Properties

Label 112.2.w.b.93.1
Level $112$
Weight $2$
Character 112.93
Analytic conductor $0.894$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [112,2,Mod(37,112)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(112, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("112.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 112.w (of order \(12\), degree \(4\), 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: \(0.894324502638\)
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: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 93.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 112.93
Dual form 112.2.w.b.53.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(0.500000 - 1.86603i) q^{3} -2.00000i q^{4} +(0.866025 + 3.23205i) q^{5} +(-1.36603 - 2.36603i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(0.500000 - 1.86603i) q^{3} -2.00000i q^{4} +(0.866025 + 3.23205i) q^{5} +(-1.36603 - 2.36603i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.633975 - 0.366025i) q^{9} +(4.09808 + 2.36603i) q^{10} +(-4.23205 - 1.13397i) q^{11} +(-3.73205 - 1.00000i) q^{12} +(0.267949 + 0.267949i) q^{13} +(0.267949 + 3.73205i) q^{14} +6.46410 q^{15} -4.00000 q^{16} +(0.232051 + 0.401924i) q^{17} +(-1.00000 + 0.267949i) q^{18} +(4.23205 - 1.13397i) q^{19} +(6.46410 - 1.73205i) q^{20} +(2.86603 + 4.23205i) q^{21} +(-5.36603 + 3.09808i) q^{22} +(2.13397 + 1.23205i) q^{23} +(-4.73205 + 2.73205i) q^{24} +(-5.36603 + 3.09808i) q^{25} +0.535898 q^{26} +(3.09808 - 3.09808i) q^{27} +(4.00000 + 3.46410i) q^{28} +(-3.73205 - 3.73205i) q^{29} +(6.46410 - 6.46410i) q^{30} +(-0.133975 - 0.232051i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(-4.23205 + 7.33013i) q^{33} +(0.633975 + 0.169873i) q^{34} +(-7.96410 - 3.86603i) q^{35} +(-0.732051 + 1.26795i) q^{36} +(-2.86603 - 10.6962i) q^{37} +(3.09808 - 5.36603i) q^{38} +(0.633975 - 0.366025i) q^{39} +(4.73205 - 8.19615i) q^{40} +8.92820i q^{41} +(7.09808 + 1.36603i) q^{42} +(-0.464102 + 0.464102i) q^{43} +(-2.26795 + 8.46410i) q^{44} +(0.633975 - 2.36603i) q^{45} +(3.36603 - 0.901924i) q^{46} +(-3.86603 + 6.69615i) q^{47} +(-2.00000 + 7.46410i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-2.26795 + 8.46410i) q^{50} +(0.866025 - 0.232051i) q^{51} +(0.535898 - 0.535898i) q^{52} +(11.0622 + 2.96410i) q^{53} -6.19615i q^{54} -14.6603i q^{55} +(7.46410 - 0.535898i) q^{56} -8.46410i q^{57} -7.46410 q^{58} +(-9.96410 - 2.66987i) q^{59} -12.9282i q^{60} +(0.133975 - 0.0358984i) q^{61} +(-0.366025 - 0.0980762i) q^{62} +(1.83013 - 0.633975i) q^{63} +8.00000i q^{64} +(-0.633975 + 1.09808i) q^{65} +(3.09808 + 11.5622i) q^{66} +(1.96410 - 7.33013i) q^{67} +(0.803848 - 0.464102i) q^{68} +(3.36603 - 3.36603i) q^{69} +(-11.8301 + 4.09808i) q^{70} +7.46410i q^{71} +(0.535898 + 2.00000i) q^{72} +(2.76795 - 1.59808i) q^{73} +(-13.5622 - 7.83013i) q^{74} +(3.09808 + 11.5622i) q^{75} +(-2.26795 - 8.46410i) q^{76} +(9.59808 - 6.50000i) q^{77} +(0.267949 - 1.00000i) q^{78} +(-0.330127 + 0.571797i) q^{79} +(-3.46410 - 12.9282i) q^{80} +(-5.33013 - 9.23205i) q^{81} +(8.92820 + 8.92820i) q^{82} +(8.46410 + 8.46410i) q^{83} +(8.46410 - 5.73205i) q^{84} +(-1.09808 + 1.09808i) q^{85} +0.928203i q^{86} +(-8.83013 + 5.09808i) q^{87} +(6.19615 + 10.7321i) q^{88} +(-4.50000 - 2.59808i) q^{89} +(-1.73205 - 3.00000i) q^{90} +(-1.00000 + 0.0717968i) q^{91} +(2.46410 - 4.26795i) q^{92} +(-0.500000 + 0.133975i) q^{93} +(2.83013 + 10.5622i) q^{94} +(7.33013 + 12.6962i) q^{95} +(5.46410 + 9.46410i) q^{96} +10.9282 q^{97} +(-7.92820 - 5.92820i) q^{98} +(2.26795 + 2.26795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 2 q^{3} - 2 q^{6} - 8 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} + 2 q^{3} - 2 q^{6} - 8 q^{8} - 6 q^{9} + 6 q^{10} - 10 q^{11} - 8 q^{12} + 8 q^{13} + 8 q^{14} + 12 q^{15} - 16 q^{16} - 6 q^{17} - 4 q^{18} + 10 q^{19} + 12 q^{20} + 8 q^{21} - 18 q^{22} + 12 q^{23} - 12 q^{24} - 18 q^{25} + 16 q^{26} + 2 q^{27} + 16 q^{28} - 8 q^{29} + 12 q^{30} - 4 q^{31} - 16 q^{32} - 10 q^{33} + 6 q^{34} - 18 q^{35} + 4 q^{36} - 8 q^{37} + 2 q^{38} + 6 q^{39} + 12 q^{40} + 18 q^{42} + 12 q^{43} - 16 q^{44} + 6 q^{45} + 10 q^{46} - 12 q^{47} - 8 q^{48} - 4 q^{49} - 16 q^{50} + 16 q^{52} + 20 q^{53} + 16 q^{56} - 16 q^{58} - 26 q^{59} + 4 q^{61} + 2 q^{62} - 10 q^{63} - 6 q^{65} + 2 q^{66} - 6 q^{67} + 24 q^{68} + 10 q^{69} - 30 q^{70} + 16 q^{72} + 18 q^{73} - 30 q^{74} + 2 q^{75} - 16 q^{76} + 28 q^{77} + 8 q^{78} + 16 q^{79} - 4 q^{81} + 8 q^{82} + 20 q^{83} + 20 q^{84} + 6 q^{85} - 18 q^{87} + 4 q^{88} - 18 q^{89} - 4 q^{91} - 4 q^{92} - 2 q^{93} - 6 q^{94} + 12 q^{95} + 8 q^{96} + 16 q^{97} - 4 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(17\) \(85\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000i 0.707107 0.707107i
\(3\) 0.500000 1.86603i 0.288675 1.07735i −0.657437 0.753510i \(-0.728359\pi\)
0.946112 0.323840i \(-0.104974\pi\)
\(4\) 2.00000i 1.00000i
\(5\) 0.866025 + 3.23205i 0.387298 + 1.44542i 0.834512 + 0.550990i \(0.185750\pi\)
−0.447214 + 0.894427i \(0.647584\pi\)
\(6\) −1.36603 2.36603i −0.557678 0.965926i
\(7\) −1.73205 + 2.00000i −0.654654 + 0.755929i
\(8\) −2.00000 2.00000i −0.707107 0.707107i
\(9\) −0.633975 0.366025i −0.211325 0.122008i
\(10\) 4.09808 + 2.36603i 1.29593 + 0.748203i
\(11\) −4.23205 1.13397i −1.27601 0.341906i −0.443680 0.896185i \(-0.646327\pi\)
−0.832331 + 0.554279i \(0.812994\pi\)
\(12\) −3.73205 1.00000i −1.07735 0.288675i
\(13\) 0.267949 + 0.267949i 0.0743157 + 0.0743157i 0.743288 0.668972i \(-0.233265\pi\)
−0.668972 + 0.743288i \(0.733265\pi\)
\(14\) 0.267949 + 3.73205i 0.0716124 + 0.997433i
\(15\) 6.46410 1.66902
\(16\) −4.00000 −1.00000
\(17\) 0.232051 + 0.401924i 0.0562806 + 0.0974808i 0.892793 0.450467i \(-0.148743\pi\)
−0.836512 + 0.547948i \(0.815409\pi\)
\(18\) −1.00000 + 0.267949i −0.235702 + 0.0631562i
\(19\) 4.23205 1.13397i 0.970899 0.260152i 0.261692 0.965152i \(-0.415720\pi\)
0.709207 + 0.705000i \(0.249053\pi\)
\(20\) 6.46410 1.73205i 1.44542 0.387298i
\(21\) 2.86603 + 4.23205i 0.625418 + 0.923509i
\(22\) −5.36603 + 3.09808i −1.14404 + 0.660512i
\(23\) 2.13397 + 1.23205i 0.444964 + 0.256900i 0.705701 0.708510i \(-0.250632\pi\)
−0.260737 + 0.965410i \(0.583965\pi\)
\(24\) −4.73205 + 2.73205i −0.965926 + 0.557678i
\(25\) −5.36603 + 3.09808i −1.07321 + 0.619615i
\(26\) 0.535898 0.105098
\(27\) 3.09808 3.09808i 0.596225 0.596225i
\(28\) 4.00000 + 3.46410i 0.755929 + 0.654654i
\(29\) −3.73205 3.73205i −0.693024 0.693024i 0.269872 0.962896i \(-0.413019\pi\)
−0.962896 + 0.269872i \(0.913019\pi\)
\(30\) 6.46410 6.46410i 1.18018 1.18018i
\(31\) −0.133975 0.232051i −0.0240625 0.0416776i 0.853743 0.520694i \(-0.174327\pi\)
−0.877806 + 0.479016i \(0.840993\pi\)
\(32\) −4.00000 + 4.00000i −0.707107 + 0.707107i
\(33\) −4.23205 + 7.33013i −0.736705 + 1.27601i
\(34\) 0.633975 + 0.169873i 0.108726 + 0.0291330i
\(35\) −7.96410 3.86603i −1.34618 0.653478i
\(36\) −0.732051 + 1.26795i −0.122008 + 0.211325i
\(37\) −2.86603 10.6962i −0.471172 1.75844i −0.635571 0.772043i \(-0.719235\pi\)
0.164399 0.986394i \(-0.447432\pi\)
\(38\) 3.09808 5.36603i 0.502574 0.870484i
\(39\) 0.633975 0.366025i 0.101517 0.0586110i
\(40\) 4.73205 8.19615i 0.748203 1.29593i
\(41\) 8.92820i 1.39435i 0.716900 + 0.697176i \(0.245560\pi\)
−0.716900 + 0.697176i \(0.754440\pi\)
\(42\) 7.09808 + 1.36603i 1.09526 + 0.210782i
\(43\) −0.464102 + 0.464102i −0.0707748 + 0.0707748i −0.741608 0.670833i \(-0.765937\pi\)
0.670833 + 0.741608i \(0.265937\pi\)
\(44\) −2.26795 + 8.46410i −0.341906 + 1.27601i
\(45\) 0.633975 2.36603i 0.0945074 0.352706i
\(46\) 3.36603 0.901924i 0.496293 0.132981i
\(47\) −3.86603 + 6.69615i −0.563918 + 0.976734i 0.433232 + 0.901283i \(0.357373\pi\)
−0.997149 + 0.0754516i \(0.975960\pi\)
\(48\) −2.00000 + 7.46410i −0.288675 + 1.07735i
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) −2.26795 + 8.46410i −0.320736 + 1.19700i
