Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [625,2,Mod(624,625)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(625, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("625.624");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 625 = 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 625.b (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: | \(4.99065012633\) |
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 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 624.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 625.624 |
Dual form | 625.2.b.a.624.3 |
$q$-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 \(\left(\mathbb{Z}/625\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.618034i | − 0.437016i | −0.975835 | − | 0.218508i | \(-0.929881\pi\) | ||||
0.975835 | − | 0.218508i | \(-0.0701190\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | 0.957427 | + | 0.288675i | \(0.0932147\pi\) | ||||
−0.957427 | + | 0.288675i | \(0.906785\pi\) | |||||||
\(4\) | 1.61803 | 0.809017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.618034 | 0.252311 | ||||||||
\(7\) | 1.61803i | 0.611559i | 0.952102 | + | 0.305780i | \(0.0989171\pi\) | ||||
−0.952102 | + | 0.305780i | \(0.901083\pi\) | |||||||
\(8\) | − 2.23607i | − 0.790569i | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.763932 | −0.230334 | −0.115167 | − | 0.993346i | \(-0.536740\pi\) | ||||
−0.115167 | + | 0.993346i | \(0.536740\pi\) | |||||||
\(12\) | 1.61803i | 0.467086i | ||||||||
\(13\) | − 4.85410i | − 1.34629i | −0.739512 | − | 0.673143i | \(-0.764944\pi\) | ||||
0.739512 | − | 0.673143i | \(-0.235056\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 0.763932i | 0.185281i | 0.995700 | + | 0.0926404i | \(0.0295307\pi\) | ||||
−0.995700 | + | 0.0926404i | \(0.970469\pi\) | |||||||
\(18\) | − 1.23607i | − 0.291344i | ||||||||
\(19\) | 5.85410 | 1.34302 | 0.671512 | − | 0.740994i | \(-0.265645\pi\) | ||||
0.671512 | + | 0.740994i | \(0.265645\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.61803 | −0.353084 | ||||||||
\(22\) | 0.472136i | 0.100660i | ||||||||
\(23\) | 8.23607i | 1.71734i | 0.512530 | + | 0.858669i | \(0.328708\pi\) | ||||
−0.512530 | + | 0.858669i | \(0.671292\pi\) | |||||||
\(24\) | 2.23607 | 0.456435 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.00000 | −0.588348 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 2.61803i | 0.494762i | ||||||||
\(29\) | 1.38197 | 0.256625 | 0.128312 | − | 0.991734i | \(-0.459044\pi\) | ||||
0.128312 | + | 0.991734i | \(0.459044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | − 5.61803i | − 0.993137i | ||||||||
\(33\) | − 0.763932i | − 0.132983i | ||||||||
\(34\) | 0.472136 | 0.0809706 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.23607 | 0.539345 | ||||||||
\(37\) | − 4.23607i | − 0.696405i | −0.937419 | − | 0.348203i | \(-0.886792\pi\) | ||||
0.937419 | − | 0.348203i | \(-0.113208\pi\) | |||||||
\(38\) | − 3.61803i | − 0.586923i | ||||||||
\(39\) | 4.85410 | 0.777278 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.23607 | −0.817736 | −0.408868 | − | 0.912593i | \(-0.634076\pi\) | ||||
−0.408868 | + | 0.912593i | \(0.634076\pi\) | |||||||
\(42\) | 1.00000i | 0.154303i | ||||||||
\(43\) | 1.85410i | 0.282748i | 0.989956 | + | 0.141374i | \(0.0451520\pi\) | ||||
−0.989956 | + | 0.141374i | \(0.954848\pi\) | |||||||
\(44\) | −1.23607 | −0.186344 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.09017 | 0.750505 | ||||||||
\(47\) | 1.61803i | 0.236015i | 0.993013 | + | 0.118007i | \(0.0376506\pi\) | ||||
−0.993013 | + | 0.118007i | \(0.962349\pi\) | |||||||
\(48\) | 1.85410i | 0.267617i | ||||||||
\(49\) | 4.38197 | 0.625995 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.763932 | −0.106972 | ||||||||
\(52\) | − 7.85410i | − 1.08917i | ||||||||
\(53\) | 5.47214i | 0.751656i | 0.926690 | + | 0.375828i | \(0.122642\pi\) | ||||
−0.926690 | + | 0.375828i | \(0.877358\pi\) | |||||||
\(54\) | 3.09017 | 0.420519 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.61803 | 0.483480 | ||||||||
\(57\) | 5.85410i | 0.775395i | ||||||||
\(58\) | − 0.854102i | − 0.112149i | ||||||||
\(59\) | 4.14590 | 0.539750 | 0.269875 | − | 0.962895i | \(-0.413018\pi\) | ||||
0.269875 | + | 0.962895i | \(0.413018\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.70820 | −0.602824 | −0.301412 | − | 0.953494i | \(-0.597458\pi\) | ||||
−0.301412 | + | 0.953494i | \(0.597458\pi\) | |||||||
\(62\) | 1.85410i | 0.235471i | ||||||||
\(63\) | 3.23607i | 0.407706i | ||||||||
\(64\) | 0.236068 | 0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.472136 | −0.0581159 | ||||||||
\(67\) | − 9.23607i | − 1.12837i | −0.825650 | − | 0.564183i | \(-0.809191\pi\) | ||||
0.825650 | − | 0.564183i | \(-0.190809\pi\) | |||||||
\(68\) | 1.23607i | 0.149895i | ||||||||
\(69\) | −8.23607 | −0.991506 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.38197 | −0.520044 | −0.260022 | − | 0.965603i | \(-0.583730\pi\) | ||||
−0.260022 | + | 0.965603i | \(0.583730\pi\) | |||||||
\(72\) | − 4.47214i | − 0.527046i | ||||||||
\(73\) | − 9.00000i | − 1.05337i | −0.850060 | − | 0.526685i | \(-0.823435\pi\) | ||||
0.850060 | − | 0.526685i | \(-0.176565\pi\) | |||||||
\(74\) | −2.61803 | −0.304340 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.47214 | 1.08653 | ||||||||
\(77\) | − 1.23607i | − 0.140863i | ||||||||
\(78\) | − 3.00000i | − 0.339683i | ||||||||
\(79\) | −3.09017 | −0.347671 | −0.173836 | − | 0.984775i | \(-0.555616\pi\) | ||||
−0.173836 | + | 0.984775i | \(0.555616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.23607i | 0.357364i | ||||||||
\(83\) | − 1.76393i | − 0.193617i | −0.995303 | − | 0.0968083i | \(-0.969137\pi\) | ||||
0.995303 | − | 0.0968083i | \(-0.0308634\pi\) | |||||||
\(84\) | −2.61803 | −0.285651 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.14590 | 0.123565 | ||||||||
\(87\) | 1.38197i | 0.148162i | ||||||||
\(88\) | 1.70820i | 0.182095i | ||||||||
\(89\) | −8.94427 | −0.948091 | −0.474045 | − | 0.880500i | \(-0.657207\pi\) | ||||
−0.474045 | + | 0.880500i | \(0.657207\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.85410 | 0.823334 | ||||||||
\(92\) | 13.3262i | 1.38936i | ||||||||
\(93\) | − 3.00000i | − 0.311086i | ||||||||
\(94\) | 1.00000 | 0.103142 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.61803 | 0.573388 | ||||||||
\(97\) | − 2.85410i | − 0.289790i | −0.989447 | − | 0.144895i | \(-0.953716\pi\) | ||||
0.989447 | − | 0.144895i | \(-0.0462845\pi\) | |||||||
\(98\) | − 2.70820i | − 0.273570i | ||||||||
\(99\) | −1.52786 | −0.153556 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.47214 | −0.743505 | −0.371753 | − | 0.928332i | \(-0.621243\pi\) | ||||
−0.371753 | + | 0.928332i | \(0.621243\pi\) | |||||||
\(102\) | 0.472136i | 0.0467484i | ||||||||
\(103\) | − 11.5623i | − 1.13927i | −0.821899 | − | 0.569634i | \(-0.807085\pi\) | ||||
0.821899 | − | 0.569634i | \(-0.192915\pi\) | |||||||
\(104\) | −10.8541 | −1.06433 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.38197 | 0.328486 | ||||||||
\(107\) | − 10.4164i | − 1.00699i | −0.863998 | − | 0.503496i | \(-0.832047\pi\) | ||||
0.863998 | − | 0.503496i | \(-0.167953\pi\) | |||||||
