Properties

Label 38.2.c.b.11.2
Level $38$
Weight $2$
Character 38.11
Analytic conductor $0.303$
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] = [38,2,Mod(7,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 38.c (of order \(3\), 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: \(0.303431527681\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.2
Root \(-1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 38.11
Dual form 38.2.c.b.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +(1.32288 + 2.29129i) q^{6} -1.64575 q^{7} +1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.82288 + 3.15731i) q^{5} +(1.32288 + 2.29129i) q^{6} -1.64575 q^{7} +1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +(-1.82288 - 3.15731i) q^{10} +0.645751 q^{11} -2.64575 q^{12} +(-1.00000 - 1.73205i) q^{13} +(0.822876 - 1.42526i) q^{14} +(4.82288 + 8.35347i) q^{15} +(-0.500000 + 0.866025i) q^{16} +4.00000 q^{18} +(4.32288 + 0.559237i) q^{19} +3.64575 q^{20} +(-2.17712 + 3.77089i) q^{21} +(-0.322876 + 0.559237i) q^{22} +(-1.82288 - 3.15731i) q^{23} +(1.32288 - 2.29129i) q^{24} +(-4.14575 - 7.18065i) q^{25} +2.00000 q^{26} -2.64575 q^{27} +(0.822876 + 1.42526i) q^{28} +(1.82288 + 3.15731i) q^{29} -9.64575 q^{30} -0.354249 q^{31} +(-0.500000 - 0.866025i) q^{32} +(0.854249 - 1.47960i) q^{33} +(3.00000 - 5.19615i) q^{35} +(-2.00000 + 3.46410i) q^{36} +5.64575 q^{37} +(-2.64575 + 3.46410i) q^{38} -5.29150 q^{39} +(-1.82288 + 3.15731i) q^{40} +(-5.14575 + 8.91270i) q^{41} +(-2.17712 - 3.77089i) q^{42} +(-0.354249 + 0.613577i) q^{43} +(-0.322876 - 0.559237i) q^{44} +14.5830 q^{45} +3.64575 q^{46} +(-4.82288 - 8.35347i) q^{47} +(1.32288 + 2.29129i) q^{48} -4.29150 q^{49} +8.29150 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-4.29150 - 7.43310i) q^{53} +(1.32288 - 2.29129i) q^{54} +(-1.17712 + 2.03884i) q^{55} -1.64575 q^{56} +(7.00000 - 9.16515i) q^{57} -3.64575 q^{58} +(-3.96863 + 6.87386i) q^{59} +(4.82288 - 8.35347i) q^{60} +(7.46863 + 12.9360i) q^{61} +(0.177124 - 0.306788i) q^{62} +(3.29150 + 5.70105i) q^{63} +1.00000 q^{64} +7.29150 q^{65} +(0.854249 + 1.47960i) q^{66} +(2.32288 + 4.02334i) q^{67} -9.64575 q^{69} +(3.00000 + 5.19615i) q^{70} +(6.64575 - 11.5108i) q^{71} +(-2.00000 - 3.46410i) q^{72} +(-6.14575 + 10.6448i) q^{73} +(-2.82288 + 4.88936i) q^{74} -21.9373 q^{75} +(-1.67712 - 4.02334i) q^{76} -1.06275 q^{77} +(2.64575 - 4.58258i) q^{78} +(2.00000 - 3.46410i) q^{79} +(-1.82288 - 3.15731i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-5.14575 - 8.91270i) q^{82} -7.93725 q^{83} +4.35425 q^{84} +(-0.354249 - 0.613577i) q^{86} +9.64575 q^{87} +0.645751 q^{88} +(-7.29150 + 12.6293i) q^{90} +(1.64575 + 2.85052i) q^{91} +(-1.82288 + 3.15731i) q^{92} +(-0.468627 + 0.811686i) q^{93} +9.64575 q^{94} +(-9.64575 + 12.6293i) q^{95} -2.64575 q^{96} +(7.14575 - 12.3768i) q^{97} +(2.14575 - 3.71655i) q^{98} +(-1.29150 - 2.23695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} + 4 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - 2 q^{4} - 2 q^{5} + 4 q^{7} + 4 q^{8} - 8 q^{9} - 2 q^{10} - 8 q^{11} - 4 q^{13} - 2 q^{14} + 14 q^{15} - 2 q^{16} + 16 q^{18} + 12 q^{19} + 4 q^{20} - 14 q^{21} + 4 q^{22} - 2 q^{23} - 6 q^{25} + 8 q^{26} - 2 q^{28} + 2 q^{29} - 28 q^{30} - 12 q^{31} - 2 q^{32} + 14 q^{33} + 12 q^{35} - 8 q^{36} + 12 q^{37} - 2 q^{40} - 10 q^{41} - 14 q^{42} - 12 q^{43} + 4 q^{44} + 16 q^{45} + 4 q^{46} - 14 q^{47} + 4 q^{49} + 12 q^{50} - 4 q^{52} + 4 q^{53} - 10 q^{55} + 4 q^{56} + 28 q^{57} - 4 q^{58} + 14 q^{60} + 14 q^{61} + 6 q^{62} - 8 q^{63} + 4 q^{64} + 8 q^{65} + 14 q^{66} + 4 q^{67} - 28 q^{69} + 12 q^{70} + 16 q^{71} - 8 q^{72} - 14 q^{73} - 6 q^{74} - 56 q^{75} - 12 q^{76} - 36 q^{77} + 8 q^{79} - 2 q^{80} + 10 q^{81} - 10 q^{82} + 28 q^{84} - 12 q^{86} + 28 q^{87} - 8 q^{88} - 8 q^{90} - 4 q^{91} - 2 q^{92} + 14 q^{93} + 28 q^{94} - 28 q^{95} + 18 q^{97} - 2 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 1.32288 2.29129i 0.763763 1.32288i −0.177136 0.984186i \(-0.556683\pi\)
0.940898 0.338689i \(-0.109984\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.82288 + 3.15731i −0.815215 + 1.41199i 0.0939588 + 0.995576i \(0.470048\pi\)
−0.909174 + 0.416417i \(0.863286\pi\)
\(6\) 1.32288 + 2.29129i 0.540062 + 0.935414i
\(7\) −1.64575 −0.622036 −0.311018 0.950404i \(-0.600670\pi\)
−0.311018 + 0.950404i \(0.600670\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 3.46410i −0.666667 1.15470i
\(10\) −1.82288 3.15731i −0.576444 0.998430i
\(11\) 0.645751 0.194701 0.0973507 0.995250i \(-0.468963\pi\)
0.0973507 + 0.995250i \(0.468963\pi\)
\(12\) −2.64575 −0.763763
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0.822876 1.42526i 0.219923 0.380917i
\(15\) 4.82288 + 8.35347i 1.24526 + 2.15686i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(18\) 4.00000 0.942809
\(19\) 4.32288 + 0.559237i 0.991736 + 0.128298i
\(20\) 3.64575 0.815215
\(21\) −2.17712 + 3.77089i −0.475087 + 0.822876i
\(22\) −0.322876 + 0.559237i −0.0688373 + 0.119230i
\(23\) −1.82288 3.15731i −0.380096 0.658345i 0.610980 0.791646i \(-0.290776\pi\)
−0.991076 + 0.133301i \(0.957442\pi\)
\(24\) 1.32288 2.29129i 0.270031 0.467707i
\(25\) −4.14575 7.18065i −0.829150 1.43613i
\(26\) 2.00000 0.392232
\(27\) −2.64575 −0.509175
\(28\) 0.822876 + 1.42526i 0.155509 + 0.269349i
\(29\) 1.82288 + 3.15731i 0.338500 + 0.586298i 0.984151 0.177334i \(-0.0567473\pi\)
−0.645651 + 0.763632i \(0.723414\pi\)
\(30\) −9.64575 −1.76107
\(31\) −0.354249 −0.0636249 −0.0318125 0.999494i \(-0.510128\pi\)
−0.0318125 + 0.999494i \(0.510128\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0.854249 1.47960i 0.148706 0.257566i
\(34\) 0 0
\(35\) 3.00000 5.19615i 0.507093 0.878310i
\(36\) −2.00000 + 3.46410i −0.333333 + 0.577350i
\(37\) 5.64575 0.928156 0.464078 0.885794i \(-0.346386\pi\)
0.464078 + 0.885794i \(0.346386\pi\)
\(38\) −2.64575 + 3.46410i −0.429198 + 0.561951i
\(39\) −5.29150 −0.847319
\(40\) −1.82288 + 3.15731i −0.288222 + 0.499215i
\(41\) −5.14575 + 8.91270i −0.803631 + 1.39193i 0.113580 + 0.993529i \(0.463768\pi\)
−0.917211 + 0.398401i \(0.869565\pi\)
\(42\) −2.17712 3.77089i −0.335938 0.581861i
\(43\) −0.354249 + 0.613577i −0.0540224 + 0.0935696i −0.891772 0.452485i \(-0.850538\pi\)
0.837750 + 0.546055i \(0.183871\pi\)
\(44\) −0.322876 0.559237i −0.0486753 0.0843082i
\(45\) 14.5830 2.17391
\(46\) 3.64575 0.537537
\(47\) −4.82288 8.35347i −0.703489 1.21848i −0.967234 0.253886i \(-0.918291\pi\)
0.263745 0.964592i \(-0.415042\pi\)
\(48\) 1.32288 + 2.29129i 0.190941 + 0.330719i
\(49\) −4.29150 −0.613072
\(50\) 8.29150 1.17260
\(51\) 0 0
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) −4.29150 7.43310i −0.589483 1.02101i −0.994300 0.106617i \(-0.965998\pi\)
0.404817 0.914398i \(-0.367335\pi\)
\(54\) 1.32288 2.29129i 0.180021 0.311805i
\(55\) −1.17712 + 2.03884i −0.158723 + 0.274917i
\(56\) −1.64575 −0.219923
\(57\) 7.00000 9.16515i 0.927173 1.21395i
\(58\) −3.64575 −0.478711
\(59\) −3.96863 + 6.87386i −0.516671 + 0.894901i 0.483141 + 0.875542i \(0.339496\pi\)
−0.999813 + 0.0193585i \(0.993838\pi\)
