Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,3,Mod(181,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.181");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.h (of order \(2\), degree \(1\), 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: | \(8.58312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-5}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.1 | ||
Root | \(-2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.181 |
Dual form | 315.3.h.b.181.2 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.500000 | 0.250000 | − | 0.968246i | \(-0.419569\pi\) | ||||
0.250000 | + | 0.968246i | \(0.419569\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.00000 | −0.750000 | ||||||||
\(5\) | − 2.23607i | − 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 1.00000 | ||||||||
\(8\) | −7.00000 | −0.875000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 2.23607i | − 0.223607i | ||||||||
\(11\) | −2.00000 | −0.181818 | −0.0909091 | − | 0.995859i | \(-0.528977\pi\) | ||||
−0.0909091 | + | 0.995859i | \(0.528977\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 13.4164i | − 1.03203i | −0.856579 | − | 0.516016i | \(-0.827415\pi\) | ||||
0.856579 | − | 0.516016i | \(-0.172585\pi\) | |||||||
\(14\) | 7.00000 | 0.500000 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | − 26.8328i | − 1.57840i | −0.614136 | − | 0.789200i | \(-0.710495\pi\) | ||||
0.614136 | − | 0.789200i | \(-0.289505\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 13.4164i | − 0.706127i | −0.935599 | − | 0.353063i | \(-0.885140\pi\) | ||||
0.935599 | − | 0.353063i | \(-0.114860\pi\) | |||||||
\(20\) | 6.70820i | 0.335410i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.00000 | −0.0909091 | ||||||||
\(23\) | −26.0000 | −1.13043 | −0.565217 | − | 0.824942i | \(-0.691208\pi\) | ||||
−0.565217 | + | 0.824942i | \(0.691208\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − 13.4164i | − 0.516016i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −21.0000 | −0.750000 | ||||||||
\(29\) | 22.0000 | 0.758621 | 0.379310 | − | 0.925270i | \(-0.376161\pi\) | ||||
0.379310 | + | 0.925270i | \(0.376161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 53.6656i | − 1.73115i | −0.500780 | − | 0.865575i | \(-0.666953\pi\) | ||||
0.500780 | − | 0.865575i | \(-0.333047\pi\) | |||||||
\(32\) | 33.0000 | 1.03125 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 26.8328i | − 0.789200i | ||||||||
\(35\) | − 15.6525i | − 0.447214i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 14.0000 | 0.378378 | 0.189189 | − | 0.981941i | \(-0.439414\pi\) | ||||
0.189189 | + | 0.981941i | \(0.439414\pi\) | |||||||
\(38\) | − 13.4164i | − 0.353063i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 15.6525i | 0.391312i | ||||||||
\(41\) | 26.8328i | 0.654459i | 0.944945 | + | 0.327229i | \(0.106115\pi\) | ||||
−0.944945 | + | 0.327229i | \(0.893885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.0000 | −0.790698 | −0.395349 | − | 0.918531i | \(-0.629376\pi\) | ||||
−0.395349 | + | 0.918531i | \(0.629376\pi\) | |||||||
\(44\) | 6.00000 | 0.136364 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −26.0000 | −0.565217 | ||||||||
\(47\) | 26.8328i | 0.570911i | 0.958392 | + | 0.285455i | \(0.0921449\pi\) | ||||
−0.958392 | + | 0.285455i | \(0.907855\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 1.00000 | ||||||||
\(50\) | −5.00000 | −0.100000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 40.2492i | 0.774024i | ||||||||
\(53\) | 34.0000 | 0.641509 | 0.320755 | − | 0.947162i | \(-0.396063\pi\) | ||||
0.320755 | + | 0.947162i | \(0.396063\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.47214i | 0.0813116i | ||||||||
\(56\) | −49.0000 | −0.875000 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 22.0000 | 0.379310 | ||||||||
\(59\) | 40.2492i | 0.682190i | 0.940029 | + | 0.341095i | \(0.110798\pi\) | ||||
−0.940029 | + | 0.341095i | \(0.889202\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 93.9149i | 1.53959i | 0.638293 | + | 0.769794i | \(0.279641\pi\) | ||||
−0.638293 | + | 0.769794i | \(0.720359\pi\) | |||||||
\(62\) | − 53.6656i | − 0.865575i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 0.203125 | ||||||||
\(65\) | −30.0000 | −0.461538 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.0000 | 0.208955 | 0.104478 | − | 0.994527i | \(-0.466683\pi\) | ||||
0.104478 | + | 0.994527i | \(0.466683\pi\) | |||||||
\(68\) | 80.4984i | 1.18380i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − 15.6525i | − 0.223607i | ||||||||
\(71\) | −62.0000 | −0.873239 | −0.436620 | − | 0.899646i | \(-0.643824\pi\) | ||||
−0.436620 | + | 0.899646i | \(0.643824\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 53.6656i | − 0.735146i | −0.929995 | − | 0.367573i | \(-0.880189\pi\) | ||||
0.929995 | − | 0.367573i | \(-0.119811\pi\) | |||||||
\(74\) | 14.0000 | 0.189189 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 40.2492i | 0.529595i | ||||||||
\(77\) | −14.0000 | −0.181818 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 38.0000 | 0.481013 | 0.240506 | − | 0.970648i | \(-0.422687\pi\) | ||||
0.240506 | + | 0.970648i | \(0.422687\pi\) | |||||||
\(80\) | − 11.1803i | − 0.139754i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 26.8328i | 0.327229i | ||||||||
\(83\) | − 40.2492i | − 0.484930i | −0.970160 | − | 0.242465i | \(-0.922044\pi\) | ||||
0.970160 | − | 0.242465i | \(-0.0779560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −60.0000 | −0.705882 | ||||||||
\(86\) | −34.0000 | −0.395349 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.0000 | 0.159091 | ||||||||
\(89\) | 26.8328i | 0.301492i | 0.988573 | + | 0.150746i | \(0.0481676\pi\) | ||||
−0.988573 | + | 0.150746i | \(0.951832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 93.9149i | − 1.03203i | ||||||||
\(92\) | 78.0000 | 0.847826 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 26.8328i | 0.285455i | ||||||||
\(95\) | −30.0000 | −0.315789 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 26.8328i | − 0.276627i | −0.990388 | − | 0.138313i | \(-0.955832\pi\) | ||||
0.990388 | − | 0.138313i | \(-0.0441681\pi\) | |||||||
\(98\) | 49.0000 | 0.500000 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 15.0000 | 0.150000 | ||||||||
\(101\) | − 67.0820i | − 0.664179i | −0.943248 | − | 0.332089i | \(-0.892246\pi\) | ||||
0.943248 | − | 0.332089i | \(-0.107754\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 160.997i | 1.56308i | 0.623857 | + | 0.781538i | \(0.285565\pi\) | ||||
−0.623857 | + | 0.781538i | \(0.714435\pi\) | |||||||
\(104\) | 93.9149i | 0.903027i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 34.0000 | 0.320755 | ||||||||
\(107\) | 106.000 | 0.990654 | 0.495327 | − | 0.868707i | \(-0.335048\pi\) | ||||
0.495327 | + | 0.868707i | \(0.335048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −142.000 | −1.30275 | −0.651376 | − | 0.758755i | \(-0.725808\pi\) | ||||
−0.651376 | + | 0.758755i | \(0.725808\pi\) | |||||||
