Properties

Label 252.2.bi.a.223.1
Level $252$
Weight $2$
Character 252.223
Analytic conductor $2.012$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,2,Mod(139,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.139");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bi (of order \(6\), degree \(2\), 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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 223.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 252.223
Dual form 252.2.bi.a.139.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 + 1.00000i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(0.633975 + 2.36603i) q^{6} +(2.59808 + 0.500000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+(-0.366025 - 1.36603i) q^{2} -1.73205 q^{3} +(-1.73205 + 1.00000i) q^{4} +(-1.50000 + 0.866025i) q^{5} +(0.633975 + 2.36603i) q^{6} +(2.59808 + 0.500000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(1.73205 + 1.73205i) q^{10} +(-0.866025 - 0.500000i) q^{11} +(3.00000 - 1.73205i) q^{12} +(1.50000 - 0.866025i) q^{13} +(-0.267949 - 3.73205i) q^{14} +(2.59808 - 1.50000i) q^{15} +(2.00000 - 3.46410i) q^{16} +3.46410i q^{17} +(-1.09808 - 4.09808i) q^{18} +6.92820 q^{19} +(1.73205 - 3.00000i) q^{20} +(-4.50000 - 0.866025i) q^{21} +(-0.366025 + 1.36603i) q^{22} +(4.33013 - 2.50000i) q^{23} +(-3.46410 - 3.46410i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(-1.73205 - 1.73205i) q^{26} -5.19615 q^{27} +(-5.00000 + 1.73205i) q^{28} +(-2.50000 + 4.33013i) q^{29} +(-3.00000 - 3.00000i) q^{30} +(4.33013 + 7.50000i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(1.50000 + 0.866025i) q^{33} +(4.73205 - 1.26795i) q^{34} +(-4.33013 + 1.50000i) q^{35} +(-5.19615 + 3.00000i) q^{36} +(-2.53590 - 9.46410i) q^{38} +(-2.59808 + 1.50000i) q^{39} +(-4.73205 - 1.26795i) q^{40} +(7.50000 - 4.33013i) q^{41} +(0.464102 + 6.46410i) q^{42} +(0.866025 + 0.500000i) q^{43} +2.00000 q^{44} +(-4.50000 + 2.59808i) q^{45} +(-5.00000 - 5.00000i) q^{46} +(-2.59808 + 4.50000i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(6.50000 + 2.59808i) q^{49} +(2.73205 + 0.732051i) q^{50} -6.00000i q^{51} +(-1.73205 + 3.00000i) q^{52} +4.00000 q^{53} +(1.90192 + 7.09808i) q^{54} +1.73205 q^{55} +(4.19615 + 6.19615i) q^{56} -12.0000 q^{57} +(6.83013 + 1.83013i) q^{58} +(-4.33013 - 7.50000i) q^{59} +(-3.00000 + 5.19615i) q^{60} +(-4.50000 - 2.59808i) q^{61} +(8.66025 - 8.66025i) q^{62} +(7.79423 + 1.50000i) q^{63} +8.00000i q^{64} +(-1.50000 + 2.59808i) q^{65} +(0.633975 - 2.36603i) q^{66} +(-12.9904 + 7.50000i) q^{67} +(-3.46410 - 6.00000i) q^{68} +(-7.50000 + 4.33013i) q^{69} +(3.63397 + 5.36603i) q^{70} -4.00000i q^{71} +(6.00000 + 6.00000i) q^{72} -10.3923i q^{73} +(1.73205 - 3.00000i) q^{75} +(-12.0000 + 6.92820i) q^{76} +(-2.00000 - 1.73205i) q^{77} +(3.00000 + 3.00000i) q^{78} +(2.59808 + 1.50000i) q^{79} +6.92820i q^{80} +9.00000 q^{81} +(-8.66025 - 8.66025i) q^{82} +(0.866025 - 1.50000i) q^{83} +(8.66025 - 3.00000i) q^{84} +(-3.00000 - 5.19615i) q^{85} +(0.366025 - 1.36603i) q^{86} +(4.33013 - 7.50000i) q^{87} +(-0.732051 - 2.73205i) q^{88} +17.3205i q^{89} +(5.19615 + 5.19615i) q^{90} +(4.33013 - 1.50000i) q^{91} +(-5.00000 + 8.66025i) q^{92} +(-7.50000 - 12.9904i) q^{93} +(7.09808 + 1.90192i) q^{94} +(-10.3923 + 6.00000i) q^{95} +(9.46410 + 2.53590i) q^{96} +(-4.50000 - 2.59808i) q^{97} +(1.16987 - 9.83013i) q^{98} +(-2.59808 - 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 6 q^{5} + 6 q^{6} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 6 q^{5} + 6 q^{6} + 8 q^{8} + 12 q^{9} + 12 q^{12} + 6 q^{13} - 8 q^{14} + 8 q^{16} + 6 q^{18} - 18 q^{21} + 2 q^{22} - 4 q^{25} - 20 q^{28} - 10 q^{29} - 12 q^{30} - 8 q^{32} + 6 q^{33} + 12 q^{34} - 24 q^{38} - 12 q^{40} + 30 q^{41} - 12 q^{42} + 8 q^{44} - 18 q^{45} - 20 q^{46} + 26 q^{49} + 4 q^{50} + 16 q^{53} + 18 q^{54} - 4 q^{56} - 48 q^{57} + 10 q^{58} - 12 q^{60} - 18 q^{61} - 6 q^{65} + 6 q^{66} - 30 q^{69} + 18 q^{70} + 24 q^{72} - 48 q^{76} - 8 q^{77} + 12 q^{78} + 36 q^{81} - 12 q^{85} - 2 q^{86} + 4 q^{88} - 20 q^{92} - 30 q^{93} + 18 q^{94} + 24 q^{96} - 18 q^{97} + 22 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 1.36603i −0.258819 0.965926i
\(3\) −1.73205 −1.00000
\(4\) −1.73205 + 1.00000i −0.866025 + 0.500000i
\(5\) −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i \(-0.793258\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) 0.633975 + 2.36603i 0.258819 + 0.965926i
\(7\) 2.59808 + 0.500000i 0.981981 + 0.188982i
\(8\) 2.00000 + 2.00000i 0.707107 + 0.707107i
\(9\) 3.00000 1.00000
\(10\) 1.73205 + 1.73205i 0.547723 + 0.547723i
\(11\) −0.866025 0.500000i −0.261116 0.150756i 0.363727 0.931505i \(-0.381504\pi\)
−0.624844 + 0.780750i \(0.714837\pi\)
\(12\) 3.00000 1.73205i 0.866025 0.500000i
\(13\) 1.50000 0.866025i 0.416025 0.240192i −0.277350 0.960769i \(-0.589456\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −0.267949 3.73205i −0.0716124 0.997433i
\(15\) 2.59808 1.50000i 0.670820 0.387298i
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 3.46410i 0.840168i 0.907485 + 0.420084i \(0.137999\pi\)
−0.907485 + 0.420084i \(0.862001\pi\)
\(18\) −1.09808 4.09808i −0.258819 0.965926i
\(19\) 6.92820 1.58944 0.794719 0.606977i \(-0.207618\pi\)
0.794719 + 0.606977i \(0.207618\pi\)
\(20\) 1.73205 3.00000i 0.387298 0.670820i
\(21\) −4.50000 0.866025i −0.981981 0.188982i
\(22\) −0.366025 + 1.36603i −0.0780369 + 0.291238i
\(23\) 4.33013 2.50000i 0.902894 0.521286i 0.0247559 0.999694i \(-0.492119\pi\)
0.878138 + 0.478407i \(0.158786\pi\)
\(24\) −3.46410 3.46410i −0.707107 0.707107i
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) −1.73205 1.73205i −0.339683 0.339683i
\(27\) −5.19615 −1.00000
\(28\) −5.00000 + 1.73205i −0.944911 + 0.327327i
\(29\) −2.50000 + 4.33013i −0.464238 + 0.804084i −0.999167 0.0408130i \(-0.987005\pi\)
0.534928 + 0.844897i \(0.320339\pi\)
\(30\) −3.00000 3.00000i −0.547723 0.547723i
\(31\) 4.33013 + 7.50000i 0.777714 + 1.34704i 0.933257 + 0.359211i \(0.116954\pi\)
−0.155543 + 0.987829i \(0.549713\pi\)
\(32\) −5.46410 1.46410i −0.965926 0.258819i
\(33\) 1.50000 + 0.866025i 0.261116 + 0.150756i
\(34\) 4.73205 1.26795i 0.811540 0.217451i
\(35\) −4.33013 + 1.50000i −0.731925 + 0.253546i
\(36\) −5.19615 + 3.00000i −0.866025 + 0.500000i
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) −2.53590 9.46410i −0.411377 1.53528i
\(39\) −2.59808 + 1.50000i −0.416025 + 0.240192i
\(40\) −4.73205 1.26795i −0.748203 0.200480i
\(41\) 7.50000 4.33013i 1.17130 0.676252i 0.217317 0.976101i \(-0.430270\pi\)
0.953987 + 0.299849i \(0.0969363\pi\)
\(42\) 0.464102 + 6.46410i 0.0716124 + 0.997433i
\(43\) 0.866025 + 0.500000i 0.132068 + 0.0762493i 0.564578 0.825380i \(-0.309039\pi\)
−0.432511 + 0.901629i \(0.642372\pi\)
\(44\) 2.00000 0.301511
\(45\) −4.50000 + 2.59808i −0.670820 + 0.387298i
\(46\) −5.00000 5.00000i −0.737210 0.737210i
\(47\) −2.59808 + 4.50000i −0.378968 + 0.656392i −0.990912 0.134509i \(-0.957054\pi\)
0.611944 + 0.790901i \(0.290388\pi\)
\(48\) −3.46410 + 6.00000i −0.500000 + 0.866025i
\(49\) 6.50000 + 2.59808i 0.928571 + 0.371154i
\(50\) 2.73205 + 0.732051i 0.386370 + 0.103528i
\(51\) 6.00000i 0.840168i
\(52\) −1.73205 + 3.00000i −0.240192 + 0.416025i
\(53\) 4.00000 0.549442 0.274721 0.961524i \(-0.411414\pi\)
0.274721 + 0.961524i \(0.411414\pi\)
\(54\) 1.90192 + 7.09808i 0.258819 + 0.965926i
\(55\) 1.73205 0.233550
\(56\) 4.19615 + 6.19615i 0.560734 + 0.827996i
