Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), degree \(2\), 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: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 9 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.193 |
Dual form | 1200.3.bg.j.1057.2 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.34847 | − | 7.34847i | 1.04978 | − | 1.04978i | 0.0510871 | − | 0.998694i | \(-0.483731\pi\) |
0.998694 | − | 0.0510871i | \(-0.0162686\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 18.0000 | 1.63636 | 0.818182 | − | 0.574960i | \(-0.194982\pi\) | ||||
0.818182 | + | 0.574960i | \(0.194982\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.34847 | + | 7.34847i | 0.565267 | + | 0.565267i | 0.930799 | − | 0.365532i | \(-0.119113\pi\) |
−0.365532 | + | 0.930799i | \(0.619113\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.89898 | − | 4.89898i | 0.288175 | − | 0.288175i | −0.548183 | − | 0.836358i | \(-0.684680\pi\) |
0.836358 | + | 0.548183i | \(0.184680\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 10.0000i | − | 0.526316i | −0.964753 | − | 0.263158i | \(-0.915236\pi\) | ||
0.964753 | − | 0.263158i | \(-0.0847640\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.0000 | 0.857143 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −19.5959 | − | 19.5959i | −0.851996 | − | 0.851996i | 0.138382 | − | 0.990379i | \(-0.455810\pi\) |
−0.990379 | + | 0.138382i | \(0.955810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −22.0000 | −0.709677 | −0.354839 | − | 0.934928i | \(-0.615464\pi\) | ||||
−0.354839 | + | 0.934928i | \(0.615464\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 22.0454 | + | 22.0454i | 0.668043 | + | 0.668043i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.34847 | + | 7.34847i | −0.198607 | + | 0.198607i | −0.799403 | − | 0.600795i | \(-0.794851\pi\) |
0.600795 | + | 0.799403i | \(0.294851\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.0000i | 0.461538i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.0000 | −0.439024 | −0.219512 | − | 0.975610i | \(-0.570447\pi\) | ||||
−0.219512 | + | 0.975610i | \(0.570447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 29.3939 | + | 29.3939i | 0.683579 | + | 0.683579i | 0.960805 | − | 0.277226i | \(-0.0894151\pi\) |
−0.277226 | + | 0.960805i | \(0.589415\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 44.0908 | − | 44.0908i | 0.938102 | − | 0.938102i | −0.0600905 | − | 0.998193i | \(-0.519139\pi\) |
0.998193 | + | 0.0600905i | \(0.0191389\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 59.0000i | − | 1.20408i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.0000 | 0.235294 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.89898 | − | 4.89898i | −0.0924336 | − | 0.0924336i | 0.659378 | − | 0.751812i | \(-0.270820\pi\) |
−0.751812 | + | 0.659378i | \(0.770820\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.2474 | − | 12.2474i | 0.214868 | − | 0.214868i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 90.0000i | − | 1.52542i | −0.646738 | − | 0.762712i | \(-0.723867\pi\) | ||
0.646738 | − | 0.762712i | \(-0.276133\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.0327869 | 0.0163934 | − | 0.999866i | \(-0.494782\pi\) | ||||
0.0163934 | + | 0.999866i | \(0.494782\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 22.0454 | + | 22.0454i | 0.349927 | + | 0.349927i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 44.0908 | − | 44.0908i | 0.658072 | − | 0.658072i | −0.296852 | − | 0.954924i | \(-0.595937\pi\) |
0.954924 | + | 0.296852i | \(0.0959367\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 48.0000i | − | 0.695652i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −72.0000 | −1.01408 | −0.507042 | − | 0.861921i | \(-0.669261\pi\) | ||||
−0.507042 | + | 0.861921i | \(0.669261\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 44.0908 | + | 44.0908i | 0.603984 | + | 0.603984i | 0.941367 | − | 0.337384i | \(-0.109542\pi\) |
−0.337384 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 132.272 | − | 132.272i | 1.71782 | − | 1.71782i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 70.0000i | 0.886076i | 0.896503 | + | 0.443038i | \(0.146099\pi\) | ||||
−0.896503 | + | 0.443038i | \(0.853901\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 53.8888 | + | 53.8888i | 0.649262 | + | 0.649262i | 0.952815 | − | 0.303552i | \(-0.0981727\pi\) |
−0.303552 | + | 0.952815i | \(0.598173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 90.0000i | 1.01124i | 0.862757 | + | 0.505618i | \(0.168735\pi\) | ||||
−0.862757 | + | 0.505618i | \(0.831265\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 108.000 | 1.18681 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −26.9444 | − | 26.9444i | −0.289725 | − | 0.289725i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 102.879 | − | 102.879i | 1.06060 | − | 1.06060i | 0.0625628 | − | 0.998041i | \(-0.480073\pi\) |
0.998041 | − | 0.0625628i | \(-0.0199274\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 54.0000i | 0.545455i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −108.000 | −1.06931 | −0.534653 | − | 0.845071i | \(-0.679558\pi\) | ||||
−0.534653 | + | 0.845071i | \(0.679558\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 66.1362 | + | 66.1362i | 0.642099 | + | 0.642099i | 0.951071 | − | 0.308972i | \(-0.0999849\pi\) |
−0.308972 | + | 0.951071i | \(0.599985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 44.0908 | − | 44.0908i | 0.412064 | − | 0.412064i | −0.470393 | − | 0.882457i | \(-0.655888\pi\) |
0.882457 | + | 0.470393i | \(0.155888\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 170.000i | 1.55963i | 0.626008 | + | 0.779817i | \(0.284688\pi\) | ||||
−0.626008 | + | 0.779817i | \(0.715312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.0000 | −0.162162 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 44.0908 | + | 44.0908i | 0.390184 | + | 0.390184i | 0.874753 | − | 0.484569i | \(-0.161024\pi\) |
