Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\), degree \(2\), 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.2 | ||
Character | \(\chi\) | \(=\) | 3150.1151 |
Dual form | 3150.2.bf.d.1601.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.34325 | + | 1.22849i | 0.885664 | + | 0.464326i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.03986 | − | 1.17771i | −0.615040 | − | 0.355093i | 0.159896 | − | 0.987134i | \(-0.448884\pi\) |
−0.774935 | + | 0.632041i | \(0.782218\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.64698i | − | 1.28884i | −0.764672 | − | 0.644420i | \(-0.777099\pi\) | ||
0.764672 | − | 0.644420i | \(-0.222901\pi\) | |||||||
\(14\) | −2.64356 | + | 0.107718i | −0.706520 | + | 0.0287888i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.28109 | − | 3.95097i | 0.553246 | − | 0.958250i | −0.444792 | − | 0.895634i | \(-0.646722\pi\) |
0.998038 | − | 0.0626158i | \(-0.0199443\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.491268 | − | 0.283634i | 0.112705 | − | 0.0650700i | −0.442588 | − | 0.896725i | \(-0.645940\pi\) |
0.555293 | + | 0.831655i | \(0.312606\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.35542 | 0.502178 | ||||||||
\(23\) | −5.04588 | + | 2.91324i | −1.05214 | + | 0.607453i | −0.923247 | − | 0.384206i | \(-0.874475\pi\) |
−0.128891 | + | 0.991659i | \(0.541142\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.32349 | + | 4.02440i | 0.455674 | + | 0.789250i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.23553 | − | 1.41507i | 0.422475 | − | 0.267422i | ||||
\(29\) | 2.55339i | 0.474153i | 0.971491 | + | 0.237077i | \(0.0761893\pi\) | ||||
−0.971491 | + | 0.237077i | \(0.923811\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.89659 | − | 1.09500i | −0.340638 | − | 0.196667i | 0.319916 | − | 0.947446i | \(-0.396345\pi\) |
−0.660554 | + | 0.750778i | \(0.729679\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.56218i | 0.782408i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.63355 | − | 8.02554i | −0.761750 | − | 1.31939i | −0.941948 | − | 0.335760i | \(-0.891007\pi\) |
0.180197 | − | 0.983630i | \(-0.442326\pi\) | |||||||
\(38\) | −0.283634 | + | 0.491268i | −0.0460114 | + | 0.0796942i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.68451 | −1.35629 | −0.678147 | − | 0.734927i | \(-0.737217\pi\) | ||||
−0.678147 | + | 0.734927i | \(0.737217\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.57695 | 1.00298 | 0.501488 | − | 0.865165i | \(-0.332786\pi\) | ||||
0.501488 | + | 0.865165i | \(0.332786\pi\) | |||||||
\(44\) | −2.03986 | + | 1.17771i | −0.307520 | + | 0.177547i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.91324 | − | 5.04588i | 0.429534 | − | 0.743975i | ||||
\(47\) | −3.15616 | − | 5.46663i | −0.460374 | − | 0.797391i | 0.538606 | − | 0.842558i | \(-0.318951\pi\) |
−0.998979 | + | 0.0451673i | \(0.985618\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.98161 | + | 5.75732i | 0.568802 | + | 0.822475i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.02440 | − | 2.32349i | −0.558084 | − | 0.322210i | ||||
\(53\) | −10.5228 | − | 6.07533i | −1.44542 | − | 0.834511i | −0.447212 | − | 0.894428i | \(-0.647583\pi\) |
−0.998203 | + | 0.0599168i | \(0.980916\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.22849 | + | 2.34325i | −0.164164 | + | 0.313130i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.27670 | − | 2.21130i | −0.167639 | − | 0.290359i | ||||
\(59\) | −1.67739 | + | 2.90532i | −0.218377 | + | 0.378241i | −0.954312 | − | 0.298812i | \(-0.903410\pi\) |
0.735935 | + | 0.677053i | \(0.236743\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.85523 | + | 3.95787i | −0.877722 | + | 0.506753i | −0.869907 | − | 0.493216i | \(-0.835821\pi\) |
−0.00781543 | + | 0.999969i | \(0.502488\pi\) | |||||||
\(62\) | 2.18999 | 0.278130 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.00143 | + | 3.46657i | −0.244513 | + | 0.423509i | −0.961995 | − | 0.273068i | \(-0.911961\pi\) |
0.717481 | + | 0.696578i | \(0.245295\pi\) | |||||||
\(68\) | −2.28109 | − | 3.95097i | −0.276623 | − | 0.479125i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.02720i | 0.240585i | 0.992738 | + | 0.120292i | \(0.0383832\pi\) | ||||
−0.992738 | + | 0.120292i | \(0.961617\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.11528 | − | 4.10801i | −0.832780 | − | 0.480806i | 0.0220235 | − | 0.999757i | \(-0.492989\pi\) |
−0.854804 | + | 0.518952i | \(0.826322\pi\) | |||||||
\(74\) | 8.02554 | + | 4.63355i | 0.932950 | + | 0.538639i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.567267i | − | 0.0650700i | ||||||
\(77\) | −3.33308 | − | 5.26562i | −0.379839 | − | 0.600073i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.13212 | + | 7.15704i | 0.464900 | + | 0.805230i | 0.999197 | − | 0.0400666i | \(-0.0127570\pi\) |
−0.534297 | + | 0.845297i | \(0.679424\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.52101 | − | 4.34226i | 0.830556 | − | 0.479522i | ||||
\(83\) | 0.171637 | 0.0188396 | 0.00941978 | − | 0.999956i | \(-0.497002\pi\) | ||||
0.00941978 | + | 0.999956i | \(0.497002\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.69581 | + | 3.28848i | −0.614195 | + | 0.354606i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.17771 | − | 2.03986i | 0.125544 | − | 0.217449i | ||||
\(89\) | 2.72938 | + | 4.72742i | 0.289313 | + | 0.501105i | 0.973646 | − | 0.228065i | \(-0.0732397\pi\) |
−0.684333 | + | 0.729170i | \(0.739906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.70878 | − | 10.8890i | 0.598443 | − | 1.14148i | ||||
\(92\) | 5.82648i | 0.607453i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.46663 | + | 3.15616i | 0.563840 | + | 0.325533i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.8564i | − | 1.10230i | −0.834406 | − | 0.551151i | \(-0.814189\pi\) | ||
0.834406 | − | 0.551151i | \(-0.185811\pi\) | |||||||
\(98\) | −6.32684 | − | 2.99518i | −0.639107 | − | 0.302559i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.74827 | − | 9.95630i | 0.571975 | − | 0.990689i | −0.424388 | − | 0.905480i | \(-0.639511\pi\) |
0.996363 | − | 0.0852090i | \(-0.0271558\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.7782 | − | 9.68690i | 1.65320 | − | 0.954478i | 0.677462 | − | 0.735558i | \(-0.263080\pi\) |
0.975743 | − | 0.218920i | \(-0.0702535\pi\) | |||||||
\(104\) | 4.64698 | 0.455674 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.1507 | 1.18018 | ||||||||
\(107\) | −9.28430 | + | 5.36029i | −0.897547 | + | 0.518199i | −0.876404 | − | 0.481577i | \(-0.840064\pi\) |
−0.0211436 | + | 0.999776i | \(0.506731\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.41186 | + | 9.37362i | −0.518363 | + | 0.897830i | 0.481410 | + | 0.876496i | \(0.340125\pi\) |
−0.999772 | + | 0.0213347i | \(0.993208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.107718 | − | 2.64356i | −0.0101784 | − | 0.249793i | ||||
\(113\) | 18.4343i | 1.73415i | 0.498176 | + | 0.867076i | \(0.334003\pi\) | ||||
−0.498176 | + | 0.867076i | \(0.665997\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.21130 | + | 1.27670i | 0.205314 | + | 0.118538i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 3.35478i | − | 0.308832i | ||||||
\(119\) | 10.1989 | − | 6.45578i | 0.934931 | − | 0.591801i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.72599 | − | 4.72156i | −0.247817 | − | 0.429232i | ||||
