Properties

Label 1340.1.bb.b.59.1
Level $1340$
Weight $1$
Character 1340.59
Analytic conductor $0.669$
Analytic rank $0$
Dimension $10$
Projective image $D_{11}$
CM discriminant -20
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1340,1,Mod(59,1340)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1340, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 12]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1340.59");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1340.bb (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: \(0.668747116928\)
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 59.1
Root \(0.142315 - 0.989821i\) of defining polynomial
Character \(\chi\) \(=\) 1340.59
Dual form 1340.1.bb.b.159.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.142315 - 0.989821i) q^{2} +(-1.25667 - 1.45027i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-1.61435 + 1.03748i) q^{6} +(-0.186393 + 1.29639i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.381761 + 2.65520i) q^{9} +O(q^{10})\) \(q+(0.142315 - 0.989821i) q^{2} +(-1.25667 - 1.45027i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(0.841254 + 0.540641i) q^{5} +(-1.61435 + 1.03748i) q^{6} +(-0.186393 + 1.29639i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.381761 + 2.65520i) q^{9} +(0.654861 - 0.755750i) q^{10} +(0.797176 + 1.74557i) q^{12} +(1.25667 + 0.368991i) q^{14} +(-0.273100 - 1.89945i) q^{15} +(0.841254 + 0.540641i) q^{16} +(2.57385 + 0.755750i) q^{18} +(-0.654861 - 0.755750i) q^{20} +(2.11435 - 1.35881i) q^{21} +(1.30972 + 1.51150i) q^{23} +(1.84125 - 0.540641i) q^{24} +(0.415415 + 0.909632i) q^{25} +(2.71616 - 1.74557i) q^{27} +(0.544078 - 1.19136i) q^{28} -1.30972 q^{29} -1.91899 q^{30} +(0.654861 - 0.755750i) q^{32} +(-0.857685 + 0.989821i) q^{35} +(1.11435 - 2.44009i) q^{36} +(-0.841254 + 0.540641i) q^{40} +(-0.797176 + 0.234072i) q^{41} +(-1.04408 - 2.28621i) q^{42} +(-1.84125 + 0.540641i) q^{43} +(-1.75667 + 2.02730i) q^{45} +(1.68251 - 1.08128i) q^{46} +(0.544078 + 0.627899i) q^{47} +(-0.273100 - 1.89945i) q^{48} +(-0.686393 - 0.201543i) q^{49} +(0.959493 - 0.281733i) q^{50} +(-1.34125 - 2.93694i) q^{54} +(-1.10181 - 0.708089i) q^{56} +(-0.186393 + 1.29639i) q^{58} +(-0.273100 + 1.89945i) q^{60} +(1.41542 - 0.909632i) q^{61} +(-3.37102 - 0.989821i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.959493 + 0.281733i) q^{67} +(0.546200 - 3.79891i) q^{69} +(0.857685 + 0.989821i) q^{70} +(-2.25667 - 1.45027i) q^{72} +(0.797176 - 1.74557i) q^{75} +(0.415415 + 0.909632i) q^{80} +(-3.37102 - 0.989821i) q^{81} +(0.118239 + 0.822373i) q^{82} +(0.239446 + 0.153882i) q^{83} +(-2.41153 + 0.708089i) q^{84} +(0.273100 + 1.89945i) q^{86} +(1.64589 + 1.89945i) q^{87} +(0.186393 - 0.215109i) q^{89} +(1.75667 + 2.02730i) q^{90} +(-0.830830 - 1.81926i) q^{92} +(0.698939 - 0.449181i) q^{94} -1.91899 q^{96} +(-0.297176 + 0.650724i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{2} + 2 q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + q^{2} + 2 q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + q^{8} - 3 q^{9} + q^{10} + 2 q^{12} - 2 q^{14} + 2 q^{15} - q^{16} + 3 q^{18} - q^{20} + 7 q^{21} + 2 q^{23} + 9 q^{24} - q^{25} + 4 q^{27} + 2 q^{28} - 2 q^{29} - 2 q^{30} + q^{32} - 9 q^{35} - 3 q^{36} + q^{40} - 2 q^{41} - 7 q^{42} - 9 q^{43} - 3 q^{45} - 2 q^{46} + 2 q^{47} + 2 q^{48} - 3 q^{49} + q^{50} - 4 q^{54} - 2 q^{56} + 2 q^{58} + 2 q^{60} + 9 q^{61} - 5 q^{63} - q^{64} + q^{67} - 4 q^{69} + 9 q^{70} - 8 q^{72} + 2 q^{75} - q^{80} - 5 q^{81} + 2 q^{82} + 2 q^{83} - 4 q^{84} - 2 q^{86} + 4 q^{87} - 2 q^{89} + 3 q^{90} + 2 q^{92} - 2 q^{94} - 2 q^{96} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times\).

