LMFDB - Embedded newform 770.2.bv.a.313.21

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			313.21
Character	$\chi$	$=$	770.313
Dual form			770.2.bv.a.647.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.838671 + 0.544639i) q^{2} +(1.54432 + 1.90707i) q^{3} +(0.406737 - 0.913545i) q^{4} +(-1.64002 + 1.51998i) q^{5} +(-2.33384 - 0.758311i) q^{6} +(1.69521 + 2.03132i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-0.628278 + 2.95582i) q^{9} +O(q^{10})$	\(q+(-0.838671 + 0.544639i) q^{2} +(1.54432 + 1.90707i) q^{3} +(0.406737 - 0.913545i) q^{4} +(-1.64002 + 1.51998i) q^{5} +(-2.33384 - 0.758311i) q^{6} +(1.69521 + 2.03132i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-0.628278 + 2.95582i) q^{9} +(0.547597 - 2.16798i) q^{10} +(-2.77172 + 1.82143i) q^{11} +(2.37033 - 0.635128i) q^{12} +(-1.00256 - 0.510828i) q^{13} +(-2.52806 - 0.780327i) q^{14} +(-5.43142 - 0.780309i) q^{15} +(-0.669131 - 0.743145i) q^{16} +(2.13742 + 1.38806i) q^{17} +(-1.08293 - 2.82114i) q^{18} +(-0.771850 + 0.343650i) q^{19} +(0.721513 + 2.11646i) q^{20} +(-1.25593 + 6.36990i) q^{21} +(1.33254 - 3.03716i) q^{22} +(-1.82967 + 0.490260i) q^{23} +(-1.64201 + 1.82364i) q^{24} +(0.379330 - 4.98559i) q^{25} +(1.11903 - 0.117615i) q^{26} +(-0.0477775 + 0.0243438i) q^{27} +(2.54521 - 0.722443i) q^{28} +(-3.35064 - 4.61176i) q^{29} +(4.98016 - 2.30374i) q^{30} +(2.94697 + 2.65346i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-7.75401 - 2.47301i) q^{33} -2.54858 q^{34} +(-5.86774 - 0.754714i) q^{35} +(2.44473 + 1.77620i) q^{36} +(5.93517 + 4.80621i) q^{37} +(0.460163 - 0.708589i) q^{38} +(-0.574079 - 2.70083i) q^{39} +(-1.75782 - 1.38205i) q^{40} +(-6.45783 + 8.88844i) q^{41} +(-2.41599 - 6.02627i) q^{42} +(-5.01217 - 5.01217i) q^{43} +(0.536596 + 3.27293i) q^{44} +(-3.46239 - 5.80257i) q^{45} +(1.26748 - 1.40768i) q^{46} +(-3.02445 - 1.16098i) q^{47} +(0.383882 - 2.42373i) q^{48} +(-1.25251 + 6.88703i) q^{49} +(2.39721 + 4.38787i) q^{50} +(0.653729 + 6.21982i) q^{51} +(-0.874441 + 0.708108i) q^{52} +(6.84997 - 0.358992i) 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} +(5.32183 + 2.04286i) q^{58} +(3.76472 + 1.67616i) q^{59} +(-2.92201 + 4.64447i) q^{60} +(6.94891 - 6.25682i) q^{61} +(-3.91672 - 0.620347i) q^{62} +(-7.06927 + 3.73451i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(2.42066 - 0.686096i) q^{65} +(7.84995 - 2.14909i) q^{66} +(-10.1105 - 2.70911i) q^{67} +(2.13742 - 1.38806i) q^{68} +(-3.76056 - 2.73221i) q^{69} +(5.33215 - 2.56285i) q^{70} +(-3.11279 + 9.58018i) q^{71} +(-3.01771 - 0.158151i) q^{72} +(10.3146 - 3.95939i) q^{73} +(-7.59530 - 0.798298i) q^{74} +(10.0937 - 6.97593i) q^{75} +0.844895i q^{76} +(-8.39854 - 2.54253i) q^{77} +(1.95244 + 1.95244i) q^{78} +(1.18376 - 5.56914i) q^{79} +(2.22695 + 0.201708i) q^{80} +(8.16159 + 3.63377i) q^{81} +(0.575000 - 10.9717i) q^{82} +(-6.46332 - 12.6850i) q^{83} +(5.30836 + 3.73822i) q^{84} +(-5.61522 + 0.972392i) q^{85} +(6.93339 + 1.47374i) q^{86} +(3.62052 - 13.5120i) q^{87} +(-2.23259 - 2.45266i) q^{88} +(-0.804950 + 1.39421i) q^{89} +(6.06411 + 2.98069i) q^{90} +(-0.661892 - 2.90247i) q^{91} +(-0.296321 + 1.87090i) q^{92} +(-0.509293 + 9.71788i) q^{93} +(3.16883 - 0.673555i) q^{94} +(0.743509 - 1.73679i) q^{95} +(0.998110 + 2.24179i) q^{96} +(-5.89844 + 11.5763i) q^{97} +(-2.70051 - 6.45812i) 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 $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.838671	+	0.544639i	−0.593030	+	0.385118i
$2$	−0.838671	+	0.544639i	−0.593030	+	0.385118i
$3$	1.54432	+	1.90707i	0.891613	+	1.10105i	0.994330	+	0.106339i	$0.0339130\pi$
$3$	1.54432	+	1.90707i	0.891613	+	1.10105i	−0.102717	+	0.994711i	$0.532754\pi$
$4$	0.406737	−	0.913545i	0.203368	−	0.456773i
$5$	−1.64002	+	1.51998i	−0.733439	+	0.679755i
$5$	−1.64002	+	1.51998i	−0.733439	+	0.679755i
$6$	−2.33384	−	0.758311i	−0.952787	−	0.309579i
$7$	1.69521	+	2.03132i	0.640730	+	0.767766i
$7$	1.69521	+	2.03132i	0.640730	+	0.767766i
$8$	0.156434	+	0.987688i	0.0553079	+	0.349201i
$9$	−0.628278	+	2.95582i	−0.209426	+	0.985272i
$10$	0.547597	−	2.16798i	0.173165	−	0.685576i
$11$	−2.77172	+	1.82143i	−0.835704	+	0.549180i
$11$	−2.77172	+	1.82143i	−0.835704	+	0.549180i
$12$	2.37033	−	0.635128i	0.684255	−	0.183346i
$13$	−1.00256	−	0.510828i	−0.278059	−	0.141678i	0.309400	−	0.950932i	$-0.399872\pi$
$13$	−1.00256	−	0.510828i	−0.278059	−	0.141678i	−0.587459	+	0.809254i	$0.699872\pi$
$14$	−2.52806	−	0.780327i	−0.675653	−	0.208551i
$15$	−5.43142	−	0.780309i	−1.40239	−	0.201475i
$16$	−0.669131	−	0.743145i	−0.167283	−	0.185786i
$17$	2.13742	+	1.38806i	0.518400	+	0.336653i	0.777175	−	0.629285i	$-0.216652\pi$
$17$	2.13742	+	1.38806i	0.518400	+	0.336653i	−0.258775	+	0.965938i	$0.583319\pi$
$18$	−1.08293	−	2.82114i	−0.255250	−	0.664949i
$19$	−0.771850	+	0.343650i	−0.177075	+	0.0788387i	−0.493359	−	0.869826i	$-0.664231\pi$
$19$	−0.771850	+	0.343650i	−0.177075	+	0.0788387i	0.316285	+	0.948664i	$0.397565\pi$
$20$	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
$23$	−1.82967	+	0.490260i	−0.381514	+	0.102226i	−0.444479	−	0.895789i	$-0.646611\pi$
$23$	−1.82967	+	0.490260i	−0.381514	+	0.102226i	0.0629650	+	0.998016i	$0.479944\pi$
$24$	−1.64201	+	1.82364i	−0.335174	+	0.372248i
$25$	0.379330	−	4.98559i	0.0758660	−	0.997118i
$26$	1.11903	−	0.117615i	0.219460	−	0.0230662i
$27$	−0.0477775	+	0.0243438i	−0.00919478	+	0.00468498i
$28$	2.54521	−	0.722443i	0.480999	−	0.136529i
$29$	−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	$0.977536\pi$
$30$	4.98016	−	2.30374i	0.909249	−	0.420604i
$31$	2.94697	+	2.65346i	0.529291	+	0.476576i	0.889909	−	0.456138i	$-0.150767\pi$
$31$	2.94697	+	2.65346i	0.529291	+	0.476576i	−0.360618	+	0.932714i	$0.617434\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−7.75401	−	2.47301i	−1.34980	−	0.430496i
$34$	−2.54858			−0.437078
$35$	−5.86774	−	0.754714i	−0.991830	−	0.127570i
$36$	2.44473	+	1.77620i	0.407455	+	0.296033i
$37$	5.93517	+	4.80621i	0.975736	+	0.790135i	0.977731	−	0.209863i	$-0.0673017\pi$
$37$	5.93517	+	4.80621i	0.975736	+	0.790135i	−0.00199506	+	0.999998i	$0.500635\pi$
$38$	0.460163	−	0.708589i	0.0746483	−	0.114948i
$39$	−0.574079	−	2.70083i	−0.0919262	−	0.432479i
$40$	−1.75782	−	1.38205i	−0.277936	−	0.218522i
$41$	−6.45783	+	8.88844i	−1.00854	+	1.38814i	−0.0886106	+	0.996066i	$0.528243\pi$
$41$	−6.45783	+	8.88844i	−1.00854	+	1.38814i	−0.919933	+	0.392075i	$0.871757\pi$
$42$	−2.41599	−	6.02627i	−0.372795	−	0.929874i
$43$	−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	$0.931756\pi$
$44$	0.536596	+	3.27293i	0.0808949	+	0.493413i
$45$	−3.46239	−	5.80257i	−0.516143	−	0.864996i
$46$	1.26748	−	1.40768i	0.186880	−	0.207551i
$47$	−3.02445	−	1.16098i	−0.441161	−	0.169346i	0.127641	−	0.991820i	$-0.459260\pi$
$47$	−3.02445	−	1.16098i	−0.441161	−	0.169346i	−0.568802	+	0.822475i	$0.692593\pi$
$48$	0.383882	−	2.42373i	0.0554086	−	0.349836i
$49$	−1.25251	+	6.88703i	−0.178929	+	0.983862i
$50$	2.39721	+	4.38787i	0.339017	+	0.620538i
$51$	0.653729	+	6.21982i	0.0915404	+	0.870949i
$52$	−0.874441	+	0.708108i	−0.121263	+	0.0981969i
$53$	6.84997	−	0.358992i	0.940916	−	0.0493113i	0.424294	−	0.905525i	$-0.360522\pi$
$53$	6.84997	−	0.358992i	0.940916	−	0.0493113i	0.516623	+	0.856213i	$0.327189\pi$
$54$	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
$58$	5.32183	+	2.04286i	0.698791	+	0.268241i
$59$	3.76472	+	1.67616i	0.490125	+	0.218218i	0.636891	−	0.770954i	$-0.280220\pi$
$59$	3.76472	+	1.67616i	0.490125	+	0.218218i	−0.146767	+	0.989171i	$0.546887\pi$
$60$	−2.92201	+	4.64447i	−0.377229	+	0.599599i
$61$	6.94891	−	6.25682i	0.889716	−	0.801104i	−0.0911398	−	0.995838i	$-0.529051\pi$
$61$	6.94891	−	6.25682i	0.889716	−	0.801104i	0.980856	+	0.194734i	$0.0623843\pi$
$62$	−3.91672	−	0.620347i	−0.497423	−	0.0787841i
$63$	−7.06927	+	3.73451i	−0.890644	+	0.470504i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	2.42066	−	0.686096i	0.300246	−	0.0850998i
$66$	7.84995	−	2.14909i	0.966262	−	0.264535i
$67$	−10.1105	−	2.70911i	−1.23520	−	0.330971i	−0.418597	−	0.908172i	$-0.637478\pi$
$67$	−10.1105	−	2.70911i	−1.23520	−	0.330971i	−0.816602	+	0.577201i	$0.804145\pi$
$68$	2.13742	−	1.38806i	0.259200	−	0.168327i
$69$	−3.76056	−	2.73221i	−0.452718	−	0.328919i
$70$	5.33215	−	2.56285i	0.637314	−	0.306319i
$71$	−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	$0.896068\pi$
$72$	−3.01771	−	0.158151i	−0.355641	−	0.0186383i
$73$	10.3146	−	3.95939i	1.20723	−	0.463412i	0.330228	−	0.943901i	$-0.392874\pi$
$73$	10.3146	−	3.95939i	1.20723	−	0.463412i	0.877001	+	0.480489i	$0.159541\pi$
$74$	−7.59530	−	0.798298i	−0.882936	−	0.0928003i
$75$	10.0937	−	6.97593i	1.16552	−	0.805511i
$76$			0.844895i			0.0969161i
$77$	−8.39854	−	2.54253i	−0.957103	−	0.289749i
$78$	1.95244	+	1.95244i	0.221070	+	0.221070i
