Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(561,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.561");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.bd (of order \(4\), 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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 561.6 | ||
Character | \(\chi\) | \(=\) | 2240.561 |
Dual form | 2240.2.bd.b.1681.6 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.56700 | + | 1.56700i | −0.904709 | + | 0.904709i | −0.995839 | − | 0.0911305i | \(-0.970952\pi\) |
0.0911305 | + | 0.995839i | \(0.470952\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.91098i | − | 0.636995i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.19408 | − | 1.19408i | −0.360027 | − | 0.360027i | 0.503796 | − | 0.863823i | \(-0.331936\pi\) |
−0.863823 | + | 0.503796i | \(0.831936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.08857 | + | 1.08857i | −0.301916 | + | 0.301916i | −0.841763 | − | 0.539847i | \(-0.818482\pi\) |
0.539847 | + | 0.841763i | \(0.318482\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.21607 | 0.572188 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.78951 | −0.919092 | −0.459546 | − | 0.888154i | \(-0.651988\pi\) | ||||
−0.459546 | + | 0.888154i | \(0.651988\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.95387 | − | 5.95387i | 1.36591 | − | 1.36591i | 0.499733 | − | 0.866180i | \(-0.333432\pi\) |
0.866180 | − | 0.499733i | \(-0.166568\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56700 | − | 1.56700i | −0.341948 | − | 0.341948i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.53073i | 0.527694i | 0.964565 | + | 0.263847i | \(0.0849914\pi\) | ||||
−0.964565 | + | 0.263847i | \(0.915009\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.70649 | − | 1.70649i | −0.328414 | − | 0.328414i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.38242 | − | 5.38242i | 0.999489 | − | 0.999489i | −0.000510422 | − | 1.00000i | \(-0.500162\pi\) |
1.00000 | 0.000510422i | \(0.000162472\pi\) | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.98299 | −0.356155 | −0.178077 | − | 0.984016i | \(-0.556988\pi\) | ||||
−0.178077 | + | 0.984016i | \(0.556988\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.74224 | 0.651440 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.707107 | − | 0.707107i | 0.119523 | − | 0.119523i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.14607 | − | 2.14607i | −0.352811 | − | 0.352811i | 0.508343 | − | 0.861155i | \(-0.330258\pi\) |
−0.861155 | + | 0.508343i | \(0.830258\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 3.41159i | − | 0.546292i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.95744i | 1.55509i | 0.628827 | + | 0.777546i | \(0.283536\pi\) | ||||
−0.628827 | + | 0.777546i | \(0.716464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.342507 | − | 0.342507i | −0.0522318 | − | 0.0522318i | 0.680508 | − | 0.732740i | \(-0.261759\pi\) |
−0.732740 | + | 0.680508i | \(0.761759\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.35127 | + | 1.35127i | −0.201435 | + | 0.201435i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.32467 | 0.630818 | 0.315409 | − | 0.948956i | \(-0.397858\pi\) | ||||
0.315409 | + | 0.948956i | \(0.397858\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.93817 | − | 5.93817i | 0.831510 | − | 0.831510i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.0660626 | − | 0.0660626i | −0.00907440 | − | 0.00907440i | 0.702555 | − | 0.711629i | \(-0.252042\pi\) |
−0.711629 | + | 0.702555i | \(0.752042\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.68868i | 0.227701i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.6595i | 2.47151i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.96474 | + | 2.96474i | 0.385976 | + | 0.385976i | 0.873250 | − | 0.487273i | \(-0.162008\pi\) |
−0.487273 | + | 0.873250i | \(0.662008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.13245 | − | 6.13245i | 0.785180 | − | 0.785180i | −0.195520 | − | 0.980700i | \(-0.562639\pi\) |
0.980700 | + | 0.195520i | \(0.0626395\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.91098 | 0.240761 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.53948 | 0.190949 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.21747 | − | 2.21747i | 0.270907 | − | 0.270907i | −0.558558 | − | 0.829465i | \(-0.688645\pi\) |
0.829465 | + | 0.558558i | \(0.188645\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.96566 | − | 3.96566i | −0.477409 | − | 0.477409i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.8350i | − | 1.40456i | −0.711902 | − | 0.702279i | \(-0.752166\pi\) | ||
0.711902 | − | 0.702279i | \(-0.247834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.17814i | − | 0.957179i | −0.878039 | − | 0.478589i | \(-0.841148\pi\) | ||
0.878039 | − | 0.478589i | \(-0.158852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.56700 | − | 1.56700i | −0.180942 | − | 0.180942i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.19408 | − | 1.19408i | 0.136078 | − | 0.136078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.46315 | 0.952179 | 0.476090 | − | 0.879397i | \(-0.342054\pi\) | ||||
0.476090 | + | 0.879397i | \(0.342054\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.0811 | 1.23123 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.79431 | + | 4.79431i | −0.526244 | + | 0.526244i | −0.919450 | − | 0.393206i | \(-0.871366\pi\) |
0.393206 | + | 0.919450i | \(0.371366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.67959 | + | 2.67959i | 0.290642 | + | 0.290642i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.8685i | 1.80849i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.9660i | 1.90439i | 0.305483 | + | 0.952197i | \(0.401182\pi\) | ||||
−0.305483 | + | 0.952197i | \(0.598818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.08857 | − | 1.08857i | −0.114114 | − | 0.114114i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.10734 | − | 3.10734i | 0.322216 | − | 0.322216i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.42005 | −0.863879 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.71168 | −0.884537 | −0.442269 | − | 0.896883i | \(-0.645826\pi\) | ||||
−0.442269 | + | 0.896883i | \(0.645826\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.28186 | + | 2.28186i | −0.229336 | + | 0.229336i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.52435 | + | 2.52435i | 0.251182 | + | 0.251182i | 0.821455 | − | 0.570273i | \(-0.193163\pi\) |
−0.570273 | + | 0.821455i | \(0.693163\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.60516i | − | 0.158161i | −0.996868 | − | 0.0790807i | \(-0.974802\pi\) | ||
0.996868 | − | 0.0790807i | \(-0.0251985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.21607i | 0.216267i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.4612 | + | 12.4612i | 1.20467 | + | 1.20467i | 0.972731 | + | 0.231936i | \(0.0745060\pi\) |
0.231936 | + | 0.972731i | \(0.425494\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.73955 | − | 2.73955i | 0.262401 | − | 0.262401i | −0.563628 | − | 0.826029i | \(-0.690595\pi\) |
0.826029 | + | 0.563628i | \(0.190595\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.72578 | 0.638383 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.1618 | 1.42630 | 0.713150 | − | 0.701012i | \(-0.247268\pi\) | ||||
