Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(649,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, 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("1950.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.f (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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.4 | ||
Root | \(2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.649 |
Dual form | 1950.2.f.p.649.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 4.56155 | 1.72410 | 0.862052 | − | 0.506819i | \(-0.169179\pi\) | ||||
0.862052 | + | 0.506819i | \(0.169179\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.56155i | 0.772337i | 0.922428 | + | 0.386169i | \(0.126202\pi\) | ||||
−0.922428 | + | 0.386169i | \(0.873798\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | −3.56155 | + | 0.561553i | −0.987797 | + | 0.155747i | ||||
\(14\) | 4.56155 | 1.21913 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.68466i | 1.37873i | 0.724413 | + | 0.689366i | \(0.242111\pi\) | ||||
−0.724413 | + | 0.689366i | \(0.757889\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.68466i | 1.07473i | 0.843348 | + | 0.537367i | \(0.180581\pi\) | ||||
−0.843348 | + | 0.537367i | \(0.819419\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.56155i | 0.995412i | ||||||||
\(22\) | 2.56155i | 0.546125i | ||||||||
\(23\) | − | 5.12311i | − | 1.06824i | −0.845408 | − | 0.534121i | \(-0.820643\pi\) | ||
0.845408 | − | 0.534121i | \(-0.179357\pi\) | |||||||
\(24\) | 1.00000i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.56155 | + | 0.561553i | −0.698478 | + | 0.110130i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 4.56155 | 0.862052 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.43845i | − | 0.258353i | −0.991622 | − | 0.129176i | \(-0.958767\pi\) | ||
0.991622 | − | 0.129176i | \(-0.0412333\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.56155 | −0.445909 | ||||||||
\(34\) | 5.68466i | 0.974911i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.438447 | 0.0720803 | 0.0360401 | − | 0.999350i | \(-0.488526\pi\) | ||||
0.0360401 | + | 0.999350i | \(0.488526\pi\) | |||||||
\(38\) | 4.68466i | 0.759952i | ||||||||
\(39\) | −0.561553 | − | 3.56155i | −0.0899204 | − | 0.570305i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.438447i | 0.0684739i | 0.999414 | + | 0.0342370i | \(0.0109001\pi\) | ||||
−0.999414 | + | 0.0342370i | \(0.989100\pi\) | |||||||
\(42\) | 4.56155i | 0.703863i | ||||||||
\(43\) | 2.87689i | 0.438722i | 0.975644 | + | 0.219361i | \(0.0703973\pi\) | ||||
−0.975644 | + | 0.219361i | \(0.929603\pi\) | |||||||
\(44\) | 2.56155i | 0.386169i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 5.12311i | − | 0.755361i | ||||||
\(47\) | −0.123106 | −0.0179568 | −0.00897840 | − | 0.999960i | \(-0.502858\pi\) | ||||
−0.00897840 | + | 0.999960i | \(0.502858\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 13.8078 | 1.97254 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.68466 | −0.796011 | ||||||||
\(52\) | −3.56155 | + | 0.561553i | −0.493899 | + | 0.0778734i | ||||
\(53\) | 5.00000i | 0.686803i | 0.939189 | + | 0.343401i | \(0.111579\pi\) | ||||
−0.939189 | + | 0.343401i | \(0.888421\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.56155 | 0.609563 | ||||||||
\(57\) | −4.68466 | −0.620498 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | − | 5.43845i | − | 0.708026i | −0.935241 | − | 0.354013i | \(-0.884817\pi\) | ||
0.935241 | − | 0.354013i | \(-0.115183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.6847 | 1.49607 | 0.748034 | − | 0.663661i | \(-0.230998\pi\) | ||||
0.748034 | + | 0.663661i | \(0.230998\pi\) | |||||||
\(62\) | − | 1.43845i | − | 0.182683i | ||||||
\(63\) | −4.56155 | −0.574702 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.56155 | −0.315305 | ||||||||
\(67\) | 4.12311 | 0.503718 | 0.251859 | − | 0.967764i | \(-0.418958\pi\) | ||||
0.251859 | + | 0.967764i | \(0.418958\pi\) | |||||||
\(68\) | 5.68466i | 0.689366i | ||||||||
\(69\) | 5.12311 | 0.616749 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.9309i | − | 1.77197i | −0.463716 | − | 0.885984i | \(-0.653484\pi\) | ||
0.463716 | − | 0.885984i | \(-0.346516\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −1.12311 | −0.131450 | −0.0657248 | − | 0.997838i | \(-0.520936\pi\) | ||||
−0.0657248 | + | 0.997838i | \(0.520936\pi\) | |||||||
\(74\) | 0.438447 | 0.0509685 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.68466i | 0.537367i | ||||||||
\(77\) | 11.6847i | 1.33159i | ||||||||
\(78\) | −0.561553 | − | 3.56155i | −0.0635833 | − | 0.403266i | ||||
\(79\) | 14.6847 | 1.65215 | 0.826077 | − | 0.563558i | \(-0.190568\pi\) | ||||
0.826077 | + | 0.563558i | \(0.190568\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.438447i | 0.0484184i | ||||||||
\(83\) | −13.9309 | −1.52911 | −0.764556 | − | 0.644558i | \(-0.777042\pi\) | ||||
−0.764556 | + | 0.644558i | \(0.777042\pi\) | |||||||
\(84\) | 4.56155i | 0.497706i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.87689i | 0.310223i | ||||||||
\(87\) | 1.00000i | 0.107211i | ||||||||
\(88\) | 2.56155i | 0.273062i | ||||||||
\(89\) | 3.12311i | 0.331049i | 0.986206 | + | 0.165524i | \(0.0529316\pi\) | ||||
−0.986206 | + | 0.165524i | \(0.947068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −16.2462 | + | 2.56155i | −1.70307 | + | 0.268524i | ||||
\(92\) | − | 5.12311i | − | 0.534121i | ||||||
\(93\) | 1.43845 | 0.149160 | ||||||||
\(94\) | −0.123106 | −0.0126974 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | −4.87689 | −0.495174 | −0.247587 | − | 0.968866i | \(-0.579638\pi\) | ||||
−0.247587 | + | 0.968866i | \(0.579638\pi\) | |||||||
\(98\) | 13.8078 | 1.39479 | ||||||||
\(99\) | − | 2.56155i | − | 0.257446i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.5616 | −1.64794 | −0.823968 | − | 0.566636i | \(-0.808244\pi\) | ||||
−0.823968 | + | 0.566636i | \(0.808244\pi\) | |||||||
\(102\) | −5.68466 | −0.562865 | ||||||||
\(103\) | − | 1.12311i | − | 0.110663i | −0.998468 | − | 0.0553314i | \(-0.982378\pi\) | ||
0.998468 | − | 0.0553314i | \(-0.0176215\pi\) | |||||||
\(104\) | −3.56155 | + | 0.561553i | −0.349239 | + | 0.0550648i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.00000i | 0.485643i | ||||||||
\(107\) | 12.6847i | 1.22627i | 0.789977 | + | 0.613136i | \(0.210092\pi\) | ||||
−0.789977 | + | 0.613136i | \(0.789908\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | − | 16.4384i | − | 1.57452i | −0.616623 | − | 0.787259i | \(-0.711500\pi\) | ||
0.616623 | − | 0.787259i | \(-0.288500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.438447i | 0.0416156i | ||||||||
\(112\) | 4.56155 | 0.431026 | ||||||||
\(113\) | 12.2462i | 1.15203i | 0.817440 | + | 0.576013i | \(0.195392\pi\) | ||||
−0.817440 | + | 0.576013i | \(0.804608\pi\) | |||||||
\(114\) | −4.68466 | −0.438758 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 3.56155 | − | 0.561553i | 0.329266 | − | 0.0519156i | ||||
\(118\) | − | 5.43845i | − | 0.500650i | ||||||
\(119\) | 25.9309i | 2.37708i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.43845 | 0.403495 | ||||||||
\(122\) | 11.6847 | 1.05788 | ||||||||