$79$	1.18376	−	5.56914i	0.133183	−	0.626577i	−0.860028	−	0.510248i	$-0.829554\pi$
$79$	1.18376	−	5.56914i	0.133183	−	0.626577i	0.993211	−	0.116330i	$-0.0371129\pi$
$80$	2.22695	+	0.201708i	0.248981	+	0.0225516i
$81$	8.16159	+	3.63377i	0.906843	+	0.403752i
$82$	0.575000	−	10.9717i	0.0634982	−	1.21162i
$83$	−6.46332	−	12.6850i	−0.709441	−	1.39236i	−0.910804	−	0.412840i	$-0.864537\pi$
$83$	−6.46332	−	12.6850i	−0.709441	−	1.39236i	0.201363	−	0.979517i	$-0.435463\pi$
$84$	5.30836	+	3.73822i	0.579190	+	0.407873i
$85$	−5.61522	+	0.972392i	−0.609057	+	0.105471i
$86$	6.93339	+	1.47374i	0.747646	+	0.158917i
$87$	3.62052	−	13.5120i	0.388160	−	1.44863i
$88$	−2.23259	−	2.45266i	−0.237995	−	0.261454i
$89$	−0.804950	+	1.39421i	−0.0853245	+	0.147786i	−0.905529	−	0.424283i	$-0.860526\pi$
$89$	−0.804950	+	1.39421i	−0.0853245	+	0.147786i	0.820205	+	0.572070i	$0.193859\pi$
$90$	6.06411	+	2.98069i	0.639213	+	0.314192i
$91$	−0.661892	−	2.90247i	−0.0693852	−	0.304262i
$92$	−0.296321	+	1.87090i	−0.0308936	+	0.195055i
$93$	−0.509293	+	9.71788i	−0.0528112	+	1.00770i
$94$	3.16883	−	0.673555i	0.326840	−	0.0694719i
$95$	0.743509	−	1.73679i	0.0762824	−	0.178191i
$96$	0.998110	+	2.24179i	0.101869	+	0.228802i
$97$	−5.89844	+	11.5763i	−0.598896	+	1.17540i	0.370255	+	0.928930i	$0.379270\pi$
$97$	−5.89844	+	11.5763i	−0.598896	+	1.17540i	−0.969151	+	0.246469i	$0.920730\pi$
$98$	−2.70051	−	6.45812i	−0.272792	−	0.652368i
$99$	−3.64239	−	9.33705i	−0.366074	−	0.938408i
$100$	−4.40028	−	2.37436i	−0.440028	−	0.237436i
$101$	7.71277	+	6.94461i	0.767450	+	0.691015i	0.956752	−	0.290904i	$-0.0939560\pi$
$101$	7.71277	+	6.94461i	0.767450	+	0.691015i	−0.189303	+	0.981919i	$0.560623\pi$
$102$	−3.93582	−	4.86033i	−0.389704	−	0.481244i
$103$	4.51332	+	3.65481i	0.444710	+	0.360119i	0.825366	−	0.564597i	$-0.190969\pi$
$103$	4.51332	+	3.65481i	0.444710	+	0.360119i	−0.380656	+	0.924717i	$0.624302\pi$
$104$	0.347704	−	1.07012i	0.0340952	−	0.104934i
$105$	−7.62237	−	12.3557i	−0.743867	−	1.20580i
$106$	−5.54935	+	4.03184i	−0.539001	+	0.391607i
$107$	−2.76821	+	7.21143i	−0.267613	+	0.697155i	0.732257	+	0.681028i	$0.238467\pi$
$107$	−2.76821	+	7.21143i	−0.267613	+	0.697155i	−0.999870	+	0.0161270i	$0.994866\pi$
$108$	0.00280636	+	0.0535484i	0.000270042	+	0.00515270i
$109$	−4.75220	+	2.74369i	−0.455178	+	0.262797i	−0.710015	−	0.704187i	$-0.751312\pi$
$109$	−4.75220	+	2.74369i	−0.455178	+	0.262797i	0.254836	+	0.966984i	$0.417978\pi$
$110$	2.43103	+	7.00643i	0.231790	+	0.668037i
$111$			18.7411i			1.77883i
$112$	0.375244	−	2.61901i	0.0354573	−	0.247473i
$113$	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	$0.712784\pi$
$114$	2.06197	−	0.216722i	0.193121	−	0.0202979i
$115$	2.25552	−	3.58510i	0.210328	−	0.334313i
$116$	−5.57589	+	1.18519i	−0.517708	+	0.110042i
$117$	2.13980	−	2.64243i	0.197824	−	0.244293i
$118$	−4.07026	+	0.644666i	−0.374698	+	0.0593463i
$119$	0.803797	+	6.69483i	0.0736840	+	0.613714i
$120$	−0.0789602	−	5.48662i	−0.00720805	−	0.500858i
$121$	4.36482	−	10.0969i	0.396802	−	0.917904i
$122$	−2.42013	+	9.03206i	−0.219109	+	0.817724i
$123$	−26.9239	+	1.41102i	−2.42764	+	0.127227i
$124$	3.62270	−	1.61293i	0.325328	−	0.144845i
$125$	6.95588	+	8.75304i	0.622153	+	0.782896i
$126$	3.89483	−	6.98222i	0.346979	−	0.622026i
$127$	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	$0.808377\pi$
$128$	0.629320	−	0.777146i	0.0556246	−	0.0686906i
$129$	1.81820	−	17.2990i	0.160083	−	1.52309i
$130$	−1.65646	+	1.89379i	−0.145281	+	0.166097i
$131$	−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
$133$	−2.00651	−	0.985314i	−0.173987	−	0.0854375i
$134$	9.95490	−	3.23454i	0.859973	−	0.279422i
$135$	0.0413539	−	0.112545i	0.00355918	−	0.00968634i
$136$	−1.03660	+	2.32824i	−0.0888878	+	0.199645i
$137$	−1.75274	+	2.69898i	−0.149747	+	0.230590i	−0.905581	−	0.424173i	$-0.860565\pi$
$137$	−1.75274	+	2.69898i	−0.149747	+	0.230590i	0.755834	+	0.654763i	$0.227231\pi$
$138$	4.64194	+	0.243274i	0.395148	+	0.0207088i
$139$	−0.880982	+	0.640071i	−0.0747239	+	0.0542901i	−0.624520	−	0.781009i	$-0.714705\pi$
$139$	−0.880982	+	0.640071i	−0.0747239	+	0.0542901i	0.549796	+	0.835299i	$0.314705\pi$
$140$	−3.07609	+	5.05348i	−0.259977	+	0.427097i
$141$	−2.45664	−	7.56076i	−0.206887	−	0.636731i
$142$	−2.60714	−	9.72996i	−0.218786	−	0.816520i
$143$	3.70924	−	0.410211i	0.310182	−	0.0343036i
$144$	2.61700	−	1.51093i	0.218083	−	0.125910i
$145$	12.5049	+	2.47048i	1.03848	+	0.205162i
$146$	−6.49408	+	8.93834i	−0.537454	+	0.739742i
$147$	−15.0684	+	8.24715i	−1.24282	+	0.680214i
$148$	6.80474	−	3.46719i	0.559346	−	0.285001i
$149$	4.82357	−	4.34316i	0.395162	−	0.355806i	−0.447466	−	0.894301i	$-0.647674\pi$
$149$	4.82357	−	4.34316i	0.395162	−	0.355806i	0.842629	+	0.538495i	$0.181007\pi$
$150$	−4.66592	+	11.3479i	−0.380971	+	0.926554i
$151$	−1.44098	+	13.7100i	−0.117265	+	1.11570i	0.764699	+	0.644387i	$0.222887\pi$
$151$	−1.44098	+	13.7100i	−0.117265	+	1.11570i	−0.881965	+	0.471316i	$0.843779\pi$
$152$	−0.460163	−	0.708589i	−0.0373241	−	0.0574741i
$153$	−5.44573	+	5.44573i	−0.440261	+	0.440261i
$154$	8.42837	−	2.44183i	0.679178	−	0.196768i
$155$	−8.86630	+	0.127598i	−0.712158	+	0.0102490i
$156$	−2.70083	−	0.574079i	−0.216239	−	0.0459631i
$157$	14.8881	−	12.0561i	1.18820	−	0.962185i	0.188398	−	0.982093i	$-0.439671\pi$
$157$	14.8881	−	12.0561i	1.18820	−	0.962185i	0.999802	+	0.0199079i	$0.00633731\pi$
$158$	2.04039	+	5.31539i	0.162325	+	0.422870i
$159$	11.2632	+	12.5090i	0.893227	+	0.992029i
$160$	−1.97754	+	1.04372i	−0.156338	+	0.0825132i
$161$	−4.09756	−	2.88556i	−0.322933	−	0.227414i
$162$	−8.82398	+	1.39758i	−0.693277	+	0.109804i
$163$	9.63147	+	14.8312i	0.754395	+	1.16167i	0.982178	+	0.187955i	$0.0601858\pi$
$163$	9.63147	+	14.8312i	0.754395	+	1.16167i	−0.227783	+	0.973712i	$0.573148\pi$
$164$	5.49336	+	9.51478i	0.428959	+	0.742979i
$165$	16.4756	−	7.73014i	1.28263	−	0.601791i
$166$	12.3293	+	7.11834i	0.956941	+	0.552490i
$167$	8.80354	−	17.2779i	0.681239	−	1.33701i	−0.248445	−	0.968646i	$-0.579919\pi$
$167$	8.80354	−	17.2779i	0.681239	−	1.33701i	0.929683	−	0.368360i	$-0.120081\pi$
$168$	−6.48794	−	0.243991i	−0.500556	−	0.0188244i
$169$	−6.89703	−	9.49295i	−0.530541	−	0.730227i
$170$	4.17972	−	3.87379i	0.320570	−	0.297106i
$171$	−0.530829	−	2.49736i	−0.0405935	−	0.190978i
$172$	−6.61748	+	2.54021i	−0.504578	+	0.193689i
$173$	2.77487	−	7.22879i	0.210970	−	0.549595i	−0.786736	−	0.617289i	$-0.788231\pi$
$173$	2.77487	−	7.22879i	0.210970	−	0.549595i	0.997706	+	0.0676943i	$0.0215643\pi$
$174$	4.32272	+	13.3040i	0.327704	+	1.00857i
$175$	10.7704	−	7.68110i	0.814163	−	0.580636i
$176$	3.20822	+	0.841015i	0.241829	+	0.0633939i
$177$	2.61736	+	9.76812i	0.196733	+	0.734217i
$178$	−0.0842556	−	1.60769i	−0.00631523	−	0.120502i
$179$	14.2487	+	1.49760i	1.06500	+	0.111936i	0.620783	−	0.783982i	$-0.286815\pi$
$179$	14.2487	+	1.49760i	1.06500	+	0.111936i	0.444218	+	0.895919i	$0.353481\pi$
$180$	−6.70919	+	0.802933i	−0.500073	+	0.0598471i
$181$	9.52413	+	3.09458i	0.707923	+	0.230018i	0.640779	−	0.767725i	$-0.278611\pi$
$181$	9.52413	+	3.09458i	0.707923	+	0.230018i	0.0671437	+	0.997743i	$0.478611\pi$
$182$	2.13591	+	2.07373i	0.158324	+	0.153715i
$183$	22.6636	+	3.58955i	1.67534	+	0.265347i
$184$	−0.770448	−	1.73045i	−0.0567982	−	0.127571i
$185$	−17.0391	+	1.13906i	−1.25274	+	0.0837453i
$186$	−4.86561	−	8.42748i	−0.356764	−	0.617933i
$187$	−8.45256	+	0.0458511i	−0.618112	+	0.00335296i
$188$	−2.29076	+	2.29076i	−0.167071	+	0.167071i
$189$	−0.130443	−	0.0557833i	−0.00948834	−	0.00405764i
$190$	0.322364	+	1.86154i	0.0233867	+	0.135050i
$191$	0.457880	+	4.35644i	0.0331311	+	0.315221i	0.998519	+	0.0544030i	$0.0173256\pi$
$191$	0.457880	+	4.35644i	0.0331311	+	0.315221i	−0.965388	+	0.260818i	$0.916008\pi$
$192$	−2.05805	−	1.33651i	−0.148527	−	0.0964546i
$193$	6.82388	+	4.43148i	0.491194	+	0.318985i	0.766360	−	0.642412i	$-0.222066\pi$
$193$	6.82388	+	4.43148i	0.491194	+	0.318985i	−0.275166	+	0.961397i	$0.588733\pi$
$194$	−1.35808	−	12.9213i	−0.0975044	−	0.927692i
$195$	5.04670	+	3.55683i	0.361402	+	0.254710i
$196$	5.78218	+	3.94543i	0.413013	+	0.281816i
$197$	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	$0.243407\pi$
$198$	8.14009	+	5.84692i	0.578491	+	0.415522i
$199$	12.8515	+	22.2595i	0.911019	+	1.57793i	0.812628	+	0.582783i	$0.198036\pi$
$199$	12.8515	+	22.2595i	0.911019	+	1.57793i	0.0983907	+	0.995148i	$0.468631\pi$
$200$	4.98355	−	0.405258i	0.352390	−	0.0286561i
$201$	−10.4474	−	23.4653i	−0.736904	−	1.65511i
$202$	−10.2508	−	1.62356i	−0.721243	−	0.114234i
$203$	3.68791	−	14.6241i	0.258840	−	1.02641i
$204$	5.94798	+	1.93262i	0.416442	+	0.135310i
$205$	−2.91927	−	24.3930i	−0.203891	−	1.70368i
$206$	−5.77574	−	0.607054i	−0.402415	−	0.0422955i
$207$	−0.299573	−	5.71620i	−0.0208218	−	0.397304i
$208$	0.291222	+	1.08686i	0.0201926	+	0.0753598i
