Properties

Label 1127.1.v.a.864.1
Level $1127$
Weight $1$
Character 1127.864
Analytic conductor $0.562$
Analytic rank $0$
Dimension $20$
Projective image $D_{11}$
CM discriminant -7
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1127,1,Mod(31,1127)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1127, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([11, 18]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1127.31");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1127 = 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1127.v (of order \(66\), degree \(20\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.562446269237\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 161)
Projective image: \(D_{11}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{11} - \cdots)\)

Embedding invariants

Embedding label 864.1
Root \(0.0475819 + 0.998867i\) of defining polynomial
Character \(\chi\) \(=\) 1127.864
Dual form 1127.1.v.a.1097.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0930932 - 0.268975i) q^{2} +(0.722372 + 0.568079i) q^{4} +(0.459493 - 0.295298i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\) \(q+(0.0930932 - 0.268975i) q^{2} +(0.722372 + 0.568079i) q^{4} +(0.459493 - 0.295298i) q^{8} +(0.580057 - 0.814576i) q^{9} +(-0.550294 - 1.58997i) q^{11} +(0.180007 + 0.741999i) q^{16} +(-0.165101 - 0.231852i) q^{18} -0.478891 q^{22} +(-0.995472 + 0.0950560i) q^{23} +(0.981929 - 0.189251i) q^{25} +(0.186393 + 1.29639i) q^{29} +(0.760064 + 0.0725773i) q^{32} +(0.881761 - 0.258908i) q^{36} +(-1.11312 + 1.56316i) q^{37} +(0.698939 + 0.449181i) q^{43} +(0.505713 - 1.46116i) q^{44} +(-0.0671040 + 0.276606i) q^{46} +(0.0405070 - 0.281733i) q^{50} +(-0.947890 + 0.903811i) q^{53} +(0.366049 + 0.0705501i) q^{58} +(-0.226900 + 0.496841i) q^{64} +(-0.279486 + 0.0538665i) q^{67} +(-1.10181 - 1.27155i) q^{71} +(0.0259893 - 0.545582i) q^{72} +(0.316827 + 0.444922i) q^{74} +(-0.947890 - 0.903811i) q^{79} +(-0.327068 - 0.945001i) q^{81} +(0.185885 - 0.146182i) q^{86} +(-0.722372 - 0.568079i) q^{88} +(-0.773100 - 0.496841i) q^{92} +(-1.61435 - 0.474017i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} + 3 q^{4} - 8 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} + 3 q^{4} - 8 q^{8} + q^{9} + 2 q^{11} - 6 q^{16} + 2 q^{18} - 8 q^{22} + q^{23} + q^{25} - 4 q^{29} - 5 q^{32} + 16 q^{36} + 2 q^{37} - 4 q^{43} - 5 q^{44} + 2 q^{46} + 18 q^{50} + 2 q^{53} - 7 q^{58} - 14 q^{64} + 2 q^{67} - 4 q^{71} + 4 q^{72} - 7 q^{74} + 2 q^{79} + q^{81} + 4 q^{86} - 3 q^{88} - 6 q^{92} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1127\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{11}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0930932 0.268975i 0.0930932 0.268975i −0.888835 0.458227i \(-0.848485\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(3\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(4\) 0.722372 + 0.568079i 0.722372 + 0.568079i
\(5\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0.459493 0.295298i 0.459493 0.295298i
\(9\) 0.580057 0.814576i 0.580057 0.814576i
\(10\) 0 0
\(11\) −0.550294 1.58997i −0.550294 1.58997i −0.786053 0.618159i \(-0.787879\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(12\) 0 0
\(13\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.180007 + 0.741999i 0.180007 + 0.741999i
\(17\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(18\) −0.165101 0.231852i −0.165101 0.231852i
\(19\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.478891 −0.478891
\(23\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(24\) 0 0
\(25\) 0.981929 0.189251i 0.981929 0.189251i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(30\) 0 0
\(31\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(32\) 0.760064 + 0.0725773i 0.760064 + 0.0725773i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.881761 0.258908i 0.881761 0.258908i
\(37\) −1.11312 + 1.56316i −1.11312 + 1.56316i −0.327068 + 0.945001i \(0.606061\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(42\) 0 0
\(43\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(44\) 0.505713 1.46116i 0.505713 1.46116i
\(45\) 0 0
\(46\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i