\(123\) | −0.438447 | −0.0395335 | ||||||||
\(124\) | − | 1.43845i | − | 0.129176i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.56155 | −0.406375 | ||||||||
\(127\) | − | 15.5616i | − | 1.38086i | −0.723397 | − | 0.690432i | \(-0.757420\pi\) | ||
0.723397 | − | 0.690432i | \(-0.242580\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.87689 | −0.253296 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.6847 | −1.63249 | −0.816243 | − | 0.577709i | \(-0.803947\pi\) | ||||
−0.816243 | + | 0.577709i | \(0.803947\pi\) | |||||||
\(132\) | −2.56155 | −0.222955 | ||||||||
\(133\) | 21.3693i | 1.85295i | ||||||||
\(134\) | 4.12311 | 0.356182 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.68466i | 0.487455i | ||||||||
\(137\) | 2.43845 | 0.208331 | 0.104165 | − | 0.994560i | \(-0.466783\pi\) | ||||
0.104165 | + | 0.994560i | \(0.466783\pi\) | |||||||
\(138\) | 5.12311 | 0.436108 | ||||||||
\(139\) | 16.4924 | 1.39887 | 0.699435 | − | 0.714697i | \(-0.253435\pi\) | ||||
0.699435 | + | 0.714697i | \(0.253435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.123106i | − | 0.0103674i | ||||||
\(142\) | − | 14.9309i | − | 1.25297i | ||||||
\(143\) | −1.43845 | − | 9.12311i | −0.120289 | − | 0.762912i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.12311 | −0.0929489 | ||||||||
\(147\) | 13.8078i | 1.13885i | ||||||||
\(148\) | 0.438447 | 0.0360401 | ||||||||
\(149\) | − | 5.36932i | − | 0.439872i | −0.975514 | − | 0.219936i | \(-0.929415\pi\) | ||
0.975514 | − | 0.219936i | \(-0.0705848\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.6847i | 1.27640i | 0.769871 | + | 0.638200i | \(0.220321\pi\) | ||||
−0.769871 | + | 0.638200i | \(0.779679\pi\) | |||||||
\(152\) | 4.68466i | 0.379976i | ||||||||
\(153\) | − | 5.68466i | − | 0.459577i | ||||||
\(154\) | 11.6847i | 0.941577i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.561553 | − | 3.56155i | −0.0449602 | − | 0.285152i | ||||
\(157\) | − | 1.68466i | − | 0.134450i | −0.997738 | − | 0.0672252i | \(-0.978585\pi\) | ||
0.997738 | − | 0.0672252i | \(-0.0214146\pi\) | |||||||
\(158\) | 14.6847 | 1.16825 | ||||||||
\(159\) | −5.00000 | −0.396526 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 23.3693i | − | 1.84176i | ||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −16.4924 | −1.29179 | −0.645893 | − | 0.763428i | \(-0.723515\pi\) | ||||
−0.645893 | + | 0.763428i | \(0.723515\pi\) | |||||||
\(164\) | 0.438447i | 0.0342370i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.9309 | −1.08125 | ||||||||
\(167\) | 17.5616 | 1.35895 | 0.679477 | − | 0.733697i | \(-0.262207\pi\) | ||||
0.679477 | + | 0.733697i | \(0.262207\pi\) | |||||||
\(168\) | 4.56155i | 0.351931i | ||||||||
\(169\) | 12.3693 | − | 4.00000i | 0.951486 | − | 0.307692i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 4.68466i | − | 0.358245i | ||||||
\(172\) | 2.87689i | 0.219361i | ||||||||
\(173\) | 8.12311i | 0.617588i | 0.951129 | + | 0.308794i | \(0.0999254\pi\) | ||||
−0.951129 | + | 0.308794i | \(0.900075\pi\) | |||||||
\(174\) | 1.00000i | 0.0758098i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.56155i | 0.193084i | ||||||||
\(177\) | 5.43845 | 0.408779 | ||||||||
\(178\) | 3.12311i | 0.234087i | ||||||||
\(179\) | 10.8769 | 0.812977 | 0.406489 | − | 0.913656i | \(-0.366753\pi\) | ||||
0.406489 | + | 0.913656i | \(0.366753\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.8078 | 1.54663 | 0.773314 | − | 0.634023i | \(-0.218597\pi\) | ||||
0.773314 | + | 0.634023i | \(0.218597\pi\) | |||||||
\(182\) | −16.2462 | + | 2.56155i | −1.20425 | + | 0.189875i | ||||
\(183\) | 11.6847i | 0.863755i | ||||||||
\(184\) | − | 5.12311i | − | 0.377680i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.43845 | 0.105472 | ||||||||
\(187\) | −14.5616 | −1.06485 | ||||||||
\(188\) | −0.123106 | −0.00897840 | ||||||||
\(189\) | − | 4.56155i | − | 0.331804i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.4924 | 1.19335 | 0.596675 | − | 0.802483i | \(-0.296488\pi\) | ||||
0.596675 | + | 0.802483i | \(0.296488\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | −13.1231 | −0.944622 | −0.472311 | − | 0.881432i | \(-0.656580\pi\) | ||||
−0.472311 | + | 0.881432i | \(0.656580\pi\) | |||||||
\(194\) | −4.87689 | −0.350141 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.8078 | 0.986269 | ||||||||
\(197\) | −4.24621 | −0.302530 | −0.151265 | − | 0.988493i | \(-0.548335\pi\) | ||||
−0.151265 | + | 0.988493i | \(0.548335\pi\) | |||||||
\(198\) | − | 2.56155i | − | 0.182042i | ||||||
\(199\) | −22.9309 | −1.62553 | −0.812763 | − | 0.582594i | \(-0.802038\pi\) | ||||
−0.812763 | + | 0.582594i | \(0.802038\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.12311i | 0.290821i | ||||||||
\(202\) | −16.5616 | −1.16527 | ||||||||
\(203\) | 4.56155 | 0.320158 | ||||||||
\(204\) | −5.68466 | −0.398006 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 1.12311i | − | 0.0782505i | ||||||
\(207\) | 5.12311i | 0.356080i | ||||||||
\(208\) | −3.56155 | + | 0.561553i | −0.246949 | + | 0.0389367i | ||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.36932 | 0.507325 | 0.253662 | − | 0.967293i | \(-0.418365\pi\) | ||||
0.253662 | + | 0.967293i | \(0.418365\pi\) | |||||||
\(212\) | 5.00000i | 0.343401i | ||||||||
\(213\) | 14.9309 | 1.02305 | ||||||||
\(214\) | 12.6847i | 0.867105i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | − | 6.56155i | − | 0.445427i | ||||||
\(218\) | − | 16.4384i | − | 1.11335i | ||||||
\(219\) | − | 1.12311i | − | 0.0758924i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.19224 | − | 20.2462i | −0.214733 | − | 1.36191i | ||||
\(222\) | 0.438447i | 0.0294266i | ||||||||
\(223\) | −9.36932 | −0.627416 | −0.313708 | − | 0.949520i | \(-0.601571\pi\) | ||||
−0.313708 | + | 0.949520i | \(0.601571\pi\) | |||||||
\(224\) | 4.56155 | 0.304782 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.2462i | 0.814606i | ||||||||
\(227\) | −15.6847 | −1.04103 | −0.520514 | − | 0.853853i | \(-0.674260\pi\) | ||||
−0.520514 | + | 0.853853i | \(0.674260\pi\) | |||||||
\(228\) | −4.68466 | −0.310249 | ||||||||
\(229\) | − | 27.8078i | − | 1.83759i | −0.394736 | − | 0.918794i | \(-0.629164\pi\) | ||
0.394736 | − | 0.918794i | \(-0.370836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.6847 | −0.768794 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | − | 5.12311i | − | 0.335626i | −0.985819 | − | 0.167813i | \(-0.946330\pi\) | ||
0.985819 | − | 0.167813i | \(-0.0536704\pi\) | |||||||
\(234\) | 3.56155 | − | 0.561553i | 0.232826 | − | 0.0367099i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 5.43845i | − | 0.354013i | ||||||
\(237\) | 14.6847i | 0.953871i | ||||||||
\(238\) | 25.9309i | 1.68085i | ||||||||
\(239\) | − | 21.9309i | − | 1.41859i | −0.704912 | − | 0.709295i | \(-0.749013\pi\) | ||
0.704912 | − | 0.709295i | \(-0.250987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3.75379i | − | 0.241803i | −0.992665 | − | 0.120901i | \(-0.961422\pi\) | ||
0.992665 | − | 0.120901i | \(-0.0385785\pi\) | |||||||
\(242\) | 4.43845 | 0.285314 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 11.6847 | 0.748034 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.438447 | −0.0279544 | ||||||||
