Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(109,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.10 | ||
Character | \(\chi\) | \(=\) | 432.109 |
Dual form | 432.2.k.c.325.10 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20402 | − | 0.741841i | 0.851373 | − | 0.524561i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.899344 | − | 1.78639i | 0.449672 | − | 0.893194i | ||||
\(5\) | 0.431497 | − | 0.431497i | 0.192971 | − | 0.192971i | −0.604007 | − | 0.796979i | \(-0.706430\pi\) |
0.796979 | + | 0.604007i | \(0.206430\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.145064i | 0.0548291i | 0.999624 | + | 0.0274145i | \(0.00872741\pi\) | ||||
−0.999624 | + | 0.0274145i | \(0.991273\pi\) | |||||||
\(8\) | −0.242383 | − | 2.81802i | −0.0856954 | − | 0.996321i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.199430 | − | 0.839634i | 0.0630654 | − | 0.265516i | ||||
\(11\) | 2.42618 | − | 2.42618i | 0.731521 | − | 0.731521i | −0.239400 | − | 0.970921i | \(-0.576951\pi\) |
0.970921 | + | 0.239400i | \(0.0769508\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.201311 | + | 0.201311i | 0.0558337 | + | 0.0558337i | 0.734472 | − | 0.678639i | \(-0.237430\pi\) |
−0.678639 | + | 0.734472i | \(0.737430\pi\) | |||||||
\(14\) | 0.107614 | + | 0.174661i | 0.0287612 | + | 0.0466800i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.38236 | − | 3.21315i | −0.595590 | − | 0.803289i | ||||
\(17\) | −3.15345 | −0.764824 | −0.382412 | − | 0.923992i | \(-0.624906\pi\) | ||||
−0.382412 | + | 0.923992i | \(0.624906\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.09482 | + | 3.09482i | 0.710000 | + | 0.710000i | 0.966535 | − | 0.256535i | \(-0.0825809\pi\) |
−0.256535 | + | 0.966535i | \(0.582581\pi\) | |||||||
\(20\) | −0.382756 | − | 1.15888i | −0.0855869 | − | 0.259134i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.12134 | − | 4.72102i | 0.239070 | − | 1.00652i | ||||
\(23\) | − | 5.99610i | − | 1.25027i | −0.780516 | − | 0.625136i | \(-0.785043\pi\) | ||
0.780516 | − | 0.625136i | \(-0.214957\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.62762i | 0.925524i | ||||||||
\(26\) | 0.391724 | + | 0.0930425i | 0.0768234 | + | 0.0182471i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.259141 | + | 0.130463i | 0.0489730 | + | 0.0246551i | ||||
\(29\) | 0.395136 | + | 0.395136i | 0.0733750 | + | 0.0733750i | 0.742842 | − | 0.669467i | \(-0.233477\pi\) |
−0.669467 | + | 0.742842i | \(0.733477\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.98888 | 0.716424 | 0.358212 | − | 0.933640i | \(-0.383387\pi\) | ||||
0.358212 | + | 0.933640i | \(0.383387\pi\) | |||||||
\(32\) | −5.25207 | − | 2.10138i | −0.928443 | − | 0.371475i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.79683 | + | 2.33936i | −0.651150 | + | 0.401196i | ||||
\(35\) | 0.0625947 | + | 0.0625947i | 0.0105804 | + | 0.0105804i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.29237 | + | 5.29237i | −0.870060 | + | 0.870060i | −0.992479 | − | 0.122419i | \(-0.960935\pi\) |
0.122419 | + | 0.992479i | \(0.460935\pi\) | |||||||
\(38\) | 6.02209 | + | 1.43037i | 0.976913 | + | 0.232037i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.32056 | − | 1.11138i | −0.208798 | − | 0.175725i | ||||
\(41\) | 1.76918i | 0.276300i | 0.990411 | + | 0.138150i | \(0.0441156\pi\) | ||||
−0.990411 | + | 0.138150i | \(0.955884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.07993 | + | 8.07993i | −1.23218 | + | 1.23218i | −0.269053 | + | 0.963125i | \(0.586711\pi\) |
−0.963125 | + | 0.269053i | \(0.913289\pi\) | |||||||
\(44\) | −2.15213 | − | 6.51607i | −0.324445 | − | 0.982334i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.44815 | − | 7.21944i | −0.655844 | − | 1.06445i | ||||
\(47\) | 5.91082 | 0.862181 | 0.431091 | − | 0.902309i | \(-0.358129\pi\) | ||||
0.431091 | + | 0.902309i | \(0.358129\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.97896 | 0.996994 | ||||||||
\(50\) | 3.43296 | + | 5.57176i | 0.485494 | + | 0.787966i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.540668 | − | 0.178572i | 0.0749771 | − | 0.0247634i | ||||
\(53\) | −7.91745 | + | 7.91745i | −1.08755 | + | 1.08755i | −0.0917652 | + | 0.995781i | \(0.529251\pi\) |
−0.995781 | + | 0.0917652i | \(0.970749\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.09378i | − | 0.282325i | ||||||
\(56\) | 0.408794 | − | 0.0351611i | 0.0546274 | − | 0.00469860i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.768882 | + | 0.182625i | 0.100959 | + | 0.0239799i | ||||
\(59\) | 6.18218 | − | 6.18218i | 0.804852 | − | 0.804852i | −0.178998 | − | 0.983849i | \(-0.557286\pi\) |
0.983849 | + | 0.178998i | \(0.0572855\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.789321 | − | 0.789321i | −0.101062 | − | 0.101062i | 0.654768 | − | 0.755830i | \(-0.272766\pi\) |
−0.755830 | + | 0.654768i | \(0.772766\pi\) | |||||||
\(62\) | 4.80270 | − | 2.95911i | 0.609944 | − | 0.375808i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.88250 | + | 1.36608i | −0.985313 | + | 0.170760i | ||||
\(65\) | 0.173730 | 0.0215486 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.34861 | + | 6.34861i | 0.775607 | + | 0.775607i | 0.979080 | − | 0.203474i | \(-0.0652232\pi\) |
−0.203474 | + | 0.979080i | \(0.565223\pi\) | |||||||
\(68\) | −2.83604 | + | 5.63328i | −0.343920 | + | 0.683136i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.121801 | + | 0.0289302i | 0.0145580 | + | 0.00345782i | ||||
\(71\) | 3.39100i | 0.402437i | 0.979546 | + | 0.201219i | \(0.0644902\pi\) | ||||
−0.979546 | + | 0.201219i | \(0.935510\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.23764i | 0.261896i | 0.991389 | + | 0.130948i | \(0.0418021\pi\) | ||||
−0.991389 | + | 0.130948i | \(0.958198\pi\) | |||||||
\(74\) | −2.44604 | + | 10.2982i | −0.284346 | + | 1.19714i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.31185 | − | 2.74524i | 0.953435 | − | 0.314900i | ||||
\(77\) | 0.351951 | + | 0.351951i | 0.0401086 | + | 0.0401086i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.01161 | −0.788867 | −0.394434 | − | 0.918924i | \(-0.629059\pi\) | ||||
−0.394434 | + | 0.918924i | \(0.629059\pi\) | |||||||
\(80\) | −2.41445 | − | 0.358486i | −0.269943 | − | 0.0400799i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.31245 | + | 2.13014i | 0.144936 | + | 0.235235i | ||||
\(83\) | −4.08882 | − | 4.08882i | −0.448807 | − | 0.448807i | 0.446151 | − | 0.894958i | \(-0.352794\pi\) |
−0.894958 | + | 0.446151i | \(0.852794\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.36070 | + | 1.36070i | −0.147589 | + | 0.147589i | ||||
\(86\) | −3.73440 | + | 15.7225i | −0.402691 | + | 1.69540i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.42509 | − | 6.24896i | −0.791518 | − | 0.666142i | ||||
\(89\) | 14.1667i | 1.50167i | 0.660489 | + | 0.750835i | \(0.270349\pi\) | ||||
−0.660489 | + | 0.750835i | \(0.729651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0292030 | + | 0.0292030i | −0.00306131 | + | 0.00306131i | ||||
\(92\) | −10.7114 | − | 5.39256i | −1.11674 | − | 0.562213i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.11676 | − | 4.38488i | 0.734038 | − | 0.452266i | ||||
\(95\) | 2.67081 | 0.274019 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.2398 | 1.75044 | 0.875219 | − | 0.483727i | \(-0.160717\pi\) | ||||
0.875219 | + | 0.483727i | \(0.160717\pi\) | |||||||
\(98\) | 8.40283 | − | 5.17727i | 0.848814 | − | 0.522984i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.26672 | + | 4.16183i | 0.826672 | + | 0.416183i | ||||
\(101\) | −10.9005 | + | 10.9005i | −1.08464 | + | 1.08464i | −0.0885752 | + | 0.996069i | \(0.528231\pi\) |
−0.996069 | + | 0.0885752i | \(0.971769\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 16.0259i | − | 1.57908i | −0.613698 | − | 0.789541i | \(-0.710319\pi\) | ||
0.613698 | − | 0.789541i | \(-0.289681\pi\) | |||||||
\(104\) | 0.518505 | − | 0.616094i | 0.0508436 | − | 0.0604130i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.65931 | + | 15.4063i | −0.355423 | + | 1.49639i | ||||
\(107\) | −2.05995 | + | 2.05995i | −0.199143 | + | 0.199143i | −0.799632 | − | 0.600490i | \(-0.794972\pi\) |
0.600490 | + | 0.799632i | \(0.294972\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7881 | − | 11.7881i | −1.12909 | − | 1.12909i | −0.990325 | − | 0.138765i | \(-0.955687\pi\) |
−0.138765 | − | 0.990325i | \(-0.544313\pi\) | |||||||
\(110\) | −1.55325 | − | 2.52096i | −0.148097 | − | 0.240364i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.466113 | − | 0.345595i | 0.0440436 | − | 0.0326556i | ||||
