Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(799,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2850.799");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.d (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: | \(22.7573645761\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2850.799 |
Dual form | 2850.2.d.w.799.3 |
$q$-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 \(\left(\mathbb{Z}/2850\mathbb{Z}\right)^\times\).
\(n\) | \(1027\) | \(1351\) | \(1901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.449490i | 0.169891i | 0.996386 | + | 0.0849456i | \(0.0270716\pi\) | ||||
−0.996386 | + | 0.0849456i | \(0.972928\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.44949 | −0.437038 | −0.218519 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218519 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | 0.449490 | 0.120131 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.449490i | 0.109017i | 0.998513 | + | 0.0545086i | \(0.0173592\pi\) | ||||
−0.998513 | + | 0.0545086i | \(0.982641\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.449490 | −0.0980867 | ||||||||
\(22\) | 1.44949i | 0.309032i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | −0.994550 | − | 0.104257i | \(-0.966753\pi\) | ||||
0.994550 | − | 0.104257i | \(-0.0332465\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.44949 | 0.480384 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 0.449490i | − 0.0849456i | ||||||||
\(29\) | −10.3485 | −1.92166 | −0.960831 | − | 0.277134i | \(-0.910615\pi\) | ||||
−0.960831 | + | 0.277134i | \(0.910615\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 1.44949i | − 0.252324i | ||||||||
\(34\) | 0.449490 | 0.0770869 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − 11.7980i | − 1.93957i | −0.243956 | − | 0.969786i | \(-0.578445\pi\) | ||||
0.243956 | − | 0.969786i | \(-0.421555\pi\) | |||||||
\(38\) | 1.00000i | 0.162221i | ||||||||
\(39\) | −2.44949 | −0.392232 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.89898 | 1.38979 | 0.694894 | − | 0.719113i | \(-0.255451\pi\) | ||||
0.694894 | + | 0.719113i | \(0.255451\pi\) | |||||||
\(42\) | 0.449490i | 0.0693578i | ||||||||
\(43\) | 2.44949i | 0.373544i | 0.982403 | + | 0.186772i | \(0.0598025\pi\) | ||||
−0.982403 | + | 0.186772i | \(0.940197\pi\) | |||||||
\(44\) | 1.44949 | 0.218519 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | − 11.7980i | − 1.72091i | −0.509527 | − | 0.860455i | \(-0.670180\pi\) | ||||
0.509527 | − | 0.860455i | \(-0.329820\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 6.79796 | 0.971137 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.449490 | −0.0629412 | ||||||||
\(52\) | − 2.44949i | − 0.339683i | ||||||||
\(53\) | − 2.55051i | − 0.350340i | −0.984538 | − | 0.175170i | \(-0.943953\pi\) | ||||
0.984538 | − | 0.175170i | \(-0.0560474\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.449490 | −0.0600656 | ||||||||
\(57\) | − 1.00000i | − 0.132453i | ||||||||
\(58\) | 10.3485i | 1.35882i | ||||||||
\(59\) | −1.55051 | −0.201859 | −0.100930 | − | 0.994894i | \(-0.532182\pi\) | ||||
−0.100930 | + | 0.994894i | \(0.532182\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.55051 | −0.582633 | −0.291317 | − | 0.956627i | \(-0.594093\pi\) | ||||
−0.291317 | + | 0.956627i | \(0.594093\pi\) | |||||||
\(62\) | 3.00000i | 0.381000i | ||||||||
\(63\) | − 0.449490i | − 0.0566304i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.44949 | −0.178420 | ||||||||
\(67\) | 9.24745i | 1.12976i | 0.825175 | + | 0.564878i | \(0.191077\pi\) | ||||
−0.825175 | + | 0.564878i | \(0.808923\pi\) | |||||||
\(68\) | − 0.449490i | − 0.0545086i | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.44949 | −0.765414 | −0.382707 | − | 0.923870i | \(-0.625008\pi\) | ||||
−0.382707 | + | 0.923870i | \(0.625008\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 1.00000i | − 0.117041i | −0.998286 | − | 0.0585206i | \(-0.981362\pi\) | ||||
0.998286 | − | 0.0585206i | \(-0.0186383\pi\) | |||||||
\(74\) | −11.7980 | −1.37148 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | − 0.651531i | − 0.0742488i | ||||||||
\(78\) | 2.44949i | 0.277350i | ||||||||
\(79\) | 5.00000 | 0.562544 | 0.281272 | − | 0.959628i | \(-0.409244\pi\) | ||||
0.281272 | + | 0.959628i | \(0.409244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 8.89898i | − 0.982728i | ||||||||
\(83\) | − 6.34847i | − 0.696835i | −0.937339 | − | 0.348418i | \(-0.886719\pi\) | ||||
0.937339 | − | 0.348418i | \(-0.113281\pi\) | |||||||
\(84\) | 0.449490 | 0.0490434 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.44949 | 0.264135 | ||||||||
\(87\) | − 10.3485i | − 1.10947i | ||||||||
\(88\) | − 1.44949i | − 0.154516i | ||||||||
\(89\) | −11.8990 | −1.26129 | −0.630645 | − | 0.776072i | \(-0.717209\pi\) | ||||
−0.630645 | + | 0.776072i | \(0.717209\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10102 | −0.115418 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | − 3.00000i | − 0.311086i | ||||||||
\(94\) | −11.7980 | −1.21687 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − 6.44949i | − 0.654846i | −0.944878 | − | 0.327423i | \(-0.893820\pi\) | ||||
0.944878 | − | 0.327423i | \(-0.106180\pi\) | |||||||
\(98\) | − 6.79796i | − 0.686698i | ||||||||
\(99\) | 1.44949 | 0.145679 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.44949 | −0.641748 | −0.320874 | − | 0.947122i | \(-0.603977\pi\) | ||||
−0.320874 | + | 0.947122i | \(0.603977\pi\) | |||||||
\(102\) | 0.449490i | 0.0445061i | ||||||||
\(103\) | − 7.89898i | − 0.778310i | −0.921172 | − | 0.389155i | \(-0.872767\pi\) | ||||
0.921172 | − | 0.389155i | \(-0.127233\pi\) | |||||||
\(104\) | −2.44949 | −0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.55051 | −0.247727 | ||||||||
\(107\) | − 2.65153i | − 0.256333i | −0.991753 | − | 0.128167i | \(-0.959091\pi\) | ||||
0.991753 | − | 0.128167i | \(-0.0409092\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −6.89898 | −0.660802 | −0.330401 | − | 0.943841i | \(-0.607184\pi\) | ||||
−0.330401 | + | 0.943841i | \(0.607184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.7980 | 1.11981 | ||||||||
\(112\) | 0.449490i | 0.0424728i | ||||||||
\(113\) | 2.79796i | 0.263210i | 0.991302 | + | 0.131605i | \(0.0420130\pi\) | ||||
−0.991302 | + | 0.131605i | \(0.957987\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.3485 | 0.960831 | ||||||||
\(117\) | − 2.44949i | − 0.226455i | ||||||||
\(118\) | 1.55051i | 0.142736i | ||||||||
\(119\) | −0.202041 | −0.0185211 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.89898 | −0.808998 | ||||||||
\(122\) | 4.55051i | 0.411984i | ||||||||
\(123\) | 8.89898i | 0.802394i | ||||||||
\(124\) | 3.00000 | 0.269408 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.449490 | −0.0400437 | ||||||||
