LMFDB - Embedded newform 1120.2.bq.b.719.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(719,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))

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

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

chi := DirichletCharacter("1120.719");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bq (of order $6$, degree $2$, not 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:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			719.1
Character	$\chi$	$=$	1120.719
Dual form			1120.2.bq.b.1039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60233 - 2.77531i) q^{3} +(2.12896 + 0.683763i) q^{5} +(-2.23600 + 1.41432i) q^{7} +(-3.63491 + 6.29586i) q^{9} +O(q^{10})$	\(q+(-1.60233 - 2.77531i) q^{3} +(2.12896 + 0.683763i) q^{5} +(-2.23600 + 1.41432i) q^{7} +(-3.63491 + 6.29586i) q^{9} +(1.23701 + 2.14257i) q^{11} -2.90697i q^{13} +(-1.51364 - 7.00414i) q^{15} +(1.21515 + 2.10471i) q^{17} +(3.38329 + 1.95334i) q^{19} +(7.50799 + 3.93940i) q^{21} +(2.86568 - 4.96350i) q^{23} +(4.06494 + 2.91141i) q^{25} +13.6833 q^{27} -4.71148i q^{29} +(3.92617 + 6.80032i) q^{31} +(3.96419 - 6.86619i) q^{33} +(-5.72741 + 1.48213i) q^{35} +(1.67865 - 2.90751i) q^{37} +(-8.06775 + 4.65792i) q^{39} +5.75850i q^{41} -0.763818i q^{43} +(-12.0435 + 10.9182i) q^{45} +(2.86896 + 1.65640i) q^{47} +(2.99940 - 6.32484i) q^{49} +(3.89415 - 6.74487i) q^{51} +(-0.474139 - 0.821232i) q^{53} +(1.16854 + 5.40726i) q^{55} -12.5196i q^{57} +(6.41474 - 3.70355i) q^{59} +(-0.145254 + 0.251587i) q^{61} +(-0.776680 - 19.2185i) q^{63} +(1.98768 - 6.18882i) q^{65} +(-4.12005 + 2.37871i) q^{67} -18.3670 q^{69} -7.87114i q^{71} +(0.915891 + 1.58637i) q^{73} +(1.56671 - 15.9465i) q^{75} +(-5.79623 - 3.04125i) q^{77} +(1.69463 + 0.978393i) q^{79} +(-11.0205 - 19.0880i) q^{81} -6.61627 q^{83} +(1.14789 + 5.31172i) q^{85} +(-13.0758 + 7.54934i) q^{87} +(3.72584 + 2.15111i) q^{89} +(4.11138 + 6.49998i) q^{91} +(12.5820 - 21.7927i) q^{93} +(5.86726 + 6.47195i) q^{95} +15.9453 q^{97} -17.9857 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 52 q^{9}+O(q^{10}) $ 80 * q - 52 * q^9	$ 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) $ 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.60233	−	2.77531i	−0.925105	−	1.60233i	−0.791392	−	0.611308i	$-0.790644\pi$
$3$	−1.60233	−	2.77531i	−0.925105	−	1.60233i	−0.133712	−	0.991020i	$-0.542690\pi$
$4$		0			0
$5$	2.12896	+	0.683763i	0.952100	+	0.305788i
$5$	2.12896	+	0.683763i	0.952100	+	0.305788i
$6$		0			0
$7$	−2.23600	+	1.41432i	−0.845129	+	0.534562i
$7$	−2.23600	+	1.41432i	−0.845129	+	0.534562i
$8$		0			0
$9$	−3.63491	+	6.29586i	−1.21164	+	2.09862i
$10$		0			0
$11$	1.23701	+	2.14257i	0.372973	+	0.646008i	0.990021	−	0.140917i	$-0.0450052\pi$
$11$	1.23701	+	2.14257i	0.372973	+	0.646008i	−0.617049	+	0.786925i	$0.711672\pi$
$12$		0			0
$13$		−	2.90697i		−	0.806248i	−0.915145	−	0.403124i	$-0.867924\pi$
$13$		−	2.90697i		−	0.806248i	0.915145	−	0.403124i	$-0.132076\pi$
$14$		0			0
$15$	−1.51364	−	7.00414i	−0.390819	−	1.80846i
$16$		0			0
$17$	1.21515	+	2.10471i	0.294718	+	0.510467i	0.974919	−	0.222559i	$-0.0714409\pi$
$17$	1.21515	+	2.10471i	0.294718	+	0.510467i	−0.680201	+	0.733026i	$0.738108\pi$
$18$		0			0
$19$	3.38329	+	1.95334i	0.776179	+	0.448127i	0.835075	−	0.550137i	$-0.185424\pi$
$19$	3.38329	+	1.95334i	0.776179	+	0.448127i	−0.0588952	+	0.998264i	$0.518758\pi$
$20$		0			0
$21$	7.50799	+	3.93940i	1.63838	+	0.859648i
$22$		0			0
$23$	2.86568	−	4.96350i	0.597535	−	1.03496i	−0.395649	−	0.918402i	$-0.629480\pi$
$23$	2.86568	−	4.96350i	0.597535	−	1.03496i	0.993184	−	0.116559i	$-0.0371864\pi$
$24$		0			0
$25$	4.06494	+	2.91141i	0.812987	+	0.582281i
$26$		0			0
$27$	13.6833			2.63336
$28$		0			0
$29$		−	4.71148i		−	0.874900i	−0.899243	−	0.437450i	$-0.855882\pi$
$29$		−	4.71148i		−	0.874900i	0.899243	−	0.437450i	$-0.144118\pi$
$30$		0			0
$31$	3.92617	+	6.80032i	0.705161	+	1.22137i	0.966634	+	0.256163i	$0.0824584\pi$
$31$	3.92617	+	6.80032i	0.705161	+	1.22137i	−0.261473	+	0.965211i	$0.584208\pi$
$32$		0			0
$33$	3.96419	−	6.86619i	0.690078	−	1.19525i
$34$		0			0
$35$	−5.72741	+	1.48213i	−0.968110	+	0.250526i
$36$		0			0
$37$	1.67865	−	2.90751i	0.275969	−	0.477991i	−0.694411	−	0.719579i	$-0.744335\pi$
$37$	1.67865	−	2.90751i	0.275969	−	0.477991i	0.970379	+	0.241588i	$0.0776681\pi$
$38$		0			0
$39$	−8.06775	+	4.65792i	−1.29187	+	0.745864i
$40$		0			0
$41$			5.75850i			0.899327i	0.893198	+	0.449664i	$0.148456\pi$
$41$			5.75850i			0.899327i	−0.893198	+	0.449664i	$0.851544\pi$
$42$		0			0
$43$		−	0.763818i		−	0.116481i	−0.998303	−	0.0582406i	$-0.981451\pi$
$43$		−	0.763818i		−	0.116481i	0.998303	−	0.0582406i	$-0.0185491\pi$
$44$		0			0
$45$	−12.0435	+	10.9182i	−1.79533	+	1.62759i
$46$		0			0
$47$	2.86896	+	1.65640i	0.418481	+	0.241610i	0.694427	−	0.719563i	$-0.255658\pi$
$47$	2.86896	+	1.65640i	0.418481	+	0.241610i	−0.275946	+	0.961173i	$0.588991\pi$
$48$		0			0
$49$	2.99940	−	6.32484i	0.428486	−	0.903548i
$50$		0			0
$51$	3.89415	−	6.74487i	0.545290	−	0.944471i
$52$		0			0
$53$	−0.474139	−	0.821232i	−0.0651280	−	0.112805i	0.831623	−	0.555341i	$-0.187412\pi$
$53$	−0.474139	−	0.821232i	−0.0651280	−	0.112805i	−0.896751	+	0.442536i	$0.854079\pi$
$54$		0			0
$55$	1.16854	+	5.40726i	0.157566	+	0.729114i
$56$		0			0
$57$		−	12.5196i		−	1.65826i
$58$		0			0
$59$	6.41474	−	3.70355i	0.835128	−	0.482161i	−0.0204773	−	0.999790i	$-0.506519\pi$
$59$	6.41474	−	3.70355i	0.835128	−	0.482161i	0.855605	+	0.517629i	$0.173185\pi$
$60$		0			0
$61$	−0.145254	+	0.251587i	−0.0185978	+	0.0322124i	−0.875175	−	0.483807i	$-0.839254\pi$
$61$	−0.145254	+	0.251587i	−0.0185978	+	0.0322124i	0.856577	+	0.516020i	$0.172587\pi$
$62$		0			0
$63$	−0.776680	−	19.2185i	−0.0978524	−	2.42130i
$64$		0			0
$65$	1.98768	−	6.18882i	0.246541	−	0.767628i
$66$		0			0
$67$	−4.12005	+	2.37871i	−0.503344	+	0.290606i	−0.730094	−	0.683347i	$-0.760524\pi$
$67$	−4.12005	+	2.37871i	−0.503344	+	0.290606i	0.226749	+	0.973953i	$0.427190\pi$
$68$		0			0
$69$	−18.3670			−2.21113
$70$		0			0
$71$		−	7.87114i		−	0.934132i	−0.884222	−	0.467066i	$-0.845311\pi$
$71$		−	7.87114i		−	0.934132i	0.884222	−	0.467066i	$-0.154689\pi$
$72$		0			0
$73$	0.915891	+	1.58637i	0.107197	+	0.185671i	0.914634	−	0.404284i	$-0.132479\pi$
$73$	0.915891	+	1.58637i	0.107197	+	0.185671i	−0.807437	+	0.589954i	$0.799146\pi$
$74$		0			0
$75$	1.56671	−	15.9465i	0.180908	−	1.84134i
$76$		0			0
$77$	−5.79623	−	3.04125i	−0.660541	−	0.346583i
$78$		0			0
$79$	1.69463	+	0.978393i	0.190660	+	0.110078i	0.592292	−	0.805724i	$-0.298223\pi$
