Properties

Label 546.2.i.j.235.2
Level $546$
Weight $2$
Character 546.235
Analytic conductor $4.360$
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] = [546,2,Mod(79,546)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(546, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("546.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.i (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: \(4.35983195036\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 235.2
Root \(1.32288 + 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 546.235
Dual form 546.2.i.j.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -1.00000 q^{6} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.82288 + 3.15731i) q^{5} -1.00000 q^{6} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.82288 + 3.15731i) q^{10} +(-0.322876 + 0.559237i) q^{11} +(-0.500000 - 0.866025i) q^{12} +1.00000 q^{13} +(-1.32288 + 2.29129i) q^{14} -3.64575 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.32288 - 5.75539i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.50000 - 4.33013i) q^{19} -3.64575 q^{20} -2.64575 q^{21} -0.645751 q^{22} +(1.17712 + 2.03884i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.14575 + 7.18065i) q^{25} +(0.500000 + 0.866025i) q^{26} +1.00000 q^{27} -2.64575 q^{28} +4.29150 q^{29} +(-1.82288 - 3.15731i) q^{30} +(-1.64575 + 2.85052i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.322876 - 0.559237i) q^{33} +6.64575 q^{34} +(-4.82288 + 8.35347i) q^{35} +1.00000 q^{36} +(-2.82288 - 4.88936i) q^{37} +(2.50000 - 4.33013i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(-1.82288 - 3.15731i) q^{40} -2.35425 q^{41} +(-1.32288 - 2.29129i) q^{42} -5.29150 q^{43} +(-0.322876 - 0.559237i) q^{44} +(1.82288 - 3.15731i) q^{45} +(-1.17712 + 2.03884i) q^{46} +(-1.50000 - 2.59808i) q^{47} +1.00000 q^{48} +(-3.50000 + 6.06218i) q^{49} -8.29150 q^{50} +(3.32288 + 5.75539i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(1.50000 - 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} -2.35425 q^{55} +(-1.32288 - 2.29129i) q^{56} +5.00000 q^{57} +(2.14575 + 3.71655i) q^{58} +(3.96863 - 6.87386i) q^{59} +(1.82288 - 3.15731i) q^{60} +(5.96863 + 10.3380i) q^{61} -3.29150 q^{62} +(1.32288 - 2.29129i) q^{63} +1.00000 q^{64} +(1.82288 + 3.15731i) q^{65} +(0.322876 - 0.559237i) q^{66} +(-3.79150 + 6.56708i) q^{67} +(3.32288 + 5.75539i) q^{68} -2.35425 q^{69} -9.64575 q^{70} +16.2915 q^{71} +(0.500000 + 0.866025i) q^{72} +(6.82288 - 11.8176i) q^{73} +(2.82288 - 4.88936i) q^{74} +(-4.14575 - 7.18065i) q^{75} +5.00000 q^{76} -1.70850 q^{77} -1.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(1.82288 - 3.15731i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.17712 - 2.03884i) q^{82} -13.2915 q^{83} +(1.32288 - 2.29129i) q^{84} +24.2288 q^{85} +(-2.64575 - 4.58258i) q^{86} +(-2.14575 + 3.71655i) q^{87} +(0.322876 - 0.559237i) q^{88} +(-8.46863 - 14.6681i) q^{89} +3.64575 q^{90} +(1.32288 + 2.29129i) q^{91} -2.35425 q^{92} +(-1.64575 - 2.85052i) q^{93} +(1.50000 - 2.59808i) q^{94} +(9.11438 - 15.7866i) q^{95} +(0.500000 + 0.866025i) q^{96} +0.937254 q^{97} -7.00000 q^{98} +0.645751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} - 4 q^{6} - 4 q^{8} - 2 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} - 10 q^{19} - 4 q^{20} + 8 q^{22} + 10 q^{23} + 2 q^{24} - 6 q^{25} + 2 q^{26} + 4 q^{27} - 4 q^{29} - 2 q^{30} + 4 q^{31} + 2 q^{32} + 4 q^{33} + 16 q^{34} - 14 q^{35} + 4 q^{36} - 6 q^{37} + 10 q^{38} - 2 q^{39} - 2 q^{40} - 20 q^{41} + 4 q^{44} + 2 q^{45} - 10 q^{46} - 6 q^{47} + 4 q^{48} - 14 q^{49} - 12 q^{50} + 8 q^{51} - 2 q^{52} + 6 q^{53} + 2 q^{54} - 20 q^{55} + 20 q^{57} - 2 q^{58} + 2 q^{60} + 8 q^{61} + 8 q^{62} + 4 q^{64} + 2 q^{65} - 4 q^{66} + 6 q^{67} + 8 q^{68} - 20 q^{69} - 28 q^{70} + 44 q^{71} + 2 q^{72} + 22 q^{73} + 6 q^{74} - 6 q^{75} + 20 q^{76} - 28 q^{77} - 4 q^{78} + 20 q^{79} + 2 q^{80} - 2 q^{81} - 10 q^{82} - 32 q^{83} + 44 q^{85} + 2 q^{87} - 4 q^{88} - 18 q^{89} + 4 q^{90} - 20 q^{92} + 4 q^{93} + 6 q^{94} + 10 q^{95} + 2 q^{96} - 28 q^{97} - 28 q^{98} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.82288 + 3.15731i 0.815215 + 1.41199i 0.909174 + 0.416417i \(0.136714\pi\)
−0.0939588 + 0.995576i \(0.529952\pi\)
\(6\) −1.00000 −0.408248
\(7\) 1.32288 + 2.29129i 0.500000 + 0.866025i
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −1.82288 + 3.15731i −0.576444 + 0.998430i
\(11\) −0.322876 + 0.559237i −0.0973507 + 0.168616i −0.910587 0.413317i \(-0.864370\pi\)
0.813237 + 0.581933i \(0.197704\pi\)
\(12\) −0.500000 0.866025i −0.144338 0.250000i
\(13\) 1.00000 0.277350
\(14\) −1.32288 + 2.29129i −0.353553 + 0.612372i
\(15\) −3.64575 −0.941329
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.32288 5.75539i 0.805916 1.39589i −0.109755 0.993959i \(-0.535007\pi\)
0.915671 0.401928i \(-0.131660\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) −3.64575 −0.815215
\(21\) −2.64575 −0.577350
\(22\) −0.645751 −0.137675
\(23\) 1.17712 + 2.03884i 0.245447 + 0.425127i 0.962257 0.272141i \(-0.0877318\pi\)
−0.716810 + 0.697269i \(0.754398\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −4.14575 + 7.18065i −0.829150 + 1.43613i
\(26\) 0.500000 + 0.866025i 0.0980581 + 0.169842i
\(27\) 1.00000 0.192450
\(28\) −2.64575 −0.500000
\(29\) 4.29150 0.796912 0.398456 0.917187i \(-0.369546\pi\)
0.398456 + 0.917187i \(0.369546\pi\)
\(30\) −1.82288 3.15731i −0.332810 0.576444i
\(31\) −1.64575 + 2.85052i −0.295586 + 0.511969i −0.975121 0.221673i \(-0.928848\pi\)
0.679535 + 0.733643i \(0.262181\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −0.322876 0.559237i −0.0562054 0.0973507i
\(34\) 6.64575 1.13974
\(35\) −4.82288 + 8.35347i −0.815215 + 1.41199i
\(36\) 1.00000 0.166667
\(37\) −2.82288 4.88936i −0.464078 0.803806i 0.535081 0.844800i \(-0.320281\pi\)
−0.999159 + 0.0409939i \(0.986948\pi\)
\(38\) 2.50000 4.33013i 0.405554 0.702439i
\(39\) −0.500000 + 0.866025i −0.0800641 + 0.138675i
\(40\) −1.82288 3.15731i −0.288222 0.499215i
\(41\) −2.35425 −0.367672 −0.183836 0.982957i \(-0.558852\pi\)
−0.183836 + 0.982957i \(0.558852\pi\)
\(42\) −1.32288 2.29129i −0.204124 0.353553i
\(43\) −5.29150 −0.806947 −0.403473 0.914991i \(-0.632197\pi\)
−0.403473 + 0.914991i \(0.632197\pi\)
\(44\) −0.322876 0.559237i −0.0486753 0.0843082i
\(45\) 1.82288 3.15731i 0.271738 0.470664i
\(46\) −1.17712 + 2.03884i −0.173558 + 0.300610i
\(47\) −1.50000 2.59808i −0.218797 0.378968i 0.735643 0.677369i \(-0.236880\pi\)
−0.954441 + 0.298401i \(0.903547\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(50\) −8.29150 −1.17260
\(51\) 3.32288 + 5.75539i 0.465296 + 0.805916i
\(52\) −0.500000 + 0.866025i −0.0693375 + 0.120096i
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −2.35425 −0.317447
\(56\) −1.32288 2.29129i −0.176777 0.306186i
\(57\) 5.00000 0.662266
\(58\) 2.14575 + 3.71655i 0.281751 + 0.488007i
\(59\) 3.96863 6.87386i 0.516671 0.894901i −0.483141 0.875542i \(-0.660504\pi\)
0.999813 0.0193585i \(-0.00616237\pi\)