\(110\) | 4.47214i | 0.0406558i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 35.0000 | 0.312500 | ||||||||
\(113\) | 34.0000 | 0.300885 | 0.150442 | − | 0.988619i | \(-0.451930\pi\) | ||||
0.150442 | + | 0.988619i | \(0.451930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 58.1378i | 0.505546i | ||||||||
\(116\) | −66.0000 | −0.568966 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 40.2492i | 0.341095i | ||||||||
\(119\) | − 187.830i | − 1.57840i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −117.000 | −0.966942 | ||||||||
\(122\) | 93.9149i | 0.769794i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 160.997i | 1.29836i | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 194.000 | 1.52756 | 0.763780 | − | 0.645477i | \(-0.223341\pi\) | ||||
0.763780 | + | 0.645477i | \(0.223341\pi\) | |||||||
\(128\) | −119.000 | −0.929688 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −30.0000 | −0.230769 | ||||||||
\(131\) | 120.748i | 0.921738i | 0.887468 | + | 0.460869i | \(0.152462\pi\) | ||||
−0.887468 | + | 0.460869i | \(0.847538\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 93.9149i | − 0.706127i | ||||||||
\(134\) | 14.0000 | 0.104478 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 187.830i | 1.38110i | ||||||||
\(137\) | 166.000 | 1.21168 | 0.605839 | − | 0.795587i | \(-0.292837\pi\) | ||||
0.605839 | + | 0.795587i | \(0.292837\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 93.9149i | − 0.675646i | −0.941210 | − | 0.337823i | \(-0.890309\pi\) | ||||
0.941210 | − | 0.337823i | \(-0.109691\pi\) | |||||||
\(140\) | 46.9574i | 0.335410i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −62.0000 | −0.436620 | ||||||||
\(143\) | 26.8328i | 0.187642i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 49.1935i | − 0.339265i | ||||||||
\(146\) | − 53.6656i | − 0.367573i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −42.0000 | −0.283784 | ||||||||
\(149\) | 142.000 | 0.953020 | 0.476510 | − | 0.879169i | \(-0.341902\pi\) | ||||
0.476510 | + | 0.879169i | \(0.341902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.00000 | 0.0132450 | 0.00662252 | − | 0.999978i | \(-0.497892\pi\) | ||||
0.00662252 | + | 0.999978i | \(0.497892\pi\) | |||||||
\(152\) | 93.9149i | 0.617861i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −14.0000 | −0.0909091 | ||||||||
\(155\) | −120.000 | −0.774194 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 67.0820i | − 0.427274i | −0.976913 | − | 0.213637i | \(-0.931469\pi\) | ||||
0.976913 | − | 0.213637i | \(-0.0685310\pi\) | |||||||
\(158\) | 38.0000 | 0.240506 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 73.7902i | − 0.461189i | ||||||||
\(161\) | −182.000 | −1.13043 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −34.0000 | −0.208589 | −0.104294 | − | 0.994546i | \(-0.533258\pi\) | ||||
−0.104294 | + | 0.994546i | \(0.533258\pi\) | |||||||
\(164\) | − 80.4984i | − 0.490844i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 40.2492i | − 0.242465i | ||||||||
\(167\) | 107.331i | 0.642702i | 0.946960 | + | 0.321351i | \(0.104137\pi\) | ||||
−0.946960 | + | 0.321351i | \(0.895863\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.0650888 | ||||||||
\(170\) | −60.0000 | −0.352941 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 102.000 | 0.593023 | ||||||||
\(173\) | − 147.580i | − 0.853066i | −0.904472 | − | 0.426533i | \(-0.859735\pi\) | ||||
0.904472 | − | 0.426533i | \(-0.140265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −35.0000 | −0.200000 | ||||||||
\(176\) | −10.0000 | −0.0568182 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 26.8328i | 0.150746i | ||||||||
\(179\) | −218.000 | −1.21788 | −0.608939 | − | 0.793217i | \(-0.708404\pi\) | ||||
−0.608939 | + | 0.793217i | \(0.708404\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 254.912i | − 1.40835i | −0.710025 | − | 0.704176i | \(-0.751317\pi\) | ||||
0.710025 | − | 0.704176i | \(-0.248683\pi\) | |||||||
\(182\) | − 93.9149i | − 0.516016i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 182.000 | 0.989130 | ||||||||
\(185\) | − 31.3050i | − 0.169216i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 53.6656i | 0.286982i | ||||||||
\(188\) | − 80.4984i | − 0.428183i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −30.0000 | −0.157895 | ||||||||
\(191\) | 58.0000 | 0.303665 | 0.151832 | − | 0.988406i | \(-0.451483\pi\) | ||||
0.151832 | + | 0.988406i | \(0.451483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 206.000 | 1.06736 | 0.533679 | − | 0.845687i | \(-0.320809\pi\) | ||||
0.533679 | + | 0.845687i | \(0.320809\pi\) | |||||||
\(194\) | − 26.8328i | − 0.138313i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −147.000 | −0.750000 | ||||||||
\(197\) | 226.000 | 1.14721 | 0.573604 | − | 0.819133i | \(-0.305545\pi\) | ||||
0.573604 | + | 0.819133i | \(0.305545\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 134.164i | 0.674191i | 0.941470 | + | 0.337096i | \(0.109445\pi\) | ||||
−0.941470 | + | 0.337096i | \(0.890555\pi\) | |||||||
\(200\) | 35.0000 | 0.175000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 67.0820i | − 0.332089i | ||||||||
\(203\) | 154.000 | 0.758621 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 60.0000 | 0.292683 | ||||||||
\(206\) | 160.997i | 0.781538i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 67.0820i | − 0.322510i | ||||||||
\(209\) | 26.8328i | 0.128387i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −118.000 | −0.559242 | −0.279621 | − | 0.960111i | \(-0.590209\pi\) | ||||
−0.279621 | + | 0.960111i | \(0.590209\pi\) | |||||||
\(212\) | −102.000 | −0.481132 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 106.000 | 0.495327 | ||||||||
\(215\) | 76.0263i | 0.353611i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 375.659i | − 1.73115i | ||||||||
\(218\) | −142.000 | −0.651376 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 13.4164i | − 0.0609837i | ||||||||
\(221\) | −360.000 | −1.62896 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 80.4984i | 0.360980i | 0.983577 | + | 0.180490i | \(0.0577683\pi\) | ||||
−0.983577 | + | 0.180490i | \(0.942232\pi\) | |||||||
\(224\) | 231.000 | 1.03125 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 34.0000 | 0.150442 | ||||||||
\(227\) | − 254.912i | − 1.12296i | −0.827491 | − | 0.561480i | \(-0.810232\pi\) | ||||
0.827491 | − | 0.561480i | \(-0.189768\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.4164i | 0.0585869i | 0.999571 | + | 0.0292935i | \(0.00932573\pi\) | ||||
−0.999571 | + | 0.0292935i | \(0.990674\pi\) | |||||||
\(230\) | 58.1378i | 0.252773i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −154.000 | −0.663793 | ||||||||
\(233\) | 214.000 | 0.918455 | 0.459227 | − | 0.888319i | \(-0.348126\pi\) | ||||
0.459227 | + | 0.888319i | \(0.348126\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 60.0000 | 0.255319 | ||||||||
\(236\) | − 120.748i | − 0.511643i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 187.830i | − 0.789200i | ||||||||