\(113\) | −12.0717 | −1.13561 | −0.567807 | − | 0.823162i | \(-0.692208\pi\) | ||||
−0.567807 | + | 0.823162i | \(0.692208\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.58730 | − | 2.58730i | −0.241267 | − | 0.241267i | ||||
\(116\) | 1.06123 | − | 0.350503i | 0.0985328 | − | 0.0325434i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.85730 | − | 12.0297i | 0.263036 | − | 1.10742i | ||||
\(119\) | − | 0.457452i | − | 0.0419346i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 0.772692i | − | 0.0702448i | ||||||
\(122\) | −1.53591 | − | 0.364811i | −0.139055 | − | 0.0330284i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.58738 | − | 7.12568i | 0.322156 | − | 0.639905i | ||||
\(125\) | 4.15429 | + | 4.15429i | 0.371571 | + | 0.371571i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2608 | 1.17671 | 0.588355 | − | 0.808603i | \(-0.299776\pi\) | ||||
0.588355 | + | 0.808603i | \(0.299776\pi\) | |||||||
\(128\) | −8.47730 | + | 7.49236i | −0.749294 | + | 0.662237i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.209175 | − | 0.128880i | 0.0183459 | − | 0.0113035i | ||||
\(131\) | 7.63558 | + | 7.63558i | 0.667124 | + | 0.667124i | 0.957049 | − | 0.289926i | \(-0.0936305\pi\) |
−0.289926 | + | 0.957049i | \(0.593631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.448947 | + | 0.448947i | −0.0389286 | + | 0.0389286i | ||||
\(134\) | 12.3535 | + | 2.93422i | 1.06718 | + | 0.253478i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.764343 | + | 8.88649i | 0.0655419 | + | 0.762010i | ||||
\(137\) | − | 2.10201i | − | 0.179586i | −0.995960 | − | 0.0897932i | \(-0.971379\pi\) | ||
0.995960 | − | 0.0897932i | \(-0.0286206\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.44119 | + | 5.44119i | −0.461516 | + | 0.461516i | −0.899152 | − | 0.437636i | \(-0.855816\pi\) |
0.437636 | + | 0.899152i | \(0.355816\pi\) | |||||||
\(140\) | 0.168113 | − | 0.0555242i | 0.0142081 | − | 0.00469265i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.51558 | + | 4.08284i | 0.211103 | + | 0.342624i | ||||
\(143\) | 0.976834 | 0.0816869 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.341000 | 0.0283185 | ||||||||
\(146\) | 1.65997 | + | 2.69417i | 0.137380 | + | 0.222971i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.69456 | + | 14.2139i | 0.385890 | + | 1.16837i | ||||
\(149\) | 15.0912 | − | 15.0912i | 1.23632 | − | 1.23632i | 0.274824 | − | 0.961495i | \(-0.411380\pi\) |
0.961495 | − | 0.274824i | \(-0.0886196\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 15.1659i | − | 1.23418i | −0.786892 | − | 0.617090i | \(-0.788311\pi\) | ||
0.786892 | − | 0.617090i | \(-0.211689\pi\) | |||||||
\(152\) | 7.97113 | − | 9.47140i | 0.646544 | − | 0.768232i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.684850 | + | 0.162666i | 0.0551868 | + | 0.0131080i | ||||
\(155\) | 1.72119 | − | 1.72119i | 0.138249 | − | 0.138249i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.6066 | − | 11.6066i | −0.926306 | − | 0.926306i | 0.0711592 | − | 0.997465i | \(-0.477330\pi\) |
−0.997465 | + | 0.0711592i | \(0.977330\pi\) | |||||||
\(158\) | −8.44214 | + | 5.20150i | −0.671620 | + | 0.413809i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.17299 | + | 1.35951i | −0.250847 | + | 0.107479i | ||||
\(161\) | 0.869818 | 0.0685513 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.06506 | + | 5.06506i | 0.396726 | + | 0.396726i | 0.877077 | − | 0.480351i | \(-0.159491\pi\) |
−0.480351 | + | 0.877077i | \(0.659491\pi\) | |||||||
\(164\) | 3.16045 | + | 1.59111i | 0.246790 | + | 0.124245i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.95630 | − | 1.88978i | −0.617528 | − | 0.146676i | ||||
\(167\) | − | 22.6665i | − | 1.75399i | −0.480501 | − | 0.876994i | \(-0.659545\pi\) | ||
0.480501 | − | 0.876994i | \(-0.340455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.9189i | − | 0.993765i | ||||||
\(170\) | −0.628893 | + | 2.64774i | −0.0482339 | + | 0.203073i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.16725 | + | 21.7005i | 0.546498 | + | 1.65465i | ||||
\(173\) | −7.67777 | − | 7.67777i | −0.583730 | − | 0.583730i | 0.352196 | − | 0.935926i | \(-0.385435\pi\) |
−0.935926 | + | 0.352196i | \(0.885435\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.671301 | −0.0507456 | ||||||||
\(176\) | −13.5757 | − | 2.01566i | −1.02331 | − | 0.151936i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10.5095 | + | 17.0571i | 0.787717 | + | 1.27848i | ||||
\(179\) | 2.05995 | + | 2.05995i | 0.153968 | + | 0.153968i | 0.779888 | − | 0.625920i | \(-0.215276\pi\) |
−0.625920 | + | 0.779888i | \(0.715276\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.82518 | + | 7.82518i | −0.581641 | + | 0.581641i | −0.935354 | − | 0.353713i | \(-0.884919\pi\) |
0.353713 | + | 0.935354i | \(0.384919\pi\) | |||||||
\(182\) | −0.0134971 | + | 0.0568251i | −0.00100047 | + | 0.00421216i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.8971 | + | 1.45335i | −1.24567 | + | 0.107143i | ||||
\(185\) | 4.56728i | 0.335793i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.65083 | + | 7.65083i | −0.559484 | + | 0.559484i | ||||
\(188\) | 5.31586 | − | 10.5590i | 0.387699 | − | 0.770095i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.21571 | − | 1.98131i | 0.233292 | − | 0.143740i | ||||
\(191\) | 3.78274 | 0.273710 | 0.136855 | − | 0.990591i | \(-0.456301\pi\) | ||||
0.136855 | + | 0.990591i | \(0.456301\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.43287 | −0.319085 | −0.159542 | − | 0.987191i | \(-0.551002\pi\) | ||||
−0.159542 | + | 0.987191i | \(0.551002\pi\) | |||||||
\(194\) | 20.7571 | − | 12.7892i | 1.49028 | − | 0.918211i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.27649 | − | 12.4671i | 0.448320 | − | 0.890509i | ||||
\(197\) | −2.97523 | + | 2.97523i | −0.211976 | + | 0.211976i | −0.805106 | − | 0.593130i | \(-0.797892\pi\) |
0.593130 | + | 0.805106i | \(0.297892\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 19.0589i | − | 1.35105i | −0.737338 | − | 0.675524i | \(-0.763917\pi\) | ||
0.737338 | − | 0.675524i | \(-0.236083\pi\) | |||||||
\(200\) | 13.0407 | − | 1.12166i | 0.922120 | − | 0.0793132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.03804 | + | 21.2110i | −0.354475 | + | 1.49240i | ||||
\(203\) | −0.0573201 | + | 0.0573201i | −0.00402308 | + | 0.00402308i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.763398 | + | 0.763398i | 0.0533180 | + | 0.0533180i | ||||
\(206\) | −11.8887 | − | 19.2956i | −0.828324 | − | 1.34439i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.167248 | − | 1.12644i | 0.0115966 | − | 0.0781045i | ||||
\(209\) | 15.0172 | 1.03876 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.44175 | − | 3.44175i | −0.236940 | − | 0.236940i | 0.578642 | − | 0.815582i | \(-0.303583\pi\) |
−0.815582 | + | 0.578642i | \(0.803583\pi\) | |||||||
\(212\) | 7.02312 | + | 21.2642i | 0.482350 | + | 1.46043i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.952072 | + | 4.00838i | −0.0650823 | + | 0.274007i | ||||
\(215\) | 6.97293i | 0.475550i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.578643i | 0.0392808i | ||||||||
\(218\) | −22.9379 | − | 5.44823i | −1.55355 | − | 0.369001i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.74030 | − | 1.88303i | −0.252171 | − | 0.126954i | ||||
\(221\) | −0.634824 | − | 0.634824i | −0.0427029 | − | 0.0427029i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.6369 | −1.38195 | −0.690975 | − | 0.722879i | \(-0.742819\pi\) | ||||
−0.690975 | + | 0.722879i | \(0.742819\pi\) | |||||||
\(224\) | 0.304835 | − | 0.761886i | 0.0203676 | − | 0.0509056i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.5347 | + | 8.95531i | −0.966831 | + | 0.595698i | ||||
\(227\) | −15.2341 | − | 15.2341i | −1.01112 | − | 1.01112i | −0.999937 | − | 0.0111848i | \(-0.996440\pi\) |
−0.0111848 | − | 0.999937i | \(-0.503560\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.28300 | + | 6.28300i | −0.415192 | + | 0.415192i | −0.883543 | − | 0.468350i | \(-0.844848\pi\) |
0.468350 | + | 0.883543i | \(0.344848\pi\) | |||||||
\(230\) | −5.03453 | − | 1.19580i | −0.331967 | − | 0.0788489i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.01773 | − | 1.20928i | 0.0668172 | − | 0.0793930i | ||||
\(233\) | − | 16.8057i | − | 1.10098i | −0.834842 | − | 0.550490i | \(-0.814441\pi\) | ||
0.834842 | − | 0.550490i | \(-0.185559\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.55050 | − | 2.55050i | 0.166376 | − | 0.166376i | ||||
\(236\) | −5.48386 | − | 16.6037i | −0.356969 | − | 1.08081i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.339357 | − | 0.550783i | −0.0219972 | − | 0.0357020i | ||||
