Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,4,Mod(767,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.767");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.c (of order \(2\), degree \(1\), 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: | \(45.3134668844\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-26}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 26 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 767.2 | ||
Root | \(-5.09902i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.767 |
Dual form | 768.4.c.d.767.1 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | + | 5.09902i | −0.192450 | + | 0.981307i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 10.1980i | − | 0.912140i | −0.889944 | − | 0.456070i | \(-0.849257\pi\) | ||
0.889944 | − | 0.456070i | \(-0.150743\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.1980i | 0.550642i | 0.961352 | + | 0.275321i | \(0.0887842\pi\) | ||||
−0.961352 | + | 0.275321i | \(0.911216\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −25.0000 | − | 10.1980i | −0.925926 | − | 0.377705i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 46.0000 | 1.26087 | 0.630433 | − | 0.776244i | \(-0.282877\pi\) | ||||
0.630433 | + | 0.776244i | \(0.282877\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −44.0000 | −0.938723 | −0.469362 | − | 0.883006i | \(-0.655516\pi\) | ||||
−0.469362 | + | 0.883006i | \(0.655516\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 52.0000 | + | 10.1980i | 0.895089 | + | 0.175541i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 20.3961i | 0.290987i | 0.989359 | + | 0.145493i | \(0.0464770\pi\) | ||||
−0.989359 | + | 0.145493i | \(0.953523\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 10.1980i | − | 0.123136i | −0.998103 | − | 0.0615682i | \(-0.980390\pi\) | ||
0.998103 | − | 0.0615682i | \(-0.0196102\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −52.0000 | − | 10.1980i | −0.540349 | − | 0.105971i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −88.0000 | −0.797794 | −0.398897 | − | 0.916996i | \(-0.630607\pi\) | ||||
−0.398897 | + | 0.916996i | \(0.630607\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 21.0000 | 0.168000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 77.0000 | − | 117.277i | 0.548839 | − | 0.835928i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 254.951i | 1.63252i | 0.577682 | + | 0.816262i | \(0.303958\pi\) | ||||
−0.577682 | + | 0.816262i | \(0.696042\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 214.159i | − | 1.24078i | −0.784295 | − | 0.620388i | \(-0.786975\pi\) | ||
0.784295 | − | 0.620388i | \(-0.213025\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −46.0000 | + | 234.555i | −0.242654 | + | 1.23730i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 104.000 | 0.502263 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −332.000 | −1.47515 | −0.737574 | − | 0.675266i | \(-0.764029\pi\) | ||||
−0.737574 | + | 0.675266i | \(0.764029\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 44.0000 | − | 224.357i | 0.180657 | − | 0.921176i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 489.506i | − | 1.86458i | −0.361706 | − | 0.932292i | \(-0.617805\pi\) | ||
0.361706 | − | 0.932292i | \(-0.382195\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 234.555i | 0.831844i | 0.909400 | + | 0.415922i | \(0.136541\pi\) | ||||
−0.909400 | + | 0.415922i | \(0.863459\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −104.000 | + | 254.951i | −0.344520 | + | 0.844574i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −384.000 | −1.19175 | −0.595874 | − | 0.803078i | \(-0.703194\pi\) | ||||
−0.595874 | + | 0.803078i | \(0.703194\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 239.000 | 0.696793 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −104.000 | − | 20.3961i | −0.285547 | − | 0.0560004i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 458.912i | − | 1.18937i | −0.803960 | − | 0.594683i | \(-0.797278\pi\) | ||
0.803960 | − | 0.594683i | \(-0.202722\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 469.110i | − | 1.15009i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 52.0000 | + | 10.1980i | 0.120835 | + | 0.0236976i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −630.000 | −1.39015 | −0.695076 | − | 0.718936i | \(-0.744629\pi\) | ||||
−0.695076 | + | 0.718936i | \(0.744629\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −236.000 | −0.495356 | −0.247678 | − | 0.968842i | \(-0.579667\pi\) | ||||
−0.247678 | + | 0.968842i | \(0.579667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 104.000 | − | 254.951i | 0.207980 | − | 0.509854i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 448.714i | 0.856247i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 50.9902i | 0.0929768i | 0.998919 | + | 0.0464884i | \(0.0148030\pi\) | ||||
−0.998919 | + | 0.0464884i | \(0.985197\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 88.0000 | − | 448.714i | 0.153536 | − | 0.782881i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 680.000 | 1.13664 | 0.568318 | − | 0.822809i | \(-0.307594\pi\) | ||||
0.568318 | + | 0.822809i | \(0.307594\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −422.000 | −0.676594 | −0.338297 | − | 0.941039i | \(-0.609851\pi\) | ||||
−0.338297 | + | 0.941039i | \(0.609851\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −21.0000 | + | 107.079i | −0.0323316 | + | 0.164860i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 469.110i | 0.694286i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 744.457i | − | 1.06023i | −0.847927 | − | 0.530114i | \(-0.822149\pi\) | ||
0.847927 | − | 0.530114i | \(-0.177851\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 521.000 | + | 509.902i | 0.714678 | + | 0.699454i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 186.000 | 0.245978 | 0.122989 | − | 0.992408i | \(-0.460752\pi\) | ||||
0.122989 | + | 0.992408i | \(0.460752\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 208.000 | 0.265421 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1300.00 | − | 254.951i | −1.60201 | − | 0.314179i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 958.616i | − | 1.14172i | −0.821048 | − | 0.570860i | \(-0.806610\pi\) | ||
0.821048 | − | 0.570860i | \(-0.193390\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 448.714i | − | 0.516901i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1092.00 | + | 214.159i | 1.21758 | + | 0.238787i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −104.000 | −0.112318 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1062.00 | −1.11165 | −0.555824 | − | 0.831300i | \(-0.687597\pi\) | ||||
−0.555824 | + | 0.831300i | \(0.687597\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1150.00 | − | 469.110i | −1.16747 | − | 0.476235i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.1980i | − | 0.0100470i | −0.999987 | − | 0.00502348i | \(-0.998401\pi\) | ||
0.999987 | − | 0.00502348i | \(-0.00159903\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1988.62i | − | 1.90237i | −0.308618 | − | 0.951186i | \(-0.599867\pi\) | ||
0.308618 | − | 0.951186i | \(-0.400133\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −104.000 | + | 530.298i | −0.0966606 | + | 0.492874i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 234.000 | 0.211417 | 0.105709 | − | 0.994397i | \(-0.466289\pi\) | ||||
