Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,3,Mod(145,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, 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("336.145");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.bh (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: | \(9.15533688251\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | 145.4 | ||
Root | \(-1.33172 + 1.34622i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.145 |
Dual form | 336.3.bh.g.241.4 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.30550 | + | 3.06313i | 1.06110 | + | 0.612627i | 0.925736 | − | 0.378169i | \(-0.123446\pi\) |
0.135364 | + | 0.990796i | \(0.456780\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.664986 | + | 6.96834i | −0.0949980 | + | 0.995477i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.89129 | − | 3.27581i | −0.171935 | − | 0.297801i | 0.767161 | − | 0.641454i | \(-0.221669\pi\) |
−0.939096 | + | 0.343654i | \(0.888335\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.29319i | 0.714861i | 0.933940 | + | 0.357431i | \(0.116347\pi\) | ||||
−0.933940 | + | 0.357431i | \(0.883653\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.6110 | −0.707400 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.84742 | − | 3.37601i | 0.343966 | − | 0.198589i | −0.318059 | − | 0.948071i | \(-0.603031\pi\) |
0.662024 | + | 0.749482i | \(0.269698\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.71544 | − | 3.29981i | −0.300813 | − | 0.173674i | 0.341995 | − | 0.939702i | \(-0.388897\pi\) |
−0.642808 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.03728 | − | 11.0284i | −0.239871 | − | 0.525162i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19.5920 | + | 33.9344i | −0.851827 | + | 1.47541i | 0.0277315 | + | 0.999615i | \(0.491172\pi\) |
−0.879558 | + | 0.475792i | \(0.842162\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.26557 | + | 10.8523i | 0.250623 | + | 0.434091i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.57302 | −0.226656 | −0.113328 | − | 0.993558i | \(-0.536151\pi\) | ||||
−0.113328 | + | 0.993558i | \(0.536151\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 18.9941 | − | 10.9662i | 0.612712 | − | 0.353750i | −0.161314 | − | 0.986903i | \(-0.551573\pi\) |
0.774026 | + | 0.633153i | \(0.218240\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.67386 | + | 3.27581i | 0.171935 | + | 0.0992669i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −24.8730 | + | 34.9336i | −0.710658 | + | 0.998103i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −33.5334 | + | 58.0816i | −0.906309 | + | 1.56977i | −0.0871580 | + | 0.996194i | \(0.527779\pi\) |
−0.819151 | + | 0.573578i | \(0.805555\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.04814 | − | 13.9398i | −0.206363 | − | 0.357431i | ||||
\(40\) | 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 | ||||||||
\(45\) | 15.9165 | − | 9.18940i | 0.353700 | − | 0.204209i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 49.8304 | + | 28.7696i | 1.06022 | + | 0.612119i | 0.925494 | − | 0.378763i | \(-0.123650\pi\) |
0.134728 | + | 0.990883i | \(0.456984\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.1156 | − | 9.26770i | −0.981951 | − | 0.189137i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.84742 | + | 10.1280i | −0.114655 | + | 0.198589i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.71091 | + | 9.89159i | 0.107753 | + | 0.186634i | 0.914860 | − | 0.403772i | \(-0.132301\pi\) |
−0.807107 | + | 0.590406i | \(0.798968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 23.1731i | − | 0.421329i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.4309 | 0.200542 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −54.0433 | + | 31.2019i | −0.915988 | + | 0.528846i | −0.882353 | − | 0.470588i | \(-0.844042\pi\) |
−0.0336351 | + | 0.999434i | \(0.510708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −103.607 | − | 59.8176i | −1.69848 | − | 0.980617i | −0.947207 | − | 0.320622i | \(-0.896108\pi\) |
−0.751271 | − | 0.659994i | \(-0.770559\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 17.1068 | + | 12.1802i | 0.271537 | + | 0.193336i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −28.4663 | + | 49.3051i | −0.437943 | + | 0.758539i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −27.8740 | − | 48.2792i | −0.416030 | − | 0.720585i | 0.579506 | − | 0.814968i | \(-0.303245\pi\) |
−0.995536 | + | 0.0943832i | \(0.969912\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 67.8687i | − | 0.983605i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 131.158 | 1.84730 | 0.923648 | − | 0.383243i | \(-0.125193\pi\) | ||||
0.923648 | + | 0.383243i | \(0.125193\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 66.7208 | − | 38.5213i | 0.913984 | − | 0.527689i | 0.0322732 | − | 0.999479i | \(-0.489725\pi\) |
0.881711 | + | 0.471790i | \(0.156392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −18.7967 | − | 10.8523i | −0.250623 | − | 0.144697i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24.0846 | − | 11.0008i | 0.312787 | − | 0.142867i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.7467 | − | 129.465i | 0.946160 | − | 1.63880i | 0.192749 | − | 0.981248i | \(-0.438260\pi\) |
0.753412 | − | 0.657549i | \(-0.228407\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 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 | ||||||||
\(87\) | 9.85953 | − | 5.69240i | 0.113328 | − | 0.0654299i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 48.4984 | + | 28.0006i | 0.544926 | + | 0.314613i | 0.747073 | − | 0.664742i | \(-0.231459\pi\) |
−0.202147 | + | 0.979355i | \(0.564792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −64.7582 | − | 6.17984i | −0.711628 | − | 0.0679104i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.9941 | + | 32.8987i | −0.204237 | + | 0.353750i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20.2155 | − | 35.0143i | −0.212795 | − | 0.368572i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 142.413i | − | 1.46818i | −0.679054 | − | 0.734089i | \(-0.737610\pi\) | ||
0.679054 | − | 0.734089i | \(-0.262390\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.3477 | −0.114624 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 127.020 | − | 73.3353i | 1.25763 | − | 0.726092i | 0.285015 | − | 0.958523i | \(-0.408001\pi\) |
0.972613 | + | 0.232431i | \(0.0746680\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.66772 | + | 3.84961i | 0.0647351 | + | 0.0373748i | 0.532018 | − | 0.846733i | \(-0.321434\pi\) |
−0.467283 | + | 0.884108i | \(0.654767\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.05617 | − | 73.9411i | 0.0672016 | − | 0.704201i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −69.7970 | + | 120.892i | −0.652308 | + | 1.12983i | 0.330253 | + | 0.943893i | \(0.392866\pi\) |