\(60\) 1.82288 3.15731i 0.235332 0.407607i
\(61\) 5.96863 + 10.3380i 0.764204 + 1.32364i 0.940666 + 0.339333i \(0.110201\pi\)
−0.176462 + 0.984307i \(0.556465\pi\)
\(62\) −3.29150 −0.418021
\(63\) 1.32288 2.29129i 0.166667 0.288675i
\(64\) 1.00000 0.125000
\(65\) 1.82288 + 3.15731i 0.226100 + 0.391617i
\(66\) 0.322876 0.559237i 0.0397432 0.0688373i
\(67\) −3.79150 + 6.56708i −0.463206 + 0.802296i −0.999119 0.0419774i \(-0.986634\pi\)
0.535913 + 0.844273i \(0.319968\pi\)
\(68\) 3.32288 + 5.75539i 0.402958 + 0.697943i
\(69\) −2.35425 −0.283418
\(70\) −9.64575 −1.15289
\(71\) 16.2915 1.93345 0.966723 0.255826i \(-0.0823474\pi\)
0.966723 + 0.255826i \(0.0823474\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 6.82288 11.8176i 0.798557 1.38314i −0.121998 0.992530i \(-0.538930\pi\)
0.920556 0.390611i \(-0.127736\pi\)
\(74\) 2.82288 4.88936i 0.328153 0.568377i
\(75\) −4.14575 7.18065i −0.478710 0.829150i
\(76\) 5.00000 0.573539
\(77\) −1.70850 −0.194701
\(78\) −1.00000 −0.113228
\(79\) 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) 1.82288 3.15731i 0.203804 0.352998i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.17712 2.03884i −0.129992 0.225152i
\(83\) −13.2915 −1.45893 −0.729466 0.684017i \(-0.760231\pi\)
−0.729466 + 0.684017i \(0.760231\pi\)
\(84\) 1.32288 2.29129i 0.144338 0.250000i
\(85\) 24.2288 2.62798
\(86\) −2.64575 4.58258i −0.285299 0.494152i
\(87\) −2.14575 + 3.71655i −0.230049 + 0.398456i
\(88\) 0.322876 0.559237i 0.0344187 0.0596149i
\(89\) −8.46863 14.6681i −0.897673 1.55481i −0.830462 0.557076i \(-0.811923\pi\)
−0.0672111 0.997739i \(-0.521410\pi\)
\(90\) 3.64575 0.384296
\(91\) 1.32288 + 2.29129i 0.138675 + 0.240192i
\(92\) −2.35425 −0.245447
\(93\) −1.64575 2.85052i −0.170656 0.295586i
\(94\) 1.50000 2.59808i 0.154713 0.267971i
\(95\) 9.11438 15.7866i 0.935115 1.61967i
\(96\) 0.500000 + 0.866025i 0.0510310 + 0.0883883i
\(97\) 0.937254 0.0951637 0.0475819 0.998867i \(-0.484849\pi\)
0.0475819 + 0.998867i \(0.484849\pi\)
\(98\) −7.00000 −0.707107
\(99\) 0.645751 0.0649004
\(100\) −4.14575 7.18065i −0.414575 0.718065i
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) −3.32288 + 5.75539i −0.329014 + 0.569868i
\(103\) 2.64575 + 4.58258i 0.260694 + 0.451535i 0.966426 0.256943i \(-0.0827154\pi\)
−0.705733 + 0.708478i \(0.749382\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −4.82288 8.35347i −0.470664 0.815215i
\(106\) 3.00000 0.291386
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 2.00000 3.46410i 0.191565 0.331801i −0.754204 0.656640i \(-0.771977\pi\)
0.945769 + 0.324840i \(0.105310\pi\)
\(110\) −1.17712 2.03884i −0.112234 0.194396i
\(111\) 5.64575 0.535871
\(112\) 1.32288 2.29129i 0.125000 0.216506i
\(113\) 15.2288 1.43260 0.716300 0.697792i \(-0.245834\pi\)
0.716300 + 0.697792i \(0.245834\pi\)
\(114\) 2.50000 + 4.33013i 0.234146 + 0.405554i
\(115\) −4.29150 + 7.43310i −0.400185 + 0.693140i
\(116\) −2.14575 + 3.71655i −0.199228 + 0.345073i
\(117\) −0.500000 0.866025i −0.0462250 0.0800641i
\(118\) 7.93725 0.730683
\(119\) 17.5830 1.61183
\(120\) 3.64575 0.332810
\(121\) 5.29150 + 9.16515i 0.481046 + 0.833196i
\(122\) −5.96863 + 10.3380i −0.540374 + 0.935955i
\(123\) 1.17712 2.03884i 0.106138 0.183836i
\(124\) −1.64575 2.85052i −0.147793 0.255985i
\(125\) −12.0000 −1.07331
\(126\) 2.64575 0.235702
\(127\) −10.2288 −0.907655 −0.453828 0.891089i \(-0.649942\pi\)
−0.453828 + 0.891089i \(0.649942\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 2.64575 4.58258i 0.232945 0.403473i
\(130\) −1.82288 + 3.15731i −0.159877 + 0.276915i
\(131\) −5.46863 9.47194i −0.477796 0.827567i 0.521880 0.853019i \(-0.325231\pi\)
−0.999676 + 0.0254518i \(0.991898\pi\)
\(132\) 0.645751 0.0562054
\(133\) 6.61438 11.4564i 0.573539 0.993399i
\(134\) −7.58301 −0.655072
\(135\) 1.82288 + 3.15731i 0.156888 + 0.271738i
\(136\) −3.32288 + 5.75539i −0.284934 + 0.493521i
\(137\) 9.76013 16.9050i 0.833864 1.44430i −0.0610877 0.998132i \(-0.519457\pi\)
0.894952 0.446163i \(-0.147210\pi\)
\(138\) −1.17712 2.03884i −0.100203 0.173558i
\(139\) −22.2288 −1.88542 −0.942709 0.333615i \(-0.891731\pi\)
−0.942709 + 0.333615i \(0.891731\pi\)
\(140\) −4.82288 8.35347i −0.407607 0.705997i
\(141\) 3.00000 0.252646
\(142\) 8.14575 + 14.1089i 0.683576 + 1.18399i
\(143\) −0.322876 + 0.559237i −0.0270002 + 0.0467658i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 7.82288 + 13.5496i 0.649654 + 1.12523i
\(146\) 13.6458 1.12933
\(147\) −3.50000 6.06218i −0.288675 0.500000i
\(148\) 5.64575 0.464078
\(149\) 3.53137 + 6.11652i 0.289301 + 0.501085i 0.973643 0.228077i \(-0.0732437\pi\)
−0.684342 + 0.729161i \(0.739910\pi\)
\(150\) 4.14575 7.18065i 0.338499 0.586298i
\(151\) −3.03137 + 5.25049i −0.246690 + 0.427279i −0.962605 0.270908i \(-0.912676\pi\)
0.715916 + 0.698187i \(0.246009\pi\)
\(152\) 2.50000 + 4.33013i 0.202777 + 0.351220i
\(153\) −6.64575 −0.537277
\(154\) −0.854249 1.47960i −0.0688373 0.119230i
\(155\) −12.0000 −0.963863
\(156\) −0.500000 0.866025i −0.0400320 0.0693375i
\(157\) −1.32288 + 2.29129i −0.105577 + 0.182865i −0.913974 0.405773i \(-0.867002\pi\)
0.808397 + 0.588638i \(0.200336\pi\)
\(158\) −5.00000 + 8.66025i −0.397779 + 0.688973i
\(159\) 1.50000 + 2.59808i 0.118958 + 0.206041i
\(160\) 3.64575 0.288222
\(161\) −3.11438 + 5.39426i −0.245447 + 0.425127i
\(162\) −1.00000 −0.0785674
\(163\) −1.20850 2.09318i −0.0946568 0.163950i 0.814809 0.579730i \(-0.196842\pi\)
−0.909465 + 0.415780i \(0.863509\pi\)
\(164\) 1.17712 2.03884i 0.0919180 0.159207i
\(165\) 1.17712 2.03884i 0.0916390 0.158723i
\(166\) −6.64575 11.5108i −0.515810 0.893410i
\(167\) −6.87451 −0.531965 −0.265983 0.963978i \(-0.585696\pi\)
−0.265983 + 0.963978i \(0.585696\pi\)
\(168\) 2.64575 0.204124
\(169\) 1.00000 0.0769231
\(170\) 12.1144 + 20.9827i 0.929130 + 1.60930i
\(171\) −2.50000 + 4.33013i −0.191180 + 0.331133i
\(172\) 2.64575 4.58258i 0.201737 0.349418i
\(173\) 11.1458 + 19.3050i 0.847396 + 1.46773i 0.883524 + 0.468385i \(0.155164\pi\)
−0.0361285 + 0.999347i \(0.511503\pi\)
\(174\) −4.29150 −0.325338
\(175\) −21.9373 −1.65830
\(176\) 0.645751 0.0486753
\(177\) 3.96863 + 6.87386i 0.298300 + 0.516671i
\(178\) 8.46863 14.6681i 0.634750 1.09942i
\(179\) 3.00000 5.19615i 0.224231 0.388379i −0.731858 0.681457i \(-0.761346\pi\)
0.956088 + 0.293079i \(0.0946798\pi\)
\(180\) 1.82288 + 3.15731i 0.135869 + 0.235332i
\(181\) 14.6458 1.08861 0.544305 0.838887i \(-0.316793\pi\)
0.544305 + 0.838887i \(0.316793\pi\)
\(182\) −1.32288 + 2.29129i −0.0980581 + 0.169842i
\(183\) −11.9373 −0.882427
\(184\) −1.17712 2.03884i −0.0867788 0.150305i
\(185\) 10.2915 17.8254i 0.756646 1.31055i
\(186\) 1.64575 2.85052i 0.120672 0.209011i
\(187\) 2.14575 + 3.71655i 0.156913 + 0.271781i
\(188\) 3.00000 0.218797
\(189\) 1.32288 + 2.29129i 0.0962250 + 0.166667i
\(190\) 18.2288 1.32245
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) −0.500000 + 0.866025i −0.0360844 + 0.0625000i
\(193\) −9.46863 + 16.4001i −0.681567 + 1.18051i 0.292936 + 0.956132i \(0.405368\pi\)
−0.974503 + 0.224376i \(0.927966\pi\)
