Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 471.2 | ||
Root | \(1.16700 + 2.02131i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.471 |
Dual form | 637.2.h.l.165.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90556 | −1.34743 | −0.673717 | − | 0.738989i | \(-0.735303\pi\) | ||||
−0.673717 | + | 0.738989i | \(0.735303\pi\) | |||||||
\(3\) | 0.214224 | − | 0.371047i | 0.123682 | − | 0.214224i | −0.797535 | − | 0.603273i | \(-0.793863\pi\) |
0.921217 | + | 0.389049i | \(0.127196\pi\) | |||||||
\(4\) | 1.63116 | 0.815580 | ||||||||
\(5\) | −0.736565 | + | 1.27577i | −0.329402 | + | 0.570541i | −0.982393 | − | 0.186825i | \(-0.940180\pi\) |
0.652991 | + | 0.757365i | \(0.273514\pi\) | |||||||
\(6\) | −0.408216 | + | 0.707051i | −0.166654 | + | 0.288653i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.702849 | 0.248495 | ||||||||
\(9\) | 1.40822 | + | 2.43910i | 0.469405 | + | 0.813034i | ||||
\(10\) | 1.40357 | − | 2.43105i | 0.443847 | − | 0.768766i | ||||
\(11\) | 2.19681 | − | 3.80498i | 0.662362 | − | 1.14725i | −0.317631 | − | 0.948214i | \(-0.602887\pi\) |
0.979993 | − | 0.199031i | \(-0.0637794\pi\) | |||||||
\(12\) | 0.349433 | − | 0.605236i | 0.100873 | − | 0.174717i | ||||
\(13\) | −2.69752 | − | 2.39236i | −0.748158 | − | 0.663520i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.315580 | + | 0.546600i | 0.0814823 | + | 0.141131i | ||||
\(16\) | −4.60164 | −1.15041 | ||||||||
\(17\) | 1.20271 | 0.291700 | 0.145850 | − | 0.989307i | \(-0.453408\pi\) | ||||
0.145850 | + | 0.989307i | \(0.453408\pi\) | |||||||
\(18\) | −2.68344 | − | 4.64786i | −0.632493 | − | 1.09551i | ||||
\(19\) | 1.62105 | + | 2.80773i | 0.371893 | + | 0.644138i | 0.989857 | − | 0.142068i | \(-0.0453753\pi\) |
−0.617963 | + | 0.786207i | \(0.712042\pi\) | |||||||
\(20\) | −1.20145 | + | 2.08098i | −0.268653 | + | 0.465321i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.18615 | + | 7.25062i | −0.892490 | + | 1.54584i | ||||
\(23\) | −4.43710 | −0.925200 | −0.462600 | − | 0.886567i | \(-0.653083\pi\) | ||||
−0.462600 | + | 0.886567i | \(0.653083\pi\) | |||||||
\(24\) | 0.150567 | − | 0.260790i | 0.0307343 | − | 0.0532334i | ||||
\(25\) | 1.41494 | + | 2.45075i | 0.282989 | + | 0.490151i | ||||
\(26\) | 5.14029 | + | 4.55878i | 1.00809 | + | 0.894050i | ||||
\(27\) | 2.49204 | 0.479593 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0837807 | − | 0.145112i | −0.0155577 | − | 0.0269467i | 0.858142 | − | 0.513413i | \(-0.171619\pi\) |
−0.873699 | + | 0.486466i | \(0.838286\pi\) | |||||||
\(30\) | −0.601356 | − | 1.04158i | −0.109792 | − | 0.190165i | ||||
\(31\) | 2.62272 | + | 4.54268i | 0.471054 | + | 0.815889i | 0.999452 | − | 0.0331076i | \(-0.0105404\pi\) |
−0.528398 | + | 0.848997i | \(0.677207\pi\) | |||||||
\(32\) | 7.36300 | 1.30161 | ||||||||
\(33\) | −0.941217 | − | 1.63024i | −0.163845 | − | 0.283788i | ||||
\(34\) | −2.29184 | −0.393047 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.29702 | + | 3.97856i | 0.382837 | + | 0.663094i | ||||
\(37\) | 7.05055 | 1.15910 | 0.579552 | − | 0.814936i | \(-0.303228\pi\) | ||||
0.579552 | + | 0.814936i | \(0.303228\pi\) | |||||||
\(38\) | −3.08900 | − | 5.35031i | −0.501102 | − | 0.867934i | ||||
\(39\) | −1.46555 | + | 0.488407i | −0.234676 | + | 0.0782077i | ||||
\(40\) | −0.517694 | + | 0.896672i | −0.0818546 | + | 0.141776i | ||||
\(41\) | 2.58195 | + | 4.47206i | 0.403233 | + | 0.698419i | 0.994114 | − | 0.108339i | \(-0.0345533\pi\) |
−0.590881 | + | 0.806758i | \(0.701220\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0113752 | + | 0.0197024i | −0.00173470 | + | 0.00300459i | −0.866891 | − | 0.498497i | \(-0.833886\pi\) |
0.865157 | + | 0.501502i | \(0.167219\pi\) | |||||||
\(44\) | 3.58334 | − | 6.20653i | 0.540209 | − | 0.935670i | ||||
\(45\) | −4.14897 | −0.618492 | ||||||||
\(46\) | 8.45516 | 1.24665 | ||||||||
\(47\) | 5.84178 | − | 10.1183i | 0.852111 | − | 1.47590i | −0.0271891 | − | 0.999630i | \(-0.508656\pi\) |
0.879300 | − | 0.476269i | \(-0.158011\pi\) | |||||||
\(48\) | −0.985780 | + | 1.70742i | −0.142285 | + | 0.246445i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.69626 | − | 4.67006i | −0.381309 | − | 0.660446i | ||||
\(51\) | 0.257649 | − | 0.446262i | 0.0360781 | − | 0.0624892i | ||||
\(52\) | −4.40009 | − | 3.90231i | −0.610183 | − | 0.541154i | ||||
\(53\) | 0.0708929 | + | 0.122790i | 0.00973788 | + | 0.0168665i | 0.870853 | − | 0.491543i | \(-0.163567\pi\) |
−0.861115 | + | 0.508410i | \(0.830234\pi\) | |||||||
\(54\) | −4.74873 | −0.646220 | ||||||||
\(55\) | 3.23618 | + | 5.60523i | 0.436367 | + | 0.755809i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.38907 | 0.183986 | ||||||||
\(58\) | 0.159649 | + | 0.276520i | 0.0209630 | + | 0.0363089i | ||||
\(59\) | 5.34354 | 0.695670 | 0.347835 | − | 0.937556i | \(-0.386917\pi\) | ||||
0.347835 | + | 0.937556i | \(0.386917\pi\) | |||||||
\(60\) | 0.514760 | + | 0.891591i | 0.0664553 | + | 0.115104i | ||||
\(61\) | 5.77287 | + | 9.99891i | 0.739141 | + | 1.28023i | 0.952883 | + | 0.303339i | \(0.0981016\pi\) |
−0.213742 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(62\) | −4.99774 | − | 8.65635i | −0.634714 | − | 1.09936i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.82736 | −0.603420 | ||||||||
\(65\) | 5.03899 | − | 1.67929i | 0.625010 | − | 0.208290i | ||||
\(66\) | 1.79355 | + | 3.10651i | 0.220770 | + | 0.382385i | ||||
\(67\) | −2.06773 | + | 3.58141i | −0.252613 | + | 0.437539i | −0.964245 | − | 0.265014i | \(-0.914623\pi\) |
0.711631 | + | 0.702553i | \(0.247957\pi\) | |||||||
\(68\) | 1.96181 | 0.237905 | ||||||||
\(69\) | −0.950533 | + | 1.64637i | −0.114431 | + | 0.198200i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.98486 | − | 8.63403i | 0.591594 | − | 1.02467i | −0.402424 | − | 0.915453i | \(-0.631832\pi\) |
0.994018 | − | 0.109217i | \(-0.0348344\pi\) | |||||||
\(72\) | 0.989763 | + | 1.71432i | 0.116645 | + | 0.202035i | ||||
\(73\) | 7.62080 | + | 13.1996i | 0.891947 | + | 1.54490i | 0.837539 | + | 0.546378i | \(0.183994\pi\) |
0.0544080 | + | 0.998519i | \(0.482673\pi\) | |||||||
\(74\) | −13.4352 | −1.56182 | ||||||||
\(75\) | 1.21246 | 0.140003 | ||||||||
\(76\) | 2.64418 | + | 4.57986i | 0.303309 | + | 0.525346i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.79269 | − | 0.930689i | 0.316210 | − | 0.105380i | ||||
\(79\) | −0.387251 | + | 0.670738i | −0.0435691 | + | 0.0754639i | −0.886988 | − | 0.461793i | \(-0.847206\pi\) |
0.843418 | + | 0.537257i | \(0.180540\pi\) | |||||||
\(80\) | 3.38941 | − | 5.87062i | 0.378947 | − | 0.656356i | ||||
\(81\) | −3.69080 | + | 6.39265i | −0.410088 | + | 0.710294i | ||||
\(82\) | −4.92006 | − | 8.52179i | −0.543329 | − | 0.941074i | ||||
\(83\) | 16.0186 | 1.75827 | 0.879136 | − | 0.476571i | \(-0.158121\pi\) | ||||
0.879136 | + | 0.476571i | \(0.158121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.885875 | + | 1.53438i | −0.0960866 | + | 0.166427i | ||||
\(86\) | 0.0216761 | − | 0.0375441i | 0.00233740 | − | 0.00404849i | ||||
\(87\) | −0.0717913 | −0.00769683 | ||||||||
\(88\) | 1.54402 | − | 2.67433i | 0.164593 | − | 0.285084i | ||||
\(89\) | −6.55760 | −0.695104 | −0.347552 | − | 0.937661i | \(-0.612987\pi\) | ||||
−0.347552 | + | 0.937661i | \(0.612987\pi\) | |||||||
\(90\) | 7.90611 | 0.833378 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.23762 | −0.754574 | ||||||||
\(93\) | 2.24739 | 0.233044 | ||||||||
\(94\) | −11.1319 | + | 19.2809i | −1.14816 | + | 1.98868i | ||||
\(95\) | −4.77602 | −0.490010 | ||||||||
\(96\) | 1.57733 | − | 2.73202i | 0.160986 | − | 0.278835i | ||||
\(97\) | 1.74583 | − | 3.02387i | 0.177262 | − | 0.307027i | −0.763680 | − | 0.645595i | \(-0.776609\pi\) |
0.940942 | + | 0.338568i | \(0.109943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.3743 | 1.24367 | ||||||||
\(100\) | 2.30800 | + | 3.99757i | 0.230800 | + | 0.399757i | ||||
\(101\) | 1.28890 | − | 2.23244i | 0.128250 | − | 0.222136i | −0.794749 | − | 0.606939i | \(-0.792397\pi\) |
0.922999 | + | 0.384803i | \(0.125731\pi\) | |||||||
\(102\) | −0.490966 | + | 0.850379i | −0.0486129 | + | 0.0842000i | ||||
\(103\) | −8.43173 | + | 14.6042i | −0.830803 | + | 1.43899i | 0.0665997 | + | 0.997780i | \(0.478785\pi\) |
−0.897402 | + | 0.441213i | \(0.854548\pi\) | |||||||
\(104\) | −1.89595 | − | 1.68146i | −0.185913 | − | 0.164881i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.135091 | − | 0.233984i | −0.0131212 | − | 0.0227265i | ||||
\(107\) | 8.68265 | 0.839383 | 0.419692 | − | 0.907667i | \(-0.362138\pi\) | ||||
0.419692 | + | 0.907667i | \(0.362138\pi\) | |||||||
\(108\) | 4.06491 | 0.391146 | ||||||||
\(109\) | 6.02026 | + | 10.4274i | 0.576637 | + | 0.998764i | 0.995862 | + | 0.0908816i | \(0.0289685\pi\) |
−0.419225 | + | 0.907882i | \(0.637698\pi\) | |||||||
\(110\) | −6.16674 | − | 10.6811i | −0.587976 | − | 1.01840i | ||||
\(111\) | 1.51040 | − | 2.61608i | 0.143360 | − | 0.248307i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.68616 | + | 8.11667i | −0.440837 | + | 0.763552i | −0.997752 | − | 0.0670176i | \(-0.978652\pi\) |
0.556915 | + | 0.830570i | \(0.311985\pi\) | |||||||
\(114\) | −2.64695 | −0.247910 | ||||||||
\(115\) | 3.26821 | − | 5.66071i | 0.304763 | − | 0.527864i | ||||
\(116\) | −0.136660 | − | 0.236701i | −0.0126885 | − | 0.0219772i | ||||
