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 | 9.2 | ||
Root | \(1.46782 - 0.476925i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.9 |
Dual form | 605.2.j.c.269.2 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.37499 | + | 0.771681i | 1.67937 | + | 0.545661i | 0.984789 | − | 0.173753i | \(-0.0555893\pi\) |
0.694582 | + | 0.719413i | \(0.255589\pi\) | |||||||
\(3\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(4\) | 3.42705 | + | 2.48990i | 1.71353 | + | 1.24495i | ||||
\(5\) | 0.690983 | + | 2.12663i | 0.309017 | + | 0.951057i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.81433 | − | 2.49721i | 0.685753 | − | 0.943857i | −0.314232 | − | 0.949346i | \(-0.601747\pi\) |
0.999985 | + | 0.00548867i | \(0.00174711\pi\) | |||||||
\(8\) | 3.28216 | + | 4.51750i | 1.16042 | + | 1.59718i | ||||
\(9\) | 0.927051 | − | 2.85317i | 0.309017 | − | 0.951057i | ||||
\(10\) | 5.58394i | 1.76580i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.81433 | − | 0.589512i | −0.503205 | − | 0.163501i | 0.0464049 | − | 0.998923i | \(-0.485224\pi\) |
−0.549610 | + | 0.835422i | \(0.685224\pi\) | |||||||
\(14\) | 6.23607 | − | 4.53077i | 1.66666 | − | 1.21090i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.69098 | + | 5.20431i | 0.422746 | + | 1.30108i | ||||
\(17\) | −7.68563 | + | 2.49721i | −1.86404 | + | 0.605663i | −0.870500 | + | 0.492168i | \(0.836204\pi\) |
−0.993539 | + | 0.113495i | \(0.963796\pi\) | |||||||
\(18\) | 4.40347 | − | 6.06086i | 1.03791 | − | 1.42856i | ||||
\(19\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(20\) | −2.92705 | + | 9.00854i | −0.654508 | + | 2.01437i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | + | 2.93893i | −0.809017 | + | 0.587785i | ||||
\(26\) | −3.85410 | − | 2.80017i | −0.755852 | − | 0.549158i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 12.4356 | − | 4.04057i | 2.35011 | − | 0.763597i | ||||
\(29\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.76393 | + | 8.50651i | −0.496417 | + | 1.52781i | 0.318320 | + | 0.947983i | \(0.396881\pi\) |
−0.814737 | + | 0.579831i | \(0.803119\pi\) | |||||||
\(32\) | 2.49721i | 0.441449i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −20.1803 | −3.46090 | ||||||||
\(35\) | 6.56431 | + | 2.13287i | 1.10957 | + | 0.360521i | ||||
\(36\) | 10.2812 | − | 7.46969i | 1.71353 | − | 1.24495i | ||||
\(37\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.33912 | + | 10.1014i | −1.16042 | + | 1.59718i | ||||
\(41\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 13.0756i | − | 1.99401i | −0.0773627 | − | 0.997003i | \(-0.524650\pi\) | ||
0.0773627 | − | 0.997003i | \(-0.475350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.70820 | 1.00000 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.781153 | − | 2.40414i | −0.111593 | − | 0.343449i | ||||
\(50\) | −11.8749 | + | 3.85840i | −1.67937 | + | 0.545661i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.74998 | − | 6.53779i | −0.658704 | − | 0.906628i | ||||
\(53\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 17.2361 | 2.30327 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.23607 | + | 2.35114i | 0.421300 | + | 0.306092i | 0.778161 | − | 0.628065i | \(-0.216153\pi\) |
−0.356861 | + | 0.934158i | \(0.616153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(62\) | −13.1286 | + | 18.0700i | −1.66734 | + | 2.29489i | ||||
\(63\) | −5.44299 | − | 7.49164i | −0.685753 | − | 0.943857i | ||||
\(64\) | 1.45492 | − | 4.47777i | 0.181864 | − | 0.559721i | ||||
\(65\) | − | 4.26575i | − | 0.529101i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | −32.5568 | − | 10.5784i | −3.94810 | − | 1.28281i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 13.9443 | + | 10.1311i | 1.66666 | + | 1.21090i | ||||
\(71\) | 2.47214 | + | 7.60845i | 0.293389 | + | 0.902957i | 0.983758 | + | 0.179500i | \(0.0574480\pi\) |
−0.690369 | + | 0.723457i | \(0.742552\pi\) | |||||||
\(72\) | 15.9319 | − | 5.17659i | 1.87759 | − | 0.610067i | ||||
\(73\) | 6.99262 | − | 9.62451i | 0.818424 | − | 1.12646i | −0.171545 | − | 0.985176i | \(-0.554876\pi\) |
0.989969 | − | 0.141287i | \(-0.0451242\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(80\) | −9.89919 | + | 7.19218i | −1.10676 | + | 0.804110i | ||||
\(81\) | −7.28115 | − | 5.29007i | −0.809017 | − | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.693013 | − | 0.225173i | 0.0760680 | − | 0.0247160i | −0.270736 | − | 0.962654i | \(-0.587267\pi\) |
0.346804 | + | 0.937938i | \(0.387267\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.6213 | − | 14.6189i | −1.15204 | − | 1.58565i | ||||
\(86\) | 10.0902 | − | 31.0543i | 1.08805 | − | 3.34868i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.4164 | 1.42214 | 0.711068 | − | 0.703123i | \(-0.248212\pi\) | ||||
0.711068 | + | 0.703123i | \(0.248212\pi\) | |||||||
\(90\) | 15.9319 | + | 5.17659i | 1.67937 | + | 0.545661i | ||||
\(91\) | −4.76393 | + | 3.46120i | −0.499396 | + | 0.362832i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(98\) | − | 6.31261i | − | 0.637670i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −21.1803 | −2.11803 | ||||||||
