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: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 616) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.3 | ||
Root | \(0.222521 + 0.385418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.529 |
Dual form | 1232.2.q.i.177.3 |
$q$-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 \(\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times\).
\(n\) | \(309\) | \(353\) | \(463\) | \(673\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −0.0990311 | + | 0.171527i | −0.0571757 | + | 0.0990311i | −0.893197 | − | 0.449667i | \(-0.851543\pi\) |
0.836021 | + | 0.548698i | \(0.184876\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.96950 | + | 3.41127i | 0.880787 | + | 1.52557i | 0.850467 | + | 0.526028i | \(0.176319\pi\) |
0.0303204 | + | 0.999540i | \(0.490347\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.167563 | + | 2.64044i | −0.0633328 | + | 0.997992i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.48039 | + | 2.56410i | 0.493462 | + | 0.854701i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.692021 | 0.191932 | 0.0959661 | − | 0.995385i | \(-0.469406\pi\) | ||||
0.0959661 | + | 0.995385i | \(0.469406\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.780167 | −0.201438 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.425428 | + | 0.736862i | −0.103181 | + | 0.178715i | −0.912994 | − | 0.407974i | \(-0.866236\pi\) |
0.809812 | + | 0.586689i | \(0.199569\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.376510 | + | 0.652135i | 0.0863774 | + | 0.149610i | 0.905977 | − | 0.423326i | \(-0.139138\pi\) |
−0.819600 | + | 0.572936i | \(0.805804\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.436313 | − | 0.290227i | −0.0952112 | − | 0.0633328i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.321552 | − | 0.556945i | −0.0670482 | − | 0.116131i | 0.830552 | − | 0.556940i | \(-0.188025\pi\) |
−0.897601 | + | 0.440809i | \(0.854691\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.25786 | + | 9.10689i | −1.05157 | + | 1.82138i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.18060 | −0.227207 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.43296 | 1.00888 | 0.504438 | − | 0.863448i | \(-0.331700\pi\) | ||||
0.504438 | + | 0.863448i | \(0.331700\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.22252 | − | 5.58157i | 0.578782 | − | 1.00248i | −0.416838 | − | 0.908981i | \(-0.636862\pi\) |
0.995619 | − | 0.0934986i | \(-0.0298051\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.0990311 | + | 0.171527i | 0.0172391 | + | 0.0298590i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.33728 | + | 4.62874i | −1.57829 | + | 0.782401i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.04892 | − | 8.74498i | −0.830037 | − | 1.43767i | −0.898008 | − | 0.439979i | \(-0.854986\pi\) |
0.0679713 | − | 0.997687i | \(-0.478347\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0685317 | + | 0.118700i | −0.0109738 | + | 0.0190073i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.89977 | 0.296695 | 0.148347 | − | 0.988935i | \(-0.452605\pi\) | ||||
0.148347 | + | 0.988935i | \(0.452605\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.97823 | −0.454176 | −0.227088 | − | 0.973874i | \(-0.572920\pi\) | ||||
−0.227088 | + | 0.973874i | \(0.572920\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.83124 | + | 10.1000i | −0.869270 | + | 1.50562i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.33728 | − | 10.9765i | −0.924388 | − | 1.60109i | −0.792543 | − | 0.609816i | \(-0.791243\pi\) |
−0.131844 | − | 0.991270i | \(-0.542090\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.94385 | − | 0.884879i | −0.991978 | − | 0.126411i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.0842611 | − | 0.145945i | −0.0117989 | − | 0.0204363i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.01089 | − | 1.75090i | 0.138856 | − | 0.240505i | −0.788208 | − | 0.615409i | \(-0.788991\pi\) |
0.927064 | + | 0.374904i | \(0.122324\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.93900 | 0.531135 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.149145 | −0.0197547 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.86778 | + | 6.69919i | −0.503542 | + | 0.872161i | 0.496449 | + | 0.868066i | \(0.334637\pi\) |
−0.999992 | + | 0.00409502i | \(0.998697\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.74094 | + | 8.21155i | 0.607015 | + | 1.05138i | 0.991730 | + | 0.128345i | \(0.0409666\pi\) |
−0.384715 | + | 0.923036i | \(0.625700\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.01842 | + | 3.47922i | −0.884238 | + | 0.438341i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.36294 | + | 2.36068i | 0.169051 | + | 0.292806i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.40581 | + | 7.63109i | −0.538256 | + | 0.932286i | 0.460742 | + | 0.887534i | \(0.347583\pi\) |
−0.998998 | + | 0.0447524i | \(0.985750\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.127375 | 0.0153341 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.313355 | 0.0371884 | 0.0185942 | − | 0.999827i | \(-0.494081\pi\) | ||||
0.0185942 | + | 0.999827i | \(0.494081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.00484 | − | 13.8648i | 0.936896 | − | 1.62275i | 0.165679 | − | 0.986180i | \(-0.447018\pi\) |
0.771217 | − | 0.636572i | \(-0.219648\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.04138 | − | 1.80373i | −0.120249 | − | 0.208277i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.20291 | + | 1.46533i | 0.251045 | + | 0.166990i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.77748 | + | 6.54279i | 0.425000 | + | 0.736121i | 0.996420 | − | 0.0845363i | \(-0.0269409\pi\) |
−0.571421 | + | 0.820657i | \(0.693608\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.32424 | + | 7.48980i | −0.480471 | + | 0.832200i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.1685 | 1.44543 | 0.722717 | − | 0.691145i | \(-0.242893\pi\) | ||||
0.722717 | + | 0.691145i | \(0.242893\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.35152 | −0.363523 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.538032 | + | 0.931899i | −0.0576831 | + | 0.0999101i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.530499 | − | 0.918852i | −0.0562328 | − | 0.0973981i | 0.836539 | − | 0.547908i | \(-0.184576\pi\) |
−0.892771 | + | 0.450510i | \(0.851242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.115957 | + | 1.82724i | −0.0121556 | + | 0.191547i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.638260 | + | 1.10550i | 0.0661845 | + | 0.114635i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.48307 | + | 2.56876i | −0.152160 | + | 0.263549i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.85623 | 0.594610 | 0.297305 | − | 0.954783i | \(-0.403912\pi\) | ||||
0.297305 | + | 0.954783i | \(0.403912\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.96077 | 0.297569 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.78836 | − | 10.0257i | 0.575964 | − | 0.997599i | −0.419972 | − | 0.907537i | \(-0.637960\pi\) |
0.995936 | − | 0.0900616i | \(-0.0287064\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.83728 | + | 4.91432i | 0.279566 | + | 0.484222i | 0.971277 | − | 0.237952i | \(-0.0764762\pi\) |
−0.691711 | + | 0.722174i | \(0.743143\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.130727 | − | 2.05999i | 0.0127577 | − | 0.201034i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.73221 | + | 9.92848i | 0.554154 | + | 0.959822i | 0.997969 | + | 0.0637039i | \(0.0202913\pi\) |
−0.443815 | + | 0.896118i | \(0.646375\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.01842 | + | 13.8883i | −0.768025 | + | 1.33026i | 0.170607 | + | 0.985339i | \(0.445427\pi\) |