\(239\) | −13.6647 | −0.883899 | −0.441950 | − | 0.897040i | \(-0.645713\pi\) | ||||
−0.441950 | + | 0.897040i | \(0.645713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 27.0347 | 1.74146 | 0.870730 | − | 0.491761i | \(-0.163647\pi\) | ||||
0.870730 | + | 0.491761i | \(0.163647\pi\) | |||||||
\(242\) | −0.573215 | − | 0.930340i | −0.0368476 | − | 0.0598045i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.11991 | + | 0.700162i | −0.135713 | + | 0.0448233i | ||||
\(245\) | 3.01140 | − | 3.01140i | 0.192391 | − | 0.192391i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.24604i | 0.0792838i | ||||||||
\(248\) | −0.966838 | − | 11.2408i | −0.0613943 | − | 0.713788i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 8.08368 | + | 1.92004i | 0.511257 | + | 0.121434i | ||||
\(251\) | −4.18483 | + | 4.18483i | −0.264144 | + | 0.264144i | −0.826735 | − | 0.562591i | \(-0.809805\pi\) |
0.562591 | + | 0.826735i | \(0.309805\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.5476 | − | 14.5476i | −0.914600 | − | 0.914600i | ||||
\(254\) | 15.9664 | − | 9.83744i | 1.00182 | − | 0.617256i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.64873 | + | 15.3098i | −0.290546 | + | 0.956861i | ||||
\(257\) | 2.12929 | 0.132821 | 0.0664106 | − | 0.997792i | \(-0.478845\pi\) | ||||
0.0664106 | + | 0.997792i | \(0.478845\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.767732 | − | 0.767732i | −0.0477046 | − | 0.0477046i | ||||
\(260\) | 0.156243 | − | 0.310349i | 0.00968980 | − | 0.0192471i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.8578 | + | 3.52903i | 0.917918 | + | 0.218024i | ||||
\(263\) | 22.3552i | 1.37848i | 0.724534 | + | 0.689239i | \(0.242055\pi\) | ||||
−0.724534 | + | 0.689239i | \(0.757945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.83271i | 0.419730i | ||||||||
\(266\) | −0.207495 | + | 0.873589i | −0.0127224 | + | 0.0535632i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 17.0507 | − | 5.63149i | 1.04154 | − | 0.343998i | ||||
\(269\) | −7.04997 | − | 7.04997i | −0.429844 | − | 0.429844i | 0.458731 | − | 0.888575i | \(-0.348304\pi\) |
−0.888575 | + | 0.458731i | \(0.848304\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1344 | 0.919351 | 0.459676 | − | 0.888087i | \(-0.347966\pi\) | ||||
0.459676 | + | 0.888087i | \(0.347966\pi\) | |||||||
\(272\) | 7.51265 | + | 10.1325i | 0.455521 | + | 0.614374i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.55935 | − | 2.53086i | −0.0942040 | − | 0.152895i | ||||
\(275\) | 11.2274 | + | 11.2274i | 0.677040 | + | 0.677040i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.2724 | − | 14.2724i | 0.857543 | − | 0.857543i | −0.133505 | − | 0.991048i | \(-0.542623\pi\) |
0.991048 | + | 0.133505i | \(0.0426232\pi\) | |||||||
\(278\) | −2.51482 | + | 10.5878i | −0.150829 | + | 0.635015i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.161221 | − | 0.191565i | 0.00963482 | − | 0.0114482i | ||||
\(281\) | − | 20.3101i | − | 1.21160i | −0.795618 | − | 0.605799i | \(-0.792854\pi\) | ||
0.795618 | − | 0.605799i | \(-0.207146\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.91438 | + | 4.91438i | −0.292130 | + | 0.292130i | −0.837921 | − | 0.545791i | \(-0.816229\pi\) |
0.545791 | + | 0.837921i | \(0.316229\pi\) | |||||||
\(284\) | 6.05763 | + | 3.04967i | 0.359454 | + | 0.180965i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.17613 | − | 0.724655i | 0.0695461 | − | 0.0428498i | ||||
\(287\) | −0.256645 | −0.0151493 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.05576 | −0.415045 | ||||||||
\(290\) | 0.410572 | − | 0.252968i | 0.0241096 | − | 0.0148548i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.99730 | + | 2.01241i | 0.233924 | + | 0.117767i | ||||
\(293\) | 11.6160 | − | 11.6160i | 0.678611 | − | 0.678611i | −0.281075 | − | 0.959686i | \(-0.590691\pi\) |
0.959686 | + | 0.281075i | \(0.0906909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 5.33518i | − | 0.310626i | ||||||
\(296\) | 16.1968 | + | 13.6312i | 0.941419 | + | 0.792299i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.97489 | − | 29.3654i | 0.404044 | − | 1.70109i | ||||
\(299\) | 1.20708 | − | 1.20708i | 0.0698073 | − | 0.0698073i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.17211 | − | 1.17211i | −0.0675592 | − | 0.0675592i | ||||
\(302\) | −11.2507 | − | 18.2601i | −0.647403 | − | 1.05075i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.57116 | − | 17.3171i | 0.147466 | − | 0.993204i | ||||
\(305\) | −0.681179 | −0.0390042 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.20459 | + | 7.20459i | 0.411188 | + | 0.411188i | 0.882152 | − | 0.470964i | \(-0.156094\pi\) |
−0.470964 | + | 0.882152i | \(0.656094\pi\) | |||||||
\(308\) | 0.945247 | − | 0.312196i | 0.0538605 | − | 0.0177890i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.795503 | − | 3.34920i | 0.0451815 | − | 0.190222i | ||||
\(311\) | 2.76925i | 0.157030i | 0.996913 | + | 0.0785148i | \(0.0250178\pi\) | ||||
−0.996913 | + | 0.0785148i | \(0.974982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 0.232921i | − | 0.0131655i | −0.999978 | − | 0.00658273i | \(-0.997905\pi\) | ||
0.999978 | − | 0.00658273i | \(-0.00209536\pi\) | |||||||
\(314\) | −22.5848 | − | 5.36436i | −1.27454 | − | 0.302728i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.30585 | + | 12.5254i | −0.354732 | + | 0.704611i | ||||
\(317\) | 16.5035 | + | 16.5035i | 0.926931 | + | 0.926931i | 0.997506 | − | 0.0705754i | \(-0.0224835\pi\) |
−0.0705754 | + | 0.997506i | \(0.522484\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.91734 | 0.107351 | ||||||||
\(320\) | −2.81181 | + | 3.99073i | −0.157185 | + | 0.223089i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.04728 | − | 0.645267i | 0.0583627 | − | 0.0359593i | ||||
\(323\) | −9.75935 | − | 9.75935i | −0.543025 | − | 0.543025i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.931592 | + | 0.931592i | −0.0516754 | + | 0.0516754i | ||||
\(326\) | 9.85592 | + | 2.34098i | 0.545869 | + | 0.129655i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.98560 | − | 0.428821i | 0.275284 | − | 0.0236777i | ||||
\(329\) | 0.857447i | 0.0472726i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.73963 | − | 1.73963i | 0.0956187 | − | 0.0956187i | −0.657679 | − | 0.753298i | \(-0.728462\pi\) |
0.753298 | + | 0.657679i | \(0.228462\pi\) | |||||||
\(332\) | −10.9815 | + | 3.62696i | −0.602687 | + | 0.199055i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.8150 | − | 27.2910i | −0.920073 | − | 1.49330i | ||||
\(335\) | 5.47881 | 0.299340 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.38998 | 0.184664 | 0.0923319 | − | 0.995728i | \(-0.470568\pi\) | ||||
0.0923319 | + | 0.995728i | \(0.470568\pi\) | |||||||
\(338\) | −9.58380 | − | 15.5547i | −0.521290 | − | 0.846065i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.20700 | + | 3.65448i | 0.0654589 | + | 0.198192i | ||||
\(341\) | 9.67774 | − | 9.67774i | 0.524079 | − | 0.524079i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.02784i | 0.109493i | ||||||||
\(344\) | 24.7279 | + | 20.8110i | 1.33324 | + | 1.12205i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.9399 | − | 3.54853i | −0.803173 | − | 0.190770i | ||||
\(347\) | −20.0204 | + | 20.0204i | −1.07475 | + | 1.07475i | −0.0777788 | + | 0.996971i | \(0.524783\pi\) |
−0.996971 | + | 0.0777788i | \(0.975217\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.9303 | + | 11.9303i | 0.638616 | + | 0.638616i | 0.950214 | − | 0.311598i | \(-0.100864\pi\) |
−0.311598 | + | 0.950214i | \(0.600864\pi\) | |||||||
\(350\) | −0.808263 | + | 0.497999i | −0.0432035 | + | 0.0266192i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −17.8408 | + | 7.64412i | −0.950917 | + | 0.407433i | ||||
\(353\) | 26.0718 | 1.38766 | 0.693830 | − | 0.720139i | \(-0.255922\pi\) | ||||
0.693830 | + | 0.720139i | \(0.255922\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.46320 | + | 1.46320i | 0.0776588 | + | 0.0776588i | ||||
\(356\) | 25.3073 | + | 12.7408i | 1.34128 | + | 0.675260i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.00838 | + | 0.952072i | 0.211849 | + | 0.0503186i | ||||
\(359\) | 11.3940i | 0.601350i | 0.953727 | + | 0.300675i | \(0.0972120\pi\) | ||||
−0.953727 | + | 0.300675i | \(0.902788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.155790i | 0.00819949i | ||||||||
\(362\) | −3.61666 | + | 15.2267i | −0.190087 | + | 0.800299i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.0259043 | + | 0.0784314i | 0.00135776 | + | 0.00411092i | ||||