\(60\) 4.82288 8.35347i 0.622631 1.07843i
\(61\) 7.46863 + 12.9360i 0.956260 + 1.65629i 0.731459 + 0.681886i \(0.238840\pi\)
0.224801 + 0.974405i \(0.427827\pi\)
\(62\) 0.177124 0.306788i 0.0224948 0.0389622i
\(63\) 3.29150 + 5.70105i 0.414690 + 0.718265i
\(64\) 1.00000 0.125000
\(65\) 7.29150 0.904400
\(66\) 0.854249 + 1.47960i 0.105151 + 0.182126i
\(67\) 2.32288 + 4.02334i 0.283784 + 0.491529i 0.972314 0.233680i \(-0.0750767\pi\)
−0.688529 + 0.725209i \(0.741743\pi\)
\(68\) 0 0
\(69\) −9.64575 −1.16121
\(70\) 3.00000 + 5.19615i 0.358569 + 0.621059i
\(71\) 6.64575 11.5108i 0.788706 1.36608i −0.138055 0.990425i \(-0.544085\pi\)
0.926760 0.375654i \(-0.122582\pi\)
\(72\) −2.00000 3.46410i −0.235702 0.408248i
\(73\) −6.14575 + 10.6448i −0.719306 + 1.24587i 0.241969 + 0.970284i \(0.422207\pi\)
−0.961275 + 0.275590i \(0.911127\pi\)
\(74\) −2.82288 + 4.88936i −0.328153 + 0.568377i
\(75\) −21.9373 −2.53310
\(76\) −1.67712 4.02334i −0.192379 0.461509i
\(77\) −1.06275 −0.121111
\(78\) 2.64575 4.58258i 0.299572 0.518875i
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) −1.82288 3.15731i −0.203804 0.352998i
\(81\) 2.50000 4.33013i 0.277778 0.481125i
\(82\) −5.14575 8.91270i −0.568253 0.984243i
\(83\) −7.93725 −0.871227 −0.435613 0.900134i \(-0.643469\pi\)
−0.435613 + 0.900134i \(0.643469\pi\)
\(84\) 4.35425 0.475087
\(85\) 0 0
\(86\) −0.354249 0.613577i −0.0381996 0.0661637i
\(87\) 9.64575 1.03413
\(88\) 0.645751 0.0688373
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) −7.29150 + 12.6293i −0.768592 + 1.33124i
\(91\) 1.64575 + 2.85052i 0.172522 + 0.298816i
\(92\) −1.82288 + 3.15731i −0.190048 + 0.329173i
\(93\) −0.468627 + 0.811686i −0.0485944 + 0.0841679i
\(94\) 9.64575 0.994883
\(95\) −9.64575 + 12.6293i −0.989633 + 1.29573i
\(96\) −2.64575 −0.270031
\(97\) 7.14575 12.3768i 0.725541 1.25667i −0.233210 0.972426i \(-0.574923\pi\)
0.958751 0.284248i \(-0.0917438\pi\)
\(98\) 2.14575 3.71655i 0.216754 0.375428i
\(99\) −1.29150 2.23695i −0.129801 0.224822i
\(100\) −4.14575 + 7.18065i −0.414575 + 0.718065i
\(101\) 4.17712 + 7.23499i 0.415639 + 0.719909i 0.995495 0.0948105i \(-0.0302245\pi\)
−0.579856 + 0.814719i \(0.696891\pi\)
\(102\) 0 0
\(103\) −2.70850 −0.266876 −0.133438 0.991057i \(-0.542602\pi\)
−0.133438 + 0.991057i \(0.542602\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) −7.93725 13.7477i −0.774597 1.34164i
\(106\) 8.58301 0.833655
\(107\) 4.70850 0.455188 0.227594 0.973756i \(-0.426914\pi\)
0.227594 + 0.973756i \(0.426914\pi\)
\(108\) 1.32288 + 2.29129i 0.127294 + 0.220479i
\(109\) 3.29150 5.70105i 0.315269 0.546062i −0.664226 0.747532i \(-0.731239\pi\)
0.979495 + 0.201470i \(0.0645720\pi\)
\(110\) −1.17712 2.03884i −0.112234 0.194396i
\(111\) 7.46863 12.9360i 0.708891 1.22783i
\(112\) 0.822876 1.42526i 0.0777544 0.134675i
\(113\) 5.58301 0.525205 0.262602 0.964904i \(-0.415419\pi\)
0.262602 + 0.964904i \(0.415419\pi\)
\(114\) 4.43725 + 10.6448i 0.415587 + 0.996973i
\(115\) 13.2915 1.23944
\(116\) 1.82288 3.15731i 0.169250 0.293149i
\(117\) −4.00000 + 6.92820i −0.369800 + 0.640513i
\(118\) −3.96863 6.87386i −0.365342 0.632790i
\(119\) 0 0
\(120\) 4.82288 + 8.35347i 0.440266 + 0.762564i
\(121\) −10.5830 −0.962091
\(122\) −14.9373 −1.35236
\(123\) 13.6144 + 23.5808i 1.22757 + 2.12621i
\(124\) 0.177124 + 0.306788i 0.0159062 + 0.0275504i
\(125\) 12.0000 1.07331
\(126\) −6.58301 −0.586461
\(127\) 1.35425 + 2.34563i 0.120170 + 0.208141i 0.919835 0.392306i \(-0.128323\pi\)
−0.799665 + 0.600447i \(0.794989\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0.937254 + 1.62337i 0.0825206 + 0.142930i
\(130\) −3.64575 + 6.31463i −0.319754 + 0.553829i
\(131\) 6.96863 12.0700i 0.608852 1.05456i −0.382578 0.923923i \(-0.624964\pi\)
0.991430 0.130639i \(-0.0417029\pi\)
\(132\) −1.70850 −0.148706
\(133\) −7.11438 0.920365i −0.616895 0.0798058i
\(134\) −4.64575 −0.401332
\(135\) 4.82288 8.35347i 0.415087 0.718952i
\(136\) 0 0
\(137\) 2.79150 + 4.83502i 0.238494 + 0.413084i 0.960282 0.279030i \(-0.0900129\pi\)
−0.721788 + 0.692114i \(0.756680\pi\)
\(138\) 4.82288 8.35347i 0.410550 0.711094i
\(139\) −6.67712 11.5651i −0.566346 0.980941i −0.996923 0.0783866i \(-0.975023\pi\)
0.430577 0.902554i \(-0.358310\pi\)
\(140\) −6.00000 −0.507093
\(141\) −25.5203 −2.14919
\(142\) 6.64575 + 11.5108i 0.557699 + 0.965963i
\(143\) −0.645751 1.11847i −0.0540004 0.0935315i
\(144\) 4.00000 0.333333
\(145\) −13.2915 −1.10380
\(146\) −6.14575 10.6448i −0.508626 0.880966i
\(147\) −5.67712 + 9.83307i −0.468241 + 0.811018i
\(148\) −2.82288 4.88936i −0.232039 0.401903i
\(149\) 2.46863 4.27579i 0.202238 0.350286i −0.747011 0.664811i \(-0.768512\pi\)
0.949249 + 0.314525i \(0.101845\pi\)
\(150\) 10.9686 18.9982i 0.895585 1.55120i
\(151\) −2.93725 −0.239030 −0.119515 0.992832i \(-0.538134\pi\)
−0.119515 + 0.992832i \(0.538134\pi\)
\(152\) 4.32288 + 0.559237i 0.350632 + 0.0453601i
\(153\) 0 0
\(154\) 0.531373 0.920365i 0.0428193 0.0741651i
\(155\) 0.645751 1.11847i 0.0518680 0.0898380i
\(156\) 2.64575 + 4.58258i 0.211830 + 0.366900i
\(157\) −5.29150 + 9.16515i −0.422308 + 0.731459i −0.996165 0.0874969i \(-0.972113\pi\)
0.573857 + 0.818956i \(0.305447\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) −22.7085 −1.80090
\(160\) 3.64575 0.288222
\(161\) 3.00000 + 5.19615i 0.236433 + 0.409514i
\(162\) 2.50000 + 4.33013i 0.196419 + 0.340207i
\(163\) −11.9373 −0.934998 −0.467499 0.883994i \(-0.654845\pi\)
−0.467499 + 0.883994i \(0.654845\pi\)
\(164\) 10.2915 0.803631
\(165\) 3.11438 + 5.39426i 0.242454 + 0.419943i
\(166\) 3.96863 6.87386i 0.308025 0.533515i
\(167\) 6.00000 + 10.3923i 0.464294 + 0.804181i 0.999169 0.0407502i \(-0.0129748\pi\)
−0.534875 + 0.844931i \(0.679641\pi\)
\(168\) −2.17712 + 3.77089i −0.167969 + 0.290930i
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) −6.70850 16.0934i −0.513012 1.23069i
\(172\) 0.708497 0.0540224
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) −4.82288 + 8.35347i −0.365621 + 0.633275i
\(175\) 6.82288 + 11.8176i 0.515761 + 0.893324i
\(176\) −0.322876 + 0.559237i −0.0243377 + 0.0421541i
\(177\) 10.5000 + 18.1865i 0.789228 + 1.36698i
\(178\) 0 0
\(179\) 19.9373 1.49018 0.745090 0.666964i \(-0.232406\pi\)
0.745090 + 0.666964i \(0.232406\pi\)
\(180\) −7.29150 12.6293i −0.543477 0.941329i
\(181\) 2.11438 + 3.66221i 0.157160 + 0.272210i 0.933844 0.357682i \(-0.116433\pi\)
−0.776683 + 0.629892i \(0.783099\pi\)
\(182\) −3.29150 −0.243982
\(183\) 39.5203 2.92142
\(184\) −1.82288 3.15731i −0.134384 0.232760i
\(185\) −10.2915 + 17.8254i −0.756646 + 1.31055i
\(186\) −0.468627 0.811686i −0.0343614 0.0595157i
\(187\) 0 0
\(188\) −4.82288 + 8.35347i −0.351744 + 0.609239i
\(189\) 4.35425 0.316725
\(190\) −6.11438 14.6681i −0.443584 1.06414i
\(191\) −14.5830 −1.05519 −0.527595 0.849496i \(-0.676906\pi\)
−0.527595 + 0.849496i \(0.676906\pi\)
\(192\) 1.32288 2.29129i 0.0954703 0.165359i
\(193\) 3.29150 5.70105i 0.236928 0.410371i −0.722904 0.690949i \(-0.757193\pi\)
0.959831 + 0.280578i \(0.0905263\pi\)
\(194\) 7.14575 + 12.3768i 0.513035 + 0.888603i
\(195\) 9.64575 16.7069i 0.690747 1.19641i
