Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(161,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.i (of order \(4\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + \cdots + 1048576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{23} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 353.7 | ||
Root | \(-1.21144 - 1.59136i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.353 |
Dual form | 384.3.i.c.161.7 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.14944 | − | 2.77106i | 0.383147 | − | 0.923687i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.80434 | + | 4.80434i | −0.960868 | + | 0.960868i | −0.999263 | − | 0.0383950i | \(-0.987775\pi\) |
0.0383950 | + | 0.999263i | \(0.487775\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.36187i | − | 1.05170i | −0.850579 | − | 0.525848i | \(-0.823748\pi\) | ||
0.850579 | − | 0.525848i | \(-0.176252\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.35757 | − | 6.37035i | −0.706397 | − | 0.707816i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.514693 | + | 0.514693i | −0.0467903 | + | 0.0467903i | −0.730115 | − | 0.683325i | \(-0.760533\pi\) |
0.683325 | + | 0.730115i | \(0.260533\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.12969 | + | 7.12969i | −0.548438 | + | 0.548438i | −0.925989 | − | 0.377551i | \(-0.876766\pi\) |
0.377551 | + | 0.925989i | \(0.376766\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.79081 | + | 18.8354i | 0.519388 | + | 1.25569i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.1126i | 0.653684i | 0.945079 | + | 0.326842i | \(0.105985\pi\) | ||||
−0.945079 | + | 0.326842i | \(0.894015\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −21.1403 | + | 21.1403i | −1.11265 | + | 1.11265i | −0.119858 | + | 0.992791i | \(0.538244\pi\) |
−0.992791 | + | 0.119858i | \(0.961756\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −20.4002 | − | 8.46203i | −0.971438 | − | 0.402954i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.80231 | 0.339231 | 0.169615 | − | 0.985510i | \(-0.445747\pi\) | ||||
0.169615 | + | 0.985510i | \(0.445747\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 21.1633i | − | 0.846533i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −24.9603 | + | 10.2949i | −0.924455 | + | 0.381292i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −34.6058 | − | 34.6058i | −1.19330 | − | 1.19330i | −0.976134 | − | 0.217169i | \(-0.930318\pi\) |
−0.217169 | − | 0.976134i | \(-0.569682\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −24.8644 | −0.802078 | −0.401039 | − | 0.916061i | \(-0.631351\pi\) | ||||
−0.401039 | + | 0.916061i | \(0.631351\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.834637 | + | 2.01786i | 0.0252920 | + | 0.0611472i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 35.3689 | + | 35.3689i | 1.01054 | + | 1.01054i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 18.2760 | + | 18.2760i | 0.493946 | + | 0.493946i | 0.909547 | − | 0.415601i | \(-0.136429\pi\) |
−0.415601 | + | 0.909547i | \(0.636429\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.5617 | + | 27.9520i | 0.296453 | + | 0.716717i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −64.2448 | −1.56695 | −0.783473 | − | 0.621426i | \(-0.786554\pi\) | ||||
−0.783473 | + | 0.621426i | \(0.786554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.24058 | + | 7.24058i | 0.168386 | + | 0.168386i | 0.786269 | − | 0.617884i | \(-0.212010\pi\) |
−0.617884 | + | 0.786269i | \(0.712010\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 61.1492 | + | 0.0613789i | 1.35887 | + | 0.00136398i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 23.0508i | 0.490442i | 0.969467 | + | 0.245221i | \(0.0788606\pi\) | ||||
−0.969467 | + | 0.245221i | \(0.921139\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.19710 | −0.106063 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 30.7938 | + | 12.7733i | 0.603800 | + | 0.250457i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31.9199 | + | 31.9199i | −0.602263 | + | 0.602263i | −0.940913 | − | 0.338650i | \(-0.890030\pi\) |
0.338650 | + | 0.940913i | \(0.390030\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.94552i | − | 0.0899185i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 34.2816 | + | 82.8807i | 0.601432 | + | 1.45405i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 17.6272 | − | 17.6272i | 0.298766 | − | 0.298766i | −0.541764 | − | 0.840530i | \(-0.682244\pi\) |
0.840530 | + | 0.541764i | \(0.182244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.3933 | − | 12.3933i | 0.203170 | − | 0.203170i | −0.598187 | − | 0.801357i | \(-0.704112\pi\) |
0.801357 | + | 0.598187i | \(0.204112\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −46.8976 | + | 46.8036i | −0.744407 | + | 0.742914i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 68.5069i | − | 1.05395i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 41.1425 | − | 41.1425i | 0.614067 | − | 0.614067i | −0.329936 | − | 0.944003i | \(-0.607027\pi\) |
0.944003 | + | 0.329936i | \(0.107027\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.96830 | − | 21.6207i | 0.129975 | − | 0.313343i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 25.6785 | 0.361669 | 0.180834 | − | 0.983514i | \(-0.442120\pi\) | ||||
0.180834 | + | 0.983514i | \(0.442120\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 56.1845i | − | 0.769650i | −0.922990 | − | 0.384825i | \(-0.874262\pi\) | ||
0.922990 | − | 0.384825i | \(-0.125738\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −58.6449 | − | 24.3260i | −0.781932 | − | 0.324347i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.78910 | + | 3.78910i | 0.0492091 | + | 0.0492091i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35.7013 | 0.451915 | 0.225957 | − | 0.974137i | \(-0.427449\pi\) | ||||
0.225957 | + | 0.974137i | \(0.427449\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.162608 | + | 80.9998i | −0.00200751 | + | 0.999998i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −94.9424 | − | 94.9424i | −1.14388 | − | 1.14388i | −0.987733 | − | 0.156151i | \(-0.950091\pi\) |
−0.156151 | − | 0.987733i | \(-0.549909\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −53.3889 | − | 53.3889i | −0.628104 | − | 0.628104i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −135.672 | + | 56.1175i | −1.55945 | + | 0.645028i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −44.8713 | −0.504172 | −0.252086 | − | 0.967705i | \(-0.581117\pi\) | ||||
−0.252086 | + | 0.967705i | \(0.581117\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 52.4878 | + | 52.4878i | 0.576789 | + | 0.576789i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28.5802 | + | 68.9008i | −0.307314 | + | 0.740869i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 203.131i | − | 2.13822i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −82.3636 | −0.849109 | −0.424554 | − | 0.905402i | \(-0.639569\pi\) | ||||
−0.424554 | + | 0.905402i | \(0.639569\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.55097 | + | 0.00657558i | 0.0661714 | + | 6.64200e-5i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 36.3420 | − | 36.3420i | 0.359822 | − | 0.359822i | −0.503925 | − | 0.863747i | \(-0.668111\pi\) |
0.863747 | + | 0.503925i | \(0.168111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 87.5176i | − | 0.849685i | −0.905267 | − | 0.424843i | \(-0.860329\pi\) | ||
0.905267 | − | 0.424843i | \(-0.139671\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 138.664 | − | 57.3550i | 1.32061 | − | 0.546238i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 104.866 | − | 104.866i | 0.980058 | − | 0.980058i | −0.0197471 | − | 0.999805i | \(-0.506286\pi\) |
0.999805 | + | 0.0197471i | \(0.00628610\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.64006 | + | 7.64006i | −0.0700923 | + | 0.0700923i | −0.741284 | − | 0.671192i | \(-0.765783\pi\) |
