Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,1,Mod(101,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(46))
chi = DirichletCharacter(H, H._module([23, 0, 32]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3525.101");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.bd (of order \(46\), degree \(22\), 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: | \(1.75920416953\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{46})\) |
Coefficient field: | \(\Q(\zeta_{92})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{44} - x^{42} + x^{40} - x^{38} + x^{36} - x^{34} + x^{32} - x^{30} + x^{28} - x^{26} + x^{24} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 705) |
Projective image: | \(D_{23}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{23} - \cdots)\) |
Embedding invariants
Embedding label | 776.1 | ||
Root | \(-0.631088 - 0.775711i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.776 |
Dual form | 3525.1.bd.a.1976.1 |
$q$-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 \(\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times\).
\(n\) | \(1552\) | \(2026\) | \(2351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{14}{23}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0911989 | − | 0.663521i | −0.0911989 | − | 0.663521i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
0.887885 | − | 0.460065i | \(-0.152174\pi\) | |||||||
\(3\) | −0.519584 | + | 0.854419i | −0.519584 | + | 0.854419i | ||||
\(4\) | 0.530974 | − | 0.148772i | 0.530974 | − | 0.148772i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.614311 | + | 0.266833i | 0.614311 | + | 0.266833i | ||||
\(7\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(8\) | −0.413970 | − | 0.953056i | −0.413970 | − | 0.953056i | ||||
\(9\) | −0.460065 | − | 0.887885i | −0.460065 | − | 0.887885i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(12\) | −0.148772 | + | 0.530974i | −0.148772 | + | 0.530974i | ||||
\(13\) | 0 | 0 | −0.816970 | − | 0.576680i | \(-0.804348\pi\) | ||||
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.123473 | + | 0.0750854i | −0.123473 | + | 0.0750854i | ||||
\(17\) | 0.0997480 | + | 0.0931581i | 0.0997480 | + | 0.0931581i | 0.730836 | − | 0.682553i | \(-0.239130\pi\) |
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(18\) | −0.547173 | + | 0.386237i | −0.547173 | + | 0.386237i | ||||
\(19\) | 0.644923 | + | 1.81464i | 0.644923 | + | 1.81464i | 0.576680 | + | 0.816970i | \(0.304348\pi\) |
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.269797 | + | 1.96292i | −0.269797 | + | 1.96292i | 1.00000i | \(0.5\pi\) | ||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(24\) | 1.02940 | + | 0.141488i | 1.02940 | + | 0.141488i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.997669 | + | 0.0682424i | 0.997669 | + | 0.0682424i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.16637 | − | 0.709287i | 1.16637 | − | 0.709287i | 0.203456 | − | 0.979084i | \(-0.434783\pi\) |
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(32\) | −0.594669 | − | 0.730947i | −0.594669 | − | 0.730947i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0527155 | − | 0.0746808i | 0.0527155 | − | 0.0746808i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.376375 | − | 0.402999i | −0.376375 | − | 0.402999i | ||||
\(37\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(38\) | 1.14523 | − | 0.593413i | 1.14523 | − | 0.593413i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.269797 | − | 0.962917i | \(-0.586957\pi\) | ||||
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.32704 | 1.32704 | ||||||||
\(47\) | 0.979084 | − | 0.203456i | 0.979084 | − | 0.203456i | ||||
\(48\) | − | 0.144511i | − | 0.144511i | ||||||
\(49\) | 0.990686 | − | 0.136167i | 0.990686 | − | 0.136167i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.131424 | + | 0.0368232i | −0.131424 | + | 0.0368232i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.366581 | − | 0.843954i | 0.366581 | − | 0.843954i | −0.631088 | − | 0.775711i | \(-0.717391\pi\) |
0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | |||||||
\(54\) | −0.0457060 | − | 0.668198i | −0.0457060 | − | 0.668198i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.88555 | − | 0.391823i | −1.88555 | − | 0.391823i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.234658 | − | 1.12924i | −0.234658 | − | 1.12924i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
0.682553 | − | 0.730836i | \(-0.260870\pi\) | |||||||
\(62\) | −0.576999 | − | 0.709227i | −0.576999 | − | 0.709227i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.529402 | + | 0.566851i | −0.529402 | + | 0.566851i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||||
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(68\) | 0.0668230 | + | 0.0346249i | 0.0668230 | + | 0.0346249i | ||||
\(69\) | −1.53697 | − | 1.25042i | −1.53697 | − | 1.25042i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(72\) | −0.655751 | + | 0.806026i | −0.655751 | + | 0.806026i | ||||
\(73\) | 0 | 0 | −0.887885 | − | 0.460065i | \(-0.847826\pi\) | ||||
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.612405 | + | 0.867580i | 0.612405 | + | 0.867580i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.05893 | − | 0.861502i | 1.05893 | − | 0.861502i | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) |
