LMFDB - Embedded newform 770.2.bv.a.423.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(3,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([45, 10, 48]))

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

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

chi := DirichletCharacter("770.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bv (of order $60$, degree $16$, 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:	$768$
Relative dimension:	$48$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			423.4
Character	$\chi$	$=$	770.423
Dual form			770.2.bv.a.537.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0523360 - 0.998630i) q^{2} +(-0.879416 + 2.29096i) q^{3} +(-0.994522 + 0.104528i) q^{4} +(0.496330 + 2.18029i) q^{5} +(2.33384 + 0.758311i) q^{6} +(-2.23996 + 1.40805i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.24567 - 2.02201i) q^{9} +O(q^{10})$	\(q+(-0.0523360 - 0.998630i) q^{2} +(-0.879416 + 2.29096i) q^{3} +(-0.994522 + 0.104528i) q^{4} +(0.496330 + 2.18029i) q^{5} +(2.33384 + 0.758311i) q^{6} +(-2.23996 + 1.40805i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.24567 - 2.02201i) q^{9} +(2.15132 - 0.609757i) q^{10} +(2.96326 + 1.48966i) q^{11} +(0.635128 - 2.37033i) q^{12} +(1.00256 + 0.510828i) q^{13} +(1.52335 + 2.16319i) q^{14} +(-5.43142 - 0.780309i) q^{15} +(0.978148 - 0.207912i) q^{16} +(-0.133382 + 2.54509i) q^{17} +(-1.90171 + 2.34842i) q^{18} +(-0.0883156 + 0.840267i) q^{19} +(-0.721513 - 2.11646i) q^{20} +(-1.25593 - 6.36990i) q^{21} +(1.33254 - 3.03716i) q^{22} +(0.490260 - 1.82967i) q^{23} +(-2.40032 - 0.510204i) q^{24} +(-4.50731 + 2.16429i) q^{25} +(0.457658 - 1.02792i) q^{26} +(0.0477775 - 0.0243438i) q^{27} +(2.08050 - 1.63447i) q^{28} +(-3.35064 - 4.61176i) q^{29} +(-0.494981 + 5.46482i) q^{30} +(-0.824482 + 3.87888i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-6.01869 + 5.47866i) q^{33} +2.54858 q^{34} +(-4.18171 - 4.18489i) q^{35} +(2.44473 + 1.77620i) q^{36} +(-7.12988 + 2.73690i) q^{37} +(0.843737 + 0.0442184i) q^{38} +(-2.05195 + 1.84758i) q^{39} +(-2.07580 + 0.831292i) q^{40} +(6.45783 - 8.88844i) q^{41} +(-6.29544 + 1.58758i) q^{42} +(-5.01217 - 5.01217i) q^{43} +(-3.10274 - 1.17176i) q^{44} +(3.29398 - 5.89980i) q^{45} +(-1.85283 - 0.393830i) q^{46} +(-2.51766 + 2.03876i) q^{47} +(-0.383882 + 2.42373i) q^{48} +(3.03480 - 6.30793i) q^{49} +(2.39721 + 4.38787i) q^{50} +(-5.71338 - 2.54376i) q^{51} +(-1.05046 - 0.403234i) q^{52} +(-3.73588 - 5.75276i) q^{53} +(-0.0268110 - 0.0464380i) q^{54} +(-1.77714 + 7.20012i) q^{55} +(-1.74112 - 1.99211i) q^{56} +(-1.84735 - 0.941271i) q^{57} +(-4.43009 + 3.58741i) q^{58} +(0.430762 + 4.09842i) q^{59} +(5.48324 + 0.208296i) q^{60} +(-1.94411 - 9.14634i) q^{61} +(3.91672 + 0.620347i) q^{62} +(7.87730 + 1.36720i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-0.616153 + 2.43940i) q^{65} +(5.78615 + 5.72371i) q^{66} +(2.70911 + 10.1105i) q^{67} +(-0.133382 - 2.54509i) q^{68} +(3.76056 + 2.73221i) q^{69} +(-3.96030 + 4.39500i) q^{70} +(-3.11279 + 9.58018i) q^{71} +(1.64582 - 2.53434i) q^{72} +(8.58622 + 6.95298i) q^{73} +(3.10630 + 6.97687i) q^{74} +(-0.994482 - 12.2294i) q^{75} -0.844895i q^{76} +(-8.73509 + 0.835631i) q^{77} +(1.95244 + 1.95244i) q^{78} +(4.23114 + 3.80973i) q^{79} +(0.938792 + 2.02945i) q^{80} +(-0.933854 - 8.88503i) q^{81} +(-9.21424 - 5.98380i) q^{82} +(6.46332 + 12.6850i) q^{83} +(1.91488 + 6.20372i) q^{84} +(-5.61522 + 0.972392i) q^{85} +(-4.74299 + 5.26762i) q^{86} +(13.5120 - 3.62052i) q^{87} +(-1.00777 + 3.15981i) q^{88} +(0.804950 + 1.39421i) q^{89} +(-6.06411 - 2.98069i) q^{90} +(-2.96495 + 0.267416i) q^{91} +(-0.296321 + 1.87090i) q^{92} +(-8.16129 - 5.30000i) q^{93} +(2.16773 + 2.40751i) q^{94} +(-1.87586 + 0.224496i) q^{95} +(2.44050 + 0.256507i) q^{96} +(5.89844 - 11.5763i) q^{97} +(-6.45812 - 2.70051i) q^{98} +(-3.64239 - 9.33705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) $ 768 * q + 24 * q^5 + 4 * q^7	$ 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) $ 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.0523360	−	0.998630i	−0.0370071	−	0.706138i
$2$	−0.0523360	−	0.998630i	−0.0370071	−	0.706138i
$3$	−0.879416	+	2.29096i	−0.507731	+	1.32268i	0.405072	+	0.914285i	$0.367246\pi$
$3$	−0.879416	+	2.29096i	−0.507731	+	1.32268i	−0.912803	+	0.408399i	$0.866087\pi$
$4$	−0.994522	+	0.104528i	−0.497261	+	0.0522642i
$5$	0.496330	+	2.18029i	0.221966	+	0.975054i
$5$	0.496330	+	2.18029i	0.221966	+	0.975054i
$6$	2.33384	+	0.758311i	0.952787	+	0.309579i
$7$	−2.23996	+	1.40805i	−0.846623	+	0.532192i
$7$	−2.23996	+	1.40805i	−0.846623	+	0.532192i
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	−2.24567	−	2.02201i	−0.748558	−	0.674004i
$10$	2.15132	−	0.609757i	0.680308	−	0.192822i
$11$	2.96326	+	1.48966i	0.893456	+	0.449151i
$11$	2.96326	+	1.48966i	0.893456	+	0.449151i
$12$	0.635128	−	2.37033i	0.183346	−	0.684255i
$13$	1.00256	+	0.510828i	0.278059	+	0.141678i	0.587459	−	0.809254i	$-0.300128\pi$
$13$	1.00256	+	0.510828i	0.278059	+	0.141678i	−0.309400	+	0.950932i	$0.600128\pi$
$14$	1.52335	+	2.16319i	0.407132	+	0.578138i
$15$	−5.43142	−	0.780309i	−1.40239	−	0.201475i
$16$	0.978148	−	0.207912i	0.244537	−	0.0519779i
$17$	−0.133382	+	2.54509i	−0.0323500	+	0.617274i	0.933564	+	0.358411i	$0.116681\pi$
$17$	−0.133382	+	2.54509i	−0.0323500	+	0.617274i	−0.965914	+	0.258863i	$0.916652\pi$
$18$	−1.90171	+	2.34842i	−0.448238	+	0.553528i
$19$	−0.0883156	+	0.840267i	−0.0202610	+	0.192770i	−0.999971	−	0.00765117i	$-0.997565\pi$
$19$	−0.0883156	+	0.840267i	−0.0202610	+	0.192770i	0.979710	+	0.200422i	$0.0642312\pi$
$20$	−0.721513	−	2.11646i	−0.161335	−	0.473256i
$21$	−1.25593	−	6.36990i	−0.274065	−	1.39003i
$22$	1.33254	−	3.03716i	0.284098	−	0.647525i
$23$	0.490260	−	1.82967i	0.102226	−	0.381514i	−0.895789	−	0.444479i	$-0.853389\pi$
$23$	0.490260	−	1.82967i	0.102226	−	0.381514i	0.998016	+	0.0629650i	$0.0200557\pi$
$24$	−2.40032	−	0.510204i	−0.489964	−	0.104145i
$25$	−4.50731	+	2.16429i	−0.901463	+	0.432857i
$26$	0.457658	−	1.02792i	0.0897541	−	0.201591i
$27$	0.0477775	−	0.0243438i	0.00919478	−	0.00468498i
$28$	2.08050	−	1.63447i	0.393178	−	0.308887i
$29$	−3.35064	−	4.61176i	−0.622199	−	0.856383i	0.375312	−	0.926899i	$-0.377536\pi$
$29$	−3.35064	−	4.61176i	−0.622199	−	0.856383i	−0.997511	+	0.0705154i	$0.977536\pi$
$30$	−0.494981	+	5.46482i	−0.0903707	+	0.997735i
$31$	−0.824482	+	3.87888i	−0.148081	+	0.696668i	0.839981	+	0.542615i	$0.182566\pi$
$31$	−0.824482	+	3.87888i	−0.148081	+	0.696668i	−0.988063	+	0.154053i	$0.950767\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−6.01869	+	5.47866i	−1.04772	+	0.953712i
$34$	2.54858			0.437078
$35$	−4.18171	−	4.18489i	−0.706838	−	0.707376i
$36$	2.44473	+	1.77620i	0.407455	+	0.296033i
$37$	−7.12988	+	2.73690i	−1.17215	+	0.449944i	−0.865026	−	0.501727i	$-0.832698\pi$
$37$	−7.12988	+	2.73690i	−1.17215	+	0.449944i	−0.307119	+	0.951671i	$0.599365\pi$
$38$	0.843737	+	0.0442184i	0.136872	+	0.00717317i
$39$	−2.05195	+	1.84758i	−0.328575	+	0.295850i
$40$	−2.07580	+	0.831292i	−0.328213	+	0.131439i
$41$	6.45783	−	8.88844i	1.00854	−	1.38814i	0.0886106	−	0.996066i	$-0.471757\pi$
$41$	6.45783	−	8.88844i	1.00854	−	1.38814i	0.919933	−	0.392075i	$-0.128243\pi$
$42$	−6.29544	+	1.58758i	−0.971407	+	0.244969i
$43$	−5.01217	−	5.01217i	−0.764349	−	0.764349i	0.212756	−	0.977105i	$-0.431756\pi$
$43$	−5.01217	−	5.01217i	−0.764349	−	0.764349i	−0.977105	+	0.212756i	$0.931756\pi$
$44$	−3.10274	−	1.17176i	−0.467755	−	0.176649i
$45$	3.29398	−	5.89980i	0.491037	−	0.879490i
$46$	−1.85283	−	0.393830i	−0.273184	−	0.0580671i
$47$	−2.51766	+	2.03876i	−0.367238	+	0.297384i	−0.795121	−	0.606450i	$-0.792593\pi$
$47$	−2.51766	+	2.03876i	−0.367238	+	0.297384i	0.427883	+	0.903834i	$0.359260\pi$
$48$	−0.383882	+	2.42373i	−0.0554086	+	0.349836i
$49$	3.03480	−	6.30793i	0.433543	−	0.901133i
$50$	2.39721	+	4.38787i	0.339017	+	0.620538i
$51$	−5.71338	−	2.54376i	−0.800034	−	0.356198i
$52$	−1.05046	−	0.403234i	−0.145673	−	0.0559185i
$53$	−3.73588	−	5.75276i	−0.513163	−	0.790202i	0.483191	−	0.875515i	$-0.339478\pi$
$53$	−3.73588	−	5.75276i	−0.513163	−	0.790202i	−0.996354	+	0.0853131i	$0.972811\pi$
$54$	−0.0268110	−	0.0464380i	−0.00364851	−	0.00631941i
$55$	−1.77714	+	7.20012i	−0.239630	+	0.970864i
$56$	−1.74112	−	1.99211i	−0.232667	−	0.266207i
$57$	−1.84735	−	0.941271i	−0.244687	−	0.124674i
$58$	−4.43009	+	3.58741i	−0.581699	+	0.471050i
$59$	0.430762	+	4.09842i	0.0560804	+	0.533569i	0.986111	+	0.166087i	$0.0531134\pi$
$59$	0.430762	+	4.09842i	0.0560804	+	0.533569i	−0.930031	+	0.367482i	$0.880220\pi$
$60$	5.48324	+	0.208296i	0.707883	+	0.0268909i
$61$	−1.94411	−	9.14634i	−0.248918	−	1.17107i	−0.907991	−	0.418990i	$-0.862384\pi$
$61$	−1.94411	−	9.14634i	−0.248918	−	1.17107i	0.659073	−	0.752079i	$-0.270949\pi$
$62$	3.91672	+	0.620347i	0.497423	+	0.0787841i
$63$	7.87730	+	1.36720i	0.992447	+	0.172251i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	−0.616153	+	2.43940i	−0.0764244	+	0.302570i
$66$	5.78615	+	5.72371i	0.712225	+	0.704540i
$67$	2.70911	+	10.1105i	0.330971	+	1.23520i	0.908172	+	0.418597i	$0.137478\pi$
$67$	2.70911	+	10.1105i	0.330971	+	1.23520i	−0.577201	+	0.816602i	$0.695855\pi$
$68$	−0.133382	−	2.54509i	−0.0161750	−	0.308637i
$69$	3.76056	+	2.73221i	0.452718	+	0.328919i
$70$	−3.96030	+	4.39500i	−0.473347	+	0.525303i
$71$	−3.11279	+	9.58018i	−0.369420	+	1.13696i	0.577746	+	0.816216i	$0.303932\pi$
$71$	−3.11279	+	9.58018i	−0.369420	+	1.13696i	−0.947167	+	0.320742i	$0.896068\pi$
$72$	1.64582	−	2.53434i	0.193962	−	0.298675i