0.671192 | + | 0.741284i | \(0.265783\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 71.6511 | − | 29.6367i | 0.645505 | − | 0.266998i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.1273i | − | 0.116171i | −0.998312 | − | 0.0580853i | \(-0.981500\pi\) | ||
0.998312 | − | 0.0580853i | \(-0.0184995\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −37.4849 | + | 37.4849i | −0.325956 | + | 0.325956i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 90.7461 | + | 0.0910869i | 0.775607 | + | 0.000778521i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 81.8098 | 0.687477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.470i | 0.995621i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −73.8456 | + | 178.026i | −0.600371 | + | 1.44737i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −18.4327 | − | 18.4327i | −0.147461 | − | 0.147461i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 88.2707 | 0.695045 | 0.347523 | − | 0.937672i | \(-0.387023\pi\) | ||||
0.347523 | + | 0.937672i | \(0.387023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 28.3867 | − | 11.7415i | 0.220052 | − | 0.0910192i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −57.0518 | − | 57.0518i | −0.435510 | − | 0.435510i | 0.454988 | − | 0.890498i | \(-0.349644\pi\) |
−0.890498 | + | 0.454988i | \(0.849644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 155.632 | + | 155.632i | 1.17017 | + | 1.17017i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 70.4575 | − | 169.378i | 0.521907 | − | 1.25465i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 165.112 | 1.20520 | 0.602599 | − | 0.798045i | \(-0.294132\pi\) | ||||
0.602599 | + | 0.798045i | \(0.294132\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −95.0802 | − | 95.0802i | −0.684030 | − | 0.684030i | 0.276875 | − | 0.960906i | \(-0.410701\pi\) |
−0.960906 | + | 0.276875i | \(0.910701\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 63.8752 | + | 26.4955i | 0.453015 | + | 0.187912i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 7.33920i | − | 0.0513231i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 332.516 | 2.29321 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.97376 | + | 14.4015i | −0.0406378 | + | 0.0979693i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 131.077 | − | 131.077i | 0.879709 | − | 0.879709i | −0.113795 | − | 0.993504i | \(-0.536301\pi\) |
0.993504 | + | 0.113795i | \(0.0363006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 123.070i | 0.815031i | 0.913198 | + | 0.407515i | \(0.133605\pi\) | ||||
−0.913198 | + | 0.407515i | \(0.866395\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 70.7913 | − | 70.6494i | 0.462688 | − | 0.461761i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 119.457 | − | 119.457i | 0.770690 | − | 0.770690i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −139.181 | + | 139.181i | −0.886503 | + | 0.886503i | −0.994185 | − | 0.107683i | \(-0.965657\pi\) |
0.107683 | + | 0.994185i | \(0.465657\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 51.7620 | + | 125.142i | 0.325547 | + | 0.787058i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 57.4396i | − | 0.356768i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.9311 | + | 19.9311i | −0.122277 | + | 0.122277i | −0.765597 | − | 0.643320i | \(-0.777556\pi\) |
0.643320 | + | 0.765597i | \(0.277556\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13.7043 | − | 5.68458i | −0.0830566 | − | 0.0344520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −60.3220 | −0.361210 | −0.180605 | − | 0.983556i | \(-0.557806\pi\) | ||||
−0.180605 | + | 0.983556i | \(0.557806\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 67.3351i | 0.398432i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 269.072 | + | 0.270083i | 1.57352 | + | 0.00157943i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −74.8292 | − | 74.8292i | −0.432539 | − | 0.432539i | 0.456952 | − | 0.889491i | \(-0.348941\pi\) |
−0.889491 | + | 0.456952i | \(0.848941\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −155.802 | −0.890295 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −28.5846 | − | 69.1074i | −0.161495 | − | 0.390438i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.96558 | + | 3.96558i | 0.0221541 | + | 0.0221541i | 0.718097 | − | 0.695943i | \(-0.245013\pi\) |
−0.695943 | + | 0.718097i | \(0.745013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −158.820 | − | 158.820i | −0.877457 | − | 0.877457i | 0.115814 | − | 0.993271i | \(-0.463052\pi\) |
−0.993271 | + | 0.115814i | \(0.963052\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −20.0973 | − | 48.5882i | −0.109821 | − | 0.265509i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −175.608 | −0.949233 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.71960 | − | 5.71960i | −0.0305861 | − | 0.0305861i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 75.7896 | + | 183.754i | 0.401003 | + | 0.972245i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 68.8639i | − | 0.360544i | −0.983617 | − | 0.180272i | \(-0.942302\pi\) | ||
0.983617 | − | 0.180272i | \(-0.0576978\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −366.645 | −1.89971 | −0.949856 | − | 0.312686i | \(-0.898771\pi\) | ||||
−0.949856 | + | 0.312686i | \(0.898771\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −189.837 | − | 78.7446i | −0.973522 | − | 0.403819i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −246.744 | + | 246.744i | −1.25251 | + | 1.25251i | −0.297912 | + | 0.954593i | \(0.596290\pi\) |
−0.954593 | + | 0.297912i | \(0.903710\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 287.802i | 1.44624i | 0.690722 | + | 0.723120i | \(0.257293\pi\) | ||||
−0.690722 | + | 0.723120i | \(0.742707\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −66.7176 | − | 161.299i | −0.331928 | − | 0.802484i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −254.763 | + | 254.763i | −1.25499 | + | 1.25499i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 308.654 | − | 308.654i | 1.50563 | − | 1.50563i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −49.6037 | − | 49.7034i | −0.239632 | − | 0.240113i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 21.7616i | − | 0.104122i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 156.146 | − | 156.146i | 0.740027 | − | 0.740027i | −0.232556 | − | 0.972583i | \(-0.574709\pi\) |
0.972583 | + | 0.232556i | \(0.0747089\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.5159 | − | 71.1567i | 0.138572 | − | 0.334069i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −69.5724 | −0.323593 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 183.048i | 0.843541i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −155.691 | − | 64.5807i | −0.710916 | − | 0.294889i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −79.2296 | − | 79.2296i | −0.358505 | − | 0.358505i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −45.2998 | −0.203138 | −0.101569 | − | 0.994828i | \(-0.532386\pi\) | ||||
−0.101569 | + | 0.994828i | \(0.532386\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −134.818 | + | 134.547i | −0.599190 | + | 0.597988i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 300.757 | + | 300.757i | 1.32492 | + | 1.32492i | 0.909737 | + | 0.415186i | \(0.136283\pi\) |
0.415186 | + | 0.909737i | \(0.363717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −65.7088 | − | 65.7088i | −0.286938 | − | 0.286938i | 0.548930 | − | 0.835868i | \(-0.315035\pi\) |
−0.835868 | + | 0.548930i | \(0.815035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 14.8552 | − | 6.14449i | 0.0643082 | − | 0.0265995i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −42.8218 | −0.183785 | −0.0918923 | − | 0.995769i | \(-0.529292\pi\) | ||||
−0.0918923 | + | 0.995769i | \(0.529292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −110.744 | − | 110.744i | −0.471250 | − | 0.471250i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 41.0365 | − | 98.9305i | 0.173150 | − | 0.417428i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 100.598i | 0.420913i | 0.977603 | + | 0.210456i | \(0.0674950\pi\) | ||||
