Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(699,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.699");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.58952814149\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 699.1 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.699 |
Dual form | 700.2.c.a.699.4 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | − | 1.00000i | −0.707107 | − | 0.707107i | ||||
\(3\) | − | 2.44949i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.44949 | + | 2.44949i | −1.00000 | + | 1.00000i | ||||
\(7\) | −1.00000 | + | 2.44949i | −0.377964 | + | 0.925820i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.00000i | 1.50756i | 0.657129 | + | 0.753778i | \(0.271771\pi\) | ||||
−0.657129 | + | 0.753778i | \(0.728229\pi\) | |||||||
\(12\) | 4.89898 | 1.41421 | ||||||||
\(13\) | 2.44949 | 0.679366 | 0.339683 | − | 0.940540i | \(-0.389680\pi\) | ||||
0.339683 | + | 0.940540i | \(0.389680\pi\) | |||||||
\(14\) | 3.44949 | − | 1.44949i | 0.921915 | − | 0.387392i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 4.89898 | 1.18818 | 0.594089 | − | 0.804400i | \(-0.297513\pi\) | ||||
0.594089 | + | 0.804400i | \(0.297513\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.707107 | + | 0.707107i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.00000 | + | 2.44949i | 1.30931 | + | 0.534522i | ||||
\(22\) | 5.00000 | − | 5.00000i | 1.06600 | − | 1.06600i | ||||
\(23\) | −1.00000 | −0.208514 | −0.104257 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104257 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(24\) | −4.89898 | − | 4.89898i | −1.00000 | − | 1.00000i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.44949 | − | 2.44949i | −0.480384 | − | 0.480384i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −4.89898 | − | 2.00000i | −0.925820 | − | 0.377964i | ||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.34847 | 1.31982 | 0.659912 | − | 0.751343i | \(-0.270594\pi\) | ||||
0.659912 | + | 0.751343i | \(0.270594\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.707107 | + | 0.707107i | ||||
\(33\) | 12.2474 | 2.13201 | ||||||||
\(34\) | −4.89898 | − | 4.89898i | −0.840168 | − | 0.840168i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | − | 6.00000i | − | 1.00000i | ||||||
\(37\) | 3.00000i | 0.493197i | 0.969118 | + | 0.246598i | \(0.0793129\pi\) | ||||
−0.969118 | + | 0.246598i | \(0.920687\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.00000i | − | 0.960769i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12.2474i | 1.91273i | 0.292174 | + | 0.956365i | \(0.405621\pi\) | ||||
−0.292174 | + | 0.956365i | \(0.594379\pi\) | |||||||
\(42\) | −3.55051 | − | 8.44949i | −0.547856 | − | 1.30378i | ||||
\(43\) | −11.0000 | −1.67748 | −0.838742 | − | 0.544529i | \(-0.816708\pi\) | ||||
−0.838742 | + | 0.544529i | \(0.816708\pi\) | |||||||
\(44\) | −10.0000 | −1.50756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | + | 1.00000i | 0.147442 | + | 0.147442i | ||||
\(47\) | 4.89898i | 0.714590i | 0.933992 | + | 0.357295i | \(0.116301\pi\) | ||||
−0.933992 | + | 0.357295i | \(0.883699\pi\) | |||||||
\(48\) | 9.79796i | 1.41421i | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 12.0000i | − | 1.68034i | ||||||
\(52\) | 4.89898i | 0.679366i | ||||||||
\(53\) | − | 4.00000i | − | 0.549442i | −0.961524 | − | 0.274721i | \(-0.911414\pi\) | ||
0.961524 | − | 0.274721i | \(-0.0885855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.89898 | + | 6.89898i | 0.387392 | + | 0.921915i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.00000 | − | 5.00000i | −0.656532 | − | 0.656532i | ||||
\(59\) | 12.2474 | 1.59448 | 0.797241 | − | 0.603661i | \(-0.206292\pi\) | ||||
0.797241 | + | 0.603661i | \(0.206292\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 12.2474i | − | 1.56813i | −0.620682 | − | 0.784063i | \(-0.713144\pi\) | ||
0.620682 | − | 0.784063i | \(-0.286856\pi\) | |||||||
\(62\) | −7.34847 | − | 7.34847i | −0.933257 | − | 0.933257i | ||||
\(63\) | 3.00000 | − | 7.34847i | 0.377964 | − | 0.925820i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −12.2474 | − | 12.2474i | −1.50756 | − | 1.50756i | ||||
\(67\) | 3.00000 | 0.366508 | 0.183254 | − | 0.983066i | \(-0.441337\pi\) | ||||
0.183254 | + | 0.983066i | \(0.441337\pi\) | |||||||
\(68\) | 9.79796i | 1.18818i | ||||||||
\(69\) | 2.44949i | 0.294884i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.00000i | − | 0.593391i | −0.954972 | − | 0.296695i | \(-0.904115\pi\) | ||
0.954972 | − | 0.296695i | \(-0.0958846\pi\) | |||||||
\(72\) | −6.00000 | + | 6.00000i | −0.707107 | + | 0.707107i | ||||
\(73\) | 2.44949 | 0.286691 | 0.143346 | − | 0.989673i | \(-0.454214\pi\) | ||||
0.143346 | + | 0.989673i | \(0.454214\pi\) | |||||||
\(74\) | 3.00000 | − | 3.00000i | 0.348743 | − | 0.348743i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.2474 | − | 5.00000i | −1.39573 | − | 0.569803i | ||||
\(78\) | −6.00000 | + | 6.00000i | −0.679366 | + | 0.679366i | ||||
\(79\) | 9.00000i | 1.01258i | 0.862364 | + | 0.506290i | \(0.168983\pi\) | ||||
−0.862364 | + | 0.506290i | \(0.831017\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 12.2474 | − | 12.2474i | 1.35250 | − | 1.35250i | ||||
\(83\) | − | 2.44949i | − | 0.268866i | −0.990923 | − | 0.134433i | \(-0.957079\pi\) | ||
0.990923 | − | 0.134433i | \(-0.0429214\pi\) | |||||||
\(84\) | −4.89898 | + | 12.0000i | −0.534522 | + | 1.30931i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.0000 | + | 11.0000i | 1.18616 | + | 1.18616i | ||||
\(87\) | − | 12.2474i | − | 1.31306i | ||||||
\(88\) | 10.0000 | + | 10.0000i | 1.06600 | + | 1.06600i | ||||
\(89\) | 2.44949i | 0.259645i | 0.991537 | + | 0.129823i | \(0.0414408\pi\) | ||||
−0.991537 | + | 0.129823i | \(0.958559\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.44949 | + | 6.00000i | −0.256776 | + | 0.628971i | ||||
\(92\) | − | 2.00000i | − | 0.208514i | ||||||
\(93\) | − | 18.0000i | − | 1.86651i | ||||||
\(94\) | 4.89898 | − | 4.89898i | 0.505291 | − | 0.505291i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796 | − | 9.79796i | 1.00000 | − | 1.00000i | ||||
\(97\) | −7.34847 | −0.746124 | −0.373062 | − | 0.927806i | \(-0.621692\pi\) | ||||
−0.373062 | + | 0.927806i | \(0.621692\pi\) | |||||||
\(98\) | 0.101021 | + | 9.89898i | 0.0102046 | + | 0.999948i | ||||
\(99\) | − | 15.0000i | − | 1.50756i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.2474i | 1.21867i | 0.792914 | + | 0.609333i | \(0.208563\pi\) | ||||
−0.792914 | + | 0.609333i | \(0.791437\pi\) | |||||||
\(102\) | −12.0000 | + | 12.0000i | −1.18818 | + | 1.18818i | ||||
\(103\) | − | 14.6969i | − | 1.44813i | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||
0.689730 | − | 0.724066i | \(-0.257729\pi\) | |||||||
\(104\) | 4.89898 | − | 4.89898i | 0.480384 | − | 0.480384i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | + | 4.00000i | −0.388514 | + | 0.388514i | ||||
\(107\) | 8.00000 | 0.773389 | 0.386695 | − | 0.922208i | \(-0.373617\pi\) | ||||
0.386695 | + | 0.922208i | \(0.373617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0000 | 1.43674 | 0.718370 | − | 0.695662i | \(-0.244889\pi\) | ||||
0.718370 | + | 0.695662i | \(0.244889\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.34847 | 0.697486 | ||||||||
\(112\) | 4.00000 | − | 9.79796i | 0.377964 | − | 0.925820i | ||||
\(113\) | 11.0000i | 1.03479i | 0.855746 | + | 0.517396i | \(0.173099\pi\) | ||||
−0.855746 | + | 0.517396i | \(0.826901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.0000i | 0.928477i | ||||||||
\(117\) | −7.34847 | −0.679366 | ||||||||
\(118\) | −12.2474 | − | 12.2474i | −1.12747 | − | 1.12747i | ||||
\(119\) | −4.89898 | + | 12.0000i | −0.449089 | + | 1.10004i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.0000 | −1.27273 | ||||||||
