Properties

Label 104.2.b.b.53.1
Level $104$
Weight $2$
Character 104.53
Analytic conductor $0.830$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [104,2,Mod(53,104)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(104, 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("104.53");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 104.b (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: \(0.830444181021\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 53.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 104.53
Dual form 104.2.b.b.53.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.366025 - 1.36603i) q^{2} +2.00000i q^{3} +(-1.73205 + 1.00000i) q^{4} +3.46410i q^{5} +(2.73205 - 0.732051i) q^{6} -1.26795 q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.366025 - 1.36603i) q^{2} +2.00000i q^{3} +(-1.73205 + 1.00000i) q^{4} +3.46410i q^{5} +(2.73205 - 0.732051i) q^{6} -1.26795 q^{7} +(2.00000 + 2.00000i) q^{8} -1.00000 q^{9} +(4.73205 - 1.26795i) q^{10} -4.73205i q^{11} +(-2.00000 - 3.46410i) q^{12} +1.00000i q^{13} +(0.464102 + 1.73205i) q^{14} -6.92820 q^{15} +(2.00000 - 3.46410i) q^{16} +5.46410 q^{17} +(0.366025 + 1.36603i) q^{18} +0.732051i q^{19} +(-3.46410 - 6.00000i) q^{20} -2.53590i q^{21} +(-6.46410 + 1.73205i) q^{22} +4.00000 q^{23} +(-4.00000 + 4.00000i) q^{24} -7.00000 q^{25} +(1.36603 - 0.366025i) q^{26} +4.00000i q^{27} +(2.19615 - 1.26795i) q^{28} +2.00000i q^{29} +(2.53590 + 9.46410i) q^{30} -6.73205 q^{31} +(-5.46410 - 1.46410i) q^{32} +9.46410 q^{33} +(-2.00000 - 7.46410i) q^{34} -4.39230i q^{35} +(1.73205 - 1.00000i) q^{36} -8.92820i q^{37} +(1.00000 - 0.267949i) q^{38} -2.00000 q^{39} +(-6.92820 + 6.92820i) q^{40} +8.92820 q^{41} +(-3.46410 + 0.928203i) q^{42} -0.535898i q^{43} +(4.73205 + 8.19615i) q^{44} -3.46410i q^{45} +(-1.46410 - 5.46410i) q^{46} +6.73205 q^{47} +(6.92820 + 4.00000i) q^{48} -5.39230 q^{49} +(2.56218 + 9.56218i) q^{50} +10.9282i q^{51} +(-1.00000 - 1.73205i) q^{52} -2.92820i q^{53} +(5.46410 - 1.46410i) q^{54} +16.3923 q^{55} +(-2.53590 - 2.53590i) q^{56} -1.46410 q^{57} +(2.73205 - 0.732051i) q^{58} -10.1962i q^{59} +(12.0000 - 6.92820i) q^{60} +2.92820i q^{61} +(2.46410 + 9.19615i) q^{62} +1.26795 q^{63} +8.00000i q^{64} -3.46410 q^{65} +(-3.46410 - 12.9282i) q^{66} +0.732051i q^{67} +(-9.46410 + 5.46410i) q^{68} +8.00000i q^{69} +(-6.00000 + 1.60770i) q^{70} -8.19615 q^{71} +(-2.00000 - 2.00000i) q^{72} -7.46410 q^{73} +(-12.1962 + 3.26795i) q^{74} -14.0000i q^{75} +(-0.732051 - 1.26795i) q^{76} +6.00000i q^{77} +(0.732051 + 2.73205i) q^{78} +5.46410 q^{79} +(12.0000 + 6.92820i) q^{80} -11.0000 q^{81} +(-3.26795 - 12.1962i) q^{82} +3.26795i q^{83} +(2.53590 + 4.39230i) q^{84} +18.9282i q^{85} +(-0.732051 + 0.196152i) q^{86} -4.00000 q^{87} +(9.46410 - 9.46410i) q^{88} -17.3205 q^{89} +(-4.73205 + 1.26795i) q^{90} -1.26795i q^{91} +(-6.92820 + 4.00000i) q^{92} -13.4641i q^{93} +(-2.46410 - 9.19615i) q^{94} -2.53590 q^{95} +(2.92820 - 10.9282i) q^{96} +6.39230 q^{97} +(1.97372 + 7.36603i) q^{98} +4.73205i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 4 q^{6} - 12 q^{7} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 4 q^{6} - 12 q^{7} + 8 q^{8} - 4 q^{9} + 12 q^{10} - 8 q^{12} - 12 q^{14} + 8 q^{16} + 8 q^{17} - 2 q^{18} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 28 q^{25} + 2 q^{26} - 12 q^{28} + 24 q^{30} - 20 q^{31} - 8 q^{32} + 24 q^{33} - 8 q^{34} + 4 q^{38} - 8 q^{39} + 8 q^{41} + 12 q^{44} + 8 q^{46} + 20 q^{47} + 20 q^{49} - 14 q^{50} - 4 q^{52} + 8 q^{54} + 24 q^{55} - 24 q^{56} + 8 q^{57} + 4 q^{58} + 48 q^{60} - 4 q^{62} + 12 q^{63} - 24 q^{68} - 24 q^{70} - 12 q^{71} - 8 q^{72} - 16 q^{73} - 28 q^{74} + 4 q^{76} - 4 q^{78} + 8 q^{79} + 48 q^{80} - 44 q^{81} - 20 q^{82} + 24 q^{84} + 4 q^{86} - 16 q^{87} + 24 q^{88} - 12 q^{90} + 4 q^{94} - 24 q^{95} - 16 q^{96} - 16 q^{97} + 46 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/104\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(53\) \(79\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 1.36603i −0.258819 0.965926i
\(3\) 2.00000i 1.15470i 0.816497 + 0.577350i \(0.195913\pi\)
−0.816497 + 0.577350i \(0.804087\pi\)
\(4\) −1.73205 + 1.00000i −0.866025 + 0.500000i
\(5\) 3.46410i 1.54919i 0.632456 + 0.774597i \(0.282047\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) 2.73205 0.732051i 1.11536 0.298858i
\(7\) −1.26795 −0.479240 −0.239620 0.970867i \(-0.577023\pi\)
−0.239620 + 0.970867i \(0.577023\pi\)
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) −1.00000 −0.333333
\(10\) 4.73205 1.26795i 1.49641 0.400961i
\(11\) 4.73205i 1.42677i −0.700774 0.713384i \(-0.747162\pi\)
0.700774 0.713384i \(-0.252838\pi\)
\(12\) −2.00000 3.46410i −0.577350 1.00000i
\(13\) 1.00000i 0.277350i
\(14\) 0.464102 + 1.73205i 0.124036 + 0.462910i
\(15\) −6.92820 −1.78885
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 5.46410 1.32524 0.662620 0.748956i \(-0.269445\pi\)
0.662620 + 0.748956i \(0.269445\pi\)
\(18\) 0.366025 + 1.36603i 0.0862730 + 0.321975i
\(19\) 0.732051i 0.167944i 0.996468 + 0.0839720i \(0.0267606\pi\)
−0.996468 + 0.0839720i \(0.973239\pi\)
\(20\) −3.46410 6.00000i −0.774597 1.34164i
\(21\) 2.53590i 0.553378i
\(22\) −6.46410 + 1.73205i −1.37815 + 0.369274i