\(239\) | −98.0000 | −0.410042 | −0.205021 | − | 0.978758i | \(-0.565726\pi\) | ||||
−0.205021 | + | 0.978758i | \(0.565726\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 160.997i | − 0.668037i | −0.942567 | − | 0.334018i | \(-0.891595\pi\) | ||||
0.942567 | − | 0.334018i | \(-0.108405\pi\) | |||||||
\(242\) | −117.000 | −0.483471 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 281.745i | − 1.15469i | ||||||||
\(245\) | − 109.567i | − 0.447214i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −180.000 | −0.728745 | ||||||||
\(248\) | 375.659i | 1.51476i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.1803i | 0.0447214i | ||||||||
\(251\) | − 335.410i | − 1.33630i | −0.744029 | − | 0.668148i | \(-0.767087\pi\) | ||||
0.744029 | − | 0.668148i | \(-0.232913\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 52.0000 | 0.205534 | ||||||||
\(254\) | 194.000 | 0.763780 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −171.000 | −0.667969 | ||||||||
\(257\) | 134.164i | 0.522039i | 0.965333 | + | 0.261020i | \(0.0840587\pi\) | ||||
−0.965333 | + | 0.261020i | \(0.915941\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 98.0000 | 0.378378 | ||||||||
\(260\) | 90.0000 | 0.346154 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 120.748i | 0.460869i | ||||||||
\(263\) | 34.0000 | 0.129278 | 0.0646388 | − | 0.997909i | \(-0.479410\pi\) | ||||
0.0646388 | + | 0.997909i | \(0.479410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 76.0263i | − 0.286892i | ||||||||
\(266\) | − 93.9149i | − 0.353063i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −42.0000 | −0.156716 | ||||||||
\(269\) | − 254.912i | − 0.947627i | −0.880625 | − | 0.473814i | \(-0.842877\pi\) | ||||
0.880625 | − | 0.473814i | \(-0.157123\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 321.994i | 1.18817i | 0.804403 | + | 0.594084i | \(0.202486\pi\) | ||||
−0.804403 | + | 0.594084i | \(0.797514\pi\) | |||||||
\(272\) | − 134.164i | − 0.493250i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 166.000 | 0.605839 | ||||||||
\(275\) | 10.0000 | 0.0363636 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0000 | 0.0505415 | 0.0252708 | − | 0.999681i | \(-0.491955\pi\) | ||||
0.0252708 | + | 0.999681i | \(0.491955\pi\) | |||||||
\(278\) | − 93.9149i | − 0.337823i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 109.567i | 0.391312i | ||||||||
\(281\) | −2.00000 | −0.00711744 | −0.00355872 | − | 0.999994i | \(-0.501133\pi\) | ||||
−0.00355872 | + | 0.999994i | \(0.501133\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 93.9149i | − 0.331855i | −0.986138 | − | 0.165927i | \(-0.946938\pi\) | ||||
0.986138 | − | 0.165927i | \(-0.0530617\pi\) | |||||||
\(284\) | 186.000 | 0.654930 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26.8328i | 0.0938210i | ||||||||
\(287\) | 187.830i | 0.654459i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −431.000 | −1.49135 | ||||||||
\(290\) | − 49.1935i | − 0.169633i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 160.997i | 0.551359i | ||||||||
\(293\) | − 335.410i | − 1.14474i | −0.819994 | − | 0.572372i | \(-0.806023\pi\) | ||||
0.819994 | − | 0.572372i | \(-0.193977\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 90.0000 | 0.305085 | ||||||||
\(296\) | −98.0000 | −0.331081 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 142.000 | 0.476510 | ||||||||
\(299\) | 348.827i | 1.16664i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −238.000 | −0.790698 | ||||||||
\(302\) | 2.00000 | 0.00662252 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 67.0820i | − 0.220665i | ||||||||
\(305\) | 210.000 | 0.688525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 201.246i | 0.655525i | 0.944760 | + | 0.327762i | \(0.106295\pi\) | ||||
−0.944760 | + | 0.327762i | \(0.893705\pi\) | |||||||
\(308\) | 42.0000 | 0.136364 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −120.000 | −0.387097 | ||||||||
\(311\) | 509.823i | 1.63930i | 0.572862 | + | 0.819652i | \(0.305833\pi\) | ||||
−0.572862 | + | 0.819652i | \(0.694167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 321.994i | 1.02873i | 0.857570 | + | 0.514367i | \(0.171973\pi\) | ||||
−0.857570 | + | 0.514367i | \(0.828027\pi\) | |||||||
\(314\) | − 67.0820i | − 0.213637i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −114.000 | −0.360759 | ||||||||
\(317\) | −374.000 | −1.17981 | −0.589905 | − | 0.807472i | \(-0.700835\pi\) | ||||
−0.589905 | + | 0.807472i | \(0.700835\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −44.0000 | −0.137931 | ||||||||
\(320\) | − 29.0689i | − 0.0908403i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −182.000 | −0.565217 | ||||||||
\(323\) | −360.000 | −1.11455 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 67.0820i | 0.206406i | ||||||||
\(326\) | −34.0000 | −0.104294 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 187.830i | − 0.572652i | ||||||||
\(329\) | 187.830i | 0.570911i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 482.000 | 1.45619 | 0.728097 | − | 0.685474i | \(-0.240405\pi\) | ||||
0.728097 | + | 0.685474i | \(0.240405\pi\) | |||||||
\(332\) | 120.748i | 0.363698i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 107.331i | 0.321351i | ||||||||
\(335\) | − 31.3050i | − 0.0934476i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 494.000 | 1.46588 | 0.732938 | − | 0.680296i | \(-0.238149\pi\) | ||||
0.732938 | + | 0.680296i | \(0.238149\pi\) | |||||||
\(338\) | −11.0000 | −0.0325444 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 180.000 | 0.529412 | ||||||||
\(341\) | 107.331i | 0.314754i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 1.00000 | ||||||||
\(344\) | 238.000 | 0.691860 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 147.580i | − 0.426533i | ||||||||
\(347\) | 346.000 | 0.997118 | 0.498559 | − | 0.866856i | \(-0.333863\pi\) | ||||
0.498559 | + | 0.866856i | \(0.333863\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 335.410i | − 0.961061i | −0.876978 | − | 0.480530i | \(-0.840444\pi\) | ||||
0.876978 | − | 0.480530i | \(-0.159556\pi\) | |||||||
\(350\) | −35.0000 | −0.100000 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −66.0000 | −0.187500 | ||||||||
\(353\) | − 26.8328i | − 0.0760136i | −0.999277 | − | 0.0380068i | \(-0.987899\pi\) | ||||
0.999277 | − | 0.0380068i | \(-0.0121009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 138.636i | 0.390525i | ||||||||
\(356\) | − 80.4984i | − 0.226119i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −218.000 | −0.608939 | ||||||||
\(359\) | −338.000 | −0.941504 | −0.470752 | − | 0.882266i | \(-0.656017\pi\) | ||||
−0.470752 | + | 0.882266i | \(0.656017\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 181.000 | 0.501385 | ||||||||
\(362\) | − 254.912i | − 0.704176i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 281.745i | 0.774024i | ||||||||
\(365\) | −120.000 | −0.328767 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 295.161i | 0.804253i | 0.915584 | + | 0.402127i | \(0.131729\pi\) | ||||
