Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(199,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(-0.409850 + 0.236627i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 675.199 |
Dual form | 675.2.k.c.424.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.409850 | + | 0.236627i | −0.289808 | + | 0.167321i | −0.637855 | − | 0.770156i | \(-0.720178\pi\) |
0.348047 | + | 0.937477i | \(0.386845\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.888015 | + | 1.53809i | −0.444008 | + | 0.769044i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.21967 | − | 1.28153i | 0.838956 | − | 0.484372i | −0.0179531 | − | 0.999839i | \(-0.505715\pi\) |
0.856909 | + | 0.515467i | \(0.172382\pi\) | |||||||
\(8\) | − | 1.78702i | − | 0.631808i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.08430 | − | 5.34217i | −0.929952 | − | 1.61072i | −0.783397 | − | 0.621522i | \(-0.786515\pi\) |
−0.146555 | − | 0.989202i | \(-0.546819\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.84662 | + | 1.06615i | 0.512161 | + | 0.295696i | 0.733722 | − | 0.679450i | \(-0.237782\pi\) |
−0.221560 | + | 0.975147i | \(0.571115\pi\) | |||||||
\(14\) | −0.606488 | + | 1.05047i | −0.162091 | + | 0.280750i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.35317 | − | 2.34376i | −0.338293 | − | 0.585941i | ||||
\(17\) | − | 3.16860i | − | 0.768500i | −0.923229 | − | 0.384250i | \(-0.874460\pi\) | ||
0.923229 | − | 0.384250i | \(-0.125540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.356267 | −0.0817332 | −0.0408666 | − | 0.999165i | \(-0.513012\pi\) | ||||
−0.0408666 | + | 0.999165i | \(0.513012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.52821 | + | 1.45966i | 0.539015 | + | 0.311201i | ||||
\(23\) | 3.64854 | + | 2.10649i | 0.760774 | + | 0.439233i | 0.829574 | − | 0.558397i | \(-0.188584\pi\) |
−0.0687995 | + | 0.997631i | \(0.521917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.00912 | −0.197905 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.55206i | 0.860259i | ||||||||
\(29\) | −0.843116 | − | 1.46032i | −0.156563 | − | 0.271174i | 0.777064 | − | 0.629421i | \(-0.216708\pi\) |
−0.933627 | + | 0.358247i | \(0.883375\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.12920 | − | 7.15199i | 0.741627 | − | 1.28453i | −0.210128 | − | 0.977674i | \(-0.567388\pi\) |
0.951754 | − | 0.306861i | \(-0.0992787\pi\) | |||||||
\(32\) | 4.20441 | + | 2.42742i | 0.743242 | + | 0.429111i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.749778 | + | 1.29865i | 0.128586 | + | 0.222717i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.63274i | 0.597219i | 0.954375 | + | 0.298609i | \(0.0965228\pi\) | ||||
−0.954375 | + | 0.298609i | \(0.903477\pi\) | |||||||
\(38\) | 0.146016 | − | 0.0843024i | 0.0236869 | − | 0.0136757i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.36677 | + | 2.36731i | −0.213453 | + | 0.369711i | −0.952793 | − | 0.303621i | \(-0.901804\pi\) |
0.739340 | + | 0.673332i | \(0.235138\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.64949 | − | 3.83908i | 1.01404 | − | 0.585455i | 0.101666 | − | 0.994819i | \(-0.467583\pi\) |
0.912371 | + | 0.409364i | \(0.134249\pi\) | |||||||
\(44\) | 10.9556 | 1.65162 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.99381 | −0.293971 | ||||||||
\(47\) | 9.89770 | − | 5.71444i | 1.44373 | − | 0.833537i | 0.445632 | − | 0.895216i | \(-0.352979\pi\) |
0.998096 | + | 0.0616792i | \(0.0196456\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.215378 | + | 0.373046i | −0.0307683 | + | 0.0532923i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.27966 | + | 1.89351i | −0.454807 | + | 0.262583i | ||||
\(53\) | − | 9.43507i | − | 1.29601i | −0.761637 | − | 0.648003i | \(-0.775604\pi\) | ||
0.761637 | − | 0.648003i | \(-0.224396\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.29012 | − | 3.96660i | −0.306030 | − | 0.530059i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.691103 | + | 0.399008i | 0.0907462 | + | 0.0523924i | ||||
\(59\) | −5.10795 | + | 8.84723i | −0.664999 | + | 1.15181i | 0.314287 | + | 0.949328i | \(0.398235\pi\) |
−0.979286 | + | 0.202484i | \(0.935099\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.00549659 | + | 0.00952038i | 0.000703767 | + | 0.00121896i | 0.866377 | − | 0.499390i | \(-0.166443\pi\) |
−0.865673 | + | 0.500609i | \(0.833109\pi\) | |||||||
\(62\) | 3.90833i | 0.496358i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.11511 | 0.389389 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.851145 | − | 0.491409i | −0.103984 | − | 0.0600351i | 0.447106 | − | 0.894481i | \(-0.352455\pi\) |
−0.551090 | + | 0.834446i | \(0.685788\pi\) | |||||||
\(68\) | 4.87359 | + | 2.81377i | 0.591010 | + | 0.341220i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.43507 | 0.763703 | 0.381851 | − | 0.924224i | \(-0.375287\pi\) | ||||
0.381851 | + | 0.924224i | \(0.375287\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.61467i | − | 0.774189i | −0.922040 | − | 0.387094i | \(-0.873479\pi\) | ||
0.922040 | − | 0.387094i | \(-0.126521\pi\) | |||||||
\(74\) | −0.859605 | − | 1.48888i | −0.0999271 | − | 0.173079i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.316370 | − | 0.547969i | 0.0362901 | − | 0.0628564i | ||||
\(77\) | −13.6923 | − | 7.90523i | −1.56038 | − | 0.900885i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.73569 | − | 8.20246i | −0.532807 | − | 0.922848i | −0.999266 | − | 0.0383057i | \(-0.987804\pi\) |
0.466459 | − | 0.884543i | \(-0.345529\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 1.29366i | − | 0.142860i | ||||||
\(83\) | −9.02378 | + | 5.20988i | −0.990489 | + | 0.571859i | −0.905420 | − | 0.424516i | \(-0.860444\pi\) |
−0.0850682 | + | 0.996375i | \(0.527111\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.81686 | + | 3.14690i | −0.195917 | + | 0.339339i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −9.54658 | + | 5.51172i | −1.01767 | + | 0.587551i | ||||
\(89\) | −6.26940 | −0.664555 | −0.332277 | − | 0.943182i | \(-0.607817\pi\) | ||||
−0.332277 | + | 0.943182i | \(0.607817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.46519 | 0.572908 | ||||||||
\(92\) | −6.47993 | + | 3.74119i | −0.675579 | + | 0.390046i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.70439 | + | 4.68413i | −0.278936 | + | 0.483131i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.24126 | − | 3.60339i | 0.633704 | − | 0.365869i | −0.148481 | − | 0.988915i | \(-0.547438\pi\) |
0.782185 | + | 0.623046i | \(0.214105\pi\) | |||||||
\(98\) | − | 0.203858i | − | 0.0205927i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.48547 | + | 6.03701i | 0.346817 | + | 0.600705i | 0.985682 | − | 0.168614i | \(-0.0539291\pi\) |
−0.638865 | + | 0.769319i | \(0.720596\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.29584 | − | 3.05756i | −0.521815 | − | 0.301270i | 0.215862 | − | 0.976424i | \(-0.430744\pi\) |
−0.737677 | + | 0.675154i | \(0.764077\pi\) | |||||||
\(104\) | 1.90523 | − | 3.29996i | 0.186823 | − | 0.323588i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.23260 | + | 3.86697i | 0.216849 | + | 0.375593i | ||||
\(107\) | 14.5349i | 1.40514i | 0.711615 | + | 0.702570i | \(0.247964\pi\) | ||||
−0.711615 | + | 0.702570i | \(0.752036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.90214 | −0.182192 | −0.0910958 | − | 0.995842i | \(-0.529037\pi\) | ||||
−0.0910958 | + | 0.995842i | \(0.529037\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.00719 | − | 3.46825i | −0.567626 | − | 0.327719i | ||||
