Properties

Label 1932.1.bi.b.1595.1
Level $1932$
Weight $1$
Character 1932.1595
Analytic conductor $0.964$
Analytic rank $0$
Dimension $10$
Projective image $D_{11}$
CM discriminant -84
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1932,1,Mod(167,1932)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1932, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 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("1932.167");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1932.bi (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: \(0.964193604407\)
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 1595.1
Root \(-0.415415 - 0.909632i\) of defining polynomial
Character \(\chi\) \(=\) 1932.1595
Dual form 1932.1.bi.b.923.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.25667 - 1.45027i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.142315 + 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.25667 - 1.45027i) q^{5} +(0.959493 - 0.281733i) q^{6} +(-0.841254 - 0.540641i) q^{7} +(0.415415 - 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(1.61435 - 1.03748i) q^{10} +(-0.239446 - 1.66538i) q^{11} +(0.142315 + 0.989821i) q^{12} +(0.654861 - 0.755750i) q^{14} +(-0.797176 + 1.74557i) q^{15} +(0.841254 + 0.540641i) q^{16} +(0.797176 - 0.234072i) q^{17} +(-0.654861 - 0.755750i) q^{18} +(-0.273100 - 0.0801894i) q^{19} +(0.797176 + 1.74557i) q^{20} +(-0.142315 + 0.989821i) q^{21} +1.68251 q^{22} +(-0.959493 - 0.281733i) q^{23} -1.00000 q^{24} +(-0.381761 + 2.65520i) q^{25} +(0.959493 + 0.281733i) q^{27} +(0.654861 + 0.755750i) q^{28} +(-1.61435 - 1.03748i) q^{30} +(-0.345139 + 0.755750i) q^{31} +(-0.654861 + 0.755750i) q^{32} +(-1.41542 + 0.909632i) q^{33} +(0.118239 + 0.822373i) q^{34} +(0.273100 + 1.89945i) q^{35} +(0.841254 - 0.540641i) q^{36} +(0.857685 - 0.989821i) q^{37} +(0.118239 - 0.258908i) q^{38} +(-1.84125 + 0.540641i) q^{40} +(-0.186393 - 0.215109i) q^{41} +(-0.959493 - 0.281733i) q^{42} +(-0.239446 + 1.66538i) q^{44} +1.91899 q^{45} +(0.415415 - 0.909632i) q^{46} +(0.142315 - 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-2.57385 - 0.755750i) q^{50} +(-0.544078 - 0.627899i) q^{51} +(-0.415415 + 0.909632i) q^{54} +(-2.11435 + 2.44009i) q^{55} +(-0.841254 + 0.540641i) q^{56} +(0.0405070 + 0.281733i) q^{57} +(1.25667 - 1.45027i) q^{60} +(-0.698939 - 0.449181i) q^{62} +(0.959493 - 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.698939 - 1.53046i) q^{66} -0.830830 q^{68} +(0.142315 + 0.989821i) q^{69} -1.91899 q^{70} +(0.186393 - 1.29639i) q^{71} +(0.415415 + 0.909632i) q^{72} +(0.857685 + 0.989821i) q^{74} +(2.57385 - 0.755750i) q^{75} +(0.239446 + 0.153882i) q^{76} +(-0.698939 + 1.53046i) q^{77} +(-0.273100 - 1.89945i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(0.239446 - 0.153882i) q^{82} +(0.415415 - 0.909632i) q^{84} +(-1.34125 - 0.861971i) q^{85} +(-1.61435 - 0.474017i) q^{88} +(0.544078 + 1.19136i) q^{89} +(-0.273100 + 1.89945i) q^{90} +(0.841254 + 0.540641i) q^{92} +0.830830 q^{93} +(0.226900 + 0.496841i) q^{95} +(0.959493 + 0.281733i) q^{96} +(-0.959493 + 0.281733i) q^{98} +(1.41542 + 0.909632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} + q^{3} - q^{4} + 2 q^{5} + q^{6} + q^{7} - q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - q^{2} + q^{3} - q^{4} + 2 q^{5} + q^{6} + q^{7} - q^{8} - q^{9} + 2 q^{10} - 2 q^{11} + q^{12} + q^{14} - 2 q^{15} - q^{16} + 2 q^{17} - q^{18} + 2 q^{19} + 2 q^{20} - q^{21} - 2 q^{22} - q^{23} - 10 q^{24} - 3 q^{25} + q^{27} + q^{28} - 2 q^{30} - 9 q^{31} - q^{32} - 9 q^{33} + 2 q^{34} - 2 q^{35} - q^{36} + 9 q^{37} + 2 q^{38} - 9 q^{40} + 2 q^{41} - q^{42} - 2 q^{44} + 2 q^{45} - q^{46} + q^{48} - q^{49} - 3 q^{50} - 2 q^{51} + q^{54} - 7 q^{55} + q^{56} + 9 q^{57} - 2 q^{60} + 2 q^{62} + q^{63} - q^{64} + 2 q^{66} + 2 q^{68} + q^{69} - 2 q^{70} - 2 q^{71} - q^{72} + 9 q^{74} + 3 q^{75} + 2 q^{76} + 2 q^{77} + 2 q^{80} - q^{81} + 2 q^{82} - q^{84} - 4 q^{85} - 2 q^{88} + 2 q^{89} + 2 q^{90} - q^{92} - 2 q^{93} + 7 q^{95} + q^{96} - q^{98} + 9 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1932\mathbb{Z}\right)^\times\).