\(122\) | −12.2474 | + | 12.2474i | −1.10883 | + | 1.10883i | ||||
\(123\) | 30.0000 | 2.70501 | ||||||||
\(124\) | 14.6969i | 1.31982i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.3485 | + | 4.34847i | −0.921915 | + | 0.387392i | ||||
\(127\) | 3.00000 | 0.266207 | 0.133103 | − | 0.991102i | \(-0.457506\pi\) | ||||
0.133103 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.707107 | + | 0.707107i | ||||
\(129\) | 26.9444i | 2.37232i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.89898 | −0.428026 | −0.214013 | − | 0.976831i | \(-0.568653\pi\) | ||||
−0.214013 | + | 0.976831i | \(0.568653\pi\) | |||||||
\(132\) | 24.4949i | 2.13201i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.00000 | − | 3.00000i | −0.259161 | − | 0.259161i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.79796 | − | 9.79796i | 0.840168 | − | 0.840168i | ||||
\(137\) | 8.00000i | 0.683486i | 0.939793 | + | 0.341743i | \(0.111017\pi\) | ||||
−0.939793 | + | 0.341743i | \(0.888983\pi\) | |||||||
\(138\) | 2.44949 | − | 2.44949i | 0.208514 | − | 0.208514i | ||||
\(139\) | 12.2474 | 1.03882 | 0.519408 | − | 0.854527i | \(-0.326153\pi\) | ||||
0.519408 | + | 0.854527i | \(0.326153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | −5.00000 | + | 5.00000i | −0.419591 | + | 0.419591i | ||||
\(143\) | 12.2474i | 1.02418i | ||||||||
\(144\) | 12.0000 | 1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.44949 | − | 2.44949i | −0.202721 | − | 0.202721i | ||||
\(147\) | −12.0000 | + | 12.2474i | −0.989743 | + | 1.01015i | ||||
\(148\) | −6.00000 | −0.493197 | ||||||||
\(149\) | 5.00000 | 0.409616 | 0.204808 | − | 0.978802i | \(-0.434343\pi\) | ||||
0.204808 | + | 0.978802i | \(0.434343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.00000i | − | 0.406894i | −0.979086 | − | 0.203447i | \(-0.934786\pi\) | ||
0.979086 | − | 0.203447i | \(-0.0652145\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.6969 | −1.18818 | ||||||||
\(154\) | 7.24745 | + | 17.2474i | 0.584016 | + | 1.38984i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 12.0000 | 0.960769 | ||||||||
\(157\) | 17.1464 | 1.36843 | 0.684217 | − | 0.729279i | \(-0.260144\pi\) | ||||
0.684217 | + | 0.729279i | \(0.260144\pi\) | |||||||
\(158\) | 9.00000 | − | 9.00000i | 0.716002 | − | 0.716002i | ||||
\(159\) | −9.79796 | −0.777029 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | − | 2.44949i | 0.0788110 | − | 0.193047i | ||||
\(162\) | 9.00000 | + | 9.00000i | 0.707107 | + | 0.707107i | ||||
\(163\) | −6.00000 | −0.469956 | −0.234978 | − | 0.972001i | \(-0.575502\pi\) | ||||
−0.234978 | + | 0.972001i | \(0.575502\pi\) | |||||||
\(164\) | −24.4949 | −1.91273 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.44949 | + | 2.44949i | −0.190117 | + | 0.190117i | ||||
\(167\) | − | 7.34847i | − | 0.568642i | −0.958729 | − | 0.284321i | \(-0.908232\pi\) | ||
0.958729 | − | 0.284321i | \(-0.0917681\pi\) | |||||||
\(168\) | 16.8990 | − | 7.10102i | 1.30378 | − | 0.547856i | ||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 22.0000i | − | 1.67748i | ||||||
\(173\) | −9.79796 | −0.744925 | −0.372463 | − | 0.928047i | \(-0.621486\pi\) | ||||
−0.372463 | + | 0.928047i | \(0.621486\pi\) | |||||||
\(174\) | −12.2474 | + | 12.2474i | −0.928477 | + | 0.928477i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 20.0000i | − | 1.50756i | ||||||
\(177\) | − | 30.0000i | − | 2.25494i | ||||||
\(178\) | 2.44949 | − | 2.44949i | 0.183597 | − | 0.183597i | ||||
\(179\) | 14.0000i | 1.04641i | 0.852207 | + | 0.523205i | \(0.175264\pi\) | ||||
−0.852207 | + | 0.523205i | \(0.824736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.2474i | − | 0.910346i | −0.890403 | − | 0.455173i | \(-0.849577\pi\) | ||
0.890403 | − | 0.455173i | \(-0.150423\pi\) | |||||||
\(182\) | 8.44949 | − | 3.55051i | 0.626318 | − | 0.263181i | ||||
\(183\) | −30.0000 | −2.21766 | ||||||||
\(184\) | −2.00000 | + | 2.00000i | −0.147442 | + | 0.147442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −18.0000 | + | 18.0000i | −1.31982 | + | 1.31982i | ||||
\(187\) | 24.4949i | 1.79124i | ||||||||
\(188\) | −9.79796 | −0.714590 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 10.0000i | − | 0.723575i | −0.932261 | − | 0.361787i | \(-0.882167\pi\) | ||
0.932261 | − | 0.361787i | \(-0.117833\pi\) | |||||||
\(192\) | −19.5959 | −1.41421 | ||||||||
\(193\) | 21.0000i | 1.51161i | 0.654795 | + | 0.755807i | \(0.272755\pi\) | ||||
−0.654795 | + | 0.755807i | \(0.727245\pi\) | |||||||
\(194\) | 7.34847 | + | 7.34847i | 0.527589 | + | 0.527589i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.79796 | − | 10.0000i | 0.699854 | − | 0.714286i | ||||
\(197\) | 23.0000i | 1.63868i | 0.573306 | + | 0.819341i | \(0.305660\pi\) | ||||
−0.573306 | + | 0.819341i | \(0.694340\pi\) | |||||||
\(198\) | −15.0000 | + | 15.0000i | −1.06600 | + | 1.06600i | ||||
\(199\) | −12.2474 | −0.868199 | −0.434099 | − | 0.900865i | \(-0.642933\pi\) | ||||
−0.434099 | + | 0.900865i | \(0.642933\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 7.34847i | − | 0.518321i | ||||||
\(202\) | 12.2474 | − | 12.2474i | 0.861727 | − | 0.861727i | ||||
\(203\) | −5.00000 | + | 12.2474i | −0.350931 | + | 0.859602i | ||||
\(204\) | 24.0000 | 1.68034 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −14.6969 | + | 14.6969i | −1.02398 | + | 1.02398i | ||||
\(207\) | 3.00000 | 0.208514 | ||||||||
\(208\) | −9.79796 | −0.679366 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000i | 0.688428i | 0.938891 | + | 0.344214i | \(0.111855\pi\) | ||||
−0.938891 | + | 0.344214i | \(0.888145\pi\) | |||||||
\(212\) | 8.00000 | 0.549442 | ||||||||
\(213\) | −12.2474 | −0.839181 | ||||||||
\(214\) | −8.00000 | − | 8.00000i | −0.546869 | − | 0.546869i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.34847 | + | 18.0000i | −0.498847 | + | 1.22192i | ||||
\(218\) | −15.0000 | − | 15.0000i | −1.01593 | − | 1.01593i | ||||
\(219\) | − | 6.00000i | − | 0.405442i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | −7.34847 | − | 7.34847i | −0.493197 | − | 0.493197i | ||||
\(223\) | − | 2.44949i | − | 0.164030i | −0.996631 | − | 0.0820150i | \(-0.973864\pi\) | ||
0.996631 | − | 0.0820150i | \(-0.0261355\pi\) | |||||||
\(224\) | −13.7980 | + | 5.79796i | −0.921915 | + | 0.387392i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.0000 | − | 11.0000i | 0.731709 | − | 0.731709i | ||||
\(227\) | − | 19.5959i | − | 1.30063i | −0.759666 | − | 0.650313i | \(-0.774638\pi\) | ||
0.759666 | − | 0.650313i | \(-0.225362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.79796i | − | 0.647467i | −0.946148 | − | 0.323734i | \(-0.895062\pi\) | ||
0.946148 | − | 0.323734i | \(-0.104938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.2474 | + | 30.0000i | −0.805823 | + | 1.97386i | ||||
\(232\) | 10.0000 | − | 10.0000i | 0.656532 | − | 0.656532i | ||||
\(233\) | 11.0000i | 0.720634i | 0.932830 | + | 0.360317i | \(0.117331\pi\) | ||||
−0.932830 | + | 0.360317i | \(0.882669\pi\) | |||||||
\(234\) | 7.34847 | + | 7.34847i | 0.480384 | + | 0.480384i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 24.4949i | 1.59448i | ||||||||
\(237\) | 22.0454 | 1.43200 | ||||||||
\(238\) | 16.8990 | − | 7.10102i | 1.09540 | − | 0.460291i | ||||
\(239\) | − | 26.0000i | − | 1.68180i | −0.541190 | − | 0.840900i | \(-0.682026\pi\) | ||
0.541190 | − | 0.840900i | \(-0.317974\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 14.0000 | + | 14.0000i | 0.899954 | + | 0.899954i | ||||
\(243\) | 22.0454i | 1.41421i | ||||||||
\(244\) | 24.4949 | 1.56813 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −30.0000 | − | 30.0000i | −1.91273 | − | 1.91273i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 14.6969 | − | 14.6969i | 0.933257 | − | 0.933257i | ||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.89898 | −0.309221 | −0.154610 | − | 0.987976i | \(-0.549412\pi\) | ||||
