Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [616,2,Mod(13,616)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(616, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 5, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("616.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 616 = 2^{3} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 616.bi (of order \(10\), degree \(4\), 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: | \(4.91878476451\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.37515625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - x^{6} + 3x^{5} - x^{4} + 6x^{3} - 4x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 293.1 | ||
Root | \(-1.41264 - 0.0667372i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 616.293 |
Dual form | 616.2.bi.b.349.1 |
$q$-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 \(\left(\mathbb{Z}/616\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(309\) | \(353\) | \(463\) |
\(\chi(n)\) | \(e\left(\frac{7}{10}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41264 | + | 0.0667372i | −0.998886 | + | 0.0471903i | ||||
\(3\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(4\) | 1.99109 | − | 0.188551i | 0.995546 | − | 0.0942755i | ||||
\(5\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.51626 | − | 0.817582i | 0.951057 | − | 0.309017i | ||||
\(8\) | −2.80011 | + | 0.399234i | −0.989988 | + | 0.141151i | ||||
\(9\) | 2.42705 | + | 1.76336i | 0.809017 | + | 0.587785i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0629004 | − | 3.31603i | 0.0189652 | − | 0.999820i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(14\) | −3.50000 | + | 1.32288i | −0.935414 | + | 0.353553i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.92890 | − | 0.750845i | 0.982224 | − | 0.187711i | ||||
\(17\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(18\) | −3.54623 | − | 2.32901i | −0.835853 | − | 0.548953i | ||||
\(19\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.132447 | + | 4.68855i | 0.0282378 | + | 0.999601i | ||||
\(23\) | 2.56038 | 0.533877 | 0.266938 | − | 0.963714i | \(-0.413988\pi\) | ||||
0.266938 | + | 0.963714i | \(0.413988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.54508 | + | 4.75528i | −0.309017 | + | 0.951057i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.85595 | − | 2.10232i | 0.917688 | − | 0.397302i | ||||
\(29\) | −2.42225 | − | 7.45492i | −0.449801 | − | 1.38434i | −0.877132 | − | 0.480249i | \(-0.840546\pi\) |
0.427331 | − | 0.904095i | \(-0.359454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(32\) | −5.50000 | + | 1.32288i | −0.972272 | + | 0.233854i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.16497 | + | 3.05338i | 0.860828 | + | 0.508897i | ||||
\(37\) | 2.31678 | − | 0.752769i | 0.380877 | − | 0.123754i | −0.112320 | − | 0.993672i | \(-0.535828\pi\) |
0.493197 | + | 0.869918i | \(0.335828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.8185 | 1.95480 | 0.977399 | − | 0.211402i | \(-0.0678028\pi\) | ||||
0.977399 | + | 0.211402i | \(0.0678028\pi\) | |||||||
\(44\) | −0.500000 | − | 6.61438i | −0.0753778 | − | 0.997155i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.61689 | + | 0.170873i | −0.533282 | + | 0.0251938i | ||||
\(47\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.66312 | − | 4.11450i | 0.809017 | − | 0.587785i | ||||
\(50\) | 1.86529 | − | 6.82061i | 0.263792 | − | 0.964580i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.57760 | + | 2.17138i | −0.216700 | + | 0.298263i | −0.903503 | − | 0.428581i | \(-0.859014\pi\) |
0.686803 | + | 0.726844i | \(0.259014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.71939 | + | 3.29390i | −0.897917 | + | 0.440165i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.91928 | + | 10.3695i | 0.514627 | + | 1.36158i | ||||
\(59\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.54878 | + | 2.45275i | 0.951057 | + | 0.309017i | ||||
\(64\) | 7.68122 | − | 2.23580i | 0.960153 | − | 0.279475i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4916i | 1.28175i | 0.767644 | + | 0.640877i | \(0.221429\pi\) | ||||
−0.767644 | + | 0.640877i | \(0.778571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9884 | − | 9.43662i | 1.54144 | − | 1.11992i | 0.592014 | − | 0.805928i | \(-0.298333\pi\) |
0.949425 | − | 0.313993i | \(-0.101667\pi\) | |||||||
\(72\) | −7.50000 | − | 3.96863i | −0.883883 | − | 0.467707i | ||||
\(73\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(74\) | −3.22254 | + | 1.21801i | −0.374613 | + | 0.141590i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.55285 | − | 8.39541i | −0.290924 | − | 0.956746i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3127 | − | 14.1942i | 1.16027 | − | 1.59698i | 0.450035 | − | 0.893011i | \(-0.351411\pi\) |