\(247\) | −2.63068 | − | 16.6847i | −0.167386 | − | 1.06162i | ||||
\(248\) | − | 1.43845i | − | 0.0913415i | ||||||
\(249\) | − | 13.9309i | − | 0.882833i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.5616 | 0.982237 | 0.491118 | − | 0.871093i | \(-0.336588\pi\) | ||||
0.491118 | + | 0.871093i | \(0.336588\pi\) | |||||||
\(252\) | −4.56155 | −0.287351 | ||||||||
\(253\) | 13.1231 | 0.825043 | ||||||||
\(254\) | − | 15.5616i | − | 0.976419i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 4.80776i | − | 0.299900i | −0.988694 | − | 0.149950i | \(-0.952089\pi\) | ||
0.988694 | − | 0.149950i | \(-0.0479113\pi\) | |||||||
\(258\) | −2.87689 | −0.179108 | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −18.6847 | −1.15434 | ||||||||
\(263\) | − | 24.7386i | − | 1.52545i | −0.646723 | − | 0.762725i | \(-0.723861\pi\) | ||
0.646723 | − | 0.762725i | \(-0.276139\pi\) | |||||||
\(264\) | −2.56155 | −0.157653 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.3693i | 1.31024i | ||||||||
\(267\) | −3.12311 | −0.191131 | ||||||||
\(268\) | 4.12311 | 0.251859 | ||||||||
\(269\) | −23.4924 | −1.43236 | −0.716179 | − | 0.697916i | \(-0.754111\pi\) | ||||
−0.716179 | + | 0.697916i | \(0.754111\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 24.8078i | − | 1.50696i | −0.657468 | − | 0.753482i | \(-0.728373\pi\) | ||
0.657468 | − | 0.753482i | \(-0.271627\pi\) | |||||||
\(272\) | 5.68466i | 0.344683i | ||||||||
\(273\) | −2.56155 | − | 16.2462i | −0.155032 | − | 0.983265i | ||||
\(274\) | 2.43845 | 0.147312 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.12311 | 0.308375 | ||||||||
\(277\) | − | 25.6155i | − | 1.53909i | −0.638594 | − | 0.769544i | \(-0.720484\pi\) | ||
0.638594 | − | 0.769544i | \(-0.279516\pi\) | |||||||
\(278\) | 16.4924 | 0.989150 | ||||||||
\(279\) | 1.43845i | 0.0861176i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.9309i | − | 1.36794i | −0.729510 | − | 0.683970i | \(-0.760252\pi\) | ||
0.729510 | − | 0.683970i | \(-0.239748\pi\) | |||||||
\(282\) | − | 0.123106i | − | 0.00733083i | ||||||
\(283\) | 17.3693i | 1.03250i | 0.856438 | + | 0.516249i | \(0.172672\pi\) | ||||
−0.856438 | + | 0.516249i | \(0.827328\pi\) | |||||||
\(284\) | − | 14.9309i | − | 0.885984i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.43845 | − | 9.12311i | −0.0850572 | − | 0.539461i | ||||
\(287\) | 2.00000i | 0.118056i | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.3153 | −0.900902 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4.87689i | − | 0.285889i | ||||||
\(292\) | −1.12311 | −0.0657248 | ||||||||
\(293\) | 25.3693 | 1.48209 | 0.741046 | − | 0.671455i | \(-0.234330\pi\) | ||||
0.741046 | + | 0.671455i | \(0.234330\pi\) | |||||||
\(294\) | 13.8078i | 0.805285i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.438447 | 0.0254842 | ||||||||
\(297\) | 2.56155 | 0.148636 | ||||||||
\(298\) | − | 5.36932i | − | 0.311036i | ||||||
\(299\) | 2.87689 | + | 18.2462i | 0.166375 | + | 1.05521i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.1231i | 0.756403i | ||||||||
\(302\) | 15.6847i | 0.902551i | ||||||||
\(303\) | − | 16.5616i | − | 0.951436i | ||||||
\(304\) | 4.68466i | 0.268684i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 5.68466i | − | 0.324970i | ||||||
\(307\) | 30.9309 | 1.76532 | 0.882659 | − | 0.470014i | \(-0.155751\pi\) | ||||
0.882659 | + | 0.470014i | \(0.155751\pi\) | |||||||
\(308\) | 11.6847i | 0.665795i | ||||||||
\(309\) | 1.12311 | 0.0638912 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.1231 | 1.31119 | 0.655596 | − | 0.755112i | \(-0.272418\pi\) | ||||
0.655596 | + | 0.755112i | \(0.272418\pi\) | |||||||
\(312\) | −0.561553 | − | 3.56155i | −0.0317917 | − | 0.201633i | ||||
\(313\) | − | 32.8617i | − | 1.85746i | −0.370763 | − | 0.928728i | \(-0.620904\pi\) | ||
0.370763 | − | 0.928728i | \(-0.379096\pi\) | |||||||
\(314\) | − | 1.68466i | − | 0.0950708i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.6847 | 0.826077 | ||||||||
\(317\) | −30.0000 | −1.68497 | −0.842484 | − | 0.538721i | \(-0.818908\pi\) | ||||
−0.842484 | + | 0.538721i | \(0.818908\pi\) | |||||||
\(318\) | −5.00000 | −0.280386 | ||||||||
\(319\) | 2.56155i | 0.143419i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.6847 | −0.707989 | ||||||||
\(322\) | − | 23.3693i | − | 1.30232i | ||||||
\(323\) | −26.6307 | −1.48177 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.4924 | −0.913431 | ||||||||
\(327\) | 16.4384 | 0.909048 | ||||||||
\(328\) | 0.438447i | 0.0242092i | ||||||||
\(329\) | −0.561553 | −0.0309594 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.49242i | 0.466786i | 0.972383 | + | 0.233393i | \(0.0749828\pi\) | ||||
−0.972383 | + | 0.233393i | \(0.925017\pi\) | |||||||
\(332\) | −13.9309 | −0.764556 | ||||||||
\(333\) | −0.438447 | −0.0240268 | ||||||||
\(334\) | 17.5616 | 0.960925 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.56155i | 0.248853i | ||||||||
\(337\) | − | 1.68466i | − | 0.0917692i | −0.998947 | − | 0.0458846i | \(-0.985389\pi\) | ||
0.998947 | − | 0.0458846i | \(-0.0146107\pi\) | |||||||
\(338\) | 12.3693 | − | 4.00000i | 0.672802 | − | 0.217571i | ||||
\(339\) | −12.2462 | −0.665123 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.68466 | 0.199535 | ||||||||
\(342\) | − | 4.68466i | − | 0.253317i | ||||||
\(343\) | 31.0540 | 1.67676 | ||||||||
\(344\) | 2.87689i | 0.155112i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.12311i | 0.436701i | ||||||||
\(347\) | − | 14.4384i | − | 0.775096i | −0.921849 | − | 0.387548i | \(-0.873322\pi\) | ||
0.921849 | − | 0.387548i | \(-0.126678\pi\) | |||||||
\(348\) | 1.00000i | 0.0536056i | ||||||||
\(349\) | 22.0000i | 1.17763i | 0.808267 | + | 0.588817i | \(0.200406\pi\) | ||||
−0.808267 | + | 0.588817i | \(0.799594\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.561553 | + | 3.56155i | 0.0299735 | + | 0.190102i | ||||
\(352\) | 2.56155i | 0.136531i | ||||||||
\(353\) | −19.5616 | −1.04116 | −0.520578 | − | 0.853814i | \(-0.674284\pi\) | ||||
−0.520578 | + | 0.853814i | \(0.674284\pi\) | |||||||
\(354\) | 5.43845 | 0.289050 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.12311i | 0.165524i | ||||||||
\(357\) | −25.9309 | −1.37241 | ||||||||
\(358\) | 10.8769 | 0.574862 | ||||||||
\(359\) | 12.1231i | 0.639833i | 0.947446 | + | 0.319917i | \(0.103655\pi\) | ||||
−0.947446 | + | 0.319917i | \(0.896345\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.94602 | −0.155054 | ||||||||
\(362\) | 20.8078 | 1.09363 | ||||||||
\(363\) | 4.43845i | 0.232958i | ||||||||
\(364\) | −16.2462 | + | 2.56155i | −0.851533 | + | 0.134262i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.6847i | 0.610767i | ||||||||
\(367\) | − | 7.31534i | − | 0.381858i | −0.981604 | − | 0.190929i | \(-0.938850\pi\) | ||
0.981604 | − | 0.190929i | \(-0.0611500\pi\) | |||||||
\(368\) | − | 5.12311i | − | 0.267060i | ||||||
\(369\) | − | 0.438447i | − | 0.0228246i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.8078i | 1.18412i | ||||||||
\(372\) | 1.43845 | 0.0745800 | ||||||||
\(373\) | − | 36.5616i | − | 1.89309i | −0.322578 | − | 0.946543i | \(-0.604550\pi\) | ||
