Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3784,1,Mod(203,3784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3784, base_ring=CyclotomicField(210))
chi = DirichletCharacter(H, H._module([105, 105, 84, 170]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3784.203");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3784 = 2^{3} \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3784.em (of order \(210\), degree \(48\), 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: | \(1.88846200780\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Coefficient field: | \(\Q(\zeta_{210})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{48} - x^{47} + x^{46} + x^{43} - x^{42} + 2 x^{41} - x^{40} + x^{39} + x^{36} - x^{35} + x^{34} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{105}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{105} - \cdots)\) |
Embedding invariants
Embedding label | 2379.1 | ||
Root | \(0.646600 - 0.762830i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3784.2379 |
Dual form | 3784.1.em.b.1115.1 |
$q$-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 \(\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times\).
\(n\) | \(89\) | \(1377\) | \(1893\) | \(2839\) |
\(\chi(n)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.473869 | − | 0.880596i | 0.473869 | − | 0.880596i | ||||
\(3\) | 1.78392 | − | 0.731119i | 1.78392 | − | 0.731119i | 0.791071 | − | 0.611724i | \(-0.209524\pi\) |
0.992847 | − | 0.119394i | \(-0.0380952\pi\) | |||||||
\(4\) | −0.550897 | − | 0.834573i | −0.550897 | − | 0.834573i | ||||
\(5\) | 0 | 0 | −0.946327 | − | 0.323210i | \(-0.895238\pi\) | ||||
0.946327 | + | 0.323210i | \(0.104762\pi\) | |||||||
\(6\) | 0.201523 | − | 1.91736i | 0.201523 | − | 1.91736i | ||||
\(7\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(8\) | −0.995974 | + | 0.0896393i | −0.995974 | + | 0.0896393i | ||||
\(9\) | 1.93545 | − | 1.90671i | 1.93545 | − | 1.90671i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.925304 | + | 0.379225i | −0.925304 | + | 0.379225i | ||||
\(12\) | −1.59293 | − | 1.08604i | −1.59293 | − | 1.08604i | ||||
\(13\) | 0 | 0 | −0.992847 | − | 0.119394i | \(-0.961905\pi\) | ||||
0.992847 | + | 0.119394i | \(0.0380952\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.393025 | + | 0.919528i | −0.393025 | + | 0.919528i | ||||
\(17\) | 0.536616 | + | 0.715821i | 0.536616 | + | 0.715821i | 0.983930 | − | 0.178557i | \(-0.0571429\pi\) |
−0.447313 | + | 0.894377i | \(0.647619\pi\) | |||||||
\(18\) | −0.761892 | − | 2.60788i | −0.761892 | − | 2.60788i | ||||
\(19\) | −0.327049 | − | 1.96945i | −0.327049 | − | 1.96945i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(23\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(24\) | −1.71120 | + | 0.888084i | −1.71120 | + | 0.888084i | ||||
\(25\) | 0.791071 | + | 0.611724i | 0.791071 | + | 0.611724i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.30093 | − | 3.04368i | 1.30093 | − | 3.04368i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.925304 | − | 0.379225i | \(-0.876190\pi\) | ||||
0.925304 | + | 0.379225i | \(0.123810\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.999552 | − | 0.0299155i | \(-0.00952381\pi\) | ||||
−0.999552 | + | 0.0299155i | \(0.990476\pi\) | |||||||
\(32\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(33\) | −1.37341 | + | 1.35301i | −1.37341 | + | 1.35301i | ||||
\(34\) | 0.884634 | − | 0.133337i | 0.884634 | − | 0.133337i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.65753 | − | 0.564875i | −2.65753 | − | 0.564875i | ||||
\(37\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(38\) | −1.88927 | − | 0.645262i | −1.88927 | − | 0.645262i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.267104 | − | 0.279369i | −0.267104 | − | 0.279369i | 0.575617 | − | 0.817719i | \(-0.304762\pi\) |
−0.842721 | + | 0.538351i | \(0.819048\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.646600 | + | 0.762830i | −0.646600 | + | 0.762830i | ||||
\(44\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.936235 | − | 0.351375i | \(-0.885714\pi\) | ||||
0.936235 | + | 0.351375i | \(0.114286\pi\) | |||||||
\(48\) | −0.0288406 | + | 1.92771i | −0.0288406 | + | 1.92771i | ||||
\(49\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(50\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(51\) | 1.48063 | + | 0.884635i | 1.48063 | + | 0.884635i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.193256 | − | 0.981148i | \(-0.438095\pi\) | ||||
−0.193256 | + | 0.981148i | \(0.561905\pi\) | |||||||
\(54\) | −2.06378 | − | 2.58790i | −2.06378 | − | 2.58790i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.02333 | − | 3.27423i | −2.02333 | − | 3.27423i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.93516 | − | 0.174167i | −1.93516 | − | 0.174167i | −0.946327 | − | 0.323210i | \(-0.895238\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.999552 | − | 0.0299155i | \(-0.990476\pi\) | ||||
0.999552 | + | 0.0299155i | \(0.00952381\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.983930 | − | 0.178557i | 0.983930 | − | 0.178557i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.540643 | + | 1.85057i | 0.540643 | + | 1.85057i | ||||
\(67\) | 1.93445 | + | 0.291571i | 1.93445 | + | 0.291571i | 0.998210 | − | 0.0598042i | \(-0.0190476\pi\) |
0.936235 | + | 0.351375i | \(0.114286\pi\) | |||||||
\(68\) | 0.301784 | − | 0.842189i | 0.301784 | − | 0.842189i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.251587 | − | 0.967835i | \(-0.419048\pi\) | ||||
−0.251587 | + | 0.967835i | \(0.580952\pi\) | |||||||
\(72\) | −1.75674 | + | 2.07253i | −1.75674 | + | 2.07253i | ||||
\(73\) | −1.59580 | + | 0.889773i | −1.59580 | + | 0.889773i | −0.599822 | + | 0.800134i | \(0.704762\pi\) |
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.85845 | + | 0.512899i | 1.85845 | + | 0.512899i | ||||
\(76\) | −1.46348 | + | 1.35791i | −1.46348 | + | 1.35791i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.0548208 | − | 3.66422i | 0.0548208 | − | 3.66422i | ||||
\(82\) | −0.372583 | + | 0.102826i | −0.372583 | + | 0.102826i | ||||