$79$	1.69463	+	0.978393i	0.190660	+	0.110078i	−0.401631	+	0.915801i	$0.631557\pi$
$80$		0			0
$81$	−11.0205	−	19.0880i	−1.22449	−	2.12089i
$82$		0			0
$83$	−6.61627			−0.726230			−0.363115	−	0.931744i	$-0.618287\pi$
$83$	−6.61627			−0.726230			−0.363115	+	0.931744i	$0.618287\pi$
$84$		0			0
$85$	1.14789	+	5.31172i	0.124506	+	0.576137i
$86$		0			0
$87$	−13.0758	+	7.54934i	−1.40188	+	0.809374i
$88$		0			0
$89$	3.72584	+	2.15111i	0.394938	+	0.228018i	0.684298	−	0.729203i	$-0.260109\pi$
$89$	3.72584	+	2.15111i	0.394938	+	0.228018i	−0.289359	+	0.957221i	$0.593442\pi$
$90$		0			0
$91$	4.11138	+	6.49998i	0.430990	+	0.681383i
$92$		0			0
$93$	12.5820	−	21.7927i	1.30469	−	2.25980i
$94$		0			0
$95$	5.86726	+	6.47195i	0.601968	+	0.664008i
$96$		0			0
$97$	15.9453			1.61900			0.809498	−	0.587123i	$-0.199739\pi$
$97$	15.9453			1.61900			0.809498	+	0.587123i	$0.199739\pi$
$98$		0			0
$99$	−17.9857			−1.80763
$100$		0			0
$101$	−6.08259	−	10.5354i	−0.605240	−	1.04831i	−0.992013	−	0.126132i	$-0.959744\pi$
$101$	−6.08259	−	10.5354i	−0.605240	−	1.04831i	0.386773	−	0.922175i	$-0.373590\pi$
$102$		0			0
$103$	10.9386	+	6.31541i	1.07781	+	0.622276i	0.930306	−	0.366785i	$-0.119542\pi$
$103$	10.9386	+	6.31541i	1.07781	+	0.622276i	0.147507	+	0.989061i	$0.452875\pi$
$104$		0			0
$105$	13.2906	+	13.5205i	1.29703	+	1.31947i
$106$		0			0
$107$	8.49616	+	4.90526i	0.821355	+	0.474209i	0.850883	−	0.525355i	$-0.176067\pi$
$107$	8.49616	+	4.90526i	0.821355	+	0.474209i	−0.0295287	+	0.999564i	$0.509401\pi$
$108$		0			0
$109$	2.87979	−	1.66265i	0.275834	−	0.159253i	−0.355702	−	0.934599i	$-0.615758\pi$
$109$	2.87979	−	1.66265i	0.275834	−	0.159253i	0.631536	+	0.775347i	$0.282425\pi$
$110$		0			0
$111$	−10.7590			−1.02120
$112$		0			0
$113$			6.24090i			0.587095i	0.955945	+	0.293547i	$0.0948358\pi$
$113$			6.24090i			0.587095i	−0.955945	+	0.293547i	$0.905164\pi$
$114$		0			0
$115$	9.49476	−	8.60764i	0.885391	−	0.802667i
$116$		0			0
$117$	18.3018	+	10.5666i	1.69201	+	0.976880i
$118$		0			0
$119$	−5.69382	−	2.98751i	−0.521951	−	0.273865i
$120$		0			0
$121$	2.43961	−	4.22553i	0.221783	−	0.384139i
$122$		0			0
$123$	15.9817	−	9.22701i	1.44102	−	0.831972i
$124$		0			0
$125$	6.66337	+	8.97772i	0.595990	+	0.802992i
$126$		0			0
$127$	−17.2612			−1.53169			−0.765843	−	0.643027i	$-0.777678\pi$
$127$	−17.2612			−1.53169			−0.765843	+	0.643027i	$0.777678\pi$
$128$		0			0
$129$	−2.11984	+	1.22389i	−0.186641	+	0.107757i
$130$		0			0
$131$	−1.77736	−	1.02616i	−0.155289	−	0.0896562i	0.420342	−	0.907366i	$-0.361910\pi$
$131$	−1.77736	−	1.02616i	−0.155289	−	0.0896562i	−0.575631	+	0.817710i	$0.695243\pi$
$132$		0			0
$133$	−10.3277	+	0.417375i	−0.895524	+	0.0361910i
$134$		0			0
$135$	29.1313	+	9.35616i	2.50722	+	0.805250i
$136$		0			0
$137$	−7.40950	+	4.27788i	−0.633036	+	0.365484i	−0.781927	−	0.623370i	$-0.785763\pi$
$137$	−7.40950	+	4.27788i	−0.633036	+	0.365484i	0.148891	+	0.988854i	$0.452430\pi$
$138$		0			0
$139$			13.3454i			1.13194i	0.824426	+	0.565970i	$0.191498\pi$
$139$			13.3454i			1.13194i	−0.824426	+	0.565970i	$0.808502\pi$
$140$		0			0
$141$		−	10.6164i		−	0.894059i
$142$		0			0
$143$	6.22837	−	3.59595i	0.520842	−	0.300708i
$144$		0			0
$145$	3.22154	−	10.0306i	0.267534	−	0.832992i
$146$		0			0
$147$	−22.3594	+	1.81019i	−1.84418	+	0.149302i
$148$		0			0
$149$	10.0494	+	5.80204i	0.823281	+	0.475321i	0.851547	−	0.524279i	$-0.175665\pi$
$149$	10.0494	+	5.80204i	0.823281	+	0.475321i	−0.0282658	+	0.999600i	$0.508998\pi$
$150$		0			0
$151$	13.4070	−	7.74053i	1.09104	−	0.629915i	0.157190	−	0.987568i	$-0.449756\pi$
$151$	13.4070	−	7.74053i	1.09104	−	0.629915i	0.933854	+	0.357653i	$0.116423\pi$
$152$		0			0
$153$	−17.6679			−1.42837
$154$		0			0
$155$	3.70884	+	17.1622i	0.297902	+	1.37850i
$156$		0			0
$157$	−1.73719	+	1.00296i	−0.138643	+	0.0800453i	−0.567717	−	0.823224i	$-0.692173\pi$
$157$	−1.73719	+	1.00296i	−0.138643	+	0.0800453i	0.429074	+	0.903269i	$0.358840\pi$
$158$		0			0
$159$	−1.51945	+	2.63177i	−0.120500	+	0.208713i
$160$		0			0
$161$	0.612315	+	15.1514i	0.0482572	+	1.19409i
$162$		0			0
$163$	−14.2898	−	8.25020i	−1.11926	−	0.646205i	−0.178048	−	0.984022i	$-0.556978\pi$
$163$	−14.2898	−	8.25020i	−1.11926	−	0.646205i	−0.941212	+	0.337816i	$0.890312\pi$
$164$		0			0
$165$	13.1345	−	11.9073i	1.02252	−	0.926979i
$166$		0			0
$167$		−	4.67196i		−	0.361527i	−0.983527	−	0.180763i	$-0.942143\pi$
$167$		−	4.67196i		−	0.361527i	0.983527	−	0.180763i	$-0.0578568\pi$
$168$		0			0
$169$	4.54954			0.349965
$170$		0			0
$171$	−24.5959	+	14.2005i	−1.88090	+	1.08594i
$172$		0			0
$173$	6.44746	+	3.72244i	0.490191	+	0.283012i	0.724654	−	0.689113i	$-0.242000\pi$
$173$	6.44746	+	3.72244i	0.490191	+	0.283012i	−0.234463	+	0.972125i	$0.575333\pi$
$174$		0			0
$175$	−13.2069	−	0.760790i	−0.998345	−	0.0575103i
$176$		0			0
$177$	−20.5570	−	11.8686i	−1.54516	−	0.892099i
$178$		0			0
$179$	4.86291	+	8.42281i	0.363471	+	0.629550i	0.988530	−	0.151028i	$-0.0482583\pi$
$179$	4.86291	+	8.42281i	0.363471	+	0.629550i	−0.625059	+	0.780578i	$0.714925\pi$
$180$		0			0
$181$	−5.72502			−0.425537			−0.212769	−	0.977103i	$-0.568248\pi$
$181$	−5.72502			−0.425537			−0.212769	+	0.977103i	$0.568248\pi$
$182$		0			0
$183$	0.930977			0.0688198
$184$		0			0
$185$	5.56183	−	5.04217i	0.408914	−	0.370708i
$186$		0			0
$187$	−3.00632	+	5.20709i	−0.219844	+	0.380780i
$188$		0			0
$189$	−30.5959	+	19.3526i	−2.22553	+	1.40769i
$190$		0			0
$191$	2.66537	+	1.53885i	0.192860	+	0.111347i	0.593321	−	0.804966i	$-0.297817\pi$
$191$	2.66537	+	1.53885i	0.192860	+	0.111347i	−0.400461	+	0.916314i	$0.631150\pi$
$192$		0			0
$193$	−16.3501	+	9.43976i	−1.17691	+	0.679488i	−0.955297	−	0.295647i	$-0.904465\pi$
$193$	−16.3501	+	9.43976i	−1.17691	+	0.679488i	−0.221611	+	0.975135i	$0.571132\pi$
$194$		0			0
$195$	−20.3608	+	4.40009i	−1.45807	+	0.315097i
$196$		0			0
$197$	4.81372			0.342964			0.171482	−	0.985187i	$-0.445145\pi$
$197$	4.81372			0.342964			0.171482	+	0.985187i	$0.445145\pi$
$198$		0			0
$199$	−12.0922	−	20.9442i	−0.857190	−	1.48470i	−0.874598	−	0.484848i	$-0.838875\pi$
$199$	−12.0922	−	20.9442i	−0.857190	−	1.48470i	0.0174086	−	0.999848i	$-0.494458\pi$
$200$		0			0
$201$	13.2034	+	7.62296i	0.931293	+	0.537682i
$202$		0			0
$203$	6.66354	+	10.5349i	0.467689	+	0.739404i
$204$		0			0
$205$	−3.93745	+	12.2596i	−0.275004	+	0.856249i
$206$		0			0
$207$	20.8330	+	36.0838i	1.44799	+	2.50800i
$208$		0			0
$209$			9.66522i			0.668557i
$210$		0			0
$211$	24.8628			1.71163			0.855814	−	0.517284i	$-0.173057\pi$
$211$	24.8628			1.71163			0.855814	+	0.517284i	$0.173057\pi$
