Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(9,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.j (of order \(10\), degree \(4\), 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.484000000.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + 16x^{4} - 66x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 444.1 | ||
Root | \(-1.46782 + 0.476925i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.444 |
Dual form | 605.2.j.a.124.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46782 | + | 2.02029i | −1.03791 | + | 1.42856i | −0.139068 | + | 0.990283i | \(0.544411\pi\) |
−0.898841 | + | 0.438276i | \(0.855589\pi\) | |||||||
\(3\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(4\) | −1.30902 | − | 4.02874i | −0.654508 | − | 2.01437i | ||||
\(5\) | −1.80902 | + | 1.31433i | −0.809017 | + | 0.587785i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.93565 | − | 0.953850i | 1.10957 | − | 0.360521i | 0.303792 | − | 0.952738i | \(-0.401747\pi\) |
0.805779 | + | 0.592217i | \(0.201747\pi\) | |||||||
\(8\) | 5.31064 | + | 1.72553i | 1.87759 | + | 0.610067i | ||||
\(9\) | −2.42705 | − | 1.76336i | −0.809017 | − | 0.587785i | ||||
\(10\) | − | 5.58394i | − | 1.76580i | ||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.12132 | − | 1.54336i | 0.310998 | − | 0.428052i | −0.624694 | − | 0.780869i | \(-0.714776\pi\) |
0.935692 | + | 0.352818i | \(0.114776\pi\) | |||||||
\(14\) | −2.38197 | + | 7.33094i | −0.636607 | + | 1.95928i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.42705 | + | 3.21644i | −1.10676 | + | 0.804110i | ||||
\(17\) | 4.74998 | + | 6.53779i | 1.15204 | + | 1.58565i | 0.737079 | + | 0.675806i | \(0.236204\pi\) |
0.414960 | + | 0.909840i | \(0.363796\pi\) | |||||||
\(18\) | 7.12497 | − | 2.31504i | 1.67937 | − | 0.545661i | ||||
\(19\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(20\) | 7.66312 | + | 5.56758i | 1.71353 | + | 1.24495i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.54508 | − | 4.75528i | 0.309017 | − | 0.951057i | ||||
\(26\) | 1.47214 | + | 4.53077i | 0.288710 | + | 0.888557i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.68563 | − | 10.5784i | −1.45245 | − | 1.99912i | ||||
\(29\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.23607 | + | 5.25731i | 1.29964 | + | 0.944241i | 0.999952 | − | 0.00979752i | \(-0.00311870\pi\) |
0.299684 | + | 0.954038i | \(0.403119\pi\) | |||||||
\(32\) | − | 2.49721i | − | 0.441449i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −20.1803 | −3.46090 | ||||||||
\(35\) | −4.05697 | + | 5.58394i | −0.685753 | + | 0.943857i | ||||
\(36\) | −3.92705 | + | 12.0862i | −0.654508 | + | 2.01437i | ||||
\(37\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.8749 | + | 3.85840i | −1.87759 | + | 0.610067i | ||||
\(41\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.0756i | 1.99401i | 0.0773627 | + | 0.997003i | \(0.475350\pi\) | ||||
−0.0773627 | + | 0.997003i | \(0.524650\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.70820 | 1.00000 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.04508 | − | 1.48584i | 0.292155 | − | 0.212263i | ||||
\(50\) | 7.33912 | + | 10.1014i | 1.03791 | + | 1.42856i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.68563 | − | 2.49721i | −1.06580 | − | 0.346301i | ||||
\(53\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 17.2361 | 2.30327 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.23607 | − | 3.80423i | −0.160922 | − | 0.495268i | 0.837790 | − | 0.545992i | \(-0.183847\pi\) |
−0.998713 | + | 0.0507240i | \(0.983847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(62\) | −21.2426 | + | 6.90212i | −2.69781 | + | 0.876571i | ||||
\(63\) | −8.80695 | − | 2.86155i | −1.10957 | − | 0.360521i | ||||
\(64\) | −3.80902 | − | 2.76741i | −0.476127 | − | 0.345927i | ||||
\(65\) | 4.26575i | 0.529101i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 20.1212 | − | 27.6945i | 2.44006 | − | 3.35845i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.32624 | − | 16.3925i | −0.636607 | − | 1.95928i | ||||
\(71\) | −6.47214 | + | 4.70228i | −0.768101 | + | 0.558058i | −0.901384 | − | 0.433020i | \(-0.857448\pi\) |
0.133283 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(72\) | −9.84647 | − | 13.5525i | −1.16042 | − | 1.59718i | ||||
\(73\) | 11.3143 | − | 3.67624i | 1.32424 | − | 0.430271i | 0.440289 | − | 0.897856i | \(-0.354876\pi\) |
0.883948 | + | 0.467585i | \(0.154876\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(80\) | 3.78115 | − | 11.6372i | 0.422746 | − | 1.30108i | ||||
\(81\) | 2.78115 | + | 8.55951i | 0.309017 | + | 0.951057i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.428305 | − | 0.589512i | −0.0470126 | − | 0.0647073i | 0.784863 | − | 0.619669i | \(-0.212733\pi\) |
−0.831876 | + | 0.554961i | \(0.812733\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −17.1856 | − | 5.58394i | −1.86404 | − | 0.605663i | ||||
\(86\) | −26.4164 | − | 19.1926i | −2.84855 | − | 2.06960i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.4164 | 1.42214 | 0.711068 | − | 0.703123i | \(-0.248212\pi\) | ||||
0.711068 | + | 0.703123i | \(0.248212\pi\) | |||||||