\(122\) | 3.95787 | − | 6.85523i | 0.358329 | − | 0.620643i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.89659 | + | 1.09500i | −0.170319 | + | 0.0983337i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.04880 | −0.359273 | −0.179637 | − | 0.983733i | \(-0.557492\pi\) | ||||
−0.179637 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.14129 | − | 12.3691i | −0.623937 | − | 1.08069i | −0.988745 | − | 0.149608i | \(-0.952199\pi\) |
0.364808 | − | 0.931083i | \(-0.381134\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.49960 | − | 0.0611049i | 0.130032 | − | 0.00529846i | ||||
\(134\) | − | 4.00285i | − | 0.345794i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.95097 | + | 2.28109i | 0.338792 | + | 0.195602i | ||||
\(137\) | 4.52794 | + | 2.61421i | 0.386848 | + | 0.223347i | 0.680794 | − | 0.732475i | \(-0.261635\pi\) |
−0.293945 | + | 0.955822i | \(0.594968\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.4726i | 1.65164i | 0.563933 | + | 0.825820i | \(0.309288\pi\) | ||||
−0.563933 | + | 0.825820i | \(0.690712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.01360 | − | 1.75561i | −0.0850596 | − | 0.147328i | ||||
\(143\) | −5.47280 | + | 9.47917i | −0.457659 | + | 0.792688i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.21601 | 0.679962 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.26709 | −0.761750 | ||||||||
\(149\) | −4.79814 | + | 2.77021i | −0.393079 | + | 0.226944i | −0.683493 | − | 0.729957i | \(-0.739540\pi\) |
0.290414 | + | 0.956901i | \(0.406207\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.23984 | − | 7.34362i | 0.345033 | − | 0.597615i | −0.640327 | − | 0.768103i | \(-0.721201\pi\) |
0.985360 | + | 0.170488i | \(0.0545343\pi\) | |||||||
\(152\) | 0.283634 | + | 0.491268i | 0.0230057 | + | 0.0398471i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.51934 | + | 2.89362i | 0.444761 | + | 0.233174i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.970763 | + | 0.560470i | 0.0774753 | + | 0.0447304i | 0.538237 | − | 0.842793i | \(-0.319090\pi\) |
−0.460762 | + | 0.887524i | \(0.652424\pi\) | |||||||
\(158\) | −7.15704 | − | 4.13212i | −0.569384 | − | 0.328734i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.4026 | + | 0.627617i | −1.21390 | + | 0.0494631i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.35749 | − | 5.81534i | −0.262979 | − | 0.455493i | 0.704053 | − | 0.710147i | \(-0.251372\pi\) |
−0.967032 | + | 0.254654i | \(0.918038\pi\) | |||||||
\(164\) | −4.34226 | + | 7.52101i | −0.339073 | + | 0.587292i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.148642 | + | 0.0858183i | −0.0115368 | + | 0.00666079i | ||||
\(167\) | −2.80110 | −0.216756 | −0.108378 | − | 0.994110i | \(-0.534566\pi\) | ||||
−0.108378 | + | 0.994110i | \(0.534566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.59442 | −0.661109 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.28848 | − | 5.69581i | 0.250744 | − | 0.434301i | ||||
\(173\) | −6.90018 | − | 11.9515i | −0.524611 | − | 0.908653i | −0.999589 | − | 0.0286558i | \(-0.990877\pi\) |
0.474978 | − | 0.879998i | \(-0.342456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.35542i | 0.177547i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.72742 | − | 2.72938i | −0.354335 | − | 0.204575i | ||||
\(179\) | −2.31980 | − | 1.33933i | −0.173390 | − | 0.100107i | 0.410794 | − | 0.911728i | \(-0.365252\pi\) |
−0.584183 | + | 0.811622i | \(0.698585\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.88082i | − | 0.511447i | −0.966750 | − | 0.255724i | \(-0.917686\pi\) | ||
0.966750 | − | 0.255724i | \(-0.0823137\pi\) | |||||||
\(182\) | 0.500563 | + | 12.2846i | 0.0371042 | + | 0.910592i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.91324 | − | 5.04588i | −0.214767 | − | 0.371987i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.30619 | + | 5.37293i | −0.680536 | + | 0.392908i | ||||
\(188\) | −6.31233 | −0.460374 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.65356 | + | 4.99614i | −0.626150 | + | 0.361508i | −0.779260 | − | 0.626701i | \(-0.784405\pi\) |
0.153110 | + | 0.988209i | \(0.451071\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.5643 | − | 21.7620i | 0.904398 | − | 1.56646i | 0.0826753 | − | 0.996577i | \(-0.473654\pi\) |
0.821723 | − | 0.569887i | \(-0.193013\pi\) | |||||||
\(194\) | 5.42821 | + | 9.40193i | 0.389723 | + | 0.675019i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.97679 | − | 0.569517i | 0.498342 | − | 0.0406798i | ||||
\(197\) | − | 20.0811i | − | 1.43072i | −0.698757 | − | 0.715359i | \(-0.746263\pi\) | ||
0.698757 | − | 0.715359i | \(-0.253737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.3028 | − | 5.94834i | −0.730348 | − | 0.421667i | 0.0882014 | − | 0.996103i | \(-0.471888\pi\) |
−0.818550 | + | 0.574436i | \(0.805221\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.4965i | 0.808894i | ||||||||
\(203\) | −3.13683 | + | 5.98323i | −0.220162 | + | 0.419941i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −9.68690 | + | 16.7782i | −0.674918 | + | 1.16899i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.02440 | + | 2.32349i | −0.279042 | + | 0.161105i | ||||
\(209\) | −1.33615 | −0.0924237 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.78640 | −0.467195 | −0.233597 | − | 0.972333i | \(-0.575050\pi\) | ||||
−0.233597 | + | 0.972333i | \(0.575050\pi\) | |||||||
\(212\) | −10.5228 | + | 6.07533i | −0.722708 | + | 0.417256i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.36029 | − | 9.28430i | 0.366422 | − | 0.634662i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.09899 | − | 4.89580i | −0.210373 | − | 0.332348i | ||||
\(218\) | − | 10.8237i | − | 0.733075i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.3601 | − | 10.6002i | −1.23503 | − | 0.713045i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 28.7684i | − | 1.92648i | −0.268646 | − | 0.963239i | \(-0.586576\pi\) | ||
0.268646 | − | 0.963239i | \(-0.413424\pi\) | |||||||
\(224\) | 1.41507 | + | 2.23553i | 0.0945480 | + | 0.149368i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.21714 | − | 15.9646i | −0.613115 | − | 1.06195i | ||||
\(227\) | −1.05185 | + | 1.82186i | −0.0698140 | + | 0.120921i | −0.898819 | − | 0.438319i | \(-0.855574\pi\) |
0.829005 | + | 0.559241i | \(0.188907\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0269 | + | 8.09841i | −0.926920 | + | 0.535158i | −0.885836 | − | 0.463998i | \(-0.846415\pi\) |
−0.0410842 | + | 0.999156i | \(0.513081\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.55339 | −0.167639 | ||||||||
\(233\) | 6.93805 | − | 4.00569i | 0.454527 | − | 0.262421i | −0.255213 | − | 0.966885i | \(-0.582146\pi\) |
0.709740 | + | 0.704464i | \(0.248812\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.67739 | + | 2.90532i | 0.109189 | + | 0.189120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.60460 | + | 10.6903i | −0.363293 | + | 0.692950i | ||||
\(239\) | − | 15.6233i | − | 1.01059i | −0.862947 | − | 0.505294i | \(-0.831384\pi\) | ||
0.862947 | − | 0.505294i | \(-0.168616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.54491 | − | 2.04665i | −0.228348 | − | 0.131837i | 0.381462 | − | 0.924385i | \(-0.375421\pi\) |
−0.609809 | + | 0.792548i | \(0.708754\pi\) | |||||||
\(242\) | 4.72156 | + | 2.72599i | 0.303513 | + | 0.175233i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.91574i | 0.506753i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.31804 | − | 2.28291i | −0.0838648 | − | 0.145258i | ||||
