Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(177,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1232.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 308) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 177.1 | ||
Root | \(0.500000 + 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.177 |
Dual form | 1232.2.q.l.529.1 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.794182 | − | 1.37556i | −0.458521 | − | 0.794182i | 0.540362 | − | 0.841433i | \(-0.318287\pi\) |
−0.998883 | + | 0.0472507i | \(0.984954\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.64400 | + | 2.84748i | −0.735217 | + | 1.27343i | 0.219411 | + | 0.975633i | \(0.429587\pi\) |
−0.954628 | + | 0.297801i | \(0.903747\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64400 | + | 0.0963576i | −0.999337 | + | 0.0364197i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.238550 | − | 0.413181i | 0.0795166 | − | 0.137727i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.98762 | −1.38332 | −0.691658 | − | 0.722225i | \(-0.743120\pi\) | ||||
−0.691658 | + | 0.722225i | \(0.743120\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.22253 | 1.34845 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.84981 | + | 3.20397i | 0.448646 | + | 0.777077i | 0.998298 | − | 0.0583162i | \(-0.0185731\pi\) |
−0.549652 | + | 0.835393i | \(0.685240\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.84981 | − | 4.93602i | 0.653792 | − | 1.13240i | −0.328403 | − | 0.944538i | \(-0.606510\pi\) |
0.982195 | − | 0.187864i | \(-0.0601563\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.23236 | + | 3.56046i | 0.487141 | + | 0.776956i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.349814 | − | 0.605896i | 0.0729413 | − | 0.126338i | −0.827248 | − | 0.561837i | \(-0.810095\pi\) |
0.900189 | + | 0.435499i | \(0.143428\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.90545 | − | 5.03238i | −0.581089 | − | 1.00648i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.52290 | −1.06288 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.68725 | 1.42749 | 0.713743 | − | 0.700408i | \(-0.246998\pi\) | ||||
0.713743 | + | 0.700408i | \(0.246998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.25526 | + | 9.10238i | 0.943873 | + | 1.63484i | 0.757993 | + | 0.652263i | \(0.226180\pi\) |
0.185880 | + | 0.982573i | \(0.440487\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.794182 | + | 1.37556i | −0.138249 | + | 0.239455i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.07234 | − | 7.68715i | 0.688351 | − | 1.29937i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.28799 | − | 9.15907i | 0.869341 | − | 1.50574i | 0.00666881 | − | 0.999978i | \(-0.497877\pi\) |
0.862672 | − | 0.505764i | \(-0.168789\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.96108 | + | 6.86079i | 0.634280 | + | 1.09861i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.81089 | 1.21986 | 0.609928 | − | 0.792457i | \(-0.291198\pi\) | ||||
0.609928 | + | 0.792457i | \(0.291198\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.63416 | −0.249208 | −0.124604 | − | 0.992207i | \(-0.539766\pi\) | ||||
−0.124604 | + | 0.992207i | \(0.539766\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.784350 | + | 1.35853i | 0.116924 | + | 0.202518i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.15019 | − | 1.99218i | 0.167772 | − | 0.290589i | −0.769864 | − | 0.638208i | \(-0.779676\pi\) |
0.937636 | + | 0.347618i | \(0.113009\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.98143 | − | 0.509538i | 0.997347 | − | 0.0727912i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.93818 | − | 5.08907i | 0.411427 | − | 0.712613i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.60507 | + | 2.78007i | 0.220474 | + | 0.381872i | 0.954952 | − | 0.296760i | \(-0.0959063\pi\) |
−0.734478 | + | 0.678632i | \(0.762573\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.28799 | 0.443353 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.05308 | −1.19911 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.88255 | + | 6.72477i | 0.505464 | + | 0.875490i | 0.999980 | + | 0.00632132i | \(0.00201215\pi\) |
−0.494516 | + | 0.869169i | \(0.664655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.47710 | + | 4.29046i | −0.317160 | + | 0.549337i | −0.979894 | − | 0.199517i | \(-0.936063\pi\) |
0.662734 | + | 0.748855i | \(0.269396\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.590912 | + | 1.11543i | −0.0744479 | + | 0.140531i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8.19963 | − | 14.2022i | 1.01704 | − | 1.76156i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.810892 | − | 1.40451i | −0.0990663 | − | 0.171588i | 0.812232 | − | 0.583334i | \(-0.198252\pi\) |
−0.911298 | + | 0.411747i | \(0.864919\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.11126 | −0.133780 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.30037 | 0.273004 | 0.136502 | − | 0.990640i | \(-0.456414\pi\) | ||||
0.136502 | + | 0.990640i | \(0.456414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.70582 | − | 4.68661i | −0.316692 | − | 0.548527i | 0.663104 | − | 0.748528i | \(-0.269239\pi\) |
−0.979796 | + | 0.200001i | \(0.935906\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.61491 | + | 7.99325i | −0.532883 | + | 0.922981i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.40545 | + | 2.24159i | 0.160165 | + | 0.255453i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.36652 | + | 2.36689i | −0.153746 | + | 0.266296i | −0.932602 | − | 0.360907i | \(-0.882467\pi\) |
0.778856 | + | 0.627203i | \(0.215800\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.67054 | + | 6.35756i | 0.407838 | + | 0.706395i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.65383 | −0.730352 | −0.365176 | − | 0.930938i | \(-0.618991\pi\) | ||||
−0.365176 | + | 0.930938i | \(0.618991\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.1643 | −1.31941 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.10507 | − | 10.5743i | −0.654533 | − | 1.13368i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.43199 | − | 11.1405i | 0.681789 | − | 1.18089i | −0.292645 | − | 0.956221i | \(-0.594535\pi\) |
0.974434 | − | 0.224673i | \(-0.0721313\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.1872 | − | 0.480595i | 1.38240 | − | 0.0503801i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.34727 | − | 14.4579i | 0.865571 | − | 1.49921i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.37017 | + | 16.2296i | 0.961359 | + | 1.66512i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.6094 | 1.88950 | 0.944749 | − | 0.327794i | \(-0.106305\pi\) | ||||
0.944749 | + | 0.327794i | \(0.106305\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.477100 | −0.0479503 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.27197 | − | 5.66722i | −0.325573 | − | 0.563909i | 0.656055 | − | 0.754713i | \(-0.272224\pi\) |
−0.981628 | + | 0.190804i | \(0.938891\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.01602 | − | 1.75980i | 0.100112 | − | 0.173398i | −0.811619 | − | 0.584187i | \(-0.801413\pi\) |
0.911730 | + | 0.410789i | \(0.134747\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.8083 | + | 0.503230i | −1.34756 | + | 0.0491102i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.74288 | − | 16.8752i | 0.941880 | − | 1.63138i | 0.179999 | − | 0.983667i | \(-0.442391\pi\) |
0.761881 | − | 0.647717i | \(-0.224276\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.53273 | − | 7.85092i | −0.434157 | − | 0.751982i | 0.563069 | − | 0.826410i | \(-0.309620\pi\) |
−0.997226 | + | 0.0744276i | \(0.976287\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.7985 | −1.59444 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.14468 | −0.766187 | −0.383094 | − | 0.923709i | \(-0.625141\pi\) | ||||