\(90\) | −9.84647 | + | 13.5525i | −1.03791 | + | 1.42856i | ||||
\(91\) | 1.81966 | − | 5.60034i | 0.190752 | − | 0.587075i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(98\) | 6.31261i | 0.637670i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −21.1803 | −2.11803 | ||||||||
\(101\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(104\) | 8.61803 | − | 6.26137i | 0.845068 | − | 0.613978i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.3069 | + | 5.94827i | 1.76980 | + | 0.575041i | 0.998138 | − | 0.0609970i | \(-0.0194280\pi\) |
0.771657 | + | 0.636038i | \(0.219428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −9.92826 | + | 13.6651i | −0.938133 | + | 1.29123i | ||||
\(113\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.44299 | + | 1.76854i | −0.503205 | + | 0.163501i | ||||
\(118\) | 9.49996 | + | 3.08672i | 0.874542 | + | 0.284156i | ||||
\(119\) | 20.1803 | + | 14.6619i | 1.84993 | + | 1.34405i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.7082 | − | 36.0341i | 1.05143 | − | 3.23596i | ||||
\(125\) | 3.45492 | + | 10.6331i | 0.309017 | + | 0.951057i | ||||
\(126\) | 18.7082 | − | 13.5923i | 1.66666 | − | 1.21090i | ||||
\(127\) | 9.92826 | + | 13.6651i | 0.880991 | + | 1.21258i | 0.976145 | + | 0.217118i | \(0.0696655\pi\) |
−0.0951544 | + | 0.995463i | \(0.530334\pi\) | |||||||
\(128\) | 15.9319 | − | 5.17659i | 1.40820 | − | 0.457551i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.61803 | − | 6.26137i | −0.755852 | − | 0.549158i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.9443 | + | 42.9161i | 1.19571 | + | 3.68002i | ||||
\(137\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(140\) | 27.8069 | + | 9.03500i | 2.35011 | + | 0.763597i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 19.9777i | − | 1.67649i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 16.4164 | 1.36803 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.18034 | + | 28.2542i | −0.759770 | + | 2.33833i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 24.2434i | − | 1.95997i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.0000 | −1.60644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.28216 | + | 4.51750i | 0.259477 | + | 0.357140i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −21.3749 | − | 6.94513i | −1.67937 | − | 0.545661i | ||||
\(163\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.81966 | 0.141233 | ||||||||
\(167\) | 6.29960 | − | 8.67066i | 0.487478 | − | 0.670956i | −0.492442 | − | 0.870345i | \(-0.663896\pi\) |
0.979920 | + | 0.199389i | \(0.0638958\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.89261 | + | 8.90254i | 0.222508 | + | 0.684810i | ||||
\(170\) | 36.5066 | − | 26.5236i | 2.79993 | − | 2.03427i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 52.6781 | − | 17.1161i | 4.01667 | − | 1.30509i | ||||
\(173\) | 9.92826 | + | 3.22589i | 0.754832 | + | 0.245260i | 0.661059 | − | 0.750334i | \(-0.270107\pi\) |
0.0937729 | + | 0.995594i | \(0.470107\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 15.4336i | − | 1.16667i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −19.6929 | + | 27.1050i | −1.47605 | + | 2.03161i | ||||
\(179\) | 5.52786 | − | 17.0130i | 0.413172 | − | 1.27161i | −0.500704 | − | 0.865619i | \(-0.666925\pi\) |
0.913876 | − | 0.405994i | \(-0.133075\pi\) | |||||||
\(180\) | −8.78115 | − | 27.0256i | −0.654508 | − | 2.01437i | ||||
\(181\) | −3.61803 | + | 2.62866i | −0.268926 | + | 0.195386i | −0.714073 | − | 0.700071i | \(-0.753152\pi\) |
0.445147 | + | 0.895458i | \(0.353152\pi\) | |||||||
\(182\) | 8.64335 | + | 11.8965i | 0.640688 | + | 0.881831i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.29180 | − | 25.5195i | −0.599973 | − | 1.84653i | −0.528224 | − | 0.849105i | \(-0.677142\pi\) |
−0.0717497 | − | 0.997423i | \(-0.522858\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0073 | − | 16.5266i | −0.864305 | − | 1.18961i | −0.980526 | − | 0.196390i | \(-0.937078\pi\) |
0.116221 | − | 0.993223i | \(-0.462922\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.66312 | − | 6.29412i | −0.618794 | − | 0.449580i | ||||
\(197\) | 21.8854i | 1.55927i | 0.626234 | + | 0.779635i | \(0.284595\pi\) | ||||
−0.626234 | + | 0.779635i | \(0.715405\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 16.4108 | − | 22.5875i | 1.16042 | − | 1.59718i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.4392i | 0.723828i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −38.8885 | + | 28.2542i | −2.65837 | + | 1.93142i | ||||
\(215\) | −17.1856 | − | 23.6539i | −1.17205 | − | 1.61318i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 26.2572 | + | 8.53149i | 1.78246 | + | 0.579156i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.4164 | 1.03702 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(224\) | −2.38197 | − | 7.33094i | −0.159152 | − | 0.489819i | ||||
\(225\) | −12.1353 | + | 8.81678i | −0.809017 | + | 0.587785i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.1782 | + | 7.85597i | −1.60476 | + | 0.521419i | −0.968279 | − | 0.249870i | \(-0.919612\pi\) |