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{6}{11}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.142315 0.989821i 0.142315 0.989821i
\(3\) −1.25667 1.45027i −1.25667 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(4\) −0.959493 0.281733i −0.959493 0.281733i
\(5\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(6\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(7\) −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(8\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(9\) −0.381761 + 2.65520i −0.381761 + 2.65520i
\(10\) 0.654861 0.755750i 0.654861 0.755750i
\(11\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(12\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(13\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(14\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(15\) −0.273100 1.89945i −0.273100 1.89945i
\(16\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(17\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(18\) 2.57385 + 0.755750i 2.57385 + 0.755750i
\(19\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(20\) −0.654861 0.755750i −0.654861 0.755750i
\(21\) 2.11435 1.35881i 2.11435 1.35881i
\(22\) 0 0
\(23\) 1.30972 + 1.51150i 1.30972 + 1.51150i 0.654861 + 0.755750i \(0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(24\) 1.84125 0.540641i 1.84125 0.540641i
\(25\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(26\) 0 0
\(27\) 2.71616 1.74557i 2.71616 1.74557i
\(28\) 0.544078 1.19136i 0.544078 1.19136i
\(29\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(30\) −1.91899 −1.91899
\(31\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(32\) 0.654861 0.755750i 0.654861 0.755750i
\(33\) 0 0
\(34\) 0 0
\(35\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(36\) 1.11435 2.44009i 1.11435 2.44009i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(41\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(42\) −1.04408 2.28621i −1.04408 2.28621i
\(43\) −1.84125 + 0.540641i −1.84125 + 0.540641i −0.841254 + 0.540641i \(0.818182\pi\)
−1.00000 \(1.00000\pi\)
\(44\) 0 0
\(45\) −1.75667 + 2.02730i −1.75667 + 2.02730i
\(46\) 1.68251 1.08128i 1.68251 1.08128i
\(47\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(48\) −0.273100 1.89945i −0.273100 1.89945i
\(49\) −0.686393 0.201543i −0.686393 0.201543i
\(50\) 0.959493 0.281733i 0.959493 0.281733i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(54\) −1.34125 2.93694i −1.34125 2.93694i
\(55\) 0 0
\(56\) −1.10181 0.708089i −1.10181 0.708089i
\(57\) 0 0
\(58\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(59\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(60\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(61\) 1.41542 0.909632i 1.41542 0.909632i 0.415415 0.909632i \(-0.363636\pi\)
1.00000 \(0\)
\(62\) 0 0
\(63\) −3.37102 0.989821i −3.37102 0.989821i
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(68\) 0 0
\(69\) 0.546200 3.79891i 0.546200 3.79891i
\(70\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(71\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(72\) −2.25667 1.45027i −2.25667 1.45027i
\(73\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(74\) 0 0
\(75\) 0.797176 1.74557i 0.797176 1.74557i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(80\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(81\) −3.37102 0.989821i −3.37102 0.989821i
\(82\) 0.118239 + 0.822373i 0.118239 + 0.822373i
\(83\) 0.239446 + 0.153882i 0.239446 + 0.153882i 0.654861 0.755750i \(-0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(84\) −2.41153 + 0.708089i −2.41153 + 0.708089i
\(85\) 0 0
\(86\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(87\) 1.64589 + 1.89945i 1.64589 + 1.89945i
\(88\) 0 0
\(89\) 0.186393 0.215109i 0.186393 0.215109i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(90\) 1.75667 + 2.02730i 1.75667 + 2.02730i
\(91\) 0 0
\(92\) −0.830830 1.81926i −0.830830 1.81926i
\(93\) 0 0
\(94\) 0.698939 0.449181i 0.698939 0.449181i
\(95\) 0 0
\(96\) −1.91899 −1.91899
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.297176 + 0.650724i −0.297176 + 0.650724i
\(99\) 0 0
\(100\) −0.142315 0.989821i −0.142315 0.989821i
\(101\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(102\) 0 0
\(103\) 0.118239 0.258908i 0.118239 0.258908i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(104\) 0 0
\(105\) 2.51334 2.51334
\(106\) 0 0
\(107\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(108\) −3.09792 + 0.909632i −3.09792 + 0.909632i
