Properties

Label 40.2.d.a.21.1
Level $40$
Weight $2$
Character 40.21
Analytic conductor $0.319$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [40,2,Mod(21,40)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(40, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("40.21");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 40 = 2^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 40.d (of order \(2\), degree \(1\), 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: \(0.319401608085\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 21.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 40.21
Dual form 40.2.d.a.21.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.36603 - 0.366025i) q^{2} +2.73205i q^{3} +(1.73205 + 1.00000i) q^{4} -1.00000i q^{5} +(1.00000 - 3.73205i) q^{6} +0.732051 q^{7} +(-2.00000 - 2.00000i) q^{8} -4.46410 q^{9} +O(q^{10})\) \(q+(-1.36603 - 0.366025i) q^{2} +2.73205i q^{3} +(1.73205 + 1.00000i) q^{4} -1.00000i q^{5} +(1.00000 - 3.73205i) q^{6} +0.732051 q^{7} +(-2.00000 - 2.00000i) q^{8} -4.46410 q^{9} +(-0.366025 + 1.36603i) q^{10} -2.00000i q^{11} +(-2.73205 + 4.73205i) q^{12} -3.46410i q^{13} +(-1.00000 - 0.267949i) q^{14} +2.73205 q^{15} +(2.00000 + 3.46410i) q^{16} +3.46410 q^{17} +(6.09808 + 1.63397i) q^{18} +0.535898i q^{19} +(1.00000 - 1.73205i) q^{20} +2.00000i q^{21} +(-0.732051 + 2.73205i) q^{22} -6.19615 q^{23} +(5.46410 - 5.46410i) q^{24} -1.00000 q^{25} +(-1.26795 + 4.73205i) q^{26} -4.00000i q^{27} +(1.26795 + 0.732051i) q^{28} +6.92820i q^{29} +(-3.73205 - 1.00000i) q^{30} -5.46410 q^{31} +(-1.46410 - 5.46410i) q^{32} +5.46410 q^{33} +(-4.73205 - 1.26795i) q^{34} -0.732051i q^{35} +(-7.73205 - 4.46410i) q^{36} -2.00000i q^{37} +(0.196152 - 0.732051i) q^{38} +9.46410 q^{39} +(-2.00000 + 2.00000i) q^{40} +1.46410 q^{41} +(0.732051 - 2.73205i) q^{42} -5.26795i q^{43} +(2.00000 - 3.46410i) q^{44} +4.46410i q^{45} +(8.46410 + 2.26795i) q^{46} +3.26795 q^{47} +(-9.46410 + 5.46410i) q^{48} -6.46410 q^{49} +(1.36603 + 0.366025i) q^{50} +9.46410i q^{51} +(3.46410 - 6.00000i) q^{52} +11.4641i q^{53} +(-1.46410 + 5.46410i) q^{54} -2.00000 q^{55} +(-1.46410 - 1.46410i) q^{56} -1.46410 q^{57} +(2.53590 - 9.46410i) q^{58} -7.46410i q^{59} +(4.73205 + 2.73205i) q^{60} -8.92820i q^{61} +(7.46410 + 2.00000i) q^{62} -3.26795 q^{63} +8.00000i q^{64} -3.46410 q^{65} +(-7.46410 - 2.00000i) q^{66} +10.7321i q^{67} +(6.00000 + 3.46410i) q^{68} -16.9282i q^{69} +(-0.267949 + 1.00000i) q^{70} +5.46410 q^{71} +(8.92820 + 8.92820i) q^{72} +7.46410 q^{73} +(-0.732051 + 2.73205i) q^{74} -2.73205i q^{75} +(-0.535898 + 0.928203i) q^{76} -1.46410i q^{77} +(-12.9282 - 3.46410i) q^{78} -1.07180 q^{79} +(3.46410 - 2.00000i) q^{80} -2.46410 q^{81} +(-2.00000 - 0.535898i) q^{82} +1.26795i q^{83} +(-2.00000 + 3.46410i) q^{84} -3.46410i q^{85} +(-1.92820 + 7.19615i) q^{86} -18.9282 q^{87} +(-4.00000 + 4.00000i) q^{88} +8.92820 q^{89} +(1.63397 - 6.09808i) q^{90} -2.53590i q^{91} +(-10.7321 - 6.19615i) q^{92} -14.9282i q^{93} +(-4.46410 - 1.19615i) q^{94} +0.535898 q^{95} +(14.9282 - 4.00000i) q^{96} -14.3923 q^{97} +(8.83013 + 2.36603i) q^{98} +8.92820i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 4 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 4 q^{6} - 4 q^{7} - 8 q^{8} - 4 q^{9} + 2 q^{10} - 4 q^{12} - 4 q^{14} + 4 q^{15} + 8 q^{16} + 14 q^{18} + 4 q^{20} + 4 q^{22} - 4 q^{23} + 8 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 8 q^{30} - 8 q^{31} + 8 q^{32} + 8 q^{33} - 12 q^{34} - 24 q^{36} - 20 q^{38} + 24 q^{39} - 8 q^{40} - 8 q^{41} - 4 q^{42} + 8 q^{44} + 20 q^{46} + 20 q^{47} - 24 q^{48} - 12 q^{49} + 2 q^{50} + 8 q^{54} - 8 q^{55} + 8 q^{56} + 8 q^{57} + 24 q^{58} + 12 q^{60} + 16 q^{62} - 20 q^{63} - 16 q^{66} + 24 q^{68} - 8 q^{70} + 8 q^{71} + 8 q^{72} + 16 q^{73} + 4 q^{74} - 16 q^{76} - 24 q^{78} - 32 q^{79} + 4 q^{81} - 8 q^{82} - 8 q^{84} + 20 q^{86} - 48 q^{87} - 16 q^{88} + 8 q^{89} + 10 q^{90} - 36 q^{92} - 4 q^{94} + 16 q^{95} + 32 q^{96} - 16 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(21\) \(31\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 0.366025i −0.965926 0.258819i
\(3\) 2.73205i 1.57735i 0.614810 + 0.788675i \(0.289233\pi\)
−0.614810 + 0.788675i \(0.710767\pi\)
\(4\) 1.73205 + 1.00000i 0.866025 + 0.500000i
\(5\) 1.00000i 0.447214i
\(6\) 1.00000 3.73205i 0.408248 1.52360i
\(7\) 0.732051 0.276689 0.138345 0.990384i \(-0.455822\pi\)
0.138345 + 0.990384i \(0.455822\pi\)
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) −4.46410 −1.48803
\(10\) −0.366025 + 1.36603i −0.115747 + 0.431975i
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) −2.73205 + 4.73205i −0.788675 + 1.36603i
\(13\) 3.46410i 0.960769i −0.877058 0.480384i \(-0.840497\pi\)
0.877058 0.480384i \(-0.159503\pi\)
\(14\) −1.00000 0.267949i −0.267261 0.0716124i
\(15\) 2.73205 0.705412
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 3.46410 0.840168 0.420084 0.907485i \(-0.362001\pi\)
0.420084 + 0.907485i \(0.362001\pi\)
\(18\) 6.09808 + 1.63397i 1.43733 + 0.385132i
\(19\) 0.535898i 0.122944i 0.998109 + 0.0614718i \(0.0195794\pi\)
−0.998109 + 0.0614718i \(0.980421\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) 2.00000i 0.436436i
\(22\) −0.732051 + 2.73205i −0.156074 + 0.582475i
\(23\) −6.19615 −1.29199 −0.645994 0.763343i \(-0.723557\pi\)
−0.645994 + 0.763343i \(0.723557\pi\)
\(24\) 5.46410 5.46410i 1.11536 1.11536i
\(25\) −1.00000 −0.200000
\(26\) −1.26795 + 4.73205i −0.248665 + 0.928032i
\(27\) 4.00000i 0.769800i
\(28\) 1.26795 + 0.732051i 0.239620 + 0.138345i
\(29\) 6.92820i 1.28654i 0.765641 + 0.643268i \(0.222422\pi\)
−0.765641 + 0.643268i \(0.777578\pi\)
\(30\) −3.73205 1.00000i −0.681376 0.182574i
\(31\) −5.46410 −0.981382 −0.490691 0.871334i \(-0.663256\pi\)
−0.490691 + 0.871334i \(0.663256\pi\)
\(32\) −1.46410 5.46410i −0.258819 0.965926i
\(33\) 5.46410 0.951178
\(34\) −4.73205 1.26795i −0.811540 0.217451i
\(35\) 0.732051i 0.123739i
\(36\) −7.73205 4.46410i −1.28868 0.744017i
\(37\) 2.00000i 0.328798i −0.986394 0.164399i \(-0.947432\pi\)
0.986394 0.164399i \(-0.0525685\pi\)
\(38\) 0.196152 0.732051i 0.0318201 0.118754i
\(39\) 9.46410 1.51547
\(40\) −2.00000 + 2.00000i −0.316228 + 0.316228i
\(41\) 1.46410 0.228654 0.114327 0.993443i \(-0.463529\pi\)
0.114327 + 0.993443i \(0.463529\pi\)
\(42\) 0.732051 2.73205i 0.112958 0.421565i
\(43\) 5.26795i 0.803355i −0.915781 0.401677i \(-0.868427\pi\)
0.915781 0.401677i \(-0.131573\pi\)
\(44\) 2.00000 3.46410i 0.301511 0.522233i
\(45\) 4.46410i 0.665469i
\(46\) 8.46410 + 2.26795i 1.24796 + 0.334391i
\(47\) 3.26795 0.476679 0.238340 0.971182i \(-0.423397\pi\)
0.238340 + 0.971182i \(0.423397\pi\)
\(48\) −9.46410 + 5.46410i −1.36603 + 0.788675i
\(49\) −6.46410 −0.923443
\(50\) 1.36603 + 0.366025i 0.193185 + 0.0517638i
\(51\) 9.46410i 1.32524i
\(52\) 3.46410 6.00000i 0.480384 0.832050i
\(53\) 11.4641i 1.57472i 0.616496 + 0.787358i \(0.288551\pi\)