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.576680 | + | 0.816970i | −0.576680 | + | 0.816970i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.34066 | − | 1.25209i | 1.34066 | − | 1.25209i | 0.398401 | − | 0.917211i | \(-0.369565\pi\) |
0.942261 | − | 0.334880i | \(-0.108696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.148772 | + | 1.08240i | 0.148772 | + | 1.08240i | ||||
\(93\) | 1.36511i | 1.36511i | ||||||||
\(94\) | −0.224289 | − | 0.631088i | −0.224289 | − | 0.631088i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.933516 | − | 0.128309i | 0.933516 | − | 0.128309i | ||||
\(97\) | 0 | 0 | 0.519584 | − | 0.854419i | \(-0.326087\pi\) | ||||
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(98\) | −0.180699 | − | 0.644923i | −0.180699 | − | 0.644923i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(102\) | 0.0364186 | + | 0.0838441i | 0.0364186 | + | 0.0838441i | ||||
\(103\) | 0 | 0 | 0.887885 | − | 0.460065i | \(-0.152174\pi\) | ||||
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.593413 | − | 0.166266i | −0.593413 | − | 0.166266i | ||||
\(107\) | 1.39607 | + | 0.985454i | 1.39607 | + | 0.985454i | 0.997669 | + | 0.0682424i | \(0.0217391\pi\) |
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(108\) | 0.539889 | − | 0.112190i | 0.539889 | − | 0.112190i | ||||
\(109\) | −1.42298 | + | 1.15768i | −1.42298 | + | 1.15768i | −0.460065 | + | 0.887885i | \(0.652174\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.383417 | − | 0.136267i | 0.383417 | − | 0.136267i | −0.136167 | − | 0.990686i | \(-0.543478\pi\) |
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(114\) | −0.0880222 | + | 1.28684i | −0.0880222 | + | 1.28684i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0682424 | + | 0.997669i | −0.0682424 | + | 0.997669i | ||||
\(122\) | −0.727872 | + | 0.258686i | −0.727872 | + | 0.258686i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.513792 | − | 0.550137i | 0.513792 | − | 0.550137i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.979084 | − | 0.203456i | \(-0.0652174\pi\) | ||||
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(128\) | −0.345426 | − | 0.243829i | −0.345426 | − | 0.243829i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.0474922 | − | 0.133630i | 0.0474922 | − | 0.133630i | ||||
\(137\) | 0.494921 | + | 1.76640i | 0.494921 | + | 1.76640i | 0.631088 | + | 0.775711i | \(0.282609\pi\) |
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(138\) | −0.689510 | + | 1.13385i | −0.689510 | + | 1.13385i | ||||
\(139\) | −1.53697 | + | 0.211252i | −1.53697 | + | 0.211252i | −0.854419 | − | 0.519584i | \(-0.826087\pi\) |
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.334880 | + | 0.942261i | −0.334880 | + | 0.942261i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.123473 | + | 0.0750854i | 0.123473 | + | 0.0750854i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.398401 | + | 0.917211i | −0.398401 | + | 0.917211i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.234658 | + | 1.12924i | −0.234658 | + | 1.12924i | 0.682553 | + | 0.730836i | \(0.260870\pi\) |
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(152\) | 1.46247 | − | 1.36585i | 1.46247 | − | 1.36585i | ||||
\(153\) | 0.0368232 | − | 0.131424i | 0.0368232 | − | 0.131424i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.519584 | − | 0.854419i | \(-0.673913\pi\) | ||||
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(158\) | −0.668198 | − | 0.624053i | −0.668198 | − | 0.624053i | ||||
\(159\) | 0.530621 | + | 0.751719i | 0.530621 | + | 0.751719i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.594669 | + | 0.308133i | 0.594669 | + | 0.308133i | ||||
\(163\) | 0 | 0 | 0.631088 | − | 0.775711i | \(-0.282609\pi\) | ||||
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.953056 | − | 0.775368i | −0.953056 | − | 0.775368i | ||||
\(167\) | −0.816970 | − | 0.423320i | −0.816970 | − | 0.423320i | − | 1.00000i | \(-0.5\pi\) | |
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.334880 | + | 0.942261i | 0.334880 | + | 0.942261i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.31448 | − | 1.40747i | 1.31448 | − | 1.40747i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.256797 | − | 0.315646i | −0.256797 | − | 0.315646i | 0.631088 | − | 0.775711i | \(-0.282609\pi\) |
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0277687 | − | 0.405963i | −0.0277687 | − | 0.405963i | −0.990686 | − | 0.136167i | \(-0.956522\pi\) |
0.962917 | − | 0.269797i | \(-0.0869565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.08677 | + | 0.386237i | 1.08677 | + | 0.386237i | ||||
\(184\) | 1.98246 | − | 0.555458i | 1.98246 | − | 0.555458i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.905777 | − | 0.124496i | 0.905777 | − | 0.124496i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0.489600 | − | 0.253690i | 0.489600 | − | 0.253690i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.854419 | − | 0.519584i | \(-0.826087\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(192\) | −0.209260 | − | 0.746857i | −0.209260 | − | 0.746857i | ||||
\(193\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.505771 | − | 0.219687i | 0.505771 | − | 0.219687i | ||||
\(197\) | −1.02405 | + | 0.530621i | −1.02405 | + | 0.530621i | −0.887885 | − | 0.460065i | \(-0.847826\pi\) |
