Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(218,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 15, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.ct (of order \(20\), degree \(8\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(256\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{20})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 218.28 | ||
Character | \(\chi\) | \(=\) | 825.218 |
Dual form | 825.2.ct.c.632.28 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.79392 | − | 0.914046i | 1.26849 | − | 0.646328i | 0.315384 | − | 0.948964i | \(-0.397867\pi\) |
0.953106 | + | 0.302636i | \(0.0978667\pi\) | |||||||
\(3\) | −0.000527682 | 1.73205i | −0.000304657 | 1.00000i | ||||||
\(4\) | 1.20708 | − | 1.66141i | 0.603542 | − | 0.830704i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.58223 | + | 3.10764i | 0.645942 | + | 1.26869i | ||||
\(7\) | −4.24105 | + | 0.671716i | −1.60296 | + | 0.253885i | −0.892901 | − | 0.450253i | \(-0.851334\pi\) |
−0.710063 | + | 0.704138i | \(0.751334\pi\) | |||||||
\(8\) | 0.0168862 | − | 0.106615i | 0.00597017 | − | 0.0376942i | ||||
\(9\) | −3.00000 | − | 0.00182794i | −1.00000 | − | 0.000609314i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09902 | + | 3.12924i | 0.331367 | + | 0.943502i | ||||
\(12\) | 2.87701 | + | 2.09161i | 0.830520 | + | 0.603795i | ||||
\(13\) | −2.03247 | + | 1.03560i | −0.563706 | + | 0.287222i | −0.712530 | − | 0.701641i | \(-0.752451\pi\) |
0.148825 | + | 0.988864i | \(0.452451\pi\) | |||||||
\(14\) | −6.99410 | + | 5.08151i | −1.86925 | + | 1.35809i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.20204 | + | 3.69951i | 0.300511 | + | 0.924878i | ||||
\(17\) | 1.14093 | − | 2.23921i | 0.276717 | − | 0.543088i | −0.710262 | − | 0.703938i | \(-0.751423\pi\) |
0.986979 | + | 0.160850i | \(0.0514234\pi\) | |||||||
\(18\) | −5.38342 | + | 2.73886i | −1.26888 | + | 0.645555i | ||||
\(19\) | 4.88242 | + | 6.72007i | 1.12010 | + | 1.54169i | 0.805625 | + | 0.592426i | \(0.201830\pi\) |
0.314479 | + | 0.949265i | \(0.398170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.16121 | − | 7.34606i | −0.253396 | − | 1.60304i | ||||
\(22\) | 4.83182 | + | 4.60904i | 1.03015 | + | 0.982651i | ||||
\(23\) | −1.84454 | + | 1.84454i | −0.384614 | + | 0.384614i | −0.872761 | − | 0.488147i | \(-0.837673\pi\) |
0.488147 | + | 0.872761i | \(0.337673\pi\) | |||||||
\(24\) | 0.184654 | + | 0.0293040i | 0.0376924 | + | 0.00598165i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.69950 | + | 3.71554i | −0.529415 | + | 0.728678i | ||||
\(27\) | 0.00474913 | − | 5.19615i | 0.000913971 | − | 1.00000i | ||||
\(28\) | −4.00330 | + | 7.85693i | −0.756553 | + | 1.48482i | ||||
\(29\) | −1.04193 | − | 0.757006i | −0.193481 | − | 0.140573i | 0.486827 | − | 0.873498i | \(-0.338154\pi\) |
−0.680309 | + | 0.732926i | \(0.738154\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0532623 | − | 0.163924i | 0.00956618 | − | 0.0294417i | −0.946159 | − | 0.323701i | \(-0.895073\pi\) |
0.955726 | + | 0.294259i | \(0.0950729\pi\) | |||||||
\(32\) | 5.69055 | + | 5.69055i | 1.00596 | + | 1.00596i | ||||
\(33\) | −5.42059 | + | 1.90191i | −0.943603 | + | 0.331079i | ||||
\(34\) | − | 5.05982i | − | 0.867752i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.62429 | + | 4.98202i | −0.604048 | + | 0.830336i | ||||
\(37\) | 8.50675 | − | 1.34734i | 1.39850 | − | 0.221501i | 0.588769 | − | 0.808301i | \(-0.299613\pi\) |
0.809732 | + | 0.586800i | \(0.199613\pi\) | |||||||
\(38\) | 14.9011 | + | 7.59249i | 2.41728 | + | 1.23166i | ||||
\(39\) | −1.79263 | − | 3.52089i | −0.287051 | − | 0.563793i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.38798 | − | 4.66315i | −0.529113 | − | 0.728262i | 0.457882 | − | 0.889013i | \(-0.348608\pi\) |
−0.986995 | + | 0.160751i | \(0.948608\pi\) | |||||||
\(42\) | −8.79774 | − | 12.1168i | −1.35752 | − | 1.86967i | ||||
\(43\) | −1.36935 | − | 1.36935i | −0.208823 | − | 0.208823i | 0.594944 | − | 0.803767i | \(-0.297174\pi\) |
−0.803767 | + | 0.594944i | \(0.797174\pi\) | |||||||
\(44\) | 6.52556 | + | 1.95134i | 0.983765 | + | 0.294175i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.62296 | + | 4.99495i | −0.239292 | + | 0.736466i | ||||
\(47\) | −7.11242 | − | 1.12650i | −1.03745 | − | 0.164317i | −0.385604 | − | 0.922664i | \(-0.626007\pi\) |
−0.651850 | + | 0.758348i | \(0.726007\pi\) | |||||||
\(48\) | −6.40838 | + | 2.08005i | −0.924970 | + | 0.300229i | ||||
\(49\) | 10.8779 | − | 3.53443i | 1.55398 | − | 0.504919i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.87782 | + | 1.97734i | 0.543004 | + | 0.276883i | ||||
\(52\) | −0.732815 | + | 4.62681i | −0.101623 | + | 0.641624i | ||||
\(53\) | −5.22707 | − | 10.2587i | −0.717993 | − | 1.40914i | −0.904407 | − | 0.426670i | \(-0.859687\pi\) |
0.186414 | − | 0.982471i | \(-0.440313\pi\) | |||||||
\(54\) | −4.74100 | − | 9.32580i | −0.645168 | − | 1.26908i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.463503i | 0.0619382i | ||||||||
\(57\) | −11.6421 | + | 8.45305i | −1.54203 | + | 1.11963i | ||||
\(58\) | −2.56107 | − | 0.405634i | −0.336285 | − | 0.0532624i | ||||
\(59\) | 7.59581 | + | 5.51868i | 0.988891 | + | 0.718471i | 0.959678 | − | 0.281102i | \(-0.0906999\pi\) |
0.0292130 | + | 0.999573i | \(0.490700\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.59408 | − | 4.90606i | −0.204100 | − | 0.628157i | −0.999749 | − | 0.0223982i | \(-0.992870\pi\) |
0.795649 | − | 0.605758i | \(-0.207130\pi\) | |||||||
\(62\) | −0.0542864 | − | 0.342751i | −0.00689438 | − | 0.0435294i | ||||
\(63\) | 12.7244 | − | 2.00739i | 1.60312 | − | 0.252908i | ||||
\(64\) | 8.01076 | + | 2.60285i | 1.00134 | + | 0.325357i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.98565 | + | 8.36652i | −0.982965 | + | 1.02985i | ||||
\(67\) | −3.78746 | + | 3.78746i | −0.462712 | + | 0.462712i | −0.899543 | − | 0.436831i | \(-0.856101\pi\) |
0.436831 | + | 0.899543i | \(0.356101\pi\) | |||||||
\(68\) | −2.34304 | − | 4.59847i | −0.284135 | − | 0.557647i | ||||
\(69\) | −3.19387 | − | 3.19582i | −0.384497 | − | 0.384731i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.245040 | + | 0.0796184i | −0.0290809 | + | 0.00944896i | −0.323521 | − | 0.946221i | \(-0.604867\pi\) |
0.294440 | + | 0.955670i | \(0.404867\pi\) | |||||||
\(72\) | −0.0508535 | + | 0.319815i | −0.00599314 | + | 0.0376905i | ||||
\(73\) | 1.18008 | + | 7.45072i | 0.138118 | + | 0.872041i | 0.955295 | + | 0.295654i | \(0.0955377\pi\) |
−0.817177 | + | 0.576386i | \(0.804462\pi\) | |||||||
\(74\) | 14.0289 | − | 10.1926i | 1.63082 | − | 1.18486i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17.0583 | 1.95672 | ||||||||
\(77\) | −6.76295 | − | 12.5330i | −0.770710 | − | 1.42827i | ||||
\(78\) | −6.43408 | − | 4.67763i | −0.728516 | − | 0.529637i | ||||
\(79\) | 5.95323 | + | 1.93432i | 0.669790 | + | 0.217628i | 0.624120 | − | 0.781328i | \(-0.285458\pi\) |
0.0456704 | + | 0.998957i | \(0.485458\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.99999 | + | 0.0109677i | 0.999999 | + | 0.00121863i | ||||
\(82\) | −10.3401 | − | 5.26853i | −1.14187 | − | 0.581812i | ||||
\(83\) | 4.72659 | + | 2.40832i | 0.518810 | + | 0.264347i | 0.693729 | − | 0.720236i | \(-0.255966\pi\) |
−0.174919 | + | 0.984583i | \(0.555966\pi\) | |||||||
\(84\) | −13.6065 | − | 6.93807i | −1.48459 | − | 0.757006i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.70814 | − | 1.20485i | −0.399859 | − | 0.129922i | ||||
\(87\) | 1.31172 | − | 1.80428i | 0.140631 | − | 0.193439i | ||||
\(88\) | 0.352183 | − | 0.0643312i | 0.0375428 | − | 0.00685773i | ||||
\(89\) | 15.7196 | 1.66628 | 0.833139 | − | 0.553064i | \(-0.186541\pi\) | ||||
0.833139 | + | 0.553064i | \(0.186541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.92417 | − | 5.75725i | 0.830679 | − | 0.603523i | ||||
\(92\) | 0.838022 | + | 5.29106i | 0.0873698 | + | 0.551631i | ||||
\(93\) | 0.283897 | + | 0.0923394i | 0.0294388 | + | 0.00957515i | ||||
\(94\) | −13.7888 | + | 4.48024i | −1.42220 | + | 0.462101i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.85932 | + | 9.85331i | −1.00626 | + | 1.00565i | ||||
\(97\) | 5.77476 | + | 11.3336i | 0.586338 | + | 1.15075i | 0.973488 | + | 0.228737i | \(0.0734594\pi\) |
−0.387150 | + | 0.922017i | \(0.626541\pi\) | |||||||
\(98\) | 16.2833 | − | 16.2833i | 1.64487 | − | 1.64487i | ||||
\(99\) | −3.29134 | − | 9.38973i | −0.330792 | − | 0.943704i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.75406 | + | 2.19453i | 0.672054 | + | 0.218364i | 0.625113 | − | 0.780534i | \(-0.285053\pi\) |
0.0469410 | + | 0.998898i | \(0.485053\pi\) | |||||||
\(102\) | 8.76387 | + | 0.00266997i | 0.867752 | + | 0.000264367i | ||||
\(103\) | 0.464392 | + | 2.93206i | 0.0457579 | + | 0.288904i | 0.999947 | − | 0.0103003i | \(-0.00327875\pi\) |
−0.954189 | + | 0.299204i | \(0.903279\pi\) | |||||||
\(104\) | 0.0760895 | + | 0.234179i | 0.00746119 | + | 0.0229632i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −18.7538 | − | 13.6255i | −1.82153 | − | 1.32342i | ||||
\(107\) | −5.17703 | − | 0.819960i | −0.500482 | − | 0.0792686i | −0.0989107 | − | 0.995096i | \(-0.531536\pi\) |
−0.401571 | + | 0.915828i | \(0.631536\pi\) | |||||||
\(108\) | −8.62720 | − | 6.28008i | −0.830152 | − | 0.604301i | ||||
\(109\) | 14.4385i | 1.38296i | 0.722397 | + | 0.691479i | \(0.243041\pi\) | ||||
−0.722397 | + | 0.691479i | \(0.756959\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.32917 | + | 14.7348i | 0.221075 | + | 1.39857i | ||||
\(112\) | −7.58294 | − | 14.8824i | −0.716521 | − | 1.40625i | ||||
\(113\) | −0.866439 | + | 5.47048i | −0.0815077 | + | 0.514619i | 0.912829 | + | 0.408342i | \(0.133893\pi\) |
−0.994337 | + | 0.106277i | \(0.966107\pi\) | |||||||