\(109\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(113\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(114\) 0 0
\(115\) 0.284630 + 1.97964i 0.284630 + 1.97964i
\(116\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(121\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(122\) −0.698939 1.53046i −0.698939 1.53046i
\(123\) 1.34125 + 0.861971i 1.34125 + 0.861971i
\(124\) 0 0
\(125\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(126\) −1.45949 + 3.19584i −1.45949 + 3.19584i
\(127\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(128\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(129\) 3.09792 + 1.99091i 3.09792 + 1.99091i
\(130\) 0 0
\(131\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.415415 0.909632i 0.415415 0.909632i
\(135\) 3.22871 3.22871
\(136\) 0 0
\(137\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(138\) −3.68251 1.08128i −3.68251 1.08128i
\(139\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(140\) 1.10181 0.708089i 1.10181 0.708089i
\(141\) 0.226900 1.57812i 0.226900 1.57812i
\(142\) 0 0
\(143\) 0 0
\(144\) −1.75667 + 2.02730i −1.75667 + 2.02730i
\(145\) −1.10181 0.708089i −1.10181 0.708089i
\(146\) 0 0
\(147\) 0.570276 + 1.24873i 0.570276 + 1.24873i
\(148\) 0 0
\(149\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(150\) −1.61435 1.03748i −1.61435 1.03748i
\(151\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.959493 0.281733i 0.959493 0.281733i
\(161\) −2.20362 + 1.41618i −2.20362 + 1.41618i
\(162\) −1.45949 + 3.19584i −1.45949 + 3.19584i
\(163\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(164\) 0.830830 0.830830
\(165\) 0 0
\(166\) 0.186393 0.215109i 0.186393 0.215109i
\(167\) −0.186393 1.29639i −0.186393 1.29639i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(168\) 0.357685 + 2.48775i 0.357685 + 2.48775i
\(169\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(170\) 0 0
\(171\) 0 0
\(172\) 1.91899 1.91899
\(173\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(174\) 2.11435 1.35881i 2.11435 1.35881i
\(175\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.186393 0.215109i −0.186393 0.215109i
\(179\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(180\) 2.25667 1.45027i 2.25667 1.45027i
\(181\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(182\) 0 0
\(183\) −3.09792 0.909632i −3.09792 0.909632i
\(184\) −1.91899 + 0.563465i −1.91899 + 0.563465i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.345139 0.755750i −0.345139 0.755750i
\(189\) 1.75667 + 3.84657i 1.75667 + 3.84657i
\(190\) 0 0
\(191\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(192\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(193\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.601808 + 0.386758i 0.601808 + 0.386758i
\(197\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(198\) 0 0
\(199\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(200\) −1.00000 −1.00000
\(201\) −0.797176 1.74557i −0.797176 1.74557i
\(202\) 0.284630 0.284630
\(203\) 0.244123 1.69791i 0.244123 1.69791i
\(204\) 0 0
\(205\) −0.797176 0.234072i −0.797176 0.234072i
\(206\) −0.239446 0.153882i −0.239446 0.153882i
\(207\) −4.51334 + 2.90055i −4.51334 + 2.90055i
\(208\) 0 0
\(209\) 0 0
\(210\) 0.357685 2.48775i 0.357685 2.48775i
\(211\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(215\) −1.84125 0.540641i −1.84125 0.540641i
\(216\) 0.459493 + 3.19584i 0.459493 + 3.19584i
\(217\) 0 0
\(218\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.10181 1.27155i 1.10181 1.27155i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(224\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(225\) −2.57385 + 0.755750i −2.57385 + 0.755750i
\(226\) 0 0
\(227\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(228\) 0 0
\(229\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(230\) 2.00000 2.00000
\(231\) 0 0
\(232\) 0.544078 1.19136i 0.544078 1.19136i
\(233\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(234\) 0 0
\(235\) 0.118239 + 0.822373i 0.118239 + 0.822373i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0.797176 1.74557i 0.797176 1.74557i
\(241\) −0.239446 + 0.153882i −0.239446 + 0.153882i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(242\) 0.959493 0.281733i 0.959493 0.281733i
\(243\) 1.45949 + 3.19584i 1.45949 + 3.19584i
\(244\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(245\) −0.468468 0.540641i −0.468468 0.540641i
