Properties

Label 920.1.bh.b.899.1
Level $920$
Weight $1$
Character 920.899
Analytic conductor $0.459$
Analytic rank $0$
Dimension $10$
Projective image $D_{11}$
CM discriminant -40
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [920,1,Mod(59,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 11, 14]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.59");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 920.bh (of order \(22\), degree \(10\), 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: \(0.459139811622\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{11}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{11} - \cdots)\)

Embedding invariants

Embedding label 899.1
Root \(-0.841254 - 0.540641i\) of defining polynomial
Character \(\chi\) \(=\) 920.899
Dual form 920.1.bh.b.219.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(1.10181 - 1.27155i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +O(q^{10})\) \(q+(-0.841254 - 0.540641i) q^{2} +(0.415415 + 0.909632i) q^{4} +(0.959493 + 0.281733i) q^{5} +(1.10181 - 1.27155i) q^{7} +(0.142315 - 0.989821i) q^{8} +(-0.959493 + 0.281733i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(0.698939 - 0.449181i) q^{11} +(-1.25667 - 1.45027i) q^{13} +(-1.61435 + 0.474017i) q^{14} +(-0.654861 + 0.755750i) q^{16} +(0.959493 + 0.281733i) q^{18} +(-0.118239 - 0.258908i) q^{19} +(0.142315 + 0.989821i) q^{20} -0.830830 q^{22} +(0.142315 + 0.989821i) q^{23} +(0.841254 + 0.540641i) q^{25} +(0.273100 + 1.89945i) q^{26} +(1.61435 + 0.474017i) q^{28} +(0.959493 - 0.281733i) q^{32} +(1.41542 - 0.909632i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-1.25667 + 0.368991i) q^{37} +(-0.0405070 + 0.281733i) q^{38} +(0.415415 - 0.909632i) q^{40} +(0.273100 + 0.0801894i) q^{41} +(0.698939 + 0.449181i) q^{44} -1.00000 q^{45} +(0.415415 - 0.909632i) q^{46} +1.30972 q^{47} +(-0.260554 - 1.81219i) q^{49} +(-0.415415 - 0.909632i) q^{50} +(0.797176 - 1.74557i) q^{52} +(-1.25667 + 1.45027i) q^{53} +(0.797176 - 0.234072i) q^{55} +(-1.10181 - 1.27155i) q^{56} +(0.857685 + 0.989821i) q^{59} +(-0.698939 + 1.53046i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-0.797176 - 1.74557i) q^{65} -1.68251 q^{70} +(0.142315 + 0.989821i) q^{72} +(1.25667 + 0.368991i) q^{74} +(0.186393 - 0.215109i) q^{76} +(0.198939 - 1.38365i) q^{77} +(-0.841254 + 0.540641i) q^{80} +(0.841254 - 0.540641i) q^{81} +(-0.186393 - 0.215109i) q^{82} +(-0.345139 - 0.755750i) q^{88} +(0.186393 + 1.29639i) q^{89} +(0.841254 + 0.540641i) q^{90} -3.22871 q^{91} +(-0.841254 + 0.540641i) q^{92} +(-1.10181 - 0.708089i) q^{94} +(-0.0405070 - 0.281733i) q^{95} +(-0.760554 + 1.66538i) q^{98} +(-0.544078 + 0.627899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{2} - q^{4} + q^{5} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + q^{2} - q^{4} + q^{5} + 2 q^{7} + q^{8} - q^{9} - q^{10} - 2 q^{11} + 2 q^{13} - 2 q^{14} - q^{16} + q^{18} - 2 q^{19} + q^{20} + 2 q^{22} + q^{23} - q^{25} - 2 q^{26} + 2 q^{28} + q^{32} + 9 q^{35} - q^{36} + 2 q^{37} - 9 q^{38} - q^{40} - 2 q^{41} - 2 q^{44} - 10 q^{45} - q^{46} + 2 q^{47} - 3 q^{49} + q^{50} + 2 q^{52} + 2 q^{53} + 2 q^{55} - 2 q^{56} + 9 q^{59} + 2 q^{63} - q^{64} - 2 q^{65} + 2 q^{70} + q^{72} - 2 q^{74} - 2 q^{76} - 7 q^{77} + q^{80} - q^{81} + 2 q^{82} - 9 q^{88} - 2 q^{89} - q^{90} - 4 q^{91} + q^{92} - 2 q^{94} - 9 q^{95} - 8 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).

