Properties

Label 65.2.l.a.49.2
Level $65$
Weight $2$
Character 65.49
Analytic conductor $0.519$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [65,2,Mod(4,65)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(65, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("65.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 65 = 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 65.l (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.519027613138\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.49787136.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.2
Root \(-0.228425 - 1.39564i\) of defining polynomial
Character \(\chi\) \(=\) 65.49
Dual form 65.2.l.a.4.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.228425 - 0.395644i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.895644 - 1.55130i) q^{4} +(2.18890 + 0.456850i) q^{5} +(0.395644 + 0.228425i) q^{6} +(0.866025 - 1.50000i) q^{7} -1.73205 q^{8} +(-1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.228425 - 0.395644i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.895644 - 1.55130i) q^{4} +(2.18890 + 0.456850i) q^{5} +(0.395644 + 0.228425i) q^{6} +(0.866025 - 1.50000i) q^{7} -1.73205 q^{8} +(-1.00000 + 1.73205i) q^{9} +(-0.319250 - 0.970381i) q^{10} +(-2.29129 + 1.32288i) q^{11} +1.79129i q^{12} +(-3.46410 + 1.00000i) q^{13} -0.791288 q^{14} +(-2.12407 + 0.698807i) q^{15} +(-1.39564 - 2.41733i) q^{16} +(3.96863 + 2.29129i) q^{17} +0.913701 q^{18} +(-1.50000 - 0.866025i) q^{19} +(2.66919 - 2.98647i) q^{20} +1.73205i q^{21} +(1.04678 + 0.604356i) q^{22} +(-3.96863 + 2.29129i) q^{23} +(1.50000 - 0.866025i) q^{24} +(4.58258 + 2.00000i) q^{25} +(1.18693 + 1.14213i) q^{26} -5.00000i q^{27} +(-1.55130 - 2.68693i) q^{28} +(2.29129 + 3.96863i) q^{29} +(0.761669 + 0.680750i) q^{30} -6.20520i q^{31} +(-2.36965 + 4.10436i) q^{32} +(1.32288 - 2.29129i) q^{33} -2.09355i q^{34} +(2.58092 - 2.88771i) q^{35} +(1.79129 + 3.10260i) q^{36} +(-3.96863 - 6.87386i) q^{37} +0.791288i q^{38} +(2.50000 - 2.59808i) q^{39} +(-3.79129 - 0.791288i) q^{40} +(2.29129 - 1.32288i) q^{41} +(0.685275 - 0.395644i) q^{42} +(9.16478 + 5.29129i) q^{43} +4.73930i q^{44} +(-2.98019 + 3.33444i) q^{45} +(1.81307 + 1.04678i) q^{46} -1.82740 q^{47} +(2.41733 + 1.39564i) q^{48} +(2.00000 + 3.46410i) q^{49} +(-0.255488 - 2.26992i) q^{50} -4.58258 q^{51} +(-1.55130 + 6.26951i) q^{52} -7.58258i q^{53} +(-1.97822 + 1.14213i) q^{54} +(-5.61976 + 1.84887i) q^{55} +(-1.50000 + 2.59808i) q^{56} +1.73205 q^{57} +(1.04678 - 1.81307i) q^{58} +(-12.0826 - 6.97588i) q^{59} +(-0.818350 + 3.92095i) q^{60} +(0.708712 - 1.22753i) q^{61} +(-2.45505 + 1.41742i) q^{62} +(1.73205 + 3.00000i) q^{63} -3.41742 q^{64} +(-8.03943 + 0.606325i) q^{65} -1.20871 q^{66} +(0.504525 + 0.873864i) q^{67} +(7.10895 - 4.10436i) q^{68} +(2.29129 - 3.96863i) q^{69} +(-1.73205 - 0.361500i) q^{70} +(6.08258 + 3.51178i) q^{71} +(1.73205 - 3.00000i) q^{72} +(-1.81307 + 3.14033i) q^{74} +(-4.96863 + 0.559237i) q^{75} +(-2.68693 + 1.55130i) q^{76} +4.58258i q^{77} +(-1.59898 - 0.395644i) q^{78} +6.00000 q^{79} +(-1.95057 - 5.92889i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.04678 - 0.604356i) q^{82} +6.01450 q^{83} +(2.68693 + 1.55130i) q^{84} +(7.64016 + 6.82847i) q^{85} -4.83465i q^{86} +(-3.96863 - 2.29129i) q^{87} +(3.96863 - 2.29129i) q^{88} +(8.29129 - 4.78698i) q^{89} +(2.00000 + 0.417424i) q^{90} +(-1.50000 + 6.06218i) q^{91} +8.20871i q^{92} +(3.10260 + 5.37386i) q^{93} +(0.417424 + 0.723000i) q^{94} +(-2.88771 - 2.58092i) q^{95} -4.73930i q^{96} +(5.70068 - 9.87386i) q^{97} +(0.913701 - 1.58258i) q^{98} -5.29150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{4} - 6 q^{6} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{4} - 6 q^{6} - 8 q^{9} - 4 q^{10} + 12 q^{14} - 6 q^{15} - 2 q^{16} - 12 q^{19} + 24 q^{20} + 12 q^{24} - 18 q^{26} - 10 q^{30} + 6 q^{35} - 4 q^{36} + 20 q^{39} - 12 q^{40} + 12 q^{45} + 42 q^{46} + 16 q^{49} - 12 q^{50} + 30 q^{54} - 14 q^{55} - 12 q^{56} - 60 q^{59} + 24 q^{61} - 64 q^{64} - 24 q^{65} - 28 q^{66} + 12 q^{71} - 42 q^{74} - 8 q^{75} + 6 q^{76} + 48 q^{79} + 18 q^{80} - 4 q^{81} - 6 q^{84} + 42 q^{85} + 48 q^{89} + 16 q^{90} - 12 q^{91} + 40 q^{94} - 6 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.228425 0.395644i −0.161521 0.279763i 0.773893 0.633316i \(-0.218307\pi\)
−0.935414 + 0.353553i \(0.884973\pi\)
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i −0.728714 0.684819i \(-0.759881\pi\)
0.228714 + 0.973494i \(0.426548\pi\)
\(4\) 0.895644 1.55130i 0.447822 0.775650i
\(5\) 2.18890 + 0.456850i 0.978906 + 0.204310i
\(6\) 0.395644 + 0.228425i 0.161521 + 0.0932542i
\(7\) 0.866025 1.50000i 0.327327 0.566947i −0.654654 0.755929i \(-0.727186\pi\)
0.981981 + 0.188982i \(0.0605189\pi\)
\(8\) −1.73205 −0.612372
\(9\) −1.00000 + 1.73205i −0.333333 + 0.577350i
\(10\) −0.319250 0.970381i −0.100956 0.306862i
\(11\) −2.29129 + 1.32288i −0.690849 + 0.398862i −0.803930 0.594724i \(-0.797261\pi\)
0.113081 + 0.993586i \(0.463928\pi\)
\(12\) 1.79129i 0.517100i
\(13\) −3.46410 + 1.00000i −0.960769 + 0.277350i
\(14\) −0.791288 −0.211481
\(15\) −2.12407 + 0.698807i −0.548432 + 0.180431i
\(16\) −1.39564 2.41733i −0.348911 0.604332i
\(17\) 3.96863 + 2.29129i 0.962533 + 0.555719i 0.896952 0.442128i \(-0.145776\pi\)
0.0655816 + 0.997847i \(0.479110\pi\)
\(18\) 0.913701 0.215361
\(19\) −1.50000 0.866025i −0.344124 0.198680i 0.317970 0.948101i \(-0.396999\pi\)
−0.662094 + 0.749421i \(0.730332\pi\)
\(20\) 2.66919 2.98647i 0.596849 0.667795i
\(21\) 1.73205i 0.377964i
\(22\) 1.04678 + 0.604356i 0.223173 + 0.128849i
\(23\) −3.96863 + 2.29129i −0.827516 + 0.477767i −0.853001 0.521909i \(-0.825220\pi\)
0.0254855 + 0.999675i \(0.491887\pi\)
\(24\) 1.50000 0.866025i 0.306186 0.176777i
\(25\) 4.58258 + 2.00000i 0.916515 + 0.400000i
\(26\) 1.18693 + 1.14213i 0.232776 + 0.223989i
\(27\) 5.00000i 0.962250i
\(28\) −1.55130 2.68693i −0.293168 0.507782i
\(29\) 2.29129 + 3.96863i 0.425481 + 0.736956i 0.996465 0.0840058i \(-0.0267714\pi\)
−0.570984 + 0.820961i \(0.693438\pi\)
\(30\) 0.761669 + 0.680750i 0.139061 + 0.124287i
\(31\) 6.20520i 1.11449i −0.830349 0.557244i \(-0.811859\pi\)
0.830349 0.557244i \(-0.188141\pi\)
\(32\) −2.36965 + 4.10436i −0.418899 + 0.725555i
\(33\) 1.32288 2.29129i 0.230283 0.398862i
\(34\) 2.09355i 0.359041i
\(35\) 2.58092 2.88771i 0.436255 0.488112i
\(36\) 1.79129 + 3.10260i 0.298548 + 0.517100i
\(37\) −3.96863 6.87386i −0.652438 1.13006i −0.982529 0.186107i \(-0.940413\pi\)
0.330091 0.943949i \(-0.392920\pi\)
\(38\) 0.791288i 0.128364i
\(39\) 2.50000 2.59808i 0.400320 0.416025i
\(40\) −3.79129 0.791288i −0.599455 0.125114i
\(41\) 2.29129 1.32288i 0.357839 0.206598i −0.310293 0.950641i \(-0.600427\pi\)
0.668132 + 0.744042i \(0.267094\pi\)
\(42\) 0.685275 0.395644i 0.105740 0.0610492i
\(43\) 9.16478 + 5.29129i 1.39762 + 0.806914i 0.994142 0.108078i \(-0.0344695\pi\)
0.403473 + 0.914991i \(0.367803\pi\)
\(44\) 4.73930i 0.714477i
\(45\) −2.98019 + 3.33444i −0.444260 + 0.497069i
\(46\) 1.81307 + 1.04678i 0.267322 + 0.154339i
\(47\) −1.82740 −0.266554 −0.133277 0.991079i \(-0.542550\pi\)
−0.133277 + 0.991079i \(0.542550\pi\)
\(48\) 2.41733 + 1.39564i 0.348911 + 0.201444i
\(49\) 2.00000 + 3.46410i 0.285714 + 0.494872i
\(50\) −0.255488 2.26992i −0.0361314 0.321015i
\(51\) −4.58258 −0.641689
\(52\) −1.55130 + 6.26951i −0.215127 + 0.869424i
\(53\) 7.58258i 1.04155i −0.853695 0.520773i \(-0.825644\pi\)
0.853695 0.520773i \(-0.174356\pi\)
\(54\) −1.97822 + 1.14213i −0.269202 + 0.155424i
\(55\) −5.61976 + 1.84887i −0.757768 + 0.249301i
\(56\) −1.50000 + 2.59808i −0.200446 + 0.347183i
\(57\) 1.73205 0.229416