\(23\) 4.00000 0.834058 0.417029 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) −4.00000 + 4.00000i −0.816497 + 0.816497i
\(25\) −7.00000 −1.40000
\(26\) 1.36603 0.366025i 0.267900 0.0717835i
\(27\) 4.00000i 0.769800i
\(28\) 2.19615 1.26795i 0.415034 0.239620i
\(29\) 2.00000i 0.371391i 0.982607 + 0.185695i \(0.0594537\pi\)
−0.982607 + 0.185695i \(0.940546\pi\)
\(30\) 2.53590 + 9.46410i 0.462990 + 1.72790i
\(31\) −6.73205 −1.20911 −0.604556 0.796563i \(-0.706649\pi\)
−0.604556 + 0.796563i \(0.706649\pi\)
\(32\) −5.46410 1.46410i −0.965926 0.258819i
\(33\) 9.46410 1.64749
\(34\) −2.00000 7.46410i −0.342997 1.28008i
\(35\) 4.39230i 0.742435i
\(36\) 1.73205 1.00000i 0.288675 0.166667i
\(37\) 8.92820i 1.46779i −0.679264 0.733894i \(-0.737701\pi\)
0.679264 0.733894i \(-0.262299\pi\)
\(38\) 1.00000 0.267949i 0.162221 0.0434671i
\(39\) −2.00000 −0.320256
\(40\) −6.92820 + 6.92820i −1.09545 + 1.09545i
\(41\) 8.92820 1.39435 0.697176 0.716900i \(-0.254440\pi\)
0.697176 + 0.716900i \(0.254440\pi\)
\(42\) −3.46410 + 0.928203i −0.534522 + 0.143225i
\(43\) 0.535898i 0.0817237i −0.999165 0.0408619i \(-0.986990\pi\)
0.999165 0.0408619i \(-0.0130104\pi\)
\(44\) 4.73205 + 8.19615i 0.713384 + 1.23562i
\(45\) 3.46410i 0.516398i
\(46\) −1.46410 5.46410i −0.215870 0.805638i
\(47\) 6.73205 0.981971 0.490985 0.871168i \(-0.336637\pi\)
0.490985 + 0.871168i \(0.336637\pi\)
\(48\) 6.92820 + 4.00000i 1.00000 + 0.577350i
\(49\) −5.39230 −0.770329
\(50\) 2.56218 + 9.56218i 0.362347 + 1.35230i
\(51\) 10.9282i 1.53025i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 2.92820i 0.402220i −0.979569 0.201110i \(-0.935545\pi\)
0.979569 0.201110i \(-0.0644548\pi\)
\(54\) 5.46410 1.46410i 0.743570 0.199239i
\(55\) 16.3923 2.21034
\(56\) −2.53590 2.53590i −0.338874 0.338874i
\(57\) −1.46410 −0.193925
\(58\) 2.73205 0.732051i 0.358736 0.0961230i
\(59\) 10.1962i 1.32743i −0.747987 0.663713i \(-0.768980\pi\)
0.747987 0.663713i \(-0.231020\pi\)
\(60\) 12.0000 6.92820i 1.54919 0.894427i
\(61\) 2.92820i 0.374918i 0.982272 + 0.187459i \(0.0600252\pi\)
−0.982272 + 0.187459i \(0.939975\pi\)
\(62\) 2.46410 + 9.19615i 0.312941 + 1.16791i
\(63\) 1.26795 0.159747
\(64\) 8.00000i 1.00000i
\(65\) −3.46410 −0.429669
\(66\) −3.46410 12.9282i −0.426401 1.59135i
\(67\) 0.732051i 0.0894342i 0.999000 + 0.0447171i \(0.0142386\pi\)
−0.999000 + 0.0447171i \(0.985761\pi\)
\(68\) −9.46410 + 5.46410i −1.14769 + 0.662620i
\(69\) 8.00000i 0.963087i
\(70\) −6.00000 + 1.60770i −0.717137 + 0.192156i
\(71\) −8.19615 −0.972704 −0.486352 0.873763i \(-0.661673\pi\)
−0.486352 + 0.873763i \(0.661673\pi\)
\(72\) −2.00000 2.00000i −0.235702 0.235702i
\(73\) −7.46410 −0.873607 −0.436804 0.899557i \(-0.643889\pi\)
−0.436804 + 0.899557i \(0.643889\pi\)
\(74\) −12.1962 + 3.26795i −1.41777 + 0.379891i
\(75\) 14.0000i 1.61658i
\(76\) −0.732051 1.26795i −0.0839720 0.145444i
\(77\) 6.00000i 0.683763i
\(78\) 0.732051 + 2.73205i 0.0828884 + 0.309344i
\(79\) 5.46410 0.614759 0.307380 0.951587i \(-0.400548\pi\)
0.307380 + 0.951587i \(0.400548\pi\)
\(80\) 12.0000 + 6.92820i 1.34164 + 0.774597i
\(81\) −11.0000 −1.22222
\(82\) −3.26795 12.1962i −0.360885 1.34684i
\(83\) 3.26795i 0.358704i 0.983785 + 0.179352i \(0.0574001\pi\)
−0.983785 + 0.179352i \(0.942600\pi\)
\(84\) 2.53590 + 4.39230i 0.276689 + 0.479240i
\(85\) 18.9282i 2.05305i
\(86\) −0.732051 + 0.196152i −0.0789391 + 0.0211517i
\(87\) −4.00000 −0.428845
\(88\) 9.46410 9.46410i 1.00888 1.00888i
\(89\) −17.3205 −1.83597 −0.917985 0.396615i \(-0.870185\pi\)
−0.917985 + 0.396615i \(0.870185\pi\)
\(90\) −4.73205 + 1.26795i −0.498802 + 0.133654i
\(91\) 1.26795i 0.132917i
\(92\) −6.92820 + 4.00000i −0.722315 + 0.417029i
\(93\) 13.4641i 1.39616i
\(94\) −2.46410 9.19615i −0.254153 0.948511i
\(95\) −2.53590 −0.260178
\(96\) 2.92820 10.9282i 0.298858 1.11536i
\(97\) 6.39230 0.649040 0.324520 0.945879i \(-0.394797\pi\)
0.324520 + 0.945879i \(0.394797\pi\)
\(98\) 1.97372 + 7.36603i 0.199376 + 0.744081i
\(99\) 4.73205i 0.475589i
\(100\) 12.1244 7.00000i 1.21244 0.700000i
\(101\) 12.0000i 1.19404i −0.802225 0.597022i \(-0.796350\pi\)
0.802225 0.597022i \(-0.203650\pi\)
\(102\) 14.9282 4.00000i 1.47811 0.396059i
\(103\) 6.92820 0.682656 0.341328 0.939944i \(-0.389123\pi\)
0.341328 + 0.939944i \(0.389123\pi\)
\(104\) −2.00000 + 2.00000i −0.196116 + 0.196116i
\(105\) 8.78461 0.857290
\(106\) −4.00000 + 1.07180i −0.388514 + 0.104102i
\(107\) 4.92820i 0.476427i 0.971213 + 0.238214i \(0.0765619\pi\)
−0.971213 + 0.238214i \(0.923438\pi\)
\(108\) −4.00000 6.92820i −0.384900 0.666667i
\(109\) 2.00000i 0.191565i −0.995402 0.0957826i \(-0.969465\pi\)
0.995402 0.0957826i \(-0.0305354\pi\)
\(110\) −6.00000 22.3923i −0.572078 2.13502i
\(111\) 17.8564 1.69486
\(112\) −2.53590 + 4.39230i −0.239620 + 0.415034i
\(113\) 2.53590 0.238557 0.119279 0.992861i \(-0.461942\pi\)
0.119279 + 0.992861i \(0.461942\pi\)
\(114\) 0.535898 + 2.00000i 0.0501915 + 0.187317i
\(115\) 13.8564i 1.29212i
\(116\) −2.00000 3.46410i −0.185695 0.321634i
\(117\) 1.00000i 0.0924500i
\(118\) −13.9282 + 3.73205i −1.28220 + 0.343563i
\(119\) −6.92820 −0.635107
\(120\) −13.8564 13.8564i −1.26491 1.26491i
\(121\) −11.3923 −1.03566
\(122\) 4.00000 1.07180i 0.362143 0.0970359i
\(123\) 17.8564i 1.61006i
\(124\) 11.6603 6.73205i 1.04712 0.604556i
\(125\) 6.92820i 0.619677i