−0.616496 + 0.787358i \(0.711449\pi\)
\(54\) −1.46410 + 5.46410i −0.199239 + 0.743570i
\(55\) −2.00000 −0.269680
\(56\) −1.46410 1.46410i −0.195649 0.195649i
\(57\) −1.46410 −0.193925
\(58\) 2.53590 9.46410i 0.332980 1.24270i
\(59\) 7.46410i 0.971743i −0.874030 0.485872i \(-0.838502\pi\)
0.874030 0.485872i \(-0.161498\pi\)
\(60\) 4.73205 + 2.73205i 0.610905 + 0.352706i
\(61\) 8.92820i 1.14314i −0.820554 0.571570i \(-0.806335\pi\)
0.820554 0.571570i \(-0.193665\pi\)
\(62\) 7.46410 + 2.00000i 0.947942 + 0.254000i
\(63\) −3.26795 −0.411723
\(64\) 8.00000i 1.00000i
\(65\) −3.46410 −0.429669
\(66\) −7.46410 2.00000i −0.918767 0.246183i
\(67\) 10.7321i 1.31113i 0.755139 + 0.655564i \(0.227569\pi\)
−0.755139 + 0.655564i \(0.772431\pi\)
\(68\) 6.00000 + 3.46410i 0.727607 + 0.420084i
\(69\) 16.9282i 2.03792i
\(70\) −0.267949 + 1.00000i −0.0320261 + 0.119523i
\(71\) 5.46410 0.648470 0.324235 0.945977i \(-0.394893\pi\)
0.324235 + 0.945977i \(0.394893\pi\)
\(72\) 8.92820 + 8.92820i 1.05220 + 1.05220i
\(73\) 7.46410 0.873607 0.436804 0.899557i \(-0.356111\pi\)
0.436804 + 0.899557i \(0.356111\pi\)
\(74\) −0.732051 + 2.73205i −0.0850992 + 0.317594i
\(75\) 2.73205i 0.315470i
\(76\) −0.535898 + 0.928203i −0.0614718 + 0.106472i
\(77\) 1.46410i 0.166850i
\(78\) −12.9282 3.46410i −1.46383 0.392232i
\(79\) −1.07180 −0.120587 −0.0602933 0.998181i \(-0.519204\pi\)
−0.0602933 + 0.998181i \(0.519204\pi\)
\(80\) 3.46410 2.00000i 0.387298 0.223607i
\(81\) −2.46410 −0.273789
\(82\) −2.00000 0.535898i −0.220863 0.0591801i
\(83\) 1.26795i 0.139176i 0.997576 + 0.0695878i \(0.0221684\pi\)
−0.997576 + 0.0695878i \(0.977832\pi\)
\(84\) −2.00000 + 3.46410i −0.218218 + 0.377964i
\(85\) 3.46410i 0.375735i
\(86\) −1.92820 + 7.19615i −0.207924 + 0.775981i
\(87\) −18.9282 −2.02932
\(88\) −4.00000 + 4.00000i −0.426401 + 0.426401i
\(89\) 8.92820 0.946388 0.473194 0.880958i \(-0.343101\pi\)
0.473194 + 0.880958i \(0.343101\pi\)
\(90\) 1.63397 6.09808i 0.172236 0.642794i
\(91\) 2.53590i 0.265834i
\(92\) −10.7321 6.19615i −1.11889 0.645994i
\(93\) 14.9282i 1.54798i
\(94\) −4.46410 1.19615i −0.460437 0.123374i
\(95\) 0.535898 0.0549820
\(96\) 14.9282 4.00000i 1.52360 0.408248i
\(97\) −14.3923 −1.46132 −0.730659 0.682743i \(-0.760787\pi\)
−0.730659 + 0.682743i \(0.760787\pi\)
\(98\) 8.83013 + 2.36603i 0.891978 + 0.239005i
\(99\) 8.92820i 0.897318i
\(100\) −1.73205 1.00000i −0.173205 0.100000i
\(101\) 2.92820i 0.291367i 0.989331 + 0.145684i \(0.0465381\pi\)
−0.989331 + 0.145684i \(0.953462\pi\)
\(102\) 3.46410 12.9282i 0.342997 1.28008i
\(103\) 15.6603 1.54305 0.771525 0.636199i \(-0.219494\pi\)
0.771525 + 0.636199i \(0.219494\pi\)
\(104\) −6.92820 + 6.92820i −0.679366 + 0.679366i
\(105\) 2.00000 0.195180
\(106\) 4.19615 15.6603i 0.407566 1.52106i
\(107\) 2.73205i 0.264117i 0.991242 + 0.132059i \(0.0421587\pi\)
−0.991242 + 0.132059i \(0.957841\pi\)
\(108\) 4.00000 6.92820i 0.384900 0.666667i
\(109\) 16.9282i 1.62143i 0.585443 + 0.810714i \(0.300921\pi\)
−0.585443 + 0.810714i \(0.699079\pi\)
\(110\) 2.73205 + 0.732051i 0.260491 + 0.0697983i
\(111\) 5.46410 0.518630
\(112\) 1.46410 + 2.53590i 0.138345 + 0.239620i
\(113\) −12.9282 −1.21618 −0.608092 0.793867i \(-0.708065\pi\)
−0.608092 + 0.793867i \(0.708065\pi\)
\(114\) 2.00000 + 0.535898i 0.187317 + 0.0501915i
\(115\) 6.19615i 0.577794i
\(116\) −6.92820 + 12.0000i −0.643268 + 1.11417i
\(117\) 15.4641i 1.42966i
\(118\) −2.73205 + 10.1962i −0.251506 + 0.938632i
\(119\) 2.53590 0.232465
\(120\) −5.46410 5.46410i −0.498802 0.498802i
\(121\) 7.00000 0.636364
\(122\) −3.26795 + 12.1962i −0.295866 + 1.10419i
\(123\) 4.00000i 0.360668i
\(124\) −9.46410 5.46410i −0.849901 0.490691i
\(125\) 1.00000i 0.0894427i
\(126\) 4.46410 + 1.19615i 0.397694 + 0.106562i
\(127\) 16.7321 1.48473 0.742365 0.669996i \(-0.233704\pi\)
0.742365 + 0.669996i \(0.233704\pi\)
\(128\) 2.92820 10.9282i 0.258819 0.965926i
\(129\) 14.3923 1.26717
\(130\) 4.73205 + 1.26795i 0.415028 + 0.111207i
\(131\) 19.8564i 1.73486i −0.497557 0.867431i \(-0.665770\pi\)
0.497557 0.867431i \(-0.334230\pi\)
\(132\) 9.46410 + 5.46410i 0.823744 + 0.475589i
\(133\) 0.392305i 0.0340171i
\(134\) 3.92820 14.6603i 0.339345 1.26645i
\(135\) −4.00000 −0.344265
\(136\) −6.92820 6.92820i −0.594089 0.594089i
\(137\) 4.92820 0.421045 0.210522 0.977589i \(-0.432484\pi\)
0.210522 + 0.977589i \(0.432484\pi\)
\(138\) −6.19615 + 23.1244i −0.527452 + 1.96848i
\(139\) 0.535898i 0.0454543i −0.999742 0.0227272i \(-0.992765\pi\)
0.999742 0.0227272i \(-0.00723490\pi\)
\(140\) 0.732051 1.26795i 0.0618696 0.107161i
\(141\) 8.92820i 0.751890i
\(142\) −7.46410 2.00000i −0.626373 0.167836i
\(143\) −6.92820 −0.579365
\(144\) −8.92820 15.4641i −0.744017 1.28868i
\(145\) 6.92820 0.575356
\(146\) −10.1962 2.73205i −0.843840 0.226106i
\(147\) 17.6603i 1.45659i
\(148\) 2.00000 3.46410i 0.164399 0.284747i
\(149\) 7.85641i 0.643622i −0.946804 0.321811i \(-0.895708\pi\)
0.946804 0.321811i \(-0.104292\pi\)
\(150\) −1.00000 + 3.73205i −0.0816497 + 0.304721i
\(151\) −12.3923 −1.00847 −0.504236 0.863566i \(-0.668226\pi\)
−0.504236 + 0.863566i \(0.668226\pi\)
\(152\) 1.07180 1.07180i 0.0869342 0.0869342i
\(153\) −15.4641 −1.25020
\(154\) −0.535898 + 2.00000i −0.0431839 + 0.161165i
\(155\) 5.46410i 0.438887i
\(156\) 16.3923 + 9.46410i 1.31243 + 0.757735i
\(157\) 3.07180i 0.245156i −0.992459 0.122578i \(-0.960884\pi\)
0.992459 0.122578i \(-0.0391162\pi\)
\(158\) 1.46410 + 0.392305i 0.116478 + 0.0312101i
\(159\) −31.3205 −2.48388
\(160\) −5.46410 + 1.46410i −0.431975 + 0.115747i
\(161\) −4.53590 −0.357479
\(162\) 3.36603 + 0.901924i 0.264460 + 0.0708618i
\(163\) 0.196152i 0.0153638i −0.999970 0.00768192i \(-0.997555\pi\)
0.999970 0.00768192i \(-0.00244526\pi\)
\(164\) 2.53590 + 1.46410i 0.198020 + 0.114327i
\(165\) 5.46410i 0.425380i
\(166\) 0.464102 1.73205i 0.0360213 0.134433i
\(167\) −9.80385 −0.758645 −0.379322 0.925265i \(-0.623843\pi\)
−0.379322 + 0.925265i \(0.623843\pi\)
\(168\) 4.00000 4.00000i 0.308607 0.308607i
\(169\) 1.00000 0.0769231
\(170\) −1.26795 + 4.73205i −0.0972473 + 0.362932i
\(171\) 2.39230i 0.182944i
\(172\) 5.26795 9.12436i 0.401677 0.695726i
\(173\) 2.00000i 0.152057i 0.997106 + 0.0760286i \(0.0242240\pi\)
−0.997106 + 0.0760286i \(0.975776\pi\)
\(174\) 25.8564 + 6.92820i 1.96017 + 0.525226i
\(175\) −0.732051 −0.0553378
\(176\) 6.92820 4.00000i 0.522233 0.301511i
\(177\) 20.3923 1.53278
\(178\) −12.1962 3.26795i −0.914140 0.244943i
\(179\) 8.53590i 0.638003i −0.947754 0.319002i \(-0.896652\pi\)
0.947754 0.319002i \(-0.103348\pi\)
\(180\) −4.46410 + 7.73205i −0.332734 + 0.576313i
\(181\) 16.0000i 1.18927i 0.803996 + 0.594635i \(0.202704\pi\)
−0.803996 + 0.594635i \(0.797296\pi\)
\(182\) −0.928203 + 3.46410i −0.0688030 + 0.256776i
\(183\) 24.3923 1.80313
\(184\) 12.3923 + 12.3923i 0.913573 + 0.913573i
\(185\) −2.00000 −0.147043
\(186\) −5.46410 + 20.3923i −0.400647 + 1.49524i
\(187\) 6.92820i 0.506640i
\(188\) 5.66025 + 3.26795i 0.412816 + 0.238340i
\(189\) 2.92820i 0.212995i