\(194\) 0.468627 + 0.811686i 0.0336455 + 0.0582756i
\(195\) −3.64575 −0.261078
\(196\) −3.50000 6.06218i −0.250000 0.433013i
\(197\) −26.8118 −1.91026 −0.955129 0.296189i \(-0.904284\pi\)
−0.955129 + 0.296189i \(0.904284\pi\)
\(198\) 0.322876 + 0.559237i 0.0229458 + 0.0397432i
\(199\) 11.1144 19.2507i 0.787877 1.36464i −0.139388 0.990238i \(-0.544513\pi\)
0.927265 0.374406i \(-0.122153\pi\)
\(200\) 4.14575 7.18065i 0.293149 0.507749i
\(201\) −3.79150 6.56708i −0.267432 0.463206i
\(202\) 0 0
\(203\) 5.67712 + 9.83307i 0.398456 + 0.690146i
\(204\) −6.64575 −0.465296
\(205\) −4.29150 7.43310i −0.299732 0.519150i
\(206\) −2.64575 + 4.58258i −0.184338 + 0.319283i
\(207\) 1.17712 2.03884i 0.0818158 0.141709i
\(208\) −0.500000 0.866025i −0.0346688 0.0600481i
\(209\) 3.22876 0.223338
\(210\) 4.82288 8.35347i 0.332810 0.576444i
\(211\) −6.35425 −0.437445 −0.218722 0.975787i \(-0.570189\pi\)
−0.218722 + 0.975787i \(0.570189\pi\)
\(212\) 1.50000 + 2.59808i 0.103020 + 0.178437i
\(213\) −8.14575 + 14.1089i −0.558138 + 0.966723i
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) −9.64575 16.7069i −0.657835 1.13940i
\(216\) −1.00000 −0.0680414
\(217\) −8.70850 −0.591171
\(218\) 4.00000 0.270914
\(219\) 6.82288 + 11.8176i 0.461047 + 0.798557i
\(220\) 1.17712 2.03884i 0.0793617 0.137459i
\(221\) 3.32288 5.75539i 0.223521 0.387149i
\(222\) 2.82288 + 4.88936i 0.189459 + 0.328153i
\(223\) −20.5203 −1.37414 −0.687069 0.726592i \(-0.741103\pi\)
−0.687069 + 0.726592i \(0.741103\pi\)
\(224\) 2.64575 0.176777
\(225\) 8.29150 0.552767
\(226\) 7.61438 + 13.1885i 0.506501 + 0.877285i
\(227\) 2.35425 4.07768i 0.156257 0.270645i −0.777259 0.629181i \(-0.783391\pi\)
0.933516 + 0.358536i \(0.116724\pi\)
\(228\) −2.50000 + 4.33013i −0.165567 + 0.286770i
\(229\) −13.2288 22.9129i −0.874181 1.51413i −0.857633 0.514263i \(-0.828066\pi\)
−0.0165480 0.999863i \(-0.505268\pi\)
\(230\) −8.58301 −0.565947
\(231\) 0.854249 1.47960i 0.0562054 0.0973507i
\(232\) −4.29150 −0.281751
\(233\) −0.322876 0.559237i −0.0211523 0.0366368i 0.855256 0.518207i \(-0.173400\pi\)
−0.876408 + 0.481570i \(0.840067\pi\)
\(234\) 0.500000 0.866025i 0.0326860 0.0566139i
\(235\) 5.46863 9.47194i 0.356734 0.617881i
\(236\) 3.96863 + 6.87386i 0.258336 + 0.447450i
\(237\) −10.0000 −0.649570
\(238\) 8.79150 + 15.2273i 0.569868 + 0.987041i
\(239\) 3.00000 0.194054 0.0970269 0.995282i \(-0.469067\pi\)
0.0970269 + 0.995282i \(0.469067\pi\)
\(240\) 1.82288 + 3.15731i 0.117666 + 0.203804i
\(241\) 6.93725 12.0157i 0.446868 0.773998i −0.551312 0.834299i \(-0.685873\pi\)
0.998180 + 0.0603011i \(0.0192061\pi\)
\(242\) −5.29150 + 9.16515i −0.340151 + 0.589158i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −11.9373 −0.764204
\(245\) −25.5203 −1.63043
\(246\) 2.35425 0.150101
\(247\) −2.50000 4.33013i −0.159071 0.275519i
\(248\) 1.64575 2.85052i 0.104505 0.181009i
\(249\) 6.64575 11.5108i 0.421157 0.729466i
\(250\) −6.00000 10.3923i −0.379473 0.657267i
\(251\) −13.2915 −0.838952 −0.419476 0.907766i \(-0.637786\pi\)
−0.419476 + 0.907766i \(0.637786\pi\)
\(252\) 1.32288 + 2.29129i 0.0833333 + 0.144338i
\(253\) −1.52026 −0.0955779
\(254\) −5.11438 8.85836i −0.320905 0.555823i
\(255\) −12.1144 + 20.9827i −0.758632 + 1.31399i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.93725 + 13.7477i 0.495112 + 0.857560i 0.999984 0.00563467i \(-0.00179358\pi\)
−0.504872 + 0.863194i \(0.668460\pi\)
\(258\) 5.29150 0.329435
\(259\) 7.46863 12.9360i 0.464078 0.803806i
\(260\) −3.64575 −0.226100
\(261\) −2.14575 3.71655i −0.132819 0.230049i
\(262\) 5.46863 9.47194i 0.337853 0.585178i
\(263\) 1.82288 3.15731i 0.112403 0.194688i −0.804335 0.594175i \(-0.797478\pi\)
0.916739 + 0.399487i \(0.130812\pi\)
\(264\) 0.322876 + 0.559237i 0.0198716 + 0.0344187i
\(265\) 10.9373 0.671870
\(266\) 13.2288 0.811107
\(267\) 16.9373 1.03654
\(268\) −3.79150 6.56708i −0.231603 0.401148i
\(269\) −3.43725 + 5.95350i −0.209573 + 0.362991i −0.951580 0.307401i \(-0.900541\pi\)
0.742007 + 0.670392i \(0.233874\pi\)
\(270\) −1.82288 + 3.15731i −0.110937 + 0.192148i
\(271\) 11.3229 + 19.6118i 0.687816 + 1.19133i 0.972543 + 0.232723i \(0.0747636\pi\)
−0.284727 + 0.958609i \(0.591903\pi\)
\(272\) −6.64575 −0.402958
\(273\) −2.64575 −0.160128
\(274\) 19.5203 1.17926
\(275\) −2.67712 4.63692i −0.161437 0.279617i
\(276\) 1.17712 2.03884i 0.0708546 0.122724i
\(277\) −9.26013 + 16.0390i −0.556387 + 0.963691i 0.441407 + 0.897307i \(0.354480\pi\)
−0.997794 + 0.0663840i \(0.978854\pi\)
\(278\) −11.1144 19.2507i −0.666596 1.15458i
\(279\) 3.29150 0.197057
\(280\) 4.82288 8.35347i 0.288222 0.499215i
\(281\) −2.58301 −0.154089 −0.0770446 0.997028i \(-0.524548\pi\)
−0.0770446 + 0.997028i \(0.524548\pi\)
\(282\) 1.50000 + 2.59808i 0.0893237 + 0.154713i
\(283\) 5.53137 9.58062i 0.328806 0.569509i −0.653469 0.756953i \(-0.726687\pi\)
0.982275 + 0.187444i \(0.0600204\pi\)
\(284\) −8.14575 + 14.1089i −0.483361 + 0.837207i
\(285\) 9.11438 + 15.7866i 0.539889 + 0.935115i
\(286\) −0.645751 −0.0381841
\(287\) −3.11438 5.39426i −0.183836 0.318413i
\(288\) −1.00000 −0.0589256
\(289\) −13.5830 23.5265i −0.799000 1.38391i
\(290\) −7.82288 + 13.5496i −0.459375 + 0.795661i
\(291\) −0.468627 + 0.811686i −0.0274714 + 0.0475819i
\(292\) 6.82288 + 11.8176i 0.399279 + 0.691571i
\(293\) 7.52026 0.439338 0.219669 0.975574i \(-0.429502\pi\)
0.219669 + 0.975574i \(0.429502\pi\)
\(294\) 3.50000 6.06218i 0.204124 0.353553i
\(295\) 28.9373 1.68479
\(296\) 2.82288 + 4.88936i 0.164076 + 0.284189i
\(297\) −0.322876 + 0.559237i −0.0187351 + 0.0324502i
\(298\) −3.53137 + 6.11652i −0.204567 + 0.354320i
\(299\) 1.17712 + 2.03884i 0.0680749 + 0.117909i
\(300\) 8.29150 0.478710
\(301\) −7.00000 12.1244i −0.403473 0.698836i
\(302\) −6.06275 −0.348872
\(303\) 0 0
\(304\) −2.50000 + 4.33013i −0.143385 + 0.248350i
\(305\) −21.7601 + 37.6897i −1.24598 + 2.15810i
\(306\) −3.32288 5.75539i −0.189956 0.329014i
\(307\) −9.58301 −0.546931 −0.273465 0.961882i \(-0.588170\pi\)
−0.273465 + 0.961882i \(0.588170\pi\)
\(308\) 0.854249 1.47960i 0.0486753 0.0843082i
\(309\) −5.29150 −0.301023
\(310\) −6.00000 10.3923i −0.340777 0.590243i
\(311\) 0.531373 0.920365i 0.0301314 0.0521891i −0.850566 0.525868i \(-0.823741\pi\)
0.880698 + 0.473678i \(0.157074\pi\)
\(312\) 0.500000 0.866025i 0.0283069 0.0490290i
\(313\) −6.58301 11.4021i −0.372093 0.644485i 0.617794 0.786340i \(-0.288027\pi\)
−0.989887 + 0.141855i \(0.954693\pi\)
\(314\) −2.64575 −0.149308
\(315\) 9.64575 0.543477
\(316\) −10.0000 −0.562544
\(317\) 6.64575 + 11.5108i 0.373263 + 0.646510i 0.990065 0.140608i \(-0.0449057\pi\)
−0.616803 + 0.787118i \(0.711572\pi\)
\(318\) −1.50000 + 2.59808i −0.0841158 + 0.145693i
\(319\) −1.38562 + 2.39997i −0.0775799 + 0.134372i
\(320\) 1.82288 + 3.15731i 0.101902 + 0.176499i
\(321\) −12.0000 −0.669775
\(322\) −6.22876 −0.347115
\(323\) −33.2288 −1.84890
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) −4.14575 + 7.18065i −0.229965 + 0.398311i
\(326\) 1.20850 2.09318i 0.0669325 0.115930i