0.710235 | − | 0.703964i | \(-0.248589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.78115 | + | 8.55951i | 0.309017 | + | 0.951057i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −18.1079 | + | 0.855469i | −1.95262 | + | 0.0922476i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.14774 | + | 9.31035i | 0.122350 | + | 0.992487i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.09796 | − | 0.482763i | 0.531499 | − | 0.0503315i | ||||
\(93\) | 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 | \(0.200000\pi\) | |||||||
\(98\) | −7.72535 | + | 6.19024i | −0.780378 | + | 0.625308i | ||||
\(99\) | 6.00000 | − | 7.93725i | 0.603023 | − | 0.797724i | ||||
\(100\) | −2.17979 | + | 9.75953i | −0.217979 | + | 0.975953i | ||||
\(101\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.08367 | − | 3.17266i | 0.202384 | − | 0.308156i | ||||
\(107\) | −3.46496 | + | 10.6641i | −0.334971 | + | 1.03093i | 0.631766 | + | 0.775159i | \(0.282330\pi\) |
−0.966736 | + | 0.255774i | \(0.917670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6273 | −1.49683 | −0.748414 | − | 0.663232i | \(-0.769184\pi\) | ||||
−0.748414 | + | 0.663232i | \(0.769184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.27225 | − | 5.10152i | 0.876145 | − | 0.482048i | ||||
\(113\) | −3.34450 | + | 10.2933i | −0.314624 | + | 0.968314i | 0.661285 | + | 0.750135i | \(0.270012\pi\) |
−0.975909 | + | 0.218179i | \(0.929988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.22856 | − | 14.3867i | −0.578307 | − | 1.33577i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9921 | − | 0.417159i | −0.999281 | − | 0.0379235i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.8274 | − | 2.96106i | −0.964580 | − | 0.263792i | ||||
\(127\) | −6.06090 | − | 8.34211i | −0.537818 | − | 0.740242i | 0.450479 | − | 0.892787i | \(-0.351253\pi\) |
−0.988297 | + | 0.152545i | \(0.951253\pi\) | |||||||
\(128\) | −10.7016 | + | 3.67100i | −0.945895 | + | 0.324473i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.700180 | − | 14.8208i | −0.0604864 | − | 1.28033i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.7856 | + | 10.0158i | −1.17778 | + | 0.855708i | −0.991920 | − | 0.126868i | \(-0.959507\pi\) |
−0.185861 | + | 0.982576i | \(0.559507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −17.7181 | + | 14.1973i | −1.48687 | + | 1.19141i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.8596 | + | 5.10570i | 0.904970 | + | 0.425475i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.47100 | − | 1.93566i | 0.367514 | − | 0.159111i | ||||
\(149\) | −17.7984 | + | 12.9313i | −1.45810 | + | 1.05937i | −0.474247 | + | 0.880392i | \(0.657280\pi\) |
−0.983853 | + | 0.178979i | \(0.942720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.2633 | − | 7.55872i | −1.89314 | − | 0.615120i | −0.976546 | − | 0.215308i | \(-0.930924\pi\) |
−0.916597 | − | 0.399811i | \(-0.869076\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.16654 | + | 11.6893i | 0.335750 | + | 0.941951i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(158\) | −13.6208 | + | 20.7395i | −1.08362 | + | 1.64995i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.44258 | − | 2.09332i | 0.507747 | − | 0.164977i | ||||
\(162\) | −4.50000 | − | 11.9059i | −0.353553 | − | 0.935414i | ||||
\(163\) | −8.29696 | + | 11.4198i | −0.649868 | + | 0.894467i | −0.999093 | − | 0.0425718i | \(-0.986445\pi\) |
0.349225 | + | 0.937039i | \(0.386445\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.01722 | + | 12.3637i | 0.309017 | + | 0.951057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 25.5228 | − | 2.41694i | 1.94609 | − | 0.184290i | ||||
\(173\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.2288i | 1.00000i | ||||||||
\(176\) | −2.24269 | − | 13.0756i | −0.169049 | − | 0.985608i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.15763 | − | 1.35090i | −0.310756 | − | 0.100971i | 0.149487 | − | 0.988764i | \(-0.452238\pi\) |
−0.460243 | + | 0.887793i | \(0.652238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.16935 | + | 1.02219i | −0.528531 | + | 0.0753570i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.80563 | − | 8.63483i | −0.203008 | − | 0.624795i | −0.999789 | − | 0.0205267i | \(-0.993466\pi\) |
0.796781 | − | 0.604268i | \(-0.206534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2839 | − | 22.4128i | −1.17214 | − | 1.61331i | −0.647834 | − | 0.761781i | \(-0.724325\pi\) |
−0.524305 | − | 0.851530i | \(-0.675675\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.5000 | − | 9.26013i | 0.750000 | − | 0.661438i | ||||
\(197\) | −2.03059 | −0.144674 | −0.0723369 | − | 0.997380i | \(-0.523046\pi\) | ||||