−0.154610 | + | 0.987976i | \(0.549412\pi\) | |||||||
\(252\) | 14.6969 | + | 6.00000i | 0.925820 | + | 0.377964i | ||||
\(253\) | − | 5.00000i | − | 0.314347i | ||||||
\(254\) | −3.00000 | − | 3.00000i | −0.188237 | − | 0.188237i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −7.34847 | −0.458385 | −0.229192 | − | 0.973381i | \(-0.573609\pi\) | ||||
−0.229192 | + | 0.973381i | \(0.573609\pi\) | |||||||
\(258\) | 26.9444 | − | 26.9444i | 1.67748 | − | 1.67748i | ||||
\(259\) | −7.34847 | − | 3.00000i | −0.456612 | − | 0.186411i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.0000 | −0.928477 | ||||||||
\(262\) | 4.89898 | + | 4.89898i | 0.302660 | + | 0.302660i | ||||
\(263\) | −1.00000 | −0.0616626 | −0.0308313 | − | 0.999525i | \(-0.509815\pi\) | ||||
−0.0308313 | + | 0.999525i | \(0.509815\pi\) | |||||||
\(264\) | 24.4949 | − | 24.4949i | 1.50756 | − | 1.50756i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00000 | 0.367194 | ||||||||
\(268\) | 6.00000i | 0.366508i | ||||||||
\(269\) | − | 22.0454i | − | 1.34413i | −0.740491 | − | 0.672066i | \(-0.765407\pi\) | ||
0.740491 | − | 0.672066i | \(-0.234593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.1464 | −1.04157 | −0.520786 | − | 0.853687i | \(-0.674361\pi\) | ||||
−0.520786 | + | 0.853687i | \(0.674361\pi\) | |||||||
\(272\) | −19.5959 | −1.18818 | ||||||||
\(273\) | 14.6969 | + | 6.00000i | 0.889499 | + | 0.363137i | ||||
\(274\) | 8.00000 | − | 8.00000i | 0.483298 | − | 0.483298i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.89898 | −0.294884 | ||||||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | −12.2474 | − | 12.2474i | −0.734553 | − | 0.734553i | ||||
\(279\) | −22.0454 | −1.31982 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.0000 | 1.01413 | 0.507067 | − | 0.861906i | \(-0.330729\pi\) | ||||
0.507067 | + | 0.861906i | \(0.330729\pi\) | |||||||
\(282\) | −12.0000 | − | 12.0000i | −0.714590 | − | 0.714590i | ||||
\(283\) | 9.79796i | 0.582428i | 0.956658 | + | 0.291214i | \(0.0940592\pi\) | ||||
−0.956658 | + | 0.291214i | \(0.905941\pi\) | |||||||
\(284\) | 10.0000 | 0.593391 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.2474 | − | 12.2474i | 0.724207 | − | 0.724207i | ||||
\(287\) | −30.0000 | − | 12.2474i | −1.77084 | − | 0.722944i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.707107 | − | 0.707107i | ||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.0000i | 1.05518i | ||||||||
\(292\) | 4.89898i | 0.286691i | ||||||||
\(293\) | 2.44949 | 0.143101 | 0.0715504 | − | 0.997437i | \(-0.477205\pi\) | ||||
0.0715504 | + | 0.997437i | \(0.477205\pi\) | |||||||
\(294\) | 24.2474 | − | 0.247449i | 1.41414 | − | 0.0144315i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.00000 | + | 6.00000i | 0.348743 | + | 0.348743i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.00000 | − | 5.00000i | −0.289642 | − | 0.289642i | ||||
\(299\) | −2.44949 | −0.141658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.0000 | − | 26.9444i | 0.634029 | − | 1.55305i | ||||
\(302\) | −5.00000 | + | 5.00000i | −0.287718 | + | 0.287718i | ||||
\(303\) | 30.0000 | 1.72345 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 14.6969 | + | 14.6969i | 0.840168 | + | 0.840168i | ||||
\(307\) | 4.89898i | 0.279600i | 0.990180 | + | 0.139800i | \(0.0446459\pi\) | ||||
−0.990180 | + | 0.139800i | \(0.955354\pi\) | |||||||
\(308\) | 10.0000 | − | 24.4949i | 0.569803 | − | 1.39573i | ||||
\(309\) | −36.0000 | −2.04797 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5959 | 1.11118 | 0.555591 | − | 0.831456i | \(-0.312492\pi\) | ||||
0.555591 | + | 0.831456i | \(0.312492\pi\) | |||||||
\(312\) | −12.0000 | − | 12.0000i | −0.679366 | − | 0.679366i | ||||
\(313\) | −9.79796 | −0.553813 | −0.276907 | − | 0.960897i | \(-0.589309\pi\) | ||||
−0.276907 | + | 0.960897i | \(0.589309\pi\) | |||||||
\(314\) | −17.1464 | − | 17.1464i | −0.967629 | − | 0.967629i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −18.0000 | −1.01258 | ||||||||
\(317\) | − | 17.0000i | − | 0.954815i | −0.878682 | − | 0.477408i | \(-0.841577\pi\) | ||
0.878682 | − | 0.477408i | \(-0.158423\pi\) | |||||||
\(318\) | 9.79796 | + | 9.79796i | 0.549442 | + | 0.549442i | ||||
\(319\) | 25.0000i | 1.39973i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 19.5959i | − | 1.09374i | ||||||
\(322\) | −3.44949 | + | 1.44949i | −0.192233 | + | 0.0807769i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 18.0000i | − | 1.00000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.00000 | + | 6.00000i | 0.332309 | + | 0.332309i | ||||
\(327\) | − | 36.7423i | − | 2.03186i | ||||||
\(328\) | 24.4949 | + | 24.4949i | 1.35250 | + | 1.35250i | ||||
\(329\) | −12.0000 | − | 4.89898i | −0.661581 | − | 0.270089i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 25.0000i | − | 1.37412i | −0.726599 | − | 0.687062i | \(-0.758900\pi\) | ||
0.726599 | − | 0.687062i | \(-0.241100\pi\) | |||||||
\(332\) | 4.89898 | 0.268866 | ||||||||
\(333\) | − | 9.00000i | − | 0.493197i | ||||||
\(334\) | −7.34847 | + | 7.34847i | −0.402090 | + | 0.402090i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −24.0000 | − | 9.79796i | −1.30931 | − | 0.534522i | ||||
\(337\) | − | 12.0000i | − | 0.653682i | −0.945079 | − | 0.326841i | \(-0.894016\pi\) | ||
0.945079 | − | 0.326841i | \(-0.105984\pi\) | |||||||
\(338\) | 7.00000 | + | 7.00000i | 0.380750 | + | 0.380750i | ||||
\(339\) | 26.9444 | 1.46342 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36.7423i | 1.98971i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | −22.0000 | + | 22.0000i | −1.18616 | + | 1.18616i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.79796 | + | 9.79796i | 0.526742 | + | 0.526742i | ||||
\(347\) | −17.0000 | −0.912608 | −0.456304 | − | 0.889824i | \(-0.650827\pi\) | ||||
−0.456304 | + | 0.889824i | \(0.650827\pi\) | |||||||
\(348\) | 24.4949 | 1.31306 | ||||||||
\(349\) | − | 9.79796i | − | 0.524473i | −0.965004 | − | 0.262236i | \(-0.915540\pi\) | ||
0.965004 | − | 0.262236i | \(-0.0844600\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.0000 | + | 20.0000i | −1.06600 | + | 1.06600i | ||||
\(353\) | −22.0454 | −1.17336 | −0.586679 | − | 0.809819i | \(-0.699565\pi\) | ||||
−0.586679 | + | 0.809819i | \(0.699565\pi\) | |||||||
\(354\) | −30.0000 | + | 30.0000i | −1.59448 | + | 1.59448i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.89898 | −0.259645 | ||||||||
\(357\) | 29.3939 | + | 12.0000i | 1.55569 | + | 0.635107i | ||||
\(358\) | 14.0000 | − | 14.0000i | 0.739923 | − | 0.739923i | ||||
\(359\) | 19.0000i | 1.00278i | 0.865221 | + | 0.501391i | \(0.167178\pi\) | ||||
−0.865221 | + | 0.501391i | \(0.832822\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | −12.2474 | + | 12.2474i | −0.643712 | + | 0.643712i | ||||
\(363\) | 34.2929i | 1.79991i | ||||||||
\(364\) | −12.0000 | − | 4.89898i | −0.628971 | − | 0.256776i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 30.0000 | + | 30.0000i | 1.56813 | + | 1.56813i | ||||
\(367\) | 17.1464i | 0.895036i | 0.894275 | + | 0.447518i | \(0.147692\pi\) | ||||
−0.894275 | + | 0.447518i | \(0.852308\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | − | 36.7423i | − | 1.91273i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.79796 | + | 4.00000i | 0.508685 | + | 0.207670i | ||||
\(372\) | 36.0000 | 1.86651 | ||||||||
\(373\) | − | 29.0000i | − | 1.50156i | −0.660551 | − | 0.750782i | \(-0.729677\pi\) | ||
0.660551 | − | 0.750782i | \(-0.270323\pi\) | |||||||
\(374\) | 24.4949 | − | 24.4949i | 1.26660 | − | 1.26660i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.79796 | + | 9.79796i | 0.505291 | + | 0.505291i | ||||