\(57\) −12.0000 −1.58944
\(58\) 6.83013 + 1.83013i 0.896840 + 0.240307i
\(59\) −4.33013 7.50000i −0.563735 0.976417i −0.997166 0.0752304i \(-0.976031\pi\)
0.433432 0.901186i \(-0.357303\pi\)
\(60\) −3.00000 + 5.19615i −0.387298 + 0.670820i
\(61\) −4.50000 2.59808i −0.576166 0.332650i 0.183442 0.983030i \(-0.441276\pi\)
−0.759608 + 0.650381i \(0.774609\pi\)
\(62\) 8.66025 8.66025i 1.09985 1.09985i
\(63\) 7.79423 + 1.50000i 0.981981 + 0.188982i
\(64\) 8.00000i 1.00000i
\(65\) −1.50000 + 2.59808i −0.186052 + 0.322252i
\(66\) 0.633975 2.36603i 0.0780369 0.291238i
\(67\) −12.9904 + 7.50000i −1.58703 + 0.916271i −0.593234 + 0.805030i \(0.702149\pi\)
−0.993793 + 0.111241i \(0.964517\pi\)
\(68\) −3.46410 6.00000i −0.420084 0.727607i
\(69\) −7.50000 + 4.33013i −0.902894 + 0.521286i
\(70\) 3.63397 + 5.36603i 0.434343 + 0.641363i
\(71\) 4.00000i 0.474713i −0.971423 0.237356i \(-0.923719\pi\)
0.971423 0.237356i \(-0.0762809\pi\)
\(72\) 6.00000 + 6.00000i 0.707107 + 0.707107i
\(73\) 10.3923i 1.21633i −0.793812 0.608164i \(-0.791906\pi\)
0.793812 0.608164i \(-0.208094\pi\)
\(74\) 0 0
\(75\) 1.73205 3.00000i 0.200000 0.346410i
\(76\) −12.0000 + 6.92820i −1.37649 + 0.794719i
\(77\) −2.00000 1.73205i −0.227921 0.197386i
\(78\) 3.00000 + 3.00000i 0.339683 + 0.339683i
\(79\) 2.59808 + 1.50000i 0.292306 + 0.168763i 0.638982 0.769222i \(-0.279356\pi\)
−0.346675 + 0.937985i \(0.612689\pi\)
\(80\) 6.92820i 0.774597i
\(81\) 9.00000 1.00000
\(82\) −8.66025 8.66025i −0.956365 0.956365i
\(83\) 0.866025 1.50000i 0.0950586 0.164646i −0.814574 0.580059i \(-0.803029\pi\)
0.909633 + 0.415413i \(0.136363\pi\)
\(84\) 8.66025 3.00000i 0.944911 0.327327i
\(85\) −3.00000 5.19615i −0.325396 0.563602i
\(86\) 0.366025 1.36603i 0.0394695 0.147302i
\(87\) 4.33013 7.50000i 0.464238 0.804084i
\(88\) −0.732051 2.73205i −0.0780369 0.291238i
\(89\) 17.3205i 1.83597i 0.396615 + 0.917985i \(0.370185\pi\)
−0.396615 + 0.917985i \(0.629815\pi\)
\(90\) 5.19615 + 5.19615i 0.547723 + 0.547723i
\(91\) 4.33013 1.50000i 0.453921 0.157243i
\(92\) −5.00000 + 8.66025i −0.521286 + 0.902894i
\(93\) −7.50000 12.9904i −0.777714 1.34704i
\(94\) 7.09808 + 1.90192i 0.732111 + 0.196168i
\(95\) −10.3923 + 6.00000i −1.06623 + 0.615587i
\(96\) 9.46410 + 2.53590i 0.965926 + 0.258819i
\(97\) −4.50000 2.59808i −0.456906 0.263795i 0.253837 0.967247i \(-0.418307\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 1.16987 9.83013i 0.118175 0.992993i
\(99\) −2.59808 1.50000i −0.261116 0.150756i
\(100\) 4.00000i 0.400000i
\(101\) 10.5000 + 6.06218i 1.04479 + 0.603209i 0.921186 0.389123i \(-0.127222\pi\)
0.123603 + 0.992332i \(0.460555\pi\)
\(102\) −8.19615 + 2.19615i −0.811540 + 0.217451i
\(103\) −4.33013 7.50000i −0.426660 0.738997i 0.569914 0.821705i \(-0.306977\pi\)
−0.996574 + 0.0827075i \(0.973643\pi\)
\(104\) 4.73205 + 1.26795i 0.464016 + 0.124333i
\(105\) 7.50000 2.59808i 0.731925 0.253546i
\(106\) −1.46410 5.46410i −0.142206 0.530720i
\(107\) 2.00000i 0.193347i −0.995316 0.0966736i \(-0.969180\pi\)
0.995316 0.0966736i \(-0.0308203\pi\)
\(108\) 9.00000 5.19615i 0.866025 0.500000i
\(109\) 12.0000 1.14939 0.574696 0.818367i \(-0.305120\pi\)
0.574696 + 0.818367i \(0.305120\pi\)
\(110\) −0.633975 2.36603i −0.0604471 0.225592i
\(111\) 0 0
\(112\) 6.92820 8.00000i 0.654654 0.755929i
\(113\) −9.50000 16.4545i −0.893685 1.54791i −0.835424 0.549606i \(-0.814778\pi\)
−0.0582609 0.998301i \(-0.518556\pi\)
\(114\) 4.39230 + 16.3923i 0.411377 + 1.53528i
\(115\) −4.33013 + 7.50000i −0.403786 + 0.699379i
\(116\) 10.0000i 0.928477i
\(117\) 4.50000 2.59808i 0.416025 0.240192i
\(118\) −8.66025 + 8.66025i −0.797241 + 0.797241i
\(119\) −1.73205 + 9.00000i −0.158777 + 0.825029i
\(120\) 8.19615 + 2.19615i 0.748203 + 0.200480i
\(121\) −5.00000 8.66025i −0.454545 0.787296i
\(122\) −1.90192 + 7.09808i −0.172192 + 0.642630i
\(123\) −12.9904 + 7.50000i −1.17130 + 0.676252i
\(124\) −15.0000 8.66025i −1.34704 0.777714i
\(125\) 12.1244i 1.08444i
\(126\) −0.803848 11.1962i −0.0716124 0.997433i
\(127\) 18.0000i 1.59724i −0.601834 0.798621i \(-0.705563\pi\)
0.601834 0.798621i \(-0.294437\pi\)
\(128\) 10.9282 2.92820i 0.965926 0.258819i
\(129\) −1.50000 0.866025i −0.132068 0.0762493i
\(130\) 4.09808 + 1.09808i 0.359425 + 0.0963077i
\(131\) 6.06218 + 10.5000i 0.529655 + 0.917389i 0.999402 + 0.0345880i \(0.0110119\pi\)
−0.469747 + 0.882801i \(0.655655\pi\)
\(132\) −3.46410 −0.301511
\(133\) 18.0000 + 3.46410i 1.56080 + 0.300376i
\(134\) 15.0000 + 15.0000i 1.29580 + 1.29580i
\(135\) 7.79423 4.50000i 0.670820 0.387298i
\(136\) −6.92820 + 6.92820i −0.594089 + 0.594089i
\(137\) −2.50000 + 4.33013i −0.213589 + 0.369948i −0.952835 0.303488i \(-0.901849\pi\)
0.739246 + 0.673436i \(0.235182\pi\)
\(138\) 8.66025 + 8.66025i 0.737210 + 0.737210i
\(139\) −4.33013 7.50000i −0.367277 0.636142i 0.621862 0.783127i \(-0.286376\pi\)
−0.989139 + 0.146985i \(0.953043\pi\)
\(140\) 6.00000 6.92820i 0.507093 0.585540i
\(141\) 4.50000 7.79423i 0.378968 0.656392i
\(142\) −5.46410 + 1.46410i −0.458537 + 0.122865i
\(143\) −1.73205 −0.144841
\(144\) 6.00000 10.3923i 0.500000 0.866025i
\(145\) 8.66025i 0.719195i
\(146\) −14.1962 + 3.80385i −1.17488 + 0.314809i
\(147\) −11.2583 4.50000i −0.928571 0.371154i
\(148\) 0 0
\(149\) 3.50000 + 6.06218i 0.286731 + 0.496633i 0.973028 0.230689i \(-0.0740980\pi\)
−0.686296 + 0.727322i \(0.740765\pi\)
\(150\) −4.73205 1.26795i −0.386370 0.103528i
\(151\) 9.52628 + 5.50000i 0.775238 + 0.447584i 0.834740 0.550645i \(-0.185618\pi\)
−0.0595022 + 0.998228i \(0.518951\pi\)
\(152\) 13.8564 + 13.8564i 1.12390 + 1.12390i
\(153\) 10.3923i 0.840168i
\(154\) −1.63397 + 3.36603i −0.131669 + 0.271242i
\(155\) −12.9904 7.50000i −1.04341 0.602414i
\(156\) 3.00000 5.19615i 0.240192 0.416025i
\(157\) 4.50000 2.59808i 0.359139 0.207349i −0.309564 0.950879i \(-0.600183\pi\)
0.668703 + 0.743530i \(0.266850\pi\)
\(158\) 1.09808 4.09808i 0.0873583 0.326025i
\(159\) −6.92820 −0.549442
\(160\) 9.46410 2.53590i 0.748203 0.200480i
\(161\) 12.5000 4.33013i 0.985138 0.341262i
\(162\) −3.29423 12.2942i −0.258819 0.965926i
\(163\) 6.00000i 0.469956i 0.972001 + 0.234978i \(0.0755019\pi\)
−0.972001 + 0.234978i \(0.924498\pi\)
\(164\) −8.66025 + 15.0000i −0.676252 + 1.17130i
\(165\) −3.00000 −0.233550
\(166\) −2.36603 0.633975i −0.183639 0.0492060i
\(167\) 6.06218 + 10.5000i 0.469105 + 0.812514i 0.999376 0.0353139i \(-0.0112431\pi\)
−0.530271 + 0.847828i \(0.677910\pi\)
\(168\) −7.26795 10.7321i −0.560734 0.827996i
\(169\) −5.00000 + 8.66025i −0.384615 + 0.666173i
\(170\) −6.00000 + 6.00000i −0.460179 + 0.460179i
\(171\) 20.7846 1.58944
\(172\) −2.00000 −0.152499
\(173\) −7.50000 4.33013i −0.570214 0.329213i 0.187021 0.982356i \(-0.440117\pi\)
−0.757235 + 0.653143i \(0.773450\pi\)
\(174\) −11.8301 3.16987i −0.896840 0.240307i
\(175\) −3.46410 + 4.00000i −0.261861 + 0.302372i
\(176\) −3.46410 + 2.00000i −0.261116 + 0.150756i
\(177\) 7.50000 + 12.9904i 0.563735 + 0.976417i
\(178\) 23.6603 6.33975i 1.77341 0.475184i
\(179\) 2.00000i 0.149487i 0.997203 + 0.0747435i \(0.0238138\pi\)
−0.997203 + 0.0747435i \(0.976186\pi\)
\(180\) 5.19615 9.00000i 0.387298 0.670820i
\(181\) 17.3205i 1.28742i 0.765268 + 0.643712i \(0.222606\pi\)
−0.765268 + 0.643712i \(0.777394\pi\)
\(182\) −3.63397 5.36603i −0.269368 0.397756i
\(183\) 7.79423 + 4.50000i 0.576166 + 0.332650i
\(184\) 13.6603 + 3.66025i 1.00705 + 0.269838i
\(185\) 0 0
\(186\) −15.0000 + 15.0000i −1.09985 + 1.09985i
\(187\) 1.73205 3.00000i 0.126660 0.219382i
