Properties

Label 784.2.x.h.765.1
Level $784$
Weight $2$
Character 784.765
Analytic conductor $6.260$
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] = [784,2,Mod(165,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.x (of order \(12\), degree \(4\), not 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: \(6.26027151847\)
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: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 765.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 784.765
Dual form 784.2.x.h.165.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(-0.500000 + 1.86603i) q^{3} -2.00000i q^{4} +(-0.866025 - 3.23205i) q^{5} +(1.36603 + 2.36603i) q^{6} +(-2.00000 - 2.00000i) q^{8} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})\) \(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} +(-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} +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} +(-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} +(-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} +(-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} +(-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} +(-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} -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} +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} +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} +(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} +(-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} +(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} +(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 \( 4 q + 4 q^{2} - 2 q^{3} + 2 q^{6} - 8 q^{8} - 6 q^{9} - 6 q^{10} - 10 q^{11} + 8 q^{12} - 8 q^{13} + 12 q^{15} - 16 q^{16} + 6 q^{17} - 4 q^{18} - 10 q^{19} - 12 q^{20} - 18 q^{22} + 12 q^{23} + 12 q^{24} - 18 q^{25} - 16 q^{26} - 2 q^{27} - 8 q^{29} + 12 q^{30} + 4 q^{31} - 16 q^{32} + 10 q^{33} - 6 q^{34} + 4 q^{36} - 8 q^{37} - 2 q^{38} + 6 q^{39} - 12 q^{40} + 12 q^{43} - 16 q^{44} - 6 q^{45} + 10 q^{46} + 12 q^{47} + 8 q^{48} - 16 q^{50} - 16 q^{52} + 20 q^{53} - 16 q^{58} + 26 q^{59} - 4 q^{61} - 2 q^{62} - 6 q^{65} - 2 q^{66} - 6 q^{67} - 24 q^{68} - 10 q^{69} + 16 q^{72} - 18 q^{73} - 30 q^{74} - 2 q^{75} + 16 q^{76} + 8 q^{78} + 16 q^{79} - 4 q^{81} - 8 q^{82} - 20 q^{83} + 6 q^{85} + 18 q^{87} + 4 q^{88} + 18 q^{89} - 4 q^{92} - 2 q^{93} + 6 q^{94} + 12 q^{95} - 8 q^{96} - 16 q^{97} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 \(0.271641\pi\)
−0.946112 + 0.323840i \(0.895026\pi\)
\(4\) 2.00000i 1.00000i
\(5\) −0.866025 3.23205i −0.387298 1.44542i −0.834512 0.550990i \(-0.814250\pi\)
0.447214 0.894427i \(-0.352416\pi\)
\(6\) 1.36603 + 2.36603i 0.557678 + 0.965926i
\(7\) 0 0
\(8\) −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 0.668972 0.743288i \(-0.266735\pi\)
−0.743288 + 0.668972i \(0.766735\pi\)
\(14\) 0 0
\(15\) 6.46410 1.66902
\(16\) −4.00000 −1.00000
\(17\) −0.232051 0.401924i −0.0562806 0.0974808i 0.836512 0.547948i \(-0.184591\pi\)
−0.892793 + 0.450467i \(0.851257\pi\)
\(18\) −1.00000 + 0.267949i −0.235702 + 0.0631562i
\(19\) −4.23205 + 1.13397i −0.970899 + 0.260152i −0.709207 0.705000i \(-0.750947\pi\)
−0.261692 + 0.965152i \(0.584280\pi\)
\(20\) −6.46410 + 1.73205i −1.44542 + 0.387298i
\(21\) 0 0
\(22\) −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
\(28\) 0 0
\(29\) −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 0.877806 0.479016i \(-0.159007\pi\)
−0.853743 + 0.520694i \(0.825673\pi\)
\(32\) −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
\(35\) 0 0
\(36\) −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 \(-0.754440\pi\)
0.716900 0.697176i \(-0.245560\pi\)
\(42\) 0 0
\(43\) −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 \(-0.642627\pi\)
0.997149 0.0754516i \(-0.0240398\pi\)
\(48\) 2.00000 7.46410i 0.288675 1.07735i
\(49\) 0 0
\(50\) −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
\(56\) 0 0
\(57\) 8.46410i 1.12110i
\(58\) −7.46410 −0.980085
\(59\) 9.96410 + 2.66987i 1.29722 + 0.347588i 0.840397 0.541972i \(-0.182322\pi\)