\(n\) \(829\) \(925\) \(967\) \(1289\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{11}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(3\) −0.415415 0.909632i −0.415415 0.909632i
\(4\) −0.959493 0.281733i −0.959493 0.281733i
\(5\) −1.25667 1.45027i −1.25667 1.45027i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(6\) 0.959493 0.281733i 0.959493 0.281733i
\(7\) −0.841254 0.540641i −0.841254 0.540641i
\(8\) 0.415415 0.909632i 0.415415 0.909632i
\(9\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(10\) 1.61435 1.03748i 1.61435 1.03748i
\(11\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(12\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(13\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(14\) 0.654861 0.755750i 0.654861 0.755750i
\(15\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(16\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(17\) 0.797176 0.234072i 0.797176 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(18\) −0.654861 0.755750i −0.654861 0.755750i
\(19\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(20\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(21\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(22\) 1.68251 1.68251
\(23\) −0.959493 0.281733i −0.959493 0.281733i
\(24\) −1.00000 −1.00000
\(25\) −0.381761 + 2.65520i −0.381761 + 2.65520i
\(26\) 0 0
\(27\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(28\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(29\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(30\) −1.61435 1.03748i −1.61435 1.03748i
\(31\) −0.345139 + 0.755750i −0.345139 + 0.755750i 0.654861 + 0.755750i \(0.272727\pi\)
−1.00000 \(\pi\)
\(32\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(33\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(34\) 0.118239 + 0.822373i 0.118239 + 0.822373i
\(35\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(36\) 0.841254 0.540641i 0.841254 0.540641i
\(37\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(38\) 0.118239 0.258908i 0.118239 0.258908i
\(39\) 0 0
\(40\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(41\) −0.186393 0.215109i −0.186393 0.215109i 0.654861 0.755750i \(-0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(42\) −0.959493 0.281733i −0.959493 0.281733i
\(43\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(44\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(45\) 1.91899 1.91899
\(46\) 0.415415 0.909632i 0.415415 0.909632i
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0.142315 0.989821i 0.142315 0.989821i
\(49\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(50\) −2.57385 0.755750i −2.57385 0.755750i
\(51\) −0.544078 0.627899i −0.544078 0.627899i
\(52\) 0 0
\(53\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(54\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(55\) −2.11435 + 2.44009i −2.11435 + 2.44009i
\(56\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(57\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(58\) 0 0
\(59\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(60\) 1.25667 1.45027i 1.25667 1.45027i
\(61\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(62\) −0.698939 0.449181i −0.698939 0.449181i
\(63\) 0.959493 0.281733i 0.959493 0.281733i
\(64\) −0.654861 0.755750i −0.654861 0.755750i
\(65\) 0 0
\(66\) −0.698939 1.53046i −0.698939 1.53046i
\(67\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(68\) −0.830830 −0.830830
\(69\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(70\) −1.91899 −1.91899
\(71\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(72\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(73\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(74\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(75\) 2.57385 0.755750i 2.57385 0.755750i
\(76\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(77\) −0.698939 + 1.53046i −0.698939 + 1.53046i
\(78\) 0 0
\(79\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(80\) −0.273100 1.89945i −0.273100 1.89945i
\(81\) −0.142315 0.989821i −0.142315 0.989821i
\(82\) 0.239446 0.153882i 0.239446 0.153882i
\(83\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(84\) 0.415415 0.909632i 0.415415 0.909632i
\(85\) −1.34125 0.861971i −1.34125 0.861971i
\(86\) 0 0
\(87\) 0 0
\(88\) −1.61435 0.474017i −1.61435 0.474017i
\(89\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(90\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(91\) 0 0
\(92\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(93\) 0.830830 0.830830
\(94\) 0 0
\(95\) 0.226900 + 0.496841i 0.226900 + 0.496841i
\(96\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(97\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(98\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(99\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(100\) 1.11435 2.44009i 1.11435 2.44009i
\(101\) −0.857685 + 0.989821i −0.857685 + 0.989821i 0.142315 + 0.989821i \(0.454545\pi\)
−1.00000 \(\pi\)
\(102\) 0.698939 0.449181i 0.698939 0.449181i
\(103\) −0.186393 1.29639i −0.186393 1.29639i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(104\) 0 0
\(105\) 1.61435 1.03748i 1.61435 1.03748i
\(106\) 0 0
\(107\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(108\) −0.841254 0.540641i −0.841254 0.540641i
\(109\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(110\) −2.11435 2.44009i −2.11435 2.44009i
\(111\) −1.25667 0.368991i −1.25667 0.368991i
\(112\) −0.415415 0.909632i −0.415415 0.909632i
\(113\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(114\) −0.284630 −0.284630