\(117\) | 2.03651 | − | 9.94849i | 0.188275 | − | 0.919738i | ||||
\(118\) | −10.1824 | −0.937369 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.221805 | + | 0.384177i | 0.0202479 | + | 0.0350704i | ||||
\(121\) | −4.15192 | − | 7.19134i | −0.377448 | − | 0.653758i | ||||
\(122\) | −11.0006 | − | 19.0535i | −0.995944 | − | 1.72503i | ||||
\(123\) | 2.21246 | 0.199491 | ||||||||
\(124\) | 4.27807 | + | 7.40983i | 0.384182 | + | 0.665423i | ||||
\(125\) | −11.5344 | −1.03167 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.94269 | − | 13.7571i | −0.704800 | − | 1.22075i | −0.966764 | − | 0.255672i | \(-0.917703\pi\) |
0.261964 | − | 0.965078i | \(-0.415630\pi\) | |||||||
\(128\) | −5.52717 | −0.488537 | ||||||||
\(129\) | 0.00487367 | + | 0.00844145i | 0.000429103 | + | 0.000743228i | ||||
\(130\) | −9.60210 | + | 3.19998i | −0.842160 | + | 0.280657i | ||||
\(131\) | 0.928725 | − | 1.60860i | 0.0811430 | − | 0.140544i | −0.822598 | − | 0.568623i | \(-0.807476\pi\) |
0.903741 | + | 0.428079i | \(0.140810\pi\) | |||||||
\(132\) | −1.53527 | − | 2.65917i | −0.133628 | − | 0.231451i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.94018 | − | 6.82459i | 0.340380 | − | 0.589555i | ||||
\(135\) | −1.83555 | + | 3.17926i | −0.157979 | + | 0.273627i | ||||
\(136\) | 0.845324 | 0.0724859 | ||||||||
\(137\) | −12.8002 | −1.09360 | −0.546798 | − | 0.837264i | \(-0.684153\pi\) | ||||
−0.546798 | + | 0.837264i | \(0.684153\pi\) | |||||||
\(138\) | 1.81130 | − | 3.13726i | 0.154188 | − | 0.267061i | ||||
\(139\) | −0.169365 | + | 0.293348i | −0.0143653 | + | 0.0248815i | −0.873119 | − | 0.487508i | \(-0.837906\pi\) |
0.858753 | + | 0.512389i | \(0.171239\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.50290 | − | 4.33514i | −0.210782 | − | 0.365085i | ||||
\(142\) | −9.49894 | + | 16.4527i | −0.797134 | + | 1.38068i | ||||
\(143\) | −15.0288 | + | 5.00848i | −1.25677 | + | 0.418830i | ||||
\(144\) | −6.48010 | − | 11.2239i | −0.540009 | − | 0.935322i | ||||
\(145\) | 0.246840 | 0.0204989 | ||||||||
\(146\) | −14.5219 | − | 25.1526i | −1.20184 | − | 2.08165i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.5006 | 0.945341 | ||||||||
\(149\) | −1.96158 | − | 3.39756i | −0.160699 | − | 0.278339i | 0.774421 | − | 0.632671i | \(-0.218041\pi\) |
−0.935120 | + | 0.354332i | \(0.884708\pi\) | |||||||
\(150\) | −2.31041 | −0.188644 | ||||||||
\(151\) | 1.05939 | + | 1.83492i | 0.0862122 | + | 0.149324i | 0.905907 | − | 0.423476i | \(-0.139190\pi\) |
−0.819695 | + | 0.572800i | \(0.805857\pi\) | |||||||
\(152\) | 1.13935 | + | 1.97341i | 0.0924135 | + | 0.160065i | ||||
\(153\) | 1.69368 | + | 2.93354i | 0.136926 | + | 0.237162i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.72721 | −0.620664 | ||||||||
\(156\) | −2.39054 | + | 0.796669i | −0.191397 | + | 0.0637846i | ||||
\(157\) | −11.0564 | − | 19.1502i | −0.882397 | − | 1.52836i | −0.848668 | − | 0.528925i | \(-0.822595\pi\) |
−0.0337285 | − | 0.999431i | \(-0.510738\pi\) | |||||||
\(158\) | 0.737929 | − | 1.27813i | 0.0587065 | − | 0.101683i | ||||
\(159\) | 0.0607478 | 0.00481761 | ||||||||
\(160\) | −5.42333 | + | 9.39348i | −0.428752 | + | 0.742620i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.03303 | − | 12.1816i | 0.552567 | − | 0.957074i | ||||
\(163\) | −1.92607 | − | 3.33605i | −0.150861 | − | 0.261299i | 0.780683 | − | 0.624927i | \(-0.214871\pi\) |
−0.931544 | + | 0.363628i | \(0.881538\pi\) | |||||||
\(164\) | 4.21157 | + | 7.29465i | 0.328868 | + | 0.569616i | ||||
\(165\) | 2.77307 | 0.215883 | ||||||||
\(166\) | −30.5244 | −2.36916 | ||||||||
\(167\) | 1.06947 | + | 1.85238i | 0.0827582 | + | 0.143341i | 0.904434 | − | 0.426614i | \(-0.140294\pi\) |
−0.821676 | + | 0.569956i | \(0.806960\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.55326 | + | 12.9069i | 0.119482 | + | 0.992836i | ||||
\(170\) | 1.68809 | − | 2.92385i | 0.129470 | − | 0.224249i | ||||
\(171\) | −4.56557 | + | 7.90779i | −0.349138 | + | 0.604724i | ||||
\(172\) | −0.0185547 | + | 0.0321378i | −0.00141479 | + | 0.00245048i | ||||
\(173\) | −8.30664 | − | 14.3875i | −0.631542 | − | 1.09386i | −0.987237 | − | 0.159260i | \(-0.949089\pi\) |
0.355695 | − | 0.934602i | \(-0.384244\pi\) | |||||||
\(174\) | 0.136803 | 0.0103710 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.1089 | + | 17.5091i | −0.761988 | + | 1.31980i | ||||
\(177\) | 1.14471 | − | 1.98270i | 0.0860419 | − | 0.149029i | ||||
\(178\) | 12.4959 | 0.936607 | ||||||||
\(179\) | 0.269748 | − | 0.467217i | 0.0201619 | − | 0.0349214i | −0.855768 | − | 0.517359i | \(-0.826915\pi\) |
0.875930 | + | 0.482438i | \(0.160248\pi\) | |||||||
\(180\) | −6.76763 | −0.504430 | ||||||||
\(181\) | −2.77164 | −0.206014 | −0.103007 | − | 0.994681i | \(-0.532846\pi\) | ||||
−0.103007 | + | 0.994681i | \(0.532846\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.94675 | 0.365674 | ||||||||
\(184\) | −3.11861 | −0.229907 | ||||||||
\(185\) | −5.19319 | + | 8.99486i | −0.381811 | + | 0.661316i | ||||
\(186\) | −4.28254 | −0.314011 | ||||||||
\(187\) | 2.64213 | − | 4.57629i | 0.193211 | − | 0.334652i | ||||
\(188\) | 9.52887 | − | 16.5045i | 0.694964 | − | 1.20371i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.10100 | 0.660256 | ||||||||
\(191\) | 10.1204 | + | 17.5290i | 0.732284 | + | 1.26835i | 0.955905 | + | 0.293677i | \(0.0948790\pi\) |
−0.223621 | + | 0.974676i | \(0.571788\pi\) | |||||||
\(192\) | −1.03414 | + | 1.79118i | −0.0746323 | + | 0.129267i | ||||
\(193\) | 8.18856 | − | 14.1830i | 0.589425 | − | 1.02091i | −0.404882 | − | 0.914369i | \(-0.632688\pi\) |
0.994308 | − | 0.106546i | \(-0.0339791\pi\) | |||||||
\(194\) | −3.32678 | + | 5.76216i | −0.238849 | + | 0.413699i | ||||
\(195\) | 0.456378 | − | 2.22944i | 0.0326819 | − | 0.159654i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.86676 | − | 17.0897i | −0.702977 | − | 1.21759i | −0.967417 | − | 0.253190i | \(-0.918520\pi\) |
0.264439 | − | 0.964402i | \(-0.414813\pi\) | |||||||
\(198\) | −23.5800 | −1.67576 | ||||||||
\(199\) | 14.1175 | 1.00076 | 0.500380 | − | 0.865806i | \(-0.333194\pi\) | ||||
0.500380 | + | 0.865806i | \(0.333194\pi\) | |||||||
\(200\) | 0.994491 | + | 1.72251i | 0.0703212 | + | 0.121800i | ||||
\(201\) | 0.885913 | + | 1.53445i | 0.0624875 | + | 0.108232i | ||||
\(202\) | −2.45607 | + | 4.25404i | −0.172809 | + | 0.299313i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.420267 | − | 0.727924i | 0.0294246 | − | 0.0509649i | ||||
\(205\) | −7.60709 | −0.531302 | ||||||||
\(206\) | 16.0672 | − | 27.8291i | 1.11945 | − | 1.93895i | ||||
\(207\) | −6.24840 | − | 10.8225i | −0.434294 | − | 0.752219i | ||||
\(208\) | 12.4130 | + | 11.0088i | 0.860688 | + | 0.763320i | ||||
\(209\) | 14.2445 | 0.985313 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.31317 | + | 4.00652i | 0.159245 | + | 0.275820i | 0.934597 | − | 0.355709i | \(-0.115761\pi\) |
−0.775352 | + | 0.631530i | \(0.782427\pi\) | |||||||
\(212\) | 0.115638 | + | 0.200290i | 0.00794202 | + | 0.0137560i | ||||
\(213\) | −2.13575 | − | 3.69923i | −0.146339 | − | 0.253467i | ||||
\(214\) | −16.5453 | −1.13101 | ||||||||
\(215\) | −0.0167571 | − | 0.0290242i | −0.00114283 | − | 0.00197943i | ||||
\(216\) | 1.75152 | 0.119176 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.4720 | − | 19.8700i | −0.776980 | − | 1.34577i | ||||
\(219\) | 6.53022 | 0.441272 | ||||||||
\(220\) | 5.27873 | + | 9.14303i | 0.355892 | + | 0.616423i | ||||
\(221\) | −3.24434 | − | 2.87731i | −0.218238 | − | 0.193549i | ||||
\(222\) | −2.87815 | + | 4.98510i | −0.193169 | + | 0.334578i | ||||
\(223\) | −10.6761 | − | 18.4916i | −0.714926 | − | 1.23829i | −0.962988 | − | 0.269545i | \(-0.913127\pi\) |
0.248061 | − | 0.968744i | \(-0.420207\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.98509 | + | 6.90239i | −0.265673 | + | 0.460159i | ||||
\(226\) | 8.92976 | − | 15.4668i | 0.593999 | − | 1.02884i | ||||
\(227\) | 10.4490 | 0.693526 | 0.346763 | − | 0.937953i | \(-0.387281\pi\) | ||||
0.346763 | + | 0.937953i | \(0.387281\pi\) | |||||||
\(228\) | 2.26579 | 0.150056 | ||||||||
\(229\) | 7.22901 | − | 12.5210i | 0.477706 | − | 0.827412i | −0.521967 | − | 0.852966i | \(-0.674802\pi\) |
0.999673 | + | 0.0255538i | \(0.00813493\pi\) | |||||||
\(230\) | −6.22778 | + | 10.7868i | −0.410648 | + | 0.711262i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.0588852 | − | 0.101992i | −0.00386600 | − | 0.00669611i | ||||
\(233\) | 4.64413 | − | 8.04388i | 0.304247 | − | 0.526972i | −0.672846 | − | 0.739783i | \(-0.734928\pi\) |
0.977093 | + | 0.212811i | \(0.0682617\pi\) | |||||||
\(234\) | −3.88068 | + | 18.9574i | −0.253688 | + | 1.23929i | ||||
\(235\) | 8.60570 | + | 14.9055i | 0.561374 | + | 0.972328i | ||||
\(236\) | 8.71616 | 0.567374 | ||||||||
\(237\) | 0.165917 | + | 0.287376i | 0.0107774 | + | 0.0186671i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.6332 | 1.26997 | 0.634983 | − | 0.772526i | \(-0.281007\pi\) | ||||
0.634983 | + | 0.772526i | \(0.281007\pi\) | |||||||
\(240\) | −1.45218 | − | 2.51525i | −0.0937380 | − | 0.162359i | ||||
\(241\) | −7.31105 | −0.470946 | −0.235473 | − | 0.971881i | \(-0.575664\pi\) | ||||
−0.235473 | + | 0.971881i | \(0.575664\pi\) | |||||||
\(242\) | 7.91174 | + | 13.7035i | 0.508586 | + | 0.880897i | ||||
