Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(227,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("931.227");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.43407242818\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 607.14 | ||
Character | \(\chi\) | \(=\) | 931.607 |
Dual form | 931.2.o.i.227.14 |
$q$-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 \(\left(\mathbb{Z}/931\mathbb{Z}\right)^\times\).
\(n\) | \(248\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.774359 | − | 0.447076i | −0.547554 | − | 0.316131i | 0.200581 | − | 0.979677i | \(-0.435717\pi\) |
−0.748135 | + | 0.663547i | \(0.769050\pi\) | |||||||
\(3\) | 0.525649 | + | 0.910452i | 0.303484 | + | 0.525649i | 0.976923 | − | 0.213594i | \(-0.0685168\pi\) |
−0.673439 | + | 0.739243i | \(0.735183\pi\) | |||||||
\(4\) | −0.600246 | − | 1.03966i | −0.300123 | − | 0.519828i | ||||
\(5\) | 0.249238 | + | 0.143898i | 0.111463 | + | 0.0643531i | 0.554695 | − | 0.832054i | \(-0.312835\pi\) |
−0.443232 | + | 0.896407i | \(0.646168\pi\) | |||||||
\(6\) | − | 0.940021i | − | 0.383762i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.86173i | 1.01177i | ||||||||
\(9\) | 0.947385 | − | 1.64092i | 0.315795 | − | 0.546973i | ||||
\(10\) | −0.128667 | − | 0.222857i | −0.0406880 | − | 0.0704736i | ||||
\(11\) | 0.238323 | + | 0.412787i | 0.0718570 | + | 0.124460i | 0.899715 | − | 0.436477i | \(-0.143774\pi\) |
−0.827858 | + | 0.560937i | \(0.810441\pi\) | |||||||
\(12\) | 0.631038 | − | 1.09299i | 0.182165 | − | 0.315519i | ||||
\(13\) | −6.36831 | −1.76625 | −0.883126 | − | 0.469135i | \(-0.844566\pi\) | ||||
−0.883126 | + | 0.469135i | \(0.844566\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.302559i | 0.0781205i | ||||||||
\(16\) | 0.0789186 | − | 0.136691i | 0.0197297 | − | 0.0341728i | ||||
\(17\) | −5.00633 | + | 2.89040i | −1.21421 | + | 0.701026i | −0.963674 | − | 0.267081i | \(-0.913941\pi\) |
−0.250538 | + | 0.968107i | \(0.580608\pi\) | |||||||
\(18\) | −1.46723 | + | 0.847107i | −0.345830 | + | 0.199665i | ||||
\(19\) | −1.73661 | − | 3.99802i | −0.398405 | − | 0.917210i | ||||
\(20\) | − | 0.345496i | − | 0.0772553i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.426194i | − | 0.0908648i | ||||||
\(23\) | 3.26497 | − | 5.65510i | 0.680794 | − | 1.17917i | −0.293945 | − | 0.955822i | \(-0.594968\pi\) |
0.974739 | − | 0.223347i | \(-0.0716984\pi\) | |||||||
\(24\) | −2.60546 | + | 1.50427i | −0.531838 | + | 0.307057i | ||||
\(25\) | −2.45859 | − | 4.25840i | −0.491717 | − | 0.851679i | ||||
\(26\) | 4.93136 | + | 2.84712i | 0.967119 | + | 0.558367i | ||||
\(27\) | 5.14587 | 0.990323 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.71402i | 1.06107i | 0.847664 | + | 0.530534i | \(0.178008\pi\) | ||||
−0.847664 | + | 0.530534i | \(0.821992\pi\) | |||||||
\(30\) | 0.135267 | − | 0.234290i | 0.0246963 | − | 0.0427752i | ||||
\(31\) | 2.16608 | + | 3.75176i | 0.389039 | + | 0.673835i | 0.992321 | − | 0.123693i | \(-0.0394738\pi\) |
−0.603282 | + | 0.797528i | \(0.706141\pi\) | |||||||
\(32\) | 4.83443 | − | 2.79116i | 0.854615 | − | 0.493412i | ||||
\(33\) | −0.250549 | + | 0.433963i | −0.0436149 | + | 0.0755432i | ||||
\(34\) | 5.16892 | 0.886463 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.27466 | −0.379109 | ||||||||
\(37\) | −1.21914 | − | 0.703868i | −0.200425 | − | 0.115715i | 0.396429 | − | 0.918065i | \(-0.370249\pi\) |
−0.596854 | + | 0.802350i | \(0.703583\pi\) | |||||||
\(38\) | −0.442664 | + | 3.87230i | −0.0718095 | + | 0.628170i | ||||
\(39\) | −3.34750 | − | 5.79804i | −0.536029 | − | 0.928430i | ||||
\(40\) | −0.411797 | + | 0.713253i | −0.0651108 | + | 0.112775i | ||||
\(41\) | −7.44541 | −1.16278 | −0.581389 | − | 0.813626i | \(-0.697490\pi\) | ||||
−0.581389 | + | 0.813626i | \(0.697490\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.20284 | −1.09842 | −0.549212 | − | 0.835683i | \(-0.685072\pi\) | ||||
−0.549212 | + | 0.835683i | \(0.685072\pi\) | |||||||
\(44\) | 0.286105 | − | 0.495548i | 0.0431319 | − | 0.0747066i | ||||
\(45\) | 0.472250 | − | 0.272654i | 0.0703988 | − | 0.0406448i | ||||
\(46\) | −5.05652 | + | 2.91938i | −0.745543 | + | 0.430440i | ||||
\(47\) | −3.58484 | − | 2.06971i | −0.522903 | − | 0.301898i | 0.215218 | − | 0.976566i | \(-0.430954\pi\) |
−0.738122 | + | 0.674668i | \(0.764287\pi\) | |||||||
\(48\) | 0.165934 | 0.0239505 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.39670i | 0.621788i | ||||||||
\(51\) | −5.26314 | − | 3.03868i | −0.736988 | − | 0.425500i | ||||
\(52\) | 3.82255 | + | 6.62086i | 0.530093 | + | 0.918148i | ||||
\(53\) | −7.21467 | + | 4.16539i | −0.991011 | + | 0.572161i | −0.905576 | − | 0.424183i | \(-0.860561\pi\) |
−0.0854348 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(54\) | −3.98475 | − | 2.30059i | −0.542255 | − | 0.313071i | ||||
\(55\) | 0.137177i | 0.0184969i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.72716 | − | 3.68266i | 0.361221 | − | 0.487780i | ||||
\(58\) | 2.55460 | − | 4.42470i | 0.335436 | − | 0.580992i | ||||
\(59\) | −0.962041 | − | 1.66630i | −0.125247 | − | 0.216934i | 0.796582 | − | 0.604530i | \(-0.206639\pi\) |
−0.921830 | + | 0.387596i | \(0.873306\pi\) | |||||||
\(60\) | 0.314558 | − | 0.181610i | 0.0406092 | − | 0.0234458i | ||||
\(61\) | −2.27164 | − | 1.31153i | −0.290853 | − | 0.167924i | 0.347473 | − | 0.937690i | \(-0.387040\pi\) |
−0.638327 | + | 0.769766i | \(0.720373\pi\) | |||||||
\(62\) | − | 3.87361i | − | 0.491948i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.30712 | −0.663390 | ||||||||
\(65\) | −1.58723 | − | 0.916387i | −0.196872 | − | 0.113664i | ||||
\(66\) | 0.388029 | − | 0.224029i | 0.0477631 | − | 0.0275760i | ||||
\(67\) | −5.71986 | + | 3.30237i | −0.698793 | + | 0.403448i | −0.806898 | − | 0.590691i | \(-0.798855\pi\) |
0.108105 | + | 0.994139i | \(0.465522\pi\) | |||||||
\(68\) | 6.01005 | + | 3.46990i | 0.728826 | + | 0.420788i | ||||
\(69\) | 6.86493 | 0.826440 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.2159i | − | 1.44976i | −0.688875 | − | 0.724880i | \(-0.741895\pi\) | ||
0.688875 | − | 0.724880i | \(-0.258105\pi\) | |||||||
\(72\) | 4.69586 | + | 2.71116i | 0.553413 | + | 0.319513i | ||||
\(73\) | −1.13940 | + | 0.657835i | −0.133357 | + | 0.0769937i | −0.565194 | − | 0.824958i | \(-0.691199\pi\) |
0.431837 | + | 0.901952i | \(0.357865\pi\) | |||||||
\(74\) | 0.629365 | + | 1.09009i | 0.0731622 | + | 0.126721i | ||||
\(75\) | 2.58471 | − | 4.47685i | 0.298457 | − | 0.516942i | ||||
\(76\) | −3.11418 | + | 4.20527i | −0.357221 | + | 0.482378i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 5.98635i | 0.677821i | ||||||||
\(79\) | −10.3899 | − | 5.99859i | −1.16895 | − | 0.674895i | −0.215519 | − | 0.976500i | \(-0.569144\pi\) |
−0.953433 | + | 0.301605i | \(0.902478\pi\) | |||||||
\(80\) | 0.0393391 | − | 0.0227124i | 0.00439825 | − | 0.00253933i | ||||
\(81\) | −0.137233 | − | 0.237695i | −0.0152481 | − | 0.0264106i | ||||
\(82\) | 5.76541 | + | 3.32866i | 0.636684 | + | 0.367589i | ||||
\(83\) | 0.627610i | 0.0688892i | 0.999407 | + | 0.0344446i | \(0.0109662\pi\) | ||||
−0.999407 | + | 0.0344446i | \(0.989034\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.66369 | −0.180453 | ||||||||
\(86\) | 5.57758 | + | 3.22022i | 0.601446 | + | 0.347245i | ||||
\(87\) | −5.20234 | + | 3.00357i | −0.557750 | + | 0.322017i | ||||
\(88\) | −1.18128 | + | 0.682015i | −0.125925 | + | 0.0727030i | ||||
\(89\) | 0.774284 | − | 1.34110i | 0.0820739 | − | 0.142156i | −0.822067 | − | 0.569391i | \(-0.807179\pi\) |
0.904141 | + | 0.427235i | \(0.140512\pi\) | |||||||
\(90\) | −0.487588 | −0.0513962 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7.83915 | −0.817287 | ||||||||
\(93\) | −2.27719 | + | 3.94422i | −0.236134 | + | 0.408996i | ||||
\(94\) | 1.85064 | + | 3.20540i | 0.190879 | + | 0.330611i | ||||
\(95\) | 0.142478 | − | 1.24636i | 0.0146179 | − | 0.127873i | ||||
\(96\) | 5.08244 | + | 2.93435i | 0.518724 | + | 0.299485i | ||||
\(97\) | −1.36169 | −0.138258 | −0.0691291 | − | 0.997608i | \(-0.522022\pi\) | ||||
−0.0691291 | + | 0.997608i | \(0.522022\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.903134 | 0.0907684 | ||||||||
\(100\) | −2.95151 | + | 5.11217i | −0.295151 | + | 0.511217i | ||||
\(101\) | 2.89060 | − | 1.66889i | 0.287626 | − | 0.166061i | −0.349245 | − | 0.937031i | \(-0.613562\pi\) |
0.636871 | + | 0.770971i | \(0.280229\pi\) | |||||||
\(102\) | 2.71704 | + | 4.70605i | 0.269027 | + | 0.465969i | ||||
\(103\) | −6.85954 | + | 11.8811i | −0.675891 | + | 1.17068i | 0.300317 | + | 0.953840i | \(0.402908\pi\) |
−0.976208 | + | 0.216838i | \(0.930426\pi\) | |||||||
\(104\) | − | 18.2244i | − | 1.78705i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.44899 | 0.723510 | ||||||||
\(107\) | 5.34029 | + | 3.08322i | 0.516266 | + | 0.298066i | 0.735405 | − | 0.677627i | \(-0.236992\pi\) |
−0.219140 | + | 0.975693i | \(0.570325\pi\) | |||||||
\(108\) | −3.08878 | − | 5.34993i | −0.297218 | − | 0.514797i | ||||
\(109\) | 11.2274 | − | 6.48217i | 1.07539 | − | 0.620879i | 0.145744 | − | 0.989322i | \(-0.453442\pi\) |
0.929650 | + | 0.368443i | \(0.120109\pi\) | |||||||
\(110\) | 0.0613284 | − | 0.106224i | 0.00584743 | − | 0.0101281i | ||||