\(196\) 2.14575 + 3.71655i 0.153268 + 0.265468i
\(197\) −2.35425 −0.167733 −0.0838666 0.996477i \(-0.526727\pi\)
−0.0838666 + 0.996477i \(0.526727\pi\)
\(198\) 2.58301 0.183566
\(199\) −5.93725 10.2836i −0.420881 0.728987i 0.575145 0.818051i \(-0.304946\pi\)
−0.996026 + 0.0890645i \(0.971612\pi\)
\(200\) −4.14575 7.18065i −0.293149 0.507749i
\(201\) 12.2915 0.866976
\(202\) −8.35425 −0.587803
\(203\) −3.00000 5.19615i −0.210559 0.364698i
\(204\) 0 0
\(205\) −18.7601 32.4935i −1.31026 2.26944i
\(206\) 1.35425 2.34563i 0.0943550 0.163428i
\(207\) −7.29150 + 12.6293i −0.506794 + 0.877794i
\(208\) 2.00000 0.138675
\(209\) 2.79150 + 0.361128i 0.193092 + 0.0249797i
\(210\) 15.8745 1.09545
\(211\) 1.35425 2.34563i 0.0932303 0.161480i −0.815638 0.578562i \(-0.803614\pi\)
0.908869 + 0.417082i \(0.136947\pi\)
\(212\) −4.29150 + 7.43310i −0.294742 + 0.510507i
\(213\) −17.5830 30.4547i −1.20477 2.08672i
\(214\) −2.35425 + 4.07768i −0.160933 + 0.278744i
\(215\) −1.29150 2.23695i −0.0880797 0.152559i
\(216\) −2.64575 −0.180021
\(217\) 0.583005 0.0395770
\(218\) 3.29150 + 5.70105i 0.222929 + 0.386124i
\(219\) 16.2601 + 28.1634i 1.09876 + 1.90310i
\(220\) 2.35425 0.158723
\(221\) 0 0
\(222\) 7.46863 + 12.9360i 0.501261 + 0.868210i
\(223\) −14.4059 + 24.9517i −0.964689 + 1.67089i −0.254241 + 0.967141i \(0.581826\pi\)
−0.710448 + 0.703750i \(0.751508\pi\)
\(224\) 0.822876 + 1.42526i 0.0549807 + 0.0952294i
\(225\) −16.5830 + 28.7226i −1.10553 + 1.91484i
\(226\) −2.79150 + 4.83502i −0.185688 + 0.321621i
\(227\) −12.6458 −0.839328 −0.419664 0.907680i \(-0.637852\pi\)
−0.419664 + 0.907680i \(0.637852\pi\)
\(228\) −11.4373 1.47960i −0.757451 0.0979890i
\(229\) 20.0000 1.32164 0.660819 0.750546i \(-0.270209\pi\)
0.660819 + 0.750546i \(0.270209\pi\)
\(230\) −6.64575 + 11.5108i −0.438208 + 0.758998i
\(231\) −1.40588 + 2.43506i −0.0925002 + 0.160215i
\(232\) 1.82288 + 3.15731i 0.119678 + 0.207288i
\(233\) 6.43725 11.1497i 0.421719 0.730438i −0.574389 0.818582i \(-0.694760\pi\)
0.996108 + 0.0881444i \(0.0280937\pi\)
\(234\) −4.00000 6.92820i −0.261488 0.452911i
\(235\) 35.1660 2.29398
\(236\) 7.93725 0.516671
\(237\) −5.29150 9.16515i −0.343720 0.595341i
\(238\) 0 0
\(239\) −12.0000 −0.776215 −0.388108 0.921614i \(-0.626871\pi\)
−0.388108 + 0.921614i \(0.626871\pi\)
\(240\) −9.64575 −0.622631
\(241\) −6.79150 11.7632i −0.437479 0.757736i 0.560015 0.828482i \(-0.310795\pi\)
−0.997494 + 0.0707462i \(0.977462\pi\)
\(242\) 5.29150 9.16515i 0.340151 0.589158i
\(243\) −10.5830 18.3303i −0.678900 1.17589i
\(244\) 7.46863 12.9360i 0.478130 0.828145i
\(245\) 7.82288 13.5496i 0.499785 0.865653i
\(246\) −27.2288 −1.73604
\(247\) −3.35425 8.04668i −0.213426 0.511998i
\(248\) −0.354249 −0.0224948
\(249\) −10.5000 + 18.1865i −0.665410 + 1.15252i
\(250\) −6.00000 + 10.3923i −0.379473 + 0.657267i
\(251\) −1.38562 2.39997i −0.0874597 0.151485i 0.818977 0.573826i \(-0.194542\pi\)
−0.906437 + 0.422342i \(0.861208\pi\)
\(252\) 3.29150 5.70105i 0.207345 0.359132i
\(253\) −1.17712 2.03884i −0.0740052 0.128181i
\(254\) −2.70850 −0.169946
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −0.854249 1.47960i −0.0532866 0.0922950i 0.838152 0.545437i \(-0.183636\pi\)
−0.891438 + 0.453142i \(0.850303\pi\)
\(258\) −1.87451 −0.116702
\(259\) −9.29150 −0.577346
\(260\) −3.64575 6.31463i −0.226100 0.391617i
\(261\) 7.29150 12.6293i 0.451333 0.781731i
\(262\) 6.96863 + 12.0700i 0.430523 + 0.745688i
\(263\) −2.46863 + 4.27579i −0.152222 + 0.263656i −0.932044 0.362345i \(-0.881976\pi\)
0.779822 + 0.626001i \(0.215310\pi\)
\(264\) 0.854249 1.47960i 0.0525754 0.0910632i
\(265\) 31.2915 1.92222
\(266\) 4.35425 5.70105i 0.266976 0.349554i
\(267\) 0 0
\(268\) 2.32288 4.02334i 0.141892 0.245765i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 4.82288 + 8.35347i 0.293511 + 0.508376i
\(271\) −8.82288 + 15.2817i −0.535952 + 0.928295i 0.463165 + 0.886272i \(0.346714\pi\)
−0.999117 + 0.0420233i \(0.986620\pi\)
\(272\) 0 0
\(273\) 8.70850 0.527062
\(274\) −5.58301 −0.337282
\(275\) −2.67712 4.63692i −0.161437 0.279617i
\(276\) 4.82288 + 8.35347i 0.290303 + 0.502820i
\(277\) 9.52026 0.572017 0.286008 0.958227i \(-0.407671\pi\)
0.286008 + 0.958227i \(0.407671\pi\)
\(278\) 13.3542 0.800935
\(279\) 0.708497 + 1.22715i 0.0424166 + 0.0734678i
\(280\) 3.00000 5.19615i 0.179284 0.310530i
\(281\) 13.7288 + 23.7789i 0.818989 + 1.41853i 0.906428 + 0.422361i \(0.138798\pi\)
−0.0874389 + 0.996170i \(0.527868\pi\)
\(282\) 12.7601 22.1012i 0.759855 1.31611i
\(283\) −12.6771 + 21.9574i −0.753577 + 1.30523i 0.192502 + 0.981297i \(0.438340\pi\)
−0.946079 + 0.323937i \(0.894993\pi\)
\(284\) −13.2915 −0.788706
\(285\) 16.1771 + 38.8081i 0.958250 + 2.29879i
\(286\) 1.29150 0.0763682
\(287\) 8.46863 14.6681i 0.499887 0.865830i
\(288\) −2.00000 + 3.46410i −0.117851 + 0.204124i
\(289\) 8.50000 + 14.7224i 0.500000 + 0.866025i
\(290\) 6.64575 11.5108i 0.390252 0.675936i
\(291\) −18.9059 32.7459i −1.10828 1.91960i
\(292\) 12.2915 0.719306
\(293\) 13.0627 0.763134 0.381567 0.924341i \(-0.375385\pi\)
0.381567 + 0.924341i \(0.375385\pi\)
\(294\) −5.67712 9.83307i −0.331097 0.573476i
\(295\) −14.4686 25.0604i −0.842396 1.45907i
\(296\) 5.64575 0.328153
\(297\) −1.70850 −0.0991371
\(298\) 2.46863 + 4.27579i 0.143004 + 0.247690i
\(299\) −3.64575 + 6.31463i −0.210839 + 0.365184i
\(300\) 10.9686 + 18.9982i 0.633274 + 1.09686i
\(301\) 0.583005 1.00979i 0.0336039 0.0582036i
\(302\) 1.46863 2.54374i 0.0845100 0.146376i
\(303\) 22.1033 1.26980
\(304\) −2.64575 + 3.46410i −0.151744 + 0.198680i
\(305\) −54.4575 −3.11823
\(306\) 0 0
\(307\) 2.32288 4.02334i 0.132574 0.229624i −0.792094 0.610399i \(-0.791009\pi\)
0.924668 + 0.380775i \(0.124343\pi\)
\(308\) 0.531373 + 0.920365i 0.0302778 + 0.0524427i
\(309\) −3.58301 + 6.20595i −0.203830 + 0.353044i
\(310\) 0.645751 + 1.11847i 0.0366762 + 0.0635251i
\(311\) 8.35425 0.473726 0.236863 0.971543i \(-0.423881\pi\)
0.236863 + 0.971543i \(0.423881\pi\)
\(312\) −5.29150 −0.299572
\(313\) 11.4373 + 19.8099i 0.646472 + 1.11972i 0.983959 + 0.178392i \(0.0570895\pi\)
−0.337488 + 0.941330i \(0.609577\pi\)
\(314\) −5.29150 9.16515i −0.298617 0.517219i
\(315\) −24.0000 −1.35225
\(316\) −4.00000 −0.225018
\(317\) 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i \(-0.112775\pi\)
−0.769395 + 0.638774i \(0.779442\pi\)
\(318\) 11.3542 19.6661i 0.636715 1.10282i
\(319\) 1.17712 + 2.03884i 0.0659063 + 0.114153i
\(320\) −1.82288 + 3.15731i −0.101902 + 0.176499i
\(321\) 6.22876 10.7885i 0.347655 0.602157i
\(322\) −6.00000 −0.334367
\(323\) 0 0
\(324\) −5.00000 −0.277778
\(325\) −8.29150 + 14.3613i −0.459930 + 0.796622i
\(326\) 5.96863 10.3380i 0.330572 0.572567i
\(327\) −8.70850 15.0836i −0.481581 0.834123i
\(328\) −5.14575 + 8.91270i −0.284127 + 0.492122i
\(329\) 7.93725 + 13.7477i 0.437595 + 0.757937i
\(330\) −6.22876 −0.342882
\(331\) −27.8118 −1.52867 −0.764336 0.644818i \(-0.776933\pi\)
−0.764336 + 0.644818i \(0.776933\pi\)
\(332\) 3.96863 + 6.87386i 0.217807 + 0.377252i
\(333\) −11.2915 19.5575i −0.618771 1.07174i
\(334\) −12.0000 −0.656611
\(335\) −16.9373 −0.925381