−0.383094 | + | 0.923709i | \(0.625141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.15019 | + | 1.99218i | 0.107255 | + | 0.185772i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.18980 | + | 2.06079i | −0.109997 | + | 0.190520i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.19963 | − | 8.29305i | −0.476649 | − | 0.760222i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.20327 | − | 10.7444i | −0.559330 | − | 0.968788i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.66621 | 0.238473 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.98762 | 0.708787 | 0.354393 | − | 0.935096i | \(-0.384687\pi\) | ||||
0.354393 | + | 0.935096i | \(0.384687\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.29782 | + | 2.24790i | 0.114267 | + | 0.197916i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.77816 | − | 4.81191i | 0.242729 | − | 0.420419i | −0.718762 | − | 0.695257i | \(-0.755291\pi\) |
0.961491 | + | 0.274838i | \(0.0886241\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.05927 | + | 13.3254i | −0.612117 | + | 1.15546i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.07963 | − | 15.7264i | 0.781450 | − | 1.35351i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.105074 | + | 0.181994i | 0.00897710 | + | 0.0155488i | 0.870479 | − | 0.492205i | \(-0.163809\pi\) |
−0.861502 | + | 0.507754i | \(0.830476\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0000 | −0.933008 | −0.466504 | − | 0.884519i | \(-0.654487\pi\) | ||||
−0.466504 | + | 0.884519i | \(0.654487\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.65383 | −0.307708 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.49381 | + | 4.31941i | 0.208543 | + | 0.361207i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.6378 | + | 21.8893i | −1.04951 | + | 1.81781i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.24543 | − | 9.19874i | −0.515114 | − | 0.758699i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.18725 | + | 10.7166i | −0.506879 | + | 0.877940i | 0.493089 | + | 0.869979i | \(0.335868\pi\) |
−0.999968 | + | 0.00796165i | \(0.997466\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.67054 | + | 6.35756i | 0.298704 | + | 0.517371i | 0.975840 | − | 0.218487i | \(-0.0701123\pi\) |
−0.677136 | + | 0.735858i | \(0.736779\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.76509 | 0.142699 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −34.5585 | −2.77581 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.68911 | + | 8.12177i | 0.374232 | + | 0.648188i | 0.990212 | − | 0.139574i | \(-0.0445732\pi\) |
−0.615980 | + | 0.787762i | \(0.711240\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.54944 | − | 4.41576i | 0.202184 | − | 0.350193i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.866524 | + | 1.63569i | −0.0682917 | + | 0.128911i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.89926 | + | 13.6819i | −0.618718 | + | 1.07165i | 0.371003 | + | 0.928632i | \(0.379014\pi\) |
−0.989720 | + | 0.143018i | \(0.954319\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.61126 | − | 4.52284i | −0.203287 | − | 0.352103i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.26323 | 0.639428 | 0.319714 | − | 0.947514i | \(-0.396413\pi\) | ||||
0.319714 | + | 0.947514i | \(0.396413\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8764 | 0.913566 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.35965 | − | 2.35498i | −0.103975 | − | 0.180089i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.30470 | − | 9.18801i | 0.403309 | − | 0.698552i | −0.590814 | − | 0.806808i | \(-0.701193\pi\) |
0.994123 | + | 0.108256i | \(0.0345266\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.16690 | + | 13.0256i | 0.617359 | + | 0.984645i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.16690 | − | 10.6814i | 0.463532 | − | 0.802862i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.28180 | + | 9.14835i | 0.394780 | + | 0.683780i | 0.993073 | − | 0.117498i | \(-0.0374873\pi\) |
−0.598293 | + | 0.801278i | \(0.704154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.4079 | −1.51691 | −0.758454 | − | 0.651726i | \(-0.774045\pi\) | ||||
−0.758454 | + | 0.651726i | \(0.774045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.86907 | 0.581699 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.3869 | + | 30.1150i | 1.27831 | + | 2.21410i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.84981 | − | 3.20397i | 0.135272 | − | 0.234298i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.6025 | − | 0.532173i | 1.06218 | − | 0.0387099i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.1996 | − | 19.3983i | 0.810377 | − | 1.40361i | −0.102224 | − | 0.994761i | \(-0.532596\pi\) |
0.912601 | − | 0.408852i | \(-0.134071\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.394926 | + | 0.684031i | 0.0284274 | + | 0.0492377i | 0.879889 | − | 0.475179i | \(-0.157617\pi\) |
−0.851462 | + | 0.524417i | \(0.824283\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −26.0480 | −1.86534 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.3214 | 0.735370 | 0.367685 | − | 0.929950i | \(-0.380150\pi\) | ||||
0.367685 | + | 0.929950i | \(0.380150\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.81020 | + | 11.7956i | 0.482763 | + | 0.836169i | 0.999804 | − | 0.0197910i | \(-0.00630009\pi\) |
−0.517042 | + | 0.855960i | \(0.672967\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.28799 | + | 2.23087i | −0.0908480 | + | 0.157353i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −20.3251 | + | 0.740725i | −1.42654 | + | 0.0519887i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.8411 | + | 22.2414i | −0.896860 | + | 1.55341i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.166896 | − | 0.289073i | −0.0116001 | − | 0.0200919i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.69963 | −0.394252 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.7738 | 1.84318 | 0.921591 | − | 0.388163i | \(-0.126890\pi\) | ||||
0.921591 | + | 0.388163i | \(0.126890\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.82691 | − | 3.16431i | −0.125178 | − | 0.216815i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.68656 | − | 4.65326i | 0.183222 | − | 0.317350i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.7720 | − | 23.5603i | −1.00279 | − | 1.59938i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.29782 | + | 7.44405i | −0.290420 | + | 0.503022i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.22617 | − | 15.9802i | −0.620619 | − | 1.07494i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.60074 | 0.375054 | 0.187527 | − | 0.982259i | \(-0.439953\pi\) | ||||
0.187527 | + | 0.982259i | \(0.439953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.77238 | −0.184825 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.89857 | + | 11.9487i | 0.457874 | + | 0.793061i | 0.998848 | − | 0.0479780i | \(-0.0152777\pi\) |
−0.540974 | + | 0.841039i | \(0.681944\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.48762 | + | 6.04074i | −0.230468 | + | 0.399183i | −0.957946 | − | 0.286948i | \(-0.907359\pi\) |
0.727478 | + | 0.686131i | \(0.240693\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.96727 | − | 3.71351i | 0.129437 | − | 0.244331i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.38874 | + | 5.86946i | −0.222003 | + | 0.384521i | −0.955416 | − | 0.295262i | \(-0.904593\pi\) |
0.733413 | + | 0.679784i | \(0.237926\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.78180 | + | 6.55027i | 0.246698 | + | 0.427293i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.34108 | 0.281983 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.43996 | −0.481251 | −0.240626 | − | 0.970618i | \(-0.577353\pi\) | ||||