−0.484569 | + | 0.874753i | \(0.661024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −22.0454 | + | 22.0454i | −0.188422 | + | 0.188422i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 72.0000i | − | 0.605042i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 203.000 | 1.67769 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.0454 | − | 22.0454i | −0.179231 | − | 0.179231i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.34847 | − | 7.34847i | 0.0578620 | − | 0.0578620i | −0.677584 | − | 0.735446i | \(-0.736973\pi\) |
0.735446 | + | 0.677584i | \(0.236973\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 72.0000i | 0.558140i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.0000 | 0.137405 | 0.0687023 | − | 0.997637i | \(-0.478114\pi\) | ||||
0.0687023 | + | 0.997637i | \(0.478114\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −73.4847 | − | 73.4847i | −0.552516 | − | 0.552516i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −142.070 | + | 142.070i | −1.03701 | + | 1.03701i | −0.0377220 | + | 0.999288i | \(0.512010\pi\) |
−0.999288 | + | 0.0377220i | \(0.987990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 170.000i | 1.22302i | 0.791236 | + | 0.611511i | \(0.209438\pi\) | ||||
−0.791236 | + | 0.611511i | \(0.790562\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 108.000 | 0.765957 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 132.272 | + | 132.272i | 0.924982 | + | 0.924982i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 72.2599 | − | 72.2599i | 0.491564 | − | 0.491564i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 180.000i | − | 1.20805i | −0.796964 | − | 0.604027i | \(-0.793562\pi\) | ||
0.796964 | − | 0.604027i | \(-0.206438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.0000 | −0.145695 | −0.0728477 | − | 0.997343i | \(-0.523209\pi\) | ||||
−0.0728477 | + | 0.997343i | \(0.523209\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.6969 | + | 14.6969i | 0.0960584 | + | 0.0960584i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 139.621 | − | 139.621i | 0.889305 | − | 0.889305i | −0.105151 | − | 0.994456i | \(-0.533533\pi\) |
0.994456 | + | 0.105151i | \(0.0335326\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 12.0000i | − | 0.0754717i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −288.000 | −1.78882 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −117.576 | − | 117.576i | −0.721322 | − | 0.721322i | 0.247552 | − | 0.968875i | \(-0.420374\pi\) |
−0.968875 | + | 0.247552i | \(0.920374\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.5959 | − | 19.5959i | 0.117341 | − | 0.117341i | −0.645998 | − | 0.763339i | \(-0.723559\pi\) |
0.763339 | + | 0.645998i | \(0.223559\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 61.0000i | − | 0.360947i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 30.0000 | 0.175439 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 142.070 | + | 142.070i | 0.821216 | + | 0.821216i | 0.986282 | − | 0.165066i | \(-0.0527838\pi\) |
−0.165066 | + | 0.986282i | \(0.552784\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 110.227 | − | 110.227i | 0.622752 | − | 0.622752i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 90.0000i | 0.502793i | 0.967884 | + | 0.251397i | \(0.0808899\pi\) | ||||
−0.967884 | + | 0.251397i | \(0.919110\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −98.0000 | −0.541436 | −0.270718 | − | 0.962659i | \(-0.587261\pi\) | ||||
−0.270718 | + | 0.962659i | \(0.587261\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.44949 | + | 2.44949i | 0.0133852 | + | 0.0133852i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 88.1816 | − | 88.1816i | 0.471560 | − | 0.471560i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 54.0000i | 0.285714i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −252.000 | −1.31937 | −0.659686 | − | 0.751541i | \(-0.729311\pi\) | ||||
−0.659686 | + | 0.751541i | \(0.729311\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 264.545 | + | 264.545i | 1.37070 | + | 1.37070i | 0.859407 | + | 0.511292i | \(0.170833\pi\) |
0.511292 | + | 0.859407i | \(0.329167\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 127.373 | − | 127.373i | 0.646566 | − | 0.646566i | −0.305596 | − | 0.952161i | \(-0.598856\pi\) |
0.952161 | + | 0.305596i | \(0.0988556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 290.000i | − | 1.45729i | −0.684893 | − | 0.728643i | \(-0.740151\pi\) | ||
0.684893 | − | 0.728643i | \(-0.259849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 108.000 | 0.537313 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 58.7878 | − | 58.7878i | 0.283999 | − | 0.283999i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 180.000i | − | 0.861244i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −122.000 | −0.578199 | −0.289100 | − | 0.957299i | \(-0.593356\pi\) | ||||
−0.289100 | + | 0.957299i | \(0.593356\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −88.1816 | − | 88.1816i | −0.413998 | − | 0.413998i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −161.666 | + | 161.666i | −0.745006 | + | 0.745006i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 108.000i | 0.493151i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 72.0000 | 0.325792 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −80.8332 | − | 80.8332i | −0.362481 | − | 0.362481i | 0.502245 | − | 0.864725i | \(-0.332508\pi\) |
−0.864725 | + | 0.502245i | \(0.832508\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −53.8888 | + | 53.8888i | −0.237395 | + | 0.237395i | −0.815771 | − | 0.578375i | \(-0.803687\pi\) |
0.578375 | + | 0.815771i | \(0.303687\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 50.0000i | − | 0.218341i | −0.994023 | − | 0.109170i | \(-0.965181\pi\) | ||
0.994023 | − | 0.109170i | \(-0.0348194\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 324.000 | 1.40260 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 44.0908 | + | 44.0908i | 0.189231 | + | 0.189231i | 0.795364 | − | 0.606133i | \(-0.207280\pi\) |
−0.606133 | + | 0.795364i | \(0.707280\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −85.7321 | + | 85.7321i | −0.361739 | + | 0.361739i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 180.000i | − | 0.753138i | −0.926389 | − | 0.376569i | \(-0.877104\pi\) | ||