\(336\) −2.17712 3.77089i −0.118772 0.205719i
\(337\) 10.1458 17.5730i 0.552674 0.957260i −0.445406 0.895329i \(-0.646941\pi\)
0.998080 0.0619313i \(-0.0197260\pi\)
\(338\) 4.50000 + 7.79423i 0.244768 + 0.423950i
\(339\) 7.38562 12.7923i 0.401132 0.694781i
\(340\) 0 0
\(341\) −0.228757 −0.0123879
\(342\) 17.2915 + 2.23695i 0.935017 + 0.120960i
\(343\) 18.5830 1.00339
\(344\) −0.354249 + 0.613577i −0.0190998 + 0.0330818i
\(345\) 17.5830 30.4547i 0.946637 1.63962i
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) −1.61438 + 2.79619i −0.0866644 + 0.150107i −0.906099 0.423065i \(-0.860954\pi\)
0.819435 + 0.573172i \(0.194287\pi\)
\(348\) −4.82288 8.35347i −0.258533 0.447793i
\(349\) −21.1660 −1.13299 −0.566495 0.824065i \(-0.691701\pi\)
−0.566495 + 0.824065i \(0.691701\pi\)
\(350\) −13.6458 −0.729396
\(351\) 2.64575 + 4.58258i 0.141220 + 0.244600i
\(352\) −0.322876 0.559237i −0.0172093 0.0298074i
\(353\) −18.8745 −1.00459 −0.502294 0.864697i \(-0.667511\pi\)
−0.502294 + 0.864697i \(0.667511\pi\)
\(354\) −21.0000 −1.11614
\(355\) 24.2288 + 41.9654i 1.28593 + 2.22729i
\(356\) 0 0
\(357\) 0 0
\(358\) −9.96863 + 17.2662i −0.526858 + 0.912545i
\(359\) −5.46863 + 9.47194i −0.288623 + 0.499910i −0.973481 0.228766i \(-0.926531\pi\)
0.684858 + 0.728676i \(0.259864\pi\)
\(360\) 14.5830 0.768592
\(361\) 18.3745 + 4.83502i 0.967079 + 0.254475i
\(362\) −4.22876 −0.222259
\(363\) −14.0000 + 24.2487i −0.734809 + 1.27273i
\(364\) 1.64575 2.85052i 0.0862608 0.149408i
\(365\) −22.4059 38.8081i −1.17278 2.03131i
\(366\) −19.7601 + 34.2255i −1.03288 + 1.78900i
\(367\) 5.11438 + 8.85836i 0.266968 + 0.462403i 0.968077 0.250651i \(-0.0806447\pi\)
−0.701109 + 0.713054i \(0.747311\pi\)
\(368\) 3.64575 0.190048
\(369\) 41.1660 2.14302
\(370\) −10.2915 17.8254i −0.535030 0.926699i
\(371\) 7.06275 + 12.2330i 0.366680 + 0.635108i
\(372\) 0.937254 0.0485944
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 15.8745 27.4955i 0.819756 1.41986i
\(376\) −4.82288 8.35347i −0.248721 0.430797i
\(377\) 3.64575 6.31463i 0.187766 0.325220i
\(378\) −2.17712 + 3.77089i −0.111979 + 0.193954i
\(379\) 21.2915 1.09367 0.546836 0.837240i \(-0.315832\pi\)
0.546836 + 0.837240i \(0.315832\pi\)
\(380\) 15.7601 + 2.03884i 0.808478 + 0.104590i
\(381\) 7.16601 0.367126
\(382\) 7.29150 12.6293i 0.373066 0.646169i
\(383\) 15.7601 27.2973i 0.805305 1.39483i −0.110780 0.993845i \(-0.535335\pi\)
0.916085 0.400984i \(-0.131332\pi\)
\(384\) 1.32288 + 2.29129i 0.0675077 + 0.116927i
\(385\) 1.93725 3.35542i 0.0987316 0.171008i
\(386\) 3.29150 + 5.70105i 0.167533 + 0.290176i
\(387\) 2.83399 0.144060
\(388\) −14.2915 −0.725541
\(389\) −6.00000 10.3923i −0.304212 0.526911i 0.672874 0.739758i \(-0.265060\pi\)
−0.977086 + 0.212847i \(0.931726\pi\)
\(390\) 9.64575 + 16.7069i 0.488432 + 0.845988i
\(391\) 0 0
\(392\) −4.29150 −0.216754
\(393\) −18.4373 31.9343i −0.930036 1.61087i
\(394\) 1.17712 2.03884i 0.0593027 0.102715i
\(395\) 7.29150 + 12.6293i 0.366875 + 0.635447i
\(396\) −1.29150 + 2.23695i −0.0649004 + 0.112411i
\(397\) −18.4686 + 31.9886i −0.926914 + 1.60546i −0.138460 + 0.990368i \(0.544215\pi\)
−0.788454 + 0.615094i \(0.789118\pi\)
\(398\) 11.8745 0.595215
\(399\) −11.5203 + 15.0836i −0.576734 + 0.755122i
\(400\) 8.29150 0.414575
\(401\) −3.20850 + 5.55728i −0.160225 + 0.277517i −0.934949 0.354782i \(-0.884555\pi\)
0.774724 + 0.632299i \(0.217889\pi\)
\(402\) −6.14575 + 10.6448i −0.306522 + 0.530912i
\(403\) 0.354249 + 0.613577i 0.0176464 + 0.0305644i
\(404\) 4.17712 7.23499i 0.207820 0.359954i
\(405\) 9.11438 + 15.7866i 0.452897 + 0.784441i
\(406\) 6.00000 0.297775
\(407\) 3.64575 0.180713
\(408\) 0 0
\(409\) −6.79150 11.7632i −0.335818 0.581654i 0.647823 0.761790i \(-0.275679\pi\)
−0.983642 + 0.180136i \(0.942346\pi\)
\(410\) 37.5203 1.85299
\(411\) 14.7712 0.728612
\(412\) 1.35425 + 2.34563i 0.0667190 + 0.115561i
\(413\) 6.53137 11.3127i 0.321388 0.556660i
\(414\) −7.29150 12.6293i −0.358358 0.620694i
\(415\) 14.4686 25.0604i 0.710237 1.23017i
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) −35.3320 −1.73022
\(418\) −1.70850 + 2.23695i −0.0835653 + 0.109413i
\(419\) 31.7490 1.55104 0.775520 0.631322i \(-0.217488\pi\)
0.775520 + 0.631322i \(0.217488\pi\)
\(420\) −7.93725 + 13.7477i −0.387298 + 0.670820i
\(421\) −11.4059 + 19.7556i −0.555889 + 0.962827i 0.441945 + 0.897042i \(0.354289\pi\)
−0.997834 + 0.0657853i \(0.979045\pi\)
\(422\) 1.35425 + 2.34563i 0.0659238 + 0.114183i
\(423\) −19.2915 + 33.4139i −0.937985 + 1.62464i
\(424\) −4.29150 7.43310i −0.208414 0.360983i
\(425\) 0 0
\(426\) 35.1660 1.70380
\(427\) −12.2915 21.2895i −0.594828 1.03027i
\(428\) −2.35425 4.07768i −0.113797 0.197102i
\(429\) −3.41699 −0.164974
\(430\) 2.58301 0.124564
\(431\) 1.93725 + 3.35542i 0.0933142 + 0.161625i 0.908904 0.417006i \(-0.136921\pi\)
−0.815590 + 0.578631i \(0.803587\pi\)
\(432\) 1.32288 2.29129i 0.0636469 0.110240i
\(433\) 6.93725 + 12.0157i 0.333383 + 0.577437i 0.983173 0.182677i \(-0.0584764\pi\)
−0.649790 + 0.760114i \(0.725143\pi\)
\(434\) −0.291503 + 0.504897i −0.0139926 + 0.0242358i
\(435\) −17.5830 + 30.4547i −0.843041 + 1.46019i
\(436\) −6.58301 −0.315269
\(437\) −6.11438 14.6681i −0.292490 0.701670i
\(438\) −32.5203 −1.55388
\(439\) 18.4059 31.8799i 0.878465 1.52155i 0.0254393 0.999676i \(-0.491902\pi\)
0.853025 0.521869i \(-0.174765\pi\)
\(440\) −1.17712 + 2.03884i −0.0561172 + 0.0971978i
\(441\) 8.58301 + 14.8662i 0.408715 + 0.707914i
\(442\) 0 0
\(443\) −2.67712 4.63692i −0.127194 0.220306i 0.795394 0.606092i \(-0.207264\pi\)
−0.922588 + 0.385786i \(0.873930\pi\)
\(444\) −14.9373 −0.708891
\(445\) 0 0
\(446\) −14.4059 24.9517i −0.682138 1.18150i
\(447\) −6.53137 11.3127i −0.308923 0.535071i
\(448\) −1.64575 −0.0777544
\(449\) −13.7085 −0.646944 −0.323472 0.946238i \(-0.604850\pi\)
−0.323472 + 0.946238i \(0.604850\pi\)
\(450\) −16.5830 28.7226i −0.781730 1.35400i
\(451\) −3.32288 + 5.75539i −0.156468 + 0.271011i
\(452\) −2.79150 4.83502i −0.131301 0.227420i
\(453\) −3.88562 + 6.73009i −0.182562 + 0.316207i
\(454\) 6.32288 10.9515i 0.296747 0.513981i
\(455\) −12.0000 −0.562569
\(456\) 7.00000 9.16515i 0.327805 0.429198i
\(457\) 1.12549 0.0526483 0.0263242 0.999653i \(-0.491620\pi\)
0.0263242 + 0.999653i \(0.491620\pi\)
\(458\) −10.0000 + 17.3205i −0.467269 + 0.809334i
\(459\) 0 0
\(460\) −6.64575 11.5108i −0.309860 0.536693i
\(461\) 11.5830 20.0624i 0.539474 0.934397i −0.459458 0.888200i \(-0.651956\pi\)
0.998932 0.0461975i \(-0.0147103\pi\)
\(462\) −1.40588 2.43506i −0.0654075 0.113289i
\(463\) 14.4575 0.671898 0.335949 0.941880i \(-0.390943\pi\)
0.335949 + 0.941880i \(0.390943\pi\)
\(464\) −3.64575 −0.169250
\(465\) −1.70850 2.95920i −0.0792297 0.137230i
\(466\) 6.43725 + 11.1497i 0.298200 + 0.516498i
\(467\) −24.6458 −1.14047 −0.570235 0.821482i \(-0.693148\pi\)
−0.570235 + 0.821482i \(0.693148\pi\)
\(468\) 8.00000 0.369800
\(469\) −3.82288 6.62141i −0.176524 0.305749i
\(470\) −17.5830 + 30.4547i −0.811044 + 1.40477i
\(471\) 14.0000 + 24.2487i 0.645086 + 1.11732i
\(472\) −3.96863 + 6.87386i −0.182671 + 0.316395i
\(473\) −0.228757 + 0.396218i −0.0105182 + 0.0182181i