\(126\) −0.464102 1.73205i −0.0413455 0.154303i
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 10.9282 2.92820i 0.965926 0.258819i
\(129\) 1.07180 0.0943664
\(130\) 1.26795 + 4.73205i 0.111207 + 0.415028i
\(131\) 19.8564i 1.73486i 0.497557 + 0.867431i \(0.334230\pi\)
−0.497557 + 0.867431i \(0.665770\pi\)
\(132\) −16.3923 + 9.46410i −1.42677 + 0.823744i
\(133\) 0.928203i 0.0804854i
\(134\) 1.00000 0.267949i 0.0863868 0.0231473i
\(135\) −13.8564 −1.19257
\(136\) 10.9282 + 10.9282i 0.937086 + 0.937086i
\(137\) 12.9282 1.10453 0.552265 0.833668i \(-0.313763\pi\)
0.552265 + 0.833668i \(0.313763\pi\)
\(138\) 10.9282 2.92820i 0.930270 0.249265i
\(139\) 10.0000i 0.848189i −0.905618 0.424094i \(-0.860592\pi\)
0.905618 0.424094i \(-0.139408\pi\)
\(140\) 4.39230 + 7.60770i 0.371218 + 0.642968i
\(141\) 13.4641i 1.13388i
\(142\) 3.00000 + 11.1962i 0.251754 + 0.939560i
\(143\) 4.73205 0.395714
\(144\) −2.00000 + 3.46410i −0.166667 + 0.288675i
\(145\) −6.92820 −0.575356
\(146\) 2.73205 + 10.1962i 0.226106 + 0.843840i
\(147\) 10.7846i 0.889500i
\(148\) 8.92820 + 15.4641i 0.733894 + 1.27114i
\(149\) 12.9282i 1.05912i −0.848273 0.529560i \(-0.822357\pi\)
0.848273 0.529560i \(-0.177643\pi\)
\(150\) −19.1244 + 5.12436i −1.56150 + 0.418402i
\(151\) −7.12436 −0.579772 −0.289886 0.957061i \(-0.593617\pi\)
−0.289886 + 0.957061i \(0.593617\pi\)
\(152\) −1.46410 + 1.46410i −0.118754 + 0.118754i
\(153\) −5.46410 −0.441746
\(154\) 8.19615 2.19615i 0.660465 0.176971i
\(155\) 23.3205i 1.87315i
\(156\) 3.46410 2.00000i 0.277350 0.160128i
\(157\) 16.9282i 1.35102i −0.737352 0.675509i \(-0.763924\pi\)
0.737352 0.675509i \(-0.236076\pi\)
\(158\) −2.00000 7.46410i −0.159111 0.593812i
\(159\) 5.85641 0.464443
\(160\) 5.07180 18.9282i 0.400961 1.49641i
\(161\) −5.07180 −0.399714
\(162\) 4.02628 + 15.0263i 0.316334 + 1.18058i
\(163\) 16.7321i 1.31056i 0.755388 + 0.655278i \(0.227448\pi\)
−0.755388 + 0.655278i \(0.772552\pi\)
\(164\) −15.4641 + 8.92820i −1.20754 + 0.697176i
\(165\) 32.7846i 2.55228i
\(166\) 4.46410 1.19615i 0.346481 0.0928394i
\(167\) −5.66025 −0.438004 −0.219002 0.975724i \(-0.570280\pi\)
−0.219002 + 0.975724i \(0.570280\pi\)
\(168\) 5.07180 5.07180i 0.391298 0.391298i
\(169\) −1.00000 −0.0769231
\(170\) 25.8564 6.92820i 1.98310 0.531369i
\(171\) 0.732051i 0.0559813i
\(172\) 0.535898 + 0.928203i 0.0408619 + 0.0707748i
\(173\) 6.92820i 0.526742i 0.964695 + 0.263371i \(0.0848343\pi\)
−0.964695 + 0.263371i \(0.915166\pi\)
\(174\) 1.46410 + 5.46410i 0.110993 + 0.414232i
\(175\) 8.87564 0.670936
\(176\) −16.3923 9.46410i −1.23562 0.713384i
\(177\) 20.3923 1.53278
\(178\) 6.33975 + 23.6603i 0.475184 + 1.77341i
\(179\) 10.3923i 0.776757i −0.921500 0.388379i \(-0.873035\pi\)
0.921500 0.388379i \(-0.126965\pi\)
\(180\) 3.46410 + 6.00000i 0.258199 + 0.447214i
\(181\) 8.92820i 0.663628i −0.943345 0.331814i \(-0.892339\pi\)
0.943345 0.331814i \(-0.107661\pi\)
\(182\) −1.73205 + 0.464102i −0.128388 + 0.0344015i
\(183\) −5.85641 −0.432918
\(184\) 8.00000 + 8.00000i 0.589768 + 0.589768i
\(185\) 30.9282 2.27389
\(186\) −18.3923 + 4.92820i −1.34859 + 0.361353i
\(187\) 25.8564i 1.89081i
\(188\) −11.6603 + 6.73205i −0.850411 + 0.490985i
\(189\) 5.07180i 0.368919i
\(190\) 0.928203 + 3.46410i 0.0673389 + 0.251312i
\(191\) −14.5359 −1.05178 −0.525890 0.850552i \(-0.676268\pi\)
−0.525890 + 0.850552i \(0.676268\pi\)
\(192\) −16.0000 −1.15470
\(193\) −1.60770 −0.115724 −0.0578622 0.998325i \(-0.518428\pi\)
−0.0578622 + 0.998325i \(0.518428\pi\)
\(194\) −2.33975 8.73205i −0.167984 0.626925i
\(195\) 6.92820i 0.496139i
\(196\) 9.33975 5.39230i 0.667125 0.385165i
\(197\) 3.07180i 0.218856i −0.993995 0.109428i \(-0.965098\pi\)
0.993995 0.109428i \(-0.0349020\pi\)
\(198\) 6.46410 1.73205i 0.459384 0.123091i
\(199\) 16.7846 1.18983 0.594915 0.803789i \(-0.297186\pi\)
0.594915 + 0.803789i \(0.297186\pi\)
\(200\) −14.0000 14.0000i −0.989949 0.989949i
\(201\) −1.46410 −0.103270
\(202\) −16.3923 + 4.39230i −1.15336 + 0.309041i
\(203\) 2.53590i 0.177985i
\(204\) −10.9282 18.9282i −0.765127 1.32524i
\(205\) 30.9282i 2.16012i
\(206\) −2.53590 9.46410i −0.176684 0.659395i
\(207\) −4.00000 −0.278019
\(208\) 3.46410 + 2.00000i 0.240192 + 0.138675i
\(209\) 3.46410 0.239617
\(210\) −3.21539 12.0000i −0.221883 0.828079i
\(211\) 7.85641i 0.540857i −0.962740 0.270429i \(-0.912835\pi\)
0.962740 0.270429i \(-0.0871654\pi\)
\(212\) 2.92820 + 5.07180i 0.201110 + 0.348332i
\(213\) 16.3923i 1.12318i
\(214\) 6.73205 1.80385i 0.460194 0.123308i
\(215\) 1.85641 0.126606
\(216\) −8.00000 + 8.00000i −0.544331 + 0.544331i
\(217\) 8.53590 0.579455
\(218\) −2.73205 + 0.732051i −0.185038 + 0.0495807i
\(219\) 14.9282i 1.00875i
\(220\) −28.3923 + 16.3923i −1.91421 + 1.10517i
\(221\) 5.46410i 0.367555i
\(222\) −6.53590 24.3923i −0.438661 1.63710i
\(223\) −0.196152 −0.0131353 −0.00656767 0.999978i \(-0.502091\pi\)
−0.00656767 + 0.999978i \(0.502091\pi\)
\(224\) 6.92820 + 1.85641i 0.462910 + 0.124036i
\(225\) 7.00000 0.466667
\(226\) −0.928203 3.46410i −0.0617432 0.230429i
\(227\) 2.87564i 0.190863i 0.995436 + 0.0954316i \(0.0304231\pi\)
−0.995436 + 0.0954316i \(0.969577\pi\)
\(228\) 2.53590 1.46410i 0.167944 0.0969625i
\(229\) 5.32051i 0.351589i −0.984427 0.175795i \(-0.943751\pi\)
0.984427 0.175795i \(-0.0562494\pi\)