\(248\) | 1.09500 | − | 1.89659i | 0.0695324 | − | 0.120434i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.9413 | 1.25869 | 0.629343 | − | 0.777128i | \(-0.283324\pi\) | ||||
0.629343 | + | 0.777128i | \(0.283324\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.7238 | 0.862810 | ||||||||
\(254\) | 3.50637 | − | 2.02440i | 0.220009 | − | 0.127022i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10.1722 | + | 17.6188i | 0.634527 | + | 1.09903i | 0.986615 | + | 0.163067i | \(0.0521385\pi\) |
−0.352088 | + | 0.935967i | \(0.614528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.998233 | − | 24.4981i | −0.0620272 | − | 1.52224i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.3691 | + | 7.14129i | 0.764164 | + | 0.441190i | ||||
\(263\) | 3.13156 | + | 1.80801i | 0.193100 | + | 0.111487i | 0.593433 | − | 0.804883i | \(-0.297772\pi\) |
−0.400333 | + | 0.916370i | \(0.631105\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.26814 | + | 0.802720i | −0.0777548 | + | 0.0492179i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.00143 | + | 3.46657i | 0.122257 | + | 0.211755i | ||||
\(269\) | 10.6172 | − | 18.3896i | 0.647345 | − | 1.12123i | −0.336410 | − | 0.941716i | \(-0.609213\pi\) |
0.983755 | − | 0.179518i | \(-0.0574539\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.9957 | + | 10.9672i | −1.15390 | + | 0.666207i | −0.949836 | − | 0.312749i | \(-0.898750\pi\) |
−0.204069 | + | 0.978956i | \(0.565417\pi\) | |||||||
\(272\) | −4.56218 | −0.276623 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.22842 | −0.315860 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.96452 | + | 8.59880i | −0.298289 | + | 0.516652i | −0.975745 | − | 0.218912i | \(-0.929749\pi\) |
0.677456 | + | 0.735564i | \(0.263083\pi\) | |||||||
\(278\) | −9.73628 | − | 16.8637i | −0.583943 | − | 1.01142i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.0696i | − | 0.660358i | −0.943918 | − | 0.330179i | \(-0.892891\pi\) | ||
0.943918 | − | 0.330179i | \(-0.107109\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.6392 | − | 11.3387i | −1.16743 | − | 0.674014i | −0.214354 | − | 0.976756i | \(-0.568765\pi\) |
−0.953072 | + | 0.302742i | \(0.902098\pi\) | |||||||
\(284\) | 1.75561 | + | 1.01360i | 0.104176 | + | 0.0601462i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 10.9456i | − | 0.647227i | ||||||
\(287\) | −20.3500 | − | 10.6689i | −1.20122 | − | 0.629763i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.90675 | − | 3.30259i | −0.112162 | − | 0.194270i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.11528 | + | 4.10801i | −0.416390 | + | 0.240403i | ||||
\(293\) | 12.3248 | 0.720020 | 0.360010 | − | 0.932949i | \(-0.382773\pi\) | ||||
0.360010 | + | 0.932949i | \(0.382773\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.02554 | − | 4.63355i | 0.466475 | − | 0.269319i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.77021 | − | 4.79814i | 0.160474 | − | 0.277949i | ||||
\(299\) | 13.5378 | + | 23.4481i | 0.782909 | + | 1.35604i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.4114 | + | 8.07974i | 0.888300 | + | 0.465708i | ||||
\(302\) | 8.47968i | 0.487951i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.491268 | − | 0.283634i | −0.0281761 | − | 0.0162675i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 8.06274i | − | 0.460165i | −0.973171 | − | 0.230082i | \(-0.926100\pi\) | ||
0.973171 | − | 0.230082i | \(-0.0738996\pi\) | |||||||
\(308\) | −6.22670 | + | 0.253721i | −0.354799 | + | 0.0144571i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.2215 | − | 22.9003i | 0.749721 | − | 1.29855i | −0.198236 | − | 0.980154i | \(-0.563521\pi\) |
0.947956 | − | 0.318400i | \(-0.103146\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.3180 | + | 8.26650i | −0.809301 | + | 0.467250i | −0.846713 | − | 0.532050i | \(-0.821422\pi\) |
0.0374122 | + | 0.999300i | \(0.488089\pi\) | |||||||
\(314\) | −1.12094 | −0.0632583 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.26424 | 0.464900 | ||||||||
\(317\) | 10.6181 | − | 6.13038i | 0.596374 | − | 0.344317i | −0.171240 | − | 0.985229i | \(-0.554777\pi\) |
0.767614 | + | 0.640913i | \(0.221444\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00716 | − | 5.20856i | 0.168369 | − | 0.291623i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.0253 | − | 8.24485i | 0.725870 | − | 0.459468i | ||||
\(323\) | − | 2.58798i | − | 0.143999i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.81534 | + | 3.35749i | 0.322082 | + | 0.185954i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.68451i | − | 0.479522i | ||||||
\(329\) | −0.679951 | − | 16.6870i | −0.0374869 | − | 0.919984i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.1942 | − | 29.7812i | −0.945077 | − | 1.63692i | −0.755598 | − | 0.655036i | \(-0.772654\pi\) |
−0.189479 | − | 0.981885i | \(-0.560680\pi\) | |||||||
\(332\) | 0.0858183 | − | 0.148642i | 0.00470989 | − | 0.00815777i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.42583 | − | 1.40055i | 0.132735 | − | 0.0766348i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.9536 | 1.30484 | 0.652418 | − | 0.757860i | \(-0.273755\pi\) | ||||
0.652418 | + | 0.757860i | \(0.273755\pi\) | |||||||
\(338\) | 7.44298 | − | 4.29721i | 0.404845 | − | 0.233737i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.57918 | + | 4.46727i | 0.139671 | + | 0.241916i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.25708 | + | 18.3822i | 0.121871 | + | 0.992546i | ||||
\(344\) | 6.57695i | 0.354606i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.9515 | + | 6.90018i | 0.642515 | + | 0.370956i | ||||
\(347\) | −24.8552 | − | 14.3501i | −1.33429 | − | 0.770355i | −0.348340 | − | 0.937368i | \(-0.613254\pi\) |
−0.985955 | + | 0.167013i | \(0.946588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.57176i | 0.191192i | 0.995420 | + | 0.0955960i | \(0.0304757\pi\) | ||||
−0.995420 | + | 0.0955960i | \(0.969524\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.17771 | − | 2.03986i | −0.0627722 | − | 0.108725i | ||||
\(353\) | −6.26984 | + | 10.8597i | −0.333710 | + | 0.578003i | −0.983236 | − | 0.182337i | \(-0.941634\pi\) |
0.649526 | + | 0.760339i | \(0.274967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.45875 | 0.289313 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.67867 | 0.141572 | ||||||||
\(359\) | 13.6940 | − | 7.90624i | 0.722742 | − | 0.417275i | −0.0930190 | − | 0.995664i | \(-0.529652\pi\) |
0.815761 | + | 0.578389i | \(0.196318\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.33910 | + | 16.1758i | −0.491532 | + | 0.851358i | ||||
\(362\) | 3.44041 | + | 5.95896i | 0.180824 | + | 0.313196i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.57578 | − | 10.3885i | −0.344664 | − | 0.544503i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.8855 | + | 17.8317i | 1.61221 | + | 0.930809i | 0.988857 | + | 0.148867i | \(0.0475627\pi\) |
0.623351 | + | 0.781942i | \(0.285771\pi\) | |||||||
\(368\) | 5.04588 | + | 2.91324i | 0.263035 | + | 0.151863i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.1940 | − | 27.1632i | −0.892667 | − | 1.41024i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.5306 | + | 19.9717i | 0.597034 | + | 1.03409i | 0.993256 | + | 0.115939i | \(0.0369876\pi\) |
−0.396222 | + | 0.918155i | \(0.629679\pi\) | |||||||
\(374\) | 5.37293 | − | 9.30619i | 0.277828 | − | 0.481212i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.46663 | − | 3.15616i | 0.281920 | − | 0.162767i | ||||