\(474\) 10.5830 0.486094
\(475\) −13.9059 33.3595i −0.638046 1.53064i
\(476\) 0 0
\(477\) −17.1660 + 29.7324i −0.785978 + 1.36135i
\(478\) 6.00000 10.3923i 0.274434 0.475333i
\(479\) 7.29150 + 12.6293i 0.333157 + 0.577045i 0.983129 0.182913i \(-0.0585527\pi\)
−0.649972 + 0.759958i \(0.725219\pi\)
\(480\) 4.82288 8.35347i 0.220133 0.381282i
\(481\) −5.64575 9.77873i −0.257424 0.445872i
\(482\) 13.5830 0.618689
\(483\) 15.8745 0.722315
\(484\) 5.29150 + 9.16515i 0.240523 + 0.416598i
\(485\) 26.0516 + 45.1228i 1.18294 + 2.04892i
\(486\) 21.1660 0.960110
\(487\) −22.2288 −1.00728 −0.503641 0.863913i \(-0.668006\pi\)
−0.503641 + 0.863913i \(0.668006\pi\)
\(488\) 7.46863 + 12.9360i 0.338089 + 0.585587i
\(489\) −15.7915 + 27.3517i −0.714116 + 1.23689i
\(490\) 7.82288 + 13.5496i 0.353401 + 0.612109i
\(491\) −14.3542 + 24.8623i −0.647798 + 1.12202i 0.335849 + 0.941916i \(0.390977\pi\)
−0.983648 + 0.180104i \(0.942357\pi\)
\(492\) 13.6144 23.5808i 0.613784 1.06310i
\(493\) 0 0
\(494\) 8.64575 + 1.11847i 0.388991 + 0.0503225i
\(495\) 9.41699 0.423262
\(496\) 0.177124 0.306788i 0.00795312 0.0137752i
\(497\) −10.9373 + 18.9439i −0.490603 + 0.849749i
\(498\) −10.5000 18.1865i −0.470516 0.814958i
\(499\) 15.6144 27.0449i 0.698996 1.21070i −0.269819 0.962911i \(-0.586964\pi\)
0.968815 0.247785i \(-0.0797026\pi\)
\(500\) −6.00000 10.3923i −0.268328 0.464758i
\(501\) 31.7490 1.41844
\(502\) 2.77124 0.123687
\(503\) 12.5314 + 21.7050i 0.558746 + 0.967777i 0.997601 + 0.0692192i \(0.0220508\pi\)
−0.438855 + 0.898558i \(0.644616\pi\)
\(504\) 3.29150 + 5.70105i 0.146615 + 0.253945i
\(505\) −30.4575 −1.35534
\(506\) 2.35425 0.104659
\(507\) −11.9059 20.6216i −0.528759 0.915837i
\(508\) 1.35425 2.34563i 0.0600851 0.104070i
\(509\) −15.8745 27.4955i −0.703625 1.21871i −0.967185 0.254072i \(-0.918230\pi\)
0.263560 0.964643i \(-0.415103\pi\)
\(510\) 0 0
\(511\) 10.1144 17.5186i 0.447434 0.774978i
\(512\) 1.00000 0.0441942
\(513\) −11.4373 1.47960i −0.504967 0.0653260i
\(514\) 1.70850 0.0753586
\(515\) 4.93725 8.55157i 0.217561 0.376827i
\(516\) 0.937254 1.62337i 0.0412603 0.0714649i
\(517\) −3.11438 5.39426i −0.136970 0.237239i
\(518\) 4.64575 8.04668i 0.204123 0.353551i
\(519\) −7.93725 13.7477i −0.348407 0.603458i
\(520\) 7.29150 0.319754
\(521\) −22.2915 −0.976608 −0.488304 0.872673i \(-0.662384\pi\)
−0.488304 + 0.872673i \(0.662384\pi\)
\(522\) 7.29150 + 12.6293i 0.319140 + 0.552767i
\(523\) −14.9373 25.8721i −0.653161 1.13131i −0.982352 0.187044i \(-0.940109\pi\)
0.329191 0.944263i \(-0.393224\pi\)
\(524\) −13.9373 −0.608852
\(525\) 36.1033 1.57568
\(526\) −2.46863 4.27579i −0.107637 0.186433i
\(527\) 0 0
\(528\) 0.854249 + 1.47960i 0.0371764 + 0.0643914i
\(529\) 4.85425 8.40781i 0.211054 0.365557i
\(530\) −15.6458 + 27.0992i −0.679608 + 1.17712i
\(531\) 31.7490 1.37779
\(532\) 2.76013 + 6.62141i 0.119667 + 0.287075i
\(533\) 20.5830 0.891549
\(534\) 0 0
\(535\) −8.58301 + 14.8662i −0.371076 + 0.642722i
\(536\) 2.32288 + 4.02334i 0.100333 + 0.173782i
\(537\) 26.3745 45.6820i 1.13814 1.97132i
\(538\) 0 0
\(539\) −2.77124 −0.119366
\(540\) −9.64575 −0.415087
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) −8.82288 15.2817i −0.378975 0.656404i
\(543\) 11.1882 0.480133
\(544\) 0 0
\(545\) 12.0000 + 20.7846i 0.514024 + 0.890315i
\(546\) −4.35425 + 7.54178i −0.186345 + 0.322758i
\(547\) −0.354249 0.613577i −0.0151466 0.0262346i 0.858353 0.513060i \(-0.171488\pi\)
−0.873499 + 0.486825i \(0.838155\pi\)
\(548\) 2.79150 4.83502i 0.119247 0.206542i
\(549\) 29.8745 51.7442i 1.27501 2.20839i
\(550\) 5.35425 0.228306
\(551\) 6.11438 + 14.6681i 0.260481 + 0.624882i
\(552\) −9.64575 −0.410550
\(553\) −3.29150 + 5.70105i −0.139969 + 0.242433i
\(554\) −4.76013 + 8.24479i −0.202239 + 0.350287i
\(555\) 27.2288 + 47.1616i 1.15580 + 2.00190i
\(556\) −6.67712 + 11.5651i −0.283173 + 0.490470i
\(557\) 13.2915 + 23.0216i 0.563179 + 0.975455i 0.997217 + 0.0745599i \(0.0237552\pi\)
−0.434037 + 0.900895i \(0.642911\pi\)
\(558\) −1.41699 −0.0599862
\(559\) 1.41699 0.0599325
\(560\) 3.00000 + 5.19615i 0.126773 + 0.219578i
\(561\) 0 0
\(562\) −27.4575 −1.15823
\(563\) 25.9373 1.09312 0.546562 0.837418i \(-0.315936\pi\)
0.546562 + 0.837418i \(0.315936\pi\)
\(564\) 12.7601 + 22.1012i 0.537298 + 0.930628i
\(565\) −10.1771 + 17.6273i −0.428155 + 0.741586i
\(566\) −12.6771 21.9574i −0.532859 0.922939i
\(567\) −4.11438 + 7.12631i −0.172788 + 0.299277i
\(568\) 6.64575 11.5108i 0.278850 0.482982i
\(569\) −14.5830 −0.611351 −0.305676 0.952136i \(-0.598882\pi\)
−0.305676 + 0.952136i \(0.598882\pi\)
\(570\) −41.6974 5.39426i −1.74651 0.225941i
\(571\) −39.8118 −1.66607 −0.833035 0.553220i \(-0.813399\pi\)
−0.833035 + 0.553220i \(0.813399\pi\)
\(572\) −0.645751 + 1.11847i −0.0270002 + 0.0467658i
\(573\) −19.2915 + 33.4139i −0.805914 + 1.39588i
\(574\) 8.46863 + 14.6681i 0.353474 + 0.612234i
\(575\) −15.1144 + 26.1789i −0.630313 + 1.09173i
\(576\) −2.00000 3.46410i −0.0833333 0.144338i
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) −17.0000 −0.707107
\(579\) −8.70850 15.0836i −0.361913 0.626851i
\(580\) 6.64575 + 11.5108i 0.275950 + 0.477959i
\(581\) 13.0627 0.541934
\(582\) 37.8118 1.56735
\(583\) −2.77124 4.79993i −0.114773 0.198793i
\(584\) −6.14575 + 10.6448i −0.254313 + 0.440483i
\(585\) −14.5830 25.2585i −0.602933 1.04431i
\(586\) −6.53137 + 11.3127i −0.269809 + 0.467322i
\(587\) 22.9373 39.7285i 0.946722 1.63977i 0.194455 0.980911i \(-0.437706\pi\)
0.752267 0.658859i \(-0.228961\pi\)
\(588\) 11.3542 0.468241
\(589\) −1.53137 0.198109i −0.0630991 0.00816294i
\(590\) 28.9373 1.19133
\(591\) −3.11438 + 5.39426i −0.128108 + 0.221890i
\(592\) −2.82288 + 4.88936i −0.116019 + 0.200952i
\(593\) −20.1458 34.8935i −0.827287 1.43290i −0.900159 0.435562i \(-0.856550\pi\)
0.0728721 0.997341i \(-0.476784\pi\)
\(594\) 0.854249 1.47960i 0.0350502 0.0607088i
\(595\) 0 0
\(596\) −4.93725 −0.202238
\(597\) −31.4170 −1.28581
\(598\) −3.64575 6.31463i −0.149086 0.258224i
\(599\) 0.531373 + 0.920365i 0.0217113 + 0.0376051i 0.876677 0.481080i \(-0.159755\pi\)
−0.854966 + 0.518685i \(0.826422\pi\)
\(600\) −21.9373 −0.895585
\(601\) 31.5830 1.28830 0.644149 0.764900i \(-0.277212\pi\)
0.644149 + 0.764900i \(0.277212\pi\)
\(602\) 0.583005 + 1.00979i 0.0237615 + 0.0411562i
\(603\) 9.29150 16.0934i 0.378379 0.655372i
\(604\) 1.46863 + 2.54374i 0.0597576 + 0.103503i
\(605\) 19.2915 33.4139i 0.784311 1.35847i
\(606\) −11.0516 + 19.1420i −0.448942 + 0.777590i
\(607\) −8.93725 −0.362752 −0.181376 0.983414i \(-0.558055\pi\)
−0.181376 + 0.983414i \(0.558055\pi\)
\(608\) −1.67712 4.02334i −0.0680164 0.163168i
\(609\) −15.8745 −0.643268
\(610\) 27.2288 47.1616i 1.10246 1.90952i
\(611\) −9.64575 + 16.7069i −0.390225 + 0.675890i
\(612\) 0 0
\(613\) −14.2915 + 24.7536i −0.577228 + 0.999789i 0.418567 + 0.908186i \(0.362532\pi\)
−0.995796 + 0.0916030i \(0.970801\pi\)
\(614\) 2.32288 + 4.02334i 0.0937436 + 0.162369i
\(615\) −99.2693 −4.00292
\(616\) −1.06275 −0.0428193
\(617\) −0.437254 0.757346i −0.0176032 0.0304896i 0.857090 0.515167i \(-0.172270\pi\)