$212$		0			0
$213$	−21.8449	+	12.6121i	−1.49679	+	0.864170i
$214$		0			0
$215$	0.522271	−	1.62614i	0.0356186	−	0.110902i
$216$		0			0
$217$	−18.3967	−	9.65267i	−1.24885	−	0.655266i
$218$		0			0
$219$	2.93512	−	5.08377i	0.198337	−	0.343529i
$220$		0			0
$221$	6.11832	−	3.53241i	0.411563	−	0.237616i
$222$		0			0
$223$			6.76281i			0.452871i	0.974026	+	0.226436i	$0.0727073\pi$
$223$			6.76281i			0.452871i	−0.974026	+	0.226436i	$0.927293\pi$
$224$		0			0
$225$	−33.1055	+	15.0095i	−2.20703	+	1.00064i
$226$		0			0
$227$	4.30970	+	7.46462i	0.286045	+	0.495444i	0.972862	−	0.231386i	$-0.0743260\pi$
$227$	4.30970	+	7.46462i	0.286045	+	0.495444i	−0.686817	+	0.726830i	$0.740993\pi$
$228$		0			0
$229$	−10.3387	+	17.9071i	−0.683200	+	1.18334i	0.290799	+	0.956784i	$0.406079\pi$
$229$	−10.3387	+	17.9071i	−0.683200	+	1.18334i	−0.973999	+	0.226552i	$0.927255\pi$
$230$		0			0
$231$	0.847038	+	20.9594i	0.0557310	+	1.37903i
$232$		0			0
$233$	19.1261	+	11.0424i	1.25299	+	0.723414i	0.971702	−	0.236210i	$-0.0759053\pi$
$233$	19.1261	+	11.0424i	1.25299	+	0.723414i	0.281287	+	0.959624i	$0.409239\pi$
$234$		0			0
$235$	4.97532	+	5.48809i	0.324554	+	0.358003i
$236$		0			0
$237$		−	6.27083i		−	0.407334i
$238$		0			0
$239$			10.7855i			0.697656i	0.937187	+	0.348828i	$0.113420\pi$
$239$			10.7855i			0.697656i	−0.937187	+	0.348828i	$0.886580\pi$
$240$		0			0
$241$	−15.4652	+	8.92882i	−0.996200	+	0.575156i	−0.907122	−	0.420868i	$-0.861725\pi$
$241$	−15.4652	+	8.92882i	−0.996200	+	0.575156i	−0.0890780	+	0.996025i	$0.528392\pi$
$242$		0			0
$243$	−14.7918	+	25.6201i	−0.948893	+	1.64353i
$244$		0			0
$245$	10.7103	−	11.4144i	0.684256	−	0.729242i
$246$		0			0
$247$	5.67830	−	9.83511i	0.361302	−	0.625793i
$248$		0			0
$249$	10.6014	+	18.3622i	0.671839	+	1.16366i
$250$		0			0
$251$		−	11.0237i		−	0.695810i	−0.937530	−	0.347905i	$-0.886893\pi$
$251$		−	11.0237i		−	0.695810i	0.937530	−	0.347905i	$-0.113107\pi$
$252$		0			0
$253$	14.1795			0.891457
$254$		0			0
$255$	12.9024	−	11.6969i	0.807979	−	0.732487i
$256$		0			0
$257$	−15.5353	+	26.9079i	−0.969065	+	1.67847i	−0.270793	+	0.962638i	$0.587286\pi$
$257$	−15.5353	+	26.9079i	−0.969065	+	1.67847i	−0.698272	+	0.715832i	$0.746048\pi$
$258$		0			0
$259$	0.358681	+	8.87534i	0.0222873	+	0.551487i
$260$		0			0
$261$	29.6628	+	17.1258i	1.83608	+	1.06006i
$262$		0			0
$263$	−9.32868	−	16.1577i	−0.575231	−	0.996329i	−0.996017	−	0.0891689i	$-0.971579\pi$
$263$	−9.32868	−	16.1577i	−0.575231	−	0.996329i	0.420786	−	0.907160i	$-0.361754\pi$
$264$		0			0
$265$	−0.447894	−	2.07257i	−0.0275139	−	0.127317i
$266$		0			0
$267$		−	13.7872i		−	0.843761i
$268$		0			0
$269$	1.41984	+	2.45923i	0.0865689	+	0.149942i	0.906059	−	0.423152i	$-0.139076\pi$
$269$	1.41984	+	2.45923i	0.0865689	+	0.149942i	−0.819490	+	0.573094i	$0.805743\pi$
$270$		0			0
$271$	9.37179	−	16.2324i	0.569296	−	0.986049i	−0.427340	−	0.904091i	$-0.640549\pi$
$271$	9.37179	−	16.2324i	0.569296	−	0.986049i	0.996636	−	0.0819580i	$-0.0261173\pi$
$272$		0			0
$273$	11.4517	−	21.8255i	0.693089	−	1.32094i
$274$		0			0
$275$	−1.20951	+	12.3108i	−0.0729362	+	0.742371i
$276$		0			0
$277$	−11.9110	−	20.6304i	−0.715661	−	1.23956i	−0.962704	−	0.270557i	$-0.912792\pi$
$277$	−11.9110	−	20.6304i	−0.715661	−	1.23956i	0.247043	−	0.969004i	$-0.420541\pi$
$278$		0			0
$279$	−57.0851			−3.41760
$280$		0			0
$281$	10.3608			0.618073			0.309037	−	0.951050i	$-0.399993\pi$
$281$	10.3608			0.618073			0.309037	+	0.951050i	$0.399993\pi$
$282$		0			0
$283$	−4.67454	−	8.09653i	−0.277872	−	0.481289i	0.692983	−	0.720953i	$-0.256296\pi$
$283$	−4.67454	−	8.09653i	−0.277872	−	0.481289i	−0.970856	+	0.239665i	$0.922963\pi$
$284$		0			0
$285$	8.56043	−	26.6537i	0.507076	−	1.57883i
$286$		0			0
$287$	−8.14436	−	12.8760i	−0.480747	−	0.760047i
$288$		0			0
$289$	5.54680	−	9.60734i	0.326282	−	0.565138i
$290$		0			0
$291$	−25.5495	−	44.2531i	−1.49774	−	2.59416i
$292$		0			0
$293$			16.0747i			0.939094i	0.882907	+	0.469547i	$0.155583\pi$
$293$			16.0747i			0.939094i	−0.882907	+	0.469547i	$0.844417\pi$
$294$		0			0
$295$	16.1891	−	3.49855i	0.942564	−	0.203693i
$296$		0			0
$297$	16.9264	+	29.3174i	0.982171	+	1.70117i
$298$		0			0
$299$	−14.4287	−	8.33043i	−0.834435	−	0.481761i
$300$		0			0
$301$	1.08028	+	1.70790i	0.0622665	+	0.0984417i
$302$		0			0
$303$	−19.4926	+	33.7622i	−1.11982	+	1.93959i
$304$		0			0
$305$	−0.481265	+	0.436299i	−0.0275572	+	0.0249824i
$306$		0			0
$307$	14.9824			0.855091			0.427545	−	0.903994i	$-0.359378\pi$
$307$	14.9824			0.855091			0.427545	+	0.903994i	$0.359378\pi$
$308$		0			0
$309$		−	40.4774i		−	2.30268i
$310$		0			0
$311$	15.4750	+	26.8036i	0.877509	+	1.51989i	0.854066	+	0.520165i	$0.174130\pi$
$311$	15.4750	+	26.8036i	0.877509	+	1.51989i	0.0234437	+	0.999725i	$0.492537\pi$
$312$		0			0
$313$	1.57151	−	2.72194i	0.0888271	−	0.153853i	−0.818189	−	0.574950i	$-0.805021\pi$
$313$	1.57151	−	2.72194i	0.0888271	−	0.153853i	0.907016	+	0.421097i	$0.138355\pi$
$314$		0			0
$315$	11.4874	−	41.4464i	0.647239	−	2.33524i
$316$		0			0
$317$	1.89262	−	3.27812i	0.106300	−	0.184118i	−0.807968	−	0.589226i	$-0.799433\pi$
$317$	1.89262	−	3.27812i	0.106300	−	0.184118i	0.914269	+	0.405108i	$0.132766\pi$
$318$		0			0
$319$	10.0947	−	5.82815i	0.565192	−	0.326314i
$320$		0			0
$321$		−	31.4393i		−	1.75477i
$322$		0			0
$323$			9.49444i			0.528285i
$324$		0			0
$325$	8.46336	−	11.8166i	0.469463	−	0.655469i
$326$		0			0
$327$	−9.22873	−	5.32821i	−0.510350	−	0.294651i
$328$		0			0
$329$	−8.75767	+	0.353925i	−0.482826	+	0.0195125i
$330$		0			0
$331$	3.83340	−	6.63965i	0.210703	−	0.364948i	−0.741232	−	0.671249i	$-0.765758\pi$
$331$	3.83340	−	6.63965i	0.210703	−	0.364948i	0.951935	+	0.306301i	$0.0990914\pi$
$332$		0			0
$333$	12.2035	+	21.1371i	0.668748	+	1.15831i
$334$		0			0
$335$	−10.3979	+	2.24704i	−0.568098	+	0.122769i
$336$		0			0
$337$		−	24.8688i		−	1.35469i	−0.735667	−	0.677344i	$-0.763131\pi$
$337$		−	24.8688i		−	1.35469i	0.735667	−	0.677344i	$-0.236869\pi$
$338$		0			0
$339$	17.3205	−	9.99998i	0.940719	−	0.543124i
$340$		0			0
$341$	−9.71342	+	16.8241i	−0.526011	+	0.911078i
$342$		0			0
$343$	2.23868	+	18.3845i	0.120877	+	0.992667i
$344$		0			0
$345$	−39.1026	−	12.5587i	−2.10522	−	0.676137i
$346$		0			0
$347$	−19.3450	+	11.1689i	−1.03850	+	0.599576i	−0.919407	−	0.393308i	$-0.871331\pi$
$347$	−19.3450	+	11.1689i	−1.03850	+	0.599576i	−0.119089	+	0.992884i	$0.537997\pi$
$348$		0			0
$349$	−6.23220			−0.333602			−0.166801	−	0.985991i	$-0.553344\pi$
$349$	−6.23220			−0.333602			−0.166801	+	0.985991i	$0.553344\pi$
$350$		0			0