\(108\) | 8.09017i | 0.778477i | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.23607 | 0.402070 | ||||||||
\(112\) | 3.00000i | 0.283473i | ||||||||
\(113\) | 10.1459i | 0.954446i | 0.878782 | + | 0.477223i | \(0.158357\pi\) | ||||
−0.878782 | + | 0.477223i | \(0.841643\pi\) | |||||||
\(114\) | 3.61803 | 0.338860 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.23607 | 0.207614 | ||||||||
\(117\) | − 9.70820i | − 0.897524i | ||||||||
\(118\) | − 2.56231i | − 0.235879i | ||||||||
\(119\) | −1.23607 | −0.113310 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4164 | −0.946946 | ||||||||
\(122\) | 2.90983i | 0.263444i | ||||||||
\(123\) | − 5.23607i | − 0.472120i | ||||||||
\(124\) | −4.85410 | −0.435911 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | 15.8885i | 1.40988i | 0.709267 | + | 0.704940i | \(0.249026\pi\) | ||||
−0.709267 | + | 0.704940i | \(0.750974\pi\) | |||||||
\(128\) | − 11.3820i | − 1.00603i | ||||||||
\(129\) | −1.85410 | −0.163245 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.7984 | −1.55505 | −0.777526 | − | 0.628851i | \(-0.783525\pi\) | ||||
−0.777526 | + | 0.628851i | \(0.783525\pi\) | |||||||
\(132\) | − 1.23607i | − 0.107586i | ||||||||
\(133\) | 9.47214i | 0.821338i | ||||||||
\(134\) | −5.70820 | −0.493114 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.70820 | 0.146477 | ||||||||
\(137\) | − 5.94427i | − 0.507853i | −0.967223 | − | 0.253927i | \(-0.918278\pi\) | ||||
0.967223 | − | 0.253927i | \(-0.0817222\pi\) | |||||||
\(138\) | 5.09017i | 0.433304i | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.61803 | −0.136263 | ||||||||
\(142\) | 2.70820i | 0.227267i | ||||||||
\(143\) | 3.70820i | 0.310096i | ||||||||
\(144\) | 3.70820 | 0.309017 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.56231 | −0.460340 | ||||||||
\(147\) | 4.38197i | 0.361418i | ||||||||
\(148\) | − 6.85410i | − 0.563404i | ||||||||
\(149\) | −13.9443 | −1.14236 | −0.571180 | − | 0.820825i | \(-0.693514\pi\) | ||||
−0.571180 | + | 0.820825i | \(0.693514\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.56231 | −0.452654 | −0.226327 | − | 0.974051i | \(-0.572672\pi\) | ||||
−0.226327 | + | 0.974051i | \(0.572672\pi\) | |||||||
\(152\) | − 13.0902i | − 1.06175i | ||||||||
\(153\) | 1.52786i | 0.123520i | ||||||||
\(154\) | −0.763932 | −0.0615594 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.85410 | 0.628831 | ||||||||
\(157\) | 9.18034i | 0.732671i | 0.930483 | + | 0.366335i | \(0.119388\pi\) | ||||
−0.930483 | + | 0.366335i | \(0.880612\pi\) | |||||||
\(158\) | 1.90983i | 0.151938i | ||||||||
\(159\) | −5.47214 | −0.433969 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.3262 | −1.05025 | ||||||||
\(162\) | − 0.618034i | − 0.0485573i | ||||||||
\(163\) | 11.0000i | 0.861586i | 0.902451 | + | 0.430793i | \(0.141766\pi\) | ||||
−0.902451 | + | 0.430793i | \(0.858234\pi\) | |||||||
\(164\) | −8.47214 | −0.661563 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.09017 | −0.0846136 | ||||||||
\(167\) | 5.56231i | 0.430424i | 0.976567 | + | 0.215212i | \(0.0690443\pi\) | ||||
−0.976567 | + | 0.215212i | \(0.930956\pi\) | |||||||
\(168\) | 3.61803i | 0.279137i | ||||||||
\(169\) | −10.5623 | −0.812485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.7082 | 0.895349 | ||||||||
\(172\) | 3.00000i | 0.228748i | ||||||||
\(173\) | − 16.8885i | − 1.28401i | −0.766700 | − | 0.642006i | \(-0.778102\pi\) | ||||
0.766700 | − | 0.642006i | \(-0.221898\pi\) | |||||||
\(174\) | 0.854102 | 0.0647493 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.41641 | −0.106766 | ||||||||
\(177\) | 4.14590i | 0.311625i | ||||||||
\(178\) | 5.52786i | 0.414331i | ||||||||
\(179\) | 9.47214 | 0.707981 | 0.353990 | − | 0.935249i | \(-0.384825\pi\) | ||||
0.353990 | + | 0.935249i | \(0.384825\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.7082 | 1.01892 | 0.509461 | − | 0.860494i | \(-0.329845\pi\) | ||||
0.509461 | + | 0.860494i | \(0.329845\pi\) | |||||||
\(182\) | − 4.85410i | − 0.359810i | ||||||||
\(183\) | − 4.70820i | − 0.348040i | ||||||||
\(184\) | 18.4164 | 1.35768 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.85410 | −0.135949 | ||||||||
\(187\) | − 0.583592i | − 0.0426765i | ||||||||
\(188\) | 2.61803i | 0.190940i | ||||||||
\(189\) | −8.09017 | −0.588473 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.1803 | −1.74963 | −0.874814 | − | 0.484459i | \(-0.839016\pi\) | ||||
−0.874814 | + | 0.484459i | \(0.839016\pi\) | |||||||
\(192\) | 0.236068i | 0.0170367i | ||||||||
\(193\) | − 5.70820i | − 0.410886i | −0.978669 | − | 0.205443i | \(-0.934137\pi\) | ||||
0.978669 | − | 0.205443i | \(-0.0658634\pi\) | |||||||
\(194\) | −1.76393 | −0.126643 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.09017 | 0.506441 | ||||||||
\(197\) | 9.70820i | 0.691681i | 0.938293 | + | 0.345840i | \(0.112406\pi\) | ||||
−0.938293 | + | 0.345840i | \(0.887594\pi\) | |||||||
\(198\) | 0.944272i | 0.0671065i | ||||||||
\(199\) | −2.56231 | −0.181637 | −0.0908185 | − | 0.995867i | \(-0.528948\pi\) | ||||
−0.0908185 | + | 0.995867i | \(0.528948\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.23607 | 0.651462 | ||||||||
\(202\) | 4.61803i | 0.324924i | ||||||||
\(203\) | 2.23607i | 0.156941i | ||||||||
\(204\) | −1.23607 | −0.0865421 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.14590 | −0.497878 | ||||||||
\(207\) | 16.4721i | 1.14489i | ||||||||
\(208\) | − 9.00000i | − 0.624038i | ||||||||
\(209\) | −4.47214 | −0.309344 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.1803 | 0.907372 | 0.453686 | − | 0.891162i | \(-0.350109\pi\) | ||||
0.453686 | + | 0.891162i | \(0.350109\pi\) | |||||||
\(212\) | 8.85410i | 0.608102i | ||||||||
\(213\) | − 4.38197i | − 0.300247i | ||||||||
\(214\) | −6.43769 | −0.440072 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.1803 | 0.760726 | ||||||||
\(217\) | − 4.85410i | − 0.329518i | ||||||||
\(218\) | 6.18034i | 0.418585i | ||||||||
\(219\) | 9.00000 | 0.608164 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.70820 | 0.249441 | ||||||||
\(222\) | − 2.61803i | − 0.175711i | ||||||||
\(223\) | 22.1803i | 1.48531i | 0.669677 | + | 0.742653i | \(0.266433\pi\) | ||||
−0.669677 | + | 0.742653i | \(0.733567\pi\) | |||||||
\(224\) | 9.09017 | 0.607363 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.27051 | 0.417108 | ||||||||
\(227\) | − 19.2361i | − 1.27674i | −0.769729 | − | 0.638371i | \(-0.779608\pi\) | ||||
0.769729 | − | 0.638371i | \(-0.220392\pi\) | |||||||
\(228\) | 9.47214i | 0.627308i | ||||||||
\(229\) | −8.29180 | −0.547937 | −0.273969 | − | 0.961739i | \(-0.588336\pi\) | ||||
−0.273969 | + | 0.961739i | \(0.588336\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.23607 | 0.0813273 | ||||||||
\(232\) | − 3.09017i | − 0.202880i | ||||||||
\(233\) | 14.9443i | 0.979032i | 0.871994 | + | 0.489516i | \(0.162826\pi\) | ||||
−0.871994 | + | 0.489516i | \(0.837174\pi\) | |||||||
\(234\) | −6.00000 | −0.392232 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.70820 | 0.436667 | ||||||||
\(237\) | − 3.09017i | − 0.200728i | ||||||||
\(238\) | 0.763932i | 0.0495184i | ||||||||
\(239\) | 29.4721 | 1.90639 | 0.953197 | − | 0.302350i | \(-0.0977711\pi\) | ||||
0.953197 | + | 0.302350i | \(0.0977711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.4721 | 0.738985 | 0.369493 | − | 0.929234i | \(-0.379532\pi\) | ||||