\(101\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(104\) | −3.29180 | − | 10.1311i | −0.322787 | − | 0.993437i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3143 | + | 15.5728i | 1.09379 | + | 1.50548i | 0.843364 | + | 0.537343i | \(0.180572\pi\) |
0.250430 | + | 0.968135i | \(0.419428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.0643 | + | 5.21960i | 1.51793 | + | 0.493206i | ||||
\(113\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.36395 | + | 4.63009i | −0.310998 | + | 0.428052i | ||||
\(118\) | 5.87130 | + | 8.08115i | 0.540497 | + | 0.743930i | ||||
\(119\) | −7.70820 | + | 23.7234i | −0.706610 | + | 2.17472i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −30.6525 | + | 22.2703i | −2.75267 | + | 1.99993i | ||||
\(125\) | −9.04508 | − | 6.57164i | −0.809017 | − | 0.587785i | ||||
\(126\) | −7.14590 | − | 21.9928i | −0.636607 | − | 1.95928i | ||||
\(127\) | −16.0643 | + | 5.21960i | −1.42547 | + | 0.463164i | −0.917337 | − | 0.398112i | \(-0.869666\pi\) |
−0.508137 | + | 0.861276i | \(0.669666\pi\) | |||||||
\(128\) | 9.84647 | − | 13.5525i | 0.870313 | − | 1.19788i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.29180 | − | 10.1311i | 0.288710 | − | 0.888557i | ||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −36.5066 | − | 26.5236i | −3.13041 | − | 2.27438i | ||||
\(137\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(140\) | 17.1856 | + | 23.6539i | 1.45245 | + | 1.99912i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 19.9777i | 1.67649i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 16.4164 | 1.36803 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 24.0344 | − | 17.4620i | 1.98910 | − | 1.44517i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 24.2434i | 1.95997i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.0000 | −1.60644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −5.31064 | + | 1.72553i | −0.419843 | + | 0.136415i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −13.2104 | − | 18.1826i | −1.03791 | − | 1.42856i | ||||
\(163\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.81966 | 0.141233 | ||||||||
\(167\) | −10.1930 | − | 3.31190i | −0.788756 | − | 0.256282i | −0.113182 | − | 0.993574i | \(-0.536104\pi\) |
−0.675574 | + | 0.737292i | \(0.736104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.57295 | − | 5.50207i | −0.582535 | − | 0.423236i | ||||
\(170\) | −13.9443 | − | 42.9161i | −1.06948 | − | 3.29151i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 32.5568 | − | 44.8107i | 2.48244 | − | 3.41678i | ||||
\(173\) | 6.13600 | + | 8.44549i | 0.466512 | + | 0.642098i | 0.975843 | − | 0.218472i | \(-0.0701072\pi\) |
−0.509331 | + | 0.860570i | \(0.670107\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.4336i | 1.16667i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 31.8638 | + | 10.3532i | 2.38830 | + | 0.776004i | ||||
\(179\) | −14.4721 | + | 10.5146i | −1.08170 | + | 0.785900i | −0.977978 | − | 0.208707i | \(-0.933075\pi\) |
−0.103720 | + | 0.994607i | \(0.533075\pi\) | |||||||
\(180\) | 22.9894 | + | 16.7027i | 1.71353 | + | 1.24495i | ||||
\(181\) | 1.38197 | + | 4.25325i | 0.102721 | + | 0.316142i | 0.989189 | − | 0.146648i | \(-0.0468485\pi\) |
−0.886468 | + | 0.462790i | \(0.846848\pi\) | |||||||
\(182\) | −13.9852 | + | 4.54408i | −1.03665 | + | 0.336829i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.7082 | + | 15.7719i | 1.57075 | + | 1.14122i | 0.926433 | + | 0.376459i | \(0.122858\pi\) |
0.644317 | + | 0.764758i | \(0.277142\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.4282 | − | 6.31261i | 1.39847 | − | 0.454392i | 0.489777 | − | 0.871848i | \(-0.337078\pi\) |
0.908697 | + | 0.417456i | \(0.137078\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.30902 | − | 10.1841i | 0.236358 | − | 0.727436i | ||||
\(197\) | − | 21.8854i | − | 1.55927i | −0.626234 | − | 0.779635i | \(-0.715405\pi\) | ||
0.626234 | − | 0.779635i | \(-0.284595\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | −26.5532 | − | 8.62766i | −1.87759 | − | 0.610067i | ||||
\(201\) | 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 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.8541 | + | 45.7162i | 1.01541 | + | 3.12510i | ||||
\(215\) | 27.8069 | − | 9.03500i | 1.89641 | − | 0.616182i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.2279 | + | 22.3357i | 1.10162 | + | 1.51625i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.4164 | 1.03702 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(224\) | 6.23607 | + | 4.53077i | 0.416665 | + | 0.302725i | ||||
\(225\) | 4.63525 | + | 14.2658i | 0.309017 | + | 0.951057i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.9430 | + | 20.5672i | −0.991799 | + | 1.36509i | −0.0615740 | + | 0.998103i | \(0.519612\pi\) |
−0.930224 | + | 0.366991i | \(0.880388\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.85410 | − | 5.70634i | 0.122523 | − | 0.377086i | −0.870919 | − | 0.491426i | \(-0.836476\pi\) |
