Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(247,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.247");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.k (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 247.4 | ||
Character | \(\chi\) | \(=\) | 930.247 |
Dual form | 930.2.k.b.433.4 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −0.899839 | + | 2.04702i | −0.402420 | + | 0.915455i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 2.95191 | + | 2.95191i | 1.11572 | + | 1.11572i | 0.992363 | + | 0.123354i | \(0.0393651\pi\) |
0.123354 | + | 0.992363i | \(0.460635\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 2.08374 | − | 0.811179i | 0.658938 | − | 0.256517i | ||||
\(11\) | 4.03469i | 1.21650i | 0.793744 | + | 0.608252i | \(0.208129\pi\) | ||||
−0.793744 | + | 0.608252i | \(0.791871\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | −2.80675 | − | 2.80675i | −0.778452 | − | 0.778452i | 0.201115 | − | 0.979568i | \(-0.435543\pi\) |
−0.979568 | + | 0.201115i | \(0.935543\pi\) | |||||||
\(14\) | − | 4.17463i | − | 1.11572i | ||||||
\(15\) | 2.08374 | − | 0.811179i | 0.538020 | − | 0.209446i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −2.66235 | + | 2.66235i | −0.645716 | + | 0.645716i | −0.951955 | − | 0.306239i | \(-0.900929\pi\) |
0.306239 | + | 0.951955i | \(0.400929\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | 1.01510i | 0.232879i | 0.993198 | + | 0.116440i | \(0.0371482\pi\) | ||||
−0.993198 | + | 0.116440i | \(0.962852\pi\) | |||||||
\(20\) | −2.04702 | − | 0.899839i | −0.457728 | − | 0.201210i | ||||
\(21\) | − | 4.17463i | − | 0.910979i | ||||||
\(22\) | 2.85296 | − | 2.85296i | 0.608252 | − | 0.608252i | ||||
\(23\) | −2.02478 | − | 2.02478i | −0.422196 | − | 0.422196i | 0.463763 | − | 0.885959i | \(-0.346499\pi\) |
−0.885959 | + | 0.463763i | \(0.846499\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | −3.38058 | − | 3.68398i | −0.676116 | − | 0.736795i | ||||
\(26\) | 3.96934i | 0.778452i | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −2.95191 | + | 2.95191i | −0.557858 | + | 0.557858i | ||||
\(29\) | −4.35667 | −0.809013 | −0.404506 | − | 0.914535i | \(-0.632557\pi\) | ||||
−0.404506 | + | 0.914535i | \(0.632557\pi\) | |||||||
\(30\) | −2.04702 | − | 0.899839i | −0.373733 | − | 0.164287i | ||||
\(31\) | −2.75488 | − | 4.83845i | −0.494791 | − | 0.869012i | ||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 2.85296 | − | 2.85296i | 0.496636 | − | 0.496636i | ||||
\(34\) | 3.76514 | 0.645716 | ||||||||
\(35\) | −8.69886 | + | 3.38637i | −1.47038 | + | 0.572402i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 4.51858 | − | 4.51858i | 0.742849 | − | 0.742849i | −0.230276 | − | 0.973125i | \(-0.573963\pi\) |
0.973125 | + | 0.230276i | \(0.0739629\pi\) | |||||||
\(38\) | 0.717783 | − | 0.717783i | 0.116440 | − | 0.116440i | ||||
\(39\) | 3.96934i | 0.635604i | ||||||||
\(40\) | 0.811179 | + | 2.08374i | 0.128259 | + | 0.329469i | ||||
\(41\) | −8.01545 | −1.25180 | −0.625902 | − | 0.779902i | \(-0.715269\pi\) | ||||
−0.625902 | + | 0.779902i | \(0.715269\pi\) | |||||||
\(42\) | −2.95191 | + | 2.95191i | −0.455490 | + | 0.455490i | ||||
\(43\) | −0.805022 | − | 0.805022i | −0.122765 | − | 0.122765i | 0.643055 | − | 0.765820i | \(-0.277667\pi\) |
−0.765820 | + | 0.643055i | \(0.777667\pi\) | |||||||
\(44\) | −4.03469 | −0.608252 | ||||||||
\(45\) | −2.04702 | − | 0.899839i | −0.305152 | − | 0.134140i | ||||
\(46\) | 2.86347i | 0.422196i | ||||||||
\(47\) | −0.485909 | − | 0.485909i | −0.0708772 | − | 0.0708772i | 0.670780 | − | 0.741657i | \(-0.265960\pi\) |
−0.741657 | + | 0.670780i | \(0.765960\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | 10.4275i | 1.48965i | ||||||||
\(50\) | −0.214533 | + | 4.99540i | −0.0303396 | + | 0.706456i | ||||
\(51\) | 3.76514 | 0.527225 | ||||||||
\(52\) | 2.80675 | − | 2.80675i | 0.389226 | − | 0.389226i | ||||
\(53\) | −2.97139 | − | 2.97139i | −0.408152 | − | 0.408152i | 0.472942 | − | 0.881094i | \(-0.343192\pi\) |
−0.881094 | + | 0.472942i | \(0.843192\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −8.25909 | − | 3.63057i | −1.11366 | − | 0.489546i | ||||
\(56\) | 4.17463 | 0.557858 | ||||||||
\(57\) | 0.717783 | − | 0.717783i | 0.0950727 | − | 0.0950727i | ||||
\(58\) | 3.08063 | + | 3.08063i | 0.404506 | + | 0.404506i | ||||
\(59\) | 12.9765i | 1.68940i | 0.535241 | + | 0.844699i | \(0.320221\pi\) | ||||
−0.535241 | + | 0.844699i | \(0.679779\pi\) | |||||||
\(60\) | 0.811179 | + | 2.08374i | 0.104723 | + | 0.269010i | ||||
\(61\) | 8.09893i | 1.03696i | 0.855089 | + | 0.518481i | \(0.173502\pi\) | ||||
−0.855089 | + | 0.518481i | \(0.826498\pi\) | |||||||
\(62\) | −1.47331 | + | 5.36930i | −0.187111 | + | 0.681901i | ||||
\(63\) | −2.95191 | + | 2.95191i | −0.371906 | + | 0.371906i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 8.27109 | − | 3.21985i | 1.02590 | − | 0.399373i | ||||
\(66\) | −4.03469 | −0.496636 | ||||||||
\(67\) | −4.92097 | − | 4.92097i | −0.601192 | − | 0.601192i | 0.339437 | − | 0.940629i | \(-0.389764\pi\) |
−0.940629 | + | 0.339437i | \(0.889764\pi\) | |||||||
\(68\) | −2.66235 | − | 2.66235i | −0.322858 | − | 0.322858i | ||||
\(69\) | 2.86347i | 0.344722i | ||||||||
\(70\) | 8.54555 | + | 3.75649i | 1.02139 | + | 0.448987i | ||||
\(71\) | 6.49419 | 0.770718 | 0.385359 | − | 0.922767i | \(-0.374078\pi\) | ||||
0.385359 | + | 0.922767i | \(0.374078\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 6.55280 | + | 6.55280i | 0.766947 | + | 0.766947i | 0.977568 | − | 0.210621i | \(-0.0675486\pi\) |
−0.210621 | + | 0.977568i | \(0.567549\pi\) | |||||||
\(74\) | −6.39023 | −0.742849 | ||||||||
\(75\) | −0.214533 | + | 4.99540i | −0.0247722 | + | 0.576819i | ||||
\(76\) | −1.01510 | −0.116440 | ||||||||
\(77\) | −11.9100 | + | 11.9100i | −1.35727 | + | 1.35727i | ||||
\(78\) | 2.80675 | − | 2.80675i | 0.317802 | − | 0.317802i | ||||
\(79\) | −9.44004 | −1.06209 | −0.531044 | − | 0.847344i | \(-0.678200\pi\) | ||||
−0.531044 | + | 0.847344i | \(0.678200\pi\) | |||||||
\(80\) | 0.899839 | − | 2.04702i | 0.100605 | − | 0.228864i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 5.66778 | + | 5.66778i | 0.625902 | + | 0.625902i | ||||
\(83\) | 7.59317 | + | 7.59317i | 0.833459 | + | 0.833459i | 0.987988 | − | 0.154529i | \(-0.0493861\pi\) |
−0.154529 | + | 0.987988i | \(0.549386\pi\) | |||||||
\(84\) | 4.17463 | 0.455490 | ||||||||
\(85\) | −3.05420 | − | 7.84558i | −0.331275 | − | 0.850973i | ||||
\(86\) | 1.13847i | 0.122765i | ||||||||
\(87\) | 3.08063 | + | 3.08063i | 0.330278 | + | 0.330278i | ||||
\(88\) | 2.85296 | + | 2.85296i | 0.304126 | + | 0.304126i | ||||
\(89\) | 5.03739 | 0.533962 | 0.266981 | − | 0.963702i | \(-0.413974\pi\) | ||||
0.266981 | + | 0.963702i | \(0.413974\pi\) | |||||||
\(90\) | 0.811179 | + | 2.08374i | 0.0855058 | + | 0.219646i | ||||
\(91\) | − | 16.5705i | − | 1.73706i | ||||||
\(92\) | 2.02478 | − | 2.02478i | 0.211098 | − | 0.211098i | ||||
\(93\) | −1.47331 | + | 5.36930i | −0.152775 | + | 0.556770i | ||||
\(94\) | 0.687180i | 0.0708772i | ||||||||
\(95\) | −2.07793 | − | 0.913425i | −0.213191 | − | 0.0937154i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 8.30027 | + | 8.30027i | 0.842764 | + | 0.842764i | 0.989218 | − | 0.146453i | \(-0.0467858\pi\) |
−0.146453 | + | 0.989218i | \(0.546786\pi\) | |||||||
\(98\) | 7.37338 | − | 7.37338i | 0.744824 | − | 0.744824i | ||||
\(99\) | −4.03469 | −0.405502 | ||||||||
\(100\) | 3.68398 | − | 3.38058i | 0.368398 | − | 0.338058i | ||||
\(101\) | −2.88110 | −0.286680 | −0.143340 | − | 0.989674i | \(-0.545784\pi\) | ||||
−0.143340 | + | 0.989674i | \(0.545784\pi\) | |||||||
\(102\) | −2.66235 | − | 2.66235i | −0.263612 | − | 0.263612i | ||||
\(103\) | 8.65254 | − | 8.65254i | 0.852560 | − | 0.852560i | −0.137888 | − | 0.990448i | \(-0.544031\pi\) |
0.990448 | + | 0.137888i | \(0.0440314\pi\) | |||||||
\(104\) | −3.96934 | −0.389226 | ||||||||
\(105\) | 8.54555 | + | 3.75649i | 0.833960 | + | 0.366596i | ||||
\(106\) | 4.20218i | 0.408152i | ||||||||
\(107\) | −11.2782 | − | 11.2782i | −1.09031 | − | 1.09031i | −0.995495 | − | 0.0948132i | \(-0.969775\pi\) |
−0.0948132 | − | 0.995495i | \(-0.530225\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 14.0311i | 1.34394i | 0.740579 | + | 0.671970i | \(0.234552\pi\) | ||||
−0.740579 | + | 0.671970i | \(0.765448\pi\) | |||||||
\(110\) | 3.27286 | + | 8.40726i | 0.312055 | + | 0.801601i | ||||
\(111\) | −6.39023 | −0.606534 | ||||||||
\(112\) | −2.95191 | − | 2.95191i | −0.278929 | − | 0.278929i | ||||
\(113\) | 6.42328 | − | 6.42328i | 0.604251 | − | 0.604251i | −0.337187 | − | 0.941438i | \(-0.609475\pi\) |
0.941438 | + | 0.337187i | \(0.109475\pi\) | |||||||
\(114\) | −1.01510 | −0.0950727 | ||||||||
\(115\) | 5.96674 | − | 2.32279i | 0.556402 | − | 0.216601i | ||||
\(116\) | − | 4.35667i | − | 0.404506i | ||||||
\(117\) | 2.80675 | − | 2.80675i | 0.259484 | − | 0.259484i | ||||
\(118\) | 9.17578 | − | 9.17578i | 0.844699 | − | 0.844699i | ||||
\(119\) | −15.7181 | −1.44087 | ||||||||
\(120\) | 0.899839 | − | 2.04702i | 0.0821437 | − | 0.186866i | ||||
\(121\) | −5.27872 | −0.479884 | ||||||||
\(122\) | 5.72681 | − | 5.72681i | 0.518481 | − | 0.518481i | ||||