\(47\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0.0405070 0.281733i 0.0405070 0.281733i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.947890 + 0.903811i −0.947890 + 0.903811i −0.995472 0.0950560i \(-0.969697\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.366049 + 0.0705501i 0.366049 + 0.0705501i
\(59\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(60\) 0 0
\(61\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.226900 + 0.496841i −0.226900 + 0.496841i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.279486 + 0.0538665i −0.279486 + 0.0538665i −0.327068 0.945001i \(-0.606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(72\) 0.0259893 0.545582i 0.0259893 0.545582i
\(73\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(74\) 0.316827 + 0.444922i 0.316827 + 0.444922i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.947890 0.903811i −0.947890 0.903811i 0.0475819 0.998867i \(-0.484848\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(80\) 0 0
\(81\) −0.327068 0.945001i −0.327068 0.945001i
\(82\) 0 0
\(83\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0.185885 0.146182i 0.185885 0.146182i
\(87\) 0 0
\(88\) −0.722372 0.568079i −0.722372 0.568079i
\(89\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.773100 0.496841i −0.773100 0.496841i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(98\) 0 0
\(99\) −1.61435 0.474017i −1.61435 0.474017i
\(100\) 0.816827 + 0.421104i 0.816827 + 0.421104i
\(101\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(102\) 0 0
\(103\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.154861 + 0.339098i 0.154861 + 0.339098i
\(107\) 1.70566 + 0.879330i 1.70566 + 0.879330i 0.981929 + 0.189251i \(0.0606061\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(108\) 0 0
\(109\) −0.264241 0.105786i −0.264241 0.105786i 0.235759 0.971812i \(-0.424242\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.601808 + 1.04236i −0.601808 + 1.04236i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.43913 + 1.13174i −1.43913 + 1.13174i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(128\) 0.665101 + 0.634173i 0.665101 + 0.634173i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.0115295 + 0.0801894i −0.0115295 + 0.0801894i
\(135\) 0 0
\(136\) 0 0
\(137\) 0.142315 0.246497i 0.142315 0.246497i −0.786053 0.618159i \(-0.787879\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.444587 + 0.177986i −0.444587 + 0.177986i
\(143\) 0 0
\(144\) 0.708829 + 0.283772i 0.708829 + 0.283772i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −1.69209 + 0.496841i −1.69209 + 0.496841i
\(149\) 0.815816 + 0.157236i 0.815816 + 0.157236i 0.580057 0.814576i \(-0.303030\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(150\) 0 0
\(151\) −0.308779 + 1.27280i −0.308779 + 1.27280i 0.580057 + 0.814576i \(0.303030\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(158\) −0.331345 + 0.170820i −0.331345 + 0.170820i
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) −0.284630 −0.284630
\(163\) 0.428368 1.23769i 0.428368 1.23769i −0.500000 0.866025i \(-0.666667\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(168\) 0 0
\(169\) 0.841254 0.540641i 0.841254 0.540641i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.249723 + 0.721528i 0.249723 + 0.721528i
\(173\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.08070 0.694523i 1.08070 0.694523i
\(177\) 0 0
\(178\) 0 0
\(179\) 0.481929 + 0.676774i 0.481929 + 0.676774i 0.981929 0.189251i \(-0.0606061\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(180\) 0 0
\(181\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.429342 + 0.337639i −0.429342 + 0.337639i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.452418 1.86489i −0.452418 1.86489i −0.500000 0.866025i \(-0.666667\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(192\) 0 0
\(193\) −1.67489 0.159932i −1.67489 0.159932i −0.786053 0.618159i \(-0.787879\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(198\) −0.277784 + 0.390093i −0.277784 + 0.390093i
\(199\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(200\) 0.395304 0.376921i 0.395304 0.376921i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(212\) −1.19817 + 0.114411i −1.19817 + 0.114411i