0.105709 | + | 0.994397i | \(0.466289\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 724.000 | 0.636208 | 0.318104 | − | 0.948056i | \(-0.396954\pi\) | ||||
0.318104 | + | 0.948056i | \(0.396954\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 332.000 | − | 1692.87i | 0.283892 | − | 1.44757i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1019.80i | − | 0.848983i | −0.905432 | − | 0.424492i | \(-0.860453\pi\) | ||
0.905432 | − | 0.424492i | \(-0.139547\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 897.427i | 0.727700i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1100.00 | + | 448.714i | 0.869188 | + | 0.354561i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −208.000 | −0.160230 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 785.000 | 0.589782 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2496.00 | + | 489.506i | 1.82973 | + | 0.358839i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1488.91i | − | 1.06538i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2253.77i | − | 1.57472i | −0.616493 | − | 0.787360i | \(-0.711447\pi\) | ||
0.616493 | − | 0.787360i | \(-0.288553\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1196.00 | − | 234.555i | −0.816294 | − | 0.160088i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1742.00 | 1.16183 | 0.580913 | − | 0.813966i | \(-0.302696\pi\) | ||||
0.580913 | + | 0.813966i | \(0.302696\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 104.000 | 0.0678041 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1196.00 | − | 785.249i | −0.762484 | − | 0.500618i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2406.74i | 1.50089i | 0.660935 | + | 0.750443i | \(0.270160\pi\) | ||||
−0.660935 | + | 0.750443i | \(0.729840\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 764.853i | − | 0.466719i | −0.972390 | − | 0.233360i | \(-0.925028\pi\) | ||
0.972390 | − | 0.233360i | \(-0.0749719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 384.000 | − | 1958.02i | 0.229352 | − | 1.16947i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2024.00 | −1.18360 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2600.00 | 1.48909 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −239.000 | + | 1218.67i | −0.134098 | + | 0.683768i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 479.308i | 0.263533i | 0.991281 | + | 0.131767i | \(0.0420649\pi\) | ||||
−0.991281 | + | 0.131767i | \(0.957935\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1499.11i | − | 0.807920i | −0.914777 | − | 0.403960i | \(-0.867633\pi\) | ||
0.914777 | − | 0.403960i | \(-0.132367\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 208.000 | − | 509.902i | 0.109907 | − | 0.269432i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2184.00 | −1.13176 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1948.00 | −0.990238 | −0.495119 | − | 0.868825i | \(-0.664875\pi\) | ||||
−0.495119 | + | 0.868825i | \(0.664875\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2340.00 | + | 458.912i | 1.16713 | + | 0.228894i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 897.427i | − | 0.439299i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3395.95i | − | 1.63185i | −0.578160 | − | 0.815924i | \(-0.696229\pi\) | ||
0.578160 | − | 0.815924i | \(-0.303771\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2392.00 | + | 469.110i | 1.12859 | + | 0.221334i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2008.00 | 0.930441 | 0.465221 | − | 0.885195i | \(-0.345975\pi\) | ||||
0.465221 | + | 0.885195i | \(0.345975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −261.000 | −0.118798 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −104.000 | + | 254.951i | −0.0465092 | + | 0.114015i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1213.57i | − | 0.533328i | −0.963790 | − | 0.266664i | \(-0.914079\pi\) | ||
0.963790 | − | 0.266664i | \(-0.0859214\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 214.159i | 0.0925079i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 630.000 | − | 3212.38i | 0.267535 | − | 1.36417i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2382.00 | 0.994632 | 0.497316 | − | 0.867570i | \(-0.334319\pi\) | ||||
0.497316 | + | 0.867570i | \(0.334319\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2652.00 | −1.08907 | −0.544535 | − | 0.838738i | \(-0.683294\pi\) | ||||
−0.544535 | + | 0.838738i | \(0.683294\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 236.000 | − | 1203.37i | 0.0953313 | − | 0.486096i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3385.75i | 1.34554i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 938.220i | 0.366895i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1196.00 | + | 785.249i | 0.460297 | + | 0.302214i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4784.00 | −1.81235 | −0.906173 | − | 0.422907i | \(-0.861010\pi\) | ||||
−0.906173 | + | 0.422907i | \(0.861010\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3074.00 | −1.14648 | −0.573242 | − | 0.819386i | \(-0.694314\pi\) | ||||
−0.573242 | + | 0.819386i | \(0.694314\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2288.00 | − | 448.714i | −0.840241 | − | 0.164785i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4844.07i | 1.75191i | 0.482396 | + | 0.875953i | \(0.339767\pi\) | ||||
−0.482396 | + | 0.875953i | \(0.660233\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1927.43i | 0.686592i | 0.939227 | + | 0.343296i | \(0.111543\pi\) | ||||
−0.939227 | + | 0.343296i | \(0.888457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −260.000 | − | 50.9902i | −0.0912387 | − | 0.0178934i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2600.00 | −0.898937 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4992.00 | −1.70076 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2200.00 | + | 897.427i | 0.738698 | + | 0.301331i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 469.110i | − | 0.155258i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3436.74i | 1.12130i | 0.828052 | + | 0.560651i | \(0.189449\pi\) | ||||
−0.828052 | + | 0.560651i | \(0.810551\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −680.000 | + | 3467.33i | −0.218746 | + | 1.11539i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2392.00 | 0.758758 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2184.00 | 0.683224 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 422.000 | − | 2151.79i | 0.130211 | − | 0.663946i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 897.427i | − | 0.273156i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1233.96i | − | 0.370548i | −0.982687 | − | 0.185274i | \(-0.940683\pi\) | ||
0.982687 | − | 0.185274i | \(-0.0593173\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −525.000 | − | 214.159i | −0.155556 | − | 0.0634545i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1270.00 | −0.371334 | −0.185667 | − | 0.982613i | \(-0.559445\pi\) | ||||
−0.185667 | + | 0.982613i | \(0.559445\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4556.00 | −1.31471 | −0.657356 | − | 0.753580i | \(-0.728325\pi\) | ||||
−0.657356 | + | 0.753580i | \(0.728325\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2392.00 | − | 469.110i | −0.681308 | − | 0.133615i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 877.031i | − | 0.246593i | −0.992370 | − | 0.123297i | \(-0.960653\pi\) | ||