\(n\) \(231\) \(281\) \(461\) \(737\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{11}\right)\) \(-1\) \(-1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.841254 0.540641i −0.841254 0.540641i
\(3\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(4\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(5\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(6\) 0 0
\(7\) 1.10181 1.27155i 1.10181 1.27155i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(8\) 0.142315 0.989821i 0.142315 0.989821i
\(9\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(10\) −0.654861 0.755750i −0.654861 0.755750i
\(11\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(12\) 0 0
\(13\) −1.25667 1.45027i −1.25667 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(14\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(15\) 0 0
\(16\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(17\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(18\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(19\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(20\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(21\) 0 0
\(22\) −0.830830 −0.830830
\(23\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(24\) 0 0
\(25\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(26\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(27\) 0 0
\(28\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(29\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(30\) 0 0
\(31\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(32\) 0.959493 0.281733i 0.959493 0.281733i
\(33\) 0 0
\(34\) 0 0
\(35\) 1.41542 0.909632i 1.41542 0.909632i
\(36\) −0.654861 0.755750i −0.654861 0.755750i
\(37\) −1.25667 + 0.368991i −1.25667 + 0.368991i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(38\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(39\) 0 0
\(40\) 0.415415 0.909632i 0.415415 0.909632i
\(41\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(42\) 0 0
\(43\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(44\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(45\) −1.00000 −1.00000
\(46\) 0.415415 0.909632i 0.415415 0.909632i
\(47\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(48\) 0 0
\(49\) −0.260554 1.81219i −0.260554 1.81219i
\(50\) −0.415415 0.909632i −0.415415 0.909632i
\(51\) 0 0
\(52\) 0.797176 1.74557i 0.797176 1.74557i
\(53\) −1.25667 + 1.45027i −1.25667 + 1.45027i −0.415415 + 0.909632i \(0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(54\) 0 0
\(55\) 0.797176 0.234072i 0.797176 0.234072i
\(56\) −1.10181 1.27155i −1.10181 1.27155i
\(57\) 0 0
\(58\) 0 0
\(59\) 0.857685 + 0.989821i 0.857685 + 0.989821i 1.00000 \(0\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(60\) 0 0
\(61\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(62\) 0 0
\(63\) −0.698939 + 1.53046i −0.698939 + 1.53046i
\(64\) −0.959493 0.281733i −0.959493 0.281733i
\(65\) −0.797176 1.74557i −0.797176 1.74557i
\(66\) 0 0
\(67\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −1.68251 −1.68251
\(71\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(72\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(73\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(74\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(75\) 0 0
\(76\) 0.186393 0.215109i 0.186393 0.215109i
\(77\) 0.198939 1.38365i 0.198939 1.38365i
\(78\) 0 0
\(79\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(80\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(81\) 0.841254 0.540641i 0.841254 0.540641i
\(82\) −0.186393 0.215109i −0.186393 0.215109i
\(83\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.345139 0.755750i −0.345139 0.755750i
\(89\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(90\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(91\) −3.22871 −3.22871
\(92\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(93\) 0 0
\(94\) −1.10181 0.708089i −1.10181 0.708089i
\(95\) −0.0405070 0.281733i −0.0405070 0.281733i
\(96\) 0 0
\(97\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(98\) −0.760554 + 1.66538i −0.760554 + 1.66538i
\(99\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(100\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(101\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(102\) 0 0