\(111\) | − | 1.47995i | − | 0.140471i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 18.6883i | − | 1.75804i | −0.476781 | − | 0.879022i | \(-0.658197\pi\) | ||
0.476781 | − | 0.879022i | \(-0.341803\pi\) | |||||||
\(114\) | −3.75823 | + | 1.63245i | −0.351990 | + | 0.152893i | ||||
\(115\) | 1.62751 | − | 0.939646i | 0.151766 | − | 0.0876224i | ||||
\(116\) | 5.94062 | − | 3.42982i | 0.551573 | − | 0.318451i | ||||
\(117\) | −6.03325 | + | 10.4499i | −0.557774 | + | 0.966093i | ||||
\(118\) | 1.72042i | 0.158378i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.865843 | −0.0790403 | ||||||||
\(121\) | 5.38640 | − | 9.32953i | 0.489673 | − | 0.848139i | ||||
\(122\) | 1.17271 | + | 2.03119i | 0.106172 | + | 0.183895i | ||||
\(123\) | −3.91367 | − | 6.77868i | −0.352884 | − | 0.611213i | ||||
\(124\) | 2.60036 | − | 4.50395i | 0.233519 | − | 0.404467i | ||||
\(125\) | − | 2.85412i | − | 0.255280i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3013i | 1.00282i | 0.865209 | + | 0.501412i | \(0.167186\pi\) | ||||
−0.865209 | + | 0.501412i | \(0.832814\pi\) | |||||||
\(128\) | −5.55925 | − | 3.20964i | −0.491373 | − | 0.283694i | ||||
\(129\) | −3.78617 | − | 6.55784i | −0.333354 | − | 0.577386i | ||||
\(130\) | 0.819390 | + | 1.41922i | 0.0718652 | + | 0.124474i | ||||
\(131\) | −0.115008 | − | 0.0663996i | −0.0100483 | − | 0.00580136i | 0.494967 | − | 0.868912i | \(-0.335180\pi\) |
−0.505016 | + | 0.863110i | \(0.668513\pi\) | |||||||
\(132\) | 0.601563 | 0.0523593 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.90564 | 0.510169 | ||||||||
\(135\) | 1.28255 | + | 0.740480i | 0.110384 | + | 0.0637303i | ||||
\(136\) | −8.27155 | − | 14.3267i | −0.709279 | − | 1.22851i | ||||
\(137\) | 9.55102 | + | 16.5429i | 0.815999 | + | 1.41335i | 0.908608 | + | 0.417649i | \(0.137146\pi\) |
−0.0926095 | + | 0.995703i | \(0.529521\pi\) | |||||||
\(138\) | −5.31592 | − | 3.06915i | −0.452521 | − | 0.261263i | ||||
\(139\) | 17.9635i | 1.52365i | 0.647786 | + | 0.761823i | \(0.275695\pi\) | ||||
−0.647786 | + | 0.761823i | \(0.724305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.35177i | − | 0.366485i | ||||||
\(142\) | −5.46144 | + | 9.45949i | −0.458314 | + | 0.793822i | ||||
\(143\) | −1.51771 | − | 2.62876i | −0.126918 | − | 0.219828i | ||||
\(144\) | −0.149533 | − | 0.258998i | −0.0124611 | − | 0.0215832i | ||||
\(145\) | −0.822236 | + | 1.42415i | −0.0682830 | + | 0.118270i | ||||
\(146\) | 1.17641 | 0.0973603 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.68998i | 0.138915i | ||||||||
\(149\) | 2.78010 | − | 4.81528i | 0.227755 | − | 0.394483i | −0.729387 | − | 0.684101i | \(-0.760195\pi\) |
0.957142 | + | 0.289618i | \(0.0935282\pi\) | |||||||
\(150\) | −4.00298 | + | 2.31112i | −0.326842 | + | 0.188703i | ||||
\(151\) | −8.43878 | + | 4.87213i | −0.686738 | + | 0.396488i | −0.802389 | − | 0.596801i | \(-0.796438\pi\) |
0.115651 | + | 0.993290i | \(0.463105\pi\) | |||||||
\(152\) | 11.4413 | − | 4.96970i | 0.928008 | − | 0.403096i | ||||
\(153\) | 10.9533i | 0.885522i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.24678i | 0.100143i | ||||||||
\(156\) | −4.01865 | + | 6.96050i | −0.321749 | + | 0.557286i | ||||
\(157\) | 19.8601 | − | 11.4662i | 1.58501 | − | 0.915106i | 0.590898 | − | 0.806746i | \(-0.298774\pi\) |
0.994112 | − | 0.108360i | \(-0.0345598\pi\) | |||||||
\(158\) | 5.36366 | + | 9.29013i | 0.426710 | + | 0.739083i | ||||
\(159\) | −7.58478 | − | 4.37907i | −0.601512 | − | 0.347283i | ||||
\(160\) | 1.60657 | 0.127010 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.245415i | 0.0192816i | ||||||||
\(163\) | −5.38555 | + | 9.32805i | −0.421829 | + | 0.730629i | −0.996118 | − | 0.0880231i | \(-0.971945\pi\) |
0.574289 | + | 0.818652i | \(0.305278\pi\) | |||||||
\(164\) | 4.46907 | + | 7.74066i | 0.348976 | + | 0.604444i | ||||
\(165\) | −0.124893 | + | 0.0721068i | −0.00972288 | + | 0.00561351i | ||||
\(166\) | 0.280590 | − | 0.485996i | 0.0217780 | − | 0.0377206i | ||||
\(167\) | −11.0372 | −0.854081 | −0.427041 | − | 0.904232i | \(-0.640444\pi\) | ||||
−0.427041 | + | 0.904232i | \(0.640444\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.5554 | 2.11965 | ||||||||
\(170\) | 1.28829 | + | 0.743797i | 0.0988077 | + | 0.0570466i | ||||
\(171\) | −8.20567 | − | 0.938035i | −0.627503 | − | 0.0717333i | ||||
\(172\) | 4.32348 | + | 7.48848i | 0.329662 | + | 0.570991i | ||||
\(173\) | −4.07400 | + | 7.05638i | −0.309741 | + | 0.536487i | −0.978306 | − | 0.207167i | \(-0.933576\pi\) |
0.668565 | + | 0.743654i | \(0.266909\pi\) | |||||||
\(174\) | 5.37131 | 0.407198 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0752324 | 0.00567086 | ||||||||
\(177\) | 1.01139 | − | 1.75178i | 0.0760210 | − | 0.131672i | ||||
\(178\) | −1.19915 | + | 0.692328i | −0.0898799 | + | 0.0518922i | ||||
\(179\) | 8.52516 | − | 4.92200i | 0.637200 | − | 0.367888i | −0.146335 | − | 0.989235i | \(-0.546748\pi\) |
0.783535 | + | 0.621347i | \(0.213414\pi\) | |||||||
\(180\) | −0.566932 | − | 0.327318i | −0.0422566 | − | 0.0243969i | ||||
\(181\) | −3.29904 | −0.245216 | −0.122608 | − | 0.992455i | \(-0.539126\pi\) | ||||
−0.122608 | + | 0.992455i | \(0.539126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.75762i | − | 0.203849i | ||||||
\(184\) | 16.1834 | + | 9.34346i | 1.19305 | + | 0.688809i | ||||
\(185\) | −0.202570 | − | 0.350862i | −0.0148933 | − | 0.0257959i | ||||
\(186\) | 3.52673 | − | 2.03616i | 0.258592 | − | 0.149298i | ||||
\(187\) | −2.38624 | − | 1.37770i | −0.174499 | − | 0.100747i | ||||
\(188\) | 4.96934i | 0.362426i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.667545 | + | 0.901428i | −0.0484288 | + | 0.0653965i | ||||
\(191\) | −5.65674 | + | 9.79777i | −0.409308 | + | 0.708941i | −0.994812 | − | 0.101728i | \(-0.967563\pi\) |
0.585505 | + | 0.810669i | \(0.300896\pi\) | |||||||
\(192\) | −2.78969 | − | 4.83188i | −0.201328 | − | 0.348711i | ||||
\(193\) | −13.1534 | + | 7.59411i | −0.946801 | + | 0.546636i | −0.892086 | − | 0.451866i | \(-0.850759\pi\) |
−0.0547156 | + | 0.998502i | \(0.517425\pi\) | |||||||
\(194\) | 1.05443 | + | 0.608777i | 0.0757039 | + | 0.0437077i | ||||
\(195\) | − | 1.92679i | − | 0.137981i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6450 | 0.758428 | 0.379214 | − | 0.925309i | \(-0.376195\pi\) | ||||
0.379214 | + | 0.925309i | \(0.376195\pi\) | |||||||
\(198\) | −0.699350 | − | 0.403770i | −0.0497006 | − | 0.0286947i | ||||
\(199\) | 16.0416 | − | 9.26165i | 1.13716 | − | 0.656541i | 0.191436 | − | 0.981505i | \(-0.438686\pi\) |
0.945726 | + | 0.324964i | \(0.105352\pi\) | |||||||
\(200\) | 12.1864 | − | 7.03580i | 0.861707 | − | 0.497507i | ||||
\(201\) | −6.01329 | − | 3.47177i | −0.424145 | − | 0.244880i | ||||
\(202\) | −2.98448 | −0.209988 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.29581i | 0.510809i | ||||||||
\(205\) | −1.85568 | − | 1.07138i | −0.129606 | − | 0.0748283i | ||||
\(206\) | 10.6235 | − | 6.13348i | 0.740174 | − | 0.427340i | ||||
\(207\) | −6.18637 | − | 10.7151i | −0.429983 | − | 0.744752i | ||||
\(208\) | −0.502579 | + | 0.870492i | −0.0348476 | + | 0.0603577i | ||||
\(209\) | 1.23646 | − | 1.66967i | 0.0855277 | − | 0.115494i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.64234i | 0.457277i | 0.973511 | + | 0.228639i | \(0.0734274\pi\) | ||||
−0.973511 | + | 0.228639i | \(0.926573\pi\) | |||||||
\(212\) | 8.66115 | + | 5.00052i | 0.594850 | + | 0.343437i | ||||
\(213\) | 11.1220 | − | 6.42128i | 0.762066 | − | 0.439979i | ||||
\(214\) | −2.75687 | − | 4.77504i | −0.188456 | − | 0.326415i | ||||
\(215\) | −1.79523 | − | 1.03647i | −0.122433 | − | 0.0706869i | ||||
\(216\) | 14.7261i | 1.00198i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.5921 | −0.785115 | ||||||||
\(219\) | −1.19785 | − | 0.691581i | −0.0809434 | − | 0.0467327i | ||||
\(220\) | 0.142617 | − | 0.0823397i | 0.00961520 | − | 0.00555134i | ||||
\(221\) | 31.8819 | − | 18.4070i | 2.14461 | − | 1.23819i | ||||
\(222\) | −0.661651 | + | 1.14601i | −0.0444071 | + | 0.0769154i | ||||
\(223\) | 26.9969 | 1.80785 | 0.903924 | − | 0.427692i | \(-0.140673\pi\) | ||||
0.903924 | + | 0.427692i | \(0.140673\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.31692 | −0.621128 | ||||||||
\(226\) | −8.35508 | + | 14.4714i | −0.555772 | + | 0.962625i | ||||
\(227\) | −10.9921 | − | 19.0388i | −0.729570 | − | 1.26365i | −0.957065 | − | 0.289873i | \(-0.906387\pi\) |
0.227496 | − | 0.973779i | \(-0.426946\pi\) | |||||||
\(228\) | −5.46566 | − | 0.624809i | −0.361972 | − | 0.0413790i | ||||
\(229\) | 8.35773 | + | 4.82534i | 0.552294 | + | 0.318867i | 0.750047 | − | 0.661385i | \(-0.230031\pi\) |
−0.197753 | + | 0.980252i | \(0.563364\pi\) | |||||||
\(230\) | −1.68037 | −0.110801 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.3520 | −1.07356 | ||||||||
\(233\) | 5.06082 | − | 8.76559i | 0.331545 | − | 0.574253i | −0.651270 | − | 0.758846i | \(-0.725763\pi\) |
0.982815 | + | 0.184593i | \(0.0590967\pi\) | |||||||
\(234\) | 9.34380 | − | 5.39464i | 0.610823 | − | 0.352659i | ||||
\(235\) | −0.595654 | − | 1.03170i | −0.0388562 | − | 0.0673009i | ||||
\(236\) | −1.15492 | + | 2.00038i | −0.0751790 | + | 0.130214i | ||||
