Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(506,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.506");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 506.1 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.506 |
Dual form | 845.2.c.c.506.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.61803i | − 1.14412i | −0.820211 | − | 0.572061i | \(-0.806144\pi\) | ||||
0.820211 | − | 0.572061i | \(-0.193856\pi\) | |||||||
\(3\) | −2.23607 | −1.29099 | −0.645497 | − | 0.763763i | \(-0.723350\pi\) | ||||
−0.645497 | + | 0.763763i | \(0.723350\pi\) | |||||||
\(4\) | −0.618034 | −0.309017 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | 3.61803i | 1.47706i | ||||||||
\(7\) | − 0.236068i | − 0.0892253i | −0.999004 | − | 0.0446127i | \(-0.985795\pi\) | ||||
0.999004 | − | 0.0446127i | \(-0.0142054\pi\) | |||||||
\(8\) | − 2.23607i | − 0.790569i | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | −1.61803 | −0.511667 | ||||||||
\(11\) | 4.23607i | 1.27722i | 0.769529 | + | 0.638611i | \(0.220491\pi\) | ||||
−0.769529 | + | 0.638611i | \(0.779509\pi\) | |||||||
\(12\) | 1.38197 | 0.398939 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −0.381966 | −0.102085 | ||||||||
\(15\) | 2.23607i | 0.577350i | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | −5.47214 | −1.32719 | −0.663594 | − | 0.748093i | \(-0.730970\pi\) | ||||
−0.663594 | + | 0.748093i | \(0.730970\pi\) | |||||||
\(18\) | − 3.23607i | − 0.762749i | ||||||||
\(19\) | 0.236068i | 0.0541577i | 0.999633 | + | 0.0270789i | \(0.00862052\pi\) | ||||
−0.999633 | + | 0.0270789i | \(0.991379\pi\) | |||||||
\(20\) | 0.618034i | 0.138197i | ||||||||
\(21\) | 0.527864i | 0.115189i | ||||||||
\(22\) | 6.85410 | 1.46130 | ||||||||
\(23\) | −8.23607 | −1.71734 | −0.858669 | − | 0.512530i | \(-0.828708\pi\) | ||||
−0.858669 | + | 0.512530i | \(0.828708\pi\) | |||||||
\(24\) | 5.00000i | 1.02062i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 0.145898i | 0.0275721i | ||||||||
\(29\) | 1.47214 | 0.273369 | 0.136684 | − | 0.990615i | \(-0.456355\pi\) | ||||
0.136684 | + | 0.990615i | \(0.456355\pi\) | |||||||
\(30\) | 3.61803 | 0.660560 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 3.38197i | 0.597853i | ||||||||
\(33\) | − 9.47214i | − 1.64889i | ||||||||
\(34\) | 8.85410i | 1.51847i | ||||||||
\(35\) | −0.236068 | −0.0399028 | ||||||||
\(36\) | −1.23607 | −0.206011 | ||||||||
\(37\) | 3.00000i | 0.493197i | 0.969118 | + | 0.246598i | \(0.0793129\pi\) | ||||
−0.969118 | + | 0.246598i | \(0.920687\pi\) | |||||||
\(38\) | 0.381966 | 0.0619631 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.23607 | −0.353553 | ||||||||
\(41\) | 5.94427i | 0.928339i | 0.885746 | + | 0.464170i | \(0.153647\pi\) | ||||
−0.885746 | + | 0.464170i | \(0.846353\pi\) | |||||||
\(42\) | 0.854102 | 0.131791 | ||||||||
\(43\) | 1.76393 | 0.268997 | 0.134499 | − | 0.990914i | \(-0.457058\pi\) | ||||
0.134499 | + | 0.990914i | \(0.457058\pi\) | |||||||
\(44\) | − 2.61803i | − 0.394683i | ||||||||
\(45\) | − 2.00000i | − 0.298142i | ||||||||
\(46\) | 13.3262i | 1.96485i | ||||||||
\(47\) | 12.9443i | 1.88812i | 0.329779 | + | 0.944058i | \(0.393026\pi\) | ||||
−0.329779 | + | 0.944058i | \(0.606974\pi\) | |||||||
\(48\) | 10.8541 | 1.56665 | ||||||||
\(49\) | 6.94427 | 0.992039 | ||||||||
\(50\) | 1.61803i | 0.228825i | ||||||||
\(51\) | 12.2361 | 1.71339 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | − 3.61803i | − 0.492352i | ||||||||
\(55\) | 4.23607 | 0.571191 | ||||||||
\(56\) | −0.527864 | −0.0705388 | ||||||||
\(57\) | − 0.527864i | − 0.0699173i | ||||||||
\(58\) | − 2.38197i | − 0.312767i | ||||||||
\(59\) | 12.7082i | 1.65447i | 0.561858 | + | 0.827234i | \(0.310087\pi\) | ||||
−0.561858 | + | 0.827234i | \(0.689913\pi\) | |||||||
\(60\) | − 1.38197i | − 0.178411i | ||||||||
\(61\) | −12.4164 | −1.58976 | −0.794879 | − | 0.606768i | \(-0.792466\pi\) | ||||
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 0.472136i | − 0.0594835i | ||||||||
\(64\) | −4.23607 | −0.529508 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −15.3262 | −1.88653 | ||||||||
\(67\) | − 10.7082i | − 1.30822i | −0.756401 | − | 0.654108i | \(-0.773044\pi\) | ||||
0.756401 | − | 0.654108i | \(-0.226956\pi\) | |||||||
\(68\) | 3.38197 | 0.410124 | ||||||||
\(69\) | 18.4164 | 2.21707 | ||||||||
\(70\) | 0.381966i | 0.0456537i | ||||||||
\(71\) | 1.76393i | 0.209340i | 0.994507 | + | 0.104670i | \(0.0333787\pi\) | ||||
−0.994507 | + | 0.104670i | \(0.966621\pi\) | |||||||
\(72\) | − 4.47214i | − 0.527046i | ||||||||
\(73\) | − 6.00000i | − 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 4.85410 | 0.564278 | ||||||||
\(75\) | 2.23607 | 0.258199 | ||||||||
\(76\) | − 0.145898i | − 0.0167357i | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 4.85410i | 0.542705i | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 9.61803 | 1.06213 | ||||||||
\(83\) | 8.94427i | 0.981761i | 0.871227 | + | 0.490881i | \(0.163325\pi\) | ||||
−0.871227 | + | 0.490881i | \(0.836675\pi\) | |||||||
\(84\) | − 0.326238i | − 0.0355955i | ||||||||
\(85\) | 5.47214i | 0.593536i | ||||||||
\(86\) | − 2.85410i | − 0.307766i | ||||||||
\(87\) | −3.29180 | −0.352918 | ||||||||
\(88\) | 9.47214 | 1.00973 | ||||||||
\(89\) | − 9.00000i | − 0.953998i | −0.878904 | − | 0.476999i | \(-0.841725\pi\) | ||||
0.878904 | − | 0.476999i | \(-0.158275\pi\) | |||||||
\(90\) | −3.23607 | −0.341112 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.09017 | 0.530687 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 20.9443 | 2.16024 | ||||||||
\(95\) | 0.236068 | 0.0242201 | ||||||||
\(96\) | − 7.56231i | − 0.771825i | ||||||||
\(97\) | − 5.47214i | − 0.555611i | −0.960637 | − | 0.277806i | \(-0.910393\pi\) | ||||
0.960637 | − | 0.277806i | \(-0.0896071\pi\) | |||||||
\(98\) | − 11.2361i | − 1.13501i | ||||||||
\(99\) | 8.47214i | 0.851482i | ||||||||
\(100\) | 0.618034 | 0.0618034 | ||||||||
\(101\) | −9.47214 | −0.942513 | −0.471256 | − | 0.881996i | \(-0.656199\pi\) | ||||
−0.471256 | + | 0.881996i | \(0.656199\pi\) | |||||||
\(102\) | − 19.7984i | − 1.96033i | ||||||||
\(103\) | 4.94427 | 0.487174 | 0.243587 | − | 0.969879i | \(-0.421676\pi\) | ||||
0.243587 | + | 0.969879i | \(0.421676\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.527864 | 0.0515143 | ||||||||
\(106\) | − 9.70820i | − 0.942944i | ||||||||
\(107\) | −10.2361 | −0.989558 | −0.494779 | − | 0.869019i | \(-0.664751\pi\) | ||||
−0.494779 | + | 0.869019i | \(0.664751\pi\) | |||||||
\(108\) | −1.38197 | −0.132980 | ||||||||
\(109\) | 2.00000i | 0.191565i | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) | ||||
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | − 6.85410i | − 0.653513i | ||||||||
\(111\) | − 6.70820i | − 0.636715i | ||||||||
\(112\) | 1.14590i | 0.108277i | ||||||||
\(113\) | −7.47214 | −0.702919 | −0.351460 | − | 0.936203i | \(-0.614315\pi\) | ||||
−0.351460 | + | 0.936203i | \(0.614315\pi\) | |||||||
\(114\) | −0.854102 | −0.0799940 | ||||||||
\(115\) | 8.23607i | 0.768017i | ||||||||
\(116\) | −0.909830 | −0.0844756 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 20.5623 | 1.89291 | ||||||||
\(119\) | 1.29180i | 0.118419i | ||||||||
\(120\) | 5.00000 | 0.456435 | ||||||||
