LMFDB - Embedded newform 1148.2.ba.a.113.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.7
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.15530i q^{3} +(-1.04872 - 3.22763i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.66528 q^{9} +O(q^{10})$	\(q-1.15530i q^{3} +(-1.04872 - 3.22763i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.66528 q^{9} +(-4.79368 - 1.55756i) q^{11} +(-0.242673 + 0.334011i) q^{13} +(-3.72888 + 1.21159i) q^{15} +(4.09880 + 1.33178i) q^{17} +(-4.03463 - 5.55319i) q^{19} +(-0.934658 + 0.679068i) q^{21} +(2.71308 + 1.97117i) q^{23} +(-5.27268 + 3.83082i) q^{25} -5.38980i q^{27} +(-5.54178 + 1.80063i) q^{29} +(1.17885 - 3.62811i) q^{31} +(-1.79945 + 5.53814i) q^{33} +(-1.99478 + 2.74558i) q^{35} +(1.51545 + 4.66407i) q^{37} +(0.385883 + 0.280360i) q^{39} +(-2.10916 + 6.04578i) q^{41} +(2.08403 + 1.51413i) q^{43} +(-1.74641 - 5.37491i) q^{45} +(-2.14962 + 2.95870i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(1.53861 - 4.73534i) q^{51} +(-4.59927 + 1.49439i) q^{53} +17.1057i q^{55} +(-6.41561 + 4.66121i) q^{57} +(2.76662 + 2.01006i) q^{59} +(9.57199 - 6.95446i) q^{61} +(-0.978828 - 1.34724i) q^{63} +(1.33256 + 0.432974i) q^{65} +(-4.00013 + 1.29972i) q^{67} +(2.27729 - 3.13442i) q^{69} +(-3.48844 - 1.13346i) q^{71} -16.2956 q^{73} +(4.42575 + 6.09152i) q^{75} +(1.55756 + 4.79368i) q^{77} -5.78329i q^{79} -1.23099 q^{81} -8.92404 q^{83} -14.6261i q^{85} +(2.08027 + 6.40242i) q^{87} +(4.55641 + 6.27135i) q^{89} +0.412860 q^{91} +(-4.19156 - 1.36192i) q^{93} +(-13.6924 + 18.8460i) q^{95} +(0.934792 - 0.303732i) q^{97} +(-7.98283 - 2.59378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

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
$3$		−	1.15530i		−	0.667013i	−0.942748	−	0.333506i	$-0.891768\pi$
$3$		−	1.15530i		−	0.667013i	0.942748	−	0.333506i	$-0.108232\pi$
$4$		0			0
$5$	−1.04872	−	3.22763i	−0.469002	−	1.44344i	−0.853879	−	0.520471i	$-0.825756\pi$
$5$	−1.04872	−	3.22763i	−0.469002	−	1.44344i	0.384878	−	0.922968i	$-0.374244\pi$
$6$		0			0
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$8$		0			0
$9$	1.66528			0.555094
$10$		0			0
$11$	−4.79368	−	1.55756i	−1.44535	−	0.469623i	−0.521789	−	0.853074i	$-0.674735\pi$
$11$	−4.79368	−	1.55756i	−1.44535	−	0.469623i	−0.923561	+	0.383452i	$0.874735\pi$
$12$		0			0
$13$	−0.242673	+	0.334011i	−0.0673054	+	0.0926379i	−0.841343	−	0.540502i	$-0.818234\pi$
$13$	−0.242673	+	0.334011i	−0.0673054	+	0.0926379i	0.774037	+	0.633140i	$0.218234\pi$
$14$		0			0
$15$	−3.72888	+	1.21159i	−0.962792	+	0.312830i
$16$		0			0
$17$	4.09880	+	1.33178i	0.994105	+	0.323004i	0.760507	−	0.649329i	$-0.224950\pi$
$17$	4.09880	+	1.33178i	0.994105	+	0.323004i	0.233597	+	0.972333i	$0.424950\pi$
$18$		0			0
$19$	−4.03463	−	5.55319i	−0.925608	−	1.27399i	−0.961548	−	0.274636i	$-0.911443\pi$
$19$	−4.03463	−	5.55319i	−0.925608	−	1.27399i	0.0359405	−	0.999354i	$-0.488557\pi$
$20$		0			0
$21$	−0.934658	+	0.679068i	−0.203959	+	0.148185i
$22$		0			0
$23$	2.71308	+	1.97117i	0.565717	+	0.411017i	0.833547	−	0.552449i	$-0.186307\pi$
$23$	2.71308	+	1.97117i	0.565717	+	0.411017i	−0.267830	+	0.963466i	$0.586307\pi$
$24$		0			0
$25$	−5.27268	+	3.83082i	−1.05454	+	0.766165i
$26$		0			0
$27$		−	5.38980i		−	1.03727i
$28$		0			0
$29$	−5.54178	+	1.80063i	−1.02908	+	0.334369i	−0.774427	−	0.632663i	$-0.781962\pi$
$29$	−5.54178	+	1.80063i	−1.02908	+	0.334369i	−0.254655	+	0.967032i	$0.581962\pi$
$30$		0			0
$31$	1.17885	−	3.62811i	0.211727	−	0.651628i	−0.787643	−	0.616132i	$-0.788699\pi$
$31$	1.17885	−	3.62811i	0.211727	−	0.651628i	0.999370	−	0.0354964i	$-0.0113012\pi$
$32$		0			0
$33$	−1.79945	+	5.53814i	−0.313244	+	0.964067i
$34$		0			0
$35$	−1.99478	+	2.74558i	−0.337180	+	0.464088i
$36$		0			0
$37$	1.51545	+	4.66407i	0.249138	+	0.766768i	0.994928	+	0.100587i	$0.0320720\pi$
$37$	1.51545	+	4.66407i	0.249138	+	0.766768i	−0.745790	+	0.666181i	$0.767928\pi$
$38$		0			0
$39$	0.385883	+	0.280360i	0.0617907	+	0.0448936i
$40$		0			0
$41$	−2.10916	+	6.04578i	−0.329395	+	0.944192i
$41$	−2.10916	+	6.04578i	−0.329395	+	0.944192i
$42$		0			0
$43$	2.08403	+	1.51413i	0.317811	+	0.230903i	0.735241	−	0.677806i	$-0.237069\pi$
$43$	2.08403	+	1.51413i	0.317811	+	0.230903i	−0.417430	+	0.908709i	$0.637069\pi$