\(58\) 1.04678 1.81307i 0.137448 0.238068i
\(59\) −12.0826 6.97588i −1.57302 0.908182i −0.995796 0.0915940i \(-0.970804\pi\)
−0.577221 0.816588i \(-0.695863\pi\)
\(60\) −0.818350 + 3.92095i −0.105649 + 0.506193i
\(61\) 0.708712 1.22753i 0.0907413 0.157169i −0.817082 0.576522i \(-0.804410\pi\)
0.907823 + 0.419353i \(0.137743\pi\)
\(62\) −2.45505 + 1.41742i −0.311792 + 0.180013i
\(63\) 1.73205 + 3.00000i 0.218218 + 0.377964i
\(64\) −3.41742 −0.427178
\(65\) −8.03943 + 0.606325i −0.997168 + 0.0752054i
\(66\) −1.20871 −0.148782
\(67\) 0.504525 + 0.873864i 0.0616376 + 0.106759i 0.895198 0.445670i \(-0.147034\pi\)
−0.833560 + 0.552429i \(0.813701\pi\)
\(68\) 7.10895 4.10436i 0.862087 0.497726i
\(69\) 2.29129 3.96863i 0.275839 0.477767i
\(70\) −1.73205 0.361500i −0.207020 0.0432075i
\(71\) 6.08258 + 3.51178i 0.721869 + 0.416771i 0.815440 0.578841i \(-0.196495\pi\)
−0.0935712 + 0.995613i \(0.529828\pi\)
\(72\) 1.73205 3.00000i 0.204124 0.353553i
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) −1.81307 + 3.14033i −0.210765 + 0.365056i
\(75\) −4.96863 + 0.559237i −0.573728 + 0.0645751i
\(76\) −2.68693 + 1.55130i −0.308212 + 0.177946i
\(77\) 4.58258i 0.522233i
\(78\) −1.59898 0.395644i −0.181048 0.0447979i
\(79\) 6.00000 0.675053 0.337526 0.941316i \(-0.390410\pi\)
0.337526 + 0.941316i \(0.390410\pi\)
\(80\) −1.95057 5.92889i −0.218080 0.662870i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.04678 0.604356i −0.115597 0.0667400i
\(83\) 6.01450 0.660177 0.330089 0.943950i \(-0.392921\pi\)
0.330089 + 0.943950i \(0.392921\pi\)
\(84\) 2.68693 + 1.55130i 0.293168 + 0.169261i
\(85\) 7.64016 + 6.82847i 0.828691 + 0.740652i
\(86\) 4.83465i 0.521334i
\(87\) −3.96863 2.29129i −0.425481 0.245652i
\(88\) 3.96863 2.29129i 0.423057 0.244252i
\(89\) 8.29129 4.78698i 0.878875 0.507419i 0.00858752 0.999963i \(-0.497266\pi\)
0.870287 + 0.492545i \(0.163933\pi\)
\(90\) 2.00000 + 0.417424i 0.210819 + 0.0440004i
\(91\) −1.50000 + 6.06218i −0.157243 + 0.635489i
\(92\) 8.20871i 0.855817i
\(93\) 3.10260 + 5.37386i 0.321725 + 0.557244i
\(94\) 0.417424 + 0.723000i 0.0430540 + 0.0745718i
\(95\) −2.88771 2.58092i −0.296273 0.264797i
\(96\) 4.73930i 0.483703i
\(97\) 5.70068 9.87386i 0.578816 1.00254i −0.416799 0.908999i \(-0.636848\pi\)
0.995615 0.0935404i \(-0.0298184\pi\)
\(98\) 0.913701 1.58258i 0.0922977 0.159864i
\(99\) 5.29150i 0.531816i
\(100\) 7.20696 5.31767i 0.720696 0.531767i
\(101\) −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i \(-0.314447\pi\)
−0.998240 + 0.0592978i \(0.981114\pi\)
\(102\) 1.04678 + 1.81307i 0.103646 + 0.179521i
\(103\) 3.16515i 0.311872i −0.987767 0.155936i \(-0.950161\pi\)
0.987767 0.155936i \(-0.0498393\pi\)
\(104\) 6.00000 1.73205i 0.588348 0.169842i
\(105\) −0.791288 + 3.79129i −0.0772218 + 0.369992i
\(106\) −3.00000 + 1.73205i −0.291386 + 0.168232i
\(107\) −9.16478 + 5.29129i −0.885993 + 0.511528i −0.872630 0.488383i \(-0.837587\pi\)
−0.0133631 + 0.999911i \(0.504254\pi\)
\(108\) −7.75650 4.47822i −0.746370 0.430917i
\(109\) 13.1334i 1.25795i 0.777425 + 0.628976i \(0.216526\pi\)
−0.777425 + 0.628976i \(0.783474\pi\)
\(110\) 2.01519 + 1.80110i 0.192141 + 0.171728i
\(111\) 6.87386 + 3.96863i 0.652438 + 0.376685i
\(112\) −4.83465 −0.456832
\(113\) −6.42368 3.70871i −0.604289 0.348886i 0.166438 0.986052i \(-0.446773\pi\)
−0.770727 + 0.637166i \(0.780107\pi\)
\(114\) −0.395644 0.685275i −0.0370554 0.0641819i
\(115\) −9.73371 + 3.20233i −0.907673 + 0.298619i
\(116\) 8.20871 0.762160
\(117\) 1.73205 7.00000i 0.160128 0.647150i
\(118\) 6.37386i 0.586762i
\(119\) 6.87386 3.96863i 0.630126 0.363803i
\(120\) 3.67900 1.21037i 0.335845 0.110491i
\(121\) −2.00000 + 3.46410i −0.181818 + 0.314918i
\(122\) −0.647551 −0.0586265
\(123\) −1.32288 + 2.29129i −0.119280 + 0.206598i
\(124\) −9.62614 5.55765i −0.864453 0.499092i
\(125\) 9.11710 + 6.47135i 0.815459 + 0.578815i
\(126\) 0.791288 1.37055i 0.0704935 0.122098i
\(127\) 15.3700 8.87386i 1.36387 0.787428i 0.373729 0.927538i \(-0.378079\pi\)
0.990136 + 0.140110i \(0.0447455\pi\)
\(128\) 5.51993 + 9.56080i 0.487897 + 0.845063i
\(129\) −10.5826 −0.931744
\(130\) 2.07630 + 3.04225i 0.182103 + 0.266823i
\(131\) −7.58258 −0.662493 −0.331246 0.943544i \(-0.607469\pi\)
−0.331246 + 0.943544i \(0.607469\pi\)
\(132\) −2.36965 4.10436i −0.206252 0.357238i
\(133\) −2.59808 + 1.50000i −0.225282 + 0.130066i
\(134\) 0.230493 0.399225i 0.0199115 0.0344878i
\(135\) 2.28425 10.9445i 0.196597 0.941953i
\(136\) −6.87386 3.96863i −0.589429 0.340307i
\(137\) −5.24383 + 9.08258i −0.448010 + 0.775977i −0.998256 0.0590258i \(-0.981201\pi\)
0.550246 + 0.835003i \(0.314534\pi\)
\(138\) −2.09355 −0.178215
\(139\) −10.8739 + 18.8341i −0.922309 + 1.59749i −0.126476 + 0.991970i \(0.540367\pi\)
−0.795833 + 0.605517i \(0.792967\pi\)
\(140\) −2.16812 6.59014i −0.183239 0.556968i
\(141\) 1.58258 0.913701i 0.133277 0.0769475i
\(142\) 3.20871i 0.269269i
\(143\) 6.61438 6.87386i 0.553122 0.574821i
\(144\) 5.58258 0.465215
\(145\) 3.20233 + 9.73371i 0.265939 + 0.808340i
\(146\) 0 0
\(147\) −3.46410 2.00000i −0.285714 0.164957i
\(148\) −14.2179 −1.16870
\(149\) −14.4564 8.34643i −1.18432 0.683766i −0.227308 0.973823i \(-0.572992\pi\)
−0.957009 + 0.290057i \(0.906326\pi\)
\(150\) 1.35622 + 1.83806i 0.110735 + 0.150077i
\(151\) 9.66930i 0.786877i 0.919351 + 0.393438i \(0.128715\pi\)
−0.919351 + 0.393438i \(0.871285\pi\)
\(152\) 2.59808 + 1.50000i 0.210732 + 0.121666i
\(153\) −7.93725 + 4.58258i −0.641689 + 0.370479i
\(154\) 1.81307 1.04678i 0.146101 0.0843516i
\(155\) 2.83485 13.5826i 0.227701 1.09098i
\(156\) −1.79129 6.20520i −0.143418 0.496814i
\(157\) 9.16515i 0.731459i 0.930721 + 0.365729i \(0.119180\pi\)
−0.930721 + 0.365729i \(0.880820\pi\)
\(158\) −1.37055 2.37386i −0.109035 0.188854i
\(159\) 3.79129 + 6.56670i 0.300669 + 0.520773i
\(160\) −7.06201 + 7.90145i −0.558301 + 0.624665i
\(161\) 7.93725i 0.625543i
\(162\) −0.228425 + 0.395644i −0.0179468 + 0.0310847i
\(163\) −10.5353 + 18.2477i −0.825191 + 1.42927i 0.0765827 + 0.997063i \(0.475599\pi\)
−0.901773 + 0.432209i \(0.857734\pi\)
\(164\) 4.73930i 0.370077i
\(165\) 3.94242 4.41105i 0.306917 0.343399i
\(166\) −1.37386 2.37960i −0.106632 0.184693i
\(167\) 4.78698 + 8.29129i 0.370427 + 0.641599i 0.989631 0.143631i \(-0.0458779\pi\)
−0.619204 + 0.785230i \(0.712545\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 11.0000 6.92820i 0.846154 0.532939i
\(170\) 0.956439 4.58258i 0.0733555 0.351468i
\(171\) 3.00000 1.73205i 0.229416 0.132453i
\(172\) 16.4168 9.47822i 1.25177 0.722707i
\(173\) −14.3609 8.29129i −1.09184 0.630375i −0.157775 0.987475i \(-0.550432\pi\)
−0.934066 + 0.357100i \(0.883766\pi\)
\(174\) 2.09355i 0.158712i
\(175\) 6.96863 5.14181i 0.526779 0.388685i
\(176\) 6.39564 + 3.69253i 0.482090 + 0.278335i
\(177\) 13.9518 1.04868
\(178\) −3.78788 2.18693i −0.283913 0.163917i
\(179\) 9.08258 + 15.7315i 0.678864 + 1.17583i 0.975323 + 0.220781i \(0.0708606\pi\)
−0.296460 + 0.955045i \(0.595806\pi\)
\(180\) 2.50353 + 7.60964i 0.186602 + 0.567189i
\(181\) 8.74773 0.650213 0.325107 0.945677i \(-0.394600\pi\)
0.325107 + 0.945677i \(0.394600\pi\)
\(182\) 2.74110 0.791288i 0.203184 0.0586542i
\(183\) 1.41742i 0.104779i
\(184\) 6.87386 3.96863i 0.506748 0.292571i
\(185\) −5.54661 16.8593i −0.407795 1.23952i
\(186\) 1.41742 2.45505i 0.103931 0.180013i
\(187\) −12.1244 −0.886621
\(188\) −1.63670 + 2.83485i −0.119369 + 0.206753i
\(189\) −7.50000 4.33013i −0.545545 0.314970i
\(190\) −0.361500 + 1.73205i −0.0262260 + 0.125656i
\(191\) 8.29129 14.3609i 0.599937 1.03912i −0.392893 0.919584i \(-0.628526\pi\)
0.992830 0.119536i \(-0.0381408\pi\)
\(192\) 2.95958 1.70871i 0.213589 0.123316i