\(365\) | 0.965536 | + | 0.965536i | 0.0505384 | + | 0.0505384i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.83069 | 0.513158 | 0.256579 | − | 0.966523i | \(-0.417405\pi\) | ||||
0.256579 | + | 0.966523i | \(0.417405\pi\) | |||||||
\(368\) | −19.2664 | + | 14.2849i | −1.00433 | + | 0.744650i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.38819 | + | 5.49911i | 0.176144 | + | 0.285885i | ||||
\(371\) | −1.14854 | − | 1.14854i | −0.0596291 | − | 0.0596291i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9304 | + | 14.9304i | −0.773067 | + | 0.773067i | −0.978641 | − | 0.205575i | \(-0.934094\pi\) |
0.205575 | + | 0.978641i | \(0.434094\pi\) | |||||||
\(374\) | −3.53608 | + | 14.8875i | −0.182846 | + | 0.769813i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.43268 | − | 16.6568i | −0.0738850 | − | 0.859009i | ||||
\(377\) | 0.159091i | 0.00819359i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.32709 | − | 2.32709i | 0.119534 | − | 0.119534i | −0.644809 | − | 0.764344i | \(-0.723063\pi\) |
0.764344 | + | 0.644809i | \(0.223063\pi\) | |||||||
\(380\) | 2.40198 | − | 4.77110i | 0.123219 | − | 0.244752i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.55451 | − | 2.80619i | 0.233029 | − | 0.143577i | ||||
\(383\) | −28.7611 | −1.46962 | −0.734811 | − | 0.678272i | \(-0.762729\pi\) | ||||
−0.734811 | + | 0.678272i | \(0.762729\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.303732 | 0.0154796 | ||||||||
\(386\) | −5.33727 | + | 3.28848i | −0.271660 | + | 0.167379i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.5045 | − | 30.7970i | 0.787123 | − | 1.56348i | ||||
\(389\) | −16.6290 | + | 16.6290i | −0.843125 | + | 0.843125i | −0.989264 | − | 0.146139i | \(-0.953315\pi\) |
0.146139 | + | 0.989264i | \(0.453315\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.9084i | 0.956238i | ||||||||
\(392\) | −1.69158 | − | 19.6669i | −0.0854378 | − | 0.993326i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.37510 | + | 5.78939i | −0.0692764 | + | 0.291665i | ||||
\(395\) | −3.02549 | + | 3.02549i | −0.152229 | + | 0.152229i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.4919 | + | 19.4919i | 0.978271 | + | 0.978271i | 0.999769 | − | 0.0214976i | \(-0.00684343\pi\) |
−0.0214976 | + | 0.999769i | \(0.506843\pi\) | |||||||
\(398\) | −14.1387 | − | 22.9473i | −0.708707 | − | 1.15025i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.8693 | − | 11.0247i | 0.743463 | − | 0.551233i | ||||
\(401\) | −34.7719 | −1.73643 | −0.868213 | − | 0.496192i | \(-0.834731\pi\) | ||||
−0.868213 | + | 0.496192i | \(0.834731\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.803006 | + | 0.803006i | 0.0400006 | + | 0.0400006i | ||||
\(404\) | 9.66925 | + | 29.2759i | 0.481063 | + | 1.45653i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0264923 | + | 0.111537i | −0.00131479 | + | 0.00553549i | ||||
\(407\) | 25.6805i | 1.27293i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.194755i | − | 0.00963004i | −0.999988 | − | 0.00481502i | \(-0.998467\pi\) | ||
0.999988 | − | 0.00481502i | \(-0.00153267\pi\) | |||||||
\(410\) | 1.48547 | + | 0.352829i | 0.0733620 | + | 0.0174250i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.6285 | − | 14.4128i | −1.41043 | − | 0.710069i | ||||
\(413\) | 0.896813 | + | 0.896813i | 0.0441293 | + | 0.0441293i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.52863 | −0.173214 | ||||||||
\(416\) | −0.634268 | − | 1.48033i | −0.0310975 | − | 0.0725792i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.0810 | − | 11.1403i | 0.884371 | − | 0.544892i | ||||
\(419\) | 26.2018 | + | 26.2018i | 1.28004 | + | 1.28004i | 0.940642 | + | 0.339400i | \(0.110224\pi\) |
0.339400 | + | 0.940642i | \(0.389776\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.73965 | − | 3.73965i | 0.182259 | − | 0.182259i | −0.610080 | − | 0.792340i | \(-0.708863\pi\) |
0.792340 | + | 0.610080i | \(0.208863\pi\) | |||||||
\(422\) | −6.69717 | − | 1.59072i | −0.326013 | − | 0.0774348i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 24.2306 | + | 20.3925i | 1.17674 | + | 0.990348i | ||||
\(425\) | − | 14.5930i | − | 0.707863i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.114502 | − | 0.114502i | 0.00554115 | − | 0.00554115i | ||||
\(428\) | 1.82726 | + | 5.53247i | 0.0883241 | + | 0.267422i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.17281 | + | 8.39557i | 0.249455 | + | 0.404870i | ||||
\(431\) | −15.9815 | −0.769803 | −0.384902 | − | 0.922958i | \(-0.625765\pi\) | ||||
−0.384902 | + | 0.922958i | \(0.625765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.4282 | −0.789487 | −0.394743 | − | 0.918791i | \(-0.629166\pi\) | ||||
−0.394743 | + | 0.918791i | \(0.629166\pi\) | |||||||
\(434\) | 0.429261 | + | 0.696700i | 0.0206052 | + | 0.0334427i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.6595 | + | 10.4565i | −1.51622 | + | 0.500776i | ||||
\(437\) | 18.5568 | − | 18.5568i | 0.887694 | − | 0.887694i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7064i | 0.797355i | 0.917091 | + | 0.398678i | \(0.130531\pi\) | ||||
−0.917091 | + | 0.398678i | \(0.869469\pi\) | |||||||
\(440\) | −5.90031 | + | 0.507497i | −0.281286 | + | 0.0241940i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.23528 | − | 0.293405i | −0.0587564 | − | 0.0139558i | ||||
\(443\) | −14.0270 | + | 14.0270i | −0.666443 | + | 0.666443i | −0.956891 | − | 0.290448i | \(-0.906196\pi\) |
0.290448 | + | 0.956891i | \(0.406196\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.11290 | + | 6.11290i | 0.289779 | + | 0.289779i | ||||
\(446\) | −24.8473 | + | 15.3093i | −1.17656 | + | 0.724917i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.198170 | − | 1.14347i | −0.00936263 | − | 0.0540238i | ||||
\(449\) | 36.1984 | 1.70831 | 0.854153 | − | 0.520022i | \(-0.174076\pi\) | ||||
0.854153 | + | 0.520022i | \(0.174076\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.29236 | + | 4.29236i | 0.202119 | + | 0.202119i | ||||
\(452\) | −10.8567 | + | 21.5648i | −0.510654 | + | 1.01432i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −29.6435 | − | 7.04093i | −1.39124 | − | 0.330447i | ||||
\(455\) | 0.0252020i | 0.00118149i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.1008i | 1.22094i | 0.792037 | + | 0.610472i | \(0.209020\pi\) | ||||
−0.792037 | + | 0.610472i | \(0.790980\pi\) | |||||||
\(458\) | −2.90389 | + | 12.2259i | −0.135690 | + | 0.571277i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.94879 | + | 2.29504i | −0.323989 | + | 0.107007i | ||||
\(461\) | −21.9138 | − | 21.9138i | −1.02063 | − | 1.02063i | −0.999783 | − | 0.0208460i | \(-0.993364\pi\) |
−0.0208460 | − | 0.999783i | \(-0.506636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.2790 | −0.570654 | −0.285327 | − | 0.958430i | \(-0.592102\pi\) | ||||
−0.285327 | + | 0.958430i | \(0.592102\pi\) | |||||||
\(464\) | 0.328278 | − | 2.21099i | 0.0152399 | − | 0.102643i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.4672 | − | 20.2345i | −0.577531 | − | 0.937345i | ||||
\(467\) | −2.75939 | − | 2.75939i | −0.127690 | − | 0.127690i | 0.640374 | − | 0.768063i | \(-0.278779\pi\) |
−0.768063 | + | 0.640374i | \(0.778779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.920956 | + | 0.920956i | −0.0425258 | + | 0.0425258i | ||||
\(470\) | 1.17880 | − | 4.96292i | 0.0543738 | − | 0.228923i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.9200 | − | 15.9231i | −0.870863 | − | 0.732919i | ||||
\(473\) | 39.2067i | 1.80273i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.3216 | + | 14.3216i | −0.657122 | + | 0.657122i | ||||
\(476\) | −0.817186 | − | 0.411407i | −0.0374557 | − | 0.0188568i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.4527 | + | 10.1371i | −0.752528 | + | 0.463659i | ||||
\(479\) | 9.23611 | 0.422008 | 0.211004 | − | 0.977485i | \(-0.432327\pi\) | ||||
0.211004 | + | 0.977485i | \(0.432327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.13082 | −0.0971572 | ||||||||
\(482\) | 32.5504 | − | 20.0555i | 1.48263 | − | 0.913501i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.38033 | − | 0.694917i | −0.0627422 | − | 0.0315871i | ||||
\(485\) | 7.43892 | − | 7.43892i | 0.337784 | − | 0.337784i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.5777i | 1.43092i | 0.698652 | + | 0.715461i | \(0.253783\pi\) | ||||
−0.698652 | + | 0.715461i | \(0.746217\pi\) | |||||||
\(488\) | −2.03301 | + | 2.41564i | −0.0920299 | + | 0.109351i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.39182 | − | 5.85977i | 0.0628758 | − | 0.264717i | ||||
\(491\) | −9.58359 | + | 9.58359i | −0.432501 | + | 0.432501i | −0.889478 | − | 0.456977i | \(-0.848932\pi\) |