−0.938632 | + | 0.344919i | \(0.887906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.6189 | −1.46931 | −0.734653 | − | 0.678443i | \(-0.762655\pi\) | ||||
−0.734653 | + | 0.678443i | \(0.762655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.26659 | − | 2.19381i | 0.118110 | − | 0.204573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.02446 | + | 1.77441i | 0.0947112 | + | 0.164045i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.87435 | − | 1.24679i | −0.171822 | − | 0.114293i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.188137 | + | 0.325862i | −0.0169637 | + | 0.0293820i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −21.7265 | −1.94327 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.1739 | 1.70141 | 0.850704 | − | 0.525645i | \(-0.176176\pi\) | ||||
0.850704 | + | 0.525645i | \(0.176176\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.294937 | − | 0.510847i | 0.0259678 | − | 0.0449775i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.40850 | + | 11.0999i | 0.559913 | + | 0.969798i | 0.997503 | + | 0.0706236i | \(0.0224989\pi\) |
−0.437590 | + | 0.899175i | \(0.644168\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.78501 | + | 0.884879i | −0.154780 | + | 0.0767287i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.32520 | − | 4.02736i | −0.200121 | − | 0.346620i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.38889 | − | 12.7979i | 0.631275 | − | 1.09340i | −0.356016 | − | 0.934480i | \(-0.615865\pi\) |
0.987291 | − | 0.158921i | \(-0.0508015\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.10992 | −0.178961 | −0.0894804 | − | 0.995989i | \(-0.528521\pi\) | ||||
−0.0894804 | + | 0.995989i | \(0.528521\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.51035 | 0.211410 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.346011 | − | 0.599308i | 0.0289349 | − | 0.0501167i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.7002 | + | 18.5333i | 0.888605 | + | 1.53911i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.839437 | − | 1.10343i | 0.0692356 | − | 0.0910090i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.65883 | − | 11.5334i | −0.545513 | − | 0.944856i | −0.998574 | − | 0.0533768i | \(-0.983002\pi\) |
0.453062 | − | 0.891479i | \(-0.350332\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.928116 | − | 1.60754i | 0.0755290 | − | 0.130820i | −0.825787 | − | 0.563982i | \(-0.809269\pi\) |
0.901316 | + | 0.433162i | \(0.142602\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.51919 | −0.203664 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.3870 | 2.03914 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.08211 | − | 10.5345i | 0.485405 | − | 0.840746i | −0.514455 | − | 0.857518i | \(-0.672006\pi\) |
0.999859 | + | 0.0167718i | \(0.00533889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.200218 | + | 0.346788i | 0.0158783 | + | 0.0275021i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.52446 | − | 0.755716i | 0.120144 | − | 0.0595587i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.65883 | + | 6.33729i | 0.286582 | + | 0.496375i | 0.972992 | − | 0.230841i | \(-0.0741476\pi\) |
−0.686410 | + | 0.727215i | \(0.740814\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.390084 | + | 0.675645i | −0.0303680 | + | 0.0525989i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.5623 | −1.74592 | −0.872960 | − | 0.487792i | \(-0.837802\pi\) | ||||
−0.872960 | + | 0.487792i | \(0.837802\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5211 | −0.963162 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.11476 | + | 1.93082i | −0.0852479 | + | 0.147654i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.53199 | − | 4.38554i | −0.192504 | − | 0.333426i | 0.753576 | − | 0.657361i | \(-0.228327\pi\) |
−0.946079 | + | 0.323935i | \(0.894994\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −23.1652 | − | 15.4091i | −1.75112 | − | 1.16481i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.766061 | − | 1.32686i | −0.0575807 | − | 0.0997327i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.12983 | + | 15.8133i | −0.682395 | + | 1.18194i | 0.291853 | + | 0.956463i | \(0.405728\pi\) |
−0.974248 | + | 0.225480i | \(0.927605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.73556 | −0.129003 | −0.0645017 | − | 0.997918i | \(-0.520546\pi\) | ||||
−0.0645017 | + | 0.997918i | \(0.520546\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.87800 | −0.138826 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 19.8877 | − | 34.4465i | 1.46217 | − | 2.53256i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.425428 | + | 0.736862i | 0.0311103 | + | 0.0538847i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.197825 | − | 3.11731i | 0.0143897 | − | 0.226751i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0036 | − | 17.3268i | −0.723839 | − | 1.25373i | −0.959450 | − | 0.281878i | \(-0.909043\pi\) |
0.235612 | − | 0.971847i | \(-0.424291\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.693218 | − | 1.20069i | 0.0498989 | − | 0.0864275i | −0.839997 | − | 0.542591i | \(-0.817443\pi\) |
0.889896 | + | 0.456163i | \(0.150777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.539893 | −0.0386625 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.3642 | 1.30839 | 0.654197 | − | 0.756324i | \(-0.273007\pi\) | ||||
0.654197 | + | 0.756324i | \(0.273007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.777479 | + | 1.34663i | −0.0551140 | + | 0.0954603i | −0.892266 | − | 0.451510i | \(-0.850886\pi\) |
0.837152 | + | 0.546970i | \(0.184219\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.872625 | − | 1.51143i | −0.0615502 | − | 0.106608i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.910362 | + | 14.3454i | −0.0638949 | + | 1.00685i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.74160 | + | 6.48065i | 0.261325 | + | 0.452628i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.952042 | − | 1.64899i | 0.0661715 | − | 0.114612i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.753020 | 0.0520875 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.5797 | 1.07255 | 0.536276 | − | 0.844043i | \(-0.319831\pi\) | ||||
0.536276 | + | 0.844043i | \(0.319831\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.0310319 | + | 0.0537489i | −0.00212627 | + | 0.00368281i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.86563 | − | 10.1596i | −0.400032 | − | 0.692876i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.1978 | + | 9.44414i | 0.963811 | + | 0.641110i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.58546 | + | 2.74609i | 0.107135 | + | 0.185564i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.294405 | + | 0.509924i | −0.0198038 | + | 0.0343012i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.9444 | −1.06771 | −0.533857 | − | 0.845575i | \(-0.679258\pi\) | ||||
−0.533857 | + | 0.845575i | \(0.679258\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.1347 | −2.07564 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.85421 | − | 8.40773i | 0.322185 | − | 0.558041i | −0.658754 | − | 0.752359i | \(-0.728916\pi\) |
0.980939 | + | 0.194318i | \(0.0622493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.41185 | + | 7.64156i | 0.291544 | + | 0.504968i | 0.974175 | − | 0.225795i | \(-0.0724979\pi\) |
−0.682631 | + | 0.730763i | \(0.739165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.469501 | + | 0.232744i | −0.0308909 | + | 0.0153134i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.65883 | + | 9.80139i | 0.370723 | + | 0.642110i | 0.989677 | − | 0.143317i | \(-0.0457768\pi\) |
−0.618954 | + | 0.785427i | \(0.712443\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.9626 | − | 43.2364i | 1.62838 | − | 2.82043i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.49635 | −0.0971985 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.77479 | 0.373540 | 0.186770 | − | 0.982404i | \(-0.440198\pi\) | ||||
