Properties

Label 462.2.k.g.353.3
Level $462$
Weight $2$
Character 462.353
Analytic conductor $3.689$
Analytic rank $0$
Dimension $20$
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] = [462,2,Mod(89,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.k (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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 6 x^{19} + 19 x^{18} - 42 x^{17} + 62 x^{16} - 42 x^{15} - 25 x^{14} + 6 x^{13} + 445 x^{12} - 1764 x^{11} + 3864 x^{10} - 5292 x^{9} + 4005 x^{8} + 162 x^{7} - 2025 x^{6} + \cdots + 59049 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 353.3
Root \(1.69321 + 0.364755i\) of defining polynomial
Character \(\chi\) \(=\) 462.353
Dual form 462.2.k.g.89.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.530717 - 1.64874i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.417958 - 0.723925i) q^{5} +(1.28398 + 1.16249i) q^{6} +(-1.42670 - 2.22812i) q^{7} +1.00000i q^{8} +(-2.43668 + 1.75003i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.530717 - 1.64874i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.417958 - 0.723925i) q^{5} +(1.28398 + 1.16249i) q^{6} +(-1.42670 - 2.22812i) q^{7} +1.00000i q^{8} +(-2.43668 + 1.75003i) q^{9} +(0.723925 + 0.417958i) q^{10} +(0.866025 + 0.500000i) q^{11} +(-1.69321 - 0.364755i) q^{12} -3.86332i q^{13} +(2.34962 + 1.21626i) q^{14} +(-0.971746 + 1.07330i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.06563 + 1.84573i) q^{17} +(1.23521 - 2.73391i) q^{18} +(-2.35922 + 1.36210i) q^{19} -0.835917 q^{20} +(-2.91642 + 3.53475i) q^{21} -1.00000 q^{22} +(-6.08555 + 3.51349i) q^{23} +(1.64874 - 0.530717i) q^{24} +(2.15062 - 3.72499i) q^{25} +(1.93166 + 3.34573i) q^{26} +(4.17853 + 3.08868i) q^{27} +(-2.64296 + 0.121493i) q^{28} +7.25640i q^{29} +(0.304905 - 1.41538i) q^{30} +(-4.85360 - 2.80223i) q^{31} +(0.866025 + 0.500000i) q^{32} +(0.364755 - 1.69321i) q^{33} -2.13127i q^{34} +(-1.01670 + 1.96408i) q^{35} +(0.297229 + 2.98524i) q^{36} +(1.76131 + 3.05069i) q^{37} +(1.36210 - 2.35922i) q^{38} +(-6.36960 + 2.05033i) q^{39} +(0.723925 - 0.417958i) q^{40} +0.835917 q^{41} +(0.758320 - 4.51940i) q^{42} -9.85086 q^{43} +(0.866025 - 0.500000i) q^{44} +(2.28532 + 1.03253i) q^{45} +(3.51349 - 6.08555i) q^{46} +(-5.84290 - 10.1202i) q^{47} +(-1.16249 + 1.28398i) q^{48} +(-2.92908 + 6.35771i) q^{49} +4.30124i q^{50} +(3.60868 + 0.777390i) q^{51} +(-3.34573 - 1.93166i) q^{52} +(-7.26395 - 4.19384i) q^{53} +(-5.16305 - 0.585609i) q^{54} -0.835917i q^{55} +(2.22812 - 1.42670i) q^{56} +(3.49783 + 3.16686i) q^{57} +(-3.62820 - 6.28423i) q^{58} +(3.60897 - 6.25091i) q^{59} +(0.443635 + 1.37821i) q^{60} +(-2.31656 + 1.33746i) q^{61} +5.60445 q^{62} +(7.37568 + 2.93247i) q^{63} -1.00000 q^{64} +(-2.79675 + 1.61471i) q^{65} +(0.530717 + 1.64874i) q^{66} +(6.35213 - 11.0022i) q^{67} +(1.06563 + 1.84573i) q^{68} +(9.02254 + 8.16881i) q^{69} +(-0.101558 - 2.20930i) q^{70} -2.66448i q^{71} +(-1.75003 - 2.43668i) q^{72} +(10.7588 + 6.21158i) q^{73} +(-3.05069 - 1.76131i) q^{74} +(-7.28290 - 1.56890i) q^{75} +2.72420i q^{76} +(-0.121493 - 2.64296i) q^{77} +(4.49107 - 4.96044i) q^{78} +(2.81072 + 4.86831i) q^{79} +(-0.417958 + 0.723925i) q^{80} +(2.87481 - 8.52851i) q^{81} +(-0.723925 + 0.417958i) q^{82} -3.41567 q^{83} +(1.60297 + 4.29307i) q^{84} +1.78156 q^{85} +(8.53109 - 4.92543i) q^{86} +(11.9639 - 3.85110i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(0.355752 + 0.616180i) q^{89} +(-2.49541 + 0.248459i) q^{90} +(-8.60795 + 5.51178i) q^{91} +7.02699i q^{92} +(-2.04425 + 9.48951i) q^{93} +(10.1202 + 5.84290i) q^{94} +(1.97212 + 1.13860i) q^{95} +(0.364755 - 1.69321i) q^{96} -9.84612i q^{97} +(-0.642202 - 6.97048i) q^{98} +(-2.98524 + 0.297229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.530717 1.64874i −0.306410 0.951900i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.417958 0.723925i −0.186917 0.323749i 0.757304 0.653063i \(-0.226516\pi\)
−0.944221 + 0.329313i \(0.893183\pi\)
\(6\) 1.28398 + 1.16249i 0.524184 + 0.474585i
\(7\) −1.42670 2.22812i −0.539240 0.842152i
\(8\) 1.00000i 0.353553i
\(9\) −2.43668 + 1.75003i −0.812226 + 0.583343i
\(10\) 0.723925 + 0.417958i 0.228925 + 0.132170i
\(11\) 0.866025 + 0.500000i 0.261116 + 0.150756i
\(12\) −1.69321 0.364755i −0.488787 0.105296i
\(13\) 3.86332i 1.07149i −0.844379 0.535746i \(-0.820031\pi\)
0.844379 0.535746i \(-0.179969\pi\)
\(14\) 2.34962 + 1.21626i 0.627962 + 0.325060i
\(15\) −0.971746 + 1.07330i −0.250904 + 0.277126i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.06563 + 1.84573i −0.258454 + 0.447656i −0.965828 0.259184i \(-0.916546\pi\)
0.707374 + 0.706840i \(0.249880\pi\)
\(18\) 1.23521 2.73391i 0.291142 0.644388i
\(19\) −2.35922 + 1.36210i −0.541243 + 0.312487i −0.745583 0.666413i \(-0.767829\pi\)
0.204339 + 0.978900i \(0.434495\pi\)
\(20\) −0.835917 −0.186917
\(21\) −2.91642 + 3.53475i −0.636416 + 0.771346i
\(22\) −1.00000 −0.213201
\(23\) −6.08555 + 3.51349i −1.26892 + 0.732614i −0.974785 0.223148i \(-0.928367\pi\)
−0.294140 + 0.955762i \(0.595033\pi\)
\(24\) 1.64874 0.530717i 0.336547 0.108332i
\(25\) 2.15062 3.72499i 0.430124 0.744997i
\(26\) 1.93166 + 3.34573i 0.378829 + 0.656152i
\(27\) 4.17853 + 3.08868i 0.804158 + 0.594416i
\(28\) −2.64296 + 0.121493i −0.499473 + 0.0229600i
\(29\) 7.25640i 1.34748i 0.738969 + 0.673740i \(0.235313\pi\)
−0.738969 + 0.673740i \(0.764687\pi\)
\(30\) 0.304905 1.41538i 0.0556677 0.258412i
\(31\) −4.85360 2.80223i −0.871732 0.503295i −0.00380865 0.999993i \(-0.501212\pi\)
−0.867923 + 0.496698i \(0.834546\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0.364755 1.69321i 0.0634957 0.294750i
\(34\) 2.13127i 0.365509i
\(35\) −1.01670 + 1.96408i −0.171853 + 0.331991i
\(36\) 0.297229 + 2.98524i 0.0495382 + 0.497540i
\(37\) 1.76131 + 3.05069i 0.289558 + 0.501530i 0.973704 0.227815i \(-0.0731583\pi\)
−0.684146 + 0.729345i \(0.739825\pi\)
\(38\) 1.36210 2.35922i 0.220962 0.382717i
\(39\) −6.36960 + 2.05033i −1.01995 + 0.328315i
\(40\) 0.723925 0.417958i 0.114463 0.0660850i
\(41\) 0.835917 0.130548 0.0652741 0.997867i \(-0.479208\pi\)
0.0652741 + 0.997867i \(0.479208\pi\)
\(42\) 0.758320 4.51940i 0.117011 0.697358i
\(43\) −9.85086 −1.50224 −0.751121 0.660165i \(-0.770486\pi\)
−0.751121 + 0.660165i \(0.770486\pi\)
\(44\) 0.866025 0.500000i 0.130558 0.0753778i
\(45\) 2.28532 + 1.03253i 0.340675 + 0.153921i
\(46\) 3.51349 6.08555i 0.518036 0.897265i
\(47\) −5.84290 10.1202i −0.852274 1.47618i −0.879151 0.476543i \(-0.841890\pi\)
0.0268770 0.999639i \(-0.491444\pi\)
\(48\) −1.16249 + 1.28398i −0.167791 + 0.185327i
\(49\) −2.92908 + 6.35771i −0.418440 + 0.908245i
\(50\) 4.30124i 0.608288i
\(51\) 3.60868 + 0.777390i 0.505316 + 0.108856i
\(52\) −3.34573 1.93166i −0.463969 0.267873i
\(53\) −7.26395 4.19384i −0.997780 0.576069i −0.0901894 0.995925i \(-0.528747\pi\)
−0.907591 + 0.419856i \(0.862081\pi\)
\(54\) −5.16305 0.585609i −0.702602 0.0796914i
\(55\) 0.835917i 0.112715i
\(56\) 2.22812 1.42670i 0.297746 0.190650i
\(57\) 3.49783 + 3.16686i 0.463298 + 0.419460i
\(58\) −3.62820 6.28423i −0.476406 0.825159i
\(59\) 3.60897 6.25091i 0.469847 0.813799i −0.529558 0.848274i \(-0.677642\pi\)
0.999406 + 0.0344741i \(0.0109756\pi\)
\(60\) 0.443635 + 1.37821i 0.0572731 + 0.177926i
\(61\) −2.31656 + 1.33746i −0.296605 + 0.171245i −0.640917 0.767611i \(-0.721446\pi\)
0.344312 + 0.938855i \(0.388112\pi\)
\(62\) 5.60445 0.711766
\(63\) 7.37568 + 2.93247i 0.929248 + 0.369456i
\(64\) −1.00000 −0.125000
