Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,3,Mod(17,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, 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("192.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.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: | \(5.23162107572\) |
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 | 17.1 | ||
Root | \(-1.21144 + 1.59136i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.17 |
Dual form | 192.3.i.b.113.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −2.77106 | − | 1.14944i | −0.923687 | − | 0.383147i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.80434 | − | 4.80434i | −0.960868 | − | 0.960868i | 0.0383950 | − | 0.999263i | \(-0.487775\pi\) |
−0.999263 | + | 0.0383950i | \(0.987775\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.36187i | 1.05170i | 0.850579 | + | 0.525848i | \(0.176252\pi\) | ||||
−0.850579 | + | 0.525848i | \(0.823748\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.35757 | + | 6.37035i | 0.706397 | + | 0.707816i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.514693 | − | 0.514693i | −0.0467903 | − | 0.0467903i | 0.683325 | − | 0.730115i | \(-0.260533\pi\) |
−0.730115 | + | 0.683325i | \(0.760533\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.12969 | + | 7.12969i | 0.548438 | + | 0.548438i | 0.925989 | − | 0.377551i | \(-0.123234\pi\) |
−0.377551 | + | 0.925989i | \(0.623234\pi\) | |||||||
\(14\) | 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 | 0.992791 | + | 0.119858i | \(0.0382440\pi\) |
0.119858 | + | 0.992791i | \(0.461756\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.46203 | − | 20.4002i | 0.402954 | − | 0.971438i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.80231 | −0.339231 | −0.169615 | − | 0.985510i | \(-0.554253\pi\) | ||||
−0.169615 | + | 0.985510i | \(0.554253\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.1633i | 0.846533i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10.2949 | − | 24.9603i | −0.381292 | − | 0.924455i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −34.6058 | + | 34.6058i | −1.19330 | + | 1.19330i | −0.217169 | + | 0.976134i | \(0.569682\pi\) |
−0.976134 | + | 0.217169i | \(0.930318\pi\) | |||||||
\(30\) | 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 | \(-0.863571\pi\) |
0.415601 | + | 0.909547i | \(0.363571\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.5617 | − | 27.9520i | −0.296453 | − | 0.716717i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 64.2448 | 1.56695 | 0.783473 | − | 0.621426i | \(-0.213446\pi\) | ||||
0.783473 | + | 0.621426i | \(0.213446\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.24058 | + | 7.24058i | −0.168386 | + | 0.168386i | −0.786269 | − | 0.617884i | \(-0.787990\pi\) |
0.617884 | + | 0.786269i | \(0.287990\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0613789 | − | 61.1492i | 0.00136398 | − | 1.35887i | ||||
\(46\) | 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 | ||||||||
\(51\) | 12.7733 | − | 30.7938i | 0.250457 | − | 0.603800i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −31.9199 | − | 31.9199i | −0.602263 | − | 0.602263i | 0.338650 | − | 0.940913i | \(-0.390030\pi\) |
−0.940913 | + | 0.338650i | \(0.890030\pi\) | |||||||
\(54\) | 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 | 0.840530 | − | 0.541764i | \(-0.182244\pi\) |
−0.541764 | + | 0.840530i | \(0.682244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3933 | − | 12.3933i | −0.203170 | − | 0.203170i | 0.598187 | − | 0.801357i | \(-0.295888\pi\) |
−0.801357 | + | 0.598187i | \(0.795888\pi\) | |||||||
\(62\) | 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 | \(-0.392973\pi\) |
−0.944003 | + | 0.329936i | \(0.892973\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.6207 | + | 8.96830i | 0.313343 | + | 0.129975i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −25.6785 | −0.361669 | −0.180834 | − | 0.983514i | \(-0.557880\pi\) | ||||
−0.180834 | + | 0.983514i | \(0.557880\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 56.1845i | 0.769650i | 0.922990 | + | 0.384825i | \(0.125738\pi\) | ||||
−0.922990 | + | 0.384825i | \(0.874262\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 24.3260 | − | 58.6449i | 0.324347 | − | 0.781932i | ||||
\(76\) | 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 | −0.156151 | + | 0.987733i | \(0.549909\pi\) |
−0.987733 | + | 0.156151i | \(0.950091\pi\) | |||||||
\(84\) | 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 | \(-0.418883\pi\) | ||||
0.252086 | + | 0.967705i | \(0.418883\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −52.4878 | + | 52.4878i | −0.576789 | + | 0.576789i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 68.9008 | + | 28.5802i | 0.740869 | + | 0.307314i | ||||