\(237\) | − | 12.6126i | − | 0.819279i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 26.4382 | 1.71014 | 0.855072 | − | 0.518509i | \(-0.173513\pi\) | ||||
0.855072 | + | 0.518509i | \(0.173513\pi\) | |||||||
\(240\) | 0.0413572 | + | 0.0238776i | 0.00266959 | + | 0.00154129i | ||||
\(241\) | 2.87291 | + | 4.97603i | 0.185060 | + | 0.320534i | 0.943597 | − | 0.331097i | \(-0.107419\pi\) |
−0.758536 | + | 0.651631i | \(0.774085\pi\) | |||||||
\(242\) | −8.34202 | + | 4.81627i | −0.536245 | + | 0.309601i | ||||
\(243\) | 7.86307 | − | 13.6192i | 0.504416 | − | 0.873675i | ||||
\(244\) | 3.14896i | 0.201592i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.99884i | 0.446230i | ||||||||
\(247\) | 11.0593 | + | 25.4607i | 0.703684 | + | 1.62002i | ||||
\(248\) | −10.7365 | + | 6.19872i | −0.681768 | + | 0.393619i | ||||
\(249\) | −0.571409 | + | 0.329903i | −0.0362116 | + | 0.0209068i | ||||
\(250\) | −1.27601 | + | 2.21011i | −0.0807019 | + | 0.139780i | ||||
\(251\) | − | 5.77064i | − | 0.364240i | −0.983276 | − | 0.182120i | \(-0.941704\pi\) | ||
0.983276 | − | 0.182120i | \(-0.0582959\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.11247 | 0.195679 | ||||||||
\(254\) | 5.05252 | − | 8.75123i | 0.317023 | − | 0.549101i | ||||
\(255\) | −0.874519 | − | 1.51471i | −0.0547645 | − | 0.0948549i | ||||
\(256\) | 8.17703 | + | 14.1630i | 0.511064 | + | 0.885189i | ||||
\(257\) | 11.4760 | − | 19.8769i | 0.715851 | − | 1.23989i | −0.246780 | − | 0.969072i | \(-0.579373\pi\) |
0.962631 | − | 0.270818i | \(-0.0872942\pi\) | |||||||
\(258\) | 6.77083i | 0.421533i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.20023i | 0.136452i | ||||||||
\(261\) | 9.37625 | + | 5.41338i | 0.580375 | + | 0.335080i | ||||
\(262\) | 0.0593714 | + | 0.102834i | 0.00366798 | + | 0.00635312i | ||||
\(263\) | 2.17844 | + | 3.77317i | 0.134328 | + | 0.232663i | 0.925341 | − | 0.379137i | \(-0.123779\pi\) |
−0.791012 | + | 0.611800i | \(0.790446\pi\) | |||||||
\(264\) | −1.24188 | − | 0.717002i | −0.0764326 | − | 0.0441284i | ||||
\(265\) | −2.39756 | −0.147281 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.62801 | 0.0996325 | ||||||||
\(268\) | 6.86665 | + | 3.96446i | 0.419447 | + | 0.242168i | ||||
\(269\) | 2.08605 | + | 3.61315i | 0.127189 | + | 0.220298i | 0.922586 | − | 0.385790i | \(-0.126071\pi\) |
−0.795397 | + | 0.606088i | \(0.792738\pi\) | |||||||
\(270\) | −0.662102 | − | 1.14679i | −0.0402942 | − | 0.0697916i | ||||
\(271\) | −23.7473 | − | 13.7105i | −1.44254 | − | 0.832853i | −0.444525 | − | 0.895766i | \(-0.646628\pi\) |
−0.998019 | + | 0.0629130i | \(0.979961\pi\) | |||||||
\(272\) | 0.912427i | 0.0553240i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 17.0801i | − | 1.03185i | ||||||
\(275\) | 1.17187 | − | 2.02975i | 0.0706667 | − | 0.122398i | ||||
\(276\) | −4.12064 | − | 7.13716i | −0.248034 | − | 0.429607i | ||||
\(277\) | −0.795257 | − | 1.37742i | −0.0477823 | − | 0.0827614i | 0.841145 | − | 0.540810i | \(-0.181882\pi\) |
−0.888927 | + | 0.458048i | \(0.848549\pi\) | |||||||
\(278\) | 8.03106 | − | 13.9102i | 0.481671 | − | 0.834278i | ||||
\(279\) | 8.20844 | 0.491426 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 29.2240i | − | 1.74336i | −0.490079 | − | 0.871678i | \(-0.663032\pi\) | ||
0.490079 | − | 0.871678i | \(-0.336968\pi\) | |||||||
\(282\) | −1.94557 | + | 3.36983i | −0.115857 | + | 0.200670i | ||||
\(283\) | −12.2556 | + | 7.07578i | −0.728521 | + | 0.420612i | −0.817881 | − | 0.575388i | \(-0.804851\pi\) |
0.0893599 | + | 0.995999i | \(0.471518\pi\) | |||||||
\(284\) | −12.7003 | + | 7.33254i | −0.753626 | + | 0.435106i | ||||
\(285\) | 1.20964 | − | 0.525427i | 0.0716529 | − | 0.0311236i | ||||
\(286\) | 2.71414i | 0.160490i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 10.5772i | − | 0.623269i | ||||||
\(289\) | 8.20886 | − | 14.2182i | 0.482874 | − | 0.836363i | ||||
\(290\) | 1.27341 | − | 0.735204i | 0.0747773 | − | 0.0431727i | ||||
\(291\) | −0.715770 | − | 1.23975i | −0.0419592 | − | 0.0726754i | ||||
\(292\) | 1.36784 | + | 0.789725i | 0.0800470 | + | 0.0462152i | ||||
\(293\) | −8.00946 | −0.467918 | −0.233959 | − | 0.972246i | \(-0.575168\pi\) | ||||
−0.233959 | + | 0.972246i | \(0.575168\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 0.553743i | − | 0.0322402i | ||||||
\(296\) | 2.01428 | − | 3.48883i | 0.117078 | − | 0.202784i | ||||
\(297\) | 1.22638 | + | 2.12415i | 0.0711617 | + | 0.123256i | ||||
\(298\) | −4.30559 | + | 2.48584i | −0.249416 | + | 0.144001i | ||||
\(299\) | −20.7924 | + | 36.0135i | −1.20245 | + | 2.08271i | ||||
\(300\) | −6.20584 | −0.358295 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.71286 | 0.501369 | ||||||||
\(303\) | 3.03889 | + | 1.75450i | 0.174580 | + | 0.100794i | ||||
\(304\) | −0.683545 | − | 0.0781397i | −0.0392040 | − | 0.00448162i | ||||
\(305\) | −0.377453 | − | 0.653767i | −0.0216129 | − | 0.0374346i | ||||
\(306\) | 4.89696 | − | 8.48178i | 0.279941 | − | 0.484871i | ||||
\(307\) | 13.3461 | 0.761701 | 0.380850 | − | 0.924637i | \(-0.375631\pi\) | ||||
0.380850 | + | 0.924637i | \(0.375631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.4229 | −0.820488 | ||||||||
\(310\) | 0.557404 | − | 0.965452i | 0.0316584 | − | 0.0548340i | ||||
\(311\) | 20.2373 | − | 11.6840i | 1.14755 | − | 0.662538i | 0.199261 | − | 0.979946i | \(-0.436146\pi\) |
0.948289 | + | 0.317408i | \(0.102812\pi\) | |||||||
\(312\) | 16.5924 | − | 9.57964i | 0.939361 | − | 0.542340i | ||||
\(313\) | −19.3478 | − | 11.1704i | −1.09360 | − | 0.631391i | −0.159068 | − | 0.987268i | \(-0.550849\pi\) |
−0.934533 | + | 0.355877i | \(0.884182\pi\) | |||||||
\(314\) | −20.5051 | −1.15717 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.4025i | 0.810205i | ||||||||
\(317\) | −4.89845 | − | 2.82812i | −0.275124 | − | 0.158843i | 0.356090 | − | 0.934452i | \(-0.384110\pi\) |
−0.631214 | + | 0.775609i | \(0.717443\pi\) | |||||||
\(318\) | 3.91556 | + | 6.78195i | 0.219574 | + | 0.380313i | ||||
\(319\) | −2.35868 | + | 1.36178i | −0.132061 | + | 0.0762452i | ||||
\(320\) | −1.32274 | − | 0.763684i | −0.0739434 | − | 0.0426912i | ||||
\(321\) | 6.48277i | 0.361833i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.2499 | + | 14.9959i | 1.12674 | + | 0.834395i | ||||
\(324\) | −0.164747 | + | 0.285351i | −0.00915263 | + | 0.0158528i | ||||
\(325\) | 15.6571 | + | 27.1188i | 0.868497 | + | 1.50428i | ||||
\(326\) | 8.34070 | − | 4.81550i | 0.461949 | − | 0.266706i | ||||
\(327\) | 11.8034 | + | 6.81470i | 0.652729 | + | 0.376854i | ||||
\(328\) | − | 21.3067i | − | 1.17647i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.128949 | 0.00709841 | ||||||||
\(331\) | −22.7878 | − | 13.1565i | −1.25253 | − | 0.723148i | −0.280918 | − | 0.959732i | \(-0.590639\pi\) |
−0.971611 | + | 0.236584i | \(0.923972\pi\) | |||||||
\(332\) | 0.652499 | − | 0.376721i | 0.0358105 | − | 0.0206752i | ||||
\(333\) | −2.30998 | + | 1.33367i | −0.126586 | + | 0.0730846i | ||||
\(334\) | 8.54672 | + | 4.93445i | 0.467656 | + | 0.270001i | ||||
\(335\) | −1.90081 | −0.103853 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.8906i | 1.30141i | 0.759333 | + | 0.650703i | \(0.225526\pi\) | ||||
−0.759333 | + | 0.650703i | \(0.774474\pi\) | |||||||
\(338\) | −21.3378 | − | 12.3194i | −1.16062 | − | 0.670086i | ||||
\(339\) | 17.0148 | − | 9.82348i | 0.924115 | − | 0.533538i | ||||
\(340\) | 0.998624 | + | 1.72967i | 0.0541580 | + | 0.0938044i | ||||
\(341\) | −1.03245 | + | 1.78826i | −0.0559104 | + | 0.0968396i | ||||
\(342\) | 5.93476 | + | 4.39494i | 0.320915 | + | 0.237651i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 20.6126i | − | 1.11136i | ||||||
\(345\) | 1.71100 | + | 0.987848i | 0.0921173 | + | 0.0531840i | ||||
\(346\) | 6.30948 | − | 3.64278i | 0.339200 | − | 0.195837i | ||||
\(347\) | 3.45781 | + | 5.98911i | 0.185625 | + | 0.321512i | 0.943787 | − | 0.330554i | \(-0.107236\pi\) |
−0.758162 | + | 0.652066i | \(0.773902\pi\) | |||||||
\(348\) | 6.24537 | + | 3.60576i | 0.334787 | + | 0.193289i | ||||
\(349\) | − | 13.1300i | − | 0.702831i | −0.936220 | − | 0.351416i | \(-0.885700\pi\) | ||
0.936220 | − | 0.351416i | \(-0.114300\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −32.7705 | −1.74916 | ||||||||
\(352\) | 2.30431 | + | 1.33040i | 0.122820 | + | 0.0709103i | ||||
\(353\) | −18.5310 | + | 10.6989i | −0.986307 | + | 0.569445i | −0.904168 | − | 0.427176i | \(-0.859508\pi\) |
−0.0821389 | + | 0.996621i | \(0.526175\pi\) | |||||||
\(354\) | −1.56636 | + | 0.904340i | −0.0832512 | + | 0.0480651i | ||||
\(355\) | 1.75784 | − | 3.04467i | 0.0932966 | − | 0.161594i | ||||
\(356\) | −1.85904 | −0.0985291 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.80204 | −0.465202 | ||||||||
\(359\) | 5.50977 | − | 9.54320i | 0.290795 | − | 0.503671i | −0.683203 | − | 0.730228i | \(-0.739414\pi\) |
0.973998 | + | 0.226557i | \(0.0727471\pi\) | |||||||
\(360\) | 0.780260 | + | 1.35145i | 0.0411233 | + | 0.0712277i | ||||
\(361\) | −12.9684 | + | 13.8860i | −0.682547 | + | 0.730842i | ||||
\(362\) | 2.55464 | + | 1.47492i | 0.134269 | + | 0.0775203i | ||||
\(363\) | 11.3254 | 0.594432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.378644 | −0.0198191 | ||||||||
\(366\) | −1.23287 | + | 2.13539i | −0.0644430 | + | 0.111618i | ||||
