Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,3,Mod(145,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cg (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.4660106475\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.35911766016.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 7x^{6} - 2x^{5} + 78x^{4} - 18x^{3} - 153x^{2} - 230x + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 577.1 | ||
Root | \(-1.33172 - 1.34622i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.577 |
Dual form | 1008.3.cg.p.145.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.30550 | + | 3.06313i | −1.06110 | + | 0.612627i | −0.925736 | − | 0.378169i | \(-0.876554\pi\) |
−0.135364 | + | 0.990796i | \(0.543220\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.664986 | − | 6.96834i | −0.0949980 | − | 0.995477i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.89129 | − | 3.27581i | 0.171935 | − | 0.297801i | −0.767161 | − | 0.641454i | \(-0.778331\pi\) |
0.939096 | + | 0.343654i | \(0.111665\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 9.29319i | − | 0.714861i | −0.933940 | − | 0.357431i | \(-0.883653\pi\) | ||
0.933940 | − | 0.357431i | \(-0.116347\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.84742 | − | 3.37601i | −0.343966 | − | 0.198589i | 0.318059 | − | 0.948071i | \(-0.396969\pi\) |
−0.662024 | + | 0.749482i | \(0.730302\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.71544 | + | 3.29981i | −0.300813 | + | 0.173674i | −0.642808 | − | 0.766027i | \(-0.722231\pi\) |
0.341995 | + | 0.939702i | \(0.388897\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19.5920 | + | 33.9344i | 0.851827 | + | 1.47541i | 0.879558 | + | 0.475792i | \(0.157838\pi\) |
−0.0277315 | + | 0.999615i | \(0.508828\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.26557 | − | 10.8523i | 0.250623 | − | 0.434091i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.57302 | 0.226656 | 0.113328 | − | 0.993558i | \(-0.463849\pi\) | ||||
0.113328 | + | 0.993558i | \(0.463849\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.9941 | + | 10.9662i | 0.612712 | + | 0.353750i | 0.774026 | − | 0.633153i | \(-0.218240\pi\) |
−0.161314 | + | 0.986903i | \(0.551573\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 24.8730 | + | 34.9336i | 0.710658 | + | 0.998103i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −33.5334 | − | 58.0816i | −0.906309 | − | 1.56977i | −0.819151 | − | 0.573578i | \(-0.805555\pi\) |
−0.0871580 | − | 0.996194i | \(-0.527779\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 53.6570i | 1.30871i | 0.756189 | + | 0.654353i | \(0.227059\pi\) | ||||
−0.756189 | + | 0.654353i | \(0.772941\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 42.0426 | 0.977734 | 0.488867 | − | 0.872358i | \(-0.337410\pi\) | ||||
0.488867 | + | 0.872358i | \(0.337410\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −49.8304 | + | 28.7696i | −1.06022 | + | 0.612119i | −0.925494 | − | 0.378763i | \(-0.876350\pi\) |
−0.134728 | + | 0.990883i | \(0.543016\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.1156 | + | 9.26770i | −0.981951 | + | 0.189137i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.71091 | + | 9.89159i | −0.107753 | + | 0.186634i | −0.914860 | − | 0.403772i | \(-0.867699\pi\) |
0.807107 | + | 0.590406i | \(0.201032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 23.1731i | 0.421329i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 54.0433 | + | 31.2019i | 0.915988 | + | 0.528846i | 0.882353 | − | 0.470588i | \(-0.155958\pi\) |
0.0336351 | + | 0.999434i | \(0.489292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −103.607 | + | 59.8176i | −1.69848 | + | 0.980617i | −0.751271 | + | 0.659994i | \(0.770559\pi\) |
−0.947207 | + | 0.320622i | \(0.896108\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 28.4663 | + | 49.3051i | 0.437943 | + | 0.758539i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −27.8740 | + | 48.2792i | −0.416030 | + | 0.720585i | −0.995536 | − | 0.0943832i | \(-0.969912\pi\) |
0.579506 | + | 0.814968i | \(0.303245\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −131.158 | −1.84730 | −0.923648 | − | 0.383243i | \(-0.874807\pi\) | ||||
−0.923648 | + | 0.383243i | \(0.874807\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 66.7208 | + | 38.5213i | 0.913984 | + | 0.527689i | 0.881711 | − | 0.471790i | \(-0.156392\pi\) |
0.0322732 | + | 0.999479i | \(0.489725\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −24.0846 | − | 11.0008i | −0.312787 | − | 0.142867i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.7467 | + | 129.465i | 0.946160 | + | 1.63880i | 0.753412 | + | 0.657549i | \(0.228407\pi\) |
0.192749 | + | 0.981248i | \(0.438260\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 39.7649i | − | 0.479096i | −0.970885 | − | 0.239548i | \(-0.923001\pi\) | ||
0.970885 | − | 0.239548i | \(-0.0769992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41.3647 | 0.486643 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −48.4984 | + | 28.0006i | −0.544926 | + | 0.314613i | −0.747073 | − | 0.664742i | \(-0.768541\pi\) |
0.202147 | + | 0.979355i | \(0.435208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −64.7582 | + | 6.17984i | −0.711628 | + | 0.0679104i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.2155 | − | 35.0143i | 0.212795 | − | 0.368572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 142.413i | 1.46818i | 0.679054 | + | 0.734089i | \(0.262390\pi\) | ||||
−0.679054 | + | 0.734089i | \(0.737610\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −127.020 | − | 73.3353i | −1.25763 | − | 0.726092i | −0.285015 | − | 0.958523i | \(-0.591999\pi\) |
−0.972613 | + | 0.232431i | \(0.925332\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.66772 | − | 3.84961i | 0.0647351 | − | 0.0373748i | −0.467283 | − | 0.884108i | \(-0.654767\pi\) |
0.532018 | + | 0.846733i | \(0.321434\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 69.7970 | + | 120.892i | 0.652308 | + | 1.12983i | 0.982561 | + | 0.185939i | \(0.0595327\pi\) |