0.186770 | + | 0.982404i | \(0.440198\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.8339 | − | 20.4970i | 0.762290 | − | 1.32033i | −0.179377 | − | 0.983780i | \(-0.557408\pi\) |
0.941667 | − | 0.336545i | \(-0.109259\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.62737 | − | 4.55075i | −0.168546 | − | 0.291931i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.6573 | − | 25.4301i | −0.680873 | − | 1.62467i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.260553 | + | 0.451291i | 0.0165786 | + | 0.0287150i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.30409 | + | 2.25876i | −0.0826436 | + | 0.143143i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.94139 | 0.248779 | 0.124389 | − | 0.992233i | \(-0.460303\pi\) | ||||
0.124389 | + | 0.992233i | \(0.460303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.643104 | −0.0404316 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.331905 | − | 0.574876i | 0.0207847 | − | 0.0360001i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.23759 | − | 16.0000i | −0.576225 | − | 0.998051i | −0.995907 | − | 0.0903797i | \(-0.971192\pi\) |
0.419683 | − | 0.907671i | \(-0.362141\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.9366 | − | 11.8660i | 1.48735 | − | 0.737319i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.04288 | + | 13.9307i | 0.497842 | + | 0.862287i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.35839 | − | 9.28100i | 0.330412 | − | 0.572291i | −0.652180 | − | 0.758064i | \(-0.726146\pi\) |
0.982593 | + | 0.185773i | \(0.0594789\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.96376 | 0.489210 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.210144 | 0.0128606 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.518418 | + | 0.897926i | −0.0316085 | + | 0.0547475i | −0.881397 | − | 0.472376i | \(-0.843396\pi\) |
0.849788 | + | 0.527124i | \(0.176730\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.2409 | − | 24.6660i | −0.865075 | − | 1.49835i | −0.866972 | − | 0.498356i | \(-0.833937\pi\) |
0.00189684 | − | 0.999998i | \(-0.499396\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.301938 | − | 0.200844i | −0.0182741 | − | 0.0121556i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.25786 | + | 9.10689i | 0.317061 | + | 0.549166i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.27897 | − | 12.6075i | 0.437351 | − | 0.757514i | −0.560133 | − | 0.828403i | \(-0.689250\pi\) |
0.997484 | + | 0.0708884i | \(0.0225834\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 19.0823 | 1.14243 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.7821 | −1.06079 | −0.530395 | − | 0.847751i | \(-0.677956\pi\) | ||||
−0.530395 | + | 0.847751i | \(0.677956\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.82520 | − | 15.2857i | 0.524604 | − | 0.908640i | −0.474986 | − | 0.879993i | \(-0.657547\pi\) |
0.999590 | − | 0.0286468i | \(-0.00911982\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.293741 | − | 0.508774i | −0.0173997 | − | 0.0301372i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.318331 | + | 5.01623i | −0.0187905 | + | 0.296099i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.13802 | + | 14.0955i | 0.478707 | + | 0.829145i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.579949 | + | 1.00450i | −0.0339972 | + | 0.0588849i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.9444 | −0.697798 | −0.348899 | − | 0.937160i | \(-0.613444\pi\) | ||||
−0.348899 | + | 0.937160i | \(0.613444\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −30.4704 | −1.77405 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.590302 | + | 1.02243i | −0.0342528 | + | 0.0593276i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.222521 | − | 0.385418i | −0.0128687 | − | 0.0222893i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.499041 | − | 7.86384i | 0.0287642 | − | 0.453264i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.14646 | + | 1.98572i | 0.0658622 | + | 0.114077i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.6746 | + | 32.3453i | −1.06930 | + | 1.85209i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.99330 | −0.570347 | −0.285174 | − | 0.958476i | \(-0.592051\pi\) | ||||
−0.285174 | + | 0.958476i | \(0.592051\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.12392 | −0.0639374 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.15010 | + | 1.99204i | −0.0652164 | + | 0.112958i | −0.896790 | − | 0.442456i | \(-0.854107\pi\) |
0.831574 | + | 0.555415i | \(0.187440\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.1054 | + | 20.9671i | 0.684236 | + | 1.18513i | 0.973676 | + | 0.227935i | \(0.0731974\pi\) |
−0.289440 | + | 0.957196i | \(0.593469\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −25.6914 | − | 17.0894i | −1.44754 | − | 0.962880i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.95593 | + | 17.2442i | 0.559181 | + | 0.968529i | 0.997565 | + | 0.0697416i | \(0.0222175\pi\) |
−0.438385 | + | 0.898788i | \(0.644449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.71648 | − | 4.70508i | 0.152094 | − | 0.263434i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.27067 | −0.126736 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.640711 | −0.0356501 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.63856 | + | 6.30216i | −0.201831 | + | 0.349581i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.58815 | − | 2.75075i | −0.0878247 | − | 0.152117i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.0447 | − | 14.8940i | 1.65642 | − | 0.821131i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.1625 | + | 24.5301i | 0.778440 | + | 1.34830i | 0.932840 | + | 0.360290i | \(0.117322\pi\) |
−0.154400 | + | 0.988008i | \(0.549344\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.9487 | − | 25.8919i | 0.819183 | − | 1.41887i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −34.7090 | −1.89636 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.49827 | 0.245036 | 0.122518 | − | 0.992466i | \(-0.460903\pi\) | ||||
0.122518 | + | 0.992466i | \(0.460903\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.54676 | − | 2.67907i | 0.0840085 | − | 0.145507i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.22252 | − | 5.58157i | −0.174509 | − | 0.302259i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.50000 | − | 18.1865i | 0.188982 | − | 0.981981i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.250864 | + | 0.434510i | 0.0135061 | + | 0.0233932i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.2322 | + | 21.1868i | −0.656659 | + | 1.13737i | 0.324816 | + | 0.945777i | \(0.394698\pi\) |
−0.981475 | + | 0.191590i | \(0.938636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.5254 | 0.991643 | 0.495821 | − | 0.868424i | \(-0.334867\pi\) | ||||
0.495821 | + | 0.868424i | \(0.334867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.817003 | −0.0436084 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.730054 | + | 1.26449i | −0.0388568 | + | 0.0673020i | −0.884800 | − | 0.465971i | \(-0.845705\pi\) |
0.845943 | + | 0.533273i | \(0.179038\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.617154 | + | 1.06894i | 0.0327551 | + | 0.0567335i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.399477 | − | 0.198032i | 0.0211426 | − | 0.0104809i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.17241 | + | 3.76272i | 0.114655 | + | 0.198589i | 0.917642 | − | 0.397408i | \(-0.130090\pi\) |
−0.802987 | + | 0.595997i | \(0.796757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.21648 | − | 15.9634i | 0.485078 | − | 0.840180i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.198062 | 0.0103956 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 63.0622 | 3.30083 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.76002 | − | 13.4408i | 0.405070 | − | 0.701601i | −0.589260 | − | 0.807944i | \(-0.700581\pi\) |