0.456819 + 0.889560i \(0.348989\pi\)
\(60\) 12.9282i 1.66902i
\(61\) −0.133975 + 0.0358984i −0.0171537 + 0.00459632i −0.267386 0.963590i \(-0.586160\pi\)
0.250232 + 0.968186i \(0.419493\pi\)
\(62\) 0.366025 + 0.0980762i 0.0464853 + 0.0124557i
\(63\) 0 0
\(64\) 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
\(70\) 0 0
\(71\) 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 −0.653158 0.757222i \(-0.726556\pi\)
0.329194 + 0.944262i \(0.393223\pi\)
\(74\) −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
\(77\) 0 0
\(78\) 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 0.0685891 0.997645i \(-0.478150\pi\)
−0.997645 + 0.0685891i \(0.978150\pi\)
\(84\) 0 0
\(85\) −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 0.719165 0.694839i \(-0.244525\pi\)
−0.242166 + 0.970235i \(0.577858\pi\)
\(90\) 1.73205 + 3.00000i 0.182574 + 0.316228i
\(91\) 0 0
\(92\) 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 \(-0.687203\pi\)
−0.554795 + 0.831987i \(0.687203\pi\)
\(98\) 0 0
\(99\) 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 0.592445 0.805611i \(-0.298163\pi\)
0.110268 + 0.993902i \(0.464829\pi\)
\(102\) 0.633975 1.09808i 0.0627728 0.108726i
\(103\) 0.401924 + 0.232051i 0.0396027 + 0.0228646i 0.519671 0.854367i \(-0.326055\pi\)
−0.480068 + 0.877231i \(0.659388\pi\)
\(104\) 1.07180i 0.105098i
\(105\) 0 0
\(106\) 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
\(112\) 0 0
\(113\) 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
\(119\) 0 0
\(120\) −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
\(126\) 0 0
\(127\) 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 0.155003 0.987914i \(-0.450461\pi\)
0.628194 + 0.778057i \(0.283794\pi\)
\(132\) −14.6603 8.46410i −1.27601 0.736705i
\(133\) 0 0
\(134\) −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 −0.784136 0.620588i \(-0.786894\pi\)
0.620588 + 0.784136i \(0.286894\pi\)
\(140\) 0 0
\(141\) 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
\(147\) 0 0
\(148\) −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
\(154\) 0 0
\(155\) 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 \(0.311315\pi\)
−0.898513 + 0.438948i \(0.855351\pi\)
\(158\) 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
\(161\) 0 0
\(162\) −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 \(-0.927242\pi\)
0.973990 0.226591i \(-0.0727581\pi\)
\(168\) 0 0
\(169\) 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 −0.0797535 0.996815i \(-0.525413\pi\)
0.429339 + 0.903144i \(0.358747\pi\)
\(174\) 3.73205 13.9282i 0.282926 1.05589i
\(175\) 0 0
\(176\) 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 −0.376821 0.926286i \(-0.622983\pi\)
0.926286 + 0.376821i \(0.122983\pi\)
\(182\) 0 0
\(183\) 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 0
\(190\) 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
\(196\) 0 0
\(197\) 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 −0.439644 0.898172i \(-0.644895\pi\)
0.558018 + 0.829829i \(0.311562\pi\)
\(200\) 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
\(203\) 0 0
\(204\) −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
\(210\) 0 0
\(211\) −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 0
\(218\) 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 \(-0.296011\pi\)
0.597877 + 0.801588i \(0.296011\pi\)
\(224\) 0 0
\(225\) 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 \(-0.626811\pi\)
0.796804 0.604238i \(-0.206522\pi\)
\(228\) −16.9282 −1.12110
\(229\) −4.66987 17.4282i −0.308594 1.15169i −0.929807 0.368047i \(-0.880027\pi\)
0.621213 0.783641i \(-0.286640\pi\)
\(230\) −5.83013 10.0981i −0.384427 0.665847i
\(231\) 0 0
\(232\) 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
\(238\) 0 0
\(239\) −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 0.867179 0.497996i \(-0.165931\pi\)
−0.864867 + 0.502001i \(0.832597\pi\)
\(242\) 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
\(245\) 0 0
\(246\) 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 −0.991066 0.133370i \(-0.957420\pi\)