−0.915584 | + | 0.402127i | \(0.868271\pi\) | |||||||
\(368\) | −130.000 | −0.353261 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 31.3050i | − 0.0846080i | ||||||||
\(371\) | 238.000 | 0.641509 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 86.0000 | 0.230563 | 0.115282 | − | 0.993333i | \(-0.463223\pi\) | ||||
0.115282 | + | 0.993333i | \(0.463223\pi\) | |||||||
\(374\) | 53.6656i | 0.143491i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 187.830i | − 0.499547i | ||||||||
\(377\) | − 295.161i | − 0.782920i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −262.000 | −0.691293 | −0.345646 | − | 0.938365i | \(-0.612340\pi\) | ||||
−0.345646 | + | 0.938365i | \(0.612340\pi\) | |||||||
\(380\) | 90.0000 | 0.236842 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 58.0000 | 0.151832 | ||||||||
\(383\) | 563.489i | 1.47125i | 0.677388 | + | 0.735625i | \(0.263112\pi\) | ||||
−0.677388 | + | 0.735625i | \(0.736888\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 31.3050i | 0.0813116i | ||||||||
\(386\) | 206.000 | 0.533679 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 80.4984i | 0.207470i | ||||||||
\(389\) | −698.000 | −1.79434 | −0.897172 | − | 0.441681i | \(-0.854382\pi\) | ||||
−0.897172 | + | 0.441681i | \(0.854382\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 697.653i | 1.78428i | ||||||||
\(392\) | −343.000 | −0.875000 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 226.000 | 0.573604 | ||||||||
\(395\) | − 84.9706i | − 0.215115i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 308.577i | 0.777273i | 0.921391 | + | 0.388636i | \(0.127054\pi\) | ||||
−0.921391 | + | 0.388636i | \(0.872946\pi\) | |||||||
\(398\) | 134.164i | 0.337096i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −25.0000 | −0.0625000 | ||||||||
\(401\) | 538.000 | 1.34165 | 0.670823 | − | 0.741618i | \(-0.265941\pi\) | ||||
0.670823 | + | 0.741618i | \(0.265941\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −720.000 | −1.78660 | ||||||||
\(404\) | 201.246i | 0.498134i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 154.000 | 0.379310 | ||||||||
\(407\) | −28.0000 | −0.0687961 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 295.161i | 0.721665i | 0.932631 | + | 0.360832i | \(0.117507\pi\) | ||||
−0.932631 | + | 0.360832i | \(0.882493\pi\) | |||||||
\(410\) | 60.0000 | 0.146341 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 482.991i | − 1.17231i | ||||||||
\(413\) | 281.745i | 0.682190i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −90.0000 | −0.216867 | ||||||||
\(416\) | − 442.741i | − 1.06428i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 26.8328i | 0.0641933i | ||||||||
\(419\) | 818.401i | 1.95322i | 0.215009 | + | 0.976612i | \(0.431022\pi\) | ||||
−0.215009 | + | 0.976612i | \(0.568978\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −118.000 | −0.280285 | −0.140143 | − | 0.990131i | \(-0.544756\pi\) | ||||
−0.140143 | + | 0.990131i | \(0.544756\pi\) | |||||||
\(422\) | −118.000 | −0.279621 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −238.000 | −0.561321 | ||||||||
\(425\) | 134.164i | 0.315680i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 657.404i | 1.53959i | ||||||||
\(428\) | −318.000 | −0.742991 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 76.0263i | 0.176805i | ||||||||
\(431\) | 718.000 | 1.66589 | 0.832947 | − | 0.553353i | \(-0.186652\pi\) | ||||
0.832947 | + | 0.553353i | \(0.186652\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 509.823i | 1.17742i | 0.808344 | + | 0.588711i | \(0.200364\pi\) | ||||
−0.808344 | + | 0.588711i | \(0.799636\pi\) | |||||||
\(434\) | − 375.659i | − 0.865575i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 426.000 | 0.977064 | ||||||||
\(437\) | 348.827i | 0.798230i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 26.8328i | − 0.0611226i | −0.999533 | − | 0.0305613i | \(-0.990271\pi\) | ||||
0.999533 | − | 0.0305613i | \(-0.00972948\pi\) | |||||||
\(440\) | − 31.3050i | − 0.0711476i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −360.000 | −0.814480 | ||||||||
\(443\) | 634.000 | 1.43115 | 0.715576 | − | 0.698535i | \(-0.246164\pi\) | ||||
0.715576 | + | 0.698535i | \(0.246164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 60.0000 | 0.134831 | ||||||||
\(446\) | 80.4984i | 0.180490i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 91.0000 | 0.203125 | ||||||||
\(449\) | −338.000 | −0.752784 | −0.376392 | − | 0.926461i | \(-0.622835\pi\) | ||||
−0.376392 | + | 0.926461i | \(0.622835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 53.6656i | − 0.118993i | ||||||||
\(452\) | −102.000 | −0.225664 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 254.912i | − 0.561480i | ||||||||
\(455\) | −210.000 | −0.461538 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −466.000 | −1.01969 | −0.509847 | − | 0.860265i | \(-0.670298\pi\) | ||||
−0.509847 | + | 0.860265i | \(0.670298\pi\) | |||||||
\(458\) | 13.4164i | 0.0292935i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 174.413i | − 0.379159i | ||||||||
\(461\) | 442.741i | 0.960394i | 0.877161 | + | 0.480197i | \(0.159435\pi\) | ||||
−0.877161 | + | 0.480197i | \(0.840565\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 206.000 | 0.444924 | 0.222462 | − | 0.974941i | \(-0.428591\pi\) | ||||
0.222462 | + | 0.974941i | \(0.428591\pi\) | |||||||
\(464\) | 110.000 | 0.237069 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 214.000 | 0.459227 | ||||||||
\(467\) | − 362.243i | − 0.775681i | −0.921727 | − | 0.387840i | \(-0.873221\pi\) | ||||
0.921727 | − | 0.387840i | \(-0.126779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 98.0000 | 0.208955 | ||||||||
\(470\) | 60.0000 | 0.127660 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 281.745i | − 0.596916i | ||||||||
\(473\) | 68.0000 | 0.143763 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 67.0820i | 0.141225i | ||||||||
\(476\) | 563.489i | 1.18380i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −98.0000 | −0.205021 | ||||||||
\(479\) | − 214.663i | − 0.448147i | −0.974572 | − | 0.224074i | \(-0.928064\pi\) | ||||
0.974572 | − | 0.224074i | \(-0.0719356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 187.830i | − 0.390498i | ||||||||
\(482\) | − 160.997i | − 0.334018i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 351.000 | 0.725207 | ||||||||
\(485\) | −60.0000 | −0.123711 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −166.000 | −0.340862 | −0.170431 | − | 0.985370i | \(-0.554516\pi\) | ||||
−0.170431 | + | 0.985370i | \(0.554516\pi\) | |||||||
\(488\) | − 657.404i | − 1.34714i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − 109.567i | − 0.223607i | ||||||||
\(491\) | 838.000 | 1.70672 | 0.853360 | − | 0.521321i | \(-0.174561\pi\) | ||||
0.853360 | + | 0.521321i | \(0.174561\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 590.322i | − 1.19741i | ||||||||