\(367\) | −21.5490 | + | 12.4413i | −1.12485 | + | 0.649432i | −0.942634 | − | 0.333827i | \(-0.891660\pi\) |
−0.182215 | + | 0.983259i | \(0.558327\pi\) | |||||||
\(368\) | −0.515334 | − | 0.892585i | −0.0268637 | − | 0.0465292i | ||||
\(369\) | −7.05367 | + | 12.2173i | −0.367199 | + | 0.636008i | ||||
\(370\) | 0.362257i | 0.0188329i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 5.46750 | 0.283477 | ||||||||
\(373\) | 5.17977 | + | 2.99054i | 0.268198 | + | 0.154844i | 0.628069 | − | 0.778158i | \(-0.283846\pi\) |
−0.359870 | + | 0.933002i | \(0.617179\pi\) | |||||||
\(374\) | 1.23187 | + | 2.13367i | 0.0636986 | + | 0.110329i | ||||
\(375\) | 2.59854 | − | 1.50027i | 0.134188 | − | 0.0774735i | ||||
\(376\) | 5.92295 | − | 10.2588i | 0.305453 | − | 0.529060i | ||||
\(377\) | − | 36.3887i | − | 1.87411i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.98456i | 0.204673i | 0.994750 | + | 0.102336i | \(0.0326318\pi\) | ||||
−0.994750 | + | 0.102336i | \(0.967368\pi\) | |||||||
\(380\) | −1.38130 | + | 0.599992i | −0.0708593 | + | 0.0307789i | ||||
\(381\) | −10.2892 | + | 5.94050i | −0.527134 | + | 0.304341i | ||||
\(382\) | 8.76070 | − | 5.05799i | 0.448236 | − | 0.258789i | ||||
\(383\) | 5.09215 | − | 8.81987i | 0.260197 | − | 0.450674i | −0.706097 | − | 0.708115i | \(-0.749546\pi\) |
0.966294 | + | 0.257441i | \(0.0828792\pi\) | |||||||
\(384\) | − | 6.74857i | − | 0.344387i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.5806 | 0.691234 | ||||||||
\(387\) | −6.82387 | + | 11.8193i | −0.346877 | + | 0.600808i | ||||
\(388\) | 0.817346 | + | 1.41569i | 0.0414945 | + | 0.0718705i | ||||
\(389\) | 5.55875 | + | 9.62803i | 0.281840 | + | 0.488161i | 0.971838 | − | 0.235651i | \(-0.0757221\pi\) |
−0.689998 | + | 0.723811i | \(0.742389\pi\) | |||||||
\(390\) | −0.861424 | + | 1.49203i | −0.0436199 | + | 0.0755518i | ||||
\(391\) | 37.7484i | 1.90902i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.139612i | − | 0.00704248i | ||||||
\(394\) | −8.24308 | − | 4.75914i | −0.415280 | − | 0.239762i | ||||
\(395\) | −1.72637 | − | 2.99016i | −0.0868631 | − | 0.150451i | ||||
\(396\) | −0.542102 | − | 0.938949i | −0.0272417 | − | 0.0471840i | ||||
\(397\) | 27.3946 | + | 15.8163i | 1.37490 | + | 0.793797i | 0.991540 | − | 0.129803i | \(-0.0414344\pi\) |
0.383358 | + | 0.923600i | \(0.374768\pi\) | |||||||
\(398\) | −16.5627 | −0.830211 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.776113 | −0.0388057 | ||||||||
\(401\) | −15.7772 | − | 9.10899i | −0.787878 | − | 0.454881i | 0.0513372 | − | 0.998681i | \(-0.483652\pi\) |
−0.839215 | + | 0.543800i | \(0.816985\pi\) | |||||||
\(402\) | 3.10429 | + | 5.37680i | 0.154828 | + | 0.268170i | ||||
\(403\) | −13.7943 | − | 23.8924i | −0.687141 | − | 1.19016i | ||||
\(404\) | −3.47014 | − | 2.00349i | −0.172646 | − | 0.0996773i | ||||
\(405\) | − | 0.0789903i | − | 0.00392506i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.670991i | − | 0.0332598i | ||||||
\(408\) | 8.69587 | − | 15.0617i | 0.430510 | − | 0.745664i | ||||
\(409\) | 2.66242 | + | 4.61145i | 0.131648 | + | 0.228021i | 0.924312 | − | 0.381638i | \(-0.124640\pi\) |
−0.792664 | + | 0.609659i | \(0.791306\pi\) | |||||||
\(410\) | 0.957975 | + | 1.65926i | 0.0473110 | + | 0.0819451i | ||||
\(411\) | −10.0410 | + | 17.3915i | −0.495285 | + | 0.857859i | ||||
\(412\) | 16.4696 | 0.811401 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 11.0631i | 0.543723i | ||||||||
\(415\) | −0.0903118 | + | 0.156425i | −0.00443323 | + | 0.00767859i | ||||
\(416\) | −30.7872 | + | 17.7750i | −1.50947 | + | 0.871491i | ||||
\(417\) | −16.3549 | + | 9.44251i | −0.800903 | + | 0.462402i | ||||
\(418\) | −1.70393 | + | 0.740132i | −0.0833421 | + | 0.0362010i | ||||
\(419\) | 8.09389i | 0.395412i | 0.980261 | + | 0.197706i | \(0.0633492\pi\) | ||||
−0.980261 | + | 0.197706i | \(0.936651\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 25.4935i | − | 1.24248i | −0.783621 | − | 0.621239i | \(-0.786629\pi\) | ||
0.783621 | − | 0.621239i | \(-0.213371\pi\) | |||||||
\(422\) | 2.96963 | − | 5.14355i | 0.144559 | − | 0.250384i | ||||
\(423\) | −6.79246 | + | 3.92163i | −0.330261 | + | 0.190676i | ||||
\(424\) | −11.9202 | − | 20.6464i | −0.578897 | − | 1.00268i | ||||
\(425\) | 24.6170 | + | 14.2126i | 1.19410 | + | 0.689413i | ||||
\(426\) | −11.4832 | −0.556363 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 7.40276i | − | 0.357826i | ||||||
\(429\) | 1.59557 | − | 2.76361i | 0.0770349 | − | 0.133428i | ||||
\(430\) | 0.926766 | + | 1.60521i | 0.0446926 | + | 0.0774099i | ||||
\(431\) | −5.56360 | + | 3.21215i | −0.267989 | + | 0.154724i | −0.627973 | − | 0.778235i | \(-0.716115\pi\) |
0.359984 | + | 0.932958i | \(0.382782\pi\) | |||||||
\(432\) | 0.406105 | − | 0.703394i | 0.0195387 | − | 0.0338421i | ||||
\(433\) | −24.2261 | −1.16423 | −0.582115 | − | 0.813106i | \(-0.697775\pi\) | ||||
−0.582115 | + | 0.813106i | \(0.697775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.72883 | −0.0828911 | ||||||||
\(436\) | −13.4785 | − | 7.78179i | −0.645501 | − | 0.372680i | ||||
\(437\) | −28.2792 | − | 3.23275i | −1.35278 | − | 0.154643i | ||||
\(438\) | 0.618379 | + | 1.07106i | 0.0295473 | + | 0.0511774i | ||||
\(439\) | 0.916950 | − | 1.58820i | 0.0437636 | − | 0.0758008i | −0.843314 | − | 0.537421i | \(-0.819398\pi\) |
0.887077 | + | 0.461621i | \(0.152732\pi\) | |||||||
\(440\) | −0.392562 | −0.0187147 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −32.9173 | −1.56572 | ||||||||
\(443\) | 5.35119 | − | 9.26854i | 0.254243 | − | 0.440361i | −0.710447 | − | 0.703751i | \(-0.751507\pi\) |
0.964690 | + | 0.263389i | \(0.0848404\pi\) | |||||||
\(444\) | −1.53864 | + | 0.888335i | −0.0730207 | + | 0.0421585i | ||||
\(445\) | 0.385963 | − | 0.222836i | 0.0182964 | − | 0.0105634i | ||||
\(446\) | −20.9053 | − | 12.0697i | −0.989895 | − | 0.571516i | ||||
\(447\) | 5.84544 | 0.276480 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.6699i | 0.928278i | 0.885762 | + | 0.464139i | \(0.153636\pi\) | ||||
−0.885762 | + | 0.464139i | \(0.846364\pi\) | |||||||
\(450\) | 7.21463 | + | 4.16537i | 0.340101 | + | 0.196357i | ||||
\(451\) | −1.77441 | − | 3.07337i | −0.0835537 | − | 0.144719i | ||||
\(452\) | −19.4294 | + | 11.2176i | −0.913881 | + | 0.527629i | ||||
\(453\) | −8.87168 | − | 5.12207i | −0.416828 | − | 0.240656i | ||||
\(454\) | 19.6572i | 0.922557i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.5388 | + | 7.80439i | 0.493523 | + | 0.365474i | ||||
\(457\) | 4.70869 | − | 8.15569i | 0.220263 | − | 0.381507i | −0.734625 | − | 0.678474i | \(-0.762642\pi\) |
0.954888 | + | 0.296967i | \(0.0959751\pi\) | |||||||
\(458\) | −4.31459 | − | 7.47308i | −0.201607 | − | 0.349194i | ||||
\(459\) | −25.7619 | + | 14.8736i | −1.20246 | + | 0.694242i | ||||
\(460\) | −1.95382 | − | 1.12804i | −0.0910972 | − | 0.0525950i | ||||
\(461\) | − | 28.3908i | − | 1.32229i | −0.750258 | − | 0.661145i | \(-0.770071\pi\) | ||
0.750258 | − | 0.661145i | \(-0.229929\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.1625 | −1.16940 | −0.584700 | − | 0.811250i | \(-0.698788\pi\) | ||||
−0.584700 | + | 0.811250i | \(0.698788\pi\) | |||||||
\(464\) | 0.781056 | + | 0.450943i | 0.0362596 | + | 0.0209345i | ||||
\(465\) | −1.13513 | + | 0.655367i | −0.0526403 | + | 0.0303919i | ||||
\(466\) | −7.83778 | + | 4.52514i | −0.363078 | + | 0.209623i | ||||
\(467\) | 14.3282 | + | 8.27241i | 0.663031 | + | 0.382801i | 0.793431 | − | 0.608660i | \(-0.208293\pi\) |
−0.130400 | + | 0.991462i | \(0.541626\pi\) | |||||||
\(468\) | 14.4857 | 0.669603 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.06521i | 0.0491345i | ||||||||
\(471\) | 20.8789 | + | 12.0545i | 0.962050 | + | 0.555440i | ||||
\(472\) | 4.76851 | − | 2.75310i | 0.219488 | − | 0.126722i | ||||
\(473\) | −1.71660 | − | 2.97324i | −0.0789294 | − | 0.136710i | ||||
\(474\) | −5.63881 | + | 9.76670i | −0.258999 | + | 0.448599i | ||||
\(475\) | −12.7556 | + | 17.2247i | −0.585266 | + | 0.790321i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 15.7849i | 0.722742i | ||||||||
\(478\) | −20.4726 | − | 11.8199i | −0.936397 | − | 0.540629i | ||||
\(479\) | 5.63404 | − | 3.25282i | 0.257426 | − | 0.148625i | −0.365734 | − | 0.930719i | \(-0.619182\pi\) |
0.623160 | + | 0.782095i | \(0.285849\pi\) | |||||||
\(480\) | 0.844492 | + | 1.46270i | 0.0385456 | + | 0.0667630i | ||||
\(481\) | 7.76384 | + | 4.48245i | 0.354001 | + | 0.204382i | ||||
\(482\) | − | 5.13764i | − | 0.234013i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.9327 | −0.587848 | ||||||||
\(485\) | −0.339385 | − | 0.195944i | −0.0154107 | − | 0.00889735i | ||||
\(486\) | −12.1777 | + | 7.03079i | −0.552391 | + | 0.318923i | ||||
\(487\) | 4.90255 | − | 2.83049i | 0.222156 | − | 0.128262i | −0.384792 | − | 0.923003i | \(-0.625727\pi\) |
0.606948 | + | 0.794741i | \(0.292394\pi\) | |||||||
\(488\) | 3.75324 | − | 6.50080i | 0.169901 | − | 0.294278i | ||||
\(489\) | −11.3237 | −0.512073 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0570 | −0.860031 | −0.430015 | − | 0.902822i | \(-0.641492\pi\) | ||||
−0.430015 | + | 0.902822i | \(0.641492\pi\) | |||||||
\(492\) | −4.69833 | + | 8.13775i | −0.211817 | + | 0.366878i | ||||
\(493\) | −16.5158 | − | 28.6063i | −0.743836 | − | 1.28836i | ||||