\(193\) −7.43273 12.8739i −0.535020 0.926681i −0.999162 0.0409206i \(-0.986971\pi\)
0.464143 0.885760i \(-0.346362\pi\)
\(194\) −5.20871 −0.373964
\(195\) 6.65918 4.54481i 0.476874 0.325460i
\(196\) 7.16515 0.511797
\(197\) 7.33738 + 12.7087i 0.522767 + 0.905458i 0.999649 + 0.0264912i \(0.00843339\pi\)
−0.476882 + 0.878967i \(0.658233\pi\)
\(198\) −2.09355 + 1.20871i −0.148782 + 0.0858994i
\(199\) 5.29129 9.16478i 0.375089 0.649674i −0.615251 0.788331i \(-0.710945\pi\)
0.990340 + 0.138657i \(0.0442787\pi\)
\(200\) −7.93725 3.46410i −0.561249 0.244949i
\(201\) −0.873864 0.504525i −0.0616376 0.0355865i
\(202\) −2.05583 + 3.56080i −0.144647 + 0.250537i
\(203\) 7.93725 0.557086
\(204\) −4.10436 + 7.10895i −0.287362 + 0.497726i
\(205\) 5.61976 1.84887i 0.392501 0.129131i
\(206\) −1.25227 + 0.723000i −0.0872500 + 0.0503738i
\(207\) 9.16515i 0.637022i
\(208\) 7.25198 + 6.97822i 0.502834 + 0.483852i
\(209\) 4.58258 0.316983
\(210\) 1.68075 0.552957i 0.115983 0.0381577i
\(211\) 0.0825757 + 0.143025i 0.00568475 + 0.00984627i 0.868854 0.495069i \(-0.164857\pi\)
−0.863169 + 0.504915i \(0.831524\pi\)
\(212\) −11.7629 6.79129i −0.807876 0.466428i
\(213\) −7.02355 −0.481246
\(214\) 4.18693 + 2.41733i 0.286213 + 0.165245i
\(215\) 17.6435 + 15.7690i 1.20327 + 1.07544i
\(216\) 8.66025i 0.589256i
\(217\) −9.30780 5.37386i −0.631855 0.364802i
\(218\) 5.19615 3.00000i 0.351928 0.203186i
\(219\) 0 0
\(220\) −2.16515 + 10.3739i −0.145974 + 0.699406i
\(221\) −16.0390 3.96863i −1.07890 0.266959i
\(222\) 3.62614i 0.243370i
\(223\) 4.33013 + 7.50000i 0.289967 + 0.502237i 0.973801 0.227400i \(-0.0730224\pi\)
−0.683835 + 0.729637i \(0.739689\pi\)
\(224\) 4.10436 + 7.10895i 0.274234 + 0.474987i
\(225\) −8.04668 + 5.93725i −0.536445 + 0.395817i
\(226\) 3.38865i 0.225410i
\(227\) −0.409175 + 0.708712i −0.0271579 + 0.0470389i −0.879285 0.476296i \(-0.841979\pi\)
0.852127 + 0.523335i \(0.175312\pi\)
\(228\) 1.55130 2.68693i 0.102737 0.177946i
\(229\) 26.2668i 1.73576i −0.496774 0.867880i \(-0.665482\pi\)
0.496774 0.867880i \(-0.334518\pi\)
\(230\) 3.49041 + 3.11959i 0.230151 + 0.205700i
\(231\) −2.29129 3.96863i −0.150756 0.261116i
\(232\) −3.96863 6.87386i −0.260553 0.451291i
\(233\) 2.83485i 0.185717i −0.995679 0.0928586i \(-0.970400\pi\)
0.995679 0.0928586i \(-0.0296004\pi\)
\(234\) −3.16515 + 0.913701i −0.206912 + 0.0597305i
\(235\) −4.00000 0.834849i −0.260931 0.0544595i
\(236\) −21.6434 + 12.4958i −1.40886 + 0.813408i
\(237\) −5.19615 + 3.00000i −0.337526 + 0.194871i
\(238\) −3.14033 1.81307i −0.203557 0.117524i
\(239\) 0.190700i 0.0123354i −0.999981 0.00616769i \(-0.998037\pi\)
0.999981 0.00616769i \(-0.00196325\pi\)
\(240\) 4.65369 + 4.15928i 0.300394 + 0.268481i
\(241\) −1.50000 0.866025i −0.0966235 0.0557856i 0.450910 0.892570i \(-0.351100\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 1.82740 0.117470
\(243\) 13.8564 + 8.00000i 0.888889 + 0.513200i
\(244\) −1.26951 2.19885i −0.0812719 0.140767i
\(245\) 2.79523 + 8.49628i 0.178580 + 0.542807i
\(246\) 1.20871 0.0770647
\(247\) 6.06218 + 1.50000i 0.385727 + 0.0954427i
\(248\) 10.7477i 0.682481i
\(249\) −5.20871 + 3.00725i −0.330089 + 0.190577i
\(250\) 0.477776 5.08535i 0.0302172 0.321626i
\(251\) 0.0825757 0.143025i 0.00521213 0.00902768i −0.863408 0.504507i \(-0.831674\pi\)
0.868620 + 0.495479i \(0.165008\pi\)
\(252\) 6.20520 0.390891
\(253\) 6.06218 10.5000i 0.381126 0.660129i
\(254\) −7.02178 4.05403i −0.440586 0.254372i
\(255\) −10.0308 2.09355i −0.628153 0.131103i
\(256\) −0.895644 + 1.55130i −0.0559777 + 0.0969563i
\(257\) −15.7315 + 9.08258i −0.981303 + 0.566556i −0.902663 0.430348i \(-0.858391\pi\)
−0.0786397 + 0.996903i \(0.525058\pi\)
\(258\) 2.41733 + 4.18693i 0.150496 + 0.260667i
\(259\) −13.7477 −0.854242
\(260\) −6.25987 + 13.0146i −0.388221 + 0.807132i
\(261\) −9.16515 −0.567309
\(262\) 1.73205 + 3.00000i 0.107006 + 0.185341i
\(263\) −7.79423 + 4.50000i −0.480613 + 0.277482i −0.720672 0.693276i \(-0.756167\pi\)
0.240059 + 0.970758i \(0.422833\pi\)
\(264\) −2.29129 + 3.96863i −0.141019 + 0.244252i
\(265\) 3.46410 16.5975i 0.212798 1.01958i
\(266\) 1.18693 + 0.685275i 0.0727755 + 0.0420169i
\(267\) −4.78698 + 8.29129i −0.292958 + 0.507419i
\(268\) 1.80750 0.110411
\(269\) −7.50000 + 12.9904i −0.457283 + 0.792038i −0.998816 0.0486418i \(-0.984511\pi\)
0.541533 + 0.840679i \(0.317844\pi\)
\(270\) −4.85191 + 1.59625i −0.295278 + 0.0971447i
\(271\) 7.50000 4.33013i 0.455593 0.263036i −0.254597 0.967047i \(-0.581943\pi\)
0.710189 + 0.704011i \(0.248609\pi\)
\(272\) 12.7913i 0.775586i
\(273\) −1.73205 6.00000i −0.104828 0.363137i
\(274\) 4.79129 0.289452
\(275\) −13.1458 + 1.47960i −0.792719 + 0.0892234i
\(276\) −4.10436 7.10895i −0.247053 0.427909i
\(277\) 6.42368 + 3.70871i 0.385961 + 0.222835i 0.680409 0.732833i \(-0.261802\pi\)
−0.294447 + 0.955668i \(0.595136\pi\)
\(278\) 9.93545 0.595889
\(279\) 10.7477 + 6.20520i 0.643450 + 0.371496i
\(280\) −4.47028 + 5.00166i −0.267151 + 0.298906i
\(281\) 3.65480i 0.218027i −0.994040 0.109014i \(-0.965231\pi\)
0.994040 0.109014i \(-0.0347692\pi\)
\(282\) −0.723000 0.417424i −0.0430540 0.0248573i
\(283\) 24.0302 13.8739i 1.42845 0.824716i 0.431451 0.902136i \(-0.358002\pi\)
0.996998 + 0.0774209i \(0.0246685\pi\)
\(284\) 10.8956 6.29060i 0.646538 0.373279i
\(285\) 3.79129 + 0.791288i 0.224577 + 0.0468718i
\(286\) −4.23049 1.04678i −0.250154 0.0618971i
\(287\) 4.58258i 0.270501i
\(288\) −4.73930 8.20871i −0.279266 0.483703i
\(289\) 2.00000 + 3.46410i 0.117647 + 0.203771i
\(290\) 3.11959 3.49041i 0.183189 0.204964i
\(291\) 11.4014i 0.668359i
\(292\) 0 0
\(293\) 9.06943 15.7087i 0.529842 0.917713i −0.469552 0.882905i \(-0.655585\pi\)
0.999394 0.0348081i \(-0.0110820\pi\)
\(294\) 1.82740i 0.106576i
\(295\) −23.2606 20.7894i −1.35429 1.21041i
\(296\) 6.87386 + 11.9059i 0.399535 + 0.692015i
\(297\) 6.61438 + 11.4564i 0.383805 + 0.664770i
\(298\) 7.62614i 0.441770i
\(299\) 11.4564 11.9059i 0.662543 0.688535i
\(300\) −3.58258 + 8.20871i −0.206840 + 0.473930i
\(301\) 15.8739 9.16478i 0.914954 0.528249i
\(302\) 3.82560 2.20871i 0.220139 0.127097i
\(303\) 7.79423 + 4.50000i 0.447767 + 0.258518i
\(304\) 4.83465i 0.277286i
\(305\) 2.11210 2.36316i 0.120938 0.135314i
\(306\) 3.62614 + 2.09355i 0.207292 + 0.119680i
\(307\) −24.2487 −1.38395 −0.691974 0.721923i \(-0.743259\pi\)
−0.691974 + 0.721923i \(0.743259\pi\)
\(308\) 7.10895 + 4.10436i 0.405070 + 0.233867i
\(309\) 1.58258 + 2.74110i 0.0900296 + 0.155936i
\(310\) −6.02141 + 1.98101i −0.341993 + 0.112514i
\(311\) 7.58258 0.429968 0.214984 0.976618i \(-0.431030\pi\)
0.214984 + 0.976618i \(0.431030\pi\)
\(312\) −4.33013 + 4.50000i −0.245145 + 0.254762i
\(313\) 3.25227i 0.183829i 0.995767 + 0.0919147i \(0.0292987\pi\)
−0.995767 + 0.0919147i \(0.970701\pi\)
\(314\) 3.62614 2.09355i 0.204635 0.118146i
\(315\) 2.42074 + 7.35799i 0.136393 + 0.414576i
\(316\) 5.37386 9.30780i 0.302303 0.523605i
\(317\) 0.190700 0.0107108 0.00535540 0.999986i \(-0.498295\pi\)
0.00535540 + 0.999986i \(0.498295\pi\)
\(318\) 1.73205 3.00000i 0.0971286 0.168232i
\(319\) −10.5000 6.06218i −0.587887 0.339417i
\(320\) −7.48040 1.56125i −0.418167 0.0872766i
\(321\) 5.29129 9.16478i 0.295331 0.511528i
\(322\) 3.14033 1.81307i 0.175004 0.101038i
\(323\) −3.96863 6.87386i −0.220820 0.382472i
\(324\) −1.79129 −0.0995160
\(325\) −17.8745 2.34563i −0.991499 0.130112i
\(326\) 9.62614 0.533142
\(327\) −6.56670 11.3739i −0.363140 0.628976i
\(328\) −3.96863 + 2.29129i −0.219131 + 0.126515i
\(329\) −1.58258 + 2.74110i −0.0872502 + 0.151122i
\(330\) −2.64575 0.552200i −0.145644 0.0303976i
\(331\) −3.87386 2.23658i −0.212927 0.122933i 0.389744 0.920923i \(-0.372563\pi\)
−0.602671 + 0.797990i \(0.705897\pi\)
\(332\) 5.38685 9.33030i 0.295642 0.512067i