\(127\) | − 9.89898i | − 0.878392i | −0.898391 | − | 0.439196i | \(-0.855263\pi\) | ||||
0.898391 | − | 0.439196i | \(-0.144737\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −2.44949 | −0.215666 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.2474 | −1.33218 | −0.666088 | − | 0.745873i | \(-0.732032\pi\) | ||||
−0.666088 | + | 0.745873i | \(0.732032\pi\) | |||||||
\(132\) | 1.44949i | 0.126162i | ||||||||
\(133\) | − 0.449490i | − 0.0389757i | ||||||||
\(134\) | 9.24745 | 0.798858 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.449490 | −0.0385434 | ||||||||
\(137\) | − 4.89898i | − 0.418548i | −0.977857 | − | 0.209274i | \(-0.932890\pi\) | ||||
0.977857 | − | 0.209274i | \(-0.0671101\pi\) | |||||||
\(138\) | − 1.00000i | − 0.0851257i | ||||||||
\(139\) | −2.24745 | −0.190626 | −0.0953131 | − | 0.995447i | \(-0.530385\pi\) | ||||
−0.0953131 | + | 0.995447i | \(0.530385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.7980 | 0.993567 | ||||||||
\(142\) | 6.44949i | 0.541229i | ||||||||
\(143\) | − 3.55051i | − 0.296909i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.00000 | −0.0827606 | ||||||||
\(147\) | 6.79796i | 0.560686i | ||||||||
\(148\) | 11.7980i | 0.969786i | ||||||||
\(149\) | 13.7980 | 1.13037 | 0.565186 | − | 0.824963i | \(-0.308804\pi\) | ||||
0.565186 | + | 0.824963i | \(0.308804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.20204 | −0.341957 | −0.170979 | − | 0.985275i | \(-0.554693\pi\) | ||||
−0.170979 | + | 0.985275i | \(0.554693\pi\) | |||||||
\(152\) | − 1.00000i | − 0.0811107i | ||||||||
\(153\) | − 0.449490i | − 0.0363391i | ||||||||
\(154\) | −0.651531 | −0.0525018 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.44949 | 0.196116 | ||||||||
\(157\) | − 4.89898i | − 0.390981i | −0.980706 | − | 0.195491i | \(-0.937370\pi\) | ||||
0.980706 | − | 0.195491i | \(-0.0626299\pi\) | |||||||
\(158\) | − 5.00000i | − 0.397779i | ||||||||
\(159\) | 2.55051 | 0.202269 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.449490 | 0.0354248 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | 0.202041i | 0.0158251i | 0.999969 | + | 0.00791254i | \(0.00251867\pi\) | ||||
−0.999969 | + | 0.00791254i | \(0.997481\pi\) | |||||||
\(164\) | −8.89898 | −0.694894 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.34847 | −0.492737 | ||||||||
\(167\) | − 18.0000i | − 1.39288i | −0.717614 | − | 0.696441i | \(-0.754766\pi\) | ||||
0.717614 | − | 0.696441i | \(-0.245234\pi\) | |||||||
\(168\) | − 0.449490i | − 0.0346789i | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | 0.0764719 | ||||||||
\(172\) | − 2.44949i | − 0.186772i | ||||||||
\(173\) | − 16.3485i | − 1.24295i | −0.783434 | − | 0.621476i | \(-0.786534\pi\) | ||||
0.783434 | − | 0.621476i | \(-0.213466\pi\) | |||||||
\(174\) | −10.3485 | −0.784515 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.44949 | −0.109259 | ||||||||
\(177\) | − 1.55051i | − 0.116543i | ||||||||
\(178\) | 11.8990i | 0.891866i | ||||||||
\(179\) | −6.20204 | −0.463562 | −0.231781 | − | 0.972768i | \(-0.574455\pi\) | ||||
−0.231781 | + | 0.972768i | \(0.574455\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.55051 | −0.709884 | −0.354942 | − | 0.934888i | \(-0.615499\pi\) | ||||
−0.354942 | + | 0.934888i | \(0.615499\pi\) | |||||||
\(182\) | 1.10102i | 0.0816131i | ||||||||
\(183\) | − 4.55051i | − 0.336383i | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | −0.219971 | ||||||||
\(187\) | − 0.651531i | − 0.0476446i | ||||||||
\(188\) | 11.7980i | 0.860455i | ||||||||
\(189\) | 0.449490 | 0.0326956 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.89898 | −0.716265 | −0.358133 | − | 0.933671i | \(-0.616586\pi\) | ||||
−0.358133 | + | 0.933671i | \(0.616586\pi\) | |||||||
\(192\) | − 1.00000i | − 0.0721688i | ||||||||
\(193\) | − 0.651531i | − 0.0468982i | −0.999725 | − | 0.0234491i | \(-0.992535\pi\) | ||||
0.999725 | − | 0.0234491i | \(-0.00746477\pi\) | |||||||
\(194\) | −6.44949 | −0.463046 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.79796 | −0.485568 | ||||||||
\(197\) | − 12.6515i | − 0.901384i | −0.892679 | − | 0.450692i | \(-0.851177\pi\) | ||||
0.892679 | − | 0.450692i | \(-0.148823\pi\) | |||||||
\(198\) | − 1.44949i | − 0.103011i | ||||||||
\(199\) | 10.0000 | 0.708881 | 0.354441 | − | 0.935079i | \(-0.384671\pi\) | ||||
0.354441 | + | 0.935079i | \(0.384671\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.24745 | −0.652265 | ||||||||
\(202\) | 6.44949i | 0.453785i | ||||||||
\(203\) | − 4.65153i | − 0.326473i | ||||||||
\(204\) | 0.449490 | 0.0314706 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.89898 | −0.550348 | ||||||||
\(207\) | 1.00000i | 0.0695048i | ||||||||
\(208\) | 2.44949i | 0.169842i | ||||||||
\(209\) | 1.44949 | 0.100263 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.3485 | −1.26316 | −0.631580 | − | 0.775310i | \(-0.717593\pi\) | ||||
−0.631580 | + | 0.775310i | \(0.717593\pi\) | |||||||
\(212\) | 2.55051i | 0.175170i | ||||||||
\(213\) | − 6.44949i | − 0.441912i | ||||||||
\(214\) | −2.65153 | −0.181255 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | − 1.34847i | − 0.0915401i | ||||||||
\(218\) | 6.89898i | 0.467258i | ||||||||
\(219\) | 1.00000 | 0.0675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.10102 | −0.0740627 | ||||||||
\(222\) | − 11.7980i | − 0.791827i | ||||||||
\(223\) | 25.8990i | 1.73432i | 0.498026 | + | 0.867162i | \(0.334058\pi\) | ||||
−0.498026 | + | 0.867162i | \(0.665942\pi\) | |||||||
\(224\) | 0.449490 | 0.0300328 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.79796 | 0.186117 | ||||||||
\(227\) | 9.59592i | 0.636903i | 0.947939 | + | 0.318452i | \(0.103163\pi\) | ||||
−0.947939 | + | 0.318452i | \(0.896837\pi\) | |||||||
\(228\) | 1.00000i | 0.0662266i | ||||||||
\(229\) | 17.2474 | 1.13974 | 0.569872 | − | 0.821734i | \(-0.306993\pi\) | ||||
0.569872 | + | 0.821734i | \(0.306993\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.651531 | 0.0428676 | ||||||||
\(232\) | − 10.3485i | − 0.679410i | ||||||||
\(233\) | − 18.2474i | − 1.19543i | −0.801709 | − | 0.597715i | \(-0.796075\pi\) | ||||
0.801709 | − | 0.597715i | \(-0.203925\pi\) | |||||||
\(234\) | −2.44949 | −0.160128 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.55051 | 0.100930 | ||||||||
\(237\) | 5.00000i | 0.324785i | ||||||||
\(238\) | 0.202041i | 0.0130964i | ||||||||
\(239\) | −20.6969 | −1.33877 | −0.669387 | − | 0.742914i | \(-0.733443\pi\) | ||||
−0.669387 | + | 0.742914i | \(0.733443\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.449490 | 0.0289542 | 0.0144771 | − | 0.999895i | \(-0.495392\pi\) | ||||
0.0144771 | + | 0.999895i | \(0.495392\pi\) | |||||||
\(242\) | 8.89898i | 0.572048i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 4.55051 | 0.291317 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.89898 | 0.567378 | ||||||||