\(494\) | −180.000 | −0.364372 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 268.328i | − 0.540984i | ||||||||
\(497\) | −434.000 | −0.873239 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −262.000 | −0.525050 | −0.262525 | − | 0.964925i | \(-0.584555\pi\) | ||||
−0.262525 | + | 0.964925i | \(0.584555\pi\) | |||||||
\(500\) | − 33.5410i | − 0.0670820i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 335.410i | − 0.668148i | ||||||||
\(503\) | − 429.325i | − 0.853529i | −0.904363 | − | 0.426764i | \(-0.859653\pi\) | ||||
0.904363 | − | 0.426764i | \(-0.140347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −150.000 | −0.297030 | ||||||||
\(506\) | 52.0000 | 0.102767 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −582.000 | −1.14567 | ||||||||
\(509\) | − 898.899i | − 1.76601i | −0.469363 | − | 0.883005i | \(-0.655516\pi\) | ||||
0.469363 | − | 0.883005i | \(-0.344484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 375.659i | − 0.735146i | ||||||||
\(512\) | 305.000 | 0.595703 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 134.164i | 0.261020i | ||||||||
\(515\) | 360.000 | 0.699029 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 53.6656i | − 0.103802i | ||||||||
\(518\) | 98.0000 | 0.189189 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 210.000 | 0.403846 | ||||||||
\(521\) | − 724.486i | − 1.39057i | −0.718735 | − | 0.695284i | \(-0.755279\pi\) | ||||
0.718735 | − | 0.695284i | \(-0.244721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 523.240i | − 1.00046i | −0.865893 | − | 0.500229i | \(-0.833249\pi\) | ||||
0.865893 | − | 0.500229i | \(-0.166751\pi\) | |||||||
\(524\) | − 362.243i | − 0.691303i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 34.0000 | 0.0646388 | ||||||||
\(527\) | −1440.00 | −2.73245 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 147.000 | 0.277883 | ||||||||
\(530\) | − 76.0263i | − 0.143446i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 281.745i | 0.529595i | ||||||||
\(533\) | 360.000 | 0.675422 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 237.023i | − 0.443034i | ||||||||
\(536\) | −98.0000 | −0.182836 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 254.912i | − 0.473814i | ||||||||
\(539\) | −98.0000 | −0.181818 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 842.000 | 1.55638 | 0.778189 | − | 0.628031i | \(-0.216139\pi\) | ||||
0.778189 | + | 0.628031i | \(0.216139\pi\) | |||||||
\(542\) | 321.994i | 0.594084i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 885.483i | − 1.62773i | ||||||||
\(545\) | 317.522i | 0.582609i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 134.000 | 0.244973 | 0.122486 | − | 0.992470i | \(-0.460913\pi\) | ||||
0.122486 | + | 0.992470i | \(0.460913\pi\) | |||||||
\(548\) | −498.000 | −0.908759 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10.0000 | 0.0181818 | ||||||||
\(551\) | − 295.161i | − 0.535682i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 266.000 | 0.481013 | ||||||||
\(554\) | 14.0000 | 0.0252708 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 281.745i | 0.506735i | ||||||||
\(557\) | 706.000 | 1.26750 | 0.633752 | − | 0.773536i | \(-0.281514\pi\) | ||||
0.633752 | + | 0.773536i | \(0.281514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 456.158i | 0.816025i | ||||||||
\(560\) | − 78.2624i | − 0.139754i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.00000 | −0.00355872 | ||||||||
\(563\) | 13.4164i | 0.0238302i | 0.999929 | + | 0.0119151i | \(0.00379279\pi\) | ||||
−0.999929 | + | 0.0119151i | \(0.996207\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 76.0263i | − 0.134560i | ||||||||
\(566\) | − 93.9149i | − 0.165927i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 434.000 | 0.764085 | ||||||||
\(569\) | 82.0000 | 0.144112 | 0.0720562 | − | 0.997401i | \(-0.477044\pi\) | ||||
0.0720562 | + | 0.997401i | \(0.477044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −118.000 | −0.206655 | −0.103327 | − | 0.994647i | \(-0.532949\pi\) | ||||
−0.103327 | + | 0.994647i | \(0.532949\pi\) | |||||||
\(572\) | − 80.4984i | − 0.140732i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 187.830i | 0.327229i | ||||||||
\(575\) | 130.000 | 0.226087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 885.483i | − 1.53463i | −0.641269 | − | 0.767316i | \(-0.721592\pi\) | ||||
0.641269 | − | 0.767316i | \(-0.278408\pi\) | |||||||
\(578\) | −431.000 | −0.745675 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 147.580i | 0.254449i | ||||||||
\(581\) | − 281.745i | − 0.484930i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −68.0000 | −0.116638 | ||||||||
\(584\) | 375.659i | 0.643252i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 335.410i | − 0.572372i | ||||||||
\(587\) | 791.568i | 1.34850i | 0.738504 | + | 0.674249i | \(0.235532\pi\) | ||||
−0.738504 | + | 0.674249i | \(0.764468\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −720.000 | −1.22241 | ||||||||
\(590\) | 90.0000 | 0.152542 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 70.0000 | 0.118243 | ||||||||
\(593\) | 134.164i | 0.226246i | 0.993581 | + | 0.113123i | \(0.0360855\pi\) | ||||
−0.993581 | + | 0.113123i | \(0.963915\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −420.000 | −0.705882 | ||||||||
\(596\) | −426.000 | −0.714765 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 348.827i | 0.583322i | ||||||||
\(599\) | −398.000 | −0.664441 | −0.332220 | − | 0.943202i | \(-0.607798\pi\) | ||||
−0.332220 | + | 0.943202i | \(0.607798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 134.164i | 0.223235i | 0.993751 | + | 0.111617i | \(0.0356031\pi\) | ||||
−0.993751 | + | 0.111617i | \(0.964397\pi\) | |||||||
\(602\) | −238.000 | −0.395349 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.00000 | −0.00993377 | ||||||||
\(605\) | 261.620i | 0.432430i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 939.149i | − 1.54720i | −0.633676 | − | 0.773598i | \(-0.718455\pi\) | ||||
0.633676 | − | 0.773598i | \(-0.281545\pi\) | |||||||
\(608\) | − 442.741i | − 0.728193i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 210.000 | 0.344262 | ||||||||
\(611\) | 360.000 | 0.589198 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 206.000 | 0.336052 | 0.168026 | − | 0.985783i | \(-0.446261\pi\) | ||||
0.168026 | + | 0.985783i | \(0.446261\pi\) | |||||||
\(614\) | 201.246i | 0.327762i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 98.0000 | 0.159091 | ||||||||
\(617\) | −494.000 | −0.800648 | −0.400324 | − | 0.916374i | \(-0.631102\pi\) | ||||
−0.400324 | + | 0.916374i | \(0.631102\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 120.748i | 0.195069i | 0.995232 | + | 0.0975345i | \(0.0310956\pi\) | ||||
−0.995232 | + | 0.0975345i | \(0.968904\pi\) | |||||||
\(620\) | 360.000 | 0.580645 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 509.823i | 0.819652i | ||||||||
\(623\) | 187.830i | 0.301492i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 321.994i | 0.514367i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 201.246i | 0.320456i | ||||||||