\(377\) | 11.8656 | 0.611108 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.20110 | 0.421262 | 0.210631 | − | 0.977566i | \(-0.432448\pi\) | ||||
0.210631 | + | 0.977566i | \(0.432448\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.99614 | − | 8.65356i | 0.255625 | − | 0.442755i | ||||
\(383\) | 2.31637 | + | 4.01207i | 0.118361 | + | 0.205007i | 0.919118 | − | 0.393982i | \(-0.128903\pi\) |
−0.800757 | + | 0.598989i | \(0.795569\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 25.1286i | 1.27901i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.40193 | − | 5.42821i | −0.477311 | − | 0.275575i | ||||
\(389\) | −29.0194 | − | 16.7544i | −1.47134 | − | 0.849480i | −0.471860 | − | 0.881673i | \(-0.656417\pi\) |
−0.999482 | + | 0.0321938i | \(0.989751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.5815i | 1.34428i | ||||||||
\(392\) | −5.75732 | + | 3.98161i | −0.290789 | + | 0.201102i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.0405 | + | 17.3907i | 0.505835 | + | 0.876132i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0748 | + | 9.28081i | −0.806772 | + | 0.465790i | −0.845834 | − | 0.533447i | \(-0.820897\pi\) |
0.0390613 | + | 0.999237i | \(0.487563\pi\) | |||||||
\(398\) | 11.8967 | 0.596327 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.1377 | + | 7.00770i | −0.606128 | + | 0.349948i | −0.771448 | − | 0.636292i | \(-0.780467\pi\) |
0.165321 | + | 0.986240i | \(0.447134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.08843 | + | 8.81342i | −0.253473 | + | 0.439028i | ||||
\(404\) | −5.74827 | − | 9.95630i | −0.285987 | − | 0.495345i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.275047 | − | 6.75005i | −0.0136503 | − | 0.334999i | ||||
\(407\) | 21.8279i | 1.08197i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.6162 | + | 11.9028i | 1.01941 | + | 0.588555i | 0.913932 | − | 0.405868i | \(-0.133031\pi\) |
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 19.3738i | − | 0.954478i | ||||||
\(413\) | −7.49970 | + | 4.74723i | −0.369036 | + | 0.233596i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.32349 | − | 4.02440i | 0.113918 | − | 0.197313i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.15714 | − | 0.668077i | 0.0565977 | − | 0.0326767i | ||||
\(419\) | 18.1374 | 0.886068 | 0.443034 | − | 0.896505i | \(-0.353902\pi\) | ||||
0.443034 | + | 0.896505i | \(0.353902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.98092 | 0.388966 | 0.194483 | − | 0.980906i | \(-0.437697\pi\) | ||||
0.194483 | + | 0.980906i | \(0.437697\pi\) | |||||||
\(422\) | 5.87719 | − | 3.39320i | 0.286097 | − | 0.165178i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.07533 | − | 10.5228i | 0.295044 | − | 0.511032i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.9257 | + | 0.852667i | −1.01267 | + | 0.0412635i | ||||
\(428\) | 10.7206i | 0.518199i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.1353 | + | 15.6666i | 1.30706 | + | 0.754632i | 0.981605 | − | 0.190925i | \(-0.0611488\pi\) |
0.325456 | + | 0.945557i | \(0.394482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.21564i | 0.250648i | 0.992116 | + | 0.125324i | \(0.0399970\pi\) | ||||
−0.992116 | + | 0.125324i | \(0.960003\pi\) | |||||||
\(434\) | 5.13170 | + | 2.69039i | 0.246329 | + | 0.129143i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.41186 | + | 9.37362i | 0.259181 | + | 0.448915i | ||||
\(437\) | −1.65259 | + | 2.86236i | −0.0790539 | + | 0.136925i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.91887 | + | 5.14931i | −0.425675 | + | 0.245763i | −0.697502 | − | 0.716583i | \(-0.745705\pi\) |
0.271828 | + | 0.962346i | \(0.412372\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.2004 | 1.00840 | ||||||||
\(443\) | 35.9968 | − | 20.7828i | 1.71026 | − | 0.987419i | 0.776067 | − | 0.630651i | \(-0.217212\pi\) |
0.934193 | − | 0.356768i | \(-0.116121\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 14.3842 | + | 24.9142i | 0.681113 | + | 1.17972i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.34325 | − | 1.22849i | −0.110708 | − | 0.0580408i | ||||
\(449\) | − | 23.7838i | − | 1.12242i | −0.827672 | − | 0.561212i | \(-0.810335\pi\) | ||
0.827672 | − | 0.561212i | \(-0.189665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.7152 | + | 10.2279i | 0.834174 | + | 0.481611i | ||||
\(452\) | 15.9646 | + | 9.21714i | 0.750910 | + | 0.433538i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 2.10371i | − | 0.0987319i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.38745 | − | 16.2595i | −0.439126 | − | 0.760589i | 0.558496 | − | 0.829507i | \(-0.311379\pi\) |
−0.997622 | + | 0.0689182i | \(0.978045\pi\) | |||||||
\(458\) | 8.09841 | − | 14.0269i | 0.378414 | − | 0.655432i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.4662 | 0.813484 | 0.406742 | − | 0.913543i | \(-0.366665\pi\) | ||||
0.406742 | + | 0.913543i | \(0.366665\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.99345 | 0.139117 | 0.0695586 | − | 0.997578i | \(-0.477841\pi\) | ||||
0.0695586 | + | 0.997578i | \(0.477841\pi\) | |||||||
\(464\) | 2.21130 | − | 1.27670i | 0.102657 | − | 0.0592692i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.00569 | + | 6.93805i | −0.185560 | + | 0.321399i | ||||
\(467\) | −12.7050 | − | 22.0058i | −0.587920 | − | 1.01831i | −0.994505 | − | 0.104694i | \(-0.966614\pi\) |
0.406585 | − | 0.913613i | \(-0.366720\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.94849 | + | 5.66430i | −0.413203 | + | 0.261553i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.90532 | − | 1.67739i | −0.133728 | − | 0.0772081i | ||||
\(473\) | −13.4160 | − | 7.74575i | −0.616870 | − | 0.356150i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.491429 | − | 12.0604i | −0.0225246 | − | 0.552787i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.81165 | + | 13.5302i | 0.357297 | + | 0.618856i | ||||
\(479\) | −11.8516 | + | 20.5276i | −0.541514 | + | 0.937929i | 0.457304 | + | 0.889311i | \(0.348815\pi\) |
−0.998817 | + | 0.0486188i | \(0.984518\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.2945 | + | 21.5320i | −1.70048 | + | 0.981774i | ||||
\(482\) | 4.09331 | 0.186445 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.45198 | −0.247817 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.10772 | + | 8.84683i | −0.231453 | + | 0.400888i | −0.958236 | − | 0.285979i | \(-0.907681\pi\) |
0.726783 | + | 0.686867i | \(0.241015\pi\) | |||||||
\(488\) | −3.95787 | − | 6.85523i | −0.179164 | − | 0.310322i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.25910i | − | 0.101952i | −0.998700 | − | 0.0509758i | \(-0.983767\pi\) | ||
0.998700 | − | 0.0509758i | \(-0.0162331\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.0884 | + | 5.82452i | 0.454357 | + | 0.262323i | ||||
\(494\) | 2.28291 | + | 1.31804i | 0.102713 | + | 0.0593014i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.18999i | 0.0983337i | ||||||||
\(497\) | −2.49041 | + | 4.75024i | −0.111710 | + | 0.213077i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.6811 | − | 30.6246i | −0.791517 | − | 1.37095i | −0.925028 | − | 0.379900i | \(-0.875958\pi\) |
0.133511 | − | 0.991047i | \(-0.457375\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.2697 | + | 9.97066i | −0.770784 | + | 0.445012i | ||||
\(503\) | 30.7297 | 1.37017 | 0.685084 | − | 0.728464i | \(-0.259766\pi\) | ||||
