LMFDB - Embedded newform 180.2.r.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(49,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("180.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.r (of order $6$, degree $2$, 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:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
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} - 4x^{10} + 10x^{8} - 6x^{6} + 90x^{4} - 324x^{2} + 729 $ x^12 - 4x^10 + 10x^8 - 6x^6 + 90x^4 - 324*x^2 + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$-1.54493 + 0.783067i$ of defining polynomial
Character	$\chi$	$=$	180.49
Dual form			180.2.r.a.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54493 + 0.783067i) q^{3} +(0.801701 - 2.08741i) q^{5} +(1.96151 - 1.13248i) q^{7} +(1.77361 - 2.41957i) q^{9} +O(q^{10})$	\(q+(-1.54493 + 0.783067i) q^{3} +(0.801701 - 2.08741i) q^{5} +(1.96151 - 1.13248i) q^{7} +(1.77361 - 2.41957i) q^{9} +(1.27361 + 2.20596i) q^{11} +(4.35186 + 2.51255i) q^{13} +(0.396010 + 3.85268i) q^{15} -5.72392i q^{17} +1.86997 q^{19} +(-2.14359 + 3.28559i) q^{21} +(-4.67413 - 2.69861i) q^{23} +(-3.71455 - 3.34696i) q^{25} +(-0.845423 + 5.12692i) q^{27} +(-1.50000 - 2.59808i) q^{29} +(-4.69081 + 8.12472i) q^{31} +(-3.69506 - 2.41073i) q^{33} +(-0.791400 - 5.00238i) q^{35} +2.59165i q^{37} +(-8.69081 - 0.473910i) q^{39} +(-1.98221 + 3.43329i) q^{41} +(8.84073 - 5.10420i) q^{43} +(-3.62872 - 5.64202i) q^{45} +(-0.927469 + 0.535475i) q^{47} +(-0.934987 + 1.61945i) q^{49} +(4.48221 + 8.84305i) q^{51} +10.7036i q^{53} +(5.62580 - 0.890028i) q^{55} +(-2.88898 + 1.46432i) q^{57} +(-0.791400 + 1.37075i) q^{59} +(-0.434987 - 0.753420i) q^{61} +(0.738852 - 6.75458i) q^{63} +(8.73361 - 7.06980i) q^{65} +(-4.20594 - 2.42830i) q^{67} +(9.33440 + 0.509005i) q^{69} -1.86997 q^{71} +3.87652i q^{73} +(8.35961 + 2.26207i) q^{75} +(4.99640 + 2.88468i) q^{77} +(-6.62580 - 11.4762i) q^{79} +(-2.70860 - 8.58274i) q^{81} +(-12.7333 + 7.35158i) q^{83} +(-11.9482 - 4.58887i) q^{85} +(4.35186 + 2.83924i) q^{87} +13.4172 q^{89} +11.3816 q^{91} +(0.884768 - 16.2253i) q^{93} +(1.49916 - 3.90340i) q^{95} +(-15.3000 + 8.83347i) q^{97} +(7.59636 + 0.830931i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{5} + 8 q^{9}+O(q^{10}) $ 12 * q + q^5 + 8 * q^9	$ 12 q + q^{5} + 8 q^{9} + 2 q^{11} - 5 q^{15} + 10 q^{21} - 3 q^{25} - 18 q^{29} + 6 q^{31} - 34 q^{35} - 42 q^{39} + 14 q^{41} - 31 q^{45} + 16 q^{51} - 6 q^{55} - 34 q^{59} + 6 q^{61} + 15 q^{65} + 14 q^{69} + 41 q^{75} - 6 q^{79} - 8 q^{81} - 12 q^{85} + 112 q^{89} + 12 q^{91} + 36 q^{95} + 82 q^{99}+O(q^{100}) $ 12 * q + q^5 + 8 * q^9 + 2 * q^11 - 5 * q^15 + 10 * q^21 - 3 * q^25 - 18 * q^29 + 6 * q^31 - 34 * q^35 - 42 * q^39 + 14 * q^41 - 31 * q^45 + 16 * q^51 - 6 * q^55 - 34 * q^59 + 6 * q^61 + 15 * q^65 + 14 * q^69 + 41 * q^75 - 6 * q^79 - 8 * q^81 - 12 * q^85 + 112 * q^89 + 12 * q^91 + 36 * q^95 + 82 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.54493	+	0.783067i	−0.891965	+	0.452104i
$3$	−1.54493	+	0.783067i	−0.891965	+	0.452104i
$4$		0			0
$5$	0.801701	−	2.08741i	0.358532	−	0.933518i
$5$	0.801701	−	2.08741i	0.358532	−	0.933518i
$6$		0			0
$7$	1.96151	−	1.13248i	0.741381	−	0.428036i	−0.0811903	−	0.996699i	$-0.525872\pi$
$7$	1.96151	−	1.13248i	0.741381	−	0.428036i	0.822571	+	0.568662i	$0.192539\pi$
$8$		0			0
$9$	1.77361	−	2.41957i	0.591204	−	0.806522i
$10$		0			0
$11$	1.27361	+	2.20596i	0.384009	+	0.665122i	0.991631	−	0.129104i	$-0.0412100\pi$
$11$	1.27361	+	2.20596i	0.384009	+	0.665122i	−0.607623	+	0.794226i	$0.707877\pi$
$12$		0			0
$13$	4.35186	+	2.51255i	1.20699	+	0.696856i	0.962100	−	0.272696i	$-0.0879152\pi$
$13$	4.35186	+	2.51255i	1.20699	+	0.696856i	0.244889	+	0.969551i	$0.421249\pi$
$14$		0			0
$15$	0.396010	+	3.85268i	0.102249	+	0.994759i
$16$		0			0
$17$		−	5.72392i		−	1.38825i	−0.719852	−	0.694127i	$-0.755791\pi$
$17$		−	5.72392i		−	1.38825i	0.719852	−	0.694127i	$-0.244209\pi$
$18$		0			0
$19$	1.86997			0.429002			0.214501	−	0.976724i	$-0.431188\pi$
$19$	1.86997			0.429002			0.214501	+	0.976724i	$0.431188\pi$
$20$		0			0
$21$	−2.14359	+	3.28559i	−0.467769	+	0.716975i
$22$		0			0
$23$	−4.67413	−	2.69861i	−0.974624	−	0.562699i	−0.0739813	−	0.997260i	$-0.523571\pi$
$23$	−4.67413	−	2.69861i	−0.974624	−	0.562699i	−0.900643	+	0.434560i	$0.856904\pi$
$24$		0			0
$25$	−3.71455	−	3.34696i	−0.742910	−	0.669391i
$26$		0			0
$27$	−0.845423	+	5.12692i	−0.162702	+	0.986675i
$28$		0			0
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	0.692480	−	0.721437i	$-0.256518\pi$
$29$	−1.50000	−	2.59808i	−0.278543	−	0.482451i	−0.971023	+	0.238987i	$0.923185\pi$
$30$		0			0
$31$	−4.69081	+	8.12472i	−0.842495	+	1.45924i	0.0452848	+	0.998974i	$0.485580\pi$
$31$	−4.69081	+	8.12472i	−0.842495	+	1.45924i	−0.887779	+	0.460269i	$0.847753\pi$
$32$		0			0
$33$	−3.69506	−	2.41073i	−0.643227	−	0.419654i
$34$		0			0
$35$	−0.791400	−	5.00238i	−0.133771	−	0.845557i
$36$		0			0
$37$			2.59165i			0.426065i	0.977045	+	0.213032i	$0.0683340\pi$
$37$			2.59165i			0.426065i	−0.977045	+	0.213032i	$0.931666\pi$
$38$		0			0
$39$	−8.69081	−	0.473910i	−1.39164	−	0.0758864i
$40$		0			0
$41$	−1.98221	+	3.43329i	−0.309569	+	0.536190i	−0.978268	−	0.207343i	$-0.933518\pi$
$41$	−1.98221	+	3.43329i	−0.309569	+	0.536190i	0.668699	+	0.743533i	$0.266852\pi$
$42$		0			0
$43$	8.84073	−	5.10420i	1.34820	−	0.778383i	0.360205	−	0.932873i	$-0.382707\pi$
$43$	8.84073	−	5.10420i	1.34820	−	0.778383i	0.987994	+	0.154490i	$0.0493735\pi$
$44$		0			0
$45$	−3.62872	−	5.64202i	−0.540937	−	0.841063i
$46$		0			0
$47$	−0.927469	+	0.535475i	−0.135285	+	0.0781070i	−0.566115	−	0.824326i	$-0.691554\pi$
$47$	−0.927469	+	0.535475i	−0.135285	+	0.0781070i	0.430830	+	0.902433i	$0.358221\pi$
$48$		0			0
$49$	−0.934987	+	1.61945i	−0.133570	+	0.231349i
$50$		0			0
$51$	4.48221	+	8.84305i	0.627635	+	1.23827i
$52$		0			0
$53$			10.7036i			1.47025i	0.677931	+	0.735125i	$0.262877\pi$
$53$			10.7036i			1.47025i	−0.677931	+	0.735125i	$0.737123\pi$
$54$		0			0
$55$	5.62580	−	0.890028i	0.758583	−	0.120011i
$56$		0			0
$57$	−2.88898	+	1.46432i	−0.382655	+	0.193953i
$58$		0			0
$59$	−0.791400	+	1.37075i	−0.103032	+	0.178456i	−0.912932	−	0.408111i	$-0.866188\pi$
$59$	−0.791400	+	1.37075i	−0.103032	+	0.178456i	0.809901	+	0.586567i	$0.199521\pi$
$60$		0			0
$61$	−0.434987	−	0.753420i	−0.0556944	−	0.0964656i	0.836834	−	0.547457i	$-0.184404\pi$
$61$	−0.434987	−	0.753420i	−0.0556944	−	0.0964656i	−0.892528	+	0.450991i	$0.851071\pi$
$62$		0			0
$63$	0.738852	−	6.75458i	0.0930866	−	0.850997i
$64$		0			0
$65$	8.73361	−	7.06980i	1.08327	−	0.876901i
$66$		0			0
$67$	−4.20594	−	2.42830i	−0.513838	−	0.296664i	0.220572	−	0.975371i	$-0.429208\pi$
$67$	−4.20594	−	2.42830i	−0.513838	−	0.296664i	−0.734410	+	0.678706i	$0.762541\pi$
$68$		0			0
$69$	9.33440	+	0.509005i	1.12373	+	0.0612770i
$70$		0			0
$71$	−1.86997			−0.221925			−0.110963	−	0.993825i	$-0.535393\pi$