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.628038 | − | 0.672464i | −0.628038 | − | 0.672464i | 0.334880 | − | 0.942261i | \(-0.391304\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0643043 | + | 0.0391043i | −0.0643043 | + | 0.0391043i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.86697 | − | 0.663521i | 1.86697 | − | 0.663521i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.69292 | − | 0.232687i | −1.69292 | − | 0.232687i | −0.775711 | − | 0.631088i | \(-0.782609\pi\) |
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(212\) | 0.0690883 | − | 0.502655i | 0.0690883 | − | 0.502655i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.526549 | − | 1.01619i | 0.526549 | − | 1.01619i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.347967 | − | 0.979084i | −0.347967 | − | 0.979084i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.897921 | + | 0.838599i | 0.897921 | + | 0.838599i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.269797 | − | 0.962917i | \(-0.413043\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.125383 | − | 0.241978i | −0.125383 | − | 0.241978i | ||||
\(227\) | −0.459500 | − | 1.05788i | −0.459500 | − | 1.05788i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
0.519584 | − | 0.854419i | \(-0.326087\pi\) | |||||||
\(228\) | −1.05947 | + | 0.0724699i | −1.05947 | + | 0.0724699i | ||||
\(229\) | −1.05788 | − | 0.459500i | −1.05788 | − | 0.459500i | −0.203456 | − | 0.979084i | \(-0.565217\pi\) |
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.125291 | − | 0.911560i | −0.125291 | − | 0.911560i | −0.942261 | − | 0.334880i | \(-0.891304\pi\) |
0.816970 | − | 0.576680i | \(-0.195652\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.185882 | + | 1.35239i | 0.185882 | + | 1.35239i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.843954 | − | 0.366581i | −0.843954 | − | 0.366581i | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) |
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(242\) | 0.668198 | − | 0.0457060i | 0.668198 | − | 0.0457060i | ||||
\(243\) | −0.398401 | − | 0.917211i | −0.398401 | − | 0.917211i | ||||
\(244\) | −0.292596 | − | 0.564685i | −0.292596 | − | 0.564685i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.15883 | − | 0.817995i | −1.15883 | − | 0.817995i | ||||
\(249\) | 0.373224 | + | 1.79605i | 0.373224 | + | 1.79605i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.487118 | + | 0.940096i | −0.487118 | + | 0.940096i | ||||
\(257\) | 0.0861339 | − | 0.105873i | 0.0861339 | − | 0.105873i | −0.730836 | − | 0.682553i | \(-0.760870\pi\) |
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.86697 | + | 0.663521i | −1.86697 | + | 0.663521i | −0.887885 | + | 0.460065i | \(0.847826\pi\) |
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.31448 | + | 1.40747i | 1.31448 | + | 1.40747i | 0.854419 | + | 0.519584i | \(0.173913\pi\) |
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(272\) | −0.0193110 | − | 0.00401286i | −0.0193110 | − | 0.00401286i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.12691 | − | 0.489484i | 1.12691 | − | 0.489484i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00212 | − | 0.435282i | −1.00212 | − | 0.435282i | ||||
\(277\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(278\) | 0.280340 | + | 1.00055i | 0.280340 | + | 1.00055i | ||||
\(279\) | −1.16637 | − | 0.709287i | −1.16637 | − | 0.709287i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0.655751 | + | 0.136267i | 0.655751 | + | 0.136267i | ||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.375410 | + | 0.864281i | −0.375410 | + | 0.864281i | ||||
\(289\) | −0.0669712 | − | 0.979084i | −0.0669712 | − | 0.979084i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.489484 | − | 0.457146i | 0.489484 | − | 0.457146i | −0.398401 | − | 0.917211i | \(-0.630435\pi\) |
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(294\) | 0.644923 | + | 0.180699i | 0.644923 | + | 0.180699i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.770673 | + | 0.0527155i | 0.770673 | + | 0.0527155i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.215883 | − | 0.175634i | −0.215883 | − | 0.175634i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0905606 | − | 0.0124473i | −0.0905606 | − | 0.0124473i | ||||
\(307\) | 0 | 0 | 0.631088 | − | 0.775711i | \(-0.282609\pi\) | ||||
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.519584 | − | 0.854419i | \(-0.673913\pi\) | ||||
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.434096 | − | 0.614974i | 0.434096 | − | 0.614974i | ||||
\(317\) | 0.461039 | − | 1.64547i | 0.461039 | − | 1.64547i | −0.269797 | − | 0.962917i | \(-0.586957\pi\) |
0.730836 | − | 0.682553i | \(-0.239130\pi\) | |||||||
\(318\) | 0.450389 | − | 0.420634i | 0.450389 | − | 0.420634i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.56737 | + | 0.680803i | −1.56737 | + | 0.680803i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.104719 | + | 0.241086i | −0.104719 | + | 0.241086i | ||||
\(324\) | −0.184660 | + | 0.519584i | −0.184660 | + | 0.519584i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.249787 | − | 1.81734i | −0.249787 | − | 1.81734i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.81734 | − | 0.249787i | 1.81734 | − | 0.249787i | 0.854419 | − | 0.519584i | \(-0.173913\pi\) |