0.322578 | − | 0.946543i | \(-0.395450\pi\) | |||||||
\(374\) | −14.5616 | −0.752960 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.123106 | −0.00634869 | ||||||||
\(377\) | −3.56155 | + | 0.561553i | −0.183429 | + | 0.0289214i | ||||
\(378\) | − | 4.56155i | − | 0.234621i | ||||||
\(379\) | 19.6847i | 1.01113i | 0.862788 | + | 0.505566i | \(0.168716\pi\) | ||||
−0.862788 | + | 0.505566i | \(0.831284\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.5616 | 0.797243 | ||||||||
\(382\) | 16.4924 | 0.843826 | ||||||||
\(383\) | −14.9309 | −0.762932 | −0.381466 | − | 0.924383i | \(-0.624581\pi\) | ||||
−0.381466 | + | 0.924383i | \(0.624581\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −13.1231 | −0.667948 | ||||||||
\(387\) | − | 2.87689i | − | 0.146241i | ||||||
\(388\) | −4.87689 | −0.247587 | ||||||||
\(389\) | −13.8078 | −0.700081 | −0.350041 | − | 0.936734i | \(-0.613832\pi\) | ||||
−0.350041 | + | 0.936734i | \(0.613832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.1231 | 1.47282 | ||||||||
\(392\) | 13.8078 | 0.697397 | ||||||||
\(393\) | − | 18.6847i | − | 0.942516i | ||||||
\(394\) | −4.24621 | −0.213921 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − | 2.56155i | − | 0.128723i | ||||||
\(397\) | 2.05398 | 0.103086 | 0.0515430 | − | 0.998671i | \(-0.483586\pi\) | ||||
0.0515430 | + | 0.998671i | \(0.483586\pi\) | |||||||
\(398\) | −22.9309 | −1.14942 | ||||||||
\(399\) | −21.3693 | −1.06980 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.0000i | 1.09863i | 0.835616 | + | 0.549314i | \(0.185111\pi\) | ||||
−0.835616 | + | 0.549314i | \(0.814889\pi\) | |||||||
\(402\) | 4.12311i | 0.205642i | ||||||||
\(403\) | 0.807764 | + | 5.12311i | 0.0402376 | + | 0.255200i | ||||
\(404\) | −16.5616 | −0.823968 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.56155 | 0.226386 | ||||||||
\(407\) | 1.12311i | 0.0556703i | ||||||||
\(408\) | −5.68466 | −0.281433 | ||||||||
\(409\) | − | 13.6155i | − | 0.673245i | −0.941640 | − | 0.336622i | \(-0.890715\pi\) | ||
0.941640 | − | 0.336622i | \(-0.109285\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.43845i | 0.120280i | ||||||||
\(412\) | − | 1.12311i | − | 0.0553314i | ||||||
\(413\) | − | 24.8078i | − | 1.22071i | ||||||
\(414\) | 5.12311i | 0.251787i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.56155 | + | 0.561553i | −0.174619 | + | 0.0275324i | ||||
\(417\) | 16.4924i | 0.807637i | ||||||||
\(418\) | −12.0000 | −0.586939 | ||||||||
\(419\) | −6.68466 | −0.326567 | −0.163283 | − | 0.986579i | \(-0.552209\pi\) | ||||
−0.163283 | + | 0.986579i | \(0.552209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 29.3693i | − | 1.43137i | −0.698422 | − | 0.715686i | \(-0.746114\pi\) | ||
0.698422 | − | 0.715686i | \(-0.253886\pi\) | |||||||
\(422\) | 7.36932 | 0.358733 | ||||||||
\(423\) | 0.123106 | 0.00598560 | ||||||||
\(424\) | 5.00000i | 0.242821i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 14.9309 | 0.723403 | ||||||||
\(427\) | 53.3002 | 2.57938 | ||||||||
\(428\) | 12.6847i | 0.613136i | ||||||||
\(429\) | 9.12311 | − | 1.43845i | 0.440468 | − | 0.0694489i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.1771i | 1.79076i | 0.445306 | + | 0.895378i | \(0.353095\pi\) | ||||
−0.445306 | + | 0.895378i | \(0.646905\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 32.0540i | 1.54042i | 0.637793 | + | 0.770208i | \(0.279848\pi\) | ||||
−0.637793 | + | 0.770208i | \(0.720152\pi\) | |||||||
\(434\) | − | 6.56155i | − | 0.314965i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 16.4384i | − | 0.787259i | ||||||
\(437\) | 24.0000 | 1.14808 | ||||||||
\(438\) | − | 1.12311i | − | 0.0536641i | ||||||
\(439\) | −26.3002 | −1.25524 | −0.627620 | − | 0.778520i | \(-0.715971\pi\) | ||||
−0.627620 | + | 0.778520i | \(0.715971\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.8078 | −0.657513 | ||||||||
\(442\) | −3.19224 | − | 20.2462i | −0.151839 | − | 0.963014i | ||||
\(443\) | 24.4384i | 1.16111i | 0.814223 | + | 0.580553i | \(0.197164\pi\) | ||||
−0.814223 | + | 0.580553i | \(0.802836\pi\) | |||||||
\(444\) | 0.438447i | 0.0208078i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −9.36932 | −0.443650 | ||||||||
\(447\) | 5.36932 | 0.253960 | ||||||||
\(448\) | 4.56155 | 0.215513 | ||||||||
\(449\) | − | 9.56155i | − | 0.451238i | −0.974216 | − | 0.225619i | \(-0.927560\pi\) | ||
0.974216 | − | 0.225619i | \(-0.0724404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.12311 | −0.0528850 | ||||||||
\(452\) | 12.2462i | 0.576013i | ||||||||
\(453\) | −15.6847 | −0.736930 | ||||||||
\(454\) | −15.6847 | −0.736117 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.68466 | −0.219379 | ||||||||
\(457\) | 20.7386 | 0.970112 | 0.485056 | − | 0.874483i | \(-0.338799\pi\) | ||||
0.485056 | + | 0.874483i | \(0.338799\pi\) | |||||||
\(458\) | − | 27.8078i | − | 1.29937i | ||||||
\(459\) | 5.68466 | 0.265337 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 5.75379i | − | 0.267981i | −0.990983 | − | 0.133990i | \(-0.957221\pi\) | ||
0.990983 | − | 0.133990i | \(-0.0427791\pi\) | |||||||
\(462\) | −11.6847 | −0.543620 | ||||||||
\(463\) | −7.43845 | −0.345694 | −0.172847 | − | 0.984949i | \(-0.555297\pi\) | ||||
−0.172847 | + | 0.984949i | \(0.555297\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 5.12311i | − | 0.237323i | ||||||
\(467\) | 20.1922i | 0.934385i | 0.884156 | + | 0.467193i | \(0.154735\pi\) | ||||
−0.884156 | + | 0.467193i | \(0.845265\pi\) | |||||||
\(468\) | 3.56155 | − | 0.561553i | 0.164633 | − | 0.0259578i | ||||
\(469\) | 18.8078 | 0.868462 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.68466 | 0.0776250 | ||||||||
\(472\) | − | 5.43845i | − | 0.250325i | ||||||
\(473\) | −7.36932 | −0.338842 | ||||||||
\(474\) | 14.6847i | 0.674489i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 25.9309i | 1.18854i | ||||||||
\(477\) | − | 5.00000i | − | 0.228934i | ||||||
\(478\) | − | 21.9309i | − | 1.00309i | ||||||
\(479\) | 23.8769i | 1.09096i | 0.838123 | + | 0.545482i | \(0.183653\pi\) | ||||
−0.838123 | + | 0.545482i | \(0.816347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.56155 | + | 0.246211i | −0.0712007 | + | 0.0112263i | ||||
\(482\) | − | 3.75379i | − | 0.170980i | ||||||
\(483\) | 23.3693 | 1.06334 | ||||||||
\(484\) | 4.43845 | 0.201748 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 5.68466 | 0.257596 | 0.128798 | − | 0.991671i | \(-0.458888\pi\) | ||||
0.128798 | + | 0.991671i | \(0.458888\pi\) | |||||||
\(488\) | 11.6847 | 0.528940 | ||||||||
\(489\) | − | 16.4924i | − | 0.745813i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.7386 | −0.484628 | −0.242314 | − | 0.970198i | \(-0.577906\pi\) | ||||
−0.242314 | + | 0.970198i | \(0.577906\pi\) | |||||||
\(492\) | −0.438447 | −0.0197667 | ||||||||
\(493\) | 5.68466i | 0.256024i | ||||||||
\(494\) | −2.63068 | − | 16.6847i | −0.118360 | − | 0.750678i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.43845i | − | 0.0645882i | ||||||
\(497\) | − | 68.1080i | − | 3.05506i | ||||||
\(498\) | − | 13.9309i | − | 0.624257i | ||||||
\(499\) | − | 19.8769i | − | 0.889812i | −0.895577 | − | 0.444906i | \(-0.853237\pi\) | ||