0.685084 | + | 0.728464i | \(0.259766\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.8852 | + | 6.86191i | −0.528361 | + | 0.305049i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.02440 | + | 3.50637i | −0.0898183 | + | 0.155570i | ||||
\(509\) | 1.03925 | + | 1.80003i | 0.0460637 | + | 0.0797847i | 0.888138 | − | 0.459577i | \(-0.151999\pi\) |
−0.842074 | + | 0.539362i | \(0.818666\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.6262 | − | 18.3671i | −0.514313 | − | 0.812514i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.6188 | − | 10.1722i | −0.777134 | − | 0.448679i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.8682i | 0.653903i | ||||||||
\(518\) | 13.1135 | + | 20.7169i | 0.576176 | + | 0.910246i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.86182 | − | 8.42093i | 0.213000 | − | 0.368927i | −0.739652 | − | 0.672990i | \(-0.765010\pi\) |
0.952652 | + | 0.304062i | \(0.0983431\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.20378 | + | 0.695001i | −0.0526375 | + | 0.0303903i | −0.526088 | − | 0.850430i | \(-0.676342\pi\) |
0.473450 | + | 0.880821i | \(0.343008\pi\) | |||||||
\(524\) | −14.2826 | −0.623937 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.61602 | −0.157666 | ||||||||
\(527\) | −8.65259 | + | 4.99558i | −0.376913 | + | 0.217611i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.47394 | − | 9.48114i | 0.237997 | − | 0.412224i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.696883 | − | 1.32925i | 0.0302137 | − | 0.0576302i | ||||
\(533\) | 40.3568i | 1.74805i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.46657 | − | 2.00143i | −0.149733 | − | 0.0864485i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21.2345i | 0.915484i | ||||||||
\(539\) | −1.34145 | − | 16.4333i | −0.0577805 | − | 0.707832i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.5510 | − | 39.0594i | −0.969541 | − | 1.67930i | −0.696884 | − | 0.717184i | \(-0.745431\pi\) |
−0.272658 | − | 0.962111i | \(-0.587903\pi\) | |||||||
\(542\) | 10.9672 | − | 18.9957i | 0.471080 | − | 0.815934i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.95097 | − | 2.28109i | 0.169396 | − | 0.0978010i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.1372 | 0.476193 | 0.238096 | − | 0.971242i | \(-0.423477\pi\) | ||||
0.238096 | + | 0.971242i | \(0.423477\pi\) | |||||||
\(548\) | 4.52794 | − | 2.61421i | 0.193424 | − | 0.111673i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.724228 | + | 1.25440i | 0.0308532 | + | 0.0534393i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.890207 | + | 21.8470i | 0.0378555 | + | 0.929029i | ||||
\(554\) | − | 9.92903i | − | 0.421844i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.8637 | + | 9.73628i | 0.715181 | + | 0.412910i | ||||
\(557\) | −23.7662 | − | 13.7214i | −1.00701 | − | 0.581395i | −0.0966925 | − | 0.995314i | \(-0.530826\pi\) |
−0.910314 | + | 0.413919i | \(0.864160\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 30.5630i | − | 1.29268i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.53481 | + | 9.58656i | 0.233472 | + | 0.404385i | ||||
\(563\) | 16.6414 | − | 28.8238i | 0.701352 | − | 1.21478i | −0.266640 | − | 0.963796i | \(-0.585914\pi\) |
0.967992 | − | 0.250981i | \(-0.0807531\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 22.6773 | 0.953200 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.02720 | −0.0850596 | ||||||||
\(569\) | −24.6215 | + | 14.2152i | −1.03219 | + | 0.595932i | −0.917610 | − | 0.397482i | \(-0.869884\pi\) |
−0.114575 | + | 0.993415i | \(0.536551\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.0784 | + | 24.3845i | −0.589162 | + | 1.02046i | 0.405181 | + | 0.914237i | \(0.367209\pi\) |
−0.994343 | + | 0.106221i | \(0.966125\pi\) | |||||||
\(572\) | 5.47280 | + | 9.47917i | 0.228829 | + | 0.396344i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 22.9580 | − | 0.935478i | 0.958249 | − | 0.0390461i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.77604 | + | 1.02540i | 0.0739377 | + | 0.0426879i | 0.536513 | − | 0.843892i | \(-0.319741\pi\) |
−0.462575 | + | 0.886580i | \(0.653075\pi\) | |||||||
\(578\) | 3.30259 | + | 1.90675i | 0.137370 | + | 0.0793103i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.402187 | + | 0.210854i | 0.0166855 | + | 0.00874771i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.3100 | + | 24.7856i | 0.592659 | + | 1.02652i | ||||
\(584\) | 4.10801 | − | 7.11528i | 0.169991 | − | 0.294432i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.6735 | + | 6.16238i | −0.440920 | + | 0.254565i | ||||
\(587\) | 36.2336 | 1.49552 | 0.747761 | − | 0.663968i | \(-0.231129\pi\) | ||||
0.747761 | + | 0.663968i | \(0.231129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.24231 | −0.0511886 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.63355 | + | 8.02554i | −0.190438 | + | 0.329848i | ||||
\(593\) | −17.3920 | − | 30.1239i | −0.714205 | − | 1.23704i | −0.963265 | − | 0.268551i | \(-0.913455\pi\) |
0.249061 | − | 0.968488i | \(-0.419878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.54041i | 0.226944i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −23.4481 | − | 13.5378i | −0.958864 | − | 0.553601i | ||||
\(599\) | 31.6459 | + | 18.2708i | 1.29302 | + | 0.746524i | 0.979188 | − | 0.202956i | \(-0.0650547\pi\) |
0.313829 | + | 0.949479i | \(0.398388\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.5137i | 1.85654i | 0.371902 | + | 0.928272i | \(0.378706\pi\) | ||||
−0.371902 | + | 0.928272i | \(0.621294\pi\) | |||||||
\(602\) | −17.3866 | + | 0.708456i | −0.708623 | + | 0.0288745i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.23984 | − | 7.34362i | −0.172517 | − | 0.298807i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.8414 | + | 18.3836i | −1.29240 | + | 0.746169i | −0.979080 | − | 0.203478i | \(-0.934776\pi\) |
−0.313323 | + | 0.949647i | \(0.601442\pi\) | |||||||
\(608\) | 0.567267 | 0.0230057 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.4033 | + | 14.6666i | −1.02771 | + | 0.593348i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.3557 | + | 28.3288i | −0.660599 | + | 1.14419i | 0.319860 | + | 0.947465i | \(0.396364\pi\) |
−0.980459 | + | 0.196726i | \(0.936969\pi\) | |||||||
\(614\) | 4.03137 | + | 6.98254i | 0.162693 | + | 0.281792i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.26562 | − | 3.33308i | 0.212158 | − | 0.134294i | ||||
\(617\) | 20.5530i | 0.827435i | 0.910405 | + | 0.413717i | \(0.135770\pi\) | ||||
−0.910405 | + | 0.413717i | \(0.864230\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.9593 | + | 8.63675i | 0.601265 | + | 0.347140i | 0.769539 | − | 0.638600i | \(-0.220486\pi\) |
−0.168274 | + | 0.985740i | \(0.553819\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 26.4429i | 1.06027i | ||||||||
\(623\) | 0.588006 | + | 14.4305i | 0.0235580 | + | 0.578147i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.26650 | − | 14.3180i | 0.330396 | − | 0.572262i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.970763 | − | 0.560470i | 0.0387377 | − | 0.0223652i | ||||
\(629\) | −42.2782 | −1.68574 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.7501 | 1.30376 | 0.651880 | − | 0.758322i | \(-0.273981\pi\) | ||||
0.651880 | + | 0.758322i | \(0.273981\pi\) | |||||||
\(632\) | −7.15704 | + | 4.13212i | −0.284692 | + | 0.164367i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.13038 | + | 10.6181i | −0.243469 | + | 0.421700i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.7542 | − | 18.5025i | 1.06004 | − | 0.733095i | ||||