0.713150 | + | 0.701012i | \(0.247268\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.78950 | − | 1.78950i | 0.166871 | − | 0.166871i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.08025 | + | 2.08025i | 0.192319 | + | 0.192319i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.78951i | − | 0.347384i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 8.14837i | − | 0.740761i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.6033 | − | 15.6033i | −1.40690 | − | 1.40690i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4711 | 1.37284 | 0.686418 | − | 0.727208i | \(-0.259182\pi\) | ||||
0.686418 | + | 0.727208i | \(0.259182\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.07342 | 0.0945091 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.44063 | + | 7.44063i | −0.650091 | + | 0.650091i | −0.953015 | − | 0.302924i | \(-0.902037\pi\) |
0.302924 | + | 0.953015i | \(0.402037\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.95387 | + | 5.95387i | 0.516266 | + | 0.516266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.41334i | 0.207707i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.2513i | 1.21757i | 0.793337 | + | 0.608783i | \(0.208342\pi\) | ||||
−0.793337 | + | 0.608783i | \(0.791658\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.6749 | + | 13.6749i | 1.15989 | + | 1.15989i | 0.984499 | + | 0.175393i | \(0.0561196\pi\) |
0.175393 | + | 0.984499i | \(0.443880\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.77677 | + | 6.77677i | −0.570707 | + | 0.570707i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.59968 | 0.217396 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.61188 | −0.632133 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.56700 | − | 1.56700i | 0.129244 | − | 0.129244i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.08027 | + | 6.08027i | 0.498115 | + | 0.498115i | 0.910851 | − | 0.412736i | \(-0.135427\pi\) |
−0.412736 | + | 0.910851i | \(0.635427\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.92748i | 0.645129i | 0.946547 | + | 0.322565i | \(0.104545\pi\) | ||||
−0.946547 | + | 0.322565i | \(0.895455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.24170i | 0.585457i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.40218 | + | 1.40218i | 0.112626 | + | 0.112626i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.779619 | − | 0.779619i | 0.0622204 | − | 0.0622204i | −0.675312 | − | 0.737532i | \(-0.735991\pi\) |
0.737532 | + | 0.675312i | \(0.235991\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.207040 | 0.0164194 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.53073 | −0.199449 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.01759 | − | 6.01759i | 0.471334 | − | 0.471334i | −0.431012 | − | 0.902346i | \(-0.641843\pi\) |
0.902346 | + | 0.431012i | \(0.141843\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.64616 | − | 2.64616i | −0.206003 | − | 0.206003i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.9564i | 1.38951i | 0.719248 | + | 0.694753i | \(0.244486\pi\) | ||||
−0.719248 | + | 0.694753i | \(0.755514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.6300i | 0.817693i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.3778 | − | 11.3778i | −0.870079 | − | 0.870079i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.5456 | − | 11.5456i | 0.877798 | − | 0.877798i | −0.115509 | − | 0.993306i | \(-0.536850\pi\) |
0.993306 | + | 0.115509i | \(0.0368498\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.29150 | −0.698392 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.30062 | − | 9.30062i | 0.695161 | − | 0.695161i | −0.268202 | − | 0.963363i | \(-0.586429\pi\) |
0.963363 | + | 0.268202i | \(0.0864295\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.1313 | − | 11.1313i | −0.827387 | − | 0.827387i | 0.159768 | − | 0.987155i | \(-0.448925\pi\) |
−0.987155 | + | 0.159768i | \(0.948925\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 19.2191i | 1.42072i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.03500i | 0.223137i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.52496 | + | 4.52496i | 0.330898 | + | 0.330898i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.70649 | − | 1.70649i | 0.124129 | − | 0.124129i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.4022 | 1.33153 | 0.665767 | − | 0.746160i | \(-0.268105\pi\) | ||||
0.665767 | + | 0.746160i | \(0.268105\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.72357 | 0.555954 | 0.277977 | − | 0.960588i | \(-0.410336\pi\) | ||||
0.277977 | + | 0.960588i | \(0.410336\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.41236 | + | 2.41236i | −0.172753 | + | 0.172753i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.23103 | + | 3.23103i | 0.230201 | + | 0.230201i | 0.812777 | − | 0.582575i | \(-0.197955\pi\) |
−0.582575 | + | 0.812777i | \(0.697955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.14152i | − | 0.577137i | −0.957459 | − | 0.288568i | \(-0.906821\pi\) | ||
0.957459 | − | 0.288568i | \(-0.0931793\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.94955i | 0.490183i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.38242 | + | 5.38242i | 0.377772 | + | 0.377772i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.04097 | − | 7.04097i | 0.491763 | − | 0.491763i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.83619 | 0.336138 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.2188 | −0.983532 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.19071 | + | 2.19071i | −0.150814 | + | 0.150814i | −0.778482 | − | 0.627667i | \(-0.784010\pi\) |
0.627667 | + | 0.778482i | \(0.284010\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.5455 | + | 18.5455i | 1.27072 | + | 1.27072i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.484378i | 0.0330343i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.98299i | − | 0.134614i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.8152 | + | 12.8152i | 0.865968 | + | 0.865968i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.12517 | − | 4.12517i | 0.277489 | − | 0.277489i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0943 | −0.675966 | −0.337983 | − | 0.941152i | \(-0.609745\pi\) | ||||
−0.337983 | + | 0.941152i | \(0.609745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.91098 | 0.127399 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.7082 | + | 14.7082i | −0.976218 | + | 0.976218i | −0.999724 | − | 0.0235056i | \(-0.992517\pi\) |
0.0235056 | + | 0.999724i | \(0.492517\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.8816 | − | 18.8816i | −1.24773 | − | 1.24773i | −0.956718 | − | 0.291016i | \(-0.906007\pi\) |
−0.291016 | − | 0.956718i | \(-0.593993\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.74224i | 0.246221i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 17.0786i | − | 1.11886i | −0.828879 | − | 0.559428i | \(-0.811021\pi\) | ||
0.828879 | − | 0.559428i | \(-0.188979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.05801 | − | 3.05801i | −0.199482 | − | 0.199482i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.2618 | + | 13.2618i | −0.861445 | + | 0.861445i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.76620 | 0.502354 | 0.251177 | − | 0.967941i | \(-0.419182\pi\) | ||||