−0.874693 + 0.484678i \(0.838937\pi\)
\(618\) −3.58301 6.20595i −0.144130 0.249640i
\(619\) 44.4575 1.78690 0.893449 0.449164i \(-0.148278\pi\)
0.893449 + 0.449164i \(0.148278\pi\)
\(620\) −1.29150 −0.0518680
\(621\) 4.82288 + 8.35347i 0.193535 + 0.335213i
\(622\) −4.17712 + 7.23499i −0.167487 + 0.290097i
\(623\) 0 0
\(624\) 2.64575 4.58258i 0.105915 0.183450i
\(625\) −1.14575 + 1.98450i −0.0458301 + 0.0793800i
\(626\) −22.8745 −0.914249
\(627\) 4.52026 5.91841i 0.180522 0.236358i
\(628\) 10.5830 0.422308
\(629\) 0 0
\(630\) 12.0000 20.7846i 0.478091 0.828079i
\(631\) −11.4059 19.7556i −0.454061 0.786457i 0.544573 0.838714i \(-0.316692\pi\)
−0.998634 + 0.0522570i \(0.983359\pi\)
\(632\) 2.00000 3.46410i 0.0795557 0.137795i
\(633\) −3.58301 6.20595i −0.142412 0.246664i
\(634\) −6.00000 −0.238290
\(635\) −9.87451 −0.391858
\(636\) 11.3542 + 19.6661i 0.450225 + 0.779813i
\(637\) 4.29150 + 7.43310i 0.170036 + 0.294510i
\(638\) −2.35425 −0.0932056
\(639\) −53.1660 −2.10321
\(640\) −1.82288 3.15731i −0.0720555 0.124804i
\(641\) 9.43725 16.3458i 0.372749 0.645620i −0.617238 0.786776i \(-0.711749\pi\)
0.989987 + 0.141156i \(0.0450819\pi\)
\(642\) 6.22876 + 10.7885i 0.245829 + 0.425789i
\(643\) −15.2601 + 26.4313i −0.601801 + 1.04235i 0.390748 + 0.920498i \(0.372217\pi\)
−0.992548 + 0.121852i \(0.961117\pi\)
\(644\) 3.00000 5.19615i 0.118217 0.204757i
\(645\) −6.83399 −0.269088
\(646\) 0 0
\(647\) 30.4575 1.19741 0.598704 0.800970i \(-0.295683\pi\)
0.598704 + 0.800970i \(0.295683\pi\)
\(648\) 2.50000 4.33013i 0.0982093 0.170103i
\(649\) −2.56275 + 4.43881i −0.100597 + 0.174238i
\(650\) −8.29150 14.3613i −0.325219 0.563297i
\(651\) 0.771243 1.33583i 0.0302274 0.0523554i
\(652\) 5.96863 + 10.3380i 0.233749 + 0.404866i
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 17.4170 0.681058
\(655\) 25.4059 + 44.0043i 0.992690 + 1.71939i
\(656\) −5.14575 8.91270i −0.200908 0.347983i
\(657\) 49.1660 1.91815
\(658\) −15.8745 −0.618853
\(659\) −1.29150 2.23695i −0.0503098 0.0871391i 0.839774 0.542936i \(-0.182688\pi\)
−0.890084 + 0.455797i \(0.849354\pi\)
\(660\) 3.11438 5.39426i 0.121227 0.209971i
\(661\) 5.11438 + 8.85836i 0.198926 + 0.344550i 0.948181 0.317732i \(-0.102921\pi\)
−0.749254 + 0.662282i \(0.769588\pi\)
\(662\) 13.9059 24.0857i 0.540467 0.936117i
\(663\) 0 0
\(664\) −7.93725 −0.308025
\(665\) 15.8745 20.7846i 0.615587 0.805993i
\(666\) 22.5830 0.875074
\(667\) 6.64575 11.5108i 0.257325 0.445699i
\(668\) 6.00000 10.3923i 0.232147 0.402090i
\(669\) 38.1144 + 66.0160i 1.47359 + 2.55233i
\(670\) 8.46863 14.6681i 0.327172 0.566678i
\(671\) 4.82288 + 8.35347i 0.186185 + 0.322482i
\(672\) 4.35425 0.167969
\(673\) 17.8745 0.689012 0.344506 0.938784i \(-0.388046\pi\)
0.344506 + 0.938784i \(0.388046\pi\)
\(674\) 10.1458 + 17.5730i 0.390800 + 0.676885i
\(675\) 10.9686 + 18.9982i 0.422183 + 0.731242i
\(676\) −9.00000 −0.346154
\(677\) −32.5830 −1.25227 −0.626133 0.779716i \(-0.715363\pi\)
−0.626133 + 0.779716i \(0.715363\pi\)
\(678\) 7.38562 + 12.7923i 0.283643 + 0.491284i
\(679\) −11.7601 + 20.3691i −0.451312 + 0.781696i
\(680\) 0 0
\(681\) −16.7288 + 28.9751i −0.641047 + 1.11033i
\(682\) 0.114378 0.198109i 0.00437977 0.00758599i
\(683\) −26.5830 −1.01717 −0.508585 0.861012i \(-0.669831\pi\)
−0.508585 + 0.861012i \(0.669831\pi\)
\(684\) −10.5830 + 13.8564i −0.404651 + 0.529813i
\(685\) −20.3542 −0.777696
\(686\) −9.29150 + 16.0934i −0.354751 + 0.614447i
\(687\) 26.4575 45.8258i 1.00942 1.74836i
\(688\) −0.354249 0.613577i −0.0135056 0.0233924i
\(689\) −8.58301 + 14.8662i −0.326986 + 0.566357i
\(690\) 17.5830 + 30.4547i 0.669374 + 1.15939i
\(691\) −18.5830 −0.706931 −0.353465 0.935448i \(-0.614997\pi\)
−0.353465 + 0.935448i \(0.614997\pi\)
\(692\) −6.00000 −0.228086
\(693\) 2.12549 + 3.68146i 0.0807408 + 0.139847i
\(694\) −1.61438 2.79619i −0.0612810 0.106142i
\(695\) 48.6863 1.84678
\(696\) 9.64575 0.365621
\(697\) 0 0
\(698\) 10.5830 18.3303i 0.400573 0.693812i
\(699\) −17.0314 29.4992i −0.644186 1.11576i
\(700\) 6.82288 11.8176i 0.257880 0.446662i
\(701\) −7.82288 + 13.5496i −0.295466 + 0.511762i −0.975093 0.221796i \(-0.928808\pi\)
0.679627 + 0.733558i \(0.262142\pi\)
\(702\) −5.29150 −0.199715
\(703\) 24.4059 + 3.15731i 0.920485 + 0.119080i
\(704\) 0.645751 0.0243377
\(705\) 46.5203 80.5755i 1.75205 3.03465i
\(706\) 9.43725 16.3458i 0.355176 0.615182i
\(707\) −6.87451 11.9070i −0.258542 0.447809i
\(708\) 10.5000 18.1865i 0.394614 0.683492i
\(709\) 0.822876 + 1.42526i 0.0309037 + 0.0535269i 0.881064 0.472998i \(-0.156828\pi\)
−0.850160 + 0.526525i \(0.823495\pi\)
\(710\) −48.4575 −1.81858
\(711\) −16.0000 −0.600047
\(712\) 0 0
\(713\) 0.645751 + 1.11847i 0.0241836 + 0.0418872i
\(714\) 0 0
\(715\) 4.70850 0.176088
\(716\) −9.96863 17.2662i −0.372545 0.645267i
\(717\) −15.8745 + 27.4955i −0.592844 + 1.02684i
\(718\) −5.46863 9.47194i −0.204087 0.353490i
\(719\) −6.64575 + 11.5108i −0.247845 + 0.429280i −0.962928 0.269760i \(-0.913056\pi\)
0.715083 + 0.699040i \(0.246389\pi\)
\(720\) −7.29150 + 12.6293i −0.271738 + 0.470664i
\(721\) 4.45751 0.166006
\(722\) −13.3745 + 13.4953i −0.497748 + 0.502242i
\(723\) −35.9373 −1.33652
\(724\) 2.11438 3.66221i 0.0785802 0.136105i
\(725\) 15.1144 26.1789i 0.561334 0.972259i
\(726\) −14.0000 24.2487i −0.519589 0.899954i
\(727\) −11.2915 + 19.5575i −0.418779 + 0.725346i −0.995817 0.0913712i \(-0.970875\pi\)
0.577038 + 0.816717i \(0.304208\pi\)
\(728\) 1.64575 + 2.85052i 0.0609956 + 0.105647i
\(729\) −41.0000 −1.51852
\(730\) 44.8118 1.65856
\(731\) 0 0
\(732\) −19.7601 34.2255i −0.730355 1.26501i
\(733\) 42.1033 1.55512 0.777560 0.628809i \(-0.216457\pi\)
0.777560 + 0.628809i \(0.216457\pi\)
\(734\) −10.2288 −0.377550
\(735\) −20.6974 35.8489i −0.763434 1.32231i
\(736\) −1.82288 + 3.15731i −0.0671921 + 0.116380i
\(737\) 1.50000 + 2.59808i 0.0552532 + 0.0957014i
\(738\) −20.5830 + 35.6508i −0.757671 + 1.31232i
\(739\) −6.90588 + 11.9613i −0.254037 + 0.440005i −0.964633 0.263595i \(-0.915092\pi\)
0.710597 + 0.703600i \(0.248425\pi\)
\(740\) 20.5830 0.756646
\(741\) −22.8745 2.95920i −0.840316 0.108709i
\(742\) −14.1255 −0.518563
\(743\) 5.23987 9.07572i 0.192232 0.332956i −0.753757 0.657153i \(-0.771761\pi\)
0.945990 + 0.324197i \(0.105094\pi\)
\(744\) −0.468627 + 0.811686i −0.0171807 + 0.0297578i
\(745\) 9.00000 + 15.5885i 0.329734 + 0.571117i
\(746\) 2.00000 3.46410i 0.0732252 0.126830i
\(747\) 15.8745 + 27.4955i 0.580818 + 1.00601i
\(748\) 0 0
\(749\) −7.74902 −0.283143
\(750\) 15.8745 + 27.4955i 0.579655 + 1.00399i
\(751\) −11.9373 20.6759i −0.435597 0.754475i 0.561748 0.827309i \(-0.310129\pi\)
−0.997344 + 0.0728333i \(0.976796\pi\)
\(752\) 9.64575 0.351744
\(753\) −7.33202 −0.267194
\(754\) 3.64575 + 6.31463i 0.132770 + 0.229965i
\(755\) 5.35425 9.27383i 0.194861 0.337509i
\(756\) −2.17712 3.77089i −0.0791812 0.137146i
\(757\) −8.29150 + 14.3613i −0.301360 + 0.521970i −0.976444 0.215770i \(-0.930774\pi\)
0.675084 + 0.737740i \(0.264107\pi\)
\(758\) −10.6458 + 18.4390i −0.386671 + 0.669734i
\(759\) −6.22876 −0.226090
\(760\) −9.64575 + 12.6293i −0.349888 + 0.458111i