\(94\) | 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 | ||||||||
\(99\) | 0.00657558 | − | 6.55097i | 6.64200e−5 | − | 0.0661714i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 36.3420 | + | 36.3420i | 0.359822 | + | 0.359822i | 0.863747 | − | 0.503925i | \(-0.168111\pi\) |
−0.503925 | + | 0.863747i | \(0.668111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 87.5176i | 0.849685i | 0.905267 | + | 0.424843i | \(0.139671\pi\) | ||||
−0.905267 | + | 0.424843i | \(0.860329\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −138.664 | + | 57.3550i | −1.32061 | + | 0.546238i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 104.866 | + | 104.866i | 0.980058 | + | 0.980058i | 0.999805 | − | 0.0197471i | \(-0.00628610\pi\) |
−0.0197471 | + | 0.999805i | \(0.506286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.64006 | + | 7.64006i | 0.0700923 | + | 0.0700923i | 0.741284 | − | 0.671192i | \(-0.234217\pi\) |
−0.671192 | + | 0.741284i | \(0.734217\pi\) | |||||||
\(110\) | 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 | ||||||||
\(117\) | −0.0910869 | + | 90.7461i | −0.000778521 | + | 0.775607i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −81.8098 | −0.687477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 120.470i | − | 0.995621i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −178.026 | − | 73.8456i | −1.44737 | − | 0.600371i | ||||
\(124\) | 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 | −0.890498 | − | 0.454988i | \(-0.849644\pi\) |
0.454988 | + | 0.890498i | \(0.349644\pi\) | |||||||
\(132\) | 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 | \(-0.705868\pi\) | ||||
−0.602599 | + | 0.798045i | \(0.705868\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 95.0802 | − | 95.0802i | 0.684030 | − | 0.684030i | −0.276875 | − | 0.960906i | \(-0.589299\pi\) |
0.960906 | + | 0.276875i | \(0.0892990\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.4955 | − | 63.8752i | 0.187912 | − | 0.453015i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 7.33920i | − | 0.0513231i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 332.516 | 2.29321 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.4015 | + | 5.97376i | 0.0979693 | + | 0.0406378i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 131.077 | + | 131.077i | 0.879709 | + | 0.879709i | 0.993504 | − | 0.113795i | \(-0.0363006\pi\) |
−0.113795 | + | 0.993504i | \(0.536301\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 123.070i | − | 0.815031i | −0.913198 | − | 0.407515i | \(-0.866395\pi\) | ||
0.913198 | − | 0.407515i | \(-0.133605\pi\) | |||||||
\(152\) | 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 | \(-0.0343430\pi\) |
−0.107683 | + | 0.994185i | \(0.534343\pi\) | |||||||
\(158\) | 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 | \(-0.222444\pi\) |
−0.643320 | + | 0.765597i | \(0.722444\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.68458 | − | 13.7043i | 0.0344520 | − | 0.0830566i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 60.3220 | 0.361210 | 0.180605 | − | 0.983556i | \(-0.442194\pi\) | ||||
0.180605 | + | 0.983556i | \(0.442194\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 67.3351i | − | 0.398432i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.270083 | + | 269.072i | −0.00157943 | + | 1.57352i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −74.8292 | + | 74.8292i | −0.432539 | + | 0.432539i | −0.889491 | − | 0.456952i | \(-0.848941\pi\) |
0.456952 | + | 0.889491i | \(0.348941\pi\) | |||||||
\(174\) | 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 | −0.695943 | − | 0.718097i | \(-0.745013\pi\) |
0.718097 | + | 0.695943i | \(0.245013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 158.820 | − | 158.820i | 0.877457 | − | 0.877457i | −0.115814 | − | 0.993271i | \(-0.536948\pi\) |
0.993271 | + | 0.115814i | \(0.0369475\pi\) | |||||||
\(182\) | 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 | ||||||||
\(189\) | 183.754 | − | 75.7896i | 0.972245 | − | 0.401003i | ||||
\(190\) | 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 | ||||||||
\(195\) | −78.7446 | + | 189.837i | −0.403819 | + | 0.973522i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −246.744 | − | 246.744i | −1.25251 | − | 1.25251i | −0.954593 | − | 0.297912i | \(-0.903710\pi\) |
−0.297912 | − | 0.954593i | \(-0.596290\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 287.802i | − | 1.44624i | −0.690722 | − | 0.723120i | \(-0.742707\pi\) | ||
0.690722 | − | 0.723120i | \(-0.257293\pi\) | |||||||
\(200\) | 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 | \(-0.425291\pi\) |
