Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(77,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("390.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.s (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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.11 | ||
Character | \(\chi\) | \(=\) | 390.77 |
Dual form | 390.2.s.c.233.11 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.14719 | + | 1.29768i | 0.662328 | + | 0.749214i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −2.23605 | + | 0.00995019i | −0.999990 | + | 0.00444986i | ||||
\(6\) | −0.106413 | + | 1.72878i | −0.0434428 | + | 0.705771i | ||||
\(7\) | −1.03162 | + | 1.03162i | −0.389917 | + | 0.389917i | −0.874658 | − | 0.484741i | \(-0.838914\pi\) |
0.484741 | + | 0.874658i | \(0.338914\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −0.367928 | + | 2.97735i | −0.122643 | + | 0.992451i | ||||
\(10\) | −1.58816 | − | 1.57409i | −0.502220 | − | 0.497770i | ||||
\(11\) | −3.70213 | −1.11623 | −0.558117 | − | 0.829762i | \(-0.688476\pi\) | ||||
−0.558117 | + | 0.829762i | \(0.688476\pi\) | |||||||
\(12\) | −1.29768 | + | 1.14719i | −0.374607 | + | 0.331164i | ||||
\(13\) | 1.20959 | + | 3.39660i | 0.335480 | + | 0.942047i | ||||
\(14\) | −1.45893 | −0.389917 | ||||||||
\(15\) | −2.57807 | − | 2.89025i | −0.665656 | − | 0.746259i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.82396 | − | 1.82396i | 0.442376 | − | 0.442376i | −0.450434 | − | 0.892810i | \(-0.648731\pi\) |
0.892810 | + | 0.450434i | \(0.148731\pi\) | |||||||
\(18\) | −2.36547 | + | 1.84514i | −0.557547 | + | 0.434904i | ||||
\(19\) | 6.37656 | 1.46288 | 0.731442 | − | 0.681904i | \(-0.238848\pi\) | ||||
0.731442 | + | 0.681904i | \(0.238848\pi\) | |||||||
\(20\) | −0.00995019 | − | 2.23605i | −0.00222493 | − | 0.499995i | ||||
\(21\) | −2.52217 | − | 0.155249i | −0.550384 | − | 0.0338781i | ||||
\(22\) | −2.61780 | − | 2.61780i | −0.558117 | − | 0.558117i | ||||
\(23\) | 3.59028 | + | 3.59028i | 0.748624 | + | 0.748624i | 0.974221 | − | 0.225596i | \(-0.0724331\pi\) |
−0.225596 | + | 0.974221i | \(0.572433\pi\) | |||||||
\(24\) | −1.72878 | − | 0.106413i | −0.352886 | − | 0.0217214i | ||||
\(25\) | 4.99980 | − | 0.0444982i | 0.999960 | − | 0.00889964i | ||||
\(26\) | −1.54645 | + | 3.25707i | −0.303284 | + | 0.638764i | ||||
\(27\) | −4.28572 | + | 2.93813i | −0.824788 | + | 0.565443i | ||||
\(28\) | −1.03162 | − | 1.03162i | −0.194958 | − | 0.194958i | ||||
\(29\) | −0.495771 | −0.0920624 | −0.0460312 | − | 0.998940i | \(-0.514657\pi\) | ||||
−0.0460312 | + | 0.998940i | \(0.514657\pi\) | |||||||
\(30\) | 0.220742 | − | 3.86669i | 0.0403018 | − | 0.705957i | ||||
\(31\) | − | 2.88858i | − | 0.518803i | −0.965770 | − | 0.259402i | \(-0.916475\pi\) | ||
0.965770 | − | 0.259402i | \(-0.0835254\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −4.24703 | − | 4.80417i | −0.739314 | − | 0.836298i | ||||
\(34\) | 2.57947 | 0.442376 | ||||||||
\(35\) | 2.29649 | − | 2.31702i | 0.388178 | − | 0.391648i | ||||
\(36\) | −2.97735 | − | 0.367928i | −0.496225 | − | 0.0613214i | ||||
\(37\) | 2.07537 | − | 2.07537i | 0.341189 | − | 0.341189i | −0.515625 | − | 0.856814i | \(-0.672440\pi\) |
0.856814 | + | 0.515625i | \(0.172440\pi\) | |||||||
\(38\) | 4.50891 | + | 4.50891i | 0.731442 | + | 0.731442i | ||||
\(39\) | −3.02006 | + | 5.46619i | −0.483597 | + | 0.875291i | ||||
\(40\) | 1.57409 | − | 1.58816i | 0.248885 | − | 0.251110i | ||||
\(41\) | −1.65794 | −0.258927 | −0.129463 | − | 0.991584i | \(-0.541325\pi\) | ||||
−0.129463 | + | 0.991584i | \(0.541325\pi\) | |||||||
\(42\) | −1.67367 | − | 1.89322i | −0.258253 | − | 0.292131i | ||||
\(43\) | 8.68616 | − | 8.68616i | 1.32463 | − | 1.32463i | 0.414643 | − | 0.909984i | \(-0.363906\pi\) |
0.909984 | − | 0.414643i | \(-0.136094\pi\) | |||||||
\(44\) | − | 3.70213i | − | 0.558117i | ||||||
\(45\) | 0.793079 | − | 6.66116i | 0.118225 | − | 0.992987i | ||||
\(46\) | 5.07742i | 0.748624i | ||||||||
\(47\) | 2.79640 | + | 2.79640i | 0.407897 | + | 0.407897i | 0.881005 | − | 0.473108i | \(-0.156868\pi\) |
−0.473108 | + | 0.881005i | \(0.656868\pi\) | |||||||
\(48\) | −1.14719 | − | 1.29768i | −0.165582 | − | 0.187303i | ||||
\(49\) | 4.87151i | 0.695930i | ||||||||
\(50\) | 3.56686 | + | 3.50393i | 0.504430 | + | 0.495530i | ||||
\(51\) | 4.45933 | + | 0.274489i | 0.624432 | + | 0.0384361i | ||||
\(52\) | −3.39660 | + | 1.20959i | −0.471024 | + | 0.167740i | ||||
\(53\) | −5.90440 | − | 5.90440i | −0.811031 | − | 0.811031i | 0.173757 | − | 0.984788i | \(-0.444409\pi\) |
−0.984788 | + | 0.173757i | \(0.944409\pi\) | |||||||
\(54\) | −5.10803 | − | 0.952895i | −0.695115 | − | 0.129673i | ||||
\(55\) | 8.27814 | − | 0.0368369i | 1.11622 | − | 0.00496709i | ||||
\(56\) | − | 1.45893i | − | 0.194958i | ||||||
\(57\) | 7.31510 | + | 8.27471i | 0.968909 | + | 1.09601i | ||||
\(58\) | −0.350563 | − | 0.350563i | −0.0460312 | − | 0.0460312i | ||||
\(59\) | − | 0.692553i | − | 0.0901628i | −0.998983 | − | 0.0450814i | \(-0.985645\pi\) | ||
0.998983 | − | 0.0450814i | \(-0.0143547\pi\) | |||||||
\(60\) | 2.89025 | − | 2.57807i | 0.373130 | − | 0.332828i | ||||
\(61\) | −12.0684 | −1.54520 | −0.772601 | − | 0.634892i | \(-0.781045\pi\) | ||||
−0.772601 | + | 0.634892i | \(0.781045\pi\) | |||||||
\(62\) | 2.04253 | − | 2.04253i | 0.259402 | − | 0.259402i | ||||
\(63\) | −2.69194 | − | 3.45107i | −0.339153 | − | 0.434793i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −2.73849 | − | 7.58292i | −0.339668 | − | 0.940545i | ||||
\(66\) | 0.393954 | − | 6.40017i | 0.0484924 | − | 0.787806i | ||||
\(67\) | −6.79503 | + | 6.79503i | −0.830145 | + | 0.830145i | −0.987536 | − | 0.157391i | \(-0.949692\pi\) |
0.157391 | + | 0.987536i | \(0.449692\pi\) | |||||||
\(68\) | 1.82396 | + | 1.82396i | 0.221188 | + | 0.221188i | ||||
\(69\) | −0.540302 | + | 8.77773i | −0.0650447 | + | 1.05671i | ||||
\(70\) | 3.26224 | − | 0.0145167i | 0.389913 | − | 0.00173507i | ||||
\(71\) | 4.41216 | 0.523627 | 0.261813 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261813 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(72\) | −1.84514 | − | 2.36547i | −0.217452 | − | 0.278773i | ||||
\(73\) | 8.02368 | + | 8.02368i | 0.939101 | + | 0.939101i | 0.998249 | − | 0.0591482i | \(-0.0188385\pi\) |
−0.0591482 | + | 0.998249i | \(0.518838\pi\) | |||||||
\(74\) | 2.93502 | 0.341189 | ||||||||
\(75\) | 5.79345 | + | 6.43708i | 0.668970 | + | 0.743290i | ||||
\(76\) | 6.37656i | 0.731442i | ||||||||
\(77\) | 3.81920 | − | 3.81920i | 0.435238 | − | 0.435238i | ||||
\(78\) | −6.00069 | + | 1.72967i | −0.679444 | + | 0.195847i | ||||
\(79\) | 6.09995i | 0.686298i | 0.939281 | + | 0.343149i | \(0.111494\pi\) | ||||
−0.939281 | + | 0.343149i | \(0.888506\pi\) | |||||||
\(80\) | 2.23605 | − | 0.00995019i | 0.249998 | − | 0.00111247i | ||||
\(81\) | −8.72926 | − | 2.19090i | −0.969918 | − | 0.243434i | ||||
\(82\) | −1.17234 | − | 1.17234i | −0.129463 | − | 0.129463i | ||||
\(83\) | 4.84469 | − | 4.84469i | 0.531774 | − | 0.531774i | −0.389326 | − | 0.921100i | \(-0.627292\pi\) |
0.921100 | + | 0.389326i | \(0.127292\pi\) | |||||||
\(84\) | 0.155249 | − | 2.52217i | 0.0169391 | − | 0.275192i | ||||
\(85\) | −4.06031 | + | 4.09661i | −0.440403 | + | 0.444340i | ||||
\(86\) | 12.2841 | 1.32463 | ||||||||
\(87\) | −0.568742 | − | 0.643350i | −0.0609755 | − | 0.0689744i | ||||
\(88\) | 2.61780 | − | 2.61780i | 0.279059 | − | 0.279059i | ||||
\(89\) | − | 2.66725i | − | 0.282728i | −0.989958 | − | 0.141364i | \(-0.954851\pi\) | ||
0.989958 | − | 0.141364i | \(-0.0451488\pi\) | |||||||
\(90\) | 5.27094 | − | 4.14936i | 0.555606 | − | 0.437381i | ||||
\(91\) | −4.75185 | − | 2.25617i | −0.498129 | − | 0.236511i | ||||
\(92\) | −3.59028 | + | 3.59028i | −0.374312 | + | 0.374312i | ||||
\(93\) | 3.74844 | − | 3.31373i | 0.388695 | − | 0.343618i | ||||
\(94\) | 3.95471i | 0.407897i | ||||||||
\(95\) | −14.2583 | + | 0.0634480i | −1.46287 | + | 0.00650963i | ||||
\(96\) | 0.106413 | − | 1.72878i | 0.0108607 | − | 0.176443i | ||||
\(97\) | 6.98302 | − | 6.98302i | 0.709019 | − | 0.709019i | −0.257310 | − | 0.966329i | \(-0.582836\pi\) |
0.966329 | + | 0.257310i | \(0.0828362\pi\) | |||||||
\(98\) | −3.44468 | + | 3.44468i | −0.347965 | + | 0.347965i | ||||
\(99\) | 1.36212 | − | 11.0226i | 0.136898 | − | 1.10781i | ||||
\(100\) | 0.0444982 | + | 4.99980i | 0.00444982 | + | 0.499980i | ||||
\(101\) | 15.5880i | 1.55106i | 0.631309 | + | 0.775531i | \(0.282518\pi\) | ||||
−0.631309 | + | 0.775531i | \(0.717482\pi\) | |||||||
\(102\) | 2.95913 | + | 3.34732i | 0.292998 | + | 0.331434i | ||||
\(103\) | 4.08174 | − | 4.08174i | 0.402185 | − | 0.402185i | −0.476817 | − | 0.879003i | \(-0.658210\pi\) |
0.879003 | + | 0.476817i | \(0.158210\pi\) | |||||||
\(104\) | −3.25707 | − | 1.54645i | −0.319382 | − | 0.151642i | ||||
\(105\) | 5.64124 | + | 0.322048i | 0.550529 | + | 0.0314287i | ||||
\(106\) | − | 8.35008i | − | 0.811031i | ||||||
\(107\) | 10.6375 | − | 10.6375i | 1.02836 | − | 1.02836i | 0.0287790 | − | 0.999586i | \(-0.490838\pi\) |
0.999586 | − | 0.0287790i | \(-0.00916189\pi\) | |||||||
\(108\) | −2.93813 | − | 4.28572i | −0.282721 | − | 0.412394i | ||||
\(109\) | 12.9928 | 1.24448 | 0.622242 | − | 0.782825i | \(-0.286222\pi\) | ||||
0.622242 | + | 0.782825i | \(0.286222\pi\) | |||||||
\(110\) | 5.87957 | + | 5.82748i | 0.560595 | + | 0.555628i | ||||
\(111\) | 5.07400 | + | 0.312323i | 0.481603 | + | 0.0296444i | ||||
\(112\) | 1.03162 | − | 1.03162i | 0.0974791 | − | 0.0974791i | ||||
\(113\) | −5.71439 | − | 5.71439i | −0.537565 | − | 0.537565i | 0.385248 | − | 0.922813i | \(-0.374116\pi\) |
−0.922813 | + | 0.385248i | \(0.874116\pi\) | |||||||
\(114\) | −0.678547 | + | 11.0237i | −0.0635518 | + | 1.03246i | ||||
\(115\) | −8.06375 | − | 7.99230i | −0.751948 | − | 0.745286i | ||||
\(116\) | − | 0.495771i | − | 0.0460312i | ||||||
