LMFDB - Embedded newform 770.2.bg.e.291.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(81,770)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("770.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bg (of order $15$, degree $8$, 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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			291.2
Character	$\chi$	$=$	770.291
Dual form			770.2.bg.e.471.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.669131 + 0.743145i) q^{2} +(-1.49289 + 0.664675i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-0.978148 + 0.207912i) q^{5} +(0.504985 - 1.55418i) q^{6} +(-1.80895 - 1.93072i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.220478 + 0.244866i) q^{9} +O(q^{10})$	\(q+(-0.669131 + 0.743145i) q^{2} +(-1.49289 + 0.664675i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-0.978148 + 0.207912i) q^{5} +(0.504985 - 1.55418i) q^{6} +(-1.80895 - 1.93072i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.220478 + 0.244866i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.50306 + 2.17593i) q^{11} +(0.817083 + 1.41523i) q^{12} +(0.697320 + 2.14613i) q^{13} +(2.64523 - 0.0524091i) q^{14} +(1.32207 - 0.960539i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-1.16784 - 1.29701i) q^{17} +(-0.0344421 - 0.327694i) q^{18} +(-0.0900475 + 0.856745i) q^{19} +(0.309017 + 0.951057i) q^{20} +(3.98386 + 1.67998i) q^{21} +(0.0578470 - 3.31612i) q^{22} +(-3.64953 - 6.32117i) q^{23} +(-1.59846 - 0.339762i) q^{24} +(0.913545 - 0.406737i) q^{25} +(-2.06148 - 0.917831i) q^{26} +(1.68135 - 5.17466i) q^{27} +(-1.73106 + 2.00086i) q^{28} +(7.84526 - 5.69991i) q^{29} +(-0.170817 + 1.62521i) q^{30} +(7.75492 + 1.64836i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.29050 - 4.91214i) q^{33} +1.74531 q^{34} +(2.17084 + 1.51243i) q^{35} +(0.266571 + 0.193675i) q^{36} +(7.73856 + 3.44543i) q^{37} +(-0.576432 - 0.640193i) q^{38} +(-2.46750 - 2.74043i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(-0.0621780 - 0.0451750i) q^{41} +(-3.91419 + 1.83646i) q^{42} -2.40375 q^{43} +(2.42565 + 2.26191i) q^{44} +(0.164750 - 0.285355i) q^{45} +(7.13956 + 1.51756i) q^{46} +(-0.177632 + 1.69005i) q^{47} +(1.32207 - 0.960539i) q^{48} +(-0.455376 + 6.98517i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(2.60554 + 1.16006i) q^{51} +(2.06148 - 0.917831i) q^{52} +(-11.5974 - 2.46511i) q^{53} +(2.72048 + 4.71201i) q^{54} +(1.99597 - 2.64880i) q^{55} +(-0.328624 - 2.62526i) q^{56} +(-0.435027 - 1.33887i) q^{57} +(-1.01364 + 9.64415i) q^{58} +(0.964723 + 9.17873i) q^{59} +(-1.09347 - 1.21442i) q^{60} +(12.9911 - 2.76135i) q^{61} +(-6.41402 + 4.66006i) q^{62} +(0.871602 - 0.0172687i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.12829 - 1.95425i) q^{65} +(2.11778 + 4.98904i) q^{66} +(7.27196 - 12.5954i) q^{67} +(-1.16784 + 1.29701i) q^{68} +(9.64985 + 7.01103i) q^{69} +(-2.57653 + 0.601238i) q^{70} +(1.84033 - 5.66396i) q^{71} +(-0.322299 + 0.0685068i) q^{72} +(0.825921 + 7.85811i) q^{73} +(-7.73856 + 3.44543i) q^{74} +(-1.09347 + 1.21442i) q^{75} +0.861464 q^{76} +(8.72904 + 0.896569i) q^{77} +3.68762 q^{78} +(4.13263 - 4.58975i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.826081 + 7.85964i) q^{81} +(0.0751768 - 0.0159793i) q^{82} +(0.146308 - 0.450288i) q^{83} +(1.25435 - 4.13765i) q^{84} +(1.41198 + 1.02586i) q^{85} +(1.60842 - 1.78633i) q^{86} +(-7.92348 + 13.7239i) q^{87} +(-3.30400 + 0.289099i) q^{88} +(-6.01497 - 10.4182i) q^{89} +(0.101821 + 0.313372i) q^{90} +(2.88216 - 5.22858i) q^{91} +(-5.90506 + 4.29028i) q^{92} +(-12.6728 + 2.69369i) q^{93} +(-1.13710 - 1.26287i) q^{94} +(-0.0900475 - 0.856745i) q^{95} +(-0.170817 + 1.62521i) q^{96} +(0.790112 + 2.43172i) q^{97} +(-4.88629 - 5.01240i) q^{98} +(0.0190606 - 1.09266i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} + 2 q^{7} + 18 q^{8} + 22 q^{9}+O(q^{10}) $ 72 * q - 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 + 2 * q^7 + 18 * q^8 + 22 * q^9	\( 72 q - 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} + 2 q^{7} + 18 q^{8} + 22 q^{9} + 36 q^{10} - 2 q^{12} + 28 q^{13} - 2 q^{14} - 6 q^{15} + 9 q^{16} - 4 q^{17} - 7 q^{18} - q^{19} - 18 q^{20} - 32 q^{21} - 20 q^{22} - 30 q^{23} + 2 q^{24} + 9 q^{25} - 11 q^{26} + 18 q^{27} + 6 q^{28} + 22 q^{29} - 3 q^{30} - 8 q^{31} + 36 q^{32} - 24 q^{33} + 32 q^{34} - 3 q^{35} - 14 q^{36} + 20 q^{37} - 4 q^{38} - 25 q^{39} - 9 q^{40} + 34 q^{41} + 22 q^{42} + 12 q^{43} - 58 q^{45} - 20 q^{46} - 13 q^{47} - 6 q^{48} + 6 q^{49} + 18 q^{50} - 37 q^{51} + 11 q^{52} + 2 q^{53} + 14 q^{54} - 10 q^{55} - 2 q^{56} - 18 q^{57} + 11 q^{58} + 29 q^{59} - 2 q^{60} + 21 q^{61} + 44 q^{62} + 31 q^{63} - 18 q^{64} + 6 q^{65} - q^{66} - 20 q^{67} - 4 q^{68} - 104 q^{69} + 4 q^{70} - 70 q^{71} - 22 q^{72} - 28 q^{73} - 20 q^{74} - 2 q^{75} + 12 q^{76} - 47 q^{77} + 20 q^{78} - 24 q^{79} + 9 q^{80} + 44 q^{81} - 28 q^{82} - 56 q^{83} - 46 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} - 5 q^{88} - 20 q^{89} + 44 q^{90} - 36 q^{91} + 10 q^{92} + 77 q^{93} - 22 q^{94} - q^{95} - 3 q^{96} - 178 q^{97} - 68 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q - 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 + 2 * q^7 + 18 * q^8 + 22 * q^9 + 36 * q^10 - 2 * q^12 + 28 * q^13 - 2 * q^14 - 6 * q^15 + 9 * q^16 - 4 * q^17 - 7 * q^18 - q^19 - 18 * q^20 - 32 * q^21 - 20 * q^22 - 30 * q^23 + 2 * q^24 + 9 * q^25 - 11 * q^26 + 18 * q^27 + 6 * q^28 + 22 * q^29 - 3 * q^30 - 8 * q^31 + 36 * q^32 - 24 * q^33 + 32 * q^34 - 3 * q^35 - 14 * q^36 + 20 * q^37 - 4 * q^38 - 25 * q^39 - 9 * q^40 + 34 * q^41 + 22 * q^42 + 12 * q^43 - 58 * q^45 - 20 * q^46 - 13 * q^47 - 6 * q^48 + 6 * q^49 + 18 * q^50 - 37 * q^51 + 11 * q^52 + 2 * q^53 + 14 * q^54 - 10 * q^55 - 2 * q^56 - 18 * q^57 + 11 * q^58 + 29 * q^59 - 2 * q^60 + 21 * q^61 + 44 * q^62 + 31 * q^63 - 18 * q^64 + 6 * q^65 - q^66 - 20 * q^67 - 4 * q^68 - 104 * q^69 + 4 * q^70 - 70 * q^71 - 22 * q^72 - 28 * q^73 - 20 * q^74 - 2 * q^75 + 12 * q^76 - 47 * q^77 + 20 * q^78 - 24 * q^79 + 9 * q^80 + 44 * q^81 - 28 * q^82 - 56 * q^83 - 46 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 - 5 * q^88 - 20 * q^89 + 44 * q^90 - 36 * q^91 + 10 * q^92 + 77 * q^93 - 22 * q^94 - q^95 - 3 * q^96 - 178 * q^97 - 68 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$2$	−0.669131	+	0.743145i	−0.473147	+	0.525483i
$3$	−1.49289	+	0.664675i	−0.861918	+	0.383751i	−0.789593	−	0.613631i	$-0.789708\pi$
$3$	−1.49289	+	0.664675i	−0.861918	+	0.383751i	−0.0723246	+	0.997381i	$0.523042\pi$
$4$	−0.104528	−	0.994522i	−0.0522642	−	0.497261i
$5$	−0.978148	+	0.207912i	−0.437441	+	0.0929809i
$5$	−0.978148	+	0.207912i	−0.437441	+	0.0929809i
$6$	0.504985	−	1.55418i	0.206159	−	0.634493i
$7$	−1.80895	−	1.93072i	−0.683720	−	0.729744i
$7$	−1.80895	−	1.93072i	−0.683720	−	0.729744i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.220478	+	0.244866i	−0.0734927	+	0.0816219i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−2.50306	+	2.17593i	−0.754702	+	0.656067i
$11$	−2.50306	+	2.17593i	−0.754702	+	0.656067i
$12$	0.817083	+	1.41523i	0.235872	+	0.408542i
$13$	0.697320	+	2.14613i	0.193402	+	0.595229i	0.999992	+	0.00411770i	$0.00131071\pi$
$13$	0.697320	+	2.14613i	0.193402	+	0.595229i	−0.806590	+	0.591112i	$0.798689\pi$
$14$	2.64523	−	0.0524091i	0.706968	−	0.0140069i
$15$	1.32207	−	0.960539i	0.341357	−	0.248010i
$16$	−0.978148	+	0.207912i	−0.244537	+	0.0519779i
$17$	−1.16784	−	1.29701i	−0.283242	−	0.314572i	0.584688	−	0.811258i	$-0.301217\pi$
$17$	−1.16784	−	1.29701i	−0.283242	−	0.314572i	−0.867930	+	0.496686i	$0.834550\pi$
$18$	−0.0344421	−	0.327694i	−0.00811807	−	0.0772383i
$19$	−0.0900475	+	0.856745i	−0.0206583	+	0.196551i	−0.999984	−	0.00574149i	$-0.998172\pi$
$19$	−0.0900475	+	0.856745i	−0.0206583	+	0.196551i	0.979325	+	0.202292i	$0.0648391\pi$
$20$	0.309017	+	0.951057i	0.0690983	+	0.212663i
$21$	3.98386	+	1.67998i	0.869350	+	0.366602i
$22$	0.0578470	−	3.31612i	0.0123330	−	0.706999i
$23$	−3.64953	−	6.32117i	−0.760979	−	1.31805i	−0.942346	−	0.334639i	$-0.891386\pi$
$23$	−3.64953	−	6.32117i	−0.760979	−	1.31805i	0.181367	−	0.983415i	$-0.441948\pi$
$24$	−1.59846	−	0.339762i	−0.326284	−	0.0693537i
$25$	0.913545	−	0.406737i	0.182709	−	0.0813473i
$26$	−2.06148	−	0.917831i	−0.404290	−	0.180002i
$27$	1.68135	−	5.17466i	0.323576	−	0.995863i
$28$	−1.73106	+	2.00086i	−0.327139	+	0.378127i
$29$	7.84526	−	5.69991i	1.45683	−	1.05845i	0.472652	−	0.881249i	$-0.343297\pi$
$29$	7.84526	−	5.69991i	1.45683	−	1.05845i	0.984175	−	0.177198i	$-0.0567033\pi$
$30$	−0.170817	+	1.62521i	−0.0311868	+	0.296722i
$31$	7.75492	+	1.64836i	1.39282	+	0.296054i	0.842410	−	0.538837i	$-0.181136\pi$
$31$	7.75492	+	1.64836i	1.39282	+	0.296054i	0.550415	+	0.834891i	$0.314470\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.29050	−	4.91214i	0.398725	−	0.855094i
$34$	1.74531			0.299317
$35$	2.17084	+	1.51243i	0.366939	+	0.255647i
$36$	0.266571	+	0.193675i	0.0444284	+	0.0322791i
$37$	7.73856	+	3.44543i	1.27221	+	0.566425i	0.928040	−	0.372481i	$-0.121493\pi$
$37$	7.73856	+	3.44543i	1.27221	+	0.566425i	0.344172	+	0.938907i	$0.388160\pi$
$38$	−0.576432	−	0.640193i	−0.0935096	−	0.103853i
$39$	−2.46750	−	2.74043i	−0.395116	−	0.438821i
$40$	−0.913545	−	0.406737i	−0.144444	−	0.0643107i
$41$	−0.0621780	−	0.0451750i	−0.00971058	−	0.00705515i	0.582919	−	0.812530i	$-0.301910\pi$
$41$	−0.0621780	−	0.0451750i	−0.00971058	−	0.00705515i	−0.592630	+	0.805475i	$0.701910\pi$
$42$	−3.91419	+	1.83646i	−0.603973	+	0.283372i
$43$	−2.40375			−0.366568			−0.183284	−	0.983060i	$-0.558673\pi$
$43$	−2.40375			−0.366568			−0.183284	+	0.983060i	$0.558673\pi$
$44$	2.42565	+	2.26191i	0.365681	+	0.340995i
$45$	0.164750	−	0.285355i	0.0245594	−	0.0425382i
$46$	7.13956	+	1.51756i	1.05267	+	0.223752i
$47$	−0.177632	+	1.69005i	−0.0259103	+	0.246520i	0.973899	+	0.226982i	$0.0728860\pi$
$47$	−0.177632	+	1.69005i	−0.0259103	+	0.246520i	−0.999809	+	0.0195373i	$0.993781\pi$
$48$	1.32207	−	0.960539i	0.190824	−	0.138642i