0.992370 | − | 0.123297i | \(-0.0393467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3916.05i | 1.08704i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3796.00 | + | 744.457i | 1.04041 | + | 0.204041i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1920.00 | 0.519642 | 0.259821 | − | 0.965657i | \(-0.416336\pi\) | ||||
0.259821 | + | 0.965657i | \(0.416336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1618.00 | −0.432467 | −0.216233 | − | 0.976342i | \(-0.569377\pi\) | ||||
−0.216233 | + | 0.976342i | \(0.569377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3121.00 | + | 2146.69i | −0.823919 | + | 0.566708i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 2437.33i | − | 0.635573i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 448.714i | 0.115591i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −186.000 | + | 948.418i | −0.0473384 | + | 0.241380i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1586.00 | −0.398834 | −0.199417 | − | 0.979915i | \(-0.563905\pi\) | ||||
−0.199417 | + | 0.979915i | \(0.563905\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4048.00 | −1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −208.000 | + | 1060.60i | −0.0510803 | + | 0.260459i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3956.84i | 0.960392i | 0.877161 | + | 0.480196i | \(0.159435\pi\) | ||||
−0.877161 | + | 0.480196i | \(0.840565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3385.75i | − | 0.812279i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2600.00 | − | 6373.77i | 0.616613 | − | 1.51160i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4344.00 | −1.01849 | −0.509244 | − | 0.860622i | \(-0.670075\pi\) | ||||
−0.509244 | + | 0.860622i | \(0.670075\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4680.00 | −1.08487 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4888.00 | + | 958.616i | 1.12038 | + | 0.219724i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2743.27i | 0.621785i | 0.950445 | + | 0.310893i | \(0.100628\pi\) | ||||
−0.950445 | + | 0.310893i | \(0.899372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3253.17i | 0.729211i | 0.931162 | + | 0.364606i | \(0.118796\pi\) | ||||
−0.931162 | + | 0.364606i | \(0.881204\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2288.00 | + | 448.714i | 0.507238 | + | 0.0994776i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 966.000 | 0.211825 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4956.00 | −1.07501 | −0.537504 | − | 0.843261i | \(-0.680633\pi\) | ||||
−0.537504 | + | 0.843261i | \(0.680633\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2184.00 | + | 5353.97i | −0.468648 | + | 1.14887i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1978.42i | − | 0.420009i | −0.977700 | − | 0.210005i | \(-0.932652\pi\) | ||
0.977700 | − | 0.210005i | \(-0.0673479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7985.06i | − | 1.67725i | −0.544706 | − | 0.838627i | \(-0.683359\pi\) | ||
0.544706 | − | 0.838627i | \(-0.316641\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 104.000 | − | 530.298i | 0.0216155 | − | 0.110218i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4992.00 | 1.02672 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4497.00 | 0.915327 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1062.00 | − | 5415.16i | 0.213937 | − | 1.09087i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1845.85i | − | 0.368039i | −0.982923 | − | 0.184019i | \(-0.941089\pi\) | ||
0.982923 | − | 0.184019i | \(-0.0589110\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6424.76i | 1.26801i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3542.00 | − | 5394.76i | 0.692012 | − | 1.05399i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3872.00 | 0.748908 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2392.00 | −0.458048 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 52.0000 | + | 10.1980i | 0.00985915 | + | 0.00193354i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2406.74i | 0.451834i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8291.01i | 1.54134i | 0.637232 | + | 0.770672i | \(0.280079\pi\) | ||||
−0.637232 | + | 0.770672i | \(0.719921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10140.0 | + | 1988.62i | 1.86681 | + | 0.366112i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10104.0 | 1.84227 | 0.921134 | − | 0.389246i | \(-0.127264\pi\) | ||||
0.921134 | + | 0.389246i | \(0.127264\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1198.00 | −0.216342 | −0.108171 | − | 0.994132i | \(-0.534499\pi\) | ||||
−0.108171 | + | 0.994132i | \(0.534499\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2600.00 | − | 1060.60i | −0.465058 | − | 0.189707i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5027.63i | 0.890789i | 0.895335 | + | 0.445394i | \(0.146937\pi\) | ||||
−0.895335 | + | 0.445394i | \(0.853063\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11727.7i | 2.05839i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −234.000 | + | 1193.17i | −0.0406872 | + | 0.207465i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 208.000 | 0.0358311 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −924.000 | −0.157706 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −724.000 | + | 3691.69i | −0.122438 | + | 0.624315i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3916.05i | − | 0.656227i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6129.02i | 1.01777i | 0.860835 | + | 0.508884i | \(0.169942\pi\) | ||||
−0.860835 | + | 0.508884i | \(0.830058\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8300.00 | + | 3385.75i | 1.36588 | + | 0.557171i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 520.000 | 0.0848079 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 390.000 | 0.0630405 | 0.0315203 | − | 0.999503i | \(-0.489965\pi\) | ||||
0.0315203 | + | 0.999503i | \(0.489965\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5200.00 | + | 1019.80i | 0.833113 | + | 0.163387i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 9851.31i | − | 1.56445i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5935.26i | 0.934326i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4576.00 | − | 897.427i | −0.714097 | − | 0.140046i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4366.00 | 0.675444 | 0.337722 | − | 0.941246i | \(-0.390344\pi\) | ||||
0.337722 | + | 0.941246i | \(0.390344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5492.00 | 0.842350 | 0.421175 | − | 0.906979i | \(-0.361618\pi\) | ||||
0.421175 | + | 0.906979i | \(0.361618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3388.00 | + | 5160.21i | −0.515208 | + | 0.784705i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 81.5843i | − | 0.0123011i | −0.999981 | − | 0.00615056i | \(-0.998042\pi\) | ||
0.999981 | − | 0.00615056i | \(-0.00195780\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 6934.67i | − | 1.03677i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 208.000 | − | 1060.60i | 0.0308362 | − | 0.157234i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2216.00 | 0.325783 | 0.162891 | − | 0.986644i | \(-0.447918\pi\) | ||||
0.162891 | + | 0.986644i | \(0.447918\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6755.00 | 0.984837 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −785.000 | + | 4002.73i | −0.113504 | + | 0.578757i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4303.57i | 0.617149i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7128.43i | 1.01390i | 0.861976 | + | 0.506950i | \(0.169227\pi\) | ||||
