Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(307,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1386.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 307.1 | ||
Root | \(1.54779 + 1.54779i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.307 |
Dual form | 1386.2.e.b.307.8 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 3.09557i | − | 1.38438i | −0.721714 | − | 0.692191i | \(-0.756645\pi\) | ||
0.721714 | − | 0.692191i | \(-0.243355\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | − | 1.00000i | −0.925820 | − | 0.377964i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.09557 | −0.978906 | ||||||||
\(11\) | 1.79129 | − | 2.79129i | 0.540094 | − | 0.841605i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.646084 | −0.179191 | −0.0895957 | − | 0.995978i | \(-0.528557\pi\) | ||||
−0.0895957 | + | 0.995978i | \(0.528557\pi\) | |||||||
\(14\) | −1.00000 | + | 2.44949i | −0.267261 | + | 0.654654i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.74166 | −0.907485 | −0.453743 | − | 0.891133i | \(-0.649911\pi\) | ||||
−0.453743 | + | 0.891133i | \(0.649911\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.80341 | 0.413730 | 0.206865 | − | 0.978370i | \(-0.433674\pi\) | ||||
0.206865 | + | 0.978370i | \(0.433674\pi\) | |||||||
\(20\) | 3.09557i | 0.692191i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.79129 | − | 1.79129i | −0.595105 | − | 0.381904i | ||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.58258 | −0.916515 | ||||||||
\(26\) | 0.646084i | 0.126707i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.44949 | + | 1.00000i | 0.462910 | + | 0.188982i | ||||
\(29\) | 1.58258i | 0.293877i | 0.989146 | + | 0.146938i | \(0.0469419\pi\) | ||||
−0.989146 | + | 0.146938i | \(0.953058\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.64064i | − | 1.55190i | −0.630792 | − | 0.775952i | \(-0.717270\pi\) | ||
0.630792 | − | 0.775952i | \(-0.282730\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.74166i | 0.641689i | ||||||||
\(35\) | −3.09557 | + | 7.58258i | −0.523247 | + | 1.28169i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.58258 | 0.588972 | 0.294486 | − | 0.955656i | \(-0.404852\pi\) | ||||
0.294486 | + | 0.955656i | \(0.404852\pi\) | |||||||
\(38\) | − | 1.80341i | − | 0.292551i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.09557 | 0.489453 | ||||||||
\(41\) | −9.93280 | −1.55124 | −0.775622 | − | 0.631198i | \(-0.782564\pi\) | ||||
−0.775622 | + | 0.631198i | \(0.782564\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.16515i | 1.09268i | 0.837565 | + | 0.546338i | \(0.183978\pi\) | ||||
−0.837565 | + | 0.546338i | \(0.816022\pi\) | |||||||
\(44\) | −1.79129 | + | 2.79129i | −0.270047 | + | 0.420802i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000i | 0.589768i | ||||||||
\(47\) | 9.93280i | 1.44885i | 0.689354 | + | 0.724424i | \(0.257894\pi\) | ||||
−0.689354 | + | 0.724424i | \(0.742106\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | + | 4.89898i | 0.714286 | + | 0.699854i | ||||
\(50\) | 4.58258i | 0.648074i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.646084 | 0.0895957 | ||||||||
\(53\) | 11.5826 | 1.59099 | 0.795495 | − | 0.605961i | \(-0.207211\pi\) | ||||
0.795495 | + | 0.605961i | \(0.207211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.64064 | − | 5.54506i | −1.16510 | − | 0.747696i | ||||
\(56\) | 1.00000 | − | 2.44949i | 0.133631 | − | 0.327327i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.58258 | 0.207802 | ||||||||
\(59\) | 0.646084i | 0.0841129i | 0.999115 | + | 0.0420565i | \(0.0133909\pi\) | ||||
−0.999115 | + | 0.0420565i | \(0.986609\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.93825 | −0.248168 | −0.124084 | − | 0.992272i | \(-0.539599\pi\) | ||||
−0.124084 | + | 0.992272i | \(0.539599\pi\) | |||||||
\(62\) | −8.64064 | −1.09736 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.00000i | 0.248069i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.58258 | −0.926359 | −0.463180 | − | 0.886264i | \(-0.653291\pi\) | ||||
−0.463180 | + | 0.886264i | \(0.653291\pi\) | |||||||
\(68\) | 3.74166 | 0.453743 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.58258 | + | 3.09557i | 0.906291 | + | 0.369992i | ||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.1240 | −1.88717 | −0.943583 | − | 0.331136i | \(-0.892568\pi\) | ||||
−0.943583 | + | 0.331136i | \(0.892568\pi\) | |||||||
\(74\) | − | 3.58258i | − | 0.416466i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.80341 | −0.206865 | ||||||||
\(77\) | −7.17903 | + | 5.04594i | −0.818126 | + | 0.575039i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | − | 3.09557i | − | 0.346096i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.93280i | 1.09689i | ||||||||
\(83\) | 12.8935 | 1.41525 | 0.707625 | − | 0.706589i | \(-0.249767\pi\) | ||||
0.707625 | + | 0.706589i | \(0.249767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.5826i | 1.25631i | ||||||||
\(86\) | 7.16515 | 0.772638 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.79129 | + | 1.79129i | 0.297552 | + | 0.190952i | ||||
\(89\) | − | 9.79796i | − | 1.03858i | −0.854598 | − | 0.519291i | \(-0.826196\pi\) | ||
0.854598 | − | 0.519291i | \(-0.173804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.58258 | + | 0.646084i | 0.165899 | + | 0.0677280i | ||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.93280 | 1.02449 | ||||||||
\(95\) | − | 5.58258i | − | 0.572760i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.50579i | − | 0.863632i | −0.901962 | − | 0.431816i | \(-0.857873\pi\) | ||
0.901962 | − | 0.431816i | \(-0.142127\pi\) | |||||||
\(98\) | 4.89898 | − | 5.00000i | 0.494872 | − | 0.505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.58258 | 0.458258 | ||||||||
\(101\) | −11.7362 | −1.16780 | −0.583898 | − | 0.811827i | \(-0.698473\pi\) | ||||
−0.583898 | + | 0.811827i | \(0.698473\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.05630i | 0.596745i | 0.954449 | + | 0.298373i | \(0.0964438\pi\) | ||||
−0.954449 | + | 0.298373i | \(0.903556\pi\) | |||||||
\(104\) | − | 0.646084i | − | 0.0633537i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 11.5826i | − | 1.12500i | ||||||
\(107\) | 17.5826i | 1.69977i | 0.526967 | + | 0.849886i | \(0.323329\pi\) | ||||
−0.526967 | + | 0.849886i | \(0.676671\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 17.1652i | − | 1.64412i | −0.569398 | − | 0.822062i | \(-0.692824\pi\) | ||
0.569398 | − | 0.822062i | \(-0.307176\pi\) | |||||||
\(110\) | −5.54506 | + | 8.64064i | −0.528701 | + | 0.823852i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.44949 | − | 1.00000i | −0.231455 | − | 0.0944911i | ||||
\(113\) | −10.7477 | −1.01106 | −0.505531 | − | 0.862809i | \(-0.668703\pi\) | ||||
−0.505531 | + | 0.862809i | \(0.668703\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.3823i | 1.15465i | ||||||||
\(116\) | − | 1.58258i | − | 0.146938i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.646084 | 0.0594768 | ||||||||
\(119\) | 9.16515 | + | 3.74166i | 0.840168 | + | 0.342997i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.58258 | − | 10.0000i | −0.416598 | − | 0.909091i | ||||
\(122\) | 1.93825i | 0.175481i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.64064i | 0.775952i | ||||||||