\(494\) | 2.81902 | − | 24.6600i | 0.126834 | − | 1.10951i | ||||
\(495\) | 0.225096 | + | 0.129959i | 0.0101173 | + | 0.00584123i | ||||
\(496\) | 0.683775 | 0.0307024 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.589967 | 0.0264371 | ||||||||
\(499\) | −0.520471 | + | 0.901483i | −0.0232995 | + | 0.0403559i | −0.877440 | − | 0.479686i | \(-0.840750\pi\) |
0.854141 | + | 0.520042i | \(0.174084\pi\) | |||||||
\(500\) | −2.96730 | + | 1.71317i | −0.132702 | + | 0.0766155i | ||||
\(501\) | −5.80168 | − | 10.0488i | −0.259200 | − | 0.448947i | ||||
\(502\) | −2.57992 | + | 4.46855i | −0.115147 | + | 0.199441i | ||||
\(503\) | − | 23.5048i | − | 1.04803i | −0.851710 | − | 0.524013i | \(-0.824434\pi\) | ||
0.851710 | − | 0.524013i | \(-0.175566\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.960599 | 0.0427461 | ||||||||
\(506\) | −2.41017 | − | 1.39151i | −0.107145 | − | 0.0618602i | ||||
\(507\) | 14.4845 | + | 25.0879i | 0.643279 | + | 1.11419i | ||||
\(508\) | 11.7494 | − | 6.78353i | 0.521296 | − | 0.300971i | ||||
\(509\) | −9.42499 | + | 16.3246i | −0.417755 | + | 0.723574i | −0.995713 | − | 0.0924929i | \(-0.970516\pi\) |
0.577958 | + | 0.816067i | \(0.303850\pi\) | |||||||
\(510\) | 1.56391i | 0.0692509i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.78447i | − | 0.0788633i | ||||||
\(513\) | −8.93635 | − | 20.5733i | −0.394550 | − | 0.908333i | ||||
\(514\) | −17.7730 | + | 10.2613i | −0.783934 | + | 0.452605i | ||||
\(515\) | −3.41932 | + | 1.97415i | −0.150673 | + | 0.0869913i | ||||
\(516\) | −4.54527 | + | 7.87263i | −0.200094 | + | 0.346573i | ||||
\(517\) | − | 1.97304i | − | 0.0867741i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.56599 | −0.376005 | ||||||||
\(520\) | 2.62245 | − | 4.54222i | 0.115002 | − | 0.199189i | ||||
\(521\) | 14.4853 | + | 25.0893i | 0.634614 | + | 1.09918i | 0.986597 | + | 0.163177i | \(0.0521742\pi\) |
−0.351983 | + | 0.936006i | \(0.614492\pi\) | |||||||
\(522\) | −4.84039 | − | 8.38380i | −0.211858 | − | 0.366949i | ||||
\(523\) | 4.98226 | − | 8.62952i | 0.217859 | − | 0.377343i | −0.736294 | − | 0.676661i | \(-0.763426\pi\) |
0.954153 | + | 0.299319i | \(0.0967594\pi\) | |||||||
\(524\) | 0.159424i | 0.00696449i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 3.89571i | − | 0.169861i | ||||||
\(527\) | −21.6882 | − | 12.5217i | −0.944752 | − | 0.545453i | ||||
\(528\) | 0.0395459 | + | 0.0684955i | 0.00172101 | + | 0.00298088i | ||||
\(529\) | −9.82010 | − | 17.0089i | −0.426961 | − | 0.739518i | ||||
\(530\) | 1.85658 | + | 1.07189i | 0.0806445 | + | 0.0465601i | ||||
\(531\) | −3.64570 | −0.158210 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.4147 | 2.05376 | ||||||||
\(534\) | −1.26066 | − | 0.727844i | −0.0545542 | − | 0.0314969i | ||||
\(535\) | 0.887338 | + | 1.53691i | 0.0383630 | + | 0.0664466i | ||||
\(536\) | −9.45047 | − | 16.3687i | −0.408198 | − | 0.707020i | ||||
\(537\) | 8.96249 | + | 5.17450i | 0.386760 | + | 0.223296i | ||||
\(538\) | − | 3.73050i | − | 0.160833i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | − | 1.77788i | − | 0.0765077i | ||||||
\(541\) | 4.62179 | − | 8.00517i | 0.198706 | − | 0.344169i | −0.749403 | − | 0.662114i | \(-0.769659\pi\) |
0.948109 | + | 0.317945i | \(0.102993\pi\) | |||||||
\(542\) | 12.2593 | + | 21.2337i | 0.526581 | + | 0.912065i | ||||
\(543\) | −1.73414 | − | 3.00362i | −0.0744191 | − | 0.128898i | ||||
\(544\) | −16.1352 | + | 27.9469i | −0.691790 | + | 1.19821i | ||||
\(545\) | 3.73108 | 0.159822 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.8556i | 1.49032i | 0.666887 | + | 0.745158i | \(0.267626\pi\) | ||||
−0.666887 | + | 0.745158i | \(0.732374\pi\) | |||||||
\(548\) | 11.4659 | − | 19.8596i | 0.489800 | − | 0.848358i | ||||
\(549\) | −4.30423 | + | 2.48505i | −0.183700 | + | 0.106059i | ||||
\(550\) | −1.81490 | + | 1.04783i | −0.0773877 | + | 0.0446798i | ||||
\(551\) | 22.8448 | − | 9.92302i | 0.973221 | − | 0.422735i | ||||
\(552\) | 19.6455i | 0.836170i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.42216i | 0.0604218i | ||||||||
\(555\) | 0.212962 | − | 0.368861i | 0.00903973 | − | 0.0156573i | ||||
\(556\) | 18.6759 | − | 10.7825i | 0.792034 | − | 0.457281i | ||||
\(557\) | 18.5283 | + | 32.0919i | 0.785068 | + | 1.35978i | 0.928958 | + | 0.370184i | \(0.120705\pi\) |
−0.143890 | + | 0.989594i | \(0.545961\pi\) | |||||||
\(558\) | −6.35627 | − | 3.66980i | −0.269083 | − | 0.155355i | ||||
\(559\) | 45.8700 | 1.94009 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 2.89675i | − | 0.122301i | ||||||
\(562\) | −13.0653 | + | 22.6298i | −0.551128 | + | 0.954582i | ||||
\(563\) | 7.30046 | + | 12.6448i | 0.307678 | + | 0.532913i | 0.977854 | − | 0.209289i | \(-0.0671148\pi\) |
−0.670176 | + | 0.742202i | \(0.733782\pi\) | |||||||
\(564\) | −4.52434 | + | 2.61213i | −0.190509 | + | 0.109991i | ||||
\(565\) | 2.68920 | − | 4.65784i | 0.113136 | − | 0.195957i | ||||
\(566\) | 12.6537 | 0.531873 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 34.9586 | 1.46683 | ||||||||
\(569\) | −14.1095 | − | 8.14614i | −0.591502 | − | 0.341504i | 0.174189 | − | 0.984712i | \(-0.444270\pi\) |
−0.765691 | + | 0.643208i | \(0.777603\pi\) | |||||||
\(570\) | −1.17160 | − | 0.133932i | −0.0490730 | − | 0.00560980i | ||||
\(571\) | −6.77687 | − | 11.7379i | −0.283603 | − | 0.491215i | 0.688666 | − | 0.725079i | \(-0.258197\pi\) |
−0.972270 | + | 0.233863i | \(0.924863\pi\) | |||||||
\(572\) | −1.82200 | + | 3.15580i | −0.0761818 | + | 0.131951i | ||||
\(573\) | −11.8939 | −0.496873 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.1089 | −1.33903 | ||||||||
\(576\) | −5.02789 | + | 8.70856i | −0.209495 | + | 0.362857i | ||||
\(577\) | −29.0158 | + | 16.7523i | −1.20794 | + | 0.697407i | −0.962310 | − | 0.271955i | \(-0.912330\pi\) |
−0.245635 | + | 0.969362i | \(0.578996\pi\) | |||||||
\(578\) | −12.7132 | + | 7.33997i | −0.528800 | + | 0.305303i | ||||
\(579\) | −13.8281 | − | 7.98368i | −0.574678 | − | 0.331790i | ||||
\(580\) | 1.97417 | 0.0819731 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.28001i | 0.0530583i | ||||||||
\(583\) | −3.43884 | − | 1.98542i | −0.142422 | − | 0.0822275i | ||||
\(584\) | −1.88254 | − | 3.26066i | −0.0779002 | − | 0.134927i | ||||
\(585\) | −3.00743 | + | 1.73634i | −0.124342 | + | 0.0717890i | ||||
\(586\) | 6.20220 | + | 3.58084i | 0.256210 | + | 0.147923i | ||||
\(587\) | 23.4332i | 0.967190i | 0.875292 | + | 0.483595i | \(0.160669\pi\) | ||||
−0.875292 | + | 0.483595i | \(0.839331\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.2380 | − | 15.1754i | 0.463053 | − | 0.625290i | ||||
\(590\) | −0.247565 | + | 0.428796i | −0.0101921 | + | 0.0176532i | ||||
\(591\) | 5.59556 | + | 9.69179i | 0.230171 | + | 0.398667i | ||||
\(592\) | −0.192425 | + | 0.111097i | −0.00790862 | + | 0.00456604i | ||||
\(593\) | −35.6805 | − | 20.6002i | −1.46522 | − | 0.845947i | −0.465979 | − | 0.884796i | \(-0.654298\pi\) |
−0.999245 | + | 0.0388484i | \(0.987631\pi\) | |||||||
\(594\) | − | 2.19314i | − | 0.0899855i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.67498 | −0.273418 | ||||||||
\(597\) | 16.8646 | + | 9.73676i | 0.690221 | + | 0.398499i | ||||
\(598\) | 32.2015 | − | 18.5916i | 1.31682 | − | 0.760265i | ||||
\(599\) | −21.1840 | + | 12.2306i | −0.865556 | + | 0.499729i | −0.865869 | − | 0.500271i | \(-0.833234\pi\) |
0.000312831 | 1.00000i | \(0.499900\pi\) | ||||||||
\(600\) | 12.8115 | + | 7.39673i | 0.523028 | + | 0.301970i | ||||
\(601\) | −24.4746 | −0.998340 | −0.499170 | − | 0.866504i | \(-0.666362\pi\) | ||||
−0.499170 | + | 0.866504i | \(0.666362\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.5144i | 0.509628i | ||||||||
\(604\) | 10.1307 | + | 5.84895i | 0.412212 | + | 0.237990i | ||||
\(605\) | 2.68500 | − | 1.55018i | 0.109161 | − | 0.0630240i | ||||
\(606\) | −1.56879 | − | 2.71723i | −0.0637278 | − | 0.110380i | ||||
\(607\) | 18.2596 | − | 31.6265i | 0.741132 | − | 1.28368i | −0.210848 | − | 0.977519i | \(-0.567622\pi\) |
0.951980 | − | 0.306160i | \(-0.0990443\pi\) | |||||||
\(608\) | −19.5546 | − | 14.4810i | −0.793046 | − | 0.587283i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.675001i | 0.0273300i | ||||||||
\(611\) | 22.8294 | + | 13.1806i | 0.923579 | + | 0.533229i | ||||
\(612\) | 11.3877 | − | 6.57467i | 0.460319 | − | 0.265765i | ||||
\(613\) | 16.1048 | + | 27.8944i | 0.650468 | + | 1.12664i | 0.983009 | + | 0.183555i | \(0.0587605\pi\) |
−0.332542 | + | 0.943089i | \(0.607906\pi\) | |||||||
\(614\) | −10.3346 | − | 5.96671i | −0.417072 | − | 0.240797i | ||||
\(615\) | − | 2.25268i | − | 0.0908367i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.7646 | −1.39957 | −0.699785 | − | 0.714354i | \(-0.746721\pi\) | ||||
−0.699785 | + | 0.714354i | \(0.746721\pi\) | |||||||
\(618\) | 11.1685 | + | 6.44812i | 0.449262 | + | 0.259381i | ||||
\(619\) | −33.8046 | + | 19.5171i | −1.35872 | + | 0.784458i | −0.989451 | − | 0.144865i | \(-0.953725\pi\) |
−0.369269 | + | 0.929323i | \(0.620392\pi\) | |||||||
\(620\) | 1.29622 | − | 0.748372i | 0.0520574 | − | 0.0300553i | ||||
\(621\) | 16.8011 | − | 29.1004i | 0.674206 | − | 1.16776i | ||||
\(622\) | −20.8945 | −0.837795 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.05672 | −0.0423027 | ||||||||