\(123\) | 5.66778 | + | 5.66778i | 0.511047 | + | 0.511047i | ||||
\(124\) | 4.83845 | − | 2.75488i | 0.434506 | − | 0.247395i | ||||
\(125\) | 10.5831 | − | 3.60513i | 0.946586 | − | 0.322453i | ||||
\(126\) | 4.17463 | 0.371906 | ||||||||
\(127\) | −0.444118 | + | 0.444118i | −0.0394091 | + | 0.0394091i | −0.726537 | − | 0.687128i | \(-0.758871\pi\) |
0.687128 | + | 0.726537i | \(0.258871\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 1.13847i | 0.100237i | ||||||||
\(130\) | −8.12532 | − | 3.57177i | −0.712638 | − | 0.313265i | ||||
\(131\) | −12.9824 | −1.13427 | −0.567137 | − | 0.823624i | \(-0.691949\pi\) | ||||
−0.567137 | + | 0.823624i | \(0.691949\pi\) | |||||||
\(132\) | 2.85296 | + | 2.85296i | 0.248318 | + | 0.248318i | ||||
\(133\) | −2.99648 | + | 2.99648i | −0.259828 | + | 0.259828i | ||||
\(134\) | 6.95930i | 0.601192i | ||||||||
\(135\) | 0.811179 | + | 2.08374i | 0.0698152 | + | 0.179340i | ||||
\(136\) | 3.76514i | 0.322858i | ||||||||
\(137\) | −13.4768 | + | 13.4768i | −1.15140 | + | 1.15140i | −0.165130 | + | 0.986272i | \(0.552804\pi\) |
−0.986272 | + | 0.165130i | \(0.947196\pi\) | |||||||
\(138\) | 2.02478 | − | 2.02478i | 0.172361 | − | 0.172361i | ||||
\(139\) | −21.5110 | −1.82454 | −0.912268 | − | 0.409593i | \(-0.865671\pi\) | ||||
−0.912268 | + | 0.409593i | \(0.865671\pi\) | |||||||
\(140\) | −3.38637 | − | 8.69886i | −0.286201 | − | 0.735188i | ||||
\(141\) | 0.687180i | 0.0578710i | ||||||||
\(142\) | −4.59208 | − | 4.59208i | −0.385359 | − | 0.385359i | ||||
\(143\) | 11.3244 | − | 11.3244i | 0.946991 | − | 0.946991i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 3.92030 | − | 8.91819i | 0.325563 | − | 0.740615i | ||||
\(146\) | − | 9.26705i | − | 0.766947i | ||||||
\(147\) | 7.37338 | − | 7.37338i | 0.608146 | − | 0.608146i | ||||
\(148\) | 4.51858 | + | 4.51858i | 0.371425 | + | 0.371425i | ||||
\(149\) | − | 0.221568i | − | 0.0181515i | −0.999959 | − | 0.00907577i | \(-0.997111\pi\) | ||
0.999959 | − | 0.00907577i | \(-0.00288895\pi\) | |||||||
\(150\) | 3.68398 | − | 3.38058i | 0.300795 | − | 0.276023i | ||||
\(151\) | 11.4689i | 0.933324i | 0.884436 | + | 0.466662i | \(0.154544\pi\) | ||||
−0.884436 | + | 0.466662i | \(0.845456\pi\) | |||||||
\(152\) | 0.717783 | + | 0.717783i | 0.0582199 | + | 0.0582199i | ||||
\(153\) | −2.66235 | − | 2.66235i | −0.215239 | − | 0.215239i | ||||
\(154\) | 16.8433 | 1.35727 | ||||||||
\(155\) | 12.3834 | − | 1.28546i | 0.994655 | − | 0.103251i | ||||
\(156\) | −3.96934 | −0.317802 | ||||||||
\(157\) | 10.0308 | + | 10.0308i | 0.800549 | + | 0.800549i | 0.983181 | − | 0.182633i | \(-0.0584619\pi\) |
−0.182633 | + | 0.983181i | \(0.558462\pi\) | |||||||
\(158\) | 6.67512 | + | 6.67512i | 0.531044 | + | 0.531044i | ||||
\(159\) | 4.20218i | 0.333255i | ||||||||
\(160\) | −2.08374 | + | 0.811179i | −0.164734 | + | 0.0641294i | ||||
\(161\) | − | 11.9539i | − | 0.942103i | ||||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −2.82330 | + | 2.82330i | −0.221138 | + | 0.221138i | −0.808977 | − | 0.587840i | \(-0.799979\pi\) |
0.587840 | + | 0.808977i | \(0.299979\pi\) | |||||||
\(164\) | − | 8.01545i | − | 0.625902i | ||||||
\(165\) | 3.27286 | + | 8.40726i | 0.254792 | + | 0.654504i | ||||
\(166\) | − | 10.7384i | − | 0.833459i | ||||||
\(167\) | 14.2859 | − | 14.2859i | 1.10547 | − | 1.10547i | 0.111736 | − | 0.993738i | \(-0.464359\pi\) |
0.993738 | − | 0.111736i | \(-0.0356410\pi\) | |||||||
\(168\) | −2.95191 | − | 2.95191i | −0.227745 | − | 0.227745i | ||||
\(169\) | 2.75569i | 0.211976i | ||||||||
\(170\) | −3.38802 | + | 7.70731i | −0.259849 | + | 0.591124i | ||||
\(171\) | −1.01510 | −0.0776265 | ||||||||
\(172\) | 0.805022 | − | 0.805022i | 0.0613823 | − | 0.0613823i | ||||
\(173\) | −12.5526 | + | 12.5526i | −0.954360 | + | 0.954360i | −0.999003 | − | 0.0446433i | \(-0.985785\pi\) |
0.0446433 | + | 0.999003i | \(0.485785\pi\) | |||||||
\(174\) | − | 4.35667i | − | 0.330278i | ||||||
\(175\) | 0.895598 | − | 20.8539i | 0.0677008 | − | 1.57641i | ||||
\(176\) | − | 4.03469i | − | 0.304126i | ||||||
\(177\) | 9.17578 | − | 9.17578i | 0.689694 | − | 0.689694i | ||||
\(178\) | −3.56197 | − | 3.56197i | −0.266981 | − | 0.266981i | ||||
\(179\) | −22.2553 | −1.66344 | −0.831720 | − | 0.555195i | \(-0.812644\pi\) | ||||
−0.831720 | + | 0.555195i | \(0.812644\pi\) | |||||||
\(180\) | 0.899839 | − | 2.04702i | 0.0670700 | − | 0.152576i | ||||
\(181\) | − | 3.14386i | − | 0.233681i | −0.993151 | − | 0.116841i | \(-0.962723\pi\) | ||
0.993151 | − | 0.116841i | \(-0.0372767\pi\) | |||||||
\(182\) | −11.7171 | + | 11.7171i | −0.868532 | + | 0.868532i | ||||
\(183\) | 5.72681 | − | 5.72681i | 0.423338 | − | 0.423338i | ||||
\(184\) | −2.86347 | −0.211098 | ||||||||
\(185\) | 5.18362 | + | 13.3156i | 0.381108 | + | 0.978983i | ||||
\(186\) | 4.83845 | − | 2.75488i | 0.354773 | − | 0.201998i | ||||
\(187\) | −10.7418 | − | 10.7418i | −0.785516 | − | 0.785516i | ||||
\(188\) | 0.485909 | − | 0.485909i | 0.0354386 | − | 0.0354386i | ||||
\(189\) | 4.17463 | 0.303660 | ||||||||
\(190\) | 0.823427 | + | 2.11520i | 0.0597377 | + | 0.153453i | ||||
\(191\) | −14.4881 | −1.04832 | −0.524162 | − | 0.851618i | \(-0.675621\pi\) | ||||
−0.524162 | + | 0.851618i | \(0.675621\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 11.6924 | − | 11.6924i | 0.841640 | − | 0.841640i | −0.147432 | − | 0.989072i | \(-0.547101\pi\) |
0.989072 | + | 0.147432i | \(0.0471007\pi\) | |||||||
\(194\) | − | 11.7383i | − | 0.842764i | ||||||
\(195\) | −8.12532 | − | 3.57177i | −0.581867 | − | 0.255780i | ||||
\(196\) | −10.4275 | −0.744824 | ||||||||
\(197\) | −15.6591 | + | 15.6591i | −1.11567 | + | 1.11567i | −0.123297 | + | 0.992370i | \(0.539347\pi\) |
−0.992370 | + | 0.123297i | \(0.960653\pi\) | |||||||
\(198\) | 2.85296 | + | 2.85296i | 0.202751 | + | 0.202751i | ||||
\(199\) | 14.4567 | 1.02481 | 0.512406 | − | 0.858743i | \(-0.328754\pi\) | ||||
0.512406 | + | 0.858743i | \(0.328754\pi\) | |||||||
\(200\) | −4.99540 | − | 0.214533i | −0.353228 | − | 0.0151698i | ||||
\(201\) | 6.95930i | 0.490871i | ||||||||
\(202\) | 2.03724 | + | 2.03724i | 0.143340 | + | 0.143340i | ||||
\(203\) | −12.8605 | − | 12.8605i | −0.902629 | − | 0.902629i | ||||
\(204\) | 3.76514i | 0.263612i | ||||||||
\(205\) | 7.21261 | − | 16.4078i | 0.503751 | − | 1.14597i | ||||
\(206\) | −12.2365 | −0.852560 | ||||||||
\(207\) | 2.02478 | − | 2.02478i | 0.140732 | − | 0.140732i | ||||
\(208\) | 2.80675 | + | 2.80675i | 0.194613 | + | 0.194613i | ||||
\(209\) | −4.09561 | −0.283299 | ||||||||
\(210\) | −3.38637 | − | 8.69886i | −0.233682 | − | 0.600278i | ||||
\(211\) | −8.27591 | −0.569737 | −0.284869 | − | 0.958567i | \(-0.591950\pi\) | ||||
−0.284869 | + | 0.958567i | \(0.591950\pi\) | |||||||
\(212\) | 2.97139 | − | 2.97139i | 0.204076 | − | 0.204076i | ||||
\(213\) | −4.59208 | − | 4.59208i | −0.314644 | − | 0.314644i | ||||
\(214\) | 15.9498i | 1.09031i | ||||||||
\(215\) | 2.37229 | − | 0.923506i | 0.161789 | − | 0.0629826i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 6.15052 | − | 22.4148i | 0.417525 | − | 1.52162i | ||||
\(218\) | 9.92151 | − | 9.92151i | 0.671970 | − | 0.671970i | ||||
\(219\) | − | 9.26705i | − | 0.626209i | ||||||
\(220\) | 3.63057 | − | 8.25909i | 0.244773 | − | 0.556828i | ||||
\(221\) | 14.9451 | 1.00532 | ||||||||
\(222\) | 4.51858 | + | 4.51858i | 0.303267 | + | 0.303267i | ||||
\(223\) | 1.91786 | + | 1.91786i | 0.128429 | + | 0.128429i | 0.768400 | − | 0.639970i | \(-0.221053\pi\) |
−0.639970 | + | 0.768400i | \(0.721053\pi\) | |||||||
\(224\) | 4.17463i | 0.278929i | ||||||||
\(225\) | 3.68398 | − | 3.38058i | 0.245598 | − | 0.225372i | ||||
\(226\) | −9.08389 | −0.604251 | ||||||||
\(227\) | −5.61156 | − | 5.61156i | −0.372452 | − | 0.372452i | 0.495917 | − | 0.868370i | \(-0.334832\pi\) |
−0.868370 | + | 0.495917i | \(0.834832\pi\) | |||||||
\(228\) | 0.717783 | + | 0.717783i | 0.0475363 | + | 0.0475363i | ||||
\(229\) | 5.55524 | 0.367101 | 0.183550 | − | 0.983010i | \(-0.441241\pi\) | ||||
0.183550 | + | 0.983010i | \(0.441241\pi\) | |||||||
\(230\) | −5.86159 | − | 2.57666i | −0.386502 | − | 0.169900i | ||||
\(231\) | 16.8433 | 1.10821 | ||||||||
\(232\) | −3.08063 | + | 3.08063i | −0.202253 | + | 0.202253i | ||||
\(233\) | 12.4453 | − | 12.4453i | 0.815317 | − | 0.815317i | −0.170108 | − | 0.985425i | \(-0.554412\pi\) |
0.985425 | + | 0.170108i | \(0.0544118\pi\) | |||||||
\(234\) | −3.96934 | −0.259484 | ||||||||
\(235\) | 1.43191 | − | 0.557426i | 0.0934073 | − | 0.0363625i | ||||
\(236\) | −12.9765 | −0.844699 | ||||||||
\(237\) | 6.67512 | + | 6.67512i | 0.433595 | + | 0.433595i | ||||
\(238\) | 11.1143 | + | 11.1143i | 0.720436 | + | 0.720436i | ||||
\(239\) | 24.6462 | 1.59423 | 0.797114 | − | 0.603829i | \(-0.206359\pi\) | ||||
0.797114 | + | 0.603829i | \(0.206359\pi\) | |||||||
\(240\) | −2.08374 | + | 0.811179i | −0.134505 | + | 0.0523614i | ||||
\(241\) | 15.1372i | 0.975071i | 0.873103 | + | 0.487535i | \(0.162104\pi\) | ||||
−0.873103 | + | 0.487535i | \(0.837896\pi\) | |||||||
\(242\) | 3.73262 | + | 3.73262i | 0.239942 | + | 0.239942i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −8.09893 | −0.518481 | ||||||||
\(245\) | −21.3454 | − | 9.38311i | −1.36371 | − | 0.599465i | ||||