0.994330 | + | 0.106342i | \(0.0339139\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.81240 | + | 4.87121i | 0.146407 | + | 0.253585i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.45377 | + | 2.96257i | 0.231228 | + | 0.153809i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.44869 | − | 16.3656i | −0.489235 | − | 0.847379i | 0.510689 | − | 0.859766i | \(-0.329390\pi\) |
−0.999923 | + | 0.0123865i | \(0.996057\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.15160 | − | 3.72667i | 0.111108 | − | 0.192445i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.75973 | 0.193636 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.3220 | 1.14660 | 0.573302 | − | 0.819344i | \(-0.305662\pi\) | ||||
0.573302 | + | 0.819344i | \(0.305662\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.89881 | + | 3.28884i | −0.0972791 | + | 0.168492i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5025 | − | 25.1190i | −0.741041 | − | 1.28352i | −0.952022 | − | 0.306030i | \(-0.900999\pi\) |
0.210981 | − | 0.977490i | \(-0.432334\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.660030 | + | 10.4007i | −0.0336382 | + | 0.530069i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.40893 | − | 7.63649i | −0.224118 | − | 0.388185i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.1766 | + | 26.2866i | −0.769484 | + | 1.33278i | 0.168360 | + | 0.985726i | \(0.446153\pi\) |
−0.937843 | + | 0.347059i | \(0.887180\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.547188 | 0.0276725 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.53856 | −0.128054 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.8795 | + | 25.7720i | −0.748669 | + | 1.29673i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.5187 | + | 33.8074i | 0.979616 | + | 1.69674i | 0.663774 | + | 0.747933i | \(0.268954\pi\) |
0.315842 | + | 0.948812i | \(0.397713\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0249911 | − | 0.393808i | 0.00125112 | − | 0.0197151i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.77293 | + | 8.26696i | 0.238349 | + | 0.412832i | 0.960241 | − | 0.279174i | \(-0.0900605\pi\) |
−0.721892 | + | 0.692006i | \(0.756727\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.23005 | − | 3.86257i | 0.111087 | − | 0.192408i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −34.0664 | −1.69277 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0978 | −0.500531 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.1169 | + | 17.5230i | −0.500249 | + | 0.866457i | 0.499751 | + | 0.866169i | \(0.333425\pi\) |
−1.00000 | 0.000287922i | \(0.999908\pi\) | ||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.46346 | + | 2.53479i | 0.0721871 | + | 0.125032i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.0407 | − | 11.3352i | −0.838519 | − | 0.557768i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.9354 | + | 44.9215i | 1.27312 | + | 2.20511i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.208947 | − | 0.361908i | 0.0102322 | − | 0.0177227i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.24267 | 0.109561 | 0.0547807 | − | 0.998498i | \(-0.482554\pi\) | ||||
0.0547807 | + | 0.998498i | \(0.482554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.4319 | 0.703368 | 0.351684 | − | 0.936119i | \(-0.385609\pi\) | ||||
0.351684 | + | 0.936119i | \(0.385609\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.7632 | − | 32.4989i | 0.912300 | − | 1.58015i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.47368 | − | 7.74864i | −0.217005 | − | 0.375864i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.4765 | + | 11.1422i | −1.08771 | + | 0.539210i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.0685317 | + | 0.118700i | 0.00330874 | + | 0.00573091i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6032 | + | 20.0974i | −0.558907 | + | 0.968055i | 0.438681 | + | 0.898643i | \(0.355446\pi\) |
−0.997588 | + | 0.0694125i | \(0.977888\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.1521 | −0.872336 | −0.436168 | − | 0.899865i | \(-0.643665\pi\) | ||||
−0.436168 | + | 0.899865i | \(0.643665\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.23862 | −0.203226 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.242135 | − | 0.419391i | 0.0115829 | − | 0.0200622i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.3148 | + | 17.8658i | 0.492301 | + | 0.852690i | 0.999961 | − | 0.00886757i | \(-0.00282267\pi\) |
−0.507660 | + | 0.861558i | \(0.669489\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.01065 | − | 19.1147i | −0.381459 | − | 0.910224i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.60052 | + | 4.50424i | 0.123555 | + | 0.214003i | 0.921167 | − | 0.389167i | \(-0.127237\pi\) |
−0.797612 | + | 0.603170i | \(0.793904\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.08964 | − | 3.61936i | 0.0990583 | − | 0.171574i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.63773 | 0.124760 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.2379 | −1.23824 | −0.619121 | − | 0.785296i | \(-0.712511\pi\) | ||||
−0.619121 | + | 0.785296i | \(0.712511\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.949886 | − | 1.64525i | 0.0447284 | − | 0.0774719i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.183825 | + | 0.318394i | 0.00863684 | + | 0.0149594i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.46160 | + | 3.20319i | −0.302924 | + | 0.150168i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.28836 | + | 2.23151i | 0.0602671 | + | 0.104386i | 0.894585 | − | 0.446898i | \(-0.147471\pi\) |
−0.834318 | + | 0.551284i | \(0.814138\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.502261 | − | 0.869942i | 0.0234436 | − | 0.0406054i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.5599 | −1.09729 | −0.548646 | − | 0.836055i | \(-0.684857\pi\) | ||||
−0.548646 | + | 0.836055i | \(0.684857\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.5429 | 1.79124 | 0.895620 | − | 0.444821i | \(-0.146733\pi\) | ||||
0.895620 | + | 0.444821i | \(0.146733\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.51411 | + | 4.35456i | −0.116589 | + | 0.201938i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.2582 | − | 28.1600i | −0.752338 | − | 1.30309i | −0.946687 | − | 0.322155i | \(-0.895593\pi\) |
0.194349 | − | 0.980932i | \(-0.437741\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.4112 | − | 12.9120i | −0.896325 | − | 0.596219i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.20464 | + | 2.08649i | 0.0555067 | + | 0.0961404i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.48911 | + | 2.57922i | −0.0684696 | + | 0.118593i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.91856 | −0.363328 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.98600 | 0.274080 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.3572 | − | 23.1353i | 0.610306 | − | 1.05708i | −0.380883 | − | 0.924623i | \(-0.624380\pi\) |
0.991189 | − | 0.132457i | \(-0.0422867\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.49396 | − | 6.05171i | −0.159311 | − | 0.275934i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0213433 | + | 0.336325i | −0.000971152 | + | 0.0153033i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.5339 | + | 19.9772i | 0.523725 | + | 0.907119i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.8949 | − | 34.4590i | 0.901525 | − | 1.56149i | 0.0760105 | − | 0.997107i | \(-0.475782\pi\) |
0.825515 | − | 0.564381i | \(-0.190885\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.44935 | −0.0655420 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.1051 | −1.17811 | −0.589054 | − | 0.808094i | \(-0.700499\pi\) | ||||