−0.0723369 | + | 0.997380i | \(0.523046\pi\) | |||||||
\(198\) | −7.94612 | + | 11.6129i | −0.564706 | + | 0.825292i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 2.42794 | − | 13.9322i | 0.171681 | − | 0.985153i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.1900 | − | 16.7781i | −0.855572 | − | 1.17759i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.21418 | + | 4.51486i | 0.431915 | + | 0.313805i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3570 | + | 16.9698i | 1.60796 | + | 1.16825i | 0.869469 | + | 0.493987i | \(0.164461\pi\) |
0.738490 | + | 0.674264i | \(0.235539\pi\) | |||||||
\(212\) | −2.73174 | + | 4.62089i | −0.187616 | + | 0.317364i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.18305 | − | 15.2957i | 0.285947 | − | 1.04559i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 22.0758 | − | 1.04293i | 1.49516 | − | 0.0706358i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(224\) | −12.7579 | + | 7.82540i | −0.852421 | + | 0.522856i | ||||
\(225\) | −12.1353 | + | 8.81678i | −0.809017 | + | 0.587785i | ||||
\(226\) | 4.03762 | − | 14.7639i | 0.268579 | − | 0.982082i | ||||
\(227\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.75883 | + | 19.9075i | 0.640698 | + | 1.30699i | ||||
\(233\) | 12.4411 | − | 17.1237i | 0.815042 | − | 1.12181i | −0.175484 | − | 0.984482i | \(-0.556149\pi\) |
0.990526 | − | 0.137326i | \(-0.0438509\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.4127 | − | 3.70821i | −0.738226 | − | 0.239864i | −0.0843185 | − | 0.996439i | \(-0.526871\pi\) |
−0.653907 | + | 0.756575i | \(0.726871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 15.5557 | − | 0.144287i | 0.999957 | − | 0.00927509i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(252\) | 15.4928 | + | 3.46031i | 0.975953 | + | 0.217979i | ||||
\(253\) | 0.161049 | − | 8.49030i | 0.0101251 | − | 0.533781i | ||||
\(254\) | 9.11858 | + | 11.3799i | 0.572151 | + | 0.714038i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.8725 | − | 5.89998i | 0.929529 | − | 0.368749i | ||||
\(257\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.21418 | − | 3.78832i | 0.323993 | − | 0.235395i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.26675 | − | 22.3648i | 0.449801 | − | 1.38434i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.0900i | 1.42379i | 0.702284 | + | 0.711897i | \(0.252164\pi\) | ||||
−0.702284 | + | 0.711897i | \(0.747836\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.97820 | + | 20.8898i | 0.120838 | + | 1.27604i | ||||
\(269\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.8056 | − | 15.0687i | 1.13609 | − | 0.910334i | ||||
\(275\) | 15.6715 | + | 5.42265i | 0.945025 | + | 0.326998i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.9284 | + | 19.5646i | 1.61797 | + | 1.17552i | 0.814289 | + | 0.580460i | \(0.197127\pi\) |
0.803679 | + | 0.595063i | \(0.202873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.08226 | + | 1.48960i | 0.0645620 | + | 0.0888620i | 0.840077 | − | 0.542467i | \(-0.182510\pi\) |
−0.775515 | + | 0.631329i | \(0.782510\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(284\) | 24.0818 | − | 21.2382i | 1.42899 | − | 1.26025i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −15.6815 | − | 6.48777i | −0.924040 | − | 0.382296i | ||||
\(289\) | −5.25329 | + | 16.1680i | −0.309017 | + | 0.951057i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.18672 | + | 3.03277i | −0.359596 | + | 0.176276i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.2797 | − | 19.4550i | 1.40648 | − | 1.12700i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.2546 | − | 10.4802i | 1.85912 | − | 0.604066i | ||||
\(302\) | 33.3671 | + | 9.12520i | 1.92006 | + | 0.525096i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | −6.66593 | − | 16.2347i | −0.379826 | − | 0.925058i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.8572 | − | 30.2065i | 1.00455 | − | 1.69925i | ||||
\(317\) | −16.7792 | + | 23.0946i | −0.942415 | + | 1.29712i | 0.0123997 | + | 0.999923i | \(0.496053\pi\) |
−0.954815 | + | 0.297200i | \(0.903947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.8731 | + | 7.56333i | −1.39263 | + | 0.423465i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.96134 | + | 3.38707i | −0.499396 | + | 0.188754i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 7.15144 | + | 16.5184i | 0.397302 | + | 0.917688i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.9585 | − | 16.6857i | 0.606934 | − | 0.924138i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 32.6029i | − | 1.79202i | −0.444038 | − | 0.896008i | \(-0.646455\pi\) | ||