−0.972583 | + | 0.232556i | \(0.925291\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 71.1567 | + | 29.5159i | 0.334069 | + | 0.138572i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 69.5724 | 0.323593 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 183.048i | − | 0.843541i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 64.5807 | − | 155.691i | 0.294889 | − | 0.710916i | ||||
\(220\) | 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 | 0.415186 | − | 0.909737i | \(-0.363717\pi\) |
0.909737 | − | 0.415186i | \(-0.136283\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 65.7088 | − | 65.7088i | 0.286938 | − | 0.286938i | −0.548930 | − | 0.835868i | \(-0.684965\pi\) |
0.835868 | + | 0.548930i | \(0.184965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.8552 | + | 6.14449i | −0.0643082 | + | 0.0265995i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 42.8218 | 0.183785 | 0.0918923 | − | 0.995769i | \(-0.470708\pi\) | ||||
0.0918923 | + | 0.995769i | \(0.470708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 110.744 | − | 110.744i | 0.471250 | − | 0.471250i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −98.9305 | − | 41.0365i | −0.417428 | − | 0.173150i | ||||
\(238\) | 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 | ||||||||
\(243\) | 93.5551 | − | 224.269i | 0.385001 | − | 0.922916i | ||||
\(244\) | 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 | 0.740990 | − | 0.671516i | \(-0.234356\pi\) |
−0.671516 | + | 0.740990i | \(0.734356\pi\) | |||||||
\(252\) | 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 | ||||||||
\(261\) | −440.460 | − | 0.442114i | −1.68758 | − | 0.00169392i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 98.0863 | 0.372952 | 0.186476 | − | 0.982460i | \(-0.440293\pi\) | ||||
0.186476 | + | 0.982460i | \(0.440293\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 306.708i | 1.15739i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −124.341 | − | 51.5769i | −0.465697 | − | 0.193172i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 126.560 | − | 126.560i | 0.470482 | − | 0.470482i | −0.431589 | − | 0.902070i | \(-0.642047\pi\) |
0.902070 | + | 0.431589i | \(0.142047\pi\) | |||||||
\(270\) | 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 | \(-0.594898\pi\) |
0.955887 | + | 0.293734i | \(0.0948980\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −158.077 | − | 158.395i | −0.566585 | − | 0.567723i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 109.143 | 0.388409 | 0.194204 | − | 0.980961i | \(-0.437787\pi\) | ||||
0.194204 | + | 0.980961i | \(0.437787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −60.4623 | + | 60.4623i | −0.213648 | + | 0.213648i | −0.805815 | − | 0.592167i | \(-0.798272\pi\) |
0.592167 | + | 0.805815i | \(0.298272\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −233.487 | + | 562.888i | −0.819252 | + | 1.97504i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 472.962i | 1.64795i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 165.509 | 0.572697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 228.235 | + | 94.6721i | 0.784311 | + | 0.325334i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.4639 | − | 19.4639i | −0.0664296 | − | 0.0664296i | 0.673111 | − | 0.739541i | \(-0.264957\pi\) |
−0.739541 | + | 0.673111i | \(0.764957\pi\) | |||||||
\(294\) | 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 | 0.905677 | + | 0.423967i | \(0.139363\pi\) |
0.423967 | + | 0.905677i | \(0.360637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 100.596 | − | 242.517i | 0.325554 | − | 0.784844i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −360.965 | −1.16066 | −0.580330 | − | 0.814381i | \(-0.697076\pi\) | ||||
−0.580330 | + | 0.814381i | \(0.697076\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 73.9217i | 0.236172i | 0.993003 | + | 0.118086i | \(0.0376758\pi\) | ||||
−0.993003 | + | 0.118086i | \(0.962324\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 450.172 | + | 0.451863i | 1.42912 | + | 0.00143449i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 172.709 | − | 172.709i | 0.544825 | − | 0.544825i | −0.380115 | − | 0.924939i | \(-0.624116\pi\) |
0.924939 | + | 0.380115i | \(0.124116\pi\) | |||||||
\(318\) | 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 | \(-0.938681\pi\) |
0.191451 | + | 0.981502i | \(0.438681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −232.615 | − | 0.233489i | −0.698544 | − | 0.000701168i | ||||
\(334\) | 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 | ||||||||
\(339\) | −15.0890 | + | 36.3765i | −0.0445104 | + | 0.107305i | ||||
\(340\) | 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 | 0.411021 | − | 0.911626i | \(-0.365172\pi\) |