\(113\) | 5.69780 | + | 3.28962i | 0.536004 | + | 0.309462i | 0.743458 | − | 0.668783i | \(-0.233184\pi\) |
−0.207454 | + | 0.978245i | \(0.566518\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.99480 | 0.278060 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4.83472i | − | 0.445072i | ||||||
\(119\) | −4.06065 | − | 7.03326i | −0.372239 | − | 0.644737i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.5258 | + | 23.4274i | −1.22962 | + | 2.12977i | ||||
\(122\) | −0.00450556 | − | 0.00260129i | −0.000407914 | − | 0.000235509i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.33359 | + | 12.7021i | 0.658576 | + | 1.14069i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.25840i | − | 0.821550i | −0.911737 | − | 0.410775i | \(-0.865258\pi\) | ||
0.911737 | − | 0.410775i | \(-0.134742\pi\) | |||||||
\(128\) | −9.68555 | + | 5.59196i | −0.856090 | + | 0.494264i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.134698 | − | 0.233305i | 0.0117687 | − | 0.0203839i | −0.860081 | − | 0.510157i | \(-0.829587\pi\) |
0.871850 | + | 0.489773i | \(0.162920\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.790794 | + | 0.456565i | −0.0685705 | + | 0.0395892i | ||||
\(134\) | 0.465123 | 0.0401805 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.66237 | −0.485544 | ||||||||
\(137\) | −3.01046 | + | 1.73809i | −0.257201 | + | 0.148495i | −0.623057 | − | 0.782176i | \(-0.714110\pi\) |
0.365856 | + | 0.930671i | \(0.380776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.37393 | − | 12.7720i | 0.625448 | − | 1.08331i | −0.363006 | − | 0.931787i | \(-0.618249\pi\) |
0.988454 | − | 0.151521i | \(-0.0484172\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.63742 | + | 1.52271i | −0.221327 | + | 0.127783i | ||||
\(143\) | − | 13.1533i | − | 1.09993i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.56521 | + | 2.71103i | 0.129538 | + | 0.224366i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.58747 | − | 3.22593i | −0.459287 | − | 0.265170i | ||||
\(149\) | 5.07665 | − | 8.79301i | 0.415895 | − | 0.720352i | −0.579627 | − | 0.814882i | \(-0.696802\pi\) |
0.995522 | + | 0.0945305i | \(0.0301350\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.15811 | + | 8.93410i | 0.419761 | + | 0.727047i | 0.995915 | − | 0.0902940i | \(-0.0287807\pi\) |
−0.576155 | + | 0.817341i | \(0.695447\pi\) | |||||||
\(152\) | 0.636657i | 0.0516397i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.48237 | 0.602947 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.920247 | − | 0.531305i | −0.0734437 | − | 0.0424028i | 0.462828 | − | 0.886448i | \(-0.346835\pi\) |
−0.536272 | + | 0.844045i | \(0.680168\pi\) | |||||||
\(158\) | 3.88185 | + | 2.24119i | 0.308823 | + | 0.178299i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.7981 | 0.851008 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.1386i | 1.34240i | 0.741278 | + | 0.671198i | \(0.234220\pi\) | ||||
−0.741278 | + | 0.671198i | \(0.765780\pi\) | |||||||
\(164\) | −2.42742 | − | 4.20441i | −0.189549 | − | 0.328309i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.46560 | − | 4.27054i | 0.191368 | − | 0.331459i | ||||
\(167\) | −3.78752 | − | 2.18672i | −0.293087 | − | 0.169214i | 0.346246 | − | 0.938144i | \(-0.387456\pi\) |
−0.639333 | + | 0.768930i | \(0.720790\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.22666 | − | 7.32078i | −0.325127 | − | 0.563137i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 13.6367i | 1.03979i | ||||||||
\(173\) | −12.6960 | + | 7.33005i | −0.965260 | + | 0.557293i | −0.897788 | − | 0.440428i | \(-0.854827\pi\) |
−0.0674723 | + | 0.997721i | \(0.521493\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.34718 | + | 14.4577i | −0.629192 | + | 1.08979i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.56952 | − | 1.48351i | 0.192593 | − | 0.111194i | ||||
\(179\) | −6.87014 | −0.513499 | −0.256749 | − | 0.966478i | \(-0.582651\pi\) | ||||
−0.256749 | + | 0.966478i | \(0.582651\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9709 | −0.815463 | −0.407732 | − | 0.913102i | \(-0.633680\pi\) | ||||
−0.407732 | + | 0.913102i | \(0.633680\pi\) | |||||||
\(182\) | −2.23991 | + | 1.29321i | −0.166033 | + | 0.0958593i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.76434 | − | 6.52003i | 0.277511 | − | 0.480663i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.9272 | + | 9.77294i | −1.23784 | + | 0.714668i | ||||
\(188\) | 20.2980i | 1.48039i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.86627 | + | 11.8927i | 0.496826 | + | 0.860528i | 0.999993 | − | 0.00366109i | \(-0.00116536\pi\) |
−0.503167 | + | 0.864189i | \(0.667832\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.417748 | − | 0.241187i | −0.0300701 | − | 0.0173610i | 0.484890 | − | 0.874575i | \(-0.338860\pi\) |
−0.514960 | + | 0.857214i | \(0.672193\pi\) | |||||||
\(194\) | −1.70532 | + | 2.95370i | −0.122435 | + | 0.212064i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.382518 | − | 0.662541i | −0.0273227 | − | 0.0473244i | ||||
\(197\) | − | 5.53488i | − | 0.394344i | −0.980369 | − | 0.197172i | \(-0.936824\pi\) | ||
0.980369 | − | 0.197172i | \(-0.0631757\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.4590 | −1.23764 | −0.618818 | − | 0.785534i | \(-0.712388\pi\) | ||||
−0.618818 | + | 0.785534i | \(0.712388\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.85704 | − | 1.64951i | −0.201021 | − | 0.116059i | ||||
\(203\) | −3.74288 | − | 2.16095i | −0.262698 | − | 0.151669i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.89401 | 0.201635 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.77073i | − | 0.400128i | ||||||
\(209\) | 1.09883 | + | 1.90324i | 0.0760079 | + | 0.131650i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.818328 | − | 1.41739i | 0.0563360 | − | 0.0975769i | −0.836482 | − | 0.547994i | \(-0.815392\pi\) |
0.892818 | + | 0.450417i | \(0.148725\pi\) | |||||||
\(212\) | 14.5120 | + | 8.37849i | 0.996686 | + | 0.575437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.43935 | − | 5.95713i | −0.235109 | − | 0.407221i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 21.1667i | − | 1.43689i | ||||||
\(218\) | 0.779592 | − | 0.450098i | 0.0528006 | − | 0.0304844i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.37820 | − | 5.85122i | 0.227243 | − | 0.393596i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.70984 | + | 3.87393i | −0.449324 | + | 0.259417i | −0.707545 | − | 0.706669i | \(-0.750197\pi\) |
0.258221 | + | 0.966086i | \(0.416864\pi\) | |||||||
\(224\) | 12.4432 | 0.831397 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.11366 | −0.207118 | ||||||||
\(227\) | 9.75169 | − | 5.63014i | 0.647242 | − | 0.373685i | −0.140157 | − | 0.990129i | \(-0.544761\pi\) |
0.787399 | + | 0.616444i | \(0.211427\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.23879 | + | 9.07384i | −0.346189 | + | 0.599616i | −0.985569 | − | 0.169274i | \(-0.945858\pi\) |
0.639380 | + | 0.768891i | \(0.279191\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.60962 | + | 1.50667i | −0.171330 | + | 0.0989176i | ||||
\(233\) | − | 2.90214i | − | 0.190125i | −0.995471 | − | 0.0950627i | \(-0.969695\pi\) | ||
0.995471 | − | 0.0950627i | \(-0.0303051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.07188 | − | 15.7130i | −0.590529 | − | 1.02283i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.32852 | + | 1.92172i | 0.215756 | + | 0.124567i | ||||
\(239\) | −8.17723 | + | 14.1634i | −0.528941 | + | 0.916153i | 0.470489 | + | 0.882406i | \(0.344077\pi\) |