0.444038 | − | 0.896008i | \(-0.353545\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.95035 | + | 2.25831i | 0.380877 | + | 0.123754i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.3558 | + | 10.8380i | −1.81701 | + | 0.590381i | −0.817102 | + | 0.576493i | \(0.804421\pi\) |
−0.999904 | + | 0.0138879i | \(0.995579\pi\) | |||||||
\(338\) | −6.50000 | − | 17.1974i | −0.353553 | − | 0.935414i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.8859 | − | 14.9832i | 0.587785 | − | 0.809017i | ||||
\(344\) | −35.8931 | + | 5.11757i | −1.93523 | + | 0.275921i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.9958 | + | 10.8951i | −0.805016 | + | 0.584878i | −0.912381 | − | 0.409342i | \(-0.865758\pi\) |
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(350\) | −0.882850 | − | 18.6874i | −0.0471903 | − | 0.998886i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.04074 | + | 18.3214i | 0.215372 | + | 0.976532i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.96339 | + | 1.63086i | 0.315175 | + | 0.0861936i | ||||
\(359\) | −3.64987 | + | 1.18591i | −0.192633 | + | 0.0625901i | −0.403745 | − | 0.914872i | \(-0.632292\pi\) |
0.211112 | + | 0.977462i | \(0.432292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3713 | − | 11.1679i | −0.809017 | − | 0.587785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(368\) | 10.0595 | − | 1.92245i | 0.524387 | − | 0.100215i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.19437 | + | 6.75359i | −0.113926 | + | 0.350629i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.4361 | − | 18.4932i | −0.690165 | − | 0.949931i | 0.309834 | − | 0.950791i | \(-0.399726\pi\) |
−1.00000 | 0.000859657i | \(0.999726\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.53960 | + | 12.0107i | 0.232266 | + | 0.614518i | ||||
\(383\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.4990 | + | 30.5745i | 1.24697 | + | 1.55620i | ||||
\(387\) | 31.1111 | + | 22.6035i | 1.58147 | + | 1.14900i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.4816 | − | 12.1785i | 1.90039 | − | 0.617475i | 0.937054 | − | 0.349185i | \(-0.113542\pi\) |
0.963338 | − | 0.268290i | \(-0.0864585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −14.2147 | + | 13.7820i | −0.717951 | + | 0.696094i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.86849 | − | 0.135516i | 0.144513 | − | 0.00682721i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.4500 | − | 16.9351i | 0.525131 | − | 0.851021i | ||||
\(397\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.50000 | + | 19.8431i | −0.125000 | + | 0.992157i | ||||
\(401\) | 24.7856 | − | 18.0078i | 1.23773 | − | 0.899265i | 0.240287 | − | 0.970702i | \(-0.422758\pi\) |
0.997445 | + | 0.0714367i | \(0.0227584\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.3398 | + | 22.8879i | 0.910190 | + | 1.13591i | ||||
\(407\) | −2.35048 | − | 7.72987i | −0.116509 | − | 0.383155i | ||||
\(408\) | 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 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −9.07969 | − | 5.96315i | −0.446243 | − | 0.293073i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.8480 | − | 10.6730i | −1.60091 | − | 0.520169i | −0.633581 | − | 0.773676i | \(-0.718416\pi\) |
−0.967333 | + | 0.253507i | \(0.918416\pi\) | |||||||
\(422\) | −34.1275 | − | 22.4134i | −1.66130 | − | 1.09107i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.55057 | − | 6.70995i | 0.172431 | − | 0.325864i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.88834 | + | 21.8865i | −0.236287 | + | 1.05792i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.6942 | + | 31.2358i | −1.09314 | + | 1.50458i | −0.248963 | + | 0.968513i | \(0.580090\pi\) |
−0.844177 | + | 0.536065i | \(0.819910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.1155 | + | 2.94655i | −1.49016 | + | 0.141114i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −39.6801 | − | 12.8928i | −1.88526 | − | 0.612557i | −0.983676 | − | 0.179949i | \(-0.942407\pi\) |
−0.901582 | − | 0.432608i | \(-0.857593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 17.5000 | − | 11.9059i | 0.826797 | − | 0.562500i | ||||
\(449\) | 33.0711 | + | 24.0276i | 1.56072 | + | 1.13393i | 0.935413 | + | 0.353556i | \(0.115028\pi\) |
0.625310 | + | 0.780376i | \(0.284972\pi\) | |||||||
\(450\) | 16.5543 | − | 13.2648i | 0.780378 | − | 0.625308i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −4.71840 | + | 21.1256i | −0.221935 | + | 0.993663i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.33490 | + | 5.96648i | 0.202778 | + | 0.279100i | 0.898279 | − | 0.439425i | \(-0.144818\pi\) |
−0.695501 | + | 0.718525i | \(0.744818\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.0299 | 1.07029 | 0.535145 | − | 0.844760i | \(-0.320257\pi\) | ||||
0.535145 | + | 0.844760i | \(0.320257\pi\) | |||||||