\(190\) −0.732051 0.196152i −0.0531085 0.0142304i
\(191\) 15.3205 1.10855 0.554277 0.832333i \(-0.312995\pi\)
0.554277 + 0.832333i \(0.312995\pi\)
\(192\) −21.8564 −1.57735
\(193\) 0.535898 0.0385748 0.0192874 0.999814i \(-0.493860\pi\)
0.0192874 + 0.999814i \(0.493860\pi\)
\(194\) 19.6603 + 5.26795i 1.41152 + 0.378217i
\(195\) 9.46410i 0.677738i
\(196\) −11.1962 6.46410i −0.799725 0.461722i
\(197\) 19.4641i 1.38676i −0.720572 0.693380i \(-0.756121\pi\)
0.720572 0.693380i \(-0.243879\pi\)
\(198\) 3.26795 12.1962i 0.232243 0.866743i
\(199\) −1.85641 −0.131597 −0.0657986 0.997833i \(-0.520959\pi\)
−0.0657986 + 0.997833i \(0.520959\pi\)
\(200\) 2.00000 + 2.00000i 0.141421 + 0.141421i
\(201\) −29.3205 −2.06811
\(202\) 1.07180 4.00000i 0.0754114 0.281439i
\(203\) 5.07180i 0.355970i
\(204\) −9.46410 + 16.3923i −0.662620 + 1.14769i
\(205\) 1.46410i 0.102257i
\(206\) −21.3923 5.73205i −1.49047 0.399371i
\(207\) 27.6603 1.92252
\(208\) 12.0000 6.92820i 0.832050 0.480384i
\(209\) 1.07180 0.0741377
\(210\) −2.73205 0.732051i −0.188529 0.0505163i
\(211\) 26.7846i 1.84393i 0.387275 + 0.921964i \(0.373416\pi\)
−0.387275 + 0.921964i \(0.626584\pi\)
\(212\) −11.4641 + 19.8564i −0.787358 + 1.36374i
\(213\) 14.9282i 1.02286i
\(214\) 1.00000 3.73205i 0.0683586 0.255118i
\(215\) −5.26795 −0.359271
\(216\) −8.00000 + 8.00000i −0.544331 + 0.544331i
\(217\) −4.00000 −0.271538
\(218\) 6.19615 23.1244i 0.419656 1.56618i
\(219\) 20.3923i 1.37798i
\(220\) −3.46410 2.00000i −0.233550 0.134840i
\(221\) 12.0000i 0.807207i
\(222\) −7.46410 2.00000i −0.500958 0.134231i
\(223\) −5.80385 −0.388654 −0.194327 0.980937i \(-0.562252\pi\)
−0.194327 + 0.980937i \(0.562252\pi\)
\(224\) −1.07180 4.00000i −0.0716124 0.267261i
\(225\) 4.46410 0.297607
\(226\) 17.6603 + 4.73205i 1.17474 + 0.314771i
\(227\) 10.0526i 0.667212i 0.942713 + 0.333606i \(0.108265\pi\)
−0.942713 + 0.333606i \(0.891735\pi\)
\(228\) −2.53590 1.46410i −0.167944 0.0969625i
\(229\) 4.00000i 0.264327i −0.991228 0.132164i \(-0.957808\pi\)
0.991228 0.132164i \(-0.0421925\pi\)
\(230\) 2.26795 8.46410i 0.149544 0.558106i
\(231\) 4.00000 0.263181
\(232\) 13.8564 13.8564i 0.909718 0.909718i
\(233\) −5.32051 −0.348558 −0.174279 0.984696i \(-0.555759\pi\)
−0.174279 + 0.984696i \(0.555759\pi\)
\(234\) 5.66025 21.1244i 0.370022 1.38094i
\(235\) 3.26795i 0.213177i
\(236\) 7.46410 12.9282i 0.485872 0.841554i
\(237\) 2.92820i 0.190207i
\(238\) −3.46410 0.928203i −0.224544 0.0601665i
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 5.46410 + 9.46410i 0.352706 + 0.610905i
\(241\) 16.3923 1.05592 0.527961 0.849269i \(-0.322957\pi\)
0.527961 + 0.849269i \(0.322957\pi\)
\(242\) −9.56218 2.56218i −0.614680 0.164703i
\(243\) 18.7321i 1.20166i
\(244\) 8.92820 15.4641i 0.571570 0.989988i
\(245\) 6.46410i 0.412976i
\(246\) 1.46410 5.46410i 0.0933477 0.348378i
\(247\) 1.85641 0.118120
\(248\) 10.9282 + 10.9282i 0.693942 + 0.693942i
\(249\) −3.46410 −0.219529
\(250\) 0.366025 1.36603i 0.0231495 0.0863950i
\(251\) 24.9282i 1.57345i 0.617301 + 0.786727i \(0.288226\pi\)
−0.617301 + 0.786727i \(0.711774\pi\)
\(252\) −5.66025 3.26795i −0.356562 0.205861i
\(253\) 12.3923i 0.779098i
\(254\) −22.8564 6.12436i −1.43414 0.384276i
\(255\) 9.46410 0.592665
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −2.00000 −0.124757 −0.0623783 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) −19.6603 5.26795i −1.22399 0.327968i
\(259\) 1.46410i 0.0909748i
\(260\) −6.00000 3.46410i −0.372104 0.214834i
\(261\) 30.9282i 1.91441i
\(262\) −7.26795 + 27.1244i −0.449015 + 1.67575i
\(263\) −11.6603 −0.719002 −0.359501 0.933145i \(-0.617053\pi\)
−0.359501 + 0.933145i \(0.617053\pi\)
\(264\) −10.9282 10.9282i −0.672584 0.672584i
\(265\) 11.4641 0.704234
\(266\) 0.143594 0.535898i 0.00880428 0.0328580i
\(267\) 24.3923i 1.49278i
\(268\) −10.7321 + 18.5885i −0.655564 + 1.13547i
\(269\) 8.92820i 0.544362i −0.962246 0.272181i \(-0.912255\pi\)
0.962246 0.272181i \(-0.0877450\pi\)
\(270\) 5.46410 + 1.46410i 0.332535 + 0.0891024i
\(271\) −19.3205 −1.17364 −0.586819 0.809718i \(-0.699620\pi\)
−0.586819 + 0.809718i \(0.699620\pi\)
\(272\) 6.92820 + 12.0000i 0.420084 + 0.727607i
\(273\) 6.92820 0.419314
\(274\) −6.73205 1.80385i −0.406698 0.108974i
\(275\) 2.00000i 0.120605i
\(276\) 16.9282 29.3205i 1.01896 1.76489i
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) −0.196152 + 0.732051i −0.0117644 + 0.0439055i
\(279\) 24.3923 1.46033
\(280\) −1.46410 + 1.46410i −0.0874968 + 0.0874968i
\(281\) 10.5359 0.628519 0.314260 0.949337i \(-0.398244\pi\)
0.314260 + 0.949337i \(0.398244\pi\)
\(282\) 3.26795 12.1962i 0.194604 0.726270i
\(283\) 9.66025i 0.574242i −0.957894 0.287121i \(-0.907302\pi\)
0.957894 0.287121i \(-0.0926983\pi\)
\(284\) 9.46410 + 5.46410i 0.561591 + 0.324235i
\(285\) 1.46410i 0.0867259i
\(286\) 9.46410 + 2.53590i 0.559624 + 0.149951i
\(287\) 1.07180 0.0632662
\(288\) 6.53590 + 24.3923i 0.385132 + 1.43733i
\(289\) −5.00000 −0.294118
\(290\) −9.46410 2.53590i −0.555751 0.148913i
\(291\) 39.3205i 2.30501i
\(292\) 12.9282 + 7.46410i 0.756566 + 0.436804i
\(293\) 15.8564i 0.926341i −0.886269 0.463171i \(-0.846712\pi\)
0.886269 0.463171i \(-0.153288\pi\)
\(294\) −6.46410 + 24.1244i −0.376994 + 1.40696i
\(295\) −7.46410 −0.434577
\(296\) −4.00000 + 4.00000i −0.232495 + 0.232495i
\(297\) −8.00000 −0.464207
\(298\) −2.87564 + 10.7321i −0.166582 + 0.621691i
\(299\) 21.4641i 1.24130i
\(300\) 2.73205 4.73205i 0.157735 0.273205i
\(301\) 3.85641i 0.222280i
\(302\) 16.9282 + 4.53590i 0.974109 + 0.261012i
\(303\) −8.00000 −0.459588
\(304\) −1.85641 + 1.07180i −0.106472 + 0.0614718i
\(305\) −8.92820 −0.511227
\(306\) 21.1244 + 5.66025i 1.20760 + 0.323575i
\(307\) 24.9808i 1.42573i −0.701303 0.712864i \(-0.747398\pi\)
0.701303 0.712864i \(-0.252602\pi\)
\(308\) 1.46410 2.53590i 0.0834249 0.144496i
\(309\) 42.7846i 2.43393i
\(310\) 2.00000 7.46410i 0.113592 0.423932i
\(311\) 31.3205 1.77602 0.888012 0.459821i \(-0.152086\pi\)
0.888012 + 0.459821i \(0.152086\pi\)
\(312\) −18.9282 18.9282i −1.07160 1.07160i
\(313\) −4.14359 −0.234210 −0.117105 0.993120i \(-0.537361\pi\)
−0.117105 + 0.993120i \(0.537361\pi\)
\(314\) −1.12436 + 4.19615i −0.0634511 + 0.236803i
\(315\) 3.26795i 0.184128i
\(316\) −1.85641 1.07180i −0.104431 0.0602933i
\(317\) 8.53590i 0.479424i 0.970844 + 0.239712i \(0.0770530\pi\)
−0.970844 + 0.239712i \(0.922947\pi\)
\(318\) 42.7846 + 11.4641i 2.39924 + 0.642875i
\(319\) 13.8564 0.775810
\(320\) 8.00000 0.447214
\(321\) −7.46410 −0.416606
\(322\) 6.19615 + 1.66025i 0.345298 + 0.0925223i
\(323\) 1.85641i 0.103293i
\(324\) −4.26795 2.46410i −0.237108 0.136895i
\(325\) 3.46410i 0.192154i
\(326\) −0.0717968 + 0.267949i −0.00397646 + 0.0148403i
\(327\) −46.2487 −2.55756
\(328\) −2.92820 2.92820i −0.161683 0.161683i
\(329\) 2.39230 0.131892
\(330\) −2.00000 + 7.46410i −0.110096 + 0.410885i
\(331\) 14.0000i 0.769510i −0.923019 0.384755i \(-0.874286\pi\)
0.923019 0.384755i \(-0.125714\pi\)