\(51\) 0.866025 0.232051i 0.121268 0.0324936i
\(52\) 0.535898 0.535898i 0.0743157 0.0743157i
\(53\) 11.0622 + 2.96410i 1.51951 + 0.407151i 0.919580 0.392904i \(-0.128529\pi\)
0.599927 + 0.800054i \(0.295196\pi\)
\(54\) 6.19615i 0.843190i
\(55\) 14.6603i 1.97679i
\(56\) 7.46410 0.535898i 0.997433 0.0716124i
\(57\) 8.46410i 1.12110i
\(58\) −7.46410 −0.980085
\(59\) −9.96410 2.66987i −1.29722 0.347588i −0.456819 0.889560i \(-0.651011\pi\)
−0.840397 + 0.541972i \(0.817678\pi\)
\(60\) 12.9282i 1.66902i
\(61\) 0.133975 0.0358984i 0.0171537 0.00459632i −0.250232 0.968186i \(-0.580507\pi\)
0.267386 + 0.963590i \(0.413840\pi\)
\(62\) −0.366025 0.0980762i −0.0464853 0.0124557i
\(63\) 1.83013 0.633975i 0.230574 0.0798733i
\(64\) 8.00000i 1.00000i
\(65\) −0.633975 + 1.09808i −0.0786349 + 0.136200i
\(66\) 3.09808 + 11.5622i 0.381347 + 1.42321i
\(67\) 1.96410 7.33013i 0.239953 0.895518i −0.735900 0.677090i \(-0.763241\pi\)
0.975853 0.218427i \(-0.0700927\pi\)
\(68\) 0.803848 0.464102i 0.0974808 0.0562806i
\(69\) 3.36603 3.36603i 0.405222 0.405222i
\(70\) −11.8301 + 4.09808i −1.41397 + 0.489814i
\(71\) 7.46410i 0.885826i 0.896565 + 0.442913i \(0.146055\pi\)
−0.896565 + 0.442913i \(0.853945\pi\)
\(72\) 0.535898 + 2.00000i 0.0631562 + 0.235702i
\(73\) 2.76795 1.59808i 0.323964 0.187041i −0.329194 0.944262i \(-0.606777\pi\)
0.653158 + 0.757222i \(0.273444\pi\)
\(74\) −13.5622 7.83013i −1.57657 0.910234i
\(75\) 3.09808 + 11.5622i 0.357735 + 1.33509i
\(76\) −2.26795 8.46410i −0.260152 0.970899i
\(77\) 9.59808 6.50000i 1.09380 0.740744i
\(78\) 0.267949 1.00000i 0.0303393 0.113228i
\(79\) −0.330127 + 0.571797i −0.0371422 + 0.0643322i −0.883999 0.467489i \(-0.845159\pi\)
0.846857 + 0.531821i \(0.178492\pi\)
\(80\) −3.46410 12.9282i −0.387298 1.44542i
\(81\) −5.33013 9.23205i −0.592236 1.02578i
\(82\) 8.92820 + 8.92820i 0.985955 + 0.985955i
\(83\) 8.46410 + 8.46410i 0.929056 + 0.929056i 0.997645 0.0685891i \(-0.0218498\pi\)
−0.0685891 + 0.997645i \(0.521850\pi\)
\(84\) 8.46410 5.73205i 0.923509 0.625418i
\(85\) −1.09808 + 1.09808i −0.119103 + 0.119103i
\(86\) 0.928203i 0.100091i
\(87\) −8.83013 + 5.09808i −0.946689 + 0.546571i
\(88\) 6.19615 + 10.7321i 0.660512 + 1.14404i
\(89\) −4.50000 2.59808i −0.476999 0.275396i 0.242166 0.970235i \(-0.422142\pi\)
−0.719165 + 0.694839i \(0.755475\pi\)
\(90\) −1.73205 3.00000i −0.182574 0.316228i
\(91\) −1.00000 + 0.0717968i −0.104828 + 0.00752635i
\(92\) 2.46410 4.26795i 0.256900 0.444964i
\(93\) −0.500000 + 0.133975i −0.0518476 + 0.0138925i
\(94\) 2.83013 + 10.5622i 0.291905 + 1.08941i
\(95\) 7.33013 + 12.6962i 0.752055 + 1.30260i
\(96\) 5.46410 + 9.46410i 0.557678 + 0.965926i
\(97\) 10.9282 1.10959 0.554795 0.831987i \(-0.312797\pi\)
0.554795 + 0.831987i \(0.312797\pi\)
\(98\) −7.92820 5.92820i −0.800869 0.598839i
\(99\) 2.26795 + 2.26795i 0.227937 + 0.227937i
\(100\) 6.19615 + 10.7321i 0.619615 + 1.07321i
\(101\) −7.06218 1.89230i −0.702713 0.188291i −0.110268 0.993902i \(-0.535171\pi\)
−0.592445 + 0.805611i \(0.701837\pi\)
\(102\) 0.633975 1.09808i 0.0627728 0.108726i
\(103\) −0.401924 0.232051i −0.0396027 0.0228646i 0.480068 0.877231i \(-0.340612\pi\)
−0.519671 + 0.854367i \(0.673945\pi\)
\(104\) 1.07180i 0.105098i
\(105\) −11.1962 + 12.9282i −1.09263 + 1.26166i
\(106\) 14.0263 8.09808i 1.36235 0.786555i
\(107\) −0.232051 0.866025i −0.0224332 0.0837218i 0.953802 0.300437i \(-0.0971324\pi\)
−0.976235 + 0.216715i \(0.930466\pi\)
\(108\) −6.19615 6.19615i −0.596225 0.596225i
\(109\) −3.86603 + 14.4282i −0.370298 + 1.38197i 0.489797 + 0.871837i \(0.337071\pi\)
−0.860095 + 0.510134i \(0.829596\pi\)
\(110\) −14.6603 14.6603i −1.39780 1.39780i
\(111\) −21.3923 −2.03047
\(112\) 6.92820 8.00000i 0.654654 0.755929i
\(113\) 5.46410 0.514019 0.257010 0.966409i \(-0.417263\pi\)
0.257010 + 0.966409i \(0.417263\pi\)
\(114\) −8.46410 8.46410i −0.792736 0.792736i
\(115\) −2.13397 + 7.96410i −0.198994 + 0.742656i
\(116\) −7.46410 + 7.46410i −0.693024 + 0.693024i
\(117\) −0.0717968 0.267949i −0.00663761 0.0247719i
\(118\) −12.6340 + 7.29423i −1.16305 + 0.671488i
\(119\) −1.20577 0.232051i −0.110533 0.0212721i
\(120\) −12.9282 12.9282i −1.18018 1.18018i
\(121\) 7.09808 + 4.09808i 0.645280 + 0.372552i
\(122\) 0.0980762 0.169873i 0.00887940 0.0153796i
\(123\) 16.6603 + 4.46410i 1.50220 + 0.402514i
\(124\) −0.464102 + 0.267949i −0.0416776 + 0.0240625i
\(125\) −2.83013 2.83013i −0.253134 0.253134i
\(126\) 1.19615 2.46410i 0.106562 0.219520i
\(127\) 2.53590 0.225025 0.112512 0.993650i \(-0.464110\pi\)
0.112512 + 0.993650i \(0.464110\pi\)
\(128\) 8.00000 + 8.00000i 0.707107 + 0.707107i
\(129\) 0.633975 + 1.09808i 0.0558184 + 0.0966802i
\(130\) 0.464102 + 1.73205i 0.0407044 + 0.151911i
\(131\) −8.96410 + 2.40192i −0.783197 + 0.209857i −0.628194 0.778057i \(-0.716206\pi\)
−0.155003 + 0.987914i \(0.549539\pi\)
\(132\) 14.6603 + 8.46410i 1.27601 + 0.736705i
\(133\) −5.06218 + 10.4282i −0.438946 + 0.904240i
\(134\) −5.36603 9.29423i −0.463554 0.802899i
\(135\) 12.6962 + 7.33013i 1.09271 + 0.630877i
\(136\) 0.339746 1.26795i 0.0291330 0.108726i
\(137\) 11.7679 6.79423i 1.00540 0.580470i 0.0955611 0.995424i \(-0.469535\pi\)
0.909843 + 0.414953i \(0.136202\pi\)
\(138\) 6.73205i 0.573070i
\(139\) 1.92820 1.92820i 0.163548 0.163548i −0.620588 0.784136i \(-0.713106\pi\)
0.784136 + 0.620588i \(0.213106\pi\)
\(140\) −7.73205 + 15.9282i −0.653478 + 1.34618i
\(141\) 10.5622 + 10.5622i 0.889496 + 0.889496i
\(142\) 7.46410 + 7.46410i 0.626373 + 0.626373i
\(143\) −0.830127 1.43782i −0.0694187 0.120237i
\(144\) 2.53590 + 1.46410i 0.211325 + 0.122008i
\(145\) 8.83013 15.2942i 0.733302 1.27012i
\(146\) 1.16987 4.36603i 0.0968194 0.361335i
\(147\) −13.4282 1.59808i −1.10754 0.131807i
\(148\) −21.3923 + 5.73205i −1.75844 + 0.471172i
\(149\) −2.40192 8.96410i −0.196773 0.734368i −0.991801 0.127794i \(-0.959210\pi\)
0.795027 0.606573i \(-0.207456\pi\)
\(150\) 14.6603 + 8.46410i 1.19700 + 0.691091i
\(151\) 8.13397 4.69615i 0.661933 0.382167i −0.131080 0.991372i \(-0.541844\pi\)
0.793013 + 0.609204i \(0.208511\pi\)
\(152\) −10.7321 6.19615i −0.870484 0.502574i
\(153\) 0.339746i 0.0274668i
\(154\) 3.09808 16.0981i 0.249650 1.29722i
\(155\) 0.633975 0.633975i 0.0509221 0.0509221i
\(156\) −0.732051 1.26795i −0.0586110 0.101517i
\(157\) 4.25833 15.8923i 0.339852 1.26834i −0.558661 0.829396i \(-0.688685\pi\)
0.898513 0.438948i \(-0.144649\pi\)
\(158\) 0.241670 + 0.901924i 0.0192262 + 0.0717532i
\(159\) 11.0622 19.1603i 0.877288 1.51951i
\(160\) −16.3923 9.46410i −1.29593 0.748203i
\(161\) −6.16025 + 2.13397i −0.485496 + 0.168181i
\(162\) −14.5622 3.90192i −1.14411 0.306564i
\(163\) −0.232051 + 0.0621778i −0.0181756 + 0.00487014i −0.267895 0.963448i \(-0.586328\pi\)
0.249720 + 0.968318i \(0.419661\pi\)
\(164\) 17.8564 1.39435
\(165\) −27.3564 7.33013i −2.12969 0.570650i
\(166\) 16.9282 1.31388
\(167\) 5.85641i 0.453182i 0.973990 + 0.226591i \(0.0727581\pi\)
−0.973990 + 0.226591i \(0.927242\pi\)
\(168\) 2.73205 14.1962i 0.210782 1.09526i
\(169\) 12.8564i 0.988954i
\(170\) 2.19615i 0.168437i
\(171\) −3.09808 0.830127i −0.236916 0.0634814i
\(172\) 0.928203 + 0.928203i 0.0707748 + 0.0707748i
\(173\) −4.59808 + 1.23205i −0.349585 + 0.0936711i −0.429339 0.903144i \(-0.641253\pi\)
0.0797535 + 0.996815i \(0.474587\pi\)
\(174\) −3.73205 + 13.9282i −0.282926 + 1.05589i
\(175\) 3.09808 16.0981i 0.234193 1.21690i
\(176\) 16.9282 + 4.53590i 1.27601 + 0.341906i
\(177\) −9.96410 + 17.2583i −0.748948 + 1.29722i
\(178\) −7.09808 + 1.90192i −0.532023 + 0.142555i
\(179\) 2.03590 7.59808i 0.152170 0.567907i −0.847161 0.531336i \(-0.821690\pi\)
0.999331 0.0365704i \(-0.0116433\pi\)
\(180\) −4.73205 1.26795i −0.352706 0.0945074i
\(181\) −7.39230 + 7.39230i −0.549466 + 0.549466i −0.926286 0.376821i \(-0.877017\pi\)
0.376821 + 0.926286i \(0.377017\pi\)
\(182\) −0.928203 + 1.07180i −0.0688030 + 0.0794469i
\(183\) 0.267949i 0.0198074i
\(184\) −1.80385 6.73205i −0.132981 0.496293i
\(185\) 32.0885 18.5263i 2.35919 1.36208i