\(65\) −2.79675 + 1.61471i −0.346895 + 0.200280i
\(66\) 0.530717 + 1.64874i 0.0653268 + 0.202946i
\(67\) 6.35213 11.0022i 0.776036 1.34413i −0.158175 0.987411i \(-0.550561\pi\)
0.934211 0.356722i \(-0.116106\pi\)
\(68\) 1.06563 + 1.84573i 0.129227 + 0.223828i
\(69\) 9.02254 + 8.16881i 1.08619 + 0.983409i
\(70\) −0.101558 2.20930i −0.0121385 0.264061i
\(71\) 2.66448i 0.316215i −0.987422 0.158108i \(-0.949461\pi\)
0.987422 0.158108i \(-0.0505393\pi\)
\(72\) −1.75003 2.43668i −0.206243 0.287165i
\(73\) 10.7588 + 6.21158i 1.25922 + 0.727011i 0.972923 0.231130i \(-0.0742422\pi\)
0.286297 + 0.958141i \(0.407576\pi\)
\(74\) −3.05069 1.76131i −0.354635 0.204749i
\(75\) −7.28290 1.56890i −0.840957 0.181161i
\(76\) 2.72420i 0.312487i
\(77\) −0.121493 2.64296i −0.0138454 0.301193i
\(78\) 4.49107 4.96044i 0.508514 0.561659i
\(79\) 2.81072 + 4.86831i 0.316231 + 0.547728i 0.979698 0.200477i \(-0.0642492\pi\)
−0.663467 + 0.748205i \(0.730916\pi\)
\(80\) −0.417958 + 0.723925i −0.0467292 + 0.0809373i
\(81\) 2.87481 8.52851i 0.319423 0.947612i
\(82\) −0.723925 + 0.417958i −0.0799442 + 0.0461558i
\(83\) −3.41567 −0.374918 −0.187459 0.982272i \(-0.560025\pi\)
−0.187459 + 0.982272i \(0.560025\pi\)
\(84\) 1.60297 + 4.29307i 0.174899 + 0.468413i
\(85\) 1.78156 0.193238
\(86\) 8.53109 4.92543i 0.919931 0.531123i
\(87\) 11.9639 3.85110i 1.28267 0.412881i
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 0.355752 + 0.616180i 0.0377096 + 0.0653150i 0.884264 0.466987i \(-0.154660\pi\)
−0.846555 + 0.532302i \(0.821327\pi\)
\(90\) −2.49541 + 0.248459i −0.263040 + 0.0261899i
\(91\) −8.60795 + 5.51178i −0.902359 + 0.577792i
\(92\) 7.02699i 0.732614i
\(93\) −2.04425 + 9.48951i −0.211979 + 0.984016i
\(94\) 10.1202 + 5.84290i 1.04382 + 0.602649i
\(95\) 1.97212 + 1.13860i 0.202335 + 0.116818i
\(96\) 0.364755 1.69321i 0.0372276 0.172812i
\(97\) 9.84612i 0.999722i −0.866106 0.499861i \(-0.833384\pi\)
0.866106 0.499861i \(-0.166616\pi\)
\(98\) −0.642202 6.97048i −0.0648722 0.704125i
\(99\) −2.98524 + 0.297229i −0.300028 + 0.0298727i
\(100\) −2.15062 3.72499i −0.215062 0.372499i
\(101\) 3.31704 5.74529i 0.330058 0.571677i −0.652465 0.757819i \(-0.726265\pi\)
0.982523 + 0.186142i \(0.0595983\pi\)
\(102\) −3.51390 + 1.13110i −0.347928 + 0.111996i
\(103\) 13.2128 7.62843i 1.30190 0.751651i 0.321169 0.947022i \(-0.395924\pi\)
0.980729 + 0.195371i \(0.0625910\pi\)
\(104\) 3.86332 0.378829
\(105\) 3.77784 + 0.633892i 0.368680 + 0.0618616i
\(106\) 8.38769 0.814684
\(107\) 3.22599 1.86253i 0.311868 0.180057i −0.335894 0.941900i \(-0.609038\pi\)
0.647762 + 0.761843i \(0.275705\pi\)
\(108\) 4.76414 2.07437i 0.458429 0.199606i
\(109\) −9.01132 + 15.6081i −0.863128 + 1.49498i 0.00576622 + 0.999983i \(0.498165\pi\)
−0.868894 + 0.494998i \(0.835169\pi\)
\(110\) 0.417958 + 0.723925i 0.0398508 + 0.0690236i
\(111\) 4.09502 4.52300i 0.388682 0.429304i
\(112\) −1.21626 + 2.34962i −0.114926 + 0.222018i
\(113\) 13.9774i 1.31488i −0.753506 0.657441i \(-0.771639\pi\)
0.753506 0.657441i \(-0.228361\pi\)
\(114\) −4.61263 0.993664i −0.432013 0.0930652i
\(115\) 5.08701 + 2.93699i 0.474366 + 0.273876i
\(116\) 6.28423 + 3.62820i 0.583476 + 0.336870i
\(117\) 6.76091 + 9.41366i 0.625047 + 0.870293i
\(118\) 7.21793i 0.664464i
\(119\) 5.63285 0.258934i 0.516363 0.0237364i
\(120\) −1.07330 0.971746i −0.0979788 0.0887079i
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 1.33746 2.31656i 0.121088 0.209731i
\(123\) −0.443635 1.37821i −0.0400013 0.124269i
\(124\) −4.85360 + 2.80223i −0.435866 + 0.251647i
\(125\) −7.77507 −0.695423
\(126\) −7.85376 + 1.14825i −0.699668 + 0.102294i
\(127\) −10.4325 −0.925737 −0.462869 0.886427i \(-0.653180\pi\)
−0.462869 + 0.886427i \(0.653180\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 5.22802 + 16.2415i 0.460301 + 1.42998i
\(130\) 1.61471 2.79675i 0.141619 0.245292i
\(131\) 5.20268 + 9.01131i 0.454561 + 0.787322i 0.998663 0.0516968i \(-0.0164629\pi\)
−0.544102 + 0.839019i \(0.683130\pi\)
\(132\) −1.28398 1.16249i −0.111756 0.101182i
\(133\) 6.40082 + 3.31334i 0.555022 + 0.287303i
\(134\) 12.7043i 1.09748i
\(135\) 0.489521 4.31588i 0.0421313 0.371452i
\(136\) −1.84573 1.06563i −0.158270 0.0913773i
\(137\) 5.61907 + 3.24417i 0.480070 + 0.277168i 0.720446 0.693511i \(-0.243937\pi\)
−0.240376 + 0.970680i \(0.577271\pi\)
\(138\) −11.8982 2.56313i −1.01284 0.218188i
\(139\) 15.0423i 1.27587i −0.770091 0.637934i \(-0.779789\pi\)
0.770091 0.637934i \(-0.220211\pi\)
\(140\) 1.19260 + 1.86253i 0.100793 + 0.157412i
\(141\) −13.5846 + 15.0044i −1.14403 + 1.26360i
\(142\) 1.33224 + 2.30750i 0.111799 + 0.193641i
\(143\) 1.93166 3.34573i 0.161533 0.279784i
\(144\) 2.73391 + 1.23521i 0.227826 + 0.102934i
\(145\) 5.25309 3.03287i 0.436246 0.251866i
\(146\) −12.4232 −1.02815
\(147\) 12.0367 + 1.45513i 0.992772 + 0.120017i
\(148\) 3.52263 0.289558
\(149\) −4.20728 + 2.42908i −0.344674 + 0.198998i −0.662337 0.749206i \(-0.730435\pi\)
0.317663 + 0.948204i \(0.397102\pi\)
\(150\) 7.09163 2.28274i 0.579029 0.186385i
\(151\) 8.45368 14.6422i 0.687951 1.19157i −0.284549 0.958662i \(-0.591844\pi\)
0.972500 0.232904i \(-0.0748229\pi\)
\(152\) −1.36210 2.35922i −0.110481 0.191358i
\(153\) −0.633475 6.36234i −0.0512134 0.514365i
\(154\) 1.42670 + 2.22812i 0.114966 + 0.179547i
\(155\) 4.68486i 0.376297i
\(156\) −1.40916 + 6.54140i −0.112823 + 0.523731i
\(157\) 3.28571 + 1.89701i 0.262229 + 0.151398i 0.625351 0.780344i \(-0.284956\pi\)
−0.363122 + 0.931742i \(0.618289\pi\)
\(158\) −4.86831 2.81072i −0.387302 0.223609i
\(159\) −3.05945 + 14.2021i −0.242630 + 1.12630i
\(160\) 0.835917i 0.0660850i
\(161\) 16.5107 + 8.54667i 1.30123 + 0.673572i
\(162\) 1.77460 + 8.82331i 0.139426 + 0.693225i
\(163\) 3.12271 + 5.40870i 0.244590 + 0.423642i 0.962016 0.272992i \(-0.0880134\pi\)
−0.717426 + 0.696634i \(0.754680\pi\)
\(164\) 0.417958 0.723925i 0.0326371 0.0565291i
\(165\) −1.37821 + 0.443635i −0.107293 + 0.0345370i
\(166\) 2.95806 1.70784i 0.229590 0.132554i
\(167\) 3.37801 0.261398 0.130699 0.991422i \(-0.458278\pi\)
0.130699 + 0.991422i \(0.458278\pi\)
\(168\) −3.53475 2.91642i −0.272712 0.225007i
\(169\) −1.92522 −0.148094
\(170\) −1.54288 + 0.890781i −0.118333 + 0.0683198i
\(171\) 3.36496 7.44771i 0.257325 0.569540i
\(172\) −4.92543 + 8.53109i −0.375560 + 0.650490i
\(173\) −5.09256 8.82057i −0.387180 0.670615i 0.604889 0.796310i \(-0.293217\pi\)
−0.992069 + 0.125694i \(0.959884\pi\)
\(174\) −8.43550 + 9.31710i −0.639494 + 0.706328i
\(175\) −11.3680 + 0.522570i −0.859341 + 0.0395026i
\(176\) 1.00000i 0.0753778i
\(177\) −12.2215 2.63278i −0.918621 0.197892i
\(178\) −0.616180 0.355752i −0.0461846 0.0266647i
\(179\) −16.5044 9.52883i −1.23360 0.712218i −0.265820 0.964023i \(-0.585643\pi\)
−0.967778 + 0.251805i \(0.918976\pi\)
\(180\) 2.03686 1.46288i 0.151819 0.109036i
\(181\) 21.3997i 1.59063i −0.606199 0.795313i \(-0.707306\pi\)
0.606199 0.795313i \(-0.292694\pi\)
\(182\) 4.69882 9.07732i 0.348299 0.672856i
\(183\) 3.43456 + 3.10958i 0.253890 + 0.229867i
\(184\) −3.51349 6.08555i −0.259018 0.448633i
\(185\) 1.47231 2.55012i 0.108247 0.187489i
\(186\) −2.97438 9.24028i −0.218092 0.677530i
\(187\) −1.84573 + 1.06563i −0.134973 + 0.0779268i
\(188\) −11.6858 −0.852274
\(189\) 0.920469 13.7169i 0.0669543 0.997756i
\(190\) −2.27720 −0.165206
\(191\) −7.70390 + 4.44785i −0.557435 + 0.321835i −0.752115 0.659032i \(-0.770966\pi\)
0.194680 + 0.980867i \(0.437633\pi\)
\(192\) 0.530717 + 1.64874i 0.0383012 + 0.118987i
\(193\) 3.07676 5.32910i 0.221470 0.383597i −0.733785 0.679382i \(-0.762248\pi\)