\(246\) | − | 8.01545i | − | 0.511047i | ||||||
\(247\) | 2.84913 | − | 2.84913i | 0.181286 | − | 0.181286i | ||||
\(248\) | −5.36930 | − | 1.47331i | −0.340951 | − | 0.0935553i | ||||
\(249\) | − | 10.7384i | − | 0.680516i | ||||||
\(250\) | −10.0326 | − | 4.93421i | −0.634519 | − | 0.312067i | ||||
\(251\) | − | 0.385808i | − | 0.0243520i | −0.999926 | − | 0.0121760i | \(-0.996124\pi\) | ||
0.999926 | − | 0.0121760i | \(-0.00387584\pi\) | |||||||
\(252\) | −2.95191 | − | 2.95191i | −0.185953 | − | 0.185953i | ||||
\(253\) | 8.16936 | − | 8.16936i | 0.513603 | − | 0.513603i | ||||
\(254\) | 0.628077 | 0.0394091 | ||||||||
\(255\) | −3.38802 | + | 7.70731i | −0.212166 | + | 0.482650i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.6768 | + | 14.6768i | 0.915514 | + | 0.915514i | 0.996699 | − | 0.0811847i | \(-0.0258703\pi\) |
−0.0811847 | + | 0.996699i | \(0.525870\pi\) | |||||||
\(258\) | 0.805022 | − | 0.805022i | 0.0501185 | − | 0.0501185i | ||||
\(259\) | 26.6769 | 1.65762 | ||||||||
\(260\) | 3.21985 | + | 8.27109i | 0.199687 | + | 0.512952i | ||||
\(261\) | − | 4.35667i | − | 0.269671i | ||||||
\(262\) | 9.17991 | + | 9.17991i | 0.567137 | + | 0.567137i | ||||
\(263\) | 21.5005 | + | 21.5005i | 1.32578 | + | 1.32578i | 0.909018 | + | 0.416757i | \(0.136833\pi\) |
0.416757 | + | 0.909018i | \(0.363167\pi\) | |||||||
\(264\) | − | 4.03469i | − | 0.248318i | ||||||
\(265\) | 8.75627 | − | 3.40873i | 0.537894 | − | 0.209396i | ||||
\(266\) | 4.23766 | 0.259828 | ||||||||
\(267\) | −3.56197 | − | 3.56197i | −0.217989 | − | 0.217989i | ||||
\(268\) | 4.92097 | − | 4.92097i | 0.300596 | − | 0.300596i | ||||
\(269\) | 20.9881 | 1.27967 | 0.639833 | − | 0.768514i | \(-0.279004\pi\) | ||||
0.639833 | + | 0.768514i | \(0.279004\pi\) | |||||||
\(270\) | 0.899839 | − | 2.04702i | 0.0547625 | − | 0.124578i | ||||
\(271\) | 13.3550i | 0.811257i | 0.914038 | + | 0.405629i | \(0.132947\pi\) | ||||
−0.914038 | + | 0.405629i | \(0.867053\pi\) | |||||||
\(272\) | 2.66235 | − | 2.66235i | 0.161429 | − | 0.161429i | ||||
\(273\) | −11.7171 | + | 11.7171i | −0.709154 | + | 0.709154i | ||||
\(274\) | 19.0591 | 1.15140 | ||||||||
\(275\) | 14.8637 | − | 13.6396i | 0.896315 | − | 0.822498i | ||||
\(276\) | −2.86347 | −0.172361 | ||||||||
\(277\) | −22.7574 | + | 22.7574i | −1.36736 | + | 1.36736i | −0.503182 | + | 0.864181i | \(0.667837\pi\) |
−0.864181 | + | 0.503182i | \(0.832163\pi\) | |||||||
\(278\) | 15.2106 | + | 15.2106i | 0.912268 | + | 0.912268i | ||||
\(279\) | 4.83845 | − | 2.75488i | 0.289671 | − | 0.164930i | ||||
\(280\) | −3.75649 | + | 8.54555i | −0.224494 | + | 0.510694i | ||||
\(281\) | 11.7181 | 0.699046 | 0.349523 | − | 0.936928i | \(-0.386344\pi\) | ||||
0.349523 | + | 0.936928i | \(0.386344\pi\) | |||||||
\(282\) | 0.485909 | − | 0.485909i | 0.0289355 | − | 0.0289355i | ||||
\(283\) | 16.4024 | − | 16.4024i | 0.975023 | − | 0.975023i | −0.0246725 | − | 0.999696i | \(-0.507854\pi\) |
0.999696 | + | 0.0246725i | \(0.00785430\pi\) | |||||||
\(284\) | 6.49419i | 0.385359i | ||||||||
\(285\) | 0.823427 | + | 2.11520i | 0.0487756 | + | 0.125294i | ||||
\(286\) | −16.0151 | −0.946991 | ||||||||
\(287\) | −23.6609 | − | 23.6609i | −1.39666 | − | 1.39666i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 2.82375i | 0.166103i | ||||||||
\(290\) | −9.07818 | + | 3.53404i | −0.533089 | + | 0.207526i | ||||
\(291\) | − | 11.7383i | − | 0.688114i | ||||||
\(292\) | −6.55280 | + | 6.55280i | −0.383473 | + | 0.383473i | ||||
\(293\) | −1.36623 | + | 1.36623i | −0.0798158 | + | 0.0798158i | −0.745888 | − | 0.666072i | \(-0.767974\pi\) |
0.666072 | + | 0.745888i | \(0.267974\pi\) | |||||||
\(294\) | −10.4275 | −0.608146 | ||||||||
\(295\) | −26.5632 | − | 11.6768i | −1.54657 | − | 0.679848i | ||||
\(296\) | − | 6.39023i | − | 0.371425i | ||||||
\(297\) | 2.85296 | + | 2.85296i | 0.165545 | + | 0.165545i | ||||
\(298\) | −0.156672 | + | 0.156672i | −0.00907577 | + | 0.00907577i | ||||
\(299\) | 11.3661i | 0.657319i | ||||||||
\(300\) | −4.99540 | − | 0.214533i | −0.288409 | − | 0.0123861i | ||||
\(301\) | − | 4.75270i | − | 0.273941i | ||||||
\(302\) | 8.10972 | − | 8.10972i | 0.466662 | − | 0.466662i | ||||
\(303\) | 2.03724 | + | 2.03724i | 0.117037 | + | 0.117037i | ||||
\(304\) | − | 1.01510i | − | 0.0582199i | ||||||
\(305\) | −16.5787 | − | 7.28774i | −0.949292 | − | 0.417295i | ||||
\(306\) | 3.76514i | 0.215239i | ||||||||
\(307\) | 0.502871 | + | 0.502871i | 0.0287004 | + | 0.0287004i | 0.721311 | − | 0.692611i | \(-0.243540\pi\) |
−0.692611 | + | 0.721311i | \(0.743540\pi\) | |||||||
\(308\) | −11.9100 | − | 11.9100i | −0.678637 | − | 0.678637i | ||||
\(309\) | −12.2365 | −0.696112 | ||||||||
\(310\) | −9.66532 | − | 7.84740i | −0.548953 | − | 0.445702i | ||||
\(311\) | 23.6115 | 1.33889 | 0.669443 | − | 0.742864i | \(-0.266533\pi\) | ||||
0.669443 | + | 0.742864i | \(0.266533\pi\) | |||||||
\(312\) | 2.80675 | + | 2.80675i | 0.158901 | + | 0.158901i | ||||
\(313\) | −12.8877 | − | 12.8877i | −0.728458 | − | 0.728458i | 0.241854 | − | 0.970313i | \(-0.422244\pi\) |
−0.970313 | + | 0.241854i | \(0.922244\pi\) | |||||||
\(314\) | − | 14.1858i | − | 0.800549i | ||||||
\(315\) | −3.38637 | − | 8.69886i | −0.190801 | − | 0.490125i | ||||
\(316\) | − | 9.44004i | − | 0.531044i | ||||||
\(317\) | −1.52562 | − | 1.52562i | −0.0856873 | − | 0.0856873i | 0.662964 | − | 0.748651i | \(-0.269298\pi\) |
−0.748651 | + | 0.662964i | \(0.769298\pi\) | |||||||
\(318\) | 2.97139 | − | 2.97139i | 0.166627 | − | 0.166627i | ||||
\(319\) | − | 17.5778i | − | 0.984168i | ||||||
\(320\) | 2.04702 | + | 0.899839i | 0.114432 | + | 0.0503025i | ||||
\(321\) | 15.9498i | 0.890233i | ||||||||
\(322\) | −8.45271 | + | 8.45271i | −0.471051 | + | 0.471051i | ||||
\(323\) | −2.70255 | − | 2.70255i | −0.150374 | − | 0.150374i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −0.851557 | + | 19.8284i | −0.0472359 | + | 1.09988i | ||||
\(326\) | 3.99275 | 0.221138 | ||||||||
\(327\) | 9.92151 | − | 9.92151i | 0.548661 | − | 0.548661i | ||||
\(328\) | −5.66778 | + | 5.66778i | −0.312951 | + | 0.312951i | ||||
\(329\) | − | 2.86872i | − | 0.158158i | ||||||
\(330\) | 3.63057 | − | 8.25909i | 0.199856 | − | 0.454648i | ||||
\(331\) | 10.2406i | 0.562872i | 0.959580 | + | 0.281436i | \(0.0908107\pi\) | ||||
−0.959580 | + | 0.281436i | \(0.909189\pi\) | |||||||
\(332\) | −7.59317 | + | 7.59317i | −0.416729 | + | 0.416729i | ||||
\(333\) | 4.51858 | + | 4.51858i | 0.247616 | + | 0.247616i | ||||
\(334\) | −20.2033 | −1.10547 | ||||||||
\(335\) | 14.5014 | − | 5.64524i | 0.792296 | − | 0.308433i | ||||
\(336\) | 4.17463i | 0.227745i | ||||||||
\(337\) | −18.5342 | + | 18.5342i | −1.00962 | + | 1.00962i | −0.00966899 | + | 0.999953i | \(0.503078\pi\) |
−0.999953 | + | 0.00966899i | \(0.996922\pi\) | |||||||
\(338\) | 1.94856 | − | 1.94856i | 0.105988 | − | 0.105988i | ||||
\(339\) | −9.08389 | −0.493369 | ||||||||
\(340\) | 7.84558 | − | 3.05420i | 0.425486 | − | 0.165637i | ||||
\(341\) | 19.5217 | − | 11.1151i | 1.05716 | − | 0.601916i | ||||
\(342\) | 0.717783 | + | 0.717783i | 0.0388132 | + | 0.0388132i | ||||
\(343\) | −10.1178 | + | 10.1178i | −0.546309 | + | 0.546309i | ||||
\(344\) | −1.13847 | −0.0613823 | ||||||||
\(345\) | −5.86159 | − | 2.57666i | −0.315577 | − | 0.138723i | ||||
\(346\) | 17.7521 | 0.954360 | ||||||||
\(347\) | 17.5456 | − | 17.5456i | 0.941899 | − | 0.941899i | −0.0565033 | − | 0.998402i | \(-0.517995\pi\) |
0.998402 | + | 0.0565033i | \(0.0179951\pi\) | |||||||
\(348\) | −3.08063 | + | 3.08063i | −0.165139 | + | 0.165139i | ||||
\(349\) | 31.1464i | 1.66723i | 0.552345 | + | 0.833616i | \(0.313733\pi\) | ||||
−0.552345 | + | 0.833616i | \(0.686267\pi\) | |||||||
\(350\) | −15.3792 | + | 14.1127i | −0.822055 | + | 0.754354i | ||||
\(351\) | −3.96934 | −0.211868 | ||||||||
\(352\) | −2.85296 | + | 2.85296i | −0.152063 | + | 0.152063i | ||||
\(353\) | −7.56467 | − | 7.56467i | −0.402627 | − | 0.402627i | 0.476531 | − | 0.879158i | \(-0.341894\pi\) |
−0.879158 | + | 0.476531i | \(0.841894\pi\) | |||||||
\(354\) | −12.9765 | −0.689694 | ||||||||
\(355\) | −5.84372 | + | 13.2937i | −0.310153 | + | 0.705558i | ||||
\(356\) | 5.03739i | 0.266981i | ||||||||
\(357\) | 11.1143 | + | 11.1143i | 0.588233 | + | 0.588233i | ||||
\(358\) | 15.7369 | + | 15.7369i | 0.831720 | + | 0.831720i | ||||
\(359\) | − | 13.4534i | − | 0.710042i | −0.934858 | − | 0.355021i | \(-0.884474\pi\) | ||
0.934858 | − | 0.355021i | \(-0.115526\pi\) | |||||||
\(360\) | −2.08374 | + | 0.811179i | −0.109823 | + | 0.0427529i | ||||
\(361\) | 17.9696 | 0.945767 | ||||||||
\(362\) | −2.22305 | + | 2.22305i | −0.116841 | + | 0.116841i | ||||
\(363\) | 3.73262 | + | 3.73262i | 0.195912 | + | 0.195912i | ||||
\(364\) | 16.5705 | 0.868532 | ||||||||
\(365\) | −19.3102 | + | 7.51724i | −1.01074 | + | 0.393470i | ||||
\(366\) | −8.09893 | −0.423338 | ||||||||
\(367\) | −15.3254 | + | 15.3254i | −0.799982 | + | 0.799982i | −0.983092 | − | 0.183111i | \(-0.941383\pi\) |
0.183111 | + | 0.983092i | \(0.441383\pi\) | |||||||
\(368\) | 2.02478 | + | 2.02478i | 0.105549 | + | 0.105549i | ||||
\(369\) | − | 8.01545i | − | 0.417268i | ||||||
\(370\) | 5.75018 | − | 13.0809i | 0.298938 | − | 0.680045i | ||||