0.369493 | + | 0.929234i | \(0.379532\pi\) | |||||||
\(242\) | 6.43769i | 0.413831i | ||||||||
\(243\) | 16.0000i | 1.02640i | ||||||||
\(244\) | −7.61803 | −0.487695 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.23607 | −0.206324 | ||||||||
\(247\) | − 28.4164i | − 1.80809i | ||||||||
\(248\) | 6.70820i | 0.425971i | ||||||||
\(249\) | 1.76393 | 0.111785 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.81966 | −0.430453 | −0.215227 | − | 0.976564i | \(-0.569049\pi\) | ||||
−0.215227 | + | 0.976564i | \(0.569049\pi\) | |||||||
\(252\) | 5.23607i | 0.329841i | ||||||||
\(253\) | − 6.29180i | − 0.395562i | ||||||||
\(254\) | 9.81966 | 0.616140 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | − 16.1459i | − 1.00715i | −0.863951 | − | 0.503577i | \(-0.832017\pi\) | ||||
0.863951 | − | 0.503577i | \(-0.167983\pi\) | |||||||
\(258\) | 1.14590i | 0.0713405i | ||||||||
\(259\) | 6.85410 | 0.425893 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.76393 | 0.171083 | ||||||||
\(262\) | 11.0000i | 0.679582i | ||||||||
\(263\) | − 22.0902i | − 1.36214i | −0.732219 | − | 0.681069i | \(-0.761515\pi\) | ||||
0.732219 | − | 0.681069i | \(-0.238485\pi\) | |||||||
\(264\) | −1.70820 | −0.105133 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.85410 | 0.358938 | ||||||||
\(267\) | − 8.94427i | − 0.547381i | ||||||||
\(268\) | − 14.9443i | − 0.912867i | ||||||||
\(269\) | 17.2361 | 1.05090 | 0.525451 | − | 0.850824i | \(-0.323897\pi\) | ||||
0.525451 | + | 0.850824i | \(0.323897\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 1.41641i | 0.0858823i | ||||||||
\(273\) | 7.85410i | 0.475352i | ||||||||
\(274\) | −3.67376 | −0.221940 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −13.3262 | −0.802145 | ||||||||
\(277\) | 11.2918i | 0.678458i | 0.940704 | + | 0.339229i | \(0.110166\pi\) | ||||
−0.940704 | + | 0.339229i | \(0.889834\pi\) | |||||||
\(278\) | 3.09017i | 0.185336i | ||||||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.09017 | −0.0650341 | −0.0325170 | − | 0.999471i | \(-0.510352\pi\) | ||||
−0.0325170 | + | 0.999471i | \(0.510352\pi\) | |||||||
\(282\) | 1.00000i | 0.0595491i | ||||||||
\(283\) | − 23.1459i | − 1.37588i | −0.725767 | − | 0.687940i | \(-0.758515\pi\) | ||||
0.725767 | − | 0.687940i | \(-0.241485\pi\) | |||||||
\(284\) | −7.09017 | −0.420724 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.29180 | 0.135517 | ||||||||
\(287\) | − 8.47214i | − 0.500094i | ||||||||
\(288\) | − 11.2361i | − 0.662092i | ||||||||
\(289\) | 16.4164 | 0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.85410 | 0.167310 | ||||||||
\(292\) | − 14.5623i | − 0.852194i | ||||||||
\(293\) | − 28.4721i | − 1.66336i | −0.555255 | − | 0.831680i | \(-0.687379\pi\) | ||||
0.555255 | − | 0.831680i | \(-0.312621\pi\) | |||||||
\(294\) | 2.70820 | 0.157946 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.47214 | −0.550557 | ||||||||
\(297\) | − 3.81966i | − 0.221639i | ||||||||
\(298\) | 8.61803i | 0.499229i | ||||||||
\(299\) | 39.9787 | 2.31203 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.00000 | −0.172917 | ||||||||
\(302\) | 3.43769i | 0.197817i | ||||||||
\(303\) | − 7.47214i | − 0.429263i | ||||||||
\(304\) | 10.8541 | 0.622525 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.944272 | 0.0539804 | ||||||||
\(307\) | − 4.76393i | − 0.271892i | −0.990716 | − | 0.135946i | \(-0.956593\pi\) | ||||
0.990716 | − | 0.135946i | \(-0.0434074\pi\) | |||||||
\(308\) | − 2.00000i | − 0.113961i | ||||||||
\(309\) | 11.5623 | 0.657757 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.5066 | −1.67316 | −0.836582 | − | 0.547841i | \(-0.815450\pi\) | ||||
−0.836582 | + | 0.547841i | \(0.815450\pi\) | |||||||
\(312\) | − 10.8541i | − 0.614493i | ||||||||
\(313\) | − 21.2361i | − 1.20033i | −0.799875 | − | 0.600167i | \(-0.795101\pi\) | ||||
0.799875 | − | 0.600167i | \(-0.204899\pi\) | |||||||
\(314\) | 5.67376 | 0.320189 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.00000 | −0.281272 | ||||||||
\(317\) | 23.6525i | 1.32846i | 0.747530 | + | 0.664228i | \(0.231239\pi\) | ||||
−0.747530 | + | 0.664228i | \(0.768761\pi\) | |||||||
\(318\) | 3.38197i | 0.189651i | ||||||||
\(319\) | −1.05573 | −0.0591094 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4164 | 0.581387 | ||||||||
\(322\) | 8.23607i | 0.458978i | ||||||||
\(323\) | 4.47214i | 0.248836i | ||||||||
\(324\) | 1.61803 | 0.0898908 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.79837 | 0.376527 | ||||||||
\(327\) | − 10.0000i | − 0.553001i | ||||||||
\(328\) | 11.7082i | 0.646477i | ||||||||
\(329\) | −2.61803 | −0.144337 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.1246 | 0.941254 | 0.470627 | − | 0.882332i | \(-0.344028\pi\) | ||||
0.470627 | + | 0.882332i | \(0.344028\pi\) | |||||||
\(332\) | − 2.85410i | − 0.156639i | ||||||||
\(333\) | − 8.47214i | − 0.464270i | ||||||||
\(334\) | 3.43769 | 0.188102 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.00000 | −0.163663 | ||||||||
\(337\) | − 1.14590i | − 0.0624210i | −0.999513 | − | 0.0312105i | \(-0.990064\pi\) | ||||
0.999513 | − | 0.0312105i | \(-0.00993623\pi\) | |||||||
\(338\) | 6.52786i | 0.355069i | ||||||||
\(339\) | −10.1459 | −0.551050 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.29180 | 0.124108 | ||||||||
\(342\) | − 7.23607i | − 0.391282i | ||||||||
\(343\) | 18.4164i | 0.994393i | ||||||||
\(344\) | 4.14590 | 0.223532 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.4377 | −0.561134 | ||||||||
\(347\) | 31.0902i | 1.66901i | 0.551002 | + | 0.834504i | \(0.314246\pi\) | ||||
−0.551002 | + | 0.834504i | \(0.685754\pi\) | |||||||
\(348\) | 2.23607i | 0.119866i | ||||||||
\(349\) | −8.29180 | −0.443850 | −0.221925 | − | 0.975064i | \(-0.571234\pi\) | ||||
−0.221925 | + | 0.975064i | \(0.571234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.2705 | 1.29546 | ||||||||
\(352\) | 4.29180i | 0.228753i | ||||||||
\(353\) | 24.0902i | 1.28219i | 0.767461 | + | 0.641095i | \(0.221520\pi\) | ||||
−0.767461 | + | 0.641095i | \(0.778480\pi\) | |||||||
\(354\) | 2.56231 | 0.136185 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −14.4721 | −0.767022 | ||||||||
\(357\) | − 1.23607i | − 0.0654197i | ||||||||
\(358\) | − 5.85410i | − 0.309399i | ||||||||
\(359\) | 28.7426 | 1.51698 | 0.758489 | − | 0.651685i | \(-0.225938\pi\) | ||||
0.758489 | + | 0.651685i | \(0.225938\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2705 | 0.803711 | ||||||||
\(362\) | − 8.47214i | − 0.445286i | ||||||||
\(363\) | − 10.4164i | − 0.546720i | ||||||||
\(364\) | 12.7082 | 0.666091 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.90983 | −0.152099 | ||||||||
\(367\) | 5.43769i | 0.283845i | 0.989878 | + | 0.141923i | \(0.0453284\pi\) | ||||
−0.989878 | + | 0.141923i | \(0.954672\pi\) | |||||||
\(368\) | 15.2705i | 0.796030i | ||||||||
\(369\) | −10.4721 | −0.545158 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.85410 | −0.459682 | ||||||||
\(372\) | − 4.85410i | − 0.251673i | ||||||||
\(373\) | 5.27051i | 0.272897i | 0.990647 | + | 0.136448i | \(0.0435688\pi\) | ||||
−0.990647 | + | 0.136448i | \(0.956431\pi\) | |||||||
