LMFDB - Embedded newform 770.2.bv.a.537.4

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			537.4
Character	$\chi$	$=$	770.537
Dual form			770.2.bv.a.423.4

$q$-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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \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	−0.912803	−	0.408399i	$-0.866087\pi$
$3$	−0.879416	−	2.29096i	−0.507731	−	1.32268i	0.405072	−	0.914285i	$-0.367246\pi$
$4$	−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	−0.309400	−	0.950932i	$-0.600128\pi$
$13$	1.00256	−	0.510828i	0.278059	−	0.141678i	0.587459	+	0.809254i	$0.300128\pi$
$14$	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	−0.965914	−	0.258863i	$-0.916652\pi$
$17$	−0.133382	−	2.54509i	−0.0323500	−	0.617274i	0.933564	−	0.358411i	$-0.116681\pi$
$18$	−1.90171	−	2.34842i	−0.448238	−	0.553528i
$19$	−0.0883156	−	0.840267i	−0.0202610	−	0.192770i	0.979710	−	0.200422i	$-0.0642312\pi$
$19$	−0.0883156	−	0.840267i	−0.0202610	−	0.192770i	−0.999971	+	0.00765117i	$0.997565\pi$
$20$	−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	0.998016	−	0.0629650i	$-0.0200557\pi$
$23$	0.490260	+	1.82967i	0.102226	+	0.381514i	−0.895789	+	0.444479i	$0.853389\pi$
$24$	−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	−0.997511	−	0.0705154i	$-0.977536\pi$
$29$	−3.35064	+	4.61176i	−0.622199	+	0.856383i	0.375312	+	0.926899i	$0.377536\pi$
$30$	−0.494981	−	5.46482i	−0.0903707	−	0.997735i
$31$	−0.824482	−	3.87888i	−0.148081	−	0.696668i	−0.988063	−	0.154053i	$-0.950767\pi$
$31$	−0.824482	−	3.87888i	−0.148081	−	0.696668i	0.839981	−	0.542615i	$-0.182566\pi$
$32$	−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	−0.307119	−	0.951671i	$-0.599365\pi$
$37$	−7.12988	−	2.73690i	−1.17215	−	0.449944i	−0.865026	+	0.501727i	$0.832698\pi$
$38$	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	0.919933	+	0.392075i	$0.128243\pi$
$41$	6.45783	+	8.88844i	1.00854	+	1.38814i	0.0886106	+	0.996066i	$0.471757\pi$
$42$	−6.29544	−	1.58758i	−0.971407	−	0.244969i
$43$	−5.01217	+	5.01217i	−0.764349	+	0.764349i	−0.977105	−	0.212756i	$-0.931756\pi$
$43$	−5.01217	+	5.01217i	−0.764349	+	0.764349i	0.212756	+	0.977105i	$0.431756\pi$
$44$	−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	0.427883	−	0.903834i	$-0.359260\pi$
$47$	−2.51766	−	2.03876i	−0.367238	−	0.297384i	−0.795121	+	0.606450i	$0.792593\pi$
$48$	−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	−0.996354	−	0.0853131i	$-0.972811\pi$
$53$	−3.73588	+	5.75276i	−0.513163	+	0.790202i	0.483191	+	0.875515i	$0.339478\pi$
$54$	−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	−0.930031	−	0.367482i	$-0.880220\pi$
$59$	0.430762	−	4.09842i	0.0560804	−	0.533569i	0.986111	−	0.166087i	$-0.0531134\pi$
$60$	5.48324	−	0.208296i	0.707883	−	0.0268909i
$61$	−1.94411	+	9.14634i	−0.248918	+	1.17107i	0.659073	+	0.752079i	$0.270949\pi$
$61$	−1.94411	+	9.14634i	−0.248918	+	1.17107i	−0.907991	+	0.418990i	$0.862384\pi$
$62$	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	−0.577201	−	0.816602i	$-0.695855\pi$
$67$	2.70911	−	10.1105i	0.330971	−	1.23520i	0.908172	−	0.418597i	$-0.137478\pi$
$68$	−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	−0.947167	−	0.320742i	$-0.896068\pi$
$71$	−3.11279	−	9.58018i	−0.369420	−	1.13696i	0.577746	−	0.816216i	$-0.303932\pi$
$72$	1.64582	+	2.53434i	0.193962	+	0.298675i
$73$	8.58622	−	6.95298i	1.00494	−	0.813785i	0.0223842	−	0.999749i	$-0.492874\pi$
$73$	8.58622	−	6.95298i	1.00494	−	0.813785i	0.982556	+	0.185965i	$0.0595410\pi$
$74$	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	−0.395861	−	0.918310i	$-0.629554\pi$
$79$	4.23114	−	3.80973i	0.476040	−	0.428629i	0.871901	+	0.489682i	$0.162887\pi$
$80$	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	−0.201363	−	0.979517i	$-0.564537\pi$
$83$	6.46332	−	12.6850i	0.709441	−	1.39236i	0.910804	−	0.412840i	$-0.135463\pi$
$84$	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	−0.820205	−	0.572070i	$-0.806141\pi$