0.251177 | + | 0.967941i | \(0.419182\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.89836 | −0.379947 | −0.189973 | − | 0.981789i | \(-0.560840\pi\) | ||||
−0.189973 | + | 0.981789i | \(0.560840\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −12.2446 | + | 12.2446i | −0.785493 | + | 0.785493i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.707107 | + | 0.707107i | 0.0451754 | + | 0.0451754i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.9625i | 0.824782i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 15.0254i | − | 0.952195i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.0065 | − | 16.0065i | −1.01032 | − | 1.01032i | −0.999946 | − | 0.0103768i | \(-0.996697\pi\) |
−0.0103768 | − | 0.999946i | \(-0.503303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.02188 | − | 3.02188i | 0.189984 | − | 0.189984i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.39784 | −0.525893 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.5127 | 1.03003 | 0.515015 | − | 0.857181i | \(-0.327786\pi\) | ||||
0.515015 | + | 0.857181i | \(0.327786\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.14607 | − | 2.14607i | 0.133350 | − | 0.133350i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.2857 | − | 10.2857i | −0.636670 | − | 0.636670i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 8.22335i | − | 0.507073i | −0.967326 | − | 0.253537i | \(-0.918406\pi\) | ||
0.967326 | − | 0.253537i | \(-0.0815939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0934267i | 0.00573915i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.1528 | − | 28.1528i | −1.72292 | − | 1.72292i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.43495 | − | 9.43495i | 0.575259 | − | 0.575259i | −0.358334 | − | 0.933593i | \(-0.616655\pi\) |
0.933593 | + | 0.358334i | \(0.116655\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.9236 | 1.69624 | 0.848118 | − | 0.529807i | \(-0.177736\pi\) | ||||
0.848118 | + | 0.529807i | \(0.177736\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.41159 | 0.206479 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.19408 | − | 1.19408i | 0.0720055 | − | 0.0720055i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.1281 | + | 20.1281i | 1.20938 | + | 1.20938i | 0.971228 | + | 0.238150i | \(0.0765410\pi\) |
0.238150 | + | 0.971228i | \(0.423459\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.78946i | 0.226869i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 29.4141i | − | 1.75470i | −0.479853 | − | 0.877349i | \(-0.659310\pi\) | ||
0.479853 | − | 0.877349i | \(-0.340690\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.3571 | − | 13.3571i | −0.793999 | − | 0.793999i | 0.188143 | − | 0.982142i | \(-0.439753\pi\) |
−0.982142 | + | 0.188143i | \(0.939753\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.1942 | − | 13.1942i | 0.781559 | − | 0.781559i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.95744 | −0.587769 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.63959 | −0.155270 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.6512 | − | 13.6512i | 0.800248 | − | 0.800248i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.359523 | + | 0.359523i | 0.0210036 | + | 0.0210036i | 0.717531 | − | 0.696527i | \(-0.245272\pi\) |
−0.696527 | + | 0.717531i | \(0.745272\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 4.19278i | − | 0.244113i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.07535i | 0.236476i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.75489 | − | 2.75489i | −0.159319 | − | 0.159319i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.342507 | − | 0.342507i | 0.0197418 | − | 0.0197418i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.91131 | −0.454493 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.67259 | −0.496591 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.1588 | + | 22.1588i | −1.26467 | + | 1.26467i | −0.315863 | + | 0.948805i | \(0.602294\pi\) |
−0.948805 | + | 0.315863i | \(0.897706\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.51529 | + | 2.51529i | 0.143090 | + | 0.143090i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.82146i | − | 0.103286i | −0.998666 | − | 0.0516429i | \(-0.983554\pi\) | ||
0.998666 | − | 0.0516429i | \(-0.0164458\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.18259i | 0.123367i | 0.998096 | + | 0.0616837i | \(0.0196470\pi\) | ||||
−0.998096 | + | 0.0616837i | \(0.980353\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.35127 | − | 1.35127i | −0.0761355 | − | 0.0761355i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.76038 | − | 4.76038i | 0.267370 | − | 0.267370i | −0.560670 | − | 0.828039i | \(-0.689456\pi\) |
0.828039 | + | 0.560670i | \(0.189456\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.8540 | −0.719687 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −39.0533 | −2.17974 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.5623 | + | 22.5623i | −1.25540 | + | 1.25540i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.08857 | − | 1.08857i | −0.0603832 | − | 0.0603832i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.58576i | 0.474794i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.32467i | 0.238427i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.31659 | + | 1.31659i | 0.0723661 | + | 0.0723661i | 0.742363 | − | 0.669997i | \(-0.233705\pi\) |
−0.669997 | + | 0.742363i | \(0.733705\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.10110 | + | 4.10110i | −0.224739 | + | 0.224739i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.13597 | −0.171336 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.65940 | −0.253813 | −0.126907 | − | 0.991915i | \(-0.540505\pi\) | ||||
−0.126907 | + | 0.991915i | \(0.540505\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −23.7585 | + | 23.7585i | −1.29039 | + | 1.29039i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.36784 | + | 2.36784i | 0.128225 | + | 0.128225i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.60829i | 0.301940i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.67385 | − | 6.67385i | −0.358271 | − | 0.358271i | 0.504904 | − | 0.863175i | \(-0.331528\pi\) |
−0.863175 | + | 0.504904i | \(0.831528\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.12213 | − | 4.12213i | 0.220653 | − | 0.220653i | −0.588121 | − | 0.808773i | \(-0.700132\pi\) |
0.808773 | + | 0.588121i | \(0.200132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.71528 | 0.198307 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0645 | 0.961478 | 0.480739 | − | 0.876864i | \(-0.340368\pi\) | ||||
0.480739 | + | 0.876864i | \(0.340368\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.36862 | + | 8.36862i | −0.444160 | + | 0.444160i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.93817 | + | 5.93817i | 0.314281 | + | 0.314281i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 23.7729i | − | 1.25469i | −0.778743 | − | 0.627343i | \(-0.784142\pi\) | ||
0.778743 | − | 0.627343i | \(-0.215858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 51.8972i | − | 2.73143i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.7685 | + | 12.7685i | 0.670172 | + | 0.670172i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.78282 | + | 5.78282i | −0.302686 | + | 0.302686i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.6120 | 1.23254 | 0.616269 | − | 0.787536i | \(-0.288643\pi\) | ||||