−0.330253 | + | 0.943893i | \(0.607134\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 75.8059 | − | 131.300i | 0.695467 | − | 1.20458i | −0.274556 | − | 0.961571i | \(-0.588531\pi\) |
0.970023 | − | 0.243013i | \(-0.0781356\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 40.4809 | 0.358238 | 0.179119 | − | 0.983827i | \(-0.442675\pi\) | ||||
0.179119 | + | 0.983827i | \(0.442675\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −207.891 | − | 120.026i | −1.80775 | − | 1.04370i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.6367 | + | 42.9918i | −0.165015 | + | 0.361276i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 53.3461 | + | 92.3981i | 0.440877 | + | 0.763621i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 76.3876i | − | 0.611101i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 88.3367 | 0.695565 | 0.347782 | − | 0.937575i | \(-0.386935\pi\) | ||||
0.347782 | + | 0.937575i | \(0.386935\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 58.5849 | − | 33.8240i | 0.447213 | − | 0.258198i | −0.259440 | − | 0.965759i | \(-0.583538\pi\) |
0.706652 | + | 0.707561i | \(0.250205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.7949 | + | 37.6328i | 0.201465 | + | 0.282954i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −82.6190 | + | 143.100i | −0.603058 | + | 1.04453i | 0.389297 | + | 0.921112i | \(0.372718\pi\) |
−0.992355 | + | 0.123415i | \(0.960615\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 73.0610i | 0.525619i | 0.964848 | + | 0.262809i | \(0.0846490\pi\) | ||||
−0.964848 | + | 0.262809i | \(0.915351\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30.4427 | − | 17.5761i | −0.212886 | − | 0.122910i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −34.8732 | + | 20.1340i | −0.240505 | + | 0.138855i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 75.2940 | + | 130.413i | 0.505329 | + | 0.875255i | 0.999981 | + | 0.00616430i | \(0.00196217\pi\) |
−0.494652 | + | 0.869091i | \(0.664704\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 69.4921 | − | 120.364i | 0.460213 | − | 0.797112i | −0.538759 | − | 0.842460i | \(-0.681107\pi\) |
0.998971 | + | 0.0453486i | \(0.0144398\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −134.364 | −0.866866 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 136.184 | + | 78.6256i | 0.867412 | + | 0.500800i | 0.866487 | − | 0.499199i | \(-0.166372\pi\) |
0.000924354 | 1.00000i | \(0.499706\pi\) | ||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 223.438 | − | 159.090i | 1.38781 | − | 0.988135i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.6613 | − | 18.4660i | −0.0654069 | − | 0.113288i | 0.831467 | − | 0.555573i | \(-0.187501\pi\) |
−0.896874 | + | 0.442285i | \(0.854168\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 177.968i | − | 1.06567i | −0.846218 | − | 0.532837i | \(-0.821126\pi\) | ||
0.846218 | − | 0.532837i | \(-0.178874\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 82.6365 | 0.488974 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −95.3511 | + | 55.0510i | −0.551163 | + | 0.318214i | −0.749591 | − | 0.661902i | \(-0.769750\pi\) |
0.198428 | + | 0.980115i | \(0.436416\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −79.7889 | − | 36.4440i | −0.455937 | − | 0.208251i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.1225 | − | 24.4608i | 0.0788964 | − | 0.136653i | −0.823878 | − | 0.566768i | \(-0.808194\pi\) |
0.902774 | + | 0.430115i | \(0.141527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 206.410i | 1.14039i | 0.821510 | + | 0.570195i | \(0.193132\pi\) | ||||
−0.821510 | + | 0.570195i | \(0.806868\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 355.823 | + | 205.435i | 1.92337 | + | 1.11046i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.1183 | + | 12.7700i | −0.118280 | + | 0.0682888i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 31.8684 | + | 55.1977i | 0.166850 | + | 0.288993i | 0.937311 | − | 0.348494i | \(-0.113307\pi\) |
−0.770460 | + | 0.637488i | \(0.779974\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 33.6762 | − | 58.3288i | 0.174488 | − | 0.302222i | −0.765496 | − | 0.643441i | \(-0.777506\pi\) |
0.939984 | + | 0.341219i | \(0.110840\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −96.0707 | −0.487668 | −0.243834 | − | 0.969817i | \(-0.578405\pi\) | ||||
−0.243834 | + | 0.969817i | \(0.578405\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −178.392 | − | 102.995i | −0.896444 | − | 0.517562i | −0.0203995 | − | 0.999792i | \(-0.506494\pi\) |
−0.876045 | + | 0.482230i | \(0.839827\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.37097 | − | 45.8030i | −0.0215319 | − | 0.225631i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −164.358 | − | 284.677i | −0.801748 | − | 1.38867i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.9636i | 0.119443i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 121.942 | 0.577925 | 0.288963 | − | 0.957340i | \(-0.406690\pi\) | ||||
0.288963 | + | 0.957340i | \(0.406690\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −223.057 | + | 128.782i | −1.03747 | + | 0.598986i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 63.7857 | − | 139.650i | 0.293943 | − | 0.643547i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.3739 | + | 54.3412i | −0.141963 | + | 0.245888i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.5026i | 0.0829712i | 0.999139 | + | 0.0414856i | \(0.0132091\pi\) | ||||
−0.999139 | + | 0.0414856i | \(0.986791\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −127.348 | − | 73.5243i | −0.561004 | − | 0.323896i | 0.192545 | − | 0.981288i | \(-0.438326\pi\) |
−0.753548 | + | 0.657393i | \(0.771659\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −311.695 | + | 179.957i | −1.36112 | + | 0.785840i | −0.989772 | − | 0.142656i | \(-0.954436\pi\) |
−0.371343 | + | 0.928496i | \(0.621103\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.0340 | + | 38.1641i | 0.0945667 | + | 0.163794i | 0.909428 | − | 0.415862i | \(-0.136520\pi\) |