$89$	0.804950	−	1.39421i	0.0853245	−	0.147786i	0.905529	+	0.424283i	$0.139474\pi$
$90$	−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	0.969151	+	0.246469i	$0.0792704\pi$
$97$	5.89844	+	11.5763i	0.598896	+	1.17540i	−0.370255	+	0.928930i	$0.620730\pi$
$98$	−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	−0.945018	−	0.327019i	$-0.893956\pi$
$101$	−2.15782	−	10.1518i	−0.214712	−	1.01014i	0.730306	−	0.683120i	$-0.239377\pi$
$102$	−2.24126	−	5.83868i	−0.221918	−	0.578116i
$103$	5.42182	+	2.08124i	0.534227	+	0.205071i	0.610500	−	0.792016i	$-0.290969\pi$
$103$	5.42182	+	2.08124i	0.534227	+	0.205071i	−0.0762725	+	0.997087i	$0.524302\pi$
$104$	−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	−0.955916	−	0.293639i	$-0.905134\pi$
$107$	−4.86118	+	6.00305i	−0.469948	+	0.580337i	0.485969	+	0.873976i	$0.338467\pi$
$108$	−0.0449711	−	0.0292046i	−0.00432735	−	0.00281021i
$109$	4.75220	−	2.74369i	0.455178	−	0.262797i	−0.254836	−	0.966984i	$-0.582022\pi$
$109$	4.75220	−	2.74369i	0.455178	−	0.262797i	0.710015	+	0.704187i	$0.248688\pi$
$110$	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	−0.619794	−	0.784764i	$-0.712784\pi$
$113$	2.25540	−	14.2401i	0.212171	−	1.33959i	0.831965	−	0.554828i	$-0.187216\pi$
$114$	−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	−0.824203	−	0.566294i	$-0.808377\pi$
$127$	1.33422	−	2.61855i	0.118393	−	0.232358i	0.942596	+	0.333935i	$0.108377\pi$
$128$	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	0.400238	−	0.916411i	$-0.368928\pi$
$131$	−2.21218	−	1.27720i	−0.193279	−	0.111590i	−0.593517	+	0.804822i	$0.702261\pi$
$132$	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	0.0854459	−	0.996343i	$-0.472769\pi$
$137$	3.21376	−	0.168426i	0.274570	−	0.0143896i	0.189124	+	0.981953i	$0.439435\pi$
$138$	2.53165	+	3.89840i	0.215508	+	0.331854i
$139$	0.880982	+	0.640071i	0.0747239	+	0.0542901i	0.624520	−	0.781009i	$-0.285295\pi$
$139$	0.880982	+	0.640071i	0.0747239	+	0.0542901i	−0.549796	+	0.835299i	$0.685295\pi$
$140$	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	−0.887665	−	0.460490i	$-0.847674\pi$
$149$	1.34950	−	6.34892i	0.110556	−	0.520123i	0.998220	−	0.0596331i	$-0.0189931\pi$
$150$	−12.1606	−	1.63315i	−0.992905	−	0.133347i
$151$	12.5937	+	5.60707i	1.02486	+	0.456297i	0.849154	−	0.528146i	$-0.177113\pi$
$151$	12.5937	+	5.60707i	1.02486	+	0.456297i	0.175706	+	0.984443i	$0.443779\pi$
$152$	−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	0.482660	−	0.875808i	$-0.339671\pi$
$157$	17.8850	−	6.86540i	1.42738	−	0.547918i	0.944716	+	0.327889i	$0.106337\pi$
$158$	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	−0.653862	−	0.756614i	$-0.726852\pi$
$163$	−17.6599	−	0.925516i	−1.38323	−	0.0724920i	−0.729368	+	0.684121i	$0.760186\pi$
$164$	−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	−0.929683	−	0.368360i	$-0.879919\pi$
$167$	−8.80354	−	17.2779i	−0.681239	−	1.33701i	0.248445	−	0.968646i	$-0.420081\pi$
$168$	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	−0.927956	−	0.372689i	$-0.878436\pi$
$173$	−4.87288	+	6.01750i	−0.370478	+	0.457502i	0.557478	+	0.830192i	$0.311769\pi$
$174$	−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	0.553779	+	0.832664i	$0.313185\pi$
$179$	−5.82741	+	13.0886i	−0.435561	+	0.978286i	−0.989340	+	0.145623i	$0.953481\pi$
$180$	−2.65923	−	6.21180i	−0.198208	−	0.463000i
$181$	−9.52413	+	3.09458i	−0.707923	+	0.230018i	−0.640779	−	0.767725i	$-0.721389\pi$
$181$	−9.52413	+	3.09458i	−0.707923	+	0.230018i	−0.0671437	+	0.997743i	$0.521389\pi$
$182$	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	−0.546374	−	0.837541i	$-0.683992\pi$
$191$	−4.00173	+	1.78168i	−0.289555	+	0.128918i	0.256819	+	0.966460i	$0.417326\pi$
$192$	0.128430	+	2.45058i	0.00926861	+	0.176856i
$193$	0.425834	+	8.12540i	0.0306522	+	0.584879i	0.970177	+	0.242398i	$0.0779339\pi$
$193$	0.425834	+	8.12540i	0.0306522	+	0.584879i	−0.939525	+	0.342481i	$0.888733\pi$