\(117\) | −10.5579 | + | 2.35167i | −0.976080 | + | 0.217412i | ||||
\(118\) | 0.489709 | − | 0.489709i | 0.0450814 | − | 0.0450814i | ||||
\(119\) | 3.76328i | 0.344979i | ||||||||
\(120\) | 3.86669 | + | 0.220742i | 0.352979 | + | 0.0201509i | ||||
\(121\) | 2.70578 | 0.245980 | ||||||||
\(122\) | −8.53366 | − | 8.53366i | −0.772601 | − | 0.772601i | ||||
\(123\) | −1.90197 | − | 2.15147i | −0.171495 | − | 0.193992i | ||||
\(124\) | 2.88858 | 0.259402 | ||||||||
\(125\) | −11.1793 | + | 0.149249i | −0.999911 | + | 0.0133492i | ||||
\(126\) | 0.536783 | − | 4.34376i | 0.0478204 | − | 0.386973i | ||||
\(127\) | −13.1211 | − | 13.1211i | −1.16431 | − | 1.16431i | −0.983522 | − | 0.180786i | \(-0.942136\pi\) |
−0.180786 | − | 0.983522i | \(-0.557864\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 21.2365 | + | 1.30718i | 1.86977 | + | 0.115091i | ||||
\(130\) | 3.42553 | − | 7.29834i | 0.300438 | − | 0.640107i | ||||
\(131\) | − | 11.4677i | − | 1.00193i | −0.865466 | − | 0.500967i | \(-0.832978\pi\) | ||
0.865466 | − | 0.500967i | \(-0.167022\pi\) | |||||||
\(132\) | 4.80417 | − | 4.24703i | 0.418149 | − | 0.369657i | ||||
\(133\) | −6.57820 | + | 6.57820i | −0.570402 | + | 0.570402i | ||||
\(134\) | −9.60963 | −0.830145 | ||||||||
\(135\) | 9.55384 | − | 6.61243i | 0.822263 | − | 0.569107i | ||||
\(136\) | 2.57947i | 0.221188i | ||||||||
\(137\) | 9.53679 | + | 9.53679i | 0.814783 | + | 0.814783i | 0.985347 | − | 0.170564i | \(-0.0545589\pi\) |
−0.170564 | + | 0.985347i | \(0.554559\pi\) | |||||||
\(138\) | −6.58885 | + | 5.82474i | −0.560880 | + | 0.495835i | ||||
\(139\) | − | 2.09695i | − | 0.177861i | −0.996038 | − | 0.0889305i | \(-0.971655\pi\) | ||
0.996038 | − | 0.0889305i | \(-0.0283449\pi\) | |||||||
\(140\) | 2.31702 | + | 2.29649i | 0.195824 | + | 0.194089i | ||||
\(141\) | −0.420831 | + | 6.83681i | −0.0354404 | + | 0.575763i | ||||
\(142\) | 3.11987 | + | 3.11987i | 0.261813 | + | 0.261813i | ||||
\(143\) | −4.47806 | − | 12.5747i | −0.374474 | − | 1.05155i | ||||
\(144\) | 0.367928 | − | 2.97735i | 0.0306607 | − | 0.248113i | ||||
\(145\) | 1.10857 | − | 0.00493302i | 0.0920615 | − | 0.000409665i | ||||
\(146\) | 11.3472i | 0.939101i | ||||||||
\(147\) | −6.32164 | + | 5.58853i | −0.521400 | + | 0.460934i | ||||
\(148\) | 2.07537 | + | 2.07537i | 0.170595 | + | 0.170595i | ||||
\(149\) | 21.4810i | 1.75980i | 0.475163 | + | 0.879898i | \(0.342389\pi\) | ||||
−0.475163 | + | 0.879898i | \(0.657611\pi\) | |||||||
\(150\) | −0.455115 | + | 8.64829i | −0.0371600 | + | 0.706130i | ||||
\(151\) | 4.31897i | 0.351473i | 0.984437 | + | 0.175736i | \(0.0562306\pi\) | ||||
−0.984437 | + | 0.175736i | \(0.943769\pi\) | |||||||
\(152\) | −4.50891 | + | 4.50891i | −0.365721 | + | 0.365721i | ||||
\(153\) | 4.75949 | + | 6.10166i | 0.384782 | + | 0.493290i | ||||
\(154\) | 5.40117 | 0.435238 | ||||||||
\(155\) | 0.0287419 | + | 6.45899i | 0.00230860 | + | 0.518798i | ||||
\(156\) | −5.46619 | − | 3.02006i | −0.437645 | − | 0.241799i | ||||
\(157\) | −2.78660 | − | 2.78660i | −0.222395 | − | 0.222395i | 0.587111 | − | 0.809506i | \(-0.300265\pi\) |
−0.809506 | + | 0.587111i | \(0.800265\pi\) | |||||||
\(158\) | −4.31332 | + | 4.31332i | −0.343149 | + | 0.343149i | ||||
\(159\) | 0.888554 | − | 14.4354i | 0.0704669 | − | 1.14480i | ||||
\(160\) | 1.58816 | + | 1.57409i | 0.125555 | + | 0.124443i | ||||
\(161\) | −7.40762 | −0.583802 | ||||||||
\(162\) | −4.62331 | − | 7.72172i | −0.363242 | − | 0.606676i | ||||
\(163\) | −13.8871 | − | 13.8871i | −1.08772 | − | 1.08772i | −0.995763 | − | 0.0919595i | \(-0.970687\pi\) |
−0.0919595 | − | 0.995763i | \(-0.529313\pi\) | |||||||
\(164\) | − | 1.65794i | − | 0.129463i | ||||||
\(165\) | 9.54436 | + | 10.7001i | 0.743028 | + | 0.833000i | ||||
\(166\) | 6.85143 | 0.531774 | ||||||||
\(167\) | −13.3857 | − | 13.3857i | −1.03582 | − | 1.03582i | −0.999334 | − | 0.0364854i | \(-0.988384\pi\) |
−0.0364854 | − | 0.999334i | \(-0.511616\pi\) | |||||||
\(168\) | 1.89322 | − | 1.67367i | 0.146065 | − | 0.129126i | ||||
\(169\) | −10.0738 | + | 8.21698i | −0.774907 | + | 0.632075i | ||||
\(170\) | −5.76782 | + | 0.0256662i | −0.442371 | + | 0.00196851i | ||||
\(171\) | −2.34612 | + | 18.9853i | −0.179412 | + | 1.45184i | ||||
\(172\) | 8.68616 | + | 8.68616i | 0.662314 | + | 0.662314i | ||||
\(173\) | 0.386807 | + | 0.386807i | 0.0294084 | + | 0.0294084i | 0.721658 | − | 0.692250i | \(-0.243380\pi\) |
−0.692250 | + | 0.721658i | \(0.743380\pi\) | |||||||
\(174\) | 0.0527564 | − | 0.857079i | 0.00399945 | − | 0.0649750i | ||||
\(175\) | −5.11200 | + | 5.20381i | −0.386431 | + | 0.393371i | ||||
\(176\) | 3.70213 | 0.279059 | ||||||||
\(177\) | 0.898710 | − | 0.794488i | 0.0675512 | − | 0.0597173i | ||||
\(178\) | 1.88603 | − | 1.88603i | 0.141364 | − | 0.141364i | ||||
\(179\) | 23.6190 | 1.76537 | 0.882684 | − | 0.469967i | \(-0.155734\pi\) | ||||
0.882684 | + | 0.469967i | \(0.155734\pi\) | |||||||
\(180\) | 6.66116 | + | 0.793079i | 0.496493 | + | 0.0591126i | ||||
\(181\) | −10.1453 | −0.754094 | −0.377047 | − | 0.926194i | \(-0.623061\pi\) | ||||
−0.377047 | + | 0.926194i | \(0.623061\pi\) | |||||||
\(182\) | −1.76471 | − | 4.95542i | −0.130809 | − | 0.367320i | ||||
\(183\) | −13.8447 | − | 15.6609i | −1.02343 | − | 1.15769i | ||||
\(184\) | −5.07742 | −0.374312 | ||||||||
\(185\) | −4.61998 | + | 4.66128i | −0.339667 | + | 0.342704i | ||||
\(186\) | 4.99371 | + | 0.307381i | 0.366156 | + | 0.0225383i | ||||
\(187\) | −6.75254 | + | 6.75254i | −0.493795 | + | 0.493795i | ||||
\(188\) | −2.79640 | + | 2.79640i | −0.203948 | + | 0.203948i | ||||
\(189\) | 1.39021 | − | 7.45228i | 0.101123 | − | 0.542074i | ||||
\(190\) | −10.1270 | − | 10.0373i | −0.734689 | − | 0.728180i | ||||
\(191\) | 15.5138i | 1.12254i | 0.827632 | + | 0.561271i | \(0.189688\pi\) | ||||
−0.827632 | + | 0.561271i | \(0.810312\pi\) | |||||||
\(192\) | 1.29768 | − | 1.14719i | 0.0936517 | − | 0.0827910i | ||||
\(193\) | 5.80655 | + | 5.80655i | 0.417965 | + | 0.417965i | 0.884502 | − | 0.466537i | \(-0.154499\pi\) |
−0.466537 | + | 0.884502i | \(0.654499\pi\) | |||||||
\(194\) | 9.87549 | 0.709019 | ||||||||
\(195\) | 6.69861 | − | 12.2527i | 0.479698 | − | 0.877434i | ||||
\(196\) | −4.87151 | −0.347965 | ||||||||
\(197\) | −8.00755 | − | 8.00755i | −0.570514 | − | 0.570514i | 0.361758 | − | 0.932272i | \(-0.382177\pi\) |
−0.932272 | + | 0.361758i | \(0.882177\pi\) | |||||||
\(198\) | 8.75728 | − | 6.83096i | 0.622353 | − | 0.485455i | ||||
\(199\) | − | 11.1959i | − | 0.793656i | −0.917893 | − | 0.396828i | \(-0.870111\pi\) | ||
0.917893 | − | 0.396828i | \(-0.129889\pi\) | |||||||
\(200\) | −3.50393 | + | 3.56686i | −0.247765 | + | 0.252215i | ||||
\(201\) | −16.6129 | − | 1.02259i | −1.17179 | − | 0.0721277i | ||||
\(202\) | −11.0224 | + | 11.0224i | −0.775531 | + | 0.775531i | ||||
\(203\) | 0.511449 | − | 0.511449i | 0.0358966 | − | 0.0358966i | ||||
\(204\) | −0.274489 | + | 4.45933i | −0.0192180 | + | 0.312216i | ||||
\(205\) | 3.70723 | − | 0.0164968i | 0.258924 | − | 0.00115219i | ||||
\(206\) | 5.77245 | 0.402185 | ||||||||
\(207\) | −12.0105 | + | 9.36856i | −0.834786 | + | 0.651160i | ||||
\(208\) | −1.20959 | − | 3.39660i | −0.0838699 | − | 0.235512i | ||||
\(209\) | −23.6069 | −1.63292 | ||||||||
\(210\) | 3.76124 | + | 4.21668i | 0.259550 | + | 0.290979i | ||||
\(211\) | 3.34994 | 0.230619 | 0.115310 | − | 0.993330i | \(-0.463214\pi\) | ||||
0.115310 | + | 0.993330i | \(0.463214\pi\) | |||||||
\(212\) | 5.90440 | − | 5.90440i | 0.405516 | − | 0.405516i | ||||
\(213\) | 5.06156 | + | 5.72555i | 0.346813 | + | 0.392308i | ||||
\(214\) | 15.0437 | 1.02836 | ||||||||
\(215\) | −19.3362 | + | 19.5091i | −1.31872 | + | 1.33051i | ||||
\(216\) | 0.952895 | − | 5.10803i | 0.0648363 | − | 0.347558i | ||||
\(217\) | 2.97992 | + | 2.97992i | 0.202290 | + | 0.202290i | ||||
\(218\) | 9.18729 | + | 9.18729i | 0.622242 | + | 0.622242i | ||||
\(219\) | −1.20749 | + | 19.6168i | −0.0815944 | + | 1.32558i | ||||
\(220\) | 0.0368369 | + | 8.27814i | 0.00248354 | + | 0.558112i | ||||
\(221\) | 8.40151 | + | 3.98902i | 0.565147 | + | 0.268331i | ||||
\(222\) | 3.36701 | + | 3.80871i | 0.225979 | + | 0.255624i | ||||
\(223\) | 8.84969 | + | 8.84969i | 0.592619 | + | 0.592619i | 0.938338 | − | 0.345719i | \(-0.112365\pi\) |
−0.345719 | + | 0.938338i | \(0.612365\pi\) | |||||||
\(224\) | 1.45893 | 0.0974791 | ||||||||
\(225\) | −1.70708 | + | 14.9025i | −0.113805 | + | 0.993503i | ||||
\(226\) | − | 8.08137i | − | 0.537565i | ||||||
\(227\) | −7.63136 | − | 7.63136i | −0.506511 | − | 0.506511i | 0.406942 | − | 0.913454i | \(-0.366595\pi\) |
−0.913454 | + | 0.406942i | \(0.866595\pi\) | |||||||
\(228\) | −8.27471 | + | 7.31510i | −0.548006 | + | 0.484454i | ||||
\(229\) | −23.0299 | −1.52186 | −0.760929 | − | 0.648836i | \(-0.775256\pi\) | ||||
−0.760929 | + | 0.648836i | \(0.775256\pi\) | |||||||
\(230\) | −0.0505213 | − | 11.3533i | −0.00333128 | − | 0.748617i | ||||
\(231\) | 9.33742 | + | 0.574753i | 0.614357 | + | 0.0378160i | ||||
\(232\) | 0.350563 | − | 0.350563i | 0.0230156 | − | 0.0230156i | ||||
\(233\) | 19.7471 | + | 19.7471i | 1.29368 | + | 1.29368i | 0.932495 | + | 0.361182i | \(0.117627\pi\) |
0.361182 | + | 0.932495i | \(0.382373\pi\) | |||||||
\(234\) | −9.12846 | − | 5.80270i | −0.596746 | − | 0.379334i | ||||
\(235\) | −6.28070 | − | 6.22505i | −0.409708 | − | 0.406078i | ||||
\(236\) | 0.692553 | 0.0450814 | ||||||||
\(237\) | −7.91576 | + | 6.99778i | −0.514184 | + | 0.454554i | ||||
\(238\) | −2.66104 | + | 2.66104i | −0.172490 | + | 0.172490i | ||||
\(239\) | − | 2.46770i | − | 0.159622i | −0.996810 | − | 0.0798112i | \(-0.974568\pi\) | ||
0.996810 | − | 0.0798112i | \(-0.0254317\pi\) | |||||||
\(240\) | 2.57807 | + | 2.89025i | 0.166414 | + | 0.186565i | ||||
\(241\) | − | 21.2063i | − | 1.36602i | −0.730410 | − | 0.683009i | \(-0.760671\pi\) | ||