\(332\) −1.26795 + 2.19615i −0.0695878 + 0.120530i
\(333\) 8.92820i 0.489263i
\(334\) 13.3923 + 3.58846i 0.732794 + 0.196352i
\(335\) 10.7321 0.586355
\(336\) −6.92820 + 4.00000i −0.377964 + 0.218218i
\(337\) −19.8564 −1.08165 −0.540824 0.841136i \(-0.681887\pi\)
−0.540824 + 0.841136i \(0.681887\pi\)
\(338\) −1.36603 0.366025i −0.0743020 0.0199092i
\(339\) 35.3205i 1.91835i
\(340\) 3.46410 6.00000i 0.187867 0.325396i
\(341\) 10.9282i 0.591795i
\(342\) −0.875644 + 3.26795i −0.0473494 + 0.176710i
\(343\) −9.85641 −0.532196
\(344\) −10.5359 + 10.5359i −0.568058 + 0.568058i
\(345\) −16.9282 −0.911384
\(346\) 0.732051 2.73205i 0.0393553 0.146876i
\(347\) 1.66025i 0.0891271i −0.999007 0.0445636i \(-0.985810\pi\)
0.999007 0.0445636i \(-0.0141897\pi\)
\(348\) −32.7846 18.9282i −1.75744 1.01466i
\(349\) 28.0000i 1.49881i −0.662114 0.749403i \(-0.730341\pi\)
0.662114 0.749403i \(-0.269659\pi\)
\(350\) 1.00000 + 0.267949i 0.0534522 + 0.0143225i
\(351\) −13.8564 −0.739600
\(352\) −10.9282 + 2.92820i −0.582475 + 0.156074i
\(353\) 12.9282 0.688099 0.344049 0.938952i \(-0.388201\pi\)
0.344049 + 0.938952i \(0.388201\pi\)
\(354\) −27.8564 7.46410i −1.48055 0.396713i
\(355\) 5.46410i 0.290004i
\(356\) 15.4641 + 8.92820i 0.819596 + 0.473194i
\(357\) 6.92820i 0.366679i
\(358\) −3.12436 + 11.6603i −0.165127 + 0.616264i
\(359\) 18.9282 0.998992 0.499496 0.866316i \(-0.333518\pi\)
0.499496 + 0.866316i \(0.333518\pi\)
\(360\) 8.92820 8.92820i 0.470558 0.470558i
\(361\) 18.7128 0.984885
\(362\) 5.85641 21.8564i 0.307806 1.14875i
\(363\) 19.1244i 1.00377i
\(364\) 2.53590 4.39230i 0.132917 0.230219i
\(365\) 7.46410i 0.390689i
\(366\) −33.3205 8.92820i −1.74169 0.466685i
\(367\) 2.87564 0.150107 0.0750537 0.997179i \(-0.476087\pi\)
0.0750537 + 0.997179i \(0.476087\pi\)
\(368\) −12.3923 21.4641i −0.645994 1.11889i
\(369\) −6.53590 −0.340245
\(370\) 2.73205 + 0.732051i 0.142033 + 0.0380575i
\(371\) 8.39230i 0.435707i
\(372\) 14.9282 25.8564i 0.773991 1.34059i
\(373\) 25.7128i 1.33136i −0.746238 0.665679i \(-0.768142\pi\)
0.746238 0.665679i \(-0.231858\pi\)
\(374\) −2.53590 + 9.46410i −0.131128 + 0.489377i
\(375\) −2.73205 −0.141082
\(376\) −6.53590 6.53590i −0.337063 0.337063i
\(377\) 24.0000 1.23606
\(378\) −1.07180 + 4.00000i −0.0551273 + 0.205738i
\(379\) 36.2487i 1.86197i −0.365056 0.930986i \(-0.618950\pi\)
0.365056 0.930986i \(-0.381050\pi\)
\(380\) 0.928203 + 0.535898i 0.0476158 + 0.0274910i
\(381\) 45.7128i 2.34194i
\(382\) −20.9282 5.60770i −1.07078 0.286915i
\(383\) 21.1244 1.07940 0.539702 0.841856i \(-0.318537\pi\)
0.539702 + 0.841856i \(0.318537\pi\)
\(384\) 29.8564 + 8.00000i 1.52360 + 0.408248i
\(385\) −1.46410 −0.0746175
\(386\) −0.732051 0.196152i −0.0372604 0.00998390i
\(387\) 23.5167i 1.19542i
\(388\) −24.9282 14.3923i −1.26554 0.730659i
\(389\) 6.78461i 0.343993i 0.985098 + 0.171997i \(0.0550218\pi\)
−0.985098 + 0.171997i \(0.944978\pi\)
\(390\) −3.46410 + 12.9282i −0.175412 + 0.654645i
\(391\) −21.4641 −1.08549
\(392\) 12.9282 + 12.9282i 0.652973 + 0.652973i
\(393\) 54.2487 2.73649
\(394\) −7.12436 + 26.5885i −0.358920 + 1.33951i
\(395\) 1.07180i 0.0539279i
\(396\) −8.92820 + 15.4641i −0.448659 + 0.777100i
\(397\) 32.2487i 1.61852i 0.587453 + 0.809258i \(0.300131\pi\)
−0.587453 + 0.809258i \(0.699869\pi\)
\(398\) 2.53590 + 0.679492i 0.127113 + 0.0340599i
\(399\) −1.07180 −0.0536570
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −7.85641 −0.392330 −0.196165 0.980571i \(-0.562849\pi\)
−0.196165 + 0.980571i \(0.562849\pi\)
\(402\) 40.0526 + 10.7321i 1.99764 + 0.535266i
\(403\) 18.9282i 0.942881i
\(404\) −2.92820 + 5.07180i −0.145684 + 0.252331i
\(405\) 2.46410i 0.122442i
\(406\) 1.85641 6.92820i 0.0921319 0.343841i
\(407\) −4.00000 −0.198273
\(408\) 18.9282 18.9282i 0.937086 0.937086i
\(409\) −11.3205 −0.559763 −0.279882 0.960035i \(-0.590295\pi\)
−0.279882 + 0.960035i \(0.590295\pi\)
\(410\) −0.535898 + 2.00000i −0.0264661 + 0.0987730i
\(411\) 13.4641i 0.664135i
\(412\) 27.1244 + 15.6603i 1.33632 + 0.771525i
\(413\) 5.46410i 0.268871i
\(414\) −37.7846 10.1244i −1.85701 0.497585i
\(415\) 1.26795 0.0622412
\(416\) −18.9282 + 5.07180i −0.928032 + 0.248665i
\(417\) 1.46410 0.0716974
\(418\) −1.46410 0.392305i −0.0716116 0.0191883i
\(419\) 18.3923i 0.898523i 0.893400 + 0.449261i \(0.148313\pi\)
−0.893400 + 0.449261i \(0.851687\pi\)
\(420\) 3.46410 + 2.00000i 0.169031 + 0.0975900i
\(421\) 0.143594i 0.00699832i 0.999994 + 0.00349916i \(0.00111382\pi\)
−0.999994 + 0.00349916i \(0.998886\pi\)
\(422\) 9.80385 36.5885i 0.477244 1.78110i
\(423\) −14.5885 −0.709315
\(424\) 22.9282 22.9282i 1.11349 1.11349i
\(425\) −3.46410 −0.168034
\(426\) 5.46410 20.3923i 0.264737 0.988010i
\(427\) 6.53590i 0.316294i
\(428\) −2.73205 + 4.73205i −0.132059 + 0.228732i
\(429\) 18.9282i 0.913862i
\(430\) 7.19615 + 1.92820i 0.347029 + 0.0929862i
\(431\) −21.4641 −1.03389 −0.516945 0.856019i \(-0.672931\pi\)
−0.516945 + 0.856019i \(0.672931\pi\)
\(432\) 13.8564 8.00000i 0.666667 0.384900i
\(433\) −19.4641 −0.935385 −0.467693 0.883891i \(-0.654915\pi\)
−0.467693 + 0.883891i \(0.654915\pi\)
\(434\) 5.46410 + 1.46410i 0.262285 + 0.0702791i
\(435\) 18.9282i 0.907538i
\(436\) −16.9282 + 29.3205i −0.810714 + 1.40420i
\(437\) 3.32051i 0.158841i
\(438\) 7.46410 27.8564i 0.356649 1.33103i
\(439\) 40.7846 1.94654 0.973272 0.229657i \(-0.0737605\pi\)
0.973272 + 0.229657i \(0.0737605\pi\)
\(440\) 4.00000 + 4.00000i 0.190693 + 0.190693i
\(441\) 28.8564 1.37411
\(442\) −4.39230 + 16.3923i −0.208921 + 0.779702i
\(443\) 20.9808i 0.996826i 0.866940 + 0.498413i \(0.166084\pi\)
−0.866940 + 0.498413i \(0.833916\pi\)
\(444\) 9.46410 + 5.46410i 0.449146 + 0.259315i
\(445\) 8.92820i 0.423237i
\(446\) 7.92820 + 2.12436i 0.375411 + 0.100591i
\(447\) 21.4641 1.01522
\(448\) 5.85641i 0.276689i
\(449\) −23.3205 −1.10056 −0.550281 0.834979i \(-0.685480\pi\)
−0.550281 + 0.834979i \(0.685480\pi\)
\(450\) −6.09808 1.63397i −0.287466 0.0770263i
\(451\) 2.92820i 0.137884i
\(452\) −22.3923 12.9282i −1.05325 0.608092i
\(453\) 33.8564i 1.59071i
\(454\) 3.67949 13.7321i 0.172687 0.644477i
\(455\) −2.53590 −0.118885
\(456\) 2.92820 + 2.92820i 0.137126 + 0.137126i
\(457\) −26.7846 −1.25293 −0.626466 0.779449i \(-0.715499\pi\)
−0.626466 + 0.779449i \(0.715499\pi\)
\(458\) −1.46410 + 5.46410i −0.0684130 + 0.255321i
\(459\) 13.8564i 0.646762i
\(460\) −6.19615 + 10.7321i −0.288897 + 0.500384i
\(461\) 10.9282i 0.508977i −0.967076 0.254489i \(-0.918093\pi\)
0.967076 0.254489i \(-0.0819071\pi\)
\(462\) −5.46410 1.46410i −0.254213 0.0681162i
\(463\) −11.2679 −0.523666 −0.261833 0.965113i \(-0.584327\pi\)
−0.261833 + 0.965113i \(0.584327\pi\)
\(464\) −24.0000 + 13.8564i −1.11417 + 0.643268i
\(465\) −14.9282 −0.692279
\(466\) 7.26795 + 1.94744i 0.336681 + 0.0902135i
\(467\) 25.6603i 1.18741i −0.804681 0.593707i \(-0.797664\pi\)
0.804681 0.593707i \(-0.202336\pi\)
\(468\) −15.4641 + 26.7846i −0.714828 + 1.23812i
\(469\) 7.85641i 0.362775i
\(470\) −1.19615 + 4.46410i −0.0551744 + 0.205914i