\(761\) 11.1255 0.403299 0.201649 0.979458i \(-0.435370\pi\)
0.201649 + 0.979458i \(0.435370\pi\)
\(762\) −3.58301 + 6.20595i −0.129799 + 0.224818i
\(763\) −5.41699 + 9.38251i −0.196108 + 0.339670i
\(764\) 7.29150 + 12.6293i 0.263797 + 0.456910i
\(765\) 0 0
\(766\) 15.7601 + 27.2973i 0.569437 + 0.986293i
\(767\) 15.8745 0.573195
\(768\) −2.64575 −0.0954703
\(769\) −12.3542 21.3982i −0.445506 0.771638i 0.552582 0.833459i \(-0.313643\pi\)
−0.998087 + 0.0618204i \(0.980309\pi\)
\(770\) 1.93725 + 3.35542i 0.0698138 + 0.120921i
\(771\) −4.52026 −0.162793
\(772\) −6.58301 −0.236928
\(773\) −5.46863 9.47194i −0.196693 0.340682i 0.750761 0.660574i \(-0.229687\pi\)
−0.947454 + 0.319892i \(0.896354\pi\)
\(774\) −1.41699 + 2.45431i −0.0509328 + 0.0882182i
\(775\) 1.46863 + 2.54374i 0.0527546 + 0.0913737i
\(776\) 7.14575 12.3768i 0.256518 0.444301i
\(777\) −12.2915 + 21.2895i −0.440955 + 0.763757i
\(778\) 12.0000 0.430221
\(779\) −27.2288 + 35.6508i −0.975571 + 1.27732i
\(780\) −19.2915 −0.690747
\(781\) 4.29150 7.43310i 0.153562 0.265977i
\(782\) 0 0
\(783\) −4.82288 8.35347i −0.172356 0.298529i
\(784\) 2.14575 3.71655i 0.0766340 0.132734i
\(785\) −19.2915 33.4139i −0.688543 1.19259i
\(786\) 36.8745 1.31527
\(787\) −5.47974 −0.195332 −0.0976658 0.995219i \(-0.531138\pi\)
−0.0976658 + 0.995219i \(0.531138\pi\)
\(788\) 1.17712 + 2.03884i 0.0419333 + 0.0726306i
\(789\) 6.53137 + 11.3127i 0.232523 + 0.402742i
\(790\) −14.5830 −0.518840
\(791\) −9.18824 −0.326696
\(792\) −1.29150 2.23695i −0.0458915 0.0794865i
\(793\) 14.9373 25.8721i 0.530437 0.918745i
\(794\) −18.4686 31.9886i −0.655427 1.13523i
\(795\) 41.3948 71.6978i 1.46812 2.54286i
\(796\) −5.93725 + 10.2836i −0.210440 + 0.364493i
\(797\) 2.81176 0.0995977 0.0497989 0.998759i \(-0.484142\pi\)
0.0497989 + 0.998759i \(0.484142\pi\)
\(798\) −7.30262 17.5186i −0.258510 0.620152i
\(799\) 0 0
\(800\) −4.14575 + 7.18065i −0.146574 + 0.253874i
\(801\) 0 0
\(802\) −3.20850 5.55728i −0.113296 0.196234i
\(803\) −3.96863 + 6.87386i −0.140050 + 0.242573i
\(804\) −6.14575 10.6448i −0.216744 0.375412i
\(805\) −21.8745 −0.770975
\(806\) −0.708497 −0.0249558
\(807\) 0 0
\(808\) 4.17712 + 7.23499i 0.146951 + 0.254526i
\(809\) −9.00000 −0.316423 −0.158212 0.987405i \(-0.550573\pi\)
−0.158212 + 0.987405i \(0.550573\pi\)
\(810\) −18.2288 −0.640493
\(811\) 10.3542 + 17.9341i 0.363587 + 0.629751i 0.988548 0.150905i \(-0.0482187\pi\)
−0.624961 + 0.780656i \(0.714885\pi\)
\(812\) −3.00000 + 5.19615i −0.105279 + 0.182349i
\(813\) 23.3431 + 40.4315i 0.818679 + 1.41799i
\(814\) −1.82288 + 3.15731i −0.0638918 + 0.110664i
\(815\) 21.7601 37.6897i 0.762224 1.32021i
\(816\) 0 0
\(817\) −1.87451 + 2.45431i −0.0655807 + 0.0858653i
\(818\) 13.5830 0.474919
\(819\) 6.58301 11.4021i 0.230029 0.398422i
\(820\) −18.7601 + 32.4935i −0.655132 + 1.13472i
\(821\) 3.00000 + 5.19615i 0.104701 + 0.181347i 0.913616 0.406578i \(-0.133278\pi\)
−0.808915 + 0.587925i \(0.799945\pi\)
\(822\) −7.38562 + 12.7923i −0.257603 + 0.446182i
\(823\) 0.0627461 + 0.108679i 0.00218719 + 0.00378832i 0.867117 0.498105i \(-0.165970\pi\)
−0.864930 + 0.501893i \(0.832637\pi\)
\(824\) −2.70850 −0.0943550
\(825\) −14.1660 −0.493197
\(826\) 6.53137 + 11.3127i 0.227256 + 0.393618i
\(827\) 23.6771 + 41.0100i 0.823334 + 1.42606i 0.903186 + 0.429250i \(0.141222\pi\)
−0.0798514 + 0.996807i \(0.525445\pi\)
\(828\) 14.5830 0.506794
\(829\) 25.1660 0.874052 0.437026 0.899449i \(-0.356032\pi\)
0.437026 + 0.899449i \(0.356032\pi\)
\(830\) 14.4686 + 25.0604i 0.502213 + 0.869859i
\(831\) 12.5941 21.8137i 0.436885 0.756707i
\(832\) −1.00000 1.73205i −0.0346688 0.0600481i
\(833\) 0 0
\(834\) 17.6660 30.5984i 0.611724 1.05954i
\(835\) −43.7490 −1.51400
\(836\) −1.08301 2.59808i −0.0374565 0.0898563i
\(837\) 0.937254 0.0323962
\(838\) −15.8745 + 27.4955i −0.548376 + 0.949815i
\(839\) 2.23987 3.87957i 0.0773289 0.133938i −0.824768 0.565472i \(-0.808694\pi\)
0.902097 + 0.431534i \(0.142028\pi\)
\(840\) −7.93725 13.7477i −0.273861 0.474342i
\(841\) 7.85425 13.6040i 0.270836 0.469102i
\(842\) −11.4059 19.7556i −0.393073 0.680822i
\(843\) 72.6458 2.50205
\(844\) −2.70850 −0.0932303
\(845\) 16.4059 + 28.4158i 0.564379 + 0.977534i
\(846\) −19.2915 33.4139i −0.663256 1.14879i
\(847\) 17.4170 0.598455
\(848\) 8.58301 0.294742
\(849\) 33.5405 + 58.0939i 1.15111 + 1.99378i
\(850\) 0 0
\(851\) −10.2915 17.8254i −0.352788 0.611047i
\(852\) −17.5830 + 30.4547i −0.602384 + 1.04336i
\(853\) 6.29150 10.8972i 0.215417 0.373113i −0.737985 0.674818i \(-0.764222\pi\)
0.953401 + 0.301705i \(0.0975556\pi\)
\(854\) 24.5830 0.841213
\(855\) 63.0405 + 8.15536i 2.15594 + 0.278907i
\(856\) 4.70850 0.160933
\(857\) −10.5000 + 18.1865i −0.358673 + 0.621240i −0.987739 0.156112i \(-0.950104\pi\)
0.629066 + 0.777352i \(0.283437\pi\)
\(858\) 1.70850 2.95920i 0.0583271 0.101026i
\(859\) 6.61438 + 11.4564i 0.225680 + 0.390889i 0.956523 0.291656i \(-0.0942064\pi\)
−0.730843 + 0.682545i \(0.760873\pi\)
\(860\) −1.29150 + 2.23695i −0.0440399 + 0.0762793i
\(861\) −22.4059 38.8081i −0.763590 1.32258i
\(862\) −3.87451 −0.131966
\(863\) −46.9373 −1.59776 −0.798881 0.601489i \(-0.794575\pi\)
−0.798881 + 0.601489i \(0.794575\pi\)
\(864\) 1.32288 + 2.29129i 0.0450051 + 0.0779512i
\(865\) 10.9373 + 18.9439i 0.371878 + 0.644111i
\(866\) −13.8745 −0.471475
\(867\) 44.9778 1.52753
\(868\) −0.291503 0.504897i −0.00989424 0.0171373i
\(869\) 1.29150 2.23695i 0.0438112 0.0758833i
\(870\) −17.5830 30.4547i −0.596120 1.03251i
\(871\) 4.64575 8.04668i 0.157415 0.272651i
\(872\) 3.29150 5.70105i 0.111464 0.193062i
\(873\) −57.1660 −1.93478
\(874\) 15.7601 + 2.03884i 0.533094 + 0.0689648i
\(875\) −19.7490 −0.667639
\(876\) 16.2601 28.1634i 0.549379 0.951552i
\(877\) 18.1771 31.4837i 0.613798 1.06313i −0.376796 0.926296i \(-0.622974\pi\)
0.990594 0.136833i \(-0.0436924\pi\)
\(878\) 18.4059 + 31.8799i 0.621168 + 1.07590i
\(879\) 17.2804 29.9305i 0.582853 1.00953i
\(880\) −1.17712 2.03884i −0.0396809 0.0687293i
\(881\) −5.12549 −0.172682 −0.0863411 0.996266i \(-0.527517\pi\)
−0.0863411 + 0.996266i \(0.527517\pi\)
\(882\) −17.1660 −0.578010
\(883\) −20.1974 34.9829i −0.679696 1.17727i −0.975072 0.221887i \(-0.928778\pi\)
0.295376 0.955381i \(-0.404555\pi\)
\(884\) 0 0
\(885\) −76.5608 −2.57356
\(886\) 5.35425 0.179880
\(887\) 19.2915 + 33.4139i 0.647745 + 1.12193i 0.983660 + 0.180035i \(0.0576212\pi\)
−0.335915 + 0.941892i \(0.609045\pi\)
\(888\) 7.46863 12.9360i 0.250631 0.434105i
\(889\) −2.22876 3.86032i −0.0747501 0.129471i
\(890\) 0 0
\(891\) 1.61438 2.79619i 0.0540837 0.0936757i
\(892\) 28.8118 0.964689
\(893\) −16.1771 38.8081i −0.541347 1.29866i
\(894\) 13.0627 0.436884
\(895\) −36.3431 + 62.9482i −1.21482 + 2.10412i
\(896\) 0.822876 1.42526i 0.0274903 0.0476147i
\(897\) 9.64575 + 16.7069i 0.322062 + 0.557828i
\(898\) 6.85425 11.8719i 0.228729 0.396171i
\(899\) −0.645751 1.11847i −0.0215370 0.0373032i
\(900\) 33.1660 1.10553
\(901\) 0 0
\(902\) −3.32288 5.75539i −0.110640 0.191634i
\(903\) −1.54249 2.67167i −0.0513307 0.0889075i
\(904\) 5.58301 0.185688
\(905\) −15.4170 −0.512478
\(906\) −3.88562 6.73009i −0.129091 0.223592i