\(188\) 10.3923i 0.757937i
\(189\) −13.5000 2.59808i −0.981981 0.188982i
\(190\) 12.0000 + 12.0000i 0.870572 + 0.870572i
\(191\) 4.33013 + 2.50000i 0.313317 + 0.180894i 0.648410 0.761291i \(-0.275434\pi\)
−0.335093 + 0.942185i \(0.608768\pi\)
\(192\) 13.8564i 1.00000i
\(193\) −4.50000 7.79423i −0.323917 0.561041i 0.657376 0.753563i \(-0.271667\pi\)
−0.981293 + 0.192522i \(0.938333\pi\)
\(194\) −1.90192 + 7.09808i −0.136550 + 0.509612i
\(195\) 2.59808 4.50000i 0.186052 0.322252i
\(196\) −13.8564 + 2.00000i −0.989743 + 0.142857i
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) −1.09808 + 4.09808i −0.0780369 + 0.291238i
\(199\) −17.3205 −1.22782 −0.613909 0.789377i \(-0.710404\pi\)
−0.613909 + 0.789377i \(0.710404\pi\)
\(200\) −5.46410 + 1.46410i −0.386370 + 0.103528i
\(201\) 22.5000 12.9904i 1.58703 0.916271i
\(202\) 4.43782 16.5622i 0.312244 1.16531i
\(203\) −8.66025 + 10.0000i −0.607831 + 0.701862i
\(204\) 6.00000 + 10.3923i 0.420084 + 0.727607i
\(205\) −7.50000 + 12.9904i −0.523823 + 0.907288i
\(206\) −8.66025 + 8.66025i −0.603388 + 0.603388i
\(207\) 12.9904 7.50000i 0.902894 0.521286i
\(208\) 6.92820i 0.480384i
\(209\) −6.00000 3.46410i −0.415029 0.239617i
\(210\) −6.29423 9.29423i −0.434343 0.641363i
\(211\) 0.866025 0.500000i 0.0596196 0.0344214i −0.469894 0.882723i \(-0.655708\pi\)
0.529514 + 0.848301i \(0.322374\pi\)
\(212\) −6.92820 + 4.00000i −0.475831 + 0.274721i
\(213\) 6.92820i 0.474713i
\(214\) −2.73205 + 0.732051i −0.186759 + 0.0500420i
\(215\) −1.73205 −0.118125
\(216\) −10.3923 10.3923i −0.707107 0.707107i
\(217\) 7.50000 + 21.6506i 0.509133 + 1.46974i
\(218\) −4.39230 16.3923i −0.297484 1.11023i
\(219\) 18.0000i 1.21633i
\(220\) −3.00000 + 1.73205i −0.202260 + 0.116775i
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) 0 0
\(223\) 0.866025 1.50000i 0.0579934 0.100447i −0.835571 0.549382i \(-0.814863\pi\)
0.893565 + 0.448935i \(0.148196\pi\)
\(224\) −13.4641 6.53590i −0.899608 0.436698i
\(225\) −3.00000 + 5.19615i −0.200000 + 0.346410i
\(226\) −19.0000 + 19.0000i −1.26386 + 1.26386i
\(227\) 2.59808 4.50000i 0.172440 0.298675i −0.766832 0.641848i \(-0.778168\pi\)
0.939272 + 0.343172i \(0.111501\pi\)
\(228\) 20.7846 12.0000i 1.37649 0.794719i
\(229\) −1.50000 + 0.866025i −0.0991228 + 0.0572286i −0.548742 0.835992i \(-0.684893\pi\)
0.449619 + 0.893220i \(0.351560\pi\)
\(230\) 11.8301 + 3.16987i 0.780055 + 0.209015i
\(231\) 3.46410 + 3.00000i 0.227921 + 0.197386i
\(232\) −13.6603 + 3.66025i −0.896840 + 0.240307i
\(233\) −14.0000 −0.917170 −0.458585 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) −5.19615 5.19615i −0.339683 0.339683i
\(235\) 9.00000i 0.587095i
\(236\) 15.0000 + 8.66025i 0.976417 + 0.563735i
\(237\) −4.50000 2.59808i −0.292306 0.168763i
\(238\) 12.9282 0.928203i 0.838011 0.0601665i
\(239\) 21.6506 12.5000i 1.40046 0.808558i 0.406023 0.913863i \(-0.366915\pi\)
0.994440 + 0.105305i \(0.0335819\pi\)
\(240\) 12.0000i 0.774597i
\(241\) −25.5000 14.7224i −1.64260 0.948355i −0.979905 0.199465i \(-0.936079\pi\)
−0.662695 0.748890i \(-0.730587\pi\)
\(242\) −10.0000 + 10.0000i −0.642824 + 0.642824i
\(243\) −15.5885 −1.00000
\(244\) 10.3923 0.665299
\(245\) −12.0000 + 1.73205i −0.766652 + 0.110657i
\(246\) 15.0000 + 15.0000i 0.956365 + 0.956365i
\(247\) 10.3923 6.00000i 0.661247 0.381771i
\(248\) −6.33975 + 23.6603i −0.402574 + 1.50243i
\(249\) −1.50000 + 2.59808i −0.0950586 + 0.164646i
\(250\) −16.5622 + 4.43782i −1.04748 + 0.280673i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −15.0000 + 5.19615i −0.944911 + 0.327327i
\(253\) −5.00000 −0.314347
\(254\) −24.5885 + 6.58846i −1.54282 + 0.413397i
\(255\) 5.19615 + 9.00000i 0.325396 + 0.563602i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −25.5000 + 14.7224i −1.59065 + 0.918360i −0.597450 + 0.801906i \(0.703819\pi\)
−0.993196 + 0.116454i \(0.962847\pi\)
\(258\) −0.633975 + 2.36603i −0.0394695 + 0.147302i
\(259\) 0 0
\(260\) 6.00000i 0.372104i
\(261\) −7.50000 + 12.9904i −0.464238 + 0.804084i
\(262\) 12.1244 12.1244i 0.749045 0.749045i
\(263\) 16.4545 + 9.50000i 1.01463 + 0.585795i 0.912543 0.408981i \(-0.134116\pi\)
0.102084 + 0.994776i \(0.467449\pi\)
\(264\) 1.26795 + 4.73205i 0.0780369 + 0.291238i
\(265\) −6.00000 + 3.46410i −0.368577 + 0.212798i
\(266\) −1.85641 25.8564i −0.113824 1.58536i
\(267\) 30.0000i 1.83597i
\(268\) 15.0000 25.9808i 0.916271 1.58703i
\(269\) 10.3923i 0.633630i −0.948487 0.316815i \(-0.897387\pi\)
0.948487 0.316815i \(-0.102613\pi\)
\(270\) −9.00000 9.00000i −0.547723 0.547723i
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 12.0000 + 6.92820i 0.727607 + 0.420084i
\(273\) −7.50000 + 2.59808i −0.453921 + 0.157243i
\(274\) 6.83013 + 1.83013i 0.412623 + 0.110562i
\(275\) 1.73205 1.00000i 0.104447 0.0603023i
\(276\) 8.66025 15.0000i 0.521286 0.902894i
\(277\) −11.5000 + 19.9186i −0.690968 + 1.19679i 0.280553 + 0.959839i \(0.409482\pi\)
−0.971521 + 0.236953i \(0.923851\pi\)
\(278\) −8.66025 + 8.66025i −0.519408 + 0.519408i
\(279\) 12.9904 + 22.5000i 0.777714 + 1.34704i
\(280\) −11.6603 5.66025i −0.696833 0.338265i
\(281\) −0.500000 + 0.866025i −0.0298275 + 0.0516627i −0.880554 0.473946i \(-0.842829\pi\)
0.850726 + 0.525609i \(0.176162\pi\)
\(282\) −12.2942 3.29423i −0.732111 0.196168i
\(283\) −7.79423 13.5000i −0.463319 0.802492i 0.535805 0.844342i \(-0.320008\pi\)
−0.999124 + 0.0418500i \(0.986675\pi\)
\(284\) 4.00000 + 6.92820i 0.237356 + 0.411113i
\(285\) 18.0000 10.3923i 1.06623 0.615587i
\(286\) 0.633975 + 2.36603i 0.0374877 + 0.139906i
\(287\) 21.6506 7.50000i 1.27800 0.442711i
\(288\) −16.3923 4.39230i −0.965926 0.258819i
\(289\) 5.00000 0.294118
\(290\) −11.8301 + 3.16987i −0.694689 + 0.186141i
\(291\) 7.79423 + 4.50000i 0.456906 + 0.263795i
\(292\) 10.3923 + 18.0000i 0.608164 + 1.05337i
\(293\) 22.5000 12.9904i 1.31446 0.758906i 0.331632 0.943409i \(-0.392401\pi\)
0.982832 + 0.184503i \(0.0590674\pi\)
\(294\) −2.02628 + 17.0263i −0.118175 + 0.992993i
\(295\) 12.9904 + 7.50000i 0.756329 + 0.436667i
\(296\) 0 0
\(297\) 4.50000 + 2.59808i 0.261116 + 0.150756i
\(298\) 7.00000 7.00000i 0.405499 0.405499i
\(299\) 4.33013 7.50000i 0.250418 0.433736i
\(300\) 6.92820i 0.400000i
\(301\) 2.00000 + 1.73205i 0.115278 + 0.0998337i
\(302\) 4.02628 15.0263i 0.231686 0.864665i
\(303\) −18.1865 10.5000i −1.04479 0.603209i
\(304\) 13.8564 24.0000i 0.794719 1.37649i
\(305\) 9.00000 0.515339
\(306\) 14.1962 3.80385i 0.811540 0.217451i
\(307\) −13.8564 −0.790827 −0.395413 0.918503i \(-0.629399\pi\)
−0.395413 + 0.918503i \(0.629399\pi\)
\(308\) 5.19615 + 1.00000i 0.296078 + 0.0569803i
\(309\) 7.50000 + 12.9904i 0.426660 + 0.738997i
\(310\) −5.49038 + 20.4904i −0.311833 + 1.16378i
\(311\) −12.9904 22.5000i −0.736617 1.27586i −0.954010 0.299774i \(-0.903089\pi\)
0.217393 0.976084i \(-0.430245\pi\)
\(312\) −8.19615 2.19615i −0.464016 0.124333i
\(313\) −7.50000 4.33013i −0.423925 0.244753i 0.272830 0.962062i \(-0.412040\pi\)
−0.696755 + 0.717309i \(0.745374\pi\)
\(314\) −5.19615 5.19615i −0.293236 0.293236i
\(315\) −12.9904 + 4.50000i −0.731925 + 0.253546i
\(316\) −6.00000 −0.337526
\(317\) 11.5000 19.9186i 0.645904 1.11874i −0.338188 0.941079i \(-0.609814\pi\)
0.984092 0.177660i \(-0.0568529\pi\)
\(318\) 2.53590 + 9.46410i 0.142206 + 0.530720i
\(319\) 4.33013 2.50000i 0.242441 0.139973i
\(320\) −6.92820 12.0000i −0.387298 0.670820i
\(321\) 3.46410i 0.193347i
\(322\) −10.4904 15.4904i −0.584606 0.863245i
\(323\) 24.0000i 1.33540i