−0.911626 | + | 0.411021i | \(0.865172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 387.899 | + | 387.899i | 1.11146 | + | 1.11146i | 0.992953 | + | 0.118506i | \(0.0378106\pi\) |
0.118506 | + | 0.992953i | \(0.462189\pi\) | |||||||
\(350\) | 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 | ||||||||
\(357\) | 226.700 | + | 94.0355i | 0.635014 | + | 0.263405i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 240.896 | 0.671020 | 0.335510 | − | 0.942037i | \(-0.391091\pi\) | ||||
0.335510 | + | 0.942037i | \(0.391091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 532.827i | 1.47598i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −138.473 | + | 333.830i | −0.381469 | + | 0.919643i | ||||
\(364\) | 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 | \(-0.987865\pi\) |
0.0381137 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(374\) | 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 | \(-0.665291\pi\) |
0.868178 | + | 0.496253i | \(0.165291\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −244.604 | − | 101.462i | −0.642004 | − | 0.266305i | ||||
\(382\) | 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 | ||||||||
\(387\) | −92.1575 | − | 0.0925037i | −0.238133 | − | 0.000239028i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 265.362 | + | 265.362i | 0.682165 | + | 0.682165i | 0.960488 | − | 0.278322i | \(-0.0897783\pi\) |
−0.278322 | + | 0.960488i | \(0.589778\pi\) | |||||||
\(390\) | 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 | \(-0.0973004\pi\) |
−0.300940 | + | 0.953643i | \(0.597300\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 389.932 | − | 388.369i | 0.962795 | − | 0.958937i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.8131 | 0.0462237 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 530.421i | − | 1.29687i | −0.761269 | − | 0.648437i | \(-0.775423\pi\) | ||
0.761269 | − | 0.648437i | \(-0.224577\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 457.536 | + | 189.787i | 1.11323 | + | 0.461768i | ||||
\(412\) | 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 | −0.999393 | − | 0.0348367i | \(-0.988909\pi\) |
0.0348367 | + | 0.999393i | \(0.488909\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −264.630 | + | 264.630i | −0.628575 | + | 0.628575i | −0.947710 | − | 0.319134i | \(-0.896608\pi\) |
0.319134 | + | 0.947710i | \(0.396608\pi\) | |||||||
\(422\) | 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 | ||||||||
\(429\) | −8.43598 | + | 20.3374i | −0.0196643 | + | 0.0474065i | ||||
\(430\) | 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 | ||||||||
\(435\) | −921.422 | − | 382.207i | −2.11821 | − | 0.878638i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −164.943 | − | 164.943i | −0.377445 | − | 0.377445i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 565.007i | 1.28703i | 0.765433 | + | 0.643516i | \(0.222525\pi\) | ||||
−0.765433 | + | 0.643516i | \(0.777475\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.0409 | − | 33.1073i | −0.0749228 | − | 0.0750733i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −100.963 | − | 100.963i | −0.227907 | − | 0.227907i | 0.583911 | − | 0.811818i | \(-0.301522\pi\) |
−0.811818 | + | 0.583911i | \(0.801522\pi\) | |||||||
\(444\) | 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 | ||||||||
\(453\) | −141.461 | + | 341.034i | −0.312277 | + | 0.752833i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 504.339 | 1.10844 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 137.963i | − | 0.301888i | −0.988542 | − | 0.150944i | \(-0.951769\pi\) | ||
0.988542 | − | 0.150944i | \(-0.0482313\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 277.374 | − | 114.403i | 0.604302 | − | 0.249245i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 303.536 | − | 303.536i | 0.658430 | − | 0.658430i | −0.296579 | − | 0.955008i | \(-0.595846\pi\) |
0.955008 | + | 0.296579i | \(0.0958457\pi\) | |||||||
\(462\) | 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 | −0.773880 | − | 0.633333i | \(-0.781687\pi\) |
0.633333 | + | 0.773880i | \(0.281687\pi\) | |||||||
\(468\) | 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 | ||||||||
\(477\) | 0.407800 | − | 406.274i | 0.000854927 | − | 0.851728i | ||||
\(478\) | 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 | ||||||||
\(483\) | −66.0234 | + | 159.169i | −0.136694 | + | 0.329542i | ||||
\(484\) | 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 | \(1.53771e-5\pi\) | |||||
−1.00000 | 4.83086e-5i | \(0.999985\pi\) | ||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.3206 | − | 78.1398i | −0.0660954 | − | 0.159795i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 273.442 | + | 273.442i | 0.556908 | + | 0.556908i | 0.928426 | − | 0.371518i | \(-0.121163\pi\) |
−0.371518 | + | 0.928426i | \(0.621163\pi\) | |||||||