0.993442 | + | 0.114341i | \(0.0364756\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9430 | + | 4.85526i | 0.978945 | + | 0.318079i | 0.754422 | − | 0.656390i | \(-0.227917\pi\) |
0.224524 | + | 0.974469i | \(0.427917\pi\) | |||||||
\(234\) | −11.5623 | + | 8.40051i | −0.755852 | + | 0.549158i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.23607 | + | 16.1150i | 0.340839 | + | 1.04899i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −36.6138 | + | 50.3946i | −2.37332 | + | 3.26660i | ||||
\(239\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.57295 | − | 3.32244i | 0.292155 | − | 0.212263i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −47.4998 | + | 15.4336i | −3.01624 | + | 0.980036i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −16.4108 | − | 22.5875i | −1.03791 | − | 1.42856i | ||||
\(251\) | 8.65248 | − | 26.6296i | 0.546139 | − | 1.68084i | −0.172126 | − | 0.985075i | \(-0.555064\pi\) |
0.718265 | − | 0.695769i | \(-0.244936\pi\) | |||||||
\(252\) | − | 39.2267i | − | 2.47105i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −42.1803 | −2.64663 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 26.2254 | − | 19.0539i | 1.63909 | − | 1.19087i | ||||
\(257\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 10.6213 | − | 14.6189i | 0.658704 | − | 0.906628i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.54408i | 0.280200i | 0.990137 | + | 0.140100i | \(0.0447424\pi\) | ||||
−0.990137 | + | 0.140100i | \(0.955258\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.32624 | − | 13.3148i | −0.263775 | − | 0.811817i | −0.991973 | − | 0.126450i | \(-0.959642\pi\) |
0.728198 | − | 0.685367i | \(-0.240358\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(272\) | −25.9925 | − | 35.7757i | −1.57603 | − | 2.16922i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.9282 | − | 9.39934i | −1.73813 | − | 0.564751i | −0.743542 | − | 0.668689i | \(-0.766856\pi\) |
−0.994584 | + | 0.103938i | \(0.966856\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 21.7082 | + | 15.7719i | 1.29964 | + | 0.944241i | ||||
\(280\) | 11.9098 | + | 36.6547i | 0.711748 | + | 2.19054i | ||||
\(281\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.7996 | − | 21.7462i | −0.939186 | − | 1.29268i | −0.956167 | − | 0.292823i | \(-0.905405\pi\) |
0.0169800 | − | 0.999856i | \(-0.494595\pi\) | |||||||
\(284\) | −10.4721 | + | 32.2299i | −0.621407 | + | 1.91249i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 7.12497 | + | 2.31504i | 0.419843 | + | 0.136415i | ||||
\(289\) | 39.0795 | − | 28.3929i | 2.29880 | − | 1.67017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 47.9281 | − | 15.5728i | 2.80478 | − | 0.911328i | ||||
\(293\) | −20.1212 | + | 27.6945i | −1.17550 | + | 1.61793i | −0.578589 | + | 0.815619i | \(0.696397\pi\) |
−0.596906 | + | 0.802311i | \(0.703603\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.76393 | + | 8.50651i | −0.160922 | + | 0.495268i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −32.6525 | − | 23.7234i | −1.88206 | − | 1.36739i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −18.7082 | + | 57.5779i | −1.06948 | + | 3.29151i | ||||
\(307\) | 33.0533i | 1.88645i | 0.332155 | + | 0.943225i | \(0.392224\pi\) | ||||
−0.332155 | + | 0.943225i | \(0.607776\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −47.4998 | − | 15.4336i | −2.69781 | − | 0.876571i | ||||
\(311\) | −25.8885 | + | 18.8091i | −1.46800 | + | 1.06657i | −0.486819 | + | 0.873503i | \(0.661843\pi\) |
−0.981186 | + | 0.193065i | \(0.938157\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.1709 | − | 16.7518i | 0.685753 | − | 0.943857i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 10.5279 | 0.588525 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −11.7812 | − | 36.2587i | −0.654508 | − | 2.01437i | ||||
\(325\) | 9.07165 | − | 2.94756i | 0.503205 | − | 0.163501i | ||||
\(326\) | 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 | \(0.941646\pi\) | |||||||
\(332\) | 2.93565 | + | 0.953850i | 0.161115 | + | 0.0523493i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.6525 | − | 15.7314i | −1.18477 | − | 0.860786i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.76467 | + | 13.4399i | −0.531915 | + | 0.732119i | −0.987421 | − | 0.158114i | \(-0.949459\pi\) |
0.455506 | + | 0.890233i | \(0.349459\pi\) | |||||||
\(338\) | −13.7398 | − | 18.9113i | −0.747348 | − | 1.02864i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 76.5457i | − | 4.15128i | ||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.1286 | + | 4.26575i | 0.708879 | + | 0.230329i | ||||
\(344\) | 59.0689 | − | 42.9161i | 3.18478 | − | 2.31388i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.05573 | + | 24.7930i | 0.433079 | + | 1.33288i | ||||
\(347\) | 11.0496 | − | 3.59023i | 0.593173 | − | 0.192733i | 0.00297954 | − | 0.999996i | \(-0.499052\pi\) |
0.590193 | + | 0.807262i | \(0.299052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(350\) | −11.9098 | + | 36.6547i | −0.636607 | + | 1.95928i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.4721 | + | 10.5146i | −0.768101 | + | 0.558058i | ||||