\(114\) | −13.1584 | + | 25.8055i | −1.23240 | + | 2.41690i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.51539 | + | 0.817301i | −0.233548 | + | 0.0758845i | ||||
\(117\) | 6.09930 | − | 3.10307i | 0.563881 | − | 0.286879i | ||||
\(118\) | 18.6706 | + | 2.95713i | 1.71877 | + | 0.272226i | ||||
\(119\) | −3.33464 | + | 10.2630i | −0.305686 | + | 0.940805i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.58431 | + | 6.87820i | −0.780392 | + | 0.625291i | ||||
\(122\) | −7.34400 | − | 7.34400i | −0.664894 | − | 0.664894i | ||||
\(123\) | 8.07860 | − | 5.86569i | 0.728423 | − | 0.528891i | ||||
\(124\) | −0.208053 | − | 0.286361i | −0.0186837 | − | 0.0257160i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 20.9916 | − | 15.2317i | 1.87008 | − | 1.35695i | ||||
\(127\) | 13.3034 | + | 6.77841i | 1.18048 | + | 0.601487i | 0.930332 | − | 0.366719i | \(-0.119519\pi\) |
0.250153 | + | 0.968206i | \(0.419519\pi\) | |||||||
\(128\) | 0.852615 | − | 0.135041i | 0.0753613 | − | 0.0119361i | ||||
\(129\) | 2.37250 | − | 2.37106i | 0.208887 | − | 0.208760i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 14.2050i | − | 1.24110i | −0.784167 | − | 0.620550i | \(-0.786909\pi\) | ||
0.784167 | − | 0.620550i | \(-0.213091\pi\) | |||||||
\(132\) | −3.38326 | + | 11.3016i | −0.294475 | + | 0.983675i | ||||
\(133\) | −25.2205 | − | 25.2205i | −2.18690 | − | 2.18690i | ||||
\(134\) | −3.33247 | + | 10.2563i | −0.287882 | + | 0.886010i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.219468 | − | 0.159453i | −0.0188192 | − | 0.0136730i | ||||
\(137\) | 3.59873 | − | 7.06291i | 0.307460 | − | 0.603425i | −0.684639 | − | 0.728883i | \(-0.740040\pi\) |
0.992099 | + | 0.125458i | \(0.0400400\pi\) | |||||||
\(138\) | −8.65066 | − | 2.81368i | −0.736393 | − | 0.239517i | ||||
\(139\) | 3.38639 | − | 4.66097i | 0.287230 | − | 0.395338i | −0.640882 | − | 0.767639i | \(-0.721431\pi\) |
0.928112 | + | 0.372301i | \(0.121431\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.95490 | − | 12.3185i | 0.164633 | − | 1.03740i | ||||
\(142\) | −0.366807 | + | 0.366807i | −0.0307817 | + | 0.0307817i | ||||
\(143\) | −5.47435 | − | 5.22195i | −0.457788 | − | 0.436681i | ||||
\(144\) | −3.59937 | − | 11.1007i | −0.299948 | − | 0.925061i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.92726 | + | 12.2873i | 0.738825 | + | 1.01691i | ||||
\(147\) | 6.11608 | + | 18.8429i | 0.504446 | + | 1.55413i | ||||
\(148\) | 8.02988 | − | 15.7595i | 0.660052 | − | 1.29543i | ||||
\(149\) | −4.51430 | − | 13.8936i | −0.369826 | − | 1.13821i | −0.946904 | − | 0.321517i | \(-0.895807\pi\) |
0.577078 | − | 0.816689i | \(-0.304193\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.8163 | + | 7.85852i | −0.880220 | + | 0.639517i | −0.933310 | − | 0.359073i | \(-0.883093\pi\) |
0.0530898 | + | 0.998590i | \(0.483093\pi\) | |||||||
\(152\) | 0.798908 | − | 0.407064i | 0.0648000 | − | 0.0330172i | ||||
\(153\) | −3.42690 | + | 6.71554i | −0.277048 | + | 0.542920i | ||||
\(154\) | −23.5879 | − | 16.3016i | −1.90077 | − | 1.31362i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.01349 | − | 1.27171i | −0.641593 | − | 0.101819i | ||||
\(157\) | −0.0978515 | + | 0.617810i | −0.00780940 | + | 0.0493066i | −0.991285 | − | 0.131732i | \(-0.957946\pi\) |
0.983476 | + | 0.181039i | \(0.0579460\pi\) | |||||||
\(158\) | 12.4476 | − | 1.97151i | 0.990282 | − | 0.156845i | ||||
\(159\) | 17.7714 | − | 9.04814i | 1.40936 | − | 0.717564i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.58378 | − | 9.06180i | 0.518875 | − | 0.714170i | ||||
\(162\) | 16.1553 | − | 8.20673i | 1.26928 | − | 0.644782i | ||||
\(163\) | 6.83345 | − | 3.48182i | 0.535237 | − | 0.272717i | −0.165410 | − | 0.986225i | \(-0.552895\pi\) |
0.700647 | + | 0.713508i | \(0.252895\pi\) | |||||||
\(164\) | −11.8370 | −0.924312 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.6804 | 0.828961 | ||||||||
\(167\) | 16.0847 | − | 8.19558i | 1.24467 | − | 0.634193i | 0.297441 | − | 0.954740i | \(-0.403867\pi\) |
0.947233 | + | 0.320547i | \(0.103867\pi\) | |||||||
\(168\) | −0.802810 | 0.000244582i | −0.0619382 | 1.88699e-5i | ||||||
\(169\) | −4.58273 | + | 6.30759i | −0.352518 | + | 0.485199i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.6350 | − | 20.1691i | −1.11916 | − | 1.54237i | ||||
\(172\) | −3.92796 | + | 0.622128i | −0.299504 | + | 0.0474368i | ||||
\(173\) | −3.11702 | + | 19.6801i | −0.236983 | + | 1.49625i | 0.526364 | + | 0.850260i | \(0.323555\pi\) |
−0.763346 | + | 0.645990i | \(0.776445\pi\) | |||||||
\(174\) | 0.703930 | − | 4.43569i | 0.0533648 | − | 0.336269i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.2556 | + | 7.82732i | −0.773045 | + | 0.590007i | ||||
\(177\) | −9.56265 | + | 13.1534i | −0.718773 | + | 0.988672i | ||||
\(178\) | 28.1997 | − | 14.3685i | 2.11366 | − | 1.07696i | ||||
\(179\) | 2.64486 | − | 1.92160i | 0.197686 | − | 0.143627i | −0.484539 | − | 0.874770i | \(-0.661013\pi\) |
0.682225 | + | 0.731143i | \(0.261013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.28307 | − | 3.94888i | −0.0953697 | − | 0.293518i | 0.891980 | − | 0.452075i | \(-0.149316\pi\) |
−0.987350 | + | 0.158557i | \(0.949316\pi\) | |||||||
\(182\) | 8.95291 | − | 17.5711i | 0.663634 | − | 1.30245i | ||||
\(183\) | 8.49838 | − | 2.75843i | 0.628219 | − | 0.203909i | ||||
\(184\) | 0.165509 | + | 0.227804i | 0.0122015 | + | 0.0167939i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.593690 | − | 0.0938459i | 0.0435315 | − | 0.00688112i | ||||
\(187\) | 8.26094 | + | 1.10932i | 0.604100 | + | 0.0811219i | ||||
\(188\) | −10.4569 | + | 10.4569i | −0.762645 | + | 0.762645i | ||||
\(189\) | 3.47019 | + | 22.0403i | 0.252419 | + | 1.60320i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.427825 | − | 0.588851i | 0.0309564 | − | 0.0426078i | −0.793258 | − | 0.608885i | \(-0.791617\pi\) |
0.824215 | + | 0.566278i | \(0.191617\pi\) | |||||||
\(192\) | −4.51250 | + | 13.8737i | −0.325662 | + | 1.00125i | ||||
\(193\) | −9.94470 | + | 19.5176i | −0.715835 | + | 1.40491i | 0.190218 | + | 0.981742i | \(0.439080\pi\) |
−0.906053 | + | 0.423164i | \(0.860920\pi\) | |||||||
\(194\) | 20.7189 | + | 15.0531i | 1.48753 | + | 1.08075i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.25836 | − | 22.3389i | 0.518454 | − | 1.59564i | ||||
\(197\) | 1.76040 | + | 1.76040i | 0.125423 | + | 0.125423i | 0.767032 | − | 0.641609i | \(-0.221733\pi\) |
−0.641609 | + | 0.767032i | \(0.721733\pi\) | |||||||
\(198\) | −14.4870 | − | 13.8360i | −1.02955 | − | 0.983279i | ||||
\(199\) | − | 18.7598i | − | 1.32984i | −0.746913 | − | 0.664922i | \(-0.768465\pi\) | ||
0.746913 | − | 0.664922i | \(-0.231535\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.55808 | − | 6.56208i | −0.462571 | − | 0.462853i | ||||
\(202\) | 14.1221 | − | 2.23672i | 0.993629 | − | 0.157375i | ||||
\(203\) | 4.92736 | + | 2.51062i | 0.345833 | + | 0.176211i | ||||
\(204\) | 7.96603 | − | 4.05584i | 0.557733 | − | 0.283965i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.51311 | + | 4.83539i | 0.244770 | + | 0.336897i | ||||
\(207\) | 5.53700 | − | 5.53026i | 0.384848 | − | 0.384380i | ||||
\(208\) | −6.27432 | − | 6.27432i | −0.435046 | − | 0.435046i | ||||
\(209\) | −15.6629 | + | 22.6638i | −1.08342 | + | 1.56769i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.93223 | − | 12.1022i | 0.270706 | − | 0.833148i | −0.719618 | − | 0.694371i | \(-0.755683\pi\) |
0.990324 | − | 0.138777i | \(-0.0443171\pi\) | |||||||
\(212\) | −23.3534 | − | 3.69882i | −1.60392 | − | 0.254036i | ||||
\(213\) | −0.137774 | − | 0.424464i | −0.00944010 | − | 0.0290838i | ||||
\(214\) | −10.0366 | + | 3.26110i | −0.686090 | + | 0.222924i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.553909 | − | 0.0882495i | −0.0376887 | − | 0.00600462i | ||||
\(217\) | −0.115777 | + | 0.730988i | −0.00785946 | + | 0.0496227i | ||||
\(218\) | 13.1975 | + | 25.9015i | 0.893844 | + | 1.75427i | ||||
\(219\) | −12.9056 | + | 2.04002i | −0.872083 | + | 0.137852i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.73267i | 0.385621i | ||||||||
\(222\) | 17.6466 | + | 24.3041i | 1.18436 | + | 1.63118i | ||||
\(223\) | 4.36169 | + | 0.690824i | 0.292080 | + | 0.0462610i | 0.300755 | − | 0.953701i | \(-0.402761\pi\) |
−0.00867482 | + | 0.999962i | \(0.502761\pi\) | |||||||
\(224\) | −27.9563 | − | 20.3114i | −1.86791 | − | 1.35711i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.44595 | + | 10.6055i | 0.229221 | + | 0.705470i | ||||
\(227\) | 2.60504 | + | 16.4476i | 0.172902 | + | 1.09166i | 0.909614 | + | 0.415455i | \(0.136378\pi\) |
−0.736711 | + | 0.676207i | \(0.763622\pi\) | |||||||
\(228\) | −0.00900134 | + | 29.5458i | −0.000596128 | + | 1.95672i | ||||
\(229\) | 6.32680 | + | 2.05570i | 0.418086 | + | 0.135845i | 0.510503 | − | 0.859876i | \(-0.329459\pi\) |
−0.0924167 | + | 0.995720i | \(0.529459\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.7114 | − | 11.7072i | 1.42851 | − | 0.770275i | ||||
\(232\) | −0.0983026 | + | 0.0983026i | −0.00645388 | + | 0.00645388i | ||||
\(233\) | −5.00895 | − | 9.83061i | −0.328147 | − | 0.644025i | 0.666710 | − | 0.745318i | \(-0.267702\pi\) |
−0.994857 | + | 0.101293i | \(0.967702\pi\) | |||||||
\(234\) | 8.10529 | − | 11.1417i | 0.529859 | − | 0.728355i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.3376 | − | 5.95824i | 1.19367 | − | 0.387848i | ||||
\(237\) | −3.35348 | + | 10.3103i | −0.217832 | + | 0.669724i | ||||
\(238\) | 3.39876 | + | 21.4589i | 0.220309 | + | 1.39098i | ||||
\(239\) | −21.7492 | + | 15.8018i | −1.40684 | + | 1.02213i | −0.413070 | + | 0.910699i | \(0.635543\pi\) |
−0.993772 | + | 0.111431i | \(0.964457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.8403 | −1.14919 | −0.574596 | − | 0.818437i | \(-0.694841\pi\) | ||||