\(230\) 18.9282 5.07180i 1.24809 0.334424i
\(231\) −12.0000 −0.789542
\(232\) −4.00000 + 4.00000i −0.262613 + 0.262613i
\(233\) 16.9282 1.10900 0.554502 0.832183i \(-0.312909\pi\)
0.554502 + 0.832183i \(0.312909\pi\)
\(234\) −1.36603 + 0.366025i −0.0892999 + 0.0239278i
\(235\) 23.3205i 1.52126i
\(236\) 10.1962 + 17.6603i 0.663713 + 1.14958i
\(237\) 10.9282i 0.709863i
\(238\) 2.53590 + 9.46410i 0.164378 + 0.613467i
\(239\) 18.7321 1.21168 0.605838 0.795588i \(-0.292838\pi\)
0.605838 + 0.795588i \(0.292838\pi\)
\(240\) −13.8564 + 24.0000i −0.894427 + 1.54919i
\(241\) −30.3923 −1.95774 −0.978870 0.204482i \(-0.934449\pi\)
−0.978870 + 0.204482i \(0.934449\pi\)
\(242\) 4.16987 + 15.5622i 0.268050 + 1.00037i
\(243\) 10.0000i 0.641500i
\(244\) −2.92820 5.07180i −0.187459 0.324689i
\(245\) 18.6795i 1.19339i
\(246\) 24.3923 6.53590i 1.55520 0.416714i
\(247\) −0.732051 −0.0465793
\(248\) −13.4641 13.4641i −0.854971 0.854971i
\(249\) −6.53590 −0.414196
\(250\) −9.46410 + 2.53590i −0.598562 + 0.160384i
\(251\) 6.39230i 0.403479i 0.979439 + 0.201739i \(0.0646594\pi\)
−0.979439 + 0.201739i \(0.935341\pi\)
\(252\) −2.19615 + 1.26795i −0.138345 + 0.0798733i
\(253\) 18.9282i 1.19001i
\(254\) 1.46410 + 5.46410i 0.0918659 + 0.342848i
\(255\) −37.8564 −2.37066
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −23.8564 −1.48812 −0.744061 0.668112i \(-0.767103\pi\)
−0.744061 + 0.668112i \(0.767103\pi\)
\(258\) −0.392305 1.46410i −0.0244238 0.0911510i
\(259\) 11.3205i 0.703422i
\(260\) 6.00000 3.46410i 0.372104 0.214834i
\(261\) 2.00000i 0.123797i
\(262\) 27.1244 7.26795i 1.67575 0.449015i
\(263\) −27.3205 −1.68465 −0.842327 0.538966i \(-0.818815\pi\)
−0.842327 + 0.538966i \(0.818815\pi\)
\(264\) 18.9282 + 18.9282i 1.16495 + 1.16495i
\(265\) 10.1436 0.623116
\(266\) −1.26795 + 0.339746i −0.0777430 + 0.0208312i
\(267\) 34.6410i 2.12000i
\(268\) −0.732051 1.26795i −0.0447171 0.0774523i
\(269\) 7.85641i 0.479014i −0.970895 0.239507i \(-0.923014\pi\)
0.970895 0.239507i \(-0.0769857\pi\)
\(270\) 5.07180 + 18.9282i 0.308660 + 1.15193i
\(271\) −20.1962 −1.22683 −0.613414 0.789761i \(-0.710204\pi\)
−0.613414 + 0.789761i \(0.710204\pi\)
\(272\) 10.9282 18.9282i 0.662620 1.14769i
\(273\) 2.53590 0.153480
\(274\) −4.73205 17.6603i −0.285874 1.06689i
\(275\) 33.1244i 1.99747i
\(276\) −8.00000 13.8564i −0.481543 0.834058i
\(277\) 1.85641i 0.111541i 0.998444 + 0.0557703i \(0.0177615\pi\)
−0.998444 + 0.0557703i \(0.982239\pi\)
\(278\) −13.6603 + 3.66025i −0.819288 + 0.219527i
\(279\) 6.73205 0.403037
\(280\) 8.78461 8.78461i 0.524981 0.524981i
\(281\) 9.32051 0.556015 0.278007 0.960579i \(-0.410326\pi\)
0.278007 + 0.960579i \(0.410326\pi\)
\(282\) 18.3923 4.92820i 1.09525 0.293470i
\(283\) 19.4641i 1.15702i 0.815675 + 0.578510i \(0.196366\pi\)
−0.815675 + 0.578510i \(0.803634\pi\)
\(284\) 14.1962 8.19615i 0.842387 0.486352i
\(285\) 5.07180i 0.300427i
\(286\) −1.73205 6.46410i −0.102418 0.382230i
\(287\) −11.3205 −0.668228
\(288\) 5.46410 + 1.46410i 0.321975 + 0.0862730i
\(289\) 12.8564 0.756259
\(290\) 2.53590 + 9.46410i 0.148913 + 0.555751i
\(291\) 12.7846i 0.749447i
\(292\) 12.9282 7.46410i 0.756566 0.436804i
\(293\) 32.9282i 1.92369i 0.273602 + 0.961843i \(0.411785\pi\)
−0.273602 + 0.961843i \(0.588215\pi\)
\(294\) −14.7321 + 3.94744i −0.859191 + 0.230219i
\(295\) 35.3205 2.05644
\(296\) 17.8564 17.8564i 1.03788 1.03788i
\(297\) 18.9282 1.09833
\(298\) −17.6603 + 4.73205i −1.02303 + 0.274120i
\(299\) 4.00000i 0.231326i
\(300\) 14.0000 + 24.2487i 0.808290 + 1.40000i
\(301\) 0.679492i 0.0391653i
\(302\) 2.60770 + 9.73205i 0.150056 + 0.560017i
\(303\) 24.0000 1.37876
\(304\) 2.53590 + 1.46410i 0.145444 + 0.0839720i
\(305\) −10.1436 −0.580820
\(306\) 2.00000 + 7.46410i 0.114332 + 0.426694i
\(307\) 0.732051i 0.0417803i 0.999782 + 0.0208902i \(0.00665003\pi\)
−0.999782 + 0.0208902i \(0.993350\pi\)
\(308\) −6.00000 10.3923i −0.341882 0.592157i
\(309\) 13.8564i 0.788263i
\(310\) −31.8564 + 8.53590i −1.80932 + 0.484806i
\(311\) 1.07180 0.0607760 0.0303880 0.999538i \(-0.490326\pi\)
0.0303880 + 0.999538i \(0.490326\pi\)
\(312\) −4.00000 4.00000i −0.226455 0.226455i
\(313\) 0.392305 0.0221744 0.0110872 0.999939i \(-0.496471\pi\)
0.0110872 + 0.999939i \(0.496471\pi\)
\(314\) −23.1244 + 6.19615i −1.30498 + 0.349669i
\(315\) 4.39230i 0.247478i
\(316\) −9.46410 + 5.46410i −0.532397 + 0.307380i
\(317\) 3.46410i 0.194563i 0.995257 + 0.0972817i \(0.0310148\pi\)
−0.995257 + 0.0972817i \(0.968985\pi\)
\(318\) −2.14359 8.00000i −0.120207 0.448618i
\(319\) 9.46410 0.529888
\(320\) −27.7128 −1.54919
\(321\) −9.85641 −0.550131
\(322\) 1.85641 + 6.92820i 0.103453 + 0.386094i
\(323\) 4.00000i 0.222566i
\(324\) 19.0526 11.0000i 1.05848 0.611111i
\(325\) 7.00000i 0.388290i
\(326\) 22.8564 6.12436i 1.26590 0.339197i
\(327\) 4.00000 0.221201
\(328\) 17.8564 + 17.8564i 0.985955 + 0.985955i
\(329\) −8.53590 −0.470599
\(330\) 44.7846 12.0000i 2.46531 0.660578i
\(331\) 17.5167i 0.962803i 0.876500 + 0.481401i \(0.159872\pi\)
−0.876500 + 0.481401i \(0.840128\pi\)
\(332\) −3.26795 5.66025i −0.179352 0.310647i
\(333\) 8.92820i 0.489263i
\(334\) 2.07180 + 7.73205i 0.113364 + 0.423079i
\(335\) −2.53590 −0.138551
\(336\) −8.78461 5.07180i −0.479240 0.276689i
\(337\) 1.46410 0.0797547 0.0398773 0.999205i \(-0.487303\pi\)
0.0398773 + 0.999205i \(0.487303\pi\)