$194$	−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	0.721599	−	0.692311i	$-0.243407\pi$
$197$	0.411078	+	0.411078i	0.0292881	+	0.0292881i	−0.692311	+	0.721599i	$0.743407\pi$
$198$	−9.13362	−	4.12606i	−0.649098	−	0.293226i
$199$	−12.8515	−	22.2595i	−0.911019	−	1.57793i	−0.812628	−	0.582783i	$-0.801964\pi$
$199$	−12.8515	−	22.2595i	−0.911019	−	1.57793i	−0.0983907	−	0.995148i	$-0.531369\pi$
$200$	−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	−0.514815	−	0.857301i	$-0.672139\pi$
$211$	5.89151	−	18.1322i	0.405588	−	1.24827i	0.920403	−	0.390971i	$-0.127861\pi$
$212$	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	−0.114670	−	0.993404i	$-0.536581\pi$
$223$	−7.92513	−	1.25522i	−0.530706	−	0.0840555i	−0.416036	+	0.909348i	$0.636581\pi$
$224$	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	−0.990785	−	0.135444i	$-0.956754\pi$
$227$	−13.8201	−	17.0664i	−0.917273	−	1.13274i	0.0735115	−	0.997294i	$-0.476579\pi$
$228$	1.93562	−	0.743014i	0.128189	−	0.0492073i
$229$	9.51262	+	10.5648i	0.628611	+	0.698144i	0.970364	−	0.241646i	$-0.0776873\pi$
$229$	9.51262	+	10.5648i	0.628611	+	0.698144i	−0.341753	+	0.939790i	$0.611021\pi$
$230$	−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	−0.0910045	−	0.995850i	$-0.529008\pi$
$233$	−4.35957	−	0.228476i	−0.285605	−	0.0149679i	−0.194601	+	0.980883i	$0.562341\pi$
$234$	−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	0.995359	−	0.0962342i	$-0.0306798\pi$
$239$	9.21783	+	12.6873i	0.596252	+	0.820670i	−0.399107	+	0.916904i	$0.630680\pi$
$240$	−5.47497	−	0.366000i	−0.353408	−	0.0236252i
$241$	14.8923	−	8.59806i	0.959296	−	0.553850i	0.0633398	−	0.997992i	$-0.479825\pi$
$241$	14.8923	−	8.59806i	0.959296	−	0.553850i	0.895956	+	0.444142i	$0.146491\pi$
$242$	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	0.241079	−	0.970506i	$-0.422499\pi$
$251$	−2.12825	−	0.691509i	−0.134334	−	0.0436477i	−0.375412	+	0.926858i	$0.622499\pi$
$252$	−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	−0.943883	−	0.330280i	$-0.892857\pi$
$257$	−0.343722	+	0.895425i	−0.0214408	+	0.0558551i	0.922442	+	0.386135i	$0.126190\pi$
$258$	−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	0.759206	−	0.650851i	$-0.225588\pi$
$263$	17.6975	+	4.74202i	1.09127	+	0.292405i	0.332066	+	0.943256i	$0.392254\pi$
$264$	−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	−0.186799	+	0.982398i	$0.559811\pi$
$269$	−18.7677	+	20.8437i	−1.14429	+	1.27086i	−0.957491	+	0.288464i	$0.906855\pi$
$270$	0.0879410	+	0.0815042i	0.00535192	+	0.00496019i
$271$	−1.34147	−	3.01298i	−0.0814883	−	0.183026i	0.868206	−	0.496204i	$-0.165273\pi$
$271$	−1.34147	−	3.01298i	−0.0814883	−	0.183026i	−0.949694	+	0.313178i	$0.898606\pi$
$272$	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	0.509515	−	0.860462i	$-0.329825\pi$
$277$	−1.15368	−	0.749211i	−0.0693181	−	0.0450157i	−0.578833	+	0.815446i	$0.696492\pi$
$278$	−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	−0.878777	−	0.477233i	$-0.841640\pi$
$281$	−7.51558	−	23.1306i	−0.448342	−	1.37985i	0.430435	−	0.902622i	$-0.358360\pi$
$282$	−7.42183	−	2.84897i	−0.441964	−	0.169654i
$283$	6.06043	+	15.7880i	0.360255	+	0.938497i	0.987208	+	0.159440i	$0.0509687\pi$
$283$	6.06043	+	15.7880i	0.360255	+	0.938497i	−0.626952	+	0.779058i	$0.715698\pi$
$284$	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	−0.599394	−	0.800454i	$-0.704592\pi$
$293$	−4.73617	−	29.9030i	−0.276690	−	1.74695i	0.322704	−	0.946500i	$-0.395408\pi$
$294$	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	0.335699	−	0.941969i	$-0.391028\pi$
$307$	22.3866	−	22.3866i	1.27767	−	1.27767i	0.941969	−	0.335699i	$-0.108972\pi$
$308$	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	−0.971624	−	0.236530i	$-0.923990\pi$
$311$	−2.56953	+	5.77126i	−0.145705	+	0.327258i	0.825920	+	0.563788i	$0.190656\pi$
$312$	−2.14583	+	1.73766i	−0.121484	+	0.0983756i
$313$	−10.5780	−	16.2887i	−0.597906	−	0.920694i	−0.999987	−	0.00509018i	$-0.998380\pi$