\(103\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(104\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(105\) 0 0
\(106\) 1.84125 0.540641i 1.84125 0.540641i
\(107\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(108\) 0 0
\(109\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(110\) −0.797176 0.234072i −0.797176 0.234072i
\(111\) 0 0
\(112\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(113\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(114\) 0 0
\(115\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(116\) 0 0
\(117\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(118\) −0.186393 1.29639i −0.186393 1.29639i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.128663 + 0.281733i −0.128663 + 0.281733i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(126\) 1.41542 0.909632i 1.41542 0.909632i
\(127\) −1.41542 + 0.909632i −1.41542 + 0.909632i −0.415415 + 0.909632i \(0.636364\pi\)
−1.00000 \(\pi\)
\(128\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(129\) 0 0
\(130\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(131\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(132\) 0 0
\(133\) −0.459493 0.134919i −0.459493 0.134919i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0.830830 0.830830 0.415415 0.909632i \(-0.363636\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(140\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(141\) 0 0
\(142\) 0 0
\(143\) −1.52977 0.449181i −1.52977 0.449181i
\(144\) 0.415415 0.909632i 0.415415 0.909632i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −0.857685 0.989821i −0.857685 0.989821i
\(149\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(150\) 0 0
\(151\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(152\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(153\) 0 0
\(154\) −0.915415 + 1.05645i −0.915415 + 1.05645i
\(155\) 0 0
\(156\) 0 0
\(157\) 0.118239 + 0.258908i 0.118239 + 0.258908i 0.959493 0.281733i \(-0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 1.00000 1.00000
\(161\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(162\) −1.00000 −1.00000
\(163\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(164\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(165\) 0 0
\(166\) 0 0
\(167\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(168\) 0 0
\(169\) −0.381761 + 2.65520i −0.381761 + 2.65520i
\(170\) 0 0
\(171\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(172\) 0 0
\(173\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(174\) 0 0
\(175\) 1.61435 0.474017i 1.61435 0.474017i
\(176\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(177\) 0 0
\(178\) 0.544078 1.19136i 0.544078 1.19136i
\(179\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(180\) −0.415415 0.909632i −0.415415 0.909632i
\(181\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(182\) 2.71616 + 1.74557i 2.71616 + 1.74557i
\(183\) 0 0
\(184\) 1.00000 1.00000
\(185\) −1.30972 −1.30972
\(186\) 0 0
\(187\) 0 0
\(188\) 0.544078 + 1.19136i 0.544078 + 1.19136i
\(189\) 0 0
\(190\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(191\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(192\) 0 0
\(193\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 1.54019 0.989821i 1.54019 0.989821i
\(197\) −0.857685 0.989821i −0.857685 0.989821i 0.142315 0.989821i \(-0.454545\pi\)
−1.00000 \(\pi\)
\(198\) 0.797176 0.234072i 0.797176 0.234072i
\(199\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(200\) 0.654861 0.755750i 0.654861 0.755750i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(206\) −1.91899 −1.91899
\(207\) −0.415415 0.909632i −0.415415 0.909632i
\(208\) 1.91899 1.91899
\(209\) −0.198939 0.127850i −0.198939 0.127850i
\(210\) 0 0
\(211\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(212\) −1.84125 0.540641i −1.84125 0.540641i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(221\) 0 0
\(222\) 0 0
\(223\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(224\) 0.698939 1.53046i 0.698939 1.53046i
\(225\) −0.959493 0.281733i −0.959493 0.281733i
\(226\) 0 0
\(227\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0.654861 0.755750i 0.654861 0.755750i
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(234\) −0.797176 1.74557i −0.797176 1.74557i
