Properties

Label 104.2.b.b.53.3
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 53.3
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 104.53
Dual form 104.2.b.b.53.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36603 - 0.366025i) q^{2} -2.00000i q^{3} +(1.73205 - 1.00000i) q^{4} +3.46410i q^{5} +(-0.732051 - 2.73205i) q^{6} -4.73205 q^{7} +(2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(1.36603 - 0.366025i) q^{2} -2.00000i q^{3} +(1.73205 - 1.00000i) q^{4} +3.46410i q^{5} +(-0.732051 - 2.73205i) q^{6} -4.73205 q^{7} +(2.00000 - 2.00000i) q^{8} -1.00000 q^{9} +(1.26795 + 4.73205i) q^{10} +1.26795i q^{11} +(-2.00000 - 3.46410i) q^{12} -1.00000i q^{13} +(-6.46410 + 1.73205i) q^{14} +6.92820 q^{15} +(2.00000 - 3.46410i) q^{16} -1.46410 q^{17} +(-1.36603 + 0.366025i) q^{18} +2.73205i q^{19} +(3.46410 + 6.00000i) q^{20} +9.46410i q^{21} +(0.464102 + 1.73205i) q^{22} +4.00000 q^{23} +(-4.00000 - 4.00000i) q^{24} -7.00000 q^{25} +(-0.366025 - 1.36603i) q^{26} -4.00000i q^{27} +(-8.19615 + 4.73205i) q^{28} -2.00000i q^{29} +(9.46410 - 2.53590i) q^{30} -3.26795 q^{31} +(1.46410 - 5.46410i) q^{32} +2.53590 q^{33} +(-2.00000 + 0.535898i) q^{34} -16.3923i q^{35} +(-1.73205 + 1.00000i) q^{36} -4.92820i q^{37} +(1.00000 + 3.73205i) q^{38} -2.00000 q^{39} +(6.92820 + 6.92820i) q^{40} -4.92820 q^{41} +(3.46410 + 12.9282i) q^{42} +7.46410i q^{43} +(1.26795 + 2.19615i) q^{44} -3.46410i q^{45} +(5.46410 - 1.46410i) q^{46} +3.26795 q^{47} +(-6.92820 - 4.00000i) q^{48} +15.3923 q^{49} +(-9.56218 + 2.56218i) q^{50} +2.92820i q^{51} +(-1.00000 - 1.73205i) q^{52} -10.9282i q^{53} +(-1.46410 - 5.46410i) q^{54} -4.39230 q^{55} +(-9.46410 + 9.46410i) q^{56} +5.46410 q^{57} +(-0.732051 - 2.73205i) q^{58} -0.196152i q^{59} +(12.0000 - 6.92820i) q^{60} +10.9282i q^{61} +(-4.46410 + 1.19615i) q^{62} +4.73205 q^{63} -8.00000i q^{64} +3.46410 q^{65} +(3.46410 - 0.928203i) q^{66} +2.73205i q^{67} +(-2.53590 + 1.46410i) q^{68} -8.00000i q^{69} +(-6.00000 - 22.3923i) q^{70} +2.19615 q^{71} +(-2.00000 + 2.00000i) q^{72} -0.535898 q^{73} +(-1.80385 - 6.73205i) q^{74} +14.0000i q^{75} +(2.73205 + 4.73205i) q^{76} -6.00000i q^{77} +(-2.73205 + 0.732051i) q^{78} -1.46410 q^{79} +(12.0000 + 6.92820i) q^{80} -11.0000 q^{81} +(-6.73205 + 1.80385i) q^{82} -6.73205i q^{83} +(9.46410 + 16.3923i) q^{84} -5.07180i q^{85} +(2.73205 + 10.1962i) q^{86} -4.00000 q^{87} +(2.53590 + 2.53590i) q^{88} +17.3205 q^{89} +(-1.26795 - 4.73205i) q^{90} +4.73205i q^{91} +(6.92820 - 4.00000i) q^{92} +6.53590i q^{93} +(4.46410 - 1.19615i) q^{94} -9.46410 q^{95} +(-10.9282 - 2.92820i) q^{96} -14.3923 q^{97} +(21.0263 - 5.63397i) q^{98} -1.26795i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 0.366025i 0.965926 0.258819i
\(3\) 2.00000i 1.15470i −0.816497 0.577350i \(-0.804087\pi\)
0.816497 0.577350i \(-0.195913\pi\)
\(4\) 1.73205 1.00000i 0.866025 0.500000i
\(5\) 3.46410i 1.54919i 0.632456 + 0.774597i \(0.282047\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) −0.732051 2.73205i −0.298858 1.11536i
\(7\) −4.73205 −1.78855 −0.894274 0.447521i \(-0.852307\pi\)
−0.894274 + 0.447521i \(0.852307\pi\)
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) −1.00000 −0.333333
\(10\) 1.26795 + 4.73205i 0.400961 + 1.49641i
\(11\) 1.26795i 0.382301i 0.981561 + 0.191151i \(0.0612219\pi\)
−0.981561 + 0.191151i \(0.938778\pi\)
\(12\) −2.00000 3.46410i −0.577350 1.00000i
\(13\) 1.00000i 0.277350i
\(14\) −6.46410 + 1.73205i −1.72760 + 0.462910i
\(15\) 6.92820 1.78885
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −1.46410 −0.355097 −0.177548 0.984112i \(-0.556817\pi\)
−0.177548 + 0.984112i \(0.556817\pi\)
\(18\) −1.36603 + 0.366025i −0.321975 + 0.0862730i
\(19\) 2.73205i 0.626775i 0.949625 + 0.313388i \(0.101464\pi\)
−0.949625 + 0.313388i \(0.898536\pi\)
\(20\) 3.46410 + 6.00000i 0.774597 + 1.34164i
\(21\) 9.46410i 2.06524i
\(22\) 0.464102 + 1.73205i 0.0989468 + 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
\(26\) −0.366025 1.36603i −0.0717835 0.267900i
\(27\) 4.00000i 0.769800i
\(28\) −8.19615 + 4.73205i −1.54893 + 0.894274i
\(29\) 2.00000i 0.371391i −0.982607 0.185695i \(-0.940546\pi\)
0.982607 0.185695i \(-0.0594537\pi\)
\(30\) 9.46410 2.53590i 1.72790 0.462990i
\(31\) −3.26795 −0.586941 −0.293471 0.955968i \(-0.594810\pi\)
−0.293471 + 0.955968i \(0.594810\pi\)
\(32\) 1.46410 5.46410i 0.258819 0.965926i
\(33\) 2.53590 0.441443
\(34\) −2.00000 + 0.535898i −0.342997 + 0.0919058i
\(35\) 16.3923i 2.77081i
\(36\) −1.73205 + 1.00000i −0.288675 + 0.166667i
\(37\) 4.92820i 0.810192i −0.914274 0.405096i \(-0.867238\pi\)
0.914274 0.405096i \(-0.132762\pi\)
\(38\) 1.00000 + 3.73205i 0.162221 + 0.605419i
\(39\) −2.00000 −0.320256
\(40\) 6.92820 + 6.92820i 1.09545 + 1.09545i
\(41\) −4.92820 −0.769656 −0.384828 0.922988i \(-0.625739\pi\)
−0.384828 + 0.922988i \(0.625739\pi\)
\(42\) 3.46410 + 12.9282i 0.534522 + 1.99487i
\(43\) 7.46410i 1.13826i 0.822246 + 0.569132i \(0.192721\pi\)
−0.822246 + 0.569132i \(0.807279\pi\)
\(44\) 1.26795 + 2.19615i 0.191151 + 0.331082i
\(45\) 3.46410i 0.516398i
\(46\) 5.46410 1.46410i 0.805638 0.215870i