$351$		−	39.7770i		−	2.12314i
$352$		0			0
$353$	5.05250	+	8.75119i	0.268918	+	0.465779i	0.968583	−	0.248692i	$-0.0800008\pi$
$353$	5.05250	+	8.75119i	0.268918	+	0.465779i	−0.699665	+	0.714471i	$0.746667\pi$
$354$		0			0
$355$	5.38199	−	16.7573i	0.285646	−	0.889387i
$356$		0			0
$357$	0.832072	+	20.5891i	0.0440379	+	1.08969i
$358$		0			0
$359$	−18.4425	−	10.6478i	−0.973359	−	0.561969i	−0.0731003	−	0.997325i	$-0.523289\pi$
$359$	−18.4425	−	10.6478i	−0.973359	−	0.561969i	−0.900259	+	0.435356i	$0.856623\pi$
$360$		0			0
$361$	−1.86891	−	3.23705i	−0.0983638	−	0.170371i
$362$		0			0
$363$	−15.6362			−0.820689
$364$		0			0
$365$	0.865194	+	4.00357i	0.0452863	+	0.209556i
$366$		0			0
$367$	26.2490	−	15.1549i	1.37019	−	0.791077i	0.379234	−	0.925301i	$-0.376187\pi$
$367$	26.2490	−	15.1549i	1.37019	−	0.791077i	0.990951	+	0.134224i	$0.0428541\pi$
$368$		0			0
$369$	−36.2547	−	20.9317i	−1.88734	−	1.08966i
$370$		0			0
$371$	2.22166	+	1.16569i	0.115343	+	0.0605198i
$372$		0			0
$373$	−11.6702	+	20.2134i	−0.604260	+	1.04661i	0.387908	+	0.921698i	$0.373198\pi$
$373$	−11.6702	+	20.2134i	−0.604260	+	1.04661i	−0.992168	+	0.124911i	$0.960136\pi$
$374$		0			0
$375$	14.2391	−	32.8782i	0.735303	−	1.69782i
$376$		0			0
$377$	−13.6961			−0.705386
$378$		0			0
$379$	−9.55433			−0.490773			−0.245387	−	0.969425i	$-0.578915\pi$
$379$	−9.55433			−0.490773			−0.245387	+	0.969425i	$0.578915\pi$
$380$		0			0
$381$	27.6582	+	47.9053i	1.41697	+	2.45427i
$382$		0			0
$383$	16.2249	+	9.36744i	0.829052	+	0.478654i	0.853528	−	0.521047i	$-0.174458\pi$
$383$	16.2249	+	9.36744i	0.829052	+	0.478654i	−0.0244757	+	0.999700i	$0.507792\pi$
$384$		0			0
$385$	−10.2604	−	10.4379i	−0.522920	−	0.531967i
$386$		0			0
$387$	4.80889	+	2.77641i	0.244450	+	0.141133i
$388$		0			0
$389$	−18.5104	+	10.6870i	−0.938515	+	0.541852i	−0.889494	−	0.456946i	$-0.848943\pi$
$389$	−18.5104	+	10.6870i	−0.938515	+	0.541852i	−0.0490204	+	0.998798i	$0.515610\pi$
$390$		0			0
$391$	13.9290			0.704417
$392$		0			0
$393$			6.57699i			0.331765i
$394$		0			0
$395$	2.93880	+	3.24168i	0.147867	+	0.163107i
$396$		0			0
$397$	−0.251200	−	0.145030i	−0.0126073	−	0.00727885i	0.493683	−	0.869642i	$-0.335650\pi$
$397$	−0.251200	−	0.145030i	−0.0126073	−	0.00727885i	−0.506290	+	0.862363i	$0.668984\pi$
$398$		0			0
$399$	17.7067	+	27.9938i	0.886443	+	1.40144i
$400$		0			0
$401$	13.4012	−	23.2115i	0.669223	−	1.15913i	−0.308899	−	0.951095i	$-0.599960\pi$
$401$	13.4012	−	23.2115i	0.669223	−	1.15913i	0.978122	−	0.208033i	$-0.0667063\pi$
$402$		0			0
$403$	19.7683	−	11.4132i	0.984730	−	0.568534i
$404$		0			0
$405$	−10.4104	−	48.1729i	−0.517299	−	2.39373i
$406$		0			0
$407$	8.30603			0.411715
$408$		0			0
$409$	11.0759	−	6.39466i	0.547667	−	0.316195i	−0.200514	−	0.979691i	$-0.564261\pi$
$409$	11.0759	−	6.39466i	0.547667	−	0.316195i	0.748180	+	0.663495i	$0.230928\pi$
$410$		0			0
$411$	23.7449	+	13.7091i	1.17125	+	0.676221i
$412$		0			0
$413$	−9.10536	+	17.3536i	−0.448045	+	0.853916i
$414$		0			0
$415$	−14.0858	−	4.52396i	−0.691444	−	0.222073i
$416$		0			0
$417$	37.0376	−	21.3837i	1.81374	−	1.04716i
$418$		0			0
$419$		−	11.3606i		−	0.555002i	−0.960725	−	0.277501i	$-0.910494\pi$
$419$		−	11.3606i		−	0.555002i	0.960725	−	0.277501i	$-0.0895062\pi$
$420$		0			0
$421$		−	36.1939i		−	1.76398i	−0.471266	−	0.881991i	$-0.656203\pi$
$421$		−	36.1939i		−	1.76398i	0.471266	−	0.881991i	$-0.343797\pi$
$422$		0			0
$423$	−20.8569	+	12.0417i	−1.01409	+	0.585488i
$424$		0			0
$425$	−1.18814	+	12.0933i	−0.0576332	+	0.586612i
$426$		0			0
$427$	−0.0310367	−	0.767984i	−0.00150197	−	0.0371654i
$428$		0			0
$429$	−19.9598	−	11.5238i	−0.963667	−	0.556374i
$430$		0			0
$431$	−26.0484	+	15.0391i	−1.25471	+	0.724406i	−0.972041	−	0.234812i	$-0.924552\pi$
$431$	−26.0484	+	15.0391i	−1.25471	+	0.724406i	−0.282667	+	0.959218i	$0.591219\pi$
$432$		0			0
$433$	−13.9510			−0.670442			−0.335221	−	0.942139i	$-0.608811\pi$
$433$	−13.9510			−0.670442			−0.335221	+	0.942139i	$0.608811\pi$
$434$		0			0
$435$	−32.9999	+	7.13147i	−1.58222	+	0.341928i
$436$		0			0
$437$	19.3908	−	11.1953i	0.927588	−	0.535543i
$438$		0			0
$439$	−5.58413	+	9.67200i	−0.266516	+	0.461619i	−0.967960	−	0.251106i	$-0.919206\pi$
$439$	−5.58413	+	9.67200i	−0.266516	+	0.461619i	0.701444	+	0.712725i	$0.252539\pi$
$440$		0			0
$441$	28.9177	+	41.8740i	1.37703	+	1.99400i
$442$		0			0
$443$	16.0785	+	9.28292i	0.763912	+	0.441045i	0.830699	−	0.556722i	$-0.187941\pi$
$443$	16.0785	+	9.28292i	0.763912	+	0.441045i	−0.0667865	+	0.997767i	$0.521275\pi$
$444$		0			0
$445$	6.46131	+	7.12722i	0.306295	+	0.337863i
$446$		0			0
$447$		−	37.1871i		−	1.75889i
$448$		0			0
$449$	−8.39895			−0.396371			−0.198186	−	0.980165i	$-0.563505\pi$
$449$	−8.39895			−0.396371			−0.198186	+	0.980165i	$0.563505\pi$
$450$		0			0
$451$	−12.3380	+	7.12333i	−0.580972	+	0.335424i
$452$		0			0
$453$	−42.9648	−	24.8057i	−2.01866	−	1.16547i
$454$		0			0
$455$	4.30852	+	16.6494i	0.201986	+	0.780536i
$456$		0			0
$457$	24.5026	+	14.1466i	1.14618	+	0.661749i	0.947954	−	0.318406i	$-0.103148\pi$
$457$	24.5026	+	14.1466i	1.14618	+	0.661749i	0.198229	+	0.980156i	$0.436481\pi$
$458$		0			0
$459$	16.6274	+	28.7994i	0.776099	+	1.34424i
$460$		0			0
$461$	−31.5889			−1.47124			−0.735621	−	0.677393i	$-0.763110\pi$
$461$	−31.5889			−1.47124			−0.735621	+	0.677393i	$0.763110\pi$
$462$		0			0
$463$	−20.6027			−0.957487			−0.478744	−	0.877955i	$-0.658908\pi$
$463$	−20.6027			−0.957487			−0.478744	+	0.877955i	$0.658908\pi$
$464$		0			0
$465$	41.6877	−	37.7927i	1.93322	−	1.75259i
$466$		0			0
$467$	8.18604	−	14.1786i	0.378805	−	0.656109i	−0.612084	−	0.790793i	$-0.709669\pi$
$467$	8.18604	−	14.1786i	0.378805	−	0.656109i	0.990889	+	0.134684i	$0.0430019\pi$
$468$		0			0
$469$	5.84818	−	11.1459i	0.270044	−	0.514669i
$470$		0			0
$471$	5.56708	+	3.21416i	0.256518	+	0.148101i
$472$		0			0
$473$	1.63653	−	0.944851i	0.0752478	−	0.0434443i
$474$		0			0
$475$	8.06588	+	17.7903i	0.370088	+	0.816277i
$476$		0			0
$477$	6.89381			0.315646
$478$		0			0
$479$	18.7679	+	32.5069i	0.857526	+	1.48528i	0.874282	+	0.485419i	$0.161333\pi$
$479$	18.7679	+	32.5069i	0.857526	+	1.48528i	−0.0167554	+	0.999860i	$0.505334\pi$
$480$		0			0
$481$	−8.45203	−	4.87978i	−0.385379	−	0.222499i
$482$		0			0
$483$	41.0687	−	25.9768i	1.86869	−	1.18199i
$484$		0			0
$485$	33.9468	+	10.9028i	1.54145	+	0.495070i
$486$		0			0
$487$	−12.1439	−	21.0339i	−0.550294	−	0.953138i	−0.998253	−	0.0590835i	$-0.981182\pi$
$487$	−12.1439	−	21.0339i	−0.550294	−	0.953138i	0.447959	−	0.894054i	$-0.352151\pi$
$488$		0			0
$489$			52.8781i			2.39123i