$313$	−10.5780	−	16.2887i	−0.597906	−	0.920694i	0.402081	−	0.915604i	$-0.368287\pi$
$314$	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	−0.500014	−	0.866018i	$-0.666672\pi$
$317$	1.56296	−	29.8230i	0.0877844	−	1.67503i	0.587798	−	0.809008i	$-0.299995\pi$
$318$	−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	−0.484783	−	0.874634i	$-0.661102\pi$
$331$	9.37076	−	16.2306i	0.515064	−	0.892117i	0.999847	−	0.0174823i	$-0.00556509\pi$
$332$	−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	0.859997	+	0.510299i	$0.170465\pi$
$337$	3.66752	+	23.1558i	0.199782	+	1.26138i	−0.660215	+	0.751077i	$0.729535\pi$
$338$	−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	−0.0705829	−	0.997506i	$-0.522486\pi$
$347$	−0.680133	+	0.0356443i	−0.0365114	+	0.00191348i	0.0340715	+	0.999419i	$0.489153\pi$
$348$	−13.0595	−	5.01307i	−0.700062	−	0.268729i
$349$	24.8855	−	18.0804i	1.33209	−	0.967819i	0.332394	−	0.943141i	$-0.392144\pi$
$349$	24.8855	−	18.0804i	1.33209	−	0.967819i	0.999695	−	0.0246787i	$-0.00785627\pi$
$350$	−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	−0.622360	−	0.782731i	$-0.713826\pi$
$353$	5.78652	−	21.5956i	0.307985	−	1.14942i	0.930345	−	0.366685i	$-0.119507\pi$
$354$	−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	0.979460	−	0.201640i	$-0.0646271\pi$
$359$	3.30110	+	7.41440i	0.174226	+	0.391317i	−0.805234	+	0.592957i	$0.797960\pi$
$360$	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	0.830641	−	0.556809i	$-0.187974\pi$
$367$	2.17051	+	2.68035i	0.113300	+	0.139913i	−0.717341	+	0.696722i	$0.754641\pi$
$368$	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	0.953886	+	0.300168i	$0.0970429\pi$
$373$	5.36677	+	20.0291i	0.277881	+	1.03707i	−0.676005	+	0.736897i	$0.736290\pi$
$374$	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	−0.569714	−	0.821843i	$-0.692946\pi$
$379$	−10.6598	+	3.46357i	−0.547556	+	0.177912i	0.0221585	+	0.999754i	$0.492946\pi$
$380$	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	0.682120	+	0.731241i	$0.261058\pi$
$383$	−1.42274	+	27.1475i	−0.0726987	+	1.38717i	−0.754818	+	0.655934i	$0.772275\pi$
$384$	−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	−0.913717	−	0.406351i	$-0.866801\pi$
$389$	−37.3151	−	3.92198i	−1.89195	−	0.198852i	−0.978235	+	0.207498i	$0.933468\pi$
$390$	−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	0.969429	+	0.245374i	$0.0789107\pi$
$397$	5.03233	+	18.7809i	0.252566	+	0.942588i	−0.716863	+	0.697214i	$0.754423\pi$
$398$	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	−0.450353	−	0.892851i	$-0.648702\pi$
$401$	−24.5291	−	5.21382i	−1.22493	−	0.260366i	−0.774573	+	0.632485i	$0.782035\pi$
$402$	−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	−0.648114	−	0.761543i	$-0.724442\pi$
$409$	−18.8172	+	3.99971i	−0.930449	+	0.197773i	−0.282335	+	0.959316i	$0.591109\pi$
$410$	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	−0.0721305	−	0.997395i	$-0.522980\pi$
$421$	17.5259	−	12.7333i	0.854159	−	0.620583i	0.926290	+	0.376812i	$0.122980\pi$
$422$	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	0.504645	−	0.863327i	$-0.331623\pi$
$431$	27.3377	−	5.81080i	1.31681	−	0.279896i	0.812163	+	0.583430i	$0.198290\pi$
$432$	0.0416721	+	0.0337454i	0.00200495	+	0.00162358i
$433$	−5.01575	−	31.6682i	−0.241041	−	1.52188i	−0.750205	−	0.661206i	$-0.770045\pi$
$433$	−5.01575	−	31.6682i	−0.241041	−	1.52188i	0.509163	−	0.860670i	$-0.329955\pi$
$434$	−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	−0.744387	−	0.667748i	$-0.767258\pi$
$439$	4.31814	−	7.47924i	0.206094	−	0.356965i	0.950481	+	0.310784i	$0.100592\pi$
$440$	−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	0.886328	+	0.463058i	$0.153248\pi$
$443$	32.0669	+	25.9673i	1.52354	+	1.23374i	0.637217	+	0.770685i	$0.280086\pi$
$444$	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	−0.408169	−	0.912906i	$-0.633833\pi$