−0.589054 | + | 0.808094i | \(0.700499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.31133 | + | 4.00334i | −0.104097 | + | 0.180301i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.83124 | + | 10.1000i | 0.262095 | + | 0.453961i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.0525067 | + | 0.827396i | −0.00235525 | + | 0.0371138i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.3300 | + | 21.3563i | 0.551969 | + | 0.956038i | 0.998132 | + | 0.0610864i | \(0.0194565\pi\) |
−0.446164 | + | 0.894951i | \(0.647210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.23437 | − | 3.87003i | 0.0998241 | − | 0.172900i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.7972 | 0.971887 | 0.485943 | − | 0.873990i | \(-0.338476\pi\) | ||||
0.485943 | + | 0.873990i | \(0.338476\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 45.6007 | 2.02921 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.23998 | − | 2.14771i | 0.0550694 | − | 0.0953830i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.96897 | − | 13.8027i | −0.353218 | − | 0.611792i | 0.633593 | − | 0.773666i | \(-0.281579\pi\) |
−0.986811 | + | 0.161874i | \(0.948246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.2678 | + | 23.4595i | 1.56016 | + | 1.03779i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.444509 | − | 0.769913i | −0.0196256 | − | 0.0339925i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.1761 | + | 19.3575i | −0.492476 | + | 0.852993i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.6746 | −0.557427 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.00298 | 0.0440261 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0746 | − | 22.6458i | 0.572807 | − | 0.992132i | −0.423469 | − | 0.905911i | \(-0.639188\pi\) |
0.996276 | − | 0.0862208i | \(-0.0274790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.80947 | − | 4.86615i | −0.122850 | − | 0.212782i | 0.798041 | − | 0.602603i | \(-0.205870\pi\) |
−0.920890 | + | 0.389822i | \(0.872537\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.93714 | − | 2.44748i | 0.215474 | − | 0.106817i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.74190 | + | 4.74911i | 0.119439 | + | 0.206874i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2932 | − | 19.5604i | 0.491009 | − | 0.850453i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.9032 | −0.993916 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.31468 | 0.0569453 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.5792 | + | 39.1083i | −0.976183 | + | 1.69080i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.80827 | − | 3.13202i | −0.0780328 | − | 0.135157i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.23825 | + | 5.57111i | −0.182554 | + | 0.239965i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.5087 | − | 21.6658i | −0.537792 | − | 0.931484i | −0.999023 | − | 0.0442031i | \(-0.985925\pi\) |
0.461230 | − | 0.887280i | \(-0.347408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.171875 | − | 0.297696i | 0.00737585 | − | 0.0127753i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −63.1691 | −2.70587 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.0194 | −1.41181 | −0.705903 | − | 0.708308i | \(-0.749459\pi\) | ||||
−0.705903 | + | 0.708308i | \(0.749459\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.0368 | + | 24.3125i | −0.599078 | + | 1.03763i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.04556 | + | 3.54302i | 0.0871440 | + | 0.150938i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.9088 | + | 8.87788i | −0.761560 | + | 0.377526i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.93900 | + | 6.82255i | 0.167201 | + | 0.289601i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.54623 | − | 13.0705i | 0.319744 | − | 0.553813i | −0.660691 | − | 0.750658i | \(-0.729736\pi\) |
0.980435 | + | 0.196846i | \(0.0630698\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.06100 | −0.0871710 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.168522 | −0.00711502 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0523 | + | 20.8751i | −0.507943 | + | 0.879782i | 0.492015 | + | 0.870587i | \(0.336260\pi\) |
−0.999958 | + | 0.00919575i | \(0.997073\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.7615 | − | 53.2805i | −1.29415 | − | 2.24153i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19.0518 | − | 12.6729i | −0.800100 | − | 0.532212i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.0383 | + | 34.7074i | 0.840050 | + | 1.45501i | 0.889851 | + | 0.456251i | \(0.150808\pi\) |
−0.0498008 | + | 0.998759i | \(0.515859\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0782 | − | 19.1880i | 0.463609 | − | 0.802995i | −0.535528 | − | 0.844517i | \(-0.679888\pi\) |
0.999138 | + | 0.0415227i | \(0.0132209\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.96269 | 0.165544 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.76271 | 0.282024 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.0903 | − | 22.6731i | 0.544956 | − | 0.943892i | −0.453653 | − | 0.891178i | \(-0.649880\pi\) |
0.998610 | − | 0.0527139i | \(-0.0167871\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.137300 | + | 0.237811i | 0.00570601 | + | 0.00988309i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.20655 | + | 34.7707i | −0.0915433 | + | 1.44253i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.01089 | − | 1.75090i | −0.0418666 | − | 0.0725151i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.03534 | + | 6.98942i | −0.166841 | + | 0.288977i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.6450 | −0.769562 | −0.384781 | − | 0.923008i | \(-0.625723\pi\) | ||||
−0.384781 | + | 0.923008i | \(0.625723\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.85325 | 0.199975 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.81863 | + | 3.14995i | −0.0748083 | + | 0.129572i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.97554 | + | 6.88584i | 0.163256 | + | 0.282768i | 0.936035 | − | 0.351908i | \(-0.114467\pi\) |
−0.772779 | + | 0.634676i | \(0.781134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.561590 | − | 8.84948i | 0.0230229 | − | 0.362793i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.153989 | − | 0.266717i | −0.00630236 | − | 0.0109160i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.63826 | + | 16.6940i | −0.393809 | + | 0.682097i | −0.992948 | − | 0.118548i | \(-0.962176\pi\) |
0.599140 | + | 0.800644i | \(0.295509\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.18896 | 0.0892897 | 0.0446449 | − | 0.999003i | \(-0.485784\pi\) | ||||
0.0446449 | + | 0.999003i | \(0.485784\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.0892 | −1.06243 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.96950 | − | 3.41127i | 0.0800716 | − | 0.138688i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.6027 | + | 28.7567i | 0.673882 | + | 1.16720i | 0.976794 | + | 0.214179i | \(0.0687077\pi\) |
−0.302912 | + | 0.953018i | \(0.597959\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.37047 | − | 1.57679i | −0.0960563 | − | 0.0638949i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.38553 | − | 7.59597i | −0.177420 | − | 0.307300i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.34481 | + | 4.06134i | −0.0947062 | + | 0.164036i | −0.909486 | − | 0.415735i | \(-0.863524\pi\) |
0.814780 | + | 0.579771i | \(0.196858\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.48214 | −0.0597657 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.00000 | −0.161034 | −0.0805170 | − | 0.996753i | \(-0.525657\pi\) | ||||
−0.0805170 | + | 0.996753i | \(0.525657\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.7114 | − | 39.3373i | 0.912848 | − | 1.58110i | 0.102827 | − | 0.994699i | \(-0.467211\pi\) |