\(115\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.797176 0.234072i −0.797176 0.234072i
\(120\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(121\) −1.75667 + 0.515804i −1.75667 + 0.515804i
\(122\) 0 0
\(123\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(124\) 0.544078 0.627899i 0.544078 0.627899i
\(125\) 2.71616 1.74557i 2.71616 1.74557i
\(126\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(127\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(128\) 0.841254 0.540641i 0.841254 0.540641i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(132\) 1.61435 0.474017i 1.61435 0.474017i
\(133\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(134\) 0 0
\(135\) −0.797176 1.74557i −0.797176 1.74557i
\(136\) 0.118239 0.822373i 0.118239 0.822373i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) −1.00000 −1.00000
\(139\) 0.284630 0.284630 0.142315 0.989821i \(-0.454545\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(140\) 0.273100 1.89945i 0.273100 1.89945i
\(141\) 0 0
\(142\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(143\) 0 0
\(144\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.654861 0.755750i 0.654861 0.755750i
\(148\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(149\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(150\) 0.381761 + 2.65520i 0.381761 + 2.65520i
\(151\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(152\) −0.186393 + 0.215109i −0.186393 + 0.215109i
\(153\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(154\) −1.41542 0.909632i −1.41542 0.909632i
\(155\) 1.52977 0.449181i 1.52977 0.449181i
\(156\) 0 0
\(157\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 1.91899 1.91899
\(161\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(162\) 1.00000 1.00000
\(163\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(164\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(165\) 3.09792 + 0.909632i 3.09792 + 0.909632i
\(166\) 0 0
\(167\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(168\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(169\) 0.415415 0.909632i 0.415415 0.909632i
\(170\) 1.04408 1.20493i 1.04408 1.20493i
\(171\) 0.239446 0.153882i 0.239446 0.153882i
\(172\) 0 0
\(173\) −0.273100 1.89945i −0.273100 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(174\) 0 0
\(175\) 1.75667 2.02730i 1.75667 2.02730i
\(176\) 0.698939 1.53046i 0.698939 1.53046i
\(177\) 0 0
\(178\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(179\) 0.857685 + 0.989821i 0.857685 + 0.989821i 1.00000 \(0\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(180\) −1.84125 0.540641i −1.84125 0.540641i
\(181\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(185\) −2.51334 −2.51334
\(186\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(187\) −0.580699 1.27155i −0.580699 1.27155i
\(188\) 0 0
\(189\) −0.654861 0.755750i −0.654861 0.755750i
\(190\) −0.524075 + 0.153882i −0.524075 + 0.153882i
\(191\) −1.10181 0.708089i −1.10181 0.708089i −0.142315 0.989821i \(-0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(192\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(193\) 1.25667 1.45027i 1.25667 1.45027i 0.415415 0.909632i \(-0.363636\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.142315 0.989821i −0.142315 0.989821i
\(197\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(198\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(199\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(200\) 2.25667 + 1.45027i 2.25667 + 1.45027i
\(201\) 0 0
\(202\) −0.857685 0.989821i −0.857685 0.989821i
\(203\) 0 0
\(204\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(205\) −0.0777324 + 0.540641i −0.0777324 + 0.540641i
\(206\) 1.30972 1.30972
\(207\) 0.841254 0.540641i 0.841254 0.540641i
\(208\) 0 0
\(209\) −0.0681534 + 0.474017i −0.0681534 + 0.474017i
\(210\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(211\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(212\) 0 0
\(213\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(214\) −0.239446 0.153882i −0.239446 0.153882i
\(215\) 0 0
\(216\) 0.654861 0.755750i 0.654861 0.755750i
\(217\) 0.698939 0.449181i 0.698939 0.449181i
\(218\) −0.118239 0.822373i −0.118239 0.822373i
\(219\) 0 0
\(220\) 2.71616 1.74557i 2.71616 1.74557i
\(221\) 0 0
\(222\) 0.544078 1.19136i 0.544078 1.19136i
\(223\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(224\) 0.959493 0.281733i 0.959493 0.281733i
\(225\) −1.75667 2.02730i −1.75667 2.02730i
\(226\) 0 0
\(227\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(228\) 0.0405070 0.281733i 0.0405070 0.281733i
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(231\) 1.68251 1.68251
\(232\) 0 0
\(233\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0.345139 0.755750i 0.345139 0.755750i
\(239\) −1.10181 + 1.27155i −1.10181 + 1.27155i −0.142315 + 0.989821i \(0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(240\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(241\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(242\) −0.260554 1.81219i −0.260554 1.81219i
\(243\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(244\) 0 0
\(245\) 0.797176 1.74557i 0.797176 1.74557i
\(246\) −0.239446 0.153882i −0.239446 0.153882i
\(247\) 0 0
\(248\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(249\) 0 0
\(250\) 1.34125 + 2.93694i 1.34125 + 2.93694i
\(251\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(252\) −1.00000 −1.00000
\(253\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(254\) 0 0