$449$	−27.0163	−	8.77812i	−1.27498	−	0.414265i	−0.866808	+	0.498641i	$0.833833\pi$
$450$	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	0.999817	+	0.0191550i	$0.00609761\pi$
$457$	13.0543	+	20.1018i	0.610654	+	0.940324i	−0.389163	+	0.921169i	$0.627236\pi$
$458$	−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	$-0.795836\pi$
$461$		−	25.6929i		−	1.19664i	0.801259	−	0.598318i	$-0.204164\pi$
$462$	−21.0200	+	4.67368i	−0.977938	+	0.217439i
$463$	3.46806	−	3.46806i	0.161174	−	0.161174i	−0.621912	−	0.783087i	$-0.713644\pi$
$463$	3.46806	−	3.46806i	0.161174	−	0.161174i	0.783087	+	0.621912i	$0.213644\pi$
$464$	−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	−0.772027	−	0.635590i	$-0.780757\pi$
$467$	−10.9217	+	7.09265i	−0.505397	+	0.328209i	0.266629	+	0.963799i	$0.414090\pi$
$468$	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	−0.823551	−	0.567242i	$-0.808011\pi$
$479$	−3.79357	+	4.21319i	−0.173333	+	0.192506i	0.650219	+	0.759747i	$0.274677\pi$
$480$	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	0.997162	−	0.0752856i	$-0.0239869\pi$
$487$	4.54051	+	11.8284i	0.205750	+	0.535998i	−0.791412	+	0.611284i	$0.790654\pi$
$488$	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	0.506457	−	0.862265i	$-0.330955\pi$
$491$	−3.48115	−	2.52920i	−0.157102	−	0.114141i	−0.663559	+	0.748124i	$0.730955\pi$
$492$	−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	0.960805	−	0.277223i	$-0.0894142\pi$
$499$	2.49930	+	5.61352i	0.111884	+	0.251296i	−0.848921	+	0.528519i	$0.822748\pi$
$500$	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	−0.729032	−	0.684479i	$-0.760030\pi$
$503$	−36.6445	−	5.80392i	−1.63390	−	0.258784i	−0.904867	+	0.425695i	$0.860030\pi$
$504$	−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	−0.867248	−	0.497877i	$-0.834113\pi$
$509$	−2.76295	−	26.2878i	−0.122466	−	1.16518i	0.744782	−	0.667308i	$-0.232553\pi$
$510$	−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	0.658734	−	0.752376i	$-0.271092\pi$
$521$	26.1727	+	2.75086i	1.14665	+	0.120517i	0.487911	+	0.872893i	$0.337759\pi$
$522$	17.2023	−	0.901535i	0.752925	−	0.0394591i
$523$	14.0454	+	21.6281i	0.614163	+	0.945729i	0.999734	+	0.0230506i	$0.00733787\pi$
$523$	14.0454	+	21.6281i	0.614163	+	0.945729i	−0.385571	+	0.922678i	$0.625995\pi$
$524$	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	0.793404	−	0.608695i	$-0.208307\pi$
$541$	2.44481	+	2.71524i	0.105111	+	0.116737i	−0.688294	+	0.725432i	$0.741640\pi$
$542$	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	−0.382167	−	0.924093i	$-0.624822\pi$
$547$	−24.1175	−	3.81983i	−1.03119	−	0.163324i	−0.649023	+	0.760769i	$0.724822\pi$
$548$	−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	−0.255857	+	0.966715i	$0.582358\pi$
$557$	−29.6106	+	23.9782i	−1.25464	+	1.01599i	−0.998785	+	0.0492748i	$0.984309\pi$
$558$	−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	0.999240	+	0.0389688i	$0.0124073\pi$
$563$	34.1979	+	22.2083i	1.44127	+	0.935970i	0.442027	+	0.897002i	$0.354259\pi$
$564$	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	0.675211	−	0.737625i	$-0.264053\pi$
$569$	35.5188	−	3.73318i	1.48903	−	0.156503i	0.813817	+	0.581122i	$0.197386\pi$
$570$	−4.54819	+	0.898545i	−0.190503	+	0.0376359i
$571$	1.40366	+	2.43121i	0.0587412	+	0.101743i	0.893901	−	0.448265i	$-0.147958\pi$
$571$	1.40366	+	2.43121i	0.0587412	+	0.101743i	−0.835159	+	0.550008i	$0.814625\pi$
$572$	−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	0.992301	+	0.123853i	$0.0395250\pi$
$577$	0.441552	+	8.42531i	0.0183820	+	0.350750i	−0.973919	+	0.226898i	$0.927142\pi$
$578$	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	−0.0126490	−	0.999920i	$-0.504026\pi$
$587$	6.88837	−	1.09101i	0.284313	−	0.0450308i	0.296962	+	0.954889i	$0.404026\pi$
$588$	−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	−0.278096	−	0.960553i	$-0.589703\pi$
$593$	−0.941362	+	0.252237i	−0.0386571	+	0.0103581i	0.239439	+	0.970911i	$0.423037\pi$