0.456977 | + | 0.889478i | \(0.348932\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.24604 | − | 1.24604i | −0.0561189 | − | 0.0561189i | ||||
\(494\) | 0.924365 | + | 1.50026i | 0.0415892 | + | 0.0675001i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.50294 | − | 12.8169i | −0.426695 | − | 0.575495i | ||||
\(497\) | −0.491912 | −0.0220653 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.34782 | + | 8.34782i | 0.373700 | + | 0.373700i | 0.868823 | − | 0.495123i | \(-0.164877\pi\) |
−0.495123 | + | 0.868823i | \(0.664877\pi\) | |||||||
\(500\) | 11.1573 | − | 3.68503i | 0.498970 | − | 0.164800i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.93415 | + | 8.14311i | −0.0863256 | + | 0.363445i | ||||
\(503\) | − | 18.7022i | − | 0.833888i | −0.908932 | − | 0.416944i | \(-0.863101\pi\) | ||
0.908932 | − | 0.416944i | \(-0.136899\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.40710i | 0.418610i | ||||||||
\(506\) | −28.3077 | − | 6.72365i | −1.25843 | − | 0.298903i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.9261 | − | 23.6890i | 0.529134 | − | 1.05103i | ||||
\(509\) | 18.0996 | + | 18.0996i | 0.802251 | + | 0.802251i | 0.983447 | − | 0.181196i | \(-0.0579968\pi\) |
−0.181196 | + | 0.983447i | \(0.557997\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.324602 | −0.0143595 | ||||||||
\(512\) | 5.76024 | + | 21.8819i | 0.254569 | + | 0.967055i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.56371 | − | 1.57959i | 0.113080 | − | 0.0696728i | ||||
\(515\) | −6.91514 | − | 6.91514i | −0.304717 | − | 0.304717i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.3407 | − | 14.3407i | 0.630703 | − | 0.630703i | ||||
\(518\) | −1.49390 | − | 0.354832i | −0.0656383 | − | 0.0155904i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0421093 | − | 0.489576i | −0.00184661 | − | 0.0214693i | ||||
\(521\) | − | 36.0316i | − | 1.57857i | −0.614024 | − | 0.789287i | \(-0.710450\pi\) | ||
0.614024 | − | 0.789287i | \(-0.289550\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.68786 | − | 7.68786i | 0.336167 | − | 0.336167i | −0.518756 | − | 0.854922i | \(-0.673605\pi\) |
0.854922 | + | 0.518756i | \(0.173605\pi\) | |||||||
\(524\) | 20.5071 | − | 6.77309i | 0.895858 | − | 0.295884i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.5840 | + | 26.9161i | 0.723096 | + | 1.17360i | ||||
\(527\) | −12.5787 | −0.547938 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.9532 | −0.563182 | ||||||||
\(530\) | 5.06878 | + | 8.22674i | 0.220174 | + | 0.357347i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.398235 | + | 1.20575i | 0.0172657 | + | 0.0522759i | ||||
\(533\) | −0.356157 | + | 0.356157i | −0.0154269 | + | 0.0154269i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.77772i | 0.0768577i | ||||||||
\(536\) | 16.3517 | − | 19.4293i | 0.706288 | − | 0.839219i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.7183 | − | 3.25837i | −0.591437 | − | 0.140478i | ||||
\(539\) | 16.9322 | − | 16.9322i | 0.729321 | − | 0.729321i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.6750 | + | 10.6750i | 0.458953 | + | 0.458953i | 0.898312 | − | 0.439358i | \(-0.144794\pi\) |
−0.439358 | + | 0.898312i | \(0.644794\pi\) | |||||||
\(542\) | 18.2222 | − | 11.2273i | 0.782711 | − | 0.482255i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.5621 | + | 6.62660i | 0.710095 | + | 0.284113i | ||||
\(545\) | −10.1730 | −0.435764 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.5460 | − | 22.5460i | −0.963997 | − | 0.963997i | 0.0353769 | − | 0.999374i | \(-0.488737\pi\) |
−0.999374 | + | 0.0353769i | \(0.988737\pi\) | |||||||
\(548\) | −3.75500 | − | 1.89043i | −0.160405 | − | 0.0807550i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 21.8471 | + | 5.18913i | 0.931562 | + | 0.221265i | ||||
\(551\) | 2.44575i | 0.104192i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.01713i | − | 0.0432529i | ||||||
\(554\) | 6.59644 | − | 27.7721i | 0.280256 | − | 1.17992i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.82657 | + | 14.6136i | 0.204692 | + | 0.619754i | ||||
\(557\) | 5.21780 | + | 5.21780i | 0.221085 | + | 0.221085i | 0.808955 | − | 0.587870i | \(-0.200033\pi\) |
−0.587870 | + | 0.808955i | \(0.700033\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.25316 | −0.137594 | ||||||||
\(560\) | 0.0520034 | − | 0.350249i | 0.00219754 | − | 0.0148007i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.0668 | − | 24.4538i | −0.635557 | − | 1.03152i | ||||
\(563\) | 2.18674 | + | 2.18674i | 0.0921602 | + | 0.0921602i | 0.751684 | − | 0.659524i | \(-0.229242\pi\) |
−0.659524 | + | 0.751684i | \(0.729242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.20892 | + | 5.20892i | −0.219141 | + | 0.219141i | ||||
\(566\) | −2.27134 | + | 9.56272i | −0.0954716 | + | 0.401951i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.55590 | − | 0.821921i | 0.400957 | − | 0.0344870i | ||||
\(569\) | 9.40319i | 0.394202i | 0.980383 | + | 0.197101i | \(0.0631527\pi\) | ||||
−0.980383 | + | 0.197101i | \(0.936847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.5674 | − | 28.5674i | 1.19551 | − | 1.19551i | 0.220014 | − | 0.975497i | \(-0.429390\pi\) |
0.975497 | − | 0.220014i | \(-0.0706102\pi\) | |||||||
\(572\) | 0.878510 | − | 1.74500i | 0.0367323 | − | 0.0729623i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.309007 | + | 0.190390i | −0.0128977 | + | 0.00794672i | ||||
\(575\) | 27.7477 | 1.15716 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.70475 | −0.362384 | −0.181192 | − | 0.983448i | \(-0.557995\pi\) | ||||
−0.181192 | + | 0.983448i | \(0.557995\pi\) | |||||||
\(578\) | −8.49531 | + | 5.23425i | −0.353358 | + | 0.217716i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.306677 | − | 0.609158i | 0.0127341 | − | 0.0252939i | ||||
\(581\) | 0.593141 | − | 0.593141i | 0.0246077 | − | 0.0246077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.4183i | 1.59112i | ||||||||
\(584\) | 6.30573 | − | 0.542367i | 0.260933 | − | 0.0224433i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.36869 | − | 22.6031i | 0.221779 | − | 0.933724i | ||||
\(587\) | −2.03359 | + | 2.03359i | −0.0839353 | + | 0.0839353i | −0.747828 | − | 0.663893i | \(-0.768903\pi\) |
0.663893 | + | 0.747828i | \(0.268903\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.3449 | + | 12.3449i | 0.508661 | + | 0.508661i | ||||
\(590\) | −3.95786 | − | 6.42369i | −0.162942 | − | 0.264459i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 29.6135 | + | 4.39688i | 1.21711 | + | 0.180710i | ||||
\(593\) | −18.8849 | −0.775508 | −0.387754 | − | 0.921763i | \(-0.626749\pi\) | ||||
−0.387754 | + | 0.921763i | \(0.626749\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.197389 | − | 0.197389i | −0.00809216 | − | 0.00809216i | ||||
\(596\) | −13.3865 | − | 40.5309i | −0.548334 | − | 1.66021i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.557892 | − | 2.34882i | 0.0228139 | − | 0.0960502i | ||||
\(599\) | − | 6.48419i | − | 0.264937i | −0.991187 | − | 0.132468i | \(-0.957710\pi\) | ||
0.991187 | − | 0.132468i | \(-0.0422903\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 11.1376i | − | 0.454313i | −0.973858 | − | 0.227156i | \(-0.927057\pi\) | ||
0.973858 | − | 0.227156i | \(-0.0729429\pi\) | |||||||
\(602\) | −2.28076 | − | 0.541728i | −0.0929570 | − | 0.0220792i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −27.0921 | − | 13.6393i | −1.10236 | − | 0.554977i | ||||
\(605\) | −0.333414 | − | 0.333414i | −0.0135552 | − | 0.0135552i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.1363 | 0.898486 | 0.449243 | − | 0.893410i | \(-0.351694\pi\) | ||||
0.449243 | + | 0.893410i | \(0.351694\pi\) | |||||||
\(608\) | −9.75079 | − | 22.7576i | −0.395447 | − | 0.922942i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.820156 | + | 0.505327i | −0.0332071 | + | 0.0204601i | ||||
\(611\) | 1.18991 | + | 1.18991i | 0.0481387 | + | 0.0481387i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.82549 | + | 2.82549i | −0.114121 | + | 0.114121i | −0.761861 | − | 0.647740i | \(-0.775714\pi\) |
0.647740 | + | 0.761861i | \(0.275714\pi\) | |||||||
\(614\) | 14.0192 | + | 3.32984i | 0.565767 | + | 0.134381i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.906500 | − | 1.07711i | 0.0365239 | − | 0.0433982i | ||||
\(617\) | − | 7.27869i | − | 0.293029i | −0.989209 | − | 0.146514i | \(-0.953194\pi\) | ||
0.989209 | − | 0.146514i | \(-0.0468055\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.7397 | − | 24.7397i | 0.994371 | − | 0.994371i | −0.00561374 | − | 0.999984i | \(-0.501787\pi\) |