−0.977603 | + | 0.210456i | \(0.932505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.23162 | −0.0217080 | −0.0108540 | − | 0.999941i | \(-0.503455\pi\) | ||||
−0.0108540 | + | 0.999941i | \(0.503455\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 224.269 | + | 93.5551i | 0.922916 | + | 0.385001i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.9686 | − | 24.9686i | 0.101913 | − | 0.101913i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 301.448i | − | 1.22044i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −372.222 | + | 153.961i | −1.49487 | + | 0.618315i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.4381 | − | 17.4381i | 0.0694747 | − | 0.0694747i | −0.671516 | − | 0.740990i | \(-0.734356\pi\) |
0.740990 | + | 0.671516i | \(0.234356\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.01579 | + | 4.01579i | −0.0158727 | + | 0.0158727i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −209.311 | + | 86.5765i | −0.820828 | + | 0.339516i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 343.676i | 1.33726i | 0.743595 | + | 0.668630i | \(0.233119\pi\) | ||||
−0.743595 | + | 0.668630i | \(0.766881\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 134.545 | − | 134.545i | 0.519480 | − | 0.519480i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.442114 | + | 440.460i | −0.00169392 | + | 1.68758i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −98.0863 | −0.372952 | −0.186476 | − | 0.982460i | \(-0.559707\pi\) | ||||
−0.186476 | + | 0.982460i | \(0.559707\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 306.708i | − | 1.15739i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −51.5769 | + | 124.341i | −0.193172 | + | 0.465697i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 126.560 | + | 126.560i | 0.470482 | + | 0.470482i | 0.902070 | − | 0.431589i | \(-0.142047\pi\) |
−0.431589 | + | 0.902070i | \(0.642047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 206.487 | 0.761945 | 0.380972 | − | 0.924586i | \(-0.375589\pi\) | ||||
0.380972 | + | 0.924586i | \(0.375589\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 205.779 | − | 85.1154i | 0.753768 | − | 0.311778i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.8926 | + | 10.8926i | 0.0396095 | + | 0.0396095i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −183.416 | − | 183.416i | −0.662153 | − | 0.662153i | 0.293734 | − | 0.955887i | \(-0.405102\pi\) |
−0.955887 | + | 0.293734i | \(0.905102\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 158.077 | + | 158.395i | 0.566585 | + | 0.567723i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −109.143 | −0.388409 | −0.194204 | − | 0.980961i | \(-0.562213\pi\) | ||||
−0.194204 | + | 0.980961i | \(0.562213\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 60.4623 | + | 60.4623i | 0.213648 | + | 0.213648i | 0.805815 | − | 0.592167i | \(-0.201728\pi\) |
−0.592167 | + | 0.805815i | \(0.701728\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −562.888 | − | 233.487i | −1.97504 | − | 0.819252i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 472.962i | 1.64795i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 165.509 | 0.572697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −94.6721 | + | 228.235i | −0.325334 | + | 0.784311i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.4639 | + | 19.4639i | −0.0664296 | + | 0.0664296i | −0.739541 | − | 0.673111i | \(-0.764957\pi\) |
0.673111 | + | 0.739541i | \(0.264957\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 169.374i | 0.574149i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.54818 | − | 18.1456i | 0.0254147 | − | 0.0610963i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −55.6280 | + | 55.6280i | −0.186047 | + | 0.186047i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 53.3042 | − | 53.3042i | 0.177090 | − | 0.177090i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −58.9329 | − | 142.479i | −0.194498 | − | 0.470227i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 119.084i | 0.390438i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −408.201 | + | 408.201i | −1.32964 | + | 1.32964i | −0.423967 | + | 0.905677i | \(0.639363\pi\) |
−0.905677 | + | 0.423967i | \(0.860637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −242.517 | − | 100.596i | −0.784844 | − | 0.325554i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 360.965 | 1.16066 | 0.580330 | − | 0.814381i | \(-0.302924\pi\) | ||||
0.580330 | + | 0.814381i | \(0.302924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 73.9217i | − | 0.236172i | −0.993003 | − | 0.118086i | \(-0.962324\pi\) | ||
0.993003 | − | 0.118086i | \(-0.0376758\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.451863 | − | 450.172i | 0.00143449 | − | 1.42912i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 172.709 | + | 172.709i | 0.544825 | + | 0.544825i | 0.924939 | − | 0.380115i | \(-0.124116\pi\) |
−0.380115 | + | 0.924939i | \(0.624116\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.6227 | 0.111670 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −170.053 | − | 411.128i | −0.529761 | − | 1.28077i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −234.925 | − | 234.925i | −0.727321 | − | 0.727321i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 150.888 | + | 150.888i | 0.464271 | + | 0.464271i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.3893 | + | 29.9529i | 0.0378877 | + | 0.0915990i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 169.697 | 0.515796 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 261.507 | + | 261.507i | 0.790051 | + | 0.790051i | 0.981502 | − | 0.191451i | \(-0.0613194\pi\) |
−0.191451 | + | 0.981502i | \(0.561319\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.233489 | − | 232.615i | 0.000701168 | − | 0.698544i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 395.325i | 1.18007i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.2211 | 0.0540684 | 0.0270342 | − | 0.999635i | \(-0.491394\pi\) | ||||
0.0270342 | + | 0.999635i | \(0.491394\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36.3765 | − | 15.0890i | −0.107305 | − | 0.0445104i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.7975 | − | 12.7975i | 0.0375294 | − | 0.0375294i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 322.471i | − | 0.940149i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 60.7863 | + | 146.960i | 0.176192 | + | 0.425970i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −173.710 | + | 173.710i | −0.500605 | + | 0.500605i | −0.911626 | − | 0.411021i | \(-0.865172\pi\) |
0.411021 | + | 0.911626i | \(0.365172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −387.899 | + | 387.899i | −1.11146 | + | 1.11146i | −0.118506 | + | 0.992953i | \(0.537811\pi\) |
−0.992953 | + | 0.118506i | \(0.962189\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 104.560 | − | 251.358i | 0.297891 | − | 0.716121i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 676.812i | − | 1.91732i | −0.284561 | − | 0.958658i | \(-0.591848\pi\) | ||
0.284561 | − | 0.958658i | \(-0.408152\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −123.368 | + | 123.368i | −0.347516 | + | 0.347516i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 94.0355 | − | 226.700i | 0.263405 | − | 0.635014i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −240.896 | −0.671020 | −0.335510 | − | 0.942037i | \(-0.608909\pi\) | ||||
−0.335510 | + | 0.942037i | \(0.608909\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 532.827i | − | 1.47598i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 333.830 | + | 138.473i | 0.919643 | + | 0.381469i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 269.929 | + | 269.929i | 0.739532 | + | 0.739532i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −666.702 | −1.81663 | −0.908313 | − | 0.418291i | \(-0.862629\pi\) | ||||