\(235\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(236\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(240\) 0 0
\(241\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(242\) 0.260554 0.167448i 0.260554 0.167448i
\(243\) 0 0
\(244\) 0 0
\(245\) 0.260554 1.81219i 0.260554 1.81219i
\(246\) 0 0
\(247\) −0.226900 + 0.496841i −0.226900 + 0.496841i
\(248\) 0 0
\(249\) 0 0
\(250\) −0.142315 0.989821i −0.142315 0.989821i
\(251\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(252\) −1.68251 −1.68251
\(253\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(254\) 1.68251 1.68251
\(255\) 0 0
\(256\) −0.142315 0.989821i −0.142315 0.989821i
\(257\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(258\) 0 0
\(259\) −0.915415 + 2.00448i −0.915415 + 2.00448i
\(260\) 1.25667 1.45027i 1.25667 1.45027i
\(261\) 0 0
\(262\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(263\) −1.25667 1.45027i −1.25667 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(264\) 0 0
\(265\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(266\) 0.313607 + 0.361922i 0.313607 + 0.361922i
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(270\) 0 0
\(271\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.830830 0.830830
\(276\) 0 0
\(277\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(278\) −0.698939 0.449181i −0.698939 0.449181i
\(279\) 0 0
\(280\) −0.698939 1.53046i −0.698939 1.53046i
\(281\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(282\) 0 0
\(283\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 1.04408 + 1.20493i 1.04408 + 1.20493i
\(287\) 0.402869 0.258908i 0.402869 0.258908i
\(288\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(289\) −0.654861 0.755750i −0.654861 0.755750i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.345139 + 0.755750i −0.345139 + 0.755750i 0.654861 + 0.755750i \(0.272727\pi\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0.544078 + 1.19136i 0.544078 + 1.19136i
\(296\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(297\) 0 0
\(298\) 0 0
\(299\) 1.25667 1.45027i 1.25667 1.45027i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(308\) 1.34125 0.393828i 1.34125 0.393828i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(312\) 0 0
\(313\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(314\) 0.0405070 0.281733i 0.0405070 0.281733i
\(315\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(316\) 0 0
\(317\) 1.61435 + 0.474017i 1.61435 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.841254 0.540641i −0.841254 0.540641i
\(321\) 0 0
\(322\) −0.698939 1.53046i −0.698939 1.53046i
\(323\) 0 0
\(324\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(325\) −0.273100 1.89945i −0.273100 1.89945i
\(326\) 0 0
\(327\) 0 0
\(328\) 0.118239 0.258908i 0.118239 0.258908i
\(329\) 1.44306 1.66538i 1.44306 1.66538i
\(330\) 0 0
\(331\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(332\) 0 0
\(333\) 1.10181 0.708089i 1.10181 0.708089i
\(334\) 1.41542 0.909632i 1.41542 0.909632i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(338\) 1.75667 2.02730i 1.75667 2.02730i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −0.0405070 0.281733i −0.0405070 0.281733i
\(343\) −1.17597 0.755750i −1.17597 0.755750i
\(344\) 0 0
\(345\) 0 0
\(346\) 0.830830 0.830830
\(347\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(348\) 0 0
\(349\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(350\) −1.61435 0.474017i −1.61435 0.474017i
\(351\) 0 0
\(352\) 0.544078 0.627899i 0.544078 0.627899i
\(353\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(357\) 0 0
\(358\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(361\) 0.601808 0.694523i 0.601808 0.694523i
\(362\) 0 0
\(363\) 0 0
\(364\) −1.34125 2.93694i −1.34125 2.93694i
\(365\) 0 0
\(366\) 0 0
\(367\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(368\) −0.841254 0.540641i −0.841254 0.540641i
\(369\) −0.284630 −0.284630
\(370\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(371\) 0.459493 + 3.19584i 0.459493 + 3.19584i
\(372\) 0 0
\(373\) 0.797176 + 0.234072i 0.797176 + 0.234072i 0.654861 0.755750i \(-0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.186393 1.29639i 0.186393 1.29639i
\(377\) 0 0
\(378\) 0 0
\(379\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(380\) 0.239446 0.153882i 0.239446 0.153882i