0.730410 | − | 0.683009i | \(-0.239329\pi\) | |||||||
\(242\) | 1.91327 | + | 1.91327i | 0.122990 | + | 0.122990i | ||||
\(243\) | −7.17100 | − | 13.8411i | −0.460020 | − | 0.887909i | ||||
\(244\) | − | 12.0684i | − | 0.772601i | ||||||
\(245\) | −0.0484725 | − | 10.8929i | −0.00309679 | − | 0.695923i | ||||
\(246\) | 0.176426 | − | 2.86621i | 0.0112485 | − | 0.182743i | ||||
\(247\) | 7.71302 | + | 21.6586i | 0.490768 | + | 1.37811i | ||||
\(248\) | 2.04253 | + | 2.04253i | 0.129701 | + | 0.129701i | ||||
\(249\) | 11.8446 | + | 0.729079i | 0.750621 | + | 0.0462035i | ||||
\(250\) | −8.01052 | − | 7.79945i | −0.506630 | − | 0.493281i | ||||
\(251\) | − | 21.0780i | − | 1.33043i | −0.746651 | − | 0.665216i | \(-0.768339\pi\) | ||
0.746651 | − | 0.665216i | \(-0.231661\pi\) | |||||||
\(252\) | 3.45107 | − | 2.69194i | 0.217397 | − | 0.169576i | ||||
\(253\) | −13.2917 | − | 13.2917i | −0.835640 | − | 0.835640i | ||||
\(254\) | − | 18.5560i | − | 1.16431i | ||||||
\(255\) | −9.97401 | − | 0.569398i | −0.624597 | − | 0.0356571i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.49660 | − | 8.49660i | 0.530003 | − | 0.530003i | −0.390570 | − | 0.920573i | \(-0.627722\pi\) |
0.920573 | + | 0.390570i | \(0.127722\pi\) | |||||||
\(258\) | 14.0921 | + | 15.9408i | 0.877338 | + | 0.992429i | ||||
\(259\) | 4.28200i | 0.266071i | ||||||||
\(260\) | 7.58292 | − | 2.73849i | 0.470273 | − | 0.169834i | ||||
\(261\) | 0.182408 | − | 1.47609i | 0.0112908 | − | 0.0913674i | ||||
\(262\) | 8.10886 | − | 8.10886i | 0.500967 | − | 0.500967i | ||||
\(263\) | 12.5564 | + | 12.5564i | 0.774263 | + | 0.774263i | 0.978849 | − | 0.204585i | \(-0.0655846\pi\) |
−0.204585 | + | 0.978849i | \(0.565585\pi\) | |||||||
\(264\) | 6.40017 | + | 0.393954i | 0.393903 | + | 0.0242462i | ||||
\(265\) | 13.2612 | + | 13.1437i | 0.814632 | + | 0.807414i | ||||
\(266\) | −9.30298 | −0.570402 | ||||||||
\(267\) | 3.46123 | − | 3.05983i | 0.211824 | − | 0.187259i | ||||
\(268\) | −6.79503 | − | 6.79503i | −0.415073 | − | 0.415073i | ||||
\(269\) | −17.2259 | −1.05028 | −0.525140 | − | 0.851016i | \(-0.675987\pi\) | ||||
−0.525140 | + | 0.851016i | \(0.675987\pi\) | |||||||
\(270\) | 11.4313 | + | 2.07989i | 0.695685 | + | 0.126578i | ||||
\(271\) | − | 9.68987i | − | 0.588617i | −0.955710 | − | 0.294309i | \(-0.904911\pi\) | ||
0.955710 | − | 0.294309i | \(-0.0950894\pi\) | |||||||
\(272\) | −1.82396 | + | 1.82396i | −0.110594 | + | 0.110594i | ||||
\(273\) | −2.52348 | − | 8.75461i | −0.152728 | − | 0.529853i | ||||
\(274\) | 13.4871i | 0.814783i | ||||||||
\(275\) | −18.5099 | + | 0.164738i | −1.11619 | + | 0.00993408i | ||||
\(276\) | −8.77773 | − | 0.540302i | −0.528357 | − | 0.0325224i | ||||
\(277\) | −15.4074 | − | 15.4074i | −0.925743 | − | 0.925743i | 0.0716840 | − | 0.997427i | \(-0.477163\pi\) |
−0.997427 | + | 0.0716840i | \(0.977163\pi\) | |||||||
\(278\) | 1.48277 | − | 1.48277i | 0.0889305 | − | 0.0889305i | ||||
\(279\) | 8.60031 | + | 1.06279i | 0.514887 | + | 0.0636275i | ||||
\(280\) | 0.0145167 | + | 3.26224i | 0.000867537 | + | 0.194956i | ||||
\(281\) | 10.7797 | 0.643064 | 0.321532 | − | 0.946899i | \(-0.395802\pi\) | ||||
0.321532 | + | 0.946899i | \(0.395802\pi\) | |||||||
\(282\) | −5.13193 | + | 4.53678i | −0.305602 | + | 0.270161i | ||||
\(283\) | −4.45748 | + | 4.45748i | −0.264970 | + | 0.264970i | −0.827069 | − | 0.562100i | \(-0.809994\pi\) |
0.562100 | + | 0.827069i | \(0.309994\pi\) | |||||||
\(284\) | 4.41216i | 0.261813i | ||||||||
\(285\) | −16.4392 | − | 18.4298i | −0.973776 | − | 1.09169i | ||||
\(286\) | 5.72516 | − | 12.0581i | 0.338536 | − | 0.713010i | ||||
\(287\) | 1.71037 | − | 1.71037i | 0.100960 | − | 0.100960i | ||||
\(288\) | 2.36547 | − | 1.84514i | 0.139387 | − | 0.108726i | ||||
\(289\) | 10.3463i | 0.608608i | ||||||||
\(290\) | 0.787363 | + | 0.780387i | 0.0462356 | + | 0.0458259i | ||||
\(291\) | 17.0725 | + | 1.05088i | 1.00081 | + | 0.0616035i | ||||
\(292\) | −8.02368 | + | 8.02368i | −0.469550 | + | 0.469550i | ||||
\(293\) | 6.26863 | − | 6.26863i | 0.366217 | − | 0.366217i | −0.499878 | − | 0.866096i | \(-0.666622\pi\) |
0.866096 | + | 0.499878i | \(0.166622\pi\) | |||||||
\(294\) | −8.42177 | − | 0.518391i | −0.491167 | − | 0.0302332i | ||||
\(295\) | 0.00689104 | + | 1.54858i | 0.000401212 | + | 0.0901619i | ||||
\(296\) | 2.93502i | 0.170595i | ||||||||
\(297\) | 15.8663 | − | 10.8773i | 0.920657 | − | 0.631167i | ||||
\(298\) | −15.1894 | + | 15.1894i | −0.879898 | + | 0.879898i | ||||
\(299\) | −7.85198 | + | 16.5375i | −0.454091 | + | 0.956388i | ||||
\(300\) | −6.43708 | + | 5.79345i | −0.371645 | + | 0.334485i | ||||
\(301\) | 17.9217i | 1.03299i | ||||||||
\(302\) | −3.05397 | + | 3.05397i | −0.175736 | + | 0.175736i | ||||
\(303\) | −20.2282 | + | 17.8823i | −1.16208 | + | 1.02731i | ||||
\(304\) | −6.37656 | −0.365721 | ||||||||
\(305\) | 26.9855 | − | 0.120083i | 1.54519 | − | 0.00687593i | ||||
\(306\) | −0.949060 | + | 7.67999i | −0.0542541 | + | 0.439036i | ||||
\(307\) | 18.3933 | − | 18.3933i | 1.04976 | − | 1.04976i | 0.0510636 | − | 0.998695i | \(-0.483739\pi\) |
0.998695 | − | 0.0510636i | \(-0.0162611\pi\) | |||||||
\(308\) | 3.81920 | + | 3.81920i | 0.217619 | + | 0.217619i | ||||
\(309\) | 9.97928 | + | 0.614262i | 0.567702 | + | 0.0349441i | ||||
\(310\) | −4.54687 | + | 4.58752i | −0.258245 | + | 0.260553i | ||||
\(311\) | 1.77908i | 0.100882i | 0.998727 | + | 0.0504412i | \(0.0160627\pi\) | ||||
−0.998727 | + | 0.0504412i | \(0.983937\pi\) | |||||||
\(312\) | −1.72967 | − | 6.00069i | −0.0979233 | − | 0.339722i | ||||
\(313\) | −14.6637 | + | 14.6637i | −0.828840 | + | 0.828840i | −0.987356 | − | 0.158516i | \(-0.949329\pi\) |
0.158516 | + | 0.987356i | \(0.449329\pi\) | |||||||
\(314\) | − | 3.94085i | − | 0.222395i | ||||||
\(315\) | 6.05364 | + | 7.68996i | 0.341084 | + | 0.433280i | ||||
\(316\) | −6.09995 | −0.343149 | ||||||||
\(317\) | 7.54686 | + | 7.54686i | 0.423874 | + | 0.423874i | 0.886535 | − | 0.462661i | \(-0.153105\pi\) |
−0.462661 | + | 0.886535i | \(0.653105\pi\) | |||||||
\(318\) | 10.8357 | − | 9.57909i | 0.607636 | − | 0.537169i | ||||
\(319\) | 1.83541 | 0.102763 | ||||||||
\(320\) | 0.00995019 | + | 2.23605i | 0.000556233 | + | 0.124999i | ||||
\(321\) | 26.0072 | + | 1.60084i | 1.45158 | + | 0.0893501i | ||||
\(322\) | −5.23798 | − | 5.23798i | −0.291901 | − | 0.291901i | ||||
\(323\) | 11.6306 | − | 11.6306i | 0.647144 | − | 0.647144i | ||||
\(324\) | 2.19090 | − | 8.72926i | 0.121717 | − | 0.484959i | ||||
\(325\) | 6.19885 | + | 16.9285i | 0.343850 | + | 0.939025i | ||||
\(326\) | − | 19.6393i | − | 1.08772i | ||||||
\(327\) | 14.9051 | + | 16.8604i | 0.824257 | + | 0.932384i | ||||
\(328\) | 1.17234 | − | 1.17234i | 0.0647317 | − | 0.0647317i | ||||
\(329\) | −5.76965 | −0.318091 | ||||||||
\(330\) | −0.817216 | + | 14.3150i | −0.0449863 | + | 0.788014i | ||||
\(331\) | − | 4.18973i | − | 0.230288i | −0.993349 | − | 0.115144i | \(-0.963267\pi\) | ||
0.993349 | − | 0.115144i | \(-0.0367330\pi\) | |||||||
\(332\) | 4.84469 | + | 4.84469i | 0.265887 | + | 0.265887i | ||||
\(333\) | 5.41553 | + | 6.94270i | 0.296769 | + | 0.380458i | ||||
\(334\) | − | 18.9303i | − | 1.03582i | ||||||
\(335\) | 15.1264 | − | 15.2616i | 0.826443 | − | 0.833831i | ||||
\(336\) | 2.52217 | + | 0.155249i | 0.137596 | + | 0.00846954i | ||||
\(337\) | 15.4822 | + | 15.4822i | 0.843371 | + | 0.843371i | 0.989296 | − | 0.145925i | \(-0.0466157\pi\) |
−0.145925 | + | 0.989296i | \(0.546616\pi\) | |||||||
\(338\) | −12.9335 | − | 1.31296i | −0.703491 | − | 0.0714157i | ||||
\(339\) | 0.859961 | − | 13.9709i | 0.0467067 | − | 0.758795i | ||||
\(340\) | −4.09661 | − | 4.06031i | −0.222170 | − | 0.220201i | ||||
\(341\) | 10.6939i | 0.579106i | ||||||||
\(342\) | −15.0836 | + | 11.7657i | −0.815626 | + | 0.636214i | ||||
\(343\) | −12.2469 | − | 12.2469i | −0.661271 | − | 0.661271i | ||||
\(344\) | 12.2841i | 0.662314i | ||||||||
\(345\) | 1.12080 | − | 19.6328i | 0.0603418 | − | 1.05699i | ||||
\(346\) | 0.547027i | 0.0294084i | ||||||||
\(347\) | 9.96769 | − | 9.96769i | 0.535094 | − | 0.535094i | −0.386990 | − | 0.922084i | \(-0.626485\pi\) |
0.922084 | + | 0.386990i | \(0.126485\pi\) | |||||||
\(348\) | 0.643350 | − | 0.568742i | 0.0344872 | − | 0.0304878i | ||||
\(349\) | −24.7426 | −1.32444 | −0.662220 | − | 0.749309i | \(-0.730386\pi\) | ||||
−0.662220 | + | 0.749309i | \(0.730386\pi\) | |||||||
\(350\) | −7.29438 | + | 0.0649199i | −0.389901 | + | 0.00347012i | ||||
\(351\) | −15.1636 | − | 11.0030i | −0.809373 | − | 0.587295i | ||||
\(352\) | 2.61780 | + | 2.61780i | 0.139529 | + | 0.139529i | ||||
\(353\) | 4.17093 | − | 4.17093i | 0.221996 | − | 0.221996i | −0.587342 | − | 0.809339i | \(-0.699826\pi\) |
0.809339 | + | 0.587342i | \(0.199826\pi\) | |||||||
\(354\) | 1.19727 | + | 0.0736965i | 0.0636343 | + | 0.00391692i | ||||
\(355\) | −9.86578 | + | 0.0439018i | −0.523621 | + | 0.00233007i | ||||
\(356\) | 2.66725 | 0.141364 | ||||||||
\(357\) | −4.88352 | + | 4.31718i | −0.258463 | + | 0.228489i | ||||
\(358\) | 16.7012 | + | 16.7012i | 0.882684 | + | 0.882684i | ||||
\(359\) | − | 2.55214i | − | 0.134697i | −0.997730 | − | 0.0673485i | \(-0.978546\pi\) | ||
0.997730 | − | 0.0673485i | \(-0.0214539\pi\) | |||||||
\(360\) | 4.14936 | + | 5.27094i | 0.218690 | + | 0.277803i | ||||
\(361\) | 21.6605 | 1.14003 | ||||||||
\(362\) | −7.17381 | − | 7.17381i | −0.377047 | − | 0.377047i | ||||
\(363\) | 3.10403 | + | 3.51122i | 0.162919 | + | 0.184291i | ||||
\(364\) | 2.25617 | − | 4.75185i | 0.118255 | − | 0.249064i | ||||
\(365\) | −18.0212 | − | 17.8615i | −0.943271 | − | 0.934913i | ||||
\(366\) | 1.28423 | − | 20.8636i | 0.0671279 | − | 1.09056i | ||||
\(367\) | 13.0614 | + | 13.0614i | 0.681800 | + | 0.681800i | 0.960406 | − | 0.278605i | \(-0.0898722\pi\) |
−0.278605 | + | 0.960406i | \(0.589872\pi\) | |||||||