$490$		0			0
$491$	−15.9769			−0.721025			−0.360513	−	0.932754i	$-0.617398\pi$
$491$	−15.9769			−0.721025			−0.360513	+	0.932754i	$0.617398\pi$
$492$		0			0
$493$	9.91630	−	5.72518i	0.446608	−	0.257849i
$494$		0			0
$495$	−38.2908	−	12.2980i	−1.72105	−	0.552752i
$496$		0			0
$497$	11.1323	+	17.5999i	0.499352	+	0.789462i
$498$		0			0
$499$	−7.03517	+	12.1853i	−0.314937	+	0.545487i	−0.979424	−	0.201813i	$-0.935317\pi$
$499$	−7.03517	+	12.1853i	−0.314937	+	0.545487i	0.664487	+	0.747300i	$0.268650\pi$
$500$		0			0
$501$	−12.9661	+	7.48601i	−0.579285	+	0.334450i
$502$		0			0
$503$			8.77499i			0.391258i	0.980678	+	0.195629i	$0.0626748\pi$
$503$			8.77499i			0.391258i	−0.980678	+	0.195629i	$0.937325\pi$
$504$		0			0
$505$	−5.74590	−	26.5884i	−0.255689	−	1.18317i
$506$		0			0
$507$	−7.28986	−	12.6264i	−0.323754	−	0.560758i
$508$		0			0
$509$	17.8686	−	30.9493i	0.792011	−	1.37180i	−0.132709	−	0.991155i	$-0.542367\pi$
$509$	17.8686	−	30.9493i	0.792011	−	1.37180i	0.924720	−	0.380649i	$-0.124299\pi$
$510$		0			0
$511$	−4.29157	−	2.25176i	−0.189848	−	0.0996121i
$512$		0			0
$513$	46.2946	+	26.7282i	2.04396	+	1.18008i
$514$		0			0
$515$	18.9696	+	20.9247i	0.835901	+	0.922051i
$516$		0			0
$517$			8.19591i			0.360456i
$518$		0			0
$519$		−	23.8583i		−	1.04726i
$520$		0			0
$521$	−34.6318	+	19.9947i	−1.51724	+	0.875982i	−0.517450	+	0.855713i	$0.673119\pi$
$521$	−34.6318	+	19.9947i	−1.51724	+	0.875982i	−0.999795	+	0.0202683i	$0.993548\pi$
$522$		0			0
$523$	−17.3266	+	30.0106i	−0.757641	+	1.31227i	0.186409	+	0.982472i	$0.440315\pi$
$523$	−17.3266	+	30.0106i	−0.757641	+	1.31227i	−0.944050	+	0.329801i	$0.893018\pi$
$524$		0			0
$525$	19.0503	+	37.8722i	0.831423	+	1.65288i
$526$		0			0
$527$	−9.54180	+	16.5269i	−0.415647	+	0.719922i
$528$		0			0
$529$	−4.92420	−	8.52897i	−0.214096	−	0.370825i
$530$		0			0
$531$			53.8484i			2.33682i
$532$		0			0
$533$	16.7398			0.725080
$534$		0			0
$535$	14.7339	+	16.2525i	0.637004	+	0.702655i
$536$		0			0
$537$	15.5840	−	26.9922i	0.672497	−	1.16480i
$538$		0			0
$539$	17.2617	−	1.39748i	0.743513	−	0.0601938i
$540$		0			0
$541$	−24.2321	−	13.9904i	−1.04182	−	0.601495i	−0.121472	−	0.992595i	$-0.538761\pi$
$541$	−24.2321	−	13.9904i	−1.04182	−	0.601495i	−0.920348	+	0.391100i	$0.872095\pi$
$542$		0			0
$543$	9.17336	+	15.8887i	0.393667	+	0.681851i
$544$		0			0
$545$	7.26781	−	1.57061i	0.311319	−	0.0672777i
$546$		0			0
$547$		−	11.5628i		−	0.494391i	−0.968966	−	0.247196i	$-0.920491\pi$
$547$		−	11.5628i		−	0.494391i	0.968966	−	0.247196i	$-0.0795090\pi$
$548$		0			0
$549$	−1.05597	−	1.82899i	−0.0450677	−	0.0780596i
$550$		0			0
$551$	9.20314	−	15.9403i	0.392067	−	0.679080i
$552$		0			0
$553$	−5.17295	+	0.209055i	−0.219976	+	0.00888993i
$554$		0			0
$555$	−22.9055	−	7.35661i	−0.972283	−	0.312271i
$556$		0			0
$557$	−22.6698	−	39.2653i	−0.960552	−	1.66372i	−0.721118	−	0.692812i	$-0.756371\pi$
$557$	−22.6698	−	39.2653i	−0.960552	−	1.66372i	−0.239434	−	0.970913i	$-0.576962\pi$
$558$		0			0
$559$	−2.22040			−0.0939127
$560$		0			0
$561$	19.2684			0.813514
$562$		0			0
$563$	−5.15902	−	8.93569i	−0.217427	−	0.376594i	0.736594	−	0.676335i	$-0.236433\pi$
$563$	−5.15902	−	8.93569i	−0.217427	−	0.376594i	−0.954021	+	0.299741i	$0.903100\pi$
$564$		0			0
$565$	−4.26730	+	13.2866i	−0.179527	+	0.558973i
$566$		0			0
$567$	51.6383	+	27.0943i	2.16860	+	1.13785i
$568$		0			0
$569$	−4.72049	+	8.17613i	−0.197893	+	0.342761i	−0.947845	−	0.318731i	$-0.896743\pi$
$569$	−4.72049	+	8.17613i	−0.197893	+	0.342761i	0.749952	+	0.661492i	$0.230077\pi$
$570$		0			0
$571$	−14.8128	−	25.6565i	−0.619895	−	1.07369i	−0.989504	−	0.144503i	$-0.953842\pi$
$571$	−14.8128	−	25.6565i	−0.619895	−	1.07369i	0.369609	−	0.929187i	$-0.379492\pi$
$572$		0			0
$573$		−	9.86299i		−	0.412032i
$574$		0			0
$575$	26.0996	−	11.8332i	1.08843	−	0.493477i
$576$		0			0
$577$	−7.61237	−	13.1850i	−0.316907	−	0.548899i	0.662934	−	0.748678i	$-0.269311\pi$
$577$	−7.61237	−	13.1850i	−0.316907	−	0.548899i	−0.979841	+	0.199779i	$0.935978\pi$
$578$		0			0
$579$	52.3966	+	30.2512i	2.17753	+	1.25720i
$580$		0			0
$581$	14.7940	−	9.35752i	0.613758	−	0.388216i
$582$		0			0
$583$	1.17303	−	2.03175i	0.0485819	−	0.0841463i
$584$		0			0
$585$	31.7389	+	35.0099i	1.31224	+	1.44748i
$586$		0			0
$587$	−24.3201			−1.00380			−0.501899	−	0.864926i	$-0.667365\pi$
$587$	−24.3201			−1.00380			−0.501899	+	0.864926i	$0.667365\pi$
$588$		0			0
$589$			30.6766i			1.26401i
$590$		0			0
$591$	−7.71317	−	13.3596i	−0.317277	−	0.549540i
$592$		0			0
$593$	4.82898	−	8.36403i	0.198302	−	0.343470i	−0.749676	−	0.661805i	$-0.769791\pi$
$593$	4.82898	−	8.36403i	0.198302	−	0.343470i	0.947978	+	0.318336i	$0.103124\pi$
$594$		0			0
$595$	−10.0792	−	10.2535i	−0.413205	−	0.420353i
$596$		0			0
$597$	−38.7512	+	67.1190i	−1.58598	+	2.74700i
$598$		0			0
$599$	9.10218	−	5.25515i	0.371905	−	0.214719i	−0.302385	−	0.953186i	$-0.597783\pi$
$599$	9.10218	−	5.25515i	0.371905	−	0.214719i	0.674290	+	0.738466i	$0.264450\pi$
$600$		0			0
$601$			9.14888i			0.373191i	0.982437	+	0.186595i	$0.0597453\pi$
$601$			9.14888i			0.373191i	−0.982437	+	0.186595i	$0.940255\pi$
$602$		0			0
$603$		−	34.5857i		−	1.40844i
$604$		0			0
$605$	8.08309	−	7.32786i	0.328624	−	0.297920i
$606$		0			0
$607$	−42.1138	−	24.3144i	−1.70935	−	0.986892i	−0.935366	−	0.353682i	$-0.884929\pi$
$607$	−42.1138	−	24.3144i	−1.70935	−	0.986892i	−0.773981	−	0.633209i	$-0.781737\pi$
$608$		0			0
$609$	18.5604	−	35.3738i	0.752106	−	1.43342i
$610$		0			0
$611$	4.81509	−	8.33998i	0.194798	−	0.337399i
$612$		0			0
$613$	2.92021	+	5.05795i	0.117946	+	0.204289i	0.918954	−	0.394366i	$-0.129036\pi$
$613$	2.92021	+	5.05795i	0.117946	+	0.204289i	−0.801008	+	0.598654i	$0.795702\pi$
$614$		0			0
$615$	40.3334	−	8.71627i	1.62640	−	0.351474i
$616$		0			0
$617$			49.5048i			1.99299i	0.0836564	+	0.996495i	$0.473340\pi$
$617$			49.5048i			1.99299i	−0.0836564	+	0.996495i	$0.526660\pi$
$618$		0			0
$619$	−8.25280	+	4.76475i	−0.331708	+	0.191512i	−0.656599	−	0.754240i	$-0.728006\pi$
$619$	−8.25280	+	4.76475i	−0.331708	+	0.191512i	0.324891	+	0.945751i	$0.394672\pi$
$620$		0			0
$621$	39.2120	−	67.9172i	1.57352	−	2.72542i
$622$		0			0
$623$	−11.3733	+	0.459633i	−0.455663	+	0.0184148i
$624$		0			0
$625$	8.04742	+	23.6694i	0.321897	+	0.946775i
$626$		0			0
$627$	26.8240	−	15.4869i	1.07125	−	0.618485i
$628$		0			0
$629$	8.15928			0.325332
$630$		0			0
$631$		−	7.60958i		−	0.302933i	−0.988462	−	0.151466i	$-0.951601\pi$
$631$		−	7.60958i		−	0.302933i	0.988462	−	0.151466i	$-0.0483995\pi$
$632$		0			0
$633$	−39.8384	−	69.0021i	−1.58343	−	2.74259i