−0.574596 | + | 0.818437i | \(0.694841\pi\) | |||||||
\(242\) | −9.11255 | + | 20.1854i | −0.585777 | + | 1.29756i | ||||
\(243\) | −0.0237457 | + | 15.5884i | −0.00152328 | + | 0.999999i | ||||
\(244\) | −10.0752 | − | 3.27362i | −0.644995 | − | 0.209572i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.13082 | − | 17.9068i | 0.582160 | − | 1.14169i | ||||
\(247\) | −16.8826 | − | 8.60214i | −1.07422 | − | 0.547341i | ||||
\(248\) | −0.0165774 | − | 0.00844663i | −0.00105267 | − | 0.000536361i | ||||
\(249\) | −4.17382 | + | 8.18542i | −0.264505 | + | 0.518730i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.8418 | + | 6.12208i | 1.18929 | + | 0.386423i | 0.835809 | − | 0.549020i | \(-0.184999\pi\) |
0.353477 | + | 0.935443i | \(0.384999\pi\) | |||||||
\(252\) | 12.0243 | − | 23.5635i | 0.757458 | − | 1.48436i | ||||
\(253\) | −7.79921 | − | 3.74483i | −0.490332 | − | 0.235436i | ||||
\(254\) | 30.0609 | 1.88619 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.2226 | + | 8.88026i | −0.763914 | + | 0.555016i | ||||
\(257\) | −1.66956 | − | 10.5412i | −0.104144 | − | 0.657539i | −0.983436 | − | 0.181256i | \(-0.941984\pi\) |
0.879292 | − | 0.476283i | \(-0.158016\pi\) | |||||||
\(258\) | 2.08881 | − | 6.42205i | 0.130044 | − | 0.399819i | ||||
\(259\) | −35.1725 | + | 11.4282i | −2.18551 | + | 0.710116i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.12440 | + | 2.27292i | 0.193396 | + | 0.140690i | ||||
\(262\) | −12.9841 | − | 25.4826i | −0.802157 | − | 1.57432i | ||||
\(263\) | −0.223294 | + | 0.223294i | −0.0137689 | + | 0.0137689i | −0.713958 | − | 0.700189i | \(-0.753099\pi\) |
0.700189 | + | 0.713958i | \(0.253099\pi\) | |||||||
\(264\) | 0.111239 | + | 0.610033i | 0.00684629 | + | 0.0375449i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −68.2962 | − | 22.1908i | −4.18751 | − | 1.36060i | ||||
\(267\) | −0.00829496 | + | 27.2272i | −0.000507643 | + | 1.66628i | ||||
\(268\) | 1.72074 | + | 10.8643i | 0.105111 | + | 0.663643i | ||||
\(269\) | −7.21029 | − | 22.1910i | −0.439619 | − | 1.35301i | −0.888278 | − | 0.459306i | \(-0.848098\pi\) |
0.448659 | − | 0.893703i | \(-0.351902\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.228534 | + | 0.166040i | 0.0138825 | + | 0.0100862i | 0.594705 | − | 0.803944i | \(-0.297269\pi\) |
−0.580822 | + | 0.814030i | \(0.697269\pi\) | |||||||
\(272\) | 9.65544 | + | 1.52927i | 0.585447 | + | 0.0927257i | ||||
\(273\) | 9.96766 | + | 13.7281i | 0.603270 | + | 0.830863i | ||||
\(274\) | − | 15.9597i | − | 0.964159i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.16483 | + | 1.44870i | −0.551658 | + | 0.0872017i | ||||
\(277\) | −14.2175 | − | 27.9035i | −0.854250 | − | 1.67656i | −0.729085 | − | 0.684424i | \(-0.760054\pi\) |
−0.125165 | − | 0.992136i | \(-0.539946\pi\) | |||||||
\(278\) | 1.81456 | − | 11.4567i | 0.108830 | − | 0.687127i | ||||
\(279\) | −0.160086 | + | 0.491676i | −0.00958412 | + | 0.0294359i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.8105 | + | 6.43682i | −1.18179 | + | 0.383988i | −0.833033 | − | 0.553223i | \(-0.813398\pi\) |
−0.348762 | + | 0.937211i | \(0.613398\pi\) | |||||||
\(282\) | −7.75273 | − | 23.8852i | −0.461668 | − | 1.42234i | ||||
\(283\) | 1.67673 | + | 0.265569i | 0.0996715 | + | 0.0157864i | 0.206071 | − | 0.978537i | \(-0.433932\pi\) |
−0.106399 | + | 0.994323i | \(0.533932\pi\) | |||||||
\(284\) | −0.163505 | + | 0.503218i | −0.00970226 | + | 0.0298605i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.5936 | − | 4.36393i | −0.862939 | − | 0.258045i | ||||
\(287\) | 17.5009 | + | 17.5009i | 1.03304 | + | 1.03304i | ||||
\(288\) | −17.0612 | − | 17.0820i | −1.00534 | − | 1.00657i | ||||
\(289\) | 6.28002 | + | 8.64370i | 0.369413 | + | 0.508453i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.6334 | + | 9.99620i | −1.15093 | + | 0.585987i | ||||
\(292\) | 13.8031 | + | 7.03305i | 0.807768 | + | 0.411578i | ||||
\(293\) | 5.84998 | − | 0.926547i | 0.341760 | − | 0.0541294i | 0.0168044 | − | 0.999859i | \(-0.494651\pi\) |
0.324955 | + | 0.945729i | \(0.394651\pi\) | |||||||
\(294\) | 28.1950 | + | 28.2122i | 1.64436 | + | 1.64537i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 0.929700i | − | 0.0540377i | ||||||
\(297\) | 16.2652 | − | 5.69581i | 0.943804 | − | 0.330504i | ||||
\(298\) | −20.7976 | − | 20.7976i | −1.20477 | − | 1.20477i | ||||
\(299\) | 1.83878 | − | 5.65918i | 0.106339 | − | 0.327279i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.72727 | + | 4.88765i | 0.387754 | + | 0.281719i | ||||
\(302\) | −12.2205 | + | 23.9841i | −0.703212 | + | 1.38013i | ||||
\(303\) | −3.80460 | + | 11.6972i | −0.218568 | + | 0.671988i | ||||
\(304\) | −18.9921 | + | 26.1404i | −1.08927 | + | 1.49925i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.00924906 | + | 15.1795i | −0.000528734 | + | 0.867752i | ||||
\(307\) | −14.2660 | + | 14.2660i | −0.814202 | + | 0.814202i | −0.985261 | − | 0.171058i | \(-0.945281\pi\) |
0.171058 | + | 0.985261i | \(0.445281\pi\) | |||||||
\(308\) | −28.9859 | − | 3.89239i | −1.65163 | − | 0.221790i | ||||
\(309\) | −5.07872 | + | 0.802803i | −0.288918 | + | 0.0456699i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.28014 | + | 11.3966i | 0.469524 | + | 0.646244i | 0.976450 | − | 0.215746i | \(-0.0692182\pi\) |
−0.506926 | + | 0.861990i | \(0.669218\pi\) | |||||||
\(312\) | −0.405651 | + | 0.131667i | −0.0229655 | + | 0.00745420i | ||||
\(313\) | 12.2903 | − | 24.1210i | 0.694688 | − | 1.36340i | −0.226395 | − | 0.974036i | \(-0.572694\pi\) |
0.921083 | − | 0.389366i | \(-0.127306\pi\) | |||||||
\(314\) | 0.389169 | + | 1.19774i | 0.0219621 | + | 0.0675923i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.3997 | − | 7.55586i | 0.585031 | − | 0.425050i | ||||
\(317\) | 13.1331 | − | 6.69163i | 0.737626 | − | 0.375839i | −0.0444587 | − | 0.999011i | \(-0.514156\pi\) |
0.782085 | + | 0.623172i | \(0.214156\pi\) | |||||||
\(318\) | 23.6099 | − | 32.4754i | 1.32398 | − | 1.82113i | ||||
\(319\) | 1.22375 | − | 4.09241i | 0.0685171 | − | 0.229131i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.42294 | − | 8.96644i | 0.0794210 | − | 0.500458i | ||||
\(322\) | 3.52785 | − | 22.2740i | 0.196600 | − | 1.24128i | ||||
\(323\) | 20.6182 | − | 3.26560i | 1.14723 | − | 0.181703i | ||||
\(324\) | 10.8820 | − | 14.9394i | 0.604554 | − | 0.829968i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.07609 | − | 12.4922i | 0.502678 | − | 0.691877i | ||||
\(327\) | −25.0082 | − | 0.00761893i | −1.38296 | − | 0.000421328i | ||||
\(328\) | −0.554373 | + | 0.282467i | −0.0306101 | + | 0.0155966i | ||||
\(329\) | 30.9208 | 1.70472 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2920 | 0.620662 | 0.310331 | − | 0.950628i | \(-0.399560\pi\) | ||||
0.310331 | + | 0.950628i | \(0.399560\pi\) | |||||||
\(332\) | 9.70659 | − | 4.94575i | 0.532718 | − | 0.271433i | ||||
\(333\) | −25.5227 | + | 4.02646i | −1.39864 | + | 0.220649i | ||||
\(334\) | 21.3635 | − | 29.4044i | 1.16896 | − | 1.60894i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 25.7810 | − | 13.1262i | 1.40647 | − | 0.716092i | ||||
\(337\) | −23.1206 | + | 3.66195i | −1.25946 | + | 0.199479i | −0.750245 | − | 0.661160i | \(-0.770064\pi\) |
−0.509216 | + | 0.860639i | \(0.670064\pi\) | |||||||
\(338\) | −2.45561 | + | 15.5041i | −0.133568 | + | 0.843313i | ||||
\(339\) | −9.47469 | − | 1.50360i | −0.514594 | − | 0.0816645i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.571495 | − | 0.0134856i | 0.0309482 | − | 0.000730285i | ||||
\(342\) | −44.6894 | − | 22.8047i | −2.41653 | − | 1.23314i | ||||
\(343\) | −16.9781 | + | 8.65076i | −0.916730 | + | 0.467097i | ||||
\(344\) | −0.169116 | + | 0.122870i | −0.00911814 | + | 0.00662472i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.3968 | + | 38.1535i | 0.666458 | + | 2.05115i | ||||
\(347\) | −4.13733 | + | 8.11998i | −0.222104 | + | 0.435903i | −0.974990 | − | 0.222247i | \(-0.928661\pi\) |
0.752887 | + | 0.658150i | \(0.228661\pi\) | |||||||
\(348\) | −1.41428 | − | 4.35722i | −0.0758133 | − | 0.233572i | ||||
\(349\) | 11.5742 | + | 15.9305i | 0.619553 | + | 0.852742i | 0.997320 | − | 0.0731589i | \(-0.0233080\pi\) |
−0.377767 | + | 0.925901i | \(0.623308\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.37145 | + | 10.5659i | 0.286707 | + | 0.563968i | ||||
\(352\) | −11.5531 | + | 24.0611i | −0.615781 | + | 1.28246i | ||||
\(353\) | 16.0974 | − | 16.0974i | 0.856776 | − | 0.856776i | −0.134180 | − | 0.990957i | \(-0.542840\pi\) |
0.990957 | + | 0.134180i | \(0.0428402\pi\) | |||||||
\(354\) | −5.13175 | + | 32.3368i | −0.272749 | + | 1.71868i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 18.9749 | − | 26.1167i | 1.00567 | − | 1.38418i | ||||
\(357\) | −17.7742 | − | 5.78119i | −0.940712 | − | 0.305973i | ||||
\(358\) | 2.98822 | − | 5.86471i | 0.157932 | − | 0.309960i | ||||
\(359\) | 4.29742 | + | 3.12226i | 0.226809 | + | 0.164786i | 0.695386 | − | 0.718636i | \(-0.255233\pi\) |
−0.468577 | + | 0.883422i | \(0.655233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.4500 | + | 47.5503i | −0.813160 | + | 2.50265i | ||||
\(362\) | −5.91117 | − | 5.91117i | −0.310684 | − | 0.310684i | ||||
\(363\) | −11.9089 | − | 14.8721i | −0.625053 | − | 0.780582i | ||||
\(364\) | − | 20.1148i | − | 1.05430i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.7241 | − | 12.7163i | 0.665097 | − | 0.664692i | ||||
\(367\) | 13.7951 | − | 2.18494i | 0.720101 | − | 0.114053i | 0.214380 | − | 0.976750i | \(-0.431227\pi\) |
0.505720 | + | 0.862698i | \(0.331227\pi\) | |||||||
\(368\) | −9.04114 | − | 4.60669i | −0.471302 | − | 0.240140i | ||||
\(369\) | 10.1554 | + | 13.9956i | 0.528669 | + | 0.728584i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 29.0592 | + | 39.9965i | 1.50868 | + | 2.07652i | ||||