\(338\) 0.366025 + 1.36603i 0.0199092 + 0.0743020i
\(339\) 5.07180i 0.275462i
\(340\) −18.9282 32.7846i −1.02653 1.77800i
\(341\) 31.8564i 1.72512i
\(342\) −1.00000 + 0.267949i −0.0540738 + 0.0144890i
\(343\) 15.7128 0.848412
\(344\) 1.07180 1.07180i 0.0577874 0.0577874i
\(345\) −27.7128 −1.49201
\(346\) 9.46410 2.53590i 0.508793 0.136331i
\(347\) 7.07180i 0.379634i −0.981819 0.189817i \(-0.939211\pi\)
0.981819 0.189817i \(-0.0607895\pi\)
\(348\) 6.92820 4.00000i 0.371391 0.214423i
\(349\) 9.60770i 0.514288i 0.966373 + 0.257144i \(0.0827815\pi\)
−0.966373 + 0.257144i \(0.917219\pi\)
\(350\) −3.24871 12.1244i −0.173651 0.648074i
\(351\) −4.00000 −0.213504
\(352\) −6.92820 + 25.8564i −0.369274 + 1.37815i
\(353\) −11.0718 −0.589292 −0.294646 0.955606i \(-0.595202\pi\)
−0.294646 + 0.955606i \(0.595202\pi\)
\(354\) −7.46410 27.8564i −0.396713 1.48055i
\(355\) 28.3923i 1.50691i
\(356\) 30.0000 17.3205i 1.59000 0.917985i
\(357\) 13.8564i 0.733359i
\(358\) −14.1962 + 3.80385i −0.750290 + 0.201040i
\(359\) 31.5167 1.66339 0.831693 0.555236i \(-0.187372\pi\)
0.831693 + 0.555236i \(0.187372\pi\)
\(360\) 6.92820 6.92820i 0.365148 0.365148i
\(361\) 18.4641 0.971795
\(362\) −12.1962 + 3.26795i −0.641016 + 0.171760i
\(363\) 22.7846i 1.19588i
\(364\) 1.26795 + 2.19615i 0.0664586 + 0.115110i
\(365\) 25.8564i 1.35339i
\(366\) 2.14359 + 8.00000i 0.112047 + 0.418167i
\(367\) −22.2487 −1.16137 −0.580687 0.814127i \(-0.697216\pi\)
−0.580687 + 0.814127i \(0.697216\pi\)
\(368\) 8.00000 13.8564i 0.417029 0.722315i
\(369\) −8.92820 −0.464784
\(370\) −11.3205 42.2487i −0.588525 2.19641i
\(371\) 3.71281i 0.192760i
\(372\) 13.4641 + 23.3205i 0.698081 + 1.20911i
\(373\) 14.7846i 0.765518i −0.923848 0.382759i \(-0.874974\pi\)
0.923848 0.382759i \(-0.125026\pi\)
\(374\) −35.3205 + 9.46410i −1.82638 + 0.489377i
\(375\) 13.8564 0.715542
\(376\) 13.4641 + 13.4641i 0.694358 + 0.694358i
\(377\) −2.00000 −0.103005
\(378\) −6.92820 + 1.85641i −0.356348 + 0.0954832i
\(379\) 14.5885i 0.749359i 0.927154 + 0.374679i \(0.122247\pi\)
−0.927154 + 0.374679i \(0.877753\pi\)
\(380\) 4.39230 2.53590i 0.225320 0.130089i
\(381\) 8.00000i 0.409852i
\(382\) 5.32051 + 19.8564i 0.272221 + 1.01594i
\(383\) −10.3397 −0.528336 −0.264168 0.964477i \(-0.585097\pi\)
−0.264168 + 0.964477i \(0.585097\pi\)
\(384\) 5.85641 + 21.8564i 0.298858 + 1.11536i
\(385\) −20.7846 −1.05928
\(386\) 0.588457 + 2.19615i 0.0299517 + 0.111781i
\(387\) 0.535898i 0.0272412i
\(388\) −11.0718 + 6.39230i −0.562085 + 0.324520i
\(389\) 2.00000i 0.101404i 0.998714 + 0.0507020i \(0.0161459\pi\)
−0.998714 + 0.0507020i \(0.983854\pi\)
\(390\) −9.46410 + 2.53590i −0.479233 + 0.128410i
\(391\) 21.8564 1.10533
\(392\) −10.7846 10.7846i −0.544705 0.544705i
\(393\) −39.7128 −2.00325
\(394\) −4.19615 + 1.12436i −0.211399 + 0.0566442i
\(395\) 18.9282i 0.952381i
\(396\) −4.73205 8.19615i −0.237795 0.411872i
\(397\) 4.53590i 0.227650i −0.993501 0.113825i \(-0.963690\pi\)
0.993501 0.113825i \(-0.0363104\pi\)
\(398\) −6.14359 22.9282i −0.307951 1.14929i
\(399\) 1.85641 0.0929366
\(400\) −14.0000 + 24.2487i −0.700000 + 1.21244i
\(401\) 4.53590 0.226512 0.113256 0.993566i \(-0.463872\pi\)
0.113256 + 0.993566i \(0.463872\pi\)
\(402\) 0.535898 + 2.00000i 0.0267282 + 0.0997509i
\(403\) 6.73205i 0.335347i
\(404\) 12.0000 + 20.7846i 0.597022 + 1.03407i
\(405\) 38.1051i 1.89346i
\(406\) −3.46410 + 0.928203i −0.171920 + 0.0460660i
\(407\) −42.2487 −2.09419
\(408\) −21.8564 + 21.8564i −1.08205 + 1.08205i
\(409\) 12.9282 0.639259 0.319629 0.947543i \(-0.396442\pi\)
0.319629 + 0.947543i \(0.396442\pi\)
\(410\) 42.2487 11.3205i 2.08652 0.559080i
\(411\) 25.8564i 1.27540i
\(412\) −12.0000 + 6.92820i −0.591198 + 0.341328i
\(413\) 12.9282i 0.636155i
\(414\) 1.46410 + 5.46410i 0.0719567 + 0.268546i
\(415\) −11.3205 −0.555702
\(416\) 1.46410 5.46410i 0.0717835 0.267900i
\(417\) 20.0000 0.979404
\(418\) −1.26795 4.73205i −0.0620174 0.231452i
\(419\) 30.7846i 1.50393i −0.659205 0.751963i \(-0.729107\pi\)
0.659205 0.751963i \(-0.270893\pi\)
\(420\) −15.2154 + 8.78461i −0.742435 + 0.428645i
\(421\) 24.2487i 1.18181i 0.806741 + 0.590905i \(0.201229\pi\)
−0.806741 + 0.590905i \(0.798771\pi\)
\(422\) −10.7321 + 2.87564i −0.522428 + 0.139984i
\(423\) −6.73205 −0.327324
\(424\) 5.85641 5.85641i 0.284412 0.284412i
\(425\) −38.2487 −1.85534
\(426\) −22.3923 + 6.00000i −1.08491 + 0.290701i
\(427\) 3.71281i 0.179676i
\(428\) −4.92820 8.53590i −0.238214 0.412598i
\(429\) 9.46410i 0.456931i
\(430\) −0.679492 2.53590i −0.0327680 0.122292i
\(431\) 39.1244 1.88455 0.942277 0.334835i \(-0.108680\pi\)
0.942277 + 0.334835i \(0.108680\pi\)
\(432\) 13.8564 + 8.00000i 0.666667 + 0.384900i
\(433\) −6.78461 −0.326048 −0.163024 0.986622i \(-0.552125\pi\)
−0.163024 + 0.986622i \(0.552125\pi\)
\(434\) −3.12436 11.6603i −0.149974 0.559710i
\(435\) 13.8564i 0.664364i
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) 2.92820i 0.140075i
\(438\) −20.3923 + 5.46410i −0.974382 + 0.261085i
\(439\) 2.92820 0.139756 0.0698778 0.997556i \(-0.477739\pi\)
0.0698778 + 0.997556i \(0.477739\pi\)
\(440\) 32.7846 + 32.7846i 1.56294 + 1.56294i
\(441\) 5.39230 0.256776
\(442\) 7.46410 2.00000i 0.355031 0.0951303i
\(443\) 30.0000i 1.42534i −0.701498 0.712672i \(-0.747485\pi\)
0.701498 0.712672i \(-0.252515\pi\)