\(625\) | −11.8822 | + | 20.5806i | −0.475289 | + | 0.823225i | ||||
\(626\) | 9.98808 | + | 17.2999i | 0.399204 | + | 0.691442i | ||||
\(627\) | 2.17010 | + | 0.248076i | 0.0866654 | + | 0.00990719i | ||||
\(628\) | −23.8419 | − | 13.7651i | −0.951395 | − | 0.549288i | ||||
\(629\) | 8.13785 | 0.324477 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.8349 | −1.14790 | −0.573950 | − | 0.818890i | \(-0.694590\pi\) | ||||
−0.573950 | + | 0.818890i | \(0.694590\pi\) | |||||||
\(632\) | 17.1663 | − | 29.7330i | 0.682840 | − | 1.18271i | ||||
\(633\) | −6.04753 | + | 3.49154i | −0.240368 | + | 0.138776i | ||||
\(634\) | 2.52877 | + | 4.37996i | 0.100430 | + | 0.173950i | ||||
\(635\) | −1.62623 | + | 2.81671i | −0.0645349 | + | 0.111778i | ||||
\(636\) | 10.5141i | 0.416910i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.43528 | 0.0964137 | ||||||||
\(639\) | −20.0453 | − | 11.5732i | −0.792980 | − | 0.457827i | ||||
\(640\) | −0.923720 | − | 1.59993i | −0.0365132 | − | 0.0632428i | ||||
\(641\) | 34.5535 | − | 19.9495i | 1.36478 | − | 0.787957i | 0.374526 | − | 0.927216i | \(-0.377805\pi\) |
0.990256 | + | 0.139259i | \(0.0444721\pi\) | |||||||
\(642\) | 2.89829 | − | 5.01999i | 0.114386 | − | 0.198123i | ||||
\(643\) | − | 20.5969i | − | 0.812263i | −0.913815 | − | 0.406132i | \(-0.866877\pi\) | ||
0.913815 | − | 0.406132i | \(-0.133123\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 2.17929i | − | 0.0858094i | ||||||
\(646\) | −8.97639 | − | 20.6655i | −0.353171 | − | 0.813072i | ||||
\(647\) | −1.85762 | + | 1.07250i | −0.0730306 | + | 0.0421642i | −0.536071 | − | 0.844173i | \(-0.680092\pi\) |
0.463040 | + | 0.886337i | \(0.346759\pi\) | |||||||
\(648\) | 0.680218 | − | 0.392724i | 0.0267215 | − | 0.0154277i | ||||
\(649\) | 0.458553 | − | 0.794237i | 0.0179998 | − | 0.0311765i | ||||
\(650\) | − | 27.9996i | − | 1.09823i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.9306 | 0.506402 | ||||||||
\(653\) | −8.38182 | + | 14.5177i | −0.328006 | + | 0.568123i | −0.982116 | − | 0.188276i | \(-0.939710\pi\) |
0.654110 | + | 0.756399i | \(0.273043\pi\) | |||||||
\(654\) | −6.09338 | − | 10.5540i | −0.238270 | − | 0.412696i | ||||
\(655\) | −0.0191095 | − | 0.0330987i | −0.000746671 | − | 0.00129327i | ||||
\(656\) | −0.587581 | + | 1.01772i | −0.0229412 | + | 0.0397353i | ||||
\(657\) | 2.49289i | 0.0972570i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 41.1006i | − | 1.60105i | −0.599297 | − | 0.800527i | \(-0.704553\pi\) | ||
0.599297 | − | 0.800527i | \(-0.295447\pi\) | |||||||
\(660\) | 0.149933 | + | 0.0865636i | 0.00583612 | + | 0.00336948i | ||||
\(661\) | −9.10759 | − | 15.7748i | −0.354244 | − | 0.613569i | 0.632744 | − | 0.774361i | \(-0.281928\pi\) |
−0.986988 | + | 0.160792i | \(0.948595\pi\) | |||||||
\(662\) | 11.7639 | + | 20.3757i | 0.457218 | + | 0.791925i | ||||
\(663\) | 33.5174 | + | 19.3513i | 1.30171 | + | 0.751541i | ||||
\(664\) | −1.79605 | −0.0697003 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.38501 | 0.0924171 | ||||||||
\(667\) | 32.3134 | + | 18.6561i | 1.25118 | + | 0.722368i | ||||
\(668\) | 6.62501 | + | 11.4749i | 0.256329 | + | 0.443975i | ||||
\(669\) | 14.1909 | + | 24.5794i | 0.548653 | + | 0.950295i | ||||
\(670\) | 1.47191 | + | 0.849809i | 0.0568649 | + | 0.0328310i | ||||
\(671\) | − | 1.25027i | − | 0.0482661i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.7582i | 1.37838i | 0.724581 | + | 0.689189i | \(0.242033\pi\) | ||||
−0.724581 | + | 0.689189i | \(0.757967\pi\) | |||||||
\(674\) | 10.6809 | − | 18.4999i | 0.411414 | − | 0.712590i | ||||
\(675\) | −12.6516 | − | 21.9131i | −0.486959 | − | 0.843437i | ||||
\(676\) | −16.5400 | − | 28.6482i | −0.636155 | − | 1.10185i | ||||
\(677\) | 16.2540 | − | 28.1527i | 0.624691 | − | 1.08200i | −0.363909 | − | 0.931434i | \(-0.618558\pi\) |
0.988600 | − | 0.150563i | \(-0.0481085\pi\) | |||||||
\(678\) | −17.5674 | −0.674671 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 4.76103i | − | 0.182577i | ||||||
\(681\) | 11.5560 | − | 20.0155i | 0.442825 | − | 0.766996i | ||||
\(682\) | 1.59898 | − | 0.923169i | 0.0612279 | − | 0.0353500i | ||||
\(683\) | 14.7801 | − | 8.53331i | 0.565546 | − | 0.326518i | −0.189823 | − | 0.981818i | \(-0.560791\pi\) |
0.755368 | + | 0.655300i | \(0.227458\pi\) | |||||||
\(684\) | 3.95019 | + | 9.09413i | 0.151039 | + | 0.347723i | ||||
\(685\) | 5.49749i | 0.210048i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.1457i | 0.387084i | ||||||||
\(688\) | −0.568438 | + | 0.984564i | −0.0216715 | + | 0.0375362i | ||||
\(689\) | 45.9453 | − | 26.5265i | 1.75038 | − | 1.01058i | ||||
\(690\) | −0.883287 | − | 1.52990i | −0.0336262 | − | 0.0582422i | ||||
\(691\) | −18.4114 | − | 10.6298i | −0.700402 | − | 0.404378i | 0.107095 | − | 0.994249i | \(-0.465845\pi\) |
−0.807497 | + | 0.589871i | \(0.799178\pi\) | |||||||
\(692\) | 9.78161 | 0.371841 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 6.18362i | − | 0.234727i | ||||||
\(695\) | −2.58491 | + | 4.47720i | −0.0980513 | + | 0.169830i | ||||
\(696\) | −8.59541 | − | 14.8877i | −0.325808 | − | 0.564316i | ||||
\(697\) | 37.2741 | − | 21.5202i | 1.41186 | − | 0.815137i | ||||
\(698\) | −5.87010 | + | 10.1673i | −0.222186 | + | 0.384838i | ||||
\(699\) | 10.6409 | 0.402474 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 47.7171 | 1.80225 | 0.901126 | − | 0.433558i | \(-0.142742\pi\) | ||||
0.901126 | + | 0.433558i | \(0.142742\pi\) | |||||||
\(702\) | 25.3761 | + | 14.6509i | 0.957760 | + | 0.552963i | ||||
\(703\) | −0.696921 | + | 6.09647i | −0.0262849 | + | 0.229933i | ||||
\(704\) | −1.26481 | − | 2.19071i | −0.0476693 | − | 0.0825656i | ||||
\(705\) | 0.626210 | − | 1.08463i | 0.0235845 | − | 0.0408495i | ||||
\(706\) | 19.1329 | 0.720076 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.42834 | −0.0912625 | ||||||||
\(709\) | 2.40313 | − | 4.16234i | 0.0902514 | − | 0.156320i | −0.817365 | − | 0.576120i | \(-0.804566\pi\) |
0.907617 | + | 0.419800i | \(0.137900\pi\) | |||||||
\(710\) | −2.72240 | + | 1.57178i | −0.102170 | + | 0.0589878i | ||||
\(711\) | −19.6864 | + | 11.3660i | −0.738298 | + | 0.426257i | ||||
\(712\) | 3.83786 | + | 2.21579i | 0.143830 | + | 0.0830402i | ||||
\(713\) | 28.2887 | 1.05942 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 0.873584i | − | 0.0326702i | ||||||
\(716\) | −10.2344 | − | 5.90882i | −0.382477 | − | 0.220823i | ||||
\(717\) | 13.8972 | + | 24.0707i | 0.519001 | + | 0.898937i | ||||
\(718\) | −8.53308 | + | 4.92657i | −0.318452 | + | 0.183858i | ||||
\(719\) | −24.3098 | − | 14.0353i | −0.906604 | − | 0.523428i | −0.0272673 | − | 0.999628i | \(-0.508681\pi\) |
−0.879337 | + | 0.476200i | \(0.842014\pi\) | |||||||
\(720\) | − | 0.0860697i | − | 0.00320763i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 16.2503 | − | 4.95489i | 0.604773 | − | 0.184402i | ||||
\(723\) | −3.02029 | + | 5.23129i | −0.112326 | + | 0.194554i | ||||
\(724\) | 1.98024 | + | 3.42987i | 0.0735949 | + | 0.127470i | ||||
\(725\) | 24.3326 | − | 14.0484i | 0.903689 | − | 0.521745i | ||||
\(726\) | −8.76996 | − | 5.06334i | −0.325484 | − | 0.187918i | ||||
\(727\) | − | 11.6510i | − | 0.432111i | −0.976381 | − | 0.216055i | \(-0.930681\pi\) | ||
0.976381 | − | 0.216055i | \(-0.0693192\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.7095 | 0.581833 | ||||||||
\(730\) | 0.293206 | + | 0.169283i | 0.0108521 | + | 0.00626544i | ||||
\(731\) | 36.0598 | − | 20.8191i | 1.33372 | − | 0.770023i | ||||
\(732\) | −2.86698 | + | 1.65525i | −0.105967 | + | 0.0611798i | ||||
\(733\) | 0.738349 | + | 0.426286i | 0.0272715 | + | 0.0157452i | 0.513574 | − | 0.858045i | \(-0.328321\pi\) |
−0.486302 | + | 0.873791i | \(0.661655\pi\) | |||||||
\(734\) | 22.2489 | 0.821221 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 36.4523i | − | 1.34365i | ||||||
\(737\) | −2.72635 | − | 1.57406i | −0.100426 | − | 0.0579812i | ||||
\(738\) | 10.9241 | − | 6.30705i | 0.402123 | − | 0.232166i | ||||
\(739\) | −12.4593 | − | 21.5802i | −0.458324 | − | 0.793841i | 0.540548 | − | 0.841313i | \(-0.318217\pi\) |
−0.998873 | + | 0.0474723i | \(0.984883\pi\) | |||||||
\(740\) | −0.243184 | + | 0.421207i | −0.00893962 | + | 0.0154839i | ||||
\(741\) | −17.3674 | + | 23.4523i | −0.638008 | + | 0.861542i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.5921i | − | 0.498646i | −0.968420 | − | 0.249323i | \(-0.919792\pi\) | ||
0.968420 | − | 0.249323i | \(-0.0802080\pi\) | |||||||
\(744\) | −11.2873 | − | 6.51671i | −0.413811 | − | 0.238914i | ||||
\(745\) | 1.38582 | − | 0.800102i | 0.0507724 | − | 0.0293135i | ||||
\(746\) | −2.67400 | − | 4.63150i | −0.0979020 | − | 0.169571i | ||||
\(747\) | 1.02986 | + | 0.594589i | 0.0376805 | + | 0.0217549i | ||||
\(748\) | 3.30783i | 0.120946i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.68294 | −0.0979669 | ||||||||
\(751\) | 26.5760 | + | 15.3437i | 0.969772 | + | 0.559898i | 0.899167 | − | 0.437606i | \(-0.144174\pi\) |
0.0706054 | + | 0.997504i | \(0.477507\pi\) | |||||||
\(752\) | −0.565822 | + | 0.326677i | −0.0206334 | + | 0.0119127i | ||||
\(753\) | 5.25389 | − | 3.03333i | 0.191462 | − | 0.110541i | ||||
\(754\) | −16.2685 | + | 28.1779i | −0.592465 | + | 1.02618i | ||||