\(247\) | − 2.44949i | − 0.155857i | ||||||||
\(248\) | − 3.00000i | − 0.190500i | ||||||||
\(249\) | 6.34847 | 0.402318 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | 0.449490i | 0.0283152i | ||||||||
\(253\) | 1.44949i | 0.0911286i | ||||||||
\(254\) | −9.89898 | −0.621117 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 27.4949i | − 1.71508i | −0.514413 | − | 0.857542i | \(-0.671990\pi\) | ||||
0.514413 | − | 0.857542i | \(-0.328010\pi\) | |||||||
\(258\) | 2.44949i | 0.152499i | ||||||||
\(259\) | 5.30306 | 0.329516 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.3485 | 0.640554 | ||||||||
\(262\) | 15.2474i | 0.941991i | ||||||||
\(263\) | 12.7980i | 0.789156i | 0.918862 | + | 0.394578i | \(0.129109\pi\) | ||||
−0.918862 | + | 0.394578i | \(0.870891\pi\) | |||||||
\(264\) | 1.44949 | 0.0892099 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.449490 | −0.0275600 | ||||||||
\(267\) | − 11.8990i | − 0.728206i | ||||||||
\(268\) | − 9.24745i | − 0.564878i | ||||||||
\(269\) | −6.89898 | −0.420638 | −0.210319 | − | 0.977633i | \(-0.567450\pi\) | ||||
−0.210319 | + | 0.977633i | \(0.567450\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.9444 | −1.87974 | −0.939869 | − | 0.341536i | \(-0.889053\pi\) | ||||
−0.939869 | + | 0.341536i | \(0.889053\pi\) | |||||||
\(272\) | 0.449490i | 0.0272543i | ||||||||
\(273\) | − 1.10102i | − 0.0666368i | ||||||||
\(274\) | −4.89898 | −0.295958 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 23.0454i | 1.38466i | 0.721579 | + | 0.692332i | \(0.243417\pi\) | ||||
−0.721579 | + | 0.692332i | \(0.756583\pi\) | |||||||
\(278\) | 2.24745i | 0.134793i | ||||||||
\(279\) | 3.00000 | 0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.00000 | 0.417585 | 0.208792 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208792 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(282\) | − 11.7980i | − 0.702558i | ||||||||
\(283\) | 10.2020i | 0.606448i | 0.952919 | + | 0.303224i | \(0.0980631\pi\) | ||||
−0.952919 | + | 0.303224i | \(0.901937\pi\) | |||||||
\(284\) | 6.44949 | 0.382707 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.55051 | −0.209946 | ||||||||
\(287\) | 4.00000i | 0.236113i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 16.7980 | 0.988115 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.44949 | 0.378076 | ||||||||
\(292\) | 1.00000i | 0.0585206i | ||||||||
\(293\) | 1.24745i | 0.0728767i | 0.999336 | + | 0.0364384i | \(0.0116013\pi\) | ||||
−0.999336 | + | 0.0364384i | \(0.988399\pi\) | |||||||
\(294\) | 6.79796 | 0.396465 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 11.7980 | 0.685742 | ||||||||
\(297\) | 1.44949i | 0.0841079i | ||||||||
\(298\) | − 13.7980i | − 0.799294i | ||||||||
\(299\) | 2.44949 | 0.141658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.10102 | −0.0634618 | ||||||||
\(302\) | 4.20204i | 0.241800i | ||||||||
\(303\) | − 6.44949i | − 0.370514i | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.449490 | −0.0256956 | ||||||||
\(307\) | 1.65153i | 0.0942578i | 0.998889 | + | 0.0471289i | \(0.0150072\pi\) | ||||
−0.998889 | + | 0.0471289i | \(0.984993\pi\) | |||||||
\(308\) | 0.651531i | 0.0371244i | ||||||||
\(309\) | 7.89898 | 0.449357 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.20204 | −0.238276 | −0.119138 | − | 0.992878i | \(-0.538013\pi\) | ||||
−0.119138 | + | 0.992878i | \(0.538013\pi\) | |||||||
\(312\) | − 2.44949i | − 0.138675i | ||||||||
\(313\) | 22.1010i | 1.24922i | 0.780935 | + | 0.624612i | \(0.214743\pi\) | ||||
−0.780935 | + | 0.624612i | \(0.785257\pi\) | |||||||
\(314\) | −4.89898 | −0.276465 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.00000 | −0.281272 | ||||||||
\(317\) | 9.24745i | 0.519388i | 0.965691 | + | 0.259694i | \(0.0836218\pi\) | ||||
−0.965691 | + | 0.259694i | \(0.916378\pi\) | |||||||
\(318\) | − 2.55051i | − 0.143026i | ||||||||
\(319\) | 15.0000 | 0.839839 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.65153 | 0.147994 | ||||||||
\(322\) | − 0.449490i | − 0.0250491i | ||||||||
\(323\) | − 0.449490i | − 0.0250103i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.202041 | 0.0111900 | ||||||||
\(327\) | − 6.89898i | − 0.381514i | ||||||||
\(328\) | 8.89898i | 0.491364i | ||||||||
\(329\) | 5.30306 | 0.292367 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.65153 | −0.420566 | −0.210283 | − | 0.977641i | \(-0.567439\pi\) | ||||
−0.210283 | + | 0.977641i | \(0.567439\pi\) | |||||||
\(332\) | 6.34847i | 0.348418i | ||||||||
\(333\) | 11.7980i | 0.646524i | ||||||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.449490 | −0.0245217 | ||||||||
\(337\) | 15.1010i | 0.822605i | 0.911499 | + | 0.411303i | \(0.134926\pi\) | ||||
−0.911499 | + | 0.411303i | \(0.865074\pi\) | |||||||
\(338\) | − 7.00000i | − 0.380750i | ||||||||
\(339\) | −2.79796 | −0.151964 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.34847 | 0.235483 | ||||||||
\(342\) | − 1.00000i | − 0.0540738i | ||||||||
\(343\) | 6.20204i | 0.334879i | ||||||||
\(344\) | −2.44949 | −0.132068 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.3485 | −0.878899 | ||||||||
\(347\) | − 15.5959i | − 0.837233i | −0.908163 | − | 0.418616i | \(-0.862515\pi\) | ||||
0.908163 | − | 0.418616i | \(-0.137485\pi\) | |||||||
\(348\) | 10.3485i | 0.554736i | ||||||||
\(349\) | −27.9444 | −1.49583 | −0.747914 | − | 0.663795i | \(-0.768945\pi\) | ||||
−0.747914 | + | 0.663795i | \(0.768945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.44949 | 0.130744 | ||||||||
\(352\) | 1.44949i | 0.0772581i | ||||||||
\(353\) | 6.24745i | 0.332518i | 0.986082 | + | 0.166259i | \(0.0531688\pi\) | ||||
−0.986082 | + | 0.166259i | \(0.946831\pi\) | |||||||
\(354\) | −1.55051 | −0.0824087 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.8990 | 0.630645 | ||||||||
\(357\) | − 0.202041i | − 0.0106931i | ||||||||
\(358\) | 6.20204i | 0.327788i | ||||||||
\(359\) | 13.1010 | 0.691445 | 0.345723 | − | 0.938337i | \(-0.387634\pi\) | ||||
0.345723 | + | 0.938337i | \(0.387634\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 9.55051i | 0.501964i | ||||||||
\(363\) | − 8.89898i | − 0.467075i | ||||||||
\(364\) | 1.10102 | 0.0577092 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.55051 | −0.237859 | ||||||||
\(367\) | 10.4495i | 0.545459i | 0.962091 | + | 0.272729i | \(0.0879264\pi\) | ||||
−0.962091 | + | 0.272729i | \(0.912074\pi\) | |||||||
\(368\) | − 1.00000i | − 0.0521286i | ||||||||
\(369\) | −8.89898 | −0.463262 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.14643 | 0.0595196 | ||||||||
\(372\) | 3.00000i | 0.155543i | ||||||||
\(373\) | − 17.5505i | − 0.908731i | −0.890815 | − | 0.454365i | \(-0.849866\pi\) | ||||