\(255\) −0.226900 + 1.57812i −0.226900 + 1.57812i
\(256\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(257\) −1.84125 0.540641i −1.84125 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(264\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(265\) 0 0
\(266\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(267\) 0.857685 0.989821i 0.857685 0.989821i
\(268\) 0 0
\(269\) −1.41542 0.909632i −1.41542 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
−1.00000 \(\pi\)
\(270\) 1.84125 0.540641i 1.84125 0.540641i
\(271\) 1.10181 + 1.27155i 1.10181 + 1.27155i 0.959493 + 0.281733i \(0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(272\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(273\) 0 0
\(274\) 0 0
\(275\) 4.51334 4.51334
\(276\) 0.142315 0.989821i 0.142315 0.989821i
\(277\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(278\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(279\) −0.345139 0.755750i −0.345139 0.755750i
\(280\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(281\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(282\) 0 0
\(283\) −1.41542 0.909632i −1.41542 0.909632i −0.415415 0.909632i \(-0.636364\pi\)
−1.00000 \(\pi\)
\(284\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(285\) 0.357685 0.412791i 0.357685 0.412791i
\(286\) 0 0
\(287\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(288\) −0.142315 0.989821i −0.142315 0.989821i
\(289\) −0.260554 + 0.167448i −0.260554 + 0.167448i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(294\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(295\) 0 0
\(296\) −0.544078 1.19136i −0.544078 1.19136i
\(297\) 0.239446 1.66538i 0.239446 1.66538i
\(298\) 0 0
\(299\) 0 0
\(300\) −2.68251 −2.68251
\(301\) 0 0
\(302\) 0 0
\(303\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(304\) −0.186393 0.215109i −0.186393 0.215109i
\(305\) 0 0
\(306\) −0.698939 0.449181i −0.698939 0.449181i
\(307\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(308\) 1.10181 1.27155i 1.10181 1.27155i
\(309\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(310\) 0.226900 + 1.57812i 0.226900 + 1.57812i
\(311\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(312\) 0 0
\(313\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(314\) 0 0
\(315\) −1.61435 1.03748i −1.61435 1.03748i
\(316\) 0 0
\(317\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(321\) 0.284630 0.284630
\(322\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(323\) −0.236479 −0.236479
\(324\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(325\) 0 0
\(326\) 0 0
\(327\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(328\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(329\) 0 0
\(330\) −1.34125 + 2.93694i −1.34125 + 2.93694i
\(331\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(332\) 0 0
\(333\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(334\) 0 0
\(335\) 0 0
\(336\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(337\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(338\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(339\) 0 0
\(340\) 1.04408 + 1.20493i 1.04408 + 1.20493i
\(341\) 1.34125 + 0.393828i 1.34125 + 0.393828i
\(342\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(343\) 0.142315 0.989821i 0.142315 0.989821i
\(344\) 0 0
\(345\) 1.25667 1.45027i 1.25667 1.45027i
\(346\) 1.91899 1.91899
\(347\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(348\) 0 0
\(349\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(350\) 1.75667 + 2.02730i 1.75667 + 2.02730i
\(351\) 0 0
\(352\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(353\) 0.118239 0.258908i 0.118239 0.258908i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(354\) 0 0
\(355\) −2.11435 + 1.35881i −2.11435 + 1.35881i
\(356\) −0.186393 1.29639i −0.186393 1.29639i
\(357\) 0.118239 + 0.822373i 0.118239 + 0.822373i
\(358\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(359\) −1.30972 + 1.51150i −1.30972 + 1.51150i −0.654861 + 0.755750i \(0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(360\) 0.797176 1.74557i 0.797176 1.74557i
\(361\) −0.773100 0.496841i −0.773100 0.496841i
\(362\) 0 0
\(363\) 1.19894 + 1.38365i 1.19894 + 1.38365i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.830830 −0.830830 −0.415415 0.909632i \(-0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(368\) −0.654861 0.755750i −0.654861 0.755750i
\(369\) 0.284630 0.284630
\(370\) 0.357685 2.48775i 0.357685 2.48775i
\(371\) 0 0
\(372\) −0.797176 0.234072i −0.797176 0.234072i
\(373\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(374\) 1.34125 0.393828i 1.34125 0.393828i
\(375\) −2.71616 1.74557i −2.71616 1.74557i
\(376\) 0 0
\(377\) 0 0
\(378\) 0.841254 0.540641i 0.841254 0.540641i
\(379\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(380\) −0.0777324 0.540641i −0.0777324 0.540641i
\(381\) 0 0
\(382\) 0.857685 0.989821i 0.857685 0.989821i
\(383\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(384\) −0.841254 0.540641i −0.841254 0.540641i
\(385\) 3.09792 0.909632i 3.09792 0.909632i
\(386\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(390\) 0 0
\(391\) −0.830830 −0.830830
\(392\) 1.00000 1.00000
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −1.10181 1.27155i −1.10181 1.27155i
\(397\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(398\) −1.41542 0.909632i −1.41542 0.909632i
\(399\) 0.118239 0.258908i 0.118239 0.258908i
\(400\) −1.75667 + 2.02730i −1.75667 + 2.02730i
