Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(37,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.n (of order \(6\), 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: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + x^{14} + 2 x^{12} - 4 x^{11} - 8 x^{9} + 4 x^{8} - 16 x^{7} - 32 x^{5} + 32 x^{4} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(0.820200 + 1.15207i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.37 |
Dual form | 216.2.n.b.181.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.587625 | − | 1.28635i | −0.415513 | − | 0.909587i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.30939 | + | 1.51178i | −0.654697 | + | 0.755891i | ||||
\(5\) | 1.97542 | + | 1.14051i | 0.883437 | + | 0.510052i | 0.871790 | − | 0.489880i | \(-0.162959\pi\) |
0.0116467 | + | 0.999932i | \(0.496293\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.907824 | − | 1.57240i | −0.343125 | − | 0.594311i | 0.641886 | − | 0.766800i | \(-0.278152\pi\) |
−0.985011 | + | 0.172490i | \(0.944819\pi\) | |||||||
\(8\) | 2.71411 | + | 0.795980i | 0.959584 | + | 0.281421i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.306290 | − | 3.21128i | 0.0968573 | − | 1.01550i | ||||
\(11\) | 4.24153 | − | 2.44885i | 1.27887 | − | 0.738355i | 0.302228 | − | 0.953236i | \(-0.402270\pi\) |
0.976640 | + | 0.214880i | \(0.0689362\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00895 | + | 2.31457i | 1.11188 | + | 0.641946i | 0.939317 | − | 0.343052i | \(-0.111461\pi\) |
0.172567 | + | 0.984998i | \(0.444794\pi\) | |||||||
\(14\) | −1.48919 | + | 2.09176i | −0.398004 | + | 0.559046i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.570971 | − | 3.95904i | −0.142743 | − | 0.989760i | ||||
\(17\) | −1.92788 | −0.467579 | −0.233790 | − | 0.972287i | \(-0.575113\pi\) | ||||
−0.233790 | + | 0.972287i | \(0.575113\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.12907i | − | 0.488442i | −0.969720 | − | 0.244221i | \(-0.921468\pi\) | ||
0.969720 | − | 0.244221i | \(-0.0785322\pi\) | |||||||
\(20\) | −4.31082 | + | 1.49303i | −0.963928 | + | 0.333852i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.64250 | − | 4.01709i | −1.20299 | − | 0.856446i | ||||
\(23\) | 1.15765 | − | 2.00511i | 0.241387 | − | 0.418094i | −0.719723 | − | 0.694261i | \(-0.755731\pi\) |
0.961109 | + | 0.276168i | \(0.0890645\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.101535 | + | 0.175863i | 0.0203069 | + | 0.0351726i | ||||
\(26\) | 0.621589 | − | 6.51702i | 0.121904 | − | 1.27809i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.56582 | + | 0.686457i | 0.673877 | + | 0.129728i | ||||
\(29\) | −3.16440 | + | 1.82697i | −0.587615 | + | 0.339260i | −0.764154 | − | 0.645034i | \(-0.776843\pi\) |
0.176539 | + | 0.984294i | \(0.443510\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.65800 | + | 4.60379i | −0.477391 | + | 0.826865i | −0.999664 | − | 0.0259130i | \(-0.991751\pi\) |
0.522273 | + | 0.852778i | \(0.325084\pi\) | |||||||
\(32\) | −4.75719 | + | 3.06090i | −0.840961 | + | 0.541095i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.13287 | + | 2.47993i | 0.194285 | + | 0.425304i | ||||
\(35\) | − | 4.14154i | − | 0.700048i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.98438i | 1.31262i | 0.754489 | + | 0.656312i | \(0.227885\pi\) | ||||
−0.754489 | + | 0.656312i | \(0.772115\pi\) | |||||||
\(38\) | −2.73873 | + | 1.25109i | −0.444280 | + | 0.202954i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.45370 | + | 4.66788i | 0.704192 | + | 0.738056i | ||||
\(41\) | 2.36240 | − | 4.09180i | 0.368946 | − | 0.639033i | −0.620455 | − | 0.784242i | \(-0.713052\pi\) |
0.989401 | + | 0.145209i | \(0.0463855\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.20800 | + | 1.27479i | −0.336717 | + | 0.194404i | −0.658819 | − | 0.752301i | \(-0.728944\pi\) |
0.322102 | + | 0.946705i | \(0.395610\pi\) | |||||||
\(44\) | −1.85171 | + | 9.61877i | −0.279156 | + | 1.45008i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.25953 | − | 0.310892i | −0.480592 | − | 0.0458386i | ||||
\(47\) | 2.02005 | + | 3.49884i | 0.294655 | + | 0.510358i | 0.974905 | − | 0.222623i | \(-0.0714619\pi\) |
−0.680249 | + | 0.732981i | \(0.738129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.85171 | − | 3.20726i | 0.264530 | − | 0.458179i | ||||
\(50\) | 0.166557 | − | 0.233951i | 0.0235548 | − | 0.0330856i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −8.74843 | + | 3.02998i | −1.21319 | + | 0.420182i | ||||
\(53\) | 8.95958i | 1.23069i | 0.788257 | + | 0.615347i | \(0.210984\pi\) | ||||
−0.788257 | + | 0.615347i | \(0.789016\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.1718 | 1.50640 | ||||||||
\(56\) | −1.21234 | − | 4.99028i | −0.162006 | − | 0.666854i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.20960 | + | 2.99696i | 0.552748 | + | 0.393520i | ||||
\(59\) | −3.05255 | − | 1.76239i | −0.397408 | − | 0.229444i | 0.287957 | − | 0.957643i | \(-0.407024\pi\) |
−0.685365 | + | 0.728200i | \(0.740357\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.71675 | − | 0.991165i | 0.219807 | − | 0.126906i | −0.386054 | − | 0.922476i | \(-0.626162\pi\) |
0.605861 | + | 0.795571i | \(0.292829\pi\) | |||||||
\(62\) | 7.48399 | + | 0.713818i | 0.950468 | + | 0.0906550i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.73283 | + | 4.32076i | 0.841604 | + | 0.540095i | ||||
\(65\) | 5.27959 | + | 9.14451i | 0.654852 | + | 1.13424i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.72723 | − | 4.46132i | −0.944031 | − | 0.545036i | −0.0528093 | − | 0.998605i | \(-0.516818\pi\) |
−0.891222 | + | 0.453568i | \(0.850151\pi\) | |||||||
\(68\) | 2.52435 | − | 2.91453i | 0.306123 | − | 0.353439i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.32747 | + | 2.43367i | −0.636754 | + | 0.290879i | ||||
\(71\) | −13.3561 | −1.58508 | −0.792539 | − | 0.609821i | \(-0.791241\pi\) | ||||
−0.792539 | + | 0.609821i | \(0.791241\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.5592 | −1.35290 | −0.676450 | − | 0.736489i | \(-0.736482\pi\) | ||||
−0.676450 | + | 0.736489i | \(0.736482\pi\) | |||||||
\(74\) | 10.2707 | − | 4.69182i | 1.19395 | − | 0.545413i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.21869 | + | 2.78779i | 0.369209 | + | 0.319782i | ||||
\(77\) | −7.70112 | − | 4.44625i | −0.877625 | − | 0.506697i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.97330 | − | 8.61401i | −0.559540 | − | 0.969151i | −0.997535 | − | 0.0701739i | \(-0.977645\pi\) |
0.437995 | − | 0.898977i | \(-0.355689\pi\) | |||||||
\(80\) | 3.38742 | − | 8.47198i | 0.378725 | − | 0.947196i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.65170 | − | 0.634435i | −0.734558 | − | 0.0700616i | ||||
\(83\) | −3.12153 | + | 1.80221i | −0.342632 | + | 0.197819i | −0.661435 | − | 0.750002i | \(-0.730052\pi\) |
0.318803 | + | 0.947821i | \(0.396719\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.80838 | − | 2.19877i | −0.413077 | − | 0.238490i | ||||
\(86\) | 2.93730 | + | 2.09116i | 0.316737 | + | 0.225496i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.4612 | − | 3.27028i | 1.43497 | − | 0.348613i | ||||
\(89\) | −2.49965 | −0.264962 | −0.132481 | − | 0.991186i | \(-0.542294\pi\) | ||||
−0.132481 | + | 0.991186i | \(0.542294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 8.40489i | − | 0.881072i | ||||||
\(92\) | 1.51547 | + | 4.37559i | 0.157998 | + | 0.456187i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.31370 | − | 4.65450i | 0.341782 | − | 0.480075i | ||||
\(95\) | 2.42823 | − | 4.20582i | 0.249131 | − | 0.431508i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.99370 | + | 12.1134i | 0.710103 | + | 1.22993i | 0.964818 | + | 0.262918i | \(0.0846849\pi\) |
−0.254715 | + | 0.967016i | \(0.581982\pi\) | |||||||
\(98\) | −5.21376 | − | 0.497285i | −0.526670 | − | 0.0502334i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.398816 | − | 0.0767760i | −0.0398816 | − | 0.00767760i | ||||
\(101\) | 1.13087 | − | 0.652911i | 0.112526 | − | 0.0649671i | −0.442681 | − | 0.896679i | \(-0.645972\pi\) |
0.555207 | + | 0.831712i | \(0.312639\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.22312 | + | 5.58261i | −0.317584 | + | 0.550071i | −0.979983 | − | 0.199080i | \(-0.936205\pi\) |
0.662400 | + | 0.749151i | \(0.269538\pi\) | |||||||
\(104\) | 9.03840 | + | 9.47305i | 0.886288 | + | 0.928909i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.5252 | − | 5.26487i | 1.11942 | − | 0.511370i | ||||
\(107\) | 3.10427i | 0.300101i | 0.988678 | + | 0.150051i | \(0.0479437\pi\) | ||||
−0.988678 | + | 0.150051i | \(0.952056\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 18.0837i | − | 1.73210i | −0.499955 | − | 0.866051i | \(-0.666650\pi\) | ||
0.499955 | − | 0.866051i | \(-0.333350\pi\) | |||||||
\(110\) | −6.56480 | − | 14.3708i | −0.625929 | − | 1.37020i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −5.70684 | + | 4.49191i | −0.539246 | + | 0.424445i | ||||