\(381\) 0 0
\(382\) 0 0
\(383\) 0.118239 0.822373i 0.118239 0.822373i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(384\) 0 0
\(385\) 0.580699 1.27155i 0.580699 1.27155i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.83083 −1.83083
\(393\) 0 0
\(394\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(395\) 0 0
\(396\) −0.797176 0.234072i −0.797176 0.234072i
\(397\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(401\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.959493 0.281733i 0.959493 0.281733i
\(406\) 0 0
\(407\) −0.712591 + 0.822373i −0.712591 + 0.822373i
\(408\) 0 0
\(409\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(410\) −0.118239 0.258908i −0.118239 0.258908i
\(411\) 0 0
\(412\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(413\) 2.20362 2.20362
\(414\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(415\) 0 0
\(416\) −1.61435 1.03748i −1.61435 1.03748i
\(417\) 0 0
\(418\) 0.0982369 + 0.215109i 0.0982369 + 0.215109i
\(419\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(420\) 0 0
\(421\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(422\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(423\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(424\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(432\) 0 0
\(433\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.239446 0.153882i 0.239446 0.153882i
\(438\) 0 0
\(439\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(440\) −0.118239 0.822373i −0.118239 0.822373i
\(441\) 0.760554 + 1.66538i 0.760554 + 1.66538i
\(442\) 0 0
\(443\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(444\) 0 0
\(445\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(446\) 0.273100 0.0801894i 0.273100 0.0801894i
\(447\) 0 0
\(448\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(449\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(450\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(451\) 0.226900 0.0666238i 0.226900 0.0666238i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.09792 0.909632i −3.09792 0.909632i
\(456\) 0 0
\(457\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) −0.273100 1.89945i −0.273100 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(468\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(469\) 0 0
\(470\) −0.857685 0.989821i −0.857685 0.989821i
\(471\) 0 0
\(472\) 1.10181 0.708089i 1.10181 0.708089i
\(473\) 0 0
\(474\) 0 0
\(475\) 0.0405070 0.281733i 0.0405070 0.281733i
\(476\) 0 0
\(477\) 0.797176 1.74557i 0.797176 1.74557i
\(478\) 0 0
\(479\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(480\) 0 0
\(481\) 2.11435 + 1.35881i 2.11435 + 1.35881i
\(482\) 1.30972 1.30972
\(483\) 0 0
\(484\) −0.309721 −0.309721
\(485\) 0 0
\(486\) 0 0
\(487\) −0.345139 0.755750i −0.345139 0.755750i 0.654861 0.755750i \(-0.272727\pi\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −1.19894 + 1.38365i −1.19894 + 1.38365i
\(491\) −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i \(0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0.459493 0.295298i 0.459493 0.295298i
\(495\) −0.698939 + 0.449181i −0.698939 + 0.449181i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(500\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(501\) 0 0
\(502\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(503\) 0.118239 + 0.822373i 0.118239 + 0.822373i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(504\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(505\) 0 0
\(506\) −0.118239 0.822373i −0.118239 0.822373i
\(507\) 0 0
\(508\) −1.41542 0.909632i −1.41542 0.909632i
\(509\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(513\) 0 0
\(514\) 0 0
\(515\) 1.84125 0.540641i 1.84125 0.540641i
\(516\) 0 0
\(517\) 0.915415 0.588302i 0.915415 0.588302i
\(518\) 1.85380 1.19136i 1.85380 1.19136i
\(519\) 0 0
\(520\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(521\) −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i \(0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(522\) 0 0
\(523\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(524\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(525\) 0 0
\(526\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(530\) 1.91899 1.91899
\(531\) −1.10181 0.708089i −1.10181 0.708089i