0.890815 | − | 0.454365i | \(-0.150134\pi\) | |||||||
\(374\) | −0.651531 | −0.0336899 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.7980 | 0.608433 | ||||||||
\(377\) | − 25.3485i | − 1.30551i | ||||||||
\(378\) | − 0.449490i | − 0.0231193i | ||||||||
\(379\) | 30.6969 | 1.57680 | 0.788398 | − | 0.615166i | \(-0.210911\pi\) | ||||
0.788398 | + | 0.615166i | \(0.210911\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.89898 | 0.507140 | ||||||||
\(382\) | 9.89898i | 0.506476i | ||||||||
\(383\) | − 8.24745i | − 0.421425i | −0.977548 | − | 0.210712i | \(-0.932422\pi\) | ||||
0.977548 | − | 0.210712i | \(-0.0675784\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.651531 | −0.0331620 | ||||||||
\(387\) | − 2.44949i | − 0.124515i | ||||||||
\(388\) | 6.44949i | 0.327423i | ||||||||
\(389\) | 17.5959 | 0.892148 | 0.446074 | − | 0.894996i | \(-0.352822\pi\) | ||||
0.446074 | + | 0.894996i | \(0.352822\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.449490 | 0.0227317 | ||||||||
\(392\) | 6.79796i | 0.343349i | ||||||||
\(393\) | − 15.2474i | − 0.769132i | ||||||||
\(394\) | −12.6515 | −0.637375 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.44949 | −0.0728396 | ||||||||
\(397\) | 29.9444i | 1.50287i | 0.659810 | + | 0.751433i | \(0.270637\pi\) | ||||
−0.659810 | + | 0.751433i | \(0.729363\pi\) | |||||||
\(398\) | − 10.0000i | − 0.501255i | ||||||||
\(399\) | 0.449490 | 0.0225026 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.7980 | 1.53798 | 0.768988 | − | 0.639263i | \(-0.220760\pi\) | ||||
0.768988 | + | 0.639263i | \(0.220760\pi\) | |||||||
\(402\) | 9.24745i | 0.461221i | ||||||||
\(403\) | − 7.34847i | − 0.366053i | ||||||||
\(404\) | 6.44949 | 0.320874 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.65153 | −0.230852 | ||||||||
\(407\) | 17.1010i | 0.847666i | ||||||||
\(408\) | − 0.449490i | − 0.0222531i | ||||||||
\(409\) | 13.1010 | 0.647804 | 0.323902 | − | 0.946091i | \(-0.395005\pi\) | ||||
0.323902 | + | 0.946091i | \(0.395005\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.89898 | 0.241649 | ||||||||
\(412\) | 7.89898i | 0.389155i | ||||||||
\(413\) | − 0.696938i | − 0.0342941i | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.44949 | 0.120096 | ||||||||
\(417\) | − 2.24745i | − 0.110058i | ||||||||
\(418\) | − 1.44949i | − 0.0708969i | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 18.3485i | 0.893190i | ||||||||
\(423\) | 11.7980i | 0.573636i | ||||||||
\(424\) | 2.55051 | 0.123864 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.44949 | −0.312479 | ||||||||
\(427\) | − 2.04541i | − 0.0989842i | ||||||||
\(428\) | 2.65153i | 0.128167i | ||||||||
\(429\) | 3.55051 | 0.171420 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.8990 | −0.717659 | −0.358829 | − | 0.933403i | \(-0.616824\pi\) | ||||
−0.358829 | + | 0.933403i | \(0.616824\pi\) | |||||||
\(432\) | − 1.00000i | − 0.0481125i | ||||||||
\(433\) | 19.3485i | 0.929828i | 0.885356 | + | 0.464914i | \(0.153915\pi\) | ||||
−0.885356 | + | 0.464914i | \(0.846085\pi\) | |||||||
\(434\) | −1.34847 | −0.0647286 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.89898 | 0.330401 | ||||||||
\(437\) | 1.00000i | 0.0478365i | ||||||||
\(438\) | − 1.00000i | − 0.0477818i | ||||||||
\(439\) | 21.8990 | 1.04518 | 0.522591 | − | 0.852584i | \(-0.324966\pi\) | ||||
0.522591 | + | 0.852584i | \(0.324966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.79796 | −0.323712 | ||||||||
\(442\) | 1.10102i | 0.0523702i | ||||||||
\(443\) | − 3.24745i | − 0.154291i | −0.997020 | − | 0.0771455i | \(-0.975419\pi\) | ||||
0.997020 | − | 0.0771455i | \(-0.0245806\pi\) | |||||||
\(444\) | −11.7980 | −0.559906 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.8990 | 1.22635 | ||||||||
\(447\) | 13.7980i | 0.652621i | ||||||||
\(448\) | − 0.449490i | − 0.0212364i | ||||||||
\(449\) | 15.0000 | 0.707894 | 0.353947 | − | 0.935266i | \(-0.384839\pi\) | ||||
0.353947 | + | 0.935266i | \(0.384839\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8990 | −0.607389 | ||||||||
\(452\) | − 2.79796i | − 0.131605i | ||||||||
\(453\) | − 4.20204i | − 0.197429i | ||||||||
\(454\) | 9.59592 | 0.450359 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 15.1010i | 0.706396i | 0.935549 | + | 0.353198i | \(0.114906\pi\) | ||||
−0.935549 | + | 0.353198i | \(0.885094\pi\) | |||||||
\(458\) | − 17.2474i | − 0.805920i | ||||||||
\(459\) | 0.449490 | 0.0209804 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0000 | 0.558896 | 0.279448 | − | 0.960161i | \(-0.409849\pi\) | ||||
0.279448 | + | 0.960161i | \(0.409849\pi\) | |||||||
\(462\) | − 0.651531i | − 0.0303120i | ||||||||
\(463\) | 14.6969i | 0.683025i | 0.939877 | + | 0.341512i | \(0.110939\pi\) | ||||
−0.939877 | + | 0.341512i | \(0.889061\pi\) | |||||||
\(464\) | −10.3485 | −0.480416 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.2474 | −0.845297 | ||||||||
\(467\) | − 8.34847i | − 0.386321i | −0.981167 | − | 0.193161i | \(-0.938126\pi\) | ||||
0.981167 | − | 0.193161i | \(-0.0618738\pi\) | |||||||
\(468\) | 2.44949i | 0.113228i | ||||||||
\(469\) | −4.15663 | −0.191935 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.89898 | 0.225733 | ||||||||
\(472\) | − 1.55051i | − 0.0713680i | ||||||||
\(473\) | − 3.55051i | − 0.163253i | ||||||||
\(474\) | 5.00000 | 0.229658 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.202041 | 0.00926054 | ||||||||
\(477\) | 2.55051i | 0.116780i | ||||||||
\(478\) | 20.6969i | 0.946656i | ||||||||
\(479\) | 22.5959 | 1.03243 | 0.516217 | − | 0.856458i | \(-0.327340\pi\) | ||||
0.516217 | + | 0.856458i | \(0.327340\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.8990 | 1.31768 | ||||||||
\(482\) | − 0.449490i | − 0.0204737i | ||||||||
\(483\) | 0.449490i | 0.0204525i | ||||||||
\(484\) | 8.89898 | 0.404499 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 32.0000i | 1.45006i | 0.688718 | + | 0.725029i | \(0.258174\pi\) | ||||
−0.688718 | + | 0.725029i | \(0.741826\pi\) | |||||||
\(488\) | − 4.55051i | − 0.205992i | ||||||||
\(489\) | −0.202041 | −0.00913661 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.40408 | 0.198753 | 0.0993767 | − | 0.995050i | \(-0.468315\pi\) | ||||
0.0993767 | + | 0.995050i | \(0.468315\pi\) | |||||||
\(492\) | − 8.89898i | − 0.401197i | ||||||||
\(493\) | − 4.65153i | − 0.209494i | ||||||||
\(494\) | −2.44949 | −0.110208 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | −0.134704 | ||||||||
\(497\) | − 2.89898i | − 0.130037i | ||||||||
\(498\) | − 6.34847i | − 0.284482i | ||||||||
\(499\) | −39.8434 | −1.78363 | −0.891817 | − | 0.452396i | \(-0.850569\pi\) | ||||
−0.891817 | + | 0.452396i | \(0.850569\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.0000 | 0.804181 | ||||||||
\(502\) | 18.0000i | 0.803379i | ||||||||