$71$	−1.86997			−0.221925			−0.110963	+	0.993825i	$0.535393\pi$
$72$		0			0
$73$			3.87652i			0.453713i	0.973928	+	0.226856i	$0.0728448\pi$
$73$			3.87652i			0.453713i	−0.973928	+	0.226856i	$0.927155\pi$
$74$		0			0
$75$	8.35961	+	2.26207i	0.965284	+	0.261201i
$76$		0			0
$77$	4.99640	+	2.88468i	0.569393	+	0.328739i
$78$		0			0
$79$	−6.62580	−	11.4762i	−0.745461	−	1.29118i	−0.949979	−	0.312313i	$-0.898896\pi$
$79$	−6.62580	−	11.4762i	−0.745461	−	1.29118i	0.204519	−	0.978863i	$-0.434437\pi$
$80$		0			0
$81$	−2.70860	−	8.58274i	−0.300956	−	0.953638i
$82$		0			0
$83$	−12.7333	+	7.35158i	−1.39766	+	0.806941i	−0.994147	−	0.108032i	$-0.965545\pi$
$83$	−12.7333	+	7.35158i	−1.39766	+	0.806941i	−0.403515	+	0.914973i	$0.632212\pi$
$84$		0			0
$85$	−11.9482	−	4.58887i	−1.29596	−	0.497733i
$86$		0			0
$87$	4.35186	+	2.83924i	0.466569	+	0.304399i
$88$		0			0
$89$	13.4172			1.42222			0.711110	−	0.703081i	$-0.248193\pi$
$89$	13.4172			1.42222			0.711110	+	0.703081i	$0.248193\pi$
$90$		0			0
$91$	11.3816			1.19312
$92$		0			0
$93$	0.884768	−	16.2253i	0.0917462	−	1.68249i
$94$		0			0
$95$	1.49916	−	3.90340i	0.153811	−	0.400481i
$96$		0			0
$97$	−15.3000	+	8.83347i	−1.55348	+	0.896903i	−0.555627	+	0.831432i	$0.687522\pi$
$97$	−15.3000	+	8.83347i	−1.55348	+	0.896903i	−0.997854	+	0.0654715i	$0.979145\pi$
$98$		0			0
$99$	7.59636	+	0.830931i	0.763463	+	0.0835117i
$100$		0			0
$101$	2.66138	+	4.60964i	0.264817	+	0.458676i	0.967516	−	0.252811i	$-0.0813552\pi$
$101$	2.66138	+	4.60964i	0.264817	+	0.458676i	−0.702699	+	0.711487i	$0.748022\pi$
$102$		0			0
$103$	5.20955	+	3.00773i	0.513312	+	0.296361i	0.734194	−	0.678940i	$-0.237560\pi$
$103$	5.20955	+	3.00773i	0.513312	+	0.296361i	−0.220882	+	0.975301i	$0.570894\pi$
$104$		0			0
$105$	5.13986	+	7.10860i	0.501599	+	0.693729i
$106$		0			0
$107$			4.69840i			0.454212i	0.973870	+	0.227106i	$0.0729263\pi$
$107$			4.69840i			0.454212i	−0.973870	+	0.227106i	$0.927074\pi$
$108$		0			0
$109$	6.64167			0.636157			0.318078	−	0.948064i	$-0.396962\pi$
$109$	6.64167			0.636157			0.318078	+	0.948064i	$0.396962\pi$
$110$		0			0
$111$	−2.02944	−	4.00392i	−0.192626	−	0.380035i
$112$		0			0
$113$	11.0852	+	6.40002i	1.04280	+	0.602064i	0.920626	−	0.390444i	$-0.127679\pi$
$113$	11.0852	+	6.40002i	1.04280	+	0.602064i	0.122178	+	0.992508i	$0.461012\pi$
$114$		0			0
$115$	−9.38036	+	7.59335i	−0.874723	+	0.708083i
$116$		0			0
$117$	13.7978	−	6.07333i	1.27561	−	0.561480i
$118$		0			0
$119$	−6.48221	−	11.2275i	−0.594223	−	1.02923i
$120$		0			0
$121$	2.25582	−	3.90720i	0.205075	−	0.355200i
$122$		0			0
$123$	0.373880	−	6.85640i	0.0337116	−	0.618220i
$124$		0			0
$125$	−9.96442	+	5.07053i	−0.891245	+	0.453522i
$126$		0			0
$127$		−	12.8103i		−	1.13673i	−0.822775	−	0.568367i	$-0.807576\pi$
$127$		−	12.8103i		−	1.13673i	0.822775	−	0.568367i	$-0.192424\pi$
$128$		0			0
$129$	−9.66138	+	14.8085i	−0.850637	+	1.30382i
$130$		0			0
$131$	4.75582	−	8.23733i	0.415518	−	0.719699i	−0.579964	−	0.814642i	$-0.696934\pi$
$131$	4.75582	−	8.23733i	0.415518	−	0.719699i	0.995483	+	0.0949430i	$0.0302669\pi$
$132$		0			0
$133$	3.66797	−	2.11771i	0.318054	−	0.183628i
$134$		0			0
$135$	10.0242	+	5.87500i	0.862745	+	0.505639i
$136$		0			0
$137$	9.95346	−	5.74663i	0.850382	−	0.490968i	−0.0103979	−	0.999946i	$-0.503310\pi$
$137$	9.95346	−	5.74663i	0.850382	−	0.490968i	0.860780	+	0.508978i	$0.169976\pi$
$138$		0			0
$139$	−5.75582	+	9.96938i	−0.488203	+	0.845592i	−0.999908	−	0.0135693i	$-0.995681\pi$
$139$	−5.75582	+	9.96938i	−0.488203	+	0.845592i	0.511705	+	0.859161i	$0.329014\pi$
$140$		0			0
$141$	1.01356	−	1.55354i	0.0853573	−	0.130832i
$142$		0			0
$143$			12.8000i			1.07039i
$144$		0			0
$145$	−6.62580	+	1.04823i	−0.550243	+	0.0870510i
$146$		0			0
$147$	0.176355	−	3.23409i	0.0145455	−	0.266743i
$148$		0			0
$149$	−9.85219	+	17.0645i	−0.807123	+	1.39798i	0.107726	+	0.994181i	$0.465643\pi$
$149$	−9.85219	+	17.0645i	−0.807123	+	1.39798i	−0.914849	+	0.403797i	$0.867690\pi$
$150$		0			0
$151$	−7.69081	−	13.3209i	−0.625869	−	1.08404i	−0.988372	−	0.152055i	$-0.951411\pi$
$151$	−7.69081	−	13.3209i	−0.625869	−	1.08404i	0.362503	−	0.931983i	$-0.381922\pi$
$152$		0			0
$153$	−13.8494	−	10.1520i	−1.11966	−	0.820742i
$154$		0			0
$155$	13.1990	+	16.3052i	1.06017	+	1.30967i
$156$		0			0
$157$	−10.8111	−	6.24182i	−0.862824	−	0.498151i	0.00213321	−	0.999998i	$-0.499321\pi$
$157$	−10.8111	−	6.24182i	−0.862824	−	0.498151i	−0.864957	+	0.501846i	$0.832654\pi$
$158$		0			0
$159$	−8.38162	−	16.5363i	−0.664706	−	1.31141i
$160$		0			0
$161$	−12.2245			−0.963424
$162$		0			0
$163$			1.93826i			0.151816i	0.997115	+	0.0759082i	$0.0241856\pi$
$163$			1.93826i			0.151816i	−0.997115	+	0.0759082i	$0.975814\pi$
$164$		0			0
$165$	−7.99451	+	5.78041i	−0.622372	+	0.450004i
$166$		0			0
$167$	0.282926	+	0.163347i	0.0218935	+	0.0126402i	0.510907	−	0.859636i	$-0.329310\pi$
$167$	0.282926	+	0.163347i	0.0218935	+	0.0126402i	−0.489013	+	0.872276i	$0.662643\pi$
$168$		0			0
$169$	6.12580	+	10.6102i	0.471215	+	0.816169i
$170$		0			0
$171$	3.31661	−	4.52453i	0.253628	−	0.345999i
$172$		0			0
$173$	−18.0126	+	10.3996i	−1.36948	+	0.790667i	−0.990861	−	0.134887i	$-0.956933\pi$
$173$	−18.0126	+	10.3996i	−1.36948	+	0.790667i	−0.378615	+	0.925554i	$0.623600\pi$
$174$		0			0
$175$	−11.0765	−	2.35844i	−0.837303	−	0.178281i
$176$		0			0
$177$	0.149272	−	2.73742i	0.0112200	−	0.205757i
$178$		0			0
$179$	−3.79882			−0.283937			−0.141969	−	0.989871i	$-0.545343\pi$
$179$	−3.79882			−0.283937			−0.141969	+	0.989871i	$0.545343\pi$
$180$		0			0
$181$	−16.5116			−1.22730			−0.613651	−	0.789578i	$-0.710300\pi$
$181$	−16.5116			−1.22730			−0.613651	+	0.789578i	$0.710300\pi$
$182$		0			0
$183$	1.26200	+	0.823357i	0.0932900	+	0.0608643i
$184$		0			0
$185$	5.40983	+	2.07773i	0.397739	+	0.152758i
$186$		0			0
$187$	12.6267	−	7.29005i	0.923359	−	0.533101i
$188$		0			0
$189$	4.14781	+	11.0139i	0.301709	+	0.801144i
$190$		0			0
$191$	−5.69081	−	9.85677i	−0.411773	−	0.713211i	0.583311	−	0.812249i	$-0.301757\pi$
$191$	−5.69081	−	9.85677i	−0.411773	−	0.713211i	−0.995084	+	0.0990377i	$0.968424\pi$
$192$		0			0
$193$	12.1979	+	7.04246i	0.878024	+	0.506927i	0.870006	−	0.493040i	$-0.164115\pi$
$193$	12.1979	+	7.04246i	0.878024	+	0.506927i	0.00801760	+	0.999968i	$0.497448\pi$
$194$		0			0
$195$	−7.95668	+	17.7613i	−0.569789	+	1.27192i
$196$		0			0
$197$		−	7.90830i		−	0.563443i	−0.959496	−	0.281721i	$-0.909095\pi$
$197$		−	7.90830i		−	0.563443i	0.959496	−	0.281721i	$-0.0909054\pi$
$198$		0			0
$199$	1.86997			0.132559			0.0662795	−	0.997801i	$-0.478887\pi$
$199$	1.86997			0.132559			0.0662795	+	0.997801i	$0.478887\pi$
$200$		0			0
$201$	8.39941	+	0.458020i	0.592449	+	0.0323063i
$202$		0			0
$203$	−5.88453	−	3.39743i	−0.413013	−	0.238453i
$204$		0			0
$205$	5.57754	+	6.89016i	0.389552	+	0.481230i
$206$		0			0
$207$	−14.8196	+	6.52308i	−1.03003	+	0.453386i