\(333\) 15.8745 0.869918
\(334\) 2.18693 3.78788i 0.119664 0.207263i
\(335\) 0.705131 + 2.14329i 0.0385254 + 0.117101i
\(336\) 4.18693 2.41733i 0.228416 0.131876i
\(337\) 30.7477i 1.67494i 0.546487 + 0.837468i \(0.315965\pi\)
−0.546487 + 0.837468i \(0.684035\pi\)
\(338\) −5.25378 2.76951i −0.285768 0.150641i
\(339\) 7.41742 0.402859
\(340\) 17.4359 5.73630i 0.945593 0.311095i
\(341\) 8.20871 + 14.2179i 0.444527 + 0.769943i
\(342\) −1.37055 0.791288i −0.0741109 0.0427879i
\(343\) 19.0526 1.02874
\(344\) −15.8739 9.16478i −0.855861 0.494132i
\(345\) 6.82847 7.64016i 0.367633 0.411332i
\(346\) 7.57575i 0.407275i
\(347\) 18.4726 + 10.6652i 0.991660 + 0.572535i 0.905770 0.423769i \(-0.139293\pi\)
0.0858901 + 0.996305i \(0.472627\pi\)
\(348\) −7.10895 + 4.10436i −0.381080 + 0.220017i
\(349\) 2.12614 1.22753i 0.113809 0.0657079i −0.442015 0.897008i \(-0.645736\pi\)
0.555824 + 0.831300i \(0.312403\pi\)
\(350\) −3.62614 1.58258i −0.193825 0.0845922i
\(351\) 5.00000 + 17.3205i 0.266880 + 0.924500i
\(352\) 12.5390i 0.668332i
\(353\) −3.41643 5.91742i −0.181838 0.314953i 0.760668 0.649141i \(-0.224871\pi\)
−0.942506 + 0.334188i \(0.891538\pi\)
\(354\) −3.18693 5.51993i −0.169384 0.293381i
\(355\) 11.7098 + 10.4658i 0.621492 + 0.555465i
\(356\) 17.1497i 0.908933i
\(357\) −3.96863 + 6.87386i −0.210042 + 0.363803i
\(358\) 4.14938 7.18693i 0.219301 0.379841i
\(359\) 19.5293i 1.03072i 0.856975 + 0.515359i \(0.172341\pi\)
−0.856975 + 0.515359i \(0.827659\pi\)
\(360\) 5.16184 5.77542i 0.272053 0.304391i
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) −1.99820 3.46099i −0.105023 0.181905i
\(363\) 4.00000i 0.209946i
\(364\) 8.06080 + 7.75650i 0.422500 + 0.406551i
\(365\) 0 0
\(366\) 0.560795 0.323775i 0.0293132 0.0169240i
\(367\) −1.51358 + 0.873864i −0.0790080 + 0.0456153i −0.538984 0.842316i \(-0.681192\pi\)
0.459976 + 0.887932i \(0.347858\pi\)
\(368\) 11.0776 + 6.39564i 0.577459 + 0.333396i
\(369\) 5.29150i 0.275465i
\(370\) −5.40329 + 6.04556i −0.280903 + 0.314294i
\(371\) −11.3739 6.56670i −0.590502 0.340926i
\(372\) 11.1153 0.576302
\(373\) −11.2583 6.50000i −0.582934 0.336557i 0.179364 0.983783i \(-0.442596\pi\)
−0.762299 + 0.647225i \(0.775929\pi\)
\(374\) 2.76951 + 4.79693i 0.143208 + 0.248043i
\(375\) −11.1313 1.04580i −0.574819 0.0540051i
\(376\) 3.16515 0.163230
\(377\) −11.9059 11.4564i −0.613184 0.590037i
\(378\) 3.95644i 0.203497i
\(379\) −9.24773 + 5.33918i −0.475024 + 0.274255i −0.718340 0.695692i \(-0.755098\pi\)
0.243317 + 0.969947i \(0.421765\pi\)
\(380\) −6.59014 + 2.16812i −0.338067 + 0.111222i
\(381\) −8.87386 + 15.3700i −0.454622 + 0.787428i
\(382\) −7.57575 −0.387609
\(383\) −11.8105 + 20.4564i −0.603490 + 1.04528i 0.388798 + 0.921323i \(0.372890\pi\)
−0.992288 + 0.123952i \(0.960443\pi\)
\(384\) −9.56080 5.51993i −0.487897 0.281688i
\(385\) −2.09355 + 10.0308i −0.106697 + 0.511217i
\(386\) −3.39564 + 5.88143i −0.172834 + 0.299357i
\(387\) −18.3296 + 10.5826i −0.931744 + 0.537943i
\(388\) −10.2116 17.6869i −0.518413 0.897918i
\(389\) 3.16515 0.160480 0.0802398 0.996776i \(-0.474431\pi\)
0.0802398 + 0.996776i \(0.474431\pi\)
\(390\) −3.31925 1.59652i −0.168077 0.0808428i
\(391\) −21.0000 −1.06202
\(392\) −3.46410 6.00000i −0.174964 0.303046i
\(393\) 6.56670 3.79129i 0.331246 0.191245i
\(394\) 3.35208 5.80598i 0.168876 0.292501i
\(395\) 13.1334 + 2.74110i 0.660813 + 0.137920i
\(396\) −8.20871 4.73930i −0.412503 0.238159i
\(397\) 10.1738 17.6216i 0.510610 0.884402i −0.489315 0.872107i \(-0.662753\pi\)
0.999924 0.0122949i \(-0.00391368\pi\)
\(398\) −4.83465 −0.242339
\(399\) 1.50000 2.59808i 0.0750939 0.130066i
\(400\) −1.56099 13.8689i −0.0780496 0.693443i
\(401\) −25.8303 + 14.9131i −1.28990 + 0.744726i −0.978637 0.205596i \(-0.934087\pi\)
−0.311267 + 0.950323i \(0.600753\pi\)
\(402\) 0.460985i 0.0229918i
\(403\) 6.20520 + 21.4955i 0.309103 + 1.07076i
\(404\) −16.1216 −0.802079
\(405\) −0.698807 2.12407i −0.0347240 0.105546i
\(406\) −1.81307 3.14033i −0.0899811 0.155852i
\(407\) 18.1865 + 10.5000i 0.901473 + 0.520466i
\(408\) 7.93725 0.392953
\(409\) 7.50000 + 4.33013i 0.370851 + 0.214111i 0.673830 0.738886i \(-0.264648\pi\)
−0.302979 + 0.952997i \(0.597981\pi\)
\(410\) −2.01519 1.80110i −0.0995230 0.0889498i
\(411\) 10.4877i 0.517318i
\(412\) −4.91010 2.83485i −0.241903 0.139663i
\(413\) −20.9276 + 12.0826i −1.02978 + 0.594545i
\(414\) −3.62614 + 2.09355i −0.178215 + 0.102892i
\(415\) 13.1652 + 2.74773i 0.646252 + 0.134881i
\(416\) 4.10436 16.5876i 0.201233 0.813272i
\(417\) 21.7477i 1.06499i
\(418\) −1.04678 1.81307i −0.0511995 0.0886801i
\(419\) −2.91742 5.05313i −0.142526 0.246861i 0.785922 0.618326i \(-0.212189\pi\)
−0.928447 + 0.371465i \(0.878856\pi\)
\(420\) 5.17272 + 4.62317i 0.252403 + 0.225588i
\(421\) 5.48220i 0.267186i −0.991036 0.133593i \(-0.957348\pi\)
0.991036 0.133593i \(-0.0426515\pi\)
\(422\) 0.0377247 0.0653411i 0.00183641 0.00318076i
\(423\) 1.82740 3.16515i 0.0888513 0.153895i
\(424\) 13.1334i 0.637815i
\(425\) 13.6040 + 18.4373i 0.659889 + 0.894338i
\(426\) 1.60436 + 2.77883i 0.0777313 + 0.134635i
\(427\) −1.22753 2.12614i −0.0594041 0.102891i
\(428\) 18.9564i 0.916294i
\(429\) −2.29129 + 9.26013i −0.110624 + 0.447083i
\(430\) 2.20871 10.5826i 0.106514 0.510337i
\(431\) 7.33485 4.23478i 0.353307 0.203982i −0.312834 0.949808i \(-0.601278\pi\)
0.666141 + 0.745826i \(0.267945\pi\)
\(432\) −12.0866 + 6.97822i −0.581518 + 0.335740i
\(433\) 8.44178 + 4.87386i 0.405686 + 0.234223i 0.688934 0.724824i \(-0.258079\pi\)
−0.283248 + 0.959047i \(0.591412\pi\)
\(434\) 4.91010i 0.235692i
\(435\) −7.64016 6.82847i −0.366317 0.327400i
\(436\) 20.3739 + 11.7629i 0.975731 + 0.563339i
\(437\) 7.93725 0.379690
\(438\) 0 0
\(439\) −7.24773 12.5534i −0.345915 0.599143i 0.639604 0.768704i \(-0.279098\pi\)
−0.985520 + 0.169562i \(0.945765\pi\)
\(440\) 9.73371 3.20233i 0.464036 0.152665i
\(441\) −8.00000 −0.380952
\(442\) 2.09355 + 7.25227i 0.0995801 + 0.344955i
\(443\) 19.9129i 0.946089i −0.881038 0.473045i \(-0.843155\pi\)
0.881038 0.473045i \(-0.156845\pi\)
\(444\) 12.3131 7.10895i 0.584352 0.337376i
\(445\) 20.3357 6.69034i 0.964007 0.317153i
\(446\) 1.97822 3.42638i 0.0936714 0.162244i
\(447\) 16.6929 0.789545
\(448\) −2.95958 + 5.12614i −0.139827 + 0.242187i
\(449\) 9.54356 + 5.50998i 0.450388 + 0.260032i 0.707994 0.706218i \(-0.249600\pi\)
−0.257606 + 0.966250i \(0.582934\pi\)
\(450\) 4.18710 + 1.82740i 0.197382 + 0.0861445i
\(451\) −3.50000 + 6.06218i −0.164809 + 0.285457i
\(452\) −11.5067 + 6.64337i −0.541228 + 0.312478i
\(453\) −4.83465 8.37386i −0.227152 0.393438i
\(454\) 0.373864 0.0175463
\(455\) −6.05286 + 12.5842i −0.283762 + 0.589958i
\(456\) −3.00000 −0.140488
\(457\) −0.866025 1.50000i −0.0405110 0.0701670i 0.845059 0.534673i \(-0.179565\pi\)
−0.885570 + 0.464506i \(0.846232\pi\)
\(458\) −10.3923 + 6.00000i −0.485601 + 0.280362i
\(459\) 11.4564 19.8431i 0.534741 0.926198i
\(460\) −3.75015 + 17.9681i −0.174852 + 0.837765i
\(461\) 31.0390 + 17.9204i 1.44563 + 0.834635i 0.998217 0.0596914i \(-0.0190117\pi\)
0.447414 + 0.894327i \(0.352345\pi\)
\(462\) −1.04678 + 1.81307i −0.0487004 + 0.0843516i
\(463\) −39.4002 −1.83108 −0.915542 0.402223i \(-0.868238\pi\)
−0.915542 + 0.402223i \(0.868238\pi\)
\(464\) 6.39564 11.0776i 0.296910 0.514264i
\(465\) 4.33624 + 13.1803i 0.201088 + 0.611221i
\(466\) −1.12159 + 0.647551i −0.0519567 + 0.0299972i
\(467\) 24.3303i 1.12587i −0.826500 0.562936i \(-0.809672\pi\)
0.826500 0.562936i \(-0.190328\pi\)
\(468\) −9.30780 8.95644i −0.430253 0.414012i
\(469\) 1.74773 0.0807025
\(470\) 0.583398 + 1.77328i 0.0269101 + 0.0817951i
\(471\) −4.58258 7.93725i −0.211154 0.365729i
\(472\) 20.9276 + 12.0826i 0.963272 + 0.556146i