$49$	−0.455376	+	6.98517i	−0.0650537	+	0.997882i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	2.60554	+	1.16006i	0.364849	+	0.162441i
$52$	2.06148	−	0.917831i	0.285876	−	0.127280i
$53$	−11.5974	−	2.46511i	−1.59303	−	0.338609i	−0.675837	−	0.737051i	$-0.736218\pi$
$53$	−11.5974	−	2.46511i	−1.59303	−	0.338609i	−0.917193	+	0.398442i	$0.869551\pi$
$54$	2.72048	+	4.71201i	0.370210	+	0.641223i
$55$	1.99597	−	2.64880i	0.269136	−	0.357164i
$56$	−0.328624	−	2.62526i	−0.0439142	−	0.350816i
$57$	−0.435027	−	1.33887i	−0.0576207	−	0.177338i
$58$	−1.01364	+	9.64415i	−0.133098	+	1.26634i
$59$	0.964723	+	9.17873i	0.125596	+	1.19497i	0.857837	+	0.513922i	$0.171808\pi$
$59$	0.964723	+	9.17873i	0.125596	+	1.19497i	−0.732240	+	0.681046i	$0.761525\pi$
$60$	−1.09347	−	1.21442i	−0.141166	−	0.156781i
$61$	12.9911	−	2.76135i	1.66335	−	0.353555i	0.722233	−	0.691650i	$-0.243116\pi$
$61$	12.9911	−	2.76135i	1.66335	−	0.353555i	0.941112	+	0.338095i	$0.109782\pi$
$62$	−6.41402	+	4.66006i	−0.814582	+	0.591828i
$63$	0.871602	−	0.0172687i	0.109812	−	0.00217566i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−1.12829	−	1.95425i	−0.139947	−	0.242395i
$66$	2.11778	+	4.98904i	0.260681	+	0.614108i
$67$	7.27196	−	12.5954i	0.888411	−	1.53877i	0.0466575	−	0.998911i	$-0.485143\pi$
$67$	7.27196	−	12.5954i	0.888411	−	1.53877i	0.841753	−	0.539862i	$-0.181524\pi$
$68$	−1.16784	+	1.29701i	−0.141621	+	0.157286i
$69$	9.64985	+	7.01103i	1.16171	+	0.844029i
$70$	−2.57653	+	0.601238i	−0.307954	+	0.0718617i
$71$	1.84033	−	5.66396i	0.218407	−	0.672189i	−0.780487	−	0.625172i	$-0.785029\pi$
$71$	1.84033	−	5.66396i	0.218407	−	0.672189i	0.998894	−	0.0470165i	$-0.0149713\pi$
$72$	−0.322299	+	0.0685068i	−0.0379833	+	0.00807360i
$73$	0.825921	+	7.85811i	0.0966667	+	0.919722i	0.930151	+	0.367178i	$0.119676\pi$
$73$	0.825921	+	7.85811i	0.0966667	+	0.919722i	−0.833484	+	0.552544i	$0.813657\pi$
$74$	−7.73856	+	3.44543i	−0.899590	+	0.400523i
$75$	−1.09347	+	1.21442i	−0.126263	+	0.140229i
$76$	0.861464			0.0988167
$77$	8.72904	+	0.896569i	0.994767	+	0.102173i
$78$	3.68762			0.417541
$79$	4.13263	−	4.58975i	0.464958	−	0.516388i	−0.464371	−	0.885641i	$-0.653720\pi$
$79$	4.13263	−	4.58975i	0.464958	−	0.516388i	0.929329	+	0.369253i	$0.120386\pi$
$80$	0.913545	−	0.406737i	0.102137	−	0.0454745i
$81$	0.826081	+	7.85964i	0.0917868	+	0.873293i
$82$	0.0751768	−	0.0159793i	0.00830189	−	0.00176462i
$83$	0.146308	−	0.450288i	0.0160593	−	0.0494256i	−0.942706	−	0.333625i	$-0.891728\pi$
$83$	0.146308	−	0.450288i	0.0160593	−	0.0494256i	0.958765	+	0.284200i	$0.0917279\pi$
$84$	1.25435	−	4.13765i	0.136861	−	0.451454i
$85$	1.41198	+	1.02586i	0.153151	+	0.111271i
$86$	1.60842	−	1.78633i	0.173440	−	0.192625i
$87$	−7.92348	+	13.7239i	−0.849486	+	1.47135i
$88$	−3.30400	+	0.289099i	−0.352208	+	0.0308180i
$89$	−6.01497	−	10.4182i	−0.637586	−	1.10433i	−0.985961	−	0.166976i	$-0.946600\pi$
$89$	−6.01497	−	10.4182i	−0.637586	−	1.10433i	0.348375	−	0.937355i	$-0.386733\pi$
$90$	0.101821	+	0.313372i	0.0107329	+	0.0330324i
$91$	2.88216	−	5.22858i	0.302133	−	0.548104i
$92$	−5.90506	+	4.29028i	−0.615645	+	0.447292i
$93$	−12.6728	+	2.69369i	−1.31411	+	0.279323i
$94$	−1.13710	−	1.26287i	−0.117282	−	0.130255i
$95$	−0.0900475	−	0.856745i	−0.00923868	−	0.0879002i
$96$	−0.170817	+	1.62521i	−0.0174339	+	0.165873i
$97$	0.790112	+	2.43172i	0.0802238	+	0.246903i	0.983122	−	0.182951i	$-0.0585649\pi$
$97$	0.790112	+	2.43172i	0.0802238	+	0.246903i	−0.902898	+	0.429854i	$0.858565\pi$
$98$	−4.88629	−	5.01240i	−0.493590	−	0.506329i
$99$	0.0190606	−	1.09266i	0.00191566	−	0.109816i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	16.6357	+	3.53603i	1.65531	+	0.351848i	0.938464	−	0.345378i	$-0.112249\pi$
$101$	16.6357	+	3.53603i	1.65531	+	0.351848i	0.716851	+	0.697226i	$0.245583\pi$
$102$	−2.60554	+	1.16006i	−0.257987	+	0.114863i
$103$	−11.0440	−	4.91708i	−1.08819	−	0.484495i	−0.217369	−	0.976090i	$-0.569747\pi$
$103$	−11.0440	−	4.91708i	−1.08819	−	0.484495i	−0.870824	+	0.491595i	$0.836414\pi$
$104$	−0.697320	+	2.14613i	−0.0683778	+	0.210445i
$105$	−4.24609	−	0.814977i	−0.414376	−	0.0795336i
$106$	9.59213	−	6.96909i	0.931670	−	0.676898i
$107$	1.43310	−	13.6350i	0.138543	−	1.31815i	−0.675507	−	0.737353i	$-0.736075\pi$
$107$	1.43310	−	13.6350i	0.138543	−	1.31815i	0.814050	−	0.580795i	$-0.197258\pi$
$108$	−5.32206	−	1.13124i	−0.512115	−	0.108853i
$109$	−1.71585	+	2.97194i	−0.164349	+	0.284660i	−0.936424	−	0.350871i	$-0.885886\pi$
$109$	−1.71585	+	2.97194i	−0.164349	+	0.284660i	0.772075	+	0.635531i	$0.219219\pi$
$110$	0.632877	+	3.25568i	0.0603425	+	0.310417i
$111$	−13.8429			−1.31391
$112$	2.17084	+	1.51243i	0.205125	+	0.142911i
$113$	6.38878	+	4.64172i	0.601006	+	0.436656i	0.846236	−	0.532809i	$-0.178863\pi$
$113$	6.38878	+	4.64172i	0.601006	+	0.436656i	−0.245230	+	0.969465i	$0.578863\pi$
$114$	1.28607	+	0.572594i	0.120451	+	0.0536283i
$115$	4.88402	+	5.42426i	0.455437	+	0.505815i
$116$	−6.48874	−	7.20648i	−0.602464	−	0.669104i
$117$	−0.679257	−	0.302425i	−0.0627974	−	0.0279592i
$118$	−7.46665	−	5.42484i	−0.687361	−	0.499397i
$119$	−0.391612	+	4.60101i	−0.0358990	+	0.421774i
$120$	1.63417			0.149178
$121$	1.53067	−	10.8930i	0.139152	−	0.990271i
$122$	−6.64068	+	11.5020i	−0.601219	+	1.04134i
$123$	0.122851	+	0.0261129i	0.0110771	+	0.00235452i
$124$	0.828719	−	7.88474i	0.0744212	−	0.708070i
$125$	−0.809017	+	0.587785i	−0.0723607	+	0.0525731i
$126$	−0.570382	+	0.659282i	−0.0508137	+	0.0587335i
$127$	4.22816	−	13.0130i	0.375189	−	1.15471i	−0.568162	−	0.822917i	$-0.692345\pi$
$127$	4.22816	−	13.0130i	0.375189	−	1.15471i	0.943351	−	0.331796i	$-0.107655\pi$
$128$	−0.913545	−	0.406737i	−0.0807468	−	0.0359508i
$129$	3.58852	−	1.59771i	0.315951	−	0.140671i
$130$	2.20726	+	0.469168i	0.193590	+	0.0411488i
$131$	−2.27547	−	3.94123i	−0.198809	−	0.344347i	0.749334	−	0.662192i	$-0.230374\pi$
$131$	−2.27547	−	3.94123i	−0.198809	−	0.344347i	−0.948142	+	0.317846i	$0.897041\pi$
$132$	−5.12465	−	1.76450i	−0.446044	−	0.153580i
$133$	1.81703	−	1.37595i	0.157556	−	0.119310i
$134$	4.49432	+	13.8321i	0.388250	+	1.19491i
$135$	−0.568735	+	5.41115i	−0.0489489	+	0.465718i
$136$	−0.182434	−	1.73574i	−0.0156436	−	0.148839i
$137$	−0.100323	−	0.111420i	−0.00857117	−	0.00951925i	0.738844	−	0.673877i	$-0.235372\pi$
$137$	−0.100323	−	0.111420i	−0.00857117	−	0.00951925i	−0.747415	+	0.664357i	$0.768705\pi$
$138$	−11.6672	+	2.47994i	−0.993180	+	0.211107i
$139$	−16.9869	+	12.3417i	−1.44081	+	1.04681i	−0.452938	+	0.891542i	$0.649624\pi$
$139$	−16.9869	+	12.3417i	−1.44081	+	1.04681i	−0.987872	+	0.155268i	$0.950376\pi$
$140$	1.27723	−	2.31704i	0.107946	−	0.195826i
$141$	−0.858153	−	2.64112i	−0.0722695	−	0.222423i
$142$	2.97772	+	5.15757i	0.249885	+	0.432813i
$143$	−6.41526	−	3.85458i	−0.536471	−	0.322336i
$144$	0.164750	−	0.285355i	0.0137291	−	0.0237796i
$145$	−6.48874	+	7.20648i	−0.538861	+	0.598465i
$146$	−6.39236	−	4.64432i	−0.529036	−	0.384367i
$147$	−3.96305	−	10.7307i	−0.326867	−	0.885057i
$148$	2.61766	−	8.05632i	0.215170	−	0.662225i
$149$	−10.3095	+	2.19136i	−0.844589	+	0.179523i	−0.609831	−	0.792531i	$-0.708763\pi$
$149$	−10.3095	+	2.19136i	−0.844589	+	0.179523i	−0.234757	+	0.972054i	$0.575430\pi$
$150$	−0.170817	−	1.62521i	−0.0139471	−	0.132698i
$151$	−15.4780	+	6.89127i	−1.25959	+	0.560804i	−0.924427	−	0.381358i	$-0.875457\pi$
$151$	−15.4780	+	6.89127i	−1.25959	+	0.560804i	−0.335158	+	0.942162i	$0.608790\pi$
$152$	−0.576432	+	0.640193i	−0.0467548	+	0.0519265i
$153$	0.575077			0.0464922
$154$	−6.50715	+	5.88702i	−0.524361	+	0.474390i
$155$	−7.92817			−0.636806
$156$	−2.46750	+	2.74043i	−0.197558	+	0.219410i
$157$	7.89199	−	3.51374i	0.629850	−	0.280427i	−0.0668800	−	0.997761i	$-0.521304\pi$
$157$	7.89199	−	3.51374i	0.629850	−	0.280427i	0.696730	+	0.717334i	$0.254638\pi$
$158$	0.645581	+	6.14229i	0.0513597	+	0.488654i
$159$	18.9521	−	4.02840i	1.50300	−	0.319473i
$160$	−0.309017	+	0.951057i	−0.0244299	+	0.0751876i
$161$	−5.60259	+	18.4809i	−0.441546	+	1.45650i
$162$	−6.39361	−	4.64523i	−0.502329	−	0.364964i
$163$	11.3670	−	12.6244i	0.890335	−	0.988817i	−0.109652	−	0.993970i	$-0.534974\pi$
$163$	11.3670	−	12.6244i	0.890335	−	0.988817i	0.999987	+	0.00515325i	$0.00164034\pi$
$164$	−0.0384281	+	0.0665595i	−0.00300073	+	0.00519742i
$165$	−1.21916	+	5.28102i	−0.0949114	+	0.411127i
$166$	0.236731	+	0.410029i	0.0183739	+	0.0318245i
$167$	0.800536	+	2.46380i	0.0619473	+	0.190654i	0.977241	−	0.212134i	$-0.0680412\pi$
$167$	0.800536	+	2.46380i	0.0619473	+	0.190654i	−0.915293	+	0.402788i	$0.868041\pi$
$168$	2.23555	+	3.70079i	0.172476	+	0.285522i
$169$	6.39760	−	4.64813i	0.492123	−	0.357549i
$170$	−1.70717	+	0.362869i	−0.130934	+	0.0278308i
$171$	−0.189934	−	0.210943i	−0.0145246	−	0.0161312i
$172$	0.251260	+	2.39058i	0.0191584	+	0.182280i
$173$	−0.553851	+	5.26954i	−0.0421085	+	0.400636i	0.953085	+	0.302704i	$0.0978894\pi$
$173$	−0.553851	+	5.26954i	−0.0421085	+	0.400636i	−0.995193	+	0.0979318i	$0.968777\pi$
$174$	−4.89698	−	15.0714i	−0.371239	−	1.14256i
$175$	−2.43786	−	1.02803i	−0.184285	−	0.0777121i
$176$	1.99597	−	2.64880i	0.150452	−	0.199661i
$177$	−7.54110	−	13.0616i	−0.566824	−	0.981767i
$178$	11.7671	+	2.50117i	0.881978	+	0.187470i
$179$	5.15440	−	2.29489i	0.385258	−	0.171528i	−0.204963	−	0.978770i	$-0.565707\pi$
$179$	5.15440	−	2.29489i	0.385258	−	0.171528i	0.590221	+	0.807242i	$0.299041\pi$
$180$	−0.301013	−	0.134019i	−0.0224362	−	0.00998922i
$181$	5.45092	−	16.7762i	0.405163	−	1.24696i	−0.515595	−	0.856832i	$-0.672429\pi$
$181$	5.45092	−	16.7762i	0.405163	−	1.24696i	0.920759	−	0.390132i	$-0.127571\pi$
$182$	1.95705	+	5.64047i	0.145066	+	0.418099i
$183$	−17.5589	+	12.7573i	−1.29799	+	0.943045i
$184$	0.762959	−	7.25907i	0.0562461	−	0.535146i
$185$	−8.28580	−	1.76120i	−0.609184	−	0.129486i
$186$	6.47798	−	11.2202i	0.474988	−	0.822704i
$187$	5.74538	+	0.705381i	0.420144	+	0.0515826i
$188$	1.69936			0.123939
$189$	−13.0323	+	6.11450i	−0.947961	+	0.444764i
$190$	0.696939	+	0.506356i	0.0505613	+	0.0367349i