$208$		0			0
$209$	2.38162	+	4.12509i	0.164740	+	0.285339i
$210$		0			0
$211$	5.69081	−	9.85677i	0.391772	−	0.678568i	−0.600912	−	0.799315i	$-0.705196\pi$
$211$	5.69081	−	9.85677i	0.391772	−	0.678568i	0.992683	+	0.120747i	$0.0385290\pi$
$212$		0			0
$213$	2.88898	−	1.46432i	0.197950	−	0.100333i
$214$		0			0
$215$	−3.56693	−	22.5463i	−0.243262	−	1.53764i
$216$		0			0
$217$			21.2490i			1.44247i
$218$		0			0
$219$	−3.03558	−	5.98895i	−0.205125	−	0.404696i
$220$		0			0
$221$	14.3816	−	24.9097i	0.967413	−	1.67561i
$222$		0			0
$223$	4.20594	−	2.42830i	0.281651	−	0.162611i	−0.352520	−	0.935804i	$-0.614675\pi$
$223$	4.20594	−	2.42830i	0.281651	−	0.162611i	0.634171	+	0.773193i	$0.281342\pi$
$224$		0			0
$225$	−14.6864	+	3.05140i	−0.979090	+	0.203427i
$226$		0			0
$227$	6.12811	−	3.53807i	0.406737	−	0.234830i	−0.282650	−	0.959223i	$-0.591213\pi$
$227$	6.12811	−	3.53807i	0.406737	−	0.234830i	0.689387	+	0.724394i	$0.257880\pi$
$228$		0			0
$229$	4.36997	−	7.56902i	0.288776	−	0.500175i	−0.684742	−	0.728786i	$-0.740085\pi$
$229$	4.36997	−	7.56902i	0.288776	−	0.500175i	0.973518	+	0.228611i	$0.0734184\pi$
$230$		0			0
$231$	−9.97799	−	0.544100i	−0.656503	−	0.0357991i
$232$		0			0
$233$		−	9.26346i		−	0.606869i	−0.952852	−	0.303435i	$-0.901867\pi$
$233$		−	9.26346i		−	0.606869i	0.952852	−	0.303435i	$-0.0981334\pi$
$234$		0			0
$235$	0.374201	+	2.36530i	0.0244102	+	0.154295i
$236$		0			0
$237$	19.2230	+	12.5415i	1.24867	+	0.814658i
$238$		0			0
$239$	−6.33862	+	10.9788i	−0.410012	+	0.710161i	−0.994891	−	0.100960i	$-0.967809\pi$
$239$	−6.33862	+	10.9788i	−0.410012	+	0.710161i	0.584879	+	0.811121i	$0.301142\pi$
$240$		0			0
$241$	5.30496	+	9.18846i	0.341723	+	0.591881i	0.984753	−	0.173960i	$-0.0556563\pi$
$241$	5.30496	+	9.18846i	0.341723	+	0.591881i	−0.643030	+	0.765841i	$0.722323\pi$
$242$		0			0
$243$	10.9055	+	11.1387i	0.699585	+	0.714549i
$244$		0			0
$245$	2.63086	+	3.25001i	0.168080	+	0.207636i
$246$		0			0
$247$	8.13787	+	4.69840i	0.517800	+	0.298952i
$248$		0			0
$249$	13.9153	−	21.3287i	0.881845	−	1.35165i
$250$		0			0
$251$	18.6332			1.17612			0.588059	−	0.808818i	$-0.299892\pi$
$251$	18.6332			1.17612			0.588059	+	0.808818i	$0.299892\pi$
$252$		0			0
$253$		−	13.7479i		−	0.864326i
$254$		0			0
$255$	22.0525	−	2.26673i	1.38098	−	0.141948i
$256$		0			0
$257$	−22.8542	−	13.1949i	−1.42561	−	0.823075i	−0.428837	−	0.903382i	$-0.641077\pi$
$257$	−22.8542	−	13.1949i	−1.42561	−	0.823075i	−0.996770	+	0.0803071i	$0.974410\pi$
$258$		0			0
$259$	2.93499	+	5.08355i	0.182371	+	0.315876i
$260$		0			0
$261$	−8.94664	−	0.978631i	−0.553783	−	0.0605757i
$262$		0			0
$263$	11.8452	−	6.83882i	0.730406	−	0.421700i	−0.0881649	−	0.996106i	$-0.528100\pi$
$263$	11.8452	−	6.83882i	0.730406	−	0.421700i	0.818571	+	0.574406i	$0.194767\pi$
$264$		0			0
$265$	22.3428	+	8.58107i	1.37250	+	0.527131i
$266$		0			0
$267$	−20.7286	+	10.5066i	−1.26857	+	0.642991i
$268$		0			0
$269$	22.6417			1.38049			0.690244	−	0.723577i	$-0.257503\pi$
$269$	22.6417			1.38049			0.690244	+	0.723577i	$0.257503\pi$
$270$		0			0
$271$	5.86997			0.356576			0.178288	−	0.983978i	$-0.442944\pi$
$271$	5.86997			0.356576			0.178288	+	0.983978i	$0.442944\pi$
$272$		0			0
$273$	−17.5838	+	8.91257i	−1.06422	+	0.539413i
$274$		0			0
$275$	2.65236	−	12.4569i	0.159943	−	0.751178i
$276$		0			0
$277$	−0.137009	+	0.0791024i	−0.00823209	+	0.00475280i	−0.504110	−	0.863639i	$-0.668180\pi$
$277$	−0.137009	+	0.0791024i	−0.00823209	+	0.00475280i	0.495878	+	0.868392i	$0.334846\pi$
$278$		0			0
$279$	11.3386	+	25.7598i	0.678826	+	1.54220i
$280$		0			0
$281$	1.69504	+	2.93589i	0.101117	+	0.175141i	0.912145	−	0.409867i	$-0.134425\pi$
$281$	1.69504	+	2.93589i	0.101117	+	0.175141i	−0.811028	+	0.585008i	$0.801092\pi$
$282$		0			0
$283$	10.3734	+	5.98908i	0.616635	+	0.356014i	0.775558	−	0.631277i	$-0.217469\pi$
$283$	10.3734	+	5.98908i	0.616635	+	0.356014i	−0.158923	+	0.987291i	$0.550802\pi$
$284$		0			0
$285$	0.740528	+	7.20442i	0.0438651	+	0.426753i
$286$		0			0
$287$			8.97924i			0.530028i
$288$		0			0
$289$	−15.7632			−0.927250
$290$		0			0
$291$	16.7202	−	25.6280i	0.980158	−	1.50234i
$292$		0			0
$293$	−13.0556	−	7.53765i	−0.762715	−	0.440354i	0.0675544	−	0.997716i	$-0.478480\pi$
$293$	−13.0556	−	7.53765i	−0.762715	−	0.440354i	−0.830270	+	0.557362i	$0.811814\pi$
$294$		0			0
$295$	2.22684	+	2.75090i	0.129652	+	0.160164i
$296$		0			0
$297$	−12.3865	+	4.66473i	−0.718739	+	0.270675i
$298$		0			0
$299$	−13.5608	−	23.4880i	−0.784241	−	1.35834i
$300$		0			0
$301$	11.5608	−	20.0239i	0.666353	−	1.15416i
$302$		0			0
$303$	−7.72129	−	5.03753i	−0.443577	−	0.289398i
$304$		0			0
$305$	−1.92143	+	0.303979i	−0.110021	+	0.0174058i
$306$		0			0
$307$		−	6.00518i		−	0.342734i	−0.985207	−	0.171367i	$-0.945182\pi$
$307$		−	6.00518i		−	0.342734i	0.985207	−	0.171367i	$-0.0548183\pi$
$308$		0			0
$309$	−10.4036	−	0.567311i	−0.591842	−	0.0322732i
$310$		0			0
$311$	−15.2025	+	26.3314i	−0.862052	+	1.49312i	0.00789212	+	0.999969i	$0.497488\pi$
$311$	−15.2025	+	26.3314i	−0.862052	+	1.49312i	−0.869944	+	0.493150i	$0.835845\pi$
$312$		0			0
$313$	15.8469	−	9.14921i	0.895720	−	0.517144i	0.0199106	−	0.999802i	$-0.493662\pi$
$313$	15.8469	−	9.14921i	0.895720	−	0.517144i	0.875809	+	0.482658i	$0.160328\pi$
$314$		0			0
$315$	−13.5072	−	6.95744i	−0.761046	−	0.392007i
$316$		0			0
$317$	−7.33850	+	4.23689i	−0.412171	+	0.237967i	−0.691722	−	0.722164i	$-0.743148\pi$
$317$	−7.33850	+	4.23689i	−0.412171	+	0.237967i	0.279551	+	0.960131i	$0.409814\pi$
$318$		0			0
$319$	3.82084	−	6.61788i	0.213926	−	0.370530i
$320$		0			0
$321$	−3.67916	−	7.25870i	−0.205351	−	0.405141i
$322$		0			0
$323$		−	10.7036i		−	0.595563i
$324$		0			0
$325$	−7.75582	−	23.8985i	−0.430216	−	1.32565i
$326$		0			0
$327$	−10.2609	+	5.20087i	−0.567430	+	0.287609i
$328$		0			0
$329$	−1.21283	+	2.10068i	−0.0668653	+	0.115814i
$330$		0			0
$331$	7.62580	+	13.2083i	0.419152	+	0.725992i	0.995854	−	0.0909620i	$-0.0289942\pi$
$331$	7.62580	+	13.2083i	0.419152	+	0.725992i	−0.576703	+	0.816954i	$0.695661\pi$
$332$		0			0
$333$	6.27067	+	4.59658i	0.343631	+	0.251891i
$334$		0			0
$335$	−8.44077	+	6.83275i	−0.461169	+	0.373313i
$336$		0			0
$337$	15.5740	+	8.99168i	0.848372	+	0.489808i	0.860101	−	0.510123i	$-0.170400\pi$
$337$	15.5740	+	8.99168i	0.848372	+	0.489808i	−0.0117293	+	0.999931i	$0.503734\pi$
$338$		0			0
$339$	−22.1374	−	1.20716i	−1.20234	−	0.0655637i
$340$		0			0
$341$	−23.8971			−1.29410
$342$		0			0
$343$			20.0901i			1.08476i
$344$		0			0
$345$	8.54590	−	19.0766i	0.460096	−	1.02705i
$346$		0			0
$347$	14.1873	+	8.19103i	0.761614	+	0.439718i	0.829875	−	0.557950i	$-0.188412\pi$
$347$	14.1873	+	8.19103i	0.761614	+	0.439718i	−0.0682612	+	0.997667i	$0.521745\pi$
$348$		0			0
$349$	8.88162	+	15.3834i	0.475422	+	0.823456i	0.999604	−	0.0281510i	$-0.00896193\pi$
$349$	8.88162	+	15.3834i	0.475422	+	0.823456i	−0.524181	+	0.851607i	$0.675629\pi$
