LMFDB - Embedded newform 765.2.t.e.64.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [765,2,Mod(64,765)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("765.64"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(765, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 765 = 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	765.t (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.10855575463$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 188x^{8} + 572x^{6} + 776x^{4} + 464x^{2} + 100 $ x^12 + 24x^10 + 188x^8 + 572x^6 + 776x^4 + 464*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			64.1
Root			$1.38621i$ of defining polynomial
Character	$\chi$	$=$	765.64
Dual form			765.2.t.e.514.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.38621 q^{2} +3.69399 q^{4} +(0.518989 + 2.17501i) q^{5} +(-0.155559 - 0.155559i) q^{7} -4.04223 q^{8} +(-1.23842 - 5.19002i) q^{10} +(-0.371196 + 0.371196i) q^{11} +1.96713i q^{13} +(0.371196 + 0.371196i) q^{14} +2.25761 q^{16} +(3.46759 + 2.23065i) q^{17} +4.00000i q^{19} +(1.91714 + 8.03446i) q^{20} +(0.885751 - 0.885751i) q^{22} +(-0.263516 - 0.263516i) q^{23} +(-4.46130 + 2.25761i) q^{25} -4.69399i q^{26} +(-0.574634 - 0.574634i) q^{28} +(-4.95160 - 4.95160i) q^{29} +(2.06519 + 2.06519i) q^{31} +2.69733 q^{32} +(-8.27440 - 5.32280i) q^{34} +(0.257608 - 0.419075i) q^{35} +(4.04223 - 4.04223i) q^{37} -9.54484i q^{38} +(-2.09787 - 8.79187i) q^{40} +(-0.563613 + 0.563613i) q^{41} -2.49417 q^{43} +(-1.37120 + 1.37120i) q^{44} +(0.628804 + 0.628804i) q^{46} +6.73955i q^{47} -6.95160i q^{49} +(10.6456 - 5.38713i) q^{50} +7.26658i q^{52} -5.92169 q^{53} +(-1.00000 - 0.614707i) q^{55} +(0.628804 + 0.628804i) q^{56} +(11.8156 + 11.8156i) q^{58} +6.00000i q^{59} +(-4.00000 + 4.00000i) q^{61} +(-4.92798 - 4.92798i) q^{62} -10.9516 q^{64} +(-4.27853 + 1.02092i) q^{65} +11.5120i q^{67} +(12.8093 + 8.24001i) q^{68} +(-0.614707 + 1.00000i) q^{70} +(5.06519 + 5.06519i) q^{71} +(0.838149 - 0.838149i) q^{73} +(-9.64560 + 9.64560i) q^{74} +14.7760i q^{76} +0.115486 q^{77} +(-4.75919 + 4.75919i) q^{79} +(1.17167 + 4.91031i) q^{80} +(1.34490 - 1.34490i) q^{82} -6.11732 q^{83} +(-3.05204 + 8.69972i) q^{85} +5.95160 q^{86} +(1.50046 - 1.50046i) q^{88} -15.9852 q^{89} +(0.306005 - 0.306005i) q^{91} +(-0.973426 - 0.973426i) q^{92} -16.0820i q^{94} +(-8.70002 + 2.07596i) q^{95} +(6.51611 - 6.51611i) q^{97} +16.5880i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{4} - 4 q^{10} - 16 q^{11} + 16 q^{14} + 4 q^{16} + 32 q^{20} - 4 q^{29} + 4 q^{31} - 20 q^{35} + 24 q^{40} - 16 q^{41} - 28 q^{44} - 4 q^{46} + 40 q^{50} - 12 q^{55} - 4 q^{56} - 48 q^{61}+ \cdots + 36 q^{91}+O(q^{100}) $ 12 * q + 12 * q^4 - 4 * q^10 - 16 * q^11 + 16 * q^14 + 4 * q^16 + 32 * q^20 - 4 * q^29 + 4 * q^31 - 20 * q^35 + 24 * q^40 - 16 * q^41 - 28 * q^44 - 4 * q^46 + 40 * q^50 - 12 * q^55 - 4 * q^56 - 48 * q^61 - 76 * q^64 - 8 * q^65 + 40 * q^71 - 28 * q^74 - 4 * q^79 - 12 * q^80 - 52 * q^85 + 16 * q^86 + 16 * q^89 + 36 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/765\mathbb{Z}\right)^\times$.

$n$	$307$	$496$	$596$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.38621			−1.68730			−0.843652	−	0.536890i	$-0.819599\pi$
$2$	−2.38621			−1.68730			−0.843652	+	0.536890i	$0.819599\pi$
$3$		0			0
$3$		0			0
$4$	3.69399			1.84700
$5$	0.518989	+	2.17501i	0.232099	+	0.972692i
$5$	0.518989	+	2.17501i	0.232099	+	0.972692i
$6$		0			0
$7$	−0.155559	−	0.155559i	−0.0587957	−	0.0587957i	0.677098	−	0.735893i	$-0.263238\pi$
$7$	−0.155559	−	0.155559i	−0.0587957	−	0.0587957i	−0.735893	+	0.677098i	$0.763238\pi$
$8$	−4.04223			−1.42914
$9$		0			0
$10$	−1.23842	−	5.19002i	−0.391622	−	1.64123i
$11$	−0.371196	+	0.371196i	−0.111920	+	0.111920i	−0.760849	−	0.648929i	$-0.775217\pi$
$11$	−0.371196	+	0.371196i	−0.111920	+	0.111920i	0.648929	+	0.760849i	$0.275217\pi$
$12$		0			0
$13$			1.96713i			0.545585i	0.962073	+	0.272792i	$0.0879472\pi$
$13$			1.96713i			0.545585i	−0.962073	+	0.272792i	$0.912053\pi$
$14$	0.371196	+	0.371196i	0.0992063	+	0.0992063i
$15$		0			0
$16$	2.25761			0.564402
$17$	3.46759	+	2.23065i	0.841015	+	0.541012i
$17$	3.46759	+	2.23065i	0.841015	+	0.541012i
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	1.91714	+	8.03446i	0.428686	+	1.79656i
$21$		0			0
$22$	0.885751	−	0.885751i	0.188843	−	0.188843i
$23$	−0.263516	−	0.263516i	−0.0549469	−	0.0549469i	0.679099	−	0.734046i	$-0.262371\pi$
$23$	−0.263516	−	0.263516i	−0.0549469	−	0.0549469i	−0.734046	+	0.679099i	$0.762371\pi$
$24$		0			0
$25$	−4.46130	+	2.25761i	−0.892260	+	0.451522i
$26$		−	4.69399i		−	0.920568i
$27$		0			0
$28$	−0.574634	−	0.574634i	−0.108596	−	0.108596i
$29$	−4.95160	−	4.95160i	−0.919490	−	0.919490i	0.0775026	−	0.996992i	$-0.475305\pi$
$29$	−4.95160	−	4.95160i	−0.919490	−	0.919490i	−0.996992	+	0.0775026i	$0.975305\pi$
$30$		0			0
$31$	2.06519	+	2.06519i	0.370919	+	0.370919i	0.867812	−	0.496893i	$-0.165526\pi$
$31$	2.06519	+	2.06519i	0.370919	+	0.370919i	−0.496893	+	0.867812i	$0.665526\pi$
$32$	2.69733			0.476825
$33$		0			0
$34$	−8.27440	−	5.32280i	−1.41905	−	0.912852i
$35$	0.257608	−	0.419075i	0.0435437	−	0.0708366i
$36$		0			0
$37$	4.04223	−	4.04223i	0.664538	−	0.664538i	−0.291908	−	0.956446i	$-0.594290\pi$
$37$	4.04223	−	4.04223i	0.664538	−	0.664538i	0.956446	+	0.291908i	$0.0942902\pi$
$38$		−	9.54484i		−	1.54838i
$39$		0			0
$40$	−2.09787	−	8.79187i	−0.331702	−	1.39012i
$41$	−0.563613	+	0.563613i	−0.0880216	+	0.0880216i	−0.749747	−	0.661725i	$-0.769825\pi$
$41$	−0.563613	+	0.563613i	−0.0880216	+	0.0880216i	0.661725	+	0.749747i	$0.269825\pi$
$42$		0			0
$43$	−2.49417			−0.380357			−0.190178	−	0.981750i	$-0.560907\pi$
$43$	−2.49417			−0.380357			−0.190178	+	0.981750i	$0.560907\pi$
$44$	−1.37120	+	1.37120i	−0.206716	+	0.206716i
$45$		0			0
$46$	0.628804	+	0.628804i	0.0927121	+	0.0927121i
$47$			6.73955i			0.983065i	0.870859	+	0.491532i	$0.163563\pi$
$47$			6.73955i			0.983065i	−0.870859	+	0.491532i	$0.836437\pi$
$48$		0			0
$49$		−	6.95160i		−	0.993086i
$50$	10.6456	−	5.38713i	1.50551	−	0.761855i
$51$		0			0
$52$			7.26658i			1.00769i
$53$	−5.92169			−0.813406			−0.406703	−	0.913560i	$-0.633322\pi$
$53$	−5.92169			−0.813406			−0.406703	+	0.913560i	$0.633322\pi$
$54$		0			0
$55$	−1.00000	−	0.614707i	−0.134840	−	0.0828870i
$56$	0.628804	+	0.628804i	0.0840275	+	0.0840275i
$57$		0			0
$58$	11.8156	+	11.8156i	1.55146	+	1.55146i
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		0			0
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	−0.915184	−	0.403036i	$-0.867955\pi$
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	0.403036	+	0.915184i	$0.367955\pi$
$62$	−4.92798	−	4.92798i	−0.625854	−	0.625854i
$63$		0			0
$64$	−10.9516			−1.36895
$65$	−4.27853	+	1.02092i	−0.530686	+	0.126630i
$66$		0			0
$67$			11.5120i			1.40641i	0.710987	+	0.703206i	$0.248249\pi$
$67$			11.5120i			1.40641i	−0.710987	+	0.703206i	$0.751751\pi$
$68$	12.8093	+	8.24001i	1.55335	+	0.999248i
$69$		0			0
$70$	−0.614707	+	1.00000i	−0.0734715	+	0.119523i
$71$	5.06519	+	5.06519i	0.601128	+	0.601128i	0.940612	−	0.339484i	$-0.110253\pi$