−0.982561 | + | 0.185939i | \(0.940467\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 75.8059 | + | 131.300i | 0.695467 | + | 1.20458i | 0.970023 | + | 0.243013i | \(0.0781356\pi\) |
−0.274556 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 116.163i | − | 1.04652i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −40.4809 | −0.358238 | −0.179119 | − | 0.983827i | \(-0.557325\pi\) | ||||
−0.179119 | + | 0.983827i | \(0.557325\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −207.891 | + | 120.026i | −1.80775 | + | 1.04370i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 24.1444 | + | 13.9398i | 0.206363 | + | 0.119144i | ||||
\(118\) | 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 | ||||||||
\(123\) | −46.4683 | − | 80.4854i | −0.377791 | − | 0.654353i | ||||
\(124\) | 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 | ||||||||
\(129\) | −63.0639 | + | 36.4099i | −0.488867 | + | 0.282248i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −58.5849 | − | 33.8240i | −0.447213 | − | 0.258198i | 0.259440 | − | 0.965759i | \(-0.416462\pi\) |
−0.706652 | + | 0.707561i | \(0.749795\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.7949 | − | 37.6328i | 0.201465 | − | 0.282954i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.9165 | + | 27.5682i | −0.117900 | + | 0.204209i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 82.6190 | + | 143.100i | 0.603058 | + | 1.04453i | 0.992355 | + | 0.123415i | \(0.0393847\pi\) |
−0.389297 | + | 0.921112i | \(0.627282\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 73.0610i | − | 0.525619i | −0.964848 | − | 0.262809i | \(-0.915351\pi\) | ||
0.964848 | − | 0.262809i | \(-0.0846490\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −99.6609 | −0.706815 | ||||||||
\(142\) | 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 | ||||||||
\(147\) | 80.1994 | − | 27.7678i | 0.545574 | − | 0.188896i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −75.2940 | + | 130.413i | −0.505329 | + | 0.875255i | 0.494652 | + | 0.869091i | \(0.335296\pi\) |
−0.999981 | + | 0.00616430i | \(0.998038\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 69.4921 | + | 120.364i | 0.460213 | + | 0.797112i | 0.998971 | − | 0.0453486i | \(-0.0144398\pi\) |
−0.538759 | + | 0.842460i | \(0.681107\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 20.2561i | − | 0.132393i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 134.364 | 0.866866 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 136.184 | − | 78.6256i | 0.867412 | − | 0.500800i | 0.000924354 | − | 1.00000i | \(-0.499706\pi\) |
0.866487 | + | 0.499199i | \(0.166372\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.1327 | − | 9.89159i | −0.107753 | − | 0.0622113i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −223.438 | − | 159.090i | −1.38781 | − | 0.988135i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.6613 | + | 18.4660i | −0.0654069 | + | 0.113288i | −0.896874 | − | 0.442285i | \(-0.854168\pi\) |
0.831467 | + | 0.555573i | \(0.187501\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 20.0685 | + | 34.7596i | 0.121627 | + | 0.210664i | ||||
\(166\) | 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 | ||||||||
\(171\) | −17.1463 | + | 9.89944i | −0.100271 | + | 0.0578914i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 95.3511 | + | 55.0510i | 0.551163 | + | 0.318214i | 0.749591 | − | 0.661902i | \(-0.230250\pi\) |
−0.198428 | + | 0.980115i | \(0.563584\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −79.7889 | + | 36.4440i | −0.455937 | + | 0.208251i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 54.0433 | − | 93.6057i | 0.305329 | − | 0.528846i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1225 | − | 24.4608i | −0.0788964 | − | 0.136653i | 0.823878 | − | 0.566768i | \(-0.191806\pi\) |
−0.902774 | + | 0.430115i | \(0.858473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 206.410i | − | 1.14039i | −0.821510 | − | 0.570195i | \(-0.806868\pi\) | ||
0.821510 | − | 0.570195i | \(-0.193132\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 207.214 | 1.13232 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | −36.2086 | − | 3.45537i | −0.191580 | − | 0.0182824i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −31.8684 | + | 55.1977i | −0.166850 | + | 0.288993i | −0.937311 | − | 0.348494i | \(-0.886693\pi\) |
0.770460 | + | 0.637488i | \(0.220026\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 33.6762 | + | 58.3288i | 0.174488 | + | 0.302222i | 0.939984 | − | 0.341219i | \(-0.110840\pi\) |
−0.765496 | + | 0.643441i | \(0.777506\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 98.6101i | − | 0.505693i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 96.0707 | 0.487668 | 0.243834 | − | 0.969817i | \(-0.421595\pi\) | ||||
0.243834 | + | 0.969817i | \(0.421595\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −178.392 | + | 102.995i | −0.896444 | + | 0.517562i | −0.876045 | − | 0.482230i | \(-0.839827\pi\) |
−0.0203995 | + | 0.999792i | \(0.506494\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 83.6220 | + | 48.2792i | 0.416030 | + | 0.240195i | ||||
\(202\) | 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 | ||||||||
\(207\) | 58.7760 | + | 101.803i | 0.283942 | + | 0.491802i | ||||
\(208\) | 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 | ||||||||
\(213\) | −196.737 | + | 113.586i | −0.923648 | + | 0.533268i | ||||
\(214\) | 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 | ||||||||
\(219\) | −66.7208 | + | 115.564i | −0.304661 | + | 0.527689i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 31.3739 | + | 54.3412i | 0.141963 | + | 0.245888i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 18.5026i | − | 0.0829712i | −0.999139 | − | 0.0414856i | \(-0.986791\pi\) | ||
0.999139 | − | 0.0414856i | \(-0.0132091\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 37.5934 | 0.167082 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 127.348 | − | 73.5243i | 0.561004 | − | 0.323896i | −0.192545 | − | 0.981288i | \(-0.561674\pi\) |
0.753548 | + | 0.657393i | \(0.228341\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −311.695 | − | 179.957i | −1.36112 | − | 0.785840i | −0.371343 | − | 0.928496i | \(-0.621103\pi\) |
−0.989772 | + | 0.142656i | \(0.954436\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −26.6000 | + | 37.3591i | −0.115151 | + | 0.161728i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.0340 | + | 38.1641i | −0.0945667 | + | 0.163794i | −0.909428 | − | 0.415862i | \(-0.863480\pi\) |
0.814861 | + | 0.579656i | \(0.196813\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 176.250 | + | 305.274i | 0.750001 | + | 1.29904i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 258.930i | 1.09253i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −165.077 | −0.690698 | −0.345349 | − | 0.938474i | \(-0.612239\pi\) | ||||