−0.636484 | + | 0.771290i | \(0.719612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.85410 | − | 3.52671i | −0.320768 | − | 0.233052i | 0.415735 | − | 0.909486i | \(-0.363524\pi\) |
−0.736503 | + | 0.676434i | \(0.763524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.23525 | + | 12.7112i | −0.605021 | + | 0.832741i | −0.996156 | − | 0.0875928i | \(-0.972083\pi\) |
0.391135 | + | 0.920333i | \(0.372083\pi\) | |||||||
\(234\) | 4.41641 | − | 13.5923i | 0.288710 | − | 0.888557i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.7082 | + | 9.95959i | −0.892328 | + | 0.648314i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −59.2424 | + | 19.2490i | −3.84011 | + | 1.24773i | ||||
\(239\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.74671 | + | 5.37582i | −0.111593 | + | 0.343449i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 29.3565 | + | 40.4057i | 1.86414 | + | 2.56577i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −26.5532 | − | 8.62766i | −1.67937 | − | 0.545661i | ||||
\(251\) | −22.6525 | − | 16.4580i | −1.42981 | − | 1.03882i | −0.990052 | − | 0.140704i | \(-0.955064\pi\) |
−0.439760 | − | 0.898115i | \(-0.644936\pi\) | |||||||
\(252\) | 39.2267i | 2.47105i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −42.1803 | −2.64663 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.0172 | + | 30.8298i | −0.626076 | + | 1.92686i | ||||
\(257\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 17.1856 | − | 5.58394i | 1.06580 | − | 0.346301i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.54408i | − | 0.280200i | −0.990137 | − | 0.140100i | \(-0.955258\pi\) | ||
0.990137 | − | 0.140100i | \(-0.0447424\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3262 | − | 8.22899i | 0.690573 | − | 0.501731i | −0.186275 | − | 0.982498i | \(-0.559642\pi\) |
0.876848 | + | 0.480767i | \(0.159642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(272\) | −42.0568 | − | 13.6651i | −2.55007 | − | 0.828567i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.8786 | − | 24.6078i | 1.07422 | − | 1.47854i | 0.208493 | − | 0.978024i | \(-0.433144\pi\) |
0.865728 | − | 0.500514i | \(-0.166856\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.29180 | − | 25.5195i | −0.496417 | − | 1.52781i | ||||
\(280\) | −31.1803 | + | 22.6538i | −1.86338 | + | 1.35383i | ||||
\(281\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.5642 | − | 8.30632i | −1.51964 | − | 0.493760i | −0.573963 | − | 0.818881i | \(-0.694595\pi\) |
−0.945672 | + | 0.325121i | \(0.894595\pi\) | |||||||
\(284\) | 27.4164 | + | 19.9192i | 1.62686 | + | 1.18199i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.40347 | + | 6.06086i | −0.259477 | + | 0.357140i | ||||
\(289\) | −14.9271 | + | 45.9407i | −0.878062 | + | 2.70240i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −29.6212 | − | 40.7701i | −1.73345 | − | 2.38589i | ||||
\(293\) | −32.5568 | + | 10.5784i | −1.90199 | + | 0.617994i | −0.947497 | + | 0.319763i | \(0.896397\pi\) |
−0.954494 | + | 0.298231i | \(0.903603\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.23607 | + | 5.25731i | 0.421300 | + | 0.306092i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.4721 | + | 38.3853i | 0.718882 | + | 2.21249i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 48.9787 | + | 35.5851i | 2.79993 | + | 2.03427i | ||||
\(307\) | − | 33.0533i | − | 1.88645i | −0.332155 | − | 0.943225i | \(-0.607776\pi\) | ||
0.332155 | − | 0.943225i | \(-0.392224\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 29.3565 | − | 40.4057i | 1.66734 | − | 2.29489i | ||||
\(311\) | 9.88854 | − | 30.4338i | 0.560728 | − | 1.72574i | −0.119588 | − | 0.992824i | \(-0.538157\pi\) |
0.680316 | − | 0.732919i | \(-0.261843\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 19.6929 | − | 6.39862i | 1.10957 | − | 0.360521i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 10.5279 | 0.588525 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 30.8435 | − | 22.4091i | 1.71353 | − | 1.24495i | ||||
\(325\) | −5.60659 | − | 7.71681i | −0.310998 | − | 0.428052i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.7771 | −1.96649 | −0.983243 | − | 0.182298i | \(-0.941646\pi\) | ||||
−0.983243 | + | 0.182298i | \(0.941646\pi\) | |||||||
\(332\) | −1.81433 | + | 2.49721i | −0.0995743 | + | 0.137052i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.27051 | + | 25.4540i | 0.452542 | + | 1.39278i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.7996 | + | 5.13359i | −0.860657 | + | 0.279644i | −0.705903 | − | 0.708309i | \(-0.749459\pi\) |
−0.154754 | + | 0.987953i | \(0.549459\pi\) | |||||||
\(338\) | −22.2315 | − | 7.22346i | −1.20924 | − | 0.392904i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 76.5457i | 4.15128i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.11393 | + | 11.1679i | −0.438111 | + | 0.603008i | ||||
\(344\) | −22.5623 | + | 69.4396i | −1.21648 | + | 3.74393i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −21.0902 | + | 15.3229i | −1.13381 | + | 0.823764i | ||||
\(347\) | −6.82902 | − | 9.39934i | −0.366601 | − | 0.504583i | 0.585372 | − | 0.810765i | \(-0.300948\pi\) |