−0.908313 | + | 0.418291i | \(0.862629\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 408.441 | + | 409.261i | 1.10689 | + | 1.10911i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 234.990 | + | 234.990i | 0.633397 | + | 0.633397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 358.513 | + | 358.513i | 0.961160 | + | 0.961160i | 0.999273 | − | 0.0381137i | \(-0.0121349\pi\) |
−0.0381137 | + | 0.999273i | \(0.512135\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −72.2653 | + | 29.8908i | −0.192708 | + | 0.0797088i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 493.457 | 1.30890 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −140.959 | − | 140.959i | −0.371925 | − | 0.371925i | 0.496253 | − | 0.868178i | \(-0.334709\pi\) |
−0.868178 | + | 0.496253i | \(0.834709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 101.462 | − | 244.604i | 0.266305 | − | 0.642004i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 69.4683i | − | 0.181379i | −0.995879 | − | 0.0906897i | \(-0.971093\pi\) | ||
0.995879 | − | 0.0906897i | \(-0.0289071\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −36.4083 | −0.0945669 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.0925037 | − | 92.1575i | 0.000239028 | − | 0.238133i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 265.362 | − | 265.362i | 0.682165 | − | 0.682165i | −0.278322 | − | 0.960488i | \(-0.589778\pi\) |
0.960488 | + | 0.278322i | \(0.0897783\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 86.7042i | 0.221750i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −223.672 | + | 92.5164i | −0.569139 | + | 0.235411i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −171.521 | + | 171.521i | −0.434230 | + | 0.434230i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −259.123 | + | 259.123i | −0.652703 | + | 0.652703i | −0.953643 | − | 0.300940i | \(-0.902700\pi\) |
0.300940 | + | 0.953643i | \(0.402700\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 610.157 | − | 252.377i | 1.52922 | − | 0.632523i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 664.163i | 1.65627i | 0.560531 | + | 0.828133i | \(0.310597\pi\) | ||||
−0.560531 | + | 0.828133i | \(0.689403\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 177.275 | − | 177.275i | 0.439889 | − | 0.439889i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −388.369 | − | 389.932i | −0.958937 | − | 0.962795i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.8131 | −0.0462237 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 530.421i | 1.29687i | 0.761269 | + | 0.648437i | \(0.224577\pi\) | ||||
−0.761269 | + | 0.648437i | \(0.775423\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 189.787 | − | 457.536i | 0.461768 | − | 1.11323i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −129.769 | − | 129.769i | −0.314211 | − | 0.314211i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 912.271 | 2.19824 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −372.762 | + | 154.184i | −0.893914 | + | 0.369746i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −404.149 | − | 404.149i | −0.964556 | − | 0.964556i | 0.0348367 | − | 0.999393i | \(-0.488909\pi\) |
−0.999393 | + | 0.0348367i | \(0.988909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 264.630 | + | 264.630i | 0.628575 | + | 0.628575i | 0.947710 | − | 0.319134i | \(-0.103392\pi\) |
−0.319134 | + | 0.947710i | \(0.603392\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 146.842 | − | 146.547i | 0.347143 | − | 0.346447i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 235.180 | 0.553366 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −91.2382 | − | 91.2382i | −0.213673 | − | 0.213673i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.3374 | − | 8.43598i | −0.0474065 | − | 0.0196643i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 766.652i | − | 1.77877i | −0.457155 | − | 0.889387i | \(-0.651132\pi\) | ||
0.457155 | − | 0.889387i | \(-0.348868\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 151.222 | 0.349243 | 0.174622 | − | 0.984636i | \(-0.444130\pi\) | ||||
0.174622 | + | 0.984636i | \(0.444130\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 382.207 | − | 921.422i | 0.878638 | − | 2.11821i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −164.943 | + | 164.943i | −0.377445 | + | 0.377445i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 565.007i | − | 1.28703i | −0.765433 | − | 0.643516i | \(-0.777475\pi\) | ||
0.765433 | − | 0.643516i | \(-0.222525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33.0409 | + | 33.1073i | 0.0749228 | + | 0.0750733i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −100.963 | + | 100.963i | −0.227907 | + | 0.227907i | −0.811818 | − | 0.583911i | \(-0.801522\pi\) |
0.583911 | + | 0.811818i | \(0.301522\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 215.577 | − | 215.577i | 0.484442 | − | 0.484442i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −212.557 | − | 513.887i | −0.475518 | − | 1.14963i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 131.725i | 0.293375i | 0.989183 | + | 0.146687i | \(0.0468611\pi\) | ||||
−0.989183 | + | 0.146687i | \(0.953139\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 33.0663 | − | 33.0663i | 0.0733178 | − | 0.0733178i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 341.034 | + | 141.461i | 0.752833 | + | 0.312277i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −504.339 | −1.10844 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 137.963i | 0.301888i | 0.988542 | + | 0.150944i | \(0.0482313\pi\) | ||||
−0.988542 | + | 0.150944i | \(0.951769\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −114.403 | − | 277.374i | −0.249245 | − | 0.604302i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 303.536 | + | 303.536i | 0.658430 | + | 0.658430i | 0.955008 | − | 0.296579i | \(-0.0958457\pi\) |
−0.296579 | + | 0.955008i | \(0.595846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −280.379 | −0.605570 | −0.302785 | − | 0.953059i | \(-0.597916\pi\) | ||||
−0.302785 | + | 0.953059i | \(0.597916\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −193.714 | − | 468.332i | −0.416589 | − | 1.00716i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −65.6355 | − | 65.6355i | −0.140547 | − | 0.140547i | 0.633333 | − | 0.773880i | \(-0.281687\pi\) |
−0.773880 | + | 0.633333i | \(0.781687\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −302.886 | − | 302.886i | −0.645812 | − | 0.645812i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 225.699 | + | 545.659i | 0.479190 | + | 1.15851i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.45335 | −0.0157576 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 447.400 | + | 447.400i | 0.941894 | + | 0.941894i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 406.274 | + | 0.407800i | 0.851728 | + | 0.000854927i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 373.272i | 0.779273i | 0.920969 | + | 0.389636i | \(0.127399\pi\) | ||||
−0.920969 | + | 0.389636i | \(0.872601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −260.604 | −0.541797 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −159.169 | − | 66.0234i | −0.329542 | − | 0.136694i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 395.702 | − | 395.702i | 0.815881 | − | 0.815881i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.0470526i | − | 9.66171e-5i | −1.00000 | 4.83086e-5i | \(-0.999985\pi\) | |||
1.00000 | 4.83086e-5i | \(-1.53771e-5\pi\) | ||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.3206 | + | 78.1398i | 0.0660954 | + | 0.159795i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 273.442 | − | 273.442i | 0.556908 | − | 0.556908i | −0.371518 | − | 0.928426i | \(-0.621163\pi\) |