−0.345349 | + | 0.938474i | \(0.612239\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −115.828 | + | 66.8732i | −0.480613 | + | 0.277482i | −0.720672 | − | 0.693276i | \(-0.756167\pi\) |
0.240059 | + | 0.970758i | \(0.422833\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 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 | ||||||||
\(249\) | 34.4374 | + | 59.6474i | 0.138303 | + | 0.239548i | ||||
\(250\) | 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 | ||||||||
\(255\) | −62.0470 | + | 35.8228i | −0.243322 | + | 0.140482i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 242.418 | + | 139.960i | 0.943260 | + | 0.544592i | 0.890981 | − | 0.454041i | \(-0.150018\pi\) |
0.0522795 | + | 0.998632i | \(0.483351\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −382.433 | − | 272.296i | −1.47658 | − | 1.05134i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.85953 | + | 17.0772i | −0.0377760 | + | 0.0654299i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −70.9462 | − | 122.882i | −0.269758 | − | 0.467234i | 0.699042 | − | 0.715081i | \(-0.253610\pi\) |
−0.968799 | + | 0.247847i | \(0.920277\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 69.9731i | 0.264050i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −96.9968 | −0.363284 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 344.508 | − | 198.902i | 1.28070 | − | 0.739411i | 0.303722 | − | 0.952761i | \(-0.401771\pi\) |
0.976976 | + | 0.213350i | \(0.0684374\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 378.562 | + | 218.563i | 1.39691 | + | 0.806505i | 0.994067 | − | 0.108765i | \(-0.0346897\pi\) |
0.402840 | + | 0.915270i | \(0.368023\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 102.489 | − | 46.8124i | 0.375418 | − | 0.171474i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23.7000 | − | 41.0496i | 0.0861818 | − | 0.149271i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.65404 | − | 4.59692i | −0.00958136 | − | 0.0165954i | 0.861195 | − | 0.508275i | \(-0.169717\pi\) |
−0.870776 | + | 0.491679i | \(0.836383\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 65.7974i | − | 0.235833i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 297.662 | 1.05930 | 0.529648 | − | 0.848217i | \(-0.322324\pi\) | ||||
0.529648 | + | 0.848217i | \(0.322324\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −178.296 | + | 102.939i | −0.630020 | + | 0.363742i | −0.780760 | − | 0.624831i | \(-0.785168\pi\) |
0.150740 | + | 0.988573i | \(0.451834\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 60.6466 | + | 35.0143i | 0.212795 | + | 0.122857i | ||||
\(286\) | 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 | ||||||||
\(291\) | 123.333 | + | 213.620i | 0.423826 | + | 0.734089i | ||||
\(292\) | 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 | ||||||||
\(297\) | 17.0216 | − | 9.82742i | 0.0573118 | − | 0.0330890i | ||||
\(298\) | 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 | ||||||||
\(303\) | −127.020 | + | 220.006i | −0.419209 | + | 0.726092i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −366.459 | − | 634.725i | −1.20150 | − | 2.08107i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 157.473i | − | 0.512941i | −0.966552 | − | 0.256471i | \(-0.917440\pi\) | ||
0.966552 | − | 0.256471i | \(-0.0825597\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.3354 | −0.0431567 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 237.994 | − | 137.406i | 0.765253 | − | 0.441819i | −0.0659254 | − | 0.997825i | \(-0.521000\pi\) |
0.831179 | + | 0.556005i | \(0.187667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 152.602 | + | 88.1048i | 0.487546 | + | 0.281485i | 0.723556 | − | 0.690266i | \(-0.242506\pi\) |
−0.236010 | + | 0.971751i | \(0.575840\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 53.4506 | + | 117.022i | 0.169685 | + | 0.371500i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 146.183 | − | 253.197i | 0.461146 | − | 0.798729i | −0.537872 | − | 0.843027i | \(-0.680772\pi\) |
0.999018 | + | 0.0442975i | \(0.0141050\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4315 | + | 21.5319i | 0.0389701 | + | 0.0674983i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 241.784i | − | 0.753221i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −44.5608 | −0.137959 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −100.852 | + | 58.2271i | −0.310315 | + | 0.179160i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −227.418 | − | 131.300i | −0.695467 | − | 0.401528i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −233.613 | + | 328.104i | −0.710070 | + | 0.997277i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 71.2984 | − | 123.492i | 0.215403 | − | 0.373089i | −0.737994 | − | 0.674807i | \(-0.764227\pi\) |
0.953397 | + | 0.301718i | \(0.0975601\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 100.600 | + | 174.245i | 0.302103 | + | 0.523258i | ||||
\(334\) | 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 | ||||||||
\(339\) | 60.7213 | − | 35.0574i | 0.179119 | − | 0.103414i | ||||
\(340\) | 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 | ||||||||
\(345\) | 207.891 | − | 360.078i | 0.602582 | − | 1.04370i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −226.686 | − | 392.632i | −0.653275 | − | 1.13151i | −0.982323 | − | 0.187192i | \(-0.940061\pi\) |
0.329048 | − | 0.944313i | \(-0.393272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 55.8211i | − | 0.159946i | −0.996797 | − | 0.0799730i | \(-0.974517\pi\) | ||
0.996797 | − | 0.0799730i | \(-0.0254834\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −48.2889 | −0.137575 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −197.638 | + | 114.107i | −0.559882 | + | 0.323248i | −0.753098 | − | 0.657908i | \(-0.771442\pi\) |
0.193216 | + | 0.981156i | \(0.438108\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 695.859 | + | 401.754i | 1.96017 | + | 1.13170i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −66.6871 | − | 47.4818i | −0.186799 | − | 0.133002i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −233.905 | + | 405.136i | −0.651547 | + | 1.12851i | 0.331201 | + | 0.943560i | \(0.392546\pi\) |
−0.982748 | + | 0.184952i | \(0.940787\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −158.722 | − | 274.915i | −0.439674 | − | 0.761539i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 184.796i | 0.509080i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 471.983 | 1.29311 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 264.699 | − | 152.824i | 0.721252 | − | 0.416415i | −0.0939615 | − | 0.995576i | \(-0.529953\pi\) |