$209$	1.51342	−	2.35837i	0.104685	−	0.163132i
$210$	13.1221	+	6.21096i	0.905509	+	0.428597i
$211$	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	$0.672139\pi$
$212$	2.45818	−	6.40378i	0.168829	−	0.439813i
$213$	−23.0773	+	8.85853i	−1.58123	+	0.606976i
$214$	−1.60601	−	7.55569i	−0.109785	−	0.516496i
$215$	15.8385	+	0.601667i	1.08017	+	0.0410334i
$216$	−0.0315182	−	0.0433811i	−0.00214454	−	0.00295171i
$217$	−0.394286	+	10.4844i	−0.0267659	+	0.711729i
$218$	2.49121	−	4.88928i	0.168726	−	0.331144i
$219$	23.4798	+	13.5561i	1.58662	+	0.916035i
$220$	−5.85481	−	4.55205i	−0.394731	−	0.306899i
$221$	−1.43382	−	2.48346i	−0.0964495	−	0.167055i
$222$	−10.2071	−	15.7176i	−0.685059	−	1.05490i
$223$	7.92513	−	1.25522i	0.530706	−	0.0840555i	0.114670	−	0.993404i	$-0.463419\pi$
$223$	7.92513	−	1.25522i	0.530706	−	0.0840555i	0.416036	+	0.909348i	$0.363419\pi$
$224$	1.11171	+	2.40086i	0.0742790	+	0.160414i
$225$	14.4982	+	4.25357i	0.966544	+	0.283571i
$226$	−9.64724	−	10.7143i	−0.641725	−	0.712708i
$227$	7.86990	+	20.5018i	0.522343	+	1.36075i	0.900438	+	0.434984i	$0.143246\pi$
$227$	7.86990	+	20.5018i	0.522343	+	1.36075i	−0.378095	+	0.925767i	$0.623421\pi$
$228$	−1.61128	+	1.30479i	−0.106710	+	0.0864117i
$229$	13.9057	+	2.95575i	0.918916	+	0.195322i	0.643005	−	0.765862i	$-0.277687\pi$
$229$	13.9057	+	2.95575i	0.918916	+	0.195322i	0.275910	+	0.961183i	$0.411021\pi$
$230$	0.0609499	+	4.23516i	0.00401892	+	0.279258i
$231$	−8.12122	−	19.9431i	−0.534337	−	1.31216i
$232$	4.03083	−	4.03083i	0.264637	−	0.264637i
$233$	2.37765	+	3.66126i	0.155765	+	0.239857i	0.907934	−	0.419113i	$-0.137659\pi$
$233$	2.37765	+	3.66126i	0.155765	+	0.239857i	−0.752169	+	0.658970i	$0.770992\pi$
$234$	−0.355415	+	3.38155i	−0.0232342	+	0.221059i
$235$	6.72481	−	2.69307i	0.438678	−	0.175677i
$236$	3.06250	−	2.75749i	0.199352	−	0.179497i
$237$	12.4489	−	6.34301i	0.808641	−	0.412023i
$238$	−4.32039	−	5.17698i	−0.280049	−	0.335573i
$239$	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	$0.0306798\pi$
$240$	3.05445	+	4.55846i	0.197164	+	0.294248i
$241$	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	$0.146491\pi$
$242$	1.83854	+	10.8453i	0.118186	+	0.697160i
$243$	5.71585	+	21.3318i	0.366672	+	1.36844i
$244$	−2.88952	−	8.89302i	−0.184982	−	0.569317i
$245$	−8.41401	−	13.1987i	−0.537551	−	0.843231i
$246$	21.8118	−	15.8472i	1.39067	−	1.01038i
$247$	0.949369	+	0.0497543i	0.0604069	+	0.00316579i
$248$	−2.15979	+	3.32578i	−0.137147	+	0.211187i
$249$	14.2098	−	31.9157i	0.900507	−	2.02257i
$250$	−10.6009	−	3.55247i	−0.670462	−	0.224678i
$251$	2.12825	−	0.691509i	0.134334	−	0.0436477i	−0.241079	−	0.970506i	$-0.577501\pi$
$251$	2.12825	−	0.691509i	0.134334	−	0.0436477i	0.375412	+	0.926858i	$0.377501\pi$
$252$	0.536310	+	7.97706i	0.0337844	+	0.502507i
$253$	4.17837	−	4.69148i	0.262692	−	0.294951i
$254$	−2.54513	−	1.46943i	−0.159696	−	0.0922004i
$255$	−10.5261	−	9.20697i	−0.659171	−	0.576563i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	0.603600	−	0.745384i	0.0376515	−	0.0464958i	−0.757972	−	0.652287i	$-0.773810\pi$
$257$	0.603600	−	0.745384i	0.0376515	−	0.0464958i	0.795624	+	0.605791i	$0.207143\pi$
$258$	7.89683	+	15.4984i	0.491635	+	0.964889i
$259$	0.298445	+	20.2038i	0.0185445	+	1.25540i
$260$	0.357791	−	2.49044i	0.0221892	−	0.154451i
$261$	15.7367	−	7.00642i	0.974075	−	0.433686i
$262$	2.55090	−	0.133687i	0.157595	−	0.00825921i
$263$	−4.74202	+	17.6975i	−0.292405	+	1.09127i	0.650851	+	0.759206i	$0.274412\pi$
$263$	−4.74202	+	17.6975i	−0.292405	+	1.09127i	−0.943256	+	0.332066i	$0.892254\pi$
$264$	1.22957	−	8.04540i	0.0756747	−	0.495160i
$265$	−10.6884	+	11.0006i	−0.656585	+	0.675760i
$266$	2.21944	−	0.266472i	0.136083	−	0.0163384i
$267$	−3.90197	+	0.618011i	−0.238797	+	0.0378217i
$268$	−6.58722	+	8.13455i	−0.402379	+	0.496896i
$269$	−27.4350	+	5.83150i	−1.67274	+	0.355553i	−0.944181	−	0.329427i	$-0.893145\pi$
$269$	−27.4350	+	5.83150i	−1.67274	+	0.355553i	−0.728563	+	0.684979i	$0.759811\pi$
$270$	0.0266142	+	0.116911i	0.00161969	+	0.00711499i
$271$	−3.28005	+	0.344747i	−0.199249	+	0.0209419i	−0.203627	−	0.979049i	$-0.565273\pi$
$271$	−3.28005	+	0.344747i	−0.199249	+	0.0209419i	0.00437819	+	0.999990i	$0.498606\pi$
$272$	−0.398686	−	2.51720i	−0.0241739	−	0.152628i
$273$	4.51306	−	5.74462i	0.273143	−	0.347680i
$274$		−	3.21817i		−	0.194417i
$275$	8.02948	+	14.5096i	0.484196	+	0.874959i
$276$	−4.02556	+	2.32416i	−0.242310	+	0.139898i
$277$	−0.0719938	−	1.37372i	−0.00432569	−	0.0825391i	0.995614	−	0.0935608i	$-0.0298249\pi$
$277$	−0.0719938	−	1.37372i	−0.00432569	−	0.0825391i	−0.999939	+	0.0110217i	$0.996492\pi$
$278$	0.390246	−	1.01663i	0.0234054	−	0.0609731i
$279$	−9.69467	+	7.04359i	−0.580405	+	0.421689i
$280$	−0.172495	−	5.91356i	−0.0103085	−	0.353403i
$281$	−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	$0.841640\pi$
$282$	6.17820	+	5.00301i	0.367906	+	0.297925i
$283$	−10.6426	−	13.1425i	−0.632635	−	0.781239i	0.355525	−	0.934667i	$-0.384302\pi$
$283$	−10.6426	−	13.1425i	−0.632635	−	0.781239i	−0.988160	+	0.153428i	$0.950969\pi$
$284$	7.48585	+	6.74029i	0.444203	+	0.399962i
$285$	4.46040	−	1.26423i	0.264211	−	0.0748863i
$286$	−2.88741	+	2.36423i	−0.170736	+	0.139800i
$287$	−29.0027	+	1.94989i	−1.71197	+	0.115099i
$288$	−1.37189	+	2.69249i	−0.0808395	+	0.158656i
$289$	−4.27266	−	9.59656i	−0.251333	−	0.564503i
$290$	−11.8330	+	4.73874i	−0.694859	+	0.278268i
$291$	−31.1860	+	6.62879i	−1.82816	+	0.388587i
$292$	0.578228	−	11.0333i	0.0338383	−	0.645672i
$293$	4.73617	−	29.9030i	0.276690	−	1.74695i	−0.322704	−	0.946500i	$-0.604592\pi$
$293$	4.73617	−	29.9030i	0.276690	−	1.74695i	0.599394	−	0.800454i	$-0.295408\pi$
$294$	8.14566	−	15.1235i	0.475065	−	0.882018i
$295$	−8.72194	+	2.97336i	−0.507811	+	0.173115i
$296$	−3.81857	+	6.61395i	−0.221950	+	0.384428i
$297$	0.0880851	−	0.154497i	0.00511122	−	0.00896485i
$298$	−1.67993	+	6.26959i	−0.0973158	+	0.363187i
$299$	2.08479	+	0.443136i	0.120567	+	0.0256272i
$300$	−2.26735	−	12.0584i	−0.130906	−	0.696193i
$301$	1.68462	−	18.6780i	0.0970997	−	1.07658i
$302$	−6.25849	−	12.2830i	−0.360136	−	0.706806i
$303$	−1.33291	+	25.4335i	−0.0765739	+	1.46112i
$304$	0.771850	+	0.343650i	0.0442687	+	0.0197097i
$305$	−1.88611	+	20.8235i	−0.107998	+	1.19235i
$306$	1.60122	−	7.53313i	0.0915355	−	0.430641i
$307$	−22.3866	−	22.3866i	−1.27767	−	1.27767i	−0.941969	−	0.335699i	$-0.891028\pi$
$307$	−22.3866	−	22.3866i	−1.27767	−	1.27767i	−0.335699	−	0.941969i	$-0.608972\pi$
$308$	−5.73871	+	6.63831i	−0.326994	+	0.378253i
$309$			14.2514i			0.810735i
$310$	7.36641	−	4.93594i	0.418384	−	0.280343i
$311$	−6.28282	−	0.660351i	−0.356266	−	0.0374451i	−0.0752949	−	0.997161i	$-0.523990\pi$
$311$	−6.28282	−	0.660351i	−0.356266	−	0.0374451i	−0.280971	+	0.959716i	$0.590656\pi$
$312$	2.57777	−	0.989514i	0.145938	−	0.0560202i
$313$	−19.3955	−	1.01647i	−1.09630	−	0.0574545i	−0.504402	−	0.863469i	$-0.668287\pi$
$313$	−19.3955	−	1.01647i	−1.09630	−	0.0574545i	−0.591896	+	0.806015i	$0.701620\pi$
$314$	−5.91996	+	18.2198i	−0.334083	+	1.02820i
$315$	5.91737	−	16.8698i	0.333406	−	0.950506i
$316$	−4.60619	−	3.34659i	−0.259118	−	0.188260i
$317$	25.0460	−	16.2650i	1.40672	−	0.913536i	0.406722	−	0.913552i	$-0.366672\pi$
$317$	25.0460	−	16.2650i	1.40672	−	0.913536i	1.00000		1.57868e-5i	$5.02510e-6\pi$
$318$	−16.2590	−	4.35658i	−0.911758	−	0.244305i
$319$	17.6870	+	6.67956i	0.990283	+	0.373983i
$320$	1.09005	−	1.95238i	0.0609358	−	0.109141i
$321$	−18.0277	+	5.85756i	−1.00621	+	0.326937i
$322$	5.00809	+	0.188339i	0.279090	+	0.0104957i
$323$	−2.12677	−	0.336848i	−0.118337	−	0.0187427i
$324$	6.63923	−	5.97799i	0.368846	−	0.332111i
$325$	−2.92708	+	4.80456i	−0.162365	+	0.266509i
$326$	−16.1553	−	7.19279i	−0.894757	−	0.398372i
$327$	−12.5713	−	4.82568i	−0.695196	−	0.266861i
$328$	−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	$-0.00556509\pi$
$332$	−14.2172	+	0.745090i	−0.780268	+	0.0408921i
$333$	−17.9352	+	14.5236i	−0.982843	+	0.795890i
$334$	2.02696	+	19.2852i	0.110910	+	1.05524i
$335$	20.6993	−	10.9248i	1.13092	−	0.596886i
$336$	5.57414	−	3.32896i	0.304094	−	0.181610i
$337$	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	$-0.170465\pi$
$338$	10.9546	+	4.20507i	0.595850	+	0.228725i
$339$	−23.6738	+	26.2924i	−1.28578	+	1.42801i
$340$	−1.39559	+	5.52527i	−0.0756867	+	0.299650i
$341$	−13.0012	−	1.98696i	−0.704057	−	0.107600i
$342$	1.80535	+	1.80535i	0.0976221	+	0.0976221i
$343$	−16.1130	+	9.13075i	−0.870021	+	0.493014i
$344$	4.16639	−	5.73454i	0.224637	−	0.309186i
$345$	10.3203	−	1.23510i	0.555626	−	0.0664955i
$346$	1.60988	+	7.57388i	0.0865475	+	0.407174i
$347$	0.370935	−	0.571190i	0.0199128	−	0.0306631i	−0.828574	−	0.559880i	$-0.810847\pi$
$347$	0.370935	−	0.571190i	0.0199128	−	0.0306631i	0.848487	+	0.529216i	$0.177514\pi$
$348$	−10.8712	−	8.80332i	−0.582757	−	0.471907i