$44$		0			0
$45$	−1.74641	−	5.37491i	−0.260340	−	0.801244i
$46$		0			0
$47$	−2.14962	+	2.95870i	−0.313554	+	0.431570i	−0.936486	−	0.350706i	$-0.885942\pi$
$47$	−2.14962	+	2.95870i	−0.313554	+	0.431570i	0.622931	+	0.782276i	$0.285942\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	1.53861	−	4.73534i	0.215448	−	0.663081i
$52$		0			0
$53$	−4.59927	+	1.49439i	−0.631758	+	0.205271i	−0.607354	−	0.794432i	$-0.707769\pi$
$53$	−4.59927	+	1.49439i	−0.631758	+	0.205271i	−0.0244041	+	0.999702i	$0.507769\pi$
$54$		0			0
$55$			17.1057i			2.30653i
$56$		0			0
$57$	−6.41561	+	4.66121i	−0.849768	+	0.617392i
$58$		0			0
$59$	2.76662	+	2.01006i	0.360183	+	0.261688i	0.753128	−	0.657874i	$-0.228544\pi$
$59$	2.76662	+	2.01006i	0.360183	+	0.261688i	−0.392946	+	0.919562i	$0.628544\pi$
$60$		0			0
$61$	9.57199	−	6.95446i	1.22557	−	0.890427i	0.229018	−	0.973422i	$-0.426449\pi$
$61$	9.57199	−	6.95446i	1.22557	−	0.890427i	0.996550	+	0.0829951i	$0.0264486\pi$
$62$		0			0
$63$	−0.978828	−	1.34724i	−0.123321	−	0.169736i
$64$		0			0
$65$	1.33256	+	0.432974i	0.165283	+	0.0537038i
$66$		0			0
$67$	−4.00013	+	1.29972i	−0.488693	+	0.158786i	−0.542991	−	0.839739i	$-0.682708\pi$
$67$	−4.00013	+	1.29972i	−0.488693	+	0.158786i	0.0542973	+	0.998525i	$0.482708\pi$
$68$		0			0
$69$	2.27729	−	3.13442i	0.274154	−	0.377340i
$70$		0			0
$71$	−3.48844	−	1.13346i	−0.414002	−	0.134517i	0.0946077	−	0.995515i	$-0.469840\pi$
$71$	−3.48844	−	1.13346i	−0.414002	−	0.134517i	−0.508610	+	0.860997i	$0.669840\pi$
$72$		0			0
$73$	−16.2956			−1.90725			−0.953627	−	0.300991i	$-0.902682\pi$
$73$	−16.2956			−1.90725			−0.953627	+	0.300991i	$0.902682\pi$
$74$		0			0
$75$	4.42575	+	6.09152i	0.511042	+	0.703389i
$76$		0			0
$77$	1.55756	+	4.79368i	0.177501	+	0.546291i
$78$		0			0
$79$		−	5.78329i		−	0.650671i	−0.945599	−	0.325336i	$-0.894523\pi$
$79$		−	5.78329i		−	0.650671i	0.945599	−	0.325336i	$-0.105477\pi$
$80$		0			0
$81$	−1.23099			−0.136777
$82$		0			0
$83$	−8.92404			−0.979541			−0.489770	−	0.871851i	$-0.662919\pi$
$83$	−8.92404			−0.979541			−0.489770	+	0.871851i	$0.662919\pi$
$84$		0			0
$85$		−	14.6261i		−	1.58642i
$86$		0			0
$87$	2.08027	+	6.40242i	0.223029	+	0.686411i
$88$		0			0
$89$	4.55641	+	6.27135i	0.482978	+	0.664762i	0.979074	−	0.203506i	$-0.0652335\pi$
$89$	4.55641	+	6.27135i	0.482978	+	0.664762i	−0.496096	+	0.868268i	$0.665234\pi$
$90$		0			0
$91$	0.412860			0.0432795
$92$		0			0
$93$	−4.19156	−	1.36192i	−0.434645	−	0.141225i
$94$		0			0
$95$	−13.6924	+	18.8460i	−1.40481	+	1.93356i
$96$		0			0
$97$	0.934792	−	0.303732i	0.0949138	−	0.0308394i	−0.261175	−	0.965291i	$-0.584110\pi$
$97$	0.934792	−	0.303732i	0.0949138	−	0.0308394i	0.356089	+	0.934452i	$0.384110\pi$
$98$		0			0
$99$	−7.98283	−	2.59378i	−0.802305	−	0.260685i
$100$		0			0
$101$	−0.0408997	−	0.0562936i	−0.00406967	−	0.00560142i	0.806977	−	0.590582i	$-0.201102\pi$
$101$	−0.0408997	−	0.0562936i	−0.00406967	−	0.00560142i	−0.811047	+	0.584981i	$0.801102\pi$
$102$		0			0
$103$	14.9785	−	10.8825i	1.47588	−	1.07229i	0.497018	−	0.867740i	$-0.334428\pi$
$103$	14.9785	−	10.8825i	1.47588	−	1.07229i	0.978857	−	0.204546i	$-0.0655717\pi$
$104$		0			0
$105$	3.17197	+	2.30457i	0.309553	+	0.224903i
$106$		0			0
$107$	−7.04598	+	5.11920i	−0.681160	+	0.494892i	−0.873742	−	0.486389i	$-0.838314\pi$
$107$	−7.04598	+	5.11920i	−0.681160	+	0.494892i	0.192582	+	0.981281i	$0.438314\pi$
$108$		0			0
$109$		−	12.2495i		−	1.17329i	−0.809844	−	0.586645i	$-0.800448\pi$
$109$		−	12.2495i		−	1.17329i	0.809844	−	0.586645i	$-0.199552\pi$
$110$		0			0
$111$	5.38840	−	1.75080i	0.511444	−	0.166178i
$112$		0			0
$113$	1.01600	−	3.12691i	0.0955768	−	0.294155i	−0.891827	−	0.452377i	$-0.850576\pi$
$113$	1.01600	−	3.12691i	0.0955768	−	0.294155i	0.987404	+	0.158222i	$0.0505761\pi$
$114$		0			0
$115$	3.51694	−	10.8240i	0.327956	−	1.00934i
$116$		0			0
$117$	−0.404119	+	0.556222i	−0.0373608	+	0.0514227i
$118$		0			0
$119$	−1.33178	−	4.09880i	−0.122084	−	0.375736i
$120$		0			0
$121$	11.6542	+	8.46729i	1.05947	+	0.769753i
$122$		0			0
$123$	6.98469	+	2.43671i	0.629788	+	0.219711i
$124$		0			0
$125$	4.16611	+	3.02685i	0.372628	+	0.270730i
$126$		0			0
$127$	−5.85134	−	18.0086i	−0.519222	−	1.59800i	−0.775466	−	0.631390i	$-0.782485\pi$