\(47\) 3.26795 0.476679 0.238340 0.971182i \(-0.423397\pi\)
0.238340 + 0.971182i \(0.423397\pi\)
\(48\) −6.92820 4.00000i −1.00000 0.577350i
\(49\) 15.3923 2.19890
\(50\) −9.56218 + 2.56218i −1.35230 + 0.362347i
\(51\) 2.92820i 0.410030i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 10.9282i 1.50110i −0.660811 0.750552i \(-0.729788\pi\)
0.660811 0.750552i \(-0.270212\pi\)
\(54\) −1.46410 5.46410i −0.199239 0.743570i
\(55\) −4.39230 −0.592258
\(56\) −9.46410 + 9.46410i −1.26469 + 1.26469i
\(57\) 5.46410 0.723738
\(58\) −0.732051 2.73205i −0.0961230 0.358736i
\(59\) 0.196152i 0.0255369i −0.999918 0.0127684i \(-0.995936\pi\)
0.999918 0.0127684i \(-0.00406443\pi\)
\(60\) 12.0000 6.92820i 1.54919 0.894427i
\(61\) 10.9282i 1.39921i 0.714528 + 0.699607i \(0.246641\pi\)
−0.714528 + 0.699607i \(0.753359\pi\)
\(62\) −4.46410 + 1.19615i −0.566941 + 0.151912i
\(63\) 4.73205 0.596182
\(64\) 8.00000i 1.00000i
\(65\) 3.46410 0.429669
\(66\) 3.46410 0.928203i 0.426401 0.114254i
\(67\) 2.73205i 0.333773i 0.985976 + 0.166887i \(0.0533714\pi\)
−0.985976 + 0.166887i \(0.946629\pi\)
\(68\) −2.53590 + 1.46410i −0.307523 + 0.177548i
\(69\) 8.00000i 0.963087i
\(70\) −6.00000 22.3923i −0.717137 2.67639i
\(71\) 2.19615 0.260635 0.130318 0.991472i \(-0.458400\pi\)
0.130318 + 0.991472i \(0.458400\pi\)
\(72\) −2.00000 + 2.00000i −0.235702 + 0.235702i
\(73\) −0.535898 −0.0627222 −0.0313611 0.999508i \(-0.509984\pi\)
−0.0313611 + 0.999508i \(0.509984\pi\)
\(74\) −1.80385 6.73205i −0.209693 0.782585i
\(75\) 14.0000i 1.61658i
\(76\) 2.73205 + 4.73205i 0.313388 + 0.542803i
\(77\) 6.00000i 0.683763i
\(78\) −2.73205 + 0.732051i −0.309344 + 0.0828884i
\(79\) −1.46410 −0.164724 −0.0823622 0.996602i \(-0.526246\pi\)
−0.0823622 + 0.996602i \(0.526246\pi\)
\(80\) 12.0000 + 6.92820i 1.34164 + 0.774597i
\(81\) −11.0000 −1.22222
\(82\) −6.73205 + 1.80385i −0.743431 + 0.199202i
\(83\) 6.73205i 0.738939i −0.929243 0.369469i \(-0.879539\pi\)
0.929243 0.369469i \(-0.120461\pi\)
\(84\) 9.46410 + 16.3923i 1.03262 + 1.78855i
\(85\) 5.07180i 0.550114i
\(86\) 2.73205 + 10.1962i 0.294605 + 1.09948i
\(87\) −4.00000 −0.428845
\(88\) 2.53590 + 2.53590i 0.270328 + 0.270328i
\(89\) 17.3205 1.83597 0.917985 0.396615i \(-0.129815\pi\)
0.917985 + 0.396615i \(0.129815\pi\)
\(90\) −1.26795 4.73205i −0.133654 0.498802i
\(91\) 4.73205i 0.496054i
\(92\) 6.92820 4.00000i 0.722315 0.417029i
\(93\) 6.53590i 0.677741i
\(94\) 4.46410 1.19615i 0.460437 0.123374i
\(95\) −9.46410 −0.970996
\(96\) −10.9282 2.92820i −1.11536 0.298858i
\(97\) −14.3923 −1.46132 −0.730659 0.682743i \(-0.760787\pi\)
−0.730659 + 0.682743i \(0.760787\pi\)
\(98\) 21.0263 5.63397i 2.12397 0.569117i
\(99\) 1.26795i 0.127434i
\(100\) −12.1244 + 7.00000i −1.21244 + 0.700000i
\(101\) 12.0000i 1.19404i 0.802225 + 0.597022i \(0.203650\pi\)
−0.802225 + 0.597022i \(0.796350\pi\)
\(102\) 1.07180 + 4.00000i 0.106124 + 0.396059i
\(103\) −6.92820 −0.682656 −0.341328 0.939944i \(-0.610877\pi\)
−0.341328 + 0.939944i \(0.610877\pi\)
\(104\) −2.00000 2.00000i −0.196116 0.196116i
\(105\) −32.7846 −3.19945
\(106\) −4.00000 14.9282i −0.388514 1.44996i
\(107\) 8.92820i 0.863122i 0.902084 + 0.431561i \(0.142037\pi\)
−0.902084 + 0.431561i \(0.857963\pi\)
\(108\) −4.00000 6.92820i −0.384900 0.666667i
\(109\) 2.00000i 0.191565i 0.995402 + 0.0957826i \(0.0305354\pi\)
−0.995402 + 0.0957826i \(0.969465\pi\)
\(110\) −6.00000 + 1.60770i −0.572078 + 0.153288i
\(111\) −9.85641 −0.935529
\(112\) −9.46410 + 16.3923i −0.894274 + 1.54893i
\(113\) 9.46410 0.890308 0.445154 0.895454i \(-0.353149\pi\)
0.445154 + 0.895454i \(0.353149\pi\)
\(114\) 7.46410 2.00000i 0.699077 0.187317i
\(115\) 13.8564i 1.29212i
\(116\) −2.00000 3.46410i −0.185695 0.321634i
\(117\) 1.00000i 0.0924500i
\(118\) −0.0717968 0.267949i −0.00660943 0.0246667i
\(119\) 6.92820 0.635107
\(120\) 13.8564 13.8564i 1.26491 1.26491i
\(121\) 9.39230 0.853846
\(122\) 4.00000 + 14.9282i 0.362143 + 1.35154i
\(123\) 9.85641i 0.888722i
\(124\) −5.66025 + 3.26795i −0.508306 + 0.293471i
\(125\) 6.92820i 0.619677i
\(126\) 6.46410 1.73205i 0.575868 0.154303i
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) −2.92820 10.9282i −0.258819 0.965926i
\(129\) 14.9282 1.31436
\(130\) 4.73205 1.26795i 0.415028 0.111207i
\(131\) 7.85641i 0.686417i 0.939259 + 0.343209i \(0.111514\pi\)
−0.939259 + 0.343209i \(0.888486\pi\)
\(132\) 4.39230 2.53590i 0.382301 0.220722i
\(133\) 12.9282i 1.12102i
\(134\) 1.00000 + 3.73205i 0.0863868 + 0.322400i
\(135\) 13.8564 1.19257
\(136\) −2.92820 + 2.92820i −0.251091 + 0.251091i
\(137\) −0.928203 −0.0793018 −0.0396509 0.999214i \(-0.512625\pi\)
−0.0396509 + 0.999214i \(0.512625\pi\)
\(138\) −2.92820 10.9282i −0.249265 0.930270i
\(139\) 10.0000i 0.848189i 0.905618 + 0.424094i \(0.139408\pi\)
−0.905618 + 0.424094i \(0.860592\pi\)
\(140\) −16.3923 28.3923i −1.38540 2.39959i
\(141\) 6.53590i 0.550422i
\(142\) 3.00000 0.803848i 0.251754 0.0674574i
\(143\) 1.26795 0.106031
\(144\) −2.00000 + 3.46410i −0.166667 + 0.288675i
\(145\) 6.92820 0.575356
\(146\) −0.732051 + 0.196152i −0.0605850 + 0.0162337i