\(372\) | 0.496101 | − | 0.360208i | 0.0257217 | − | 0.0186759i | ||||
\(373\) | 14.5386 | + | 14.5386i | 0.752778 | + | 0.752778i | 0.974997 | − | 0.222219i | \(-0.0713299\pi\) |
−0.222219 | + | 0.974997i | \(0.571330\pi\) | |||||||
\(374\) | 15.8334 | − | 5.56084i | 0.818726 | − | 0.287544i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.240204 | + | 0.739270i | −0.0123876 | + | 0.0381250i | ||||
\(377\) | 2.90164 | + | 0.459575i | 0.149442 | + | 0.0236693i | ||||
\(378\) | 26.3711 | + | 36.3665i | 1.35638 | + | 1.87049i | ||||
\(379\) | 13.7037 | − | 4.45259i | 0.703910 | − | 0.228714i | 0.0648769 | − | 0.997893i | \(-0.479335\pi\) |
0.639033 | + | 0.769179i | \(0.279335\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.7476 | + | 23.0386i | −0.601846 | + | 1.18030i | ||||
\(382\) | 0.229246 | − | 1.44740i | 0.0117292 | − | 0.0740555i | ||||
\(383\) | −6.14584 | − | 12.0619i | −0.314038 | − | 0.616334i | 0.678999 | − | 0.734139i | \(-0.262414\pi\) |
−0.993037 | + | 0.117805i | \(0.962414\pi\) | |||||||
\(384\) | 0.233448 | + | 1.47684i | 0.0119131 | + | 0.0753649i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 44.1028i | 2.24477i | ||||||||
\(387\) | 4.10554 | + | 4.11054i | 0.208696 | + | 0.208951i | ||||
\(388\) | 25.8004 | + | 4.08638i | 1.30982 | + | 0.207454i | ||||
\(389\) | −22.2934 | − | 16.1971i | −1.13032 | − | 0.821227i | −0.144580 | − | 0.989493i | \(-0.546183\pi\) |
−0.985742 | + | 0.168267i | \(0.946183\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.02582 | + | 6.23483i | 0.102450 | + | 0.315309i | ||||
\(392\) | −0.193139 | − | 1.21943i | −0.00975497 | − | 0.0615905i | ||||
\(393\) | 24.6038 | + | 0.00749573i | 1.24110 | + | 0.000378110i | ||||
\(394\) | 4.76708 | + | 1.54892i | 0.240162 | + | 0.0780334i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −19.5731 | − | 5.86594i | −0.983586 | − | 0.294775i | ||||
\(397\) | 21.5841 | − | 21.5841i | 1.08327 | − | 1.08327i | 0.0870716 | − | 0.996202i | \(-0.472249\pi\) |
0.996202 | − | 0.0870716i | \(-0.0277509\pi\) | |||||||
\(398\) | −17.1473 | − | 33.6534i | −0.859516 | − | 1.68689i | ||||
\(399\) | 43.6966 | − | 43.6699i | 2.18756 | − | 2.18623i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.9335 | − | 9.72597i | 1.49481 | − | 0.485692i | 0.556307 | − | 0.830977i | \(-0.312218\pi\) |
0.938498 | + | 0.345285i | \(0.112218\pi\) | |||||||
\(402\) | −17.7627 | − | 5.77743i | −0.885922 | − | 0.288152i | ||||
\(403\) | 0.0615053 | + | 0.388329i | 0.00306380 | + | 0.0193441i | ||||
\(404\) | 11.7987 | − | 8.57228i | 0.587009 | − | 0.426487i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.1341 | 0.552576 | ||||||||
\(407\) | 13.5652 | + | 25.1389i | 0.672403 | + | 1.24609i | ||||
\(408\) | 0.276296 | − | 0.380045i | 0.0136787 | − | 0.0188150i | ||||
\(409\) | 3.19892 | + | 1.03939i | 0.158176 | + | 0.0513946i | 0.387035 | − | 0.922065i | \(-0.373499\pi\) |
−0.228858 | + | 0.973460i | \(0.573499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.2314 | + | 6.23691i | 0.603331 | + | 0.307644i | ||||
\(412\) | 5.43190 | + | 2.76769i | 0.267611 | + | 0.136354i | ||||
\(413\) | −35.9212 | − | 18.3028i | −1.76757 | − | 0.900620i | ||||
\(414\) | 4.87801 | − | 14.9819i | 0.239741 | − | 0.736320i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −17.4590 | − | 5.67276i | −0.855996 | − | 0.278130i | ||||
\(417\) | 8.07125 | + | 5.86786i | 0.395251 | + | 0.287350i | ||||
\(418\) | −7.38214 | + | 54.9735i | −0.361072 | + | 2.68884i | ||||
\(419\) | −8.06076 | −0.393794 | −0.196897 | − | 0.980424i | \(-0.563086\pi\) | ||||
−0.196897 | + | 0.980424i | \(0.563086\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.76470 | + | 4.18830i | −0.280954 | + | 0.204125i | −0.719334 | − | 0.694665i | \(-0.755553\pi\) |
0.438379 | + | 0.898790i | \(0.355553\pi\) | |||||||
\(422\) | −4.00784 | − | 25.3045i | −0.195099 | − | 1.23180i | ||||
\(423\) | 21.3352 | + | 3.39249i | 1.03735 | + | 0.164949i | ||||
\(424\) | −1.18200 | + | 0.384055i | −0.0574030 | + | 0.0186514i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.635134 | − | 0.635521i | −0.0307723 | − | 0.0307911i | ||||
\(427\) | 10.0560 | + | 19.7361i | 0.486645 | + | 0.955095i | ||||
\(428\) | −7.61139 | + | 7.61139i | −0.367911 | + | 0.367911i | ||||
\(429\) | 9.04757 | − | 9.47910i | 0.436821 | − | 0.457655i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.2784 | − | 8.86330i | −1.31396 | − | 0.426930i | −0.433541 | − | 0.901134i | \(-0.642736\pi\) |
−0.880415 | + | 0.474203i | \(0.842736\pi\) | |||||||
\(432\) | 19.2289 | − | 6.22843i | 0.925152 | − | 0.299666i | ||||
\(433\) | −1.53811 | − | 9.71124i | −0.0739168 | − | 0.466692i | −0.996686 | − | 0.0813403i | \(-0.974080\pi\) |
0.922770 | − | 0.385352i | \(-0.125920\pi\) | |||||||
\(434\) | 0.460462 | + | 1.41716i | 0.0221029 | + | 0.0680257i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 23.9883 | + | 17.4285i | 1.14883 | + | 0.834673i | ||||
\(437\) | −21.4013 | − | 3.38963i | −1.02376 | − | 0.162148i | ||||
\(438\) | −21.2870 | + | 15.4560i | −1.01713 | + | 0.738515i | ||||
\(439\) | − | 25.0058i | − | 1.19346i | −0.802441 | − | 0.596732i | \(-0.796466\pi\) | ||
0.802441 | − | 0.596732i | \(-0.203534\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.6401 | + | 10.5834i | −1.55429 | + | 0.503972i | ||||
\(442\) | 5.23993 | + | 10.2839i | 0.249238 | + | 0.489157i | ||||
\(443\) | 1.86666 | − | 11.7856i | 0.0886877 | − | 0.559952i | −0.902832 | − | 0.429994i | \(-0.858516\pi\) |
0.991519 | − | 0.129958i | \(-0.0414843\pi\) | |||||||
\(444\) | 27.2921 | + | 13.9165i | 1.29522 | + | 0.660447i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.45595 | − | 2.74750i | 0.400401 | − | 0.130098i | ||||
\(447\) | 24.0668 | − | 7.81166i | 1.13832 | − | 0.369479i | ||||
\(448\) | −35.7224 | − | 5.65787i | −1.68772 | − | 0.267309i | ||||
\(449\) | 9.37694 | − | 28.8593i | 0.442525 | − | 1.36195i | −0.442650 | − | 0.896695i | \(-0.645961\pi\) |
0.885175 | − | 0.465258i | \(-0.154039\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8687 | − | 15.7267i | 0.511786 | − | 0.740541i | ||||
\(452\) | 8.04284 | + | 8.04284i | 0.378303 | + | 0.378303i | ||||
\(453\) | −13.6056 | − | 18.7386i | −0.639249 | − | 0.880415i | ||||
\(454\) | 19.7070 | + | 27.1244i | 0.924897 | + | 1.27301i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.704633 | + | 1.38396i | 0.0329975 | + | 0.0648100i | ||||
\(457\) | 4.56388 | + | 2.32541i | 0.213489 | + | 0.108778i | 0.557465 | − | 0.830200i | \(-0.311774\pi\) |
−0.343976 | + | 0.938978i | \(0.611774\pi\) | |||||||
\(458\) | 13.2287 | − | 2.09523i | 0.618139 | − | 0.0979035i | ||||
\(459\) | −11.6299 | − | 5.93910i | −0.542835 | − | 0.277214i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 33.6658i | − | 1.56797i | −0.620778 | − | 0.783986i | \(-0.713183\pi\) | ||
0.620778 | − | 0.783986i | \(-0.286817\pi\) | |||||||
\(462\) | 28.2476 | − | 40.8469i | 1.31420 | − | 1.90037i | ||||
\(463\) | 17.1185 | + | 17.1185i | 0.795563 | + | 0.795563i | 0.982392 | − | 0.186830i | \(-0.0598212\pi\) |
−0.186830 | + | 0.982392i | \(0.559821\pi\) | |||||||
\(464\) | 1.54811 | − | 4.76459i | 0.0718691 | − | 0.221190i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.9713 | − | 13.0569i | −0.832502 | − | 0.604848i | ||||
\(467\) | 15.4438 | − | 30.3102i | 0.714655 | − | 1.40259i | −0.192290 | − | 0.981338i | \(-0.561591\pi\) |
0.906944 | − | 0.421250i | \(-0.138409\pi\) | |||||||
\(468\) | 2.20690 | − | 13.8791i | 0.102014 | − | 0.641561i | ||||
\(469\) | 13.5187 | − | 18.6069i | 0.624236 | − | 0.859187i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.07003 | − | 0.169810i | −0.0493042 | − | 0.00782442i | ||||
\(472\) | 0.716640 | − | 0.716640i | 0.0329860 | − | 0.0329860i | ||||
\(473\) | 2.78008 | − | 5.78996i | 0.127828 | − | 0.266222i | ||||
\(474\) | 3.40819 | + | 21.5610i | 0.156544 | + | 0.990329i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.0258 | + | 17.9285i | 0.597037 | + | 0.821750i | ||||
\(477\) | 15.6625 | + | 30.7857i | 0.717135 | + | 1.40958i | ||||
\(478\) | −24.5728 | + | 48.2268i | −1.12393 | + | 2.20584i | ||||
\(479\) | 5.70396 | + | 17.5550i | 0.260621 | + | 0.802108i | 0.992670 | + | 0.120857i | \(0.0385641\pi\) |
−0.732049 | + | 0.681252i | \(0.761436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.8944 | + | 11.5480i | −0.724723 | + | 0.526542i | ||||
\(482\) | −32.0039 | + | 16.3068i | −1.45774 | + | 0.742755i | ||||
\(483\) | 15.6920 | + | 11.4082i | 0.714012 | + | 0.519092i | ||||
\(484\) | 1.06551 | + | 22.5646i | 0.0484322 | + | 1.02566i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.2059 | + | 27.9861i | 0.644395 | + | 1.26947i | ||||
\(487\) | −0.655610 | + | 4.13936i | −0.0297085 | + | 0.187572i | −0.998080 | − | 0.0619415i | \(-0.980271\pi\) |
0.968371 | + | 0.249514i | \(0.0802708\pi\) | |||||||
\(488\) | −0.549978 | + | 0.0871080i | −0.0248964 | + | 0.00394320i | ||||
\(489\) | 6.02708 | + | 11.8377i | 0.272554 | + | 0.535320i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.612517 | − | 0.843058i | 0.0276425 | − | 0.0380467i | −0.794972 | − | 0.606646i | \(-0.792515\pi\) |
0.822615 | + | 0.568599i | \(0.192515\pi\) | |||||||
\(492\) | 0.00624615 | − | 20.5022i | 0.000281598 | − | 0.924312i | ||||
\(493\) | −2.88387 | + | 1.46940i | −0.129883 | + | 0.0661787i | ||||
\(494\) | −38.1488 | −1.71640 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.670464 | 0.0301047 | ||||||||
\(497\) | 0.985745 | − | 0.502262i | 0.0442167 | − | 0.0225295i | ||||
\(498\) | −0.00563586 | + | 18.4990i | −0.000252549 | + | 0.828961i | ||||
\(499\) | −9.34149 | + | 12.8575i | −0.418182 | + | 0.575579i | −0.965190 | − | 0.261549i | \(-0.915767\pi\) |