\(327\) 2.00000 + 3.46410i 0.110600 + 0.191565i
\(328\) 2.35425 0.129992
\(329\) 3.96863 6.87386i 0.218797 0.378968i
\(330\) 2.35425 0.129597
\(331\) −5.70850 9.88741i −0.313767 0.543461i 0.665407 0.746480i \(-0.268258\pi\)
−0.979175 + 0.203019i \(0.934925\pi\)
\(332\) 6.64575 11.5108i 0.364733 0.631736i
\(333\) −2.82288 + 4.88936i −0.154693 + 0.267935i
\(334\) −3.43725 5.95350i −0.188078 0.325761i
\(335\) −27.6458 −1.51045
\(336\) 1.32288 + 2.29129i 0.0721688 + 0.125000i
\(337\) −15.5830 −0.848860 −0.424430 0.905461i \(-0.639526\pi\)
−0.424430 + 0.905461i \(0.639526\pi\)
\(338\) 0.500000 + 0.866025i 0.0271964 + 0.0471056i
\(339\) −7.61438 + 13.1885i −0.413556 + 0.716300i
\(340\) −12.1144 + 20.9827i −0.656994 + 1.13795i
\(341\) −1.06275 1.84073i −0.0575509 0.0996811i
\(342\) −5.00000 −0.270369
\(343\) −18.5203 −1.00000
\(344\) 5.29150 0.285299
\(345\) −4.29150 7.43310i −0.231047 0.400185i
\(346\) −11.1458 + 19.3050i −0.599199 + 1.03784i
\(347\) −0.114378 + 0.198109i −0.00614015 + 0.0106350i −0.869079 0.494673i \(-0.835288\pi\)
0.862939 + 0.505308i \(0.168621\pi\)
\(348\) −2.14575 3.71655i −0.115024 0.199228i
\(349\) 18.9373 1.01369 0.506844 0.862038i \(-0.330812\pi\)
0.506844 + 0.862038i \(0.330812\pi\)
\(350\) −10.9686 18.9982i −0.586298 1.01550i
\(351\) 1.00000 0.0533761
\(352\) 0.322876 + 0.559237i 0.0172093 + 0.0298074i
\(353\) 10.2915 17.8254i 0.547761 0.948751i −0.450666 0.892693i \(-0.648813\pi\)
0.998428 0.0560580i \(-0.0178532\pi\)
\(354\) −3.96863 + 6.87386i −0.210930 + 0.365342i
\(355\) 29.6974 + 51.4374i 1.57617 + 2.73001i
\(356\) 16.9373 0.897673
\(357\) −8.79150 + 15.2273i −0.465296 + 0.805916i
\(358\) 6.00000 0.317110
\(359\) 3.00000 + 5.19615i 0.158334 + 0.274242i 0.934268 0.356572i \(-0.116054\pi\)
−0.775934 + 0.630814i \(0.782721\pi\)
\(360\) −1.82288 + 3.15731i −0.0960740 + 0.166405i
\(361\) −3.00000 + 5.19615i −0.157895 + 0.273482i
\(362\) 7.32288 + 12.6836i 0.384882 + 0.666635i
\(363\) −10.5830 −0.555464
\(364\) −2.64575 −0.138675
\(365\) 49.7490 2.60398
\(366\) −5.96863 10.3380i −0.311985 0.540374i
\(367\) 0.291503 0.504897i 0.0152163 0.0263554i −0.858317 0.513120i \(-0.828490\pi\)
0.873533 + 0.486764i \(0.161823\pi\)
\(368\) 1.17712 2.03884i 0.0613618 0.106282i
\(369\) 1.17712 + 2.03884i 0.0612786 + 0.106138i
\(370\) 20.5830 1.07006
\(371\) 7.93725 0.412082
\(372\) 3.29150 0.170656
\(373\) −7.32288 12.6836i −0.379164 0.656732i 0.611777 0.791030i \(-0.290455\pi\)
−0.990941 + 0.134299i \(0.957122\pi\)
\(374\) −2.14575 + 3.71655i −0.110954 + 0.192178i
\(375\) 6.00000 10.3923i 0.309839 0.536656i
\(376\) 1.50000 + 2.59808i 0.0773566 + 0.133986i
\(377\) 4.29150 0.221024
\(378\) −1.32288 + 2.29129i −0.0680414 + 0.117851i
\(379\) −9.16601 −0.470826 −0.235413 0.971895i \(-0.575644\pi\)
−0.235413 + 0.971895i \(0.575644\pi\)
\(380\) 9.11438 + 15.7866i 0.467558 + 0.809834i
\(381\) 5.11438 8.85836i 0.262018 0.453828i
\(382\) 0 0
\(383\) −12.8745 22.2993i −0.657857 1.13944i −0.981169 0.193149i \(-0.938130\pi\)
0.323313 0.946292i \(-0.395203\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −3.11438 5.39426i −0.158723 0.274917i
\(386\) −18.9373 −0.963881
\(387\) 2.64575 + 4.58258i 0.134491 + 0.232945i
\(388\) −0.468627 + 0.811686i −0.0237909 + 0.0412071i
\(389\) −3.85425 + 6.67575i −0.195418 + 0.338474i −0.947038 0.321123i \(-0.895940\pi\)
0.751619 + 0.659597i \(0.229273\pi\)
\(390\) −1.82288 3.15731i −0.0923049 0.159877i
\(391\) 15.6458 0.791240
\(392\) 3.50000 6.06218i 0.176777 0.306186i
\(393\) 10.9373 0.551711
\(394\) −13.4059 23.2197i −0.675379 1.16979i
\(395\) −18.2288 + 31.5731i −0.917188 + 1.58862i
\(396\) −0.322876 + 0.559237i −0.0162251 + 0.0281027i
\(397\) 7.46863 + 12.9360i 0.374840 + 0.649241i 0.990303 0.138924i \(-0.0443644\pi\)
−0.615463 + 0.788165i \(0.711031\pi\)
\(398\) 22.2288 1.11423
\(399\) 6.61438 + 11.4564i 0.331133 + 0.573539i
\(400\) 8.29150 0.414575
\(401\) 9.11438 + 15.7866i 0.455150 + 0.788343i 0.998697 0.0510356i \(-0.0162522\pi\)
−0.543547 + 0.839379i \(0.682919\pi\)
\(402\) 3.79150 6.56708i 0.189103 0.327536i
\(403\) −1.64575 + 2.85052i −0.0819807 + 0.141995i
\(404\) 0 0
\(405\) −3.64575 −0.181159
\(406\) −5.67712 + 9.83307i −0.281751 + 0.488007i
\(407\) 3.64575 0.180713
\(408\) −3.32288 5.75539i −0.164507 0.284934i
\(409\) 13.4686 23.3283i 0.665981 1.15351i −0.313038 0.949741i \(-0.601347\pi\)
0.979018 0.203772i \(-0.0653201\pi\)
\(410\) 4.29150 7.43310i 0.211942 0.367095i
\(411\) 9.76013 + 16.9050i 0.481432 + 0.833864i
\(412\) −5.29150 −0.260694
\(413\) 21.0000 1.03334
\(414\) 2.35425 0.115705
\(415\) −24.2288 41.9654i −1.18934 2.06000i
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) 11.1144 19.2507i 0.544273 0.942709i
\(418\) 1.61438 + 2.79619i 0.0789618 + 0.136766i
\(419\) 30.4575 1.48795 0.743973 0.668209i \(-0.232939\pi\)
0.743973 + 0.668209i \(0.232939\pi\)
\(420\) 9.64575 0.470664
\(421\) −24.3542 −1.18695 −0.593477 0.804851i \(-0.702245\pi\)
−0.593477 + 0.804851i \(0.702245\pi\)
\(422\) −3.17712 5.50294i −0.154660 0.267879i
\(423\) −1.50000 + 2.59808i −0.0729325 + 0.126323i
\(424\) −1.50000 + 2.59808i −0.0728464 + 0.126174i
\(425\) 27.5516 + 47.7208i 1.33645 + 2.31480i
\(426\) −16.2915 −0.789326
\(427\) −15.7915 + 27.3517i −0.764204 + 1.32364i
\(428\) −12.0000 −0.580042
\(429\) −0.322876 0.559237i −0.0155886 0.0270002i
\(430\) 9.64575 16.7069i 0.465159 0.805680i
\(431\) −10.2915 + 17.8254i −0.495724 + 0.858620i −0.999988 0.00493021i \(-0.998431\pi\)
0.504264 + 0.863550i \(0.331764\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −33.5830 −1.61390 −0.806948 0.590622i \(-0.798882\pi\)
−0.806948 + 0.590622i \(0.798882\pi\)
\(434\) −4.35425 7.54178i −0.209011 0.362017i
\(435\) −15.6458 −0.750156
\(436\) 2.00000 + 3.46410i 0.0957826 + 0.165900i
\(437\) 5.88562 10.1942i 0.281547 0.487655i
\(438\) −6.82288 + 11.8176i −0.326010 + 0.564665i
\(439\) −11.8229 20.4778i −0.564275 0.977353i −0.997117 0.0758831i \(-0.975822\pi\)
0.432842 0.901470i \(-0.357511\pi\)
\(440\) 2.35425 0.112234
\(441\) 7.00000 0.333333
\(442\) 6.64575 0.316106
\(443\) −9.53137 16.5088i −0.452849 0.784358i 0.545713 0.837972i \(-0.316259\pi\)
−0.998562 + 0.0536147i \(0.982926\pi\)
\(444\) −2.82288 + 4.88936i −0.133968 + 0.232039i
\(445\) 30.8745 53.4762i 1.46359 2.53502i
\(446\) −10.2601 17.7711i −0.485831 0.841484i
\(447\) −7.06275 −0.334056
\(448\) 1.32288 + 2.29129i 0.0625000 + 0.108253i
\(449\) 12.0000 0.566315 0.283158 0.959073i \(-0.408618\pi\)
0.283158 + 0.959073i \(0.408618\pi\)
\(450\) 4.14575 + 7.18065i 0.195433 + 0.338499i
\(451\) 0.760130 1.31658i 0.0357931 0.0619955i
\(452\) −7.61438 + 13.1885i −0.358150 + 0.620334i
\(453\) −3.03137 5.25049i −0.142426 0.246690i
\(454\) 4.70850 0.220981
\(455\) −4.82288 + 8.35347i −0.226100 + 0.391617i
\(456\) −5.00000 −0.234146
\(457\) −16.1144 27.9109i −0.753799 1.30562i −0.945969 0.324256i \(-0.894886\pi\)
0.192170 0.981362i \(-0.438447\pi\)
\(458\) 13.2288 22.9129i 0.618139 1.07065i
\(459\) 3.32288 5.75539i 0.155099 0.268639i
\(460\) −4.29150 7.43310i −0.200092 0.346570i