$73$	8.58622	+	6.95298i	1.00494	+	0.813785i	0.982556	−	0.185965i	$-0.0595410\pi$
$73$	8.58622	+	6.95298i	1.00494	+	0.813785i	0.0223842	+	0.999749i	$0.492874\pi$
$74$	3.10630	+	6.97687i	0.361100	+	0.811045i
$75$	−0.994482	−	12.2294i	−0.114833	−	1.41213i
$76$		−	0.844895i		−	0.0969161i
$77$	−8.73509	+	0.835631i	−0.995455	+	0.0952290i
$78$	1.95244	+	1.95244i	0.221070	+	0.221070i
$79$	4.23114	+	3.80973i	0.476040	+	0.428629i	0.871901	−	0.489682i	$-0.162887\pi$
$79$	4.23114	+	3.80973i	0.476040	+	0.428629i	−0.395861	+	0.918310i	$0.629554\pi$
$80$	0.938792	+	2.02945i	0.104960	+	0.226899i
$81$	−0.933854	−	8.88503i	−0.103762	−	0.987225i
$82$	−9.21424	−	5.98380i	−1.01754	−	0.660800i
$83$	6.46332	+	12.6850i	0.709441	+	1.39236i	0.910804	+	0.412840i	$0.135463\pi$
$83$	6.46332	+	12.6850i	0.709441	+	1.39236i	−0.201363	+	0.979517i	$0.564537\pi$
$84$	1.91488	+	6.20372i	0.208931	+	0.676882i
$85$	−5.61522	+	0.972392i	−0.609057	+	0.105471i
$86$	−4.74299	+	5.26762i	−0.511450	+	0.568022i
$87$	13.5120	−	3.62052i	1.44863	−	0.388160i
$88$	−1.00777	+	3.15981i	−0.107428	+	0.336837i
$89$	0.804950	+	1.39421i	0.0853245	+	0.147786i	0.905529	−	0.424283i	$-0.139474\pi$
$89$	0.804950	+	1.39421i	0.0853245	+	0.147786i	−0.820205	+	0.572070i	$0.806141\pi$
$90$	−6.06411	−	2.98069i	−0.639213	−	0.314192i
$91$	−2.96495	+	0.267416i	−0.310811	+	0.0280328i
$92$	−0.296321	+	1.87090i	−0.0308936	+	0.195055i
$93$	−8.16129	−	5.30000i	−0.846286	−	0.549585i
$94$	2.16773	+	2.40751i	0.223584	+	0.248316i
$95$	−1.87586	+	0.224496i	−0.192459	+	0.0230328i
$96$	2.44050	+	0.256507i	0.249083	+	0.0261797i
$97$	5.89844	−	11.5763i	0.598896	−	1.17540i	−0.370255	−	0.928930i	$-0.620730\pi$
$97$	5.89844	−	11.5763i	0.598896	−	1.17540i	0.969151	−	0.246469i	$-0.0792704\pi$
$98$	−6.45812	−	2.70051i	−0.652368	−	0.272792i
$99$	−3.64239	−	9.33705i	−0.366074	−	0.938408i
$100$	4.25639	−	2.62357i	0.425639	−	0.262357i
$101$	−2.15782	+	10.1518i	−0.214712	+	1.01014i	0.730306	+	0.683120i	$0.239377\pi$
$101$	−2.15782	+	10.1518i	−0.214712	+	1.01014i	−0.945018	+	0.327019i	$0.893956\pi$
$102$	−2.24126	+	5.83868i	−0.221918	+	0.578116i
$103$	5.42182	−	2.08124i	0.534227	−	0.205071i	−0.0762725	−	0.997087i	$-0.524302\pi$
$103$	5.42182	−	2.08124i	0.534227	−	0.205071i	0.610500	+	0.792016i	$0.290969\pi$
$104$	−0.347704	+	1.07012i	−0.0340952	+	0.104934i
$105$	13.2649	−	5.89985i	1.29452	−	0.575767i
$106$	−5.54935	+	4.03184i	−0.539001	+	0.391607i
$107$	−4.86118	−	6.00305i	−0.469948	−	0.580337i	0.485969	−	0.873976i	$-0.338467\pi$
$107$	−4.86118	−	6.00305i	−0.469948	−	0.580337i	−0.955916	+	0.293639i	$0.905134\pi$
$108$	−0.0449711	+	0.0292046i	−0.00432735	+	0.00281021i
$109$	4.75220	+	2.74369i	0.455178	+	0.262797i	0.710015	−	0.704187i	$-0.248688\pi$
$109$	4.75220	+	2.74369i	0.455178	+	0.262797i	−0.254836	+	0.966984i	$0.582022\pi$
$110$	7.28326	+	1.39788i	0.694432	+	0.133283i
$111$		−	18.7411i		−	1.77883i
$112$	−1.89826	+	1.84299i	−0.179368	+	0.174146i
$113$	2.25540	+	14.2401i	0.212171	+	1.33959i	0.831965	+	0.554828i	$0.187216\pi$
$113$	2.25540	+	14.2401i	0.212171	+	1.33959i	−0.619794	+	0.784764i	$0.712784\pi$
$114$	−0.843298	+	1.89408i	−0.0789821	+	0.177397i
$115$	4.23255	+	0.160785i	0.394687	+	0.0149933i
$116$	3.81435	+	4.23626i	0.354153	+	0.393327i
$117$	−1.21851	−	3.17433i	−0.112652	−	0.293467i
$118$	4.07026	−	0.644666i	0.374698	−	0.0593463i
$119$	−3.28484	−	5.88869i	−0.301120	−	0.539815i
$120$	−0.0789602	−	5.48662i	−0.00720805	−	0.500858i
$121$	6.56180	+	8.82852i	0.596527	+	0.802593i
$122$	−9.03206	+	2.42013i	−0.817724	+	0.219109i
$123$	14.6839	+	22.6112i	1.32400	+	2.03879i
$124$	0.414512	−	3.94382i	0.0372242	−	0.354165i
$125$	−6.95588	−	8.75304i	−0.622153	−	0.782896i
$126$	0.953062	−	7.93806i	0.0849055	−	0.707178i
$127$	1.33422	+	2.61855i	0.118393	+	0.232358i	0.942596	−	0.333935i	$-0.108377\pi$
$127$	1.33422	+	2.61855i	0.118393	+	0.232358i	−0.824203	+	0.566294i	$0.808377\pi$
$128$	0.358368	+	0.933580i	0.0316756	+	0.0825176i
$129$	15.8905	−	7.07489i	1.39908	−	0.622909i
$130$	2.46830	+	0.487640i	0.216485	+	0.0427689i
$131$	−2.21218	+	1.27720i	−0.193279	+	0.111590i	−0.593517	−	0.804822i	$-0.702261\pi$
$131$	−2.21218	+	1.27720i	−0.193279	+	0.111590i	0.400238	+	0.916411i	$0.368928\pi$
$132$	5.41304	−	6.07777i	0.471145	−	0.529002i
$133$	−0.985314	−	2.00651i	−0.0854375	−	0.173987i
$134$	9.95490	−	3.23454i	0.859973	−	0.279422i
$135$	0.0767900	+	0.0920861i	0.00660903	+	0.00792551i
$136$	−2.53462	+	0.266399i	−0.217342	+	0.0228435i
$137$	3.21376	+	0.168426i	0.274570	+	0.0143896i	0.189124	−	0.981953i	$-0.439435\pi$
$137$	3.21376	+	0.168426i	0.274570	+	0.0143896i	0.0854459	+	0.996343i	$0.472769\pi$
$138$	2.53165	−	3.89840i	0.215508	−	0.331854i
$139$	0.880982	−	0.640071i	0.0747239	−	0.0542901i	−0.549796	−	0.835299i	$-0.685295\pi$
$139$	0.880982	−	0.640071i	0.0747239	−	0.0542901i	0.624520	+	0.781009i	$0.285295\pi$
$140$	4.59624	+	3.72486i	0.388453	+	0.314808i
$141$	−2.45664	−	7.56076i	−0.206887	−	0.636731i
$142$	9.72996	+	2.60714i	0.816520	+	0.218786i
$143$	2.20987	+	3.00719i	0.184799	+	0.251474i
$144$	−2.61700	−	1.51093i	−0.218083	−	0.125910i
$145$	8.39195	−	9.59433i	0.696914	−	0.796765i
$146$	6.49408	−	8.93834i	0.537454	−	0.739742i
$147$	11.7823	+	12.4999i	0.971791	+	1.03097i
$148$	6.80474	−	3.46719i	0.559346	−	0.285001i
$149$	1.34950	+	6.34892i	0.110556	+	0.520123i	0.998220	+	0.0596331i	$0.0189931\pi$
$149$	1.34950	+	6.34892i	0.110556	+	0.520123i	−0.887665	+	0.460490i	$0.847674\pi$
$150$	−12.1606	+	1.63315i	−0.992905	+	0.133347i
$151$	12.5937	−	5.60707i	1.02486	−	0.456297i	0.175706	−	0.984443i	$-0.443779\pi$
$151$	12.5937	−	5.60707i	1.02486	−	0.456297i	0.849154	+	0.528146i	$0.177113\pi$
$152$	−0.843737	+	0.0442184i	−0.0684361	+	0.00358659i
$153$	5.44573	−	5.44573i	0.440261	−	0.440261i
$154$	1.29164	+	8.67938i	0.104084	+	0.699404i
$155$	−8.86630	+	0.127598i	−0.712158	+	0.0102490i
$156$	1.84758	−	2.05195i	0.147925	−	0.164287i
$157$	17.8850	+	6.86540i	1.42738	+	0.547918i	0.944716	−	0.327889i	$-0.106337\pi$
$157$	17.8850	+	6.86540i	1.42738	+	0.547918i	0.482660	+	0.875808i	$0.339671\pi$
$158$	3.58307	−	4.42473i	0.285054	−	0.352012i
$159$	16.4647	−	3.49968i	1.30574	−	0.277543i
$160$	1.97754	−	1.04372i	0.156338	−	0.0825132i
$161$	1.47811	+	4.78870i	0.116491	+	0.377402i
$162$	−8.82398	+	1.39758i	−0.693277	+	0.109804i
$163$	−17.6599	+	0.925516i	−1.38323	+	0.0724920i	−0.729368	−	0.684121i	$-0.760186\pi$
$163$	−17.6599	+	0.925516i	−1.38323	+	0.0724920i	−0.653862	+	0.756614i	$0.726852\pi$
$164$	−5.49336	+	9.51478i	−0.428959	+	0.742979i
$165$	−14.9323	−	10.4033i	−1.16248	−	0.809892i
$166$	12.3293	−	7.11834i	0.956941	−	0.552490i
$167$	−8.80354	+	17.2779i	−0.681239	+	1.33701i	0.248445	+	0.968646i	$0.420081\pi$
$167$	−8.80354	+	17.2779i	−0.681239	+	1.33701i	−0.929683	+	0.368360i	$0.879919\pi$
$168$	6.09500	−	2.23693i	0.470240	−	0.172583i
$169$	−6.89703	−	9.49295i	−0.530541	−	0.730227i
$170$	1.26494	+	5.55664i	0.0970162	+	0.426175i
$171$	1.89736	−	1.70839i	0.145095	−	0.130644i
$172$	5.50863	+	4.46080i	0.420029	+	0.340133i
$173$	−4.87288	−	6.01750i	−0.370478	−	0.457502i	0.557478	−	0.830192i	$-0.311769\pi$
$173$	−4.87288	−	6.01750i	−0.370478	−	0.457502i	−0.927956	+	0.372689i	$0.878436\pi$
$174$	−4.32272	−	13.3040i	−0.327704	−	1.00857i
$175$	7.04876	−	11.1944i	0.532836	−	0.846218i
$176$	3.20822	+	0.841015i	0.241829	+	0.0633939i
$177$	−9.76812	−	2.61736i	−0.734217	−	0.196733i
$178$	1.35018	−	0.876814i	0.101200	−	0.0657200i
$179$	−5.82741	−	13.0886i	−0.435561	−	0.978286i	−0.989340	−	0.145623i	$-0.953481\pi$
$179$	−5.82741	−	13.0886i	−0.435561	−	0.978286i	0.553779	−	0.832664i	$-0.313185\pi$
$180$	−2.65923	+	6.21180i	−0.198208	+	0.463000i
$181$	−9.52413	−	3.09458i	−0.707923	−	0.230018i	−0.0671437	−	0.997743i	$-0.521389\pi$
$181$	−9.52413	−	3.09458i	−0.707923	−	0.230018i	−0.640779	+	0.767725i	$0.721389\pi$
$182$	0.422223	+	2.94689i	0.0312973	+	0.218438i
$183$	22.6636	+	3.58955i	1.67534	+	0.265347i
$184$	1.88384	+	0.198000i	0.138879	+	0.0145967i
$185$	−9.50602	−	14.1868i	−0.698896	−	1.04303i
$186$	−4.86561	+	8.42748i	−0.356764	+	0.617933i
$187$	−4.18657	+	7.34306i	−0.306152	+	0.536977i
$188$	2.29076	−	2.29076i	0.167071	−	0.167071i
$189$	−0.0727421	+	0.121802i	−0.00529121	+	0.00885980i
$190$	0.322364	+	1.86154i	0.0233867	+	0.135050i
$191$	−4.00173	−	1.78168i	−0.289555	−	0.128918i	0.256819	−	0.966460i	$-0.417326\pi$
$191$	−4.00173	−	1.78168i	−0.289555	−	0.128918i	−0.546374	+	0.837541i	$0.683992\pi$
$192$	0.128430	−	2.45058i	0.00926861	−	0.176856i
$193$	0.425834	−	8.12540i	0.0306522	−	0.584879i	−0.939525	−	0.342481i	$-0.888733\pi$
$193$	0.425834	−	8.12540i	0.0306522	−	0.584879i	0.970177	−	0.242398i	$-0.0779339\pi$
$194$	−11.8692	−	5.28450i	−0.852157	−	0.379405i
$195$	−5.04670	−	3.55683i	−0.361402	−	0.254710i
$196$	−2.35882	+	6.59060i	−0.168487	+	0.470757i
$197$	0.411078	−	0.411078i	0.0292881	−	0.0292881i	−0.692311	−	0.721599i	$-0.743407\pi$
$197$	0.411078	−	0.411078i	0.0292881	−	0.0292881i	0.721599	+	0.692311i	$0.243407\pi$
$198$	−9.13362	+	4.12606i	−0.649098	+	0.293226i
$199$	−12.8515	+	22.2595i	−0.911019	+	1.57793i	−0.0983907	+	0.995148i	$0.531369\pi$
$199$	−12.8515	+	22.2595i	−0.911019	+	1.57793i	−0.812628	+	0.582783i	$0.801964\pi$
$200$	−2.84274	−	4.11325i	−0.201012	−	0.290851i
$201$	−25.5452	−	2.68491i	−1.80182	−	0.189379i
$202$	10.2508	+	1.62356i	0.721243	+	0.114234i
$203$	13.9989	+	5.61228i	0.982529	+	0.393905i
$204$	5.94798	+	1.93262i	0.416442	+	0.135310i
$205$	22.5846	+	9.66833i	1.57738	+	0.675265i
$206$	−2.36214	−	5.30546i	−0.164578	−	0.369649i
$207$	−4.80059	+	3.11754i	−0.333664	+	0.216684i