0.928426 | + | 0.371518i | \(0.121163\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 384.562 | − | 384.562i | 0.780044 | − | 0.780044i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −31.5047 | + | 31.4415i | −0.0636458 | + | 0.0635182i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 189.042i | − | 0.380365i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −46.2637 | + | 46.2637i | −0.0927129 | + | 0.0927129i | −0.751942 | − | 0.659229i | \(-0.770883\pi\) |
0.659229 | + | 0.751942i | \(0.270883\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −69.3366 | + | 167.156i | −0.138396 | + | 0.333645i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −864.426 | −1.71854 | −0.859270 | − | 0.511522i | \(-0.829082\pi\) | ||||
−0.859270 | + | 0.511522i | \(0.829082\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 349.198i | 0.691482i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 186.590 | + | 77.3977i | 0.368027 | + | 0.152658i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 171.041 | + | 171.041i | 0.336033 | + | 0.336033i | 0.854872 | − | 0.518839i | \(-0.173635\pi\) |
−0.518839 | + | 0.854872i | \(0.673635\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −413.623 | −0.809438 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 310.031 | − | 745.306i | 0.604349 | − | 1.45284i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 420.464 | + | 420.464i | 0.816435 | + | 0.816435i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.8641 | − | 11.8641i | −0.0229479 | − | 0.0229479i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −293.368 | + | 121.345i | −0.565257 | + | 0.233805i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 351.572 | 0.674802 | 0.337401 | − | 0.941361i | \(-0.390452\pi\) | ||||
0.337401 | + | 0.941361i | \(0.390452\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −287.638 | − | 287.638i | −0.549977 | − | 0.549977i | 0.376457 | − | 0.926434i | \(-0.377142\pi\) |
−0.926434 | + | 0.376457i | \(0.877142\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −179.085 | + | 431.736i | −0.341114 | + | 0.822354i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 276.309i | − | 0.524306i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −468.124 | −0.884922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −224.357 | − | 0.225200i | −0.422519 | − | 0.000424106i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 458.045 | − | 458.045i | 0.859372 | − | 0.859372i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1007.63i | 1.88341i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.5471 | − | 6.43067i | 0.0289517 | − | 0.0119752i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.67491 | − | 2.67491i | 0.00496273 | − | 0.00496273i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −419.846 | + | 419.846i | −0.776056 | + | 0.776056i | −0.979158 | − | 0.203102i | \(-0.934898\pi\) |
0.203102 | + | 0.979158i | \(0.434898\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −622.654 | + | 257.545i | −1.14669 | + | 0.474301i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 73.4108i | − | 0.134699i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 517.346 | − | 517.346i | 0.945789 | − | 0.945789i | −0.0528155 | − | 0.998604i | \(-0.516820\pi\) |
0.998604 | + | 0.0528155i | \(0.0168195\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −157.742 | − | 0.158334i | −0.287325 | − | 0.000288404i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1463.16 | 2.65546 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 262.828i | − | 0.475277i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −201.851 | + | 486.621i | −0.363696 | + | 0.876794i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.8976 | − | 31.8976i | −0.0572667 | − | 0.0572667i | 0.677893 | − | 0.735160i | \(-0.262893\pi\) |
−0.735160 | + | 0.677893i | \(0.762893\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −103.246 | −0.184698 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.4237 | + | 9.27502i | −0.0399709 | + | 0.0165330i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.9214 | − | 32.9214i | −0.0584750 | − | 0.0584750i | 0.677265 | − | 0.735740i | \(-0.263165\pi\) |
−0.735740 | + | 0.677265i | \(0.763165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 63.0679 | + | 63.0679i | 0.111625 | + | 0.111625i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 596.310 | + | 1.19710i | 1.05169 | + | 0.00211129i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 647.095 | 1.13725 | 0.568624 | − | 0.822597i | \(-0.307476\pi\) | ||||
0.568624 | + | 0.822597i | \(0.307476\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 451.861 | + | 451.861i | 0.791350 | + | 0.791350i | 0.981714 | − | 0.190363i | \(-0.0609666\pi\) |
−0.190363 | + | 0.981714i | \(0.560967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −190.826 | − | 79.1550i | −0.333030 | − | 0.138141i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 165.123i | − | 0.287170i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 532.176 | 0.922315 | 0.461157 | − | 0.887318i | \(-0.347434\pi\) | ||||
0.461157 | + | 0.887318i | \(0.347434\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −421.436 | + | 1015.99i | −0.727869 | + | 1.75474i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −698.953 | + | 698.953i | −1.20302 | + | 1.20302i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 32.8579i | − | 0.0563601i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −436.412 | + | 435.537i | −0.746004 | + | 0.744508i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 532.393 | − | 532.393i | 0.906973 | − | 0.906973i | −0.0890534 | − | 0.996027i | \(-0.528384\pi\) |
0.996027 | + | 0.0890534i | \(0.0283842\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 525.642 | − | 525.642i | 0.892431 | − | 0.892431i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 400.124 | + | 967.359i | 0.677029 | + | 1.63682i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 254.750i | − | 0.429595i | −0.976659 | − | 0.214798i | \(-0.931091\pi\) | ||
0.976659 | − | 0.214798i | \(-0.0689092\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −393.042 | + | 393.042i | −0.660574 | + | 0.660574i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 797.517 | + | 330.811i | 1.33587 | + | 0.554123i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −624.772 | −1.04303 | −0.521513 | − | 0.853244i | \(-0.674632\pi\) | ||||
−0.521513 | + | 0.853244i | \(0.674632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 386.910i | − | 0.643777i | −0.946778 | − | 0.321889i | \(-0.895682\pi\) | ||
0.946778 | − | 0.321889i | \(-0.104318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −523.658 | − | 0.525625i | −0.868422 | − | 0.000871684i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −578.779 | − | 578.779i | −0.956660 | − | 0.956660i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 951.141 | 1.56695 | 0.783477 | − | 0.621421i | \(-0.213444\pi\) | ||||
0.783477 | + | 0.621421i | \(0.213444\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 413.129 | + | 998.800i | 0.678373 | + | 1.64007i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −164.345 | − | 164.345i | −0.268977 | − | 0.268977i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −387.896 | − | 387.896i | −0.632783 | − | 0.632783i | 0.315982 | − | 0.948765i | \(-0.397666\pi\) |
−0.948765 | + | 0.315982i | \(0.897666\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −500.519 | − | 1210.08i | −0.813852 | − | 1.96761i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −882.945 | −1.43103 | −0.715514 | − | 0.698598i | \(-0.753808\pi\) | ||||
−0.715514 | + | 0.698598i | \(0.753808\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −694.731 | − | 694.731i | −1.12234 | − | 1.12234i | −0.991388 | − | 0.130955i | \(-0.958196\pi\) |
−0.130955 | − | 0.991388i | \(-0.541804\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −194.748 | + | 80.3239i | −0.313604 | + | 0.129346i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 330.337i | 0.530235i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 706.197 | 1.12991 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −60.3027 | − | 25.0136i | −0.0961765 | − | 0.0398942i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −203.094 | + | 203.094i | −0.322885 | + | 0.322885i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 927.845i | − | 1.47044i | −0.677831 | − | 0.735218i | \(-0.737080\pi\) | ||