$71$	5.06519	+	5.06519i	0.601128	+	0.601128i	−0.339484	+	0.940612i	$0.610253\pi$
$72$		0			0
$73$	0.838149	−	0.838149i	0.0980980	−	0.0980980i	−0.656355	−	0.754453i	$-0.727902\pi$
$73$	0.838149	−	0.838149i	0.0980980	−	0.0980980i	0.754453	+	0.656355i	$0.227902\pi$
$74$	−9.64560	+	9.64560i	−1.12128	+	1.12128i
$75$		0			0
$76$			14.7760i			1.69492i
$77$	0.115486			0.0131608
$78$		0			0
$79$	−4.75919	+	4.75919i	−0.535450	+	0.535450i	−0.922189	−	0.386739i	$-0.873601\pi$
$79$	−4.75919	+	4.75919i	−0.535450	+	0.535450i	0.386739	+	0.922189i	$0.373601\pi$
$80$	1.17167	+	4.91031i	0.130997	+	0.548989i
$81$		0			0
$82$	1.34490	−	1.34490i	0.148519	−	0.148519i
$83$	−6.11732			−0.671463			−0.335731	−	0.941958i	$-0.608983\pi$
$83$	−6.11732			−0.671463			−0.335731	+	0.941958i	$0.608983\pi$
$84$		0			0
$85$	−3.05204	+	8.69972i	−0.331040	+	0.943617i
$86$	5.95160			0.641778
$87$		0			0
$88$	1.50046	−	1.50046i	0.159949	−	0.159949i
$89$	−15.9852			−1.69443			−0.847213	−	0.531253i	$-0.821721\pi$
$89$	−15.9852			−1.69443			−0.847213	+	0.531253i	$0.821721\pi$
$90$		0			0
$91$	0.306005	−	0.306005i	0.0320781	−	0.0320781i
$92$	−0.973426	−	0.973426i	−0.101487	−	0.101487i
$93$		0			0
$94$		−	16.0820i		−	1.65873i
$95$	−8.70002	+	2.07596i	−0.892604	+	0.212989i
$96$		0			0
$97$	6.51611	−	6.51611i	0.661611	−	0.661611i	−0.294149	−	0.955760i	$-0.595036\pi$
$97$	6.51611	−	6.51611i	0.661611	−	0.661611i	0.955760	+	0.294149i	$0.0950361\pi$
$98$			16.5880i			1.67564i
$99$		0			0
$100$	−16.4800	+	8.33959i	−1.64800	+	0.833959i
$101$	7.20921			0.717343			0.358672	−	0.933464i	$-0.383230\pi$
$101$	7.20921			0.717343			0.358672	+	0.933464i	$0.383230\pi$
$102$		0			0
$103$			9.52456i			0.938482i	0.883070	+	0.469241i	$0.155472\pi$
$103$			9.52456i			0.938482i	−0.883070	+	0.469241i	$0.844528\pi$
$104$		−	7.95160i		−	0.779719i
$105$		0			0
$106$	14.1304			1.37246
$107$	−7.62530	+	7.62530i	−0.737166	+	0.737166i	−0.972029	−	0.234863i	$-0.924536\pi$
$107$	−7.62530	+	7.62530i	−0.737166	+	0.737166i	0.234863	+	0.972029i	$0.424536\pi$
$108$		0			0
$109$	−9.95160	+	9.95160i	−0.953191	+	0.953191i	−0.998952	−	0.0457617i	$-0.985429\pi$
$109$	−9.95160	+	9.95160i	−0.953191	+	0.953191i	0.0457617	+	0.998952i	$0.485429\pi$
$110$	2.38621	+	1.46682i	0.227516	+	0.139856i
$111$		0			0
$112$	−0.351191	−	0.351191i	−0.0331844	−	0.0331844i
$113$	5.08354	+	5.08354i	0.478219	+	0.478219i	0.904562	−	0.426343i	$-0.140198\pi$
$113$	5.08354	+	5.08354i	0.478219	+	0.478219i	−0.426343	+	0.904562i	$0.640198\pi$
$114$		0			0
$115$	0.436387	−	0.709910i	0.0406933	−	0.0661995i
$116$	−18.2912	−	18.2912i	−1.69829	−	1.69829i
$117$		0			0
$118$		−	14.3173i		−	1.31801i
$119$	−0.192417	−	0.886412i	−0.0176389	−	0.0812573i
$120$		0			0
$121$			10.7244i			0.974948i
$122$	9.54484	−	9.54484i	0.864149	−	0.864149i
$123$		0			0
$124$	7.62880	+	7.62880i	0.685087	+	0.685087i
$125$	−7.22568	−	8.53168i	−0.646284	−	0.763097i
$126$		0			0
$127$	−9.74047			−0.864327			−0.432163	−	0.901795i	$-0.642250\pi$
$127$	−9.74047			−0.864327			−0.432163	+	0.901795i	$0.642250\pi$
$128$	20.7382			1.83301
$129$		0			0
$130$	10.2095	−	2.43613i	0.895429	−	0.213663i
$131$	13.9200	+	13.9200i	1.21620	+	1.21620i	0.968954	+	0.247242i	$0.0795244\pi$
$131$	13.9200	+	13.9200i	1.21620	+	1.21620i	0.247242	+	0.968954i	$0.420476\pi$
$132$		0			0
$133$	0.622235	−	0.622235i	0.0539547	−	0.0539547i
$134$		−	27.4700i		−	2.37304i
$135$		0			0
$136$	−14.0168	−	9.01679i	−1.20193	−	0.773184i
$137$			4.65693i			0.397869i	0.980013	+	0.198934i	$0.0637480\pi$
$137$			4.65693i			0.397869i	−0.980013	+	0.198934i	$0.936252\pi$
$138$		0			0
$139$	−3.71079	−	3.71079i	−0.314745	−	0.314745i	0.532000	−	0.846745i	$-0.321441\pi$
$139$	−3.71079	−	3.71079i	−0.314745	−	0.314745i	−0.846745	+	0.532000i	$0.821441\pi$
$140$	0.951603	−	1.54806i	0.0804251	−	0.130835i
$141$		0			0
$142$	−12.0866	−	12.0866i	−1.01429	−	1.01429i
$143$	−0.730192	−	0.730192i	−0.0610618	−	0.0610618i
$144$		0			0
$145$	8.19994	−	13.3396i	0.680968	−	1.10779i
$146$	−2.00000	+	2.00000i	−0.165521	+	0.165521i
$147$		0			0
$148$	14.9320	−	14.9320i	1.22740	−	1.22740i
$149$	−8.74239			−0.716205			−0.358102	−	0.933682i	$-0.616576\pi$
$149$	−8.74239			−0.716205			−0.358102	+	0.933682i	$0.616576\pi$
$150$		0			0
$151$		−	15.9032i		−	1.29418i	−0.762412	−	0.647092i	$-0.775985\pi$
$151$		−	15.9032i		−	1.29418i	0.762412	−	0.647092i	$-0.224015\pi$
$152$		−	16.1689i		−	1.31147i
$153$		0			0
$154$	−0.275573			−0.0222063
$155$	−3.41999	+	5.56361i	−0.274700	+	0.446880i
$156$		0			0
$157$		−	10.0719i		−	0.803823i	−0.915679	−	0.401911i	$-0.868346\pi$
$157$		−	10.0719i		−	0.803823i	0.915679	−	0.401911i	$-0.131654\pi$
$158$	11.3564	−	11.3564i	0.903468	−	0.903468i
$159$		0			0
$160$	1.39988	+	5.86670i	0.110670	+	0.463804i
$161$			0.0819845i			0.00646128i
$162$		0			0
$163$	6.77963	+	6.77963i	0.531021	+	0.531021i	0.920876	−	0.389855i	$-0.127475\pi$
$163$	6.77963	+	6.77963i	0.531021	+	0.531021i	−0.389855	+	0.920876i	$0.627475\pi$
$164$	−2.08198	+	2.08198i	−0.162576	+	0.162576i
$165$		0			0
$166$	14.5972			1.13296
$167$	3.77871	−	3.77871i	0.292405	−	0.292405i	−0.545624	−	0.838030i	$-0.683707\pi$
$167$	3.77871	−	3.77871i	0.292405	−	0.292405i	0.838030	+	0.545624i	$0.183707\pi$
$168$		0			0
$169$	9.13038			0.702337
$170$	7.28280	−	20.7593i	0.558565	−	1.59217i
$171$		0			0
$172$	−9.21344			−0.702518
$173$	12.3426	−	12.3426i	0.938390	−	0.938390i	−0.0598193	−	0.998209i	$-0.519052\pi$
$173$	12.3426	−	12.3426i	0.938390	−	0.938390i	0.998209	+	0.0598193i	$0.0190524\pi$
$174$		0			0
$175$	1.04519	+	0.342804i	0.0790086	+	0.0259135i
$176$	−0.838015	+	0.838015i	−0.0631678	+	0.0631678i
$177$		0			0
$178$	38.1440			2.85901
$179$		−	21.3248i		−	1.59389i	−0.604052	−	0.796945i	$-0.706448\pi$
$179$		−	21.3248i		−	1.59389i	0.604052	−	0.796945i	$-0.293552\pi$
$180$		0			0
$181$	10.2092	−	10.2092i	0.758845	−	0.758845i	−0.217267	−	0.976112i	$-0.569714\pi$
$181$	10.2092	−	10.2092i	0.758845	−	0.758845i	0.976112	+	0.217267i	$0.0697144\pi$
$182$	−0.730192	+	0.730192i	−0.0541255	+	0.0541255i
$183$		0			0
$184$	1.06519	+	1.06519i	0.0785269	+	0.0785269i
$185$	10.8897	+	6.69399i	0.800629	+	0.492152i
$186$		0			0
$187$	−2.11516	+	0.459148i	−0.154676	+	0.0335762i
$188$			24.8959i			1.81572i
$189$		0			0
$190$	20.7601	−	4.95367i	1.50609	−	0.359377i
$191$	6.74239			0.487862			0.243931	−	0.969793i	$-0.421563\pi$
$191$	6.74239			0.487862			0.243931	+	0.969793i	$0.421563\pi$
$192$		0			0
$193$	−10.3627	−	10.3627i	−0.745924	−	0.745924i	0.227787	−	0.973711i	$-0.426851\pi$
$193$	−10.3627	−	10.3627i	−0.745924	−	0.745924i	−0.973711	+	0.227787i	$0.926851\pi$
$194$	−15.5488	+	15.5488i	−1.11634	+	1.11634i
$195$		0			0
$196$		−	25.6792i		−	1.83423i
$197$	0.614707	+	0.614707i	0.0437960	+	0.0437960i	0.728666	−	0.684870i	$-0.240141\pi$
$197$	0.614707	+	0.614707i	0.0437960	+	0.0437960i	−0.684870	+	0.728666i	$0.740141\pi$
$198$		0			0
$199$	9.40478	+	9.40478i	0.666687	+	0.666687i	0.956948	−	0.290260i	$-0.0937419\pi$
$199$	9.40478	+	9.40478i	0.666687	+	0.666687i	−0.290260	+	0.956948i	$0.593742\pi$
$200$	18.0336	−	9.12576i	1.27517	−	0.645289i
$201$		0			0