\(368\) | −3.59028 | − | 3.59028i | −0.187156 | − | 0.187156i | ||||
\(369\) | 0.610003 | − | 4.93627i | 0.0317555 | − | 0.256972i | ||||
\(370\) | −6.56284 | + | 0.0292040i | −0.341186 | + | 0.00151824i | ||||
\(371\) | 12.1822 | 0.632469 | ||||||||
\(372\) | 3.31373 | + | 3.74844i | 0.171809 | + | 0.194347i | ||||
\(373\) | 12.4877 | − | 12.4877i | 0.646591 | − | 0.646591i | −0.305577 | − | 0.952167i | \(-0.598849\pi\) |
0.952167 | + | 0.305577i | \(0.0988492\pi\) | |||||||
\(374\) | −9.54954 | −0.493795 | ||||||||
\(375\) | −13.0185 | − | 14.3360i | −0.672271 | − | 0.740305i | ||||
\(376\) | −3.95471 | −0.203948 | ||||||||
\(377\) | −0.599679 | − | 1.68394i | −0.0308851 | − | 0.0867271i | ||||
\(378\) | 6.25259 | − | 4.28653i | 0.321598 | − | 0.220475i | ||||
\(379\) | −1.70213 | −0.0874324 | −0.0437162 | − | 0.999044i | \(-0.513920\pi\) | ||||
−0.0437162 | + | 0.999044i | \(0.513920\pi\) | |||||||
\(380\) | −0.0634480 | − | 14.2583i | −0.00325481 | − | 0.731434i | ||||
\(381\) | 1.97460 | − | 32.0793i | 0.101162 | − | 1.64347i | ||||
\(382\) | −10.9699 | + | 10.9699i | −0.561271 | + | 0.561271i | ||||
\(383\) | 24.8875 | − | 24.8875i | 1.27169 | − | 1.27169i | 0.326494 | − | 0.945199i | \(-0.394133\pi\) |
0.945199 | − | 0.326494i | \(-0.105867\pi\) | |||||||
\(384\) | 1.72878 | + | 0.106413i | 0.0882214 | + | 0.00543035i | ||||
\(385\) | −8.50191 | + | 8.57791i | −0.433297 | + | 0.437171i | ||||
\(386\) | 8.21170i | 0.417965i | ||||||||
\(387\) | 22.6659 | + | 29.0576i | 1.15217 | + | 1.47708i | ||||
\(388\) | 6.98302 | + | 6.98302i | 0.354509 | + | 0.354509i | ||||
\(389\) | 18.6976 | 0.948005 | 0.474002 | − | 0.880524i | \(-0.342809\pi\) | ||||
0.474002 | + | 0.880524i | \(0.342809\pi\) | |||||||
\(390\) | 13.4006 | − | 3.92733i | 0.678566 | − | 0.198868i | ||||
\(391\) | 13.0971 | 0.662346 | ||||||||
\(392\) | −3.44468 | − | 3.44468i | −0.173983 | − | 0.173983i | ||||
\(393\) | 14.8813 | − | 13.1555i | 0.750663 | − | 0.663609i | ||||
\(394\) | − | 11.3244i | − | 0.570514i | ||||||
\(395\) | −0.0606957 | − | 13.6398i | −0.00305393 | − | 0.686291i | ||||
\(396\) | 11.0226 | + | 1.36212i | 0.553904 | + | 0.0684490i | ||||
\(397\) | 6.85449 | − | 6.85449i | 0.344017 | − | 0.344017i | −0.513858 | − | 0.857875i | \(-0.671784\pi\) |
0.857875 | + | 0.513858i | \(0.171784\pi\) | |||||||
\(398\) | 7.91669 | − | 7.91669i | 0.396828 | − | 0.396828i | ||||
\(399\) | −16.0828 | − | 0.989956i | −0.805147 | − | 0.0495598i | ||||
\(400\) | −4.99980 | + | 0.0444982i | −0.249990 | + | 0.00222491i | ||||
\(401\) | −19.0194 | −0.949781 | −0.474891 | − | 0.880045i | \(-0.657512\pi\) | ||||
−0.474891 | + | 0.880045i | \(0.657512\pi\) | |||||||
\(402\) | −11.0240 | − | 12.4702i | −0.549829 | − | 0.621956i | ||||
\(403\) | 9.81134 | − | 3.49399i | 0.488737 | − | 0.174048i | ||||
\(404\) | −15.5880 | −0.775531 | ||||||||
\(405\) | 19.5408 | + | 4.81210i | 0.970991 | + | 0.239115i | ||||
\(406\) | 0.723297 | 0.0358966 | ||||||||
\(407\) | −7.68330 | + | 7.68330i | −0.380847 | + | 0.380847i | ||||
\(408\) | −3.34732 | + | 2.95913i | −0.165717 | + | 0.146499i | ||||
\(409\) | −22.4228 | −1.10874 | −0.554368 | − | 0.832272i | \(-0.687040\pi\) | ||||
−0.554368 | + | 0.832272i | \(0.687040\pi\) | |||||||
\(410\) | 2.63307 | + | 2.60974i | 0.130038 | + | 0.128886i | ||||
\(411\) | −1.43519 | + | 23.3161i | −0.0707929 | + | 1.15010i | ||||
\(412\) | 4.08174 | + | 4.08174i | 0.201093 | + | 0.201093i | ||||
\(413\) | 0.714453 | + | 0.714453i | 0.0351560 | + | 0.0351560i | ||||
\(414\) | −15.1173 | − | 1.86812i | −0.742973 | − | 0.0918133i | ||||
\(415\) | −10.7847 | + | 10.8812i | −0.529402 | + | 0.534135i | ||||
\(416\) | 1.54645 | − | 3.25707i | 0.0758210 | − | 0.159691i | ||||
\(417\) | 2.72116 | − | 2.40559i | 0.133256 | − | 0.117802i | ||||
\(418\) | −16.6926 | − | 16.6926i | −0.816460 | − | 0.816460i | ||||
\(419\) | −0.535876 | −0.0261792 | −0.0130896 | − | 0.999914i | \(-0.504167\pi\) | ||||
−0.0130896 | + | 0.999914i | \(0.504167\pi\) | |||||||
\(420\) | −0.322048 | + | 5.64124i | −0.0157143 | + | 0.275264i | ||||
\(421\) | − | 23.5915i | − | 1.14978i | −0.818231 | − | 0.574890i | \(-0.805045\pi\) | ||
0.818231 | − | 0.574890i | \(-0.194955\pi\) | |||||||
\(422\) | 2.36877 | + | 2.36877i | 0.115310 | + | 0.115310i | ||||
\(423\) | −9.35474 | + | 7.29699i | −0.454843 | + | 0.354792i | ||||
\(424\) | 8.35008 | 0.405516 | ||||||||
\(425\) | 9.03828 | − | 9.20061i | 0.438421 | − | 0.446295i | ||||
\(426\) | −0.469510 | + | 7.62764i | −0.0227478 | + | 0.369561i | ||||
\(427\) | 12.4500 | − | 12.4500i | 0.602500 | − | 0.602500i | ||||
\(428\) | 10.6375 | + | 10.6375i | 0.514182 | + | 0.514182i | ||||
\(429\) | 11.1807 | − | 20.2365i | 0.539808 | − | 0.977030i | ||||
\(430\) | −27.4678 | + | 0.122229i | −1.32461 | + | 0.00589441i | ||||
\(431\) | 15.0604 | 0.725432 | 0.362716 | − | 0.931900i | \(-0.381849\pi\) | ||||
0.362716 | + | 0.931900i | \(0.381849\pi\) | |||||||
\(432\) | 4.28572 | − | 2.93813i | 0.206197 | − | 0.141361i | ||||
\(433\) | 8.41585 | − | 8.41585i | 0.404440 | − | 0.404440i | −0.475355 | − | 0.879794i | \(-0.657680\pi\) |
0.879794 | + | 0.475355i | \(0.157680\pi\) | |||||||
\(434\) | 4.21424i | 0.202290i | ||||||||
\(435\) | 1.27813 | + | 1.43290i | 0.0612818 | + | 0.0687024i | ||||
\(436\) | 12.9928i | 0.622242i | ||||||||
\(437\) | 22.8936 | + | 22.8936i | 1.09515 | + | 1.09515i | ||||
\(438\) | −14.7250 | + | 13.0174i | −0.703587 | + | 0.621993i | ||||
\(439\) | − | 35.6347i | − | 1.70075i | −0.526176 | − | 0.850376i | \(-0.676375\pi\) | ||
0.526176 | − | 0.850376i | \(-0.323625\pi\) | |||||||
\(440\) | −5.82748 | + | 5.87957i | −0.277814 | + | 0.280298i | ||||
\(441\) | −14.5042 | − | 1.79237i | −0.690676 | − | 0.0853508i | ||||
\(442\) | 3.12010 | + | 8.76143i | 0.148408 | + | 0.416739i | ||||
\(443\) | 13.8316 | + | 13.8316i | 0.657158 | + | 0.657158i | 0.954707 | − | 0.297549i | \(-0.0961691\pi\) |
−0.297549 | + | 0.954707i | \(0.596169\pi\) | |||||||
\(444\) | −0.312323 | + | 5.07400i | −0.0148222 | + | 0.240801i | ||||
\(445\) | 0.0265397 | + | 5.96409i | 0.00125810 | + | 0.282725i | ||||
\(446\) | 12.5153i | 0.592619i | ||||||||
\(447\) | −27.8755 | + | 24.6428i | −1.31846 | + | 1.16556i | ||||
\(448\) | 1.03162 | + | 1.03162i | 0.0487396 | + | 0.0487396i | ||||
\(449\) | − | 17.9365i | − | 0.846477i | −0.906018 | − | 0.423239i | \(-0.860893\pi\) | ||
0.906018 | − | 0.423239i | \(-0.139107\pi\) | |||||||
\(450\) | −11.7448 | + | 9.33060i | −0.553654 | + | 0.439849i | ||||
\(451\) | 6.13791 | 0.289023 | ||||||||
\(452\) | 5.71439 | − | 5.71439i | 0.268782 | − | 0.268782i | ||||
\(453\) | −5.60462 | + | 4.95466i | −0.263328 | + | 0.232790i | ||||
\(454\) | − | 10.7924i | − | 0.506511i | ||||||
\(455\) | 10.6478 | + | 4.99762i | 0.499176 | + | 0.234292i | ||||
\(456\) | −11.0237 | − | 0.678547i | −0.516230 | − | 0.0317759i | ||||
\(457\) | 23.6112 | − | 23.6112i | 1.10449 | − | 1.10449i | 0.110624 | − | 0.993862i | \(-0.464715\pi\) |
0.993862 | − | 0.110624i | \(-0.0352850\pi\) | |||||||
\(458\) | −16.2846 | − | 16.2846i | −0.760929 | − | 0.760929i | ||||
\(459\) | −2.45796 | + | 13.1760i | −0.114728 | + | 0.615004i | ||||
\(460\) | 7.99230 | − | 8.06375i | 0.372643 | − | 0.375974i | ||||
\(461\) | −25.8095 | −1.20207 | −0.601035 | − | 0.799223i | \(-0.705245\pi\) | ||||
−0.601035 | + | 0.799223i | \(0.705245\pi\) | |||||||
\(462\) | 6.19614 | + | 7.00897i | 0.288271 | + | 0.326087i | ||||
\(463\) | 20.9097 | + | 20.9097i | 0.971756 | + | 0.971756i | 0.999612 | − | 0.0278563i | \(-0.00886808\pi\) |
−0.0278563 | + | 0.999612i | \(0.508868\pi\) | |||||||
\(464\) | 0.495771 | 0.0230156 | ||||||||
\(465\) | −8.34870 | + | 7.44696i | −0.387162 | + | 0.345344i | ||||
\(466\) | 27.9267i | 1.29368i | ||||||||
\(467\) | 3.81021 | − | 3.81021i | 0.176315 | − | 0.176315i | −0.613432 | − | 0.789747i | \(-0.710212\pi\) |
0.789747 | + | 0.613432i | \(0.210212\pi\) | |||||||
\(468\) | −2.35167 | − | 10.5579i | −0.108706 | − | 0.488040i | ||||
\(469\) | − | 14.0198i | − | 0.647375i | ||||||
\(470\) | −0.0393501 | − | 8.84290i | −0.00181508 | − | 0.407893i | ||||
\(471\) | 0.419356 | − | 6.81285i | 0.0193229 | − | 0.313920i | ||||
\(472\) | 0.489709 | + | 0.489709i | 0.0225407 | + | 0.0225407i | ||||
\(473\) | −32.1573 | + | 32.1573i | −1.47859 | + | 1.47859i | ||||
\(474\) | −10.5455 | − | 0.649112i | −0.484369 | − | 0.0298147i | ||||
\(475\) | 31.8815 | − | 0.283745i | 1.46283 | − | 0.0130191i | ||||
\(476\) | −3.76328 | −0.172490 | ||||||||
\(477\) | 19.7519 | − | 15.4071i | 0.904376 | − | 0.705441i | ||||
\(478\) | 1.74493 | − | 1.74493i | 0.0798112 | − | 0.0798112i | ||||
\(479\) | 11.7705i | 0.537807i | 0.963167 | + | 0.268903i | \(0.0866612\pi\) | ||||
−0.963167 | + | 0.268903i | \(0.913339\pi\) | |||||||
\(480\) | −0.220742 | + | 3.86669i | −0.0100754 | + | 0.176489i | ||||
\(481\) | 9.55956 | + | 4.53886i | 0.435878 | + | 0.206954i | ||||
\(482\) | 14.9951 | − | 14.9951i | 0.683009 | − | 0.683009i | ||||
\(483\) | −8.49792 | − | 9.61269i | −0.386669 | − | 0.437393i | ||||
\(484\) | 2.70578i | 0.122990i | ||||||||
\(485\) | −15.5449 | + | 15.6838i | −0.705857 | + | 0.712167i | ||||
\(486\) | 4.71649 | − | 14.8578i | 0.213944 | − | 0.673964i | ||||
\(487\) | 3.51182 | − | 3.51182i | 0.159136 | − | 0.159136i | −0.623048 | − | 0.782184i | \(-0.714106\pi\) |
0.782184 | + | 0.623048i | \(0.214106\pi\) | |||||||
\(488\) | 8.53366 | − | 8.53366i | 0.386300 | − | 0.386300i | ||||
\(489\) | 2.08988 | − | 33.9521i | 0.0945074 | − | 1.53537i | ||||
\(490\) | 7.66818 | − | 7.73673i | 0.346413 | − | 0.349510i | ||||
\(491\) | 32.8608i | 1.48299i | 0.670960 | + | 0.741494i | \(0.265882\pi\) | ||||
−0.670960 | + | 0.741494i | \(0.734118\pi\) | |||||||
\(492\) | 2.15147 | − | 1.90197i | 0.0969958 | − | 0.0857473i | ||||
\(493\) | −0.904267 | + | 0.904267i | −0.0407262 | + | 0.0407262i | ||||