0.616269 | + | 0.787536i | \(0.288643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.0285 | 0.990585 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0660626 | − | 0.0660626i | 0.00342980 | − | 0.00342980i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.1118 | − | 19.1118i | −0.989572 | − | 0.989572i | 0.0103739 | − | 0.999946i | \(-0.496698\pi\) |
−0.999946 | + | 0.0103739i | \(0.996698\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.21607i | 0.114438i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.7183i | 0.603524i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.04493 | − | 2.04493i | −0.105041 | − | 0.105041i | 0.652633 | − | 0.757674i | \(-0.273664\pi\) |
−0.757674 | + | 0.652633i | \(0.773664\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.2432 | + | 24.2432i | −1.24202 | + | 1.24202i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.5359 | 1.71360 | 0.856801 | − | 0.515647i | \(-0.172448\pi\) | ||||
0.856801 | + | 0.515647i | \(0.172448\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.68868 | −0.0860630 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.654525 | + | 0.654525i | −0.0332714 | + | 0.0332714i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.06325 | − | 4.06325i | −0.206015 | − | 0.206015i | 0.596556 | − | 0.802571i | \(-0.296535\pi\) |
−0.802571 | + | 0.596556i | \(0.796535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 9.59023i | − | 0.484999i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 23.3190i | − | 1.17629i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.98435 | − | 5.98435i | −0.301106 | − | 0.301106i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.3755 | − | 24.3755i | 1.22337 | − | 1.22337i | 0.256946 | − | 0.966426i | \(-0.417284\pi\) |
0.966426 | − | 0.256946i | \(-0.0827163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.6595 | −0.934141 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.6859 | −0.733378 | −0.366689 | − | 0.930344i | \(-0.619509\pi\) | ||||
−0.366689 | + | 0.930344i | \(0.619509\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.15863 | − | 2.15863i | 0.107529 | − | 0.107529i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.83551 | − | 7.83551i | −0.389350 | − | 0.389350i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.12513i | 0.254043i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.67269i | 0.379390i | 0.981843 | + | 0.189695i | \(0.0607499\pi\) | ||||
−0.981843 | + | 0.189695i | \(0.939250\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.3317 | − | 22.3317i | −1.10154 | − | 1.10154i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.96474 | + | 2.96474i | −0.145885 | + | 0.145885i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.78018 | 0.332826 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −42.8572 | −2.09873 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.61593 | + | 7.61593i | −0.372062 | + | 0.372062i | −0.868228 | − | 0.496166i | \(-0.834741\pi\) |
0.496166 | + | 0.868228i | \(0.334741\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.83236 | − | 6.83236i | −0.332989 | − | 0.332989i | 0.520732 | − | 0.853720i | \(-0.325659\pi\) |
−0.853720 | + | 0.520732i | \(0.825659\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 8.26439i | − | 0.401828i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.78951i | − | 0.183818i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.13245 | + | 6.13245i | 0.296770 | + | 0.296770i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.07370 | + | 4.07370i | −0.196680 | + | 0.196680i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.1817 | −1.30930 | −0.654649 | − | 0.755933i | \(-0.727183\pi\) | ||||
−0.654649 | + | 0.755933i | \(0.727183\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.58371 | 0.364450 | 0.182225 | − | 0.983257i | \(-0.441670\pi\) | ||||
0.182225 | + | 0.983257i | \(0.441670\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.9278 | − | 11.9278i | 0.571896 | − | 0.571896i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.0676 | + | 15.0676i | 0.720783 | + | 0.720783i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 39.4963i | − | 1.88506i | −0.334126 | − | 0.942528i | \(-0.608441\pi\) | ||
0.334126 | − | 0.942528i | \(-0.391559\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.91098i | 0.0909993i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.7530 | − | 20.7530i | −0.986005 | − | 0.986005i | 0.0138986 | − | 0.999903i | \(-0.495576\pi\) |
−0.999903 | + | 0.0138986i | \(0.995576\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.7039 | − | 12.7039i | 0.602223 | − | 0.602223i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.0556 | −0.901298 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.5264 | 0.968702 | 0.484351 | − | 0.874874i | \(-0.339056\pi\) | ||||
0.484351 | + | 0.874874i | \(0.339056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.8899 | − | 11.8899i | 0.559875 | − | 0.559875i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.4224 | − | 12.4224i | −0.583654 | − | 0.583654i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.53948i | 0.0721718i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16.9359i | − | 0.792227i | −0.918201 | − | 0.396114i | \(-0.870359\pi\) | ||
0.918201 | − | 0.396114i | \(-0.129641\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.46676 | + | 6.46676i | 0.301842 | + | 0.301842i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.72100 | − | 8.72100i | 0.406178 | − | 0.406178i | −0.474226 | − | 0.880403i | \(-0.657272\pi\) |
0.880403 | + | 0.474226i | \(0.157272\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.9544 | 0.555567 | 0.277783 | − | 0.960644i | \(-0.410400\pi\) | ||||
0.277783 | + | 0.960644i | \(0.410400\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.39444 | −0.203787 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.9823 | − | 13.9823i | 0.647024 | − | 0.647024i | −0.305249 | − | 0.952273i | \(-0.598740\pi\) |
0.952273 | + | 0.305249i | \(0.0987397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.21747 | + | 2.21747i | 0.102393 | + | 0.102393i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.44333i | 0.112583i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.817958i | 0.0376097i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.95387 | + | 5.95387i | 0.273182 | + | 0.273182i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.126245 | + | 0.126245i | −0.00578035 | + | 0.00578035i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.6487 | −1.30899 | −0.654497 | − | 0.756064i | \(-0.727120\pi\) | ||||
−0.654497 | + | 0.756064i | \(0.727120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.67231 | 0.213039 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.96566 | − | 3.96566i | 0.180444 | − | 0.180444i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.16009 | + | 6.16009i | 0.279715 | + | 0.279715i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.1238i | − | 1.00253i | −0.865295 | − | 0.501263i | \(-0.832869\pi\) | ||
0.865295 | − | 0.501263i | \(-0.167131\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.8591i | 0.852840i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.29198 | + | 2.29198i | 0.103436 | + | 0.103436i | 0.756931 | − | 0.653495i | \(-0.226698\pi\) |