$191$	−12.9852	−	5.78137i	−0.939573	−	0.418325i	−0.120952	−	0.992658i	$-0.538595\pi$
$191$	−12.9852	−	5.78137i	−0.939573	−	0.418325i	−0.818621	+	0.574333i	$0.805261\pi$
$192$	−1.09347	−	1.21442i	−0.0789145	−	0.0876434i
$193$	−9.97141	−	11.0744i	−0.717758	−	0.797151i	0.268339	−	0.963325i	$-0.413525\pi$
$193$	−9.97141	−	11.0744i	−0.717758	−	0.797151i	−0.986096	+	0.166174i	$0.946859\pi$
$194$	−2.33581	−	1.03997i	−0.167701	−	0.0746653i
$195$	2.98335	+	2.16753i	0.213642	+	0.155220i
$196$	6.99451	−	0.277268i	0.499608	−	0.0198049i
$197$	6.17801			0.440165			0.220082	−	0.975481i	$-0.429367\pi$
$197$	6.17801			0.440165			0.220082	+	0.975481i	$0.429367\pi$
$198$	0.799250	+	0.745296i	0.0568002	+	0.0529659i
$199$	1.19146	−	2.06367i	0.0844606	−	0.146290i	−0.820701	−	0.571358i	$-0.806417\pi$
$199$	1.19146	−	2.06367i	0.0844606	−	0.146290i	0.905161	+	0.425068i	$0.139750\pi$
$200$	0.978148	+	0.207912i	0.0691655	+	0.0147016i
$201$	−2.48435	+	23.6370i	−0.175232	+	1.66722i
$202$	−13.7592	+	9.99667i	−0.968097	+	0.703364i
$203$	−25.1966	−	4.83613i	−1.76846	−	0.339430i
$204$	0.881353	−	2.71253i	0.0617071	−	0.189915i
$205$	0.0702117	+	0.0312603i	0.00490380	+	0.00218331i
$206$	11.0440	−	4.91708i	0.769468	−	0.342589i
$207$	2.35248	+	0.500035i	0.163509	+	0.0347548i
$208$	−1.12829	−	1.95425i	−0.0782326	−	0.135503i
$209$	−1.63882	−	2.34042i	−0.113360	−	0.161891i
$210$	3.44684	−	2.61014i	0.237854	−	0.180117i
$211$	−3.32957	−	10.2474i	−0.229217	−	0.705457i	−0.997836	−	0.0657506i	$-0.979056\pi$
$211$	−3.32957	−	10.2474i	−0.229217	−	0.705457i	0.768619	−	0.639707i	$-0.220944\pi$
$212$	−1.23934	+	11.7916i	−0.0851185	+	0.809849i
$213$	1.01729	+	9.67887i	0.0697036	+	0.663185i
$214$	9.17387	+	10.1886i	0.627113	+	0.696479i
$215$	2.35122	−	0.499767i	0.160352	−	0.0340838i
$216$	4.40183	−	3.19811i	0.299506	−	0.217604i
$217$	−10.8458	−	17.9544i	−0.736259	−	1.21882i
$218$	−1.06045	−	3.26374i	−0.0718231	−	0.221049i
$219$	−6.45610	−	11.1823i	−0.436263	−	0.755629i
$220$	−2.84292	−	1.70816i	−0.191670	−	0.115164i
$221$	1.96921	−	3.41076i	0.132463	−	0.229433i
$222$	9.26270	−	10.2873i	0.621671	−	0.690436i
$223$	−0.215707	−	0.156720i	−0.0144448	−	0.0104948i	0.580539	−	0.814232i	$-0.302842\pi$
$223$	−0.215707	−	0.156720i	−0.0144448	−	0.0104948i	−0.594984	+	0.803737i	$0.702842\pi$
$224$	−2.57653	+	0.601238i	−0.172152	+	0.0401719i
$225$	−0.101821	+	0.313372i	−0.00678806	+	0.0208915i
$226$	−7.72440	+	1.64187i	−0.513819	+	0.109216i
$227$	0.534579	+	5.08618i	0.0354812	+	0.337581i	0.997834	+	0.0657787i	$0.0209532\pi$
$227$	0.534579	+	5.08618i	0.0354812	+	0.337581i	−0.962353	+	0.271803i	$0.912380\pi$
$228$	−1.28607	+	0.572594i	−0.0851719	+	0.0379210i
$229$	0.199013	−	0.221026i	0.0131511	−	0.0146058i	−0.736533	−	0.676401i	$-0.763539\pi$
$229$	0.199013	−	0.221026i	0.0131511	−	0.0146058i	0.749685	+	0.661795i	$0.230205\pi$
$230$	−7.29906			−0.481286
$231$	−13.6274	+	4.46351i	−0.896616	+	0.293677i
$232$	9.69727			0.636657
$233$	−6.32176	+	7.02102i	−0.414152	+	0.459962i	−0.913739	−	0.406301i	$-0.866818\pi$
$233$	−6.32176	+	7.02102i	−0.414152	+	0.459962i	0.499587	+	0.866264i	$0.333485\pi$
$234$	0.679257	−	0.302425i	0.0444044	−	0.0197701i
$235$	−0.177632	−	1.69005i	−0.0115874	−	0.110247i
$236$	9.02761	−	1.91888i	0.587647	−	0.124908i
$237$	−3.11885	+	9.59884i	−0.202591	+	0.623512i
$238$	−3.15718	−	3.36970i	−0.204649	−	0.218425i
$239$	9.88886	+	7.18468i	0.639657	+	0.464738i	0.859732	−	0.510745i	$-0.170630\pi$
$239$	9.88886	+	7.18468i	0.639657	+	0.464738i	−0.220075	+	0.975483i	$0.570630\pi$
$240$	−1.09347	+	1.21442i	−0.0705832	+	0.0783906i
$241$	−12.1228	+	20.9973i	−0.780896	+	1.35255i	0.150524	+	0.988606i	$0.451904\pi$
$241$	−12.1228	+	20.9973i	−0.780896	+	1.35255i	−0.931420	+	0.363946i	$0.881429\pi$
$242$	7.07085	+	8.42634i	0.454531	+	0.541665i
$243$	1.70408	+	2.95155i	0.109317	+	0.189342i
$244$	−4.10417	−	12.6313i	−0.262742	−	0.808638i
$245$	−1.00687	−	6.92721i	−0.0643268	−	0.442563i
$246$	−0.101609	+	0.0738234i	−0.00647837	+	0.00470681i
$247$	−1.90148	+	0.404171i	−0.120988	+	0.0257168i
$248$	5.30498	+	5.89178i	0.336867	+	0.374128i
$249$	0.0808752	+	0.769476i	0.00512526	+	0.0487636i
$250$	0.104528	−	0.994522i	0.00661096	−	0.0628991i
$251$	−7.41030	−	22.8065i	−0.467734	−	1.43954i	−0.855512	−	0.517784i	$-0.826757\pi$
$251$	−7.41030	−	22.8065i	−0.467734	−	1.43954i	0.387778	−	0.921753i	$-0.373243\pi$
$252$	−0.108281	−	0.865022i	−0.00682109	−	0.0544913i
$253$	22.8894	+	7.88118i	1.43905	+	0.495486i
$254$	6.84131	+	11.8495i	0.429262	+	0.743504i
$255$	−2.78979	−	0.592989i	−0.174704	−	0.0371344i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	25.6819	+	11.4343i	1.60200	+	0.713254i	0.996578	−	0.0826540i	$-0.0263396\pi$
$257$	25.6819	+	11.4343i	1.60200	+	0.713254i	0.605417	+	0.795908i	$0.293006\pi$
$258$	−1.21386	+	3.73586i	−0.0755714	+	0.232585i
$259$	−7.34653	−	21.1736i	−0.456491	−	1.31567i
$260$	−1.82561	+	1.32638i	−0.113219	+	0.0822587i
$261$	−0.333994	+	3.17774i	−0.0206737	+	0.196697i
$262$	4.45149	+	0.946193i	0.275014	+	0.0584560i
$263$	−11.8417	+	20.5105i	−0.730193	+	1.26473i	0.226608	+	0.973986i	$0.427236\pi$
$263$	−11.8417	+	20.5105i	−0.730193	+	1.26473i	−0.956801	+	0.290745i	$0.906097\pi$
$264$	4.74034	−	2.62768i	0.291748	−	0.161723i
$265$	11.8565			0.728341
$266$	−0.193295	+	2.27101i	−0.0118517	+	0.139244i
$267$	15.9044	+	11.5552i	0.973334	+	0.707169i
$268$	−13.2865	−	5.91554i	−0.811604	−	0.361349i
$269$	−10.3388	−	11.4824i	−0.630367	−	0.700094i	0.340355	−	0.940297i	$-0.389453\pi$
$269$	−10.3388	−	11.4824i	−0.630367	−	0.700094i	−0.970723	+	0.240203i	$0.922786\pi$
$270$	−3.64071	−	4.04342i	−0.221567	−	0.246075i
$271$	27.3544	+	12.1790i	1.66166	+	0.739819i	0.999951	−	0.00994139i	$-0.00316449\pi$
$271$	27.3544	+	12.1790i	1.66166	+	0.739819i	0.661710	+	0.749760i	$0.269831\pi$
$272$	1.41198	+	1.02586i	0.0856140	+	0.0622022i
$273$	−0.827428	+	9.72137i	−0.0500782	+	0.588364i
$274$	0.149930			0.00905763
$275$	−1.40163	+	3.00590i	−0.0845217	+	0.181262i
$276$	5.96394	−	10.3298i	0.358987	−	0.621784i
$277$	15.8516	+	3.36936i	0.952429	+	0.202445i	0.657822	−	0.753173i	$-0.271478\pi$
$277$	15.8516	+	3.36936i	0.952429	+	0.202445i	0.294607	+	0.955618i	$0.404811\pi$
$278$	2.19478	−	20.8819i	0.131634	−	1.25242i
$279$	−2.11342	+	1.53549i	−0.126527	+	0.0919272i
$280$	0.867266	+	2.49957i	0.0518290	+	0.149378i
$281$	2.52917	−	7.78397i	0.150877	−	0.464353i	−0.846842	−	0.531844i	$-0.821499\pi$
$281$	2.52917	−	7.78397i	0.150877	−	0.464353i	0.997720	+	0.0674909i	$0.0214993\pi$
$282$	2.53695	+	1.12952i	0.151073	+	0.0672622i
$283$	4.27434	−	1.90306i	0.254083	−	0.113125i	−0.275743	−	0.961231i	$-0.588924\pi$
$283$	4.27434	−	1.90306i	0.254083	−	0.113125i	0.529826	+	0.848106i	$0.322257\pi$
$284$	−5.82530	−	1.23821i	−0.345668	−	0.0734740i
$285$	0.703888	+	1.21917i	0.0416947	+	0.0722174i
$286$	7.15716	−	2.18825i	0.423212	−	0.129394i
$287$	0.0252568	+	0.201768i	0.00149086	+	0.0119100i
$288$	0.101821	+	0.313372i	0.00599985	+	0.0184656i
$289$	1.45858	−	13.8775i	0.0857989	−	0.816322i
$290$	−1.01364	−	9.64415i	−0.0595230	−	0.566324i
$291$	−2.79585	−	3.10511i	−0.163896	−	0.182025i
$292$	7.72873	−	1.64279i	0.452290	−	0.0961372i
$293$	1.74310	−	1.26644i	0.101833	−	0.0739860i	−0.535704	−	0.844406i	$-0.679954\pi$
$293$	1.74310	−	1.26644i	0.101833	−	0.0739860i	0.637536	+	0.770420i	$0.279954\pi$
$294$	10.6263	+	4.23515i	0.619738	+	0.246999i
$295$	−2.85201	−	8.77757i	−0.166050	−	0.511050i
$296$	4.23546	+	7.33602i	0.246181	+	0.426398i
$297$	7.05116	+	16.6110i	0.409150	+	0.963868i
$298$	5.26992	−	9.12777i	0.305278	−	0.528757i
$299$	11.0212	−	12.2402i	0.637370	−	0.707871i
$300$	1.32207	+	0.960539i	0.0763297	+	0.0554567i
$301$	4.34826	+	4.64096i	0.250630	+	0.267501i
$302$	5.23562	−	16.1136i	0.301276	−	0.927233i
$303$	−27.1855	+	5.77846i	−1.56177	+	0.331964i
$304$	−0.0900475	−	0.856745i	−0.00516458	−	0.0491377i
$305$	−12.1331	+	5.40202i	−0.694741	+	0.309319i
$306$	−0.384802	+	0.427365i	−0.0219976	+	0.0244309i
$307$	22.4519			1.28140			0.640698	−	0.767793i	$-0.278645\pi$
$307$	22.4519			1.28140			0.640698	+	0.767793i	$0.278645\pi$
$308$	−0.0207760	−	8.77494i	−0.00118382	−	0.499999i
$309$	19.7556			1.12386
$310$	5.30498	−	5.89178i	0.301303	−	0.334631i
$311$	−0.620375	+	0.276209i	−0.0351782	+	0.0156624i	−0.424250	−	0.905545i	$-0.639462\pi$
$311$	−0.620375	+	0.276209i	−0.0351782	+	0.0156624i	0.389072	+	0.921207i	$0.372796\pi$
$312$	−0.385461	−	3.66742i	−0.0218224	−	0.207627i
$313$	−19.5332	+	4.15190i	−1.10408	+	0.234679i	−0.723675	−	0.690141i	$-0.757549\pi$
$313$	−19.5332	+	4.15190i	−1.10408	+	0.234679i	−0.380404	+	0.924820i	$0.624215\pi$
$314$	−2.66955	+	8.21604i	−0.150652	+	0.463658i
$315$	−0.848965	+	0.198108i	−0.0478338	+	0.0111621i
$316$	−4.99659	−	3.63023i	−0.281080	−	0.204217i
$317$	−12.0332	+	13.3642i	−0.675850	+	0.750607i	−0.979338	−	0.202228i	$-0.935182\pi$
$317$	−12.0332	+	13.3642i	−0.675850	+	0.750607i	0.303489	+	0.952835i	$0.401849\pi$
$318$	−9.68777	+	16.7797i	−0.543263	+	0.940960i
$319$	−7.23458	+	31.3380i	−0.405059	+	1.75459i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	6.92342	+	21.3081i	0.386427	+	1.18930i
$322$	−9.98514	−	16.5297i	−0.556450	−	0.921164i
$323$	1.21637	−	0.883746i	0.0676807	−	0.0491729i
$324$	7.73023	−	1.64311i	0.429457	−	0.0912840i
$325$	1.50994	+	1.67696i	0.0837566	+	0.0930211i
$326$	1.77570	+	16.8947i	0.0983472	+	0.935711i
$327$	0.586193	−	5.57725i	0.0324166	−	0.308423i
$328$	−0.0237499	−	0.0730946i	−0.00131137	−	0.00403598i
$329$	3.58435	−	2.71427i	0.197612	−	0.149643i
$330$	−3.10879	−	4.43970i	−0.171133	−	0.244398i
$331$	−11.8708	−	20.5608i	−0.652477	−	1.13012i	−0.982520	−	0.186157i	$-0.940397\pi$
$331$	−11.8708	−	20.5608i	−0.652477	−	1.13012i	0.330043	−	0.943966i	$-0.392937\pi$
$332$	−0.463115	−	0.0984381i	−0.0254167	−	0.00540249i
$333$	−2.54985	+	1.13527i	−0.139731	+	0.0622122i
$334$	−2.36662	−	1.05369i	−0.129496	−	0.0576552i
$335$	−4.49432	+	13.8321i	−0.245551	+	0.755728i
$336$	−4.24609	−	0.814977i	−0.231643	−	0.0444606i
$337$	−15.0013	+	10.8991i	−0.817174	+	0.593712i	−0.915902	−	0.401403i	$-0.868523\pi$