\(494\) | −9.86104 | + | 20.7689i | −0.443669 | + | 0.934436i | ||||
\(495\) | −2.93608 | + | 24.6605i | −0.131967 | + | 1.10841i | ||||
\(496\) | 2.88858i | 0.129701i | ||||||||
\(497\) | −4.55168 | + | 4.55168i | −0.204171 | + | 0.204171i | ||||
\(498\) | 7.85986 | + | 8.89094i | 0.352209 | + | 0.398412i | ||||
\(499\) | −18.0149 | −0.806460 | −0.403230 | − | 0.915099i | \(-0.632112\pi\) | ||||
−0.403230 | + | 0.915099i | \(0.632112\pi\) | |||||||
\(500\) | −0.149249 | − | 11.1793i | −0.00667462 | − | 0.499955i | ||||
\(501\) | 2.01442 | − | 32.7263i | 0.0899978 | − | 1.46210i | ||||
\(502\) | 14.9044 | − | 14.9044i | 0.665216 | − | 0.665216i | ||||
\(503\) | 2.42308 | + | 2.42308i | 0.108040 | + | 0.108040i | 0.759060 | − | 0.651020i | \(-0.225659\pi\) |
−0.651020 | + | 0.759060i | \(0.725659\pi\) | |||||||
\(504\) | 4.34376 | + | 0.536783i | 0.193487 | + | 0.0239102i | ||||
\(505\) | −0.155103 | − | 34.8554i | −0.00690201 | − | 1.55105i | ||||
\(506\) | − | 18.7973i | − | 0.835640i | ||||||
\(507\) | −22.2195 | − | 3.64611i | −0.986802 | − | 0.161929i | ||||
\(508\) | 13.1211 | − | 13.1211i | 0.582154 | − | 0.582154i | ||||
\(509\) | − | 3.24224i | − | 0.143710i | −0.997415 | − | 0.0718550i | \(-0.977108\pi\) | ||
0.997415 | − | 0.0718550i | \(-0.0228919\pi\) | |||||||
\(510\) | −6.65006 | − | 7.45531i | −0.294470 | − | 0.330127i | ||||
\(511\) | −16.5548 | −0.732342 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −27.3282 | + | 18.7351i | −1.20657 | + | 0.827176i | ||||
\(514\) | 12.0160 | 0.530003 | ||||||||
\(515\) | −9.08633 | + | 9.16756i | −0.400392 | + | 0.403971i | ||||
\(516\) | −1.30718 | + | 21.2365i | −0.0575455 | + | 0.934883i | ||||
\(517\) | −10.3526 | − | 10.3526i | −0.455308 | − | 0.455308i | ||||
\(518\) | −3.02783 | + | 3.02783i | −0.133035 | + | 0.133035i | ||||
\(519\) | −0.0582106 | + | 0.945689i | −0.00255516 | + | 0.0415111i | ||||
\(520\) | 7.29834 | + | 3.42553i | 0.320053 | + | 0.150219i | ||||
\(521\) | 22.6886i | 0.994006i | 0.867749 | + | 0.497003i | \(0.165566\pi\) | ||||
−0.867749 | + | 0.497003i | \(0.834434\pi\) | |||||||
\(522\) | 1.17273 | − | 0.914768i | 0.0513291 | − | 0.0400383i | ||||
\(523\) | −31.3120 | + | 31.3120i | −1.36918 | + | 1.36918i | −0.507563 | + | 0.861615i | \(0.669453\pi\) |
−0.861615 | + | 0.507563i | \(0.830547\pi\) | |||||||
\(524\) | 11.4677 | 0.500967 | ||||||||
\(525\) | −12.6173 | − | 0.663983i | −0.550663 | − | 0.0289786i | ||||
\(526\) | 17.7575i | 0.774263i | ||||||||
\(527\) | −5.26865 | − | 5.26865i | −0.229506 | − | 0.229506i | ||||
\(528\) | 4.24703 | + | 4.80417i | 0.184828 | + | 0.209075i | ||||
\(529\) | 2.78017i | 0.120877i | ||||||||
\(530\) | 0.0830849 | + | 18.6712i | 0.00360898 | + | 0.811023i | ||||
\(531\) | 2.06198 | + | 0.254810i | 0.0894821 | + | 0.0110578i | ||||
\(532\) | −6.57820 | − | 6.57820i | −0.285201 | − | 0.285201i | ||||
\(533\) | −2.00543 | − | 5.63136i | −0.0868647 | − | 0.243921i | ||||
\(534\) | 4.61109 | + | 0.283829i | 0.199541 | + | 0.0122825i | ||||
\(535\) | −23.6801 | + | 23.8918i | −1.02378 | + | 1.03293i | ||||
\(536\) | − | 9.60963i | − | 0.415073i | ||||||
\(537\) | 27.0954 | + | 30.6498i | 1.16925 | + | 1.32264i | ||||
\(538\) | −12.1805 | − | 12.1805i | −0.525140 | − | 0.525140i | ||||
\(539\) | − | 18.0350i | − | 0.776821i | ||||||
\(540\) | 6.61243 | + | 9.55384i | 0.284554 | + | 0.411132i | ||||
\(541\) | 23.3486i | 1.00383i | 0.864916 | + | 0.501916i | \(0.167371\pi\) | ||||
−0.864916 | + | 0.501916i | \(0.832629\pi\) | |||||||
\(542\) | 6.85177 | − | 6.85177i | 0.294309 | − | 0.294309i | ||||
\(543\) | −11.6386 | − | 13.1653i | −0.499458 | − | 0.564978i | ||||
\(544\) | −2.57947 | −0.110594 | ||||||||
\(545\) | −29.0525 | + | 0.129281i | −1.24447 | + | 0.00553778i | ||||
\(546\) | 4.40608 | − | 7.97481i | 0.188563 | − | 0.341290i | ||||
\(547\) | 0.00983851 | + | 0.00983851i | 0.000420664 | + | 0.000420664i | 0.707317 | − | 0.706896i | \(-0.249905\pi\) |
−0.706896 | + | 0.707317i | \(0.749905\pi\) | |||||||
\(548\) | −9.53679 | + | 9.53679i | −0.407391 | + | 0.407391i | ||||
\(549\) | 4.44031 | − | 35.9319i | 0.189508 | − | 1.53354i | ||||
\(550\) | −13.2050 | − | 12.9720i | −0.563062 | − | 0.553128i | ||||
\(551\) | −3.16131 | −0.134677 | ||||||||
\(552\) | −5.82474 | − | 6.58885i | −0.247918 | − | 0.280440i | ||||
\(553\) | −6.29284 | − | 6.29284i | −0.267599 | − | 0.267599i | ||||
\(554\) | − | 21.7894i | − | 0.925743i | ||||||
\(555\) | −11.3488 | − | 0.647882i | −0.481730 | − | 0.0275011i | ||||
\(556\) | 2.09695 | 0.0889305 | ||||||||
\(557\) | 20.4431 | + | 20.4431i | 0.866200 | + | 0.866200i | 0.992049 | − | 0.125849i | \(-0.0401655\pi\) |
−0.125849 | + | 0.992049i | \(0.540165\pi\) | |||||||
\(558\) | 5.32983 | + | 6.83284i | 0.225630 | + | 0.289257i | ||||
\(559\) | 40.0101 | + | 18.9967i | 1.69225 | + | 0.803476i | ||||
\(560\) | −2.29649 | + | 2.31702i | −0.0970444 | + | 0.0979119i | ||||
\(561\) | −16.5090 | − | 1.01619i | −0.697012 | − | 0.0429037i | ||||
\(562\) | 7.62241 | + | 7.62241i | 0.321532 | + | 0.321532i | ||||
\(563\) | −4.05212 | − | 4.05212i | −0.170777 | − | 0.170777i | 0.616544 | − | 0.787321i | \(-0.288532\pi\) |
−0.787321 | + | 0.616544i | \(0.788532\pi\) | |||||||
\(564\) | −6.83681 | − | 0.420831i | −0.287882 | − | 0.0177202i | ||||
\(565\) | 12.8345 | + | 12.7208i | 0.539952 | + | 0.535167i | ||||
\(566\) | −6.30383 | −0.264970 | ||||||||
\(567\) | 11.2655 | − | 6.74511i | 0.473106 | − | 0.283268i | ||||
\(568\) | −3.11987 | + | 3.11987i | −0.130907 | + | 0.130907i | ||||
\(569\) | −21.1653 | −0.887297 | −0.443648 | − | 0.896201i | \(-0.646316\pi\) | ||||
−0.443648 | + | 0.896201i | \(0.646316\pi\) | |||||||
\(570\) | 1.40757 | − | 24.6562i | 0.0589568 | − | 1.03273i | ||||
\(571\) | 2.14561 | 0.0897912 | 0.0448956 | − | 0.998992i | \(-0.485704\pi\) | ||||
0.0448956 | + | 0.998992i | \(0.485704\pi\) | |||||||
\(572\) | 12.5747 | − | 4.47806i | 0.525773 | − | 0.187237i | ||||
\(573\) | −20.1320 | + | 17.7973i | −0.841024 | + | 0.743492i | ||||
\(574\) | 2.41883 | 0.100960 | ||||||||
\(575\) | 18.1104 | + | 17.7909i | 0.755257 | + | 0.741932i | ||||
\(576\) | 2.97735 | + | 0.367928i | 0.124056 | + | 0.0153303i | ||||
\(577\) | −20.9845 | + | 20.9845i | −0.873597 | + | 0.873597i | −0.992862 | − | 0.119266i | \(-0.961946\pi\) |
0.119266 | + | 0.992862i | \(0.461946\pi\) | |||||||
\(578\) | −7.31596 | + | 7.31596i | −0.304304 | + | 0.304304i | ||||
\(579\) | −0.873829 | + | 14.1962i | −0.0363151 | + | 0.589974i | ||||
\(580\) | 0.00493302 | + | 1.10857i | 0.000204832 | + | 0.0460307i | ||||
\(581\) | 9.99578i | 0.414695i | ||||||||
\(582\) | 11.3290 | + | 12.8152i | 0.469603 | + | 0.531207i | ||||
\(583\) | 21.8588 | + | 21.8588i | 0.905301 | + | 0.905301i | ||||
\(584\) | −11.3472 | −0.469550 | ||||||||
\(585\) | 23.5846 | − | 5.36349i | 0.975103 | − | 0.221753i | ||||
\(586\) | 8.86519 | 0.366217 | ||||||||
\(587\) | −25.6210 | − | 25.6210i | −1.05749 | − | 1.05749i | −0.998243 | − | 0.0592474i | \(-0.981130\pi\) |
−0.0592474 | − | 0.998243i | \(-0.518870\pi\) | |||||||
\(588\) | −5.58853 | − | 6.32164i | −0.230467 | − | 0.260700i | ||||
\(589\) | − | 18.4192i | − | 0.758949i | ||||||
\(590\) | −1.09014 | + | 1.09988i | −0.0448803 | + | 0.0452815i | ||||
\(591\) | 1.20506 | − | 19.5774i | 0.0495695 | − | 0.805305i | ||||
\(592\) | −2.07537 | + | 2.07537i | −0.0852973 | + | 0.0852973i | ||||
\(593\) | −33.6720 | + | 33.6720i | −1.38274 | + | 1.38274i | −0.543033 | + | 0.839712i | \(0.682724\pi\) |
−0.839712 | + | 0.543033i | \(0.817276\pi\) | |||||||
\(594\) | 18.9106 | + | 3.52774i | 0.775912 | + | 0.144745i | ||||
\(595\) | −0.0374453 | − | 8.41486i | −0.00153511 | − | 0.344976i | ||||
\(596\) | −21.4810 | −0.879898 | ||||||||
\(597\) | 14.5286 | − | 12.8438i | 0.594618 | − | 0.525661i | ||||
\(598\) | −17.2460 | + | 6.14159i | −0.705240 | + | 0.251148i | ||||
\(599\) | 28.6778 | 1.17174 | 0.585871 | − | 0.810404i | \(-0.300753\pi\) | ||||
0.585871 | + | 0.810404i | \(0.300753\pi\) | |||||||
\(600\) | −8.64829 | − | 0.455115i | −0.353065 | − | 0.0185800i | ||||
\(601\) | 35.1548 | 1.43399 | 0.716997 | − | 0.697077i | \(-0.245516\pi\) | ||||
0.716997 | + | 0.697077i | \(0.245516\pi\) | |||||||
\(602\) | −12.6725 | + | 12.6725i | −0.516494 | + | 0.516494i | ||||
\(603\) | −17.7311 | − | 22.7313i | −0.722067 | − | 0.925690i | ||||
\(604\) | −4.31897 | −0.175736 | ||||||||
\(605\) | −6.05024 | + | 0.0269230i | −0.245977 | + | 0.00109458i | ||||
\(606\) | −26.9482 | − | 1.65876i | −1.09469 | − | 0.0673825i | ||||
\(607\) | 3.38326 | + | 3.38326i | 0.137322 | + | 0.137322i | 0.772426 | − | 0.635104i | \(-0.219043\pi\) |
−0.635104 | + | 0.772426i | \(0.719043\pi\) | |||||||
\(608\) | −4.50891 | − | 4.50891i | −0.182860 | − | 0.182860i | ||||
\(609\) | 1.25042 | + | 0.0769681i | 0.0506696 | + | 0.00311890i | ||||
\(610\) | 19.1666 | + | 18.9967i | 0.776031 | + | 0.769155i | ||||
\(611\) | −6.11576 | + | 12.8807i | −0.247417 | + | 0.521099i | ||||
\(612\) | −6.10166 | + | 4.75949i | −0.246645 | + | 0.192391i | ||||
\(613\) | 20.5151 | + | 20.5151i | 0.828596 | + | 0.828596i | 0.987323 | − | 0.158727i | \(-0.0507388\pi\) |
−0.158727 | + | 0.987323i | \(0.550739\pi\) | |||||||
\(614\) | 26.0120 | 1.04976 | ||||||||
\(615\) | 4.27429 | + | 4.79186i | 0.172356 | + | 0.193227i | ||||
\(616\) | 5.40117i | 0.217619i | ||||||||
\(617\) | −4.49927 | − | 4.49927i | −0.181134 | − | 0.181134i | 0.610716 | − | 0.791850i | \(-0.290882\pi\) |
−0.791850 | + | 0.610716i | \(0.790882\pi\) | |||||||
\(618\) | 6.62207 | + | 7.49077i | 0.266379 | + | 0.301323i | ||||
\(619\) | −5.23035 | −0.210226 | −0.105113 | − | 0.994460i | \(-0.533520\pi\) | ||||
−0.105113 | + | 0.994460i | \(0.533520\pi\) | |||||||
\(620\) | −6.45899 | + | 0.0287419i | −0.259399 | + | 0.00115430i | ||||
\(621\) | −25.9356 | − | 4.83824i | −1.04076 | − | 0.194152i | ||||