\(444\) −30.9282 + 17.8564i −1.46779 + 0.847428i
\(445\) 60.0000i 2.84427i
\(446\) 0.0717968 + 0.267949i 0.00339968 + 0.0126878i
\(447\) 25.8564 1.22297
\(448\) 10.1436i 0.479240i
\(449\) 17.6077 0.830959 0.415479 0.909603i \(-0.363614\pi\)
0.415479 + 0.909603i \(0.363614\pi\)
\(450\) −2.56218 9.56218i −0.120782 0.450765i
\(451\) 42.2487i 1.98941i
\(452\) −4.39230 + 2.53590i −0.206597 + 0.119279i
\(453\) 14.2487i 0.669463i
\(454\) 3.92820 1.05256i 0.184360 0.0493990i
\(455\) 4.39230 0.205914
\(456\) −2.92820 2.92820i −0.137126 0.137126i
\(457\) −14.0000 −0.654892 −0.327446 0.944870i \(-0.606188\pi\)
−0.327446 + 0.944870i \(0.606188\pi\)
\(458\) −7.26795 + 1.94744i −0.339609 + 0.0909979i
\(459\) 21.8564i 1.02017i
\(460\) −13.8564 24.0000i −0.646058 1.11901i
\(461\) 20.9282i 0.974724i 0.873200 + 0.487362i \(0.162041\pi\)
−0.873200 + 0.487362i \(0.837959\pi\)
\(462\) 4.39230 + 16.3923i 0.204349 + 0.762639i
\(463\) 1.66025 0.0771585 0.0385793 0.999256i \(-0.487717\pi\)
0.0385793 + 0.999256i \(0.487717\pi\)
\(464\) 6.92820 + 4.00000i 0.321634 + 0.185695i
\(465\) 46.6410 2.16293
\(466\) −6.19615 23.1244i −0.287031 1.07122i
\(467\) 36.2487i 1.67739i 0.544601 + 0.838695i \(0.316681\pi\)
−0.544601 + 0.838695i \(0.683319\pi\)
\(468\) 1.00000 + 1.73205i 0.0462250 + 0.0800641i
\(469\) 0.928203i 0.0428604i
\(470\) 31.8564 8.53590i 1.46943 0.393732i
\(471\) 33.8564 1.56002
\(472\) 20.3923 20.3923i 0.938632 0.938632i
\(473\) −2.53590 −0.116601
\(474\) 14.9282 4.00000i 0.685675 0.183726i
\(475\) 5.12436i 0.235122i
\(476\) 12.0000 6.92820i 0.550019 0.317554i
\(477\) 2.92820i 0.134073i
\(478\) −6.85641 25.5885i −0.313605 1.17039i
\(479\) 21.2679 0.971757 0.485879 0.874026i \(-0.338500\pi\)
0.485879 + 0.874026i \(0.338500\pi\)
\(480\) 37.8564 + 10.1436i 1.72790 + 0.462990i
\(481\) 8.92820 0.407091
\(482\) 11.1244 + 41.5167i 0.506701 + 1.89103i
\(483\) 10.1436i 0.461549i
\(484\) 19.7321 11.3923i 0.896911 0.517832i
\(485\) 22.1436i 1.00549i
\(486\) −13.6603 + 3.66025i −0.619642 + 0.166032i
\(487\) −42.4449 −1.92336 −0.961680 0.274174i \(-0.911596\pi\)
−0.961680 + 0.274174i \(0.911596\pi\)
\(488\) −5.85641 + 5.85641i −0.265107 + 0.265107i
\(489\) −33.4641 −1.51330
\(490\) −25.5167 + 6.83717i −1.15273 + 0.308872i
\(491\) 24.2487i 1.09433i −0.837025 0.547165i \(-0.815707\pi\)
0.837025 0.547165i \(-0.184293\pi\)
\(492\) −17.8564 30.9282i −0.805029 1.39435i
\(493\) 10.9282i 0.492182i
\(494\) 0.267949 + 1.00000i 0.0120556 + 0.0449921i
\(495\) −16.3923 −0.736779
\(496\) −13.4641 + 23.3205i −0.604556 + 1.04712i
\(497\) 10.3923 0.466159
\(498\) 2.39230 + 8.92820i 0.107202 + 0.400082i
\(499\) 7.26795i 0.325358i −0.986679 0.162679i \(-0.947986\pi\)
0.986679 0.162679i \(-0.0520135\pi\)
\(500\) 6.92820 + 12.0000i 0.309839 + 0.536656i
\(501\) 11.3205i 0.505763i
\(502\) 8.73205 2.33975i 0.389731 0.104428i
\(503\) 30.5359 1.36153 0.680764 0.732503i \(-0.261648\pi\)
0.680764 + 0.732503i \(0.261648\pi\)
\(504\) 2.53590 + 2.53590i 0.112958 + 0.112958i
\(505\) 41.5692 1.84981
\(506\) −25.8564 + 6.92820i −1.14946 + 0.307996i
\(507\) 2.00000i 0.0888231i
\(508\) 6.92820 4.00000i 0.307389 0.177471i
\(509\) 14.3923i 0.637928i 0.947767 + 0.318964i \(0.103335\pi\)
−0.947767 + 0.318964i \(0.896665\pi\)
\(510\) 13.8564 + 51.7128i 0.613572 + 2.28988i
\(511\) 9.46410 0.418667
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) −2.92820 −0.129283
\(514\) 8.73205 + 32.5885i 0.385154 + 1.43742i
\(515\) 24.0000i 1.05757i
\(516\) −1.85641 + 1.07180i −0.0817237 + 0.0471832i
\(517\) 31.8564i 1.40104i
\(518\) 15.4641 4.14359i 0.679454 0.182059i
\(519\) −13.8564 −0.608229
\(520\) −6.92820 6.92820i −0.303822 0.303822i
\(521\) −25.1769 −1.10302 −0.551510 0.834168i \(-0.685948\pi\)
−0.551510 + 0.834168i \(0.685948\pi\)
\(522\) −2.73205 + 0.732051i −0.119579 + 0.0320410i
\(523\) 14.0000i 0.612177i 0.952003 + 0.306089i \(0.0990204\pi\)
−0.952003 + 0.306089i \(0.900980\pi\)
\(524\) −19.8564 34.3923i −0.867431 1.50243i
\(525\) 17.7513i 0.774730i
\(526\) 10.0000 + 37.3205i 0.436021 + 1.62725i
\(527\) −36.7846 −1.60236
\(528\) 18.9282 32.7846i 0.823744 1.42677i
\(529\) −7.00000 −0.304348
\(530\) −3.71281 13.8564i −0.161274 0.601884i
\(531\) 10.1962i 0.442475i
\(532\) 0.928203 + 1.60770i 0.0402427 + 0.0697024i
\(533\) 8.92820i 0.386723i
\(534\) −47.3205 + 12.6795i −2.04776 + 0.548695i
\(535\) −17.0718 −0.738078
\(536\) −1.46410 + 1.46410i −0.0632396 + 0.0632396i
\(537\) 20.7846 0.896922
\(538\) −10.7321 + 2.87564i −0.462692 + 0.123978i
\(539\) 25.5167i 1.09908i
\(540\) 24.0000 13.8564i 1.03280 0.596285i
\(541\) 3.07180i 0.132067i −0.997817 0.0660334i \(-0.978966\pi\)
0.997817 0.0660334i \(-0.0210344\pi\)
\(542\) 7.39230 + 27.5885i 0.317527 + 1.18503i
\(543\) 17.8564 0.766292
\(544\) −29.8564 8.00000i −1.28008 0.342997i
\(545\) 6.92820 0.296772
\(546\) −0.928203 3.46410i −0.0397234 0.148250i
\(547\) 11.8564i 0.506943i −0.967343 0.253472i \(-0.918428\pi\)
0.967343 0.253472i \(-0.0815725\pi\)
\(548\) −22.3923 + 12.9282i −0.956552 + 0.552265i
\(549\) 2.92820i 0.124973i
\(550\) 45.2487 12.1244i 1.92941 0.516984i
\(551\) −1.46410 −0.0623728
\(552\) −16.0000 + 16.0000i −0.681005 + 0.681005i
\(553\) −6.92820 −0.294617
\(554\) 2.53590 0.679492i 0.107740 0.0288688i
\(555\) 61.8564i 2.62566i