$634$		0			0
$635$	−36.7485	−	11.8026i	−1.45832	−	0.468371i
$636$		0			0
$637$	−18.3861	−	8.71916i	−0.728484	−	0.345466i
$638$		0			0
$639$	49.5555	+	28.6109i	1.96039	+	1.13183i
$640$		0			0
$641$	−10.7911	−	18.6907i	−0.426222	−	0.738238i	0.570312	−	0.821428i	$-0.306822\pi$
$641$	−10.7911	−	18.6907i	−0.426222	−	0.738238i	−0.996534	+	0.0831906i	$0.973489\pi$
$642$		0			0
$643$	35.1575			1.38648			0.693239	−	0.720708i	$-0.256183\pi$
$643$	35.1575			1.38648			0.693239	+	0.720708i	$0.256183\pi$
$644$		0			0
$645$	−5.34990	+	1.15614i	−0.210652	+	0.0455231i
$646$		0			0
$647$	0.0712919	−	0.0411604i	0.00280277	−	0.00161818i	−0.498598	−	0.866833i	$-0.666152\pi$
$647$	0.0712919	−	0.0411604i	0.00280277	−	0.00161818i	0.501401	+	0.865215i	$0.332818\pi$
$648$		0			0
$649$	15.8702	+	9.16266i	0.622960	+	0.359666i
$650$		0			0
$651$	2.68843	+	66.5235i	0.105368	+	2.60726i
$652$		0			0
$653$	−12.0368	+	20.8484i	−0.471037	+	0.815859i	−0.999451	−	0.0331271i	$-0.989453\pi$
$653$	−12.0368	+	20.8484i	−0.471037	+	0.815859i	0.528415	+	0.848987i	$0.322787\pi$
$654$		0			0
$655$	−3.08229	−	3.39995i	−0.120435	−	0.132847i
$656$		0			0
$657$	−13.3167			−0.519536
$658$		0			0
$659$	−41.3082			−1.60914			−0.804569	−	0.593859i	$-0.797604\pi$
$659$	−41.3082			−1.60914			−0.804569	+	0.593859i	$0.797604\pi$
$660$		0			0
$661$	−9.80101	−	16.9759i	−0.381215	−	0.660284i	0.610021	−	0.792385i	$-0.291161\pi$
$661$	−9.80101	−	16.9759i	−0.381215	−	0.660284i	−0.991236	+	0.132101i	$0.957828\pi$
$662$		0			0
$663$	−19.6071	−	11.3202i	−0.761477	−	0.439639i
$664$		0			0
$665$	−22.2726	−	6.17311i	−0.863695	−	0.239383i
$666$		0			0
$667$	−23.3854	−	13.5016i	−0.905487	−	0.522783i
$668$		0			0
$669$	18.7689	−	10.8362i	0.725648	−	0.418953i
$670$		0			0
$671$	−0.718722			−0.0277460
$672$		0			0
$673$		−	38.8213i		−	1.49645i	−0.663444	−	0.748226i	$-0.730906\pi$
$673$		−	38.8213i		−	1.49645i	0.663444	−	0.748226i	$-0.269094\pi$
$674$		0			0
$675$	55.6219	+	39.8377i	2.14089	+	1.53336i
$676$		0			0
$677$	−33.5675	−	19.3802i	−1.29010	−	0.744842i	−0.311431	−	0.950269i	$-0.600808\pi$
$677$	−33.5675	−	19.3802i	−1.29010	−	0.744842i	−0.978672	+	0.205427i	$0.934142\pi$
$678$		0			0
$679$	−35.6536	+	22.5517i	−1.36826	+	0.865454i
$680$		0			0
$681$	13.8111	−	23.9216i	0.529243	−	0.916676i
$682$		0			0
$683$	−31.8093	+	18.3651i	−1.21715	+	0.702721i	−0.964307	−	0.264786i	$-0.914699\pi$
$683$	−31.8093	+	18.3651i	−1.21715	+	0.702721i	−0.252842	+	0.967508i	$0.581365\pi$
$684$		0			0
$685$	−18.6996	+	4.04108i	−0.714474	+	0.154402i
$686$		0			0
$687$	66.2639			2.52812
$688$		0			0
$689$	−2.38730	+	1.37831i	−0.0909487	+	0.0525093i
$690$		0			0
$691$	−23.1244	−	13.3509i	−0.879693	−	0.507891i	−0.00913605	−	0.999958i	$-0.502908\pi$
$691$	−23.1244	−	13.3509i	−0.879693	−	0.507891i	−0.870557	+	0.492067i	$0.836241\pi$
$692$		0			0
$693$	40.2161	−	25.4375i	1.52768	−	0.966292i
$694$		0			0
$695$	−9.12507	+	28.4118i	−0.346134	+	1.07772i
$696$		0			0
$697$	−12.1200	+	6.99747i	−0.459077	+	0.265048i
$698$		0			0
$699$		−	70.7744i		−	2.67693i
$700$		0			0
$701$			28.7252i			1.08494i	0.840076	+	0.542468i	$0.182510\pi$
$701$			28.7252i			1.08494i	−0.840076	+	0.542468i	$0.817490\pi$
$702$		0			0
$703$	11.3587	−	6.55796i	0.428402	−	0.247338i
$704$		0			0
$705$	7.25907	−	22.6018i	0.273392	−	0.851233i
$706$		0			0
$707$	28.5010	+	14.9543i	1.07189	+	0.562416i
$708$		0			0
$709$	26.2847	+	15.1755i	0.987142	+	0.569927i	0.904419	−	0.426646i	$-0.140305\pi$
$709$	26.2847	+	15.1755i	0.987142	+	0.569927i	0.0827230	+	0.996573i	$0.473638\pi$
$710$		0			0
$711$	−12.3196	+	7.11275i	−0.462023	+	0.266749i
$712$		0			0
$713$	45.0045			1.68543
$714$		0			0
$715$	15.7187	−	3.39690i	0.587847	−	0.127037i
$716$		0			0
$717$	29.9332	−	17.2819i	1.11787	−	0.645405i
$718$		0			0
$719$	23.6997	−	41.0491i	0.883849	−	1.53087i	0.0368218	−	0.999322i	$-0.488277\pi$
$719$	23.6997	−	41.0491i	0.883849	−	1.53087i	0.847027	−	0.531549i	$-0.178390\pi$
$720$		0			0
$721$	−33.3907	+	1.34943i	−1.24354	+	0.0502553i
$722$		0			0
$723$	49.5606	+	28.6138i	1.84318	+	1.06416i
$724$		0			0
$725$	13.7170	−	19.1519i	0.509438	−	0.711283i
$726$		0			0
$727$			14.3064i			0.530595i	0.964167	+	0.265297i	$0.0854701\pi$
$727$			14.3064i			0.530595i	−0.964167	+	0.265297i	$0.914530\pi$
$728$		0			0
$729$	28.6824			1.06231
$730$		0			0
$731$	1.60762	−	0.928157i	0.0594598	−	0.0343291i
$732$		0			0
$733$	6.48221	+	3.74251i	0.239426	+	0.138233i	0.614913	−	0.788595i	$-0.289191\pi$
$733$	6.48221	+	3.74251i	0.239426	+	0.138233i	−0.375487	+	0.926828i	$0.622524\pi$
$734$		0			0
$735$	−48.8401	−	11.4347i	−1.80149	−	0.421777i
$736$		0			0
$737$	−10.1931	−	5.88498i	−0.375467	−	0.216776i
$738$		0			0
$739$	−11.8579	−	20.5385i	−0.436199	−	0.755519i	0.561193	−	0.827685i	$-0.310342\pi$
$739$	−11.8579	−	20.5385i	−0.436199	−	0.755519i	−0.997393	+	0.0721655i	$0.977009\pi$
$740$		0			0
$741$	−36.3940			−1.33697
$742$		0			0
$743$	4.32810			0.158783			0.0793914	−	0.996844i	$-0.474702\pi$
$743$	4.32810			0.158783			0.0793914	+	0.996844i	$0.474702\pi$
$744$		0			0
$745$	17.4276	+	19.2237i	0.638498	+	0.704303i
$746$		0			0
$747$	24.0496	−	41.6551i	0.879928	−	1.52408i
$748$		0			0
$749$	−25.9350	+	1.04812i	−0.947645	+	0.0382974i
$750$		0			0
$751$	−1.87523	−	1.08267i	−0.0684282	−	0.0395071i	0.465396	−	0.885103i	$-0.345912\pi$
$751$	−1.87523	−	1.08267i	−0.0684282	−	0.0395071i	−0.533824	+	0.845596i	$0.679245\pi$
$752$		0			0
$753$	−30.5942	+	17.6636i	−1.11492	+	0.643697i
$754$		0			0
$755$	33.8356	−	7.31207i	1.23140	−	0.266113i
$756$		0			0
$757$	−21.9602			−0.798158			−0.399079	−	0.916917i	$-0.630670\pi$
$757$	−21.9602			−0.798158			−0.399079	+	0.916917i	$0.630670\pi$
$758$		0			0
$759$	−22.7202	−	39.3525i	−0.824691	−	1.42841i
$760$		0			0
$761$	−5.54542	−	3.20165i	−0.201021	−	0.116060i	0.396110	−	0.918203i	$-0.370360\pi$
$761$	−5.54542	−	3.20165i	−0.201021	−	0.116060i	−0.597132	+	0.802143i	$0.703693\pi$
$762$		0			0
$763$	−4.08769	+	7.79062i	−0.147984	+	0.282039i
$764$		0			0
$765$	−37.6143	−	12.0807i	−1.35995	−	0.436777i
$766$		0			0
$767$	−10.7661	−	18.6474i	−0.388741	−	0.673320i
$768$		0			0
$769$			12.2214i			0.440714i	0.975419	+	0.220357i	$0.0707222\pi$
$769$			12.2214i			0.440714i	−0.975419	+	0.220357i	$0.929278\pi$
$770$		0			0
$771$	99.5706			3.58595
$772$		0			0
$773$	41.6408	−	24.0413i	1.49772	−	0.864706i	0.497719	−	0.867338i	$-0.334171\pi$
$773$	41.6408	−	24.0413i	1.49772	−	0.864706i	0.999997	+	0.00263190i	$0.000837761\pi$
$774$		0			0
$775$	−3.83888	+	39.0736i	−0.137897	+	1.40356i
$776$		0			0