\(374\) | −0.360680 | −0.0186503 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.61803 | 0.186586 | ||||||||
\(377\) | − 6.70820i | − 0.345490i | ||||||||
\(378\) | 5.00000i | 0.257172i | ||||||||
\(379\) | 34.5967 | 1.77712 | 0.888558 | − | 0.458765i | \(-0.151708\pi\) | ||||
0.888558 | + | 0.458765i | \(0.151708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8885 | −0.813995 | ||||||||
\(382\) | 14.9443i | 0.764615i | ||||||||
\(383\) | − 11.3607i | − 0.580504i | −0.956950 | − | 0.290252i | \(-0.906261\pi\) | ||||
0.956950 | − | 0.290252i | \(-0.0937391\pi\) | |||||||
\(384\) | 11.3820 | 0.580834 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.52786 | −0.179564 | ||||||||
\(387\) | 3.70820i | 0.188499i | ||||||||
\(388\) | − 4.61803i | − 0.234445i | ||||||||
\(389\) | −15.0000 | −0.760530 | −0.380265 | − | 0.924878i | \(-0.624167\pi\) | ||||
−0.380265 | + | 0.924878i | \(0.624167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.29180 | −0.318190 | ||||||||
\(392\) | − 9.79837i | − 0.494893i | ||||||||
\(393\) | − 17.7984i | − 0.897809i | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.47214 | −0.124230 | ||||||||
\(397\) | 0.0344419i | 0.00172859i | 1.00000 | 0.000864294i | \(0.000275113\pi\) | |||||
−1.00000 | 0.000864294i | \(0.999725\pi\) | ||||||||
\(398\) | 1.58359i | 0.0793783i | ||||||||
\(399\) | −9.47214 | −0.474200 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.5967 | −1.12843 | −0.564214 | − | 0.825629i | \(-0.690821\pi\) | ||||
−0.564214 | + | 0.825629i | \(0.690821\pi\) | |||||||
\(402\) | − 5.70820i | − 0.284699i | ||||||||
\(403\) | 14.5623i | 0.725400i | ||||||||
\(404\) | −12.0902 | −0.601508 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.38197 | 0.0685858 | ||||||||
\(407\) | 3.23607i | 0.160406i | ||||||||
\(408\) | 1.70820i | 0.0845687i | ||||||||
\(409\) | −28.4164 | −1.40510 | −0.702550 | − | 0.711634i | \(-0.747955\pi\) | ||||
−0.702550 | + | 0.711634i | \(0.747955\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.94427 | 0.293209 | ||||||||
\(412\) | − 18.7082i | − 0.921687i | ||||||||
\(413\) | 6.70820i | 0.330089i | ||||||||
\(414\) | 10.1803 | 0.500336 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −27.2705 | −1.33705 | ||||||||
\(417\) | − 5.00000i | − 0.244851i | ||||||||
\(418\) | 2.76393i | 0.135188i | ||||||||
\(419\) | 0.527864 | 0.0257878 | 0.0128939 | − | 0.999917i | \(-0.495896\pi\) | ||||
0.0128939 | + | 0.999917i | \(0.495896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | − 8.14590i | − 0.396536i | ||||||||
\(423\) | 3.23607i | 0.157343i | ||||||||
\(424\) | 12.2361 | 0.594236 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.70820 | −0.131213 | ||||||||
\(427\) | − 7.61803i | − 0.368663i | ||||||||
\(428\) | − 16.8541i | − 0.814674i | ||||||||
\(429\) | −3.70820 | −0.179034 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.8328 | 1.14799 | 0.573993 | − | 0.818860i | \(-0.305394\pi\) | ||||
0.573993 | + | 0.818860i | \(0.305394\pi\) | |||||||
\(432\) | 9.27051i | 0.446028i | ||||||||
\(433\) | 20.1459i | 0.968150i | 0.875026 | + | 0.484075i | \(0.160844\pi\) | ||||
−0.875026 | + | 0.484075i | \(0.839156\pi\) | |||||||
\(434\) | −3.00000 | −0.144005 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.1803 | −0.774898 | ||||||||
\(437\) | 48.2148i | 2.30643i | ||||||||
\(438\) | − 5.56231i | − 0.265777i | ||||||||
\(439\) | −5.97871 | −0.285348 | −0.142674 | − | 0.989770i | \(-0.545570\pi\) | ||||
−0.142674 | + | 0.989770i | \(0.545570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.76393 | 0.417330 | ||||||||
\(442\) | − 2.29180i | − 0.109010i | ||||||||
\(443\) | 12.0557i | 0.572785i | 0.958112 | + | 0.286392i | \(0.0924561\pi\) | ||||
−0.958112 | + | 0.286392i | \(0.907544\pi\) | |||||||
\(444\) | 6.85410 | 0.325281 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.7082 | 0.649102 | ||||||||
\(447\) | − 13.9443i | − 0.659541i | ||||||||
\(448\) | 0.381966i | 0.0180462i | ||||||||
\(449\) | −20.3262 | −0.959254 | −0.479627 | − | 0.877472i | \(-0.659228\pi\) | ||||
−0.479627 | + | 0.877472i | \(0.659228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | 0.188353 | ||||||||
\(452\) | 16.4164i | 0.772163i | ||||||||
\(453\) | − 5.56231i | − 0.261340i | ||||||||
\(454\) | −11.8885 | −0.557957 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13.0902 | 0.613003 | ||||||||
\(457\) | − 5.41641i | − 0.253369i | −0.991943 | − | 0.126684i | \(-0.959566\pi\) | ||||
0.991943 | − | 0.126684i | \(-0.0404336\pi\) | |||||||
\(458\) | 5.12461i | 0.239457i | ||||||||
\(459\) | −3.81966 | −0.178286 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.1803 | 1.07962 | 0.539808 | − | 0.841788i | \(-0.318497\pi\) | ||||
0.539808 | + | 0.841788i | \(0.318497\pi\) | |||||||
\(462\) | − 0.763932i | − 0.0355413i | ||||||||
\(463\) | 16.1246i | 0.749374i | 0.927151 | + | 0.374687i | \(0.122250\pi\) | ||||
−0.927151 | + | 0.374687i | \(0.877750\pi\) | |||||||
\(464\) | 2.56231 | 0.118952 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.23607 | 0.427853 | ||||||||
\(467\) | 28.4508i | 1.31655i | 0.752778 | + | 0.658274i | \(0.228713\pi\) | ||||
−0.752778 | + | 0.658274i | \(0.771287\pi\) | |||||||
\(468\) | − 15.7082i | − 0.726112i | ||||||||
\(469\) | 14.9443 | 0.690062 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.18034 | −0.423008 | ||||||||
\(472\) | − 9.27051i | − 0.426710i | ||||||||
\(473\) | − 1.41641i | − 0.0651265i | ||||||||
\(474\) | −1.90983 | −0.0877214 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 10.9443i | 0.501104i | ||||||||
\(478\) | − 18.2148i | − 0.833125i | ||||||||
\(479\) | 4.14590 | 0.189431 | 0.0947155 | − | 0.995504i | \(-0.469806\pi\) | ||||
0.0947155 | + | 0.995504i | \(0.469806\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.5623 | −0.937560 | ||||||||
\(482\) | − 7.09017i | − 0.322948i | ||||||||
\(483\) | − 13.3262i | − 0.606365i | ||||||||
\(484\) | −16.8541 | −0.766096 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 9.88854 | 0.448553 | ||||||||
\(487\) | 9.58359i | 0.434274i | 0.976141 | + | 0.217137i | \(0.0696718\pi\) | ||||
−0.976141 | + | 0.217137i | \(0.930328\pi\) | |||||||
\(488\) | 10.5279i | 0.476574i | ||||||||
\(489\) | −11.0000 | −0.497437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.2492 | 1.68103 | 0.840517 | − | 0.541785i | \(-0.182251\pi\) | ||||
0.840517 | + | 0.541785i | \(0.182251\pi\) | |||||||
\(492\) | − 8.47214i | − 0.381953i | ||||||||
\(493\) | 1.05573i | 0.0475476i | ||||||||
\(494\) | −17.5623 | −0.790165 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.56231 | −0.249755 | ||||||||
\(497\) | − 7.09017i | − 0.318038i | ||||||||
\(498\) | − 1.09017i | − 0.0488517i | ||||||||
\(499\) | 12.5623 | 0.562366 | 0.281183 | − | 0.959654i | \(-0.409273\pi\) | ||||
0.281183 | + | 0.959654i | \(0.409273\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.56231 | −0.248506 | ||||||||
\(502\) | 4.21478i | 0.188115i | ||||||||
\(503\) | − 10.5836i | − 0.471899i | −0.971765 | − | 0.235950i | \(-0.924180\pi\) | ||||
0.971765 | − | 0.235950i | \(-0.0758200\pi\) | |||||||
\(504\) | 7.23607 | 0.322320 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.88854 | −0.172867 | ||||||||
\(507\) | − 10.5623i | − 0.469088i | ||||||||
\(508\) | 25.7082i | 1.14062i | ||||||||