\(461\) −36.4575 −1.69800 −0.848998 0.528396i \(-0.822794\pi\)
−0.848998 + 0.528396i \(0.822794\pi\)
\(462\) 1.70850 0.0794865
\(463\) 25.1660 1.16956 0.584782 0.811191i \(-0.301180\pi\)
0.584782 + 0.811191i \(0.301180\pi\)
\(464\) −2.14575 3.71655i −0.0996140 0.172537i
\(465\) 6.00000 10.3923i 0.278243 0.481932i
\(466\) 0.322876 0.559237i 0.0149569 0.0259062i
\(467\) 18.7601 + 32.4935i 0.868115 + 1.50362i 0.863920 + 0.503629i \(0.168002\pi\)
0.00419497 + 0.999991i \(0.498665\pi\)
\(468\) 1.00000 0.0462250
\(469\) −20.0627 −0.926412
\(470\) 10.9373 0.504498
\(471\) −1.32288 2.29129i −0.0609549 0.105577i
\(472\) −3.96863 + 6.87386i −0.182671 + 0.316395i
\(473\) 1.70850 2.95920i 0.0785568 0.136064i
\(474\) −5.00000 8.66025i −0.229658 0.397779i
\(475\) 41.4575 1.90220
\(476\) −8.79150 + 15.2273i −0.402958 + 0.697943i
\(477\) −3.00000 −0.137361
\(478\) 1.50000 + 2.59808i 0.0686084 + 0.118833i
\(479\) 17.3745 30.0935i 0.793862 1.37501i −0.129698 0.991554i \(-0.541401\pi\)
0.923560 0.383455i \(-0.125266\pi\)
\(480\) −1.82288 + 3.15731i −0.0832025 + 0.144111i
\(481\) −2.82288 4.88936i −0.128712 0.222936i
\(482\) 13.8745 0.631967
\(483\) −3.11438 5.39426i −0.141709 0.245447i
\(484\) −10.5830 −0.481046
\(485\) 1.70850 + 2.95920i 0.0775789 + 0.134371i
\(486\) 0.500000 0.866025i 0.0226805 0.0392837i
\(487\) 11.9686 20.7303i 0.542350 0.939378i −0.456418 0.889765i \(-0.650868\pi\)
0.998769 0.0496129i \(-0.0157987\pi\)
\(488\) −5.96863 10.3380i −0.270187 0.467978i
\(489\) 2.41699 0.109300
\(490\) −12.7601 22.1012i −0.576444 0.998430i
\(491\) 11.1660 0.503915 0.251957 0.967738i \(-0.418926\pi\)
0.251957 + 0.967738i \(0.418926\pi\)
\(492\) 1.17712 + 2.03884i 0.0530689 + 0.0919180i
\(493\) 14.2601 24.6993i 0.642244 1.11240i
\(494\) 2.50000 4.33013i 0.112480 0.194822i
\(495\) 1.17712 + 2.03884i 0.0529078 + 0.0916390i
\(496\) 3.29150 0.147793
\(497\) 21.5516 + 37.3285i 0.966723 + 1.67441i
\(498\) 13.2915 0.595606
\(499\) 14.6458 + 25.3672i 0.655634 + 1.13559i 0.981734 + 0.190256i \(0.0609318\pi\)
−0.326101 + 0.945335i \(0.605735\pi\)
\(500\) 6.00000 10.3923i 0.268328 0.464758i
\(501\) 3.43725 5.95350i 0.153565 0.265983i
\(502\) −6.64575 11.5108i −0.296614 0.513751i
\(503\) 36.4575 1.62556 0.812780 0.582571i \(-0.197953\pi\)
0.812780 + 0.582571i \(0.197953\pi\)
\(504\) −1.32288 + 2.29129i −0.0589256 + 0.102062i
\(505\) 0 0
\(506\) −0.760130 1.31658i −0.0337919 0.0585293i
\(507\) −0.500000 + 0.866025i −0.0222058 + 0.0384615i
\(508\) 5.11438 8.85836i 0.226914 0.393026i
\(509\) −12.0000 20.7846i −0.531891 0.921262i −0.999307 0.0372243i \(-0.988148\pi\)
0.467416 0.884037i \(-0.345185\pi\)
\(510\) −24.2288 −1.07287
\(511\) 36.1033 1.59711
\(512\) −1.00000 −0.0441942
\(513\) −2.50000 4.33013i −0.110378 0.191180i
\(514\) −7.93725 + 13.7477i −0.350097 + 0.606386i
\(515\) −9.64575 + 16.7069i −0.425043 + 0.736195i
\(516\) 2.64575 + 4.58258i 0.116473 + 0.201737i
\(517\) 1.93725 0.0852003
\(518\) 14.9373 0.656305
\(519\) −22.2915 −0.978488
\(520\) −1.82288 3.15731i −0.0799384 0.138457i
\(521\) −9.00000 + 15.5885i −0.394297 + 0.682943i −0.993011 0.118020i \(-0.962345\pi\)
0.598714 + 0.800963i \(0.295679\pi\)
\(522\) 2.14575 3.71655i 0.0939170 0.162669i
\(523\) 13.3542 + 23.1302i 0.583941 + 1.01141i 0.995007 + 0.0998091i \(0.0318232\pi\)
−0.411066 + 0.911606i \(0.634843\pi\)
\(524\) 10.9373 0.477796
\(525\) 10.9686 18.9982i 0.478710 0.829150i
\(526\) 3.64575 0.158962
\(527\) 10.9373 + 18.9439i 0.476434 + 0.825208i
\(528\) −0.322876 + 0.559237i −0.0140514 + 0.0243377i
\(529\) 8.72876 15.1186i 0.379511 0.657333i
\(530\) 5.46863 + 9.47194i 0.237542 + 0.411435i
\(531\) −7.93725 −0.344447
\(532\) 6.61438 + 11.4564i 0.286770 + 0.496700i
\(533\) −2.35425 −0.101974
\(534\) 8.46863 + 14.6681i 0.366473 + 0.634750i
\(535\) −21.8745 + 37.8878i −0.945717 + 1.63803i
\(536\) 3.79150 6.56708i 0.163768 0.283654i
\(537\) 3.00000 + 5.19615i 0.129460 + 0.224231i
\(538\) −6.87451 −0.296381
\(539\) −2.26013 3.91466i −0.0973507 0.168616i
\(540\) −3.64575 −0.156888
\(541\) −20.8229 36.0663i −0.895245 1.55061i −0.833501 0.552518i \(-0.813667\pi\)
−0.0617447 0.998092i \(-0.519666\pi\)
\(542\) −11.3229 + 19.6118i −0.486359 + 0.842399i
\(543\) −7.32288 + 12.6836i −0.314255 + 0.544305i
\(544\) −3.32288 5.75539i −0.142467 0.246760i
\(545\) 14.5830 0.624667
\(546\) −1.32288 2.29129i −0.0566139 0.0980581i
\(547\) −20.9373 −0.895212 −0.447606 0.894231i \(-0.647723\pi\)
−0.447606 + 0.894231i \(0.647723\pi\)
\(548\) 9.76013 + 16.9050i 0.416932 + 0.722148i
\(549\) 5.96863 10.3380i 0.254735 0.441214i
\(550\) 2.67712 4.63692i 0.114153 0.197719i
\(551\) −10.7288 18.5828i −0.457060 0.791652i
\(552\) 2.35425 0.100203
\(553\) −13.2288 + 22.9129i −0.562544 + 0.974355i
\(554\) −18.5203 −0.786850
\(555\) 10.2915 + 17.8254i 0.436850 + 0.756646i
\(556\) 11.1144 19.2507i 0.471355 0.816410i
\(557\) −5.58301 + 9.67005i −0.236560 + 0.409733i −0.959725 0.280942i \(-0.909353\pi\)
0.723165 + 0.690675i \(0.242686\pi\)
\(558\) 1.64575 + 2.85052i 0.0696702 + 0.120672i
\(559\) −5.29150 −0.223807
\(560\) 9.64575 0.407607
\(561\) −4.29150 −0.181187
\(562\) −1.29150 2.23695i −0.0544788 0.0943600i
\(563\) 13.5203 23.4178i 0.569811 0.986942i −0.426773 0.904359i \(-0.640350\pi\)
0.996584 0.0825829i \(-0.0263169\pi\)
\(564\) −1.50000 + 2.59808i −0.0631614 + 0.109399i
\(565\) 27.7601 + 48.0820i 1.16788 + 2.02282i
\(566\) 11.0627 0.465002
\(567\) −2.64575 −0.111111
\(568\) −16.2915 −0.683576
\(569\) 16.6144 + 28.7769i 0.696511 + 1.20639i 0.969669 + 0.244423i \(0.0785986\pi\)
−0.273158 + 0.961969i \(0.588068\pi\)
\(570\) −9.11438 + 15.7866i −0.381759 + 0.661226i
\(571\) 8.00000 13.8564i 0.334790 0.579873i −0.648655 0.761083i \(-0.724668\pi\)
0.983444 + 0.181210i \(0.0580014\pi\)
\(572\) −0.322876 0.559237i −0.0135001 0.0233829i
\(573\) 0 0
\(574\) 3.11438 5.39426i 0.129992 0.225152i
\(575\) −19.5203 −0.814051
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 6.29150 10.8972i 0.261919 0.453656i −0.704833 0.709373i \(-0.748978\pi\)
0.966752 + 0.255717i \(0.0823114\pi\)
\(578\) 13.5830 23.5265i 0.564979 0.978572i
\(579\) −9.46863 16.4001i −0.393503 0.681567i
\(580\) −15.6458 −0.649654
\(581\) −17.5830 30.4547i −0.729466 1.26347i
\(582\) −0.937254 −0.0388504
\(583\) 0.968627 + 1.67771i 0.0401164 + 0.0694837i
\(584\) −6.82288 + 11.8176i −0.282333 + 0.489014i
\(585\) 1.82288 3.15731i 0.0753666 0.130539i
\(586\) 3.76013 + 6.51274i 0.155330 + 0.269039i
\(587\) 31.9373 1.31819 0.659096 0.752059i \(-0.270939\pi\)
0.659096 + 0.752059i \(0.270939\pi\)
\(588\) 7.00000 0.288675
\(589\) 16.4575 0.678120
\(590\) 14.4686 + 25.0604i 0.595664 + 1.03172i
\(591\) 13.4059 23.2197i 0.551444 0.955129i
\(592\) −2.82288 + 4.88936i −0.116019 + 0.200952i
\(593\) −21.7601 37.6897i −0.893581 1.54773i −0.835551 0.549414i \(-0.814851\pi\)
−0.0580309 0.998315i \(-0.518482\pi\)
\(594\) −0.645751 −0.0264955
\(595\) 32.0516 + 55.5151i 1.31399 + 2.27590i
\(596\) −7.06275 −0.289301
\(597\) 11.1144 + 19.2507i 0.454881 + 0.787877i
\(598\) −1.17712 + 2.03884i −0.0481362 + 0.0833743i