$202$	−17.2027			−1.21038
$203$			1.54053i			0.108124i
$204$		0			0
$205$	−1.51837	−	0.933353i	−0.106048	−	0.0651882i
$206$		−	22.7276i		−	1.58351i
$207$		0			0
$208$			4.44102i			0.307929i
$209$	−1.48478	−	1.48478i	−0.102705	−	0.102705i
$210$		0			0
$211$	−12.5804	+	12.5804i	−0.866071	+	0.866071i	−0.992035	−	0.125964i	$-0.959798\pi$
$211$	−12.5804	+	12.5804i	−0.866071	+	0.866071i	0.125964	+	0.992035i	$0.459798\pi$
$212$	−21.8747			−1.50236
$213$		0			0
$214$	18.1956	−	18.1956i	1.24382	−	1.24382i
$215$	−1.29444	−	5.42483i	−0.0882804	−	0.369970i
$216$		0			0
$217$		−	0.642517i		−	0.0436169i
$218$	23.7466	−	23.7466i	1.60832	−	1.60832i
$219$		0			0
$220$	−3.69399	−	2.27072i	−0.249049	−	0.153092i
$221$	−4.38799	+	6.82122i	−0.295168	+	0.458845i
$222$		0			0
$223$	−1.96713			−0.131729			−0.0658645	−	0.997829i	$-0.520981\pi$
$223$	−1.96713			−0.131729			−0.0658645	+	0.997829i	$0.520981\pi$
$224$	−0.419593	−	0.419593i	−0.0280352	−	0.0280352i
$225$		0			0
$226$	−12.1304	−	12.1304i	−0.806901	−	0.806901i
$227$	−8.45593	−	8.45593i	−0.561239	−	0.561239i	0.368420	−	0.929659i	$-0.379899\pi$
$227$	−8.45593	−	8.45593i	−0.561239	−	0.561239i	−0.929659	+	0.368420i	$0.879899\pi$
$228$		0			0
$229$		−	9.30601i		−	0.614958i	−0.951555	−	0.307479i	$-0.900515\pi$
$229$		−	9.30601i		−	0.614958i	0.951555	−	0.307479i	$-0.0994854\pi$
$230$	−1.04131	+	1.69399i	−0.0686620	+	0.111699i
$231$		0			0
$232$	20.0155	+	20.0155i	1.31408	+	1.31408i
$233$	−18.2440	+	18.2440i	−1.19520	+	1.19520i	−0.219618	+	0.975586i	$0.570481\pi$
$233$	−18.2440	+	18.2440i	−1.19520	+	1.19520i	−0.975586	+	0.219618i	$0.929519\pi$
$234$		0			0
$235$	−14.6586	+	3.49775i	−0.956220	+	0.228168i
$236$			22.1640i			1.44275i
$237$		0			0
$238$	0.459148	+	2.11516i	0.0297621	+	0.137106i
$239$	29.2912			1.89469			0.947345	−	0.320215i	$-0.103755\pi$
$239$	29.2912			1.89469			0.947345	+	0.320215i	$0.103755\pi$
$240$		0			0
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	0.873435	−	0.486941i	$-0.161887\pi$
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	−0.486941	+	0.873435i	$0.661887\pi$
$242$		−	25.5907i		−	1.64503i
$243$		0			0
$244$	−14.7760	+	14.7760i	−0.945935	+	0.945935i
$245$	15.1198	−	3.60781i	0.965967	−	0.230494i
$246$		0			0
$247$	−7.86854			−0.500663
$248$	−8.34797	−	8.34797i	−0.530097	−	0.530097i
$249$		0			0
$250$	17.2420	+	20.3584i	1.09048	+	1.28758i
$251$	1.77282			0.111900			0.0559498	−	0.998434i	$-0.482181\pi$
$251$	1.77282			0.111900			0.0559498	+	0.998434i	$0.482181\pi$
$252$		0			0
$253$	0.195632			0.0122993
$254$	23.2428			1.45838
$255$		0			0
$256$	−27.5824			−1.72390
$257$	7.40235			0.461746			0.230873	−	0.972984i	$-0.425842\pi$
$257$	7.40235			0.461746			0.230873	+	0.972984i	$0.425842\pi$
$258$		0			0
$259$	−1.25761			−0.0781440
$260$	−15.8049	+	3.77128i	−0.980176	+	0.233885i
$261$		0			0
$262$	−33.2160	−	33.2160i	−2.05209	−	2.05209i
$263$	−7.67291			−0.473132			−0.236566	−	0.971615i	$-0.576022\pi$
$263$	−7.67291			−0.473132			−0.236566	+	0.971615i	$0.576022\pi$
$264$		0			0
$265$	−3.07329	−	12.8797i	−0.188791	−	0.791194i
$266$	−1.48478	+	1.48478i	−0.0910379	+	0.0910379i
$267$		0			0
$268$			42.5252i			2.59764i
$269$	5.56677	+	5.56677i	0.339412	+	0.339412i	0.856146	−	0.516734i	$-0.172852\pi$
$269$	5.56677	+	5.56677i	0.339412	+	0.339412i	−0.516734	+	0.856146i	$0.672852\pi$
$270$		0			0
$271$	18.0672			1.09750			0.548751	−	0.835986i	$-0.315103\pi$
$271$	18.0672			1.09750			0.548751	+	0.835986i	$0.315103\pi$
$272$	7.82847	+	5.03593i	0.474670	+	0.305348i
$273$		0			0
$274$		−	11.1124i		−	0.671326i
$275$	0.818002	−	2.49403i	0.0493274	−	0.150396i
$276$		0			0
$277$	−18.7786	+	18.7786i	−1.12829	+	1.12829i	−0.137840	+	0.990455i	$0.544016\pi$
$277$	−18.7786	+	18.7786i	−1.12829	+	1.12829i	−0.990455	+	0.137840i	$0.955984\pi$
$278$	8.85472	+	8.85472i	0.531071	+	0.531071i
$279$		0			0
$280$	−1.04131	+	1.69399i	−0.0622302	+	0.101236i
$281$		−	13.7728i		−	0.821618i	−0.911721	−	0.410809i	$-0.865246\pi$
$281$		−	13.7728i		−	0.821618i	0.911721	−	0.410809i	$-0.134754\pi$
$282$		0			0
$283$	−9.72068	−	9.72068i	−0.577834	−	0.577834i	0.356472	−	0.934306i	$-0.383980\pi$
$283$	−9.72068	−	9.72068i	−0.577834	−	0.577834i	−0.934306	+	0.356472i	$0.883980\pi$
$284$	18.7108	+	18.7108i	1.11028	+	1.11028i
$285$		0			0
$286$	1.74239	+	1.74239i	0.103030	+	0.103030i
$287$	0.175350			0.0103506
$288$		0			0
$289$	7.04840	+	15.4700i	0.414612	+	0.909998i
$290$	−19.5668	+	31.8311i	−1.14900	+	1.86918i
$291$		0			0
$292$	3.09612	−	3.09612i	0.181187	−	0.181187i
$293$		−	19.8873i		−	1.16183i	−0.813966	−	0.580913i	$-0.802696\pi$
$293$		−	19.8873i		−	1.16183i	0.813966	−	0.580913i	$-0.197304\pi$
$294$		0			0
$295$	−13.0500	+	3.11393i	−0.759802	+	0.181300i
$296$	−16.3396	+	16.3396i	−0.949720	+	0.949720i
$297$		0			0
$298$	20.8612			1.20846
$299$	0.518371	−	0.518371i	0.0299782	−	0.0299782i
$300$		0			0
$301$	0.387990	+	0.387990i	0.0223634	+	0.0223634i
$302$			37.9484i			2.18368i
$303$		0			0
$304$			9.03043i			0.517931i
$305$	−10.7760	−	6.62407i	−0.617031	−	0.379293i
$306$		0			0
$307$		−	14.9598i		−	0.853799i	−0.904299	−	0.426900i	$-0.859606\pi$
$307$		−	14.9598i		−	0.853799i	0.904299	−	0.426900i	$-0.140394\pi$
$308$	0.426603			0.0243080
$309$		0			0
$310$	8.16081	−	13.2759i	0.463503	−	0.754023i
$311$	20.9684	+	20.9684i	1.18901	+	1.18901i	0.977342	+	0.211667i	$0.0678892\pi$
$311$	20.9684	+	20.9684i	1.18901	+	1.18901i	0.211667	+	0.977342i	$0.432111\pi$
$312$		0			0
$313$	10.1671	+	10.1671i	0.574677	+	0.574677i	0.933432	−	0.358755i	$-0.116799\pi$
$313$	10.1671	+	10.1671i	0.574677	+	0.574677i	−0.358755	+	0.933432i	$0.616799\pi$
$314$			24.0336i			1.35629i
$315$		0			0
$316$	−17.5804	+	17.5804i	−0.988975	+	0.988975i
$317$	9.74047	+	9.74047i	0.547079	+	0.547079i	0.925595	−	0.378516i	$-0.123565\pi$
$317$	9.74047	+	9.74047i	0.547079	+	0.547079i	−0.378516	+	0.925595i	$0.623565\pi$
$318$		0			0
$319$	3.67603			0.205818
$320$	−5.68376	−	23.8198i	−0.317732	−	1.33157i
$321$		0			0
$322$		−	0.195632i		−	0.0109021i
$323$	−8.92260	+	13.8704i	−0.496467	+	0.771768i
$324$		0			0
$325$	−4.44102	−	8.77598i	−0.246343	−	0.486804i
$326$	−16.1776	−	16.1776i	−0.895995	−	0.895995i
$327$		0			0
$328$	2.27825	−	2.27825i	0.125795	−	0.125795i
$329$	1.04840	−	1.04840i	0.0578000	−	0.0578000i
$330$		0			0
$331$		−	20.1640i		−	1.10831i	−0.832413	−	0.554156i	$-0.813041\pi$
$331$		−	20.1640i		−	1.10831i	0.832413	−	0.554156i	$-0.186959\pi$
$332$	−22.5973			−1.24019
$333$		0			0
$334$	−9.01679	+	9.01679i	−0.493377	+	0.493377i
$335$	−25.0386	+	5.97459i	−1.36801	+	0.326427i
$336$		0			0
$337$	20.2111	−	20.2111i	1.10097	−	1.10097i	0.106677	−	0.994294i	$-0.465979\pi$
$337$	20.2111	−	20.2111i	1.10097	−	1.10097i	0.994294	−	0.106677i	$-0.0340210\pi$
$338$	−21.7870			−1.18506
$339$		0			0
$340$	−11.2742	+	32.1367i	−0.611430	+	1.74286i
$341$	−1.53318			−0.0830264
$342$		0			0
$343$	−2.17030	+	2.17030i	−0.117185	+	0.117185i
$344$	10.0820			0.543584
$345$		0			0
$346$	−29.4520	+	29.4520i	−1.58335	+	1.58335i
$347$	−7.73326	−	7.73326i	−0.415143	−	0.415143i	0.468383	−	0.883526i	$-0.344837\pi$