−0.653495 | + | 0.756931i | \(0.726698\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −20.3967 | + | 20.3967i | −0.918623 | + | 0.918623i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.22704 | 0.145045 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.8350 | 0.530873 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.9222 | − | 25.9222i | 1.16044 | − | 1.16044i | 0.176055 | − | 0.984380i | \(-0.443666\pi\) |
0.984380 | − | 0.176055i | \(-0.0563338\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.1377 | − | 28.1377i | −1.25710 | − | 1.25710i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 12.3871i | − | 0.552314i | −0.961113 | − | 0.276157i | \(-0.910939\pi\) | ||
0.961113 | − | 0.276157i | \(-0.0890609\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.56997i | − | 0.158861i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.6572 | − | 16.6572i | −0.739774 | − | 0.739774i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.8833 | + | 25.8833i | −1.14726 | + | 1.14726i | −0.160167 | + | 0.987090i | \(0.551203\pi\) |
−0.987090 | + | 0.160167i | \(0.948797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.17814 | 0.361780 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.3204 | −0.897169 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.13502 | + | 1.13502i | −0.0500151 | + | 0.0500151i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.16399 | − | 5.16399i | −0.227112 | − | 0.227112i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 36.1840i | 1.58830i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.6954i | 0.687626i | 0.939038 | + | 0.343813i | \(0.111719\pi\) | ||||
−0.939038 | + | 0.343813i | \(0.888281\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.54028 | + | 1.54028i | 0.0673516 | + | 0.0673516i | 0.739980 | − | 0.672629i | \(-0.234835\pi\) |
−0.672629 | + | 0.739980i | \(0.734835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.56700 | − | 1.56700i | 0.0683895 | − | 0.0683895i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.51455 | 0.327339 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.5954 | 0.721539 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.66557 | − | 5.66557i | 0.245865 | − | 0.245865i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.8394 | − | 10.8394i | −0.469507 | − | 0.469507i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 17.6228i | − | 0.761898i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 29.1481i | 1.25784i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.19408 | + | 1.19408i | 0.0514325 | + | 0.0514325i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.33236 | − | 8.33236i | 0.358236 | − | 0.358236i | −0.504926 | − | 0.863162i | \(-0.668480\pi\) |
0.863162 | + | 0.504926i | \(0.168480\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 34.8857 | 1.49709 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.87431 | −0.165957 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.4887 | − | 19.4887i | 0.833277 | − | 0.833277i | −0.154687 | − | 0.987964i | \(-0.549437\pi\) |
0.987964 | + | 0.154687i | \(0.0494369\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.7190 | − | 11.7190i | −0.500155 | − | 0.500155i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 64.0924i | − | 2.73043i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.46315i | 0.359890i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.75584 | − | 4.75584i | −0.201874 | − | 0.201874i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.10316 | + | 4.10316i | −0.173856 | + | 0.173856i | −0.788671 | − | 0.614815i | \(-0.789231\pi\) |
0.614815 | + | 0.788671i | \(0.289231\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.745688 | 0.0315392 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.1812 | −0.598733 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.37360 | − | 1.37360i | 0.0578902 | − | 0.0578902i | −0.677569 | − | 0.735459i | \(-0.736966\pi\) |
0.735459 | + | 0.677569i | \(0.236966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.7210 | − | 10.7210i | −0.451036 | − | 0.451036i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.0811i | 0.465362i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 34.6455i | 1.45241i | 0.687476 | + | 0.726207i | \(0.258719\pi\) | ||||
−0.687476 | + | 0.726207i | \(0.741281\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.0843 | + | 28.0843i | 1.17529 | + | 1.17529i | 0.980930 | + | 0.194361i | \(0.0622632\pi\) |
0.194361 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.8362 | + | 28.8362i | −1.20465 | + | 1.20465i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.53073 | −0.105539 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.3949 | −0.973941 | −0.486971 | − | 0.873418i | \(-0.661898\pi\) | ||||
−0.486971 | + | 0.873418i | \(0.661898\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.1028 | + | 12.1028i | −0.502977 | + | 0.502977i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.79431 | − | 4.79431i | −0.198902 | − | 0.198902i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.157768i | 0.00653406i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.94192i | − | 0.121633i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.4086 | − | 14.4086i | −0.594705 | − | 0.594705i | 0.344194 | − | 0.938899i | \(-0.388152\pi\) |
−0.938899 | + | 0.344194i | \(0.888152\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.8064 | + | 11.8064i | −0.486476 | + | 0.486476i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.1260 | −0.416530 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.97073 | −0.286253 | −0.143127 | − | 0.989704i | \(-0.545716\pi\) | ||||
−0.143127 | + | 0.989704i | \(0.545716\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.67959 | + | 2.67959i | −0.109852 | + | 0.109852i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.7578 | + | 12.7578i | 0.522141 | + | 0.522141i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 0.671165i | − | 0.0274231i | −0.999906 | − | 0.0137115i | \(-0.995635\pi\) | ||
0.999906 | − | 0.0137115i | \(-0.00436465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.3989i | 1.36237i | 0.732111 | + | 0.681185i | \(0.238535\pi\) | ||||
−0.732111 | + | 0.681185i | \(0.761465\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.23755 | − | 4.23755i | −0.172566 | − | 0.172566i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.76177 | + | 5.76177i | −0.234249 | + | 0.234249i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.5572 | −0.753212 | −0.376606 | − | 0.926374i | \(-0.622909\pi\) | ||||
−0.376606 | + | 0.926374i | \(0.622909\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.8685 | −0.683546 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.70773 | + | 4.70773i | −0.190454 | + | 0.190454i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6712 | + | 16.6712i | 0.673345 | + | 0.673345i | 0.958486 | − | 0.285141i | \(-0.0920403\pi\) |
−0.285141 | + | 0.958486i | \(0.592040\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.0664i | 0.889804i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.1103i | 1.41349i | 0.707470 | + | 0.706744i | \(0.249837\pi\) | ||||
−0.707470 | + | 0.706744i | \(0.750163\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.33010 | + | 6.33010i | 0.254428 | + | 0.254428i | 0.822783 | − | 0.568355i | \(-0.192420\pi\) |