\(638\) | 6.01432i | 0.238109i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.9300 | − | 10.9292i | −0.747688 | − | 0.431678i | 0.0771698 | − | 0.997018i | \(-0.475412\pi\) |
−0.824858 | + | 0.565340i | \(0.808745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 4.13643i | − | 0.163125i | −0.996668 | − | 0.0815624i | \(-0.974009\pi\) | ||
0.996668 | − | 0.0815624i | \(-0.0259910\pi\) | |||||||
\(644\) | −7.15779 | + | 13.6529i | −0.282056 | + | 0.537999i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.29399 | + | 2.24125i | 0.0509113 | + | 0.0881809i | ||||
\(647\) | 15.4046 | − | 26.6816i | 0.605618 | − | 1.04896i | −0.386335 | − | 0.922358i | \(-0.626259\pi\) |
0.991953 | − | 0.126603i | \(-0.0404075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.84327 | − | 3.95096i | 0.268622 | − | 0.155089i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.71498 | −0.262979 | ||||||||
\(653\) | −5.97747 | + | 3.45110i | −0.233917 | + | 0.135052i | −0.612378 | − | 0.790565i | \(-0.709787\pi\) |
0.378461 | + | 0.925617i | \(0.376453\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.34226 | + | 7.52101i | 0.169537 | + | 0.293646i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.93235 | + | 14.1114i | 0.348219 | + | 0.550119i | ||||
\(659\) | 11.0895i | 0.431985i | 0.976395 | + | 0.215992i | \(0.0692986\pi\) | ||||
−0.976395 | + | 0.215992i | \(0.930701\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7077 | + | 7.91416i | 0.533169 | + | 0.307825i | 0.742306 | − | 0.670061i | \(-0.233732\pi\) |
−0.209137 | + | 0.977886i | \(0.567065\pi\) | |||||||
\(662\) | 29.7812 | + | 17.1942i | 1.15748 | + | 0.668270i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.171637i | 0.00666079i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.43865 | − | 12.8841i | −0.288026 | − | 0.498875i | ||||
\(668\) | −1.40055 | + | 2.42583i | −0.0541890 | + | 0.0938581i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.6449 | 0.719779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.8980 | −1.07539 | −0.537695 | − | 0.843139i | \(-0.680705\pi\) | ||||
−0.537695 | + | 0.843139i | \(0.680705\pi\) | |||||||
\(674\) | −20.7444 | + | 11.9768i | −0.799045 | + | 0.461329i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.29721 | + | 7.44298i | −0.165277 | + | 0.286269i | ||||
\(677\) | 15.5739 | + | 26.9749i | 0.598555 | + | 1.03673i | 0.993035 | + | 0.117823i | \(0.0375916\pi\) |
−0.394479 | + | 0.918905i | \(0.629075\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.3370 | − | 25.4393i | 0.511828 | − | 0.976269i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.46727 | − | 2.57918i | −0.171061 | − | 0.0987620i | ||||
\(683\) | 21.8168 | + | 12.5960i | 0.834798 | + | 0.481971i | 0.855493 | − | 0.517815i | \(-0.173254\pi\) |
−0.0206948 | + | 0.999786i | \(0.506588\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.1458 | − | 14.7909i | −0.425548 | − | 0.564720i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.28848 | − | 5.69581i | −0.125372 | − | 0.217151i | ||||
\(689\) | −28.2319 | + | 48.8992i | −1.07555 | + | 1.86291i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.2549 | + | 15.7356i | −1.03683 | + | 0.598612i | −0.918933 | − | 0.394414i | \(-0.870948\pi\) |
−0.117894 | + | 0.993026i | \(0.537614\pi\) | |||||||
\(692\) | −13.8004 | −0.524611 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.7003 | 1.08945 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.8102 | + | 34.3122i | −0.750363 | + | 1.29967i | ||||
\(698\) | −1.78588 | − | 3.09324i | −0.0675966 | − | 0.117081i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.19395i | − | 0.196173i | −0.995178 | − | 0.0980864i | \(-0.968728\pi\) | ||
0.995178 | − | 0.0980864i | \(-0.0312721\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.55262 | − | 2.62846i | −0.171705 | − | 0.0991342i | ||||
\(704\) | 2.03986 | + | 1.17771i | 0.0768800 | + | 0.0443867i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 12.5397i | − | 0.471937i | ||||||
\(707\) | 25.7009 | − | 16.2684i | 0.966581 | − | 0.611835i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.9440 | − | 31.0800i | −0.673903 | − | 1.16723i | −0.976788 | − | 0.214207i | \(-0.931283\pi\) |
0.302885 | − | 0.953027i | \(-0.402050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.72742 | + | 2.72938i | −0.177167 | + | 0.102288i | ||||
\(713\) | 12.7600 | 0.477864 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.31980 | + | 1.33933i | −0.0866948 | + | 0.0500533i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.90624 | + | 13.6940i | −0.295058 | + | 0.511056i | ||||
\(719\) | −13.0548 | − | 22.6115i | −0.486861 | − | 0.843268i | 0.513025 | − | 0.858374i | \(-0.328525\pi\) |
−0.999886 | + | 0.0151058i | \(0.995191\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 51.2157 | − | 2.08691i | 1.90737 | − | 0.0777204i | ||||
\(722\) | − | 18.6782i | − | 0.695131i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.95896 | − | 3.44041i | −0.221463 | − | 0.127862i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.0193i | 0.705386i | 0.935739 | + | 0.352693i | \(0.114734\pi\) | ||||
−0.935739 | + | 0.352693i | \(0.885266\pi\) | |||||||
\(728\) | 10.8890 | + | 5.70878i | 0.403574 | + | 0.211581i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0026 | − | 25.9853i | 0.554892 | − | 0.961101i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.65553 | − | 4.41992i | 0.282763 | − | 0.163254i | −0.351910 | − | 0.936034i | \(-0.614468\pi\) |
0.634674 | + | 0.772780i | \(0.281134\pi\) | |||||||
\(734\) | −35.6635 | −1.31636 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.82648 | −0.214767 | ||||||||
\(737\) | 8.16524 | − | 4.71421i | 0.300771 | − | 0.173650i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.20546 | − | 14.2123i | 0.301843 | − | 0.522807i | −0.674711 | − | 0.738082i | \(-0.735732\pi\) |
0.976553 | + | 0.215276i | \(0.0690650\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 28.4720 | + | 14.9270i | 1.04524 | + | 0.547987i | ||||
\(743\) | 47.4829i | 1.74198i | 0.491302 | + | 0.870989i | \(0.336521\pi\) | ||||
−0.491302 | + | 0.870989i | \(0.663479\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −19.9717 | − | 11.5306i | −0.731214 | − | 0.422167i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.7459i | 0.392908i | ||||||||
\(749\) | −28.3405 | + | 1.15480i | −1.03554 | + | 0.0421955i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.4048 | + | 30.1459i | 0.635109 | + | 1.10004i | 0.986492 | + | 0.163809i | \(0.0523781\pi\) |
−0.351383 | + | 0.936232i | \(0.614289\pi\) | |||||||
\(752\) | −3.15616 | + | 5.46663i | −0.115093 | + | 0.199348i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.2759 | + | 5.93279i | −0.374226 | + | 0.216059i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.68581 | −0.352037 | −0.176018 | − | 0.984387i | \(-0.556322\pi\) | ||||
−0.176018 | + | 0.984387i | \(0.556322\pi\) | |||||||
\(758\) | −7.10236 | + | 4.10055i | −0.257969 | + | 0.148939i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.2236 | + | 38.4924i | 0.805605 | + | 1.39535i | 0.915882 | + | 0.401448i | \(0.131493\pi\) |
−0.110277 | + | 0.993901i | \(0.535174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.1968 | + | 15.3163i | −0.875982 | + | 0.554487i | ||||