0.810022 | − | 0.586400i | \(-0.199455\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.379626 | + | 0.657531i | 0.0152339 | + | 0.0263858i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.51507 | − | 1.24679i | 0.100764 | − | 0.0499514i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.5010 | − | 28.5805i | −0.660038 | − | 1.14322i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0745725 | + | 0.129163i | −0.00297814 | + | 0.00515829i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.59179 | 0.342577 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.9239 | 0.673731 | 0.336866 | − | 0.941553i | \(-0.390633\pi\) | ||||
0.336866 | + | 0.941553i | \(0.390633\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.54288 | + | 2.67234i | −0.0613238 | + | 0.106216i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 37.7630 | + | 65.4074i | 1.49858 | + | 2.59562i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.80529 | − | 0.612355i | −0.190393 | − | 0.0242624i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.463887 | + | 0.803475i | 0.0183511 | + | 0.0317850i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15.4695 | + | 26.7940i | −0.611009 | + | 1.05830i | 0.380062 | + | 0.924961i | \(0.375903\pi\) |
−0.991071 | + | 0.133337i | \(0.957431\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.83446 | −0.0723441 | −0.0361721 | − | 0.999346i | \(-0.511516\pi\) | ||||
−0.0361721 | + | 0.999346i | \(0.511516\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.32352 | 0.0914884 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.0586060 | − | 0.101509i | 0.00230404 | − | 0.00399071i | −0.864871 | − | 0.501994i | \(-0.832600\pi\) |
0.867175 | + | 0.498003i | \(0.165933\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.86778 | + | 6.69919i | 0.151824 | + | 0.262966i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.02595 | + | 1.50005i | −0.118596 | + | 0.0587914i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.92812 | − | 6.80370i | −0.153719 | − | 0.266249i | 0.778873 | − | 0.627182i | \(-0.215792\pi\) |
−0.932592 | + | 0.360933i | \(0.882458\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.2431 | + | 43.7223i | −0.986329 | + | 1.70837i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 47.4010 | 1.84929 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.3314 | 1.10363 | 0.551817 | − | 0.833965i | \(-0.313935\pi\) | ||||
0.551817 | + | 0.833965i | \(0.313935\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.9792 | + | 41.5332i | −0.932682 | + | 1.61545i | −0.153967 | + | 0.988076i | \(0.549205\pi\) |
−0.778715 | + | 0.627377i | \(0.784128\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.0583105 | − | 0.100997i | −0.00226459 | − | 0.00392239i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.53415 | − | 4.34640i | −0.253383 | − | 0.168546i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.74698 | − | 3.02586i | −0.0676433 | − | 0.117162i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.57899 | − | 2.73489i | 0.0610473 | − | 0.105737i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.48188 | 0.366044 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.4698 | −0.711958 | −0.355979 | − | 0.934494i | \(-0.615853\pi\) | ||||
−0.355979 | + | 0.934494i | \(0.615853\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.20746 | − | 10.7516i | 0.238925 | − | 0.413830i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.98039 | + | 15.5545i | 0.345144 | + | 0.597807i | 0.985380 | − | 0.170371i | \(-0.0544967\pi\) |
−0.640236 | + | 0.768179i | \(0.721163\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.981287 | + | 15.4630i | −0.0376583 | + | 0.593417i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.961435 | + | 1.66525i | 0.0368423 | + | 0.0638127i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.5591 | + | 25.2172i | −0.557090 | + | 0.964908i | 0.440648 | + | 0.897680i | \(0.354749\pi\) |
−0.997738 | + | 0.0672280i | \(0.978585\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 58.2097 | 2.22408 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.74764 | −0.0666768 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.699554 | − | 1.21166i | 0.0266509 | − | 0.0461607i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0422 | − | 19.1257i | −0.420066 | − | 0.727575i | 0.575880 | − | 0.817534i | \(-0.304660\pi\) |
−0.995945 | + | 0.0899594i | \(0.971326\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.496115 | + | 7.81774i | −0.0188459 | + | 0.296971i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.15548 | − | 7.19750i | −0.157626 | − | 0.273017i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.808216 | + | 1.39987i | −0.0306133 | + | 0.0530239i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.24160 | −0.0847852 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.5056 | −0.736715 | −0.368358 | − | 0.929684i | \(-0.620080\pi\) | ||||
−0.368358 | + | 0.929684i | \(0.620080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.80194 | − | 6.58515i | 0.143393 | − | 0.248364i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.94414 | + | 8.56350i | 0.186207 | + | 0.322520i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.5025 | + | 16.9638i | 0.959118 | + | 0.637988i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.0516 | + | 36.4625i | 0.790610 | + | 1.36938i | 0.925590 | + | 0.378528i | \(0.123570\pi\) |
−0.134980 | + | 0.990848i | \(0.543097\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.1843 | + | 19.3717i | −0.419442 | + | 0.726495i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.14483 | −0.155225 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.72587 | 0.101942 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.571884 | + | 0.990532i | −0.0213574 | + | 0.0369921i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.27210 | + | 3.93540i | 0.0847351 | + | 0.146766i | 0.905278 | − | 0.424819i | \(-0.139662\pi\) |
−0.820543 | + | 0.571585i | \(0.806329\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.4514 | + | 6.66821i | −0.500956 | + | 0.248337i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.34385 | + | 4.05968i | 0.0871689 | + | 0.150981i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.5658 | + | 49.4774i | −1.06091 | + | 1.83754i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.46442 | −0.165576 | −0.0827881 | − | 0.996567i | \(-0.526382\pi\) | ||||
−0.0827881 | + | 0.996567i | \(0.526382\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.9047 | −0.922395 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.26702 | − | 2.19454i | 0.0468625 | − | 0.0811682i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.7136 | − | 37.6090i | −0.802008 | − | 1.38912i | −0.918292 | − | 0.395903i | \(-0.870432\pi\) |
0.116284 | − | 0.993216i | \(-0.462902\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.41736 | + | 0.690354i | 0.199822 | + | 0.0254641i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.40581 | + | 7.63109i | 0.162290 | + | 0.281095i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.650341 | − | 1.12642i | 0.0239232 | − | 0.0414362i | −0.853816 | − | 0.520575i | \(-0.825718\pi\) |
0.877739 | + | 0.479139i | \(0.159051\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.103211 | −0.00379157 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.37867 | −0.0505784 | −0.0252892 | − | 0.999680i | \(-0.508051\pi\) | ||||
−0.0252892 | + | 0.999680i | \(0.508051\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.2292 | − | 45.4302i | 0.960962 | − | 1.66443i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.4945 | + | 33.7655i | 0.713266 | + | 1.23541i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.1761 | + | 13.4719i | −0.992991 | + | 0.492253i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.2262 | − | 22.9084i | −0.482630 | − | 0.835939i | 0.517171 | − | 0.855882i | \(-0.326985\pi\) |