−0.951973 | + | 0.306182i | \(0.900948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(350\) | 31.1803 | + | 22.6538i | 1.66666 | + | 1.21090i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.52786 | − | 17.0130i | 0.293389 | − | 0.902957i | ||||
\(356\) | −17.5623 | − | 54.0512i | −0.930800 | − | 2.86471i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.2572 | + | 36.1400i | 1.38774 | + | 1.91006i | ||||
\(359\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(360\) | 35.6248 | + | 11.5752i | 1.87759 | + | 0.610067i | ||||
\(361\) | 15.3713 | + | 11.1679i | 0.809017 | + | 0.587785i | ||||
\(362\) | − | 11.1679i | − | 0.586970i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.9443 | −1.30744 | ||||||||
\(365\) | −15.6360 | + | 21.5211i | −0.818424 | + | 1.12646i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.62379i | − | 0.342967i | −0.985187 | − | 0.171484i | \(-0.945144\pi\) | ||
0.985187 | − | 0.171484i | \(-0.0548560\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.1246 | − | 21.1603i | 1.49603 | − | 1.08693i | 0.524102 | − | 0.851656i | \(-0.324401\pi\) |
0.971929 | − | 0.235274i | \(-0.0755989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 63.7277 | + | 20.7064i | 3.26059 | + | 1.05943i | ||||
\(383\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 51.0132 | 2.59650 | ||||||||
\(387\) | 23.0569 | − | 31.7351i | 1.17205 | − | 1.61318i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.03444 | − | 24.7275i | −0.407362 | − | 1.25373i | −0.918906 | − | 0.394475i | \(-0.870926\pi\) |
0.511544 | − | 0.859257i | \(-0.329074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 13.4246 | − | 4.36191i | 0.678043 | − | 0.220310i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −44.2148 | − | 32.1239i | −2.22751 | − | 1.61838i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | −35.2278 | + | 48.4869i | −1.76581 | + | 2.43043i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.45492 | + | 26.0216i | 0.422746 | + | 1.30108i | ||||
\(401\) | −3.61803 | + | 2.62866i | −0.180676 | + | 0.131269i | −0.674447 | − | 0.738323i | \(-0.735618\pi\) |
0.493771 | + | 0.869592i | \(0.335618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2279 | − | 5.27275i | 0.808368 | − | 0.262655i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.2812 | − | 11.8290i | −0.809017 | − | 0.587785i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.25732 | − | 9.98885i | −0.357110 | − | 0.491519i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.54962 | + | 0.503503i | 0.0760680 | + | 0.0247160i | ||||
\(416\) | −3.85410 | − | 2.80017i | −0.188963 | − | 0.137290i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −35.7771 | −1.74783 | −0.873913 | − | 0.486083i | \(-0.838425\pi\) | ||||
−0.873913 | + | 0.486083i | \(0.838425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.67376 | + | 29.7728i | −0.471470 | + | 1.45104i | 0.379189 | + | 0.925319i | \(0.376203\pi\) |
−0.850659 | + | 0.525717i | \(0.823797\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.4281 | − | 12.4861i | 1.86404 | − | 0.605663i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 81.5402i | − | 3.94139i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 73.0132 | 3.52101 | ||||||||
\(431\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(434\) | −55.7771 | + | 40.5244i | −2.67739 | + | 1.94523i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.58359 | −0.361123 | ||||||||
\(442\) | −22.6286 | + | 31.1456i | −1.07633 | + | 1.48144i | ||||
\(443\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.2705 | + | 17.6336i | −1.15053 | + | 0.835911i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13.8216 | − | 4.49092i | −0.653011 | − | 0.212176i | ||||
\(449\) | −32.5623 | − | 23.6579i | −1.53671 | − | 1.11649i | −0.952357 | − | 0.304986i | \(-0.901348\pi\) |
−0.584353 | − | 0.811499i | \(-0.698652\pi\) | |||||||
\(450\) | − | 37.4582i | − | 1.76580i | ||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.6180 | − | 60.3781i | 0.920720 | − | 2.83368i | ||||
\(455\) | 4.06888 | + | 12.5227i | 0.190752 | + | 0.587075i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.5073 | + | 29.6022i | 1.00607 | + | 1.38473i | 0.921528 | + | 0.388313i | \(0.126942\pi\) |
0.0845396 | + | 0.996420i | \(0.473058\pi\) | |||||||
\(458\) | 14.2499 | − | 4.63009i | 0.665856 | − | 0.216350i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.1246 | − | 37.3157i | −0.561662 | − | 1.72862i | ||||
\(467\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(468\) | 14.2499 | + | 19.6134i | 0.658704 | + | 0.906628i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 22.3357i | − | 1.02809i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 32.6525 | − | 100.494i | 1.49662 | − | 4.60613i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.29684 | − | 11.4196i | −0.374813 | − | 0.515886i | ||||
\(491\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −48.9443 | −2.19766 | ||||||||
\(497\) | −14.5146 | + | 19.9777i | −0.651071 | + | 0.896122i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.23607 | − | 3.80423i | −0.0553340 | − | 0.170301i | 0.919570 | − | 0.392926i | \(-0.128537\pi\) |
−0.974904 | + | 0.222626i | \(0.928537\pi\) | |||||||