\(492\) | 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 | \(-0.229117\pi\) |
−0.659229 | + | 0.751942i | \(0.729117\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −167.156 | − | 69.3366i | −0.333645 | − | 0.138396i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 864.426 | 1.71854 | 0.859270 | − | 0.511522i | \(-0.170918\pi\) | ||||
0.859270 | + | 0.511522i | \(0.170918\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 349.198i | − | 0.691482i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −77.3977 | + | 186.590i | −0.152658 | + | 0.368027i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 171.041 | − | 171.041i | 0.336033 | − | 0.336033i | −0.518839 | − | 0.854872i | \(-0.673635\pi\) |
0.854872 | + | 0.518839i | \(0.173635\pi\) | |||||||
\(510\) | 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 | \(-0.609548\pi\) | ||||
−0.337401 | + | 0.941361i | \(0.609548\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 287.638 | − | 287.638i | 0.549977 | − | 0.549977i | −0.376457 | − | 0.926434i | \(-0.622858\pi\) |
0.926434 | + | 0.376457i | \(0.122858\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 431.736 | + | 179.085i | 0.822354 | + | 0.341114i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 276.309i | − | 0.524306i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −468.124 | −0.884922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.225200 | + | 224.357i | −0.000424106 | + | 0.422519i | ||||
\(532\) | 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 | \(-0.0651021\pi\) |
−0.203102 | + | 0.979158i | \(0.565102\pi\) | |||||||
\(542\) | 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 | \(-0.483180\pi\) |
−0.998604 | + | 0.0528155i | \(0.983180\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.158334 | − | 157.742i | 0.000288404 | − | 0.287325i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1463.16 | −2.65546 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 262.828i | 0.475277i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −486.621 | − | 201.851i | −0.876794 | − | 0.363696i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.8976 | + | 31.8976i | −0.0572667 | + | 0.0572667i | −0.735160 | − | 0.677893i | \(-0.762893\pi\) |
0.677893 | + | 0.735160i | \(0.262893\pi\) | |||||||
\(558\) | 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 | −0.735740 | − | 0.677265i | \(-0.763165\pi\) |
0.677265 | + | 0.735740i | \(0.263165\pi\) | |||||||
\(564\) | 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 | \(-0.692524\pi\) | ||||
−0.568624 | + | 0.822597i | \(0.692524\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −451.861 | + | 451.861i | −0.791350 | + | 0.791350i | −0.981714 | − | 0.190363i | \(-0.939033\pi\) |
0.190363 | + | 0.981714i | \(0.439033\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −79.1550 | + | 190.826i | −0.138141 | + | 0.333030i | ||||
\(574\) | 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 | ||||||||
\(579\) | 1015.99 | + | 421.436i | 1.75474 | + | 0.727869i | ||||
\(580\) | 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 | 0.996027 | − | 0.0890534i | \(-0.0283842\pi\) |
−0.0890534 | + | 0.996027i | \(0.528384\pi\) | |||||||
\(588\) | 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 | ||||||||
\(597\) | −330.811 | + | 797.517i | −0.554123 | + | 1.33587i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 624.772 | 1.04303 | 0.521513 | − | 0.853244i | \(-0.325368\pi\) | ||||
0.521513 | + | 0.853244i | \(0.325368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 386.910i | 0.643777i | 0.946778 | + | 0.321889i | \(0.104318\pi\) | ||||
−0.946778 | + | 0.321889i | \(0.895682\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.525625 | − | 523.658i | 0.000871684 | − | 0.868422i | ||||
\(604\) | 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 | \(-0.602334\pi\) |
0.948765 | + | 0.315982i | \(0.102334\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 500.519 | + | 1210.08i | 0.813852 | + | 1.96761i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 882.945 | 1.43103 | 0.715514 | − | 0.698598i | \(-0.246192\pi\) | ||||
0.715514 | + | 0.698598i | \(0.246192\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 694.731 | − | 694.731i | 1.12234 | − | 1.12234i | 0.130955 | − | 0.991388i | \(-0.458196\pi\) |
0.991388 | − | 0.130955i | \(-0.0418043\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 80.3239 | + | 194.748i | 0.129346 | + | 0.313604i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 330.337i | 0.530235i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 706.197 | 1.12991 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.0136 | + | 60.3027i | −0.0398942 | + | 0.0961765i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −203.094 | − | 203.094i | −0.322885 | − | 0.322885i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 927.845i | 1.47044i | 0.677831 | + | 0.735218i | \(0.262920\pi\) | ||||