\(599\) 16.4059 28.4158i 0.670326 1.16104i −0.307485 0.951553i \(-0.599488\pi\)
0.977812 0.209486i \(-0.0671791\pi\)
\(600\) 4.14575 + 7.18065i 0.169250 + 0.293149i
\(601\) 14.8745 0.606744 0.303372 0.952872i \(-0.401888\pi\)
0.303372 + 0.952872i \(0.401888\pi\)
\(602\) 7.00000 12.1244i 0.285299 0.494152i
\(603\) 7.58301 0.308804
\(604\) −3.03137 5.25049i −0.123345 0.213639i
\(605\) −19.2915 + 33.4139i −0.784311 + 1.35847i
\(606\) 0 0
\(607\) −8.40588 14.5594i −0.341184 0.590948i 0.643469 0.765472i \(-0.277495\pi\)
−0.984653 + 0.174524i \(0.944161\pi\)
\(608\) −5.00000 −0.202777
\(609\) −11.3542 −0.460097
\(610\) −43.5203 −1.76208
\(611\) −1.50000 2.59808i −0.0606835 0.105107i
\(612\) 3.32288 5.75539i 0.134319 0.232648i
\(613\) −20.9373 + 36.2644i −0.845648 + 1.46470i 0.0394098 + 0.999223i \(0.487452\pi\)
−0.885058 + 0.465482i \(0.845881\pi\)
\(614\) −4.79150 8.29913i −0.193369 0.334925i
\(615\) 8.58301 0.346100
\(616\) 1.70850 0.0688373
\(617\) −10.7085 −0.431108 −0.215554 0.976492i \(-0.569156\pi\)
−0.215554 + 0.976492i \(0.569156\pi\)
\(618\) −2.64575 4.58258i −0.106428 0.184338i
\(619\) 20.8745 36.1557i 0.839017 1.45322i −0.0516999 0.998663i \(-0.516464\pi\)
0.890717 0.454558i \(-0.150203\pi\)
\(620\) 6.00000 10.3923i 0.240966 0.417365i
\(621\) 1.17712 + 2.03884i 0.0472364 + 0.0818158i
\(622\) 1.06275 0.0426122
\(623\) 22.4059 38.8081i 0.897673 1.55481i
\(624\) 1.00000 0.0400320
\(625\) −1.14575 1.98450i −0.0458301 0.0793800i
\(626\) 6.58301 11.4021i 0.263110 0.455720i
\(627\) −1.61438 + 2.79619i −0.0644721 + 0.111669i
\(628\) −1.32288 2.29129i −0.0527885 0.0914323i
\(629\) −37.5203 −1.49603
\(630\) 4.82288 + 8.35347i 0.192148 + 0.332810i
\(631\) 14.4575 0.575545 0.287772 0.957699i \(-0.407085\pi\)
0.287772 + 0.957699i \(0.407085\pi\)
\(632\) −5.00000 8.66025i −0.198889 0.344486i
\(633\) 3.17712 5.50294i 0.126279 0.218722i
\(634\) −6.64575 + 11.5108i −0.263937 + 0.457151i
\(635\) −18.6458 32.2954i −0.739934 1.28160i
\(636\) −3.00000 −0.118958
\(637\) −3.50000 + 6.06218i −0.138675 + 0.240192i
\(638\) −2.77124 −0.109715
\(639\) −8.14575 14.1089i −0.322241 0.558138i
\(640\) −1.82288 + 3.15731i −0.0720555 + 0.124804i
\(641\) 10.7085 18.5477i 0.422960 0.732589i −0.573267 0.819368i \(-0.694324\pi\)
0.996228 + 0.0867798i \(0.0276577\pi\)
\(642\) −6.00000 10.3923i −0.236801 0.410152i
\(643\) −10.8745 −0.428849 −0.214424 0.976741i \(-0.568788\pi\)
−0.214424 + 0.976741i \(0.568788\pi\)
\(644\) −3.11438 5.39426i −0.122724 0.212564i
\(645\) 19.2915 0.759602
\(646\) −16.6144 28.7769i −0.653684 1.13221i
\(647\) −12.8745 + 22.2993i −0.506149 + 0.876676i 0.493826 + 0.869561i \(0.335598\pi\)
−0.999975 + 0.00711502i \(0.997735\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 2.56275 + 4.43881i 0.100597 + 0.174238i
\(650\) −8.29150 −0.325219
\(651\) 4.35425 7.54178i 0.170656 0.295586i
\(652\) 2.41699 0.0946568
\(653\) −6.00000 10.3923i −0.234798 0.406682i 0.724416 0.689363i \(-0.242110\pi\)
−0.959214 + 0.282681i \(0.908776\pi\)
\(654\) −2.00000 + 3.46410i −0.0782062 + 0.135457i
\(655\) 19.9373 34.5323i 0.779013 1.34929i
\(656\) 1.17712 + 2.03884i 0.0459590 + 0.0796033i
\(657\) −13.6458 −0.532371
\(658\) 7.93725 0.309426
\(659\) −16.9373 −0.659782 −0.329891 0.944019i \(-0.607012\pi\)
−0.329891 + 0.944019i \(0.607012\pi\)
\(660\) 1.17712 + 2.03884i 0.0458195 + 0.0793617i
\(661\) −7.76013 + 13.4409i −0.301834 + 0.522792i −0.976551 0.215284i \(-0.930932\pi\)
0.674717 + 0.738076i \(0.264266\pi\)
\(662\) 5.70850 9.88741i 0.221867 0.384285i
\(663\) 3.32288 + 5.75539i 0.129050 + 0.223521i
\(664\) 13.2915 0.515810
\(665\) 48.2288 1.87023
\(666\) −5.64575 −0.218768
\(667\) 5.05163 + 8.74968i 0.195600 + 0.338789i
\(668\) 3.43725 5.95350i 0.132991 0.230348i
\(669\) 10.2601 17.7711i 0.396680 0.687069i
\(670\) −13.8229 23.9419i −0.534024 0.924957i
\(671\) −7.70850 −0.297583
\(672\) −1.32288 + 2.29129i −0.0510310 + 0.0883883i
\(673\) −6.58301 −0.253756 −0.126878 0.991918i \(-0.540496\pi\)
−0.126878 + 0.991918i \(0.540496\pi\)
\(674\) −7.79150 13.4953i −0.300117 0.519819i
\(675\) −4.14575 + 7.18065i −0.159570 + 0.276383i
\(676\) −0.500000 + 0.866025i −0.0192308 + 0.0333087i
\(677\) −10.0830 17.4643i −0.387521 0.671207i 0.604594 0.796534i \(-0.293335\pi\)
−0.992115 + 0.125327i \(0.960002\pi\)
\(678\) −15.2288 −0.584857
\(679\) 1.23987 + 2.14752i 0.0475819 + 0.0824142i
\(680\) −24.2288 −0.929130
\(681\) 2.35425 + 4.07768i 0.0902150 + 0.156257i
\(682\) 1.06275 1.84073i 0.0406947 0.0704852i
\(683\) −9.64575 + 16.7069i −0.369084 + 0.639273i −0.989423 0.145061i \(-0.953662\pi\)
0.620338 + 0.784334i \(0.286995\pi\)
\(684\) −2.50000 4.33013i −0.0955899 0.165567i
\(685\) 71.1660 2.71911
\(686\) −9.26013 16.0390i −0.353553 0.612372i
\(687\) 26.4575 1.00942
\(688\) 2.64575 + 4.58258i 0.100868 + 0.174709i
\(689\) 1.50000 2.59808i 0.0571454 0.0989788i
\(690\) 4.29150 7.43310i 0.163375 0.282973i
\(691\) 20.0203 + 34.6761i 0.761607 + 1.31914i 0.942022 + 0.335551i \(0.108922\pi\)
−0.180416 + 0.983590i \(0.557744\pi\)
\(692\) −22.2915 −0.847396
\(693\) 0.854249 + 1.47960i 0.0324502 + 0.0562054i
\(694\) −0.228757 −0.00868348
\(695\) −40.5203 70.1831i −1.53702 2.66220i
\(696\) 2.14575 3.71655i 0.0813345 0.140875i
\(697\) −7.82288 + 13.5496i −0.296313 + 0.513228i
\(698\) 9.46863 + 16.4001i 0.358393 + 0.620755i
\(699\) 0.645751 0.0244246
\(700\) 10.9686 18.9982i 0.414575 0.718065i
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 0.500000 + 0.866025i 0.0188713 + 0.0326860i
\(703\) −14.1144 + 24.4468i −0.532334 + 0.922029i
\(704\) −0.322876 + 0.559237i −0.0121688 + 0.0210770i
\(705\) 5.46863 + 9.47194i 0.205960 + 0.356734i
\(706\) 20.5830 0.774652
\(707\) 0 0
\(708\) −7.93725 −0.298300
\(709\) −3.23987 5.61162i −0.121676 0.210749i 0.798753 0.601659i \(-0.205494\pi\)
−0.920429 + 0.390911i \(0.872160\pi\)
\(710\) −29.6974 + 51.4374i −1.11452 + 1.93041i
\(711\) 5.00000 8.66025i 0.187515 0.324785i
\(712\) 8.46863 + 14.6681i 0.317375 + 0.549710i
\(713\) −7.74902 −0.290203
\(714\) −17.5830 −0.658027
\(715\) −2.35425 −0.0880439
\(716\) 3.00000 + 5.19615i 0.112115 + 0.194189i
\(717\) −1.50000 + 2.59808i −0.0560185 + 0.0970269i
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) −22.2915 38.6100i −0.831333 1.43991i −0.896982 0.442068i \(-0.854245\pi\)
0.0656489 0.997843i \(-0.479088\pi\)
\(720\) −3.64575 −0.135869
\(721\) −7.00000 + 12.1244i −0.260694 + 0.451535i
\(722\) −6.00000 −0.223297
\(723\) 6.93725 + 12.0157i 0.257999 + 0.446868i
\(724\) −7.32288 + 12.6836i −0.272153 + 0.471382i
\(725\) −17.7915 + 30.8158i −0.660760 + 1.14447i
\(726\) −5.29150 9.16515i −0.196386 0.340151i
\(727\) −16.4575 −0.610375 −0.305188 0.952292i \(-0.598719\pi\)
−0.305188 + 0.952292i \(0.598719\pi\)
\(728\) −1.32288 2.29129i −0.0490290 0.0849208i
\(729\) 1.00000 0.0370370
\(730\) 24.8745 + 43.0839i 0.920647 + 1.59461i
\(731\) −17.5830 + 30.4547i −0.650331 + 1.12641i
\(732\) 5.96863 10.3380i 0.220607 0.382102i
\(733\) −7.11438 12.3225i −0.262776 0.455141i 0.704203 0.709999i \(-0.251305\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(734\) 0.583005 0.0215191