\(464\) | −15.1143 | − | 27.4709i | −0.701662 | − | 1.27530i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.4319 | + | 25.0198i | −0.761195 | + | 1.15902i | ||||
\(467\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.57775 | + | 26.3996i | 0.396084 | + | 1.21902i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.806287 | − | 42.5064i | 0.0370731 | − | 1.95445i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.65785 | + | 2.48818i | −0.350629 | + | 0.113926i | ||||
\(478\) | 16.3695 | + | 4.47670i | 0.748722 | + | 0.204760i | ||||
\(479\) | 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 | ||||||||
\(484\) | −21.9649 | + | 1.24197i | −0.998405 | + | 0.0564531i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.7279 | + | 39.1724i | −0.576755 | + | 1.77507i | 0.0533681 | + | 0.998575i | \(0.483004\pi\) |
−0.630123 | + | 0.776495i | \(0.716996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.5967 | − | 41.8465i | −0.613613 | − | 1.88851i | −0.420363 | − | 0.907356i | \(-0.638097\pi\) |
−0.193249 | − | 0.981150i | \(-0.561903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.9670 | − | 34.3641i | 1.11992 | − | 1.54144i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.232351 | − | 0.0754955i | 0.0104015 | − | 0.00337964i | −0.303812 | − | 0.952732i | \(-0.598259\pi\) |
0.314213 | + | 0.949352i | \(0.398259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(504\) | −22.1166 | − | 3.85423i | −0.985153 | − | 0.171681i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.339115 | + | 12.0045i | 0.0150755 | + | 0.533664i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.6407 | − | 15.4671i | −0.605209 | − | 0.686242i | ||||
\(509\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −20.6157 | + | 9.32709i | −0.911092 | + | 0.412203i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −7.11292 | + | 5.69951i | −0.312524 | + | 0.250422i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(522\) | −8.77273 | + | 32.0783i | −0.383972 | + | 1.40403i | ||||
\(523\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.54096 | − | 32.6179i | −0.0671893 | − | 1.42221i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.4444 | −0.714976 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.18861 | − | 29.3776i | −0.180920 | − | 1.26892i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.2876 | − | 19.0379i | −0.572336 | − | 0.820019i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9284 | + | 11.5726i | 0.684814 | + | 0.497546i | 0.874951 | − | 0.484211i | \(-0.160893\pi\) |
−0.190138 | + | 0.981757i | \(0.560893\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5967 | + | 41.8465i | −0.581355 | + | 1.78923i | 0.0320849 | + | 0.999485i | \(0.489785\pi\) |
−0.613440 | + | 0.789741i | \(0.710215\pi\) | |||||||
\(548\) | −25.5599 | + | 22.5417i | −1.09186 | + | 0.962932i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.5000 | − | 6.61438i | −0.959403 | − | 0.282038i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.3445 | − | 44.1478i | 0.609990 | − | 1.87736i | ||||
\(554\) | −39.3457 | − | 25.8406i | −1.67164 | − | 1.09786i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.4223 | + | 41.3094i | 0.568719 | + | 1.75034i | 0.656634 | + | 0.754209i | \(0.271980\pi\) |
−0.0879152 | + | 0.996128i | \(0.528020\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.62825 | − | 2.03204i | −0.0686835 | − | 0.0857163i | ||||
\(563\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.9962 | + | 19.2641i | 0.587785 | + | 0.809017i | ||||
\(568\) | −32.6015 | + | 31.6090i | −1.36793 | + | 1.32628i | ||||
\(569\) | 40.2601 | + | 13.0813i | 1.68779 | + | 0.548397i | 0.986398 | − | 0.164375i | \(-0.0525608\pi\) |
0.701395 | + | 0.712773i | \(0.252561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.5287 | −1.94717 | −0.973583 | − | 0.228332i | \(-0.926673\pi\) | ||||
−0.973583 | + | 0.228332i | \(0.926673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.95601 | + | 12.1753i | −0.164977 | + | 0.507747i | ||||
\(576\) | 22.5852 | + | 8.11833i | 0.941051 | + | 0.338264i | ||||
\(577\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(578\) | 6.34199 | − | 23.1901i | 0.263792 | − | 0.964580i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.10114 | + | 5.36796i | 0.294099 | + | 0.222318i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.53719 | − | 4.69710i | 0.350876 | − | 0.193049i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −33.0000 | + | 29.1033i | −1.35173 | + | 1.19212i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.4997 | + | 26.5186i | −1.49134 | + | 1.08352i | −0.517663 | + | 0.855584i | \(0.673198\pi\) |
−0.973676 | + | 0.227937i | \(0.926802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(602\) | −44.8646 | + | 16.9572i | −1.82855 | + | 0.691126i | ||||