−0.677831 | + | 0.735218i | \(0.737080\pi\) | |||||||
\(632\) | 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 | \(-0.347582\pi\) |
−0.887532 | + | 0.460746i | \(0.847582\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −192.789 | − | 79.9694i | −0.298898 | − | 0.123984i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −747.683 | −1.15561 | −0.577807 | − | 0.816173i | \(-0.696092\pi\) | ||||
−0.577807 | + | 0.816173i | \(0.696092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18.1452i | − | 0.0279587i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −210.403 | + | 507.239i | −0.323200 | + | 0.779168i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −605.127 | + | 605.127i | −0.926688 | + | 0.926688i | −0.997490 | − | 0.0708022i | \(-0.977444\pi\) |
0.0708022 | + | 0.997490i | \(0.477444\pi\) | |||||||
\(654\) | 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 | −0.101418 | − | 0.994844i | \(-0.532338\pi\) |
0.994844 | + | 0.101418i | \(0.0323381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.60334 | − | 3.60334i | 0.00545135 | − | 0.00545135i | −0.704376 | − | 0.709827i | \(-0.748773\pi\) |
0.709827 | + | 0.704376i | \(0.248773\pi\) | |||||||
\(662\) | 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 | ||||||||
\(669\) | 125.529 | + | 52.0695i | 0.187636 | + | 0.0778319i | ||||
\(670\) | 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 | ||||||||
\(675\) | 528.242 | − | 217.874i | 0.782581 | − | 0.322776i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −150.713 | − | 150.713i | −0.222618 | − | 0.222618i | 0.586982 | − | 0.809600i | \(-0.300316\pi\) |
−0.809600 | + | 0.586982i | \(0.800316\pi\) | |||||||
\(678\) | 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 | 0.143536 | − | 0.989645i | \(-0.454153\pi\) |
−0.989645 | + | 0.143536i | \(0.954153\pi\) | |||||||
\(684\) | 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 | \(-0.0616737\pi\) |
−0.192544 | + | 0.981288i | \(0.561674\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 48.2274 | + | 0.0484085i | 0.0695922 | + | 6.98536e-5i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −913.595 | −1.31453 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 713.929i | 1.02429i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −118.662 | − | 49.2212i | −0.169760 | − | 0.0704165i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 413.745 | − | 413.745i | 0.590221 | − | 0.590221i | −0.347470 | − | 0.937691i | \(-0.612959\pi\) |
0.937691 | + | 0.347470i | \(0.112959\pi\) | |||||||
\(702\) | 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 | \(-0.575721\pi\) |
0.971839 | + | 0.235648i | \(0.0757212\pi\) | |||||||
\(710\) | 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 | ||||||||
\(717\) | 115.632 | − | 278.764i | 0.161272 | − | 0.388792i | ||||
\(718\) | 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 | ||||||||
\(723\) | 14.4972 | + | 6.01344i | 0.0200514 | + | 0.00831735i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −732.374 | − | 732.374i | −1.01017 | − | 1.01017i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 635.396i | − | 0.873998i | −0.899462 | − | 0.436999i | \(-0.856041\pi\) | ||
0.899462 | − | 0.436999i | \(-0.143959\pi\) | |||||||
\(728\) | 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 | \(-0.460788\pi\) |
−0.992422 | + | 0.122875i | \(0.960788\pi\) | |||||||
\(734\) | 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 | \(-0.374128\pi\) |
−0.922827 | + | 0.385214i | \(0.874128\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 346.497 | − | 835.331i | 0.467607 | − | 1.12730i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1160.78 | 1.56229 | 0.781145 | − | 0.624349i | \(-0.214636\pi\) | ||||
0.781145 | + | 0.624349i | \(0.214636\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1259.47i | − | 1.69057i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1208.42 | − | 1.21296i | −1.61770 | − | 0.00162377i | ||||
\(748\) | 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 | \(-0.689388\pi\) |
0.828159 | + | 0.560493i | \(0.189388\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.51210 | − | 15.7439i | −0.00857984 | − | 0.0207430i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 694.461 | 0.912563 | 0.456282 | − | 0.889835i | \(-0.349181\pi\) | ||||
0.456282 | + | 0.889835i | \(0.349181\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −56.2451 | + | 56.2451i | −0.0737157 | + | 0.0737157i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 679.529 | + | 0.682081i | 0.888273 | + | 0.000891610i | ||||