0.926389 | − | 0.376569i | \(-0.122896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −178.000 | −0.738589 | −0.369295 | − | 0.929312i | \(-0.620401\pi\) | ||||
−0.369295 | + | 0.929312i | \(0.620401\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 73.4847 | − | 73.4847i | 0.297509 | − | 0.297509i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 132.000i | 0.530120i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −342.000 | −1.36255 | −0.681275 | − | 0.732028i | \(-0.738574\pi\) | ||||
−0.681275 | + | 0.732028i | \(0.738574\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −352.727 | − | 352.727i | −1.39418 | − | 1.39418i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −289.040 | + | 289.040i | −1.12467 | + | 1.12467i | −0.133638 | + | 0.991030i | \(0.542666\pi\) |
−0.991030 | + | 0.133638i | \(0.957334\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 108.000i | 0.416988i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −264.545 | − | 264.545i | −1.00587 | − | 1.00587i | −0.999983 | − | 0.00589147i | \(-0.998125\pi\) |
−0.00589147 | − | 0.999983i | \(-0.501875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −110.227 | + | 110.227i | −0.412835 | + | 0.412835i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 478.000 | 1.76384 | 0.881919 | − | 0.471401i | \(-0.156252\pi\) | ||||
0.881919 | + | 0.471401i | \(0.156252\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 132.272 | + | 132.272i | 0.484514 | + | 0.484514i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −80.8332 | + | 80.8332i | −0.291816 | + | 0.291816i | −0.837798 | − | 0.545981i | \(-0.816157\pi\) |
0.545981 | + | 0.837798i | \(0.316157\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 66.0000i | − | 0.236559i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 162.000 | 0.576512 | 0.288256 | − | 0.957553i | \(-0.406925\pi\) | ||||
0.288256 | + | 0.957553i | \(0.406925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 249.848 | + | 249.848i | 0.882855 | + | 0.882855i | 0.993824 | − | 0.110969i | \(-0.0353954\pi\) |
−0.110969 | + | 0.993824i | \(0.535395\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −132.272 | + | 132.272i | −0.460880 | + | 0.460880i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 241.000i | 0.833910i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 252.000 | 0.865979 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −372.322 | − | 372.322i | −1.27073 | − | 1.27073i | −0.945708 | − | 0.325017i | \(-0.894630\pi\) |
−0.325017 | − | 0.945708i | \(-0.605370\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −66.1362 | + | 66.1362i | −0.222681 | + | 0.222681i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 288.000i | − | 0.963211i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 432.000 | 1.43522 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −132.272 | − | 132.272i | −0.436543 | − | 0.436543i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −396.817 | + | 396.817i | −1.29256 | + | 1.29256i | −0.359369 | + | 0.933195i | \(0.617008\pi\) |
−0.933195 | + | 0.359369i | \(0.882992\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 162.000i | 0.524272i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −252.000 | −0.810289 | −0.405145 | − | 0.914253i | \(-0.632779\pi\) | ||||
−0.405145 | + | 0.914253i | \(0.632779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 117.576 | + | 117.576i | 0.375641 | + | 0.375641i | 0.869527 | − | 0.493886i | \(-0.164424\pi\) |
−0.493886 | + | 0.869527i | \(0.664424\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 274.343 | − | 274.343i | 0.865435 | − | 0.865435i | −0.126528 | − | 0.991963i | \(-0.540383\pi\) |
0.991963 | + | 0.126528i | \(0.0403834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 108.000 | 0.336449 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −48.9898 | − | 48.9898i | −0.151671 | − | 0.151671i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −208.207 | + | 208.207i | −0.636718 | + | 0.636718i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 648.000i | − | 1.96960i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 418.000 | 1.26284 | 0.631420 | − | 0.775441i | \(-0.282472\pi\) | ||||
0.631420 | + | 0.775441i | \(0.282472\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.0454 | − | 22.0454i | −0.0662024 | − | 0.0662024i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −191.060 | + | 191.060i | −0.566944 | + | 0.566944i | −0.931271 | − | 0.364327i | \(-0.881299\pi\) |
0.364327 | + | 0.931271i | \(0.381299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 108.000i | 0.318584i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −396.000 | −1.16129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −73.4847 | − | 73.4847i | −0.214241 | − | 0.214241i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 44.0908 | − | 44.0908i | 0.127063 | − | 0.127063i | −0.640716 | − | 0.767778i | \(-0.721362\pi\) |
0.767778 | + | 0.640716i | \(0.221362\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 70.0000i | 0.200573i | 0.994959 | + | 0.100287i | \(0.0319759\pi\) | ||||
−0.994959 | + | 0.100287i | \(0.968024\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −54.0000 | −0.153846 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 44.0908 | + | 44.0908i | 0.124903 | + | 0.124903i | 0.766795 | − | 0.641892i | \(-0.221850\pi\) |
−0.641892 | + | 0.766795i | \(0.721850\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 88.1816 | − | 88.1816i | 0.247007 | − | 0.247007i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 540.000i | 1.50418i | 0.659061 | + | 0.752089i | \(0.270954\pi\) | ||||
−0.659061 | + | 0.752089i | \(0.729046\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 261.000 | 0.722992 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 248.623 | + | 248.623i | 0.684912 | + | 0.684912i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −66.1362 | + | 66.1362i | −0.180208 | + | 0.180208i | −0.791446 | − | 0.611239i | \(-0.790672\pi\) |
0.611239 | + | 0.791446i | \(0.290672\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 54.0000i | − | 0.146341i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −72.0000 | −0.194070 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −213.106 | − | 213.106i | −0.571329 | − | 0.571329i | 0.361171 | − | 0.932500i | \(-0.382377\pi\) |