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(332\) | 0.525581 | − | 0.864281i | 0.525581 | − | 0.864281i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.206375 | + | 0.580683i | −0.206375 | + | 0.580683i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.398401 | − | 0.917211i | \(-0.630435\pi\) | ||||
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(338\) | 0.594669 | − | 0.308133i | 0.594669 | − | 0.308133i | ||||
\(339\) | −0.0827887 | + | 0.398401i | −0.0827887 | + | 0.398401i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.05376 | − | 0.743829i | −1.05376 | − | 0.743829i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.186018 | + | 0.199177i | −0.186018 | + | 0.199177i | ||||
\(347\) | −0.332435 | + | 0.234658i | −0.332435 | + | 0.234658i | −0.730836 | − | 0.682553i | \(-0.760870\pi\) |
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.105873 | + | 1.54781i | −0.105873 | + | 1.54781i | 0.576680 | + | 0.816970i | \(0.304348\pi\) |
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.262234 | − | 1.90790i | 0.262234 | − | 1.90790i | −0.136167 | − | 0.990686i | \(-0.543478\pi\) |
0.398401 | − | 0.917211i | \(-0.369565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.10128 | + | 1.70952i | −2.10128 | + | 1.70952i | ||||
\(362\) | −0.266833 | + | 0.0554485i | −0.266833 | + | 0.0554485i | ||||
\(363\) | −0.816970 | − | 0.576680i | −0.816970 | − | 0.576680i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.157164 | − | 0.756317i | 0.157164 | − | 0.756317i | ||||
\(367\) | 0 | 0 | 0.887885 | − | 0.460065i | \(-0.152174\pi\) | ||||
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(368\) | −0.114074 | − | 0.262624i | −0.114074 | − | 0.262624i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.203090 | + | 0.724836i | 0.203090 | + | 0.724836i | ||||
\(373\) | 0 | 0 | 0.519584 | − | 0.854419i | \(-0.326087\pi\) | ||||
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.599217 | − | 0.848897i | −0.599217 | − | 0.848897i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.46007 | − | 0.887885i | −1.46007 | − | 0.887885i | −0.460065 | − | 0.887885i | \(-0.652174\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.405963 | − | 0.0277687i | 0.405963 | − | 0.0277687i | 0.136167 | − | 0.990686i | \(-0.456522\pi\) |
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(384\) | 0.387810 | − | 0.168450i | 0.387810 | − | 0.168450i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.209773 | + | 0.170663i | −0.209773 | + | 0.170663i | ||||
\(392\) | −0.539889 | − | 0.887810i | −0.539889 | − | 0.887810i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.445471 | + | 0.631088i | 0.445471 | + | 0.631088i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.887885 | − | 0.460065i | \(-0.847826\pi\) | ||||
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(398\) | −0.388918 | + | 0.478044i | −0.388918 | + | 0.478044i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.0895000 | + | 0.110010i | 0.0895000 | + | 0.110010i | ||||
\(409\) | 0.315646 | + | 1.51897i | 0.315646 | + | 1.51897i | 0.775711 | + | 0.631088i | \(0.217391\pi\) |
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.76640 | − | 0.494921i | −1.76640 | − | 0.494921i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.610526 | − | 1.17826i | −0.610526 | − | 1.17826i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.618088 | − | 1.42298i | 0.618088 | − | 1.42298i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.69292 | + | 0.232687i | −1.69292 | + | 0.232687i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(422\) | 1.14451i | 1.14451i | ||||||||
\(423\) | −0.631088 | − | 0.775711i | −0.631088 | − | 0.775711i | ||||
\(424\) | −0.956088 | −0.956088 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.887885 | + | 0.315554i | 0.887885 | + | 0.315554i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(432\) | −0.128309 | + | 0.0664843i | −0.128309 | + | 0.0664843i | ||||
\(433\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.583336 | + | 0.826399i | −0.583336 | + | 0.826399i | ||||
\(437\) | −3.73598 | + | 0.776346i | −3.73598 | + | 0.776346i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.56737 | − | 0.953137i | 1.56737 | − | 0.953137i | 0.576680 | − | 0.816970i | \(-0.304348\pi\) |
0.990686 | − | 0.136167i | \(-0.0434783\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.576680 | − | 0.816970i | −0.576680 | − | 0.816970i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.83015 | + | 0.125185i | 1.83015 | + | 0.125185i | 0.942261 | − | 0.334880i | \(-0.108696\pi\) |
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.183312 | − | 0.129396i | 0.183312 | − | 0.129396i | ||||
\(453\) | −0.842917 | − | 0.787230i | −0.842917 | − | 0.787230i | ||||
\(454\) | −0.660017 | + | 0.401365i | −0.660017 | + | 0.401365i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.407135 | + | 1.95924i | 0.407135 | + | 1.95924i | ||||
\(457\) | 0 | 0 | −0.816970 | − | 0.576680i | \(-0.804348\pi\) | ||||
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(458\) | −0.208411 | + | 0.743829i | −0.208411 | + | 0.743829i | ||||
\(459\) | 0.0931581 | + | 0.0997480i | 0.0931581 | + | 0.0997480i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.593413 | + | 0.166266i | −0.593413 | + | 0.166266i | ||||
\(467\) | −0.806094 | + | 1.32557i | −0.806094 | + | 1.32557i | 0.136167 | + | 0.990686i | \(0.456522\pi\) |