\(532\) −0.0681534 0.474017i −0.0681534 0.474017i
\(533\) −0.226900 0.496841i −0.226900 0.496841i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.996114 1.14958i −0.996114 1.14958i
\(540\) 0 0
\(541\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −0.698939 0.449181i −0.698939 0.449181i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −0.239446 0.153882i −0.239446 0.153882i
\(555\) 0 0
\(556\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(557\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(561\) 0 0
\(562\) −0.186393 0.215109i −0.186393 0.215109i
\(563\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.239446 1.66538i 0.239446 1.66538i
\(568\) 0 0
\(569\) 0.830830 1.81926i 0.830830 1.81926i 0.415415 0.909632i \(-0.363636\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(570\) 0 0
\(571\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(572\) −0.226900 1.57812i −0.226900 1.57812i
\(573\) 0 0
\(574\) −0.478891 −0.478891
\(575\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(576\) 1.00000 1.00000
\(577\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(578\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.226900 + 1.57812i −0.226900 + 1.57812i
\(584\) 0 0
\(585\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(586\) 0.698939 0.449181i 0.698939 0.449181i
\(587\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0.186393 1.29639i 0.186393 1.29639i
\(591\) 0 0
\(592\) 0.544078 1.19136i 0.544078 1.19136i
\(593\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.202824 + 0.234072i −0.202824 + 0.234072i
\(606\) 0 0
\(607\) −1.84125 + 0.540641i −1.84125 + 0.540641i −0.841254 + 0.540641i \(0.818182\pi\)
−1.00000 \(1.00000\pi\)
\(608\) −0.186393 0.215109i −0.186393 0.215109i
\(609\) 0 0
\(610\) 0 0
\(611\) −1.64589 1.89945i −1.64589 1.89945i
\(612\) 0 0
\(613\) −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.34125 0.393828i −1.34125 0.393828i
\(617\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(618\) 0 0
\(619\) 1.68251 + 1.08128i 1.68251 + 1.08128i 0.841254 + 0.540641i \(0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.85380 + 1.19136i 1.85380 + 1.19136i
\(624\) 0 0
\(625\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.186393 + 0.215109i −0.186393 + 0.215109i
\(629\) 0 0
\(630\) 1.61435 0.474017i 1.61435 0.474017i
\(631\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −1.10181 1.27155i −1.10181 1.27155i
\(635\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(636\) 0 0
\(637\) −2.30075 + 2.65520i −2.30075 + 2.65520i
\(638\) 0 0
\(639\) 0 0
\(640\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(641\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(645\) 0 0
\(646\) 0 0
\(647\) 0.239446 + 1.66538i 0.239446 + 1.66538i 0.654861 + 0.755750i \(0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(648\) −0.415415 0.909632i −0.415415 0.909632i
\(649\) 1.04408 + 0.306569i 1.04408 + 0.306569i
\(650\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(651\) 0 0
\(652\) 0 0
\(653\) 0.797176 0.234072i 0.797176 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(654\) 0 0
\(655\) 0.239446 0.153882i 0.239446 0.153882i
\(656\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(657\) 0 0
\(658\) −2.11435 + 0.620830i −2.11435 + 0.620830i
\(659\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(660\) 0 0
\(661\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(662\) −0.273100 0.0801894i −0.273100 0.0801894i
\(663\) 0 0
\(664\) 0 0
\(665\) −0.402869 0.258908i −0.402869 0.258908i
\(666\) −1.30972 −1.30972
\(667\) 0 0
\(668\) −1.68251 −1.68251
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) −2.57385 + 0.755750i −2.57385 + 0.755750i
\(677\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(684\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(685\) 0 0
\(686\) 0.580699 + 1.27155i 0.580699 + 1.27155i
\(687\) 0 0
\(688\) 0 0
\(689\) 3.68251 3.68251
\(690\) 0 0
\(691\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(692\) −0.698939 0.449181i −0.698939 0.449181i
\(693\) 0.198939 + 1.38365i 0.198939 + 1.38365i
\(694\) 0 0
\(695\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(701\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(702\) 0 0
\(703\) 0.244123 + 0.281733i 0.244123 + 0.281733i