\(186\) −0.366025 + 0.633975i −0.0268383 + 0.0464853i
\(187\) −0.526279 1.96410i −0.0384854 0.143629i
\(188\) 13.3923 + 7.73205i 0.976734 + 0.563918i
\(189\) 0.830127 + 11.5622i 0.0603829 + 0.841025i
\(190\) 20.0263 + 5.36603i 1.45286 + 0.389292i
\(191\) 4.33013 7.50000i 0.313317 0.542681i −0.665761 0.746165i \(-0.731893\pi\)
0.979078 + 0.203484i \(0.0652264\pi\)
\(192\) 14.9282 + 4.00000i 1.07735 + 0.288675i
\(193\) 11.5000 + 19.9186i 0.827788 + 1.43377i 0.899770 + 0.436365i \(0.143734\pi\)
−0.0719816 + 0.997406i \(0.522932\pi\)
\(194\) 10.9282 10.9282i 0.784599 0.784599i
\(195\) 1.73205 + 1.73205i 0.124035 + 0.124035i
\(196\) −13.8564 + 2.00000i −0.989743 + 0.142857i
\(197\) 0.660254 0.660254i 0.0470412 0.0470412i −0.683195 0.730236i \(-0.739410\pi\)
0.730236 + 0.683195i \(0.239410\pi\)
\(198\) 4.53590 0.322352
\(199\) −1.66987 + 0.964102i −0.118374 + 0.0683434i −0.558018 0.829829i \(-0.688438\pi\)
0.439644 + 0.898172i \(0.355105\pi\)
\(200\) 16.9282 + 4.53590i 1.19700 + 0.320736i
\(201\) −12.6962 7.33013i −0.895518 0.517027i
\(202\) −8.95448 + 5.16987i −0.630035 + 0.363751i
\(203\) 13.9282 1.00000i 0.977568 0.0701862i
\(204\) −0.464102 1.73205i −0.0324936 0.121268i
\(205\) −28.8564 + 7.73205i −2.01542 + 0.540030i
\(206\) −0.633975 + 0.169873i −0.0441711 + 0.0118356i
\(207\) −0.901924 1.56218i −0.0626880 0.108579i
\(208\) −1.07180 1.07180i −0.0743157 0.0743157i
\(209\) −19.1962 −1.32783
\(210\) 1.73205 + 24.1244i 0.119523 + 1.66474i
\(211\) −2.07180 2.07180i −0.142628 0.142628i 0.632187 0.774816i \(-0.282157\pi\)
−0.774816 + 0.632187i \(0.782157\pi\)
\(212\) 5.92820 22.1244i 0.407151 1.51951i
\(213\) 13.9282 + 3.73205i 0.954345 + 0.255716i
\(214\) −1.09808 0.633975i −0.0750629 0.0433376i
\(215\) −1.90192 1.09808i −0.129710 0.0748882i
\(216\) −12.3923 −0.843190
\(217\) 0.696152 + 0.133975i 0.0472579 + 0.00909479i
\(218\) 10.5622 + 18.2942i 0.715361 + 1.23904i
\(219\) −1.59808 5.96410i −0.107988 0.403017i
\(220\) −29.3205 −1.97679
\(221\) −0.0455173 + 0.169873i −0.00306183 + 0.0114269i
\(222\) −21.3923 + 21.3923i −1.43576 + 1.43576i
\(223\) −17.8564 −1.19575 −0.597877 0.801588i \(-0.703989\pi\)
−0.597877 + 0.801588i \(0.703989\pi\)
\(224\) −1.07180 14.9282i −0.0716124 0.997433i
\(225\) 4.53590 0.302393
\(226\) 5.46410 5.46410i 0.363467 0.363467i
\(227\) −6.16025 + 22.9904i −0.408870 + 1.52593i 0.387934 + 0.921687i \(0.373189\pi\)
−0.796804 + 0.604238i \(0.793478\pi\)
\(228\) −16.9282 −1.12110
\(229\) 4.66987 + 17.4282i 0.308594 + 1.15169i 0.929807 + 0.368047i \(0.119973\pi\)
−0.621213 + 0.783641i \(0.713360\pi\)
\(230\) 5.83013 + 10.0981i 0.384427 + 0.665847i
\(231\) −7.33013 21.1603i −0.482287 1.39224i
\(232\) 14.9282i 0.980085i
\(233\) −9.69615 5.59808i −0.635216 0.366742i 0.147553 0.989054i \(-0.452860\pi\)
−0.782769 + 0.622312i \(0.786194\pi\)
\(234\) −0.339746 0.196152i −0.0222099 0.0128229i
\(235\) −24.9904 6.69615i −1.63019 0.436809i
\(236\) −5.33975 + 19.9282i −0.347588 + 1.29722i
\(237\) 0.901924 + 0.901924i 0.0585862 + 0.0585862i
\(238\) −1.43782 + 0.973721i −0.0932002 + 0.0631169i
\(239\) −15.4641 −1.00029 −0.500145 0.865942i \(-0.666720\pi\)
−0.500145 + 0.865942i \(0.666720\pi\)
\(240\) −25.8564 −1.66902
\(241\) −0.0358984 0.0621778i −0.00231242 0.00400523i 0.864867 0.502001i \(-0.167403\pi\)
−0.867179 + 0.497996i \(0.834069\pi\)
\(242\) 11.1962 3.00000i 0.719716 0.192847i
\(243\) −7.19615 + 1.92820i −0.461633 + 0.123694i
\(244\) −0.0717968 0.267949i −0.00459632 0.0171537i
\(245\) 21.5263 9.23205i 1.37526 0.589814i
\(246\) 21.1244 12.1962i 1.34684 0.777598i
\(247\) 1.43782 + 0.830127i 0.0914864 + 0.0528197i
\(248\) −0.196152 + 0.732051i −0.0124557 + 0.0464853i
\(249\) 20.0263 11.5622i 1.26911 0.732723i
\(250\) −5.66025 −0.357986
\(251\) 13.5885 13.5885i 0.857696 0.857696i −0.133370 0.991066i \(-0.542580\pi\)
0.991066 + 0.133370i \(0.0425800\pi\)
\(252\) −1.26795 3.66025i −0.0798733 0.230574i
\(253\) −7.63397 7.63397i −0.479944 0.479944i
\(254\) 2.53590 2.53590i 0.159116 0.159116i
\(255\) 1.50000 + 2.59808i 0.0939336 + 0.162698i
\(256\) 16.0000 1.00000
\(257\) −0.696152 + 1.20577i −0.0434248 + 0.0752140i −0.886921 0.461921i \(-0.847160\pi\)
0.843496 + 0.537135i \(0.180494\pi\)
\(258\) 1.73205 + 0.464102i 0.107833 + 0.0288937i
\(259\) 26.3564 + 12.7942i 1.63771 + 0.794995i
\(260\) 2.19615 + 1.26795i 0.136200 + 0.0786349i
\(261\) 1.00000 + 3.73205i 0.0618984 + 0.231008i
\(262\) −6.56218 + 11.3660i −0.405413 + 0.702195i
\(263\) −21.9904 + 12.6962i −1.35598 + 0.782878i −0.989080 0.147380i \(-0.952916\pi\)
−0.366905 + 0.930258i \(0.619583\pi\)
\(264\) 23.1244 6.19615i 1.42321 0.381347i
\(265\) 38.3205i 2.35401i
\(266\) 5.36603 + 15.4904i 0.329012 + 0.949776i
\(267\) −7.09808 + 7.09808i −0.434395 + 0.434395i
\(268\) −14.6603 3.92820i −0.895518 0.239953i
\(269\) −5.79423 + 21.6244i −0.353280 + 1.31846i 0.529354 + 0.848401i \(0.322434\pi\)
−0.882635 + 0.470059i \(0.844232\pi\)
\(270\) 20.0263 5.36603i 1.21876 0.326566i
\(271\) 6.06218 10.5000i 0.368251 0.637830i −0.621041 0.783778i \(-0.713290\pi\)
0.989292 + 0.145948i \(0.0466233\pi\)
\(272\) −0.928203 1.60770i −0.0562806 0.0974808i
\(273\) −0.366025 + 1.90192i −0.0221529 + 0.115110i
\(274\) 4.97372 18.5622i 0.300473 1.12138i
\(275\) 26.2224 7.02628i 1.58127 0.423701i
\(276\) −6.73205 6.73205i −0.405222 0.405222i
\(277\) −16.7942 4.50000i −1.00907 0.270379i −0.283828 0.958875i \(-0.591604\pi\)
−0.725240 + 0.688496i \(0.758271\pi\)
\(278\) 3.85641i 0.231292i
\(279\) 0.196152i 0.0117433i
\(280\) 8.19615 + 23.6603i 0.489814 + 1.41397i
\(281\) 12.9282i 0.771232i 0.922659 + 0.385616i \(0.126011\pi\)
−0.922659 + 0.385616i \(0.873989\pi\)
\(282\) 21.1244 1.25794
\(283\) 16.8923 + 4.52628i 1.00414 + 0.269059i 0.723180 0.690659i \(-0.242680\pi\)
0.280963 + 0.959719i \(0.409346\pi\)
\(284\) 14.9282 0.885826
\(285\) 27.3564 7.33013i 1.62045 0.434199i
\(286\) −2.26795 0.607695i −0.134107 0.0359338i
\(287\) −17.8564 15.4641i −1.05403 0.912817i
\(288\) 4.00000 1.07180i 0.235702 0.0631562i
\(289\) 8.39230 14.5359i 0.493665 0.855053i
\(290\) −6.46410 24.1244i −0.379585 1.41663i
\(291\) 5.46410 20.3923i 0.320311 1.19542i
\(292\) −3.19615 5.53590i −0.187041 0.323964i
\(293\) 5.92820 5.92820i 0.346329 0.346329i −0.512411 0.858740i \(-0.671248\pi\)
0.858740 + 0.512411i \(0.171248\pi\)
\(294\) −15.0263 + 11.8301i −0.876350 + 0.689947i
\(295\) 34.5167i 2.00964i
\(296\) −15.6603 + 27.1244i −0.910234 + 1.57657i
\(297\) −16.6244 + 9.59808i −0.964643 + 0.556937i
\(298\) −11.3660 6.56218i −0.658416 0.380137i
\(299\) 0.241670 + 0.901924i 0.0139761 + 0.0521596i
\(300\) 23.1244 6.19615i 1.33509 0.357735i
\(301\) −0.124356 1.73205i −0.00716774 0.0998337i
\(302\) 3.43782 12.8301i 0.197824 0.738291i
\(303\) −7.06218 + 12.2321i −0.405712 + 0.702713i
\(304\) −16.9282 + 4.53590i −0.970899 + 0.260152i
\(305\) 0.232051 + 0.401924i 0.0132872 + 0.0230141i
\(306\) −0.339746 0.339746i −0.0194220 0.0194220i
\(307\) 9.00000 + 9.00000i 0.513657 + 0.513657i 0.915645 0.401988i \(-0.131681\pi\)
−0.401988 + 0.915645i \(0.631681\pi\)
\(308\) −13.0000 19.1962i −0.740744 1.09380i
\(309\) −0.633975 + 0.633975i −0.0360656 + 0.0360656i
\(310\) 1.26795i 0.0720147i
\(311\) 0.401924 0.232051i 0.0227910 0.0131584i −0.488561 0.872530i \(-0.662478\pi\)
0.511352 + 0.859371i \(0.329145\pi\)
\(312\) −2.00000 0.535898i −0.113228 0.0303393i
\(313\) −8.30385 4.79423i −0.469361 0.270986i 0.246611 0.969115i \(-0.420683\pi\)
−0.715972 + 0.698129i \(0.754016\pi\)
\(314\) −11.6340 20.1506i −0.656543 1.13717i
\(315\) 3.63397 + 5.36603i 0.204751 + 0.302341i
\(316\) 1.14359 + 0.660254i 0.0643322 + 0.0371422i
\(317\) 11.7942 3.16025i 0.662430 0.177498i 0.0880875 0.996113i \(-0.471924\pi\)
0.574342 + 0.818615i \(0.305258\pi\)
\(318\) −8.09808 30.2224i −0.454118 1.69479i
\(319\) 11.5622 + 20.0263i 0.647358 + 1.12126i
\(320\) −25.8564 + 6.92820i −1.44542 + 0.387298i
\(321\) −1.73205 −0.0966736
\(322\) −4.02628 + 8.29423i −0.224376 + 0.462219i