\(500\) | 38.3156 | − | 27.8379i | 1.71353 | − | 1.24495i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 66.4997 | − | 21.6071i | 2.96803 | − | 0.964371i | ||||
\(503\) | 35.0642 | + | 11.3930i | 1.56343 | + | 0.507991i | 0.957723 | − | 0.287693i | \(-0.0928883\pi\) |
0.605712 | + | 0.795684i | \(0.292888\pi\) | |||||||
\(504\) | −41.8328 | − | 30.3933i | −1.86338 | − | 1.35383i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 42.0568 | − | 57.8862i | 1.86597 | − | 2.56829i | ||||
\(509\) | −10.5066 | + | 32.3359i | −0.465696 | + | 1.43326i | 0.392409 | + | 0.919791i | \(0.371642\pi\) |
−0.858105 | + | 0.513474i | \(0.828358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.7082 | − | 21.5843i | 1.31421 | − | 0.954832i | ||||
\(512\) | −27.8887 | − | 38.3855i | −1.23252 | − | 1.69641i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.36068 | + | 22.6538i | −0.322787 | + | 0.993437i | ||||
\(521\) | 6.90983 | + | 21.2663i | 0.302725 | + | 0.931692i | 0.980516 | + | 0.196438i | \(0.0629374\pi\) |
−0.677791 | + | 0.735254i | \(0.737063\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.6855 | + | 36.7295i | 1.16688 | + | 1.60607i | 0.681643 | + | 0.731685i | \(0.261266\pi\) |
0.485235 | + | 0.874384i | \(0.338734\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.18034 | + | 6.66991i | 0.400282 | + | 0.290822i | ||||
\(527\) | 72.2800i | 3.14857i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.70820 | + | 11.4127i | −0.160922 | + | 0.495268i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.9355 | + | 13.3007i | −1.76980 | + | 0.575041i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 34.9610i | 1.50727i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.3262 | − | 11.8617i | 0.699982 | − | 0.508566i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.95034 | + | 2.58322i | 0.339932 | + | 0.110451i | 0.474008 | − | 0.880520i | \(-0.342807\pi\) |
−0.134076 | + | 0.990971i | \(0.542807\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 23.4721 | + | 72.2398i | 0.997235 | + | 3.06918i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.6709 | − | 7.04129i | 0.918224 | − | 0.298349i | 0.188486 | − | 0.982076i | \(-0.439642\pi\) |
0.729738 | + | 0.683727i | \(0.239642\pi\) | |||||||
\(558\) | 63.7277 | + | 20.7064i | 2.69781 | + | 0.876571i | ||||
\(559\) | 20.1803 | + | 14.6619i | 0.853537 | + | 0.620131i | ||||
\(560\) | − | 37.7694i | − | 1.59605i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.4577 | + | 14.3938i | −0.440739 | + | 0.606625i | −0.970376 | − | 0.241599i | \(-0.922328\pi\) |
0.529637 | + | 0.848224i | \(0.322328\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 54.3050 | − | 39.4549i | 2.28261 | − | 1.65841i | ||||
\(567\) | 16.3290 | + | 22.4749i | 0.685753 | + | 0.943857i | ||||
\(568\) | −42.4851 | + | 13.8042i | −1.78264 | + | 0.579213i | ||||
\(569\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.36475 | + | 13.4333i | 0.181864 | + | 0.559721i | ||||
\(577\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(578\) | −70.9032 | − | 97.5899i | −2.94918 | − | 4.05920i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.81966 | − | 1.32206i | −0.0754922 | − | 0.0548483i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 66.4296 | 2.74887 | ||||||||
\(585\) | 7.52203 | − | 10.3532i | 0.310998 | − | 0.428052i | ||||
\(586\) | 26.4164 | − | 81.3013i | 1.09125 | − | 3.35853i | ||||
\(587\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −21.2426 | + | 6.90212i | −0.874542 | + | 0.284156i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.7749i | 1.34591i | 0.739686 | + | 0.672953i | \(0.234974\pi\) | ||||
−0.739686 | + | 0.672953i | \(0.765026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −55.7771 | −2.28664 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.1803 | − | 26.2866i | 1.47829 | − | 1.07404i | 0.500186 | − | 0.865918i | \(-0.333265\pi\) |
0.978103 | − | 0.208121i | \(-0.0667349\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(602\) | −95.8562 | − | 31.1456i | −3.90681 | − | 1.26940i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.4135 | + | 19.8385i | −0.585027 | + | 0.805221i | −0.994235 | − | 0.107220i | \(-0.965805\pi\) |
0.409208 | + | 0.912441i | \(0.365805\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −97.6705 | + | 31.7351i | −3.94810 | + | 1.28281i | ||||
\(613\) | −44.2994 | − | 14.3938i | −1.78924 | − | 0.581359i | −0.789752 | − | 0.613426i | \(-0.789791\pi\) |
−0.999486 | + | 0.0320680i | \(0.989791\pi\) | |||||||
\(614\) | 66.7771 | + | 48.5164i | 2.69490 | + | 1.95796i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.52786 | − | 17.0130i | 0.222184 | − | 0.683811i | −0.776382 | − | 0.630263i | \(-0.782947\pi\) |
0.998565 | − | 0.0535478i | \(-0.0170530\pi\) | |||||||
\(620\) | 26.1803 | + | 80.5748i | 1.05143 | + | 3.23596i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 46.9704 | + | 64.6492i | 1.88334 | + | 2.59220i | ||||
\(623\) | 39.3859 | − | 12.7972i | 1.57796 | − | 0.512711i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.2254 | − | 14.6946i | −0.809017 | − | 0.587785i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −15.9787 | + | 49.1774i | −0.636607 | + | 1.95928i | ||||