\(121\) | −6.94427 | −0.631297 | ||||||||
\(122\) | 20.0902i | 1.81888i | ||||||||
\(123\) | − 13.2918i | − 1.19848i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −0.763932 | −0.0680565 | ||||||||
\(127\) | −0.236068 | −0.0209476 | −0.0104738 | − | 0.999945i | \(-0.503334\pi\) | ||||
−0.0104738 | + | 0.999945i | \(0.503334\pi\) | |||||||
\(128\) | 13.6180i | 1.20368i | ||||||||
\(129\) | −3.94427 | −0.347274 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 5.85410i | 0.509534i | ||||||||
\(133\) | 0.0557281 | 0.00483224 | ||||||||
\(134\) | −17.3262 | −1.49676 | ||||||||
\(135\) | − 2.23607i | − 0.192450i | ||||||||
\(136\) | 12.2361i | 1.04923i | ||||||||
\(137\) | − 7.47214i | − 0.638388i | −0.947689 | − | 0.319194i | \(-0.896588\pi\) | ||||
0.947689 | − | 0.319194i | \(-0.103412\pi\) | |||||||
\(138\) | − 29.7984i | − 2.53661i | ||||||||
\(139\) | −3.29180 | −0.279206 | −0.139603 | − | 0.990208i | \(-0.544583\pi\) | ||||
−0.139603 | + | 0.990208i | \(0.544583\pi\) | |||||||
\(140\) | 0.145898 | 0.0123306 | ||||||||
\(141\) | − 28.9443i | − 2.43755i | ||||||||
\(142\) | 2.85410 | 0.239511 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −9.70820 | −0.809017 | ||||||||
\(145\) | − 1.47214i | − 0.122254i | ||||||||
\(146\) | −9.70820 | −0.803457 | ||||||||
\(147\) | −15.5279 | −1.28072 | ||||||||
\(148\) | − 1.85410i | − 0.152406i | ||||||||
\(149\) | − 13.4721i | − 1.10368i | −0.833950 | − | 0.551840i | \(-0.813926\pi\) | ||||
0.833950 | − | 0.551840i | \(-0.186074\pi\) | |||||||
\(150\) | − 3.61803i | − 0.295411i | ||||||||
\(151\) | 8.00000i | 0.651031i | 0.945537 | + | 0.325515i | \(0.105538\pi\) | ||||
−0.945537 | + | 0.325515i | \(0.894462\pi\) | |||||||
\(152\) | 0.527864 | 0.0428154 | ||||||||
\(153\) | −10.9443 | −0.884792 | ||||||||
\(154\) | − 1.61803i | − 0.130385i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.0000 | −1.43656 | −0.718278 | − | 0.695756i | \(-0.755069\pi\) | ||||
−0.718278 | + | 0.695756i | \(0.755069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.4164 | −1.06399 | ||||||||
\(160\) | 3.38197 | 0.267368 | ||||||||
\(161\) | 1.94427i | 0.153230i | ||||||||
\(162\) | 17.7984i | 1.39837i | ||||||||
\(163\) | 1.29180i | 0.101181i | 0.998719 | + | 0.0505906i | \(0.0161104\pi\) | ||||
−0.998719 | + | 0.0505906i | \(0.983890\pi\) | |||||||
\(164\) | − 3.67376i | − 0.286873i | ||||||||
\(165\) | −9.47214 | −0.737405 | ||||||||
\(166\) | 14.4721 | 1.12326 | ||||||||
\(167\) | 5.18034i | 0.400867i | 0.979707 | + | 0.200433i | \(0.0642350\pi\) | ||||
−0.979707 | + | 0.200433i | \(0.935765\pi\) | |||||||
\(168\) | 1.18034 | 0.0910652 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 8.85410 | 0.679079 | ||||||||
\(171\) | 0.472136i | 0.0361051i | ||||||||
\(172\) | −1.09017 | −0.0831247 | ||||||||
\(173\) | −16.8885 | −1.28401 | −0.642006 | − | 0.766700i | \(-0.721898\pi\) | ||||
−0.642006 | + | 0.766700i | \(0.721898\pi\) | |||||||
\(174\) | 5.32624i | 0.403781i | ||||||||
\(175\) | 0.236068i | 0.0178451i | ||||||||
\(176\) | − 20.5623i | − 1.54994i | ||||||||
\(177\) | − 28.4164i | − 2.13591i | ||||||||
\(178\) | −14.5623 | −1.09149 | ||||||||
\(179\) | 3.76393 | 0.281329 | 0.140665 | − | 0.990057i | \(-0.455076\pi\) | ||||
0.140665 | + | 0.990057i | \(0.455076\pi\) | |||||||
\(180\) | 1.23607i | 0.0921311i | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 27.7639 | 2.05237 | ||||||||
\(184\) | 18.4164i | 1.35768i | ||||||||
\(185\) | 3.00000 | 0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 23.1803i | − 1.69511i | ||||||||
\(188\) | − 8.00000i | − 0.583460i | ||||||||
\(189\) | − 0.527864i | − 0.0383965i | ||||||||
\(190\) | − 0.381966i | − 0.0277107i | ||||||||
\(191\) | −4.81966 | −0.348738 | −0.174369 | − | 0.984680i | \(-0.555789\pi\) | ||||
−0.174369 | + | 0.984680i | \(0.555789\pi\) | |||||||
\(192\) | 9.47214 | 0.683593 | ||||||||
\(193\) | 5.47214i | 0.393893i | 0.980414 | + | 0.196946i | \(0.0631025\pi\) | ||||
−0.980414 | + | 0.196946i | \(0.936897\pi\) | |||||||
\(194\) | −8.85410 | −0.635687 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.29180 | −0.306557 | ||||||||
\(197\) | − 3.00000i | − 0.213741i | −0.994273 | − | 0.106871i | \(-0.965917\pi\) | ||||
0.994273 | − | 0.106871i | \(-0.0340831\pi\) | |||||||
\(198\) | 13.7082 | 0.974200 | ||||||||
\(199\) | 14.7082 | 1.04264 | 0.521318 | − | 0.853362i | \(-0.325440\pi\) | ||||
0.521318 | + | 0.853362i | \(0.325440\pi\) | |||||||
\(200\) | 2.23607i | 0.158114i | ||||||||
\(201\) | 23.9443i | 1.68890i | ||||||||
\(202\) | 15.3262i | 1.07835i | ||||||||
\(203\) | − 0.347524i | − 0.0243914i | ||||||||
\(204\) | −7.56231 | −0.529467 | ||||||||
\(205\) | 5.94427 | 0.415166 | ||||||||
\(206\) | − 8.00000i | − 0.557386i | ||||||||
\(207\) | −16.4721 | −1.14489 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | − 0.854102i | − 0.0589386i | ||||||||
\(211\) | 9.18034 | 0.632001 | 0.316000 | − | 0.948759i | \(-0.397660\pi\) | ||||
0.316000 | + | 0.948759i | \(0.397660\pi\) | |||||||
\(212\) | −3.70820 | −0.254680 | ||||||||
\(213\) | − 3.94427i | − 0.270257i | ||||||||
\(214\) | 16.5623i | 1.13218i | ||||||||
\(215\) | − 1.76393i | − 0.120299i | ||||||||
\(216\) | − 5.00000i | − 0.340207i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.23607 | 0.219174 | ||||||||
\(219\) | 13.4164i | 0.906597i | ||||||||
\(220\) | −2.61803 | −0.176508 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.8541 | −0.728480 | ||||||||
\(223\) | 12.7082i | 0.851004i | 0.904957 | + | 0.425502i | \(0.139903\pi\) | ||||
−0.904957 | + | 0.425502i | \(0.860097\pi\) | |||||||
\(224\) | 0.798374 | 0.0533436 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | 12.0902i | 0.804226i | ||||||||
\(227\) | 1.76393i | 0.117076i | 0.998285 | + | 0.0585381i | \(0.0186439\pi\) | ||||
−0.998285 | + | 0.0585381i | \(0.981356\pi\) | |||||||
\(228\) | 0.326238i | 0.0216056i | ||||||||
\(229\) | − 19.8885i | − 1.31427i | −0.753772 | − | 0.657136i | \(-0.771768\pi\) | ||||
0.753772 | − | 0.657136i | \(-0.228232\pi\) | |||||||
\(230\) | 13.3262 | 0.878706 | ||||||||
\(231\) | −2.23607 | −0.147122 | ||||||||
\(232\) | − 3.29180i | − 0.216117i | ||||||||
\(233\) | −19.8885 | −1.30294 | −0.651471 | − | 0.758674i | \(-0.725848\pi\) | ||||
−0.651471 | + | 0.758674i | \(0.725848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.9443 | 0.844391 | ||||||||
\(236\) | − 7.85410i | − 0.511258i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.09017 | 0.135486 | ||||||||
\(239\) | − 9.88854i | − 0.639637i | −0.947479 | − | 0.319818i | \(-0.896378\pi\) | ||||
0.947479 | − | 0.319818i | \(-0.103622\pi\) | |||||||
\(240\) | − 10.8541i | − 0.700629i | ||||||||
\(241\) | 15.0000i | 0.966235i | 0.875556 | + | 0.483117i | \(0.160496\pi\) | ||||
−0.875556 | + | 0.483117i | \(0.839504\pi\) | |||||||
\(242\) | 11.2361i | 0.722282i | ||||||||
\(243\) | 17.8885 | 1.14755 | ||||||||
\(244\) | 7.67376 | 0.491262 | ||||||||
\(245\) | − 6.94427i | − 0.443653i | ||||||||
\(246\) | −21.5066 | −1.37121 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − 20.0000i | − 1.26745i | ||||||||
\(250\) | 1.61803 | 0.102333 | ||||||||
\(251\) | −15.7639 | −0.995011 | −0.497505 | − | 0.867461i | \(-0.665750\pi\) | ||||