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) 34.7846i 1.47387i 0.675963 + 0.736936i \(0.263728\pi\)
−0.675963 + 0.736936i \(0.736272\pi\)
\(558\) −2.46410 9.19615i −0.104314 0.389304i
\(559\) 0.535898 0.0226661
\(560\) −15.2154 8.78461i −0.642968 0.371218i
\(561\) 51.7128 2.18332
\(562\) −3.41154 12.7321i −0.143907 0.537069i
\(563\) 7.46410i 0.314574i −0.987553 0.157287i \(-0.949725\pi\)
0.987553 0.157287i \(-0.0502748\pi\)
\(564\) −13.4641 23.3205i −0.566941 0.981971i
\(565\) 8.78461i 0.369571i
\(566\) 26.5885 7.12436i 1.11760 0.299459i
\(567\) 13.9474 0.585737
\(568\) −16.3923 16.3923i −0.687806 0.687806i
\(569\) −14.0000 −0.586911 −0.293455 0.955973i \(-0.594805\pi\)
−0.293455 + 0.955973i \(0.594805\pi\)
\(570\) −6.92820 + 1.85641i −0.290191 + 0.0777563i
\(571\) 2.67949i 0.112133i 0.998427 + 0.0560666i \(0.0178559\pi\)
−0.998427 + 0.0560666i \(0.982144\pi\)
\(572\) −8.19615 + 4.73205i −0.342698 + 0.197857i
\(573\) 29.0718i 1.21449i
\(574\) 4.14359 + 15.4641i 0.172950 + 0.645459i
\(575\) −28.0000 −1.16768
\(576\) 8.00000i 0.333333i
\(577\) −7.07180 −0.294403 −0.147201 0.989107i \(-0.547027\pi\)
−0.147201 + 0.989107i \(0.547027\pi\)
\(578\) −4.70577 17.5622i −0.195734 0.730490i
\(579\) 3.21539i 0.133627i
\(580\) 12.0000 6.92820i 0.498273 0.287678i
\(581\) 4.14359i 0.171905i
\(582\) 17.4641 4.67949i 0.723910 0.193971i
\(583\) −13.8564 −0.573874
\(584\) −14.9282 14.9282i −0.617733 0.617733i
\(585\) 3.46410 0.143223
\(586\) 44.9808 12.0526i 1.85814 0.497887i
\(587\) 4.33975i 0.179120i −0.995981 0.0895602i \(-0.971454\pi\)
0.995981 0.0895602i \(-0.0285462\pi\)
\(588\) 10.7846 + 18.6795i 0.444750 + 0.770329i
\(589\) 4.92820i 0.203063i
\(590\) −12.9282 48.2487i −0.532246 1.98637i
\(591\) 6.14359 0.252714
\(592\) −30.9282 17.8564i −1.27114 0.733894i
\(593\) −7.85641 −0.322624 −0.161312 0.986903i \(-0.551573\pi\)
−0.161312 + 0.986903i \(0.551573\pi\)
\(594\) −6.92820 25.8564i −0.284268 1.06090i
\(595\) 24.0000i 0.983904i
\(596\) 12.9282 + 22.3923i 0.529560 + 0.917225i
\(597\) 33.5692i 1.37390i
\(598\) 5.46410 1.46410i 0.223444 0.0598716i
\(599\) −45.1769 −1.84588 −0.922939 0.384945i \(-0.874220\pi\)
−0.922939 + 0.384945i \(0.874220\pi\)
\(600\) 28.0000 28.0000i 1.14310 1.14310i
\(601\) −4.39230 −0.179166 −0.0895829 0.995979i \(-0.528553\pi\)
−0.0895829 + 0.995979i \(0.528553\pi\)
\(602\) 0.928203 0.248711i 0.0378307 0.0101367i
\(603\) 0.732051i 0.0298114i
\(604\) 12.3397 7.12436i 0.502097 0.289886i
\(605\) 39.4641i 1.60444i
\(606\) −8.78461 32.7846i −0.356850 1.33178i
\(607\) 7.32051 0.297130 0.148565 0.988903i \(-0.452535\pi\)
0.148565 + 0.988903i \(0.452535\pi\)
\(608\) 1.07180 4.00000i 0.0434671 0.162221i
\(609\) 5.07180 0.205520
\(610\) 3.71281 + 13.8564i 0.150327 + 0.561029i
\(611\) 6.73205i 0.272350i
\(612\) 9.46410 5.46410i 0.382564 0.220873i
\(613\) 24.6410i 0.995241i 0.867395 + 0.497621i \(0.165793\pi\)
−0.867395 + 0.497621i \(0.834207\pi\)
\(614\) 1.00000 0.267949i 0.0403567 0.0108135i
\(615\) −61.8564 −2.49429
\(616\) −12.0000 + 12.0000i −0.483494 + 0.483494i
\(617\) 41.3205 1.66350 0.831751 0.555150i \(-0.187339\pi\)
0.831751 + 0.555150i \(0.187339\pi\)
\(618\) 18.9282 5.07180i 0.761404 0.204018i
\(619\) 18.5885i 0.747133i −0.927603 0.373567i \(-0.878135\pi\)
0.927603 0.373567i \(-0.121865\pi\)
\(620\) 23.3205 + 40.3923i 0.936574 + 1.62219i
\(621\) 16.0000i 0.642058i
\(622\) −0.392305 1.46410i −0.0157300 0.0587051i
\(623\) 21.9615 0.879870
\(624\) −4.00000 + 6.92820i −0.160128 + 0.277350i
\(625\) −11.0000 −0.440000
\(626\) −0.143594 0.535898i −0.00573915 0.0214188i
\(627\) 6.92820i 0.276686i
\(628\) 16.9282 + 29.3205i 0.675509 + 1.17002i
\(629\) 48.7846i 1.94517i
\(630\) 6.00000 1.60770i 0.239046 0.0640521i
\(631\) −42.0526 −1.67409 −0.837043 0.547137i \(-0.815718\pi\)
−0.837043 + 0.547137i \(0.815718\pi\)
\(632\) 10.9282 + 10.9282i 0.434701 + 0.434701i
\(633\) 15.7128 0.624528
\(634\) 4.73205 1.26795i 0.187934 0.0503567i
\(635\) 13.8564i 0.549875i
\(636\) −10.1436 + 5.85641i −0.402220 + 0.232222i
\(637\) 5.39230i 0.213651i
\(638\) −3.46410 12.9282i −0.137145 0.511832i
\(639\) 8.19615 0.324235
\(640\) 10.1436 + 37.8564i 0.400961 + 1.49641i
\(641\) −22.2487 −0.878771 −0.439386 0.898299i \(-0.644804\pi\)
−0.439386 + 0.898299i \(0.644804\pi\)
\(642\) 3.60770 + 13.4641i 0.142384 + 0.531386i
\(643\) 12.7321i 0.502103i −0.967974 0.251052i \(-0.919224\pi\)
0.967974 0.251052i \(-0.0807764\pi\)
\(644\) 8.78461 5.07180i 0.346162 0.199857i
\(645\) 3.71281i 0.146192i
\(646\) 5.46410 1.46410i 0.214982 0.0576043i
\(647\) 37.8564 1.48829 0.744144 0.668019i \(-0.232857\pi\)
0.744144 + 0.668019i \(0.232857\pi\)
\(648\) −22.0000 22.0000i −0.864242 0.864242i
\(649\) −48.2487 −1.89393
\(650\) −9.56218 + 2.56218i −0.375059 + 0.100497i
\(651\) 17.0718i 0.669096i
\(652\) −16.7321 28.9808i −0.655278 1.13497i
\(653\) 3.07180i 0.120209i −0.998192 0.0601043i \(-0.980857\pi\)
0.998192 0.0601043i \(-0.0191433\pi\)
\(654\) −1.46410 5.46410i −0.0572509 0.213663i
\(655\) −68.7846 −2.68764
\(656\) 17.8564 30.9282i 0.697176 1.20754i
\(657\) 7.46410 0.291202
\(658\) 3.12436 + 11.6603i 0.121800 + 0.454564i
\(659\) 14.0000i 0.545363i 0.962104 + 0.272681i \(0.0879105\pi\)
−0.962104 + 0.272681i \(0.912090\pi\)
\(660\) −32.7846 56.7846i −1.27614 2.21034i
\(661\) 17.3205i 0.673690i 0.941560 + 0.336845i \(0.109360\pi\)