$349$	−24.8855	−	18.0804i	−1.33209	−	0.967819i	−0.999695	−	0.0246787i	$-0.992144\pi$
$349$	−24.8855	−	18.0804i	−1.33209	−	0.967819i	−0.332394	−	0.943141i	$-0.607856\pi$
$350$	−4.84936	+	12.3079i	−0.259209	+	0.657883i
$351$	0.0603351			0.00322045
$352$	−3.14869	+	1.04199i	−0.167826	+	0.0555382i
$353$	21.5956	+	5.78652i	1.14942	+	0.307985i	0.782731	−	0.622360i	$-0.213826\pi$
$353$	21.5956	+	5.78652i	1.14942	+	0.307985i	0.366685	+	0.930345i	$0.380493\pi$
$354$	−7.51521	−	6.76672i	−0.399429	−	0.359647i
$355$	−9.45664	−	20.4431i	−0.501906	−	1.08501i
$356$	0.946275	+	1.30244i	0.0501525	+	0.0690290i
$357$	−11.5262	+	11.8718i	−0.610032	+	0.628325i
$358$	−12.7657	+	6.50443i	−0.674686	+	0.343770i
$359$	−8.07161	+	0.848360i	−0.426003	+	0.0447747i	−0.315105	−	0.949057i	$-0.602040\pi$
$359$	−8.07161	+	0.848360i	−0.426003	+	0.0447747i	−0.110899	+	0.993832i	$0.535373\pi$
$360$	5.18949	−	4.32748i	0.273510	−	0.228078i
$361$	−12.2358	+	13.5893i	−0.643991	+	0.715224i
$362$	−9.67303	+	2.59188i	−0.508403	+	0.136226i
$363$	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
$366$	−20.9623	+	9.33300i	−1.09572	+	0.487844i
$367$	−1.23600	−	3.21989i	−0.0645187	−	0.168077i	0.897531	−	0.440952i	$-0.145359\pi$
$367$	−1.23600	−	3.21989i	−0.0645187	−	0.168077i	−0.962050	+	0.272875i	$0.912026\pi$
$368$	1.58863	+	1.03167i	0.0828128	+	0.0537793i
$369$	−22.2153	−	24.6726i	−1.15648	−	1.28440i
$370$	13.6698	−	10.2355i	0.710661	−	0.532117i
$371$	12.3414	+	13.3059i	0.640733	+	0.690808i
$372$	8.67058	+	4.41788i	0.449549	+	0.229056i
$373$	−20.0291	+	5.36677i	−1.03707	+	0.277881i	−0.736897	−	0.676005i	$-0.763710\pi$
$373$	−20.0291	+	5.36677i	−1.03707	+	0.277881i	−0.300168	+	0.953886i	$0.597043\pi$
$374$	7.06394	−	4.64205i	0.365268	−	0.240035i
$375$	−5.95060	+	26.7829i	−0.307288	+	1.38306i
$376$	0.673555	−	3.16883i	0.0347360	−	0.163420i
$377$	1.00339	+	6.33516i	0.0516772	+	0.326277i
$378$	0.139781	−	0.0242606i	0.00718954	−	0.00124783i
$379$	−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	$0.692946\pi$
$380$	−1.28422	−	1.38565i	−0.0658792	−	0.0710821i
$381$	−2.93331	+	6.58832i	−0.150278	+	0.337530i
$382$	−2.75670	−	3.40424i	−0.141045	−	0.174176i
$383$	22.7991	−	14.8059i	1.16498	−	0.756546i	0.190646	−	0.981659i	$-0.438942\pi$
$383$	22.7991	−	14.8059i	1.16498	−	0.756546i	0.974333	+	0.225113i	$0.0722750\pi$
$384$	2.45395			0.125227
$385$	17.6384	−	8.59580i	0.898935	−	0.438083i
$386$	−8.13655			−0.414139
$387$	17.9641	−	11.6660i	0.913167	−	0.593017i
$388$	8.17640	+	10.0970i	0.415094	+	0.512598i
$389$	15.2610	−	34.2768i	0.773765	−	1.73791i	0.104949	−	0.994478i	$-0.466532\pi$
$389$	15.2610	−	34.2768i	0.773765	−	1.73791i	0.668817	−	0.743427i	$-0.266801\pi$
$390$	−6.16971	−	0.234373i	−0.312415	−	0.0118680i
$391$	−4.59129	−	1.49180i	−0.232191	−	0.0754436i
$392$	−6.99818	−	0.159716i	−0.353461	−	0.00806685i
$393$	−0.980588	−	6.19119i	−0.0494641	−	0.312304i
$394$	−0.120870	+	0.568648i	−0.00608934	+	0.0286481i
$395$	6.52359	+	10.9328i	0.328237	+	0.550088i
$396$	−10.0113	−	0.470230i	−0.503087	−	0.0236300i
$397$	18.7809	−	5.03233i	0.942588	−	0.252566i	0.245374	−	0.969429i	$-0.421089\pi$
$397$	18.7809	−	5.03233i	0.942588	−	0.252566i	0.697214	+	0.716863i	$0.254423\pi$
$398$	−22.9015	−	11.6689i	−1.14795	−	0.584910i
$399$	−1.21963	−	5.34821i	−0.0610578	−	0.267745i
$400$	−3.95884	+	3.05411i	−0.197942	+	0.152706i
$401$	16.7799	+	18.6359i	0.837946	+	0.930633i	0.998408	−	0.0564087i	$-0.0179650\pi$
$401$	16.7799	+	18.6359i	0.837946	+	0.930633i	−0.160462	+	0.987042i	$0.551298\pi$
$402$	21.5421	+	13.9896i	1.07442	+	0.697736i
$403$	−1.59904	−	4.16564i	−0.0796538	−	0.207505i
$404$	9.48129	−	4.22134i	0.471712	−	0.210020i
$405$	−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
$408$	−6.04097	+	1.61867i	−0.299073	+	0.0801363i
$409$	−12.8724	+	14.2963i	−0.636501	+	0.706906i	−0.971959	−	0.235149i	$-0.924442\pi$
$409$	−12.8724	+	14.2963i	−0.636501	+	0.706906i	0.335458	+	0.942055i	$0.391109\pi$
$410$	15.7337	+	18.8677i	0.777031	+	0.931811i
$411$	−7.85395	+	0.825484i	−0.387407	+	0.0407181i
$412$	5.17457	−	2.63657i	0.254933	−	0.129895i
$413$	2.97719	+	10.4888i	0.146498	+	0.516120i
$414$	3.36451	+	4.63085i	0.165357	+	0.227594i
$415$	29.8808	+	10.9795i	1.46679	+	0.538963i
$416$	−0.836183	−	0.752902i	−0.0409972	−	0.0369141i
$417$	−2.58118	−	0.691625i	−0.126401	−	0.0338690i
$418$	0.0152004	+	2.80216i	0.000743475	+	0.137058i
$419$	−7.97366			−0.389539			−0.194769	−	0.980849i	$-0.562396\pi$
$419$	−7.97366			−0.389539			−0.194769	+	0.980849i	$0.562396\pi$
$420$	−14.3878	+	1.93785i	−0.702054	+	0.0945572i
$421$	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	$0.522980\pi$
$422$	−14.8165	−	11.9982i	−0.721258	−	0.584063i
$423$	5.33183	−	8.21030i	0.259242	−	0.399198i
$424$	1.42614	+	6.70948i	0.0692597	+	0.325841i
$425$	7.73106	−	10.1298i	0.375012	−	0.491366i
$426$	14.5295	−	19.9982i	0.703957	−	0.968914i
$427$	24.4895	+	3.50879i	1.18513	+	0.169802i
$428$	5.46204	+	5.46204i	0.264018	+	0.264018i
$429$	6.51054	+	6.44029i	0.314332	+	0.310940i
$430$	−13.6109	+	8.12164i	−0.656378	+	0.391660i
$431$	−18.7011	+	20.7697i	−0.900802	+	1.00044i	0.0991841	+	0.995069i	$0.468377\pi$
$431$	−18.7011	+	20.7697i	−0.900802	+	1.00044i	−0.999986	+	0.00537232i	$0.998290\pi$
$432$	0.0500604	+	0.0192164i	0.00240853	+	0.000924549i
$433$	5.01575	−	31.6682i	0.241041	−	1.52188i	−0.509163	−	0.860670i	$-0.670045\pi$
$433$	5.01575	−	31.6682i	0.241041	−	1.52188i	0.750205	−	0.661206i	$-0.229955\pi$
$434$	−5.37955	−	9.00772i	−0.258227	−	0.432384i
$435$	14.6002	+	27.6630i	0.700024	+	1.32634i
$436$	0.573586	+	5.45731i	0.0274698	+	0.261358i
$437$	1.24376	−	1.00717i	0.0594970	−	0.0481797i
$438$	−27.0750	+	1.41894i	−1.29369	+	0.0677996i
$439$	−4.31814	+	7.47924i	−0.206094	+	0.356965i	−0.950481	−	0.310784i	$-0.899408\pi$
$439$	−4.31814	+	7.47924i	−0.206094	+	0.356965i	0.744387	+	0.667748i	$0.232742\pi$
$440$	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
$443$	−38.5218	−	14.7871i	−1.83022	−	0.702557i	−0.986041	−	0.166503i	$-0.946752\pi$
$443$	−38.5218	−	14.7871i	−1.83022	−	0.702557i	−0.844184	−	0.536054i	$-0.819914\pi$
$444$	17.1209	+	7.62270i	0.812520	+	0.361757i
$445$	−0.799042	−	3.51005i	−0.0378782	−	0.166392i
$446$	−5.96293	+	5.36905i	−0.282353	+	0.254232i
$447$	15.7319	+	2.49168i	0.744092	+	0.117853i
$448$	−2.23996	−	1.40805i	−0.105828	−	0.0665240i
$449$	−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	$0.633833\pi$
$450$	−14.4758	+	4.32893i	−0.682398	+	0.204067i
$451$	1.70964	−	36.3987i	0.0805040	−	1.71395i
$452$	13.9263	+	3.73154i	0.655038	+	0.175517i
$453$	−28.3713	+	18.4245i	−1.33300	+	0.865660i
$454$	−17.7663	−	12.9080i	−0.833815	−	0.605802i
$455$	5.49721	+	3.75405i	0.257713	+	0.175993i
$456$	0.640693	−	1.97185i	0.0300032	−	0.0923404i
$457$	−23.9358	−	1.25442i	−1.11967	−	0.0586795i	−0.516497	−	0.856289i	$-0.672764\pi$
$457$	−23.9358	−	1.25442i	−1.11967	−	0.0586795i	−0.603174	+	0.797610i	$0.706098\pi$
$458$	−13.2721	+	5.09470i	−0.620166	+	0.238059i
$459$	−0.135911	−	0.0142848i	−0.00634379	−	0.000666759i
$460$	−2.35775	−	3.51871i	−0.109931	−	0.164061i
$461$		−	25.6929i		−	1.19664i	−0.801259	−	0.598318i	$-0.795836\pi$
$461$		−	25.6929i		−	1.19664i	0.801259	−	0.598318i	$-0.204164\pi$
$462$	17.6728	+	12.3026i	0.822215	+	0.572368i
$463$	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	$0.713644\pi$
$464$	−1.18519	+	5.57589i	−0.0550211	+	0.258854i
$465$	−13.9357	−	16.7116i	−0.646254	−	0.774983i
$466$	−3.98814	−	1.77563i	−0.184747	−	0.0822546i
$467$	0.681554	−	13.0048i	0.0315385	−	0.601791i	−0.936451	−	0.350799i	$-0.885910\pi$
$467$	0.681554	−	13.0048i	0.0315385	−	0.601791i	0.967989	−	0.250992i	$-0.0807568\pi$
$468$	−1.54365	−	3.02958i	−0.0713551	−	0.140042i
$469$	−11.6365	−	25.1302i	−0.537322	−	1.16041i
$470$	−4.17315	+	5.92120i	−0.192493	+	0.273124i
$471$	45.9839	+	9.77418i	2.11883	+	0.450371i
$472$	−1.06659	+	3.98058i	−0.0490939	+	0.183221i
$473$	23.0216	+	4.76302i	1.05854	+	0.219004i
$474$	−6.98584	+	12.0998i	−0.320870	+	0.555764i
$475$	1.42051	+	3.97849i	0.0651775	+	0.182545i
$476$	6.44296	+	1.98873i	0.295313	+	0.0911531i
$477$	−3.24258	+	20.4728i	−0.148467	+	0.937386i
$478$	−0.820749	+	15.6608i	−0.0375402	+	0.716309i
$479$	−5.54552	+	1.17874i	−0.253381	+	0.0538578i	−0.332851	−	0.942979i	$-0.608011\pi$
$479$	−5.54552	+	1.17874i	−0.253381	+	0.0538578i	0.0794699	+	0.996837i	$0.474677\pi$
$480$	−5.04439	−	2.15948i	−0.230244	−	0.0985662i
$481$	−3.49520	−	7.85034i	−0.159367	−	0.357945i
$482$	−7.80688	+	15.3219i	−0.355594	+	0.697892i
$483$	−0.824970	−	12.2706i	−0.0375374	−	0.558330i
$484$	−7.44869	−	8.09426i	−0.338577	−	0.367921i
$485$	−7.92223	−	27.9509i	−0.359730	−	1.26919i
$486$	−16.4119	−	14.7773i	−0.744457	−	0.670312i
$487$	7.97347	+	9.84642i	0.361313	+	0.446184i	0.925093	−	0.379741i	$-0.123987\pi$
$487$	7.97347	+	9.84642i	0.361313	+	0.446184i	−0.563780	+	0.825925i	$0.690654\pi$