\(629\) | − 375.659i | − 0.597233i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 542.000 | 0.858954 | 0.429477 | − | 0.903078i | \(-0.358698\pi\) | ||||
0.429477 | + | 0.903078i | \(0.358698\pi\) | |||||||
\(632\) | −266.000 | −0.420886 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −374.000 | −0.589905 | ||||||||
\(635\) | − 433.797i | − 0.683145i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 657.404i | − 1.03203i | ||||||||
\(638\) | −44.0000 | −0.0689655 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 266.092i | 0.415769i | ||||||||
\(641\) | 298.000 | 0.464899 | 0.232449 | − | 0.972609i | \(-0.425326\pi\) | ||||
0.232449 | + | 0.972609i | \(0.425326\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1006.23i | 1.56490i | 0.622714 | + | 0.782450i | \(0.286030\pi\) | ||||
−0.622714 | + | 0.782450i | \(0.713970\pi\) | |||||||
\(644\) | 546.000 | 0.847826 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −360.000 | −0.557276 | ||||||||
\(647\) | − 643.988i | − 0.995344i | −0.867365 | − | 0.497672i | \(-0.834188\pi\) | ||||
0.867365 | − | 0.497672i | \(-0.165812\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 80.4984i | − 0.124035i | ||||||||
\(650\) | 67.0820i | 0.103203i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 102.000 | 0.156442 | ||||||||
\(653\) | 154.000 | 0.235835 | 0.117917 | − | 0.993023i | \(-0.462378\pi\) | ||||
0.117917 | + | 0.993023i | \(0.462378\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 270.000 | 0.412214 | ||||||||
\(656\) | 134.164i | 0.204518i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 187.830i | 0.285455i | ||||||||
\(659\) | −338.000 | −0.512898 | −0.256449 | − | 0.966558i | \(-0.582553\pi\) | ||||
−0.256449 | + | 0.966558i | \(0.582553\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 576.906i | − 0.872777i | −0.899758 | − | 0.436388i | \(-0.856257\pi\) | ||||
0.899758 | − | 0.436388i | \(-0.143743\pi\) | |||||||
\(662\) | 482.000 | 0.728097 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 281.745i | 0.424314i | ||||||||
\(665\) | −210.000 | −0.315789 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −572.000 | −0.857571 | ||||||||
\(668\) | − 321.994i | − 0.482027i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 31.3050i | − 0.0467238i | ||||||||
\(671\) | − 187.830i | − 0.279925i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −814.000 | −1.20951 | −0.604755 | − | 0.796412i | \(-0.706729\pi\) | ||||
−0.604755 | + | 0.796412i | \(0.706729\pi\) | |||||||
\(674\) | 494.000 | 0.732938 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 33.0000 | 0.0488166 | ||||||||
\(677\) | 684.237i | 1.01069i | 0.862918 | + | 0.505345i | \(0.168635\pi\) | ||||
−0.862918 | + | 0.505345i | \(0.831365\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 187.830i | − 0.276627i | ||||||||
\(680\) | 420.000 | 0.617647 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 107.331i | 0.157377i | ||||||||
\(683\) | −926.000 | −1.35578 | −0.677892 | − | 0.735162i | \(-0.737106\pi\) | ||||
−0.677892 | + | 0.735162i | \(0.737106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 371.187i | − 0.541879i | ||||||||
\(686\) | 343.000 | 0.500000 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −170.000 | −0.247093 | ||||||||
\(689\) | − 456.158i | − 0.662058i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 576.906i | 0.834885i | 0.908703 | + | 0.417443i | \(0.137073\pi\) | ||||
−0.908703 | + | 0.417443i | \(0.862927\pi\) | |||||||
\(692\) | 442.741i | 0.639800i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 346.000 | 0.498559 | ||||||||
\(695\) | −210.000 | −0.302158 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 720.000 | 1.03300 | ||||||||
\(698\) | − 335.410i | − 0.480530i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 105.000 | 0.150000 | ||||||||
\(701\) | −362.000 | −0.516405 | −0.258203 | − | 0.966091i | \(-0.583130\pi\) | ||||
−0.258203 | + | 0.966091i | \(0.583130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 187.830i | − 0.267183i | ||||||||
\(704\) | −26.0000 | −0.0369318 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 26.8328i | − 0.0380068i | ||||||||
\(707\) | − 469.574i | − 0.664179i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1058.00 | 1.49224 | 0.746121 | − | 0.665810i | \(-0.231914\pi\) | ||||
0.746121 | + | 0.665810i | \(0.231914\pi\) | |||||||
\(710\) | 138.636i | 0.195262i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 187.830i | − 0.263806i | ||||||||
\(713\) | 1395.31i | 1.95695i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 60.0000 | 0.0839161 | ||||||||
\(716\) | 654.000 | 0.913408 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −338.000 | −0.470752 | ||||||||
\(719\) | 482.991i | 0.671753i | 0.941906 | + | 0.335877i | \(0.109033\pi\) | ||||
−0.941906 | + | 0.335877i | \(0.890967\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1126.98i | 1.56308i | ||||||||
\(722\) | 181.000 | 0.250693 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 764.735i | 1.05626i | ||||||||
\(725\) | −110.000 | −0.151724 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1126.98i | 1.55018i | 0.631853 | + | 0.775088i | \(0.282295\pi\) | ||||
−0.631853 | + | 0.775088i | \(0.717705\pi\) | |||||||
\(728\) | 657.404i | 0.903027i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −120.000 | −0.164384 | ||||||||
\(731\) | 912.316i | 1.24804i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1301.39i | − 1.77543i | −0.460392 | − | 0.887716i | \(-0.652291\pi\) | ||||
0.460392 | − | 0.887716i | \(-0.347709\pi\) | |||||||
\(734\) | 295.161i | 0.402127i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −858.000 | −1.16576 | ||||||||
\(737\) | −28.0000 | −0.0379919 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −982.000 | −1.32882 | −0.664411 | − | 0.747367i | \(-0.731318\pi\) | ||||
−0.664411 | + | 0.747367i | \(0.731318\pi\) | |||||||
\(740\) | 93.9149i | 0.126912i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 238.000 | 0.320755 | ||||||||
\(743\) | 694.000 | 0.934051 | 0.467026 | − | 0.884244i | \(-0.345326\pi\) | ||||
0.467026 | + | 0.884244i | \(0.345326\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 317.522i | − 0.426204i | ||||||||
\(746\) | 86.0000 | 0.115282 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 160.997i | − 0.215236i | ||||||||
\(749\) | 742.000 | 0.990654 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 242.000 | 0.322237 | 0.161119 | − | 0.986935i | \(-0.448490\pi\) | ||||
0.161119 | + | 0.986935i | \(0.448490\pi\) | |||||||
\(752\) | 134.164i | 0.178410i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 295.161i | − 0.391460i | ||||||||
\(755\) | − 4.47214i | − 0.00592336i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −106.000 | −0.140026 | −0.0700132 | − | 0.997546i | \(-0.522304\pi\) | ||||
−0.0700132 | + | 0.997546i | \(0.522304\pi\) | |||||||