0.133370 + 0.991066i \(0.457420\pi\)
\(252\) 0 0
\(253\) −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 −0.843496 0.537135i \(-0.819506\pi\)
0.886921 + 0.461921i \(0.152840\pi\)
\(258\) −1.73205 0.464102i −0.107833 0.0288937i
\(259\) 0 0
\(260\) 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
\(266\) 0 0
\(267\) −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 \(-0.677566\pi\)
0.882635 0.470059i \(-0.155768\pi\)
\(270\) 20.0263 5.36603i 1.21876 0.326566i
\(271\) −6.06218 + 10.5000i −0.368251 + 0.637830i −0.989292 0.145948i \(-0.953377\pi\)
0.621041 + 0.783778i \(0.286710\pi\)
\(272\) 0.928203 + 1.60770i 0.0562806 + 0.0974808i
\(273\) 0 0
\(274\) 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
\(280\) 0 0
\(281\) 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 −0.280963 0.959719i \(-0.590654\pi\)
−0.723180 + 0.690659i \(0.757320\pi\)
\(284\) 14.9282 0.885826
\(285\) −27.3564 + 7.33013i −1.62045 + 0.434199i
\(286\) 2.26795 + 0.607695i 0.134107 + 0.0359338i
\(287\) 0 0
\(288\) 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 −0.858740 0.512411i \(-0.828752\pi\)
0.512411 + 0.858740i \(0.328752\pi\)
\(294\) 0 0
\(295\) 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 0
\(302\) 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 0.401988 0.915645i \(-0.368319\pi\)
−0.915645 + 0.401988i \(0.868319\pi\)
\(308\) 0 0
\(309\) −0.633975 + 0.633975i −0.0360656 + 0.0360656i
\(310\) 1.26795i 0.0720147i
\(311\) −0.401924 + 0.232051i −0.0227910 + 0.0131584i −0.511352 0.859371i \(-0.670855\pi\)
0.488561 + 0.872530i \(0.337522\pi\)
\(312\) −2.00000 0.535898i −0.113228 0.0303393i
\(313\) 8.30385 + 4.79423i 0.469361 + 0.270986i 0.715972 0.698129i \(-0.245984\pi\)
−0.246611 + 0.969115i \(0.579317\pi\)
\(314\) 11.6340 + 20.1506i 0.656543 + 1.13717i
\(315\) 0 0
\(316\) 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
\(322\) 0 0
\(323\) 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
\(329\) 0 0
\(330\) −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
\(336\) 0 0
\(337\) −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
\(343\) 0 0
\(344\) 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 0.999568 0.0293934i \(-0.00935756\pi\)
−0.0293934 + 0.999568i \(0.509358\pi\)
\(350\) 0 0
\(351\) 1.66025 0.0886178
\(352\) 21.4641 12.3923i 1.14404 0.660512i
\(353\) 6.89230 + 11.9378i 0.366840 + 0.635386i 0.989070 0.147449i \(-0.0471062\pi\)
−0.622229 + 0.782835i \(0.713773\pi\)
\(354\) 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
\(357\) 0 0
\(358\) −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 0
\(365\) 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 0.526482 0.850186i \(-0.323511\pi\)
−0.999524 + 0.0308537i \(0.990177\pi\)
\(368\) −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
\(371\) 0 0
\(372\) 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
\(378\) 0 0
\(379\) −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 −0.990803 0.135309i \(-0.956797\pi\)
0.612583 + 0.790406i \(0.290131\pi\)
\(384\) −18.9282 + 10.9282i −0.965926 + 0.557678i
\(385\) 0 0
\(386\) 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
\(392\) 0 0
\(393\) 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 −0.385340 0.922775i \(-0.625916\pi\)
0.127673 + 0.991816i \(0.459249\pi\)
\(398\) 0.705771 2.63397i 0.0353771 0.132029i
\(399\) 0 0
\(400\) 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
\(406\) 0 0
\(407\) 48.5167i 2.40488i
\(408\) −2.19615 1.26795i −0.108726 0.0627728i
\(409\) 7.50000 4.33013i 0.370851 0.214111i −0.302979 0.952997i \(-0.597981\pi\)
0.673830 + 0.738886i \(0.264648\pi\)
\(410\) −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
\(413\) 0 0
\(414\) −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 0.997590 0.0693796i \(-0.0221020\pi\)
−0.0693796 + 0.997590i \(0.522102\pi\)
\(420\) 0 0
\(421\) −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 0
\(428\) −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 \(-0.747297\pi\)
−0.701077 + 0.713086i \(0.747297\pi\)