−0.497505 | + | 0.867461i | \(0.665750\pi\) | |||||||
\(252\) | 0.291796i | 0.0183814i | ||||||||
\(253\) | − 34.8885i | − 2.19342i | ||||||||
\(254\) | 0.381966i | 0.0239667i | ||||||||
\(255\) | − 12.2361i | − 0.766252i | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | −8.52786 | −0.531954 | −0.265977 | − | 0.963979i | \(-0.585694\pi\) | ||||
−0.265977 | + | 0.963979i | \(0.585694\pi\) | |||||||
\(258\) | 6.38197i | 0.397324i | ||||||||
\(259\) | 0.708204 | 0.0440057 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.94427 | 0.182246 | ||||||||
\(262\) | 19.4164i | 1.19955i | ||||||||
\(263\) | 8.23607 | 0.507858 | 0.253929 | − | 0.967223i | \(-0.418277\pi\) | ||||
0.253929 | + | 0.967223i | \(0.418277\pi\) | |||||||
\(264\) | −21.1803 | −1.30356 | ||||||||
\(265\) | − 6.00000i | − 0.368577i | ||||||||
\(266\) | − 0.0901699i | − 0.00552867i | ||||||||
\(267\) | 20.1246i | 1.23161i | ||||||||
\(268\) | 6.61803i | 0.404261i | ||||||||
\(269\) | −15.4721 | −0.943353 | −0.471676 | − | 0.881772i | \(-0.656351\pi\) | ||||
−0.471676 | + | 0.881772i | \(0.656351\pi\) | |||||||
\(270\) | −3.61803 | −0.220187 | ||||||||
\(271\) | 14.7082i | 0.893460i | 0.894669 | + | 0.446730i | \(0.147411\pi\) | ||||
−0.894669 | + | 0.446730i | \(0.852589\pi\) | |||||||
\(272\) | 26.5623 | 1.61058 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0902 | −0.730394 | ||||||||
\(275\) | − 4.23607i | − 0.255445i | ||||||||
\(276\) | −11.3820 | −0.685114 | ||||||||
\(277\) | 18.8885 | 1.13490 | 0.567451 | − | 0.823407i | \(-0.307930\pi\) | ||||
0.567451 | + | 0.823407i | \(0.307930\pi\) | |||||||
\(278\) | 5.32624i | 0.319447i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.527864i | 0.0315459i | ||||||||
\(281\) | 19.8885i | 1.18645i | 0.805036 | + | 0.593226i | \(0.202146\pi\) | ||||
−0.805036 | + | 0.593226i | \(0.797854\pi\) | |||||||
\(282\) | −46.8328 | −2.78885 | ||||||||
\(283\) | −2.70820 | −0.160986 | −0.0804930 | − | 0.996755i | \(-0.525649\pi\) | ||||
−0.0804930 | + | 0.996755i | \(0.525649\pi\) | |||||||
\(284\) | − 1.09017i | − 0.0646897i | ||||||||
\(285\) | −0.527864 | −0.0312680 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.40325 | 0.0828314 | ||||||||
\(288\) | 6.76393i | 0.398569i | ||||||||
\(289\) | 12.9443 | 0.761428 | ||||||||
\(290\) | −2.38197 | −0.139874 | ||||||||
\(291\) | 12.2361i | 0.717291i | ||||||||
\(292\) | 3.70820i | 0.217006i | ||||||||
\(293\) | − 12.0557i | − 0.704303i | −0.935943 | − | 0.352152i | \(-0.885450\pi\) | ||||
0.935943 | − | 0.352152i | \(-0.114550\pi\) | |||||||
\(294\) | 25.1246i | 1.46530i | ||||||||
\(295\) | 12.7082 | 0.739900 | ||||||||
\(296\) | 6.70820 | 0.389906 | ||||||||
\(297\) | 9.47214i | 0.549629i | ||||||||
\(298\) | −21.7984 | −1.26275 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.38197 | −0.0797878 | ||||||||
\(301\) | − 0.416408i | − 0.0240014i | ||||||||
\(302\) | 12.9443 | 0.744859 | ||||||||
\(303\) | 21.1803 | 1.21678 | ||||||||
\(304\) | − 1.14590i | − 0.0657218i | ||||||||
\(305\) | 12.4164i | 0.710961i | ||||||||
\(306\) | 17.7082i | 1.01231i | ||||||||
\(307\) | 7.05573i | 0.402692i | 0.979520 | + | 0.201346i | \(0.0645315\pi\) | ||||
−0.979520 | + | 0.201346i | \(0.935468\pi\) | |||||||
\(308\) | −0.618034 | −0.0352158 | ||||||||
\(309\) | −11.0557 | −0.628938 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.8885 | −1.80245 | −0.901224 | − | 0.433355i | \(-0.857330\pi\) | ||||
−0.901224 | + | 0.433355i | \(0.857330\pi\) | |||||||
\(314\) | 29.1246i | 1.64360i | ||||||||
\(315\) | −0.472136 | −0.0266018 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 23.8885i | − 1.34171i | −0.741587 | − | 0.670857i | \(-0.765926\pi\) | ||||
0.741587 | − | 0.670857i | \(-0.234074\pi\) | |||||||
\(318\) | 21.7082i | 1.21734i | ||||||||
\(319\) | 6.23607i | 0.349153i | ||||||||
\(320\) | 4.23607i | 0.236803i | ||||||||
\(321\) | 22.8885 | 1.27751 | ||||||||
\(322\) | 3.14590 | 0.175314 | ||||||||
\(323\) | − 1.29180i | − 0.0718775i | ||||||||
\(324\) | 6.79837 | 0.377687 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.09017 | 0.115764 | ||||||||
\(327\) | − 4.47214i | − 0.247310i | ||||||||
\(328\) | 13.2918 | 0.733917 | ||||||||
\(329\) | 3.05573 | 0.168468 | ||||||||
\(330\) | 15.3262i | 0.843682i | ||||||||
\(331\) | − 25.6525i | − 1.40999i | −0.709213 | − | 0.704994i | \(-0.750950\pi\) | ||||
0.709213 | − | 0.704994i | \(-0.249050\pi\) | |||||||
\(332\) | − 5.52786i | − 0.303381i | ||||||||
\(333\) | 6.00000i | 0.328798i | ||||||||
\(334\) | 8.38197 | 0.458641 | ||||||||
\(335\) | −10.7082 | −0.585052 | ||||||||
\(336\) | − 2.56231i | − 0.139785i | ||||||||
\(337\) | −27.8885 | −1.51919 | −0.759593 | − | 0.650399i | \(-0.774602\pi\) | ||||
−0.759593 | + | 0.650399i | \(0.774602\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.7082 | 0.907465 | ||||||||
\(340\) | − 3.38197i | − 0.183413i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.763932 | 0.0413087 | ||||||||
\(343\) | − 3.29180i | − 0.177740i | ||||||||
\(344\) | − 3.94427i | − 0.212661i | ||||||||
\(345\) | − 18.4164i | − 0.991506i | ||||||||
\(346\) | 27.3262i | 1.46907i | ||||||||
\(347\) | 17.2918 | 0.928272 | 0.464136 | − | 0.885764i | \(-0.346365\pi\) | ||||
0.464136 | + | 0.885764i | \(0.346365\pi\) | |||||||
\(348\) | 2.03444 | 0.109058 | ||||||||
\(349\) | − 24.4164i | − 1.30698i | −0.756935 | − | 0.653490i | \(-0.773304\pi\) | ||||
0.756935 | − | 0.653490i | \(-0.226696\pi\) | |||||||
\(350\) | 0.381966 | 0.0204169 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −14.3262 | −0.763591 | ||||||||
\(353\) | 10.5279i | 0.560342i | 0.959950 | + | 0.280171i | \(0.0903911\pi\) | ||||
−0.959950 | + | 0.280171i | \(0.909609\pi\) | |||||||
\(354\) | −45.9787 | −2.44374 | ||||||||
\(355\) | 1.76393 | 0.0936198 | ||||||||
\(356\) | 5.56231i | 0.294802i | ||||||||
\(357\) | − 2.88854i | − 0.152878i | ||||||||
\(358\) | − 6.09017i | − 0.321875i | ||||||||
\(359\) | − 17.8885i | − 0.944121i | −0.881566 | − | 0.472061i | \(-0.843510\pi\) | ||||
0.881566 | − | 0.472061i | \(-0.156490\pi\) | |||||||
\(360\) | −4.47214 | −0.235702 | ||||||||
\(361\) | 18.9443 | 0.997067 | ||||||||
\(362\) | 9.70820i | 0.510252i | ||||||||
\(363\) | 15.5279 | 0.815001 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | − 44.9230i | − 2.34816i | ||||||||
\(367\) | −25.6525 | −1.33905 | −0.669524 | − | 0.742790i | \(-0.733502\pi\) | ||||
−0.669524 | + | 0.742790i | \(0.733502\pi\) | |||||||
\(368\) | 39.9787 | 2.08403 | ||||||||
\(369\) | 11.8885i | 0.618893i | ||||||||
\(370\) | − 4.85410i | − 0.252353i | ||||||||
\(371\) | − 1.41641i | − 0.0735362i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0557 | 0.520666 | 0.260333 | − | 0.965519i | \(-0.416168\pi\) | ||||
0.260333 | + | 0.965519i | \(0.416168\pi\) | |||||||
\(374\) | −37.5066 | −1.93942 | ||||||||
\(375\) | − 2.23607i | − 0.115470i | ||||||||
\(376\) | 28.9443 | 1.49269 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −0.854102 | −0.0439303 | ||||||||
\(379\) | − 33.1803i | − 1.70436i | −0.523249 | − | 0.852180i | \(-0.675280\pi\) | ||||
0.523249 | − | 0.852180i | \(-0.324720\pi\) | |||||||
\(380\) | −0.145898 | −0.00748441 | ||||||||
\(381\) | 0.527864 | 0.0270433 | ||||||||
\(382\) | 7.79837i | 0.399000i | ||||||||