0.999984 | + | 0.00561374i | \(0.00178692\pi\) | |||||||
\(620\) | −1.52677 | − | 4.62265i | −0.0613165 | − | 0.185650i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.05434 | + | 3.33424i | 0.0823715 | + | 0.133691i | ||||
\(623\) | −2.05508 | −0.0823352 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.5530 | −0.782119 | ||||||||
\(626\) | −0.172790 | − | 0.280442i | −0.00690608 | − | 0.0112087i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −31.1722 | + | 10.2955i | −1.24390 | + | 0.410836i | ||||
\(629\) | 16.6892 | − | 16.6892i | 0.665442 | − | 0.665442i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 16.3145i | − | 0.649471i | −0.945805 | − | 0.324736i | \(-0.894725\pi\) | ||
0.945805 | − | 0.324736i | \(-0.105275\pi\) | |||||||
\(632\) | 1.69950 | + | 19.7589i | 0.0676023 | + | 0.785965i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 32.1136 | + | 7.62765i | 1.27540 | + | 0.302933i | ||||
\(635\) | 5.72201 | − | 5.72201i | 0.227071 | − | 0.227071i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.40494 | + | 1.40494i | 0.0556658 | + | 0.0556658i | ||||
\(638\) | 2.30853 | − | 1.42236i | 0.0913955 | − | 0.0563119i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.424999 | + | 6.89085i | −0.0167996 | + | 0.272385i | ||||
\(641\) | 14.6358 | 0.578080 | 0.289040 | − | 0.957317i | \(-0.406664\pi\) | ||||
0.289040 | + | 0.957317i | \(0.406664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.9564 | − | 11.9564i | −0.471515 | − | 0.471515i | 0.430890 | − | 0.902405i | \(-0.358200\pi\) |
−0.902405 | + | 0.430890i | \(0.858200\pi\) | |||||||
\(644\) | 0.782266 | − | 1.55383i | 0.0308256 | − | 0.0612296i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.9904 | − | 4.51060i | −0.747166 | − | 0.177467i | ||||
\(647\) | − | 16.0163i | − | 0.629667i | −0.949147 | − | 0.314834i | \(-0.898051\pi\) | ||
0.949147 | − | 0.314834i | \(-0.101949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 29.9982i | − | 1.17753i | ||||||
\(650\) | −0.430565 | + | 1.81275i | −0.0168882 | + | 0.0711019i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.6034 | − | 4.49292i | 0.532750 | − | 0.175957i | ||||
\(653\) | −14.1903 | − | 14.1903i | −0.555310 | − | 0.555310i | 0.372658 | − | 0.927969i | \(-0.378446\pi\) |
−0.927969 | + | 0.372658i | \(0.878446\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.58946 | 0.257471 | ||||||||
\(656\) | 5.68466 | − | 4.21483i | 0.221949 | − | 0.164562i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.636089 | + | 1.03239i | 0.0247973 | + | 0.0402466i | ||||
\(659\) | −27.2275 | − | 27.2275i | −1.06063 | − | 1.06063i | −0.998039 | − | 0.0625942i | \(-0.980063\pi\) |
−0.0625942 | − | 0.998039i | \(-0.519937\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.4007 | − | 32.4007i | 1.26024 | − | 1.26024i | 0.309267 | − | 0.950975i | \(-0.399916\pi\) |
0.950975 | − | 0.309267i | \(-0.100084\pi\) | |||||||
\(662\) | 0.804027 | − | 3.38508i | 0.0312494 | − | 0.131565i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.5313 | + | 12.5135i | −0.408695 | + | 0.485617i | ||||
\(665\) | 0.387438i | 0.0150242i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.36928 | − | 2.36928i | 0.0917388 | − | 0.0917388i | ||||
\(668\) | −40.4912 | − | 20.3850i | −1.56665 | − | 0.788720i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.59662 | − | 4.06441i | 0.254850 | − | 0.157022i | ||||
\(671\) | −3.83007 | −0.147858 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.0948 | −1.50700 | −0.753498 | − | 0.657451i | \(-0.771635\pi\) | ||||
−0.753498 | + | 0.657451i | \(0.771635\pi\) | |||||||
\(674\) | 4.08161 | − | 2.51482i | 0.157218 | − | 0.0968674i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23.0782 | − | 11.6186i | −0.887625 | − | 0.446869i | ||||
\(677\) | −31.1264 | + | 31.1264i | −1.19628 | + | 1.19628i | −0.221014 | + | 0.975271i | \(0.570937\pi\) |
−0.975271 | + | 0.221014i | \(0.929063\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.50088i | 0.0959749i | ||||||||
\(680\) | 4.16430 | + | 3.50468i | 0.159694 | + | 0.134398i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.47288 | − | 18.8316i | 0.171275 | − | 0.721098i | ||||
\(683\) | 12.1168 | − | 12.1168i | 0.463637 | − | 0.463637i | −0.436208 | − | 0.899846i | \(-0.643679\pi\) |
0.899846 | + | 0.436208i | \(0.143679\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.907009 | − | 0.907009i | −0.0346550 | − | 0.0346550i | ||||
\(686\) | 1.50434 | + | 2.44157i | 0.0574359 | + | 0.0932196i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 45.2114 | + | 6.71278i | 1.72367 | + | 0.255922i | ||||
\(689\) | −3.18774 | −0.121443 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.5013 | + | 10.5013i | 0.399488 | + | 0.399488i | 0.878052 | − | 0.478565i | \(-0.158843\pi\) |
−0.478565 | + | 0.878052i | \(0.658843\pi\) | |||||||
\(692\) | −20.6204 | + | 6.81051i | −0.783871 | + | 0.258897i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.25306 | + | 38.9569i | −0.351241 | + | 1.47878i | ||||
\(695\) | 4.69571i | 0.178119i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 5.57903i | − | 0.211321i | ||||||
\(698\) | 23.2148 | + | 5.51399i | 0.878693 | + | 0.208707i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.603731 | + | 1.19920i | −0.0228189 | + | 0.0453257i | ||||
\(701\) | −19.5107 | − | 19.5107i | −0.736908 | − | 0.736908i | 0.235071 | − | 0.971978i | \(-0.424468\pi\) |
−0.971978 | + | 0.235071i | \(0.924468\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.7578 | −1.23548 | ||||||||
\(704\) | −15.8100 | + | 22.4387i | −0.595862 | + | 0.845691i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.3910 | − | 19.3411i | 1.18142 | − | 0.727912i | ||||
\(707\) | −1.58128 | − | 1.58128i | −0.0594701 | − | 0.0594701i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.35461 | − | 1.35461i | 0.0508736 | − | 0.0508736i | −0.681212 | − | 0.732086i | \(-0.738547\pi\) |
0.732086 | + | 0.681212i | \(0.238547\pi\) | |||||||
\(710\) | 2.84720 | + | 0.676267i | 0.106853 | + | 0.0253799i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 39.9222 | − | 3.43378i | 1.49615 | − | 0.128686i | ||||
\(713\) | − | 23.9177i | − | 0.895725i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.421501 | − | 0.421501i | 0.0157632 | − | 0.0157632i | ||||
\(716\) | 5.53247 | − | 1.82726i | 0.206758 | − | 0.0682880i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.45251 | + | 13.7186i | 0.315445 | + | 0.511974i | ||||
\(719\) | 47.1881 | 1.75982 | 0.879910 | − | 0.475140i | \(-0.157603\pi\) | ||||
0.879910 | + | 0.475140i | \(0.157603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.32479 | 0.0865796 | ||||||||
\(722\) | 0.115572 | + | 0.187575i | 0.00430113 | + | 0.00698083i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.94127 | + | 21.0163i | 0.257970 | + | 0.781066i | ||||
\(725\) | −1.82854 | + | 1.82854i | −0.0679103 | + | 0.0679103i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 13.6590i | − | 0.506585i | −0.967390 | − | 0.253292i | \(-0.918487\pi\) | ||
0.967390 | − | 0.253292i | \(-0.0815134\pi\) | |||||||
\(728\) | 0.0893731 | + | 0.0752164i | 0.00331239 | + | 0.00278771i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.87880 | + | 0.446254i | 0.0695376 | + | 0.0165166i | ||||
\(731\) | 25.4797 | − | 25.4797i | 0.942399 | − | 0.942399i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.9287 | + | 14.9287i | 0.551404 | + | 0.551404i | 0.926846 | − | 0.375442i | \(-0.122509\pi\) |
−0.375442 | + | 0.926846i | \(0.622509\pi\) | |||||||
\(734\) | 11.8364 | − | 7.29280i | 0.436889 | − | 0.269182i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.6001 | + | 31.4919i | −0.464446 | + | 1.16081i | ||||
\(737\) | 30.8058 | 1.13474 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.4837 | − | 28.4837i | −1.04779 | − | 1.04779i | −0.998799 | − | 0.0489898i | \(-0.984400\pi\) |
−0.0489898 | − | 0.998799i | \(-0.515600\pi\) | |||||||
\(740\) | 8.15893 | + | 4.10756i | 0.299928 | + | 0.150997i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.23490 | − | 0.530834i | −0.0820457 | − | 0.0194875i | ||||
\(743\) | − | 19.7331i | − | 0.723937i | −0.932190 | − | 0.361968i | \(-0.882105\pi\) | ||
0.932190 | − | 0.361968i | \(-0.117895\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.0236i | − | 0.477148i | ||||||
\(746\) | −6.90057 | + | 29.0525i | −0.252648 | + | 1.06369i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.78661 | + | 20.5481i | 0.248143 | + | 0.751312i | ||||
\(749\) | −0.298825 | − | 0.298825i | −0.0109188 | − | 0.0109188i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.72525 | −0.318389 | −0.159194 | − | 0.987247i | \(-0.550890\pi\) | ||||