\(503\) | 10.2020i | 0.454887i | 0.973791 | + | 0.227443i | \(0.0730366\pi\) | ||||
−0.973791 | + | 0.227443i | \(0.926963\pi\) | |||||||
\(504\) | 0.449490 | 0.0200219 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.44949 | 0.0644377 | ||||||||
\(507\) | 7.00000i | 0.310881i | ||||||||
\(508\) | 9.89898i | 0.439196i | ||||||||
\(509\) | −4.14643 | −0.183787 | −0.0918936 | − | 0.995769i | \(-0.529292\pi\) | ||||
−0.0918936 | + | 0.995769i | \(0.529292\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.449490 | 0.0198843 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | −27.4949 | −1.21275 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.44949 | 0.107833 | ||||||||
\(517\) | 17.1010i | 0.752102i | ||||||||
\(518\) | − 5.30306i | − 0.233003i | ||||||||
\(519\) | 16.3485 | 0.717618 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.6969 | −0.600074 | −0.300037 | − | 0.953928i | \(-0.596999\pi\) | ||||
−0.300037 | + | 0.953928i | \(0.596999\pi\) | |||||||
\(522\) | − 10.3485i | − 0.452940i | ||||||||
\(523\) | 25.3939i | 1.11040i | 0.831718 | + | 0.555198i | \(0.187358\pi\) | ||||
−0.831718 | + | 0.555198i | \(0.812642\pi\) | |||||||
\(524\) | 15.2474 | 0.666088 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.7980 | 0.558018 | ||||||||
\(527\) | − 1.34847i | − 0.0587402i | ||||||||
\(528\) | − 1.44949i | − 0.0630809i | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.55051 | 0.0672864 | ||||||||
\(532\) | 0.449490i | 0.0194879i | ||||||||
\(533\) | 21.7980i | 0.944174i | ||||||||
\(534\) | −11.8990 | −0.514919 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.24745 | −0.399429 | ||||||||
\(537\) | − 6.20204i | − 0.267638i | ||||||||
\(538\) | 6.89898i | 0.297436i | ||||||||
\(539\) | −9.85357 | −0.424423 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.1464 | −0.522216 | −0.261108 | − | 0.965310i | \(-0.584088\pi\) | ||||
−0.261108 | + | 0.965310i | \(0.584088\pi\) | |||||||
\(542\) | 30.9444i | 1.32918i | ||||||||
\(543\) | − 9.55051i | − 0.409852i | ||||||||
\(544\) | 0.449490 | 0.0192717 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.10102 | −0.0471193 | ||||||||
\(547\) | − 36.6413i | − 1.56667i | −0.621600 | − | 0.783335i | \(-0.713517\pi\) | ||||
0.621600 | − | 0.783335i | \(-0.286483\pi\) | |||||||
\(548\) | 4.89898i | 0.209274i | ||||||||
\(549\) | 4.55051 | 0.194211 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.3485 | 0.440860 | ||||||||
\(552\) | 1.00000i | 0.0425628i | ||||||||
\(553\) | 2.24745i | 0.0955712i | ||||||||
\(554\) | 23.0454 | 0.979106 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.24745 | 0.0953131 | ||||||||
\(557\) | − 12.6515i | − 0.536063i | −0.963410 | − | 0.268031i | \(-0.913627\pi\) | ||||
0.963410 | − | 0.268031i | \(-0.0863731\pi\) | |||||||
\(558\) | − 3.00000i | − 0.127000i | ||||||||
\(559\) | −6.00000 | −0.253773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.651531 | 0.0275077 | ||||||||
\(562\) | − 7.00000i | − 0.295277i | ||||||||
\(563\) | − 18.2474i | − 0.769038i | −0.923117 | − | 0.384519i | \(-0.874367\pi\) | ||||
0.923117 | − | 0.384519i | \(-0.125633\pi\) | |||||||
\(564\) | −11.7980 | −0.496784 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.2020 | 0.428824 | ||||||||
\(567\) | 0.449490i | 0.0188768i | ||||||||
\(568\) | − 6.44949i | − 0.270615i | ||||||||
\(569\) | −45.1918 | −1.89454 | −0.947270 | − | 0.320436i | \(-0.896171\pi\) | ||||
−0.947270 | + | 0.320436i | \(0.896171\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2474 | 0.596237 | 0.298119 | − | 0.954529i | \(-0.403641\pi\) | ||||
0.298119 | + | 0.954529i | \(0.403641\pi\) | |||||||
\(572\) | 3.55051i | 0.148454i | ||||||||
\(573\) | − 9.89898i | − 0.413536i | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 9.89898i | − 0.412100i | −0.978541 | − | 0.206050i | \(-0.933939\pi\) | ||||
0.978541 | − | 0.206050i | \(-0.0660609\pi\) | |||||||
\(578\) | − 16.7980i | − 0.698703i | ||||||||
\(579\) | 0.651531 | 0.0270767 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.85357 | 0.118386 | ||||||||
\(582\) | − 6.44949i | − 0.267340i | ||||||||
\(583\) | 3.69694i | 0.153112i | ||||||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.24745 | 0.0515316 | ||||||||
\(587\) | 28.5505i | 1.17841i | 0.807985 | + | 0.589203i | \(0.200558\pi\) | ||||
−0.807985 | + | 0.589203i | \(0.799442\pi\) | |||||||
\(588\) | − 6.79796i | − 0.280343i | ||||||||
\(589\) | 3.00000 | 0.123613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.6515 | 0.520414 | ||||||||
\(592\) | − 11.7980i | − 0.484893i | ||||||||
\(593\) | − 40.4949i | − 1.66293i | −0.555580 | − | 0.831463i | \(-0.687504\pi\) | ||||
0.555580 | − | 0.831463i | \(-0.312496\pi\) | |||||||
\(594\) | 1.44949 | 0.0594733 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.7980 | −0.565186 | ||||||||
\(597\) | 10.0000i | 0.409273i | ||||||||
\(598\) | − 2.44949i | − 0.100167i | ||||||||
\(599\) | −11.5505 | −0.471941 | −0.235971 | − | 0.971760i | \(-0.575827\pi\) | ||||
−0.235971 | + | 0.971760i | \(0.575827\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.1464 | −0.699417 | −0.349709 | − | 0.936858i | \(-0.613719\pi\) | ||||
−0.349709 | + | 0.936858i | \(0.613719\pi\) | |||||||
\(602\) | 1.10102i | 0.0448742i | ||||||||
\(603\) | − 9.24745i | − 0.376585i | ||||||||
\(604\) | 4.20204 | 0.170979 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.44949 | −0.261993 | ||||||||
\(607\) | 32.1918i | 1.30663i | 0.757088 | + | 0.653313i | \(0.226621\pi\) | ||||
−0.757088 | + | 0.653313i | \(0.773379\pi\) | |||||||
\(608\) | 1.00000i | 0.0405554i | ||||||||
\(609\) | 4.65153 | 0.188490 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 28.8990 | 1.16913 | ||||||||
\(612\) | 0.449490i | 0.0181695i | ||||||||
\(613\) | − 41.1918i | − 1.66372i | −0.554984 | − | 0.831861i | \(-0.687275\pi\) | ||||
0.554984 | − | 0.831861i | \(-0.312725\pi\) | |||||||
\(614\) | 1.65153 | 0.0666504 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.651531 | 0.0262509 | ||||||||
\(617\) | 40.2929i | 1.62213i | 0.584957 | + | 0.811065i | \(0.301112\pi\) | ||||
−0.584957 | + | 0.811065i | \(0.698888\pi\) | |||||||
\(618\) | − 7.89898i | − 0.317744i | ||||||||
\(619\) | −10.8536 | −0.436242 | −0.218121 | − | 0.975922i | \(-0.569993\pi\) | ||||
−0.218121 | + | 0.975922i | \(0.569993\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 4.20204i | 0.168486i | ||||||||
\(623\) | − 5.34847i | − 0.214282i | ||||||||
\(624\) | −2.44949 | −0.0980581 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22.1010 | 0.883334 | ||||||||
\(627\) | 1.44949i | 0.0578870i | ||||||||
\(628\) | 4.89898i | 0.195491i | ||||||||
\(629\) | 5.30306 | 0.211447 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0000 | −1.11466 | −0.557331 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557331 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(632\) | 5.00000i | 0.198889i | ||||||||