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.880388 | − | 0.246673i | 0.880388 | − | 0.246673i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.917985 | + | 0.0627919i | −0.917985 | + | 0.0627919i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.166266 | + | 0.593413i | −0.166266 | + | 0.593413i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.112190 | + | 0.539889i | 0.112190 | + | 0.539889i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.572255 | + | 0.347996i | −0.572255 | + | 0.347996i | ||||
\(487\) | 0 | 0 | −0.730836 | − | 0.682553i | \(-0.760870\pi\) | ||||
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(488\) | −0.979084 | + | 0.691113i | −0.979084 | + | 0.691113i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.0907581 | + | 0.175155i | −0.0907581 | + | 0.175155i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.15768 | − | 0.411440i | 1.15768 | − | 0.411440i | ||||
\(499\) | −1.14262 | − | 1.61872i | −1.14262 | − | 1.61872i | −0.682553 | − | 0.730836i | \(-0.739130\pi\) |
−0.460065 | − | 0.887885i | \(-0.652174\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.786177 | − | 0.478085i | 0.786177 | − | 0.478085i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.655751 | − | 0.136267i | 0.655751 | − | 0.136267i | 0.136167 | − | 0.990686i | \(-0.456522\pi\) |
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.979084 | − | 0.203456i | −0.979084 | − | 0.203456i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.269797 | + | 0.0958858i | 0.269797 | + | 0.0958858i | ||||
\(513\) | 0.519584 | + | 1.85442i | 0.519584 | + | 1.85442i | ||||
\(514\) | −0.0781042 | − | 0.0474962i | −0.0781042 | − | 0.0474962i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.403122 | − | 0.0554078i | 0.403122 | − | 0.0554078i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.398401 | − | 0.917211i | \(-0.369565\pi\) | ||||
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.610526 | + | 1.17826i | 0.610526 | + | 1.17826i | ||||
\(527\) | 0.182419 | + | 0.0379072i | 0.182419 | + | 0.0379072i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.81734 | − | 0.789381i | −2.81734 | − | 0.789381i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.35239 | − | 0.185882i | −1.35239 | − | 0.185882i | −0.576680 | − | 0.816970i | \(-0.695652\pi\) |
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(542\) | 0.814006 | − | 1.00055i | 0.814006 | − | 1.00055i | ||||
\(543\) | 0.361291 | + | 0.187206i | 0.361291 | + | 0.187206i | ||||
\(544\) | 0.00877656 | − | 0.128309i | 0.00877656 | − | 0.128309i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.730836 | − | 0.682553i | \(-0.760870\pi\) | ||||
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(548\) | 0.525581 | + | 0.864281i | 0.525581 | + | 0.864281i | ||||
\(549\) | −0.894675 | + | 0.727872i | −0.894675 | + | 0.727872i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.555458 | + | 1.98246i | −0.555458 | + | 1.98246i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.784665 | + | 0.340828i | −0.784665 | + | 0.340828i | ||||
\(557\) | 0.136167 | − | 0.00931405i | 0.136167 | − | 0.00931405i | − | 1.00000i | \(-0.5\pi\) | |
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(558\) | −0.364255 | + | 0.838599i | −0.364255 | + | 0.838599i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 0.136485i | − | 0.136485i | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||
0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | |||||||
\(564\) | −0.0376304 | + | 0.550137i | −0.0376304 | + | 0.550137i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.131424 | − | 1.92135i | −0.131424 | − | 1.92135i | −0.334880 | − | 0.942261i | \(-0.608696\pi\) |
0.203456 | − | 0.979084i | \(-0.434783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.746857 | + | 0.209260i | 0.746857 | + | 0.209260i | ||||
\(577\) | 0 | 0 | −0.816970 | − | 0.576680i | \(-0.804348\pi\) | ||||
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(578\) | −0.643535 | + | 0.133728i | −0.643535 | + | 0.133728i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.347967 | − | 0.283092i | −0.347967 | − | 0.283092i | ||||
\(587\) | −0.262234 | + | 1.90790i | −0.262234 | + | 1.90790i | 0.136167 | + | 0.990686i | \(0.456522\pi\) |
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(588\) | −0.0750854 | + | 0.546287i | −0.0750854 | + | 0.546287i | ||||
\(589\) | 2.03932 | + | 1.65911i | 2.03932 | + | 1.65911i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.0787081 | − | 1.15067i | 0.0787081 | − | 1.15067i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.547173 | + | 0.386237i | −0.547173 | + | 0.386237i | −0.816970 | − | 0.576680i | \(-0.804348\pi\) |
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.900885 | − | 0.187206i | 0.900885 | − | 0.187206i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0827887 | − | 0.398401i | 0.0827887 | − | 0.398401i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
1.00000 | \(0\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.0434014 | + | 0.634506i | 0.0434014 | + | 0.634506i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.269797 | − | 0.962917i | \(-0.586957\pi\) | ||||
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(608\) | 0.942889 | − | 1.55051i | 0.942889 | − | 1.55051i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 0.0752608i | − | 0.0752608i | ||||||