$127$	−5.85134	−	18.0086i	−0.519222	−	1.59800i	0.256244	−	0.966612i	$-0.417515\pi$
$128$		0			0
$129$	1.74928	−	2.40768i	0.154016	−	0.211984i
$130$		0			0
$131$	1.90333	−	5.85786i	0.166295	−	0.511803i	−0.832834	−	0.553522i	$-0.813283\pi$
$131$	1.90333	−	5.85786i	0.166295	−	0.511803i	0.999129	+	0.0417190i	$0.0132834\pi$
$132$		0			0
$133$	−2.12113	+	6.52817i	−0.183925	+	0.566064i
$134$		0			0
$135$	−17.3963	+	5.65239i	−1.49723	+	0.486480i
$136$		0			0
$137$		−	8.52526i		−	0.728362i	−0.931328	−	0.364181i	$-0.881349\pi$
$137$		−	8.52526i		−	0.728362i	0.931328	−	0.364181i	$-0.118651\pi$
$138$		0			0
$139$	13.6500	−	9.91729i	1.15778	−	0.841174i	0.168281	−	0.985739i	$-0.446178\pi$
$139$	13.6500	−	9.91729i	1.15778	−	0.841174i	0.989495	+	0.144565i	$0.0461783\pi$
$140$		0			0
$141$	3.41818	+	2.48345i	0.287863	+	0.209145i
$142$		0			0
$143$	1.68354	−	1.22316i	0.140785	−	0.102286i
$144$		0			0
$145$	11.6235	+	15.9984i	0.965283	+	1.32860i
$146$		0			0
$147$	1.09876	+	0.357007i	0.0906239	+	0.0294455i
$148$		0			0
$149$	−11.5183	+	3.74252i	−0.943615	+	0.306599i	−0.740118	−	0.672477i	$-0.765231\pi$
$149$	−11.5183	+	3.74252i	−0.943615	+	0.306599i	−0.203497	+	0.979076i	$0.565231\pi$
$150$		0			0
$151$	5.96279	−	8.20708i	0.485245	−	0.667882i	−0.494257	−	0.869316i	$-0.664560\pi$
$151$	5.96279	−	8.20708i	0.485245	−	0.667882i	0.979502	+	0.201433i	$0.0645599\pi$
$152$		0			0
$153$	6.82565	+	2.21779i	0.551821	+	0.179298i
$154$		0			0
$155$	−12.9465			−1.03989
$156$		0			0
$157$	2.29599	+	3.16016i	0.183240	+	0.252209i	0.890749	−	0.454496i	$-0.150181\pi$
$157$	2.29599	+	3.16016i	0.183240	+	0.252209i	−0.707508	+	0.706705i	$0.750181\pi$
$158$		0			0
$159$	1.72647	+	5.31353i	0.136918	+	0.421391i
$160$		0			0
$161$		−	3.35355i		−	0.264297i
$162$		0			0
$163$	5.83646			0.457147			0.228573	−	0.973527i	$-0.426594\pi$
$163$	5.83646			0.457147			0.228573	+	0.973527i	$0.426594\pi$
$164$		0			0
$165$	19.7622			1.53848
$166$		0			0
$167$		−	13.5723i		−	1.05026i	−0.851023	−	0.525128i	$-0.824017\pi$
$167$		−	13.5723i		−	1.05026i	0.851023	−	0.525128i	$-0.175983\pi$
$168$		0			0
$169$	3.96455	+	12.2016i	0.304965	+	0.938586i
$170$		0			0
$171$	−6.71880	−	9.24763i	−0.513799	−	0.707184i
$172$		0			0
$173$	18.5650			1.41147			0.705734	−	0.708477i	$-0.250617\pi$
$173$	18.5650			1.41147			0.705734	+	0.708477i	$0.250617\pi$
$174$		0			0
$175$	6.19840	+	2.01398i	0.468555	+	0.152243i
$176$		0			0
$177$	2.32223	−	3.19627i	0.174549	−	0.240247i
$178$		0			0
$179$	−20.6874	+	6.72174i	−1.54625	+	0.502406i	−0.953092	−	0.302682i	$-0.902118\pi$
$179$	−20.6874	+	6.72174i	−1.54625	+	0.502406i	−0.593155	+	0.805088i	$0.702118\pi$
$180$		0			0
$181$	−17.1455	−	5.57091i	−1.27441	−	0.414082i	−0.407805	−	0.913069i	$-0.633706\pi$
$181$	−17.1455	−	5.57091i	−1.27441	−	0.414082i	−0.866609	+	0.498987i	$0.833706\pi$
$182$		0			0
$183$	−8.03449	−	11.0585i	−0.593926	−	0.817470i
$184$		0			0
$185$	13.4646	−	9.78259i	0.989936	−	0.719230i
$186$		0			0
$187$	−17.5740	−	12.7683i	−1.28514	−	0.933708i
$188$		0			0
$189$	−4.36044	+	3.16805i	−0.317175	+	0.230441i
$190$		0			0
$191$		−	5.75897i		−	0.416704i	−0.978054	−	0.208352i	$-0.933190\pi$
$191$		−	5.75897i		−	0.416704i	0.978054	−	0.208352i	$-0.0668100\pi$
$192$		0			0
$193$	−9.59712	+	3.11829i	−0.690816	+	0.224460i	−0.633325	−	0.773886i	$-0.718310\pi$
$193$	−9.59712	+	3.11829i	−0.690816	+	0.224460i	−0.0574914	+	0.998346i	$0.518310\pi$
$194$		0			0
$195$	0.500215	−	1.53950i	0.0358212	−	0.110246i
$196$		0			0
$197$	4.66718	−	14.3641i	0.332523	−	1.02340i	−0.635406	−	0.772178i	$-0.719167\pi$
$197$	4.66718	−	14.3641i	0.332523	−	1.02340i	0.967929	−	0.251223i	$-0.0808327\pi$
$198$		0			0
$199$	2.12212	−	2.92085i	0.150433	−	0.207054i	−0.727149	−	0.686480i	$-0.759155\pi$
$199$	2.12212	−	2.92085i	0.150433	−	0.207054i	0.877582	+	0.479426i	$0.159155\pi$
$200$		0			0
$201$	1.50157	+	4.62135i	0.105912	+	0.325965i
$202$		0			0
$203$	4.71412	+	3.42501i	0.330866	+	0.240388i
$204$		0			0
$205$	21.7254	+	0.467247i	1.51737	+	0.0326339i
$206$		0			0
$207$	4.51804	+	3.28255i	0.314026	+	0.228153i
$208$		0			0
$209$	10.6913	+	32.9044i	0.739533	+	2.27605i
$210$		0			0
$211$	−10.6477	+	14.6553i	−0.733017	+	1.00891i	0.265973	+	0.963981i	$0.414307\pi$