\(83\) | 0.498210 | − | 0.806221i | 0.498210 | − | 0.806221i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.998210 | + | 0.0598042i | \(0.0190476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.887586 | − | 0.460642i | 0.887586 | − | 0.460642i | ||||
\(89\) | 0.148391 | + | 1.98014i | 0.148391 | + | 1.98014i | 0.193256 | + | 0.981148i | \(0.438095\pi\) |
−0.0448648 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.68387 | + | 0.938878i | 1.68387 | + | 0.938878i | ||||
\(97\) | 1.24660 | + | 0.344039i | 1.24660 | + | 0.344039i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
0.420357 | + | 0.907359i | \(0.361905\pi\) | |||||||
\(98\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(99\) | −1.06781 | + | 2.49826i | −1.06781 | + | 2.49826i | ||||
\(100\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(101\) | 0 | 0 | −0.842721 | − | 0.538351i | \(-0.819048\pi\) | ||||
0.842721 | + | 0.538351i | \(0.180952\pi\) | |||||||
\(102\) | 1.48063 | − | 0.884635i | 1.48063 | − | 0.884635i | ||||
\(103\) | 0 | 0 | 0.575617 | − | 0.817719i | \(-0.304762\pi\) | ||||
−0.575617 | + | 0.817719i | \(0.695238\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.161032 | + | 1.18879i | −0.161032 | + | 1.18879i | 0.712376 | + | 0.701798i | \(0.247619\pi\) |
−0.873408 | + | 0.486989i | \(0.838095\pi\) | |||||||
\(108\) | −3.25686 | + | 0.591032i | −3.25686 | + | 0.591032i | ||||
\(109\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.281259 | + | 0.168044i | −0.281259 | + | 0.168044i | −0.646600 | − | 0.762830i | \(-0.723810\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(114\) | −3.84206 | + | 0.230183i | −3.84206 | + | 0.230183i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.07038 | + | 1.62156i | −1.07038 | + | 1.62156i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.712376 | − | 0.701798i | 0.712376 | − | 0.701798i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.680743 | − | 0.303086i | −0.680743 | − | 0.303086i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.983930 | − | 0.178557i | \(-0.942857\pi\) | ||||
0.983930 | + | 0.178557i | \(0.0571429\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(129\) | −0.595762 | + | 1.83357i | −0.595762 | + | 1.83357i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0269559 | + | 0.0129813i | −0.0269559 | + | 0.0129813i | −0.447313 | − | 0.894377i | \(-0.647619\pi\) |
0.420357 | + | 0.907359i | \(0.361905\pi\) | |||||||
\(132\) | 1.88580 | + | 0.400838i | 1.88580 | + | 0.400838i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.17343 | − | 1.56530i | 1.17343 | − | 1.56530i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.598622 | − | 0.664837i | −0.598622 | − | 0.664837i | ||||
\(137\) | 1.48194 | − | 1.29473i | 1.48194 | − | 1.29473i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
0.858449 | − | 0.512899i | \(-0.171429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.803364 | + | 1.73409i | 0.803364 | + | 1.73409i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.134233 | + | 0.990950i | \(0.457143\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.992594 | + | 2.52909i | 0.992594 | + | 2.52909i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0273322 | + | 1.82689i | 0.0273322 | + | 1.82689i | ||||
\(147\) | 0.540643 | + | 1.85057i | 0.540643 | + | 1.85057i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.842721 | − | 0.538351i | \(-0.180952\pi\) | ||||
−0.842721 | + | 0.538351i | \(0.819048\pi\) | |||||||
\(150\) | 1.33232 | − | 1.39349i | 1.33232 | − | 1.39349i | ||||
\(151\) | 0 | 0 | 0.134233 | − | 0.990950i | \(-0.457143\pi\) | ||||
−0.134233 | + | 0.990950i | \(0.542857\pi\) | |||||||
\(152\) | 0.502273 | + | 1.93220i | 0.502273 | + | 1.93220i | ||||
\(153\) | 2.40346 | + | 0.362263i | 2.40346 | + | 0.362263i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.772417 | − | 0.635116i | \(-0.219048\pi\) | ||||
−0.772417 | + | 0.635116i | \(0.780952\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.20072 | − | 1.78464i | −3.20072 | − | 1.78464i | ||||
\(163\) | 0.820112 | − | 0.807934i | 0.820112 | − | 0.807934i | −0.163818 | − | 0.986491i | \(-0.552381\pi\) |
0.983930 | + | 0.178557i | \(0.0571429\pi\) | |||||||
\(164\) | −0.0860070 | + | 0.376821i | −0.0860070 | + | 0.376821i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.473869 | − | 0.820765i | −0.473869 | − | 0.820765i | ||||
\(167\) | 0 | 0 | 0.599822 | − | 0.800134i | \(-0.295238\pi\) | ||||
−0.599822 | + | 0.800134i | \(0.704762\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.971490 | + | 0.237080i | 0.971490 | + | 0.237080i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.38816 | − | 3.18819i | −4.38816 | − | 3.18819i | ||||
\(172\) | 0.992847 | + | 0.119394i | 0.992847 | + | 0.119394i | ||||
\(173\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0149594 | − | 0.999888i | 0.0149594 | − | 0.999888i | ||||
\(177\) | −3.57950 | + | 1.10413i | −3.57950 | + | 1.10413i | ||||
\(178\) | 1.81402 | + | 0.807654i | 1.81402 | + | 0.807654i | ||||
\(179\) | −1.90052 | − | 0.403968i | −1.90052 | − | 0.403968i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
−0.999552 | + | 0.0299155i | \(0.990476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.887586 | − | 0.460642i | \(-0.847619\pi\) | ||||
0.887586 | + | 0.460642i | \(0.152381\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.767991 | − | 0.458853i | −0.767991 | − | 0.458853i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.447313 | − | 0.894377i | \(-0.352381\pi\) | ||||
−0.447313 | + | 0.894377i | \(0.647619\pi\) | |||||||
\(192\) | 1.62470 | − | 1.03790i | 1.62470 | − | 1.03790i | ||||
\(193\) | −0.853882 | − | 1.58678i | −0.853882 | − | 1.58678i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.0448648 | − | 0.998993i | \(-0.514286\pi\) | |||||||
\(194\) | 0.893682 | − | 0.934718i | 0.893682 | − | 0.934718i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.887586 | − | 0.460642i | 0.887586 | − | 0.460642i | ||||
\(197\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(198\) | 1.69396 | + | 2.12416i | 1.69396 | + | 2.12416i | ||||
\(199\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(200\) | −0.842721 | − | 0.538351i | −0.842721 | − | 0.538351i | ||||