\(758\) | −262.000 | −0.345646 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 210.000 | 0.276316 | ||||||||
\(761\) | − 1100.15i | − 1.44566i | −0.691027 | − | 0.722829i | \(-0.742842\pi\) | ||||
0.691027 | − | 0.722829i | \(-0.257158\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −994.000 | −1.30275 | ||||||||
\(764\) | −174.000 | −0.227749 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 563.489i | 0.735625i | ||||||||
\(767\) | 540.000 | 0.704042 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1126.98i | 1.46551i | 0.680492 | + | 0.732756i | \(0.261766\pi\) | ||||
−0.680492 | + | 0.732756i | \(0.738234\pi\) | |||||||
\(770\) | 31.3050i | 0.0406558i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −618.000 | −0.800518 | ||||||||
\(773\) | − 818.401i | − 1.05873i | −0.848393 | − | 0.529367i | \(-0.822430\pi\) | ||||
0.848393 | − | 0.529367i | \(-0.177570\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 268.328i | 0.346230i | ||||||||
\(776\) | 187.830i | 0.242049i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −698.000 | −0.897172 | ||||||||
\(779\) | 360.000 | 0.462131 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 124.000 | 0.158771 | ||||||||
\(782\) | 697.653i | 0.892140i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 245.000 | 0.312500 | ||||||||
\(785\) | −150.000 | −0.191083 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 684.237i | 0.869424i | 0.900569 | + | 0.434712i | \(0.143150\pi\) | ||||
−0.900569 | + | 0.434712i | \(0.856850\pi\) | |||||||
\(788\) | −678.000 | −0.860406 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 84.9706i | − 0.107558i | ||||||||
\(791\) | 238.000 | 0.300885 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1260.00 | 1.58890 | ||||||||
\(794\) | 308.577i | 0.388636i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 402.492i | − 0.505644i | ||||||||
\(797\) | − 308.577i | − 0.387174i | −0.981083 | − | 0.193587i | \(-0.937988\pi\) | ||||
0.981083 | − | 0.193587i | \(-0.0620121\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 720.000 | 0.901126 | ||||||||
\(800\) | −165.000 | −0.206250 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 538.000 | 0.670823 | ||||||||
\(803\) | 107.331i | 0.133663i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 406.964i | 0.505546i | ||||||||
\(806\) | −720.000 | −0.893300 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 469.574i | 0.581156i | ||||||||
\(809\) | −1358.00 | −1.67862 | −0.839308 | − | 0.543657i | \(-0.817039\pi\) | ||||
−0.839308 | + | 0.543657i | \(0.817039\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 308.577i | − 0.380490i | −0.981737 | − | 0.190245i | \(-0.939072\pi\) | ||||
0.981737 | − | 0.190245i | \(-0.0609282\pi\) | |||||||
\(812\) | −462.000 | −0.568966 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −28.0000 | −0.0343980 | ||||||||
\(815\) | 76.0263i | 0.0932838i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 456.158i | 0.558333i | ||||||||
\(818\) | 295.161i | 0.360832i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −180.000 | −0.219512 | ||||||||
\(821\) | −482.000 | −0.587089 | −0.293544 | − | 0.955945i | \(-0.594835\pi\) | ||||
−0.293544 | + | 0.955945i | \(0.594835\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 926.000 | 1.12515 | 0.562576 | − | 0.826746i | \(-0.309810\pi\) | ||||
0.562576 | + | 0.826746i | \(0.309810\pi\) | |||||||
\(824\) | − 1126.98i | − 1.36769i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 281.745i | 0.341095i | ||||||||
\(827\) | 226.000 | 0.273277 | 0.136638 | − | 0.990621i | \(-0.456370\pi\) | ||||
0.136638 | + | 0.990621i | \(0.456370\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1462.39i | − 1.76404i | −0.471213 | − | 0.882020i | \(-0.656184\pi\) | ||||
0.471213 | − | 0.882020i | \(-0.343816\pi\) | |||||||
\(830\) | −90.0000 | −0.108434 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 174.413i | − 0.209631i | ||||||||
\(833\) | − 1314.81i | − 1.57840i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 240.000 | 0.287425 | ||||||||
\(836\) | − 80.4984i | − 0.0962900i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 818.401i | 0.976612i | ||||||||
\(839\) | 831.817i | 0.991439i | 0.868483 | + | 0.495719i | \(0.165096\pi\) | ||||
−0.868483 | + | 0.495719i | \(0.834904\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −357.000 | −0.424495 | ||||||||
\(842\) | −118.000 | −0.140143 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 354.000 | 0.419431 | ||||||||
\(845\) | 24.5967i | 0.0291086i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −819.000 | −0.966942 | ||||||||
\(848\) | 170.000 | 0.200472 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 134.164i | 0.157840i | ||||||||
\(851\) | −364.000 | −0.427732 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 40.2492i | − 0.0471855i | −0.999722 | − | 0.0235927i | \(-0.992489\pi\) | ||||
0.999722 | − | 0.0235927i | \(-0.00751050\pi\) | |||||||
\(854\) | 657.404i | 0.769794i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −742.000 | −0.866822 | ||||||||
\(857\) | − 268.328i | − 0.313102i | −0.987670 | − | 0.156551i | \(-0.949962\pi\) | ||||
0.987670 | − | 0.156551i | \(-0.0500375\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 308.577i | − 0.359229i | −0.983737 | − | 0.179614i | \(-0.942515\pi\) | ||||
0.983737 | − | 0.179614i | \(-0.0574850\pi\) | |||||||
\(860\) | − 228.079i | − 0.265208i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 718.000 | 0.832947 | ||||||||
\(863\) | 514.000 | 0.595597 | 0.297798 | − | 0.954629i | \(-0.403748\pi\) | ||||
0.297798 | + | 0.954629i | \(0.403748\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −330.000 | −0.381503 | ||||||||
\(866\) | 509.823i | 0.588711i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1126.98i | 1.29836i | ||||||||
\(869\) | −76.0000 | −0.0874568 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 187.830i | − 0.215648i | ||||||||
\(872\) | 994.000 | 1.13991 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 348.827i | 0.399115i | ||||||||
\(875\) | 78.2624i | 0.0894427i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1306.00 | −1.48917 | −0.744584 | − | 0.667529i | \(-0.767352\pi\) | ||||
−0.744584 | + | 0.667529i | \(0.767352\pi\) | |||||||
\(878\) | − 26.8328i | − 0.0305613i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 22.3607i | 0.0254099i | ||||||||
\(881\) | 1126.98i | 1.27920i | 0.768706 | + | 0.639602i | \(0.220901\pi\) | ||||
−0.768706 | + | 0.639602i | \(0.779099\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1526.00 | 1.72820 | 0.864100 | − | 0.503321i | \(-0.167889\pi\) | ||||
0.864100 | + | 0.503321i | \(0.167889\pi\) | |||||||
\(884\) | 1080.00 | 1.22172 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 634.000 | 0.715576 | ||||||||
\(887\) | − 1556.30i | − 1.75457i | −0.479970 | − | 0.877285i | \(-0.659352\pi\) | ||||
0.479970 | − | 0.877285i | \(-0.340648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1358.00 | 1.52756 | ||||||||