0.677831 | − | 0.735218i | \(-0.262920\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −253.209 | − | 612.170i | −0.400014 | − | 0.967093i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −424.082 | + | 424.082i | −0.667846 | + | 0.667846i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 37.0537 | − | 37.0537i | 0.0581691 | − | 0.0581691i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −163.253 | − | 163.581i | −0.255482 | − | 0.255995i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 759.287i | 1.18453i | 0.805741 | + | 0.592267i | \(0.201767\pi\) | ||||
−0.805741 | + | 0.592267i | \(0.798233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 274.424 | − | 274.424i | 0.426787 | − | 0.426787i | −0.460746 | − | 0.887532i | \(-0.652418\pi\) |
0.887532 | + | 0.460746i | \(0.152418\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −79.9694 | + | 192.789i | −0.123984 | + | 0.298898i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 747.683 | 1.15561 | 0.577807 | − | 0.816173i | \(-0.303908\pi\) | ||||
0.577807 | + | 0.816173i | \(0.303908\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18.1452i | 0.0279587i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 507.239 | + | 210.403i | 0.779168 | + | 0.323200i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −605.127 | − | 605.127i | −0.926688 | − | 0.926688i | 0.0708022 | − | 0.997490i | \(-0.477444\pi\) |
−0.997490 | + | 0.0708022i | \(0.977444\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 548.192 | 0.836935 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −357.914 | + | 357.197i | −0.544771 | + | 0.543678i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 588.767 | + | 588.767i | 0.893425 | + | 0.893425i | 0.994844 | − | 0.101418i | \(-0.0323381\pi\) |
−0.101418 | + | 0.994844i | \(0.532338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.60334 | − | 3.60334i | −0.00545135 | − | 0.00545135i | 0.704376 | − | 0.709827i | \(-0.251227\pi\) |
−0.709827 | + | 0.704376i | \(0.751227\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −310.620 | + | 128.480i | −0.468507 | + | 0.193786i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1495.42 | −2.24875 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −270.005 | − | 270.005i | −0.404805 | − | 0.404805i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −52.0695 | + | 125.529i | −0.0778319 | + | 0.187636i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.7575i | 0.0190127i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −460.445 | −0.684167 | −0.342084 | − | 0.939670i | \(-0.611133\pi\) | ||||
−0.342084 | + | 0.939670i | \(0.611133\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 217.874 | + | 528.242i | 0.322776 | + | 0.782581i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −150.713 | + | 150.713i | −0.222618 | + | 0.222618i | −0.809600 | − | 0.586982i | \(-0.800316\pi\) |
0.586982 | + | 0.809600i | \(0.300316\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 606.350i | 0.893004i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1179.12 | − | 487.714i | 1.73145 | − | 0.716174i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −577.893 | + | 577.893i | −0.846109 | + | 0.846109i | −0.989645 | − | 0.143536i | \(-0.954153\pi\) |
0.143536 | + | 0.989645i | \(0.454153\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −793.254 | + | 793.254i | −1.15803 | + | 1.15803i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −257.612 | + | 106.555i | −0.374981 | + | 0.155102i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 455.158i | − | 0.660607i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −545.023 | + | 545.023i | −0.788745 | + | 0.788745i | −0.981288 | − | 0.192544i | \(-0.938326\pi\) |
0.192544 | + | 0.981288i | \(0.438326\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0484085 | − | 48.2274i | 6.98536e−5 | − | 0.0695922i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 913.595 | 1.31453 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 713.929i | − | 1.02429i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −49.2212 | + | 118.662i | −0.0704165 | + | 0.169760i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 413.745 | + | 413.745i | 0.590221 | + | 0.590221i | 0.937691 | − | 0.347470i | \(-0.112959\pi\) |
−0.347470 | + | 0.937691i | \(0.612959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −772.721 | −1.09918 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −434.171 | + | 179.584i | −0.615846 | + | 0.254730i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −267.545 | − | 267.545i | −0.378423 | − | 0.378423i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −521.959 | − | 521.959i | −0.736191 | − | 0.736191i | 0.235648 | − | 0.971839i | \(-0.424279\pi\) |
−0.971839 | + | 0.235648i | \(0.924279\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −226.973 | − | 227.429i | −0.319231 | − | 0.319873i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −194.000 | −0.272089 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.2600 | + | 35.2600i | 0.0493147 | + | 0.0493147i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 278.764 | + | 115.632i | 0.388792 | + | 0.161272i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 567.983i | 0.789963i | 0.918689 | + | 0.394981i | \(0.129249\pi\) | ||||
−0.918689 | + | 0.394981i | \(0.870751\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −644.293 | −0.893610 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.01344 | + | 14.4972i | −0.00831735 | + | 0.0200514i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −732.374 | + | 732.374i | −1.01017 | + | 1.01017i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 635.396i | 0.873998i | 0.899462 | + | 0.436999i | \(0.143959\pi\) | ||||
−0.899462 | + | 0.436999i | \(0.856041\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 517.031 | − | 513.926i | 0.709233 | − | 0.704974i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −80.4619 | + | 80.4619i | −0.110071 | + | 0.110071i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 637.378 | − | 637.378i | 0.869547 | − | 0.869547i | −0.122875 | − | 0.992422i | \(-0.539212\pi\) |
0.992422 | + | 0.122875i | \(0.0392116\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −40.4897 | − | 97.8896i | −0.0550880 | − | 0.133183i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42.3515i | 0.0574648i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 397.296 | − | 397.296i | 0.537613 | − | 0.537613i | −0.385214 | − | 0.922827i | \(-0.625872\pi\) |
0.922827 | + | 0.385214i | \(0.125872\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −835.331 | − | 346.497i | −1.12730 | − | 0.467607i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1160.78 | −1.56229 | −0.781145 | − | 0.624349i | \(-0.785364\pi\) | ||||
−0.781145 | + | 0.624349i | \(0.785364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1259.47i | 1.69057i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.21296 | + | 1208.42i | −0.00162377 | + | 1.61770i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −772.011 | − | 772.011i | −1.03072 | − | 1.03072i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1220.14 | −1.62469 | −0.812343 | − | 0.583181i | \(-0.801808\pi\) | ||||
−0.812343 | + | 0.583181i | \(0.801808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.2781 | − | 68.3663i | −0.0375539 | − | 0.0907919i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −591.268 | − | 591.268i | −0.783136 | − | 0.783136i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −202.623 | − | 202.623i | −0.267666 | − | 0.267666i | 0.560493 | − | 0.828159i | \(-0.310612\pi\) |