−0.932500 | + | 0.361171i | \(0.882377\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 170.000i | 0.448549i | 0.974526 | + | 0.224274i | \(0.0720012\pi\) | ||||
−0.974526 | + | 0.224274i | \(0.927999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0000 | 0.0472441 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 151.868 | + | 151.868i | 0.396523 | + | 0.396523i | 0.877005 | − | 0.480482i | \(-0.159538\pi\) |
−0.480482 | + | 0.877005i | \(0.659538\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −88.1816 | + | 88.1816i | −0.227860 | + | 0.227860i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 360.000i | − | 0.925450i | −0.886502 | − | 0.462725i | \(-0.846872\pi\) | ||
0.886502 | − | 0.462725i | \(-0.153128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −192.000 | −0.491049 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.0454 | + | 22.0454i | 0.0560952 | + | 0.0560952i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −301.287 | + | 301.287i | −0.758910 | + | 0.758910i | −0.976124 | − | 0.217214i | \(-0.930303\pi\) |
0.217214 | + | 0.976124i | \(0.430303\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 180.000i | − | 0.451128i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −558.000 | −1.39152 | −0.695761 | − | 0.718274i | \(-0.744933\pi\) | ||||
−0.695761 | + | 0.718274i | \(0.744933\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −161.666 | − | 161.666i | −0.401157 | − | 0.401157i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −132.272 | + | 132.272i | −0.324994 | + | 0.324994i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 670.000i | 1.63814i | 0.573692 | + | 0.819071i | \(0.305511\pi\) | ||||
−0.573692 | + | 0.819071i | \(0.694489\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −348.000 | −0.846715 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −661.362 | − | 661.362i | −1.60136 | − | 1.60136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −208.207 | + | 208.207i | −0.499296 | + | 0.499296i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 630.000i | − | 1.50358i | −0.659403 | − | 0.751790i | \(-0.729191\pi\) | ||
0.659403 | − | 0.751790i | \(-0.270809\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 142.000 | 0.337292 | 0.168646 | − | 0.985677i | \(-0.446061\pi\) | ||||
0.168646 | + | 0.985677i | \(0.446061\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 132.272 | + | 132.272i | 0.312701 | + | 0.312701i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.6969 | − | 14.6969i | 0.0344191 | − | 0.0344191i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 324.000i | 0.755245i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −612.000 | −1.41995 | −0.709977 | − | 0.704225i | \(-0.751295\pi\) | ||||
−0.709977 | + | 0.704225i | \(0.751295\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −102.879 | − | 102.879i | −0.237595 | − | 0.237595i | 0.578259 | − | 0.815853i | \(-0.303732\pi\) |
−0.815853 | + | 0.578259i | \(0.803732\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −195.959 | + | 195.959i | −0.448419 | + | 0.448419i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 430.000i | 0.979499i | 0.871863 | + | 0.489749i | \(0.162912\pi\) | ||||
−0.871863 | + | 0.489749i | \(0.837088\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 177.000 | 0.401361 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −582.979 | − | 582.979i | −1.31598 | − | 1.31598i | −0.916930 | − | 0.399049i | \(-0.869340\pi\) |
−0.399049 | − | 0.916930i | \(-0.630660\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 220.454 | − | 220.454i | 0.493186 | − | 0.493186i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 90.0000i | 0.200445i | 0.994965 | + | 0.100223i | \(0.0319555\pi\) | ||||
−0.994965 | + | 0.100223i | \(0.968044\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −324.000 | −0.718404 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −26.9444 | − | 26.9444i | −0.0594799 | − | 0.0594799i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −191.060 | + | 191.060i | −0.418075 | + | 0.418075i | −0.884540 | − | 0.466465i | \(-0.845527\pi\) |
0.466465 | + | 0.884540i | \(0.345527\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 36.0000i | 0.0784314i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −828.000 | −1.79610 | −0.898048 | − | 0.439898i | \(-0.855015\pi\) | ||||
−0.898048 | + | 0.439898i | \(0.855015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.34847 | − | 7.34847i | −0.0158714 | − | 0.0158714i | 0.699127 | − | 0.714998i | \(-0.253572\pi\) |
−0.714998 | + | 0.699127i | \(0.753572\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −347.828 | + | 347.828i | −0.744813 | + | 0.744813i | −0.973500 | − | 0.228687i | \(-0.926557\pi\) |
0.228687 | + | 0.973500i | \(0.426557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 648.000i | − | 1.38166i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 342.000 | 0.726115 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 529.090 | + | 529.090i | 1.11858 | + | 1.11858i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.6969 | − | 14.6969i | 0.0308112 | − | 0.0308112i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 360.000i | 0.751566i | 0.926708 | + | 0.375783i | \(0.122626\pi\) | ||||
−0.926708 | + | 0.375783i | \(0.877374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −108.000 | −0.224532 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −352.727 | − | 352.727i | −0.730283 | − | 0.730283i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −580.529 | + | 580.529i | −1.19205 | + | 1.19205i | −0.215561 | + | 0.976490i | \(0.569158\pi\) |
−0.976490 | + | 0.215561i | \(0.930842\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 288.000i | − | 0.588957i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.0000 | 0.0366599 | 0.0183299 | − | 0.999832i | \(-0.494165\pi\) | ||||
0.0183299 | + | 0.999832i | \(0.494165\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −529.090 | + | 529.090i | −1.06457 | + | 1.06457i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 590.000i | − | 1.18236i | −0.806538 | − | 0.591182i | \(-0.798661\pi\) | ||