\(243\) | 5.31937 | + | 9.21341i | 0.341238 | + | 0.591041i | ||||
\(244\) | 9.41648 | + | 16.3098i | 0.602828 | + | 1.04413i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.21597 | −0.268801 | ||||||||
\(247\) | 2.34429 | − | 11.4520i | 0.149164 | − | 0.728676i | ||||
\(248\) | 1.84337 | + | 3.19282i | 0.117054 | + | 0.202744i | ||||
\(249\) | 3.43157 | − | 5.94365i | 0.217467 | − | 0.376664i | ||||
\(250\) | 21.9796 | 1.39011 | ||||||||
\(251\) | −5.93191 | + | 10.2744i | −0.374419 | + | 0.648512i | −0.990240 | − | 0.139374i | \(-0.955491\pi\) |
0.615821 | + | 0.787886i | \(0.288824\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.74746 | + | 16.8831i | −0.612817 | + | 1.06143i | ||||
\(254\) | 15.1353 | + | 26.2151i | 0.949672 | + | 1.64488i | ||||
\(255\) | 0.379551 | + | 0.657402i | 0.0237684 | + | 0.0411681i | ||||
\(256\) | 20.1871 | 1.26169 | ||||||||
\(257\) | 15.1722 | 0.946413 | 0.473206 | − | 0.880952i | \(-0.343096\pi\) | ||||
0.473206 | + | 0.880952i | \(0.343096\pi\) | |||||||
\(258\) | −0.00928708 | − | 0.0160857i | −0.000578188 | − | 0.00100145i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.21940 | − | 2.73919i | 0.509745 | − | 0.169877i | ||||
\(261\) | 0.235963 | − | 0.408699i | 0.0146057 | − | 0.0252979i | ||||
\(262\) | −1.76974 | + | 3.06528i | −0.109335 | + | 0.189374i | ||||
\(263\) | −8.59820 | + | 14.8925i | −0.530187 | + | 0.918312i | 0.469192 | + | 0.883096i | \(0.344545\pi\) |
−0.999380 | + | 0.0352156i | \(0.988788\pi\) | |||||||
\(264\) | −0.661533 | − | 1.14581i | −0.0407145 | − | 0.0705196i | ||||
\(265\) | −0.208869 | −0.0128307 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.40479 | + | 2.43317i | −0.0859719 | + | 0.148908i | ||||
\(268\) | −3.37279 | + | 5.84185i | −0.206026 | + | 0.356848i | ||||
\(269\) | −18.9220 | −1.15370 | −0.576849 | − | 0.816851i | \(-0.695718\pi\) | ||||
−0.576849 | + | 0.816851i | \(0.695718\pi\) | |||||||
\(270\) | 3.49774 | − | 6.05827i | 0.212866 | − | 0.368695i | ||||
\(271\) | −32.1334 | −1.95196 | −0.975982 | − | 0.217853i | \(-0.930095\pi\) | ||||
−0.975982 | + | 0.217853i | \(0.930095\pi\) | |||||||
\(272\) | −5.53444 | −0.335575 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 24.3916 | 1.47355 | ||||||||
\(275\) | 12.4334 | 0.749764 | ||||||||
\(276\) | −1.55047 | + | 2.68549i | −0.0933273 | + | 0.161648i | ||||
\(277\) | 18.4054 | 1.10587 | 0.552936 | − | 0.833224i | \(-0.313507\pi\) | ||||
0.552936 | + | 0.833224i | \(0.313507\pi\) | |||||||
\(278\) | 0.322734 | − | 0.558992i | 0.0193563 | − | 0.0335261i | ||||
\(279\) | −7.38671 | + | 12.7942i | −0.442231 | + | 0.765966i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.2252 | −0.848603 | −0.424302 | − | 0.905521i | \(-0.639480\pi\) | ||||
−0.424302 | + | 0.905521i | \(0.639480\pi\) | |||||||
\(282\) | 4.76942 | + | 8.26087i | 0.284015 | + | 0.491928i | ||||
\(283\) | −5.71446 | + | 9.89773i | −0.339689 | + | 0.588359i | −0.984374 | − | 0.176089i | \(-0.943655\pi\) |
0.644685 | + | 0.764448i | \(0.276989\pi\) | |||||||
\(284\) | 8.13109 | − | 14.0835i | 0.482492 | − | 0.835700i | ||||
\(285\) | −1.02314 | + | 1.77213i | −0.0606055 | + | 0.104972i | ||||
\(286\) | 28.6383 | − | 9.54396i | 1.69342 | − | 0.564346i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 10.3687 | + | 17.9591i | 0.610981 | + | 1.05825i | ||||
\(289\) | −15.5535 | −0.914911 | ||||||||
\(290\) | −0.470368 | −0.0276210 | ||||||||
\(291\) | −0.747997 | − | 1.29557i | −0.0438483 | − | 0.0759476i | ||||
\(292\) | 12.4307 | + | 21.5307i | 0.727453 | + | 1.25999i | ||||
\(293\) | −6.60231 | + | 11.4355i | −0.385711 | + | 0.668071i | −0.991868 | − | 0.127274i | \(-0.959377\pi\) |
0.606156 | + | 0.795345i | \(0.292711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.93586 | + | 6.81712i | −0.229155 | + | 0.396908i | ||||
\(296\) | 4.95547 | 0.288031 | ||||||||
\(297\) | 5.47452 | − | 9.48215i | 0.317664 | − | 0.550210i | ||||
\(298\) | 3.73791 | + | 6.47425i | 0.216531 | + | 0.375043i | ||||
\(299\) | 11.9692 | + | 10.6151i | 0.692196 | + | 0.613889i | ||||
\(300\) | 1.97771 | 0.114183 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.01874 | − | 3.49656i | −0.116165 | − | 0.201204i | ||||
\(303\) | −0.552225 | − | 0.956482i | −0.0317245 | − | 0.0549484i | ||||
\(304\) | −7.45947 | − | 12.9202i | −0.427830 | − | 0.741023i | ||||
\(305\) | −17.0084 | −0.973898 | ||||||||
\(306\) | −3.22740 | − | 5.59003i | −0.184498 | − | 0.319561i | ||||
\(307\) | 6.65903 | 0.380051 | 0.190026 | − | 0.981779i | \(-0.439143\pi\) | ||||
0.190026 | + | 0.981779i | \(0.439143\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.61255 | + | 6.25713i | 0.205511 | + | 0.355955i | ||||
\(310\) | 14.7247 | 0.836304 | ||||||||
\(311\) | −1.02298 | − | 1.77186i | −0.0580081 | − | 0.100473i | 0.835563 | − | 0.549395i | \(-0.185142\pi\) |
−0.893571 | + | 0.448922i | \(0.851808\pi\) | |||||||
\(312\) | −1.03006 | + | 0.343276i | −0.0583156 | + | 0.0194342i | ||||
\(313\) | 4.70883 | − | 8.15594i | 0.266159 | − | 0.461001i | −0.701708 | − | 0.712465i | \(-0.747579\pi\) |
0.967867 | + | 0.251464i | \(0.0809120\pi\) | |||||||
\(314\) | 21.0686 | + | 36.4919i | 1.18897 | + | 2.05936i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.631667 | + | 1.09408i | −0.0355341 | + | 0.0615468i | ||||
\(317\) | 16.6856 | − | 28.9004i | 0.937159 | − | 1.62321i | 0.166421 | − | 0.986055i | \(-0.446779\pi\) |
0.770738 | − | 0.637153i | \(-0.219888\pi\) | |||||||
\(318\) | −0.115758 | −0.00649141 | ||||||||
\(319\) | −0.736200 | −0.0412193 | ||||||||
\(320\) | 3.55567 | − | 6.15860i | 0.198768 | − | 0.344276i | ||||
\(321\) | 1.86003 | − | 3.22167i | 0.103817 | − | 0.179816i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.94965 | + | 3.37689i | 0.108481 | + | 0.187895i | ||||
\(324\) | −6.02027 | + | 10.4274i | −0.334460 | + | 0.579301i | ||||
\(325\) | 2.04624 | − | 9.99602i | 0.113505 | − | 0.554479i | ||||
\(326\) | 3.67024 | + | 6.35704i | 0.203276 | + | 0.352084i | ||||
\(327\) | 5.15873 | 0.285279 | ||||||||
\(328\) | 1.81472 | + | 3.14318i | 0.100201 | + | 0.173553i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −5.28425 | −0.290888 | ||||||||
\(331\) | −9.53298 | − | 16.5116i | −0.523980 | − | 0.907560i | −0.999610 | − | 0.0279144i | \(-0.991113\pi\) |
0.475631 | − | 0.879645i | \(-0.342220\pi\) | |||||||
\(332\) | 26.1289 | 1.43401 | ||||||||
\(333\) | 9.92870 | + | 17.1970i | 0.544089 | + | 0.942390i | ||||
\(334\) | −2.03794 | − | 3.52982i | −0.111511 | − | 0.193143i | ||||
\(335\) | −3.04603 | − | 5.27588i | −0.166423 | − | 0.288252i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.2849 | −1.70420 | −0.852098 | − | 0.523382i | \(-0.824670\pi\) | ||||
−0.852098 | + | 0.523382i | \(0.824670\pi\) | |||||||
\(338\) | −2.95983 | − | 24.5948i | −0.160994 | − | 1.33778i | ||||
\(339\) | 2.00777 | + | 3.47757i | 0.109047 | + | 0.188876i | ||||
\(340\) | −1.44500 | + | 2.50282i | −0.0783663 | + | 0.135734i | ||||
\(341\) | 23.0464 | 1.24803 | ||||||||
\(342\) | 8.69996 | − | 15.0688i | 0.470440 | − | 0.814826i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.00799504 | + | 0.0138478i | −0.000431064 | + | 0.000746624i | ||||
\(345\) | −1.40026 | − | 2.42532i | −0.0753874 | − | 0.130575i | ||||
\(346\) | 15.8288 | + | 27.4163i | 0.850961 | + | 1.47391i | ||||
\(347\) | 11.6752 | 0.626757 | 0.313378 | − | 0.949628i | \(-0.398539\pi\) | ||||
0.313378 | + | 0.949628i | \(0.398539\pi\) | |||||||
\(348\) | −0.117103 | −0.00627738 | ||||||||
\(349\) | 11.9952 | + | 20.7763i | 0.642089 | + | 1.11213i | 0.984966 | + | 0.172750i | \(0.0552652\pi\) |
−0.342877 | + | 0.939380i | \(0.611401\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.72233 | − | 5.96184i | −0.358811 | − | 0.318219i | ||||
\(352\) | 16.1751 | − | 28.0161i | 0.862135 | − | 1.49326i | ||||
\(353\) | 6.39668 | − | 11.0794i | 0.340461 | − | 0.589696i | −0.644057 | − | 0.764977i | \(-0.722750\pi\) |
0.984518 | + | 0.175282i | \(0.0560836\pi\) | |||||||
\(354\) | −2.18132 | + | 3.77816i | −0.115936 | + | 0.200807i | ||||
\(355\) | 7.34334 | + | 12.7190i | 0.389744 | + | 0.675057i | ||||
\(356\) | −10.6965 | −0.566912 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.514021 | + | 0.890310i | −0.0271668 | + | 0.0470544i | ||||
\(359\) | −6.16986 | + | 10.6865i | −0.325633 | + | 0.564012i | −0.981640 | − | 0.190742i | \(-0.938911\pi\) |
0.656008 | + | 0.754754i | \(0.272244\pi\) | |||||||
\(360\) | −2.91610 | −0.153692 | ||||||||
\(361\) | 4.24442 | − | 7.35155i | 0.223390 | − | 0.386924i | ||||
\(362\) | 5.28152 | 0.277591 | ||||||||
\(363\) | −3.55776 | −0.186734 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.4528 | −1.17524 | ||||||||
\(366\) | −9.42633 | −0.492722 | ||||||||
\(367\) | 1.01538 | − | 1.75870i | 0.0530026 | − | 0.0918032i | −0.838307 | − | 0.545199i | \(-0.816454\pi\) |
0.891309 | + | 0.453396i | \(0.149788\pi\) | |||||||
\(368\) | 20.4179 | 1.06436 | ||||||||
\(369\) | −7.27188 | + | 12.5953i | −0.378559 | + | 0.655684i | ||||
\(370\) | 9.89593 | − | 17.1403i | 0.514465 | − | 0.891079i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.66586 | 0.190066 | ||||||||
\(373\) | 1.93700 | + | 3.35498i | 0.100294 | + | 0.173714i | 0.911806 | − | 0.410622i | \(-0.134688\pi\) |
−0.811512 | + | 0.584336i | \(0.801355\pi\) | |||||||