−0.828159 | + | 0.560493i | \(0.810612\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.51210 | + | 15.7439i | 0.00857984 | + | 0.0207430i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −694.461 | −0.912563 | −0.456282 | − | 0.889835i | \(-0.650819\pi\) | ||||
−0.456282 | + | 0.889835i | \(0.650819\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 56.2451 | + | 56.2451i | 0.0737157 | + | 0.0737157i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.682081 | + | 679.529i | −0.000891610 | + | 0.888273i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 251.353i | 0.327709i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 405.268 | 0.527007 | 0.263503 | − | 0.964658i | \(-0.415122\pi\) | ||||
0.263503 | + | 0.964658i | \(0.415122\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 952.347 | + | 395.035i | 1.23521 | + | 0.512367i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −142.479 | + | 142.479i | −0.184320 | + | 0.184320i | −0.793235 | − | 0.608916i | \(-0.791605\pi\) |
0.608916 | + | 0.793235i | \(0.291605\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 526.214i | 0.678985i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −218.182 | − | 527.486i | −0.280800 | − | 0.678875i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1358.16 | − | 1358.16i | 1.74346 | − | 1.74346i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.2165 | + | 13.2165i | −0.0169226 | + | 0.0169226i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1220.03 | + | 507.507i | 1.55815 | + | 0.648158i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1337.34i | − | 1.70362i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −482.883 | + | 482.883i | −0.613574 | + | 0.613574i | −0.943876 | − | 0.330301i | \(-0.892850\pi\) |
0.330301 | + | 0.943876i | \(0.392850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −112.744 | + | 271.803i | −0.142895 | + | 0.344491i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −96.6413 | −0.122176 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 176.721i | 0.222852i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −849.908 | − | 352.543i | −1.06907 | − | 0.443451i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 552.965 | + | 552.965i | 0.693808 | + | 0.693808i | 0.963068 | − | 0.269260i | \(-0.0867791\pi\) |
−0.269260 | + | 0.963068i | \(0.586779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −256.155 | −0.320595 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 285.272 | + | 285.846i | 0.356145 | + | 0.356861i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.9178 | + | 28.9178i | 0.0360122 | + | 0.0360122i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 275.959 | + | 275.959i | 0.342806 | + | 0.342806i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 496.177 | − | 205.232i | 0.614842 | − | 0.254314i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −930.240 | −1.14986 | −0.574932 | − | 0.818201i | \(-0.694972\pi\) | ||||
−0.574932 | + | 0.818201i | \(0.694972\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −611.506 | − | 611.506i | −0.754015 | − | 0.754015i | 0.221211 | − | 0.975226i | \(-0.428999\pi\) |
−0.975226 | + | 0.221211i | \(0.928999\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 237.345 | − | 572.188i | 0.291937 | − | 0.703799i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 191.511i | − | 0.234983i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −306.137 | −0.374708 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.670570 | − | 668.061i | 0.000818767 | − | 0.815703i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 963.577 | − | 963.577i | 1.17366 | − | 1.17366i | 0.192334 | − | 0.981330i | \(-0.438394\pi\) |
0.981330 | − | 0.192334i | \(-0.0616056\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1112.81i | − | 1.35214i | −0.736836 | − | 0.676071i | \(-0.763681\pi\) | ||
0.736836 | − | 0.676071i | \(-0.236319\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42.7046 | − | 17.6637i | 0.0517631 | − | 0.0214105i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 600.156 | − | 600.156i | 0.725703 | − | 0.725703i | −0.244058 | − | 0.969761i | \(-0.578479\pi\) |
0.969761 | + | 0.244058i | \(0.0784786\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 921.578 | − | 921.578i | 1.11167 | − | 1.11167i | 0.118750 | − | 0.992924i | \(-0.462111\pi\) |
0.992924 | − | 0.118750i | \(-0.0378887\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −719.085 | + | 297.432i | −0.865324 | + | 0.357920i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 57.7535i | − | 0.0693319i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 289.807 | − | 289.807i | 0.347075 | − | 0.347075i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 620.622 | − | 255.976i | 0.741484 | − | 0.305826i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1230.19 | 1.46625 | 0.733127 | − | 0.680091i | \(-0.238060\pi\) | ||||
0.733127 | + | 0.680091i | \(0.238060\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1554.12i | 1.84794i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −125.453 | + | 302.442i | −0.148818 | + | 0.358768i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −323.501 | − | 323.501i | −0.382841 | − | 0.382841i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 886.886 | 1.04709 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 237.043 | − | 98.0470i | 0.279202 | − | 0.115485i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 142.595 | + | 142.595i | 0.167562 | + | 0.167562i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1032.73 | + | 1032.73i | 1.21070 | + | 1.21070i | 0.970797 | + | 0.239902i | \(0.0771152\pi\) |
0.239902 | + | 0.970797i | \(0.422885\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1294.01 | + | 1291.42i | −1.51346 | + | 1.51043i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 609.799 | 0.711550 | 0.355775 | − | 0.934572i | \(-0.384217\pi\) | ||||
0.355775 | + | 0.934572i | \(0.384217\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 889.225 | + | 889.225i | 1.03519 | + | 1.03519i | 0.999358 | + | 0.0358288i | \(0.0114071\pi\) |
0.0358288 | + | 0.999358i | \(0.488593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1310.61 | + | 543.642i | 1.52219 | + | 0.631407i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1322.86i | − | 1.53286i | −0.642329 | − | 0.766429i | \(-0.722032\pi\) | ||
0.642329 | − | 0.766429i | \(-0.277968\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 719.010 | 0.831225 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 190.243 | − | 458.637i | 0.219427 | − | 0.528993i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.3752 | + | 18.3752i | −0.0211452 | + | 0.0211452i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 586.667i | 0.673555i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 523.632 | + | 524.684i | 0.599808 | + | 0.601013i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −135.699 | + | 135.699i | −0.155084 | + | 0.155084i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −853.500 | + | 853.500i | −0.973204 | + | 0.973204i | −0.999650 | − | 0.0264461i | \(-0.991581\pi\) |
0.0264461 | + | 0.999650i | \(0.491581\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 31.5630 | + | 76.3081i | 0.0359078 | + | 0.0868124i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1075.39i | 1.22064i | 0.792153 | + | 0.610322i | \(0.208960\pi\) | ||||
−0.792153 | + | 0.610322i | \(0.791040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 283.702 | − | 283.702i | 0.321294 | − | 0.321294i | −0.527970 | − | 0.849263i | \(-0.677046\pi\) |
0.849263 | + | 0.527970i | \(0.177046\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 469.346 | + | 194.685i | 0.530334 | + | 0.219983i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 282.642 | 0.318650 | 0.159325 | − | 0.987226i | \(-0.449068\pi\) | ||||