$594$	−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	0.392865	−	0.919596i	$-0.371484\pi$
$599$	−11.7631	−	10.5915i	−0.480627	−	0.432759i	−0.873493	+	0.486837i	$0.838150\pi$
$600$	11.9232	+	2.89533i	0.486764	+	0.118201i
$601$	−2.49263	+	3.43081i	−0.101677	+	0.139946i	−0.856824	−	0.515610i	$-0.827565\pi$
$601$	−2.49263	+	3.43081i	−0.101677	+	0.139946i	0.755147	+	0.655555i	$0.227565\pi$
$602$	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	−0.00457601	−	0.999990i	$-0.501457\pi$
$607$	−2.80014	−	0.146749i	−0.113654	−	0.00595637i	−0.109078	+	0.994033i	$0.534790\pi$
$608$	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	−0.983557	−	0.180600i	$-0.942196\pi$
$613$	−39.4566	+	15.1460i	−1.59364	+	0.611740i	−0.610080	+	0.792340i	$0.708863\pi$
$614$	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	0.936431	−	0.350850i	$-0.114107\pi$
$617$	14.5455	+	14.5455i	0.585581	+	0.585581i	−0.350850	+	0.936431i	$0.614107\pi$
$618$	14.2319	+	0.745862i	0.572490	+	0.0300030i
$619$	29.9252	+	13.3236i	1.20280	+	0.535520i	0.907567	−	0.419906i	$-0.137937\pi$
$619$	29.9252	+	13.3236i	1.20280	+	0.535520i	0.295230	+	0.955426i	$0.404604\pi$
$620$	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	0.311599	−	0.950214i	$-0.399136\pi$
$631$	−12.4548	−	9.04897i	−0.495819	−	0.360234i	−0.807418	+	0.589980i	$0.799136\pi$
$632$	−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	0.199916	−	0.979813i	$-0.435933\pi$
$641$	−9.98685	−	4.44643i	−0.394457	−	0.175624i	−0.594373	+	0.804189i	$0.702600\pi$
$642$	−6.79303	+	17.6965i	−0.268100	+	0.698424i
$643$	−3.66250	+	7.18807i	−0.144435	+	0.283470i	−0.951879	−	0.306475i	$-0.900850\pi$
$643$	−3.66250	+	7.18807i	−0.144435	+	0.283470i	0.807444	+	0.589945i	$0.200850\pi$
$644$	−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	0.174613	+	0.984637i	$0.444133\pi$
$647$	−20.2452	+	31.1748i	−0.795920	+	1.22561i	−0.970532	+	0.240971i	$0.922534\pi$
$648$	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	−0.817514	−	0.575909i	$-0.804648\pi$
$653$	4.48152	−	11.6748i	0.175376	−	0.456869i	0.992889	+	0.119040i	$0.0379816\pi$
$654$	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	$-0.839430\pi$
$659$		−	24.8147i		−	0.966643i	0.875443	−	0.483321i	$-0.160570\pi$
$660$	15.9380	−	8.78541i	0.620384	−	0.341972i
$661$	−3.31863	+	1.91601i	−0.129080	+	0.0745243i	−0.563150	−	0.826355i	$-0.690410\pi$
$661$	−3.31863	+	1.91601i	−0.129080	+	0.0745243i	0.434070	+	0.900879i	$0.357077\pi$
$662$	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	0.997516	+	0.0704402i	$0.0224404\pi$
$673$	12.1456	+	23.8371i	0.468178	+	0.918851i	−0.529338	+	0.848411i	$0.677560\pi$
$674$	−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	−0.960473	−	0.278372i	$-0.910205\pi$
$677$	−28.5386	+	18.5332i	−1.09683	+	0.712288i	−0.136354	+	0.990660i	$0.543539\pi$
$678$	−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	0.355722	−	0.934592i	$-0.384235\pi$
$683$	5.13514	+	1.37596i	0.196491	+	0.0526496i	−0.159231	+	0.987241i	$0.550902\pi$
$684$	−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	0.445212	−	0.895425i	$-0.353128\pi$
$691$	36.3355	−	32.7167i	1.38227	−	1.24460i	0.937057	−	0.349176i	$-0.113538\pi$
$692$	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	−0.349219	−	0.937041i	$-0.613553\pi$
$701$	11.4920	−	8.34941i	0.434046	−	0.315353i	0.783265	+	0.621688i	$0.213553\pi$
$702$	−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	−0.789756	−	0.613421i	$-0.789793\pi$
$709$	4.82543	−	22.7018i	0.181223	−	0.852586i	0.970979	−	0.239165i	$-0.0768737\pi$
$710$	−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	−0.0329908	−	0.999456i	$-0.510503\pi$
$719$	18.4394	−	8.20976i	0.687674	−	0.306172i	0.720665	+	0.693283i	$0.243837\pi$
$720$	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	−0.328517	+	0.944498i	$0.606549\pi$
$727$	−34.3242	+	34.3242i	−1.27301	+	1.27301i	−0.944498	+	0.328517i	$0.893451\pi$