\(622\) | −1.25800 | + | 1.25800i | −0.0504412 | + | 0.0504412i | ||||
\(623\) | 2.75159 | + | 2.75159i | 0.110240 | + | 0.110240i | ||||
\(624\) | 3.02006 | − | 5.46619i | 0.120899 | − | 0.218823i | ||||
\(625\) | 24.9960 | − | 0.444964i | 0.999842 | − | 0.0177986i | ||||
\(626\) | −20.7376 | −0.828840 | ||||||||
\(627\) | −27.0815 | − | 30.6341i | −1.08153 | − | 1.22341i | ||||
\(628\) | 2.78660 | − | 2.78660i | 0.111197 | − | 0.111197i | ||||
\(629\) | − | 7.57080i | − | 0.301867i | ||||||
\(630\) | −1.15705 | + | 9.71819i | −0.0460980 | + | 0.387182i | ||||
\(631\) | − | 31.1770i | − | 1.24114i | −0.784152 | − | 0.620568i | \(-0.786902\pi\) | ||
0.784152 | − | 0.620568i | \(-0.213098\pi\) | |||||||
\(632\) | −4.31332 | − | 4.31332i | −0.171574 | − | 0.171574i | ||||
\(633\) | 3.84301 | + | 4.34714i | 0.152746 | + | 0.172783i | ||||
\(634\) | 10.6729i | 0.423874i | ||||||||
\(635\) | 29.4699 | + | 29.2088i | 1.16948 | + | 1.15912i | ||||
\(636\) | 14.4354 | + | 0.888554i | 0.572402 | + | 0.0352335i | ||||
\(637\) | −16.5466 | + | 5.89253i | −0.655599 | + | 0.233470i | ||||
\(638\) | 1.29783 | + | 1.29783i | 0.0513816 | + | 0.0513816i | ||||
\(639\) | −1.62336 | + | 13.1365i | −0.0642190 | + | 0.519674i | ||||
\(640\) | −1.57409 | + | 1.58816i | −0.0622213 | + | 0.0627775i | ||||
\(641\) | − | 4.46954i | − | 0.176536i | −0.996097 | − | 0.0882681i | \(-0.971867\pi\) | ||
0.996097 | − | 0.0882681i | \(-0.0281332\pi\) | |||||||
\(642\) | 17.2579 | + | 19.5218i | 0.681115 | + | 0.770465i | ||||
\(643\) | 9.58366 | + | 9.58366i | 0.377943 | + | 0.377943i | 0.870359 | − | 0.492417i | \(-0.163886\pi\) |
−0.492417 | + | 0.870359i | \(0.663886\pi\) | |||||||
\(644\) | − | 7.40762i | − | 0.291901i | ||||||
\(645\) | −47.4987 | − | 2.71161i | −1.87026 | − | 0.106770i | ||||
\(646\) | 16.4482 | 0.647144 | ||||||||
\(647\) | −12.0307 | + | 12.0307i | −0.472977 | + | 0.472977i | −0.902877 | − | 0.429900i | \(-0.858549\pi\) |
0.429900 | + | 0.902877i | \(0.358549\pi\) | |||||||
\(648\) | 7.72172 | − | 4.62331i | 0.303338 | − | 0.181621i | ||||
\(649\) | 2.56392i | 0.100643i | ||||||||
\(650\) | −7.58701 | + | 16.3535i | −0.297587 | + | 0.641437i | ||||
\(651\) | −0.448449 | + | 7.28549i | −0.0175761 | + | 0.285541i | ||||
\(652\) | 13.8871 | − | 13.8871i | 0.543861 | − | 0.543861i | ||||
\(653\) | −7.52183 | − | 7.52183i | −0.294352 | − | 0.294352i | 0.544445 | − | 0.838797i | \(-0.316740\pi\) |
−0.838797 | + | 0.544445i | \(0.816740\pi\) | |||||||
\(654\) | −1.38260 | + | 22.4617i | −0.0540639 | + | 0.878321i | ||||
\(655\) | 0.114105 | + | 25.6422i | 0.00445847 | + | 1.00192i | ||||
\(656\) | 1.65794 | 0.0647317 | ||||||||
\(657\) | −26.8415 | + | 20.9372i | −1.04719 | + | 0.816838i | ||||
\(658\) | −4.07976 | − | 4.07976i | −0.159046 | − | 0.159046i | ||||
\(659\) | −35.5017 | −1.38295 | −0.691475 | − | 0.722400i | \(-0.743039\pi\) | ||||
−0.691475 | + | 0.722400i | \(0.743039\pi\) | |||||||
\(660\) | −10.7001 | + | 9.54436i | −0.416500 | + | 0.371514i | ||||
\(661\) | 22.1943i | 0.863260i | 0.902051 | + | 0.431630i | \(0.142061\pi\) | ||||
−0.902051 | + | 0.431630i | \(0.857939\pi\) | |||||||
\(662\) | 2.96259 | − | 2.96259i | 0.115144 | − | 0.115144i | ||||
\(663\) | 4.46163 | + | 15.4786i | 0.173276 | + | 0.601139i | ||||
\(664\) | 6.85143i | 0.265887i | ||||||||
\(665\) | 14.6437 | − | 14.7746i | 0.567859 | − | 0.572935i | ||||
\(666\) | −1.07988 | + | 8.73859i | −0.0418444 | + | 0.338613i | ||||
\(667\) | −1.77996 | − | 1.77996i | −0.0689202 | − | 0.0689202i | ||||
\(668\) | 13.3857 | − | 13.3857i | 0.517910 | − | 0.517910i | ||||
\(669\) | −1.33179 | + | 21.6363i | −0.0514901 | + | 0.836507i | ||||
\(670\) | 21.4876 | − | 0.0956176i | 0.830137 | − | 0.00369403i | ||||
\(671\) | 44.6788 | 1.72481 | ||||||||
\(672\) | 1.67367 | + | 1.89322i | 0.0645632 | + | 0.0730327i | ||||
\(673\) | 9.51386 | − | 9.51386i | 0.366732 | − | 0.366732i | −0.499552 | − | 0.866284i | \(-0.666502\pi\) |
0.866284 | + | 0.499552i | \(0.166502\pi\) | |||||||
\(674\) | 21.8952i | 0.843371i | ||||||||
\(675\) | −21.2970 | + | 14.8808i | −0.819723 | + | 0.572761i | ||||
\(676\) | −8.21698 | − | 10.0738i | −0.316038 | − | 0.387453i | ||||
\(677\) | −17.0253 | + | 17.0253i | −0.654337 | + | 0.654337i | −0.954034 | − | 0.299697i | \(-0.903114\pi\) |
0.299697 | + | 0.954034i | \(0.403114\pi\) | |||||||
\(678\) | 10.4870 | − | 9.27084i | 0.402751 | − | 0.356044i | ||||
\(679\) | 14.4077i | 0.552916i | ||||||||
\(680\) | −0.0256662 | − | 5.76782i | −0.000984255 | − | 0.221186i | ||||
\(681\) | 1.14845 | − | 18.6576i | 0.0440086 | − | 0.714962i | ||||
\(682\) | −7.56172 | + | 7.56172i | −0.289553 | + | 0.289553i | ||||
\(683\) | −28.1737 | + | 28.1737i | −1.07804 | + | 1.07804i | −0.0813495 | + | 0.996686i | \(0.525923\pi\) |
−0.996686 | + | 0.0813495i | \(0.974077\pi\) | |||||||
\(684\) | −18.9853 | − | 2.34612i | −0.725920 | − | 0.0897060i | ||||
\(685\) | −21.4196 | − | 21.2298i | −0.818400 | − | 0.811149i | ||||
\(686\) | − | 17.3198i | − | 0.661271i | ||||||
\(687\) | −26.4196 | − | 29.8853i | −1.00797 | − | 1.14020i | ||||
\(688\) | −8.68616 | + | 8.68616i | −0.331157 | + | 0.331157i | ||||
\(689\) | 12.9130 | − | 27.1968i | 0.491945 | − | 1.03611i | ||||
\(690\) | 14.6750 | − | 13.0900i | 0.558668 | − | 0.498326i | ||||
\(691\) | 7.58330i | 0.288482i | 0.989543 | + | 0.144241i | \(0.0460741\pi\) | ||||
−0.989543 | + | 0.144241i | \(0.953926\pi\) | |||||||
\(692\) | −0.386807 | + | 0.386807i | −0.0147042 | + | 0.0147042i | ||||
\(693\) | 9.96592 | + | 12.7763i | 0.378574 | + | 0.485332i | ||||
\(694\) | 14.0964 | 0.535094 | ||||||||
\(695\) | 0.0208651 | + | 4.68888i | 0.000791457 | + | 0.177859i | ||||
\(696\) | 0.857079 | + | 0.0527564i | 0.0324875 | + | 0.00199972i | ||||
\(697\) | −3.02402 | + | 3.02402i | −0.114543 | + | 0.114543i | ||||
\(698\) | −17.4957 | − | 17.4957i | −0.662220 | − | 0.662220i | ||||
\(699\) | −2.97175 | + | 48.2790i | −0.112402 | + | 1.82608i | ||||
\(700\) | −5.20381 | − | 5.11200i | −0.196686 | − | 0.193216i | ||||
\(701\) | − | 19.1834i | − | 0.724547i | −0.932072 | − | 0.362273i | \(-0.882001\pi\) | ||
0.932072 | − | 0.362273i | \(-0.117999\pi\) | |||||||
\(702\) | −2.94202 | − | 18.5026i | −0.111039 | − | 0.698334i | ||||
\(703\) | 13.2337 | − | 13.2337i | 0.499120 | − | 0.499120i | ||||
\(704\) | 3.70213i | 0.139529i | ||||||||
\(705\) | 0.872970 | − | 15.2916i | 0.0328779 | − | 0.575915i | ||||
\(706\) | 5.89859 | 0.221996 | ||||||||
\(707\) | −16.0809 | − | 16.0809i | −0.604785 | − | 0.604785i | ||||
\(708\) | 0.794488 | + | 0.898710i | 0.0298587 | + | 0.0337756i | ||||
\(709\) | −2.73514 | −0.102720 | −0.0513602 | − | 0.998680i | \(-0.516356\pi\) | ||||
−0.0513602 | + | 0.998680i | \(0.516356\pi\) | |||||||
\(710\) | −7.00721 | − | 6.94512i | −0.262976 | − | 0.260646i | ||||
\(711\) | −18.1617 | − | 2.24434i | −0.681117 | − | 0.0841694i | ||||
\(712\) | 1.88603 | + | 1.88603i | 0.0706820 | + | 0.0706820i | ||||
\(713\) | 10.3708 | − | 10.3708i | 0.388389 | − | 0.388389i | ||||
\(714\) | −6.50588 | − | 0.400461i | −0.243476 | − | 0.0149869i | ||||
\(715\) | 10.1383 | + | 28.0730i | 0.379150 | + | 1.04987i | ||||
\(716\) | 23.6190i | 0.882684i | ||||||||
\(717\) | 3.20228 | − | 2.83091i | 0.119591 | − | 0.105722i | ||||
\(718\) | 1.80464 | − | 1.80464i | 0.0673485 | − | 0.0673485i | ||||
\(719\) | 52.8821 | 1.97217 | 0.986084 | − | 0.166248i | \(-0.0531652\pi\) | ||||
0.986084 | + | 0.166248i | \(0.0531652\pi\) | |||||||
\(720\) | −0.793079 | + | 6.66116i | −0.0295563 | + | 0.248247i | ||||
\(721\) | 8.42162i | 0.313637i | ||||||||
\(722\) | 15.3163 | + | 15.3163i | 0.570014 | + | 0.570014i | ||||
\(723\) | 27.5189 | − | 24.3276i | 1.02344 | − | 0.904752i | ||||
\(724\) | − | 10.1453i | − | 0.377047i | ||||||
\(725\) | −2.47876 | + | 0.0220609i | −0.0920587 | + | 0.000819322i | ||||
\(726\) | −0.287929 | + | 4.67769i | −0.0106860 | + | 0.173605i | ||||
\(727\) | −2.36804 | − | 2.36804i | −0.0878259 | − | 0.0878259i | 0.661829 | − | 0.749655i | \(-0.269781\pi\) |
−0.749655 | + | 0.661829i | \(0.769781\pi\) | |||||||
\(728\) | 4.95542 | − | 1.76471i | 0.183660 | − | 0.0654045i | ||||
\(729\) | 9.73483 | − | 25.1840i | 0.360549 | − | 0.932740i | ||||
\(730\) | −0.112907 | − | 25.3729i | −0.00417887 | − | 0.939092i | ||||
\(731\) | − | 31.6864i | − | 1.17197i | ||||||
\(732\) | 15.6609 | − | 13.8447i | 0.578843 | − | 0.511715i | ||||
\(733\) | −3.85830 | − | 3.85830i | −0.142510 | − | 0.142510i | 0.632253 | − | 0.774762i | \(-0.282130\pi\) |
−0.774762 | + | 0.632253i | \(0.782130\pi\) | |||||||
\(734\) | 18.4716i | 0.681800i | ||||||||
\(735\) | 14.0799 | − | 12.5591i | 0.519344 | − | 0.463250i | ||||
\(736\) | − | 5.07742i | − | 0.187156i | ||||||
\(737\) | 25.1561 | − | 25.1561i | 0.926637 | − | 0.926637i | ||||
\(738\) | 3.92181 | − | 3.05914i | 0.144364 | − | 0.112608i | ||||
\(739\) | −31.7224 | −1.16693 | −0.583464 | − | 0.812139i | \(-0.698303\pi\) | ||||
−0.583464 | + | 0.812139i | \(0.698303\pi\) | |||||||
\(740\) | −4.66128 | − | 4.61998i | −0.171352 | − | 0.169834i | ||||
\(741\) | −19.2576 | + | 34.8555i | −0.707446 | + | 1.28045i | ||||
\(742\) | 8.61412 | + | 8.61412i | 0.316234 | + | 0.316234i | ||||
\(743\) | −13.7641 | + | 13.7641i | −0.504957 | + | 0.504957i | −0.912974 | − | 0.408017i | \(-0.866220\pi\) |
0.408017 | + | 0.912974i | \(0.366220\pi\) | |||||||
\(744\) | −0.307381 | + | 4.99371i | −0.0112691 | + | 0.183078i | ||||
\(745\) | −0.213741 | − | 48.0326i | −0.00783085 | − | 1.75978i | ||||
\(746\) | 17.6603 | 0.646591 | ||||||||
\(747\) | 12.6419 | + | 16.2069i | 0.462541 | + | 0.592978i | ||||
\(748\) | −6.75254 | − | 6.75254i | −0.246897 | − | 0.246897i | ||||
\(749\) | 21.9477i | 0.801953i | ||||||||
\(750\) | 0.931606 | − | 19.3425i | 0.0340174 | − | 0.706288i | ||||
\(751\) | −36.2372 | −1.32231 | −0.661157 | − | 0.750247i | \(-0.729934\pi\) | ||||
−0.661157 | + | 0.750247i | \(0.729934\pi\) | |||||||