\(125\) | − | 1.29217i | − | 0.115575i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.58258i | 0.317902i | 0.987286 | + | 0.158951i | \(0.0508112\pi\) | ||||
−0.987286 | + | 0.158951i | \(0.949189\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | 0.175412 | ||||||||
\(131\) | −16.7700 | −1.46520 | −0.732602 | − | 0.680657i | \(-0.761694\pi\) | ||||
−0.732602 | + | 0.680657i | \(0.761694\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.41742 | − | 1.80341i | −0.383039 | − | 0.156375i | ||||
\(134\) | 7.58258i | 0.655035i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.74166i | − | 0.320844i | ||||||
\(137\) | 3.16515 | 0.270417 | 0.135209 | − | 0.990817i | \(-0.456830\pi\) | ||||
0.135209 | + | 0.990817i | \(0.456830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4779 | 1.31282 | 0.656408 | − | 0.754406i | \(-0.272075\pi\) | ||||
0.656408 | + | 0.754406i | \(0.272075\pi\) | |||||||
\(140\) | 3.09557 | − | 7.58258i | 0.261624 | − | 0.640845i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000i | 0.167836i | ||||||||
\(143\) | −1.15732 | + | 1.80341i | −0.0967801 | + | 0.150808i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.89898 | 0.406838 | ||||||||
\(146\) | 16.1240i | 1.33443i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.58258 | −0.294486 | ||||||||
\(149\) | − | 14.0000i | − | 1.14692i | −0.819232 | − | 0.573462i | \(-0.805600\pi\) | ||
0.819232 | − | 0.573462i | \(-0.194400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.58258i | − | 0.454304i | −0.973859 | − | 0.227152i | \(-0.927059\pi\) | ||
0.973859 | − | 0.227152i | \(-0.0729414\pi\) | |||||||
\(152\) | 1.80341i | 0.146276i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.04594 | + | 7.17903i | 0.406614 | + | 0.578503i | ||||
\(155\) | −26.7477 | −2.14843 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 13.1632i | − | 1.05054i | −0.850936 | − | 0.525270i | \(-0.823964\pi\) | ||
0.850936 | − | 0.525270i | \(-0.176036\pi\) | |||||||
\(158\) | 4.00000 | 0.318223 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.09557 | −0.244727 | ||||||||
\(161\) | 9.79796 | + | 4.00000i | 0.772187 | + | 0.315244i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | 9.93280 | 0.775622 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 12.8935i | − | 1.00073i | ||||||
\(167\) | 1.29217 | 0.0999909 | 0.0499955 | − | 0.998749i | \(-0.484079\pi\) | ||||
0.0499955 | + | 0.998749i | \(0.484079\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5826 | −0.967890 | ||||||||
\(170\) | 11.5826 | 0.888343 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 7.16515i | − | 0.546338i | ||||||
\(173\) | 10.7137 | 0.814550 | 0.407275 | − | 0.913306i | \(-0.366479\pi\) | ||||
0.407275 | + | 0.913306i | \(0.366479\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.2250 | + | 4.58258i | 0.848528 | + | 0.346410i | ||||
\(176\) | 1.79129 | − | 2.79129i | 0.135023 | − | 0.210401i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.79796 | −0.734388 | ||||||||
\(179\) | −11.1652 | −0.834523 | −0.417261 | − | 0.908787i | \(-0.637010\pi\) | ||||
−0.417261 | + | 0.908787i | \(0.637010\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.41022i | 0.402138i | 0.979577 | + | 0.201069i | \(0.0644416\pi\) | ||||
−0.979577 | + | 0.201069i | \(0.935558\pi\) | |||||||
\(182\) | 0.646084 | − | 1.58258i | 0.0478909 | − | 0.117308i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 4.00000i | − | 0.294884i | ||||||
\(185\) | − | 11.0901i | − | 0.815362i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.70239 | + | 10.4440i | −0.490127 | + | 0.763744i | ||||
\(188\) | − | 9.93280i | − | 0.724424i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.58258 | −0.405003 | ||||||||
\(191\) | 18.0000 | 1.30243 | 0.651217 | − | 0.758891i | \(-0.274259\pi\) | ||||
0.651217 | + | 0.758891i | \(0.274259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 16.3303i | − | 1.17548i | −0.809050 | − | 0.587740i | \(-0.800018\pi\) | ||
0.809050 | − | 0.587740i | \(-0.199982\pi\) | |||||||
\(194\) | −8.50579 | −0.610680 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.00000 | − | 4.89898i | −0.357143 | − | 0.349927i | ||||
\(197\) | 8.74773i | 0.623250i | 0.950205 | + | 0.311625i | \(0.100873\pi\) | ||||
−0.950205 | + | 0.311625i | \(0.899127\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 9.66311i | − | 0.685000i | −0.939518 | − | 0.342500i | \(-0.888726\pi\) | ||
0.939518 | − | 0.342500i | \(-0.111274\pi\) | |||||||
\(200\) | − | 4.58258i | − | 0.324037i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.7362i | 0.825757i | ||||||||
\(203\) | 1.58258 | − | 3.87650i | 0.111075 | − | 0.272077i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.7477i | 2.14751i | ||||||||
\(206\) | 6.05630 | 0.421963 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.646084 | −0.0447979 | ||||||||
\(209\) | 3.23042 | − | 5.03383i | 0.223453 | − | 0.348197i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 16.7477i | − | 1.15296i | −0.817111 | − | 0.576481i | \(-0.804426\pi\) | ||
0.817111 | − | 0.576481i | \(-0.195574\pi\) | |||||||
\(212\) | −11.5826 | −0.795495 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 17.5826 | 1.20192 | ||||||||
\(215\) | 22.1803 | 1.51268 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.64064 | + | 21.1652i | −0.586565 | + | 1.43678i | ||||
\(218\) | −17.1652 | −1.16257 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8.64064 | + | 5.54506i | 0.582552 | + | 0.373848i | ||||
\(221\) | 2.41742 | 0.162614 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1240i | 1.07974i | 0.841749 | + | 0.539870i | \(0.181527\pi\) | ||||
−0.841749 | + | 0.539870i | \(0.818473\pi\) | |||||||
\(224\) | −1.00000 | + | 2.44949i | −0.0668153 | + | 0.163663i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.7477i | 0.714928i | ||||||||
\(227\) | −0.511238 | −0.0339321 | −0.0169660 | − | 0.999856i | \(-0.505401\pi\) | ||||
−0.0169660 | + | 0.999856i | \(0.505401\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.67991i | − | 0.375339i | −0.982232 | − | 0.187669i | \(-0.939907\pi\) | ||
0.982232 | − | 0.187669i | \(-0.0600934\pi\) | |||||||
\(230\) | 12.3823 | 0.816464 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.58258 | −0.103901 | ||||||||
\(233\) | − | 27.1652i | − | 1.77965i | −0.456304 | − | 0.889824i | \(-0.650827\pi\) | ||
0.456304 | − | 0.889824i | \(-0.349173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.7477 | 2.00576 | ||||||||
\(236\) | − | 0.646084i | − | 0.0420565i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.74166 | − | 9.16515i | 0.242536 | − | 0.594089i | ||||
\(239\) | − | 8.41742i | − | 0.544478i | −0.962230 | − | 0.272239i | \(-0.912236\pi\) | ||
0.962230 | − | 0.272239i | \(-0.0877641\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.47197 | 0.223649 | 0.111825 | − | 0.993728i | \(-0.464331\pi\) | ||||
0.111825 | + | 0.993728i | \(0.464331\pi\) | |||||||
\(242\) | −10.0000 | + | 4.58258i | −0.642824 | + | 0.294579i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.93825 | 0.124084 | ||||||||
\(245\) | 15.1652 | − | 15.4779i | 0.968866 | − | 0.988845i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.16515 | −0.0741368 | ||||||||
\(248\) | 8.64064 | 0.548681 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.29217 | −0.0817239 | ||||||||
\(251\) | − | 24.1185i | − | 1.52235i | −0.648549 | − | 0.761173i | \(-0.724624\pi\) | ||