0.806538 | − | 0.591182i | \(-0.201339\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 48.0000 | 0.0958084 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −93.0806 | − | 93.0806i | −0.185051 | − | 0.185051i | 0.608502 | − | 0.793553i | \(-0.291771\pi\) |
−0.793553 | + | 0.608502i | \(0.791771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 74.7094 | − | 74.7094i | 0.147356 | − | 0.147356i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 540.000i | 1.06090i | 0.847715 | + | 0.530452i | \(0.177978\pi\) | ||||
−0.847715 | + | 0.530452i | \(0.822022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 648.000 | 1.26810 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.7423 | + | 36.7423i | 0.0716225 | + | 0.0716225i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 793.635 | − | 793.635i | 1.53508 | − | 1.53508i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 348.000i | 0.670520i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 342.000 | 0.656430 | 0.328215 | − | 0.944603i | \(-0.393553\pi\) | ||||
0.328215 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −264.545 | − | 264.545i | −0.505822 | − | 0.505822i | 0.407419 | − | 0.913241i | \(-0.366429\pi\) |
−0.913241 | + | 0.407419i | \(0.866429\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −107.778 | + | 107.778i | −0.204511 | + | 0.204511i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 239.000i | 0.451796i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 270.000 | 0.508475 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −132.272 | − | 132.272i | −0.248166 | − | 0.248166i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −110.227 | + | 110.227i | −0.205265 | + | 0.205265i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1062.00i | − | 1.97032i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.00369686 | 0.00184843 | − | 0.999998i | \(-0.499412\pi\) | ||||
0.00184843 | + | 0.999998i | \(0.499412\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −120.025 | − | 120.025i | −0.221041 | − | 0.221041i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 264.545 | − | 264.545i | 0.483629 | − | 0.483629i | −0.422660 | − | 0.906288i | \(-0.638903\pi\) |
0.906288 | + | 0.422660i | \(0.138903\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.00000i | 0.0109290i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 514.393 | + | 514.393i | 0.930186 | + | 0.930186i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −484.999 | + | 484.999i | −0.870734 | + | 0.870734i | −0.992552 | − | 0.121818i | \(-0.961128\pi\) |
0.121818 | + | 0.992552i | \(0.461128\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 432.000i | 0.772809i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 216.000 | 0.385027 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 396.817 | + | 396.817i | 0.704827 | + | 0.704827i | 0.965443 | − | 0.260616i | \(-0.0839256\pi\) |
−0.260616 | + | 0.965443i | \(0.583926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −66.1362 | + | 66.1362i | −0.116642 | + | 0.116642i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 630.000i | 1.10721i | 0.832781 | + | 0.553603i | \(0.186747\pi\) | ||||
−0.832781 | + | 0.553603i | \(0.813253\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −302.000 | −0.528897 | −0.264448 | − | 0.964400i | \(-0.585190\pi\) | ||||
−0.264448 | + | 0.964400i | \(0.585190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −308.636 | − | 308.636i | −0.538631 | − | 0.538631i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −484.999 | + | 484.999i | −0.840553 | + | 0.840553i | −0.988931 | − | 0.148378i | \(-0.952595\pi\) |
0.148378 | + | 0.988931i | \(0.452595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 648.000i | 1.11917i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 792.000 | 1.36317 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −88.1816 | − | 88.1816i | −0.151255 | − | 0.151255i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 582.979 | − | 582.979i | 0.993149 | − | 0.993149i | −0.00682753 | − | 0.999977i | \(-0.502173\pi\) |
0.999977 | + | 0.00682753i | \(0.00217329\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 220.000i | 0.373514i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 312.000 | 0.527919 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 533.989 | + | 533.989i | 0.900487 | + | 0.900487i | 0.995478 | − | 0.0949912i | \(-0.0302823\pi\) |
−0.0949912 | + | 0.995478i | \(0.530282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 355.176 | − | 355.176i | 0.594935 | − | 0.594935i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 540.000i | 0.901503i | 0.892650 | + | 0.450751i | \(0.148844\pi\) | ||||
−0.892650 | + | 0.450751i | \(0.851156\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −758.000 | −1.26123 | −0.630616 | − | 0.776095i | \(-0.717198\pi\) | ||||
−0.630616 | + | 0.776095i | \(0.717198\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 132.272 | + | 132.272i | 0.219357 | + | 0.219357i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 668.711 | − | 668.711i | 1.10167 | − | 1.10167i | 0.107455 | − | 0.994210i | \(-0.465730\pi\) |
0.994210 | − | 0.107455i | \(-0.0342702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 648.000 | 1.06056 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −66.1362 | − | 66.1362i | −0.107889 | − | 0.107889i | 0.651101 | − | 0.758991i | \(-0.274307\pi\) |
−0.758991 | + | 0.651101i | \(0.774307\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 592.777 | − | 592.777i | 0.960740 | − | 0.960740i | −0.0385180 | − | 0.999258i | \(-0.512264\pi\) |
0.999258 | + | 0.0385180i | \(0.0122637\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1030.00i | 1.66397i | 0.554795 | + | 0.831987i | \(0.312797\pi\) | ||||
−0.554795 | + | 0.831987i | \(0.687203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 144.000 | 0.231884 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 661.362 | + | 661.362i | 1.06158 | + | 1.06158i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 220.454 | − | 220.454i | 0.351601 | − | 0.351601i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 72.0000i | 0.114467i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −242.000 | −0.383518 | −0.191759 | − | 0.981442i | \(-0.561419\pi\) | ||||