\(401\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 1.10181 0.708089i 1.10181 0.708089i
\(405\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(406\) 0 0
\(407\) −1.85380 1.19136i −1.85380 1.19136i
\(408\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(409\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(410\) −0.524075 0.153882i −0.524075 0.153882i
\(411\) 0 0
\(412\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(413\) 0 0
\(414\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(415\) 0 0
\(416\) 0 0
\(417\) −0.118239 0.258908i −0.118239 0.258908i
\(418\) −0.459493 0.134919i −0.459493 0.134919i
\(419\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(420\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(421\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.317178 + 2.20602i 0.317178 + 2.20602i
\(426\) −0.186393 1.29639i −0.186393 1.29639i
\(427\) 0 0
\(428\) 0.186393 0.215109i 0.186393 0.215109i
\(429\) 0 0
\(430\) 0 0
\(431\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(432\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(433\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(434\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(435\) 0 0
\(436\) 0.830830 0.830830
\(437\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(438\) 0 0
\(439\) 0.118239 0.822373i 0.118239 0.822373i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(440\) 1.34125 + 2.93694i 1.34125 + 2.93694i
\(441\) −0.959493 0.281733i −0.959493 0.281733i
\(442\) 0 0
\(443\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(444\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(445\) 1.04408 2.28621i 1.04408 2.28621i
\(446\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(447\) 0 0
\(448\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(449\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(450\) 2.25667 1.45027i 2.25667 1.45027i
\(451\) −0.313607 + 0.361922i −0.313607 + 0.361922i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i
\(457\) −0.797176 1.74557i −0.797176 1.74557i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(458\) 0 0
\(459\) 0.830830 0.830830
\(460\) −0.273100 1.89945i −0.273100 1.89945i
\(461\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(462\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(463\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(464\) 0 0
\(465\) −1.04408 1.20493i −1.04408 1.20493i
\(466\) 0 0
\(467\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.317178 0.694523i 0.317178 0.694523i
\(476\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(477\) 0 0
\(478\) −1.10181 1.27155i −1.10181 1.27155i
\(479\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(480\) −0.797176 1.74557i −0.797176 1.74557i
\(481\) 0 0
\(482\) 0 0
\(483\) 0.415415 0.909632i 0.415415 0.909632i
\(484\) 1.83083 1.83083
\(485\) 0 0
\(486\) −0.415415 0.909632i −0.415415 0.909632i
\(487\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(491\) −0.118239 + 0.258908i −0.118239 + 0.258908i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(492\) 0.186393 0.215109i 0.186393 0.215109i
\(493\) 0 0
\(494\) 0 0
\(495\) −0.459493 3.19584i −0.459493 3.19584i
\(496\) −0.698939 + 0.449181i −0.698939 + 0.449181i
\(497\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(498\) 0 0
\(499\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(500\) −3.09792 + 0.909632i −3.09792 + 0.909632i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(504\) 0.142315 0.989821i 0.142315 0.989821i
\(505\) 2.51334 2.51334
\(506\) −1.61435 0.474017i −1.61435 0.474017i
\(507\) −1.00000 −1.00000
\(508\) 0 0
\(509\) −0.345139 0.755750i −0.345139 0.755750i 0.654861 0.755750i \(-0.272727\pi\)
−1.00000 \(\pi\)
\(510\) −1.52977 0.449181i −1.52977 0.449181i
\(511\) 0 0
\(512\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(513\) −0.239446 0.153882i −0.239446 0.153882i
\(514\) 0.797176 1.74557i 0.797176 1.74557i
\(515\) −1.64589 + 1.89945i −1.64589 + 1.89945i
\(516\) 0 0
\(517\) 0 0
\(518\) −0.186393 1.29639i −0.186393 1.29639i
\(519\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(520\) 0 0
\(521\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(522\) 0 0
\(523\) 1.61435 0.474017i 1.61435 0.474017i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(524\) 0 0
\(525\) −2.57385 0.755750i −2.57385 0.755750i
\(526\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(527\) −0.0982369 + 0.683252i −0.0982369 + 0.683252i
\(528\) −1.68251 −1.68251
\(529\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.118239 0.258908i −0.118239 0.258908i
\(533\) 0 0
\(534\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(535\) 0.524075 0.153882i 0.524075 0.153882i
\(536\) 0 0
\(537\) 0.544078 1.19136i 0.544078 1.19136i
\(538\) 1.10181 1.27155i 1.10181 1.27155i
\(539\) 1.41542 0.909632i 1.41542 0.909632i
\(540\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(541\) −0.118239 0.822373i −0.118239 0.822373i −0.959493 0.281733i \(-0.909091\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(542\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(543\) 0 0
\(544\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(545\) 1.34125 + 0.861971i 1.34125 + 0.861971i
\(546\) 0 0
\(547\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) −0.642315 + 4.46740i −0.642315 + 4.46740i
\(551\) 0 0
\(552\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(553\) 0 0
\(554\) 0.273100 1.89945i 0.273100 1.89945i
\(555\) 1.04408 + 2.28621i 1.04408 + 2.28621i
\(556\) −0.273100 0.0801894i −0.273100 0.0801894i