$347$	−7.73326	−	7.73326i	−0.415143	−	0.415143i	−0.883526	+	0.468383i	$0.844837\pi$
$348$		0			0
$349$		−	0.645598i		−	0.0345581i	−0.999851	−	0.0172790i	$-0.994500\pi$
$349$		−	0.645598i		−	0.0345581i	0.999851	−	0.0172790i	$-0.00550036\pi$
$350$	−2.49403	−	0.818002i	−0.133312	−	0.0437240i
$351$		0			0
$352$	−1.00124	+	1.00124i	−0.0533661	+	0.0533661i
$353$		−	14.3022i		−	0.761229i	−0.924734	−	0.380615i	$-0.875712\pi$
$353$		−	14.3022i		−	0.761229i	0.924734	−	0.380615i	$-0.124288\pi$
$354$		0			0
$355$	−8.38804	+	13.6456i	−0.445191	+	0.724233i
$356$	−59.0492			−3.12960
$357$		0			0
$358$			50.8854i			2.68938i
$359$			15.6760i			0.827349i	0.910425	+	0.413675i	$0.135755\pi$
$359$			15.6760i			0.827349i	−0.910425	+	0.413675i	$0.864245\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−24.3613	+	24.3613i	−1.28040	+	1.28040i
$363$		0			0
$364$	1.13038	−	1.13038i	0.0592481	−	0.0592481i
$365$	2.25797	+	1.38799i	0.118188	+	0.0726507i
$366$		0			0
$367$	15.4863	+	15.4863i	0.808379	+	0.808379i	0.984388	−	0.176009i	$-0.0563189\pi$
$367$	15.4863	+	15.4863i	0.808379	+	0.808379i	−0.176009	+	0.984388i	$0.556319\pi$
$368$	−0.594916	−	0.594916i	−0.0310121	−	0.0310121i
$369$		0			0
$370$	−25.9852	−	15.9733i	−1.35091	−	0.830411i
$371$	0.921171	+	0.921171i	0.0478248	+	0.0478248i
$372$		0			0
$373$		−	6.50858i		−	0.337002i	−0.985702	−	0.168501i	$-0.946107\pi$
$373$		−	6.50858i		−	0.337002i	0.985702	−	0.168501i	$-0.0538926\pi$
$374$	5.04723	−	1.09562i	0.260986	−	0.0566533i
$375$		0			0
$376$		−	27.2428i		−	1.40494i
$377$	9.74047	−	9.74047i	0.501660	−	0.501660i
$378$		0			0
$379$	−5.32280	−	5.32280i	−0.273414	−	0.273414i	0.557059	−	0.830473i	$-0.311930\pi$
$379$	−5.32280	−	5.32280i	−0.273414	−	0.273414i	−0.830473	+	0.557059i	$0.811930\pi$
$380$	−32.1378	+	7.66857i	−1.64864	+	0.393389i
$381$		0			0
$382$	−16.0888			−0.823172
$383$	24.7752			1.26595			0.632976	−	0.774172i	$-0.281833\pi$
$383$	24.7752			1.26595			0.632976	+	0.774172i	$0.281833\pi$
$384$		0			0
$385$	0.0599358	+	0.251182i	0.00305461	+	0.0128014i
$386$	24.7276	+	24.7276i	1.25860	+	1.25860i
$387$		0			0
$388$	24.0705	−	24.0705i	1.22199	−	1.22199i
$389$		−	23.6971i		−	1.20149i	−0.799440	−	0.600747i	$-0.794870\pi$
$389$		−	23.6971i		−	1.20149i	0.799440	−	0.600747i	$-0.205130\pi$
$390$		0			0
$391$	−0.325954	−	1.50158i	−0.0164842	−	0.0759380i
$392$			28.1000i			1.41926i
$393$		0			0
$394$	−1.46682	−	1.46682i	−0.0738973	−	0.0738973i
$395$	−12.8212	−	7.88129i	−0.645106	−	0.396551i
$396$		0			0
$397$	19.5964	+	19.5964i	0.983516	+	0.983516i	0.999866	−	0.0163500i	$-0.00520460\pi$
$397$	19.5964	+	19.5964i	0.983516	+	0.983516i	−0.0163500	+	0.999866i	$0.505205\pi$
$398$	−22.4418	−	22.4418i	−1.12490	−	1.12490i
$399$		0			0
$400$	−10.0719	+	5.09679i	−0.503593	+	0.254840i
$401$	21.5972	−	21.5972i	1.07851	−	1.07851i	0.0818697	−	0.996643i	$-0.473911\pi$
$401$	21.5972	−	21.5972i	1.07851	−	1.07851i	0.996643	−	0.0818697i	$-0.0260891\pi$
$402$		0			0
$403$	−4.06251	+	4.06251i	−0.202368	+	0.202368i
$404$	26.6308			1.32493
$405$		0			0
$406$		−	3.67603i		−	0.182438i
$407$			3.00092i			0.148750i
$408$		0			0
$409$	5.90321			0.291895			0.145947	−	0.989292i	$-0.453377\pi$
$409$	5.90321			0.291895			0.145947	+	0.989292i	$0.453377\pi$
$410$	3.62315	+	2.22718i	0.178935	+	0.109992i
$411$		0			0
$412$			35.1837i			1.73337i
$413$	0.933353	−	0.933353i	0.0459273	−	0.0459273i
$414$		0			0
$415$	−3.17482	−	13.3052i	−0.155846	−	0.653127i
$416$			5.30601i			0.260148i
$417$		0			0
$418$	3.54301	+	3.54301i	0.173294	+	0.173294i
$419$	−22.9716	+	22.9716i	−1.12223	+	1.12223i	−0.130829	+	0.991405i	$0.541764\pi$
$419$	−22.9716	+	22.9716i	−1.12223	+	1.12223i	−0.991405	+	0.130829i	$0.958236\pi$
$420$		0			0
$421$	30.1156			1.46774			0.733872	−	0.679288i	$-0.237711\pi$
$421$	30.1156			1.46774			0.733872	+	0.679288i	$0.237711\pi$
$422$	30.0195	−	30.0195i	1.46133	−	1.46133i
$423$		0			0
$424$	23.9368			1.16247
$425$	−20.5059	−	2.12314i	−0.994683	−	0.102987i
$426$		0			0
$427$	1.24447			0.0602242
$428$	−28.1678	+	28.1678i	−1.36154	+	1.36154i
$429$		0			0
$430$	3.08882	+	12.9448i	0.148956	+	0.624252i
$431$	5.88641	−	5.88641i	0.283538	−	0.283538i	−0.550980	−	0.834518i	$-0.685746\pi$
$431$	5.88641	−	5.88641i	0.283538	−	0.283538i	0.834518	+	0.550980i	$0.185746\pi$
$432$		0			0
$433$	−13.5795			−0.652591			−0.326295	−	0.945268i	$-0.605800\pi$
$433$	−13.5795			−0.652591			−0.326295	+	0.945268i	$0.605800\pi$
$434$			1.53318i			0.0735950i
$435$		0			0
$436$	−36.7612	+	36.7612i	−1.76054	+	1.76054i
$437$	1.05406	−	1.05406i	0.0504227	−	0.0504227i
$438$		0			0
$439$	14.4048	+	14.4048i	0.687503	+	0.687503i	0.961679	−	0.274177i	$-0.0884053\pi$
$439$	14.4048	+	14.4048i	0.687503	+	0.687503i	−0.274177	+	0.961679i	$0.588405\pi$
$440$	4.04223	+	2.48478i	0.192706	+	0.118457i
$441$		0			0
$442$	10.4707	−	16.2769i	0.498039	−	0.774211i
$443$			2.45360i			0.116574i	0.998300	+	0.0582871i	$0.0185639\pi$
$443$			2.45360i			0.116574i	−0.998300	+	0.0582871i	$0.981436\pi$
$444$		0			0
$445$	−8.29614	−	34.7679i	−0.393275	−	1.64816i
$446$	4.69399			0.222267
$447$		0			0
$448$	1.70362	+	1.70362i	0.0804884	+	0.0804884i
$449$	−2.26076	+	2.26076i	−0.106692	+	0.106692i	−0.758438	−	0.651746i	$-0.774037\pi$
$449$	−2.26076	+	2.26076i	−0.106692	+	0.106692i	0.651746	+	0.758438i	$0.274037\pi$
$450$		0			0
$451$		−	0.418422i		−	0.0197027i
$452$	18.7786	+	18.7786i	0.883269	+	0.883269i
$453$		0			0
$454$	20.1776	+	20.1776i	0.946982	+	0.946982i
$455$	0.824376	+	0.506750i	0.0386474	+	0.0237568i
$456$		0			0
$457$	30.1803			1.41177			0.705887	−	0.708325i	$-0.250549\pi$
$457$	30.1803			1.41177			0.705887	+	0.708325i	$0.250549\pi$
$458$			22.2061i			1.03762i
$459$		0			0
$460$	1.61201	−	2.62241i	0.0751604	−	0.122270i
$461$			5.41527i			0.252214i	0.992017	+	0.126107i	$0.0402483\pi$
$461$			5.41527i			0.252214i	−0.992017	+	0.126107i	$0.959752\pi$
$462$		0			0
$463$		−	15.7574i		−	0.732307i	−0.930555	−	0.366153i	$-0.880675\pi$
$463$		−	15.7574i		−	0.732307i	0.930555	−	0.366153i	$-0.119325\pi$
$464$	−11.1788	−	11.1788i	−0.518962	−	0.518962i
$465$		0			0
$466$	43.5340	−	43.5340i	2.01667	−	2.01667i
$467$	10.7690			0.498331			0.249166	−	0.968461i	$-0.419844\pi$
$467$	10.7690			0.498331			0.249166	+	0.968461i	$0.419844\pi$
$468$		0			0
$469$	1.79079	−	1.79079i	0.0826910	−	0.0826910i
$470$	34.9784	−	8.34637i	1.61343	−	0.384989i
$471$		0			0
$472$		−	24.2534i		−	1.11635i
$473$	0.925824	−	0.925824i	0.0425695	−	0.0425695i
$474$		0			0
$475$	−9.03043	−	17.8452i	−0.414345	−	0.818794i
$476$	−0.710788	−	3.27440i	−0.0325789	−	0.150082i
$477$		0			0
$478$	−69.8949			−3.19692
$479$	−26.0988	−	26.0988i	−1.19248	−	1.19248i	−0.976368	−	0.216116i	$-0.930661\pi$
$479$	−26.0988	−	26.0988i	−1.19248	−	1.19248i	−0.216116	−	0.976368i	$-0.569339\pi$
$480$		0			0
$481$	7.95160	+	7.95160i	0.362562	+	0.362562i
$482$	−14.3173	−	14.3173i	−0.652133	−	0.652133i
$483$		0			0
$484$			39.6160i			1.80073i
$485$	17.5544	+	10.7908i	0.797103	+	0.489984i
$486$		0			0
$487$	27.0987	+	27.0987i	1.22796	+	1.22796i	0.964734	+	0.263226i	$0.0847864\pi$
$487$	27.0987	+	27.0987i	1.22796	+	1.22796i	0.263226	+	0.964734i	$0.415214\pi$