−0.999430 | + | 0.0337471i | \(0.989256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.76194 | − | 15.1761i | −0.564406 | − | 0.977580i | −0.997105 | − | 0.0760416i | \(-0.975772\pi\) |
0.432698 | − | 0.901539i | \(-0.357562\pi\) | |||||||
\(242\) | − | 12.8023i | − | 0.822965i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.0195242 | −0.00124991 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.657890 | − | 0.379833i | −0.0418605 | − | 0.0241682i | ||||
\(248\) | −12.7808 | − | 7.37898i | −0.811580 | − | 0.468566i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −8.46999 | −0.534621 | −0.267311 | − | 0.963610i | \(-0.586135\pi\) | ||||
−0.267311 | + | 0.963610i | \(0.586135\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 25.9882i | − | 1.63386i | ||||||
\(254\) | 2.19079 | + | 3.79456i | 0.137462 | + | 0.238092i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.468695 | + | 0.811804i | −0.0292934 | + | 0.0507377i | ||||
\(257\) | −2.48766 | − | 1.43625i | −0.155176 | − | 0.0895910i | 0.420401 | − | 0.907338i | \(-0.361889\pi\) |
−0.575577 | + | 0.817747i | \(0.695223\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.65545 | + | 8.06348i | 0.289276 | + | 0.501040i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.127493i | 0.00787656i | ||||||||
\(263\) | 22.1909 | − | 12.8119i | 1.36835 | − | 0.790017i | 0.377633 | − | 0.925955i | \(-0.376738\pi\) |
0.990717 | + | 0.135938i | \(0.0434048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.216072 | − | 0.374247i | 0.0132482 | − | 0.0229465i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.51166 | − | 0.872756i | 0.0923392 | − | 0.0533121i | ||||
\(269\) | 0.337210 | 0.0205600 | 0.0102800 | − | 0.999947i | \(-0.496728\pi\) | ||||
0.0102800 | + | 0.999947i | \(0.496728\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.5927 | 1.31166 | 0.655831 | − | 0.754908i | \(-0.272318\pi\) | ||||
0.655831 | + | 0.754908i | \(0.272318\pi\) | |||||||
\(272\) | −7.42646 | + | 4.28767i | −0.450295 | + | 0.259978i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.822560 | − | 1.42472i | 0.0496927 | − | 0.0860702i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9004 | − | 12.0669i | 1.25579 | − | 0.725028i | 0.283533 | − | 0.958962i | \(-0.408493\pi\) |
0.972252 | + | 0.233934i | \(0.0751600\pi\) | |||||||
\(278\) | 6.97949i | 0.418602i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.68363 | + | 2.91613i | 0.100437 | + | 0.173962i | 0.911865 | − | 0.410491i | \(-0.134643\pi\) |
−0.811428 | + | 0.584453i | \(0.801309\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.9224 | + | 10.9249i | 1.12482 | + | 0.649415i | 0.942627 | − | 0.333848i | \(-0.108347\pi\) |
0.182193 | + | 0.983263i | \(0.441681\pi\) | |||||||
\(284\) | −5.71444 | + | 9.89770i | −0.339090 | + | 0.587321i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.11243 | + | 5.39088i | 0.184042 | + | 0.318770i | ||||
\(287\) | 7.00619i | 0.413562i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.95994 | 0.409408 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.1739 | + | 5.87393i | 0.595385 | + | 0.343746i | ||||
\(293\) | −11.9114 | − | 6.87702i | −0.695869 | − | 0.401760i | 0.109938 | − | 0.993938i | \(-0.464935\pi\) |
−0.805807 | + | 0.592179i | \(0.798268\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.49179 | 0.377328 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.80509i | 0.278352i | ||||||||
\(299\) | 4.49166 | + | 7.77978i | 0.259759 | + | 0.449916i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.83978 | − | 17.0430i | 0.567155 | − | 0.982342i | ||||
\(302\) | −4.22810 | − | 2.44110i | −0.243300 | − | 0.140469i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.482090 | + | 0.835004i | 0.0276498 | + | 0.0478908i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.2183i | 1.95294i | 0.215644 | + | 0.976472i | \(0.430815\pi\) | ||||
−0.215644 | + | 0.976472i | \(0.569185\pi\) | |||||||
\(308\) | 24.3179 | − | 14.0399i | 1.38564 | − | 0.799999i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.5199 | − | 19.9530i | 0.653232 | − | 1.13143i | −0.329102 | − | 0.944294i | \(-0.606746\pi\) |
0.982334 | − | 0.187136i | \(-0.0599206\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.11016 | − | 1.79565i | 0.175796 | − | 0.101496i | −0.409520 | − | 0.912301i | \(-0.634304\pi\) |
0.585316 | + | 0.810805i | \(0.300970\pi\) | |||||||
\(314\) | 0.502885 | 0.0283794 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.8215 | 0.946281 | ||||||||
\(317\) | −11.4148 | + | 6.59033i | −0.641118 | + | 0.370150i | −0.785045 | − | 0.619439i | \(-0.787360\pi\) |
0.143927 | + | 0.989588i | \(0.454027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.20085 | + | 9.00813i | −0.291192 | + | 0.504359i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.42560 | + | 2.55512i | −0.246629 | + | 0.142391i | ||||
\(323\) | 1.12887i | 0.0628119i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.05545 | − | 7.02424i | −0.224611 | − | 0.389037i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.23044 | + | 2.44244i | 0.233587 | + | 0.134861i | ||||
\(329\) | 14.6464 | − | 25.3683i | 0.807483 | − | 1.39860i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.591264 | − | 1.02410i | −0.0324988 | − | 0.0562896i | 0.849319 | − | 0.527881i | \(-0.177013\pi\) |
−0.881817 | + | 0.471591i | \(0.843680\pi\) | |||||||
\(332\) | − | 18.5058i | − | 1.01564i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.06975 | 0.113252 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.4770 | + | 12.3997i | 1.16993 | + | 0.675457i | 0.953662 | − | 0.300879i | \(-0.0972799\pi\) |
0.216263 | + | 0.976335i | \(0.430613\pi\) | |||||||
\(338\) | 3.46459 | + | 2.00028i | 0.188449 | + | 0.108801i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −50.9428 | −2.75871 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0454i | 1.02836i | ||||||||
\(344\) | −6.86053 | − | 11.8828i | −0.369895 | − | 0.640677i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.46898 | − | 6.00845i | 0.186493 | − | 0.323016i | ||||
\(347\) | 19.1991 | + | 11.0846i | 1.03066 | + | 0.595052i | 0.917174 | − | 0.398488i | \(-0.130465\pi\) |
0.113486 | + | 0.993540i | \(0.463798\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.45925 | + | 12.9198i | 0.399285 | + | 0.691581i | 0.993638 | − | 0.112623i | \(-0.0359252\pi\) |
−0.594353 | + | 0.804204i | \(0.702592\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 29.9476i | − | 1.59621i | ||||||
\(353\) | 14.6484 | − | 8.45726i | 0.779656 | − | 0.450134i | −0.0566525 | − | 0.998394i | \(-0.518043\pi\) |
0.836308 | + | 0.548260i | \(0.184709\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.56732 | − | 9.64288i | 0.295067 | − | 0.511072i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.81573 | − | 1.62566i | 0.148816 | − | 0.0859190i | ||||
\(359\) | 0.636657 | 0.0336015 | 0.0168007 | − | 0.999859i | \(-0.494652\pi\) | ||||
0.0168007 | + | 0.999859i | \(0.494652\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8731 | −0.993320 | ||||||||
\(362\) | 4.49644 | − | 2.59602i | 0.236328 | − | 0.136444i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.85317 | + | 8.40594i | −0.254375 | + | 0.440591i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4053 | − | 10.0490i | 0.908550 | − | 0.524552i | 0.0285858 | − | 0.999591i | \(-0.490900\pi\) |
0.879964 | + | 0.475040i | \(0.157566\pi\) | |||||||
\(368\) | − | 11.4018i | − | 0.594358i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0913 | − | 20.9427i | −0.627749 | − | 1.08729i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.0113 | − | 9.82146i | −0.880810 | − | 0.508536i | −0.00988448 | − | 0.999951i | \(-0.503146\pi\) |