\(147\) 30.7846i 2.53907i
\(148\) −4.92820 8.53590i −0.405096 0.701647i
\(149\) 0.928203i 0.0760414i −0.999277 0.0380207i \(-0.987895\pi\)
0.999277 0.0380207i \(-0.0121053\pi\)
\(150\) 5.12436 + 19.1244i 0.418402 + 1.56150i
\(151\) 17.1244 1.39356 0.696780 0.717285i \(-0.254615\pi\)
0.696780 + 0.717285i \(0.254615\pi\)
\(152\) 5.46410 + 5.46410i 0.443197 + 0.443197i
\(153\) 1.46410 0.118366
\(154\) −2.19615 8.19615i −0.176971 0.660465i
\(155\) 11.3205i 0.909285i
\(156\) −3.46410 + 2.00000i −0.277350 + 0.160128i
\(157\) 3.07180i 0.245156i 0.992459 + 0.122578i \(0.0391162\pi\)
−0.992459 + 0.122578i \(0.960884\pi\)
\(158\) −2.00000 + 0.535898i −0.159111 + 0.0426338i
\(159\) −21.8564 −1.73333
\(160\) 18.9282 + 5.07180i 1.49641 + 0.400961i
\(161\) −18.9282 −1.49175
\(162\) −15.0263 + 4.02628i −1.18058 + 0.316334i
\(163\) 13.2679i 1.03923i −0.854402 0.519613i \(-0.826076\pi\)
0.854402 0.519613i \(-0.173924\pi\)
\(164\) −8.53590 + 4.92820i −0.666542 + 0.384828i
\(165\) 8.78461i 0.683881i
\(166\) −2.46410 9.19615i −0.191251 0.713760i
\(167\) 11.6603 0.902298 0.451149 0.892449i \(-0.351014\pi\)
0.451149 + 0.892449i \(0.351014\pi\)
\(168\) 18.9282 + 18.9282i 1.46034 + 1.46034i
\(169\) −1.00000 −0.0769231
\(170\) −1.85641 6.92820i −0.142380 0.531369i
\(171\) 2.73205i 0.208925i
\(172\) 7.46410 + 12.9282i 0.569132 + 0.985766i
\(173\) 6.92820i 0.526742i 0.964695 + 0.263371i \(0.0848343\pi\)
−0.964695 + 0.263371i \(0.915166\pi\)
\(174\) −5.46410 + 1.46410i −0.414232 + 0.110993i
\(175\) 33.1244 2.50397
\(176\) 4.39230 + 2.53590i 0.331082 + 0.191151i
\(177\) −0.392305 −0.0294874
\(178\) 23.6603 6.33975i 1.77341 0.475184i
\(179\) 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
\(181\) 4.92820i 0.366310i −0.983084 0.183155i \(-0.941369\pi\)
0.983084 0.183155i \(-0.0586311\pi\)
\(182\) 1.73205 + 6.46410i 0.128388 + 0.479151i
\(183\) 21.8564 1.61567
\(184\) 8.00000 8.00000i 0.589768 0.589768i
\(185\) 17.0718 1.25514
\(186\) 2.39230 + 8.92820i 0.175412 + 0.654648i
\(187\) 1.85641i 0.135754i
\(188\) 5.66025 3.26795i 0.412816 0.238340i
\(189\) 18.9282i 1.37682i
\(190\) −12.9282 + 3.46410i −0.937910 + 0.251312i
\(191\) −21.4641 −1.55309 −0.776544 0.630063i \(-0.783029\pi\)
−0.776544 + 0.630063i \(0.783029\pi\)
\(192\) −16.0000 −1.15470
\(193\) −22.3923 −1.61183 −0.805917 0.592029i \(-0.798327\pi\)
−0.805917 + 0.592029i \(0.798327\pi\)
\(194\) −19.6603 + 5.26795i −1.41152 + 0.378217i
\(195\) 6.92820i 0.496139i
\(196\) 26.6603 15.3923i 1.90430 1.09945i
\(197\) 16.9282i 1.20608i 0.797709 + 0.603042i \(0.206045\pi\)
−0.797709 + 0.603042i \(0.793955\pi\)
\(198\) −0.464102 1.73205i −0.0329823 0.123091i
\(199\) −24.7846 −1.75693 −0.878467 0.477803i \(-0.841433\pi\)
−0.878467 + 0.477803i \(0.841433\pi\)
\(200\) −14.0000 + 14.0000i −0.989949 + 0.989949i
\(201\) 5.46410 0.385408
\(202\) 4.39230 + 16.3923i 0.309041 + 1.15336i
\(203\) 9.46410i 0.664250i
\(204\) 2.92820 + 5.07180i 0.205015 + 0.355097i
\(205\) 17.0718i 1.19235i
\(206\) −9.46410 + 2.53590i −0.659395 + 0.176684i
\(207\) −4.00000 −0.278019
\(208\) −3.46410 2.00000i −0.240192 0.138675i
\(209\) −3.46410 −0.239617
\(210\) −44.7846 + 12.0000i −3.09043 + 0.828079i
\(211\) 19.8564i 1.36697i −0.729964 0.683486i \(-0.760463\pi\)
0.729964 0.683486i \(-0.239537\pi\)
\(212\) −10.9282 18.9282i −0.750552 1.29999i
\(213\) 4.39230i 0.300956i
\(214\) 3.26795 + 12.1962i 0.223392 + 0.833712i
\(215\) −25.8564 −1.76339
\(216\) −8.00000 8.00000i −0.544331 0.544331i
\(217\) 15.4641 1.04977
\(218\) 0.732051 + 2.73205i 0.0495807 + 0.185038i
\(219\) 1.07180i 0.0724253i
\(220\) −7.60770 + 4.39230i −0.512911 + 0.296129i
\(221\) 1.46410i 0.0984861i
\(222\) −13.4641 + 3.60770i −0.903651 + 0.242133i
\(223\) 10.1962 0.682785 0.341392 0.939921i \(-0.389101\pi\)
0.341392 + 0.939921i \(0.389101\pi\)
\(224\) −6.92820 + 25.8564i −0.462910 + 1.72760i
\(225\) 7.00000 0.466667
\(226\) 12.9282 3.46410i 0.859971 0.230429i
\(227\) 27.1244i 1.80031i −0.435573 0.900153i \(-0.643454\pi\)
0.435573 0.900153i \(-0.356546\pi\)
\(228\) 9.46410 5.46410i 0.626775 0.361869i
\(229\) 29.3205i 1.93755i −0.247934 0.968777i \(-0.579752\pi\)
0.247934 0.968777i \(-0.420248\pi\)
\(230\) 5.07180 + 18.9282i 0.334424 + 1.24809i
\(231\) −12.0000 −0.789542
\(232\) −4.00000 4.00000i −0.262613 0.262613i
\(233\) 3.07180 0.201240 0.100620 0.994925i \(-0.467917\pi\)
0.100620 + 0.994925i \(0.467917\pi\)
\(234\) 0.366025 + 1.36603i 0.0239278 + 0.0892999i
\(235\) 11.3205i 0.738469i
\(236\) −0.196152 0.339746i −0.0127684 0.0221156i
\(237\) 2.92820i 0.190207i
\(238\) 9.46410 2.53590i 0.613467 0.164378i
\(239\) 15.2679 0.987602 0.493801 0.869575i \(-0.335607\pi\)
0.493801 + 0.869575i \(0.335607\pi\)
\(240\) 13.8564 24.0000i 0.894427 1.54919i
\(241\) −9.60770 −0.618886 −0.309443 0.950918i \(-0.600143\pi\)
−0.309443 + 0.950918i \(0.600143\pi\)
\(242\) 12.8301 3.43782i 0.824752 0.220992i
\(243\) 10.0000i 0.641500i
\(244\) 10.9282 + 18.9282i 0.699607 + 1.21175i
\(245\) 53.3205i 3.40652i
\(246\) 3.60770 + 13.4641i 0.230018 + 0.858440i
\(247\) 2.73205 0.173836
\(248\) −6.53590 + 6.53590i −0.415030 + 0.415030i
\(249\) −13.4641 −0.853253