\(113\) | 1.41718 | − | 2.45463i | 0.133317 | − | 0.230913i | −0.791636 | − | 0.610993i | \(-0.790770\pi\) |
0.924953 | + | 0.380080i | \(0.124104\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.57370 | − | 2.64063i | 0.426500 | − | 0.246240i | ||||
\(116\) | 1.38147 | − | 7.17611i | 0.128267 | − | 0.666285i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.473298 | + | 4.96227i | −0.0435706 | + | 0.456814i | ||||
\(119\) | 1.75018 | + | 3.03139i | 0.160438 | + | 0.277887i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.49370 | − | 11.2474i | 0.590337 | − | 1.02249i | ||||
\(122\) | −2.28379 | − | 1.62591i | −0.206764 | − | 0.147203i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.47956 | − | 10.0465i | −0.312474 | − | 0.902202i | ||||
\(125\) | − | 10.9419i | − | 0.978674i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.44962 | −0.661047 | −0.330523 | − | 0.943798i | \(-0.607225\pi\) | ||||
−0.330523 | + | 0.943798i | \(0.607225\pi\) | |||||||
\(128\) | 1.60163 | − | 11.1998i | 0.141566 | − | 0.989929i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.66063 | − | 12.1649i | 0.759588 | − | 1.06694i | ||||
\(131\) | 3.12153 | + | 1.80221i | 0.272729 | + | 0.157460i | 0.630127 | − | 0.776492i | \(-0.283003\pi\) |
−0.357398 | + | 0.933952i | \(0.616336\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.34774 | + | 1.93282i | −0.290286 | + | 0.167597i | ||||
\(134\) | −1.19811 | + | 12.5615i | −0.103501 | + | 1.08515i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.23248 | − | 1.53455i | −0.448682 | − | 0.131587i | ||||
\(137\) | −5.88147 | − | 10.1870i | −0.502488 | − | 0.870335i | −0.999996 | − | 0.00287543i | \(-0.999085\pi\) |
0.497508 | − | 0.867460i | \(-0.334249\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.0400 | + | 6.37395i | 0.936400 | + | 0.540631i | 0.888830 | − | 0.458237i | \(-0.151519\pi\) |
0.0475703 | + | 0.998868i | \(0.484852\pi\) | |||||||
\(140\) | 6.26110 | + | 5.42291i | 0.529160 | + | 0.458319i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.84838 | + | 17.1806i | 0.658621 | + | 1.44177i | ||||
\(143\) | 22.6721 | 1.89594 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.33472 | −0.692161 | ||||||||
\(146\) | 6.79246 | + | 14.8692i | 0.562148 | + | 1.23058i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.0706 | − | 10.4547i | −0.992201 | − | 0.859372i | ||||
\(149\) | 6.59790 | + | 3.80930i | 0.540521 | + | 0.312070i | 0.745290 | − | 0.666740i | \(-0.232311\pi\) |
−0.204769 | + | 0.978810i | \(0.565644\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.26988 | + | 3.93155i | 0.184720 | + | 0.319945i | 0.943482 | − | 0.331423i | \(-0.107529\pi\) |
−0.758762 | + | 0.651368i | \(0.774195\pi\) | |||||||
\(152\) | 1.69470 | − | 5.77854i | 0.137458 | − | 0.468701i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.19406 | + | 12.5191i | −0.0962201 | + | 1.00882i | ||||
\(155\) | −10.5014 | + | 6.06296i | −0.843489 | + | 0.486989i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4105 | − | 6.58787i | −0.910659 | − | 0.525769i | −0.0300161 | − | 0.999549i | \(-0.509556\pi\) |
−0.880643 | + | 0.473780i | \(0.842889\pi\) | |||||||
\(158\) | −8.15820 | + | 11.4592i | −0.649031 | + | 0.911645i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.8885 | + | 0.620936i | −1.01892 | + | 0.0490893i | ||||
\(161\) | −4.20377 | −0.331303 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.5911i | 1.61282i | 0.591358 | + | 0.806409i | \(0.298592\pi\) | ||||
−0.591358 | + | 0.806409i | \(0.701408\pi\) | |||||||
\(164\) | 3.09260 | + | 8.92923i | 0.241491 | + | 0.697256i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.15257 | + | 2.95635i | 0.322302 | + | 0.229457i | ||||
\(167\) | −2.53912 | + | 4.39789i | −0.196483 | + | 0.340319i | −0.947386 | − | 0.320094i | \(-0.896285\pi\) |
0.750903 | + | 0.660413i | \(0.229619\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.21446 | + | 7.29967i | 0.324190 | + | 0.561513i | ||||
\(170\) | −0.590490 | + | 6.19096i | −0.0452885 | + | 0.474825i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.963939 | − | 5.00722i | 0.0734997 | − | 0.381797i | ||||
\(173\) | 11.0398 | − | 6.37385i | 0.839343 | − | 0.484595i | −0.0176977 | − | 0.999843i | \(-0.505634\pi\) |
0.857041 | + | 0.515248i | \(0.172300\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.184351 | − | 0.319306i | 0.0139356 | − | 0.0241372i | ||||
\(176\) | −12.1169 | − | 15.3942i | −0.913344 | − | 1.16038i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.46886 | + | 3.21543i | 0.110095 | + | 0.241006i | ||||
\(179\) | 8.82019i | 0.659252i | 0.944112 | + | 0.329626i | \(0.106923\pi\) | ||||
−0.944112 | + | 0.329626i | \(0.893077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.4369i | 1.14741i | 0.819061 | + | 0.573707i | \(0.194495\pi\) | ||||
−0.819061 | + | 0.573707i | \(0.805505\pi\) | |||||||
\(182\) | −10.8116 | + | 4.93892i | −0.801412 | + | 0.366097i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.73802 | − | 4.52063i | 0.349291 | − | 0.333265i | ||||
\(185\) | −9.10628 | + | 15.7725i | −0.669507 | + | 1.15962i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.17715 | + | 4.72108i | −0.597972 | + | 0.345239i | ||||
\(188\) | −7.93453 | − | 1.52748i | −0.578685 | − | 0.111403i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.83704 | − | 0.652112i | −0.496011 | − | 0.0473092i | ||||
\(191\) | −4.81698 | − | 8.34326i | −0.348545 | − | 0.603697i | 0.637446 | − | 0.770495i | \(-0.279991\pi\) |
−0.985991 | + | 0.166797i | \(0.946657\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.49335 | − | 6.05066i | 0.251457 | − | 0.435536i | −0.712470 | − | 0.701702i | \(-0.752424\pi\) |
0.963927 | + | 0.266166i | \(0.0857570\pi\) | |||||||
\(194\) | 11.4725 | − | 16.1145i | 0.823675 | − | 1.15695i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.42405 | + | 6.99894i | 0.173147 | + | 0.499925i | ||||
\(197\) | − | 4.31842i | − | 0.307675i | −0.988096 | − | 0.153837i | \(-0.950837\pi\) | ||
0.988096 | − | 0.153837i | \(-0.0491632\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.90649 | 0.418700 | 0.209350 | − | 0.977841i | \(-0.432865\pi\) | ||||
0.209350 | + | 0.977841i | \(0.432865\pi\) | |||||||
\(200\) | 0.135593 | + | 0.558132i | 0.00958787 | + | 0.0394659i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.50440 | − | 1.07103i | −0.105849 | − | 0.0753577i | ||||
\(203\) | 5.74544 | + | 3.31713i | 0.403251 | + | 0.232817i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.33350 | − | 5.38870i | 0.651880 | − | 0.376363i | ||||
\(206\) | 9.07518 | + | 0.865585i | 0.632298 | + | 0.0603082i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.87447 | − | 17.1932i | 0.476659 | − | 1.19213i | ||||
\(209\) | −5.21376 | − | 9.03050i | −0.360644 | − | 0.624653i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.8781 | + | 9.16723i | 1.09309 | + | 0.631098i | 0.934399 | − | 0.356229i | \(-0.115938\pi\) |
0.158696 | + | 0.987328i | \(0.449271\pi\) | |||||||
\(212\) | −13.5449 | − | 11.7316i | −0.930270 | − | 0.805732i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.99318 | − | 1.82415i | 0.272968 | − | 0.124696i | ||||
\(215\) | −5.81565 | −0.396624 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.65199 | 0.655220 | ||||||||
\(218\) | −23.2619 | + | 10.6264i | −1.57550 | + | 0.719712i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −14.6282 | + | 16.8893i | −0.986236 | + | 1.13867i | ||||
\(221\) | −7.72877 | − | 4.46221i | −0.519893 | − | 0.300161i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.63263 | − | 4.55986i | −0.176294 | − | 0.305350i | 0.764314 | − | 0.644844i | \(-0.223078\pi\) |
−0.940608 | + | 0.339494i | \(0.889744\pi\) | |||||||
\(224\) | 9.13165 | + | 4.70145i | 0.610134 | + | 0.314129i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.99029 | − | 0.380591i | −0.265430 | − | 0.0253166i | ||||
\(227\) | 1.53638 | − | 0.887027i | 0.101973 | − | 0.0588741i | −0.448146 | − | 0.893960i | \(-0.647916\pi\) |
0.550119 | + | 0.835086i | \(0.314582\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.30687 | + | 1.90922i | 0.218524 | + | 0.126165i | 0.605267 | − | 0.796023i | \(-0.293066\pi\) |
−0.386742 | + | 0.922188i | \(0.626400\pi\) | |||||||
\(230\) | −6.08439 | − | 4.33168i | −0.401193 | − | 0.285623i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.0428 | + | 2.43980i | −0.659341 | + | 0.160181i | ||||
\(233\) | 20.3207 | 1.33125 | 0.665627 | − | 0.746284i | \(-0.268164\pi\) | ||||
0.665627 | + | 0.746284i | \(0.268164\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.21558i | 0.601158i | ||||||||
\(236\) | 6.66134 | − | 2.30713i | 0.433616 | − | 0.150181i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.87099 | − | 4.03266i | 0.186098 | − | 0.261398i | ||||
\(239\) | −8.69811 | + | 15.0656i | −0.562634 | + | 0.974510i | 0.434632 | + | 0.900608i | \(0.356879\pi\) |