−0.861976 | + | 0.506950i | \(0.830773\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4992.00 | + | 12237.6i | −0.704263 | + | 1.72647i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4680.00 | 0.654915 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2028.00 | −0.281517 | −0.140759 | − | 0.990044i | \(-0.544954\pi\) | ||||
−0.140759 | + | 0.990044i | \(0.544954\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7592.00 | + | 1488.91i | 1.04546 | + | 0.205032i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 11217.8i | − | 1.53249i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1315.55i | − | 0.178298i | −0.996018 | − | 0.0891492i | \(-0.971585\pi\) | ||
0.996018 | − | 0.0891492i | \(-0.0284148\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11492.0 | + | 2253.77i | 1.54528 | + | 0.303055i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2128.00 | −0.283905 | −0.141953 | − | 0.989873i | \(-0.545338\pi\) | ||||
−0.141953 | + | 0.989873i | \(0.545338\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4784.00 | 0.633286 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2392.00 | − | 5863.87i | 0.314192 | − | 0.770226i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 1927.43i | − | 0.251220i | −0.992080 | − | 0.125610i | \(-0.959911\pi\) | ||
0.992080 | − | 0.125610i | \(-0.0400888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1794.85i | − | 0.232148i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1742.00 | + | 8882.49i | −0.223594 | + | 1.14011i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7592.00 | −0.967076 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6220.00 | −0.786330 | −0.393165 | − | 0.919468i | \(-0.628620\pi\) | ||||
−0.393165 | + | 0.919468i | \(0.628620\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −104.000 | + | 530.298i | −0.0130489 | + | 0.0665366i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1937.63i | 0.241298i | 0.992695 | + | 0.120649i | \(0.0384976\pi\) | ||||
−0.992695 | + | 0.120649i | \(0.961502\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9422.99i | 1.16475i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5200.00 | − | 5313.18i | 0.638000 | − | 0.651886i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15272.0 | −1.85996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1270.00 | 0.153539 | 0.0767695 | − | 0.997049i | \(-0.475539\pi\) | ||||
0.0767695 | + | 0.997049i | \(0.475539\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12272.0 | − | 2406.74i | −1.47283 | − | 0.288846i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6424.76i | − | 0.765477i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1896.84i | − | 0.224366i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3900.00 | + | 764.853i | 0.457995 | + | 0.0898202i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9126.00 | −1.06404 | −0.532022 | − | 0.846731i | \(-0.678568\pi\) | ||||
−0.532022 | + | 0.846731i | \(0.678568\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3436.00 | −0.397768 | −0.198884 | − | 0.980023i | \(-0.563732\pi\) | ||||
−0.198884 | + | 0.980023i | \(0.563732\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9600.00 | + | 3916.05i | 1.10347 | + | 0.450129i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 428.318i | 0.0488858i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2406.74i | − | 0.272764i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2024.00 | − | 10320.4i | 0.227785 | − | 1.16148i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1920.00 | 0.214578 | 0.107289 | − | 0.994228i | \(-0.465783\pi\) | ||||
0.107289 | + | 0.994228i | \(0.465783\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15766.0 | −1.74981 | −0.874903 | − | 0.484299i | \(-0.839075\pi\) | ||||
−0.874903 | + | 0.484299i | \(0.839075\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2600.00 | + | 13257.5i | −0.286576 | + | 1.46126i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 897.427i | 0.0982375i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7311.99i | 0.794949i | 0.917613 | + | 0.397474i | \(0.130113\pi\) | ||||
−0.917613 | + | 0.397474i | \(0.869887\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5975.00 | − | 2437.33i | −0.645179 | − | 0.263182i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8190.00 | 0.878372 | 0.439186 | − | 0.898396i | \(-0.355267\pi\) | ||||
0.439186 | + | 0.898396i | \(0.355267\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9776.00 | −1.04141 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2444.00 | − | 479.308i | −0.258607 | − | 0.0507170i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 13767.4i | − | 1.44704i | −0.690303 | − | 0.723521i | \(-0.742523\pi\) | ||
0.690303 | − | 0.723521i | \(-0.257477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 22517.3i | − | 2.35099i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7644.00 | + | 1499.11i | 0.792818 | + | 0.155484i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4576.00 | −0.471486 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10682.0 | −1.09340 | −0.546699 | − | 0.837329i | \(-0.684116\pi\) | ||||
−0.546699 | + | 0.837329i | \(0.684116\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2392.00 | + | 1570.50i | 0.243244 | + | 0.159705i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3090.01i | − | 0.312182i | −0.987743 | − | 0.156091i | \(-0.950111\pi\) | ||
0.987743 | − | 0.156091i | \(-0.0498893\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2661.69i | − | 0.267169i | −0.991037 | − | 0.133584i | \(-0.957351\pi\) | ||
0.991037 | − | 0.133584i | \(-0.0426487\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2184.00 | − | 11136.3i | 0.217808 | − | 1.11061i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12246.0 | −1.21344 | −0.606721 | − | 0.794915i | \(-0.707515\pi\) | ||||
−0.606721 | + | 0.794915i | \(0.707515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −520.000 | −0.0511969 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1948.00 | − | 9932.89i | 0.190571 | − | 0.971727i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10789.5i | 1.04884i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 214.159i | − | 0.0206869i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4680.00 | + | 11472.8i | −0.449230 | + | 1.10126i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15008.0 | 1.43159 | 0.715796 | − | 0.698309i | \(-0.246064\pi\) | ||||
0.715796 | + | 0.698309i | \(0.246064\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14608.0 | 1.38476 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4576.00 | + | 897.427i | 0.431087 | + | 0.0845432i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10830.3i | 1.01398i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5721.10i | 0.532336i | 0.963927 | + | 0.266168i | \(0.0857576\pi\) | ||||
−0.963927 | + | 0.266168i | \(0.914242\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17316.0 | + | 3395.95i | 1.60134 | + | 0.314049i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5018.00 | 0.461220 | 0.230610 | − | 0.973046i | \(-0.425928\pi\) | ||||