\(377\) | 12.2474 | 0.630776 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.00000i | − | 0.0513665i | −0.999670 | − | 0.0256833i | \(-0.991824\pi\) | ||
0.999670 | − | 0.0256833i | \(-0.00817614\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 7.34847i | − | 0.376473i | ||||||
\(382\) | −10.0000 | + | 10.0000i | −0.511645 | + | 0.511645i | ||||
\(383\) | − | 2.44949i | − | 0.125163i | −0.998040 | − | 0.0625815i | \(-0.980067\pi\) | ||
0.998040 | − | 0.0625815i | \(-0.0199333\pi\) | |||||||
\(384\) | 19.5959 | + | 19.5959i | 1.00000 | + | 1.00000i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.0000 | − | 21.0000i | 1.06887 | − | 1.06887i | ||||
\(387\) | 33.0000 | 1.67748 | ||||||||
\(388\) | − | 14.6969i | − | 0.746124i | ||||||
\(389\) | −5.00000 | −0.253510 | −0.126755 | − | 0.991934i | \(-0.540456\pi\) | ||||
−0.126755 | + | 0.991934i | \(0.540456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.89898 | −0.247752 | ||||||||
\(392\) | −19.7980 | + | 0.202041i | −0.999948 | + | 0.0102046i | ||||
\(393\) | 12.0000i | 0.605320i | ||||||||
\(394\) | 23.0000 | − | 23.0000i | 1.15872 | − | 1.15872i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 30.0000 | 1.50756 | ||||||||
\(397\) | −19.5959 | −0.983491 | −0.491745 | − | 0.870739i | \(-0.663641\pi\) | ||||
−0.491745 | + | 0.870739i | \(0.663641\pi\) | |||||||
\(398\) | 12.2474 | + | 12.2474i | 0.613909 | + | 0.613909i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.0000 | −1.14857 | −0.574283 | − | 0.818657i | \(-0.694719\pi\) | ||||
−0.574283 | + | 0.818657i | \(0.694719\pi\) | |||||||
\(402\) | −7.34847 | + | 7.34847i | −0.366508 | + | 0.366508i | ||||
\(403\) | 18.0000 | 0.896644 | ||||||||
\(404\) | −24.4949 | −1.21867 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.2474 | − | 7.24745i | 0.855977 | − | 0.359685i | ||||
\(407\) | −15.0000 | −0.743522 | ||||||||
\(408\) | −24.0000 | − | 24.0000i | −1.18818 | − | 1.18818i | ||||
\(409\) | − | 34.2929i | − | 1.69567i | −0.530258 | − | 0.847836i | \(-0.677905\pi\) | ||
0.530258 | − | 0.847836i | \(-0.322095\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.5959 | 0.966595 | ||||||||
\(412\) | 29.3939 | 1.44813 | ||||||||
\(413\) | −12.2474 | + | 30.0000i | −0.602658 | + | 1.47620i | ||||
\(414\) | −3.00000 | − | 3.00000i | −0.147442 | − | 0.147442i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.79796 | + | 9.79796i | 0.480384 | + | 0.480384i | ||||
\(417\) | − | 30.0000i | − | 1.46911i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.2474 | 0.598327 | 0.299164 | − | 0.954202i | \(-0.403292\pi\) | ||||
0.299164 | + | 0.954202i | \(0.403292\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0000 | −1.12095 | −0.560476 | − | 0.828171i | \(-0.689382\pi\) | ||||
−0.560476 | + | 0.828171i | \(0.689382\pi\) | |||||||
\(422\) | 10.0000 | − | 10.0000i | 0.486792 | − | 0.486792i | ||||
\(423\) | − | 14.6969i | − | 0.714590i | ||||||
\(424\) | −8.00000 | − | 8.00000i | −0.388514 | − | 0.388514i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.2474 | + | 12.2474i | 0.593391 | + | 0.593391i | ||||
\(427\) | 30.0000 | + | 12.2474i | 1.45180 | + | 0.592696i | ||||
\(428\) | 16.0000i | 0.773389i | ||||||||
\(429\) | 30.0000 | 1.44841 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.0000i | − | 0.481683i | −0.970564 | − | 0.240842i | \(-0.922577\pi\) | ||
0.970564 | − | 0.240842i | \(-0.0774234\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 39.1918 | 1.88344 | 0.941720 | − | 0.336399i | \(-0.109209\pi\) | ||||
0.941720 | + | 0.336399i | \(0.109209\pi\) | |||||||
\(434\) | 25.3485 | − | 10.6515i | 1.21677 | − | 0.511290i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 30.0000i | 1.43674i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6.00000 | + | 6.00000i | −0.286691 | + | 0.286691i | ||||
\(439\) | −12.2474 | −0.584539 | −0.292269 | − | 0.956336i | \(-0.594410\pi\) | ||||
−0.292269 | + | 0.956336i | \(0.594410\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 15.0000 | + | 14.6969i | 0.714286 | + | 0.699854i | ||||
\(442\) | −12.0000 | − | 12.0000i | −0.570782 | − | 0.570782i | ||||
\(443\) | 14.0000 | 0.665160 | 0.332580 | − | 0.943075i | \(-0.392081\pi\) | ||||
0.332580 | + | 0.943075i | \(0.392081\pi\) | |||||||
\(444\) | 14.6969i | 0.697486i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.44949 | + | 2.44949i | −0.115987 | + | 0.115987i | ||||
\(447\) | − | 12.2474i | − | 0.579284i | ||||||
\(448\) | 19.5959 | + | 8.00000i | 0.925820 | + | 0.377964i | ||||
\(449\) | 25.0000 | 1.17982 | 0.589911 | − | 0.807468i | \(-0.299163\pi\) | ||||
0.589911 | + | 0.807468i | \(0.299163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −61.2372 | −2.88355 | ||||||||
\(452\) | −22.0000 | −1.03479 | ||||||||
\(453\) | −12.2474 | −0.575435 | ||||||||
\(454\) | −19.5959 | + | 19.5959i | −0.919682 | + | 0.919682i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00000i | 0.140334i | 0.997535 | + | 0.0701670i | \(0.0223532\pi\) | ||||
−0.997535 | + | 0.0701670i | \(0.977647\pi\) | |||||||
\(458\) | −9.79796 | + | 9.79796i | −0.457829 | + | 0.457829i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.2474i | 0.570421i | 0.958465 | + | 0.285210i | \(0.0920634\pi\) | ||||
−0.958465 | + | 0.285210i | \(0.907937\pi\) | |||||||
\(462\) | 42.2474 | − | 17.7526i | 1.96553 | − | 0.825923i | ||||
\(463\) | −36.0000 | −1.67306 | −0.836531 | − | 0.547920i | \(-0.815420\pi\) | ||||
−0.836531 | + | 0.547920i | \(0.815420\pi\) | |||||||
\(464\) | −20.0000 | −0.928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.0000 | − | 11.0000i | 0.509565 | − | 0.509565i | ||||
\(467\) | 4.89898i | 0.226698i | 0.993555 | + | 0.113349i | \(0.0361578\pi\) | ||||
−0.993555 | + | 0.113349i | \(0.963842\pi\) | |||||||
\(468\) | − | 14.6969i | − | 0.679366i | ||||||
\(469\) | −3.00000 | + | 7.34847i | −0.138527 | + | 0.339321i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 42.0000i | − | 1.93526i | ||||||
\(472\) | 24.4949 | − | 24.4949i | 1.12747 | − | 1.12747i | ||||
\(473\) | − | 55.0000i | − | 2.52890i | ||||||
\(474\) | −22.0454 | − | 22.0454i | −1.01258 | − | 1.01258i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −24.0000 | − | 9.79796i | −1.10004 | − | 0.449089i | ||||
\(477\) | 12.0000i | 0.549442i | ||||||||
\(478\) | −26.0000 | + | 26.0000i | −1.18921 | + | 1.18921i | ||||
\(479\) | −36.7423 | −1.67880 | −0.839400 | − | 0.543514i | \(-0.817094\pi\) | ||||
−0.839400 | + | 0.543514i | \(0.817094\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.34847i | 0.335061i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.00000 | − | 2.44949i | −0.273009 | − | 0.111456i | ||||
\(484\) | − | 28.0000i | − | 1.27273i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454 | − | 22.0454i | 1.00000 | − | 1.00000i | ||||
\(487\) | −7.00000 | −0.317200 | −0.158600 | − | 0.987343i | \(-0.550698\pi\) | ||||
−0.158600 | + | 0.987343i | \(0.550698\pi\) | |||||||
\(488\) | −24.4949 | − | 24.4949i | −1.10883 | − | 1.10883i | ||||
\(489\) | 14.6969i | 0.664619i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.00000i | 0.225647i | 0.993615 | + | 0.112823i | \(0.0359894\pi\) | ||||
−0.993615 | + | 0.112823i | \(0.964011\pi\) | |||||||
\(492\) | 60.0000i | 2.70501i | ||||||||
\(493\) | 24.4949 | 1.10319 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −29.3939 | −1.31982 | ||||||||
\(497\) | 12.2474 | + | 5.00000i | 0.549373 | + | 0.224281i | ||||
\(498\) | 6.00000 | + | 6.00000i | 0.268866 | + | 0.268866i | ||||
\(499\) | − | 16.0000i | − | 0.716258i | −0.933672 | − | 0.358129i | \(-0.883415\pi\) | ||
0.933672 | − | 0.358129i | \(-0.116585\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.0000 | −0.804181 | ||||||||