\(471\) 8.39230 0.386697
\(472\) −14.9282 + 14.9282i −0.687126 + 0.687126i
\(473\) −10.5359 −0.484441
\(474\) −1.07180 + 4.00000i −0.0492293 + 0.183726i
\(475\) 0.535898i 0.0245887i
\(476\) 4.39230 + 2.53590i 0.201321 + 0.116233i
\(477\) 51.1769i 2.34323i
\(478\) 27.3205 + 7.32051i 1.24961 + 0.334832i
\(479\) 5.85641 0.267586 0.133793 0.991009i \(-0.457284\pi\)
0.133793 + 0.991009i \(0.457284\pi\)
\(480\) −4.00000 14.9282i −0.182574 0.681376i
\(481\) −6.92820 −0.315899
\(482\) −22.3923 6.00000i −1.01994 0.273293i
\(483\) 12.3923i 0.563869i
\(484\) 12.1244 + 7.00000i 0.551107 + 0.318182i
\(485\) 14.3923i 0.653521i
\(486\) −6.85641 + 25.5885i −0.311013 + 1.16072i
\(487\) 6.58846 0.298551 0.149276 0.988796i \(-0.452306\pi\)
0.149276 + 0.988796i \(0.452306\pi\)
\(488\) −17.8564 + 17.8564i −0.808322 + 0.808322i
\(489\) 0.535898 0.0242342
\(490\) 2.36603 8.83013i 0.106886 0.398904i
\(491\) 16.9282i 0.763959i −0.924171 0.381980i \(-0.875242\pi\)
0.924171 0.381980i \(-0.124758\pi\)
\(492\) −4.00000 + 6.92820i −0.180334 + 0.312348i
\(493\) 24.0000i 1.08091i
\(494\) −2.53590 0.679492i −0.114095 0.0305718i
\(495\) 8.92820 0.401293
\(496\) −10.9282 18.9282i −0.490691 0.849901i
\(497\) 4.00000 0.179425
\(498\) 4.73205 + 1.26795i 0.212048 + 0.0568182i
\(499\) 31.4641i 1.40853i 0.709939 + 0.704263i \(0.248723\pi\)
−0.709939 + 0.704263i \(0.751277\pi\)
\(500\) −1.00000 + 1.73205i −0.0447214 + 0.0774597i
\(501\) 26.7846i 1.19665i
\(502\) 9.12436 34.0526i 0.407240 1.51984i
\(503\) −0.339746 −0.0151485 −0.00757426 0.999971i \(-0.502411\pi\)
−0.00757426 + 0.999971i \(0.502411\pi\)
\(504\) 6.53590 + 6.53590i 0.291132 + 0.291132i
\(505\) 2.92820 0.130303
\(506\) 4.53590 16.9282i 0.201645 0.752550i
\(507\) 2.73205i 0.121335i
\(508\) 28.9808 + 16.7321i 1.28581 + 0.742365i
\(509\) 1.85641i 0.0822838i −0.999153 0.0411419i \(-0.986900\pi\)
0.999153 0.0411419i \(-0.0130996\pi\)
\(510\) −12.9282 3.46410i −0.572470 0.153393i
\(511\) 5.46410 0.241718
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 2.14359 0.0946420
\(514\) 2.73205 + 0.732051i 0.120506 + 0.0322894i
\(515\) 15.6603i 0.690073i
\(516\) 24.9282 + 14.3923i 1.09740 + 0.633586i
\(517\) 6.53590i 0.287448i
\(518\) −0.535898 + 2.00000i −0.0235460 + 0.0878750i
\(519\) −5.46410 −0.239847
\(520\) 6.92820 + 6.92820i 0.303822 + 0.303822i
\(521\) −43.8564 −1.92138 −0.960692 0.277616i \(-0.910456\pi\)
−0.960692 + 0.277616i \(0.910456\pi\)
\(522\) −11.3205 + 42.2487i −0.495485 + 1.84918i
\(523\) 11.8038i 0.516146i −0.966125 0.258073i \(-0.916912\pi\)
0.966125 0.258073i \(-0.0830875\pi\)
\(524\) 19.8564 34.3923i 0.867431 1.50243i
\(525\) 2.00000i 0.0872872i
\(526\) 15.9282 + 4.26795i 0.694503 + 0.186091i
\(527\) −18.9282 −0.824525
\(528\) 10.9282 + 18.9282i 0.475589 + 0.823744i
\(529\) 15.3923 0.669231
\(530\) −15.6603 4.19615i −0.680238 0.182269i
\(531\) 33.3205i 1.44599i
\(532\) −0.392305 + 0.679492i −0.0170086 + 0.0294597i
\(533\) 5.07180i 0.219684i
\(534\) 8.92820 33.3205i 0.386361 1.44192i
\(535\) 2.73205 0.118117
\(536\) 21.4641 21.4641i 0.927108 0.927108i
\(537\) 23.3205 1.00635
\(538\) −3.26795 + 12.1962i −0.140891 + 0.525813i
\(539\) 12.9282i 0.556857i
\(540\) −6.92820 4.00000i −0.298142 0.172133i
\(541\) 26.9282i 1.15773i −0.815422 0.578867i \(-0.803495\pi\)
0.815422 0.578867i \(-0.196505\pi\)
\(542\) 26.3923 + 7.07180i 1.13365 + 0.303760i
\(543\) −43.7128 −1.87590
\(544\) −5.07180 18.9282i −0.217451 0.811540i
\(545\) 16.9282 0.725125
\(546\) −9.46410 2.53590i −0.405026 0.108526i
\(547\) 33.2679i 1.42243i 0.702972 + 0.711217i \(0.251856\pi\)
−0.702972 + 0.711217i \(0.748144\pi\)
\(548\) 8.53590 + 4.92820i 0.364636 + 0.210522i
\(549\) 39.8564i 1.70103i
\(550\) 0.732051 2.73205i 0.0312148 0.116495i
\(551\) −3.71281 −0.158171
\(552\) −33.8564 + 33.8564i −1.44102 + 1.44102i
\(553\) −0.784610 −0.0333650
\(554\) 0.732051 2.73205i 0.0311019 0.116074i
\(555\) 5.46410i 0.231938i
\(556\) 0.535898 0.928203i 0.0227272 0.0393646i
\(557\) 14.7846i 0.626444i 0.949680 + 0.313222i \(0.101408\pi\)
−0.949680 + 0.313222i \(0.898592\pi\)
\(558\) −33.3205 8.92820i −1.41057 0.377961i
\(559\) −18.2487 −0.771838
\(560\) 2.53590 1.46410i 0.107161 0.0618696i
\(561\) 18.9282 0.799149
\(562\) −14.3923 3.85641i −0.607103 0.162673i
\(563\) 22.0526i 0.929405i −0.885467 0.464702i \(-0.846161\pi\)
0.885467 0.464702i \(-0.153839\pi\)
\(564\) −8.92820 + 15.4641i −0.375945 + 0.651156i
\(565\) 12.9282i 0.543894i
\(566\) −3.53590 + 13.1962i −0.148625 + 0.554676i
\(567\) −1.80385 −0.0757545
\(568\) −10.9282 10.9282i −0.458537 0.458537i
\(569\) −13.4641 −0.564445 −0.282222 0.959349i \(-0.591072\pi\)
−0.282222 + 0.959349i \(0.591072\pi\)
\(570\) 0.535898 2.00000i 0.0224463 0.0837708i
\(571\) 6.78461i 0.283927i 0.989872 + 0.141964i \(0.0453416\pi\)
−0.989872 + 0.141964i \(0.954658\pi\)
\(572\) −12.0000 6.92820i −0.501745 0.289683i
\(573\) 41.8564i 1.74858i
\(574\) −1.46410 0.392305i −0.0611104 0.0163745i
\(575\) 6.19615 0.258397
\(576\) 35.7128i 1.48803i
\(577\) 39.5692 1.64729 0.823644 0.567107i \(-0.191937\pi\)
0.823644 + 0.567107i \(0.191937\pi\)
\(578\) 6.83013 + 1.83013i 0.284096 + 0.0761232i
\(579\) 1.46410i 0.0608460i
\(580\) 12.0000 + 6.92820i 0.498273 + 0.287678i
\(581\) 0.928203i 0.0385084i
\(582\) −14.3923 + 53.7128i −0.596580 + 2.22647i
\(583\) 22.9282 0.949589
\(584\) −14.9282 14.9282i −0.617733 0.617733i
\(585\) 15.4641 0.639362
\(586\) −5.80385 + 21.6603i −0.239755 + 0.894777i
\(587\) 3.80385i 0.157002i −0.996914 0.0785008i \(-0.974987\pi\)
0.996914 0.0785008i \(-0.0250133\pi\)
\(588\) 17.6603 30.5885i 0.728297 1.26145i
\(589\) 2.92820i 0.120655i
\(590\) 10.1962 + 2.73205i 0.419769 + 0.112477i
\(591\) 53.1769 2.18741
\(592\) 6.92820 4.00000i 0.284747 0.164399i
\(593\) 32.6410 1.34041 0.670203 0.742178i \(-0.266207\pi\)
0.670203 + 0.742178i \(0.266207\pi\)
\(594\) 10.9282 + 2.92820i 0.448390 + 0.120146i
\(595\) 2.53590i 0.103962i
\(596\) 7.85641 13.6077i 0.321811 0.557393i
\(597\) 5.07180i 0.207575i
\(598\) 7.85641 29.3205i 0.321272 1.19900i
\(599\) −34.6410 −1.41539 −0.707697 0.706516i \(-0.750266\pi\)
−0.707697 + 0.706516i \(0.750266\pi\)
\(600\) −5.46410 + 5.46410i −0.223071 + 0.223071i
\(601\) 18.5359 0.756095 0.378048 0.925786i \(-0.376596\pi\)
0.378048 + 0.925786i \(0.376596\pi\)
\(602\) −1.41154 + 5.26795i −0.0575302 + 0.214706i
\(603\) 47.9090i 1.95100i
\(604\) −21.4641 12.3923i −0.873362 0.504236i
\(605\) 7.00000i 0.284590i
\(606\) 10.9282 + 2.92820i 0.443928 + 0.118950i
\(607\) 30.9808 1.25747 0.628735 0.777619i \(-0.283573\pi\)
0.628735 + 0.777619i \(0.283573\pi\)
\(608\) 2.92820 0.784610i 0.118754 0.0318201i
\(609\) −13.8564 −0.561490
\(610\) 12.1962 + 3.26795i 0.493808 + 0.132315i
\(611\) 11.3205i 0.457979i
\(612\) −26.7846 15.4641i −1.08270 0.625099i
\(613\) 26.3923i 1.06598i 0.846123 + 0.532988i \(0.178931\pi\)
−0.846123 + 0.532988i \(0.821069\pi\)
\(614\) −9.14359 + 34.1244i −0.369005 + 1.37715i
\(615\) 4.00000 0.161296
\(616\) −2.92820 + 2.92820i −0.117981 + 0.117981i