$337$	−15.0013	+	10.8991i	−0.817174	+	0.593712i	0.0987276	+	0.995114i	$0.468523\pi$
$338$	−0.826598	+	7.86455i	−0.0449610	+	0.427775i
$339$	−12.6230	−	2.68309i	−0.685585	−	0.145726i
$340$	0.872653	−	1.51148i	0.0473262	−	0.0819714i
$341$	−22.9978	+	12.7482i	−1.24540	+	0.690354i
$342$	0.283852			0.0153489
$343$	14.3102	−	11.7566i	0.772677	−	0.634799i
$344$	−1.94467	−	1.41289i	−0.104850	−	0.0761777i
$345$	−10.8967	−	4.85150i	−0.586656	−	0.261196i
$346$	−3.54543	−	3.93760i	−0.190604	−	0.211687i
$347$	5.43154	+	6.03234i	0.291580	+	0.323833i	0.871081	−	0.491139i	$-0.163419\pi$
$347$	5.43154	+	6.03234i	0.291580	+	0.323833i	−0.579501	+	0.814972i	$0.696753\pi$
$348$	14.4769	+	6.44554i	0.776044	+	0.345517i
$349$	8.08919	+	5.87714i	0.433005	+	0.314596i	0.782849	−	0.622212i	$-0.213766\pi$
$349$	8.08919	+	5.87714i	0.433005	+	0.314596i	−0.349845	+	0.936808i	$0.613766\pi$
$350$	2.39522	−	1.12379i	0.128030	−	0.0600692i
$351$	12.2779			0.655347
$352$	0.632877	+	3.25568i	0.0337325	+	0.173528i
$353$	14.4775	−	25.0758i	0.770562	−	1.33465i	−0.166694	−	0.986009i	$-0.553309\pi$
$353$	14.4775	−	25.0758i	0.770562	−	1.33465i	0.937256	−	0.348643i	$-0.113357\pi$
$354$	14.7526	+	3.13576i	0.784093	+	0.166664i
$355$	−0.622513	+	5.92282i	−0.0330396	+	0.314351i
$356$	−9.73243	+	7.07102i	−0.515818	+	0.374763i
$357$	−2.47355	−	7.12907i	−0.130914	−	0.377311i
$358$	−1.74354	+	5.36605i	−0.0921487	+	0.283605i
$359$	−1.85465	−	0.825744i	−0.0978847	−	0.0435811i	0.357210	−	0.934024i	$-0.383728\pi$
$359$	−1.85465	−	0.825744i	−0.0978847	−	0.0435811i	−0.455095	+	0.890443i	$0.650395\pi$
$360$	0.301013	−	0.134019i	0.0158648	−	0.00706344i
$361$	17.8589	+	3.79603i	0.939942	+	0.199791i
$362$	8.81977	+	15.2763i	0.463557	+	0.802904i
$363$	4.95519	+	17.2794i	0.260080	+	0.906932i
$364$	−5.50120	−	2.31984i	−0.288341	−	0.121592i
$365$	−2.44167	−	7.51467i	−0.127803	−	0.393336i
$366$	2.26868	−	21.5851i	0.118586	−	1.12827i
$367$	−1.56609	−	14.9003i	−0.0817490	−	0.777790i	−0.956208	−	0.292689i	$-0.905450\pi$
$367$	−1.56609	−	14.9003i	−0.0817490	−	0.777790i	0.874459	−	0.485100i	$-0.161217\pi$
$368$	4.88402	+	5.42426i	0.254597	+	0.282759i
$369$	0.0247707	−	0.00526517i	0.00128951	−	0.000274094i
$370$	6.85311	−	4.97908i	0.356276	−	0.258850i
$371$	16.2198	+	26.8507i	0.842089	+	1.39402i
$372$	4.00361	+	12.3218i	0.207577	+	0.638858i
$373$	3.57577	+	6.19342i	0.185146	+	0.320683i	0.943626	−	0.331014i	$-0.107391\pi$
$373$	3.57577	+	6.19342i	0.185146	+	0.320683i	−0.758479	+	0.651697i	$0.774057\pi$
$374$	−4.36861	+	3.79766i	−0.225896	+	0.196372i
$375$	0.817083	−	1.41523i	0.0421940	−	0.0730822i
$376$	−1.13710	+	1.26287i	−0.0586412	+	0.0651277i
$377$	17.7034	+	12.8623i	0.911772	+	0.662441i
$378$	4.17636	−	13.7763i	0.214809	−	0.708576i
$379$	3.82683	−	11.7778i	0.196571	−	0.604983i	−0.803384	−	0.595462i	$-0.796969\pi$
$379$	3.82683	−	11.7778i	0.196571	−	0.604983i	0.999955	−	0.00952159i	$-0.00303086\pi$
$380$	−0.842639	+	0.179108i	−0.0432265	+	0.00918807i
$381$	2.33722	+	22.2372i	0.119740	+	1.13925i
$382$	12.9852	−	5.78137i	0.664379	−	0.295800i
$383$	−1.52660	+	1.69547i	−0.0780058	+	0.0866343i	−0.780884	−	0.624676i	$-0.785231\pi$
$383$	−1.52660	+	1.69547i	−0.0780058	+	0.0866343i	0.702878	+	0.711310i	$0.251898\pi$
$384$	1.63417			0.0833932
$385$	−8.72470	+	0.937893i	−0.444652	+	0.0477995i
$386$	14.9020			0.758494
$387$	0.529973	−	0.588595i	0.0269400	−	0.0299199i
$388$	2.33581	−	1.03997i	0.118583	−	0.0527964i
$389$	−2.89221	−	27.5176i	−0.146641	−	1.39520i	−0.782144	−	0.623097i	$-0.785874\pi$
$389$	−2.89221	−	27.5176i	−0.146641	−	1.39520i	0.635503	−	0.772098i	$-0.280793\pi$
$390$	−3.60704	+	0.766699i	−0.182649	+	0.0388233i
$391$	−3.93659	+	12.1156i	−0.199082	+	0.612712i
$392$	−4.47419	+	5.38346i	−0.225981	+	0.271906i
$393$	6.01665	+	4.37135i	0.303500	+	0.220506i
$394$	−4.13389	+	4.59116i	−0.208263	+	0.231299i
$395$	−3.08806	+	5.34868i	−0.155377	+	0.269121i
$396$	−1.08867	+	0.0952579i	−0.0547075	+	0.00478689i
$397$	−5.28824	−	9.15950i	−0.265409	−	0.459702i	0.702262	−	0.711919i	$-0.252174\pi$
$397$	−5.28824	−	9.15950i	−0.265409	−	0.459702i	−0.967671	+	0.252217i	$0.918840\pi$
$398$	0.736364	+	2.26630i	0.0369106	+	0.113599i
$399$	−1.79805	+	3.26188i	−0.0900152	+	0.163298i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	21.0903	−	4.48289i	1.05320	−	0.223865i	0.351391	−	0.936229i	$-0.385709\pi$
$401$	21.0903	−	4.48289i	1.05320	−	0.223865i	0.701810	+	0.712364i	$0.252376\pi$
$402$	−15.9033	−	17.6625i	−0.793187	−	0.880923i
$403$	1.87007	+	17.7925i	0.0931547	+	0.886308i
$404$	1.77775	−	16.9142i	0.0884465	−	0.841512i
$405$	−2.44214	−	7.51614i	−0.121351	−	0.373480i
$406$	20.4538	−	15.4888i	1.01510	−	0.768694i
$407$	−26.8671	+	8.21443i	−1.33175	+	0.407174i
$408$	1.42606	+	2.47001i	0.0706005	+	0.122284i
$409$	37.5976	+	7.99162i	1.85908	+	0.395160i	0.994267	−	0.106929i	$-0.0341019\pi$
$409$	37.5976	+	7.99162i	1.85908	+	0.395160i	0.864816	+	0.502089i	$0.167435\pi$
$410$	−0.0702117	+	0.0312603i	−0.00346751	+	0.00154383i
$411$	0.223829	+	0.0996551i	0.0110407	+	0.00491562i
$412$	−3.73574	+	11.4974i	−0.184047	+	0.566438i
$413$	15.9764	−	18.4665i	0.786149	−	0.908677i
$414$	−1.94571	+	1.41364i	−0.0956266	+	0.0694768i
$415$	−0.0494902	+	0.470868i	−0.00242938	+	0.0231140i
$416$	2.20726	+	0.469168i	0.108220	+	0.0230029i
$417$	17.1563	−	29.7155i	0.840146	−	1.45518i
$418$	2.83586	+	0.348169i	0.138706	+	0.0170295i
$419$	−16.2170			−0.792250			−0.396125	−	0.918196i	$-0.629645\pi$
$419$	−16.2170			−0.792250			−0.396125	+	0.918196i	$0.629645\pi$
$420$	−0.366674	+	4.30802i	−0.0178919	+	0.210210i
$421$	0.503386	+	0.365732i	0.0245336	+	0.0178247i	0.599984	−	0.800012i	$-0.295173\pi$
$421$	0.503386	+	0.365732i	0.0245336	+	0.0178247i	−0.575451	+	0.817836i	$0.695173\pi$
$422$	9.84319	+	4.38247i	0.479159	+	0.213335i
$423$	−0.374672	−	0.416116i	−0.0182172	−	0.0202322i
$424$	−7.93357	−	8.81112i	−0.385288	−	0.427906i
$425$	−1.59442	−	0.709880i	−0.0773405	−	0.0344342i
$426$	−7.87351	−	5.72044i	−0.381473	−	0.277156i
$427$	−28.8318	−	20.0871i	−1.39527	−	0.972084i
$428$	−13.7101			−0.662704
$429$	12.1393	+	1.49038i	0.586091	+	0.0719564i
$430$	−1.20187	+	2.08170i	−0.0579594	+	0.100389i
$431$	−32.6081	−	6.93107i	−1.57068	−	0.333858i	−0.661395	−	0.750038i	$-0.730035\pi$
$431$	−32.6081	−	6.93107i	−1.57068	−	0.333858i	−0.909282	+	0.416180i	$0.863369\pi$
$432$	−0.568735	+	5.41115i	−0.0273633	+	0.260344i
$433$	18.4417	−	13.3987i	0.886250	−	0.643898i	−0.0486478	−	0.998816i	$-0.515491\pi$
$433$	18.4417	−	13.3987i	0.886250	−	0.643898i	0.934897	+	0.354918i	$0.115491\pi$
$434$	20.6000	+	3.95387i	0.988830	+	0.189792i
$435$	4.89698	−	15.0714i	0.234792	−	0.722616i
$436$	3.13502	+	1.39580i	0.150140	+	0.0668467i
$437$	5.74426	−	2.55751i	0.274785	−	0.122342i
$438$	12.6300	+	2.68460i	0.603486	+	0.128275i
$439$	8.52409	+	14.7642i	0.406833	+	0.704655i	0.994533	−	0.104424i	$-0.0332998\pi$
$439$	8.52409	+	14.7642i	0.406833	+	0.704655i	−0.587700	+	0.809079i	$0.699967\pi$
$440$	3.17169	−	0.969722i	0.151205	−	0.0462297i
$441$	−1.61003	−	1.65158i	−0.0766680	−	0.0786468i
$442$	1.21704	+	3.74565i	0.0578885	+	0.178162i
$443$	−1.44025	+	13.7031i	−0.0684285	+	0.651054i	0.905523	+	0.424297i	$0.139479\pi$
$443$	−1.44025	+	13.7031i	−0.0684285	+	0.651054i	−0.973951	+	0.226757i	$0.927188\pi$
$444$	1.44698	+	13.7670i	0.0686704	+	0.653355i
$445$	8.04960	+	8.93999i	0.381588	+	0.423796i
$446$	0.260802	−	0.0554352i	0.0123493	−	0.00262493i
$447$	13.9344	−	10.1239i	0.659074	−	0.478845i
$448$	1.27723	−	2.31704i	0.0603434	−	0.109470i
$449$	1.07094	+	3.29600i	0.0505406	+	0.155548i	0.973141	−	0.230208i	$-0.0739407\pi$
$449$	1.07094	+	3.29600i	0.0505406	+	0.155548i	−0.922601	+	0.385756i	$0.873941\pi$
$450$	−0.164750	−	0.285355i	−0.00776637	−	0.0134518i
$451$	0.253933	−	0.0222191i	0.0119572	−	0.00104625i
$452$	3.94848	−	6.83897i	0.185721	−	0.321678i
$453$	18.5265	−	20.5758i	0.870451	−	0.966734i
$454$	−4.13747	−	3.00605i	−0.194181	−	0.141081i
$455$	−1.73210	+	5.71356i	−0.0812019	+	0.267856i
$456$	0.435027	−	1.33887i	0.0203720	−	0.0626985i
$457$	−15.3934	+	3.27196i	−0.720071	+	0.153056i	−0.553351	−	0.832948i	$-0.686651\pi$
$457$	−15.3934	+	3.27196i	−0.720071	+	0.153056i	−0.166720	+	0.986004i	$0.553318\pi$
$458$	0.0310888	+	0.295790i	0.00145269	+	0.0138214i
$459$	−8.67515	+	3.86242i	−0.404921	+	0.180283i
$460$	4.88402	−	5.42426i	0.227719	−	0.252907i
$461$	13.6185			0.634275			0.317138	−	0.948380i	$-0.397278\pi$
$461$	13.6185			0.634275			0.317138	+	0.948380i	$0.397278\pi$
$462$	5.80147	−	13.1138i	0.269909	−	0.610109i
$463$	23.0561			1.07151			0.535755	−	0.844374i	$-0.320027\pi$
$463$	23.0561			1.07151			0.535755	+	0.844374i	$0.320027\pi$
$464$	−6.48874	+	7.20648i	−0.301232	+	0.334552i
$465$	11.8359	−	5.26966i	0.548874	−	0.244375i
$466$	−0.987555	−	9.39596i	−0.0457476	−	0.435259i
$467$	−14.4056	+	3.06200i	−0.666610	+	0.141692i	−0.528774	−	0.848763i	$-0.677348\pi$
$467$	−14.4056	+	3.06200i	−0.666610	+	0.141692i	−0.137836	+	0.990455i	$0.544015\pi$
$468$	−0.229766	+	0.707148i	−0.0106210	+	0.0326879i
$469$	−37.4728	+	8.74436i	−1.73034	+	0.403777i
$470$	1.37481	+	0.998861i	0.0634154	+	0.0460740i
$471$	−9.44634	+	10.4912i	−0.435265	+	0.483410i
$472$	−4.61464	+	7.99280i	−0.212406	+	0.367898i
$473$	6.01673	−	5.23038i	0.276650	−	0.240493i
$474$	−5.04641	−	8.74064i	−0.231789	−	0.401471i
$475$	0.266207	+	0.819301i	0.0122144	+	0.0375921i
$476$	4.61674	−	0.0914698i	0.211608	−	0.00419251i
$477$	3.16060	−	2.29631i	0.144714	−	0.105141i
$478$	−11.9562	+	2.54137i	−0.546864	+	0.116239i
$479$	−13.2831	−	14.7523i	−0.606919	−	0.674052i	0.358868	−	0.933388i	$-0.383163\pi$
$479$	−13.2831	−	14.7523i	−0.606919	−	0.674052i	−0.965787	+	0.259337i	$0.916496\pi$
$480$	−0.170817	−	1.62521i	−0.00779669	−	0.0741806i
$481$	−1.99809	+	19.0105i	−0.0911049	+	0.866805i
$482$	−7.49228	−	23.0589i	−0.341264	−	1.05030i
$483$	−3.91979	−	31.3138i	−0.178356	−	1.42483i
$484$	−10.9933	−	0.383655i	−0.499696	−	0.0174389i
$485$	−1.27843	−	2.21430i	−0.0580505	−	0.100546i