−0.814861 | + | 0.579656i | \(0.803187\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 176.250 | − | 305.274i | 0.750001 | − | 1.29904i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 165.077 | 0.690698 | 0.345349 | − | 0.938474i | \(-0.387761\pi\) | ||||
0.345349 | + | 0.938474i | \(0.387761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −115.828 | − | 66.8732i | −0.480613 | − | 0.277482i | 0.240059 | − | 0.970758i | \(-0.422833\pi\) |
−0.720672 | + | 0.693276i | \(0.756167\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 226.889 | − | 196.554i | 0.926078 | − | 0.802262i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.6658 | + | 53.1147i | 0.124153 | + | 0.215039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 403.639i | 1.60812i | 0.594545 | + | 0.804062i | \(0.297332\pi\) | ||||
−0.594545 | + | 0.804062i | \(0.702668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 148.217 | 0.585836 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −242.418 | + | 139.960i | −0.943260 | + | 0.544592i | −0.890981 | − | 0.454041i | \(-0.849982\pi\) |
−0.0522795 | + | 0.998632i | \(0.516649\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −382.433 | + | 272.296i | −1.47658 | + | 1.05134i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 70.9462 | − | 122.882i | 0.269758 | − | 0.467234i | −0.699042 | − | 0.715081i | \(-0.746390\pi\) |
0.968799 | + | 0.247847i | \(0.0797231\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 69.9731i | − | 0.264050i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −344.508 | − | 198.902i | −1.28070 | − | 0.739411i | −0.303722 | − | 0.952761i | \(-0.598229\pi\) |
−0.976976 | + | 0.213350i | \(0.931563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 378.562 | − | 218.563i | 1.39691 | − | 0.806505i | 0.402840 | − | 0.915270i | \(-0.368023\pi\) |
0.994067 | + | 0.108765i | \(0.0346897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.7000 | − | 41.0496i | −0.0861818 | − | 0.149271i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.65404 | + | 4.59692i | −0.00958136 | + | 0.0165954i | −0.870776 | − | 0.491679i | \(-0.836383\pi\) |
0.861195 | + | 0.508275i | \(0.169717\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −297.662 | −1.05930 | −0.529648 | − | 0.848217i | \(-0.677676\pi\) | ||||
−0.529648 | + | 0.848217i | \(0.677676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −178.296 | − | 102.939i | −0.630020 | − | 0.363742i | 0.150740 | − | 0.988573i | \(-0.451834\pi\) |
−0.780760 | + | 0.624831i | \(0.785168\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 373.900 | − | 35.6811i | 1.30279 | − | 0.124325i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −121.705 | − | 210.799i | −0.421125 | − | 0.729410i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 138.398i | − | 0.472347i | −0.971711 | − | 0.236173i | \(-0.924107\pi\) | ||
0.971711 | − | 0.236173i | \(-0.0758933\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −382.302 | −1.29594 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 315.359 | − | 182.072i | 1.05471 | − | 0.608938i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.9577 | − | 292.967i | −0.0928828 | − | 0.973312i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 366.459 | − | 634.725i | 1.20150 | − | 2.08107i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 157.473i | 0.512941i | 0.966552 | + | 0.256471i | \(0.0825597\pi\) | ||||
−0.966552 | + | 0.256471i | \(0.917440\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −237.994 | − | 137.406i | −0.765253 | − | 0.441819i | 0.0659254 | − | 0.997825i | \(-0.479000\pi\) |
−0.831179 | + | 0.556005i | \(0.812333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 152.602 | − | 88.1048i | 0.487546 | − | 0.281485i | −0.236010 | − | 0.971751i | \(-0.575840\pi\) |
0.723556 | + | 0.690266i | \(0.242506\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −146.183 | − | 253.197i | −0.461146 | − | 0.798729i | 0.537872 | − | 0.843027i | \(-0.319228\pi\) |
−0.999018 | + | 0.0442975i | \(0.985895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4315 | − | 21.5319i | 0.0389701 | − | 0.0674983i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 44.5608 | 0.137959 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −100.852 | − | 58.2271i | −0.310315 | − | 0.179160i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 233.613 | + | 328.104i | 0.710070 | + | 0.997277i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 71.2984 | + | 123.492i | 0.215403 | + | 0.373089i | 0.953397 | − | 0.301718i | \(-0.0975601\pi\) |
−0.737994 | + | 0.674807i | \(0.764227\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 341.527i | − | 1.01948i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 477.413 | 1.41666 | 0.708328 | − | 0.705884i | \(-0.249450\pi\) | ||||
0.708328 | + | 0.705884i | \(0.249450\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 71.8466 | − | 41.4806i | 0.210694 | − | 0.121644i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 96.5767 | + | 329.123i | 0.281565 | + | 0.959542i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 226.686 | − | 392.632i | 0.653275 | − | 1.13151i | −0.329048 | − | 0.944313i | \(-0.606728\pi\) |
0.982323 | − | 0.187192i | \(-0.0599387\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 55.8211i | 0.159946i | 0.996797 | + | 0.0799730i | \(0.0254834\pi\) | ||||
−0.996797 | + | 0.0799730i | \(0.974517\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 197.638 | + | 114.107i | 0.559882 | + | 0.323248i | 0.753098 | − | 0.657908i | \(-0.228558\pi\) |
−0.193216 | + | 0.981156i | \(0.561892\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 695.859 | − | 401.754i | 1.96017 | − | 1.13170i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 233.905 | + | 405.136i | 0.651547 | + | 1.12851i | 0.982748 | + | 0.184952i | \(0.0592128\pi\) |