\(631\) | −14.8328 | − | 45.6507i | −0.590485 | − | 1.81733i | −0.576027 | − | 0.817431i | \(-0.695398\pi\) |
−0.0144581 | − | 0.999895i | \(-0.504602\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.9208 | − | 11.6714i | −1.42547 | − | 0.463164i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4.82241i | − | 0.191071i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0000 | 0.949425 | ||||||||
\(640\) | −22.0174 | + | 30.3043i | −0.870313 | + | 1.19788i | ||||
\(641\) | −9.67376 | + | 29.7728i | −0.382091 | + | 1.17595i | 0.556478 | + | 0.830862i | \(0.312152\pi\) |
−0.938569 | + | 0.345092i | \(0.887848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(648\) | 50.2554i | 1.97422i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 23.8197 | 0.934284 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.9429 | − | 11.0287i | −1.32424 | − | 0.430271i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.0000 | −1.63361 | −0.816805 | − | 0.576913i | \(-0.804257\pi\) | ||||
−0.816805 | + | 0.576913i | \(0.804257\pi\) | |||||||
\(662\) | 52.5145 | − | 72.2800i | 2.04103 | − | 2.80924i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.25735 | − | 3.86974i | −0.0487948 | − | 0.150175i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −43.1781 | − | 14.0294i | −1.67061 | − | 0.542815i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.2352 | − | 38.8624i | 1.08839 | − | 1.49803i | 0.238445 | − | 0.971156i | \(-0.423362\pi\) |
0.849941 | − | 0.526879i | \(-0.176638\pi\) | |||||||
\(674\) | 12.8197 | − | 39.4549i | 0.493795 | − | 1.51974i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 32.0795 | − | 23.3071i | 1.23383 | − | 0.896428i | ||||
\(677\) | −1.65073 | − | 2.27204i | −0.0634428 | − | 0.0873215i | 0.776117 | − | 0.630589i | \(-0.217187\pi\) |
−0.839559 | + | 0.543268i | \(0.817187\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −81.6312 | − | 59.3085i | −3.13041 | − | 2.27438i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10.6525 | − | 32.7849i | −0.406713 | − | 1.25174i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −42.0568 | − | 57.8862i | −1.60340 | − | 2.20689i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.6525 | − | 16.4580i | −0.861741 | − | 0.626091i | 0.0666172 | − | 0.997779i | \(-0.478779\pi\) |
−0.928358 | + | 0.371687i | \(0.878779\pi\) | |||||||
\(692\) | − | 44.2211i | − | 1.68104i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 29.0132 | 1.10132 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −62.1780 | + | 20.2029i | −2.35011 | + | 0.763597i | ||||
\(701\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.61803 | + | 2.62866i | −0.135878 | + | 0.0987212i | −0.653648 | − | 0.756799i | \(-0.726762\pi\) |
0.517770 | + | 0.855520i | \(0.326762\pi\) | |||||||
\(710\) | 26.2572 | + | 36.1400i | 0.985417 | + | 1.35631i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 71.2497 | + | 23.1504i | 2.67020 | + | 0.867599i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −75.7771 | −2.83192 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.29180 | − | 25.5195i | −0.309232 | − | 0.951718i | −0.978064 | − | 0.208304i | \(-0.933206\pi\) |
0.668832 | − | 0.743413i | \(-0.266794\pi\) | |||||||
\(720\) | −29.6976 | + | 21.5765i | −1.10676 | + | 0.804110i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −45.1248 | + | 14.6619i | −1.67937 | + | 0.545661i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.3262 | + | 11.1352i | 0.569595 | + | 0.413835i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 19.3271 | − | 26.6015i | 0.716311 | − | 0.985917i | ||||
\(729\) | 8.34346 | − | 25.6785i | 0.309017 | − | 0.951057i | ||||
\(730\) | −20.5279 | − | 63.1783i | −0.759770 | − | 2.33833i | ||||
\(731\) | −85.4853 | + | 62.1087i | −3.16179 | + | 2.29717i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.0716 | − | 9.12101i | 1.03685 | − | 0.336892i | 0.259353 | − | 0.965783i | \(-0.416491\pi\) |
0.777494 | + | 0.628890i | \(0.216491\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.7849 | − | 14.8441i | −0.395659 | − | 0.544577i | 0.563989 | − | 0.825782i | \(-0.309266\pi\) |
−0.959648 | + | 0.281205i | \(0.909266\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13.3820 | + | 9.72257i | 0.489949 | + | 0.355968i | ||||
\(747\) | 2.18603i | 0.0799827i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 59.4164 | 2.17103 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.88854 | − | 30.4338i | 0.360838 | − | 1.11055i | −0.591708 | − | 0.806152i | \(-0.701546\pi\) |
0.952546 | − | 0.304393i | \(-0.0984537\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(758\) | 89.8996i | 3.26530i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −91.9574 | + | 66.8110i | −3.32690 | + | 2.41714i | ||||
\(765\) | 31.8638 | + | 43.8568i | 1.15204 | + | 1.58565i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.25732 | − | 2.35805i | −0.262047 | − | 0.0851441i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −50.8637 | + | 70.0079i | −1.83063 | + | 2.51964i | ||||
\(773\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(774\) | 30.2705 | + | 93.1630i | 1.08805 | + | 3.34868i | ||||