0.648549 | − | 0.761173i | \(-0.275376\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.16515 | + | 11.1652i | −0.450469 | + | 0.701947i | ||||
\(254\) | 3.58258 | 0.224791 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.89898i | 0.305590i | 0.988258 | + | 0.152795i | \(0.0488274\pi\) | ||||
−0.988258 | + | 0.152795i | \(0.951173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.77548 | − | 3.58258i | −0.545282 | − | 0.222610i | ||||
\(260\) | − | 2.00000i | − | 0.124035i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.7700i | 1.03606i | ||||||||
\(263\) | − | 8.33030i | − | 0.513668i | −0.966455 | − | 0.256834i | \(-0.917321\pi\) | ||
0.966455 | − | 0.256834i | \(-0.0826794\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 35.8547i | − | 2.20254i | ||||||
\(266\) | −1.80341 | + | 4.41742i | −0.110574 | + | 0.270850i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.58258 | 0.463180 | ||||||||
\(269\) | 16.5003i | 1.00604i | 0.864274 | + | 0.503022i | \(0.167778\pi\) | ||||
−0.864274 | + | 0.503022i | \(0.832222\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.89898 | 0.297592 | 0.148796 | − | 0.988868i | \(-0.452460\pi\) | ||||
0.148796 | + | 0.988868i | \(0.452460\pi\) | |||||||
\(272\) | −3.74166 | −0.226871 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 3.16515i | − | 0.191214i | ||||||
\(275\) | −8.20871 | + | 12.7913i | −0.495004 | + | 0.771344i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | − | 15.4779i | − | 0.928301i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7.58258 | − | 3.09557i | −0.453146 | − | 0.184996i | ||||
\(281\) | 11.1652i | 0.666057i | 0.942917 | + | 0.333029i | \(0.108071\pi\) | ||||
−0.942917 | + | 0.333029i | \(0.891929\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.0622 | 1.07369 | 0.536843 | − | 0.843682i | \(-0.319617\pi\) | ||||
0.536843 | + | 0.843682i | \(0.319617\pi\) | |||||||
\(284\) | 2.00000 | 0.118678 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.80341 | + | 1.15732i | 0.106638 | + | 0.0684339i | ||||
\(287\) | 24.3303 | + | 9.93280i | 1.43617 | + | 0.586315i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.00000 | −0.176471 | ||||||||
\(290\) | − | 4.89898i | − | 0.287678i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.1240 | 0.943583 | ||||||||
\(293\) | 25.1410 | 1.46875 | 0.734376 | − | 0.678743i | \(-0.237475\pi\) | ||||
0.734376 | + | 0.678743i | \(0.237475\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | 0.116445 | ||||||||
\(296\) | 3.58258i | 0.208233i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.0000 | −0.810998 | ||||||||
\(299\) | 2.58434 | 0.149456 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.16515 | − | 17.5510i | 0.412992 | − | 1.01162i | ||||
\(302\) | −5.58258 | −0.321241 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.80341 | 0.103432 | ||||||||
\(305\) | 6.00000i | 0.343559i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.5789 | 0.603769 | 0.301885 | − | 0.953344i | \(-0.402384\pi\) | ||||
0.301885 | + | 0.953344i | \(0.402384\pi\) | |||||||
\(308\) | 7.17903 | − | 5.04594i | 0.409063 | − | 0.287519i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 26.7477i | 1.51917i | ||||||||
\(311\) | − | 5.03383i | − | 0.285442i | −0.989763 | − | 0.142721i | \(-0.954415\pi\) | ||
0.989763 | − | 0.142721i | \(-0.0455852\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 23.4724i | − | 1.32674i | −0.748292 | − | 0.663370i | \(-0.769126\pi\) | ||
0.748292 | − | 0.663370i | \(-0.230874\pi\) | |||||||
\(314\) | −13.1632 | −0.742844 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 4.00000i | − | 0.225018i | ||||||
\(317\) | −9.16515 | −0.514766 | −0.257383 | − | 0.966309i | \(-0.582860\pi\) | ||||
−0.257383 | + | 0.966309i | \(0.582860\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.41742 | + | 2.83485i | 0.247328 | + | 0.158721i | ||||
\(320\) | 3.09557i | 0.173048i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.00000 | − | 9.79796i | 0.222911 | − | 0.546019i | ||||
\(323\) | −6.74773 | −0.375454 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.96073 | 0.164232 | ||||||||
\(326\) | − | 4.00000i | − | 0.221540i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 9.93280i | − | 0.548447i | ||||||
\(329\) | 9.93280 | − | 24.3303i | 0.547613 | − | 1.34137i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.5826 | −1.29622 | −0.648108 | − | 0.761549i | \(-0.724439\pi\) | ||||
−0.648108 | + | 0.761549i | \(0.724439\pi\) | |||||||
\(332\) | −12.8935 | −0.707625 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 1.29217i | − | 0.0707043i | ||||||
\(335\) | 23.4724i | 1.28244i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.8348i | − | 0.590212i | −0.955465 | − | 0.295106i | \(-0.904645\pi\) | ||
0.955465 | − | 0.295106i | \(-0.0953549\pi\) | |||||||
\(338\) | 12.5826i | 0.684402i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 11.5826i | − | 0.628153i | ||||||
\(341\) | −24.1185 | − | 15.4779i | −1.30609 | − | 0.838174i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.34847 | − | 17.0000i | −0.396780 | − | 0.917914i | ||||
\(344\) | −7.16515 | −0.386319 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 10.7137i | − | 0.575974i | ||||||
\(347\) | − | 19.1652i | − | 1.02884i | −0.857539 | − | 0.514420i | \(-0.828007\pi\) | ||
0.857539 | − | 0.514420i | \(-0.171993\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.1185 | −1.29103 | −0.645517 | − | 0.763746i | \(-0.723358\pi\) | ||||
−0.645517 | + | 0.763746i | \(0.723358\pi\) | |||||||
\(350\) | 4.58258 | − | 11.2250i | 0.244949 | − | 0.600000i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.79129 | − | 1.79129i | −0.148776 | − | 0.0954760i | ||||
\(353\) | − | 7.48331i | − | 0.398297i | −0.979969 | − | 0.199148i | \(-0.936182\pi\) | ||
0.979969 | − | 0.199148i | \(-0.0638176\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.19115i | 0.328592i | ||||||||
\(356\) | 9.79796i | 0.519291i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.1652i | 0.590097i | ||||||||
\(359\) | − | 9.58258i | − | 0.505749i | −0.967499 | − | 0.252875i | \(-0.918624\pi\) | ||
0.967499 | − | 0.252875i | \(-0.0813760\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.7477 | −0.828828 | ||||||||
\(362\) | 5.41022 | 0.284355 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.58258 | − | 0.646084i | −0.0829495 | − | 0.0338640i | ||||
\(365\) | 49.9129i | 2.61256i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.0229i | 1.09739i | 0.836023 | + | 0.548694i | \(0.184875\pi\) | ||||
−0.836023 | + | 0.548694i | \(0.815125\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.0901 | −0.576548 | ||||||||
\(371\) | −28.3714 | − | 11.5826i | −1.47297 | − | 0.601337i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9.58258i | − | 0.496167i | −0.968739 | − | 0.248083i | \(-0.920199\pi\) | ||
0.968739 | − | 0.248083i | \(-0.0798007\pi\) | |||||||
\(374\) | 10.4440 | + | 6.70239i | 0.540049 | + | 0.346572i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.93280 | −0.512245 | ||||||||
\(377\) | − | 1.02248i | − | 0.0526602i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.3303 | −1.14703 | −0.573515 | − | 0.819195i | \(-0.694421\pi\) | ||||
−0.573515 | + | 0.819195i | \(0.694421\pi\) | |||||||
\(380\) | 5.58258i | 0.286380i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 18.0000i | − | 0.920960i | ||||||