\(371\) | − | 17.5426i | − | 0.910765i | ||||||
\(372\) | −5.36930 | − | 1.47331i | −0.278385 | − | 0.0763876i | ||||
\(373\) | −18.1490 | + | 18.1490i | −0.939721 | + | 0.939721i | −0.998284 | − | 0.0585625i | \(-0.981348\pi\) |
0.0585625 | + | 0.998284i | \(0.481348\pi\) | |||||||
\(374\) | 15.1912i | 0.785516i | ||||||||
\(375\) | −10.0326 | − | 4.93421i | −0.518083 | − | 0.254801i | ||||
\(376\) | −0.687180 | −0.0354386 | ||||||||
\(377\) | 12.2281 | + | 12.2281i | 0.629778 | + | 0.629778i | ||||
\(378\) | −2.95191 | − | 2.95191i | −0.151830 | − | 0.151830i | ||||
\(379\) | − | 12.0805i | − | 0.620535i | −0.950649 | − | 0.310267i | \(-0.899581\pi\) | ||
0.950649 | − | 0.310267i | \(-0.100419\pi\) | |||||||
\(380\) | 0.913425 | − | 2.07793i | 0.0468577 | − | 0.106595i | ||||
\(381\) | 0.628077 | 0.0321774 | ||||||||
\(382\) | 10.2447 | + | 10.2447i | 0.524162 | + | 0.524162i | ||||
\(383\) | 5.18617 | + | 5.18617i | 0.265001 | + | 0.265001i | 0.827082 | − | 0.562081i | \(-0.189999\pi\) |
−0.562081 | + | 0.827082i | \(0.689999\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −13.6630 | − | 35.0972i | −0.696329 | − | 1.78872i | ||||
\(386\) | −16.5356 | −0.841640 | ||||||||
\(387\) | 0.805022 | − | 0.805022i | 0.0409216 | − | 0.0409216i | ||||
\(388\) | −8.30027 | + | 8.30027i | −0.421382 | + | 0.421382i | ||||
\(389\) | −5.33947 | −0.270722 | −0.135361 | − | 0.990796i | \(-0.543219\pi\) | ||||
−0.135361 | + | 0.990796i | \(0.543219\pi\) | |||||||
\(390\) | 3.21985 | + | 8.27109i | 0.163043 | + | 0.418823i | ||||
\(391\) | 10.7814 | 0.545237 | ||||||||
\(392\) | 7.37338 | + | 7.37338i | 0.372412 | + | 0.372412i | ||||
\(393\) | 9.17991 | + | 9.17991i | 0.463065 | + | 0.463065i | ||||
\(394\) | 22.1453 | 1.11567 | ||||||||
\(395\) | 8.49451 | − | 19.3239i | 0.427405 | − | 0.972293i | ||||
\(396\) | − | 4.03469i | − | 0.202751i | ||||||
\(397\) | −1.41370 | − | 1.41370i | −0.0709514 | − | 0.0709514i | 0.670741 | − | 0.741692i | \(-0.265976\pi\) |
−0.741692 | + | 0.670741i | \(0.765976\pi\) | |||||||
\(398\) | −10.2225 | − | 10.2225i | −0.512406 | − | 0.512406i | ||||
\(399\) | 4.23766 | 0.212148 | ||||||||
\(400\) | 3.38058 | + | 3.68398i | 0.169029 | + | 0.184199i | ||||
\(401\) | − | 3.16248i | − | 0.157927i | −0.996878 | − | 0.0789633i | \(-0.974839\pi\) | ||
0.996878 | − | 0.0789633i | \(-0.0251610\pi\) | |||||||
\(402\) | 4.92097 | − | 4.92097i | 0.245436 | − | 0.245436i | ||||
\(403\) | −5.84807 | + | 21.3126i | −0.291313 | + | 1.06166i | ||||
\(404\) | − | 2.88110i | − | 0.143340i | ||||||
\(405\) | 0.899839 | − | 2.04702i | 0.0447134 | − | 0.101717i | ||||
\(406\) | 18.1875i | 0.902629i | ||||||||
\(407\) | 18.2311 | + | 18.2311i | 0.903680 | + | 0.903680i | ||||
\(408\) | 2.66235 | − | 2.66235i | 0.131806 | − | 0.131806i | ||||
\(409\) | −5.32872 | −0.263488 | −0.131744 | − | 0.991284i | \(-0.542058\pi\) | ||||
−0.131744 | + | 0.991284i | \(0.542058\pi\) | |||||||
\(410\) | −16.7021 | + | 6.50197i | −0.824860 | + | 0.321109i | ||||
\(411\) | 19.0591 | 0.940115 | ||||||||
\(412\) | 8.65254 | + | 8.65254i | 0.426280 | + | 0.426280i | ||||
\(413\) | −38.3055 | + | 38.3055i | −1.88489 | + | 1.88489i | ||||
\(414\) | −2.86347 | −0.140732 | ||||||||
\(415\) | −22.3760 | + | 8.71074i | −1.09839 | + | 0.427593i | ||||
\(416\) | − | 3.96934i | − | 0.194613i | ||||||
\(417\) | 15.2106 | + | 15.2106i | 0.744864 | + | 0.744864i | ||||
\(418\) | 2.89603 | + | 2.89603i | 0.141649 | + | 0.141649i | ||||
\(419\) | 21.2866i | 1.03992i | 0.854191 | + | 0.519959i | \(0.174053\pi\) | ||||
−0.854191 | + | 0.519959i | \(0.825947\pi\) | |||||||
\(420\) | −3.75649 | + | 8.54555i | −0.183298 | + | 0.416980i | ||||
\(421\) | 23.1425 | 1.12790 | 0.563949 | − | 0.825809i | \(-0.309281\pi\) | ||||
0.563949 | + | 0.825809i | \(0.309281\pi\) | |||||||
\(422\) | 5.85196 | + | 5.85196i | 0.284869 | + | 0.284869i | ||||
\(423\) | 0.485909 | − | 0.485909i | 0.0236257 | − | 0.0236257i | ||||
\(424\) | −4.20218 | −0.204076 | ||||||||
\(425\) | 18.8083 | + | 0.807748i | 0.912339 | + | 0.0391815i | ||||
\(426\) | 6.49419i | 0.314644i | ||||||||
\(427\) | −23.9073 | + | 23.9073i | −1.15696 | + | 1.15696i | ||||
\(428\) | 11.2782 | − | 11.2782i | 0.545154 | − | 0.545154i | ||||
\(429\) | −16.0151 | −0.773215 | ||||||||
\(430\) | −2.33048 | − | 1.02444i | −0.112386 | − | 0.0494030i | ||||
\(431\) | 29.9524 | 1.44276 | 0.721379 | − | 0.692541i | \(-0.243509\pi\) | ||||
0.721379 | + | 0.692541i | \(0.243509\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | −3.11417 | − | 3.11417i | −0.149658 | − | 0.149658i | 0.628307 | − | 0.777965i | \(-0.283748\pi\) |
−0.777965 | + | 0.628307i | \(0.783748\pi\) | |||||||
\(434\) | −20.1988 | + | 11.5006i | −0.969571 | + | 0.552047i | ||||
\(435\) | −9.07818 | + | 3.53404i | −0.435265 | + | 0.169444i | ||||
\(436\) | −14.0311 | −0.671970 | ||||||||
\(437\) | 2.05535 | − | 2.05535i | 0.0983208 | − | 0.0983208i | ||||
\(438\) | −6.55280 | + | 6.55280i | −0.313105 | + | 0.313105i | ||||
\(439\) | 28.7403i | 1.37170i | 0.727743 | + | 0.685850i | \(0.240570\pi\) | ||||
−0.727743 | + | 0.685850i | \(0.759430\pi\) | |||||||
\(440\) | −8.40726 | + | 3.27286i | −0.400800 | + | 0.156027i | ||||
\(441\) | −10.4275 | −0.496550 | ||||||||
\(442\) | −10.5678 | − | 10.5678i | −0.502659 | − | 0.502659i | ||||
\(443\) | −3.15593 | + | 3.15593i | −0.149943 | + | 0.149943i | −0.778092 | − | 0.628150i | \(-0.783812\pi\) |
0.628150 | + | 0.778092i | \(0.283812\pi\) | |||||||
\(444\) | − | 6.39023i | − | 0.303267i | ||||||
\(445\) | −4.53284 | + | 10.3116i | −0.214877 | + | 0.488818i | ||||
\(446\) | − | 2.71227i | − | 0.128429i | ||||||
\(447\) | −0.156672 | + | 0.156672i | −0.00741033 | + | 0.00741033i | ||||
\(448\) | 2.95191 | − | 2.95191i | 0.139465 | − | 0.139465i | ||||
\(449\) | −18.9024 | −0.892060 | −0.446030 | − | 0.895018i | \(-0.647162\pi\) | ||||
−0.446030 | + | 0.895018i | \(0.647162\pi\) | |||||||
\(450\) | −4.99540 | − | 0.214533i | −0.235485 | − | 0.0101132i | ||||
\(451\) | − | 32.3399i | − | 1.52282i | ||||||
\(452\) | 6.42328 | + | 6.42328i | 0.302126 | + | 0.302126i | ||||
\(453\) | 8.10972 | − | 8.10972i | 0.381028 | − | 0.381028i | ||||
\(454\) | 7.93594i | 0.372452i | ||||||||
\(455\) | 33.9202 | + | 14.9108i | 1.59020 | + | 0.699030i | ||||
\(456\) | − | 1.01510i | − | 0.0475363i | ||||||
\(457\) | 3.87894 | − | 3.87894i | 0.181449 | − | 0.181449i | −0.610538 | − | 0.791987i | \(-0.709047\pi\) |
0.791987 | + | 0.610538i | \(0.209047\pi\) | |||||||
\(458\) | −3.92815 | − | 3.92815i | −0.183550 | − | 0.183550i | ||||
\(459\) | 3.76514i | 0.175742i | ||||||||
\(460\) | 2.32279 | + | 5.96674i | 0.108301 | + | 0.278201i | ||||
\(461\) | 8.68105i | 0.404317i | 0.979353 | + | 0.202158i | \(0.0647956\pi\) | ||||
−0.979353 | + | 0.202158i | \(0.935204\pi\) | |||||||
\(462\) | −11.9100 | − | 11.9100i | −0.554105 | − | 0.554105i | ||||
\(463\) | −17.7693 | − | 17.7693i | −0.825808 | − | 0.825808i | 0.161126 | − | 0.986934i | \(-0.448488\pi\) |
−0.986934 | + | 0.161126i | \(0.948488\pi\) | |||||||
\(464\) | 4.35667 | 0.202253 | ||||||||
\(465\) | −9.66532 | − | 7.84740i | −0.448218 | − | 0.363914i | ||||
\(466\) | −17.6003 | −0.815317 | ||||||||
\(467\) | −8.74361 | − | 8.74361i | −0.404606 | − | 0.404606i | 0.475247 | − | 0.879853i | \(-0.342359\pi\) |
−0.879853 | + | 0.475247i | \(0.842359\pi\) | |||||||
\(468\) | 2.80675 | + | 2.80675i | 0.129742 | + | 0.129742i | ||||
\(469\) | − | 29.0525i | − | 1.34152i | ||||||
\(470\) | −1.40667 | − | 0.618351i | −0.0648849 | − | 0.0285224i | ||||
\(471\) | − | 14.1858i | − | 0.653645i | ||||||
\(472\) | 9.17578 | + | 9.17578i | 0.422350 | + | 0.422350i | ||||
\(473\) | 3.24801 | − | 3.24801i | 0.149344 | − | 0.149344i | ||||
\(474\) | − | 9.44004i | − | 0.433595i | ||||||
\(475\) | 3.73960 | − | 3.43162i | 0.171584 | − | 0.157454i | ||||
\(476\) | − | 15.7181i | − | 0.720436i | ||||||
\(477\) | 2.97139 | − | 2.97139i | 0.136051 | − | 0.136051i | ||||
\(478\) | −17.4275 | − | 17.4275i | −0.797114 | − | 0.797114i | ||||
\(479\) | 9.39464i | 0.429252i | 0.976696 | + | 0.214626i | \(0.0688532\pi\) | ||||
−0.976696 | + | 0.214626i | \(0.931147\pi\) | |||||||
\(480\) | 2.04702 | + | 0.899839i | 0.0934332 | + | 0.0410718i | ||||
\(481\) | −25.3650 | −1.15655 | ||||||||
\(482\) | 10.7036 | − | 10.7036i | 0.487535 | − | 0.487535i | ||||
\(483\) | −8.45271 | + | 8.45271i | −0.384612 | + | 0.384612i | ||||
\(484\) | − | 5.27872i | − | 0.239942i | ||||||
\(485\) | −24.4597 | + | 9.52191i | −1.11066 | + | 0.432367i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | −22.3244 | + | 22.3244i | −1.01162 | + | 1.01162i | −0.0116856 | + | 0.999932i | \(0.503720\pi\) |
−0.999932 | + | 0.0116856i | \(0.996280\pi\) | |||||||
\(488\) | 5.72681 | + | 5.72681i | 0.259241 | + | 0.259241i | ||||
\(489\) | 3.99275 | 0.180558 | ||||||||
\(490\) | 8.45861 | + | 21.7283i | 0.382121 | + | 0.981585i | ||||
\(491\) | 5.51033i | 0.248678i | 0.992240 | + | 0.124339i | \(0.0396810\pi\) | ||||
−0.992240 | + | 0.124339i | \(0.960319\pi\) | |||||||
\(492\) | −5.66778 | + | 5.66778i | −0.255523 | + | 0.255523i | ||||
\(493\) | 11.5990 | − | 11.5990i | 0.522392 | − | 0.522392i | ||||
\(494\) | −4.02927 | −0.181286 | ||||||||
\(495\) | 3.63057 | − | 8.25909i | 0.163182 | − | 0.371218i | ||||