−0.997266 | + | 0.0739020i | \(0.976455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.85611 | − | 11.8751i | −0.441641 | − | 0.764944i | 0.556171 | − | 0.831068i | \(-0.312270\pi\) |
−0.997811 | + | 0.0661240i | \(0.978937\pi\) | |||||||
\(242\) | −18.2840 | − | 1.74391i | −1.17534 | − | 0.112103i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.749475 | + | 3.89317i | −0.0479802 | + | 0.249235i | ||||
\(245\) | 7.31583 | − | 4.22379i | 0.467391 | − | 0.269848i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.92788 | − | 8.53534i | 0.313553 | − | 0.543090i | ||||
\(248\) | −10.8786 | + | 10.3795i | −0.690794 | + | 0.659099i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.0751 | + | 6.42974i | −0.890190 | + | 0.406652i | ||||
\(251\) | 4.50751i | 0.284512i | 0.989830 | + | 0.142256i | \(0.0454356\pi\) | ||||
−0.989830 | + | 0.142256i | \(0.954564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 11.3396i | − | 0.712916i | ||||||
\(254\) | 4.37758 | + | 9.58282i | 0.274674 | + | 0.601280i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.3480 | + | 4.52100i | −0.959249 | + | 0.282562i | ||||
\(257\) | 4.11258 | − | 7.12320i | 0.256536 | − | 0.444333i | −0.708776 | − | 0.705434i | \(-0.750752\pi\) |
0.965311 | + | 0.261101i | \(0.0840856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.5546 | − | 7.24842i | 0.780106 | − | 0.450395i | ||||
\(260\) | −20.7376 | − | 3.99219i | −1.28609 | − | 0.247585i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.483993 | − | 5.07440i | 0.0299012 | − | 0.313498i | ||||
\(263\) | −2.51376 | − | 4.35395i | −0.155005 | − | 0.268476i | 0.778056 | − | 0.628195i | \(-0.216206\pi\) |
−0.933061 | + | 0.359719i | \(0.882873\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.2185 | + | 17.6990i | −0.627718 | + | 1.08724i | ||||
\(266\) | 4.45350 | + | 3.17060i | 0.273062 | + | 0.194402i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.8625 | − | 5.84026i | 1.03004 | − | 0.356751i | ||||
\(269\) | − | 23.1577i | − | 1.41195i | −0.708236 | − | 0.705976i | \(-0.750509\pi\) | ||
0.708236 | − | 0.705976i | \(-0.249491\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.9367 | 1.27181 | 0.635906 | − | 0.771766i | \(-0.280627\pi\) | ||||
0.635906 | + | 0.771766i | \(0.280627\pi\) | |||||||
\(272\) | 1.10076 | + | 7.63255i | 0.0667436 | + | 0.462791i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.64797 | + | 13.5518i | −0.582855 | + | 0.818693i | ||||
\(275\) | 0.861323 | + | 0.497285i | 0.0519398 | + | 0.0299874i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.2687 | + | 11.1248i | −1.15775 | + | 0.668425i | −0.950763 | − | 0.309920i | \(-0.899698\pi\) |
−0.206983 | + | 0.978345i | \(0.566364\pi\) | |||||||
\(278\) | 1.71175 | − | 17.9468i | 0.102664 | − | 1.07638i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.29658 | − | 11.2406i | 0.197008 | − | 0.671755i | ||||
\(281\) | 9.28029 | + | 16.0739i | 0.553616 | + | 0.958890i | 0.998010 | + | 0.0630590i | \(0.0200856\pi\) |
−0.444394 | + | 0.895831i | \(0.646581\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.75962 | − | 1.01592i | −0.104599 | − | 0.0603901i | 0.446788 | − | 0.894640i | \(-0.352568\pi\) |
−0.551387 | + | 0.834250i | \(0.685901\pi\) | |||||||
\(284\) | 17.4884 | − | 20.1915i | 1.03775 | − | 1.19815i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −13.3227 | − | 29.1643i | −0.787787 | − | 1.72452i | ||||
\(287\) | −8.57859 | −0.506378 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2833 | −0.781370 | ||||||||
\(290\) | 4.89768 | + | 10.7214i | 0.287602 | + | 0.629580i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.1355 | − | 17.4750i | 0.885739 | − | 1.02264i | ||||
\(293\) | 29.5484 | + | 17.0598i | 1.72623 | + | 0.996642i | 0.904057 | + | 0.427411i | \(0.140574\pi\) |
0.822178 | + | 0.569231i | \(0.192759\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.02005 | − | 6.96294i | −0.234057 | − | 0.405398i | ||||
\(296\) | −6.35541 | + | 21.6705i | −0.369401 | + | 1.25957i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.02300 | − | 10.7256i | 0.0592611 | − | 0.621320i | ||||
\(299\) | 9.28192 | − | 5.35892i | 0.536787 | − | 0.309914i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00895 | + | 2.31457i | 0.231072 | + | 0.133410i | ||||
\(302\) | 3.72351 | − | 5.23013i | 0.214264 | − | 0.300960i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.42907 | + | 1.21564i | −0.483440 | + | 0.0697216i | ||||
\(305\) | 4.52174 | 0.258914 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.77588i | − | 0.272574i | −0.990669 | − | 0.136287i | \(-0.956483\pi\) | ||
0.990669 | − | 0.136287i | \(-0.0435169\pi\) | |||||||
\(308\) | 16.8056 | − | 5.82053i | 0.957586 | − | 0.331656i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.9699 | + | 9.94568i | 0.793440 | + | 0.564876i | ||||
\(311\) | 11.1771 | − | 19.3592i | 0.633793 | − | 1.09776i | −0.352976 | − | 0.935632i | \(-0.614830\pi\) |
0.986769 | − | 0.162130i | \(-0.0518364\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.22411 | + | 2.12022i | 0.0691907 | + | 0.119842i | 0.898545 | − | 0.438881i | \(-0.144625\pi\) |
−0.829355 | + | 0.558723i | \(0.811292\pi\) | |||||||
\(314\) | −1.76920 | + | 18.5491i | −0.0998420 | + | 1.04679i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 19.5345 | + | 3.76059i | 1.09890 | + | 0.211550i | ||||
\(317\) | −14.2886 | + | 8.24953i | −0.802528 | + | 0.463340i | −0.844354 | − | 0.535785i | \(-0.820016\pi\) |
0.0418263 | + | 0.999125i | \(0.486682\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.94793 | + | 15.4983i | −0.500988 | + | 0.867737i | ||||
\(320\) | 8.37232 | + | 16.2142i | 0.468027 | + | 0.906402i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.47024 | + | 5.40752i | 0.137661 | + | 0.301349i | ||||
\(323\) | 4.10459i | 0.228385i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.940035i | 0.0521438i | ||||||||
\(326\) | 26.4874 | − | 12.0998i | 1.46700 | − | 0.670148i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.66883 | − | 9.22520i | 0.533872 | − | 0.509376i | ||||
\(329\) | 3.66771 | − | 6.35266i | 0.202207 | − | 0.350233i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.329200 | − | 0.190064i | 0.0180945 | − | 0.0104469i | −0.490925 | − | 0.871202i | \(-0.663341\pi\) |
0.509020 | + | 0.860755i | \(0.330008\pi\) | |||||||
\(332\) | 1.36275 | − | 7.07888i | 0.0747909 | − | 0.388504i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.14928 | + | 0.681893i | 0.391191 | + | 0.0373115i | ||||
\(335\) | −10.1764 | − | 17.6260i | −0.555994 | − | 0.963010i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.51872 | + | 4.36255i | −0.137203 | + | 0.237643i | −0.926437 | − | 0.376450i | \(-0.877145\pi\) |
0.789234 | + | 0.614093i | \(0.210478\pi\) | |||||||
\(338\) | 6.91341 | − | 9.71074i | 0.376040 | − | 0.528195i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.31073 | − | 2.87838i | 0.450713 | − | 0.156102i | ||||
\(341\) | 26.0361i | 1.40994i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.4337 | −1.04932 | ||||||||
\(344\) | −7.00747 | + | 1.70240i | −0.377817 | + | 0.0917873i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.6863 | − | 10.4557i | −0.789540 | − | 0.562100i | ||||
\(347\) | −8.40337 | − | 4.85169i | −0.451116 | − | 0.260452i | 0.257185 | − | 0.966362i | \(-0.417205\pi\) |
−0.708302 | + | 0.705910i | \(0.750538\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.1239 | − | 15.0827i | 1.39838 | − | 0.807356i | 0.404158 | − | 0.914689i | \(-0.367564\pi\) |
0.994223 | + | 0.107333i | \(0.0342312\pi\) | |||||||
\(350\) | −0.519068 | − | 0.0495084i | −0.0277454 | − | 0.00264633i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.6821 | + | 24.6325i | −0.675958 | + | 1.31292i | ||||
\(353\) | −13.2376 | − | 22.9282i | −0.704565 | − | 1.22034i | −0.966848 | − | 0.255352i | \(-0.917809\pi\) |
0.262283 | − | 0.964991i | \(-0.415525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.3840 | − | 15.2328i | −1.40032 | − | 0.808473i | ||||
\(356\) | 3.27303 | − | 3.77893i | 0.173470 | − | 0.200283i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.3458 | − | 5.18296i | 0.599647 | − | 0.273928i | ||||
\(359\) | 23.4619 | 1.23827 | 0.619135 | − | 0.785285i | \(-0.287483\pi\) | ||||
0.619135 | + | 0.785285i | \(0.287483\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4671 | 0.761424 | ||||||||
\(362\) | 19.8572 | − | 9.07108i | 1.04367 | − | 0.476766i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.7064 | + | 11.0053i | 0.665995 | + | 0.576835i | ||||
\(365\) | −22.8343 | − | 13.1834i | −1.19520 | − | 0.690050i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.62599 | + | 16.6727i | 0.502472 | + | 0.870308i | 0.999996 | + | 0.00285720i | \(0.000909476\pi\) |
−0.497524 | + | 0.867450i | \(0.665757\pi\) | |||||||
\(368\) | −8.59928 | − | 3.43832i | −0.448269 | − | 0.179235i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 25.6401 | + | 2.44553i | 1.33296 | + | 0.127137i | ||||