\(201\) | 3.66406 | − | 0.894170i | 3.66406 | − | 0.894170i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.0773817 | − | 1.72304i | −0.0773817 | − | 1.72304i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.04949 | + | 1.69831i | 1.04949 | + | 1.69831i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0352660 | − | 0.785259i | 0.0352660 | − | 0.785259i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.936235 | − | 0.351375i | \(-0.114286\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.970532 | + | 0.705133i | 0.970532 | + | 0.705133i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.02286 | + | 3.14805i | −1.02286 | + | 3.14805i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.19624 | + | 2.75400i | −2.19624 | + | 2.75400i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.995974 | − | 0.0896393i | \(-0.0285714\pi\) | ||||
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.69746 | − | 0.324382i | 2.69746 | − | 0.324382i | ||||
\(226\) | 0.0146993 | + | 0.327306i | 0.0146993 | + | 0.327306i | ||||
\(227\) | −0.443676 | + | 0.343088i | −0.443676 | + | 0.343088i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(228\) | −1.61793 | + | 3.49238i | −1.61793 | + | 3.49238i | ||||
\(229\) | 0 | 0 | −0.525684 | − | 0.850680i | \(-0.676190\pi\) | ||||
0.525684 | + | 0.850680i | \(0.323810\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.169736 | + | 0.473681i | −0.169736 | + | 0.473681i | −0.995974 | − | 0.0896393i | \(-0.971429\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.920717 | + | 1.71098i | 0.920717 | + | 1.71098i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.163818 | − | 0.986491i | \(-0.552381\pi\) | ||||
0.163818 | + | 0.986491i | \(0.447619\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.256539 | + | 0.0791319i | 0.256539 | + | 0.0791319i | 0.420357 | − | 0.907359i | \(-0.361905\pi\) |
−0.163818 | + | 0.986491i | \(0.552381\pi\) | |||||||
\(242\) | −0.280427 | − | 0.959875i | −0.280427 | − | 0.959875i | ||||
\(243\) | −1.37189 | − | 3.49552i | −1.37189 | − | 3.49552i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.589479 | + | 0.455836i | −0.589479 | + | 0.455836i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.299323 | − | 1.80248i | 0.299323 | − | 1.80248i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.104528 | + | 0.994522i | 0.104528 | + | 0.994522i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.691063 | − | 0.722795i | −0.691063 | − | 0.722795i | ||||
\(257\) | −0.0646021 | + | 0.198825i | −0.0646021 | + | 0.198825i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(258\) | 1.33232 | + | 1.39349i | 1.33232 | + | 1.39349i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.00134230 | + | 0.0298887i | −0.00134230 | + | 0.0298887i | ||||
\(263\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(264\) | 1.24660 | − | 1.47068i | 1.24660 | − | 1.47068i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.71244 | + | 3.42392i | 1.71244 | + | 3.42392i | ||||
\(268\) | −0.822343 | − | 1.77506i | −0.822343 | − | 1.77506i | ||||
\(269\) | 0 | 0 | −0.0448648 | − | 0.998993i | \(-0.514286\pi\) | ||||
0.0448648 | + | 0.998993i | \(0.485714\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.873408 | − | 0.486989i | \(-0.161905\pi\) | ||||
−0.873408 | + | 0.486989i | \(0.838095\pi\) | |||||||
\(272\) | −0.869121 | + | 0.212098i | −0.869121 | + | 0.212098i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.437890 | − | 1.91852i | −0.437890 | − | 1.91852i | ||||
\(275\) | −0.963963 | − | 0.266037i | −0.963963 | − | 0.266037i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.887586 | − | 0.460642i | \(-0.152381\pi\) | ||||
−0.887586 | + | 0.460642i | \(0.847619\pi\) | |||||||
\(278\) | 1.90772 | + | 0.114294i | 1.90772 | + | 0.114294i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.53973 | + | 0.983616i | −1.53973 | + | 0.983616i | −0.550897 | + | 0.834573i | \(0.685714\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.578021 | + | 0.446976i | 0.578021 | + | 0.446976i | 0.858449 | − | 0.512899i | \(-0.171429\pi\) |
−0.280427 | + | 0.959875i | \(0.590476\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.69746 | + | 0.324382i | 2.69746 | + | 0.324382i | ||||
\(289\) | 0.0559856 | − | 0.191633i | 0.0559856 | − | 0.191633i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.47536 | − | 0.297673i | 2.47536 | − | 0.297673i | ||||
\(292\) | 1.62170 | + | 0.841636i | 1.62170 | + | 0.841636i | ||||
\(293\) | 0 | 0 | −0.858449 | − | 0.512899i | \(-0.828571\pi\) | ||||
0.858449 | + | 0.512899i | \(0.171429\pi\) | |||||||
\(294\) | 1.88580 | + | 0.400838i | 1.88580 | + | 0.400838i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0495164 | + | 3.30968i | −0.0495164 | + | 3.30968i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.595762 | − | 1.83357i | −0.595762 | − | 1.83357i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.93950 | + | 0.473312i | 1.93950 | + | 0.473312i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.45793 | − | 1.94481i | 1.45793 | − | 1.94481i | ||||
\(307\) | −0.712376 | − | 1.23387i | −0.712376 | − | 1.23387i | −0.963963 | − | 0.266037i | \(-0.914286\pi\) |
0.251587 | − | 0.967835i | \(-0.419048\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.873408 | − | 0.486989i | \(-0.838095\pi\) | ||||
0.873408 | + | 0.486989i | \(0.161905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.579161 | − | 1.61626i | −0.579161 | − | 1.61626i | −0.772417 | − | 0.635116i | \(-0.780952\pi\) |
0.193256 | − | 0.981148i | \(-0.438095\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.753071 | − | 0.657939i | \(-0.771429\pi\) | ||||
0.753071 | + | 0.657939i | \(0.228571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.581876 | + | 2.23843i | 0.581876 | + | 2.23843i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.23427 | − | 1.29095i | 1.23427 | − | 1.29095i | ||||