0.895577 | − | 0.444906i | \(-0.146763\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.5616i | 0.784592i | ||||||||
\(502\) | 15.5616 | 0.694546 | ||||||||
\(503\) | − | 40.7386i | − | 1.81645i | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||
0.418487 | − | 0.908223i | \(-0.362561\pi\) | |||||||
\(504\) | −4.56155 | −0.203188 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 13.1231 | 0.583393 | ||||||||
\(507\) | 4.00000 | + | 12.3693i | 0.177646 | + | 0.549341i | ||||
\(508\) | − | 15.5616i | − | 0.690432i | ||||||
\(509\) | − | 10.4924i | − | 0.465068i | −0.972588 | − | 0.232534i | \(-0.925298\pi\) | ||
0.972588 | − | 0.232534i | \(-0.0747018\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.12311 | −0.226633 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.68466 | 0.206833 | ||||||||
\(514\) | − | 4.80776i | − | 0.212061i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.87689 | −0.126648 | ||||||||
\(517\) | − | 0.315342i | − | 0.0138687i | ||||||
\(518\) | 2.00000 | 0.0878750 | ||||||||
\(519\) | −8.12311 | −0.356565 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.246211 | 0.0107867 | 0.00539336 | − | 0.999985i | \(-0.498283\pi\) | ||||
0.00539336 | + | 0.999985i | \(0.498283\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | 25.3693i | 1.10932i | 0.832076 | + | 0.554661i | \(0.187152\pi\) | ||||
−0.832076 | + | 0.554661i | \(0.812848\pi\) | |||||||
\(524\) | −18.6847 | −0.816243 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 24.7386i | − | 1.07866i | ||||||
\(527\) | 8.17708 | 0.356199 | ||||||||
\(528\) | −2.56155 | −0.111477 | ||||||||
\(529\) | −3.24621 | −0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.43845i | 0.236009i | ||||||||
\(532\) | 21.3693i | 0.926477i | ||||||||
\(533\) | −0.246211 | − | 1.56155i | −0.0106646 | − | 0.0676384i | ||||
\(534\) | −3.12311 | −0.135150 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.12311 | 0.178091 | ||||||||
\(537\) | 10.8769i | 0.469373i | ||||||||
\(538\) | −23.4924 | −1.01283 | ||||||||
\(539\) | 35.3693i | 1.52346i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.7538i | 0.677308i | 0.940911 | + | 0.338654i | \(0.109972\pi\) | ||||
−0.940911 | + | 0.338654i | \(0.890028\pi\) | |||||||
\(542\) | − | 24.8078i | − | 1.06558i | ||||||
\(543\) | 20.8078i | 0.892947i | ||||||||
\(544\) | 5.68466i | 0.243728i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.56155 | − | 16.2462i | −0.109624 | − | 0.695274i | ||||
\(547\) | 1.12311i | 0.0480205i | 0.999712 | + | 0.0240103i | \(0.00764344\pi\) | ||||
−0.999712 | + | 0.0240103i | \(0.992357\pi\) | |||||||
\(548\) | 2.43845 | 0.104165 | ||||||||
\(549\) | −11.6847 | −0.498689 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.68466i | 0.199573i | ||||||||
\(552\) | 5.12311 | 0.218054 | ||||||||
\(553\) | 66.9848 | 2.84849 | ||||||||
\(554\) | − | 25.6155i | − | 1.08830i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4924 | 0.699435 | ||||||||
\(557\) | −15.8617 | −0.672083 | −0.336042 | − | 0.941847i | \(-0.609088\pi\) | ||||
−0.336042 | + | 0.941847i | \(0.609088\pi\) | |||||||
\(558\) | 1.43845i | 0.0608943i | ||||||||
\(559\) | −1.61553 | − | 10.2462i | −0.0683296 | − | 0.433369i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 14.5616i | − | 0.614789i | ||||||
\(562\) | − | 22.9309i | − | 0.967280i | ||||||
\(563\) | − | 10.3002i | − | 0.434101i | −0.976160 | − | 0.217051i | \(-0.930356\pi\) | ||
0.976160 | − | 0.217051i | \(-0.0696436\pi\) | |||||||
\(564\) | − | 0.123106i | − | 0.00518368i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17.3693i | 0.730087i | ||||||||
\(567\) | 4.56155 | 0.191567 | ||||||||
\(568\) | − | 14.9309i | − | 0.626485i | ||||||
\(569\) | 19.6847 | 0.825224 | 0.412612 | − | 0.910907i | \(-0.364617\pi\) | ||||
0.412612 | + | 0.910907i | \(0.364617\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.8769 | 0.789973 | 0.394987 | − | 0.918687i | \(-0.370749\pi\) | ||||
0.394987 | + | 0.918687i | \(0.370749\pi\) | |||||||
\(572\) | −1.43845 | − | 9.12311i | −0.0601445 | − | 0.381456i | ||||
\(573\) | 16.4924i | 0.688981i | ||||||||
\(574\) | 2.00000i | 0.0834784i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −33.3693 | −1.38918 | −0.694591 | − | 0.719404i | \(-0.744415\pi\) | ||||
−0.694591 | + | 0.719404i | \(0.744415\pi\) | |||||||
\(578\) | −15.3153 | −0.637034 | ||||||||
\(579\) | − | 13.1231i | − | 0.545378i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −63.5464 | −2.63635 | ||||||||
\(582\) | − | 4.87689i | − | 0.202154i | ||||||
\(583\) | −12.8078 | −0.530443 | ||||||||
\(584\) | −1.12311 | −0.0464744 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.3693 | 1.04800 | ||||||||
\(587\) | −9.93087 | −0.409891 | −0.204945 | − | 0.978773i | \(-0.565702\pi\) | ||||
−0.204945 | + | 0.978773i | \(0.565702\pi\) | |||||||
\(588\) | 13.8078i | 0.569423i | ||||||||
\(589\) | 6.73863 | 0.277661 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 4.24621i | − | 0.174666i | ||||||
\(592\) | 0.438447 | 0.0180201 | ||||||||
\(593\) | −4.19224 | −0.172154 | −0.0860772 | − | 0.996288i | \(-0.527433\pi\) | ||||
−0.0860772 | + | 0.996288i | \(0.527433\pi\) | |||||||
\(594\) | 2.56155 | 0.105102 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5.36932i | − | 0.219936i | ||||||
\(597\) | − | 22.9309i | − | 0.938498i | ||||||
\(598\) | 2.87689 | + | 18.2462i | 0.117645 | + | 0.746143i | ||||
\(599\) | −42.9848 | −1.75631 | −0.878157 | − | 0.478373i | \(-0.841227\pi\) | ||||
−0.878157 | + | 0.478373i | \(0.841227\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.7386 | −1.53939 | −0.769695 | − | 0.638411i | \(-0.779592\pi\) | ||||
−0.769695 | + | 0.638411i | \(0.779592\pi\) | |||||||
\(602\) | 13.1231i | 0.534858i | ||||||||
\(603\) | −4.12311 | −0.167906 | ||||||||
\(604\) | 15.6847i | 0.638200i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 16.5616i | − | 0.672767i | ||||||
\(607\) | − | 9.94602i | − | 0.403697i | −0.979417 | − | 0.201848i | \(-0.935305\pi\) | ||
0.979417 | − | 0.201848i | \(-0.0646948\pi\) | |||||||
\(608\) | 4.68466i | 0.189988i | ||||||||
\(609\) | 4.56155i | 0.184843i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.438447 | − | 0.0691303i | 0.0177377 | − | 0.00279671i | ||||
\(612\) | − | 5.68466i | − | 0.229789i | ||||||
\(613\) | −14.6307 | −0.590928 | −0.295464 | − | 0.955354i | \(-0.595474\pi\) | ||||
−0.295464 | + | 0.955354i | \(0.595474\pi\) | |||||||
\(614\) | 30.9309 | 1.24827 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.6847i | 0.470788i | ||||||||
\(617\) | −15.3153 | −0.616572 | −0.308286 | − | 0.951294i | \(-0.599755\pi\) | ||||
−0.308286 | + | 0.951294i | \(0.599755\pi\) | |||||||
\(618\) | 1.12311 | 0.0451779 | ||||||||
\(619\) | 14.2462i | 0.572604i | 0.958139 | + | 0.286302i | \(0.0924260\pi\) | ||||
−0.958139 | + | 0.286302i | \(0.907574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.12311 | −0.205583 | ||||||||
\(622\) | 23.1231 | 0.927152 | ||||||||
\(623\) | 14.2462i | 0.570762i | ||||||||
\(624\) | −0.561553 | − | 3.56155i | −0.0224801 | − | 0.142576i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 32.8617i | − | 1.31342i | ||||||