0.547008 | + | 0.837128i | \(0.315767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.1867 | + | 27.8639i | 0.633814 | + | 1.24487i | ||||
\(502\) | 39.3965 | − | 6.23980i | 1.75835 | − | 0.278496i | ||||
\(503\) | −1.17084 | + | 7.39239i | −0.0522051 | + | 0.329610i | 0.947739 | + | 0.319047i | \(0.103363\pi\) |
−0.999944 | + | 0.0105638i | \(0.996637\pi\) | |||||||
\(504\) | 0.000847256 | − | 1.39051i | 3.77398e−5 | − | 0.0619381i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −17.4141 | + | 0.410920i | −0.774150 | + | 0.0182676i | ||||
\(507\) | −10.9226 | − | 7.94085i | −0.485092 | − | 0.352666i | ||||
\(508\) | 27.3200 | − | 13.9202i | 1.21213 | − | 0.617611i | ||||
\(509\) | −20.5132 | + | 14.9037i | −0.909231 | + | 0.660595i | −0.940820 | − | 0.338906i | \(-0.889943\pi\) |
0.0315895 | + | 0.999501i | \(0.489943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0095 | − | 30.8062i | −0.442795 | − | 1.36278i | ||||
\(512\) | −14.5932 | + | 28.6408i | −0.644935 | + | 1.26576i | ||||
\(513\) | 34.9417 | − | 25.3379i | 1.54271 | − | 1.11869i | ||||
\(514\) | −12.6301 | − | 17.3839i | −0.557092 | − | 0.766771i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.07548 | − | 6.80376i | −0.0473456 | − | 0.299519i | ||||
\(517\) | −4.29161 | − | 23.4945i | −0.188745 | − | 1.03329i | ||||
\(518\) | −52.6505 | + | 52.6505i | −2.31333 | + | 2.31333i | ||||
\(519\) | −34.0853 | − | 5.40922i | −1.49618 | − | 0.237438i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.12955 | + | 12.5657i | −0.399973 | + | 0.550515i | −0.960737 | − | 0.277460i | \(-0.910507\pi\) |
0.560764 | + | 0.827975i | \(0.310507\pi\) | |||||||
\(522\) | 7.68247 | + | 1.22158i | 0.336253 | + | 0.0534673i | ||||
\(523\) | −8.39391 | + | 16.4740i | −0.367040 | + | 0.720357i | −0.998483 | − | 0.0550660i | \(-0.982463\pi\) |
0.631443 | + | 0.775423i | \(0.282463\pi\) | |||||||
\(524\) | −23.6004 | − | 17.1467i | −1.03099 | − | 0.749056i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.196470 | + | 0.604673i | −0.00856650 | + | 0.0263650i | ||||
\(527\) | −0.306292 | − | 0.306292i | −0.0133423 | − | 0.0133423i | ||||
\(528\) | −13.5519 | − | 17.7673i | −0.589771 | − | 0.773225i | ||||
\(529\) | 16.1953i | 0.704144i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.7774 | − | 16.5699i | −0.988453 | − | 0.719074i | ||||
\(532\) | −72.3449 | + | 11.4583i | −3.13655 | + | 0.496781i | ||||
\(533\) | 11.7151 | + | 5.96914i | 0.507437 | + | 0.258552i | ||||
\(534\) | 24.8720 | + | 48.8509i | 1.07632 | + | 2.11399i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.339845 | + | 0.467757i | 0.0146791 | + | 0.0202040i | ||||
\(537\) | 3.32691 | + | 4.58204i | 0.143567 | + | 0.197730i | ||||
\(538\) | −33.2183 | − | 33.2183i | −1.43214 | − | 1.43214i | ||||
\(539\) | 23.0151 | + | 30.1551i | 0.991330 | + | 1.29887i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.619332 | − | 1.90611i | 0.0266272 | − | 0.0819500i | −0.936860 | − | 0.349705i | \(-0.886282\pi\) |
0.963487 | + | 0.267755i | \(0.0862818\pi\) | |||||||
\(542\) | 0.561739 | + | 0.0889707i | 0.0241288 | + | 0.00382162i | ||||
\(543\) | 6.84033 | − | 2.22025i | 0.293547 | − | 0.0952803i | ||||
\(544\) | 19.2349 | − | 6.24979i | 0.824688 | − | 0.267957i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 30.4293 | + | 15.5162i | 1.30225 | + | 0.664030i | ||||
\(547\) | 3.39919 | − | 21.4617i | 0.145339 | − | 0.917635i | −0.801982 | − | 0.597348i | \(-0.796221\pi\) |
0.947321 | − | 0.320286i | \(-0.103779\pi\) | |||||||
\(548\) | −7.39040 | − | 14.5045i | −0.315702 | − | 0.619601i | ||||
\(549\) | 4.77326 | + | 14.7211i | 0.203718 | + | 0.628281i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 10.6979i | − | 0.455744i | ||||||
\(552\) | −0.394655 | + | 0.286550i | −0.0167976 | + | 0.0121964i | ||||
\(553\) | −26.5472 | − | 4.20467i | −1.12890 | − | 0.178801i | ||||
\(554\) | −51.0102 | − | 37.0611i | −2.16721 | − | 1.57457i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.65611 | − | 11.2524i | −0.155054 | − | 0.477206i | ||||
\(557\) | 1.85285 | + | 11.6984i | 0.0785077 | + | 0.495678i | 0.995342 | + | 0.0964096i | \(0.0307359\pi\) |
−0.916834 | + | 0.399269i | \(0.869264\pi\) | |||||||
\(558\) | 0.162233 | + | 1.02835i | 0.00686785 | + | 0.0435336i | ||||
\(559\) | 4.20124 | + | 1.36507i | 0.177694 | + | 0.0577362i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.92577 | + | 14.3078i | −0.0813059 | + | 0.604075i | ||||
\(562\) | −29.6548 | + | 29.6548i | −1.25091 | + | 1.25091i | ||||
\(563\) | 13.4469 | + | 26.3911i | 0.566720 | + | 1.11225i | 0.979505 | + | 0.201422i | \(0.0645563\pi\) |
−0.412784 | + | 0.910829i | \(0.635444\pi\) | |||||||
\(564\) | −18.1063 | − | 18.1173i | −0.762413 | − | 0.762878i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.25066 | − | 1.05620i | 0.136636 | − | 0.0443956i | ||||
\(567\) | −38.1767 | + | 5.99892i | −1.60327 | + | 0.251931i | ||||
\(568\) | 0.00435074 | + | 0.0274695i | 0.000182553 | + | 0.00115259i | ||||
\(569\) | −10.8034 | + | 7.84911i | −0.452901 | + | 0.329052i | −0.790740 | − | 0.612152i | \(-0.790304\pi\) |
0.337839 | + | 0.941204i | \(0.390304\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.25098 | 0.345293 | 0.172646 | − | 0.984984i | \(-0.444768\pi\) | ||||
0.172646 | + | 0.984984i | \(0.444768\pi\) | |||||||
\(572\) | −15.2838 | + | 2.79180i | −0.639048 | + | 0.116731i | ||||
\(573\) | 1.01969 | + | 0.741326i | 0.0425983 | + | 0.0309693i | ||||
\(574\) | 47.3917 | + | 15.3985i | 1.97809 | + | 0.642721i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0275 | − | 7.82320i | −1.00115 | − | 0.325967i | ||||
\(577\) | 18.7627 | + | 9.56008i | 0.781102 | + | 0.397991i | 0.798605 | − | 0.601856i | \(-0.205572\pi\) |
−0.0175032 | + | 0.999847i | \(0.505572\pi\) | |||||||
\(578\) | 19.1666 | + | 9.76585i | 0.797224 | + | 0.406206i | ||||
\(579\) | −33.8002 | − | 17.2350i | −1.40469 | − | 0.716263i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.6634 | − | 7.03886i | −0.898748 | − | 0.292021i | ||||
\(582\) | −26.0837 | + | 35.8782i | −1.08121 | + | 1.48720i | ||||
\(583\) | 26.3573 | − | 27.6313i | 1.09161 | − | 1.14437i | ||||
\(584\) | 0.814287 | 0.0336954 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.64747 | − | 7.00930i | 0.398534 | − | 0.289552i | ||||
\(587\) | −5.45777 | − | 34.4590i | −0.225266 | − | 1.42228i | −0.798061 | − | 0.602576i | \(-0.794141\pi\) |
0.572795 | − | 0.819699i | \(-0.305859\pi\) | |||||||
\(588\) | 38.6883 | + | 12.5836i | 1.59548 | + | 0.518940i | ||||
\(589\) | 1.36163 | − | 0.442421i | 0.0561051 | − | 0.0182296i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.05002 | + | 3.04817i | −0.125461 | + | 0.125385i | ||||
\(592\) | 15.2100 | + | 29.8513i | 0.625126 | + | 1.22688i | ||||
\(593\) | 4.91375 | − | 4.91375i | 0.201784 | − | 0.201784i | −0.598980 | − | 0.800764i | \(-0.704427\pi\) |
0.800764 | + | 0.598980i | \(0.204427\pi\) | |||||||
\(594\) | 23.9722 | − | 25.0850i | 0.983592 | − | 1.02925i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −28.5320 | − | 9.27062i | −1.16872 | − | 0.379740i | ||||
\(597\) | 32.4929 | + | 0.00989918i | 1.32984 | + | 0.000405147i | ||||
\(598\) | −1.87413 | − | 11.8328i | −0.0766391 | − | 0.483880i | ||||
\(599\) | −7.90381 | − | 24.3254i | −0.322941 | − | 0.993910i | −0.972361 | − | 0.233481i | \(-0.924988\pi\) |
0.649420 | − | 0.760430i | \(-0.275012\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.4898 | − | 14.1601i | −0.795004 | − | 0.577605i | 0.114440 | − | 0.993430i | \(-0.463493\pi\) |
−0.909444 | + | 0.415826i | \(0.863493\pi\) | |||||||
\(602\) | 16.5357 | + | 2.61900i | 0.673945 | + | 0.106742i | ||||
\(603\) | 11.3693 | − | 11.3555i | 0.462994 | − | 0.462430i | ||||
\(604\) | 27.4562i | 1.11718i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.86667 | + | 24.4614i | 0.157073 | + | 0.993677i | ||||
\(607\) | −0.572319 | − | 1.12324i | −0.0232297 | − | 0.0455909i | 0.879100 | − | 0.476637i | \(-0.158145\pi\) |
−0.902330 | + | 0.431046i | \(0.858145\pi\) | |||||||
\(608\) | −10.4573 | + | 66.0245i | −0.424098 | + | 2.67765i | ||||
\(609\) | −4.35112 | + | 8.53312i | −0.176316 | + | 0.345779i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.6224 | − | 5.07602i | 0.632014 | − | 0.205354i | ||||
\(612\) | 7.02071 | + | 13.7997i | 0.283795 | + | 0.557820i | ||||
\(613\) | −32.9838 | − | 5.22412i | −1.33220 | − | 0.211000i | −0.550596 | − | 0.834772i | \(-0.685599\pi\) |
−0.781606 | + | 0.623772i | \(0.785599\pi\) | |||||||
\(614\) | −12.5522 | + | 38.6317i | −0.506566 | + | 1.55905i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.45041 | + | 0.509399i | −0.0584388 | + | 0.0205243i | ||||
\(617\) | 0.184767 | + | 0.184767i | 0.00743843 | + | 0.00743843i | 0.710816 | − | 0.703378i | \(-0.248326\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(618\) | −8.37699 | + | 6.08234i | −0.336972 | + | 0.244668i | ||||
\(619\) | −9.40644 | − | 12.9469i | −0.378077 | − | 0.520378i | 0.576997 | − | 0.816746i | \(-0.304224\pi\) |
−0.955074 | + | 0.296368i | \(0.904224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.57577 | + | 9.59329i | 0.384262 | + | 0.384965i | ||||
\(622\) | 25.2709 | + | 12.8762i | 1.01327 | + | 0.516288i | ||||
\(623\) | −66.6677 | + | 10.5591i | −2.67098 | + | 0.423042i | ||||
\(624\) | 10.8707 | − | 10.8641i | 0.435178 | − | 0.434913i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 54.5050i | − | 2.17846i | ||||||
\(627\) | −39.2465 | − | 27.1408i | −1.56736 | − | 1.08390i | ||||
\(628\) | 0.908320 | + | 0.908320i | 0.0362459 | + | 0.0362459i | ||||
\(629\) | 6.68867 | − | 20.5856i | 0.266695 | − | 0.820802i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.3117 | + | 13.3042i | 0.728977 | + | 0.529633i | 0.889240 | − | 0.457442i | \(-0.151234\pi\) |