$211$	−10.6477	+	14.6553i	−0.733017	+	1.00891i	−0.998990	+	0.0449311i	$0.985693\pi$
$212$		0			0
$213$	−1.30949	+	4.03020i	−0.0897248	+	0.276145i
$214$		0			0
$215$	2.70150	−	8.31436i	0.184241	−	0.567035i
$216$		0			0
$217$	−3.62811	+	1.17885i	−0.246292	+	0.0800253i
$218$		0			0
$219$			18.8263i			1.27216i
$220$		0			0
$221$	−1.43950	+	1.04586i	−0.0968310	+	0.0703518i
$222$		0			0
$223$	−1.11339	−	0.808922i	−0.0745579	−	0.0541695i	0.549882	−	0.835242i	$-0.314673\pi$
$223$	−1.11339	−	0.808922i	−0.0745579	−	0.0541695i	−0.624440	+	0.781073i	$0.714673\pi$
$224$		0			0
$225$	−8.78049	+	6.37940i	−0.585366	+	0.425293i
$226$		0			0
$227$	5.87373	+	8.08449i	0.389853	+	0.536587i	0.958161	−	0.286229i	$-0.0924019\pi$
$227$	5.87373	+	8.08449i	0.389853	+	0.536587i	−0.568308	+	0.822816i	$0.692402\pi$
$228$		0			0
$229$	19.2691	+	6.26092i	1.27334	+	0.413733i	0.866230	−	0.499646i	$-0.166536\pi$
$229$	19.2691	+	6.26092i	1.27334	+	0.413733i	0.407110	+	0.913379i	$0.366536\pi$
$230$		0			0
$231$	5.53814	−	1.79945i	0.364383	−	0.118395i
$232$		0			0
$233$	7.03542	−	9.68342i	0.460905	−	0.634382i	−0.513791	−	0.857916i	$-0.671759\pi$
$233$	7.03542	−	9.68342i	0.460905	−	0.634382i	0.974696	+	0.223534i	$0.0717592\pi$
$234$		0			0
$235$	11.8039	+	3.83532i	0.770002	+	0.250189i
$236$		0			0
$237$	−6.68144			−0.434006
$238$		0			0
$239$	−4.02745	−	5.54331i	−0.260514	−	0.358567i	0.658645	−	0.752454i	$-0.271130\pi$
$239$	−4.02745	−	5.54331i	−0.260514	−	0.358567i	−0.919159	+	0.393887i	$0.871130\pi$
$240$		0			0
$241$	0.114728	+	0.353096i	0.00739028	+	0.0227449i	0.954684	−	0.297622i	$-0.0961936\pi$
$241$	0.114728	+	0.353096i	0.00739028	+	0.0227449i	−0.947293	+	0.320367i	$0.896194\pi$
$242$		0			0
$243$		−	14.7472i		−	0.946036i
$244$		0			0
$245$	3.39373			0.216817
$246$		0			0
$247$	2.83392			0.180318
$248$		0			0
$249$			10.3099i			0.653366i
$250$		0			0
$251$	0.428825	+	1.31979i	0.0270672	+	0.0833043i	0.963678	−	0.267068i	$-0.0860550\pi$
$251$	0.428825	+	1.31979i	0.0270672	+	0.0833043i	−0.936610	+	0.350373i	$0.886055\pi$
$252$		0			0
$253$	−9.93544	−	13.6750i	−0.624636	−	0.859737i
$254$		0			0
$255$	−16.8975			−1.05816
$256$		0			0
$257$	5.36241	+	1.74235i	0.334498	+	0.108685i	0.471450	−	0.881893i	$-0.343731\pi$
$257$	5.36241	+	1.74235i	0.334498	+	0.108685i	−0.136952	+	0.990578i	$0.543731\pi$
$258$		0			0
$259$	2.88255	−	3.96749i	0.179113	−	0.246528i
$260$		0			0
$261$	−9.22862	+	2.99856i	−0.571237	+	0.185606i
$262$		0			0
$263$	25.0333	+	8.13381i	1.54362	+	0.501552i	0.952372	−	0.304938i	$-0.0986359\pi$
$263$	25.0333	+	8.13381i	1.54362	+	0.501552i	0.591247	+	0.806491i	$0.298636\pi$
$264$		0			0
$265$	9.64668	+	13.2775i	0.592591	+	0.815631i
$266$		0			0
$267$	7.24530	−	5.26402i	0.443405	−	0.322153i
$268$		0			0
$269$	−4.14563	−	3.01197i	−0.252763	−	0.183643i	0.454187	−	0.890906i	$-0.349930\pi$
$269$	−4.14563	−	3.01197i	−0.252763	−	0.183643i	−0.706951	+	0.707263i	$0.749930\pi$
$270$		0			0
$271$	−23.7992	+	17.2911i	−1.44570	+	1.05036i	−0.458885	+	0.888496i	$0.651751\pi$
$271$	−23.7992	+	17.2911i	−1.44570	+	1.05036i	−0.986813	+	0.161865i	$0.948249\pi$
$272$		0			0
$273$		−	0.476977i		−	0.0288680i
$274$		0			0
$275$	31.2423	−	10.1512i	1.88398	−	0.612142i
$276$		0			0
$277$	9.91362	−	30.5110i	0.595652	−	1.83323i	0.0441978	−	0.999023i	$-0.485927\pi$
$277$	9.91362	−	30.5110i	0.595652	−	1.83323i	0.551454	−	0.834205i	$-0.314073\pi$
$278$		0			0
$279$	1.96311	−	6.04183i	0.117528	−	0.361715i
$280$		0			0
$281$	18.4782	−	25.4330i	1.10232	−	1.51721i	0.270036	−	0.962850i	$-0.412965\pi$
$281$	18.4782	−	25.4330i	1.10232	−	1.51721i	0.832280	−	0.554356i	$-0.187035\pi$
$282$		0			0
$283$	−0.429565	−	1.32207i	−0.0255350	−	0.0785886i	0.937477	−	0.348047i	$-0.113155\pi$
$283$	−0.429565	−	1.32207i	−0.0255350	−	0.0785886i	−0.963012	+	0.269459i	$0.913155\pi$
$284$		0			0
$285$	21.7728	+	15.8189i	1.28971	+	0.937029i
$286$		0			0
$287$	6.13087	−	1.84728i	0.361894	−	0.109041i
$288$		0			0
$289$	1.27322	+	0.925049i	0.0748954	+	0.0544147i
$290$		0			0
$291$	−0.350902	−	1.07997i	−0.0205702	−	0.0633087i
$292$		0			0
$293$	7.54333	−	10.3825i	0.440686	−	0.606552i	−0.529678	−	0.848199i	$-0.677687\pi$
$293$	7.54333	−	10.3825i	0.440686	−	0.606552i	0.970364	+	0.241646i	$0.0776874\pi$