\(613\) | 0 | 0 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.543860 | + | 1.25209i | −0.543860 | + | 1.25209i | 0.398401 | + | 0.917211i | \(0.369565\pi\) |
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.05788 | + | 0.459500i | −1.05788 | + | 0.459500i | −0.854419 | − | 0.519584i | \(-0.826087\pi\) |
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.403122 | + | 1.93993i | −0.403122 | + | 1.93993i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.135214 | − | 1.97675i | 0.135214 | − | 1.97675i | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) |
0.203456 | − | 0.979084i | \(-0.434783\pi\) | |||||||
\(632\) | −1.25942 | − | 0.652581i | −1.25942 | − | 0.652581i | ||||
\(633\) | 1.07843 | − | 1.32557i | 1.07843 | − | 1.32557i | ||||
\(634\) | −1.13385 | − | 0.155844i | −1.13385 | − | 0.155844i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.393581 | + | 0.320202i | 0.393581 | + | 0.320202i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(642\) | 0.594669 | + | 0.977892i | 0.594669 | + | 0.977892i | ||||
\(643\) | 0 | 0 | −0.631088 | − | 0.775711i | \(-0.717391\pi\) | ||||
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.169516 | + | 0.0474962i | 0.169516 | + | 0.0474962i | ||||
\(647\) | 0.672464 | − | 0.628038i | 0.672464 | − | 0.628038i | −0.269797 | − | 0.962917i | \(-0.586957\pi\) |
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(648\) | 1.01735 | + | 0.211407i | 1.01735 | + | 0.211407i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.81464 | − | 0.644923i | −1.81464 | − | 0.644923i | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) |
−0.816970 | − | 0.576680i | \(-0.804348\pi\) | |||||||
\(654\) | −1.18306 | + | 0.331478i | −1.18306 | + | 0.331478i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.116615 | − | 0.0709153i | −0.116615 | − | 0.0709153i | 0.460065 | − | 0.887885i | \(-0.347826\pi\) |
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(662\) | −0.331478 | − | 1.18306i | −0.331478 | − | 1.18306i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.74831 | − | 0.759397i | −1.74831 | − | 0.759397i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −0.496768 | − | 0.103230i | −0.496768 | − | 0.103230i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.631088 | − | 0.775711i | \(-0.717391\pi\) | ||||
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.317995 | + | 0.450496i | 0.317995 | + | 0.450496i | ||||
\(677\) | 1.46184 | − | 0.519540i | 1.46184 | − | 0.519540i | 0.519584 | − | 0.854419i | \(-0.326087\pi\) |
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(678\) | 0.271898 | + | 0.0185983i | 0.271898 | + | 0.0185983i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.14262 | + | 0.157049i | 1.14262 | + | 0.157049i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.25042 | + | 1.53697i | −1.25042 | + | 1.53697i | −0.519584 | + | 0.854419i | \(0.673913\pi\) |
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(684\) | 0.488565 | − | 0.942889i | 0.488565 | − | 0.942889i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.942261 | − | 0.665120i | 0.942261 | − | 0.665120i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.0277687 | − | 0.133630i | −0.0277687 | − | 0.133630i | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) |
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(692\) | −0.183312 | − | 0.129396i | −0.183312 | − | 0.129396i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.186018 | + | 0.199177i | 0.186018 | + | 0.199177i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.03666 | − | 0.0709093i | 1.03666 | − | 0.0709093i | ||||
\(699\) | 0.843954 | + | 0.366581i | 0.843954 | + | 0.366581i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.28985 | −1.28985 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.90790 | − | 0.534568i | 1.90790 | − | 0.534568i | 0.917211 | − | 0.398401i | \(-0.130435\pi\) |
0.990686 | − | 0.136167i | \(-0.0434783\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.25209 | − | 0.543860i | −1.25209 | − | 0.543860i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.07759 | + | 2.48086i | 1.07759 | + | 2.48086i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.32593 | + | 1.23834i | 1.32593 | + | 1.23834i | ||||
\(723\) | 0.751719 | − | 0.530621i | 0.751719 | − | 0.530621i | ||||
\(724\) | −0.0751404 | − | 0.211425i | −0.0751404 | − | 0.211425i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.308133 | + | 0.594669i | −0.308133 | + | 0.594669i | ||||
\(727\) | 0 | 0 | 0.631088 | − | 0.775711i | \(-0.282609\pi\) | ||||
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.990686 | + | 0.136167i | 0.990686 | + | 0.136167i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.634506 | + | 0.0434014i | 0.634506 | + | 0.0434014i | ||||
\(733\) | 0 | 0 | 0.942261 | − | 0.334880i | \(-0.108696\pi\) | ||||
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.59523 | − | 0.970080i | 1.59523 | − | 0.970080i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.234658 | − | 0.332435i | 0.234658 | − | 0.332435i | −0.682553 | − | 0.730836i | \(-0.739130\pi\) |
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.70992 | + | 0.886009i | −1.70992 | + | 0.886009i | −0.730836 | + | 0.682553i | \(0.760870\pi\) |