0.815213 | + | 0.579161i | \(0.196620\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 139.405 | + | 80.4854i | 0.377791 | + | 0.218118i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −72.7257 | + | 33.2178i | −0.196026 | + | 0.0895359i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −131.217 | + | 227.274i | −0.351787 | + | 0.609313i | −0.986563 | − | 0.163383i | \(-0.947759\pi\) |
0.634776 | + | 0.772697i | \(0.281093\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 66.1536 | + | 114.581i | 0.176410 | + | 0.305550i | ||||
\(376\) | 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 | ||||||||
\(381\) | −132.505 | + | 76.5019i | −0.347782 | + | 0.200792i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −289.022 | − | 166.867i | −0.754627 | − | 0.435684i | 0.0727364 | − | 0.997351i | \(-0.476827\pi\) |
−0.827363 | + | 0.561667i | \(0.810160\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 161.478 | + | 15.4098i | 0.419423 | + | 0.0400254i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 63.0639 | − | 109.230i | 0.162956 | − | 0.282248i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −298.042 | − | 516.223i | −0.766174 | − | 1.32705i | −0.939624 | − | 0.342210i | \(-0.888825\pi\) |
0.173449 | − | 0.984843i | \(-0.444509\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 264.571i | 0.676653i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 117.170 | 0.298142 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 793.137 | − | 457.918i | 2.00794 | − | 1.15929i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 268.394 | + | 154.957i | 0.676055 | + | 0.390321i | 0.798367 | − | 0.602171i | \(-0.205697\pi\) |
−0.122312 | + | 0.992492i | \(0.539031\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.60138 | + | 79.6543i | −0.0190511 | + | 0.199635i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 167.573 | − | 290.245i | 0.417888 | − | 0.723803i | −0.577839 | − | 0.816151i | \(-0.696104\pi\) |
0.995727 | + | 0.0923475i | \(0.0294371\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 101.911 | + | 176.516i | 0.252882 | + | 0.438004i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 55.1364i | − | 0.136139i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 253.685 | 0.623306 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −302.456 | + | 174.623i | −0.739501 | + | 0.426951i | −0.821888 | − | 0.569649i | \(-0.807079\pi\) |
0.0823869 | + | 0.996600i | \(0.473746\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −247.857 | − | 143.100i | −0.603058 | − | 0.348176i | ||||
\(412\) | 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 | ||||||||
\(417\) | 63.2727 | + | 109.591i | 0.151733 | + | 0.262809i | ||||
\(418\) | 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 | ||||||||
\(423\) | 149.491 | − | 86.3088i | 0.353407 | − | 0.204040i | ||||
\(424\) | 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 | ||||||||
\(429\) | −30.4427 | + | 52.7283i | −0.0709620 | + | 0.122910i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 161.420 | + | 279.587i | 0.374524 | + | 0.648694i | 0.990256 | − | 0.139262i | \(-0.0444729\pi\) |
−0.615732 | + | 0.787956i | \(0.711140\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 523.962i | − | 1.21007i | −0.796197 | − | 0.605037i | \(-0.793158\pi\) | ||
0.796197 | − | 0.605037i | \(-0.206842\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 69.7463 | 0.160336 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 223.954 | − | 129.300i | 0.512481 | − | 0.295881i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −606.881 | − | 350.383i | −1.38242 | − | 0.798138i | −0.389971 | − | 0.920827i | \(-0.627515\pi\) |
−0.992445 | + | 0.122689i | \(0.960848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −96.2516 | + | 111.106i | −0.218258 | + | 0.251942i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −48.4446 | + | 83.9086i | −0.109356 | + | 0.189410i | −0.915509 | − | 0.402296i | \(-0.868212\pi\) |
0.806154 | + | 0.591706i | \(0.201545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 171.539 | + | 297.114i | 0.385481 | + | 0.667672i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 260.826i | − | 0.583504i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −499.063 | −1.11150 | −0.555749 | − | 0.831350i | \(-0.687568\pi\) | ||||
−0.555749 | + | 0.831350i | \(0.687568\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 175.770 | − | 101.481i | 0.389734 | − | 0.225013i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −208.476 | − | 120.364i | −0.460213 | − | 0.265704i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −324.645 | − | 231.150i | −0.713505 | − | 0.508022i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −158.284 | + | 274.156i | −0.346354 | + | 0.599903i | −0.985599 | − | 0.169100i | \(-0.945914\pi\) |
0.639245 | + | 0.769003i | \(0.279247\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.5423 | + | 30.3841i | 0.0382184 | + | 0.0661963i | ||||
\(460\) | 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 | ||||||||
\(465\) | −201.546 | + | 116.363i | −0.433433 | + | 0.250243i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.4408 | + | 22.1938i | 0.0823143 | + | 0.0475242i | 0.540592 | − | 0.841285i | \(-0.318200\pi\) |
−0.458278 | + | 0.888809i | \(0.651534\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 354.962 | − | 162.131i | 0.756848 | − | 0.345694i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −136.184 | + | 235.877i | −0.289137 | + | 0.500800i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −79.5146 | − | 137.723i | −0.168107 | − | 0.291170i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 82.7008i | − | 0.174107i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.2655 | 0.0718354 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −129.513 | + | 74.7741i | −0.270381 | + | 0.156105i | −0.629061 | − | 0.777356i | \(-0.716560\pi\) |
0.358680 | + | 0.933461i | \(0.383227\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −539.764 | − | 311.633i | −1.12217 | − | 0.647885i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 472.932 | + | 45.1318i | 0.979156 | + | 0.0934405i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 436.230 | − | 755.573i | 0.899444 | − | 1.55788i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5141 | + | 49.3879i | 0.0585505 | + | 0.101413i | 0.893815 | − | 0.448436i | \(-0.148019\pi\) |
−0.835264 | + | 0.549848i | \(0.814685\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 36.9319i | − | 0.0755254i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 563.958 | 1.14859 | 0.574296 | − | 0.818648i | \(-0.305276\pi\) | ||||
0.574296 | + | 0.818648i | \(0.305276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.4352 | + | 22.1906i | −0.0779619 | + | 0.0450113i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −60.2054 | − | 34.7596i | −0.121627 | − | 0.0702214i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −87.2182 | + | 913.954i | −0.175489 | + | 1.83894i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −194.019 | + | 336.050i | −0.388815 | + | 0.673447i | −0.992290 | − | 0.123935i | \(-0.960449\pi\) |