0.955254 + 0.295785i \(0.0955813\pi\)
\(194\) 4.92306 + 8.52699i 0.353455 + 0.612202i
\(195\) 4.14651 + 3.75416i 0.296938 + 0.268841i
\(196\) 4.04140 + 5.71551i 0.288672 + 0.408251i
\(197\) 19.4741i 1.38748i −0.720228 0.693738i \(-0.755963\pi\)
0.720228 0.693738i \(-0.244037\pi\)
\(198\) 2.43668 1.75003i 0.173167 0.124369i
\(199\) −11.4944 6.63628i −0.814815 0.470433i 0.0338105 0.999428i \(-0.489236\pi\)
−0.848625 + 0.528995i \(0.822569\pi\)
\(200\) 3.72499 + 2.15062i 0.263396 + 0.152072i
\(201\) −21.5109 4.63394i −1.51726 0.326853i
\(202\) 6.63409i 0.466773i
\(203\) 16.1682 10.3527i 1.13478 0.726615i
\(204\) 2.47758 2.73651i 0.173465 0.191594i
\(205\) −0.349379 0.605141i −0.0244017 0.0422649i
\(206\) −7.62843 + 13.2128i −0.531498 + 0.920581i
\(207\) 8.67982 19.2111i 0.603289 1.33527i
\(208\) −3.34573 + 1.93166i −0.231985 + 0.133936i
\(209\) −2.72420 −0.188437
\(210\) −3.58865 + 1.33995i −0.247641 + 0.0924656i
\(211\) −16.8085 −1.15715 −0.578574 0.815630i \(-0.696391\pi\)
−0.578574 + 0.815630i \(0.696391\pi\)
\(212\) −7.26395 + 4.19384i −0.498890 + 0.288034i
\(213\) −4.39302 + 1.41408i −0.301005 + 0.0968913i
\(214\) −1.86253 + 3.22599i −0.127320 + 0.220524i
\(215\) 4.11725 + 7.13129i 0.280794 + 0.486350i
\(216\) −3.08868 + 4.17853i −0.210158 + 0.284313i
\(217\) 0.680901 + 14.8123i 0.0462226 + 1.00553i
\(218\) 18.0226i 1.22065i
\(219\) 4.53141 21.0350i 0.306204 1.42141i
\(220\) −0.723925 0.417958i −0.0488070 0.0281788i
\(221\) 7.13065 + 4.11688i 0.479659 + 0.276931i
\(222\) −1.28490 + 5.96454i −0.0862365 + 0.400314i
\(223\) 5.99627i 0.401540i 0.979638 + 0.200770i \(0.0643444\pi\)
−0.979638 + 0.200770i \(0.935656\pi\)
\(224\) −0.121493 2.64296i −0.00811758 0.176590i
\(225\) 1.27846 + 12.8402i 0.0852303 + 0.856016i
\(226\) 6.98869 + 12.1048i 0.464881 + 0.805197i
\(227\) −3.71163 + 6.42873i −0.246350 + 0.426690i −0.962510 0.271246i \(-0.912564\pi\)
0.716161 + 0.697935i \(0.245898\pi\)
\(228\) 4.49149 1.44578i 0.297456 0.0957490i
\(229\) −10.1281 + 5.84744i −0.669281 + 0.386410i −0.795804 0.605554i \(-0.792952\pi\)
0.126523 + 0.991964i \(0.459618\pi\)
\(230\) −5.87398 −0.387319
\(231\) −4.29307 + 1.60297i −0.282463 + 0.105468i
\(232\) −7.25640 −0.476406
\(233\) −12.0947 + 6.98286i −0.792348 + 0.457462i −0.840788 0.541364i \(-0.817908\pi\)
0.0484405 + 0.998826i \(0.484575\pi\)
\(234\) −10.5620 4.77201i −0.690457 0.311956i
\(235\) −4.88418 + 8.45964i −0.318609 + 0.551846i
\(236\) −3.60897 6.25091i −0.234924 0.406900i
\(237\) 6.53488 7.21785i 0.424486 0.468849i
\(238\) −4.74873 + 3.04067i −0.307814 + 0.197097i
\(239\) 9.25345i 0.598556i −0.954166 0.299278i \(-0.903254\pi\)
0.954166 0.299278i \(-0.0967458\pi\)
\(240\) 1.41538 + 0.304905i 0.0913625 + 0.0196815i
\(241\) −4.12181 2.37973i −0.265509 0.153292i 0.361336 0.932436i \(-0.382321\pi\)
−0.626845 + 0.779144i \(0.715654\pi\)
\(242\) −0.866025 0.500000i −0.0556702 0.0321412i
\(243\) −15.5870 0.213576i −0.999906 0.0137009i
\(244\) 2.67493i 0.171245i
\(245\) 5.82674 0.536827i 0.372257 0.0342966i
\(246\) 1.07330 + 0.971746i 0.0684314 + 0.0619563i
\(247\) 5.26222 + 9.11443i 0.334827 + 0.579938i
\(248\) 2.80223 4.85360i 0.177942 0.308204i
\(249\) 1.81275 + 5.63155i 0.114879 + 0.356885i
\(250\) 6.73341 3.88753i 0.425858 0.245869i
\(251\) −20.1964 −1.27478 −0.637392 0.770540i \(-0.719987\pi\)
−0.637392 + 0.770540i \(0.719987\pi\)
\(252\) 6.22743 4.92129i 0.392291 0.310012i
\(253\) −7.02699 −0.441783
\(254\) 9.03483 5.21626i 0.566896 0.327298i
\(255\) −0.945506 2.93733i −0.0592099 0.183943i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 14.1698 + 24.5429i 0.883890 + 1.53094i 0.846980 + 0.531624i \(0.178418\pi\)
0.0369100 + 0.999319i \(0.488249\pi\)
\(258\) −12.6483 11.4515i −0.787451 0.712941i
\(259\) 4.28445 8.27683i 0.266223 0.514297i
\(260\) 3.22941i 0.200280i
\(261\) −12.6989 17.6815i −0.786042 1.09446i
\(262\) −9.01131 5.20268i −0.556721 0.321423i
\(263\) −16.5761 9.57022i −1.02213 0.590125i −0.107407 0.994215i \(-0.534255\pi\)
−0.914719 + 0.404090i \(0.867588\pi\)
\(264\) 1.69321 + 0.364755i 0.104210 + 0.0224491i
\(265\) 7.01141i 0.430707i
\(266\) −7.19995 + 0.330971i −0.441457 + 0.0202931i
\(267\) 0.827116 0.913559i 0.0506187 0.0559089i
\(268\) −6.35213 11.0022i −0.388018 0.672067i
\(269\) −4.24434 + 7.35142i −0.258782 + 0.448224i −0.965916 0.258856i \(-0.916655\pi\)
0.707134 + 0.707080i \(0.249988\pi\)
\(270\) 1.73400 + 3.98242i 0.105528 + 0.242362i
\(271\) 13.3069 7.68275i 0.808338 0.466694i −0.0380407 0.999276i \(-0.512112\pi\)
0.846378 + 0.532582i \(0.178778\pi\)
\(272\) 2.13127 0.129227
\(273\) 13.6559 + 11.2671i 0.826491 + 0.681914i
\(274\) −6.48835 −0.391975
\(275\) 3.72499 2.15062i 0.224625 0.129687i
\(276\) 11.5857 3.72934i 0.697375 0.224480i
\(277\) 10.1508 17.5818i 0.609904 1.05638i −0.381352 0.924430i \(-0.624541\pi\)
0.991256 0.131955i \(-0.0421254\pi\)
\(278\) 7.52113 + 13.0270i 0.451088 + 0.781307i
\(279\) 16.7306 1.66581i 1.00164 0.0997293i
\(280\) −1.96408 1.01670i −0.117377 0.0607592i
\(281\) 11.7320i 0.699870i 0.936774 + 0.349935i \(0.113796\pi\)
−0.936774 + 0.349935i \(0.886204\pi\)
\(282\) 4.26245 19.7865i 0.253825 1.17827i
\(283\) 12.3521 + 7.13151i 0.734258 + 0.423924i 0.819978 0.572395i \(-0.193986\pi\)
−0.0857197 + 0.996319i \(0.527319\pi\)
\(284\) −2.30750 1.33224i −0.136925 0.0790538i
\(285\) 0.830621 3.85578i 0.0492017 0.228397i
\(286\) 3.86332i 0.228443i
\(287\) −1.19260 1.86253i −0.0703969 0.109941i
\(288\) −2.98524 + 0.297229i −0.175907 + 0.0175144i
\(289\) 6.22885 + 10.7887i 0.366403 + 0.634629i
\(290\) −3.03287 + 5.25309i −0.178096 + 0.308472i
\(291\) −16.2337 + 5.22550i −0.951635 + 0.306324i
\(292\) 10.7588 6.21158i 0.629610 0.363505i
\(293\) −6.45384 −0.377038 −0.188519 0.982070i \(-0.560369\pi\)
−0.188519 + 0.982070i \(0.560369\pi\)
\(294\) −11.1517 + 4.75818i −0.650379 + 0.277502i
\(295\) −6.03359 −0.351289
\(296\) −3.05069 + 1.76131i −0.177317 + 0.102374i
\(297\) 2.07437 + 4.76414i 0.120367 + 0.276443i
\(298\) 2.42908 4.20728i 0.140713 0.243721i
\(299\) 13.5737 + 23.5104i 0.784990 + 1.35964i
\(300\) −5.00016 + 5.52273i −0.288684 + 0.318855i
\(301\) 14.0542 + 21.9489i 0.810070 + 1.26512i
\(302\) 16.9074i 0.972910i
\(303\) −11.2329 2.41981i −0.645313 0.139015i
\(304\) 2.35922 + 1.36210i 0.135311 + 0.0781217i
\(305\) 1.93645 + 1.11801i 0.110881 + 0.0640170i
\(306\) 3.72978 + 5.19321i 0.213217 + 0.296876i
\(307\) 11.6367i 0.664141i 0.943255 + 0.332071i \(0.107747\pi\)
−0.943255 + 0.332071i \(0.892253\pi\)
\(308\) −2.34962 1.21626i −0.133882 0.0693031i
\(309\) −19.5896 17.7360i −1.11441 1.00896i
\(310\) −2.34243 4.05721i −0.133041 0.230434i
\(311\) 14.3269 24.8149i 0.812405 1.40713i −0.0987717 0.995110i \(-0.531491\pi\)
0.911177 0.412016i \(-0.135175\pi\)
\(312\) −2.05033 6.36960i −0.116077 0.360608i
\(313\) 19.4240 11.2144i 1.09791 0.633878i 0.162238 0.986752i \(-0.448129\pi\)
0.935671 + 0.352874i \(0.114796\pi\)
\(314\) −3.79402 −0.214109
\(315\) −0.959842 6.56509i −0.0540810 0.369901i
\(316\) 5.62145 0.316231
\(317\) 9.12201 5.26659i 0.512343 0.295801i −0.221453 0.975171i \(-0.571080\pi\)
0.733796 + 0.679370i \(0.237747\pi\)
\(318\) −4.45149 13.8291i −0.249627 0.775498i
\(319\) −3.62820 + 6.28423i −0.203140 + 0.351849i
\(320\) 0.417958 + 0.723925i 0.0233646 + 0.0404687i
\(321\) −4.78291 4.33034i −0.266956 0.241696i
\(322\) −18.5720 + 0.853729i −1.03498 + 0.0475764i
\(323\) 5.80599i 0.323054i
\(324\) −5.94850 6.75391i −0.330472 0.375217i
\(325\) −14.3908 8.30853i −0.798258 0.460875i