$208$	1.08686	+	0.291222i	0.0753598	+	0.0201926i
$209$	−1.51342	+	2.35837i	−0.104685	+	0.163132i
$210$	−6.58600	−	12.9379i	−0.454477	−	0.892800i
$211$	5.89151	+	18.1322i	0.405588	+	1.24827i	0.920403	+	0.390971i	$0.127861\pi$
$211$	5.89151	+	18.1322i	0.405588	+	1.24827i	−0.514815	+	0.857301i	$0.672139\pi$
$212$	4.31674	+	5.33074i	0.296475	+	0.366116i
$213$	−19.2103	−	15.5562i	−1.31627	−	1.06590i
$214$	−5.74041	+	5.16869i	−0.392407	+	0.353324i
$215$	8.44029	−	13.4157i	0.575623	−	0.914942i
$216$	0.0315182	+	0.0433811i	0.00214454	+	0.00295171i
$217$	−3.61485	−	9.84943i	−0.245392	−	0.668623i
$218$	2.49121	−	4.88928i	0.168726	−	0.331144i
$219$	−23.4798	+	13.5561i	−1.58662	+	0.916035i
$220$	1.01479	−	7.34644i	0.0684171	−	0.495297i
$221$	−1.43382	+	2.48346i	−0.0964495	+	0.167055i
$222$	−18.7154	+	0.980834i	−1.25610	+	0.0658293i
$223$	−7.92513	+	1.25522i	−0.530706	+	0.0840555i	−0.416036	−	0.909348i	$-0.636581\pi$
$223$	−7.92513	+	1.25522i	−0.530706	+	0.0840555i	−0.114670	+	0.993404i	$0.536581\pi$
$224$	1.93981	+	1.79920i	0.129609	+	0.120214i
$225$	14.4982	+	4.25357i	0.966544	+	0.283571i
$226$	14.1025	−	2.99758i	0.938085	−	0.199396i
$227$	−13.8201	+	17.0664i	−0.917273	+	1.13274i	0.0735115	+	0.997294i	$0.476579\pi$
$227$	−13.8201	+	17.0664i	−0.917273	+	1.13274i	−0.990785	+	0.135444i	$0.956754\pi$
$228$	1.93562	+	0.743014i	0.128189	+	0.0492073i
$229$	9.51262	−	10.5648i	0.628611	−	0.698144i	−0.341753	−	0.939790i	$-0.611021\pi$
$229$	9.51262	−	10.5648i	0.628611	−	0.698144i	0.970364	+	0.241646i	$0.0776873\pi$
$230$	−0.0609499	−	4.23516i	−0.00401892	−	0.279258i
$231$	5.76738	−	20.7466i	0.379466	−	1.36502i
$232$	4.03083	−	4.03083i	0.264637	−	0.264637i
$233$	−4.35957	+	0.228476i	−0.285605	+	0.0149679i	−0.194601	−	0.980883i	$-0.562341\pi$
$233$	−4.35957	+	0.228476i	−0.285605	+	0.0149679i	−0.0910045	+	0.995850i	$0.529008\pi$
$234$	−3.10621	+	1.38297i	−0.203059	+	0.0904079i
$235$	−5.69467	−	4.47732i	−0.371480	−	0.292068i
$236$	−0.856804	−	4.03094i	−0.0557732	−	0.262392i
$237$	−12.4489	+	6.34301i	−0.808641	+	0.412023i
$238$	−5.70870	+	3.58852i	−0.370040	+	0.232609i
$239$	9.21783	−	12.6873i	0.596252	−	0.820670i	−0.399107	−	0.916904i	$-0.630680\pi$
$239$	9.21783	−	12.6873i	0.596252	−	0.820670i	0.995359	+	0.0962342i	$0.0306798\pi$
$240$	−5.47497	+	0.366000i	−0.353408	+	0.0236252i
$241$	14.8923	+	8.59806i	0.959296	+	0.553850i	0.895956	−	0.444142i	$-0.146491\pi$
$241$	14.8923	+	8.59806i	0.959296	+	0.553850i	0.0633398	+	0.997992i	$0.479825\pi$
$242$	8.47300	−	7.01486i	0.544665	−	0.450932i
$243$	21.3318	+	5.71585i	1.36844	+	0.366672i
$244$	2.88952	+	8.89302i	0.184982	+	0.569317i
$245$	15.2594	+	3.48592i	0.974885	+	0.222707i
$246$	21.8118	−	15.8472i	1.39067	−	1.01038i
$247$	−0.517773	+	0.797301i	−0.0329451	+	0.0507310i
$248$	−3.96010	−	0.207540i	−0.251467	−	0.0131788i
$249$	−34.7447	+	3.65181i	−2.20185	+	0.231424i
$250$	−8.37700	+	7.40445i	−0.529808	+	0.468298i
$251$	−2.12825	+	0.691509i	−0.134334	+	0.0436477i	−0.375412	−	0.926858i	$-0.622499\pi$
$251$	−2.12825	+	0.691509i	−0.134334	+	0.0436477i	0.241079	+	0.970506i	$0.422499\pi$
$252$	−7.97706	−	0.536310i	−0.502507	−	0.0337844i
$253$	4.17837	−	4.69148i	0.262692	−	0.294951i
$254$	2.54513	−	1.46943i	0.159696	−	0.0922004i
$255$	2.71041	−	13.7194i	0.169732	−	0.859140i
$256$	0.913545	−	0.406737i	0.0570966	−	0.0254210i
$257$	−0.343722	−	0.895425i	−0.0214408	−	0.0558551i	0.922442	−	0.386135i	$-0.126190\pi$
$257$	−0.343722	−	0.895425i	−0.0214408	−	0.0558551i	−0.943883	+	0.330280i	$0.892857\pi$
$258$	−7.89683	−	15.4984i	−0.491635	−	0.964889i
$259$	12.1169	−	16.1698i	0.752909	−	1.00474i
$260$	0.357791	−	2.49044i	0.0221892	−	0.154451i
$261$	−1.80060	+	17.1316i	−0.111454	+	1.06042i
$262$	1.39123	+	2.14230i	0.0859503	+	0.132352i
$263$	17.6975	−	4.74202i	1.09127	−	0.292405i	0.332066	−	0.943256i	$-0.392254\pi$
$263$	17.6975	−	4.74202i	1.09127	−	0.292405i	0.759206	+	0.650851i	$0.225588\pi$
$264$	−6.35274	−	5.08754i	−0.390984	−	0.313116i
$265$	10.6884	−	11.0006i	0.656585	−	0.675760i
$266$	−1.95220	+	1.08898i	−0.119697	+	0.0667694i
$267$	−3.90197	+	0.618011i	−0.238797	+	0.0378217i
$268$	−3.75111	−	9.77198i	−0.229136	−	0.596918i
$269$	−18.7677	−	20.8437i	−1.14429	−	1.27086i	−0.957491	−	0.288464i	$-0.906855\pi$
$269$	−18.7677	−	20.8437i	−1.14429	−	1.27086i	−0.186799	−	0.982398i	$-0.559811\pi$
$270$	0.0879410	−	0.0815042i	0.00535192	−	0.00496019i
$271$	−1.34147	+	3.01298i	−0.0814883	+	0.183026i	−0.949694	−	0.313178i	$-0.898606\pi$
$271$	−1.34147	+	3.01298i	−0.0814883	+	0.183026i	0.868206	+	0.496204i	$0.165273\pi$
$272$	0.398686	+	2.51720i	0.0241739	+	0.152628i
$273$	1.99479	−	7.02774i	0.120730	−	0.425338i
$274$		−	3.21817i		−	0.194417i
$275$	−16.5804	−	0.301043i	−0.999835	−	0.0181536i
$276$	−4.02556	−	2.32416i	−0.242310	−	0.139898i
$277$	−1.15368	+	0.749211i	−0.0693181	+	0.0450157i	−0.578833	−	0.815446i	$-0.696492\pi$
$277$	−1.15368	+	0.749211i	−0.0693181	+	0.0450157i	0.509515	+	0.860462i	$0.329825\pi$
$278$	−0.685300	−	0.846276i	−0.0411016	−	0.0507562i
$279$	9.69467	−	7.04359i	0.580405	−	0.421689i
$280$	3.47920	−	4.78489i	0.207922	−	0.285952i
$281$	−7.51558	+	23.1306i	−0.448342	+	1.37985i	0.430435	+	0.902622i	$0.358360\pi$
$281$	−7.51558	+	23.1306i	−0.448342	+	1.37985i	−0.878777	+	0.477233i	$0.841640\pi$
$282$	−7.42183	+	2.84897i	−0.441964	+	0.169654i
$283$	6.06043	−	15.7880i	0.360255	−	0.938497i	−0.626952	−	0.779058i	$-0.715698\pi$
$283$	6.06043	−	15.7880i	0.360255	−	0.938497i	0.987208	−	0.159440i	$-0.0509687\pi$
$284$	2.09434	−	9.85308i	0.124276	−	0.584673i
$285$	1.13535	−	4.49493i	0.0672522	−	0.266257i
$286$	2.88741	−	2.36423i	0.170736	−	0.139800i
$287$	−1.94989	+	29.0027i	−0.115099	+	1.71197i
$288$	−1.37189	+	2.69249i	−0.0808395	+	0.158656i
$289$	10.4472	+	1.09804i	0.614541	+	0.0645909i
$290$	−10.0204	−	7.87832i	−0.588417	−	0.462631i
$291$	21.3337	+	23.6935i	1.25060	+	1.38894i
$292$	−9.26596	−	6.01739i	−0.542250	−	0.352141i
$293$	−4.73617	+	29.9030i	−0.276690	+	1.74695i	0.322704	+	0.946500i	$0.395408\pi$
$293$	−4.73617	+	29.9030i	−0.276690	+	1.74695i	−0.599394	+	0.800454i	$0.704592\pi$
$294$	11.8661	−	12.4204i	0.692046	−	0.724372i
$295$	−8.72194	+	2.97336i	−0.507811	+	0.173115i
$296$	−3.81857	−	6.61395i	−0.221950	−	0.384428i
$297$	0.177841		0.000964704i	0.0103194		5.59778e-5i
$298$	6.26959	−	1.67993i	0.363187	−	0.0973158i
$299$	1.42616	−	1.58391i	0.0824771	−	0.0916001i
$300$	2.26735	+	12.0584i	0.130906	+	0.696193i
$301$	18.2844	+	4.16966i	1.05390	+	0.240335i
$302$	−6.25849	−	12.2830i	−0.360136	−	0.706806i
$303$	−21.3596	−	13.8711i	−1.22708	−	0.796874i
$304$	0.0883156	+	0.840267i	0.00506525	+	0.0481926i
$305$	18.9767	−	8.77834i	1.08660	−	0.502646i
$306$	−5.72328	−	5.15326i	−0.327178	−	0.294592i
$307$	22.3866	+	22.3866i	1.27767	+	1.27767i	0.941969	+	0.335699i	$0.108972\pi$
$307$	22.3866	+	22.3866i	1.27767	+	1.27767i	0.335699	+	0.941969i	$0.391028\pi$
$308$	8.59989	−	1.74412i	0.490024	−	0.0993804i
$309$			14.2514i			0.810735i
$310$	0.591450	+	8.84747i	0.0335921	+	0.502502i
$311$	−2.56953	−	5.77126i	−0.145705	−	0.327258i	0.825920	−	0.563788i	$-0.190656\pi$
$311$	−2.56953	−	5.77126i	−0.145705	−	0.327258i	−0.971624	+	0.236530i	$0.923990\pi$
$312$	−2.14583	−	1.73766i	−0.121484	−	0.0983756i
$313$	−10.5780	+	16.2887i	−0.597906	+	0.920694i	0.402081	+	0.915604i	$0.368287\pi$
$313$	−10.5780	+	16.2887i	−0.597906	+	0.920694i	−0.999987	+	0.00509018i	$0.998380\pi$
$314$	5.91996	−	18.2198i	0.334083	−	1.02820i
$315$	0.928847	+	17.8534i	0.0523346	+	1.00592i
$316$	−4.60619	−	3.34659i	−0.259118	−	0.188260i
$317$	1.56296	+	29.8230i	0.0877844	+	1.67503i	0.587798	+	0.809008i	$0.299995\pi$
$317$	1.56296	+	29.8230i	0.0877844	+	1.67503i	−0.500014	+	0.866018i	$0.666672\pi$
$318$	−4.35658	−	16.2590i	−0.244305	−	0.911758i
$319$	−3.05884	−	18.6572i	−0.171262	−	1.04460i
$320$	−1.14578	−	1.92020i	−0.0640513	−	0.107343i
$321$	18.0277	−	5.85756i	1.00621	−	0.326937i
$322$	4.70478	−	1.72671i	0.262187	−	0.0962256i
$323$	−2.12677	−	0.336848i	−0.118337	−	0.0187427i
$324$	1.85748	+	8.73874i	0.103193	+	0.485486i
$325$	−5.62441	−	0.132643i	−0.311986	−	0.00735771i
$326$	1.84850	+	17.5873i	0.102379	+	0.974068i
$327$	−10.4648	+	8.47425i	−0.578706	+	0.468627i
$328$	9.78924	+	4.98787i	0.540520	+	0.275409i
$329$	2.76877	−	8.11172i	0.152647	−	0.447213i
$330$	−9.60750	+	15.4563i	−0.528875	+	0.850842i
$331$	9.37076	+	16.2306i	0.515064	+	0.892117i	0.999847	+	0.0174823i	$0.00556509\pi$
$331$	9.37076	+	16.2306i	0.515064	+	0.892117i	−0.484783	+	0.874634i	$0.661102\pi$
$332$	−7.75385	−	11.9399i	−0.425548	−	0.655286i
$333$	21.5454	+	8.27052i	1.18068	+	0.453222i
$334$	17.7150	+	7.88722i	0.969321	+	0.431570i
$335$	−20.6993	+	10.9248i	−1.13092	+	0.596886i
$336$	−2.55286	−	5.96958i	−0.139270	−	0.325667i
$337$	3.66752	−	23.1558i	0.199782	−	1.26138i	−0.660215	−	0.751077i	$-0.729535\pi$
$337$	3.66752	−	23.1558i	0.199782	−	1.26138i	0.859997	−	0.510299i	$-0.170465\pi$
$338$	−9.11898	+	7.38441i	−0.496007	+	0.401659i
$339$	−34.6068	−	7.35590i	−1.87958	−	0.399518i
$340$	5.48282	−	1.55402i	0.297348	−	0.0842783i
$341$	−8.22138	+	10.2659i	−0.445213	+	0.555931i
$342$	−1.80535	−	1.80535i	−0.0976221	−	0.0976221i
$343$	2.08406	+	18.4026i	0.112529	+	0.993648i
$344$	4.16639	−	5.73454i	0.224637	−	0.309186i
$345$	−4.09052	+	9.55519i	−0.220226	+	0.514434i
$346$	−5.75423	+	5.18113i	−0.309349	+	0.278539i
$347$	−0.680133	−	0.0356443i	−0.0365114	−	0.00191348i	0.0340715	−	0.999419i	$-0.489153\pi$
$347$	−0.680133	−	0.0356443i	−0.0365114	−	0.00191348i	−0.0705829	+	0.997506i	$0.522486\pi$
$348$	−13.0595	+	5.01307i	−0.700062	+	0.268729i