\(766\) | 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 | ||||||||
\(771\) | 395.035 | − | 952.347i | 0.512367 | − | 1.23521i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −142.479 | − | 142.479i | −0.184320 | − | 0.184320i | 0.608916 | − | 0.793235i | \(-0.291605\pi\) |
−0.793235 | + | 0.608916i | \(0.791605\pi\) | |||||||
\(774\) | 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 | \(-0.107150\pi\) |
−0.330301 | + | 0.943876i | \(0.607150\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −271.803 | − | 112.744i | −0.344491 | − | 0.142895i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 96.6413 | 0.122176 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 176.721i | − | 0.222852i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 352.543 | − | 849.908i | 0.443451 | − | 1.06907i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 552.965 | − | 552.965i | 0.693808 | − | 0.693808i | −0.269260 | − | 0.963068i | \(-0.586779\pi\) |
0.963068 | + | 0.269260i | \(0.0867791\pi\) | |||||||
\(798\) | 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 | \(-0.305028\pi\) | ||||
0.574932 | + | 0.818201i | \(0.305028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 611.506 | − | 611.506i | 0.754015 | − | 0.754015i | −0.221211 | − | 0.975226i | \(-0.571001\pi\) |
0.975226 | + | 0.221211i | \(0.0710010\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −572.188 | − | 237.345i | −0.703799 | − | 0.291937i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 191.511i | − | 0.234983i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −306.137 | −0.374708 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −668.061 | − | 0.670570i | −0.815703 | − | 0.000818767i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 963.577 | + | 963.577i | 1.17366 | + | 1.17366i | 0.981330 | + | 0.192334i | \(0.0616056\pi\) |
0.192334 | + | 0.981330i | \(0.438394\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1112.81i | 1.35214i | 0.736836 | + | 0.676071i | \(0.236319\pi\) | ||||
−0.736836 | + | 0.676071i | \(0.763681\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −42.7046 | + | 17.6637i | −0.0517631 | + | 0.0214105i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 600.156 | + | 600.156i | 0.725703 | + | 0.725703i | 0.969761 | − | 0.244058i | \(-0.0784786\pi\) |
−0.244058 | + | 0.969761i | \(0.578479\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −921.578 | − | 921.578i | −1.11167 | − | 1.11167i | −0.992924 | − | 0.118750i | \(-0.962111\pi\) |
−0.118750 | − | 0.992924i | \(-0.537889\pi\) | |||||||
\(830\) | 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 | ||||||||
\(837\) | 255.976 | + | 620.622i | 0.305826 | + | 0.741484i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1230.19 | −1.46625 | −0.733127 | − | 0.680091i | \(-0.761940\pi\) | ||||
−0.733127 | + | 0.680091i | \(0.761940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 1554.12i | − | 1.84794i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −302.442 | − | 125.453i | −0.358768 | − | 0.148818i | ||||
\(844\) | 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 | −0.239902 | + | 0.970797i | \(0.577115\pi\) |
−0.970797 | + | 0.239902i | \(0.922885\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1294.01 | − | 1291.42i | 1.51346 | − | 1.51043i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −609.799 | −0.711550 | −0.355775 | − | 0.934572i | \(-0.615783\pi\) | ||||
−0.355775 | + | 0.934572i | \(0.615783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −889.225 | + | 889.225i | −1.03519 | + | 1.03519i | −0.0358288 | + | 0.999358i | \(0.511407\pi\) |
−0.999358 | + | 0.0358288i | \(0.988593\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 543.642 | − | 1310.61i | 0.631407 | − | 1.52219i | ||||
\(862\) | 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 | ||||||||
\(867\) | −458.637 | − | 190.243i | −0.528993 | − | 0.219427i | ||||
\(868\) | 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 | \(-0.00841905\pi\) |
−0.0264461 | + | 0.999650i | \(0.508419\pi\) | |||||||
\(878\) | 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 | \(-0.322954\pi\) |
−0.849263 | + | 0.527970i | \(0.822954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −194.685 | + | 469.346i | −0.219983 | + | 0.530334i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −282.642 | −0.318650 | −0.159325 | − | 0.987226i | \(-0.550932\pi\) | ||||
−0.159325 | + | 0.987226i | \(0.550932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 649.838i | 0.730976i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41.7738 | − | 41.6064i | 0.0468841 | − | 0.0466963i | ||||
\(892\) | 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 | \(-0.695936\pi\) |