\(326\) −5.40870 3.12271i −0.299560 0.172951i
\(327\) 30.5161 + 6.57384i 1.68754 + 0.363534i
\(328\) 0.835917i 0.0461558i
\(329\) −14.2130 + 27.4571i −0.783589 + 1.51376i
\(330\) 0.971746 1.07330i 0.0534929 0.0590834i
\(331\) 15.4645 + 26.7852i 0.850003 + 1.47225i 0.881204 + 0.472735i \(0.156733\pi\)
−0.0312013 + 0.999513i \(0.509933\pi\)
\(332\) −1.70784 + 2.95806i −0.0937296 + 0.162344i
\(333\) −9.63054 4.35119i −0.527750 0.238444i
\(334\) −2.92544 + 1.68901i −0.160073 + 0.0924183i
\(335\) −10.6197 −0.580216
\(336\) 4.51940 + 0.758320i 0.246553 + 0.0413697i
\(337\) 8.74219 0.476217 0.238109 0.971239i \(-0.423473\pi\)
0.238109 + 0.971239i \(0.423473\pi\)
\(338\) 1.66729 0.962611i 0.0906887 0.0523591i
\(339\) −23.0451 + 7.41804i −1.25164 + 0.402892i
\(340\) 0.890781 1.54288i 0.0483094 0.0836743i
\(341\) −2.80223 4.85360i −0.151749 0.262837i
\(342\) 0.809711 + 8.13238i 0.0437842 + 0.439749i
\(343\) 18.3447 2.54418i 0.990519 0.137373i
\(344\) 9.85086i 0.531123i
\(345\) 2.14256 9.94587i 0.115352 0.535467i
\(346\) 8.82057 + 5.09256i 0.474197 + 0.273778i
\(347\) 1.10854 + 0.640018i 0.0595098 + 0.0343580i 0.529460 0.848335i \(-0.322395\pi\)
−0.469950 + 0.882693i \(0.655728\pi\)
\(348\) 2.64681 12.2866i 0.141884 0.658631i
\(349\) 13.1540i 0.704117i 0.935978 + 0.352058i \(0.114518\pi\)
−0.935978 + 0.352058i \(0.885482\pi\)
\(350\) 9.58370 6.13657i 0.512271 0.328013i
\(351\) 11.9325 16.1430i 0.636912 0.861648i
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) −7.51019 + 13.0080i −0.399727 + 0.692347i −0.993692 0.112143i \(-0.964228\pi\)
0.593965 + 0.804491i \(0.297562\pi\)
\(354\) 11.9005 3.83068i 0.632504 0.203598i
\(355\) −1.92888 + 1.11364i −0.102374 + 0.0591059i
\(356\) 0.711503 0.0377096
\(357\) −3.41637 9.14968i −0.180813 0.484253i
\(358\) 19.0577 1.00723
\(359\) −27.0726 + 15.6304i −1.42884 + 0.824940i −0.997029 0.0770249i \(-0.975458\pi\)
−0.431809 + 0.901965i \(0.642125\pi\)
\(360\) −1.03253 + 2.28532i −0.0544193 + 0.120447i
\(361\) −5.78937 + 10.0275i −0.304704 + 0.527763i
\(362\) 10.6998 + 18.5327i 0.562371 + 0.974056i
\(363\) 1.16249 1.28398i 0.0610150 0.0673917i
\(364\) 0.469366 + 10.2106i 0.0246014 + 0.535181i
\(365\) 10.3847i 0.543562i
\(366\) −4.52921 0.975693i −0.236746 0.0510003i
\(367\) −8.94931 5.16689i −0.467150 0.269709i 0.247896 0.968787i \(-0.420261\pi\)
−0.715046 + 0.699077i \(0.753594\pi\)
\(368\) 6.08555 + 3.51349i 0.317231 + 0.183154i
\(369\) −2.03686 + 1.46288i −0.106035 + 0.0761544i
\(370\) 2.94462i 0.153084i
\(371\) 1.01904 + 22.1683i 0.0529061 + 1.15092i
\(372\) 7.19603 + 6.51513i 0.373097 + 0.337794i
\(373\) −6.99037 12.1077i −0.361947 0.626911i 0.626334 0.779555i \(-0.284555\pi\)
−0.988281 + 0.152644i \(0.951221\pi\)
\(374\) 1.06563 1.84573i 0.0551026 0.0954405i
\(375\) 4.12636 + 12.8191i 0.213084 + 0.661973i
\(376\) 10.1202 5.84290i 0.521909 0.301324i
\(377\) 28.0338 1.44381
\(378\) 6.06129 + 12.3394i 0.311759 + 0.634670i
\(379\) −2.40372 −0.123471 −0.0617353 0.998093i \(-0.519663\pi\)
−0.0617353 + 0.998093i \(0.519663\pi\)
\(380\) 1.97212 1.13860i 0.101167 0.0584090i
\(381\) 5.53672 + 17.2005i 0.283655 + 0.881209i
\(382\) 4.44785 7.70390i 0.227572 0.394166i
\(383\) −11.4425 19.8189i −0.584683 1.01270i −0.994915 0.100720i \(-0.967886\pi\)
0.410232 0.911981i \(-0.365448\pi\)
\(384\) −1.28398 1.16249i −0.0655230 0.0593231i
\(385\) −1.86253 + 1.19260i −0.0949232 + 0.0607805i
\(386\) 6.15351i 0.313206i
\(387\) 24.0034 17.2393i 1.22016 0.876322i
\(388\) −8.52699 4.92306i −0.432892 0.249930i
\(389\) 15.3333 + 8.85268i 0.777428 + 0.448849i 0.835518 0.549463i \(-0.185168\pi\)
−0.0580897 + 0.998311i \(0.518501\pi\)
\(390\) −5.46807 1.17794i −0.276886 0.0596475i
\(391\) 14.9764i 0.757388i
\(392\) −6.35771 2.92908i −0.321113 0.147941i
\(393\) 12.0961 13.3603i 0.610170 0.673939i
\(394\) 9.73707 + 16.8651i 0.490547 + 0.849652i
\(395\) 2.34953 4.06951i 0.118218 0.204759i
\(396\) −1.23521 + 2.73391i −0.0620717 + 0.137384i
\(397\) −31.0739 + 17.9405i −1.55955 + 0.900408i −0.562254 + 0.826965i \(0.690066\pi\)
−0.997299 + 0.0734435i \(0.976601\pi\)
\(398\) 13.2726 0.665293
\(399\) 2.06581 12.3117i 0.103420 0.616358i
\(400\) −4.30124 −0.215062
\(401\) 22.4661 12.9708i 1.12191 0.647733i 0.180019 0.983663i \(-0.442384\pi\)
0.941887 + 0.335931i \(0.109051\pi\)
\(402\) 20.9460 6.74236i 1.04469 0.336279i
\(403\) −10.8259 + 18.7510i −0.539276 + 0.934054i
\(404\) −3.31704 5.74529i −0.165029 0.285839i
\(405\) −7.37555 + 1.48342i −0.366494 + 0.0737117i
\(406\) −8.82570 + 17.0498i −0.438012 + 0.846165i
\(407\) 3.52263i 0.174610i
\(408\) −0.777390 + 3.60868i −0.0384865 + 0.178656i
\(409\) 8.55454 + 4.93897i 0.422995 + 0.244216i 0.696358 0.717695i \(-0.254803\pi\)
−0.273363 + 0.961911i \(0.588136\pi\)
\(410\) 0.605141 + 0.349379i 0.0298858 + 0.0172546i
\(411\) 2.36666 10.9861i 0.116739 0.541905i
\(412\) 15.2569i 0.751651i
\(413\) −19.0767 + 0.876927i −0.938703 + 0.0431508i
\(414\) 2.08863 + 20.9772i 0.102650 + 1.03098i
\(415\) 1.42761 + 2.47269i 0.0700785 + 0.121380i
\(416\) 1.93166 3.34573i 0.0947074 0.164038i
\(417\) −24.8008 + 7.98319i −1.21450 + 0.390939i
\(418\) 2.35922 1.36210i 0.115393 0.0666224i
\(419\) 7.14212 0.348916 0.174458 0.984665i \(-0.444183\pi\)
0.174458 + 0.984665i \(0.444183\pi\)
\(420\) 2.43789 2.95476i 0.118957 0.144178i
\(421\) 2.83262 0.138053 0.0690267 0.997615i \(-0.478011\pi\)
0.0690267 + 0.997615i \(0.478011\pi\)
\(422\) 14.5566 8.40427i 0.708606 0.409114i
\(423\) 31.9479 + 14.4344i 1.55336 + 0.701826i
\(424\) 4.19384 7.26395i 0.203671 0.352769i
\(425\) 4.58355 + 7.93894i 0.222335 + 0.385095i
\(426\) 3.09743 3.42114i 0.150071 0.165755i
\(427\) 6.28506 + 3.25342i 0.304155 + 0.157444i
\(428\) 3.72505i 0.180057i
\(429\) −6.54140 1.40916i −0.315822 0.0680351i
\(430\) −7.13129 4.11725i −0.343901 0.198551i
\(431\) 22.0931 + 12.7555i 1.06419 + 0.614410i 0.926588 0.376078i \(-0.122728\pi\)
0.137601 + 0.990488i \(0.456061\pi\)
\(432\) 0.585609 5.16305i 0.0281752 0.248407i
\(433\) 17.6085i 0.846213i 0.906080 + 0.423106i \(0.139060\pi\)
−0.906080 + 0.423106i \(0.860940\pi\)
\(434\) −7.99585 12.4874i −0.383813 0.599415i
\(435\) −7.78832 7.05138i −0.373421 0.338088i
\(436\) 9.01132 + 15.6081i 0.431564 + 0.747491i
\(437\) 9.57145 16.5782i 0.457865 0.793045i
\(438\) 6.59319 + 20.4826i 0.315035 + 0.978695i
\(439\) 20.3880 11.7710i 0.973068 0.561801i 0.0728977 0.997339i \(-0.476775\pi\)
0.900170 + 0.435538i \(0.143442\pi\)
\(440\) 0.835917 0.0398508
\(441\) −3.98896 20.6177i −0.189950 0.981794i
\(442\) −8.23376 −0.391640
\(443\) −8.86868 + 5.12033i −0.421363 + 0.243274i −0.695661 0.718371i \(-0.744888\pi\)
0.274297 + 0.961645i \(0.411555\pi\)
\(444\) −1.86952 5.80789i −0.0887235 0.275630i
\(445\) 0.297379 0.515075i 0.0140971 0.0244169i
\(446\) −2.99814 5.19292i −0.141966 0.245892i
\(447\) 6.23779 + 5.64756i 0.295037 + 0.267120i
\(448\) 1.42670 + 2.22812i 0.0674051 + 0.105269i
\(449\) 17.4205i 0.822123i −0.911608 0.411061i \(-0.865158\pi\)
0.911608 0.411061i \(-0.134842\pi\)
\(450\) −7.52729 10.4807i −0.354840 0.494067i
\(451\) 0.723925 + 0.417958i 0.0340883 + 0.0196809i
\(452\) −12.1048 6.98869i −0.569360 0.328720i
\(453\) −28.6277 6.16704i −1.34505 0.289753i
\(454\) 7.42326i 0.348391i
\(455\) 7.58788 + 3.92782i 0.355725 + 0.184139i
\(456\) −3.16686 + 3.49783i −0.148302 + 0.163801i
\(457\) −3.44330 5.96396i −0.161071 0.278982i 0.774182 0.632963i \(-0.218161\pi\)
−0.935253 + 0.353980i \(0.884828\pi\)
\(458\) 5.84744 10.1281i 0.273233 0.473253i
\(459\) −10.1536 + 4.42104i −0.473931 + 0.206356i