−0.331201 | + | 0.943560i | \(0.607454\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −158.722 | + | 274.915i | −0.439674 | + | 0.761539i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −471.983 | −1.29311 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 264.699 | + | 152.824i | 0.721252 | + | 0.416415i | 0.815213 | − | 0.579161i | \(-0.196620\pi\) |
−0.0939615 | + | 0.995576i | \(0.529953\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 72.7257 | + | 33.2178i | 0.196026 | + | 0.0895359i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −131.217 | − | 227.274i | −0.351787 | − | 0.609313i | 0.634776 | − | 0.772697i | \(-0.281093\pi\) |
−0.986563 | + | 0.163383i | \(0.947759\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 61.0843i | − | 0.162027i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 489.503 | 1.29156 | 0.645782 | − | 0.763522i | \(-0.276531\pi\) | ||||
0.645782 | + | 0.763522i | \(0.276531\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 289.022 | − | 166.867i | 0.754627 | − | 0.435684i | −0.0727364 | − | 0.997351i | \(-0.523173\pi\) |
0.827363 | + | 0.561667i | \(0.189840\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 161.478 | − | 15.4098i | 0.419423 | − | 0.0400254i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 298.042 | − | 516.223i | 0.766174 | − | 1.32705i | −0.173449 | − | 0.984843i | \(-0.555491\pi\) |
0.939624 | − | 0.342210i | \(-0.111175\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 264.571i | − | 0.676653i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −793.137 | − | 457.918i | −2.00794 | − | 1.15929i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 268.394 | − | 154.957i | 0.676055 | − | 0.390321i | −0.122312 | − | 0.992492i | \(-0.539031\pi\) |
0.798367 | + | 0.602171i | \(0.205697\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −167.573 | − | 290.245i | −0.417888 | − | 0.723803i | 0.577839 | − | 0.816151i | \(-0.303896\pi\) |
−0.995727 | + | 0.0923475i | \(0.970563\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 101.911 | − | 176.516i | 0.252882 | − | 0.438004i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −253.685 | −0.623306 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −302.456 | − | 174.623i | −0.739501 | − | 0.426951i | 0.0823869 | − | 0.996600i | \(-0.473746\pi\) |
−0.821888 | + | 0.569649i | \(0.807079\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 181.488 | − | 397.341i | 0.439437 | − | 0.962085i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 121.805 | + | 210.973i | 0.293507 | + | 0.508369i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 359.369i | − | 0.857683i | −0.903380 | − | 0.428841i | \(-0.858922\pi\) | ||
0.903380 | − | 0.428841i | \(-0.141078\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −831.803 | −1.97578 | −0.987890 | − | 0.155159i | \(-0.950411\pi\) | ||||
−0.987890 | + | 0.155159i | \(0.950411\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −73.2748 | + | 42.3052i | −0.172411 | + | 0.0995417i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 485.727 | + | 682.192i | 1.13753 | + | 1.59764i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −161.420 | + | 279.587i | −0.374524 | + | 0.648694i | −0.990256 | − | 0.139262i | \(-0.955527\pi\) |
0.615732 | + | 0.787956i | \(0.288860\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 523.962i | 1.21007i | 0.796197 | + | 0.605037i | \(0.206842\pi\) | ||||
−0.796197 | + | 0.605037i | \(0.793158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −223.954 | − | 129.300i | −0.512481 | − | 0.295881i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −606.881 | + | 350.383i | −1.38242 | + | 0.798138i | −0.992445 | − | 0.122689i | \(-0.960848\pi\) |
−0.389971 | + | 0.920827i | \(0.627515\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 48.4446 | + | 83.9086i | 0.109356 | + | 0.189410i | 0.915509 | − | 0.402296i | \(-0.131788\pi\) |
−0.806154 | + | 0.591706i | \(0.798455\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 171.539 | − | 297.114i | 0.385481 | − | 0.667672i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 499.063 | 1.11150 | 0.555749 | − | 0.831350i | \(-0.312432\pi\) | ||||
0.555749 | + | 0.831350i | \(0.312432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 175.770 | + | 101.481i | 0.389734 | + | 0.225013i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 324.645 | − | 231.150i | 0.713505 | − | 0.508022i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −158.284 | − | 274.156i | −0.346354 | − | 0.599903i | 0.639245 | − | 0.769003i | \(-0.279247\pi\) |
−0.985599 | + | 0.169100i | \(0.945914\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 387.287i | 0.840103i | 0.907500 | + | 0.420051i | \(0.137988\pi\) | ||||
−0.907500 | + | 0.420051i | \(0.862012\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −909.661 | −1.96471 | −0.982355 | − | 0.187027i | \(-0.940115\pi\) | ||||
−0.982355 | + | 0.187027i | \(0.940115\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −38.4408 | + | 22.1938i | −0.0823143 | + | 0.0475242i | −0.540592 | − | 0.841285i | \(-0.681800\pi\) |
0.458278 | + | 0.888809i | \(0.348466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 354.962 | + | 162.131i | 0.756848 | + | 0.345694i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 79.5146 | − | 137.723i | 0.168107 | − | 0.291170i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 82.7008i | 0.174107i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 129.513 | + | 74.7741i | 0.270381 | + | 0.156105i | 0.629061 | − | 0.777356i | \(-0.283440\pi\) |
−0.358680 | + | 0.933461i | \(0.616773\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −539.764 | + | 311.633i | −1.12217 | + | 0.647885i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −436.230 | − | 755.573i | −0.899444 | − | 1.55788i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5141 | − | 49.3879i | 0.0585505 | − | 0.101413i | −0.835264 | − | 0.549848i | \(-0.814685\pi\) |
0.893815 | + | 0.448436i | \(0.148019\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −563.958 | −1.14859 | −0.574296 | − | 0.818648i | \(-0.694724\pi\) | ||||