\(374\) | −5.03473 | + | 8.72040i | −0.260340 | + | 0.450921i | ||||
\(375\) | −2.47095 | + | 4.27981i | −0.127599 | + | 0.221009i | ||||
\(376\) | 4.10588 | − | 7.11160i | 0.211745 | − | 0.366753i | ||||
\(377\) | −0.121160 | + | 0.591877i | −0.00624007 | + | 0.0304832i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.28396 | + | 12.6162i | 0.374152 | + | 0.648050i | 0.990200 | − | 0.139659i | \(-0.0446006\pi\) |
−0.616048 | + | 0.787709i | \(0.711267\pi\) | |||||||
\(380\) | −7.79045 | −0.399642 | ||||||||
\(381\) | −6.80606 | −0.348685 | ||||||||
\(382\) | −19.2850 | − | 33.4025i | −0.986705 | − | 1.70902i | ||||
\(383\) | −13.3909 | − | 23.1937i | −0.684243 | − | 1.18514i | −0.973674 | − | 0.227945i | \(-0.926799\pi\) |
0.289430 | − | 0.957199i | \(-0.406534\pi\) | |||||||
\(384\) | −1.18405 | + | 2.05084i | −0.0604234 | + | 0.104656i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15.6038 | + | 27.0266i | −0.794212 | + | 1.37562i | ||||
\(387\) | −0.0640749 | −0.00325711 | ||||||||
\(388\) | 2.84773 | − | 4.93241i | 0.144571 | − | 0.250405i | ||||
\(389\) | −6.00738 | − | 10.4051i | −0.304586 | − | 0.527559i | 0.672583 | − | 0.740022i | \(-0.265185\pi\) |
−0.977169 | + | 0.212463i | \(0.931852\pi\) | |||||||
\(390\) | −0.869656 | + | 4.24834i | −0.0440368 | + | 0.215123i | ||||
\(391\) | −5.33655 | −0.269881 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.397910 | − | 0.689200i | −0.0200719 | − | 0.0347655i | ||||
\(394\) | 18.8017 | + | 32.5655i | 0.947216 | + | 1.64063i | ||||
\(395\) | −0.570470 | − | 0.988084i | −0.0287035 | − | 0.0497159i | ||||
\(396\) | 20.1845 | 1.01431 | ||||||||
\(397\) | −0.828825 | − | 1.43557i | −0.0415975 | − | 0.0720491i | 0.844477 | − | 0.535592i | \(-0.179911\pi\) |
−0.886075 | + | 0.463543i | \(0.846578\pi\) | |||||||
\(398\) | −26.9017 | −1.34846 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.51106 | − | 11.2775i | −0.325553 | − | 0.563874i | ||||
\(401\) | −20.4828 | −1.02286 | −0.511430 | − | 0.859325i | \(-0.670884\pi\) | ||||
−0.511430 | + | 0.859325i | \(0.670884\pi\) | |||||||
\(402\) | −1.68816 | − | 2.92398i | −0.0841978 | − | 0.145835i | ||||
\(403\) | 3.79287 | − | 18.5285i | 0.188936 | − | 0.922968i | ||||
\(404\) | 2.10240 | − | 3.64146i | 0.104598 | − | 0.181169i | ||||
\(405\) | −5.43702 | − | 9.41720i | −0.270168 | − | 0.467944i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.4887 | − | 26.8272i | 0.767746 | − | 1.32978i | ||||
\(408\) | 0.181089 | − | 0.313655i | 0.00896522 | − | 0.0155282i | ||||
\(409\) | −14.8659 | −0.735070 | −0.367535 | − | 0.930010i | \(-0.619798\pi\) | ||||
−0.367535 | + | 0.930010i | \(0.619798\pi\) | |||||||
\(410\) | 14.4958 | 0.715895 | ||||||||
\(411\) | −2.74211 | + | 4.74948i | −0.135258 | + | 0.234274i | ||||
\(412\) | −13.7535 | + | 23.8217i | −0.677586 | + | 1.17361i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 11.9067 | + | 20.6230i | 0.585182 | + | 1.01357i | ||||
\(415\) | −11.7988 | + | 20.4360i | −0.579178 | + | 1.00317i | ||||
\(416\) | −19.8619 | − | 17.6149i | −0.973808 | − | 0.863643i | ||||
\(417\) | 0.0725639 | + | 0.125684i | 0.00355347 | + | 0.00615479i | ||||
\(418\) | −27.1438 | −1.32764 | ||||||||
\(419\) | −11.8087 | − | 20.4533i | −0.576895 | − | 0.999211i | −0.995833 | − | 0.0911962i | \(-0.970931\pi\) |
0.418938 | − | 0.908015i | \(-0.362402\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0822 | 1.27117 | 0.635585 | − | 0.772031i | \(-0.280759\pi\) | ||||
0.635585 | + | 0.772031i | \(0.280759\pi\) | |||||||
\(422\) | −4.40788 | − | 7.63467i | −0.214572 | − | 0.371650i | ||||
\(423\) | 32.9059 | 1.59994 | ||||||||
\(424\) | 0.0498269 | + | 0.0863028i | 0.00241981 | + | 0.00419123i | ||||
\(425\) | 1.70177 | + | 2.94755i | 0.0825479 | + | 0.142977i | ||||
\(426\) | 4.06980 | + | 7.04910i | 0.197182 | + | 0.341530i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14.1628 | 0.684584 | ||||||||
\(429\) | −1.36115 | + | 6.64932i | −0.0657169 | + | 0.321032i | ||||
\(430\) | 0.0319317 | + | 0.0553074i | 0.00153988 | + | 0.00266716i | ||||
\(431\) | 6.65859 | − | 11.5330i | 0.320733 | − | 0.555526i | −0.659906 | − | 0.751348i | \(-0.729404\pi\) |
0.980640 | + | 0.195822i | \(0.0627374\pi\) | |||||||
\(432\) | −11.4675 | −0.551728 | ||||||||
\(433\) | 10.2110 | − | 17.6860i | 0.490711 | − | 0.849937i | −0.509232 | − | 0.860629i | \(-0.670070\pi\) |
0.999943 | + | 0.0106929i | \(0.00340371\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.0528790 | − | 0.0915890i | 0.00253535 | − | 0.00439136i | ||||
\(436\) | 9.82001 | + | 17.0087i | 0.470293 | + | 0.814571i | ||||
\(437\) | −7.19275 | − | 12.4582i | −0.344076 | − | 0.595957i | ||||
\(438\) | −12.4437 | −0.594585 | ||||||||
\(439\) | 9.77074 | 0.466332 | 0.233166 | − | 0.972437i | \(-0.425091\pi\) | ||||
0.233166 | + | 0.972437i | \(0.425091\pi\) | |||||||
\(440\) | 2.27455 | + | 3.93963i | 0.108435 | + | 0.187814i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.18229 | + | 5.48290i | 0.294061 | + | 0.260795i | ||||
\(443\) | −10.5819 | + | 18.3285i | −0.502763 | + | 0.870811i | 0.497232 | + | 0.867618i | \(0.334350\pi\) |
−0.999995 | + | 0.00319331i | \(0.998984\pi\) | |||||||
\(444\) | 2.46370 | − | 4.26725i | 0.116922 | − | 0.202514i | ||||
\(445\) | 4.83010 | − | 8.36597i | 0.228968 | − | 0.396585i | ||||
\(446\) | 20.3440 | + | 35.2368i | 0.963317 | + | 1.66851i | ||||
\(447\) | −1.68087 | −0.0795023 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.07320 | − | 15.7152i | 0.428191 | − | 0.741648i | −0.568522 | − | 0.822668i | \(-0.692484\pi\) |
0.996712 | + | 0.0810200i | \(0.0258178\pi\) | |||||||
\(450\) | 7.59384 | − | 13.1529i | 0.357977 | − | 0.620034i | ||||
\(451\) | 22.6882 | 1.06834 | ||||||||
\(452\) | −7.64387 | + | 13.2396i | −0.359538 | + | 0.622737i | ||||
\(453\) | 0.907789 | 0.0426517 | ||||||||
\(454\) | −19.9112 | −0.934480 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.976304 | 0.0457196 | ||||||||
\(457\) | −18.0198 | −0.842932 | −0.421466 | − | 0.906844i | \(-0.638484\pi\) | ||||
−0.421466 | + | 0.906844i | \(0.638484\pi\) | |||||||
\(458\) | −13.7753 | + | 23.8595i | −0.643678 | + | 1.11488i | ||||
\(459\) | 2.99720 | 0.139897 | ||||||||
\(460\) | 5.33098 | − | 9.23352i | 0.248558 | − | 0.430515i | ||||
\(461\) | −14.8873 | + | 25.7855i | −0.693370 | + | 1.20095i | 0.277357 | + | 0.960767i | \(0.410542\pi\) |
−0.970727 | + | 0.240185i | \(0.922792\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7067 | 0.822900 | 0.411450 | − | 0.911432i | \(-0.365023\pi\) | ||||
0.411450 | + | 0.911432i | \(0.365023\pi\) | |||||||
\(464\) | 0.385529 | + | 0.667755i | 0.0178977 | + | 0.0309997i | ||||
\(465\) | −1.65535 | + | 2.86715i | −0.0767651 | + | 0.132961i | ||||
\(466\) | −8.84968 | + | 15.3281i | −0.409953 | + | 0.710060i | ||||
\(467\) | −2.91461 | + | 5.04825i | −0.134872 | + | 0.233605i | −0.925549 | − | 0.378629i | \(-0.876396\pi\) |
0.790677 | + | 0.612234i | \(0.209729\pi\) | |||||||
\(468\) | 3.32186 | − | 16.2276i | 0.153553 | − | 0.750120i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.3987 | − | 28.4033i | −0.756414 | − | 1.31015i | ||||
\(471\) | −9.47418 | −0.436547 | ||||||||
\(472\) | 3.75570 | 0.172870 | ||||||||
\(473\) | 0.0499782 | + | 0.0865648i | 0.00229800 | + | 0.00398025i | ||||
\(474\) | −0.316164 | − | 0.547612i | −0.0145219 | − | 0.0251527i | ||||
\(475\) | −4.58738 | + | 7.94557i | −0.210483 | + | 0.364568i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.199665 | + | 0.345830i | −0.00914203 | + | 0.0158345i | ||||
\(478\) | −37.4122 | −1.71120 | ||||||||
\(479\) | 7.24565 | − | 12.5498i | 0.331062 | − | 0.573417i | −0.651658 | − | 0.758513i | \(-0.725926\pi\) |
0.982720 | + | 0.185096i | \(0.0592596\pi\) | |||||||
\(480\) | 2.32361 | + | 4.02461i | 0.106058 | + | 0.183698i | ||||
\(481\) | −19.0190 | − | 16.8674i | −0.867193 | − | 0.769088i | ||||
\(482\) | 13.9316 | 0.634569 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.77245 | − | 11.7302i | −0.307839 | − | 0.533192i | ||||
\(485\) | 2.57183 | + | 4.45455i | 0.116781 | + | 0.202271i | ||||
\(486\) | −10.1364 | − | 17.5567i | −0.459795 | − | 0.796389i | ||||
\(487\) | −17.9601 | −0.813851 | −0.406926 | − | 0.913461i | \(-0.633399\pi\) | ||||
−0.406926 | + | 0.913461i | \(0.633399\pi\) | |||||||
\(488\) | 4.05746 | + | 7.02772i | 0.183672 | + | 0.318130i | ||||
\(489\) | −1.65044 | −0.0746354 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.1505 | + | 31.4375i | 0.819119 | + | 1.41876i | 0.906332 | + | 0.422566i | \(0.138870\pi\) |
−0.0872134 | + | 0.996190i | \(0.527796\pi\) | |||||||
\(492\) | 3.60887 | 0.162701 | ||||||||
\(493\) | −0.100764 | − | 0.174528i | −0.00453818 | − | 0.00786036i | ||||
\(494\) | −4.46719 | + | 21.8226i | −0.200988 | + | 0.981844i | ||||
\(495\) | −9.11449 | + | 15.7868i | −0.409666 | + | 0.709562i | ||||
\(496\) | −12.0688 | − | 20.9038i | −0.541905 | − | 0.938607i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6.53906 | + | 11.3260i | −0.293022 | + | 0.507530i | ||||
\(499\) | −11.8538 | + | 20.5314i | −0.530649 | + | 0.919112i | 0.468711 | + | 0.883352i | \(0.344719\pi\) |
−0.999360 | + | 0.0357602i | \(0.988615\pi\) | |||||||
\(500\) | −18.8145 | −0.841410 | ||||||||
\(501\) | 0.916426 | 0.0409429 | ||||||||
\(502\) | 11.3036 | − | 19.5784i | 0.504505 | − | 0.873828i | ||||