\(603\) | −18.5004 | + | 25.4637i | −0.753396 | + | 1.03696i | ||||
\(604\) | −47.7447 | − | 10.6638i | −1.94270 | − | 0.433903i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.73325 | − | 11.4898i | 0.150784 | − | 0.464067i | −0.846925 | − | 0.531712i | \(-0.821549\pi\) |
0.997709 | + | 0.0676456i | \(0.0215487\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.5000 | + | 22.4889i | 0.423057 | + | 0.906103i | ||||
\(617\) | 3.84770 | 0.154902 | 0.0774512 | − | 0.996996i | \(-0.475322\pi\) | ||||
0.0774512 | + | 0.996996i | \(0.475322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.2254 | − | 14.6946i | −0.809017 | − | 0.587785i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.5241 | − | 47.7782i | −0.618003 | − | 1.90202i | −0.318475 | − | 0.947931i | \(-0.603171\pi\) |
−0.299528 | − | 0.954087i | \(-0.596829\pi\) | |||||||
\(632\) | −23.2099 | + | 43.8626i | −0.923240 | + | 1.74476i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.1617 | − | 33.7441i | 0.880154 | − | 1.34015i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34.6319 | − | 12.3442i | 1.37109 | − | 0.488712i | ||||
\(639\) | 48.1636 | 1.90532 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.65550 | − | 23.5612i | 0.302374 | − | 0.930611i | −0.678270 | − | 0.734813i | \(-0.737270\pi\) |
0.980644 | − | 0.195799i | \(-0.0627300\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(644\) | 12.4331 | − | 5.38275i | 0.489932 | − | 0.212110i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(648\) | −11.2048 | − | 22.8572i | −0.440165 | − | 0.897917i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.3668 | + | 24.3023i | −0.562648 | + | 0.951750i | ||||
\(653\) | 42.1152 | − | 13.6840i | 1.64809 | − | 0.535498i | 0.669768 | − | 0.742571i | \(-0.266394\pi\) |
0.978326 | + | 0.207072i | \(0.0663936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.0000 | 1.71400 | 0.856998 | − | 0.515319i | \(-0.172327\pi\) | ||||
0.856998 | + | 0.515319i | \(0.172327\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(662\) | 2.17582 | + | 46.0561i | 0.0845658 | + | 1.79002i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.96904 | − | 2.72632i | −0.386293 | − | 0.105643i | ||||
\(667\) | −6.20189 | − | 19.0874i | −0.240138 | − | 0.739069i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.76533 | − | 13.4408i | 0.376426 | − | 0.518106i | −0.578208 | − | 0.815890i | \(-0.696248\pi\) |
0.954633 | + | 0.297784i | \(0.0962476\pi\) | |||||||
\(674\) | 46.3964 | − | 17.5362i | 1.78712 | − | 0.675468i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.3299 | + | 23.8599i | 0.397302 | + | 0.917688i | ||||
\(677\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 51.0901i | − | 1.95491i | −0.211147 | − | 0.977454i | \(-0.567720\pi\) | ||
0.211147 | − | 0.977454i | \(-0.432280\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −14.3779 | + | 21.8923i | −0.548953 | + | 0.835853i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 50.3625 | − | 9.62468i | 1.92005 | − | 0.366938i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.60820 | − | 24.8777i | 0.326998 | − | 0.945025i | ||||
\(694\) | 20.4565 | − | 16.3916i | 0.776518 | − | 0.622215i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.49430 | + | 26.3397i | 0.0942755 | + | 0.995546i | ||||
\(701\) | −15.7423 | + | 48.4499i | −0.594579 | + | 1.82993i | −0.0377695 | + | 0.999286i | \(0.512025\pi\) |
−0.556810 | + | 0.830640i | \(0.687975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −6.93082 | − | 25.6118i | −0.261215 | − | 0.965281i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.0896 | − | 31.7802i | −0.867150 | − | 1.19353i | −0.979817 | − | 0.199896i | \(-0.935939\pi\) |
0.112667 | − | 0.993633i | \(-0.464061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 50.0589 | − | 16.2651i | 1.87736 | − | 0.609990i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.53295 | − | 1.90583i | −0.318891 | − | 0.0712244i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.07680 | − | 1.91885i | 0.189464 | − | 0.0716108i | ||||
\(719\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 22.4594 | + | 14.7504i | 0.835853 | + | 0.548953i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 39.1928 | 1.45559 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.34346 | + | 25.6785i | −0.309017 | + | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.0821 | + | 3.38707i | −0.519073 | + | 0.124849i | ||||
\(737\) | 34.7905 | + | 0.659926i | 1.28152 | + | 0.0243087i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.4857 | + | 19.2430i | 0.974291 | + | 0.707864i | 0.956425 | − | 0.291977i | \(-0.0943129\pi\) |
0.0178655 | + | 0.999840i | \(0.494313\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.64914 | − | 9.68682i | 0.0972530 | − | 0.355614i | ||||