\(324\) | −3.08826 | + | 1.97286i | −3.08826 | + | 1.97286i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.322838 | − | 1.10504i | −0.322838 | − | 1.10504i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.291071 | + | 0.254301i | 0.291071 | + | 0.254301i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.770707 | − | 0.715112i | −0.770707 | − | 0.715112i | 0.193256 | − | 0.981148i | \(-0.438095\pi\) |
−0.963963 | + | 0.266037i | \(0.914286\pi\) | |||||||
\(332\) | −0.947313 | + | 0.0283520i | −0.947313 | + | 0.0283520i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.05866 | + | 1.17576i | 1.05866 | + | 1.17576i | 0.983930 | + | 0.178557i | \(0.0571429\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(338\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(339\) | −0.378882 | + | 0.505410i | −0.378882 | + | 0.505410i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −4.88692 | + | 2.35342i | −4.88692 | + | 2.35342i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.575617 | − | 0.817719i | 0.575617 | − | 0.817719i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.172233 | + | 0.278713i | −0.172233 | + | 0.278713i | −0.925304 | − | 0.379225i | \(-0.876190\pi\) |
0.753071 | + | 0.657939i | \(0.228571\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.575617 | − | 0.817719i | \(-0.695238\pi\) | ||||
0.575617 | + | 0.817719i | \(0.304762\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.873408 | − | 0.486989i | −0.873408 | − | 0.486989i | ||||
\(353\) | −1.13838 | + | 0.171583i | −1.13838 | + | 0.171583i | −0.691063 | − | 0.722795i | \(-0.742857\pi\) |
−0.447313 | + | 0.894377i | \(0.647619\pi\) | |||||||
\(354\) | −0.723921 | + | 3.67530i | −0.723921 | + | 3.67530i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.57082 | − | 1.21470i | 1.57082 | − | 1.21470i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.25633 | + | 1.48216i | −1.25633 | + | 1.48216i | ||||
\(359\) | 0 | 0 | 0.998210 | − | 0.0598042i | \(-0.0190476\pi\) | ||||
−0.998210 | + | 0.0598042i | \(0.980952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.82544 | + | 0.965005i | −2.82544 | + | 0.965005i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.757723 | − | 1.77278i | 0.757723 | − | 1.77278i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.772417 | − | 0.635116i | \(-0.780952\pi\) | ||||
0.772417 | + | 0.635116i | \(0.219048\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.04964 | − | 0.0314146i | −1.04964 | − | 0.0314146i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(374\) | −0.767991 | + | 0.458853i | −0.767991 | + | 0.458853i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.791755 | − | 0.691735i | 0.791755 | − | 0.691735i | −0.163818 | − | 0.986491i | \(-0.552381\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.0448648 | − | 0.998993i | \(-0.485714\pi\) | ||||
−0.0448648 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(384\) | −0.144074 | − | 1.92253i | −0.144074 | − | 1.92253i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.80194 | −1.80194 | ||||||||
\(387\) | 0.203034 | + | 2.70930i | 0.203034 | + | 2.70930i | ||||
\(388\) | −0.399621 | − | 1.22991i | −0.399621 | − | 1.22991i | ||||
\(389\) | 0 | 0 | −0.134233 | − | 0.990950i | \(-0.542857\pi\) | ||||
0.134233 | + | 0.990950i | \(0.457143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.0149594 | − | 0.999888i | 0.0149594 | − | 0.999888i | ||||
\(393\) | −0.0385963 | + | 0.0428655i | −0.0385963 | + | 0.0428655i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.67324 | − | 0.485121i | 2.67324 | − | 0.485121i | ||||
\(397\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.873408 | + | 0.486989i | −0.873408 | + | 0.486989i | ||||
\(401\) | −1.27242 | + | 1.50114i | −1.27242 | + | 1.50114i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.772417 | + | 0.635116i | \(0.780952\pi\) | |||||||
\(402\) | 0.948883 | − | 3.65028i | 0.948883 | − | 3.65028i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −1.55397 | − | 0.748351i | −1.55397 | − | 0.748351i | ||||
\(409\) | −1.44254 | + | 0.261783i | −1.44254 | + | 0.261783i | −0.842721 | − | 0.538351i | \(-0.819048\pi\) |
−0.599822 | + | 0.800134i | \(0.704762\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.69706 | − | 3.39317i | 1.69706 | − | 3.39317i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.70096 | + | 2.50613i | 2.70096 | + | 2.50613i | ||||
\(418\) | 1.99285 | − | 0.119394i | 1.99285 | − | 0.119394i | ||||
\(419\) | 0.939065 | + | 1.17755i | 0.939065 | + | 1.17755i | 0.983930 | + | 0.178557i | \(0.0571429\pi\) |
−0.0448648 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.447313 | − | 0.894377i | \(-0.647619\pi\) | ||||
0.447313 | + | 0.894377i | \(0.352381\pi\) | |||||||
\(422\) | −0.674784 | − | 0.403165i | −0.674784 | − | 0.403165i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.0133831 | + | 0.894526i | −0.0133831 | + | 0.894526i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.08084 | − | 0.520506i | 1.08084 | − | 0.520506i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(432\) | 2.28745 | + | 2.39249i | 2.28745 | + | 2.39249i | ||||
\(433\) | −1.93516 | − | 0.472252i | −1.93516 | − | 0.472252i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.946327 | − | 0.323210i | \(-0.895238\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1.38443 | + | 3.23903i | 1.38443 | + | 3.23903i | ||||
\(439\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.69396 | + | 2.12416i | 1.69396 | + | 2.12416i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.633118 | − | 1.36661i | 0.633118 | − | 1.36661i | −0.280427 | − | 0.959875i | \(-0.590476\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.64257 | + | 0.852469i | −1.64257 | + | 0.852469i | −0.646600 | + | 0.762830i | \(0.723810\pi\) |
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(450\) | 0.992594 | − | 2.52909i | 0.992594 | − | 2.52909i | ||||
\(451\) | 0.353096 | + | 0.157209i | 0.353096 | + | 0.157209i | ||||
\(452\) | 0.295190 | + | 0.142156i | 0.295190 | + | 0.142156i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.0918781 | + | 0.553278i | 0.0918781 | + | 0.553278i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.30868 | + | 3.07967i | 2.30868 | + | 3.07967i | ||||