$294$		0			0
$295$	3.58633	−	11.0376i	0.208804	−	0.642634i
$296$		0			0
$297$	−8.39495	+	25.8370i	−0.487124	+	1.49922i
$298$		0			0
$299$	−1.31678	+	0.427849i	−0.0761515	+	0.0247431i
$300$		0			0
$301$		−	2.57600i		−	0.148478i
$302$		0			0
$303$	−0.0650360	+	0.0472514i	−0.00373622	+	0.00271452i
$304$		0			0
$305$	−32.4847	−	23.6015i	−1.86007	−	1.35142i
$306$		0			0
$307$	18.9952	−	13.8008i	1.08411	−	0.787653i	0.105716	−	0.994396i	$-0.466287\pi$
$307$	18.9952	−	13.8008i	1.08411	−	0.787653i	0.978395	+	0.206744i	$0.0662867\pi$
$308$		0			0
$309$	−12.5726	−	17.3047i	−0.715229	−	0.984428i
$310$		0			0
$311$	−11.5910	−	3.76614i	−0.657265	−	0.213558i	−0.0386503	−	0.999253i	$-0.512306\pi$
$311$	−11.5910	−	3.76614i	−0.657265	−	0.213558i	−0.618615	+	0.785694i	$0.712306\pi$
$312$		0			0
$313$	25.4243	−	8.26086i	1.43707	−	0.466931i	0.516085	−	0.856537i	$-0.327389\pi$
$313$	25.4243	−	8.26086i	1.43707	−	0.466931i	0.920982	+	0.389606i	$0.127389\pi$
$314$		0			0
$315$	−3.32187	+	4.57217i	−0.187166	+	0.257612i
$316$		0			0
$317$	−7.65607	−	2.48761i	−0.430008	−	0.139718i	0.0860130	−	0.996294i	$-0.472587\pi$
$317$	−7.65607	−	2.48761i	−0.430008	−	0.139718i	−0.516021	+	0.856576i	$0.672587\pi$
$318$		0			0
$319$	29.3701			1.64441
$320$		0			0
$321$	5.91422	+	8.14022i	0.330099	+	0.454343i
$322$		0			0
$323$	−9.14151	−	28.1347i	−0.508647	−	1.56545i
$324$		0			0
$325$		−	2.69077i		−	0.149257i
$326$		0			0
$327$	−14.1519			−0.782600
$328$		0			0
$329$	3.65715			0.201625
$330$		0			0
$331$			16.3613i			0.899300i	0.893205	+	0.449650i	$0.148451\pi$
$331$			16.3613i			0.899300i	−0.893205	+	0.449650i	$0.851549\pi$
$332$		0			0
$333$	2.52364	+	7.76698i	0.138295	+	0.425628i
$334$		0			0
$335$	8.39002	+	11.5479i	0.458396	+	0.630928i
$336$		0			0
$337$	21.1433			1.15175			0.575875	−	0.817538i	$-0.304662\pi$
$337$	21.1433			1.15175			0.575875	+	0.817538i	$0.304662\pi$
$338$		0			0
$339$	−3.61252	−	1.17378i	−0.196205	−	0.0637510i
$340$		0			0
$341$	−11.3020	+	15.5559i	−0.612039	+	0.842400i
$342$		0			0
$343$	0.951057	−	0.309017i	0.0513522	−	0.0166853i
$344$		0			0
$345$	−12.5050	−	4.06312i	−0.673246	−	0.218751i
$346$		0			0
$347$	−9.89619	−	13.6209i	−0.531255	−	0.731210i	0.456066	−	0.889946i	$-0.349258\pi$
$347$	−9.89619	−	13.6209i	−0.531255	−	0.731210i	−0.987321	+	0.158736i	$0.949258\pi$
$348$		0			0
$349$	18.1720	−	13.2028i	0.972727	−	0.706727i	0.0166552	−	0.999861i	$-0.494698\pi$
$349$	18.1720	−	13.2028i	0.972727	−	0.706727i	0.956071	+	0.293134i	$0.0946982\pi$
$350$		0			0
$351$	1.80025	+	1.30796i	0.0960903	+	0.0698137i
$352$		0			0
$353$	−18.0279	+	13.0981i	−0.959530	+	0.697139i	−0.953041	−	0.302840i	$-0.902065\pi$
$353$	−18.0279	+	13.0981i	−0.959530	+	0.697139i	−0.00648827	+	0.999979i	$0.502065\pi$
$354$		0			0
$355$			12.4481i			0.660675i
$356$		0			0
$357$	−4.73534	+	1.53861i	−0.250621	+	0.0814317i
$358$		0			0
$359$	1.87799	−	5.77986i	0.0991166	−	0.305049i	−0.889188	−	0.457542i	$-0.848730\pi$
$359$	1.87799	−	5.77986i	0.0991166	−	0.305049i	0.988305	+	0.152492i	$0.0487300\pi$
$360$		0			0
$361$	−8.68838	+	26.7401i	−0.457283	+	1.40737i
$362$		0			0
$363$	9.78226	−	13.4641i	0.513435	−	0.706683i
$364$		0			0
$365$	17.0895	+	52.5961i	0.894505	+	2.75300i
$366$		0			0
$367$	−17.6647	−	12.8342i	−0.922089	−	0.669937i	0.0219537	−	0.999759i	$-0.493011\pi$
$367$	−17.6647	−	12.8342i	−0.922089	−	0.669937i	−0.944043	+	0.329822i	$0.893011\pi$
$368$		0			0
$369$	−3.51234	+	10.0679i	−0.182845	+	0.524115i
$370$		0			0
$371$	3.91237	+	2.84250i	0.203120	+	0.147575i
$372$		0			0
$373$	1.12547	+	3.46385i	0.0582748	+	0.179351i	0.975957	−	0.217964i	$-0.0699417\pi$
$373$	1.12547	+	3.46385i	0.0582748	+	0.179351i	−0.917682	+	0.397316i	$0.869942\pi$
$374$		0			0
$375$	3.49693	−	4.81310i	0.180580	−	0.248548i
$376$		0			0
$377$	0.743409	−	2.28798i	0.0382875	−	0.117837i
$378$		0			0
$379$	−5.02114	+	15.4535i	−0.257918	+	0.793791i	0.735322	+	0.677718i	$0.237031\pi$
$379$	−5.02114	+	15.4535i	−0.257918	+	0.793791i	−0.993241	+	0.116074i	$0.962969\pi$
$380$		0			0
$381$	−20.8053	+	6.76005i	−1.06589	+	0.346328i
$382$		0			0
$383$		−	27.9579i		−	1.42858i	−0.699848	−	0.714292i	$-0.746749\pi$
$383$		−	27.9579i		−	1.42858i	0.699848	−	0.714292i	$-0.253251\pi$
$384$		0			0