\(323\) 1.43782 + 1.43782i 0.0800026 + 0.0800026i
\(324\) −18.4641 + 10.6603i −1.02578 + 0.592236i
\(325\) −2.26795 0.607695i −0.125803 0.0337089i
\(326\) −0.169873 + 0.294229i −0.00940839 + 0.0162958i
\(327\) 24.9904 + 14.4282i 1.38197 + 0.797881i
\(328\) 17.8564 17.8564i 0.985955 0.985955i
\(329\) −6.69615 19.3301i −0.369171 1.06570i
\(330\) −34.6865 + 20.0263i −1.90943 + 1.10241i
\(331\) 4.62436 + 17.2583i 0.254178 + 0.948604i 0.968546 + 0.248834i \(0.0800474\pi\)
−0.714369 + 0.699770i \(0.753286\pi\)
\(332\) 16.9282 16.9282i 0.929056 0.929056i
\(333\) −2.09808 + 7.83013i −0.114974 + 0.429088i
\(334\) 5.85641 + 5.85641i 0.320448 + 0.320448i
\(335\) 25.3923 1.38733
\(336\) −11.4641 16.9282i −0.625418 0.923509i
\(337\) −33.8564 −1.84428 −0.922138 0.386861i \(-0.873559\pi\)
−0.922138 + 0.386861i \(0.873559\pi\)
\(338\) −12.8564 12.8564i −0.699296 0.699296i
\(339\) 2.73205 10.1962i 0.148385 0.553779i
\(340\) 2.19615 + 2.19615i 0.119103 + 0.119103i
\(341\) 0.303848 + 1.13397i 0.0164543 + 0.0614082i
\(342\) −3.92820 + 2.26795i −0.212413 + 0.122637i
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) 1.85641 0.100091
\(345\) 13.7942 + 7.96410i 0.742656 + 0.428773i
\(346\) −3.36603 + 5.83013i −0.180959 + 0.313430i
\(347\) −16.6962 4.47372i −0.896296 0.240162i −0.218871 0.975754i \(-0.570238\pi\)
−0.677425 + 0.735592i \(0.736904\pi\)
\(348\) 10.1962 + 17.6603i 0.546571 + 0.946689i
\(349\) −18.1244 18.1244i −0.970175 0.970175i 0.0293934 0.999568i \(-0.490642\pi\)
−0.999568 + 0.0293934i \(0.990642\pi\)
\(350\) −13.0000 19.1962i −0.694879 1.02608i
\(351\) 1.66025 0.0886178
\(352\) 21.4641 12.3923i 1.14404 0.660512i
\(353\) −6.89230 11.9378i −0.366840 0.635386i 0.622229 0.782835i \(-0.286227\pi\)
−0.989070 + 0.147449i \(0.952894\pi\)
\(354\) 7.29423 + 27.2224i 0.387684 + 1.44686i
\(355\) −24.1244 + 6.46410i −1.28039 + 0.343079i
\(356\) −5.19615 + 9.00000i −0.275396 + 0.476999i
\(357\) −1.03590 + 2.13397i −0.0548256 + 0.112942i
\(358\) −5.56218 9.63397i −0.293970 0.509171i
\(359\) −2.13397 1.23205i −0.112627 0.0650252i 0.442628 0.896705i \(-0.354046\pi\)
−0.555255 + 0.831680i \(0.687379\pi\)
\(360\) −6.00000 + 3.46410i −0.316228 + 0.182574i
\(361\) 0.169873 0.0980762i 0.00894068 0.00516191i
\(362\) 14.7846i 0.777062i
\(363\) 11.1962 11.1962i 0.587646 0.587646i
\(364\) 0.143594 + 2.00000i 0.00752635 + 0.104828i
\(365\) 7.56218 + 7.56218i 0.395822 + 0.395822i
\(366\) −0.267949 0.267949i −0.0140059 0.0140059i
\(367\) 9.06218 + 15.6962i 0.473042 + 0.819332i 0.999524 0.0308537i \(-0.00982261\pi\)
−0.526482 + 0.850186i \(0.676489\pi\)
\(368\) −8.53590 4.92820i −0.444964 0.256900i
\(369\) 3.26795 5.66025i 0.170123 0.294661i
\(370\) 13.5622 50.6147i 0.705064 2.63133i
\(371\) −25.0885 + 16.9904i −1.30253 + 0.882097i
\(372\) 0.267949 + 1.00000i 0.0138925 + 0.0518476i
\(373\) −0.866025 3.23205i −0.0448411 0.167349i 0.939874 0.341521i \(-0.110942\pi\)
−0.984715 + 0.174171i \(0.944275\pi\)
\(374\) −2.49038 1.43782i −0.128775 0.0743480i
\(375\) −6.69615 + 3.86603i −0.345788 + 0.199641i
\(376\) 21.1244 5.66025i 1.08941 0.291905i
\(377\) 2.00000i 0.103005i
\(378\) 12.3923 + 10.7321i 0.637391 + 0.551997i
\(379\) −24.1244 + 24.1244i −1.23918 + 1.23918i −0.278850 + 0.960335i \(0.589953\pi\)
−0.960335 + 0.278850i \(0.910047\pi\)
\(380\) 25.3923 14.6603i 1.30260 0.752055i
\(381\) 1.26795 4.73205i 0.0649590 0.242430i
\(382\) −3.16987 11.8301i −0.162185 0.605282i
\(383\) 7.40192 12.8205i 0.378221 0.655097i −0.612583 0.790406i \(-0.709869\pi\)
0.990803 + 0.135309i \(0.0432027\pi\)
\(384\) 18.9282 10.9282i 0.965926 0.557678i
\(385\) 29.3205 + 25.3923i 1.49431 + 1.29411i
\(386\) 31.4186 + 8.41858i 1.59916 + 0.428495i
\(387\) 0.464102 0.124356i 0.0235916 0.00632135i
\(388\) 21.8564i 1.10959i
\(389\) −19.9904 5.35641i −1.01355 0.271581i −0.286440 0.958098i \(-0.592472\pi\)
−0.727113 + 0.686518i \(0.759138\pi\)
\(390\) 3.46410 0.175412
\(391\) 1.14359i 0.0578340i
\(392\) −11.8564 + 15.8564i −0.598839 + 0.800869i
\(393\) 17.9282i 0.904358i
\(394\) 1.32051i 0.0665262i
\(395\) −2.13397 0.571797i −0.107372 0.0287702i
\(396\) 4.53590 4.53590i 0.227937 0.227937i
\(397\) 5.13397 1.37564i 0.257667 0.0690416i −0.127673 0.991816i \(-0.540751\pi\)
0.385340 + 0.922775i \(0.374084\pi\)
\(398\) −0.705771 + 2.63397i −0.0353771 + 0.132029i
\(399\) 16.9282 + 14.6603i 0.847470 + 0.733931i
\(400\) 21.4641 12.3923i 1.07321 0.619615i
\(401\) 7.50000 12.9904i 0.374532 0.648709i −0.615725 0.787961i \(-0.711137\pi\)
0.990257 + 0.139253i \(0.0444700\pi\)
\(402\) −20.0263 + 5.36603i −0.998820 + 0.267633i
\(403\) 0.0262794 0.0980762i 0.00130907 0.00488552i
\(404\) −3.78461 + 14.1244i −0.188291 + 0.702713i
\(405\) 25.2224 25.2224i 1.25331 1.25331i
\(406\) 12.9282 14.9282i 0.641616 0.740874i
\(407\) 48.5167i 2.40488i
\(408\) −2.19615 1.26795i −0.108726 0.0627728i
\(409\) −7.50000 + 4.33013i −0.370851 + 0.214111i −0.673830 0.738886i \(-0.735352\pi\)
0.302979 + 0.952997i \(0.402019\pi\)
\(410\) −21.1244 + 36.5885i −1.04326 + 1.80698i
\(411\) −6.79423 25.3564i −0.335135 1.25074i
\(412\) −0.464102 + 0.803848i −0.0228646 + 0.0396027i
\(413\) 22.5981 15.3038i 1.11198 0.753053i
\(414\) −2.46410 0.660254i −0.121104 0.0324497i
\(415\) −20.0263 + 34.6865i −0.983051 + 1.70269i
\(416\) −2.14359 −0.105098
\(417\) −2.63397 4.56218i −0.128986 0.223411i
\(418\) −19.1962 + 19.1962i −0.938915 + 0.938915i
\(419\) −19.0000 19.0000i −0.928211 0.928211i 0.0693796 0.997590i \(-0.477898\pi\)
−0.997590 + 0.0693796i \(0.977898\pi\)
\(420\) 25.8564 + 22.3923i 1.26166 + 1.09263i
\(421\) −8.66025 + 8.66025i −0.422075 + 0.422075i −0.885918 0.463843i \(-0.846470\pi\)
0.463843 + 0.885918i \(0.346470\pi\)
\(422\) −4.14359 −0.201707
\(423\) 4.90192 2.83013i 0.238340 0.137605i
\(424\) −16.1962 28.0526i −0.786555 1.36235i
\(425\) −2.49038 1.43782i −0.120801 0.0697446i
\(426\) 17.6603 10.1962i 0.855642 0.494005i
\(427\) −0.160254 + 0.330127i −0.00775524 + 0.0159760i
\(428\) −1.73205 + 0.464102i −0.0837218 + 0.0224332i
\(429\) −3.09808 + 0.830127i −0.149577 + 0.0400789i
\(430\) −3.00000 + 0.803848i −0.144673 + 0.0387650i
\(431\) −6.66987 11.5526i −0.321276 0.556467i 0.659475 0.751726i \(-0.270779\pi\)
−0.980752 + 0.195259i \(0.937445\pi\)
\(432\) −12.3923 + 12.3923i −0.596225 + 0.596225i
\(433\) 29.1769 1.40215 0.701077 0.713086i \(-0.252703\pi\)
0.701077 + 0.713086i \(0.252703\pi\)
\(434\) 0.830127 0.562178i 0.0398474 0.0269854i
\(435\) −24.1244 24.1244i −1.15667 1.15667i
\(436\) 28.8564 + 7.73205i 1.38197 + 0.370298i
\(437\) 10.4282 + 2.79423i 0.498849 + 0.133666i
\(438\) −7.56218 4.36603i −0.361335 0.208617i
\(439\) −12.5263 7.23205i −0.597847 0.345167i 0.170347 0.985384i \(-0.445511\pi\)
−0.768194 + 0.640217i \(0.778844\pi\)
\(440\) −29.3205 + 29.3205i −1.39780 + 1.39780i
\(441\) −1.90192 + 4.75833i −0.0905678 + 0.226587i
\(442\) 0.124356 + 0.215390i 0.00591500 + 0.0102451i
\(443\) 3.42820 + 12.7942i 0.162879 + 0.607872i 0.998301 + 0.0582637i \(0.0185564\pi\)
−0.835422 + 0.549608i \(0.814777\pi\)
\(444\) 42.7846i 2.03047i
\(445\) 4.50000 16.7942i 0.213320 0.796123i
\(446\) −17.8564 + 17.8564i −0.845525 + 0.845525i
\(447\) −17.9282 −0.847975
\(448\) −16.0000 13.8564i −0.755929 0.654654i
\(449\) 11.3205 0.534248 0.267124 0.963662i \(-0.413927\pi\)
0.267124 + 0.963662i \(0.413927\pi\)
\(450\) 4.53590 4.53590i 0.213824 0.213824i
\(451\) 10.1244 37.7846i 0.476737 1.77921i
\(452\) 10.9282i 0.514019i
\(453\) −4.69615 17.5263i −0.220644 0.823456i
\(454\) 16.8301 + 29.1506i 0.789877 + 1.36811i
\(455\) −1.09808 3.16987i −0.0514786 0.148606i
\(456\) −16.9282 + 16.9282i −0.792736 + 0.792736i
\(457\) −25.2846 14.5981i −1.18276 0.682869i −0.226112 0.974101i \(-0.572601\pi\)
−0.956652 + 0.291232i \(0.905935\pi\)
\(458\) 22.0981 + 12.7583i 1.03258 + 0.596158i
\(459\) 1.96410 + 0.526279i 0.0916764 + 0.0245646i
\(460\) 15.9282 + 4.26795i 0.742656 + 0.198994i
\(461\) 1.33975 + 1.33975i 0.0623982 + 0.0623982i 0.737617 0.675219i \(-0.235951\pi\)