\(496\) | 2.75488 | + | 4.83845i | 0.123698 | + | 0.217253i | ||||
\(497\) | 19.1702 | + | 19.1702i | 0.859903 | + | 0.859903i | ||||
\(498\) | −7.59317 | + | 7.59317i | −0.340258 | + | 0.340258i | ||||
\(499\) | 12.0284 | 0.538464 | 0.269232 | − | 0.963075i | \(-0.413230\pi\) | ||||
0.269232 | + | 0.963075i | \(0.413230\pi\) | |||||||
\(500\) | 3.60513 | + | 10.5831i | 0.161226 | + | 0.473293i | ||||
\(501\) | −20.2033 | −0.902615 | ||||||||
\(502\) | −0.272808 | + | 0.272808i | −0.0121760 | + | 0.0121760i | ||||
\(503\) | 4.36837 | − | 4.36837i | 0.194776 | − | 0.194776i | −0.602980 | − | 0.797756i | \(-0.706020\pi\) |
0.797756 | + | 0.602980i | \(0.206020\pi\) | |||||||
\(504\) | 4.17463i | 0.185953i | ||||||||
\(505\) | 2.59252 | − | 5.89767i | 0.115366 | − | 0.262443i | ||||
\(506\) | −11.5532 | −0.513603 | ||||||||
\(507\) | 1.94856 | − | 1.94856i | 0.0865388 | − | 0.0865388i | ||||
\(508\) | −0.444118 | − | 0.444118i | −0.0197045 | − | 0.0197045i | ||||
\(509\) | 14.7406 | 0.653367 | 0.326684 | − | 0.945134i | \(-0.394069\pi\) | ||||
0.326684 | + | 0.945134i | \(0.394069\pi\) | |||||||
\(510\) | 7.84558 | − | 3.05420i | 0.347408 | − | 0.135242i | ||||
\(511\) | 38.6865i | 1.71139i | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0.717783 | + | 0.717783i | 0.0316909 | + | 0.0316909i | ||||
\(514\) | − | 20.7561i | − | 0.915514i | ||||||
\(515\) | 9.92603 | + | 25.4978i | 0.437393 | + | 1.12357i | ||||
\(516\) | −1.13847 | −0.0501185 | ||||||||
\(517\) | 1.96049 | − | 1.96049i | 0.0862224 | − | 0.0862224i | ||||
\(518\) | −18.8634 | − | 18.8634i | −0.828810 | − | 0.828810i | ||||
\(519\) | 17.7521 | 0.779231 | ||||||||
\(520\) | 3.57177 | − | 8.12532i | 0.156632 | − | 0.356319i | ||||
\(521\) | 5.07786 | 0.222465 | 0.111233 | − | 0.993794i | \(-0.464520\pi\) | ||||
0.111233 | + | 0.993794i | \(0.464520\pi\) | |||||||
\(522\) | −3.08063 | + | 3.08063i | −0.134835 | + | 0.134835i | ||||
\(523\) | −11.5844 | − | 11.5844i | −0.506552 | − | 0.506552i | 0.406915 | − | 0.913466i | \(-0.366605\pi\) |
−0.913466 | + | 0.406915i | \(0.866605\pi\) | |||||||
\(524\) | − | 12.9824i | − | 0.567137i | ||||||
\(525\) | −15.3792 | + | 14.1127i | −0.671205 | + | 0.615928i | ||||
\(526\) | − | 30.4062i | − | 1.32578i | ||||||
\(527\) | 20.2161 | + | 5.54721i | 0.880629 | + | 0.241640i | ||||
\(528\) | −2.85296 | + | 2.85296i | −0.124159 | + | 0.124159i | ||||
\(529\) | − | 14.8005i | − | 0.643501i | ||||||
\(530\) | −8.60195 | − | 3.78129i | −0.373645 | − | 0.164249i | ||||
\(531\) | −12.9765 | −0.563133 | ||||||||
\(532\) | −2.99648 | − | 2.99648i | −0.129914 | − | 0.129914i | ||||
\(533\) | 22.4974 | + | 22.4974i | 0.974469 | + | 0.974469i | ||||
\(534\) | 5.03739i | 0.217989i | ||||||||
\(535\) | 33.2354 | − | 12.9382i | 1.43689 | − | 0.559366i | ||||
\(536\) | −6.95930 | −0.300596 | ||||||||
\(537\) | 15.7369 | + | 15.7369i | 0.679097 | + | 0.679097i | ||||
\(538\) | −14.8408 | − | 14.8408i | −0.639833 | − | 0.639833i | ||||
\(539\) | −42.0719 | −1.81216 | ||||||||
\(540\) | −2.08374 | + | 0.811179i | −0.0896701 | + | 0.0349076i | ||||
\(541\) | 5.34555 | 0.229823 | 0.114911 | − | 0.993376i | \(-0.463342\pi\) | ||||
0.114911 | + | 0.993376i | \(0.463342\pi\) | |||||||
\(542\) | 9.44340 | − | 9.44340i | 0.405629 | − | 0.405629i | ||||
\(543\) | −2.22305 | + | 2.22305i | −0.0954000 | + | 0.0954000i | ||||
\(544\) | −3.76514 | −0.161429 | ||||||||
\(545\) | −28.7220 | − | 12.6258i | −1.23032 | − | 0.540828i | ||||
\(546\) | 16.5705 | 0.709154 | ||||||||
\(547\) | −30.0130 | − | 30.0130i | −1.28326 | − | 1.28326i | −0.938800 | − | 0.344464i | \(-0.888061\pi\) |
−0.344464 | − | 0.938800i | \(-0.611939\pi\) | |||||||
\(548\) | −13.4768 | − | 13.4768i | −0.575701 | − | 0.575701i | ||||
\(549\) | −8.09893 | −0.345654 | ||||||||
\(550\) | −20.1549 | − | 0.865576i | −0.859407 | − | 0.0369083i | ||||
\(551\) | − | 4.42245i | − | 0.188403i | ||||||
\(552\) | 2.02478 | + | 2.02478i | 0.0861804 | + | 0.0861804i | ||||
\(553\) | −27.8661 | − | 27.8661i | −1.18499 | − | 1.18499i | ||||
\(554\) | 32.1839 | 1.36736 | ||||||||
\(555\) | 5.75018 | − | 13.0809i | 0.244081 | − | 0.555255i | ||||
\(556\) | − | 21.5110i | − | 0.912268i | ||||||
\(557\) | 26.7109 | − | 26.7109i | 1.13178 | − | 1.13178i | 0.141895 | − | 0.989882i | \(-0.454680\pi\) |
0.989882 | − | 0.141895i | \(-0.0453196\pi\) | |||||||
\(558\) | −5.36930 | − | 1.47331i | −0.227300 | − | 0.0623702i | ||||
\(559\) | 4.51899i | 0.191133i | ||||||||
\(560\) | 8.69886 | − | 3.38637i | 0.367594 | − | 0.143100i | ||||
\(561\) | 15.1912i | 0.641371i | ||||||||
\(562\) | −8.28598 | − | 8.28598i | −0.349523 | − | 0.349523i | ||||
\(563\) | 16.5013 | − | 16.5013i | 0.695446 | − | 0.695446i | −0.267978 | − | 0.963425i | \(-0.586356\pi\) |
0.963425 | + | 0.267978i | \(0.0863556\pi\) | |||||||
\(564\) | −0.687180 | −0.0289355 | ||||||||
\(565\) | 7.36866 | + | 18.9285i | 0.310002 | + | 0.796328i | ||||
\(566\) | −23.1965 | −0.975023 | ||||||||
\(567\) | −2.95191 | − | 2.95191i | −0.123969 | − | 0.123969i | ||||
\(568\) | 4.59208 | − | 4.59208i | 0.192680 | − | 0.192680i | ||||
\(569\) | 24.1381 | 1.01192 | 0.505962 | − | 0.862556i | \(-0.331138\pi\) | ||||
0.505962 | + | 0.862556i | \(0.331138\pi\) | |||||||
\(570\) | 0.913425 | − | 2.07793i | 0.0382592 | − | 0.0870347i | ||||
\(571\) | 4.16201i | 0.174175i | 0.996201 | + | 0.0870875i | \(0.0277560\pi\) | ||||
−0.996201 | + | 0.0870875i | \(0.972244\pi\) | |||||||
\(572\) | 11.3244 | + | 11.3244i | 0.473495 | + | 0.473495i | ||||
\(573\) | 10.2447 | + | 10.2447i | 0.427977 | + | 0.427977i | ||||
\(574\) | 33.4615i | 1.39666i | ||||||||
\(575\) | −0.614311 | + | 14.3042i | −0.0256185 | + | 0.596526i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 7.51725 | + | 7.51725i | 0.312947 | + | 0.312947i | 0.846050 | − | 0.533103i | \(-0.178974\pi\) |
−0.533103 | + | 0.846050i | \(0.678974\pi\) | |||||||
\(578\) | 1.99669 | − | 1.99669i | 0.0830514 | − | 0.0830514i | ||||
\(579\) | −16.5356 | −0.687197 | ||||||||
\(580\) | 8.91819 | + | 3.92030i | 0.370308 | + | 0.162782i | ||||
\(581\) | 44.8287i | 1.85981i | ||||||||
\(582\) | −8.30027 | + | 8.30027i | −0.344057 | + | 0.344057i | ||||
\(583\) | 11.9886 | − | 11.9886i | 0.496519 | − | 0.496519i | ||||
\(584\) | 9.26705 | 0.383473 | ||||||||
\(585\) | 3.21985 | + | 8.27109i | 0.133124 | + | 0.341968i | ||||
\(586\) | 1.93214 | 0.0798158 | ||||||||
\(587\) | −13.1654 | + | 13.1654i | −0.543396 | + | 0.543396i | −0.924523 | − | 0.381127i | \(-0.875536\pi\) |
0.381127 | + | 0.924523i | \(0.375536\pi\) | |||||||
\(588\) | 7.37338 | + | 7.37338i | 0.304073 | + | 0.304073i | ||||
\(589\) | 4.91151 | − | 2.79647i | 0.202375 | − | 0.115227i | ||||
\(590\) | 10.5263 | + | 27.0397i | 0.433360 | + | 1.11321i | ||||
\(591\) | 22.1453 | 0.910938 | ||||||||
\(592\) | −4.51858 | + | 4.51858i | −0.185712 | + | 0.185712i | ||||
\(593\) | 7.98738 | − | 7.98738i | 0.328002 | − | 0.328002i | −0.523824 | − | 0.851826i | \(-0.675495\pi\) |
0.851826 | + | 0.523824i | \(0.175495\pi\) | |||||||
\(594\) | − | 4.03469i | − | 0.165545i | ||||||
\(595\) | 14.1437 | − | 32.1752i | 0.579836 | − | 1.31905i | ||||
\(596\) | 0.221568 | 0.00907577 | ||||||||
\(597\) | −10.2225 | − | 10.2225i | −0.418378 | − | 0.418378i | ||||
\(598\) | 8.03705 | − | 8.03705i | 0.328659 | − | 0.328659i | ||||
\(599\) | 3.56015i | 0.145464i | 0.997352 | + | 0.0727318i | \(0.0231717\pi\) | ||||
−0.997352 | + | 0.0727318i | \(0.976828\pi\) | |||||||
\(600\) | 3.38058 | + | 3.68398i | 0.138012 | + | 0.150398i | ||||
\(601\) | 21.1871i | 0.864239i | 0.901816 | + | 0.432120i | \(0.142234\pi\) | ||||
−0.901816 | + | 0.432120i | \(0.857766\pi\) | |||||||
\(602\) | −3.36067 | + | 3.36067i | −0.136971 | + | 0.136971i | ||||
\(603\) | 4.92097 | − | 4.92097i | 0.200397 | − | 0.200397i | ||||
\(604\) | −11.4689 | −0.466662 | ||||||||
\(605\) | 4.75000 | − | 10.8056i | 0.193115 | − | 0.439312i | ||||
\(606\) | − | 2.88110i | − | 0.117037i | ||||||
\(607\) | −11.0204 | − | 11.0204i | −0.447305 | − | 0.447305i | 0.447153 | − | 0.894458i | \(-0.352438\pi\) |
−0.894458 | + | 0.447153i | \(0.852438\pi\) | |||||||
\(608\) | −0.717783 | + | 0.717783i | −0.0291099 | + | 0.0291099i | ||||
\(609\) | 18.1875i | 0.736994i | ||||||||
\(610\) | 6.56969 | + | 16.8761i | 0.265999 | + | 0.683293i | ||||
\(611\) | 2.72765i | 0.110349i | ||||||||
\(612\) | 2.66235 | − | 2.66235i | 0.107619 | − | 0.107619i | ||||
\(613\) | −29.3900 | − | 29.3900i | −1.18705 | − | 1.18705i | −0.977879 | − | 0.209171i | \(-0.932923\pi\) |
−0.209171 | − | 0.977879i | \(-0.567077\pi\) | |||||||
\(614\) | − | 0.711167i | − | 0.0287004i | ||||||
\(615\) | −16.7021 | + | 6.50197i | −0.673496 | + | 0.262185i | ||||
\(616\) | 16.8433i | 0.678637i | ||||||||
\(617\) | −7.25887 | − | 7.25887i | −0.292231 | − | 0.292231i | 0.545730 | − | 0.837961i | \(-0.316252\pi\) |
−0.837961 | + | 0.545730i | \(0.816252\pi\) | |||||||
\(618\) | 8.65254 | + | 8.65254i | 0.348056 | + | 0.348056i | ||||
\(619\) | 42.3564 | 1.70245 | 0.851224 | − | 0.524803i | \(-0.175861\pi\) | ||||
0.851224 | + | 0.524803i | \(0.175861\pi\) | |||||||
\(620\) | 1.28546 | + | 12.3834i | 0.0516255 | + | 0.497328i | ||||
\(621\) | −2.86347 | −0.114907 | ||||||||