\(383\) | − | 19.7308i | − | 1.00819i | −0.863647 | − | 0.504097i | \(-0.831825\pi\) | ||
0.863647 | − | 0.504097i | \(-0.168175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.6201 | + | 22.2232i | 0.796073 | + | 1.13260i | ||||
\(386\) | −16.3303 | −0.831191 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.50579i | 0.431816i | ||||||||
\(389\) | −10.0000 | −0.507020 | −0.253510 | − | 0.967333i | \(-0.581585\pi\) | ||||
−0.253510 | + | 0.967333i | \(0.581585\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.9666 | 0.756895 | ||||||||
\(392\) | −4.89898 | + | 5.00000i | −0.247436 | + | 0.252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.74773 | 0.440704 | ||||||||
\(395\) | 12.3823 | 0.623021 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 27.5905i | − | 1.38473i | −0.721549 | − | 0.692363i | \(-0.756570\pi\) | ||
0.721549 | − | 0.692363i | \(-0.243430\pi\) | |||||||
\(398\) | −9.66311 | −0.484368 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.58258 | −0.229129 | ||||||||
\(401\) | −7.58258 | −0.378656 | −0.189328 | − | 0.981914i | \(-0.560631\pi\) | ||||
−0.189328 | + | 0.981914i | \(0.560631\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.58258i | 0.278088i | ||||||||
\(404\) | 11.7362 | 0.583898 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.87650 | − | 1.58258i | −0.192388 | − | 0.0785419i | ||||
\(407\) | 6.41742 | − | 10.0000i | 0.318100 | − | 0.495682i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.03383 | 0.248907 | 0.124453 | − | 0.992225i | \(-0.460282\pi\) | ||||
0.124453 | + | 0.992225i | \(0.460282\pi\) | |||||||
\(410\) | 30.7477 | 1.51852 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 6.05630i | − | 0.298373i | ||||||
\(413\) | 0.646084 | − | 1.58258i | 0.0317917 | − | 0.0778735i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 39.9129i | − | 1.95925i | ||||||
\(416\) | 0.646084i | 0.0316769i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.03383 | − | 3.23042i | −0.246212 | − | 0.158005i | ||||
\(419\) | − | 13.0284i | − | 0.636478i | −0.948011 | − | 0.318239i | \(-0.896909\pi\) | ||
0.948011 | − | 0.318239i | \(-0.103091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.58258 | 0.369552 | 0.184776 | − | 0.982781i | \(-0.440844\pi\) | ||||
0.184776 | + | 0.982781i | \(0.440844\pi\) | |||||||
\(422\) | −16.7477 | −0.815267 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.5826i | 0.562500i | ||||||||
\(425\) | 17.1464 | 0.831724 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.74773 | + | 1.93825i | 0.229759 | + | 0.0937986i | ||||
\(428\) | − | 17.5826i | − | 0.849886i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 22.1803i | − | 1.06963i | ||||||
\(431\) | − | 27.9129i | − | 1.34452i | −0.740317 | − | 0.672258i | \(-0.765325\pi\) | ||
0.740317 | − | 0.672258i | \(-0.234675\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.5850i | 1.71011i | 0.518540 | + | 0.855054i | \(0.326476\pi\) | ||||
−0.518540 | + | 0.855054i | \(0.673524\pi\) | |||||||
\(434\) | 21.1652 | + | 8.64064i | 1.01596 | + | 0.414764i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.1652i | 0.822062i | ||||||||
\(437\) | −7.21362 | −0.345074 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.2813 | −0.824790 | −0.412395 | − | 0.911005i | \(-0.635308\pi\) | ||||
−0.412395 | + | 0.911005i | \(0.635308\pi\) | |||||||
\(440\) | 5.54506 | − | 8.64064i | 0.264351 | − | 0.411926i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.41742i | − | 0.114985i | ||||||
\(443\) | −15.1652 | −0.720518 | −0.360259 | − | 0.932852i | \(-0.617312\pi\) | ||||
−0.360259 | + | 0.932852i | \(0.617312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.3303 | −1.43779 | ||||||||
\(446\) | 16.1240 | 0.763491 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.44949 | + | 1.00000i | 0.115728 | + | 0.0472456i | ||||
\(449\) | −31.1652 | −1.47077 | −0.735387 | − | 0.677647i | \(-0.763000\pi\) | ||||
−0.735387 | + | 0.677647i | \(0.763000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.7925 | + | 27.7253i | −0.837817 | + | 1.30553i | ||||
\(452\) | 10.7477 | 0.505531 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.511238i | 0.0239936i | ||||||||
\(455\) | 2.00000 | − | 4.89898i | 0.0937614 | − | 0.229668i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 33.1652i | − | 1.55140i | −0.631102 | − | 0.775700i | \(-0.717397\pi\) | ||
0.631102 | − | 0.775700i | \(-0.282603\pi\) | |||||||
\(458\) | −5.67991 | −0.265405 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 12.3823i | − | 0.577327i | ||||||
\(461\) | 30.0400 | 1.39910 | 0.699550 | − | 0.714583i | \(-0.253384\pi\) | ||||
0.699550 | + | 0.714583i | \(0.253384\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.16515 | 0.240045 | 0.120022 | − | 0.992771i | \(-0.461703\pi\) | ||||
0.120022 | + | 0.992771i | \(0.461703\pi\) | |||||||
\(464\) | 1.58258i | 0.0734692i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.1652 | −1.25840 | ||||||||
\(467\) | 11.7362i | 0.543087i | 0.962426 | + | 0.271544i | \(0.0875341\pi\) | ||||
−0.962426 | + | 0.271544i | \(0.912466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.5734 | + | 7.58258i | 0.857642 | + | 0.350131i | ||||
\(470\) | − | 30.7477i | − | 1.41829i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.646084 | −0.0297384 | ||||||||
\(473\) | 20.0000 | + | 12.8348i | 0.919601 | + | 0.590147i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.26424 | −0.379190 | ||||||||
\(476\) | −9.16515 | − | 3.74166i | −0.420084 | − | 0.171499i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.41742 | −0.385004 | ||||||||
\(479\) | 30.9557 | 1.41440 | 0.707202 | − | 0.707012i | \(-0.249957\pi\) | ||||
0.707202 | + | 0.707012i | \(0.249957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.31464 | −0.105539 | ||||||||
\(482\) | − | 3.47197i | − | 0.158144i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.58258 | + | 10.0000i | 0.208299 | + | 0.454545i | ||||
\(485\) | −26.3303 | −1.19560 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.4955 | 0.974052 | 0.487026 | − | 0.873387i | \(-0.338082\pi\) | ||||
0.487026 | + | 0.873387i | \(0.338082\pi\) | |||||||
\(488\) | − | 1.93825i | − | 0.0877405i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.4779 | − | 15.1652i | −0.699219 | − | 0.685092i | ||||
\(491\) | 33.4955i | 1.51163i | 0.654786 | + | 0.755814i | \(0.272759\pi\) | ||||
−0.654786 | + | 0.755814i | \(0.727241\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.92146i | − | 0.266689i | ||||||
\(494\) | 1.16515i | 0.0524226i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 8.64064i | − | 0.387976i | ||||||
\(497\) | 4.89898 | + | 2.00000i | 0.219749 | + | 0.0897123i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.9129 | −0.801891 | −0.400945 | − | 0.916102i | \(-0.631318\pi\) | ||||
−0.400945 | + | 0.916102i | \(0.631318\pi\) | |||||||
\(500\) | 1.29217i | 0.0577875i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.1185 | −1.07646 | ||||||||
\(503\) | −17.0116 | −0.758509 | −0.379254 | − | 0.925292i | \(-0.623820\pi\) | ||||
−0.379254 | + | 0.925292i | \(0.623820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.3303i | 1.61668i | ||||||||
\(506\) | 11.1652 | + | 7.16515i | 0.496352 | + | 0.318530i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 3.58258i | − | 0.158951i | ||||||