−0.574296 | + | 0.818648i | \(0.694724\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.4352 | − | 22.1906i | −0.0779619 | − | 0.0450113i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 87.2182 | + | 913.954i | 0.175489 | + | 1.83894i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −194.019 | − | 336.050i | −0.388815 | − | 0.673447i | 0.603476 | − | 0.797381i | \(-0.293782\pi\) |
−0.992290 | + | 0.123935i | \(0.960449\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 712.944i | 1.41738i | 0.705518 | + | 0.708692i | \(0.250714\pi\) | ||||
−0.705518 | + | 0.708692i | \(0.749286\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 898.543 | 1.77929 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −446.040 | + | 257.521i | −0.876306 | + | 0.505935i | −0.869439 | − | 0.494041i | \(-0.835519\pi\) |
−0.00686712 | + | 0.999976i | \(0.502186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 224.061 | − | 490.550i | 0.438476 | − | 0.959980i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.5837 | + | 40.8482i | −0.0457936 | + | 0.0793169i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 217.647i | 0.420980i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.7063 | − | 15.9962i | −0.0531791 | − | 0.0307030i | 0.473175 | − | 0.880969i | \(-0.343108\pi\) |
−0.526354 | + | 0.850266i | \(0.676441\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −275.525 | + | 159.075i | −0.526817 | + | 0.304158i | −0.739719 | − | 0.672916i | \(-0.765042\pi\) |
0.212902 | + | 0.977073i | \(0.431708\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −74.0443 | − | 128.248i | −0.140501 | − | 0.243356i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −503.194 | + | 871.557i | −0.951217 | + | 1.64756i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 498.645 | 0.935543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −740.616 | − | 427.595i | −1.38433 | − | 0.799243i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −60.6412 | + | 175.145i | −0.112507 | + | 0.324945i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −119.509 | − | 206.995i | −0.220903 | − | 0.382615i | 0.734179 | − | 0.678956i | \(-0.237567\pi\) |
−0.955082 | + | 0.296340i | \(0.904234\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 928.814i | 1.70425i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −436.346 | −0.797707 | −0.398854 | − | 0.917015i | \(-0.630592\pi\) | ||||
−0.398854 | + | 0.917015i | \(0.630592\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −37.5677 | + | 21.6897i | −0.0681810 | + | 0.0393643i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 852.451 | − | 606.953i | 1.54150 | − | 1.09756i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −442.789 | + | 766.932i | −0.794953 | + | 1.37690i | 0.127917 | + | 0.991785i | \(0.459171\pi\) |
−0.922869 | + | 0.385113i | \(0.874162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 390.710i | − | 0.698944i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −154.219 | − | 89.0382i | −0.273923 | − | 0.158150i | 0.356746 | − | 0.934201i | \(-0.383886\pi\) |
−0.630669 | + | 0.776052i | \(0.717219\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −214.771 | + | 123.998i | −0.380126 | + | 0.219466i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 451.288 | + | 781.654i | 0.793125 | + | 1.37373i | 0.924023 | + | 0.382336i | \(0.124880\pi\) |
−0.130898 | + | 0.991396i | \(0.541786\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0141 | − | 69.3064i | 0.0700771 | − | 0.121377i | −0.828858 | − | 0.559459i | \(-0.811009\pi\) |
0.898935 | + | 0.438082i | \(0.144342\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 491.020 | 0.853948 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 436.345 | + | 251.924i | 0.756231 | + | 0.436610i | 0.827941 | − | 0.560815i | \(-0.189512\pi\) |
−0.0717099 | + | 0.997426i | \(0.522846\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −277.096 | + | 26.4431i | −0.476929 | + | 0.0455131i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.6020 | + | 37.4157i | 0.0370531 | + | 0.0641779i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 458.274i | 0.780706i | 0.920665 | + | 0.390353i | \(0.127647\pi\) | ||||
−0.920665 | + | 0.390353i | \(0.872353\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −144.746 | −0.245749 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 580.642 | − | 335.234i | 0.979160 | − | 0.565318i | 0.0771438 | − | 0.997020i | \(-0.475420\pi\) |
0.902017 | + | 0.431701i | \(0.142087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.5069 | − | 288.243i | −0.0462301 | − | 0.484442i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 220.065 | − | 381.163i | 0.367387 | − | 0.636332i | −0.621770 | − | 0.783200i | \(-0.713586\pi\) |
0.989156 | + | 0.146868i | \(0.0469193\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 732.160i | 1.21824i | 0.793080 | + | 0.609118i | \(0.208476\pi\) | ||||
−0.793080 | + | 0.609118i | \(0.791524\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −566.055 | − | 326.812i | −0.935628 | − | 0.540185i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 283.101 | − | 163.449i | 0.466394 | − | 0.269273i | −0.248335 | − | 0.968674i | \(-0.579883\pi\) |
0.714729 | + | 0.699401i | \(0.246550\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 267.362 | + | 463.084i | 0.437580 | + | 0.757911i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 494.332 | − | 856.207i | 0.806414 | − | 1.39675i | −0.108919 | − | 0.994051i | \(-0.534739\pi\) |
0.915333 | − | 0.402699i | \(-0.131928\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −280.536 | −0.454678 | −0.227339 | − | 0.973816i | \(-0.573003\pi\) | ||||
−0.227339 | + | 0.973816i | \(0.573003\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −894.439 | − | 516.405i | −1.44497 | − | 0.834256i | −0.446799 | − | 0.894634i | \(-0.647436\pi\) |
−0.998176 | + | 0.0603780i | \(0.980769\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 227.368 | + | 319.334i | 0.364957 | + | 0.512574i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390.625 | + | 676.582i | 0.624999 | + | 1.08253i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 452.837i | 0.719931i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −178.252 | −0.282491 | −0.141245 | − | 0.989975i | \(-0.545111\pi\) | ||||