$349$	24.8855	+	18.0804i	1.33209	+	0.967819i	0.999695	+	0.0246787i	$0.00785627\pi$
$349$	24.8855	+	18.0804i	1.33209	+	0.967819i	0.332394	+	0.943141i	$0.392144\pi$
$350$	−11.5480	−	6.45323i	−0.617266	−	0.344940i
$351$	0.0603351			0.00322045
$352$	0.671957	−	3.24784i	0.0358154	−	0.173111i
$353$	5.78652	+	21.5956i	0.307985	+	1.14942i	0.930345	+	0.366685i	$0.119507\pi$
$353$	5.78652	+	21.5956i	0.307985	+	1.14942i	−0.622360	+	0.782731i	$0.713826\pi$
$354$	−2.10255	+	9.89172i	−0.111749	+	0.525739i
$355$	−22.4325	−	2.03185i	−1.19060	−	0.107839i
$356$	−0.946275	−	1.30244i	−0.0501525	−	0.0690290i
$357$	16.3795	−	2.34681i	0.866893	−	0.124206i
$358$	−12.7657	+	6.50443i	−0.674686	+	0.343770i
$359$	3.30110	−	7.41440i	0.174226	−	0.391317i	−0.805234	−	0.592957i	$-0.797960\pi$
$359$	3.30110	−	7.41440i	0.174226	−	0.391317i	0.979460	+	0.201640i	$0.0646271\pi$
$360$	6.34246	+	2.33049i	0.334277	+	0.122828i
$361$	17.8866	+	3.80190i	0.941398	+	0.200100i
$362$	−2.59188	+	9.67303i	−0.136226	+	0.508403i
$363$	−25.9963	+	7.26886i	−1.36445	+	0.381516i
$364$	2.92076	−	0.575873i	0.153089	−	0.0301839i
$365$	−10.8979	+	22.1714i	−0.570422	+	1.16050i
$366$	2.39852	−	22.8204i	0.125372	−	1.19284i
$367$	2.17051	−	2.68035i	0.113300	−	0.139913i	−0.717341	−	0.696722i	$-0.754641\pi$
$367$	2.17051	−	2.68035i	0.113300	−	0.139913i	0.830641	+	0.556809i	$0.187974\pi$
$368$	0.0991357	−	1.89162i	0.00516781	−	0.0986077i
$369$	−32.4747	+	6.90272i	−1.69057	+	0.359341i
$370$	−13.6698	+	10.2355i	−0.710661	+	0.532117i
$371$	16.4684	+	7.62561i	0.854995	+	0.395902i
$372$	8.67058	+	4.41788i	0.449549	+	0.229056i
$373$	5.36677	−	20.0291i	0.277881	−	1.03707i	−0.676005	−	0.736897i	$-0.736290\pi$
$373$	5.36677	−	20.0291i	0.277881	−	1.03707i	0.953886	−	0.300168i	$-0.0970429\pi$
$374$	7.55210	+	3.79653i	0.390510	+	0.196314i
$375$	26.1699	−	8.23806i	1.35141	−	0.425412i
$376$	−2.40751	−	2.16773i	−0.124158	−	0.111792i
$377$	−1.00339	−	6.33516i	−0.0516772	−	0.326277i
$378$	0.125442	+	0.0662678i	0.00645205	+	0.00340845i
$379$	−10.6598	−	3.46357i	−0.547556	−	0.177912i	0.0221585	−	0.999754i	$-0.492946\pi$
$379$	−10.6598	−	3.46357i	−0.547556	−	0.177912i	−0.569714	+	0.821843i	$0.692946\pi$
$380$	1.84212	−	0.419347i	0.0944985	−	0.0215121i
$381$	−7.17231	+	0.753840i	−0.367448	+	0.0386204i
$382$	−1.56981	+	4.08949i	−0.0803184	+	0.209237i
$383$	−1.42274	−	27.1475i	−0.0726987	−	1.38717i	−0.754818	−	0.655934i	$-0.772275\pi$
$383$	−1.42274	−	27.1475i	−0.0726987	−	1.38717i	0.682120	−	0.731241i	$-0.261058\pi$
$384$	−2.45395			−0.125227
$385$	−6.15740	−	18.6303i	−0.313810	−	0.949486i
$386$	−8.13655			−0.414139
$387$	1.12102	+	21.3904i	0.0569848	+	1.08733i
$388$	−4.65607	+	12.1295i	−0.236376	+	0.615781i
$389$	−37.3151	+	3.92198i	−1.89195	+	0.198852i	−0.978235	−	0.207498i	$-0.933468\pi$
$389$	−37.3151	+	3.92198i	−1.89195	+	0.198852i	−0.913717	+	0.406351i	$0.866801\pi$
$390$	−3.28783	+	5.22594i	−0.166486	+	0.264626i
$391$	4.59129	+	1.49180i	0.232191	+	0.0754436i
$392$	6.70502	+	2.01066i	0.338655	+	0.101554i
$393$	−0.980588	−	6.19119i	−0.0494641	−	0.312304i
$394$	−0.432029	−	0.389001i	−0.0217653	−	0.0195976i
$395$	−6.20628	+	11.1160i	−0.312272	+	0.559306i
$396$	4.59842	+	8.90516i	0.231079	+	0.447501i
$397$	5.03233	−	18.7809i	0.252566	−	0.942588i	−0.716863	−	0.697214i	$-0.754423\pi$
$397$	5.03233	−	18.7809i	0.252566	−	0.942588i	0.969429	−	0.245374i	$-0.0789107\pi$
$398$	22.9015	+	11.6689i	1.14795	+	0.584910i
$399$	5.46333	−	0.492751i	0.273509	−	0.0246684i
$400$	−3.95884	+	3.05411i	−0.197942	+	0.152706i
$401$	−24.5291	+	5.21382i	−1.22493	+	0.260366i	−0.774573	−	0.632485i	$-0.782035\pi$
$401$	−24.5291	+	5.21382i	−1.22493	+	0.260366i	−0.450353	+	0.892851i	$0.648702\pi$
$402$	−1.34430	+	25.6508i	−0.0670475	+	1.27934i
$403$	−2.80803	+	3.46763i	−0.139878	+	0.172735i
$404$	1.08485	−	10.3217i	0.0539736	−	0.513524i
$405$	18.9084	−	6.44598i	0.939567	−	0.320303i
$406$	4.87194	−	14.2734i	0.241790	−	0.708378i
$407$	−25.2047	−	2.51097i	−1.24935	−	0.124464i
$408$	1.61867	−	6.04097i	0.0801363	−	0.299073i
$409$	−18.8172	−	3.99971i	−0.930449	−	0.197773i	−0.282335	−	0.959316i	$-0.591109\pi$
$409$	−18.8172	−	3.99971i	−0.930449	−	0.197773i	−0.648114	+	0.761543i	$0.724442\pi$
$410$	8.47309	−	23.0596i	0.418456	−	1.13883i
$411$	−3.21209	+	7.21446i	−0.158441	+	0.355863i
$412$	−5.17457	+	2.63657i	−0.254933	+	0.129895i
$413$	−6.73566	−	8.57375i	−0.331440	−	0.421887i
$414$	3.36451	+	4.63085i	0.165357	+	0.227594i
$415$	−24.4490	+	20.3878i	−1.20015	+	1.00080i
$416$	0.233941	−	1.10061i	0.0114699	−	0.0539617i
$417$	0.691625	+	2.58118i	0.0338690	+	0.126401i
$418$	2.43434	+	1.38792i	0.119068	+	0.0678852i
$419$	7.97366			0.389539			0.194769	−	0.980849i	$-0.437604\pi$
$419$	7.97366			0.389539			0.194769	+	0.980849i	$0.437604\pi$
$420$	−12.5755	+	7.25409i	−0.613621	+	0.353963i
$421$	17.5259	+	12.7333i	0.854159	+	0.620583i	0.926290	−	0.376812i	$-0.122980\pi$
$421$	17.5259	+	12.7333i	0.854159	+	0.620583i	−0.0721305	+	0.997395i	$0.522980\pi$
$422$	17.7990	−	6.83240i	0.866443	−	0.332596i
$423$	9.77624	+	0.512351i	0.475337	+	0.0249114i
$424$	5.09751	−	4.58982i	0.247557	−	0.222901i
$425$	−4.90710	−	11.7602i	−0.238029	−	0.570453i
$426$	−14.5295	+	19.9982i	−0.703957	+	0.968914i
$427$	17.2332	+	17.7500i	0.833974	+	0.858982i
$428$	5.46204	+	5.46204i	0.264018	+	0.264018i
$429$	−8.83273	+	2.41815i	−0.426448	+	0.116749i
$430$	−13.8390	−	7.72660i	−0.667377	−	0.372610i
$431$	27.3377	+	5.81080i	1.31681	+	0.279896i	0.812163	−	0.583430i	$-0.198290\pi$
$431$	27.3377	+	5.81080i	1.31681	+	0.279896i	0.504645	+	0.863327i	$0.331623\pi$
$432$	0.0416721	−	0.0337454i	0.00200495	−	0.00162358i
$433$	−5.01575	+	31.6682i	−0.241041	+	1.52188i	0.509163	+	0.860670i	$0.329955\pi$
$433$	−5.01575	+	31.6682i	−0.241041	+	1.52188i	−0.750205	+	0.661206i	$0.770045\pi$
$434$	−9.64675	+	4.12538i	−0.463059	+	0.198024i
$435$	14.6002	+	27.6630i	0.700024	+	1.32634i
$436$	−5.01296	−	2.23191i	−0.240077	−	0.106889i
$437$	1.49412	+	0.573538i	0.0714733	+	0.0274360i
$438$	14.7663	+	22.7382i	0.705563	+	1.08647i
$439$	4.31814	+	7.47924i	0.206094	+	0.356965i	0.950481	−	0.310784i	$-0.100592\pi$
$439$	4.31814	+	7.47924i	0.206094	+	0.356965i	−0.744387	+	0.667748i	$0.767258\pi$
$440$	−7.38948	−	0.628915i	−0.352280	−	0.0299824i
$441$	−19.5699	+	8.02915i	−0.931899	+	0.382340i
$442$	2.55509	+	1.30189i	0.121533	+	0.0619244i
$443$	32.0669	−	25.9673i	1.52354	−	1.23374i	0.637217	−	0.770685i	$-0.280086\pi$
$443$	32.0669	−	25.9673i	1.52354	−	1.23374i	0.886328	−	0.463058i	$-0.153248\pi$
$444$	1.95898	+	18.6385i	0.0929691	+	0.884542i
$445$	−2.64027	+	2.44701i	−0.125161	+	0.116000i
$446$	1.66827	+	7.84857i	0.0789947	+	0.371641i
$447$	−15.7319	−	2.49168i	−0.744092	−	0.117853i
$448$	1.69521	−	2.03132i	0.0800913	−	0.0959708i
$449$	−27.0163	+	8.77812i	−1.27498	+	0.414265i	−0.866808	−	0.498641i	$-0.833833\pi$
$449$	−27.0163	+	8.77812i	−1.27498	+	0.414265i	−0.408169	+	0.912906i	$0.633833\pi$
$450$	3.48896	−	14.7009i	0.164471	−	0.693008i
$451$	32.3770	−	16.7188i	1.52457	−	0.787255i
$452$	−3.73154	−	13.9263i	−0.175517	−	0.655038i
$453$	1.77047	+	33.7825i	0.0831838	+	1.58724i
$454$	17.7663	+	12.9080i	0.833815	+	0.605802i
$455$	−2.05464	−	6.33172i	−0.0963230	−	0.296836i
$456$	0.640693	−	1.97185i	0.0300032	−	0.0923404i
$457$	13.0543	−	20.1018i	0.610654	−	0.940324i	−0.389163	−	0.921169i	$-0.627236\pi$
$457$	13.0543	−	20.1018i	0.610654	−	0.940324i	0.999817	−	0.0191550i	$-0.00609761\pi$
$458$	−11.0482	−	8.94666i	−0.516249	−	0.418050i
$459$	0.0555845	+	0.124845i	0.00259446	+	0.00582726i
$460$	−4.22617	+	0.282518i	−0.197046	+	0.0131725i
$461$			25.6929i			1.19664i	0.801259	+	0.598318i	$0.204164\pi$
$461$			25.6929i			1.19664i	−0.801259	+	0.598318i	$0.795836\pi$
$462$	−21.0200	−	4.67368i	−0.977938	−	0.217439i
$463$	3.46806	+	3.46806i	0.161174	+	0.161174i	0.783087	−	0.621912i	$-0.213644\pi$
$463$	3.46806	+	3.46806i	0.161174	+	0.161174i	−0.621912	+	0.783087i	$0.713644\pi$
$464$	−4.23626	−	3.81435i	−0.196664	−	0.177077i
$465$	7.50484	−	20.4245i	0.348028	−	0.947164i
$466$	0.456325	+	4.34164i	0.0211388	+	0.201123i
$467$	−10.9217	−	7.09265i	−0.505397	−	0.328209i	0.266629	−	0.963799i	$-0.414090\pi$
$467$	−10.9217	−	7.09265i	−0.505397	−	0.328209i	−0.772027	+	0.635590i	$0.780757\pi$
$468$	1.54365	+	3.02958i	0.0713551	+	0.140042i
$469$	−20.3044	−	18.8326i	−0.937571	−	0.869609i
$470$	−4.17315	+	5.92120i	−0.192493	+	0.273124i
$471$	−31.4567	+	34.9361i	−1.44945	+	1.60977i
$472$	−3.98058	+	1.06659i	−0.183221	+	0.0490939i
$473$	−7.38591	−	22.3188i	−0.339605	−	1.02622i
$474$	6.98584	+	12.0998i	0.320870	+	0.555764i
$475$	−1.42051	−	3.97849i	−0.0651775	−	0.182545i
$476$	3.88238	+	5.51307i	0.177948	+	0.252691i
$477$	−3.24258	+	20.4728i	−0.148467	+	0.937386i
$478$	−13.1523	−	8.54120i	−0.601572	−	0.390665i
$479$	−3.79357	−	4.21319i	−0.173333	−	0.192506i	0.650219	−	0.759747i	$-0.274677\pi$
$479$	−3.79357	−	4.21319i	−0.173333	−	0.192506i	−0.823551	+	0.567242i	$0.808011\pi$
$480$	0.652036	+	5.44831i	0.0297612	+	0.248680i
$481$	−8.54619	−	0.898241i	−0.389673	−	0.0409563i
$482$	7.80688	−	15.3219i	0.355594	−	0.697892i
$483$	−12.2706	−	0.824970i	−0.558330	−	0.0375374i
$484$	−7.44869	−	8.09426i	−0.338577	−	0.367921i
$485$	28.1673	+	7.11461i	1.27901	+	0.323058i
$486$	4.59159	−	21.6017i	0.208279	−	0.979875i
$487$	4.54051	−	11.8284i	0.205750	−	0.535998i	−0.791412	−	0.611284i	$-0.790654\pi$
$487$	4.54051	−	11.8284i	0.205750	−	0.535998i	0.997162	+	0.0752856i	$0.0239869\pi$
$488$	8.72961	−	3.35098i	0.395171	−	0.151692i
$489$	13.4101	−	41.2720i	0.606425	−	1.86638i
$490$	2.68253	−	15.4209i	0.121184	−	0.696645i
$491$	−3.48115	+	2.52920i	−0.157102	+	0.114141i	−0.663559	−	0.748124i	$-0.730955\pi$