0.230610 | + | 0.973046i | \(0.425928\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5200.00 | −0.475043 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4784.00 | + | 11727.7i | −0.434394 | + | 1.06489i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6934.67i | 0.625880i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16082.3i | 1.44277i | 0.692533 | + | 0.721386i | \(0.256494\pi\) | ||||
−0.692533 | + | 0.721386i | \(0.743506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2008.00 | + | 10238.8i | −0.179064 | + | 0.913048i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10632.0 | −0.942460 | −0.471230 | − | 0.882010i | \(-0.656190\pi\) | ||||
−0.471230 | + | 0.882010i | \(0.656190\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −104.000 | −0.00916424 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 261.000 | − | 1330.84i | 0.0228628 | − | 0.116578i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 3579.51i | − | 0.311707i | −0.987780 | − | 0.155854i | \(-0.950187\pi\) | ||
0.987780 | − | 0.155854i | \(-0.0498128\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4303.57i | − | 0.372561i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1196.00 | − | 785.249i | −0.102933 | − | 0.0675820i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20280.0 | −1.73523 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17664.0 | −1.50263 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6188.00 | + | 1213.57i | 0.523358 | + | 0.102639i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1590.89i | − | 0.133778i | −0.997760 | − | 0.0668890i | \(-0.978693\pi\) | ||
0.997760 | − | 0.0668890i | \(-0.0213073\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4109.81i | 0.343613i | 0.985131 | + | 0.171806i | \(0.0549603\pi\) | ||||
−0.985131 | + | 0.171806i | \(0.945040\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1092.00 | − | 214.159i | −0.0907786 | − | 0.0178032i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4368.00 | 0.361049 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4423.00 | −0.363524 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15750.0 | + | 6424.76i | 1.28718 | + | 0.525068i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21538.3i | 1.75033i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2386.34i | − | 0.192842i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2382.00 | + | 12145.9i | −0.191417 | + | 0.976039i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10994.0 | 0.878562 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9484.00 | −0.753695 | −0.376848 | − | 0.926275i | \(-0.622992\pi\) | ||||
−0.376848 | + | 0.926275i | \(0.622992\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2652.00 | − | 13522.6i | 0.209592 | − | 1.06871i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7383.38i | − | 0.580311i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5476.35i | − | 0.428065i | −0.976827 | − | 0.214033i | \(-0.931340\pi\) | ||
0.976827 | − | 0.214033i | \(-0.0686599\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5900.00 | + | 2406.74i | 0.458663 | + | 0.187098i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2600.00 | 0.201023 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7592.00 | 0.583806 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17264.0 | − | 3385.75i | −1.32039 | − | 0.258950i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1091.19i | − | 0.0830076i | −0.999138 | − | 0.0415038i | \(-0.986785\pi\) | ||
0.999138 | − | 0.0415038i | \(-0.0132149\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10320.4i | − | 0.780871i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4784.00 | − | 938.220i | −0.360037 | − | 0.0706090i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17898.0 | 1.33981 | 0.669903 | − | 0.742449i | \(-0.266336\pi\) | ||||
0.669903 | + | 0.742449i | \(0.266336\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10400.0 | −0.774392 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5200.00 | + | 5313.18i | −0.385149 | + | 0.393532i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21089.5i | 1.55381i | 0.629616 | + | 0.776907i | \(0.283212\pi\) | ||||
−0.629616 | + | 0.776907i | \(0.716788\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3334.76i | − | 0.244405i | −0.992505 | − | 0.122203i | \(-0.961004\pi\) | ||
0.992505 | − | 0.122203i | \(-0.0389958\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4784.00 | − | 24393.7i | 0.348786 | − | 1.77847i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1848.00 | −0.134029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5066.00 | −0.365512 | −0.182756 | − | 0.983158i | \(-0.558502\pi\) | ||||
−0.182756 | + | 0.983158i | \(0.558502\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3074.00 | − | 15674.4i | 0.220641 | − | 1.12505i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1896.84i | 0.135446i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 21109.9i | − | 1.49963i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4576.00 | − | 11217.8i | 0.323409 | − | 0.792822i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20042.0 | 1.40924 | 0.704618 | − | 0.709587i | \(-0.251118\pi\) | ||||
0.704618 | + | 0.709587i | \(0.251118\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2184.00 | −0.152785 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24700.0 | − | 4844.07i | −1.71916 | − | 0.337155i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 26351.7i | − | 1.82485i | −0.409244 | − | 0.912425i | \(-0.634208\pi\) | ||
0.409244 | − | 0.912425i | \(-0.365792\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2121.19i | 0.146152i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9828.00 | − | 1927.43i | −0.673758 | − | 0.132135i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4344.00 | −0.296312 | −0.148156 | − | 0.988964i | \(-0.547334\pi\) | ||||
−0.148156 | + | 0.988964i | \(0.547334\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18250.0 | 1.23866 | 0.619329 | − | 0.785132i | \(-0.287405\pi\) | ||||
0.619329 | + | 0.785132i | \(0.287405\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 520.000 | − | 1274.75i | 0.0351178 | − | 0.0860896i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 8005.46i | − | 0.537964i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5272.39i | − | 0.352553i | −0.984341 | − | 0.176276i | \(-0.943595\pi\) | ||
0.984341 | − | 0.176276i | \(-0.0564053\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2600.00 | − | 13257.5i | 0.173001 | − | 0.882133i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16896.0 | 1.11872 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11748.0 | 0.774058 | 0.387029 | − | 0.922068i | \(-0.373501\pi\) | ||||
0.387029 | + | 0.922068i | \(0.373501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4992.00 | − | 25454.3i | 0.327312 | − | 1.66897i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3895.65i | 0.254186i | 0.991891 | + | 0.127093i | \(0.0405647\pi\) | ||||
−0.991891 | + | 0.127093i | \(0.959435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7189.62i | 0.466842i | 0.972376 | + | 0.233421i | \(0.0749920\pi\) | ||||