−0.160263 | + | 0.987074i | \(0.551234\pi\) | |||||||
\(632\) | 0.306755 | − | 0.602041i | 0.0122021 | − | 0.0239479i | ||||
\(633\) | 20.9595 | + | 6.81721i | 0.833065 | + | 0.270960i | ||||
\(634\) | 17.4432 | − | 24.0084i | 0.692756 | − | 0.953497i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.41886 | − | 40.4473i | 0.254524 | − | 1.60384i | ||||
\(637\) | −18.4487 | + | 18.4487i | −0.730964 | + | 0.730964i | ||||
\(638\) | −1.54534 | − | 8.46002i | −0.0611807 | − | 0.334935i | ||||
\(639\) | 0.735266 | − | 0.238407i | 0.0290867 | − | 0.00943124i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.413955 | + | 0.569760i | 0.0163502 | + | 0.0225042i | 0.817114 | − | 0.576476i | \(-0.195573\pi\) |
−0.800764 | + | 0.598980i | \(0.795573\pi\) | |||||||
\(642\) | −5.64309 | − | 17.3857i | −0.222715 | − | 0.686158i | ||||
\(643\) | −0.536739 | + | 1.05341i | −0.0211669 | + | 0.0415424i | −0.901348 | − | 0.433096i | \(-0.857421\pi\) |
0.880181 | + | 0.474638i | \(0.157421\pi\) | |||||||
\(644\) | −7.10817 | − | 21.8767i | −0.280101 | − | 0.862063i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.0024 | − | 24.7042i | 1.33781 | − | 0.971972i | ||||
\(647\) | 4.86138 | − | 2.47700i | 0.191121 | − | 0.0973808i | −0.355812 | − | 0.934558i | \(-0.615796\pi\) |
0.546932 | + | 0.837177i | \(0.315796\pi\) | |||||||
\(648\) | 0.153145 | − | 0.959351i | 0.00601610 | − | 0.0376869i | ||||
\(649\) | −8.92135 | + | 29.8343i | −0.350193 | + | 1.17110i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.26605 | − | 0.200918i | −0.0496203 | − | 0.00787458i | ||||
\(652\) | 2.46383 | − | 15.5560i | 0.0964909 | − | 0.609220i | ||||
\(653\) | −32.7635 | + | 5.18923i | −1.28213 | + | 0.203070i | −0.760073 | − | 0.649838i | \(-0.774837\pi\) |
−0.522061 | + | 0.852908i | \(0.674837\pi\) | |||||||
\(654\) | −44.8696 | + | 22.8450i | −1.75454 | + | 0.893310i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 13.1789 | − | 18.1392i | 0.514549 | − | 0.708216i | ||||
\(657\) | −3.52661 | − | 22.3543i | −0.137586 | − | 0.872125i | ||||
\(658\) | 55.4693 | − | 28.2630i | 2.16242 | − | 1.10181i | ||||
\(659\) | −19.7145 | −0.767966 | −0.383983 | − | 0.923340i | \(-0.625448\pi\) | ||||
−0.383983 | + | 0.923340i | \(0.625448\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8276 | 0.771202 | 0.385601 | − | 0.922666i | \(-0.373994\pi\) | ||||
0.385601 | + | 0.922666i | \(0.373994\pi\) | |||||||
\(662\) | 20.2568 | − | 10.3214i | 0.787304 | − | 0.401151i | ||||
\(663\) | −9.92928 | − | 0.00302503i | −0.385621 | − | 0.000117482i | ||||
\(664\) | 0.336577 | − | 0.463259i | 0.0130617 | − | 0.0179779i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −42.1052 | + | 30.5520i | −1.63154 | + | 1.18387i | ||||
\(667\) | 3.31822 | − | 0.525554i | 0.128482 | − | 0.0203495i | ||||
\(668\) | 5.79942 | − | 36.6161i | 0.224386 | − | 1.41672i | ||||
\(669\) | −1.19884 | + | 7.55430i | −0.0463500 | + | 0.292066i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.6003 | − | 10.3801i | 0.525035 | − | 0.400719i | ||||
\(672\) | 35.1952 | − | 48.4110i | 1.35768 | − | 1.86749i | ||||
\(673\) | −10.2260 | + | 5.21043i | −0.394185 | + | 0.200847i | −0.639837 | − | 0.768511i | \(-0.720998\pi\) |
0.245652 | + | 0.969358i | \(0.420998\pi\) | |||||||
\(674\) | −38.1293 | + | 27.7025i | −1.46868 | + | 1.06706i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.94774 | + | 15.2276i | 0.190298 | + | 0.585676i | ||||
\(677\) | 9.07185 | − | 17.8045i | 0.348660 | − | 0.684283i | −0.648368 | − | 0.761327i | \(-0.724548\pi\) |
0.997028 | + | 0.0770440i | \(0.0245482\pi\) | |||||||
\(678\) | −18.3712 | + | 5.96296i | −0.705540 | + | 0.229006i | ||||
\(679\) | −32.1040 | − | 44.1873i | −1.23204 | − | 1.69575i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −28.4894 | + | 4.50338i | −1.09171 | + | 0.172570i | ||||
\(682\) | 1.01289 | − | 0.546565i | 0.0387855 | − | 0.0209291i | ||||
\(683\) | −20.8418 | + | 20.8418i | −0.797488 | + | 0.797488i | −0.982699 | − | 0.185211i | \(-0.940703\pi\) |
0.185211 | + | 0.982699i | \(0.440703\pi\) | |||||||
\(684\) | −51.1748 | − | 0.0311815i | −1.95672 | − | 0.00119226i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −22.5500 | + | 31.0375i | −0.860965 | + | 1.18502i | ||||
\(687\) | −3.56392 | + | 10.9572i | −0.135972 | + | 0.418045i | ||||
\(688\) | 3.41990 | − | 6.71193i | 0.130382 | − | 0.255890i | ||||
\(689\) | 21.2477 | + | 15.4374i | 0.809474 | + | 0.588117i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.960137 | + | 2.95500i | −0.0365253 | + | 0.112413i | −0.967657 | − | 0.252270i | \(-0.918823\pi\) |
0.931132 | + | 0.364684i | \(0.118823\pi\) | |||||||
\(692\) | 28.9342 | + | 28.9342i | 1.09991 | + | 1.09991i | ||||
\(693\) | 20.2659 | + | 37.6114i | 0.769839 | + | 1.42874i | ||||
\(694\) | 18.3483i | 0.696491i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.170213 | − | 0.170317i | −0.00645192 | − | 0.00645585i | ||||
\(697\) | −14.3072 | + | 2.26604i | −0.541925 | + | 0.0858325i | ||||
\(698\) | 35.3244 | + | 17.9987i | 1.33705 | + | 0.681260i | ||||
\(699\) | 17.0298 | − | 8.67056i | 0.644125 | − | 0.327951i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.4277 | + | 22.6108i | 0.620465 | + | 0.853997i | 0.997387 | − | 0.0722484i | \(-0.0230174\pi\) |
−0.376922 | + | 0.926245i | \(0.623017\pi\) | |||||||
\(702\) | 19.2937 | + | 14.0446i | 0.728193 | + | 0.530081i | ||||
\(703\) | 50.5877 | + | 50.5877i | 1.90795 | + | 1.90795i | ||||
\(704\) | 0.659022 | + | 27.9282i | 0.0248378 | + | 1.05258i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.1636 | − | 43.5911i | 0.533054 | − | 1.64057i | ||||
\(707\) | −30.1184 | − | 4.77028i | −1.13272 | − | 0.179405i | ||||
\(708\) | 10.3103 | + | 31.7648i | 0.387485 | + | 1.19379i | ||||
\(709\) | −26.9408 | + | 8.75358i | −1.01178 | + | 0.328748i | −0.767564 | − | 0.640973i | \(-0.778531\pi\) |
−0.244218 | + | 0.969720i | \(0.578531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.8561 | − | 5.81384i | −0.669658 | − | 0.218036i | ||||
\(712\) | 0.265445 | − | 1.67595i | 0.00994797 | − | 0.0628090i | ||||
\(713\) | 0.204121 | + | 0.400610i | 0.00764440 | + | 0.0150030i | ||||
\(714\) | −37.1697 | + | 5.87550i | −1.39104 | + | 0.219885i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 6.71372i | − | 0.250904i | ||||||
\(717\) | −27.3580 | − | 37.6791i | −1.02170 | − | 1.40715i | ||||
\(718\) | 10.5631 | + | 1.67303i | 0.394211 | + | 0.0624369i | ||||
\(719\) | 24.8692 | + | 18.0685i | 0.927465 | + | 0.673843i | 0.945371 | − | 0.325997i | \(-0.105700\pi\) |
−0.0179059 | + | 0.999840i | \(0.505700\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.93902 | − | 12.1230i | −0.146697 | − | 0.451486i | ||||
\(722\) | 15.7471 | + | 99.4234i | 0.586047 | + | 3.70015i | ||||
\(723\) | 0.00941398 | − | 30.9002i | 0.000350110 | − | 1.14919i | ||||
\(724\) | −8.10947 | − | 2.63493i | −0.301386 | − | 0.0979263i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −34.9573 | − | 15.7940i | −1.29739 | − | 0.586172i | ||||
\(727\) | −12.2759 | + | 12.2759i | −0.455287 | + | 0.455287i | −0.897105 | − | 0.441818i | \(-0.854334\pi\) |
0.441818 | + | 0.897105i | \(0.354334\pi\) | |||||||
\(728\) | −0.480001 | − | 0.942055i | −0.0177900 | − | 0.0349149i | ||||
\(729\) | −27.0000 | − | 0.0493544i | −0.999998 | − | 0.00182794i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.62859 | + | 1.50392i | −0.171195 | + | 0.0556245i | ||||
\(732\) | 5.67538 | − | 17.4489i | 0.209768 | − | 0.644932i | ||||
\(733\) | −1.33901 | − | 8.45420i | −0.0494576 | − | 0.312263i | −0.999999 | − | 0.00166396i | \(-0.999470\pi\) |
0.950541 | − | 0.310599i | \(-0.100530\pi\) | |||||||
\(734\) | 22.7502 | − | 16.5290i | 0.839725 | − | 0.610096i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.9929 | −0.773809 | ||||||||
\(737\) | −16.0144 | − | 7.68939i | −0.589897 | − | 0.283242i | ||||
\(738\) | 31.0106 | + | 15.8245i | 1.14152 | + | 0.582508i | ||||
\(739\) | 7.40702 | + | 2.40669i | 0.272472 | + | 0.0885314i | 0.442066 | − | 0.896983i | \(-0.354246\pi\) |
−0.169594 | + | 0.985514i | \(0.554246\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.9082 | − | 29.2371i | 0.547668 | − | 1.07405i | ||||
\(742\) | 88.6884 | + | 45.1890i | 3.25585 | + | 1.65894i | ||||
\(743\) | 10.1177 | + | 5.15521i | 0.371181 | + | 0.189126i | 0.629623 | − | 0.776900i | \(-0.283209\pi\) |
−0.258442 | + | 0.966027i | \(0.583209\pi\) | |||||||
\(744\) | 0.0146387 | − | 0.0287085i | 0.000536682 | − | 0.00105251i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 39.3699 | + | 12.7920i | 1.44143 | + | 0.468350i | ||||
\(747\) | −14.1754 | − | 7.23359i | −0.518649 | − | 0.264663i | ||||
\(748\) | 11.8147 | − | 12.3857i | 0.431988 | − | 0.452868i | ||||
\(749\) | 22.5068 | 0.822380 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.36088 | − | 1.71528i | 0.0861498 | − | 0.0625915i | −0.543877 | − | 0.839165i | \(-0.683044\pi\) |
0.630026 | + | 0.776574i | \(0.283044\pi\) | |||||||
\(752\) | −4.38196 | − | 27.6666i | −0.159794 | − | 1.00890i | ||||
\(753\) | −10.6137 | + | 32.6318i | −0.386785 | + | 1.18917i | ||||
\(754\) | 5.62537 | − | 1.82780i | 0.204864 | − | 0.0665644i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 40.8068 | + | 20.8391i | 1.48413 | + | 0.757910i | ||||
\(757\) | 7.66252 | + | 15.0385i | 0.278499 | + | 0.546585i | 0.987308 | − | 0.158815i | \(-0.0507674\pi\) |
−0.708809 | + | 0.705400i | \(0.750767\pi\) | |||||||
\(758\) | 20.5134 | − | 20.5134i | 0.745079 | − | 0.745079i | ||||
\(759\) | 6.49036 | − | 13.5067i | 0.235585 | − | 0.490261i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.1857 | + | 4.93415i | 0.550483 | + | 0.178863i | 0.571035 | − | 0.820926i | \(-0.306542\pi\) |