\(250\) −2.53590 9.46410i −0.160384 0.598562i
\(251\) 14.3923i 0.908434i 0.890891 + 0.454217i \(0.150081\pi\)
−0.890891 + 0.454217i \(0.849919\pi\)
\(252\) 8.19615 4.73205i 0.516309 0.298091i
\(253\) 5.07180i 0.318861i
\(254\) −5.46410 + 1.46410i −0.342848 + 0.0918659i
\(255\) −10.1436 −0.635216
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) 3.85641 0.240556 0.120278 0.992740i \(-0.461621\pi\)
0.120278 + 0.992740i \(0.461621\pi\)
\(258\) 20.3923 5.46410i 1.26957 0.340180i
\(259\) 23.3205i 1.44907i
\(260\) 6.00000 3.46410i 0.372104 0.214834i
\(261\) 2.00000i 0.123797i
\(262\) 2.87564 + 10.7321i 0.177658 + 0.663028i
\(263\) 7.32051 0.451402 0.225701 0.974197i \(-0.427533\pi\)
0.225701 + 0.974197i \(0.427533\pi\)
\(264\) 5.07180 5.07180i 0.312148 0.312148i
\(265\) 37.8564 2.32550
\(266\) −4.73205 17.6603i −0.290141 1.08282i
\(267\) 34.6410i 2.12000i
\(268\) 2.73205 + 4.73205i 0.166887 + 0.289056i
\(269\) 19.8564i 1.21067i −0.795972 0.605333i \(-0.793040\pi\)
0.795972 0.605333i \(-0.206960\pi\)
\(270\) 18.9282 5.07180i 1.15193 0.308660i
\(271\) −9.80385 −0.595541 −0.297771 0.954637i \(-0.596243\pi\)
−0.297771 + 0.954637i \(0.596243\pi\)
\(272\) −2.92820 + 5.07180i −0.177548 + 0.307523i
\(273\) 9.46410 0.572793
\(274\) −1.26795 + 0.339746i −0.0765996 + 0.0205248i
\(275\) 8.87564i 0.535221i
\(276\) −8.00000 13.8564i −0.481543 0.834058i
\(277\) 25.8564i 1.55356i 0.629771 + 0.776780i \(0.283149\pi\)
−0.629771 + 0.776780i \(0.716851\pi\)
\(278\) 3.66025 + 13.6603i 0.219527 + 0.819288i
\(279\) 3.26795 0.195647
\(280\) −32.7846 32.7846i −1.95926 1.95926i
\(281\) −25.3205 −1.51049 −0.755247 0.655440i \(-0.772483\pi\)
−0.755247 + 0.655440i \(0.772483\pi\)
\(282\) −2.39230 8.92820i −0.142460 0.531667i
\(283\) 12.5359i 0.745182i −0.927996 0.372591i \(-0.878469\pi\)
0.927996 0.372591i \(-0.121531\pi\)
\(284\) 3.80385 2.19615i 0.225717 0.130318i
\(285\) 18.9282i 1.12121i
\(286\) 1.73205 0.464102i 0.102418 0.0274429i
\(287\) 23.3205 1.37657
\(288\) −1.46410 + 5.46410i −0.0862730 + 0.321975i
\(289\) −14.8564 −0.873906
\(290\) 9.46410 2.53590i 0.555751 0.148913i
\(291\) 28.7846i 1.68738i
\(292\) −0.928203 + 0.535898i −0.0543190 + 0.0313611i
\(293\) 19.0718i 1.11419i −0.830450 0.557093i \(-0.811917\pi\)
0.830450 0.557093i \(-0.188083\pi\)
\(294\) −11.2679 42.0526i −0.657160 2.45256i
\(295\) 0.679492 0.0395615
\(296\) −9.85641 9.85641i −0.572892 0.572892i
\(297\) 5.07180 0.294295
\(298\) −0.339746 1.26795i −0.0196810 0.0734503i
\(299\) 4.00000i 0.231326i
\(300\) 14.0000 + 24.2487i 0.808290 + 1.40000i
\(301\) 35.3205i 2.03584i
\(302\) 23.3923 6.26795i 1.34608 0.360680i
\(303\) 24.0000 1.37876
\(304\) 9.46410 + 5.46410i 0.542803 + 0.313388i
\(305\) −37.8564 −2.16765
\(306\) 2.00000 0.535898i 0.114332 0.0306353i
\(307\) 2.73205i 0.155926i 0.996956 + 0.0779632i \(0.0248417\pi\)
−0.996956 + 0.0779632i \(0.975158\pi\)
\(308\) −6.00000 10.3923i −0.341882 0.592157i
\(309\) 13.8564i 0.788263i
\(310\) −4.14359 15.4641i −0.235340 0.878302i
\(311\) 14.9282 0.846501 0.423250 0.906013i \(-0.360889\pi\)
0.423250 + 0.906013i \(0.360889\pi\)
\(312\) −4.00000 + 4.00000i −0.226455 + 0.226455i
\(313\) −20.3923 −1.15264 −0.576321 0.817224i \(-0.695512\pi\)
−0.576321 + 0.817224i \(0.695512\pi\)
\(314\) 1.12436 + 4.19615i 0.0634511 + 0.236803i
\(315\) 16.3923i 0.923602i
\(316\) −2.53590 + 1.46410i −0.142655 + 0.0823622i
\(317\) 3.46410i 0.194563i 0.995257 + 0.0972817i \(0.0310148\pi\)
−0.995257 + 0.0972817i \(0.968985\pi\)
\(318\) −29.8564 + 8.00000i −1.67426 + 0.448618i
\(319\) 2.53590 0.141983
\(320\) 27.7128 1.54919
\(321\) 17.8564 0.996647
\(322\) −25.8564 + 6.92820i −1.44092 + 0.386094i
\(323\) 4.00000i 0.222566i
\(324\) −19.0526 + 11.0000i −1.05848 + 0.611111i
\(325\) 7.00000i 0.388290i
\(326\) −4.85641 18.1244i −0.268971 1.00382i
\(327\) 4.00000 0.221201
\(328\) −9.85641 + 9.85641i −0.544229 + 0.544229i
\(329\) −15.4641 −0.852564
\(330\) 3.21539 + 12.0000i 0.177001 + 0.660578i
\(331\) 27.5167i 1.51245i 0.654310 + 0.756226i \(0.272959\pi\)
−0.654310 + 0.756226i \(0.727041\pi\)
\(332\) −6.73205 11.6603i −0.369469 0.639940i
\(333\) 4.92820i 0.270064i
\(334\) 15.9282 4.26795i 0.871553 0.233532i
\(335\) −9.46410 −0.517079
\(336\) 32.7846 + 18.9282i 1.78855 + 1.03262i
\(337\) −5.46410 −0.297649 −0.148824 0.988864i \(-0.547549\pi\)
−0.148824 + 0.988864i \(0.547549\pi\)
\(338\) −1.36603 + 0.366025i −0.0743020 + 0.0199092i
\(339\) 18.9282i 1.02804i
\(340\) −5.07180 8.78461i −0.275057 0.476412i
\(341\) 4.14359i 0.224388i
\(342\) −1.00000 3.73205i −0.0540738 0.201806i
\(343\) −39.7128 −2.14429
\(344\) 14.9282 + 14.9282i 0.804875 + 0.804875i
\(345\) 27.7128 1.49201
\(346\) 2.53590 + 9.46410i 0.136331 + 0.508793i
\(347\) 20.9282i 1.12348i 0.827312 + 0.561742i \(0.189869\pi\)
−0.827312 + 0.561742i \(0.810131\pi\)
\(348\) −6.92820 + 4.00000i −0.371391 + 0.214423i
\(349\) 30.3923i 1.62686i −0.581661 0.813431i \(-0.697597\pi\)
0.581661 0.813431i \(-0.302403\pi\)
\(350\) 45.2487 12.1244i 2.41865 0.648074i
\(351\) −4.00000 −0.213504
\(352\) 6.92820 + 1.85641i 0.369274 + 0.0989468i