$350$		0			0
$351$	−16.5608	+	20.1875i	−0.883949	+	1.07753i
$352$		0			0
$353$	17.9340	−	10.3542i	0.954528	−	0.551097i	0.0600434	−	0.998196i	$-0.480876\pi$
$353$	17.9340	−	10.3542i	0.954528	−	0.551097i	0.894485	+	0.447099i	$0.147543\pi$
$354$		0			0
$355$	−1.49916	+	3.90340i	−0.0795672	+	0.207171i
$356$		0			0
$357$	18.8065	+	12.2697i	0.995343	+	0.649382i
$358$		0			0
$359$	34.3732			1.81415			0.907073	−	0.420973i	$-0.138311\pi$
$359$	34.3732			1.81415			0.907073	+	0.420973i	$0.138311\pi$
$360$		0			0
$361$	−15.5032			−0.815958
$362$		0			0
$363$	−0.425488	+	7.80281i	−0.0223323	+	0.409541i
$364$		0			0
$365$	8.09189	+	3.10781i	0.423549	+	0.162670i
$366$		0			0
$367$	0.994695	−	0.574287i	0.0519226	−	0.0299776i	−0.473814	−	0.880625i	$-0.657123\pi$
$367$	0.994695	−	0.574287i	0.0519226	−	0.0299776i	0.525737	+	0.850647i	$0.323790\pi$
$368$		0			0
$369$	4.79140	+	10.8854i	0.249430	+	0.566672i
$370$		0			0
$371$	12.1216	+	20.9952i	0.629321	+	1.09002i
$372$		0			0
$373$	−18.6572	−	10.7717i	−0.966032	−	0.557739i	−0.0680081	−	0.997685i	$-0.521664\pi$
$373$	−18.6572	−	10.7717i	−0.966032	−	0.557739i	−0.898024	+	0.439946i	$0.854998\pi$
$374$		0			0
$375$	11.4238	−	15.6364i	0.589921	−	0.807461i
$376$		0			0
$377$		−	15.0753i		−	0.776417i
$378$		0			0
$379$	−24.7632			−1.27200			−0.636001	−	0.771688i	$-0.719413\pi$
$379$	−24.7632			−1.27200			−0.636001	+	0.771688i	$0.719413\pi$
$380$		0			0
$381$	10.0313	+	19.7911i	0.513922	+	1.01393i
$382$		0			0
$383$	−3.06278	−	1.76829i	−0.156501	−	0.0903556i	0.419705	−	0.907661i	$-0.362134\pi$
$383$	−3.06278	−	1.76829i	−0.156501	−	0.0903556i	−0.576205	+	0.817305i	$0.695467\pi$
$384$		0			0
$385$	10.0271	−	8.11689i	0.511029	−	0.413675i
$386$		0			0
$387$	3.33008	−	30.4436i	0.169278	−	1.54754i
$388$		0			0
$389$	−15.3994	−	26.6726i	−0.780781	−	1.35235i	−0.931487	−	0.363774i	$-0.881488\pi$
$389$	−15.3994	−	26.6726i	−0.780781	−	1.35235i	0.150706	−	0.988579i	$-0.451845\pi$
$390$		0			0
$391$	−15.4466	+	26.7544i	−0.781170	+	1.35303i
$392$		0			0
$393$	−0.897031	+	16.4502i	−0.0452492	+	0.829804i
$394$		0			0
$395$	−29.2675	+	4.63025i	−1.47261	+	0.232973i
$396$		0			0
$397$		−	18.1196i		−	0.909399i	−0.890645	−	0.454700i	$-0.849747\pi$
$397$		−	18.1196i		−	0.909399i	0.890645	−	0.454700i	$-0.150253\pi$
$398$		0			0
$399$	−4.00845	+	6.14397i	−0.200674	+	0.307583i
$400$		0			0
$401$	6.79140	−	11.7631i	0.339146	−	0.587419i	−0.645126	−	0.764076i	$-0.723195\pi$
$401$	6.79140	−	11.7631i	0.339146	−	0.587419i	0.984272	+	0.176657i	$0.0565285\pi$
$402$		0			0
$403$	−40.8275	+	23.5718i	−2.03376	+	1.17419i
$404$		0			0
$405$	−20.0872	−	1.22684i	−0.998140	−	0.0609621i
$406$		0			0
$407$	−5.71708	+	3.30076i	−0.283385	+	0.163613i
$408$		0			0
$409$	14.1374	−	24.4868i	0.699052	−	1.21079i	−0.269744	−	0.962932i	$-0.586939\pi$
$409$	14.1374	−	24.4868i	0.699052	−	1.21079i	0.968796	−	0.247861i	$-0.0797276\pi$
$410$		0			0
$411$	−10.8774	+	16.6724i	−0.536542	+	0.822387i
$412$		0			0
$413$			3.58497i			0.176405i
$414$		0			0
$415$	5.13745	+	32.4734i	0.252187	+	1.59406i
$416$		0			0
$417$	1.08565	−	19.9092i	0.0531644	−	0.974957i
$418$		0			0
$419$	−11.0136	+	19.0760i	−0.538048	+	0.931926i	0.460961	+	0.887420i	$0.347505\pi$
$419$	−11.0136	+	19.0760i	−0.538048	+	0.931926i	−0.999009	+	0.0445058i	$0.985829\pi$
$420$		0			0
$421$	8.13745	+	14.0945i	0.396595	+	0.686922i	0.993303	−	0.115536i	$-0.0368584\pi$
$421$	8.13745	+	14.0945i	0.396595	+	0.686922i	−0.596708	+	0.802458i	$0.703525\pi$
$422$		0			0
$423$	−0.349355	+	3.19380i	−0.0169862	+	0.155288i
$424$		0			0
$425$	−19.1577	+	21.2618i	−0.929285	+	1.03135i
$426$		0			0
$427$	−1.70646	−	0.985227i	−0.0825816	−	0.0476785i
$428$		0			0
$429$	−10.0233	−	19.7752i	−0.483929	−	0.954754i
$430$		0			0
$431$	−18.6921			−0.900366			−0.450183	−	0.892936i	$-0.648641\pi$
$431$	−18.6921			−0.900366			−0.450183	+	0.892936i	$0.648641\pi$
$432$		0			0
$433$		−	11.9885i		−	0.576128i	−0.957611	−	0.288064i	$-0.906988\pi$
$433$		−	11.9885i		−	0.576128i	0.957611	−	0.288064i	$-0.0930116\pi$
$434$		0			0
$435$	9.41555	−	6.80789i	0.451441	−	0.326413i
$436$		0			0
$437$	−8.74051	−	5.04634i	−0.418115	−	0.241399i
$438$		0			0
$439$	−6.62580	−	11.4762i	−0.316232	−	0.547730i	0.663467	−	0.748206i	$-0.269085\pi$
$439$	−6.62580	−	11.4762i	−0.316232	−	0.547730i	−0.979699	+	0.200476i	$0.935751\pi$
$440$		0			0
$441$	2.26005	+	5.13453i	0.107621	+	0.244502i
$442$		0			0
$443$	20.1899	−	11.6566i	0.959249	−	0.553823i	0.0633071	−	0.997994i	$-0.479835\pi$
$443$	20.1899	−	11.6566i	0.959249	−	0.553823i	0.895942	+	0.444172i	$0.146502\pi$
$444$		0			0
$445$	10.7566	−	28.0072i	0.509911	−	1.32767i
$446$		0			0
$447$	1.85829	−	34.0783i	0.0878943	−	1.61185i
$448$		0			0
$449$	−10.7632			−0.507949			−0.253974	−	0.967211i	$-0.581738\pi$
$449$	−10.7632			−0.507949			−0.253974	+	0.967211i	$0.581738\pi$
$450$		0			0
$451$	−10.0983			−0.475509
$452$		0			0
$453$	22.3129	+	14.5574i	1.04835	+	0.683966i
$454$		0			0
$455$	9.12466	−	23.7581i	0.427771	−	1.11380i
$456$		0			0
$457$	−8.27488	+	4.77750i	−0.387083	+	0.223482i	−0.680895	−	0.732381i	$-0.738409\pi$
$457$	−8.27488	+	4.77750i	−0.387083	+	0.223482i	0.293813	+	0.955863i	$0.405076\pi$
$458$		0			0
$459$	29.3460	+	4.83913i	1.36976	+	0.225871i
$460$		0			0
$461$	8.63003	+	14.9476i	0.401940	+	0.696181i	0.993960	−	0.109742i	$-0.0350026\pi$
$461$	8.63003	+	14.9476i	0.401940	+	0.696181i	−0.592020	+	0.805923i	$0.701669\pi$
$462$		0			0
$463$	−31.0289	−	17.9145i	−1.44203	−	0.832559i	−0.444049	−	0.896002i	$-0.646458\pi$
$463$	−31.0289	−	17.9145i	−1.44203	−	0.832559i	−0.997985	+	0.0634435i	$0.979792\pi$
$464$		0			0
$465$	−33.1596	−	14.8547i	−1.53774	−	0.688872i
$466$		0			0
$467$			28.5287i			1.32015i	0.751199	+	0.660076i	$0.229476\pi$
$467$			28.5287i			1.32015i	−0.751199	+	0.660076i	$0.770524\pi$
$468$		0			0
$469$	−11.0000			−0.507933
$470$		0			0
$471$	21.5902	+	1.17732i	0.994825	+	0.0542478i
$472$		0			0
$473$	22.5193	+	13.0015i	1.03544	+	0.597811i
$474$		0			0
$475$	−6.94612	−	6.25872i	−0.318710	−	0.287170i
$476$		0			0
$477$	25.8980	+	18.9840i	1.18579	+	0.869218i
$478$		0			0
$479$	12.9130	+	22.3659i	0.590009	+	1.02193i	0.994231	+	0.107264i	$0.0342091\pi$
$479$	12.9130	+	22.3659i	0.590009	+	1.02193i	−0.404222	+	0.914661i	$0.632458\pi$
$480$		0			0
$481$	−6.51165	+	11.2785i	−0.296906	+	0.514256i
$482$		0			0
$483$	18.8859	−	9.57258i	0.859340	−	0.435568i
$484$		0			0
$485$	6.17302	+	39.0192i	0.280303	+	1.77177i
$486$		0			0
$487$		−	4.88880i		−	0.221533i	−0.993846	−	0.110766i	$-0.964669\pi$
$487$		−	4.88880i		−	0.221533i	0.993846	−	0.110766i	$-0.0353305\pi$
$488$		0			0
$489$	−1.51779	−	2.99448i	−0.0686368	−	0.135415i
$490$		0			0
$491$	4.75582	−	8.23733i	0.214627	−	0.371745i	−0.738530	−	0.674221i	$-0.764480\pi$
$491$	4.75582	−	8.23733i	0.214627	−	0.371745i	0.953157	+	0.302475i	$0.0978130\pi$
$492$		0			0
$493$	−14.8712	+	8.58588i	−0.669764	+	0.386688i