\(502\) | 4.89898 | + | 4.89898i | 0.218652 | + | 0.218652i | ||||
\(503\) | − | 14.6969i | − | 0.655304i | −0.944798 | − | 0.327652i | \(-0.893743\pi\) | ||
0.944798 | − | 0.327652i | \(-0.106257\pi\) | |||||||
\(504\) | −8.69694 | − | 20.6969i | −0.387392 | − | 0.921915i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.00000 | + | 5.00000i | −0.222277 | + | 0.222277i | ||||
\(507\) | 17.1464i | 0.761500i | ||||||||
\(508\) | 6.00000i | 0.266207i | ||||||||
\(509\) | 26.9444i | 1.19429i | 0.802134 | + | 0.597144i | \(0.203698\pi\) | ||||
−0.802134 | + | 0.597144i | \(0.796302\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.44949 | + | 6.00000i | −0.108359 | + | 0.265424i | ||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.34847 | + | 7.34847i | 0.324127 | + | 0.324127i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −53.8888 | −2.37232 | ||||||||
\(517\) | −24.4949 | −1.07728 | ||||||||
\(518\) | 4.34847 | + | 10.3485i | 0.191061 | + | 0.454686i | ||||
\(519\) | 24.0000i | 1.05348i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 15.0000 | + | 15.0000i | 0.656532 | + | 0.656532i | ||||
\(523\) | 9.79796i | 0.428435i | 0.976786 | + | 0.214217i | \(0.0687201\pi\) | ||||
−0.976786 | + | 0.214217i | \(0.931280\pi\) | |||||||
\(524\) | − | 9.79796i | − | 0.428026i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.00000 | + | 1.00000i | 0.0436021 | + | 0.0436021i | ||||
\(527\) | 36.0000 | 1.56818 | ||||||||
\(528\) | −48.9898 | −2.13201 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −36.7423 | −1.59448 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.0000i | 1.29944i | ||||||||
\(534\) | −6.00000 | − | 6.00000i | −0.259645 | − | 0.259645i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.00000 | − | 6.00000i | 0.259161 | − | 0.259161i | ||||
\(537\) | 34.2929 | 1.47985 | ||||||||
\(538\) | −22.0454 | + | 22.0454i | −0.950445 | + | 0.950445i | ||||
\(539\) | 24.4949 | − | 25.0000i | 1.05507 | − | 1.07683i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.0000 | −0.558914 | −0.279457 | − | 0.960158i | \(-0.590154\pi\) | ||||
−0.279457 | + | 0.960158i | \(0.590154\pi\) | |||||||
\(542\) | 17.1464 | + | 17.1464i | 0.736502 | + | 0.736502i | ||||
\(543\) | −30.0000 | −1.28742 | ||||||||
\(544\) | 19.5959 | + | 19.5959i | 0.840168 | + | 0.840168i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.69694 | − | 20.6969i | −0.372195 | − | 0.885747i | ||||
\(547\) | −27.0000 | −1.15444 | −0.577218 | − | 0.816590i | \(-0.695862\pi\) | ||||
−0.577218 | + | 0.816590i | \(0.695862\pi\) | |||||||
\(548\) | −16.0000 | −0.683486 | ||||||||
\(549\) | 36.7423i | 1.56813i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 4.89898 | + | 4.89898i | 0.208514 | + | 0.208514i | ||||
\(553\) | −22.0454 | − | 9.00000i | −0.937466 | − | 0.382719i | ||||
\(554\) | −2.00000 | + | 2.00000i | −0.0849719 | + | 0.0849719i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24.4949i | 1.03882i | ||||||||
\(557\) | − | 37.0000i | − | 1.56774i | −0.620925 | − | 0.783870i | \(-0.713243\pi\) | ||
0.620925 | − | 0.783870i | \(-0.286757\pi\) | |||||||
\(558\) | 22.0454 | + | 22.0454i | 0.933257 | + | 0.933257i | ||||
\(559\) | −26.9444 | −1.13963 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 60.0000 | 2.53320 | ||||||||
\(562\) | −17.0000 | − | 17.0000i | −0.717102 | − | 0.717102i | ||||
\(563\) | − | 14.6969i | − | 0.619402i | −0.950834 | − | 0.309701i | \(-0.899771\pi\) | ||
0.950834 | − | 0.309701i | \(-0.100229\pi\) | |||||||
\(564\) | 24.0000i | 1.01058i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.79796 | − | 9.79796i | 0.411839 | − | 0.411839i | ||||
\(567\) | 9.00000 | − | 22.0454i | 0.377964 | − | 0.925820i | ||||
\(568\) | −10.0000 | − | 10.0000i | −0.419591 | − | 0.419591i | ||||
\(569\) | −5.00000 | −0.209611 | −0.104805 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104805 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 15.0000i | − | 0.627730i | −0.949468 | − | 0.313865i | \(-0.898376\pi\) | ||
0.949468 | − | 0.313865i | \(-0.101624\pi\) | |||||||
\(572\) | −24.4949 | −1.02418 | ||||||||
\(573\) | −24.4949 | −1.02329 | ||||||||
\(574\) | 17.7526 | + | 42.2474i | 0.740977 | + | 1.76337i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.0000i | 1.00000i | ||||||||
\(577\) | −44.0908 | −1.83552 | −0.917762 | − | 0.397130i | \(-0.870006\pi\) | ||||
−0.917762 | + | 0.397130i | \(0.870006\pi\) | |||||||
\(578\) | −7.00000 | − | 7.00000i | −0.291162 | − | 0.291162i | ||||
\(579\) | 51.4393 | 2.13774 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | + | 2.44949i | 0.248922 | + | 0.101622i | ||||
\(582\) | 18.0000 | − | 18.0000i | 0.746124 | − | 0.746124i | ||||
\(583\) | 20.0000 | 0.828315 | ||||||||
\(584\) | 4.89898 | − | 4.89898i | 0.202721 | − | 0.202721i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.44949 | − | 2.44949i | −0.101187 | − | 0.101187i | ||||
\(587\) | 17.1464i | 0.707709i | 0.935301 | + | 0.353854i | \(0.115129\pi\) | ||||
−0.935301 | + | 0.353854i | \(0.884871\pi\) | |||||||
\(588\) | −24.4949 | − | 24.0000i | −1.01015 | − | 0.989743i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 56.3383 | 2.31745 | ||||||||
\(592\) | − | 12.0000i | − | 0.493197i | ||||||
\(593\) | −9.79796 | −0.402354 | −0.201177 | − | 0.979555i | \(-0.564477\pi\) | ||||
−0.201177 | + | 0.979555i | \(0.564477\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.0000i | 0.409616i | ||||||||
\(597\) | 30.0000i | 1.22782i | ||||||||
\(598\) | 2.44949 | + | 2.44949i | 0.100167 | + | 0.100167i | ||||
\(599\) | − | 11.0000i | − | 0.449448i | −0.974422 | − | 0.224724i | \(-0.927852\pi\) | ||
0.974422 | − | 0.224724i | \(-0.0721480\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | −37.9444 | + | 15.9444i | −1.54650 | + | 0.649845i | ||||
\(603\) | −9.00000 | −0.366508 | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −30.0000 | − | 30.0000i | −1.21867 | − | 1.21867i | ||||
\(607\) | − | 7.34847i | − | 0.298265i | −0.988817 | − | 0.149133i | \(-0.952352\pi\) | ||
0.988817 | − | 0.149133i | \(-0.0476481\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.0000 | + | 12.2474i | 1.21566 | + | 0.496292i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.0000i | 0.485468i | ||||||||
\(612\) | − | 29.3939i | − | 1.18818i | ||||||
\(613\) | 11.0000i | 0.444286i | 0.975014 | + | 0.222143i | \(0.0713052\pi\) | ||||
−0.975014 | + | 0.222143i | \(0.928695\pi\) | |||||||
\(614\) | 4.89898 | − | 4.89898i | 0.197707 | − | 0.197707i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −34.4949 | + | 14.4949i | −1.38984 | + | 0.584016i | ||||
\(617\) | 13.0000i | 0.523360i | 0.965155 | + | 0.261680i | \(0.0842766\pi\) | ||||
−0.965155 | + | 0.261680i | \(0.915723\pi\) | |||||||
\(618\) | 36.0000 | + | 36.0000i | 1.44813 | + | 1.44813i | ||||
\(619\) | −12.2474 | −0.492267 | −0.246133 | − | 0.969236i | \(-0.579160\pi\) | ||||
−0.246133 | + | 0.969236i | \(0.579160\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −19.5959 | − | 19.5959i | −0.785725 | − | 0.785725i | ||||
\(623\) | −6.00000 | − | 2.44949i | −0.240385 | − | 0.0981367i | ||||
\(624\) | 24.0000i | 0.960769i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.79796 | + | 9.79796i | 0.391605 | + | 0.391605i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 34.2929i | 1.36843i | ||||||||
\(629\) | 14.6969i | 0.586005i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.0000i | 1.79142i | 0.444637 | + | 0.895711i | \(0.353333\pi\) | ||||
−0.444637 | + | 0.895711i | \(0.646667\pi\) | |||||||
\(632\) | 18.0000 | + | 18.0000i | 0.716002 | + | 0.716002i | ||||
\(633\) | 24.4949 | 0.973585 | ||||||||
\(634\) | −17.0000 | + | 17.0000i | −0.675156 | + | 0.675156i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 19.5959i | − | 0.777029i | ||||||