\(557\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(558\) 0.797176 0.234072i 0.797176 0.234072i
\(559\) 0 0
\(560\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(561\) −0.915415 + 1.05645i −0.915415 + 1.05645i
\(562\) 0 0
\(563\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 1.10181 1.27155i 1.10181 1.27155i
\(567\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(568\) −1.10181 0.708089i −1.10181 0.708089i
\(569\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(570\) 0.357685 + 0.412791i 0.357685 + 0.412791i
\(571\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(572\) 0 0
\(573\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(574\) −0.284630 −0.284630
\(575\) 1.11435 2.44009i 1.11435 2.44009i
\(576\) 1.00000 1.00000
\(577\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(578\) −0.128663 0.281733i −0.128663 0.281733i
\(579\) −1.84125 0.540641i −1.84125 0.540641i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −0.0405070 0.281733i −0.0405070 0.281733i
\(587\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(588\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(589\) 0.154861 0.178719i 0.154861 0.178719i
\(590\) 0 0
\(591\) 0 0
\(592\) 1.25667 0.368991i 1.25667 0.368991i
\(593\) 1.10181 + 1.27155i 1.10181 + 1.27155i 0.959493 + 0.281733i \(0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(594\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(595\) 0.662317 + 1.45027i 0.662317 + 1.45027i
\(596\) 0 0
\(597\) 1.68251 1.68251
\(598\) 0 0
\(599\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(600\) 0.381761 2.65520i 0.381761 2.65520i
\(601\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.95561 + 1.89945i 2.95561 + 1.89945i
\(606\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(607\) 1.10181 1.27155i 1.10181 1.27155i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(608\) 0.239446 0.153882i 0.239446 0.153882i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.544078 0.627899i 0.544078 0.627899i
\(613\) 0.830830 1.81926i 0.830830 1.81926i 0.415415 0.909632i \(-0.363636\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(614\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(615\) 0.524075 0.153882i 0.524075 0.153882i
\(616\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(617\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(618\) −0.544078 1.19136i −0.544078 1.19136i
\(619\) −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(620\) −1.59435 −1.59435
\(621\) −0.841254 0.540641i −0.841254 0.540641i
\(622\) 0 0
\(623\) 0.186393 1.29639i 0.186393 1.29639i
\(624\) 0 0
\(625\) −3.37102 0.989821i −3.37102 0.989821i
\(626\) 0 0
\(627\) 0.459493 0.134919i 0.459493 0.134919i
\(628\) 0 0
\(629\) 0.452036 0.989821i 0.452036 0.989821i
\(630\) 1.25667 1.45027i 1.25667 1.45027i
\(631\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(640\) −1.84125 0.540641i −1.84125 0.540641i
\(641\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(642\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(643\) −1.68251 −1.68251 −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(644\) −0.415415 0.909632i −0.415415 0.909632i
\(645\) 0 0
\(646\) 0.0336545 0.234072i 0.0336545 0.234072i
\(647\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(648\) −0.959493 0.281733i −0.959493 0.281733i
\(649\) 0 0
\(650\) 0 0
\(651\) −0.698939 0.449181i −0.698939 0.449181i
\(652\) 0 0
\(653\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(654\) −0.698939 + 0.449181i −0.698939 + 0.449181i
\(655\) 0 0
\(656\) −0.0405070 0.281733i −0.0405070 0.281733i
\(657\) 0 0
\(658\) 0 0
\(659\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(660\) −2.71616 1.74557i −2.71616 1.74557i
\(661\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0.0777324 0.540641i 0.0777324 0.540641i
\(666\) −1.30972 −1.30972
\(667\) 0 0
\(668\) 0 0
\(669\) 0.273100 1.89945i 0.273100 1.89945i
\(670\) 0 0
\(671\) 0 0
\(672\) −0.654861 0.755750i −0.654861 0.755750i
\(673\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(674\) −0.239446 0.153882i −0.239446 0.153882i
\(675\) −1.11435 + 2.44009i −1.11435 + 2.44009i
\(676\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(677\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.34125 + 0.861971i −1.34125 + 0.861971i
\(681\) 0 0
\(682\) −0.580699 + 1.27155i −0.580699 + 1.27155i
\(683\) −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(684\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(685\) 0 0
\(686\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(691\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(692\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(693\) −0.698939 1.53046i −0.698939 1.53046i
\(694\) −1.61435 0.474017i −1.61435 0.474017i
\(695\) −0.357685 0.412791i −0.357685 0.412791i
\(696\) 0 0
\(697\) −0.198939 0.127850i −0.198939 0.127850i
\(698\) 0 0
\(699\) 0 0
\(700\) −2.25667 + 1.45027i −2.25667 + 1.45027i
\(701\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(702\) 0 0
\(703\) −0.313607 + 0.201543i −0.313607 + 0.201543i
\(704\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(705\) 0 0
\(706\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(707\) 1.25667 0.368991i 1.25667 0.368991i
\(708\) 0 0
\(709\) −1.61435 0.474017i −1.61435 0.474017i −0.654861 0.755750i \(-0.727273\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(710\) −1.04408 2.28621i −1.04408 2.28621i
\(711\) 0 0
\(712\) 1.30972 1.30972
\(713\) 0.544078 0.627899i 0.544078 0.627899i
\(714\) −0.830830 −0.830830
\(715\) 0 0