−0.675219 + 0.737617i \(0.735951\pi\)
\(462\) −28.4904 13.8301i −1.32549 0.643436i
\(463\) 29.8564 1.38754 0.693772 0.720194i \(-0.255947\pi\)
0.693772 + 0.720194i \(0.255947\pi\)
\(464\) 14.9282 + 14.9282i 0.693024 + 0.693024i
\(465\) −0.866025 1.50000i −0.0401610 0.0695608i
\(466\) −15.2942 + 4.09808i −0.708491 + 0.189840i
\(467\) −0.0358984 + 0.00961894i −0.00166118 + 0.000445112i −0.259650 0.965703i \(-0.583607\pi\)
0.257988 + 0.966148i \(0.416940\pi\)
\(468\) −0.535898 + 0.143594i −0.0247719 + 0.00663761i
\(469\) 11.2583 + 16.6244i 0.519861 + 0.767641i
\(470\) −31.6865 + 18.2942i −1.46159 + 0.843850i
\(471\) −27.5263 15.8923i −1.26834 0.732279i
\(472\) 14.5885 + 25.2679i 0.671488 + 1.16305i
\(473\) 2.49038 1.43782i 0.114508 0.0661111i
\(474\) 1.80385 0.0828535
\(475\) −19.1962 + 19.1962i −0.880780 + 0.880780i
\(476\) −0.464102 + 2.41154i −0.0212721 + 0.110533i
\(477\) −5.92820 5.92820i −0.271434 0.271434i
\(478\) −15.4641 + 15.4641i −0.707312 + 0.707312i
\(479\) 7.79423 + 13.5000i 0.356127 + 0.616831i 0.987310 0.158803i \(-0.0507636\pi\)
−0.631183 + 0.775634i \(0.717430\pi\)
\(480\) −25.8564 + 25.8564i −1.18018 + 1.18018i
\(481\) 2.09808 3.63397i 0.0956640 0.165695i
\(482\) −0.0980762 0.0262794i −0.00446725 0.00119700i
\(483\) 0.901924 + 12.5622i 0.0410390 + 0.571599i
\(484\) 8.19615 14.1962i 0.372552 0.645280i
\(485\) 9.46410 + 35.3205i 0.429743 + 1.60382i
\(486\) −5.26795 + 9.12436i −0.238959 + 0.413889i
\(487\) 19.3301 11.1603i 0.875932 0.505719i 0.00661681 0.999978i \(-0.497894\pi\)
0.869315 + 0.494259i \(0.164560\pi\)
\(488\) −0.339746 0.196152i −0.0153796 0.00887940i
\(489\) 0.464102i 0.0209874i
\(490\) 12.2942 30.7583i 0.555397 1.38952i
\(491\) 27.5885 27.5885i 1.24505 1.24505i 0.287170 0.957880i \(-0.407286\pi\)
0.957880 0.287170i \(-0.0927145\pi\)
\(492\) 8.92820 33.3205i 0.402514 1.50220i
\(493\) 0.633975 2.36603i 0.0285528 0.106560i
\(494\) 2.26795 0.607695i 0.102040 0.0273415i
\(495\) −5.36603 + 9.29423i −0.241185 + 0.417745i
\(496\) 0.535898 + 0.928203i 0.0240625 + 0.0416776i
\(497\) −14.9282 12.9282i −0.669621 0.579909i
\(498\) 8.46410 31.5885i 0.379285 1.41551i
\(499\) −3.69615 + 0.990381i −0.165463 + 0.0443355i −0.340599 0.940209i \(-0.610630\pi\)
0.175137 + 0.984544i \(0.443963\pi\)
\(500\) −5.66025 + 5.66025i −0.253134 + 0.253134i
\(501\) 10.9282 + 2.92820i 0.488236 + 0.130822i
\(502\) 27.1769i 1.21297i
\(503\) 4.14359i 0.184754i −0.995724 0.0923769i \(-0.970554\pi\)
0.995724 0.0923769i \(-0.0294464\pi\)
\(504\) −4.92820 2.39230i −0.219520 0.106562i
\(505\) 24.4641i 1.08864i
\(506\) −15.2679 −0.678743
\(507\) −23.9904 6.42820i −1.06545 0.285487i
\(508\) 5.07180i 0.225025i
\(509\) −16.5263 + 4.42820i −0.732514 + 0.196277i −0.605749 0.795656i \(-0.707126\pi\)
−0.126766 + 0.991933i \(0.540460\pi\)
\(510\) 4.09808 + 1.09808i 0.181466 + 0.0486236i
\(511\) −1.59808 + 8.30385i −0.0706947 + 0.367341i
\(512\) 16.0000 16.0000i 0.707107 0.707107i
\(513\) 9.59808 16.6244i 0.423765 0.733983i
\(514\) 0.509619 + 1.90192i 0.0224783 + 0.0838903i
\(515\) 0.401924 1.50000i 0.0177109 0.0660979i
\(516\) 2.19615 1.26795i 0.0966802 0.0558184i
\(517\) 23.9545 23.9545i 1.05352 1.05352i
\(518\) 39.1506 13.5622i 1.72018 0.595888i
\(519\) 9.19615i 0.403666i
\(520\) 3.46410 0.928203i 0.151911 0.0407044i
\(521\) −37.6244 + 21.7224i −1.64835 + 0.951677i −0.670626 + 0.741796i \(0.733974\pi\)
−0.977727 + 0.209881i \(0.932692\pi\)
\(522\) 4.73205 + 2.73205i 0.207116 + 0.119579i
\(523\) 9.28461 + 34.6506i 0.405988 + 1.51517i 0.802227 + 0.597019i \(0.203648\pi\)
−0.396239 + 0.918147i \(0.629685\pi\)
\(524\) 4.80385 + 17.9282i 0.209857 + 0.783197i
\(525\) −28.4904 13.8301i −1.24342 0.603596i
\(526\) −9.29423 + 34.6865i −0.405248 + 1.51240i
\(527\) 0.0621778 0.107695i 0.00270851 0.00469127i
\(528\) 16.9282 29.3205i 0.736705 1.27601i
\(529\) −8.46410 14.6603i −0.368004 0.637402i
\(530\) 38.3205 + 38.3205i 1.66454 + 1.66454i
\(531\) 5.33975 + 5.33975i 0.231725 + 0.231725i
\(532\) 20.8564 + 10.1244i 0.904240 + 0.438946i
\(533\) −2.39230 + 2.39230i −0.103622 + 0.103622i
\(534\) 14.1962i 0.614328i
\(535\) 2.59808 1.50000i 0.112325 0.0648507i
\(536\) −18.5885 + 10.7321i −0.802899 + 0.463554i
\(537\) −13.1603 7.59808i −0.567907 0.327881i
\(538\) 15.8301 + 27.4186i 0.682485 + 1.18210i
\(539\) −3.62436 + 30.4545i −0.156112 + 1.31177i
\(540\) 14.6603 25.3923i 0.630877 1.09271i
\(541\) 21.5263 5.76795i 0.925487 0.247984i 0.235558 0.971860i \(-0.424308\pi\)
0.689929 + 0.723877i \(0.257642\pi\)
\(542\) −4.43782 16.5622i −0.190621 0.711406i
\(543\) 10.0981 + 17.4904i 0.433350 + 0.750584i
\(544\) −2.53590 0.679492i −0.108726 0.0291330i
\(545\) −49.9808 −2.14094
\(546\) 1.53590 + 2.26795i 0.0657304 + 0.0970593i
\(547\) 15.0526 + 15.0526i 0.643601 + 0.643601i 0.951439 0.307838i \(-0.0996054\pi\)
−0.307838 + 0.951439i \(0.599605\pi\)
\(548\) −13.5885 23.5359i −0.580470 1.00540i
\(549\) −0.0980762 0.0262794i −0.00418579 0.00112158i
\(550\) 19.1962 33.2487i 0.818527 1.41773i
\(551\) −20.0263 11.5622i −0.853148 0.492565i
\(552\) −13.4641 −0.573070
\(553\) −0.571797 1.65064i −0.0243153 0.0701921i
\(554\) −21.2942 + 12.2942i −0.904705 + 0.522332i
\(555\) −18.5263 69.1410i −0.786397 2.93487i
\(556\) −3.85641 3.85641i −0.163548 0.163548i
\(557\) 1.40192 5.23205i 0.0594014 0.221689i −0.929844 0.367954i \(-0.880058\pi\)
0.989245 + 0.146265i \(0.0467251\pi\)
\(558\) 0.196152 + 0.196152i 0.00830379 + 0.00830379i
\(559\) −0.248711 −0.0105194
\(560\) 31.8564 + 15.4641i 1.34618 + 0.653478i
\(561\) −3.92820 −0.165849
\(562\) 12.9282 + 12.9282i 0.545343 + 0.545343i
\(563\) 11.4282 42.6506i 0.481641 1.79751i −0.113089 0.993585i \(-0.536075\pi\)
0.594731 0.803925i \(-0.297259\pi\)
\(564\) 21.1244 21.1244i 0.889496 0.889496i
\(565\) 4.73205 + 17.6603i 0.199079 + 0.742972i
\(566\) 21.4186 12.3660i 0.900290 0.519783i
\(567\) 27.6962 + 5.33013i 1.16313 + 0.223844i
\(568\) 14.9282 14.9282i 0.626373 0.626373i
\(569\) 26.0885 + 15.0622i 1.09369 + 0.631439i 0.934555 0.355818i \(-0.115798\pi\)
0.159130 + 0.987258i \(0.449131\pi\)
\(570\) 20.0263 34.6865i 0.838809 1.45286i
\(571\) 10.1603 + 2.72243i 0.425193 + 0.113930i 0.465069 0.885274i \(-0.346030\pi\)
−0.0398756 + 0.999205i \(0.512696\pi\)
\(572\) −2.87564 + 1.66025i −0.120237 + 0.0694187i
\(573\) −11.8301 11.8301i −0.494211 0.494211i
\(574\) −33.3205 + 2.39230i −1.39077 + 0.0998529i
\(575\) −15.2679 −0.636717
\(576\) 2.92820 5.07180i 0.122008 0.211325i
\(577\) 17.6244 + 30.5263i 0.733712 + 1.27083i 0.955286 + 0.295682i \(0.0955470\pi\)
−0.221575 + 0.975143i \(0.571120\pi\)
\(578\) −6.14359 22.9282i −0.255540 0.953688i
\(579\) 42.9186 11.5000i 1.78364 0.477924i
\(580\) −30.5885 17.6603i −1.27012 0.733302i
\(581\) −31.5885 + 2.26795i −1.31051 + 0.0940904i
\(582\) −14.9282 25.8564i −0.618794 1.07178i
\(583\) −43.4545 25.0885i −1.79970 1.03906i
\(584\) −8.73205 2.33975i −0.361335 0.0968194i
\(585\) 0.803848 0.464102i 0.0332350 0.0191882i
\(586\) 11.8564i 0.489784i
\(587\) 8.07180 8.07180i 0.333159 0.333159i −0.520626 0.853785i \(-0.674301\pi\)
0.853785 + 0.520626i \(0.174301\pi\)
\(588\) −3.19615 + 26.8564i −0.131807 + 1.10754i
\(589\) −0.830127 0.830127i −0.0342048 0.0342048i
\(590\) −34.5167 34.5167i −1.42103 1.42103i
\(591\) −0.901924 1.56218i −0.0371002 0.0642594i
\(592\) 11.4641 + 42.7846i 0.471172 + 1.75844i
\(593\) −4.69615 + 8.13397i −0.192848 + 0.334022i −0.946193 0.323603i \(-0.895106\pi\)
0.753345 + 0.657625i \(0.228439\pi\)
\(594\) −7.02628 + 26.2224i −0.288292 + 1.07592i
\(595\) −0.294229 4.09808i −0.0120622 0.168005i
\(596\) −17.9282 + 4.80385i −0.734368 + 0.196773i
\(597\) 0.964102 + 3.59808i 0.0394581 + 0.147259i
\(598\) 1.14359 + 0.660254i 0.0467650 + 0.0269998i
\(599\) 25.3301 14.6244i 1.03496 0.597535i 0.116559 0.993184i \(-0.462814\pi\)
0.918402 + 0.395649i \(0.129480\pi\)
\(600\) 16.9282 29.3205i 0.691091 1.19700i
\(601\) 10.0000i 0.407909i 0.978980 + 0.203954i \(0.0653794\pi\)
−0.978980 + 0.203954i \(0.934621\pi\)