−0.159194 | + | 0.987247i | \(0.550890\pi\) | |||||||
\(752\) | −14.0817 | − | 18.9924i | −0.513506 | − | 0.692580i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.118020 | + | 0.191549i | 0.00429803 | + | 0.00697580i | ||||
\(755\) | −6.54402 | − | 6.54402i | −0.238161 | − | 0.238161i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.7284 | − | 28.7284i | 1.04415 | − | 1.04415i | 0.0451715 | − | 0.998979i | \(-0.485617\pi\) |
0.998979 | − | 0.0451715i | \(-0.0143834\pi\) | |||||||
\(758\) | 1.07554 | − | 4.52819i | 0.0390653 | − | 0.164471i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.647359 | − | 7.52640i | −0.0234822 | − | 0.273011i | ||||
\(761\) | 41.3046i | 1.49729i | 0.662971 | + | 0.748645i | \(0.269295\pi\) | ||||
−0.662971 | + | 0.748645i | \(0.730705\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.71002 | − | 1.71002i | 0.0619070 | − | 0.0619070i | ||||
\(764\) | 3.40199 | − | 6.75744i | 0.123080 | − | 0.244476i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34.6290 | + | 21.3361i | −1.25120 | + | 0.770906i | ||||
\(767\) | 2.48908 | 0.0898756 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.72628 | 0.278617 | 0.139308 | − | 0.990249i | \(-0.455512\pi\) | ||||
0.139308 | + | 0.990249i | \(0.455512\pi\) | |||||||
\(770\) | 0.365700 | − | 0.225321i | 0.0131789 | − | 0.00811999i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.98667 | + | 7.91881i | −0.143483 | + | 0.285004i | ||||
\(773\) | −27.0058 | + | 27.0058i | −0.971330 | + | 0.971330i | −0.999600 | − | 0.0282699i | \(-0.991000\pi\) |
0.0282699 | + | 0.999600i | \(0.491000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.4590i | 0.663068i | ||||||||
\(776\) | −4.17864 | − | 48.5822i | −0.150005 | − | 1.74400i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.68564 | + | 32.3578i | −0.275544 | + | 1.16008i | ||||
\(779\) | −5.47530 | + | 5.47530i | −0.196173 | + | 0.196173i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.22717 | + | 8.22717i | 0.294391 | + | 0.294391i | ||||
\(782\) | 14.0270 | + | 22.7661i | 0.501605 | + | 0.814115i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −16.6264 | − | 22.4245i | −0.593799 | − | 0.800874i | ||||
\(785\) | −10.0164 | −0.357501 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.6837 | − | 29.6837i | −1.05811 | − | 1.05811i | −0.998204 | − | 0.0599063i | \(-0.980920\pi\) |
−0.0599063 | − | 0.998204i | \(-0.519080\pi\) | |||||||
\(788\) | 2.63915 | + | 7.99066i | 0.0940160 | + | 0.284656i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.39833 | + | 5.88718i | −0.0497502 | + | 0.209457i | ||||
\(791\) | − | 1.75118i | − | 0.0622646i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.317798i | − | 0.0112854i | ||||||
\(794\) | 37.9286 | + | 9.00882i | 1.34604 | + | 0.319711i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −34.0466 | − | 17.1405i | −1.20675 | − | 0.607529i | ||||
\(797\) | 22.5646 | + | 22.5646i | 0.799279 | + | 0.799279i | 0.982982 | − | 0.183703i | \(-0.0588083\pi\) |
−0.183703 | + | 0.982982i | \(0.558808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.6395 | −0.659416 | ||||||||
\(800\) | 9.72440 | − | 24.3046i | 0.343810 | − | 0.859296i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −41.8662 | + | 25.7952i | −1.47835 | + | 0.910861i | ||||
\(803\) | 5.42892 | + | 5.42892i | 0.191583 | + | 0.191583i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.375324 | − | 0.375324i | 0.0132284 | − | 0.0132284i | ||||
\(806\) | 1.56254 | + | 0.371135i | 0.0550381 | + | 0.0130727i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 33.3601 | + | 28.0759i | 1.17360 | + | 0.987706i | ||||
\(809\) | 12.6040i | 0.443133i | 0.975145 | + | 0.221566i | \(0.0711169\pi\) | ||||
−0.975145 | + | 0.221566i | \(0.928883\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.45783 | + | 4.45783i | −0.156536 | + | 0.156536i | −0.781030 | − | 0.624494i | \(-0.785305\pi\) |
0.624494 | + | 0.781030i | \(0.285305\pi\) | |||||||
\(812\) | 0.0508454 | + | 0.153946i | 0.00178432 | + | 0.00540246i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 19.0508 | + | 30.9199i | 0.667731 | + | 1.08374i | ||||
\(815\) | 4.37111 | 0.153113 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −50.0118 | −1.74969 | ||||||||
\(818\) | −0.144478 | − | 0.234490i | −0.00505154 | − | 0.00819876i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.05028 | − | 0.677166i | 0.0715989 | − | 0.0236477i | ||||
\(821\) | 0.309854 | − | 0.309854i | 0.0108140 | − | 0.0108140i | −0.701679 | − | 0.712493i | \(-0.747566\pi\) |
0.712493 | + | 0.701679i | \(0.247566\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.5835i | 1.13579i | 0.823101 | + | 0.567895i | \(0.192242\pi\) | ||||
−0.823101 | + | 0.567895i | \(0.807758\pi\) | |||||||
\(824\) | −45.1614 | + | 3.88442i | −1.57327 | + | 0.135320i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.74508 | + | 0.414491i | 0.0607189 | + | 0.0144220i | ||||
\(827\) | 6.09935 | − | 6.09935i | 0.212095 | − | 0.212095i | −0.593062 | − | 0.805157i | \(-0.702081\pi\) |
0.805157 | + | 0.593062i | \(0.202081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.6929 | + | 12.6929i | 0.440843 | + | 0.440843i | 0.892295 | − | 0.451452i | \(-0.149094\pi\) |
−0.451452 | + | 0.892295i | \(0.649094\pi\) | |||||||
\(830\) | −4.24855 | + | 2.61768i | −0.147469 | + | 0.0908610i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.86184 | − | 1.31183i | −0.0645478 | − | 0.0454794i | ||||
\(833\) | −22.0078 | −0.762524 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.78053 | − | 9.78053i | −0.338469 | − | 0.338469i | ||||
\(836\) | 13.5056 | − | 26.8265i | 0.467101 | − | 0.927813i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 50.9852 | + | 12.1100i | 1.76125 | + | 0.418334i | ||||
\(839\) | 5.30930i | 0.183297i | 0.995791 | + | 0.0916487i | \(0.0292137\pi\) | ||||
−0.995791 | + | 0.0916487i | \(0.970786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.6877i | − | 0.989232i | ||||||
\(842\) | 1.72840 | − | 7.27685i | 0.0595646 | − | 0.250777i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.24361 | + | 3.05298i | −0.318178 | + | 0.105088i | ||||
\(845\) | −5.57448 | − | 5.57448i | −0.191768 | − | 0.191768i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.112090 | 0.00385145 | ||||||||
\(848\) | 44.3022 | + | 6.57779i | 1.52134 | + | 0.225882i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.8257 | − | 17.5703i | −0.371317 | − | 0.602655i | ||||
\(851\) | 31.7336 | + | 31.7336i | 1.08781 | + | 1.08781i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.6932 | + | 20.6932i | −0.708520 | + | 0.708520i | −0.966224 | − | 0.257704i | \(-0.917034\pi\) |
0.257704 | + | 0.966224i | \(0.417034\pi\) | |||||||
\(854\) | 0.0529209 | − | 0.222806i | 0.00181092 | − | 0.00762425i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.30428 | + | 5.30568i | 0.215476 | + | 0.181345i | ||||
\(857\) | 35.7478i | 1.22112i | 0.791970 | + | 0.610560i | \(0.209056\pi\) | ||||
−0.791970 | + | 0.610560i | \(0.790944\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 21.4421 | − | 21.4421i | 0.731595 | − | 0.731595i | −0.239341 | − | 0.970936i | \(-0.576931\pi\) |
0.970936 | + | 0.239341i | \(0.0769314\pi\) | |||||||
\(860\) | 12.4564 | + | 6.27107i | 0.424758 | + | 0.213842i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.2421 | + | 11.8558i | −0.655390 | + | 0.403809i | ||||
\(863\) | −39.2457 | −1.33594 | −0.667970 | − | 0.744188i | \(-0.732837\pi\) | ||||
−0.667970 | + | 0.744188i | \(0.732837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.62586 | −0.225286 | ||||||||
\(866\) | −19.7799 | + | 12.1871i | −0.672148 | + | 0.414134i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.03368 | + | 0.520399i | 0.0350854 | + | 0.0176635i | ||||
\(869\) | −17.0114 | + | 17.0114i | −0.577073 | + | 0.577073i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.55609i | 0.0866099i | ||||||||
\(872\) | −30.3618 | + | 36.0762i | −1.02818 | + | 1.22170i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.57664 | − | 36.1091i | 0.290109 | − | 1.22141i | ||||
\(875\) | −0.602638 | + | 0.602638i | −0.0203729 | + | 0.0203729i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.6404 | − | 17.6404i | −0.595675 | − | 0.595675i | 0.343484 | − | 0.939159i | \(-0.388393\pi\) |
−0.939159 | + | 0.343484i | \(0.888393\pi\) | |||||||
\(878\) | 12.3935 | + | 20.1150i | 0.418261 | + | 0.678847i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.72763 | + | 4.98813i | −0.226788 | + | 0.168150i | ||||
\(881\) | −45.9065 | −1.54663 | −0.773314 | − | 0.634023i | \(-0.781402\pi\) | ||||