\(353\) −24.9282 −1.32679 −0.663397 0.748267i \(-0.730886\pi\)
−0.663397 + 0.748267i \(0.730886\pi\)
\(354\) −0.535898 + 0.143594i −0.0284827 + 0.00763191i
\(355\) 7.60770i 0.403775i
\(356\) 30.0000 17.3205i 1.59000 0.917985i
\(357\) 13.8564i 0.733359i
\(358\) −3.80385 14.1962i −0.201040 0.750290i
\(359\) −13.5167 −0.713382 −0.356691 0.934222i \(-0.616095\pi\)
−0.356691 + 0.934222i \(0.616095\pi\)
\(360\) −6.92820 6.92820i −0.365148 0.365148i
\(361\) 11.5359 0.607153
\(362\) −1.80385 6.73205i −0.0948081 0.353829i
\(363\) 18.7846i 0.985936i
\(364\) 4.73205 + 8.19615i 0.248027 + 0.429595i
\(365\) 1.85641i 0.0971688i
\(366\) 29.8564 8.00000i 1.56062 0.418167i
\(367\) 26.2487 1.37017 0.685086 0.728462i \(-0.259765\pi\)
0.685086 + 0.728462i \(0.259765\pi\)
\(368\) 8.00000 13.8564i 0.417029 0.722315i
\(369\) 4.92820 0.256552
\(370\) 23.3205 6.24871i 1.21238 0.324855i
\(371\) 51.7128i 2.68480i
\(372\) 6.53590 + 11.3205i 0.338871 + 0.586941i
\(373\) 26.7846i 1.38685i −0.720527 0.693427i \(-0.756100\pi\)
0.720527 0.693427i \(-0.243900\pi\)
\(374\) −0.679492 2.53590i −0.0351357 0.131128i
\(375\) −13.8564 −0.715542
\(376\) 6.53590 6.53590i 0.337063 0.337063i
\(377\) −2.00000 −0.103005
\(378\) 6.92820 + 25.8564i 0.356348 + 1.32991i
\(379\) 16.5885i 0.852092i 0.904702 + 0.426046i \(0.140094\pi\)
−0.904702 + 0.426046i \(0.859906\pi\)
\(380\) −16.3923 + 9.46410i −0.840907 + 0.485498i
\(381\) 8.00000i 0.409852i
\(382\) −29.3205 + 7.85641i −1.50017 + 0.401969i
\(383\) −27.6603 −1.41337 −0.706686 0.707527i \(-0.749811\pi\)
−0.706686 + 0.707527i \(0.749811\pi\)
\(384\) −21.8564 + 5.85641i −1.11536 + 0.298858i
\(385\) 20.7846 1.05928
\(386\) −30.5885 + 8.19615i −1.55691 + 0.417173i
\(387\) 7.46410i 0.379422i
\(388\) −24.9282 + 14.3923i −1.26554 + 0.730659i
\(389\) 2.00000i 0.101404i −0.998714 0.0507020i \(-0.983854\pi\)
0.998714 0.0507020i \(-0.0161459\pi\)
\(390\) −2.53590 9.46410i −0.128410 0.479233i
\(391\) −5.85641 −0.296171
\(392\) 30.7846 30.7846i 1.55486 1.55486i
\(393\) 15.7128 0.792607
\(394\) 6.19615 + 23.1244i 0.312158 + 1.16499i
\(395\) 5.07180i 0.255190i
\(396\) −1.26795 2.19615i −0.0637168 0.110361i
\(397\) 11.4641i 0.575367i 0.957726 + 0.287683i \(0.0928851\pi\)
−0.957726 + 0.287683i \(0.907115\pi\)
\(398\) −33.8564 + 9.07180i −1.69707 + 0.454728i
\(399\) −25.8564 −1.29444
\(400\) −14.0000 + 24.2487i −0.700000 + 1.21244i
\(401\) 11.4641 0.572490 0.286245 0.958156i \(-0.407593\pi\)
0.286245 + 0.958156i \(0.407593\pi\)
\(402\) 7.46410 2.00000i 0.372276 0.0997509i
\(403\) 3.26795i 0.162788i
\(404\) 12.0000 + 20.7846i 0.597022 + 1.03407i
\(405\) 38.1051i 1.89346i
\(406\) 3.46410 + 12.9282i 0.171920 + 0.641616i
\(407\) 6.24871 0.309737
\(408\) 5.85641 + 5.85641i 0.289935 + 0.289935i
\(409\) −0.928203 −0.0458967 −0.0229483 0.999737i \(-0.507305\pi\)
−0.0229483 + 0.999737i \(0.507305\pi\)
\(410\) −6.24871 23.3205i −0.308602 1.15172i
\(411\) 1.85641i 0.0915698i
\(412\) −12.0000 + 6.92820i −0.591198 + 0.341328i
\(413\) 0.928203i 0.0456739i
\(414\) −5.46410 + 1.46410i −0.268546 + 0.0719567i
\(415\) 23.3205 1.14476
\(416\) −5.46410 1.46410i −0.267900 0.0717835i
\(417\) 20.0000 0.979404
\(418\) −4.73205 + 1.26795i −0.231452 + 0.0620174i
\(419\) 10.7846i 0.526863i −0.964678 0.263431i \(-0.915146\pi\)
0.964678 0.263431i \(-0.0848542\pi\)
\(420\) −56.7846 + 32.7846i −2.77081 + 1.59973i
\(421\) 24.2487i 1.18181i 0.806741 + 0.590905i \(0.201229\pi\)
−0.806741 + 0.590905i \(0.798771\pi\)
\(422\) −7.26795 27.1244i −0.353798 1.32039i
\(423\) −3.26795 −0.158893
\(424\) −21.8564 21.8564i −1.06144 1.06144i
\(425\) 10.2487 0.497136
\(426\) −1.60770 6.00000i −0.0778931 0.290701i
\(427\) 51.7128i 2.50256i
\(428\) 8.92820 + 15.4641i 0.431561 + 0.747486i
\(429\) 2.53590i 0.122434i
\(430\) −35.3205 + 9.46410i −1.70331 + 0.456400i
\(431\) 14.8756 0.716535 0.358267 0.933619i \(-0.383368\pi\)
0.358267 + 0.933619i \(0.383368\pi\)
\(432\) −13.8564 8.00000i −0.666667 0.384900i
\(433\) 34.7846 1.67164 0.835821 0.549002i \(-0.184992\pi\)
0.835821 + 0.549002i \(0.184992\pi\)
\(434\) 21.1244 5.66025i 1.01400 0.271701i
\(435\) 13.8564i 0.664364i
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) 10.9282i 0.522767i
\(438\) 0.392305 + 1.46410i 0.0187451 + 0.0699575i
\(439\) −10.9282 −0.521575 −0.260787 0.965396i \(-0.583982\pi\)
−0.260787 + 0.965396i \(0.583982\pi\)
\(440\) −8.78461 + 8.78461i −0.418790 + 0.418790i
\(441\) −15.3923 −0.732967
\(442\) 0.535898 + 2.00000i 0.0254901 + 0.0951303i
\(443\) 30.0000i 1.42534i 0.701498 + 0.712672i \(0.252515\pi\)
−0.701498 + 0.712672i \(0.747485\pi\)
\(444\) −17.0718 + 9.85641i −0.810192 + 0.467764i
\(445\) 60.0000i 2.84427i
\(446\) 13.9282 3.73205i 0.659520 0.176718i
\(447\) −1.85641 −0.0878050
\(448\) 37.8564i 1.78855i
\(449\) 38.3923 1.81184 0.905922 0.423444i \(-0.139179\pi\)
0.905922 + 0.423444i \(0.139179\pi\)
\(450\) 9.56218 2.56218i 0.450765 0.120782i
\(451\) 6.24871i 0.294240i
\(452\) 16.3923 9.46410i 0.771029 0.445154i
\(453\) 34.2487i 1.60914i
\(454\) −9.92820 37.0526i −0.465954 1.73896i
\(455\) −16.3923 −0.768483
\(456\) 10.9282 10.9282i 0.511760 0.511760i
\(457\) −14.0000 −0.654892 −0.327446 0.944870i \(-0.606188\pi\)