−0.141245 | + | 0.989975i | \(0.545111\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −468.671 | + | 270.587i | −0.738064 | + | 0.426122i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 86.1265 | + | 447.148i | 0.135207 | + | 0.701958i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 334.263 | − | 578.961i | 0.521471 | − | 0.903215i | −0.478217 | − | 0.878242i | \(-0.658717\pi\) |
0.999688 | − | 0.0249729i | \(-0.00794996\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 313.584i | 0.487690i | 0.969814 | + | 0.243845i | \(0.0784088\pi\) | ||||
−0.969814 | + | 0.243845i | \(0.921591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −292.310 | − | 168.765i | −0.451793 | − | 0.260843i | 0.256794 | − | 0.966466i | \(-0.417334\pi\) |
−0.708587 | + | 0.705623i | \(0.750667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 204.423 | − | 118.024i | 0.314981 | − | 0.181855i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 451.677 | + | 782.328i | 0.691695 | + | 1.19805i | 0.971282 | + | 0.237931i | \(0.0764692\pi\) |
−0.279587 | + | 0.960120i | \(0.590197\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −207.215 | + | 358.907i | −0.316358 | + | 0.547949i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 768.092 | 1.16554 | 0.582771 | − | 0.812637i | \(-0.301969\pi\) | ||||
0.582771 | + | 0.812637i | \(0.301969\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 356.130 | + | 205.612i | 0.538774 | + | 0.311062i | 0.744582 | − | 0.667531i | \(-0.232649\pi\) |
−0.205808 | + | 0.978592i | \(0.565982\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −257.435 | − | 117.585i | −0.387120 | − | 0.176819i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 128.779 | + | 223.051i | 0.193071 | + | 0.334410i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 452.529i | 0.674410i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −818.448 | −1.21612 | −0.608060 | − | 0.793891i | \(-0.708052\pi\) | ||||
−0.608060 | + | 0.793891i | \(0.708052\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.0858 | − | 27.7623i | 0.0710277 | − | 0.0410079i | −0.464066 | − | 0.885801i | \(-0.653610\pi\) |
0.535093 | + | 0.844793i | \(0.320276\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 992.384 | − | 94.7028i | 1.46154 | − | 0.139474i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −38.1419 | + | 66.0637i | −0.0558447 | + | 0.0967258i | −0.892596 | − | 0.450857i | \(-0.851118\pi\) |
0.836752 | + | 0.547583i | \(0.184452\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1012.29i | − | 1.47780i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 91.9245 | + | 53.0726i | 0.133417 | + | 0.0770285i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.4780 | − | 11.2456i | 0.0281881 | − | 0.0162744i | −0.485840 | − | 0.874048i | \(-0.661486\pi\) |
0.514028 | + | 0.857774i | \(0.328153\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −223.796 | − | 387.625i | −0.322008 | − | 0.557734i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 181.146 | − | 313.755i | 0.259894 | − | 0.450150i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 854.197 | 1.21854 | 0.609270 | − | 0.792963i | \(-0.291462\pi\) | ||||
0.609270 | + | 0.792963i | \(0.291462\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 383.317 | + | 221.308i | 0.545258 | + | 0.314805i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −426.558 | + | 933.889i | −0.603336 | + | 1.32092i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 79.3009 | + | 137.353i | 0.111849 | + | 0.193728i | 0.916516 | − | 0.399999i | \(-0.130989\pi\) |
−0.804667 | + | 0.593727i | \(0.797656\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 859.403i | 1.20533i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 215.352 | 0.301191 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −329.191 | + | 190.059i | −0.457846 | + | 0.264338i | −0.711138 | − | 0.703052i | \(-0.751820\pi\) |
0.253292 | + | 0.967390i | \(0.418487\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.2593 | − | 43.9030i | −0.0433555 | − | 0.0608918i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.1837 | − | 71.3322i | 0.0568051 | − | 0.0983893i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 159.283i | 0.219096i | 0.993981 | + | 0.109548i | \(0.0349404\pi\) | ||||
−0.993981 | + | 0.109548i | \(0.965060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −245.841 | − | 141.936i | −0.336307 | − | 0.194167i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −154.308 | + | 89.0895i | −0.210515 | + | 0.121541i | −0.601551 | − | 0.798835i | \(-0.705450\pi\) |
0.391036 | + | 0.920376i | \(0.372117\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 105.436 | + | 182.620i | 0.143060 | + | 0.247788i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 158.693 | − | 274.864i | 0.214740 | − | 0.371941i | −0.738452 | − | 0.674306i | \(-0.764443\pi\) |
0.953192 | + | 0.302365i | \(0.0977762\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1055.73 | −1.42090 | −0.710450 | − | 0.703748i | \(-0.751508\pi\) | ||||
−0.710450 | + | 0.703748i | \(0.751508\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −798.945 | − | 461.271i | −1.07241 | − | 0.619156i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 796.003 | − | 566.761i | 1.06275 | − | 0.756690i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 153.605 | + | 266.051i | 0.204533 | + | 0.354262i | 0.949984 | − | 0.312299i | \(-0.101099\pi\) |
−0.745451 | + | 0.666561i | \(0.767766\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 851.454i | 1.12775i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −711.179 | −0.939470 | −0.469735 | − | 0.882808i | \(-0.655651\pi\) | ||||
−0.469735 | + | 0.882808i | \(0.655651\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −457.221 | + | 263.977i | −0.600816 | + | 0.346881i | −0.769363 | − | 0.638812i | \(-0.779426\pi\) |