\(460\) 5.08701 2.93699i 0.237183 0.136938i
\(461\) 6.62247 0.308439 0.154220 0.988037i \(-0.450714\pi\)
0.154220 + 0.988037i \(0.450714\pi\)
\(462\) 2.91642 3.53475i 0.135684 0.164452i
\(463\) 21.3829 0.993749 0.496874 0.867822i \(-0.334481\pi\)
0.496874 + 0.867822i \(0.334481\pi\)
\(464\) 6.28423 3.62820i 0.291738 0.168435i
\(465\) 7.72411 2.48633i 0.358197 0.115301i
\(466\) 6.98286 12.0947i 0.323475 0.560275i
\(467\) −12.4871 21.6284i −0.577836 1.00084i −0.995727 0.0923444i \(-0.970564\pi\)
0.417891 0.908497i \(-0.362769\pi\)
\(468\) 11.5329 1.14829i 0.533110 0.0530798i
\(469\) −33.5768 + 1.54348i −1.55043 + 0.0712711i
\(470\) 9.76835i 0.450581i
\(471\) 1.38389 6.42406i 0.0637661 0.296005i
\(472\) 6.25091 + 3.60897i 0.287722 + 0.166116i
\(473\) −8.53109 4.92543i −0.392260 0.226471i
\(474\) −2.05045 + 9.51828i −0.0941803 + 0.437189i
\(475\) 11.7174i 0.537633i
\(476\) 2.59218 5.00766i 0.118813 0.229526i
\(477\) 25.0392 2.49307i 1.14647 0.114150i
\(478\) 4.62673 + 8.01372i 0.211622 + 0.366539i
\(479\) −14.4998 + 25.1144i −0.662512 + 1.14750i 0.317442 + 0.948278i \(0.397176\pi\)
−0.979954 + 0.199226i \(0.936157\pi\)
\(480\) −1.37821 + 0.443635i −0.0629063 + 0.0202491i
\(481\) 11.7858 6.80452i 0.537385 0.310259i
\(482\) 4.75945 0.216787
\(483\) 5.32870 31.7577i 0.242464 1.44503i
\(484\) 1.00000 0.0454545
\(485\) −7.12785 + 4.11527i −0.323659 + 0.186865i
\(486\) 13.6055 7.60853i 0.617159 0.345130i
\(487\) −7.81129 + 13.5296i −0.353963 + 0.613082i −0.986940 0.161088i \(-0.948500\pi\)
0.632977 + 0.774171i \(0.281833\pi\)
\(488\) −1.33746 2.31656i −0.0605441 0.104866i
\(489\) 7.26025 8.01903i 0.328320 0.362633i
\(490\) −4.77769 + 3.37828i −0.215834 + 0.152615i
\(491\) 32.5285i 1.46799i −0.679154 0.733996i \(-0.737653\pi\)
0.679154 0.733996i \(-0.262347\pi\)
\(492\) −1.41538 0.304905i −0.0638103 0.0137462i
\(493\) −13.3934 7.73266i −0.603207 0.348262i
\(494\) −9.11443 5.26222i −0.410078 0.236759i
\(495\) 1.46288 + 2.03686i 0.0657515 + 0.0915501i
\(496\) 5.60445i 0.251647i
\(497\) −5.93678 + 3.80140i −0.266301 + 0.170516i
\(498\) −4.38567 3.97069i −0.196526 0.177931i
\(499\) 7.65028 + 13.2507i 0.342473 + 0.593181i 0.984891 0.173173i \(-0.0554020\pi\)
−0.642418 + 0.766354i \(0.722069\pi\)
\(500\) −3.88753 + 6.73341i −0.173856 + 0.301127i
\(501\) −1.79277 5.56946i −0.0800950 0.248825i
\(502\) 17.4906 10.0982i 0.780642 0.450704i
\(503\) 31.3069 1.39590 0.697952 0.716145i \(-0.254095\pi\)
0.697952 + 0.716145i \(0.254095\pi\)
\(504\) −2.93247 + 7.37568i −0.130622 + 0.328539i
\(505\) −5.54554 −0.246773
\(506\) 6.08555 3.51349i 0.270536 0.156194i
\(507\) 1.02175 + 3.17419i 0.0453774 + 0.140971i
\(508\) −5.21626 + 9.03483i −0.231434 + 0.400856i
\(509\) −13.5445 23.4597i −0.600348 1.03983i −0.992768 0.120048i \(-0.961695\pi\)
0.392420 0.919786i \(-0.371638\pi\)
\(510\) 2.28750 + 2.07105i 0.101292 + 0.0917076i
\(511\) −1.50933 32.8339i −0.0667687 1.45249i
\(512\) 1.00000i 0.0441942i
\(513\) −14.0652 1.59532i −0.620992 0.0704349i
\(514\) −24.5429 14.1698i −1.08254 0.625005i
\(515\) −11.0448 6.37673i −0.486693 0.280992i
\(516\) 16.6796 + 3.59315i 0.734276 + 0.158180i
\(517\) 11.6858i 0.513941i
\(518\) 0.427974 + 9.31017i 0.0188041 + 0.409065i
\(519\) −11.8401 + 13.0775i −0.519723 + 0.574040i
\(520\) −1.61471 2.79675i −0.0708096 0.122646i
\(521\) 7.87689 13.6432i 0.345093 0.597718i −0.640278 0.768143i \(-0.721181\pi\)
0.985371 + 0.170425i \(0.0545142\pi\)
\(522\) 19.8383 + 8.96319i 0.868300 + 0.392308i
\(523\) 15.4013 8.89196i 0.673453 0.388818i −0.123931 0.992291i \(-0.539550\pi\)
0.797384 + 0.603473i \(0.206217\pi\)
\(524\) 10.4054 0.454561
\(525\) 6.89478 + 18.4655i 0.300913 + 0.805903i
\(526\) 19.1404 0.834563
\(527\) 10.3443 5.97229i 0.450605 0.260157i
\(528\) −1.64874 + 0.530717i −0.0717521 + 0.0230965i
\(529\) 13.1893 22.8445i 0.573447 0.993239i
\(530\) −3.50570 6.07206i −0.152278 0.263753i
\(531\) 2.14538 + 21.5473i 0.0931016 + 0.935071i
\(532\) 6.06985 3.88660i 0.263161 0.168506i
\(533\) 3.22941i 0.139881i
\(534\) −0.259524 + 1.20472i −0.0112307 + 0.0521335i
\(535\) −2.69666 1.55692i −0.116587 0.0673114i
\(536\) 11.0022 + 6.35213i 0.475223 + 0.274370i
\(537\) −6.95137 + 32.2686i −0.299974 + 1.39249i
\(538\) 8.48869i 0.365973i
\(539\) −5.71551 + 4.04140i −0.246184 + 0.174076i
\(540\) −3.49290 2.58188i −0.150311 0.111106i
\(541\) 17.3541 + 30.0582i 0.746111 + 1.29230i 0.949674 + 0.313241i \(0.101415\pi\)
−0.203563 + 0.979062i \(0.565252\pi\)
\(542\) −7.68275 + 13.3069i −0.330002 + 0.571581i
\(543\) −35.2825 + 11.3572i −1.51412 + 0.487383i
\(544\) −1.84573 + 1.06563i −0.0791351 + 0.0456887i
\(545\) 15.0654 0.645332
\(546\) −17.4599 2.92963i −0.747213 0.125377i
\(547\) −9.06564 −0.387619 −0.193809 0.981039i \(-0.562084\pi\)
−0.193809 + 0.981039i \(0.562084\pi\)
\(548\) 5.61907 3.24417i 0.240035 0.138584i
\(549\) 3.30410 7.31301i 0.141016 0.312111i
\(550\) −2.15062 + 3.72499i −0.0917028 + 0.158834i
\(551\) −9.88393 17.1195i −0.421070 0.729314i
\(552\) −8.16881 + 9.02254i −0.347688 + 0.384025i
\(553\) 6.83716 13.2082i 0.290746 0.561672i
\(554\) 20.3017i 0.862535i
\(555\) −4.98586 1.07407i −0.211638 0.0455916i
\(556\) −13.0270 7.52113i −0.552467 0.318967i
\(557\) −5.76379 3.32773i −0.244220 0.141000i 0.372895 0.927874i \(-0.378365\pi\)
−0.617115 + 0.786873i \(0.711699\pi\)
\(558\) −13.6563 + 9.80795i −0.578115 + 0.415204i
\(559\) 38.0570i 1.60964i
\(560\) 2.20930 0.101558i 0.0933598 0.00429161i
\(561\) 2.73651 + 2.47758i 0.115536 + 0.104603i
\(562\) −5.86598 10.1602i −0.247441 0.428581i
\(563\) −20.7720 + 35.9782i −0.875435 + 1.51630i −0.0191372 + 0.999817i \(0.506092\pi\)
−0.856298 + 0.516482i \(0.827241\pi\)
\(564\) 6.20185 + 19.2668i 0.261145 + 0.811279i
\(565\) −10.1186 + 5.84197i −0.425692 + 0.245773i
\(566\) −14.2630 −0.599519
\(567\) −23.1041 + 5.76217i −0.970279 + 0.241988i
\(568\) 2.66448 0.111799
\(569\) 19.0011 10.9703i 0.796566 0.459898i −0.0457028 0.998955i \(-0.514553\pi\)
0.842269 + 0.539057i \(0.181219\pi\)
\(570\) 1.20855 + 3.75451i 0.0506206 + 0.157259i
\(571\) −12.8656 + 22.2839i −0.538409 + 0.932551i 0.460581 + 0.887618i \(0.347641\pi\)
−0.998990 + 0.0449337i \(0.985692\pi\)
\(572\) −1.93166 3.34573i −0.0807667 0.139892i
\(573\) 11.4219 + 10.3412i 0.477158 + 0.432009i
\(574\) 1.96408 + 1.01670i 0.0819793 + 0.0424361i
\(575\) 30.2248i 1.26046i
\(576\) 2.43668 1.75003i 0.101528 0.0729178i
\(577\) 9.60562 + 5.54581i 0.399887 + 0.230875i 0.686435 0.727191i \(-0.259175\pi\)
−0.286548 + 0.958066i \(0.592508\pi\)
\(578\) −10.7887 6.22885i −0.448750 0.259086i
\(579\) −10.4192 2.24452i −0.433006 0.0932792i
\(580\) 6.06575i 0.251866i
\(581\) 4.87312 + 7.61054i 0.202171 + 0.315738i
\(582\) 11.4460 12.6423i 0.474453 0.524038i
\(583\) −4.19384 7.26395i −0.173691 0.300842i
\(584\) −6.21158 + 10.7588i −0.257037 + 0.445201i
\(585\) 3.98901 8.82892i 0.164925 0.365031i
\(586\) 5.58919 3.22692i 0.230887 0.133303i
\(587\) −39.3634 −1.62470 −0.812351 0.583169i \(-0.801813\pi\)
−0.812351 + 0.583169i \(0.801813\pi\)
\(588\) 7.27854 9.69654i 0.300162 0.399878i
\(589\) 15.2676 0.629092
\(590\) 5.22524 3.01680i 0.215120 0.124200i
\(591\) −32.1078 + 10.3353i −1.32074 + 0.425136i
\(592\) 1.76131 3.05069i 0.0723896 0.125382i
\(593\) 4.17903 + 7.23829i 0.171612 + 0.297241i 0.938984 0.343962i \(-0.111769\pi\)
−0.767371 + 0.641203i \(0.778436\pi\)
\(594\) −4.17853 3.08868i −0.171447 0.126730i
\(595\) −2.54175 3.96954i −0.104201 0.162735i
\(596\) 4.85815i 0.198998i
\(597\) −4.84123 + 22.4732i −0.198138 + 0.919767i
\(598\) −23.5104 13.5737i −0.961412 0.555072i