\(509\) | 4.67376 | 0.207161 | 0.103580 | − | 0.994621i | \(-0.466970\pi\) | ||||
0.103580 | + | 0.994621i | \(0.466970\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.5623 | 0.644198 | ||||||||
\(512\) | − 18.7082i | − 0.826794i | ||||||||
\(513\) | 29.2705i | 1.29232i | ||||||||
\(514\) | −9.97871 | −0.440142 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.00000 | −0.132068 | ||||||||
\(517\) | − 1.23607i | − 0.0543622i | ||||||||
\(518\) | − 4.23607i | − 0.186122i | ||||||||
\(519\) | 16.8885 | 0.741325 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.3607 | −0.672964 | −0.336482 | − | 0.941690i | \(-0.609237\pi\) | ||||
−0.336482 | + | 0.941690i | \(0.609237\pi\) | |||||||
\(522\) | − 1.70820i | − 0.0747661i | ||||||||
\(523\) | − 19.8541i | − 0.868159i | −0.900875 | − | 0.434080i | \(-0.857074\pi\) | ||||
0.900875 | − | 0.434080i | \(-0.142926\pi\) | |||||||
\(524\) | −28.7984 | −1.25806 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.6525 | −0.595276 | ||||||||
\(527\) | − 2.29180i | − 0.0998322i | ||||||||
\(528\) | − 1.41641i | − 0.0616412i | ||||||||
\(529\) | −44.8328 | −1.94925 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.29180 | 0.359833 | ||||||||
\(532\) | 15.3262i | 0.664477i | ||||||||
\(533\) | 25.4164i | 1.10091i | ||||||||
\(534\) | −5.52786 | −0.239214 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −20.6525 | −0.892051 | ||||||||
\(537\) | 9.47214i | 0.408753i | ||||||||
\(538\) | − 10.6525i | − 0.459261i | ||||||||
\(539\) | −3.34752 | −0.144188 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1246 | −0.564271 | −0.282136 | − | 0.959375i | \(-0.591043\pi\) | ||||
−0.282136 | + | 0.959375i | \(0.591043\pi\) | |||||||
\(542\) | 4.94427i | 0.212375i | ||||||||
\(543\) | 13.7082i | 0.588275i | ||||||||
\(544\) | 4.29180 | 0.184009 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.85410 | 0.207736 | ||||||||
\(547\) | 34.7082i | 1.48402i | 0.670391 | + | 0.742008i | \(0.266126\pi\) | ||||
−0.670391 | + | 0.742008i | \(0.733874\pi\) | |||||||
\(548\) | − 9.61803i | − 0.410862i | ||||||||
\(549\) | −9.41641 | −0.401882 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.09017 | 0.344653 | ||||||||
\(552\) | 18.4164i | 0.783854i | ||||||||
\(553\) | − 5.00000i | − 0.212622i | ||||||||
\(554\) | 6.97871 | 0.296497 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.09017 | −0.343100 | ||||||||
\(557\) | − 9.23607i | − 0.391345i | −0.980669 | − | 0.195672i | \(-0.937311\pi\) | ||||
0.980669 | − | 0.195672i | \(-0.0626889\pi\) | |||||||
\(558\) | 3.70820i | 0.156981i | ||||||||
\(559\) | 9.00000 | 0.380659 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.583592 | 0.0246393 | ||||||||
\(562\) | 0.673762i | 0.0284209i | ||||||||
\(563\) | 9.61803i | 0.405352i | 0.979246 | + | 0.202676i | \(0.0649638\pi\) | ||||
−0.979246 | + | 0.202676i | \(0.935036\pi\) | |||||||
\(564\) | −2.61803 | −0.110239 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.3050 | −0.601282 | ||||||||
\(567\) | 1.61803i | 0.0679510i | ||||||||
\(568\) | 9.79837i | 0.411131i | ||||||||
\(569\) | −29.4721 | −1.23554 | −0.617768 | − | 0.786360i | \(-0.711963\pi\) | ||||
−0.617768 | + | 0.786360i | \(0.711963\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.1246 | 1.34437 | 0.672187 | − | 0.740382i | \(-0.265355\pi\) | ||||
0.672187 | + | 0.740382i | \(0.265355\pi\) | |||||||
\(572\) | 6.00000i | 0.250873i | ||||||||
\(573\) | − 24.1803i | − 1.01015i | ||||||||
\(574\) | −5.23607 | −0.218549 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.472136 | 0.0196723 | ||||||||
\(577\) | − 37.7771i | − 1.57268i | −0.617794 | − | 0.786340i | \(-0.711973\pi\) | ||||
0.617794 | − | 0.786340i | \(-0.288027\pi\) | |||||||
\(578\) | − 10.1459i | − 0.422014i | ||||||||
\(579\) | 5.70820 | 0.237225 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.85410 | 0.118408 | ||||||||
\(582\) | − 1.76393i | − 0.0731173i | ||||||||
\(583\) | − 4.18034i | − 0.173132i | ||||||||
\(584\) | −20.1246 | −0.832762 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.5967 | −0.726915 | ||||||||
\(587\) | − 18.7082i | − 0.772170i | −0.922463 | − | 0.386085i | \(-0.873827\pi\) | ||||
0.922463 | − | 0.386085i | \(-0.126173\pi\) | |||||||
\(588\) | 7.09017i | 0.292394i | ||||||||
\(589\) | −17.5623 | −0.723642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.70820 | −0.399342 | ||||||||
\(592\) | − 7.85410i | − 0.322802i | ||||||||
\(593\) | − 22.0902i | − 0.907135i | −0.891222 | − | 0.453567i | \(-0.850151\pi\) | ||||
0.891222 | − | 0.453567i | \(-0.149849\pi\) | |||||||
\(594\) | −2.36068 | −0.0968599 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −22.5623 | −0.924188 | ||||||||
\(597\) | − 2.56231i | − 0.104868i | ||||||||
\(598\) | − 24.7082i | − 1.01039i | ||||||||
\(599\) | 0.527864 | 0.0215679 | 0.0107840 | − | 0.999942i | \(-0.496567\pi\) | ||||
0.0107840 | + | 0.999942i | \(0.496567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2705 | 1.47950 | 0.739752 | − | 0.672879i | \(-0.234943\pi\) | ||||
0.739752 | + | 0.672879i | \(0.234943\pi\) | |||||||
\(602\) | 1.85410i | 0.0755676i | ||||||||
\(603\) | − 18.4721i | − 0.752244i | ||||||||
\(604\) | −9.00000 | −0.366205 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.61803 | −0.187595 | ||||||||
\(607\) | 15.4377i | 0.626597i | 0.949655 | + | 0.313298i | \(0.101434\pi\) | ||||
−0.949655 | + | 0.313298i | \(0.898566\pi\) | |||||||
\(608\) | − 32.8885i | − 1.33381i | ||||||||
\(609\) | −2.23607 | −0.0906100 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.85410 | 0.317743 | ||||||||
\(612\) | 2.47214i | 0.0999302i | ||||||||
\(613\) | 31.9787i | 1.29161i | 0.763503 | + | 0.645804i | \(0.223478\pi\) | ||||
−0.763503 | + | 0.645804i | \(0.776522\pi\) | |||||||
\(614\) | −2.94427 | −0.118821 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.76393 | −0.111362 | ||||||||
\(617\) | − 9.76393i | − 0.393081i | −0.980496 | − | 0.196541i | \(-0.937029\pi\) | ||||
0.980496 | − | 0.196541i | \(-0.0629707\pi\) | |||||||
\(618\) | − 7.14590i | − 0.287450i | ||||||||
\(619\) | −39.4721 | −1.58652 | −0.793260 | − | 0.608884i | \(-0.791618\pi\) | ||||
−0.793260 | + | 0.608884i | \(0.791618\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −41.1803 | −1.65251 | ||||||||
\(622\) | 18.2361i | 0.731200i | ||||||||
\(623\) | − 14.4721i | − 0.579814i | ||||||||
\(624\) | 9.00000 | 0.360288 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13.1246 | −0.524565 | ||||||||
\(627\) | − 4.47214i | − 0.178600i | ||||||||
\(628\) | 14.8541i | 0.592743i | ||||||||
\(629\) | 3.23607 | 0.129030 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.76393 | −0.229459 | −0.114729 | − | 0.993397i | \(-0.536600\pi\) | ||||
−0.114729 | + | 0.993397i | \(0.536600\pi\) | |||||||
\(632\) | 6.90983i | 0.274858i | ||||||||
\(633\) | 13.1803i | 0.523871i | ||||||||
\(634\) | 14.6180 | 0.580556 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.85410 | −0.351088 | ||||||||
\(637\) | − 21.2705i | − 0.842768i | ||||||||
\(638\) | 0.652476i | 0.0258318i | ||||||||
\(639\) | −8.76393 | −0.346696 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.0902 | 0.398538 | 0.199269 | − | 0.979945i | \(-0.436143\pi\) | ||||
0.199269 | + | 0.979945i | \(0.436143\pi\) | |||||||