0.603476 | + | 0.797381i | \(0.293782\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 154.125 | + | 266.951i | 0.307634 | + | 0.532837i | ||||
\(502\) | 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 | ||||||||
\(507\) | −123.955 | + | 71.5653i | −0.244487 | + | 0.141155i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 446.040 | + | 257.521i | 0.876306 | + | 0.505935i | 0.869439 | − | 0.494041i | \(-0.164481\pi\) |
0.00686712 | + | 0.999976i | \(0.497814\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 224.061 | + | 490.550i | 0.438476 | + | 0.959980i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.1463 | − | 29.6983i | 0.0334236 | − | 0.0578914i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.5837 | + | 40.8482i | 0.0457936 | + | 0.0793169i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 217.647i | − | 0.420980i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −190.702 | −0.367442 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.7063 | − | 15.9962i | 0.0531791 | − | 0.0307030i | −0.473175 | − | 0.880969i | \(-0.656892\pi\) |
0.526354 | + | 0.850266i | \(0.323559\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −275.525 | − | 159.075i | −0.526817 | − | 0.304158i | 0.212902 | − | 0.977073i | \(-0.431708\pi\) |
−0.739719 | + | 0.672916i | \(0.765042\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 88.1219 | − | 123.765i | 0.167851 | − | 0.235743i | ||||
\(526\) | 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 | ||||||||
\(531\) | 187.211i | 0.352564i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −498.645 | −0.935543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −740.616 | + | 427.595i | −1.38433 | + | 0.799243i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 42.3674 | + | 24.4608i | 0.0788964 | + | 0.0455509i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 60.6412 | + | 175.145i | 0.112507 | + | 0.324945i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −119.509 | + | 206.995i | −0.220903 | + | 0.382615i | −0.955082 | − | 0.296340i | \(-0.904234\pi\) |
0.734179 | + | 0.678956i | \(0.237567\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 178.757 | + | 309.616i | 0.329202 | + | 0.570195i | ||||
\(544\) | 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 | ||||||||
\(549\) | −310.821 | + | 179.453i | −0.566159 | + | 0.326872i | ||||
\(550\) | 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 | ||||||||
\(555\) | 355.823 | − | 616.304i | 0.641123 | − | 1.11046i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 442.789 | + | 766.932i | 0.794953 | + | 1.37690i | 0.922869 | + | 0.385113i | \(0.125838\pi\) |
−0.127917 | + | 0.991785i | \(0.540829\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 390.710i | 0.698944i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 44.2366 | 0.0788532 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 154.219 | − | 89.0382i | 0.273923 | − | 0.158150i | −0.356746 | − | 0.934201i | \(-0.616114\pi\) |
0.630669 | + | 0.776052i | \(0.282781\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −214.771 | − | 123.998i | −0.380126 | − | 0.219466i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 57.3053 | − | 26.1745i | 0.101068 | − | 0.0461631i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −451.288 | + | 781.654i | −0.793125 | + | 1.37373i | 0.130898 | + | 0.991396i | \(0.458214\pi\) |
−0.924023 | + | 0.382336i | \(0.875120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.0141 | + | 69.3064i | 0.0700771 | + | 0.121377i | 0.898935 | − | 0.438082i | \(-0.144342\pi\) |
−0.828858 | + | 0.559459i | \(0.811009\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 110.395i | − | 0.192662i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −491.020 | −0.853948 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 436.345 | − | 251.924i | 0.756231 | − | 0.436610i | −0.0717099 | − | 0.997426i | \(-0.522846\pi\) |
0.827941 | + | 0.560815i | \(0.189512\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −101.028 | − | 58.3288i | −0.174488 | − | 0.100741i | ||||
\(580\) | 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 | ||||||||
\(585\) | 85.3989 | + | 147.915i | 0.145981 | + | 0.252846i | ||||
\(586\) | 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 | ||||||||
\(591\) | −144.106 | + | 83.1997i | −0.243834 | + | 0.140778i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −580.642 | − | 335.234i | −0.979160 | − | 0.565318i | −0.0771438 | − | 0.997020i | \(-0.524580\pi\) |
−0.902017 | + | 0.431701i | \(0.857913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.5069 | + | 288.243i | −0.0462301 | + | 0.484442i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 178.392 | − | 308.985i | 0.298815 | − | 0.517562i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −220.065 | − | 381.163i | −0.367387 | − | 0.636332i | 0.621770 | − | 0.783200i | \(-0.286414\pi\) |
−0.989156 | + | 0.146868i | \(0.953081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 732.160i | − | 1.21824i | −0.793080 | − | 0.609118i | \(-0.791524\pi\) | ||
0.793080 | − | 0.609118i | \(-0.208476\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −167.244 | −0.277353 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 566.055 | − | 326.812i | 0.935628 | − | 0.540185i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 283.101 | + | 163.449i | 0.466394 | + | 0.269273i | 0.714729 | − | 0.699401i | \(-0.246550\pi\) |
−0.248335 | + | 0.968674i | \(0.579883\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.1102 | + | 72.4899i | 0.0543681 | + | 0.119031i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −267.362 | + | 463.084i | −0.437580 | + | 0.757911i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 494.332 | + | 856.207i | 0.806414 | + | 1.39675i | 0.915333 | + | 0.402699i | \(0.131928\pi\) |
−0.108919 | + | 0.994051i | \(0.534739\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 569.354i | − | 0.925779i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 280.536 | 0.454678 | 0.227339 | − | 0.973816i | \(-0.426997\pi\) | ||||
0.227339 | + | 0.973816i | \(0.426997\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −894.439 | + | 516.405i | −1.44497 | + | 0.834256i | −0.998176 | − | 0.0603780i | \(-0.980769\pi\) |
−0.446799 | + | 0.894634i | \(0.647436\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −176.328 | − | 101.803i | −0.283942 | − | 0.163934i | ||||
\(622\) | 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 | ||||||||
\(627\) | −21.6191 | − | 37.4454i | −0.0344802 | − | 0.0597215i | ||||
\(628\) | 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 | ||||||||