−0.327446 + 0.944870i \(0.606188\pi\)
\(458\) −10.7321 40.0526i −0.501476 1.87153i
\(459\) 5.85641i 0.273354i
\(460\) 13.8564 + 24.0000i 0.646058 + 1.11901i
\(461\) 7.07180i 0.329366i −0.986347 0.164683i \(-0.947340\pi\)
0.986347 0.164683i \(-0.0526602\pi\)
\(462\) −16.3923 + 4.39230i −0.762639 + 0.204349i
\(463\) −15.6603 −0.727794 −0.363897 0.931439i \(-0.618554\pi\)
−0.363897 + 0.931439i \(0.618554\pi\)
\(464\) −6.92820 4.00000i −0.321634 0.185695i
\(465\) −22.6410 −1.04995
\(466\) 4.19615 1.12436i 0.194383 0.0520848i
\(467\) 12.2487i 0.566803i 0.959001 + 0.283401i \(0.0914629\pi\)
−0.959001 + 0.283401i \(0.908537\pi\)
\(468\) 1.00000 + 1.73205i 0.0462250 + 0.0800641i
\(469\) 12.9282i 0.596969i
\(470\) 4.14359 + 15.4641i 0.191130 + 0.713306i
\(471\) 6.14359 0.283082
\(472\) −0.392305 0.392305i −0.0180573 0.0180573i
\(473\) −9.46410 −0.435160
\(474\) 1.07180 + 4.00000i 0.0492293 + 0.183726i
\(475\) 19.1244i 0.877486i
\(476\) 12.0000 6.92820i 0.550019 0.317554i
\(477\) 10.9282i 0.500368i
\(478\) 20.8564 5.58846i 0.953950 0.255610i
\(479\) 24.7321 1.13004 0.565018 0.825078i \(-0.308869\pi\)
0.565018 + 0.825078i \(0.308869\pi\)
\(480\) 10.1436 37.8564i 0.462990 1.72790i
\(481\) −4.92820 −0.224707
\(482\) −13.1244 + 3.51666i −0.597798 + 0.160179i
\(483\) 37.8564i 1.72253i
\(484\) 16.2679 9.39230i 0.739452 0.426923i
\(485\) 49.8564i 2.26386i
\(486\) 3.66025 + 13.6603i 0.166032 + 0.619642i
\(487\) 16.4449 0.745188 0.372594 0.927994i \(-0.378468\pi\)
0.372594 + 0.927994i \(0.378468\pi\)
\(488\) 21.8564 + 21.8564i 0.989393 + 0.989393i
\(489\) −26.5359 −1.19999
\(490\) 19.5167 + 72.8372i 0.881673 + 3.29045i
\(491\) 24.2487i 1.09433i −0.837025 0.547165i \(-0.815707\pi\)
0.837025 0.547165i \(-0.184293\pi\)
\(492\) 9.85641 + 17.0718i 0.444361 + 0.769656i
\(493\) 2.92820i 0.131880i
\(494\) 3.73205 1.00000i 0.167913 0.0449921i
\(495\) 4.39230 0.197419
\(496\) −6.53590 + 11.3205i −0.293471 + 0.508306i
\(497\) −10.3923 −0.466159
\(498\) −18.3923 + 4.92820i −0.824179 + 0.220838i
\(499\) 10.7321i 0.480433i 0.970719 + 0.240216i \(0.0772184\pi\)
−0.970719 + 0.240216i \(0.922782\pi\)
\(500\) −6.92820 12.0000i −0.309839 0.536656i
\(501\) 23.3205i 1.04188i
\(502\) 5.26795 + 19.6603i 0.235120 + 0.877480i
\(503\) 37.4641 1.67044 0.835221 0.549915i \(-0.185340\pi\)
0.835221 + 0.549915i \(0.185340\pi\)
\(504\) 9.46410 9.46410i 0.421565 0.421565i
\(505\) −41.5692 −1.84981
\(506\) 1.85641 + 6.92820i 0.0825273 + 0.307996i
\(507\) 2.00000i 0.0888231i
\(508\) −6.92820 + 4.00000i −0.307389 + 0.177471i
\(509\) 6.39230i 0.283334i 0.989914 + 0.141667i \(0.0452462\pi\)
−0.989914 + 0.141667i \(0.954754\pi\)
\(510\) −13.8564 + 3.71281i −0.613572 + 0.164406i
\(511\) 2.53590 0.112182
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 10.9282 0.482492
\(514\) 5.26795 1.41154i 0.232359 0.0622605i
\(515\) 24.0000i 1.05757i
\(516\) 25.8564 14.9282i 1.13826 0.657178i
\(517\) 4.14359i 0.182235i
\(518\) 8.53590 + 31.8564i 0.375046 + 1.39969i
\(519\) 13.8564 0.608229
\(520\) 6.92820 6.92820i 0.303822 0.303822i
\(521\) 37.1769 1.62875 0.814375 0.580339i \(-0.197080\pi\)
0.814375 + 0.580339i \(0.197080\pi\)
\(522\) 0.732051 + 2.73205i 0.0320410 + 0.119579i
\(523\) 14.0000i 0.612177i −0.952003 0.306089i \(-0.900980\pi\)
0.952003 0.306089i \(-0.0990204\pi\)
\(524\) 7.85641 + 13.6077i 0.343209 + 0.594455i
\(525\) 66.2487i 2.89133i
\(526\) 10.0000 2.67949i 0.436021 0.116831i
\(527\) 4.78461 0.208421
\(528\) 5.07180 8.78461i 0.220722 0.382301i
\(529\) −7.00000 −0.304348
\(530\) 51.7128 13.8564i 2.24626 0.601884i
\(531\) 0.196152i 0.00851229i
\(532\) −12.9282 22.3923i −0.560509 0.970830i
\(533\) 4.92820i 0.213464i
\(534\) −12.6795 47.3205i −0.548695 2.04776i
\(535\) −30.9282 −1.33714
\(536\) 5.46410 + 5.46410i 0.236013 + 0.236013i
\(537\) −20.7846 −0.896922
\(538\) −7.26795 27.1244i −0.313344 1.16941i
\(539\) 19.5167i 0.840642i
\(540\) 24.0000 13.8564i 1.03280 0.596285i
\(541\) 16.9282i 0.727800i 0.931438 + 0.363900i \(0.118555\pi\)
−0.931438 + 0.363900i \(0.881445\pi\)
\(542\) −13.3923 + 3.58846i −0.575249 + 0.154137i
\(543\) −9.85641 −0.422979
\(544\) −2.14359 + 8.00000i −0.0919058 + 0.342997i
\(545\) −6.92820 −0.296772
\(546\) 12.9282 3.46410i 0.553276 0.148250i
\(547\) 15.8564i 0.677971i −0.940792 0.338985i \(-0.889916\pi\)
0.940792 0.338985i \(-0.110084\pi\)
\(548\) −1.60770 + 0.928203i −0.0686773 + 0.0396509i
\(549\) 10.9282i 0.466404i
\(550\) −3.24871 12.1244i −0.138526 0.516984i
\(551\) 5.46410 0.232779
\(552\) −16.0000 16.0000i −0.681005 0.681005i
\(553\) 6.92820 0.294617
\(554\) 9.46410 + 35.3205i 0.402091 + 1.50062i
\(555\) 34.1436i 1.44931i
\(556\) 10.0000 + 17.3205i 0.424094 + 0.734553i
\(557\) 6.78461i 0.287473i 0.989616 + 0.143737i \(0.0459118\pi\)
−0.989616 + 0.143737i \(0.954088\pi\)
\(558\) 4.46410 1.19615i 0.188980 0.0506372i
\(559\) 7.46410 0.315698
\(560\) −56.7846 32.7846i −2.39959 1.38540i
\(561\) −3.71281 −0.156755
\(562\) −34.5885 + 9.26795i −1.45903 + 0.390945i
\(563\) 0.535898i 0.0225854i 0.999936 + 0.0112927i \(0.00359466\pi\)
−0.999936 + 0.0112927i \(0.996405\pi\)