\(324\) −15.5885 + 9.00000i −0.866025 + 0.500000i
\(325\) 3.46410i 0.192154i
\(326\) 8.19615 2.19615i 0.453943 0.121634i
\(327\) −20.7846 −1.14939
\(328\) 23.6603 + 6.33975i 1.30642 + 0.350054i
\(329\) −9.00000 + 10.3923i −0.496186 + 0.572946i
\(330\) 1.09808 + 4.09808i 0.0604471 + 0.225592i
\(331\) −25.1147 14.5000i −1.38043 0.796992i −0.388221 0.921567i \(-0.626910\pi\)
−0.992210 + 0.124574i \(0.960243\pi\)
\(332\) 3.46410i 0.190117i
\(333\) 0 0
\(334\) 12.1244 12.1244i 0.663415 0.663415i
\(335\) 12.9904 22.5000i 0.709740 1.22931i
\(336\) −12.0000 + 13.8564i −0.654654 + 0.755929i
\(337\) −7.50000 12.9904i −0.408551 0.707631i 0.586177 0.810183i \(-0.300632\pi\)
−0.994728 + 0.102552i \(0.967299\pi\)
\(338\) 13.6603 + 3.66025i 0.743020 + 0.199092i
\(339\) 16.4545 + 28.5000i 0.893685 + 1.54791i
\(340\) 10.3923 + 6.00000i 0.563602 + 0.325396i
\(341\) 8.66025i 0.468979i
\(342\) −7.60770 28.3923i −0.411377 1.53528i
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) 0.732051 + 2.73205i 0.0394695 + 0.147302i
\(345\) 7.50000 12.9904i 0.403786 0.699379i
\(346\) −3.16987 + 11.8301i −0.170413 + 0.635992i
\(347\) 4.33013 2.50000i 0.232453 0.134207i −0.379250 0.925294i \(-0.623818\pi\)
0.611703 + 0.791087i \(0.290485\pi\)
\(348\) 17.3205i 0.928477i
\(349\) 22.5000 + 12.9904i 1.20440 + 0.695359i 0.961530 0.274700i \(-0.0885786\pi\)
0.242867 + 0.970059i \(0.421912\pi\)
\(350\) 6.73205 + 3.26795i 0.359843 + 0.174679i
\(351\) −7.79423 + 4.50000i −0.416025 + 0.240192i
\(352\) 4.00000 + 4.00000i 0.213201 + 0.213201i
\(353\) 7.50000 + 4.33013i 0.399185 + 0.230469i 0.686132 0.727477i \(-0.259307\pi\)
−0.286947 + 0.957946i \(0.592641\pi\)
\(354\) 15.0000 15.0000i 0.797241 0.797241i
\(355\) 3.46410 + 6.00000i 0.183855 + 0.318447i
\(356\) −17.3205 30.0000i −0.917985 1.59000i
\(357\) 3.00000 15.5885i 0.158777 0.825029i
\(358\) 2.73205 0.732051i 0.144393 0.0386901i
\(359\) 10.0000i 0.527780i 0.964553 + 0.263890i \(0.0850056\pi\)
−0.964553 + 0.263890i \(0.914994\pi\)
\(360\) −14.1962 3.80385i −0.748203 0.200480i
\(361\) 29.0000 1.52632
\(362\) 23.6603 6.33975i 1.24356 0.333210i
\(363\) 8.66025 + 15.0000i 0.454545 + 0.787296i
\(364\) −6.00000 + 6.92820i −0.314485 + 0.363137i
\(365\) 9.00000 + 15.5885i 0.471082 + 0.815937i
\(366\) 3.29423 12.2942i 0.172192 0.642630i
\(367\) −11.2583 + 19.5000i −0.587680 + 1.01789i 0.406855 + 0.913493i \(0.366625\pi\)
−0.994535 + 0.104399i \(0.966708\pi\)
\(368\) 20.0000i 1.04257i
\(369\) 22.5000 12.9904i 1.17130 0.676252i
\(370\) 0 0
\(371\) 10.3923 + 2.00000i 0.539542 + 0.103835i
\(372\) 25.9808 + 15.0000i 1.34704 + 0.777714i
\(373\) −0.500000 0.866025i −0.0258890 0.0448411i 0.852791 0.522253i \(-0.174908\pi\)
−0.878680 + 0.477412i \(0.841575\pi\)
\(374\) −4.73205 1.26795i −0.244689 0.0655641i
\(375\) 21.0000i 1.08444i
\(376\) −14.1962 + 3.80385i −0.732111 + 0.196168i
\(377\) 8.66025i 0.446026i
\(378\) 1.39230 + 19.3923i 0.0716124 + 0.997433i
\(379\) 8.00000i 0.410932i −0.978664 0.205466i \(-0.934129\pi\)
0.978664 0.205466i \(-0.0658711\pi\)
\(380\) 12.0000 20.7846i 0.615587 1.06623i
\(381\) 31.1769i 1.59724i
\(382\) 1.83013 6.83013i 0.0936374 0.349460i
\(383\) −0.866025 1.50000i −0.0442518 0.0766464i 0.843051 0.537833i \(-0.180757\pi\)
−0.887303 + 0.461187i \(0.847424\pi\)
\(384\) −18.9282 + 5.07180i −0.965926 + 0.258819i
\(385\) 4.50000 + 0.866025i 0.229341 + 0.0441367i
\(386\) −9.00000 + 9.00000i −0.458088 + 0.458088i
\(387\) 2.59808 + 1.50000i 0.132068 + 0.0762493i
\(388\) 10.3923 0.527589
\(389\) 8.50000 14.7224i 0.430967 0.746457i −0.565990 0.824412i \(-0.691506\pi\)
0.996957 + 0.0779554i \(0.0248392\pi\)
\(390\) −7.09808 1.90192i −0.359425 0.0963077i
\(391\) 8.66025 + 15.0000i 0.437968 + 0.758583i
\(392\) 7.80385 + 18.1962i 0.394154 + 0.919044i
\(393\) −10.5000 18.1865i −0.529655 0.917389i
\(394\) −0.732051 2.73205i −0.0368802 0.137639i
\(395\) −5.19615 −0.261447
\(396\) 6.00000 0.301511
\(397\) 17.3205i 0.869291i 0.900602 + 0.434646i \(0.143126\pi\)
−0.900602 + 0.434646i \(0.856874\pi\)
\(398\) 6.33975 + 23.6603i 0.317783 + 1.18598i
\(399\) −31.1769 6.00000i −1.56080 0.300376i
\(400\) 4.00000 + 6.92820i 0.200000 + 0.346410i
\(401\) −2.50000 4.33013i −0.124844 0.216236i 0.796828 0.604206i \(-0.206510\pi\)
−0.921672 + 0.387970i \(0.873176\pi\)
\(402\) −25.9808 25.9808i −1.29580 1.29580i
\(403\) 12.9904 + 7.50000i 0.647097 + 0.373602i
\(404\) −24.2487 −1.20642
\(405\) −13.5000 + 7.79423i −0.670820 + 0.387298i
\(406\) 16.8301 + 8.16987i 0.835265 + 0.405464i
\(407\) 0 0
\(408\) 12.0000 12.0000i 0.594089 0.594089i
\(409\) −13.5000 + 7.79423i −0.667532 + 0.385400i −0.795141 0.606425i \(-0.792603\pi\)
0.127609 + 0.991825i \(0.459270\pi\)
\(410\) 20.4904 + 5.49038i 1.01195 + 0.271151i
\(411\) 4.33013 7.50000i 0.213589 0.369948i
\(412\) 15.0000 + 8.66025i 0.738997 + 0.426660i
\(413\) −7.50000 21.6506i −0.369051 1.06536i
\(414\) −15.0000 15.0000i −0.737210 0.737210i
\(415\) 3.00000i 0.147264i
\(416\) −9.46410 + 2.53590i −0.464016 + 0.124333i
\(417\) 7.50000 + 12.9904i 0.367277 + 0.636142i
\(418\) −2.53590 + 9.46410i −0.124035 + 0.462904i
\(419\) −12.9904 22.5000i −0.634622 1.09920i −0.986595 0.163187i \(-0.947823\pi\)
0.351974 0.936010i \(-0.385511\pi\)
\(420\) −10.3923 + 12.0000i −0.507093 + 0.585540i
\(421\) 5.50000 9.52628i 0.268054 0.464282i −0.700306 0.713843i \(-0.746953\pi\)
0.968359 + 0.249561i \(0.0802862\pi\)
\(422\) −1.00000 1.00000i −0.0486792 0.0486792i
\(423\) −7.79423 + 13.5000i −0.378968 + 0.656392i
\(424\) 8.00000 + 8.00000i 0.388514 + 0.388514i
\(425\) −6.00000 3.46410i −0.291043 0.168034i
\(426\) 9.46410 2.53590i 0.458537 0.122865i
\(427\) −10.3923 9.00000i −0.502919 0.435541i
\(428\) 2.00000 + 3.46410i 0.0966736 + 0.167444i
\(429\) 3.00000 0.144841
\(430\) 0.633975 + 2.36603i 0.0305730 + 0.114100i
\(431\) 26.0000i 1.25238i −0.779672 0.626188i \(-0.784614\pi\)
0.779672 0.626188i \(-0.215386\pi\)
\(432\) −10.3923 + 18.0000i −0.500000 + 0.866025i
\(433\) 17.3205i 0.832370i −0.909280 0.416185i \(-0.863367\pi\)
0.909280 0.416185i \(-0.136633\pi\)
\(434\) 26.8301 18.1699i 1.28789 0.872182i
\(435\) 15.0000i 0.719195i
\(436\) −20.7846 + 12.0000i −0.995402 + 0.574696i
\(437\) 30.0000 17.3205i 1.43509 0.828552i
\(438\) 24.5885 6.58846i 1.17488 0.314809i
\(439\) 9.52628 16.5000i 0.454665 0.787502i −0.544004 0.839082i \(-0.683092\pi\)
0.998669 + 0.0515804i \(0.0164258\pi\)
\(440\) 3.46410 + 3.46410i 0.165145 + 0.165145i
\(441\) 19.5000 + 7.79423i 0.928571 + 0.371154i
\(442\) 6.00000 6.00000i 0.285391 0.285391i
\(443\) −30.3109 17.5000i −1.44011 0.831450i −0.442257 0.896888i \(-0.645822\pi\)
−0.997857 + 0.0654382i \(0.979155\pi\)
\(444\) 0 0
\(445\) −15.0000 25.9808i −0.711068 1.23161i
\(446\) −2.36603 0.633975i −0.112035 0.0300196i
\(447\) −6.06218 10.5000i −0.286731 0.496633i
\(448\) −4.00000 + 20.7846i −0.188982 + 0.981981i
\(449\) −20.0000 −0.943858 −0.471929 0.881636i \(-0.656442\pi\)
−0.471929 + 0.881636i \(0.656442\pi\)
\(450\) 8.19615 + 2.19615i 0.386370 + 0.103528i
\(451\) −8.66025 −0.407795
\(452\) 32.9090 + 19.0000i 1.54791 + 0.893685i
\(453\) −16.5000 9.52628i −0.775238 0.447584i
\(454\) −7.09808 1.90192i −0.333129 0.0892617i
\(455\) −5.19615 + 6.00000i −0.243599 + 0.281284i
\(456\) −24.0000 24.0000i −1.12390 1.12390i
\(457\) 7.50000 12.9904i 0.350835 0.607664i −0.635561 0.772051i \(-0.719231\pi\)
0.986396 + 0.164386i \(0.0525644\pi\)
\(458\) 1.73205 + 1.73205i 0.0809334 + 0.0809334i
\(459\) 18.0000i 0.840168i
\(460\) 17.3205i 0.807573i