\(743\) | −3.79415 | − | 5.22220i | −0.139194 | − | 0.191584i | 0.733729 | − | 0.679442i | \(-0.237778\pi\) |
−0.872923 | + | 0.487858i | \(0.837778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 31.0780 | − | 1.46822i | 1.13785 | − | 0.0537553i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.6664i | 1.08399i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.3593 | − | 38.0379i | 0.450996 | − | 1.38802i | −0.424777 | − | 0.905298i | \(-0.639647\pi\) |
0.875772 | − | 0.482724i | \(-0.160353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6240 | + | 18.7519i | −0.495174 | + | 0.681548i | −0.981332 | − | 0.192323i | \(-0.938398\pi\) |
0.486158 | + | 0.873871i | \(0.338398\pi\) | |||||||
\(758\) | 20.2145 | + | 25.2275i | 0.734224 | + | 0.916303i | ||||
\(759\) | 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 | ||||||||
\(763\) | −39.3224 | + | 12.7766i | −1.42357 | + | 0.462545i | ||||
\(764\) | −7.21437 | − | 16.6637i | −0.261007 | − | 0.602873i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −36.6487 | − | 41.5557i | −1.31901 | − | 1.49562i | ||||
\(773\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(774\) | −45.4572 | − | 29.8543i | −1.63393 | − | 1.07309i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −52.1352 | + | 19.7052i | −1.86914 | + | 0.706467i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.4751 | − | 43.6635i | −1.09049 | − | 1.56240i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 19.1605 | − | 20.4176i | 0.684302 | − | 0.729199i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(788\) | −4.04310 | + | 0.382871i | −0.144029 | + | 0.0136392i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.6351i | 1.01815i | ||||||||
\(792\) | −13.6318 | + | 24.6206i | −0.484386 | + | 0.874854i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 2.20732 | − | 28.1980i | 0.0780405 | − | 0.996950i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −33.8113 | + | 27.0926i | −1.19392 | + | 0.956672i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.9316 | + | 39.8210i | 1.01718 | + | 1.40003i | 0.914160 | + | 0.405353i | \(0.132851\pi\) |
0.103022 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(812\) | −27.4350 | − | 31.1084i | −0.962779 | − | 1.09169i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.83624 | + | 10.7626i | 0.134460 | + | 0.377230i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.79837 | + | 20.9232i | 0.237265 | + | 0.730226i | 0.996813 | + | 0.0797750i | \(0.0254202\pi\) |
−0.759548 | + | 0.650451i | \(0.774580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.70206 | + | 1.23662i | 0.0593301 | + | 0.0431058i | 0.617055 | − | 0.786920i | \(-0.288326\pi\) |
−0.557725 | + | 0.830026i | \(0.688326\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.5967 | + | 25.8626i | 1.23782 | + | 0.899329i | 0.997451 | − | 0.0713526i | \(-0.0227315\pi\) |
0.240369 | + | 0.970682i | \(0.422732\pi\) | |||||||
\(828\) | 13.2243 | + | 7.81782i | 0.459576 | + | 0.271688i | ||||
\(829\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2471 | + | 19.0696i | −0.905071 | + | 0.657573i | ||||
\(842\) | 47.1146 | + | 12.8849i | 1.62368 | + | 0.444042i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 49.7055 | + | 29.3845i | 1.71094 | + | 1.01146i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −28.0000 | + | 7.93725i | −0.962091 | + | 0.272727i | ||||
\(848\) | −4.56787 | + | 9.71568i | −0.156861 | + | 0.333638i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.93185 | − | 1.92738i | 0.203341 | − | 0.0660696i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.44482 | − | 31.2439i | 0.186100 | − | 1.06789i | ||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 29.9741 | − | 45.6395i | 1.02092 | − | 1.55449i | ||||
\(863\) | 6.47214 | − | 4.70228i | 0.220314 | − | 0.160068i | −0.472154 | − | 0.881516i | \(-0.656523\pi\) |
0.692468 | + | 0.721449i | \(0.256523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −46.4198 | − | 35.0901i | −1.57468 | − | 1.19035i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 43.7583 | − | 6.23897i | 1.48184 | − | 0.211278i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.2668 | − | 56.2193i | 0.616824 | − | 1.89839i | 0.248939 | − | 0.968519i | \(-0.419918\pi\) |
0.367885 | − | 0.929871i | \(-0.380082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −29.6654 | + | 1.40148i | −0.998886 | + | 0.0471903i | ||||
\(883\) | 55.3577 | + | 17.9868i | 1.86293 | + | 0.605304i | 0.993863 | + | 0.110619i | \(0.0352832\pi\) |
0.869072 | + | 0.494686i | \(0.164717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 56.9140 | + | 15.5648i | 1.91206 | + | 0.522909i | ||||