\(907\) −12.0314 + 20.8389i −0.399495 + 0.691946i −0.993664 0.112395i \(-0.964148\pi\)
0.594168 + 0.804341i \(0.297481\pi\)
\(908\) 6.32288 + 10.9515i 0.209832 + 0.363440i
\(909\) 16.7085 28.9400i 0.554186 0.959878i
\(910\) 6.00000 10.3923i 0.198898 0.344502i
\(911\) 1.06275 0.0352103 0.0176052 0.999845i \(-0.494396\pi\)
0.0176052 + 0.999845i \(0.494396\pi\)
\(912\) 4.43725 + 10.6448i 0.146932 + 0.352483i
\(913\) −5.12549 −0.169629
\(914\) −0.562746 + 0.974705i −0.0186140 + 0.0322404i
\(915\) −72.0405 + 124.778i −2.38159 + 4.12503i
\(916\) −10.0000 17.3205i −0.330409 0.572286i
\(917\) −11.4686 + 19.8642i −0.378727 + 0.655975i
\(918\) 0 0
\(919\) 11.8745 0.391704 0.195852 0.980633i \(-0.437253\pi\)
0.195852 + 0.980633i \(0.437253\pi\)
\(920\) 13.2915 0.438208
\(921\) −6.14575 10.6448i −0.202509 0.350757i
\(922\) 11.5830 + 20.0624i 0.381466 + 0.660718i
\(923\) −26.5830 −0.874990
\(924\) 2.81176 0.0925002
\(925\) −23.4059 40.5402i −0.769581 1.33295i
\(926\) −7.22876 + 12.5206i −0.237552 + 0.411452i
\(927\) 5.41699 + 9.38251i 0.177917 + 0.308162i
\(928\) 1.82288 3.15731i 0.0598388 0.103644i
\(929\) −5.79150 + 10.0312i −0.190013 + 0.329112i −0.945254 0.326335i \(-0.894186\pi\)
0.755241 + 0.655447i \(0.227520\pi\)
\(930\) 3.41699 0.112048
\(931\) −18.5516 2.39997i −0.608005 0.0786557i
\(932\) −12.8745 −0.421719
\(933\) 11.0516 19.1420i 0.361814 0.626681i
\(934\) 12.3229 21.3438i 0.403217 0.698392i
\(935\) 0 0
\(936\) −4.00000 + 6.92820i −0.130744 + 0.226455i
\(937\) −19.4373 33.6663i −0.634987 1.09983i −0.986518 0.163654i \(-0.947672\pi\)
0.351530 0.936176i \(-0.385661\pi\)
\(938\) 7.64575 0.249643
\(939\) 60.5203 1.97500
\(940\) −17.5830 30.4547i −0.573494 0.993321i
\(941\) −29.5830 51.2393i −0.964378 1.67035i −0.711276 0.702913i \(-0.751882\pi\)
−0.253103 0.967439i \(-0.581451\pi\)
\(942\) −28.0000 −0.912289
\(943\) 37.5203 1.22183
\(944\) −3.96863 6.87386i −0.129168 0.223725i
\(945\) −7.93725 + 13.7477i −0.258199 + 0.447214i
\(946\) −0.228757 0.396218i −0.00743752 0.0128822i
\(947\) −27.8745 + 48.2801i −0.905800 + 1.56889i −0.0859598 + 0.996299i \(0.527396\pi\)
−0.819840 + 0.572593i \(0.805938\pi\)
\(948\) −5.29150 + 9.16515i −0.171860 + 0.297670i
\(949\) 24.5830 0.797998
\(950\) 35.8431 + 4.63692i 1.16290 + 0.150441i
\(951\) 15.8745 0.514766
\(952\) 0 0
\(953\) −19.7288 + 34.1712i −0.639077 + 1.10691i 0.346559 + 0.938028i \(0.387350\pi\)
−0.985636 + 0.168886i \(0.945983\pi\)
\(954\) −17.1660 29.7324i −0.555770 0.962622i
\(955\) 26.5830 46.0431i 0.860206 1.48992i
\(956\) 6.00000 + 10.3923i 0.194054 + 0.336111i
\(957\) 6.22876 0.201347
\(958\) −14.5830 −0.471156
\(959\) −4.59412 7.95725i −0.148352 0.256953i
\(960\) 4.82288 + 8.35347i 0.155658 + 0.269607i
\(961\) −30.8745 −0.995952
\(962\) 11.2915 0.364053
\(963\) −9.41699 16.3107i −0.303458 0.525605i
\(964\) −6.79150 + 11.7632i −0.218740 + 0.378868i
\(965\) 12.0000 + 20.7846i 0.386294 + 0.669080i
\(966\) −7.93725 + 13.7477i −0.255377 + 0.442326i
\(967\) 1.35425 2.34563i 0.0435497 0.0754303i −0.843429 0.537241i \(-0.819467\pi\)
0.886979 + 0.461810i \(0.152800\pi\)
\(968\) −10.5830 −0.340151
\(969\) 0 0
\(970\) −52.1033 −1.67293
\(971\) −7.19738 + 12.4662i −0.230975 + 0.400060i −0.958095 0.286450i \(-0.907525\pi\)
0.727120 + 0.686510i \(0.240858\pi\)
\(972\) −10.5830 + 18.3303i −0.339450 + 0.587945i
\(973\) 10.9889 + 19.0333i 0.352288 + 0.610180i
\(974\) 11.1144 19.2507i 0.356128 0.616831i
\(975\) 21.9373 + 37.9964i 0.702554 + 1.21686i
\(976\) −14.9373 −0.478130
\(977\) 45.4575 1.45431 0.727157 0.686471i \(-0.240841\pi\)
0.727157 + 0.686471i \(0.240841\pi\)
\(978\) −15.7915 27.3517i −0.504957 0.874610i
\(979\) 0 0
\(980\) −15.6458 −0.499785
\(981\) −26.3320 −0.840717
\(982\) −14.3542 24.8623i −0.458062 0.793387i
\(983\) 15.8745 27.4955i 0.506318 0.876969i −0.493655 0.869658i \(-0.664339\pi\)
0.999973 0.00731102i \(-0.00232719\pi\)
\(984\) 13.6144 + 23.5808i 0.434011 + 0.751728i
\(985\) 4.29150 7.43310i 0.136739 0.236838i
\(986\) 0 0
\(987\) 42.0000 1.33687
\(988\) −5.29150 + 6.92820i −0.168345 + 0.220416i
\(989\) 2.58301 0.0821348
\(990\) −4.70850 + 8.15536i −0.149646 + 0.259194i
\(991\) 22.5830 39.1149i 0.717373 1.24253i −0.244664 0.969608i \(-0.578678\pi\)
0.962037 0.272918i \(-0.0879889\pi\)
\(992\) 0.177124 + 0.306788i 0.00562370 + 0.00974054i
\(993\) −36.7915 + 63.7248i −1.16754 + 2.02224i
\(994\) −10.9373 18.9439i −0.346909 0.600863i
\(995\) 43.2915 1.37243
\(996\) 21.0000 0.665410
\(997\) 5.11438 + 8.85836i 0.161974 + 0.280547i 0.935577 0.353124i \(-0.114881\pi\)
−0.773603 + 0.633671i \(0.781547\pi\)
\(998\) 15.6144 + 27.0449i 0.494265 + 0.856091i
\(999\) −14.9373 −0.472594
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 38.2.c.b.11.2 yes 4
3.2 odd 2 342.2.g.f.163.2 4
4.3 odd 2 304.2.i.e.49.1 4
5.2 odd 4 950.2.j.g.49.1 8
5.3 odd 4 950.2.j.g.49.4 8
5.4 even 2 950.2.e.k.201.1 4
8.3 odd 2 1216.2.i.k.961.2 4
8.5 even 2 1216.2.i.l.961.1 4
12.11 even 2 2736.2.s.v.1873.2 4
19.2 odd 18 722.2.e.o.595.1 12
19.3 odd 18 722.2.e.o.99.2 12
19.4 even 9 722.2.e.n.423.1 12
19.5 even 9 722.2.e.n.389.1 12
19.6 even 9 722.2.e.n.415.2 12
19.7 even 3 inner 38.2.c.b.7.2 4
19.8 odd 6 722.2.a.g.1.2 2
19.9 even 9 722.2.e.n.245.1 12
19.10 odd 18 722.2.e.o.245.2 12
19.11 even 3 722.2.a.j.1.1 2
19.12 odd 6 722.2.c.j.653.1 4
19.13 odd 18 722.2.e.o.415.1 12
19.14 odd 18 722.2.e.o.389.2 12
19.15 odd 18 722.2.e.o.423.2 12
19.16 even 9 722.2.e.n.99.1 12
19.17 even 9 722.2.e.n.595.2 12
19.18 odd 2 722.2.c.j.429.1 4
57.8 even 6 6498.2.a.bg.1.1 2
57.11 odd 6 6498.2.a.ba.1.1 2
57.26 odd 6 342.2.g.f.235.2 4
76.7 odd 6 304.2.i.e.273.1 4
76.11 odd 6 5776.2.a.ba.1.2 2
76.27 even 6 5776.2.a.z.1.1 2
95.7 odd 12 950.2.j.g.349.4 8
95.64 even 6 950.2.e.k.501.1 4
95.83 odd 12 950.2.j.g.349.1 8
152.45 even 6 1216.2.i.l.577.1 4
152.83 odd 6 1216.2.i.k.577.2 4
228.83 even 6 2736.2.s.v.577.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.2.c.b.7.2 4 19.7 even 3 inner
38.2.c.b.11.2 yes 4 1.1 even 1 trivial
304.2.i.e.49.1 4 4.3 odd 2
304.2.i.e.273.1 4 76.7 odd 6
342.2.g.f.163.2 4 3.2 odd 2
342.2.g.f.235.2 4 57.26 odd 6
722.2.a.g.1.2 2 19.8 odd 6
722.2.a.j.1.1 2 19.11 even 3
722.2.c.j.429.1 4 19.18 odd 2
722.2.c.j.653.1 4 19.12 odd 6
722.2.e.n.99.1 12 19.16 even 9
722.2.e.n.245.1 12 19.9 even 9
722.2.e.n.389.1 12 19.5 even 9
722.2.e.n.415.2 12 19.6 even 9
722.2.e.n.423.1 12 19.4 even 9
722.2.e.n.595.2 12 19.17 even 9
722.2.e.o.99.2 12 19.3 odd 18
722.2.e.o.245.2 12 19.10 odd 18
722.2.e.o.389.2 12 19.14 odd 18
722.2.e.o.415.1 12 19.13 odd 18
722.2.e.o.423.2 12 19.15 odd 18
722.2.e.o.595.1 12 19.2 odd 18
950.2.e.k.201.1 4 5.4 even 2
950.2.e.k.501.1 4 95.64 even 6
950.2.j.g.49.1 8 5.2 odd 4
950.2.j.g.49.4 8 5.3 odd 4
950.2.j.g.349.1 8 95.83 odd 12
950.2.j.g.349.4 8 95.7 odd 12
1216.2.i.k.577.2 4 152.83 odd 6
1216.2.i.k.961.2 4 8.3 odd 2
1216.2.i.l.577.1 4 152.45 even 6
1216.2.i.l.961.1 4 8.5 even 2
2736.2.s.v.577.2 4 228.83 even 6
2736.2.s.v.1873.2 4 12.11 even 2
5776.2.a.z.1.1 2 76.27 even 6
5776.2.a.ba.1.2 2 76.11 odd 6
6498.2.a.ba.1.1 2 57.11 odd 6
6498.2.a.bg.1.1 2 57.8 even 6