\(602\) −1.85641 1.60770i −0.0756615 0.0655248i
\(603\) −3.92820 + 3.92820i −0.159969 + 0.159969i
\(604\) −9.39230 16.2679i −0.382167 0.661933i
\(605\) −7.09808 + 26.4904i −0.288578 + 1.07699i
\(606\) 5.16987 + 19.2942i 0.210012 + 0.783774i
\(607\) 10.5263 18.2321i 0.427249 0.740016i −0.569379 0.822075i \(-0.692816\pi\)
0.996627 + 0.0820591i \(0.0261496\pi\)
\(608\) −12.3923 + 21.4641i −0.502574 + 0.870484i
\(609\) 5.09808 26.4904i 0.206584 1.07344i
\(610\) 0.633975 + 0.169873i 0.0256689 + 0.00687796i
\(611\) −2.83013 + 0.758330i −0.114495 + 0.0306788i
\(612\) −0.679492 −0.0274668
\(613\) 21.5263 + 5.76795i 0.869438 + 0.232965i 0.665845 0.746090i \(-0.268071\pi\)
0.203593 + 0.979056i \(0.434738\pi\)
\(614\) 18.0000 0.726421
\(615\) 57.7128i 2.32721i
\(616\) −32.1962 6.19615i −1.29722 0.249650i
\(617\) 7.46410i 0.300493i 0.988649 + 0.150247i \(0.0480068\pi\)
−0.988649 + 0.150247i \(0.951993\pi\)
\(618\) 1.26795i 0.0510044i
\(619\) 25.8923 + 6.93782i 1.04070 + 0.278855i 0.738403 0.674359i \(-0.235580\pi\)
0.302296 + 0.953214i \(0.402247\pi\)
\(620\) −1.26795 1.26795i −0.0509221 0.0509221i
\(621\) 10.4282 2.79423i 0.418469 0.112129i
\(622\) 0.169873 0.633975i 0.00681129 0.0254201i
\(623\) 12.9904 4.50000i 0.520449 0.180289i
\(624\) −2.53590 + 1.46410i −0.101517 + 0.0586110i
\(625\) −8.79423 + 15.2321i −0.351769 + 0.609282i
\(626\) −13.0981 + 3.50962i −0.523504 + 0.140273i
\(627\) −9.59808 + 35.8205i −0.383310 + 1.43053i
\(628\) −31.7846 8.51666i −1.26834 0.339852i
\(629\) 3.63397 3.63397i 0.144896 0.144896i
\(630\) 9.00000 + 1.73205i 0.358569 + 0.0690066i
\(631\) 16.2487i 0.646851i −0.946254 0.323425i \(-0.895165\pi\)
0.946254 0.323425i \(-0.104835\pi\)
\(632\) 1.80385 0.483340i 0.0717532 0.0192262i
\(633\) −4.90192 + 2.83013i −0.194834 + 0.112487i
\(634\) 8.63397 14.9545i 0.342899 0.593918i
\(635\) 2.19615 + 8.19615i 0.0871517 + 0.325254i
\(636\) −38.3205 22.1244i −1.51951 0.877288i
\(637\) 1.58846 2.12436i 0.0629370 0.0841700i
\(638\) 31.5885 + 8.46410i 1.25060 + 0.335097i
\(639\) 2.73205 4.73205i 0.108078 0.187197i
\(640\) −18.9282 + 32.7846i −0.748203 + 1.29593i
\(641\) 19.4282 + 33.6506i 0.767368 + 1.32912i 0.938986 + 0.343957i \(0.111767\pi\)
−0.171618 + 0.985164i \(0.554899\pi\)
\(642\) −1.73205 + 1.73205i −0.0683586 + 0.0683586i
\(643\) 15.3923 + 15.3923i 0.607013 + 0.607013i 0.942164 0.335151i \(-0.108787\pi\)
−0.335151 + 0.942164i \(0.608787\pi\)
\(644\) 4.26795 + 12.3205i 0.168181 + 0.485496i
\(645\) −3.00000 + 3.00000i −0.118125 + 0.118125i
\(646\) 2.87564 0.113141
\(647\) 29.1340 16.8205i 1.14537 0.661282i 0.197619 0.980279i \(-0.436679\pi\)
0.947756 + 0.318997i \(0.103346\pi\)
\(648\) −7.80385 + 29.1244i −0.306564 + 1.14411i
\(649\) 39.1410 + 22.5981i 1.53642 + 0.887052i
\(650\) −2.87564 + 1.66025i −0.112792 + 0.0651205i
\(651\) 0.598076 1.23205i 0.0234405 0.0482879i
\(652\) 0.124356 + 0.464102i 0.00487014 + 0.0181756i
\(653\) 20.7224 5.55256i 0.810931 0.217288i 0.170554 0.985348i \(-0.445444\pi\)
0.640378 + 0.768060i \(0.278778\pi\)
\(654\) 39.4186 10.5622i 1.54139 0.413014i
\(655\) −15.5263 26.8923i −0.606662 1.05077i
\(656\) 35.7128i 1.39435i
\(657\) −2.33975 −0.0912822
\(658\) −26.0263 12.6340i −1.01461 0.492524i
\(659\) −8.85641 8.85641i −0.344997 0.344997i 0.513245 0.858242i \(-0.328443\pi\)
−0.858242 + 0.513245i \(0.828443\pi\)
\(660\) −14.6603 + 54.7128i −0.570650 + 2.12969i
\(661\) −18.0622 4.83975i −0.702537 0.188244i −0.110170 0.993913i \(-0.535140\pi\)
−0.592367 + 0.805668i \(0.701806\pi\)
\(662\) 21.8827 + 12.6340i 0.850495 + 0.491033i
\(663\) 0.294229 + 0.169873i 0.0114269 + 0.00659732i
\(664\) 33.8564i 1.31388i
\(665\) −38.0885 7.33013i −1.47701 0.284250i
\(666\) 5.73205 + 9.92820i 0.222112 + 0.384710i
\(667\) −3.36603 12.5622i −0.130333 0.486409i
\(668\) 11.7128 0.453182
\(669\) −8.92820 + 33.3205i −0.345184 + 1.28825i
\(670\) 25.3923 25.3923i 0.980990 0.980990i
\(671\) −0.607695 −0.0234598
\(672\) −28.3923 5.46410i −1.09526 0.210782i
\(673\) −0.784610 −0.0302445 −0.0151222 0.999886i \(-0.504814\pi\)
−0.0151222 + 0.999886i \(0.504814\pi\)
\(674\) −33.8564 + 33.8564i −1.30410 + 1.30410i
\(675\) −7.02628 + 26.2224i −0.270442 + 1.00930i
\(676\) −25.7128 −0.988954
\(677\) −13.2776 49.5526i −0.510298 1.90446i −0.417233 0.908800i \(-0.637000\pi\)
−0.0930654 0.995660i \(-0.529667\pi\)
\(678\) −7.46410 12.9282i −0.286657 0.496505i
\(679\) −18.9282 + 21.8564i −0.726398 + 0.838772i
\(680\) 4.39230 0.168437
\(681\) 39.8205 + 22.9904i 1.52593 + 0.880993i
\(682\) 1.43782 + 0.830127i 0.0550571 + 0.0317872i
\(683\) −43.2128 11.5788i −1.65349 0.443052i −0.692905 0.721029i \(-0.743669\pi\)
−0.960588 + 0.277977i \(0.910336\pi\)
\(684\) −1.66025 + 6.19615i −0.0634814 + 0.236916i
\(685\) 32.1506 + 32.1506i 1.22841 + 1.22841i
\(686\) 25.5885 5.58846i 0.976972 0.213368i
\(687\) 34.8564 1.32985
\(688\) 1.85641 1.85641i 0.0707748 0.0707748i
\(689\) 2.16987 + 3.75833i 0.0826656 + 0.143181i
\(690\) 21.7583 5.83013i 0.828325 0.221949i
\(691\) −11.1603 + 2.99038i −0.424556 + 0.113759i −0.464770 0.885432i \(-0.653863\pi\)
0.0402135 + 0.999191i \(0.487196\pi\)
\(692\) 2.46410 + 9.19615i 0.0936711 + 0.349585i
\(693\) −8.46410 + 0.607695i −0.321525 + 0.0230844i
\(694\) −21.1699 + 12.2224i −0.803597 + 0.463957i
\(695\) 7.90192 + 4.56218i 0.299737 + 0.173053i
\(696\) 27.8564 + 7.46410i 1.05589 + 0.282926i
\(697\) −3.58846 + 2.07180i −0.135923 + 0.0784749i
\(698\) −36.2487 −1.37203
\(699\) −15.2942 + 15.2942i −0.578481 + 0.578481i
\(700\) −32.1962 6.19615i −1.21690 0.234193i
\(701\) 7.39230 + 7.39230i 0.279204 + 0.279204i 0.832791 0.553588i \(-0.186742\pi\)
−0.553588 + 0.832791i \(0.686742\pi\)
\(702\) 1.66025 1.66025i 0.0626623 0.0626623i
\(703\) −24.2583 42.0167i −0.914920 1.58469i
\(704\) 9.07180 33.8564i 0.341906 1.27601i
\(705\) −24.9904 + 43.2846i −0.941192 + 1.63019i
\(706\) −18.8301 5.04552i −0.708681 0.189891i
\(707\) 16.0167 10.8468i 0.602369 0.407935i
\(708\) 34.5167 + 19.9282i 1.29722 + 0.748948i
\(709\) 2.34936 + 8.76795i 0.0882323 + 0.329287i 0.995907 0.0903879i \(-0.0288107\pi\)
−0.907674 + 0.419675i \(0.862144\pi\)
\(710\) −17.6603 + 30.5885i −0.662778 + 1.14796i
\(711\) 0.418584 0.241670i 0.0156981 0.00906332i
\(712\) 3.80385 + 14.1962i 0.142555 + 0.532023i
\(713\) 0.660254i 0.0247267i
\(714\) 1.09808 + 3.16987i 0.0410945 + 0.118630i
\(715\) 3.92820 3.92820i 0.146906 0.146906i
\(716\) −15.1962 4.07180i −0.567907 0.152170i
\(717\) −7.73205 + 28.8564i −0.288759 + 1.07766i
\(718\) −3.36603 + 0.901924i −0.125619 + 0.0336595i
\(719\) −15.7942 + 27.3564i −0.589025 + 1.02022i 0.405335 + 0.914168i \(0.367155\pi\)
−0.994360 + 0.106054i \(0.966178\pi\)
\(720\) −2.53590 + 9.46410i −0.0945074 + 0.352706i
\(721\) 1.16025 0.401924i 0.0432101 0.0149684i
\(722\) 0.0717968 0.267949i 0.00267200 0.00997204i
\(723\) −0.133975 + 0.0358984i −0.00498257 + 0.00133508i
\(724\) 14.7846 + 14.7846i 0.549466 + 0.549466i
\(725\) 31.5885 + 8.46410i 1.17317 + 0.314349i
\(726\) 22.3923i 0.831056i
\(727\) 6.67949i 0.247729i −0.992299 0.123864i \(-0.960471\pi\)
0.992299 0.123864i \(-0.0395288\pi\)
\(728\) 2.14359 + 1.85641i 0.0794469 + 0.0688030i
\(729\) 17.5885i 0.651424i
\(730\) 15.1244 0.559778
\(731\) −0.294229 0.0788383i −0.0108824 0.00291594i
\(732\) −0.535898 −0.0198074
\(733\) −45.1865 + 12.1077i −1.66900 + 0.447208i −0.964842 0.262832i \(-0.915343\pi\)
−0.704161 + 0.710040i \(0.748677\pi\)
\(734\) 24.7583 + 6.63397i 0.913847 + 0.244864i
\(735\) −6.46410 44.7846i −0.238432 1.65191i
\(736\) −13.4641 + 3.60770i −0.496293 + 0.132981i
\(737\) −16.6244 + 28.7942i −0.612366 + 1.06065i
\(738\) −2.39230 8.92820i −0.0880620 0.328652i
\(739\) −13.4808 + 50.3109i −0.495898 + 1.85072i 0.0290444 + 0.999578i \(0.490754\pi\)
−0.524942 + 0.851138i \(0.675913\pi\)
\(740\) −37.0526 64.1769i −1.36208 2.35919i
\(741\) 2.26795 2.26795i 0.0833152 0.0833152i
\(742\) −8.09808 + 42.0788i −0.297290 + 1.54476i
\(743\) 24.9282i 0.914527i −0.889331 0.457264i \(-0.848830\pi\)