\(213\) 0 0
\(214\) 0.395304 0.376921i 0.395304 0.376921i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −0.0530529 + 0.0612263i −0.0530529 + 0.0612263i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(224\) 0 0
\(225\) 0.415415 0.909632i 0.415415 0.909632i
\(226\) −0.219539 + 0.0878903i −0.219539 + 0.0878903i
\(227\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(228\) 0 0
\(229\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.468468 + 0.540641i 0.468468 + 0.540641i
\(233\) −0.0913090 + 1.91681i −0.0913090 + 1.91681i 0.235759 + 0.971812i \(0.424242\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(240\) 0 0
\(241\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(242\) 0.170438 + 0.492448i 0.170438 + 0.492448i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(252\) 0 0
\(253\) 0.698939 + 1.53046i 0.698939 + 1.53046i
\(254\) 0.118239 + 0.204797i 0.118239 + 0.204797i
\(255\) 0 0
\(256\) −0.252989 + 0.130425i −0.252989 + 0.130425i
\(257\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1.16413 + 0.600149i 1.16413 + 0.600149i
\(262\) 0 0
\(263\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i −0.995472 0.0950560i \(-0.969697\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.232493 0.119859i −0.232493 0.119859i
\(269\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(270\) 0 0
\(271\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.0530529 0.0612263i −0.0530529 0.0612263i
\(275\) −0.841254 1.45709i −0.841254 1.45709i
\(276\) 0 0
\(277\) 0.959493 1.66189i 0.959493 1.66189i 0.235759 0.971812i \(-0.424242\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(282\) 0 0
\(283\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(284\) −0.0735712 1.54445i −0.0735712 1.54445i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.500000 0.577031i 0.500000 0.577031i
\(289\) 0.723734 + 0.690079i 0.723734 + 0.690079i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.0498730 + 1.04696i −0.0498730 + 1.04696i
\(297\) 0 0
\(298\) 0.118239 0.204797i 0.118239 0.204797i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0.313607 + 0.201543i 0.313607 + 0.201543i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(312\) 0 0
\(313\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.171292 1.19136i −0.171292 1.19136i
\(317\) 1.91030 0.182411i 1.91030 0.182411i 0.928368 0.371662i \(-0.121212\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(318\) 0 0
\(319\) 1.95865 1.00976i 1.95865 1.00976i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.300571 0.868442i 0.300571 0.868442i
\(325\) 0 0
\(326\) −0.293029 0.230441i −0.293029 0.230441i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.481929 0.676774i 0.481929 0.676774i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(332\) 0 0
\(333\) 0.627639 + 1.81344i 0.627639 + 1.81344i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(338\) −0.0671040 0.276606i −0.0671040 0.276606i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0.453800 0.453800
\(345\) 0 0
\(346\) 0 0
\(347\) −1.88431 + 0.363170i −1.88431 + 0.363170i −0.995472 0.0950560i \(-0.969697\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(348\) 0 0
\(349\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.302863 1.24842i −0.302863 1.24842i
\(353\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.226900 0.0666238i 0.226900 0.0666238i
\(359\) 0.481929 0.676774i 0.481929 0.676774i −0.500000 0.866025i \(-0.666667\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(360\) 0 0
\(361\) 0.723734 0.690079i 0.723734 0.690079i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(368\) −0.249723 0.721528i −0.249723 0.721528i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −1.67489 + 0.159932i −1.67489 + 0.159932i −0.888835 0.458227i \(-0.848485\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(380\) 0 0
\(381\) 0 0
\(382\) −0.543727 0.0519196i −0.543727 0.0519196i
\(383\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.198939 + 0.435615i −0.198939 + 0.435615i
\(387\) 0.771316 0.308788i 0.771316 0.308788i
\(388\) 0 0