$728$	−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	0.430876	−	0.902411i	$-0.358205\pi$
$733$	3.98659	+	1.53031i	0.147248	+	0.0565232i	−0.283628	+	0.958934i	$0.591538\pi$
$734$	−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	−0.993804	−	0.111143i	$-0.964549\pi$
$739$	−3.56457	−	16.7700i	−0.131125	−	0.616894i	0.862680	−	0.505751i	$-0.168784\pi$
$740$	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	0.822896	−	0.568191i	$-0.192357\pi$
$743$	23.0850	+	11.7624i	0.846906	+	0.431520i	0.0240100	+	0.999712i	$0.492357\pi$
$744$	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	0.999995	+	0.00309066i	$0.000983790\pi$
$751$	0.616458	+	5.86521i	0.0224949	+	0.214024i	−0.977500	+	0.210934i	$0.932350\pi$
$752$	−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	0.410370	−	0.911919i	$-0.365399\pi$
$757$	38.2257	−	19.4770i	1.38934	−	0.707903i	0.978968	+	0.204016i	$0.0653995\pi$
$758$	−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	−0.745726	−	0.666252i	$-0.767897\pi$
$761$	−4.44341	+	4.00086i	−0.161073	+	0.145031i	0.584653	+	0.811284i	$0.301231\pi$
$762$	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	0.996120	+	0.0880007i	$0.0280478\pi$
$773$	8.75075	+	22.7965i	0.314743	+	0.819933i	−0.681378	+	0.731932i	$0.738619\pi$
$774$	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	−0.671411	−	0.741086i	$-0.734311\pi$
$787$	−2.27634	−	43.4351i	−0.0811426	−	1.54829i	0.590268	−	0.807207i	$-0.299022\pi$
$788$	−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	0.680904	−	0.732373i	$-0.261587\pi$
$797$	13.7945	+	7.02866i	0.488627	+	0.248968i	−0.192277	+	0.981341i	$0.561587\pi$
$798$	−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	0.999881	−	0.0154468i	$-0.00491706\pi$
$809$	30.9753	+	27.8903i	1.08903	+	0.980571i	0.0891538	+	0.996018i	$0.471584\pi$
$810$	−7.42673	+	18.5451i	−0.260949	+	0.651610i
$811$	11.7862	+	16.2224i	0.413871	+	0.569644i	0.964157	−	0.265332i	$-0.0854815\pi$
$811$	11.7862	+	16.2224i	0.413871	+	0.569644i	−0.550287	+	0.834976i	$0.685482\pi$
$812$	−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	−0.400752	−	0.916187i	$-0.631251\pi$
$821$	0.342466	−	0.152476i	0.0119521	−	0.00532143i	0.412704	+	0.910865i	$0.364584\pi$
$822$	7.37268	−	2.83011i	0.257152	−	0.0987114i
$823$	−12.5148	+	19.2711i	−0.436239	+	0.671749i	−0.986596	−	0.163180i	$-0.947825\pi$
$823$	−12.5148	+	19.2711i	−0.436239	+	0.671749i	0.550357	+	0.834929i	$0.314492\pi$
$824$	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	−0.460113	−	0.887860i	$-0.652191\pi$
$827$	−0.352774	+	0.179747i	−0.0122672	+	0.00625043i	0.447846	+	0.894111i	$0.352191\pi$
$828$	4.44842	+	3.60226i	0.154593	+	0.125187i
$829$	5.42524	−	51.6177i	0.188426	−	1.79276i	−0.336577	−	0.941656i	$-0.609269\pi$
$829$	5.42524	−	51.6177i	0.188426	−	1.79276i	0.525004	−	0.851100i	$-0.324064\pi$
$830$	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	−0.575531	−	0.817780i	$-0.695205\pi$
$839$	0.706010	−	0.512947i	0.0243742	−	0.0177089i	0.599906	+	0.800071i	$0.295205\pi$
$840$	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	−0.956611	−	0.291369i	$-0.905889\pi$
$853$	−4.63228	+	9.09136i	−0.158606	+	0.311282i	0.798004	+	0.602652i	$0.205889\pi$
$854$	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	0.940307	−	0.340328i	$-0.110538\pi$
$857$	46.3848	+	12.4288i	1.58447	+	0.424558i	0.644166	+	0.764886i	$0.277205\pi$
$858$	2.87711	−	8.69407i	0.0982228	−	0.296811i
$859$	−2.22378	+	3.85169i	−0.0758743	+	0.131418i	−0.901466	−	0.432850i	$-0.857508\pi$
$859$	−2.22378	+	3.85169i	−0.0758743	+	0.131418i	0.825592	+	0.564268i	$0.190841\pi$
$860$	−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	0.0446881	−	0.999001i	$-0.485771\pi$
$863$	28.6570	−	18.6101i	0.975497	−	0.633495i	0.930809	+	0.365506i	$0.119104\pi$
$864$	−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	−0.206935	+	0.978355i	$0.566349\pi$
$877$	−33.1941	+	40.9913i	−1.12089	+	1.38418i	−0.913951	+	0.405824i	$0.866985\pi$