\(716\) −0.544078 1.19136i −0.544078 1.19136i
\(717\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(718\) −1.30972 1.51150i −1.30972 1.51150i
\(719\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(720\) 1.61435 + 1.03748i 1.61435 + 1.03748i
\(721\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(722\) 0.601808 0.694523i 0.601808 0.694523i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −1.54019 + 0.989821i −1.54019 + 0.989821i
\(727\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(728\) 0 0
\(729\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(734\) 0.118239 0.822373i 0.118239 0.822373i
\(735\) −1.91899 −1.91899
\(736\) 0.841254 0.540641i 0.841254 0.540641i
\(737\) 0 0
\(738\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(739\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(740\) 2.41153 + 0.708089i 2.41153 + 0.708089i
\(741\) 0 0
\(742\) 0 0
\(743\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(744\) 0.345139 0.755750i 0.345139 0.755750i
\(745\) 0 0
\(746\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(747\) 0 0
\(748\) 0.198939 + 1.38365i 0.198939 + 1.38365i
\(749\) 0.239446 0.153882i 0.239446 0.153882i
\(750\) 2.11435 2.44009i 2.11435 2.44009i
\(751\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(757\) 0.186393 1.29639i 0.186393 1.29639i −0.654861 0.755750i \(-0.727273\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(758\) 0 0
\(759\) 1.61435 0.474017i 1.61435 0.474017i
\(760\) 0.546200 0.546200
\(761\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(762\) 0 0
\(763\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(764\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(765\) 1.52977 0.449181i 1.52977 0.449181i
\(766\) 0 0
\(767\) 0 0
\(768\) 0.654861 0.755750i 0.654861 0.755750i
\(769\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(770\) 0.459493 + 3.19584i 0.459493 + 3.19584i
\(771\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(772\) −1.61435 + 1.03748i −1.61435 + 1.03748i
\(773\) 1.10181 1.27155i 1.10181 1.27155i 0.142315 0.989821i \(-0.454545\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(774\) 0 0
\(775\) −1.87491 1.20493i −1.87491 1.20493i
\(776\) 0 0
\(777\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(778\) 0 0
\(779\) 0.0336545 + 0.0736930i 0.0336545 + 0.0736930i
\(780\) 0 0
\(781\) −2.20362 −2.20362
\(782\) 0.118239 0.822373i 0.118239 0.822373i
\(783\) 0 0
\(784\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.186393 0.215109i −0.186393 0.215109i 0.654861 0.755750i \(-0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(788\) 0 0
\(789\) −0.698939 0.449181i −0.698939 0.449181i
\(790\) 0 0
\(791\) 0 0
\(792\) 1.41542 0.909632i 1.41542 0.909632i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 1.10181 1.27155i 1.10181 1.27155i
\(797\) −0.830830 + 1.81926i −0.830830 + 1.81926i −0.415415 + 0.909632i \(0.636364\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(798\) 0.239446 + 0.153882i 0.239446 + 0.153882i
\(799\) 0 0
\(800\) −1.75667 2.02730i −1.75667 2.02730i
\(801\) −1.25667 0.368991i −1.25667 0.368991i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0.273100 1.89945i 0.273100 1.89945i
\(806\) 0 0
\(807\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(808\) 0.544078 + 1.19136i 0.544078 + 1.19136i
\(809\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(810\) −1.25667 1.45027i −1.25667 1.45027i
\(811\) −1.84125 + 0.540641i −1.84125 + 0.540641i −0.841254 + 0.540641i \(0.818182\pi\)
−1.00000 \(1.00000\pi\)
\(812\) 0 0
\(813\) 0.698939 1.53046i 0.698939 1.53046i
\(814\) 1.44306 1.66538i 1.44306 1.66538i
\(815\) 0 0
\(816\) −0.118239 0.822373i −0.118239 0.822373i
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0.226900 0.496841i 0.226900 0.496841i
\(821\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(822\) 0 0
\(823\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(824\) −1.25667 0.368991i −1.25667 0.368991i
\(825\) −1.87491 4.10548i −1.87491 4.10548i
\(826\) 0 0
\(827\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(828\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(832\) 0 0
\(833\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(834\) 0.273100 0.0801894i 0.273100 0.0801894i
\(835\) 0 0
\(836\) 0.198939 0.435615i 0.198939 0.435615i
\(837\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(838\) 0 0
\(839\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(840\) −0.273100 1.89945i −0.273100 1.89945i
\(841\) 0.841254 0.540641i 0.841254 0.540641i
\(842\) 1.25667 1.45027i 1.25667 1.45027i
\(843\) 0 0
\(844\) 0 0
\(845\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(846\) 0 0
\(847\) 1.75667 + 0.515804i 1.75667 + 0.515804i
\(848\) 0 0
\(849\) −0.239446 + 1.66538i −0.239446 + 1.66538i
\(850\) −2.22871 −2.22871
\(851\) −1.10181 + 0.708089i −1.10181 + 0.708089i
\(852\) 1.30972 1.30972
\(853\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(854\) 0 0
\(855\) −0.524075 0.153882i −0.524075 0.153882i
\(856\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(857\) 0.797176 0.234072i 0.797176 0.234072i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(858\) 0 0
\(859\) 0.544078 1.19136i 0.544078 1.19136i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(860\) 0 0
\(861\) 0.239446 0.153882i 0.239446 0.153882i
\(862\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i
\(863\) −0.239446 1.66538i −0.239446 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(864\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(865\) −2.41153 + 2.78305i −2.41153 + 2.78305i