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(744\) | 1.30102 | − | 0.565114i | 1.30102 | − | 0.565114i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.72850 | − | 0.614311i | −1.72850 | − | 0.614311i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.70884 | 1.70884 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(752\) | −0.105614 | + | 0.0986361i | −0.105614 | + | 0.0986361i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(758\) | −0.455974 | + | 1.04976i | −0.455974 | + | 1.04976i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.0554485 | − | 0.266833i | −0.0554485 | − | 0.266833i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.550137 | − | 0.904662i | −0.550137 | − | 0.904662i | ||||
\(769\) | 0.0931581 | − | 0.0997480i | 0.0931581 | − | 0.0997480i | −0.682553 | − | 0.730836i | \(-0.739130\pi\) |
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.0457060 | + | 0.128604i | 0.0457060 | + | 0.128604i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.37749 | − | 0.713755i | −1.37749 | − | 0.713755i | −0.398401 | − | 0.917211i | \(-0.630435\pi\) |
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.132370 | + | 0.123625i | 0.132370 | + | 0.123625i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.112098 | + | 0.0911989i | −0.112098 | + | 0.0911989i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.269797 | − | 0.962917i | \(-0.413043\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(788\) | −0.464804 | + | 0.434096i | −0.464804 | + | 0.434096i | ||||
\(789\) | 0.403122 | − | 1.93993i | 0.403122 | − | 1.93993i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.433516 | − | 0.263627i | −0.433516 | − | 0.263627i | ||||
\(797\) | −0.211252 | − | 1.53697i | −0.211252 | − | 1.53697i | −0.730836 | − | 0.682553i | \(-0.760870\pi\) |
0.519584 | − | 0.854419i | \(-0.326087\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.116615 | + | 0.0709153i | 0.116615 | + | 0.0709153i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.391823 | + | 0.109784i | 0.391823 | + | 0.109784i | 0.460065 | − | 0.887885i | \(-0.347826\pi\) |
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.88555 | + | 0.391823i | −1.88555 | + | 0.391823i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.0134623 | − | 0.0144146i | 0.0134623 | − | 0.0144146i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.979084 | − | 0.347967i | 0.979084 | − | 0.347967i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(822\) | −0.167297 | + | 1.21718i | −0.167297 | + | 1.21718i | ||||
\(823\) | 0 | 0 | 0.136167 | − | 0.990686i | \(-0.456522\pi\) | ||||
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.46184 | − | 0.519540i | 1.46184 | − | 0.519540i | 0.519584 | − | 0.854419i | \(-0.326087\pi\) |
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(828\) | 0.892599 | − | 0.630065i | 0.892599 | − | 0.630065i | ||||
\(829\) | 0.457146 | − | 0.489484i | 0.457146 | − | 0.489484i | −0.460065 | − | 0.887885i | \(-0.652174\pi\) |
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.111504 | + | 0.0787081i | 0.111504 | + | 0.0787081i | ||||
\(834\) | −1.00055 | − | 0.280340i | −1.00055 | − | 0.280340i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.21206 | − | 0.628038i | 1.21206 | − | 0.628038i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.334880 | + | 0.942261i | −0.334880 | + | 0.942261i | ||||
\(842\) | 0.308785 | + | 1.10207i | 0.308785 | + | 1.10207i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.933516 | + | 0.128309i | −0.933516 | + | 0.128309i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.457146 | + | 0.489484i | −0.457146 | + | 0.489484i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.0181059 | + | 0.131730i | 0.0181059 | + | 0.131730i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.361260 | − | 1.73848i | 0.361260 | − | 1.73848i | ||||
\(857\) | 1.24888 | − | 1.16637i | 1.24888 | − | 1.16637i | 0.269797 | − | 0.962917i | \(-0.413043\pi\) |
0.979084 | − | 0.203456i | \(-0.0652174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.386237 | + | 0.547173i | −0.386237 | + | 0.547173i | −0.962917 | − | 0.269797i | \(-0.913043\pi\) |
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.997669 | + | 0.931758i | 0.997669 | + | 0.931758i | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | −0.543401 | − | 0.769824i | −0.543401 | − | 0.769824i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.871346 | + | 0.451495i | 0.871346 | + | 0.451495i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.69241 | + | 0.876935i | 1.69241 | + | 0.876935i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.855840 | + | 2.40810i | 0.855840 | + | 2.40810i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.519584 | − | 0.854419i | \(-0.673913\pi\) | ||||
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(878\) | −0.775368 | − | 0.953056i | −0.775368 | − | 0.953056i | ||||
\(879\) | 0.136267 | + | 0.655751i | 0.136267 | + | 0.655751i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(882\) | −0.489484 | + | 0.457146i | −0.489484 | + | 0.457146i | ||||
\(883\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.0838441 | − | 1.22576i | −0.0838441 | − | 1.22576i | ||||
\(887\) | −0.767255 | + | 1.76640i | −0.767255 | + | 1.76640i | −0.136167 | + | 0.990686i | \(0.543478\pi\) |