\(457\) | 0.743861 | − | 1.74035i | 0.743861 | − | 1.74035i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.87683 | − | 0.702056i | 2.87683 | − | 0.702056i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.336689 | + | 0.373931i | 0.336689 | + | 0.373931i | ||||
\(467\) | 0.153250 | − | 1.45807i | 0.153250 | − | 1.45807i | −0.599822 | − | 0.800134i | \(-0.704762\pi\) |
0.753071 | − | 0.657939i | \(-0.228571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.94298 | 1.94298 | ||||||||
\(473\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.946041 | − | 1.75804i | 0.946041 | − | 1.75804i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.191249 | − | 0.188409i | 0.191249 | − | 0.188409i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.72823 | − | 0.448336i | −3.72823 | − | 0.448336i | ||||
\(487\) | 0 | 0 | 0.971490 | − | 0.237080i | \(-0.0761905\pi\) | ||||
−0.971490 | + | 0.237080i | \(0.923810\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.872317 | − | 2.04089i | 0.872317 | − | 2.04089i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.399540 | − | 1.36758i | −0.399540 | − | 1.36758i | −0.873408 | − | 0.486989i | \(-0.838095\pi\) |
0.473869 | − | 0.880596i | \(-0.342857\pi\) | |||||||
\(492\) | 0.122072 | + | 0.735099i | 0.122072 | + | 0.735099i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.44542 | − | 1.11772i | −1.44542 | − | 1.11772i | ||||
\(499\) | −0.744388 | + | 1.05747i | −0.744388 | + | 1.05747i | 0.251587 | + | 0.967835i | \(0.419048\pi\) |
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.925304 | + | 0.379225i | 0.925304 | + | 0.379225i | ||||
\(503\) | 0 | 0 | 0.420357 | − | 0.907359i | \(-0.361905\pi\) | ||||
−0.420357 | + | 0.907359i | \(0.638095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.90639 | − | 0.287342i | 1.90639 | − | 0.287342i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.963963 | + | 0.266037i | −0.963963 | + | 0.266037i | ||||
\(513\) | −6.41985 | − | 1.56669i | −6.41985 | − | 1.56669i | ||||
\(514\) | 0.144471 | + | 0.151105i | 0.144471 | + | 0.151105i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.85845 | − | 0.512899i | 1.85845 | − | 0.512899i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.000447568 | − | 0.0299155i | 0.000447568 | − | 0.0299155i | −0.999552 | − | 0.0299155i | \(-0.990476\pi\) |
1.00000 | \(0\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.59580 | + | 0.710494i | −1.59580 | + | 0.710494i | −0.995974 | − | 0.0896393i | \(-0.971429\pi\) |
−0.599822 | + | 0.800134i | \(0.704762\pi\) | |||||||
\(524\) | 0.0256838 | + | 0.0153453i | 0.0256838 | + | 0.0153453i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.704350 | − | 1.79466i | −0.704350 | − | 1.79466i | ||||
\(529\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.07749 | + | 3.35270i | −4.07749 | + | 3.35270i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.82656 | + | 0.114524i | 3.82656 | + | 0.114524i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.95279 | − | 0.116995i | −1.95279 | − | 0.116995i | ||||
\(537\) | −3.68572 | + | 0.668860i | −3.68572 | + | 0.668860i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.280427 | − | 0.959875i | −0.280427 | − | 0.959875i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.337330 | − | 0.941386i | \(-0.390476\pi\) | ||||
−0.337330 | + | 0.941386i | \(0.609524\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.225076 | + | 0.865850i | −0.225076 | + | 0.865850i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.558597 | − | 1.91202i | 0.558597 | − | 1.91202i | 0.193256 | − | 0.981148i | \(-0.438095\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(548\) | −1.89694 | − | 0.523523i | −1.89694 | − | 0.523523i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.691063 | + | 0.722795i | −0.691063 | + | 0.722795i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.00466 | − | 1.62577i | 1.00466 | − | 1.62577i | ||||
\(557\) | 0 | 0 | −0.134233 | − | 0.990950i | \(-0.542857\pi\) | ||||
0.134233 | + | 0.990950i | \(0.457143\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.70551 | − | 0.257064i | −1.70551 | − | 0.257064i | ||||
\(562\) | 0.136539 | + | 1.82198i | 0.136539 | + | 1.82198i | ||||
\(563\) | −0.0675728 | + | 1.50463i | −0.0675728 | + | 1.50463i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−0.691063 | + | 0.722795i | \(0.742857\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.667511 | − | 0.297195i | 0.667511 | − | 0.297195i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.61634 | + | 0.901226i | 1.61634 | + | 0.901226i | 0.992847 | + | 0.119394i | \(0.0380952\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.48883 | − | 1.01507i | −1.48883 | − | 1.01507i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.56389 | − | 2.22166i | 1.56389 | − | 2.22166i | ||||
\(577\) | −0.268346 | − | 0.00803130i | −0.268346 | − | 0.00803130i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
−0.163818 | + | 0.986491i | \(0.552381\pi\) | |||||||
\(578\) | −0.142221 | − | 0.140110i | −0.142221 | − | 0.140110i | ||||
\(579\) | −2.68338 | − | 2.20639i | −2.68338 | − | 2.20639i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.910865 | − | 2.32085i | 0.910865 | − | 2.32085i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.50961 | − | 1.02924i | 1.50961 | − | 1.02924i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.559851 | + | 0.0335414i | −0.559851 | + | 0.0335414i | −0.337330 | − | 0.941386i | \(-0.609524\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(588\) | 1.24660 | − | 1.47068i | 1.24660 | − | 1.47068i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.52758 | − | 0.230246i | 1.52758 | − | 0.230246i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.858449 | + | 0.512899i | \(0.171429\pi\) | |||||||
\(594\) | 2.89103 | + | 1.61196i | 2.89103 | + | 1.61196i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.525684 | − | 0.850680i | \(-0.323810\pi\) | ||||
−0.525684 | + | 0.850680i | \(0.676190\pi\) | |||||||
\(600\) | −1.89694 | − | 0.344244i | −1.89694 | − | 0.344244i | ||||
\(601\) | 0.324890 | − | 0.999910i | 0.324890 | − | 0.999910i | −0.646600 | − | 0.762830i | \(-0.723810\pi\) |