\(383\) | 0.236068i | 0.0120625i | 0.999982 | + | 0.00603126i | \(0.00191982\pi\) | ||||
−0.999982 | + | 0.00603126i | \(0.998080\pi\) | |||||||
\(384\) | − 30.4508i | − 1.55394i | ||||||||
\(385\) | − 1.00000i | − 0.0509647i | ||||||||
\(386\) | 8.85410 | 0.450662 | ||||||||
\(387\) | 3.52786 | 0.179331 | ||||||||
\(388\) | 3.38197i | 0.171693i | ||||||||
\(389\) | 35.8885 | 1.81962 | 0.909811 | − | 0.415023i | \(-0.136227\pi\) | ||||
0.909811 | + | 0.415023i | \(0.136227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.0689 | 2.27923 | ||||||||
\(392\) | − 15.5279i | − 0.784276i | ||||||||
\(393\) | 26.8328 | 1.35354 | ||||||||
\(394\) | −4.85410 | −0.244546 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − 5.23607i | − 0.263122i | ||||||||
\(397\) | 10.0557i | 0.504683i | 0.967638 | + | 0.252341i | \(0.0812006\pi\) | ||||
−0.967638 | + | 0.252341i | \(0.918799\pi\) | |||||||
\(398\) | − 23.7984i | − 1.19290i | ||||||||
\(399\) | −0.124612 | −0.00623839 | ||||||||
\(400\) | 4.85410 | 0.242705 | ||||||||
\(401\) | − 26.8885i | − 1.34275i | −0.741118 | − | 0.671375i | \(-0.765704\pi\) | ||||
0.741118 | − | 0.671375i | \(-0.234296\pi\) | |||||||
\(402\) | 38.7426 | 1.93231 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.85410 | 0.291252 | ||||||||
\(405\) | 11.0000i | 0.546594i | ||||||||
\(406\) | −0.562306 | −0.0279068 | ||||||||
\(407\) | −12.7082 | −0.629922 | ||||||||
\(408\) | − 27.3607i | − 1.35456i | ||||||||
\(409\) | 10.8885i | 0.538404i | 0.963084 | + | 0.269202i | \(0.0867599\pi\) | ||||
−0.963084 | + | 0.269202i | \(0.913240\pi\) | |||||||
\(410\) | − 9.61803i | − 0.475001i | ||||||||
\(411\) | 16.7082i | 0.824155i | ||||||||
\(412\) | −3.05573 | −0.150545 | ||||||||
\(413\) | 3.00000 | 0.147620 | ||||||||
\(414\) | 26.6525i | 1.30990i | ||||||||
\(415\) | 8.94427 | 0.439057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.36068 | 0.360454 | ||||||||
\(418\) | 1.61803i | 0.0791406i | ||||||||
\(419\) | −13.6525 | −0.666967 | −0.333484 | − | 0.942756i | \(-0.608224\pi\) | ||||
−0.333484 | + | 0.942756i | \(0.608224\pi\) | |||||||
\(420\) | −0.326238 | −0.0159188 | ||||||||
\(421\) | − 6.00000i | − 0.292422i | −0.989253 | − | 0.146211i | \(-0.953292\pi\) | ||||
0.989253 | − | 0.146211i | \(-0.0467079\pi\) | |||||||
\(422\) | − 14.8541i | − 0.723086i | ||||||||
\(423\) | 25.8885i | 1.25874i | ||||||||
\(424\) | − 13.4164i | − 0.651558i | ||||||||
\(425\) | 5.47214 | 0.265438 | ||||||||
\(426\) | −6.38197 | −0.309207 | ||||||||
\(427\) | 2.93112i | 0.141847i | ||||||||
\(428\) | 6.32624 | 0.305790 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.85410 | −0.137637 | ||||||||
\(431\) | − 4.81966i | − 0.232155i | −0.993240 | − | 0.116077i | \(-0.962968\pi\) | ||||
0.993240 | − | 0.116077i | \(-0.0370321\pi\) | |||||||
\(432\) | −10.8541 | −0.522218 | ||||||||
\(433\) | 23.4721 | 1.12800 | 0.563999 | − | 0.825775i | \(-0.309262\pi\) | ||||
0.563999 | + | 0.825775i | \(0.309262\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.29180i | 0.157830i | ||||||||
\(436\) | − 1.23607i | − 0.0591969i | ||||||||
\(437\) | − 1.94427i | − 0.0930071i | ||||||||
\(438\) | 21.7082 | 1.03726 | ||||||||
\(439\) | 9.29180 | 0.443473 | 0.221737 | − | 0.975107i | \(-0.428827\pi\) | ||||
0.221737 | + | 0.975107i | \(0.428827\pi\) | |||||||
\(440\) | − 9.47214i | − 0.451566i | ||||||||
\(441\) | 13.8885 | 0.661359 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.9443 | −0.805047 | −0.402523 | − | 0.915410i | \(-0.631867\pi\) | ||||
−0.402523 | + | 0.915410i | \(0.631867\pi\) | |||||||
\(444\) | 4.14590i | 0.196756i | ||||||||
\(445\) | −9.00000 | −0.426641 | ||||||||
\(446\) | 20.5623 | 0.973653 | ||||||||
\(447\) | 30.1246i | 1.42485i | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | − 13.9443i | − 0.658071i | −0.944318 | − | 0.329035i | \(-0.893276\pi\) | ||||
0.944318 | − | 0.329035i | \(-0.106724\pi\) | |||||||
\(450\) | 3.23607i | 0.152550i | ||||||||
\(451\) | −25.1803 | −1.18570 | ||||||||
\(452\) | 4.61803 | 0.217214 | ||||||||
\(453\) | − 17.8885i | − 0.840477i | ||||||||
\(454\) | 2.85410 | 0.133950 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.18034 | −0.0552745 | ||||||||
\(457\) | 28.4164i | 1.32926i | 0.747171 | + | 0.664632i | \(0.231412\pi\) | ||||
−0.747171 | + | 0.664632i | \(0.768588\pi\) | |||||||
\(458\) | −32.1803 | −1.50369 | ||||||||
\(459\) | −12.2361 | −0.571131 | ||||||||
\(460\) | − 5.09017i | − 0.237330i | ||||||||
\(461\) | 28.4164i | 1.32348i | 0.749732 | + | 0.661742i | \(0.230183\pi\) | ||||
−0.749732 | + | 0.661742i | \(0.769817\pi\) | |||||||
\(462\) | 3.61803i | 0.168326i | ||||||||
\(463\) | 28.9443i | 1.34515i | 0.740027 | + | 0.672577i | \(0.234813\pi\) | ||||
−0.740027 | + | 0.672577i | \(0.765187\pi\) | |||||||
\(464\) | −7.14590 | −0.331740 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 32.1803i | 1.49073i | ||||||||
\(467\) | 8.94427 | 0.413892 | 0.206946 | − | 0.978352i | \(-0.433648\pi\) | ||||
0.206946 | + | 0.978352i | \(0.433648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.52786 | −0.116726 | ||||||||
\(470\) | − 20.9443i | − 0.966087i | ||||||||
\(471\) | 40.2492 | 1.85459 | ||||||||
\(472\) | 28.4164 | 1.30797 | ||||||||
\(473\) | 7.47214i | 0.343569i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.236068i | − 0.0108315i | ||||||||
\(476\) | − 0.798374i | − 0.0365934i | ||||||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | −16.0000 | −0.731823 | ||||||||
\(479\) | − 8.12461i | − 0.371223i | −0.982623 | − | 0.185611i | \(-0.940573\pi\) | ||||
0.982623 | − | 0.185611i | \(-0.0594266\pi\) | |||||||
\(480\) | −7.56231 | −0.345170 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 24.2705 | 1.10549 | ||||||||
\(483\) | − 4.34752i | − 0.197819i | ||||||||
\(484\) | 4.29180 | 0.195082 | ||||||||
\(485\) | −5.47214 | −0.248477 | ||||||||
\(486\) | − 28.9443i | − 1.31294i | ||||||||
\(487\) | 26.1246i | 1.18382i | 0.806004 | + | 0.591910i | \(0.201626\pi\) | ||||
−0.806004 | + | 0.591910i | \(0.798374\pi\) | |||||||
\(488\) | 27.7639i | 1.25681i | ||||||||
\(489\) | − 2.88854i | − 0.130624i | ||||||||
\(490\) | −11.2361 | −0.507594 | ||||||||
\(491\) | −4.23607 | −0.191171 | −0.0955855 | − | 0.995421i | \(-0.530472\pi\) | ||||
−0.0955855 | + | 0.995421i | \(0.530472\pi\) | |||||||
\(492\) | 8.21478i | 0.370351i | ||||||||
\(493\) | −8.05573 | −0.362812 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.47214 | 0.380794 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.416408 | 0.0186784 | ||||||||
\(498\) | −32.3607 | −1.45012 | ||||||||
\(499\) | − 13.8885i | − 0.621737i | −0.950453 | − | 0.310868i | \(-0.899380\pi\) | ||||
0.950453 | − | 0.310868i | \(-0.100620\pi\) | |||||||
\(500\) | − 0.618034i | − 0.0276393i | ||||||||
\(501\) | − 11.5836i | − 0.517517i | ||||||||
\(502\) | 25.5066i | 1.13841i | ||||||||
\(503\) | −13.1803 | −0.587682 | −0.293841 | − | 0.955854i | \(-0.594934\pi\) | ||||
−0.293841 | + | 0.955854i | \(0.594934\pi\) | |||||||
\(504\) | −1.05573 | −0.0470259 | ||||||||
\(505\) | 9.47214i | 0.421505i | ||||||||
\(506\) | −56.4508 | −2.50955 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.145898 | 0.00647318 | ||||||||
\(509\) | − 11.3607i | − 0.503553i | −0.967785 | − | 0.251777i | \(-0.918985\pi\) | ||||