\(564\) −6.53590 11.3205i −0.275211 0.476679i
\(565\) 32.7846i 1.37926i
\(566\) −4.58846 17.1244i −0.192867 0.719790i
\(567\) 52.0526 2.18600
\(568\) 4.39230 4.39230i 0.184297 0.184297i
\(569\) −14.0000 −0.586911 −0.293455 0.955973i \(-0.594805\pi\)
−0.293455 + 0.955973i \(0.594805\pi\)
\(570\) 6.92820 + 25.8564i 0.290191 + 1.08301i
\(571\) 37.3205i 1.56181i −0.624647 0.780907i \(-0.714757\pi\)
0.624647 0.780907i \(-0.285243\pi\)
\(572\) 2.19615 1.26795i 0.0918257 0.0530156i
\(573\) 42.9282i 1.79335i
\(574\) 31.8564 8.53590i 1.32966 0.356282i
\(575\) −28.0000 −1.16768
\(576\) 8.00000i 0.333333i
\(577\) −20.9282 −0.871253 −0.435626 0.900128i \(-0.643473\pi\)
−0.435626 + 0.900128i \(0.643473\pi\)
\(578\) −20.2942 + 5.43782i −0.844129 + 0.226184i
\(579\) 44.7846i 1.86118i
\(580\) 12.0000 6.92820i 0.498273 0.287678i
\(581\) 31.8564i 1.32163i
\(582\) 10.5359 + 39.3205i 0.436727 + 1.62989i
\(583\) 13.8564 0.573874
\(584\) −1.07180 + 1.07180i −0.0443513 + 0.0443513i
\(585\) −3.46410 −0.143223
\(586\) −6.98076 26.0526i −0.288373 1.07622i
\(587\) 21.6603i 0.894014i 0.894530 + 0.447007i \(0.147510\pi\)
−0.894530 + 0.447007i \(0.852490\pi\)
\(588\) −30.7846 53.3205i −1.26954 2.19890i
\(589\) 8.92820i 0.367880i
\(590\) 0.928203 0.248711i 0.0382135 0.0102393i
\(591\) 33.8564 1.39267
\(592\) −17.0718 9.85641i −0.701647 0.405096i
\(593\) 19.8564 0.815405 0.407702 0.913115i \(-0.366330\pi\)
0.407702 + 0.913115i \(0.366330\pi\)
\(594\) 6.92820 1.85641i 0.284268 0.0761693i
\(595\) 24.0000i 0.983904i
\(596\) −0.928203 1.60770i −0.0380207 0.0658538i
\(597\) 49.5692i 2.02873i
\(598\) −1.46410 5.46410i −0.0598716 0.223444i
\(599\) 17.1769 0.701830 0.350915 0.936407i \(-0.385871\pi\)
0.350915 + 0.936407i \(0.385871\pi\)
\(600\) 28.0000 + 28.0000i 1.14310 + 1.14310i
\(601\) 16.3923 0.668656 0.334328 0.942457i \(-0.391491\pi\)
0.334328 + 0.942457i \(0.391491\pi\)
\(602\) −12.9282 48.2487i −0.526914 1.96647i
\(603\) 2.73205i 0.111258i
\(604\) 29.6603 17.1244i 1.20686 0.696780i
\(605\) 32.5359i 1.32277i
\(606\) 32.7846 8.78461i 1.33178 0.356850i
\(607\) −27.3205 −1.10891 −0.554453 0.832215i \(-0.687072\pi\)
−0.554453 + 0.832215i \(0.687072\pi\)
\(608\) 14.9282 + 4.00000i 0.605419 + 0.162221i
\(609\) 18.9282 0.767010
\(610\) −51.7128 + 13.8564i −2.09379 + 0.561029i
\(611\) 3.26795i 0.132207i
\(612\) 2.53590 1.46410i 0.102508 0.0591828i
\(613\) 44.6410i 1.80303i 0.432744 + 0.901517i \(0.357545\pi\)
−0.432744 + 0.901517i \(0.642455\pi\)
\(614\) 1.00000 + 3.73205i 0.0403567 + 0.150613i
\(615\) −34.1436 −1.37680
\(616\) −12.0000 12.0000i −0.483494 0.483494i
\(617\) 6.67949 0.268906 0.134453 0.990920i \(-0.457072\pi\)
0.134453 + 0.990920i \(0.457072\pi\)
\(618\) 5.07180 + 18.9282i 0.204018 + 0.761404i
\(619\) 12.5885i 0.505973i −0.967470 0.252986i \(-0.918587\pi\)
0.967470 0.252986i \(-0.0814128\pi\)
\(620\) −11.3205 19.6077i −0.454643 0.787464i
\(621\) 16.0000i 0.642058i
\(622\) 20.3923 5.46410i 0.817657 0.219091i
\(623\) −81.9615 −3.28372
\(624\) −4.00000 + 6.92820i −0.160128 + 0.277350i
\(625\) −11.0000 −0.440000
\(626\) −27.8564 + 7.46410i −1.11337 + 0.298325i
\(627\) 6.92820i 0.276686i
\(628\) 3.07180 + 5.32051i 0.122578 + 0.212311i
\(629\) 7.21539i 0.287696i
\(630\) 6.00000 + 22.3923i 0.239046 + 0.892131i
\(631\) −3.94744 −0.157145 −0.0785726 0.996908i \(-0.525036\pi\)
−0.0785726 + 0.996908i \(0.525036\pi\)
\(632\) −2.92820 + 2.92820i −0.116478 + 0.116478i
\(633\) −39.7128 −1.57844
\(634\) 1.26795 + 4.73205i 0.0503567 + 0.187934i
\(635\) 13.8564i 0.549875i
\(636\) −37.8564 + 21.8564i −1.50110 + 0.866663i
\(637\) 15.3923i 0.609865i
\(638\) 3.46410 0.928203i 0.137145 0.0367479i
\(639\) −2.19615 −0.0868784
\(640\) 37.8564 10.1436i 1.49641 0.400961i
\(641\) 26.2487 1.03676 0.518381 0.855150i \(-0.326535\pi\)
0.518381 + 0.855150i \(0.326535\pi\)
\(642\) 24.3923 6.53590i 0.962687 0.257951i
\(643\) 9.26795i 0.365492i 0.983160 + 0.182746i \(0.0584986\pi\)
−0.983160 + 0.182746i \(0.941501\pi\)
\(644\) −32.7846 + 18.9282i −1.29189 + 0.745876i
\(645\) 51.7128i 2.03619i
\(646\) −1.46410 5.46410i −0.0576043 0.214982i
\(647\) 10.1436 0.398786 0.199393 0.979920i \(-0.436103\pi\)
0.199393 + 0.979920i \(0.436103\pi\)
\(648\) −22.0000 + 22.0000i −0.864242 + 0.864242i
\(649\) 0.248711 0.00976277
\(650\) 2.56218 + 9.56218i 0.100497 + 0.375059i
\(651\) 30.9282i 1.21217i
\(652\) −13.2679 22.9808i −0.519613 0.899996i
\(653\) 16.9282i 0.662452i 0.943551 + 0.331226i \(0.107462\pi\)
−0.943551 + 0.331226i \(0.892538\pi\)
\(654\) 5.46410 1.46410i 0.213663 0.0572509i
\(655\) −27.2154 −1.06339
\(656\) −9.85641 + 17.0718i −0.384828 + 0.666542i
\(657\) 0.535898 0.0209074
\(658\) −21.1244 + 5.66025i −0.823513 + 0.220660i
\(659\) 14.0000i 0.545363i −0.962104 0.272681i \(-0.912090\pi\)
0.962104 0.272681i \(-0.0879105\pi\)
\(660\) 8.78461 + 15.2154i 0.341940 + 0.592258i
\(661\) 17.3205i 0.673690i 0.941560 + 0.336845i \(0.109360\pi\)
−0.941560 + 0.336845i \(0.890640\pi\)
\(662\) 10.0718 + 37.5885i 0.391451 + 1.46092i
\(663\) 2.92820 0.113722
\(664\) −13.4641 13.4641i −0.522508 0.522508i
\(665\) 44.7846 1.73667