$486$	−3.33369	−	0.708597i	−0.151219	−	0.0321426i
$487$	17.6185	−	7.84427i	0.798372	−	0.355458i	0.0333346	−	0.999444i	$-0.489387\pi$
$487$	17.6185	−	7.84427i	0.798372	−	0.355458i	0.765037	+	0.643986i	$0.222721\pi$
$488$	12.1331	+	5.40202i	0.549241	+	0.244538i
$489$	−8.57857	+	26.4021i	−0.387936	+	1.19395i
$490$	5.82165	+	3.88695i	0.262995	+	0.175595i
$491$	14.6904	−	10.6732i	0.662969	−	0.481675i	−0.204695	−	0.978826i	$-0.565620\pi$
$491$	14.6904	−	10.6732i	0.662969	−	0.481675i	0.867664	+	0.497151i	$0.165620\pi$
$492$	0.0131284	−	0.124908i	0.000591872	−	0.00563128i
$493$	−16.5549	−	3.51884i	−0.745593	−	0.158481i
$494$	0.971979	−	1.68352i	0.0437314	−	0.0757450i
$495$	0.208533	+	1.07274i	0.00937284	+	0.0482163i
$496$	−7.92817			−0.355985
$497$	−14.2646	+	6.69267i	−0.639855	+	0.300207i
$498$	−0.625948	−	0.454778i	−0.0280494	−	0.0203791i
$499$	17.1804	+	7.64920i	0.769100	+	0.342425i	0.753496	−	0.657453i	$-0.228366\pi$
$499$	17.1804	+	7.64920i	0.769100	+	0.342425i	0.0156044	+	0.999878i	$0.495033\pi$
$500$	0.669131	+	0.743145i	0.0299244	+	0.0332344i
$501$	−2.83273	−	3.14607i	−0.126557	−	0.140556i
$502$	21.9070	+	9.75363i	0.977758	+	0.435326i
$503$	27.3161	+	19.8463i	1.21797	+	0.884905i	0.995930	−	0.0901334i	$-0.0287294\pi$
$503$	27.3161	+	19.8463i	1.21797	+	0.884905i	0.222037	+	0.975038i	$0.428729\pi$
$504$	0.715291	+	0.498344i	0.0318616	+	0.0221980i
$505$	−17.0074			−0.756817
$506$	−21.1729	+	11.7366i	−0.941249	+	0.521756i
$507$	−6.46139	+	11.1915i	−0.286960	+	0.497030i
$508$	−13.3836	−	2.84478i	−0.593802	−	0.126217i
$509$	1.71175	−	16.2862i	0.0758720	−	0.721874i	−0.888778	−	0.458338i	$-0.848445\pi$
$509$	1.71175	−	16.2862i	0.0758720	−	0.721874i	0.964650	−	0.263535i	$-0.0848885\pi$
$510$	2.30741	−	1.67643i	0.102174	−	0.0742337i
$511$	13.6778	−	15.8096i	0.605069	−	0.699375i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	4.28196	+	1.90645i	0.189053	+	0.0841719i
$514$	−25.6819	+	11.4343i	−1.13278	+	0.504347i
$515$	11.8249	+	2.51347i	0.521069	+	0.110757i
$516$	−1.96406	−	3.40185i	−0.0864629	−	0.149758i
$517$	−3.23281	−	4.61683i	−0.142179	−	0.203048i
$518$	20.6509	+	8.70839i	0.907347	+	0.382625i
$519$	−2.67570	−	8.23495i	−0.117450	−	0.361474i
$520$	0.235876	−	2.24421i	0.0103439	−	0.0984152i
$521$	−2.48131	−	23.6080i	−0.108708	−	1.03429i	−0.903846	−	0.427858i	$-0.859268\pi$
$521$	−2.48131	−	23.6080i	−0.108708	−	1.03429i	0.795138	−	0.606429i	$-0.207398\pi$
$522$	−2.13804	−	2.37453i	−0.0935793	−	0.103930i
$523$	20.9743	−	4.45822i	0.917142	−	0.194944i	0.274923	−	0.961466i	$-0.411348\pi$
$523$	20.9743	−	4.45822i	0.917142	−	0.194944i	0.642218	+	0.766522i	$0.278014\pi$
$524$	−3.68179	+	2.67497i	−0.160840	+	0.116857i
$525$	4.32275	−	0.0856451i	0.188660	−	0.00373786i
$526$	−7.31859	−	22.5243i	−0.319106	−	0.982107i
$527$	−6.91854	−	11.9833i	−0.301376	−	0.521999i
$528$	−1.21916	+	5.28102i	−0.0530571	+	0.229827i
$529$	−15.1381	+	26.2200i	−0.658179	+	1.14000i
$530$	−7.93357	+	8.81112i	−0.344612	+	0.382731i
$531$	−2.46026	−	1.78748i	−0.106766	−	0.0775701i
$532$	−1.55835	−	1.66325i	−0.0675630	−	0.0721109i
$533$	0.0535934	−	0.164944i	0.00232139	−	0.00714450i
$534$	−19.2293	+	4.08732i	−0.832135	+	0.176876i
$535$	1.43310	+	13.6350i	0.0619583	+	0.589494i
$536$	13.2865	−	5.91554i	0.573891	−	0.255513i
$537$	−6.16958	+	6.85201i	−0.266237	+	0.295686i
$538$	15.4511			0.666144
$539$	−14.0594	−	18.4752i	−0.605581	−	0.795783i
$540$	5.44096			0.234141
$541$	22.6115	−	25.1126i	0.972143	−	1.07967i	−0.0246537	−	0.999696i	$-0.507848\pi$
$541$	22.6115	−	25.1126i	0.972143	−	1.07967i	0.996797	−	0.0799781i	$-0.0254850\pi$
$542$	−27.3544	+	12.1790i	−1.17497	+	0.523131i
$543$	3.01313	+	28.6680i	0.129306	+	1.23026i
$544$	−1.70717	+	0.362869i	−0.0731941	+	0.0155579i
$545$	1.06045	−	3.26374i	0.0454249	−	0.139803i
$546$	−6.67073	−	7.11977i	−0.285481	−	0.304698i
$547$	23.5000	+	17.0738i	1.00479	+	0.730021i	0.963109	−	0.269110i	$-0.0867296\pi$
$547$	23.5000	+	17.0738i	1.00479	+	0.730021i	0.0416781	+	0.999131i	$0.486730\pi$
$548$	−0.100323	+	0.111420i	−0.00428559	+	0.00475963i
$549$	−2.18810	+	3.78990i	−0.0933859	+	0.161749i
$550$	−1.29594	−	3.05296i	−0.0552591	−	0.130178i
$551$	4.17692	+	7.23465i	0.177943	+	0.308206i
$552$	3.68592	+	11.3441i	0.156883	+	0.482836i
$553$	−16.3373	+	0.323685i	−0.694732	+	0.0137645i
$554$	−13.1107	+	9.52548i	−0.557020	+	0.404699i
$555$	13.5404	−	2.87810i	0.574757	−	0.122168i
$556$	14.0497	+	15.6038i	0.595841	+	0.661748i
$557$	−0.150559	−	1.43248i	−0.00637940	−	0.0606960i	0.990869	−	0.134828i	$-0.0430481\pi$
$557$	−0.150559	−	1.43248i	−0.00637940	−	0.0606960i	−0.997248	+	0.0741318i	$0.976381\pi$
$558$	0.273062	−	2.59802i	0.0115597	−	0.109983i
$559$	−1.67618	−	5.15875i	−0.0708948	−	0.218192i
$560$	−2.43786	−	1.02803i	−0.103018	−	0.0434424i
$561$	−9.04605	+	2.76576i	−0.381925	+	0.116771i
$562$	4.09228	+	7.08803i	0.172622	+	0.298991i
$563$	−13.6373	−	2.89870i	−0.574744	−	0.122166i	−0.0886358	−	0.996064i	$-0.528251\pi$
$563$	−13.6373	−	2.89870i	−0.574744	−	0.122166i	−0.486109	+	0.873898i	$0.661584\pi$
$564$	−2.53695	+	1.12952i	−0.106825	+	0.0475616i
$565$	−7.21424	−	3.21199i	−0.303505	−	0.135129i
$566$	−1.44584	+	4.44985i	−0.0607734	+	0.187041i
$567$	13.6804	−	15.8127i	0.574524	−	0.664069i
$568$	4.81806	−	3.50052i	0.202161	−	0.146879i
$569$	0.311319	−	2.96200i	0.0130512	−	0.124174i	−0.986056	−	0.166411i	$-0.946782\pi$
$569$	0.311319	−	2.96200i	0.0130512	−	0.124174i	0.999108	+	0.0422377i	$0.0134487\pi$
$570$	−1.37701	−	0.292693i	−0.0576767	−	0.0122596i
$571$	−3.58149	+	6.20333i	−0.149881	+	0.259601i	−0.931183	−	0.364552i	$-0.881222\pi$
$571$	−3.58149	+	6.20333i	−0.149881	+	0.259601i	0.781302	+	0.624153i	$0.214556\pi$
$572$	−3.16289	+	6.78303i	−0.132247	+	0.283613i
$573$	23.2281			0.970367
$574$	−0.166843	−	0.116240i	−0.00696389	−	0.00485175i
$575$	−5.90506	−	4.29028i	−0.246258	−	0.178917i
$576$	−0.301013	−	0.134019i	−0.0125422	−	0.00558414i
$577$	−15.5497	−	17.2697i	−0.647341	−	0.718946i	0.326747	−	0.945112i	$-0.394047\pi$
$577$	−15.5497	−	17.2697i	−0.647341	−	0.718946i	−0.974089	+	0.226166i	$0.927381\pi$
$578$	9.33699	+	10.3698i	0.388367	+	0.431326i
$579$	22.2470	+	9.90502i	0.924555	+	0.411639i
$580$	7.84526	+	5.69991i	0.325757	+	0.236676i
$581$	−1.13405	+	0.532071i	−0.0470481	+	0.0220740i
$582$	4.17833			0.173197
$583$	34.3930	−	19.0649i	1.42441	−	0.789586i
$584$	−3.95070	+	6.84281i	−0.163481	+	0.283157i
$585$	0.727291	+	0.154591i	0.0300698	+	0.00639153i
$586$	−0.225216	+	2.14279i	−0.00930359	+	0.0885177i
$587$	−2.38783	+	1.73486i	−0.0985562	+	0.0716053i	−0.635972	−	0.771712i	$-0.719401\pi$
$587$	−2.38783	+	1.73486i	−0.0985562	+	0.0716053i	0.537416	+	0.843317i	$0.319401\pi$
$588$	−10.2577	+	5.06301i	−0.423021	+	0.208795i
$589$	−2.11053	+	6.49556i	−0.0869631	+	0.267645i
$590$	8.43137	+	3.75389i	0.347114	+	0.154545i
$591$	−9.22306	+	4.10637i	−0.379386	+	0.168914i
$592$	−8.28580	−	1.76120i	−0.340544	−	0.0723849i
$593$	−16.1850	−	28.0333i	−0.664639	−	1.15119i	−0.979383	−	0.202012i	$-0.935252\pi$
$593$	−16.1850	−	28.0333i	−0.664639	−	1.15119i	0.314744	−	0.949176i	$-0.398081\pi$
$594$	−17.0625	−	5.87489i	−0.700084	−	0.241050i
$595$	−0.573549	−	4.58189i	−0.0235132	−	0.187839i
$596$	3.25699	+	10.0240i	0.133411	+	0.410598i
$597$	−0.407044	+	3.87277i	−0.0166592	+	0.158502i
$598$	1.72167	+	16.3806i	0.0704045	+	0.669854i
$599$	−0.594703	−	0.660484i	−0.0242989	−	0.0269867i	0.730873	−	0.682514i	$-0.239113\pi$
$599$	−0.594703	−	0.660484i	−0.0242989	−	0.0269867i	−0.755172	+	0.655527i	$0.772447\pi$
$600$	−1.59846	+	0.339762i	−0.0652567	+	0.0138707i
$601$	−22.9546	+	16.6775i	−0.936340	+	0.680291i	−0.947537	−	0.319647i	$-0.896436\pi$
$601$	−22.9546	+	16.6775i	−0.936340	+	0.680291i	0.0111971	+	0.999937i	$0.496436\pi$
$602$	−6.35846	+	0.125978i	−0.259152	+	0.00513448i
$603$	1.48087	+	4.55766i	0.0603059	+	0.185602i
$604$	8.47142	+	14.6729i	0.344697	+	0.597033i
$605$	0.767560	+	10.9732i	0.0312057	+	0.446124i
$606$	13.8964	−	24.0693i	0.564504	−	0.977749i
$607$	−8.47605	+	9.41361i	−0.344032	+	0.382087i	−0.890185	−	0.455599i	$-0.849425\pi$
$607$	−8.47605	+	9.41361i	−0.344032	+	0.382087i	0.546153	+	0.837686i	$0.316092\pi$
$608$	0.696939	+	0.506356i	0.0282646	+	0.0205354i
$609$	40.8302	−	9.52780i	1.65452	−	0.386086i
$610$	4.10417	−	12.6313i	0.166173	−	0.511428i
$611$	−3.75094	+	0.797287i	−0.151747	+	0.0322548i
$612$	−0.0601119	−	0.571926i	−0.00242988	−	0.0231188i
$613$	−32.7681	+	14.5893i	−1.32349	+	0.589257i	−0.942154	−	0.335179i	$-0.891203\pi$
$613$	−32.7681	+	14.5893i	−1.32349	+	0.589257i	−0.381338	+	0.924436i	$0.624537\pi$
$614$	−15.0232	+	16.6850i	−0.606288	+	0.673352i
$615$	−0.125596			−0.00506452
$616$	6.53495	+	5.85614i	0.263301	+	0.235951i
$617$	2.72334			0.109637			0.0548187	−	0.998496i	$-0.482542\pi$
$617$	2.72334			0.109637			0.0548187	+	0.998496i	$0.482542\pi$
$618$	−13.2191	+	14.6813i	−0.531750	+	0.590568i
$619$	9.15818	−	4.07748i	0.368098	−	0.163888i	−0.214348	−	0.976757i	$-0.568763\pi$
$619$	9.15818	−	4.07748i	0.368098	−	0.163888i	0.582446	+	0.812870i	$0.302096\pi$
$620$	0.828719	+	7.88474i	0.0332822	+	0.316659i
$621$	−38.8460	+	8.25697i	−1.55884	+	0.331341i
$622$	0.209849	−	0.645848i	0.00841417	−	0.0258961i
$623$	−9.23392	+	30.4593i	−0.369949	+	1.22033i
$624$	2.98335	+	2.16753i	0.119429	+	0.0867706i
$625$	0.669131	−	0.743145i	0.0267652	−	0.0297258i
$626$	9.98477	−	17.2941i	0.399072	−	0.691212i
$627$	4.00220	+	2.40470i	0.159832	+	0.0960346i
$628$	−4.31943	−	7.48147i	−0.172364	−	0.298543i
$629$	−4.56861	−	14.0607i	−0.182162	−	0.560638i
$630$	0.420846	−	0.763464i	0.0167669	−	0.0304171i
$631$	−24.9516	+	18.1284i	−0.993308	+	0.721680i	−0.960643	−	0.277786i	$-0.910399\pi$
$631$	−24.9516	+	18.1284i	−0.993308	+	0.721680i	−0.0326649	+	0.999466i	$0.510399\pi$
$632$	6.04116	−	1.28409i	0.240304	−	0.0510783i
$633$	11.7818	+	13.0851i	0.468286	+	0.520084i
$634$	−1.87976	−	17.8848i	−0.0746550	−	0.710295i
$635$	−1.43022	+	13.6077i	−0.0567567	+	0.540004i
$636$	−5.98737	−	18.4272i	−0.237415	−	0.730688i