−0.191759 | + | 0.981442i | \(0.561419\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −149.419 | − | 149.419i | −0.236049 | − | 0.236049i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 433.560 | − | 433.560i | 0.680627 | − | 0.680627i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 216.000i | − | 0.338028i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 162.000 | 0.252730 | 0.126365 | − | 0.991984i | \(-0.459669\pi\) | ||||
0.126365 | + | 0.991984i | \(0.459669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −264.545 | − | 264.545i | −0.411423 | − | 0.411423i | 0.470811 | − | 0.882234i | \(-0.343961\pi\) |
−0.882234 | + | 0.470811i | \(0.843961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 93.0806 | − | 93.0806i | 0.143865 | − | 0.143865i | −0.631506 | − | 0.775371i | \(-0.717563\pi\) |
0.775371 | + | 0.631506i | \(0.217563\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1620.00i | − | 2.49615i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −396.000 | −0.608295 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 68.5857 | + | 68.5857i | 0.105032 | + | 0.105032i | 0.757670 | − | 0.652638i | \(-0.226338\pi\) |
−0.652638 | + | 0.757670i | \(0.726338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −132.272 | + | 132.272i | −0.201328 | + | 0.201328i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 630.000i | − | 0.955994i | −0.878361 | − | 0.477997i | \(-0.841363\pi\) | ||
0.878361 | − | 0.477997i | \(-0.158637\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 622.000 | 0.940998 | 0.470499 | − | 0.882400i | \(-0.344074\pi\) | ||||
0.470499 | + | 0.882400i | \(0.344074\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 88.1816 | + | 88.1816i | 0.133004 | + | 0.133004i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 198.000i | − | 0.295964i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.0000 | 0.0536513 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −102.879 | − | 102.879i | −0.152866 | − | 0.152866i | 0.626531 | − | 0.779397i | \(-0.284474\pi\) |
−0.779397 | + | 0.626531i | \(0.784474\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 176.363 | − | 176.363i | 0.260507 | − | 0.260507i | −0.564753 | − | 0.825260i | \(-0.691029\pi\) |
0.825260 | + | 0.564753i | \(0.191029\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1512.00i | − | 2.22680i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −132.000 | −0.193833 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 445.807 | + | 445.807i | 0.652719 | + | 0.652719i | 0.953647 | − | 0.300928i | \(-0.0972963\pi\) |
−0.300928 | + | 0.953647i | \(0.597296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 61.2372 | − | 61.2372i | 0.0891372 | − | 0.0891372i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 72.0000i | − | 0.104499i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −682.000 | −0.986975 | −0.493488 | − | 0.869753i | \(-0.664278\pi\) | ||||
−0.493488 | + | 0.869753i | \(0.664278\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 396.817 | + | 396.817i | 0.572608 | + | 0.572608i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −88.1816 | + | 88.1816i | −0.126516 | + | 0.126516i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 108.000i | 0.154506i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −468.000 | −0.667618 | −0.333809 | − | 0.942641i | \(-0.608334\pi\) | ||||
−0.333809 | + | 0.942641i | \(0.608334\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 73.4847 | + | 73.4847i | 0.104530 | + | 0.104530i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −793.635 | + | 793.635i | −1.12254 | + | 1.12254i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 310.000i | 0.437236i | 0.975811 | + | 0.218618i | \(0.0701548\pi\) | ||||
−0.975811 | + | 0.218618i | \(0.929845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −210.000 | −0.295359 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 431.110 | + | 431.110i | 0.604643 | + | 0.604643i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 220.454 | − | 220.454i | 0.307467 | − | 0.307467i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 180.000i | − | 0.250348i | −0.992135 | − | 0.125174i | \(-0.960051\pi\) | ||
0.992135 | − | 0.125174i | \(-0.0399489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 972.000 | 1.34813 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −218.005 | − | 218.005i | −0.301528 | − | 0.301528i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −507.044 | + | 507.044i | −0.697448 | + | 0.697448i | −0.963859 | − | 0.266412i | \(-0.914162\pi\) |
0.266412 | + | 0.963859i | \(0.414162\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 288.000 | 0.393981 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −800.983 | − | 800.983i | −1.09275 | − | 1.09275i | −0.995234 | − | 0.0975121i | \(-0.968912\pi\) |
−0.0975121 | − | 0.995234i | \(-0.531088\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 793.635 | − | 793.635i | 1.07684 | − | 1.07684i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 350.000i | 0.473613i | 0.971557 | + | 0.236806i | \(0.0761007\pi\) | ||||
−0.971557 | + | 0.236806i | \(0.923899\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 180.000 | 0.242915 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −925.907 | − | 925.907i | −1.24617 | − | 1.24617i | −0.957396 | − | 0.288778i | \(-0.906751\pi\) |
−0.288778 | − | 0.957396i | \(-0.593249\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −161.666 | + | 161.666i | −0.216421 | + | 0.216421i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 648.000i | − | 0.865154i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 338.000 | 0.450067 | 0.225033 | − | 0.974351i | \(-0.427751\pi\) | ||||
0.225033 | + | 0.974351i | \(0.427751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −418.863 | − | 418.863i | −0.556259 | − | 0.556259i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 286.590 | − | 286.590i | 0.378587 | − | 0.378587i | −0.492005 | − | 0.870592i | \(-0.663736\pi\) |