−0.870925 | + | 0.491415i | \(0.836480\pi\) | |||||||
\(374\) | 4.62509 | − | 8.01088i | 0.239157 | − | 0.414233i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.2118 | − | 17.6874i | −0.526635 | − | 0.912159i | ||||
\(377\) | − | 3.59555i | − | 0.185180i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.94219 | 0.407963 | 0.203982 | − | 0.978975i | \(-0.434612\pi\) | ||||
0.203982 | + | 0.978975i | \(0.434612\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.62829 | − | 3.24949i | −0.287968 | − | 0.166259i | ||||
\(383\) | 27.0103 | + | 15.5944i | 1.38016 | + | 0.796836i | 0.992178 | − | 0.124830i | \(-0.0398387\pi\) |
0.387983 | + | 0.921667i | \(0.373172\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.228285 | 0.0116194 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.7995i | 0.649795i | ||||||||
\(389\) | 15.7247 | + | 27.2360i | 0.797274 | + | 1.38092i | 0.921385 | + | 0.388650i | \(0.127059\pi\) |
−0.124111 | + | 0.992268i | \(0.539608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.67463 | − | 11.5608i | 0.337550 | − | 0.584655i | ||||
\(392\) | 0.666642 | + | 0.384886i | 0.0336705 | + | 0.0194397i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.30970 | + | 2.26847i | 0.0659819 | + | 0.114284i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.7174i | 0.889211i | 0.895726 | + | 0.444606i | \(0.146656\pi\) | ||||
−0.895726 | + | 0.444606i | \(0.853344\pi\) | |||||||
\(398\) | 7.15558 | − | 4.13128i | 0.358677 | − | 0.207082i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.57124 | + | 6.18556i | −0.178339 | + | 0.308892i | −0.941312 | − | 0.337538i | \(-0.890406\pi\) |
0.762973 | + | 0.646431i | \(0.223739\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.2502 | − | 8.80468i | 0.759665 | − | 0.438593i | ||||
\(404\) | −12.3806 | −0.615958 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.04536 | 0.101509 | ||||||||
\(407\) | 19.4067 | − | 11.2045i | 0.961955 | − | 0.555385i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.3759 | − | 21.4357i | 0.611948 | − | 1.05993i | −0.378964 | − | 0.925412i | \(-0.623719\pi\) |
0.990912 | − | 0.134514i | \(-0.0429472\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.40558 | − | 5.43031i | 0.463380 | − | 0.267532i | ||||
\(413\) | 26.1839i | 1.28843i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.17598 | + | 8.96505i | 0.253773 | + | 0.439548i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.900715 | − | 0.520028i | −0.0440554 | − | 0.0254354i | ||||
\(419\) | 5.32956 | − | 9.23106i | 0.260366 | − | 0.450967i | −0.705973 | − | 0.708238i | \(-0.749490\pi\) |
0.966339 | + | 0.257272i | \(0.0828235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.08931 | + | 7.08288i | 0.199301 | + | 0.345199i | 0.948302 | − | 0.317370i | \(-0.102800\pi\) |
−0.749001 | + | 0.662569i | \(0.769466\pi\) | |||||||
\(422\) | 0.774555i | 0.0377048i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −16.8607 | −0.818828 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0244012 | + | 0.0140881i | 0.00118086 | + | 0.000681769i | ||||
\(428\) | −22.3559 | − | 12.9072i | −1.08061 | − | 0.623893i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.67248 | −0.0805604 | −0.0402802 | − | 0.999188i | \(-0.512825\pi\) | ||||
−0.0402802 | + | 0.999188i | \(0.512825\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.95994i | 0.478644i | 0.970940 | + | 0.239322i | \(0.0769252\pi\) | ||||
−0.970940 | + | 0.239322i | \(0.923075\pi\) | |||||||
\(434\) | 5.00863 | + | 8.67519i | 0.240422 | + | 0.416423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.68913 | − | 2.92565i | 0.0808945 | − | 0.140113i | ||||
\(437\) | −1.29985 | − | 0.750471i | −0.0621805 | − | 0.0358999i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.40788 | + | 11.0988i | 0.305832 | + | 0.529716i | 0.977446 | − | 0.211185i | \(-0.0677322\pi\) |
−0.671615 | + | 0.740901i | \(0.734399\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.19750i | 0.152090i | ||||||||
\(443\) | −6.71520 | + | 3.87702i | −0.319049 | + | 0.184203i | −0.650968 | − | 0.759105i | \(-0.725637\pi\) |
0.331920 | + | 0.943308i | \(0.392304\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.83335 | − | 3.17546i | 0.0868118 | − | 0.150362i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.91452 | − | 3.99210i | 0.326681 | − | 0.188609i | ||||
\(449\) | −33.3401 | −1.57342 | −0.786709 | − | 0.617324i | \(-0.788217\pi\) | ||||
−0.786709 | + | 0.617324i | \(0.788217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.8621 | 0.794004 | ||||||||
\(452\) | −10.1195 | + | 5.84247i | −0.475979 | + | 0.274807i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.66449 | + | 4.61503i | −0.125051 | + | 0.216594i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.0988 | + | 19.1096i | −1.54830 | + | 0.893910i | −0.550026 | + | 0.835148i | \(0.685382\pi\) |
−0.998272 | + | 0.0587626i | \(0.981285\pi\) | |||||||
\(458\) | − | 4.95856i | − | 0.231698i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.6517 | + | 27.1095i | 0.728971 | + | 1.26261i | 0.957319 | + | 0.289035i | \(0.0933343\pi\) |
−0.228348 | + | 0.973580i | \(0.573332\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.4661 | + | 6.04258i | 0.486399 | + | 0.280823i | 0.723079 | − | 0.690765i | \(-0.242726\pi\) |
−0.236680 | + | 0.971588i | \(0.576059\pi\) | |||||||
\(464\) | −2.28176 | + | 3.95212i | −0.105928 | + | 0.183473i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.686725 | + | 1.18944i | 0.0318119 | + | 0.0550998i | ||||
\(467\) | 7.60466i | 0.351902i | 0.984399 | + | 0.175951i | \(0.0563000\pi\) | ||||
−0.984399 | + | 0.175951i | \(0.943700\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.51901 | −0.116317 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.8102 | + | 9.12803i | 0.727724 | + | 0.420152i | ||||
\(473\) | −41.0181 | − | 23.6818i | −1.88601 | − | 1.08889i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.4237 | 0.661108 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 7.73982i | − | 0.354011i | ||||||
\(479\) | 16.2417 | + | 28.1314i | 0.742101 | + | 1.28536i | 0.951537 | + | 0.307534i | \(0.0995037\pi\) |
−0.209437 | + | 0.977822i | \(0.567163\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.87304 | + | 6.70830i | −0.176595 | + | 0.305872i | ||||
\(482\) | 7.18217 | + | 4.14663i | 0.327139 | + | 0.188874i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −24.0223 | − | 41.6079i | −1.09192 | − | 1.89127i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.46121i | − | 0.202157i | −0.994878 | − | 0.101078i | \(-0.967771\pi\) | ||
0.994878 | − | 0.101078i | \(-0.0322293\pi\) | |||||||
\(488\) | 0.0170131 | − | 0.00982254i | 0.000770148 | − | 0.000444645i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4210 | − | 28.4420i | 0.741070 | − | 1.28357i | −0.210938 | − | 0.977499i | \(-0.567652\pi\) |
0.952008 | − | 0.306072i | \(-0.0990148\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.62717 | + | 2.67150i | −0.208397 | + | 0.120318i | ||||
\(494\) | 0.359515 | 0.0161754 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −22.3501 | −1.00355 | ||||||||
\(497\) | 14.2837 | − | 8.24672i | 0.640713 | − | 0.369916i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.1010 | + | 29.6198i | −0.765547 | + | 1.32597i | 0.174410 | + | 0.984673i | \(0.444198\pi\) |
−0.939957 | + | 0.341293i | \(0.889135\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.47143 | − | 2.00423i | 0.154938 | − | 0.0894532i | ||||