−0.972376 | + | 0.233421i | \(0.925008\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6776.00 | + | 10320.4i | −0.437861 | + | 0.666899i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9776.00 | 0.628679 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12559.0 | −0.803776 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2392.00 | + | 469.110i | 0.152356 | + | 0.0298795i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 6771.50i | − | 0.429248i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 26831.0i | − | 1.69275i | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||
0.532585 | − | 0.846376i | \(-0.321221\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17524.0 | − | 3436.74i | −1.10034 | − | 0.215795i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22984.0 | −1.43637 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10516.0 | −0.654096 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17000.0 | − | 6934.67i | −1.05244 | − | 0.429313i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23639.1i | 1.45661i | 0.685254 | + | 0.728305i | \(0.259691\pi\) | ||||
−0.685254 | + | 0.728305i | \(0.740309\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 16245.5i | − | 0.996359i | −0.867074 | − | 0.498180i | \(-0.834002\pi\) | ||
0.867074 | − | 0.498180i | \(-0.165998\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2392.00 | + | 12196.9i | −0.146023 | + | 0.744575i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7384.00 | 0.448679 | 0.224339 | − | 0.974511i | \(-0.427978\pi\) | ||||
0.224339 | + | 0.974511i | \(0.427978\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28980.0 | −1.75280 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2184.00 | + | 11136.3i | −0.131486 | + | 0.670452i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 15082.9i | − | 0.903889i | −0.892046 | − | 0.451944i | \(-0.850731\pi\) | ||
0.892046 | − | 0.451944i | \(-0.149269\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 17765.0i | − | 1.05975i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10550.0 | + | 4303.57i | 0.626476 | + | 0.255553i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20434.0 | −1.20788 | −0.603942 | − | 0.797028i | \(-0.706404\pi\) | ||||
−0.603942 | + | 0.797028i | \(0.706404\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12148.0 | 0.714830 | 0.357415 | − | 0.933946i | \(-0.383658\pi\) | ||||
0.357415 | + | 0.933946i | \(0.383658\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4576.00 | + | 897.427i | 0.268050 | + | 0.0525689i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1060.60i | − | 0.0618468i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 22435.7i | − | 1.30242i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6292.00 | + | 1233.96i | 0.363621 | + | 0.0713120i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10856.0 | −0.624577 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12730.0 | 0.729131 | 0.364566 | − | 0.931178i | \(-0.381217\pi\) | ||||
0.364566 | + | 0.931178i | \(0.381217\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1617.00 | − | 2462.83i | 0.0922050 | − | 0.140436i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 19672.0i | − | 1.11678i | −0.829580 | − | 0.558388i | \(-0.811420\pi\) | ||
0.829580 | − | 0.558388i | \(-0.188580\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 10830.3i | − | 0.612120i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1270.00 | − | 6475.75i | 0.0714633 | − | 0.364393i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6558.00 | 0.367401 | 0.183701 | − | 0.982982i | \(-0.441192\pi\) | ||||
0.183701 | + | 0.982982i | \(0.441192\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24544.0 | 1.36902 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4556.00 | − | 23231.1i | 0.253016 | − | 1.29014i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20192.1i | 1.11649i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30461.5i | 1.67701i | 0.544896 | + | 0.838503i | \(0.316569\pi\) | ||||
−0.544896 | + | 0.838503i | \(0.683431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4784.00 | − | 11727.7i | 0.262235 | − | 0.642857i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7800.00 | −0.425713 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9984.00 | 0.542570 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4472.00 | + | 877.031i | 0.241984 | + | 0.0474569i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31461.0i | 1.69510i | 0.530717 | + | 0.847549i | \(0.321923\pi\) | ||||
−0.530717 | + | 0.847549i | \(0.678077\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3385.75i | 0.181644i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −19968.0 | − | 3916.05i | −1.06672 | − | 0.209201i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 104.000 | 0.00553228 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25396.0 | 1.34523 | 0.672614 | − | 0.739993i | \(-0.265171\pi\) | ||||
0.672614 | + | 0.739993i | \(0.265171\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7592.00 | + | 18611.4i | −0.400453 | + | 0.981692i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18846.0i | 0.989884i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20640.8i | 1.07961i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1920.00 | + | 9790.12i | −0.100005 | + | 0.509928i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7888.00 | −0.409142 | −0.204571 | − | 0.978852i | \(-0.565580\pi\) | ||||
−0.204571 | + | 0.978852i | \(0.565580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20280.0 | 1.04753 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1618.00 | − | 8250.21i | 0.0832283 | − | 0.424383i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5353.97i | 0.274264i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6475.75i | − | 0.330361i | −0.986263 | − | 0.165181i | \(-0.947179\pi\) | ||
0.986263 | − | 0.165181i | \(-0.0528207\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7825.00 | − | 18060.7i | −0.397551 | − | 0.917580i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4784.00 | −0.242056 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14772.0 | 0.744361 | 0.372180 | − | 0.928160i | \(-0.378610\pi\) | ||||
0.372180 | + | 0.928160i | \(0.378610\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12428.0 | + | 2437.33i | 0.623692 | + | 0.122316i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2345.55i | 0.117231i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22364.3i | 1.11324i | 0.830767 | + | 0.556620i | \(0.187902\pi\) | ||||
−0.830767 | + | 0.556620i | \(0.812098\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2288.00 | − | 448.714i | −0.113430 | − | 0.0222455i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19080.0 | −0.942096 | −0.471048 | − | 0.882108i | \(-0.656124\pi\) | ||||
−0.471048 | + | 0.882108i | \(0.656124\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4888.00 | 0.240379 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4650.00 | − | 1896.84i | −0.227757 | − | 0.0929071i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2386.34i | 0.116415i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 20324.7i | − | 0.987561i | −0.869586 | − | 0.493781i | \(-0.835615\pi\) | ||
0.869586 | − | 0.493781i | \(-0.164385\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1586.00 | − | 8087.04i | 0.0767557 | − | 0.391379i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15288.0 | −0.736937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4188.00 | −0.201077 | −0.100539 | − | 0.994933i | \(-0.532057\pi\) | ||||