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.00063 | + | 1.64547i | 1.00063 | + | 1.64547i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.115187 | − | 0.0500327i | 0.115187 | − | 0.0500327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.288593 | − | 0.309008i | −0.288593 | − | 0.309008i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.445471 | + | 0.631088i | −0.445471 | + | 0.631088i | ||||
\(907\) | 0 | 0 | 0.979084 | − | 0.203456i | \(-0.0652174\pi\) | ||||
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(908\) | −0.401365 | − | 0.493344i | −0.401365 | − | 0.493344i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(912\) | 0.262234 | − | 0.0931981i | 0.262234 | − | 0.0931981i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.630065 | − | 0.0866005i | −0.630065 | − | 0.0866005i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.0576890 | − | 0.0709093i | 0.0576890 | − | 0.0709093i | ||||
\(919\) | 0.911560 | − | 1.75923i | 0.911560 | − | 1.75923i | 0.334880 | − | 0.942261i | \(-0.391304\pi\) |
0.576680 | − | 0.816970i | \(-0.304348\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.886009 | + | 1.70992i | 0.886009 | + | 1.70992i | ||||
\(932\) | −0.202141 | − | 0.465375i | −0.202141 | − | 0.465375i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.953056 | + | 0.413970i | 0.953056 | + | 0.413970i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.519584 | − | 0.854419i | \(-0.326087\pi\) | ||||
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.54781 | − | 0.105873i | 1.54781 | − | 0.105873i | 0.730836 | − | 0.682553i | \(-0.239130\pi\) |
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(948\) | 0.299897 | + | 0.690431i | 0.299897 | + | 0.690431i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.16637 | + | 1.24888i | 1.16637 | + | 1.24888i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.547173 | + | 0.386237i | 0.547173 | + | 0.386237i | 0.816970 | − | 0.576680i | \(-0.195652\pi\) |
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(954\) | 0.125383 | + | 0.603376i | 0.125383 | + | 0.603376i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.397273 | − | 0.766702i | 0.397273 | − | 0.766702i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.232687 | − | 1.69292i | 0.232687 | − | 1.69292i | ||||
\(964\) | −0.502655 | − | 0.0690883i | −0.502655 | − | 0.0690883i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||||
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(968\) | 0.979084 | − | 0.347967i | 0.979084 | − | 0.347967i | ||||
\(969\) | −0.151579 | − | 0.214738i | −0.151579 | − | 0.214738i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(972\) | −0.347996 | − | 0.427745i | −0.347996 | − | 0.427745i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.113763 | + | 0.121810i | 0.113763 | + | 0.121810i | ||||
\(977\) | −0.398401 | − | 0.0827887i | −0.398401 | − | 0.0827887i | − | 1.00000i | \(-0.5\pi\) | |
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.68255 | + | 0.730836i | 1.68255 | + | 0.730836i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.311173 | − | 1.11059i | −0.311173 | − | 1.11059i | −0.942261 | − | 0.334880i | \(-0.891304\pi\) |
0.631088 | − | 0.775711i | \(-0.282609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.64547 | − | 0.461039i | 1.64547 | − | 0.461039i | 0.682553 | − | 0.730836i | \(-0.260870\pi\) |
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(992\) | −1.21206 | − | 0.430765i | −1.21206 | − | 0.430765i | ||||
\(993\) | −0.730836 | + | 1.68255i | −0.730836 | + | 1.68255i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.465375 | + | 0.898133i | 0.465375 | + | 0.898133i | ||||
\(997\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(998\) | −0.969850 | + | 0.905777i | −0.969850 | + | 0.905777i | ||||
\(999\) | 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 | 3525.1.bd.a.776.1 | 44 | ||
3.2 | odd | 2 | inner | 3525.1.bd.a.776.2 | 44 | ||
5.2 | odd | 4 | 705.1.p.a.494.1 | yes | 22 | ||
5.3 | odd | 4 | 705.1.p.b.494.1 | yes | 22 | ||
5.4 | even | 2 | inner | 3525.1.bd.a.776.2 | 44 | ||
15.2 | even | 4 | 705.1.p.b.494.1 | yes | 22 | ||
15.8 | even | 4 | 705.1.p.a.494.1 | yes | 22 | ||
15.14 | odd | 2 | CM | 3525.1.bd.a.776.1 | 44 | ||
47.2 | even | 23 | inner | 3525.1.bd.a.1976.2 | 44 | ||
141.2 | odd | 46 | inner | 3525.1.bd.a.1976.1 | 44 | ||
235.2 | odd | 92 | 705.1.p.a.284.1 | ✓ | 22 | ||
235.49 | even | 46 | inner | 3525.1.bd.a.1976.1 | 44 | ||
235.143 | odd | 92 | 705.1.p.b.284.1 | yes | 22 | ||
705.2 | even | 92 | 705.1.p.b.284.1 | yes | 22 | ||
705.143 | even | 92 | 705.1.p.a.284.1 | ✓ | 22 | ||
705.284 | odd | 46 | inner | 3525.1.bd.a.1976.2 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.1.p.a.284.1 | ✓ | 22 | 235.2 | odd | 92 | ||
705.1.p.a.284.1 | ✓ | 22 | 705.143 | even | 92 | ||
705.1.p.a.494.1 | yes | 22 | 5.2 | odd | 4 | ||
705.1.p.a.494.1 | yes | 22 | 15.8 | even | 4 | ||
705.1.p.b.284.1 | yes | 22 | 235.143 | odd | 92 | ||
705.1.p.b.284.1 | yes | 22 | 705.2 | even | 92 | ||
705.1.p.b.494.1 | yes | 22 | 5.3 | odd | 4 | ||
705.1.p.b.494.1 | yes | 22 | 15.2 | even | 4 | ||
3525.1.bd.a.776.1 | 44 | 1.1 | even | 1 | trivial | ||
3525.1.bd.a.776.1 | 44 | 15.14 | odd | 2 | CM | ||
3525.1.bd.a.776.2 | 44 | 3.2 | odd | 2 | inner | ||
3525.1.bd.a.776.2 | 44 | 5.4 | even | 2 | inner | ||
3525.1.bd.a.1976.1 | 44 | 141.2 | odd | 46 | inner | ||
3525.1.bd.a.1976.1 | 44 | 235.49 | even | 46 | inner | ||
3525.1.bd.a.1976.2 | 44 | 47.2 | even | 23 | inner | ||
3525.1.bd.a.1976.2 | 44 | 705.284 | odd | 46 | inner |