\(389\) 1.65210 0.318417i 1.65210 0.318417i 0.723734 0.690079i \(-0.242424\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −0.0112521 + 0.236211i −0.0112521 + 0.236211i
\(395\) 0 0
\(396\) −0.896884 1.25950i −0.896884 1.25950i
\(397\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.317178 + 0.694523i 0.317178 + 0.694523i
\(401\) −1.38884 1.32425i −1.38884 1.32425i −0.888835 0.458227i \(-0.848485\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.09792 + 0.909632i 3.09792 + 0.909632i
\(408\) 0 0
\(409\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(420\) 0 0
\(421\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(422\) 0.425656 + 0.219441i 0.425656 + 0.219441i
\(423\) 0 0
\(424\) −0.168655 + 0.695205i −0.168655 + 0.695205i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0.732593 + 1.60416i 0.732593 + 1.60416i
\(429\) 0 0
\(430\) 0 0
\(431\) 0.771316 + 0.308788i 0.771316 + 0.308788i 0.723734 0.690079i \(-0.242424\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(432\) 0 0
\(433\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.130785 0.226527i −0.130785 0.226527i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.32254 + 1.04006i −1.32254 + 1.04006i −0.327068 + 0.945001i \(0.606061\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(450\) −0.205996 0.196417i −0.205996 0.196417i
\(451\) 0 0
\(452\) −0.0363298 0.762656i −0.0363298 0.762656i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.0623191 + 1.30824i −0.0623191 + 1.30824i 0.723734 + 0.690079i \(0.242424\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(464\) −0.928368 + 0.371662i −0.928368 + 0.371662i
\(465\) 0 0
\(466\) 0.507075 + 0.203002i 0.507075 + 0.203002i
\(467\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.329562 1.35847i 0.329562 1.35847i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(478\) −0.543727 + 0.0519196i −0.543727 + 0.0519196i
\(479\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.68251 −1.68251
\(485\) 0 0
\(486\) 0 0
\(487\) −0.653077 0.513585i −0.653077 0.513585i 0.235759 0.971812i \(-0.424242\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.239446 + 0.153882i −0.239446 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −0.0671040 0.276606i −0.0671040 0.276606i 0.928368 0.371662i \(-0.121212\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0.476723 0.0455215i 0.476723 0.0455215i
\(507\) 0 0
\(508\) −0.749723 + 0.144497i −0.749723 + 0.144497i
\(509\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(522\) 0.269798 0.257252i 0.269798 0.257252i
\(523\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.0681534 + 0.0437995i 0.0681534 + 0.0437995i
\(527\) 0 0
\(528\) 0 0
\(529\) 0.981929 0.189251i 0.981929 0.189251i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −0.112515 + 0.107283i −0.112515 + 0.107283i
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −0.279486 0.0538665i −0.279486 0.0538665i 0.0475819 0.998867i \(-0.484848\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(548\) 0.242834 0.0972160i 0.242834 0.0972160i
\(549\) 0 0
\(550\) −0.470237 + 0.0906308i −0.470237 + 0.0906308i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −0.357685 0.412791i −0.357685 0.412791i
\(555\) 0 0
\(556\) 0 0
\(557\) 1.16011 + 1.62915i 1.16011 + 1.62915i 0.580057 + 0.814576i \(0.303030\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.269798 + 0.257252i 0.269798 + 0.257252i
\(563\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −0.881761 0.258908i −0.881761 0.258908i
\(569\) 1.50842 1.18624i 1.50842 1.18624i 0.580057 0.814576i \(-0.303030\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(570\) 0 0
\(571\) 1.50842 + 1.18624i 1.50842 + 1.18624i 0.928368 + 0.371662i \(0.121212\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(576\) 0.273100 + 0.473023i 0.273100 + 0.473023i
\(577\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(578\) 0.252989 0.130425i 0.252989 0.130425i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1.95865 + 1.00976i 1.95865 + 1.00976i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.36023 0.544555i −1.36023 0.544555i
\(593\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.500000 + 0.577031i 0.500000 + 0.577031i
\(597\) 0 0