0.967785 | − | 0.251777i | \(-0.0810148\pi\) | |||||||
\(510\) | −19.7984 | −0.876687 | ||||||||
\(511\) | −1.41641 | −0.0626582 | ||||||||
\(512\) | 5.29180i | 0.233867i | ||||||||
\(513\) | 0.527864i | 0.0233058i | ||||||||
\(514\) | 13.7984i | 0.608620i | ||||||||
\(515\) | − 4.94427i | − 0.217871i | ||||||||
\(516\) | 2.43769 | 0.107313 | ||||||||
\(517\) | −54.8328 | −2.41154 | ||||||||
\(518\) | − 1.14590i | − 0.0503479i | ||||||||
\(519\) | 37.7639 | 1.65765 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.7771 | −1.83029 | −0.915144 | − | 0.403128i | \(-0.867923\pi\) | ||||
−0.915144 | + | 0.403128i | \(0.867923\pi\) | |||||||
\(522\) | − 4.76393i | − 0.208512i | ||||||||
\(523\) | 18.7082 | 0.818053 | 0.409026 | − | 0.912523i | \(-0.365868\pi\) | ||||
0.409026 | + | 0.912523i | \(0.365868\pi\) | |||||||
\(524\) | 7.41641 | 0.323987 | ||||||||
\(525\) | − 0.527864i | − 0.0230379i | ||||||||
\(526\) | − 13.3262i | − 0.581052i | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 45.9787i | 2.00097i | ||||||||
\(529\) | 44.8328 | 1.94925 | ||||||||
\(530\) | −9.70820 | −0.421697 | ||||||||
\(531\) | 25.4164i | 1.10298i | ||||||||
\(532\) | −0.0344419 | −0.00149324 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 32.5623 | 1.40911 | ||||||||
\(535\) | 10.2361i | 0.442544i | ||||||||
\(536\) | −23.9443 | −1.03424 | ||||||||
\(537\) | −8.41641 | −0.363195 | ||||||||
\(538\) | 25.0344i | 1.07931i | ||||||||
\(539\) | 29.4164i | 1.26705i | ||||||||
\(540\) | 1.38197i | 0.0594703i | ||||||||
\(541\) | 7.88854i | 0.339155i | 0.985517 | + | 0.169577i | \(0.0542403\pi\) | ||||
−0.985517 | + | 0.169577i | \(0.945760\pi\) | |||||||
\(542\) | 23.7984 | 1.02223 | ||||||||
\(543\) | 13.4164 | 0.575753 | ||||||||
\(544\) | − 18.5066i | − 0.793463i | ||||||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.8328 | −1.48934 | −0.744672 | − | 0.667431i | \(-0.767394\pi\) | ||||
−0.744672 | + | 0.667431i | \(0.767394\pi\) | |||||||
\(548\) | 4.61803i | 0.197273i | ||||||||
\(549\) | −24.8328 | −1.05984 | ||||||||
\(550\) | −6.85410 | −0.292260 | ||||||||
\(551\) | 0.347524i | 0.0148050i | ||||||||
\(552\) | − 41.1803i | − 1.75275i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 30.5623i | − 1.29847i | ||||||||
\(555\) | −6.70820 | −0.284747 | ||||||||
\(556\) | 2.03444 | 0.0862796 | ||||||||
\(557\) | 7.94427i | 0.336610i | 0.985735 | + | 0.168305i | \(0.0538293\pi\) | ||||
−0.985735 | + | 0.168305i | \(0.946171\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.14590 | 0.0484230 | ||||||||
\(561\) | 51.8328i | 2.18838i | ||||||||
\(562\) | 32.1803 | 1.35745 | ||||||||
\(563\) | −17.2918 | −0.728762 | −0.364381 | − | 0.931250i | \(-0.618719\pi\) | ||||
−0.364381 | + | 0.931250i | \(0.618719\pi\) | |||||||
\(564\) | 17.8885i | 0.753244i | ||||||||
\(565\) | 7.47214i | 0.314355i | ||||||||
\(566\) | 4.38197i | 0.184188i | ||||||||
\(567\) | 2.59675i | 0.109053i | ||||||||
\(568\) | 3.94427 | 0.165498 | ||||||||
\(569\) | 18.8885 | 0.791849 | 0.395924 | − | 0.918283i | \(-0.370424\pi\) | ||||
0.395924 | + | 0.918283i | \(0.370424\pi\) | |||||||
\(570\) | 0.854102i | 0.0357744i | ||||||||
\(571\) | −28.0000 | −1.17176 | −0.585882 | − | 0.810397i | \(-0.699252\pi\) | ||||
−0.585882 | + | 0.810397i | \(0.699252\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.7771 | 0.450219 | ||||||||
\(574\) | − 2.27051i | − 0.0947692i | ||||||||
\(575\) | 8.23607 | 0.343468 | ||||||||
\(576\) | −8.47214 | −0.353006 | ||||||||
\(577\) | 7.88854i | 0.328404i | 0.986427 | + | 0.164202i | \(0.0525050\pi\) | ||||
−0.986427 | + | 0.164202i | \(0.947495\pi\) | |||||||
\(578\) | − 20.9443i | − 0.871167i | ||||||||
\(579\) | − 12.2361i | − 0.508514i | ||||||||
\(580\) | 0.909830i | 0.0377786i | ||||||||
\(581\) | 2.11146 | 0.0875980 | ||||||||
\(582\) | 19.7984 | 0.820669 | ||||||||
\(583\) | 25.4164i | 1.05264i | ||||||||
\(584\) | −13.4164 | −0.555175 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.5066 | −0.805809 | ||||||||
\(587\) | − 5.76393i | − 0.237903i | −0.992900 | − | 0.118951i | \(-0.962047\pi\) | ||||
0.992900 | − | 0.118951i | \(-0.0379533\pi\) | |||||||
\(588\) | 9.59675 | 0.395763 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | − 20.5623i | − 0.846537i | ||||||||
\(591\) | 6.70820i | 0.275939i | ||||||||
\(592\) | − 14.5623i | − 0.598507i | ||||||||
\(593\) | 27.8885i | 1.14525i | 0.819819 | + | 0.572623i | \(0.194074\pi\) | ||||
−0.819819 | + | 0.572623i | \(0.805926\pi\) | |||||||
\(594\) | 15.3262 | 0.628843 | ||||||||
\(595\) | 1.29180 | 0.0529585 | ||||||||
\(596\) | 8.32624i | 0.341056i | ||||||||
\(597\) | −32.8885 | −1.34604 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | − 5.00000i | − 0.204124i | ||||||||
\(601\) | 26.0557 | 1.06284 | 0.531418 | − | 0.847110i | \(-0.321659\pi\) | ||||
0.531418 | + | 0.847110i | \(0.321659\pi\) | |||||||
\(602\) | −0.673762 | −0.0274605 | ||||||||
\(603\) | − 21.4164i | − 0.872144i | ||||||||
\(604\) | − 4.94427i | − 0.201180i | ||||||||
\(605\) | 6.94427i | 0.282325i | ||||||||
\(606\) | − 34.2705i | − 1.39214i | ||||||||
\(607\) | 12.7082 | 0.515810 | 0.257905 | − | 0.966170i | \(-0.416968\pi\) | ||||
0.257905 | + | 0.966170i | \(0.416968\pi\) | |||||||
\(608\) | −0.798374 | −0.0323783 | ||||||||
\(609\) | 0.777088i | 0.0314892i | ||||||||
\(610\) | 20.0902 | 0.813427 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.76393 | 0.273416 | ||||||||
\(613\) | − 22.0557i | − 0.890822i | −0.895326 | − | 0.445411i | \(-0.853057\pi\) | ||||
0.895326 | − | 0.445411i | \(-0.146943\pi\) | |||||||
\(614\) | 11.4164 | 0.460729 | ||||||||
\(615\) | −13.2918 | −0.535977 | ||||||||
\(616\) | − 2.23607i | − 0.0900937i | ||||||||
\(617\) | 13.5836i | 0.546855i | 0.961893 | + | 0.273427i | \(0.0881573\pi\) | ||||
−0.961893 | + | 0.273427i | \(0.911843\pi\) | |||||||
\(618\) | 17.8885i | 0.719583i | ||||||||
\(619\) | 12.0000i | 0.482321i | 0.970485 | + | 0.241160i | \(0.0775280\pi\) | ||||
−0.970485 | + | 0.241160i | \(0.922472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18.4164 | −0.739025 | ||||||||
\(622\) | − 38.8328i | − 1.55705i | ||||||||
\(623\) | −2.12461 | −0.0851208 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 51.5967i | 2.06222i | ||||||||
\(627\) | 2.23607 | 0.0893000 | ||||||||
\(628\) | 11.1246 | 0.443920 | ||||||||
\(629\) | − 16.4164i | − 0.654565i | ||||||||
\(630\) | 0.763932i | 0.0304358i | ||||||||
\(631\) | 24.1246i | 0.960386i | 0.877163 | + | 0.480193i | \(0.159433\pi\) | ||||
−0.877163 | + | 0.480193i | \(0.840567\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.5279 | −0.815909 | ||||||||
\(634\) | −38.6525 | −1.53509 | ||||||||
\(635\) | 0.236068i | 0.00936807i | ||||||||
\(636\) | 8.29180 | 0.328791 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 10.0902 | 0.399474 | ||||||||
\(639\) | 3.52786i | 0.139560i | ||||||||
\(640\) | 13.6180 | 0.538300 | ||||||||
\(641\) | 26.8885 | 1.06203 | 0.531017 | − | 0.847361i | \(-0.321810\pi\) | ||||
0.531017 | + | 0.847361i | \(0.321810\pi\) | |||||||
\(642\) | − 37.0344i | − 1.46163i | ||||||||
\(643\) | 30.7082i | 1.21101i | 0.795840 | + | 0.605507i | \(0.207030\pi\) | ||||
−0.795840 | + | 0.605507i | \(0.792970\pi\) | |||||||