\(503\) | 22.1773i | 0.988837i | 0.869224 | + | 0.494419i | \(0.164619\pi\) | ||||
−0.869224 | + | 0.494419i | \(0.835381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.14951 | + | 10.6513i | 0.273379 | + | 0.473507i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.2402 | + | 8.22160i | 0.631808 | + | 0.364775i | ||||
\(509\) | 10.7816 | − | 18.6743i | 0.477887 | − | 0.827724i | −0.521792 | − | 0.853073i | \(-0.674736\pi\) |
0.999679 | + | 0.0253489i | \(0.00806968\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.47688 | − | 14.6824i | −0.374995 | − | 0.649510i | ||||
\(512\) | − | 22.8115i | − | 1.00813i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.35943 | 0.0599617 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −61.0550 | − | 35.2501i | −2.68520 | − | 1.55030i | ||||
\(518\) | −3.81608 | − | 2.20321i | −0.167669 | − | 0.0968037i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.2626 | −0.887718 | −0.443859 | − | 0.896097i | \(-0.646391\pi\) | ||||
−0.443859 | + | 0.896097i | \(0.646391\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 31.8114i | − | 1.39101i | −0.718520 | − | 0.695507i | \(-0.755180\pi\) | ||
0.718520 | − | 0.695507i | \(-0.244820\pi\) | |||||||
\(524\) | 0.239229 | + | 0.414356i | 0.0104507 | + | 0.0181012i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.06330 | + | 10.5019i | −0.264373 | + | 0.457907i | ||||
\(527\) | −22.6618 | − | 13.0838i | −0.987164 | − | 0.569940i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.62541 | − | 4.54735i | −0.114148 | − | 0.197711i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 1.62175i | − | 0.0703117i | ||||||
\(533\) | −5.04780 | + | 2.91435i | −0.218645 | + | 0.126235i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.878159 | + | 1.52102i | −0.0379307 | + | 0.0656978i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.138205 | + | 0.0797930i | −0.00595846 | + | 0.00344012i | ||||
\(539\) | 2.65717 | 0.114452 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.1315 | −0.650553 | −0.325277 | − | 0.945619i | \(-0.605457\pi\) | ||||
−0.325277 | + | 0.945619i | \(0.605457\pi\) | |||||||
\(542\) | −8.84977 | + | 5.10942i | −0.380130 | + | 0.219468i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.69153 | − | 13.3221i | 0.329772 | − | 0.571181i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.53982 | + | 2.04372i | −0.151352 | + | 0.0873831i | −0.573763 | − | 0.819021i | \(-0.694517\pi\) |
0.422411 | + | 0.906404i | \(0.361184\pi\) | |||||||
\(548\) | − | 6.17381i | − | 0.263732i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.300374 | + | 0.520263i | 0.0127964 | + | 0.0221639i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.0233 | − | 12.1378i | −0.894003 | − | 0.516153i | ||||
\(554\) | −5.71070 | + | 9.89123i | −0.242625 | + | 0.420238i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.0963 | + | 22.6835i | 0.555408 | + | 0.961994i | ||||
\(557\) | 13.1425i | 0.556864i | 0.960456 | + | 0.278432i | \(0.0898147\pi\) | ||||
−0.960456 | + | 0.278432i | \(0.910185\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.3721 | 0.692467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.38007 | − | 0.796785i | −0.0582149 | − | 0.0336104i | ||||
\(563\) | 21.2368 | + | 12.2611i | 0.895023 | + | 0.516742i | 0.875582 | − | 0.483069i | \(-0.160478\pi\) |
0.0194410 | + | 0.999811i | \(0.493811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.3405 | −0.434642 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 11.4996i | − | 0.482514i | ||||||
\(569\) | −11.3649 | − | 19.6846i | −0.476442 | − | 0.825223i | 0.523193 | − | 0.852214i | \(-0.324741\pi\) |
−0.999636 | + | 0.0269915i | \(0.991407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.247093 | − | 0.427977i | 0.0103405 | − | 0.0179103i | −0.860809 | − | 0.508928i | \(-0.830042\pi\) |
0.871149 | + | 0.491018i | \(0.163375\pi\) | |||||||
\(572\) | 20.2309 | + | 11.6803i | 0.845897 | + | 0.488379i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.65786 | − | 2.87149i | −0.0691976 | − | 0.119854i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9.41187i | − | 0.391821i | −0.980622 | − | 0.195911i | \(-0.937234\pi\) | ||
0.980622 | − | 0.195911i | \(-0.0627662\pi\) | |||||||
\(578\) | −2.85254 | + | 1.64691i | −0.118650 | + | 0.0685025i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.3532 | + | 23.1284i | −0.553984 | + | 0.959529i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −50.4037 | + | 29.1006i | −2.08751 | + | 1.20522i | ||||
\(584\) | −11.8206 | −0.489139 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.50916 | 0.268891 | ||||||||
\(587\) | −8.63705 | + | 4.98661i | −0.356489 | + | 0.205819i | −0.667540 | − | 0.744574i | \(-0.732653\pi\) |
0.311050 | + | 0.950393i | \(0.399319\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.47110 | + | 2.54801i | −0.0606155 | + | 0.104989i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.51428 | − | 4.91572i | 0.349935 | − | 0.202035i | ||||
\(593\) | 38.3421i | 1.57452i | 0.616621 | + | 0.787260i | \(0.288501\pi\) | ||||
−0.616621 | + | 0.787260i | \(0.711499\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.01628 | + | 15.6167i | 0.369321 | + | 0.639683i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.68182 | − | 2.12570i | −0.150561 | − | 0.0869262i | ||||
\(599\) | 5.07665 | − | 8.79301i | 0.207426 | − | 0.359273i | −0.743477 | − | 0.668762i | \(-0.766825\pi\) |
0.950903 | + | 0.309489i | \(0.100158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.6371 | + | 18.4241i | 0.433898 | + | 0.751533i | 0.997205 | − | 0.0747146i | \(-0.0238046\pi\) |
−0.563307 | + | 0.826248i | \(0.690471\pi\) | |||||||
\(602\) | 9.31344i | 0.379587i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −18.3219 | −0.745508 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.6799 | + | 18.8678i | 1.32644 | + | 0.765819i | 0.984747 | − | 0.173993i | \(-0.0556671\pi\) |
0.341691 | + | 0.939812i | \(0.389000\pi\) | |||||||
\(608\) | −1.49789 | − | 0.864808i | −0.0607475 | − | 0.0350726i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24.3698 | 0.985895 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.2633i | 1.30310i | 0.758605 | + | 0.651551i | \(0.225881\pi\) | ||||
−0.758605 | + | 0.651551i | \(0.774119\pi\) | |||||||
\(614\) | −8.09699 | − | 14.0244i | −0.326768 | − | 0.565979i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −14.1268 | + | 24.4684i | −0.569186 | + | 0.985860i | ||||
\(617\) | −22.5321 | − | 13.0089i | −0.907108 | − | 0.523719i | −0.0276084 | − | 0.999619i | \(-0.508789\pi\) |
−0.879499 | + | 0.475900i | \(0.842122\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.94077 | − | 10.2897i | −0.238780 | − | 0.413578i | 0.721585 | − | 0.692326i | \(-0.243414\pi\) |
−0.960364 | + | 0.278748i | \(0.910081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.9037i | 0.437197i | ||||||||
\(623\) | −13.9160 | + | 8.03440i | −0.557532 | + | 0.321891i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.849799 | + | 1.47189i | −0.0339648 | + | 0.0588288i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.63439 | − | 0.943614i | 0.0652191 | − | 0.0376543i | ||||
\(629\) | 11.5107 | 0.458962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.2726 | −0.528372 | −0.264186 | − | 0.964472i | \(-0.585103\pi\) | ||||
−0.264186 | + | 0.964472i | \(0.585103\pi\) | |||||||
\(632\) | −14.6580 | + | 8.46279i | −0.583063 | + | 0.336632i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.11890 | − | 5.40210i | 0.123867 | − | 0.214545i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.795445 | + | 0.459251i | −0.0315167 | + | 0.0181962i | ||||