\(503\) | 13.8876 | − | 24.0540i | 0.619217 | − | 1.07252i | −0.370411 | − | 0.928868i | \(-0.620783\pi\) |
0.989629 | − | 0.143648i | \(-0.0458834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.89871 | + | 3.28867i | 0.0844916 | + | 0.146344i | ||||
\(506\) | 18.5744 | − | 32.1717i | 0.825731 | − | 1.43021i | ||||
\(507\) | 5.12180 | + | 2.18863i | 0.227467 | + | 0.0972003i | ||||
\(508\) | −12.9558 | − | 22.4401i | −0.574820 | − | 0.995618i | ||||
\(509\) | −8.70416 | −0.385805 | −0.192902 | − | 0.981218i | \(-0.561790\pi\) | ||||
−0.192902 | + | 0.981218i | \(0.561790\pi\) | |||||||
\(510\) | −0.723257 | − | 1.25272i | −0.0320264 | − | 0.0554713i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −27.4134 | −1.21151 | ||||||||
\(513\) | 4.03971 | + | 6.99698i | 0.178357 | + | 0.308924i | ||||
\(514\) | −28.9114 | −1.27523 | ||||||||
\(515\) | −12.4210 | − | 21.5139i | −0.547336 | − | 0.948014i | ||||
\(516\) | 0.00794974 | + | 0.0137693i | 0.000349968 | + | 0.000606162i | ||||
\(517\) | −25.6665 | − | 44.4557i | −1.12881 | − | 1.95516i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.11792 | −0.312442 | ||||||||
\(520\) | 3.54165 | − | 1.18028i | 0.155312 | − | 0.0517589i | ||||
\(521\) | −4.28573 | − | 7.42310i | −0.187761 | − | 0.325212i | 0.756742 | − | 0.653713i | \(-0.226790\pi\) |
−0.944504 | + | 0.328501i | \(0.893456\pi\) | |||||||
\(522\) | −0.449641 | + | 0.778801i | −0.0196803 | + | 0.0340872i | ||||
\(523\) | −29.9493 | −1.30959 | −0.654796 | − | 0.755806i | \(-0.727245\pi\) | ||||
−0.654796 | + | 0.755806i | \(0.727245\pi\) | |||||||
\(524\) | 1.51490 | − | 2.62388i | 0.0661786 | − | 0.114625i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.3844 | − | 28.3786i | 0.714393 | − | 1.23736i | ||||
\(527\) | 3.15437 | + | 5.46353i | 0.137407 | + | 0.237995i | ||||
\(528\) | 4.33114 | + | 7.50175i | 0.188489 | + | 0.326472i | ||||
\(529\) | −3.31212 | −0.144005 | ||||||||
\(530\) | 0.398012 | 0.0172885 | ||||||||
\(531\) | 7.52486 | + | 13.0334i | 0.326551 | + | 0.565603i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.73391 | − | 18.2404i | 0.161734 | − | 0.790081i | ||||
\(534\) | 2.67692 | − | 4.63656i | 0.115842 | − | 0.200643i | ||||
\(535\) | −6.39534 | + | 11.0770i | −0.276494 | + | 0.478902i | ||||
\(536\) | −1.45330 | + | 2.51719i | −0.0627730 | + | 0.108726i | ||||
\(537\) | −0.115573 | − | 0.200178i | −0.00498734 | − | 0.00863832i | ||||
\(538\) | 36.0571 | 1.55453 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.99407 | + | 5.18588i | −0.128844 | + | 0.223165i | ||||
\(541\) | −5.24095 | + | 9.07760i | −0.225326 | + | 0.390276i | −0.956417 | − | 0.292003i | \(-0.905678\pi\) |
0.731091 | + | 0.682280i | \(0.239011\pi\) | |||||||
\(542\) | 61.2321 | 2.63014 | ||||||||
\(543\) | −0.593751 | + | 1.02841i | −0.0254803 | + | 0.0441331i | ||||
\(544\) | 8.85557 | 0.379679 | ||||||||
\(545\) | −17.7373 | −0.759781 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.2216 | 0.650829 | 0.325415 | − | 0.945571i | \(-0.394496\pi\) | ||||
0.325415 | + | 0.945571i | \(0.394496\pi\) | |||||||
\(548\) | −20.8792 | −0.891915 | ||||||||
\(549\) | −16.2589 | + | 28.1613i | −0.693914 | + | 1.20189i | ||||
\(550\) | −23.6927 | −1.01026 | ||||||||
\(551\) | 0.271625 | − | 0.470468i | 0.0115716 | − | 0.0200426i | ||||
\(552\) | −0.668081 | + | 1.15715i | −0.0284354 | + | 0.0492516i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −35.0726 | −1.49009 | ||||||||
\(555\) | 2.22501 | + | 3.85383i | 0.0944464 | + | 0.163586i | ||||
\(556\) | −0.276261 | + | 0.478497i | −0.0117161 | + | 0.0202928i | ||||
\(557\) | −5.92986 | + | 10.2708i | −0.251256 | + | 0.435189i | −0.963872 | − | 0.266366i | \(-0.914177\pi\) |
0.712616 | + | 0.701555i | \(0.247510\pi\) | |||||||
\(558\) | 14.0758 | − | 24.3800i | 0.595877 | − | 1.03209i | ||||
\(559\) | 0.0778200 | − | 0.0259342i | 0.00329144 | − | 0.00109690i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.13201 | − | 1.96070i | −0.0477936 | − | 0.0827809i | ||||
\(562\) | 27.1069 | 1.14344 | ||||||||
\(563\) | −7.69349 | −0.324242 | −0.162121 | − | 0.986771i | \(-0.551834\pi\) | ||||
−0.162121 | + | 0.986771i | \(0.551834\pi\) | |||||||
\(564\) | −4.08262 | − | 7.07131i | −0.171909 | − | 0.297756i | ||||
\(565\) | −6.90332 | − | 11.9569i | −0.290425 | − | 0.503031i | ||||
\(566\) | 10.8892 | − | 18.8607i | 0.457709 | − | 0.792775i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.50360 | − | 6.06841i | 0.147008 | − | 0.254625i | ||||
\(569\) | 37.4196 | 1.56871 | 0.784355 | − | 0.620312i | \(-0.212994\pi\) | ||||
0.784355 | + | 0.620312i | \(0.212994\pi\) | |||||||
\(570\) | 1.94965 | − | 3.37689i | 0.0816619 | − | 0.141443i | ||||
\(571\) | −7.08285 | − | 12.2679i | −0.296408 | − | 0.513394i | 0.678903 | − | 0.734228i | \(-0.262456\pi\) |
−0.975311 | + | 0.220834i | \(0.929122\pi\) | |||||||
\(572\) | −24.5144 | + | 8.16963i | −1.02500 | + | 0.341589i | ||||
\(573\) | 8.67209 | 0.362282 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.27825 | − | 10.8742i | −0.261821 | − | 0.453488i | ||||
\(576\) | −6.79797 | − | 11.7744i | −0.283249 | − | 0.490601i | ||||
\(577\) | −7.48776 | − | 12.9692i | −0.311720 | − | 0.539914i | 0.667015 | − | 0.745044i | \(-0.267572\pi\) |
−0.978735 | + | 0.205130i | \(0.934238\pi\) | |||||||
\(578\) | 29.6381 | 1.23278 | ||||||||
\(579\) | −3.50837 | − | 6.07667i | −0.145803 | − | 0.252538i | ||||
\(580\) | 0.402635 | 0.0167185 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.42535 | + | 2.46878i | 0.0590828 | + | 0.102334i | ||||
\(583\) | 0.622952 | 0.0258000 | ||||||||
\(584\) | 5.35627 | + | 9.27732i | 0.221644 | + | 0.383898i | ||||
\(585\) | 11.1919 | + | 9.92582i | 0.462730 | + | 0.410382i | ||||
\(586\) | 12.5811 | − | 21.7911i | 0.519720 | − | 0.900182i | ||||
\(587\) | −6.58821 | − | 11.4111i | −0.271925 | − | 0.470987i | 0.697430 | − | 0.716653i | \(-0.254327\pi\) |
−0.969355 | + | 0.245666i | \(0.920993\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.50309 | + | 14.7278i | −0.350364 | + | 0.606848i | ||||
\(590\) | 7.50003 | − | 12.9904i | 0.308771 | − | 0.534807i | ||||
\(591\) | −8.45478 | −0.347783 | ||||||||
\(592\) | −32.4441 | −1.33344 | ||||||||
\(593\) | −22.0663 | + | 38.2200i | −0.906156 | + | 1.56951i | −0.0867989 | + | 0.996226i | \(0.527664\pi\) |
−0.819357 | + | 0.573283i | \(0.805670\pi\) | |||||||
\(594\) | −10.4320 | + | 18.0688i | −0.428032 | + | 0.741372i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.19965 | − | 5.54195i | −0.131063 | − | 0.227007i | ||||
\(597\) | 3.02429 | − | 5.23823i | 0.123776 | − | 0.214387i | ||||
\(598\) | −22.8080 | − | 20.2278i | −0.932689 | − | 0.827175i | ||||
\(599\) | 3.01349 | + | 5.21952i | 0.123128 | + | 0.213264i | 0.921000 | − | 0.389564i | \(-0.127374\pi\) |
−0.797872 | + | 0.602827i | \(0.794041\pi\) | |||||||
\(600\) | 0.852175 | 0.0347899 | ||||||||
\(601\) | 1.86260 | + | 3.22612i | 0.0759770 | + | 0.131596i | 0.901511 | − | 0.432757i | \(-0.142459\pi\) |
−0.825534 | + | 0.564353i | \(0.809126\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.6472 | −0.474312 | ||||||||
\(604\) | 1.72804 | + | 2.99305i | 0.0703129 | + | 0.121786i | ||||
\(605\) | 12.2326 | 0.497328 | ||||||||
\(606\) | 1.05230 | + | 1.82263i | 0.0427467 | + | 0.0740394i | ||||
\(607\) | −3.00825 | − | 5.21045i | −0.122101 | − | 0.211486i | 0.798495 | − | 0.602002i | \(-0.205630\pi\) |
−0.920596 | + | 0.390516i | \(0.872297\pi\) | |||||||
\(608\) | 11.9358 | + | 20.6733i | 0.484059 | + | 0.838415i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 32.4105 | 1.31226 | ||||||||
\(611\) | −39.9648 | + | 13.3186i | −1.61680 | + | 0.538813i | ||||
\(612\) | 2.76266 | + | 4.78506i | 0.111674 | + | 0.193425i | ||||
\(613\) | −4.90413 | + | 8.49420i | −0.198076 | + | 0.343077i | −0.947904 | − | 0.318555i | \(-0.896803\pi\) |
0.749829 | + | 0.661632i | \(0.230136\pi\) | |||||||
\(614\) | −12.6892 | −0.512094 | ||||||||
\(615\) | −1.62962 | + | 2.82258i | −0.0657126 | + | 0.113818i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.8838 | + | 29.2436i | −0.679716 | + | 1.17730i | 0.295350 | + | 0.955389i | \(0.404564\pi\) |
−0.975066 | + | 0.221914i | \(0.928770\pi\) | |||||||
\(618\) | −6.88394 | − | 11.9233i | −0.276913 | − | 0.479627i | ||||
\(619\) | 2.04671 | + | 3.54501i | 0.0822644 | + | 0.142486i | 0.904222 | − | 0.427062i | \(-0.140451\pi\) |
−0.821958 | + | 0.569548i | \(0.807118\pi\) | |||||||
\(620\) | −12.6043 | −0.506201 | ||||||||
\(621\) | −11.0574 | −0.443719 | ||||||||
\(622\) | 1.94936 | + | 3.37639i | 0.0781621 | + | 0.135381i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.74393 | − | 2.24747i | 0.269973 | − | 0.0899709i | ||||
\(625\) | 1.42115 | − | 2.46150i | 0.0568459 | − | 0.0984599i | ||||
\(626\) | −8.97297 | + | 15.5416i | −0.358632 | + | 0.621169i | ||||
\(627\) | 3.05151 | − | 5.28537i | 0.121866 | − | 0.211077i | ||||
\(628\) | −18.0347 | − | 31.2371i | −0.719665 | − | 1.24650i | ||||
\(629\) | 8.47978 | 0.338111 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.3868 | − | 23.1866i | 0.532921 | − | 0.923046i | −0.466340 | − | 0.884605i | \(-0.654428\pi\) |
0.999261 | − | 0.0384402i | \(-0.0122389\pi\) | |||||||
\(632\) | −0.272179 | + | 0.471427i | −0.0108267 | + | 0.0187524i | ||||