\(356\) | 45.9787 | + | 33.4055i | 2.43687 | + | 1.77049i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −42.4851 | + | 13.8042i | −2.24541 | + | 0.729577i | ||||
\(359\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(360\) | 22.0174 | + | 30.3043i | 1.16042 | + | 1.59718i | ||||
\(361\) | −5.87132 | + | 18.0701i | −0.309017 | + | 0.951057i | ||||
\(362\) | 11.1679i | 0.586970i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.9443 | −1.30744 | ||||||||
\(365\) | 25.2995 | + | 8.22031i | 1.32424 | + | 0.430271i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.62379i | 0.342967i | 0.985187 | + | 0.171484i | \(0.0548560\pi\) | ||||
−0.985187 | + | 0.171484i | \(0.945144\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1246 | − | 34.2380i | −0.571433 | − | 1.75869i | −0.648016 | − | 0.761627i | \(-0.724401\pi\) |
0.0765833 | − | 0.997063i | \(-0.475599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 39.3859 | + | 54.2100i | 2.01516 | + | 2.77362i | ||||
\(383\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 51.0132 | 2.59650 | ||||||||
\(387\) | −37.3068 | − | 12.1217i | −1.89641 | − | 0.616182i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.0344 | + | 15.2824i | 1.06649 | + | 0.774849i | 0.975278 | − | 0.220982i | \(-0.0709263\pi\) |
0.0912107 | + | 0.995832i | \(0.470926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 8.29684 | − | 11.4196i | 0.419054 | − | 0.576778i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.8885 | − | 51.9776i | 0.850833 | − | 2.61859i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 56.9998 | + | 18.5203i | 2.85714 | + | 0.928341i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −22.1353 | − | 16.0822i | −1.10676 | − | 0.804110i | ||||
\(401\) | 1.38197 | + | 4.25325i | 0.0690121 | + | 0.212397i | 0.979615 | − | 0.200886i | \(-0.0643820\pi\) |
−0.910603 | + | 0.413283i | \(0.864382\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0294 | − | 13.8042i | 0.499599 | − | 0.687639i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.21885 | − | 19.1396i | 0.309017 | − | 0.951057i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.7426 | − | 3.81540i | 0.577815 | − | 0.187744i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.957720 | + | 1.31819i | 0.0470126 | + | 0.0647073i | ||||
\(416\) | 1.47214 | − | 4.53077i | 0.0721774 | − | 0.222139i | ||||
\(417\) | 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 | ||||||||
\(421\) | 25.3262 | − | 18.4006i | 1.23433 | − | 0.896790i | 0.237119 | − | 0.971481i | \(-0.423797\pi\) |
0.997207 | + | 0.0746909i | \(0.0237970\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.7499 | − | 32.6889i | 1.15204 | − | 1.58565i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 81.5402i | 3.94139i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 73.0132 | 3.52101 | ||||||||
\(431\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(434\) | 21.3050 | + | 65.5699i | 1.02267 | + | 3.14746i | ||||
\(435\) | 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 | ||||||||
\(442\) | 36.6138 | + | 11.8965i | 1.74154 | + | 0.565861i | ||||
\(443\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.27051 | + | 28.5317i | 0.439464 | + | 1.35253i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.54224 | − | 11.7574i | −0.403583 | − | 0.555484i | ||||
\(449\) | 12.4377 | − | 38.2793i | 0.586971 | − | 1.80651i | −0.00423548 | − | 0.999991i | \(-0.501348\pi\) |
0.591207 | − | 0.806520i | \(-0.298652\pi\) | |||||||
\(450\) | 37.4582i | 1.76580i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −51.3607 | + | 37.3157i | −2.41048 | + | 1.75131i | ||||
\(455\) | −10.6525 | − | 7.73948i | −0.499396 | − | 0.362832i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.7995 | + | 11.3070i | −1.62785 | + | 0.528921i | −0.973776 | − | 0.227509i | \(-0.926942\pi\) |
−0.654075 | + | 0.756430i | \(0.726942\pi\) | |||||||
\(458\) | 8.80695 | − | 12.1217i | 0.411522 | − | 0.566411i | ||||
\(459\) | 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 | ||||||||
\(466\) | 31.7426 | + | 23.0624i | 1.47045 | + | 1.06834i | ||||
\(467\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(468\) | −23.0569 | + | 7.49164i | −1.06580 | + | 0.346301i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 22.3357i | 1.02809i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −85.4853 | + | 62.1087i | −3.91821 | + | 2.84675i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.4246 | − | 4.36191i | 0.606460 | − | 0.197051i | ||||
\(491\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −48.9443 | −2.19766 | ||||||||
\(497\) | 23.4852 | + | 7.63080i | 1.05345 | + | 0.342288i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.23607 | + | 2.35114i | 0.144866 | + | 0.105252i | 0.657858 | − | 0.753142i | \(-0.271463\pi\) |
−0.512992 | + | 0.858394i | \(0.671463\pi\) | |||||||
\(500\) | −14.6353 | − | 45.0427i | −0.654508 | − | 2.01437i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 41.0991 | − | 56.5680i | 1.83434 | − | 2.52475i | ||||