$488$	16.1689	−	16.1689i	0.731932	−	0.731932i
$489$		0			0
$490$	−36.0790	+	8.60898i	−1.62988	+	0.388914i
$491$			38.0336i			1.71643i	0.513289	+	0.858216i	$0.328427\pi$
$491$			38.0336i			1.71643i	−0.513289	+	0.858216i	$0.671573\pi$
$492$		0			0
$493$	−6.12485	−	28.2154i	−0.275849	−	1.27076i
$494$	18.7760			0.844771
$495$		0			0
$496$	4.66239	+	4.66239i	0.209348	+	0.209348i
$497$		−	1.57587i		−	0.0706875i
$498$		0			0
$499$	6.58041	−	6.58041i	0.294579	−	0.294579i	−0.544307	−	0.838886i	$-0.683207\pi$
$499$	6.58041	−	6.58041i	0.294579	−	0.294579i	0.838886	+	0.544307i	$0.183207\pi$
$500$	−26.6916	−	31.5160i	−1.19369	−	1.40944i
$501$		0			0
$502$	−4.23033			−0.188809
$503$	1.10919	+	1.10919i	0.0494565	+	0.0494565i	0.731403	−	0.681946i	$-0.238866\pi$
$503$	1.10919	+	1.10919i	0.0494565	+	0.0494565i	−0.681946	+	0.731403i	$0.738866\pi$
$504$		0			0
$505$	3.74150	+	15.6801i	0.166495	+	0.697754i
$506$	−0.466819			−0.0207526
$507$		0			0
$508$	−35.9812			−1.59641
$509$	24.4247			1.08261			0.541304	−	0.840827i	$-0.317931\pi$
$509$	24.4247			1.08261			0.541304	+	0.840827i	$0.317931\pi$
$510$		0			0
$511$	−0.260763			−0.0115355
$512$	24.3410			1.07573
$513$		0			0
$514$	−17.6636			−0.779106
$515$	−20.7160	+	4.94314i	−0.912854	+	0.217821i
$516$		0			0
$517$	−2.50169	−	2.50169i	−0.110024	−	0.110024i
$518$	3.00092			0.131853
$519$		0			0
$520$	17.2948	−	4.12679i	0.758426	−	0.180972i
$521$	5.30916	−	5.30916i	0.232599	−	0.232599i	−0.581178	−	0.813776i	$-0.697408\pi$
$521$	5.30916	−	5.30916i	0.232599	−	0.232599i	0.813776	+	0.581178i	$0.197408\pi$
$522$		0			0
$523$		−	8.98247i		−	0.392776i	−0.980526	−	0.196388i	$-0.937079\pi$
$523$		−	8.98247i		−	0.392776i	0.980526	−	0.196388i	$-0.0629212\pi$
$524$	51.4204	+	51.4204i	2.24631	+	2.24631i
$525$		0			0
$526$	18.3092			0.798317
$527$	2.55452	+	11.7680i	0.111277	+	0.512620i
$528$		0			0
$529$		−	22.8611i		−	0.993962i
$530$	7.33351	+	30.7337i	0.318547	+	1.33498i
$531$		0			0
$532$	2.29853	−	2.29853i	0.0996541	−	0.0996541i
$533$	−1.10870	−	1.10870i	−0.0480233	−	0.0480233i
$534$		0			0
$535$	−20.5425	−	12.6276i	−0.888131	−	0.545940i
$536$		−	46.5340i		−	2.00996i
$537$		0			0
$538$	−13.2835	−	13.2835i	−0.572691	−	0.572691i
$539$	2.58041	+	2.58041i	0.111146	+	0.111146i
$540$		0			0
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	−43.1121			−1.85182
$543$		0			0
$544$	9.35323	+	6.01679i	0.401016	+	0.257968i
$545$	−26.8096	−	16.4800i	−1.14840	−	0.705927i
$546$		0			0
$547$	1.81910	−	1.81910i	0.0777793	−	0.0777793i	−0.667147	−	0.744926i	$-0.732485\pi$
$547$	1.81910	−	1.81910i	0.0777793	−	0.0777793i	0.744926	+	0.667147i	$0.232485\pi$
$548$			17.2027i			0.734862i
$549$		0			0
$550$	−1.95192	+	5.95128i	−0.0832303	+	0.253764i
$551$	19.8064	−	19.8064i	0.843782	−	0.843782i
$552$		0			0
$553$	1.48067			0.0629644
$554$	44.8096	−	44.8096i	1.90378	−	1.90378i
$555$		0			0
$556$	−13.7076	−	13.7076i	−0.581333	−	0.581333i
$557$		−	21.0162i		−	0.890487i	−0.895410	−	0.445243i	$-0.853117\pi$
$557$		−	21.0162i		−	0.890487i	0.895410	−	0.445243i	$-0.146883\pi$
$558$		0			0
$559$		−	4.90636i		−	0.207517i
$560$	0.581578	−	0.946106i	0.0245762	−	0.0399803i
$561$		0			0
$562$			32.8648i			1.38632i
$563$	−40.5377			−1.70846			−0.854231	−	0.519893i	$-0.825972\pi$
$563$	−40.5377			−1.70846			−0.854231	+	0.519893i	$0.825972\pi$
$564$		0			0
$565$	−8.41842	+	13.6950i	−0.354166	+	0.576154i
$566$	23.1956	+	23.1956i	0.974983	+	0.974983i
$567$		0			0
$568$	−20.4746	−	20.4746i	−0.859097	−	0.859097i
$569$		−	0.612010i		−	0.0256568i	−0.999918	−	0.0128284i	$-0.995916\pi$
$569$		−	0.612010i		−	0.0256568i	0.999918	−	0.0128284i	$-0.00408352\pi$
$570$		0			0
$571$	−10.5320	+	10.5320i	−0.440751	+	0.440751i	−0.892264	−	0.451513i	$-0.850884\pi$
$571$	−10.5320	+	10.5320i	−0.440751	+	0.440751i	0.451513	+	0.892264i	$0.350884\pi$
$572$	−2.69733	−	2.69733i	−0.112781	−	0.112781i
$573$		0			0
$574$	−0.418422			−0.0174646
$575$	1.77054	+	0.580708i	0.0738366	+	0.0242172i
$576$		0			0
$577$			37.2107i			1.54910i	0.632513	+	0.774550i	$0.282024\pi$
$577$			37.2107i			1.54910i	−0.632513	+	0.774550i	$0.717976\pi$
$578$	−16.8190	−	36.9146i	−0.699576	−	1.53544i
$579$		0			0
$580$	30.2905	−	49.2764i	1.25775	−	2.04609i
$581$	0.951603	+	0.951603i	0.0394791	+	0.0394791i
$582$		0			0
$583$	2.19811	−	2.19811i	0.0910362	−	0.0910362i
$584$	−3.38799	+	3.38799i	−0.140196	+	0.140196i
$585$		0			0
$586$			47.4552i			1.96035i
$587$	9.60470			0.396428			0.198214	−	0.980159i	$-0.436486\pi$
$587$	9.60470			0.396428			0.198214	+	0.980159i	$0.436486\pi$
$588$		0			0
$589$	−8.26076	+	8.26076i	−0.340379	+	0.340379i
$590$	31.1401	−	7.43050i	1.28202	−	0.305909i
$591$		0			0
$592$	9.12576	−	9.12576i	0.375067	−	0.375067i
$593$	16.5206			0.678419			0.339210	−	0.940711i	$-0.389840\pi$
$593$	16.5206			0.678419			0.339210	+	0.940711i	$0.389840\pi$
$594$		0			0
$595$	1.82809	−	0.878547i	0.0749443	−	0.0360169i
$596$	−32.2944			−1.32283
$597$		0			0
$598$	−1.23694	+	1.23694i	−0.0505823	+	0.0505823i
$599$	−34.8096			−1.42228			−0.711140	−	0.703050i	$-0.751821\pi$
$599$	−34.8096			−1.42228			−0.711140	+	0.703050i	$0.751821\pi$
$600$		0			0
$601$	−8.26076	+	8.26076i	−0.336964	+	0.336964i	−0.855223	−	0.518260i	$-0.826580\pi$
$601$	−8.26076	+	8.26076i	−0.336964	+	0.336964i	0.518260	+	0.855223i	$0.326580\pi$
$602$	−0.925824	−	0.925824i	−0.0377338	−	0.0377338i
$603$		0			0
$604$		−	58.7464i		−	2.39036i
$605$	−23.3257	+	5.56586i	−0.948324	+	0.226284i
$606$		0			0
$607$	19.0421	−	19.0421i	0.772894	−	0.772894i	−0.205718	−	0.978611i	$-0.565953\pi$
$607$	19.0421	−	19.0421i	0.772894	−	0.772894i	0.978611	+	0.205718i	$0.0659528\pi$
$608$			10.7893i			0.437564i
$609$		0			0
$610$	25.7137	+	15.8064i	1.04112	+	0.639983i
$611$	−13.2576			−0.536345
$612$		0			0
$613$			5.43522i			0.219526i	0.993958	+	0.109763i	$0.0350092\pi$
$613$			5.43522i			0.219526i	−0.993958	+	0.109763i	$0.964991\pi$
$614$			35.6971i			1.44062i
$615$		0			0
$616$	−0.466819			−0.0188087
$617$	−2.47388	+	2.47388i	−0.0995948	+	0.0995948i	−0.755149	−	0.655554i	$-0.772435\pi$
$617$	−2.47388	+	2.47388i	−0.0995948	+	0.0995948i	0.655554	+	0.755149i	$0.272435\pi$
$618$		0			0
$619$	8.57725	−	8.57725i	0.344749	−	0.344749i	−0.513400	−	0.858149i	$-0.671614\pi$
$619$	8.57725	−	8.57725i	0.344749	−	0.344749i	0.858149	+	0.513400i	$0.171614\pi$
$620$	−12.6334	+	20.5520i	−0.507371	+	0.825387i
$621$		0			0
$622$	−50.0350	−	50.0350i	−2.00622	−	2.00622i
$623$	2.48664	+	2.48664i	0.0996250	+	0.0996250i
$624$		0			0
$625$	14.8064	−	20.1437i	0.592256	−	0.805750i
$626$	−24.2608	−	24.2608i	−0.969655	−	0.969655i
$627$		0			0
$628$		−	37.2054i		−	1.48466i
$629$	23.0336	−	5.00000i	0.918409	−	0.199363i
$630$		0			0
$631$		−	12.6183i		−	0.502327i	−0.967945	−	0.251164i	$-0.919187\pi$
$631$		−	12.6183i		−	0.502327i	0.967945	−	0.251164i	$-0.0808132\pi$
$632$	19.2377	−	19.2377i	0.765235	−	0.765235i
$633$		0			0
$634$	−23.2428	−	23.2428i	−0.923089	−	0.923089i
$635$	−5.05520	−	21.1856i	−0.200609	−	0.840724i
$636$		0			0
$637$	13.6747			0.541813
$638$	−8.77178			−0.347278
$639$		0			0
$640$	10.7629	+	45.1056i	0.425440	+	1.78296i