\(599\) 10.5034 + 6.06417i 0.429159 + 0.247775i 0.698988 0.715133i \(-0.253634\pi\)
−0.269829 + 0.962908i \(0.586967\pi\)
\(600\) 1.56890 7.28290i 0.0640500 0.297323i
\(601\) 41.6196i 1.69770i −0.528634 0.848850i \(-0.677295\pi\)
0.528634 0.848850i \(-0.322705\pi\)
\(602\) −23.1457 11.9812i −0.943350 0.488319i
\(603\) 3.77607 + 37.9252i 0.153774 + 1.54443i
\(604\) −8.45368 14.6422i −0.343975 0.595783i
\(605\) 0.417958 0.723925i 0.0169924 0.0294317i
\(606\) 10.9379 3.52082i 0.444321 0.143024i
\(607\) −18.6709 + 10.7797i −0.757830 + 0.437533i −0.828516 0.559965i \(-0.810814\pi\)
0.0706862 + 0.997499i \(0.477481\pi\)
\(608\) −2.72420 −0.110481
\(609\) −25.6496 21.1627i −1.03937 0.857557i
\(610\) −2.23602 −0.0905337
\(611\) −39.0975 + 22.5730i −1.58172 + 0.913204i
\(612\) −5.82669 2.63257i −0.235530 0.106415i
\(613\) 2.42873 4.20669i 0.0980955 0.169906i −0.812801 0.582542i \(-0.802058\pi\)
0.910896 + 0.412635i \(0.135392\pi\)
\(614\) −5.81835 10.0777i −0.234809 0.406702i
\(615\) −0.812299 + 0.897193i −0.0327551 + 0.0361783i
\(616\) 2.64296 0.121493i 0.106488 0.00489509i
\(617\) 20.6685i 0.832084i 0.909345 + 0.416042i \(0.136583\pi\)
−0.909345 + 0.416042i \(0.863417\pi\)
\(618\) 25.8330 + 5.56501i 1.03916 + 0.223858i
\(619\) −15.9542 9.21116i −0.641253 0.370228i 0.143844 0.989600i \(-0.454054\pi\)
−0.785097 + 0.619373i \(0.787387\pi\)
\(620\) 4.05721 + 2.34243i 0.162941 + 0.0940742i
\(621\) −36.2807 4.11507i −1.45589 0.165132i
\(622\) 28.6538i 1.14891i
\(623\) 0.865376 1.67176i 0.0346706 0.0669777i
\(624\) 4.96044 + 4.49107i 0.198576 + 0.179787i
\(625\) −7.50345 12.9964i −0.300138 0.519854i
\(626\) −11.2144 + 19.4240i −0.448219 + 0.776338i
\(627\) 1.44578 + 4.49149i 0.0577388 + 0.179373i
\(628\) 3.28571 1.89701i 0.131114 0.0756989i
\(629\) −7.50766 −0.299350
\(630\) 4.11379 + 5.20561i 0.163897 + 0.207397i
\(631\) −21.1539 −0.842125 −0.421063 0.907032i \(-0.638343\pi\)
−0.421063 + 0.907032i \(0.638343\pi\)
\(632\) −4.86831 + 2.81072i −0.193651 + 0.111805i
\(633\) 8.92059 + 27.7129i 0.354561 + 1.10149i
\(634\) −5.26659 + 9.12201i −0.209163 + 0.362281i
\(635\) 4.36036 + 7.55237i 0.173036 + 0.299707i
\(636\) 10.7697 + 9.75061i 0.427045 + 0.386637i
\(637\) 24.5619 + 11.3160i 0.973176 + 0.448354i
\(638\) 7.25640i 0.287284i
\(639\) 4.66291 + 6.49247i 0.184462 + 0.256838i
\(640\) −0.723925 0.417958i −0.0286157 0.0165213i
\(641\) 29.6480 + 17.1173i 1.17102 + 0.676091i 0.953921 0.300058i \(-0.0970059\pi\)
0.217103 + 0.976149i \(0.430339\pi\)
\(642\) 6.30729 + 1.35873i 0.248929 + 0.0536248i
\(643\) 37.5930i 1.48252i −0.671215 0.741262i \(-0.734227\pi\)
0.671215 0.741262i \(-0.265773\pi\)
\(644\) 15.6570 10.0254i 0.616972 0.395055i
\(645\) 9.57253 10.5730i 0.376918 0.416310i
\(646\) 2.90300 + 5.02814i 0.114217 + 0.197829i
\(647\) 20.3948 35.3248i 0.801802 1.38876i −0.116628 0.993176i \(-0.537208\pi\)
0.918429 0.395585i \(-0.129458\pi\)
\(648\) 8.52851 + 2.87481i 0.335032 + 0.112933i
\(649\) 6.25091 3.60897i 0.245370 0.141664i
\(650\) 16.6171 0.651775
\(651\) 24.0603 8.98380i 0.942998 0.352103i
\(652\) 6.24543 0.244590
\(653\) 36.7047 21.1915i 1.43637 0.829286i 0.438771 0.898599i \(-0.355414\pi\)
0.997595 + 0.0693127i \(0.0220806\pi\)
\(654\) −29.7146 + 9.56492i −1.16193 + 0.374018i
\(655\) 4.34901 7.53271i 0.169930 0.294327i
\(656\) −0.417958 0.723925i −0.0163185 0.0282645i
\(657\) −37.0861 + 3.69253i −1.44687 + 0.144059i
\(658\) −1.41974 30.8851i −0.0553472 1.20403i
\(659\) 44.3754i 1.72862i 0.502961 + 0.864309i \(0.332244\pi\)
−0.502961 + 0.864309i \(0.667756\pi\)
\(660\) −0.304905 + 1.41538i −0.0118684 + 0.0550936i
\(661\) −15.0119 8.66712i −0.583895 0.337112i 0.178785 0.983888i \(-0.442783\pi\)
−0.762680 + 0.646776i \(0.776117\pi\)
\(662\) −26.7852 15.4645i −1.04104 0.601043i
\(663\) 3.00330 13.9415i 0.116639 0.541442i
\(664\) 3.41567i 0.132554i
\(665\) −0.276664 6.01856i −0.0107286 0.233390i
\(666\) 10.5159 1.04703i 0.407482 0.0405715i
\(667\) −25.4953 44.1592i −0.987182 1.70985i
\(668\) 1.68901 2.92544i 0.0653496 0.113189i
\(669\) 9.88629 3.18232i 0.382226 0.123036i
\(670\) 9.19693 5.30985i 0.355308 0.205137i
\(671\) −2.67493 −0.103264
\(672\) −4.29307 + 1.60297i −0.165609 + 0.0618361i
\(673\) 8.22070 0.316885 0.158442 0.987368i \(-0.449353\pi\)
0.158442 + 0.987368i \(0.449353\pi\)
\(674\) −7.57096 + 4.37109i −0.291622 + 0.168368i
\(675\) 20.4917 8.92237i 0.788726 0.343422i
\(676\) −0.962611 + 1.66729i −0.0370235 + 0.0641266i
\(677\) −9.52599 16.4995i −0.366113 0.634127i 0.622841 0.782349i \(-0.285978\pi\)
−0.988954 + 0.148222i \(0.952645\pi\)
\(678\) 16.2486 17.9467i 0.624023 0.689240i
\(679\) −21.9384 + 14.0474i −0.841917 + 0.539090i
\(680\) 1.78156i 0.0683198i
\(681\) 12.5691 + 2.70767i 0.481650 + 0.103758i
\(682\) 4.85360 + 2.80223i 0.185854 + 0.107303i
\(683\) 41.1088 + 23.7342i 1.57299 + 0.908164i 0.995800 + 0.0915501i \(0.0291822\pi\)
0.577185 + 0.816613i \(0.304151\pi\)
\(684\) −4.76742 6.63799i −0.182287 0.253810i
\(685\) 5.42372i 0.207230i
\(686\) −14.6149 + 11.3757i −0.557998 + 0.434325i
\(687\) 15.0160 + 13.5952i 0.572897 + 0.518689i
\(688\) 4.92543 + 8.53109i 0.187780 + 0.325245i
\(689\) −16.2021 + 28.0629i −0.617253 + 1.06911i
\(690\) 3.11742 + 9.68465i 0.118678 + 0.368688i
\(691\) 18.7810 10.8432i 0.714464 0.412496i −0.0982480 0.995162i \(-0.531324\pi\)
0.812712 + 0.582666i \(0.197991\pi\)
\(692\) −10.1851 −0.387180
\(693\) 4.92129 + 6.22743i 0.186944 + 0.236560i
\(694\) −1.28004 −0.0485895
\(695\) −10.8895 + 6.28704i −0.413061 + 0.238481i
\(696\) 3.85110 + 11.9639i 0.145975 + 0.453491i
\(697\) −0.890781 + 1.54288i −0.0337407 + 0.0584407i
\(698\) −6.57699 11.3917i −0.248943 0.431182i
\(699\) 17.9318 + 16.2350i 0.678241 + 0.614065i
\(700\) −5.23145 + 10.1063i −0.197730 + 0.381981i
\(701\) 51.9746i 1.96305i −0.191328 0.981526i \(-0.561280\pi\)
0.191328 0.981526i \(-0.438720\pi\)
\(702\) −2.26240 + 19.9465i −0.0853886 + 0.752832i
\(703\) −8.31067 4.79817i −0.313443 0.180966i
\(704\) −0.866025 0.500000i −0.0326396 0.0188445i
\(705\) 16.5399 + 3.56305i 0.622927 + 0.134192i
\(706\) 15.0204i 0.565299i
\(707\) −17.5336 + 0.805994i −0.659420 + 0.0303125i
\(708\) −8.39078 + 9.26771i −0.315345 + 0.348302i
\(709\) 9.83314 + 17.0315i 0.369291 + 0.639632i 0.989455 0.144841i \(-0.0462671\pi\)
−0.620163 + 0.784473i \(0.712934\pi\)
\(710\) 1.11364 1.92888i 0.0417942 0.0723896i
\(711\) −15.3685 6.94368i −0.576364 0.260408i
\(712\) −0.616180 + 0.355752i −0.0230923 + 0.0133324i
\(713\) 39.3824 1.47488
\(714\) 7.53350 + 6.21567i 0.281934 + 0.232616i
\(715\) −3.22941 −0.120773
\(716\) −16.5044 + 9.52883i −0.616799 + 0.356109i
\(717\) −15.2565 + 4.91097i −0.569765 + 0.183403i
\(718\) 15.6304 27.0726i 0.583321 1.01034i
\(719\) 7.00169 + 12.1273i 0.261119 + 0.452271i 0.966540 0.256518i \(-0.0825752\pi\)
−0.705421 + 0.708789i \(0.749242\pi\)
\(720\) −0.248459 2.49541i −0.00925952 0.0929985i
\(721\) −35.8478 18.5564i −1.33504 0.691075i
\(722\) 11.5787i 0.430916i
\(723\) −1.73603 + 8.05874i −0.0645638 + 0.299708i
\(724\) −18.5327 10.6998i −0.688761 0.397657i
\(725\) 27.0300 + 15.6058i 1.00387 + 0.579584i
\(726\) −0.364755 + 1.69321i −0.0135373 + 0.0628408i
\(727\) 11.1514i 0.413582i −0.978385 0.206791i \(-0.933698\pi\)
0.978385 0.206791i \(-0.0663020\pi\)
\(728\) −5.51178 8.60795i −0.204280 0.319032i
\(729\) 7.92015 + 25.8122i 0.293339 + 0.956008i
\(730\) 5.19237 + 8.99345i 0.192178 + 0.332862i
\(731\) 10.4974 18.1820i 0.388260 0.672487i
\(732\) 4.41026 1.41963i 0.163008 0.0524710i