\(666\) 1.80385 + 6.73205i 0.0698977 + 0.260862i
\(667\) 8.00000i 0.309761i
\(668\) 20.1962 11.6603i 0.781413 0.451149i
\(669\) 20.3923i 0.788412i
\(670\) −12.9282 + 3.46410i −0.499460 + 0.133830i
\(671\) −13.8564 −0.534921
\(672\) 51.7128 + 13.8564i 1.99487 + 0.534522i
\(673\) −29.1769 −1.12469 −0.562344 0.826904i \(-0.690100\pi\)
−0.562344 + 0.826904i \(0.690100\pi\)
\(674\) −7.46410 + 2.00000i −0.287506 + 0.0770371i
\(675\) 28.0000i 1.07772i
\(676\) −1.73205 + 1.00000i −0.0666173 + 0.0384615i
\(677\) 34.9282i 1.34240i −0.741276 0.671200i \(-0.765779\pi\)
0.741276 0.671200i \(-0.234221\pi\)
\(678\) −6.92820 25.8564i −0.266076 0.993009i
\(679\) 68.1051 2.61363
\(680\) −10.1436 10.1436i −0.388989 0.388989i
\(681\) −54.2487 −2.07882
\(682\) −1.51666 5.66025i −0.0580759 0.216742i
\(683\) 28.1962i 1.07890i 0.842019 + 0.539448i \(0.181367\pi\)
−0.842019 + 0.539448i \(0.818633\pi\)
\(684\) −2.73205 4.73205i −0.104463 0.180934i
\(685\) 3.21539i 0.122854i
\(686\) −54.2487 + 14.5359i −2.07123 + 0.554983i
\(687\) −58.6410 −2.23729
\(688\) 25.8564 + 14.9282i 0.985766 + 0.569132i
\(689\) −10.9282 −0.416331
\(690\) 37.8564 10.1436i 1.44117 0.386160i
\(691\) 46.8372i 1.78177i −0.454229 0.890885i \(-0.650085\pi\)
0.454229 0.890885i \(-0.349915\pi\)
\(692\) 6.92820 + 12.0000i 0.263371 + 0.456172i
\(693\) 6.00000i 0.227921i
\(694\) 7.66025 + 28.5885i 0.290779 + 1.08520i
\(695\) −34.6410 −1.31401
\(696\) −8.00000 + 8.00000i −0.303239 + 0.303239i
\(697\) 7.21539 0.273302
\(698\) −11.1244 41.5167i −0.421063 1.57143i
\(699\) 6.14359i 0.232372i
\(700\) 57.3731 33.1244i 2.16850 1.25198i
\(701\) 28.6410i 1.08176i −0.841101 0.540878i \(-0.818092\pi\)
0.841101 0.540878i \(-0.181908\pi\)
\(702\) −5.46410 + 1.46410i −0.206229 + 0.0552590i
\(703\) 13.4641 0.507808
\(704\) 10.1436 0.382301
\(705\) 22.6410 0.852710
\(706\) −34.0526 + 9.12436i −1.28158 + 0.343400i
\(707\) 56.7846i 2.13561i
\(708\) −0.679492 + 0.392305i −0.0255369 + 0.0147437i
\(709\) 5.32051i 0.199816i 0.994997 + 0.0999079i \(0.0318548\pi\)
−0.994997 + 0.0999079i \(0.968145\pi\)
\(710\) 2.78461 + 10.3923i 0.104505 + 0.390016i
\(711\) 1.46410 0.0549081
\(712\) 34.6410 34.6410i 1.29823 1.29823i
\(713\) −13.0718 −0.489543
\(714\) −5.07180 18.9282i −0.189807 0.708370i
\(715\) 4.39230i 0.164263i
\(716\) −10.3923 18.0000i −0.388379 0.672692i
\(717\) 30.5359i 1.14038i
\(718\) −18.4641 + 4.94744i −0.689074 + 0.184637i
\(719\) 17.0718 0.636671 0.318335 0.947978i \(-0.396876\pi\)
0.318335 + 0.947978i \(0.396876\pi\)
\(720\) −12.0000 6.92820i −0.447214 0.258199i
\(721\) 32.7846 1.22096
\(722\) 15.7583 4.22243i 0.586464 0.157143i
\(723\) 19.2154i 0.714628i
\(724\) −4.92820 8.53590i −0.183155 0.317234i
\(725\) 14.0000i 0.519947i
\(726\) −6.87564 25.6603i −0.255179 0.952341i
\(727\) −9.07180 −0.336454 −0.168227 0.985748i \(-0.553804\pi\)
−0.168227 + 0.985748i \(0.553804\pi\)
\(728\) 9.46410 + 9.46410i 0.350763 + 0.350763i
\(729\) −13.0000 −0.481481
\(730\) −0.679492 2.53590i −0.0251491 0.0938578i
\(731\) 10.9282i 0.404194i
\(732\) 37.8564 21.8564i 1.39921 0.807836i
\(733\) 2.67949i 0.0989693i −0.998775 0.0494846i \(-0.984242\pi\)
0.998775 0.0494846i \(-0.0157579\pi\)
\(734\) 35.8564 9.60770i 1.32348 0.354626i
\(735\) 106.641 3.93351
\(736\) 5.85641 21.8564i 0.215870 0.805638i
\(737\) −3.46410 −0.127602
\(738\) 6.73205 1.80385i 0.247810 0.0664005i
\(739\) 53.7654i 1.97779i 0.148612 + 0.988896i \(0.452519\pi\)
−0.148612 + 0.988896i \(0.547481\pi\)
\(740\) 29.5692 17.0718i 1.08699 0.627572i
\(741\) 5.46410i 0.200729i
\(742\) 18.9282 + 70.6410i 0.694876 + 2.59331i
\(743\) −21.8038 −0.799906 −0.399953 0.916536i \(-0.630973\pi\)
−0.399953 + 0.916536i \(0.630973\pi\)
\(744\) 13.0718 + 13.0718i 0.479235 + 0.479235i
\(745\) 3.21539 0.117803
\(746\) −9.80385 36.5885i −0.358944 1.33960i
\(747\) 6.73205i 0.246313i
\(748\) −1.85641 3.21539i −0.0678769 0.117566i
\(749\) 42.2487i 1.54373i
\(750\) −18.9282 + 5.07180i −0.691160 + 0.185196i
\(751\) 14.9282 0.544738 0.272369 0.962193i \(-0.412193\pi\)
0.272369 + 0.962193i \(0.412193\pi\)
\(752\) 6.53590 11.3205i 0.238340 0.412816i
\(753\) 28.7846 1.04897
\(754\) −2.73205 + 0.732051i −0.0994954 + 0.0266597i
\(755\) 59.3205i 2.15889i
\(756\) 18.9282 + 32.7846i 0.688412 + 1.19236i
\(757\) 0.784610i 0.0285171i 0.999898 + 0.0142586i \(0.00453880\pi\)
−0.999898 + 0.0142586i \(0.995461\pi\)
\(758\) 6.07180 + 22.6603i 0.220538 + 0.823057i
\(759\) 10.1436 0.368189
\(760\) −18.9282 + 18.9282i −0.686598 + 0.686598i
\(761\) −22.7846 −0.825941 −0.412971 0.910744i \(-0.635509\pi\)
−0.412971 + 0.910744i \(0.635509\pi\)
\(762\) 2.92820 + 10.9282i 0.106078 + 0.395887i
\(763\) 9.46410i 0.342623i
\(764\) −37.1769 + 21.4641i −1.34501 + 0.776544i
\(765\) 5.07180i 0.183371i
\(766\) −37.7846 + 10.1244i −1.36521 + 0.365808i
\(767\) −0.196152 −0.00708265
\(768\) −27.7128 + 16.0000i −1.00000 + 0.577350i
\(769\) 24.5359 0.884787 0.442394 0.896821i \(-0.354129\pi\)
0.442394 + 0.896821i \(0.354129\pi\)
\(770\) 28.3923 7.60770i 1.02319 0.274162i
\(771\) 7.71281i 0.277770i
\(772\) −38.7846 + 22.3923i −1.39589 + 0.805917i
\(773\) 20.5359i 0.738625i −0.929305 0.369312i