−0.240626 | + | 0.970618i | \(0.577353\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.35965 | + | 12.7473i | 0.474076 | + | 0.821125i | 0.999559 | − | 0.0296796i | \(-0.00944869\pi\) |
−0.525483 | + | 0.850804i | \(0.676115\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.45420 | + | 4.25080i | −0.157437 | + | 0.272689i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.0265 | + | 20.7172i | −0.640572 | + | 1.32357i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.2138 | + | 24.6190i | −0.904402 | + | 1.56647i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.28435 | + | 9.15276i | 0.334882 | + | 0.580033i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.0741 | 1.58266 | 0.791332 | − | 0.611386i | \(-0.209388\pi\) | ||||
0.791332 | + | 0.611386i | \(0.209388\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.699628 | −0.0439852 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.66071 | + | 16.7328i | 0.604977 | + | 1.04785i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.65452 | + | 9.79391i | −0.352719 | + | 0.610927i | −0.986725 | − | 0.162401i | \(-0.948076\pi\) |
0.634006 | + | 0.773328i | \(0.281410\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.0989 | + | 24.7261i | −0.813925 | + | 1.53640i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.83379 | − | 3.17622i | 0.113509 | − | 0.196603i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.16071 | − | 3.74245i | −0.133235 | − | 0.230770i | 0.791687 | − | 0.610927i | \(-0.209203\pi\) |
−0.924922 | + | 0.380157i | \(0.875870\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.5549 | −0.648385 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.4327 | −1.25046 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.32072 | − | 4.01961i | −0.141497 | − | 0.245080i | 0.786564 | − | 0.617509i | \(-0.211858\pi\) |
−0.928061 | + | 0.372429i | \(0.878525\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.88688 | + | 10.1964i | −0.357602 | + | 0.619385i | −0.987560 | − | 0.157244i | \(-0.949739\pi\) |
0.629957 | + | 0.776630i | \(0.283072\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.1342 | − | 17.7582i | −0.673870 | − | 1.07478i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.90545 | + | 5.03238i | −0.175205 | + | 0.303464i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.28180 | − | 10.8804i | −0.377437 | − | 0.653740i | 0.613252 | − | 0.789888i | \(-0.289861\pi\) |
−0.990689 | + | 0.136148i | \(0.956528\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.01457 | 0.300214 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.9949 | −1.07349 | −0.536743 | − | 0.843746i | \(-0.680346\pi\) | ||||
−0.536743 | + | 0.843746i | \(0.680346\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.86033 | − | 3.22219i | −0.110585 | − | 0.191540i | 0.805421 | − | 0.592703i | \(-0.201939\pi\) |
−0.916006 | + | 0.401164i | \(0.868606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.8832 | − | 25.7785i | 0.881607 | − | 1.52699i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.6520 | + | 0.752639i | −1.21905 | + | 0.0444269i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.65638 | − | 2.86893i | 0.0974339 | − | 0.168760i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.7793 | − | 25.5984i | −0.866375 | − | 1.50061i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.8654 | 1.51107 | 0.755535 | − | 0.655108i | \(-0.227377\pi\) | ||||
0.755535 | + | 0.655108i | \(0.227377\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −25.5316 | −1.48650 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.76145 | + | 4.78297i | 0.160236 | + | 0.277536i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.74474 | + | 3.02198i | −0.100901 | + | 0.174765i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.32072 | − | 0.157464i | 0.249042 | − | 0.00907608i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.19708 | + | 9.00161i | −0.298564 | + | 0.517129i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.14468 | − | 14.1070i | −0.466363 | − | 0.807765i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.3090 | −0.930806 | −0.465403 | − | 0.885099i | \(-0.654091\pi\) | ||||
−0.465403 | + | 0.885099i | \(0.654091\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.22762 | −0.183613 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.244740 | − | 0.423902i | −0.0138779 | − | 0.0240373i | 0.859003 | − | 0.511970i | \(-0.171084\pi\) |
−0.872881 | + | 0.487933i | \(0.837751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.91528 | + | 11.9776i | −0.390875 | + | 0.677015i | −0.992565 | − | 0.121715i | \(-0.961161\pi\) |
0.601691 | + | 0.798729i | \(0.294494\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.20472 | − | 3.51638i | −0.124222 | − | 0.198126i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.77128 | − | 15.1923i | 0.492644 | − | 0.853285i | −0.507320 | − | 0.861758i | \(-0.669364\pi\) |
0.999964 | + | 0.00847294i | \(0.00269705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.84362 | − | 6.65735i | −0.215202 | − | 0.372740i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.9505 | −1.72749 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.0865 | 1.17328 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.4913 | + | 25.0996i | 0.803831 | + | 1.39228i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.19963 | + | 12.4701i | −0.398140 | + | 0.689599i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.84913 | + | 5.37815i | −0.157077 | + | 0.296507i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.31089 | − | 7.46668i | 0.236948 | − | 0.410406i | −0.722889 | − | 0.690964i | \(-0.757186\pi\) |
0.959837 | + | 0.280558i | \(0.0905195\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.52290 | − | 4.36979i | −0.138254 | − | 0.239463i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.33242 | 0.291341 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.0073 | 1.36223 | 0.681117 | − | 0.732175i | \(-0.261495\pi\) | ||||
0.681117 | + | 0.732175i | \(0.261495\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.46836 | + | 11.2035i | 0.351313 | + | 0.608492i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.25526 | − | 9.10238i | 0.284588 | − | 0.492921i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4098 | + | 2.01993i | −0.994035 | + | 0.109066i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.82691 | − | 3.16431i | 0.0983577 | − | 0.170361i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.1774 | − | 17.6278i | −0.546352 | − | 0.946310i | −0.998520 | − | 0.0543773i | \(-0.982683\pi\) |
0.452168 | − | 0.891933i | \(-0.350651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.7775 | −0.576905 | −0.288452 | − | 0.957494i | \(-0.593141\pi\) | ||||
−0.288452 | + | 0.957494i | \(0.593141\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 27.5461 | 1.47030 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.4691 | − | 19.8650i | −0.610436 | − | 1.05731i | −0.991167 | − | 0.132620i | \(-0.957661\pi\) |
0.380731 | − | 0.924686i | \(-0.375672\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.78180 | + | 6.55027i | −0.200717 | + | 0.347652i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.27816 | + | 13.7386i | −0.385201 | + | 0.727124i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.42766 | − | 16.3292i | 0.497573 | − | 0.861821i | −0.502423 | − | 0.864622i | \(-0.667558\pi\) |
0.999996 | + | 0.00280050i | \(0.000891427\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.74288 | − | 11.6790i | −0.354888 | − | 0.614685i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.58836 | 0.0833675 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.7934 | 0.931350 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.2553 | + | 19.4947i | 0.587520 | + | 1.01761i | 0.994556 | + | 0.104202i | \(0.0332289\pi\) |