\(866\) 0 0
\(867\) 0.260554 + 0.167448i 0.260554 + 0.167448i
\(868\) −0.797176 + 0.234072i −0.797176 + 0.234072i
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(873\) 0 0
\(874\) −0.186393 + 0.215109i −0.186393 + 0.215109i
\(875\) −3.22871 −3.22871
\(876\) 0 0
\(877\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(878\) 0.797176 + 0.234072i 0.797176 + 0.234072i
\(879\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(880\) −3.09792 + 0.909632i −3.09792 + 0.909632i
\(881\) −1.68251 1.08128i −1.68251 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 0.540641i \(-0.818182\pi\)
\(882\) 0.415415 0.909632i 0.415415 0.909632i
\(883\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −0.118239 0.822373i −0.118239 0.822373i
\(887\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(888\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(889\) 0 0
\(890\) 2.11435 + 1.35881i 2.11435 + 1.35881i
\(891\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(892\) −1.25667 1.45027i −1.25667 1.45027i
\(893\) 0 0
\(894\) 0 0
\(895\) 0.357685 2.48775i 0.357685 2.48775i
\(896\) −1.00000 −1.00000
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 1.11435 + 2.44009i 1.11435 + 2.44009i
\(901\) 0 0
\(902\) −0.313607 0.361922i −0.313607 0.361922i
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(908\) 0 0
\(909\) −0.186393 1.29639i −0.186393 1.29639i
\(910\) 0 0
\(911\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(912\) −0.118239 + 0.258908i −0.118239 + 0.258908i
\(913\) 0 0
\(914\) 1.84125 0.540641i 1.84125 0.540641i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 1.91899 1.91899
\(921\) −1.91899 −1.91899
\(922\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(923\) 0 0
\(924\) −1.61435 0.474017i −1.61435 0.474017i
\(925\) 2.30075 + 2.65520i 2.30075 + 2.65520i
\(926\) 0 0
\(927\) 1.10181 + 0.708089i 1.10181 + 0.708089i
\(928\) 0 0
\(929\) −1.25667 + 1.45027i −1.25667 + 1.45027i −0.415415 + 0.909632i \(0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(930\) 1.34125 0.861971i 1.34125 0.861971i
\(931\) −0.0405070 0.281733i −0.0405070 0.281733i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.11435 + 2.44009i −1.11435 + 2.44009i
\(936\) 0 0
\(937\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i 0.959493 + 0.281733i \(0.0909091\pi\)
−1.00000 \(1.00000\pi\)
\(942\) 0 0
\(943\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(944\) 0 0
\(945\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(946\) 0 0
\(947\) 1.25667 + 0.368991i 1.25667 + 0.368991i 0.841254 0.540641i \(-0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.642315 + 0.412791i 0.642315 + 0.412791i
\(951\) 0 0
\(952\) −0.544078 + 0.627899i −0.544078 + 0.627899i
\(953\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(954\) 0 0
\(955\) 0.357685 + 2.48775i 0.357685 + 2.48775i
\(956\) 1.41542 0.909632i 1.41542 0.909632i
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.84125 0.540641i 1.84125 0.540641i
\(961\) 0.202824 + 0.234072i 0.202824 + 0.234072i
\(962\) 0 0
\(963\) −0.118239 0.258908i −0.118239 0.258908i
\(964\) 0 0
\(965\) −3.68251 −3.68251
\(966\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) −0.260554 + 1.81219i −0.260554 + 1.81219i
\(969\) 0.0982369 + 0.215109i 0.0982369 + 0.215109i
\(970\) 0 0
\(971\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(972\) 0.959493 0.281733i 0.959493 0.281733i
\(973\) −0.239446 0.153882i −0.239446 0.153882i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(978\) 0 0
\(979\) 1.85380 1.19136i 1.85380 1.19136i
\(980\) −1.25667 + 1.45027i −1.25667 + 1.45027i
\(981\) 0.345139 0.755750i 0.345139 0.755750i
\(982\) −0.239446 0.153882i −0.239446 0.153882i
\(983\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(984\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 3.22871 3.22871
\(991\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(992\) −0.345139 0.755750i −0.345139 0.755750i
\(993\) 0 0
\(994\) −0.857685 0.989821i −0.857685 0.989821i
\(995\) 3.09792 0.909632i 3.09792 0.909632i
\(996\) 0 0
\(997\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(998\) 0 0
\(999\) 1.10181 0.708089i 1.10181 0.708089i
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 1932.1.bi.b.1595.1 yes 10
3.2 odd 2 1932.1.bi.d.1595.1 yes 10
4.3 odd 2 1932.1.bi.c.1595.1 yes 10
7.6 odd 2 1932.1.bi.a.1595.1 yes 10
12.11 even 2 1932.1.bi.a.1595.1 yes 10
21.20 even 2 1932.1.bi.c.1595.1 yes 10
23.3 even 11 inner 1932.1.bi.b.923.1 yes 10
28.27 even 2 1932.1.bi.d.1595.1 yes 10
69.26 odd 22 1932.1.bi.d.923.1 yes 10
84.83 odd 2 CM 1932.1.bi.b.1595.1 yes 10
92.3 odd 22 1932.1.bi.c.923.1 yes 10
161.118 odd 22 1932.1.bi.a.923.1 10
276.95 even 22 1932.1.bi.a.923.1 10
483.440 even 22 1932.1.bi.c.923.1 yes 10
644.279 even 22 1932.1.bi.d.923.1 yes 10
1932.923 odd 22 inner 1932.1.bi.b.923.1 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1932.1.bi.a.923.1 10 161.118 odd 22
1932.1.bi.a.923.1 10 276.95 even 22
1932.1.bi.a.1595.1 yes 10 7.6 odd 2
1932.1.bi.a.1595.1 yes 10 12.11 even 2
1932.1.bi.b.923.1 yes 10 23.3 even 11 inner
1932.1.bi.b.923.1 yes 10 1932.923 odd 22 inner
1932.1.bi.b.1595.1 yes 10 1.1 even 1 trivial
1932.1.bi.b.1595.1 yes 10 84.83 odd 2 CM
1932.1.bi.c.923.1 yes 10 92.3 odd 22
1932.1.bi.c.923.1 yes 10 483.440 even 22
1932.1.bi.c.1595.1 yes 10 4.3 odd 2
1932.1.bi.c.1595.1 yes 10 21.20 even 2
1932.1.bi.d.923.1 yes 10 69.26 odd 22
1932.1.bi.d.923.1 yes 10 644.279 even 22
1932.1.bi.d.1595.1 yes 10 3.2 odd 2
1932.1.bi.d.1595.1 yes 10 28.27 even 2