\(633\) | −182.913 | + | 105.605i | −0.288963 | + | 0.166833i | ||||
\(634\) | 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 | ||||||||
\(639\) | 196.737 | − | 340.758i | 0.307883 | − | 0.533268i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −334.263 | − | 578.961i | −0.521471 | − | 0.903215i | −0.999688 | − | 0.0249729i | \(-0.992050\pi\) |
0.478217 | − | 0.878242i | \(-0.341283\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 313.584i | − | 0.487690i | −0.969814 | − | 0.243845i | \(-0.921591\pi\) | ||
0.969814 | − | 0.243845i | \(-0.0784088\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −446.114 | −0.691649 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 292.310 | − | 168.765i | 0.451793 | − | 0.260843i | −0.256794 | − | 0.966466i | \(-0.582666\pi\) |
0.708587 | + | 0.705623i | \(0.249333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 204.423 | + | 118.024i | 0.314981 | + | 0.181855i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −216.619 | − | 154.234i | −0.332748 | − | 0.236919i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −451.677 | + | 782.328i | −0.691695 | + | 1.19805i | 0.279587 | + | 0.960120i | \(0.409803\pi\) |
−0.971282 | + | 0.237931i | \(0.923531\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −207.215 | − | 358.907i | −0.316358 | − | 0.547949i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 231.128i | − | 0.351793i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −768.092 | −1.16554 | −0.582771 | − | 0.812637i | \(-0.698031\pi\) | ||||
−0.582771 | + | 0.812637i | \(0.698031\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 356.130 | − | 205.612i | 0.538774 | − | 0.311062i | −0.205808 | − | 0.978592i | \(-0.565982\pi\) |
0.744582 | + | 0.667531i | \(0.232649\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −94.1217 | − | 54.3412i | −0.141963 | − | 0.0819626i | ||||
\(664\) | 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 | ||||||||
\(669\) | 16.0237 | + | 27.7539i | 0.0239517 | + | 0.0414856i | ||||
\(670\) | 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 | ||||||||
\(675\) | −56.3901 | + | 32.5568i | −0.0835409 | + | 0.0482323i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −48.0858 | − | 27.7623i | −0.0710277 | − | 0.0410079i | 0.464066 | − | 0.885801i | \(-0.346390\pi\) |
−0.535093 | + | 0.844793i | \(0.679724\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 992.384 | + | 94.7028i | 1.46154 | + | 0.139474i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −127.348 | + | 220.573i | −0.187001 | + | 0.323896i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.1419 | + | 66.0637i | 0.0558447 | + | 0.0967258i | 0.892596 | − | 0.450857i | \(-0.148882\pi\) |
−0.836752 | + | 0.547583i | \(0.815548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1012.29i | 1.47780i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 623.391 | 0.907410 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −91.9245 | + | 53.0726i | −0.133417 | + | 0.0770285i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.4780 | + | 11.2456i | 0.0281881 | + | 0.0162744i | 0.514028 | − | 0.857774i | \(-0.328153\pi\) |
−0.485840 | + | 0.874048i | \(0.661486\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.54608 | − | 79.0749i | 0.0108890 | − | 0.114105i | ||||
\(694\) | 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 | ||||||||
\(699\) | − | 76.3282i | − | 0.109196i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −854.197 | −1.21854 | −0.609270 | − | 0.792963i | \(-0.708538\pi\) | ||||
−0.609270 | + | 0.792963i | \(0.708538\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 383.317 | − | 221.308i | 0.545258 | − | 0.314805i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −528.751 | − | 305.274i | −0.750001 | − | 0.433013i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 426.558 | + | 933.889i | 0.603336 | + | 1.32092i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 79.3009 | − | 137.353i | 0.111849 | − | 0.193728i | −0.804667 | − | 0.593727i | \(-0.797656\pi\) |
0.916516 | + | 0.399999i | \(0.130989\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −224.240 | − | 388.395i | −0.315387 | − | 0.546266i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 859.403i | 1.20533i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 215.352 | 0.301191 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 247.615 | − | 142.961i | 0.345349 | − | 0.199387i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 329.191 | + | 190.059i | 0.457846 | + | 0.264338i | 0.711138 | − | 0.703052i | \(-0.248180\pi\) |
−0.253292 | + | 0.967390i | \(0.581513\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.2593 | + | 43.9030i | −0.0433555 | + | 0.0608918i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 115.828 | − | 200.620i | 0.160204 | − | 0.277482i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −41.1837 | − | 71.3322i | −0.0568051 | − | 0.0983893i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 159.283i | − | 0.219096i | −0.993981 | − | 0.109548i | \(-0.965060\pi\) | ||
0.993981 | − | 0.109548i | \(-0.0349404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 245.841 | − | 141.936i | 0.336307 | − | 0.194167i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −154.308 | − | 89.0895i | −0.210515 | − | 0.121541i | 0.391036 | − | 0.920376i | \(-0.372117\pi\) |
−0.601551 | + | 0.798835i | \(0.705450\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 510.555 | + | 98.3396i | 0.694632 | + | 0.133795i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −105.436 | + | 182.620i | −0.143060 | + | 0.247788i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 158.693 | + | 274.864i | 0.214740 | + | 0.371941i | 0.953192 | − | 0.302365i | \(-0.0977762\pi\) |
−0.738452 | + | 0.674306i | \(0.764443\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 106.229i | 0.143360i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1055.73 | 1.42090 | 0.710450 | − | 0.703748i | \(-0.248492\pi\) | ||||
0.710450 | + | 0.703748i | \(0.248492\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −798.945 | + | 461.271i | −1.07241 | + | 0.619156i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −103.312 | − | 59.6474i | −0.138303 | − | 0.0798493i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −796.003 | − | 566.761i | −1.06275 | − | 0.756690i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 153.605 | − | 266.051i | 0.204533 | − | 0.354262i | −0.745451 | − | 0.666561i | \(-0.767766\pi\) |
0.949984 | + | 0.312299i | \(0.101099\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −349.562 | − | 605.459i | −0.464226 | − | 0.804062i | ||||
\(754\) | 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 | ||||||||