\(642\) | − 6.43769i | − 0.254076i | ||||||||
\(643\) | 22.8328i | 0.900438i | 0.892918 | + | 0.450219i | \(0.148654\pi\) | ||||
−0.892918 | + | 0.450219i | \(0.851346\pi\) | |||||||
\(644\) | −21.5623 | −0.849674 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.76393 | 0.108745 | ||||||||
\(647\) | − 30.5410i | − 1.20069i | −0.799741 | − | 0.600346i | \(-0.795030\pi\) | ||||
0.799741 | − | 0.600346i | \(-0.204970\pi\) | |||||||
\(648\) | − 2.23607i | − 0.0878410i | ||||||||
\(649\) | −3.16718 | −0.124323 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.85410 | 0.190247 | ||||||||
\(652\) | 17.7984i | 0.697038i | ||||||||
\(653\) | 7.90983i | 0.309536i | 0.987951 | + | 0.154768i | \(0.0494629\pi\) | ||||
−0.987951 | + | 0.154768i | \(0.950537\pi\) | |||||||
\(654\) | −6.18034 | −0.241670 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.70820 | −0.379042 | ||||||||
\(657\) | − 18.0000i | − 0.702247i | ||||||||
\(658\) | 1.61803i | 0.0630775i | ||||||||
\(659\) | −24.4721 | −0.953299 | −0.476650 | − | 0.879093i | \(-0.658149\pi\) | ||||
−0.476650 | + | 0.879093i | \(0.658149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.6869 | −1.58254 | −0.791269 | − | 0.611468i | \(-0.790579\pi\) | ||||
−0.791269 | + | 0.611468i | \(0.790579\pi\) | |||||||
\(662\) | − 10.5836i | − 0.411343i | ||||||||
\(663\) | 3.70820i | 0.144015i | ||||||||
\(664\) | −3.94427 | −0.153067 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.23607 | −0.202894 | ||||||||
\(667\) | 11.3820i | 0.440711i | ||||||||
\(668\) | 9.00000i | 0.348220i | ||||||||
\(669\) | −22.1803 | −0.857541 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.59675 | 0.138851 | ||||||||
\(672\) | 9.09017i | 0.350661i | ||||||||
\(673\) | − 10.1803i | − 0.392423i | −0.980562 | − | 0.196212i | \(-0.937136\pi\) | ||||
0.980562 | − | 0.196212i | \(-0.0628640\pi\) | |||||||
\(674\) | −0.708204 | −0.0272790 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.0902 | −0.657314 | ||||||||
\(677\) | − 8.38197i | − 0.322145i | −0.986943 | − | 0.161073i | \(-0.948505\pi\) | ||||
0.986943 | − | 0.161073i | \(-0.0514953\pi\) | |||||||
\(678\) | 6.27051i | 0.240817i | ||||||||
\(679\) | 4.61803 | 0.177224 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.2361 | 0.737128 | ||||||||
\(682\) | − 1.41641i | − 0.0542371i | ||||||||
\(683\) | − 4.52786i | − 0.173254i | −0.996241 | − | 0.0866270i | \(-0.972391\pi\) | ||||
0.996241 | − | 0.0866270i | \(-0.0276088\pi\) | |||||||
\(684\) | 18.9443 | 0.724352 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11.3820 | 0.434565 | ||||||||
\(687\) | − 8.29180i | − 0.316352i | ||||||||
\(688\) | 3.43769i | 0.131061i | ||||||||
\(689\) | 26.5623 | 1.01194 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.72949 | 0.103835 | 0.0519173 | − | 0.998651i | \(-0.483467\pi\) | ||||
0.0519173 | + | 0.998651i | \(0.483467\pi\) | |||||||
\(692\) | − 27.3262i | − 1.03879i | ||||||||
\(693\) | − 2.47214i | − 0.0939087i | ||||||||
\(694\) | 19.2148 | 0.729383 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.09017 | 0.117133 | ||||||||
\(697\) | − 4.00000i | − 0.151511i | ||||||||
\(698\) | 5.12461i | 0.193969i | ||||||||
\(699\) | −14.9443 | −0.565244 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 35.0132 | 1.32243 | 0.661214 | − | 0.750197i | \(-0.270041\pi\) | ||||
0.661214 | + | 0.750197i | \(0.270041\pi\) | |||||||
\(702\) | − 15.0000i | − 0.566139i | ||||||||
\(703\) | − 24.7984i | − 0.935288i | ||||||||
\(704\) | −0.180340 | −0.00679682 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.8885 | 0.560338 | ||||||||
\(707\) | − 12.0902i | − 0.454698i | ||||||||
\(708\) | 6.70820i | 0.252110i | ||||||||
\(709\) | −33.5410 | −1.25966 | −0.629830 | − | 0.776733i | \(-0.716875\pi\) | ||||
−0.629830 | + | 0.776733i | \(0.716875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.18034 | −0.231781 | ||||||||
\(712\) | 20.0000i | 0.749532i | ||||||||
\(713\) | − 24.7082i | − 0.925330i | ||||||||
\(714\) | −0.763932 | −0.0285894 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15.3262 | 0.572768 | ||||||||
\(717\) | 29.4721i | 1.10066i | ||||||||
\(718\) | − 17.7639i | − 0.662944i | ||||||||
\(719\) | 36.7082 | 1.36899 | 0.684493 | − | 0.729020i | \(-0.260024\pi\) | ||||
0.684493 | + | 0.729020i | \(0.260024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.7082 | 0.696730 | ||||||||
\(722\) | − 9.43769i | − 0.351235i | ||||||||
\(723\) | 11.4721i | 0.426653i | ||||||||
\(724\) | 22.1803 | 0.824326 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.43769 | −0.238925 | ||||||||
\(727\) | − 4.43769i | − 0.164585i | −0.996608 | − | 0.0822925i | \(-0.973776\pi\) | ||||
0.996608 | − | 0.0822925i | \(-0.0262242\pi\) | |||||||
\(728\) | − 17.5623i | − 0.650902i | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.41641 | −0.0523877 | ||||||||
\(732\) | − 7.61803i | − 0.281571i | ||||||||
\(733\) | 26.9787i | 0.996482i | 0.867039 | + | 0.498241i | \(0.166020\pi\) | ||||
−0.867039 | + | 0.498241i | \(0.833980\pi\) | |||||||
\(734\) | 3.36068 | 0.124045 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 46.2705 | 1.70555 | ||||||||
\(737\) | 7.05573i | 0.259901i | ||||||||
\(738\) | 6.47214i | 0.238243i | ||||||||
\(739\) | 30.9787 | 1.13957 | 0.569785 | − | 0.821794i | \(-0.307026\pi\) | ||||
0.569785 | + | 0.821794i | \(0.307026\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 28.4164 | 1.04390 | ||||||||
\(742\) | 5.47214i | 0.200888i | ||||||||
\(743\) | − 16.3607i | − 0.600215i | −0.953905 | − | 0.300108i | \(-0.902977\pi\) | ||||
0.953905 | − | 0.300108i | \(-0.0970226\pi\) | |||||||
\(744\) | −6.70820 | −0.245935 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.25735 | 0.119260 | ||||||||
\(747\) | − 3.52786i | − 0.129078i | ||||||||
\(748\) | − 0.944272i | − 0.0345260i | ||||||||
\(749\) | 16.8541 | 0.615835 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.8885 | −1.49204 | −0.746022 | − | 0.665921i | \(-0.768039\pi\) | ||||
−0.746022 | + | 0.665921i | \(0.768039\pi\) | |||||||
\(752\) | 3.00000i | 0.109399i | ||||||||
\(753\) | − 6.81966i | − 0.248522i | ||||||||
\(754\) | −4.14590 | −0.150985 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −13.0902 | −0.476085 | ||||||||
\(757\) | − 3.58359i | − 0.130248i | −0.997877 | − | 0.0651239i | \(-0.979256\pi\) | ||||
0.997877 | − | 0.0651239i | \(-0.0207443\pi\) | |||||||
\(758\) | − 21.3820i | − 0.776628i | ||||||||
\(759\) | 6.29180 | 0.228378 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.4508 | 1.35759 | 0.678796 | − | 0.734327i | \(-0.262502\pi\) | ||||
0.678796 | + | 0.734327i | \(0.262502\pi\) | |||||||
\(762\) | 9.81966i | 0.355729i | ||||||||
\(763\) | − 16.1803i | − 0.585768i | ||||||||
\(764\) | −39.1246 | −1.41548 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.02129 | −0.253689 | ||||||||
\(767\) | − 20.1246i | − 0.726658i | ||||||||
\(768\) | − 6.56231i | − 0.236797i | ||||||||
\(769\) | 13.4164 | 0.483808 | 0.241904 | − | 0.970300i | \(-0.422228\pi\) | ||||
0.241904 | + | 0.970300i | \(0.422228\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.1459 | 0.581480 | ||||||||
\(772\) | − 9.23607i | − 0.332413i | ||||||||
\(773\) | 33.1591i | 1.19265i | 0.802744 | + | 0.596324i | \(0.203373\pi\) | ||||
−0.802744 | + | 0.596324i | \(0.796627\pi\) | |||||||