\(246\) 1.04408 1.20493i 1.04408 1.20493i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.0777324 0.540641i −0.0777324 0.540641i
\(250\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(251\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(252\) 2.95561 + 1.89945i 2.95561 + 1.89945i
\(253\) 0 0
\(254\) −1.61435 0.474017i −1.61435 0.474017i
\(255\) 0 0
\(256\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(257\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(258\) 2.41153 2.78305i 2.41153 2.78305i
\(259\) 0 0
\(260\) 0 0
\(261\) 0.500000 3.47758i 0.500000 3.47758i
\(262\) 0 0
\(263\) −1.41542 0.909632i −1.41542 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.546200 −0.546200
\(268\) −0.841254 0.540641i −0.841254 0.540641i
\(269\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(270\) 0.459493 3.19584i 0.459493 3.19584i
\(271\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.59435 + 3.49114i −1.59435 + 3.49114i
\(277\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −0.544078 1.19136i −0.544078 1.19136i
\(281\) 0.345139 + 0.755750i 0.345139 + 0.755750i 1.00000 \(0\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(282\) −1.52977 0.449181i −1.52977 0.449181i
\(283\) 0.239446 + 1.66538i 0.239446 + 1.66538i 0.654861 + 0.755750i \(0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.154861 1.07708i −0.154861 1.07708i
\(288\) 1.75667 + 2.02730i 1.75667 + 2.02730i
\(289\) 0.841254 0.540641i 0.841254 0.540641i
\(290\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(294\) 1.31718 0.386758i 1.31718 0.386758i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.830830 −0.830830
\(299\) 0 0
\(300\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(301\) −0.357685 2.48775i −0.357685 2.48775i
\(302\) 0 0
\(303\) 0.357685 0.412791i 0.357685 0.412791i
\(304\) 0 0
\(305\) 1.68251 1.68251
\(306\) 0 0
\(307\) −0.345139 + 0.755750i −0.345139 + 0.755750i 0.654861 + 0.755750i \(0.272727\pi\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −0.524075 + 0.153882i −0.524075 + 0.153882i
\(310\) 0 0
\(311\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(312\) 0 0
\(313\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(314\) 0 0
\(315\) −2.30075 2.65520i −2.30075 2.65520i
\(316\) 0 0
\(317\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.142315 0.989821i −0.142315 0.989821i
\(321\) 1.52977 + 0.449181i 1.52977 + 0.449181i
\(322\) 1.08816 + 2.38273i 1.08816 + 2.38273i
\(323\) 0 0
\(324\) 2.95561 + 1.89945i 2.95561 + 1.89945i
\(325\) 0 0
\(326\) 0.273100 1.89945i 0.273100 1.89945i
\(327\) −0.226900 + 0.496841i −0.226900 + 0.496841i
\(328\) 0.118239 0.822373i 0.118239 0.822373i
\(329\) −0.915415 + 0.588302i −0.915415 + 0.588302i
\(330\) 0 0
\(331\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(332\) −0.186393 0.215109i −0.186393 0.215109i
\(333\) 0 0
\(334\) −1.30972 −1.30972
\(335\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(336\) 2.51334 2.51334
\(337\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(338\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.154861 + 0.339098i −0.154861 + 0.339098i
\(344\) 0.273100 1.89945i 0.273100 1.89945i
\(345\) 2.51334 2.90055i 2.51334 2.90055i
\(346\) 0 0
\(347\) −0.698939 1.53046i −0.698939 1.53046i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(348\) −1.04408 2.28621i −1.04408 2.28621i
\(349\) 1.84125 + 0.540641i 1.84125 + 0.540641i 1.00000 \(0\)
0.841254 + 0.540641i \(0.181818\pi\)
\(350\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(360\) −1.11435 2.44009i −1.11435 2.44009i
\(361\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(362\) 1.61435 1.03748i 1.61435 1.03748i
\(363\) 0.797176 1.74557i 0.797176 1.74557i
\(364\) 0 0
\(365\) 0 0
\(366\) −1.34125 + 2.93694i −1.34125 + 2.93694i
\(367\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(368\) 0.284630 + 1.97964i 0.284630 + 1.97964i
\(369\) −0.317178 2.20602i −0.317178 2.20602i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 1.61435 1.03748i 1.61435 1.03748i
\(376\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(377\) 0 0
\(378\) 4.05742 1.19136i 4.05742 1.19136i
\(379\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(380\) 0 0
\(381\) −2.71616 + 1.74557i −2.71616 + 1.74557i
\(382\) 0 0
\(383\) 0.118239 + 0.822373i 0.118239 + 0.822373i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(384\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(385\) 0 0
\(386\) 0 0
\(387\) −0.732593 5.09530i −0.732593 5.09530i
\(388\) 0 0