\(509\) | − | 0.780929i | − | 0.0346141i | −0.999850 | − | 0.0173070i | \(-0.994491\pi\) | ||
0.999850 | − | 0.0173070i | \(-0.00550928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.4955 | + | 16.1240i | 1.74718 | + | 0.713282i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.89898 | 0.216085 | ||||||||
\(515\) | 18.7477 | 0.826124 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.7253 | + | 17.7925i | 1.21936 | + | 0.782514i | ||||
\(518\) | −3.58258 | + | 8.77548i | −0.157409 | + | 0.385573i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.00000 | −0.0877058 | ||||||||
\(521\) | 28.1017i | 1.23116i | 0.788075 | + | 0.615579i | \(0.211078\pi\) | ||||
−0.788075 | + | 0.615579i | \(0.788922\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.4554 | 0.632090 | 0.316045 | − | 0.948744i | \(-0.397645\pi\) | ||||
0.316045 | + | 0.948744i | \(0.397645\pi\) | |||||||
\(524\) | 16.7700 | 0.732602 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.33030 | −0.363218 | ||||||||
\(527\) | 32.3303i | 1.40833i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −35.8547 | −1.55743 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.41742 | + | 1.80341i | 0.191520 | + | 0.0781876i | ||||
\(533\) | 6.41742 | 0.277970 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 54.4282 | 2.35313 | ||||||||
\(536\) | − | 7.58258i | − | 0.327517i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.5003 | 0.711380 | ||||||||
\(539\) | 22.6309 | − | 5.18096i | 0.974782 | − | 0.223160i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.7477i | 1.57991i | 0.613166 | + | 0.789954i | \(0.289896\pi\) | ||||
−0.613166 | + | 0.789954i | \(0.710104\pi\) | |||||||
\(542\) | − | 4.89898i | − | 0.210429i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.74166i | 0.160422i | ||||||||
\(545\) | −53.1360 | −2.27610 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.7477i | 1.05814i | 0.848579 | + | 0.529068i | \(0.177458\pi\) | ||||
−0.848579 | + | 0.529068i | \(0.822542\pi\) | |||||||
\(548\) | −3.16515 | −0.135209 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.7913 | + | 8.20871i | 0.545422 | + | 0.350021i | ||||
\(551\) | 2.85403i | 0.121586i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | − | 9.79796i | 0.170097 | − | 0.416652i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.4779 | −0.656408 | ||||||||
\(557\) | − | 35.9129i | − | 1.52168i | −0.648941 | − | 0.760839i | \(-0.724788\pi\) | ||
0.648941 | − | 0.760839i | \(-0.275212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.62929i | − | 0.195798i | ||||||
\(560\) | −3.09557 | + | 7.58258i | −0.130812 | + | 0.320422i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.1652 | 0.470973 | ||||||||
\(563\) | 23.7140 | 0.999425 | 0.499712 | − | 0.866191i | \(-0.333439\pi\) | ||||
0.499712 | + | 0.866191i | \(0.333439\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.2704i | 1.39970i | ||||||||
\(566\) | − | 18.0622i | − | 0.759211i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 2.00000i | − | 0.0839181i | ||||||
\(569\) | 39.4955i | 1.65574i | 0.560923 | + | 0.827868i | \(0.310446\pi\) | ||||
−0.560923 | + | 0.827868i | \(0.689554\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.58258i | 0.233624i | 0.993154 | + | 0.116812i | \(0.0372674\pi\) | ||||
−0.993154 | + | 0.116812i | \(0.962733\pi\) | |||||||
\(572\) | 1.15732 | − | 1.80341i | 0.0483901 | − | 0.0754042i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.93280 | − | 24.3303i | 0.414587 | − | 1.01553i | ||||
\(575\) | 18.3303 | 0.764426 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.6636i | 1.23491i | 0.786606 | + | 0.617455i | \(0.211836\pi\) | ||||
−0.786606 | + | 0.617455i | \(0.788164\pi\) | |||||||
\(578\) | 3.00000i | 0.124784i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.89898 | −0.203419 | ||||||||
\(581\) | −31.5826 | − | 12.8935i | −1.31027 | − | 0.534914i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7477 | − | 32.3303i | 0.859283 | − | 1.33898i | ||||
\(584\) | − | 16.1240i | − | 0.667214i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 25.1410i | − | 1.03856i | ||||||
\(587\) | 39.0851i | 1.61322i | 0.591087 | + | 0.806608i | \(0.298699\pi\) | ||||
−0.591087 | + | 0.806608i | \(0.701301\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 15.5826i | − | 0.642069i | ||||||
\(590\) | − | 2.00000i | − | 0.0823387i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.58258 | 0.147243 | ||||||||
\(593\) | −14.8318 | −0.609068 | −0.304534 | − | 0.952501i | \(-0.598501\pi\) | ||||
−0.304534 | + | 0.952501i | \(0.598501\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.5826 | − | 28.3714i | 0.474839 | − | 1.16311i | ||||
\(596\) | 14.0000i | 0.573462i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 2.58434i | − | 0.105681i | ||||||
\(599\) | 21.1652 | 0.864785 | 0.432392 | − | 0.901686i | \(-0.357670\pi\) | ||||
0.432392 | + | 0.901686i | \(0.357670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0229 | −0.857543 | −0.428772 | − | 0.903413i | \(-0.641053\pi\) | ||||
−0.428772 | + | 0.903413i | \(0.641053\pi\) | |||||||
\(602\) | −17.5510 | − | 7.16515i | −0.715324 | − | 0.292030i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.58258i | 0.227152i | ||||||||
\(605\) | −30.9557 | + | 14.1857i | −1.25853 | + | 0.576731i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.04495 | −0.0830021 | −0.0415010 | − | 0.999138i | \(-0.513214\pi\) | ||||
−0.0415010 | + | 0.999138i | \(0.513214\pi\) | |||||||
\(608\) | − | 1.80341i | − | 0.0731378i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | − | 6.41742i | − | 0.259621i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 31.9129i | − | 1.28895i | −0.764626 | − | 0.644475i | \(-0.777076\pi\) | ||
0.764626 | − | 0.644475i | \(-0.222924\pi\) | |||||||
\(614\) | − | 10.5789i | − | 0.426929i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.04594 | − | 7.17903i | −0.203307 | − | 0.289251i | ||||
\(617\) | 19.9129 | 0.801662 | 0.400831 | − | 0.916152i | \(-0.368721\pi\) | ||||
0.400831 | + | 0.916152i | \(0.368721\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 17.9274i | − | 0.720561i | −0.932844 | − | 0.360281i | \(-0.882681\pi\) | ||
0.932844 | − | 0.360281i | \(-0.117319\pi\) | |||||||
\(620\) | 26.7477 | 1.07421 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.03383 | −0.201838 | ||||||||
\(623\) | −9.79796 | + | 24.0000i | −0.392547 | + | 0.961540i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.9129 | −1.07652 | ||||||||
\(626\) | −23.4724 | −0.938147 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.1632i | 0.525270i | ||||||||
\(629\) | −13.4048 | −0.534483 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.1652 | 0.524096 | 0.262048 | − | 0.965055i | \(-0.415602\pi\) | ||||
0.262048 | + | 0.965055i | \(0.415602\pi\) | |||||||
\(632\) | −4.00000 | −0.159111 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.16515i | 0.363995i | ||||||||
\(635\) | 11.0901 | 0.440098 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.23042 | − | 3.16515i | −0.127994 | − | 0.125408i | ||||
\(638\) | 2.83485 | − | 4.41742i | 0.112233 | − | 0.174888i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.09557 | 0.122363 | ||||||||
\(641\) | 15.9129 | 0.628521 | 0.314260 | − | 0.949337i | \(-0.398243\pi\) | ||||