−0.407036 | + | 0.913412i | \(0.633438\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.86329 | − | 3.22731i | 0.0969989 | − | 0.168007i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.51169 | − | 7.19583i | −0.234235 | − | 0.373589i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.82141 | + | 11.8150i | −0.353199 | + | 0.611759i | −0.986808 | − | 0.161894i | \(-0.948240\pi\) |
0.633609 | + | 0.773654i | \(0.281573\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.11745 | − | 3.66754i | −0.109345 | − | 0.189391i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −38.3411 | −1.97467 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.69963 | 0.395503 | 0.197752 | − | 0.980252i | \(-0.436636\pi\) | ||||
0.197752 | + | 0.980252i | \(0.436636\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.34362 | − | 10.9875i | −0.324994 | − | 0.562906i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.95853 | − | 10.3205i | 0.304467 | − | 0.527352i | −0.672676 | − | 0.739937i | \(-0.734855\pi\) |
0.977142 | + | 0.212586i | \(0.0681884\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.69344 | + | 0.316823i | −0.443059 | + | 0.0161468i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.389830 | + | 0.675205i | −0.0198162 | + | 0.0343226i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.6545 | + | 25.3824i | 0.743013 | + | 1.28694i | 0.951117 | + | 0.308830i | \(0.0999375\pi\) |
−0.208104 | + | 0.978107i | \(0.566729\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58836 | 0.130899 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.82546 | −0.445186 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.49312 | − | 7.78231i | −0.226073 | − | 0.391571i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.4647 | − | 18.1254i | 0.525209 | − | 0.909689i | −0.474360 | − | 0.880331i | \(-0.657320\pi\) |
0.999569 | − | 0.0293580i | \(-0.00934628\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 23.9363 | − | 0.872333i | 1.19831 | − | 0.0436713i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.8578 | − | 20.5383i | 0.592150 | − | 1.02563i | −0.401793 | − | 0.915731i | \(-0.631613\pi\) |
0.993942 | − | 0.109903i | \(-0.0350539\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.2112 | − | 45.3992i | −1.30567 | − | 2.26150i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −24.1374 | −1.19940 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.5760 | −0.524232 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.9215 | − | 18.9165i | −0.540032 | − | 0.935363i | −0.998902 | − | 0.0468590i | \(-0.985079\pi\) |
0.458870 | − | 0.888504i | \(-0.348254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.166896 | − | 0.289073i | 0.00823238 | − | 0.0142589i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.9134 | − | 17.4061i | −0.537014 | − | 0.856500i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.9389 | − | 18.9467i | 0.536968 | − | 0.930056i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.73600 | + | 15.1312i | 0.427804 | + | 0.740978i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.5970 | 1.00623 | 0.503115 | − | 0.864219i | \(-0.332187\pi\) | ||||
0.503115 | + | 0.864219i | \(0.332187\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.3607 | 1.86959 | 0.934794 | − | 0.355190i | \(-0.115584\pi\) | ||||
0.934794 | + | 0.355190i | \(0.115584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.548754 | − | 0.950469i | −0.0266813 | − | 0.0462134i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.7491 | − | 18.6179i | 0.521407 | − | 0.903103i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.13602 | − | 11.5827i | 0.296943 | − | 0.560524i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.96108 | − | 6.86079i | 0.191243 | − | 0.331242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.8535 | − | 30.9231i | −0.859971 | − | 1.48951i | −0.871956 | − | 0.489585i | \(-0.837148\pi\) |
0.0119850 | − | 0.999928i | \(-0.496185\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.08513 | 0.340489 | 0.170245 | − | 0.985402i | \(-0.445544\pi\) | ||||
0.170245 | + | 0.985402i | \(0.445544\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 40.1469 | 1.92490 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.99381 | − | 3.45338i | −0.0953769 | − | 0.165198i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.63781 | − | 13.2291i | 0.364533 | − | 0.631389i | −0.624168 | − | 0.781290i | \(-0.714562\pi\) |
0.988701 | + | 0.149901i | \(0.0478954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.45489 | − | 3.00614i | 0.0692804 | − | 0.143150i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.9320 | + | 24.1309i | −0.661929 | + | 1.14649i | 0.318180 | + | 0.948030i | \(0.396929\pi\) |
−0.980108 | + | 0.198464i | \(0.936405\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.1483 | + | 36.6300i | 1.00253 | + | 1.73643i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.6552 | 0.929659 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.0879 | −0.476077 | −0.238038 | − | 0.971256i | \(-0.576504\pi\) | ||||
−0.238038 | + | 0.971256i | \(0.576504\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.90545 | − | 6.76443i | −0.183900 | − | 0.318525i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.83015 | − | 10.0981i | 0.273924 | − | 0.474451i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −20.3113 | + | 38.3406i | −0.952208 | + | 1.79743i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.45056 | − | 9.44064i | 0.254966 | − | 0.441615i | −0.709920 | − | 0.704282i | \(-0.751269\pi\) |
0.964886 | + | 0.262668i | \(0.0846023\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.2163 | − | 17.6952i | −0.476858 | − | 0.825942i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.4313 | −1.32418 | −0.662089 | − | 0.749425i | \(-0.730330\pi\) | ||||
−0.662089 | + | 0.749425i | \(0.730330\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.11498 | −0.0982916 | −0.0491458 | − | 0.998792i | \(-0.515650\pi\) | ||||
−0.0491458 | + | 0.998792i | \(0.515650\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 27.4457 | + | 47.5374i | 1.27277 | + | 2.20450i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.1483 | + | 31.4338i | −0.839804 | + | 1.45458i | 0.0502535 | + | 0.998736i | \(0.483997\pi\) |
−0.890058 | + | 0.455847i | \(0.849336\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.27933 | + | 3.63537i | 0.105250 | + | 0.167866i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.44801 | − | 12.9003i | 0.343186 | − | 0.594416i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.817082 | + | 1.41523i | 0.0375695 | + | 0.0650722i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.1199 | −1.51965 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.53156 | 0.0701254 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.49745 | − | 12.9860i | −0.342567 | − | 0.593344i | 0.642341 | − | 0.766419i | \(-0.277963\pi\) |
−0.984909 | + | 0.173075i | \(0.944630\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.3745 | + | 45.6820i | −1.20257 | + | 2.08292i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.93818 | − | 0.107079i | 0.133692 | − | 0.00487225i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30.5938 | + | 52.9900i | −1.38919 | + | 2.40615i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.77128 | + | 6.53205i | 0.170893 | + | 0.295996i | 0.938732 | − | 0.344647i | \(-0.112001\pi\) |
−0.767839 | + | 0.640643i | \(0.778668\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.0938 | 1.13478 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.5302 | 0.836255 | 0.418128 | − | 0.908388i | \(-0.362686\pi\) | ||||