\(617\) −20.5359 −0.826744 −0.413372 0.910562i \(-0.635649\pi\)
−0.413372 + 0.910562i \(0.635649\pi\)
\(618\) 15.6603 58.4449i 0.629948 2.35100i
\(619\) 1.32051i 0.0530757i 0.999648 + 0.0265379i \(0.00844825\pi\)
−0.999648 + 0.0265379i \(0.991552\pi\)
\(620\) −5.46410 + 9.46410i −0.219444 + 0.380087i
\(621\) 24.7846i 0.994572i
\(622\) −42.7846 11.4641i −1.71551 0.459669i
\(623\) 6.53590 0.261855
\(624\) 18.9282 + 32.7846i 0.757735 + 1.31243i
\(625\) 1.00000 0.0400000
\(626\) 5.66025 + 1.51666i 0.226229 + 0.0606179i
\(627\) 2.92820i 0.116941i
\(628\) 3.07180 5.32051i 0.122578 0.212311i
\(629\) 6.92820i 0.276246i
\(630\) 1.19615 4.46410i 0.0476559 0.177854i
\(631\) −23.3205 −0.928375 −0.464187 0.885737i \(-0.653654\pi\)
−0.464187 + 0.885737i \(0.653654\pi\)
\(632\) 2.14359 + 2.14359i 0.0852676 + 0.0852676i
\(633\) −73.1769 −2.90852
\(634\) 3.12436 11.6603i 0.124084 0.463088i
\(635\) 16.7321i 0.663991i
\(636\) −54.2487 31.3205i −2.15110 1.24194i
\(637\) 22.3923i 0.887215i
\(638\) −18.9282 5.07180i −0.749375 0.200794i
\(639\) −24.3923 −0.964945
\(640\) −10.9282 2.92820i −0.431975 0.115747i
\(641\) 0.392305 0.0154951 0.00774755 0.999970i \(-0.497534\pi\)
0.00774755 + 0.999970i \(0.497534\pi\)
\(642\) 10.1962 + 2.73205i 0.402410 + 0.107825i
\(643\) 39.1244i 1.54291i 0.636281 + 0.771457i \(0.280472\pi\)
−0.636281 + 0.771457i \(0.719528\pi\)
\(644\) −7.85641 4.53590i −0.309586 0.178739i
\(645\) 14.3923i 0.566696i
\(646\) 0.679492 2.53590i 0.0267343 0.0997736i
\(647\) 16.7321 0.657805 0.328902 0.944364i \(-0.393321\pi\)
0.328902 + 0.944364i \(0.393321\pi\)
\(648\) 4.92820 + 4.92820i 0.193598 + 0.193598i
\(649\) −14.9282 −0.585983
\(650\) 1.26795 4.73205i 0.0497331 0.185606i
\(651\) 10.9282i 0.428310i
\(652\) 0.196152 0.339746i 0.00768192 0.0133055i
\(653\) 12.2487i 0.479329i 0.970856 + 0.239665i \(0.0770375\pi\)
−0.970856 + 0.239665i \(0.922963\pi\)
\(654\) 63.1769 + 16.9282i 2.47041 + 0.661945i
\(655\) −19.8564 −0.775854
\(656\) 2.92820 + 5.07180i 0.114327 + 0.198020i
\(657\) −33.3205 −1.29996
\(658\) −3.26795 0.875644i −0.127398 0.0341362i
\(659\) 17.3205i 0.674711i −0.941377 0.337356i \(-0.890468\pi\)
0.941377 0.337356i \(-0.109532\pi\)
\(660\) 5.46410 9.46410i 0.212690 0.368390i
\(661\) 8.14359i 0.316749i −0.987379 0.158375i \(-0.949375\pi\)
0.987379 0.158375i \(-0.0506253\pi\)
\(662\) −5.12436 + 19.1244i −0.199164 + 0.743289i
\(663\) 32.7846 1.27325
\(664\) 2.53590 2.53590i 0.0984119 0.0984119i
\(665\) 0.392305 0.0152129
\(666\) 3.26795 12.1962i 0.126630 0.472591i
\(667\) 42.9282i 1.66219i
\(668\) −16.9808 9.80385i −0.657005 0.379322i
\(669\) 15.8564i 0.613044i
\(670\) −14.6603 3.92820i −0.566375 0.151760i
\(671\) −17.8564 −0.689339
\(672\) 10.9282 2.92820i 0.421565 0.112958i
\(673\) 12.5359 0.483223 0.241612 0.970373i \(-0.422324\pi\)
0.241612 + 0.970373i \(0.422324\pi\)
\(674\) 27.1244 + 7.26795i 1.04479 + 0.279951i
\(675\) 4.00000i 0.153960i
\(676\) 1.73205 + 1.00000i 0.0666173 + 0.0384615i
\(677\) 17.6077i 0.676719i 0.941017 + 0.338359i \(0.109872\pi\)
−0.941017 + 0.338359i \(0.890128\pi\)
\(678\) −12.9282 + 48.2487i −0.496505 + 1.85298i
\(679\) −10.5359 −0.404331
\(680\) −6.92820 + 6.92820i −0.265684 + 0.265684i
\(681\) −27.4641 −1.05243
\(682\) 4.00000 14.9282i 0.153168 0.571630i
\(683\) 16.9808i 0.649751i −0.945757 0.324875i \(-0.894678\pi\)
0.945757 0.324875i \(-0.105322\pi\)
\(684\) 2.39230 4.14359i 0.0914721 0.158434i
\(685\) 4.92820i 0.188297i
\(686\) 13.4641 + 3.60770i 0.514062 + 0.137742i
\(687\) 10.9282 0.416937
\(688\) 18.2487 10.5359i 0.695726 0.401677i
\(689\) 39.7128 1.51294
\(690\) 23.1244 + 6.19615i 0.880329 + 0.235883i
\(691\) 18.0000i 0.684752i 0.939563 + 0.342376i \(0.111232\pi\)
−0.939563 + 0.342376i \(0.888768\pi\)
\(692\) −2.00000 + 3.46410i −0.0760286 + 0.131685i
\(693\) 6.53590i 0.248278i
\(694\) −0.607695 + 2.26795i −0.0230678 + 0.0860902i
\(695\) −0.535898 −0.0203278
\(696\) 37.8564 + 37.8564i 1.43494 + 1.43494i
\(697\) 5.07180 0.192108
\(698\) −10.2487 + 38.2487i −0.387919 + 1.44774i
\(699\) 14.5359i 0.549798i
\(700\) −1.26795 0.732051i −0.0479240 0.0276689i
\(701\) 19.0718i 0.720332i 0.932888 + 0.360166i \(0.117280\pi\)
−0.932888 + 0.360166i \(0.882720\pi\)
\(702\) 18.9282 + 5.07180i 0.714399 + 0.191423i
\(703\) 1.07180 0.0404236
\(704\) 16.0000 0.603023
\(705\) 8.92820 0.336256
\(706\) −17.6603 4.73205i −0.664652 0.178093i
\(707\) 2.14359i 0.0806181i
\(708\) 35.3205 + 20.3923i 1.32743 + 0.766390i
\(709\) 12.7846i 0.480136i −0.970756 0.240068i \(-0.922830\pi\)
0.970756 0.240068i \(-0.0771698\pi\)
\(710\) −2.00000 + 7.46410i −0.0750587 + 0.280123i
\(711\) 4.78461 0.179437
\(712\) −17.8564 17.8564i −0.669197 0.669197i
\(713\) 33.8564 1.26793
\(714\) 2.53590 9.46410i 0.0949036 0.354185i
\(715\) 6.92820i 0.259100i
\(716\) 8.53590 14.7846i 0.319002 0.552527i
\(717\) 54.6410i 2.04061i
\(718\) −25.8564 6.92820i −0.964953 0.258558i
\(719\) −1.85641 −0.0692323 −0.0346161 0.999401i \(-0.511021\pi\)
−0.0346161 + 0.999401i \(0.511021\pi\)
\(720\) −15.4641 + 8.92820i −0.576313 + 0.332734i
\(721\) 11.4641 0.426945
\(722\) −25.5622 6.84936i −0.951326 0.254907i
\(723\) 44.7846i 1.66556i
\(724\) −16.0000 + 27.7128i −0.594635 + 1.02994i
\(725\) 6.92820i 0.257307i
\(726\) 7.00000 26.1244i 0.259794 0.969566i
\(727\) −24.0526 −0.892060 −0.446030 0.895018i \(-0.647163\pi\)
−0.446030 + 0.895018i \(0.647163\pi\)
\(728\) −5.07180 + 5.07180i −0.187973 + 0.187973i
\(729\) 43.7846 1.62165
\(730\) −2.73205 + 10.1962i −0.101118 + 0.377377i
\(731\) 18.2487i 0.674953i
\(732\) 42.2487 + 24.3923i 1.56156 + 0.901566i
\(733\) 35.0718i 1.29541i −0.761893 0.647703i \(-0.775730\pi\)
0.761893 0.647703i \(-0.224270\pi\)
\(734\) −3.92820 1.05256i −0.144993 0.0388507i
\(735\) −17.6603 −0.651408
\(736\) 9.07180 + 33.8564i 0.334391 + 1.24796i
\(737\) 21.4641 0.790640
\(738\) 8.92820 + 2.39230i 0.328652 + 0.0880620i
\(739\) 29.3205i 1.07857i 0.842123 + 0.539286i \(0.181306\pi\)
−0.842123 + 0.539286i \(0.818694\pi\)
\(740\) −3.46410 2.00000i −0.127343 0.0735215i
\(741\) 5.07180i 0.186317i
\(742\) 3.07180 11.4641i 0.112769 0.420860i
\(743\) 10.9808 0.402845 0.201423 0.979504i \(-0.435444\pi\)
0.201423 + 0.979504i \(0.435444\pi\)
\(744\) −29.8564 + 29.8564i −1.09459 + 1.09459i
\(745\) −7.85641 −0.287836
\(746\) −9.41154 + 35.1244i −0.344581 + 1.28599i
\(747\) 5.66025i 0.207098i
\(748\) 6.92820 12.0000i 0.253320 0.438763i
\(749\) 2.00000i 0.0730784i
\(750\) 3.73205 + 1.00000i 0.136275 + 0.0365148i
\(751\) 26.2487 0.957829 0.478915 0.877862i \(-0.341030\pi\)
0.478915 + 0.877862i \(0.341030\pi\)
\(752\) 6.53590 + 11.3205i 0.238340 + 0.412816i
\(753\) −68.1051 −2.48189
\(754\) −32.7846 8.78461i −1.19395 0.319917i
\(755\) 12.3923i 0.451002i
\(756\) 2.92820 5.07180i 0.106498 0.184459i
\(757\) 19.0718i 0.693176i −0.938017 0.346588i \(-0.887340\pi\)
0.938017 0.346588i \(-0.112660\pi\)
\(758\) −13.2679 + 49.5167i −0.481914 + 1.79853i
\(759\) −33.8564 −1.22891
\(760\) −1.07180 1.07180i −0.0388782 0.0388782i