\(389\) −0.118239 0.258908i −0.118239 0.258908i 0.841254 0.540641i \(-0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.468468 0.540641i 0.468468 0.540641i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(401\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(402\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(403\) 0 0
\(404\) 0.0405070 0.281733i 0.0405070 0.281733i
\(405\) −2.30075 2.65520i −2.30075 2.65520i
\(406\) −1.64589 0.483276i −1.64589 0.483276i
\(407\) 0 0
\(408\) 0 0
\(409\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(410\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(411\) 0 0
\(412\) −0.186393 + 0.215109i −0.186393 + 0.215109i
\(413\) 0 0
\(414\) 2.22871 + 4.88019i 2.22871 + 4.88019i
\(415\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(420\) −2.41153 0.708089i −2.41153 0.708089i
\(421\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(422\) 0 0
\(423\) −1.87491 + 1.20493i −1.87491 + 1.20493i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.915415 + 2.00448i 0.915415 + 2.00448i
\(428\) 0.797176 0.234072i 0.797176 0.234072i
\(429\) 0 0
\(430\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 3.22871 3.22871
\(433\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(434\) 0 0
\(435\) 0.357685 + 2.48775i 0.357685 + 2.48775i
\(436\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0.797176 1.74557i 0.797176 1.74557i
\(442\) 0 0
\(443\) −1.25667 + 0.368991i −1.25667 + 0.368991i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(444\) 0 0
\(445\) 0.273100 0.0801894i 0.273100 0.0801894i
\(446\) −1.10181 1.27155i −1.10181 1.27155i
\(447\) −1.04408 + 1.20493i −1.04408 + 1.20493i
\(448\) 1.10181 0.708089i 1.10181 0.708089i
\(449\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(450\) 0.381761 + 2.65520i 0.381761 + 2.65520i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(458\) −1.41542 0.909632i −1.41542 0.909632i
\(459\) 0 0
\(460\) 0.284630 1.97964i 0.284630 1.97964i
\(461\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(462\) 0 0
\(463\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(464\) −1.10181 0.708089i −1.10181 0.708089i
\(465\) 0 0
\(466\) 0 0
\(467\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(468\) 0 0
\(469\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(470\) 0.830830 0.830830
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(480\) −1.61435 1.03748i −1.61435 1.03748i
\(481\) 0 0
\(482\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(483\) 4.82306 + 1.41618i 4.82306 + 1.41618i
\(484\) −0.142315 0.989821i −0.142315 0.989821i
\(485\) 0 0
\(486\) 3.37102 0.989821i 3.37102 0.989821i
\(487\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(488\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(489\) −2.41153 2.78305i −2.41153 2.78305i
\(490\) −0.601808 + 0.386758i −0.601808 + 0.386758i
\(491\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(492\) −1.04408 1.20493i −1.04408 1.20493i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.546200 −0.546200
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 0.415415 0.909632i 0.415415 0.909632i
\(501\) −1.64589 + 1.89945i −1.64589 + 1.89945i
\(502\) 0 0
\(503\) 0.118239 + 0.822373i 0.118239 + 0.822373i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(504\) 2.30075 2.65520i 2.30075 2.65520i
\(505\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(506\) 0 0
\(507\) 1.91899 1.91899
\(508\) −0.698939 + 1.53046i −0.698939 + 1.53046i
\(509\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.959493 0.281733i 0.959493 0.281733i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.239446 0.153882i 0.239446 0.153882i
\(516\) −2.41153 2.78305i −2.41153 2.78305i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.284630 1.97964i −0.284630 1.97964i −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(522\) −3.37102 0.989821i −3.37102 0.989821i
\(523\) 0.797176 + 1.74557i 0.797176 + 1.74557i 0.654861 + 0.755750i \(0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(524\) 0 0
\(525\) 2.11435 + 1.35881i 2.11435 + 1.35881i
\(526\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.426945 + 2.96946i −0.426945 + 2.96946i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.0777324 + 0.540641i −0.0777324 + 0.540641i
\(535\) −0.830830 −0.830830
\(536\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(537\) 0 0
\(538\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(539\) 0 0
\(540\) −3.09792 0.909632i −3.09792 0.909632i