$488$	7.26684	+	5.88457i	0.328954	+	0.266382i
$489$	−13.4101	+	41.2720i	−0.606425	+	1.86638i
$490$	14.2451	+	6.48672i	0.643527	+	0.293040i
$491$	−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	$0.330955\pi$
$492$	−9.66189	+	25.1701i	−0.435592	+	1.13476i
$493$	−0.760340	−	14.5082i	−0.0342440	−	0.653414i
$494$	−0.823306	+	0.475336i	−0.0370423	+	0.0213864i
$495$	20.1657	+	9.77659i	0.906381	+	0.439425i
$496$		−	3.96554i		−	0.178058i
$497$	−24.7372	+	9.91738i	−1.10962	+	0.444856i
$498$	5.46520	+	34.5059i	0.244901	+	1.54625i
$499$	−6.11110	+	0.642302i	−0.273570	+	0.0287534i	−0.240320	−	0.970694i	$-0.577252\pi$
$499$	−6.11110	+	0.642302i	−0.273570	+	0.0287534i	−0.0332501	+	0.999447i	$0.510586\pi$
$500$	10.8255	−	2.79433i	0.484132	−	0.124966i
$501$	46.5458	−	9.89361i	2.07951	−	0.442014i
$502$	−1.40827	+	1.73907i	−0.0628544	+	0.0776187i
$503$	36.6445	−	5.80392i	1.63390	−	0.258784i	0.729032	−	0.684479i	$-0.239970\pi$
$503$	36.6445	−	5.80392i	1.63390	−	0.258784i	0.904867	+	0.425695i	$0.139970\pi$
$504$	−4.79441	−	6.39803i	−0.213560	−	0.284991i
$505$	−23.2048	+	0.333949i	−1.03260	+	0.0148605i
$506$	−0.949112	+	6.21031i	−0.0421932	+	0.276082i
$507$	7.45255	−	27.8133i	0.330979	−	1.23523i
$508$	2.93484	−	0.153808i	0.130212	−	0.00682414i
$509$	−24.1473	+	10.7511i	−1.07031	+	0.476534i	−0.864798	−	0.502120i	$-0.832553\pi$
$509$	−24.1473	+	10.7511i	−1.07031	+	0.476534i	−0.205515	+	0.978654i	$0.565887\pi$
$510$	13.8424	+	1.98868i	0.612953	+	0.0880602i
$511$	25.5282	+	14.2402i	1.12930	+	0.629947i
$512$	−0.453990	−	0.891007i	−0.0200637	−	0.0393773i
$513$	0.0285113	−	0.0352085i	0.00125881	−	0.00155449i
$514$	−0.100256	+	0.953876i	−0.00442212	+	0.0420737i
$515$	−12.9572	+	0.866181i	−0.570961	+	0.0381685i
$516$	−15.0639	−	8.69713i	−0.663150	−	0.382870i
$517$	10.4975	−	2.29091i	0.461681	−	0.100754i
$518$	−11.2541	−	16.7818i	−0.494475	−	0.737348i
$519$	18.0711	−	5.87166i	0.793234	−	0.257737i
$520$	1.05632	+	2.28353i	0.0463229	+	0.100139i
$521$	10.7040	−	24.0416i	0.468952	−	1.05328i	−0.511992	−	0.858990i	$-0.671092\pi$
$521$	10.7040	−	24.0416i	0.468952	−	1.05328i	0.980944	−	0.194292i	$-0.0622411\pi$
$522$	−9.38191	+	14.4469i	−0.410635	+	0.632323i
$523$	25.7532	+	1.34967i	1.12611	+	0.0590168i	0.606277	−	0.795253i	$-0.292662\pi$
$523$	25.7532	+	1.34967i	1.12611	+	0.0590168i	0.519830	+	0.854270i	$0.325995\pi$
$524$	−2.06655	+	1.50144i	−0.0902778	+	0.0655907i
$525$	31.2813	+	8.67782i	1.36523	+	0.378731i
$526$	−5.66173	−	17.4250i	−0.246863	−	0.759767i
$527$	2.61575	+	9.76212i	0.113944	+	0.425245i
$528$	3.35064	+	7.41711i	0.145818	+	0.322788i
$529$	−16.8112	+	9.70597i	−0.730923	+	0.421999i
$530$	2.97274	−	15.0472i	0.129127	−	0.653608i
$531$	−7.31972	+	10.0747i	−0.317649	+	0.437206i
$532$	−1.71625	+	1.43228i	−0.0744089	+	0.0620971i
$533$	11.0148	−	5.61232i	0.477104	−	0.243097i
$534$	2.93587	−	2.64347i	0.127048	−	0.114394i
$535$	−6.42130	−	16.0345i	−0.277617	−	0.693232i
$536$	1.09412	−	10.4099i	0.0472588	−	0.449638i
$537$	19.1486	+	29.4862i	0.826321	+	1.27242i
$538$	19.8329	−	19.8329i	0.855057	−	0.855057i
$539$	−9.07263	−	21.3702i	−0.390786	−	0.920482i
$540$	−0.0859950	−	0.0835549i	−0.00370063	−	0.00359563i
$541$	−3.57387	−	0.759650i	−0.153653	−	0.0326599i	0.130443	−	0.991456i	$-0.458360\pi$
$541$	−3.57387	−	0.759650i	−0.153653	−	0.0326599i	−0.284096	+	0.958796i	$0.591693\pi$
$542$	2.56312	−	2.07557i	0.110095	−	0.0891535i
$543$	8.80670	+	22.9422i	0.377932	+	0.984545i
$544$	1.70533	+	1.89396i	0.0731155	+	0.0812030i
$545$	3.62336	−	11.7229i	0.155208	−	0.502156i
$546$	−0.656225	+	7.27583i	−0.0280838	+	0.311377i
$547$	−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	$0.624822\pi$
$548$	1.75274	+	2.69898i	0.0748734	+	0.115295i
$549$	14.1282	+	24.4707i	0.602976	+	1.04438i
$550$	−14.6366	−	7.79557i	−0.624105	−	0.332404i
$551$	4.17103	+	2.40814i	0.177692	+	0.102590i
$552$	2.11029	−	4.14168i	0.0898199	−	0.176281i
$553$	13.3194	−	7.03629i	0.566399	−	0.299214i
$554$	0.808563	+	1.11289i	0.0343525	+	0.0472822i
$555$	−28.4861	−	30.7358i	−1.20917	−	1.30466i
$556$	0.226406	+	1.06516i	0.00960176	+	0.0451727i
$557$	35.5711	−	13.6544i	1.50719	−	0.578558i	0.542066	−	0.840336i	$-0.317642\pi$
$557$	35.5711	−	13.6544i	1.50719	−	0.578558i	0.965128	+	0.261779i	$0.0843090\pi$
$558$	4.29442	−	11.1873i	0.181797	−	0.473598i
$559$	2.46463	+	7.58534i	0.104243	+	0.320826i
$560$	3.36542	+	4.86559i	0.142215	+	0.205608i
$561$	−13.1409	−	16.0488i	−0.554808	−	0.677583i
$562$	−6.29472	−	23.4922i	−0.265527	−	0.990959i
$563$	−2.13407	−	40.7204i	−0.0899401	−	1.71616i	−0.555812	−	0.831308i	$-0.687593\pi$
$563$	−2.13407	−	40.7204i	−0.0899401	−	1.71616i	0.465872	−	0.884852i	$-0.345741\pi$
$564$	−7.90631	−	0.830986i	−0.332916	−	0.0349908i
$565$	−25.3435	−	19.9258i	−1.06621	−	0.838286i
$566$	16.0835	+	5.22585i	0.676040	+	0.219659i
$567$	6.45428	+	22.7388i	0.271054	+	0.954940i
$568$	−9.94918	−	1.57580i	−0.417458	−	0.0661189i
$569$	−14.5264	−	32.6268i	−0.608978	−	1.36779i	−0.910174	−	0.414225i	$-0.864053\pi$
$569$	−14.5264	−	32.6268i	−0.608978	−	1.36779i	0.301196	−	0.953562i	$-0.402614\pi$
$570$	−3.05226	+	3.48958i	−0.127845	+	0.146162i
$571$	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	$0.814625\pi$
$572$	1.13394	−	3.55540i	0.0474122	−	0.148659i
$573$	−7.60094	+	7.60094i	−0.317534	+	0.317534i
$574$	23.2617	−	17.4313i	0.970924	−	0.727568i
$575$	1.75018	+	9.30798i	0.0729877	+	0.388170i
$576$	−0.315869	−	3.00530i	−0.0131612	−	0.125221i
$577$	−7.07576	−	4.59505i	−0.294568	−	0.191294i	0.388891	−	0.921284i	$-0.372858\pi$
$577$	−7.07576	−	4.59505i	−0.294568	−	0.191294i	−0.683458	+	0.729989i	$0.739525\pi$
$578$	8.81002	+	5.72129i	0.366448	+	0.237974i
$579$	2.08708	+	19.8573i	0.0867362	+	0.825240i
$580$	7.34310	−	10.4190i	0.304906	−	0.432624i
$581$	14.8105	−	34.6328i	0.614444	−	1.43681i
$582$	22.5445	−	22.5445i	0.934499	−	0.934499i
$583$	−18.3323	+	13.4717i	−0.759247	+	0.557942i
$584$	5.52420	+	9.56819i	0.228593	+	0.395935i
$585$	0.507127	+	7.58608i	0.0209671	+	0.313646i
$586$	12.3143	+	27.6583i	0.508698	+	1.14255i
$587$	−6.88837	−	1.09101i	−0.284313	−	0.0450308i	0.0126490	−	0.999920i	$-0.495974\pi$
$587$	−6.88837	−	1.09101i	−0.284313	−	0.0450308i	−0.296962	+	0.954889i	$0.595974\pi$
$588$	1.40530	+	17.1200i	0.0579535	+	0.706019i
$589$	−3.18648	−	1.03535i	−0.131297	−	0.0426609i
$590$	5.69543	−	7.24398i	0.234477	−	0.298230i
$591$	1.41879	+	0.149121i	0.0583613	+	0.00613402i
$592$	−0.399697	−	7.62667i	−0.0164274	−	0.313454i
$593$	−0.252237	−	0.941362i	−0.0103581	−	0.0386571i	0.960553	−	0.278096i	$-0.0897033\pi$
$593$	−0.252237	−	0.941362i	−0.0103581	−	0.0386571i	−0.970911	+	0.239439i	$0.923037\pi$
$594$	0.0102709	+	0.177547i	0.000421419	+	0.00728484i
$595$	−11.4942	−	9.75790i	−0.471218	−	0.400035i
$596$	−2.00575	−	6.17307i	−0.0821589	−	0.252859i
$597$	−22.6036	+	58.8844i	−0.925105	+	2.40998i
$598$	−1.98980	+	0.763813i	−0.0813690	+	0.0312346i
$599$	−3.29100	−	15.4829i	−0.134466	−	0.632615i	−0.992826	−	0.119567i	$-0.961850\pi$
$599$	−3.29100	−	15.4829i	−0.134466	−	0.632615i	0.858360	−	0.513048i	$-0.171484\pi$
$600$	8.46904	+	8.87815i	0.345747	+	0.362449i
$601$	2.49263	+	3.43081i	0.101677	+	0.139946i	0.856824	−	0.515610i	$-0.172435\pi$
$601$	2.49263	+	3.43081i	0.101677	+	0.139946i	−0.755147	+	0.655555i	$0.772435\pi$
$602$	8.75994	+	16.5822i	0.357029	+	0.675841i
$603$	14.3599	−	28.1828i	0.584779	−	1.14769i
$604$	11.9386	+	6.89275i	0.485775	+	0.280462i
$605$	8.18875	+	23.1936i	0.332920	+	0.942955i
$606$	−12.7342	−	22.0563i	−0.517292	−	0.895976i
$607$	−1.52716	−	2.35162i	−0.0619855	−	0.0954493i	0.806319	−	0.591481i	$-0.201457\pi$
$607$	−1.52716	−	2.35162i	−0.0619855	−	0.0954493i	−0.868304	+	0.496032i	$0.834790\pi$
$608$	−0.834493	+	0.132171i	−0.0338432	+	0.00536023i
$609$	33.5846	−	15.5512i	1.36092	−	0.630167i
$610$	−9.75947	−	18.4913i	−0.395149	−	0.748691i
$611$	2.43912	+	2.70892i	0.0986762	+	0.109591i
$612$	2.75995	+	7.18990i	0.111564	+	0.290635i
$613$	32.8451	−	26.5974i	1.32660	−	1.07426i	0.335374	−	0.942085i	$-0.391137\pi$
$613$	32.8451	−	26.5974i	1.32660	−	1.07426i	0.991226	−	0.132175i	$-0.0421960\pi$
$614$	30.9675	+	6.58235i	1.24975	+	0.265642i
$615$	42.0110	−	43.2378i	1.69405	−	1.74352i
$616$	1.19741	−	8.69288i	0.0482450	−	0.350246i
$617$	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	$0.114107\pi$
$618$	−7.76188	−	11.9522i	−0.312229	−	0.480790i
$619$	3.42407	−	32.5778i	0.137625	−	1.30941i	−0.679809	−	0.733390i	$-0.737937\pi$
$619$	3.42407	−	32.5778i	0.137625	−	1.30941i	0.817433	−	0.576023i	$-0.195396\pi$
$620$	−3.48968	+	8.15166i	−0.140149	+	0.327379i
$621$	0.0754825	−	0.0679647i	0.00302901	−	0.00272733i
$622$	5.62887	−	2.86805i	0.225697	−	0.114998i
$623$	−4.19665	+	0.728381i	−0.168135	+	0.0291820i
$624$	−1.62297	+	2.23383i	−0.0649710	+	0.0894248i
$625$	−24.7122	−	3.78237i	−0.988489	−	0.151295i