0.314260 | + | 0.949337i | \(0.398243\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.42157i | − | 0.371550i | −0.982592 | − | 0.185775i | \(-0.940520\pi\) | ||
0.982592 | − | 0.185775i | \(-0.0594796\pi\) | |||||||
\(644\) | −9.79796 | − | 4.00000i | −0.386094 | − | 0.157622i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.74773i | 0.265486i | ||||||||
\(647\) | 30.0681i | 1.18210i | 0.806635 | + | 0.591050i | \(0.201286\pi\) | ||||
−0.806635 | + | 0.591050i | \(0.798714\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.80341 | + | 1.15732i | 0.0707899 | + | 0.0454289i | ||||
\(650\) | − | 2.96073i | − | 0.116129i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | 6.00000 | 0.234798 | 0.117399 | − | 0.993085i | \(-0.462544\pi\) | ||||
0.117399 | + | 0.993085i | \(0.462544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 51.9129i | 2.02840i | ||||||||
\(656\) | −9.93280 | −0.387811 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.3303 | − | 9.93280i | −0.948494 | − | 0.387221i | ||||
\(659\) | − | 6.33030i | − | 0.246594i | −0.992370 | − | 0.123297i | \(-0.960653\pi\) | ||
0.992370 | − | 0.123297i | \(-0.0393467\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.26424i | 0.321442i | 0.987000 | + | 0.160721i | \(0.0513819\pi\) | ||||
−0.987000 | + | 0.160721i | \(0.948618\pi\) | |||||||
\(662\) | 23.5826i | 0.916563i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.8935i | 0.500366i | ||||||||
\(665\) | −5.58258 | + | 13.6745i | −0.216483 | + | 0.530273i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.33030i | − | 0.245110i | ||||||
\(668\) | −1.29217 | −0.0499955 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.4724 | 0.906819 | ||||||||
\(671\) | −3.47197 | + | 5.41022i | −0.134034 | + | 0.208859i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.3303i | 0.706581i | 0.935514 | + | 0.353291i | \(0.114937\pi\) | ||||
−0.935514 | + | 0.353291i | \(0.885063\pi\) | |||||||
\(674\) | −10.8348 | −0.417343 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.5826 | 0.483945 | ||||||||
\(677\) | 5.27537 | 0.202749 | 0.101375 | − | 0.994848i | \(-0.467676\pi\) | ||||
0.101375 | + | 0.994848i | \(0.467676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.50579 | + | 20.8348i | −0.326422 | + | 0.799568i | ||||
\(680\) | −11.5826 | −0.444172 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.4779 | + | 24.1185i | −0.592678 | + | 0.923545i | ||||
\(683\) | 9.49545 | 0.363333 | 0.181667 | − | 0.983360i | \(-0.441851\pi\) | ||||
0.181667 | + | 0.983360i | \(0.441851\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 9.79796i | − | 0.374361i | ||||||
\(686\) | −17.0000 | + | 7.34847i | −0.649063 | + | 0.280566i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.16515i | 0.273169i | ||||||||
\(689\) | −7.48331 | −0.285092 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.98320i | − | 0.151528i | −0.997126 | − | 0.0757641i | \(-0.975860\pi\) | ||
0.997126 | − | 0.0757641i | \(-0.0241396\pi\) | |||||||
\(692\) | −10.7137 | −0.407275 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.1652 | −0.727499 | ||||||||
\(695\) | − | 47.9129i | − | 1.81744i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37.1652 | 1.40773 | ||||||||
\(698\) | 24.1185i | 0.912899i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.2250 | − | 4.58258i | −0.424264 | − | 0.173205i | ||||
\(701\) | 12.3303i | 0.465709i | 0.972512 | + | 0.232855i | \(0.0748066\pi\) | ||||
−0.972512 | + | 0.232855i | \(0.925193\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.46084 | 0.243675 | ||||||||
\(704\) | −1.79129 | + | 2.79129i | −0.0675117 | + | 0.105201i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.48331 | −0.281638 | ||||||||
\(707\) | 28.7477 | + | 11.7362i | 1.08117 | + | 0.441386i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 52.3303 | 1.96531 | 0.982653 | − | 0.185454i | \(-0.0593757\pi\) | ||||
0.982653 | + | 0.185454i | \(0.0593757\pi\) | |||||||
\(710\) | 6.19115 | 0.232350 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.79796 | 0.367194 | ||||||||
\(713\) | 34.5625i | 1.29438i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.58258 | + | 3.58258i | 0.208776 | + | 0.133981i | ||||
\(716\) | 11.1652 | 0.417261 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.58258 | −0.357619 | ||||||||
\(719\) | 23.3376i | 0.870345i | 0.900347 | + | 0.435172i | \(0.143313\pi\) | ||||
−0.900347 | + | 0.435172i | \(0.856687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.05630 | − | 14.8348i | 0.225548 | − | 0.552479i | ||||
\(722\) | 15.7477i | 0.586070i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 5.41022i | − | 0.201069i | ||||||
\(725\) | − | 7.25227i | − | 0.269343i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.5514i | 1.39271i | 0.717700 | + | 0.696353i | \(0.245195\pi\) | ||||
−0.717700 | + | 0.696353i | \(0.754805\pi\) | |||||||
\(728\) | −0.646084 | + | 1.58258i | −0.0239455 | + | 0.0586542i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 49.9129 | 1.84736 | ||||||||
\(731\) | − | 26.8095i | − | 0.991587i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.7137 | −0.395721 | −0.197860 | − | 0.980230i | \(-0.563399\pi\) | ||||
−0.197860 | + | 0.980230i | \(0.563399\pi\) | |||||||
\(734\) | 21.0229 | 0.775971 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000i | 0.147442i | ||||||||
\(737\) | −13.5826 | + | 21.1652i | −0.500321 | + | 0.779628i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.58258i | − | 0.0582160i | −0.999576 | − | 0.0291080i | \(-0.990733\pi\) | ||
0.999576 | − | 0.0291080i | \(-0.00926667\pi\) | |||||||
\(740\) | 11.0901i | 0.407681i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.5826 | + | 28.3714i | −0.425210 | + | 1.04155i | ||||
\(743\) | 1.91288i | 0.0701767i | 0.999384 | + | 0.0350884i | \(0.0111713\pi\) | ||||
−0.999384 | + | 0.0350884i | \(0.988829\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.3380 | −1.58778 | ||||||||
\(746\) | −9.58258 | −0.350843 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.70239 | − | 10.4440i | 0.245063 | − | 0.381872i | ||||
\(749\) | 17.5826 | − | 43.0683i | 0.642453 | − | 1.57368i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.4955 | −1.51419 | −0.757095 | − | 0.653304i | \(-0.773382\pi\) | ||||
−0.757095 | + | 0.653304i | \(0.773382\pi\) | |||||||
\(752\) | 9.93280i | 0.362212i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.02248 | −0.0372364 | ||||||||
\(755\) | −17.2813 | −0.628930 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.8348 | −1.12071 | −0.560356 | − | 0.828252i | \(-0.689336\pi\) | ||||
−0.560356 | + | 0.828252i | \(0.689336\pi\) | |||||||
\(758\) | 22.3303i | 0.811073i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.58258 | 0.202501 | ||||||||
\(761\) | 28.2366 | 1.02357 | 0.511787 | − | 0.859112i | \(-0.328984\pi\) | ||||
0.511787 | + | 0.859112i | \(0.328984\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.1652 | + | 42.0459i | −0.621420 | + | 1.52216i | ||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.7308 | −0.712901 | ||||||||
\(767\) | − | 0.417424i | − | 0.0150723i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.1015 | 0.544573 | 0.272287 | − | 0.962216i | \(-0.412220\pi\) | ||||
0.272287 | + | 0.962216i | \(0.412220\pi\) | |||||||
\(770\) | 22.2232 | − | 15.6201i | 0.800869 | − | 0.562909i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.3303i | 0.587740i | ||||||||