\(434\) 0 0
\(435\) −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 0.768194 0.640217i \(-0.221156\pi\)
−0.170347 + 0.985384i \(0.554489\pi\)
\(440\) 29.3205 29.3205i 1.39780 1.39780i
\(441\) 0 0
\(442\) 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
\(448\) 0 0
\(449\) 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
\(455\) 0 0
\(456\) −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 0.675219 0.737617i \(-0.264049\pi\)
−0.737617 + 0.675219i \(0.764049\pi\)
\(462\) 0 0
\(463\) 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 −0.257988 0.966148i \(-0.583060\pi\)
0.259650 + 0.965703i \(0.416393\pi\)
\(468\) 0.535898 0.143594i 0.0247719 0.00663761i
\(469\) 0 0
\(470\) −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 0
\(477\) −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 0.631183 0.775634i \(-0.282570\pi\)
−0.987310 + 0.158803i \(0.949236\pi\)
\(480\) −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 0
\(484\) 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
\(490\) 0 0
\(491\) 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
\(497\) 0 0
\(498\) 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 \(0.0294464\pi\)
−0.995724 + 0.0923769i \(0.970554\pi\)
\(504\) 0 0
\(505\) 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 0.126766 0.991933i \(-0.459540\pi\)
0.605749 + 0.795656i \(0.292874\pi\)
\(510\) −4.09808 1.09808i −0.181466 0.0486236i
\(511\) 0 0
\(512\) 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
\(518\) 0 0
\(519\) 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 \(-0.266026\pi\)
0.977727 0.209881i \(-0.0673078\pi\)
\(522\) 4.73205 + 2.73205i 0.207116 + 0.119579i
\(523\) −9.28461 34.6506i −0.405988 1.51517i −0.802227 0.597019i \(-0.796352\pi\)
0.396239 0.918147i \(-0.370315\pi\)
\(524\) −4.80385 17.9282i −0.209857 0.783197i
\(525\) 0 0
\(526\) −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
\(532\) 0 0
\(533\) −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
\(539\) 0 0
\(540\) 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
\(546\) 0 0
\(547\) 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 0
\(554\) −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
\(560\) 0 0
\(561\) −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 \(0.463925\pi\)
−0.594731 + 0.803925i \(0.702741\pi\)
\(564\) 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
\(567\) 0 0
\(568\) 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
\(574\) 0 0
\(575\) −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 \(-0.904453\pi\)
0.221575 0.975143i \(-0.428880\pi\)
\(578\) −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
\(581\) 0 0
\(582\) −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 −0.853785 0.520626i \(-0.825699\pi\)
0.520626 + 0.853785i \(0.325699\pi\)
\(588\) 0 0
\(589\) −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 −0.753345 0.657625i \(-0.771561\pi\)
0.946193 + 0.323603i \(0.104894\pi\)
\(594\) 7.02628 26.2224i 0.288292 1.07592i
\(595\) 0 0
\(596\) −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 \(-0.934621\pi\)
0.978980 0.203954i \(-0.0653794\pi\)
\(602\) 0 0
\(603\) −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 −0.996627 0.0820591i \(-0.973850\pi\)
0.569379 + 0.822075i \(0.307184\pi\)
\(608\) 12.3923 21.4641i 0.502574 0.870484i
\(609\) 0 0
\(610\) 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
\(616\) 0 0
\(617\) 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 −0.302296 0.953214i \(-0.597753\pi\)
−0.738403 + 0.674359i \(0.764420\pi\)
\(620\) −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
\(623\) 0 0
\(624\) −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
\(630\) 0 0
\(631\) 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
\(637\) 0 0
\(638\) 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 0.335151 0.942164i \(-0.391213\pi\)
−0.942164 + 0.335151i \(0.891213\pi\)
\(644\) 0 0
\(645\) −3.00000 + 3.00000i −0.118125 + 0.118125i
\(646\) 2.87564 0.113141
\(647\) −29.1340 + 16.8205i −1.14537 + 0.661282i −0.947756 0.318997i \(-0.896654\pi\)