\(775\) | 36.1803 | − | 26.2866i | 1.29964 | − | 0.944241i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 61.7497 | + | 20.0637i | 2.21384 | + | 0.719319i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.27458 | + | 13.1558i | −0.152663 | + | 0.469850i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.5422 | − | 37.9085i | −0.981772 | − | 1.35129i | −0.935869 | − | 0.352347i | \(-0.885384\pi\) |
−0.0459025 | − | 0.998946i | \(-0.514616\pi\) | |||||||
\(788\) | 88.1706 | − | 28.6484i | 3.14095 | − | 1.02056i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −31.4164 | − | 96.6898i | −1.11353 | − | 3.42708i | ||||
\(797\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −11.8749 | − | 3.85840i | −0.419843 | − | 0.136415i | ||||
\(801\) | −32.5623 | − | 23.6579i | −1.15053 | − | 0.835911i | ||||
\(802\) | − | 11.1679i | − | 0.394351i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.1672 | + | 40.5244i | −0.463794 | + | 1.42741i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(810\) | 47.7957 | − | 15.5298i | 1.67937 | − | 0.545661i | ||||
\(811\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.2918 | + | 10.3836i | −0.499396 | + | 0.362832i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.8328 | 1.07281 | ||||||||
\(827\) | −31.1708 | + | 42.9030i | −1.08392 | + | 1.49188i | −0.228779 | + | 0.973478i | \(0.573473\pi\) |
−0.855136 | + | 0.518404i | \(0.826527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.90983 | + | 21.2663i | 0.239988 | + | 0.738608i | 0.996420 | + | 0.0845359i | \(0.0269408\pi\) |
−0.756432 | + | 0.654072i | \(0.773059\pi\) | |||||||
\(830\) | −3.29180 | + | 2.39163i | −0.114260 | + | 0.0830147i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.54224 | + | 2.77554i | −0.296149 | + | 0.0962246i | ||||
\(833\) | 19.4282 | + | 6.31261i | 0.673148 | + | 0.218719i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.9651i | 0.829347i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 52.5145 | − | 72.2800i | 1.81408 | − | 2.49687i | ||||
\(839\) | −17.3050 | + | 53.2592i | −0.597433 | + | 1.83871i | −0.0552123 | + | 0.998475i | \(0.517584\pi\) |
−0.542221 | + | 0.840236i | \(0.682416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4615 | − | 17.0458i | 0.809017 | − | 0.587785i | ||||
\(842\) | −45.9502 | − | 63.2450i | −1.58355 | − | 2.17957i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.9336 | − | 12.3030i | −0.582535 | − | 0.423236i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −31.1803 | + | 95.9632i | −1.06948 | + | 3.29151i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.1507 | + | 15.3476i | 0.381792 | + | 0.525492i | 0.956058 | − | 0.293177i | \(-0.0947124\pi\) |
−0.574266 | + | 0.818669i | \(0.694712\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 86.9574 | + | 63.1783i | 2.97214 | + | 2.15939i | ||||
\(857\) | − | 52.7526i | − | 1.80200i | −0.433824 | − | 0.900998i | \(-0.642836\pi\) | ||
0.433824 | − | 0.900998i | \(-0.357164\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.7771 | −1.22070 | −0.610349 | − | 0.792132i | \(-0.708971\pi\) | ||||
−0.610349 | + | 0.792132i | \(0.708971\pi\) | |||||||
\(860\) | −72.7993 | + | 100.200i | −2.48244 | + | 3.41678i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.2003 | + | 7.21331i | −0.754832 | + | 0.245260i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 116.951i | − | 3.96959i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.2848 | + | 27.9197i | 0.685753 | + | 0.943857i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.0421 | + | 12.0357i | 1.25082 | + | 0.406417i | 0.858216 | − | 0.513289i | \(-0.171573\pi\) |
0.392608 | + | 0.919706i | \(0.371573\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 11.1314 | − | 15.3210i | 0.374813 | − | 0.515886i | ||||
\(883\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(884\) | −20.1803 | − | 62.1087i | −0.678738 | − | 2.08894i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.2922 | − | 4.31890i | 0.446309 | − | 0.145015i | −0.0772356 | − | 0.997013i | \(-0.524609\pi\) |
0.523545 | + | 0.851998i | \(0.324609\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.1803 | + | 30.6458i | 1.41468 | + | 1.02783i | ||||
\(890\) | − | 74.9164i | − | 2.51120i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.3607 | + | 38.0423i | 0.413172 | + | 1.27161i | ||||
\(896\) | 41.8328 | − | 30.3933i | 1.39754 | − | 1.01537i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 95.5915 | − | 31.0596i | 3.18993 | − | 1.03647i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 51.4058 | + | 37.3485i | 1.71353 | + | 1.24495i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.09017 | − | 9.51057i | 0.102721 | − | 0.316142i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(908\) | 63.2994 | + | 87.1241i | 2.10066 | + | 2.89131i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −31.2719 | − | 10.1609i | −1.03665 | − | 0.336829i | ||||
\(911\) | 7.23607 | + | 5.25731i | 0.239742 | + | 0.174182i | 0.701168 | − | 0.712996i | \(-0.252662\pi\) |