\(627\) | − | 12.0000i | − | 0.479234i | ||||||
\(628\) | − | 1.68466i | − | 0.0672252i | ||||||
\(629\) | 2.49242i | 0.0993794i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31.1231i | − | 1.23899i | −0.785000 | − | 0.619496i | \(-0.787337\pi\) | ||
0.785000 | − | 0.619496i | \(-0.212663\pi\) | |||||||
\(632\) | 14.6847 | 0.584124 | ||||||||
\(633\) | 7.36932i | 0.292904i | ||||||||
\(634\) | −30.0000 | −1.19145 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −5.00000 | −0.198263 | ||||||||
\(637\) | −49.1771 | + | 7.75379i | −1.94847 | + | 0.307216i | ||||
\(638\) | 2.56155i | 0.101413i | ||||||||
\(639\) | 14.9309i | 0.590656i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.4233 | 1.67562 | 0.837810 | − | 0.545962i | \(-0.183836\pi\) | ||||
0.837810 | + | 0.545962i | \(0.183836\pi\) | |||||||
\(642\) | −12.6847 | −0.500624 | ||||||||
\(643\) | 3.31534 | 0.130744 | 0.0653722 | − | 0.997861i | \(-0.479177\pi\) | ||||
0.0653722 | + | 0.997861i | \(0.479177\pi\) | |||||||
\(644\) | − | 23.3693i | − | 0.920880i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −26.6307 | −1.04777 | ||||||||
\(647\) | 19.1231i | 0.751807i | 0.926659 | + | 0.375903i | \(0.122668\pi\) | ||||
−0.926659 | + | 0.375903i | \(0.877332\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 13.9309 | 0.546834 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.56155 | 0.257168 | ||||||||
\(652\) | −16.4924 | −0.645893 | ||||||||
\(653\) | 7.30019i | 0.285678i | 0.989746 | + | 0.142839i | \(0.0456232\pi\) | ||||
−0.989746 | + | 0.142839i | \(0.954377\pi\) | |||||||
\(654\) | 16.4384 | 0.642794 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.438447i | 0.0171185i | ||||||||
\(657\) | 1.12311 | 0.0438165 | ||||||||
\(658\) | −0.561553 | −0.0218916 | ||||||||
\(659\) | 8.43845 | 0.328715 | 0.164358 | − | 0.986401i | \(-0.447445\pi\) | ||||
0.164358 | + | 0.986401i | \(0.447445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.3002i | 1.48970i | 0.667229 | + | 0.744852i | \(0.267480\pi\) | ||||
−0.667229 | + | 0.744852i | \(0.732520\pi\) | |||||||
\(662\) | 8.49242i | 0.330067i | ||||||||
\(663\) | 20.2462 | − | 3.19224i | 0.786298 | − | 0.123976i | ||||
\(664\) | −13.9309 | −0.540623 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.438447 | −0.0169895 | ||||||||
\(667\) | − | 5.12311i | − | 0.198367i | ||||||
\(668\) | 17.5616 | 0.679477 | ||||||||
\(669\) | − | 9.36932i | − | 0.362239i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.9309i | 1.15547i | ||||||||
\(672\) | 4.56155i | 0.175966i | ||||||||
\(673\) | 13.8769i | 0.534915i | 0.963570 | + | 0.267457i | \(0.0861835\pi\) | ||||
−0.963570 | + | 0.267457i | \(0.913817\pi\) | |||||||
\(674\) | − | 1.68466i | − | 0.0648906i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.3693 | − | 4.00000i | 0.475743 | − | 0.153846i | ||||
\(677\) | 19.7538i | 0.759200i | 0.925151 | + | 0.379600i | \(0.123938\pi\) | ||||
−0.925151 | + | 0.379600i | \(0.876062\pi\) | |||||||
\(678\) | −12.2462 | −0.470313 | ||||||||
\(679\) | −22.2462 | −0.853731 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 15.6847i | − | 0.601037i | ||||||
\(682\) | 3.68466 | 0.141093 | ||||||||
\(683\) | −42.6695 | −1.63270 | −0.816352 | − | 0.577555i | \(-0.804007\pi\) | ||||
−0.816352 | + | 0.577555i | \(0.804007\pi\) | |||||||
\(684\) | − | 4.68466i | − | 0.179122i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 31.0540 | 1.18565 | ||||||||
\(687\) | 27.8078 | 1.06093 | ||||||||
\(688\) | 2.87689i | 0.109681i | ||||||||
\(689\) | −2.80776 | − | 17.8078i | −0.106967 | − | 0.678422i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.0000i | 1.33146i | 0.746191 | + | 0.665731i | \(0.231880\pi\) | ||||
−0.746191 | + | 0.665731i | \(0.768120\pi\) | |||||||
\(692\) | 8.12311i | 0.308794i | ||||||||
\(693\) | − | 11.6847i | − | 0.443863i | ||||||
\(694\) | − | 14.4384i | − | 0.548076i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.00000i | 0.0379049i | ||||||||
\(697\) | −2.49242 | −0.0944072 | ||||||||
\(698\) | 22.0000i | 0.832712i | ||||||||
\(699\) | 5.12311 | 0.193774 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.3153 | 0.540683 | 0.270341 | − | 0.962764i | \(-0.412863\pi\) | ||||
0.270341 | + | 0.962764i | \(0.412863\pi\) | |||||||
\(702\) | 0.561553 | + | 3.56155i | 0.0211944 | + | 0.134422i | ||||
\(703\) | 2.05398i | 0.0774671i | ||||||||
\(704\) | 2.56155i | 0.0965422i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.5616 | −0.736209 | ||||||||
\(707\) | −75.5464 | −2.84121 | ||||||||
\(708\) | 5.43845 | 0.204389 | ||||||||
\(709\) | 26.4924i | 0.994944i | 0.867480 | + | 0.497472i | \(0.165738\pi\) | ||||
−0.867480 | + | 0.497472i | \(0.834262\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.6847 | −0.550718 | ||||||||
\(712\) | 3.12311i | 0.117043i | ||||||||
\(713\) | −7.36932 | −0.275983 | ||||||||
\(714\) | −25.9309 | −0.970438 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.8769 | 0.406489 | ||||||||
\(717\) | 21.9309 | 0.819023 | ||||||||
\(718\) | 12.1231i | 0.452430i | ||||||||
\(719\) | −0.630683 | −0.0235205 | −0.0117603 | − | 0.999931i | \(-0.503743\pi\) | ||||
−0.0117603 | + | 0.999931i | \(0.503743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 5.12311i | − | 0.190794i | ||||||
\(722\) | −2.94602 | −0.109640 | ||||||||
\(723\) | 3.75379 | 0.139605 | ||||||||
\(724\) | 20.8078 | 0.773314 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.43845i | 0.164726i | ||||||||
\(727\) | 41.6155i | 1.54343i | 0.635966 | + | 0.771717i | \(0.280602\pi\) | ||||
−0.635966 | + | 0.771717i | \(0.719398\pi\) | |||||||
\(728\) | −16.2462 | + | 2.56155i | −0.602125 | + | 0.0949375i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.3542 | −0.604881 | ||||||||
\(732\) | 11.6847i | 0.431877i | ||||||||
\(733\) | 27.3153 | 1.00892 | 0.504458 | − | 0.863436i | \(-0.331692\pi\) | ||||
0.504458 | + | 0.863436i | \(0.331692\pi\) | |||||||
\(734\) | − | 7.31534i | − | 0.270014i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.12311i | − | 0.188840i | ||||||
\(737\) | 10.5616i | 0.389040i | ||||||||
\(738\) | − | 0.438447i | − | 0.0161395i | ||||||
\(739\) | 14.5076i | 0.533670i | 0.963742 | + | 0.266835i | \(0.0859779\pi\) | ||||
−0.963742 | + | 0.266835i | \(0.914022\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.6847 | − | 2.63068i | 0.612926 | − | 0.0966406i | ||||
\(742\) | 22.8078i | 0.837299i | ||||||||
\(743\) | 1.63068 | 0.0598240 | 0.0299120 | − | 0.999553i | \(-0.490477\pi\) | ||||
0.0299120 | + | 0.999553i | \(0.490477\pi\) | |||||||
\(744\) | 1.43845 | 0.0527360 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 36.5616i | − | 1.33861i | ||||||
\(747\) | 13.9309 | 0.509704 | ||||||||
\(748\) | −14.5616 | −0.532423 | ||||||||
\(749\) | 57.8617i | 2.11422i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.80776 | 0.211928 | 0.105964 | − | 0.994370i | \(-0.466207\pi\) | ||||
0.105964 | + | 0.994370i | \(0.466207\pi\) | |||||||
\(752\) | −0.123106 | −0.00448920 | ||||||||
\(753\) | 15.5616i | 0.567095i | ||||||||
\(754\) | −3.56155 | + | 0.561553i | −0.129704 | + | 0.0204505i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 4.56155i | − | 0.165902i | ||||||