0.418128 | + | 0.908388i | \(0.362686\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.2200 | + | 24.6297i | 0.640436 | + | 1.10927i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.784350 | − | 1.35853i | 0.0352539 | − | 0.0610616i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.08217 | + | 0.221658i | −0.272823 | + | 0.00994273i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.99931 | − | 8.65906i | 0.223800 | − | 0.387633i | −0.732159 | − | 0.681134i | \(-0.761487\pi\) |
0.955959 | + | 0.293501i | \(0.0948205\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.56251 | − | 11.3666i | −0.293191 | − | 0.507822i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.34479 | −0.193725 | −0.0968624 | − | 0.995298i | \(-0.530881\pi\) | ||||
−0.0968624 | + | 0.995298i | \(0.530881\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.5164 | 0.957468 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.43199 | − | 16.3367i | −0.418889 | − | 0.725538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.0036 | − | 32.9153i | 0.842322 | − | 1.45894i | −0.0456054 | − | 0.998960i | \(-0.514522\pi\) |
0.887927 | − | 0.459984i | \(-0.152145\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.60576 | + | 12.1307i | 0.336459 | + | 0.536629i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.7392 | + | 27.2612i | −0.694904 | + | 1.20361i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.34067 | + | 5.78621i | 0.147208 | + | 0.254971i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.30037 | −0.101170 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.8516 | −0.739703 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.40290 | + | 9.35809i | 0.236705 | + | 0.409986i | 0.959767 | − | 0.280798i | \(-0.0905991\pi\) |
−0.723062 | + | 0.690784i | \(0.757266\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.4134 | − | 18.0366i | 0.455347 | − | 0.788684i | −0.543361 | − | 0.839499i | \(-0.682849\pi\) |
0.998708 | + | 0.0508150i | \(0.0161819\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.4316 | − | 21.5788i | 0.498915 | − | 0.941776i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.4425 | + | 33.6754i | −0.846929 | + | 1.46692i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2553 | + | 19.4947i | 0.489359 | + | 0.847595i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.70472 | 0.160771 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.9578 | −1.68745 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.0345 | + | 55.4854i | 1.38497 | + | 2.39884i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.38942 | − | 14.5309i | 0.362030 | − | 0.627055i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.93199 | − | 5.79133i | −0.169363 | − | 0.249450i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.55563 | − | 4.42648i | 0.109875 | − | 0.190309i | −0.805844 | − | 0.592127i | \(-0.798288\pi\) |
0.915720 | + | 0.401818i | \(0.131622\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.2076 | + | 28.0724i | 0.695535 | + | 1.20470i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.8072 | 1.27680 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.04580 | −0.0874721 | −0.0437361 | − | 0.999043i | \(-0.513926\pi\) | ||||
−0.0437361 | + | 0.999043i | \(0.513926\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.18182 | + | 2.04698i | 0.0504390 | + | 0.0873629i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.9072 | − | 37.9444i | 0.933279 | − | 1.61649i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.38502 | − | 6.38972i | 0.143946 | − | 0.271719i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.6167 | − | 47.8335i | 1.17226 | − | 2.03042i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.6316 | − | 30.5389i | −0.747076 | − | 1.29397i | −0.949219 | − | 0.314617i | \(-0.898124\pi\) |
0.202143 | − | 0.979356i | \(-0.435209\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.15059 | 0.344733 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.87636 | −0.248100 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.77630 | − | 13.4689i | −0.327732 | − | 0.567649i | 0.654329 | − | 0.756210i | \(-0.272951\pi\) |
−0.982061 | + | 0.188561i | \(0.939618\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.3898 | − | 23.1919i | 0.563314 | − | 0.975689i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.3175 | − | 16.4557i | −0.433294 | − | 0.691073i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.14833 | − | 5.45306i | 0.131985 | − | 0.228604i | −0.792457 | − | 0.609928i | \(-0.791198\pi\) |
0.924442 | + | 0.381324i | \(0.124532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.47160 | + | 6.01299i | 0.145282 | + | 0.251636i | 0.929478 | − | 0.368877i | \(-0.120258\pi\) |
−0.784196 | + | 0.620513i | \(0.786924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.5782 | −1.48630 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.06546 | −0.169542 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.09201 | + | 1.89141i | 0.0454608 | + | 0.0787404i | 0.887860 | − | 0.460113i | \(-0.152191\pi\) |
−0.842400 | + | 0.538853i | \(0.818858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.627286 | − | 1.08649i | 0.0260691 | − | 0.0451530i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.5927 | − | 0.641147i | 0.729868 | − | 0.0265993i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.60507 | − | 2.78007i | 0.0664754 | − | 0.115139i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.91204 | − | 6.77585i | −0.161743 | − | 0.280147i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.4574 | 1.00947 | 0.504733 | − | 0.863275i | \(-0.331591\pi\) | ||||
0.504733 | + | 0.863275i | \(0.331591\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 59.9061 | 2.46839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.19708 | − | 14.1978i | −0.337183 | − | 0.584018i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.2095 | + | 22.8795i | −0.542448 | + | 0.939547i | 0.456315 | + | 0.889818i | \(0.349169\pi\) |
−0.998763 | + | 0.0497285i | \(0.984164\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 32.1625 | − | 1.17213i | 1.31853 | − | 0.0480525i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.8171 | − | 18.7357i | 0.442714 | − | 0.766803i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0679 | + | 41.6869i | 0.983389 | + | 1.70328i | 0.648887 | + | 0.760885i | \(0.275235\pi\) |
0.334503 | + | 0.942395i | \(0.391432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.00138 | −0.204010 | −0.102005 | − | 0.994784i | \(-0.532526\pi\) | ||||
−0.102005 | + | 0.994784i | \(0.532526\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.773753 | −0.0315097 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.64400 | − | 2.84748i | −0.0668379 | − | 0.115767i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.839982 | − | 1.45489i | 0.0340938 | − | 0.0590522i | −0.848475 | − | 0.529235i | \(-0.822479\pi\) |
0.882569 | + | 0.470183i | \(0.155812\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.1607 | + | 27.3701i | 0.695387 | + | 1.10909i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.73669 | + | 9.93624i | −0.232082 | + | 0.401977i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.52290 | + | 16.4941i | 0.384626 | + | 0.666192i | 0.991717 | − | 0.128440i | \(-0.0409970\pi\) |
−0.607091 | + | 0.794632i | \(0.707664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 40.7926 | 1.64492 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.3955 | 1.30420 | 0.652098 | − | 0.758135i | \(-0.273889\pi\) | ||||
0.652098 | + | 0.758135i | \(0.273889\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.98762 | + | 8.63881i | 0.200469 | + | 0.347223i | 0.948680 | − | 0.316238i | \(-0.102420\pi\) |