−0.197619 + 0.980279i \(0.563321\pi\)
\(648\) −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 0
\(652\) 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
\(658\) 0 0
\(659\) −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 0.592367 0.805668i \(-0.298194\pi\)
0.110170 + 0.993913i \(0.464860\pi\)
\(662\) 21.8827 + 12.6340i 0.850495 + 0.491033i
\(663\) −0.294229 0.169873i −0.0114269 0.00659732i
\(664\) 33.8564i 1.31388i
\(665\) 0 0
\(666\) 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
\(672\) 0 0
\(673\) −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 \(0.363000\pi\)
0.0930654 + 0.995660i \(0.470333\pi\)
\(678\) 7.46410 + 12.9282i 0.286657 + 0.496505i
\(679\) 0 0
\(680\) 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
\(686\) 0 0
\(687\) 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 −0.0402135 0.999191i \(-0.512804\pi\)
0.464770 + 0.885432i \(0.346137\pi\)
\(692\) −2.46410 9.19615i −0.0936711 0.349585i
\(693\) 0 0
\(694\) −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
\(700\) 0 0
\(701\) 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
\(707\) 0 0
\(708\) 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
\(714\) 0 0
\(715\) 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 \(-0.632845\pi\)
0.994360 0.106054i \(-0.0338215\pi\)
\(720\) 2.53590 9.46410i 0.0945074 0.352706i
\(721\) 0 0
\(722\) 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 \(0.0395288\pi\)
−0.992299 + 0.123864i \(0.960471\pi\)
\(728\) 0 0
\(729\) 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 0.704161 0.710040i \(-0.251323\pi\)
0.964842 + 0.262832i \(0.0846566\pi\)
\(734\) −24.7583 6.63397i −0.913847 0.244864i
\(735\) 0 0
\(736\) −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
\(742\) 0 0
\(743\) 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
\(749\) 0 0
\(750\) −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
\(756\) 0 0
\(757\) −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 0.197832 0.980236i \(-0.436610\pi\)
−0.749993 + 0.661445i \(0.769943\pi\)
\(762\) 3.46410 + 6.00000i 0.125491 + 0.217357i
\(763\) 0 0
\(764\) −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 \(-0.395659\pi\)
0.321959 + 0.946754i \(0.395659\pi\)
\(770\) 0 0
\(771\) 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 0.519308 0.854587i \(-0.326190\pi\)
0.0224406 + 0.999748i \(0.492856\pi\)
\(774\) 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
\(777\) 0 0
\(778\) −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
\(784\) 0 0
\(785\) 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 \(0.175821\pi\)
−0.999586 + 0.0287557i \(0.990846\pi\)
\(788\) −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
\(791\) 0 0
\(792\) 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 \(0.0287219\pi\)
0.0901101 + 0.995932i \(0.471278\pi\)
\(798\) 0 0
\(799\) −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
\(805\) 0 0
\(806\) −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 −0.502295 0.864697i \(-0.667511\pi\)
0.864697 + 0.502295i \(0.167511\pi\)
\(812\) 0 0
\(813\) −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 0
\(820\) 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
\(826\) 0 0
\(827\) 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 \(0.291376\pi\)
−0.924229 + 0.381838i \(0.875291\pi\)
\(830\) 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
\(833\) 0 0
\(834\) −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 \(0.225648\pi\)
−0.759082 + 0.650995i \(0.774352\pi\)
\(840\) 0 0
\(841\) 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
\(847\) 0 0
\(848\) −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 \(-0.411123\pi\)
0.961272 0.275603i \(-0.0888774\pi\)
\(854\) 0 0
\(855\) 10.7321i 0.367028i
\(856\) −1.26795 + 2.19615i −0.0433376 + 0.0750629i
\(857\) 8.89230 5.13397i 0.303755 0.175373i −0.340373 0.940290i \(-0.610553\pi\)
0.644129 + 0.764917i \(0.277220\pi\)
\(858\) −2.26795 + 3.92820i −0.0774265 + 0.134107i
\(859\) 10.6244 + 39.6506i 0.362498 + 1.35286i 0.870781 + 0.491672i \(0.163614\pi\)