−0.461427 | + | 0.887178i | \(0.652662\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −91.3738 | −3.02238 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.85410 | + | 24.1724i | −0.259507 | + | 0.798680i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.2616i | 0.502342i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.3262 | − | 8.22899i | 0.371602 | − | 0.269985i | −0.386273 | − | 0.922384i | \(-0.626238\pi\) |
0.757875 | + | 0.652400i | \(0.226238\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 63.2994 | + | 20.5672i | 2.07344 | + | 0.673701i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −31.9574 | −1.04456 | ||||||||
\(937\) | −5.27939 | + | 7.26646i | −0.172470 | + | 0.237385i | −0.886498 | − | 0.462732i | \(-0.846869\pi\) |
0.714028 | + | 0.700117i | \(0.246869\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 17.7082 | + | 12.8658i | 0.576353 | + | 0.418745i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.01316 | − | 21.5843i | 0.227657 | − | 0.700655i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 81.8710 | + | 112.686i | 2.65345 | + | 3.65217i | ||||
\(953\) | −49.3141 | + | 16.0231i | −1.59744 | + | 0.519040i | −0.966473 | − | 0.256768i | \(-0.917342\pi\) |
−0.630968 | + | 0.775809i | \(0.717342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.5410 | + | 35.2671i | 1.57075 | + | 1.14122i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1418 | + | 46.6018i | 0.488446 | + | 1.50328i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −33.9429 | − | 46.7184i | −1.09379 | − | 1.50548i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.4428 | + | 14.1154i | 1.39847 | + | 0.454392i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 61.5625i | − | 1.97972i | −0.142063 | − | 0.989858i | \(-0.545374\pi\) | ||
0.142063 | − | 0.989858i | \(-0.454626\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.52786 | − | 17.0130i | 0.177398 | − | 0.545974i | −0.822337 | − | 0.569000i | \(-0.807330\pi\) |
0.999735 | + | 0.0230267i | \(0.00733028\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 23.9443 | 0.764872 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −28.7646 | − | 39.5911i | −0.916516 | − | 1.26148i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 62.6099 | 1.98887 | 0.994435 | − | 0.105356i | \(-0.0335982\pi\) | ||||
0.994435 | + | 0.105356i | \(0.0335982\pi\) | |||||||
\(992\) | 13.1286 | − | 18.0700i | 0.416834 | − | 0.573723i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −19.0557 | − | 58.6475i | −0.604411 | − | 1.86019i | ||||
\(995\) | −43.4164 | + | 31.5439i | −1.37639 | + | 1.00001i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.1854 | − | 17.9308i | 1.74774 | − | 0.567875i | 0.751923 | − | 0.659250i | \(-0.229126\pi\) |
0.995817 | + | 0.0913754i | \(0.0291263\pi\) | |||||||
\(998\) | 9.49996 | + | 3.08672i | 0.300716 | + | 0.0977085i | ||||
\(999\) | 0 | 0 |
(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 | 605.2.j.a.444.1 | 8 | ||
5.4 | even | 2 | inner | 605.2.j.a.444.2 | 8 | ||
11.2 | odd | 10 | 605.2.j.c.269.1 | 8 | |||
11.3 | even | 5 | inner | 605.2.j.a.124.2 | 8 | ||
11.4 | even | 5 | 605.2.j.c.9.1 | 8 | |||
11.5 | even | 5 | 605.2.b.b.364.1 | ✓ | 4 | ||
11.6 | odd | 10 | 605.2.b.b.364.4 | yes | 4 | ||
11.7 | odd | 10 | 605.2.j.c.9.2 | 8 | |||
11.8 | odd | 10 | inner | 605.2.j.a.124.1 | 8 | ||
11.9 | even | 5 | 605.2.j.c.269.2 | 8 | |||
11.10 | odd | 2 | inner | 605.2.j.a.444.2 | 8 | ||
55.4 | even | 10 | 605.2.j.c.9.2 | 8 | |||
55.9 | even | 10 | 605.2.j.c.269.1 | 8 | |||
55.14 | even | 10 | inner | 605.2.j.a.124.1 | 8 | ||
55.17 | even | 20 | 3025.2.a.bb.1.1 | 4 | |||
55.19 | odd | 10 | inner | 605.2.j.a.124.2 | 8 | ||
55.24 | odd | 10 | 605.2.j.c.269.2 | 8 | |||
55.27 | odd | 20 | 3025.2.a.bb.1.4 | 4 | |||
55.28 | even | 20 | 3025.2.a.bb.1.4 | 4 | |||
55.29 | odd | 10 | 605.2.j.c.9.1 | 8 | |||
55.38 | odd | 20 | 3025.2.a.bb.1.1 | 4 | |||
55.39 | odd | 10 | 605.2.b.b.364.1 | ✓ | 4 | ||
55.49 | even | 10 | 605.2.b.b.364.4 | yes | 4 | ||
55.54 | odd | 2 | CM | 605.2.j.a.444.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.b.364.1 | ✓ | 4 | 11.5 | even | 5 | ||
605.2.b.b.364.1 | ✓ | 4 | 55.39 | odd | 10 | ||
605.2.b.b.364.4 | yes | 4 | 11.6 | odd | 10 | ||
605.2.b.b.364.4 | yes | 4 | 55.49 | even | 10 | ||
605.2.j.a.124.1 | 8 | 11.8 | odd | 10 | inner | ||
605.2.j.a.124.1 | 8 | 55.14 | even | 10 | inner | ||
605.2.j.a.124.2 | 8 | 11.3 | even | 5 | inner | ||
605.2.j.a.124.2 | 8 | 55.19 | odd | 10 | inner | ||
605.2.j.a.444.1 | 8 | 1.1 | even | 1 | trivial | ||
605.2.j.a.444.1 | 8 | 55.54 | odd | 2 | CM | ||
605.2.j.a.444.2 | 8 | 5.4 | even | 2 | inner | ||
605.2.j.a.444.2 | 8 | 11.10 | odd | 2 | inner | ||
605.2.j.c.9.1 | 8 | 11.4 | even | 5 | |||
605.2.j.c.9.1 | 8 | 55.29 | odd | 10 | |||
605.2.j.c.9.2 | 8 | 11.7 | odd | 10 | |||
605.2.j.c.9.2 | 8 | 55.4 | even | 10 | |||
605.2.j.c.269.1 | 8 | 11.2 | odd | 10 | |||
605.2.j.c.269.1 | 8 | 55.9 | even | 10 | |||
605.2.j.c.269.2 | 8 | 11.9 | even | 5 | |||
605.2.j.c.269.2 | 8 | 55.24 | odd | 10 | |||
3025.2.a.bb.1.1 | 4 | 55.17 | even | 20 | |||
3025.2.a.bb.1.1 | 4 | 55.38 | odd | 20 | |||
3025.2.a.bb.1.4 | 4 | 55.27 | odd | 20 | |||
3025.2.a.bb.1.4 | 4 | 55.28 | even | 20 |