\(633\) | − 18.3485i | − 0.729286i | ||||||||
\(634\) | 9.24745 | 0.367263 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.55051 | −0.101134 | ||||||||
\(637\) | 16.6515i | 0.659758i | ||||||||
\(638\) | − 15.0000i | − 0.593856i | ||||||||
\(639\) | 6.44949 | 0.255138 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.2020 | 0.718937 | 0.359469 | − | 0.933157i | \(-0.382958\pi\) | ||||
0.359469 | + | 0.933157i | \(0.382958\pi\) | |||||||
\(642\) | − 2.65153i | − 0.104648i | ||||||||
\(643\) | − 19.7980i | − 0.780755i | −0.920655 | − | 0.390378i | \(-0.872344\pi\) | ||||
0.920655 | − | 0.390378i | \(-0.127656\pi\) | |||||||
\(644\) | −0.449490 | −0.0177124 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.449490 | −0.0176849 | ||||||||
\(647\) | − 16.1010i | − 0.632996i | −0.948593 | − | 0.316498i | \(-0.897493\pi\) | ||||
0.948593 | − | 0.316498i | \(-0.102507\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 2.24745 | 0.0882201 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.34847 | 0.0528507 | ||||||||
\(652\) | − 0.202041i | − 0.00791254i | ||||||||
\(653\) | 14.6969i | 0.575136i | 0.957760 | + | 0.287568i | \(0.0928467\pi\) | ||||
−0.957760 | + | 0.287568i | \(0.907153\pi\) | |||||||
\(654\) | −6.89898 | −0.269771 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.89898 | 0.347447 | ||||||||
\(657\) | 1.00000i | 0.0390137i | ||||||||
\(658\) | − 5.30306i | − 0.206735i | ||||||||
\(659\) | −26.0454 | −1.01459 | −0.507293 | − | 0.861774i | \(-0.669354\pi\) | ||||
−0.507293 | + | 0.861774i | \(0.669354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5959 | −0.606611 | −0.303305 | − | 0.952893i | \(-0.598090\pi\) | ||||
−0.303305 | + | 0.952893i | \(0.598090\pi\) | |||||||
\(662\) | 7.65153i | 0.297385i | ||||||||
\(663\) | − 1.10102i | − 0.0427601i | ||||||||
\(664\) | 6.34847 | 0.246368 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 11.7980 | 0.457162 | ||||||||
\(667\) | 10.3485i | 0.400694i | ||||||||
\(668\) | 18.0000i | 0.696441i | ||||||||
\(669\) | −25.8990 | −1.00131 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.59592 | 0.254633 | ||||||||
\(672\) | 0.449490i | 0.0173394i | ||||||||
\(673\) | − 30.6515i | − 1.18153i | −0.806844 | − | 0.590765i | \(-0.798826\pi\) | ||||
0.806844 | − | 0.590765i | \(-0.201174\pi\) | |||||||
\(674\) | 15.1010 | 0.581670 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.00000 | −0.269231 | ||||||||
\(677\) | − 7.65153i | − 0.294072i | −0.989131 | − | 0.147036i | \(-0.953027\pi\) | ||||
0.989131 | − | 0.147036i | \(-0.0469734\pi\) | |||||||
\(678\) | 2.79796i | 0.107455i | ||||||||
\(679\) | 2.89898 | 0.111253 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.59592 | −0.367716 | ||||||||
\(682\) | − 4.34847i | − 0.166511i | ||||||||
\(683\) | 47.6413i | 1.82294i | 0.411361 | + | 0.911472i | \(0.365053\pi\) | ||||
−0.411361 | + | 0.911472i | \(0.634947\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.20204 | 0.236795 | ||||||||
\(687\) | 17.2474i | 0.658031i | ||||||||
\(688\) | 2.44949i | 0.0933859i | ||||||||
\(689\) | 6.24745 | 0.238009 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.2474 | 1.30283 | 0.651417 | − | 0.758720i | \(-0.274175\pi\) | ||||
0.651417 | + | 0.758720i | \(0.274175\pi\) | |||||||
\(692\) | 16.3485i | 0.621476i | ||||||||
\(693\) | 0.651531i | 0.0247496i | ||||||||
\(694\) | −15.5959 | −0.592013 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.3485 | 0.392258 | ||||||||
\(697\) | 4.00000i | 0.151511i | ||||||||
\(698\) | 27.9444i | 1.05771i | ||||||||
\(699\) | 18.2474 | 0.690182 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.4949 | 0.623004 | 0.311502 | − | 0.950246i | \(-0.399168\pi\) | ||||
0.311502 | + | 0.950246i | \(0.399168\pi\) | |||||||
\(702\) | − 2.44949i | − 0.0924500i | ||||||||
\(703\) | 11.7980i | 0.444968i | ||||||||
\(704\) | 1.44949 | 0.0546297 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.24745 | 0.235126 | ||||||||
\(707\) | − 2.89898i | − 0.109027i | ||||||||
\(708\) | 1.55051i | 0.0582717i | ||||||||
\(709\) | 37.2474 | 1.39886 | 0.699429 | − | 0.714702i | \(-0.253438\pi\) | ||||
0.699429 | + | 0.714702i | \(0.253438\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.00000 | −0.187515 | ||||||||
\(712\) | − 11.8990i | − 0.445933i | ||||||||
\(713\) | 3.00000i | 0.112351i | ||||||||
\(714\) | −0.202041 | −0.00756120 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.20204 | 0.231781 | ||||||||
\(717\) | − 20.6969i | − 0.772941i | ||||||||
\(718\) | − 13.1010i | − 0.488926i | ||||||||
\(719\) | 38.7980 | 1.44692 | 0.723460 | − | 0.690366i | \(-0.242551\pi\) | ||||
0.723460 | + | 0.690366i | \(0.242551\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.55051 | 0.132228 | ||||||||
\(722\) | − 1.00000i | − 0.0372161i | ||||||||
\(723\) | 0.449490i | 0.0167167i | ||||||||
\(724\) | 9.55051 | 0.354942 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.89898 | −0.330272 | ||||||||
\(727\) | 26.4949i | 0.982641i | 0.870979 | + | 0.491321i | \(0.163486\pi\) | ||||
−0.870979 | + | 0.491321i | \(0.836514\pi\) | |||||||
\(728\) | − 1.10102i | − 0.0408065i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.10102 | −0.0407227 | ||||||||
\(732\) | 4.55051i | 0.168192i | ||||||||
\(733\) | − 30.1464i | − 1.11348i | −0.830686 | − | 0.556742i | \(-0.812051\pi\) | ||||
0.830686 | − | 0.556742i | \(-0.187949\pi\) | |||||||
\(734\) | 10.4495 | 0.385698 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | − 13.4041i | − 0.493746i | ||||||||
\(738\) | 8.89898i | 0.327576i | ||||||||
\(739\) | −23.1010 | −0.849785 | −0.424892 | − | 0.905244i | \(-0.639688\pi\) | ||||
−0.424892 | + | 0.905244i | \(0.639688\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.44949 | 0.0899843 | ||||||||
\(742\) | − 1.14643i | − 0.0420867i | ||||||||
\(743\) | 5.39388i | 0.197882i | 0.995093 | + | 0.0989411i | \(0.0315455\pi\) | ||||
−0.995093 | + | 0.0989411i | \(0.968454\pi\) | |||||||
\(744\) | 3.00000 | 0.109985 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.5505 | −0.642570 | ||||||||
\(747\) | 6.34847i | 0.232278i | ||||||||
\(748\) | 0.651531i | 0.0238223i | ||||||||
\(749\) | 1.19184 | 0.0435487 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.20204 | −0.153335 | −0.0766673 | − | 0.997057i | \(-0.524428\pi\) | ||||
−0.0766673 | + | 0.997057i | \(0.524428\pi\) | |||||||
\(752\) | − 11.7980i | − 0.430227i | ||||||||
\(753\) | − 18.0000i | − 0.655956i | ||||||||
\(754\) | −25.3485 | −0.923137 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.449490 | −0.0163478 | ||||||||
\(757\) | − 13.8536i | − 0.503517i | −0.967790 | − | 0.251758i | \(-0.918991\pi\) | ||||