\(644\) | − 1.20163i | − 0.0473507i | ||||||||
\(645\) | 3.94427i | 0.155306i | ||||||||
\(646\) | −2.09017 | −0.0822366 | ||||||||
\(647\) | 46.5967 | 1.83191 | 0.915954 | − | 0.401284i | \(-0.131436\pi\) | ||||
0.915954 | + | 0.401284i | \(0.131436\pi\) | |||||||
\(648\) | 24.5967i | 0.966252i | ||||||||
\(649\) | −53.8328 | −2.11312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 0.798374i | − 0.0312667i | ||||||||
\(653\) | −21.0000 | −0.821794 | −0.410897 | − | 0.911682i | \(-0.634784\pi\) | ||||
−0.410897 | + | 0.911682i | \(0.634784\pi\) | |||||||
\(654\) | −7.23607 | −0.282953 | ||||||||
\(655\) | 12.0000i | 0.468879i | ||||||||
\(656\) | − 28.8541i | − 1.12656i | ||||||||
\(657\) | − 12.0000i | − 0.468165i | ||||||||
\(658\) | − 4.94427i | − 0.192748i | ||||||||
\(659\) | −48.2361 | −1.87901 | −0.939505 | − | 0.342535i | \(-0.888715\pi\) | ||||
−0.939505 | + | 0.342535i | \(0.888715\pi\) | |||||||
\(660\) | 5.85410 | 0.227871 | ||||||||
\(661\) | 3.36068i | 0.130715i | 0.997862 | + | 0.0653576i | \(0.0208188\pi\) | ||||
−0.997862 | + | 0.0653576i | \(0.979181\pi\) | |||||||
\(662\) | −41.5066 | −1.61320 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.0000 | 0.776151 | ||||||||
\(665\) | − 0.0557281i | − 0.00216104i | ||||||||
\(666\) | 9.70820 | 0.376185 | ||||||||
\(667\) | −12.1246 | −0.469467 | ||||||||
\(668\) | − 3.20163i | − 0.123875i | ||||||||
\(669\) | − 28.4164i | − 1.09864i | ||||||||
\(670\) | 17.3262i | 0.669371i | ||||||||
\(671\) | − 52.5967i | − 2.03047i | ||||||||
\(672\) | −1.78522 | −0.0688663 | ||||||||
\(673\) | 36.4164 | 1.40375 | 0.701875 | − | 0.712300i | \(-0.252347\pi\) | ||||
0.701875 | + | 0.712300i | \(0.252347\pi\) | |||||||
\(674\) | 45.1246i | 1.73814i | ||||||||
\(675\) | −2.23607 | −0.0860663 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 47.8885 | 1.84051 | 0.920253 | − | 0.391324i | \(-0.127983\pi\) | ||||
0.920253 | + | 0.391324i | \(0.127983\pi\) | |||||||
\(678\) | − 27.0344i | − 1.03825i | ||||||||
\(679\) | −1.29180 | −0.0495746 | ||||||||
\(680\) | 12.2361 | 0.469232 | ||||||||
\(681\) | − 3.94427i | − 0.151145i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.2361i | 1.15695i | 0.815700 | + | 0.578475i | \(0.196352\pi\) | ||||
−0.815700 | + | 0.578475i | \(0.803648\pi\) | |||||||
\(684\) | − 0.291796i | − 0.0111571i | ||||||||
\(685\) | −7.47214 | −0.285496 | ||||||||
\(686\) | −5.32624 | −0.203357 | ||||||||
\(687\) | 44.4721i | 1.69672i | ||||||||
\(688\) | −8.56231 | −0.326435 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −29.7984 | −1.13440 | ||||||||
\(691\) | 10.5967i | 0.403119i | 0.979476 | + | 0.201560i | \(0.0646010\pi\) | ||||
−0.979476 | + | 0.201560i | \(0.935399\pi\) | |||||||
\(692\) | 10.4377 | 0.396782 | ||||||||
\(693\) | 2.00000 | 0.0759737 | ||||||||
\(694\) | − 27.9787i | − 1.06206i | ||||||||
\(695\) | 3.29180i | 0.124865i | ||||||||
\(696\) | 7.36068i | 0.279006i | ||||||||
\(697\) | − 32.5279i | − 1.23208i | ||||||||
\(698\) | −39.5066 | −1.49535 | ||||||||
\(699\) | 44.4721 | 1.68209 | ||||||||
\(700\) | − 0.145898i | − 0.00551443i | ||||||||
\(701\) | 27.8885 | 1.05334 | 0.526668 | − | 0.850071i | \(-0.323441\pi\) | ||||
0.526668 | + | 0.850071i | \(0.323441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.708204 | −0.0267104 | ||||||||
\(704\) | − 17.9443i | − 0.676300i | ||||||||
\(705\) | −28.9443 | −1.09010 | ||||||||
\(706\) | 17.0344 | 0.641100 | ||||||||
\(707\) | 2.23607i | 0.0840960i | ||||||||
\(708\) | 17.5623i | 0.660032i | ||||||||
\(709\) | − 38.3050i | − 1.43857i | −0.694714 | − | 0.719286i | \(-0.744469\pi\) | ||||
0.694714 | − | 0.719286i | \(-0.255531\pi\) | |||||||
\(710\) | − 2.85410i | − 0.107113i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.1246 | −0.754202 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −4.67376 | −0.174911 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.32624 | −0.0869356 | ||||||||
\(717\) | 22.1115i | 0.825767i | ||||||||
\(718\) | −28.9443 | −1.08019 | ||||||||
\(719\) | −8.12461 | −0.302997 | −0.151498 | − | 0.988457i | \(-0.548410\pi\) | ||||
−0.151498 | + | 0.988457i | \(0.548410\pi\) | |||||||
\(720\) | 9.70820i | 0.361803i | ||||||||
\(721\) | − 1.16718i | − 0.0434682i | ||||||||
\(722\) | − 30.6525i | − 1.14077i | ||||||||
\(723\) | − 33.5410i | − 1.24740i | ||||||||
\(724\) | 3.70820 | 0.137814 | ||||||||
\(725\) | −1.47214 | −0.0546738 | ||||||||
\(726\) | − 25.1246i | − 0.932462i | ||||||||
\(727\) | −11.0557 | −0.410034 | −0.205017 | − | 0.978758i | \(-0.565725\pi\) | ||||
−0.205017 | + | 0.978758i | \(0.565725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | 9.70820i | 0.359317i | ||||||||
\(731\) | −9.65248 | −0.357010 | ||||||||
\(732\) | −17.1591 | −0.634217 | ||||||||
\(733\) | 8.11146i | 0.299603i | 0.988716 | + | 0.149802i | \(0.0478635\pi\) | ||||
−0.988716 | + | 0.149802i | \(0.952136\pi\) | |||||||
\(734\) | 41.5066i | 1.53204i | ||||||||
\(735\) | 15.5279i | 0.572754i | ||||||||
\(736\) | − 27.8541i | − 1.02672i | ||||||||
\(737\) | 45.3607 | 1.67088 | ||||||||
\(738\) | 19.2361 | 0.708089 | ||||||||
\(739\) | − 39.5410i | − 1.45454i | −0.686352 | − | 0.727270i | \(-0.740789\pi\) | ||||
0.686352 | − | 0.727270i | \(-0.259211\pi\) | |||||||
\(740\) | −1.85410 | −0.0681581 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.29180 | −0.0841345 | ||||||||
\(743\) | − 2.12461i | − 0.0779444i | −0.999240 | − | 0.0389722i | \(-0.987592\pi\) | ||||
0.999240 | − | 0.0389722i | \(-0.0124084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.4721 | −0.493581 | ||||||||
\(746\) | − 16.2705i | − 0.595706i | ||||||||
\(747\) | 17.8885i | 0.654508i | ||||||||
\(748\) | 14.3262i | 0.523819i | ||||||||
\(749\) | 2.41641i | 0.0882936i | ||||||||
\(750\) | −3.61803 | −0.132112 | ||||||||
\(751\) | 17.2918 | 0.630987 | 0.315493 | − | 0.948928i | \(-0.397830\pi\) | ||||
0.315493 | + | 0.948928i | \(0.397830\pi\) | |||||||
\(752\) | − 62.8328i | − 2.29128i | ||||||||
\(753\) | 35.2492 | 1.28455 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.00000 | 0.291150 | ||||||||
\(756\) | 0.326238i | 0.0118652i | ||||||||
\(757\) | 28.8885 | 1.04997 | 0.524986 | − | 0.851111i | \(-0.324071\pi\) | ||||
0.524986 | + | 0.851111i | \(0.324071\pi\) | |||||||
\(758\) | −53.6869 | −1.95000 | ||||||||
\(759\) | 78.0132i | 2.83170i | ||||||||
\(760\) | − 0.527864i | − 0.0191476i | ||||||||
\(761\) | − 20.0557i | − 0.727020i | −0.931590 | − | 0.363510i | \(-0.881578\pi\) | ||||
0.931590 | − | 0.363510i | \(-0.118422\pi\) | |||||||
\(762\) | − 0.854102i | − 0.0309408i | ||||||||
\(763\) | 0.472136 | 0.0170925 | ||||||||
\(764\) | 2.97871 | 0.107766 | ||||||||
\(765\) | 10.9443i | 0.395691i | ||||||||
\(766\) | 0.381966 | 0.0138010 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −30.3262 | −1.09430 | ||||||||
\(769\) | 23.8328i | 0.859433i | 0.902964 | + | 0.429717i | \(0.141387\pi\) | ||||
−0.902964 | + | 0.429717i | \(0.858613\pi\) | |||||||
\(770\) | −1.61803 | −0.0583099 | ||||||||
\(771\) | 19.0689 | 0.686749 | ||||||||
\(772\) | − 3.38197i | − 0.121720i | ||||||||
\(773\) | 37.9443i | 1.36476i | 0.730997 | + | 0.682380i | \(0.239055\pi\) | ||||
−0.730997 | + | 0.682380i | \(0.760945\pi\) | |||||||