\(371\) | 14.0880 | − | 8.13373i | 0.731414 | − | 0.422282i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.09206 | + | 5.24930i | 0.470769 | + | 0.271799i | 0.716562 | − | 0.697524i | \(-0.245715\pi\) |
−0.245793 | + | 0.969322i | \(0.579048\pi\) | |||||||
\(374\) | 10.8781 | + | 7.74446i | 0.562491 | + | 0.400456i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.69765 | + | 11.1042i | 0.139121 | + | 0.572653i | ||||
\(377\) | −16.9146 | −0.871145 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 35.5203i | − | 1.82455i | −0.409574 | − | 0.912277i | \(-0.634323\pi\) | ||
0.409574 | − | 0.912277i | \(-0.365677\pi\) | |||||||
\(380\) | 3.17877 | + | 9.17802i | 0.163067 | + | 0.470823i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.90178 | + | 11.0990i | −0.404290 | + | 0.567876i | ||||
\(383\) | −18.0395 | + | 31.2453i | −0.921774 | + | 1.59656i | −0.125105 | + | 0.992144i | \(0.539927\pi\) |
−0.796669 | + | 0.604416i | \(0.793407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.1420 | − | 17.5664i | −0.516884 | − | 0.895269i | ||||
\(386\) | −9.83605 | − | 0.938156i | −0.500642 | − | 0.0477509i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.4704 | − | 5.28833i | −1.39460 | − | 0.268474i | ||||
\(389\) | −17.5243 | + | 10.1177i | −0.888519 | + | 0.512987i | −0.873458 | − | 0.486900i | \(-0.838128\pi\) |
−0.0150612 | + | 0.999887i | \(0.504794\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.23181 | + | 3.86560i | −0.112867 | + | 0.195492i | ||||
\(392\) | 7.57866 | − | 7.23093i | 0.382780 | − | 0.365217i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.55500 | + | 2.53761i | −0.279857 | + | 0.127843i | ||||
\(395\) | − | 22.6884i | − | 1.14158i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.99499i | − | 0.200503i | −0.994962 | − | 0.100251i | \(-0.968035\pi\) | ||
0.994962 | − | 0.100251i | \(-0.0319647\pi\) | |||||||
\(398\) | −3.47080 | − | 7.59781i | −0.173975 | − | 0.380844i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.638275 | − | 0.502392i | 0.0319138 | − | 0.0251196i | ||||
\(401\) | −14.0124 | + | 24.2702i | −0.699747 | + | 1.21200i | 0.268807 | + | 0.963194i | \(0.413371\pi\) |
−0.968554 | + | 0.248803i | \(0.919963\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −21.3116 | + | 12.3042i | −1.06161 | + | 0.612918i | ||||
\(404\) | −0.493702 | + | 2.56455i | −0.0245626 | + | 0.127591i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.890832 | − | 9.33988i | 0.0442112 | − | 0.463531i | ||||
\(407\) | 19.5525 | + | 33.8660i | 0.969183 | + | 1.67867i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.22481 | − | 14.2458i | 0.406691 | − | 0.704409i | −0.587826 | − | 0.808987i | \(-0.700016\pi\) |
0.994517 | + | 0.104579i | \(0.0333494\pi\) | |||||||
\(410\) | −12.4164 | − | 8.83962i | −0.613200 | − | 0.436558i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.21936 | − | 12.1825i | −0.207873 | − | 0.600189i | ||||
\(413\) | 6.39976i | 0.314912i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.22179 | −0.403592 | ||||||||
\(416\) | −26.1560 | + | 1.26014i | −1.28240 | + | 0.0617832i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.55266 | + | 12.0133i | −0.418324 | + | 0.587588i | ||||
\(419\) | −20.5573 | − | 11.8688i | −1.00429 | − | 0.579827i | −0.0947752 | − | 0.995499i | \(-0.530213\pi\) |
−0.909515 | + | 0.415672i | \(0.863547\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.9420 | + | 14.9776i | −1.26433 | + | 0.729963i | −0.973910 | − | 0.226935i | \(-0.927130\pi\) |
−0.290424 | + | 0.956898i | \(0.593796\pi\) | |||||||
\(422\) | 2.46190 | − | 25.8117i | 0.119844 | − | 1.25649i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.13165 | + | 24.3173i | −0.346343 | + | 1.18095i | ||||
\(425\) | −0.195746 | − | 0.339043i | −0.00949509 | − | 0.0164460i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.11701 | − | 1.79961i | −0.150843 | − | 0.0870891i | ||||
\(428\) | −4.69298 | − | 4.06472i | −0.226844 | − | 0.196475i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.41742 | + | 7.48096i | 0.164803 | + | 0.360764i | ||||
\(431\) | 11.0367 | 0.531621 | 0.265810 | − | 0.964025i | \(-0.414360\pi\) | ||||
0.265810 | + | 0.964025i | \(0.414360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.9394 | 1.67908 | 0.839541 | − | 0.543297i | \(-0.182824\pi\) | ||||
0.839541 | + | 0.543297i | \(0.182824\pi\) | |||||||
\(434\) | −5.67175 | − | 12.4158i | −0.272252 | − | 0.595979i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.3386 | + | 23.6787i | 1.30928 | + | 1.13400i | ||||
\(437\) | −4.26901 | − | 2.46472i | −0.204215 | − | 0.117903i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.58518 | − | 11.4059i | −0.314293 | − | 0.544372i | 0.664994 | − | 0.746849i | \(-0.268434\pi\) |
−0.979287 | + | 0.202477i | \(0.935101\pi\) | |||||||
\(440\) | 30.3214 | + | 8.89249i | 1.44552 | + | 0.423933i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.19835 | + | 12.5640i | −0.0569996 | + | 0.597609i | ||||
\(443\) | −23.6849 | + | 13.6745i | −1.12530 | + | 0.649694i | −0.942749 | − | 0.333502i | \(-0.891770\pi\) |
−0.182554 | + | 0.983196i | \(0.558436\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.93787 | − | 2.85088i | −0.234077 | − | 0.135145i | ||||
\(446\) | −4.31857 | + | 6.06597i | −0.204490 | + | 0.287232i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.681725 | − | 14.5092i | 0.0322085 | − | 0.685495i | ||||
\(449\) | 13.8225 | 0.652323 | 0.326161 | − | 0.945314i | \(-0.394245\pi\) | ||||
0.326161 | + | 0.945314i | \(0.394245\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 23.1407i | − | 1.08965i | ||||||
\(452\) | 1.85522 | + | 5.35656i | 0.0872622 | + | 0.251951i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.04384 | − | 1.45508i | −0.0959222 | − | 0.0682902i | ||||
\(455\) | 9.58588 | − | 16.6032i | 0.449393 | − | 0.778371i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.86205 | − | 4.95722i | −0.133881 | − | 0.231889i | 0.791288 | − | 0.611443i | \(-0.209411\pi\) |
−0.925170 | + | 0.379554i | \(0.876077\pi\) | |||||||
\(458\) | 0.512731 | − | 5.37570i | 0.0239584 | − | 0.251190i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.99672 | + | 10.3721i | −0.0930977 | + | 0.483600i | ||||
\(461\) | −19.3717 | + | 11.1843i | −0.902231 | + | 0.520903i | −0.877923 | − | 0.478801i | \(-0.841071\pi\) |
−0.0243074 | + | 0.999705i | \(0.507738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.5733 | − | 32.1699i | 0.863174 | − | 1.49506i | −0.00567564 | − | 0.999984i | \(-0.501807\pi\) |
0.868849 | − | 0.495077i | \(-0.164860\pi\) | |||||||
\(464\) | 9.03982 | + | 11.4848i | 0.419663 | + | 0.533171i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.9410 | − | 26.1396i | −0.553154 | − | 1.21089i | ||||
\(467\) | − | 22.6850i | − | 1.04974i | −0.851184 | − | 0.524868i | \(-0.824115\pi\) | ||
0.851184 | − | 0.524868i | \(-0.175885\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.2004i | 0.748063i | ||||||||
\(470\) | 11.8545 | − | 5.41530i | 0.546806 | − | 0.249789i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.88214 | − | 7.21310i | −0.316776 | − | 0.332010i | ||||
\(473\) | −6.24353 | + | 10.8141i | −0.287078 | + | 0.497233i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.374425 | − | 0.216174i | 0.0171798 | − | 0.00991875i | ||||
\(476\) | −6.87447 | − | 1.32340i | −0.315091 | − | 0.0606582i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.4908 | + | 2.33592i | 1.12018 | + | 0.106842i | ||||
\(479\) | −13.1576 | − | 22.7897i | −0.601188 | − | 1.04129i | −0.992641 | − | 0.121091i | \(-0.961361\pi\) |
0.391453 | − | 0.920198i | \(-0.371973\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.4804 | + | 32.0090i | −0.842634 | + | 1.45948i | ||||
\(482\) | −11.2468 | + | 15.7975i | −0.512276 | + | 0.719555i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.50083 | + | 24.5444i | 0.386402 | + | 1.11565i | ||||
\(485\) | 31.9056i | 1.44876i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.0388 | −1.08930 | −0.544652 | − | 0.838662i | \(-0.683338\pi\) | ||||
−0.544652 | + | 0.838662i | \(0.683338\pi\) | |||||||
\(488\) | 5.44840 | − | 1.32364i | 0.246637 | − | 0.0599183i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.73224 | − | 6.92871i | −0.439658 | − | 0.313007i | ||||
\(491\) | 27.2256 | + | 15.7187i | 1.22867 | + | 0.709374i | 0.966752 | − | 0.255715i | \(-0.0823109\pi\) |
0.261920 | + | 0.965090i | \(0.415644\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.10058 | − | 3.52217i | 0.274756 | − | 0.158631i | ||||
\(494\) | −13.8752 | − | 1.32340i | −0.624274 | − | 0.0595428i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 19.7442 | + | 7.89449i | 0.886542 | + | 0.354473i | ||||
\(497\) | 12.1250 | + | 21.0011i | 0.543881 | + | 0.942029i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.08156 | − | 2.93384i | −0.227482 | − | 0.131337i | 0.381928 | − | 0.924192i | \(-0.375260\pi\) |
−0.609410 | + | 0.792855i | \(0.708594\pi\) | |||||||