$641$	−21.3544	−	21.3544i	−0.843448	−	0.843448i	0.145857	−	0.989306i	$-0.453406\pi$
$641$	−21.3544	−	21.3544i	−0.843448	−	0.843448i	−0.989306	+	0.145857i	$0.953406\pi$
$642$		0			0
$643$	13.9383	−	13.9383i	0.549671	−	0.549671i	−0.376675	−	0.926346i	$-0.622932\pi$
$643$	13.9383	−	13.9383i	0.549671	−	0.549671i	0.926346	+	0.376675i	$0.122932\pi$
$644$			0.302850i			0.0119340i
$645$		0			0
$646$	21.2912	−	33.0976i	0.837691	−	1.30221i
$647$		−	21.0418i		−	0.827237i	−0.910450	−	0.413618i	$-0.864265\pi$
$647$		−	21.0418i		−	0.827237i	0.910450	−	0.413618i	$-0.135735\pi$
$648$		0			0
$649$	−2.22718	−	2.22718i	−0.0874243	−	0.0874243i
$650$	10.5972	+	20.9413i	0.415656	+	0.821386i
$651$		0			0
$652$	25.0439	+	25.0439i	0.980795	+	0.980795i
$653$	27.3773	+	27.3773i	1.07136	+	1.07136i	0.997250	+	0.0741056i	$0.0236102\pi$
$653$	27.3773	+	27.3773i	1.07136	+	1.07136i	0.0741056	+	0.997250i	$0.476390\pi$
$654$		0			0
$655$	−23.0518	+	37.5004i	−0.900707	+	1.46526i
$656$	−1.27242	+	1.27242i	−0.0496796	+	0.0496796i
$657$		0			0
$658$	−2.50169	+	2.50169i	−0.0975262	+	0.0975262i
$659$	24.1577			0.941049			0.470524	−	0.882387i	$-0.344065\pi$
$659$	24.1577			0.941049			0.470524	+	0.882387i	$0.344065\pi$
$660$		0			0
$661$			25.7432i			1.00129i	0.865651	+	0.500647i	$0.166905\pi$
$661$			25.7432i			1.00129i	−0.865651	+	0.500647i	$0.833095\pi$
$662$			48.1155i			1.87006i
$663$		0			0
$664$	24.7276			0.959616
$665$	1.67630	+	1.03043i	0.0650041	+	0.0399585i
$666$		0			0
$667$			2.60965i			0.101046i
$668$	13.9585	−	13.9585i	0.540072	−	0.540072i
$669$		0			0
$670$	59.7474	−	14.2566i	2.30824	−	0.550781i
$671$		−	2.96957i		−	0.114639i
$672$		0			0
$673$	−7.42165	−	7.42165i	−0.286084	−	0.286084i	0.549446	−	0.835529i	$-0.314839\pi$
$673$	−7.42165	−	7.42165i	−0.286084	−	0.286084i	−0.835529	+	0.549446i	$0.814839\pi$
$674$	−48.2280	+	48.2280i	−1.85767	+	1.85767i
$675$		0			0
$676$	33.7276			1.29721
$677$	6.00183	−	6.00183i	0.230669	−	0.230669i	−0.582303	−	0.812972i	$-0.697848\pi$
$677$	6.00183	−	6.00183i	0.230669	−	0.230669i	0.812972	+	0.582303i	$0.197848\pi$
$678$		0			0
$679$	−2.02728			−0.0777998
$680$	12.3370	−	35.1662i	0.473103	−	1.34856i
$681$		0			0
$682$	3.65849			0.140091
$683$	−10.1044	+	10.1044i	−0.386635	+	0.386635i	−0.873485	−	0.486851i	$-0.838146\pi$
$683$	−10.1044	+	10.1044i	−0.386635	+	0.386635i	0.486851	+	0.873485i	$0.338146\pi$
$684$		0			0
$685$	−10.1289	+	2.41690i	−0.387004	+	0.0923449i
$686$	5.17878	−	5.17878i	0.197727	−	0.197727i
$687$		0			0
$688$	−5.63085			−0.214674
$689$		−	11.6488i		−	0.443782i
$690$		0			0
$691$	−6.24081	+	6.24081i	−0.237412	+	0.237412i	−0.815778	−	0.578366i	$-0.803691\pi$
$691$	−6.24081	+	6.24081i	−0.237412	+	0.237412i	0.578366	+	0.815778i	$0.303691\pi$
$692$	45.5935	−	45.5935i	1.73320	−	1.73320i
$693$		0			0
$694$	18.4532	+	18.4532i	0.700473	+	0.700473i
$695$	6.14513	−	9.99684i	0.233098	−	0.379202i
$696$		0			0
$697$	−3.21161	+	0.697157i	−0.121648	+	0.0264067i
$698$			1.54053i			0.0583100i
$699$		0			0
$700$	3.86091	+	1.26632i	0.145929	+	0.0478622i
$701$	−18.5340			−0.700019			−0.350010	−	0.936746i	$-0.613822\pi$
$701$	−18.5340			−0.700019			−0.350010	+	0.936746i	$0.613822\pi$
$702$		0			0
$703$	16.1689	+	16.1689i	0.609822	+	0.609822i
$704$	4.06519	−	4.06519i	0.153213	−	0.153213i
$705$		0			0
$706$			34.1280i			1.28443i
$707$	−1.12146	−	1.12146i	−0.0421767	−	0.0421767i
$708$		0			0
$709$	−18.0304	−	18.0304i	−0.677147	−	0.677147i	0.282207	−	0.959354i	$-0.408934\pi$
$709$	−18.0304	−	18.0304i	−0.677147	−	0.677147i	−0.959354	+	0.282207i	$0.908934\pi$
$710$	20.0156	−	32.5613i	0.751173	−	1.22200i
$711$		0			0
$712$	64.6158			2.42158
$713$		−	1.08842i		−	0.0407617i
$714$		0			0
$715$	1.20921	−	1.96713i	0.0452219	−	0.0735667i
$716$		−	78.7736i		−	2.94391i
$717$		0			0
$718$		−	37.4063i		−	1.39599i
$719$	−3.36804	−	3.36804i	−0.125607	−	0.125607i	0.641509	−	0.767116i	$-0.278309\pi$
$719$	−3.36804	−	3.36804i	−0.125607	−	0.125607i	−0.767116	+	0.641509i	$0.778309\pi$
$720$		0			0
$721$	1.48163	−	1.48163i	0.0551787	−	0.0551787i
$722$	−7.15863			−0.266417
$723$		0			0
$724$	37.7128	−	37.7128i	1.40158	−	1.40158i
$725$	33.2694	+	10.9118i	1.23559	+	0.405255i
$726$		0			0
$727$		−	11.1858i		−	0.414858i	−0.978250	−	0.207429i	$-0.933490\pi$
$727$		−	11.1858i		−	0.414858i	0.978250	−	0.207429i	$-0.0665096\pi$
$728$	−1.23694	+	1.23694i	−0.0458441	+	0.0458441i
$729$		0			0
$730$	−5.38799	−	3.31203i	−0.199418	−	0.122584i
$731$	−8.64875	−	5.56361i	−0.319886	−	0.205778i
$732$		0			0
$733$	−26.2804			−0.970687			−0.485344	−	0.874324i	$-0.661305\pi$
$733$	−26.2804			−0.970687			−0.485344	+	0.874324i	$0.661305\pi$
$734$	−36.9536	−	36.9536i	−1.36398	−	1.36398i
$735$		0			0
$736$	−0.710788	−	0.710788i	−0.0262000	−	0.0262000i
$737$	−4.27320	−	4.27320i	−0.157405	−	0.157405i
$738$		0			0
$739$		−	6.00000i		−	0.220714i	−0.993892	−	0.110357i	$-0.964801\pi$
$739$		−	6.00000i		−	0.220714i	0.993892	−	0.110357i	$-0.0351994\pi$
$740$	40.2266	+	24.7276i	1.47876	+	0.909004i
$741$		0			0
$742$	−2.19811	−	2.19811i	−0.0806950	−	0.0806950i
$743$	24.0700	−	24.0700i	0.883042	−	0.883042i	−0.110800	−	0.993843i	$-0.535341\pi$
$743$	24.0700	−	24.0700i	0.883042	−	0.883042i	0.993843	+	0.110800i	$0.0353415\pi$
$744$		0			0
$745$	−4.53720	−	19.0148i	−0.166230	−	0.696647i
$746$			15.5308i			0.568624i
$747$		0			0
$748$	−7.81341	+	1.69609i	−0.285686	+	0.0620152i
$749$	2.37237			0.0866844
$750$		0			0
$751$	−9.22285	−	9.22285i	−0.336547	−	0.336547i	0.518519	−	0.855066i	$-0.326483\pi$
$751$	−9.22285	−	9.22285i	−0.336547	−	0.336547i	−0.855066	+	0.518519i	$0.826483\pi$
$752$			15.2153i			0.554844i
$753$		0			0
$754$	−23.2428	+	23.2428i	−0.846453	+	0.846453i
$755$	34.5896	−	8.25359i	1.25884	−	0.300379i
$756$		0			0
$757$	31.8716			1.15839			0.579197	−	0.815188i	$-0.303366\pi$
$757$	31.8716			1.15839			0.579197	+	0.815188i	$0.303366\pi$
$758$	12.7013	+	12.7013i	0.461332	+	0.461332i
$759$		0			0
$760$	35.1675	−	8.39148i	1.27566	−	0.304391i
$761$	−18.7549			−0.679863			−0.339932	−	0.940450i	$-0.610404\pi$
$761$	−18.7549			−0.679863			−0.339932	+	0.940450i	$0.610404\pi$
$762$		0			0
$763$	3.09612			0.112087
$764$	24.9064			0.901081
$765$		0			0
$766$	−59.1187			−2.13605
$767$	−11.8028			−0.426175
$768$		0			0
$769$	−47.7916			−1.72341			−0.861705	−	0.507410i	$-0.830603\pi$
$769$	−47.7916			−1.72341			−0.861705	+	0.507410i	$0.830603\pi$
$770$	−0.143019	−	0.599373i	−0.00515406	−	0.0215999i
$771$		0			0
$772$	−38.2798	−	38.2798i	−1.37772	−	1.37772i
$773$	28.3286			1.01891			0.509455	−	0.860497i	$-0.329847\pi$
$773$	28.3286			1.01891			0.509455	+	0.860497i	$0.329847\pi$
$774$		0			0
$775$	−13.8758	−	4.55105i	−0.498434	−	0.163478i
$776$	−26.3396	+	26.3396i	−0.945536	+	0.945536i
$777$		0			0
$778$			56.5464i			2.02729i
$779$	−2.25445	−	2.25445i	−0.0807742	−	0.0807742i
$780$		0			0
$781$	−3.76036			−0.134556
$782$	0.777794	+	3.58308i	0.0278139	+	0.128131i
$783$		0			0
$784$		−	15.6940i		−	0.560500i
$785$	21.9064	−	5.22719i	0.781872	−	0.186566i
$786$		0			0
$787$	−29.9191	+	29.9191i	−1.06650	+	1.06650i	−0.0688738	+	0.997625i	$0.521941\pi$