$491$	−3.48115	+	2.52920i	−0.157102	+	0.114141i	0.506457	+	0.862265i	$0.330955\pi$
$492$	−16.9670	−	20.9525i	−0.764931	−	0.944611i
$493$	12.1843	−	7.91255i	0.548751	−	0.356363i
$494$	0.823306	+	0.475336i	0.0370423	+	0.0213864i
$495$	18.5496	−	12.5757i	0.833744	−	0.565236i
$496$			3.96554i			0.178058i
$497$	−6.51685	−	25.8421i	−0.292321	−	1.15918i
$498$	5.46520	+	34.5059i	0.244901	+	1.54625i
$499$	2.49930	−	5.61352i	0.111884	−	0.251296i	−0.848921	−	0.528519i	$-0.822748\pi$
$499$	2.49930	−	5.61352i	0.111884	−	0.251296i	0.960805	+	0.277223i	$0.0894142\pi$
$500$	7.83272	+	7.97800i	0.350290	+	0.356787i
$501$	−31.8410	−	35.3630i	−1.42255	−	1.57990i
$502$	0.801945	+	2.08914i	0.0357926	+	0.0932428i
$503$	−36.6445	+	5.80392i	−1.63390	+	0.258784i	−0.904867	−	0.425695i	$-0.860030\pi$
$503$	−36.6445	+	5.80392i	−1.63390	+	0.258784i	−0.729032	+	0.684479i	$0.760030\pi$
$504$	−0.118088	+	7.99419i	−0.00526008	+	0.356090i
$505$	−23.2048	+	0.333949i	−1.03260	+	0.0148605i
$506$	−4.90373	−	3.92711i	−0.217997	−	0.174581i
$507$	27.8133	−	7.45255i	1.23523	−	0.330979i
$508$	−1.60062	−	2.46474i	−0.0710160	−	0.109355i
$509$	−2.76295	+	26.2878i	−0.122466	+	1.16518i	0.744782	+	0.667308i	$0.232553\pi$
$509$	−2.76295	+	26.2878i	−0.122466	+	1.16518i	−0.867248	+	0.497877i	$0.834113\pi$
$510$	−13.8424	−	1.98868i	−0.612953	−	0.0880602i
$511$	−29.0229	−	3.48456i	−1.28390	−	0.154148i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	0.0162358	+	0.0422958i	0.000716829	+	0.00186740i
$514$	−0.876209	+	0.390113i	−0.0386479	+	0.0172072i
$515$	7.22872	+	10.7881i	0.318535	+	0.475382i
$516$	−15.0639	+	8.69713i	−0.663150	+	0.382870i
$517$	−10.4975	+	2.29091i	−0.461681	+	0.100754i
$518$	−16.7818	−	11.2541i	−0.737348	−	0.494475i
$519$	18.0711	−	5.87166i	0.793234	−	0.257737i
$520$	−2.50576	−	0.226961i	−0.109885	−	0.00995289i
$521$	26.1727	−	2.75086i	1.14665	−	0.120517i	0.487911	−	0.872893i	$-0.337759\pi$
$521$	26.1727	−	2.75086i	1.14665	−	0.120517i	0.658734	+	0.752376i	$0.271092\pi$
$522$	17.2023	+	0.901535i	0.752925	+	0.0394591i
$523$	14.0454	−	21.6281i	0.614163	−	0.945729i	−0.385571	−	0.922678i	$-0.625995\pi$
$523$	14.0454	−	21.6281i	0.614163	−	0.945729i	0.999734	−	0.0230506i	$-0.00733787\pi$
$524$	2.06655	−	1.50144i	0.0902778	−	0.0655907i
$525$	19.4471	+	25.9929i	0.848742	+	1.13443i
$526$	−5.66173	−	17.4250i	−0.246863	−	0.759767i
$527$	−9.76212	−	2.61575i	−0.425245	−	0.113944i
$528$	−4.74809	+	6.61030i	−0.206634	+	0.287676i
$529$	16.8112	+	9.70597i	0.730923	+	0.421999i
$530$	−11.5449	−	10.0981i	−0.501478	−	0.438632i
$531$	7.31972	−	10.0747i	0.317649	−	0.437206i
$532$	1.18965	+	1.89253i	0.0515780	+	0.0820515i
$533$	11.0148	−	5.61232i	0.477104	−	0.243097i
$534$	0.821377	+	3.86428i	0.0355445	+	0.167224i
$535$	10.6756	−	13.5783i	0.461548	−	0.587040i
$536$	−9.56227	+	4.25740i	−0.413027	+	0.183891i
$537$	35.1101	−	1.84004i	1.51511	−	0.0794036i
$538$	−19.8329	+	19.8329i	−0.855057	+	0.855057i
$539$	18.3896	−	14.1712i	0.792096	−	0.610397i
$540$	−0.0859950	−	0.0835549i	−0.00370063	−	0.00359563i
$541$	2.44481	−	2.71524i	0.105111	−	0.116737i	−0.688294	−	0.725432i	$-0.741640\pi$
$541$	2.44481	−	2.71524i	0.105111	−	0.116737i	0.793404	+	0.608695i	$0.208307\pi$
$542$	3.07906	+	1.18194i	0.132257	+	0.0507687i
$543$	15.4652	−	19.0979i	0.663675	−	0.819571i
$544$	2.49289	−	0.529880i	0.106882	−	0.0227184i
$545$	−3.62336	+	11.7229i	−0.155208	+	0.502156i
$546$	−7.12251	−	1.62425i	−0.304815	−	0.0695114i
$547$	−24.1175	+	3.81983i	−1.03119	+	0.163324i	−0.649023	−	0.760769i	$-0.724822\pi$
$547$	−24.1175	+	3.81983i	−1.03119	+	0.163324i	−0.382167	+	0.924093i	$0.624822\pi$
$548$	−3.21376	+	0.168426i	−0.137285	+	0.00719480i
$549$	−14.1282	+	24.4707i	−0.602976	+	1.04438i
$550$	0.567120	+	16.5734i	0.0241821	+	0.706693i
$551$	4.17103	−	2.40814i	0.177692	−	0.102590i
$552$	−2.11029	+	4.14168i	−0.0898199	+	0.176281i
$553$	−14.8419	−	2.57599i	−0.631140	−	0.109542i
$554$	0.808563	+	1.11289i	0.0343525	+	0.0472822i
$555$	40.8610	−	9.30178i	1.73445	−	0.394839i
$556$	−0.809250	+	0.728652i	−0.0343198	+	0.0309017i
$557$	−29.6106	−	23.9782i	−1.25464	−	1.01599i	−0.998785	−	0.0492748i	$-0.984309\pi$
$557$	−29.6106	−	23.9782i	−1.25464	−	1.01599i	−0.255857	−	0.966715i	$-0.582358\pi$
$558$	−7.54132	−	9.31275i	−0.319249	−	0.394240i
$559$	−2.46463	−	7.58534i	−0.104243	−	0.320826i
$560$	−4.96042	−	3.22401i	−0.209616	−	0.136239i
$561$	−13.1409	−	16.0488i	−0.554808	−	0.677583i
$562$	23.4922	+	6.29472i	0.990959	+	0.265527i
$563$	34.1979	−	22.2083i	1.44127	−	0.935970i	0.442027	−	0.897002i	$-0.354259\pi$
$563$	34.1979	−	22.2083i	1.44127	−	0.935970i	0.999240	−	0.0389688i	$-0.0124073\pi$
$564$	3.23350	+	7.26256i	0.136155	+	0.305809i
$565$	−29.9280	+	11.9852i	−1.25908	+	0.504221i
$566$	−16.0835	−	5.22585i	−0.676040	−	0.219659i
$567$	14.6023	+	18.5872i	0.613241	+	0.780587i
$568$	−9.94918	−	1.57580i	−0.417458	−	0.0661189i
$569$	35.5188	+	3.73318i	1.48903	+	0.156503i	0.813817	−	0.581122i	$-0.197386\pi$
$569$	35.5188	+	3.73318i	1.48903	+	0.156503i	0.675211	+	0.737625i	$0.264053\pi$
$570$	−4.54819	−	0.898545i	−0.190503	−	0.0376359i
$571$	1.40366	−	2.43121i	0.0587412	−	0.101743i	−0.835159	−	0.550008i	$-0.814625\pi$
$571$	1.40366	−	2.43121i	0.0587412	−	0.101743i	0.893901	+	0.448265i	$0.147958\pi$
$572$	−2.51210	−	2.75972i	−0.105036	−	0.115390i
$573$	7.60094	−	7.60094i	0.317534	−	0.317534i
$574$	29.0650	+	0.429341i	1.21315	+	0.0179203i
$575$	1.75018	+	9.30798i	0.0729877	+	0.388170i
$576$	2.76060	+	1.22910i	0.115025	+	0.0512124i
$577$	0.441552	−	8.42531i	0.0183820	−	0.350750i	−0.973919	−	0.226898i	$-0.927142\pi$
$577$	0.441552	−	8.42531i	0.0183820	−	0.350750i	0.992301	−	0.123853i	$-0.0395250\pi$
$578$	0.549776	−	10.4903i	0.0228677	−	0.436341i
$579$	18.2404	+	8.12117i	0.758047	+	0.337504i
$580$	−7.34310	+	10.4190i	−0.304906	+	0.432624i
$581$	−32.3386	−	19.3131i	−1.34163	−	0.801243i
$582$	22.5445	−	22.5445i	0.934499	−	0.934499i
$583$	−2.50071	−	22.6121i	−0.103569	−	0.936498i
$584$	−5.52420	+	9.56819i	−0.228593	+	0.395935i
$585$	6.31618	−	4.23223i	0.261142	−	0.174981i
$586$	30.1099	+	3.16468i	1.24383	+	0.130732i
$587$	6.88837	+	1.09101i	0.284313	+	0.0450308i	0.296962	−	0.954889i	$-0.404026\pi$
$587$	6.88837	+	1.09101i	0.284313	+	0.0450308i	−0.0126490	+	0.999920i	$0.504026\pi$
$588$	−13.0244	−	11.1998i	−0.537117	−	0.461873i
$589$	−3.18648	−	1.03535i	−0.131297	−	0.0426609i
$590$	3.42575	+	8.55438i	0.141036	+	0.352178i
$591$	0.580253	+	1.30327i	0.0238684	+	0.0536094i
$592$	−6.40504	+	4.15948i	−0.263246	+	0.170954i
$593$	−0.941362	−	0.252237i	−0.0386571	−	0.0103581i	0.239439	−	0.970911i	$-0.423037\pi$
$593$	−0.941362	−	0.252237i	−0.0386571	−	0.0103581i	−0.278096	+	0.960553i	$0.589703\pi$
$594$	−0.0102709	−	0.177547i	−0.000421419	−	0.00728484i
$595$	11.2087	−	10.0846i	0.459511	−	0.413429i
$596$	−2.00575	−	6.17307i	−0.0821589	−	0.252859i
$597$	−39.6936	−	49.0175i	−1.62455	−	2.00615i
$598$	−1.65638	−	1.34131i	−0.0677345	−	0.0548503i
$599$	−11.7631	+	10.5915i	−0.480627	+	0.432759i	−0.873493	−	0.486837i	$-0.838150\pi$
$599$	−11.7631	+	10.5915i	−0.480627	+	0.432759i	0.392865	+	0.919596i	$0.371484\pi$
$600$	11.9232	−	2.89533i	0.486764	−	0.118201i
$601$	−2.49263	−	3.43081i	−0.101677	−	0.139946i	0.755147	−	0.655555i	$-0.227565\pi$
$601$	−2.49263	−	3.43081i	−0.101677	−	0.139946i	−0.856824	+	0.515610i	$0.827565\pi$
$602$	3.20701	−	18.4776i	0.130708	−	0.753091i
$603$	14.3599	−	28.1828i	0.584779	−	1.14769i
$604$	−11.9386	+	6.89275i	−0.485775	+	0.280462i
$605$	−15.9919	+	18.6885i	−0.650163	+	0.759795i
$606$	−12.7342	+	22.0563i	−0.517292	+	0.895976i
$607$	−2.80014	+	0.146749i	−0.113654	+	0.00595637i	−0.109078	−	0.994033i	$-0.534790\pi$
$607$	−2.80014	+	0.146749i	−0.113654	+	0.00595637i	−0.00457601	+	0.999990i	$0.501457\pi$
$608$	0.834493	−	0.132171i	0.0338432	−	0.00536023i
$609$	−25.1683	+	27.1353i	−1.01987	+	1.09958i
$610$	−9.75947	−	18.4913i	−0.395149	−	0.748691i
$611$	−3.56555	+	0.757881i	−0.144247	+	0.0306606i
$612$	−4.84667	+	5.98513i	−0.195915	+	0.241935i
$613$	−39.4566	−	15.1460i	−1.59364	−	0.611740i	−0.610080	−	0.792340i	$-0.708863\pi$
$613$	−39.4566	−	15.1460i	−1.59364	−	0.611740i	−0.983557	+	0.180600i	$0.942196\pi$
$614$	21.1843	−	23.5275i	0.854927	−	0.949492i
$615$	−42.0110	+	43.2378i	−1.69405	+	1.74352i
$616$	−2.19181	−	8.49682i	−0.0883106	−	0.342347i
$617$	14.5455	−	14.5455i	0.585581	−	0.585581i	−0.350850	−	0.936431i	$-0.614107\pi$
$617$	14.5455	−	14.5455i	0.585581	−	0.585581i	0.936431	+	0.350850i	$0.114107\pi$
$618$	14.2319	−	0.745862i	0.572490	−	0.0300030i
$619$	29.9252	−	13.3236i	1.20280	−	0.535520i	0.295230	−	0.955426i	$-0.404604\pi$
$619$	29.9252	−	13.3236i	1.20280	−	0.535520i	0.907567	+	0.419906i	$0.137937\pi$
$620$	8.80439	−	1.05368i	0.353593	−	0.0423168i
$621$	−0.0211179	−	0.0993521i	−0.000847434	−	0.00398686i
$622$	−5.62887	+	2.86805i	−0.225697	+	0.114998i
$623$	−3.76617	−	1.98957i	−0.150889	−	0.0797104i
$624$	−1.62297	+	2.23383i	−0.0649710	+	0.0894248i
$625$	15.6317	−	19.5102i	0.625269	−	0.780409i
$626$	16.8200	+	9.71105i	0.672264	+	0.388132i
$627$	−4.07199	−	5.54116i	−0.162620	−	0.221293i
$628$	−18.5046	−	4.95830i	−0.738415	−	0.197858i
$629$	−6.01466	−	18.5112i	−0.239820	−	0.738091i
$630$	17.7803	−	1.86195i	0.708384	−	0.0741818i
$631$	−12.4548	+	9.04897i	−0.495819	+	0.360234i	−0.807418	−	0.589980i	$-0.799136\pi$
$631$	−12.4548	+	9.04897i	−0.495819	+	0.360234i	0.311599	+	0.950214i	$0.399136\pi$
$632$	−3.10093	+	4.77502i	−0.123349	+	0.189940i
$633$	−46.7212	−	2.44855i	−1.85700	−	0.0973212i
$634$	29.7003	−	3.12163i	1.17955	−	0.123976i
$635$	−5.04698	+	4.20864i	−0.200283	+	0.167015i