\(752\) | −2.79640 | − | 2.79640i | −0.101974 | − | 0.101974i | ||||
\(753\) | 27.3524 | − | 24.1804i | 0.996779 | − | 0.881183i | ||||
\(754\) | 0.766686 | − | 1.61476i | 0.0279210 | − | 0.0588061i | ||||
\(755\) | −0.0429746 | − | 9.65741i | −0.00156400 | − | 0.351469i | ||||
\(756\) | 7.45228 | + | 1.39021i | 0.271037 | + | 0.0505615i | ||||
\(757\) | −21.7590 | − | 21.7590i | −0.790845 | − | 0.790845i | 0.190787 | − | 0.981632i | \(-0.438896\pi\) |
−0.981632 | + | 0.190787i | \(0.938896\pi\) | |||||||
\(758\) | −1.20359 | − | 1.20359i | −0.0437162 | − | 0.0437162i | ||||
\(759\) | 2.00027 | − | 32.4963i | 0.0726051 | − | 1.17954i | ||||
\(760\) | 10.0373 | − | 10.1270i | 0.364090 | − | 0.367345i | ||||
\(761\) | −14.1444 | −0.512735 | −0.256367 | − | 0.966579i | \(-0.582526\pi\) | ||||
−0.256367 | + | 0.966579i | \(0.582526\pi\) | |||||||
\(762\) | 24.0797 | − | 21.2872i | 0.872316 | − | 0.771155i | ||||
\(763\) | −13.4037 | + | 13.4037i | −0.485245 | + | 0.485245i | ||||
\(764\) | −15.5138 | −0.561271 | ||||||||
\(765\) | −10.7031 | − | 13.5962i | −0.386973 | − | 0.491573i | ||||
\(766\) | 35.1963 | 1.27169 | ||||||||
\(767\) | 2.35233 | − | 0.837705i | 0.0849376 | − | 0.0302478i | ||||
\(768\) | 1.14719 | + | 1.29768i | 0.0413955 | + | 0.0468259i | ||||
\(769\) | 17.8477 | 0.643604 | 0.321802 | − | 0.946807i | \(-0.395712\pi\) | ||||
0.321802 | + | 0.946807i | \(0.395712\pi\) | |||||||
\(770\) | −12.0773 | + | 0.0537426i | −0.435234 | + | 0.00193675i | ||||
\(771\) | 20.7730 | + | 1.27866i | 0.748122 | + | 0.0460497i | ||||
\(772\) | −5.80655 | + | 5.80655i | −0.208982 | + | 0.208982i | ||||
\(773\) | 17.8480 | − | 17.8480i | 0.641948 | − | 0.641948i | −0.309086 | − | 0.951034i | \(-0.600023\pi\) |
0.951034 | + | 0.309086i | \(0.100023\pi\) | |||||||
\(774\) | −4.51966 | + | 36.5741i | −0.162456 | + | 1.31463i | ||||
\(775\) | −0.128536 | − | 14.4423i | −0.00461716 | − | 0.518783i | ||||
\(776\) | 9.87549i | 0.354509i | ||||||||
\(777\) | −5.55665 | + | 4.91225i | −0.199344 | + | 0.176226i | ||||
\(778\) | 13.2212 | + | 13.2212i | 0.474002 | + | 0.474002i | ||||
\(779\) | −10.5720 | −0.378780 | ||||||||
\(780\) | 12.2527 | + | 6.69861i | 0.438717 | + | 0.239849i | ||||
\(781\) | −16.3344 | −0.584490 | ||||||||
\(782\) | 9.26101 | + | 9.26101i | 0.331173 | + | 0.331173i | ||||
\(783\) | 2.12474 | − | 1.45664i | 0.0759319 | − | 0.0520560i | ||||
\(784\) | − | 4.87151i | − | 0.173983i | ||||||
\(785\) | 6.25869 | + | 6.20324i | 0.223382 | + | 0.221403i | ||||
\(786\) | 19.8251 | + | 1.22031i | 0.707136 | + | 0.0435268i | ||||
\(787\) | −7.56156 | + | 7.56156i | −0.269540 | + | 0.269540i | −0.828915 | − | 0.559375i | \(-0.811041\pi\) |
0.559375 | + | 0.828915i | \(0.311041\pi\) | |||||||
\(788\) | 8.00755 | − | 8.00755i | 0.285257 | − | 0.285257i | ||||
\(789\) | −1.88962 | + | 30.6988i | −0.0672723 | + | 1.09291i | ||||
\(790\) | 9.60185 | − | 9.68769i | 0.341619 | − | 0.344673i | ||||
\(791\) | 11.7902 | 0.419211 | ||||||||
\(792\) | 6.83096 | + | 8.75728i | 0.242727 | + | 0.311177i | ||||
\(793\) | −14.5978 | − | 40.9916i | −0.518384 | − | 1.45565i | ||||
\(794\) | 9.69372 | 0.344017 | ||||||||
\(795\) | −1.84321 | + | 32.2871i | −0.0653720 | + | 1.14511i | ||||
\(796\) | 11.1959 | 0.396828 | ||||||||
\(797\) | 12.1869 | − | 12.1869i | 0.431680 | − | 0.431680i | −0.457519 | − | 0.889200i | \(-0.651262\pi\) |
0.889200 | + | 0.457519i | \(0.151262\pi\) | |||||||
\(798\) | −10.6723 | − | 12.0723i | −0.377794 | − | 0.427353i | ||||
\(799\) | 10.2010 | 0.360887 | ||||||||
\(800\) | −3.56686 | − | 3.50393i | −0.126108 | − | 0.123883i | ||||
\(801\) | 7.94134 | + | 0.981356i | 0.280594 | + | 0.0346745i | ||||
\(802\) | −13.4487 | − | 13.4487i | −0.474891 | − | 0.474891i | ||||
\(803\) | −29.7047 | − | 29.7047i | −1.04826 | − | 1.04826i | ||||
\(804\) | 1.02259 | − | 16.6129i | 0.0360638 | − | 0.585893i | ||||
\(805\) | 16.5638 | − | 0.0737072i | 0.583796 | − | 0.00259784i | ||||
\(806\) | 9.40828 | + | 4.46704i | 0.331393 | + | 0.157345i | ||||
\(807\) | −19.7613 | − | 22.3536i | −0.695630 | − | 0.786884i | ||||
\(808\) | −11.0224 | − | 11.0224i | −0.387766 | − | 0.387766i | ||||
\(809\) | −27.7750 | −0.976516 | −0.488258 | − | 0.872699i | \(-0.662368\pi\) | ||||
−0.488258 | + | 0.872699i | \(0.662368\pi\) | |||||||
\(810\) | 10.4148 | + | 17.2201i | 0.365938 | + | 0.605053i | ||||
\(811\) | − | 5.31945i | − | 0.186791i | −0.995629 | − | 0.0933957i | \(-0.970228\pi\) | ||
0.995629 | − | 0.0933957i | \(-0.0297722\pi\) | |||||||
\(812\) | 0.511449 | + | 0.511449i | 0.0179483 | + | 0.0179483i | ||||
\(813\) | 12.5743 | − | 11.1161i | 0.441000 | − | 0.389858i | ||||
\(814\) | −10.8658 | −0.380847 | ||||||||
\(815\) | 31.1904 | + | 30.9140i | 1.09255 | + | 1.08287i | ||||
\(816\) | −4.45933 | − | 0.274489i | −0.156108 | − | 0.00960902i | ||||
\(817\) | 55.3878 | − | 55.3878i | 1.93777 | − | 1.93777i | ||||
\(818\) | −15.8553 | − | 15.8553i | −0.554368 | − | 0.554368i | ||||
\(819\) | 8.46575 | − | 13.3178i | 0.295817 | − | 0.465362i | ||||
\(820\) | 0.0164968 | + | 3.70723i | 0.000576094 | + | 0.129462i | ||||
\(821\) | 35.6438 | 1.24398 | 0.621989 | − | 0.783026i | \(-0.286325\pi\) | ||||
0.621989 | + | 0.783026i | \(0.286325\pi\) | |||||||
\(822\) | −17.5018 | + | 15.4722i | −0.610447 | + | 0.539654i | ||||
\(823\) | 19.4031 | − | 19.4031i | 0.676350 | − | 0.676350i | −0.282822 | − | 0.959172i | \(-0.591271\pi\) |
0.959172 | + | 0.282822i | \(0.0912706\pi\) | |||||||
\(824\) | 5.77245i | 0.201093i | ||||||||
\(825\) | −21.4481 | − | 23.8309i | −0.746727 | − | 0.829686i | ||||
\(826\) | 1.01039i | 0.0351560i | ||||||||
\(827\) | −18.4487 | − | 18.4487i | −0.641525 | − | 0.641525i | 0.309406 | − | 0.950930i | \(-0.399870\pi\) |
−0.950930 | + | 0.309406i | \(0.899870\pi\) | |||||||
\(828\) | −9.36856 | − | 12.0105i | −0.325580 | − | 0.417393i | ||||
\(829\) | − | 21.9653i | − | 0.762885i | −0.924393 | − | 0.381443i | \(-0.875427\pi\) | ||
0.924393 | − | 0.381443i | \(-0.124573\pi\) | |||||||
\(830\) | −15.3201 | + | 0.0681730i | −0.531769 | + | 0.00236632i | ||||
\(831\) | 2.31867 | − | 37.6691i | 0.0804338 | − | 1.30673i | ||||
\(832\) | 3.39660 | − | 1.20959i | 0.117756 | − | 0.0419350i | ||||
\(833\) | 8.88545 | + | 8.88545i | 0.307863 | + | 0.307863i | ||||
\(834\) | 3.62516 | + | 0.223142i | 0.125529 | + | 0.00772678i | ||||
\(835\) | 30.0643 | + | 29.7979i | 1.04042 | + | 1.03120i | ||||
\(836\) | − | 23.6069i | − | 0.816460i | ||||||
\(837\) | 8.48700 | + | 12.3796i | 0.293354 | + | 0.427903i | ||||
\(838\) | −0.378921 | − | 0.378921i | −0.0130896 | − | 0.0130896i | ||||
\(839\) | − | 28.4339i | − | 0.981647i | −0.871259 | − | 0.490823i | \(-0.836696\pi\) | ||
0.871259 | − | 0.490823i | \(-0.163304\pi\) | |||||||
\(840\) | −4.21668 | + | 3.76124i | −0.145489 | + | 0.129775i | ||||
\(841\) | −28.7542 | −0.991525 | ||||||||
\(842\) | 16.6817 | − | 16.6817i | 0.574890 | − | 0.574890i | ||||
\(843\) | 12.3663 | + | 13.9886i | 0.425919 | + | 0.481792i | ||||
\(844\) | 3.34994i | 0.115310i | ||||||||
\(845\) | 22.4437 | − | 18.4738i | 0.772086 | − | 0.635517i | ||||
\(846\) | −11.7746 | − | 1.45505i | −0.404817 | − | 0.0500256i | ||||
\(847\) | −2.79134 | + | 2.79134i | −0.0959115 | + | 0.0959115i | ||||
\(848\) | 5.90440 | + | 5.90440i | 0.202758 | + | 0.202758i | ||||
\(849\) | −10.8979 | − | 0.670808i | −0.374016 | − | 0.0230221i | ||||
\(850\) | 12.8968 | − | 0.114782i | 0.442358 | − | 0.00393698i | ||||
\(851\) | 14.9023 | 0.510845 | ||||||||
\(852\) | −5.72555 | + | 5.06156i | −0.196154 | + | 0.173406i | ||||
\(853\) | −13.9812 | − | 13.9812i | −0.478707 | − | 0.478707i | 0.426011 | − | 0.904718i | \(-0.359918\pi\) |
−0.904718 | + | 0.426011i | \(0.859918\pi\) | |||||||
\(854\) | 17.6070 | 0.602500 | ||||||||
\(855\) | 5.05712 | − | 42.4753i | 0.172950 | − | 1.45262i | ||||
\(856\) | 15.0437i | 0.514182i | ||||||||
\(857\) | −37.1382 | + | 37.1382i | −1.26862 | + | 1.26862i | −0.321815 | + | 0.946803i | \(0.604293\pi\) |
−0.946803 | + | 0.321815i | \(0.895707\pi\) | |||||||
\(858\) | 22.2153 | − | 6.40347i | 0.758419 | − | 0.218611i | ||||
\(859\) | 28.5944i | 0.975628i | 0.872948 | + | 0.487814i | \(0.162205\pi\) | ||||
−0.872948 | + | 0.487814i | \(0.837795\pi\) | |||||||
\(860\) | −19.5091 | − | 19.3362i | −0.665254 | − | 0.659360i | ||||
\(861\) | 4.18162 | + | 0.257394i | 0.142509 | + | 0.00877196i | ||||
\(862\) | 10.6493 | + | 10.6493i | 0.362716 | + | 0.362716i | ||||
\(863\) | 28.9597 | − | 28.9597i | 0.985800 | − | 0.985800i | −0.0141001 | − | 0.999901i | \(-0.504488\pi\) |
0.999901 | + | 0.0141001i | \(0.00448836\pi\) | |||||||
\(864\) | 5.10803 | + | 0.952895i | 0.173779 | + | 0.0324181i | ||||
\(865\) | −0.868766 | − | 0.861068i | −0.0295389 | − | 0.0292772i | ||||
\(866\) | 11.9018 | 0.404440 | ||||||||
\(867\) | −13.4262 | + | 11.8692i | −0.455977 | + | 0.403098i | ||||
\(868\) | −2.97992 | + | 2.97992i | −0.101145 | + | 0.101145i | ||||
\(869\) | − | 22.5828i | − | 0.766070i | ||||||
\(870\) | −0.109438 | + | 1.91699i | −0.00371028 | + | 0.0649921i | ||||
\(871\) | −31.2992 | − | 14.8608i | −1.06053 | − | 0.503539i | ||||
\(872\) | −9.18729 | + | 9.18729i | −0.311121 | + | 0.311121i | ||||
\(873\) | 18.2217 | + | 23.3602i | 0.616710 | + | 0.790622i | ||||
\(874\) | 32.3765i | 1.09515i | ||||||||
\(875\) | 11.3789 | − | 11.6868i | 0.384677 | − | 0.395087i | ||||
\(876\) | −19.6168 | − | 1.20749i | −0.662790 | − | 0.0407972i | ||||
\(877\) | −28.6850 | + | 28.6850i | −0.968623 | + | 0.968623i | −0.999522 | − | 0.0308995i | \(-0.990163\pi\) |
0.0308995 | + | 0.999522i | \(0.490163\pi\) | |||||||
\(878\) | 25.1975 | − | 25.1975i | 0.850376 | − | 0.850376i | ||||
\(879\) | 15.3259 | + | 0.943369i | 0.516931 | + | 0.0318190i | ||||
\(880\) | −8.27814 | + | 0.0368369i | −0.279056 | + | 0.00124177i | ||||
\(881\) | − | 32.8722i | − | 1.10749i | −0.832686 | − | 0.553746i | \(-0.813198\pi\) | ||