\(704\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.30972 1.30972
\(713\) 0 0
\(714\) 0 0
\(715\) −1.34125 0.861971i −1.34125 0.861971i
\(716\) −0.118239 0.822373i −0.118239 0.822373i
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(720\) 0.654861 0.755750i 0.654861 0.755750i
\(721\) 0.459493 3.19584i 0.459493 3.19584i
\(722\) −0.881761 + 0.258908i −0.881761 + 0.258908i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −1.25667 + 0.368991i −1.25667 + 0.368991i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(728\) −0.459493 + 3.19584i −0.459493 + 3.19584i
\(729\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.273100 1.89945i −0.273100 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(734\) −1.61435 1.03748i −1.61435 1.03748i
\(735\) 0 0
\(736\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(737\) 0 0
\(738\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(739\) 0.273100 + 1.89945i 0.273100 + 1.89945i 0.415415 + 0.909632i \(0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(740\) −0.544078 1.19136i −0.544078 1.19136i
\(741\) 0 0
\(742\) 1.34125 2.93694i 1.34125 2.93694i
\(743\) −0.857685 + 0.989821i −0.857685 + 0.989821i 0.142315 + 0.989821i \(0.454545\pi\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −0.544078 0.627899i −0.544078 0.627899i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(752\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.41542 0.909632i −1.41542 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
−1.00000 \(\pi\)
\(758\) −1.68251 −1.68251
\(759\) 0 0
\(760\) −0.284630 −0.284630
\(761\) 0.698939 + 0.449181i 0.698939 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(767\) 0.357685 2.48775i 0.357685 2.48775i
\(768\) 0 0
\(769\) −1.10181 1.27155i −1.10181 1.27155i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(770\) −1.17597 + 0.755750i −1.17597 + 0.755750i
\(771\) 0 0
\(772\) 0 0
\(773\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −0.0115295 0.0801894i −0.0115295 0.0801894i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.54019 + 0.989821i 1.54019 + 0.989821i
\(785\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(786\) 0 0
\(787\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(788\) 0.544078 1.19136i 0.544078 1.19136i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(793\) 0 0
\(794\) 1.41542 0.909632i 1.41542 0.909632i
\(795\) 0 0
\(796\) 0 0
\(797\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(801\) −0.544078 1.19136i −0.544078 1.19136i
\(802\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(803\) 0 0
\(804\) 0 0
\(805\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(810\) −0.959493 0.281733i −0.959493 0.281733i
\(811\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 1.04408 0.306569i 1.04408 0.306569i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(819\) 3.09792 0.909632i 3.09792 0.909632i
\(820\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(821\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(822\) 0 0
\(823\) 1.61435 + 0.474017i 1.61435 + 0.474017i 0.959493 0.281733i \(-0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(824\) −0.797176 1.74557i −0.797176 1.74557i
\(825\) 0 0
\(826\) −1.85380 1.19136i −1.85380 1.19136i
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0.654861 0.755750i 0.654861 0.755750i
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(833\) 0 0
\(834\) 0 0
\(835\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(836\) 0.0336545 0.234072i 0.0336545 0.234072i
\(837\) 0 0
\(838\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(839\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(840\) 0 0
\(841\) −0.654861 0.755750i −0.654861 0.755750i
\(842\) 0 0
\(843\) 0 0
\(844\) 1.25667 1.45027i 1.25667 1.45027i
\(845\) −1.11435 + 2.44009i −1.11435 + 2.44009i
\(846\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(847\) 0.216476 + 0.474017i 0.216476 + 0.474017i
\(848\) −0.273100 1.89945i −0.273100 1.89945i
\(849\) 0 0
\(850\) 0 0
\(851\) −0.544078 1.19136i −0.544078 1.19136i
\(852\) 0 0
\(853\) −1.41542 0.909632i −1.41542 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(856\) 0 0
\(857\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(858\) 0 0
\(859\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(864\) 0 0