\(503\) | 21.6709 | + | 29.8274i | 0.966256 | + | 1.32994i | 0.943916 | + | 0.330187i | \(0.107112\pi\) |
0.0223402 | + | 0.999750i | \(0.492888\pi\) | |||||||
\(504\) | 15.9787 | − | 49.1774i | 0.711748 | − | 2.19054i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −68.0493 | − | 22.1106i | −3.01920 | − | 0.980998i | ||||
\(509\) | 27.5066 | − | 19.9847i | 1.21921 | − | 0.885806i | 0.223174 | − | 0.974779i | \(-0.428358\pi\) |
0.996034 | + | 0.0889725i | \(0.0283583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3475 | − | 34.9241i | −0.501985 | − | 1.54495i | ||||
\(512\) | 45.1248 | − | 14.6619i | 1.99425 | − | 0.647972i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 19.2705 | − | 14.0008i | 0.845068 | − | 0.613978i | ||||
\(521\) | −18.0902 | − | 13.1433i | −0.792545 | − | 0.575817i | 0.116173 | − | 0.993229i | \(-0.462937\pi\) |
−0.908718 | + | 0.417412i | \(0.862937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.1781 | + | 14.0294i | −1.88805 | + | 0.613464i | −0.906513 | + | 0.422178i | \(0.861266\pi\) |
−0.981534 | + | 0.191286i | \(0.938734\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.50658 | + | 10.7921i | −0.152894 | + | 0.470560i | ||||
\(527\) | − | 72.2800i | − | 3.14857i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.70820 | − | 7.05342i | 0.421300 | − | 0.306092i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.2995 | + | 34.8218i | −1.09379 | + | 1.50548i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 34.9610i | − | 1.50727i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.23607 | − | 19.1926i | −0.267369 | − | 0.822878i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.91358 | + | 6.76296i | 0.210089 | + | 0.289163i | 0.901038 | − | 0.433741i | \(-0.142807\pi\) |
−0.690948 | + | 0.722904i | \(0.742807\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −61.4508 | − | 44.6467i | −2.61080 | − | 1.89685i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.3933 | − | 18.4343i | 0.567494 | − | 0.781088i | −0.424762 | − | 0.905305i | \(-0.639642\pi\) |
0.992255 | + | 0.124217i | \(0.0396420\pi\) | |||||||
\(558\) | 39.3859 | + | 54.2100i | 1.66734 | + | 2.29489i | ||||
\(559\) | −7.70820 | + | 23.7234i | −0.326022 | + | 1.00339i | ||||
\(560\) | 37.7694i | 1.59605i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.9209 | + | 5.49793i | 0.713130 | + | 0.231710i | 0.643042 | − | 0.765831i | \(-0.277672\pi\) |
0.0700880 | + | 0.997541i | \(0.477672\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.7426 | − | 63.8393i | −0.871878 | − | 2.68337i | ||||
\(567\) | −26.4208 | + | 8.58465i | −1.10957 | + | 0.360521i | ||||
\(568\) | −26.2572 | + | 36.1400i | −1.10173 | + | 1.51640i | ||||
\(569\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(570\) | 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 | ||||||||
\(576\) | −11.4271 | − | 8.30224i | −0.476127 | − | 0.345927i | ||||
\(577\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(578\) | 114.724 | − | 37.2760i | 4.77188 | − | 1.55048i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.695048 | − | 2.13914i | 0.0288355 | − | 0.0887464i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 66.4296 | 2.74887 | ||||||||
\(585\) | −12.1709 | − | 3.95457i | −0.503205 | − | 0.163501i | ||||
\(586\) | −69.1591 | + | 50.2470i | −2.85693 | + | 2.07568i | ||||
\(587\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −13.1286 | + | 18.0700i | −0.540497 | + | 0.743930i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 32.7749i | − | 1.34591i | −0.739686 | − | 0.672953i | \(-0.765026\pi\) | ||
0.739686 | − | 0.672953i | \(-0.234974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −55.7771 | −2.28664 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.8197 | − | 42.5325i | −0.564656 | − | 1.73783i | −0.668971 | − | 0.743288i | \(-0.733265\pi\) |
0.104315 | − | 0.994544i | \(-0.466735\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(602\) | −59.2424 | − | 81.5402i | −2.41454 | − | 3.32333i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.3216 | + | 7.57764i | 0.946594 | + | 0.307567i | 0.741331 | − | 0.671140i | \(-0.234195\pi\) |
0.205263 | + | 0.978707i | \(0.434195\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −60.3637 | + | 83.0835i | −2.44006 | + | 3.35845i | ||||
\(613\) | −27.3786 | − | 37.6834i | −1.10581 | − | 1.52202i | −0.827450 | − | 0.561539i | \(-0.810209\pi\) |
−0.278360 | − | 0.960477i | \(-0.589791\pi\) | |||||||
\(614\) | −25.5066 | + | 78.5012i | −1.02936 | + | 3.16805i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.4721 | + | 10.5146i | −0.581684 | + | 0.422618i | −0.839331 | − | 0.543621i | \(-0.817053\pi\) |
0.257647 | + | 0.966239i | \(0.417053\pi\) | |||||||
\(620\) | −68.5410 | − | 49.7980i | −2.75267 | − | 1.99993i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −75.9997 | + | 24.6938i | −3.04731 | + | 0.990131i | ||||
\(623\) | 24.3418 | − | 33.5036i | 0.975234 | − | 1.34229i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.72542 | − | 23.7764i | 0.309017 | − | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 41.8328 | − | 30.3933i | 1.66666 | − | 1.21090i | ||||