\(774\) | 2.29180 | 0.0823769 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.38197 | −0.229099 | ||||||||
\(777\) | 6.85410i | 0.245890i | ||||||||
\(778\) | 9.27051i | 0.332364i | ||||||||
\(779\) | −30.6525 | −1.09824 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.34752 | 0.119784 | ||||||||
\(782\) | 3.88854i | 0.139054i | ||||||||
\(783\) | 6.90983i | 0.246937i | ||||||||
\(784\) | 8.12461 | 0.290165 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −11.0000 | −0.392357 | ||||||||
\(787\) | 34.1803i | 1.21840i | 0.793018 | + | 0.609199i | \(0.208509\pi\) | ||||
−0.793018 | + | 0.609199i | \(0.791491\pi\) | |||||||
\(788\) | 15.7082i | 0.559582i | ||||||||
\(789\) | 22.0902 | 0.786431 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.4164 | −0.583700 | ||||||||
\(792\) | 3.41641i | 0.121397i | ||||||||
\(793\) | 22.8541i | 0.811573i | ||||||||
\(794\) | 0.0212862 | 0.000755420 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.14590 | −0.146947 | ||||||||
\(797\) | − 14.2361i | − 0.504267i | −0.967692 | − | 0.252134i | \(-0.918868\pi\) | ||||
0.967692 | − | 0.252134i | \(-0.0811323\pi\) | |||||||
\(798\) | 5.85410i | 0.207233i | ||||||||
\(799\) | −1.23607 | −0.0437289 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.8885 | −0.632061 | ||||||||
\(802\) | 13.9656i | 0.493141i | ||||||||
\(803\) | 6.87539i | 0.242627i | ||||||||
\(804\) | 14.9443 | 0.527044 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9.00000 | 0.317011 | ||||||||
\(807\) | 17.2361i | 0.606738i | ||||||||
\(808\) | 16.7082i | 0.587793i | ||||||||
\(809\) | 15.9787 | 0.561782 | 0.280891 | − | 0.959740i | \(-0.409370\pi\) | ||||
0.280891 | + | 0.959740i | \(0.409370\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.29180 | −0.0453611 | −0.0226805 | − | 0.999743i | \(-0.507220\pi\) | ||||
−0.0226805 | + | 0.999743i | \(0.507220\pi\) | |||||||
\(812\) | 3.61803i | 0.126968i | ||||||||
\(813\) | − 8.00000i | − 0.280572i | ||||||||
\(814\) | 2.00000 | 0.0701000 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.41641 | −0.0495842 | ||||||||
\(817\) | 10.8541i | 0.379737i | ||||||||
\(818\) | 17.5623i | 0.614052i | ||||||||
\(819\) | 15.7082 | 0.548889 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6869 | 0.687078 | 0.343539 | − | 0.939138i | \(-0.388374\pi\) | ||||
0.343539 | + | 0.939138i | \(0.388374\pi\) | |||||||
\(822\) | − 3.67376i | − 0.128137i | ||||||||
\(823\) | 34.2918i | 1.19534i | 0.801743 | + | 0.597668i | \(0.203906\pi\) | ||||
−0.801743 | + | 0.597668i | \(0.796094\pi\) | |||||||
\(824\) | −25.8541 | −0.900670 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.14590 | 0.144254 | ||||||||
\(827\) | 30.0344i | 1.04440i | 0.852823 | + | 0.522200i | \(0.174889\pi\) | ||||
−0.852823 | + | 0.522200i | \(0.825111\pi\) | |||||||
\(828\) | 26.6525i | 0.926238i | ||||||||
\(829\) | 29.1459 | 1.01228 | 0.506139 | − | 0.862452i | \(-0.331072\pi\) | ||||
0.506139 | + | 0.862452i | \(0.331072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.2918 | −0.391708 | ||||||||
\(832\) | − 1.14590i | − 0.0397269i | ||||||||
\(833\) | 3.34752i | 0.115985i | ||||||||
\(834\) | −3.09017 | −0.107004 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.23607 | −0.250265 | ||||||||
\(837\) | − 15.0000i | − 0.518476i | ||||||||
\(838\) | − 0.326238i | − 0.0112697i | ||||||||
\(839\) | −4.14590 | −0.143132 | −0.0715661 | − | 0.997436i | \(-0.522800\pi\) | ||||
−0.0715661 | + | 0.997436i | \(0.522800\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0902 | −0.934144 | ||||||||
\(842\) | − 19.7771i | − 0.681563i | ||||||||
\(843\) | − 1.09017i | − 0.0375474i | ||||||||
\(844\) | 21.3262 | 0.734079 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.00000 | 0.0687614 | ||||||||
\(847\) | − 16.8541i | − 0.579114i | ||||||||
\(848\) | 10.1459i | 0.348412i | ||||||||
\(849\) | 23.1459 | 0.794365 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 34.8885 | 1.19596 | ||||||||
\(852\) | − 7.09017i | − 0.242905i | ||||||||
\(853\) | 47.3050i | 1.61969i | 0.586643 | + | 0.809845i | \(0.300449\pi\) | ||||
−0.586643 | + | 0.809845i | \(0.699551\pi\) | |||||||
\(854\) | −4.70820 | −0.161111 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −23.2918 | −0.796097 | ||||||||
\(857\) | 40.6869i | 1.38984i | 0.719088 | + | 0.694919i | \(0.244560\pi\) | ||||
−0.719088 | + | 0.694919i | \(0.755440\pi\) | |||||||
\(858\) | 2.29180i | 0.0782406i | ||||||||
\(859\) | 28.4164 | 0.969555 | 0.484778 | − | 0.874637i | \(-0.338901\pi\) | ||||
0.484778 | + | 0.874637i | \(0.338901\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.47214 | 0.288730 | ||||||||
\(862\) | − 14.7295i | − 0.501688i | ||||||||
\(863\) | − 41.5623i | − 1.41480i | −0.706815 | − | 0.707399i | \(-0.749869\pi\) | ||||
0.706815 | − | 0.707399i | \(-0.250131\pi\) | |||||||
\(864\) | 28.0902 | 0.955647 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.4508 | 0.423097 | ||||||||
\(867\) | 16.4164i | 0.557530i | ||||||||
\(868\) | − 7.85410i | − 0.266586i | ||||||||
\(869\) | 2.36068 | 0.0800806 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.8328 | −1.51910 | ||||||||
\(872\) | 22.3607i | 0.757228i | ||||||||
\(873\) | − 5.70820i | − 0.193193i | ||||||||
\(874\) | 29.7984 | 1.00795 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14.5623 | 0.492015 | ||||||||
\(877\) | − 30.5410i | − 1.03130i | −0.856800 | − | 0.515648i | \(-0.827551\pi\) | ||||
0.856800 | − | 0.515648i | \(-0.172449\pi\) | |||||||
\(878\) | 3.69505i | 0.124702i | ||||||||
\(879\) | 28.4721 | 0.960341 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.36068 | 0.146915 | 0.0734575 | − | 0.997298i | \(-0.476597\pi\) | ||||
0.0734575 | + | 0.997298i | \(0.476597\pi\) | |||||||
\(882\) | − 5.41641i | − 0.182380i | ||||||||
\(883\) | − 47.4164i | − 1.59569i | −0.602863 | − | 0.797845i | \(-0.705974\pi\) | ||||
0.602863 | − | 0.797845i | \(-0.294026\pi\) | |||||||
\(884\) | 6.00000 | 0.201802 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.45085 | 0.250316 | ||||||||
\(887\) | 5.88854i | 0.197718i | 0.995101 | + | 0.0988590i | \(0.0315193\pi\) | ||||
−0.995101 | + | 0.0988590i | \(0.968481\pi\) | |||||||
\(888\) | − 9.47214i | − 0.317864i | ||||||||
\(889\) | −25.7082 | −0.862225 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.763932 | −0.0255927 | ||||||||
\(892\) | 35.8885i | 1.20164i | ||||||||
\(893\) | 9.47214i | 0.316973i | ||||||||
\(894\) | −8.61803 | −0.288230 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 18.4164 | 0.615249 | ||||||||
\(897\) | 39.9787i | 1.33485i | ||||||||
\(898\) | 12.5623i | 0.419210i | ||||||||
\(899\) | −4.14590 | −0.138273 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.18034 | −0.139267 | ||||||||
\(902\) | − 2.47214i | − 0.0823131i | ||||||||
\(903\) | − 3.00000i | − 0.0998337i | ||||||||
\(904\) | 22.6869 | 0.754556 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.43769 | −0.114210 | ||||||||
\(907\) | − 47.2492i | − 1.56888i | −0.620202 | − | 0.784442i | \(-0.712949\pi\) | ||||
0.620202 | − | 0.784442i | \(-0.287051\pi\) | |||||||
\(908\) | − 31.1246i | − 1.03291i | ||||||||
\(909\) | −14.9443 | −0.495670 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.7639 | −1.18491 | −0.592456 | − | 0.805603i | \(-0.701842\pi\) | ||||