\(865\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) −0.284630 −0.284630
\(875\) 1.68251 1.68251
\(876\) 0 0
\(877\) 0.118239 + 0.822373i 0.118239 + 0.822373i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(881\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(882\) 0.260554 1.81219i 0.260554 1.81219i
\(883\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.25667 1.45027i −1.25667 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(888\) 0 0
\(889\) −0.402869 + 2.80202i −0.402869 + 2.80202i
\(890\) 0.857685 0.989821i 0.857685 0.989821i
\(891\) 0.345139 0.755750i 0.345139 0.755750i
\(892\) −0.273100 0.0801894i −0.273100 0.0801894i
\(893\) −0.154861 0.339098i −0.154861 0.339098i
\(894\) 0 0
\(895\) −0.698939 0.449181i −0.698939 0.449181i
\(896\) 1.68251 1.68251
\(897\) 0 0
\(898\) −0.830830 −0.830830
\(899\) 0 0
\(900\) −0.142315 0.989821i −0.142315 0.989821i
\(901\) 0 0
\(902\) −0.226900 0.0666238i −0.226900 0.0666238i
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 2.11435 + 2.44009i 2.11435 + 2.44009i
\(911\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −0.0681534 0.474017i −0.0681534 0.474017i
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1.25667 0.368991i −1.25667 0.368991i
\(926\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(927\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(928\) 0 0
\(929\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(930\) 0 0
\(931\) −0.438384 + 0.281733i −0.438384 + 0.281733i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 1.25667 1.45027i 1.25667 1.45027i
\(937\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(941\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(942\) 0 0
\(943\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(944\) −1.30972 −1.30972
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −0.186393 + 0.215109i −0.186393 + 0.215109i
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(954\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.959493 0.281733i −0.959493 0.281733i
\(962\) −1.04408 2.28621i −1.04408 2.28621i
\(963\) 0 0
\(964\) −1.10181 0.708089i −1.10181 0.708089i
\(965\) 0 0
\(966\) 0 0
\(967\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(968\) 0.260554 + 0.167448i 0.260554 + 0.167448i
\(969\) 0 0
\(970\) 0 0
\(971\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(972\) 0 0
\(973\) 0.915415 1.05645i 0.915415 1.05645i
\(974\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(978\) 0 0
\(979\) 0.712591 + 0.822373i 0.712591 + 0.822373i
\(980\) 1.75667 0.515804i 1.75667 0.515804i
\(981\) 0 0
\(982\) 0.544078 0.627899i 0.544078 0.627899i
\(983\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(984\) 0 0
\(985\) −0.544078 1.19136i −0.544078 1.19136i
\(986\) 0 0
\(987\) 0 0
\(988\) −0.546200 −0.546200
\(989\) 0 0
\(990\) 0.830830 0.830830
\(991\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0.118239 0.822373i 0.118239 0.822373i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(998\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(999\) 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 920.1.bh.b.899.1 yes 10
4.3 odd 2 3680.1.cn.b.1359.1 10
5.4 even 2 920.1.bh.a.899.1 yes 10
8.3 odd 2 920.1.bh.a.899.1 yes 10
8.5 even 2 3680.1.cn.a.1359.1 10
20.19 odd 2 3680.1.cn.a.1359.1 10
23.12 even 11 inner 920.1.bh.b.219.1 yes 10
40.19 odd 2 CM 920.1.bh.b.899.1 yes 10
40.29 even 2 3680.1.cn.b.1359.1 10
92.35 odd 22 3680.1.cn.b.3439.1 10
115.104 even 22 920.1.bh.a.219.1 10
184.35 odd 22 920.1.bh.a.219.1 10
184.173 even 22 3680.1.cn.a.3439.1 10
460.219 odd 22 3680.1.cn.a.3439.1 10
920.219 odd 22 inner 920.1.bh.b.219.1 yes 10
920.909 even 22 3680.1.cn.b.3439.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
920.1.bh.a.219.1 10 115.104 even 22
920.1.bh.a.219.1 10 184.35 odd 22
920.1.bh.a.899.1 yes 10 5.4 even 2
920.1.bh.a.899.1 yes 10 8.3 odd 2
920.1.bh.b.219.1 yes 10 23.12 even 11 inner
920.1.bh.b.219.1 yes 10 920.219 odd 22 inner
920.1.bh.b.899.1 yes 10 1.1 even 1 trivial
920.1.bh.b.899.1 yes 10 40.19 odd 2 CM
3680.1.cn.a.1359.1 10 8.5 even 2
3680.1.cn.a.1359.1 10 20.19 odd 2
3680.1.cn.a.3439.1 10 184.173 even 22
3680.1.cn.a.3439.1 10 460.219 odd 22
3680.1.cn.b.1359.1 10 4.3 odd 2
3680.1.cn.b.1359.1 10 40.29 even 2
3680.1.cn.b.3439.1 10 92.35 odd 22
3680.1.cn.b.3439.1 10 920.909 even 22