\(757\) | − | 25.9309i | − | 0.942473i | −0.882007 | − | 0.471237i | \(-0.843808\pi\) | ||
0.882007 | − | 0.471237i | \(-0.156192\pi\) | |||||||
\(758\) | 19.6847i | 0.714979i | ||||||||
\(759\) | 13.1231i | 0.476339i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 35.6695i | − | 1.29302i | −0.762906 | − | 0.646509i | \(-0.776228\pi\) | ||
0.762906 | − | 0.646509i | \(-0.223772\pi\) | |||||||
\(762\) | 15.5616 | 0.563736 | ||||||||
\(763\) | − | 74.9848i | − | 2.71463i | ||||||
\(764\) | 16.4924 | 0.596675 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.9309 | −0.539474 | ||||||||
\(767\) | 3.05398 | + | 19.3693i | 0.110273 | + | 0.699385i | ||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | − | 14.2462i | − | 0.513732i | −0.966447 | − | 0.256866i | \(-0.917310\pi\) | ||
0.966447 | − | 0.256866i | \(-0.0826898\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.80776 | 0.173147 | ||||||||
\(772\) | −13.1231 | −0.472311 | ||||||||
\(773\) | 51.2311 | 1.84265 | 0.921327 | − | 0.388790i | \(-0.127107\pi\) | ||||
0.921327 | + | 0.388790i | \(0.127107\pi\) | |||||||
\(774\) | − | 2.87689i | − | 0.103408i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.87689 | −0.175070 | ||||||||
\(777\) | 2.00000i | 0.0717496i | ||||||||
\(778\) | −13.8078 | −0.495032 | ||||||||
\(779\) | −2.05398 | −0.0735913 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.2462 | 1.36856 | ||||||||
\(782\) | 29.1231 | 1.04144 | ||||||||
\(783\) | − | 1.00000i | − | 0.0357371i | ||||||
\(784\) | 13.8078 | 0.493134 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 18.6847i | − | 0.666460i | ||||||
\(787\) | 2.06913 | 0.0737565 | 0.0368783 | − | 0.999320i | \(-0.488259\pi\) | ||||
0.0368783 | + | 0.999320i | \(0.488259\pi\) | |||||||
\(788\) | −4.24621 | −0.151265 | ||||||||
\(789\) | 24.7386 | 0.880719 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 55.8617i | 1.98621i | ||||||||
\(792\) | − | 2.56155i | − | 0.0910208i | ||||||
\(793\) | −41.6155 | + | 6.56155i | −1.47781 | + | 0.233008i | ||||
\(794\) | 2.05398 | 0.0728929 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.9309 | −0.812763 | ||||||||
\(797\) | − | 21.5464i | − | 0.763213i | −0.924325 | − | 0.381606i | \(-0.875371\pi\) | ||
0.924325 | − | 0.381606i | \(-0.124629\pi\) | |||||||
\(798\) | −21.3693 | −0.756466 | ||||||||
\(799\) | − | 0.699813i | − | 0.0247576i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.12311i | − | 0.110350i | ||||||
\(802\) | 22.0000i | 0.776847i | ||||||||
\(803\) | − | 2.87689i | − | 0.101523i | ||||||
\(804\) | 4.12311i | 0.145411i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.807764 | + | 5.12311i | 0.0284523 | + | 0.180454i | ||||
\(807\) | − | 23.4924i | − | 0.826972i | ||||||
\(808\) | −16.5616 | −0.582633 | ||||||||
\(809\) | −1.12311 | −0.0394863 | −0.0197431 | − | 0.999805i | \(-0.506285\pi\) | ||||
−0.0197431 | + | 0.999805i | \(0.506285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.1771i | 0.427595i | 0.976878 | + | 0.213798i | \(0.0685833\pi\) | ||||
−0.976878 | + | 0.213798i | \(0.931417\pi\) | |||||||
\(812\) | 4.56155 | 0.160079 | ||||||||
\(813\) | 24.8078 | 0.870046 | ||||||||
\(814\) | 1.12311i | 0.0393648i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5.68466 | −0.199003 | ||||||||
\(817\) | −13.4773 | −0.471510 | ||||||||
\(818\) | − | 13.6155i | − | 0.476056i | ||||||
\(819\) | 16.2462 | − | 2.56155i | 0.567689 | − | 0.0895079i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 29.6155i | − | 1.03359i | −0.856109 | − | 0.516795i | \(-0.827125\pi\) | ||
0.856109 | − | 0.516795i | \(-0.172875\pi\) | |||||||
\(822\) | 2.43845i | 0.0850506i | ||||||||
\(823\) | − | 8.19224i | − | 0.285563i | −0.989754 | − | 0.142782i | \(-0.954395\pi\) | ||
0.989754 | − | 0.142782i | \(-0.0456047\pi\) | |||||||
\(824\) | − | 1.12311i | − | 0.0391252i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 24.8078i | − | 0.863173i | ||||||
\(827\) | 53.6847 | 1.86680 | 0.933399 | − | 0.358840i | \(-0.116827\pi\) | ||||
0.933399 | + | 0.358840i | \(0.116827\pi\) | |||||||
\(828\) | 5.12311i | 0.178040i | ||||||||
\(829\) | 1.19224 | 0.0414081 | 0.0207040 | − | 0.999786i | \(-0.493409\pi\) | ||||
0.0207040 | + | 0.999786i | \(0.493409\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 25.6155 | 0.888593 | ||||||||
\(832\) | −3.56155 | + | 0.561553i | −0.123475 | + | 0.0194683i | ||||
\(833\) | 78.4924i | 2.71960i | ||||||||
\(834\) | 16.4924i | 0.571086i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | −1.43845 | −0.0497200 | ||||||||
\(838\) | −6.68466 | −0.230918 | ||||||||
\(839\) | − | 40.0000i | − | 1.38095i | −0.723355 | − | 0.690477i | \(-0.757401\pi\) | ||
0.723355 | − | 0.690477i | \(-0.242599\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | − | 29.3693i | − | 1.01213i | ||||||
\(843\) | 22.9309 | 0.789781 | ||||||||
\(844\) | 7.36932 | 0.253662 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.123106 | 0.00423246 | ||||||||
\(847\) | 20.2462 | 0.695668 | ||||||||
\(848\) | 5.00000i | 0.171701i | ||||||||
\(849\) | −17.3693 | −0.596113 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.24621i | − | 0.0769991i | ||||||
\(852\) | 14.9309 | 0.511523 | ||||||||
\(853\) | −8.19224 | −0.280497 | −0.140248 | − | 0.990116i | \(-0.544790\pi\) | ||||
−0.140248 | + | 0.990116i | \(0.544790\pi\) | |||||||
\(854\) | 53.3002 | 1.82389 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.6847i | 0.433553i | ||||||||
\(857\) | − | 9.61553i | − | 0.328460i | −0.986422 | − | 0.164230i | \(-0.947486\pi\) | ||
0.986422 | − | 0.164230i | \(-0.0525140\pi\) | |||||||
\(858\) | 9.12311 | − | 1.43845i | 0.311458 | − | 0.0491078i | ||||
\(859\) | 36.7386 | 1.25351 | 0.626753 | − | 0.779218i | \(-0.284384\pi\) | ||||
0.626753 | + | 0.779218i | \(0.284384\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.00000 | −0.0681598 | ||||||||
\(862\) | 37.1771i | 1.26626i | ||||||||
\(863\) | 12.8617 | 0.437819 | 0.218909 | − | 0.975745i | \(-0.429750\pi\) | ||||
0.218909 | + | 0.975745i | \(0.429750\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 32.0540i | 1.08924i | ||||||||
\(867\) | − | 15.3153i | − | 0.520136i | ||||||
\(868\) | − | 6.56155i | − | 0.222714i | ||||||
\(869\) | 37.6155i | 1.27602i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.6847 | + | 2.31534i | −0.497571 | + | 0.0784524i | ||||
\(872\) | − | 16.4384i | − | 0.556676i | ||||||
\(873\) | 4.87689 | 0.165058 | ||||||||
\(874\) | 24.0000 | 0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 1.12311i | − | 0.0379462i | ||||||
\(877\) | −13.1771 | −0.444958 | −0.222479 | − | 0.974937i | \(-0.571415\pi\) | ||||
−0.222479 | + | 0.974937i | \(0.571415\pi\) | |||||||
\(878\) | −26.3002 | −0.887588 | ||||||||
\(879\) | 25.3693i | 0.855686i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.0388 | 1.75323 | 0.876616 | − | 0.481190i | \(-0.159795\pi\) | ||||
0.876616 | + | 0.481190i | \(0.159795\pi\) | |||||||
\(882\) | −13.8078 | −0.464932 | ||||||||
\(883\) | 23.6155i | 0.794726i | 0.917662 | + | 0.397363i | \(0.130075\pi\) | ||||
−0.917662 | + | 0.397363i | \(0.869925\pi\) | |||||||