\(890\) | 60.0000 | 0.0674157 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 241.495i | − 0.270735i | ||||||||
\(893\) | 360.000 | 0.403135 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 487.463i | 0.544651i | ||||||||
\(896\) | −833.000 | −0.929688 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −338.000 | −0.376392 | ||||||||
\(899\) | − 1180.64i | − 1.31329i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 912.316i | − 1.01256i | ||||||||
\(902\) | − 53.6656i | − 0.0594963i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −238.000 | −0.263274 | ||||||||
\(905\) | −570.000 | −0.629834 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 734.000 | 0.809261 | 0.404631 | − | 0.914480i | \(-0.367400\pi\) | ||||
0.404631 | + | 0.914480i | \(0.367400\pi\) | |||||||
\(908\) | 764.735i | 0.842219i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −210.000 | −0.230769 | ||||||||
\(911\) | −1202.00 | −1.31943 | −0.659715 | − | 0.751516i | \(-0.729323\pi\) | ||||
−0.659715 | + | 0.751516i | \(0.729323\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 80.4984i | 0.0881692i | ||||||||
\(914\) | −466.000 | −0.509847 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 40.2492i | − 0.0439402i | ||||||||
\(917\) | 845.234i | 0.921738i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1282.00 | −1.39499 | −0.697497 | − | 0.716587i | \(-0.745703\pi\) | ||||
−0.697497 | + | 0.716587i | \(0.745703\pi\) | |||||||
\(920\) | − 406.964i | − 0.442353i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 442.741i | 0.480197i | ||||||||
\(923\) | 831.817i | 0.901210i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −70.0000 | −0.0756757 | ||||||||
\(926\) | 206.000 | 0.222462 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 726.000 | 0.782328 | ||||||||
\(929\) | 1126.98i | 1.21311i | 0.795042 | + | 0.606554i | \(0.207449\pi\) | ||||
−0.795042 | + | 0.606554i | \(0.792551\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 657.404i | − 0.706127i | ||||||||
\(932\) | −642.000 | −0.688841 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 362.243i | − 0.387840i | ||||||||
\(935\) | 120.000 | 0.128342 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 214.663i | 0.229096i | 0.993418 | + | 0.114548i | \(0.0365419\pi\) | ||||
−0.993418 | + | 0.114548i | \(0.963458\pi\) | |||||||
\(938\) | 98.0000 | 0.104478 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −180.000 | −0.191489 | ||||||||
\(941\) | − 845.234i | − 0.898229i | −0.893474 | − | 0.449115i | \(-0.851739\pi\) | ||||
0.893474 | − | 0.449115i | \(-0.148261\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 697.653i | − 0.739823i | ||||||||
\(944\) | 201.246i | 0.213184i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 68.0000 | 0.0718816 | ||||||||
\(947\) | −734.000 | −0.775079 | −0.387540 | − | 0.921853i | \(-0.626675\pi\) | ||||
−0.387540 | + | 0.921853i | \(0.626675\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −720.000 | −0.758693 | ||||||||
\(950\) | 67.0820i | 0.0706127i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1314.81i | 1.38110i | ||||||||
\(953\) | 934.000 | 0.980063 | 0.490031 | − | 0.871705i | \(-0.336985\pi\) | ||||
0.490031 | + | 0.871705i | \(0.336985\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 129.692i | − 0.135803i | ||||||||
\(956\) | 294.000 | 0.307531 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 214.663i | − 0.224074i | ||||||||
\(959\) | 1162.00 | 1.21168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1919.00 | −1.99688 | ||||||||
\(962\) | − 187.830i | − 0.195249i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 482.991i | 0.501028i | ||||||||
\(965\) | − 460.630i | − 0.477337i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 314.000 | 0.324716 | 0.162358 | − | 0.986732i | \(-0.448090\pi\) | ||||
0.162358 | + | 0.986732i | \(0.448090\pi\) | |||||||
\(968\) | 819.000 | 0.846074 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −60.0000 | −0.0618557 | ||||||||
\(971\) | 147.580i | 0.151988i | 0.997108 | + | 0.0759941i | \(0.0242130\pi\) | ||||
−0.997108 | + | 0.0759941i | \(0.975787\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 657.404i | − 0.675646i | ||||||||
\(974\) | −166.000 | −0.170431 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 469.574i | 0.481121i | ||||||||
\(977\) | 1486.00 | 1.52098 | 0.760491 | − | 0.649348i | \(-0.224958\pi\) | ||||
0.760491 | + | 0.649348i | \(0.224958\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 53.6656i | − 0.0548168i | ||||||||
\(980\) | 328.702i | 0.335410i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 838.000 | 0.853360 | ||||||||
\(983\) | 965.981i | 0.982687i | 0.870966 | + | 0.491344i | \(0.163494\pi\) | ||||
−0.870966 | + | 0.491344i | \(0.836506\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 505.351i | − 0.513047i | ||||||||
\(986\) | − 590.322i | − 0.598704i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 540.000 | 0.546559 | ||||||||
\(989\) | 884.000 | 0.893832 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.0000 | −0.0585267 | −0.0292634 | − | 0.999572i | \(-0.509316\pi\) | ||||
−0.0292634 | + | 0.999572i | \(0.509316\pi\) | |||||||
\(992\) | − 1770.97i | − 1.78525i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −434.000 | −0.436620 | ||||||||
\(995\) | 300.000 | 0.301508 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 630.571i | − 0.632469i | −0.948681 | − | 0.316234i | \(-0.897581\pi\) | ||||
0.948681 | − | 0.316234i | \(-0.102419\pi\) | |||||||
\(998\) | −262.000 | −0.262525 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.3.h.b.181.1 | 2 | ||
3.2 | odd | 2 | 35.3.d.a.6.2 | yes | 2 | ||
7.6 | odd | 2 | inner | 315.3.h.b.181.2 | 2 | ||
12.11 | even | 2 | 560.3.f.a.321.1 | 2 | |||
15.2 | even | 4 | 175.3.c.d.174.2 | 4 | |||
15.8 | even | 4 | 175.3.c.d.174.3 | 4 | |||
15.14 | odd | 2 | 175.3.d.f.76.1 | 2 | |||
21.2 | odd | 6 | 245.3.h.b.31.1 | 4 | |||
21.5 | even | 6 | 245.3.h.b.31.2 | 4 | |||
21.11 | odd | 6 | 245.3.h.b.166.2 | 4 | |||
21.17 | even | 6 | 245.3.h.b.166.1 | 4 | |||
21.20 | even | 2 | 35.3.d.a.6.1 | ✓ | 2 | ||
84.83 | odd | 2 | 560.3.f.a.321.2 | 2 | |||
105.62 | odd | 4 | 175.3.c.d.174.1 | 4 | |||
105.83 | odd | 4 | 175.3.c.d.174.4 | 4 | |||
105.104 | even | 2 | 175.3.d.f.76.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.3.d.a.6.1 | ✓ | 2 | 21.20 | even | 2 | ||
35.3.d.a.6.2 | yes | 2 | 3.2 | odd | 2 | ||
175.3.c.d.174.1 | 4 | 105.62 | odd | 4 | |||
175.3.c.d.174.2 | 4 | 15.2 | even | 4 | |||
175.3.c.d.174.3 | 4 | 15.8 | even | 4 | |||
175.3.c.d.174.4 | 4 | 105.83 | odd | 4 | |||
175.3.d.f.76.1 | 2 | 15.14 | odd | 2 | |||
175.3.d.f.76.2 | 2 | 105.104 | even | 2 | |||
245.3.h.b.31.1 | 4 | 21.2 | odd | 6 | |||
245.3.h.b.31.2 | 4 | 21.5 | even | 6 | |||
245.3.h.b.166.1 | 4 | 21.17 | even | 6 | |||
245.3.h.b.166.2 | 4 | 21.11 | odd | 6 | |||
315.3.h.b.181.1 | 2 | 1.1 | even | 1 | trivial | ||
315.3.h.b.181.2 | 2 | 7.6 | odd | 2 | inner | ||
560.3.f.a.321.1 | 2 | 12.11 | even | 2 | |||
560.3.f.a.321.2 | 2 | 84.83 | odd | 2 |