−0.748210 | + | 0.663462i | \(0.769087\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.93199 | + | 3.34630i | −0.0775280 | + | 0.134282i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.9327 | + | 30.0753i | −0.638329 | + | 1.20494i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.1440 | − | 17.5699i | 0.405760 | − | 0.702797i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.52654 | + | 7.84020i | 0.180773 | + | 0.313107i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.1272 | 1.56010 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.4290 | −1.17155 | −0.585774 | − | 0.810474i | \(-0.699209\pi\) | ||||
−0.585774 | + | 0.810474i | \(0.699209\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.2632 | − | 36.8290i | −0.845138 | − | 1.46382i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.1316 | + | 22.7446i | −0.521112 | + | 0.902593i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.8207 | + | 2.54138i | −1.37965 | + | 0.100693i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.548754 | − | 0.950469i | 0.0217084 | − | 0.0376000i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.0116910 | − | 0.0202494i | −0.000461767 | − | 0.000799804i | 0.865794 | − | 0.500400i | \(-0.166814\pi\) |
−0.866256 | + | 0.499600i | \(0.833480\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.9963 | 0.433651 | 0.216826 | − | 0.976210i | \(-0.430430\pi\) | ||||
0.216826 | + | 0.976210i | \(0.430430\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.53447 | −0.336044 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.20877 | − | 14.2180i | −0.322720 | − | 0.558968i | 0.658328 | − | 0.752731i | \(-0.271264\pi\) |
−0.981048 | + | 0.193763i | \(0.937931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.88255 | − | 6.72477i | 0.152403 | − | 0.263970i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.6770 | + | 39.0309i | −0.810396 | + | 1.52974i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.90545 | + | 11.9606i | −0.270231 | + | 0.468054i | −0.968921 | − | 0.247371i | \(-0.920433\pi\) |
0.698690 | + | 0.715425i | \(0.253767\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.13457 | + | 15.8215i | 0.356917 | + | 0.618199i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.58189 | −0.100729 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.0283 | 0.741238 | 0.370619 | − | 0.928785i | \(-0.379146\pi\) | ||||
0.370619 | + | 0.928785i | \(0.379146\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.14214 | − | 5.44234i | −0.122215 | − | 0.211683i | 0.798426 | − | 0.602093i | \(-0.205666\pi\) |
−0.920641 | + | 0.390411i | \(0.872333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.6545 | + | 25.3824i | −0.569134 | + | 0.985769i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −26.3385 | − | 42.0081i | −1.02136 | − | 1.62901i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.68911 | − | 4.65767i | 0.104123 | − | 0.180346i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.44801 | − | 7.70418i | −0.171970 | − | 0.297861i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.95420 | 0.191255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.3497 | 1.43973 | 0.719863 | − | 0.694116i | \(-0.244204\pi\) | ||||
0.719863 | + | 0.694116i | \(0.244204\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.0465 | + | 27.7933i | 0.617630 | + | 1.06977i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.1451 | − | 38.3564i | 0.851105 | − | 1.47416i | −0.0291070 | − | 0.999576i | \(-0.509266\pi\) |
0.880212 | − | 0.474581i | \(-0.157400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49.2032 | + | 1.79316i | −1.88825 | + | 0.0688151i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.9574 | − | 18.9788i | 0.419890 | − | 0.727271i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.59269 | + | 4.49068i | 0.0992067 | + | 0.171831i | 0.911357 | − | 0.411618i | \(-0.135036\pi\) |
−0.812150 | + | 0.583449i | \(0.801703\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.690967 | −0.0264005 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.0792 | 0.422699 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.00550 | − | 13.8659i | −0.304985 | − | 0.528250i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.02104 | + | 1.76849i | −0.0388422 | + | 0.0672767i | −0.884793 | − | 0.465984i | \(-0.845700\pi\) |
0.845951 | + | 0.533261i | \(0.179034\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.26145 | − | 0.0459722i | 0.0479185 | − | 0.00174634i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.0840 | − | 31.3223i | 0.685964 | − | 1.18812i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.4487 | + | 25.0259i | 0.547283 | + | 0.947923i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.7651 | 0.407173 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.6291 | −1.68562 | −0.842808 | − | 0.538214i | \(-0.819099\pi\) | ||||
−0.842808 | + | 0.538214i | \(0.819099\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.1396 | − | 52.2033i | −1.13674 | − | 1.96888i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.00688 | − | 10.4042i | 0.226232 | − | 0.391846i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.19716 | + | 14.6688i | 0.345895 | + | 0.551678i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.9301 | + | 34.5200i | −0.748492 | + | 1.29643i | 0.200054 | + | 0.979785i | \(0.435888\pi\) |
−0.948546 | + | 0.316641i | \(0.897445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.651969 | + | 1.12924i | 0.0244507 | + | 0.0423499i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.35346 | 0.275389 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.3993 | −0.613297 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.90868 | + | 10.2341i | 0.220664 | + | 0.382201i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.99745 | − | 15.5840i | 0.335548 | − | 0.581187i | −0.648042 | − | 0.761605i | \(-0.724412\pi\) |
0.983590 | + | 0.180418i | \(0.0577451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.51679 | + | 4.75081i | −0.0937300 | + | 0.176929i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6898 | − | 20.2473i | 0.434748 | − | 0.753006i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.3349 | − | 38.6852i | −0.829497 | − | 1.43673i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9491 | −0.517344 | −0.258672 | − | 0.965965i | \(-0.583285\pi\) | ||||
−0.258672 | + | 0.965965i | \(0.583285\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8196 | 1.10443 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.02290 | − | 5.23582i | −0.111806 | − | 0.193654i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.88323 | + | 17.1183i | −0.365046 | + | 0.632278i | −0.988783 | − | 0.149356i | \(-0.952280\pi\) |
0.623738 | + | 0.781634i | \(0.285613\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 36.4607 | − | 2.66108i | 1.34487 | − | 0.0981553i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.810892 | + | 1.40451i | −0.0298696 | + | 0.0517357i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.458530 | − | 0.794198i | −0.0168673 | − | 0.0292150i | 0.857469 | − | 0.514536i | \(-0.172036\pi\) |
−0.874336 | + | 0.485321i | \(0.838703\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.1533 | 1.65875 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.22391 | −0.228333 | −0.114166 | − | 0.993462i | \(-0.536420\pi\) | ||||
−0.114166 | + | 0.993462i | \(0.536420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.3436 | − | 35.2362i | −0.745333 | − | 1.29095i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.58727 | + | 2.74923i | −0.0580752 | + | 0.100589i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −24.1341 | + | 45.5567i | −0.881840 | + | 1.66460i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5400 | + | 39.0405i | −0.822497 | + | 1.42461i | 0.0813205 | + | 0.996688i | \(0.474086\pi\) |
−0.903817 | + | 0.427918i | \(0.859247\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.9134 | − | 34.4911i | −0.725685 | − | 1.25692i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.1374 | −0.878450 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.46844 | 0.126063 | 0.0630313 | − | 0.998012i | \(-0.479923\pi\) | ||||