0.870592 | + | 0.492005i | \(0.163736\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 864.000i | − | 1.13834i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1278.00 | −1.67937 | −0.839685 | − | 0.543074i | \(-0.817260\pi\) | ||||
−0.839685 | + | 0.543074i | \(0.817260\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1249.24 | + | 1249.24i | 1.63727 | + | 1.63727i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 661.362 | − | 661.362i | 0.862271 | − | 0.862271i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 590.000i | 0.767230i | 0.923493 | + | 0.383615i | \(0.125321\pi\) | ||||
−0.923493 | + | 0.383615i | \(0.874679\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −708.000 | −0.918288 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −127.373 | − | 127.373i | −0.164778 | − | 0.164778i | 0.619902 | − | 0.784680i | \(-0.287173\pi\) |
−0.784680 | + | 0.619902i | \(0.787173\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −132.272 | + | 132.272i | −0.170235 | + | 0.170235i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 180.000i | 0.231065i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1296.00 | −1.65941 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 264.545 | − | 264.545i | 0.336143 | − | 0.336143i | −0.518770 | − | 0.854914i | \(-0.673610\pi\) |
0.854914 | + | 0.518770i | \(0.173610\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 648.000i | − | 0.821293i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 648.000 | 0.819216 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.6969 | + | 14.6969i | 0.0185333 | + | 0.0185333i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 200.858 | − | 200.858i | 0.252018 | − | 0.252018i | −0.569780 | − | 0.821797i | \(-0.692971\pi\) |
0.821797 | + | 0.569780i | \(0.192971\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 432.000i | − | 0.540676i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −270.000 | −0.337079 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 793.635 | + | 793.635i | 0.988337 | + | 0.988337i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 630.000i | − | 0.778739i | −0.921082 | − | 0.389370i | \(-0.872693\pi\) | ||
0.921082 | − | 0.389370i | \(-0.127307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 218.000 | 0.268804 | 0.134402 | − | 0.990927i | \(-0.457089\pi\) | ||||
0.134402 | + | 0.990927i | \(0.457089\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 585.428 | + | 585.428i | 0.720084 | + | 0.720084i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 293.939 | − | 293.939i | 0.359778 | − | 0.359778i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 324.000i | 0.395604i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 432.000 | 0.526188 | 0.263094 | − | 0.964770i | \(-0.415257\pi\) | ||||
0.263094 | + | 0.964770i | \(0.415257\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 360.075 | + | 360.075i | 0.437515 | + | 0.437515i | 0.891175 | − | 0.453660i | \(-0.149882\pi\) |
−0.453660 | + | 0.891175i | \(0.649882\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 876.917 | − | 876.917i | 1.06036 | − | 1.06036i | 0.0623022 | − | 0.998057i | \(-0.480156\pi\) |
0.998057 | − | 0.0623022i | \(-0.0198443\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 70.0000i | 0.0844391i | 0.999108 | + | 0.0422195i | \(0.0134429\pi\) | ||||
−0.999108 | + | 0.0422195i | \(0.986557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −198.000 | −0.238267 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −289.040 | − | 289.040i | −0.346987 | − | 0.346987i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 80.8332 | − | 80.8332i | 0.0965749 | − | 0.0965749i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 540.000i | 0.643623i | 0.946804 | + | 0.321812i | \(0.104292\pi\) | ||||
−0.946804 | + | 0.321812i | \(0.895708\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 198.409 | + | 198.409i | 0.235360 | + | 0.235360i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1491.74 | − | 1491.74i | 1.76120 | − | 1.76120i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 612.000i | 0.720848i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 288.000 | 0.338425 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 815.680 | + | 815.680i | 0.956249 | + | 0.956249i | 0.999082 | − | 0.0428336i | \(-0.0136385\pi\) |
−0.0428336 | + | 0.999082i | \(0.513639\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 298.838 | − | 298.838i | 0.348702 | − | 0.348702i | −0.510924 | − | 0.859626i | \(-0.670697\pi\) |
0.859626 | + | 0.510924i | \(0.170697\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 310.000i | 0.360885i | 0.983586 | + | 0.180442i | \(0.0577529\pi\) | ||||
−0.983586 | + | 0.180442i | \(0.942247\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −324.000 | −0.376307 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 225.353 | + | 225.353i | 0.261128 | + | 0.261128i | 0.825512 | − | 0.564385i | \(-0.190886\pi\) |
−0.564385 | + | 0.825512i | \(0.690886\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −295.164 | + | 295.164i | −0.340442 | + | 0.340442i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1260.00i | 1.44994i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 648.000 | 0.743972 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 308.636 | + | 308.636i | 0.353535 | + | 0.353535i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 213.106 | − | 213.106i | 0.242994 | − | 0.242994i | −0.575094 | − | 0.818088i | \(-0.695034\pi\) |
0.818088 | + | 0.575094i | \(0.195034\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 912.000i | − | 1.03754i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1062.00 | 1.20545 | 0.602724 | − | 0.797950i | \(-0.294082\pi\) | ||||
0.602724 | + | 0.797950i | \(0.294082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −117.576 | − | 117.576i | −0.133155 | − | 0.133155i | 0.637388 | − | 0.770543i | \(-0.280015\pi\) |
−0.770543 | + | 0.637388i | \(0.780015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 509.494 | − | 509.494i | 0.574401 | − | 0.574401i | −0.358954 | − | 0.933355i | \(-0.616867\pi\) |