−0.0205516 | + | 0.999789i | \(0.506542\pi\) | |||||||
\(762\) | −0.0158626 | + | 52.0671i | −0.000574641 | + | 1.88619i | ||||
\(763\) | −9.69857 | − | 61.2343i | −0.351112 | − | 2.21683i | ||||
\(764\) | −0.461901 | − | 1.42159i | −0.0167110 | − | 0.0514312i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.0502 | − | 16.0204i | −0.796708 | − | 0.578842i | ||||
\(767\) | −21.1534 | − | 3.35037i | −0.763804 | − | 0.120975i | ||||
\(768\) | −15.3746 | − | 21.1749i | −0.554783 | − | 0.764083i | ||||
\(769\) | − | 2.12397i | − | 0.0765925i | −0.999266 | − | 0.0382962i | \(-0.987807\pi\) | ||
0.999266 | − | 0.0382962i | \(-0.0121931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.2587 | − | 2.88619i | 0.657571 | − | 0.103944i | ||||
\(772\) | 20.4226 | + | 40.0816i | 0.735024 | + | 1.44257i | ||||
\(773\) | 2.88604 | − | 18.2217i | 0.103804 | − | 0.655390i | −0.879841 | − | 0.475269i | \(-0.842351\pi\) |
0.983644 | − | 0.180122i | \(-0.0576492\pi\) | |||||||
\(774\) | 11.1222 | + | 3.62132i | 0.399780 | + | 0.130166i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.30585 | − | 0.424296i | 0.0468772 | − | 0.0152313i | ||||
\(777\) | −19.7757 | − | 60.9265i | −0.709450 | − | 2.18573i | ||||
\(778\) | −54.7974 | − | 8.67906i | −1.96458 | − | 0.311159i | ||||
\(779\) | 14.7952 | − | 45.5349i | 0.530093 | − | 1.63146i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.518449 | − | 0.679288i | −0.0185516 | − | 0.0243068i | ||||
\(782\) | 9.33306 | + | 9.33306i | 0.333750 | + | 0.333750i | ||||
\(783\) | −3.93847 | + | 5.41043i | −0.140749 | + | 0.193353i | ||||
\(784\) | 26.1514 | + | 35.9943i | 0.933977 | + | 1.28551i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 44.1441 | − | 22.4756i | 1.57457 | − | 0.801678i | ||||
\(787\) | −25.1479 | − | 12.8135i | −0.896424 | − | 0.456751i | −0.0558449 | − | 0.998439i | \(-0.517785\pi\) |
−0.840579 | + | 0.541689i | \(0.817785\pi\) | |||||||
\(788\) | 5.04968 | − | 0.799791i | 0.179887 | − | 0.0284914i | ||||
\(789\) | −0.386639 | − | 0.386875i | −0.0137647 | − | 0.0137731i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 23.7825i | − | 0.845610i | ||||||
\(792\) | −1.05667 | + | 0.192350i | −0.0375470 | + | 0.00683486i | ||||
\(793\) | 8.32060 | + | 8.32060i | 0.295473 | + | 0.295473i | ||||
\(794\) | 18.9912 | − | 58.4489i | 0.673972 | − | 2.07427i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.1676 | − | 22.6446i | −1.10471 | − | 0.802617i | ||||
\(797\) | −2.37050 | + | 4.65237i | −0.0839674 | + | 0.164795i | −0.929172 | − | 0.369647i | \(-0.879478\pi\) |
0.845205 | + | 0.534443i | \(0.179478\pi\) | |||||||
\(798\) | 38.4716 | − | 118.281i | 1.36188 | − | 4.18710i | ||||
\(799\) | −10.6373 | + | 14.6410i | −0.376320 | + | 0.517960i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.1589 | − | 0.0287346i | −1.66628 | − | 0.00101529i | ||||
\(802\) | 44.8081 | − | 44.8081i | 1.58223 | − | 1.58223i | ||||
\(803\) | −22.0182 | + | 11.8812i | −0.777004 | + | 0.419280i | ||||
\(804\) | −18.8184 | + | 2.97467i | −0.663675 | + | 0.104909i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.465286 | + | 0.640412i | 0.0163890 | + | 0.0225575i | ||||
\(807\) | 38.4397 | − | 12.4769i | 1.35314 | − | 0.439207i | ||||
\(808\) | 0.348021 | − | 0.683029i | 0.0122433 | − | 0.0240289i | ||||
\(809\) | −8.59306 | − | 26.4467i | −0.302116 | − | 0.929817i | −0.980738 | − | 0.195329i | \(-0.937422\pi\) |
0.678622 | − | 0.734488i | \(-0.262578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.5008 | − | 20.7071i | 1.00080 | − | 0.727123i | 0.0385397 | − | 0.999257i | \(-0.487729\pi\) |
0.962259 | + | 0.272134i | \(0.0877294\pi\) | |||||||
\(812\) | 10.1189 | − | 5.15584i | 0.355104 | − | 0.180934i | ||||
\(813\) | −0.287710 | + | 0.395745i | −0.0100904 | + | 0.0138794i | ||||
\(814\) | 47.3130 | + | 32.6979i | 1.65832 | + | 1.14606i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.65387 | + | 16.7229i | −0.0929041 | + | 0.585419i | ||||
\(817\) | 2.51639 | − | 15.8878i | 0.0880372 | − | 0.555845i | ||||
\(818\) | 6.68864 | − | 1.05938i | 0.233863 | − | 0.0370403i | ||||
\(819\) | −23.7830 | + | 17.2573i | −0.831046 | + | 0.603017i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.77774 | − | 5.19962i | 0.131844 | − | 0.181468i | −0.737991 | − | 0.674811i | \(-0.764225\pi\) |
0.869835 | + | 0.493343i | \(0.164225\pi\) | |||||||
\(822\) | 27.6430 | + | 0.00842162i | 0.964159 | + | 0.000293738i | ||||
\(823\) | 7.27496 | − | 3.70678i | 0.253589 | − | 0.129210i | −0.322576 | − | 0.946544i | \(-0.604549\pi\) |
0.576165 | + | 0.817334i | \(0.304549\pi\) | |||||||
\(824\) | 0.320444 | 0.0111632 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −81.1691 | −2.82424 | ||||||||
\(827\) | 38.1983 | − | 19.4630i | 1.32829 | − | 0.676796i | 0.361498 | − | 0.932373i | \(-0.382266\pi\) |
0.966789 | + | 0.255577i | \(0.0822655\pi\) | |||||||
\(828\) | −2.50439 | − | 15.8747i | −0.0870337 | − | 0.551684i | ||||
\(829\) | 28.7225 | − | 39.5331i | 0.997573 | − | 1.37304i | 0.0707706 | − | 0.997493i | \(-0.477454\pi\) |
0.926803 | − | 0.375549i | \(-0.122546\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 48.3378 | − | 24.6108i | 1.67682 | − | 0.853739i | ||||
\(832\) | −18.9771 | + | 3.00568i | −0.657913 | + | 0.104203i | ||||
\(833\) | 4.49660 | − | 28.3904i | 0.155798 | − | 0.983669i | ||||
\(834\) | 19.8426 | + | 3.14896i | 0.687094 | + | 0.109040i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 18.7474 | + | 53.3795i | 0.648392 | + | 1.84617i | ||||
\(837\) | −0.851523 | − | 0.277537i | −0.0294329 | − | 0.00959309i | ||||
\(838\) | −14.4603 | + | 7.36791i | −0.499524 | + | 0.254520i | ||||
\(839\) | 2.49994 | − | 1.81631i | 0.0863075 | − | 0.0627061i | −0.543795 | − | 0.839218i | \(-0.683013\pi\) |
0.630102 | + | 0.776512i | \(0.283013\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.44893 | − | 26.0031i | −0.291343 | − | 0.896660i | ||||
\(842\) | −6.51309 | + | 12.7827i | −0.224456 | + | 0.440519i | ||||
\(843\) | −11.1384 | − | 34.3162i | −0.383628 | − | 1.18191i | ||||
\(844\) | −15.3601 | − | 21.1414i | −0.528717 | − | 0.727716i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 41.3745 | − | 13.4155i | 1.42248 | − | 0.461235i | ||||
\(847\) | 31.7863 | − | 34.9370i | 1.09219 | − | 1.20045i | ||||
\(848\) | 31.6690 | − | 31.6690i | 1.08752 | − | 1.08752i | ||||
\(849\) | −0.460863 | + | 2.90405i | −0.0158168 | + | 0.0996667i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.2058 | + | 18.1763i | −0.452691 | + | 0.623075i | ||||
\(852\) | −0.871513 | − | 0.283465i | −0.0298575 | − | 0.00971136i | ||||
\(853\) | 1.26597 | − | 2.48460i | 0.0433458 | − | 0.0850710i | −0.868318 | − | 0.496008i | \(-0.834799\pi\) |
0.911664 | + | 0.410937i | \(0.134799\pi\) | |||||||
\(854\) | 36.0793 | + | 26.2132i | 1.23461 | + | 0.896996i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.174841 | + | 0.538104i | −0.00597593 | + | 0.0183920i | ||||
\(857\) | 23.9356 | + | 23.9356i | 0.817625 | + | 0.817625i | 0.985763 | − | 0.168138i | \(-0.0537755\pi\) |
−0.168138 | + | 0.985763i | \(0.553775\pi\) | |||||||
\(858\) | 7.56625 | − | 25.2746i | 0.258308 | − | 0.862861i | ||||
\(859\) | 17.2076i | 0.587115i | 0.955941 | + | 0.293558i | \(0.0948393\pi\) | ||||
−0.955941 | + | 0.293558i | \(0.905161\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.3216 | + | 30.3032i | −1.03336 | + | 1.03273i | ||||
\(862\) | −57.0367 | + | 9.03373i | −1.94268 | + | 0.307690i | ||||
\(863\) | 21.2153 | + | 10.8097i | 0.722177 | + | 0.367968i | 0.776128 | − | 0.630576i | \(-0.217181\pi\) |
−0.0539502 | + | 0.998544i | \(0.517181\pi\) | |||||||
\(864\) | 29.5960 | − | 29.5419i | 1.00688 | − | 1.00504i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11.6358 | − | 16.0152i | −0.395399 | − | 0.544220i | ||||
\(867\) | −14.9746 | + | 10.8727i | −0.508566 | + | 0.369258i | ||||
\(868\) | 1.07472 | + | 1.07472i | 0.0364783 | + | 0.0364783i | ||||
\(869\) | 0.489755 | + | 20.7549i | 0.0166138 | + | 0.704063i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.77563 | − | 11.6202i | 0.127932 | − | 0.393735i | ||||
\(872\) | 1.53936 | + | 0.243811i | 0.0521295 | + | 0.00825650i | ||||
\(873\) | −17.3036 | − | 34.0114i | −0.585637 | − | 1.15111i | ||||
\(874\) | −41.4904 | + | 13.4811i | −1.40343 | + | 0.456003i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.1889 | + | 23.9040i | −0.411824 | + | 0.807642i | ||||
\(877\) | −7.38610 | + | 46.6340i | −0.249411 | + | 1.57472i | 0.471611 | + | 0.881806i | \(0.343673\pi\) |
−0.721022 | + | 0.692912i | \(0.756327\pi\) | |||||||
\(878\) | −22.8565 | − | 44.8584i | −0.771369 | − | 1.51390i | ||||
\(879\) | 1.60174 | + | 10.1330i | 0.0540253 | + | 0.341776i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 31.5604i | − | 1.06330i | −0.846965 | − | 0.531649i | \(-0.821573\pi\) | ||
0.846965 | − | 0.531649i | \(-0.178427\pi\) | |||||||
\(882\) | −48.8798 | + | 48.8203i | −1.64587 | + | 1.64386i | ||||
\(883\) | 54.0724 | + | 8.56422i | 1.81968 | + | 0.288209i | 0.970714 | − | 0.240238i | \(-0.0772255\pi\) |
0.848966 | + | 0.528447i | \(0.177226\pi\) | |||||||
\(884\) | 9.52431 | + | 6.91982i | 0.320337 | + | 0.232739i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.42397 | − | 22.8486i | −0.249413 | − | 0.767615i | ||||
\(887\) | −6.45512 | − | 40.7560i | −0.216742 | − | 1.36845i | −0.820665 | − | 0.571410i | \(-0.806397\pi\) |
0.603923 | − | 0.797042i | \(-0.293603\pi\) | |||||||
\(888\) | 1.61029 | 0.000490586i | 0.0540377 | 1.64630e-5i | ||||||
\(889\) | −60.9734 | − | 19.8115i | −2.04498 | − | 0.664455i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.85685 | + | 28.1752i | 0.330217 | + | 0.943905i | ||||
\(892\) | 6.41267 | − | 6.41267i | 0.214712 | − | 0.214712i | ||||