0.0630313 | + | 0.998012i | \(0.479923\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.555632 | + | 0.962383i | 0.0201682 | + | 0.0349323i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.0371 | − | 19.1168i | 0.400093 | − | 0.692982i | −0.593644 | − | 0.804728i | \(-0.702311\pi\) |
0.993737 | + | 0.111746i | \(0.0356444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.7410 | + | 20.3210i | 0.461256 | + | 0.735671i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.90180 | + | 5.02607i | −0.104915 | + | 0.181718i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.3647 | − | 33.5406i | −0.699218 | − | 1.21108i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −47.9468 | −1.72900 | −0.864502 | − | 0.502629i | \(-0.832366\pi\) | ||||
−0.864502 | + | 0.502629i | \(0.832366\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.9629 | 0.646917 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.0796 | + | 41.7071i | 0.866084 | + | 1.50010i | 0.865967 | + | 0.500101i | \(0.166704\pi\) |
0.000117116 | 1.00000i | \(0.499963\pi\) | ||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.5378 | − | 52.8929i | 1.09695 | − | 1.89997i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 44.4152 | − | 1.61866i | 1.59339 | − | 0.0580693i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.2596 | − | 38.5547i | 0.797533 | − | 1.38137i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.15019 | − | 1.99218i | −0.0411569 | − | 0.0712858i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −42.4559 | −1.51725 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.8355 | −1.10057 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.4814 | − | 21.6185i | −0.444915 | − | 0.770615i | 0.553131 | − | 0.833094i | \(-0.313433\pi\) |
−0.998046 | + | 0.0624788i | \(0.980099\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.43199 | + | 5.94438i | −0.122182 | + | 0.211625i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.5345 | − | 0.784802i | 0.765679 | − | 0.0279044i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.3548 | − | 21.3992i | 0.438733 | − | 0.759908i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.38255 | + | 14.5190i | 0.297298 | + | 0.514936i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.02832 | 0.0364251 | 0.0182126 | − | 0.999834i | \(-0.494202\pi\) | ||||
0.0182126 | + | 0.999834i | \(0.494202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.51052 | 0.301081 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.06870 | − | 5.31515i | −0.108427 | − | 0.187801i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.70582 | + | 4.68661i | −0.0954862 | + | 0.165387i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.23305 | − | 5.15649i | −0.113950 | − | 0.181742i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.68615 | + | 6.38461i | −0.129759 | + | 0.224749i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.3516 | + | 26.5897i | 0.539733 | + | 0.934846i | 0.998918 | + | 0.0465048i | \(0.0148083\pi\) |
−0.459185 | + | 0.888341i | \(0.651858\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.8887 | −1.18999 | −0.594997 | − | 0.803728i | \(-0.702847\pi\) | ||||
−0.594997 | + | 0.803728i | \(0.702847\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.7010 | 0.655873 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.9727 | − | 44.9860i | −0.909784 | − | 1.57579i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.65706 | + | 8.06627i | −0.162930 | + | 0.282203i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.94724 | − | 5.56336i | 0.102985 | − | 0.194400i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.4759 | − | 25.0730i | 0.505213 | − | 0.875055i | −0.494768 | − | 0.869025i | \(-0.664747\pi\) |
0.999982 | − | 0.00603043i | \(-0.00191956\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.41961 | − | 16.3152i | −0.328347 | − | 0.568714i | 0.653837 | − | 0.756635i | \(-0.273158\pi\) |
−0.982184 | + | 0.187922i | \(0.939825\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.22981 | 0.321341 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.7366 | 1.52087 | 0.760436 | − | 0.649413i | \(-0.224986\pi\) | ||||
0.760436 | + | 0.649413i | \(0.224986\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8898 | − | 37.9143i | −0.760265 | − | 1.31682i | −0.942714 | − | 0.333603i | \(-0.891736\pi\) |
0.182449 | − | 0.983215i | \(-0.441598\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.97779 | + | 17.2820i | −0.346126 | + | 0.599507i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.5469 | + | 21.4258i | 0.504020 | + | 0.742358i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.5847 | + | 23.5294i | −0.470119 | + | 0.814269i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.0243 | − | 50.2715i | −1.00323 | − | 1.73764i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.9766 | −0.931336 | −0.465668 | − | 0.884959i | \(-0.654186\pi\) | ||||
−0.465668 | + | 0.884959i | \(0.654186\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 30.0938 | 1.03772 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.2912 | + | 24.7531i | 0.492216 | + | 0.852543i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.5247 | + | 33.8177i | −0.671670 | + | 1.16337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.23855 | − | 2.33795i | 0.0425571 | − | 0.0803328i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.95489 | + | 5.11802i | −0.101412 | + | 0.175650i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.69963 | − | 6.40794i | −0.126822 | − | 0.219661i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.5082 | −1.21578 | −0.607888 | − | 0.794022i | \(-0.707983\pi\) | ||||
−0.607888 | + | 0.794022i | \(0.707983\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.94101 | 0.305776 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.2509 | + | 28.1474i | 0.555121 | + | 0.961498i | 0.997894 | + | 0.0648643i | \(0.0206615\pi\) |
−0.442773 | + | 0.896634i | \(0.646005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.75704 | + | 3.04329i | −0.0599495 | + | 0.103836i | −0.894443 | − | 0.447183i | \(-0.852427\pi\) |
0.834493 | + | 0.551019i | \(0.185761\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.4367 | + | 27.8104i | 0.594242 | + | 0.947775i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.4549 | − | 31.9648i | 0.628212 | − | 1.08809i | −0.359699 | − | 0.933069i | \(-0.617121\pi\) |
0.987910 | − | 0.155026i | \(-0.0495462\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.4418 | + | 30.2101i | 0.593040 | + | 1.02717i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.26186 | −0.178702 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.73305 | 0.0927123 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.04442 | + | 7.00515i | 0.137040 | + | 0.237360i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.43927 | − | 7.68904i | 0.150247 | − | 0.260235i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.04944 | + | 0.256909i | −0.238315 | + | 0.00868512i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.4672 | − | 37.1823i | 0.724896 | − | 1.25556i | −0.234121 | − | 0.972207i | \(-0.575221\pi\) |
0.959017 | − | 0.283349i | \(-0.0914453\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.5418 | − | 35.5794i | −0.692858 | − | 1.20006i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.2980 | −1.15553 | −0.577765 | − | 0.816203i | \(-0.696075\pi\) | ||||
−0.577765 | + | 0.816203i | \(0.696075\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.436395 | −0.0146859 | −0.00734294 | − | 0.999973i | \(-0.502337\pi\) | ||||