0.168546 | + | 0.985694i | \(0.446093\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −965.350 | − | 440.929i | −1.26520 | − | 0.577888i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 289.965 | − | 502.235i | 0.378051 | − | 0.654804i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 831.961i | − | 1.08187i | −0.841063 | − | 0.540937i | \(-0.818070\pi\) | ||
0.841063 | − | 0.540937i | \(-0.181930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −657.060 | − | 379.354i | −0.850012 | − | 0.490755i | 0.0106426 | − | 0.999943i | \(-0.496612\pi\) |
−0.860655 | + | 0.509188i | \(0.829946\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 238.017 | − | 137.419i | 0.307119 | − | 0.177315i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −177.058 | − | 306.673i | −0.227289 | − | 0.393676i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −248.058 | + | 429.648i | −0.317615 | + | 0.550126i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −963.363 | −1.22721 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 595.121 | + | 343.593i | 0.756190 | + | 0.436586i | 0.827926 | − | 0.560837i | \(-0.189521\pi\) |
−0.0717363 | + | 0.997424i | \(0.522854\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.9192 | − | 282.084i | −0.0340319 | − | 0.356617i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 555.897 | + | 962.841i | 0.701005 | + | 1.21418i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 716.069i | 0.898456i | 0.893417 | + | 0.449228i | \(0.148301\pi\) | ||||
−0.893417 | + | 0.449228i | \(0.851699\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 388.506 | 0.486240 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 252.377 | − | 145.710i | 0.314292 | − | 0.181457i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −698.137 | + | 1528.47i | −0.867251 | + | 1.89872i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −68.0836 | + | 117.924i | −0.0841577 | + | 0.145765i | −0.905032 | − | 0.425344i | \(-0.860153\pi\) |
0.820874 | + | 0.571109i | \(0.193487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 421.599i | 0.519851i | 0.965629 | + | 0.259926i | \(0.0836981\pi\) | ||||
−0.965629 | + | 0.259926i | \(0.916302\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 113.127 | + | 65.3141i | 0.138807 | + | 0.0801401i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −240.292 | + | 138.733i | −0.294115 | + | 0.169807i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8238 | + | 68.9769i | 0.0485065 | + | 0.0840157i | 0.889259 | − | 0.457404i | \(-0.151221\pi\) |
−0.840753 | + | 0.541419i | \(0.817887\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −666.149 | + | 1153.80i | −0.809416 | + | 1.40195i | 0.103853 | + | 0.994593i | \(0.466883\pi\) |
−0.913269 | + | 0.407357i | \(0.866451\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 468.548 | 0.566564 | 0.283282 | − | 0.959037i | \(-0.408577\pi\) | ||||
0.283282 | + | 0.959037i | \(0.408577\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 426.112 | + | 246.016i | 0.514007 | + | 0.296762i | 0.734479 | − | 0.678631i | \(-0.237426\pi\) |
−0.220472 | + | 0.975393i | \(0.570760\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 312.640 | + | 108.247i | 0.375318 | + | 0.129948i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 545.139 | + | 944.208i | 0.652861 | + | 1.13079i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1045.41i | 1.24602i | 0.782214 | + | 0.623010i | \(0.214090\pi\) | ||||
−0.782214 | + | 0.623010i | \(0.785910\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −797.795 | −0.948627 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −438.428 | + | 253.127i | −0.518850 | + | 0.299558i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 608.387 | − | 433.177i | 0.718285 | − | 0.511425i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1313.97 | − | 2275.87i | 1.54404 | − | 2.67435i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 339.686i | − | 0.398225i | −0.979977 | − | 0.199113i | \(-0.936194\pi\) | ||
0.979977 | − | 0.199113i | \(-0.0638060\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1216.76 | − | 702.497i | −1.41979 | − | 0.819717i | −0.423511 | − | 0.905891i | \(-0.639203\pi\) |
−0.996280 | + | 0.0861737i | \(0.972536\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1047.21 | + | 604.609i | −1.21911 | + | 0.703853i | −0.964727 | − | 0.263251i | \(-0.915205\pi\) |
−0.254381 | + | 0.967104i | \(0.581872\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −497.129 | − | 861.052i | −0.576047 | − | 0.997743i | −0.995927 | − | 0.0901632i | \(-0.971261\pi\) |
0.419880 | − | 0.907580i | \(-0.362072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 337.257 | − | 584.146i | 0.389893 | − | 0.675314i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 565.470 | 0.650713 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 448.668 | + | 259.038i | 0.515118 | + | 0.297403i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −532.295 | + | 50.7967i | −0.608337 | + | 0.0580534i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 777.369 | + | 1346.44i | 0.886396 | + | 1.53528i | 0.844105 | + | 0.536177i | \(0.180132\pi\) |
0.0422903 | + | 0.999105i | \(0.486535\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 921.015i | − | 1.04542i | −0.852511 | − | 0.522710i | \(-0.824921\pi\) | ||
0.852511 | − | 0.522710i | \(-0.175079\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 156.823 | 0.177603 | 0.0888014 | − | 0.996049i | \(-0.471696\pi\) | ||||
0.0888014 | + | 0.996049i | \(0.471696\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1401.86 | + | 809.362i | −1.58045 | + | 0.912471i | −0.585653 | + | 0.810562i | \(0.699162\pi\) |