\(759\) | −222.325 | + | 128.359i | −0.292918 | + | 0.169116i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 457.221 | + | 263.977i | 0.600816 | + | 0.346881i | 0.769363 | − | 0.638812i | \(-0.220574\pi\) |
−0.168546 | + | 0.985694i | \(0.553907\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −965.350 | + | 440.929i | −1.26520 | + | 0.577888i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 62.0470 | − | 107.469i | 0.0811072 | − | 0.140482i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −289.965 | − | 502.235i | −0.378051 | − | 0.654804i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 831.961i | 1.08187i | 0.841063 | + | 0.540937i | \(0.181930\pi\) | ||||
−0.841063 | + | 0.540937i | \(0.818070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −484.836 | −0.628840 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 657.060 | − | 379.354i | 0.850012 | − | 0.490755i | −0.0106426 | − | 0.999943i | \(-0.503388\pi\) |
0.860655 | + | 0.509188i | \(0.170054\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 238.017 | + | 137.419i | 0.307119 | + | 0.177315i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 809.465 | + | 77.2469i | 1.04178 | + | 0.0994169i | ||||
\(778\) | 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 | ||||||||
\(783\) | − | 34.1544i | − | 0.0436199i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 963.363 | 1.22721 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 595.121 | − | 343.593i | 0.756190 | − | 0.436586i | −0.0717363 | − | 0.997424i | \(-0.522854\pi\) |
0.827926 | + | 0.560837i | \(0.189521\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 212.839 | + | 122.882i | 0.269758 | + | 0.155745i | ||||
\(790\) | 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 | ||||||||
\(795\) | −60.5985 | − | 104.960i | −0.0762245 | − | 0.132025i | ||||
\(796\) | 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 | ||||||||
\(801\) | 145.495 | − | 84.0017i | 0.181642 | − | 0.104871i | ||||
\(802\) | 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 | ||||||||
\(807\) | −344.508 | + | 596.705i | −0.426899 | + | 0.739411i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 68.0836 | + | 117.924i | 0.0841577 | + | 0.145765i | 0.905032 | − | 0.425344i | \(-0.139847\pi\) |
−0.820874 | + | 0.571109i | \(0.806513\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 421.599i | − | 0.519851i | −0.965629 | − | 0.259926i | \(-0.916302\pi\) | ||
0.965629 | − | 0.259926i | \(-0.0836981\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −757.124 | −0.931272 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | −113.193 | + | 158.977i | −0.138209 | + | 0.194111i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.8238 | + | 68.9769i | −0.0485065 | + | 0.0840157i | −0.889259 | − | 0.457404i | \(-0.848779\pi\) |
0.840753 | + | 0.541419i | \(0.182113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −666.149 | − | 1153.80i | −0.809416 | − | 1.40195i | −0.913269 | − | 0.407357i | \(-0.866451\pi\) |
0.103853 | − | 0.994593i | \(-0.466883\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 82.0991i | 0.0995141i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −468.548 | −0.566564 | −0.283282 | − | 0.959037i | \(-0.591423\pi\) | ||||
−0.283282 | + | 0.959037i | \(0.591423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 426.112 | − | 246.016i | 0.514007 | − | 0.296762i | −0.220472 | − | 0.975393i | \(-0.570760\pi\) |
0.734479 | + | 0.678631i | \(0.237426\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.96211 | + | 4.59692i | 0.00958136 | + | 0.00553180i | ||||
\(832\) | 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 | ||||||||
\(837\) | 56.9823 | + | 98.6962i | 0.0680792 | + | 0.117917i | ||||
\(838\) | 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 | ||||||||
\(843\) | −446.493 | + | 257.783i | −0.529648 | + | 0.305792i | ||||
\(844\) | 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 | ||||||||
\(849\) | 178.296 | − | 308.817i | 0.210007 | − | 0.363742i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1313.97 | − | 2275.87i | −1.54404 | − | 2.67435i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 339.686i | 0.398225i | 0.979977 | + | 0.199113i | \(0.0638060\pi\) | ||||
−0.979977 | + | 0.199113i | \(0.936194\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −121.293 | −0.141863 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1216.76 | − | 702.497i | 1.41979 | − | 0.819717i | 0.423511 | − | 0.905891i | \(-0.360797\pi\) |
0.996280 | + | 0.0861737i | \(0.0274640\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1047.21 | − | 604.609i | −1.21911 | − | 0.703853i | −0.254381 | − | 0.967104i | \(-0.581872\pi\) |
−0.964727 | + | 0.263251i | \(0.915205\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 591.751 | − | 270.285i | 0.687283 | − | 0.313920i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 497.129 | − | 861.052i | 0.576047 | − | 0.997743i | −0.419880 | − | 0.907580i | \(-0.637928\pi\) |
0.995927 | − | 0.0901632i | \(-0.0287389\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 337.257 | + | 584.146i | 0.389893 | + | 0.675314i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 421.599i | − | 0.486273i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −565.470 | −0.650713 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 448.668 | − | 259.038i | 0.515118 | − | 0.297403i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −370.000 | − | 213.620i | −0.423826 | − | 0.244696i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 532.295 | + | 50.7967i | 0.608337 | + | 0.0580534i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 777.369 | − | 1346.44i | 0.886396 | − | 1.53528i | 0.0422903 | − | 0.999105i | \(-0.486535\pi\) |
0.844105 | − | 0.536177i | \(-0.180132\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 119.856 | + | 207.596i | 0.136355 | + | 0.236173i | ||||
\(880\) | 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 | ||||||||
\(885\) | 573.454 | − | 331.084i | 0.647970 | − | 0.374106i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1401.86 | + | 809.362i | 1.58045 | + | 0.912471i | 0.994794 | + | 0.101909i | \(0.0324950\pi\) |
0.585653 | + | 0.810562i | \(0.300838\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −58.7427 | + | 615.561i | −0.0660773 | + | 0.692419i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.0216 | + | 29.4823i | −0.0191039 | + | 0.0330890i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −189.869 | − | 328.862i | −0.212619 | − | 0.368267i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 173.036i | − | 0.193336i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 630.717 | 0.703141 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | −211.780 | − | 463.663i | −0.234530 | − | 0.513469i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 632.263 | − | 1095.11i | 0.698633 | − | 1.21007i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −279.345 | − | 483.839i | −0.307988 | − | 0.533450i | 0.669934 | − | 0.742420i | \(-0.266322\pi\) |