\(637\) | −12.2474 | − | 12.0000i | −0.485262 | − | 0.475457i | ||||
\(638\) | 25.0000 | − | 25.0000i | 0.989759 | − | 0.989759i | ||||
\(639\) | 15.0000i | 0.593391i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.0000 | 0.671460 | 0.335730 | − | 0.941958i | \(-0.391017\pi\) | ||||
0.335730 | + | 0.941958i | \(0.391017\pi\) | |||||||
\(642\) | −19.5959 | + | 19.5959i | −0.773389 | + | 0.773389i | ||||
\(643\) | − | 39.1918i | − | 1.54558i | −0.634665 | − | 0.772788i | \(-0.718862\pi\) | ||
0.634665 | − | 0.772788i | \(-0.281138\pi\) | |||||||
\(644\) | 4.89898 | + | 2.00000i | 0.193047 | + | 0.0788110i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.3939i | 1.15559i | 0.816181 | + | 0.577796i | \(0.196087\pi\) | ||||
−0.816181 | + | 0.577796i | \(0.803913\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.707107 | + | 0.707107i | ||||
\(649\) | 61.2372i | 2.40377i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 44.0908 | + | 18.0000i | 1.72806 | + | 0.705476i | ||||
\(652\) | − | 12.0000i | − | 0.469956i | ||||||
\(653\) | 16.0000i | 0.626128i | 0.949732 | + | 0.313064i | \(0.101356\pi\) | ||||
−0.949732 | + | 0.313064i | \(0.898644\pi\) | |||||||
\(654\) | −36.7423 | + | 36.7423i | −1.43674 | + | 1.43674i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 48.9898i | − | 1.91273i | ||||||
\(657\) | −7.34847 | −0.286691 | ||||||||
\(658\) | 7.10102 | + | 16.8990i | 0.276827 | + | 0.658791i | ||||
\(659\) | − | 16.0000i | − | 0.623272i | −0.950202 | − | 0.311636i | \(-0.899123\pi\) | ||
0.950202 | − | 0.311636i | \(-0.100877\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 24.4949i | − | 0.952741i | −0.879245 | − | 0.476371i | \(-0.841952\pi\) | ||
0.879245 | − | 0.476371i | \(-0.158048\pi\) | |||||||
\(662\) | −25.0000 | + | 25.0000i | −0.971653 | + | 0.971653i | ||||
\(663\) | − | 29.3939i | − | 1.14156i | ||||||
\(664\) | −4.89898 | − | 4.89898i | −0.190117 | − | 0.190117i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9.00000 | + | 9.00000i | −0.348743 | + | 0.348743i | ||||
\(667\) | −5.00000 | −0.193601 | ||||||||
\(668\) | 14.6969 | 0.568642 | ||||||||
\(669\) | −6.00000 | −0.231973 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 61.2372 | 2.36404 | ||||||||
\(672\) | 14.2020 | + | 33.7980i | 0.547856 | + | 1.30378i | ||||
\(673\) | − | 24.0000i | − | 0.925132i | −0.886585 | − | 0.462566i | \(-0.846929\pi\) | ||
0.886585 | − | 0.462566i | \(-0.153071\pi\) | |||||||
\(674\) | −12.0000 | + | 12.0000i | −0.462223 | + | 0.462223i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 14.0000i | − | 0.538462i | ||||||
\(677\) | 29.3939 | 1.12970 | 0.564849 | − | 0.825194i | \(-0.308934\pi\) | ||||
0.564849 | + | 0.825194i | \(0.308934\pi\) | |||||||
\(678\) | −26.9444 | − | 26.9444i | −1.03479 | − | 1.03479i | ||||
\(679\) | 7.34847 | − | 18.0000i | 0.282008 | − | 0.690777i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −48.0000 | −1.83936 | ||||||||
\(682\) | 36.7423 | − | 36.7423i | 1.40694 | − | 1.40694i | ||||
\(683\) | −11.0000 | −0.420903 | −0.210452 | − | 0.977604i | \(-0.567493\pi\) | ||||
−0.210452 | + | 0.977604i | \(0.567493\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.3485 | − | 9.65153i | −0.929629 | − | 0.368497i | ||||
\(687\) | −24.0000 | −0.915657 | ||||||||
\(688\) | 44.0000 | 1.67748 | ||||||||
\(689\) | − | 9.79796i | − | 0.373273i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.8434 | 1.21138 | 0.605689 | − | 0.795701i | \(-0.292897\pi\) | ||||
0.605689 | + | 0.795701i | \(0.292897\pi\) | |||||||
\(692\) | − | 19.5959i | − | 0.744925i | ||||||
\(693\) | 36.7423 | + | 15.0000i | 1.39573 | + | 0.569803i | ||||
\(694\) | 17.0000 | + | 17.0000i | 0.645311 | + | 0.645311i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −24.4949 | − | 24.4949i | −0.928477 | − | 0.928477i | ||||
\(697\) | 60.0000i | 2.27266i | ||||||||
\(698\) | −9.79796 | + | 9.79796i | −0.370858 | + | 0.370858i | ||||
\(699\) | 26.9444 | 1.01913 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.0000 | 0.830929 | 0.415464 | − | 0.909610i | \(-0.363619\pi\) | ||||
0.415464 | + | 0.909610i | \(0.363619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 40.0000 | 1.50756 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.0454 | + | 22.0454i | 0.829690 | + | 0.829690i | ||||
\(707\) | −30.0000 | − | 12.2474i | −1.12827 | − | 0.460613i | ||||
\(708\) | 60.0000 | 2.25494 | ||||||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 27.0000i | − | 1.01258i | ||||||
\(712\) | 4.89898 | + | 4.89898i | 0.183597 | + | 0.183597i | ||||
\(713\) | −7.34847 | −0.275202 | ||||||||
\(714\) | −17.3939 | − | 41.3939i | −0.650949 | − | 1.54913i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −28.0000 | −1.04641 | ||||||||
\(717\) | −63.6867 | −2.37842 | ||||||||
\(718\) | 19.0000 | − | 19.0000i | 0.709074 | − | 0.709074i | ||||
\(719\) | 12.2474 | 0.456753 | 0.228376 | − | 0.973573i | \(-0.426658\pi\) | ||||
0.228376 | + | 0.973573i | \(0.426658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.0000 | + | 14.6969i | 1.34071 | + | 0.547343i | ||||
\(722\) | 19.0000 | + | 19.0000i | 0.707107 | + | 0.707107i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24.4949 | 0.910346 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 34.2929 | − | 34.2929i | 1.27273 | − | 1.27273i | ||||
\(727\) | 29.3939i | 1.09016i | 0.838385 | + | 0.545079i | \(0.183500\pi\) | ||||
−0.838385 | + | 0.545079i | \(0.816500\pi\) | |||||||
\(728\) | 7.10102 | + | 16.8990i | 0.263181 | + | 0.626318i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.8888 | −1.99315 | ||||||||
\(732\) | − | 60.0000i | − | 2.21766i | ||||||
\(733\) | 39.1918 | 1.44758 | 0.723792 | − | 0.690018i | \(-0.242398\pi\) | ||||
0.723792 | + | 0.690018i | \(0.242398\pi\) | |||||||
\(734\) | 17.1464 | − | 17.1464i | 0.632886 | − | 0.632886i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | − | 4.00000i | −0.147442 | − | 0.147442i | ||||
\(737\) | 15.0000i | 0.552532i | ||||||||
\(738\) | −36.7423 | + | 36.7423i | −1.35250 | + | 1.35250i | ||||
\(739\) | 9.00000i | 0.331070i | 0.986204 | + | 0.165535i | \(0.0529351\pi\) | ||||
−0.986204 | + | 0.165535i | \(0.947065\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.79796 | − | 13.7980i | −0.212850 | − | 0.506539i | ||||
\(743\) | 34.0000 | 1.24734 | 0.623670 | − | 0.781688i | \(-0.285641\pi\) | ||||
0.623670 | + | 0.781688i | \(0.285641\pi\) | |||||||
\(744\) | −36.0000 | − | 36.0000i | −1.31982 | − | 1.31982i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −29.0000 | + | 29.0000i | −1.06177 | + | 1.06177i | ||||
\(747\) | 7.34847i | 0.268866i | ||||||||
\(748\) | −48.9898 | −1.79124 | ||||||||
\(749\) | −8.00000 | + | 19.5959i | −0.292314 | + | 0.716019i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.0000i | 0.729810i | 0.931045 | + | 0.364905i | \(0.118899\pi\) | ||||
−0.931045 | + | 0.364905i | \(0.881101\pi\) | |||||||
\(752\) | − | 19.5959i | − | 0.714590i | ||||||
\(753\) | 12.0000i | 0.437304i | ||||||||
\(754\) | −12.2474 | − | 12.2474i | −0.446026 | − | 0.446026i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.00000i | 0.109037i | 0.998513 | + | 0.0545184i | \(0.0173624\pi\) | ||||
−0.998513 | + | 0.0545184i | \(0.982638\pi\) | |||||||
\(758\) | −1.00000 | + | 1.00000i | −0.0363216 | + | 0.0363216i | ||||
\(759\) | −12.2474 | −0.444554 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 24.4949i | − | 0.887939i | −0.896042 | − | 0.443970i | \(-0.853570\pi\) | ||
0.896042 | − | 0.443970i | \(-0.146430\pi\) | |||||||
\(762\) | −7.34847 | + | 7.34847i | −0.266207 | + | 0.266207i | ||||
\(763\) | −15.0000 | + | 36.7423i | −0.543036 | + | 1.33016i | ||||