\(631\) | 38.8328 | + | 28.2137i | 1.54591 | + | 1.12317i | 0.946489 | + | 0.322735i | \(0.104602\pi\) |
0.599421 | + | 0.800434i | \(0.295398\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.2003 | − | 30.5561i | −0.880991 | − | 1.21258i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.82241i | 0.191071i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0000 | 0.949425 | ||||||||
\(640\) | 35.6248 | + | 11.5752i | 1.40820 | + | 0.457551i | ||||
\(641\) | 25.3262 | − | 18.4006i | 1.00033 | − | 0.726780i | 0.0381681 | − | 0.999271i | \(-0.487848\pi\) |
0.962158 | + | 0.272492i | \(0.0878478\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(648\) | − | 50.2554i | − | 1.97422i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 23.8197 | 0.934284 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.9778 | − | 28.8735i | −0.818424 | − | 1.12646i | ||||
\(658\) | 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 | \(0.804257\pi\) | |||||||
\(662\) | −84.9702 | − | 27.6085i | −3.30246 | − | 1.07303i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.29180 | + | 2.39163i | 0.127746 | + | 0.0928132i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −26.6855 | − | 36.7295i | −1.03249 | − | 1.42111i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −45.6855 | − | 14.8441i | −1.76105 | − | 0.572198i | −0.763737 | − | 0.645527i | \(-0.776638\pi\) |
−0.997308 | + | 0.0733287i | \(0.976638\pi\) | |||||||
\(674\) | −33.5623 | + | 24.3844i | −1.29277 | + | 0.939254i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.2533 | − | 37.7117i | −0.471280 | − | 1.45045i | ||||
\(677\) | 2.67094 | − | 0.867842i | 0.102653 | − | 0.0333539i | −0.257240 | − | 0.966347i | \(-0.582813\pi\) |
0.359893 | + | 0.932994i | \(0.382813\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 31.1803 | − | 95.9632i | 1.19571 | − | 3.68002i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.8885 | + | 20.2622i | 1.06479 | + | 0.773615i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 68.0493 | − | 22.1106i | 2.59436 | − | 0.842958i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.65248 | − | 26.6296i | 0.329156 | − | 1.01304i | −0.640374 | − | 0.768063i | \(-0.721221\pi\) |
0.969530 | − | 0.244974i | \(-0.0787794\pi\) | |||||||
\(692\) | 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 | ||||||||
\(700\) | −38.4281 | + | 52.8918i | −1.45245 | + | 1.99912i | ||||
\(701\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.38197 | + | 4.25325i | 0.0519008 | + | 0.159734i | 0.973647 | − | 0.228058i | \(-0.0732377\pi\) |
−0.921747 | + | 0.387793i | \(0.873238\pi\) | |||||||
\(710\) | −42.4851 | + | 13.8042i | −1.59444 | + | 0.518064i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 44.0347 | + | 60.6086i | 1.65027 | + | 2.27140i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −75.7771 | −2.83192 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.7082 | + | 15.7719i | 0.809579 | + | 0.588194i | 0.913709 | − | 0.406370i | \(-0.133206\pi\) |
−0.104129 | + | 0.994564i | \(0.533206\pi\) | |||||||
\(720\) | 11.3435 | + | 34.9116i | 0.422746 | + | 1.30108i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −27.8887 | + | 38.3855i | −1.03791 | + | 1.42856i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.85410 | + | 18.0171i | −0.217566 | + | 0.669599i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | −31.2719 | − | 10.1609i | −1.15901 | − | 0.376587i | ||||
\(729\) | −21.8435 | + | 15.8702i | −0.809017 | + | 0.587785i | ||||
\(730\) | 53.7426 | + | 39.0463i | 1.98910 | + | 1.44517i | ||||
\(731\) | 32.6525 | + | 100.494i | 1.20770 | + | 3.71690i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.3492 | − | 23.8791i | 0.640807 | − | 0.881995i | −0.357852 | − | 0.933778i | \(-0.616491\pi\) |
0.998658 | + | 0.0517836i | \(0.0164906\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.4503 | − | 5.66994i | 0.640189 | − | 0.208010i | 0.0291059 | − | 0.999576i | \(-0.490734\pi\) |
0.611083 | + | 0.791566i | \(0.290734\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.11146 | + | 15.7314i | −0.187144 | + | 0.575969i | ||||
\(747\) | − | 2.18603i | − | 0.0799827i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 59.4164 | 2.17103 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.8885 | + | 18.8091i | −0.944686 | + | 0.686355i | −0.949544 | − | 0.313633i | \(-0.898454\pi\) |
0.00485778 | + | 0.999988i | \(0.498454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(758\) | − | 89.8996i | − | 3.26530i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 35.1246 | + | 108.102i | 1.27076 | + | 3.91101i | ||||
\(765\) | −51.5568 | + | 16.7518i | −1.86404 | + | 0.605663i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.48527 | − | 6.17345i | −0.161954 | − | 0.222910i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 82.2993 | + | 26.7407i | 2.96202 | + | 0.962417i | ||||
\(773\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(774\) | −79.2492 | − | 57.5779i | −2.84855 | − | 2.06960i | ||||