0.967790 | − | 0.251758i | \(-0.0810088\pi\) | |||||||
\(758\) | − 30.6969i | − 1.11496i | ||||||||
\(759\) | −1.44949 | −0.0526131 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.6515 | 1.32862 | 0.664308 | − | 0.747459i | \(-0.268726\pi\) | ||||
0.664308 | + | 0.747459i | \(0.268726\pi\) | |||||||
\(762\) | − 9.89898i | − 0.358602i | ||||||||
\(763\) | − 3.10102i | − 0.112264i | ||||||||
\(764\) | 9.89898 | 0.358133 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.24745 | −0.297992 | ||||||||
\(767\) | − 3.79796i | − 0.137136i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −1.89898 | −0.0684790 | −0.0342395 | − | 0.999414i | \(-0.510901\pi\) | ||||
−0.0342395 | + | 0.999414i | \(0.510901\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.4949 | 0.990205 | ||||||||
\(772\) | 0.651531i | 0.0234491i | ||||||||
\(773\) | − 30.4949i | − 1.09683i | −0.836208 | − | 0.548413i | \(-0.815232\pi\) | ||||
0.836208 | − | 0.548413i | \(-0.184768\pi\) | |||||||
\(774\) | −2.44949 | −0.0880451 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.44949 | 0.231523 | ||||||||
\(777\) | 5.30306i | 0.190246i | ||||||||
\(778\) | − 17.5959i | − 0.630844i | ||||||||
\(779\) | −8.89898 | −0.318839 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.34847 | 0.334515 | ||||||||
\(782\) | − 0.449490i | − 0.0160737i | ||||||||
\(783\) | 10.3485i | 0.369824i | ||||||||
\(784\) | 6.79796 | 0.242784 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.2474 | −0.543858 | ||||||||
\(787\) | 28.5505i | 1.01772i | 0.860851 | + | 0.508858i | \(0.169932\pi\) | ||||
−0.860851 | + | 0.508858i | \(0.830068\pi\) | |||||||
\(788\) | 12.6515i | 0.450692i | ||||||||
\(789\) | −12.7980 | −0.455619 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.25765 | −0.0447170 | ||||||||
\(792\) | 1.44949i | 0.0515054i | ||||||||
\(793\) | − 11.1464i | − 0.395821i | ||||||||
\(794\) | 29.9444 | 1.06269 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.0000 | −0.354441 | ||||||||
\(797\) | − 52.4949i | − 1.85946i | −0.368236 | − | 0.929732i | \(-0.620038\pi\) | ||||
0.368236 | − | 0.929732i | \(-0.379962\pi\) | |||||||
\(798\) | − 0.449490i | − 0.0159118i | ||||||||
\(799\) | 5.30306 | 0.187609 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.8990 | 0.420430 | ||||||||
\(802\) | − 30.7980i | − 1.08751i | ||||||||
\(803\) | 1.44949i | 0.0511514i | ||||||||
\(804\) | 9.24745 | 0.326132 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.34847 | −0.258839 | ||||||||
\(807\) | − 6.89898i | − 0.242856i | ||||||||
\(808\) | − 6.44949i | − 0.226892i | ||||||||
\(809\) | 8.44949 | 0.297068 | 0.148534 | − | 0.988907i | \(-0.452545\pi\) | ||||
0.148534 | + | 0.988907i | \(0.452545\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.5505 | −0.510938 | −0.255469 | − | 0.966817i | \(-0.582230\pi\) | ||||
−0.255469 | + | 0.966817i | \(0.582230\pi\) | |||||||
\(812\) | 4.65153i | 0.163237i | ||||||||
\(813\) | − 30.9444i | − 1.08527i | ||||||||
\(814\) | 17.1010 | 0.599390 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.449490 | −0.0157353 | ||||||||
\(817\) | − 2.44949i | − 0.0856968i | ||||||||
\(818\) | − 13.1010i | − 0.458066i | ||||||||
\(819\) | 1.10102 | 0.0384728 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1464 | 0.389013 | 0.194507 | − | 0.980901i | \(-0.437689\pi\) | ||||
0.194507 | + | 0.980901i | \(0.437689\pi\) | |||||||
\(822\) | − 4.89898i | − 0.170872i | ||||||||
\(823\) | − 12.2020i | − 0.425336i | −0.977124 | − | 0.212668i | \(-0.931785\pi\) | ||||
0.977124 | − | 0.212668i | \(-0.0682153\pi\) | |||||||
\(824\) | 7.89898 | 0.275174 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.696938 | −0.0242496 | ||||||||
\(827\) | 24.2474i | 0.843166i | 0.906790 | + | 0.421583i | \(0.138525\pi\) | ||||
−0.906790 | + | 0.421583i | \(0.861475\pi\) | |||||||
\(828\) | − 1.00000i | − 0.0347524i | ||||||||
\(829\) | −43.6413 | −1.51573 | −0.757863 | − | 0.652414i | \(-0.773756\pi\) | ||||
−0.757863 | + | 0.652414i | \(0.773756\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.0454 | −0.799436 | ||||||||
\(832\) | − 2.44949i | − 0.0849208i | ||||||||
\(833\) | 3.05561i | 0.105871i | ||||||||
\(834\) | −2.24745 | −0.0778228 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.44949 | −0.0501317 | ||||||||
\(837\) | 3.00000i | 0.103695i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.3485 | −0.875126 | −0.437563 | − | 0.899188i | \(-0.644158\pi\) | ||||
−0.437563 | + | 0.899188i | \(0.644158\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 78.0908 | 2.69279 | ||||||||
\(842\) | − 22.0000i | − 0.758170i | ||||||||
\(843\) | 7.00000i | 0.241093i | ||||||||
\(844\) | 18.3485 | 0.631580 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 11.7980 | 0.405622 | ||||||||
\(847\) | − 4.00000i | − 0.137442i | ||||||||
\(848\) | − 2.55051i | − 0.0875849i | ||||||||
\(849\) | −10.2020 | −0.350133 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.7980 | −0.404429 | ||||||||
\(852\) | 6.44949i | 0.220956i | ||||||||
\(853\) | 10.8990i | 0.373174i | 0.982438 | + | 0.186587i | \(0.0597426\pi\) | ||||
−0.982438 | + | 0.186587i | \(0.940257\pi\) | |||||||
\(854\) | −2.04541 | −0.0699924 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.65153 | 0.0906275 | ||||||||
\(857\) | − 12.4949i | − 0.426818i | −0.976963 | − | 0.213409i | \(-0.931543\pi\) | ||||
0.976963 | − | 0.213409i | \(-0.0684566\pi\) | |||||||
\(858\) | − 3.55051i | − 0.121212i | ||||||||
\(859\) | 23.7980 | 0.811976 | 0.405988 | − | 0.913878i | \(-0.366927\pi\) | ||||
0.405988 | + | 0.913878i | \(0.366927\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.00000 | −0.136320 | ||||||||
\(862\) | 14.8990i | 0.507461i | ||||||||
\(863\) | − 46.6969i | − 1.58958i | −0.606883 | − | 0.794791i | \(-0.707580\pi\) | ||||
0.606883 | − | 0.794791i | \(-0.292420\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.3485 | 0.657488 | ||||||||
\(867\) | 16.7980i | 0.570489i | ||||||||
\(868\) | 1.34847i | 0.0457700i | ||||||||
\(869\) | −7.24745 | −0.245853 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.6515 | −0.767518 | ||||||||
\(872\) | − 6.89898i | − 0.233629i | ||||||||
\(873\) | 6.44949i | 0.218282i | ||||||||
\(874\) | 1.00000 | 0.0338255 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.00000 | −0.0337869 | ||||||||
\(877\) | 18.8990i | 0.638173i | 0.947726 | + | 0.319087i | \(0.103376\pi\) | ||||
−0.947726 | + | 0.319087i | \(0.896624\pi\) | |||||||
\(878\) | − 21.8990i | − 0.739055i | ||||||||
\(879\) | −1.24745 | −0.0420754 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.3031 | 0.717718 | 0.358859 | − | 0.933392i | \(-0.383166\pi\) | ||||
0.358859 | + | 0.933392i | \(0.383166\pi\) | |||||||
\(882\) | 6.79796i | 0.228899i | ||||||||
\(883\) | 49.3485i | 1.66071i | 0.557236 | + | 0.830354i | \(0.311862\pi\) | ||||