$636$	−16.0087	+	5.20154i	−0.634786	+	0.206254i
$637$	6.26482	−	4.77380i	0.248221	−	0.189145i
$638$	−18.4715	+	4.03109i	−0.731295	+	0.159592i
$639$	26.3616	−	15.2199i	1.04285	−	0.602088i
$640$	−1.85761	+	1.24471i	−0.0734283	+	0.0492015i
$641$	−9.98685	+	4.44643i	−0.394457	+	0.175624i	−0.594373	−	0.804189i	$-0.702600\pi$
$641$	−9.98685	+	4.44643i	−0.394457	+	0.175624i	0.199916	+	0.979813i	$0.435933\pi$
$642$	−6.79303	−	17.6965i	−0.268100	−	0.698424i
$643$	−3.66250	−	7.18807i	−0.144435	−	0.283470i	0.807444	−	0.589945i	$-0.200850\pi$
$643$	−3.66250	−	7.18807i	−0.144435	−	0.283470i	−0.951879	+	0.306475i	$0.900850\pi$
$644$	−1.97057	−	4.60796i	−0.0776513	−	0.181579i
$645$	23.3122	+	31.1343i	0.917917	+	1.22591i
$646$	−0.225079	+	2.14149i	−0.00885563	+	0.0842557i
$647$	−20.2452	−	31.1748i	−0.795920	−	1.22561i	−0.970532	−	0.240971i	$-0.922534\pi$
$647$	−20.2452	−	31.1748i	−0.795920	−	1.22561i	0.174613	−	0.984637i	$-0.444133\pi$
$648$	8.62955	−	2.31228i	0.339001	−	0.0908350i
$649$	−4.82882	+	12.7864i	−0.189548	+	0.501909i
$650$	0.161898	+	5.62365i	0.00635015	+	0.220578i
$651$	25.7436	+	0.380278i	1.00897	+	0.0149043i
$652$	17.4664	−	2.76641i	0.684038	−	0.108341i
$653$	4.48152	+	11.6748i	0.175376	+	0.456869i	0.992889	−	0.119040i	$-0.0379816\pi$
$653$	4.48152	+	11.6748i	0.175376	+	0.456869i	−0.817514	+	0.575909i	$0.804648\pi$
$654$	9.01032	+	10.0070i	0.352331	+	0.391304i
$655$	−3.88264	−	4.18927i	−0.151707	−	0.163688i
$656$	4.46870	−	10.0369i	0.174473	−	0.391874i
$657$	−5.22282	−	32.9756i	−0.203761	−	1.28650i
$658$	−8.24551	−	2.34044i	−0.321443	−	0.0912399i
$659$			24.8147i			0.966643i	0.875443	+	0.483321i	$0.160570\pi$
$659$			24.8147i			0.966643i	−0.875443	+	0.483321i	$0.839430\pi$
$660$	15.9380	+	8.78541i	0.620384	+	0.341972i
$661$	−3.31863	−	1.91601i	−0.129080	−	0.0745243i	0.434070	−	0.900879i	$-0.357077\pi$
$661$	−3.31863	−	1.91601i	−0.129080	−	0.0745243i	−0.563150	+	0.826355i	$0.690410\pi$
$662$	15.7180	−	10.2074i	0.610896	−	0.396721i
$663$	−4.42856	−	5.46882i	−0.171991	−	0.212391i
$664$	−11.5177	+	8.36811i	−0.446974	+	0.324746i
$665$	3.88574	−	3.14416i	0.150682	−	0.121925i
$666$	7.13158	−	21.9488i	0.276343	−	0.850497i
$667$	−10.0807	+	3.86962i	−0.390327	+	0.149832i
$668$	6.94928	−	18.1035i	0.268876	−	0.700445i
$669$	4.09383	−	19.2600i	0.158277	−	0.744634i
$670$	11.9932	+	20.0992i	0.463336	+	0.776498i
$671$	7.86406	−	29.9991i	0.303589	−	1.15810i
$672$	−5.82779	+	2.86178i	−0.224812	+	0.110396i
$673$	12.1456	−	23.8371i	0.468178	−	0.918851i	−0.529338	−	0.848411i	$-0.677560\pi$
$673$	12.1456	−	23.8371i	0.468178	−	0.918851i	0.997516	−	0.0704402i	$-0.0224404\pi$
$674$	−23.3160	−	2.45061i	−0.898099	−	0.0943940i
$675$	−0.162661	+	0.213129i	−0.00626083	+	0.00820336i
$676$	7.85154	+	8.72001i	0.301982	+	0.335385i
$677$	−28.5386	−	18.5332i	−1.09683	−	0.712288i	−0.136354	−	0.990660i	$-0.543539\pi$
$677$	−28.5386	−	18.5332i	−1.09683	−	0.712288i	−0.960473	+	0.278372i	$0.910205\pi$
$678$	−5.53464	+	34.9444i	−0.212557	+	1.34203i
$679$	3.08781	+	34.2358i	0.118499	+	1.31385i
$680$	−1.83883	−	5.39398i	−0.0705161	−	0.206850i
$681$	−26.9448	−	46.6698i	−1.03253	−	1.78839i
$682$	10.6821	+	7.67284i	0.409040	+	0.293808i
$683$	5.13514	−	1.37596i	0.196491	−	0.0526496i	−0.159231	−	0.987241i	$-0.550902\pi$
$683$	5.13514	−	1.37596i	0.196491	−	0.0526496i	0.355722	+	0.934592i	$0.384235\pi$
$684$	−1.70839	+	1.89736i	−0.0653219	+	0.0725473i
$685$	1.22787	+	7.09051i	0.0469144	+	0.270915i
$686$	18.2683	−	3.04432i	0.697488	−	0.116233i
$687$	15.8380	+	31.0839i	0.604258	+	1.18592i
$688$	−5.94474	−	3.86056i	−0.226641	−	0.147182i
$689$	−0.806765	−	7.67585i	−0.0307353	−	0.292427i
$690$	9.75617	+	3.58484i	0.371411	+	0.136472i
$691$	36.3355	+	32.7167i	1.38227	+	1.24460i	0.937057	+	0.349176i	$0.113538\pi$
$691$	36.3355	+	32.7167i	1.38227	+	1.24460i	0.445212	+	0.895425i	$0.353128\pi$
$692$	5.47519	+	5.47519i	0.208135	+	0.208135i
$693$	21.3058	+	15.7859i	0.809341	+	0.599657i
$694$			0.681066i			0.0258529i
$695$	1.83280	+	1.60311i	0.0695219	+	0.0608093i
$696$	5.68968	+	12.7792i	0.215667	+	0.484395i
$697$	21.7605	+	17.6213i	0.824238	+	0.667454i
$698$	16.7532	−	25.7976i	0.634117	−	0.976455i
$699$	3.31045	−	10.1885i	0.125213	−	0.385365i
$700$	−5.84001	+	11.8699i	−0.220732	+	0.448640i
$701$	11.4920	+	8.34941i	0.434046	+	0.315353i	0.783265	−	0.621688i	$-0.213553\pi$
$701$	11.4920	+	8.34941i	0.434046	+	0.315353i	−0.349219	+	0.937041i	$0.613553\pi$
$702$	−0.00315770	−	0.0602524i	−0.000119180	−	0.00227408i
$703$	−1.67005	−	6.23271i	−0.0629872	−	0.235071i
$704$	−3.27856	−	0.501057i	−0.123565	−	0.0188843i
$705$	15.2653	−	9.10882i	0.574926	−	0.343058i
$706$	21.2631	−	6.90881i	0.800248	−	0.260016i
$707$	−9.46075	−	25.7778i	−0.355808	−	0.969475i
$708$	9.98820	+	1.58198i	0.375380	+	0.0594543i
$709$	4.82543	+	22.7018i	0.181223	+	0.852586i	0.970979	+	0.239165i	$0.0768737\pi$
$709$	4.82543	+	22.7018i	0.181223	+	0.852586i	−0.789756	+	0.613421i	$0.789793\pi$
$710$	−0.855033	+	22.5081i	−0.0320888	+	0.844715i
$711$	−1.79842	−	17.1108i	−0.0674461	−	0.641706i
$712$	−1.25113	+	1.01314i	−0.0468880	+	0.0379691i
$713$	6.69288	+	3.41019i	0.250650	+	0.127713i
$714$	−3.20083	−	16.2342i	−0.119788	−	0.607549i
$715$	−5.45971	+	6.31071i	−0.204182	+	0.236007i
$716$	7.16362	+	12.4077i	0.267717	+	0.463699i
$717$	20.9596	+	32.2750i	0.782752	+	1.20533i
$718$	−7.57700	−	2.90854i	−0.282771	−	0.108546i
$719$	18.4394	+	8.20976i	0.687674	+	0.306172i	0.720665	−	0.693283i	$-0.243837\pi$
$719$	18.4394	+	8.20976i	0.687674	+	0.306172i	−0.0329908	+	0.999456i	$0.510503\pi$
$720$	1.99536	−	6.45573i	0.0743626	−	0.240591i
$721$	−9.21414	+	12.2961i	−0.343152	+	0.457929i
$722$	2.86058	−	18.0610i	0.106460	−	0.672162i
$723$	−32.7943	+	26.5563i	−1.21963	+	0.987639i
$724$	9.79542	+	2.08208i	0.364044	+	0.0773800i
$725$	25.0836	+	13.5349i	0.931581	+	0.502674i
$726$	8.61944	+	25.5803i	0.319897	+	0.949372i
$727$	−34.3242	−	34.3242i	−1.27301	−	1.27301i	−0.944498	−	0.328517i	$-0.893451\pi$
$727$	−34.3242	−	34.3242i	−1.27301	−	1.27301i	−0.328517	−	0.944498i	$-0.606549\pi$
$728$	−0.727944	−	2.88661i	−0.0269794	−	0.106985i
$729$	−16.1005	+	22.1605i	−0.596316	+	0.820759i
$730$	22.7114	+	9.72261i	0.840585	+	0.359850i
$731$	13.4250	−	12.0879i	0.496540	−	0.447086i
$732$	−22.9146	−	1.20090i	−0.846948	−	0.0443867i
$733$	3.98659	−	1.53031i	0.147248	−	0.0565232i	−0.283628	−	0.958934i	$-0.591538\pi$
$733$	3.98659	−	1.53031i	0.147248	−	0.0565232i	0.430876	+	0.902411i	$0.358205\pi$
$734$	−2.79028	−	2.02725i	−0.102991	−	0.0748273i
$735$	−21.4054	+	31.8930i	−0.789551	+	1.17639i
$736$	−1.89422			−0.0698218
$737$	−7.03351	+	33.9958i	−0.259083	+	1.25225i
$738$	8.59285	+	32.0690i	0.316307	+	1.18047i
$739$	−3.56457	+	16.7700i	−0.131125	+	0.616894i	0.862680	+	0.505751i	$0.168784\pi$
$739$	−3.56457	+	16.7700i	−0.131125	+	0.616894i	−0.993804	+	0.111143i	$0.964549\pi$
$740$	10.9369	+	13.1154i	0.402047	+	0.482132i
$741$	−1.37124	−	1.88735i	−0.0503739	−	0.0693337i
$742$	6.75327	−	16.8449i	0.247920	−	0.618396i
$743$	23.0850	−	11.7624i	0.846906	−	0.431520i	0.0240100	−	0.999712i	$-0.492357\pi$
$743$	23.0850	−	11.7624i	0.846906	−	0.431520i	0.822896	+	0.568191i	$0.192357\pi$
$744$	3.95804	−	8.88991i	0.145109	−	0.325920i
$745$	−13.1727	+	6.09347i	−0.482609	+	0.223247i
$746$	−20.2825	−	4.31117i	−0.742594	−	0.157843i
$747$	11.1347	−	41.5552i	0.407397	−	1.52043i
$748$	3.39608	−	7.74045i	0.124173	−	0.283019i
$749$	19.3414	+	6.60180i	0.706720	+	0.241224i
$750$	−9.59640	−	25.7029i	−0.350411	−	0.938538i
$751$	0.616458	−	5.86521i	0.0224949	−	0.214024i	−0.977500	−	0.210934i	$-0.932350\pi$
$751$	0.616458	−	5.86521i	0.0224949	−	0.214024i	0.999995	−	0.00309066i	$-0.000983790\pi$
$752$	−2.03876	+	2.51766i	−0.0743459	+	0.0918096i
$753$	0.287396	−	5.48384i	0.0104733	−	0.199842i
$754$	−6.27396	+	1.33357i	−0.228484	+	0.0485658i
$755$	18.4757	+	24.6749i	0.672398	+	0.898012i
$756$	0.0596118	−	0.128739i	0.00216806	−	0.00468218i
$757$	38.2257	+	19.4770i	1.38934	+	0.707903i	0.978968	−	0.204016i	$-0.0653995\pi$
$757$	38.2257	+	19.4770i	1.38934	+	0.707903i	0.410370	+	0.911919i	$0.365399\pi$
$758$	−2.90093	+	10.8264i	−0.105367	+	0.393234i
$759$	7.07345	+	13.6982i	0.256750	+	0.497214i
$760$	−0.515181	−	1.81764i	−0.0186876	−	0.0659329i
$761$	−4.44341	−	4.00086i	−0.161073	−	0.145031i	0.584653	−	0.811284i	$-0.301231\pi$
$761$	−4.44341	−	4.00086i	−0.161073	−	0.145031i	−0.745726	+	0.666252i	$0.767897\pi$
$762$	1.12818	+	7.12303i	0.0408695	+	0.258040i
$763$	−14.5080	+	0.545600i	−0.525224	+	0.0197520i
$764$	4.16604	+	1.35363i	0.150722	+	0.0489726i
$765$	14.5761	+	9.17038i	0.527002	+	0.331556i
$766$	−27.0359	+	2.84158i	−0.976846	+	0.102671i
$767$	−1.66173	+	4.32894i	−0.0600014	+	0.156309i
$768$	0.128430	+	2.45058i	0.00463430	+	0.0884278i
$769$	36.3829			1.31200			0.656001	−	0.754760i	$-0.272247\pi$
$769$	36.3829			1.31200			0.656001	+	0.754760i	$0.272247\pi$
$770$	−18.2825	+	7.12400i	−0.658854	+	0.256731i
$771$	2.35365			0.0847648
$772$	0.425834	+	8.12540i	0.0153261	+	0.292440i
$773$	8.75075	−	22.7965i	0.314743	−	0.819933i	−0.681378	−	0.731932i	$-0.738619\pi$
$773$	8.75075	−	22.7965i	0.314743	−	0.819933i	0.996120	−	0.0880007i	$-0.0280478\pi$
$774$	21.3024	−	2.23897i	0.765699	−	0.0804782i
$775$	−4.67881	−	19.2677i	−0.168068	−	0.692118i
$776$	12.3565	+	4.01488i	0.443574	+	0.144126i
$777$	26.3884	+	41.9793i	0.946679	+	1.50600i
$778$	5.86953	+	37.0587i	0.210433	+	1.32862i
$779$	6.89834	+	6.21129i	0.247159	+	0.222543i
$780$	5.39085	+	3.00982i	0.193023	+	0.107769i
$781$	−23.4953	+	23.7515i	−0.840726	+	0.849897i
$782$	1.24947	−	4.66307i	0.0446808	−	0.166751i