$494$		0			0
$495$	7.82450	−	15.1906i	0.351685	−	0.682765i
$496$		0			0
$497$	−3.66797	+	2.11771i	−0.164531	+	0.0949921i
$498$		0			0
$499$	4.75582	−	8.23733i	0.212900	−	0.368753i	−0.739721	−	0.672914i	$-0.765043\pi$
$499$	4.75582	−	8.23733i	0.212900	−	0.368753i	0.952621	+	0.304160i	$0.0983758\pi$
$500$		0			0
$501$	−0.565013	−	0.0308102i	−0.0252429	−	0.00137650i
$502$		0			0
$503$		−	13.7801i		−	0.614426i	−0.951641	−	0.307213i	$-0.900604\pi$
$503$		−	13.7801i		−	0.614426i	0.951641	−	0.307213i	$-0.0993964\pi$
$504$		0			0
$505$	11.7558	−	1.85983i	0.523127	−	0.0827612i
$506$		0			0
$507$	−17.7724	−	11.5951i	−0.789301	−	0.514956i
$508$		0			0
$509$	−0.988352	+	1.71188i	−0.0438079	+	0.0758776i	−0.887098	−	0.461581i	$-0.847282\pi$
$509$	−0.988352	+	1.71188i	−0.0438079	+	0.0758776i	0.843290	+	0.537459i	$0.180616\pi$
$510$		0			0
$511$	4.39008	+	7.60383i	0.194206	+	0.336374i
$512$		0			0
$513$	−1.58092	+	9.58720i	−0.0697993	+	0.423285i
$514$		0			0
$515$	10.4549	−	8.46315i	0.460697	−	0.372931i
$516$		0			0
$517$	−2.36247	−	1.36397i	−0.103901	−	0.0599875i
$518$		0			0
$519$	19.6847	−	30.1718i	0.864061	−	1.32439i
$520$		0			0
$521$	18.1804			0.796500			0.398250	−	0.917277i	$-0.369618\pi$
$521$	18.1804			0.796500			0.398250	+	0.917277i	$0.369618\pi$
$522$		0			0
$523$		−	15.0431i		−	0.657789i	−0.944367	−	0.328894i	$-0.893324\pi$
$523$		−	15.0431i		−	0.657789i	0.944367	−	0.328894i	$-0.106676\pi$
$524$		0			0
$525$	18.9592	−	5.03001i	0.827447	−	0.219528i
$526$		0			0
$527$	46.5053	+	26.8498i	2.02580	+	1.16960i
$528$		0			0
$529$	3.06501	+	5.30876i	0.133261	+	0.230816i
$530$		0			0
$531$	1.91297	+	4.34602i	0.0830159	+	0.188601i
$532$		0			0
$533$	−17.2526	+	9.96081i	−0.747294	+	0.431450i
$534$		0			0
$535$	9.80749	+	3.76671i	0.424015	+	0.162849i
$536$		0			0
$537$	5.86891	−	2.97473i	0.253262	−	0.128369i
$538$		0			0
$539$	−4.76325			−0.205167
$540$		0			0
$541$	12.7717			0.549098			0.274549	−	0.961573i	$-0.411471\pi$
$541$	12.7717			0.549098			0.274549	+	0.961573i	$0.411471\pi$
$542$		0			0
$543$	25.5093	−	12.9297i	1.09471	−	0.554868i
$544$		0			0
$545$	5.32464	−	13.8639i	0.228082	−	0.593864i
$546$		0			0
$547$	8.16575	−	4.71450i	0.349142	−	0.201577i	−0.315165	−	0.949037i	$-0.602060\pi$
$547$	8.16575	−	4.71450i	0.349142	−	0.201577i	0.664307	+	0.747459i	$0.268727\pi$
$548$		0			0
$549$	−2.59445	−	0.283795i	−0.110728	−	0.0121121i
$550$		0			0
$551$	−2.80496	−	4.85834i	−0.119495	−	0.206972i
$552$		0			0
$553$	−25.9931	−	15.0071i	−1.10534	−	0.638169i
$554$		0			0
$555$	−9.98481	+	1.02632i	−0.423832	+	0.0435648i
$556$		0			0
$557$			5.85726i			0.248180i	0.992271	+	0.124090i	$0.0396012\pi$
$557$			5.85726i			0.248180i	−0.992271	+	0.124090i	$0.960399\pi$
$558$		0			0
$559$	51.2982			2.16968
$560$		0			0
$561$	−13.7988	+	21.1502i	−0.582587	+	0.892962i
$562$		0			0
$563$	27.1173	+	15.6562i	1.14286	+	0.659830i	0.947137	−	0.320829i	$-0.103962\pi$
$563$	27.1173	+	15.6562i	1.14286	+	0.659830i	0.195722	+	0.980659i	$0.437295\pi$
$564$		0			0
$565$	22.2465	−	18.0084i	0.935915	−	0.757618i
$566$		0			0
$567$	−15.0327	−	13.7677i	−0.631315	−	0.578189i
$568$		0			0
$569$	−17.7202	−	30.6924i	−0.742871	−	1.28669i	−0.951183	−	0.308628i	$-0.900130\pi$
$569$	−17.7202	−	30.6924i	−0.742871	−	1.28669i	0.208311	−	0.978063i	$-0.433203\pi$
$570$		0			0
$571$	19.3975	−	33.5975i	0.811760	−	1.40601i	−0.0998712	−	0.995000i	$-0.531843\pi$
$571$	19.3975	−	33.5975i	0.811760	−	1.40601i	0.911631	−	0.411009i	$-0.134824\pi$
$572$		0			0
$573$	16.5104	+	10.7717i	0.689732	+	0.449996i
$574$		0			0
$575$	8.33017	+	25.6682i	0.347392	+	1.07044i
$576$		0			0
$577$			19.7634i			0.822761i	0.911464	+	0.411381i	$0.134953\pi$
$577$			19.7634i			0.822761i	−0.911464	+	0.411381i	$0.865047\pi$
$578$		0			0
$579$	−24.3596	−	1.32833i	−1.01235	−	0.0552035i
$580$		0			0
$581$	−16.6510	+	28.8404i	−0.690800	+	1.19650i
$582$		0			0
$583$	−23.6117	+	13.6322i	−0.977896	+	0.564589i
$584$		0			0
$585$	−1.61582	−	33.6706i	−0.0668059	−	1.39211i
$586$		0			0
$587$	−18.2194	+	10.5190i	−0.751997	+	0.434165i	−0.826415	−	0.563062i	$-0.809623\pi$
$587$	−18.2194	+	10.5190i	−0.751997	+	0.434165i	0.0744183	+	0.997227i	$0.476290\pi$
$588$		0			0
$589$	−8.77170	+	15.1930i	−0.361432	+	0.626018i
$590$		0			0
$591$	6.19273	+	12.2178i	0.254735	+	0.502571i
$592$		0			0
$593$		−	14.9390i		−	0.613471i	−0.951795	−	0.306735i	$-0.900763\pi$
$593$		−	14.9390i		−	0.613471i	0.951795	−	0.306735i	$-0.0992367\pi$
$594$		0			0
$595$	−28.6332	+	4.52991i	−1.17385	+	0.185708i
$596$		0			0
$597$	−2.88898	+	1.46432i	−0.118238	+	0.0599304i
$598$		0			0
$599$	10.7558	−	18.6296i	0.439471	−	0.761186i	−0.558178	−	0.829721i	$-0.688499\pi$
$599$	10.7558	−	18.6296i	0.439471	−	0.761186i	0.997649	+	0.0685353i	$0.0218326\pi$
$600$		0			0
$601$	−2.75582	−	4.77323i	−0.112412	−	0.194704i	0.804330	−	0.594183i	$-0.202524\pi$
$601$	−2.75582	−	4.77323i	−0.112412	−	0.194704i	−0.916742	+	0.399479i	$0.869191\pi$
$602$		0			0
$603$	−13.3352	+	5.86969i	−0.543049	+	0.239032i
$604$		0			0
$605$	−6.34743	−	7.84123i	−0.258060	−	0.318792i
$606$		0			0
$607$	−8.40298	−	4.85146i	−0.341067	−	0.196915i	0.319677	−	0.947527i	$-0.396426\pi$
$607$	−8.40298	−	4.85146i	−0.341067	−	0.196915i	−0.660744	+	0.750612i	$0.729759\pi$
$608$		0			0
$609$	11.7516	+	0.640815i	0.476199	+	0.0259671i
$610$		0			0
$611$	−5.38162			−0.217717
$612$		0			0
$613$			2.25467i			0.0910653i	0.998963	+	0.0455326i	$0.0144985\pi$
$613$			2.25467i			0.0910653i	−0.998963	+	0.0455326i	$0.985501\pi$
$614$		0			0
$615$	−14.0124	−	6.27722i	−0.565033	−	0.253122i
$616$		0			0
$617$	−34.7755	−	20.0777i	−1.40001	−	0.808297i	−0.405618	−	0.914043i	$-0.632944\pi$
$617$	−34.7755	−	20.0777i	−1.40001	−	0.808297i	−0.994393	+	0.105746i	$0.966277\pi$
$618$		0			0
$619$	2.56079	+	4.43541i	0.102927	+	0.178274i	0.912889	−	0.408207i	$-0.133846\pi$
$619$	2.56079	+	4.43541i	0.102927	+	0.178274i	−0.809963	+	0.586482i	$0.800513\pi$
$620$		0			0
$621$	17.7872	−	21.6824i	0.713775	−	0.870085i
$622$		0			0
$623$	26.3180	−	15.1947i	1.05441	−	0.608762i
$624$		0			0
$625$	2.59578	+	24.8649i	0.103831	+	0.994595i
$626$		0			0
$627$	−6.90966	−	4.50800i	−0.275945	−	0.180032i
$628$		0			0
$629$	14.8344			0.591486
$630$		0			0
$631$	−1.28335			−0.0510892			−0.0255446	−	0.999674i	$-0.508132\pi$
$631$	−1.28335			−0.0510892			−0.0255446	+	0.999674i	$0.508132\pi$
$632$		0			0
$633$	−1.07339	+	19.6843i	−0.0426633	+	0.782381i
$634$		0			0
$635$	−26.7404	−	10.2701i	−1.06116	−	0.407555i
$636$		0			0
$637$	−8.13787	+	4.69840i	−0.322434	+	0.186157i
$638$		0			0
$639$	−3.31661	+	4.52453i	−0.131203	+	0.178988i
$640$		0			0
$641$	14.2694	+	24.7153i	0.563607	+	0.976196i	0.997178	+	0.0750763i	$0.0239200\pi$
$641$	14.2694	+	24.7153i	0.563607	+	0.976196i	−0.433571	+	0.901119i	$0.642747\pi$
$642$		0			0
$643$	−20.1899	−	11.6566i	−0.796210	−	0.459692i	0.0459341	−	0.998944i	$-0.485374\pi$