−0.100539 | + | 0.994933i | \(0.532057\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4048.00 | − | 20640.8i | 0.193588 | − | 0.987108i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 30757.3i | − | 1.46511i | −0.680706 | − | 0.732556i | \(-0.738327\pi\) | ||
0.680706 | − | 0.732556i | \(-0.261673\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7383.38i | 0.350323i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5200.00 | − | 2121.19i | −0.245760 | − | 0.100251i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27720.0 | 1.30497 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10370.0 | −0.486283 | −0.243142 | − | 0.969991i | \(-0.578178\pi\) | ||||
−0.243142 | + | 0.969991i | \(0.578178\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20176.0 | − | 3956.84i | −0.942440 | − | 0.184828i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 10779.3i | − | 0.501559i | −0.968044 | − | 0.250780i | \(-0.919313\pi\) | ||
0.968044 | − | 0.250780i | \(-0.0806870\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4497.34i | − | 0.208450i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17264.0 | + | 3385.75i | 0.797095 | + | 0.156323i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4992.00 | −0.229598 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 31280.0 | 1.43315 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 29900.0 | + | 19631.2i | 1.36467 | + | 0.895993i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19865.8i | 0.903236i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 23384.1i | − | 1.05915i | −0.848262 | − | 0.529576i | \(-0.822351\pi\) | ||
0.848262 | − | 0.529576i | \(-0.177649\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4344.00 | − | 22150.1i | 0.196008 | − | 0.999450i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10400.0 | 0.467486 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10384.0 | 0.465002 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4680.00 | − | 23863.4i | 0.208783 | − | 1.06459i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3232.78i | 0.143677i | 0.997416 | + | 0.0718387i | \(0.0228867\pi\) | ||||
−0.997416 | + | 0.0718387i | \(0.977113\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 7832.09i | − | 0.346783i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9776.00 | + | 23965.4i | −0.431233 | + | 1.05715i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19412.0 | −0.853094 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9152.00 | −0.400703 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13988.0 | − | 2743.27i | −0.610162 | − | 0.119663i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 33857.5i | − | 1.47140i | −0.677305 | − | 0.735702i | \(-0.736852\pi\) | ||
0.677305 | − | 0.735702i | \(-0.263148\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10493.8i | − | 0.454361i | −0.973853 | − | 0.227180i | \(-0.927049\pi\) | ||
0.973853 | − | 0.227180i | \(-0.0729507\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16588.0 | − | 3253.17i | −0.715580 | − | 0.140337i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −34632.0 | −1.48847 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2392.00 | 0.102430 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4576.00 | + | 11217.8i | −0.195236 | + | 0.478612i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 15103.3i | − | 0.642032i | −0.947074 | − | 0.321016i | \(-0.895976\pi\) | ||
0.947074 | − | 0.321016i | \(-0.104024\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17958.7i | 0.760635i | 0.924856 | + | 0.380317i | \(0.124185\pi\) | ||||
−0.924856 | + | 0.380317i | \(0.875815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −966.000 | + | 4925.65i | −0.0407658 | + | 0.207866i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6598.00 | −0.277430 | −0.138715 | − | 0.990332i | \(-0.544297\pi\) | ||||
−0.138715 | + | 0.990332i | \(0.544297\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41028.0 | 1.71889 | 0.859446 | − | 0.511227i | \(-0.170809\pi\) | ||||
0.859446 | + | 0.511227i | \(0.170809\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4956.00 | − | 25270.7i | 0.206885 | − | 1.05491i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4874.66i | 0.202758i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 20477.7i | − | 0.848693i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25116.0 | − | 16490.2i | −1.03720 | − | 0.680987i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17816.0 | −0.733107 | −0.366553 | − | 0.930397i | \(-0.619462\pi\) | ||||
−0.366553 | + | 0.930397i | \(0.619462\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −40611.0 | −1.66514 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10088.0 | + | 1978.42i | 0.412158 | + | 0.0808308i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2661.69i | 0.108361i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8005.46i | 0.324759i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 40716.0 | + | 7985.06i | 1.64590 | + | 0.322788i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 29216.0 | 1.17686 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28308.0 | 1.13628 | 0.568140 | − | 0.822932i | \(-0.307663\pi\) | ||||
0.568140 | + | 0.822932i | \(0.307663\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2600.00 | + | 1060.60i | 0.103998 | + | 0.0424229i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 33735.1i | − | 1.34466i | −0.740254 | − | 0.672328i | \(-0.765295\pi\) | ||
0.740254 | − | 0.672328i | \(-0.234705\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 336.535i | − | 0.0133672i | −0.999978 | − | 0.00668361i | \(-0.997873\pi\) | ||
0.999978 | − | 0.00668361i | \(-0.00212747\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4992.00 | + | 25454.3i | −0.197592 | + | 1.00753i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48208.0 | −1.90153 | −0.950764 | − | 0.309915i | \(-0.899700\pi\) | ||||
−0.950764 | + | 0.309915i | \(0.899700\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12376.0 | −0.486470 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4497.00 | + | 22930.3i | −0.176155 | + | 0.898216i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 34245.0i | − | 1.33680i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2243.57i | − | 0.0872795i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26550.0 | + | 10830.3i | 1.02930 | + | 0.419875i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15184.0 | 0.586643 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42844.0 | −1.64965 | −0.824823 | − | 0.565391i | \(-0.808725\pi\) | ||||
−0.824823 | + | 0.565391i | \(0.808725\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9412.00 | + | 1845.85i | 0.361159 | + | 0.0708291i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 6975.46i | − | 0.266753i | −0.991065 | − | 0.133376i | \(-0.957418\pi\) | ||
0.991065 | − | 0.133376i | \(-0.0425819\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4803.28i | 0.183061i | 0.995802 | + | 0.0915306i | \(0.0291759\pi\) | ||||
−0.995802 | + | 0.0915306i | \(0.970824\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −32760.0 | − | 6424.76i | −1.24431 | − | 0.244029i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37336.0 | 1.41333 | 0.706663 | − | 0.707550i | \(-0.250200\pi\) | ||||