$637$	−15.3086	+	3.89360i	−0.606550	+	0.154270i
$638$	−18.4478	−	26.3455i	−0.730354	−	1.04303i
$639$	0.981157	+	1.69941i	0.0388140	+	0.0672278i
$640$	0.978148	+	0.207912i	0.0386647	+	0.00821843i
$641$	15.5075	−	6.90437i	0.612508	−	0.272706i	−0.0769464	−	0.997035i	$-0.524517\pi$
$641$	15.5075	−	6.90437i	0.612508	−	0.272706i	0.689454	+	0.724329i	$0.257850\pi$
$642$	−20.4677	−	9.11279i	−0.807794	−	0.359653i
$643$	−4.43740	+	13.6569i	−0.174994	+	0.538576i	−0.999633	−	0.0270829i	$-0.991378\pi$
$643$	−4.43740	+	13.6569i	−0.174994	+	0.538576i	0.824639	+	0.565659i	$0.191378\pi$
$644$	18.9653	+	3.64012i	0.747338	+	0.143441i
$645$	−3.17792	+	2.30889i	−0.125130	+	0.0909125i
$646$	−0.157160	+	1.49528i	−0.00618339	+	0.0588311i
$647$	−5.66725	−	1.20461i	−0.222803	−	0.0473582i	0.0951576	−	0.995462i	$-0.469665\pi$
$647$	−5.66725	−	1.20461i	−0.222803	−	0.0473582i	−0.317960	+	0.948104i	$0.602998\pi$
$648$	−3.95147	+	6.84414i	−0.155228	+	0.268863i
$649$	−22.3870	−	20.8758i	−0.878768	−	0.819446i
$650$	−2.25657			−0.0885101
$651$	28.1253	+	19.5950i	1.10232	+	0.767987i
$652$	−13.7434	−	9.98516i	−0.538233	−	0.391049i
$653$	43.7460	+	19.4770i	1.71191	+	0.762193i	0.998084	+	0.0618720i	$0.0197071\pi$
$653$	43.7460	+	19.4770i	1.71191	+	0.762193i	0.713828	+	0.700321i	$0.246960\pi$
$654$	3.75247	+	4.16754i	0.146733	+	0.162964i
$655$	3.04517	+	3.38201i	0.118985	+	0.132146i
$656$	0.0702117	+	0.0312603i	0.00274131	+	0.00122051i
$657$	−2.10628	−	1.53030i	−0.0821738	−	0.0597027i
$658$	−0.381303	+	4.47989i	−0.0148647	+	0.174644i
$659$	22.7006			0.884291			0.442145	−	0.896943i	$-0.354218\pi$
$659$	22.7006			0.884291			0.442145	+	0.896943i	$0.354218\pi$
$660$	5.37953	+	0.660463i	0.209398	+	0.0257085i
$661$	16.6863	−	28.9016i	0.649023	−	1.12414i	−0.334333	−	0.942455i	$-0.608511\pi$
$661$	16.6863	−	28.9016i	0.649023	−	1.12414i	0.983357	−	0.181686i	$-0.0581556\pi$
$662$	23.2227	+	4.93615i	0.902577	+	0.191849i
$663$	−0.672747	+	6.40076i	−0.0261273	+	0.248585i
$664$	0.383038	−	0.278294i	0.0148648	−	0.0107999i
$665$	−1.49124	+	1.72367i	−0.0578280	+	0.0668410i
$666$	0.862516	−	2.65455i	0.0334218	−	0.102862i
$667$	−64.6616	−	28.7892i	−2.50371	−	1.11472i
$668$	2.36662	−	1.05369i	0.0915673	−	0.0407684i
$669$	0.426194	+	0.0905904i	0.0164776	+	0.00350243i
$670$	−7.27196	−	12.5954i	−0.280940	−	0.486603i
$671$	−26.5092	+	35.1796i	−1.02337	+	1.35809i
$672$	3.44684	−	2.61014i	0.132965	−	0.100688i
$673$	−9.65846	−	29.7257i	−0.372306	−	1.14584i	−0.945278	−	0.326266i	$-0.894210\pi$
$673$	−9.65846	−	29.7257i	−0.372306	−	1.14584i	0.572972	−	0.819575i	$-0.305790\pi$
$674$	1.93823	−	18.4411i	0.0746580	−	0.710324i
$675$	−0.568735	−	5.41115i	−0.0218906	−	0.208275i
$676$	−5.29140	−	5.87669i	−0.203515	−	0.226027i
$677$	25.0212	−	5.31842i	0.961642	−	0.204403i	0.299763	−	0.954014i	$-0.403092\pi$
$677$	25.0212	−	5.31842i	0.961642	−	0.204403i	0.661879	+	0.749610i	$0.269759\pi$
$678$	10.4403	−	7.58535i	0.400959	−	0.291313i
$679$	3.26569	−	5.92435i	0.125326	−	0.227356i
$680$	0.539329	+	1.65988i	0.0206823	+	0.0636536i
$681$	−4.17872	−	7.23776i	−0.160129	−	0.277352i
$682$	5.91476	−	25.6209i	0.226488	−	0.981075i
$683$	18.6916	−	32.3748i	0.715213	−	1.23879i	−0.247664	−	0.968846i	$-0.579663\pi$
$683$	18.6916	−	32.3748i	0.715213	−	1.23879i	0.962877	−	0.269940i	$-0.0870037\pi$
$684$	−0.189934	+	0.210943i	−0.00726230	+	0.00806561i
$685$	0.121296	+	0.0881269i	0.00463449	+	0.00336716i
$686$	−0.838488	+	18.5013i	−0.0320136	+	0.706382i
$687$	−0.150193	+	0.462245i	−0.00573020	+	0.0176358i
$688$	2.35122	−	0.499767i	0.0896393	−	0.0190534i
$689$	−2.79667	−	26.6086i	−0.106545	−	1.01371i
$690$	10.8967	−	4.85150i	0.414829	−	0.184694i
$691$	−13.9986	+	15.5470i	−0.532530	+	0.591435i	−0.948039	−	0.318154i	$-0.896937\pi$
$691$	−13.9986	+	15.5470i	−0.532530	+	0.591435i	0.415509	+	0.909589i	$0.363604\pi$
$692$	5.29857			0.201421
$693$	−2.14410	+	1.93977i	−0.0814477	+	0.0736857i
$694$	−8.11731			−0.308129
$695$	14.0497	−	15.6038i	0.532936	−	0.591885i
$696$	−14.4769	+	6.44554i	−0.548746	+	0.244317i
$697$	0.0140212	+	0.133403i	0.000531091	+	0.00505299i
$698$	−9.78029	+	2.07887i	−0.370190	+	0.0786862i
$699$	4.77096	−	14.6835i	0.180454	−	0.555381i
$700$	−0.767578	+	2.53196i	−0.0290117	+	0.0956991i
$701$	−20.9632	−	15.2307i	−0.791771	−	0.575255i	0.116718	−	0.993165i	$-0.462763\pi$
$701$	−20.9632	−	15.2307i	−0.791771	−	0.575255i	−0.908488	+	0.417910i	$0.862763\pi$
$702$	−8.21553	+	9.12427i	−0.310075	+	0.344374i
$703$	−3.64869	+	6.31972i	−0.137613	+	0.238353i
$704$	−2.84292	−	1.70816i	−0.107147	−	0.0643786i
$705$	1.38852	+	2.40499i	0.0522947	+	0.0905771i
$706$	8.94761	+	27.5379i	0.336748	+	1.03640i
$707$	−23.2661	−	38.5154i	−0.875013	−	1.44852i
$708$	−12.2018	+	8.86509i	−0.458570	+	0.333171i
$709$	−42.1102	+	8.95080i	−1.58148	+	0.336154i	−0.913123	−	0.407684i	$-0.866336\pi$
$709$	−42.1102	+	8.95080i	−1.58148	+	0.336154i	−0.668359	+	0.743839i	$0.733003\pi$
$710$	−3.98497	−	4.42576i	−0.149553	−	0.166096i
$711$	0.212718	+	2.02388i	0.00797756	+	0.0759014i
$712$	1.25747	−	11.9640i	0.0471257	−	0.448371i
$713$	−17.8822	−	55.0359i	−0.669695	−	2.06111i
$714$	6.95306	+	2.93208i	0.260212	+	0.109730i
$715$	7.07649	+	2.43654i	0.264646	+	0.0911216i
$716$	−2.82110	−	4.88629i	−0.105429	−	0.182609i
$717$	−19.5384	−	4.15302i	−0.729676	−	0.155097i
$718$	1.85465	−	0.825744i	0.0692149	−	0.0308165i
$719$	11.5941	+	5.16204i	0.432388	+	0.192512i	0.611377	−	0.791340i	$-0.290616\pi$
$719$	11.5941	+	5.16204i	0.432388	+	0.192512i	−0.178989	+	0.983851i	$0.557283\pi$
$720$	−0.101821	+	0.313372i	−0.00379464	+	0.0116787i
$721$	10.4845	+	30.2176i	0.390462	+	1.12536i
$722$	−14.7709	+	10.7317i	−0.549717	+	0.399393i
$723$	4.14155	−	39.4042i	0.154026	−	1.46546i
$724$	−17.2541	−	3.66746i	−0.641242	−	0.136300i
$725$	4.84863	−	8.39808i	0.180074	−	0.311897i
$726$	−16.1567	−	7.87974i	−0.599633	−	0.292444i
$727$	−48.1652			−1.78635			−0.893175	−	0.449709i	$-0.851528\pi$
$727$	−48.1652			−1.78635			−0.893175	+	0.449709i	$0.851528\pi$
$728$	5.40500	−	2.53592i	0.200323	−	0.0939874i
$729$	−23.6866	−	17.2094i	−0.877283	−	0.637383i
$730$	7.21828	+	3.21379i	0.267161	+	0.118948i
$731$	2.80718	+	3.11769i	0.103827	+	0.115312i
$732$	14.5228	+	16.1292i	0.536778	+	0.596152i
$733$	−0.559361	−	0.249044i	−0.0206605	−	0.00919863i	0.396380	−	0.918086i	$-0.370266\pi$
$733$	−0.559361	−	0.249044i	−0.0206605	−	0.00919863i	−0.417041	+	0.908888i	$0.636933\pi$
$734$	12.1210	+	8.80642i	0.447394	+	0.325051i
$735$	6.10749	+	9.67228i	0.225278	+	0.356768i
$736$	−7.29906			−0.269047
$737$	9.20451	+	47.3504i	0.339053	+	1.74417i
$738$	−0.0126620	+	0.0219313i	−0.000466096	+	0.000807302i
$739$	42.3408	+	8.99982i	1.55753	+	0.331064i	0.904570	−	0.426326i	$-0.140192\pi$
$739$	42.3408	+	8.99982i	1.55753	+	0.331064i	0.652963	+	0.757390i	$0.273526\pi$
$740$	−0.885451	+	8.42451i	−0.0325498	+	0.309691i
$741$	2.57005	−	1.86725i	0.0944130	−	0.0685950i
$742$	−30.8071	−	5.91298i	−1.13096	−	0.217072i
$743$	−4.13506	+	12.7264i	−0.151701	+	0.466886i	−0.997812	−	0.0661203i	$-0.978938\pi$
$743$	−4.13506	+	12.7264i	−0.151701	+	0.466886i	0.846111	+	0.533007i	$0.178938\pi$
$744$	−11.8359	−	5.26966i	−0.433923	−	0.193195i
$745$	9.62862	−	4.28694i	0.352765	−	0.157061i
$746$	−6.99526	−	1.48689i	−0.256115	−	0.0544389i
$747$	0.0780026	+	0.135104i	0.00285396	+	0.00494321i
$748$	0.100961	−	5.78764i	0.00369149	−	0.211617i
$749$	−28.9179	+	21.8982i	−1.05664	+	0.800143i
$750$	0.504985	+	1.55418i	0.0184395	+	0.0567508i
$751$	1.74690	−	16.6207i	0.0637454	−	0.606497i	−0.915288	−	0.402799i	$-0.868037\pi$
$751$	1.74690	−	16.6207i	0.0637454	−	0.606497i	0.979034	−	0.203698i	$-0.0652960\pi$
$752$	−0.177632	−	1.69005i	−0.00647757	−	0.0616299i
$753$	26.2217	+	29.1221i	0.955571	+	1.06127i
$754$	−21.4044	+	4.54965i	−0.779503	+	0.165688i
$755$	13.7070	−	9.95875i	0.498850	−	0.362436i
$756$	7.44325	+	12.3218i	0.270708	+	0.448139i
$757$	5.44192	+	16.7485i	0.197790	+	0.608735i	0.999933	+	0.0116025i	$0.00369326\pi$
$757$	5.44192	+	16.7485i	0.197790	+	0.608735i	−0.802143	+	0.597132i	$0.796307\pi$
$758$	6.19194	+	10.7248i	0.224901	+	0.389541i
$759$	−39.4097	+	3.44833i	−1.43048	+	0.125167i
$760$	0.430732	−	0.746050i	0.0156243	−	0.0270621i
$761$	−26.7428	+	29.7009i	−0.969426	+	1.07666i	0.0276027	+	0.999619i	$0.491213\pi$
$761$	−26.7428	+	29.7009i	−0.969426	+	1.07666i	−0.997028	+	0.0770371i	$0.975454\pi$
$762$	−18.0894	−	13.1427i	−0.655309	−	0.476110i
$763$	8.84189	−	2.06327i	0.320098	−	0.0746955i
$764$	−4.39238	+	13.5183i	−0.158911	+	0.489077i
$765$	−0.562510	+	0.119565i	−0.0203376	+	0.00432289i
$766$	−0.238479	−	2.26898i	−0.00861660	−	0.0819814i
$767$	−19.0260	+	8.47093i	−0.686990	+	0.305868i
$768$	−1.09347	+	1.21442i	−0.0394572	+	0.0438217i
$769$	−17.3166			−0.624454			−0.312227	−	0.950008i	$-0.601075\pi$
$769$	−17.3166			−0.624454			−0.312227	+	0.950008i	$0.601075\pi$
$770$	5.14097	−	7.11129i	0.185268	−	0.256273i
$771$	−45.9403			−1.65450
$772$	−9.97141	+	11.0744i	−0.358879	+	0.398575i
$773$	32.9868	−	14.6867i	1.18645	−	0.528242i	0.283912	−	0.958850i	$-0.408367\pi$
$773$	32.9868	−	14.6867i	1.18645	−	0.528242i	0.902539	+	0.430608i	$0.141701\pi$
$774$	0.0827899	+	0.787693i	0.00297582	+	0.0283131i
$775$	7.75492	−	1.64836i	0.278565	−	0.0592108i
$776$	−0.790112	+	2.43172i	−0.0283634	+	0.0872935i
$777$	25.0411	+	26.7268i	0.898345	+	0.958817i
$778$	22.3848	+	16.2635i	0.802534	+	0.583075i
$779$	0.0443024	−	0.0492028i	0.00158730	−	0.00176287i
$780$	1.84381	−	3.19357i	0.0660190	−	0.114348i
$781$	7.71791	+	18.1817i	0.276168	+	0.650592i
$782$	−6.36954	−	11.0324i	−0.227774	−	0.394517i
$783$	−16.3045	−	50.1800i	−0.582675	−	1.79329i
$784$	−1.00687	−	6.92721i	−0.0359598	−	0.247400i
$785$	−6.98899	+	5.07779i	−0.249448	+	0.181234i
$786$	−7.27447	+	1.54624i	−0.259472	+	0.0551525i
$787$	−6.66192	−	7.39881i	−0.237472	−	0.263739i	0.612615	−	0.790381i	$-0.290118\pi$
$787$	−6.66192	−	7.39881i	−0.237472	−	0.263739i	−0.850087	+	0.526642i	$0.823451\pi$
$788$	−0.645778	−	6.14416i	−0.0230049	−	0.218877i
$789$	4.04554	−	38.4907i	0.144025	−	1.37031i