0.816456 | + | 0.577408i | \(0.195936\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.464295 | + | 462.558i | −0.000510776 | + | 0.508864i | ||||
\(910\) | 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 | ||||||||
\(915\) | 136.880 | − | 329.988i | 0.149595 | − | 0.360643i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −420.008 | − | 420.008i | −0.458024 | − | 0.458024i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 345.202i | − | 0.375628i | −0.982205 | − | 0.187814i | \(-0.939860\pi\) | ||
0.982205 | − | 0.187814i | \(-0.0601402\pi\) | |||||||
\(920\) | 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 | ||||||||
\(933\) | 1000.26 | + | 414.908i | 1.07209 | + | 0.444704i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −54.9578 | −0.0587784 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 182.650i | 0.194931i | 0.995239 | + | 0.0974656i | \(0.0310736\pi\) | ||||
−0.995239 | + | 0.0974656i | \(0.968926\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 84.9687 | − | 204.842i | 0.0904885 | − | 0.218149i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 524.733 | − | 524.733i | 0.557634 | − | 0.557634i | −0.371000 | − | 0.928633i | \(-0.620985\pi\) |
0.928633 | + | 0.371000i | \(0.120985\pi\) | |||||||
\(942\) | 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 | −0.838606 | − | 0.544739i | \(-0.816629\pi\) |
0.544739 | + | 0.838606i | \(0.316629\pi\) | |||||||
\(948\) | 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 | \(-0.592383\pi\) | ||||
−0.286174 | + | 0.958178i | \(0.592383\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −330.845 | + | 330.845i | −0.346435 | + | 0.346435i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −98.7128 | − | 40.9462i | −0.103148 | − | 0.0427860i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1215.53i | − | 1.26750i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −342.761 | −0.356672 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.33974 | + | 1334.73i | −0.00139122 | + | 1.38601i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1761.48 | + | 1761.48i | 1.82537 | + | 1.82537i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 216.237i | − | 0.223616i | −0.993730 | − | 0.111808i | \(-0.964336\pi\) | ||
0.993730 | − | 0.111808i | \(-0.0356642\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 921.024 | − | 380.959i | 0.950489 | − | 0.393147i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −147.926 | − | 147.926i | −0.152344 | − | 0.152344i | 0.626820 | − | 0.779164i | \(-0.284356\pi\) |
−0.779164 | + | 0.626820i | \(0.784356\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | −0.0976072 | + | 97.2420i | −9.94977e−5 | + | 0.0991254i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1107.13 | 1.12628 | 0.563139 | − | 0.826362i | \(-0.309594\pi\) | ||||
0.563139 | + | 0.826362i | \(0.309594\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2370.88i | 2.40698i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 470.241 | + | 195.057i | 0.476434 | + | 0.197626i | ||||
\(988\) | 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 | \(-0.715586\pi\) |
0.779277 | + | 0.626679i | \(0.215586\pi\) | |||||||
\(998\) | 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 | 192.3.i.b.17.1 | 20 | ||
3.2 | odd | 2 | inner | 192.3.i.b.17.4 | 20 | ||
4.3 | odd | 2 | 48.3.i.b.29.7 | yes | 20 | ||
8.3 | odd | 2 | 384.3.i.d.161.1 | 20 | |||
8.5 | even | 2 | 384.3.i.c.161.10 | 20 | |||
12.11 | even | 2 | 48.3.i.b.29.4 | yes | 20 | ||
16.3 | odd | 4 | 384.3.i.d.353.4 | 20 | |||
16.5 | even | 4 | inner | 192.3.i.b.113.4 | 20 | ||
16.11 | odd | 4 | 48.3.i.b.5.4 | ✓ | 20 | ||
16.13 | even | 4 | 384.3.i.c.353.7 | 20 | |||
24.5 | odd | 2 | 384.3.i.c.161.7 | 20 | |||
24.11 | even | 2 | 384.3.i.d.161.4 | 20 | |||
48.5 | odd | 4 | inner | 192.3.i.b.113.1 | 20 | ||
48.11 | even | 4 | 48.3.i.b.5.7 | yes | 20 | ||
48.29 | odd | 4 | 384.3.i.c.353.10 | 20 | |||
48.35 | even | 4 | 384.3.i.d.353.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.i.b.5.4 | ✓ | 20 | 16.11 | odd | 4 | ||
48.3.i.b.5.7 | yes | 20 | 48.11 | even | 4 | ||
48.3.i.b.29.4 | yes | 20 | 12.11 | even | 2 | ||
48.3.i.b.29.7 | yes | 20 | 4.3 | odd | 2 | ||
192.3.i.b.17.1 | 20 | 1.1 | even | 1 | trivial | ||
192.3.i.b.17.4 | 20 | 3.2 | odd | 2 | inner | ||
192.3.i.b.113.1 | 20 | 48.5 | odd | 4 | inner | ||
192.3.i.b.113.4 | 20 | 16.5 | even | 4 | inner | ||
384.3.i.c.161.7 | 20 | 24.5 | odd | 2 | |||
384.3.i.c.161.10 | 20 | 8.5 | even | 2 | |||
384.3.i.c.353.7 | 20 | 16.13 | even | 4 | |||
384.3.i.c.353.10 | 20 | 48.29 | odd | 4 | |||
384.3.i.d.161.1 | 20 | 8.3 | odd | 2 | |||
384.3.i.d.161.4 | 20 | 24.11 | even | 2 | |||
384.3.i.d.353.1 | 20 | 48.35 | even | 4 | |||
384.3.i.d.353.4 | 20 | 16.3 | odd | 4 |