−0.941560 + 0.336845i \(0.890640\pi\)
\(662\) 23.9282 6.41154i 0.929996 0.249192i
\(663\) −10.9282 −0.424416
\(664\) −6.53590 + 6.53590i −0.253642 + 0.253642i
\(665\) 3.21539 0.124687
\(666\) 12.1962 3.26795i 0.472591 0.126630i
\(667\) 8.00000i 0.309761i
\(668\) 9.80385 5.66025i 0.379322 0.219002i
\(669\) 0.392305i 0.0151674i
\(670\) 0.928203 + 3.46410i 0.0358596 + 0.133830i
\(671\) 13.8564 0.534921
\(672\) −3.71281 + 13.8564i −0.143225 + 0.534522i
\(673\) 33.1769 1.27888 0.639438 0.768843i \(-0.279167\pi\)
0.639438 + 0.768843i \(0.279167\pi\)
\(674\) −0.535898 2.00000i −0.0206420 0.0770371i
\(675\) 28.0000i 1.07772i
\(676\) 1.73205 1.00000i 0.0666173 0.0384615i
\(677\) 21.0718i 0.809855i 0.914349 + 0.404927i \(0.132703\pi\)
−0.914349 + 0.404927i \(0.867297\pi\)
\(678\) 6.92820 1.85641i 0.266076 0.0712949i
\(679\) −8.10512 −0.311046
\(680\) −37.8564 + 37.8564i −1.45173 + 1.45173i
\(681\) −5.75129 −0.220390
\(682\) 43.5167 11.6603i 1.66634 0.446494i
\(683\) 17.8038i 0.681245i −0.940200 0.340623i \(-0.889362\pi\)
0.940200 0.340623i \(-0.110638\pi\)
\(684\) 0.732051 + 1.26795i 0.0279907 + 0.0484812i
\(685\) 44.7846i 1.71113i
\(686\) −5.75129 21.4641i −0.219585 0.819503i
\(687\) 10.6410 0.405980
\(688\) −1.85641 1.07180i −0.0707748 0.0408619i
\(689\) 2.92820 0.111556
\(690\) 10.1436 + 37.8564i 0.386160 + 1.44117i
\(691\) 32.8372i 1.24918i −0.780951 0.624592i \(-0.785265\pi\)
0.780951 0.624592i \(-0.214735\pi\)
\(692\) −6.92820 12.0000i −0.263371 0.456172i
\(693\) 6.00000i 0.227921i
\(694\) −9.66025 + 2.58846i −0.366698 + 0.0982565i
\(695\) 34.6410 1.31401
\(696\) −8.00000 8.00000i −0.303239 0.303239i
\(697\) 48.7846 1.84785
\(698\) 13.1244 3.51666i 0.496764 0.133108i
\(699\) 33.8564i 1.28057i
\(700\) −15.3731 + 8.87564i −0.581047 + 0.335468i
\(701\) 40.6410i 1.53499i −0.641055 0.767495i \(-0.721503\pi\)
0.641055 0.767495i \(-0.278497\pi\)
\(702\) 1.46410 + 5.46410i 0.0552590 + 0.206229i
\(703\) 6.53590 0.246506
\(704\) 37.8564 1.42677
\(705\) −46.6410 −1.75660
\(706\) 4.05256 + 15.1244i 0.152520 + 0.569213i
\(707\) 15.2154i 0.572234i
\(708\) −35.3205 + 20.3923i −1.32743 + 0.766390i
\(709\) 29.3205i 1.10115i 0.834784 + 0.550577i \(0.185592\pi\)
−0.834784 + 0.550577i \(0.814408\pi\)
\(710\) −38.7846 + 10.3923i −1.45556 + 0.390016i
\(711\) −5.46410 −0.204920
\(712\) −34.6410 34.6410i −1.29823 1.29823i
\(713\) −26.9282 −1.00847
\(714\) −18.9282 + 5.07180i −0.708370 + 0.189807i
\(715\) 16.3923i 0.613037i
\(716\) 10.3923 + 18.0000i 0.388379 + 0.672692i
\(717\) 37.4641i 1.39912i
\(718\) −11.5359 43.0526i −0.430516 1.60671i
\(719\) 30.9282 1.15343 0.576714 0.816946i \(-0.304335\pi\)
0.576714 + 0.816946i \(0.304335\pi\)
\(720\) −12.0000 6.92820i −0.447214 0.258199i
\(721\) −8.78461 −0.327156
\(722\) −6.75833 25.2224i −0.251519 0.938682i
\(723\) 60.7846i 2.26060i
\(724\) 8.92820 + 15.4641i 0.331814 + 0.574719i
\(725\) 14.0000i 0.519947i
\(726\) −31.1244 + 8.33975i −1.15513 + 0.309517i
\(727\) −22.9282 −0.850360 −0.425180 0.905109i \(-0.639789\pi\)
−0.425180 + 0.905109i \(0.639789\pi\)
\(728\) 2.53590 2.53590i 0.0939866 0.0939866i
\(729\) −13.0000 −0.481481
\(730\) −35.3205 + 9.46410i −1.30727 + 0.350282i
\(731\) 2.92820i 0.108304i
\(732\) 10.1436 5.85641i 0.374918 0.216459i
\(733\) 37.3205i 1.37846i 0.724541 + 0.689232i \(0.242052\pi\)
−0.724541 + 0.689232i \(0.757948\pi\)
\(734\) 8.14359 + 30.3923i 0.300586 + 1.12180i
\(735\) 37.3590 1.37801
\(736\) −21.8564 5.85641i −0.805638 0.215870i
\(737\) 3.46410 0.127602
\(738\) 3.26795 + 12.1962i 0.120295 + 0.448947i
\(739\) 39.7654i 1.46279i 0.681953 + 0.731396i \(0.261131\pi\)
−0.681953 + 0.731396i \(0.738869\pi\)
\(740\) −53.5692 + 30.9282i −1.96924 + 1.13694i
\(741\) 1.46410i 0.0537851i
\(742\) 5.07180 1.35898i 0.186192 0.0498899i
\(743\) −32.1962 −1.18116 −0.590581 0.806978i \(-0.701101\pi\)
−0.590581 + 0.806978i \(0.701101\pi\)
\(744\) 26.9282 26.9282i 0.987236 0.987236i
\(745\) 44.7846 1.64078
\(746\) −20.1962 + 5.41154i −0.739434 + 0.198131i
\(747\) 3.26795i 0.119568i
\(748\) 25.8564 + 44.7846i 0.945404 + 1.63749i
\(749\) 6.24871i 0.228323i
\(750\) −5.07180 18.9282i −0.185196 0.691160i
\(751\) 1.07180 0.0391104 0.0195552 0.999809i \(-0.493775\pi\)
0.0195552 + 0.999809i \(0.493775\pi\)
\(752\) 13.4641 23.3205i 0.490985 0.850411i
\(753\) −12.7846 −0.465897
\(754\) 0.732051 + 2.73205i 0.0266597 + 0.0994954i
\(755\) 24.6795i 0.898179i
\(756\) 5.07180 + 8.78461i 0.184459 + 0.319493i
\(757\) 40.7846i 1.48234i 0.671316 + 0.741171i \(0.265729\pi\)
−0.671316 + 0.741171i \(0.734271\pi\)
\(758\) 19.9282 5.33975i 0.723825 0.193948i
\(759\) 37.8564 1.37410
\(760\) −5.07180 5.07180i −0.183973 0.183973i
\(761\) 18.7846 0.680942 0.340471 0.940255i \(-0.389414\pi\)
0.340471 + 0.940255i \(0.389414\pi\)
\(762\) −10.9282 + 2.92820i −0.395887 + 0.106078i
\(763\) 2.53590i 0.0918057i
\(764\) 25.1769 14.5359i 0.910869 0.525890i
\(765\) 18.9282i 0.684351i
\(766\) 3.78461 + 14.1244i 0.136744 + 0.510334i
\(767\) 10.1962 0.368162
\(768\) 27.7128 16.0000i 1.00000 0.577350i
\(769\) 31.4641 1.13462 0.567312 0.823503i \(-0.307983\pi\)
0.567312 + 0.823503i \(0.307983\pi\)
\(770\) 7.60770 + 28.3923i 0.274162 + 1.02319i
\(771\) 47.7128i 1.71833i
\(772\) 2.78461 1.60770i 0.100220 0.0578622i
\(773\) 27.4641i 0.987815i 0.869514 + 0.493908i \(0.16443