\(541\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(542\) 0 0
\(543\) 0.524075 3.64502i 0.524075 3.64502i
\(544\) 0 0
\(545\) 0.0405070 0.281733i 0.0405070 0.281733i
\(546\) 0 0
\(547\) −1.41542 0.909632i −1.41542 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 1.87491 + 4.10548i 1.87491 + 4.10548i
\(550\) 0 0
\(551\) 0 0
\(552\) 3.22871 + 2.07496i 3.22871 + 2.07496i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(561\) 0 0
\(562\) 0.797176 0.234072i 0.797176 0.234072i
\(563\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(564\) −0.662317 + 1.45027i −0.662317 + 1.45027i
\(565\) 0 0
\(566\) 1.68251 1.68251
\(567\) 1.91153 4.18567i 1.91153 4.18567i
\(568\) 0 0
\(569\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(570\) 0 0
\(571\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −1.08816 −1.08816
\(575\) −0.830830 + 1.81926i −0.830830 + 1.81926i
\(576\) 2.25667 1.45027i 2.25667 1.45027i
\(577\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(578\) −0.415415 0.909632i −0.415415 0.909632i
\(579\) 0 0
\(580\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(581\) −0.244123 + 0.281733i −0.244123 + 0.281733i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.698939 0.449181i −0.698939 0.449181i 0.142315 0.989821i \(-0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(588\) −0.195368 1.35881i −0.195368 1.35881i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(600\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(601\) 0.273100 1.89945i 0.273100 1.89945i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(602\) −2.51334 −2.51334
\(603\) −1.11435 + 2.44009i −1.11435 + 2.44009i
\(604\) 0 0
\(605\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(606\) −0.357685 0.412791i −0.357685 0.412791i
\(607\) 0.797176 + 0.234072i 0.797176 + 0.234072i 0.654861 0.755750i \(-0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(608\) 0 0
\(609\) −2.76921 + 1.77967i −2.76921 + 1.77967i
\(610\) 0.239446 1.66538i 0.239446 1.66538i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(614\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(615\) 0.662317 + 1.45027i 0.662317 + 1.45027i
\(616\) 0 0
\(617\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(618\) 0.0777324 + 0.540641i 0.0777324 + 0.540641i
\(619\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(620\) 0 0
\(621\) 6.19584 + 1.81926i 6.19584 + 1.81926i
\(622\) 0 0
\(623\) 0.244123 + 0.281733i 0.244123 + 0.281733i
\(624\) 0 0
\(625\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −2.95561 + 1.89945i −2.95561 + 1.89945i
\(631\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.10181 1.27155i 1.10181 1.27155i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −1.00000
\(641\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(642\) 0.662317 1.45027i 0.662317 1.45027i
\(643\) 1.10181 0.708089i 1.10181 0.708089i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(644\) 2.51334 0.737982i 2.51334 0.737982i
\(645\) 1.52977 + 3.34973i 1.52977 + 3.34973i
\(646\) 0 0
\(647\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(648\) 2.30075 2.65520i 2.30075 2.65520i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −1.84125 0.540641i −1.84125 0.540641i
\(653\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(654\) 0.459493 + 0.295298i 0.459493 + 0.295298i
\(655\) 0 0
\(656\) −0.797176 0.234072i −0.797176 0.234072i
\(657\) 0 0
\(658\) 0.452036 + 0.989821i 0.452036 + 0.989821i
\(659\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(660\) 0 0
\(661\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(665\) 0 0
\(666\) 0 0
\(667\) −1.71537 1.97964i −1.71537 1.97964i
\(668\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(669\) −3.22871 −3.22871
\(670\) 0.841254 0.540641i 0.841254 0.540641i
\(671\) 0 0
\(672\) 0.357685 2.48775i 0.357685 2.48775i
\(673\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(674\) 0 0
\(675\) 2.71616 + 1.74557i 2.71616 + 1.74557i
\(676\) 0.841254 0.540641i 0.841254 0.540641i
\(677\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.459493 + 0.295298i 0.459493 + 0.295298i
\(682\) 0 0
\(683\) −0.345139 0.755750i −0.345139 0.755750i 0.654861 0.755750i \(-0.272727\pi\)
−1.00000 \(\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.313607 + 0.201543i 0.313607 + 0.201543i
\(687\) −3.09792 + 0.909632i −3.09792 + 0.909632i
\(688\) −1.84125 0.540641i −1.84125 0.540641i
\(689\) 0 0
\(690\) −2.51334 2.90055i −2.51334 2.90055i
\(691\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(695\) 0 0