0.159325 | + | 0.987226i | \(0.449068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 649.838i | − | 0.730976i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −41.6064 | − | 41.7738i | −0.0466963 | − | 0.0468841i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −487.301 | − | 487.301i | −0.545690 | − | 0.545690i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −38.1040 | −0.0425743 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 90.2076 | + | 218.090i | 0.100566 | + | 0.243133i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 860.452 | + | 860.452i | 0.957122 | + | 0.957122i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −354.715 | − | 354.715i | −0.393690 | − | 0.393690i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −86.4392 | − | 208.979i | −0.0957245 | − | 0.231428i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1526.05 | 1.68624 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −216.816 | − | 216.816i | −0.239047 | − | 0.239047i | 0.577408 | − | 0.816456i | \(-0.304064\pi\) |
−0.816456 | + | 0.577408i | \(0.804064\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −462.558 | − | 0.464295i | −0.508864 | − | 0.000510776i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1193.35i | − | 1.30994i | −0.755657 | − | 0.654968i | \(-0.772682\pi\) | ||
0.755657 | − | 0.654968i | \(-0.227318\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 97.7324 | 0.107045 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 329.988 | + | 136.880i | 0.360643 | + | 0.149595i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −420.008 | + | 420.008i | −0.458024 | + | 0.458024i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 345.202i | 0.375628i | 0.982205 | + | 0.187814i | \(0.0601402\pi\) | ||||
−0.982205 | + | 0.187814i | \(0.939860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 661.947 | + | 1600.35i | 0.718727 | + | 1.73763i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −183.080 | + | 183.080i | −0.198353 | + | 0.198353i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 386.781 | − | 386.781i | 0.418141 | − | 0.418141i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −557.517 | + | 556.399i | −0.601421 | + | 0.600215i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1417.53i | − | 1.52587i | −0.646475 | − | 0.762935i | \(-0.723758\pi\) | ||
0.646475 | − | 0.762935i | \(-0.276242\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 109.868 | − | 109.868i | 0.118011 | − | 0.118011i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 414.908 | − | 1000.26i | 0.444704 | − | 1.07209i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 54.9578 | 0.0587784 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 182.650i | − | 0.194931i | −0.995239 | − | 0.0974656i | \(-0.968926\pi\) | ||
0.995239 | − | 0.0974656i | \(-0.0310736\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −204.842 | − | 84.9687i | −0.218149 | − | 0.0904885i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 524.733 | + | 524.733i | 0.557634 | + | 0.557634i | 0.928633 | − | 0.371000i | \(-0.120985\pi\) |
−0.371000 | + | 0.928633i | \(0.620985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −501.258 | −0.531556 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1246.94 | − | 518.699i | −1.31951 | − | 0.548888i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −278.292 | − | 278.292i | −0.293867 | − | 0.293867i | 0.544739 | − | 0.838606i | \(-0.316629\pi\) |
−0.838606 | + | 0.544739i | \(0.816629\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 400.578 | + | 400.578i | 0.422105 | + | 0.422105i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 677.108 | − | 280.069i | 0.711996 | − | 0.294500i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 545.447 | 0.572348 | 0.286174 | − | 0.958178i | \(-0.407617\pi\) | ||||
0.286174 | + | 0.958178i | \(0.407617\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 330.845 | + | 330.845i | 0.346435 | + | 0.346435i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.9462 | − | 98.7128i | 0.0427860 | − | 0.103148i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1215.53i | − | 1.26750i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −342.761 | −0.356672 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1334.73 | − | 1.33974i | −1.38601 | − | 0.00139122i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1761.48 | − | 1761.48i | 1.82537 | − | 1.82537i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 216.237i | 0.223616i | 0.993730 | + | 0.111808i | \(0.0356642\pi\) | ||||
−0.993730 | + | 0.111808i | \(0.964336\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −921.024 | + | 380.959i | −0.950489 | + | 0.393147i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −147.926 | + | 147.926i | −0.152344 | + | 0.152344i | −0.779164 | − | 0.626820i | \(-0.784356\pi\) |
0.626820 | + | 0.779164i | \(0.284356\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −699.968 | + | 699.968i | −0.719392 | + | 0.719392i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 591.557 | − | 244.683i | 0.606725 | − | 0.250957i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 553.321i | 0.566347i | 0.959069 | + | 0.283174i | \(0.0913873\pi\) | ||||
−0.959069 | + | 0.283174i | \(0.908613\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.0949 | − | 23.0949i | 0.0235903 | − | 0.0235903i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 97.2420 | + | 0.0976072i | 0.0991254 | + | 9.94977e-5i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1107.13 | −1.12628 | −0.563139 | − | 0.826362i | \(-0.690406\pi\) | ||||
−0.563139 | + | 0.826362i | \(0.690406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2370.88i | − | 2.40698i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 195.057 | − | 470.241i | 0.197626 | − | 0.476434i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 56.4932 | + | 56.4932i | 0.0571216 | + | 0.0571216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1635.60 | 1.65046 | 0.825228 | − | 0.564800i | \(-0.191047\pi\) | ||||
0.825228 | + | 0.564800i | \(0.191047\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1025.24 | − | 424.065i | 1.03247 | − | 0.427054i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1382.70 | − | 1382.70i | −1.38965 | − | 1.38965i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −152.140 | − | 152.140i | −0.152598 | − | 0.152598i | 0.626679 | − | 0.779277i | \(-0.284414\pi\) |
−0.779277 | + | 0.626679i | \(0.784414\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −644.323 | − | 268.025i | −0.644968 | − | 0.268293i |
(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 | 384.3.i.c.353.7 | 20 | ||
3.2 | odd | 2 | inner | 384.3.i.c.353.10 | 20 | ||
4.3 | odd | 2 | 384.3.i.d.353.4 | 20 | |||
8.3 | odd | 2 | 48.3.i.b.5.4 | ✓ | 20 | ||
8.5 | even | 2 | 192.3.i.b.113.4 | 20 | |||
12.11 | even | 2 | 384.3.i.d.353.1 | 20 | |||
16.3 | odd | 4 | 384.3.i.d.161.1 | 20 | |||
16.5 | even | 4 | 192.3.i.b.17.1 | 20 | |||
16.11 | odd | 4 | 48.3.i.b.29.7 | yes | 20 | ||
16.13 | even | 4 | inner | 384.3.i.c.161.10 | 20 | ||
24.5 | odd | 2 | 192.3.i.b.113.1 | 20 | |||
24.11 | even | 2 | 48.3.i.b.5.7 | yes | 20 | ||
48.5 | odd | 4 | 192.3.i.b.17.4 | 20 | |||
48.11 | even | 4 | 48.3.i.b.29.4 | yes | 20 | ||
48.29 | odd | 4 | inner | 384.3.i.c.161.7 | 20 | ||
48.35 | even | 4 | 384.3.i.d.161.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.4 | ✓ | 20 | 8.3 | odd | 2 | ||
48.3.i.b.5.7 | yes | 20 | 24.11 | even | 2 | ||
48.3.i.b.29.4 | yes | 20 | 48.11 | even | 4 | ||
48.3.i.b.29.7 | yes | 20 | 16.11 | odd | 4 | ||
192.3.i.b.17.1 | 20 | 16.5 | even | 4 | |||
192.3.i.b.17.4 | 20 | 48.5 | odd | 4 | |||
192.3.i.b.113.1 | 20 | 24.5 | odd | 2 | |||
192.3.i.b.113.4 | 20 | 8.5 | even | 2 | |||
384.3.i.c.161.7 | 20 | 48.29 | odd | 4 | inner | ||
384.3.i.c.161.10 | 20 | 16.13 | even | 4 | inner | ||
384.3.i.c.353.7 | 20 | 1.1 | even | 1 | trivial | ||
384.3.i.c.353.10 | 20 | 3.2 | odd | 2 | inner | ||
384.3.i.d.161.1 | 20 | 16.3 | odd | 4 | |||
384.3.i.d.161.4 | 20 | 48.35 | even | 4 | |||
384.3.i.d.353.1 | 20 | 12.11 | even | 2 | |||
384.3.i.d.353.4 | 20 | 4.3 | odd | 2 |