\(887\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.0711 | − | 16.0356i | −0.740242 | − | 0.537818i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.5585 | − | 8.68399i | 0.956746 | − | 0.290924i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −23.9266 | + | 17.9866i | −0.799332 | + | 0.600890i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −48.3211 | − | 31.7352i | −1.61250 | − | 1.05902i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −22.5000 | + | 19.8431i | −0.750000 | + | 0.661438i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.25553 | − | 30.1577i | 0.174796 | − | 1.00303i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.2132 | − | 25.0684i | −0.604760 | − | 0.832381i | 0.391373 | − | 0.920232i | \(-0.372000\pi\) |
−0.996134 | + | 0.0878507i | \(0.972000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.9443 | + | 9.40456i | 0.428863 | + | 0.311587i | 0.781194 | − | 0.624288i | \(-0.214611\pi\) |
−0.352331 | + | 0.935875i | \(0.614611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −6.52183 | − | 8.13918i | −0.215723 | − | 0.269220i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.1974 | + | 47.0687i | 1.12807 | + | 1.55265i | 0.791687 | + | 0.610927i | \(0.209203\pi\) |
0.336381 | + | 0.941726i | \(0.390797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.1801i | 0.400478i | ||||||||
\(926\) | −32.5329 | + | 1.53695i | −1.06910 | + | 0.0505073i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.1843 | + | 37.7977i | 0.761062 | + | 1.24077i | ||||
\(929\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 21.5426 | − | 36.4406i | 0.705652 | − | 1.19365i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(938\) | −13.8791 | − | 36.7206i | −0.453168 | − | 1.19897i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.69777 | + | 60.1000i | 0.0551992 | + | 1.95402i | ||||
\(947\) | − | 58.2065i | − | 1.89146i | −0.324956 | − | 0.945729i | \(-0.605350\pi\) | ||
0.324956 | − | 0.945729i | \(-0.394650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −46.2410 | + | 15.0246i | −1.49789 | + | 0.486694i | −0.939402 | − | 0.342817i | \(-0.888619\pi\) |
−0.558489 | + | 0.829512i | \(0.688619\pi\) | |||||||
\(954\) | 10.6517 | − | 4.02597i | 0.344862 | − | 0.130346i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −23.4229 | − | 5.23151i | −0.757551 | − | 0.169199i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.4993 | + | 36.4732i | −0.855708 | + | 1.17778i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.57953 | + | 29.4828i | 0.309017 | + | 0.951057i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.2142 | + | 19.7723i | −0.876965 | + | 0.637152i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 52.7587i | − | 1.69661i | −0.529511 | − | 0.848303i | \(-0.677624\pi\) | ||
0.529511 | − | 0.848303i | \(-0.322376\pi\) | |||||||
\(968\) | 30.9456 | − | 3.22033i | 0.994629 | − | 0.103505i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 15.3656 | − | 56.1858i | 0.492347 | − | 1.80031i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.0711 | + | 32.0196i | 1.40996 | + | 1.02440i | 0.993328 | + | 0.115321i | \(0.0367898\pi\) |
0.416632 | + | 0.909075i | \(0.363210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.9284 | − | 27.5566i | −1.21096 | − | 0.879813i | ||||
\(982\) | 22.0000 | + | 58.2065i | 0.702048 | + | 1.85744i | ||||
\(983\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.8202 | 1.04362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.0000 | −0.762385 | −0.381193 | − | 0.924496i | \(-0.624487\pi\) | ||||
−0.381193 | + | 0.924496i | \(0.624487\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −32.9759 | + | 50.2102i | −1.04593 | + | 1.59257i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(998\) | −0.323190 | + | 0.122154i | −0.0102304 | + | 0.00386673i | ||||
\(999\) | 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 | 616.2.bi.b.293.1 | yes | 8 | |
7.6 | odd | 2 | CM | 616.2.bi.b.293.1 | yes | 8 | |
8.5 | even | 2 | 616.2.bi.a.293.2 | ✓ | 8 | ||
11.8 | odd | 10 | 616.2.bi.a.349.2 | yes | 8 | ||
56.13 | odd | 2 | 616.2.bi.a.293.2 | ✓ | 8 | ||
77.41 | even | 10 | 616.2.bi.a.349.2 | yes | 8 | ||
88.85 | odd | 10 | inner | 616.2.bi.b.349.1 | yes | 8 | |
616.349 | even | 10 | inner | 616.2.bi.b.349.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.2.bi.a.293.2 | ✓ | 8 | 8.5 | even | 2 | ||
616.2.bi.a.293.2 | ✓ | 8 | 56.13 | odd | 2 | ||
616.2.bi.a.349.2 | yes | 8 | 11.8 | odd | 10 | ||
616.2.bi.a.349.2 | yes | 8 | 77.41 | even | 10 | ||
616.2.bi.b.293.1 | yes | 8 | 1.1 | even | 1 | trivial | |
616.2.bi.b.293.1 | yes | 8 | 7.6 | odd | 2 | CM | |
616.2.bi.b.349.1 | yes | 8 | 88.85 | odd | 10 | inner | |
616.2.bi.b.349.1 | yes | 8 | 616.349 | even | 10 | inner |