$790$	−1.90853	−	5.87384i	−0.0679024	−	0.208982i
$791$	−2.59513	−	20.7316i	−0.0922723	−	0.737131i
$792$	0.657669	−	0.872776i	0.0233693	−	0.0310128i
$793$	14.9852	+	25.9551i	0.532140	+	0.921694i
$794$	10.3454	+	2.19897i	0.367143	+	0.0780386i
$795$	−17.7004	+	7.88074i	−0.627770	+	0.279501i
$796$	−2.17691	−	0.969223i	−0.0771586	−	0.0343532i
$797$	2.24337	−	6.90437i	0.0794641	−	0.244565i	−0.903430	−	0.428735i	$-0.858959\pi$
$797$	2.24337	−	6.90437i	0.0794641	−	0.244565i	0.982895	+	0.184169i	$0.0589595\pi$
$798$	−1.22092	−	3.51883i	−0.0432199	−	0.124565i
$799$	2.39947	−	1.74332i	0.0848871	−	0.0616741i
$800$	0.104528	−	0.994522i	0.00369564	−	0.0351617i
$801$	3.87724	+	0.824132i	0.136995	+	0.0291193i
$802$	−10.7807	+	18.6728i	−0.380681	+	0.659360i
$803$	−19.1660	−	17.8722i	−0.676354	−	0.630697i
$804$	23.7672			0.838204
$805$	1.63776	−	19.2419i	0.0577236	−	0.678188i
$806$	−14.4737	−	10.5158i	−0.509815	−	0.370402i
$807$	23.0667	+	10.2700i	0.811986	+	0.361520i
$808$	11.3801	+	12.6389i	0.400352	+	0.444636i
$809$	−8.49578	−	9.43552i	−0.298696	−	0.331735i	0.575050	−	0.818118i	$-0.304983\pi$
$809$	−8.49578	−	9.43552i	−0.298696	−	0.331735i	−0.873746	+	0.486383i	$0.838316\pi$
$810$	7.21969	+	3.21441i	0.253674	+	0.112943i
$811$	−8.22129	−	5.97312i	−0.288689	−	0.209745i	0.434010	−	0.900908i	$-0.357098\pi$
$811$	−8.22129	−	5.97312i	−0.288689	−	0.209745i	−0.722698	+	0.691164i	$0.757098\pi$
$812$	−2.17587	+	25.5641i	−0.0763582	+	0.897125i
$813$	−48.9320			−1.71612
$814$	11.8731	−	25.4627i	0.416152	−	0.892467i
$815$	−8.49388	+	14.7118i	−0.297528	+	0.515333i
$816$	−2.78979	−	0.592989i	−0.0976623	−	0.0207588i
$817$	0.216451	−	2.05940i	0.00757267	−	0.0720492i
$818$	−31.0966	+	22.5930i	−1.08727	+	0.789947i
$819$	0.644846	+	1.85853i	0.0225328	+	0.0649423i
$820$	0.0237499	−	0.0730946i	0.000829382	−	0.00255258i
$821$	29.3599	+	13.0719i	1.02467	+	0.456211i	0.849087	−	0.528254i	$-0.177153\pi$
$821$	29.3599	+	13.0719i	1.02467	+	0.456211i	0.175581	+	0.984465i	$0.443820\pi$
$822$	−0.223829	+	0.0996551i	−0.00780693	+	0.00347587i
$823$	−8.09554	−	1.72076i	−0.282193	−	0.0599819i	0.0646409	−	0.997909i	$-0.479410\pi$
$823$	−8.09554	−	1.72076i	−0.282193	−	0.0599819i	−0.346834	+	0.937927i	$0.612743\pi$
$824$	−6.04455	−	10.4695i	−0.210572	−	0.364721i
$825$	0.0945317	−	5.41909i	0.00329117	−	0.188669i
$826$	3.03297	+	24.2293i	0.105530	+	0.843045i
$827$	6.10766	+	18.7975i	0.212384	+	0.653652i	0.999329	+	0.0366281i	$0.0116617\pi$
$827$	6.10766	+	18.7975i	0.212384	+	0.653652i	−0.786945	+	0.617024i	$0.788338\pi$
$828$	0.251395	−	2.39186i	0.00873656	−	0.0831228i
$829$	−2.65069	−	25.2197i	−0.0920623	−	0.875915i	−0.938929	−	0.344110i	$-0.888181\pi$
$829$	−2.65069	−	25.2197i	−0.0920623	−	0.875915i	0.846867	−	0.531805i	$-0.178486\pi$
$830$	−0.316807	−	0.351850i	−0.0109965	−	0.0122129i
$831$	−25.9041	+	5.50609i	−0.898604	+	0.191004i
$832$	−1.82561	+	1.32638i	−0.0632915	+	0.0459840i
$833$	9.59167	−	7.56692i	0.332332	−	0.262178i
$834$	10.6032	+	32.6332i	0.367157	+	1.12999i
$835$	−1.29529	−	2.24352i	−0.0448255	−	0.0776400i
$836$	−2.15630	+	1.87448i	−0.0745772	+	0.0648304i
$837$	21.5684	−	37.3576i	0.745514	−	1.29127i
$838$	10.8513	−	12.0516i	0.374851	−	0.416314i
$839$	24.6461	+	17.9065i	0.850879	+	0.618200i	0.925388	−	0.379020i	$-0.123739\pi$
$839$	24.6461	+	17.9065i	0.850879	+	0.618200i	−0.0745091	+	0.997220i	$0.523739\pi$
$840$	−2.95613	−	3.15512i	−0.101996	−	0.108862i
$841$	20.0976	−	61.8539i	0.693019	−	2.13289i
$842$	−0.608623	+	0.129367i	−0.0209745	+	0.00445827i
$843$	1.39806	+	13.3017i	0.0481518	+	0.458133i
$844$	−9.84319	+	4.38247i	−0.338817	+	0.150851i
$845$	−5.29140	+	5.87669i	−0.182030	+	0.202164i
$846$	0.559939			0.0192511
$847$	−23.8002	+	16.7496i	−0.817785	+	0.575523i
$848$	11.8565			0.407155
$849$	−5.11619	+	5.68210i	−0.175587	+	0.195009i
$850$	1.59442	−	0.709880i	0.0546880	−	0.0243487i
$851$	−6.46296	−	61.4910i	−0.221547	−	2.10788i
$852$	9.51952	−	2.02344i	0.326133	−	0.0693218i
$853$	−6.08809	+	18.7372i	−0.208452	+	0.641550i	0.791102	+	0.611685i	$0.209508\pi$
$853$	−6.08809	+	18.7372i	−0.208452	+	0.641550i	−0.999554	+	0.0298655i	$0.990492\pi$
$854$	34.2199	−	7.98527i	1.17098	−	0.273250i
$855$	0.229641	+	0.166844i	0.00785355	+	0.00570594i
$856$	9.17387	−	10.1886i	0.313556	−	0.348240i
$857$	−12.7669	+	22.1130i	−0.436111	+	0.755366i	−0.997386	−	0.0722637i	$-0.976978\pi$
$857$	−12.7669	+	22.1130i	−0.436111	+	0.755366i	0.561275	+	0.827629i	$0.310311\pi$
$858$	−9.23035	+	8.02400i	−0.315119	+	0.273935i
$859$	18.4295	+	31.9208i	0.628806	+	1.08912i	0.987792	+	0.155780i	$0.0497892\pi$
$859$	18.4295	+	31.9208i	0.628806	+	1.08912i	−0.358986	+	0.933343i	$0.616877\pi$
$860$	−0.742798	−	2.28610i	−0.0253292	−	0.0779553i
$861$	−0.171816	−	0.284429i	−0.00585546	−	0.00969331i
$862$	26.9699	−	19.5948i	0.918598	−	0.667400i
$863$	4.87198	−	1.03557i	0.165844	−	0.0352513i	−0.124241	−	0.992252i	$-0.539650\pi$
$863$	4.87198	−	1.03557i	0.165844	−	0.0352513i	0.290085	+	0.957001i	$0.406316\pi$
$864$	−3.64071	−	4.04342i	−0.123859	−	0.137560i
$865$	−0.553851	−	5.26954i	−0.0188315	−	0.179170i
$866$	−2.38274	+	22.6703i	−0.0809689	+	0.770367i
$867$	7.04652	+	21.6870i	0.239312	+	0.736528i
$868$	−16.7224	+	12.6631i	−0.567594	+	0.429814i
$869$	−0.357270	+	20.4808i	−0.0121196	+	0.694763i
$870$	7.92348	+	13.7239i	0.268631	+	0.465283i
$871$	32.1022	+	6.82354i	1.08774	+	0.231207i
$872$	−3.13502	+	1.39580i	−0.106165	+	0.0472677i
$873$	−0.769646	−	0.342669i	−0.0260486	−	0.0115976i
$874$	−1.94306	+	5.98012i	−0.0657250	+	0.202281i
$875$	2.59832	+	0.498711i	0.0878394	+	0.0168595i
$876$	−10.4462	+	7.58960i	−0.352944	+	0.256429i
$877$	4.05807	−	38.6100i	0.137031	−	1.30377i	−0.682565	−	0.730825i	$-0.739136\pi$
$877$	4.05807	−	38.6100i	0.137031	−	1.30377i	0.819596	−	0.572941i	$-0.194198\pi$
$878$	−16.6756	−	3.54452i	−0.562776	−	0.119622i
$879$	−1.76048	+	3.04924i	−0.0593795	+	0.102848i
$880$	−1.40163	+	3.00590i	−0.0472491	+	0.101329i
$881$	−17.4902			−0.589260			−0.294630	−	0.955611i	$-0.595196\pi$
$881$	−17.4902			−0.589260			−0.294630	+	0.955611i	$0.595196\pi$
$882$	2.30468	−	0.0913597i	0.0776028	−	0.00307624i
$883$	−17.9556	−	13.0455i	−0.604255	−	0.439017i	0.243131	−	0.969993i	$-0.421825\pi$
$883$	−17.9556	−	13.0455i	−0.604255	−	0.439017i	−0.847387	+	0.530976i	$0.821825\pi$
$884$	−3.59792	−	1.60190i	−0.121011	−	0.0538776i
$885$	10.0920	+	11.2083i	0.339237	+	0.376761i
$886$	−9.21967	−	10.2395i	−0.309741	−	0.344002i
$887$	−4.77888	−	2.12769i	−0.160459	−	0.0714409i	0.324936	−	0.945736i	$-0.394657\pi$
$887$	−4.77888	−	2.12769i	−0.160459	−	0.0714409i	−0.485395	+	0.874295i	$0.661324\pi$
$888$	−11.1991	−	8.13664i	−0.375818	−	0.273048i
$889$	−32.7729	+	15.3764i	−1.09917	+	0.515708i
$890$	−12.0299			−0.403245
$891$	−19.1698	−	17.8757i	−0.642211	−	0.598858i
$892$	−0.133314	+	0.230907i	−0.00446370	+	0.00773135i
$893$	−1.43195	−	0.304370i	−0.0479184	−	0.0101854i
$894$	−1.80038	+	17.1295i	−0.0602138	+	0.572896i
$895$	−4.56463	+	3.31640i	−0.152579	+	0.110855i
$896$	0.867266	+	2.49957i	0.0289733	+	0.0835048i
$897$	−8.31754	+	25.5988i	−0.277715	+	0.854718i
$898$	−3.16600	−	1.40960i	−0.105651	−	0.0470388i
$899$	70.2348	−	31.2706i	2.34246	−	1.04293i
$900$	0.322299	+	0.0685068i	0.0107433	+	0.00228356i
$901$	10.3466	+	17.9209i	0.344696	+	0.597031i
$902$	−0.153402	+	0.203577i	−0.00510774	+	0.00677836i
$903$	−9.57619	−	4.03824i	−0.318676	−	0.134384i
$904$	2.44030	+	7.51046i	0.0811631	+	0.249794i
$905$	−1.84383	+	17.5429i	−0.0612911	+	0.583146i
$906$	2.89412	+	27.5357i	0.0961508	+	0.914814i
$907$	33.8603	+	37.6057i	1.12431	+	1.24868i	0.965228	+	0.261411i	$0.0841876\pi$
$907$	33.8603	+	37.6057i	1.12431	+	1.24868i	0.159085	+	0.987265i	$0.449146\pi$
$908$	5.00244	−	1.06330i	0.166012	−	0.0352869i
$909$	−4.53366	+	3.29390i	−0.150372	+	0.109252i
$910$	−3.08700	−	5.11031i	−0.102333	−	0.169405i
$911$	13.2345	+	40.7316i	0.438479	+	1.34950i	0.889479	+	0.456976i	$0.151067\pi$
$911$	13.2345	+	40.7316i	0.438479	+	1.34950i	−0.451000	+	0.892524i	$0.648933\pi$
$912$	0.703888	+	1.21917i	0.0233081	+	0.0403707i
$913$	0.613578	+	1.44546i	0.0203065	+	0.0478376i
$914$	7.86863	−	13.6289i	0.260271	−	0.450803i
$915$	14.5228	−	16.1292i	0.480109	−	0.533215i
$916$	−0.240618	−	0.174819i	−0.00795023	−	0.00577618i
$917$	−3.49320	+	11.5228i	−0.115356	+	0.380516i
$918$	2.93447	−	9.03136i	0.0968518	−	0.298079i
$919$	21.3475	−	4.53754i	0.704187	−	0.149680i	0.158119	−	0.987420i	$-0.449457\pi$
$919$	21.3475	−	4.53754i	0.704187	−	0.149680i	0.546069	+	0.837740i	$0.316124\pi$
$920$	0.762959	+	7.25907i	0.0251540	+	0.239325i
$921$	−33.5181	+	14.9232i	−1.10446	+	0.491736i
$922$	−9.11253	+	10.1205i	−0.300105	+	0.333301i
$923$	13.4389			0.442347
$924$	5.86350	+	13.0862i	0.192895	+	0.430503i
$925$	8.47091			0.278522
$926$	−15.4276	+	17.1340i	−0.506981	+	0.563060i
$927$	3.63897	−	1.62018i	0.119520	−	0.0532135i
$928$	−1.01364	−	9.64415i	−0.0332744	−	0.316585i
$929$	−1.00399	+	0.213405i	−0.0329399	+	0.00700159i	−0.224352	−	0.974508i	$-0.572027\pi$
$929$	−1.00399	+	0.213405i	−0.0329399	+	0.00700159i	0.191412	+	0.981510i	$0.438693\pi$
$930$	−4.00361	+	12.3218i	−0.131284	+	0.404049i
$931$	−5.94351	−	1.01914i	−0.194791	−	0.0334009i
$932$	7.64336	+	5.55323i	0.250367	+	0.181902i
$933$	0.742559	−	0.824696i	0.0243103	−	0.0269993i
$934$	7.36370	−	12.7543i	0.240948	−	0.417334i
$935$	−5.76649	+	0.504566i	−0.188584	+	0.0165011i
$936$	−0.371770	−	0.643924i	−0.0121517	−	0.0210473i
$937$	3.44085	+	10.5899i	0.112408	+	0.345955i	0.991398	−	0.130885i	$-0.0417819\pi$
$937$	3.44085	+	10.5899i	0.112408	+	0.345955i	−0.878990	+	0.476841i	$0.841782\pi$
$938$	18.5759	−	33.6989i	0.606525	−	1.10031i
$939$	26.4011	−	19.1815i	0.861567	−	0.625965i
$940$	−1.66223	+	0.353317i	−0.0542159	+	0.0115239i
$941$	12.1218	+	13.4626i	0.395159	+	0.438869i	0.907589	−	0.419861i	$-0.137921\pi$
$941$	12.1218	+	13.4626i	0.395159	+	0.438869i	−0.512430	+	0.858729i	$0.671254\pi$
$942$	−1.47566	−	14.0400i	−0.0480797	−	0.457448i
$943$	−0.0586382	+	0.557905i	−0.00190952	+	0.0181679i