\(598\) 0 0
\(599\) 0.142315 0.246497i 0.142315 0.246497i −0.786053 0.618159i \(-0.787879\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(600\) 0 0
\(601\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(602\) 0 0
\(603\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(604\) −0.946106 + 0.744026i −0.946106 + 0.744026i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.0135432 0.284307i −0.0135432 0.284307i −0.995472 0.0950560i \(-0.969697\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(618\) 0 0
\(619\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.928368 0.371662i 0.928368 0.371662i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(632\) −0.702443 0.135385i −0.702443 0.135385i
\(633\) 0 0
\(634\) 0.128772 0.530804i 0.128772 0.530804i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −0.0892619 0.620830i −0.0892619 0.620830i
\(639\) −1.67489 + 0.159932i −1.67489 + 0.159932i
\(640\) 0 0
\(641\) −1.77767 + 0.916453i −1.77767 + 0.916453i −0.888835 + 0.458227i \(0.848485\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(648\) −0.429342 0.337639i −0.429342 0.337639i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1.01255 0.650724i 1.01255 0.650724i
\(653\) −0.165101 + 0.231852i −0.165101 + 0.231852i −0.888835 0.458227i \(-0.848485\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(660\) 0 0
\(661\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(662\) −0.137171 0.192630i −0.137171 0.192630i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.546200 0.546200
\(667\) −0.308779 1.27280i −0.308779 1.27280i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(674\) −0.112903 0.465392i −0.112903 0.465392i
\(675\) 0 0
\(676\) 0.914825 + 0.0873552i 0.914825 + 0.0873552i
\(677\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.38884 + 1.32425i −1.38884 + 1.32425i −0.500000 + 0.866025i \(0.666667\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) −0.207478 + 0.599467i −0.207478 + 0.599467i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.0777324 + 0.540641i −0.0777324 + 0.540641i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.914825 + 0.0873552i 0.914825 + 0.0873552i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.56199 0.625325i 1.56199 0.625325i 0.580057 0.814576i \(-0.303030\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(710\) 0 0
\(711\) −1.28605 + 0.247866i −1.28605 + 0.247866i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.0363298 + 0.762656i −0.0363298 + 0.762656i
\(717\) 0 0
\(718\) −0.137171 0.192630i −0.137171 0.192630i
\(719\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.118239 0.258908i −0.118239 0.258908i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.428368 + 1.23769i 0.428368 + 1.23769i
\(726\) 0 0
\(727\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(728\) 0 0
\(729\) −0.959493 0.281733i −0.959493 0.281733i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.763521 −0.763521
\(737\) 0.239446 + 0.414732i 0.239446 + 0.414732i
\(738\) 0 0
\(739\) 0.252989 0.130425i 0.252989 0.130425i −0.327068 0.945001i \(-0.606061\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.112903 + 0.465392i −0.112903 + 0.465392i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.16413 + 0.600149i 1.16413 + 0.600149i 0.928368 0.371662i \(-0.121212\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(758\) −0.186393 0.322842i −0.186393 0.322842i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.732593 1.60416i 0.732593 1.60416i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.11904 1.06700i −1.11904 1.06700i
\(773\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(774\) −0.0112521 0.236211i −0.0112521 0.236211i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.0681534 0.474017i 0.0681534 0.474017i
\(779\) 0 0
\(780\) 0 0
\(781\) −1.41542 + 2.45157i −1.41542 + 2.45157i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(788\) −0.708829 0.283772i −0.708829 0.283772i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.881761 + 0.258908i −0.881761 + 0.258908i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.760064 0.0725773i 0.760064 0.0725773i
\(801\) 0 0