−0.999801 | + | 0.0199426i | \(0.993652\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.390321 | + | 0.676055i | −0.0142241 | + | 0.0246368i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.31170 | 0.266100 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.2083 | −0.807176 | −0.403588 | − | 0.914941i | \(-0.632237\pi\) | ||||
−0.403588 | + | 0.914941i | \(0.632237\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.0636873 | − | 0.110310i | 0.00231170 | − | 0.00400399i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9351 | + | 25.8684i | 0.541398 | + | 0.937728i | 0.998824 | + | 0.0484807i | \(0.0154379\pi\) |
−0.457427 | + | 0.889247i | \(0.651229\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.3277 | − | 23.4993i | −1.27895 | − | 0.850732i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.96154 | − | 8.59364i | −0.179385 | − | 0.310704i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.67659 | + | 4.63599i | −0.0966460 | + | 0.167396i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.16554 | −0.186274 | −0.0931370 | − | 0.995653i | \(-0.529689\pi\) | ||||
−0.0931370 | + | 0.995653i | \(0.529689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.65923 | 0.131784 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.45689 | + | 11.1837i | −0.232238 | + | 0.402248i | −0.958466 | − | 0.285205i | \(-0.907938\pi\) |
0.726228 | + | 0.687454i | \(0.241272\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.8872 | + | 58.6943i | 1.21726 | + | 2.10836i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.335126 | + | 5.28088i | −0.0120226 | + | 0.189451i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.715284 | + | 1.23891i | 0.0256277 | + | 0.0443885i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.156678 | − | 0.271374i | 0.00560637 | − | 0.00971051i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.41417 | −0.229224 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.9148 | 1.71015 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.21193 | + | 15.9555i | −0.328370 | + | 0.568753i | −0.982189 | − | 0.187898i | \(-0.939833\pi\) |
0.653819 | + | 0.756651i | \(0.273166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.06129 | + | 1.83822i | 0.0377831 | + | 0.0654422i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.61715 | − | 41.2409i | 0.0930553 | − | 1.46636i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.28083 | + | 5.68257i | 0.116506 | + | 0.201794i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.788660 | + | 1.36600i | −0.0279709 | + | 0.0484470i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.7469 | 1.23080 | 0.615399 | − | 0.788216i | \(-0.288995\pi\) | ||||
0.615399 | + | 0.788216i | \(0.288995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.7842 | 0.381518 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.57069 | − | 2.72051i | 0.0554975 | − | 0.0961245i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.00484 | − | 13.8648i | −0.282485 | − | 0.489278i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.58038 | + | 3.71197i | 0.196682 | + | 0.130830i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.102679 | − | 0.177845i | −0.00361447 | − | 0.00626045i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.37502 | + | 5.84570i | −0.118659 | + | 0.205524i | −0.919237 | − | 0.393706i | \(-0.871193\pi\) |
0.800577 | + | 0.599230i | \(0.204526\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.3062 | 0.923735 | 0.461867 | − | 0.886949i | \(-0.347180\pi\) | ||||
0.461867 | + | 0.886949i | \(0.347180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.64119 | 0.197845 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.4121 | + | 24.9626i | −0.504836 | + | 0.874401i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.12133 | − | 1.94221i | −0.0392305 | − | 0.0679492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.85690 | + | 2.40770i | −0.169714 | + | 0.0841317i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.26002 | − | 9.11062i | −0.183576 | − | 0.317963i | 0.759520 | − | 0.650484i | \(-0.225434\pi\) |
−0.943096 | + | 0.332521i | \(0.892101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.66517 | − | 2.88416i | 0.0580442 | − | 0.100535i | −0.835543 | − | 0.549425i | \(-0.814847\pi\) |
0.893587 | + | 0.448889i | \(0.148180\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.08277 | −0.0725127 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.25236 | −0.0783221 | −0.0391611 | − | 0.999233i | \(-0.512469\pi\) | ||||
−0.0391611 | + | 0.999233i | \(0.512469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.824240 | + | 1.42763i | −0.0286271 | + | 0.0495835i | −0.879984 | − | 0.475003i | \(-0.842447\pi\) |
0.851357 | + | 0.524587i | \(0.175780\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.44169 | + | 2.49708i | 0.0500117 | + | 0.0866227i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.60614 | − | 4.74020i | 0.124945 | − | 0.164238i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44.4364 | − | 76.9661i | −1.53778 | − | 2.66352i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.80452 | + | 6.58962i | −0.131503 | + | 0.227771i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.7144 | 0.680616 | 0.340308 | − | 0.940314i | \(-0.389469\pi\) | ||||
0.340308 | + | 0.940314i | \(0.389469\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.517057 | 0.0178296 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.76098 | − | 3.05011i | 0.0606514 | − | 0.105051i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.6603 | − | 42.7129i | −0.848341 | − | 1.46937i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.37047 | − | 1.17511i | 0.0814503 | − | 0.0403771i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.74794 | + | 3.02752i | 0.0599891 | + | 0.103904i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.24698 | + | 5.62393i | −0.111305 | + | 0.192786i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.77884 | 0.0951457 | 0.0475728 | − | 0.998868i | \(-0.484851\pi\) | ||||
0.0475728 | + | 0.998868i | \(0.484851\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.78209 | −0.300341 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.23878 | + | 10.8059i | −0.213113 | + | 0.369122i | −0.952687 | − | 0.303953i | \(-0.901694\pi\) |
0.739574 | + | 0.673075i | \(0.235027\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.2753 | + | 24.7256i | 0.487068 | + | 0.843626i | 0.999889 | − | 0.0148691i | \(-0.00473314\pi\) |
−0.512822 | + | 0.858495i | \(0.671400\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.828895 | − | 0.551366i | −0.0282487 | − | 0.0187905i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.3535 | − | 33.5213i | −0.658802 | − | 1.14108i | −0.980926 | − | 0.194381i | \(-0.937730\pi\) |
0.322124 | − | 0.946698i | \(-0.395603\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.97352 | − | 17.2746i | 0.339110 | − | 0.587355i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.22367 | −0.109482 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.55496 | 0.256284 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.04892 | + | 5.28088i | −0.103309 | + | 0.178936i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.66948 | + | 15.0160i | 0.293418 | + | 0.508214i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.64055 | − | 57.3674i | 0.123073 | − | 1.93937i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.6824 | + | 37.5550i | 0.732162 | + | 1.26814i | 0.955957 | + | 0.293506i | \(0.0948221\pi\) |
−0.223795 | + | 0.974636i | \(0.571845\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.18287 | − | 2.04878i | 0.0398971 | − | 0.0691037i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.9675 | −0.807485 | −0.403742 | − | 0.914873i | \(-0.632291\pi\) | ||||