\(638\) | − | 4.92265i | − | 0.194890i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.4075 | + | 38.8109i | 0.885042 | + | 1.53294i | 0.845665 | + | 0.533713i | \(0.179204\pi\) |
0.0393765 | + | 0.999224i | \(0.487463\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.9259 | − | 7.46275i | −0.509747 | − | 0.294302i | 0.222983 | − | 0.974822i | \(-0.428421\pi\) |
−0.732729 | + | 0.680520i | \(0.761754\pi\) | |||||||
\(644\) | −9.58886 | + | 16.6084i | −0.377854 | + | 0.654462i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.267121 | − | 0.462667i | −0.0105097 | − | 0.0182034i | ||||
\(647\) | 41.2684i | 1.62243i | 0.584749 | + | 0.811214i | \(0.301193\pi\) | ||||
−0.584749 | + | 0.811214i | \(0.698807\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 63.0179 | 2.47367 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −26.3606 | − | 15.2193i | −1.03236 | − | 0.596034i | ||||
\(653\) | −23.9241 | − | 13.8126i | −0.936223 | − | 0.540528i | −0.0474484 | − | 0.998874i | \(-0.515109\pi\) |
−0.888774 | + | 0.458345i | \(0.848442\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.39788 | 0.288839 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.8630i | 0.540435i | ||||||||
\(659\) | −20.0112 | − | 34.6605i | −0.779527 | − | 1.35018i | −0.932215 | − | 0.361905i | \(-0.882126\pi\) |
0.152688 | − | 0.988274i | \(-0.451207\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4965 | + | 21.6445i | −0.486056 | + | 0.841874i | −0.999872 | − | 0.0160270i | \(-0.994898\pi\) |
0.513816 | + | 0.857901i | \(0.328232\pi\) | |||||||
\(662\) | 0.484659 | + | 0.279818i | 0.0188368 | + | 0.0108754i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.31018 | + | 16.1257i | 0.361305 | + | 0.625799i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 7.10405i | − | 0.275070i | ||||||
\(668\) | 6.72675 | − | 3.88369i | 0.260266 | − | 0.150264i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.0339063 | − | 0.0587274i | 0.00130894 | − | 0.00226715i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.3380 | − | 20.4024i | 1.36218 | − | 0.786454i | 0.372265 | − | 0.928126i | \(-0.378581\pi\) |
0.989914 | + | 0.141672i | \(0.0452479\pi\) | |||||||
\(674\) | −11.7365 | −0.452072 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.0133 | 0.577436 | ||||||||
\(677\) | −35.6710 | + | 20.5947i | −1.37095 | + | 0.791518i | −0.991048 | − | 0.133509i | \(-0.957375\pi\) |
−0.379901 | + | 0.925027i | \(0.624042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.23569 | − | 15.9967i | 0.354433 | − | 0.613896i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 20.8789 | − | 12.0545i | 0.799496 | − | 0.461589i | ||||
\(683\) | 1.33820i | 0.0512047i | 0.999672 | + | 0.0256023i | \(0.00815037\pi\) | ||||
−0.999672 | + | 0.0256023i | \(0.991850\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.50667 | − | 7.80578i | −0.172065 | − | 0.298026i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17.9958 | − | 10.3899i | −0.686083 | − | 0.396110i | ||||
\(689\) | 10.0592 | − | 17.4230i | 0.383225 | − | 0.663764i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.6407 | + | 21.8943i | 0.480874 | + | 0.832898i | 0.999759 | − | 0.0219459i | \(-0.00698617\pi\) |
−0.518885 | + | 0.854844i | \(0.673653\pi\) | |||||||
\(692\) | − | 26.0368i | − | 0.989770i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.4917 | −0.398258 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.50106 | + | 4.33074i | 0.284123 | + | 0.164039i | ||||
\(698\) | −6.11435 | − | 3.53012i | −0.231432 | − | 0.133617i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.2064 | 0.687645 | 0.343822 | − | 0.939035i | \(-0.388278\pi\) | ||||
0.343822 | + | 0.939035i | \(0.388278\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.29422i | − | 0.0488126i | ||||||
\(704\) | −9.60795 | − | 16.6415i | −0.362113 | − | 0.627199i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.00244 | + | 6.93242i | −0.150634 | + | 0.260905i | ||||
\(707\) | 15.4732 | + | 8.93344i | 0.581929 | + | 0.335977i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.9103 | + | 36.2177i | 0.785304 | + | 1.36019i | 0.928818 | + | 0.370537i | \(0.120826\pi\) |
−0.143514 | + | 0.989648i | \(0.545840\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.2036i | 0.419871i | ||||||||
\(713\) | 30.1312 | − | 17.3962i | 1.12842 | − | 0.651494i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.10079 | − | 10.5669i | 0.227997 | − | 0.394903i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.260934 | + | 0.150650i | −0.00973797 | + | 0.00562222i | ||||
\(719\) | 48.9786 | 1.82660 | 0.913298 | − | 0.407293i | \(-0.133527\pi\) | ||||
0.913298 | + | 0.407293i | \(0.133527\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6734 | −0.583707 | ||||||||
\(722\) | 7.73514 | − | 4.46588i | 0.287872 | − | 0.166203i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.74236 | − | 16.8743i | 0.362072 | − | 0.627127i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −37.9327 | + | 21.9005i | −1.40685 | + | 0.812243i | −0.995083 | − | 0.0990474i | \(-0.968420\pi\) |
−0.411764 | + | 0.911291i | \(0.635087\pi\) | |||||||
\(728\) | − | 9.76642i | − | 0.361968i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.1645 | − | 21.0696i | −0.449922 | − | 0.779287i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.87740 | − | 3.39332i | −0.217087 | − | 0.125335i | 0.387514 | − | 0.921864i | \(-0.373334\pi\) |
−0.604601 | + | 0.796529i | \(0.706667\pi\) | |||||||
\(734\) | −4.75572 | + | 8.23715i | −0.175537 | + | 0.304039i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.2267 | + | 17.7131i | 0.376960 | + | 0.652913i | ||||
\(737\) | 6.06261i | 0.223319i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.7245 | −1.05665 | −0.528324 | − | 0.849043i | \(-0.677179\pi\) | ||||
−0.528324 | + | 0.849043i | \(0.677179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.91125 | + | 5.72226i | 0.363853 | + | 0.210071i | ||||
\(743\) | 27.2385 | + | 15.7262i | 0.999284 | + | 0.576937i | 0.908036 | − | 0.418891i | \(-0.137581\pi\) |
0.0912477 | + | 0.995828i | \(0.470915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.29610 | 0.340354 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 34.7141i | − | 1.26927i | ||||||
\(749\) | 18.6268 | + | 32.2626i | 0.680610 | + | 1.17885i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.47659 | + | 9.48574i | −0.199844 | + | 0.346139i | −0.948478 | − | 0.316844i | \(-0.897377\pi\) |
0.748634 | + | 0.662984i | \(0.230710\pi\) | |||||||
\(752\) | −26.7866 | − | 15.4652i | −0.976806 | − | 0.563959i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.850804 | + | 1.47364i | 0.0309845 | + | 0.0536667i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 45.7942i | − | 1.66442i | −0.554461 | − | 0.832210i | \(-0.687075\pi\) | ||
0.554461 | − | 0.832210i | \(-0.312925\pi\) | |||||||
\(758\) | −3.25511 | + | 1.87934i | −0.118231 | + | 0.0682607i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.9569 | + | 29.3702i | −0.614687 | + | 1.06467i | 0.375753 | + | 0.926720i | \(0.377384\pi\) |
−0.990439 | + | 0.137948i | \(0.955949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.22212 | + | 2.43764i | −0.152851 | + | 0.0882485i | ||||
\(764\) | −24.3894 | −0.882378 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.7602 | −0.533309 | ||||||||
\(767\) | −18.8649 | + | 10.8917i | −0.681173 | + | 0.393275i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.57986 | − | 6.20050i | 0.129093 | − | 0.223596i | −0.794232 | − | 0.607614i | \(-0.792127\pi\) |