\(755\) | −2.80436 | −0.102061 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.7950 | −1.22830 | −0.614150 | − | 0.789189i | \(-0.710501\pi\) | ||||
−0.614150 | + | 0.789189i | \(0.710501\pi\) | |||||||
\(758\) | 1.78140 | − | 3.08548i | 0.0647034 | − | 0.112070i | ||||
\(759\) | 1.63607 | + | 2.83375i | 0.0593855 | + | 0.102859i | ||||
\(760\) | 3.56673 | + | 0.407732i | 0.129379 | + | 0.0147900i | ||||
\(761\) | 28.5566 | + | 16.4871i | 1.03517 | + | 0.597658i | 0.918463 | − | 0.395507i | \(-0.129431\pi\) |
0.116712 | + | 0.993166i | \(0.462765\pi\) | |||||||
\(762\) | 10.6234 | 0.384846 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 13.5817 | 0.491370 | ||||||||
\(765\) | −1.57616 | + | 2.72998i | −0.0569861 | + | 0.0987028i | ||||
\(766\) | −7.88631 | + | 4.55316i | −0.284944 | + | 0.164512i | ||||
\(767\) | 6.12658 | + | 10.6116i | 0.221218 | + | 0.383161i | ||||
\(768\) | −8.59650 | + | 14.8896i | −0.310199 | + | 0.537281i | ||||
\(769\) | − | 39.5435i | − | 1.42598i | −0.701176 | − | 0.712988i | \(-0.747341\pi\) | ||
0.701176 | − | 0.712988i | \(-0.252659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.1293 | 0.868996 | ||||||||
\(772\) | 15.7905 | + | 9.11667i | 0.568314 | + | 0.328116i | ||||
\(773\) | −9.89411 | − | 17.1371i | −0.355866 | − | 0.616379i | 0.631400 | − | 0.775458i | \(-0.282481\pi\) |
−0.987266 | + | 0.159079i | \(0.949147\pi\) | |||||||
\(774\) | 10.5682 | − | 6.10158i | 0.379868 | − | 0.219317i | ||||
\(775\) | 10.6510 | − | 18.4480i | 0.382594 | − | 0.662673i | ||||
\(776\) | − | 3.89677i | − | 0.139886i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 9.94073i | − | 0.356393i | ||||||
\(779\) | 12.9298 | + | 29.7669i | 0.463256 | + | 1.06651i | ||||
\(780\) | −2.00320 | + | 1.15655i | −0.0717262 | + | 0.0414111i | ||||
\(781\) | 5.04257 | − | 2.91133i | 0.180437 | − | 0.104175i | ||||
\(782\) | 16.8764 | − | 29.2308i | 0.603499 | − | 1.04529i | ||||
\(783\) | 29.4036i | 1.05080i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.59987 | 0.235560 | ||||||||
\(786\) | −0.0624171 | + | 0.108110i | −0.00222634 | + | 0.00385614i | ||||
\(787\) | −8.72110 | − | 15.1054i | −0.310874 | − | 0.538449i | 0.667678 | − | 0.744450i | \(-0.267288\pi\) |
−0.978552 | + | 0.206001i | \(0.933955\pi\) | |||||||
\(788\) | −6.38964 | − | 11.0672i | −0.227621 | − | 0.394252i | ||||
\(789\) | −2.29019 | + | 3.96673i | −0.0815329 | + | 0.141219i | ||||
\(790\) | 3.08728i | 0.109840i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.58452i | 0.0918371i | ||||||||
\(793\) | 14.4665 | + | 8.35224i | 0.513720 | + | 0.296597i | ||||
\(794\) | −14.1422 | − | 24.4950i | −0.501887 | − | 0.869294i | ||||
\(795\) | −1.26028 | − | 2.18287i | −0.0446975 | − | 0.0774183i | ||||
\(796\) | −19.2579 | − | 11.1185i | −0.682577 | − | 0.394086i | ||||
\(797\) | −23.8795 | −0.845854 | −0.422927 | − | 0.906164i | \(-0.638997\pi\) | ||||
−0.422927 | + | 0.906164i | \(0.638997\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.9292 | 0.846554 | ||||||||
\(800\) | −23.7718 | − | 13.7246i | −0.840458 | − | 0.485239i | ||||
\(801\) | −1.46709 | − | 2.54108i | −0.0518371 | − | 0.0897845i | ||||
\(802\) | 8.14483 | + | 14.1073i | 0.287604 | + | 0.498144i | ||||
\(803\) | −0.543092 | − | 0.313554i | −0.0191653 | − | 0.0110651i | ||||
\(804\) | 8.33567i | 0.293976i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 24.6683i | 0.868905i | ||||||||
\(807\) | −2.19307 | + | 3.79850i | −0.0771996 | + | 0.133714i | ||||
\(808\) | 4.77591 | + | 8.27212i | 0.168016 | + | 0.291012i | ||||
\(809\) | 8.26901 | + | 14.3223i | 0.290723 | + | 0.503547i | 0.973981 | − | 0.226630i | \(-0.0727709\pi\) |
−0.683258 | + | 0.730177i | \(0.739438\pi\) | |||||||
\(810\) | −0.0353147 | + | 0.0611668i | −0.00124083 | + | 0.00214918i | ||||
\(811\) | −35.1379 | −1.23386 | −0.616930 | − | 0.787018i | \(-0.711624\pi\) | ||||
−0.616930 | + | 0.787018i | \(0.711624\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 28.8277i | − | 1.01103i | ||||||
\(814\) | −0.299984 | + | 0.519588i | −0.0105144 | + | 0.0182116i | ||||
\(815\) | −2.68457 | + | 1.54994i | −0.0940365 | + | 0.0542920i | ||||
\(816\) | −0.830720 | + | 0.479617i | −0.0290810 | + | 0.0167899i | ||||
\(817\) | 12.5085 | + | 28.7971i | 0.437618 | + | 1.00748i | ||||
\(818\) | − | 4.76122i | − | 0.166472i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.57236i | 0.0898307i | ||||||||
\(821\) | −25.0660 | + | 43.4156i | −0.874809 | + | 1.51521i | −0.0178426 | + | 0.999841i | \(0.505680\pi\) |
−0.856966 | + | 0.515373i | \(0.827654\pi\) | |||||||
\(822\) | 15.5506 | − | 8.97817i | 0.542391 | − | 0.313150i | ||||
\(823\) | 3.09005 | + | 5.35212i | 0.107712 | + | 0.186563i | 0.914843 | − | 0.403810i | \(-0.132314\pi\) |
−0.807131 | + | 0.590373i | \(0.798981\pi\) | |||||||
\(824\) | −34.0004 | − | 19.6301i | −1.18446 | − | 0.683848i | ||||
\(825\) | 2.46398 | 0.0857848 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.4829i | 1.37296i | 0.727151 | + | 0.686478i | \(0.240844\pi\) | ||||
−0.727151 | + | 0.686478i | \(0.759156\pi\) | |||||||
\(828\) | −7.42669 | + | 12.8634i | −0.258095 | + | 0.447034i | ||||
\(829\) | 7.17020 | + | 12.4192i | 0.249031 | + | 0.431335i | 0.963257 | − | 0.268580i | \(-0.0865544\pi\) |
−0.714226 | + | 0.699915i | \(0.753221\pi\) | |||||||
\(830\) | 0.139868 | − | 0.0807525i | 0.00485487 | − | 0.00280296i | ||||
\(831\) | 0.836052 | − | 1.44809i | 0.0290023 | − | 0.0502335i | ||||
\(832\) | 33.7974 | 1.17171 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.8861 | 0.584717 | ||||||||
\(835\) | −2.75089 | − | 1.58822i | −0.0951983 | − | 0.0549628i | ||||
\(836\) | −2.47806 | − | 0.283281i | −0.0857056 | − | 0.00979747i | ||||
\(837\) | 11.1463 | + | 19.3060i | 0.385274 | + | 0.667314i | ||||
\(838\) | 3.61859 | − | 6.26757i | 0.125002 | − | 0.216510i | ||||
\(839\) | −38.1902 | −1.31847 | −0.659237 | − | 0.751935i | \(-0.729121\pi\) | ||||
−0.659237 | + | 0.751935i | \(0.729121\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.65007 | −0.125864 | ||||||||
\(842\) | −11.3976 | + | 19.7411i | −0.392786 | + | 0.680325i | ||||
\(843\) | 26.6070 | − | 15.3616i | 0.916394 | − | 0.529080i | ||||
\(844\) | 6.90575 | − | 3.98704i | 0.237706 | − | 0.137239i | ||||
\(845\) | 6.86787 | + | 3.96517i | 0.236262 | + | 0.136406i | ||||
\(846\) | 7.01306 | 0.241114 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.31491i | 0.0451541i | ||||||||
\(849\) | −12.8843 | − | 7.43876i | −0.442189 | − | 0.255298i | ||||
\(850\) | −12.7082 | − | 22.0113i | −0.435889 | − | 0.754982i | ||||
\(851\) | −7.96089 | + | 4.59622i | −0.272896 | + | 0.157556i | ||||
\(852\) | −13.3518 | − | 7.70869i | −0.457427 | − | 0.264095i | ||||
\(853\) | 42.6408i | 1.45999i | 0.683450 | + | 0.729997i | \(0.260479\pi\) | ||||
−0.683450 | + | 0.729997i | \(0.739521\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.91019 | − | 1.41457i | −0.0653270 | − | 0.0483774i | ||||
\(856\) | −8.82333 | + | 15.2825i | −0.301575 | + | 0.522344i | ||||
\(857\) | −15.7382 | − | 27.2594i | −0.537607 | − | 0.931162i | −0.999032 | − | 0.0439830i | \(-0.985995\pi\) |
0.461426 | − | 0.887179i | \(-0.347338\pi\) | |||||||
\(858\) | −2.47109 | + | 1.42668i | −0.0843616 | + | 0.0487062i | ||||
\(859\) | −9.72197 | − | 5.61298i | −0.331709 | − | 0.191512i | 0.324890 | − | 0.945752i | \(-0.394673\pi\) |
−0.656600 | + | 0.754239i | \(0.728006\pi\) | |||||||
\(860\) | 2.48856i | 0.0848591i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.74430 | 0.195652 | ||||||||
\(863\) | 20.2175 | + | 11.6726i | 0.688210 | + | 0.397338i | 0.802941 | − | 0.596058i | \(-0.203267\pi\) |
−0.114731 | + | 0.993397i | \(0.536601\pi\) | |||||||
\(864\) | 24.8774 | − | 14.3629i | 0.846345 | − | 0.488637i | ||||
\(865\) | −2.03080 | + | 1.17248i | −0.0690492 | + | 0.0398656i | ||||
\(866\) | 18.7597 | + | 10.8309i | 0.637479 | + | 0.368049i | ||||
\(867\) | 17.2599 | 0.586178 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 5.71841i | − | 0.193984i | ||||||
\(870\) | 1.33874 | + | 0.772920i | 0.0453874 | + | 0.0262044i | ||||
\(871\) | 36.4259 | − | 21.0305i | 1.23424 | − | 0.712591i | ||||
\(872\) | 18.5502 | + | 32.1299i | 0.628189 | + | 1.08806i | ||||
\(873\) | −1.29004 | + | 2.23442i | −0.0436613 | + | 0.0756236i | ||||
\(874\) | 20.4530 | + | 15.1463i | 0.691832 | + | 0.512330i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.66047i | 0.0561022i | ||||||||
\(877\) | −0.0709141 | − | 0.0409423i | −0.00239460 | − | 0.00138252i | 0.498802 | − | 0.866716i | \(-0.333773\pi\) |
−0.501197 | + | 0.865333i | \(0.667107\pi\) | |||||||
\(878\) | −1.42010 | + | 0.819893i | −0.0479259 | + | 0.0276700i | ||||
\(879\) | −4.21017 | − | 7.29223i | −0.142005 | − | 0.245961i | ||||
\(880\) | 0.0187508 | + | 0.0108258i | 0.000632090 | + | 0.000364937i | ||||
\(881\) | 4.56861i | 0.153920i | 0.997034 | + | 0.0769602i | \(0.0245215\pi\) | ||||
−0.997034 | + | 0.0769602i | \(0.975479\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.5387 | −1.29693 | −0.648466 | − | 0.761244i | \(-0.724589\pi\) | ||||
−0.648466 | + | 0.761244i | \(0.724589\pi\) | |||||||
\(884\) | −38.2739 | − | 22.0974i | −1.28729 | − | 0.743217i | ||||
\(885\) | 0.504156 | − | 0.291075i | 0.0169470 | − | 0.00978437i | ||||