−0.568355 | + | 0.822783i | \(0.692420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.31866 | − | 4.31866i | 0.173302 | − | 0.173302i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.9660 | −0.719794 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22.2808 | − | 22.2808i | 0.889809 | − | 0.889809i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.13255 | + | 8.13255i | 0.324266 | + | 0.324266i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.80873i | − | 0.111814i | −0.998436 | − | 0.0559069i | \(-0.982195\pi\) | ||
0.998436 | − | 0.0559069i | \(-0.0178050\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.86568i | − | 0.272886i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.9397 | − | 10.9397i | −0.434129 | − | 0.434129i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.08857 | − | 1.08857i | 0.0431309 | − | 0.0431309i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.6165 | −0.894696 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3083 | 0.446650 | 0.223325 | − | 0.974744i | \(-0.428309\pi\) | ||||
0.223325 | + | 0.974744i | \(0.428309\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.41909 | − | 2.41909i | 0.0953997 | − | 0.0953997i | −0.657796 | − | 0.753196i | \(-0.728511\pi\) |
0.753196 | + | 0.657796i | \(0.228511\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.759020 | − | 0.759020i | −0.0298864 | − | 0.0298864i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.4567i | 1.82640i | 0.407512 | + | 0.913200i | \(0.366396\pi\) | ||||
−0.407512 | + | 0.913200i | \(0.633604\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 7.08025i | − | 0.277924i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.10734 | + | 3.10734i | 0.121786 | + | 0.121786i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.9851 | + | 27.9851i | −1.09514 | + | 1.09514i | −0.100170 | + | 0.994970i | \(0.531939\pi\) |
−0.994970 | + | 0.100170i | \(0.968061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.5226 | 0.411154 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.6283 | −0.609718 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.2972 | + | 29.2972i | −1.14126 | + | 1.14126i | −0.153039 | + | 0.988220i | \(0.548906\pi\) |
−0.988220 | + | 0.153039i | \(0.951094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.4083 | + | 27.4083i | 1.06606 | + | 1.06606i | 0.997658 | + | 0.0684007i | \(0.0217896\pi\) |
0.0684007 | + | 0.997658i | \(0.478210\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.9283i | 0.502093i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 8.42005i | − | 0.326516i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.6214 | + | 13.6214i | 0.527424 | + | 0.527424i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 15.8178 | − | 15.8178i | 0.611552 | − | 0.611552i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.6452 | −0.565372 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.8026 | −1.22590 | −0.612950 | − | 0.790122i | \(-0.710017\pi\) | ||||
−0.612950 | + | 0.790122i | \(0.710017\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.70649 | − | 1.70649i | 0.0656827 | − | 0.0656827i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.3856 | − | 13.3856i | −0.514451 | − | 0.514451i | 0.401436 | − | 0.915887i | \(-0.368511\pi\) |
−0.915887 | + | 0.401436i | \(0.868511\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 8.71168i | − | 0.334324i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 46.0956i | − | 1.76639i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.17288 | − | 3.17288i | −0.121407 | − | 0.121407i | 0.643793 | − | 0.765200i | \(-0.277360\pi\) |
−0.765200 | + | 0.643793i | \(0.777360\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.0772 | − | 10.0772i | 0.385028 | − | 0.385028i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 59.1751 | 2.25767 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.143828 | 0.00547942 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.7745 | − | 19.7745i | 0.752257 | − | 0.752257i | −0.222643 | − | 0.974900i | \(-0.571468\pi\) |
0.974900 | + | 0.222643i | \(0.0714684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.28186 | − | 2.28186i | −0.0866807 | − | 0.0866807i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 19.3393i | − | 0.733580i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 37.7339i | − | 1.42927i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.7622 | + | 26.7622i | 1.01224 | + | 1.01224i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.7909 | + | 16.7909i | −0.634183 | + | 0.634183i | −0.949114 | − | 0.314931i | \(-0.898018\pi\) |
0.314931 | + | 0.949114i | \(0.398018\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.5548 | −0.963819 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.58380 | 0.360947 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.52435 | + | 2.52435i | −0.0949379 | + | 0.0949379i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0620 | + | 10.0620i | 0.377888 | + | 0.377888i | 0.870340 | − | 0.492452i | \(-0.163899\pi\) |
−0.492452 | + | 0.870340i | \(0.663899\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 16.1730i | − | 0.606533i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.01840i | − | 0.187941i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.83825 | − | 1.83825i | −0.0687467 | − | 0.0687467i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.1696 | + | 12.1696i | −0.454484 | + | 0.454484i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.0270 | −1.41817 | −0.709083 | − | 0.705125i | \(-0.750891\pi\) | ||||
−0.709083 | + | 0.705125i | \(0.750891\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.60516 | 0.0597794 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.24274 | − | 9.24274i | 0.343741 | − | 0.343741i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.38242 | + | 5.38242i | 0.199898 | + | 0.199898i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.5488i | 0.613761i | 0.951748 | + | 0.306881i | \(0.0992852\pi\) | ||||
−0.951748 | + | 0.306881i | \(0.900715\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 5.13139i | − | 0.190051i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.29793 | + | 1.29793i | 0.0480058 | + | 0.0480058i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.9078 | − | 23.9078i | 0.883055 | − | 0.883055i | −0.110789 | − | 0.993844i | \(-0.535338\pi\) |
0.993844 | + | 0.110789i | \(0.0353376\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.21607 | −0.0817411 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.29565 | −0.195068 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.69669 | − | 1.69669i | 0.0624138 | − | 0.0624138i | −0.675211 | − | 0.737625i | \(-0.735947\pi\) |
0.737625 | + | 0.675211i | \(0.235947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.3122 | − | 20.3122i | −0.746187 | − | 0.746187i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.32561i | 0.0486318i | 0.999704 | + | 0.0243159i | \(0.00774075\pi\) | ||||
−0.999704 | + | 0.0243159i | \(0.992259\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 8.59880i | − | 0.315036i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.16186 | + | 9.16186i | 0.335215 | + | 0.335215i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.4612 | + | 12.4612i | −0.455321 | + | 0.455321i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −49.2984 | −1.79893 | −0.899463 | − | 0.436998i | \(-0.856042\pi\) | ||||