−0.403742 | + | 0.914873i | \(0.632291\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.6571 | 0.897083 | 0.448541 | − | 0.893762i | \(-0.351944\pi\) | ||||
0.448541 | + | 0.893762i | \(0.351944\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.01752 | − | 5.22649i | 0.101433 | − | 0.175687i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.6821 | − | 25.4301i | −0.492977 | − | 0.853860i | 0.506991 | − | 0.861952i | \(-0.330758\pi\) |
−0.999967 | + | 0.00809111i | \(0.997424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.21283 | + | 50.6275i | −0.107755 | + | 1.69799i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.32424 | + | 7.48980i | 0.144868 | + | 0.250918i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.77210 | − | 8.26552i | 0.159692 | − | 0.276595i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −71.9248 | −2.40418 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0881460 | 0.00294311 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.5078 | − | 30.3244i | 0.583919 | − | 1.01138i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.860117 | + | 1.48977i | 0.0286546 | + | 0.0496313i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.29944 | + | 0.864364i | 0.0432426 | + | 0.0287642i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.41819 | − | 5.92048i | −0.113624 | − | 0.196803i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.07673 | − | 8.79315i | 0.168570 | − | 0.291972i | −0.769347 | − | 0.638831i | \(-0.779418\pi\) |
0.937917 | + | 0.346859i | \(0.112752\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 34.2760 | 1.13686 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.4330 | −1.80344 | −0.901722 | − | 0.432316i | \(-0.857697\pi\) | ||||
−0.901722 | + | 0.432316i | \(0.857697\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.58426 | − | 11.4043i | 0.217907 | − | 0.377426i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.69873 | − | 6.40638i | −0.122276 | − | 0.211788i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.3823 | + | 15.0613i | −1.00331 | + | 0.497369i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.9983 | + | 20.7816i | 0.395786 | + | 0.685522i | 0.993201 | − | 0.116410i | \(-0.0371387\pi\) |
−0.597415 | + | 0.801932i | \(0.703805\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.989647 | − | 1.71412i | 0.0326100 | − | 0.0564822i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.216849 | 0.00713766 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 106.186 | 3.49138 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.40054 | + | 14.5502i | −0.275910 | + | 0.477890i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.1990 | − | 22.8614i | −0.433046 | − | 0.750057i | 0.564088 | − | 0.825715i | \(-0.309228\pi\) |
−0.997134 | + | 0.0756572i | \(0.975895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.03737 | − | 4.86149i | −0.0667720 | − | 0.159329i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.227792 | − | 0.394548i | −0.00745758 | − | 0.0129169i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.67576 | + | 2.90250i | −0.0548032 | + | 0.0949219i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.2519 | −0.498257 | −0.249129 | − | 0.968470i | \(-0.580144\pi\) | ||||
−0.249129 | + | 0.968470i | \(0.580144\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.79523 | −0.156487 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.8611 | − | 30.9363i | 0.582254 | − | 1.00849i | −0.412957 | − | 0.910750i | \(-0.635504\pi\) |
0.995212 | − | 0.0977438i | \(-0.0311626\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.610876 | − | 1.05807i | −0.0198929 | − | 0.0344554i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.0236 | − | 5.46471i | 0.358599 | − | 0.177767i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.8451 | − | 39.5689i | −0.742366 | − | 1.28582i | −0.951415 | − | 0.307911i | \(-0.900370\pi\) |
0.209049 | − | 0.977905i | \(-0.432963\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.53952 | − | 9.59474i | 0.179821 | − | 0.311458i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.94379 | −0.127886 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.55389 | 0.0827287 | 0.0413644 | − | 0.999144i | \(-0.486830\pi\) | ||||
0.0413644 | + | 0.999144i | \(0.486830\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.4044 | − | 68.2504i | 1.27510 | − | 2.20853i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.538032 | + | 0.931899i | 0.0173921 | + | 0.0301240i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 32.5541 | + | 21.6544i | 1.05123 | + | 0.699256i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.26928 | − | 9.12666i | −0.169977 | − | 0.294409i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.9718 | + | 29.3960i | −0.546907 | + | 0.947271i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.46117 | 0.175801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.4843 | −0.980308 | −0.490154 | − | 0.871636i | \(-0.663059\pi\) | ||||
−0.490154 | + | 0.871636i | \(0.663059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.0634504 | − | 0.109899i | 0.00203832 | − | 0.00353047i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.4006 | − | 37.0669i | −0.686778 | − | 1.18953i | −0.972875 | − | 0.231334i | \(-0.925691\pi\) |
0.286097 | − | 0.958201i | \(-0.407642\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.353543 | − | 5.57111i | 0.0113341 | − | 0.178601i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.720660 | − | 1.24822i | −0.0230796 | − | 0.0399751i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.96897 | − | 17.2668i | 0.318936 | − | 0.552413i | −0.661331 | − | 0.750094i | \(-0.730008\pi\) |
0.980266 | + | 0.197682i | \(0.0633413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.06100 | −0.0339097 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −47.4814 | −1.51596 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.84063 | − | 11.8483i | 0.218182 | − | 0.377903i | −0.736070 | − | 0.676905i | \(-0.763321\pi\) |
0.954252 | + | 0.299003i | \(0.0966539\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.1683 | + | 62.6453i | 1.15242 | + | 1.99605i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.420642 | + | 6.62844i | −0.0133892 | + | 0.210985i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.957656 | + | 1.65871i | 0.0304517 | + | 0.0527439i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1054 | + | 19.2351i | −0.352774 | + | 0.611022i | −0.986734 | − | 0.162343i | \(-0.948095\pi\) |
0.633961 | + | 0.773365i | \(0.281428\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.61011 | −0.178031 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.12498 | −0.194175 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0109 | + | 20.8035i | −0.380389 | + | 0.658852i | −0.991118 | − | 0.132987i | \(-0.957543\pi\) |
0.610729 | + | 0.791840i | \(0.290876\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.96077 | + | 10.3244i | 0.188590 | + | 0.326648i |
(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.i.529.3 | 6 | ||
4.3 | odd | 2 | 616.2.q.c.529.1 | yes | 6 | ||
7.2 | even | 3 | inner | 1232.2.q.i.177.3 | 6 | ||
7.3 | odd | 6 | 8624.2.a.cf.1.3 | 3 | |||
7.4 | even | 3 | 8624.2.a.cq.1.1 | 3 | |||
28.3 | even | 6 | 4312.2.a.x.1.1 | 3 | |||
28.11 | odd | 6 | 4312.2.a.v.1.3 | 3 | |||
28.23 | odd | 6 | 616.2.q.c.177.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.2.q.c.177.1 | ✓ | 6 | 28.23 | odd | 6 | ||
616.2.q.c.529.1 | yes | 6 | 4.3 | odd | 2 | ||
1232.2.q.i.177.3 | 6 | 7.2 | even | 3 | inner | ||
1232.2.q.i.529.3 | 6 | 1.1 | even | 1 | trivial | ||
4312.2.a.v.1.3 | 3 | 28.11 | odd | 6 | |||
4312.2.a.x.1.1 | 3 | 28.3 | even | 6 | |||
8624.2.a.cf.1.3 | 3 | 7.3 | odd | 6 | |||
8624.2.a.cq.1.1 | 3 | 7.4 | even | 3 |