\(764\) | 9.99228i | 0.361508i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.01207 | − | 2.31637i | −0.144962 | − | 0.0836939i | ||||
\(767\) | 13.5010 | + | 7.79479i | 0.487492 | + | 0.281454i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.0290i | 1.47954i | 0.672858 | + | 0.739771i | \(0.265066\pi\) | ||||
−0.672858 | + | 0.739771i | \(0.734934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.5643 | − | 21.7620i | −0.452199 | − | 0.783232i | ||||
\(773\) | −17.4971 | + | 30.3059i | −0.629327 | + | 1.09003i | 0.358360 | + | 0.933583i | \(0.383336\pi\) |
−0.987687 | + | 0.156443i | \(0.949997\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.8564 | 0.389723 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 33.5087 | 1.20135 | ||||||||
\(779\) | −4.26642 | + | 2.46322i | −0.152860 | + | 0.0882540i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.38746 | − | 4.13521i | 0.0854301 | − | 0.147969i | ||||
\(782\) | −13.2907 | − | 23.0202i | −0.475276 | − | 0.823201i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.99518 | − | 6.32684i | 0.106971 | − | 0.225959i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.3139 | + | 11.1509i | 0.688465 | + | 0.397485i | 0.803037 | − | 0.595930i | \(-0.203216\pi\) |
−0.114572 | + | 0.993415i | \(0.536550\pi\) | |||||||
\(788\) | −17.3907 | − | 10.0405i | −0.619519 | − | 0.357679i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.6464 | + | 43.1961i | −0.805212 | + | 1.53588i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.3921 | + | 31.8561i | 0.653124 | + | 1.13124i | ||||
\(794\) | 9.28081 | − | 16.0748i | 0.329363 | − | 0.570474i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.3028 | + | 5.94834i | −0.365174 | + | 0.210833i | ||||
\(797\) | 49.1382 | 1.74057 | 0.870283 | − | 0.492553i | \(-0.163936\pi\) | ||||
0.870283 | + | 0.492553i | \(0.163936\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −28.7980 | −1.01880 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.00770 | − | 12.1377i | 0.247451 | − | 0.428597i | ||||
\(803\) | 9.67609 | + | 16.7595i | 0.341462 | + | 0.591429i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 10.1769i | − | 0.358465i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.95630 | + | 5.74827i | 0.350262 | + | 0.202224i | ||||
\(809\) | −32.5217 | − | 18.7764i | −1.14340 | − | 0.660144i | −0.196132 | − | 0.980578i | \(-0.562838\pi\) |
−0.947271 | + | 0.320434i | \(0.896171\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 32.3972i | − | 1.13762i | −0.822469 | − | 0.568810i | \(-0.807404\pi\) | ||
0.822469 | − | 0.568810i | \(-0.192596\pi\) | |||||||
\(812\) | 3.61322 | + | 5.70819i | 0.126799 | + | 0.200318i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.9140 | − | 18.9035i | −0.382534 | − | 0.662569i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.23104 | − | 1.86544i | 0.113040 | − | 0.0652636i | ||||
\(818\) | −23.8056 | −0.832342 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.8756 | − | 9.74316i | 0.588964 | − | 0.340039i | −0.175724 | − | 0.984440i | \(-0.556227\pi\) |
0.764688 | + | 0.644401i | \(0.222893\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.3974 | + | 24.9370i | −0.501861 | + | 0.869250i | 0.498136 | + | 0.867099i | \(0.334018\pi\) |
−0.999998 | + | 0.00215079i | \(0.999315\pi\) | |||||||
\(824\) | 9.68690 | + | 16.7782i | 0.337459 | + | 0.584496i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.12132 | − | 7.86107i | 0.143399 | − | 0.273522i | ||||
\(827\) | − | 32.2720i | − | 1.12221i | −0.827745 | − | 0.561104i | \(-0.810377\pi\) | ||
0.827745 | − | 0.561104i | \(-0.189623\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.2675 | + | 27.2899i | 1.64167 | + | 0.947817i | 0.980241 | + | 0.197806i | \(0.0633816\pi\) |
0.661426 | + | 0.750011i | \(0.269952\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.64698i | 0.161105i | ||||||||
\(833\) | 31.8294 | − | 2.59824i | 1.10282 | − | 0.0900237i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.668077 | + | 1.15714i | −0.0231059 | + | 0.0400206i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.7074 | + | 9.06868i | −0.542604 | + | 0.313272i | ||||
\(839\) | 47.8295 | 1.65126 | 0.825629 | − | 0.564213i | \(-0.190820\pi\) | ||||
0.825629 | + | 0.564213i | \(0.190820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.4802 | 0.775179 | ||||||||
\(842\) | −6.91168 | + | 3.99046i | −0.238192 | + | 0.137520i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.39320 | + | 5.87719i | −0.116799 | + | 0.202301i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.587277 | − | 14.4126i | −0.0201791 | − | 0.495224i | ||||
\(848\) | 12.1507i | 0.417256i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46.7606 | + | 26.9973i | 1.60293 | + | 0.925455i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.9274i | 0.374148i | 0.982346 | + | 0.187074i | \(0.0599004\pi\) | ||||
−0.982346 | + | 0.187074i | \(0.940100\pi\) | |||||||
\(854\) | 17.6959 | − | 11.2013i | 0.605540 | − | 0.383300i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.36029 | − | 9.28430i | −0.183211 | − | 0.317331i | ||||
\(857\) | −11.1878 | + | 19.3778i | −0.382167 | + | 0.661932i | −0.991372 | − | 0.131081i | \(-0.958155\pi\) |
0.609205 | + | 0.793013i | \(0.291489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.2119 | − | 16.2881i | 0.962577 | − | 0.555744i | 0.0656116 | − | 0.997845i | \(-0.479100\pi\) |
0.896965 | + | 0.442101i | \(0.145767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −31.3331 | −1.06721 | ||||||||
\(863\) | 36.2871 | − | 20.9504i | 1.23523 | − | 0.713160i | 0.267113 | − | 0.963665i | \(-0.413930\pi\) |
0.968115 | + | 0.250506i | \(0.0805969\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.60782 | − | 4.51688i | −0.0886174 | − | 0.153490i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.78938 | + | 0.235902i | −0.196504 | + | 0.00800703i | ||||
\(869\) | − | 19.4658i | − | 0.660331i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.1091 | + | 9.30059i | 0.545836 | + | 0.315138i | ||||
\(872\) | −9.37362 | − | 5.41186i | −0.317431 | − | 0.183269i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 3.30517i | − | 0.111799i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.3084 | − | 50.7637i | −0.989675 | − | 1.71417i | −0.618965 | − | 0.785419i | \(-0.712448\pi\) |
−0.370710 | − | 0.928749i | \(-0.620886\pi\) | |||||||
\(878\) | 5.14931 | − | 8.91887i | 0.173781 | − | 0.300997i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.97791 | −0.167710 | −0.0838550 | − | 0.996478i | \(-0.526723\pi\) | ||||
−0.0838550 | + | 0.996478i | \(0.526723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.8600 | 0.701995 | 0.350998 | − | 0.936376i | \(-0.385843\pi\) | ||||
0.350998 | + | 0.936376i | \(0.385843\pi\) | |||||||
\(884\) | −18.3601 | + | 10.6002i | −0.617515 | + | 0.356523i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20.7828 | + | 35.9968i | −0.698211 | + | 1.20934i | ||||
\(887\) | 24.9109 | + | 43.1470i | 0.836427 | + | 1.44873i | 0.892864 | + | 0.450327i | \(0.148693\pi\) |
−0.0564371 | + | 0.998406i | \(0.517974\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.48735 | − | 4.97392i | −0.318195 | − | 0.166820i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.9142 | − | 14.3842i | −0.834189 | − | 0.481619i | ||||
\(893\) | −3.10104 | − | 1.79039i | −0.103772 | − | 0.0599130i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.64356 | − | 0.107718i | 0.0883151 | − | 0.00359861i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.8919 | + | 20.5973i | 0.396837 | + | 0.687342i | ||||