\(696\) −2.41153 + 0.708089i −2.41153 + 0.708089i
\(697\) 0 0
\(698\) 0.797176 1.74557i 0.797176 1.74557i
\(699\) 0 0
\(700\) 1.30972 1.30972
\(701\) 0.830830 1.81926i 0.830830 1.81926i 0.415415 0.909632i \(-0.363636\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 1.04408 1.20493i 1.04408 1.20493i
\(706\) 0 0
\(707\) −0.372786 −0.372786
\(708\) 0 0
\(709\) 0.830830 1.81926i 0.830830 1.81926i 0.415415 0.909632i \(-0.363636\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(720\) −2.57385 + 0.755750i −2.57385 + 0.755750i
\(721\) 0.313607 + 0.201543i 0.313607 + 0.201543i
\(722\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(723\) 0.524075 + 0.153882i 0.524075 + 0.153882i
\(724\) −0.797176 1.74557i −0.797176 1.74557i
\(725\) −0.544078 1.19136i −0.544078 1.19136i
\(726\) −1.61435 1.03748i −1.61435 1.03748i
\(727\) 0.544078 0.627899i 0.544078 0.627899i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(728\) 0 0
\(729\) 1.34125 2.93694i 1.34125 2.93694i
\(730\) 0 0
\(731\) 0 0
\(732\) 2.71616 + 1.74557i 2.71616 + 1.74557i
\(733\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(734\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(735\) −0.195368 + 1.35881i −0.195368 + 1.35881i
\(736\) 2.00000 2.00000
\(737\) 0 0
\(738\) −2.22871 −2.22871
\(739\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(744\) 0 0
\(745\) 0.345139 0.755750i 0.345139 0.755750i
\(746\) 0 0
\(747\) −0.500000 + 0.577031i −0.500000 + 0.577031i
\(748\) 0 0
\(749\) −0.452036 0.989821i −0.452036 0.989821i
\(750\) −0.797176 1.74557i −0.797176 1.74557i
\(751\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(752\) 0.118239 + 0.822373i 0.118239 + 0.822373i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −0.601808 4.18567i −0.601808 4.18567i
\(757\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(762\) 1.34125 + 2.93694i 1.34125 + 2.93694i
\(763\) 0.357685 0.105026i 0.357685 0.105026i
\(764\) 0 0
\(765\) 0 0
\(766\) 0.830830 0.830830
\(767\) 0 0
\(768\) 0.797176 1.74557i 0.797176 1.74557i
\(769\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(774\) −5.14769 −5.14769
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −3.55742 + 2.28621i −3.55742 + 2.28621i
\(784\) −0.468468 0.540641i −0.468468 0.540641i
\(785\) 0 0
\(786\) 0 0
\(787\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(788\) 0 0
\(789\) 0.459493 + 3.19584i 0.459493 + 3.19584i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(801\) 0.500000 + 0.577031i 0.500000 + 0.577031i
\(802\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(803\) 0 0
\(804\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(805\) −2.61944 −2.61944
\(806\) 0 0
\(807\) 2.41153 + 2.78305i 2.41153 + 2.78305i
\(808\) −0.273100 0.0801894i −0.273100 0.0801894i
\(809\) 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 \(0\)
0.415415 + 0.909632i \(0.363636\pi\)
\(810\) −2.95561 + 1.89945i −2.95561 + 1.89945i
\(811\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(812\) −0.712591 + 1.56036i −0.712591 + 1.56036i
\(813\) 0 0
\(814\) 0 0
\(815\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(816\) 0 0
\(817\) 0 0
\(818\) −1.84125 0.540641i −1.84125 0.540641i
\(819\) 0 0
\(820\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(821\) −1.61435 + 0.474017i −1.61435 + 0.474017i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(822\) 0 0
\(823\) −0.186393 1.29639i −0.186393 1.29639i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(824\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(825\) 0 0
\(826\) 0 0
\(827\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(828\) 5.14769 1.51150i 5.14769 1.51150i
\(829\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(830\) 0.273100 0.0801894i 0.273100 0.0801894i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0.544078 1.19136i 0.544078 1.19136i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(840\) −1.04408 + 2.28621i −1.04408 + 2.28621i
\(841\) 0.715370 0.715370
\(842\) 1.30972 1.30972
\(843\) 0.662317 1.45027i 0.662317 1.45027i
\(844\) 0 0
\(845\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(846\) 0.925839 + 2.02730i 0.925839 + 2.02730i
\(847\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(848\) 0 0
\(849\) 2.11435 2.44009i 2.11435 2.44009i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(854\) 2.11435 0.620830i 2.11435 0.620830i
\(855\) 0 0
\(856\) −0.118239 0.822373i −0.118239 0.822373i
\(857\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(858\) 0 0