−0.557236 | + | 0.830354i | \(0.688138\pi\) | |||||||
\(884\) | 1.10102 | 0.0370313 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.24745 | −0.109100 | ||||||||
\(887\) | − 4.89898i | − 0.164492i | −0.996612 | − | 0.0822458i | \(-0.973791\pi\) | ||||
0.996612 | − | 0.0822458i | \(-0.0262093\pi\) | |||||||
\(888\) | 11.7980i | 0.395914i | ||||||||
\(889\) | 4.44949 | 0.149231 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.44949 | −0.0485597 | ||||||||
\(892\) | − 25.8990i | − 0.867162i | ||||||||
\(893\) | 11.7980i | 0.394804i | ||||||||
\(894\) | 13.7980 | 0.461473 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.449490 | −0.0150164 | ||||||||
\(897\) | 2.44949i | 0.0817861i | ||||||||
\(898\) | − 15.0000i | − 0.500556i | ||||||||
\(899\) | 31.0454 | 1.03542 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14643 | 0.0381931 | ||||||||
\(902\) | 12.8990i | 0.429489i | ||||||||
\(903\) | − 1.10102i | − 0.0366397i | ||||||||
\(904\) | −2.79796 | −0.0930587 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.20204 | −0.139603 | ||||||||
\(907\) | 22.0000i | 0.730498i | 0.930910 | + | 0.365249i | \(0.119016\pi\) | ||||
−0.930910 | + | 0.365249i | \(0.880984\pi\) | |||||||
\(908\) | − 9.59592i | − 0.318452i | ||||||||
\(909\) | 6.44949 | 0.213916 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.4949 | −1.40792 | −0.703959 | − | 0.710240i | \(-0.748586\pi\) | ||||
−0.703959 | + | 0.710240i | \(0.748586\pi\) | |||||||
\(912\) | − 1.00000i | − 0.0331133i | ||||||||
\(913\) | 9.20204i | 0.304543i | ||||||||
\(914\) | 15.1010 | 0.499497 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.2474 | −0.569872 | ||||||||
\(917\) | − 6.85357i | − 0.226325i | ||||||||
\(918\) | − 0.449490i | − 0.0148354i | ||||||||
\(919\) | 39.8434 | 1.31431 | 0.657156 | − | 0.753755i | \(-0.271759\pi\) | ||||
0.657156 | + | 0.753755i | \(0.271759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.65153 | −0.0544198 | ||||||||
\(922\) | − 12.0000i | − 0.395199i | ||||||||
\(923\) | − 15.7980i | − 0.519996i | ||||||||
\(924\) | −0.651531 | −0.0214338 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 14.6969 | 0.482971 | ||||||||
\(927\) | 7.89898i | 0.259437i | ||||||||
\(928\) | 10.3485i | 0.339705i | ||||||||
\(929\) | −7.59592 | −0.249214 | −0.124607 | − | 0.992206i | \(-0.539767\pi\) | ||||
−0.124607 | + | 0.992206i | \(0.539767\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.79796 | −0.222794 | ||||||||
\(932\) | 18.2474i | 0.597715i | ||||||||
\(933\) | − 4.20204i | − 0.137569i | ||||||||
\(934\) | −8.34847 | −0.273170 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.44949 | 0.0800641 | ||||||||
\(937\) | − 39.3939i | − 1.28694i | −0.765471 | − | 0.643471i | \(-0.777494\pi\) | ||||
0.765471 | − | 0.643471i | \(-0.222506\pi\) | |||||||
\(938\) | 4.15663i | 0.135719i | ||||||||
\(939\) | −22.1010 | −0.721240 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.6413 | −1.52046 | −0.760232 | − | 0.649652i | \(-0.774915\pi\) | ||||
−0.760232 | + | 0.649652i | \(0.774915\pi\) | |||||||
\(942\) | − 4.89898i | − 0.159617i | ||||||||
\(943\) | − 8.89898i | − 0.289791i | ||||||||
\(944\) | −1.55051 | −0.0504648 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.55051 | −0.115437 | ||||||||
\(947\) | − 8.00000i | − 0.259965i | −0.991516 | − | 0.129983i | \(-0.958508\pi\) | ||||
0.991516 | − | 0.129983i | \(-0.0414921\pi\) | |||||||
\(948\) | − 5.00000i | − 0.162392i | ||||||||
\(949\) | 2.44949 | 0.0795138 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.24745 | −0.299869 | ||||||||
\(952\) | − 0.202041i | − 0.00654819i | ||||||||
\(953\) | 33.4949i | 1.08501i | 0.840054 | + | 0.542503i | \(0.182523\pi\) | ||||
−0.840054 | + | 0.542503i | \(0.817477\pi\) | |||||||
\(954\) | 2.55051 | 0.0825758 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.6969 | 0.669387 | ||||||||
\(957\) | 15.0000i | 0.484881i | ||||||||
\(958\) | − 22.5959i | − 0.730041i | ||||||||
\(959\) | 2.20204 | 0.0711076 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | − 28.8990i | − 0.931740i | ||||||||
\(963\) | 2.65153i | 0.0854444i | ||||||||
\(964\) | −0.449490 | −0.0144771 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.449490 | 0.0144621 | ||||||||
\(967\) | 25.1010i | 0.807194i | 0.914937 | + | 0.403597i | \(0.132240\pi\) | ||||
−0.914937 | + | 0.403597i | \(0.867760\pi\) | |||||||
\(968\) | − 8.89898i | − 0.286024i | ||||||||
\(969\) | 0.449490 | 0.0144397 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −41.6413 | −1.33633 | −0.668167 | − | 0.744011i | \(-0.732921\pi\) | ||||
−0.668167 | + | 0.744011i | \(0.732921\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | − 1.01021i | − 0.0323857i | ||||||||
\(974\) | 32.0000 | 1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.55051 | −0.145658 | ||||||||
\(977\) | 19.5959i | 0.626929i | 0.949600 | + | 0.313464i | \(0.101490\pi\) | ||||
−0.949600 | + | 0.313464i | \(0.898510\pi\) | |||||||
\(978\) | 0.202041i | 0.00646056i | ||||||||
\(979\) | 17.2474 | 0.551231 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.89898 | 0.220267 | ||||||||
\(982\) | − 4.40408i | − 0.140540i | ||||||||
\(983\) | 45.5505i | 1.45284i | 0.687253 | + | 0.726418i | \(0.258816\pi\) | ||||
−0.687253 | + | 0.726418i | \(0.741184\pi\) | |||||||
\(984\) | −8.89898 | −0.283689 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.65153 | −0.148135 | ||||||||
\(987\) | 5.30306i | 0.168798i | ||||||||
\(988\) | 2.44949i | 0.0779287i | ||||||||
\(989\) | 2.44949 | 0.0778892 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.8990 | 1.71216 | 0.856079 | − | 0.516845i | \(-0.172894\pi\) | ||||
0.856079 | + | 0.516845i | \(0.172894\pi\) | |||||||
\(992\) | 3.00000i | 0.0952501i | ||||||||
\(993\) | − 7.65153i | − 0.242814i | ||||||||
\(994\) | −2.89898 | −0.0919500 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.34847 | −0.201159 | ||||||||
\(997\) | − 34.5505i | − 1.09423i | −0.837059 | − | 0.547113i | \(-0.815727\pi\) | ||||
0.837059 | − | 0.547113i | \(-0.184273\pi\) | |||||||
\(998\) | 39.8434i | 1.26122i | ||||||||
\(999\) | −11.7980 | −0.373271 |
(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 | 2850.2.d.w.799.2 | 4 | ||
5.2 | odd | 4 | 2850.2.a.bj.1.1 | yes | 2 | ||
5.3 | odd | 4 | 2850.2.a.bc.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 2850.2.d.w.799.3 | 4 | ||
15.2 | even | 4 | 8550.2.a.bu.1.1 | 2 | |||
15.8 | even | 4 | 8550.2.a.bv.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.bc.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
2850.2.a.bj.1.1 | yes | 2 | 5.2 | odd | 4 | ||
2850.2.d.w.799.2 | 4 | 1.1 | even | 1 | trivial | ||
2850.2.d.w.799.3 | 4 | 5.4 | even | 2 | inner | ||
8550.2.a.bu.1.1 | 2 | 15.2 | even | 4 | |||
8550.2.a.bv.1.2 | 2 | 15.8 | even | 4 |