−0.508282 + 0.861191i \(0.669719\pi\)
\(860\) 2.19615 3.80385i 0.0748882 0.129710i
\(861\) 0 0
\(862\) −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 0
\(869\) 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
\(875\) 0 0
\(876\) −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 \(-0.818782\pi\)
−0.842271 + 0.539054i \(0.818782\pi\)
\(882\) 0 0
\(883\) −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 −0.0449622 0.998989i \(-0.514317\pi\)
−0.887631 + 0.460556i \(0.847650\pi\)
\(888\) −42.7846 42.7846i −1.43576 1.43576i
\(889\) 0 0
\(890\) −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
\(896\) 0 0
\(897\) 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
\(903\) 0 0
\(904\) −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
\(910\) 0 0
\(911\) −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
\(917\) 0 0
\(918\) 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
\(924\) 0 0
\(925\) 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 \(0.394726\pi\)
−0.981458 + 0.191676i \(0.938608\pi\)
\(930\) 2.36603 + 0.633975i 0.0775850 + 0.0207888i
\(931\) 0 0
\(932\) −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 \(0.247353\pi\)
−0.712963 + 0.701202i \(0.752647\pi\)
\(938\) 0 0
\(939\) −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 \(-0.825755\pi\)
0.999717 0.0238050i \(-0.00757808\pi\)
\(942\) −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
\(945\) 0 0
\(946\) 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
\(952\) 0 0
\(953\) 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
\(959\) 0 0
\(960\) 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
\(966\) 0 0
\(967\) 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 \(-0.770929\pi\)
0.321723 0.946834i \(-0.395738\pi\)
\(972\) −3.85641 14.3923i −0.123694 0.461633i
\(973\) 0 0
\(974\) 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
\(980\) 0 0
\(981\) 7.73205 7.73205i 0.246865 0.246865i
\(982\) 55.1769i 1.76077i
\(983\) −18.8660 + 10.8923i −0.601733 + 0.347411i −0.769723 0.638378i \(-0.779606\pi\)
0.167990 + 0.985789i \(0.446272\pi\)
\(984\) −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
\(987\) 0 0
\(988\) 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
\(994\) 0 0
\(995\) −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 0.169080 0.985602i \(-0.445920\pi\)
−0.346373 + 0.938097i \(0.612587\pi\)
\(998\) −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 784.2.x.h.765.1 4
7.2 even 3 784.2.m.d.589.1 4
7.3 odd 6 112.2.w.a.109.1 yes 4
7.4 even 3 784.2.x.a.557.1 4
7.5 odd 6 784.2.m.e.589.1 4
7.6 odd 2 112.2.w.b.93.1 yes 4
16.5 even 4 784.2.x.a.373.1 4
28.3 even 6 448.2.ba.b.81.1 4
28.27 even 2 448.2.ba.a.401.1 4
56.3 even 6 896.2.ba.a.417.1 4
56.13 odd 2 896.2.ba.b.289.1 4
56.27 even 2 896.2.ba.c.289.1 4
56.45 odd 6 896.2.ba.d.417.1 4
112.3 even 12 896.2.ba.c.865.1 4
112.5 odd 12 784.2.m.e.197.1 4
112.13 odd 4 896.2.ba.d.737.1 4
112.27 even 4 448.2.ba.b.177.1 4
112.37 even 12 784.2.m.d.197.1 4
112.45 odd 12 896.2.ba.b.865.1 4
112.53 even 12 inner 784.2.x.h.165.1 4
112.59 even 12 448.2.ba.a.305.1 4
112.69 odd 4 112.2.w.a.37.1 4
112.83 even 4 896.2.ba.a.737.1 4
112.101 odd 12 112.2.w.b.53.1 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.a.37.1 4 112.69 odd 4
112.2.w.a.109.1 yes 4 7.3 odd 6
112.2.w.b.53.1 yes 4 112.101 odd 12
112.2.w.b.93.1 yes 4 7.6 odd 2
448.2.ba.a.305.1 4 112.59 even 12
448.2.ba.a.401.1 4 28.27 even 2
448.2.ba.b.81.1 4 28.3 even 6
448.2.ba.b.177.1 4 112.27 even 4
784.2.m.d.197.1 4 112.37 even 12
784.2.m.d.589.1 4 7.2 even 3
784.2.m.e.197.1 4 112.5 odd 12
784.2.m.e.589.1 4 7.5 odd 6
784.2.x.a.373.1 4 16.5 even 4
784.2.x.a.557.1 4 7.4 even 3
784.2.x.h.165.1 4 112.53 even 12 inner
784.2.x.h.765.1 4 1.1 even 1 trivial
896.2.ba.a.417.1 4 56.3 even 6
896.2.ba.a.737.1 4 112.83 even 4
896.2.ba.b.289.1 4 56.13 odd 2
896.2.ba.b.865.1 4 112.45 odd 12
896.2.ba.c.289.1 4 56.27 even 2
896.2.ba.c.865.1 4 112.3 even 12
896.2.ba.d.417.1 4 56.45 odd 6
896.2.ba.d.737.1 4 112.13 odd 4