\(473\) −27.9989 −1.28739
\(474\) 2.37386 + 1.37055i 0.109035 + 0.0629515i
\(475\) −5.14181 6.96863i −0.235923 0.319743i
\(476\) 14.2179i 0.651677i
\(477\) 13.1334 + 7.58258i 0.601337 + 0.347182i
\(478\) −0.0754495 + 0.0435608i −0.00345098 + 0.00199242i
\(479\) 4.03901 2.33193i 0.184547 0.106548i −0.404880 0.914370i \(-0.632687\pi\)
0.589427 + 0.807821i \(0.299353\pi\)
\(480\) 2.16515 10.3739i 0.0988252 0.473500i
\(481\) 20.6216 + 19.8431i 0.940264 + 0.904769i
\(482\) 0.791288i 0.0360422i
\(483\) −3.96863 6.87386i −0.180579 0.312772i
\(484\) 3.58258 + 6.20520i 0.162844 + 0.282055i
\(485\) 16.9891 19.0086i 0.771435 0.863134i
\(486\) 7.30960i 0.331570i
\(487\) −5.33918 + 9.24773i −0.241941 + 0.419055i −0.961267 0.275618i \(-0.911117\pi\)
0.719326 + 0.694673i \(0.244451\pi\)
\(488\) −1.22753 + 2.12614i −0.0555675 + 0.0962457i
\(489\) 21.0707i 0.952848i
\(490\) 2.72300 3.04668i 0.123013 0.137635i
\(491\) −9.70871 16.8160i −0.438148 0.758895i 0.559399 0.828899i \(-0.311032\pi\)
−0.997547 + 0.0700041i \(0.977699\pi\)
\(492\) 2.36965 + 4.10436i 0.106832 + 0.185039i
\(493\) 21.0000i 0.945792i
\(494\) −0.791288 2.74110i −0.0356017 0.123328i
\(495\) 2.41742 11.5826i 0.108655 0.520598i
\(496\) −15.0000 + 8.66025i −0.673520 + 0.388857i
\(497\) 10.5353 6.08258i 0.472574 0.272841i
\(498\) 2.37960 + 1.37386i 0.106632 + 0.0615643i
\(499\) 0.723000i 0.0323659i −0.999869 0.0161830i \(-0.994849\pi\)
0.999869 0.0161830i \(-0.00515142\pi\)
\(500\) 18.2047 8.34734i 0.814139 0.373305i
\(501\) −8.29129 4.78698i −0.370427 0.213866i
\(502\) −0.0754495 −0.00336747
\(503\) 0.143025 + 0.0825757i 0.00637718 + 0.00368187i 0.503185 0.864179i \(-0.332161\pi\)
−0.496808 + 0.867860i \(0.665495\pi\)
\(504\) −3.00000 5.19615i −0.133631 0.231455i
\(505\) −6.28926 19.1166i −0.279868 0.850678i
\(506\) −5.53901 −0.246239
\(507\) −6.06218 + 11.5000i −0.269231 + 0.510733i
\(508\) 31.7913i 1.41051i
\(509\) −7.33485 + 4.23478i −0.325111 + 0.187703i −0.653669 0.756781i \(-0.726771\pi\)
0.328557 + 0.944484i \(0.393438\pi\)
\(510\) 1.46299 + 4.44685i 0.0647822 + 0.196910i
\(511\) 0 0
\(512\) 22.8981 1.01196
\(513\) −4.33013 + 7.50000i −0.191180 + 0.331133i
\(514\) 7.18693 + 4.14938i 0.317002 + 0.183021i
\(515\) 1.44600 6.92820i 0.0637184 0.305293i
\(516\) −9.47822 + 16.4168i −0.417255 + 0.722707i
\(517\) 4.18710 2.41742i 0.184149 0.106318i
\(518\) 3.14033 + 5.43920i 0.137978 + 0.238985i
\(519\) 16.5826 0.727894
\(520\) 13.9247 1.05019i 0.610638 0.0460537i
\(521\) 27.4955 1.20460 0.602299 0.798271i \(-0.294252\pi\)
0.602299 + 0.798271i \(0.294252\pi\)
\(522\) 2.09355 + 3.62614i 0.0916322 + 0.158712i
\(523\) −0.143025 + 0.0825757i −0.00625406 + 0.00361078i −0.503124 0.864214i \(-0.667816\pi\)
0.496870 + 0.867825i \(0.334483\pi\)
\(524\) −6.79129 + 11.7629i −0.296679 + 0.513863i
\(525\) −3.46410 + 7.93725i −0.151186 + 0.346410i
\(526\) 3.56080 + 2.05583i 0.155258 + 0.0896383i
\(527\) 14.2179 24.6261i 0.619342 1.07273i
\(528\) −7.38505 −0.321393
\(529\) −1.00000 + 1.73205i −0.0434783 + 0.0753066i
\(530\) −7.35799 + 2.42074i −0.319611 + 0.105150i
\(531\) 24.1652 13.9518i 1.04868 0.605455i
\(532\) 5.37386i 0.232987i
\(533\) −6.61438 + 6.87386i −0.286501 + 0.297740i
\(534\) 4.37386 0.189276
\(535\) −22.4781 + 7.39517i −0.971814 + 0.319721i
\(536\) −0.873864 1.51358i −0.0377452 0.0653765i
\(537\) −15.7315 9.08258i −0.678864 0.391942i
\(538\) 6.85275 0.295443
\(539\) −9.16515 5.29150i −0.394771 0.227921i
\(540\) −14.9323 13.3459i −0.642586 0.574318i
\(541\) 10.3923i 0.446800i 0.974727 + 0.223400i \(0.0717156\pi\)
−0.974727 + 0.223400i \(0.928284\pi\)
\(542\) −3.42638 1.97822i −0.147175 0.0849718i
\(543\) −7.57575 + 4.37386i −0.325107 + 0.187700i
\(544\) −18.8085 + 10.8591i −0.806409 + 0.465580i
\(545\) −6.00000 + 28.7477i −0.257012 + 1.23142i
\(546\) −1.97822 + 2.05583i −0.0846600 + 0.0879812i
\(547\) 28.7477i 1.22916i 0.788853 + 0.614582i \(0.210675\pi\)
−0.788853 + 0.614582i \(0.789325\pi\)
\(548\) 9.39320 + 16.2695i 0.401258 + 0.694999i
\(549\) 1.41742 + 2.45505i 0.0604942 + 0.104779i
\(550\) 3.58822 + 4.86306i 0.153002 + 0.207362i
\(551\) 7.93725i 0.338138i
\(552\) −3.96863 + 6.87386i −0.168916 + 0.292571i
\(553\) 5.19615 9.00000i 0.220963 0.382719i
\(554\) 3.38865i 0.143970i
\(555\) 13.2331 + 11.8273i 0.561715 + 0.502039i
\(556\) 19.4782 + 33.7373i 0.826061 + 1.43078i
\(557\) −3.87328 6.70871i −0.164116 0.284257i 0.772225 0.635349i \(-0.219144\pi\)
−0.936341 + 0.351092i \(0.885810\pi\)
\(558\) 5.66970i 0.240017i
\(559\) −37.0390 9.16478i −1.56658 0.387629i
\(560\) −10.5826 2.20871i −0.447195 0.0933351i
\(561\) 10.5000 6.06218i 0.443310 0.255945i
\(562\) −1.44600 + 0.834849i −0.0609958 + 0.0352160i
\(563\) −7.79423 4.50000i −0.328488 0.189652i 0.326682 0.945134i \(-0.394069\pi\)
−0.655169 + 0.755482i \(0.727403\pi\)
\(564\) 3.27340i 0.137835i
\(565\) −12.3665 11.0527i −0.520261 0.464989i
\(566\) −10.9782 6.33828i −0.461449 0.266418i
\(567\) −1.73205 −0.0727393
\(568\) −10.5353 6.08258i −0.442053 0.255219i
\(569\) 3.87386 + 6.70973i 0.162401 + 0.281286i 0.935729 0.352719i \(-0.114743\pi\)
−0.773328 + 0.634006i \(0.781410\pi\)
\(570\) −0.552957 1.68075i −0.0231608 0.0703989i
\(571\) −35.0780 −1.46797 −0.733985 0.679166i \(-0.762342\pi\)
−0.733985 + 0.679166i \(0.762342\pi\)
\(572\) −4.73930 16.4174i −0.198160 0.686447i
\(573\) 16.5826i 0.692747i
\(574\) −1.81307 + 1.04678i −0.0756760 + 0.0436916i
\(575\) −22.7691 + 2.56275i −0.949537 + 0.106874i
\(576\) 3.41742 5.91915i 0.142393 0.246631i
\(577\) 6.92820 0.288425 0.144212 0.989547i \(-0.453935\pi\)
0.144212 + 0.989547i \(0.453935\pi\)
\(578\) 0.913701 1.58258i 0.0380049 0.0658265i
\(579\) 12.8739 + 7.43273i 0.535020 + 0.308894i
\(580\) 17.9681 + 3.75015i 0.746083 + 0.155717i
\(581\) 5.20871 9.02175i 0.216094 0.374285i
\(582\) 4.51088 2.60436i 0.186982 0.107954i
\(583\) 10.0308 + 17.3739i 0.415433 + 0.719552i
\(584\) 0 0
\(585\) 6.98924 14.5310i 0.288969 0.600784i
\(586\) −8.28674 −0.342322
\(587\) −19.7478 34.2042i −0.815078 1.41176i −0.909272 0.416203i \(-0.863361\pi\)
0.0941934 0.995554i \(-0.469973\pi\)
\(588\) −6.20520 + 3.58258i −0.255898 + 0.147743i
\(589\) −5.37386 + 9.30780i −0.221426 + 0.383521i
\(590\) −2.91190 + 13.9518i −0.119881 + 0.574385i
\(591\) −12.7087 7.33738i −0.522767 0.301819i
\(592\) −11.0776 + 19.1869i −0.455286 + 0.788578i
\(593\) 21.1660 0.869184 0.434592 0.900627i \(-0.356893\pi\)
0.434592 + 0.900627i \(0.356893\pi\)
\(594\) 3.02178 5.23388i 0.123985 0.214749i
\(595\) 16.8593 5.54661i 0.691163 0.227389i
\(596\) −25.8956 + 14.9509i −1.06073 + 0.612411i
\(597\) 10.5826i 0.433116i
\(598\) −7.32743 1.81307i −0.299641 0.0741419i
\(599\) −15.4955 −0.633127 −0.316564 0.948571i \(-0.602529\pi\)
−0.316564 + 0.948571i \(0.602529\pi\)
\(600\) 8.60591 0.968627i 0.351335 0.0395440i
\(601\) −8.45644 14.6470i −0.344945 0.597463i 0.640398 0.768043i \(-0.278769\pi\)
−0.985344 + 0.170580i \(0.945436\pi\)
\(602\) −7.25198 4.18693i −0.295569 0.170647i
\(603\) −2.01810 −0.0821834
\(604\) 15.0000 + 8.66025i 0.610341 + 0.352381i
\(605\) −5.96038 + 6.66888i −0.242324 + 0.271128i
\(606\) 4.11165i 0.167024i
\(607\) −6.70973 3.87386i −0.272339 0.157235i 0.357611 0.933871i \(-0.383591\pi\)
−0.629950 + 0.776635i \(0.716925\pi\)
\(608\) 7.10895 4.10436i 0.288306 0.166454i
\(609\) −6.87386 + 3.96863i −0.278543 + 0.160817i
\(610\) −1.41742 0.295834i −0.0573898 0.0119780i
\(611\) 6.33030 1.82740i 0.256097 0.0739287i
\(612\) 16.4174i 0.663635i
\(613\) 2.95958 + 5.12614i 0.119536 + 0.207043i 0.919584 0.392894i \(-0.128526\pi\)
−0.800048 + 0.599936i \(0.795193\pi\)
\(614\) 5.53901 + 9.59386i 0.223536 + 0.387176i
\(615\) −3.94242 + 4.41105i −0.158974 + 0.177871i