\(859\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(860\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(861\) −1.36745 + 1.57812i −1.36745 + 1.57812i
\(862\) 0 0
\(863\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(864\) 0.459493 3.19584i 0.459493 3.19584i
\(865\) 0 0
\(866\) 0 0
\(867\) −1.84125 0.540641i −1.84125 0.540641i
\(868\) 0 0
\(869\) 0 0
\(870\) 2.51334 2.51334
\(871\) 0 0
\(872\) 0.284630 0.284630
\(873\) 0 0
\(874\) 0 0
\(875\) −1.25667 0.368991i −1.25667 0.368991i
\(876\) 0 0
\(877\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.30972 + 1.51150i −1.30972 + 1.51150i −0.654861 + 0.755750i \(0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(882\) −1.61435 1.03748i −1.61435 1.03748i
\(883\) −0.345139 0.755750i −0.345139 0.755750i 0.654861 0.755750i \(-0.272727\pi\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(887\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(888\) 0 0
\(889\) 2.11435 + 0.620830i 2.11435 + 0.620830i
\(890\) −0.0405070 0.281733i −0.0405070 0.281733i
\(891\) 0 0
\(892\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(893\) 0 0
\(894\) 1.04408 + 1.20493i 1.04408 + 1.20493i
\(895\) 0 0
\(896\) −0.544078 1.19136i −0.544078 1.19136i
\(897\) 0 0
\(898\) −0.698939 + 0.449181i −0.698939 + 0.449181i
\(899\) 0 0
\(900\) 2.68251 2.68251
\(901\) 0 0
\(902\) 0 0
\(903\) −3.15843 + 3.64502i −3.15843 + 3.64502i
\(904\) 0 0
\(905\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(906\) 0 0
\(907\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(908\) 0.284630 0.284630
\(909\) −0.763521 −0.763521
\(910\) 0 0
\(911\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −2.11435 2.44009i −2.11435 2.44009i
\(916\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(920\) −1.91899 0.563465i −1.91899 0.563465i
\(921\) 1.52977 0.449181i 1.52977 0.449181i
\(922\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −0.797176 1.74557i −0.797176 1.74557i
\(927\) 0.642315 + 0.412791i 0.642315 + 0.412791i
\(928\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(929\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −1.61435 0.474017i −1.61435 0.474017i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(939\) 0 0
\(940\) 0.118239 0.822373i 0.118239 0.822373i
\(941\) −0.544078 0.627899i −0.544078 0.627899i 0.415415 0.909632i \(-0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(942\) 0 0
\(943\) −1.39788 0.898361i −1.39788 0.898361i
\(944\) 0 0
\(945\) −0.601808 + 4.18567i −0.601808 + 4.18567i
\(946\) 0 0
\(947\) −0.273100 + 1.89945i −0.273100 + 1.89945i 0.142315 + 0.989821i \(0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(961\) −0.654861 0.755750i −0.654861 0.755750i
\(962\) 0 0
\(963\) −0.925839 2.02730i −0.925839 2.02730i
\(964\) 0.273100 0.0801894i 0.273100 0.0801894i
\(965\) 0 0
\(966\) 2.08816 4.57242i 2.08816 4.57242i
\(967\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(972\) −0.500000 3.47758i −0.500000 3.47758i
\(973\) 0 0
\(974\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(975\) 0 0
\(976\) 1.68251 1.68251
\(977\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(978\) −3.09792 + 1.99091i −3.09792 + 1.99091i
\(979\) 0 0
\(980\) 0.297176 + 0.650724i 0.297176 + 0.650724i
\(981\) 0.732593 0.215109i 0.732593 0.215109i
\(982\) 0 0
\(983\) −0.857685 + 0.989821i −0.857685 + 0.989821i 0.142315 + 0.989821i \(0.454545\pi\)
−1.00000 \(\pi\)
\(984\) −1.34125 + 0.861971i −1.34125 + 0.861971i
\(985\) 0 0
\(986\) 0 0
\(987\) 2.00357 + 0.588302i 2.00357 + 0.588302i
\(988\) 0 0
\(989\) −3.22871 2.07496i −3.22871 2.07496i
\(990\) 0 0
\(991\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) −0.0777324 + 0.540641i −0.0777324 + 0.540641i
\(997\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(998\) 0 0
\(999\) 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 1340.1.bb.b.59.1 yes 10
4.3 odd 2 1340.1.bb.a.59.1 10
5.4 even 2 1340.1.bb.a.59.1 10
20.19 odd 2 CM 1340.1.bb.b.59.1 yes 10
67.25 even 11 inner 1340.1.bb.b.159.1 yes 10
268.159 odd 22 1340.1.bb.a.159.1 yes 10
335.159 even 22 1340.1.bb.a.159.1 yes 10
1340.159 odd 22 inner 1340.1.bb.b.159.1 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1340.1.bb.a.59.1 10 4.3 odd 2
1340.1.bb.a.59.1 10 5.4 even 2
1340.1.bb.a.159.1 yes 10 268.159 odd 22
1340.1.bb.a.159.1 yes 10 335.159 even 22
1340.1.bb.b.59.1 yes 10 1.1 even 1 trivial
1340.1.bb.b.59.1 yes 10 20.19 odd 2 CM
1340.1.bb.b.159.1 yes 10 67.25 even 11 inner
1340.1.bb.b.159.1 yes 10 1340.159 odd 22 inner