\(461\) −10.5000 6.06218i −0.489034 0.282344i 0.235140 0.971962i \(-0.424445\pi\)
−0.724174 + 0.689618i \(0.757779\pi\)
\(462\) 2.83013 5.83013i 0.131669 0.271242i
\(463\) −33.7750 + 19.5000i −1.56966 + 0.906242i −0.573449 + 0.819242i \(0.694395\pi\)
−0.996208 + 0.0870004i \(0.972272\pi\)
\(464\) 10.0000 + 17.3205i 0.464238 + 0.804084i
\(465\) 22.5000 + 12.9904i 1.04341 + 0.602414i
\(466\) 5.12436 + 19.1244i 0.237381 + 0.885919i
\(467\) 20.7846 0.961797 0.480899 0.876776i \(-0.340311\pi\)
0.480899 + 0.876776i \(0.340311\pi\)
\(468\) −5.19615 + 9.00000i −0.240192 + 0.416025i
\(469\) −37.5000 + 12.9904i −1.73159 + 0.599840i
\(470\) −12.2942 + 3.29423i −0.567090 + 0.151951i
\(471\) −7.79423 + 4.50000i −0.359139 + 0.207349i
\(472\) 6.33975 23.6603i 0.291810 1.08905i
\(473\) −0.500000 0.866025i −0.0229900 0.0398199i
\(474\) −1.90192 + 7.09808i −0.0873583 + 0.326025i
\(475\) −6.92820 + 12.0000i −0.317888 + 0.550598i
\(476\) −6.00000 17.3205i −0.275010 0.793884i
\(477\) 12.0000 0.549442
\(478\) −25.0000 25.0000i −1.14347 1.14347i
\(479\) 16.4545 28.5000i 0.751825 1.30220i −0.195113 0.980781i \(-0.562507\pi\)
0.946938 0.321417i \(-0.104159\pi\)
\(480\) −16.3923 + 4.39230i −0.748203 + 0.200480i
\(481\) 0 0
\(482\) −10.7776 + 40.2224i −0.490905 + 1.83208i
\(483\) −21.6506 + 7.50000i −0.985138 + 0.341262i
\(484\) 17.3205 + 10.0000i 0.787296 + 0.454545i
\(485\) 9.00000 0.408669
\(486\) 5.70577 + 21.2942i 0.258819 + 0.965926i
\(487\) 10.0000i 0.453143i −0.973995 0.226572i \(-0.927248\pi\)
0.973995 0.226572i \(-0.0727517\pi\)
\(488\) −3.80385 14.1962i −0.172192 0.642630i
\(489\) 10.3923i 0.469956i
\(490\) 6.75833 + 15.7583i 0.305310 + 0.711889i
\(491\) 16.4545 9.50000i 0.742580 0.428729i −0.0804264 0.996761i \(-0.525628\pi\)
0.823007 + 0.568032i \(0.192295\pi\)
\(492\) 15.0000 25.9808i 0.676252 1.17130i
\(493\) −15.0000 8.66025i −0.675566 0.390038i
\(494\) −12.0000 12.0000i −0.539906 0.539906i
\(495\) 5.19615 0.233550
\(496\) 34.6410 1.55543
\(497\) 2.00000 10.3923i 0.0897123 0.466159i
\(498\) 4.09808 + 1.09808i 0.183639 + 0.0492060i
\(499\) 6.06218 3.50000i 0.271380 0.156682i −0.358134 0.933670i \(-0.616587\pi\)
0.629515 + 0.776989i \(0.283254\pi\)
\(500\) 12.1244 + 21.0000i 0.542218 + 0.939149i
\(501\) −10.5000 18.1865i −0.469105 0.812514i
\(502\) 0 0
\(503\) −17.3205 −0.772283 −0.386142 0.922440i \(-0.626192\pi\)
−0.386142 + 0.922440i \(0.626192\pi\)
\(504\) 12.5885 + 18.5885i 0.560734 + 0.827996i
\(505\) −21.0000 −0.934488
\(506\) 1.83013 + 6.83013i 0.0813591 + 0.303636i
\(507\) 8.66025 15.0000i 0.384615 0.666173i
\(508\) 18.0000 + 31.1769i 0.798621 + 1.38325i
\(509\) −22.5000 + 12.9904i −0.997295 + 0.575789i −0.907447 0.420167i \(-0.861972\pi\)
−0.0898481 + 0.995955i \(0.528638\pi\)
\(510\) 10.3923 10.3923i 0.460179 0.460179i
\(511\) 5.19615 27.0000i 0.229864 1.19441i
\(512\) −16.0000 + 16.0000i −0.707107 + 0.707107i
\(513\) −36.0000 −1.58944
\(514\) 29.4449 + 29.4449i 1.29876 + 1.29876i
\(515\) 12.9904 + 7.50000i 0.572425 + 0.330489i
\(516\) 3.46410 0.152499
\(517\) 4.50000 2.59808i 0.197910 0.114263i
\(518\) 0 0
\(519\) 12.9904 + 7.50000i 0.570214 + 0.329213i
\(520\) −8.19615 + 2.19615i −0.359425 + 0.0963077i
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 20.4904 + 5.49038i 0.896840 + 0.240307i
\(523\) 24.2487 1.06032 0.530161 0.847897i \(-0.322131\pi\)
0.530161 + 0.847897i \(0.322131\pi\)
\(524\) −21.0000 12.1244i −0.917389 0.529655i
\(525\) 6.00000 6.92820i 0.261861 0.302372i
\(526\) 6.95448 25.9545i 0.303230 1.13167i
\(527\) −25.9808 + 15.0000i −1.13174 + 0.653410i
\(528\) 6.00000 3.46410i 0.261116 0.150756i
\(529\) 1.00000 1.73205i 0.0434783 0.0753066i
\(530\) 6.92820 + 6.92820i 0.300942 + 0.300942i
\(531\) −12.9904 22.5000i −0.563735 0.976417i
\(532\) −34.6410 + 12.0000i −1.50188 + 0.520266i
\(533\) 7.50000 12.9904i 0.324861 0.562676i
\(534\) −40.9808 + 10.9808i −1.77341 + 0.475184i
\(535\) 1.73205 + 3.00000i 0.0748831 + 0.129701i
\(536\) −40.9808 10.9808i −1.77010 0.474297i
\(537\) 3.46410i 0.149487i
\(538\) −14.1962 + 3.80385i −0.612040 + 0.163996i
\(539\) −4.33013 5.50000i −0.186512 0.236902i
\(540\) −9.00000 + 15.5885i −0.387298 + 0.670820i
\(541\) 26.0000 1.11783 0.558914 0.829226i \(-0.311218\pi\)
0.558914 + 0.829226i \(0.311218\pi\)
\(542\) 0 0
\(543\) 30.0000i 1.28742i
\(544\) 5.07180 18.9282i 0.217451 0.811540i
\(545\) −18.0000 + 10.3923i −0.771035 + 0.445157i
\(546\) 6.29423 + 9.29423i 0.269368 + 0.397756i
\(547\) 23.3827 + 13.5000i 0.999771 + 0.577218i 0.908181 0.418578i \(-0.137471\pi\)
0.0915908 + 0.995797i \(0.470805\pi\)
\(548\) 10.0000i 0.427179i
\(549\) −13.5000 7.79423i −0.576166 0.332650i
\(550\) −2.00000 2.00000i −0.0852803 0.0852803i
\(551\) −17.3205 + 30.0000i −0.737878 + 1.27804i
\(552\) −23.6603 6.33975i −1.00705 0.269838i
\(553\) 6.00000 + 5.19615i 0.255146 + 0.220963i
\(554\) 31.4186 + 8.41858i 1.33485 + 0.357671i
\(555\) 0 0
\(556\) 15.0000 + 8.66025i 0.636142 + 0.367277i
\(557\) −40.0000 −1.69485 −0.847427 0.530912i \(-0.821850\pi\)
−0.847427 + 0.530912i \(0.821850\pi\)
\(558\) 25.9808 25.9808i 1.09985 1.09985i
\(559\) 1.73205 0.0732579
\(560\) −3.46410 + 18.0000i −0.146385 + 0.760639i
\(561\) −3.00000 + 5.19615i −0.126660 + 0.219382i
\(562\) 1.36603 + 0.366025i 0.0576223 + 0.0154398i
\(563\) 0.866025 + 1.50000i 0.0364986 + 0.0632175i 0.883698 0.468058i \(-0.155046\pi\)
−0.847199 + 0.531276i \(0.821713\pi\)
\(564\) 18.0000i 0.757937i
\(565\) 28.5000 + 16.4545i 1.19900 + 0.692245i
\(566\) −15.5885 + 15.5885i −0.655232 + 0.655232i
\(567\) 23.3827 + 4.50000i 0.981981 + 0.188982i
\(568\) 8.00000 8.00000i 0.335673 0.335673i
\(569\) −3.50000 + 6.06218i −0.146728 + 0.254140i −0.930016 0.367519i \(-0.880207\pi\)
0.783289 + 0.621658i \(0.213541\pi\)
\(570\) −20.7846 20.7846i −0.870572 0.870572i
\(571\) 7.79423 4.50000i 0.326178 0.188319i −0.327965 0.944690i \(-0.606363\pi\)
0.654143 + 0.756371i \(0.273029\pi\)
\(572\) 3.00000 1.73205i 0.125436 0.0724207i
\(573\) −7.50000 4.33013i −0.313317 0.180894i
\(574\) −18.1699 26.8301i −0.758396 1.11987i
\(575\) 10.0000i 0.417029i
\(576\) 24.0000i 1.00000i
\(577\) 38.1051i 1.58634i −0.609002 0.793168i \(-0.708430\pi\)
0.609002 0.793168i \(-0.291570\pi\)
\(578\) −1.83013 6.83013i −0.0761232 0.284096i
\(579\) 7.79423 + 13.5000i 0.323917 + 0.561041i
\(580\) 8.66025 + 15.0000i 0.359597 + 0.622841i
\(581\) 3.00000 3.46410i 0.124461 0.143715i
\(582\) 3.29423 12.2942i 0.136550 0.509612i
\(583\) −3.46410 2.00000i −0.143468 0.0828315i
\(584\) 20.7846 20.7846i 0.860073 0.860073i
\(585\) −4.50000 + 7.79423i −0.186052 + 0.322252i
\(586\) −25.9808 25.9808i −1.07326 1.07326i
\(587\) −12.9904 + 22.5000i −0.536170 + 0.928674i 0.462935 + 0.886392i \(0.346796\pi\)
−0.999106 + 0.0422823i \(0.986537\pi\)
\(588\) 24.0000 3.46410i 0.989743 0.142857i
\(589\) 30.0000 + 51.9615i 1.23613 + 2.14104i
\(590\) 5.49038 20.4904i 0.226035 0.843576i
\(591\) −3.46410 −0.142494
\(592\) 0 0
\(593\) 31.1769i 1.28028i 0.768257 + 0.640141i \(0.221124\pi\)
−0.768257 + 0.640141i \(0.778876\pi\)
\(594\) 1.90192 7.09808i 0.0780369 0.291238i
\(595\) −5.19615 15.0000i −0.213021 0.614940i
\(596\) −12.1244 7.00000i −0.496633 0.286731i
\(597\) 30.0000 1.22782
\(598\) −11.8301 3.16987i −0.483770 0.129626i
\(599\) −14.7224 + 8.50000i −0.601542 + 0.347301i −0.769648 0.638468i \(-0.779568\pi\)
0.168106 + 0.985769i \(0.446235\pi\)
\(600\) 9.46410 2.53590i 0.386370 0.103528i
\(601\) −4.50000 2.59808i −0.183559 0.105978i 0.405405 0.914137i \(-0.367131\pi\)