0.889331 0.457264i \(-0.151170\pi\)
\(744\) 1.26795 + 0.732051i 0.0464853 + 0.0268383i
\(745\) 26.8923 15.5263i 0.985258 0.568839i
\(746\) −4.09808 2.36603i −0.150041 0.0866263i
\(747\) −2.26795 8.46410i −0.0829799 0.309685i
\(748\) −3.92820 + 1.05256i −0.143629 + 0.0384854i
\(749\) 2.13397 + 1.03590i 0.0779737 + 0.0378509i
\(750\) −2.83013 + 10.5622i −0.103342 + 0.385676i
\(751\) 12.5263 21.6962i 0.457090 0.791704i −0.541715 0.840562i \(-0.682225\pi\)
0.998806 + 0.0488582i \(0.0155582\pi\)
\(752\) 15.4641 26.7846i 0.563918 0.976734i
\(753\) −18.5622 32.1506i −0.676443 1.17163i
\(754\) −2.00000 2.00000i −0.0728357 0.0728357i
\(755\) 22.2224 + 22.2224i 0.808757 + 0.808757i
\(756\) 23.1244 1.66025i 0.841025 0.0603829i
\(757\) −1.33975 + 1.33975i −0.0486939 + 0.0486939i −0.731034 0.682341i \(-0.760962\pi\)
0.682341 + 0.731034i \(0.260962\pi\)
\(758\) 48.2487i 1.75247i
\(759\) −18.0622 + 10.4282i −0.655616 + 0.378520i
\(760\) 10.7321 40.0526i 0.389292 1.45286i
\(761\) 15.2321 + 8.79423i 0.552161 + 0.318791i 0.749993 0.661445i \(-0.230057\pi\)
−0.197832 + 0.980236i \(0.563390\pi\)
\(762\) −3.46410 6.00000i −0.125491 0.217357i
\(763\) −22.1603 32.7224i −0.802255 1.18463i
\(764\) −15.0000 8.66025i −0.542681 0.313317i
\(765\) 1.09808 0.294229i 0.0397010 0.0106379i
\(766\) −5.41858 20.2224i −0.195781 0.730666i
\(767\) −1.95448 3.38526i −0.0705723 0.122235i
\(768\) 8.00000 29.8564i 0.288675 1.07735i
\(769\) −17.8564 −0.643918 −0.321959 0.946754i \(-0.604341\pi\)
−0.321959 + 0.946754i \(0.604341\pi\)
\(770\) 54.7128 3.92820i 1.97171 0.141563i
\(771\) 1.90192 + 1.90192i 0.0684961 + 0.0684961i
\(772\) 39.8372 23.0000i 1.43377 0.827788i
\(773\) −15.0622 4.03590i −0.541749 0.145161i −0.0224406 0.999748i \(-0.507144\pi\)
−0.519308 + 0.854587i \(0.673810\pi\)
\(774\) 0.339746 0.588457i 0.0122119 0.0211517i
\(775\) 1.43782 + 0.830127i 0.0516481 + 0.0298190i
\(776\) −21.8564 21.8564i −0.784599 0.784599i
\(777\) 37.0526 42.7846i 1.32925 1.53489i
\(778\) −25.3468 + 14.6340i −0.908726 + 0.524653i
\(779\) 10.1244 + 37.7846i 0.362743 + 1.35377i
\(780\) 3.46410 3.46410i 0.124035 0.124035i
\(781\) 8.46410 31.5885i 0.302869 1.13032i
\(782\) 1.14359 + 1.14359i 0.0408948 + 0.0408948i
\(783\) −23.1244 −0.826397
\(784\) 4.00000 + 27.7128i 0.142857 + 0.989743i
\(785\) 55.0526 1.96491
\(786\) 17.9282 + 17.9282i 0.639478 + 0.639478i
\(787\) 4.16025 15.5263i 0.148297 0.553452i −0.851289 0.524696i \(-0.824179\pi\)
0.999586 0.0287557i \(-0.00915448\pi\)
\(788\) −1.32051 1.32051i −0.0470412 0.0470412i
\(789\) 12.6962 + 47.3827i 0.451995 + 1.68687i
\(790\) −2.70577 + 1.56218i −0.0962670 + 0.0555798i
\(791\) −9.46410 + 10.9282i −0.336505 + 0.388562i
\(792\) 9.07180i 0.322352i
\(793\) 0.0455173 + 0.0262794i 0.00161637 + 0.000933210i
\(794\) 3.75833 6.50962i 0.133378 0.231018i
\(795\) 71.5070 + 19.1603i 2.53609 + 0.679544i
\(796\) 1.92820 + 3.33975i 0.0683434 + 0.118374i
\(797\) −30.6603 30.6603i −1.08604 1.08604i −0.995932 0.0901101i \(-0.971278\pi\)
−0.0901101 0.995932i \(-0.528722\pi\)
\(798\) 31.5885 2.26795i 1.11822 0.0802845i
\(799\) −3.58846 −0.126950
\(800\) 9.07180 33.8564i 0.320736 1.19700i
\(801\) 1.90192 + 3.29423i 0.0672012 + 0.116396i
\(802\) −5.49038 20.4904i −0.193872 0.723541i
\(803\) −13.5263 + 3.62436i −0.477332 + 0.127901i
\(804\) −14.6603 + 25.3923i −0.517027 + 0.895518i
\(805\) −12.2321 18.0622i −0.431123 0.636608i
\(806\) −0.0717968 0.124356i −0.00252893 0.00438024i
\(807\) 37.4545 + 21.6244i 1.31846 + 0.761213i
\(808\) 10.3397 + 17.9090i 0.363751 + 0.630035i
\(809\) −15.5718 + 8.99038i −0.547475 + 0.316085i −0.748103 0.663583i \(-0.769035\pi\)
0.200628 + 0.979668i \(0.435702\pi\)
\(810\) 50.4449i 1.77245i
\(811\) −10.3205 + 10.3205i −0.362402 + 0.362402i −0.864697 0.502295i \(-0.832489\pi\)
0.502295 + 0.864697i \(0.332489\pi\)
\(812\) −2.00000 27.8564i −0.0701862 0.977568i
\(813\) −16.5622 16.5622i −0.580861 0.580861i
\(814\) 48.5167 + 48.5167i 1.70051 + 1.70051i
\(815\) −0.401924 0.696152i −0.0140788 0.0243852i
\(816\) −3.46410 + 0.928203i −0.121268 + 0.0324936i
\(817\) −1.43782 + 2.49038i −0.0503030 + 0.0871274i
\(818\) −3.16987 + 11.8301i −0.110832 + 0.413631i
\(819\) 0.660254 + 0.320508i 0.0230711 + 0.0111995i
\(820\) 15.4641 + 57.7128i 0.540030 + 2.01542i
\(821\) −4.59808 17.1603i −0.160474 0.598897i −0.998574 0.0533808i \(-0.983000\pi\)
0.838100 0.545516i \(-0.183666\pi\)
\(822\) −32.1506 18.5622i −1.12138 0.647430i
\(823\) −27.0622 + 15.6244i −0.943328 + 0.544631i −0.891002 0.453999i \(-0.849997\pi\)
−0.0523262 + 0.998630i \(0.516664\pi\)
\(824\) 0.339746 + 1.26795i 0.0118356 + 0.0441711i
\(825\) 52.4449i 1.82590i
\(826\) 7.29423 37.9019i 0.253799 1.31878i
\(827\) 37.7846 37.7846i 1.31390 1.31390i 0.395383 0.918516i \(-0.370612\pi\)
0.918516 0.395383i \(-0.129388\pi\)
\(828\) −3.12436 + 1.80385i −0.108579 + 0.0626880i
\(829\) 9.06218 33.8205i 0.314742 1.17463i −0.609487 0.792796i \(-0.708624\pi\)
0.924229 0.381838i \(-0.124709\pi\)
\(830\) 14.6603 + 54.7128i 0.508865 + 1.89911i
\(831\) −16.7942 + 29.0885i −0.582585 + 1.00907i
\(832\) −2.14359 + 2.14359i −0.0743157 + 0.0743157i
\(833\) 2.55256 2.00962i 0.0884409 0.0696292i
\(834\) −7.19615 1.92820i −0.249182 0.0667682i
\(835\) −18.9282 + 5.07180i −0.655037 + 0.175517i
\(836\) 38.3923i 1.32783i
\(837\) −1.13397 0.303848i −0.0391959 0.0105025i
\(838\) −38.0000 −1.31269
\(839\) 37.7128i 1.30199i −0.759082 0.650995i \(-0.774352\pi\)
0.759082 0.650995i \(-0.225648\pi\)
\(840\) 48.2487 3.46410i 1.66474 0.119523i
\(841\) 1.14359i 0.0394343i
\(842\) 17.3205i 0.596904i
\(843\) 24.1244 + 6.46410i 0.830887 + 0.222635i
\(844\) −4.14359 + 4.14359i −0.142628 + 0.142628i
\(845\) 41.5526 11.1340i 1.42945 0.383020i
\(846\) 2.07180 7.73205i 0.0712298 0.265833i
\(847\) −20.4904 + 7.09808i −0.704058 + 0.243893i
\(848\) −44.2487 11.8564i −1.51951 0.407151i
\(849\) 16.8923 29.2583i 0.579742 1.00414i
\(850\) −3.92820 + 1.05256i −0.134736 + 0.0361025i
\(851\) 7.06218 26.3564i 0.242088 0.903486i
\(852\) 7.46410 27.8564i 0.255716 0.954345i
\(853\) −36.1244 + 36.1244i −1.23687 + 1.23687i −0.275603 + 0.961272i \(0.588877\pi\)
−0.961272 + 0.275603i \(0.911123\pi\)
\(854\) 0.169873 + 0.490381i 0.00581293 + 0.0167805i
\(855\) 10.7321i 0.367028i
\(856\) −1.26795 + 2.19615i −0.0433376 + 0.0750629i
\(857\) −8.89230 + 5.13397i −0.303755 + 0.175373i −0.644129 0.764917i \(-0.722780\pi\)
0.340373 + 0.940290i \(0.389447\pi\)
\(858\) −2.26795 + 3.92820i −0.0774265 + 0.134107i
\(859\) −10.6244 39.6506i −0.362498 1.35286i −0.870781 0.491672i \(-0.836386\pi\)
0.508282 0.861191i \(-0.330281\pi\)
\(860\) −2.19615 + 3.80385i −0.0748882 + 0.129710i
\(861\) −37.7846 + 25.5885i −1.28770 + 0.872052i
\(862\) −18.2224 4.88269i −0.620658 0.166305i
\(863\) 7.66987 13.2846i 0.261086 0.452213i −0.705445 0.708765i \(-0.749253\pi\)
0.966531 + 0.256551i \(0.0825862\pi\)
\(864\) 24.7846i 0.843190i
\(865\) −7.96410 13.7942i −0.270788 0.469018i
\(866\) 29.1769 29.1769i 0.991472 0.991472i
\(867\) −22.9282 22.9282i −0.778683 0.778683i
\(868\) 0.267949 1.39230i 0.00909479 0.0472579i
\(869\) 2.04552 2.04552i 0.0693894 0.0693894i
\(870\) −48.2487 −1.63578
\(871\) 2.49038 1.43782i 0.0843833 0.0487187i
\(872\) 36.5885 21.1244i 1.23904 0.715361i
\(873\) −6.92820 4.00000i −0.234484 0.135379i
\(874\) 13.2224 7.63397i 0.447255 0.258223i
\(875\) 10.5622 0.758330i 0.357067 0.0256362i
\(876\) −11.9282 + 3.19615i −0.403017 + 0.107988i
\(877\) −28.1865 + 7.55256i −0.951792 + 0.255032i −0.701122 0.713041i \(-0.747317\pi\)
−0.250669 + 0.968073i \(0.580651\pi\)
\(878\) −19.7583 + 5.29423i −0.666811 + 0.178672i
\(879\) −8.09808 14.0263i −0.273141 0.473095i
\(880\) 58.6410i 1.97679i
\(881\) 50.0000 1.68454 0.842271 0.539054i \(-0.181218\pi\)
0.842271 + 0.539054i \(0.181218\pi\)
\(882\) 2.85641 + 6.66025i 0.0961802 + 0.224262i
\(883\) −5.00000 5.00000i −0.168263 0.168263i 0.617952 0.786216i \(-0.287963\pi\)
−0.786216 + 0.617952i \(0.787963\pi\)