\(899\) | 2.79596 | − | 4.84275i | 0.0932505 | − | 0.161515i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0069 | + | 27.7168i | −1.59934 | + | 0.923379i | ||||
\(902\) | −20.4557 | −0.681100 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.4343 | −0.613115 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.0797 | + | 31.3149i | −0.600326 | + | 1.03980i | 0.392445 | + | 0.919775i | \(0.371629\pi\) |
−0.992771 | + | 0.120020i | \(0.961704\pi\) | |||||||
\(908\) | 1.05185 | + | 1.82186i | 0.0349070 | + | 0.0604607i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.05205i | 0.0679873i | 0.999422 | + | 0.0339937i | \(0.0108226\pi\) | ||||
−0.999422 | + | 0.0339937i | \(0.989177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.350114 | − | 0.202138i | −0.0115871 | − | 0.00668980i | ||||
\(914\) | 16.2595 | + | 9.38745i | 0.537818 | + | 0.310509i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.1968i | 0.535158i | ||||||||
\(917\) | −1.53849 | − | 37.7568i | −0.0508054 | − | 1.24684i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.696500 | − | 1.20637i | −0.0229754 | − | 0.0397946i | 0.854309 | − | 0.519765i | \(-0.173981\pi\) |
−0.877285 | + | 0.479971i | \(0.840647\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.1262 | + | 8.73312i | −0.498155 | + | 0.287610i | ||||
\(923\) | 9.42038 | 0.310076 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.59240 | + | 1.49672i | −0.0851916 | + | 0.0491854i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.27670 | + | 2.21130i | −0.0419096 | + | 0.0725896i | ||||
\(929\) | 16.5276 | + | 28.6266i | 0.542252 | + | 0.939208i | 0.998774 | + | 0.0494960i | \(0.0157615\pi\) |
−0.456522 | + | 0.889712i | \(0.650905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.58901 | + | 1.69907i | 0.117625 | + | 0.0556847i | ||||
\(932\) | − | 8.01137i | − | 0.262421i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.0058 | + | 12.7050i | 0.720051 | + | 0.415722i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.53551i | − | 0.0828314i | −0.999142 | − | 0.0414157i | \(-0.986813\pi\) | ||
0.999142 | − | 0.0414157i | \(-0.0131868\pi\) | |||||||
\(938\) | 4.91747 | − | 9.37967i | 0.160561 | − | 0.306257i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.8858 | − | 32.7112i | 0.615659 | − | 1.06635i | −0.374609 | − | 0.927183i | \(-0.622223\pi\) |
0.990268 | − | 0.139171i | \(-0.0444436\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.8210 | − | 25.3001i | 1.42701 | − | 0.823884i | ||||
\(944\) | 3.35478 | 0.109189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.4915 | 0.503672 | ||||||||
\(947\) | −49.0138 | + | 28.2981i | −1.59274 | + | 0.919566i | −0.599900 | + | 0.800075i | \(0.704793\pi\) |
−0.992835 | + | 0.119491i | \(0.961874\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.0898 | + | 33.0645i | −0.619682 | + | 1.07332i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.45578 | + | 10.1989i | 0.209233 | + | 0.330548i | ||||
\(953\) | − | 34.3234i | − | 1.11184i | −0.831234 | − | 0.555922i | \(-0.812365\pi\) | ||
0.831234 | − | 0.555922i | \(-0.187635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.5302 | − | 7.81165i | −0.437597 | − | 0.252647i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 23.7032i | − | 0.765816i | ||||||
\(959\) | 7.39855 | + | 11.6883i | 0.238912 | + | 0.377434i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.1020 | − | 22.6933i | −0.422644 | − | 0.732041i | ||||
\(962\) | 21.5320 | − | 37.2945i | 0.694219 | − | 1.20242i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.54491 | + | 2.04665i | −0.114174 | + | 0.0659183i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.903990 | −0.0290703 | −0.0145352 | − | 0.999894i | \(-0.504627\pi\) | ||||
−0.0145352 | + | 0.999894i | \(0.504627\pi\) | |||||||
\(968\) | 4.72156 | − | 2.72599i | 0.151757 | − | 0.0876167i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.2293 | + | 36.7703i | 0.681282 | + | 1.18001i | 0.974590 | + | 0.223997i | \(0.0719105\pi\) |
−0.293308 | + | 0.956018i | \(0.594756\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.9219 | + | 45.6290i | −0.766901 | + | 1.46280i | ||||
\(974\) | − | 10.2154i | − | 0.327324i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.85523 | + | 3.95787i | 0.219431 | + | 0.126688i | ||||
\(977\) | 5.32079 | + | 3.07196i | 0.170227 | + | 0.0982807i | 0.582693 | − | 0.812692i | \(-0.301999\pi\) |
−0.412466 | + | 0.910973i | \(0.635332\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12.8577i | − | 0.410933i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.12955 | + | 1.95643i | 0.0360453 | + | 0.0624323i | ||||
\(983\) | −19.7933 | + | 34.2830i | −0.631309 | + | 1.09346i | 0.355976 | + | 0.934495i | \(0.384149\pi\) |
−0.987284 | + | 0.158964i | \(0.949185\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11.6490 | −0.370981 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.63608 | −0.0838648 | ||||||||
\(989\) | −33.1865 | + | 19.1602i | −1.05527 | + | 0.609260i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.4602 | − | 33.7060i | 0.618172 | − | 1.07071i | −0.371647 | − | 0.928374i | \(-0.621207\pi\) |
0.989819 | − | 0.142331i | \(-0.0454599\pi\) | |||||||
\(992\) | −1.09500 | − | 1.89659i | −0.0347662 | − | 0.0602168i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.218366 | − | 5.35903i | −0.00692616 | − | 0.169978i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.5522 | + | 10.7111i | 0.587555 | + | 0.339225i | 0.764130 | − | 0.645062i | \(-0.223168\pi\) |
−0.176575 | + | 0.984287i | \(0.556502\pi\) | |||||||
\(998\) | 30.6246 | + | 17.6811i | 0.969406 | + | 0.559687i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.bf.d.1151.2 | ✓ | 24 | |
3.2 | odd | 2 | inner | 3150.2.bf.d.1151.11 | yes | 24 | |
5.2 | odd | 4 | 3150.2.bp.g.899.5 | 24 | |||
5.3 | odd | 4 | 3150.2.bp.h.899.8 | 24 | |||
5.4 | even | 2 | 3150.2.bf.e.1151.11 | yes | 24 | ||
7.5 | odd | 6 | inner | 3150.2.bf.d.1601.11 | yes | 24 | |
15.2 | even | 4 | 3150.2.bp.h.899.5 | 24 | |||
15.8 | even | 4 | 3150.2.bp.g.899.8 | 24 | |||
15.14 | odd | 2 | 3150.2.bf.e.1151.2 | yes | 24 | ||
21.5 | even | 6 | inner | 3150.2.bf.d.1601.2 | yes | 24 | |
35.12 | even | 12 | 3150.2.bp.g.1349.8 | 24 | |||
35.19 | odd | 6 | 3150.2.bf.e.1601.2 | yes | 24 | ||
35.33 | even | 12 | 3150.2.bp.h.1349.5 | 24 | |||
105.47 | odd | 12 | 3150.2.bp.h.1349.8 | 24 | |||
105.68 | odd | 12 | 3150.2.bp.g.1349.5 | 24 | |||
105.89 | even | 6 | 3150.2.bf.e.1601.11 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.bf.d.1151.2 | ✓ | 24 | 1.1 | even | 1 | trivial | |
3150.2.bf.d.1151.11 | yes | 24 | 3.2 | odd | 2 | inner | |
3150.2.bf.d.1601.2 | yes | 24 | 21.5 | even | 6 | inner | |
3150.2.bf.d.1601.11 | yes | 24 | 7.5 | odd | 6 | inner | |
3150.2.bf.e.1151.2 | yes | 24 | 15.14 | odd | 2 | ||
3150.2.bf.e.1151.11 | yes | 24 | 5.4 | even | 2 | ||
3150.2.bf.e.1601.2 | yes | 24 | 35.19 | odd | 6 | ||
3150.2.bf.e.1601.11 | yes | 24 | 105.89 | even | 6 | ||
3150.2.bp.g.899.5 | 24 | 5.2 | odd | 4 | |||
3150.2.bp.g.899.8 | 24 | 15.8 | even | 4 | |||
3150.2.bp.g.1349.5 | 24 | 105.68 | odd | 12 | |||
3150.2.bp.g.1349.8 | 24 | 35.12 | even | 12 | |||
3150.2.bp.h.899.5 | 24 | 15.2 | even | 4 | |||
3150.2.bp.h.899.8 | 24 | 5.3 | odd | 4 | |||
3150.2.bp.h.1349.5 | 24 | 35.33 | even | 12 | |||
3150.2.bp.h.1349.8 | 24 | 105.47 | odd | 12 |