0.923325 | + | 0.384018i | \(0.125460\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.741933 | − | 0.428355i | 0.0267027 | − | 0.0154168i | ||||
\(773\) | − | 14.5998i | − | 0.525117i | −0.964916 | − | 0.262558i | \(-0.915434\pi\) | ||
0.964916 | − | 0.262558i | \(-0.0845663\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.43935 | − | 11.1533i | −0.231159 | − | 0.400379i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.8895 | − | 7.44178i | −0.462113 | − | 0.266801i | ||||
\(779\) | 0.486933 | − | 0.843393i | 0.0174462 | − | 0.0302177i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.8477 | − | 34.3772i | −0.710207 | − | 1.23011i | ||||
\(782\) | 6.31760i | 0.225917i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.16578 | 0.0416348 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.9979 | − | 9.23638i | −0.570263 | − | 0.329242i | 0.186991 | − | 0.982362i | \(-0.440126\pi\) |
−0.757254 | + | 0.653120i | \(0.773460\pi\) | |||||||
\(788\) | 8.51312 | + | 4.91505i | 0.303267 | + | 0.175092i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.8630 | 0.599578 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0234407i | 0.000832405i | ||||||||
\(794\) | −4.19242 | − | 7.26149i | −0.148783 | − | 0.257700i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.5039 | − | 26.8535i | 0.549520 | − | 0.951796i | ||||
\(797\) | 35.5395 | + | 20.5187i | 1.25887 | + | 0.726810i | 0.972855 | − | 0.231414i | \(-0.0743353\pi\) |
0.286017 | + | 0.958225i | \(0.407669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.1068 | − | 31.3619i | −0.640573 | − | 1.10950i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 3.38021i | − | 0.119359i | ||||||
\(803\) | −35.3367 | + | 20.4016i | −1.24700 | + | 0.719958i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.16686 | + | 7.21721i | −0.146771 | + | 0.254215i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.7883 | − | 6.22861i | 0.379530 | − | 0.219122i | ||||
\(809\) | 7.19375 | 0.252919 | 0.126459 | − | 0.991972i | \(-0.459639\pi\) | ||||
0.126459 | + | 0.991972i | \(0.459639\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.2183 | 1.34203 | 0.671014 | − | 0.741445i | \(-0.265859\pi\) | ||||
0.671014 | + | 0.741445i | \(0.265859\pi\) | |||||||
\(812\) | 6.64746 | − | 3.83791i | 0.233280 | − | 0.134684i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.30257 | + | 9.18431i | −0.185855 | + | 0.321910i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.36899 | + | 1.36774i | −0.0828805 | + | 0.0478511i | ||||
\(818\) | 11.7139i | 0.409566i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.334280 | − | 0.578990i | −0.0116665 | − | 0.0202069i | 0.860133 | − | 0.510069i | \(-0.170380\pi\) |
−0.871800 | + | 0.489863i | \(0.837047\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.23004 | − | 0.710165i | −0.0428766 | − | 0.0247548i | 0.478408 | − | 0.878137i | \(-0.341214\pi\) |
−0.521285 | + | 0.853383i | \(0.674547\pi\) | |||||||
\(824\) | −5.46393 | + | 9.46380i | −0.190345 | + | 0.329687i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.19583 | − | 10.7315i | −0.215580 | − | 0.373396i | ||||
\(827\) | − | 49.8169i | − | 1.73230i | −0.499782 | − | 0.866152i | \(-0.666586\pi\) | ||
0.499782 | − | 0.866152i | \(-0.333414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.4150 | −1.26475 | −0.632373 | − | 0.774664i | \(-0.717919\pi\) | ||||
−0.632373 | + | 0.774664i | \(0.717919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.75244 | + | 3.32117i | 0.199430 | + | 0.115141i | ||||
\(833\) | 1.18204 | + | 0.682449i | 0.0409551 | + | 0.0236455i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.90312 | −0.134992 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.04447i | 0.174258i | ||||||||
\(839\) | 10.0445 | + | 17.3976i | 0.346774 | + | 0.600631i | 0.985674 | − | 0.168659i | \(-0.0539436\pi\) |
−0.638900 | + | 0.769290i | \(0.720610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0783 | − | 22.6523i | 0.450976 | − | 0.781114i | ||||
\(842\) | −3.35201 | − | 1.93528i | −0.115518 | − | 0.0666942i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.45338 | + | 2.51732i | 0.0500273 | + | 0.0866498i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 69.3349i | 2.38238i | ||||||||
\(848\) | −22.1136 | + | 12.7673i | −0.759383 | + | 0.438430i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.65232 | + | 13.2542i | −0.262318 | + | 0.454349i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.3034 | + | 13.4542i | −0.797892 | + | 0.460663i | −0.842733 | − | 0.538331i | \(-0.819055\pi\) |
0.0448418 | + | 0.998994i | \(0.485722\pi\) | |||||||
\(854\) | −0.0133345 | −0.000456296 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.9742 | 0.887779 | ||||||||
\(857\) | 42.2973 | − | 24.4204i | 1.44485 | − | 0.834184i | 0.446682 | − | 0.894693i | \(-0.352606\pi\) |
0.998168 | + | 0.0605088i | \(0.0192723\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.7047 | + | 35.8616i | −0.706435 | + | 1.22358i | 0.259736 | + | 0.965680i | \(0.416365\pi\) |
−0.966171 | + | 0.257902i | \(0.916969\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.685465 | − | 0.395754i | 0.0233470 | − | 0.0134794i | ||||
\(863\) | − | 50.8101i | − | 1.72960i | −0.502119 | − | 0.864799i | \(-0.667446\pi\) | ||
0.502119 | − | 0.864799i | \(-0.332554\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.35679 | − | 4.08209i | −0.0800871 | − | 0.138715i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.5563 | + | 18.7964i | 1.10503 | + | 0.637991i | ||||
\(869\) | −29.2126 | + | 50.5977i | −0.990970 | + | 1.71641i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.04783 | − | 1.81489i | −0.0355043 | − | 0.0614953i | ||||
\(872\) | 3.39916i | 0.115110i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.710328 | 0.0240272 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.354715 | + | 0.204795i | 0.0119779 | + | 0.00691542i | 0.505977 | − | 0.862547i | \(-0.331132\pi\) |
−0.493999 | + | 0.869462i | \(0.664465\pi\) | |||||||
\(878\) | −5.25255 | − | 3.03256i | −0.177265 | − | 0.102344i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.32851 | 0.179522 | 0.0897610 | − | 0.995963i | \(-0.471390\pi\) | ||||
0.0897610 | + | 0.995963i | \(0.471390\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.2064i | 0.478083i | 0.971009 | + | 0.239042i | \(0.0768333\pi\) | ||||
−0.971009 | + | 0.239042i | \(0.923167\pi\) | |||||||
\(884\) | 5.99979 | + | 10.3919i | 0.201795 | + | 0.349519i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.83482 | − | 3.17800i | 0.0616419 | − | 0.106767i | ||||
\(887\) | −6.26304 | − | 3.61597i | −0.210292 | − | 0.121412i | 0.391155 | − | 0.920325i | \(-0.372076\pi\) |
−0.601447 | + | 0.798913i | \(0.705409\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.8649 | − | 20.5506i | −0.397936 | − | 0.689245i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 13.7604i | − | 0.460733i | ||||||
\(893\) | −3.52622 | + | 2.03586i | −0.118000 | + | 0.0681276i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −14.3325 | + | 24.8246i | −0.478815 | + | 0.829331i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.6645 | − | 7.88919i | 0.455989 | − | 0.263266i | ||||
\(899\) | −13.9256 | −0.464444 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8960 | −0.995981 | ||||||||
\(902\) | −6.91093 | + | 3.99003i | −0.230109 | + | 0.132853i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.87864 | − | 10.1821i | 0.195521 | − | 0.338651i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.6106 | − | 19.4051i | 1.11602 | − | 0.644335i | 0.175639 | − | 0.984455i | \(-0.443801\pi\) |