$777$	24.0571	−	15.2167i	0.863045	−	0.545895i
$778$		0			0
$779$	−11.2483	+	19.4827i	−0.403013	+	0.698039i
$780$		0			0
$781$	16.8644	−	9.73668i	0.603456	−	0.348406i
$782$		0			0
$783$		−	64.4688i		−	2.30393i
$784$		0			0
$785$	−4.38419	+	0.947448i	−0.156478	+	0.0338159i
$786$		0			0
$787$	−13.4764	−	23.3419i	−0.480384	−	0.832049i	0.519363	−	0.854554i	$-0.326169\pi$
$787$	−13.4764	−	23.3419i	−0.480384	−	0.832049i	−0.999747	+	0.0225049i	$0.992836\pi$
$788$		0			0
$789$	−29.8952	+	51.7800i	−1.06430	+	1.84342i
$790$		0			0
$791$	−8.82663	−	13.9547i	−0.313839	−	0.496171i
$792$		0			0
$793$	0.731355	+	0.422248i	0.0259712	+	0.0149945i
$794$		0			0
$795$	−5.03436	+	4.56398i	−0.178550	+	0.161868i
$796$		0			0
$797$			1.04481i			0.0370090i	0.999829	+	0.0185045i	$0.00589050\pi$
$797$			1.04481i			0.0370090i	−0.999829	+	0.0185045i	$0.994109\pi$
$798$		0			0
$799$			8.05110i			0.284828i
$800$		0			0
$801$	−27.0862	+	15.6382i	−0.957044	+	0.552550i
$802$		0			0
$803$	−2.26593	+	3.92471i	−0.0799631	+	0.138500i
$804$		0			0
$805$	−9.05635	+	32.6753i	−0.319194	+	1.15165i
$806$		0			0
$807$	4.55009	−	7.88098i	0.160171	−	0.277424i
$808$		0			0
$809$	−20.5368	−	35.5707i	−0.722034	−	1.25060i	−0.960183	−	0.279371i	$-0.909874\pi$
$809$	−20.5368	−	35.5707i	−0.722034	−	1.25060i	0.238150	−	0.971229i	$-0.423459\pi$
$810$		0			0
$811$		−	52.7552i		−	1.85249i	−0.376926	−	0.926244i	$-0.623019\pi$
$811$		−	52.7552i		−	1.85249i	0.376926	−	0.926244i	$-0.376981\pi$
$812$		0			0
$813$	−60.0667			−2.10663
$814$		0			0
$815$	−24.7811	−	27.3351i	−0.868046	−	0.957508i
$816$		0			0
$817$	1.49200	−	2.58422i	0.0521984	−	0.0904103i
$818$		0			0
$819$	−55.8675	+	2.25778i	−1.95217	+	0.0788933i
$820$		0			0
$821$	25.0058	+	14.4371i	0.872710	+	0.503859i	0.868248	−	0.496131i	$-0.165246\pi$
$821$	25.0058	+	14.4371i	0.872710	+	0.503859i	0.00446216	+	0.999990i	$0.498580\pi$
$822$		0			0
$823$	−6.70757	−	11.6178i	−0.233811	−	0.404973i	0.725115	−	0.688627i	$-0.241786\pi$
$823$	−6.70757	−	11.6178i	−0.233811	−	0.404973i	−0.958926	+	0.283655i	$0.908453\pi$
$824$		0			0
$825$	36.1045	−	16.3692i	1.25700	−	0.569903i
$826$		0			0
$827$			30.8083i			1.07131i	0.844437	+	0.535655i	$0.179935\pi$
$827$			30.8083i			1.07131i	−0.844437	+	0.535655i	$0.820065\pi$
$828$		0			0
$829$	8.18705	+	14.1804i	0.284348	+	0.492505i	0.972451	−	0.233108i	$-0.0748896\pi$
$829$	8.18705	+	14.1804i	0.284348	+	0.492505i	−0.688103	+	0.725613i	$0.741556\pi$
$830$		0			0
$831$	−38.1706	+	66.1134i	−1.32412	+	2.29345i
$832$		0			0
$833$	16.9567	−	1.37279i	0.587514	−	0.0475643i
$834$		0			0
$835$	3.19451	−	9.94640i	0.110551	−	0.344210i
$836$		0			0
$837$	53.7231	+	93.0511i	1.85694	+	3.21632i
$838$		0			0
$839$	−23.6109			−0.815137			−0.407569	−	0.913175i	$-0.633623\pi$
$839$	−23.6109			−0.815137			−0.407569	+	0.913175i	$0.633623\pi$
$840$		0			0
$841$	6.80193			0.234549
$842$		0			0
$843$	−16.6014	−	28.7545i	−0.571783	−	0.990356i
$844$		0			0
$845$	9.68579	+	3.11081i	0.333201	+	0.107015i
$846$		0			0
$847$	0.521277	+	12.8987i	0.0179113	+	0.443204i
$848$		0			0
$849$	−14.9803	+	25.9466i	−0.514122	+	0.890485i
$850$		0			0
$851$	−9.62094	−	16.6640i	−0.329802	−	0.571233i
$852$		0			0
$853$		−	38.4550i		−	1.31667i	−0.752724	−	0.658336i	$-0.771260\pi$
$853$		−	38.4550i		−	1.31667i	0.752724	−	0.658336i	$-0.228740\pi$
$854$		0			0
$855$	−62.0734	+	13.4144i	−2.12287	+	0.458764i
$856$		0			0
$857$	−8.83986	−	15.3111i	−0.301964	−	0.523017i	0.674617	−	0.738168i	$-0.264309\pi$
$857$	−8.83986	−	15.3111i	−0.301964	−	0.523017i	−0.976581	+	0.215151i	$0.930976\pi$
$858$		0			0
$859$	−10.4581	−	6.03798i	−0.356825	−	0.206013i	0.310862	−	0.950455i	$-0.399382\pi$
$859$	−10.4581	−	6.03798i	−0.356825	−	0.206013i	−0.667687	+	0.744442i	$0.732716\pi$
$860$		0			0
$861$	−22.6851	+	43.2348i	−0.773105	+	1.47344i
$862$		0			0
$863$	3.86108	−	6.68759i	0.131433	−	0.227648i	−0.792796	−	0.609487i	$-0.791376\pi$
$863$	3.86108	−	6.68759i	0.131433	−	0.227648i	0.924229	+	0.381838i	$0.124709\pi$
$864$		0			0
$865$	11.1811	+	12.3335i	0.380169	+	0.419350i
$866$		0			0
$867$	−35.5512			−1.20738
$868$		0			0
$869$			4.84113i			0.164224i
$870$		0			0
$871$	6.91484	+	11.9769i	0.234300	+	0.405820i
$872$		0			0
$873$	−57.9596	+	100.389i	−1.96164	+	3.39765i
$874$		0			0
$875$	−27.5967	−	10.6501i	−0.932938	−	0.360038i
$876$		0			0
$877$	4.57193	−	7.91882i	0.154383	−	0.267399i	−0.778451	−	0.627705i	$-0.783994\pi$
$877$	4.57193	−	7.91882i	0.154383	−	0.267399i	0.932834	+	0.360306i	$0.117328\pi$
$878$		0			0
$879$	44.6123	−	25.7570i	1.50474	−	0.868760i
$880$		0			0
$881$		−	4.52233i		−	0.152361i	−0.997094	−	0.0761805i	$-0.975727\pi$
$881$		−	4.52233i		−	0.152361i	0.997094	−	0.0761805i	$-0.0242725\pi$
$882$		0			0
$883$		−	37.8342i		−	1.27322i	−0.771185	−	0.636611i	$-0.780336\pi$
$883$		−	37.8342i		−	1.27322i	0.771185	−	0.636611i	$-0.219664\pi$
$884$		0			0
$885$	−35.6498	−	39.3239i	−1.19835	−	1.32186i
$886$		0			0
$887$	13.0412	+	7.52933i	0.437880	+	0.252810i	0.702698	−	0.711488i	$-0.251979\pi$
$887$	13.0412	+	7.52933i	0.437880	+	0.252810i	−0.264818	+	0.964298i	$0.585312\pi$
$888$		0			0
$889$	38.5961	−	24.4129i	1.29447	−	0.818782i
$890$		0			0
$891$	27.2648	−	47.2241i	0.913406	−	1.58207i
$892$		0			0
$893$	6.47101	+	11.2081i	0.216544	+	0.375066i
$894$		0			0
$895$	4.59373	+	21.2569i	0.153552	+	0.710539i
$896$		0			0
$897$			53.3923i			1.78272i
$898$		0			0
$899$	32.0396	−	18.4981i	1.06858	−	0.616945i
$900$		0			0
$901$	1.15230	−	1.99585i	0.0383888	−	0.0664913i
$902$		0			0
$903$	3.00899	−	5.73474i	0.100133	−	0.190840i
$904$		0			0
$905$	−12.1883	−	3.91456i	−0.405154	−	0.130124i
$906$		0			0
$907$	−38.3608	+	22.1476i	−1.27375	+	0.735400i	−0.975692	−	0.219148i	$-0.929672\pi$
$907$	−38.3608	+	22.1476i	−1.27375	+	0.735400i	−0.298058	+	0.954548i	$0.596339\pi$
$908$		0			0
$909$	88.4388			2.93333
$910$		0			0
$911$			41.0968i			1.36160i	0.732470	+	0.680799i	$0.238367\pi$
$911$			41.0968i			1.36160i	−0.732470	+	0.680799i	$0.761633\pi$
$912$		0			0
$913$	−8.18440	−	14.1758i	−0.270864	−	0.469150i
$914$		0			0
$915$	1.98201	+	0.636568i	0.0655233	+	0.0210443i
$916$		0			0
$917$	5.42551	−	0.219262i	0.179166	−	0.00724068i
$918$		0			0
$919$	−13.1904	−	7.61549i	−0.435112	−	0.251212i	0.266410	−	0.963860i	$-0.414162\pi$
$919$	−13.1904	−	7.61549i	−0.435112	−	0.251212i	−0.701522	+	0.712648i	$0.747496\pi$
$920$		0			0
$921$	−24.0067	−	41.5809i	−0.791049	−	1.37014i
$922$		0			0
$923$	−22.8811			−0.753142
$924$		0			0
$925$	15.2886	−	6.93160i	0.502684	−	0.227910i
$926$		0			0
$927$	−79.5218	+	45.9119i	−2.61184	+	1.50795i
$928$		0			0