\(616\) 7.93725i 0.319801i
\(617\) 6.97588 12.0826i 0.280838 0.486426i −0.690753 0.723091i \(-0.742721\pi\)
0.971591 + 0.236664i \(0.0760542\pi\)
\(618\) 0.723000 1.25227i 0.0290833 0.0503738i
\(619\) 29.7309i 1.19499i 0.801874 + 0.597493i \(0.203836\pi\)
−0.801874 + 0.597493i \(0.796164\pi\)
\(620\) −18.5316 16.5629i −0.744249 0.665180i
\(621\) 11.4564 + 19.8431i 0.459731 + 0.796278i
\(622\) −1.73205 3.00000i −0.0694489 0.120289i
\(623\) 16.5826i 0.664367i
\(624\) −9.76951 2.41733i −0.391093 0.0967705i
\(625\) 17.0000 + 18.3303i 0.680000 + 0.733212i
\(626\) 1.28674 0.742901i 0.0514286 0.0296923i
\(627\) −3.96863 + 2.29129i −0.158492 + 0.0915052i
\(628\) 14.2179 + 8.20871i 0.567356 + 0.327563i
\(629\) 36.3731i 1.45029i
\(630\) 2.35819 2.63850i 0.0939524 0.105120i
\(631\) −5.12614 2.95958i −0.204068 0.117819i 0.394483 0.918903i \(-0.370924\pi\)
−0.598552 + 0.801084i \(0.704257\pi\)
\(632\) −10.3923 −0.413384
\(633\) −0.143025 0.0825757i −0.00568475 0.00328209i
\(634\) −0.0435608 0.0754495i −0.00173002 0.00299648i
\(635\) 37.6974 12.4022i 1.49598 0.492167i
\(636\) 13.5826 0.538584
\(637\) −10.3923 10.0000i −0.411758 0.396214i
\(638\) 5.53901i 0.219292i
\(639\) −12.1652 + 7.02355i −0.481246 + 0.277847i
\(640\) 7.71472 + 23.4494i 0.304951 + 0.926920i
\(641\) −9.08258 + 15.7315i −0.358740 + 0.621356i −0.987751 0.156041i \(-0.950127\pi\)
0.629010 + 0.777397i \(0.283460\pi\)
\(642\) −4.83465 −0.190809
\(643\) 10.8968 18.8739i 0.429729 0.744313i −0.567120 0.823635i \(-0.691942\pi\)
0.996849 + 0.0793227i \(0.0252757\pi\)
\(644\) 12.3131 + 7.10895i 0.485203 + 0.280132i
\(645\) −23.1642 4.83465i −0.912090 0.190364i
\(646\) −1.81307 + 3.14033i −0.0713342 + 0.123554i
\(647\) 23.3827 13.5000i 0.919268 0.530740i 0.0358667 0.999357i \(-0.488581\pi\)
0.883402 + 0.468617i \(0.155247\pi\)
\(648\) 0.866025 + 1.50000i 0.0340207 + 0.0589256i
\(649\) 36.9129 1.44896
\(650\) 3.15495 + 7.60774i 0.123747 + 0.298400i
\(651\) 10.7477 0.421237
\(652\) 18.8718 + 32.6869i 0.739077 + 1.28012i
\(653\) 37.0882 21.4129i 1.45137 0.837951i 0.452814 0.891605i \(-0.350420\pi\)
0.998560 + 0.0536545i \(0.0170870\pi\)
\(654\) −3.00000 + 5.19615i −0.117309 + 0.203186i
\(655\) −16.5975 3.46410i −0.648518 0.135354i
\(656\) −6.39564 3.69253i −0.249708 0.144169i
\(657\) 0 0
\(658\) 1.44600 0.0563710
\(659\) 15.2477 26.4098i 0.593967 1.02878i −0.399725 0.916635i \(-0.630894\pi\)
0.993692 0.112146i \(-0.0357724\pi\)
\(660\) −3.31186 10.0666i −0.128914 0.391842i
\(661\) 15.8739 9.16478i 0.617422 0.356469i −0.158443 0.987368i \(-0.550647\pi\)
0.775865 + 0.630900i \(0.217314\pi\)
\(662\) 2.04356i 0.0794252i
\(663\) 15.8745 4.58258i 0.616515 0.177972i
\(664\) −10.4174 −0.404274
\(665\) −6.37221 + 2.09642i −0.247104 + 0.0812957i
\(666\) −3.62614 6.28065i −0.140510 0.243370i
\(667\) −18.1865 10.5000i −0.704185 0.406562i
\(668\) 17.1497 0.663542
\(669\) −7.50000 4.33013i −0.289967 0.167412i
\(670\) 0.686911 0.768563i 0.0265377 0.0296922i
\(671\) 3.75015i 0.144773i
\(672\) −7.10895 4.10436i −0.274234 0.158329i
\(673\) 20.9276 12.0826i 0.806701 0.465749i −0.0391079 0.999235i \(-0.512452\pi\)
0.845809 + 0.533486i \(0.179118\pi\)
\(674\) 12.1652 7.02355i 0.468584 0.270537i
\(675\) 10.0000 22.9129i 0.384900 0.881917i
\(676\) −0.895644 23.2695i −0.0344478 0.894981i
\(677\) 2.83485i 0.108952i −0.998515 0.0544760i \(-0.982651\pi\)
0.998515 0.0544760i \(-0.0173489\pi\)
\(678\) −1.69433 2.93466i −0.0650702 0.112705i
\(679\) −9.87386 17.1020i −0.378924 0.656316i
\(680\) −13.2331 11.8273i −0.507468 0.453555i
\(681\) 0.818350i 0.0313593i
\(682\) 3.75015 6.49545i 0.143601 0.248724i
\(683\) −16.5498 + 28.6652i −0.633262 + 1.09684i 0.353619 + 0.935390i \(0.384951\pi\)
−0.986881 + 0.161452i \(0.948382\pi\)
\(684\) 6.20520i 0.237262i
\(685\) −15.6276 + 17.4852i −0.597100 + 0.668076i
\(686\) −4.35208 7.53803i −0.166163 0.287803i
\(687\) 13.1334 + 22.7477i 0.501071 + 0.867880i
\(688\) 29.5390i 1.12616i
\(689\) 7.58258 + 26.2668i 0.288873 + 1.00069i
\(690\) −4.58258 0.956439i −0.174456 0.0364110i
\(691\) 17.1261 9.88778i 0.651509 0.376149i −0.137525 0.990498i \(-0.543915\pi\)
0.789034 + 0.614349i \(0.210581\pi\)
\(692\) −25.7246 + 14.8521i −0.977901 + 0.564591i
\(693\) −7.93725 4.58258i −0.301511 0.174078i
\(694\) 9.74475i 0.369906i
\(695\) −32.4062 + 36.2582i −1.22924 + 1.37535i
\(696\) 6.87386 + 3.96863i 0.260553 + 0.150430i
\(697\) 12.1244 0.459243
\(698\) −0.971326 0.560795i −0.0367652 0.0212264i
\(699\) 1.41742 + 2.45505i 0.0536119 + 0.0928586i
\(700\) −1.73509 15.4157i −0.0655802 0.582658i
\(701\) −21.1652 −0.799397 −0.399698 0.916647i \(-0.630885\pi\)
−0.399698 + 0.916647i \(0.630885\pi\)
\(702\) 5.71063 5.93466i 0.215534 0.223989i
\(703\) 13.7477i 0.518505i
\(704\) 7.83030 4.52083i 0.295116 0.170385i
\(705\) 3.88153 1.27700i 0.146187 0.0480946i
\(706\) −1.56080 + 2.70338i −0.0587413 + 0.101743i
\(707\) −15.5885 −0.586264
\(708\) 12.4958 21.6434i 0.469621 0.813408i
\(709\) 31.5000 + 18.1865i 1.18301 + 0.683010i 0.956708 0.291048i \(-0.0940040\pi\)
0.226299 + 0.974058i \(0.427337\pi\)
\(710\) 1.46590 7.02355i 0.0550143 0.263589i
\(711\) −6.00000 + 10.3923i −0.225018 + 0.389742i
\(712\) −14.3609 + 8.29129i −0.538199 + 0.310729i
\(713\) 14.2179 + 24.6261i 0.532465 + 0.922256i
\(714\) 3.62614 0.135705
\(715\) 17.6185 12.0244i 0.658896 0.449688i
\(716\) 32.5390 1.21604
\(717\) 0.0953502 + 0.165151i 0.00356092 + 0.00616769i
\(718\) 7.72665 4.46099i 0.288356 0.166482i
\(719\) −12.2477 + 21.2137i −0.456763 + 0.791137i −0.998788 0.0492257i \(-0.984325\pi\)
0.542025 + 0.840363i \(0.317658\pi\)
\(720\) 12.2197 + 2.55040i 0.455402 + 0.0950478i
\(721\) −4.74773 2.74110i −0.176815 0.102084i
\(722\) −3.65480 + 6.33030i −0.136018 + 0.235589i
\(723\) 1.73205 0.0644157
\(724\) 7.83485 13.5704i 0.291180 0.504338i
\(725\) 2.56275 + 22.7691i 0.0951780 + 0.845623i
\(726\) −1.58258 + 0.913701i −0.0587349 + 0.0339106i
\(727\) 15.2523i 0.565675i −0.959168 0.282838i \(-0.908724\pi\)
0.959168 0.282838i \(-0.0912758\pi\)
\(728\) 2.59808 10.5000i 0.0962911 0.389156i
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 24.2477 + 41.9983i 0.896835 + 1.55336i
\(732\) 2.19885 + 1.26951i 0.0812719 + 0.0469223i
\(733\) −22.8027 −0.842237 −0.421119 0.907006i \(-0.638362\pi\)
−0.421119 + 0.907006i \(0.638362\pi\)
\(734\) 0.691478 + 0.399225i 0.0255229 + 0.0147357i
\(735\) −6.66888 5.96038i −0.245985 0.219852i
\(736\) 21.7182i 0.800544i
\(737\) −2.31203 1.33485i −0.0851646 0.0491698i
\(738\) 2.09355 1.20871i 0.0770647 0.0444933i
\(739\) −14.7523 + 8.51723i −0.542671 + 0.313311i −0.746161 0.665766i \(-0.768105\pi\)
0.203490 + 0.979077i \(0.434772\pi\)
\(740\) −31.1216 6.49545i −1.14405 0.238778i
\(741\) −6.00000 + 1.73205i −0.220416 + 0.0636285i
\(742\) 6.00000i 0.220267i
\(743\) −2.86423 4.96099i −0.105078 0.182001i 0.808692 0.588232i \(-0.200176\pi\)
−0.913770 + 0.406232i \(0.866843\pi\)
\(744\) −5.37386 9.30780i −0.197015 0.341241i
\(745\) −27.8306 24.8739i −1.01964 0.911310i
\(746\) 5.93905i 0.217444i
\(747\) −6.01450 + 10.4174i −0.220059 + 0.381154i
\(748\) −10.8591 + 18.8085i −0.397048 + 0.687708i
\(749\) 18.3296i 0.669748i
\(750\) 2.12891 + 4.64293i 0.0777367 + 0.169536i
\(751\) −5.87386 10.1738i −0.214340 0.371248i 0.738728 0.674004i \(-0.235427\pi\)
−0.953068 + 0.302755i \(0.902093\pi\)
\(752\) 2.55040 + 4.41742i 0.0930036 + 0.161087i
\(753\) 0.165151i 0.00601845i
\(754\) −1.81307 + 7.32743i −0.0660281 + 0.266849i
\(755\) −4.41742 + 21.1652i −0.160767 + 0.770279i
\(756\) −13.4347 + 7.75650i −0.488614 + 0.282101i
\(757\) 8.44178 4.87386i 0.306822 0.177144i −0.338682 0.940901i \(-0.609981\pi\)
0.645503 + 0.763757i \(0.276648\pi\)
\(758\) 4.22483 + 2.43920i 0.153453 + 0.0885959i