−0.00734294 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.2767 | + | 35.1203i | 0.681594 | + | 1.18056i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.4789 | − | 38.9346i | 0.754767 | − | 1.30729i | −0.190723 | − | 0.981644i | \(-0.561083\pi\) |
0.945490 | − | 0.325651i | \(-0.105583\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.1192 | + | 0.769668i | −0.708316 | + | 0.0258138i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.67054 | − | 6.35756i | 0.122968 | − | 0.212986i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.55563 | − | 11.3547i | −0.219376 | − | 0.379970i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.7330 | −1.16100 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.54256 | 0.185061 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.3985 | + | 69.9722i | 1.34737 | + | 2.33370i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.93818 | + | 10.2852i | −0.197829 | + | 0.342651i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.64804 | − | 5.81838i | −0.121399 | − | 0.193623i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33.5505 | − | 58.1112i | 1.11526 | − | 1.93168i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.9079 | + | 37.9456i | 0.727440 | + | 1.25996i | 0.957962 | + | 0.286897i | \(0.0926236\pi\) |
−0.230521 | + | 0.973067i | \(0.574043\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.12211 | −0.103554 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.7046 | 1.34860 | 0.674301 | − | 0.738456i | \(-0.264445\pi\) | ||||
0.674301 | + | 0.738456i | \(0.264445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.32691 | + | 5.76238i | 0.110105 | + | 0.190707i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.9367 | + | 22.4071i | −0.427675 | + | 0.740755i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.88178 | + | 12.9904i | −0.227256 | + | 0.428980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.66435 | − | 4.61479i | 0.0878887 | − | 0.152228i | −0.818730 | − | 0.574179i | \(-0.805321\pi\) |
0.906619 | + | 0.421951i | \(0.138655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.9523 | + | 22.4341i | 0.426794 | + | 0.739229i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.4734 | −0.377651 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −61.4559 | −2.02066 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.484744 | − | 0.839601i | −0.0159211 | − | 0.0275761i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.25340 | − | 10.8312i | 0.205167 | − | 0.355360i | −0.745019 | − | 0.667044i | \(-0.767559\pi\) |
0.950186 | + | 0.311683i | \(0.100893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.3807 | − | 35.9126i | 0.569629 | − | 1.17699i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.388736 | + | 0.673310i | −0.0127266 | + | 0.0220432i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.08217 | + | 10.5346i | 0.198908 | + | 0.344519i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.4152 | 1.35298 | 0.676488 | − | 0.736454i | \(-0.263501\pi\) | ||||
0.676488 | + | 0.736454i | \(0.263501\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.9680 | 0.716897 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.82437 | − | 13.5522i | −0.255067 | − | 0.441789i | 0.709847 | − | 0.704356i | \(-0.248764\pi\) |
−0.964914 | + | 0.262567i | \(0.915431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.73236 | − | 4.73259i | 0.0889779 | − | 0.154114i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.4911 | + | 42.4554i | −0.731637 | + | 1.38107i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.91095 | + | 10.2381i | −0.192080 | + | 0.332692i | −0.945939 | − | 0.324343i | \(-0.894857\pi\) |
0.753859 | + | 0.657036i | \(0.228190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.4956 | + | 23.3751i | 0.438085 | + | 0.758786i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.8640 | −0.903551 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.8946 | −0.871203 | −0.435601 | − | 0.900140i | \(-0.643464\pi\) | ||||
−0.435601 | + | 0.900140i | \(0.643464\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.8243 | + | 63.7815i | 1.19161 | + | 2.06392i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.10507 | + | 10.5743i | −0.197349 | + | 0.341819i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.295353 | − | 0.471067i | −0.00953743 | − | 0.0152115i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39.7355 | + | 68.8239i | −1.28179 | + | 2.22013i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.64833 | − | 8.05114i | −0.149790 | − | 0.259444i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.59703 | −0.0836012 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.21015 | 0.135389 | 0.0676946 | − | 0.997706i | \(-0.478436\pi\) | ||||
0.0676946 | + | 0.997706i | \(0.478436\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.7465 | − | 29.0058i | −0.537976 | − | 0.931801i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.5883 | − | 44.3202i | 0.821167 | − | 1.42230i | −0.0836464 | − | 0.996495i | \(-0.526657\pi\) |
0.904814 | − | 0.425808i | \(-0.140010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.0840 | − | 1.05993i | 0.932389 | − | 0.0339799i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.0174 | − | 39.8673i | 0.737147 | − | 1.27678i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.0778 | + | 39.9719i | 0.738323 | + | 1.27881i | 0.953250 | + | 0.302183i | \(0.0977154\pi\) |
−0.214927 | + | 0.976630i | \(0.568951\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.8640 | −0.411134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.32513 | −0.138091 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.1792 | − | 43.6117i | −0.803092 | − | 1.39100i | −0.917572 | − | 0.397570i | \(-0.869854\pi\) |
0.114480 | − | 0.993426i | \(-0.463480\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.9684 | + | 29.3901i | −0.540657 | + | 0.936445i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.66071 | − | 0.352074i | 0.307504 | − | 0.0112066i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.571654 | + | 0.990133i | −0.0181775 | + | 0.0314844i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.8003 | − | 39.4913i | −0.724275 | − | 1.25448i | −0.959272 | − | 0.282485i | \(-0.908841\pi\) |
0.234996 | − | 0.971996i | \(-0.424492\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.6945 | −0.434583 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −44.7838 | −1.41974 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.1811 | + | 33.2226i | 0.607470 | + | 1.05217i | 0.991656 | + | 0.128913i | \(0.0411489\pi\) |
−0.384186 | + | 0.923256i | \(0.625518\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −29.2051 | + | 50.5846i | −0.924007 | + | 1.60043i |
(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 | 1232.2.q.l.177.1 | 6 | ||
4.3 | odd | 2 | 308.2.i.a.177.3 | ✓ | 6 | ||
7.2 | even | 3 | 8624.2.a.ci.1.3 | 3 | |||
7.4 | even | 3 | inner | 1232.2.q.l.529.1 | 6 | ||
7.5 | odd | 6 | 8624.2.a.cn.1.1 | 3 | |||
12.11 | even | 2 | 2772.2.s.f.793.3 | 6 | |||
28.3 | even | 6 | 2156.2.i.l.1145.1 | 6 | |||
28.11 | odd | 6 | 308.2.i.a.221.3 | yes | 6 | ||
28.19 | even | 6 | 2156.2.a.h.1.3 | 3 | |||
28.23 | odd | 6 | 2156.2.a.i.1.1 | 3 | |||
28.27 | even | 2 | 2156.2.i.l.177.1 | 6 | |||
84.11 | even | 6 | 2772.2.s.f.2377.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
308.2.i.a.177.3 | ✓ | 6 | 4.3 | odd | 2 | ||
308.2.i.a.221.3 | yes | 6 | 28.11 | odd | 6 | ||
1232.2.q.l.177.1 | 6 | 1.1 | even | 1 | trivial | ||
1232.2.q.l.529.1 | 6 | 7.4 | even | 3 | inner | ||
2156.2.a.h.1.3 | 3 | 28.19 | even | 6 | |||
2156.2.a.i.1.1 | 3 | 28.23 | odd | 6 | |||
2156.2.i.l.177.1 | 6 | 28.27 | even | 2 | |||
2156.2.i.l.1145.1 | 6 | 28.3 | even | 6 | |||
2772.2.s.f.793.3 | 6 | 12.11 | even | 2 | |||
2772.2.s.f.2377.3 | 6 | 84.11 | even | 6 | |||
8624.2.a.ci.1.3 | 3 | 7.2 | even | 3 | |||
8624.2.a.cn.1.1 | 3 | 7.5 | odd | 6 |