\(893\) | −27.1557 | − | 53.2960i | −0.908730 | − | 1.78348i | ||||
\(894\) | 36.0335 | − | 36.0116i | 1.20514 | − | 1.20441i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.52527 | + | 1.14543i | −0.117771 | + | 0.0382661i | ||||
\(897\) | 9.80102 | + | 3.18784i | 0.327246 | + | 0.106439i | ||||
\(898\) | −9.55724 | − | 60.3421i | −0.318929 | − | 2.01364i | ||||
\(899\) | −0.179587 | + | 0.130478i | −0.00598957 | + | 0.00435168i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.9351 | −0.963969 | ||||||||
\(902\) | 5.12257 | − | 38.1468i | 0.170563 | − | 1.27015i | ||||
\(903\) | −8.46921 | + | 11.6494i | −0.281838 | + | 0.387668i | ||||
\(904\) | 0.568606 | + | 0.184751i | 0.0189115 | + | 0.00614473i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −41.5353 | − | 21.1792i | −1.37992 | − | 0.703633i | ||||
\(907\) | −34.4665 | − | 17.5616i | −1.14444 | − | 0.583122i | −0.224227 | − | 0.974537i | \(-0.571986\pi\) |
−0.920214 | + | 0.391415i | \(0.871986\pi\) | |||||||
\(908\) | 30.4706 | + | 15.5255i | 1.01120 | + | 0.515233i | ||||
\(909\) | −20.2582 | − | 6.59593i | −0.671921 | − | 0.218773i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.4299 | − | 9.23742i | −0.941923 | − | 0.306049i | −0.202494 | − | 0.979284i | \(-0.564905\pi\) |
−0.739429 | + | 0.673234i | \(0.764905\pi\) | |||||||
\(912\) | −45.2665 | − | 32.9091i | −1.49892 | − | 1.08973i | ||||
\(913\) | −2.34159 | + | 17.4374i | −0.0774954 | + | 0.577094i | ||||
\(914\) | 10.3128 | 0.341116 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11.0523 | − | 8.02999i | 0.365179 | − | 0.265318i | ||||
\(917\) | 9.54174 | + | 60.2442i | 0.315096 | + | 1.98944i | ||||
\(918\) | −26.2916 | − | 0.0240298i | −0.867752 | − | 0.000793100i | ||||
\(919\) | 10.7020 | − | 3.47729i | 0.353026 | − | 0.114705i | −0.127135 | − | 0.991885i | \(-0.540578\pi\) |
0.480161 | + | 0.877180i | \(0.340578\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.7019 | − | 24.7169i | −0.813954 | − | 0.814450i | ||||
\(922\) | −30.7721 | − | 60.3936i | −1.01342 | − | 1.98896i | ||||
\(923\) | 0.415584 | − | 0.415584i | 0.0136791 | − | 0.0136791i | ||||
\(924\) | 6.75712 | − | 50.2031i | 0.222293 | − | 1.65156i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 46.3562 | + | 15.0620i | 1.52336 | + | 0.494969i | ||||
\(927\) | −1.38782 | − | 8.79702i | −0.0455819 | − | 0.288932i | ||||
\(928\) | −1.62137 | − | 10.2369i | −0.0532241 | − | 0.336044i | ||||
\(929\) | −2.06011 | − | 6.34037i | −0.0675900 | − | 0.208021i | 0.911557 | − | 0.411174i | \(-0.134881\pi\) |
−0.979147 | + | 0.203153i | \(0.934881\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 76.8619 | + | 55.8435i | 2.51905 | + | 1.83020i | ||||
\(932\) | −22.3789 | − | 3.54447i | −0.733045 | − | 0.116103i | ||||
\(933\) | −19.7439 | + | 14.3356i | −0.646387 | + | 0.469327i | ||||
\(934\) | − | 68.4903i | − | 2.24107i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.227840 | − | 0.702677i | −0.00744720 | − | 0.0229677i | ||||
\(937\) | 2.76808 | + | 5.43267i | 0.0904294 | + | 0.177478i | 0.931791 | − | 0.362995i | \(-0.118246\pi\) |
−0.841362 | + | 0.540472i | \(0.818246\pi\) | |||||||
\(938\) | 7.24386 | − | 45.7359i | 0.236520 | − | 1.49333i | ||||
\(939\) | 41.7724 | + | 21.3001i | 1.36319 | + | 0.695103i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.9005 | + | 5.49131i | −0.550941 | + | 0.179012i | −0.571241 | − | 0.820782i | \(-0.693538\pi\) |
0.0203001 | + | 0.999794i | \(0.493538\pi\) | |||||||
\(942\) | −2.07475 | + | 0.673429i | −0.0675990 | + | 0.0219415i | ||||
\(943\) | 14.8507 | + | 2.35211i | 0.483604 | + | 0.0765953i | ||||
\(944\) | −11.2859 | + | 34.7345i | −0.367326 | + | 1.13051i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.305058 | − | 12.9278i | −0.00991829 | − | 0.420320i | ||||
\(947\) | −21.8913 | − | 21.8913i | −0.711371 | − | 0.711371i | 0.255451 | − | 0.966822i | \(-0.417776\pi\) |
−0.966822 | + | 0.255451i | \(0.917776\pi\) | |||||||
\(948\) | 13.0816 | + | 18.0169i | 0.424872 | + | 0.585161i | ||||
\(949\) | −10.1144 | − | 13.9213i | −0.328327 | − | 0.451904i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.5833 | + | 22.7507i | 0.375615 | + | 0.737741i | ||||
\(952\) | 1.03788 | + | 0.528826i | 0.0336379 | + | 0.0171394i | ||||
\(953\) | 42.2131 | − | 6.68589i | 1.36742 | − | 0.216577i | 0.570813 | − | 0.821080i | \(-0.306628\pi\) |
0.796603 | + | 0.604503i | \(0.206628\pi\) | |||||||
\(954\) | 56.2366 | + | 40.9107i | 1.82073 | + | 1.32453i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 55.2084i | 1.78557i | ||||||||
\(957\) | 7.08762 | + | 2.12176i | 0.229110 | + | 0.0685869i | ||||
\(958\) | 26.2785 | + | 26.2785i | 0.849020 | + | 0.849020i | ||||
\(959\) | −10.5181 | + | 32.3714i | −0.339648 | + | 1.04533i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0555 | + | 18.2039i | 0.808242 | + | 0.587222i | ||||
\(962\) | −17.9579 | + | 35.2443i | −0.578985 | + | 1.13632i | ||||
\(963\) | 15.5296 | + | 2.46934i | 0.500434 | + | 0.0795735i | ||||
\(964\) | −21.5347 | + | 29.6400i | −0.693586 | + | 0.954639i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 38.5778 | + | 6.12217i | 1.24122 | + | 0.196978i | ||||
\(967\) | 10.9192 | − | 10.9192i | 0.351136 | − | 0.351136i | −0.509396 | − | 0.860532i | \(-0.670131\pi\) |
0.860532 | + | 0.509396i | \(0.170131\pi\) | |||||||
\(968\) | 0.588364 | + | 1.03136i | 0.0189107 | + | 0.0331493i | ||||
\(969\) | 5.64530 | + | 35.7135i | 0.181353 | + | 1.14728i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.41292 | + | 3.32110i | 0.0774342 | + | 0.106579i | 0.845977 | − | 0.533219i | \(-0.179018\pi\) |
−0.768543 | + | 0.639798i | \(0.779018\pi\) | |||||||
\(972\) | 25.8701 | + | 18.8560i | 0.829784 | + | 0.604807i | ||||
\(973\) | −11.2310 | + | 22.0421i | −0.360049 | + | 0.706636i | ||||
\(974\) | 2.60745 | + | 8.02492i | 0.0835482 | + | 0.257135i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.2339 | − | 11.7946i | 0.519634 | − | 0.377536i | ||||
\(977\) | −25.9582 | + | 13.2264i | −0.830477 | + | 0.423149i | −0.816914 | − | 0.576759i | \(-0.804317\pi\) |
−0.0135622 | + | 0.999908i | \(0.504317\pi\) | |||||||
\(978\) | 21.6323 | + | 15.7268i | 0.691724 | + | 0.502889i | ||||
\(979\) | 17.2762 | + | 49.1906i | 0.552149 | + | 1.57214i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.0263928 | − | 43.3155i | 0.000842656 | − | 1.38296i | ||||
\(982\) | 0.328211 | − | 2.07224i | 0.0104736 | − | 0.0661279i | ||||
\(983\) | 11.5604 | − | 1.83099i | 0.368720 | − | 0.0583995i | 0.0306749 | − | 0.999529i | \(-0.490234\pi\) |
0.338045 | + | 0.941130i | \(0.390234\pi\) | |||||||
\(984\) | −0.488955 | − | 0.960351i | −0.0155873 | − | 0.0306149i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.83032 | + | 5.27198i | −0.121982 | + | 0.167894i | ||||
\(987\) | −0.0163163 | + | 53.5564i | −0.000519355 | + | 1.70472i | ||||
\(988\) | −34.6704 | + | 17.6655i | −1.10301 | + | 0.562013i | ||||
\(989\) | 5.05164 | 0.160633 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.1007 | −0.860882 | −0.430441 | − | 0.902619i | \(-0.641642\pi\) | ||||
−0.430441 | + | 0.902619i | \(0.641642\pi\) | |||||||
\(992\) | 1.23591 | − | 0.629728i | 0.0392402 | − | 0.0199939i | ||||
\(993\) | −0.00595856 | + | 19.5583i | −0.000189089 | + | 0.620662i | ||||
\(994\) | 1.30925 | − | 1.80203i | 0.0415270 | − | 0.0571570i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.56117 | + | 16.8149i | 0.271271 | + | 0.532801i | ||||
\(997\) | 8.97216 | − | 1.42105i | 0.284151 | − | 0.0450051i | −0.0127320 | − | 0.999919i | \(-0.504053\pi\) |
0.296883 | + | 0.954914i | \(0.404053\pi\) | |||||||
\(998\) | −5.00554 | + | 31.6037i | −0.158448 | + | 1.00040i | ||||
\(999\) | −6.96056 | − | 44.2087i | −0.220222 | − | 1.39870i |
(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 | 825.2.ct.c.218.28 | yes | 256 | |
3.2 | odd | 2 | inner | 825.2.ct.c.218.6 | yes | 256 | |
5.2 | odd | 4 | inner | 825.2.ct.c.482.28 | yes | 256 | |
5.3 | odd | 4 | inner | 825.2.ct.c.482.5 | yes | 256 | |
5.4 | even | 2 | inner | 825.2.ct.c.218.5 | ✓ | 256 | |
11.5 | even | 5 | inner | 825.2.ct.c.368.6 | yes | 256 | |
15.2 | even | 4 | inner | 825.2.ct.c.482.6 | yes | 256 | |
15.8 | even | 4 | inner | 825.2.ct.c.482.27 | yes | 256 | |
15.14 | odd | 2 | inner | 825.2.ct.c.218.27 | yes | 256 | |
33.5 | odd | 10 | inner | 825.2.ct.c.368.28 | yes | 256 | |
55.27 | odd | 20 | inner | 825.2.ct.c.632.6 | yes | 256 | |
55.38 | odd | 20 | inner | 825.2.ct.c.632.27 | yes | 256 | |
55.49 | even | 10 | inner | 825.2.ct.c.368.27 | yes | 256 | |
165.38 | even | 20 | inner | 825.2.ct.c.632.5 | yes | 256 | |
165.104 | odd | 10 | inner | 825.2.ct.c.368.5 | yes | 256 | |
165.137 | even | 20 | inner | 825.2.ct.c.632.28 | yes | 256 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.2.ct.c.218.5 | ✓ | 256 | 5.4 | even | 2 | inner | |
825.2.ct.c.218.6 | yes | 256 | 3.2 | odd | 2 | inner | |
825.2.ct.c.218.27 | yes | 256 | 15.14 | odd | 2 | inner | |
825.2.ct.c.218.28 | yes | 256 | 1.1 | even | 1 | trivial | |
825.2.ct.c.368.5 | yes | 256 | 165.104 | odd | 10 | inner | |
825.2.ct.c.368.6 | yes | 256 | 11.5 | even | 5 | inner | |
825.2.ct.c.368.27 | yes | 256 | 55.49 | even | 10 | inner | |
825.2.ct.c.368.28 | yes | 256 | 33.5 | odd | 10 | inner | |
825.2.ct.c.482.5 | yes | 256 | 5.3 | odd | 4 | inner | |
825.2.ct.c.482.6 | yes | 256 | 15.2 | even | 4 | inner | |
825.2.ct.c.482.27 | yes | 256 | 15.8 | even | 4 | inner | |
825.2.ct.c.482.28 | yes | 256 | 5.2 | odd | 4 | inner | |
825.2.ct.c.632.5 | yes | 256 | 165.38 | even | 20 | inner | |
825.2.ct.c.632.6 | yes | 256 | 55.27 | odd | 20 | inner | |
825.2.ct.c.632.27 | yes | 256 | 55.38 | odd | 20 | inner | |
825.2.ct.c.632.28 | yes | 256 | 165.137 | even | 20 | inner |