−0.592456 | + | 0.805603i | \(0.701842\pi\) | |||||||
\(912\) | 10.8541i | 0.359415i | ||||||||
\(913\) | 1.34752i | 0.0445965i | ||||||||
\(914\) | −3.34752 | −0.110726 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.4164 | −0.443291 | ||||||||
\(917\) | − 28.7984i | − 0.951006i | ||||||||
\(918\) | 2.36068i | 0.0779140i | ||||||||
\(919\) | 1.78522 | 0.0588889 | 0.0294445 | − | 0.999566i | \(-0.490626\pi\) | ||||
0.0294445 | + | 0.999566i | \(0.490626\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.76393 | 0.156977 | ||||||||
\(922\) | − 14.3262i | − 0.471810i | ||||||||
\(923\) | 21.2705i | 0.700127i | ||||||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.96556 | 0.327489 | ||||||||
\(927\) | − 23.1246i | − 0.759512i | ||||||||
\(928\) | − 7.76393i | − 0.254864i | ||||||||
\(929\) | 36.6312 | 1.20183 | 0.600915 | − | 0.799313i | \(-0.294803\pi\) | ||||
0.600915 | + | 0.799313i | \(0.294803\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.6525 | 0.840726 | ||||||||
\(932\) | 24.1803i | 0.792053i | ||||||||
\(933\) | − 29.5066i | − 0.966002i | ||||||||
\(934\) | 17.5836 | 0.575353 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −21.7082 | −0.709555 | ||||||||
\(937\) | − 51.2705i | − 1.67493i | −0.546487 | − | 0.837467i | \(-0.684035\pi\) | ||||
0.546487 | − | 0.837467i | \(-0.315965\pi\) | |||||||
\(938\) | − 9.23607i | − 0.301568i | ||||||||
\(939\) | 21.2361 | 0.693013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.5836 | −0.638407 | −0.319203 | − | 0.947686i | \(-0.603415\pi\) | ||||
−0.319203 | + | 0.947686i | \(0.603415\pi\) | |||||||
\(942\) | 5.67376i | 0.184861i | ||||||||
\(943\) | − 43.1246i | − 1.40433i | ||||||||
\(944\) | 7.68692 | 0.250188 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.875388 | −0.0284613 | ||||||||
\(947\) | 28.6525i | 0.931080i | 0.885027 | + | 0.465540i | \(0.154140\pi\) | ||||
−0.885027 | + | 0.465540i | \(0.845860\pi\) | |||||||
\(948\) | − 5.00000i | − 0.162392i | ||||||||
\(949\) | −43.6869 | −1.41814 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.6525 | −0.766984 | ||||||||
\(952\) | 2.76393i | 0.0895796i | ||||||||
\(953\) | 34.7426i | 1.12542i | 0.826653 | + | 0.562712i | \(0.190242\pi\) | ||||
−0.826653 | + | 0.562712i | \(0.809758\pi\) | |||||||
\(954\) | 6.76393 | 0.218990 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 47.6869 | 1.54231 | ||||||||
\(957\) | − 1.05573i | − 0.0341268i | ||||||||
\(958\) | − 2.56231i | − 0.0827843i | ||||||||
\(959\) | 9.61803 | 0.310583 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 12.7082i | 0.409729i | ||||||||
\(963\) | − 20.8328i | − 0.671328i | ||||||||
\(964\) | 18.5623 | 0.597852 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.23607 | −0.264991 | ||||||||
\(967\) | − 39.8885i | − 1.28273i | −0.767236 | − | 0.641365i | \(-0.778369\pi\) | ||||
0.767236 | − | 0.641365i | \(-0.221631\pi\) | |||||||
\(968\) | 23.2918i | 0.748627i | ||||||||
\(969\) | −4.47214 | −0.143666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.38197 | 0.108532 | 0.0542662 | − | 0.998527i | \(-0.482718\pi\) | ||||
0.0542662 | + | 0.998527i | \(0.482718\pi\) | |||||||
\(972\) | 25.8885i | 0.830375i | ||||||||
\(973\) | − 8.09017i | − 0.259359i | ||||||||
\(974\) | 5.92299 | 0.189785 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.72949 | −0.279424 | ||||||||
\(977\) | 33.6525i | 1.07664i | 0.842741 | + | 0.538319i | \(0.180940\pi\) | ||||
−0.842741 | + | 0.538319i | \(0.819060\pi\) | |||||||
\(978\) | 6.79837i | 0.217388i | ||||||||
\(979\) | 6.83282 | 0.218378 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −20.0000 | −0.638551 | ||||||||
\(982\) | − 23.0213i | − 0.734639i | ||||||||
\(983\) | 7.38197i | 0.235448i | 0.993046 | + | 0.117724i | \(0.0375598\pi\) | ||||
−0.993046 | + | 0.117724i | \(0.962440\pi\) | |||||||
\(984\) | −11.7082 | −0.373244 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.652476 | 0.0207791 | ||||||||
\(987\) | − 2.61803i | − 0.0833329i | ||||||||
\(988\) | − 45.9787i | − 1.46278i | ||||||||
\(989\) | −15.2705 | −0.485574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.3607 | 0.932673 | 0.466336 | − | 0.884607i | \(-0.345574\pi\) | ||||
0.466336 | + | 0.884607i | \(0.345574\pi\) | |||||||
\(992\) | 16.8541i | 0.535118i | ||||||||
\(993\) | 17.1246i | 0.543433i | ||||||||
\(994\) | −4.38197 | −0.138988 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.85410 | 0.0904357 | ||||||||
\(997\) | 10.8885i | 0.344844i | 0.985023 | + | 0.172422i | \(0.0551592\pi\) | ||||
−0.985023 | + | 0.172422i | \(0.944841\pi\) | |||||||
\(998\) | − 7.76393i | − 0.245763i | ||||||||
\(999\) | 21.1803 | 0.670116 |
(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 | 625.2.b.a.624.2 | 4 | ||
5.2 | odd | 4 | 625.2.a.b.1.2 | 2 | |||
5.3 | odd | 4 | 625.2.a.c.1.1 | 2 | |||
5.4 | even | 2 | inner | 625.2.b.a.624.3 | 4 | ||
15.2 | even | 4 | 5625.2.a.f.1.1 | 2 | |||
15.8 | even | 4 | 5625.2.a.d.1.2 | 2 | |||
20.3 | even | 4 | 10000.2.a.l.1.1 | 2 | |||
20.7 | even | 4 | 10000.2.a.c.1.2 | 2 | |||
25.2 | odd | 20 | 625.2.d.h.501.1 | 4 | |||
25.3 | odd | 20 | 125.2.d.a.76.1 | 4 | |||
25.4 | even | 10 | 125.2.e.a.49.2 | 8 | |||
25.6 | even | 5 | 125.2.e.a.74.2 | 8 | |||
25.8 | odd | 20 | 125.2.d.a.51.1 | 4 | |||
25.9 | even | 10 | 625.2.e.c.499.1 | 8 | |||
25.11 | even | 5 | 625.2.e.c.124.1 | 8 | |||
25.12 | odd | 20 | 625.2.d.h.126.1 | 4 | |||
25.13 | odd | 20 | 625.2.d.b.126.1 | 4 | |||
25.14 | even | 10 | 625.2.e.c.124.2 | 8 | |||
25.16 | even | 5 | 625.2.e.c.499.2 | 8 | |||
25.17 | odd | 20 | 25.2.d.a.11.1 | ✓ | 4 | ||
25.19 | even | 10 | 125.2.e.a.74.1 | 8 | |||
25.21 | even | 5 | 125.2.e.a.49.1 | 8 | |||
25.22 | odd | 20 | 25.2.d.a.16.1 | yes | 4 | ||
25.23 | odd | 20 | 625.2.d.b.501.1 | 4 | |||
75.17 | even | 20 | 225.2.h.b.136.1 | 4 | |||
75.47 | even | 20 | 225.2.h.b.91.1 | 4 | |||
100.47 | even | 20 | 400.2.u.b.241.1 | 4 | |||
100.67 | even | 20 | 400.2.u.b.161.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.d.a.11.1 | ✓ | 4 | 25.17 | odd | 20 | ||
25.2.d.a.16.1 | yes | 4 | 25.22 | odd | 20 | ||
125.2.d.a.51.1 | 4 | 25.8 | odd | 20 | |||
125.2.d.a.76.1 | 4 | 25.3 | odd | 20 | |||
125.2.e.a.49.1 | 8 | 25.21 | even | 5 | |||
125.2.e.a.49.2 | 8 | 25.4 | even | 10 | |||
125.2.e.a.74.1 | 8 | 25.19 | even | 10 | |||
125.2.e.a.74.2 | 8 | 25.6 | even | 5 | |||
225.2.h.b.91.1 | 4 | 75.47 | even | 20 | |||
225.2.h.b.136.1 | 4 | 75.17 | even | 20 | |||
400.2.u.b.161.1 | 4 | 100.67 | even | 20 | |||
400.2.u.b.241.1 | 4 | 100.47 | even | 20 | |||
625.2.a.b.1.2 | 2 | 5.2 | odd | 4 | |||
625.2.a.c.1.1 | 2 | 5.3 | odd | 4 | |||
625.2.b.a.624.2 | 4 | 1.1 | even | 1 | trivial | ||
625.2.b.a.624.3 | 4 | 5.4 | even | 2 | inner | ||
625.2.d.b.126.1 | 4 | 25.13 | odd | 20 | |||
625.2.d.b.501.1 | 4 | 25.23 | odd | 20 | |||
625.2.d.h.126.1 | 4 | 25.12 | odd | 20 | |||
625.2.d.h.501.1 | 4 | 25.2 | odd | 20 | |||
625.2.e.c.124.1 | 8 | 25.11 | even | 5 | |||
625.2.e.c.124.2 | 8 | 25.14 | even | 10 | |||
625.2.e.c.499.1 | 8 | 25.9 | even | 10 | |||
625.2.e.c.499.2 | 8 | 25.16 | even | 5 | |||
5625.2.a.d.1.2 | 2 | 15.8 | even | 4 | |||
5625.2.a.f.1.1 | 2 | 15.2 | even | 4 | |||
10000.2.a.c.1.2 | 2 | 20.7 | even | 4 | |||
10000.2.a.l.1.1 | 2 | 20.3 | even | 4 |