\(773\) | − | 10.0395i | − | 0.361096i | −0.983566 | − | 0.180548i | \(-0.942213\pi\) | ||
0.983566 | − | 0.180548i | \(-0.0577871\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 39.5964i | 1.42234i | ||||||||
\(776\) | 8.50579 | 0.305340 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10.0000i | 0.358517i | ||||||||
\(779\) | −17.9129 | −0.641795 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.58258 | + | 5.58258i | −0.128195 | + | 0.199760i | ||||
\(782\) | − | 14.9666i | − | 0.535206i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.00000 | + | 4.89898i | 0.178571 | + | 0.174964i | ||||
\(785\) | −40.7477 | −1.45435 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.2309 | −0.828091 | −0.414046 | − | 0.910256i | \(-0.635885\pi\) | ||||
−0.414046 | + | 0.910256i | \(0.635885\pi\) | |||||||
\(788\) | − | 8.74773i | − | 0.311625i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 12.3823i | − | 0.440542i | ||||||
\(791\) | 26.3264 | + | 10.7477i | 0.936061 | + | 0.382145i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.25227 | 0.0444695 | ||||||||
\(794\) | −27.5905 | −0.979149 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.66311i | 0.342500i | ||||||||
\(797\) | − | 25.0061i | − | 0.885763i | −0.896580 | − | 0.442881i | \(-0.853956\pi\) | ||
0.896580 | − | 0.442881i | \(-0.146044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 37.1652i | − | 1.31481i | ||||||
\(800\) | 4.58258i | 0.162019i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.58258i | 0.267750i | ||||||||
\(803\) | −28.8826 | + | 45.0066i | −1.01925 | + | 1.58825i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.3823 | − | 30.3303i | 0.436419 | − | 1.06900i | ||||
\(806\) | 5.58258 | 0.196638 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 11.7362i | − | 0.412878i | ||||||
\(809\) | 14.8348i | 0.521566i | 0.965398 | + | 0.260783i | \(0.0839806\pi\) | ||||
−0.965398 | + | 0.260783i | \(0.916019\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.36526 | −0.118170 | −0.0590852 | − | 0.998253i | \(-0.518818\pi\) | ||||
−0.0590852 | + | 0.998253i | \(0.518818\pi\) | |||||||
\(812\) | −1.58258 | + | 3.87650i | −0.0555375 | + | 0.136039i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.0000 | − | 6.41742i | −0.350500 | − | 0.224931i | ||||
\(815\) | − | 12.3823i | − | 0.433733i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.9217i | 0.452072i | ||||||||
\(818\) | − | 5.03383i | − | 0.176004i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 30.7477i | − | 1.07376i | ||||||
\(821\) | − | 43.4955i | − | 1.51800i | −0.651090 | − | 0.759001i | \(-0.725688\pi\) | ||
0.651090 | − | 0.759001i | \(-0.274312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.66970 | −0.127918 | −0.0639588 | − | 0.997953i | \(-0.520373\pi\) | ||||
−0.0639588 | + | 0.997953i | \(0.520373\pi\) | |||||||
\(824\) | −6.05630 | −0.210981 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.58258 | − | 0.646084i | −0.0550649 | − | 0.0224801i | ||||
\(827\) | 3.16515i | 0.110063i | 0.998485 | + | 0.0550315i | \(0.0175259\pi\) | ||||
−0.998485 | + | 0.0550315i | \(0.982474\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.99455i | 0.277662i | 0.990316 | + | 0.138831i | \(0.0443345\pi\) | ||||
−0.990316 | + | 0.138831i | \(0.955665\pi\) | |||||||
\(830\) | −39.9129 | −1.38540 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.646084 | 0.0223989 | ||||||||
\(833\) | −18.7083 | − | 18.3303i | −0.648204 | − | 0.635107i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4.00000i | − | 0.138426i | ||||||
\(836\) | −3.23042 | + | 5.03383i | −0.111726 | + | 0.174098i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.0284 | −0.450058 | ||||||||
\(839\) | 9.66311i | 0.333608i | 0.985990 | + | 0.166804i | \(0.0533447\pi\) | ||||
−0.985990 | + | 0.166804i | \(0.946655\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.4955 | 0.913636 | ||||||||
\(842\) | − | 7.58258i | − | 0.261313i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.7477i | 0.576481i | ||||||||
\(845\) | 38.9503i | 1.33993i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.22497 | + | 29.0775i | 0.0420905 | + | 0.999114i | ||||
\(848\) | 11.5826 | 0.397747 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 17.1464i | − | 0.588118i | ||||||
\(851\) | −14.3303 | −0.491236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.4665 | −0.392606 | −0.196303 | − | 0.980543i | \(-0.562894\pi\) | ||||
−0.196303 | + | 0.980543i | \(0.562894\pi\) | |||||||
\(854\) | 1.93825 | − | 4.74773i | 0.0663256 | − | 0.162464i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.5826 | −0.600960 | ||||||||
\(857\) | −31.0906 | −1.06203 | −0.531017 | − | 0.847361i | \(-0.678190\pi\) | ||||
−0.531017 | + | 0.847361i | \(0.678190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 24.3882i | − | 0.832115i | −0.909338 | − | 0.416057i | \(-0.863412\pi\) | ||
0.909338 | − | 0.416057i | \(-0.136588\pi\) | |||||||
\(860\) | −22.1803 | −0.756340 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.9129 | −0.950716 | ||||||||
\(863\) | 14.8348 | 0.504984 | 0.252492 | − | 0.967599i | \(-0.418750\pi\) | ||||
0.252492 | + | 0.967599i | \(0.418750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 33.1652i | − | 1.12765i | ||||||
\(866\) | 35.5850 | 1.20923 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.64064 | − | 21.1652i | 0.293282 | − | 0.718392i | ||||
\(869\) | 11.1652 | + | 7.16515i | 0.378752 | + | 0.243061i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.89898 | 0.165996 | ||||||||
\(872\) | 17.1652 | 0.581285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.21362i | 0.244004i | ||||||||
\(875\) | −1.29217 | + | 3.16515i | −0.0436832 | + | 0.107002i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.83485i | 0.230796i | 0.993319 | + | 0.115398i | \(0.0368144\pi\) | ||||
−0.993319 | + | 0.115398i | \(0.963186\pi\) | |||||||
\(878\) | 17.2813i | 0.583215i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.64064 | − | 5.54506i | −0.291276 | − | 0.186924i | ||||
\(881\) | − | 7.21362i | − | 0.243033i | −0.992589 | − | 0.121517i | \(-0.961224\pi\) | ||
0.992589 | − | 0.121517i | \(-0.0387758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8348 | 0.431927 | 0.215964 | − | 0.976401i | \(-0.430711\pi\) | ||||
0.215964 | + | 0.976401i | \(0.430711\pi\) | |||||||
\(884\) | −2.41742 | −0.0813068 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.1652i | 0.509483i | ||||||||
\(887\) | −53.4057 | −1.79319 | −0.896594 | − | 0.442854i | \(-0.853966\pi\) | ||||
−0.896594 | + | 0.442854i | \(0.853966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.58258 | − | 8.77548i | 0.120156 | − | 0.294320i | ||||
\(890\) | 30.3303i | 1.01667i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 16.1240i | − | 0.539870i | ||||||
\(893\) | 17.9129i | 0.599432i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.5625i | 1.15530i | ||||||||
\(896\) | 1.00000 | − | 2.44949i | 0.0334077 | − | 0.0818317i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.1652i | 1.03999i | ||||||||
\(899\) | 13.6745 | 0.456069 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.3380 | −1.44380 | ||||||||
\(902\) | 27.7253 | + | 17.7925i | 0.923152 | + | 0.592426i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 10.7477i | − | 0.357464i | ||||||