\(622\) | −16.6959 | − | 16.6959i | −0.669443 | − | 0.669443i | ||||
\(623\) | 14.8699 | + | 14.8699i | 0.595750 | + | 0.595750i | ||||
\(624\) | − | 3.96934i | − | 0.158901i | ||||||
\(625\) | −2.14336 | + | 24.9080i | −0.0857343 | + | 0.996318i | ||||
\(626\) | 18.2260i | 0.728458i | ||||||||
\(627\) | 2.89603 | + | 2.89603i | 0.115656 | + | 0.115656i | ||||
\(628\) | −10.0308 | + | 10.0308i | −0.400274 | + | 0.400274i | ||||
\(629\) | 24.0601i | 0.959339i | ||||||||
\(630\) | −3.75649 | + | 8.54555i | −0.149662 | + | 0.340463i | ||||
\(631\) | 34.7320i | 1.38266i | 0.722540 | + | 0.691329i | \(0.242975\pi\) | ||||
−0.722540 | + | 0.691329i | \(0.757025\pi\) | |||||||
\(632\) | −6.67512 | + | 6.67512i | −0.265522 | + | 0.265522i | ||||
\(633\) | 5.85196 | + | 5.85196i | 0.232594 | + | 0.232594i | ||||
\(634\) | 2.15755i | 0.0856873i | ||||||||
\(635\) | −0.509483 | − | 1.30875i | −0.0202182 | − | 0.0519362i | ||||
\(636\) | −4.20218 | −0.166627 | ||||||||
\(637\) | 29.2675 | − | 29.2675i | 1.15962 | − | 1.15962i | ||||
\(638\) | −12.4294 | + | 12.4294i | −0.492084 | + | 0.492084i | ||||
\(639\) | 6.49419i | 0.256906i | ||||||||
\(640\) | −0.811179 | − | 2.08374i | −0.0320647 | − | 0.0823672i | ||||
\(641\) | − | 24.4321i | − | 0.965011i | −0.875893 | − | 0.482505i | \(-0.839727\pi\) | ||
0.875893 | − | 0.482505i | \(-0.160273\pi\) | |||||||
\(642\) | 11.2782 | − | 11.2782i | 0.445116 | − | 0.445116i | ||||
\(643\) | 29.6839 | + | 29.6839i | 1.17062 | + | 1.17062i | 0.982062 | + | 0.188557i | \(0.0603809\pi\) |
0.188557 | + | 0.982062i | \(0.439619\pi\) | |||||||
\(644\) | 11.9539 | 0.471051 | ||||||||
\(645\) | −2.33048 | − | 1.02444i | −0.0917624 | − | 0.0403374i | ||||
\(646\) | 3.82198i | 0.150374i | ||||||||
\(647\) | 1.52435 | − | 1.52435i | 0.0599282 | − | 0.0599282i | −0.676507 | − | 0.736436i | \(-0.736507\pi\) |
0.736436 | + | 0.676507i | \(0.236507\pi\) | |||||||
\(648\) | −0.707107 | + | 0.707107i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | −52.3562 | −2.05516 | ||||||||
\(650\) | 14.6230 | − | 13.4187i | 0.573560 | − | 0.526324i | ||||
\(651\) | −20.1988 | + | 11.5006i | −0.791652 | + | 0.450744i | ||||
\(652\) | −2.82330 | − | 2.82330i | −0.110569 | − | 0.110569i | ||||
\(653\) | −23.7269 | + | 23.7269i | −0.928504 | + | 0.928504i | −0.997609 | − | 0.0691055i | \(-0.977985\pi\) |
0.0691055 | + | 0.997609i | \(0.477985\pi\) | |||||||
\(654\) | −14.0311 | −0.548661 | ||||||||
\(655\) | 11.6820 | − | 26.5751i | 0.456455 | − | 1.03838i | ||||
\(656\) | 8.01545 | 0.312951 | ||||||||
\(657\) | −6.55280 | + | 6.55280i | −0.255649 | + | 0.255649i | ||||
\(658\) | −2.02849 | + | 2.02849i | −0.0790789 | + | 0.0790789i | ||||
\(659\) | − | 39.5459i | − | 1.54049i | −0.637747 | − | 0.770246i | \(-0.720134\pi\) | ||
0.637747 | − | 0.770246i | \(-0.279866\pi\) | |||||||
\(660\) | −8.40726 | + | 3.27286i | −0.327252 | + | 0.127396i | ||||
\(661\) | 15.6588 | 0.609057 | 0.304529 | − | 0.952503i | \(-0.401501\pi\) | ||||
0.304529 | + | 0.952503i | \(0.401501\pi\) | |||||||
\(662\) | 7.24116 | − | 7.24116i | 0.281436 | − | 0.281436i | ||||
\(663\) | −10.5678 | − | 10.5678i | −0.410419 | − | 0.410419i | ||||
\(664\) | 10.7384 | 0.416729 | ||||||||
\(665\) | −3.43750 | − | 8.83020i | −0.133301 | − | 0.342420i | ||||
\(666\) | − | 6.39023i | − | 0.247616i | ||||||
\(667\) | 8.82130 | + | 8.82130i | 0.341562 | + | 0.341562i | ||||
\(668\) | 14.2859 | + | 14.2859i | 0.552737 | + | 0.552737i | ||||
\(669\) | − | 2.71227i | − | 0.104862i | ||||||
\(670\) | −14.2458 | − | 6.26225i | −0.550365 | − | 0.241932i | ||||
\(671\) | −32.6767 | −1.26147 | ||||||||
\(672\) | 2.95191 | − | 2.95191i | 0.113872 | − | 0.113872i | ||||
\(673\) | −12.3713 | − | 12.3713i | −0.476880 | − | 0.476880i | 0.427253 | − | 0.904132i | \(-0.359481\pi\) |
−0.904132 | + | 0.427253i | \(0.859481\pi\) | |||||||
\(674\) | 26.2113 | 1.00962 | ||||||||
\(675\) | −4.99540 | − | 0.214533i | −0.192273 | − | 0.00825740i | ||||
\(676\) | −2.75569 | −0.105988 | ||||||||
\(677\) | −27.6460 | + | 27.6460i | −1.06252 | + | 1.06252i | −0.0646102 | + | 0.997911i | \(0.520580\pi\) |
−0.997911 | + | 0.0646102i | \(0.979420\pi\) | |||||||
\(678\) | 6.42328 | + | 6.42328i | 0.246685 | + | 0.246685i | ||||
\(679\) | 49.0033i | 1.88057i | ||||||||
\(680\) | −7.70731 | − | 3.38802i | −0.295562 | − | 0.129924i | ||||
\(681\) | 7.93594i | 0.304106i | ||||||||
\(682\) | −21.6634 | − | 5.94435i | −0.829536 | − | 0.227621i | ||||
\(683\) | −16.3646 | + | 16.3646i | −0.626174 | + | 0.626174i | −0.947103 | − | 0.320929i | \(-0.896005\pi\) |
0.320929 | + | 0.947103i | \(0.396005\pi\) | |||||||
\(684\) | − | 1.01510i | − | 0.0388132i | ||||||
\(685\) | −15.4603 | − | 39.7143i | −0.590709 | − | 1.51740i | ||||
\(686\) | 14.3087 | 0.546309 | ||||||||
\(687\) | −3.92815 | − | 3.92815i | −0.149868 | − | 0.149868i | ||||
\(688\) | 0.805022 | + | 0.805022i | 0.0306912 | + | 0.0306912i | ||||
\(689\) | 16.6799i | 0.635454i | ||||||||
\(690\) | 2.32279 | + | 5.96674i | 0.0884271 | + | 0.227150i | ||||
\(691\) | −34.2989 | −1.30479 | −0.652395 | − | 0.757879i | \(-0.726236\pi\) | ||||
−0.652395 | + | 0.757879i | \(0.726236\pi\) | |||||||
\(692\) | −12.5526 | − | 12.5526i | −0.477180 | − | 0.477180i | ||||
\(693\) | −11.9100 | − | 11.9100i | −0.452425 | − | 0.452425i | ||||
\(694\) | −24.8133 | −0.941899 | ||||||||
\(695\) | 19.3564 | − | 44.0334i | 0.734230 | − | 1.67028i | ||||
\(696\) | 4.35667 | 0.165139 | ||||||||
\(697\) | 21.3400 | − | 21.3400i | 0.808309 | − | 0.808309i | ||||
\(698\) | 22.0239 | − | 22.0239i | 0.833616 | − | 0.833616i | ||||
\(699\) | −17.6003 | −0.665703 | ||||||||
\(700\) | 20.8539 | + | 0.895598i | 0.788204 | + | 0.0338504i | ||||
\(701\) | 26.5443 | 1.00257 | 0.501283 | − | 0.865283i | \(-0.332862\pi\) | ||||
0.501283 | + | 0.865283i | \(0.332862\pi\) | |||||||
\(702\) | 2.80675 | + | 2.80675i | 0.105934 | + | 0.105934i | ||||
\(703\) | 4.58680 | + | 4.58680i | 0.172994 | + | 0.172994i | ||||
\(704\) | 4.03469 | 0.152063 | ||||||||
\(705\) | −1.40667 | − | 0.618351i | −0.0529783 | − | 0.0232884i | ||||
\(706\) | 10.6981i | 0.402627i | ||||||||
\(707\) | −8.50474 | − | 8.50474i | −0.319854 | − | 0.319854i | ||||
\(708\) | 9.17578 | + | 9.17578i | 0.344847 | + | 0.344847i | ||||
\(709\) | 42.1917 | 1.58454 | 0.792272 | − | 0.610169i | \(-0.208898\pi\) | ||||
0.792272 | + | 0.610169i | \(0.208898\pi\) | |||||||
\(710\) | 13.5322 | − | 5.26795i | 0.507855 | − | 0.197703i | ||||
\(711\) | − | 9.44004i | − | 0.354029i | ||||||
\(712\) | 3.56197 | − | 3.56197i | 0.133490 | − | 0.133490i | ||||
\(713\) | −4.21878 | + | 15.3748i | −0.157995 | + | 0.575792i | ||||
\(714\) | − | 15.7181i | − | 0.588233i | ||||||
\(715\) | 12.9911 | + | 33.3713i | 0.485839 | + | 1.24802i | ||||
\(716\) | − | 22.2553i | − | 0.831720i | ||||||
\(717\) | −17.4275 | − | 17.4275i | −0.650841 | − | 0.650841i | ||||
\(718\) | −9.51297 | + | 9.51297i | −0.355021 | + | 0.355021i | ||||
\(719\) | −39.9630 | −1.49037 | −0.745183 | − | 0.666860i | \(-0.767638\pi\) | ||||
−0.745183 | + | 0.666860i | \(0.767638\pi\) | |||||||
\(720\) | 2.04702 | + | 0.899839i | 0.0762879 | + | 0.0335350i | ||||
\(721\) | 51.0830 | 1.90243 | ||||||||
\(722\) | −12.7064 | − | 12.7064i | −0.472884 | − | 0.472884i | ||||
\(723\) | 10.7036 | − | 10.7036i | 0.398071 | − | 0.398071i | ||||
\(724\) | 3.14386 | 0.116841 | ||||||||
\(725\) | 14.7281 | + | 16.0499i | 0.546987 | + | 0.596077i | ||||
\(726\) | − | 5.27872i | − | 0.195912i | ||||||
\(727\) | −27.1518 | − | 27.1518i | −1.00700 | − | 1.00700i | −0.999975 | − | 0.00702780i | \(-0.997763\pi\) |
−0.00702780 | − | 0.999975i | \(-0.502237\pi\) | |||||||
\(728\) | −11.7171 | − | 11.7171i | −0.434266 | − | 0.434266i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 18.9698 | + | 8.33885i | 0.702105 | + | 0.308635i | ||||
\(731\) | 4.28651 | 0.158542 | ||||||||
\(732\) | 5.72681 | + | 5.72681i | 0.211669 | + | 0.211669i | ||||
\(733\) | 34.0779 | − | 34.0779i | 1.25870 | − | 1.25870i | 0.306979 | − | 0.951716i | \(-0.400682\pi\) |
0.951716 | − | 0.306979i | \(-0.0993183\pi\) | |||||||
\(734\) | 21.6734 | 0.799982 | ||||||||
\(735\) | 8.45861 | + | 21.7283i | 0.312000 | + | 0.801461i | ||||
\(736\) | − | 2.86347i | − | 0.105549i | ||||||
\(737\) | 19.8546 | − | 19.8546i | 0.731353 | − | 0.731353i | ||||
\(738\) | −5.66778 | + | 5.66778i | −0.208634 | + | 0.208634i | ||||
\(739\) | −16.9876 | −0.624897 | −0.312449 | − | 0.949935i | \(-0.601149\pi\) | ||||
−0.312449 | + | 0.949935i | \(0.601149\pi\) | |||||||
\(740\) | −13.3156 | + | 5.18362i | −0.489491 | + | 0.190554i | ||||
\(741\) | −4.02927 | −0.148019 | ||||||||
\(742\) | −12.4045 | + | 12.4045i | −0.455382 | + | 0.455382i | ||||
\(743\) | 19.2665 | + | 19.2665i | 0.706818 | + | 0.706818i | 0.965865 | − | 0.259047i | \(-0.0834084\pi\) |
−0.259047 | + | 0.965865i | \(0.583408\pi\) | |||||||
\(744\) | 2.75488 | + | 4.83845i | 0.100999 | + | 0.177386i | ||||
\(745\) | 0.453553 | + | 0.199375i | 0.0166169 | + | 0.00730454i | ||||
\(746\) | 25.6666 | 0.939721 | ||||||||
\(747\) | −7.59317 | + | 7.59317i | −0.277820 | + | 0.277820i | ||||
\(748\) | 10.7418 | − | 10.7418i | 0.392758 | − | 0.392758i | ||||
\(749\) | − | 66.5847i | − | 2.43295i | ||||||
\(750\) | 3.60513 | + | 10.5831i | 0.131641 | + | 0.386442i | ||||