\(774\) | − 5.70820i | − 0.205177i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.2361 | −0.439249 | ||||||||
\(777\) | −1.58359 | −0.0568111 | ||||||||
\(778\) | − 58.0689i | − 2.08187i | ||||||||
\(779\) | −1.40325 | −0.0502767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.47214 | −0.267374 | ||||||||
\(782\) | − 72.9230i | − 2.60772i | ||||||||
\(783\) | 3.29180 | 0.117639 | ||||||||
\(784\) | −33.7082 | −1.20386 | ||||||||
\(785\) | 18.0000i | 0.642448i | ||||||||
\(786\) | − 43.4164i | − 1.54861i | ||||||||
\(787\) | − 37.5410i | − 1.33819i | −0.743176 | − | 0.669096i | \(-0.766681\pi\) | ||||
0.743176 | − | 0.669096i | \(-0.233319\pi\) | |||||||
\(788\) | 1.85410i | 0.0660496i | ||||||||
\(789\) | −18.4164 | −0.655641 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.76393i | 0.0627182i | ||||||||
\(792\) | 18.9443 | 0.673155 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 16.2705 | 0.577419 | ||||||||
\(795\) | 13.4164i | 0.475831i | ||||||||
\(796\) | −9.09017 | −0.322193 | ||||||||
\(797\) | −0.167184 | −0.00592197 | −0.00296099 | − | 0.999996i | \(-0.500943\pi\) | ||||
−0.00296099 | + | 0.999996i | \(0.500943\pi\) | |||||||
\(798\) | 0.201626i | 0.00713749i | ||||||||
\(799\) | − 70.8328i | − 2.50588i | ||||||||
\(800\) | − 3.38197i | − 0.119571i | ||||||||
\(801\) | − 18.0000i | − 0.635999i | ||||||||
\(802\) | −43.5066 | −1.53627 | ||||||||
\(803\) | 25.4164 | 0.896926 | ||||||||
\(804\) | − 14.7984i | − 0.521898i | ||||||||
\(805\) | 1.94427 | 0.0685266 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.5967 | 1.21786 | ||||||||
\(808\) | 21.1803i | 0.745122i | ||||||||
\(809\) | 32.8885 | 1.15630 | 0.578150 | − | 0.815931i | \(-0.303775\pi\) | ||||
0.578150 | + | 0.815931i | \(0.303775\pi\) | |||||||
\(810\) | 17.7984 | 0.625371 | ||||||||
\(811\) | 39.7771i | 1.39676i | 0.715726 | + | 0.698381i | \(0.246096\pi\) | ||||
−0.715726 | + | 0.698381i | \(0.753904\pi\) | |||||||
\(812\) | 0.214782i | 0.00753736i | ||||||||
\(813\) | − 32.8885i | − 1.15345i | ||||||||
\(814\) | 20.5623i | 0.720708i | ||||||||
\(815\) | 1.29180 | 0.0452496 | ||||||||
\(816\) | −59.3951 | −2.07925 | ||||||||
\(817\) | 0.416408i | 0.0145683i | ||||||||
\(818\) | 17.6180 | 0.616000 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.67376 | −0.128293 | ||||||||
\(821\) | − 19.3607i | − 0.675692i | −0.941201 | − | 0.337846i | \(-0.890302\pi\) | ||||
0.941201 | − | 0.337846i | \(-0.109698\pi\) | |||||||
\(822\) | 27.0344 | 0.942934 | ||||||||
\(823\) | −22.5967 | −0.787673 | −0.393837 | − | 0.919180i | \(-0.628852\pi\) | ||||
−0.393837 | + | 0.919180i | \(0.628852\pi\) | |||||||
\(824\) | − 11.0557i | − 0.385145i | ||||||||
\(825\) | 9.47214i | 0.329777i | ||||||||
\(826\) | − 4.85410i | − 0.168896i | ||||||||
\(827\) | 8.94427i | 0.311023i | 0.987834 | + | 0.155511i | \(0.0497025\pi\) | ||||
−0.987834 | + | 0.155511i | \(0.950297\pi\) | |||||||
\(828\) | 10.1803 | 0.353791 | ||||||||
\(829\) | −37.2492 | −1.29372 | −0.646860 | − | 0.762609i | \(-0.723918\pi\) | ||||
−0.646860 | + | 0.762609i | \(0.723918\pi\) | |||||||
\(830\) | − 14.4721i | − 0.502335i | ||||||||
\(831\) | −42.2361 | −1.46515 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.0000 | −1.31662 | ||||||||
\(834\) | − 11.9098i | − 0.412404i | ||||||||
\(835\) | 5.18034 | 0.179273 | ||||||||
\(836\) | 0.618034 | 0.0213752 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 22.0902i | 0.763092i | ||||||||
\(839\) | 17.2918i | 0.596979i | 0.954413 | + | 0.298490i | \(0.0964828\pi\) | ||||
−0.954413 | + | 0.298490i | \(0.903517\pi\) | |||||||
\(840\) | − 1.18034i | − 0.0407256i | ||||||||
\(841\) | −26.8328 | −0.925270 | ||||||||
\(842\) | −9.70820 | −0.334567 | ||||||||
\(843\) | − 44.4721i | − 1.53170i | ||||||||
\(844\) | −5.67376 | −0.195299 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 41.8885 | 1.44016 | ||||||||
\(847\) | 1.63932i | 0.0563277i | ||||||||
\(848\) | −29.1246 | −1.00014 | ||||||||
\(849\) | 6.05573 | 0.207832 | ||||||||
\(850\) | − 8.85410i | − 0.303693i | ||||||||
\(851\) | − 24.7082i | − 0.846986i | ||||||||
\(852\) | 2.43769i | 0.0835140i | ||||||||
\(853\) | 6.00000i | 0.205436i | 0.994711 | + | 0.102718i | \(0.0327539\pi\) | ||||
−0.994711 | + | 0.102718i | \(0.967246\pi\) | |||||||
\(854\) | 4.74265 | 0.162290 | ||||||||
\(855\) | 0.472136 | 0.0161467 | ||||||||
\(856\) | 22.8885i | 0.782314i | ||||||||
\(857\) | −0.111456 | −0.00380727 | −0.00190364 | − | 0.999998i | \(-0.500606\pi\) | ||||
−0.00190364 | + | 0.999998i | \(0.500606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.8885 | −0.473871 | −0.236935 | − | 0.971525i | \(-0.576143\pi\) | ||||
−0.236935 | + | 0.971525i | \(0.576143\pi\) | |||||||
\(860\) | 1.09017i | 0.0371745i | ||||||||
\(861\) | −3.13777 | −0.106935 | ||||||||
\(862\) | −7.79837 | −0.265614 | ||||||||
\(863\) | 38.8328i | 1.32188i | 0.750437 | + | 0.660942i | \(0.229843\pi\) | ||||
−0.750437 | + | 0.660942i | \(0.770157\pi\) | |||||||
\(864\) | 7.56231i | 0.257275i | ||||||||
\(865\) | 16.8885i | 0.574228i | ||||||||
\(866\) | − 37.9787i | − 1.29057i | ||||||||
\(867\) | −28.9443 | −0.982999 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 5.32624 | 0.180576 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 4.47214 | 0.151446 | ||||||||
\(873\) | − 10.9443i | − 0.370407i | ||||||||
\(874\) | −3.14590 | −0.106412 | ||||||||
\(875\) | 0.236068 | 0.00798055 | ||||||||
\(876\) | − 8.29180i | − 0.280154i | ||||||||
\(877\) | − 55.7214i | − 1.88158i | −0.338995 | − | 0.940788i | \(-0.610087\pi\) | ||||
0.338995 | − | 0.940788i | \(-0.389913\pi\) | |||||||
\(878\) | − 15.0344i | − 0.507388i | ||||||||
\(879\) | 26.9574i | 0.909251i | ||||||||
\(880\) | −20.5623 | −0.693155 | ||||||||
\(881\) | −15.0000 | −0.505363 | −0.252681 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252681 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(882\) | − 22.4721i | − 0.756676i | ||||||||
\(883\) | −10.8328 | −0.364553 | −0.182277 | − | 0.983247i | \(-0.558347\pi\) | ||||
−0.182277 | + | 0.983247i | \(0.558347\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.4164 | −0.955207 | ||||||||
\(886\) | 27.4164i | 0.921072i | ||||||||
\(887\) | −40.4853 | −1.35936 | −0.679682 | − | 0.733507i | \(-0.737882\pi\) | ||||
−0.679682 | + | 0.733507i | \(0.737882\pi\) | |||||||
\(888\) | −15.0000 | −0.503367 | ||||||||
\(889\) | 0.0557281i | 0.00186906i | ||||||||
\(890\) | 14.5623i | 0.488130i | ||||||||
\(891\) | − 46.5967i | − 1.56105i | ||||||||
\(892\) | − 7.85410i | − 0.262975i | ||||||||
\(893\) | −3.05573 | −0.102256 | ||||||||
\(894\) | 48.7426 | 1.63020 | ||||||||
\(895\) | − 3.76393i | − 0.125814i | ||||||||
\(896\) | 3.21478 | 0.107398 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −22.5623 | −0.752914 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.23607 | 0.0412023 | ||||||||
\(901\) | −32.8328 | −1.09382 | ||||||||
\(902\) | 40.7426i | 1.35658i | ||||||||
\(903\) | 0.931116i | 0.0309856i | ||||||||
\(904\) | 16.7082i | 0.555707i | ||||||||
\(905\) | 6.00000i | 0.199447i | ||||||||
\(906\) | −28.9443 | −0.961609 | ||||||||
\(907\) | 20.1246 | 0.668227 | 0.334113 | − | 0.942533i | \(-0.391563\pi\) | ||||
0.334113 | + | 0.942533i | \(0.391563\pi\) | |||||||