$643$	−20.1899	−	11.6566i	−0.796210	−	0.459692i	−0.842144	+	0.539252i	$0.818707\pi$
$644$		0			0
$645$	23.1659	+	32.0392i	0.912156	+	1.26154i
$646$		0			0
$647$			8.93381i			0.351224i	0.984459	+	0.175612i	$0.0561905\pi$
$647$			8.93381i			0.351224i	−0.984459	+	0.175612i	$0.943810\pi$
$648$		0			0
$649$	−4.03175			−0.158260
$650$		0			0
$651$	−16.6394	−	32.8281i	−0.652148	−	1.28664i
$652$		0			0
$653$	−12.4110	−	7.16552i	−0.485682	−	0.280408i	0.237100	−	0.971485i	$-0.423803\pi$
$653$	−12.4110	−	7.16552i	−0.485682	−	0.280408i	−0.722781	+	0.691077i	$0.757137\pi$
$654$		0			0
$655$	−13.3819	−	16.5312i	−0.522875	−	0.645928i
$656$		0			0
$657$	9.37950	+	6.87545i	0.365929	+	0.268237i
$658$		0			0
$659$	−3.79140	−	6.56690i	−0.147692	−	0.255810i	0.782682	−	0.622422i	$-0.213851\pi$
$659$	−3.79140	−	6.56690i	−0.147692	−	0.255810i	−0.930374	+	0.366612i	$0.880518\pi$
$660$		0			0
$661$	−14.7558	+	25.5578i	−0.573935	+	0.994085i	0.422221	+	0.906493i	$0.361250\pi$
$661$	−14.7558	+	25.5578i	−0.573935	+	0.994085i	−0.996156	+	0.0875919i	$0.972083\pi$
$662$		0			0
$663$	−2.71262	+	49.7455i	−0.105350	+	1.93196i
$664$		0			0
$665$	−1.47990	−	9.35433i	−0.0573880	−	0.362745i
$666$		0			0
$667$			16.1917i			0.626944i
$668$		0			0
$669$	−4.59636	+	7.04509i	−0.177706	+	0.272379i
$670$		0			0
$671$	1.10801	−	1.91913i	0.0427743	−	0.0740872i
$672$		0			0
$673$	−6.04942	+	3.49263i	−0.233188	+	0.134631i	−0.612042	−	0.790825i	$-0.709652\pi$
$673$	−6.04942	+	3.49263i	−0.233188	+	0.134631i	0.378854	+	0.925456i	$0.376318\pi$
$674$		0			0
$675$	20.2999	−	16.2146i	0.781344	−	0.624100i
$676$		0			0
$677$	−17.4100	+	10.0517i	−0.669121	+	0.386317i	−0.795743	−	0.605634i	$-0.792920\pi$
$677$	−17.4100	+	10.0517i	−0.669121	+	0.386317i	0.126623	+	0.991951i	$0.459586\pi$
$678$		0			0
$679$	−20.0074	+	34.6539i	−0.767814	+	1.32989i
$680$		0			0
$681$	−6.69695	+	10.2648i	−0.256628	+	0.393347i
$682$		0			0
$683$		−	44.5270i		−	1.70378i	−0.523721	−	0.851890i	$-0.675456\pi$
$683$		−	44.5270i		−	1.70378i	0.523721	−	0.851890i	$-0.324544\pi$
$684$		0			0
$685$	−4.01587	−	25.3840i	−0.153439	−	0.969874i
$686$		0			0
$687$	−0.824253	+	15.1156i	−0.0314472	+	0.576695i
$688$		0			0
$689$	−26.8933	+	46.5805i	−1.02455	+	1.77458i
$690$		0			0
$691$	−16.8858	−	29.2471i	−0.642368	−	1.11261i	−0.984903	−	0.173109i	$-0.944619\pi$
$691$	−16.8858	−	29.2471i	−0.642368	−	1.11261i	0.342535	−	0.939505i	$-0.388715\pi$
$692$		0			0
$693$	15.8413	−	6.97283i	0.601763	−	0.264876i
$694$		0			0
$695$	16.1957	+	20.0072i	0.614339	+	0.758917i
$696$		0			0
$697$	19.6519	+	11.3460i	0.744368	+	0.429761i
$698$		0			0
$699$	7.25391	+	14.3114i	0.274368	+	0.541307i
$700$		0			0
$701$	−6.78398			−0.256227			−0.128114	−	0.991759i	$-0.540892\pi$
$701$	−6.78398			−0.256227			−0.128114	+	0.991759i	$0.540892\pi$
$702$		0			0
$703$			4.84632i			0.182782i
$704$		0			0
$705$	−2.43030	−	3.36119i	−0.0915304	−	0.126590i
$706$		0			0
$707$	10.4406	+	6.02790i	0.392660	+	0.226702i
$708$		0			0
$709$	−22.3933	−	38.7863i	−0.840997	−	1.45665i	−0.889053	−	0.457805i	$-0.848636\pi$
$709$	−22.3933	−	38.7863i	−0.840997	−	1.45665i	0.0480558	−	0.998845i	$-0.484697\pi$
$710$		0			0
$711$	−39.5191	−	4.32281i	−1.48208	−	0.162118i
$712$		0			0
$713$	43.8510	−	25.3174i	1.64223	−	0.948143i
$714$		0			0
$715$	26.7189	+	10.2618i	0.999232	+	0.383770i
$716$		0			0
$717$	1.19557	−	21.9251i	0.0446496	−	0.818807i
$718$		0			0
$719$	−5.55105			−0.207019			−0.103510	−	0.994628i	$-0.533007\pi$
$719$	−5.55105			−0.207019			−0.103510	+	0.994628i	$0.533007\pi$
$720$		0			0
$721$	13.6248			0.507413
$722$		0			0
$723$	−15.3910	−	10.0414i	−0.572396	−	0.373443i
$724$		0			0
$725$	−3.12382	+	14.6711i	−0.116016	+	0.544872i
$726$		0			0
$727$	32.5248	−	18.7782i	1.20628	−	0.696444i	0.244333	−	0.969691i	$-0.421431\pi$
$727$	32.5248	−	18.7782i	1.20628	−	0.696444i	0.961944	+	0.273247i	$0.0880977\pi$
$728$		0			0
$729$	−25.5705	−	8.66882i	−0.947056	−	0.321068i
$730$		0			0
$731$	−29.2160	−	50.6036i	−1.08059	−	1.87164i
$732$		0			0
$733$	29.9162	+	17.2721i	1.10498	+	0.637959i	0.937524	−	0.347920i	$-0.113112\pi$
$733$	29.9162	+	17.2721i	1.10498	+	0.637959i	0.167454	+	0.985880i	$0.446445\pi$
$734$		0			0
$735$	−6.60948	−	2.96089i	−0.243794	−	0.109214i
$736$		0			0
$737$		−	12.3709i		−	0.455687i
$738$		0			0
$739$	0.520101			0.0191322			0.00956612	−	0.999954i	$-0.496955\pi$
$739$	0.520101			0.0191322			0.00956612	+	0.999954i	$0.496955\pi$
$740$		0			0
$741$	−16.2516	−	0.886200i	−0.597017	−	0.0325554i
$742$		0			0
$743$	−36.1927	−	20.8959i	−1.32778	−	0.766596i	−0.342826	−	0.939399i	$-0.611384\pi$
$743$	−36.1927	−	20.8959i	−1.32778	−	0.766596i	−0.984956	+	0.172803i	$0.944718\pi$
$744$		0			0
$745$	27.7221	+	34.2462i	1.01566	+	1.25468i
$746$		0			0
$747$	−4.79632	+	43.8479i	−0.175488	+	1.60431i
$748$		0			0
$749$	5.32084	+	9.21596i	0.194419	+	0.336744i
$750$		0			0
$751$	−8.56079	+	14.8277i	−0.312388	+	0.541071i	−0.978879	−	0.204442i	$-0.934462\pi$
$751$	−8.56079	+	14.8277i	−0.312388	+	0.541071i	0.666491	+	0.745513i	$0.267795\pi$
$752$		0			0
$753$	−28.7870	+	14.5911i	−1.04906	+	0.531728i
$754$		0			0
$755$	−33.9718	+	5.37451i	−1.23636	+	0.195598i
$756$		0			0
$757$		−	6.80515i		−	0.247337i	−0.992324	−	0.123669i	$-0.960534\pi$
$757$		−	6.80515i		−	0.247337i	0.992324	−	0.123669i	$-0.0394660\pi$
$758$		0			0
$759$	10.7656	+	21.2396i	0.390765	+	0.770948i
$760$		0			0
$761$	22.6216	−	39.1817i	0.820031	−	1.42034i	−0.0856268	−	0.996327i	$-0.527289\pi$
$761$	22.6216	−	39.1817i	0.820031	−	1.42034i	0.905658	−	0.424009i	$-0.139377\pi$
$762$		0			0
$763$	13.0277	−	7.52155i	0.471635	−	0.272298i
$764$		0			0
$765$	−32.2945	+	20.7705i	−1.16761	+	0.750958i
$766$		0			0
$767$	−6.88813	+	3.97686i	−0.248716	+	0.143596i
$768$		0			0
$769$	−7.62157	+	13.2009i	−0.274841	+	0.476038i	−0.970095	−	0.242726i	$-0.921959\pi$
$769$	−7.62157	+	13.2009i	−0.274841	+	0.476038i	0.695254	+	0.718764i	$0.255292\pi$
$770$		0			0
$771$	45.6406	+	2.48879i	1.64371	+	0.0896314i
$772$		0			0
$773$		0			0		1.00000			$0$
$773$		0			0		−1.00000			$\pi$
$774$		0			0
$775$	44.6173	−	14.4798i	1.60270	−	0.520128i
$776$		0			0
$777$	−8.51511	−	5.55543i	−0.305478	−	0.199300i
$778$		0			0
$779$	−3.70669	+	6.42017i	−0.132806	+	0.230026i
$780$		0			0
$781$	−2.38162	−	4.12509i	−0.0852212	−	0.147607i
$782$		0			0
$783$	14.5883	−	5.49390i	0.521342	−	0.196336i
$784$		0			0
$785$	−21.6965	+	17.5632i	−0.774383	+	0.626858i
$786$		0			0
$787$	17.5445	+	10.1293i	0.625392	+	0.361070i	0.778965	−	0.627067i	$-0.215745\pi$
$787$	17.5445	+	10.1293i	0.625392	+	0.361070i	−0.153573	+	0.988137i	$0.549078\pi$
$788$		0			0
$789$	−12.9447	+	19.8411i	−0.460844	+	0.706361i
$790$		0			0
$791$	28.9915			1.03082
$792$		0			0
$793$		−	4.37171i		−	0.155244i
$794$		0			0
$795$	−41.2375	+	4.23872i	−1.46254	+	0.150332i
$796$		0			0
$797$	−9.75929	−	5.63453i	−0.345692	−	0.199585i	0.317094	−	0.948394i	$-0.397293\pi$