\(759\) 12.1244i 0.440086i
\(760\) 5.00166 + 4.47028i 0.181429 + 0.162154i
\(761\) −30.7087 17.7297i −1.11319 0.642701i −0.173536 0.984827i \(-0.555519\pi\)
−0.939654 + 0.342127i \(0.888853\pi\)
\(762\) 8.10805 0.293724
\(763\) 19.7001 + 11.3739i 0.713192 + 0.411762i
\(764\) −14.8521 25.7246i −0.537330 0.930682i
\(765\) −19.4674 + 6.40467i −0.703846 + 0.231561i
\(766\) 10.7913 0.389905
\(767\) 48.8311 + 12.0826i 1.76319 + 0.436277i
\(768\) 1.79129i 0.0646375i
\(769\) −13.5000 + 7.79423i −0.486822 + 0.281067i −0.723255 0.690581i \(-0.757355\pi\)
0.236433 + 0.971648i \(0.424022\pi\)
\(770\) 4.44685 1.46299i 0.160253 0.0527224i
\(771\) 9.08258 15.7315i 0.327101 0.566556i
\(772\) −26.6283 −0.958374
\(773\) 12.0767 20.9174i 0.434368 0.752347i −0.562876 0.826541i \(-0.690305\pi\)
0.997244 + 0.0741940i \(0.0236384\pi\)
\(774\) 8.37386 + 4.83465i 0.300992 + 0.173778i
\(775\) 12.4104 28.4358i 0.445795 1.02144i
\(776\) −9.87386 + 17.1020i −0.354451 + 0.613927i
\(777\) 11.9059 6.87386i 0.427121 0.246598i
\(778\) −0.723000 1.25227i −0.0259208 0.0448962i
\(779\) −4.58258 −0.164188
\(780\) −1.08610 14.4009i −0.0388887 0.515636i
\(781\) −18.5826 −0.664937
\(782\) 4.79693 + 8.30852i 0.171538 + 0.297112i
\(783\) 19.8431 11.4564i 0.709136 0.409420i
\(784\) 5.58258 9.66930i 0.199378 0.345332i
\(785\) −4.18710 + 20.0616i −0.149444 + 0.716030i
\(786\) −3.00000 1.73205i −0.107006 0.0617802i
\(787\) −8.15573 + 14.1261i −0.290720 + 0.503542i −0.973980 0.226633i \(-0.927228\pi\)
0.683260 + 0.730175i \(0.260562\pi\)
\(788\) 26.2867 0.936425
\(789\) 4.50000 7.79423i 0.160204 0.277482i
\(790\) −1.91550 5.82229i −0.0681504 0.207148i
\(791\) −11.1261 + 6.42368i −0.395600 + 0.228400i
\(792\) 9.16515i 0.325669i
\(793\) −1.22753 + 4.96099i −0.0435907 + 0.176170i
\(794\) −9.29583 −0.329897
\(795\) 5.29875 + 16.1059i 0.187927 + 0.571218i
\(796\) −9.47822 16.4168i −0.335947 0.581877i
\(797\) −38.1727 22.0390i −1.35215 0.780662i −0.363596 0.931557i \(-0.618451\pi\)
−0.988550 + 0.150895i \(0.951785\pi\)
\(798\) −1.37055 −0.0485170
\(799\) −7.25227 4.18710i −0.256567 0.148129i
\(800\) −19.0678 + 14.0692i −0.674149 + 0.497422i
\(801\) 19.1479i 0.676558i
\(802\) 11.8006 + 6.81307i 0.416693 + 0.240578i
\(803\) 0 0
\(804\) −1.56534 + 0.903750i −0.0552053 + 0.0318728i
\(805\) −3.62614 + 17.3739i −0.127805 + 0.612348i
\(806\) 7.08712 7.36515i 0.249633 0.259426i
\(807\) 15.0000i 0.528025i
\(808\) 7.79423 + 13.5000i 0.274200 + 0.474928i
\(809\) −27.4129 47.4805i −0.963785 1.66933i −0.712843 0.701323i \(-0.752593\pi\)
−0.250942 0.968002i \(-0.580740\pi\)
\(810\) −0.680750 + 0.761669i −0.0239191 + 0.0267623i
\(811\) 50.5155i 1.77384i 0.461923 + 0.886920i \(0.347160\pi\)
−0.461923 + 0.886920i \(0.652840\pi\)
\(812\) 7.10895 12.3131i 0.249475 0.432104i
\(813\) −4.33013 + 7.50000i −0.151864 + 0.263036i
\(814\) 9.59386i 0.336264i
\(815\) −31.3973 + 35.1294i −1.09980 + 1.23053i
\(816\) 6.39564 + 11.0776i 0.223892 + 0.387793i
\(817\) −9.16478 15.8739i −0.320635 0.555356i
\(818\) 3.95644i 0.138334i
\(819\) −9.00000 8.66025i −0.314485 0.302614i
\(820\) 2.16515 10.3739i 0.0756104 0.362271i
\(821\) 15.7087 9.06943i 0.548238 0.316525i −0.200173 0.979761i \(-0.564150\pi\)
0.748411 + 0.663235i \(0.230817\pi\)
\(822\) −4.14938 + 2.39564i −0.144726 + 0.0835577i
\(823\) −27.2083 15.7087i −0.948421 0.547571i −0.0558311 0.998440i \(-0.517781\pi\)
−0.892590 + 0.450869i \(0.851114\pi\)
\(824\) 5.48220i 0.190982i
\(825\) 10.6448 7.85425i 0.370603 0.273450i
\(826\) 9.56080 + 5.51993i 0.332663 + 0.192063i
\(827\) −10.7737 −0.374638 −0.187319 0.982299i \(-0.559980\pi\)
−0.187319 + 0.982299i \(0.559980\pi\)
\(828\) −14.2179 8.20871i −0.494106 0.285272i
\(829\) −16.6652 28.8649i −0.578805 1.00252i −0.995617 0.0935264i \(-0.970186\pi\)
0.416812 0.908993i \(-0.363147\pi\)
\(830\) −1.92013 5.83636i −0.0666487 0.202583i
\(831\) −7.41742 −0.257308
\(832\) 11.8383 3.41742i 0.410419 0.118478i
\(833\) 18.3303i 0.635107i
\(834\) −8.60436 + 4.96773i −0.297944 + 0.172018i
\(835\) 6.69034 + 20.3357i 0.231529 + 0.703747i
\(836\) 4.10436 7.10895i 0.141952 0.245868i
\(837\) −31.0260 −1.07242
\(838\) −1.33283 + 2.30852i −0.0460417 + 0.0797466i
\(839\) 37.8303 + 21.8413i 1.30605 + 0.754047i 0.981434 0.191800i \(-0.0614326\pi\)
0.324613 + 0.945847i \(0.394766\pi\)
\(840\) 1.37055 6.56670i 0.0472885 0.226573i
\(841\) 4.00000 6.92820i 0.137931 0.238904i
\(842\) −2.16900 + 1.25227i −0.0747487 + 0.0431562i
\(843\) 1.82740 + 3.16515i 0.0629390 + 0.109014i
\(844\) 0.295834 0.0101830
\(845\) 27.2431 10.1398i 0.937190 0.348820i
\(846\) −1.66970 −0.0574054
\(847\) 3.46410 + 6.00000i 0.119028 + 0.206162i
\(848\) −18.3296 + 10.5826i −0.629440 + 0.363407i
\(849\) −13.8739 + 24.0302i −0.476150 + 0.824716i
\(850\) 4.18710 9.59386i 0.143616 0.329067i
\(851\) 31.5000 + 18.1865i 1.07981 + 0.623426i
\(852\) −6.29060 + 10.8956i −0.215513 + 0.373279i
\(853\) 5.63310 0.192874 0.0964369 0.995339i \(-0.469255\pi\)
0.0964369 + 0.995339i \(0.469255\pi\)
\(854\) −0.560795 + 0.971326i −0.0191900 + 0.0332381i
\(855\) 7.35799 2.42074i 0.251638 0.0827875i
\(856\) 15.8739 9.16478i 0.542557 0.313246i
\(857\) 4.74773i 0.162179i −0.996707 0.0810896i \(-0.974160\pi\)
0.996707 0.0810896i \(-0.0258400\pi\)
\(858\) 4.18710 1.20871i 0.142945 0.0412648i
\(859\) 44.2432 1.50956 0.754779 0.655979i \(-0.227744\pi\)
0.754779 + 0.655979i \(0.227744\pi\)
\(860\) 40.2648 13.2469i 1.37302 0.451715i
\(861\) 2.29129 + 3.96863i 0.0780869 + 0.135250i
\(862\) −3.35093 1.93466i −0.114133 0.0658947i
\(863\) −13.6657 −0.465186 −0.232593 0.972574i \(-0.574721\pi\)
−0.232593 + 0.972574i \(0.574721\pi\)
\(864\) 20.5218 + 11.8483i 0.698165 + 0.403086i
\(865\) −27.6468 24.7096i −0.940019 0.840152i
\(866\) 4.45325i 0.151328i
\(867\) −3.46410 2.00000i −0.117647 0.0679236i
\(868\) −16.6730 + 9.62614i −0.565917 + 0.326732i
\(869\) −13.7477 + 7.93725i −0.466360 + 0.269253i
\(870\) −0.956439 + 4.58258i −0.0324263 + 0.155364i
\(871\) −2.62159 2.52263i −0.0888292 0.0854759i
\(872\) 22.7477i 0.770335i
\(873\) 11.4014 + 19.7477i 0.385877 + 0.668359i
\(874\) −1.81307 3.14033i −0.0613279 0.106223i
\(875\) 17.6027 8.07130i 0.595079 0.272860i
\(876\) 0 0
\(877\) 3.96863 6.87386i 0.134011 0.232114i −0.791208 0.611547i \(-0.790548\pi\)
0.925219 + 0.379433i \(0.123881\pi\)
\(878\) −3.31113 + 5.73504i −0.111745 + 0.193548i
\(879\) 18.1389i 0.611809i
\(880\) 12.3125 + 11.0044i 0.415054 + 0.370959i
\(881\) −18.2477 31.6060i −0.614782 1.06483i −0.990423 0.138068i \(-0.955911\pi\)
0.375641 0.926765i \(-0.377422\pi\)
\(882\) 1.82740 + 3.16515i 0.0615318 + 0.106576i
\(883\) 36.2432i 1.21968i −0.792524 0.609840i \(-0.791234\pi\)
0.792524 0.609840i \(-0.208766\pi\)
\(884\) −20.5218 + 21.3269i −0.690222 + 0.717300i
\(885\) 30.5390 + 6.37386i 1.02656 + 0.214255i
\(886\) −7.87841 + 4.54860i −0.264680 + 0.152813i
\(887\) 47.1944 27.2477i 1.58463 0.914889i 0.590465 0.807064i \(-0.298945\pi\)
0.994170 0.107826i \(-0.0343888\pi\)
\(888\) −11.9059 6.87386i −0.399535 0.230672i
\(889\) 30.7400i 1.03099i
\(890\) −7.29219 6.51747i −0.244435 0.218466i
\(891\) 2.29129 + 1.32288i 0.0767610 + 0.0443180i
\(892\) 15.5130 0.519414
\(893\) 2.74110 + 1.58258i 0.0917275 + 0.0529589i
\(894\) −3.81307 6.60443i −0.127528 0.220885i
\(895\) 12.6939 + 38.5840i 0.424311 + 1.28972i
\(896\) 19.1216 0.638808
\(897\) −3.96863 + 16.0390i −0.132509 + 0.535527i
\(898\) 5.03447i 0.168002i
\(899\) 24.6261 14.2179i 0.821328 0.474194i
\(900\) 2.00351 + 17.8005i 0.0667836 + 0.593349i
\(901\) 17.3739 30.0924i 0.578807 1.00252i
\(902\) 3.19795 0.106480
\(903\) −9.16478 + 15.8739i −0.304985 + 0.528249i
\(904\) 11.1261 + 6.42368i 0.370050 + 0.213648i
\(905\) 19.1479 + 3.99640i 0.636498 + 0.132845i