−0.588964 + 0.808160i \(0.700464\pi\)
\(602\) 1.63397 3.36603i 0.0665958 0.137189i
\(603\) −38.9711 + 22.5000i −1.58703 + 0.916271i
\(604\) −22.0000 −0.895167
\(605\) 15.0000 + 8.66025i 0.609837 + 0.352089i
\(606\) −7.68653 + 28.6865i −0.312244 + 1.16531i
\(607\) −4.33013 7.50000i −0.175754 0.304416i 0.764668 0.644425i \(-0.222903\pi\)
−0.940422 + 0.340009i \(0.889570\pi\)
\(608\) −37.8564 10.1436i −1.53528 0.411377i
\(609\) 15.0000 17.3205i 0.607831 0.701862i
\(610\) −3.29423 12.2942i −0.133379 0.497779i
\(611\) 9.00000i 0.364101i
\(612\) −10.3923 18.0000i −0.420084 0.727607i
\(613\) −40.0000 −1.61558 −0.807792 0.589467i \(-0.799338\pi\)
−0.807792 + 0.589467i \(0.799338\pi\)
\(614\) 5.07180 + 18.9282i 0.204681 + 0.763880i
\(615\) 12.9904 22.5000i 0.523823 0.907288i
\(616\) −0.535898 7.46410i −0.0215920 0.300737i
\(617\) 17.5000 + 30.3109i 0.704523 + 1.22027i 0.966863 + 0.255295i \(0.0821725\pi\)
−0.262340 + 0.964976i \(0.584494\pi\)
\(618\) 15.0000 15.0000i 0.603388 0.603388i
\(619\) −4.33013 + 7.50000i −0.174042 + 0.301450i −0.939829 0.341644i \(-0.889016\pi\)
0.765787 + 0.643094i \(0.222350\pi\)
\(620\) 30.0000 1.20483
\(621\) −22.5000 + 12.9904i −0.902894 + 0.521286i
\(622\) −25.9808 + 25.9808i −1.04173 + 1.04173i
\(623\) −8.66025 + 45.0000i −0.346966 + 1.80289i
\(624\) 12.0000i 0.480384i
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) −3.16987 + 11.8301i −0.126694 + 0.472827i
\(627\) 10.3923 + 6.00000i 0.415029 + 0.239617i
\(628\) −5.19615 + 9.00000i −0.207349 + 0.359139i
\(629\) 0 0
\(630\) 10.9019 + 16.0981i 0.434343 + 0.641363i
\(631\) 6.00000i 0.238856i 0.992843 + 0.119428i \(0.0381061\pi\)
−0.992843 + 0.119428i \(0.961894\pi\)
\(632\) 2.19615 + 8.19615i 0.0873583 + 0.326025i
\(633\) −1.50000 + 0.866025i −0.0596196 + 0.0344214i
\(634\) −31.4186 8.41858i −1.24779 0.334345i
\(635\) 15.5885 + 27.0000i 0.618609 + 1.07146i
\(636\) 12.0000 6.92820i 0.475831 0.274721i
\(637\) 12.0000 1.73205i 0.475457 0.0686264i
\(638\) −5.00000 5.00000i −0.197952 0.197952i
\(639\) 12.0000i 0.474713i
\(640\) −13.8564 + 13.8564i −0.547723 + 0.547723i
\(641\) 2.50000 4.33013i 0.0987441 0.171030i −0.812421 0.583071i \(-0.801851\pi\)
0.911165 + 0.412042i \(0.135184\pi\)
\(642\) 4.73205 1.26795i 0.186759 0.0500420i
\(643\) 0.866025 + 1.50000i 0.0341527 + 0.0591542i 0.882597 0.470131i \(-0.155793\pi\)
−0.848444 + 0.529285i \(0.822460\pi\)
\(644\) −17.3205 + 20.0000i −0.682524 + 0.788110i
\(645\) 3.00000 0.118125
\(646\) 32.7846 8.78461i 1.28989 0.345626i
\(647\) 34.6410 1.36188 0.680939 0.732340i \(-0.261572\pi\)
0.680939 + 0.732340i \(0.261572\pi\)
\(648\) 18.0000 + 18.0000i 0.707107 + 0.707107i
\(649\) 8.66025i 0.339945i
\(650\) 4.73205 1.26795i 0.185606 0.0497331i
\(651\) −12.9904 37.5000i −0.509133 1.46974i
\(652\) −6.00000 10.3923i −0.234978 0.406994i
\(653\) 0.500000 + 0.866025i 0.0195665 + 0.0338902i 0.875643 0.482959i \(-0.160438\pi\)
−0.856076 + 0.516849i \(0.827105\pi\)
\(654\) 7.60770 + 28.3923i 0.297484 + 1.11023i
\(655\) −18.1865 10.5000i −0.710607 0.410269i
\(656\) 34.6410i 1.35250i
\(657\) 31.1769i 1.21633i
\(658\) 17.4904 + 8.49038i 0.681846 + 0.330990i
\(659\) −14.7224 8.50000i −0.573505 0.331113i 0.185043 0.982730i \(-0.440757\pi\)
−0.758548 + 0.651617i \(0.774091\pi\)
\(660\) 5.19615 3.00000i 0.202260 0.116775i
\(661\) −7.50000 + 4.33013i −0.291716 + 0.168422i −0.638716 0.769443i \(-0.720534\pi\)
0.346999 + 0.937865i \(0.387201\pi\)
\(662\) −10.6147 + 39.6147i −0.412553 + 1.53967i
\(663\) −5.19615 9.00000i −0.201802 0.349531i
\(664\) 4.73205 1.26795i 0.183639 0.0492060i
\(665\) −30.0000 + 10.3923i −1.16335 + 0.402996i
\(666\) 0 0
\(667\) 25.0000i 0.968004i
\(668\) −21.0000 12.1244i −0.812514 0.469105i
\(669\) −1.50000 + 2.59808i −0.0579934 + 0.100447i
\(670\) −35.4904 9.50962i −1.37111 0.367389i
\(671\) 2.59808 + 4.50000i 0.100298 + 0.173721i
\(672\) 23.3205 + 11.3205i 0.899608 + 0.436698i
\(673\) 19.5000 33.7750i 0.751670 1.30193i −0.195343 0.980735i \(-0.562582\pi\)
0.947013 0.321195i \(-0.104085\pi\)
\(674\) −15.0000 + 15.0000i −0.577778 + 0.577778i
\(675\) 5.19615 9.00000i 0.200000 0.346410i
\(676\) 20.0000i 0.769231i
\(677\) 4.50000 + 2.59808i 0.172949 + 0.0998522i 0.583976 0.811771i \(-0.301496\pi\)
−0.411027 + 0.911623i \(0.634830\pi\)
\(678\) 32.9090 32.9090i 1.26386 1.26386i
\(679\) −10.3923 9.00000i −0.398820 0.345388i
\(680\) 4.39230 16.3923i 0.168437 0.628616i
\(681\) −4.50000 + 7.79423i −0.172440 + 0.298675i
\(682\) −11.8301 + 3.16987i −0.452999 + 0.121381i
\(683\) 14.0000i 0.535695i −0.963461 0.267848i \(-0.913688\pi\)
0.963461 0.267848i \(-0.0863124\pi\)
\(684\) −36.0000 + 20.7846i −1.37649 + 0.794719i
\(685\) 8.66025i 0.330891i
\(686\) 7.95448 24.9545i 0.303704 0.952767i
\(687\) 2.59808 1.50000i 0.0991228 0.0572286i
\(688\) 3.46410 2.00000i 0.132068 0.0762493i
\(689\) 6.00000 3.46410i 0.228582 0.131972i
\(690\) −20.4904 5.49038i −0.780055 0.209015i
\(691\) 4.33013 7.50000i 0.164726 0.285313i −0.771832 0.635826i \(-0.780659\pi\)
0.936558 + 0.350513i \(0.113993\pi\)
\(692\) 17.3205 0.658427
\(693\) −6.00000 5.19615i −0.227921 0.197386i
\(694\) −5.00000 5.00000i −0.189797 0.189797i
\(695\) 12.9904 + 7.50000i 0.492753 + 0.284491i
\(696\) 23.6603 6.33975i 0.896840 0.240307i
\(697\) 15.0000 + 25.9808i 0.568166 + 0.984092i
\(698\) 9.50962 35.4904i 0.359944 1.34333i
\(699\) 24.2487 0.917170
\(700\) 2.00000 10.3923i 0.0755929 0.392792i
\(701\) 44.0000 1.66186 0.830929 0.556379i \(-0.187810\pi\)
0.830929 + 0.556379i \(0.187810\pi\)
\(702\) 9.00000 + 9.00000i 0.339683 + 0.339683i
\(703\) 0 0
\(704\) 4.00000 6.92820i 0.150756 0.261116i
\(705\) 15.5885i 0.587095i
\(706\) 3.16987 11.8301i 0.119300 0.445233i
\(707\) 24.2487 + 21.0000i 0.911967 + 0.789786i
\(708\) −25.9808 15.0000i −0.976417 0.563735i
\(709\) −7.50000 + 12.9904i −0.281668 + 0.487864i −0.971796 0.235824i \(-0.924221\pi\)
0.690127 + 0.723688i \(0.257554\pi\)
\(710\) 6.92820 6.92820i 0.260011 0.260011i
\(711\) 7.79423 + 4.50000i 0.292306 + 0.168763i
\(712\) −34.6410 + 34.6410i −1.29823 + 1.29823i
\(713\) 37.5000 + 21.6506i 1.40439 + 0.810823i
\(714\) −22.3923 + 1.60770i −0.838011 + 0.0601665i
\(715\) 2.59808 1.50000i 0.0971625 0.0560968i
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) −37.5000 + 21.6506i −1.40046 + 0.808558i
\(718\) 13.6603 3.66025i 0.509796 0.136599i
\(719\) −34.6410 −1.29189 −0.645946 0.763383i \(-0.723537\pi\)
−0.645946 + 0.763383i \(0.723537\pi\)
\(720\) 20.7846i 0.774597i
\(721\) −7.50000 21.6506i −0.279315 0.806312i
\(722\) −10.6147 39.6147i −0.395040 1.47431i
\(723\) 44.1673 + 25.5000i 1.64260 + 0.948355i
\(724\) −17.3205 30.0000i −0.643712 1.11494i
\(725\) −5.00000 8.66025i −0.185695 0.321634i
\(726\) 17.3205 17.3205i 0.642824 0.642824i
\(727\) −14.7224 + 25.5000i −0.546025 + 0.945743i 0.452517 + 0.891756i \(0.350526\pi\)
−0.998542 + 0.0539868i \(0.982807\pi\)
\(728\) 11.6603 + 5.66025i 0.432158 + 0.209783i
\(729\) 27.0000 1.00000
\(730\) 18.0000 18.0000i 0.666210 0.666210i
\(731\) −1.73205 + 3.00000i −0.0640622 + 0.110959i
\(732\) −18.0000 −0.665299
\(733\) 19.5000 11.2583i 0.720249 0.415836i −0.0945954 0.995516i \(-0.530156\pi\)
0.814844 + 0.579680i \(0.196822\pi\)
\(734\) 30.7583 + 8.24167i 1.13531 + 0.304206i
\(735\) 20.7846 3.00000i 0.766652 0.110657i
\(736\) −27.3205 + 7.32051i −1.00705 + 0.269838i
\(737\) 15.0000 0.552532
\(738\) −25.9808 25.9808i −0.956365 0.956365i
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) −18.0000 + 10.3923i −0.661247 + 0.381771i