$783$	−0.272353	−	0.138771i	−0.00973312	−	0.00495927i
$784$	1.65699	−	6.80106i	0.0591782	−	0.242895i
$785$	−6.09169	+	42.4019i	−0.217422	+	1.51339i
$786$	−6.13138	+	1.30327i	−0.218699	+	0.0464860i
$787$	−2.27634	+	43.4351i	−0.0811426	+	1.54829i	0.590268	+	0.807207i	$0.299022\pi$
$787$	−2.27634	+	43.4351i	−0.0811426	+	1.54829i	−0.671411	+	0.741086i	$0.734311\pi$
$788$	−0.365857	+	0.451796i	−0.0130331	+	0.0160946i
$789$	−4.69966	+	44.7143i	−0.167312	+	1.59187i
$790$	11.4256	+	5.61600i	0.406503	+	0.199808i
$791$	−25.1027	−	28.7214i	−0.892550	−	1.02122i
$792$	8.65230	−	5.05818i	0.307446	−	0.179735i
$793$	2.72312	−	10.1628i	0.0967009	−	0.360893i
$794$	−19.0186	−	4.04252i	−0.674944	−	0.143464i
$795$	15.8022	+	34.1608i	0.560448	+	1.21156i
$796$	10.4544	−	23.4809i	0.370545	−	0.832257i
$797$	13.7945	−	7.02866i	0.488627	−	0.248968i	−0.192277	−	0.981341i	$-0.561587\pi$
$797$	13.7945	−	7.02866i	0.488627	−	0.248968i	0.680904	+	0.732373i	$0.261587\pi$
$798$	−0.778005	−	5.43006i	−0.0275411	−	0.192222i
$799$	−4.85301	−	6.67960i	−0.171687	−	0.236307i
$800$	3.25712	+	3.79357i	0.115157	+	0.134123i
$801$	1.01146	−	4.75857i	0.0357384	−	0.168136i
$802$	6.49043	+	24.2226i	0.229185	+	0.855330i
$803$	15.0856	+	33.3941i	0.532358	+	1.17845i
$804$	25.6860			0.905874
$805$	−9.70711	+	5.59948i	−0.342131	+	0.197356i
$806$	3.60984	+	2.62270i	0.127151	+	0.0923807i
$807$	64.2566	−	24.6658i	2.26194	−	0.868278i
$808$	−10.3643	−	0.543172i	−0.364616	−	0.0191087i
$809$	30.9753	−	27.8903i	1.08903	−	0.980571i	0.0891538	−	0.996018i	$-0.471584\pi$
$809$	30.9753	−	27.8903i	1.08903	−	0.980571i	0.999881	+	0.0154468i	$0.00491706\pi$
$810$	−7.42673	−	18.5451i	−0.260949	−	0.651610i
$811$	11.7862	−	16.2224i	0.413871	−	0.569644i	−0.550287	−	0.834976i	$-0.685482\pi$
$811$	11.7862	−	16.2224i	0.413871	−	0.569644i	0.964157	+	0.265332i	$0.0854815\pi$
$812$	−14.5088	−	4.11825i	−0.509160	−	0.144522i
$813$	−5.72290	−	5.72290i	−0.200711	−	0.200711i
$814$	−1.18841	+	25.3016i	−0.0416539	+	0.886821i
$815$	−10.7830	−	38.0443i	−0.377713	−	1.33263i
$816$	−6.11741	−	1.30030i	−0.214152	−	0.0455195i
$817$	4.65422	−	3.76891i	0.162830	−	0.131857i
$818$	−3.00942	+	19.0007i	−0.105222	+	0.664344i
$819$	7.19903	+	5.39464i	0.251554	+	0.188504i
$820$	−23.4715	−	7.25463i	−0.819660	−	0.253343i
$821$	0.342466	+	0.152476i	0.0119521	+	0.00532143i	0.412704	−	0.910865i	$-0.364584\pi$
$821$	0.342466	+	0.152476i	0.0119521	+	0.00532143i	−0.400752	+	0.916187i	$0.631251\pi$
$822$	7.37268	+	2.83011i	0.257152	+	0.0987114i
$823$	−12.5148	−	19.2711i	−0.436239	−	0.671749i	0.550357	−	0.834929i	$-0.314492\pi$
$823$	−12.5148	−	19.2711i	−0.436239	−	0.671749i	−0.986596	+	0.163180i	$0.947825\pi$
$824$	2.90378	+	5.02949i	0.101158	+	0.175210i
$825$	15.2707	−	37.7202i	0.531659	−	1.31325i
$826$	−8.20948	+	7.17515i	−0.285644	+	0.249655i
$827$	−0.352774	−	0.179747i	−0.0122672	−	0.00625043i	0.447846	−	0.894111i	$-0.352191\pi$
$827$	−0.352774	−	0.179747i	−0.0122672	−	0.00625043i	−0.460113	+	0.887860i	$0.652191\pi$
$828$	4.44842	−	3.60226i	0.154593	−	0.125187i
$829$	5.42524	+	51.6177i	0.188426	+	1.79276i	0.525004	+	0.851100i	$0.324064\pi$
$829$	5.42524	+	51.6177i	0.188426	+	1.79276i	−0.336577	+	0.941656i	$0.609269\pi$
$830$	21.6394	+	23.3484i	0.751116	+	0.810436i
$831$	−0.701842	−	3.30191i	−0.0243466	−	0.114542i
$832$	−1.11134	−	0.176019i	−0.0385289	−	0.00610237i
$833$	15.6494	+	8.56519i	0.542221	+	0.296766i
$834$	2.54144	−	0.825765i	0.0880030	−	0.0285939i
$835$	−42.0403	−	10.6187i	−1.45487	−	0.367475i
$836$	1.25861	−	2.50364i	0.0435299	−	0.0865903i
$837$	0.0550352	+	0.205394i	0.00190230	+	0.00709947i
$838$	−0.417309	−	7.96274i	−0.0144157	−	0.275068i
$839$	0.706010	+	0.512947i	0.0243742	+	0.0177089i	0.599906	−	0.800071i	$-0.295205\pi$
$839$	0.706010	+	0.512947i	0.0243742	+	0.0177089i	−0.575531	+	0.817780i	$0.695205\pi$
$840$	7.90230	+	12.1786i	0.272655	+	0.420202i
$841$	−1.08007	+	3.32412i	−0.0372439	+	0.114625i
$842$	11.7986	−	18.1683i	0.406607	−	0.626120i
$843$	−46.3818	−	37.5592i	−1.59747	−	1.29361i
$844$	−7.75457	−	17.4170i	−0.266923	−	0.599519i
$845$	17.2742	−	19.7492i	0.594249	−	0.679392i
$846$		−	9.78966i		−	0.336575i
$847$	−27.1291	−	10.5362i	−0.932168	−	0.362026i
$848$	−4.85031	−	4.85031i	−0.166560	−	0.166560i
$849$	30.8399	+	27.7684i	1.05842	+	0.953008i
$850$	−11.4872	+	5.51585i	−0.394009	+	0.189192i
$851$	1.51215	+	14.3872i	0.0518359	+	0.493185i
$852$	20.7312	+	13.4630i	0.710238	+	0.461234i
$853$	−4.63228	−	9.09136i	−0.158606	−	0.311282i	0.798004	−	0.602652i	$-0.205889\pi$
$853$	−4.63228	−	9.09136i	−0.158606	−	0.311282i	−0.956611	+	0.291369i	$0.905889\pi$
$854$	16.8237	−	18.1386i	0.575697	−	0.620689i
$855$	4.66650	+	3.28886i	0.159591	+	0.112477i
$856$	5.16869	−	5.74041i	0.176662	−	0.196203i
$857$	46.3848	−	12.4288i	1.58447	−	0.424558i	0.644166	−	0.764886i	$-0.277205\pi$
$857$	46.3848	−	12.4288i	1.58447	−	0.424558i	0.940307	+	0.340328i	$0.110538\pi$
$858$	2.87711	+	8.69407i	0.0982228	+	0.296811i
$859$	−2.22378	−	3.85169i	−0.0758743	−	0.131418i	0.825592	−	0.564268i	$-0.190841\pi$
$859$	−2.22378	−	3.85169i	−0.0758743	−	0.131418i	−0.901466	+	0.432850i	$0.857508\pi$
$860$	−6.99173	+	14.2244i	−0.238416	+	0.485049i
$861$	−64.7290	−	29.9725i	−2.20596	−	1.02146i
$862$	4.37209	−	27.6043i	0.148914	−	0.940206i
$863$	28.6570	+	18.6101i	0.975497	+	0.633495i	0.930809	−	0.365506i	$-0.119104\pi$
$863$	28.6570	+	18.6101i	0.975497	+	0.633495i	0.0446881	+	0.999001i	$0.485771\pi$
$864$	−0.0358801	−	0.0398489i	−0.00122066	−	0.00135569i
$865$	10.7013	−	13.6109i	0.363856	−	0.462786i
$866$	31.8873	+	3.35149i	1.08357	+	0.113888i
$867$	−11.7030	+	22.9684i	−0.397455	+	0.780049i
$868$	4.62460	+	9.41762i	0.156969	+	0.319655i
$869$	6.86273	+	17.5922i	0.232802	+	0.596775i
$870$	26.8610	−	16.0279i	0.910672	−	0.543398i
$871$	−2.44871	+	11.5203i	−0.0829714	+	0.390350i
$872$	−1.96650	+	5.12290i	−0.0665940	+	0.173483i
$873$	−36.6535	+	14.0700i	−1.24053	+	0.476196i
$874$	0.494556	−	1.52209i	0.0167286	−	0.0514853i
$875$	27.9056	+	9.81220i	0.943380	+	0.331713i
$876$	21.9342	−	15.9361i	0.741088	−	0.538432i
$877$	−33.1941	−	40.9913i	−1.12089	−	1.38418i	−0.913951	−	0.405824i	$-0.866985\pi$
$877$	−33.1941	−	40.9913i	−1.12089	−	1.38418i	−0.206935	−	0.978355i	$-0.566349\pi$
$878$	7.24300	−	4.70366i	0.244439	−	0.158741i
$879$	−64.3415	−	37.1476i	−2.17018	−	1.25296i
$880$	−0.241318	+	7.41227i	−0.00813481	+	0.249868i
$881$		−	12.6086i		−	0.424796i	−0.977183	−	0.212398i	$-0.931873\pi$
$881$		−	12.6086i		−	0.424796i	0.977183	−	0.212398i	$-0.0681273\pi$
$882$	9.04235	+	19.1229i	0.304472	+	0.643900i
$883$	−2.28850	−	14.4490i	−0.0770143	−	0.486249i	−0.995805	−	0.0915035i	$-0.970833\pi$
$883$	−2.28850	−	14.4490i	−0.0770143	−	0.486249i	0.918790	−	0.394746i	$-0.129167\pi$
$884$	1.16638	−	2.61973i	0.0392295	−	0.0881110i
$885$	0.858386	−	22.5964i	0.0288543	−	0.759570i
$886$	−27.6099	−	30.6639i	−0.927574	−	1.03018i
$887$	−4.43451	−	11.5523i	−0.148896	−	0.387888i	0.838765	−	0.544494i	$-0.183278\pi$
$887$	−4.43451	−	11.5523i	−0.148896	−	0.387888i	−0.987661	+	0.156606i	$0.949945\pi$
$888$	18.5104	−	2.93176i	0.621168	−	0.0983833i
$889$	−6.67563	−	3.98679i	−0.223893	−	0.133713i
$890$	2.58184	+	2.50858i	0.0865435	+	0.0840879i
$891$	10.4685	−	27.7198i	0.350706	−	0.928647i
$892$	7.75051	−	2.07674i	0.259506	−	0.0695345i
$893$	−1.49075	−	2.29556i	−0.0498862	−	0.0768180i
$894$	−1.66493	+	15.8407i	−0.0556834	+	0.529792i
$895$	25.6446	−	19.2017i	0.857203	−	0.641842i
$896$	−2.11725	−	1.58658i	−0.0707325	−	0.0530039i
$897$	2.37449	+	4.66019i	0.0792818	+	0.155599i
$898$	10.1800	+	26.5198i	0.339712	+	0.884979i
$899$	20.6510	−	9.19443i	0.688751	−	0.306652i
$900$	−14.8634	−	2.71479i	−0.495445	−	0.0904932i
$901$	15.1396	−	8.74083i	0.504372	−	0.291199i
$902$	−18.3903	−	31.4577i	−0.612331	−	1.04743i
$903$	−25.6321	+	38.2220i	−0.852984	+	1.27195i
$904$	−13.7119	+	4.45527i	−0.456052	+	0.148180i
$905$	2.01996	−	22.3013i	0.0671456	−	0.741319i
$906$	33.6436	−	3.53608i	1.11773	−	0.117478i
$907$	−12.8171	−	0.671718i	−0.425586	−	0.0223040i	−0.161659	−	0.986847i	$-0.551684\pi$
$907$	−12.8171	−	0.671718i	−0.425586	−	0.0223040i	−0.263927	+	0.964543i	$0.585018\pi$
$908$	11.9605	−	18.4175i	0.396923	−	0.611207i
$909$	25.3728	−	18.4344i	0.841562	−	0.611430i
$910$	−6.21551	+	2.38320i	−0.206042	+	0.0790023i
$911$	−5.33637	−	16.4237i	−0.176802	−	0.544140i	0.822909	−	0.568173i	$-0.192349\pi$
$911$	−5.33637	−	16.4237i	−0.176802	−	0.544140i	−0.999711	+	0.0240327i	$0.992349\pi$
$912$	−2.00268	−	0.536617i	−0.0663154	−	0.0177692i
$913$	0.256130	+	47.2170i	0.00847666	+	1.56266i
$914$	−20.7575	−	11.9843i	−0.686597	−	0.396407i
$915$	3.42234	+	51.1947i	0.113139	+	1.69244i
$916$	−8.35618	+	11.5013i	−0.276096	+	0.380013i
$917$	3.15682	−	5.97572i	0.104247	−	0.197336i
$918$	0.121765	−	0.0620422i	0.00401884	−	0.00204770i
$919$	−8.54393	−	40.1960i	−0.281838	−	1.32594i	−0.860113	−	0.510103i	$-0.829607\pi$
$919$	−8.54393	−	40.1960i	−0.281838	−	1.32594i	0.578275	−	0.815842i	$-0.303726\pi$
$920$	0.503311	+	4.20559i	0.0165937	+	0.138654i
$921$	−70.9737	+	31.5995i	−2.33866	+	1.04124i
$922$	25.6577	−	1.34466i	0.844990	−	0.0442840i
$923$	−8.01457	+	8.01457i	−0.263803	+	0.263803i
$924$	−3.56718	+	21.2358i	−0.117351	+	0.698605i
$925$	26.2132	−	27.7672i	0.861883	−	0.912979i
$926$	3.28180	−	3.64481i	0.107847	−	0.119776i
$927$	−16.3839	−	6.28920i	−0.538119	−	0.206564i
$928$	−3.58741	+	4.43009i	−0.117763	+	0.145425i
$929$	8.85029	−	1.88119i	0.290369	−	0.0617198i	−0.0604243	−	0.998173i	$-0.519245\pi$
$929$	8.85029	−	1.88119i	0.290369	−	0.0617198i	0.350793	+	0.936453i	$0.385912\pi$