$385$	13.8388	−	10.0545i	0.705289	−	0.512423i
$386$		0			0
$387$	3.47049	+	2.52146i	0.176415	+	0.128173i
$388$		0			0
$389$	14.8202	−	10.7675i	0.751416	−	0.545935i	−0.144850	−	0.989454i	$-0.546270\pi$
$389$	14.8202	−	10.7675i	0.751416	−	0.545935i	0.896265	+	0.443518i	$0.146270\pi$
$390$		0			0
$391$	8.49521	+	11.6927i	0.429621	+	0.591323i
$392$		0			0
$393$	−6.76758	−	2.19892i	−0.341379	−	0.110921i
$394$		0			0
$395$	−18.6663	+	6.06505i	−0.939204	+	0.305166i
$396$		0			0
$397$	−11.3115	+	15.5689i	−0.567706	+	0.781381i	−0.992281	−	0.124012i	$-0.960424\pi$
$397$	−11.3115	+	15.5689i	−0.567706	+	0.781381i	0.424574	+	0.905393i	$0.360424\pi$
$398$		0			0
$399$	7.54200	+	2.45054i	0.377572	+	0.122681i
$400$		0			0
$401$	17.2859			0.863215			0.431607	−	0.902062i	$-0.357947\pi$
$401$	17.2859			0.863215			0.431607	+	0.902062i	$0.357947\pi$
$402$		0			0
$403$	0.925755	+	1.27419i	0.0461151	+	0.0634720i
$404$		0			0
$405$	1.29097	+	3.97319i	0.0641487	+	0.197429i
$406$		0			0
$407$		−	24.7185i		−	1.22525i
$408$		0			0
$409$	−27.4513			−1.35738			−0.678689	−	0.734426i	$-0.737452\pi$
$409$	−27.4513			−1.35738			−0.678689	+	0.734426i	$0.737452\pi$
$410$		0			0
$411$	−9.84923			−0.485827
$412$		0			0
$413$		−	3.41973i		−	0.168274i
$414$		0			0
$415$	9.35881	+	28.8035i	0.459406	+	1.41391i
$416$		0			0
$417$	−11.4575	−	15.7698i	−0.561074	−	0.772252i
$418$		0			0
$419$	−14.7604			−0.721091			−0.360546	−	0.932742i	$-0.617409\pi$
$419$	−14.7604			−0.721091			−0.360546	+	0.932742i	$0.617409\pi$
$420$		0			0
$421$	−13.3618	−	4.34150i	−0.651212	−	0.211592i	−0.0352636	−	0.999378i	$-0.511227\pi$
$421$	−13.3618	−	4.34150i	−0.651212	−	0.211592i	−0.615949	+	0.787786i	$0.711227\pi$
$422$		0			0
$423$	−3.57972	+	4.92706i	−0.174052	+	0.239562i
$424$		0			0
$425$	−26.7134	+	8.67973i	−1.29579	+	0.421029i
$426$		0			0
$427$	−11.2525	−	3.65618i	−0.544549	−	0.176935i
$428$		0			0
$429$	−1.41312	−	1.94499i	−0.0682261	−	0.0939052i
$430$		0			0
$431$	−3.96353	+	2.87968i	−0.190917	+	0.138709i	−0.679138	−	0.734011i	$-0.737646\pi$
$431$	−3.96353	+	2.87968i	−0.190917	+	0.138709i	0.488221	+	0.872720i	$0.337646\pi$
$432$		0			0
$433$	1.96971	+	1.43108i	0.0946583	+	0.0687733i	0.634108	−	0.773245i	$-0.281368\pi$
$433$	1.96971	+	1.43108i	0.0946583	+	0.0687733i	−0.539449	+	0.842018i	$0.681368\pi$
$434$		0			0
$435$	18.4830	−	13.4287i	0.886192	−	0.643856i
$436$		0			0
$437$		−	23.0192i		−	1.10116i
$438$		0			0
$439$	34.3307	−	11.1547i	1.63852	−	0.532386i	0.662310	−	0.749230i	$-0.269576\pi$
$439$	34.3307	−	11.1547i	1.63852	−	0.532386i	0.976206	+	0.216844i	$0.0695763\pi$
$440$		0			0
$441$	−0.514600	+	1.58378i	−0.0245048	+	0.0754179i
$442$		0			0
$443$	−12.3084	+	37.8815i	−0.584792	+	1.79980i	0.0153139	+	0.999883i	$0.495125\pi$
$443$	−12.3084	+	37.8815i	−0.584792	+	1.79980i	−0.600106	+	0.799921i	$0.704875\pi$
$444$		0			0
$445$	15.4632	−	21.2833i	0.733026	−	1.00892i
$446$		0			0
$447$	4.32373	+	13.3071i	0.204506	+	0.629403i
$448$		0			0
$449$	4.10203	+	2.98030i	0.193587	+	0.140649i	0.680357	−	0.732881i	$-0.261825\pi$
$449$	4.10203	+	2.98030i	0.193587	+	0.140649i	−0.486770	+	0.873530i	$0.661825\pi$
$450$		0			0
$451$	19.5273	−	25.6964i	0.919505	−	1.21000i
$452$		0			0
$453$	−9.48164	−	6.88881i	−0.445486	−	0.323665i
$454$		0			0
$455$	−0.432974	−	1.33256i	−0.0202981	−	0.0624713i
$456$		0			0
$457$	2.68451	−	3.69492i	0.125576	−	0.172841i	−0.741600	−	0.670843i	$-0.765933\pi$
$457$	2.68451	−	3.69492i	0.125576	−	0.172841i	0.867176	+	0.498002i	$0.165933\pi$
$458$		0			0
$459$	7.17803	−	22.0917i	0.335042	−	1.03115i
$460$		0			0
$461$	−12.6223	+	38.8475i	−0.587880	+	1.80931i	−0.000494251		1.00000i	$0.500157\pi$
$461$	−12.6223	+	38.8475i	−0.587880	+	1.80931i	−0.587385	+	0.809307i	$0.699843\pi$
$462$		0			0
$463$	−5.48043	+	1.78070i	−0.254697	+	0.0827562i	−0.433583	−	0.901114i	$-0.642751\pi$
$463$	−5.48043	+	1.78070i	−0.254697	+	0.0827562i	0.178886	+	0.983870i	$0.442751\pi$
$464$		0			0
$465$			14.9571i			0.693617i
$466$		0			0
$467$	−17.1600	+	12.4675i	−0.794072	+	0.576927i	−0.909169	−	0.416427i	$-0.863282\pi$
$467$	−17.1600	+	12.4675i	−0.794072	+	0.576927i	0.115097	+	0.993354i	$0.463282\pi$
$468$		0			0
$469$	3.40271	+	2.47222i	0.157123	+	0.114156i
$470$		0			0