0.971490 | − | 0.237080i | \(-0.0761905\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.29997 | − | 3.12411i | 4.29997 | − | 3.12411i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.599822 | − | 0.800134i | \(-0.295238\pi\) | ||||
−0.599822 | + | 0.800134i | \(0.704762\pi\) | |||||||
\(608\) | 1.33587 | − | 1.48363i | 1.33587 | − | 1.48363i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.02172 | − | 2.20543i | −1.02172 | − | 2.20543i | ||||
\(613\) | 0 | 0 | 0.550897 | − | 0.834573i | \(-0.314286\pi\) | ||||
−0.550897 | + | 0.834573i | \(0.685714\pi\) | |||||||
\(614\) | −1.42411 | + | 0.0426221i | −1.42411 | + | 0.0426221i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.684090 | + | 1.74303i | 0.684090 | + | 1.74303i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.0149594 | + | 0.999888i | \(0.495238\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.0164822 | − | 1.10167i | −0.0164822 | − | 1.10167i | −0.842721 | − | 0.538351i | \(-0.819048\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.251587 | + | 0.967835i | 0.251587 | + | 0.967835i | ||||
\(626\) | −1.69772 | − | 0.255890i | −1.69772 | − | 0.255890i | ||||
\(627\) | 3.11387 | + | 2.26236i | 3.11387 | + | 2.26236i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.925304 | − | 0.379225i | \(-0.876190\pi\) | ||||
0.925304 | + | 0.379225i | \(0.123810\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.511205 | − | 1.42662i | −0.511205 | − | 1.42662i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.631640 | − | 0.237059i | −0.631640 | − | 0.237059i | 0.0149594 | − | 0.999888i | \(-0.495238\pi\) |
−0.646600 | + | 0.762830i | \(0.723810\pi\) | |||||||
\(642\) | 2.24689 | + | 0.548325i | 2.24689 | + | 0.548325i | ||||
\(643\) | −1.65836 | − | 0.300947i | −1.65836 | − | 0.300947i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.925304 | + | 0.379225i | \(0.876190\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.551920 | − | 1.69863i | −0.551920 | − | 1.69863i | ||||
\(647\) | 0 | 0 | 0.473869 | − | 0.880596i | \(-0.342857\pi\) | ||||
−0.473869 | + | 0.880596i | \(0.657143\pi\) | |||||||
\(648\) | 0.273859 | + | 3.65439i | 0.273859 | + | 3.65439i | ||||
\(649\) | 1.85666 | − | 0.572703i | 1.85666 | − | 0.572703i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.12608 | − | 0.239355i | −1.12608 | − | 0.239355i | ||||
\(653\) | 0 | 0 | −0.858449 | − | 0.512899i | \(-0.828571\pi\) | ||||
0.858449 | + | 0.512899i | \(0.171429\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.361866 | − | 0.135811i | 0.361866 | − | 0.135811i | ||||
\(657\) | −1.39205 | + | 4.76484i | −1.39205 | + | 4.76484i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.0823372 | + | 1.09871i | −0.0823372 | + | 1.09871i | 0.791071 | + | 0.611724i | \(0.209524\pi\) |
−0.873408 | + | 0.486989i | \(0.838095\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(662\) | −0.994938 | + | 0.339812i | −0.994938 | + | 0.339812i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.423935 | + | 0.847635i | −0.423935 | + | 0.847635i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.708488 | − | 0.452599i | −0.708488 | − | 0.452599i | 0.134233 | − | 0.990950i | \(-0.457143\pi\) |
−0.842721 | + | 0.538351i | \(0.819048\pi\) | |||||||
\(674\) | 1.53704 | − | 0.375095i | 1.53704 | − | 0.375095i | ||||
\(675\) | 2.89103 | − | 1.61196i | 2.89103 | − | 1.61196i | ||||
\(676\) | −0.337330 | − | 0.941386i | −0.337330 | − | 0.941386i | ||||
\(677\) | 0 | 0 | −0.0448648 | − | 0.998993i | \(-0.514286\pi\) | ||||
0.0448648 | + | 0.998993i | \(0.485714\pi\) | |||||||
\(678\) | 0.265522 | + | 0.573140i | 0.265522 | + | 0.573140i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.540643 | + | 0.936421i | −0.540643 | + | 0.936421i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.19158 | − | 0.367554i | 1.19158 | − | 0.367554i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(684\) | −0.243350 | + | 5.41861i | −0.243350 | + | 5.41861i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.447313 | − | 0.894377i | −0.447313 | − | 0.894377i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.865319 | − | 1.02087i | −0.865319 | − | 1.02087i | −0.999552 | − | 0.0299155i | \(-0.990476\pi\) |
0.134233 | − | 0.990950i | \(-0.457143\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.163818 | + | 0.283741i | 0.163818 | + | 0.283741i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0566456 | − | 0.341112i | 0.0566456 | − | 0.341112i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.0435225 | + | 0.969104i | 0.0435225 | + | 0.969104i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.420357 | − | 0.907359i | \(-0.361905\pi\) | ||||
−0.420357 | + | 0.907359i | \(0.638095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.842721 | + | 0.538351i | −0.842721 | + | 0.538351i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.388346 | + | 1.08376i | −0.388346 | + | 1.08376i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.89341 | + | 2.37909i | 2.89341 | + | 2.37909i | ||||
\(709\) | 0 | 0 | −0.473869 | − | 0.880596i | \(-0.657143\pi\) | ||||
0.473869 | + | 0.880596i | \(0.342857\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.325292 | − | 1.95887i | −0.325292 | − | 1.95887i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.709850 | + | 1.80867i | 0.709850 | + | 1.80867i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.791071 | − | 0.611724i | \(-0.209524\pi\) | ||||
−0.791071 | + | 0.611724i | \(0.790476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.489110 | + | 2.94536i | −0.489110 | + | 2.94536i | ||||
\(723\) | 0.515500 | − | 0.0463958i | 0.515500 | − | 0.0463958i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.20204 | − | 1.50731i | −1.20204 | − | 1.50731i | ||||
\(727\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.47048 | − | 2.58392i | −2.47048 | − | 2.58392i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.893025 | − | 0.0535024i | −0.893025 | − | 0.0535024i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.134233 | − | 0.990950i | \(-0.542857\pi\) | ||||
0.134233 | + | 0.990950i | \(0.457143\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.90052 | + | 0.463799i | −1.90052 | + | 0.463799i | ||||