−0.977922 | + | 0.208970i | \(0.932989\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 440.012i | − | 0.484061i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −510.774 | −0.560674 | −0.280337 | − | 0.959902i | \(-0.590446\pi\) | ||||
−0.280337 | + | 0.959902i | \(0.590446\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −130.262 | + | 75.2070i | −0.142675 | + | 0.0823735i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1099.38 | + | 634.725i | 1.20150 | + | 0.693688i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 274.655 | − | 385.747i | 0.299515 | − | 0.420662i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 333.677 | − | 577.945i | 0.363087 | − | 0.628885i | −0.625380 | − | 0.780320i | \(-0.715056\pi\) |
0.988467 | + | 0.151435i | \(0.0483894\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 136.376 | + | 236.209i | 0.148073 | + | 0.256471i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1218.88i | 1.32056i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −840.424 | −0.908566 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.0032 | − | 11.5488i | 0.0215784 | − | 0.0124583i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 760.086 | + | 438.836i | 0.818177 | + | 0.472375i | 0.849787 | − | 0.527126i | \(-0.176730\pi\) |
−0.0316106 | + | 0.999500i | \(0.510064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 244.420 | + | 211.741i | 0.262535 | + | 0.227434i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −237.994 | + | 412.217i | −0.255084 | + | 0.441819i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −78.2325 | − | 135.503i | −0.0836711 | − | 0.144923i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 211.107i | 0.225301i | 0.993635 | + | 0.112650i | \(0.0359340\pi\) | ||||
−0.993635 | + | 0.112650i | \(0.964066\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −305.204 | −0.325031 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1321.72 | − | 763.093i | 1.40459 | − | 0.810938i | 0.409727 | − | 0.912208i | \(-0.365624\pi\) |
0.994859 | + | 0.101270i | \(0.0322908\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1820.81 | − | 1051.25i | −1.93087 | − | 1.11479i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −181.520 | − | 129.244i | −0.192085 | − | 0.136766i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −321.155 | + | 556.256i | −0.339129 | + | 0.587388i | −0.984269 | − | 0.176676i | \(-0.943466\pi\) |
0.645140 | + | 0.764064i | \(0.276799\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 357.986 | + | 620.050i | 0.377224 | + | 0.653372i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 506.394i | 0.532486i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 208.041 | 0.218302 | 0.109151 | − | 0.994025i | \(-0.465187\pi\) | ||||
0.109151 | + | 0.994025i | \(0.465187\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −338.156 | + | 195.234i | −0.354090 | + | 0.204434i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −37.2944 | − | 21.5319i | −0.0389701 | − | 0.0224994i | ||||
\(958\) | 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 | ||||||||
\(963\) | 209.391 | + | 362.676i | 0.217436 | + | 0.376610i | ||||
\(964\) | 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 | ||||||||
\(969\) | 66.8412 | − | 38.5908i | 0.0689795 | − | 0.0398254i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −296.922 | − | 171.428i | −0.305790 | − | 0.176548i | 0.339251 | − | 0.940696i | \(-0.389826\pi\) |
−0.645041 | + | 0.764148i | \(0.723160\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 509.114 | + | 48.5845i | 0.523241 | + | 0.0499327i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 100.852 | − | 174.681i | 0.103438 | − | 0.179160i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −835.089 | − | 1446.42i | −0.854748 | − | 1.48047i | −0.876878 | − | 0.480713i | \(-0.840378\pi\) |
0.0221298 | − | 0.999755i | \(-0.492955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 211.829i | − | 0.216372i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 454.835 | 0.463644 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −697.316 | + | 402.596i | −0.709376 | + | 0.409558i | −0.810830 | − | 0.585282i | \(-0.800984\pi\) |
0.101454 | + | 0.994840i | \(0.467650\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 509.703 | + | 294.277i | 0.517465 | + | 0.298759i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 66.2731 | − | 694.471i | 0.0671460 | − | 0.703618i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −823.698 | + | 1426.69i | −0.832860 | + | 1.44256i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 751.501 | + | 1301.64i | 0.758326 | + | 1.31346i | 0.943704 | + | 0.330792i | \(0.107316\pi\) |
−0.185378 | + | 0.982667i | \(0.559351\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 246.985i | 0.248726i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1261.95 | −1.26829 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 609.714 | − | 352.019i | 0.611549 | − | 0.353078i | −0.162023 | − | 0.986787i | \(-0.551802\pi\) |
0.773571 | + | 0.633709i | \(0.218468\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −301.801 | − | 174.245i | −0.302103 | − | 0.174419i |
(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 | 336.3.bh.g.145.4 | 8 | ||
3.2 | odd | 2 | 1008.3.cg.p.145.1 | 8 | |||
4.3 | odd | 2 | 168.3.z.b.145.4 | yes | 8 | ||
7.2 | even | 3 | 2352.3.f.g.97.1 | 8 | |||
7.3 | odd | 6 | inner | 336.3.bh.g.241.4 | 8 | ||
7.5 | odd | 6 | 2352.3.f.g.97.8 | 8 | |||
12.11 | even | 2 | 504.3.by.c.145.1 | 8 | |||
21.17 | even | 6 | 1008.3.cg.p.577.1 | 8 | |||
28.3 | even | 6 | 168.3.z.b.73.4 | ✓ | 8 | ||
28.11 | odd | 6 | 1176.3.z.c.913.1 | 8 | |||
28.19 | even | 6 | 1176.3.f.c.97.4 | 8 | |||
28.23 | odd | 6 | 1176.3.f.c.97.5 | 8 | |||
28.27 | even | 2 | 1176.3.z.c.313.1 | 8 | |||
84.23 | even | 6 | 3528.3.f.b.2449.7 | 8 | |||
84.47 | odd | 6 | 3528.3.f.b.2449.2 | 8 | |||
84.59 | odd | 6 | 504.3.by.c.73.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.3.z.b.73.4 | ✓ | 8 | 28.3 | even | 6 | ||
168.3.z.b.145.4 | yes | 8 | 4.3 | odd | 2 | ||
336.3.bh.g.145.4 | 8 | 1.1 | even | 1 | trivial | ||
336.3.bh.g.241.4 | 8 | 7.3 | odd | 6 | inner | ||
504.3.by.c.73.1 | 8 | 84.59 | odd | 6 | |||
504.3.by.c.145.1 | 8 | 12.11 | even | 2 | |||
1008.3.cg.p.145.1 | 8 | 3.2 | odd | 2 | |||
1008.3.cg.p.577.1 | 8 | 21.17 | even | 6 | |||
1176.3.f.c.97.4 | 8 | 28.19 | even | 6 | |||
1176.3.f.c.97.5 | 8 | 28.23 | odd | 6 | |||
1176.3.z.c.313.1 | 8 | 28.27 | even | 2 | |||
1176.3.z.c.913.1 | 8 | 28.11 | odd | 6 | |||
2352.3.f.g.97.1 | 8 | 7.2 | even | 3 | |||
2352.3.f.g.97.8 | 8 | 7.5 | odd | 6 | |||
3528.3.f.b.2449.2 | 8 | 84.47 | odd | 6 | |||
3528.3.f.b.2449.7 | 8 | 84.23 | even | 6 |