$471$	3.65094	−	2.65256i	0.168226	−	0.122224i
$472$		0			0
$473$	−7.63181	−	10.5043i	−0.350911	−	0.482988i
$474$		0			0
$475$	42.5466	+	13.8242i	1.95217	+	0.634299i
$476$		0			0
$477$	−7.65907	+	2.48858i	−0.350685	+	0.113944i
$478$		0			0
$479$	−12.5858	+	17.3228i	−0.575058	+	0.791500i	−0.993143	−	0.116909i	$-0.962702\pi$
$479$	−12.5858	+	17.3228i	−0.575058	+	0.791500i	0.418085	+	0.908408i	$0.362702\pi$
$480$		0			0
$481$	−1.92561	−	0.625667i	−0.0878001	−	0.0285280i
$482$		0			0
$483$	−3.87436			−0.176290
$484$		0			0
$485$	−1.96067	−	2.69863i	−0.0890294	−	0.122538i
$486$		0			0
$487$	5.50329	+	16.9374i	0.249378	+	0.767506i	0.994886	+	0.101009i	$0.0322071\pi$
$487$	5.50329	+	16.9374i	0.249378	+	0.767506i	−0.745508	+	0.666497i	$0.767793\pi$
$488$		0			0
$489$		−	6.74286i		−	0.304923i
$490$		0			0
$491$	−43.1063			−1.94536			−0.972681	−	0.232147i	$-0.925425\pi$
$491$	−43.1063			−1.94536			−0.972681	+	0.232147i	$0.925425\pi$
$492$		0			0
$493$	−25.1127			−1.13102
$494$		0			0
$495$			28.4858i			1.28034i
$496$		0			0
$497$	1.13346	+	3.48844i	0.0508428	+	0.156478i
$498$		0			0
$499$	−1.83093	−	2.52006i	−0.0819636	−	0.112813i	0.766066	−	0.642761i	$-0.222211\pi$
$499$	−1.83093	−	2.52006i	−0.0819636	−	0.112813i	−0.848030	+	0.529948i	$0.822211\pi$
$500$		0			0
$501$	−15.6801			−0.700535
$502$		0			0
$503$	9.34227	+	3.03549i	0.416551	+	0.135346i	0.509792	−	0.860298i	$-0.329723\pi$
$503$	9.34227	+	3.03549i	0.416551	+	0.135346i	−0.0932404	+	0.995644i	$0.529723\pi$
$504$		0			0
$505$	−0.138802	+	0.191045i	−0.00617662	+	0.00850139i
$506$		0			0
$507$	14.0965	−	4.58024i	0.626049	−	0.203416i
$508$		0			0
$509$	23.3169	+	7.57613i	1.03351	+	0.335806i	0.776175	−	0.630517i	$-0.217157\pi$
$509$	23.3169	+	7.57613i	1.03351	+	0.335806i	0.257330	+	0.966324i	$0.417157\pi$
$510$		0			0
$511$	9.57830	+	13.1834i	0.423719	+	0.583199i
$512$		0			0
$513$	−29.9306	+	21.7459i	−1.32147	+	0.960103i
$514$		0			0
$515$	−50.8329	−	36.9323i	−2.23997	−	1.62743i
$516$		0			0
$517$	14.9129	−	10.8349i	0.655871	−	0.476518i
$518$		0			0
$519$		−	21.4481i		−	0.941468i
$520$		0			0
$521$	−27.4453	+	8.91750i	−1.20240	+	0.390683i	−0.840643	−	0.541590i	$-0.817823\pi$
$521$	−27.4453	+	8.91750i	−1.20240	+	0.390683i	−0.361756	+	0.932273i	$0.617823\pi$
$522$		0			0
$523$	−1.20554	+	3.71028i	−0.0527147	+	0.162239i	−0.973948	−	0.226771i	$-0.927183\pi$
$523$	−1.20554	+	3.71028i	−0.0527147	+	0.162239i	0.921233	+	0.389010i	$0.127183\pi$
$524$		0			0
$525$	2.32675	−	7.16102i	0.101548	−	0.312532i
$526$		0			0
$527$	9.66370	−	13.3009i	0.420957	−	0.579398i
$528$		0			0
$529$	−3.63209	−	11.1784i	−0.157917	−	0.486018i
$530$		0			0
$531$	4.60719	+	3.34732i	0.199935	+	0.145261i
$532$		0			0
$533$	−1.50752	−	2.17163i	−0.0652979	−	0.0940637i
$534$		0			0
$535$	23.9121	+	17.3732i	1.03381	+	0.751108i
$536$		0			0
$537$	7.76562	+	23.9001i	0.335111	+	1.03137i
$538$		0			0
$539$	2.96266	−	4.07775i	0.127611	−	0.175641i
$540$		0			0
$541$	7.35324	−	22.6310i	0.316141	−	0.972981i	−0.659142	−	0.752019i	$-0.729080\pi$
$541$	7.35324	−	22.6310i	0.316141	−	0.972981i	0.975282	−	0.220962i	$-0.0709197\pi$
$542$		0			0
$543$	−6.43607	+	19.8082i	−0.276198	+	0.850051i
$544$		0			0
$545$	−39.5368	+	12.8463i	−1.69357	+	0.550275i
$546$		0			0
$547$		−	17.4613i		−	0.746590i	−0.927713	−	0.373295i	$-0.878228\pi$
$547$		−	17.4613i		−	0.746590i	0.927713	−	0.373295i	$-0.121772\pi$
$548$		0			0
$549$	15.9401	−	11.5811i	0.680305	−	0.494271i
$550$		0			0
$551$	32.3583	+	23.5097i	1.37851	+	1.00155i
$552$		0			0
$553$	−4.67878	+	3.39933i	−0.198962	+	0.144554i
$554$		0			0
$555$	−11.3018	−	15.5556i	−0.479736	−	0.660300i
$556$		0			0
$557$	−1.91316	−	0.621625i	−0.0810634	−	0.0263391i	0.268205	−	0.963362i	$-0.413570\pi$
$557$	−1.91316	−	0.621625i	−0.0810634	−	0.0263391i	−0.349268	+	0.937023i	$0.613570\pi$
$558$		0			0
$559$	−1.01147	+	0.328648i	−0.0427808	+	0.0139003i
$560$		0			0
$561$	−14.7512	+	20.3033i	−0.622796	+	0.857204i
$562$		0			0
$563$	13.0919	+	4.25381i	0.551757	+	0.179277i	0.571609	−	0.820526i	$-0.306319\pi$
$563$	13.0919	+	4.25381i	0.551757	+	0.179277i	−0.0198518	+	0.999803i	$0.506319\pi$
$564$		0			0
$565$	−11.1580			−0.469421
$566$		0			0
$567$	0.723560	+	0.995895i	0.0303867	+	0.0418237i
$568$		0			0