−0.899463 | + | 0.436998i | \(0.856042\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 50.1645 | 1.82810 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.60558 | − | 5.60558i | 0.204008 | − | 0.204008i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.110528 | + | 0.110528i | 0.00401720 | + | 0.00401720i | 0.709113 | − | 0.705095i | \(-0.249096\pi\) |
−0.705095 | + | 0.709113i | \(0.749096\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.47059i | 0.343761i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.0380i | 1.66888i | 0.551101 | + | 0.834438i | \(0.314208\pi\) | ||||
−0.551101 | + | 0.834438i | \(0.685792\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.73955 | + | 2.73955i | 0.0991784 | + | 0.0991784i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.12066 | − | 5.12066i | 0.185138 | − | 0.185138i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.45468 | −0.233065 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.8023 | 1.75986 | 0.879929 | − | 0.475106i | \(-0.157590\pi\) | ||||
0.879929 | + | 0.475106i | \(0.157590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.8753 | + | 25.8753i | −0.931878 | + | 0.931878i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.1791 | + | 10.1791i | 0.366116 | + | 0.366116i | 0.866058 | − | 0.499943i | \(-0.166646\pi\) |
−0.499943 | + | 0.866058i | \(0.666646\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.98299i | − | 0.0712310i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.72578i | 0.241286i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 59.2854 | + | 59.2854i | 2.12412 | + | 2.12412i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.1319 | + | 14.1319i | −0.505679 | + | 0.505679i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.3701 | −0.656492 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.10255 | −0.0393516 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.0676 | − | 25.0676i | 0.893562 | − | 0.893562i | −0.101294 | − | 0.994857i | \(-0.532298\pi\) |
0.994857 | + | 0.101294i | \(0.0322983\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.8860 | + | 12.8860i | 0.458754 | + | 0.458754i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.1618i | 0.539091i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.3512i | 0.474117i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.146400 | − | 0.146400i | −0.00519226 | − | 0.00519226i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.7500 | − | 26.7500i | 0.947533 | − | 0.947533i | −0.0511580 | − | 0.998691i | \(-0.516291\pi\) |
0.998691 | + | 0.0511580i | \(0.0162912\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.3884 | −0.579780 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.3328 | 1.21309 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.76532 | + | 9.76532i | −0.344610 | + | 0.344610i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.78950 | + | 1.78950i | 0.0630715 | + | 0.0630715i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.5692i | 1.04088i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 32.3562i | − | 1.13758i | −0.822481 | − | 0.568792i | \(-0.807411\pi\) | ||
0.822481 | − | 0.568792i | \(-0.192589\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.1442 | + | 14.1442i | 0.496670 | + | 0.496670i | 0.910400 | − | 0.413730i | \(-0.135774\pi\) |
−0.413730 | + | 0.910400i | \(0.635774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −43.7563 | + | 43.7563i | −1.53460 | + | 1.53460i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.51016 | −0.298098 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.07848 | −0.142688 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.08025 | + | 2.08025i | −0.0726898 | + | 0.0726898i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.55314 | + | 9.55314i | 0.333407 | + | 0.333407i | 0.853879 | − | 0.520472i | \(-0.174244\pi\) |
−0.520472 | + | 0.853879i | \(0.674244\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.435281i | 0.0151729i | 0.999971 | + | 0.00758647i | \(0.00241487\pi\) | ||||
−0.999971 | + | 0.00758647i | \(0.997585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.74224i | 0.130288i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.50281 | + | 4.50281i | 0.156578 | + | 0.156578i | 0.781048 | − | 0.624470i | \(-0.214685\pi\) |
−0.624470 | + | 0.781048i | \(0.714685\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.1416 | + | 28.1416i | −0.977399 | + | 0.977399i | −0.999750 | − | 0.0223513i | \(-0.992885\pi\) |
0.0223513 | + | 0.999750i | \(0.492885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −63.0814 | −2.18827 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.78951 | 0.131299 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.6971 | − | 12.6971i | 0.439400 | − | 0.439400i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.38394 | + | 3.38394i | 0.116966 | + | 0.116966i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 10.4652i | − | 0.361299i | −0.983548 | − | 0.180649i | \(-0.942180\pi\) | ||
0.983548 | − | 0.180649i | \(-0.0578200\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 28.9408i | − | 0.997958i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 46.0919 | + | 46.0919i | 1.58749 | + | 1.58749i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.51655 | − | 7.51655i | 0.258577 | − | 0.258577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.14837 | 0.279981 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.8613 | 1.43668 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.43112 | − | 5.43112i | 0.186176 | − | 0.186176i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.20752 | − | 3.20752i | −0.109823 | − | 0.109823i | 0.650060 | − | 0.759883i | \(-0.274744\pi\) |
−0.759883 | + | 0.650060i | \(0.774744\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.0906i | 0.550286i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.88694i | − | 0.0644566i | −0.999481 | − | 0.0322283i | \(-0.989740\pi\) | ||
0.999481 | − | 0.0322283i | \(-0.0102604\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.8963 | − | 18.8963i | −0.644735 | − | 0.644735i | 0.306981 | − | 0.951716i | \(-0.400681\pi\) |
−0.951716 | + | 0.306981i | \(0.900681\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.6033 | − | 15.6033i | 0.531760 | − | 0.531760i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.3749 | −0.795689 | −0.397845 | − | 0.917453i | \(-0.630242\pi\) | ||||
−0.397845 | + | 0.917453i | \(0.630242\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.3280 | −0.555168 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.13624 | − | 4.13624i | 0.140474 | − | 0.140474i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.1056 | − | 10.1056i | −0.342811 | − | 0.342811i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.82775i | 0.163582i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.6479i | 0.563446i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.707107 | + | 0.707107i | 0.0239046 | + | 0.0239046i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.2855 | − | 35.2855i | 1.19151 | − | 1.19151i | 0.214864 | − | 0.976644i | \(-0.431069\pi\) |