$626$	16.8200	−	9.71105i	0.672264	−	0.388132i
$627$	6.83478	−	0.755871i	0.272955	−	0.0301866i
$628$	−4.95830	−	18.5046i	−0.197858	−	0.738415i
$629$	6.01466	+	18.5112i	0.239820	+	0.738091i
$630$	4.22523	+	17.3710i	0.168337	+	0.692079i
$631$	−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	$0.399136\pi$
$632$	5.68576	+	0.297978i	0.226167	+	0.0118529i
$633$	−25.4811	+	39.2374i	−1.01278	+	1.55955i
$634$	−12.1467	+	27.2820i	−0.482409	+	1.08351i
$635$	−6.16828	−	2.26649i	−0.244781	−	0.0899429i
$636$	16.0087	−	5.20154i	0.634786	−	0.206254i
$637$	4.77380	−	6.26482i	0.189145	−	0.248221i
$638$	−18.4715	+	4.03109i	−0.731295	+	0.159592i
$639$	−26.3616	−	15.2199i	−1.04285	−	0.602088i
$640$	0.149147	+	2.23109i	0.00589557	+	0.0881915i
$641$	1.14270	−	10.8721i	0.0451340	−	0.429421i	−0.948501	−	0.316774i	$-0.897400\pi$
$641$	1.14270	−	10.8721i	0.0451340	−	0.429421i	0.993635	−	0.112647i	$-0.0359330\pi$
$642$	11.9291	−	14.7312i	0.470803	−	0.581393i
$643$	3.66250	+	7.18807i	0.144435	+	0.283470i	0.951879	−	0.306475i	$-0.0991496\pi$
$643$	3.66250	+	7.18807i	0.144435	+	0.283470i	−0.807444	+	0.589945i	$0.799150\pi$
$644$	−4.30272	+	2.56965i	−0.169551	+	0.101258i
$645$	23.3122	+	31.1343i	0.917917	+	1.22591i
$646$	1.96712	−	0.875819i	0.0773954	−	0.0344586i
$647$	−37.1208	+	1.94542i	−1.45937	+	0.0764822i	−0.765414	−	0.643538i	$-0.777466\pi$
$647$	−37.1208	+	1.94542i	−1.45937	+	0.0764822i	−0.693953	+	0.720020i	$0.744133\pi$
$648$	−2.31228	+	8.62955i	−0.0908350	+	0.339001i
$649$	−13.4877	+	2.21131i	−0.529440	+	0.0868016i
$650$	−0.161898	−	5.62365i	−0.00635015	−	0.220578i
$651$	−20.6035	+	15.4393i	−0.807514	+	0.605116i
$652$	17.4664	−	2.76641i	0.684038	−	0.108341i
$653$	7.86988	−	9.71850i	0.307972	−	0.380314i	−0.599536	−	0.800348i	$-0.704648\pi$
$653$	7.86988	−	9.71850i	0.307972	−	0.380314i	0.907509	+	0.420033i	$0.137982\pi$
$654$	13.1715	−	2.79968i	0.515045	−	0.109476i
$655$	5.56933	−	1.26783i	0.217612	−	0.0495381i
$656$	10.9265	−	1.14842i	0.426609	−	0.0448385i
$657$	5.22282	+	32.9756i	0.203761	+	1.28650i
$658$	6.74004	+	5.29508i	0.262754	+	0.206424i
$659$			24.8147i			0.966643i	0.875443	+	0.483321i	$0.160570\pi$
$659$			24.8147i			0.966643i	−0.875443	+	0.483321i	$0.839430\pi$
$660$	−0.360586	−	18.1954i	−0.0140358	−	0.708254i
$661$	−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	$0.357077\pi$
$662$	0.980856	+	18.7158i	0.0381220	+	0.727412i
$663$	2.52186	−	6.56966i	0.0979408	−	0.255144i
$664$	11.5177	−	8.36811i	0.446974	−	0.324746i
$665$	4.78838	−	1.43392i	0.185685	−	0.0556051i
$666$	7.13158	−	21.9488i	0.276343	−	0.850497i
$667$	8.39155	+	6.79534i	0.324922	+	0.263117i
$668$	−12.2034	−	15.0700i	−0.472166	−	0.583076i
$669$	14.6327	+	13.1754i	0.565733	+	0.509389i
$670$	−11.4098	+	20.4360i	−0.440799	+	0.789510i
$671$	−7.86406	+	29.9991i	−0.303589	+	1.15810i
$672$	−2.86178	+	5.82779i	−0.110396	+	0.224812i
$673$	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	$-0.0224404\pi$
$674$	9.53571	+	21.4176i	0.367302	+	0.824973i
$675$	0.103245	+	0.247433i	0.00397390	+	0.00952371i
$676$	−11.4775	+	2.43962i	−0.441443	+	0.0938316i
$677$	1.78091	−	33.9817i	0.0684459	−	1.30602i	−0.721314	−	0.692608i	$-0.756461\pi$
$677$	1.78091	−	33.9817i	0.0684459	−	1.30602i	0.789760	−	0.613416i	$-0.210205\pi$
$678$	5.53464	−	34.9444i	0.212557	−	1.34203i
$679$	−33.5144	+	7.64276i	−1.28616	+	0.293302i
$680$	−1.83883	−	5.39398i	−0.0705161	−	0.206850i
$681$	−26.9448	+	46.6698i	−1.03253	+	1.78839i
$682$	11.9859	−	5.41458i	0.458965	−	0.207335i
$683$	−1.37596	+	5.13514i	−0.0526496	+	0.196491i	−0.987241	−	0.159231i	$-0.949098\pi$
$683$	−1.37596	+	5.13514i	−0.0526496	+	0.196491i	0.934592	+	0.355722i	$0.115765\pi$
$684$	−2.49736	−	0.530829i	−0.0954888	−	0.0202968i
$685$	−1.22787	−	7.09051i	−0.0469144	−	0.270915i
$686$	8.54055	−	16.4335i	0.326080	−	0.627433i
$687$	15.8380	+	31.0839i	0.604258	+	1.18592i
$688$	−0.370972	+	7.07857i	−0.0141432	+	0.269868i
$689$	−7.05087	−	3.13925i	−0.268617	−	0.119596i
$690$	−7.98264	+	6.65668i	−0.303894	+	0.253415i
$691$	−10.1657	+	47.8258i	−0.386721	+	1.81938i	0.166133	+	0.986103i	$0.446872\pi$
$691$	−10.1657	+	47.8258i	−0.386721	+	1.81938i	−0.552855	+	0.833278i	$0.686462\pi$
$692$	−5.47519	−	5.47519i	−0.208135	−	0.208135i
$693$	12.7919	−	23.2271i	0.485923	−	0.882326i
$694$			0.681066i			0.0258529i
$695$	0.471934	−	2.38880i	0.0179015	−	0.0906124i
$696$	13.9120	+	1.46221i	0.527332	+	0.0554248i
$697$	−26.1407	+	10.0345i	−0.990151	+	0.380083i
$698$	30.7180	+	1.60986i	1.16269	+	0.0609342i
$699$	−3.31045	+	10.1885i	−0.125213	+	0.385365i
$700$	−2.63633	−	12.9634i	−0.0996439	−	0.489970i
$701$	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	$0.613553\pi$
$702$	−0.0506013	+	0.0328609i	−0.00190982	+	0.00124025i
$703$	−6.23271	−	1.67005i	−0.235071	−	0.0629872i
$704$	2.07321	−	2.58879i	0.0781369	−	0.0975685i
$705$	15.5211	+	8.66576i	0.584560	+	0.326371i
$706$	−21.2631	+	6.90881i	−0.800248	+	0.260016i
$707$	−1.03192	+	27.4397i	−0.0388094	+	1.03198i
$708$	9.98820	+	1.58198i	0.375380	+	0.0594543i
$709$	17.2477	−	15.5299i	0.647750	−	0.583236i	−0.278366	−	0.960475i	$-0.589793\pi$
$709$	17.2477	−	15.5299i	0.647750	−	0.583236i	0.926116	+	0.377239i	$0.123126\pi$
$710$	19.0651	+	11.9945i	0.715500	+	0.450147i
$711$	15.7176	+	6.99794i	0.589457	+	0.262443i
$712$	−1.50297	−	0.576936i	−0.0563262	−	0.0216216i
$713$	−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
$717$	38.4308	−	2.01407i	1.43522	−	0.0752169i
$718$	6.30737	−	5.10761i	0.235389	−	0.190614i
$719$	2.10985	+	20.0739i	0.0786841	+	0.748630i	0.960734	+	0.277473i	$0.0894968\pi$
$719$	2.10985	+	20.0739i	0.0786841	+	0.748630i	−0.882049	+	0.471157i	$0.843837\pi$
$720$	−1.99536	+	6.45573i	−0.0743626	+	0.240591i
$721$	0.226948	+	15.3637i	0.00845200	+	0.572173i
$722$	2.86058	−	18.0610i	0.106460	−	0.672162i
$723$	39.3956	+	15.1225i	1.46514	+	0.562413i
$724$	6.70085	−	7.44205i	0.249035	−	0.276581i
$725$	−24.2634	+	14.9556i	−0.901119	+	0.555435i
$726$	−17.8434	+	20.2548i	−0.662232	+	0.751725i
$727$	34.3242	+	34.3242i	1.27301	+	1.27301i	0.944498	+	0.328517i	$0.106549\pi$
$727$	34.3242	+	34.3242i	1.27301	+	1.27301i	0.328517	+	0.944498i	$0.393451\pi$
$728$	2.76320	−	1.10779i	0.102411	−	0.0410574i
$729$	−16.1005	+	22.1605i	−0.596316	+	0.820759i
$730$	−2.93566	−	24.5299i	−0.108654	−	0.907893i
$731$	−3.75594	−	17.6703i	−0.138918	−	0.653559i
$732$	12.4973	−	19.2442i	0.461914	−	0.711285i
$733$	3.31858	+	2.68733i	0.122574	+	0.0992589i	0.688648	−	0.725096i	$-0.258205\pi$
$733$	3.31858	+	2.68733i	0.122574	+	0.0992589i	−0.566073	+	0.824355i	$0.691538\pi$
$734$	2.79028	+	2.02725i	0.102991	+	0.0748273i
$735$	12.1769	−	36.4291i	0.449152	−	1.34371i
$736$	−1.89422			−0.0698218
$737$	32.9580	−	10.9067i	1.21402	−	0.401754i
$738$	32.0690	+	8.59285i	1.18047	+	0.316307i
$739$	−12.7409	−	11.4720i	−0.468683	−	0.422004i	0.400650	−	0.916231i	$-0.368784\pi$
$739$	−12.7409	−	11.4720i	−0.468683	−	0.422004i	−0.869333	+	0.494227i	$0.835451\pi$
$740$	−5.88985	+	16.0293i	−0.216515	+	0.589249i
$741$	1.37124	+	1.88735i	0.0503739	+	0.0693337i
$742$	−17.5973	−	4.43767i	−0.646016	−	0.162912i
$743$	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	$0.192357\pi$
$744$	−9.67791	+	1.01719i	−0.354809	+	0.0372920i
$745$	−1.30924	+	14.4546i	−0.0479667	+	0.529575i
$746$	13.8748	−	15.4096i	0.507993	−	0.564184i
$747$	41.5552	−	11.1347i	1.52043	−	0.407397i
$748$	−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
$751$	−5.38765	+	2.39874i	−0.196598	+	0.0875311i	−0.502674	−	0.864476i	$-0.667650\pi$
$751$	−5.38765	+	2.39874i	−0.196598	+	0.0875311i	0.306076	+	0.952007i	$0.400984\pi$
$752$	1.16098	+	3.02445i	0.0423365	+	0.110290i
$753$	4.60545	+	2.99081i	0.167832	+	0.108991i
$754$	−4.29189	−	4.76662i	−0.156301	−	0.173590i
$755$	−18.4757	−	24.6749i	−0.672398	−	0.898012i
$756$	−0.104017	+	0.0964766i	−0.00378305	+	0.00350882i
$757$	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	$0.365399\pi$
$758$	10.8264	−	2.90093i	0.393234	−	0.105367i
$759$	15.3997	+	0.723324i	0.558975	+	0.0262550i
$760$	1.83172	+	0.462662i	0.0664433	+	0.0167825i
$761$	1.24314	−	5.84853i	0.0450639	−	0.212009i	−0.949855	−	0.312692i	$-0.898769\pi$
$761$	1.24314	−	5.84853i	0.0450639	−	0.212009i	0.994919	+	0.100683i	$0.0321026\pi$
$762$	−1.12818	−	7.12303i	−0.0408695	−	0.258040i
$763$	−13.6293	−	5.00210i	−0.493414	−	0.181088i
$764$	4.16604	+	1.35363i	0.150722	+	0.0489726i
$765$	0.653712	−	17.2085i	0.0236350	−	0.622175i
$766$	−11.0571	+	24.8345i	−0.399508	+	0.897309i
$767$	−2.91811	−	3.60357i	−0.105367	−	0.130117i
$768$	−2.05805	+	1.33651i	−0.0742636	+	0.0482273i
$769$	−36.3829			−1.31200			−0.656001	−	0.754760i	$-0.727753\pi$
$769$	−36.3829			−1.31200			−0.656001	+	0.754760i	$0.727753\pi$
$770$	−10.1112	+	16.8156i	−0.364381	+	0.605992i
$771$	2.35365			0.0847648
$772$	6.82388	−	4.43148i	0.245597	−	0.159493i