\(500\) | 16.5418 | + | 14.3273i | 0.739771 | + | 0.640736i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.79824 | − | 2.64873i | 0.258788 | − | 0.118218i | ||||
\(503\) | −32.4317 | −1.44606 | −0.723029 | − | 0.690818i | \(-0.757251\pi\) | ||||
−0.723029 | + | 0.690818i | \(0.757251\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.97861 | 0.132546 | ||||||||
\(506\) | −14.5867 | + | 6.66344i | −0.648459 | + | 0.296226i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.75449 | − | 11.2622i | 0.432786 | − | 0.499679i | ||||
\(509\) | −13.6855 | − | 7.90133i | −0.606599 | − | 0.350220i | 0.165034 | − | 0.986288i | \(-0.447227\pi\) |
−0.771633 | + | 0.636068i | \(0.780560\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.4937 | + | 18.1756i | 0.464214 | + | 0.804042i | ||||
\(512\) | 14.8344 | + | 17.0862i | 0.655596 | + | 0.755112i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −11.5796 | − | 1.10445i | −0.510753 | − | 0.0487153i | ||||
\(515\) | −12.7341 | + | 7.35202i | −0.561130 | + | 0.323969i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.1362 | + | 9.89361i | 0.753650 | + | 0.435120i | ||||
\(518\) | −16.7014 | − | 11.8903i | −0.733818 | − | 0.522430i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.05056 | + | 29.0217i | 0.309187 | + | 1.27269i | ||||
\(521\) | −5.50310 | −0.241095 | −0.120548 | − | 0.992708i | \(-0.538465\pi\) | ||||
−0.120548 | + | 0.992708i | \(0.538465\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.5894i | 1.68740i | 0.536818 | + | 0.843698i | \(0.319626\pi\) | ||||
−0.536818 | + | 0.843698i | \(0.680374\pi\) | |||||||
\(524\) | −6.81187 | + | 2.35926i | −0.297578 | + | 0.103065i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.12356 | + | 5.79206i | −0.179796 | + | 0.252546i | ||||
\(527\) | 5.12430 | − | 8.87555i | 0.223218 | − | 0.386625i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.81970 | + | 15.2762i | 0.383465 | + | 0.664181i | ||||
\(530\) | 28.7717 | + | 2.74423i | 1.24976 | + | 0.119202i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.46151 | − | 7.59189i | 0.0633647 | − | 0.329150i | ||||
\(533\) | 18.9415 | − | 10.9359i | 0.820449 | − | 0.473686i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.54046 | + | 6.13225i | −0.153067 | + | 0.265120i | ||||
\(536\) | −17.4215 | − | 18.2592i | −0.752492 | − | 0.788679i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −29.7889 | + | 13.6080i | −1.28429 | + | 0.586685i | ||||
\(539\) | − | 18.1382i | − | 0.781268i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5666i | 0.970214i | 0.874455 | + | 0.485107i | \(0.161219\pi\) | ||||
−0.874455 | + | 0.485107i | \(0.838781\pi\) | |||||||
\(542\) | −12.3029 | − | 26.9319i | −0.528455 | − | 1.15682i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9.17129 | − | 5.90104i | 0.393216 | − | 0.253005i | ||||
\(545\) | 20.6246 | − | 35.7229i | 0.883463 | − | 1.53020i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2679 | − | 6.50552i | 0.481780 | − | 0.278156i | −0.239378 | − | 0.970927i | \(-0.576943\pi\) |
0.721158 | + | 0.692770i | \(0.243610\pi\) | |||||||
\(548\) | 23.1017 | + | 4.44731i | 0.986856 | + | 0.189980i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.133548 | − | 1.40018i | 0.00569452 | − | 0.0597039i | ||||
\(551\) | 3.88974 | + | 6.73723i | 0.165709 | + | 0.287016i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.02976 | + | 15.6400i | −0.383985 | + | 0.665081i | ||||
\(554\) | 25.6332 | + | 18.2491i | 1.08905 | + | 0.775331i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −24.0917 | + | 8.34406i | −1.02172 | + | 0.353867i | ||||
\(557\) | 5.73693i | 0.243081i | 0.992586 | + | 0.121541i | \(0.0387835\pi\) | ||||
−0.992586 | + | 0.121541i | \(0.961217\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.8024 | −0.499186 | ||||||||
\(560\) | −16.3965 | + | 2.36470i | −0.692879 | + | 0.0999268i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.2234 | − | 21.3831i | 0.642160 | − | 0.901993i | ||||
\(563\) | 13.2510 | + | 7.65045i | 0.558462 | + | 0.322428i | 0.752528 | − | 0.658560i | \(-0.228834\pi\) |
−0.194066 | + | 0.980988i | \(0.562168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.59908 | − | 3.23263i | 0.235555 | − | 0.135998i | ||||
\(566\) | −0.272830 | + | 2.86047i | −0.0114679 | + | 0.120235i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −36.2500 | − | 10.6312i | −1.52102 | − | 0.446075i | ||||
\(569\) | −6.63095 | − | 11.4851i | −0.277984 | − | 0.481482i | 0.692900 | − | 0.721034i | \(-0.256333\pi\) |
−0.970884 | + | 0.239552i | \(0.922999\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.4262 | − | 13.5251i | −0.980357 | − | 0.566009i | −0.0779788 | − | 0.996955i | \(-0.524847\pi\) |
−0.902378 | + | 0.430946i | \(0.858180\pi\) | |||||||
\(572\) | −29.6867 | + | 34.2753i | −1.24126 | + | 1.43312i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.04099 | + | 11.0351i | 0.210407 | + | 0.460595i | ||||
\(575\) | 0.470166 | 0.0196073 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.78434 | −0.199174 | −0.0995872 | − | 0.995029i | \(-0.531752\pi\) | ||||
−0.0995872 | + | 0.995029i | \(0.531752\pi\) | |||||||
\(578\) | 7.80559 | + | 17.0870i | 0.324670 | + | 0.710724i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.9134 | − | 12.6003i | 0.453156 | − | 0.523198i | ||||
\(581\) | 5.66760 | + | 3.27219i | 0.235132 | + | 0.135753i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.9406 | + | 38.0023i | 0.908689 | + | 1.57390i | ||||
\(584\) | −31.3729 | − | 9.20087i | −1.29822 | − | 0.380735i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.58148 | − | 48.0343i | 0.189259 | − | 1.98428i | ||||
\(587\) | 37.0796 | − | 21.4079i | 1.53044 | − | 0.883598i | 0.531095 | − | 0.847312i | \(-0.321781\pi\) |
0.999341 | − | 0.0362861i | \(-0.0115528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.80179 | + | 5.65906i | 0.403876 | + | 0.233178i | ||||
\(590\) | −6.59449 | + | 9.26279i | −0.271491 | + | 0.381343i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 31.6105 | − | 4.55885i | 1.29918 | − | 0.187368i | ||||
\(593\) | 0.825572 | 0.0339022 | 0.0169511 | − | 0.999856i | \(-0.494604\pi\) | ||||
0.0169511 | + | 0.999856i | \(0.494604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.98438i | 0.327328i | ||||||||
\(596\) | −14.3981 | + | 4.98671i | −0.589768 | + | 0.204264i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.3477 | − | 8.79077i | −0.504936 | − | 0.359481i | ||||
\(599\) | 0.961228 | − | 1.66490i | 0.0392747 | − | 0.0680258i | −0.845720 | − | 0.533627i | \(-0.820829\pi\) |
0.884995 | + | 0.465601i | \(0.154162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.5937 | − | 37.4014i | −0.880825 | − | 1.52563i | −0.850425 | − | 0.526096i | \(-0.823655\pi\) |
−0.0303994 | − | 0.999538i | \(-0.509678\pi\) | |||||||
\(602\) | 0.621589 | − | 6.51702i | 0.0253341 | − | 0.265614i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.91581 | − | 1.71638i | −0.362779 | − | 0.0698386i | ||||
\(605\) | 25.6556 | − | 14.8123i | 1.04305 | − | 0.602205i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.5078 | − | 35.5206i | 0.832386 | − | 1.44174i | −0.0637546 | − | 0.997966i | \(-0.520307\pi\) |
0.896141 | − | 0.443770i | \(-0.146359\pi\) | |||||||
\(608\) | 6.51686 | + | 10.1284i | 0.264294 | + | 0.410761i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.65709 | − | 5.81654i | −0.107582 | − | 0.235505i | ||||
\(611\) | 18.7022i | 0.756611i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.05878i | − | 0.204322i | −0.994768 | − | 0.102161i | \(-0.967424\pi\) | ||
0.994768 | − | 0.102161i | \(-0.0325757\pi\) | |||||||
\(614\) | −6.14345 | + | 2.80642i | −0.247930 | + | 0.113258i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.3626 | − | 18.1976i | −0.699559 | − | 0.733201i | ||||
\(617\) | 16.0739 | − | 27.8408i | 0.647112 | − | 1.12083i | −0.336698 | − | 0.941613i | \(-0.609310\pi\) |
0.983809 | − | 0.179217i | \(-0.0573566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.3562 | − | 15.7941i | 1.09954 | − | 0.634820i | 0.163440 | − | 0.986553i | \(-0.447741\pi\) |
0.936100 | + | 0.351734i | \(0.114408\pi\) | |||||||
\(620\) | 4.58454 | − | 23.8146i | 0.184120 | − | 0.956416i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.4707 | − | 3.00165i | −1.26186 | − | 0.120355i | ||||
\(623\) | 2.26924 | + | 3.93044i | 0.0909153 | + | 0.157470i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.9871 | − | 22.4942i | 0.519482 | − | 0.899770i | ||||
\(626\) | 2.00803 | − | 2.82053i | 0.0802569 | − | 0.112731i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 24.9003 | − | 8.62411i | 0.993631 | − | 0.344139i | ||||
\(629\) | − | 15.3929i | − | 0.613756i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.4885 | −0.616586 | −0.308293 | − | 0.951292i | \(-0.599758\pi\) | ||||
−0.308293 | + | 0.951292i | \(0.599758\pi\) | |||||||
\(632\) | −6.64153 | − | 27.3380i | −0.264186 | − | 1.08745i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 19.0081 | + | 13.5325i | 0.754909 | + | 0.537445i | ||||