\(802\) −0.485482 + 0.250283i −0.485482 + 0.250283i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.02951 + 0.809616i 1.02951 + 0.809616i 0.981929 0.189251i \(-0.0606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(810\) 0 0
\(811\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0.533064 0.748584i 0.533064 0.748584i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0.396666 + 1.63508i 0.396666 + 1.63508i 0.723734 + 0.690079i \(0.242424\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(822\) 0 0
\(823\) −0.759713 1.06687i −0.759713 1.06687i −0.995472 0.0950560i \(-0.969697\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(828\) −0.853157 + 0.341553i −0.853157 + 0.341553i
\(829\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(840\) 0 0
\(841\) −0.686393 + 0.201543i −0.686393 + 0.201543i
\(842\) −0.137171 + 0.192630i −0.137171 + 0.192630i
\(843\) 0 0
\(844\) −1.11904 + 1.06700i −1.11904 + 1.06700i
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −0.841254 0.540641i −0.841254 0.540641i
\(849\) 0 0
\(850\) 0 0
\(851\) 0.959493 1.66189i 0.959493 1.66189i
\(852\) 0 0
\(853\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.04340 0.0996331i 1.04340 0.0996331i
\(857\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(858\) 0 0
\(859\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.154861 0.178719i 0.154861 0.178719i
\(863\) 1.65210 + 0.318417i 1.65210 + 0.318417i 0.928368 0.371662i \(-0.121212\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −0.915415 + 2.00448i −0.915415 + 2.00448i
\(870\) 0 0
\(871\) 0 0
\(872\) −0.152655 + 0.0294219i −0.152655 + 0.0294219i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0.0800569 1.68060i 0.0800569 1.68060i −0.500000 0.866025i \(-0.666667\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(882\) 0 0
\(883\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.156630 + 0.452553i 0.156630 + 0.452553i
\(887\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −1.32254 + 1.04006i −1.32254 + 1.04006i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −0.273100 0.473023i −0.273100 0.473023i
\(899\) 0 0
\(900\) 0.816827 0.421104i 0.816827 0.421104i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −0.435418 0.127850i −0.435418 0.127850i
\(905\) 0 0
\(906\) 0 0
\(907\) −0.0671040 + 0.276606i −0.0671040 + 0.276606i −0.995472 0.0950560i \(-0.969697\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.346082 + 0.138550i 0.346082 + 0.138550i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0.959493 + 1.66189i 0.959493 + 1.66189i 0.723734 + 0.690079i \(0.242424\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(926\) −0.0636813 + 0.0500796i −0.0636813 + 0.0500796i
\(927\) 0 0
\(928\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(929\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −1.15486 + 1.33278i −1.15486 + 1.33278i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −0.334716 0.215109i −0.334716 0.215109i
\(947\) −1.78153 + 0.713215i −1.78153 + 0.713215i −0.786053 + 0.618159i \(0.787879\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(954\) 0.366049 + 0.0705501i 0.366049 + 0.0705501i
\(955\) 0 0
\(956\) 0.415766 1.71381i 0.415766 1.71381i
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(962\) 0 0
\(963\) 1.70566 0.879330i 1.70566 0.879330i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(968\) −0.327068 + 0.945001i −0.327068 + 0.945001i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −0.198939 + 0.127850i −0.198939 + 0.127850i
\(975\) 0 0
\(976\) 0 0
\(977\) −0.654136 1.89000i −0.654136 1.89000i −0.327068 0.945001i \(-0.606061\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(982\) 0.0190998 + 0.0787304i 0.0190998 + 0.0787304i
\(983\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −0.738471 0.380708i −0.738471 0.380708i
\(990\) 0 0
\(991\) −0.279486 + 0.0538665i −0.279486 + 0.0538665i −0.327068 0.945001i \(-0.606061\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(998\) −0.0806472 0.00770088i −0.0806472 0.00770088i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 1127.1.v.a.864.1 20
7.2 even 3 inner 1127.1.v.a.1048.1 20
7.3 odd 6 161.1.l.a.13.1 10
7.4 even 3 161.1.l.a.13.1 10
7.5 odd 6 inner 1127.1.v.a.1048.1 20