$787$	−29.9191	+	29.9191i	−1.06650	+	1.06650i	−0.997625	+	0.0688738i	$0.978059\pi$
$788$	2.27072	+	2.27072i	0.0808912	+	0.0808912i
$789$		0			0
$790$	30.5941	+	18.8064i	1.08849	+	0.669102i
$791$		−	1.58158i		−	0.0562344i
$792$		0			0
$793$	−7.86854	−	7.86854i	−0.279420	−	0.279420i
$794$	−46.7612	−	46.7612i	−1.65949	−	1.65949i
$795$		0			0
$796$	34.7412	+	34.7412i	1.23137	+	1.23137i
$797$	54.1578			1.91837			0.959185	−	0.282780i	$-0.0912568\pi$
$797$	54.1578			1.91837			0.959185	+	0.282780i	$0.0912568\pi$
$798$		0			0
$799$	−15.0336	+	23.3700i	−0.531850	+	0.826772i
$800$	−12.0336	+	6.08951i	−0.425452	+	0.215297i
$801$		0			0
$802$	−51.5354	+	51.5354i	−1.81978	+	1.81978i
$803$			0.622235i			0.0219582i
$804$		0			0
$805$	−0.178317	+	0.0425490i	−0.00628484	+	0.00149966i
$806$	9.69399	−	9.69399i	0.341456	−	0.341456i
$807$		0			0
$808$	−29.1413			−1.02519
$809$	−21.9064	+	21.9064i	−0.770187	+	0.770187i	−0.978139	−	0.207952i	$-0.933320\pi$
$809$	−21.9064	+	21.9064i	−0.770187	+	0.770187i	0.207952	+	0.978139i	$0.433320\pi$
$810$		0			0
$811$	−2.93481	−	2.93481i	−0.103055	−	0.103055i	0.653699	−	0.756754i	$-0.273216\pi$
$811$	−2.93481	−	2.93481i	−0.103055	−	0.103055i	−0.756754	+	0.653699i	$0.773216\pi$
$812$			5.69071i			0.199705i
$813$		0			0
$814$		−	7.16081i		−	0.250986i
$815$	−11.2272	+	18.2643i	−0.393271	+	0.639770i
$816$		0			0
$817$		−	9.97667i		−	0.349039i
$818$	−14.0863			−0.492515
$819$		0			0
$820$	−5.60886	−	3.44780i	−0.195870	−	0.120402i
$821$	0.996845	+	0.996845i	0.0347901	+	0.0347901i	0.724288	−	0.689498i	$-0.242169\pi$
$821$	0.996845	+	0.996845i	0.0347901	+	0.0347901i	−0.689498	+	0.724288i	$0.742169\pi$
$822$		0			0
$823$	14.2899	+	14.2899i	0.498116	+	0.498116i	0.910851	−	0.412735i	$-0.135427\pi$
$823$	14.2899	+	14.2899i	0.498116	+	0.498116i	−0.412735	+	0.910851i	$0.635427\pi$
$824$		−	38.5004i		−	1.34123i
$825$		0			0
$826$	−2.22718	+	2.22718i	−0.0774934	+	0.0774934i
$827$	8.03163	+	8.03163i	0.279287	+	0.279287i	0.832824	−	0.553537i	$-0.186722\pi$
$827$	8.03163	+	8.03163i	0.279287	+	0.279287i	−0.553537	+	0.832824i	$0.686722\pi$
$828$		0			0
$829$	−10.9336			−0.379741			−0.189870	−	0.981809i	$-0.560807\pi$
$829$	−10.9336			−0.379741			−0.189870	+	0.981809i	$0.560807\pi$
$830$	7.57579	+	31.7490i	0.262959	+	1.10202i
$831$		0			0
$832$		−	21.5433i		−	0.746879i
$833$	15.5066	−	24.1053i	0.537272	−	0.835200i
$834$		0			0
$835$	10.1798	+	6.25761i	0.352287	+	0.216553i
$836$	−5.48478	−	5.48478i	−0.189695	−	0.189695i
$837$		0			0
$838$	54.8149	−	54.8149i	1.89355	−	1.89355i
$839$	−27.4836	+	27.4836i	−0.948840	+	0.948840i	−0.998754	−	0.0499138i	$-0.984105\pi$
$839$	−27.4836	+	27.4836i	−0.948840	+	0.948840i	0.0499138	+	0.998754i	$0.484105\pi$
$840$		0			0
$841$			20.0367i			0.690922i
$842$	−71.8621			−2.47653
$843$		0			0
$844$	−46.4720	+	46.4720i	−1.59963	+	1.59963i
$845$	4.73857	+	19.8586i	0.163012	+	0.683158i
$846$		0			0
$847$	1.66828	−	1.66828i	0.0573228	−	0.0573228i
$848$	−13.3688			−0.459088
$849$		0			0
$850$	48.9314	+	5.06625i	1.67833	+	0.173771i
$851$	−2.13038			−0.0730285
$852$		0			0
$853$	−22.6454	+	22.6454i	−0.775365	+	0.775365i	−0.979039	−	0.203674i	$-0.934712\pi$
$853$	−22.6454	+	22.6454i	−0.775365	+	0.775365i	0.203674	+	0.979039i	$0.434712\pi$
$854$	−2.96957			−0.101617
$855$		0			0
$856$	30.8232	−	30.8232i	1.05352	−	1.05352i
$857$	18.1563	+	18.1563i	0.620208	+	0.620208i	0.945585	−	0.325376i	$-0.105491\pi$
$857$	18.1563	+	18.1563i	0.620208	+	0.620208i	−0.325376	+	0.945585i	$0.605491\pi$
$858$		0			0
$859$			38.7065i			1.32065i	0.750981	+	0.660324i	$0.229581\pi$
$859$			38.7065i			1.32065i	−0.750981	+	0.660324i	$0.770419\pi$
$860$	−4.78167	−	20.0393i	−0.163054	−	0.683334i
$861$		0			0
$862$	−14.0462	+	14.0462i	−0.478416	+	0.478416i
$863$			29.5881i			1.00719i	0.863939	+	0.503596i	$0.167990\pi$
$863$			29.5881i			1.00719i	−0.863939	+	0.503596i	$0.832010\pi$
$864$		0			0
$865$	33.2509	+	20.4395i	1.13056	+	0.694965i
$866$	32.4036			1.10112
$867$		0			0
$868$		−	2.37346i		−	0.0805603i
$869$		−	3.53318i		−	0.119855i
$870$		0			0
$871$	−22.6456			−0.767317
$872$	40.2266	−	40.2266i	1.36225	−	1.36225i
$873$		0			0
$874$	−2.51522	+	2.51522i	−0.0850785	+	0.0850785i
$875$	−0.203161	+	2.45120i	−0.00686808	+	0.0828656i
$876$		0			0
$877$	18.7380	+	18.7380i	0.632737	+	0.632737i	0.948754	−	0.316017i	$-0.102346\pi$
$877$	18.7380	+	18.7380i	0.632737	+	0.632737i	−0.316017	+	0.948754i	$0.602346\pi$
$878$	−34.3728	−	34.3728i	−1.16003	−	1.16003i
$879$		0			0
$880$	−2.25761	−	1.38777i	−0.0761040	−	0.0467816i
$881$	7.77282	+	7.77282i	0.261873	+	0.261873i	0.825815	−	0.563942i	$-0.190716\pi$
$881$	7.77282	+	7.77282i	0.261873	+	0.261873i	−0.563942	+	0.825815i	$0.690716\pi$
$882$		0			0
$883$			56.2202i			1.89196i	0.324225	+	0.945980i	$0.394896\pi$
$883$			56.2202i			1.89196i	−0.324225	+	0.945980i	$0.605104\pi$
$884$	−16.2092	+	25.1976i	−0.545175	+	0.847486i
$885$		0			0
$886$		−	5.85481i		−	0.196696i
$887$	−4.87988	+	4.87988i	−0.163850	+	0.163850i	−0.784270	−	0.620420i	$-0.786962\pi$
$887$	−4.87988	+	4.87988i	−0.163850	+	0.163850i	0.620420	+	0.784270i	$0.286962\pi$
$888$		0			0
$889$	1.51522	+	1.51522i	0.0508187	+	0.0508187i
$890$	19.7963	+	82.9634i	0.663574	+	2.78094i
$891$		0			0
$892$	−7.26658			−0.243303
$893$	−26.9582			−0.902122
$894$		0			0
$895$	46.3815	−	11.0673i	1.55036	−	0.369940i
$896$	−3.22600	−	3.22600i	−0.107773	−	0.107773i
$897$		0			0
$898$	5.39465	−	5.39465i	0.180022	−	0.180022i
$899$		−	20.4520i		−	0.682113i
$900$		0			0
$901$	−20.5340	−	13.2092i	−0.684087	−	0.440063i
$902$			0.998442i			0.0332445i
$903$		0			0
$904$	−20.5488	−	20.5488i	−0.683443	−	0.683443i
$905$	27.5036	+	16.9066i	0.914249	+	0.561995i
$906$		0			0
$907$	−22.0708	−	22.0708i	−0.732849	−	0.732849i	0.238334	−	0.971183i	$-0.423399\pi$
$907$	−22.0708	−	22.0708i	−0.732849	−	0.732849i	−0.971183	+	0.238334i	$0.923399\pi$
$908$	−31.2361	−	31.2361i	−1.03661	−	1.03661i
$909$		0			0
$910$	−1.96713	−	1.20921i	−0.0652099	−	0.0400850i
$911$	−30.0472	+	30.0472i	−0.995509	+	0.995509i	−0.999990	−	0.00448095i	$-0.998574\pi$
$911$	−30.0472	+	30.0472i	−0.995509	+	0.995509i	0.00448095	+	0.999990i	$0.498574\pi$
$912$		0			0
$913$	2.27072	−	2.27072i	0.0751500	−	0.0751500i
$914$	−72.0164			−2.38209
$915$		0			0
$916$		−	34.3763i		−	1.13583i
$917$		−	4.33076i		−	0.143014i
$918$		0			0
$919$	−29.1312			−0.960949			−0.480475	−	0.877009i	$-0.659536\pi$
$919$	−29.1312			−0.960949			−0.480475	+	0.877009i	$0.659536\pi$
$920$	−1.76397	+	2.86962i	−0.0581565	+	0.0946085i
$921$		0			0
$922$		−	12.9220i		−	0.425562i
$923$	−9.96391	+	9.96391i	−0.327966	+	0.327966i
$924$		0			0
$925$	−8.90782	+	27.1593i	−0.292887	+	0.892994i
$926$			37.6004i			1.23562i
$927$		0			0
$928$	−13.3561	−	13.3561i	−0.438435	−	0.438435i
$929$	−0.921171	+	0.921171i	−0.0302226	+	0.0302226i	−0.722057	−	0.691834i	$-0.756803\pi$
$929$	−0.921171	+	0.921171i	−0.0302226	+	0.0302226i	0.691834	+	0.722057i	$0.256803\pi$
$930$		0			0
$931$	27.8064			0.911318
$932$	−67.3932	+	67.3932i	−2.20754	+	2.20754i
$933$		0			0
$934$	−25.6971			−0.840836
$935$	−2.09640	−	4.36220i	−0.0685595	−	0.142659i
$936$		0			0