\(735\) 12.7601 22.1012i 0.470664 0.815215i
\(736\) 2.35425 0.0867788
\(737\) −2.44837 4.24070i −0.0901868 0.156208i
\(738\) −1.17712 + 2.03884i −0.0433305 + 0.0750507i
\(739\) 8.64575 14.9749i 0.318039 0.550860i −0.662040 0.749469i \(-0.730309\pi\)
0.980079 + 0.198609i \(0.0636423\pi\)
\(740\) 10.2915 + 17.8254i 0.378323 + 0.655275i
\(741\) 5.00000 0.183680
\(742\) 3.96863 + 6.87386i 0.145693 + 0.252347i
\(743\) −51.4575 −1.88779 −0.943897 0.330241i \(-0.892870\pi\)
−0.943897 + 0.330241i \(0.892870\pi\)
\(744\) 1.64575 + 2.85052i 0.0603362 + 0.104505i
\(745\) −12.8745 + 22.2993i −0.471685 + 0.816983i
\(746\) 7.32288 12.6836i 0.268110 0.464379i
\(747\) 6.64575 + 11.5108i 0.243155 + 0.421157i
\(748\) −4.29150 −0.156913
\(749\) −15.8745 + 27.4955i −0.580042 + 1.00466i
\(750\) 12.0000 0.438178
\(751\) 16.5830 + 28.7226i 0.605122 + 1.04810i 0.992032 + 0.125985i \(0.0402092\pi\)
−0.386910 + 0.922118i \(0.626457\pi\)
\(752\) −1.50000 + 2.59808i −0.0546994 + 0.0947421i
\(753\) 6.64575 11.5108i 0.242185 0.419476i
\(754\) 2.14575 + 3.71655i 0.0781437 + 0.135349i
\(755\) −22.1033 −0.804420
\(756\) −2.64575 −0.0962250
\(757\) 26.6458 0.968456 0.484228 0.874942i \(-0.339100\pi\)
0.484228 + 0.874942i \(0.339100\pi\)
\(758\) −4.58301 7.93800i −0.166462 0.288321i
\(759\) 0.760130 1.31658i 0.0275910 0.0477889i
\(760\) −9.11438 + 15.7866i −0.330613 + 0.572639i
\(761\) −3.64575 6.31463i −0.132158 0.228905i 0.792350 0.610067i \(-0.208857\pi\)
−0.924508 + 0.381162i \(0.875524\pi\)
\(762\) 10.2288 0.370549
\(763\) 10.5830 0.383131
\(764\) 0 0
\(765\) −12.1144 20.9827i −0.437996 0.758632i
\(766\) 12.8745 22.2993i 0.465175 0.805707i
\(767\) 3.96863 6.87386i 0.143299 0.248201i
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 5.64575 0.203591 0.101795 0.994805i \(-0.467541\pi\)
0.101795 + 0.994805i \(0.467541\pi\)
\(770\) 3.11438 5.39426i 0.112234 0.194396i
\(771\) −15.8745 −0.571706
\(772\) −9.46863 16.4001i −0.340783 0.590254i
\(773\) −20.1660 + 34.9286i −0.725321 + 1.25629i 0.233521 + 0.972352i \(0.424975\pi\)
−0.958842 + 0.283941i \(0.908358\pi\)
\(774\) −2.64575 + 4.58258i −0.0950996 + 0.164717i
\(775\) −13.6458 23.6351i −0.490170 0.848999i
\(776\) −0.937254 −0.0336455
\(777\) 7.46863 + 12.9360i 0.267935 + 0.464078i
\(778\) −7.70850 −0.276363
\(779\) 5.88562 + 10.1942i 0.210874 + 0.365245i
\(780\) 1.82288 3.15731i 0.0652694 0.113050i
\(781\) −5.26013 + 9.11081i −0.188222 + 0.326010i
\(782\) 7.82288 + 13.5496i 0.279745 + 0.484533i
\(783\) 4.29150 0.153366
\(784\) 7.00000 0.250000
\(785\) −9.64575 −0.344272
\(786\) 5.46863 + 9.47194i 0.195059 + 0.337853i
\(787\) −26.3118 + 45.5733i −0.937913 + 1.62451i −0.168558 + 0.985692i \(0.553911\pi\)
−0.769355 + 0.638821i \(0.779422\pi\)
\(788\) 13.4059 23.2197i 0.477565 0.827166i
\(789\) 1.82288 + 3.15731i 0.0648961 + 0.112403i
\(790\) −36.4575 −1.29710
\(791\) 20.1458 + 34.8935i 0.716300 + 1.24067i
\(792\) −0.645751 −0.0229458
\(793\) 5.96863 + 10.3380i 0.211952 + 0.367112i
\(794\) −7.46863 + 12.9360i −0.265052 + 0.459083i
\(795\) −5.46863 + 9.47194i −0.193952 + 0.335935i
\(796\) 11.1144 + 19.2507i 0.393939 + 0.682322i
\(797\) −45.8745 −1.62496 −0.812479 0.582990i \(-0.801883\pi\)
−0.812479 + 0.582990i \(0.801883\pi\)
\(798\) −6.61438 + 11.4564i −0.234146 + 0.405554i
\(799\) −19.9373 −0.705329
\(800\) 4.14575 + 7.18065i 0.146574 + 0.253874i
\(801\) −8.46863 + 14.6681i −0.299224 + 0.518272i
\(802\) −9.11438 + 15.7866i −0.321840 + 0.557443i
\(803\) 4.40588 + 7.63121i 0.155480 + 0.269300i
\(804\) 7.58301 0.267432
\(805\) −22.7085 −0.800369
\(806\) −3.29150 −0.115938
\(807\) −3.43725 5.95350i −0.120997 0.209573i
\(808\) 0 0
\(809\) −11.9059 + 20.6216i −0.418588 + 0.725017i −0.995798 0.0915798i \(-0.970808\pi\)
0.577209 + 0.816596i \(0.304142\pi\)
\(810\) −1.82288 3.15731i −0.0640493 0.110937i
\(811\) 38.0000 1.33436 0.667180 0.744896i \(-0.267501\pi\)
0.667180 + 0.744896i \(0.267501\pi\)
\(812\) −11.3542 −0.398456
\(813\) −22.6458 −0.794221
\(814\) 1.82288 + 3.15731i 0.0638918 + 0.110664i
\(815\) 4.40588 7.63121i 0.154331 0.267310i
\(816\) 3.32288 5.75539i 0.116324 0.201479i
\(817\) 13.2288 + 22.9129i 0.462816 + 0.801620i
\(818\) 26.9373 0.941839
\(819\) 1.32288 2.29129i 0.0462250 0.0800641i
\(820\) 8.58301 0.299732
\(821\) 2.88562 + 4.99804i 0.100709 + 0.174433i 0.911977 0.410242i \(-0.134556\pi\)
−0.811268 + 0.584674i \(0.801222\pi\)
\(822\) −9.76013 + 16.9050i −0.340424 + 0.589631i
\(823\) −7.76013 + 13.4409i −0.270501 + 0.468522i −0.968990 0.247099i \(-0.920523\pi\)
0.698489 + 0.715621i \(0.253856\pi\)
\(824\) −2.64575 4.58258i −0.0921691 0.159642i
\(825\) 5.35425 0.186411
\(826\) 10.5000 + 18.1865i 0.365342 + 0.632790i
\(827\) 35.3542 1.22939 0.614694 0.788766i \(-0.289280\pi\)
0.614694 + 0.788766i \(0.289280\pi\)
\(828\) 1.17712 + 2.03884i 0.0409079 + 0.0708546i
\(829\) −23.6144 + 40.9013i −0.820161 + 1.42056i 0.0854006 + 0.996347i \(0.472783\pi\)
−0.905562 + 0.424214i \(0.860550\pi\)
\(830\) 24.2288 41.9654i 0.840992 1.45664i
\(831\) −9.26013 16.0390i −0.321230 0.556387i
\(832\) 1.00000 0.0346688
\(833\) 23.2601 + 40.2877i 0.805916 + 1.39589i
\(834\) 22.2288 0.769719
\(835\) −12.5314 21.7050i −0.433666 0.751132i
\(836\) −1.61438 + 2.79619i −0.0558344 + 0.0967081i
\(837\) −1.64575 + 2.85052i −0.0568855 + 0.0985286i
\(838\) 15.2288 + 26.3770i 0.526069 + 0.911178i
\(839\) 21.0000 0.725001 0.362500 0.931984i \(-0.381923\pi\)
0.362500 + 0.931984i \(0.381923\pi\)
\(840\) 4.82288 + 8.35347i 0.166405 + 0.288222i
\(841\) −10.5830 −0.364931
\(842\) −12.1771 21.0914i −0.419651 0.726858i
\(843\) 1.29150 2.23695i 0.0444817 0.0770446i
\(844\) 3.17712 5.50294i 0.109361 0.189419i
\(845\) 1.82288 + 3.15731i 0.0627088 + 0.108615i
\(846\) −3.00000 −0.103142
\(847\) −14.0000 + 24.2487i −0.481046 + 0.833196i
\(848\) −3.00000 −0.103020
\(849\) 5.53137 + 9.58062i 0.189836 + 0.328806i
\(850\) −27.5516 + 47.7208i −0.945013 + 1.63681i
\(851\) 6.64575 11.5108i 0.227813 0.394584i
\(852\) −8.14575 14.1089i −0.279069 0.483361i
\(853\) −20.1033 −0.688323 −0.344161 0.938911i \(-0.611837\pi\)
−0.344161 + 0.938911i \(0.611837\pi\)
\(854\) −31.5830 −1.08075
\(855\) −18.2288 −0.623410
\(856\) −6.00000 10.3923i −0.205076 0.355202i
\(857\) −6.96863 + 12.0700i −0.238044 + 0.412304i −0.960153 0.279475i \(-0.909840\pi\)
0.722109 + 0.691779i \(0.243173\pi\)
\(858\) 0.322876 0.559237i 0.0110228 0.0190920i
\(859\) −22.2288 38.5013i −0.758435 1.31365i −0.943648 0.330950i \(-0.892631\pi\)
0.185213 0.982698i \(-0.440703\pi\)
\(860\) 19.2915 0.657835
\(861\) 6.22876 0.212275
\(862\) −20.5830 −0.701060
\(863\) −15.8745 27.4955i −0.540375 0.935956i −0.998882 0.0472658i \(-0.984949\pi\)
0.458508 0.888690i \(-0.348384\pi\)
\(864\) 0.500000 0.866025i 0.0170103 0.0294628i
\(865\) −40.6346 + 70.3813i −1.38162 + 2.39303i
\(866\) −16.7915 29.0837i −0.570598 0.988306i
\(867\) 27.1660 0.922606
\(868\) 4.35425 7.54178i 0.147793 0.255985i
\(869\) −6.45751 −0.219056
\(870\) −7.82288 13.5496i −0.265220 0.459375i