\(751\) | −40.8167 | −1.48942 | −0.744710 | − | 0.667388i | \(-0.767412\pi\) | ||||
−0.744710 | + | 0.667388i | \(0.767412\pi\) | |||||||
\(752\) | 0.485909 | + | 0.485909i | 0.0177193 | + | 0.0177193i | ||||
\(753\) | −0.272808 | + | 0.272808i | −0.00994166 | + | 0.00994166i | ||||
\(754\) | − | 17.2931i | − | 0.629778i | ||||||
\(755\) | −23.4770 | − | 10.3201i | −0.854416 | − | 0.375588i | ||||
\(756\) | 4.17463i | 0.151830i | ||||||||
\(757\) | 16.0389 | − | 16.0389i | 0.582943 | − | 0.582943i | −0.352768 | − | 0.935711i | \(-0.614759\pi\) |
0.935711 | + | 0.352768i | \(0.114759\pi\) | |||||||
\(758\) | −8.54222 | + | 8.54222i | −0.310267 | + | 0.310267i | ||||
\(759\) | −11.5532 | −0.419355 | ||||||||
\(760\) | −2.11520 | + | 0.823427i | −0.0767265 | + | 0.0298688i | ||||
\(761\) | − | 16.2603i | − | 0.589437i | −0.955584 | − | 0.294718i | \(-0.904774\pi\) | ||
0.955584 | − | 0.294718i | \(-0.0952258\pi\) | |||||||
\(762\) | −0.444118 | − | 0.444118i | −0.0160887 | − | 0.0160887i | ||||
\(763\) | −41.4187 | + | 41.4187i | −1.49946 | + | 1.49946i | ||||
\(764\) | − | 14.4881i | − | 0.524162i | ||||||
\(765\) | 7.84558 | − | 3.05420i | 0.283658 | − | 0.110425i | ||||
\(766\) | − | 7.33434i | − | 0.265001i | ||||||
\(767\) | 36.4218 | − | 36.4218i | 1.31512 | − | 1.31512i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | 7.52534i | 0.271371i | 0.990752 | + | 0.135685i | \(0.0433236\pi\) | ||||
−0.990752 | + | 0.135685i | \(0.956676\pi\) | |||||||
\(770\) | −15.1563 | + | 34.4786i | −0.546195 | + | 1.24252i | ||||
\(771\) | − | 20.7561i | − | 0.747514i | ||||||
\(772\) | 11.6924 | + | 11.6924i | 0.420820 | + | 0.420820i | ||||
\(773\) | 6.55832 | + | 6.55832i | 0.235886 | + | 0.235886i | 0.815144 | − | 0.579258i | \(-0.196658\pi\) |
−0.579258 | + | 0.815144i | \(0.696658\pi\) | |||||||
\(774\) | −1.13847 | −0.0409216 | ||||||||
\(775\) | −8.51166 | + | 26.5057i | −0.305748 | + | 0.952113i | ||||
\(776\) | 11.7383 | 0.421382 | ||||||||
\(777\) | −18.8634 | − | 18.8634i | −0.676720 | − | 0.676720i | ||||
\(778\) | 3.77557 | + | 3.77557i | 0.135361 | + | 0.135361i | ||||
\(779\) | − | 8.13647i | − | 0.291519i | ||||||
\(780\) | 3.57177 | − | 8.12532i | 0.127890 | − | 0.290933i | ||||
\(781\) | 26.2020i | 0.937582i | ||||||||
\(782\) | −7.62358 | − | 7.62358i | −0.272619 | − | 0.272619i | ||||
\(783\) | −3.08063 | + | 3.08063i | −0.110093 | + | 0.110093i | ||||
\(784\) | − | 10.4275i | − | 0.372412i | ||||||
\(785\) | −29.5595 | + | 11.5072i | −1.05502 | + | 0.410709i | ||||
\(786\) | − | 12.9824i | − | 0.463065i | ||||||
\(787\) | 30.6420 | − | 30.6420i | 1.09227 | − | 1.09227i | 0.0969850 | − | 0.995286i | \(-0.469080\pi\) |
0.995286 | − | 0.0969850i | \(-0.0309199\pi\) | |||||||
\(788\) | −15.6591 | − | 15.6591i | −0.557833 | − | 0.557833i | ||||
\(789\) | − | 30.4062i | − | 1.08249i | ||||||
\(790\) | −19.6706 | + | 7.65756i | −0.699849 | + | 0.272444i | ||||
\(791\) | 37.9219 | 1.34835 | ||||||||
\(792\) | −2.85296 | + | 2.85296i | −0.101375 | + | 0.101375i | ||||
\(793\) | 22.7317 | − | 22.7317i | 0.807226 | − | 0.807226i | ||||
\(794\) | 1.99927i | 0.0709514i | ||||||||
\(795\) | −8.60195 | − | 3.78129i | −0.305080 | − | 0.134108i | ||||
\(796\) | 14.4567i | 0.512406i | ||||||||
\(797\) | −2.53778 | + | 2.53778i | −0.0898928 | + | 0.0898928i | −0.750623 | − | 0.660730i | \(-0.770247\pi\) |
0.660730 | + | 0.750623i | \(0.270247\pi\) | |||||||
\(798\) | −2.99648 | − | 2.99648i | −0.106074 | − | 0.106074i | ||||
\(799\) | 2.58733 | 0.0915330 | ||||||||
\(800\) | 0.214533 | − | 4.99540i | 0.00758490 | − | 0.176614i | ||||
\(801\) | 5.03739i | 0.177987i | ||||||||
\(802\) | −2.23621 | + | 2.23621i | −0.0789633 | + | 0.0789633i | ||||
\(803\) | −26.4385 | + | 26.4385i | −0.932994 | + | 0.932994i | ||||
\(804\) | −6.95930 | −0.245436 | ||||||||
\(805\) | 24.4700 | + | 10.7566i | 0.862453 | + | 0.379121i | ||||
\(806\) | 19.2055 | − | 10.9351i | 0.676484 | − | 0.385171i | ||||
\(807\) | −14.8408 | − | 14.8408i | −0.522421 | − | 0.522421i | ||||
\(808\) | −2.03724 | + | 2.03724i | −0.0716700 | + | 0.0716700i | ||||
\(809\) | −5.85839 | −0.205970 | −0.102985 | − | 0.994683i | \(-0.532839\pi\) | ||||
−0.102985 | + | 0.994683i | \(0.532839\pi\) | |||||||
\(810\) | −2.08374 | + | 0.811179i | −0.0732153 | + | 0.0285019i | ||||
\(811\) | −39.7619 | −1.39623 | −0.698115 | − | 0.715986i | \(-0.745977\pi\) | ||||
−0.698115 | + | 0.715986i | \(0.745977\pi\) | |||||||
\(812\) | 12.8605 | − | 12.8605i | 0.451315 | − | 0.451315i | ||||
\(813\) | 9.44340 | − | 9.44340i | 0.331194 | − | 0.331194i | ||||
\(814\) | − | 25.7826i | − | 0.903680i | ||||||
\(815\) | −3.23884 | − | 8.31986i | −0.113451 | − | 0.291432i | ||||
\(816\) | −3.76514 | −0.131806 | ||||||||
\(817\) | 0.817176 | − | 0.817176i | 0.0285894 | − | 0.0285894i | ||||
\(818\) | 3.76797 | + | 3.76797i | 0.131744 | + | 0.131744i | ||||
\(819\) | 16.5705 | 0.579022 | ||||||||
\(820\) | 16.4078 | + | 7.21261i | 0.572985 | + | 0.251875i | ||||
\(821\) | − | 50.6248i | − | 1.76682i | −0.468604 | − | 0.883408i | \(-0.655243\pi\) | ||
0.468604 | − | 0.883408i | \(-0.344757\pi\) | |||||||
\(822\) | −13.4768 | − | 13.4768i | −0.470058 | − | 0.470058i | ||||
\(823\) | 32.2721 | + | 32.2721i | 1.12493 | + | 1.12493i | 0.990989 | + | 0.133945i | \(0.0427645\pi\) |
0.133945 | + | 0.990989i | \(0.457236\pi\) | |||||||
\(824\) | − | 12.2365i | − | 0.426280i | ||||||
\(825\) | −20.1549 | − | 0.865576i | −0.701702 | − | 0.0301355i | ||||
\(826\) | 54.1722 | 1.88489 | ||||||||
\(827\) | −19.7409 | + | 19.7409i | −0.686460 | + | 0.686460i | −0.961448 | − | 0.274988i | \(-0.911326\pi\) |
0.274988 | + | 0.961448i | \(0.411326\pi\) | |||||||
\(828\) | 2.02478 | + | 2.02478i | 0.0703660 | + | 0.0703660i | ||||
\(829\) | 52.4332 | 1.82108 | 0.910540 | − | 0.413421i | \(-0.135666\pi\) | ||||
0.910540 | + | 0.413421i | \(0.135666\pi\) | |||||||
\(830\) | 21.9816 | + | 9.66280i | 0.762994 | + | 0.335401i | ||||
\(831\) | 32.1839 | 1.11645 | ||||||||
\(832\) | −2.80675 | + | 2.80675i | −0.0973065 | + | 0.0973065i | ||||
\(833\) | −27.7618 | − | 27.7618i | −0.961889 | − | 0.961889i | ||||
\(834\) | − | 21.5110i | − | 0.744864i | ||||||
\(835\) | 16.3885 | + | 42.0984i | 0.567147 | + | 1.45688i | ||||
\(836\) | − | 4.09561i | − | 0.141649i | ||||||
\(837\) | −5.36930 | − | 1.47331i | −0.185590 | − | 0.0509250i | ||||
\(838\) | 15.0519 | − | 15.0519i | 0.519959 | − | 0.519959i | ||||
\(839\) | − | 35.4933i | − | 1.22537i | −0.790329 | − | 0.612683i | \(-0.790090\pi\) | ||
0.790329 | − | 0.612683i | \(-0.209910\pi\) | |||||||
\(840\) | 8.69886 | − | 3.38637i | 0.300139 | − | 0.116841i | ||||
\(841\) | −10.0194 | −0.345498 | ||||||||
\(842\) | −16.3643 | − | 16.3643i | −0.563949 | − | 0.563949i | ||||
\(843\) | −8.28598 | − | 8.28598i | −0.285384 | − | 0.285384i | ||||
\(844\) | − | 8.27591i | − | 0.284869i | ||||||
\(845\) | −5.64095 | − | 2.47967i | −0.194054 | − | 0.0853034i | ||||
\(846\) | −0.687180 | −0.0236257 | ||||||||
\(847\) | −15.5823 | − | 15.5823i | −0.535414 | − | 0.535414i | ||||
\(848\) | 2.97139 | + | 2.97139i | 0.102038 | + | 0.102038i | ||||
\(849\) | −23.1965 | −0.796103 | ||||||||
\(850\) | −12.7283 | − | 13.8707i | −0.436579 | − | 0.475760i | ||||
\(851\) | −18.2983 | −0.627256 | ||||||||
\(852\) | 4.59208 | − | 4.59208i | 0.157322 | − | 0.157322i | ||||
\(853\) | −20.1909 | + | 20.1909i | −0.691323 | + | 0.691323i | −0.962523 | − | 0.271200i | \(-0.912580\pi\) |
0.271200 | + | 0.962523i | \(0.412580\pi\) | |||||||
\(854\) | 33.8101 | 1.15696 | ||||||||
\(855\) | 0.913425 | − | 2.07793i | 0.0312385 | − | 0.0710636i | ||||
\(856\) | −15.9498 | −0.545154 | ||||||||
\(857\) | 31.3119 | + | 31.3119i | 1.06959 | + | 1.06959i | 0.997390 | + | 0.0722034i | \(0.0230031\pi\) |
0.0722034 | + | 0.997390i | \(0.476997\pi\) | |||||||
\(858\) | 11.3244 | + | 11.3244i | 0.386607 | + | 0.386607i | ||||
\(859\) | 24.2766 | 0.828308 | 0.414154 | − | 0.910207i | \(-0.364078\pi\) | ||||
0.414154 | + | 0.910207i | \(0.364078\pi\) | |||||||
\(860\) | 0.923506 | + | 2.37229i | 0.0314913 | + | 0.0808943i | ||||
\(861\) | 33.4615i | 1.14037i | ||||||||
\(862\) | −21.1796 | − | 21.1796i | −0.721379 | − | 0.721379i | ||||
\(863\) | −20.5511 | − | 20.5511i | −0.699568 | − | 0.699568i | 0.264749 | − | 0.964317i | \(-0.414711\pi\) |
−0.964317 | + | 0.264749i | \(0.914711\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −14.4002 | − | 36.9909i | −0.489620 | − | 1.25773i | ||||
\(866\) | 4.40411i | 0.149658i | ||||||||
\(867\) | 1.99669 | − | 1.99669i | 0.0678112 | − | 0.0678112i | ||||
\(868\) | 22.4148 | + | 6.15052i | 0.760809 | + | 0.208762i | ||||
\(869\) | − | 38.0876i | − | 1.29203i | ||||||
\(870\) | 8.91819 | + | 3.92030i | 0.302355 | + | 0.132911i | ||||
\(871\) | 27.6239i | 0.935999i | ||||||||
\(872\) | 9.92151 | + | 9.92151i | 0.335985 | + | 0.335985i | ||||
\(873\) | −8.30027 | + | 8.30027i | −0.280921 | + | 0.280921i | ||||
\(874\) | −2.90671 | −0.0983208 | ||||||||
\(875\) | 41.8825 | + | 20.5985i | 1.41589 | + | 0.696356i | ||||
\(876\) | 9.26705 | 0.313105 | ||||||||
\(877\) | −4.50607 | − | 4.50607i | −0.152159 | − | 0.152159i | 0.626922 | − | 0.779082i | \(-0.284314\pi\) |
−0.779082 | + | 0.626922i | \(0.784314\pi\) | |||||||