\(742\) −1.07180 14.9282i −0.0393469 0.548032i
\(743\) −25.1147 + 14.5000i −0.921370 + 0.531953i −0.884072 0.467351i \(-0.845209\pi\)
−0.0372984 + 0.999304i \(0.511875\pi\)
\(744\) 10.9808 40.9808i 0.402574 1.50243i
\(745\) −10.5000 6.06218i −0.384690 0.222101i
\(746\) −1.00000 + 1.00000i −0.0366126 + 0.0366126i
\(747\) 2.59808 4.50000i 0.0950586 0.164646i
\(748\) 6.92820i 0.253320i
\(749\) 1.00000 5.19615i 0.0365392 0.189863i
\(750\) 28.6865 7.68653i 1.04748 0.280673i
\(751\) 30.3109 17.5000i 1.10606 0.638584i 0.168254 0.985744i \(-0.446187\pi\)
0.937806 + 0.347160i \(0.112854\pi\)
\(752\) 10.3923 + 18.0000i 0.378968 + 0.656392i
\(753\) 0 0
\(754\) 11.8301 3.16987i 0.430828 0.115440i
\(755\) −19.0526 −0.693394
\(756\) 25.9808 9.00000i 0.944911 0.327327i
\(757\) 30.0000 1.09037 0.545184 0.838316i \(-0.316460\pi\)
0.545184 + 0.838316i \(0.316460\pi\)
\(758\) −10.9282 + 2.92820i −0.396930 + 0.106357i
\(759\) 8.66025 0.314347
\(760\) −32.7846 8.78461i −1.18922 0.318651i
\(761\) 19.5000 11.2583i 0.706874 0.408114i −0.103028 0.994678i \(-0.532853\pi\)
0.809903 + 0.586564i \(0.199520\pi\)
\(762\) 42.5885 11.4115i 1.54282 0.413397i
\(763\) 31.1769 + 6.00000i 1.12868 + 0.217215i
\(764\) −10.0000 −0.361787
\(765\) −9.00000 15.5885i −0.325396 0.563602i
\(766\) −1.73205 + 1.73205i −0.0625815 + 0.0625815i
\(767\) −12.9904 7.50000i −0.469055 0.270809i
\(768\) 13.8564 + 24.0000i 0.500000 + 0.866025i
\(769\) 22.5000 12.9904i 0.811371 0.468445i −0.0360609 0.999350i \(-0.511481\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) −0.464102 6.46410i −0.0167251 0.232950i
\(771\) 44.1673 25.5000i 1.59065 0.918360i
\(772\) 15.5885 + 9.00000i 0.561041 + 0.323917i
\(773\) 24.2487i 0.872166i −0.899907 0.436083i \(-0.856365\pi\)
0.899907 0.436083i \(-0.143635\pi\)
\(774\) 1.09808 4.09808i 0.0394695 0.147302i
\(775\) −17.3205 −0.622171
\(776\) −3.80385 14.1962i −0.136550 0.509612i
\(777\) 0 0
\(778\) −23.2224 6.22243i −0.832565 0.223085i
\(779\) 51.9615 30.0000i 1.86171 1.07486i
\(780\) 10.3923i 0.372104i
\(781\) −2.00000 + 3.46410i −0.0715656 + 0.123955i
\(782\) 17.3205 17.3205i 0.619380 0.619380i
\(783\) 12.9904 22.5000i 0.464238 0.804084i
\(784\) 22.0000 17.3205i 0.785714 0.618590i
\(785\) −4.50000 + 7.79423i −0.160612 + 0.278188i
\(786\) −21.0000 + 21.0000i −0.749045 + 0.749045i
\(787\) 6.06218 + 10.5000i 0.216093 + 0.374285i 0.953610 0.301044i \(-0.0973351\pi\)
−0.737517 + 0.675329i \(0.764002\pi\)
\(788\) −3.46410 + 2.00000i −0.123404 + 0.0712470i
\(789\) −28.5000 16.4545i −1.01463 0.585795i
\(790\) 1.90192 + 7.09808i 0.0676674 + 0.252538i
\(791\) −16.4545 47.5000i −0.585054 1.68891i
\(792\) −2.19615 8.19615i −0.0780369 0.291238i
\(793\) −9.00000 −0.319599
\(794\) 23.6603 6.33975i 0.839671 0.224989i
\(795\) 10.3923 6.00000i 0.368577 0.212798i
\(796\) 30.0000 17.3205i 1.06332 0.613909i
\(797\) −4.50000 + 2.59808i −0.159398 + 0.0920286i −0.577577 0.816336i \(-0.696002\pi\)
0.418179 + 0.908365i \(0.362668\pi\)
\(798\) 3.21539 + 44.7846i 0.113824 + 1.58536i
\(799\) −15.5885 9.00000i −0.551480 0.318397i
\(800\) 8.00000 8.00000i 0.282843 0.282843i
\(801\) 51.9615i 1.83597i
\(802\) −5.00000 + 5.00000i −0.176556 + 0.176556i
\(803\) −5.19615 + 9.00000i −0.183368 + 0.317603i
\(804\) −25.9808 + 45.0000i −0.916271 + 1.58703i
\(805\) −15.0000 + 17.3205i −0.528681 + 0.610468i
\(806\) 5.49038 20.4904i 0.193390 0.721743i
\(807\) 18.0000i 0.633630i
\(808\) 8.87564 + 33.1244i 0.312244 + 1.16531i
\(809\) 8.00000 0.281265 0.140633 0.990062i \(-0.455086\pi\)
0.140633 + 0.990062i \(0.455086\pi\)
\(810\) 15.5885 + 15.5885i 0.547723 + 0.547723i
\(811\) 20.7846 0.729846 0.364923 0.931038i \(-0.381095\pi\)
0.364923 + 0.931038i \(0.381095\pi\)
\(812\) 5.00000 25.9808i 0.175466 0.911746i
\(813\) 0 0
\(814\) 0 0
\(815\) −5.19615 9.00000i −0.182013 0.315256i
\(816\) −20.7846 12.0000i −0.727607 0.420084i
\(817\) 6.00000 + 3.46410i 0.209913 + 0.121194i
\(818\) 15.5885 + 15.5885i 0.545038 + 0.545038i
\(819\) 12.9904 4.50000i 0.453921 0.157243i
\(820\) 30.0000i 1.04765i
\(821\) −20.5000 + 35.5070i −0.715455 + 1.23920i 0.247329 + 0.968932i \(0.420447\pi\)
−0.962784 + 0.270273i \(0.912886\pi\)
\(822\) −11.8301 3.16987i −0.412623 0.110562i
\(823\) 7.79423 4.50000i 0.271690 0.156860i −0.357966 0.933735i \(-0.616529\pi\)
0.629655 + 0.776875i \(0.283196\pi\)
\(824\) 6.33975 23.6603i 0.220856 0.824244i
\(825\) −3.00000 + 1.73205i −0.104447 + 0.0603023i
\(826\) −26.8301 + 18.1699i −0.933540 + 0.632211i
\(827\) 50.0000i 1.73867i 0.494223 + 0.869335i \(0.335453\pi\)
−0.494223 + 0.869335i \(0.664547\pi\)
\(828\) −15.0000 + 25.9808i −0.521286 + 0.902894i
\(829\) 10.3923i 0.360940i −0.983581 0.180470i \(-0.942238\pi\)
0.983581 0.180470i \(-0.0577618\pi\)
\(830\) 4.09808 1.09808i 0.142246 0.0381148i
\(831\) 19.9186 34.5000i 0.690968 1.19679i
\(832\) 6.92820 + 12.0000i 0.240192 + 0.416025i
\(833\) −9.00000 + 22.5167i −0.311832 + 0.780156i
\(834\) 15.0000 15.0000i 0.519408 0.519408i
\(835\) −18.1865 10.5000i −0.629371 0.363367i
\(836\) 13.8564 0.479234
\(837\) −22.5000 38.9711i −0.777714 1.34704i
\(838\) −25.9808 + 25.9808i −0.897491 + 0.897491i
\(839\) 0.866025 1.50000i 0.0298985 0.0517858i −0.850689 0.525669i \(-0.823815\pi\)
0.880587 + 0.473884i \(0.157148\pi\)
\(840\) 20.1962 + 9.80385i 0.696833 + 0.338265i
\(841\) 2.00000 + 3.46410i 0.0689655 + 0.119452i
\(842\) −15.0263 4.02628i −0.517840 0.138755i
\(843\) 0.866025 1.50000i 0.0298275 0.0516627i
\(844\) −1.00000 + 1.73205i −0.0344214 + 0.0596196i
\(845\) 17.3205i 0.595844i
\(846\) 21.2942 + 5.70577i 0.732111 + 0.196168i
\(847\) −8.66025 25.0000i −0.297570 0.859010i
\(848\) 8.00000 13.8564i 0.274721 0.475831i
\(849\) 13.5000 + 23.3827i 0.463319 + 0.802492i
\(850\) −2.53590 + 9.46410i −0.0869806 + 0.324616i
\(851\) 0 0
\(852\) −6.92820 12.0000i −0.237356 0.411113i
\(853\) −34.5000 19.9186i −1.18126 0.681999i −0.224952 0.974370i \(-0.572223\pi\)
−0.956305 + 0.292370i \(0.905556\pi\)
\(854\) −8.49038 + 17.4904i −0.290535 + 0.598509i
\(855\) −31.1769 + 18.0000i −1.06623 + 0.615587i
\(856\) 4.00000 4.00000i 0.136717 0.136717i
\(857\) 25.5000 + 14.7224i 0.871063 + 0.502909i 0.867701 0.497086i \(-0.165597\pi\)
0.00336193 + 0.999994i \(0.498930\pi\)
\(858\) −1.09808 4.09808i −0.0374877 0.139906i
\(859\) 18.1865 + 31.5000i 0.620517 + 1.07477i 0.989390 + 0.145286i \(0.0464103\pi\)
−0.368873 + 0.929480i \(0.620256\pi\)
\(860\) 3.00000 1.73205i 0.102299 0.0590624i
\(861\) −37.5000 + 12.9904i −1.27800 + 0.442711i
\(862\) −35.5167 + 9.51666i −1.20970 + 0.324139i
\(863\) 10.0000i 0.340404i −0.985409 0.170202i \(-0.945558\pi\)
0.985409 0.170202i \(-0.0544420\pi\)
\(864\) 28.3923 + 7.60770i 0.965926 + 0.258819i
\(865\) 15.0000 0.510015
\(866\) −23.6603 + 6.33975i −0.804008 + 0.215433i
\(867\) −8.66025 −0.294118
\(868\) −34.6410 30.0000i −1.17579 1.01827i
\(869\) −1.50000 2.59808i −0.0508840 0.0881337i
\(870\) 20.4904 5.49038i 0.694689 0.186141i
\(871\) −12.9904 + 22.5000i −0.440162 + 0.762383i
\(872\) 24.0000 + 24.0000i 0.812743 + 0.812743i
\(873\) −13.5000 7.79423i −0.456906 0.263795i
\(874\) −34.6410 34.6410i −1.17175 1.17175i
\(875\) 6.06218 31.5000i 0.204939 1.06489i
\(876\) −18.0000 31.1769i −0.608164 1.05337i
\(877\) −12.5000 21.6506i −0.422095 0.731090i 0.574049 0.818821i \(-0.305372\pi\)
−0.996144 + 0.0877308i \(0.972038\pi\)
\(878\) −26.0263 6.97372i −0.878344 0.235352i
\(879\) −38.9711 + 22.5000i −1.31446 + 0.758906i
\(880\) 3.46410 6.00000i 0.116775 0.202260i