$929$	−6.33630	−	3.65826i	−0.207887	−	0.120024i	0.392442	−	0.919777i	$-0.371630\pi$
$929$	−6.33630	−	3.65826i	−0.207887	−	0.120024i	−0.600329	+	0.799753i	$0.704964\pi$
$930$		0			0
$931$	22.5024	−	15.5399i	0.737487	−	0.509299i
$932$		0			0
$933$	49.5922	−	85.8962i	1.62358	−	2.81212i
$934$		0			0
$935$	−9.96074	+	9.03008i	−0.325751	+	0.295315i
$936$		0			0
$937$	−18.5605			−0.606347			−0.303173	−	0.952935i	$-0.598046\pi$
$937$	−18.5605			−0.606347			−0.303173	+	0.952935i	$0.598046\pi$
$938$		0			0
$939$	−10.0723			−0.328698
$940$		0			0
$941$	7.91298	+	13.7057i	0.257956	+	0.446792i	0.965694	−	0.259682i	$-0.0836178\pi$
$941$	7.91298	+	13.7057i	0.257956	+	0.446792i	−0.707738	+	0.706475i	$0.750284\pi$
$942$		0			0
$943$	28.5823	+	16.5020i	0.930768	+	0.537379i
$944$		0			0
$945$	−78.3701	+	20.2805i	−2.54938	+	0.659726i
$946$		0			0
$947$	−13.2327	−	7.63993i	−0.430006	−	0.248264i	0.269343	−	0.963044i	$-0.413193\pi$
$947$	−13.2327	−	7.63993i	−0.430006	−	0.248264i	−0.699349	+	0.714780i	$0.746527\pi$
$948$		0			0
$949$	4.61153	−	2.66247i	0.149696	−	0.0864273i
$950$		0			0
$951$	−12.1304			−0.393356
$952$		0			0
$953$			13.4292i			0.435014i	0.976059	+	0.217507i	$0.0697924\pi$
$953$			13.4292i			0.435014i	−0.976059	+	0.217507i	$0.930208\pi$
$954$		0			0
$955$	4.62226	+	5.09864i	0.149573	+	0.164988i
$956$		0			0
$957$	−32.3499	−	18.6772i	−1.04572	−	0.603749i
$958$		0			0
$959$	10.5174	−	20.0447i	0.339623	−	0.647278i
$960$		0			0
$961$	−15.3296	+	26.5516i	−0.494503	+	0.856504i
$962$		0			0
$963$	−61.7656	+	35.6604i	−1.99037	+	1.14914i
$964$		0			0
$965$	−41.2633	+	8.91724i	−1.32831	+	0.287056i
$966$		0			0
$967$	−20.1963			−0.649468			−0.324734	−	0.945805i	$-0.605275\pi$
$967$	−20.1963			−0.649468			−0.324734	+	0.945805i	$0.605275\pi$
$968$		0			0
$969$	26.3501	−	15.2132i	0.846486	−	0.488719i
$970$		0			0
$971$	24.0745	+	13.8994i	0.772587	+	0.446053i	0.833797	−	0.552071i	$-0.186162\pi$
$971$	24.0745	+	13.8994i	0.772587	+	0.446053i	−0.0612095	+	0.998125i	$0.519496\pi$
$972$		0			0
$973$	−18.8746	−	29.8403i	−0.605092	−	0.956635i
$974$		0			0
$975$	−46.3560	−	4.55436i	−1.48458	−	0.145856i
$976$		0			0
$977$	35.2559	−	20.3550i	1.12794	−	0.651214i	0.184521	−	0.982829i	$-0.440927\pi$
$977$	35.2559	−	20.3550i	1.12794	−	0.651214i	0.943415	+	0.331615i	$0.107593\pi$
$978$		0			0
$979$			10.6438i			0.340177i
$980$		0			0
$981$			24.1743i			0.771826i
$982$		0			0
$983$	34.7777	−	20.0789i	1.10924	−	0.640418i	0.170605	−	0.985339i	$-0.445428\pi$
$983$	34.7777	−	20.0789i	1.10924	−	0.640418i	0.938632	+	0.344921i	$0.112094\pi$
$984$		0			0
$985$	10.2482	+	3.29145i	0.326536	+	0.104874i
$986$		0			0
$987$	15.0149	+	23.7382i	0.477930	+	0.755595i
$988$		0			0
$989$	−3.79121	−	2.18886i	−0.120553	−	0.0696016i
$990$		0			0
$991$	6.03398	−	3.48372i	0.191676	−	0.110664i	−0.401091	−	0.916038i	$-0.631369\pi$
$991$	6.03398	−	3.48372i	0.191676	−	0.110664i	0.592767	+	0.805374i	$0.298036\pi$
$992$		0			0
$993$	−24.5695			−0.779689
$994$		0			0
$995$	−11.4228	−	52.8576i	−0.362128	−	1.67570i
$996$		0			0
$997$	−13.7596	+	7.94408i	−0.435770	+	0.251592i	−0.701802	−	0.712373i	$-0.747621\pi$
$997$	−13.7596	+	7.94408i	−0.435770	+	0.251592i	0.266032	+	0.963964i	$0.414287\pi$
$998$		0			0
$999$	22.9695	−	39.7844i	0.726724	−	1.25872i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bq.b.719.1		80
4.3	odd	2		280.2.ba.b.19.12	yes	80
5.4	even	2	inner	1120.2.bq.b.719.39		80
7.3	odd	6	inner	1120.2.bq.b.1039.40		80
8.3	odd	2	inner	1120.2.bq.b.719.2		80
8.5	even	2		280.2.ba.b.19.3	✓	80
20.19	odd	2		280.2.ba.b.19.29	yes	80
28.3	even	6		280.2.ba.b.59.38	yes	80
35.24	odd	6	inner	1120.2.bq.b.1039.2		80
40.19	odd	2	inner	1120.2.bq.b.719.40		80
40.29	even	2		280.2.ba.b.19.38	yes	80
56.3	even	6	inner	1120.2.bq.b.1039.39		80
56.45	odd	6		280.2.ba.b.59.29	yes	80
140.59	even	6		280.2.ba.b.59.3	yes	80
280.59	even	6	inner	1120.2.bq.b.1039.1		80
280.269	odd	6		280.2.ba.b.59.12	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.ba.b.19.3	✓	80	8.5	even	2
280.2.ba.b.19.12	yes	80	4.3	odd	2
280.2.ba.b.19.29	yes	80	20.19	odd	2
280.2.ba.b.19.38	yes	80	40.29	even	2
280.2.ba.b.59.3	yes	80	140.59	even	6
280.2.ba.b.59.12	yes	80	280.269	odd	6
280.2.ba.b.59.29	yes	80	56.45	odd	6
280.2.ba.b.59.38	yes	80	28.3	even	6
1120.2.bq.b.719.1		80	1.1	even	1	trivial
1120.2.bq.b.719.2		80	8.3	odd	2	inner
1120.2.bq.b.719.39		80	5.4	even	2	inner
1120.2.bq.b.719.40		80	40.19	odd	2	inner
1120.2.bq.b.1039.1		80	280.59	even	6	inner
1120.2.bq.b.1039.2		80	35.24	odd	6	inner
1120.2.bq.b.1039.39		80	56.3	even	6	inner
1120.2.bq.b.1039.40		80	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.60233 - 2.77531i) q^{3} +(2.12896 + 0.683763i) q^{5} +(-2.23600 + 1.41432i) q^{7} +(-3.63491 + 6.29586i) q^{9} +O(q^{10})\)	\(q+(-1.60233 - 2.77531i) q^{3} +(2.12896 + 0.683763i) q^{5} +(-2.23600 + 1.41432i) q^{7} +(-3.63491 + 6.29586i) q^{9} +(1.23701 + 2.14257i) q^{11} -2.90697i q^{13} +(-1.51364 - 7.00414i) q^{15} +(1.21515 + 2.10471i) q^{17} +(3.38329 + 1.95334i) q^{19} +(7.50799 + 3.93940i) q^{21} +(2.86568 - 4.96350i) q^{23} +(4.06494 + 2.91141i) q^{25} +13.6833 q^{27} -4.71148i q^{29} +(3.92617 + 6.80032i) q^{31} +(3.96419 - 6.86619i) q^{33} +(-5.72741 + 1.48213i) q^{35} +(1.67865 - 2.90751i) q^{37} +(-8.06775 + 4.65792i) q^{39} +5.75850i q^{41} -0.763818i q^{43} +(-12.0435 + 10.9182i) q^{45} +(2.86896 + 1.65640i) q^{47} +(2.99940 - 6.32484i) q^{49} +(3.89415 - 6.74487i) q^{51} +(-0.474139 - 0.821232i) q^{53} +(1.16854 + 5.40726i) q^{55} -12.5196i q^{57} +(6.41474 - 3.70355i) q^{59} +(-0.145254 + 0.251587i) q^{61} +(-0.776680 - 19.2185i) q^{63} +(1.98768 - 6.18882i) q^{65} +(-4.12005 + 2.37871i) q^{67} -18.3670 q^{69} -7.87114i q^{71} +(0.915891 + 1.58637i) q^{73} +(1.56671 - 15.9465i) q^{75} +(-5.79623 - 3.04125i) q^{77} +(1.69463 + 0.978393i) q^{79} +(-11.0205 - 19.0880i) q^{81} -6.61627 q^{83} +(1.14789 + 5.31172i) q^{85} +(-13.0758 + 7.54934i) q^{87} +(3.72584 + 2.15111i) q^{89} +(4.11138 + 6.49998i) q^{91} +(12.5820 - 21.7927i) q^{93} +(5.86726 + 6.47195i) q^{95} +15.9453 q^{97} -17.9857 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 52 q^{9}+O(q^{10}) \) 80 * q - 52 * q^9	\( 80 q - 52 q^{9} + 48 q^{19} - 22 q^{25} + 22 q^{35} + 16 q^{49} - 20 q^{51} + 60 q^{59} - 12 q^{65} + 6 q^{75} - 36 q^{89} - 72 q^{91} - 104 q^{99}+O(q^{100}) \) 80 * q - 52 * q^9 + 48 * q^19 - 22 * q^25 + 22 * q^35 + 16 * q^49 - 20 * q^51 + 60 * q^59 - 12 * q^65 + 6 * q^75 - 36 * q^89 - 72 * q^91 - 104 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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