\(761\) −5.71281 −0.207089 −0.103545 0.994625i \(-0.533018\pi\)
−0.103545 + 0.994625i \(0.533018\pi\)
\(762\) 16.7321 62.4449i 0.606138 2.26214i
\(763\) 12.3923i 0.448632i
\(764\) 26.5359 + 15.3205i 0.960035 + 0.554277i
\(765\) 15.4641i 0.559106i
\(766\) −28.8564 7.73205i −1.04262 0.279370i
\(767\) −25.8564 −0.933621
\(768\) −37.8564 21.8564i −1.36603 0.788675i
\(769\) 12.9282 0.466203 0.233101 0.972452i \(-0.425113\pi\)
0.233101 + 0.972452i \(0.425113\pi\)
\(770\) 2.00000 + 0.535898i 0.0720750 + 0.0193124i
\(771\) 5.46410i 0.196785i
\(772\) 0.928203 + 0.535898i 0.0334068 + 0.0192874i
\(773\) 22.3923i 0.805395i −0.915333 0.402698i \(-0.868073\pi\)
0.915333 0.402698i \(-0.131927\pi\)
\(774\) 8.60770 32.1244i 0.309397 1.15469i
\(775\) 5.46410 0.196276
\(776\) 28.7846 + 28.7846i 1.03331 + 1.03331i
\(777\) 4.00000 0.143499
\(778\) 2.48334 9.26795i 0.0890320 0.332272i
\(779\) 0.784610i 0.0281116i
\(780\) 9.46410 16.3923i 0.338869 0.586939i
\(781\) 10.9282i 0.391042i
\(782\) 29.3205 + 7.85641i 1.04850 + 0.280945i
\(783\) 27.7128 0.990375
\(784\) −12.9282 22.3923i −0.461722 0.799725i
\(785\) −3.07180 −0.109637
\(786\) −74.1051 19.8564i −2.64324 0.708255i
\(787\) 16.5885i 0.591315i 0.955294 + 0.295657i \(0.0955387\pi\)
−0.955294 + 0.295657i \(0.904461\pi\)
\(788\) 19.4641 33.7128i 0.693380 1.20097i
\(789\) 31.8564i 1.13412i
\(790\) 0.392305 1.46410i 0.0139576 0.0520904i
\(791\) −9.46410 −0.336505
\(792\) 17.8564 17.8564i 0.634500 0.634500i
\(793\) −30.9282 −1.09829
\(794\) 11.8038 44.0526i 0.418903 1.56337i
\(795\) 31.3205i 1.11082i
\(796\) −3.21539 1.85641i −0.113966 0.0657986i
\(797\) 50.1051i 1.77481i 0.460986 + 0.887407i \(0.347496\pi\)
−0.460986 + 0.887407i \(0.652504\pi\)
\(798\) 1.46410 + 0.392305i 0.0518286 + 0.0138874i
\(799\) 11.3205 0.400491
\(800\) 1.46410 + 5.46410i 0.0517638 + 0.193185i
\(801\) −39.8564 −1.40826
\(802\) 10.7321 + 2.87564i 0.378962 + 0.101543i
\(803\) 14.9282i 0.526805i
\(804\) −50.7846 29.3205i −1.79104 1.03405i
\(805\) 4.53590i 0.159869i
\(806\) 6.92820 25.8564i 0.244036 0.910753i
\(807\) 24.3923 0.858650
\(808\) 5.85641 5.85641i 0.206028 0.206028i
\(809\) 23.8564 0.838747 0.419373 0.907814i \(-0.362250\pi\)
0.419373 + 0.907814i \(0.362250\pi\)
\(810\) 0.901924 3.36603i 0.0316904 0.118270i
\(811\) 28.9282i 1.01581i −0.861414 0.507903i \(-0.830421\pi\)
0.861414 0.507903i \(-0.169579\pi\)
\(812\) −5.07180 + 8.78461i −0.177985 + 0.308279i
\(813\) 52.7846i 1.85124i
\(814\) 5.46410 + 1.46410i 0.191517 + 0.0513167i
\(815\) −0.196152 −0.00687092
\(816\) −32.7846 + 18.9282i −1.14769 + 0.662620i
\(817\) 2.82309 0.0987673
\(818\) 15.4641 + 4.14359i 0.540690 + 0.144877i
\(819\) 11.3205i 0.395571i
\(820\) 1.46410 2.53590i 0.0511286 0.0885574i
\(821\) 34.7846i 1.21399i 0.794705 + 0.606996i \(0.207625\pi\)
−0.794705 + 0.606996i \(0.792375\pi\)
\(822\) 4.92820 18.3923i 0.171891 0.641505i
\(823\) −9.12436 −0.318055 −0.159028 0.987274i \(-0.550836\pi\)
−0.159028 + 0.987274i \(0.550836\pi\)
\(824\) −31.3205 31.3205i −1.09110 1.09110i
\(825\) −5.46410 −0.190236
\(826\) −2.00000 + 7.46410i −0.0695889 + 0.259709i
\(827\) 23.1244i 0.804113i 0.915615 + 0.402056i \(0.131704\pi\)
−0.915615 + 0.402056i \(0.868296\pi\)
\(828\) 47.9090 + 27.6603i 1.66495 + 0.961260i
\(829\) 28.9282i 1.00472i 0.864659 + 0.502359i \(0.167534\pi\)
−0.864659 + 0.502359i \(0.832466\pi\)
\(830\) −1.73205 0.464102i −0.0601204 0.0161092i
\(831\) −5.46410 −0.189548
\(832\) 27.7128 0.960769
\(833\) −22.3923 −0.775847
\(834\) −2.00000 0.535898i −0.0692543 0.0185566i
\(835\) 9.80385i 0.339276i
\(836\) 1.85641 + 1.07180i 0.0642052 + 0.0370689i
\(837\) 21.8564i 0.755468i
\(838\) 6.73205 25.1244i 0.232555 0.867906i
\(839\) 24.7846 0.855660 0.427830 0.903859i \(-0.359278\pi\)
0.427830 + 0.903859i \(0.359278\pi\)
\(840\) −4.00000 4.00000i −0.138013 0.138013i
\(841\) −19.0000 −0.655172
\(842\) 0.0525589 0.196152i 0.00181130 0.00675986i
\(843\) 28.7846i 0.991395i
\(844\) −26.7846 + 46.3923i −0.921964 + 1.59689i
\(845\) 1.00000i 0.0344010i
\(846\) 19.9282 + 5.33975i 0.685146 + 0.183584i
\(847\) 5.12436 0.176075
\(848\) −39.7128 + 22.9282i −1.36374 + 0.787358i
\(849\) 26.3923 0.905782
\(850\) 4.73205 + 1.26795i 0.162308 + 0.0434903i
\(851\) 12.3923i 0.424803i
\(852\) −14.9282 + 25.8564i −0.511432 + 0.885826i
\(853\) 21.6077i 0.739833i −0.929065 0.369917i \(-0.879386\pi\)
0.929065 0.369917i \(-0.120614\pi\)
\(854\) −2.39230 + 8.92820i −0.0818630 + 0.305517i
\(855\) −2.39230 −0.0818151
\(856\) 5.46410 5.46410i 0.186759 0.186759i
\(857\) −19.8564 −0.678282 −0.339141 0.940736i \(-0.610136\pi\)
−0.339141 + 0.940736i \(0.610136\pi\)
\(858\) −6.92820 + 25.8564i −0.236525 + 0.882723i
\(859\) 28.2487i 0.963834i 0.876217 + 0.481917i \(0.160059\pi\)
−0.876217 + 0.481917i \(0.839941\pi\)
\(860\) −9.12436 5.26795i −0.311138 0.179636i
\(861\) 2.92820i 0.0997929i
\(862\) 29.3205 + 7.85641i 0.998660 + 0.267590i
\(863\) 47.6603 1.62237 0.811187 0.584787i \(-0.198822\pi\)
0.811187 + 0.584787i \(0.198822\pi\)
\(864\) −21.8564 + 5.85641i −0.743570 + 0.199239i
\(865\) 2.00000 0.0680020
\(866\) 26.5885 + 7.12436i 0.903513 + 0.242095i
\(867\) 13.6603i 0.463927i
\(868\) −6.92820 4.00000i −0.235159 0.135769i
\(869\) 2.14359i 0.0727164i
\(870\) 6.92820 25.8564i 0.234888 0.876614i
\(871\) 37.1769 1.25969
\(872\) 33.8564 33.8564i 1.14652 1.14652i
\(873\) 64.2487 2.17449
\(874\) −1.21539 + 4.53590i −0.0411112 + 0.153429i
\(875\) 0.732051i 0.0247478i
\(876\) −20.3923 + 35.3205i −0.688992 + 1.19337i
\(877\) 1.71281i 0.0578376i −0.999582 0.0289188i \(-0.990794\pi\)
0.999582 0.0289188i \(-0.00920642\pi\)
\(878\) −55.7128 14.9282i −1.88022 0.503802i
\(879\) 43.3205 1.46116
\(880\) −4.00000 6.92820i −0.134840 0.233550i
\(881\) 9.46410 0.318854 0.159427 0.987210i \(-0.449035\pi\)
0.159427 + 0.987210i \(0.449035\pi\)
\(882\) −39.4186 10.5622i −1.32729 0.355647i
\(883\) 27.9090i 0.939211i −0.882876 0.469606i \(-0.844396\pi\)
0.882876 0.469606i \(-0.155604\pi\)
\(884\) 12.0000 20.7846i 0.403604 0.699062i
\(885\) 20.3923i 0.685480i
\(886\) 7.67949 28.6603i 0.257998 0.962860i
\(887\) −13.9090 −0.467017 −0.233509 0.972355i \(-0.575021\pi\)
−0.233509 + 0.972355i \(0.575021\pi\)
\(888\) −10.9282 10.9282i −0.366726 0.366726i
\(889\) 12.2487 0.410809
\(890\) −3.26795 + 12.1962i −0.109542 + 0.408816i
\(891\) 4.92820i 0.165101i
\(892\) −10.0526 5.80385i −0.336585 0.194327i
\(893\) 1.75129i 0.0586046i
\(894\) −29.3205 7.85641i −0.980624 0.262758i
\(895\) −8.53590 −0.285324
\(896\) 2.14359 8.00000i 0.0716124 0.267261i
\(897\) −58.6410 −1.95797
\(898\) 31.8564 + 8.53590i 1.06306 + 0.284847i
\(899\) 37.8564i 1.26258i
\(900\) 7.73205 + 4.46410i 0.257735 + 0.148803i
\(901\) 39.7128i 1.32303i
\(902\) −1.07180 + 4.00000i −0.0356869 + 0.133185i
\(903\) 10.5359 0.350613
\(904\) 25.8564 + 25.8564i 0.859971 + 0.859971i
\(905\) 16.0000 0.531858
\(906\) −12.3923 + 46.2487i −0.411707 + 1.53651i
\(907\) 4.87564i 0.161893i 0.996718 + 0.0809466i \(0.0257943\pi\)