0.933355 | + | 0.358954i | \(0.116867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 108.000i | − | 0.121485i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −162.000 | −0.181818 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −440.908 | − | 440.908i | −0.493738 | − | 0.493738i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 352.727 | − | 352.727i | 0.393229 | − | 0.393229i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0000 | −0.0532741 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 529.090 | + | 529.090i | 0.585924 | + | 0.585924i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 411.514 | − | 411.514i | 0.453709 | − | 0.453709i | −0.442874 | − | 0.896584i | \(-0.646041\pi\) |
0.896584 | + | 0.442874i | \(0.146041\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 324.000i | − | 0.356436i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −792.000 | −0.869374 | −0.434687 | − | 0.900582i | \(-0.643141\pi\) | ||||
−0.434687 | + | 0.900582i | \(0.643141\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 969.998 | + | 969.998i | 1.06243 | + | 1.06243i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 132.272 | − | 132.272i | 0.144245 | − | 0.144245i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 430.000i | − | 0.467900i | −0.972249 | − | 0.233950i | \(-0.924835\pi\) | ||
0.972249 | − | 0.233950i | \(-0.0751652\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −972.000 | −1.05537 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −529.090 | − | 529.090i | −0.573228 | − | 0.573228i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −198.409 | + | 198.409i | −0.214033 | + | 0.214033i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1530.00i | 1.64693i | 0.567365 | + | 0.823466i | \(0.307963\pi\) | ||||
−0.567365 | + | 0.823466i | \(0.692037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −590.000 | −0.633727 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −308.636 | − | 308.636i | −0.330799 | − | 0.330799i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 323.333 | − | 323.333i | 0.345072 | − | 0.345072i | −0.513198 | − | 0.858270i | \(-0.671539\pi\) |
0.858270 | + | 0.513198i | \(0.171539\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 288.000i | 0.306709i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1152.00 | 1.22423 | 0.612115 | − | 0.790769i | \(-0.290319\pi\) | ||||
0.612115 | + | 0.790769i | \(0.290319\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 352.727 | + | 352.727i | 0.374047 | + | 0.374047i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −739.746 | + | 739.746i | −0.781147 | + | 0.781147i | −0.980024 | − | 0.198878i | \(-0.936270\pi\) |
0.198878 | + | 0.980024i | \(0.436270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 648.000i | 0.682824i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 672.000 | 0.706625 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.0908 | + | 44.0908i | 0.0462653 | + | 0.0462653i | 0.729861 | − | 0.683596i | \(-0.239585\pi\) |
−0.683596 | + | 0.729861i | \(0.739585\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2088.00i | 2.17727i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −477.000 | −0.496358 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 132.272 | + | 132.272i | 0.137355 | + | 0.137355i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −727.498 | + | 727.498i | −0.752325 | + | 0.752325i | −0.974913 | − | 0.222588i | \(-0.928550\pi\) |
0.222588 | + | 0.974913i | \(0.428550\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 120.000i | − | 0.123839i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1278.00 | 1.31617 | 0.658084 | − | 0.752944i | \(-0.271367\pi\) | ||||
0.658084 | + | 0.752944i | \(0.271367\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1249.24 | + | 1249.24i | 1.28391 | + | 1.28391i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 396.817 | − | 396.817i | 0.406159 | − | 0.406159i | −0.474238 | − | 0.880397i | \(-0.657276\pi\) |
0.880397 | + | 0.474238i | \(0.157276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1620.00i | 1.65475i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −510.000 | −0.519878 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −827.928 | − | 827.928i | −0.842246 | − | 0.842246i | 0.146905 | − | 0.989151i | \(-0.453069\pi\) |
−0.989151 | + | 0.146905i | \(0.953069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 793.635 | − | 793.635i | 0.804088 | − | 0.804088i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1152.00i | − | 1.16481i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 118.000 | 0.119072 | 0.0595358 | − | 0.998226i | \(-0.481038\pi\) | ||||
0.0595358 | + | 0.998226i | \(0.481038\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 511.943 | + | 511.943i | 0.515552 | + | 0.515552i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −815.680 | + | 815.680i | −0.818134 | + | 0.818134i | −0.985838 | − | 0.167703i | \(-0.946365\pi\) |
0.167703 | + | 0.985838i | \(0.446365\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 54.0000i | − | 0.0540541i |
(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 | 1200.3.bg.j.193.2 | 4 | ||
4.3 | odd | 2 | 75.3.f.a.43.1 | yes | 4 | ||
5.2 | odd | 4 | inner | 1200.3.bg.j.1057.2 | 4 | ||
5.3 | odd | 4 | inner | 1200.3.bg.j.1057.1 | 4 | ||
5.4 | even | 2 | inner | 1200.3.bg.j.193.1 | 4 | ||
12.11 | even | 2 | 225.3.g.f.118.2 | 4 | |||
20.3 | even | 4 | 75.3.f.a.7.2 | yes | 4 | ||
20.7 | even | 4 | 75.3.f.a.7.1 | ✓ | 4 | ||
20.19 | odd | 2 | 75.3.f.a.43.2 | yes | 4 | ||
60.23 | odd | 4 | 225.3.g.f.82.1 | 4 | |||
60.47 | odd | 4 | 225.3.g.f.82.2 | 4 | |||
60.59 | even | 2 | 225.3.g.f.118.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.f.a.7.1 | ✓ | 4 | 20.7 | even | 4 | ||
75.3.f.a.7.2 | yes | 4 | 20.3 | even | 4 | ||
75.3.f.a.43.1 | yes | 4 | 4.3 | odd | 2 | ||
75.3.f.a.43.2 | yes | 4 | 20.19 | odd | 2 | ||
225.3.g.f.82.1 | 4 | 60.23 | odd | 4 | |||
225.3.g.f.82.2 | 4 | 60.47 | odd | 4 | |||
225.3.g.f.118.1 | 4 | 60.59 | even | 2 | |||
225.3.g.f.118.2 | 4 | 12.11 | even | 2 | |||
1200.3.bg.j.193.1 | 4 | 5.4 | even | 2 | inner | ||
1200.3.bg.j.193.2 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.j.1057.1 | 4 | 5.3 | odd | 4 | inner | ||
1200.3.bg.j.1057.2 | 4 | 5.2 | odd | 4 | inner |