$878$	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	$0.0681273\pi$
$881$			12.6086i			0.424796i	−0.977183	+	0.212398i	$0.931873\pi$
$882$	9.04235	−	19.1229i	0.304472	−	0.643900i
$883$	−2.28850	+	14.4490i	−0.0770143	+	0.486249i	0.918790	+	0.394746i	$0.129167\pi$
$883$	−2.28850	+	14.4490i	−0.0770143	+	0.486249i	−0.995805	+	0.0915035i	$0.970833\pi$
$884$	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	−0.987661	−	0.156606i	$-0.949945\pi$
$887$	−4.43451	+	11.5523i	−0.148896	+	0.387888i	0.838765	+	0.544494i	$0.183278\pi$
$888$	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	−0.263927	−	0.964543i	$-0.585018\pi$
$907$	−12.8171	+	0.671718i	−0.425586	+	0.0223040i	−0.161659	+	0.986847i	$0.551684\pi$
$908$	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	−0.999711	−	0.0240327i	$-0.992349\pi$
$911$	−5.33637	+	16.4237i	−0.176802	+	0.544140i	0.822909	+	0.568173i	$0.192349\pi$
$912$	−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	0.578275	+	0.815842i	$0.303726\pi$
$919$	−8.54393	+	40.1960i	−0.281838	+	1.32594i	−0.860113	+	0.510103i	$0.829607\pi$
$920$	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	0.350793	−	0.936453i	$-0.385912\pi$
$929$	8.85029	+	1.88119i	0.290369	+	0.0617198i	−0.0604243	+	0.998173i	$0.519245\pi$
$930$	−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	0.809747	−	0.586779i	$-0.199604\pi$
$937$	−4.31375	−	8.46621i	−0.140924	−	0.276579i	−0.950671	+	0.310200i	$0.899604\pi$
$938$	−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	0.564041	−	0.825747i	$-0.309246\pi$
$941$	−6.08068	−	5.47507i	−0.198225	−	0.178482i	−0.762265	+	0.647265i	$0.775913\pi$
$942$	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	−0.606940	−	0.794748i	$-0.707603\pi$
$947$	−22.6243	+	6.06216i	−0.735191	+	0.196994i	−0.128251	+	0.991742i	$0.540936\pi$
$948$	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	0.753114	−	0.657890i	$-0.228551\pi$
$953$	51.6364	−	8.17841i	1.67267	−	0.264925i	0.919553	+	0.392965i	$0.128551\pi$
$954$	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	0.947233	−	0.320546i	$-0.103867\pi$
$967$	19.4878	+	19.4878i	0.626686	+	0.626686i	−0.320546	+	0.947233i	$0.603867\pi$
$968$	−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	−0.698072	−	0.716028i	$-0.745958\pi$
$971$	−38.3908	+	4.03503i	−1.23202	+	0.129490i	−0.533946	+	0.845518i	$0.679292\pi$
$972$	−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	0.239222	−	0.970965i	$-0.423108\pi$
$977$	−17.2069	−	11.1743i	−0.550498	−	0.357498i	−0.789720	+	0.613467i	$0.789774\pi$
$978$	−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	−0.831553	−	0.555446i	$-0.812548\pi$
$983$	−14.4579	+	11.7078i	−0.461135	+	0.373419i	0.370418	+	0.928865i	$0.379214\pi$
$984$	−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	−0.989377	−	0.145375i	$-0.953561\pi$
$991$	−19.5362	−	33.8376i	−0.620586	−	1.07489i	0.368790	−	0.929513i	$-0.379772\pi$
$992$	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	0.441033	−	0.897491i	$-0.354612\pi$
$997$	−16.6889	−	20.6090i	−0.528542	−	0.652695i	−0.969575	+	0.244796i	$0.921279\pi$
$998$	−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.537.4	yes	768
5.3	odd	4	inner	770.2.bv.a.383.45	yes	768
7.3	odd	6	inner	770.2.bv.a.647.21	yes	768
11.5	even	5	inner	770.2.bv.a.467.21	yes	768
35.3	even	12	inner	770.2.bv.a.493.21	yes	768
55.38	odd	20	inner	770.2.bv.a.313.21	✓	768
77.38	odd	30	inner	770.2.bv.a.577.45	yes	768
385.38	even	60	inner	770.2.bv.a.423.4	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.313.21	✓	768	55.38	odd	20	inner
770.2.bv.a.383.45	yes	768	5.3	odd	4	inner
770.2.bv.a.423.4	yes	768	385.38	even	60	inner
770.2.bv.a.467.21	yes	768	11.5	even	5	inner
770.2.bv.a.493.21	yes	768	35.3	even	12	inner
770.2.bv.a.537.4	yes	768	1.1	even	1	trivial
770.2.bv.a.577.45	yes	768	77.38	odd	30	inner
770.2.bv.a.647.21	yes	768	7.3	odd	6	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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