−0.996718 + 0.0809466i \(0.974206\pi\)
\(908\) −10.0526 + 17.4115i −0.333606 + 0.577822i
\(909\) 13.0718i 0.433564i
\(910\) 3.46410 + 0.928203i 0.114834 + 0.0307696i
\(911\) −49.1769 −1.62930 −0.814652 0.579950i \(-0.803072\pi\)
−0.814652 + 0.579950i \(0.803072\pi\)
\(912\) −2.92820 5.07180i −0.0969625 0.167944i
\(913\) 2.53590 0.0839260
\(914\) 36.5885 + 9.80385i 1.21024 + 0.324282i
\(915\) 24.3923i 0.806385i
\(916\) 4.00000 6.92820i 0.132164 0.228914i
\(917\) 14.5359i 0.480018i
\(918\) −5.07180 + 18.9282i −0.167394 + 0.624724i
\(919\) −38.9282 −1.28412 −0.642061 0.766653i \(-0.721921\pi\)
−0.642061 + 0.766653i \(0.721921\pi\)
\(920\) 12.3923 12.3923i 0.408562 0.408562i
\(921\) 68.2487 2.24887
\(922\) −4.00000 + 14.9282i −0.131733 + 0.491634i
\(923\) 18.9282i 0.623029i
\(924\) 6.92820 + 4.00000i 0.227921 + 0.131590i
\(925\) 2.00000i 0.0657596i
\(926\) 15.3923 + 4.12436i 0.505823 + 0.135535i
\(927\) −69.9090 −2.29611
\(928\) 37.8564 10.1436i 1.24270 0.332980i
\(929\) −17.4641 −0.572979 −0.286489 0.958083i \(-0.592488\pi\)
−0.286489 + 0.958083i \(0.592488\pi\)
\(930\) 20.3923 + 5.46410i 0.668690 + 0.179175i
\(931\) 3.46410i 0.113531i
\(932\) −9.21539 5.32051i −0.301860 0.174279i
\(933\) 85.5692i 2.80141i
\(934\) −9.39230 + 35.0526i −0.307326 + 1.14695i
\(935\) −6.92820 −0.226576
\(936\) 30.9282 30.9282i 1.01092 1.01092i
\(937\) 4.24871 0.138799 0.0693997 0.997589i \(-0.477892\pi\)
0.0693997 + 0.997589i \(0.477892\pi\)
\(938\) 2.87564 10.7321i 0.0938931 0.350414i
\(939\) 11.3205i 0.369431i
\(940\) 3.26795 5.66025i 0.106589 0.184617i
\(941\) 32.0000i 1.04317i −0.853199 0.521585i \(-0.825341\pi\)
0.853199 0.521585i \(-0.174659\pi\)
\(942\) −11.4641 3.07180i −0.373521 0.100085i
\(943\) −9.07180 −0.295418
\(944\) 25.8564 14.9282i 0.841554 0.485872i
\(945\) −2.92820 −0.0952545
\(946\) 14.3923 + 3.85641i 0.467934 + 0.125383i
\(947\) 3.12436i 0.101528i −0.998711 0.0507640i \(-0.983834\pi\)
0.998711 0.0507640i \(-0.0161656\pi\)
\(948\) 2.92820 5.07180i 0.0951036 0.164724i
\(949\) 25.8564i 0.839334i
\(950\) −0.196152 + 0.732051i −0.00636402 + 0.0237509i
\(951\) −23.3205 −0.756219
\(952\) −5.07180 5.07180i −0.164378 0.164378i
\(953\) −17.2154 −0.557661 −0.278831 0.960340i \(-0.589947\pi\)
−0.278831 + 0.960340i \(0.589947\pi\)
\(954\) −18.7321 + 69.9090i −0.606473 + 2.26339i
\(955\) 15.3205i 0.495760i
\(956\) −34.6410 20.0000i −1.12037 0.646846i
\(957\) 37.8564i 1.22372i
\(958\) −8.00000 2.14359i −0.258468 0.0692564i
\(959\) 3.60770 0.116499
\(960\) 21.8564i 0.705412i
\(961\) −1.14359 −0.0368901
\(962\) 9.46410 + 2.53590i 0.305135 + 0.0817606i
\(963\) 12.1962i 0.393016i
\(964\) 28.3923 + 16.3923i 0.914455 + 0.527961i
\(965\) 0.535898i 0.0172512i
\(966\) −4.53590 + 16.9282i −0.145940 + 0.544656i
\(967\) 16.3397 0.525451 0.262725 0.964871i \(-0.415379\pi\)
0.262725 + 0.964871i \(0.415379\pi\)
\(968\) −14.0000 14.0000i −0.449977 0.449977i
\(969\) −5.07180 −0.162930
\(970\) 5.26795 19.6603i 0.169144 0.631253i
\(971\) 36.9282i 1.18508i 0.805540 + 0.592541i \(0.201875\pi\)
−0.805540 + 0.592541i \(0.798125\pi\)
\(972\) 18.7321 32.4449i 0.600831 1.04067i
\(973\) 0.392305i 0.0125767i
\(974\) −9.00000 2.41154i −0.288379 0.0772708i
\(975\) −9.46410 −0.303094
\(976\) 30.9282 17.8564i 0.989988 0.571570i
\(977\) −24.5359 −0.784973 −0.392486 0.919758i \(-0.628385\pi\)
−0.392486 + 0.919758i \(0.628385\pi\)
\(978\) −0.732051 0.196152i −0.0234084 0.00627226i
\(979\) 17.8564i 0.570693i
\(980\) −6.46410 + 11.1962i −0.206488 + 0.357648i
\(981\) 75.5692i 2.41274i
\(982\) −6.19615 + 23.1244i −0.197727 + 0.737928i
\(983\) −48.7321 −1.55431 −0.777156 0.629309i \(-0.783338\pi\)
−0.777156 + 0.629309i \(0.783338\pi\)
\(984\) 8.00000 8.00000i 0.255031 0.255031i
\(985\) −19.4641 −0.620178
\(986\) 8.78461 32.7846i 0.279759 1.04407i
\(987\) 6.53590i 0.208040i
\(988\) 3.21539 + 1.85641i 0.102295 + 0.0590602i
\(989\) 32.6410i 1.03792i
\(990\) −12.1962 3.26795i −0.387619 0.103862i
\(991\) 41.4641 1.31715 0.658575 0.752515i \(-0.271159\pi\)
0.658575 + 0.752515i \(0.271159\pi\)
\(992\) 8.00000 + 29.8564i 0.254000 + 0.947942i
\(993\) 38.2487 1.21379
\(994\) −5.46410 1.46410i −0.173311 0.0464385i
\(995\) 1.85641i 0.0588520i
\(996\) −6.00000 3.46410i −0.190117 0.109764i
\(997\) 11.1769i 0.353976i −0.984213 0.176988i \(-0.943365\pi\)
0.984213 0.176988i \(-0.0566354\pi\)
\(998\) 11.5167 42.9808i 0.364554 1.36053i
\(999\) −8.00000 −0.253109
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 40.2.d.a.21.1 4
3.2 odd 2 360.2.k.e.181.4 4
4.3 odd 2 160.2.d.a.81.1 4
5.2 odd 4 200.2.f.c.149.3 4
5.3 odd 4 200.2.f.e.149.2 4
5.4 even 2 200.2.d.f.101.4 4
8.3 odd 2 160.2.d.a.81.4 4
8.5 even 2 inner 40.2.d.a.21.2 yes 4
12.11 even 2 1440.2.k.e.721.3 4
15.2 even 4 1800.2.d.p.1549.2 4
15.8 even 4 1800.2.d.l.1549.3 4
15.14 odd 2 1800.2.k.j.901.1 4
16.3 odd 4 1280.2.a.n.1.2 2
16.5 even 4 1280.2.a.o.1.2 2
16.11 odd 4 1280.2.a.d.1.1 2
16.13 even 4 1280.2.a.a.1.1 2
20.3 even 4 800.2.f.e.49.4 4
20.7 even 4 800.2.f.c.49.1 4
20.19 odd 2 800.2.d.e.401.4 4
24.5 odd 2 360.2.k.e.181.3 4
24.11 even 2 1440.2.k.e.721.1 4
40.3 even 4 800.2.f.c.49.2 4
40.13 odd 4 200.2.f.c.149.4 4
40.19 odd 2 800.2.d.e.401.1 4
40.27 even 4 800.2.f.e.49.3 4
40.29 even 2 200.2.d.f.101.3 4
40.37 odd 4 200.2.f.e.149.1 4
60.23 odd 4 7200.2.d.n.2449.3 4
60.47 odd 4 7200.2.d.o.2449.2 4
60.59 even 2 7200.2.k.j.3601.3 4
80.19 odd 4 6400.2.a.be.1.1 2
80.29 even 4 6400.2.a.ce.1.2 2
80.59 odd 4 6400.2.a.cj.1.2 2
80.69 even 4 6400.2.a.z.1.1 2
120.29 odd 2 1800.2.k.j.901.2 4
120.53 even 4 1800.2.d.p.1549.1 4
120.59 even 2 7200.2.k.j.3601.4 4
120.77 even 4 1800.2.d.l.1549.4 4
120.83 odd 4 7200.2.d.o.2449.3 4
120.107 odd 4 7200.2.d.n.2449.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.2.d.a.21.1 4 1.1 even 1 trivial
40.2.d.a.21.2 yes 4 8.5 even 2 inner
160.2.d.a.81.1 4 4.3 odd 2
160.2.d.a.81.4 4 8.3 odd 2
200.2.d.f.101.3 4 40.29 even 2
200.2.d.f.101.4 4 5.4 even 2
200.2.f.c.149.3 4 5.2 odd 4
200.2.f.c.149.4 4 40.13 odd 4
200.2.f.e.149.1 4 40.37 odd 4
200.2.f.e.149.2 4 5.3 odd 4
360.2.k.e.181.3 4 24.5 odd 2
360.2.k.e.181.4 4 3.2 odd 2
800.2.d.e.401.1 4 40.19 odd 2
800.2.d.e.401.4 4 20.19 odd 2
800.2.f.c.49.1 4 20.7 even 4
800.2.f.c.49.2 4 40.3 even 4
800.2.f.e.49.3 4 40.27 even 4
800.2.f.e.49.4 4 20.3 even 4
1280.2.a.a.1.1 2 16.13 even 4
1280.2.a.d.1.1 2 16.11 odd 4
1280.2.a.n.1.2 2 16.3 odd 4
1280.2.a.o.1.2 2 16.5 even 4
1440.2.k.e.721.1 4 24.11 even 2
1440.2.k.e.721.3 4 12.11 even 2
1800.2.d.l.1549.3 4 15.8 even 4
1800.2.d.l.1549.4 4 120.77 even 4
1800.2.d.p.1549.1 4 120.53 even 4
1800.2.d.p.1549.2 4 15.2 even 4
1800.2.k.j.901.1 4 15.14 odd 2
1800.2.k.j.901.2 4 120.29 odd 2
6400.2.a.z.1.1 2 80.69 even 4
6400.2.a.be.1.1 2 80.19 odd 4
6400.2.a.ce.1.2 2 80.29 even 4
6400.2.a.cj.1.2 2 80.59 odd 4
7200.2.d.n.2449.2 4 120.107 odd 4
7200.2.d.n.2449.3 4 60.23 odd 4
7200.2.d.o.2449.2 4 60.47 odd 4
7200.2.d.o.2449.3 4 120.83 odd 4
7200.2.k.j.3601.3 4 60.59 even 2
7200.2.k.j.3601.4 4 120.59 even 2