\(635\) | −14.7162 | − | 8.49638i | −0.583993 | − | 0.337168i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.8468 | − | 8.57182i | 0.588253 | − | 0.339628i | ||||
\(638\) | 25.1942 | + | 2.40301i | 0.997449 | + | 0.0951361i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 15.9374 | − | 20.2976i | 0.629980 | − | 0.802334i | ||||
\(641\) | 15.2248 | + | 26.3701i | 0.601344 | + | 1.04156i | 0.992618 | + | 0.121284i | \(0.0387011\pi\) |
−0.391274 | + | 0.920274i | \(0.627966\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5911 | + | 8.42419i | 0.575418 | + | 0.332218i | 0.759310 | − | 0.650729i | \(-0.225537\pi\) |
−0.183893 | + | 0.982946i | \(0.558870\pi\) | |||||||
\(644\) | 5.50439 | − | 6.35518i | 0.216903 | − | 0.250429i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.27994 | − | 2.41196i | 0.207736 | − | 0.0948971i | ||||
\(647\) | −18.6734 | −0.734126 | −0.367063 | − | 0.930196i | \(-0.619637\pi\) | ||||
−0.367063 | + | 0.930196i | \(0.619637\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.2633 | −0.677644 | ||||||||
\(650\) | 1.20922 | − | 0.552388i | 0.0474293 | − | 0.0216664i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −31.1292 | − | 26.9619i | −1.21912 | − | 1.05591i | ||||
\(653\) | 31.4276 | + | 18.1448i | 1.22986 | + | 0.710059i | 0.967000 | − | 0.254775i | \(-0.0820015\pi\) |
0.262858 | + | 0.964834i | \(0.415335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.11089 | + | 7.12028i | 0.160626 | + | 0.278212i | ||||
\(656\) | −17.5485 | − | 7.01655i | −0.685153 | − | 0.273950i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.3270 | − | 0.984980i | −0.402588 | − | 0.0383985i | ||||
\(659\) | 19.3088 | − | 11.1480i | 0.752166 | − | 0.434263i | −0.0743103 | − | 0.997235i | \(-0.523676\pi\) |
0.826476 | + | 0.562972i | \(0.190342\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.19793 | − | 3.00103i | −0.202176 | − | 0.116726i | 0.395494 | − | 0.918469i | \(-0.370573\pi\) |
−0.597670 | + | 0.801742i | \(0.703907\pi\) | |||||||
\(662\) | −0.437935 | − | 0.311781i | −0.0170208 | − | 0.0121177i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.90671 | + | 2.40674i | −0.384455 | + | 0.0933998i | ||||
\(665\) | −8.81762 | −0.341933 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.45996i | 0.327571i | ||||||||
\(668\) | −3.32394 | − | 9.59717i | −0.128607 | − | 0.371326i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.6933 | + | 23.4478i | −0.644919 | + | 0.905869i | ||||
\(671\) | 4.85442 | − | 8.40810i | 0.187403 | − | 0.324591i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.70444 | − | 6.41629i | −0.142796 | − | 0.247330i | 0.785753 | − | 0.618541i | \(-0.212276\pi\) |
−0.928548 | + | 0.371211i | \(0.878943\pi\) | |||||||
\(674\) | 7.09183 | + | 0.676414i | 0.273167 | + | 0.0260545i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.5539 | − | 3.18679i | −0.636689 | − | 0.122569i | ||||
\(677\) | 8.57613 | − | 4.95143i | 0.329607 | − | 0.190299i | −0.326059 | − | 0.945349i | \(-0.605721\pi\) |
0.655667 | + | 0.755050i | \(0.272388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.6981 | − | 21.9938i | 0.487309 | − | 0.844043i | ||||
\(680\) | −8.58620 | − | 8.99910i | −0.329266 | − | 0.345100i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.4916 | − | 15.2995i | 1.28246 | − | 0.585847i | ||||
\(683\) | 39.0736i | 1.49511i | 0.664200 | + | 0.747555i | \(0.268772\pi\) | ||||
−0.664200 | + | 0.747555i | \(0.731228\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 26.8316i | − | 1.02518i | ||||||
\(686\) | 11.4197 | + | 24.9985i | 0.436006 | + | 0.954447i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.30765 | + | 8.01369i | 0.240477 | + | 0.305519i | ||||
\(689\) | −20.7376 | + | 35.9185i | −0.790039 | + | 1.36839i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.07502 | + | 1.19801i | −0.0789375 | + | 0.0455746i | −0.538949 | − | 0.842338i | \(-0.681179\pi\) |
0.460012 | + | 0.887913i | \(0.347845\pi\) | |||||||
\(692\) | −4.81962 | + | 25.0357i | −0.183215 | + | 0.951715i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.30294 | + | 13.6606i | −0.0494590 | + | 0.518551i | ||||
\(695\) | 14.5391 | + | 25.1825i | 0.551500 | + | 0.955227i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.55443 | + | 7.88850i | −0.172511 | + | 0.298798i | ||||
\(698\) | −34.7526 | − | 24.7416i | −1.31541 | − | 0.936483i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.241332 | + | 0.696796i | 0.00912150 | + | 0.0263364i | ||||
\(701\) | − | 30.9184i | − | 1.16777i | −0.811836 | − | 0.583885i | \(-0.801532\pi\) | ||
0.811836 | − | 0.583885i | \(-0.198468\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9993 | 0.641141 | ||||||||
\(704\) | 39.1384 | + | 1.83895i | 1.47508 | + | 0.0693079i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.7149 | + | 30.5013i | −0.817252 | + | 1.14793i | ||||
\(707\) | −2.05327 | − | 1.18546i | −0.0772212 | − | 0.0445837i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.46959 | − | 2.58052i | 0.167859 | − | 0.0969133i | −0.413717 | − | 0.910406i | \(-0.635770\pi\) |
0.581576 | + | 0.813492i | \(0.302436\pi\) | |||||||
\(710\) | −4.09084 | + | 42.8902i | −0.153526 | + | 1.60964i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.78434 | − | 1.98967i | −0.254254 | − | 0.0745661i | ||||
\(713\) | 6.15406 | + | 10.6591i | 0.230471 | + | 0.399188i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 44.7870 | + | 25.8578i | 1.67494 | + | 0.967027i | ||||
\(716\) | −13.3342 | − | 11.5491i | −0.498322 | − | 0.431610i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.7868 | − | 30.1802i | −0.514518 | − | 1.12631i | ||||
\(719\) | −14.7871 | −0.551465 | −0.275733 | − | 0.961234i | \(-0.588920\pi\) | ||||
−0.275733 | + | 0.961234i | \(0.588920\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.7041 | 0.435884 | ||||||||
\(722\) | −8.50120 | − | 18.6097i | −0.316382 | − | 0.692582i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.3372 | − | 20.2130i | −0.867320 | − | 0.751208i | ||||
\(725\) | −0.642593 | − | 0.371001i | −0.0238653 | − | 0.0137786i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.06681 | − | 1.84777i | −0.0395658 | − | 0.0685299i | 0.845564 | − | 0.533873i | \(-0.179264\pi\) |
−0.885130 | + | 0.465344i | \(0.845931\pi\) | |||||||
\(728\) | 6.69012 | − | 22.8118i | 0.247952 | − | 0.845463i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.54046 | + | 37.1198i | −0.131038 | + | 1.37386i | ||||
\(731\) | 4.25675 | − | 2.45764i | 0.157442 | − | 0.0908990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.2298 | − | 12.8344i | −0.821076 | − | 0.474048i | 0.0297113 | − | 0.999559i | \(-0.490541\pi\) |
−0.850787 | + | 0.525510i | \(0.823875\pi\) | |||||||
\(734\) | 15.7905 | − | 22.1797i | 0.582837 | − | 0.818667i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.630266 | + | 13.0821i | 0.0232319 | + | 0.482214i | ||||
\(737\) | −43.7003 | −1.60972 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.46282i | − | 0.200953i | −0.994939 | − | 0.100476i | \(-0.967963\pi\) | ||
0.994939 | − | 0.100476i | \(-0.0320367\pi\) | |||||||
\(740\) | −11.9209 | − | 34.4192i | −0.438222 | − | 1.26527i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.7413 | − | 13.3426i | −0.688015 | − | 0.489821i | ||||
\(743\) | 16.8170 | − | 29.1279i | 0.616955 | − | 1.06860i | −0.373083 | − | 0.927798i | \(-0.621699\pi\) |
0.990038 | − | 0.140800i | \(-0.0449674\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.68910 | + | 15.0500i | 0.318344 | + | 0.551388i | ||||
\(746\) | 1.40972 | − | 14.7802i | 0.0516137 | − | 0.541141i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.56987 | − | 18.5438i | 0.130527 | − | 0.678029i | ||||
\(749\) | 4.88115 | − | 2.81813i | 0.178353 | − | 0.102972i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.6727 | + | 21.9498i | −0.462435 | + | 0.800961i | −0.999082 | − | 0.0428462i | \(-0.986357\pi\) |
0.536647 | + | 0.843807i | \(0.319691\pi\) | |||||||
\(752\) | 12.6986 | − | 9.99521i | 0.463072 | − | 0.364488i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.93943 | + | 21.7581i | 0.361973 | + | 0.792383i | ||||
\(755\) | 10.3553i | 0.376868i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.95103i | 0.143603i | 0.997419 | + | 0.0718014i | \(0.0228748\pi\) | ||||
−0.997419 | + | 0.0718014i | \(0.977125\pi\) | |||||||
\(758\) | −45.6915 | + | 20.8726i | −1.65959 | + | 0.758126i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.93823 | − | 9.48224i | 0.360498 | − | 0.343957i | ||||
\(761\) | 23.3979 | − | 40.5264i | 0.848175 | − | 1.46908i | −0.0346607 | − | 0.999399i | \(-0.511035\pi\) |
0.882835 | − | 0.469682i | \(-0.155632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.4347 | + | 16.4168i | −1.02941 | + | 0.594328i | ||||
\(764\) | 18.9205 | + | 3.64239i | 0.684521 | + | 0.131777i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50.7928 | + | 4.84459i | 1.83522 | + | 0.175042i | ||||