−0.994794 | + | 0.101909i | \(0.967505\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −58.7427 | − | 615.561i | −0.0660773 | − | 0.692419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 189.869 | − | 328.862i | 0.212619 | − | 0.368267i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 173.036i | 0.193336i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 124.848 | + | 72.0813i | 0.138875 | + | 0.0801794i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 66.7882 | − | 38.5602i | 0.0741267 | − | 0.0427971i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −632.263 | − | 1095.11i | −0.698633 | − | 1.21007i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −279.345 | + | 483.839i | −0.307988 | + | 0.533450i | −0.977922 | − | 0.208970i | \(-0.932989\pi\) |
0.669934 | + | 0.742420i | \(0.266322\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 510.774 | 0.560674 | 0.280337 | − | 0.959902i | \(-0.409554\pi\) | ||||
0.280337 | + | 0.959902i | \(0.409554\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −130.262 | − | 75.2070i | −0.142675 | − | 0.0823735i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −274.655 | − | 385.747i | −0.299515 | − | 0.420662i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 333.677 | + | 577.945i | 0.363087 | + | 0.628885i | 0.988467 | − | 0.151435i | \(-0.0483894\pi\) |
−0.625380 | + | 0.780320i | \(0.715056\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1218.88i | 1.32056i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −840.424 | −0.908566 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −760.086 | + | 438.836i | −0.818177 | + | 0.472375i | −0.849787 | − | 0.527126i | \(-0.823270\pi\) |
0.0316106 | + | 0.999500i | \(0.489936\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 244.420 | − | 211.741i | 0.262535 | − | 0.227434i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 78.2325 | − | 135.503i | 0.0836711 | − | 0.144923i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 211.107i | − | 0.225301i | −0.993635 | − | 0.112650i | \(-0.964066\pi\) | ||
0.993635 | − | 0.112650i | \(-0.0359340\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1321.72 | − | 763.093i | −1.40459 | − | 0.810938i | −0.409727 | − | 0.912208i | \(-0.634376\pi\) |
−0.994859 | + | 0.101270i | \(0.967709\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1820.81 | + | 1051.25i | −1.93087 | + | 1.11479i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 321.155 | + | 556.256i | 0.339129 | + | 0.587388i | 0.984269 | − | 0.176676i | \(-0.0565345\pi\) |
−0.645140 | + | 0.764064i | \(0.723201\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 357.986 | − | 620.050i | 0.377224 | − | 0.653372i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −208.041 | −0.218302 | −0.109151 | − | 0.994025i | \(-0.534813\pi\) | ||||
−0.109151 | + | 0.994025i | \(0.534813\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −338.156 | − | 195.234i | −0.354090 | − | 0.204434i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1052.11 | + | 480.558i | 1.09709 | + | 0.501103i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −239.983 | − | 415.663i | −0.249722 | − | 0.432532i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 412.618i | 0.427584i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1485.38 | 1.53607 | 0.768034 | − | 0.640409i | \(-0.221235\pi\) | ||||
0.768034 | + | 0.640409i | \(0.221235\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 296.922 | − | 171.428i | 0.305790 | − | 0.176548i | −0.339251 | − | 0.940696i | \(-0.610174\pi\) |
0.645041 | + | 0.764148i | \(0.276840\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 509.114 | − | 48.5845i | 0.523241 | − | 0.0499327i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 835.089 | − | 1446.42i | 0.854748 | − | 1.48047i | −0.0221298 | − | 0.999755i | \(-0.507045\pi\) |
0.876878 | − | 0.480713i | \(-0.159622\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 211.829i | 0.216372i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 697.316 | + | 402.596i | 0.709376 | + | 0.409558i | 0.810830 | − | 0.585282i | \(-0.199016\pi\) |
−0.101454 | + | 0.994840i | \(0.532350\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 509.703 | − | 294.277i | 0.517465 | − | 0.298759i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 823.698 | + | 1426.69i | 0.832860 | + | 1.44256i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 751.501 | − | 1301.64i | 0.758326 | − | 1.31346i | −0.185378 | − | 0.982667i | \(-0.559351\pi\) |
0.943704 | − | 0.330792i | \(-0.107316\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1261.95 | 1.26829 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 609.714 | + | 352.019i | 0.611549 | + | 0.353078i | 0.773571 | − | 0.633709i | \(-0.218468\pi\) |
−0.162023 | + | 0.986787i | \(0.551802\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1008.3.cg.p.577.1 | 8 | ||
3.2 | odd | 2 | 336.3.bh.g.241.4 | 8 | |||
4.3 | odd | 2 | 504.3.by.c.73.1 | 8 | |||
7.5 | odd | 6 | inner | 1008.3.cg.p.145.1 | 8 | ||
12.11 | even | 2 | 168.3.z.b.73.4 | ✓ | 8 | ||
21.5 | even | 6 | 336.3.bh.g.145.4 | 8 | |||
21.11 | odd | 6 | 2352.3.f.g.97.8 | 8 | |||
21.17 | even | 6 | 2352.3.f.g.97.1 | 8 | |||
28.3 | even | 6 | 3528.3.f.b.2449.7 | 8 | |||
28.11 | odd | 6 | 3528.3.f.b.2449.2 | 8 | |||
28.19 | even | 6 | 504.3.by.c.145.1 | 8 | |||
84.11 | even | 6 | 1176.3.f.c.97.4 | 8 | |||
84.23 | even | 6 | 1176.3.z.c.313.1 | 8 | |||
84.47 | odd | 6 | 168.3.z.b.145.4 | yes | 8 | ||
84.59 | odd | 6 | 1176.3.f.c.97.5 | 8 | |||
84.83 | odd | 2 | 1176.3.z.c.913.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.3.z.b.73.4 | ✓ | 8 | 12.11 | even | 2 | ||
168.3.z.b.145.4 | yes | 8 | 84.47 | odd | 6 | ||
336.3.bh.g.145.4 | 8 | 21.5 | even | 6 | |||
336.3.bh.g.241.4 | 8 | 3.2 | odd | 2 | |||
504.3.by.c.73.1 | 8 | 4.3 | odd | 2 | |||
504.3.by.c.145.1 | 8 | 28.19 | even | 6 | |||
1008.3.cg.p.145.1 | 8 | 7.5 | odd | 6 | inner | ||
1008.3.cg.p.577.1 | 8 | 1.1 | even | 1 | trivial | ||
1176.3.f.c.97.4 | 8 | 84.11 | even | 6 | |||
1176.3.f.c.97.5 | 8 | 84.59 | odd | 6 | |||
1176.3.z.c.313.1 | 8 | 84.23 | even | 6 | |||
1176.3.z.c.913.1 | 8 | 84.83 | odd | 2 | |||
2352.3.f.g.97.1 | 8 | 21.17 | even | 6 | |||
2352.3.f.g.97.8 | 8 | 21.11 | odd | 6 | |||
3528.3.f.b.2449.2 | 8 | 28.11 | odd | 6 | |||
3528.3.f.b.2449.7 | 8 | 28.3 | even | 6 |