\(884\) | −3.19224 | − | 20.2462i | −0.107367 | − | 0.680954i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 24.4384i | 0.821026i | ||||||||
\(887\) | 1.61553i | 0.0542441i | 0.999632 | + | 0.0271221i | \(0.00863428\pi\) | ||||
−0.999632 | + | 0.0271221i | \(0.991366\pi\) | |||||||
\(888\) | 0.438447i | 0.0147133i | ||||||||
\(889\) | − | 70.9848i | − | 2.38076i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.56155i | 0.0858152i | ||||||||
\(892\) | −9.36932 | −0.313708 | ||||||||
\(893\) | − | 0.576708i | − | 0.0192988i | ||||||
\(894\) | 5.36932 | 0.179577 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.56155 | 0.152391 | ||||||||
\(897\) | −18.2462 | + | 2.87689i | −0.609223 | + | 0.0960567i | ||||
\(898\) | − | 9.56155i | − | 0.319073i | ||||||
\(899\) | − | 1.43845i | − | 0.0479749i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.4233 | −0.946917 | ||||||||
\(902\) | −1.12311 | −0.0373953 | ||||||||
\(903\) | −13.1231 | −0.436710 | ||||||||
\(904\) | 12.2462i | 0.407303i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.6847 | −0.521088 | ||||||||
\(907\) | 55.6155i | 1.84668i | 0.383979 | + | 0.923342i | \(0.374553\pi\) | ||||
−0.383979 | + | 0.923342i | \(0.625447\pi\) | |||||||
\(908\) | −15.6847 | −0.520514 | ||||||||
\(909\) | 16.5616 | 0.549312 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −47.3693 | −1.56942 | −0.784708 | − | 0.619866i | \(-0.787187\pi\) | ||||
−0.784708 | + | 0.619866i | \(0.787187\pi\) | |||||||
\(912\) | −4.68466 | −0.155125 | ||||||||
\(913\) | − | 35.6847i | − | 1.18099i | ||||||
\(914\) | 20.7386 | 0.685973 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 27.8078i | − | 0.918794i | ||||||
\(917\) | −85.2311 | −2.81458 | ||||||||
\(918\) | 5.68466 | 0.187622 | ||||||||
\(919\) | 14.4384 | 0.476280 | 0.238140 | − | 0.971231i | \(-0.423462\pi\) | ||||
0.238140 | + | 0.971231i | \(0.423462\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.9309i | 1.01921i | ||||||||
\(922\) | − | 5.75379i | − | 0.189491i | ||||||
\(923\) | 8.38447 | + | 53.1771i | 0.275978 | + | 1.75034i | ||||
\(924\) | −11.6847 | −0.384397 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.43845 | −0.244443 | ||||||||
\(927\) | 1.12311i | 0.0368876i | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 11.4233i | 0.374786i | 0.982285 | + | 0.187393i | \(0.0600038\pi\) | ||||
−0.982285 | + | 0.187393i | \(0.939996\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 64.6847i | 2.11995i | ||||||||
\(932\) | − | 5.12311i | − | 0.167813i | ||||||
\(933\) | 23.1231i | 0.757016i | ||||||||
\(934\) | 20.1922i | 0.660710i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.56155 | − | 0.561553i | 0.116413 | − | 0.0183549i | ||||
\(937\) | 39.9309i | 1.30448i | 0.758011 | + | 0.652242i | \(0.226172\pi\) | ||||
−0.758011 | + | 0.652242i | \(0.773828\pi\) | |||||||
\(938\) | 18.8078 | 0.614095 | ||||||||
\(939\) | 32.8617 | 1.07240 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.73863i | 0.284871i | 0.989804 | + | 0.142436i | \(0.0454934\pi\) | ||||
−0.989804 | + | 0.142436i | \(0.954507\pi\) | |||||||
\(942\) | 1.68466 | 0.0548891 | ||||||||
\(943\) | 2.24621 | 0.0731467 | ||||||||
\(944\) | − | 5.43845i | − | 0.177006i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.36932 | −0.239597 | ||||||||
\(947\) | 11.9309 | 0.387701 | 0.193851 | − | 0.981031i | \(-0.437902\pi\) | ||||
0.193851 | + | 0.981031i | \(0.437902\pi\) | |||||||
\(948\) | 14.6847i | 0.476936i | ||||||||
\(949\) | 4.00000 | − | 0.630683i | 0.129845 | − | 0.0204728i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 30.0000i | − | 0.972817i | ||||||
\(952\) | 25.9309i | 0.840424i | ||||||||
\(953\) | − | 18.8078i | − | 0.609243i | −0.952473 | − | 0.304622i | \(-0.901470\pi\) | ||
0.952473 | − | 0.304622i | \(-0.0985300\pi\) | |||||||
\(954\) | − | 5.00000i | − | 0.161881i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 21.9309i | − | 0.709295i | ||||||
\(957\) | −2.56155 | −0.0828032 | ||||||||
\(958\) | 23.8769i | 0.771427i | ||||||||
\(959\) | 11.1231 | 0.359184 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.9309 | 0.933254 | ||||||||
\(962\) | −1.56155 | + | 0.246211i | −0.0503465 | + | 0.00793817i | ||||
\(963\) | − | 12.6847i | − | 0.408757i | ||||||
\(964\) | − | 3.75379i | − | 0.120901i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 23.3693 | 0.751895 | ||||||||
\(967\) | 34.6695 | 1.11490 | 0.557448 | − | 0.830212i | \(-0.311781\pi\) | ||||
0.557448 | + | 0.830212i | \(0.311781\pi\) | |||||||
\(968\) | 4.43845 | 0.142657 | ||||||||
\(969\) | − | 26.6307i | − | 0.855501i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.9309 | −0.864253 | −0.432126 | − | 0.901813i | \(-0.642237\pi\) | ||||
−0.432126 | + | 0.901813i | \(0.642237\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 75.2311 | 2.41180 | ||||||||
\(974\) | 5.68466 | 0.182148 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.6847 | 0.374017 | ||||||||
\(977\) | 6.63068 | 0.212134 | 0.106067 | − | 0.994359i | \(-0.466174\pi\) | ||||
0.106067 | + | 0.994359i | \(0.466174\pi\) | |||||||
\(978\) | − | 16.4924i | − | 0.527370i | ||||||
\(979\) | −8.00000 | −0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.4384i | 0.524839i | ||||||||
\(982\) | −10.7386 | −0.342684 | ||||||||
\(983\) | 37.9309 | 1.20981 | 0.604903 | − | 0.796299i | \(-0.293212\pi\) | ||||
0.604903 | + | 0.796299i | \(0.293212\pi\) | |||||||
\(984\) | −0.438447 | −0.0139772 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.68466i | 0.181036i | ||||||||
\(987\) | − | 0.561553i | − | 0.0178744i | ||||||
\(988\) | −2.63068 | − | 16.6847i | −0.0836932 | − | 0.530810i | ||||
\(989\) | 14.7386 | 0.468661 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3153 | −0.422976 | −0.211488 | − | 0.977381i | \(-0.567831\pi\) | ||||
−0.211488 | + | 0.977381i | \(0.567831\pi\) | |||||||
\(992\) | − | 1.43845i | − | 0.0456707i | ||||||
\(993\) | −8.49242 | −0.269499 | ||||||||
\(994\) | − | 68.1080i | − | 2.16025i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 13.9309i | − | 0.441416i | ||||||
\(997\) | − | 24.6695i | − | 0.781291i | −0.920541 | − | 0.390646i | \(-0.872252\pi\) | ||
0.920541 | − | 0.390646i | \(-0.127748\pi\) | |||||||
\(998\) | − | 19.8769i | − | 0.629192i | ||||||
\(999\) | − | 0.438447i | − | 0.0138719i |
(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 | 1950.2.f.p.649.4 | 4 | ||
5.2 | odd | 4 | 1950.2.b.j.1351.4 | yes | 4 | ||
5.3 | odd | 4 | 1950.2.b.i.1351.1 | ✓ | 4 | ||
5.4 | even | 2 | 1950.2.f.k.649.1 | 4 | |||
13.12 | even | 2 | 1950.2.f.k.649.3 | 4 | |||
65.12 | odd | 4 | 1950.2.b.j.1351.1 | yes | 4 | ||
65.38 | odd | 4 | 1950.2.b.i.1351.4 | yes | 4 | ||
65.64 | even | 2 | inner | 1950.2.f.p.649.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.b.i.1351.1 | ✓ | 4 | 5.3 | odd | 4 | ||
1950.2.b.i.1351.4 | yes | 4 | 65.38 | odd | 4 | ||
1950.2.b.j.1351.1 | yes | 4 | 65.12 | odd | 4 | ||
1950.2.b.j.1351.4 | yes | 4 | 5.2 | odd | 4 | ||
1950.2.f.k.649.1 | 4 | 5.4 | even | 2 | |||
1950.2.f.k.649.3 | 4 | 13.12 | even | 2 | |||
1950.2.f.p.649.2 | 4 | 65.64 | even | 2 | inner | ||
1950.2.f.p.649.4 | 4 | 1.1 | even | 1 | trivial |