$773$	−15.3670	−	18.9766i	−0.552711	−	0.682541i	0.421849	−	0.906666i	$-0.361381\pi$
$773$	−15.3670	−	18.9766i	−0.552711	−	0.682541i	−0.974561	+	0.224124i	$0.928048\pi$
$774$	−8.71219	+	19.5679i	−0.313153	+	0.703354i
$775$	14.3470	−	13.6858i	0.515358	−	0.491610i
$776$	−12.3565	−	4.01488i	−0.443574	−	0.144126i
$777$	−38.0692	+	31.7702i	−1.36572	+	1.13975i
$778$	5.86953	+	37.0587i	0.210433	+	1.32862i
$779$	1.92997	−	9.07978i	0.0691482	−	0.325317i
$780$	5.30200	−	3.16370i	0.189842	−	0.113279i
$781$	−8.82182	−	32.2233i	−0.315669	−	1.15304i
$782$	4.66307	−	1.24947i	0.166751	−	0.0446808i
$783$	0.272353	+	0.138771i	0.00973312	+	0.00495927i
$784$	5.95615	−	3.67753i	0.212720	−	0.131340i
$785$	−6.09169	+	42.4019i	−0.217422	+	1.51339i
$786$	4.19435	+	4.65830i	0.149608	+	0.166156i
$787$	36.4777	+	23.6889i	1.30029	+	0.844418i	0.994196	−	0.107583i	$-0.0343113\pi$
$787$	36.4777	+	23.6889i	1.30029	+	0.844418i	0.306094	+	0.952001i	$0.400978\pi$
$788$	−0.208338	−	0.542739i	−0.00742173	−	0.0193343i
$789$	−41.0736	+	18.2871i	−1.46226	+	0.651039i
$790$	−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
$793$	−10.1628	+	2.72312i	−0.360893	+	0.0967009i
$794$	−13.0102	+	14.4493i	−0.461715	+	0.512786i
$795$	−37.4852	−	3.39526i	−1.32946	−	0.120417i
$796$	25.5622	−	2.68670i	0.906028	−	0.0952274i
$797$	−13.7945	+	7.02866i	−0.488627	+	0.248968i	−0.680904	−	0.732373i	$-0.738413\pi$
$797$	−13.7945	+	7.02866i	−0.488627	+	0.248968i	0.192277	+	0.981341i	$0.438413\pi$
$798$	3.93571	+	3.82113i	0.139323	+	0.135266i
$799$	−4.85301	−	6.67960i	−0.171687	−	0.236307i
$800$	1.65677	−	4.71753i	0.0585757	−	0.166790i
$801$	−3.61531	−	3.25524i	−0.127741	−	0.115018i
$802$	−24.2226	−	6.49043i	−0.855330	−	0.229185i
$803$	−21.3773	+	29.7615i	−0.754389	+	1.05026i
$804$	−25.6860			−0.905874
$805$	11.1061	−	1.49584i	0.391437	−	0.0527214i
$806$	3.60984	+	2.62270i	0.127151	+	0.0923807i
$807$	−53.4895	−	43.3150i	−1.88292	−	1.52476i
$808$	−5.65257	+	8.70419i	−0.198857	+	0.306212i
$809$	8.66605	+	40.7706i	0.304682	+	1.43342i	0.818000	+	0.575218i	$0.195083\pi$
$809$	8.66605	+	40.7706i	0.304682	+	1.43342i	−0.513318	+	0.858199i	$0.671584\pi$
$810$	12.3472	−	15.7043i	0.433837	−	0.551793i
$811$	−11.7862	+	16.2224i	−0.413871	+	0.569644i	−0.964157	−	0.265332i	$-0.914518\pi$
$811$	−11.7862	+	16.2224i	−0.413871	+	0.569644i	0.550287	+	0.834976i	$0.314518\pi$
$812$	−11.8598	−	9.31725i	−0.416198	−	0.326971i
$813$	−5.72290	−	5.72290i	−0.200711	−	0.200711i
$814$	22.5061	−	11.6216i	0.788837	−	0.407337i
$815$	−38.3389	−	9.68378i	−1.34295	−	0.339208i
$816$	4.18479	−	4.64768i	0.146497	−	0.162702i
$817$	5.59108	+	2.14621i	0.195607	+	0.0750866i
$818$	3.00942	−	19.0007i	0.105222	−	0.664344i
$819$	8.99503	−	0.132872i	0.314312	−	0.00464294i
$820$	−23.4715	−	7.25463i	−0.819660	−	0.253343i
$821$	−0.0391852	−	0.372822i	−0.00136757	−	0.0130116i	0.993817	−	0.111032i	$-0.0354156\pi$
$821$	−0.0391852	−	0.372822i	−0.00136757	−	0.0130116i	−0.995184	+	0.0980204i	$0.968749\pi$
$822$	6.13729	−	4.96988i	0.214062	−	0.173344i
$823$	22.9467	−	1.20259i	0.799872	−	0.0419195i	0.351980	−	0.936007i	$-0.385508\pi$
$823$	22.9467	−	1.20259i	0.799872	−	0.0419195i	0.447891	+	0.894088i	$0.352175\pi$
$824$	−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	$0.652191\pi$
$828$	−5.34386	−	2.05132i	−0.185712	−	0.0712881i
$829$	47.4148	+	21.1104i	1.64679	+	0.733196i	0.999576	−	0.0291166i	$-0.00926941\pi$
$829$	47.4148	+	21.1104i	1.64679	+	0.733196i	0.647209	+	0.762313i	$0.275936\pi$
$830$	−31.0401	+	7.06609i	−1.07742	+	0.245268i
$831$	2.50861	−	2.25877i	0.0870228	−	0.0783557i
$832$	1.11134	+	0.176019i	0.0385289	+	0.00610237i
$833$	−12.2367	+	12.9819i	−0.423977	+	0.449797i
$834$	2.54144	−	0.825765i	0.0880030	−	0.0285939i
$835$	11.8241	+	41.7173i	0.409190	+	1.44369i
$836$	−1.53891	−	2.34181i	−0.0532244	−	0.0809932i
$837$	−0.205394	−	0.0550352i	−0.00709947	−	0.00190230i
$838$	6.68728	−	4.34277i	0.231008	−	0.150018i
$839$	−0.706010	−	0.512947i	−0.0243742	−	0.0177089i	0.575531	−	0.817780i	$-0.304795\pi$
$839$	−0.706010	−	0.512947i	−0.0243742	−	0.0177089i	−0.599906	+	0.800071i	$0.704795\pi$
$840$	11.0112	−	9.46139i	0.379923	−	0.326449i
$841$	−1.08007	+	3.32412i	−0.0372439	+	0.114625i
$842$	−21.6335	−	1.13376i	−0.745539	−	0.0390721i
$843$	−55.7182	+	21.3882i	−1.91904	+	0.736649i
$844$	18.9609	+	1.99287i	0.652661	+	0.0685974i
$845$	25.7404	+	5.08529i	0.885495	+	0.174939i
$846$			9.78966i			0.336575i
$847$	27.9094	−	8.25014i	0.958979	−	0.283478i
$848$	−4.85031	−	4.85031i	−0.166560	−	0.166560i
$849$	8.62816	−	40.5923i	0.296118	−	1.39312i
$850$	−0.966752	+	12.7062i	−0.0331593	+	0.435818i
$851$	−13.2157	−	5.88402i	−0.453029	−	0.201702i
$852$	−1.29370	+	24.6852i	−0.0443213	+	0.845702i
$853$	4.63228	+	9.09136i	0.158606	+	0.311282i	0.956611	−	0.291369i	$-0.0941109\pi$
$853$	4.63228	+	9.09136i	0.158606	+	0.311282i	−0.798004	+	0.602652i	$0.794111\pi$
$854$	−22.4496	+	10.3952i	−0.768210	+	0.355717i
$855$	4.66650	+	3.28886i	0.159591	+	0.112477i
$856$	−7.55569	−	1.60601i	−0.258248	−	0.0548923i
$857$	12.4288	−	46.3848i	0.424558	−	1.58447i	−0.340328	−	0.940307i	$-0.610538\pi$
$857$	12.4288	−	46.3848i	0.424558	−	1.58447i	0.764886	−	0.644166i	$-0.222795\pi$
$858$	−8.96784	−	1.85539i	−0.306157	−	0.0633419i
$859$	2.22378	−	3.85169i	0.0758743	−	0.131418i	−0.825592	−	0.564268i	$-0.809159\pi$
$859$	2.22378	−	3.85169i	0.0758743	−	0.131418i	0.901466	+	0.432850i	$0.142492\pi$
$860$	6.99173	−	14.2244i	0.238416	−	0.485049i
$861$	−48.5079	−	52.2990i	−1.65315	−	1.78234i
$862$	4.37209	−	27.6043i	0.148914	−	0.940206i
$863$	1.78830	−	34.1228i	0.0608744	−	1.16155i	−0.781942	−	0.623352i	$-0.785771\pi$
$863$	1.78830	−	34.1228i	0.0608744	−	1.16155i	0.842816	−	0.538202i	$-0.180896\pi$
$864$	−0.0524502	+	0.0111486i	−0.00178439	+	0.000379284i
$865$	6.43676	+	16.0731i	0.218856	+	0.546502i
$866$	13.0412	+	29.2909i	0.443157	+	0.995347i
$867$	11.7030	−	22.9684i	0.397455	−	0.780049i
$868$	9.41762	+	4.62460i	0.319655	+	0.156969i
$869$	6.86273	+	17.5922i	0.232802	+	0.596775i
$870$	−27.3111	−	15.2483i	−0.925932	−	0.516966i
$871$	8.75250	+	7.88078i	0.296567	+	0.267030i
$872$	−3.45331	−	4.26449i	−0.116944	−	0.144414i
$873$	−30.5117	−	24.7079i	−1.03266	−	0.836235i
$874$	−0.494556	+	1.52209i	−0.0167286	+	0.0514853i
$875$	−5.98850	+	28.9679i	−0.202448	+	0.979293i
$876$	21.9342	−	15.9361i	0.741088	−	0.538432i
$877$	−18.9025	+	49.2426i	−0.638291	+	1.66281i	0.105522	+	0.994417i	$0.466349\pi$
$877$	−18.9025	+	49.2426i	−0.638291	+	1.66281i	−0.743813	+	0.668388i	$0.766985\pi$
$878$	−0.451988	−	8.62445i	−0.0152539	−	0.291061i
$879$	64.3415	−	37.1476i	2.17018	−	1.25296i
$880$	−6.53987	+	3.49715i	−0.220459	+	0.117889i
$881$			12.6086i			0.424796i	0.977183	+	0.212398i	$0.0681273\pi$
$881$			12.6086i			0.424796i	−0.977183	+	0.212398i	$0.931873\pi$
$882$	20.7857	−	3.92471i	0.699890	−	0.132152i
$883$	−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	$-0.129167\pi$
$884$	−2.85194	+	0.299751i	−0.0959211	+	0.0100817i
$885$	−19.1399	−	12.0416i	−0.643380	−	0.404773i
$886$	40.3607	−	8.57894i	1.35594	−	0.288215i
$887$	7.78733	−	9.61655i	0.261473	−	0.322892i	−0.629455	−	0.777037i	$-0.716722\pi$
$887$	7.78733	−	9.61655i	0.261473	−	0.322892i	0.890928	+	0.454145i	$0.150055\pi$
$888$	−18.5104	+	2.93176i	−0.621168	+	0.0983833i
$889$	−3.05732	+	7.14921i	−0.102539	+	0.239777i
$890$	2.58184	+	2.50858i	0.0865435	+	0.0840879i
$891$	−29.2402	+	4.79393i	−0.979585	+	0.160603i
$892$	2.07674	−	7.75051i	0.0695345	−	0.259506i
$893$	2.73339	−	0.143251i	0.0914694	−	0.00479371i
$894$	−14.5509	+	6.47849i	−0.486655	+	0.216673i
$895$	−25.6446	+	19.2017i	−0.857203	+	0.641842i
$896$	2.64546	−	0.0390782i	0.0883787	−	0.00130551i
$897$	2.37449	+	4.66019i	0.0792818	+	0.155599i
$898$	17.8769	−	22.0761i	0.596558	−	0.736688i
$899$	2.36291	−	22.4815i	0.0788073	−	0.749801i
$900$	9.78276	−	11.5147i	0.326092	−	0.383822i
$901$	15.1396	+	8.74083i	0.504372	+	0.291199i
$902$	18.3903	+	31.4577i	0.612331	+	1.04743i
$903$	38.2220	−	25.6321i	1.27195	−	0.852984i
$904$	−13.7119	+	4.45527i	−0.456052	+	0.148180i
$905$	−20.3234	+	9.40130i	−0.675574	+	0.312510i
$906$	13.7594	−	30.9042i	0.457127	−	1.02672i
$907$	6.99029	−	10.7641i	0.232109	−	0.357416i	−0.703355	−	0.710839i	$-0.748316\pi$
$907$	6.99029	−	10.7641i	0.232109	−	0.357416i	0.935464	+	0.353423i	$0.114982\pi$
$908$	21.9303	+	1.14932i	0.727782	+	0.0381414i
$909$	−25.3728	+	18.4344i	−0.841562	+	0.611430i
$910$	−6.65495	−	0.154414i	−0.220610	−	0.00511879i
$911$	−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	$0.992349\pi$
$912$	0.536617	+	2.00268i	0.0177692	+	0.0663154i
$913$	41.0192	+	23.3867i	1.35754	+	0.773987i
$914$	20.7575	−	11.9843i	0.686597	−	0.396407i
$915$	−42.6247	+	28.5612i	−1.40913	+	0.944203i
$916$	8.35618	−	11.5013i	0.276096	−	0.380013i
$917$	−1.15571	−	6.65876i	−0.0381649	−	0.219892i