0.706663 | + | 0.707550i | \(0.250200\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22984.0 | 0.867108 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23966.0 | + | 23455.5i | 0.901112 | + | 0.881917i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3916.05i | 0.146747i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 24291.7i | − | 0.907244i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3872.00 | + | 19743.4i | −0.144127 | + | 0.734909i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 54600.0 | 2.02560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9360.00 | 0.346090 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2392.00 | − | 12196.9i | 0.0881515 | − | 0.449486i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27045.2i | 0.993384i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 16490.2i | − | 0.603692i | −0.953357 | − | 0.301846i | \(-0.902397\pi\) | ||
0.953357 | − | 0.301846i | \(-0.0976029\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −104.000 | + | 254.951i | −0.00379479 | + | 0.00930274i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35360.0 | 1.28598 | 0.642991 | − | 0.765874i | \(-0.277693\pi\) | ||||
0.642991 | + | 0.765874i | \(0.277693\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8556.00 | 0.310145 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12272.0 | − | 2406.74i | −0.443388 | − | 0.0869555i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17765.0i | 0.639751i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 4395.35i | − | 0.157769i | −0.996884 | − | 0.0788843i | \(-0.974864\pi\) | ||
0.996884 | − | 0.0788843i | \(-0.0251358\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −42276.0 | − | 8291.01i | −1.51253 | − | 0.296632i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29920.0 | −1.06699 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6972.00 | −0.247825 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20280.0 | + | 49715.4i | −0.718536 | + | 1.76146i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1815.25i | − | 0.0641081i | −0.999486 | − | 0.0320541i | \(-0.989795\pi\) | ||
0.999486 | − | 0.0320541i | \(-0.0102049\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2437.33i | − | 0.0858005i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10104.0 | + | 51520.5i | −0.354545 | + | 1.80783i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9568.00 | 0.334660 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34034.0 | −1.18660 | −0.593299 | − | 0.804982i | \(-0.702175\pi\) | ||||
−0.593299 | + | 0.804982i | \(0.702175\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1198.00 | − | 6108.63i | 0.0416350 | − | 0.212298i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36967.9i | 1.28068i | 0.768092 | + | 0.640339i | \(0.221206\pi\) | ||||
−0.768092 | + | 0.640339i | \(0.778794\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43076.5i | 1.48756i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8008.00 | − | 12196.9i | 0.275662 | − | 0.419856i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24862.0 | 0.853122 | 0.426561 | − | 0.904459i | \(-0.359725\pi\) | ||||
0.426561 | + | 0.904459i | \(0.359725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18568.0 | 0.635135 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25636.0 | − | 5027.63i | −0.874137 | − | 0.171432i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22802.8i | 0.775085i | 0.921852 | + | 0.387542i | \(0.126676\pi\) | ||||
−0.921852 | + | 0.387542i | \(0.873324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48787.4i | 1.65311i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −59800.0 | − | 11727.7i | −2.01992 | − | 0.396138i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24544.0 | −0.826452 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16073.0 | −0.539525 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5850.00 | − | 2386.34i | −0.195757 | − | 0.0798533i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31348.8i | 1.04575i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40068.1i | 1.33247i | 0.745740 | + | 0.666237i | \(0.232096\pi\) | ||||
−0.745740 | + | 0.666237i | \(0.767904\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −208.000 | + | 1060.60i | −0.00689569 | + | 0.0351613i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43522.0 | −1.43840 | −0.719201 | − | 0.694803i | \(-0.755492\pi\) | ||||
−0.719201 | + | 0.694803i | \(0.755492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7800.00 | 0.256995 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 924.000 | − | 4711.49i | 0.0303504 | − | 0.154758i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 17683.4i | − | 0.579060i | −0.957169 | − | 0.289530i | \(-0.906501\pi\) | ||
0.957169 | − | 0.289530i | \(-0.0934991\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 44096.3i | − | 1.43956i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18100.0 | − | 7383.38i | −0.589081 | − | 0.240299i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 42360.0 | 1.37444 | 0.687220 | − | 0.726450i | \(-0.258831\pi\) | ||||
0.687220 | + | 0.726450i | \(0.258831\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49400.0 | 1.59798 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19968.0 | + | 3916.05i | 0.643960 | + | 0.126291i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 20640.8i | − | 0.663640i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25199.4i | 0.807754i | 0.914813 | + | 0.403877i | \(0.132338\pi\) | ||||
−0.914813 | + | 0.403877i | \(0.867662\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31252.0 | − | 6129.02i | −0.998743 | − | 0.195870i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19656.0 | 0.626268 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5356.00 | −0.170137 | −0.0850683 | − | 0.996375i | \(-0.527111\pi\) | ||||
−0.0850683 | + | 0.996375i | \(0.527111\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −25564.0 | + | 38936.1i | −0.809619 | + | 1.23312i |
(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 | 768.4.c.d.767.2 | 2 | ||
3.2 | odd | 2 | 768.4.c.f.767.2 | 2 | |||
4.3 | odd | 2 | 768.4.c.f.767.1 | 2 | |||
8.3 | odd | 2 | 768.4.c.e.767.2 | 2 | |||
8.5 | even | 2 | 768.4.c.g.767.1 | 2 | |||
12.11 | even | 2 | inner | 768.4.c.d.767.1 | 2 | ||
16.3 | odd | 4 | 384.4.f.e.191.4 | yes | 4 | ||
16.5 | even | 4 | 384.4.f.f.191.4 | yes | 4 | ||
16.11 | odd | 4 | 384.4.f.e.191.1 | ✓ | 4 | ||
16.13 | even | 4 | 384.4.f.f.191.1 | yes | 4 | ||
24.5 | odd | 2 | 768.4.c.e.767.1 | 2 | |||
24.11 | even | 2 | 768.4.c.g.767.2 | 2 | |||
48.5 | odd | 4 | 384.4.f.e.191.3 | yes | 4 | ||
48.11 | even | 4 | 384.4.f.f.191.2 | yes | 4 | ||
48.29 | odd | 4 | 384.4.f.e.191.2 | yes | 4 | ||
48.35 | even | 4 | 384.4.f.f.191.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.f.e.191.1 | ✓ | 4 | 16.11 | odd | 4 | ||
384.4.f.e.191.2 | yes | 4 | 48.29 | odd | 4 | ||
384.4.f.e.191.3 | yes | 4 | 48.5 | odd | 4 | ||
384.4.f.e.191.4 | yes | 4 | 16.3 | odd | 4 | ||
384.4.f.f.191.1 | yes | 4 | 16.13 | even | 4 | ||
384.4.f.f.191.2 | yes | 4 | 48.11 | even | 4 | ||
384.4.f.f.191.3 | yes | 4 | 48.35 | even | 4 | ||
384.4.f.f.191.4 | yes | 4 | 16.5 | even | 4 | ||
768.4.c.d.767.1 | 2 | 12.11 | even | 2 | inner | ||
768.4.c.d.767.2 | 2 | 1.1 | even | 1 | trivial | ||
768.4.c.e.767.1 | 2 | 24.5 | odd | 2 | |||
768.4.c.e.767.2 | 2 | 8.3 | odd | 2 | |||
768.4.c.f.767.1 | 2 | 4.3 | odd | 2 | |||
768.4.c.f.767.2 | 2 | 3.2 | odd | 2 | |||
768.4.c.g.767.1 | 2 | 8.5 | even | 2 | |||
768.4.c.g.767.2 | 2 | 24.11 | even | 2 |