\(633\) | 1.98214 | 0.0787831 | ||||||||
\(634\) | −31.7955 | + | 55.0714i | −1.26276 | + | 2.18717i | ||||
\(635\) | 23.4012 | 0.928650 | ||||||||
\(636\) | 0.0990892 | 0.00392914 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.40287 | 0.0555403 | ||||||||
\(639\) | 28.0790 | 1.11079 | ||||||||
\(640\) | 4.07112 | − | 7.05139i | 0.160925 | − | 0.278731i | ||||
\(641\) | −18.5722 | −0.733558 | −0.366779 | − | 0.930308i | \(-0.619539\pi\) | ||||
−0.366779 | + | 0.930308i | \(0.619539\pi\) | |||||||
\(642\) | −3.54440 | + | 6.13908i | −0.139886 | + | 0.242290i | ||||
\(643\) | −1.96695 | + | 3.40686i | −0.0775690 | + | 0.134353i | −0.902201 | − | 0.431317i | \(-0.858049\pi\) |
0.824632 | + | 0.565670i | \(0.191382\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0143591 | −0.000565389 | ||||||||
\(646\) | −3.71518 | − | 6.43487i | −0.146172 | − | 0.253177i | ||||
\(647\) | −0.0985378 | + | 0.170672i | −0.00387392 | + | 0.00670983i | −0.867956 | − | 0.496641i | \(-0.834566\pi\) |
0.864082 | + | 0.503351i | \(0.167900\pi\) | |||||||
\(648\) | −2.59407 | + | 4.49306i | −0.101905 | + | 0.176504i | ||||
\(649\) | 11.7387 | − | 20.3321i | 0.460785 | − | 0.798104i | ||||
\(650\) | −3.89922 | + | 19.0480i | −0.152940 | + | 0.747125i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.14172 | − | 5.44163i | −0.123039 | − | 0.213110i | ||||
\(653\) | −14.4673 | −0.566148 | −0.283074 | − | 0.959098i | \(-0.591354\pi\) | ||||
−0.283074 | + | 0.959098i | \(0.591354\pi\) | |||||||
\(654\) | −9.83028 | −0.384394 | ||||||||
\(655\) | 1.36813 | + | 2.36967i | 0.0534573 | + | 0.0925908i | ||||
\(656\) | −11.8812 | − | 20.5788i | −0.463883 | − | 0.803468i | ||||
\(657\) | −21.4635 | + | 37.1758i | −0.837369 | + | 1.45037i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.7066 | − | 20.2764i | 0.456024 | − | 0.789857i | −0.542722 | − | 0.839912i | \(-0.682606\pi\) |
0.998746 | + | 0.0500552i | \(0.0159397\pi\) | |||||||
\(660\) | 4.52332 | 0.176070 | ||||||||
\(661\) | −2.02409 | + | 3.50582i | −0.0787278 | + | 0.136361i | −0.902701 | − | 0.430268i | \(-0.858419\pi\) |
0.823973 | + | 0.566628i | \(0.191752\pi\) | |||||||
\(662\) | 18.1657 | + | 31.4638i | 0.706028 | + | 1.22288i | ||||
\(663\) | −1.76263 | + | 0.587412i | −0.0684550 | + | 0.0228132i | ||||
\(664\) | 11.2587 | 0.436921 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −18.9197 | − | 32.7699i | −0.733125 | − | 1.26981i | ||||
\(667\) | 0.371744 | + | 0.643879i | 0.0143940 | + | 0.0249311i | ||||
\(668\) | 1.74448 | + | 3.02153i | 0.0674959 | + | 0.116906i | ||||
\(669\) | −9.14832 | −0.353695 | ||||||||
\(670\) | 5.80440 | + | 10.0535i | 0.224243 | + | 0.388401i | ||||
\(671\) | 50.7276 | 1.95832 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.64704 | − | 6.31685i | −0.140583 | − | 0.243497i | 0.787133 | − | 0.616783i | \(-0.211564\pi\) |
−0.927716 | + | 0.373286i | \(0.878231\pi\) | |||||||
\(674\) | 59.6152 | 2.29629 | ||||||||
\(675\) | 3.52609 | + | 6.10737i | 0.135719 | + | 0.235073i | ||||
\(676\) | 2.53362 | + | 21.0532i | 0.0974468 | + | 0.809737i | ||||
\(677\) | −7.87553 | + | 13.6408i | −0.302681 | + | 0.524259i | −0.976742 | − | 0.214416i | \(-0.931215\pi\) |
0.674061 | + | 0.738676i | \(0.264548\pi\) | |||||||
\(678\) | −3.82593 | − | 6.62671i | −0.146934 | − | 0.254497i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.622636 | + | 1.07844i | −0.0238770 | + | 0.0413562i | ||||
\(681\) | 2.23843 | − | 3.87707i | 0.0857767 | − | 0.148570i | ||||
\(682\) | −43.9163 | −1.68164 | ||||||||
\(683\) | 41.4854 | 1.58739 | 0.793697 | − | 0.608314i | \(-0.208154\pi\) | ||||
0.793697 | + | 0.608314i | \(0.208154\pi\) | |||||||
\(684\) | −7.44717 | + | 12.8989i | −0.284750 | + | 0.493201i | ||||
\(685\) | 9.42819 | − | 16.3301i | 0.360233 | − | 0.623941i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.09725 | − | 5.36460i | −0.118168 | − | 0.204672i | ||||
\(688\) | 0.0523445 | − | 0.0906634i | 0.00199562 | − | 0.00345651i | ||||
\(689\) | 0.102522 | − | 0.500830i | 0.00390579 | − | 0.0190801i | ||||
\(690\) | 2.66828 | + | 4.62159i | 0.101580 | + | 0.175941i | ||||
\(691\) | 46.8216 | 1.78118 | 0.890589 | − | 0.454809i | \(-0.150292\pi\) | ||||
0.890589 | + | 0.454809i | \(0.150292\pi\) | |||||||
\(692\) | −13.5494 | − | 23.4683i | −0.515073 | − | 0.892132i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.2478 | −0.844514 | ||||||||
\(695\) | −0.249496 | − | 0.432140i | −0.00946392 | − | 0.0163920i | ||||
\(696\) | −0.0504584 | −0.00191262 | ||||||||
\(697\) | 3.10534 | + | 5.37860i | 0.117623 | + | 0.203729i | ||||
\(698\) | −22.8576 | − | 39.5905i | −0.865172 | − | 1.49852i | ||||
\(699\) | −1.98977 | − | 3.44638i | −0.0752600 | − | 0.130354i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.8626 | 1.12790 | 0.563948 | − | 0.825810i | \(-0.309282\pi\) | ||||
0.563948 | + | 0.825810i | \(0.309282\pi\) | |||||||
\(702\) | 12.8098 | + | 11.3606i | 0.483475 | + | 0.428780i | ||||
\(703\) | 11.4293 | + | 19.7961i | 0.431063 | + | 0.746623i | ||||
\(704\) | −10.6048 | + | 18.3680i | −0.399683 | + | 0.692271i | ||||
\(705\) | 7.37418 | 0.277728 | ||||||||
\(706\) | −12.1893 | + | 21.1124i | −0.458749 | + | 0.794576i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.86721 | − | 3.23410i | 0.0701740 | − | 0.121545i | ||||
\(709\) | −13.4666 | − | 23.3249i | −0.505750 | − | 0.875984i | −0.999978 | − | 0.00665185i | \(-0.997883\pi\) |
0.494228 | − | 0.869332i | \(-0.335451\pi\) | |||||||
\(710\) | −13.9932 | − | 24.2369i | −0.525155 | − | 0.909595i | ||||
\(711\) | −2.18133 | −0.0818063 | ||||||||
\(712\) | −4.60900 | −0.172729 | ||||||||
\(713\) | −11.6373 | − | 20.1563i | −0.435819 | − | 0.754861i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.68004 | − | 22.8623i | 0.175023 | − | 0.855003i | ||||
\(716\) | 0.440002 | − | 0.762105i | 0.0164436 | − | 0.0284812i | ||||
\(717\) | 4.20590 | − | 7.28483i | 0.157072 | − | 0.272057i | ||||
\(718\) | 11.7570 | − | 20.3638i | 0.438769 | − | 0.759969i | ||||
\(719\) | −7.24938 | − | 12.5563i | −0.270356 | − | 0.468271i | 0.698597 | − | 0.715516i | \(-0.253808\pi\) |
−0.968953 | + | 0.247245i | \(0.920475\pi\) | |||||||
\(720\) | 19.0921 | 0.711519 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.08799 | + | 14.0088i | −0.301004 | + | 0.521354i | ||||
\(723\) | −1.56620 | + | 2.71274i | −0.0582476 | + | 0.100888i | ||||
\(724\) | −4.52098 | −0.168021 | ||||||||
\(725\) | 0.237090 | − | 0.410652i | 0.00880530 | − | 0.0152512i | ||||
\(726\) | 6.77953 | 0.251612 | ||||||||
\(727\) | 6.26424 | 0.232328 | 0.116164 | − | 0.993230i | \(-0.462940\pi\) | ||||
0.116164 | + | 0.993230i | \(0.462940\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.5866 | −0.651357 | ||||||||
\(730\) | 42.7852 | 1.58355 | ||||||||
\(731\) | −0.0136811 | + | 0.0236963i | −0.000506013 | + | 0.000876440i | ||||
\(732\) | 8.06893 | 0.298236 | ||||||||
\(733\) | −5.99189 | + | 10.3783i | −0.221316 | + | 0.383330i | −0.955208 | − | 0.295936i | \(-0.904368\pi\) |
0.733892 | + | 0.679266i | \(0.237702\pi\) | |||||||
\(734\) | −1.93487 | + | 3.35130i | −0.0714175 | + | 0.123699i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −32.6704 | −1.20425 | ||||||||
\(737\) | 9.08480 | + | 15.7353i | 0.334643 | + | 0.579619i | ||||
\(738\) | 13.8570 | − | 24.0010i | 0.510084 | − | 0.883491i | ||||
\(739\) | −6.76269 | + | 11.7133i | −0.248770 | + | 0.430882i | −0.963185 | − | 0.268840i | \(-0.913360\pi\) |
0.714415 | + | 0.699722i | \(0.246693\pi\) | |||||||
\(740\) | −8.47091 | + | 14.6721i | −0.311397 | + | 0.539355i | ||||
\(741\) | −3.74704 | − | 3.32314i | −0.137651 | − | 0.122079i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.2299 | + | 33.3072i | 0.705477 | + | 1.22192i | 0.966519 | + | 0.256594i | \(0.0826003\pi\) |
−0.261043 | + | 0.965327i | \(0.584066\pi\) | |||||||
\(744\) | 1.57958 | 0.0579101 | ||||||||
\(745\) | 5.77932 | 0.211738 | ||||||||
\(746\) | −3.69107 | − | 6.39312i | −0.135140 | − | 0.234069i | ||||
\(747\) | 22.5577 | + | 39.0710i | 0.825342 | + | 1.42953i | ||||
\(748\) | 4.30973 | − | 7.46466i | 0.157579 | − | 0.272935i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4.70855 | − | 8.15544i | 0.171932 | − | 0.297795i | ||||
\(751\) | 11.7115 | 0.427357 | 0.213679 | − | 0.976904i | \(-0.431455\pi\) | ||||
0.213679 | + | 0.976904i | \(0.431455\pi\) | |||||||
\(752\) | −26.8817 | + | 46.5605i | −0.980276 | + | 1.69789i | ||||
\(753\) | 2.54151 | + | 4.40203i | 0.0926178 | + | 0.160419i | ||||
\(754\) | 0.230878 | − | 1.12786i | 0.00840809 | − | 0.0410742i | ||||
\(755\) | −3.12125 | −0.113594 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.65791 | − | 8.06773i | −0.169295 | − | 0.293227i | 0.768877 | − | 0.639396i | \(-0.220816\pi\) |
−0.938172 | + | 0.346169i | \(0.887482\pi\) | |||||||
\(758\) | −13.8800 | − | 24.0409i | −0.504145 | − | 0.873205i | ||||
\(759\) | 4.17627 | + | 7.23352i | 0.151589 | + | 0.262560i | ||||
\(760\) | −3.35682 | −0.121765 | ||||||||
\(761\) | −21.9691 | − | 38.0515i | −0.796378 | − | 1.37937i | −0.921960 | − | 0.387284i | \(-0.873413\pi\) |
0.125582 | − | 0.992083i | \(-0.459920\pi\) | |||||||
\(762\) | 12.9693 | 0.469830 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.5079 | + | 28.5926i | 0.597236 | + | 1.03444i | ||||
\(765\) | −4.99002 | −0.180414 | ||||||||