\(884\) 0.339746 + 0.0910347i 0.0114269 + 0.00306183i
\(885\) −64.4090 17.2583i −2.16508 0.580132i
\(886\) 16.2224 + 9.36603i 0.545003 + 0.314658i
\(887\) 27.7750 + 16.0359i 0.932593 + 0.538433i 0.887631 0.460556i \(-0.152350\pi\)
0.0449622 + 0.998989i \(0.485683\pi\)
\(888\) 42.7846 + 42.7846i 1.43576 + 1.43576i
\(889\) −4.39230 + 5.07180i −0.147313 + 0.170103i
\(890\) −12.2942 21.2942i −0.412103 0.713784i
\(891\) 12.0885 + 45.1147i 0.404979 + 1.51140i
\(892\) 35.7128i 1.19575i
\(893\) −8.76795 + 32.7224i −0.293408 + 1.09501i
\(894\) −17.9282 + 17.9282i −0.599609 + 0.599609i
\(895\) 26.3205 0.879798
\(896\) −29.8564 + 2.14359i −0.997433 + 0.0716124i
\(897\) 1.80385 0.0602287
\(898\) 11.3205 11.3205i 0.377770 0.377770i
\(899\) −0.366025 + 1.36603i −0.0122076 + 0.0455595i
\(900\) 9.07180i 0.302393i
\(901\) 1.37564 + 5.13397i 0.0458294 + 0.171037i
\(902\) −27.6603 47.9090i −0.920986 1.59519i
\(903\) −3.29423 0.633975i −0.109625 0.0210974i
\(904\) −10.9282 10.9282i −0.363467 0.363467i
\(905\) −30.2942 17.4904i −1.00701 0.581400i
\(906\) −22.2224 12.8301i −0.738291 0.426252i
\(907\) −10.1603 2.72243i −0.337366 0.0903969i 0.0861591 0.996281i \(-0.472541\pi\)
−0.423525 + 0.905885i \(0.639207\pi\)
\(908\) 45.9808 + 12.3205i 1.52593 + 0.408870i
\(909\) 3.78461 + 3.78461i 0.125528 + 0.125528i
\(910\) −4.26795 2.07180i −0.141481 0.0686794i
\(911\) −27.3205 −0.905169 −0.452584 0.891722i \(-0.649498\pi\)
−0.452584 + 0.891722i \(0.649498\pi\)
\(912\) 33.8564i 1.12110i
\(913\) −26.2224 45.4186i −0.867836 1.50314i
\(914\) −39.8827 + 10.6865i −1.31920 + 0.353479i
\(915\) 0.866025 0.232051i 0.0286299 0.00767136i
\(916\) 34.8564 9.33975i 1.15169 0.308594i
\(917\) 10.7224 22.0885i 0.354086 0.729425i
\(918\) 2.49038 1.43782i 0.0821948 0.0474552i
\(919\) −14.1340 8.16025i −0.466237 0.269182i 0.248426 0.968651i \(-0.420087\pi\)
−0.714663 + 0.699469i \(0.753420\pi\)
\(920\) 20.1962 11.6603i 0.665847 0.384427i
\(921\) 21.2942 12.2942i 0.701669 0.405109i
\(922\) 2.67949 0.0882444
\(923\) −2.00000 + 2.00000i −0.0658308 + 0.0658308i
\(924\) −42.3205 + 14.6603i −1.39224 + 0.482287i
\(925\) 48.5167 + 48.5167i 1.59522 + 1.59522i
\(926\) 29.8564 29.8564i 0.981142 0.981142i
\(927\) 0.169873 + 0.294229i 0.00557936 + 0.00966374i
\(928\) 29.8564 0.980085
\(929\) 20.0167 34.6699i 0.656725 1.13748i −0.324733 0.945806i \(-0.605274\pi\)
0.981458 0.191676i \(-0.0613922\pi\)
\(930\) −2.36603 0.633975i −0.0775850 0.0207888i
\(931\) −12.0885 28.1865i −0.396183 0.923776i
\(932\) −11.1962 + 19.3923i −0.366742 + 0.635216i
\(933\) −0.232051 0.866025i −0.00759700 0.0283524i
\(934\) −0.0262794 + 0.0455173i −0.000859890 + 0.00148937i
\(935\) 5.89230 3.40192i 0.192699 0.111255i
\(936\) −0.392305 + 0.679492i −0.0128229 + 0.0222099i
\(937\) 42.9282i 1.40240i −0.712963 0.701202i \(-0.752647\pi\)
0.712963 0.701202i \(-0.247353\pi\)
\(938\) 27.8827 + 5.36603i 0.910402 + 0.175207i
\(939\) −13.0981 + 13.0981i −0.427440 + 0.427440i
\(940\) −13.3923 + 49.9808i −0.436809 + 1.63019i
\(941\) −4.47372 + 16.6962i −0.145839 + 0.544279i 0.853877 + 0.520474i \(0.174245\pi\)
−0.999717 + 0.0238050i \(0.992422\pi\)
\(942\) −43.4186 + 11.6340i −1.41465 + 0.379055i
\(943\) −11.0000 + 19.0526i −0.358209 + 0.620437i
\(944\) 39.8564 + 10.6795i 1.29722 + 0.347588i
\(945\) −36.6506 + 12.6962i −1.19225 + 0.413006i
\(946\) 1.05256 3.92820i 0.0342216 0.127717i
\(947\) −39.5526 + 10.5981i −1.28529 + 0.344391i −0.835868 0.548931i \(-0.815035\pi\)
−0.449418 + 0.893322i \(0.648368\pi\)
\(948\) 1.80385 1.80385i 0.0585862 0.0585862i
\(949\) 1.16987 + 0.313467i 0.0379757 + 0.0101756i
\(950\) 38.3923i 1.24561i
\(951\) 23.5885i 0.764908i
\(952\) 1.94744 + 2.87564i 0.0631169 + 0.0932002i
\(953\) 23.4641i 0.760077i 0.924971 + 0.380038i \(0.124089\pi\)
−0.924971 + 0.380038i \(0.875911\pi\)
\(954\) −11.8564 −0.383865
\(955\) 27.9904 + 7.50000i 0.905747 + 0.242694i
\(956\) 30.9282i 1.00029i
\(957\) 43.1506 11.5622i 1.39486 0.373752i
\(958\) 21.2942 + 5.70577i 0.687985 + 0.184345i
\(959\) −6.79423 + 35.3038i −0.219397 + 1.14002i
\(960\) 51.7128i 1.66902i
\(961\) 15.4641 26.7846i 0.498842 0.864020i
\(962\) −1.53590 5.73205i −0.0495194 0.184809i
\(963\) −0.169873 + 0.633975i −0.00547408 + 0.0204295i
\(964\) −0.124356 + 0.0717968i −0.00400523 + 0.00231242i
\(965\) −54.4186 + 54.4186i −1.75180 + 1.75180i
\(966\) 13.4641 + 11.6603i 0.433200 + 0.375163i
\(967\) 11.7513i 0.377896i −0.981987 0.188948i \(-0.939492\pi\)
0.981987 0.188948i \(-0.0605078\pi\)
\(968\) −6.00000 22.3923i −0.192847 0.719716i
\(969\) 3.40192 1.96410i 0.109286 0.0630960i
\(970\) 44.7846 + 25.8564i 1.43795 + 0.830199i
\(971\) 13.4090 + 50.0429i 0.430314 + 1.60595i 0.752037 + 0.659121i \(0.229071\pi\)
−0.321723 + 0.946834i \(0.604262\pi\)
\(972\) 3.85641 + 14.3923i 0.123694 + 0.461633i
\(973\) 0.516660 + 7.19615i 0.0165634 + 0.230698i
\(974\) 8.16987 30.4904i 0.261780 0.976975i
\(975\) −2.26795 + 3.92820i −0.0726325 + 0.125803i
\(976\) −0.535898 + 0.143594i −0.0171537 + 0.00459632i
\(977\) 22.4282 + 38.8468i 0.717542 + 1.24282i 0.961971 + 0.273152i \(0.0880661\pi\)
−0.244429 + 0.969667i \(0.578601\pi\)
\(978\) 0.464102 + 0.464102i 0.0148403 + 0.0148403i
\(979\) 16.0981 + 16.0981i 0.514497 + 0.514497i
\(980\) −18.4641 43.0526i −0.589814 1.37526i
\(981\) 7.73205 7.73205i 0.246865 0.246865i
\(982\) 55.1769i 1.76077i
\(983\) 18.8660 10.8923i 0.601733 0.347411i −0.167990 0.985789i \(-0.553728\pi\)
0.769723 + 0.638378i \(0.220394\pi\)
\(984\) −24.3923 42.2487i −0.777598 1.34684i
\(985\) 2.70577 + 1.56218i 0.0862130 + 0.0497751i
\(986\) −1.73205 3.00000i −0.0551597 0.0955395i
\(987\) −39.4186 + 2.83013i −1.25471 + 0.0900839i
\(988\) 1.66025 2.87564i 0.0528197 0.0914864i
\(989\) −1.56218 + 0.418584i −0.0496744 + 0.0133102i
\(990\) 3.92820 + 14.6603i 0.124846 + 0.465933i
\(991\) 19.7942 + 34.2846i 0.628784 + 1.08909i 0.987796 + 0.155753i \(0.0497805\pi\)
−0.359012 + 0.933333i \(0.616886\pi\)
\(992\) 1.46410 + 0.392305i 0.0464853 + 0.0124557i
\(993\) 34.5167 1.09535
\(994\) −27.8564 + 2.00000i −0.883552 + 0.0634361i
\(995\) −4.56218 4.56218i −0.144631 0.144631i
\(996\) −23.1244 40.0526i −0.732723 1.26911i
\(997\) 5.59808 + 1.50000i 0.177293 + 0.0475055i 0.346373 0.938097i \(-0.387413\pi\)
−0.169080 + 0.985602i \(0.554080\pi\)
\(998\) −2.70577 + 4.68653i −0.0856497 + 0.148350i
\(999\) −42.0167 24.2583i −1.32935 0.767500i
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 112.2.w.b.93.1 yes 4
4.3 odd 2 448.2.ba.a.401.1 4
7.2 even 3 784.2.m.e.589.1 4
7.3 odd 6 784.2.x.a.557.1 4
7.4 even 3 112.2.w.a.109.1 yes 4
7.5 odd 6 784.2.m.d.589.1 4
7.6 odd 2 784.2.x.h.765.1 4
8.3 odd 2 896.2.ba.c.289.1 4
8.5 even 2 896.2.ba.b.289.1 4
16.3 odd 4 896.2.ba.a.737.1 4
16.5 even 4 112.2.w.a.37.1 4
16.11 odd 4 448.2.ba.b.177.1 4
16.13 even 4 896.2.ba.d.737.1 4
28.11 odd 6 448.2.ba.b.81.1 4
56.11 odd 6 896.2.ba.a.417.1 4
56.53 even 6 896.2.ba.d.417.1 4
112.5 odd 12 784.2.m.d.197.1 4
112.11 odd 12 448.2.ba.a.305.1 4
112.37 even 12 784.2.m.e.197.1 4
112.53 even 12 inner 112.2.w.b.53.1 yes 4
112.67 odd 12 896.2.ba.c.865.1 4
112.69 odd 4 784.2.x.a.373.1 4
112.101 odd 12 784.2.x.h.165.1 4
112.109 even 12 896.2.ba.b.865.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.a.37.1 4 16.5 even 4
112.2.w.a.109.1 yes 4 7.4 even 3
112.2.w.b.53.1 yes 4 112.53 even 12 inner
112.2.w.b.93.1 yes 4 1.1 even 1 trivial
448.2.ba.a.305.1 4 112.11 odd 12
448.2.ba.a.401.1 4 4.3 odd 2
448.2.ba.b.81.1 4 28.11 odd 6
448.2.ba.b.177.1 4 16.11 odd 4
784.2.m.d.197.1 4 112.5 odd 12
784.2.m.d.589.1 4 7.5 odd 6
784.2.m.e.197.1 4 112.37 even 12
784.2.m.e.589.1 4 7.2 even 3
784.2.x.a.373.1 4 112.69 odd 4
784.2.x.a.557.1 4 7.3 odd 6
784.2.x.h.165.1 4 112.101 odd 12
784.2.x.h.765.1 4 7.6 odd 2
896.2.ba.a.417.1 4 56.11 odd 6
896.2.ba.a.737.1 4 16.3 odd 4
896.2.ba.b.289.1 4 8.5 even 2
896.2.ba.b.865.1 4 112.109 even 12
896.2.ba.c.289.1 4 8.3 odd 2
896.2.ba.c.865.1 4 112.67 odd 12
896.2.ba.d.417.1 4 56.53 even 6
896.2.ba.d.737.1 4 16.13 even 4