\(738\) | −0.525057 | + | 0.909425i | −0.525057 | + | 0.909425i | ||||
\(739\) | 0.782886 | + | 1.83165i | 0.782886 | + | 1.83165i | 0.473869 | + | 0.880596i | \(0.342857\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.337330 | − | 0.941386i | \(-0.609524\pi\) | ||||
0.337330 | + | 0.941386i | \(0.390476\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.572970 | − | 2.51035i | −0.572970 | − | 2.51035i | ||||
\(748\) | 0.0401373 | + | 0.893725i | 0.0401373 | + | 0.893725i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.998210 | − | 0.0598042i | \(-0.980952\pi\) | ||||
0.998210 | + | 0.0598042i | \(0.0190476\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.913584 | + | 1.69772i | 0.913584 | + | 1.69772i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.946327 | − | 0.323210i | \(-0.104762\pi\) | ||||
−0.946327 | + | 0.323210i | \(0.895238\pi\) | |||||||
\(758\) | −0.233951 | − | 1.02501i | −0.233951 | − | 1.02501i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.97770 | − | 0.237827i | −1.97770 | − | 0.237827i | −0.999552 | − | 0.0299155i | \(-0.990476\pi\) |
−0.978148 | − | 0.207912i | \(-0.933333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.76125 | − | 0.784158i | −1.76125 | − | 0.784158i | ||||
\(769\) | 1.57906 | − | 0.487076i | 1.57906 | − | 0.487076i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.0301197 | + | 0.401919i | 0.0301197 | + | 0.401919i | ||||
\(772\) | −0.853882 | + | 1.58678i | −0.853882 | + | 1.58678i | ||||
\(773\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(774\) | 2.48201 | + | 1.10506i | 2.48201 | + | 1.10506i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.27242 | − | 0.230910i | −1.27242 | − | 0.230910i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.462847 | + | 0.617415i | −0.462847 | + | 0.617415i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.873408 | − | 0.486989i | −0.873408 | − | 0.486989i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.0194576 | + | 0.0543003i | 0.0194576 | + | 0.0543003i | ||||
\(787\) | 0.361866 | + | 1.83717i | 0.361866 | + | 1.83717i | 0.525684 | + | 0.850680i | \(0.323810\pi\) |
−0.163818 | + | 0.986491i | \(0.552381\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.839568 | − | 2.58392i | 0.839568 | − | 2.58392i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.842721 | − | 0.538351i | \(-0.180952\pi\) | ||||
−0.842721 | + | 0.538351i | \(0.819048\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.0149594 | + | 0.999888i | 0.0149594 | + | 0.999888i | ||||
\(801\) | 4.06277 | + | 3.54953i | 4.06277 | + | 3.54953i | ||||
\(802\) | 0.718940 | + | 1.83183i | 0.718940 | + | 1.83183i | ||||
\(803\) | 1.13917 | − | 1.42848i | 1.13917 | − | 1.42848i | ||||
\(804\) | −2.76477 | − | 2.56533i | −2.76477 | − | 2.56533i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.41010 | − | 1.23197i | 1.41010 | − | 1.23197i | 0.473869 | − | 0.880596i | \(-0.342857\pi\) |
0.936235 | − | 0.351375i | \(-0.114286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.139886 | + | 0.155360i | −0.139886 | + | 0.155360i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.39537 | + | 1.01380i | −1.39537 | + | 1.01380i | ||||
\(817\) | 1.71382 | + | 1.02396i | 1.71382 | + | 1.02396i | ||||
\(818\) | −0.453051 | + | 1.39435i | −0.453051 | + | 1.39435i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.550897 | − | 0.834573i | \(-0.685714\pi\) | ||||
0.550897 | + | 0.834573i | \(0.314286\pi\) | |||||||
\(822\) | −2.18383 | − | 3.10233i | −2.18383 | − | 3.10233i | ||||
\(823\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.91414 | + | 0.230183i | −1.91414 | + | 0.230183i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.162473 | − | 0.824866i | 0.162473 | − | 0.824866i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.971490 | − | 0.237080i | \(-0.0761905\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.791071 | − | 0.611724i | \(-0.209524\pi\) | ||||
−0.791071 | + | 0.611724i | \(0.790476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.767991 | + | 0.458853i | −0.767991 | + | 0.458853i | ||||
\(834\) | 3.48679 | − | 1.19088i | 3.48679 | − | 1.19088i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.839210 | − | 1.81147i | 0.839210 | − | 1.81147i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.48194 | − | 0.268932i | 1.48194 | − | 0.268932i | ||||
\(839\) | 0 | 0 | 0.134233 | − | 0.990950i | \(-0.457143\pi\) | ||||
−0.134233 | + | 0.990950i | \(0.542857\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.712376 | + | 0.701798i | 0.712376 | + | 0.701798i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.02761 | + | 2.88041i | −2.02761 | + | 2.88041i | ||||
\(844\) | −0.674784 | + | 0.403165i | −0.674784 | + | 0.403165i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.35794 | + | 0.374766i | 1.35794 | + | 0.374766i | ||||
\(850\) | 0.781374 | + | 0.435673i | 0.781374 | + | 0.435673i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0538218 | − | 1.19844i | 0.0538218 | − | 1.19844i | ||||
\(857\) | −0.00670551 | − | 0.0894788i | −0.00670551 | − | 0.0894788i | 0.992847 | − | 0.119394i | \(-0.0380952\pi\) |
−0.999552 | + | 0.0299155i | \(0.990476\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.0299188 | 0.0299188 | 0.0149594 | − | 0.999888i | \(-0.495238\pi\) | ||||
0.0149594 | + | 0.999888i | \(0.495238\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.525684 | − | 0.850680i | \(-0.323810\pi\) | ||||
−0.525684 | + | 0.850680i | \(0.676190\pi\) | |||||||
\(864\) | 3.19077 | − | 0.880596i | 3.19077 | − | 0.880596i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.33287 | + | 1.48031i | −1.33287 | + | 1.48031i | ||||
\(867\) | −0.0402328 | − | 0.382790i | −0.0402328 | − | 0.382790i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.06871 | − | 1.71103i | 3.06871 | − | 1.71103i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.50832 | + | 0.315754i | 3.50832 | + | 0.315754i | ||||
\(877\) | 0 | 0 | −0.0149594 | − | 0.999888i | \(-0.504762\pi\) | ||||
0.0149594 | + | 0.999888i | \(0.495238\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.51853 | + | 0.731286i | 1.51853 | + | 0.731286i | 0.992847 | − | 0.119394i | \(-0.0380952\pi\) |