$944$	−2.85201	−	8.77757i	−0.0928249	−	0.285686i
$945$	11.4762	−	8.69045i	0.373322	−	0.282700i
$946$	−0.139049	+	7.97111i	−0.00452089	+	0.259163i
$947$	5.62755	+	9.74721i	0.182871	+	0.316742i	0.942857	−	0.333198i	$-0.108128\pi$
$947$	5.62755	+	9.74721i	0.182871	+	0.316742i	−0.759986	+	0.649939i	$0.774794\pi$
$948$	9.87226	+	2.09841i	0.320636	+	0.0681533i
$949$	−16.2886	+	7.25215i	−0.528750	+	0.235415i
$950$	−0.786987	−	0.350389i	−0.0255332	−	0.0113681i
$951$	9.08129	−	27.9493i	0.294481	−	0.906319i
$952$	−3.02123	+	3.49211i	−0.0979185	+	0.113180i
$953$	−16.6320	+	12.0838i	−0.538762	+	0.391434i	−0.823625	−	0.567134i	$-0.808052\pi$
$953$	−16.6320	+	12.0838i	−0.538762	+	0.391434i	0.284863	+	0.958568i	$0.408052\pi$
$954$	−0.408363	+	3.88532i	−0.0132212	+	0.125792i
$955$	13.9034	+	2.95526i	0.449904	+	0.0956301i
$956$	6.11165	−	10.5857i	0.197665	−	0.342366i
$957$	−10.0292	−	51.5927i	−0.324197	−	1.66775i
$958$	19.8512			0.641364
$959$	−0.0336414	+	0.395249i	−0.00108634	+	0.0127633i
$960$	1.32207	+	0.960539i	0.0426696	+	0.0310013i
$961$	29.1018	+	12.9570i	0.938768	+	0.417966i
$962$	−12.7906	−	14.2054i	−0.412385	−	0.458000i
$963$	3.02278	+	3.35714i	0.0974078	+	0.108182i
$964$	22.1494	+	9.86155i	0.713384	+	0.317619i
$965$	12.0560	+	8.75920i	0.388097	+	0.281969i
$966$	25.8935	+	18.0401i	0.833111	+	0.580429i
$967$	−0.0297591			−0.000956987			−0.000478494	−	1.00000i	$-0.500152\pi$
$967$	−0.0297591			−0.000956987			−0.000478494		1.00000i	$0.500152\pi$
$968$	7.64107	−	7.91290i	0.245593	−	0.254330i
$969$	−1.22850	+	2.12782i	−0.0394651	+	0.0683555i
$970$	2.50098	+	0.531601i	0.0803018	+	0.0170687i
$971$	−2.38755	+	22.7160i	−0.0766200	+	0.728990i	0.887010	+	0.461750i	$0.152778\pi$
$971$	−2.38755	+	22.7160i	−0.0766200	+	0.728990i	−0.963630	+	0.267240i	$0.913888\pi$
$972$	2.75726	−	2.00327i	0.0884392	−	0.0642548i
$973$	54.5569	+	10.4714i	1.74901	+	0.335698i
$974$	−5.95966	+	18.3420i	−0.190960	+	0.587714i
$975$	−3.36881	−	1.49989i	−0.107888	−	0.0480349i
$976$	−12.1331	+	5.40202i	−0.388372	+	0.172914i
$977$	−23.7022	−	5.03806i	−0.758300	−	0.161182i	−0.187493	−	0.982266i	$-0.560036\pi$
$977$	−23.7022	−	5.03806i	−0.758300	−	0.161182i	−0.570807	+	0.821084i	$0.693370\pi$
$978$	−13.8804	−	24.0416i	−0.443847	−	0.768765i
$979$	37.7252	+	12.9894i	1.20570	+	0.415142i
$980$	−6.78401	+	1.72545i	−0.216707	+	0.0551174i
$981$	−0.349419	−	1.07540i	−0.0111561	−	0.0343349i
$982$	−1.89806	+	18.0589i	−0.0605696	+	0.576282i
$983$	−1.32921	−	12.6466i	−0.0423953	−	0.403365i	−0.995055	−	0.0993258i	$-0.968331\pi$
$983$	−1.32921	−	12.6466i	−0.0423953	−	0.403365i	0.952660	−	0.304039i	$-0.0983353\pi$
$984$	0.0840401	+	0.0933360i	0.00267910	+	0.00297544i
$985$	−6.04300	+	1.28448i	−0.192546	+	0.0409269i
$986$	13.6924	−	9.94809i	0.436054	−	0.316812i
$987$	−3.54692	+	6.43453i	−0.112900	+	0.204813i
$988$	0.600716	+	1.84881i	0.0191113	+	0.0588186i
$989$	8.77254	+	15.1945i	0.278950	+	0.483156i
$990$	−0.936740	−	0.562837i	−0.0297716	−	0.0178881i
$991$	1.76185	−	3.05161i	0.0559669	−	0.0969374i	−0.836685	−	0.547685i	$-0.815509\pi$
$991$	1.76185	−	3.05161i	0.0559669	−	0.0969374i	0.892651	+	0.450748i	$0.148843\pi$
$992$	5.30498	−	5.89178i	0.168433	−	0.187064i
$993$	31.3880	+	22.8047i	0.996067	+	0.723685i
$994$	4.57127	−	15.0789i	0.144992	−	0.478275i
$995$	−0.736364	+	2.26630i	−0.0233443	+	0.0718464i
$996$	0.756807	−	0.160864i	0.0239803	−	0.00509718i
$997$	−2.78602	−	26.5072i	−0.0882342	−	0.839492i	−0.945720	−	0.324984i	$-0.894641\pi$
$997$	−2.78602	−	26.5072i	−0.0882342	−	0.839492i	0.857485	−	0.514508i	$-0.172026\pi$
$998$	−17.1804	+	7.64920i	−0.543836	+	0.242131i
$999$	30.8401	−	34.2514i	0.975739	−	1.08367i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bg.e.291.2	✓	72
7.2	even	3	inner	770.2.bg.e.401.8	yes	72
11.9	even	5	inner	770.2.bg.e.361.8	yes	72
77.9	even	15	inner	770.2.bg.e.471.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bg.e.291.2	✓	72	1.1	even	1	trivial
770.2.bg.e.361.8	yes	72	11.9	even	5	inner
770.2.bg.e.401.8	yes	72	7.2	even	3	inner
770.2.bg.e.471.2	yes	72	77.9	even	15	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.669131 + 0.743145i) q^{2} +(-1.49289 + 0.664675i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-0.978148 + 0.207912i) q^{5} +(0.504985 - 1.55418i) q^{6} +(-1.80895 - 1.93072i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.220478 + 0.244866i) q^{9} +O(q^{10})\)	\(q+(-0.669131 + 0.743145i) q^{2} +(-1.49289 + 0.664675i) q^{3} +(-0.104528 - 0.994522i) q^{4} +(-0.978148 + 0.207912i) q^{5} +(0.504985 - 1.55418i) q^{6} +(-1.80895 - 1.93072i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.220478 + 0.244866i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-2.50306 + 2.17593i) q^{11} +(0.817083 + 1.41523i) q^{12} +(0.697320 + 2.14613i) q^{13} +(2.64523 - 0.0524091i) q^{14} +(1.32207 - 0.960539i) q^{15} +(-0.978148 + 0.207912i) q^{16} +(-1.16784 - 1.29701i) q^{17} +(-0.0344421 - 0.327694i) q^{18} +(-0.0900475 + 0.856745i) q^{19} +(0.309017 + 0.951057i) q^{20} +(3.98386 + 1.67998i) q^{21} +(0.0578470 - 3.31612i) q^{22} +(-3.64953 - 6.32117i) q^{23} +(-1.59846 - 0.339762i) q^{24} +(0.913545 - 0.406737i) q^{25} +(-2.06148 - 0.917831i) q^{26} +(1.68135 - 5.17466i) q^{27} +(-1.73106 + 2.00086i) q^{28} +(7.84526 - 5.69991i) q^{29} +(-0.170817 + 1.62521i) q^{30} +(7.75492 + 1.64836i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.29050 - 4.91214i) q^{33} +1.74531 q^{34} +(2.17084 + 1.51243i) q^{35} +(0.266571 + 0.193675i) q^{36} +(7.73856 + 3.44543i) q^{37} +(-0.576432 - 0.640193i) q^{38} +(-2.46750 - 2.74043i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(-0.0621780 - 0.0451750i) q^{41} +(-3.91419 + 1.83646i) q^{42} -2.40375 q^{43} +(2.42565 + 2.26191i) q^{44} +(0.164750 - 0.285355i) q^{45} +(7.13956 + 1.51756i) q^{46} +(-0.177632 + 1.69005i) q^{47} +(1.32207 - 0.960539i) q^{48} +(-0.455376 + 6.98517i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(2.60554 + 1.16006i) q^{51} +(2.06148 - 0.917831i) q^{52} +(-11.5974 - 2.46511i) q^{53} +(2.72048 + 4.71201i) q^{54} +(1.99597 - 2.64880i) q^{55} +(-0.328624 - 2.62526i) q^{56} +(-0.435027 - 1.33887i) q^{57} +(-1.01364 + 9.64415i) q^{58} +(0.964723 + 9.17873i) q^{59} +(-1.09347 - 1.21442i) q^{60} +(12.9911 - 2.76135i) q^{61} +(-6.41402 + 4.66006i) q^{62} +(0.871602 - 0.0172687i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-1.12829 - 1.95425i) q^{65} +(2.11778 + 4.98904i) q^{66} +(7.27196 - 12.5954i) q^{67} +(-1.16784 + 1.29701i) q^{68} +(9.64985 + 7.01103i) q^{69} +(-2.57653 + 0.601238i) q^{70} +(1.84033 - 5.66396i) q^{71} +(-0.322299 + 0.0685068i) q^{72} +(0.825921 + 7.85811i) q^{73} +(-7.73856 + 3.44543i) q^{74} +(-1.09347 + 1.21442i) q^{75} +0.861464 q^{76} +(8.72904 + 0.896569i) q^{77} +3.68762 q^{78} +(4.13263 - 4.58975i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.826081 + 7.85964i) q^{81} +(0.0751768 - 0.0159793i) q^{82} +(0.146308 - 0.450288i) q^{83} +(1.25435 - 4.13765i) q^{84} +(1.41198 + 1.02586i) q^{85} +(1.60842 - 1.78633i) q^{86} +(-7.92348 + 13.7239i) q^{87} +(-3.30400 + 0.289099i) q^{88} +(-6.01497 - 10.4182i) q^{89} +(0.101821 + 0.313372i) q^{90} +(2.88216 - 5.22858i) q^{91} +(-5.90506 + 4.29028i) q^{92} +(-12.6728 + 2.69369i) q^{93} +(-1.13710 - 1.26287i) q^{94} +(-0.0900475 - 0.856745i) q^{95} +(-0.170817 + 1.62521i) q^{96} +(0.790112 + 2.43172i) q^{97} +(-4.88629 - 5.01240i) q^{98} +(0.0190606 - 1.09266i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} + 2 q^{7} + 18 q^{8} + 22 q^{9}+O(q^{10}) \) 72 * q - 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 + 2 * q^7 + 18 * q^8 + 22 * q^9	\( 72 q - 9 q^{2} + 3 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} + 2 q^{7} + 18 q^{8} + 22 q^{9} + 36 q^{10} - 2 q^{12} + 28 q^{13} - 2 q^{14} - 6 q^{15} + 9 q^{16} - 4 q^{17} - 7 q^{18} - q^{19} - 18 q^{20} - 32 q^{21} - 20 q^{22} - 30 q^{23} + 2 q^{24} + 9 q^{25} - 11 q^{26} + 18 q^{27} + 6 q^{28} + 22 q^{29} - 3 q^{30} - 8 q^{31} + 36 q^{32} - 24 q^{33} + 32 q^{34} - 3 q^{35} - 14 q^{36} + 20 q^{37} - 4 q^{38} - 25 q^{39} - 9 q^{40} + 34 q^{41} + 22 q^{42} + 12 q^{43} - 58 q^{45} - 20 q^{46} - 13 q^{47} - 6 q^{48} + 6 q^{49} + 18 q^{50} - 37 q^{51} + 11 q^{52} + 2 q^{53} + 14 q^{54} - 10 q^{55} - 2 q^{56} - 18 q^{57} + 11 q^{58} + 29 q^{59} - 2 q^{60} + 21 q^{61} + 44 q^{62} + 31 q^{63} - 18 q^{64} + 6 q^{65} - q^{66} - 20 q^{67} - 4 q^{68} - 104 q^{69} + 4 q^{70} - 70 q^{71} - 22 q^{72} - 28 q^{73} - 20 q^{74} - 2 q^{75} + 12 q^{76} - 47 q^{77} + 20 q^{78} - 24 q^{79} + 9 q^{80} + 44 q^{81} - 28 q^{82} - 56 q^{83} - 46 q^{84} + 8 q^{85} + 11 q^{86} - 88 q^{87} - 5 q^{88} - 20 q^{89} + 44 q^{90} - 36 q^{91} + 10 q^{92} + 77 q^{93} - 22 q^{94} - q^{95} - 3 q^{96} - 178 q^{97} - 68 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q - 9 * q^2 + 3 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 + 2 * q^7 + 18 * q^8 + 22 * q^9 + 36 * q^10 - 2 * q^12 + 28 * q^13 - 2 * q^14 - 6 * q^15 + 9 * q^16 - 4 * q^17 - 7 * q^18 - q^19 - 18 * q^20 - 32 * q^21 - 20 * q^22 - 30 * q^23 + 2 * q^24 + 9 * q^25 - 11 * q^26 + 18 * q^27 + 6 * q^28 + 22 * q^29 - 3 * q^30 - 8 * q^31 + 36 * q^32 - 24 * q^33 + 32 * q^34 - 3 * q^35 - 14 * q^36 + 20 * q^37 - 4 * q^38 - 25 * q^39 - 9 * q^40 + 34 * q^41 + 22 * q^42 + 12 * q^43 - 58 * q^45 - 20 * q^46 - 13 * q^47 - 6 * q^48 + 6 * q^49 + 18 * q^50 - 37 * q^51 + 11 * q^52 + 2 * q^53 + 14 * q^54 - 10 * q^55 - 2 * q^56 - 18 * q^57 + 11 * q^58 + 29 * q^59 - 2 * q^60 + 21 * q^61 + 44 * q^62 + 31 * q^63 - 18 * q^64 + 6 * q^65 - q^66 - 20 * q^67 - 4 * q^68 - 104 * q^69 + 4 * q^70 - 70 * q^71 - 22 * q^72 - 28 * q^73 - 20 * q^74 - 2 * q^75 + 12 * q^76 - 47 * q^77 + 20 * q^78 - 24 * q^79 + 9 * q^80 + 44 * q^81 - 28 * q^82 - 56 * q^83 - 46 * q^84 + 8 * q^85 + 11 * q^86 - 88 * q^87 - 5 * q^88 - 20 * q^89 + 44 * q^90 - 36 * q^91 + 10 * q^92 + 77 * q^93 - 22 * q^94 - q^95 - 3 * q^96 - 178 * q^97 - 68 * q^98 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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