\(886\) | −8.28748 | + | 4.78478i | −0.278423 | + | 0.160748i | ||||
\(887\) | −9.31331 | + | 16.1311i | −0.312710 | + | 0.541630i | −0.978948 | − | 0.204109i | \(-0.934570\pi\) |
0.666238 | + | 0.745739i | \(0.267904\pi\) | |||||||
\(888\) | 4.23522 | 0.142125 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.398498 | −0.0133577 | ||||||||
\(891\) | 0.0654117 | − | 0.113296i | 0.00219137 | − | 0.00379557i | ||||
\(892\) | −16.2048 | − | 28.0675i | −0.542577 | − | 0.939770i | ||||
\(893\) | −2.04928 | + | 17.9266i | −0.0685766 | + | 0.599890i | ||||
\(894\) | −4.52647 | − | 2.61336i | −0.151388 | − | 0.0874037i | ||||
\(895\) | 2.83306 | 0.0946989 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −43.7180 | −1.45970 | ||||||||
\(898\) | 8.79392 | − | 15.2315i | 0.293457 | − | 0.508282i | ||||
\(899\) | −21.4376 | + | 12.3770i | −0.714985 | + | 0.412797i | ||||
\(900\) | 5.59244 | + | 9.68639i | 0.186415 | + | 0.322880i | ||||
\(901\) | 24.0793 | − | 41.7066i | 0.802199 | − | 1.38945i | ||||
\(902\) | 3.17319i | 0.105656i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 53.4807 | 1.77874 | ||||||||
\(905\) | −0.822249 | − | 0.474726i | −0.0273325 | − | 0.0157804i | ||||
\(906\) | 4.57991 | + | 7.93263i | 0.152157 | + | 0.263544i | ||||
\(907\) | −22.0220 | + | 12.7144i | −0.731227 | + | 0.422174i | −0.818871 | − | 0.573978i | \(-0.805400\pi\) |
0.0876439 | + | 0.996152i | \(0.472066\pi\) | |||||||
\(908\) | −13.1959 | + | 22.8560i | −0.437921 | + | 0.758502i | ||||
\(909\) | − | 6.32433i | − | 0.209765i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7634i | 0.687921i | 0.938984 | + | 0.343961i | \(0.111769\pi\) | ||||
−0.938984 | + | 0.343961i | \(0.888231\pi\) | |||||||
\(912\) | −0.288163 | − | 0.663409i | −0.00954202 | − | 0.0219677i | ||||
\(913\) | −0.259070 | + | 0.149574i | −0.00857395 | + | 0.00495017i | ||||
\(914\) | −7.29243 | + | 4.21028i | −0.241212 | + | 0.139264i | ||||
\(915\) | 0.396816 | − | 0.687305i | 0.0131183 | − | 0.0227216i | ||||
\(916\) | − | 11.5855i | − | 0.382797i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 26.5986 | 0.877884 | ||||||||
\(919\) | −11.4561 | + | 19.8425i | −0.377901 | + | 0.654544i | −0.990757 | − | 0.135651i | \(-0.956687\pi\) |
0.612856 | + | 0.790195i | \(0.290021\pi\) | |||||||
\(920\) | 2.68901 | + | 4.65750i | 0.0886540 | + | 0.153553i | ||||
\(921\) | 7.01536 | + | 12.1510i | 0.231164 | + | 0.400388i | ||||
\(922\) | −12.6928 | + | 21.9846i | −0.418017 | + | 0.724026i | ||||
\(923\) | 77.7947i | 2.56064i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.92208i | 0.227597i | ||||||||
\(926\) | 19.4848 | + | 11.2496i | 0.640310 | + | 0.369683i | ||||
\(927\) | 12.9973 | + | 22.5119i | 0.426886 | + | 0.739388i | ||||
\(928\) | 15.9488 | + | 27.6241i | 0.523544 | + | 0.906805i | ||||
\(929\) | 29.7938 | + | 17.2015i | 0.977504 | + | 0.564362i | 0.901516 | − | 0.432746i | \(-0.142455\pi\) |
0.0759886 | + | 0.997109i | \(0.475789\pi\) | |||||||
\(930\) | 1.17200 | 0.0384313 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.1509 | −0.398017 | ||||||||
\(933\) | 21.2754 | + | 12.2834i | 0.696526 | + | 0.402139i | ||||
\(934\) | −7.39679 | − | 12.8116i | −0.242030 | − | 0.419209i | ||||
\(935\) | −0.396496 | − | 0.686751i | −0.0129668 | − | 0.0224592i | ||||
\(936\) | −29.9047 | − | 17.2655i | −0.977467 | − | 0.564341i | ||||
\(937\) | − | 27.7349i | − | 0.906058i | −0.891496 | − | 0.453029i | \(-0.850343\pi\) | ||
0.891496 | − | 0.453029i | \(-0.149657\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 23.4870i | − | 0.766468i | ||||||
\(940\) | −0.715078 | + | 1.23855i | −0.0233233 | + | 0.0403971i | ||||
\(941\) | −27.5423 | − | 47.7046i | −0.897853 | − | 1.55513i | −0.830234 | − | 0.557416i | \(-0.811793\pi\) |
−0.0676192 | − | 0.997711i | \(-0.521540\pi\) | |||||||
\(942\) | −10.7785 | − | 18.6689i | −0.351183 | − | 0.608267i | ||||
\(943\) | −24.3091 | + | 42.1045i | −0.791612 | + | 1.37111i | ||||
\(944\) | −0.303692 | −0.00988433 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.06981i | 0.0998081i | ||||||||
\(947\) | −29.4083 | + | 50.9367i | −0.955641 | + | 1.65522i | −0.222747 | + | 0.974876i | \(0.571502\pi\) |
−0.732894 | + | 0.680343i | \(0.761831\pi\) | |||||||
\(948\) | −13.1128 | + | 7.57068i | −0.425884 | + | 0.245884i | ||||
\(949\) | 7.25608 | − | 4.18930i | 0.235542 | − | 0.135990i | ||||
\(950\) | 17.5781 | − | 7.63535i | 0.570310 | − | 0.247723i | ||||
\(951\) | − | 5.94640i | − | 0.192825i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.64330i | 0.118018i | 0.998257 | + | 0.0590090i | \(0.0187941\pi\) | ||||
−0.998257 | + | 0.0590090i | \(0.981206\pi\) | |||||||
\(954\) | 7.05706 | − | 12.2232i | 0.228481 | − | 0.395740i | ||||
\(955\) | −2.81976 | + | 1.62799i | −0.0912452 | + | 0.0526804i | ||||
\(956\) | −15.8694 | − | 27.4866i | −0.513254 | − | 0.888981i | ||||
\(957\) | −2.47967 | − | 1.43164i | −0.0801565 | − | 0.0462784i | ||||
\(958\) | −5.81702 | −0.187940 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | − | 1.60572i | − | 0.0518244i | ||||||
\(961\) | 6.11622 | − | 10.5936i | 0.197298 | − | 0.341729i | ||||
\(962\) | −4.00800 | − | 6.94205i | −0.129223 | − | 0.223821i | ||||
\(963\) | 10.1186 | − | 5.84199i | 0.326068 | − | 0.188256i | ||||
\(964\) | 3.44890 | − | 5.97368i | 0.111082 | − | 0.192399i | ||||
\(965\) | −4.37111 | −0.140711 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.538006 | 0.0173011 | 0.00865055 | − | 0.999963i | \(-0.497246\pi\) | ||||
0.00865055 | + | 0.999963i | \(0.497246\pi\) | |||||||
\(968\) | 26.6986 | + | 15.4144i | 0.858124 | + | 0.495438i | ||||
\(969\) | −3.00869 | + | 26.3192i | −0.0966529 | + | 0.845494i | ||||
\(970\) | 0.175204 | + | 0.303462i | 0.00562545 | + | 0.00974356i | ||||
\(971\) | −27.0391 | + | 46.8330i | −0.867725 | + | 1.50294i | −0.00340911 | + | 0.999994i | \(0.501085\pi\) |
−0.864316 | + | 0.502949i | \(0.832248\pi\) | |||||||
\(972\) | −18.8791 | −0.605548 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.06178 | −0.162190 | ||||||||
\(975\) | −16.4602 | + | 28.5100i | −0.527150 | + | 0.913050i | ||||
\(976\) | −0.358549 | + | 0.207008i | −0.0114769 | + | 0.00662617i | ||||
\(977\) | 39.8029 | − | 22.9802i | 1.27341 | − | 0.735202i | 0.297780 | − | 0.954634i | \(-0.403754\pi\) |
0.975628 | + | 0.219432i | \(0.0704204\pi\) | |||||||
\(978\) | 8.76857 | + | 5.06253i | 0.280388 | + | 0.161882i | ||||
\(979\) | 0.738118 | 0.0235904 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 24.5644i | − | 0.784282i | ||||||
\(982\) | 14.7570 | + | 8.51994i | 0.470914 | + | 0.271882i | ||||
\(983\) | 4.26160 | + | 7.38130i | 0.135924 | + | 0.235427i | 0.925950 | − | 0.377646i | \(-0.123266\pi\) |
−0.790026 | + | 0.613073i | \(0.789933\pi\) | |||||||
\(984\) | 19.3987 | − | 11.1999i | 0.618409 | − | 0.357039i | ||||
\(985\) | 2.65315 | + | 1.53180i | 0.0845365 | + | 0.0488072i | ||||
\(986\) | 29.5353i | 0.940597i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 19.8321 | − | 26.7805i | 0.630942 | − | 0.852001i | ||||
\(989\) | −23.5171 | + | 40.7328i | −0.747800 | + | 1.29523i | ||||
\(990\) | −0.116203 | − | 0.201270i | −0.00369318 | − | 0.00639678i | ||||
\(991\) | 40.0810 | − | 23.1408i | 1.27321 | − | 0.735091i | 0.297623 | − | 0.954683i | \(-0.403806\pi\) |
0.975592 | + | 0.219593i | \(0.0704728\pi\) | |||||||
\(992\) | 20.9435 | + | 12.0917i | 0.664957 | + | 0.383913i | ||||
\(993\) | − | 27.6629i | − | 0.877855i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.33093 | 0.169002 | ||||||||
\(996\) | 0.685972 | + | 0.396046i | 0.0217358 | + | 0.0125492i | ||||
\(997\) | 23.0463 | − | 13.3058i | 0.729883 | − | 0.421398i | −0.0884962 | − | 0.996077i | \(-0.528206\pi\) |
0.818379 | + | 0.574678i | \(0.194873\pi\) | |||||||
\(998\) | 0.806063 | − | 0.465381i | 0.0255155 | − | 0.0147314i | ||||
\(999\) | −6.27351 | − | 3.62201i | −0.198485 | − | 0.114595i |
(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 | 931.2.o.i.607.14 | 80 | ||
7.2 | even | 3 | 931.2.c.f.930.27 | yes | 40 | ||
7.3 | odd | 6 | inner | 931.2.o.i.227.27 | 80 | ||
7.4 | even | 3 | inner | 931.2.o.i.227.28 | 80 | ||
7.5 | odd | 6 | 931.2.c.f.930.28 | yes | 40 | ||
7.6 | odd | 2 | inner | 931.2.o.i.607.13 | 80 | ||
19.18 | odd | 2 | inner | 931.2.o.i.607.27 | 80 | ||
133.18 | odd | 6 | inner | 931.2.o.i.227.13 | 80 | ||
133.37 | odd | 6 | 931.2.c.f.930.14 | yes | 40 | ||
133.75 | even | 6 | 931.2.c.f.930.13 | ✓ | 40 | ||
133.94 | even | 6 | inner | 931.2.o.i.227.14 | 80 | ||
133.132 | even | 2 | inner | 931.2.o.i.607.28 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
931.2.c.f.930.13 | ✓ | 40 | 133.75 | even | 6 | ||
931.2.c.f.930.14 | yes | 40 | 133.37 | odd | 6 | ||
931.2.c.f.930.27 | yes | 40 | 7.2 | even | 3 | ||
931.2.c.f.930.28 | yes | 40 | 7.5 | odd | 6 | ||
931.2.o.i.227.13 | 80 | 133.18 | odd | 6 | inner | ||
931.2.o.i.227.14 | 80 | 133.94 | even | 6 | inner | ||
931.2.o.i.227.27 | 80 | 7.3 | odd | 6 | inner | ||
931.2.o.i.227.28 | 80 | 7.4 | even | 3 | inner | ||
931.2.o.i.607.13 | 80 | 7.6 | odd | 2 | inner | ||
931.2.o.i.607.14 | 80 | 1.1 | even | 1 | trivial | ||
931.2.o.i.607.27 | 80 | 19.18 | odd | 2 | inner | ||
931.2.o.i.607.28 | 80 | 133.132 | even | 2 | inner |