0.525684 | + | 0.850680i | \(0.323810\pi\) | |||||||
\(882\) | 2.67324 | − | 0.485121i | 2.67324 | − | 0.485121i | ||||
\(883\) | −0.0895691 | − | 0.00536621i | −0.0895691 | − | 0.00536621i | 0.0149594 | − | 0.999888i | \(-0.495238\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.903418 | − | 1.20512i | −0.903418 | − | 1.20512i | ||||
\(887\) | 0 | 0 | −0.995974 | − | 0.0896393i | \(-0.971429\pi\) | ||||
0.995974 | + | 0.0896393i | \(0.0285714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.33884 | + | 3.41131i | 1.33884 | + | 3.41131i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.0276840 | + | 1.85040i | −0.0276840 | + | 1.85040i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.75674 | − | 2.07253i | −1.75674 | − | 2.07253i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.305758 | − | 0.236439i | 0.305758 | − | 0.236439i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.265063 | − | 0.192580i | 0.265063 | − | 0.192580i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.68387 | − | 0.464718i | 1.68387 | − | 0.464718i | 0.712376 | − | 0.701798i | \(-0.247619\pi\) |
0.971490 | + | 0.237080i | \(0.0761905\pi\) | |||||||
\(908\) | 0.530752 | + | 0.181274i | 0.530752 | + | 0.181274i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.393025 | − | 0.919528i | \(-0.628571\pi\) | ||||
0.393025 | + | 0.919528i | \(0.371429\pi\) | |||||||
\(912\) | 3.80596 | − | 0.573656i | 3.80596 | − | 0.573656i | ||||
\(913\) | −0.155256 | + | 0.934934i | −0.155256 | + | 0.934934i | ||||
\(914\) | −1.18005 | − | 1.47974i | −1.18005 | − | 1.47974i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.745013 | − | 2.86601i | 0.745013 | − | 2.86601i | ||||
\(919\) | 0 | 0 | 0.393025 | − | 0.919528i | \(-0.371429\pi\) | ||||
−0.393025 | + | 0.919528i | \(0.628571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.17293 | − | 1.68029i | −2.17293 | − | 1.68029i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.802718 | − | 1.07079i | −0.802718 | − | 1.07079i | −0.995974 | − | 0.0896393i | \(-0.971429\pi\) |
0.193256 | − | 0.981148i | \(-0.438095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.99285 | − | 0.119394i | 1.99285 | − | 0.119394i | ||||
\(932\) | 0.488828 | − | 0.119293i | 0.488828 | − | 0.119293i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.21135 | − | 0.825886i | −1.21135 | − | 0.825886i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.31833 | + | 1.29875i | −1.31833 | + | 1.29875i | −0.393025 | + | 0.919528i | \(0.628571\pi\) |
−0.925304 | + | 0.379225i | \(0.876190\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.21486 | − | 2.45985i | −2.21486 | − | 2.45985i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.946327 | − | 0.323210i | \(-0.895238\pi\) | ||||
0.946327 | + | 0.323210i | \(0.104762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.920717 | − | 1.71098i | 0.920717 | − | 1.71098i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.691063 | − | 0.722795i | −0.691063 | − | 0.722795i | ||||
\(947\) | −1.54483 | −1.54483 | −0.772417 | − | 0.635116i | \(-0.780952\pi\) | ||||
−0.772417 | + | 0.635116i | \(0.780952\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −1.09982 | − | 1.66616i | −1.09982 | − | 1.66616i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.00781 | + | 1.11928i | 1.00781 | + | 1.11928i | 0.992847 | + | 0.119394i | \(0.0380952\pi\) |
0.0149594 | + | 0.999888i | \(0.495238\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.998210 | − | 0.0598042i | 0.998210 | − | 0.0598042i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.95501 | + | 2.60788i | 1.95501 | + | 2.60788i | ||||
\(964\) | −0.0752854 | − | 0.257694i | −0.0752854 | − | 0.257694i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(968\) | −0.646600 | + | 0.762830i | −0.646600 | + | 0.762830i | ||||
\(969\) | 1.25801 | − | 3.20534i | 1.25801 | − | 3.20534i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.352060 | − | 0.272243i | −0.352060 | − | 0.272243i | 0.420357 | − | 0.907359i | \(-0.361905\pi\) |
−0.772417 | + | 0.635116i | \(0.780952\pi\) | |||||||
\(972\) | −2.16150 | + | 3.07061i | −2.16150 | + | 3.07061i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.730355 | + | 0.0218587i | −0.730355 | + | 0.0218587i | −0.393025 | − | 0.919528i | \(-0.628571\pi\) |
−0.337330 | + | 0.941386i | \(0.609524\pi\) | |||||||
\(978\) | −1.38383 | − | 1.73527i | −1.38383 | − | 1.73527i | ||||
\(979\) | −0.888227 | − | 1.77596i | −0.888227 | − | 1.77596i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.39362 | − | 0.296223i | −1.39362 | − | 0.296223i | ||||
\(983\) | 0 | 0 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(984\) | 0.705171 | + | 0.240845i | 0.705171 | + | 0.240845i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.89771 | − | 0.712222i | −1.89771 | − | 0.712222i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.66920 | + | 0.743176i | −1.66920 | + | 0.743176i | ||||
\(997\) | 0 | 0 | −0.858449 | − | 0.512899i | \(-0.828571\pi\) | ||||
0.858449 | + | 0.512899i | \(0.171429\pi\) | |||||||
\(998\) | 0.578465 | + | 1.15661i | 0.578465 | + | 1.15661i | ||||
\(999\) | 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 | 3784.1.em.b.2379.1 | yes | 48 | |
8.3 | odd | 2 | CM | 3784.1.em.b.2379.1 | yes | 48 | |
11.4 | even | 5 | 3784.1.em.a.3755.1 | yes | 48 | ||
43.40 | even | 21 | 3784.1.em.a.3523.1 | ✓ | 48 | ||
88.59 | odd | 10 | 3784.1.em.a.3755.1 | yes | 48 | ||
344.83 | odd | 42 | 3784.1.em.a.3523.1 | ✓ | 48 | ||
473.169 | even | 105 | inner | 3784.1.em.b.1115.1 | yes | 48 | |
3784.1115 | odd | 210 | inner | 3784.1.em.b.1115.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3784.1.em.a.3523.1 | ✓ | 48 | 43.40 | even | 21 | ||
3784.1.em.a.3523.1 | ✓ | 48 | 344.83 | odd | 42 | ||
3784.1.em.a.3755.1 | yes | 48 | 11.4 | even | 5 | ||
3784.1.em.a.3755.1 | yes | 48 | 88.59 | odd | 10 | ||
3784.1.em.b.1115.1 | yes | 48 | 473.169 | even | 105 | inner | |
3784.1.em.b.1115.1 | yes | 48 | 3784.1115 | odd | 210 | inner | |
3784.1.em.b.2379.1 | yes | 48 | 1.1 | even | 1 | trivial | |
3784.1.em.b.2379.1 | yes | 48 | 8.3 | odd | 2 | CM |