0.976644 | − | 0.214864i | \(-0.0689307\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.12675 | −0.0380042 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 36.7860 | 1.23935 | 0.619675 | − | 0.784858i | \(-0.287264\pi\) | ||||
0.619675 | + | 0.784858i | \(0.287264\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.2710 | + | 17.2710i | −0.581216 | + | 0.581216i | −0.935237 | − | 0.354022i | \(-0.884814\pi\) |
0.354022 | + | 0.935237i | \(0.384814\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.57008 | + | 6.57008i | 0.220851 | + | 0.220851i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 38.2383i | − | 1.28391i | −0.766740 | − | 0.641957i | \(-0.778123\pi\) | ||
0.766740 | − | 0.641957i | \(-0.221877\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15.4711i | 0.518883i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.2317 | − | 13.2317i | −0.443277 | − | 0.443277i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.7486 | − | 25.7486i | 0.861643 | − | 0.861643i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.1531 | −0.439658 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.63382 | 0.288275 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.6733 | + | 10.6733i | −0.355973 | + | 0.355973i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.250345 | + | 0.250345i | 0.00834021 | + | 0.00834021i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.07342i | 0.0357211i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 15.7421i | 0.523285i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.62813 | − | 3.62813i | −0.120470 | − | 0.120470i | 0.644302 | − | 0.764772i | \(-0.277148\pi\) |
−0.764772 | + | 0.644302i | \(0.777148\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.82399 | − | 4.82399i | 0.160002 | − | 0.160002i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.8481 | 1.32023 | 0.660114 | − | 0.751166i | \(-0.270508\pi\) | ||||
0.660114 | + | 0.751166i | \(0.270508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.4495 | 0.378924 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.5900 | − | 13.5900i | 0.449270 | − | 0.449270i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.44063 | − | 7.44063i | −0.245711 | − | 0.245711i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 47.4733i | 1.56600i | 0.622022 | + | 0.783000i | \(0.286311\pi\) | ||||
−0.622022 | + | 0.783000i | \(0.713689\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 69.4456i | − | 2.28831i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.8833 | + | 12.8833i | 0.424059 | + | 0.424059i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.14607 | − | 2.14607i | 0.0705623 | − | 0.0705623i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.06744 | −0.100748 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.9057 | −0.685894 | −0.342947 | − | 0.939355i | \(-0.611425\pi\) | ||||
−0.342947 | + | 0.939355i | \(0.611425\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.95387 | + | 5.95387i | −0.195130 | + | 0.195130i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.85424 | + | 2.85424i | 0.0934435 | + | 0.0934435i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 6.39927i | − | 0.209278i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.7301i | 0.350536i | 0.984521 | + | 0.175268i | \(0.0560793\pi\) | ||||
−0.984521 | + | 0.175268i | \(0.943921\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.42012 | − | 3.42012i | −0.111611 | − | 0.111611i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.3926 | − | 10.3926i | 0.338790 | − | 0.338790i | −0.517122 | − | 0.855912i | \(-0.672997\pi\) |
0.855912 | + | 0.517122i | \(0.172997\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.1996 | −0.820612 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.41334 | −0.0785059 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.2724 | − | 28.2724i | 0.918731 | − | 0.918731i | −0.0782060 | − | 0.996937i | \(-0.524919\pi\) |
0.996937 | + | 0.0782060i | \(0.0249192\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.90251 | + | 8.90251i | 0.288988 | + | 0.288988i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.9190i | 0.483783i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.9583i | − | 0.387366i | −0.981064 | − | 0.193683i | \(-0.937957\pi\) | ||
0.981064 | − | 0.193683i | \(-0.0620433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.0123 | − | 13.0123i | −0.421068 | − | 0.421068i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.1423 | − | 20.1423i | 0.651107 | − | 0.651107i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.2513 | −0.460197 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0678 | −0.873154 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 23.8131 | − | 23.8131i | 0.767367 | − | 0.767367i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.46139 | − | 5.46139i | −0.175808 | − | 0.175808i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.2546i | 0.715660i | 0.933787 | + | 0.357830i | \(0.116483\pi\) | ||||
−0.933787 | + | 0.357830i | \(0.883517\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 70.7102i | − | 2.27154i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.7588 | + | 21.7588i | 0.698274 | + | 0.698274i | 0.964038 | − | 0.265764i | \(-0.0856243\pi\) |
−0.265764 | + | 0.964038i | \(0.585624\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.6749 | + | 13.6749i | −0.438398 | + | 0.438398i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.41159 | 0.109258 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 57.4976 | 1.83951 | 0.919756 | − | 0.392491i | \(-0.128387\pi\) | ||||
0.919756 | + | 0.392491i | \(0.128387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.4528 | − | 21.4528i | 0.685634 | − | 0.685634i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.23524 | − | 5.23524i | −0.167148 | − | 0.167148i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.6196i | 1.07230i | 0.844123 | + | 0.536149i | \(0.180121\pi\) | ||||
−0.844123 | + | 0.536149i | \(0.819879\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 4.56936i | − | 0.145592i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.77677 | − | 6.77677i | −0.215707 | − | 0.215707i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.866792 | − | 0.866792i | 0.0275624 | − | 0.0275624i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.02283 | 0.159555 | 0.0797777 | − | 0.996813i | \(-0.474579\pi\) | ||||
0.0797777 | + | 0.996813i | \(0.474579\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.12618 | −0.130940 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.75692 | + | 5.75692i | −0.182507 | + | 0.182507i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.7235 | − | 17.7235i | −0.561308 | − | 0.561308i | 0.368371 | − | 0.929679i | \(-0.379916\pi\) |
−0.929679 | + | 0.368371i | \(0.879916\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.32448i | 0.231736i |
(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 | 2240.2.bd.b.561.6 | 52 | ||
4.3 | odd | 2 | 560.2.bd.b.421.26 | yes | 52 | ||
16.3 | odd | 4 | 560.2.bd.b.141.26 | ✓ | 52 | ||
16.13 | even | 4 | inner | 2240.2.bd.b.1681.6 | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.bd.b.141.26 | ✓ | 52 | 16.3 | odd | 4 | ||
560.2.bd.b.421.26 | yes | 52 | 4.3 | odd | 2 | ||
2240.2.bd.b.561.6 | 52 | 1.1 | even | 1 | trivial | ||
2240.2.bd.b.1681.6 | 52 | 16.13 | even | 4 | inner |