\(881\) 31.1769i 1.05038i 0.850986 + 0.525188i \(0.176005\pi\)
−0.850986 + 0.525188i \(0.823995\pi\)
\(882\) 3.50962 29.4904i 0.118175 0.992993i
\(883\) 26.0000i 0.874970i 0.899226 + 0.437485i \(0.144131\pi\)
−0.899226 + 0.437485i \(0.855869\pi\)
\(884\) −10.3923 6.00000i −0.349531 0.201802i
\(885\) −22.5000 12.9904i −0.756329 0.436667i
\(886\) −12.8109 + 47.8109i −0.430390 + 1.60624i
\(887\) 4.33013 + 7.50000i 0.145391 + 0.251825i 0.929519 0.368774i \(-0.120223\pi\)
−0.784127 + 0.620600i \(0.786889\pi\)
\(888\) 0 0
\(889\) 9.00000 46.7654i 0.301850 1.56846i
\(890\) −30.0000 + 30.0000i −1.00560 + 1.00560i
\(891\) −7.79423 4.50000i −0.261116 0.150756i
\(892\) 3.46410i 0.115987i
\(893\) −18.0000 + 31.1769i −0.602347 + 1.04330i
\(894\) −12.1244 + 12.1244i −0.405499 + 0.405499i
\(895\) −1.73205 3.00000i −0.0578961 0.100279i
\(896\) 29.8564 2.14359i 0.997433 0.0716124i
\(897\) −7.50000 + 12.9904i −0.250418 + 0.433736i
\(898\) 7.32051 + 27.3205i 0.244289 + 0.911697i
\(899\) −43.3013 −1.44418
\(900\) 12.0000i 0.400000i
\(901\) 13.8564i 0.461624i
\(902\) 3.16987 + 11.8301i 0.105545 + 0.393900i
\(903\) −3.46410 3.00000i −0.115278 0.0998337i
\(904\) 13.9090 51.9090i 0.462605 1.72647i
\(905\) −15.0000 25.9808i −0.498617 0.863630i
\(906\) −6.97372 + 26.0263i −0.231686 + 0.864665i
\(907\) −19.9186 11.5000i −0.661386 0.381851i 0.131419 0.991327i \(-0.458047\pi\)
−0.792805 + 0.609476i \(0.791380\pi\)
\(908\) 10.3923i 0.344881i
\(909\) 31.5000 + 18.1865i 1.04479 + 0.603209i
\(910\) 10.0981 + 4.90192i 0.334748 + 0.162497i
\(911\) −35.5070 20.5000i −1.17640 0.679195i −0.221222 0.975224i \(-0.571004\pi\)
−0.955179 + 0.296028i \(0.904338\pi\)
\(912\) −24.0000 + 41.5692i −0.794719 + 1.37649i
\(913\) −1.50000 + 0.866025i −0.0496428 + 0.0286613i
\(914\) −20.4904 5.49038i −0.677762 0.181606i
\(915\) −15.5885 −0.515339
\(916\) 1.73205 3.00000i 0.0572286 0.0991228i
\(917\) 10.5000 + 30.3109i 0.346741 + 1.00095i
\(918\) −24.5885 + 6.58846i −0.811540 + 0.217451i
\(919\) 50.0000i 1.64935i 0.565608 + 0.824674i \(0.308641\pi\)
−0.565608 + 0.824674i \(0.691359\pi\)
\(920\) −23.6603 + 6.33975i −0.780055 + 0.209015i
\(921\) 24.0000 0.790827
\(922\) −4.43782 + 16.5622i −0.146152 + 0.545446i
\(923\) −3.46410 6.00000i −0.114022 0.197492i
\(924\) −9.00000 1.73205i −0.296078 0.0569803i
\(925\) 0 0
\(926\) 39.0000 + 39.0000i 1.28162 + 1.28162i
\(927\) −12.9904 22.5000i −0.426660 0.738997i
\(928\) 20.0000 20.0000i 0.656532 0.656532i
\(929\) −22.5000 12.9904i −0.738201 0.426201i 0.0832138 0.996532i \(-0.473482\pi\)
−0.821415 + 0.570331i \(0.806815\pi\)
\(930\) 9.50962 35.4904i 0.311833 1.16378i
\(931\) 45.0333 + 18.0000i 1.47591 + 0.589926i
\(932\) 24.2487 14.0000i 0.794293 0.458585i
\(933\) 22.5000 + 38.9711i 0.736617 + 1.27586i
\(934\) −7.60770 28.3923i −0.248931 0.929025i
\(935\) 6.00000i 0.196221i
\(936\) 14.1962 + 3.80385i 0.464016 + 0.124333i
\(937\) 38.1051i 1.24484i −0.782683 0.622420i \(-0.786150\pi\)
0.782683 0.622420i \(-0.213850\pi\)
\(938\) 31.4711 + 46.4711i 1.02757 + 1.51734i
\(939\) 12.9904 + 7.50000i 0.423925 + 0.244753i
\(940\) 9.00000 + 15.5885i 0.293548 + 0.508439i
\(941\) 4.50000 2.59808i 0.146696 0.0846949i −0.424856 0.905261i \(-0.639675\pi\)
0.571551 + 0.820566i \(0.306342\pi\)
\(942\) 9.00000 + 9.00000i 0.293236 + 0.293236i
\(943\) 21.6506 37.5000i 0.705042 1.22117i
\(944\) −34.6410 −1.12747
\(945\) 22.5000 7.79423i 0.731925 0.253546i
\(946\) −1.00000 + 1.00000i −0.0325128 + 0.0325128i
\(947\) 30.3109 + 17.5000i 0.984972 + 0.568674i 0.903767 0.428024i \(-0.140790\pi\)
0.0812041 + 0.996697i \(0.474123\pi\)
\(948\) 10.3923 0.337526
\(949\) −9.00000 15.5885i −0.292152 0.506023i
\(950\) 18.9282 + 5.07180i 0.614112 + 0.164551i
\(951\) −19.9186 + 34.5000i −0.645904 + 1.11874i
\(952\) −21.4641 + 14.5359i −0.695656 + 0.471111i
\(953\) −40.0000 −1.29573 −0.647864 0.761756i \(-0.724337\pi\)
−0.647864 + 0.761756i \(0.724337\pi\)
\(954\) −4.39230 16.3923i −0.142206 0.530720i
\(955\) −8.66025 −0.280239
\(956\) −25.0000 + 43.3013i −0.808558 + 1.40046i
\(957\) −7.50000 + 4.33013i −0.242441 + 0.139973i
\(958\) −44.9545 12.0455i −1.45241 0.389173i
\(959\) −8.66025 + 10.0000i −0.279654 + 0.322917i
\(960\) 12.0000 + 20.7846i 0.387298 + 0.670820i
\(961\) −22.0000 + 38.1051i −0.709677 + 1.22920i
\(962\) 0 0
\(963\) 6.00000i 0.193347i
\(964\) 58.8897 1.89671
\(965\) 13.5000 + 7.79423i 0.434580 + 0.250905i
\(966\) 18.1699 + 26.8301i 0.584606 + 0.863245i
\(967\) −12.9904 + 7.50000i −0.417742 + 0.241184i −0.694111 0.719868i \(-0.744202\pi\)
0.276368 + 0.961052i \(0.410869\pi\)
\(968\) 7.32051 27.3205i 0.235290 0.878114i
\(969\) 41.5692i 1.33540i
\(970\) −3.29423 12.2942i −0.105771 0.394744i
\(971\) 3.46410 0.111168 0.0555842 0.998454i \(-0.482298\pi\)
0.0555842 + 0.998454i \(0.482298\pi\)
\(972\) 27.0000 15.5885i 0.866025 0.500000i
\(973\) −7.50000 21.6506i −0.240439 0.694087i
\(974\) −13.6603 + 3.66025i −0.437703 + 0.117282i
\(975\) 6.00000i 0.192154i
\(976\) −18.0000 + 10.3923i −0.576166 + 0.332650i
\(977\) 2.50000 + 4.33013i 0.0799821 + 0.138533i 0.903242 0.429132i \(-0.141180\pi\)
−0.823260 + 0.567665i \(0.807847\pi\)
\(978\) −14.1962 + 3.80385i −0.453943 + 0.121634i
\(979\) 8.66025 15.0000i 0.276783 0.479402i
\(980\) 19.0526 15.0000i 0.608612 0.479157i
\(981\) 36.0000 1.14939
\(982\) −19.0000 19.0000i −0.606314 0.606314i
\(983\) −0.866025 + 1.50000i −0.0276219 + 0.0478426i −0.879506 0.475888i \(-0.842127\pi\)
0.851884 + 0.523731i \(0.175460\pi\)
\(984\) −40.9808 10.9808i −1.30642 0.350054i
\(985\) −3.00000 + 1.73205i −0.0955879 + 0.0551877i
\(986\) −6.33975 + 23.6603i −0.201899 + 0.753496i
\(987\) 15.5885 18.0000i 0.496186 0.572946i
\(988\) −12.0000 + 20.7846i −0.381771 + 0.661247i
\(989\) 5.00000 0.158991
\(990\) −1.90192 7.09808i −0.0604471 0.225592i
\(991\) 34.0000i 1.08005i 0.841650 + 0.540023i \(0.181584\pi\)
−0.841650 + 0.540023i \(0.818416\pi\)
\(992\) −12.6795 47.3205i −0.402574 1.50243i
\(993\) 43.5000 + 25.1147i 1.38043 + 0.796992i
\(994\) −14.9282 + 1.07180i −0.473494 + 0.0339953i
\(995\) 25.9808 15.0000i 0.823646 0.475532i
\(996\) 6.00000i 0.190117i
\(997\) 22.5000 + 12.9904i 0.712582 + 0.411409i 0.812016 0.583635i \(-0.198370\pi\)
−0.0994342 + 0.995044i \(0.531703\pi\)
\(998\) −7.00000 7.00000i −0.221581 0.221581i
\(999\) 0 0
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 252.2.bi.a.223.1 yes 4
3.2 odd 2 756.2.bi.b.559.2 4
4.3 odd 2 inner 252.2.bi.a.223.2 yes 4
7.6 odd 2 252.2.bi.b.223.1 yes 4
9.4 even 3 252.2.bi.b.139.2 yes 4
9.5 odd 6 756.2.bi.a.307.1 4
12.11 even 2 756.2.bi.b.559.1 4
21.20 even 2 756.2.bi.a.559.2 4
28.27 even 2 252.2.bi.b.223.2 yes 4
36.23 even 6 756.2.bi.a.307.2 4
36.31 odd 6 252.2.bi.b.139.1 yes 4
63.13 odd 6 inner 252.2.bi.a.139.2 yes 4
63.41 even 6 756.2.bi.b.307.1 4
84.83 odd 2 756.2.bi.a.559.1 4
252.139 even 6 inner 252.2.bi.a.139.1 4
252.167 odd 6 756.2.bi.b.307.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.bi.a.139.1 4 252.139 even 6 inner
252.2.bi.a.139.2 yes 4 63.13 odd 6 inner
252.2.bi.a.223.1 yes 4 1.1 even 1 trivial
252.2.bi.a.223.2 yes 4 4.3 odd 2 inner
252.2.bi.b.139.1 yes 4 36.31 odd 6
252.2.bi.b.139.2 yes 4 9.4 even 3
252.2.bi.b.223.1 yes 4 7.6 odd 2
252.2.bi.b.223.2 yes 4 28.27 even 2
756.2.bi.a.307.1 4 9.5 odd 6
756.2.bi.a.307.2 4 36.23 even 6
756.2.bi.a.559.1 4 84.83 odd 2
756.2.bi.a.559.2 4 21.20 even 2
756.2.bi.b.307.1 4 63.41 even 6
756.2.bi.b.307.2 4 252.167 odd 6
756.2.bi.b.559.1 4 12.11 even 2
756.2.bi.b.559.2 4 3.2 odd 2