\(905\) | 16.7477 | 0.556713 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.91288 | 0.196334 | 0.0981670 | − | 0.995170i | \(-0.468702\pi\) | ||||
0.0981670 | + | 0.995170i | \(0.468702\pi\) | |||||||
\(908\) | 0.511238 | 0.0169660 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.89898 | − | 2.00000i | −0.162400 | − | 0.0662994i | ||||
\(911\) | −3.16515 | −0.104866 | −0.0524331 | − | 0.998624i | \(-0.516698\pi\) | ||||
−0.0524331 | + | 0.998624i | \(0.516698\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.0960 | − | 35.9896i | 0.764367 | − | 1.19108i | ||||
\(914\) | −33.1652 | −1.09701 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.67991i | 0.187669i | ||||||||
\(917\) | 41.0780 | + | 16.7700i | 1.35652 | + | 0.553795i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 19.4955i | − | 0.643096i | −0.946893 | − | 0.321548i | \(-0.895797\pi\) | ||
0.946893 | − | 0.321548i | \(-0.104203\pi\) | |||||||
\(920\) | −12.3823 | −0.408232 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 30.0400i | − | 0.989313i | ||||||
\(923\) | 1.29217 | 0.0425322 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.4174 | −0.539802 | ||||||||
\(926\) | − | 5.16515i | − | 0.169737i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.58258 | 0.0519506 | ||||||||
\(929\) | − | 43.6077i | − | 1.43072i | −0.698755 | − | 0.715361i | \(-0.746262\pi\) | ||
0.698755 | − | 0.715361i | \(-0.253738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.01703 | + | 8.83485i | 0.295521 | + | 0.289550i | ||||
\(932\) | 27.1652i | 0.889824i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.7362 | 0.384021 | ||||||||
\(935\) | 32.3303 | + | 20.7477i | 1.05731 | + | 0.678523i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0681 | −0.982282 | −0.491141 | − | 0.871080i | \(-0.663420\pi\) | ||||
−0.491141 | + | 0.871080i | \(0.663420\pi\) | |||||||
\(938\) | 7.58258 | − | 18.5734i | 0.247580 | − | 0.606444i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30.7477 | −1.00288 | ||||||||
\(941\) | −5.27537 | −0.171972 | −0.0859861 | − | 0.996296i | \(-0.527404\pi\) | ||||
−0.0859861 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39.7312 | 1.29383 | ||||||||
\(944\) | 0.646084i | 0.0210282i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.8348 | − | 20.0000i | 0.417297 | − | 0.650256i | ||||
\(947\) | −3.58258 | −0.116418 | −0.0582090 | − | 0.998304i | \(-0.518539\pi\) | ||||
−0.0582090 | + | 0.998304i | \(0.518539\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.4174 | 0.338164 | ||||||||
\(950\) | 8.26424i | 0.268127i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.74166 | + | 9.16515i | −0.121268 | + | 0.297044i | ||||
\(953\) | − | 18.3303i | − | 0.593777i | −0.954912 | − | 0.296888i | \(-0.904051\pi\) | ||
0.954912 | − | 0.296888i | \(-0.0959489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 55.7203i | − | 1.80307i | ||||||
\(956\) | 8.41742i | 0.272239i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 30.9557i | − | 1.00013i | ||||||
\(959\) | −7.75301 | − | 3.16515i | −0.250358 | − | 0.102208i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −43.6606 | −1.40841 | ||||||||
\(962\) | 2.31464i | 0.0746271i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.47197 | −0.111825 | ||||||||
\(965\) | −50.5517 | −1.62732 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.4174i | 0.720896i | 0.932779 | + | 0.360448i | \(0.117376\pi\) | ||||
−0.932779 | + | 0.360448i | \(0.882624\pi\) | |||||||
\(968\) | 10.0000 | − | 4.58258i | 0.321412 | − | 0.147290i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 26.3303i | 0.845415i | ||||||||
\(971\) | − | 14.0509i | − | 0.450913i | −0.974253 | − | 0.225457i | \(-0.927613\pi\) | ||
0.974253 | − | 0.225457i | \(-0.0723874\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −37.9129 | − | 15.4779i | −1.21543 | − | 0.496198i | ||||
\(974\) | − | 21.4955i | − | 0.688759i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.93825 | −0.0620419 | ||||||||
\(977\) | −9.16515 | −0.293219 | −0.146610 | − | 0.989194i | \(-0.546836\pi\) | ||||
−0.146610 | + | 0.989194i | \(0.546836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −27.3489 | − | 17.5510i | −0.874075 | − | 0.560931i | ||||
\(980\) | −15.1652 | + | 15.4779i | −0.484433 | + | 0.494422i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.4955 | 1.06888 | ||||||||
\(983\) | − | 50.6865i | − | 1.61665i | −0.588738 | − | 0.808324i | \(-0.700375\pi\) | ||
0.588738 | − | 0.808324i | \(-0.299625\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0792 | 0.862816 | ||||||||
\(986\) | −5.92146 | −0.188578 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.16515 | 0.0370684 | ||||||||
\(989\) | − | 28.6606i | − | 0.911354i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.6606 | 1.48222 | 0.741111 | − | 0.671382i | \(-0.234299\pi\) | ||||
0.741111 | + | 0.671382i | \(0.234299\pi\) | |||||||
\(992\) | −8.64064 | −0.274340 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.00000 | − | 4.89898i | 0.0634361 | − | 0.155386i | ||||
\(995\) | −29.9129 | −0.948302 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.5566 | −0.714376 | −0.357188 | − | 0.934032i | \(-0.616264\pi\) | ||||
−0.357188 | + | 0.934032i | \(0.616264\pi\) | |||||||
\(998\) | 17.9129i | 0.567022i | ||||||||
\(999\) | 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 | 1386.2.e.b.307.1 | 8 | ||
3.2 | odd | 2 | 154.2.c.a.153.7 | yes | 8 | ||
7.6 | odd | 2 | inner | 1386.2.e.b.307.4 | 8 | ||
11.10 | odd | 2 | inner | 1386.2.e.b.307.5 | 8 | ||
12.11 | even | 2 | 1232.2.e.e.769.4 | 8 | |||
21.2 | odd | 6 | 1078.2.i.b.1011.6 | 16 | |||
21.5 | even | 6 | 1078.2.i.b.1011.7 | 16 | |||
21.11 | odd | 6 | 1078.2.i.b.901.3 | 16 | |||
21.17 | even | 6 | 1078.2.i.b.901.2 | 16 | |||
21.20 | even | 2 | 154.2.c.a.153.6 | yes | 8 | ||
33.32 | even | 2 | 154.2.c.a.153.3 | yes | 8 | ||
77.76 | even | 2 | inner | 1386.2.e.b.307.8 | 8 | ||
84.83 | odd | 2 | 1232.2.e.e.769.5 | 8 | |||
132.131 | odd | 2 | 1232.2.e.e.769.3 | 8 | |||
231.32 | even | 6 | 1078.2.i.b.901.7 | 16 | |||
231.65 | even | 6 | 1078.2.i.b.1011.2 | 16 | |||
231.131 | odd | 6 | 1078.2.i.b.1011.3 | 16 | |||
231.164 | odd | 6 | 1078.2.i.b.901.6 | 16 | |||
231.230 | odd | 2 | 154.2.c.a.153.2 | ✓ | 8 | ||
924.923 | even | 2 | 1232.2.e.e.769.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.c.a.153.2 | ✓ | 8 | 231.230 | odd | 2 | ||
154.2.c.a.153.3 | yes | 8 | 33.32 | even | 2 | ||
154.2.c.a.153.6 | yes | 8 | 21.20 | even | 2 | ||
154.2.c.a.153.7 | yes | 8 | 3.2 | odd | 2 | ||
1078.2.i.b.901.2 | 16 | 21.17 | even | 6 | |||
1078.2.i.b.901.3 | 16 | 21.11 | odd | 6 | |||
1078.2.i.b.901.6 | 16 | 231.164 | odd | 6 | |||
1078.2.i.b.901.7 | 16 | 231.32 | even | 6 | |||
1078.2.i.b.1011.2 | 16 | 231.65 | even | 6 | |||
1078.2.i.b.1011.3 | 16 | 231.131 | odd | 6 | |||
1078.2.i.b.1011.6 | 16 | 21.2 | odd | 6 | |||
1078.2.i.b.1011.7 | 16 | 21.5 | even | 6 | |||
1232.2.e.e.769.3 | 8 | 132.131 | odd | 2 | |||
1232.2.e.e.769.4 | 8 | 12.11 | even | 2 | |||
1232.2.e.e.769.5 | 8 | 84.83 | odd | 2 | |||
1232.2.e.e.769.6 | 8 | 924.923 | even | 2 | |||
1386.2.e.b.307.1 | 8 | 1.1 | even | 1 | trivial | ||
1386.2.e.b.307.4 | 8 | 7.6 | odd | 2 | inner | ||
1386.2.e.b.307.5 | 8 | 11.10 | odd | 2 | inner | ||
1386.2.e.b.307.8 | 8 | 77.76 | even | 2 | inner |