\(766\) | 25.5172 | + | 44.1971i | 0.921973 | + | 1.59690i | ||||
\(767\) | −14.4143 | − | 12.7837i | −0.520471 | − | 0.461591i | ||||
\(768\) | 4.32455 | − | 7.49035i | 0.156049 | − | 0.270285i | ||||
\(769\) | 12.6771 | + | 21.9573i | 0.457147 | + | 0.791802i | 0.998809 | − | 0.0487946i | \(-0.0155380\pi\) |
−0.541662 | + | 0.840597i | \(0.682205\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.25024 | − | 5.62957i | 0.117054 | − | 0.202744i | ||||
\(772\) | 13.3568 | − | 23.1347i | 0.480723 | − | 0.832637i | ||||
\(773\) | 23.1084 | 0.831152 | 0.415576 | − | 0.909559i | \(-0.363580\pi\) | ||||
0.415576 | + | 0.909559i | \(0.363580\pi\) | |||||||
\(774\) | 0.122099 | 0.00438874 | ||||||||
\(775\) | −7.42200 | + | 12.8553i | −0.266606 | + | 0.461775i | ||||
\(776\) | 1.22705 | − | 2.12532i | 0.0440487 | − | 0.0762946i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.4474 | + | 19.8275i | 0.410410 | + | 0.710851i | ||||
\(779\) | −8.37091 | + | 14.4988i | −0.299919 | + | 0.519475i | ||||
\(780\) | 0.744426 | − | 3.63658i | 0.0266547 | − | 0.130210i | ||||
\(781\) | −21.9015 | − | 37.9346i | −0.783699 | − | 1.35741i | ||||
\(782\) | 10.1691 | 0.363647 | ||||||||
\(783\) | −0.208785 | − | 0.361626i | −0.00746135 | − | 0.0129234i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.5750 | 1.16265 | ||||||||
\(786\) | 0.758241 | + | 1.31331i | 0.0270456 | + | 0.0468443i | ||||
\(787\) | 24.6692 | 0.879364 | 0.439682 | − | 0.898154i | \(-0.355091\pi\) | ||||
0.439682 | + | 0.898154i | \(0.355091\pi\) | |||||||
\(788\) | −16.0943 | − | 27.8761i | −0.573334 | − | 0.993044i | ||||
\(789\) | 3.68388 | + | 6.38066i | 0.131149 | + | 0.227158i | ||||
\(790\) | 1.08707 | + | 1.88285i | 0.0386761 | + | 0.0669889i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 8.69727 | 0.309044 | ||||||||
\(793\) | 8.34850 | − | 40.7831i | 0.296464 | − | 1.44825i | ||||
\(794\) | 1.57938 | + | 2.73556i | 0.0560500 | + | 0.0970814i | ||||
\(795\) | −0.0447447 | + | 0.0775000i | −0.00158693 | + | 0.00274864i | ||||
\(796\) | 23.0278 | 0.816199 | ||||||||
\(797\) | 5.65686 | − | 9.79797i | 0.200376 | − | 0.347062i | −0.748273 | − | 0.663390i | \(-0.769117\pi\) |
0.948650 | + | 0.316329i | \(0.102450\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.02597 | − | 12.1693i | 0.248561 | − | 0.430520i | ||||
\(800\) | 10.4182 | + | 18.0449i | 0.368340 | + | 0.637984i | ||||
\(801\) | −9.23451 | − | 15.9946i | −0.326285 | − | 0.565143i | ||||
\(802\) | 39.0311 | 1.37824 | ||||||||
\(803\) | 66.9657 | 2.36317 | ||||||||
\(804\) | 1.44507 | + | 2.50293i | 0.0509635 | + | 0.0882714i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.22754 | + | 35.3071i | −0.254579 | + | 1.24364i | ||||
\(807\) | −4.05355 | + | 7.02096i | −0.142692 | + | 0.247149i | ||||
\(808\) | 0.905900 | − | 1.56906i | 0.0318694 | − | 0.0551995i | ||||
\(809\) | −8.18540 | + | 14.1775i | −0.287783 | + | 0.498455i | −0.973280 | − | 0.229620i | \(-0.926252\pi\) |
0.685497 | + | 0.728075i | \(0.259585\pi\) | |||||||
\(810\) | 10.3606 | + | 17.9450i | 0.364033 | + | 0.630524i | ||||
\(811\) | 29.0412 | 1.01978 | 0.509888 | − | 0.860241i | \(-0.329687\pi\) | ||||
0.509888 | + | 0.860241i | \(0.329687\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.88373 | + | 11.9230i | −0.241423 | + | 0.418157i | ||||
\(814\) | −29.5146 | + | 51.1209i | −1.03449 | + | 1.79179i | ||||
\(815\) | 5.67470 | 0.198776 | ||||||||
\(816\) | −1.18561 | + | 2.05354i | −0.0415046 | + | 0.0718881i | ||||
\(817\) | −0.0737588 | −0.00258050 | ||||||||
\(818\) | 28.3278 | 0.990458 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.4084 | −0.433319 | ||||||||
\(821\) | −13.7518 | −0.479940 | −0.239970 | − | 0.970780i | \(-0.577138\pi\) | ||||
−0.239970 | + | 0.970780i | \(0.577138\pi\) | |||||||
\(822\) | 5.22526 | − | 9.05041i | 0.182252 | − | 0.315669i | ||||
\(823\) | −29.1153 | −1.01490 | −0.507448 | − | 0.861682i | \(-0.669411\pi\) | ||||
−0.507448 | + | 0.861682i | \(0.669411\pi\) | |||||||
\(824\) | −5.92623 | + | 10.2645i | −0.206450 | + | 0.357582i | ||||
\(825\) | 2.66354 | − | 4.61338i | 0.0927325 | − | 0.160617i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.9118 | −0.796722 | −0.398361 | − | 0.917229i | \(-0.630421\pi\) | ||||
−0.398361 | + | 0.917229i | \(0.630421\pi\) | |||||||
\(828\) | −10.1921 | − | 17.6533i | −0.354201 | − | 0.613494i | ||||
\(829\) | −11.6914 | + | 20.2502i | −0.406061 | + | 0.703317i | −0.994444 | − | 0.105264i | \(-0.966431\pi\) |
0.588384 | + | 0.808582i | \(0.299764\pi\) | |||||||
\(830\) | 22.4832 | − | 38.9421i | 0.780404 | − | 1.35170i | ||||
\(831\) | 3.94287 | − | 6.82925i | 0.136777 | − | 0.236904i | ||||
\(832\) | 13.0219 | + | 11.5488i | 0.451454 | + | 0.400382i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.138275 | − | 0.239499i | −0.00478806 | − | 0.00829317i | ||||
\(835\) | −3.15094 | −0.109043 | ||||||||
\(836\) | 23.2350 | 0.803601 | ||||||||
\(837\) | 6.53591 | + | 11.3205i | 0.225914 | + | 0.391295i | ||||
\(838\) | 22.5023 | + | 38.9751i | 0.777328 | + | 1.34637i | ||||
\(839\) | 0.367168 | − | 0.635954i | 0.0126761 | − | 0.0219556i | −0.859618 | − | 0.510938i | \(-0.829298\pi\) |
0.872294 | + | 0.488982i | \(0.162632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4860 | − | 25.0904i | 0.499516 | − | 0.865187i | ||||
\(842\) | −49.7013 | −1.71282 | ||||||||
\(843\) | −3.04737 | + | 5.27820i | −0.104957 | + | 0.181791i | ||||
\(844\) | 3.77314 | + | 6.53528i | 0.129877 | + | 0.224954i | ||||
\(845\) | −17.6103 | − | 7.52515i | −0.605811 | − | 0.258873i | ||||
\(846\) | −62.7042 | −2.15582 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.326223 | − | 0.565035i | −0.0112026 | − | 0.0194034i | ||||
\(849\) | 2.44834 | + | 4.24066i | 0.0840270 | + | 0.145539i | ||||
\(850\) | −3.24282 | − | 5.61674i | −0.111228 | − | 0.192652i | ||||
\(851\) | −31.2840 | −1.07240 | ||||||||
\(852\) | −3.48375 | − | 6.03403i | −0.119351 | − | 0.206722i | ||||
\(853\) | −54.3567 | −1.86114 | −0.930569 | − | 0.366118i | \(-0.880687\pi\) | ||||
−0.930569 | + | 0.366118i | \(0.880687\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.72567 | − | 11.6492i | −0.230013 | − | 0.398395i | ||||
\(856\) | 6.10259 | 0.208582 | ||||||||
\(857\) | −10.5106 | − | 18.2048i | −0.359034 | − | 0.621864i | 0.628766 | − | 0.777595i | \(-0.283560\pi\) |
−0.987800 | + | 0.155730i | \(0.950227\pi\) | |||||||
\(858\) | 2.59375 | − | 12.6707i | 0.0885493 | − | 0.432570i | ||||
\(859\) | −25.6814 | + | 44.4816i | −0.876240 | + | 1.51769i | −0.0208035 | + | 0.999784i | \(0.506622\pi\) |
−0.855436 | + | 0.517908i | \(0.826711\pi\) | |||||||
\(860\) | −0.0273336 | − | 0.0473431i | −0.000932066 | − | 0.00161439i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.6884 | + | 21.9769i | −0.432167 | + | 0.748535i | ||||
\(863\) | −3.55660 | + | 6.16021i | −0.121068 | + | 0.209696i | −0.920189 | − | 0.391474i | \(-0.871965\pi\) |
0.799121 | + | 0.601170i | \(0.205299\pi\) | |||||||
\(864\) | 18.3489 | 0.624241 | ||||||||
\(865\) | 24.4735 | 0.832124 | ||||||||
\(866\) | −19.4577 | + | 33.7018i | −0.661201 | + | 1.14523i | ||||
\(867\) | −3.33193 | + | 5.77107i | −0.113158 | + | 0.195996i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.70143 | + | 2.94696i | 0.0577171 | + | 0.0999689i | ||||
\(870\) | −0.100764 | + | 0.174528i | −0.00341622 | + | 0.00591707i | ||||
\(871\) | 14.1458 | − | 4.71419i | 0.479311 | − | 0.159734i | ||||
\(872\) | 4.23133 | + | 7.32888i | 0.143291 | + | 0.248187i | ||||
\(873\) | 9.83403 | 0.332831 | ||||||||
\(874\) | 13.7062 | + | 23.7399i | 0.463620 | + | 0.803013i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.6518 | 0.359892 | ||||||||
\(877\) | −0.256238 | − | 0.443818i | −0.00865255 | − | 0.0149867i | 0.861667 | − | 0.507475i | \(-0.169421\pi\) |
−0.870319 | + | 0.492488i | \(0.836088\pi\) | |||||||
\(878\) | −18.6187 | −0.628352 | ||||||||
\(879\) | 2.82874 | + | 4.89953i | 0.0954112 | + | 0.165257i | ||||
\(880\) | −14.8917 | − | 25.7933i | −0.502000 | − | 0.869490i | ||||
\(881\) | −18.5464 | − | 32.1232i | −0.624843 | − | 1.08226i | −0.988571 | − | 0.150754i | \(-0.951830\pi\) |
0.363729 | − | 0.931505i | \(-0.381503\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.5667 | −0.523860 | −0.261930 | − | 0.965087i | \(-0.584359\pi\) | ||||
−0.261930 | + | 0.965087i | \(0.584359\pi\) | |||||||
\(884\) | −5.29204 | − | 4.69336i | −0.177990 | − | 0.157855i | ||||
\(885\) | 1.68631 | + | 2.92078i | 0.0566847 | + | 0.0981809i | ||||
\(886\) | 20.1645 | − | 34.9260i | 0.677440 | − | 1.17336i | ||||
\(887\) | −27.5799 | −0.926043 | −0.463022 | − | 0.886347i | \(-0.653235\pi\) | ||||
−0.463022 | + | 0.886347i | \(0.653235\pi\) | |||||||
\(888\) | 1.06158 | − | 1.83871i | 0.0356243 | − | 0.0617030i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.20404 | + | 15.9419i | −0.308520 | + | 0.534372i | ||||
\(891\) | 16.2159 | + | 28.0868i | 0.543254 | + | 0.940944i | ||||
\(892\) | −17.4145 | − | 30.1627i | −0.583079 | − | 1.00992i | ||||
\(893\) | 37.8792 | 1.26758 | ||||||||
\(894\) | 3.20300 | 0.107124 | ||||||||
\(895\) | 0.397374 | + | 0.688272i | 0.0132827 | + | 0.0230064i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.50279 | − | 2.16711i | 0.217122 | − | 0.0723577i | ||||
\(898\) | −17.2895 | + | 29.9463i | −0.576959 | + | 0.999323i | ||||