$797$	−9.75929	−	5.63453i	−0.345692	−	0.199585i	−0.662786	+	0.748809i	$0.730626\pi$
$798$		0			0
$799$	3.06501	+	5.30876i	0.108432	+	0.187810i
$800$		0			0
$801$	23.7969	−	32.4638i	0.840822	−	1.14705i
$802$		0			0
$803$	−8.55146	+	4.93719i	−0.301774	+	0.174230i
$804$		0			0
$805$	−9.80037	+	25.5175i	−0.345418	+	0.899373i
$806$		0			0
$807$	−34.9798	+	17.7299i	−1.23135	+	0.624124i
$808$		0			0
$809$	26.5032			0.931803			0.465901	−	0.884837i	$-0.345730\pi$
$809$	26.5032			0.931803			0.465901	+	0.884837i	$0.345730\pi$
$810$		0			0
$811$	−1.54340			−0.0541960			−0.0270980	−	0.999633i	$-0.508627\pi$
$811$	−1.54340			−0.0541960			−0.0270980	+	0.999633i	$0.508627\pi$
$812$		0			0
$813$	−9.06870	+	4.59658i	−0.318053	+	0.161209i
$814$		0			0
$815$	4.04594	+	1.55391i	0.141723	+	0.0544309i
$816$		0			0
$817$	16.5319	−	9.54472i	0.578380	−	0.333928i
$818$		0			0
$819$	20.1866	−	27.5386i	0.705376	−	0.962276i
$820$		0			0
$821$	−5.65946	−	9.80247i	−0.197517	−	0.342109i	0.750206	−	0.661204i	$-0.229954\pi$
$821$	−5.65946	−	9.80247i	−0.197517	−	0.342109i	−0.947723	+	0.319095i	$0.896621\pi$
$822$		0			0
$823$	8.42080	+	4.86175i	0.293531	+	0.169470i	0.639533	−	0.768764i	$-0.279128\pi$
$823$	8.42080	+	4.86175i	0.293531	+	0.169470i	−0.346002	+	0.938234i	$0.612461\pi$
$824$		0			0
$825$	5.65687	+	21.3220i	0.196947	+	0.742336i
$826$		0			0
$827$		−	25.9722i		−	0.903143i	−0.892235	−	0.451571i	$-0.850864\pi$
$827$		−	25.9722i		−	0.903143i	0.892235	−	0.451571i	$-0.149136\pi$
$828$		0			0
$829$	9.61838			0.334060			0.167030	−	0.985952i	$-0.446582\pi$
$829$	9.61838			0.334060			0.167030	+	0.985952i	$0.446582\pi$
$830$		0			0
$831$	0.149727	−	0.229495i	0.00519398	−	0.00796110i
$832$		0			0
$833$	9.26957	+	5.35179i	0.321172	+	0.185429i
$834$		0			0
$835$	0.567795	−	0.459626i	0.0196494	−	0.0159060i
$836$		0			0
$837$	−37.6890	−	30.9182i	−1.30272	−	1.06869i
$838$		0			0
$839$	10.0453	+	17.3990i	0.346803	+	0.600680i	0.985680	−	0.168629i	$-0.0539340\pi$
$839$	10.0453	+	17.3990i	0.346803	+	0.600680i	−0.638877	+	0.769309i	$0.720601\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	−4.91771	−	3.20842i	−0.169375	−	0.110504i
$844$		0			0
$845$	27.0589	−	4.28084i	0.930854	−	0.147265i
$846$		0			0
$847$		−	10.2187i		−	0.351118i
$848$		0			0
$849$	−20.7160	−	1.12965i	−0.710972	−	0.0387693i
$850$		0			0
$851$	6.99386	−	12.1137i	0.239746	−	0.415253i
$852$		0			0
$853$	16.3949	−	9.46562i	0.561352	−	0.324097i	−0.192336	−	0.981329i	$-0.561606\pi$
$853$	16.3949	−	9.46562i	0.561352	−	0.324097i	0.753688	+	0.657232i	$0.228273\pi$
$854$		0			0
$855$	−6.78561	−	10.5504i	−0.232063	−	0.360817i
$856$		0			0
$857$	32.9625	−	19.0309i	1.12598	−	0.650084i	0.183058	−	0.983102i	$-0.441400\pi$
$857$	32.9625	−	19.0309i	1.12598	−	0.650084i	0.942920	+	0.333019i	$0.108067\pi$
$858$		0			0
$859$	3.17916	−	5.50647i	0.108472	−	0.187878i	−0.806680	−	0.590989i	$-0.798738\pi$
$859$	3.17916	−	5.50647i	0.108472	−	0.187878i	0.915151	+	0.403111i	$0.132071\pi$
$860$		0			0
$861$	−7.03135	−	13.8723i	−0.239628	−	0.472767i
$862$		0			0
$863$		−	6.61609i		−	0.225214i	−0.993640	−	0.112607i	$-0.964080\pi$
$863$		−	6.61609i		−	0.225214i	0.993640	−	0.112607i	$-0.0359202\pi$
$864$		0			0
$865$	7.26747	+	45.9371i	0.247101	+	1.56191i
$866$		0			0
$867$	24.3531	−	12.3437i	0.827075	−	0.419213i
$868$		0			0
$869$	16.8774	−	29.2325i	0.572526	−	0.991645i
$870$		0			0
$871$	−12.2025	−	21.1353i	−0.413465	−	0.716142i
$872$		0			0
$873$	−5.76314	+	52.6866i	−0.195053	+	1.78317i
$874$		0			0
$875$	−13.8030	+	21.2304i	−0.466628	+	0.717718i
$876$		0			0
$877$	−18.6762	−	10.7827i	−0.630649	−	0.364105i	0.150354	−	0.988632i	$-0.451959\pi$
$877$	−18.6762	−	10.7827i	−0.630649	−	0.364105i	−0.781003	+	0.624527i	$0.785292\pi$
$878$		0			0
$879$	26.0724	+	1.42173i	0.879401	+	0.0479538i
$880$		0			0
$881$	−43.1449			−1.45359			−0.726794	−	0.686856i	$-0.758990\pi$
$881$	−43.1449			−1.45359			−0.726794	+	0.686856i	$0.758990\pi$
$882$		0			0
$883$			18.3306i			0.616874i	0.951245	+	0.308437i	$0.0998060\pi$
$883$			18.3306i			0.616874i	−0.951245	+	0.308437i	$0.900194\pi$
$884$		0			0
$885$	−5.59445	−	2.50619i	−0.188055	−	0.0842446i
$886$		0			0
$887$	−32.9625	−	19.0309i	−1.10677	−	0.638996i	−0.168781	−	0.985654i	$-0.553983\pi$
$887$	−32.9625	−	19.0309i	−1.10677	−	0.638996i	−0.937992	+	0.346658i	$0.887316\pi$
$888$		0			0
$889$	−14.5074	−	25.1276i	−0.486563	−	0.842752i
$890$		0			0
$891$	15.4835	−	16.9062i	0.518717	−	0.566377i
$892$		0			0
$893$	−1.73434	+	1.00132i	−0.0580376	+	0.0335080i
$894$		0			0
$895$	−3.04552	+	7.92969i	−0.101800	+	0.265060i
$896$		0			0
$897$	39.3431	+	25.6682i	1.31363	+	0.857038i
$898$		0			0
$899$	28.1449			0.938684
$900$		0			0
$901$	61.2664			2.04108
$902$		0			0
$903$	−2.18056	+	39.9883i	−0.0725647	+	1.33073i
$904$		0			0
$905$	−13.2374	+	34.4666i	−0.440026	+	1.14571i
$906$		0			0
$907$	25.2624	−	14.5852i	0.838824	−	0.484295i	−0.0180404	−	0.999837i	$-0.505743\pi$
$907$	25.2624	−	14.5852i	0.838824	−	0.484295i	0.856864	+	0.515542i	$0.172409\pi$
$908$		0			0
$909$	15.8736	+	1.73634i	0.526493	+	0.0575906i
$910$		0			0
$911$	1.75582	+	3.04118i	0.0581730	+	0.100759i	0.893645	−	0.448774i	$-0.148139\pi$
$911$	1.75582	+	3.04118i	0.0581730	+	0.100759i	−0.835472	+	0.549533i	$0.814806\pi$
$912$		0			0
$913$	−32.4346	−	18.7261i	−1.07343	−	0.619744i
$914$		0			0
$915$	2.73043	−	1.97423i	0.0902653	−	0.0652661i
$916$		0			0
$917$		−	21.5435i		−	0.711428i
$918$		0			0
$919$	24.2431			0.799708			0.399854	−	0.916579i	$-0.369061\pi$
$919$	24.2431			0.799708			0.399854	+	0.916579i	$0.369061\pi$
$920$		0			0
$921$	4.70246	+	9.27758i	0.154951	+	0.305707i
$922$		0			0
$923$	−8.13787	−	4.69840i	−0.267861	−	0.154650i
$924$		0			0
$925$	8.67414	−	9.62682i	0.285204	−	0.316528i
$926$		0			0
$927$	16.5171	−	7.27029i	0.542494	−	0.238788i
$928$		0			0
$929$	−4.36575	−	7.56170i	−0.143236	−	0.248091i	0.785478	−	0.618890i	$-0.212417\pi$
$929$	−4.36575	−	7.56170i	−0.143236	−	0.248091i	−0.928713	+	0.370799i	$0.879084\pi$
$930$		0			0
$931$	−1.74840	+	3.02832i	−0.0573016	+	0.0992493i
$932$		0			0
$933$	2.86745	−	52.5847i	0.0938760	−	1.72155i
$934$		0			0
$935$	−5.09445	−	32.2016i	−0.166606	−	1.05311i
$936$		0			0
$937$			35.9873i			1.17565i	0.808987	+	0.587826i	$0.200016\pi$
$937$			35.9873i			1.17565i	−0.808987	+	0.587826i	$0.799984\pi$
$938$		0			0
$939$	−17.3179	+	26.5441i	−0.565148	+	0.866233i
$940$		0			0
$941$	13.3344	−	23.0959i	0.434689	−	0.752903i	−0.562581	−	0.826742i	$-0.690192\pi$
$941$	13.3344	−	23.0959i	0.434689	−	0.752903i	0.997270	+	0.0738386i	$0.0235250\pi$
$942$		0			0
$943$	18.5302	−	10.6984i	0.603428	−	0.348389i
$944$		0			0
$945$	26.3158	+	0.171684i	0.856055	+	0.00558489i
$946$		0			0
$947$	6.97944	−	4.02958i	0.226801	−	0.130944i	−0.382294	−	0.924041i	$-0.624866\pi$
$947$	6.97944	−	4.02958i	0.226801	−	0.130944i	0.609096	+	0.793097i	$0.291533\pi$
$948$		0			0
$949$	−9.73995	+	16.8701i	−0.316172	+	0.547626i
$950$		0			0