\(878\) | 20.3225 | − | 20.3225i | 0.685850 | − | 0.685850i | ||||
\(879\) | 1.93214 | 0.0651694 | ||||||||
\(880\) | 8.25909 | + | 3.63057i | 0.278414 | + | 0.122387i | ||||
\(881\) | − | 9.83063i | − | 0.331202i | −0.986193 | − | 0.165601i | \(-0.947044\pi\) | ||
0.986193 | − | 0.165601i | \(-0.0529565\pi\) | |||||||
\(882\) | 7.37338 | + | 7.37338i | 0.248275 | + | 0.248275i | ||||
\(883\) | −18.4307 | − | 18.4307i | −0.620241 | − | 0.620241i | 0.325352 | − | 0.945593i | \(-0.394517\pi\) |
−0.945593 | + | 0.325352i | \(0.894517\pi\) | |||||||
\(884\) | 14.9451i | 0.502659i | ||||||||
\(885\) | 10.5263 | + | 27.0397i | 0.353837 | + | 0.908931i | ||||
\(886\) | 4.46315 | 0.149943 | ||||||||
\(887\) | 6.97326 | + | 6.97326i | 0.234139 | + | 0.234139i | 0.814418 | − | 0.580279i | \(-0.197056\pi\) |
−0.580279 | + | 0.814418i | \(0.697056\pi\) | |||||||
\(888\) | −4.51858 | + | 4.51858i | −0.151633 | + | 0.151633i | ||||
\(889\) | −2.62199 | −0.0879387 | ||||||||
\(890\) | 10.4966 | − | 4.08622i | 0.351848 | − | 0.136971i | ||||
\(891\) | − | 4.03469i | − | 0.135167i | ||||||
\(892\) | −1.91786 | + | 1.91786i | −0.0642147 | + | 0.0642147i | ||||
\(893\) | 0.493246 | − | 0.493246i | 0.0165058 | − | 0.0165058i | ||||
\(894\) | 0.221568 | 0.00741033 | ||||||||
\(895\) | 20.0262 | − | 45.5571i | 0.669402 | − | 1.52281i | ||||
\(896\) | −4.17463 | −0.139465 | ||||||||
\(897\) | 8.03705 | − | 8.03705i | 0.268349 | − | 0.268349i | ||||
\(898\) | 13.3660 | + | 13.3660i | 0.446030 | + | 0.446030i | ||||
\(899\) | 12.0021 | + | 21.0795i | 0.400292 | + | 0.703042i | ||||
\(900\) | 3.38058 | + | 3.68398i | 0.112686 | + | 0.122799i | ||||
\(901\) | 15.8218 | 0.527100 | ||||||||
\(902\) | −22.8677 | + | 22.8677i | −0.761412 | + | 0.761412i | ||||
\(903\) | −3.36067 | + | 3.36067i | −0.111836 | + | 0.111836i | ||||
\(904\) | − | 9.08389i | − | 0.302126i | ||||||
\(905\) | 6.43555 | + | 2.82897i | 0.213925 | + | 0.0940381i | ||||
\(906\) | −11.4689 | −0.381028 | ||||||||
\(907\) | 36.7566 | + | 36.7566i | 1.22048 | + | 1.22048i | 0.967461 | + | 0.253020i | \(0.0814240\pi\) |
0.253020 | + | 0.967461i | \(0.418576\pi\) | |||||||
\(908\) | 5.61156 | − | 5.61156i | 0.186226 | − | 0.186226i | ||||
\(909\) | − | 2.88110i | − | 0.0955600i | ||||||
\(910\) | −13.4417 | − | 34.5288i | −0.445587 | − | 1.14462i | ||||
\(911\) | − | 53.0903i | − | 1.75896i | −0.475935 | − | 0.879481i | \(-0.657890\pi\) | ||
0.475935 | − | 0.879481i | \(-0.342110\pi\) | |||||||
\(912\) | −0.717783 | + | 0.717783i | −0.0237682 | + | 0.0237682i | ||||
\(913\) | −30.6361 | + | 30.6361i | −1.01391 | + | 1.01391i | ||||
\(914\) | −5.48565 | −0.181449 | ||||||||
\(915\) | 6.56969 | + | 16.8761i | 0.217187 | + | 0.557907i | ||||
\(916\) | 5.55524i | 0.183550i | ||||||||
\(917\) | −38.3227 | − | 38.3227i | −1.26553 | − | 1.26553i | ||||
\(918\) | 2.66235 | − | 2.66235i | 0.0878708 | − | 0.0878708i | ||||
\(919\) | − | 20.9427i | − | 0.690836i | −0.938449 | − | 0.345418i | \(-0.887737\pi\) | ||
0.938449 | − | 0.345418i | \(-0.112263\pi\) | |||||||
\(920\) | 2.57666 | − | 5.86159i | 0.0849501 | − | 0.193251i | ||||
\(921\) | − | 0.711167i | − | 0.0234338i | ||||||
\(922\) | 6.13843 | − | 6.13843i | 0.202158 | − | 0.202158i | ||||
\(923\) | −18.2276 | − | 18.2276i | −0.599967 | − | 0.599967i | ||||
\(924\) | 16.8433i | 0.554105i | ||||||||
\(925\) | −31.9217 | − | 1.37092i | −1.04958 | − | 0.0450755i | ||||
\(926\) | 25.1296i | 0.825808i | ||||||||
\(927\) | 8.65254 | + | 8.65254i | 0.284187 | + | 0.284187i | ||||
\(928\) | −3.08063 | − | 3.08063i | −0.101127 | − | 0.101127i | ||||
\(929\) | −7.44039 | −0.244111 | −0.122056 | − | 0.992523i | \(-0.538949\pi\) | ||||
−0.122056 | + | 0.992523i | \(0.538949\pi\) | |||||||
\(930\) | 1.28546 | + | 12.3834i | 0.0421520 | + | 0.406066i | ||||
\(931\) | −10.5850 | −0.346909 | ||||||||
\(932\) | 12.4453 | + | 12.4453i | 0.407658 | + | 0.407658i | ||||
\(933\) | −16.6959 | − | 16.6959i | −0.546598 | − | 0.546598i | ||||
\(934\) | 12.3653i | 0.404606i | ||||||||
\(935\) | 31.6545 | − | 12.3228i | 1.03521 | − | 0.402997i | ||||
\(936\) | − | 3.96934i | − | 0.129742i | ||||||
\(937\) | 5.93410 | + | 5.93410i | 0.193859 | + | 0.193859i | 0.797361 | − | 0.603502i | \(-0.206229\pi\) |
−0.603502 | + | 0.797361i | \(0.706229\pi\) | |||||||
\(938\) | −20.5432 | + | 20.5432i | −0.670760 | + | 0.670760i | ||||
\(939\) | 18.2260i | 0.594784i | ||||||||
\(940\) | 0.557426 | + | 1.43191i | 0.0181812 | + | 0.0467036i | ||||
\(941\) | 54.9327i | 1.79076i | 0.445308 | + | 0.895378i | \(0.353094\pi\) | ||||
−0.445308 | + | 0.895378i | \(0.646906\pi\) | |||||||
\(942\) | −10.0308 | + | 10.0308i | −0.326823 | + | 0.326823i | ||||
\(943\) | 16.2295 | + | 16.2295i | 0.528506 | + | 0.528506i | ||||
\(944\) | − | 12.9765i | − | 0.422350i | ||||||
\(945\) | −3.75649 | + | 8.54555i | −0.122199 | + | 0.277987i | ||||
\(946\) | −4.59338 | −0.149344 | ||||||||
\(947\) | 32.0224 | − | 32.0224i | 1.04059 | − | 1.04059i | 0.0414489 | − | 0.999141i | \(-0.486803\pi\) |
0.999141 | − | 0.0414489i | \(-0.0131974\pi\) | |||||||
\(948\) | −6.67512 | + | 6.67512i | −0.216798 | + | 0.216798i | ||||
\(949\) | − | 36.7841i | − | 1.19406i | ||||||
\(950\) | −5.07082 | − | 0.217772i | −0.164519 | − | 0.00706547i | ||||
\(951\) | 2.15755i | 0.0699634i | ||||||||
\(952\) | −11.1143 | + | 11.1143i | −0.360218 | + | 0.360218i | ||||
\(953\) | 26.2199 | + | 26.2199i | 0.849345 | + | 0.849345i | 0.990051 | − | 0.140707i | \(-0.0449374\pi\) |
−0.140707 | + | 0.990051i | \(0.544937\pi\) | |||||||
\(954\) | −4.20218 | −0.136051 | ||||||||
\(955\) | 13.0370 | − | 29.6575i | 0.421867 | − | 0.959694i | ||||
\(956\) | 24.6462i | 0.797114i | ||||||||
\(957\) | −12.4294 | + | 12.4294i | −0.401785 | + | 0.401785i | ||||
\(958\) | 6.64301 | − | 6.64301i | 0.214626 | − | 0.214626i | ||||
\(959\) | −79.5646 | −2.56928 | ||||||||
\(960\) | −0.811179 | − | 2.08374i | −0.0261807 | − | 0.0672525i | ||||
\(961\) | −15.8213 | + | 26.6587i | −0.510364 | + | 0.859959i | ||||
\(962\) | 17.9358 | + | 17.9358i | 0.578273 | + | 0.578273i | ||||
\(963\) | 11.2782 | − | 11.2782i | 0.363436 | − | 0.363436i | ||||
\(964\) | −15.1372 | −0.487535 | ||||||||
\(965\) | 13.4133 | + | 34.4560i | 0.431791 | + | 1.10918i | ||||
\(966\) | 11.9539 | 0.384612 | ||||||||
\(967\) | −18.2620 | + | 18.2620i | −0.587267 | + | 0.587267i | −0.936890 | − | 0.349623i | \(-0.886310\pi\) |
0.349623 | + | 0.936890i | \(0.386310\pi\) | |||||||
\(968\) | −3.73262 | + | 3.73262i | −0.119971 | + | 0.119971i | ||||
\(969\) | 3.82198i | 0.122780i | ||||||||
\(970\) | 24.0286 | + | 10.5626i | 0.771513 | + | 0.339145i | ||||
\(971\) | −21.3719 | −0.685858 | −0.342929 | − | 0.939361i | \(-0.611419\pi\) | ||||
−0.342929 | + | 0.939361i | \(0.611419\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −63.4984 | − | 63.4984i | −2.03567 | − | 2.03567i | ||||
\(974\) | 31.5715 | 1.01162 | ||||||||
\(975\) | 14.6230 | − | 13.4187i | 0.468310 | − | 0.429742i | ||||
\(976\) | − | 8.09893i | − | 0.259241i | ||||||
\(977\) | −13.4924 | − | 13.4924i | −0.431659 | − | 0.431659i | 0.457533 | − | 0.889193i | \(-0.348733\pi\) |
−0.889193 | + | 0.457533i | \(0.848733\pi\) | |||||||
\(978\) | −2.82330 | − | 2.82330i | −0.0902792 | − | 0.0902792i | ||||
\(979\) | 20.3243i | 0.649567i | ||||||||
\(980\) | 9.38311 | − | 21.3454i | 0.299732 | − | 0.681853i | ||||
\(981\) | −14.0311 | −0.447980 | ||||||||
\(982\) | 3.89639 | − | 3.89639i | 0.124339 | − | 0.124339i | ||||
\(983\) | −5.92278 | − | 5.92278i | −0.188907 | − | 0.188907i | 0.606316 | − | 0.795224i | \(-0.292647\pi\) |
−0.795224 | + | 0.606316i | \(0.792647\pi\) | |||||||
\(984\) | 8.01545 | 0.255523 | ||||||||
\(985\) | −17.9638 | − | 46.1452i | −0.572376 | − | 1.47031i | ||||
\(986\) | −16.4035 | −0.522392 | ||||||||
\(987\) | −2.02849 | + | 2.02849i | −0.0645676 | + | 0.0645676i | ||||
\(988\) | 2.84913 | + | 2.84913i | 0.0906428 | + | 0.0906428i | ||||
\(989\) | 3.25999i | 0.103662i | ||||||||
\(990\) | −8.40726 | + | 3.27286i | −0.267200 | + | 0.104018i | ||||
\(991\) | − | 15.0645i | − | 0.478541i | −0.970953 | − | 0.239270i | \(-0.923092\pi\) | ||
0.970953 | − | 0.239270i | \(-0.0769083\pi\) | |||||||
\(992\) | 1.47331 | − | 5.36930i | 0.0467776 | − | 0.170475i | ||||
\(993\) | 7.24116 | − | 7.24116i | 0.229791 | − | 0.229791i | ||||
\(994\) | − | 27.1108i | − | 0.859903i | ||||||
\(995\) | −13.0087 | + | 29.5932i | −0.412405 | + | 0.938169i | ||||
\(996\) | 10.7384 | 0.340258 | ||||||||
\(997\) | 22.5763 | + | 22.5763i | 0.714998 | + | 0.714998i | 0.967576 | − | 0.252579i | \(-0.0812787\pi\) |
−0.252579 | + | 0.967576i | \(0.581279\pi\) | |||||||
\(998\) | −8.50535 | − | 8.50535i | −0.269232 | − | 0.269232i | ||||
\(999\) | − | 6.39023i | − | 0.202178i |
(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 | 930.2.k.b.247.4 | yes | 32 | |
5.3 | odd | 4 | 930.2.k.a.433.4 | yes | 32 | ||
31.30 | odd | 2 | 930.2.k.a.247.4 | ✓ | 32 | ||
155.123 | even | 4 | inner | 930.2.k.b.433.4 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.k.a.247.4 | ✓ | 32 | 31.30 | odd | 2 | ||
930.2.k.a.433.4 | yes | 32 | 5.3 | odd | 4 | ||
930.2.k.b.247.4 | yes | 32 | 1.1 | even | 1 | trivial | |
930.2.k.b.433.4 | yes | 32 | 155.123 | even | 4 | inner |