0.832686 | − | 0.553746i | \(-0.186802\pi\) | |||||||
\(882\) | −8.98863 | − | 11.5234i | −0.302663 | − | 0.388014i | ||||
\(883\) | 10.1933 | − | 10.1933i | 0.343032 | − | 0.343032i | −0.514474 | − | 0.857506i | \(-0.672013\pi\) |
0.857506 | + | 0.514474i | \(0.172013\pi\) | |||||||
\(884\) | −3.98902 | + | 8.40151i | −0.134165 | + | 0.282573i | ||||
\(885\) | −2.00165 | + | 1.78545i | −0.0672848 | + | 0.0600173i | ||||
\(886\) | 19.5608i | 0.657158i | ||||||||
\(887\) | 0.276224 | − | 0.276224i | 0.00927471 | − | 0.00927471i | −0.702454 | − | 0.711729i | \(-0.747912\pi\) |
0.711729 | + | 0.702454i | \(0.247912\pi\) | |||||||
\(888\) | −3.80871 | + | 3.36701i | −0.127812 | + | 0.112990i | ||||
\(889\) | 27.0720 | 0.907967 | ||||||||
\(890\) | −4.19848 | + | 4.23602i | −0.140734 | + | 0.141992i | ||||
\(891\) | 32.3169 | + | 8.11101i | 1.08266 | + | 0.271729i | ||||
\(892\) | −8.84969 | + | 8.84969i | −0.296309 | + | 0.296309i | ||||
\(893\) | 17.8314 | + | 17.8314i | 0.596705 | + | 0.596705i | ||||
\(894\) | −37.1360 | − | 2.28586i | −1.24201 | − | 0.0764505i | ||||
\(895\) | −52.8132 | + | 0.235014i | −1.76535 | + | 0.00785564i | ||||
\(896\) | 1.45893i | 0.0487396i | ||||||||
\(897\) | −30.4680 | + | 8.78226i | −1.01730 | + | 0.293231i | ||||
\(898\) | 12.6830 | − | 12.6830i | 0.423239 | − | 0.423239i | ||||
\(899\) | 1.43207i | 0.0477623i | ||||||||
\(900\) | −14.9025 | − | 1.70708i | −0.496752 | − | 0.0569027i | ||||
\(901\) | −21.5388 | −0.717561 | ||||||||
\(902\) | 4.34016 | + | 4.34016i | 0.144512 | + | 0.144512i | ||||
\(903\) | −23.2565 | + | 20.5595i | −0.773929 | + | 0.684177i | ||||
\(904\) | 8.08137 | 0.268782 | ||||||||
\(905\) | 22.6854 | − | 0.100948i | 0.754087 | − | 0.00335562i | ||||
\(906\) | −7.46654 | − | 0.459593i | −0.248059 | − | 0.0152690i | ||||
\(907\) | −11.6761 | − | 11.6761i | −0.387698 | − | 0.387698i | 0.486168 | − | 0.873866i | \(-0.338394\pi\) |
−0.873866 | + | 0.486168i | \(0.838394\pi\) | |||||||
\(908\) | 7.63136 | − | 7.63136i | 0.253256 | − | 0.253256i | ||||
\(909\) | −46.4109 | − | 5.73526i | −1.53935 | − | 0.190226i | ||||
\(910\) | 3.99528 | + | 11.0630i | 0.132442 | + | 0.366734i | ||||
\(911\) | − | 22.6478i | − | 0.750355i | −0.926953 | − | 0.375177i | \(-0.877582\pi\) | ||
0.926953 | − | 0.375177i | \(-0.122418\pi\) | |||||||
\(912\) | −7.31510 | − | 8.27471i | −0.242227 | − | 0.274003i | ||||
\(913\) | −17.9357 | + | 17.9357i | −0.593585 | + | 0.593585i | ||||
\(914\) | 33.3913 | 1.10449 | ||||||||
\(915\) | 31.1132 | + | 34.8807i | 1.02857 | + | 1.15312i | ||||
\(916\) | − | 23.0299i | − | 0.760929i | ||||||
\(917\) | 11.8303 | + | 11.8303i | 0.390671 | + | 0.390671i | ||||
\(918\) | −11.0549 | + | 7.57881i | −0.364866 | + | 0.250138i | ||||
\(919\) | 13.8196i | 0.455867i | 0.973677 | + | 0.227933i | \(0.0731969\pi\) | ||||
−0.973677 | + | 0.227933i | \(0.926803\pi\) | |||||||
\(920\) | 11.3533 | − | 0.0505213i | 0.374309 | − | 0.00166564i | ||||
\(921\) | 44.9690 | + | 2.76801i | 1.48178 | + | 0.0912090i | ||||
\(922\) | −18.2501 | − | 18.2501i | −0.601035 | − | 0.601035i | ||||
\(923\) | 5.33690 | + | 14.9863i | 0.175666 | + | 0.493281i | ||||
\(924\) | −0.574753 | + | 9.33742i | −0.0189080 | + | 0.307179i | ||||
\(925\) | 10.2841 | − | 10.4688i | 0.338139 | − | 0.344212i | ||||
\(926\) | 29.5708i | 0.971756i | ||||||||
\(927\) | 10.6510 | + | 13.6546i | 0.349824 | + | 0.448474i | ||||
\(928\) | 0.350563 | + | 0.350563i | 0.0115078 | + | 0.0115078i | ||||
\(929\) | 5.46712i | 0.179371i | 0.995970 | + | 0.0896853i | \(0.0285861\pi\) | ||||
−0.995970 | + | 0.0896853i | \(0.971414\pi\) | |||||||
\(930\) | −11.1692 | − | 0.637630i | −0.366253 | − | 0.0209087i | ||||
\(931\) | 31.0635i | 1.01806i | ||||||||
\(932\) | −19.7471 | + | 19.7471i | −0.646839 | + | 0.646839i | ||||
\(933\) | −2.30867 | + | 2.04094i | −0.0755825 | + | 0.0668172i | ||||
\(934\) | 5.38845 | 0.176315 | ||||||||
\(935\) | 15.0318 | − | 15.1662i | 0.491593 | − | 0.495987i | ||||
\(936\) | 5.80270 | − | 9.12846i | 0.189667 | − | 0.298373i | ||||
\(937\) | 23.3846 | + | 23.3846i | 0.763942 | + | 0.763942i | 0.977033 | − | 0.213090i | \(-0.0683529\pi\) |
−0.213090 | + | 0.977033i | \(0.568353\pi\) | |||||||
\(938\) | 9.91351 | − | 9.91351i | 0.323687 | − | 0.323687i | ||||
\(939\) | −35.8507 | − | 2.20674i | −1.16994 | − | 0.0720143i | ||||
\(940\) | 6.22505 | − | 6.28070i | 0.203039 | − | 0.204854i | ||||
\(941\) | −32.6174 | −1.06330 | −0.531648 | − | 0.846965i | \(-0.678427\pi\) | ||||
−0.531648 | + | 0.846965i | \(0.678427\pi\) | |||||||
\(942\) | 5.11394 | − | 4.52088i | 0.166621 | − | 0.147298i | ||||
\(943\) | −5.95247 | − | 5.95247i | −0.193839 | − | 0.193839i | ||||
\(944\) | 0.692553i | 0.0225407i | ||||||||
\(945\) | −3.03442 | + | 16.6775i | −0.0987098 | + | 0.542518i | ||||
\(946\) | −45.4773 | −1.47859 | ||||||||
\(947\) | 17.6795 | + | 17.6795i | 0.574506 | + | 0.574506i | 0.933384 | − | 0.358879i | \(-0.116841\pi\) |
−0.358879 | + | 0.933384i | \(0.616841\pi\) | |||||||
\(948\) | −6.99778 | − | 7.91576i | −0.227277 | − | 0.257092i | ||||
\(949\) | −17.5479 | + | 36.9586i | −0.569628 | + | 1.19973i | ||||
\(950\) | 22.7443 | + | 22.3430i | 0.737922 | + | 0.724903i | ||||
\(951\) | −1.13573 | + | 18.4510i | −0.0368285 | + | 0.598316i | ||||
\(952\) | −2.66104 | − | 2.66104i | −0.0862448 | − | 0.0862448i | ||||
\(953\) | 33.1565 | + | 33.1565i | 1.07404 | + | 1.07404i | 0.997030 | + | 0.0770143i | \(0.0245387\pi\) |
0.0770143 | + | 0.997030i | \(0.475461\pi\) | |||||||
\(954\) | 24.8611 | + | 3.07223i | 0.804908 | + | 0.0994670i | ||||
\(955\) | −0.154366 | − | 34.6897i | −0.00499516 | − | 1.12253i | ||||
\(956\) | 2.46770 | 0.0798112 | ||||||||
\(957\) | 2.10556 | + | 2.38177i | 0.0680630 | + | 0.0769916i | ||||
\(958\) | −8.32298 | + | 8.32298i | −0.268903 | + | 0.268903i | ||||
\(959\) | −19.6767 | −0.635395 | ||||||||
\(960\) | −2.89025 | + | 2.57807i | −0.0932824 | + | 0.0832069i | ||||
\(961\) | 22.6561 | 0.730843 | ||||||||
\(962\) | 3.55017 | + | 9.96909i | 0.114462 | + | 0.321416i | ||||
\(963\) | 27.7577 | + | 35.5854i | 0.894480 | + | 1.14672i | ||||
\(964\) | 21.2063 | 0.683009 | ||||||||
\(965\) | −13.0415 | − | 12.9259i | −0.419820 | − | 0.416100i | ||||
\(966\) | 0.788265 | − | 12.8061i | 0.0253620 | − | 0.412031i | ||||
\(967\) | −20.1304 | + | 20.1304i | −0.647349 | + | 0.647349i | −0.952351 | − | 0.305003i | \(-0.901343\pi\) |
0.305003 | + | 0.952351i | \(0.401343\pi\) | |||||||
\(968\) | −1.91327 | + | 1.91327i | −0.0614949 | + | 0.0614949i | ||||
\(969\) | 28.4352 | + | 1.75029i | 0.913471 | + | 0.0562275i | ||||
\(970\) | −22.0820 | + | 0.0982630i | −0.709012 | + | 0.00315504i | ||||
\(971\) | − | 32.3175i | − | 1.03712i | −0.855042 | − | 0.518559i | \(-0.826469\pi\) | ||
0.855042 | − | 0.518559i | \(-0.173531\pi\) | |||||||
\(972\) | 13.8411 | − | 7.17100i | 0.443954 | − | 0.230010i | ||||
\(973\) | 2.16326 | + | 2.16326i | 0.0693509 | + | 0.0693509i | ||||
\(974\) | 4.96646 | 0.159136 | ||||||||
\(975\) | −14.8565 | + | 27.4642i | −0.475788 | + | 0.879560i | ||||
\(976\) | 12.0684 | 0.386300 | ||||||||
\(977\) | 14.1829 | + | 14.1829i | 0.453752 | + | 0.453752i | 0.896598 | − | 0.442846i | \(-0.146031\pi\) |
−0.442846 | + | 0.896598i | \(0.646031\pi\) | |||||||
\(978\) | 25.4855 | − | 22.5300i | 0.814937 | − | 0.720429i | ||||
\(979\) | 9.87451i | 0.315591i | ||||||||
\(980\) | 10.8929 | − | 0.0484725i | 0.347962 | − | 0.00154840i | ||||
\(981\) | −4.78041 | + | 38.6841i | −0.152627 | + | 1.23509i | ||||
\(982\) | −23.2361 | + | 23.2361i | −0.741494 | + | 0.741494i | ||||
\(983\) | −12.7080 | + | 12.7080i | −0.405323 | + | 0.405323i | −0.880104 | − | 0.474781i | \(-0.842527\pi\) |
0.474781 | + | 0.880104i | \(0.342527\pi\) | |||||||
\(984\) | 2.86621 | + | 0.176426i | 0.0913715 | + | 0.00562426i | ||||
\(985\) | 17.9849 | + | 17.8256i | 0.573047 | + | 0.567970i | ||||
\(986\) | −1.27883 | −0.0407262 | ||||||||
\(987\) | −6.61887 | − | 7.48715i | −0.210681 | − | 0.238318i | ||||
\(988\) | −21.6586 | + | 7.71302i | −0.689053 | + | 0.245384i | ||||
\(989\) | 62.3714 | 1.98330 | ||||||||
\(990\) | −19.5137 | + | 15.3615i | −0.620187 | + | 0.488220i | ||||
\(991\) | −5.24927 | −0.166748 | −0.0833742 | − | 0.996518i | \(-0.526570\pi\) | ||||
−0.0833742 | + | 0.996518i | \(0.526570\pi\) | |||||||
\(992\) | −2.04253 | + | 2.04253i | −0.0648504 | + | 0.0648504i | ||||
\(993\) | 5.43692 | − | 4.80640i | 0.172535 | − | 0.152527i | ||||
\(994\) | −6.43705 | −0.204171 | ||||||||
\(995\) | 0.111401 | + | 25.0345i | 0.00353166 | + | 0.793648i | ||||
\(996\) | −0.729079 | + | 11.8446i | −0.0231018 | + | 0.375311i | ||||
\(997\) | −20.0308 | − | 20.0308i | −0.634381 | − | 0.634381i | 0.314782 | − | 0.949164i | \(-0.398068\pi\) |
−0.949164 | + | 0.314782i | \(0.898068\pi\) | |||||||
\(998\) | −12.7385 | − | 12.7385i | −0.403230 | − | 0.403230i | ||||
\(999\) | −2.79676 | + | 14.9922i | −0.0884857 | + | 0.474331i |
(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 | 390.2.s.c.77.11 | yes | 24 | |
3.2 | odd | 2 | 390.2.s.b.77.2 | ✓ | 24 | ||
5.3 | odd | 4 | 390.2.s.b.233.8 | yes | 24 | ||
13.12 | even | 2 | inner | 390.2.s.c.77.5 | yes | 24 | |
15.8 | even | 4 | inner | 390.2.s.c.233.5 | yes | 24 | |
39.38 | odd | 2 | 390.2.s.b.77.8 | yes | 24 | ||
65.38 | odd | 4 | 390.2.s.b.233.2 | yes | 24 | ||
195.38 | even | 4 | inner | 390.2.s.c.233.11 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.s.b.77.2 | ✓ | 24 | 3.2 | odd | 2 | ||
390.2.s.b.77.8 | yes | 24 | 39.38 | odd | 2 | ||
390.2.s.b.233.2 | yes | 24 | 65.38 | odd | 4 | ||
390.2.s.b.233.8 | yes | 24 | 5.3 | odd | 4 | ||
390.2.s.c.77.5 | yes | 24 | 13.12 | even | 2 | inner | |
390.2.s.c.77.11 | yes | 24 | 1.1 | even | 1 | trivial | |
390.2.s.c.233.5 | yes | 24 | 15.8 | even | 4 | inner | |
390.2.s.c.233.11 | yes | 24 | 195.38 | even | 4 | inner |