\(764\) | 20.0000 | 0.723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.44949 | + | 2.44949i | −0.0885037 | + | 0.0885037i | ||||
\(767\) | 30.0000 | 1.08324 | ||||||||
\(768\) | − | 39.1918i | − | 1.41421i | ||||||
\(769\) | − | 22.0454i | − | 0.794978i | −0.917607 | − | 0.397489i | \(-0.869882\pi\) | ||
0.917607 | − | 0.397489i | \(-0.130118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000i | 0.648254i | ||||||||
\(772\) | −42.0000 | −1.51161 | ||||||||
\(773\) | 26.9444 | 0.969122 | 0.484561 | − | 0.874757i | \(-0.338979\pi\) | ||||
0.484561 | + | 0.874757i | \(0.338979\pi\) | |||||||
\(774\) | −33.0000 | − | 33.0000i | −1.18616 | − | 1.18616i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −14.6969 | + | 14.6969i | −0.527589 | + | 0.527589i | ||||
\(777\) | −7.34847 | + | 18.0000i | −0.263625 | + | 0.645746i | ||||
\(778\) | 5.00000 | + | 5.00000i | 0.179259 | + | 0.179259i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.0000 | 0.894570 | ||||||||
\(782\) | 4.89898 | + | 4.89898i | 0.175187 | + | 0.175187i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.0000 | + | 19.5959i | 0.714286 | + | 0.699854i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.0000 | − | 12.0000i | 0.428026 | − | 0.428026i | ||||
\(787\) | 17.1464i | 0.611204i | 0.952159 | + | 0.305602i | \(0.0988577\pi\) | ||||
−0.952159 | + | 0.305602i | \(0.901142\pi\) | |||||||
\(788\) | −46.0000 | −1.63868 | ||||||||
\(789\) | 2.44949i | 0.0872041i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.9444 | − | 11.0000i | −0.958032 | − | 0.391115i | ||||
\(792\) | −30.0000 | − | 30.0000i | −1.06600 | − | 1.06600i | ||||
\(793\) | − | 30.0000i | − | 1.06533i | ||||||
\(794\) | 19.5959 | + | 19.5959i | 0.695433 | + | 0.695433i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 24.4949i | − | 0.868199i | ||||||
\(797\) | −44.0908 | −1.56178 | −0.780888 | − | 0.624671i | \(-0.785233\pi\) | ||||
−0.780888 | + | 0.624671i | \(0.785233\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000i | 0.849059i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 7.34847i | − | 0.259645i | ||||||
\(802\) | 23.0000 | + | 23.0000i | 0.812158 | + | 0.812158i | ||||
\(803\) | 12.2474i | 0.432203i | ||||||||
\(804\) | 14.6969 | 0.518321 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −18.0000 | − | 18.0000i | −0.634023 | − | 0.634023i | ||||
\(807\) | −54.0000 | −1.90089 | ||||||||
\(808\) | 24.4949 | + | 24.4949i | 0.861727 | + | 0.861727i | ||||
\(809\) | 5.00000 | 0.175791 | 0.0878953 | − | 0.996130i | \(-0.471986\pi\) | ||||
0.0878953 | + | 0.996130i | \(0.471986\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.5959 | 0.688106 | 0.344053 | − | 0.938950i | \(-0.388200\pi\) | ||||
0.344053 | + | 0.938950i | \(0.388200\pi\) | |||||||
\(812\) | −24.4949 | − | 10.0000i | −0.859602 | − | 0.350931i | ||||
\(813\) | 42.0000i | 1.47300i | ||||||||
\(814\) | 15.0000 | + | 15.0000i | 0.525750 | + | 0.525750i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 48.0000i | 1.68034i | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −34.2929 | + | 34.2929i | −1.19902 | + | 1.19902i | ||||
\(819\) | 7.34847 | − | 18.0000i | 0.256776 | − | 0.628971i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.00000 | −0.279202 | −0.139601 | − | 0.990208i | \(-0.544582\pi\) | ||||
−0.139601 | + | 0.990208i | \(0.544582\pi\) | |||||||
\(822\) | −19.5959 | − | 19.5959i | −0.683486 | − | 0.683486i | ||||
\(823\) | −21.0000 | −0.732014 | −0.366007 | − | 0.930612i | \(-0.619275\pi\) | ||||
−0.366007 | + | 0.930612i | \(0.619275\pi\) | |||||||
\(824\) | −29.3939 | − | 29.3939i | −1.02398 | − | 1.02398i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 42.2474 | − | 17.7526i | 1.46998 | − | 0.617690i | ||||
\(827\) | 13.0000 | 0.452054 | 0.226027 | − | 0.974121i | \(-0.427426\pi\) | ||||
0.226027 | + | 0.974121i | \(0.427426\pi\) | |||||||
\(828\) | 6.00000i | 0.208514i | ||||||||
\(829\) | − | 9.79796i | − | 0.340297i | −0.985418 | − | 0.170149i | \(-0.945575\pi\) | ||
0.985418 | − | 0.170149i | \(-0.0544248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.89898 | −0.169944 | ||||||||
\(832\) | − | 19.5959i | − | 0.679366i | ||||||
\(833\) | −24.4949 | − | 24.0000i | −0.848698 | − | 0.831551i | ||||
\(834\) | −30.0000 | + | 30.0000i | −1.03882 | + | 1.03882i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.2474 | − | 12.2474i | −0.423081 | − | 0.423081i | ||||
\(839\) | 36.7423 | 1.26849 | 0.634243 | − | 0.773133i | \(-0.281312\pi\) | ||||
0.634243 | + | 0.773133i | \(0.281312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 23.0000 | + | 23.0000i | 0.792632 | + | 0.792632i | ||||
\(843\) | − | 41.6413i | − | 1.43420i | ||||||
\(844\) | −20.0000 | −0.688428 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −14.6969 | + | 14.6969i | −0.505291 | + | 0.505291i | ||||
\(847\) | 14.0000 | − | 34.2929i | 0.481046 | − | 1.17832i | ||||
\(848\) | 16.0000i | 0.549442i | ||||||||
\(849\) | 24.0000 | 0.823678 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.00000i | − | 0.102839i | ||||||
\(852\) | − | 24.4949i | − | 0.839181i | ||||||
\(853\) | 14.6969 | 0.503214 | 0.251607 | − | 0.967830i | \(-0.419041\pi\) | ||||
0.251607 | + | 0.967830i | \(0.419041\pi\) | |||||||
\(854\) | −17.7526 | − | 42.2474i | −0.607480 | − | 1.44568i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.0000 | − | 16.0000i | 0.546869 | − | 0.546869i | ||||
\(857\) | 41.6413 | 1.42244 | 0.711220 | − | 0.702969i | \(-0.248143\pi\) | ||||
0.711220 | + | 0.702969i | \(0.248143\pi\) | |||||||
\(858\) | −30.0000 | − | 30.0000i | −1.02418 | − | 1.02418i | ||||
\(859\) | −24.4949 | −0.835755 | −0.417878 | − | 0.908503i | \(-0.637226\pi\) | ||||
−0.417878 | + | 0.908503i | \(0.637226\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.0000 | + | 73.4847i | −1.02240 | + | 2.50435i | ||||
\(862\) | −10.0000 | + | 10.0000i | −0.340601 | + | 0.340601i | ||||
\(863\) | −31.0000 | −1.05525 | −0.527626 | − | 0.849477i | \(-0.676918\pi\) | ||||
−0.527626 | + | 0.849477i | \(0.676918\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −39.1918 | − | 39.1918i | −1.33179 | − | 1.33179i | ||||
\(867\) | − | 17.1464i | − | 0.582323i | ||||||
\(868\) | −36.0000 | − | 14.6969i | −1.22192 | − | 0.498847i | ||||
\(869\) | −45.0000 | −1.52652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.34847 | 0.248993 | ||||||||
\(872\) | 30.0000 | − | 30.0000i | 1.01593 | − | 1.01593i | ||||
\(873\) | 22.0454 | 0.746124 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | − | 52.0000i | − | 1.75592i | −0.478738 | − | 0.877958i | \(-0.658906\pi\) | ||
0.478738 | − | 0.877958i | \(-0.341094\pi\) | |||||||
\(878\) | 12.2474 | + | 12.2474i | 0.413331 | + | 0.413331i | ||||
\(879\) | − | 6.00000i | − | 0.202375i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.2474i | 0.412627i | 0.978486 | + | 0.206314i | \(0.0661467\pi\) | ||||
−0.978486 | + | 0.206314i | \(0.933853\pi\) | |||||||
\(882\) | −0.303062 | − | 29.6969i | −0.0102046 | − | 0.999948i | ||||
\(883\) | 19.0000 | 0.639401 | 0.319700 | − | 0.947519i | \(-0.396418\pi\) | ||||
0.319700 | + | 0.947519i | \(0.396418\pi\) | |||||||
\(884\) | 24.0000i | 0.807207i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.0000 | − | 14.0000i | −0.470339 | − | 0.470339i | ||||
\(887\) | − | 56.3383i | − | 1.89165i | −0.324671 | − | 0.945827i | \(-0.605254\pi\) | ||
0.324671 | − | 0.945827i | \(-0.394746\pi\) | |||||||
\(888\) | 14.6969 | − | 14.6969i | 0.493197 | − | 0.493197i | ||||
\(889\) | −3.00000 | + | 7.34847i | −0.100617 | + | 0.246460i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 45.0000i | − | 1.50756i | ||||||
\(892\) | 4.89898 | 0.164030 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −12.2474 | + | 12.2474i | −0.409616 | + | 0.409616i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −11.5959 | − | 27.5959i | −0.387392 | − | 0.921915i | ||||