$937$	−9.43458			−0.308214			−0.154107	−	0.988054i	$-0.549250\pi$
$937$	−9.43458			−0.308214			−0.154107	+	0.988054i	$0.549250\pi$
$938$	−4.27320	+	4.27320i	−0.139525	+	0.139525i
$939$		0			0
$940$	−54.1487	+	12.9207i	−1.76613	+	0.421426i
$941$	17.8033	−	17.8033i	0.580370	−	0.580370i	−0.354635	−	0.935005i	$-0.615395\pi$
$941$	17.8033	−	17.8033i	0.580370	−	0.580370i	0.935005	+	0.354635i	$0.115395\pi$
$942$		0			0
$943$	0.297042			0.00967302
$944$			13.5456i			0.440873i
$945$		0			0
$946$	−2.20921	+	2.20921i	−0.0718276	+	0.0718276i
$947$	−19.5564	+	19.5564i	−0.635496	+	0.635496i	−0.949441	−	0.313945i	$-0.898349\pi$
$947$	−19.5564	+	19.5564i	−0.635496	+	0.635496i	0.313945	+	0.949441i	$0.398349\pi$
$948$		0			0
$949$	1.64875	+	1.64875i	0.0535208	+	0.0535208i
$950$	21.5485	+	42.5824i	0.699126	+	1.38156i
$951$		0			0
$952$	0.777794	+	3.58308i	0.0252085	+	0.116128i
$953$		−	16.0279i		−	0.519195i	−0.965717	−	0.259598i	$-0.916410\pi$
$953$		−	16.0279i		−	0.519195i	0.965717	−	0.259598i	$-0.0835899\pi$
$954$		0			0
$955$	3.49923	+	14.6647i	0.113232	+	0.474540i
$956$	108.202			3.49949
$957$		0			0
$958$	62.2771	+	62.2771i	2.01208	+	2.01208i
$959$	0.724427	−	0.724427i	0.0233930	−	0.0233930i
$960$		0			0
$961$		−	22.4700i		−	0.724838i
$962$	−18.9742	−	18.9742i	−0.611752	−	0.611752i
$963$		0			0
$964$	22.1640	+	22.1640i	0.713853	+	0.713853i
$965$	17.1608	−	27.9171i	0.552426	−	0.898682i
$966$		0			0
$967$	10.9849			0.353252			0.176626	−	0.984278i	$-0.443482\pi$
$967$	10.9849			0.353252			0.176626	+	0.984278i	$0.443482\pi$
$968$		−	43.3506i		−	1.39334i
$969$		0			0
$970$	−41.8884	−	25.7491i	−1.34496	−	0.826753i
$971$			32.2944i			1.03638i	0.855267	+	0.518188i	$0.173393\pi$
$971$			32.2944i			1.03638i	−0.855267	+	0.518188i	$0.826607\pi$
$972$		0			0
$973$			1.15449i			0.0370113i
$974$	−64.6632	−	64.6632i	−2.07194	−	2.07194i
$975$		0			0
$976$	−9.03043	+	9.03043i	−0.289057	+	0.289057i
$977$	−2.59459			−0.0830084			−0.0415042	−	0.999138i	$-0.513215\pi$
$977$	−2.59459			−0.0830084			−0.0415042	+	0.999138i	$0.513215\pi$
$978$		0			0
$979$	5.93364	−	5.93364i	0.189640	−	0.189640i
$980$	55.8524	−	13.3272i	1.78414	−	0.425722i
$981$		0			0
$982$		−	90.7561i		−	2.89614i
$983$	6.79991	−	6.79991i	0.216883	−	0.216883i	−0.590300	−	0.807184i	$-0.700991\pi$
$983$	6.79991	−	6.79991i	0.216883	−	0.216883i	0.807184	+	0.590300i	$0.200991\pi$
$984$		0			0
$985$	−1.01796	+	1.65602i	−0.0324351	+	0.0527651i
$986$	14.6152	+	67.3279i	0.465442	+	2.14416i
$987$		0			0
$988$	−29.0663			−0.924723
$989$	0.657252	+	0.657252i	0.0208994	+	0.0208994i
$990$		0			0
$991$	19.9864	+	19.9864i	0.634888	+	0.634888i	0.949290	−	0.314402i	$-0.101804\pi$
$991$	19.9864	+	19.9864i	0.634888	+	0.634888i	−0.314402	+	0.949290i	$0.601804\pi$
$992$	5.57049	+	5.57049i	0.176863	+	0.176863i
$993$		0			0
$994$			3.76036i			0.119271i
$995$	−15.5745	+	25.3364i	−0.493744	+	0.803219i
$996$		0			0
$997$	−2.36593	−	2.36593i	−0.0749297	−	0.0749297i	0.668649	−	0.743578i	$-0.266873\pi$
$997$	−2.36593	−	2.36593i	−0.0749297	−	0.0749297i	−0.743578	+	0.668649i	$0.766873\pi$
$998$	−15.7022	+	15.7022i	−0.497045	+	0.497045i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	765.2.t.e.64.1		12
3.2	odd	2		85.2.j.c.64.6	yes	12
5.4	even	2	inner	765.2.t.e.64.6		12
15.2	even	4		425.2.e.d.251.6		12
15.8	even	4		425.2.e.d.251.1		12
15.14	odd	2		85.2.j.c.64.1	yes	12
17.4	even	4	inner	765.2.t.e.514.6		12
51.2	odd	8		1445.2.b.f.579.12		12
51.32	odd	8		1445.2.b.f.579.11		12
51.38	odd	4		85.2.j.c.4.1	✓	12
85.4	even	4	inner	765.2.t.e.514.1		12
255.2	even	8		7225.2.a.bp.1.2		12
255.32	even	8		7225.2.a.bp.1.1		12
255.38	even	4		425.2.e.d.276.6		12
255.53	even	8		7225.2.a.bp.1.11		12
255.83	even	8		7225.2.a.bp.1.12		12
255.89	odd	4		85.2.j.c.4.6	yes	12
255.104	odd	8		1445.2.b.f.579.1		12
255.134	odd	8		1445.2.b.f.579.2		12
255.242	even	4		425.2.e.d.276.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.1	✓	12	51.38	odd	4
85.2.j.c.4.6	yes	12	255.89	odd	4
85.2.j.c.64.1	yes	12	15.14	odd	2
85.2.j.c.64.6	yes	12	3.2	odd	2
425.2.e.d.251.1		12	15.8	even	4
425.2.e.d.251.6		12	15.2	even	4
425.2.e.d.276.1		12	255.242	even	4
425.2.e.d.276.6		12	255.38	even	4
765.2.t.e.64.1		12	1.1	even	1	trivial
765.2.t.e.64.6		12	5.4	even	2	inner
765.2.t.e.514.1		12	85.4	even	4	inner
765.2.t.e.514.6		12	17.4	even	4	inner
1445.2.b.f.579.1		12	255.104	odd	8
1445.2.b.f.579.2		12	255.134	odd	8
1445.2.b.f.579.11		12	51.32	odd	8
1445.2.b.f.579.12		12	51.2	odd	8
7225.2.a.bp.1.1		12	255.32	even	8
7225.2.a.bp.1.2		12	255.2	even	8
7225.2.a.bp.1.11		12	255.53	even	8
7225.2.a.bp.1.12		12	255.83	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 765 = 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	765.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.38621 q^{2} +3.69399 q^{4} +(0.518989 + 2.17501i) q^{5} +(-0.155559 - 0.155559i) q^{7} -4.04223 q^{8} +(-1.23842 - 5.19002i) q^{10} +(-0.371196 + 0.371196i) q^{11} +1.96713i q^{13} +(0.371196 + 0.371196i) q^{14} +2.25761 q^{16} +(3.46759 + 2.23065i) q^{17} +4.00000i q^{19} +(1.91714 + 8.03446i) q^{20} +(0.885751 - 0.885751i) q^{22} +(-0.263516 - 0.263516i) q^{23} +(-4.46130 + 2.25761i) q^{25} -4.69399i q^{26} +(-0.574634 - 0.574634i) q^{28} +(-4.95160 - 4.95160i) q^{29} +(2.06519 + 2.06519i) q^{31} +2.69733 q^{32} +(-8.27440 - 5.32280i) q^{34} +(0.257608 - 0.419075i) q^{35} +(4.04223 - 4.04223i) q^{37} -9.54484i q^{38} +(-2.09787 - 8.79187i) q^{40} +(-0.563613 + 0.563613i) q^{41} -2.49417 q^{43} +(-1.37120 + 1.37120i) q^{44} +(0.628804 + 0.628804i) q^{46} +6.73955i q^{47} -6.95160i q^{49} +(10.6456 - 5.38713i) q^{50} +7.26658i q^{52} -5.92169 q^{53} +(-1.00000 - 0.614707i) q^{55} +(0.628804 + 0.628804i) q^{56} +(11.8156 + 11.8156i) q^{58} +6.00000i q^{59} +(-4.00000 + 4.00000i) q^{61} +(-4.92798 - 4.92798i) q^{62} -10.9516 q^{64} +(-4.27853 + 1.02092i) q^{65} +11.5120i q^{67} +(12.8093 + 8.24001i) q^{68} +(-0.614707 + 1.00000i) q^{70} +(5.06519 + 5.06519i) q^{71} +(0.838149 - 0.838149i) q^{73} +(-9.64560 + 9.64560i) q^{74} +14.7760i q^{76} +0.115486 q^{77} +(-4.75919 + 4.75919i) q^{79} +(1.17167 + 4.91031i) q^{80} +(1.34490 - 1.34490i) q^{82} -6.11732 q^{83} +(-3.05204 + 8.69972i) q^{85} +5.95160 q^{86} +(1.50046 - 1.50046i) q^{88} -15.9852 q^{89} +(0.306005 - 0.306005i) q^{91} +(-0.973426 - 0.973426i) q^{92} -16.0820i q^{94} +(-8.70002 + 2.07596i) q^{95} +(6.51611 - 6.51611i) q^{97} +16.5880i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{4} - 4 q^{10} - 16 q^{11} + 16 q^{14} + 4 q^{16} + 32 q^{20} - 4 q^{29} + 4 q^{31} - 20 q^{35} + 24 q^{40} - 16 q^{41} - 28 q^{44} - 4 q^{46} + 40 q^{50} - 12 q^{55} - 4 q^{56} - 48 q^{61}+ \cdots + 36 q^{91}+O(q^{100}) \) 12 * q + 12 * q^4 - 4 * q^10 - 16 * q^11 + 16 * q^14 + 4 * q^16 + 32 * q^20 - 4 * q^29 + 4 * q^31 - 20 * q^35 + 24 * q^40 - 16 * q^41 - 28 * q^44 - 4 * q^46 + 40 * q^50 - 12 * q^55 - 4 * q^56 - 48 * q^61 - 76 * q^64 - 8 * q^65 + 40 * q^71 - 28 * q^74 - 4 * q^79 - 12 * q^80 - 52 * q^85 + 16 * q^86 + 16 * q^89 + 36 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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