\(908\) | − 1.09017i | − 0.0361786i | ||||||||
\(909\) | −18.9443 | −0.628342 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 2.56231i | 0.0848464i | ||||||||
\(913\) | −37.8885 | −1.25393 | ||||||||
\(914\) | 45.9787 | 1.52084 | ||||||||
\(915\) | − 27.7639i | − 0.917847i | ||||||||
\(916\) | 12.2918i | 0.406132i | ||||||||
\(917\) | 2.83282i | 0.0935478i | ||||||||
\(918\) | 19.7984i | 0.653444i | ||||||||
\(919\) | 33.2918 | 1.09820 | 0.549098 | − | 0.835758i | \(-0.314972\pi\) | ||||
0.549098 | + | 0.835758i | \(0.314972\pi\) | |||||||
\(920\) | 18.4164 | 0.607171 | ||||||||
\(921\) | − 15.7771i | − 0.519873i | ||||||||
\(922\) | 45.9787 | 1.51423 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.38197 | 0.0454633 | ||||||||
\(925\) | − 3.00000i | − 0.0986394i | ||||||||
\(926\) | 46.8328 | 1.53902 | ||||||||
\(927\) | 9.88854 | 0.324782 | ||||||||
\(928\) | 4.97871i | 0.163434i | ||||||||
\(929\) | − 2.05573i | − 0.0674463i | −0.999431 | − | 0.0337231i | \(-0.989264\pi\) | ||||
0.999431 | − | 0.0337231i | \(-0.0107364\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.63932i | 0.0537266i | ||||||||
\(932\) | 12.2918 | 0.402631 | ||||||||
\(933\) | −53.6656 | −1.75693 | ||||||||
\(934\) | − 14.4721i | − 0.473543i | ||||||||
\(935\) | −23.1803 | −0.758078 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.00000 | −0.196011 | −0.0980057 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980057 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(938\) | 4.09017i | 0.133549i | ||||||||
\(939\) | 71.3050 | 2.32695 | ||||||||
\(940\) | −8.00000 | −0.260931 | ||||||||
\(941\) | − 23.8885i | − 0.778744i | −0.921081 | − | 0.389372i | \(-0.872692\pi\) | ||||
0.921081 | − | 0.389372i | \(-0.127308\pi\) | |||||||
\(942\) | − 65.1246i | − 2.12187i | ||||||||
\(943\) | − 48.9574i | − 1.59427i | ||||||||
\(944\) | − 61.6869i | − 2.00774i | ||||||||
\(945\) | −0.527864 | −0.0171714 | ||||||||
\(946\) | 12.0902 | 0.393085 | ||||||||
\(947\) | 16.8197i | 0.546566i | 0.961934 | + | 0.273283i | \(0.0881095\pi\) | ||||
−0.961934 | + | 0.273283i | \(0.911891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.381966 | −0.0123926 | ||||||||
\(951\) | 53.4164i | 1.73215i | ||||||||
\(952\) | 2.88854 | 0.0936182 | ||||||||
\(953\) | 56.1935 | 1.82029 | 0.910143 | − | 0.414294i | \(-0.135972\pi\) | ||||
0.910143 | + | 0.414294i | \(0.135972\pi\) | |||||||
\(954\) | − 19.4164i | − 0.628629i | ||||||||
\(955\) | 4.81966i | 0.155961i | ||||||||
\(956\) | 6.11146i | 0.197659i | ||||||||
\(957\) | − 13.9443i | − 0.450754i | ||||||||
\(958\) | −13.1459 | −0.424725 | ||||||||
\(959\) | −1.76393 | −0.0569603 | ||||||||
\(960\) | − 9.47214i | − 0.305712i | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.4721 | −0.659705 | ||||||||
\(964\) | − 9.27051i | − 0.298583i | ||||||||
\(965\) | 5.47214 | 0.176154 | ||||||||
\(966\) | −7.03444 | −0.226329 | ||||||||
\(967\) | 1.16718i | 0.0375341i | 0.999824 | + | 0.0187671i | \(0.00597409\pi\) | ||||
−0.999824 | + | 0.0187671i | \(0.994026\pi\) | |||||||
\(968\) | 15.5279i | 0.499084i | ||||||||
\(969\) | 2.88854i | 0.0927934i | ||||||||
\(970\) | 8.85410i | 0.284288i | ||||||||
\(971\) | −16.2361 | −0.521040 | −0.260520 | − | 0.965468i | \(-0.583894\pi\) | ||||
−0.260520 | + | 0.965468i | \(0.583894\pi\) | |||||||
\(972\) | −11.0557 | −0.354613 | ||||||||
\(973\) | 0.777088i | 0.0249123i | ||||||||
\(974\) | 42.2705 | 1.35443 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 60.2705 | 1.92921 | ||||||||
\(977\) | − 34.4164i | − 1.10108i | −0.834809 | − | 0.550539i | \(-0.814422\pi\) | ||||
0.834809 | − | 0.550539i | \(-0.185578\pi\) | |||||||
\(978\) | −4.67376 | −0.149450 | ||||||||
\(979\) | 38.1246 | 1.21847 | ||||||||
\(980\) | 4.29180i | 0.137096i | ||||||||
\(981\) | 4.00000i | 0.127710i | ||||||||
\(982\) | 6.85410i | 0.218723i | ||||||||
\(983\) | − 14.8328i | − 0.473093i | −0.971620 | − | 0.236547i | \(-0.923984\pi\) | ||||
0.971620 | − | 0.236547i | \(-0.0760156\pi\) | |||||||
\(984\) | −29.7214 | −0.947482 | ||||||||
\(985\) | −3.00000 | −0.0955879 | ||||||||
\(986\) | 13.0344i | 0.415101i | ||||||||
\(987\) | −6.83282 | −0.217491 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.5279 | −0.461959 | ||||||||
\(990\) | − 13.7082i | − 0.435675i | ||||||||
\(991\) | −33.2918 | −1.05755 | −0.528774 | − | 0.848762i | \(-0.677348\pi\) | ||||
−0.528774 | + | 0.848762i | \(0.677348\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 57.3607i | 1.82029i | ||||||||
\(994\) | − 0.673762i | − 0.0213704i | ||||||||
\(995\) | − 14.7082i | − 0.466281i | ||||||||
\(996\) | 12.3607i | 0.391663i | ||||||||
\(997\) | 16.8885 | 0.534866 | 0.267433 | − | 0.963577i | \(-0.413825\pi\) | ||||
0.267433 | + | 0.963577i | \(0.413825\pi\) | |||||||
\(998\) | −22.4721 | −0.711343 | ||||||||
\(999\) | 6.70820i | 0.212238i |
(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 | 845.2.c.c.506.1 | 4 | ||
13.2 | odd | 12 | 845.2.e.g.191.2 | 4 | |||
13.3 | even | 3 | 845.2.m.e.316.4 | 8 | |||
13.4 | even | 6 | 845.2.m.e.361.4 | 8 | |||
13.5 | odd | 4 | 845.2.a.b.1.1 | 2 | |||
13.6 | odd | 12 | 845.2.e.g.146.2 | 4 | |||
13.7 | odd | 12 | 65.2.e.a.16.1 | ✓ | 4 | ||
13.8 | odd | 4 | 845.2.a.e.1.2 | 2 | |||
13.9 | even | 3 | 845.2.m.e.361.1 | 8 | |||
13.10 | even | 6 | 845.2.m.e.316.1 | 8 | |||
13.11 | odd | 12 | 65.2.e.a.61.1 | yes | 4 | ||
13.12 | even | 2 | inner | 845.2.c.c.506.4 | 4 | ||
39.5 | even | 4 | 7605.2.a.bf.1.2 | 2 | |||
39.8 | even | 4 | 7605.2.a.ba.1.1 | 2 | |||
39.11 | even | 12 | 585.2.j.e.451.2 | 4 | |||
39.20 | even | 12 | 585.2.j.e.406.2 | 4 | |||
52.7 | even | 12 | 1040.2.q.n.81.1 | 4 | |||
52.11 | even | 12 | 1040.2.q.n.321.1 | 4 | |||
65.7 | even | 12 | 325.2.o.a.224.4 | 8 | |||
65.24 | odd | 12 | 325.2.e.b.126.2 | 4 | |||
65.33 | even | 12 | 325.2.o.a.224.1 | 8 | |||
65.34 | odd | 4 | 4225.2.a.u.1.1 | 2 | |||
65.37 | even | 12 | 325.2.o.a.74.1 | 8 | |||
65.44 | odd | 4 | 4225.2.a.y.1.2 | 2 | |||
65.59 | odd | 12 | 325.2.e.b.276.2 | 4 | |||
65.63 | even | 12 | 325.2.o.a.74.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.e.a.16.1 | ✓ | 4 | 13.7 | odd | 12 | ||
65.2.e.a.61.1 | yes | 4 | 13.11 | odd | 12 | ||
325.2.e.b.126.2 | 4 | 65.24 | odd | 12 | |||
325.2.e.b.276.2 | 4 | 65.59 | odd | 12 | |||
325.2.o.a.74.1 | 8 | 65.37 | even | 12 | |||
325.2.o.a.74.4 | 8 | 65.63 | even | 12 | |||
325.2.o.a.224.1 | 8 | 65.33 | even | 12 | |||
325.2.o.a.224.4 | 8 | 65.7 | even | 12 | |||
585.2.j.e.406.2 | 4 | 39.20 | even | 12 | |||
585.2.j.e.451.2 | 4 | 39.11 | even | 12 | |||
845.2.a.b.1.1 | 2 | 13.5 | odd | 4 | |||
845.2.a.e.1.2 | 2 | 13.8 | odd | 4 | |||
845.2.c.c.506.1 | 4 | 1.1 | even | 1 | trivial | ||
845.2.c.c.506.4 | 4 | 13.12 | even | 2 | inner | ||
845.2.e.g.146.2 | 4 | 13.6 | odd | 12 | |||
845.2.e.g.191.2 | 4 | 13.2 | odd | 12 | |||
845.2.m.e.316.1 | 8 | 13.10 | even | 6 | |||
845.2.m.e.316.4 | 8 | 13.3 | even | 3 | |||
845.2.m.e.361.1 | 8 | 13.9 | even | 3 | |||
845.2.m.e.361.4 | 8 | 13.4 | even | 6 | |||
1040.2.q.n.81.1 | 4 | 52.7 | even | 12 | |||
1040.2.q.n.321.1 | 4 | 52.11 | even | 12 | |||
4225.2.a.u.1.1 | 2 | 65.34 | odd | 4 | |||
4225.2.a.y.1.2 | 2 | 65.44 | odd | 4 | |||
7605.2.a.ba.1.1 | 2 | 39.8 | even | 4 | |||
7605.2.a.bf.1.2 | 2 | 39.5 | even | 4 |