\(733\) 9.63547 5.56304i 0.355894 0.205476i −0.311384 0.950284i \(-0.600793\pi\)
0.667278 + 0.744809i \(0.267459\pi\)
\(734\) 10.3338 0.381427
\(735\) −3.97744 9.32187i −0.146710 0.343842i
\(736\) −7.02699 −0.259018
\(737\) 11.0022 6.35213i 0.405271 0.233984i
\(738\) 1.03253 2.28532i 0.0380081 0.0841238i
\(739\) −19.4856 + 33.7501i −0.716790 + 1.24152i 0.245476 + 0.969403i \(0.421056\pi\)
−0.962265 + 0.272113i \(0.912277\pi\)
\(740\) −1.47231 2.55012i −0.0541233 0.0937443i
\(741\) 12.2346 13.5132i 0.449448 0.496420i
\(742\) −11.9667 18.6888i −0.439311 0.686088i
\(743\) 6.23560i 0.228762i −0.993437 0.114381i \(-0.963512\pi\)
0.993437 0.114381i \(-0.0364884\pi\)
\(744\) −9.48951 2.04425i −0.347902 0.0749459i
\(745\) 3.51694 + 2.03051i 0.128851 + 0.0743920i
\(746\) 12.1077 + 6.99037i 0.443293 + 0.255936i
\(747\) 8.32289 5.97752i 0.304519 0.218706i
\(748\) 2.13127i 0.0779268i
\(749\) −8.75245 4.53065i −0.319808 0.165546i
\(750\) −9.98306 9.03845i −0.364530 0.330037i
\(751\) 10.7770 + 18.6663i 0.393257 + 0.681142i 0.992877 0.119143i \(-0.0380148\pi\)
−0.599620 + 0.800285i \(0.704681\pi\)
\(752\) −5.84290 + 10.1202i −0.213069 + 0.369045i
\(753\) 10.7186 + 33.2985i 0.390606 + 1.21347i
\(754\) −24.2780 + 14.0169i −0.884151 + 0.510465i
\(755\) −14.1332 −0.514358
\(756\) −11.4189 7.65559i −0.415302 0.278431i
\(757\) −33.0536 −1.20135 −0.600676 0.799492i \(-0.705102\pi\)
−0.600676 + 0.799492i \(0.705102\pi\)
\(758\) 2.08168 1.20186i 0.0756100 0.0436535i
\(759\) 3.72934 + 11.5857i 0.135367 + 0.420533i
\(760\) −1.13860 + 1.97212i −0.0413014 + 0.0715362i
\(761\) −14.3382 24.8345i −0.519759 0.900249i −0.999736 0.0229682i \(-0.992688\pi\)
0.479977 0.877281i \(-0.340645\pi\)
\(762\) −13.3952 12.1277i −0.485257 0.439341i
\(763\) 47.6331 2.18962i 1.72443 0.0792696i
\(764\) 8.89570i 0.321835i
\(765\) −4.34109 + 3.11778i −0.156953 + 0.112724i
\(766\) 19.8189 + 11.4425i 0.716088 + 0.413433i
\(767\) −24.1493 13.9426i −0.871979 0.503437i
\(768\) 1.69321 + 0.364755i 0.0610984 + 0.0131620i
\(769\) 41.1250i 1.48301i −0.670950 0.741503i \(-0.734114\pi\)
0.670950 0.741503i \(-0.265886\pi\)
\(770\) 1.01670 1.96408i 0.0366392 0.0707807i
\(771\) 32.9446 36.3877i 1.18647 1.31047i
\(772\) −3.07676 5.32910i −0.110735 0.191798i
\(773\) −4.24621 + 7.35464i −0.152725 + 0.264528i −0.932228 0.361870i \(-0.882138\pi\)
0.779503 + 0.626398i \(0.215472\pi\)
\(774\) −12.1679 + 26.9313i −0.437366 + 0.968027i
\(775\) −20.8765 + 12.0531i −0.749906 + 0.432959i
\(776\) 9.84612 0.353455
\(777\) −15.9202 2.67128i −0.571132 0.0958316i
\(778\) −17.7054 −0.634768
\(779\) −1.97212 + 1.13860i −0.0706584 + 0.0407946i
\(780\) 5.32446 1.71390i 0.190646 0.0613676i
\(781\) 1.33224 2.30750i 0.0476712 0.0825690i
\(782\) 7.48819 + 12.9699i 0.267777 + 0.463804i
\(783\) −22.4127 + 30.3211i −0.800964 + 1.08359i
\(784\) 6.97048 0.642202i 0.248946 0.0229358i
\(785\) 3.17148i 0.113195i
\(786\) −3.79541 + 17.6185i −0.135378 + 0.628430i
\(787\) −39.8454 23.0048i −1.42034 0.820032i −0.424009 0.905658i \(-0.639378\pi\)
−0.996327 + 0.0856262i \(0.972711\pi\)
\(788\) −16.8651 9.73707i −0.600795 0.346869i
\(789\) −6.98157 + 32.4087i −0.248550 + 1.15378i
\(790\) 4.69906i 0.167185i
\(791\) −31.1433 + 19.9415i −1.10733 + 0.709037i
\(792\) −0.297229 2.98524i −0.0105616 0.106076i
\(793\) 5.16705 + 8.94959i 0.183487 + 0.317809i
\(794\) 17.9405 31.0739i 0.636685 1.10277i
\(795\) 11.5600 3.72107i 0.409990 0.131973i
\(796\) −11.4944 + 6.63628i −0.407407 + 0.235217i
\(797\) −29.2744 −1.03695 −0.518476 0.855092i \(-0.673500\pi\)
−0.518476 + 0.855092i \(0.673500\pi\)
\(798\) 4.36682 + 11.6952i 0.154584 + 0.414005i
\(799\) 24.9055 0.881095
\(800\) 3.72499 2.15062i 0.131698 0.0760359i
\(801\) −1.94518 0.878857i −0.0687297 0.0310529i
\(802\) −12.9708 + 22.4661i −0.458016 + 0.793307i
\(803\) 6.21158 + 10.7588i 0.219202 + 0.379669i
\(804\) −14.7686 + 16.3121i −0.520848 + 0.575282i
\(805\) −0.713646 15.5247i −0.0251527 0.547173i
\(806\) 21.6518i 0.762652i
\(807\) 14.3731 + 3.09629i 0.505958 + 0.108995i
\(808\) 5.74529 + 3.31704i 0.202118 + 0.116693i
\(809\) 37.5875 + 21.7011i 1.32151 + 0.762972i 0.983969 0.178341i \(-0.0570729\pi\)
0.337537 + 0.941312i \(0.390406\pi\)
\(810\) 5.64571 4.97246i 0.198370 0.174714i
\(811\) 3.75467i 0.131844i 0.997825 + 0.0659221i \(0.0209989\pi\)
−0.997825 + 0.0659221i \(0.979001\pi\)
\(812\) −0.881601 19.1784i −0.0309381 0.673029i
\(813\) −19.7291 17.8623i −0.691928 0.626457i
\(814\) −1.76131 3.05069i −0.0617340 0.106926i
\(815\) 2.61033 4.52122i 0.0914358 0.158371i
\(816\) −1.13110 3.51390i −0.0395964 0.123011i
\(817\) 23.2404 13.4178i 0.813078 0.469431i
\(818\) −9.87793 −0.345374
\(819\) 11.3290 28.4946i 0.395869 0.995682i
\(820\) −0.698757 −0.0244017
\(821\) 35.4502 20.4672i 1.23722 0.714310i 0.268696 0.963225i \(-0.413407\pi\)
0.968525 + 0.248915i \(0.0800741\pi\)
\(822\) 3.44348 + 10.6976i 0.120105 + 0.373121i
\(823\) 14.6468 25.3690i 0.510556 0.884309i −0.489369 0.872077i \(-0.662773\pi\)
0.999925 0.0122325i \(-0.00389383\pi\)
\(824\) 7.62843 + 13.2128i 0.265749 + 0.460291i
\(825\) −5.52273 5.00016i −0.192277 0.174083i
\(826\) 16.0825 10.2978i 0.559580 0.358306i
\(827\) 41.9854i 1.45998i 0.683460 + 0.729988i \(0.260474\pi\)
−0.683460 + 0.729988i \(0.739526\pi\)
\(828\) −12.2974 17.1225i −0.427365 0.595048i
\(829\) −33.3726 19.2677i −1.15908 0.669195i −0.207996 0.978130i \(-0.566694\pi\)
−0.951083 + 0.308935i \(0.900027\pi\)
\(830\) −2.47269 1.42761i −0.0858283 0.0495530i
\(831\) −34.3749 7.40513i −1.19245 0.256881i
\(832\) 3.86332i 0.133936i
\(833\) −8.61331 12.1813i −0.298433 0.422056i
\(834\) 17.4865 19.3140i 0.605508 0.668790i
\(835\) −1.41187 2.44543i −0.0488597 0.0846275i
\(836\) −1.36210 + 2.35922i −0.0471092 + 0.0815955i
\(837\) −11.6257 26.7004i −0.401844 0.922900i
\(838\) −6.18526 + 3.57106i −0.213666 + 0.123360i
\(839\) 19.4169 0.670345 0.335172 0.942157i \(-0.391205\pi\)
0.335172 + 0.942157i \(0.391205\pi\)
\(840\) −0.633892 + 3.77784i −0.0218714 + 0.130348i
\(841\) −23.6553 −0.815701
\(842\) −2.45312 + 1.41631i −0.0845401 + 0.0488092i
\(843\) 19.3429 6.22635i 0.666206 0.214447i
\(844\) −8.40427 + 14.5566i −0.289287 + 0.501060i
\(845\) 0.804663 + 1.39372i 0.0276812 + 0.0479453i
\(846\) −34.8849 + 3.47336i −1.19937 + 0.119417i
\(847\) 1.21626 2.34962i 0.0417913 0.0807338i
\(848\) 8.38769i 0.288034i
\(849\) 5.20250 24.1503i 0.178549 0.828835i
\(850\) −7.93894 4.58355i −0.272303 0.157214i
\(851\) −21.4371 12.3767i −0.734855 0.424269i
\(852\) −0.971880 + 4.51151i −0.0332961 + 0.154562i
\(853\) 44.3922i 1.51996i 0.649946 + 0.759980i \(0.274791\pi\)
−0.649946 + 0.759980i \(0.725209\pi\)
\(854\) −7.06973 + 0.324985i −0.241921 + 0.0111207i
\(855\) −6.79800 + 0.676851i −0.232487 + 0.0231478i
\(856\) 1.86253 + 3.22599i 0.0636599 + 0.110262i
\(857\) −19.3914 + 33.5868i −0.662396 + 1.14730i 0.317588 + 0.948229i \(0.397127\pi\)
−0.979984 + 0.199075i \(0.936206\pi\)
\(858\) 6.36960 2.05033i 0.217455 0.0699971i
\(859\) 23.2887 13.4458i 0.794601 0.458763i −0.0469785 0.998896i \(-0.514959\pi\)
0.841580 + 0.540133i \(0.181626\pi\)
\(860\) 8.23450 0.280794
\(861\) −2.43789 + 2.95476i −0.0830830 + 0.100698i
\(862\) −25.5110 −0.868907
\(863\) −25.5304 + 14.7400i −0.869063 + 0.501754i −0.867037 0.498244i \(-0.833978\pi\)
−0.00202656 + 0.999998i \(0.500645\pi\)
\(864\) 2.07437 + 4.76414i 0.0705715 + 0.162079i
\(865\) −4.25696 + 7.37326i −0.144741 + 0.250698i
\(866\) −8.80427 15.2494i −0.299181 0.518197i
\(867\) 14.4820 15.9955i 0.491833 0.543235i
\(868\) 13.1683 + 6.81650i 0.446962 + 0.231367i