\(899\) | 0.439466 | − | 0.761178i | 0.0146570 | − | 0.0253867i | ||||
\(900\) | −6.50032 | + | 11.2589i | −0.216677 | + | 0.375296i | ||||
\(901\) | 0.0852637 | + | 0.147681i | 0.00284054 | + | 0.00491997i | ||||
\(902\) | −43.2337 | −1.43952 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.29366 | + | 5.70479i | −0.109546 | + | 0.189738i | ||||
\(905\) | 2.04149 | − | 3.53597i | 0.0678615 | − | 0.117539i | ||||
\(906\) | −1.72985 | −0.0574703 | ||||||||
\(907\) | 22.5236 | − | 39.0119i | 0.747882 | − | 1.29537i | −0.200954 | − | 0.979601i | \(-0.564404\pi\) |
0.948836 | − | 0.315769i | \(-0.102263\pi\) | |||||||
\(908\) | 17.0440 | 0.565625 | ||||||||
\(909\) | 7.26019 | 0.240805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.4678 | 1.17510 | 0.587550 | − | 0.809188i | \(-0.300093\pi\) | ||||
0.587550 | + | 0.809188i | \(0.300093\pi\) | |||||||
\(912\) | −6.39198 | −0.211660 | ||||||||
\(913\) | 35.1898 | − | 60.9505i | 1.16461 | − | 2.01717i | ||||
\(914\) | 34.3379 | 1.13580 | ||||||||
\(915\) | −3.64360 | + | 6.31090i | −0.120454 | + | 0.208632i | ||||
\(916\) | 11.7917 | − | 20.4238i | 0.389608 | − | 0.674820i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.71135 | −0.188503 | ||||||||
\(919\) | −8.68622 | − | 15.0450i | −0.286532 | − | 0.496288i | 0.686447 | − | 0.727179i | \(-0.259169\pi\) |
−0.972980 | + | 0.230891i | \(0.925836\pi\) | |||||||
\(920\) | 2.29706 | − | 3.97862i | 0.0757318 | − | 0.131171i | ||||
\(921\) | 1.42652 | − | 2.47081i | 0.0470056 | − | 0.0814160i | ||||
\(922\) | 28.3686 | − | 49.1359i | 0.934271 | − | 1.61820i | ||||
\(923\) | −34.1024 | + | 11.3649i | −1.12250 | + | 0.374081i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.97613 | + | 17.2792i | 0.328013 | + | 0.568136i | ||||
\(926\) | −33.7412 | −1.10880 | ||||||||
\(927\) | −47.4948 | −1.55993 | ||||||||
\(928\) | −0.616877 | − | 1.06846i | −0.0202500 | − | 0.0350740i | ||||
\(929\) | 5.38001 | + | 9.31845i | 0.176512 | + | 0.305729i | 0.940684 | − | 0.339285i | \(-0.110185\pi\) |
−0.764171 | + | 0.645013i | \(0.776852\pi\) | |||||||
\(930\) | 3.15437 | − | 5.46353i | 0.103436 | − | 0.179156i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 7.57532 | − | 13.1208i | 0.248138 | − | 0.429788i | ||||
\(933\) | −0.876590 | −0.0286983 | ||||||||
\(934\) | 5.55396 | − | 9.61975i | 0.181731 | − | 0.314768i | ||||
\(935\) | 3.89219 | + | 6.74148i | 0.127288 | + | 0.220470i | ||||
\(936\) | 1.43136 | − | 6.99228i | 0.0467853 | − | 0.228550i | ||||
\(937\) | 10.9816 | 0.358755 | 0.179377 | − | 0.983780i | \(-0.442592\pi\) | ||||
0.179377 | + | 0.983780i | \(0.442592\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.01749 | − | 3.49439i | −0.0658383 | − | 0.114035i | ||||
\(940\) | 14.0373 | + | 24.3132i | 0.457845 | + | 0.793011i | ||||
\(941\) | 4.08897 | + | 7.08231i | 0.133297 | + | 0.230877i | 0.924946 | − | 0.380100i | \(-0.124110\pi\) |
−0.791649 | + | 0.610976i | \(0.790777\pi\) | |||||||
\(942\) | 18.0536 | 0.588219 | ||||||||
\(943\) | −11.4564 | − | 19.8430i | −0.373071 | − | 0.646177i | ||||
\(944\) | −24.5890 | −0.800305 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0952365 | − | 0.164954i | −0.00309640 | − | 0.00536313i | ||||
\(947\) | −4.59378 | −0.149278 | −0.0746389 | − | 0.997211i | \(-0.523780\pi\) | ||||
−0.0746389 | + | 0.997211i | \(0.523780\pi\) | |||||||
\(948\) | 0.270636 | + | 0.468756i | 0.00878986 | + | 0.0152245i | ||||
\(949\) | 11.0209 | − | 53.8379i | 0.357753 | − | 1.74765i | ||||
\(950\) | 8.74153 | − | 15.1408i | 0.283613 | − | 0.491231i | ||||
\(951\) | −7.14892 | − | 12.3823i | −0.231820 | − | 0.401524i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.5714 | + | 18.3102i | −0.342442 | + | 0.593126i | −0.984886 | − | 0.173206i | \(-0.944587\pi\) |
0.642444 | + | 0.766333i | \(0.277921\pi\) | |||||||
\(954\) | 0.380474 | − | 0.659000i | 0.0123183 | − | 0.0213359i | ||||
\(955\) | −29.8172 | −0.964863 | ||||||||
\(956\) | 32.0249 | 1.03576 | ||||||||
\(957\) | −0.157712 | + | 0.273165i | −0.00509809 | + | 0.00883016i | ||||
\(958\) | −13.8070 | + | 23.9145i | −0.446085 | + | 0.772641i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.52342 | − | 2.63864i | −0.0491681 | − | 0.0851616i | ||||
\(961\) | 1.74271 | − | 3.01846i | 0.0562164 | − | 0.0973697i | ||||
\(962\) | 36.2419 | + | 32.1419i | 1.16849 | + | 1.03630i | ||||
\(963\) | 12.2270 | + | 21.1779i | 0.394011 | + | 0.682447i | ||||
\(964\) | −11.9255 | −0.384094 | ||||||||
\(965\) | 12.0628 | + | 20.8934i | 0.388316 | + | 0.672582i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.0750 | −1.03146 | −0.515731 | − | 0.856750i | \(-0.672480\pi\) | ||||
−0.515731 | + | 0.856750i | \(0.672480\pi\) | |||||||
\(968\) | −2.91817 | − | 5.05442i | −0.0937936 | − | 0.162455i | ||||
\(969\) | 1.67065 | 0.0536689 | ||||||||
\(970\) | −4.90079 | − | 8.48841i | −0.157355 | − | 0.272546i | ||||
\(971\) | −26.0417 | − | 45.1056i | −0.835719 | − | 1.44751i | −0.893444 | − | 0.449175i | \(-0.851718\pi\) |
0.0577245 | − | 0.998333i | \(-0.481616\pi\) | |||||||
\(972\) | 8.67673 | + | 15.0285i | 0.278306 | + | 0.482041i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 34.2241 | 1.09661 | ||||||||
\(975\) | −3.27064 | − | 2.90063i | −0.104744 | − | 0.0928946i | ||||
\(976\) | −26.5647 | − | 46.0114i | −0.850315 | − | 1.47279i | ||||
\(977\) | −9.62898 | + | 16.6779i | −0.308058 | + | 0.533573i | −0.977938 | − | 0.208897i | \(-0.933013\pi\) |
0.669879 | + | 0.742470i | \(0.266346\pi\) | |||||||
\(978\) | 3.14501 | 0.100566 | ||||||||
\(979\) | −14.4058 | + | 24.9515i | −0.460410 | + | 0.797454i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.9557 | + | 29.3681i | −0.541353 | + | 0.937650i | ||||
\(982\) | −34.5868 | − | 59.9061i | −1.10371 | − | 1.91168i | ||||
\(983\) | −8.03657 | − | 13.9197i | −0.256327 | − | 0.443971i | 0.708928 | − | 0.705280i | \(-0.249179\pi\) |
−0.965255 | + | 0.261310i | \(0.915846\pi\) | |||||||
\(984\) | 1.55502 | 0.0495723 | ||||||||
\(985\) | 29.0700 | 0.926248 | ||||||||
\(986\) | 0.192012 | + | 0.332574i | 0.00611490 | + | 0.0105913i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.82391 | − | 18.6801i | 0.121655 | − | 0.594294i | ||||
\(989\) | 0.0504729 | − | 0.0874216i | 0.00160494 | − | 0.00277985i | ||||
\(990\) | 17.3682 | − | 30.0826i | 0.551998 | − | 0.956088i | ||||
\(991\) | −10.7132 | + | 18.5559i | −0.340317 | + | 0.589447i | −0.984492 | − | 0.175432i | \(-0.943868\pi\) |
0.644174 | + | 0.764879i | \(0.277201\pi\) | |||||||
\(992\) | 19.3111 | + | 33.4478i | 0.613127 | + | 1.06197i | ||||
\(993\) | −8.16876 | −0.259228 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.3984 | + | 18.0106i | −0.329652 | + | 0.570974i | ||||
\(996\) | 5.59743 | − | 9.69504i | 0.177362 | − | 0.307199i | ||||
\(997\) | 16.9537 | 0.536931 | 0.268465 | − | 0.963289i | \(-0.413484\pi\) | ||||
0.268465 | + | 0.963289i | \(0.413484\pi\) | |||||||
\(998\) | 22.5881 | − | 39.1238i | 0.715015 | − | 1.23844i | ||||
\(999\) | 17.5702 | 0.555897 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 637.2.h.l.471.2 | 12 | ||
7.2 | even | 3 | 637.2.f.j.393.5 | 12 | |||
7.3 | odd | 6 | 91.2.g.b.81.5 | yes | 12 | ||
7.4 | even | 3 | 637.2.g.l.263.5 | 12 | |||
7.5 | odd | 6 | 637.2.f.k.393.5 | 12 | |||
7.6 | odd | 2 | 91.2.h.b.16.2 | yes | 12 | ||
13.9 | even | 3 | 637.2.g.l.373.5 | 12 | |||
21.17 | even | 6 | 819.2.n.d.172.2 | 12 | |||
21.20 | even | 2 | 819.2.s.d.289.5 | 12 | |||
91.3 | odd | 6 | 1183.2.e.h.508.5 | 12 | |||
91.9 | even | 3 | 637.2.f.j.295.5 | 12 | |||
91.10 | odd | 6 | 1183.2.e.g.508.2 | 12 | |||
91.16 | even | 3 | 8281.2.a.ca.1.2 | 6 | |||
91.23 | even | 6 | 8281.2.a.cf.1.5 | 6 | |||
91.48 | odd | 6 | 91.2.g.b.9.5 | ✓ | 12 | ||
91.55 | odd | 6 | 1183.2.e.h.170.5 | 12 | |||
91.61 | odd | 6 | 637.2.f.k.295.5 | 12 | |||
91.62 | odd | 6 | 1183.2.e.g.170.2 | 12 | |||
91.68 | odd | 6 | 8281.2.a.bz.1.2 | 6 | |||
91.74 | even | 3 | inner | 637.2.h.l.165.2 | 12 | ||
91.75 | odd | 6 | 8281.2.a.ce.1.5 | 6 | |||
91.87 | odd | 6 | 91.2.h.b.74.2 | yes | 12 | ||
273.230 | even | 6 | 819.2.n.d.100.2 | 12 | |||
273.269 | even | 6 | 819.2.s.d.802.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.5 | ✓ | 12 | 91.48 | odd | 6 | ||
91.2.g.b.81.5 | yes | 12 | 7.3 | odd | 6 | ||
91.2.h.b.16.2 | yes | 12 | 7.6 | odd | 2 | ||
91.2.h.b.74.2 | yes | 12 | 91.87 | odd | 6 | ||
637.2.f.j.295.5 | 12 | 91.9 | even | 3 | |||
637.2.f.j.393.5 | 12 | 7.2 | even | 3 | |||
637.2.f.k.295.5 | 12 | 91.61 | odd | 6 | |||
637.2.f.k.393.5 | 12 | 7.5 | odd | 6 | |||
637.2.g.l.263.5 | 12 | 7.4 | even | 3 | |||
637.2.g.l.373.5 | 12 | 13.9 | even | 3 | |||
637.2.h.l.165.2 | 12 | 91.74 | even | 3 | inner | ||
637.2.h.l.471.2 | 12 | 1.1 | even | 1 | trivial | ||
819.2.n.d.100.2 | 12 | 273.230 | even | 6 | |||
819.2.n.d.172.2 | 12 | 21.17 | even | 6 | |||
819.2.s.d.289.5 | 12 | 21.20 | even | 2 | |||
819.2.s.d.802.5 | 12 | 273.269 | even | 6 | |||
1183.2.e.g.170.2 | 12 | 91.62 | odd | 6 | |||
1183.2.e.g.508.2 | 12 | 91.10 | odd | 6 | |||
1183.2.e.h.170.5 | 12 | 91.55 | odd | 6 | |||
1183.2.e.h.508.5 | 12 | 91.3 | odd | 6 | |||
8281.2.a.bz.1.2 | 6 | 91.68 | odd | 6 | |||
8281.2.a.ca.1.2 | 6 | 91.16 | even | 3 | |||
8281.2.a.ce.1.5 | 6 | 91.75 | odd | 6 | |||
8281.2.a.cf.1.5 | 6 | 91.23 | even | 6 |