7.6 odd 2 CM 1127.1.v.a.864.1 20
21.11 odd 6 1449.1.bq.a.496.1 10
21.17 even 6 1449.1.bq.a.496.1 10
23.16 even 11 inner 1127.1.v.a.913.1 20
28.3 even 6 2576.1.cj.a.657.1 10
28.11 odd 6 2576.1.cj.a.657.1 10
161.3 odd 66 3703.1.l.c.3429.1 10
161.4 even 33 3703.1.b.c.1588.3 5
161.10 even 66 3703.1.l.g.1392.1 10
161.11 odd 66 3703.1.l.d.699.1 10
161.16 even 33 inner 1127.1.v.a.1097.1 20
161.17 even 66 3703.1.l.i.3044.1 10
161.18 even 33 3703.1.l.h.118.1 10
161.25 even 33 3703.1.l.a.2582.1 10
161.31 odd 66 3703.1.l.a.2603.1 10
161.32 even 33 3703.1.l.b.2617.1 10
161.38 even 66 3703.1.l.e.2603.1 10
161.39 even 33 161.1.l.a.62.1 yes 10
161.45 even 6 3703.1.l.f.2911.1 10
161.52 odd 66 3703.1.l.h.3044.1 10
161.53 odd 66 3703.1.l.f.706.1 10
161.59 odd 66 3703.1.l.c.1392.1 10
161.60 odd 66 3703.1.l.d.2617.1 10
161.62 odd 22 inner 1127.1.v.a.913.1 20
161.66 even 66 3703.1.l.g.3429.1 10
161.67 odd 66 3703.1.l.e.2582.1 10
161.73 odd 66 3703.1.b.c.1588.3 5
161.74 odd 66 3703.1.l.i.118.1 10
161.80 even 66 3703.1.l.d.699.1 10
161.81 even 33 3703.1.l.b.699.1 10
161.87 odd 66 3703.1.l.h.118.1 10
161.88 odd 66 3703.1.b.b.1588.3 5
161.94 odd 66 3703.1.l.a.2582.1 10
161.95 even 33 3703.1.l.c.3429.1 10
161.101 odd 66 3703.1.l.b.2617.1 10
161.102 odd 66 3703.1.l.g.1392.1 10
161.108 odd 66 161.1.l.a.62.1 yes 10
161.109 odd 66 3703.1.l.i.3044.1 10
161.122 even 66 3703.1.l.f.706.1 10
161.123 even 33 3703.1.l.a.2603.1 10
161.129 even 66 3703.1.l.d.2617.1 10
161.130 odd 66 3703.1.l.e.2603.1 10
161.131 odd 66 inner 1127.1.v.a.1097.1 20
161.136 even 66 3703.1.l.e.2582.1 10
161.137 odd 6 3703.1.l.f.2911.1 10
161.143 even 66 3703.1.l.i.118.1 10
161.144 even 33 3703.1.l.h.3044.1 10
161.150 odd 66 3703.1.l.b.699.1 10
161.151 even 33 3703.1.l.c.1392.1 10
161.157 even 66 3703.1.b.b.1588.3 5
161.158 odd 66 3703.1.l.g.3429.1 10
483.200 odd 66 1449.1.bq.a.1189.1 10
483.269 even 66 1449.1.bq.a.1189.1 10
644.39 odd 66 2576.1.cj.a.545.1 10
644.591 even 66 2576.1.cj.a.545.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
161.1.l.a.13.1 10 7.3 odd 6
161.1.l.a.13.1 10 7.4 even 3
161.1.l.a.62.1 yes 10 161.39 even 33
161.1.l.a.62.1 yes 10 161.108 odd 66
1127.1.v.a.864.1 20 1.1 even 1 trivial
1127.1.v.a.864.1 20 7.6 odd 2 CM
1127.1.v.a.913.1 20 23.16 even 11 inner
1127.1.v.a.913.1 20 161.62 odd 22 inner
1127.1.v.a.1048.1 20 7.2 even 3 inner
1127.1.v.a.1048.1 20 7.5 odd 6 inner
1127.1.v.a.1097.1 20 161.16 even 33 inner
1127.1.v.a.1097.1 20 161.131 odd 66 inner
1449.1.bq.a.496.1 10 21.11 odd 6
1449.1.bq.a.496.1 10 21.17 even 6
1449.1.bq.a.1189.1 10 483.200 odd 66
1449.1.bq.a.1189.1 10 483.269 even 66
2576.1.cj.a.545.1 10 644.39 odd 66
2576.1.cj.a.545.1 10 644.591 even 66
2576.1.cj.a.657.1 10 28.3 even 6
2576.1.cj.a.657.1 10 28.11 odd 6
3703.1.b.b.1588.3 5 161.88 odd 66
3703.1.b.b.1588.3 5 161.157 even 66
3703.1.b.c.1588.3 5 161.4 even 33
3703.1.b.c.1588.3 5 161.73 odd 66
3703.1.l.a.2582.1 10 161.25 even 33
3703.1.l.a.2582.1 10 161.94 odd 66
3703.1.l.a.2603.1 10 161.31 odd 66
3703.1.l.a.2603.1 10 161.123 even 33
3703.1.l.b.699.1 10 161.81 even 33
3703.1.l.b.699.1 10 161.150 odd 66
3703.1.l.b.2617.1 10 161.32 even 33
3703.1.l.b.2617.1 10 161.101 odd 66
3703.1.l.c.1392.1 10 161.59 odd 66
3703.1.l.c.1392.1 10 161.151 even 33
3703.1.l.c.3429.1 10 161.3 odd 66
3703.1.l.c.3429.1 10 161.95 even 33
3703.1.l.d.699.1 10 161.11 odd 66
3703.1.l.d.699.1 10 161.80 even 66
3703.1.l.d.2617.1 10 161.60 odd 66
3703.1.l.d.2617.1 10 161.129 even 66
3703.1.l.e.2582.1 10 161.67 odd 66
3703.1.l.e.2582.1 10 161.136 even 66
3703.1.l.e.2603.1 10 161.38 even 66
3703.1.l.e.2603.1 10 161.130 odd 66
3703.1.l.f.706.1 10 161.53 odd 66
3703.1.l.f.706.1 10 161.122 even 66
3703.1.l.f.2911.1 10 161.45 even 6
3703.1.l.f.2911.1 10 161.137 odd 6
3703.1.l.g.1392.1 10 161.10 even 66
3703.1.l.g.1392.1 10 161.102 odd 66
3703.1.l.g.3429.1 10 161.66 even 66
3703.1.l.g.3429.1 10 161.158 odd 66
3703.1.l.h.118.1 10 161.18 even 33
3703.1.l.h.118.1 10 161.87 odd 66
3703.1.l.h.3044.1 10 161.52 odd 66
3703.1.l.h.3044.1 10 161.144 even 33
3703.1.l.i.118.1 10 161.74 odd 66
3703.1.l.i.118.1 10 161.143 even 66
3703.1.l.i.3044.1 10 161.17 even 66
3703.1.l.i.3044.1 10 161.109 odd 66