\(869\) 5.62145i 0.190694i
\(870\) 10.2706 + 2.21251i 0.348205 + 0.0750111i
\(871\) −42.5050 24.5403i −1.44023 0.831516i
\(872\) −15.6081 9.01132i −0.528556 0.305162i
\(873\) 17.2310 + 23.9918i 0.583180 + 0.812000i
\(874\) 19.1429i 0.647518i
\(875\) 11.0927 + 17.3238i 0.375000 + 0.585652i
\(876\) −15.9511 14.4418i −0.538939 0.487944i
\(877\) −6.00638 10.4034i −0.202821 0.351296i 0.746615 0.665256i \(-0.231678\pi\)
−0.949436 + 0.313960i \(0.898344\pi\)
\(878\) −11.7710 + 20.3880i −0.397253 + 0.688063i
\(879\) 3.42517 + 10.6407i 0.115528 + 0.358902i
\(880\) −0.723925 + 0.417958i −0.0244035 + 0.0140894i
\(881\) 15.9253 0.536538 0.268269 0.963344i \(-0.413548\pi\)
0.268269 + 0.963344i \(0.413548\pi\)
\(882\) 13.7634 + 15.8609i 0.463437 + 0.534066i
\(883\) 29.0733 0.978396 0.489198 0.872173i \(-0.337290\pi\)
0.489198 + 0.872173i \(0.337290\pi\)
\(884\) 7.13065 4.11688i 0.239830 0.138466i
\(885\) 3.20213 + 9.94782i 0.107638 + 0.334392i
\(886\) 5.12033 8.86868i 0.172021 0.297949i
\(887\) −2.94979 5.10919i −0.0990443 0.171550i 0.812245 0.583316i \(-0.198245\pi\)
−0.911289 + 0.411767i \(0.864912\pi\)
\(888\) 4.52300 + 4.09502i 0.151782 + 0.137420i
\(889\) 14.8840 + 23.2450i 0.499195 + 0.779611i
\(890\) 0.594758i 0.0199363i
\(891\) 6.75391 5.94850i 0.226264 0.199282i
\(892\) 5.19292 + 2.99814i 0.173872 + 0.100385i
\(893\) 27.5694 + 15.9172i 0.922575 + 0.532649i
\(894\) −8.22586 1.77203i −0.275114 0.0592657i
\(895\) 15.9306i 0.532502i
\(896\) −2.34962 1.21626i −0.0784952 0.0406325i
\(897\) 31.5587 34.8569i 1.05371 1.16384i
\(898\) 8.71024 + 15.0866i 0.290664 + 0.503445i
\(899\) 20.3341 35.2197i 0.678179 1.17464i
\(900\) 11.7592 + 5.31295i 0.391973 + 0.177098i
\(901\) 15.4814 8.93820i 0.515761 0.297775i
\(902\) −0.835917 −0.0278330
\(903\) 28.7293 34.8203i 0.956050 1.15875i
\(904\) 13.9774 0.464881
\(905\) −15.4918 + 8.94418i −0.514964 + 0.297315i
\(906\) 27.8758 8.97303i 0.926112 0.298109i
\(907\) 9.72266 16.8401i 0.322836 0.559168i −0.658236 0.752811i \(-0.728697\pi\)
0.981072 + 0.193644i \(0.0620306\pi\)
\(908\) 3.71163 + 6.42873i 0.123175 + 0.213345i
\(909\) 1.97184 + 19.8043i 0.0654019 + 0.656868i
\(910\) −8.53521 + 0.392351i −0.282939 + 0.0130063i
\(911\) 14.8351i 0.491510i −0.969332 0.245755i \(-0.920964\pi\)
0.969332 0.245755i \(-0.0790359\pi\)
\(912\) 0.993664 4.61263i 0.0329035 0.152740i
\(913\) −2.95806 1.70784i −0.0978974 0.0565211i
\(914\) 5.96396 + 3.44330i 0.197270 + 0.113894i
\(915\) 0.815598 3.78604i 0.0269628 0.125163i
\(916\) 11.6949i 0.386410i
\(917\) 12.6557 24.4486i 0.417927 0.807365i
\(918\) 6.58279 8.90555i 0.217265 0.293927i
\(919\) 18.3711 + 31.8197i 0.606007 + 1.04964i 0.991891 + 0.127088i \(0.0405630\pi\)
−0.385884 + 0.922547i \(0.626104\pi\)
\(920\) −2.93699 + 5.08701i −0.0968297 + 0.167714i
\(921\) 19.1859 6.17579i 0.632196 0.203499i
\(922\) −5.73523 + 3.31124i −0.188880 + 0.109050i
\(923\) −10.2937 −0.338822
\(924\) −0.758320 + 4.51940i −0.0249469 + 0.148677i
\(925\) 15.1517 0.498184
\(926\) −18.5182 + 10.6915i −0.608544 + 0.351343i
\(927\) −18.8454 + 41.7108i −0.618966 + 1.36996i
\(928\) −3.62820 + 6.28423i −0.119101 + 0.206290i
\(929\) −10.2616 17.7737i −0.336674 0.583136i 0.647131 0.762379i \(-0.275969\pi\)
−0.983805 + 0.179243i \(0.942635\pi\)
\(930\) −5.44610 + 6.01528i −0.178585 + 0.197249i
\(931\) −1.74948 18.9890i −0.0573370 0.622338i
\(932\) 13.9657i 0.457462i
\(933\) −48.5169 10.4516i −1.58837 0.342171i
\(934\) 21.6284 + 12.4871i 0.707702 + 0.408592i
\(935\) 1.54288 + 0.890781i 0.0504575 + 0.0291317i
\(936\) −9.41366 + 6.76091i −0.307695 + 0.220987i
\(937\) 36.6682i 1.19790i −0.800788 0.598948i \(-0.795586\pi\)
0.800788 0.598948i \(-0.204414\pi\)
\(938\) 28.3066 18.1251i 0.924245 0.591806i
\(939\) −28.7983 26.0734i −0.939798 0.850872i
\(940\) 4.88418 + 8.45964i 0.159304 + 0.275923i
\(941\) 4.81705 8.34338i 0.157031 0.271987i −0.776765 0.629790i \(-0.783141\pi\)
0.933797 + 0.357804i \(0.116474\pi\)
\(942\) 2.01355 + 6.25534i 0.0656050 + 0.203810i
\(943\) −5.08701 + 2.93699i −0.165656 + 0.0956415i
\(944\) −7.21793 −0.234924
\(945\) −10.3147 + 5.06673i −0.335538 + 0.164821i
\(946\) 9.85086 0.320279
\(947\) −9.23315 + 5.33076i −0.300037 + 0.173227i −0.642460 0.766320i \(-0.722086\pi\)
0.342422 + 0.939546i \(0.388753\pi\)
\(948\) −2.98340 9.26829i −0.0968962 0.301020i
\(949\) 23.9973 41.5646i 0.778986 1.34924i
\(950\) −5.85872 10.1476i −0.190082 0.329232i
\(951\) −13.5244 12.2447i −0.438560 0.397063i
\(952\) 0.258934 + 5.63285i 0.00839209 + 0.182562i
\(953\) 20.5160i 0.664579i −0.943177 0.332290i \(-0.892179\pi\)
0.943177 0.332290i \(-0.107821\pi\)
\(954\) −20.4381 + 14.6787i −0.661708 + 0.475240i
\(955\) 6.43982 + 3.71803i 0.208388 + 0.120313i
\(956\) −8.01372 4.62673i −0.259182 0.149639i
\(957\) 12.2866 + 2.64681i 0.397169 + 0.0855591i
\(958\) 28.9996i 0.936933i
\(959\) −0.788288 17.1484i −0.0254551 0.553752i
\(960\) 0.971746 1.07330i 0.0313630 0.0346407i
\(961\) 0.204948 + 0.354981i 0.00661124 + 0.0114510i
\(962\) −6.80452 + 11.7858i −0.219386 + 0.379988i
\(963\) −4.60123 + 10.1840i −0.148273 + 0.328173i
\(964\) −4.12181 + 2.37973i −0.132754 + 0.0766458i
\(965\) −5.14382 −0.165586
\(966\) 11.2641 + 30.1674i 0.362416 + 0.970619i
\(967\) 38.6686 1.24350 0.621749 0.783217i \(-0.286423\pi\)
0.621749 + 0.783217i \(0.286423\pi\)
\(968\) −0.866025 + 0.500000i −0.0278351 + 0.0160706i
\(969\) −9.57256 + 3.08134i −0.307515 + 0.0989869i
\(970\) 4.11527 7.12785i 0.132133 0.228862i
\(971\) 24.3770 + 42.2221i 0.782294 + 1.35497i 0.930602 + 0.366032i \(0.119284\pi\)
−0.148309 + 0.988941i \(0.547383\pi\)
\(972\) −7.97846 + 13.3919i −0.255909 + 0.429547i
\(973\) −33.5160 + 21.4607i −1.07448 + 0.688000i
\(974\) 15.6226i 0.500580i
\(975\) −6.06116 + 28.1362i −0.194112 + 0.901078i
\(976\) 2.31656 + 1.33746i 0.0741511 + 0.0428112i
\(977\) 14.6963 + 8.48489i 0.470175 + 0.271456i 0.716313 0.697779i \(-0.245828\pi\)
−0.246138 + 0.969235i \(0.579162\pi\)
\(978\) −2.27805 + 10.5748i −0.0728440 + 0.338145i
\(979\) 0.711503i 0.0227397i
\(980\) 2.44846 5.31452i 0.0782133 0.169766i
\(981\) −5.35686 53.8019i −0.171031 1.71776i
\(982\) 16.2643 + 28.1705i 0.519014 + 0.898958i
\(983\) −11.3004 + 19.5728i −0.360426 + 0.624276i −0.988031 0.154256i \(-0.950702\pi\)
0.627605 + 0.778532i \(0.284035\pi\)
\(984\) 1.37821 0.443635i 0.0439357 0.0141426i
\(985\) −14.0978 + 8.13939i −0.449194 + 0.259342i
\(986\) 15.4653 0.492516
\(987\) 52.8127 + 8.86157i 1.68105 + 0.282067i
\(988\) 10.5244 0.334827
\(989\) 59.9479 34.6109i 1.90623 1.10056i
\(990\) −2.28532 1.03253i −0.0726322 0.0328161i
\(991\) 3.09848 5.36672i 0.0984264 0.170479i −0.812607 0.582812i \(-0.801952\pi\)
0.911033 + 0.412332i \(0.135286\pi\)
\(992\) −2.80223 4.85360i −0.0889708 0.154102i
\(993\) 35.9546 39.7122i 1.14098 1.26023i
\(994\) 3.24071 6.26050i 0.102789 0.198571i
\(995\) 11.0948i 0.351727i
\(996\) 5.78344 + 1.24588i 0.183255 + 0.0394773i
\(997\) −36.9714 21.3455i −1.17090 0.676017i −0.217005 0.976170i \(-0.569629\pi\)
−0.953891 + 0.300153i \(0.902962\pi\)
\(998\) −13.2507 7.65028i −0.419443 0.242165i
\(999\) −2.06288 + 18.1875i −0.0652668 + 0.575427i
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 462.2.k.g.353.3 yes 20
3.2 odd 2 inner 462.2.k.g.353.6 yes 20
7.5 odd 6 inner 462.2.k.g.89.6 yes 20
21.5 even 6 inner 462.2.k.g.89.3 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.k.g.89.3 20 21.5 even 6 inner
462.2.k.g.89.6 yes 20 7.5 odd 6 inner
462.2.k.g.353.3 yes 20 1.1 even 1 trivial
462.2.k.g.353.6 yes 20 3.2 odd 2 inner