0.940382 | + | 0.340120i | \(0.110468\pi\) | |||||||
\(908\) | 19.9986i | 0.663677i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.1390 | − | 34.8819i | −0.667236 | − | 1.15569i | −0.978674 | − | 0.205421i | \(-0.934144\pi\) |
0.311437 | − | 0.950267i | \(-0.399190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 55.6641 | + | 32.1377i | 1.84221 | + | 1.06360i | ||||
\(914\) | 9.04371 | − | 15.6642i | 0.299139 | − | 0.518125i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.30424 | − | 16.1154i | −0.307421 | − | 0.532468i | ||||
\(917\) | − | 0.690479i | − | 0.0228016i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.0468 | 0.430375 | 0.215187 | − | 0.976573i | \(-0.430964\pi\) | ||||
0.215187 | + | 0.976573i | \(0.430964\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.8297 | − | 7.40722i | −0.422523 | − | 0.243944i | ||||
\(923\) | 11.8832 | + | 6.86074i | 0.391139 | + | 0.225824i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.71936 | −0.187950 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 8.18638i | − | 0.268731i | ||||||
\(929\) | −0.146912 | − | 0.254460i | −0.00482004 | − | 0.00834855i | 0.863605 | − | 0.504168i | \(-0.168201\pi\) |
−0.868425 | + | 0.495820i | \(0.834868\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0767321 | − | 0.132904i | 0.00251479 | − | 0.00435575i | ||||
\(932\) | 4.46374 | + | 2.57714i | 0.146215 | + | 0.0844171i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.79947 | − | 3.11678i | −0.0588805 | − | 0.101984i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.9141i | − | 0.552559i | −0.961077 | − | 0.276280i | \(-0.910898\pi\) | ||
0.961077 | − | 0.276280i | \(-0.0891016\pi\) | |||||||
\(938\) | 1.03242 | − | 0.596067i | 0.0337097 | − | 0.0194623i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.6046 | − | 49.5447i | 0.932485 | − | 1.61511i | 0.153426 | − | 0.988160i | \(-0.450969\pi\) |
0.779059 | − | 0.626951i | \(-0.215697\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9.97342 | + | 5.75815i | −0.324779 | + | 0.187511i | ||||
\(944\) | 27.6478 | 0.899858 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.4150 | 0.728775 | ||||||||
\(947\) | 33.6664 | − | 19.4373i | 1.09401 | − | 0.631627i | 0.159369 | − | 0.987219i | \(-0.449054\pi\) |
0.934641 | + | 0.355592i | \(0.115721\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.05222 | − | 12.2148i | 0.228925 | − | 0.396509i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −12.5686 | + | 7.25648i | −0.407350 | + | 0.235184i | ||||
\(953\) | − | 54.4516i | − | 1.76386i | −0.471381 | − | 0.881930i | \(-0.656244\pi\) | ||
0.471381 | − | 0.881930i | \(-0.343756\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.5230 | − | 25.1546i | −0.469708 | − | 0.813557i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.3133 | − | 7.68644i | −0.430133 | − | 0.248338i | ||||
\(959\) | −4.45482 | + | 7.71598i | −0.143854 | + | 0.249162i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.6006 | − | 32.2172i | −0.600020 | − | 1.03926i | ||||
\(962\) | − | 3.66587i | − | 0.118192i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 31.1229 | 1.00240 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.9482 | + | 9.78507i | 0.545018 | + | 0.314666i | 0.747110 | − | 0.664700i | \(-0.231441\pi\) |
−0.202092 | + | 0.979367i | \(0.564774\pi\) | |||||||
\(968\) | 41.8654 | + | 24.1710i | 1.34560 | + | 0.776885i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.31009 | −0.202500 | −0.101250 | − | 0.994861i | \(-0.532284\pi\) | ||||
−0.101250 | + | 0.994861i | \(0.532284\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 37.7995i | − | 1.21180i | ||||||
\(974\) | 1.05564 | + | 1.82843i | 0.0338250 | + | 0.0585866i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.0148757 | − | 0.0257654i | 0.000476158 | − | 0.000824731i | ||||
\(977\) | 6.42514 | + | 3.70955i | 0.205558 | + | 0.118679i | 0.599245 | − | 0.800565i | \(-0.295467\pi\) |
−0.393687 | + | 0.919244i | \(0.628801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.3367 | + | 33.4922i | 0.618004 | + | 1.07041i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.5426i | 0.495986i | ||||||||
\(983\) | −9.51134 | + | 5.49137i | −0.303365 | + | 0.175148i | −0.643953 | − | 0.765065i | \(-0.722707\pi\) |
0.340589 | + | 0.940212i | \(0.389374\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.26430 | − | 2.18983i | 0.0402635 | − | 0.0697384i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.16843 | − | 0.674595i | 0.0371728 | − | 0.0214617i | ||||
\(989\) | 32.3479 | 1.02860 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3721 | −0.678908 | −0.339454 | − | 0.940623i | \(-0.610242\pi\) | ||||
−0.339454 | + | 0.940623i | \(0.610242\pi\) | |||||||
\(992\) | 34.7217 | − | 20.0466i | 1.10242 | − | 0.636480i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.90280 | + | 6.75984i | −0.123789 | + | 0.214409i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.4439 | + | 15.2674i | −0.837487 | + | 0.483524i | −0.856409 | − | 0.516297i | \(-0.827310\pi\) |
0.0189220 | + | 0.999821i | \(0.493977\pi\) | |||||||
\(998\) | − | 16.1863i | − | 0.512368i | ||||||
\(999\) | 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 | 675.2.k.c.199.4 | 16 | ||
3.2 | odd | 2 | 225.2.k.c.49.5 | 16 | |||
5.2 | odd | 4 | 675.2.e.e.226.2 | 8 | |||
5.3 | odd | 4 | 675.2.e.c.226.3 | 8 | |||
5.4 | even | 2 | inner | 675.2.k.c.199.5 | 16 | ||
9.2 | odd | 6 | 225.2.k.c.124.4 | 16 | |||
9.4 | even | 3 | 2025.2.b.o.649.4 | 8 | |||
9.5 | odd | 6 | 2025.2.b.n.649.5 | 8 | |||
9.7 | even | 3 | inner | 675.2.k.c.424.5 | 16 | ||
15.2 | even | 4 | 225.2.e.c.76.3 | ✓ | 8 | ||
15.8 | even | 4 | 225.2.e.e.76.2 | yes | 8 | ||
15.14 | odd | 2 | 225.2.k.c.49.4 | 16 | |||
45.2 | even | 12 | 225.2.e.c.151.3 | yes | 8 | ||
45.4 | even | 6 | 2025.2.b.o.649.5 | 8 | |||
45.7 | odd | 12 | 675.2.e.e.451.2 | 8 | |||
45.13 | odd | 12 | 2025.2.a.z.1.2 | 4 | |||
45.14 | odd | 6 | 2025.2.b.n.649.4 | 8 | |||
45.22 | odd | 12 | 2025.2.a.p.1.3 | 4 | |||
45.23 | even | 12 | 2025.2.a.q.1.3 | 4 | |||
45.29 | odd | 6 | 225.2.k.c.124.5 | 16 | |||
45.32 | even | 12 | 2025.2.a.y.1.2 | 4 | |||
45.34 | even | 6 | inner | 675.2.k.c.424.4 | 16 | ||
45.38 | even | 12 | 225.2.e.e.151.2 | yes | 8 | ||
45.43 | odd | 12 | 675.2.e.c.451.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.3 | ✓ | 8 | 15.2 | even | 4 | ||
225.2.e.c.151.3 | yes | 8 | 45.2 | even | 12 | ||
225.2.e.e.76.2 | yes | 8 | 15.8 | even | 4 | ||
225.2.e.e.151.2 | yes | 8 | 45.38 | even | 12 | ||
225.2.k.c.49.4 | 16 | 15.14 | odd | 2 | |||
225.2.k.c.49.5 | 16 | 3.2 | odd | 2 | |||
225.2.k.c.124.4 | 16 | 9.2 | odd | 6 | |||
225.2.k.c.124.5 | 16 | 45.29 | odd | 6 | |||
675.2.e.c.226.3 | 8 | 5.3 | odd | 4 | |||
675.2.e.c.451.3 | 8 | 45.43 | odd | 12 | |||
675.2.e.e.226.2 | 8 | 5.2 | odd | 4 | |||
675.2.e.e.451.2 | 8 | 45.7 | odd | 12 | |||
675.2.k.c.199.4 | 16 | 1.1 | even | 1 | trivial | ||
675.2.k.c.199.5 | 16 | 5.4 | even | 2 | inner | ||
675.2.k.c.424.4 | 16 | 45.34 | even | 6 | inner | ||
675.2.k.c.424.5 | 16 | 9.7 | even | 3 | inner | ||
2025.2.a.p.1.3 | 4 | 45.22 | odd | 12 | |||
2025.2.a.q.1.3 | 4 | 45.23 | even | 12 | |||
2025.2.a.y.1.2 | 4 | 45.32 | even | 12 | |||
2025.2.a.z.1.2 | 4 | 45.13 | odd | 12 | |||
2025.2.b.n.649.4 | 8 | 45.14 | odd | 6 | |||
2025.2.b.n.649.5 | 8 | 9.5 | odd | 6 | |||
2025.2.b.o.649.4 | 8 | 9.4 | even | 3 | |||
2025.2.b.o.649.5 | 8 | 45.4 | even | 6 |