$951$	8.01970	−	12.2922i	0.260057	−	0.398603i
$952$		0			0
$953$			23.7733i			0.770092i	0.922897	+	0.385046i	$0.125814\pi$
$953$			23.7733i			0.770092i	−0.922897	+	0.385046i	$0.874186\pi$
$954$		0			0
$955$	−25.1374	+	3.97686i	−0.813429	+	0.128688i
$956$		0			0
$957$	−0.720676	+	13.2161i	−0.0232961	+	0.427217i
$958$		0			0
$959$	13.0159	−	22.5442i	0.420305	−	0.727989i
$960$		0			0
$961$	−28.5074	−	49.3763i	−0.919594	−	1.59278i
$962$		0			0
$963$	11.3681	+	8.33314i	0.366332	+	0.268532i
$964$		0			0
$965$	24.4796	−	19.8161i	0.788025	−	0.637901i
$966$		0			0
$967$	29.2044	+	16.8612i	0.939150	+	0.542218i	0.889694	−	0.456558i	$-0.150918\pi$
$967$	29.2044	+	16.8612i	0.939150	+	0.542218i	0.0494560	+	0.998776i	$0.484251\pi$
$968$		0			0
$969$	8.38162	+	16.5363i	0.269257	+	0.531222i
$970$		0			0
$971$	36.1766			1.16096			0.580481	−	0.814273i	$-0.302864\pi$
$971$	36.1766			1.16096			0.580481	+	0.814273i	$0.302864\pi$
$972$		0			0
$973$			26.0734i			0.835874i
$974$		0			0
$975$	30.6963	+	30.8481i	0.983069	+	0.987931i
$976$		0			0
$977$	43.3638	+	25.0361i	1.38733	+	0.800976i	0.993014	−	0.117999i	$-0.0376479\pi$
$977$	43.3638	+	25.0361i	1.38733	+	0.800976i	0.394317	+	0.918975i	$0.370981\pi$
$978$		0			0
$979$	17.0883	+	29.5978i	0.546145	+	0.945950i
$980$		0			0
$981$	11.7798	−	16.0700i	0.376099	−	0.513075i
$982$		0			0
$983$	−34.9823	+	20.1971i	−1.11576	+	0.644186i	−0.940316	−	0.340303i	$-0.889471\pi$
$983$	−34.9823	+	20.1971i	−1.11576	+	0.644186i	−0.175447	+	0.984489i	$0.556137\pi$
$984$		0			0
$985$	−16.5078	−	6.34009i	−0.525984	−	0.202012i
$986$		0			0
$987$	0.228760	−	4.19512i	0.00728151	−	0.133532i
$988$		0			0
$989$	−55.0970			−1.75198
$990$		0			0
$991$	−32.0000			−1.01651			−0.508257	−	0.861206i	$-0.669710\pi$
$991$	−32.0000			−1.01651			−0.508257	+	0.861206i	$0.669710\pi$
$992$		0			0
$993$	−22.1243	−	14.4343i	−0.702093	−	0.458060i
$994$		0			0
$995$	1.49916	−	3.90340i	0.0475266	−	0.123746i
$996$		0			0
$997$	−37.1963	+	21.4753i	−1.17802	+	0.680130i	−0.955556	−	0.294811i	$-0.904743\pi$
$997$	−37.1963	+	21.4753i	−1.17802	+	0.680130i	−0.222464	+	0.974941i	$0.571410\pi$
$998$		0			0
$999$	−13.2872	−	2.19104i	−0.420388	−	0.0693215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.r.a.49.2	✓	12
3.2	odd	2		540.2.r.a.469.3		12
4.3	odd	2		720.2.by.e.49.5		12
5.2	odd	4		900.2.i.f.301.5		12
5.3	odd	4		900.2.i.f.301.2		12
5.4	even	2	inner	180.2.r.a.49.5	yes	12
9.2	odd	6		540.2.r.a.289.2		12
9.4	even	3		1620.2.d.c.649.2		6
9.5	odd	6		1620.2.d.d.649.5		6
9.7	even	3	inner	180.2.r.a.169.5	yes	12
12.11	even	2		2160.2.by.e.1009.3		12
15.2	even	4		2700.2.i.f.901.5		12
15.8	even	4		2700.2.i.f.901.2		12
15.14	odd	2		540.2.r.a.469.2		12
20.19	odd	2		720.2.by.e.49.2		12
36.7	odd	6		720.2.by.e.529.2		12
36.11	even	6		2160.2.by.e.289.2		12
45.2	even	12		2700.2.i.f.1801.5		12
45.4	even	6		1620.2.d.c.649.1		6
45.7	odd	12		900.2.i.f.601.5		12
45.13	odd	12		8100.2.a.bc.1.5		6
45.14	odd	6		1620.2.d.d.649.6		6
45.22	odd	12		8100.2.a.bc.1.2		6
45.23	even	12		8100.2.a.bd.1.5		6
45.29	odd	6		540.2.r.a.289.3		12
45.32	even	12		8100.2.a.bd.1.2		6
45.34	even	6	inner	180.2.r.a.169.2	yes	12
45.38	even	12		2700.2.i.f.1801.2		12
45.43	odd	12		900.2.i.f.601.2		12
60.59	even	2		2160.2.by.e.1009.2		12
180.79	odd	6		720.2.by.e.529.5		12
180.119	even	6		2160.2.by.e.289.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.r.a.49.2	✓	12	1.1	even	1	trivial
180.2.r.a.49.5	yes	12	5.4	even	2	inner
180.2.r.a.169.2	yes	12	45.34	even	6	inner
180.2.r.a.169.5	yes	12	9.7	even	3	inner
540.2.r.a.289.2		12	9.2	odd	6
540.2.r.a.289.3		12	45.29	odd	6
540.2.r.a.469.2		12	15.14	odd	2
540.2.r.a.469.3		12	3.2	odd	2
720.2.by.e.49.2		12	20.19	odd	2
720.2.by.e.49.5		12	4.3	odd	2
720.2.by.e.529.2		12	36.7	odd	6
720.2.by.e.529.5		12	180.79	odd	6
900.2.i.f.301.2		12	5.3	odd	4
900.2.i.f.301.5		12	5.2	odd	4
900.2.i.f.601.2		12	45.43	odd	12
900.2.i.f.601.5		12	45.7	odd	12
1620.2.d.c.649.1		6	45.4	even	6
1620.2.d.c.649.2		6	9.4	even	3
1620.2.d.d.649.5		6	9.5	odd	6
1620.2.d.d.649.6		6	45.14	odd	6
2160.2.by.e.289.2		12	36.11	even	6
2160.2.by.e.289.3		12	180.119	even	6
2160.2.by.e.1009.2		12	60.59	even	2
2160.2.by.e.1009.3		12	12.11	even	2
2700.2.i.f.901.2		12	15.8	even	4
2700.2.i.f.901.5		12	15.2	even	4
2700.2.i.f.1801.2		12	45.38	even	12
2700.2.i.f.1801.5		12	45.2	even	12
8100.2.a.bc.1.2		6	45.22	odd	12
8100.2.a.bc.1.5		6	45.13	odd	12
8100.2.a.bd.1.2		6	45.32	even	12
8100.2.a.bd.1.5		6	45.23	even	12

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54493 + 0.783067i) q^{3} +(0.801701 - 2.08741i) q^{5} +(1.96151 - 1.13248i) q^{7} +(1.77361 - 2.41957i) q^{9} +O(q^{10})\)	\(q+(-1.54493 + 0.783067i) q^{3} +(0.801701 - 2.08741i) q^{5} +(1.96151 - 1.13248i) q^{7} +(1.77361 - 2.41957i) q^{9} +(1.27361 + 2.20596i) q^{11} +(4.35186 + 2.51255i) q^{13} +(0.396010 + 3.85268i) q^{15} -5.72392i q^{17} +1.86997 q^{19} +(-2.14359 + 3.28559i) q^{21} +(-4.67413 - 2.69861i) q^{23} +(-3.71455 - 3.34696i) q^{25} +(-0.845423 + 5.12692i) q^{27} +(-1.50000 - 2.59808i) q^{29} +(-4.69081 + 8.12472i) q^{31} +(-3.69506 - 2.41073i) q^{33} +(-0.791400 - 5.00238i) q^{35} +2.59165i q^{37} +(-8.69081 - 0.473910i) q^{39} +(-1.98221 + 3.43329i) q^{41} +(8.84073 - 5.10420i) q^{43} +(-3.62872 - 5.64202i) q^{45} +(-0.927469 + 0.535475i) q^{47} +(-0.934987 + 1.61945i) q^{49} +(4.48221 + 8.84305i) q^{51} +10.7036i q^{53} +(5.62580 - 0.890028i) q^{55} +(-2.88898 + 1.46432i) q^{57} +(-0.791400 + 1.37075i) q^{59} +(-0.434987 - 0.753420i) q^{61} +(0.738852 - 6.75458i) q^{63} +(8.73361 - 7.06980i) q^{65} +(-4.20594 - 2.42830i) q^{67} +(9.33440 + 0.509005i) q^{69} -1.86997 q^{71} +3.87652i q^{73} +(8.35961 + 2.26207i) q^{75} +(4.99640 + 2.88468i) q^{77} +(-6.62580 - 11.4762i) q^{79} +(-2.70860 - 8.58274i) q^{81} +(-12.7333 + 7.35158i) q^{83} +(-11.9482 - 4.58887i) q^{85} +(4.35186 + 2.83924i) q^{87} +13.4172 q^{89} +11.3816 q^{91} +(0.884768 - 16.2253i) q^{93} +(1.49916 - 3.90340i) q^{95} +(-15.3000 + 8.83347i) q^{97} +(7.59636 + 0.830931i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{5} + 8 q^{9}+O(q^{10}) \) 12 * q + q^5 + 8 * q^9	\( 12 q + q^{5} + 8 q^{9} + 2 q^{11} - 5 q^{15} + 10 q^{21} - 3 q^{25} - 18 q^{29} + 6 q^{31} - 34 q^{35} - 42 q^{39} + 14 q^{41} - 31 q^{45} + 16 q^{51} - 6 q^{55} - 34 q^{59} + 6 q^{61} + 15 q^{65} + 14 q^{69} + 41 q^{75} - 6 q^{79} - 8 q^{81} - 12 q^{85} + 112 q^{89} + 12 q^{91} + 36 q^{95} + 82 q^{99}+O(q^{100}) \) 12 * q + q^5 + 8 * q^9 + 2 * q^11 - 5 * q^15 + 10 * q^21 - 3 * q^25 - 18 * q^29 + 6 * q^31 - 34 * q^35 - 42 * q^39 + 14 * q^41 - 31 * q^45 + 16 * q^51 - 6 * q^55 - 34 * q^59 + 6 * q^61 + 15 * q^65 + 14 * q^69 + 41 * q^75 - 6 * q^79 - 8 * q^81 - 12 * q^85 + 112 * q^89 + 12 * q^91 + 36 * q^95 + 82 * q^99

Introduction

L-functions

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Database

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