\(775\) | −13.8197 | − | 42.5325i | −0.496417 | − | 1.52781i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.1634 | + | 52.5275i | 1.36823 | + | 1.88320i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.1910 | − | 8.13073i | 0.399678 | − | 0.290383i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.5641 | − | 14.4798i | 1.58854 | − | 0.516148i | 0.624302 | − | 0.781183i | \(-0.285384\pi\) |
0.964239 | + | 0.265035i | \(0.0853836\pi\) | |||||||
\(788\) | 54.4924 | − | 75.0024i | 1.94121 | − | 2.67185i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 82.2492 | + | 59.7576i | 2.91525 | + | 2.11805i | ||||
\(797\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −7.33912 | − | 10.1014i | −0.259477 | − | 0.357140i | ||||
\(801\) | 12.4377 | − | 38.2793i | 0.439464 | − | 1.35253i | ||||
\(802\) | 11.1679i | 0.394351i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 34.4721 | − | 25.0455i | 1.21423 | − | 0.882189i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(810\) | 29.5394 | − | 40.6575i | 1.03791 | − | 1.42856i | ||||
\(811\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.45898 | + | 16.8010i | 0.190752 | + | 0.587075i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 30.8328 | 1.07281 | ||||||||
\(827\) | 50.4354 | + | 16.3875i | 1.75381 | + | 0.569848i | 0.996530 | − | 0.0832391i | \(-0.0265265\pi\) |
0.757283 | + | 0.653087i | \(0.226527\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0902 | − | 13.1433i | −0.628298 | − | 0.456485i | 0.227512 | − | 0.973775i | \(-0.426941\pi\) |
−0.855810 | + | 0.517290i | \(0.826941\pi\) | |||||||
\(830\) | 1.25735 | + | 3.86974i | 0.0436434 | + | 0.134321i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.27939 | + | 7.26646i | −0.183030 | + | 0.251919i | ||||
\(833\) | 12.0073 | + | 16.5266i | 0.416028 | + | 0.572614i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 23.9651i | − | 0.829347i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −84.9702 | − | 27.6085i | −2.93525 | − | 0.953720i | ||||
\(839\) | 45.3050 | − | 32.9160i | 1.56410 | − | 1.13639i | 0.631556 | − | 0.775330i | \(-0.282416\pi\) |
0.932544 | − | 0.361056i | \(-0.117584\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.96149 | − | 27.5806i | −0.309017 | − | 0.951057i | ||||
\(842\) | 74.3489 | − | 24.1574i | 2.56223 | − | 0.832520i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.46807 | − | 19.9067i | 0.222508 | − | 0.684810i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 81.6312 | − | 59.3085i | 2.79993 | − | 2.03427i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.0422 | + | 5.86227i | −0.617753 | + | 0.200720i | −0.601142 | − | 0.799142i | \(-0.705288\pi\) |
−0.0166106 | + | 0.999862i | \(0.505288\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −33.2148 | + | 102.225i | −1.13526 | + | 3.49396i | ||||
\(857\) | 52.7526i | 1.80200i | 0.433824 | + | 0.900998i | \(0.357164\pi\) | ||||
−0.433824 | + | 0.900998i | \(0.642836\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.7771 | −1.22070 | −0.610349 | − | 0.792132i | \(-0.708971\pi\) | ||||
−0.610349 | + | 0.792132i | \(0.708971\pi\) | |||||||
\(860\) | 117.792 | + | 38.2729i | 4.01667 | + | 1.30509i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.7205 | + | 18.8847i | −0.466512 | + | 0.642098i | ||||
\(866\) | 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 | ||||||||
\(875\) | −32.8216 | + | 10.6644i | −1.10957 | + | 0.360521i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.8933 | + | 31.5099i | 0.773051 | + | 1.06401i | 0.996015 | + | 0.0891871i | \(0.0284269\pi\) |
−0.222964 | + | 0.974827i | \(0.571573\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | −18.0110 | − | 5.85211i | −0.606460 | − | 0.197051i | ||||
\(883\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(884\) | 52.8328 | + | 38.3853i | 1.77696 | + | 1.29104i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.21504 | − | 11.3070i | 0.275834 | − | 0.379653i | −0.648514 | − | 0.761202i | \(-0.724609\pi\) |
0.924348 | + | 0.381549i | \(0.124609\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.1115 | + | 49.5860i | −0.540361 | + | 1.66306i | ||||
\(890\) | 74.9164i | 2.51120i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.3607 | − | 23.5114i | −1.08170 | − | 0.785900i | ||||
\(896\) | −15.9787 | − | 49.1774i | −0.533811 | − | 1.64290i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 59.0788 | − | 81.3150i | 1.97148 | − | 2.71352i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −19.6353 | + | 60.4311i | −0.654508 | + | 2.01437i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.09017 | + | 5.87785i | −0.268926 | + | 0.195386i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(908\) | −102.421 | + | 33.2784i | −3.39894 | + | 1.10438i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −19.3271 | − | 26.6015i | −0.640688 | − | 0.881831i | ||||
\(911\) | −2.76393 | + | 8.50651i | −0.0915732 | + | 0.281833i | −0.986345 | − | 0.164690i | \(-0.947338\pi\) |