\(767\) | −8.15835 | − | 14.1307i | −0.294581 | − | 0.510229i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.60083 | − | 4.50478i | 0.0937885 | − | 0.162446i | −0.815314 | − | 0.579019i | \(-0.803436\pi\) |
0.909102 | + | 0.416573i | \(0.136769\pi\) | |||||||
\(770\) | −16.6369 | + | 23.3686i | −0.599553 | + | 0.842147i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.57311 | + | 13.2039i | 0.164590 | + | 0.475219i | ||||
\(773\) | − | 38.8477i | − | 1.39725i | −0.715486 | − | 0.698627i | \(-0.753795\pi\) | ||
0.715486 | − | 0.698627i | \(-0.246205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.07952 | −0.0387773 | ||||||||
\(776\) | 9.33965 | + | 38.4441i | 0.335274 | + | 1.38006i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.3126 | + | 16.5970i | 0.835798 | + | 0.595033i | ||||
\(779\) | −8.71173 | − | 5.02972i | −0.312130 | − | 0.180209i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −56.6503 | + | 32.7071i | −2.02711 | + | 1.17035i | ||||
\(782\) | 6.28399 | + | 0.599362i | 0.224715 | + | 0.0214332i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13.7549 | − | 5.49974i | −0.491247 | − | 0.196419i | ||||
\(785\) | −15.0271 | − | 26.0277i | −0.536340 | − | 0.928968i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40.8579 | + | 23.5893i | 1.45643 | + | 0.840869i | 0.998833 | − | 0.0482918i | \(-0.0153777\pi\) |
0.457595 | + | 0.889161i | \(0.348711\pi\) | |||||||
\(788\) | 6.52851 | + | 5.65451i | 0.232568 | + | 0.201434i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −29.1853 | + | 13.3323i | −1.03836 | + | 0.474341i | ||||
\(791\) | −5.14621 | −0.182978 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.17648 | 0.325866 | ||||||||
\(794\) | −5.13895 | + | 2.34755i | −0.182375 | + | 0.0833115i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.73392 | + | 8.92932i | −0.274122 | + | 0.316492i | ||||
\(797\) | 6.35645 | + | 3.66990i | 0.225157 | + | 0.129995i | 0.608336 | − | 0.793680i | \(-0.291837\pi\) |
−0.383179 | + | 0.923674i | \(0.625171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.89442 | − | 6.74533i | −0.137775 | − | 0.238633i | ||||
\(800\) | −1.02132 | − | 0.525828i | −0.0361091 | − | 0.0185908i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 39.4541 | + | 3.76310i | 1.39317 | + | 0.132880i | ||||
\(803\) | −49.0286 | + | 28.3067i | −1.73018 | + | 0.998920i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.30423 | − | 4.79445i | −0.292686 | − | 0.168982i | ||||
\(806\) | 28.3508 | + | 20.1839i | 0.998614 | + | 0.710947i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.58903 | − | 0.871921i | 0.126262 | − | 0.0306741i | ||||
\(809\) | −2.25520 | −0.0792887 | −0.0396443 | − | 0.999214i | \(-0.512622\pi\) | ||||
−0.0396443 | + | 0.999214i | \(0.512622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.9986i | 0.561785i | 0.959739 | + | 0.280893i | \(0.0906305\pi\) | ||||
−0.959739 | + | 0.280893i | \(0.909369\pi\) | |||||||
\(812\) | −12.5378 | + | 4.34242i | −0.439992 | + | 0.152389i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 32.0740 | − | 45.0519i | 1.12419 | − | 1.57907i | ||||
\(815\) | −23.4844 | + | 40.6761i | −0.822622 | + | 1.42482i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.71411 | + | 4.70098i | 0.0949548 | + | 0.164467i | ||||
\(818\) | −23.1582 | − | 2.20881i | −0.809707 | − | 0.0772293i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.07470 | + | 21.1662i | −0.142295 | + | 0.739154i | ||||
\(821\) | −25.2413 | + | 14.5731i | −0.880928 | + | 0.508604i | −0.870964 | − | 0.491347i | \(-0.836505\pi\) |
−0.00996351 | + | 0.999950i | \(0.503172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.15695 | + | 7.20005i | −0.144902 | + | 0.250978i | −0.929336 | − | 0.369234i | \(-0.879620\pi\) |
0.784434 | + | 0.620212i | \(0.212953\pi\) | |||||||
\(824\) | −13.1916 | + | 12.5863i | −0.459550 | + | 0.438465i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.23234 | − | 3.76066i | 0.286440 | − | 0.130850i | ||||
\(827\) | 43.5035i | 1.51277i | 0.654129 | + | 0.756383i | \(0.273035\pi\) | ||||
−0.654129 | + | 0.756383i | \(0.726965\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 15.9248i | − | 0.553092i | −0.961001 | − | 0.276546i | \(-0.910810\pi\) | ||
0.961001 | − | 0.276546i | \(-0.0891897\pi\) | |||||||
\(830\) | 4.83132 | + | 10.5761i | 0.167698 | + | 0.367102i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.9909 | + | 32.9053i | 0.589054 | + | 1.14079i | ||||
\(833\) | −3.56987 | + | 6.18320i | −0.123689 | + | 0.214235i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.0317 | + | 5.79180i | −0.347161 | + | 0.200433i | ||||
\(836\) | 20.4790 | + | 3.94242i | 0.708282 | + | 0.136351i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.18741 | + | 33.4183i | −0.110107 | + | 1.15442i | ||||
\(839\) | 21.0582 | + | 36.4739i | 0.727009 | + | 1.25922i | 0.958142 | + | 0.286295i | \(0.0924237\pi\) |
−0.231132 | + | 0.972922i | \(0.574243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.82437 | + | 13.5522i | −0.269806 | + | 0.467318i | ||||
\(842\) | 34.5106 | + | 24.5692i | 1.18931 | + | 0.846712i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −34.6496 | + | 12.0007i | −1.19269 | + | 0.413082i | ||||
\(845\) | 19.2266i | 0.661415i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.5806 | −0.810238 | ||||||||
\(848\) | 35.4713 | − | 5.11567i | 1.21809 | − | 0.175673i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.321102 | + | 0.451028i | −0.0110137 | + | 0.0154701i | ||||
\(851\) | 16.0095 | + | 9.24311i | 0.548800 | + | 0.316850i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.2013 | − | 19.7461i | 1.17103 | − | 0.676095i | 0.217108 | − | 0.976148i | \(-0.430338\pi\) |
0.953923 | + | 0.300053i | \(0.0970043\pi\) | |||||||
\(854\) | −0.483293 | + | 5.06706i | −0.0165379 | + | 0.173391i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.47094 | + | 8.42535i | −0.0844549 | + | 0.287972i | ||||
\(857\) | 12.6170 | + | 21.8532i | 0.430988 | + | 0.746493i | 0.996959 | − | 0.0779326i | \(-0.0248319\pi\) |
−0.565971 | + | 0.824425i | \(0.691499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.5539 | − | 27.4552i | −1.62252 | − | 0.936761i | −0.986244 | − | 0.165297i | \(-0.947142\pi\) |
−0.636274 | − | 0.771463i | \(-0.719525\pi\) | |||||||
\(860\) | 7.61498 | − | 8.79199i | 0.259669 | − | 0.299805i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.48546 | − | 14.1971i | −0.220896 | − | 0.483555i | ||||
\(863\) | 54.3877 | 1.85138 | 0.925689 | − | 0.378285i | \(-0.123486\pi\) | ||||
0.925689 | + | 0.378285i | \(0.123486\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.0778 | 0.988675 | ||||||||
\(866\) | −20.5313 | − | 44.9443i | −0.697681 | − | 1.52727i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −12.6383 | + | 14.5917i | −0.428971 | + | 0.495275i | ||||
\(869\) | −42.1888 | − | 24.3577i | −1.43116 | − | 0.826278i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.6521 | − | 35.7704i | −0.699768 | − | 1.21203i | ||||
\(872\) | 14.3942 | − | 49.0812i | 0.487451 | − | 1.66210i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.661911 | + | 6.93977i | −0.0223895 | + | 0.234741i | ||||
\(875\) | −17.2050 | + | 9.93334i | −0.581637 | + | 0.335808i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.90001 | − | 3.40637i | −0.199229 | − | 0.115025i | 0.397067 | − | 0.917790i | \(-0.370028\pi\) |
−0.596296 | + | 0.802765i | \(0.703361\pi\) | |||||||
\(878\) | −10.8023 | + | 15.1732i | −0.364561 | + | 0.512071i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.37875 | − | 44.2294i | −0.215028 | − | 1.49097i | ||||
\(881\) | 43.2881 | 1.45841 | 0.729207 | − | 0.684293i | \(-0.239889\pi\) | ||||
0.729207 | + | 0.684293i | \(0.239889\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1510i | 1.04832i | 0.851621 | + | 0.524158i | \(0.175620\pi\) | ||||
−0.851621 | + | 0.524158i | \(0.824380\pi\) | |||||||
\(884\) | 16.8659 | − | 5.84143i | 0.567262 | − | 0.196469i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 31.5080 | + | 22.4316i | 1.05853 | + | 0.753605i | ||||
\(887\) | 24.8886 | − | 43.1083i | 0.835677 | − | 1.44743i | −0.0578015 | − | 0.998328i | \(-0.518409\pi\) |
0.893478 | − | 0.449107i | \(-0.148258\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.76295 | + | 11.7138i | 0.226822 | + | 0.392867i | ||||
\(890\) | −0.765617 | + | 8.02708i | −0.0256636 | + | 0.269068i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.3407 | + | 1.99068i | 0.346231 | + | 0.0666529i | ||||
\(893\) | 7.44926 | − | 4.30083i | 0.249280 | − | 0.143922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.0595 | + | 17.4236i | −0.336253 | + | 0.582407i | ||||
\(896\) | −19.0645 | + | 7.64902i | −0.636900 | + | 0.255536i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.12242 | − | 17.7805i | −0.271049 | − | 0.593344i | ||||