\(871\) −3.79150 + 6.56708i −0.128470 + 0.222517i
\(872\) −2.00000 + 3.46410i −0.0677285 + 0.117309i
\(873\) −0.468627 0.811686i −0.0158606 0.0274714i
\(874\) 11.7712 0.398168
\(875\) −15.8745 27.4955i −0.536656 0.929516i
\(876\) −13.6458 −0.461047
\(877\) 27.4059 + 47.4684i 0.925431 + 1.60289i 0.790867 + 0.611988i \(0.209630\pi\)
0.134564 + 0.990905i \(0.457037\pi\)
\(878\) 11.8229 20.4778i 0.399003 0.691093i
\(879\) −3.76013 + 6.51274i −0.126826 + 0.219669i
\(880\) 1.17712 + 2.03884i 0.0396809 + 0.0687293i
\(881\) −10.7085 −0.360778 −0.180389 0.983595i \(-0.557736\pi\)
−0.180389 + 0.983595i \(0.557736\pi\)
\(882\) 3.50000 + 6.06218i 0.117851 + 0.204124i
\(883\) −29.0627 −0.978039 −0.489020 0.872273i \(-0.662645\pi\)
−0.489020 + 0.872273i \(0.662645\pi\)
\(884\) 3.32288 + 5.75539i 0.111760 + 0.193575i
\(885\) −14.4686 + 25.0604i −0.486358 + 0.842396i
\(886\) 9.53137 16.5088i 0.320213 0.554625i
\(887\) −10.2915 17.8254i −0.345555 0.598519i 0.639900 0.768459i \(-0.278976\pi\)
−0.985454 + 0.169940i \(0.945643\pi\)
\(888\) −5.64575 −0.189459
\(889\) −13.5314 23.4370i −0.453828 0.786053i
\(890\) 61.7490 2.06983
\(891\) −0.322876 0.559237i −0.0108167 0.0187351i
\(892\) 10.2601 17.7711i 0.343535 0.595019i
\(893\) −7.50000 + 12.9904i −0.250978 + 0.434707i
\(894\) −3.53137 6.11652i −0.118107 0.204567i
\(895\) 21.8745 0.731184
\(896\) −1.32288 + 2.29129i −0.0441942 + 0.0765466i
\(897\) −2.35425 −0.0786061
\(898\) 6.00000 + 10.3923i 0.200223 + 0.346796i
\(899\) −7.06275 + 12.2330i −0.235556 + 0.407995i
\(900\) −4.14575 + 7.18065i −0.138192 + 0.239355i
\(901\) −9.96863 17.2662i −0.332103 0.575219i
\(902\) 1.52026 0.0506191
\(903\) 14.0000 0.465891
\(904\) −15.2288 −0.506501
\(905\) 26.6974 + 46.2412i 0.887451 + 1.53711i
\(906\) 3.03137 5.25049i 0.100711 0.174436i
\(907\) 1.88562 3.26599i 0.0626110 0.108446i −0.833021 0.553242i \(-0.813391\pi\)
0.895632 + 0.444796i \(0.146724\pi\)
\(908\) 2.35425 + 4.07768i 0.0781285 + 0.135323i
\(909\) 0 0
\(910\) −9.64575 −0.319754
\(911\) −37.7490 −1.25068 −0.625340 0.780352i \(-0.715040\pi\)
−0.625340 + 0.780352i \(0.715040\pi\)
\(912\) −2.50000 4.33013i −0.0827833 0.143385i
\(913\) 4.29150 7.43310i 0.142028 0.246000i
\(914\) 16.1144 27.9109i 0.533016 0.923211i
\(915\) −21.7601 37.6897i −0.719368 1.24598i
\(916\) 26.4575 0.874181
\(917\) 14.4686 25.0604i 0.477796 0.827567i
\(918\) 6.64575 0.219342
\(919\) −23.9373 41.4605i −0.789617 1.36766i −0.926202 0.377029i \(-0.876946\pi\)
0.136584 0.990628i \(-0.456387\pi\)
\(920\) 4.29150 7.43310i 0.141487 0.245062i
\(921\) 4.79150 8.29913i 0.157885 0.273465i
\(922\) −18.2288 31.5731i −0.600332 1.03981i
\(923\) 16.2915 0.536241
\(924\) 0.854249 + 1.47960i 0.0281027 + 0.0486753i
\(925\) 46.8118 1.53916
\(926\) 12.5830 + 21.7944i 0.413503 + 0.716209i
\(927\) 2.64575 4.58258i 0.0868979 0.150512i
\(928\) 2.14575 3.71655i 0.0704377 0.122002i
\(929\) 6.87451 + 11.9070i 0.225545 + 0.390656i 0.956483 0.291788i \(-0.0942503\pi\)
−0.730938 + 0.682444i \(0.760917\pi\)
\(930\) 12.0000 0.393496
\(931\) 35.0000 1.14708
\(932\) 0.645751 0.0211523
\(933\) 0.531373 + 0.920365i 0.0173964 + 0.0301314i
\(934\) −18.7601 + 32.4935i −0.613850 + 1.06322i
\(935\) −7.82288 + 13.5496i −0.255835 + 0.443120i
\(936\) 0.500000 + 0.866025i 0.0163430 + 0.0283069i
\(937\) −31.4575 −1.02767 −0.513836 0.857888i \(-0.671776\pi\)
−0.513836 + 0.857888i \(0.671776\pi\)
\(938\) −10.0314 17.3748i −0.327536 0.567309i
\(939\) 13.1660 0.429657
\(940\) 5.46863 + 9.47194i 0.178367 + 0.308941i
\(941\) 8.58301 14.8662i 0.279798 0.484624i −0.691536 0.722342i \(-0.743066\pi\)
0.971334 + 0.237717i \(0.0763992\pi\)
\(942\) 1.32288 2.29129i 0.0431016 0.0746542i
\(943\) −2.77124 4.79993i −0.0902441 0.156307i
\(944\) −7.93725 −0.258336
\(945\) −4.82288 + 8.35347i −0.156888 + 0.271738i
\(946\) 3.41699 0.111096
\(947\) 5.26013 + 9.11081i 0.170931 + 0.296062i 0.938746 0.344611i \(-0.111989\pi\)
−0.767814 + 0.640672i \(0.778656\pi\)
\(948\) 5.00000 8.66025i 0.162392 0.281272i
\(949\) 6.82288 11.8176i 0.221480 0.383614i
\(950\) 20.7288 + 35.9033i 0.672530 + 1.16486i
\(951\) −13.2915 −0.431007
\(952\) −17.5830 −0.569868
\(953\) −25.1033 −0.813174 −0.406587 0.913612i \(-0.633281\pi\)
−0.406587 + 0.913612i \(0.633281\pi\)
\(954\) −1.50000 2.59808i −0.0485643 0.0841158i
\(955\) 0 0
\(956\) −1.50000 + 2.59808i −0.0485135 + 0.0840278i
\(957\) −1.38562 2.39997i −0.0447908 0.0775799i
\(958\) 34.7490 1.12269
\(959\) 51.6458 1.66773
\(960\) −3.64575 −0.117666
\(961\) 10.0830 + 17.4643i 0.325258 + 0.563364i
\(962\) 2.82288 4.88936i 0.0910132 0.157639i
\(963\) 6.00000 10.3923i 0.193347 0.334887i
\(964\) 6.93725 + 12.0157i 0.223434 + 0.386999i
\(965\) −69.0405 −2.22249
\(966\) 3.11438 5.39426i 0.100203 0.173558i
\(967\) 9.10326 0.292741 0.146371 0.989230i \(-0.453241\pi\)
0.146371 + 0.989230i \(0.453241\pi\)
\(968\) −5.29150 9.16515i −0.170075 0.294579i
\(969\) 16.6144 28.7769i 0.533731 0.924449i
\(970\) −1.70850 + 2.95920i −0.0548565 + 0.0950143i
\(971\) −8.46863 14.6681i −0.271771 0.470721i 0.697544 0.716542i \(-0.254276\pi\)
−0.969315 + 0.245820i \(0.920943\pi\)
\(972\) 1.00000 0.0320750
\(973\) −29.4059 50.9325i −0.942709 1.63282i
\(974\) 23.9373 0.766999
\(975\) −4.14575 7.18065i −0.132770 0.229965i
\(976\) 5.96863 10.3380i 0.191051 0.330910i
\(977\) −10.0627 + 17.4292i −0.321936 + 0.557609i −0.980887 0.194576i \(-0.937667\pi\)
0.658952 + 0.752185i \(0.271000\pi\)
\(978\) 1.20850 + 2.09318i 0.0386435 + 0.0669325i
\(979\) 10.9373 0.349556
\(980\) 12.7601 22.1012i 0.407607 0.705997i
\(981\) −4.00000 −0.127710
\(982\) 5.58301 + 9.67005i 0.178161 + 0.308584i
\(983\) 15.0203 26.0159i 0.479072 0.829777i −0.520640 0.853776i \(-0.674307\pi\)
0.999712 + 0.0239994i \(0.00763999\pi\)
\(984\) −1.17712 + 2.03884i −0.0375254 + 0.0649958i
\(985\) −48.8745 84.6531i −1.55727 2.69727i
\(986\) 28.5203 0.908270
\(987\) 3.96863 + 6.87386i 0.126323 + 0.218797i
\(988\) 5.00000 0.159071
\(989\) −6.22876 10.7885i −0.198063 0.343055i
\(990\) −1.17712 + 2.03884i −0.0374115 + 0.0647986i
\(991\) −2.70850 + 4.69126i −0.0860383 + 0.149023i −0.905833 0.423635i \(-0.860754\pi\)
0.819795 + 0.572657i \(0.194087\pi\)
\(992\) 1.64575 + 2.85052i 0.0522527 + 0.0905043i
\(993\) 11.4170 0.362307
\(994\) −21.5516 + 37.3285i −0.683576 + 1.18399i
\(995\) 81.0405 2.56916
\(996\) 6.64575 + 11.5108i 0.210579 + 0.364733i
\(997\) 0.614378 1.06413i 0.0194576 0.0337015i −0.856133 0.516756i \(-0.827139\pi\)
0.875590 + 0.483055i \(0.160473\pi\)
\(998\) −14.6458 + 25.3672i −0.463603 + 0.802984i
\(999\) −2.82288 4.88936i −0.0893118 0.154693i
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 546.2.i.j.235.2 yes 4
3.2 odd 2 1638.2.j.k.235.1 4
7.2 even 3 inner 546.2.i.j.79.2 4
7.3 odd 6 3822.2.a.bi.1.2 2
7.4 even 3 3822.2.a.bk.1.1 2
21.2 odd 6 1638.2.j.k.1171.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.i.j.79.2 4 7.2 even 3 inner
546.2.i.j.235.2 yes 4 1.1 even 1 trivial
1638.2.j.k.235.1 4 3.2 odd 2
1638.2.j.k.1171.1 4 21.2 odd 6
3822.2.a.bi.1.2 2 7.3 odd 6
3822.2.a.bk.1.1 2 7.4 even 3