0.894772 | + | 0.446523i | \(0.147338\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −91.3738 | −3.02238 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.5623 | − | 14.9394i | 0.679398 | − | 0.493611i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(920\) | 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 | ||||||||
\(929\) | −4.32624 | − | 13.3148i | −0.141939 | − | 0.436844i | 0.854665 | − | 0.519179i | \(-0.173762\pi\) |
−0.996605 | + | 0.0823350i | \(0.973762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 39.1212 | + | 53.8456i | 1.28146 | + | 1.76377i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −31.9574 | −1.04456 | ||||||||
\(937\) | 8.54224 | + | 2.77554i | 0.279063 | + | 0.0906730i | 0.445205 | − | 0.895429i | \(-0.353131\pi\) |
−0.166142 | + | 0.986102i | \(0.553131\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −6.76393 | + | 20.8172i | −0.220147 | + | 0.677544i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.3607 | + | 13.3398i | −0.596013 | + | 0.433029i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −132.470 | + | 43.0421i | −4.29338 | + | 1.39500i | ||||
\(953\) | −30.4778 | + | 41.9491i | −0.987273 | + | 1.35886i | −0.0544552 | + | 0.998516i | \(0.517342\pi\) |
−0.932818 | + | 0.360348i | \(0.882658\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.5410 | + | 57.0634i | −0.599973 | + | 1.84653i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −39.6418 | − | 28.8015i | −1.27877 | − | 0.929080i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 54.9207 | − | 17.8448i | 1.76980 | − | 0.575041i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.8491 | + | 36.9547i | 0.864305 | + | 1.18961i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 61.5625i | 1.97972i | 0.142063 | + | 0.989858i | \(0.454626\pi\) | ||||
−0.142063 | + | 0.989858i | \(0.545374\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.4721 | + | 10.5146i | −0.464433 | + | 0.337430i | −0.795268 | − | 0.606258i | \(-0.792670\pi\) |
0.330835 | + | 0.943689i | \(0.392670\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 23.9443 | 0.764872 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 46.5421 | − | 15.1224i | 1.48295 | − | 0.481841i | ||||
\(986\) | 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 | \(0.0335982\pi\) | |||||||
\(992\) | −21.2426 | − | 6.90212i | −0.674452 | − | 0.219143i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 49.8885 | + | 36.2461i | 1.58237 | + | 1.14966i | ||||
\(995\) | 16.5836 | + | 51.0390i | 0.525735 | + | 1.61805i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.1065 | − | 46.9435i | 1.08016 | − | 1.48672i | 0.220821 | − | 0.975314i | \(-0.429126\pi\) |
0.859342 | − | 0.511402i | \(-0.170874\pi\) | |||||||
\(998\) | 5.87130 | + | 8.08115i | 0.185853 | + | 0.255804i | ||||
\(999\) | 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.c.9.2 | 8 | ||
5.4 | even | 2 | inner | 605.2.j.c.9.1 | 8 | ||
11.2 | odd | 10 | 605.2.j.a.124.2 | 8 | |||
11.3 | even | 5 | 605.2.j.a.444.2 | 8 | |||
11.4 | even | 5 | 605.2.b.b.364.4 | yes | 4 | ||
11.5 | even | 5 | inner | 605.2.j.c.269.1 | 8 | ||
11.6 | odd | 10 | inner | 605.2.j.c.269.2 | 8 | ||
11.7 | odd | 10 | 605.2.b.b.364.1 | ✓ | 4 | ||
11.8 | odd | 10 | 605.2.j.a.444.1 | 8 | |||
11.9 | even | 5 | 605.2.j.a.124.1 | 8 | |||
11.10 | odd | 2 | inner | 605.2.j.c.9.1 | 8 | ||
55.4 | even | 10 | 605.2.b.b.364.1 | ✓ | 4 | ||
55.7 | even | 20 | 3025.2.a.bb.1.4 | 4 | |||
55.9 | even | 10 | 605.2.j.a.124.2 | 8 | |||
55.14 | even | 10 | 605.2.j.a.444.1 | 8 | |||
55.18 | even | 20 | 3025.2.a.bb.1.1 | 4 | |||
55.19 | odd | 10 | 605.2.j.a.444.2 | 8 | |||
55.24 | odd | 10 | 605.2.j.a.124.1 | 8 | |||
55.29 | odd | 10 | 605.2.b.b.364.4 | yes | 4 | ||
55.37 | odd | 20 | 3025.2.a.bb.1.1 | 4 | |||
55.39 | odd | 10 | inner | 605.2.j.c.269.1 | 8 | ||
55.48 | odd | 20 | 3025.2.a.bb.1.4 | 4 | |||
55.49 | even | 10 | inner | 605.2.j.c.269.2 | 8 | ||
55.54 | odd | 2 | CM | 605.2.j.c.9.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.b.364.1 | ✓ | 4 | 11.7 | odd | 10 | ||
605.2.b.b.364.1 | ✓ | 4 | 55.4 | even | 10 | ||
605.2.b.b.364.4 | yes | 4 | 11.4 | even | 5 | ||
605.2.b.b.364.4 | yes | 4 | 55.29 | odd | 10 | ||
605.2.j.a.124.1 | 8 | 11.9 | even | 5 | |||
605.2.j.a.124.1 | 8 | 55.24 | odd | 10 | |||
605.2.j.a.124.2 | 8 | 11.2 | odd | 10 | |||
605.2.j.a.124.2 | 8 | 55.9 | even | 10 | |||
605.2.j.a.444.1 | 8 | 11.8 | odd | 10 | |||
605.2.j.a.444.1 | 8 | 55.14 | even | 10 | |||
605.2.j.a.444.2 | 8 | 11.3 | even | 5 | |||
605.2.j.a.444.2 | 8 | 55.19 | odd | 10 | |||
605.2.j.c.9.1 | 8 | 5.4 | even | 2 | inner | ||
605.2.j.c.9.1 | 8 | 11.10 | odd | 2 | inner | ||
605.2.j.c.9.2 | 8 | 1.1 | even | 1 | trivial | ||
605.2.j.c.9.2 | 8 | 55.54 | odd | 2 | CM | ||
605.2.j.c.269.1 | 8 | 11.5 | even | 5 | inner | ||
605.2.j.c.269.1 | 8 | 55.39 | odd | 10 | inner | ||
605.2.j.c.269.2 | 8 | 11.6 | odd | 10 | inner | ||
605.2.j.c.269.2 | 8 | 55.49 | even | 10 | inner | ||
3025.2.a.bb.1.1 | 4 | 55.18 | even | 20 | |||
3025.2.a.bb.1.1 | 4 | 55.37 | odd | 20 | |||
3025.2.a.bb.1.4 | 4 | 55.7 | even | 20 | |||
3025.2.a.bb.1.4 | 4 | 55.48 | odd | 20 |