\(899\) | − | 19.4243i | − | 0.647838i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 17.2730i | − | 0.575447i | ||||||
\(902\) | −29.7670 | + | 13.5980i | −0.991133 | + | 0.452765i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.80024 | − | 5.53411i | 0.192913 | − | 0.184062i | ||||
\(905\) | −17.6059 | + | 30.4944i | −0.585241 | + | 1.01367i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.6712 | − | 9.62515i | 0.553559 | − | 0.319598i | −0.196997 | − | 0.980404i | \(-0.563119\pi\) |
0.750556 | + | 0.660806i | \(0.229786\pi\) | |||||||
\(908\) | −0.670731 | + | 3.48413i | −0.0222590 | + | 0.115625i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26.9905 | − | 2.57433i | −0.894725 | − | 0.0853383i | ||||
\(911\) | −11.1396 | − | 19.2944i | −0.369072 | − | 0.639252i | 0.620348 | − | 0.784326i | \(-0.286991\pi\) |
−0.989421 | + | 0.145074i | \(0.953658\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.82669 | + | 15.2883i | −0.292121 | + | 0.505968i | ||||
\(914\) | −4.69491 | + | 6.59459i | −0.155294 | + | 0.218130i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.21633 | + | 2.49934i | −0.238434 | + | 0.0825807i | ||||
\(917\) | − | 6.54438i | − | 0.216114i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.0122 | 0.924039 | 0.462019 | − | 0.886870i | \(-0.347125\pi\) | ||||
0.462019 | + | 0.886870i | \(0.347125\pi\) | |||||||
\(920\) | 14.5154 | − | 3.52639i | 0.478559 | − | 0.116262i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.7702 | + | 18.3467i | 0.848696 | + | 0.604215i | ||||
\(923\) | −53.5440 | − | 30.9136i | −1.76242 | − | 1.01753i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.40416 | + | 0.810691i | −0.0461684 | + | 0.0266554i | ||||
\(926\) | −52.2958 | − | 4.98794i | −1.71855 | − | 0.163914i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.46151 | − | 18.3772i | 0.310589 | − | 0.603260i | ||||
\(929\) | 3.94220 | + | 6.82809i | 0.129339 | + | 0.224022i | 0.923421 | − | 0.383789i | \(-0.125381\pi\) |
−0.794081 | + | 0.607811i | \(0.792048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.82847 | − | 3.94242i | −0.223794 | − | 0.129208i | ||||
\(932\) | −26.6078 | + | 30.7205i | −0.871569 | + | 1.00628i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29.1808 | + | 13.3303i | −0.954827 | + | 0.436179i | ||||
\(935\) | −21.5378 | −0.704361 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.98600 | −0.293560 | −0.146780 | − | 0.989169i | \(-0.546891\pi\) | ||||
−0.146780 | + | 0.989169i | \(0.546891\pi\) | |||||||
\(938\) | 20.8393 | − | 9.51973i | 0.680429 | − | 0.310830i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −13.9320 | − | 12.0668i | −0.454410 | − | 0.393577i | ||||
\(941\) | −21.0227 | − | 12.1375i | −0.685322 | − | 0.395671i | 0.116535 | − | 0.993187i | \(-0.462821\pi\) |
−0.801857 | + | 0.597516i | \(0.796155\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.46967 | − | 9.47375i | −0.178117 | − | 0.308508i | ||||
\(944\) | −5.23445 | + | 13.0914i | −0.170367 | + | 0.426090i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.5796 | + | 1.67673i | 0.571561 | + | 0.0545151i | ||||
\(947\) | −1.71382 | + | 0.989473i | −0.0556916 | + | 0.0321536i | −0.527587 | − | 0.849501i | \(-0.676903\pi\) |
0.471896 | + | 0.881654i | \(0.343570\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −46.3402 | − | 26.7545i | −1.50427 | − | 0.868488i | ||||
\(950\) | −0.498097 | − | 0.354612i | −0.0161604 | − | 0.0115051i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.33725 | + | 9.62065i | 0.0757506 | + | 0.311807i | ||||
\(953\) | −28.9674 | −0.938347 | −0.469173 | − | 0.883106i | \(-0.655448\pi\) | ||||
−0.469173 | + | 0.883106i | \(0.655448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 21.9753i | − | 0.711104i | ||||||
\(956\) | −11.3866 | − | 32.8764i | −0.368269 | − | 1.06330i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.5838 | + | 30.3171i | −0.697341 | + | 0.979503i | ||||
\(959\) | −10.6787 | + | 18.4960i | −0.344833 | + | 0.597268i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.37008 | + | 2.37304i | 0.0441961 | + | 0.0765498i | ||||
\(962\) | 52.0343 | + | 4.96300i | 1.67765 | + | 0.160014i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.9300 | + | 5.18428i | 0.867355 | + | 0.166975i | ||||
\(965\) | 13.8017 | − | 7.96842i | 0.444293 | − | 0.256512i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.00531192 | − | 0.00920052i | 0.000170820 | − | 0.000295869i | −0.865940 | − | 0.500148i | \(-0.833279\pi\) |
0.866111 | + | 0.499852i | \(0.166612\pi\) | |||||||
\(968\) | 26.5774 | − | 25.3579i | 0.854229 | − | 0.815035i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 41.0418 | − | 18.7485i | 1.31777 | − | 0.601979i | ||||
\(971\) | − | 17.0984i | − | 0.548715i | −0.961628 | − | 0.274357i | \(-0.911535\pi\) | ||
0.961628 | − | 0.274357i | \(-0.0884651\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 23.1457i | − | 0.742017i | ||||||
\(974\) | 14.1258 | + | 30.9224i | 0.452620 | + | 0.990817i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.90427 | − | 6.23074i | −0.156982 | − | 0.199441i | ||||
\(977\) | 5.50612 | − | 9.53688i | 0.176156 | − | 0.305112i | −0.764404 | − | 0.644737i | \(-0.776967\pi\) |
0.940561 | + | 0.339625i | \(0.110300\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.6023 | + | 6.12126i | −0.338852 | + | 0.195636i | ||||
\(980\) | −3.19385 | + | 16.5905i | −0.102024 | + | 0.529966i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.22133 | − | 44.2583i | 0.134708 | − | 1.41234i | ||||
\(983\) | −22.7443 | − | 39.3943i | −0.725432 | − | 1.25648i | −0.958796 | − | 0.284095i | \(-0.908307\pi\) |
0.233364 | − | 0.972389i | \(-0.425027\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.92521 | − | 8.53071i | 0.156930 | − | 0.271811i | ||||
\(986\) | −8.11560 | − | 5.77777i | −0.258453 | − | 0.184002i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.45103 | + | 18.6260i | 0.205235 | + | 0.592572i | ||||
\(989\) | 5.90304i | 0.187706i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.93737 | 0.125075 | 0.0625374 | − | 0.998043i | \(-0.480081\pi\) | ||||
0.0625374 | + | 0.998043i | \(0.480081\pi\) | |||||||
\(992\) | −1.44711 | − | 30.0370i | −0.0459458 | − | 0.953675i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.8898 | − | 27.9378i | 0.630868 | − | 0.886132i | ||||
\(995\) | 11.6678 | + | 6.73642i | 0.369895 | + | 0.213559i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.16558 | + | 1.25030i | −0.0685847 | + | 0.0395974i | −0.533900 | − | 0.845547i | \(-0.679274\pi\) |
0.465316 | + | 0.885145i | \(0.345941\pi\) | |||||||
\(998\) | −0.787897 | + | 8.26066i | −0.0249404 | + | 0.261487i | ||||
\(999\) | 0 | 0 |
(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 | 216.2.n.b.37.4 | 16 | ||
3.2 | odd | 2 | 72.2.n.b.13.5 | ✓ | 16 | ||
4.3 | odd | 2 | 864.2.r.b.145.7 | 16 | |||
8.3 | odd | 2 | 864.2.r.b.145.2 | 16 | |||
8.5 | even | 2 | inner | 216.2.n.b.37.3 | 16 | ||
9.2 | odd | 6 | 72.2.n.b.61.6 | yes | 16 | ||
9.4 | even | 3 | 648.2.d.k.325.8 | 8 | |||
9.5 | odd | 6 | 648.2.d.j.325.1 | 8 | |||
9.7 | even | 3 | inner | 216.2.n.b.181.3 | 16 | ||
12.11 | even | 2 | 288.2.r.b.49.1 | 16 | |||
24.5 | odd | 2 | 72.2.n.b.13.6 | yes | 16 | ||
24.11 | even | 2 | 288.2.r.b.49.8 | 16 | |||
36.7 | odd | 6 | 864.2.r.b.721.2 | 16 | |||
36.11 | even | 6 | 288.2.r.b.241.8 | 16 | |||
36.23 | even | 6 | 2592.2.d.j.1297.7 | 8 | |||
36.31 | odd | 6 | 2592.2.d.k.1297.2 | 8 | |||
72.5 | odd | 6 | 648.2.d.j.325.2 | 8 | |||
72.11 | even | 6 | 288.2.r.b.241.1 | 16 | |||
72.13 | even | 6 | 648.2.d.k.325.7 | 8 | |||
72.29 | odd | 6 | 72.2.n.b.61.5 | yes | 16 | ||
72.43 | odd | 6 | 864.2.r.b.721.7 | 16 | |||
72.59 | even | 6 | 2592.2.d.j.1297.2 | 8 | |||
72.61 | even | 6 | inner | 216.2.n.b.181.4 | 16 | ||
72.67 | odd | 6 | 2592.2.d.k.1297.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.n.b.13.5 | ✓ | 16 | 3.2 | odd | 2 | ||
72.2.n.b.13.6 | yes | 16 | 24.5 | odd | 2 | ||
72.2.n.b.61.5 | yes | 16 | 72.29 | odd | 6 | ||
72.2.n.b.61.6 | yes | 16 | 9.2 | odd | 6 | ||
216.2.n.b.37.3 | 16 | 8.5 | even | 2 | inner | ||
216.2.n.b.37.4 | 16 | 1.1 | even | 1 | trivial | ||
216.2.n.b.181.3 | 16 | 9.7 | even | 3 | inner | ||
216.2.n.b.181.4 | 16 | 72.61 | even | 6 | inner | ||
288.2.r.b.49.1 | 16 | 12.11 | even | 2 | |||
288.2.r.b.49.8 | 16 | 24.11 | even | 2 | |||
288.2.r.b.241.1 | 16 | 72.11 | even | 6 | |||
288.2.r.b.241.8 | 16 | 36.11 | even | 6 | |||
648.2.d.j.325.1 | 8 | 9.5 | odd | 6 | |||
648.2.d.j.325.2 | 8 | 72.5 | odd | 6 | |||
648.2.d.k.325.7 | 8 | 72.13 | even | 6 | |||
648.2.d.k.325.8 | 8 | 9.4 | even | 3 | |||
864.2.r.b.145.2 | 16 | 8.3 | odd | 2 | |||
864.2.r.b.145.7 | 16 | 4.3 | odd | 2 | |||
864.2.r.b.721.2 | 16 | 36.7 | odd | 6 | |||
864.2.r.b.721.7 | 16 | 72.43 | odd | 6 | |||
2592.2.d.j.1297.2 | 8 | 72.59 | even | 6 | |||
2592.2.d.j.1297.7 | 8 | 36.23 | even | 6 | |||
2592.2.d.k.1297.2 | 8 | 36.31 | odd | 6 | |||
2592.2.d.k.1297.7 | 8 | 72.67 | odd | 6 |