$918$	0.121765	−	0.0620422i	0.00401884	−	0.00204770i
$919$	−30.5388	+	27.4973i	−1.00738	+	0.907051i	−0.995677	−	0.0928802i	$-0.970393\pi$
$919$	−30.5388	+	27.4973i	−1.00738	+	0.907051i	−0.0117052	+	0.999931i	$0.503726\pi$
$920$	3.89380	+	1.66692i	0.128375	+	0.0549566i
$921$	8.12086	−	77.2648i	0.267591	−	2.54596i
$922$	13.9933	+	21.5479i	0.460846	+	0.709641i
$923$	8.01457	−	8.01457i	0.263803	−	0.263803i
$924$	−21.5222	−	0.692493i	−0.708027	−	0.0227813i
$925$	26.2132	−	27.7672i	0.861883	−	0.912979i
$926$	−4.79740	−	1.01972i	−0.157652	−	0.0335100i
$927$	−13.6386	+	11.0443i	−0.447949	+	0.362742i
$928$	−2.04286	−	5.32183i	−0.0670602	−	0.174698i
$929$	6.05430	+	6.72399i	0.198635	+	0.220607i	0.834231	−	0.551415i	$-0.185912\pi$
$929$	6.05430	+	6.72399i	0.198635	+	0.220607i	−0.635596	+	0.772022i	$0.719245\pi$
$930$	20.7893	+	6.42562i	0.681708	+	0.210704i
$931$	−1.39998	−	5.74618i	−0.0458825	−	0.188324i
$932$	4.31181	−	0.682924i	0.141238	−	0.0223699i
$933$	−8.44333	−	13.0016i	−0.276422	−	0.425653i
$934$	6.51133	+	11.2780i	0.213057	+	0.369026i
$935$	13.7927	−	12.9229i	0.451069	−	0.422624i
$936$	2.94464	+	1.70009i	0.0962484	+	0.0555691i
$937$	4.31375	−	8.46621i	0.140924	−	0.276579i	−0.809747	−	0.586779i	$-0.800396\pi$
$937$	4.31375	−	8.46621i	0.140924	−	0.276579i	0.950671	+	0.310200i	$0.100396\pi$
$938$	23.4461	+	14.7383i	0.765541	+	0.481224i
$939$	−28.0143	−	38.5584i	−0.914212	−	1.25831i
$940$	0.274985	−	7.23879i	0.00896903	−	0.236103i
$941$	1.70121	+	8.00356i	0.0554579	+	0.260909i	0.997138	−	0.0755999i	$-0.0240872\pi$
$941$	1.70121	+	8.00356i	0.0554579	+	0.260909i	−0.941680	+	0.336509i	$0.890754\pi$
$942$	−43.8888	+	16.8473i	−1.42997	+	0.548915i
$943$	7.45808	−	19.4290i	0.242869	−	0.632694i
$944$	−1.27346	−	3.91930i	−0.0414475	−	0.127562i
$945$	0.298719	−	0.106785i	0.00971732	−	0.00347372i
$946$	−21.9017	+	8.54387i	−0.712085	+	0.277785i
$947$	6.06216	+	22.6243i	0.196994	+	0.735191i	0.991742	+	0.128251i	$0.0409364\pi$
$947$	6.06216	+	22.6243i	0.196994	+	0.735191i	−0.794748	+	0.606940i	$0.792397\pi$
$948$	−0.731221	−	13.9525i	−0.0237490	−	0.453157i
$949$	−12.3635	−	1.29946i	−0.401336	−	0.0421821i
$950$	−3.35818	−	2.56297i	−0.108954	−	0.0831538i
$951$	69.6976	+	22.6461i	2.26010	+	0.734351i
$952$	−6.48666	+	1.84120i	−0.210234	+	0.0596737i
$953$	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	$0.228551\pi$
$954$	−8.43084	−	18.9360i	−0.272959	−	0.613075i
$955$	−7.37263	−	6.44868i	−0.238573	−	0.208674i
$956$	−7.84115	−	13.5813i	−0.253601	−	0.439250i
$957$	14.5760	+	44.0458i	0.471174	+	1.42380i
$958$	4.00887	−	4.00887i	0.129521	−	0.129521i
$959$	−8.45376	+	1.01498i	−0.272986	+	0.0327754i
$960$	5.40672	−	0.936285i	0.174501	−	0.0302185i
$961$	−1.59662	−	15.1908i	−0.0515039	−	0.490027i
$962$	7.20692	+	4.68023i	0.232360	+	0.150897i
$963$	−19.5765	−	12.7131i	−0.630843	−	0.409674i
$964$	−1.79748	−	17.1019i	−0.0578931	−	0.550816i
$965$	−17.9271	+	3.10444i	−0.577093	+	0.0999355i
$966$	7.37491	+	9.84166i	0.237284	+	0.316650i
$967$	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	$0.103867\pi$
$968$	10.6554	+	2.73157i	0.342479	+	0.0877961i
$969$	−2.64202	−	4.57611i	−0.0848739	−	0.147006i
$970$	21.8673	+	19.1269i	0.702117	+	0.614127i
$971$	−15.7009	−	35.2649i	−0.503867	−	1.13170i	−0.969134	−	0.246534i	$-0.920708\pi$
$971$	−15.7009	−	35.2649i	−0.503867	−	1.13170i	0.465267	−	0.885170i	$-0.345958\pi$
$972$	21.8124	+	3.45475i	0.699635	+	0.110811i
$973$	−2.79364	−	0.704498i	−0.0895599	−	0.0225852i
$974$	−12.0499	−	3.91524i	−0.386103	−	0.125452i
$975$	−13.6830	+	1.83762i	−0.438207	+	0.0588509i
$976$	−9.29945	−	0.977412i	−0.297668	−	0.0312862i
$977$	−1.07377	−	20.4888i	−0.0343530	−	0.655495i	−0.960491	−	0.278310i	$-0.910226\pi$
$977$	−1.07377	−	20.4888i	−0.0343530	−	0.655495i	0.926138	−	0.377184i	$-0.123108\pi$
$978$	−11.2317	−	41.9172i	−0.359150	−	1.34037i
$979$	−0.308364	−	5.33052i	−0.00985536	−	0.170364i
$980$	−15.4799	+	2.31821i	−0.494486	+	0.0740523i
$981$	−5.12413	−	15.7704i	−0.163601	−	0.503511i
$982$	1.54203	−	4.01714i	0.0492083	−	0.128192i
$983$	−17.3681	+	6.66701i	−0.553958	+	0.212645i	−0.619212	−	0.785224i	$-0.712548\pi$
$983$	−17.3681	+	6.66701i	−0.553958	+	0.212645i	0.0652536	+	0.997869i	$0.479214\pi$
$984$	−5.60547	−	26.3717i	−0.178696	−	0.840698i
$985$	−0.0493463	+	1.29901i	−0.00157230	+	0.0413898i
$986$	8.53938	+	11.7535i	0.271949	+	0.374306i
$987$	11.1938	−	17.8073i	0.356302	−	0.566813i
$988$	0.431596	−	0.847055i	0.0137309	−	0.0269484i
$989$	11.6279	+	6.71338i	0.369746	+	0.213473i
$990$	−22.2371	+	2.78369i	−0.706741	+	0.0884716i
$991$	−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	$-0.379772\pi$
$992$	2.15979	+	3.32578i	0.0685733	+	0.105594i
$993$	45.4245	−	7.19453i	1.44150	−	0.228312i
$994$	15.3450	−	21.7903i	0.486714	−	0.691146i
$995$	−54.9106	−	16.9719i	−1.74078	−	0.538046i
$996$	−23.3768	−	25.9625i	−0.740721	−	0.822654i
$997$	9.50351	+	24.7575i	0.300979	+	0.784078i	0.997766	+	0.0667999i	$0.0212789\pi$
$997$	9.50351	+	24.7575i	0.300979	+	0.784078i	−0.696787	+	0.717278i	$0.745388\pi$
$998$	4.77538	−	3.86702i	0.151162	−	0.122408i
$999$	−0.400569	−	0.0851436i	−0.0126734	−	0.00269382i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bv.a.313.21	✓	768	1.1	even	1	trivial
770.2.bv.a.383.45	yes	768	11.9	even	5	inner
770.2.bv.a.423.4	yes	768	7.3	odd	6	inner
770.2.bv.a.467.21	yes	768	5.2	odd	4	inner
770.2.bv.a.493.21	yes	768	77.31	odd	30	inner
770.2.bv.a.537.4	yes	768	55.42	odd	20	inner
770.2.bv.a.577.45	yes	768	35.17	even	12	inner
770.2.bv.a.647.21	yes	768	385.262	even	60	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)

\(f(q)\)	\(=\)	\(q+(-0.838671 + 0.544639i) q^{2} +(1.54432 + 1.90707i) q^{3} +(0.406737 - 0.913545i) q^{4} +(-1.64002 + 1.51998i) q^{5} +(-2.33384 - 0.758311i) q^{6} +(1.69521 + 2.03132i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-0.628278 + 2.95582i) q^{9} +O(q^{10})\)	\(q+(-0.838671 + 0.544639i) q^{2} +(1.54432 + 1.90707i) q^{3} +(0.406737 - 0.913545i) q^{4} +(-1.64002 + 1.51998i) q^{5} +(-2.33384 - 0.758311i) q^{6} +(1.69521 + 2.03132i) q^{7} +(0.156434 + 0.987688i) q^{8} +(-0.628278 + 2.95582i) q^{9} +(0.547597 - 2.16798i) q^{10} +(-2.77172 + 1.82143i) q^{11} +(2.37033 - 0.635128i) q^{12} +(-1.00256 - 0.510828i) q^{13} +(-2.52806 - 0.780327i) q^{14} +(-5.43142 - 0.780309i) q^{15} +(-0.669131 - 0.743145i) q^{16} +(2.13742 + 1.38806i) q^{17} +(-1.08293 - 2.82114i) q^{18} +(-0.771850 + 0.343650i) q^{19} +(0.721513 + 2.11646i) q^{20} +(-1.25593 + 6.36990i) q^{21} +(1.33254 - 3.03716i) q^{22} +(-1.82967 + 0.490260i) q^{23} +(-1.64201 + 1.82364i) q^{24} +(0.379330 - 4.98559i) q^{25} +(1.11903 - 0.117615i) q^{26} +(-0.0477775 + 0.0243438i) q^{27} +(2.54521 - 0.722443i) q^{28} +(-3.35064 - 4.61176i) q^{29} +(4.98016 - 2.30374i) q^{30} +(2.94697 + 2.65346i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-7.75401 - 2.47301i) q^{33} -2.54858 q^{34} +(-5.86774 - 0.754714i) q^{35} +(2.44473 + 1.77620i) q^{36} +(5.93517 + 4.80621i) q^{37} +(0.460163 - 0.708589i) q^{38} +(-0.574079 - 2.70083i) q^{39} +(-1.75782 - 1.38205i) q^{40} +(-6.45783 + 8.88844i) q^{41} +(-2.41599 - 6.02627i) q^{42} +(-5.01217 - 5.01217i) q^{43} +(0.536596 + 3.27293i) q^{44} +(-3.46239 - 5.80257i) q^{45} +(1.26748 - 1.40768i) q^{46} +(-3.02445 - 1.16098i) q^{47} +(0.383882 - 2.42373i) q^{48} +(-1.25251 + 6.88703i) q^{49} +(2.39721 + 4.38787i) q^{50} +(0.653729 + 6.21982i) q^{51} +(-0.874441 + 0.708108i) q^{52} +(6.84997 - 0.358992i) 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} +(5.32183 + 2.04286i) q^{58} +(3.76472 + 1.67616i) q^{59} +(-2.92201 + 4.64447i) q^{60} +(6.94891 - 6.25682i) q^{61} +(-3.91672 - 0.620347i) q^{62} +(-7.06927 + 3.73451i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(2.42066 - 0.686096i) q^{65} +(7.84995 - 2.14909i) q^{66} +(-10.1105 - 2.70911i) q^{67} +(2.13742 - 1.38806i) q^{68} +(-3.76056 - 2.73221i) q^{69} +(5.33215 - 2.56285i) q^{70} +(-3.11279 + 9.58018i) q^{71} +(-3.01771 - 0.158151i) q^{72} +(10.3146 - 3.95939i) q^{73} +(-7.59530 - 0.798298i) q^{74} +(10.0937 - 6.97593i) q^{75} +0.844895i q^{76} +(-8.39854 - 2.54253i) q^{77} +(1.95244 + 1.95244i) q^{78} +(1.18376 - 5.56914i) q^{79} +(2.22695 + 0.201708i) q^{80} +(8.16159 + 3.63377i) q^{81} +(0.575000 - 10.9717i) q^{82} +(-6.46332 - 12.6850i) q^{83} +(5.30836 + 3.73822i) q^{84} +(-5.61522 + 0.972392i) q^{85} +(6.93339 + 1.47374i) q^{86} +(3.62052 - 13.5120i) q^{87} +(-2.23259 - 2.45266i) q^{88} +(-0.804950 + 1.39421i) q^{89} +(6.06411 + 2.98069i) q^{90} +(-0.661892 - 2.90247i) q^{91} +(-0.296321 + 1.87090i) q^{92} +(-0.509293 + 9.71788i) q^{93} +(3.16883 - 0.673555i) q^{94} +(0.743509 - 1.73679i) q^{95} +(0.998110 + 2.24179i) q^{96} +(-5.89844 + 11.5763i) q^{97} +(-2.70051 - 6.45812i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more