\(906\) −2.20871 + 3.82560i −0.0733795 + 0.127097i
\(907\) −5.41463 + 3.12614i −0.179790 + 0.103802i −0.587194 0.809446i \(-0.699767\pi\)
0.407404 + 0.913248i \(0.366434\pi\)
\(908\) 0.732950 + 1.26951i 0.0243238 + 0.0421301i
\(909\) 18.0000 0.597022
\(910\) 6.36150 0.479778i 0.210882 0.0159045i
\(911\) −7.91288 −0.262165 −0.131083 0.991371i \(-0.541845\pi\)
−0.131083 + 0.991371i \(0.541845\pi\)
\(912\) −2.41733 4.18693i −0.0800457 0.138643i
\(913\) −13.7810 + 7.95644i −0.456083 + 0.263320i
\(914\) −0.395644 + 0.685275i −0.0130867 + 0.0226669i
\(915\) −0.647551 + 3.10260i −0.0214074 + 0.102569i
\(916\) −40.7477 23.5257i −1.34634 0.777311i
\(917\) −6.56670 + 11.3739i −0.216852 + 0.375598i
\(918\) −10.4678 −0.345487
\(919\) 27.0826 46.9084i 0.893372 1.54737i 0.0575648 0.998342i \(-0.481666\pi\)
0.835807 0.549023i \(-0.185000\pi\)
\(920\) 16.8593 5.54661i 0.555834 0.182866i
\(921\) 21.0000 12.1244i 0.691974 0.399511i
\(922\) 16.3739i 0.539244i
\(923\) −24.5824 6.08258i −0.809141 0.200210i
\(924\) −8.20871 −0.270047
\(925\) −4.43881 39.4373i −0.145947 1.29669i
\(926\) 9.00000 + 15.5885i 0.295758 + 0.512268i
\(927\) 5.48220 + 3.16515i 0.180059 + 0.103957i
\(928\) −21.7182 −0.712935
\(929\) 22.8303 + 13.1811i 0.749038 + 0.432457i 0.825346 0.564627i \(-0.190980\pi\)
−0.0763082 + 0.997084i \(0.524313\pi\)
\(930\) 4.22419 4.72631i 0.138517 0.154982i
\(931\) 6.92820i 0.227063i
\(932\) −4.39770 2.53901i −0.144052 0.0831682i
\(933\) −6.56670 + 3.79129i −0.214984 + 0.124121i
\(934\) −9.62614 + 5.55765i −0.314977 + 0.181852i
\(935\) −26.5390 5.53901i −0.867919 0.181145i
\(936\) −3.00000 + 12.1244i −0.0980581 + 0.396297i
\(937\) 31.4955i 1.02891i 0.857517 + 0.514456i \(0.172006\pi\)
−0.857517 + 0.514456i \(0.827994\pi\)
\(938\) −0.399225 0.691478i −0.0130352 0.0225775i
\(939\) −1.62614 2.81655i −0.0530670 0.0919147i
\(940\) −4.87768 + 5.45748i −0.159092 + 0.178003i
\(941\) 26.4575i 0.862490i 0.902235 + 0.431245i \(0.141926\pi\)
−0.902235 + 0.431245i \(0.858074\pi\)
\(942\) −2.09355 + 3.62614i −0.0682116 + 0.118146i
\(943\) −6.06218 + 10.5000i −0.197412 + 0.341927i
\(944\) 38.9434i 1.26750i
\(945\) −14.4385 12.9046i −0.469686 0.419787i
\(946\) 6.39564 + 11.0776i 0.207940 + 0.360163i
\(947\) −7.16658 12.4129i −0.232883 0.403364i 0.725773 0.687935i \(-0.241482\pi\)
−0.958655 + 0.284570i \(0.908149\pi\)
\(948\) 10.7477i 0.349070i
\(949\) 0 0
\(950\) −1.58258 + 3.62614i −0.0513455 + 0.117647i
\(951\) −0.165151 + 0.0953502i −0.00535540 + 0.00309194i
\(952\) −11.9059 + 6.87386i −0.385872 + 0.222783i
\(953\) −6.99578 4.03901i −0.226616 0.130837i 0.382394 0.923999i \(-0.375100\pi\)
−0.609010 + 0.793163i \(0.708433\pi\)
\(954\) 6.92820i 0.224309i
\(955\) 24.7096 27.6468i 0.799584 0.894629i
\(956\) −0.295834 0.170800i −0.00956794 0.00552406i
\(957\) 12.1244 0.391925
\(958\) −1.84522 1.06534i −0.0596165 0.0344196i
\(959\) 9.08258 + 15.7315i 0.293292 + 0.507996i
\(960\) 7.25885 2.38812i 0.234278 0.0770762i
\(961\) −7.50455 −0.242082
\(962\) 3.14033 12.6915i 0.101248 0.409190i
\(963\) 21.1652i 0.682037i
\(964\) −2.68693 + 1.55130i −0.0865402 + 0.0499640i
\(965\) −10.3881 31.5753i −0.334404 1.01644i
\(966\) −1.81307 + 3.14033i −0.0583345 + 0.101038i
\(967\) 37.3821 1.20213 0.601064 0.799201i \(-0.294744\pi\)
0.601064 + 0.799201i \(0.294744\pi\)
\(968\) 3.46410 6.00000i 0.111340 0.192847i
\(969\) 6.87386 + 3.96863i 0.220820 + 0.127491i
\(970\) −11.4014 2.37960i −0.366075 0.0764044i
\(971\) 9.24773 16.0175i 0.296774 0.514027i −0.678622 0.734487i \(-0.737423\pi\)
0.975396 + 0.220460i \(0.0707560\pi\)
\(972\) 24.8208 14.3303i 0.796128 0.459645i
\(973\) 18.8341 + 32.6216i 0.603793 + 1.04580i
\(974\) 4.87841 0.156314
\(975\) 16.6526 6.90588i 0.533310 0.221165i
\(976\) −3.95644 −0.126643
\(977\) 17.6542 + 30.5780i 0.564809 + 0.978278i 0.997067 + 0.0765281i \(0.0243835\pi\)
−0.432258 + 0.901750i \(0.642283\pi\)
\(978\) −8.33648 + 4.81307i −0.266571 + 0.153905i
\(979\) −12.6652 + 21.9367i −0.404780 + 0.701100i
\(980\) 15.6838 + 3.27340i 0.501001 + 0.104565i
\(981\) −22.7477 13.1334i −0.726279 0.419317i
\(982\) −4.43543 + 7.68239i −0.141540 + 0.245155i
\(983\) −55.0840 −1.75691 −0.878454 0.477827i \(-0.841424\pi\)
−0.878454 + 0.477827i \(0.841424\pi\)
\(984\) 2.29129 3.96863i 0.0730436 0.126515i
\(985\) 10.2548 + 31.1702i 0.326746 + 0.993165i
\(986\) 8.30852 4.79693i 0.264597 0.152765i
\(987\) 3.16515i 0.100748i
\(988\) 7.75650 8.06080i 0.246767 0.256448i
\(989\) −48.4955 −1.54207
\(990\) −5.13478 + 1.68931i −0.163194 + 0.0536899i
\(991\) 6.50000 + 11.2583i 0.206479 + 0.357633i 0.950603 0.310409i \(-0.100466\pi\)
−0.744124 + 0.668042i \(0.767133\pi\)
\(992\) 25.4684 + 14.7042i 0.808621 + 0.466858i
\(993\) 4.47315 0.141951
\(994\) −4.81307 2.77883i −0.152661 0.0881390i
\(995\) 15.7690 17.6435i 0.499912 0.559336i
\(996\) 10.7737i 0.341378i
\(997\) −0.143025 0.0825757i −0.00452966 0.00261520i 0.497733 0.867330i \(-0.334166\pi\)
−0.502263 + 0.864715i \(0.667499\pi\)
\(998\) −0.286051 + 0.165151i −0.00905477 + 0.00522778i
\(999\) −34.3693 + 19.8431i −1.08740 + 0.627809i
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 65.2.l.a.49.2 yes 8
3.2 odd 2 585.2.bf.a.244.3 8
4.3 odd 2 1040.2.df.b.49.4 8
5.2 odd 4 325.2.n.b.101.2 4
5.3 odd 4 325.2.n.c.101.1 4
5.4 even 2 inner 65.2.l.a.49.3 yes 8
13.2 odd 12 845.2.b.f.339.3 8
13.3 even 3 845.2.d.c.844.5 8
13.4 even 6 inner 65.2.l.a.4.3 yes 8
13.5 odd 4 845.2.n.d.484.1 8
13.6 odd 12 845.2.n.c.529.4 8
13.7 odd 12 845.2.n.d.529.2 8
13.8 odd 4 845.2.n.c.484.3 8
13.9 even 3 845.2.l.c.654.2 8
13.10 even 6 845.2.d.c.844.3 8
13.11 odd 12 845.2.b.f.339.5 8
13.12 even 2 845.2.l.c.699.3 8
15.14 odd 2 585.2.bf.a.244.2 8
20.19 odd 2 1040.2.df.b.49.1 8
39.17 odd 6 585.2.bf.a.199.2 8
52.43 odd 6 1040.2.df.b.849.1 8
65.2 even 12 4225.2.a.bj.1.3 4
65.4 even 6 inner 65.2.l.a.4.2 8
65.9 even 6 845.2.l.c.654.3 8
65.17 odd 12 325.2.n.b.251.2 4
65.19 odd 12 845.2.n.d.529.1 8
65.24 odd 12 845.2.b.f.339.4 8
65.28 even 12 4225.2.a.bk.1.2 4
65.29 even 6 845.2.d.c.844.4 8
65.34 odd 4 845.2.n.d.484.2 8
65.37 even 12 4225.2.a.bj.1.2 4
65.43 odd 12 325.2.n.c.251.1 4
65.44 odd 4 845.2.n.c.484.4 8
65.49 even 6 845.2.d.c.844.6 8
65.54 odd 12 845.2.b.f.339.6 8
65.59 odd 12 845.2.n.c.529.3 8
65.63 even 12 4225.2.a.bk.1.3 4
65.64 even 2 845.2.l.c.699.2 8
195.134 odd 6 585.2.bf.a.199.3 8
260.199 odd 6 1040.2.df.b.849.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.l.a.4.2 8 65.4 even 6 inner
65.2.l.a.4.3 yes 8 13.4 even 6 inner
65.2.l.a.49.2 yes 8 1.1 even 1 trivial
65.2.l.a.49.3 yes 8 5.4 even 2 inner
325.2.n.b.101.2 4 5.2 odd 4
325.2.n.b.251.2 4 65.17 odd 12
325.2.n.c.101.1 4 5.3 odd 4
325.2.n.c.251.1 4 65.43 odd 12
585.2.bf.a.199.2 8 39.17 odd 6
585.2.bf.a.199.3 8 195.134 odd 6
585.2.bf.a.244.2 8 15.14 odd 2
585.2.bf.a.244.3 8 3.2 odd 2
845.2.b.f.339.3 8 13.2 odd 12
845.2.b.f.339.4 8 65.24 odd 12
845.2.b.f.339.5 8 13.11 odd 12
845.2.b.f.339.6 8 65.54 odd 12
845.2.d.c.844.3 8 13.10 even 6
845.2.d.c.844.4 8 65.29 even 6
845.2.d.c.844.5 8 13.3 even 3
845.2.d.c.844.6 8 65.49 even 6
845.2.l.c.654.2 8 13.9 even 3
845.2.l.c.654.3 8 65.9 even 6
845.2.l.c.699.2 8 65.64 even 2
845.2.l.c.699.3 8 13.12 even 2
845.2.n.c.484.3 8 13.8 odd 4
845.2.n.c.484.4 8 65.44 odd 4
845.2.n.c.529.3 8 65.59 odd 12
845.2.n.c.529.4 8 13.6 odd 12
845.2.n.d.484.1 8 13.5 odd 4
845.2.n.d.484.2 8 65.34 odd 4
845.2.n.d.529.1 8 65.19 odd 12
845.2.n.d.529.2 8 13.7 odd 12
1040.2.df.b.49.1 8 20.19 odd 2
1040.2.df.b.49.4 8 4.3 odd 2
1040.2.df.b.849.1 8 52.43 odd 6
1040.2.df.b.849.4 8 260.199 odd 6
4225.2.a.bj.1.2 4 65.37 even 12
4225.2.a.bj.1.3 4 65.2 even 12
4225.2.a.bk.1.2 4 65.28 even 12
4225.2.a.bk.1.3 4 65.63 even 12