−0.773314 | + | 0.634023i | \(0.781402\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.7147 | − | 28.7147i | −0.966326 | − | 0.966326i | 0.0331251 | − | 0.999451i | \(-0.489454\pi\) |
−0.999451 | + | 0.0331251i | \(0.989454\pi\) | |||||||
\(884\) | −1.70497 | + | 0.563116i | −0.0573443 | + | 0.0189397i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.48304 | + | 27.2947i | −0.217802 | + | 0.916982i | ||||
\(887\) | − | 46.2815i | − | 1.55398i | −0.629513 | − | 0.776990i | \(-0.716746\pi\) | ||
0.629513 | − | 0.776990i | \(-0.283254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.92367i | 0.0645179i | ||||||||
\(890\) | 11.8949 | + | 2.82528i | 0.398717 | + | 0.0947034i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −18.5597 | + | 36.8655i | −0.621425 | + | 1.23435i | ||||
\(893\) | 18.2929 | + | 18.2929i | 0.612148 | + | 0.612148i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.77772 | 0.0594227 | ||||||||
\(896\) | −1.08687 | − | 1.22975i | −0.0363098 | − | 0.0410831i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 43.5837 | − | 26.8534i | 1.45441 | − | 0.896110i | ||||
\(899\) | 1.57615 | + | 1.57615i | 0.0525676 | + | 0.0525676i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.9673 | − | 24.9673i | 0.831781 | − | 0.831781i | ||||
\(902\) | 8.35235 | + | 1.98385i | 0.278103 | + | 0.0660551i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.92599 | + | 34.0184i | 0.0973169 | + | 1.13144i | ||||
\(905\) | 6.75308i | 0.224480i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.0957 | − | 35.0957i | 1.16533 | − | 1.16533i | 0.182043 | − | 0.983291i | \(-0.441729\pi\) |
0.983291 | − | 0.182043i | \(-0.0582710\pi\) | |||||||
\(908\) | −40.9147 | + | 13.5133i | −1.35780 | + | 0.448454i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.0186959 | + | 0.0303438i | 0.000619762 | + | 0.00100589i | ||||
\(911\) | 50.7142 | 1.68024 | 0.840119 | − | 0.542403i | \(-0.182485\pi\) | ||||
0.840119 | + | 0.542403i | \(0.182485\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.8404 | −0.656623 | ||||||||
\(914\) | 19.3627 | + | 31.4260i | 0.640460 | + | 1.03948i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.57329 | + | 16.8745i | 0.184147 | + | 0.557548i | ||||
\(917\) | −1.10765 | + | 1.10765i | −0.0365778 | + | 0.0365778i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.7717i | 0.949090i | 0.880231 | + | 0.474545i | \(0.157387\pi\) | ||||
−0.880231 | + | 0.474545i | \(0.842613\pi\) | |||||||
\(920\) | −6.66394 | + | 7.91818i | −0.219704 | + | 0.261055i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −42.6413 | − | 10.1282i | −1.40432 | − | 0.333554i | ||||
\(923\) | −0.682645 | + | 0.682645i | −0.0224695 | + | 0.0224695i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.4911 | − | 24.4911i | −0.805261 | − | 0.805261i | ||||
\(926\) | −14.7842 | + | 9.10907i | −0.485839 | + | 0.299343i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.24495 | − | 2.90562i | −0.0408675 | − | 0.0953815i | ||||
\(929\) | −12.7259 | −0.417523 | −0.208761 | − | 0.977967i | \(-0.566943\pi\) | ||||
−0.208761 | + | 0.977967i | \(0.566943\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.5986 | + | 21.5986i | 0.707865 | + | 0.707865i | ||||
\(932\) | −30.0216 | − | 15.1141i | −0.983389 | − | 0.495080i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.36941 | − | 1.27534i | −0.175692 | − | 0.0417305i | ||||
\(935\) | 6.60262i | 0.215929i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.2582i | 1.21717i | 0.793488 | + | 0.608586i | \(0.208263\pi\) | ||||
−0.793488 | + | 0.608586i | \(0.791737\pi\) | |||||||
\(938\) | −0.425650 | + | 1.79205i | −0.0138980 | + | 0.0585127i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.26240 | − | 6.84995i | −0.0737914 | − | 0.223421i | ||||
\(941\) | −24.8783 | − | 24.8783i | −0.811009 | − | 0.811009i | 0.173776 | − | 0.984785i | \(-0.444403\pi\) |
−0.984785 | + | 0.173776i | \(0.944403\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6082 | 0.345451 | ||||||||
\(944\) | −34.5925 | − | 5.13613i | −1.12589 | − | 0.167167i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.0852 | + | 47.2058i | 0.945640 | + | 1.53479i | ||||
\(947\) | 2.27042 | + | 2.27042i | 0.0737787 | + | 0.0737787i | 0.743033 | − | 0.669255i | \(-0.233386\pi\) |
−0.669255 | + | 0.743033i | \(0.733386\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.450462 | + | 0.450462i | −0.0146226 | + | 0.0146226i | ||||
\(950\) | −6.61921 | + | 27.8680i | −0.214756 | + | 0.904156i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.28911 | + | 0.110879i | −0.0417803 | + | 0.00359360i | ||||
\(953\) | 25.8831i | 0.838436i | 0.907885 | + | 0.419218i | \(0.137696\pi\) | ||||
−0.907885 | + | 0.419218i | \(0.862304\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.63224 | − | 1.63224i | 0.0528181 | − | 0.0528181i | ||||
\(956\) | −12.2893 | + | 24.4105i | −0.397465 | + | 0.789493i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.1205 | − | 6.85172i | 0.359287 | − | 0.221369i | ||||
\(959\) | 0.304925 | 0.00984656 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0888 | −0.486737 | ||||||||
\(962\) | −2.56556 | + | 1.58073i | −0.0827171 | + | 0.0509649i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.3135 | − | 48.2945i | 0.783086 | − | 1.55546i | ||||
\(965\) | −1.91277 | + | 1.91277i | −0.0615742 | + | 0.0615742i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.4733i | − | 1.62311i | −0.584275 | − | 0.811555i | \(-0.698621\pi\) | ||
0.584275 | − | 0.811555i | \(-0.301379\pi\) | |||||||
\(968\) | −2.17746 | + | 0.187288i | −0.0699864 | + | 0.00601966i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.43814 | − | 14.4751i | 0.110392 | − | 0.464769i | ||||
\(971\) | 0.328660 | − | 0.328660i | 0.0105472 | − | 0.0105472i | −0.701814 | − | 0.712361i | \(-0.747626\pi\) |
0.712361 | + | 0.701814i | \(0.247626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.789321 | − | 0.789321i | −0.0253045 | − | 0.0253045i | ||||
\(974\) | 23.4256 | + | 38.0203i | 0.750606 | + | 1.21825i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.655765 | + | 4.41666i | −0.0209905 | + | 0.141374i | ||||
\(977\) | −26.5125 | −0.848210 | −0.424105 | − | 0.905613i | \(-0.639411\pi\) | ||||
−0.424105 | + | 0.905613i | \(0.639411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.3710 | + | 34.3710i | 1.09850 | + | 1.09850i | ||||
\(980\) | −2.67124 | − | 8.08781i | −0.0853296 | − | 0.258355i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.42937 | + | 18.6484i | −0.141347 | + | 0.595093i | ||||
\(983\) | − | 4.92322i | − | 0.157026i | −0.996913 | − | 0.0785131i | \(-0.974983\pi\) | ||
0.996913 | − | 0.0785131i | \(-0.0250172\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.56760i | 0.0818106i | ||||||||
\(986\) | −2.42463 | − | 0.575899i | −0.0772159 | − | 0.0183404i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.22591 | + | 1.12062i | 0.0708158 | + | 0.0356517i | ||||
\(989\) | 48.4481 | + | 48.4481i | 1.54056 | + | 1.54056i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.57207 | 0.0499385 | 0.0249693 | − | 0.999688i | \(-0.492051\pi\) | ||||
0.0249693 | + | 0.999688i | \(0.492051\pi\) | |||||||
\(992\) | −20.9499 | − | 8.38216i | −0.665159 | − | 0.266134i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.592273 | + | 0.364920i | −0.0187858 | + | 0.0115746i | ||||
\(995\) | −8.22385 | − | 8.22385i | −0.260714 | − | 0.260714i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.35740 | − | 2.35740i | 0.0746596 | − | 0.0746596i | −0.668791 | − | 0.743451i | \(-0.733188\pi\) |
0.743451 | + | 0.668791i | \(0.233188\pi\) | |||||||
\(998\) | 16.2437 | + | 3.85822i | 0.514186 | + | 0.122130i | ||||
\(999\) | 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 | 432.2.k.c.109.10 | yes | 24 | |
3.2 | odd | 2 | inner | 432.2.k.c.109.3 | ✓ | 24 | |
4.3 | odd | 2 | 1728.2.k.c.1297.7 | 24 | |||
12.11 | even | 2 | 1728.2.k.c.1297.6 | 24 | |||
16.5 | even | 4 | inner | 432.2.k.c.325.10 | yes | 24 | |
16.11 | odd | 4 | 1728.2.k.c.433.7 | 24 | |||
48.5 | odd | 4 | inner | 432.2.k.c.325.3 | yes | 24 | |
48.11 | even | 4 | 1728.2.k.c.433.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.k.c.109.3 | ✓ | 24 | 3.2 | odd | 2 | inner | |
432.2.k.c.109.10 | yes | 24 | 1.1 | even | 1 | trivial | |
432.2.k.c.325.3 | yes | 24 | 48.5 | odd | 4 | inner | |
432.2.k.c.325.10 | yes | 24 | 16.5 | even | 4 | inner | |
1728.2.k.c.433.6 | 24 | 48.11 | even | 4 | |||
1728.2.k.c.433.7 | 24 | 16.11 | odd | 4 | |||
1728.2.k.c.1297.6 | 24 | 12.11 | even | 2 | |||
1728.2.k.c.1297.7 | 24 | 4.3 | odd | 2 |