\(897\) | 6.00000i | 0.200334i | ||||||||
\(898\) | −25.0000 | − | 25.0000i | −0.834261 | − | 0.834261i | ||||
\(899\) | 36.7423 | 1.22543 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 19.5959i | − | 0.652835i | ||||||
\(902\) | 61.2372 | + | 61.2372i | 2.03898 | + | 2.03898i | ||||
\(903\) | −66.0000 | − | 26.9444i | −2.19634 | − | 0.896653i | ||||
\(904\) | 22.0000 | + | 22.0000i | 0.731709 | + | 0.731709i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 12.2474 | + | 12.2474i | 0.406894 | + | 0.406894i | ||||
\(907\) | 38.0000 | 1.26177 | 0.630885 | − | 0.775877i | \(-0.282692\pi\) | ||||
0.630885 | + | 0.775877i | \(0.282692\pi\) | |||||||
\(908\) | 39.1918 | 1.30063 | ||||||||
\(909\) | − | 36.7423i | − | 1.21867i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 35.0000i | − | 1.15960i | −0.814758 | − | 0.579801i | \(-0.803130\pi\) | ||
0.814758 | − | 0.579801i | \(-0.196870\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.2474 | 0.405331 | ||||||||
\(914\) | 3.00000 | − | 3.00000i | 0.0992312 | − | 0.0992312i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.5959 | 0.647467 | ||||||||
\(917\) | 4.89898 | − | 12.0000i | 0.161779 | − | 0.396275i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 41.0000i | − | 1.35247i | −0.736688 | − | 0.676233i | \(-0.763611\pi\) | ||
0.736688 | − | 0.676233i | \(-0.236389\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.0000 | 0.395413 | ||||||||
\(922\) | 12.2474 | − | 12.2474i | 0.403348 | − | 0.403348i | ||||
\(923\) | − | 12.2474i | − | 0.403130i | ||||||
\(924\) | −60.0000 | − | 24.4949i | −1.97386 | − | 0.805823i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 36.0000 | + | 36.0000i | 1.18303 | + | 1.18303i | ||||
\(927\) | 44.0908i | 1.44813i | ||||||||
\(928\) | 20.0000 | + | 20.0000i | 0.656532 | + | 0.656532i | ||||
\(929\) | 26.9444i | 0.884017i | 0.897011 | + | 0.442008i | \(0.145734\pi\) | ||||
−0.897011 | + | 0.442008i | \(0.854266\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −22.0000 | −0.720634 | ||||||||
\(933\) | − | 48.0000i | − | 1.57145i | ||||||
\(934\) | 4.89898 | − | 4.89898i | 0.160300 | − | 0.160300i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −14.6969 | + | 14.6969i | −0.480384 | + | 0.480384i | ||||
\(937\) | −7.34847 | −0.240064 | −0.120032 | − | 0.992770i | \(-0.538300\pi\) | ||||
−0.120032 | + | 0.992770i | \(0.538300\pi\) | |||||||
\(938\) | 10.3485 | − | 4.34847i | 0.337889 | − | 0.141983i | ||||
\(939\) | 24.0000i | 0.783210i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 12.2474i | − | 0.399255i | −0.979872 | − | 0.199628i | \(-0.936027\pi\) | ||
0.979872 | − | 0.199628i | \(-0.0639733\pi\) | |||||||
\(942\) | −42.0000 | + | 42.0000i | −1.36843 | + | 1.36843i | ||||
\(943\) | − | 12.2474i | − | 0.398832i | ||||||
\(944\) | −48.9898 | −1.59448 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −55.0000 | + | 55.0000i | −1.78820 | + | 1.78820i | ||||
\(947\) | 38.0000 | 1.23483 | 0.617417 | − | 0.786636i | \(-0.288179\pi\) | ||||
0.617417 | + | 0.786636i | \(0.288179\pi\) | |||||||
\(948\) | 44.0908i | 1.43200i | ||||||||
\(949\) | 6.00000 | 0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −41.6413 | −1.35031 | ||||||||
\(952\) | 14.2020 | + | 33.7980i | 0.460291 | + | 1.09540i | ||||
\(953\) | − | 59.0000i | − | 1.91120i | −0.294671 | − | 0.955599i | \(-0.595210\pi\) | ||
0.294671 | − | 0.955599i | \(-0.404790\pi\) | |||||||
\(954\) | 12.0000 | − | 12.0000i | 0.388514 | − | 0.388514i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 52.0000 | 1.68180 | ||||||||
\(957\) | 61.2372 | 1.97952 | ||||||||
\(958\) | 36.7423 | + | 36.7423i | 1.18709 | + | 1.18709i | ||||
\(959\) | −19.5959 | − | 8.00000i | −0.632785 | − | 0.258333i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | 7.34847 | − | 7.34847i | 0.236924 | − | 0.236924i | ||||
\(963\) | −24.0000 | −0.773389 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.55051 | + | 8.44949i | 0.114236 | + | 0.271858i | ||||
\(967\) | 18.0000 | 0.578841 | 0.289420 | − | 0.957202i | \(-0.406537\pi\) | ||||
0.289420 | + | 0.957202i | \(0.406537\pi\) | |||||||
\(968\) | −28.0000 | + | 28.0000i | −0.899954 | + | 0.899954i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.0908 | 1.41494 | 0.707471 | − | 0.706743i | \(-0.249836\pi\) | ||||
0.707471 | + | 0.706743i | \(0.249836\pi\) | |||||||
\(972\) | −44.0908 | −1.41421 | ||||||||
\(973\) | −12.2474 | + | 30.0000i | −0.392635 | + | 0.961756i | ||||
\(974\) | 7.00000 | + | 7.00000i | 0.224294 | + | 0.224294i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 48.9898i | 1.56813i | ||||||||
\(977\) | − | 17.0000i | − | 0.543878i | −0.962314 | − | 0.271939i | \(-0.912335\pi\) | ||
0.962314 | − | 0.271939i | \(-0.0876649\pi\) | |||||||
\(978\) | 14.6969 | − | 14.6969i | 0.469956 | − | 0.469956i | ||||
\(979\) | −12.2474 | −0.391430 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −45.0000 | −1.43674 | ||||||||
\(982\) | 5.00000 | − | 5.00000i | 0.159556 | − | 0.159556i | ||||
\(983\) | 22.0454i | 0.703139i | 0.936162 | + | 0.351570i | \(0.114352\pi\) | ||||
−0.936162 | + | 0.351570i | \(0.885648\pi\) | |||||||
\(984\) | 60.0000 | − | 60.0000i | 1.91273 | − | 1.91273i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −24.4949 | − | 24.4949i | −0.780076 | − | 0.780076i | ||||
\(987\) | −12.0000 | + | 29.3939i | −0.381964 | + | 0.935617i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0000 | 0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 35.0000i | − | 1.11181i | −0.831245 | − | 0.555906i | \(-0.812372\pi\) | ||
0.831245 | − | 0.555906i | \(-0.187628\pi\) | |||||||
\(992\) | 29.3939 | + | 29.3939i | 0.933257 | + | 0.933257i | ||||
\(993\) | −61.2372 | −1.94331 | ||||||||
\(994\) | −7.24745 | − | 17.2474i | −0.229875 | − | 0.547056i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 12.0000i | − | 0.380235i | ||||||
\(997\) | 4.89898 | 0.155152 | 0.0775761 | − | 0.996986i | \(-0.475282\pi\) | ||||
0.0775761 | + | 0.996986i | \(0.475282\pi\) | |||||||
\(998\) | −16.0000 | + | 16.0000i | −0.506471 | + | 0.506471i | ||||
\(999\) | 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 | 700.2.c.a.699.1 | 4 | ||
4.3 | odd | 2 | 700.2.c.g.699.2 | 4 | |||
5.2 | odd | 4 | 700.2.g.h.251.1 | yes | 4 | ||
5.3 | odd | 4 | 700.2.g.b.251.4 | yes | 4 | ||
5.4 | even | 2 | 700.2.c.g.699.4 | 4 | |||
7.6 | odd | 2 | inner | 700.2.c.a.699.2 | 4 | ||
20.3 | even | 4 | 700.2.g.b.251.1 | ✓ | 4 | ||
20.7 | even | 4 | 700.2.g.h.251.4 | yes | 4 | ||
20.19 | odd | 2 | inner | 700.2.c.a.699.3 | 4 | ||
28.27 | even | 2 | 700.2.c.g.699.1 | 4 | |||
35.13 | even | 4 | 700.2.g.b.251.3 | yes | 4 | ||
35.27 | even | 4 | 700.2.g.h.251.2 | yes | 4 | ||
35.34 | odd | 2 | 700.2.c.g.699.3 | 4 | |||
140.27 | odd | 4 | 700.2.g.h.251.3 | yes | 4 | ||
140.83 | odd | 4 | 700.2.g.b.251.2 | yes | 4 | ||
140.139 | even | 2 | inner | 700.2.c.a.699.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.c.a.699.1 | 4 | 1.1 | even | 1 | trivial | ||
700.2.c.a.699.2 | 4 | 7.6 | odd | 2 | inner | ||
700.2.c.a.699.3 | 4 | 20.19 | odd | 2 | inner | ||
700.2.c.a.699.4 | 4 | 140.139 | even | 2 | inner | ||
700.2.c.g.699.1 | 4 | 28.27 | even | 2 | |||
700.2.c.g.699.2 | 4 | 4.3 | odd | 2 | |||
700.2.c.g.699.3 | 4 | 35.34 | odd | 2 | |||
700.2.c.g.699.4 | 4 | 5.4 | even | 2 | |||
700.2.g.b.251.1 | ✓ | 4 | 20.3 | even | 4 | ||
700.2.g.b.251.2 | yes | 4 | 140.83 | odd | 4 | ||
700.2.g.b.251.3 | yes | 4 | 35.13 | even | 4 | ||
700.2.g.b.251.4 | yes | 4 | 5.3 | odd | 4 | ||
700.2.g.h.251.1 | yes | 4 | 5.2 | odd | 4 | ||
700.2.g.h.251.2 | yes | 4 | 35.27 | even | 4 | ||
700.2.g.h.251.3 | yes | 4 | 140.27 | odd | 4 | ||
700.2.g.h.251.4 | yes | 4 | 20.7 | even | 4 |