$930$	−20.7893	−	6.42562i	−0.681708	−	0.210704i
$931$	5.03233	+	3.10713i	0.164928	+	0.101832i
$932$	4.31181	−	0.682924i	0.141238	−	0.0223699i
$933$	15.4814	−	0.811345i	0.506838	−	0.0265622i
$934$	−6.51133	+	11.2780i	−0.213057	+	0.369026i
$935$	−18.0879	−	5.48335i	−0.591538	−	0.179325i
$936$	2.94464	−	1.70009i	0.0962484	−	0.0555691i
$937$	−4.31375	+	8.46621i	−0.140924	+	0.276579i	−0.950671	−	0.310200i	$-0.899604\pi$
$937$	−4.31375	+	8.46621i	−0.140924	+	0.276579i	0.809747	+	0.586779i	$0.199604\pi$
$938$	−17.7441	+	21.2622i	−0.579367	+	0.694236i
$939$	−28.0143	−	38.5584i	−0.914212	−	1.25831i
$940$	6.13149	+	3.85754i	0.199987	+	0.125819i
$941$	−6.08068	+	5.47507i	−0.198225	+	0.178482i	−0.762265	−	0.647265i	$-0.775913\pi$
$941$	−6.08068	+	5.47507i	−0.198225	+	0.178482i	0.564041	+	0.825747i	$0.309246\pi$
$942$	36.5346	+	29.5851i	1.19036	+	0.963935i
$943$	−13.0969	−	16.1734i	−0.426495	−	0.526678i
$944$	1.27346	+	3.91930i	0.0414475	+	0.127562i
$945$	−0.301668	−	0.0981447i	−0.00981326	−	0.00319265i
$946$	−21.9017	+	8.54387i	−0.712085	+	0.277785i
$947$	−22.6243	−	6.06216i	−0.735191	−	0.196994i	−0.128251	−	0.991742i	$-0.540936\pi$
$947$	−22.6243	−	6.06216i	−0.735191	−	0.196994i	−0.606940	+	0.794748i	$0.707603\pi$
$948$	11.7176	−	7.60952i	0.380571	−	0.247146i
$949$	5.05639	+	11.3568i	0.164137	+	0.368658i
$950$	−3.89869	+	1.62678i	−0.126490	+	0.0527798i
$951$	−69.6976	−	22.6461i	−2.26010	−	0.734351i
$952$	5.30233	−	4.16559i	0.171849	−	0.135007i
$953$	51.6364	+	8.17841i	1.67267	+	0.264925i	0.919553	−	0.392965i	$-0.128551\pi$
$953$	51.6364	+	8.17841i	1.67267	+	0.264925i	0.753114	+	0.657890i	$0.228551\pi$
$954$	20.6145	+	2.16667i	0.667418	+	0.0701484i
$955$	1.89841	−	9.60923i	0.0614310	−	0.310947i
$956$	−7.84115	+	13.5813i	−0.253601	+	0.439250i
$957$	45.4328	+	9.39975i	1.46863	+	0.303851i
$958$	−4.00887	+	4.00887i	−0.129521	+	0.129521i
$959$	−7.43583	+	4.14786i	−0.240115	+	0.133941i
$960$	5.40672	−	0.936285i	0.174501	−	0.0302185i
$961$	13.9540	+	6.21270i	0.450127	+	0.200410i
$962$	−0.449737	+	8.58149i	−0.0145001	+	0.276678i
$963$	−1.22164	+	23.3103i	−0.0393668	+	0.751163i
$964$	−15.7094	−	6.99429i	−0.505967	−	0.225271i
$965$	17.9271	−	3.10444i	0.577093	−	0.0999355i
$966$	−0.181647	+	12.2969i	−0.00584441	+	0.395647i
$967$	19.4878	−	19.4878i	0.626686	−	0.626686i	−0.320546	−	0.947233i	$-0.603867\pi$
$967$	19.4878	−	19.4878i	0.626686	−	0.626686i	0.947233	+	0.320546i	$0.103867\pi$
$968$	−7.69333	+	7.86210i	−0.247273	+	0.252697i
$969$	2.64202	−	4.57611i	0.0848739	−	0.147006i
$970$	5.63070	−	28.5011i	0.180791	−	0.915115i
$971$	−38.3908	−	4.03503i	−1.23202	−	0.129490i	−0.533946	−	0.845518i	$-0.679292\pi$
$971$	−38.3908	−	4.03503i	−1.23202	−	0.129490i	−0.698072	+	0.716028i	$0.745958\pi$
$972$	−21.8124	−	3.45475i	−0.699635	−	0.110811i
$973$	−1.07211	+	2.67419i	−0.0343702	+	0.0857307i
$974$	−12.0499	−	3.91524i	−0.386103	−	0.125452i
$975$	5.25007	−	12.7686i	0.168137	−	0.408923i
$976$	−3.80326	−	8.54227i	−0.121739	−	0.273431i
$977$	−17.2069	+	11.1743i	−0.550498	+	0.357498i	−0.789720	−	0.613467i	$-0.789774\pi$
$977$	−17.2069	+	11.1743i	−0.550498	+	0.357498i	0.239222	+	0.970965i	$0.423108\pi$
$978$	−41.9172	−	11.2317i	−1.34037	−	0.359150i
$979$	0.308364	+	5.33052i	0.00985536	+	0.170364i
$980$	−15.5402	−	1.87178i	−0.496412	−	0.0597919i
$981$	−5.12413	−	15.7704i	−0.163601	−	0.503511i
$982$	2.70793	+	3.34401i	0.0864134	+	0.106712i
$983$	−14.4579	−	11.7078i	−0.461135	−	0.373419i	0.370418	−	0.928865i	$-0.379214\pi$
$983$	−14.4579	−	11.7078i	−0.461135	−	0.373419i	−0.831553	+	0.555446i	$0.812548\pi$
$984$	−20.0358	+	18.0403i	−0.638718	+	0.575104i
$985$	1.10030	+	0.692238i	0.0350584	+	0.0220565i
$986$	−8.53938	−	11.7535i	−0.271949	−	0.374306i
$987$	16.1487	+	13.4767i	0.514018	+	0.428968i
$988$	0.431596	−	0.847055i	0.0137309	−	0.0269484i
$989$	−11.6279	+	6.71338i	−0.369746	+	0.213473i
$990$	−13.5293	−	17.8660i	−0.429989	−	0.567820i
$991$	−19.5362	+	33.8376i	−0.620586	+	1.07489i	0.368790	+	0.929513i	$0.379772\pi$
$991$	−19.5362	+	33.8376i	−0.620586	+	1.07489i	−0.989377	+	0.145375i	$0.953561\pi$
$992$	3.96010	−	0.207540i	0.125733	−	0.00658941i
$993$	−45.4245	+	7.19453i	−1.44150	+	0.228312i
$994$	−25.4657	+	7.86039i	−0.807722	+	0.249317i
$995$	−54.9106	−	16.9719i	−1.74078	−	0.538046i
$996$	34.1726	−	7.26361i	1.08280	−	0.230156i
$997$	−16.6889	+	20.6090i	−0.528542	+	0.652695i	−0.969575	−	0.244796i	$-0.921279\pi$
$997$	−16.6889	+	20.6090i	−0.528542	+	0.652695i	0.441033	+	0.897491i	$0.354612\pi$
$998$	−5.73663	−	2.20209i	−0.181590	−	0.0697058i
$999$	−0.274021	+	0.304331i	−0.00866964	+	0.00962861i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bv.a.423.4	yes	768
5.2	odd	4	inner	770.2.bv.a.577.45	yes	768
7.5	odd	6	inner	770.2.bv.a.313.21	✓	768
11.9	even	5	inner	770.2.bv.a.493.21	yes	768
35.12	even	12	inner	770.2.bv.a.467.21	yes	768
55.42	odd	20	inner	770.2.bv.a.647.21	yes	768
77.75	odd	30	inner	770.2.bv.a.383.45	yes	768
385.152	even	60	inner	770.2.bv.a.537.4	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.313.21	✓	768	7.5	odd	6	inner
770.2.bv.a.383.45	yes	768	77.75	odd	30	inner
770.2.bv.a.423.4	yes	768	1.1	even	1	trivial
770.2.bv.a.467.21	yes	768	35.12	even	12	inner
770.2.bv.a.493.21	yes	768	11.9	even	5	inner
770.2.bv.a.537.4	yes	768	385.152	even	60	inner
770.2.bv.a.577.45	yes	768	5.2	odd	4	inner
770.2.bv.a.647.21	yes	768	55.42	odd	20	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.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0523360 - 0.998630i) q^{2} +(-0.879416 + 2.29096i) q^{3} +(-0.994522 + 0.104528i) q^{4} +(0.496330 + 2.18029i) q^{5} +(2.33384 + 0.758311i) q^{6} +(-2.23996 + 1.40805i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.24567 - 2.02201i) q^{9} +O(q^{10})\)	\(q+(-0.0523360 - 0.998630i) q^{2} +(-0.879416 + 2.29096i) q^{3} +(-0.994522 + 0.104528i) q^{4} +(0.496330 + 2.18029i) q^{5} +(2.33384 + 0.758311i) q^{6} +(-2.23996 + 1.40805i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-2.24567 - 2.02201i) q^{9} +(2.15132 - 0.609757i) q^{10} +(2.96326 + 1.48966i) q^{11} +(0.635128 - 2.37033i) q^{12} +(1.00256 + 0.510828i) q^{13} +(1.52335 + 2.16319i) q^{14} +(-5.43142 - 0.780309i) q^{15} +(0.978148 - 0.207912i) q^{16} +(-0.133382 + 2.54509i) q^{17} +(-1.90171 + 2.34842i) q^{18} +(-0.0883156 + 0.840267i) q^{19} +(-0.721513 - 2.11646i) q^{20} +(-1.25593 - 6.36990i) q^{21} +(1.33254 - 3.03716i) q^{22} +(0.490260 - 1.82967i) q^{23} +(-2.40032 - 0.510204i) q^{24} +(-4.50731 + 2.16429i) q^{25} +(0.457658 - 1.02792i) q^{26} +(0.0477775 - 0.0243438i) q^{27} +(2.08050 - 1.63447i) q^{28} +(-3.35064 - 4.61176i) q^{29} +(-0.494981 + 5.46482i) q^{30} +(-0.824482 + 3.87888i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-6.01869 + 5.47866i) q^{33} +2.54858 q^{34} +(-4.18171 - 4.18489i) q^{35} +(2.44473 + 1.77620i) q^{36} +(-7.12988 + 2.73690i) q^{37} +(0.843737 + 0.0442184i) q^{38} +(-2.05195 + 1.84758i) q^{39} +(-2.07580 + 0.831292i) q^{40} +(6.45783 - 8.88844i) q^{41} +(-6.29544 + 1.58758i) q^{42} +(-5.01217 - 5.01217i) q^{43} +(-3.10274 - 1.17176i) q^{44} +(3.29398 - 5.89980i) q^{45} +(-1.85283 - 0.393830i) q^{46} +(-2.51766 + 2.03876i) q^{47} +(-0.383882 + 2.42373i) q^{48} +(3.03480 - 6.30793i) q^{49} +(2.39721 + 4.38787i) q^{50} +(-5.71338 - 2.54376i) q^{51} +(-1.05046 - 0.403234i) q^{52} +(-3.73588 - 5.75276i) q^{53} +(-0.0268110 - 0.0464380i) q^{54} +(-1.77714 + 7.20012i) q^{55} +(-1.74112 - 1.99211i) q^{56} +(-1.84735 - 0.941271i) q^{57} +(-4.43009 + 3.58741i) q^{58} +(0.430762 + 4.09842i) q^{59} +(5.48324 + 0.208296i) q^{60} +(-1.94411 - 9.14634i) q^{61} +(3.91672 + 0.620347i) q^{62} +(7.87730 + 1.36720i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(-0.616153 + 2.43940i) q^{65} +(5.78615 + 5.72371i) q^{66} +(2.70911 + 10.1105i) q^{67} +(-0.133382 - 2.54509i) q^{68} +(3.76056 + 2.73221i) q^{69} +(-3.96030 + 4.39500i) q^{70} +(-3.11279 + 9.58018i) q^{71} +(1.64582 - 2.53434i) q^{72} +(8.58622 + 6.95298i) q^{73} +(3.10630 + 6.97687i) q^{74} +(-0.994482 - 12.2294i) q^{75} -0.844895i q^{76} +(-8.73509 + 0.835631i) q^{77} +(1.95244 + 1.95244i) q^{78} +(4.23114 + 3.80973i) q^{79} +(0.938792 + 2.02945i) q^{80} +(-0.933854 - 8.88503i) q^{81} +(-9.21424 - 5.98380i) q^{82} +(6.46332 + 12.6850i) q^{83} +(1.91488 + 6.20372i) q^{84} +(-5.61522 + 0.972392i) q^{85} +(-4.74299 + 5.26762i) q^{86} +(13.5120 - 3.62052i) q^{87} +(-1.00777 + 3.15981i) q^{88} +(0.804950 + 1.39421i) q^{89} +(-6.06411 - 2.98069i) q^{90} +(-2.96495 + 0.267416i) q^{91} +(-0.296321 + 1.87090i) q^{92} +(-8.16129 - 5.30000i) q^{93} +(2.16773 + 2.40751i) q^{94} +(-1.87586 + 0.224496i) q^{95} +(2.44050 + 0.256507i) q^{96} +(5.89844 - 11.5763i) q^{97} +(-6.45812 - 2.70051i) q^{98} +(-3.64239 - 9.33705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q + 24 q^{5} + 4 q^{7}+O(q^{10}) \) 768 * q + 24 * q^5 + 4 * q^7	\( 768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98}+O(q^{100}) \) 768 * q + 24 * q^5 + 4 * q^7 + 24 * q^10 + 12 * q^11 - 24 * q^15 - 96 * q^16 + 8 * q^22 + 8 * q^23 + 16 * q^25 - 24 * q^26 - 28 * q^28 - 16 * q^30 + 252 * q^33 - 40 * q^35 + 160 * q^36 - 8 * q^37 - 44 * q^42 + 80 * q^43 + 96 * q^45 - 8 * q^46 - 24 * q^47 + 64 * q^50 - 8 * q^51 + 40 * q^53 + 16 * q^56 + 64 * q^57 - 48 * q^58 - 164 * q^63 - 88 * q^65 + 32 * q^67 - 100 * q^70 + 32 * q^71 + 120 * q^73 - 336 * q^75 - 96 * q^77 - 36 * q^80 - 24 * q^81 + 48 * q^82 - 112 * q^85 - 24 * q^87 + 4 * q^88 - 12 * q^91 - 16 * q^92 - 88 * q^93 - 44 * q^95 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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