$569$	4.33035	+	13.3274i	0.181538	+	0.558715i	0.999872	−	0.0160279i	$-0.00510204\pi$
$569$	4.33035	+	13.3274i	0.181538	+	0.558715i	−0.818334	+	0.574743i	$0.805102\pi$
$570$		0			0
$571$			12.1249i			0.507412i	0.967281	+	0.253706i	$0.0816495\pi$
$571$			12.1249i			0.507412i	−0.967281	+	0.253706i	$0.918351\pi$
$572$		0			0
$573$	−6.65334			−0.277947
$574$		0			0
$575$	−21.8564			−0.911475
$576$		0			0
$577$		−	45.6732i		−	1.90140i	−0.310109	−	0.950701i	$-0.600365\pi$
$577$		−	45.6732i		−	1.90140i	0.310109	−	0.950701i	$-0.399635\pi$
$578$		0			0
$579$	3.60257	+	11.0876i	0.149718	+	0.460783i
$580$		0			0
$581$	5.24542	+	7.21970i	0.217617	+	0.299524i
$582$		0			0
$583$	24.3750			1.00951
$584$		0			0
$585$	2.21908	+	0.721024i	0.0917478	+	0.0298107i
$586$		0			0
$587$	3.92364	−	5.40043i	0.161946	−	0.222900i	−0.720331	−	0.693631i	$-0.756010\pi$
$587$	3.92364	−	5.40043i	0.161946	−	0.222900i	0.882277	+	0.470731i	$0.156010\pi$
$588$		0			0
$589$	−24.9038	+	8.09174i	−1.02614	+	0.333414i
$590$		0			0
$591$	−16.5949	−	5.39200i	−0.682622	−	0.221797i
$592$		0			0
$593$	−12.3908	−	17.0545i	−0.508831	−	0.700346i	0.474891	−	0.880045i	$-0.342488\pi$
$593$	−12.3908	−	17.0545i	−0.508831	−	0.700346i	−0.983722	+	0.179699i	$0.942488\pi$
$594$		0			0
$595$	−11.8327	+	8.59698i	−0.485094	+	0.352442i
$596$		0			0
$597$	−3.37446	−	2.45169i	−0.138108	−	0.100341i
$598$		0			0
$599$	−17.6596	+	12.8304i	−0.721551	+	0.524238i	−0.886879	−	0.462001i	$-0.847132\pi$
$599$	−17.6596	+	12.8304i	−0.721551	+	0.524238i	0.165328	+	0.986239i	$0.447132\pi$
$600$		0			0
$601$		−	0.602524i		−	0.0245775i	−0.999924	−	0.0122887i	$-0.996088\pi$
$601$		−	0.602524i		−	0.0245775i	0.999924	−	0.0122887i	$-0.00391172\pi$
$602$		0			0
$603$	−6.66134	+	2.16440i	−0.271271	+	0.0881412i
$604$		0			0
$605$	15.1072	−	46.4953i	0.614196	−	1.89030i
$606$		0			0
$607$	1.85120	−	5.69740i	0.0751377	−	0.231250i	−0.906433	−	0.422350i	$-0.861205\pi$
$607$	1.85120	−	5.69740i	0.0751377	−	0.231250i	0.981571	+	0.191100i	$0.0612054\pi$
$608$		0			0
$609$	3.95691	−	5.44622i	0.160342	−	0.220692i
$610$		0			0
$611$	−0.466582	−	1.43599i	−0.0188759	−	0.0580940i
$612$		0			0
$613$	1.40076	+	1.01771i	0.0565762	+	0.0411050i	0.615714	−	0.787970i	$-0.288868\pi$
$613$	1.40076	+	1.01771i	0.0565762	+	0.0411050i	−0.559138	+	0.829075i	$0.688868\pi$
$614$		0			0
$615$	0.539811	−	25.0994i	0.0217673	−	1.01211i
$616$		0			0
$617$	−21.0097	−	15.2644i	−0.845819	−	0.614524i	0.0781710	−	0.996940i	$-0.475092\pi$
$617$	−21.0097	−	15.2644i	−0.845819	−	0.614524i	−0.923990	+	0.382416i	$0.875092\pi$
$618$		0			0
$619$	−13.7261	−	42.2446i	−0.551698	−	1.69795i	−0.704507	−	0.709697i	$-0.748832\pi$
$619$	−13.7261	−	42.2446i	−0.551698	−	1.69795i	0.152809	−	0.988256i	$-0.451168\pi$
$620$		0			0
$621$	10.6242	−	14.6230i	0.426335	−	0.586799i
$622$		0			0
$623$	2.39544	−	7.37242i	0.0959714	−	0.295370i
$624$		0			0
$625$	−4.66944	+	14.3710i	−0.186777	+	0.574842i
$626$		0			0
$627$	38.0145	−	12.3517i	1.51815	−	0.493278i
$628$		0			0
$629$			21.1353i			0.842720i
$630$		0			0
$631$	−24.0201	+	17.4516i	−0.956224	+	0.694737i	−0.952271	−	0.305255i	$-0.901258\pi$
$631$	−24.0201	+	17.4516i	−0.956224	+	0.694737i	−0.00395328	+	0.999992i	$0.501258\pi$
$632$		0			0
$633$	16.9313	+	12.3013i	0.672957	+	0.488932i
$634$		0			0
$635$	−51.9885	+	37.7719i	−2.06310	+	1.49893i
$636$		0			0
$637$	−0.242673	−	0.334011i	−0.00961505	−	0.0132340i
$638$		0			0
$639$	−5.80924	−	1.88754i	−0.229810	−	0.0746697i
$640$		0			0
$641$	−22.9307	+	7.45065i	−0.905710	+	0.294283i	−0.724592	−	0.689178i	$-0.757972\pi$
$641$	−22.9307	+	7.45065i	−0.905710	+	0.294283i	−0.181118	+	0.983461i	$0.557972\pi$
$642$		0			0
$643$	−10.9189	+	15.0285i	−0.430598	+	0.592667i	−0.968090	−	0.250601i	$-0.919372\pi$
$643$	−10.9189	+	15.0285i	−0.430598	+	0.592667i	0.537492	+	0.843269i	$0.319372\pi$
$644$		0			0
$645$	−9.60559	−	3.12104i	−0.378220	−	0.122891i
$646$		0			0
$647$	46.6864			1.83543			0.917717	−	0.397236i	$-0.130031\pi$
$647$	46.6864			1.83543			0.917717	+	0.397236i	$0.130031\pi$
$648$		0			0
$649$	−10.1315	−	13.9448i	−0.397696	−	0.547381i
$650$		0			0
$651$	1.36192	+	4.19156i	0.0533779	+	0.164280i
$652$		0			0
$653$		−	45.6865i		−	1.78785i	−0.448215	−	0.893926i	$-0.647940\pi$
$653$		−	45.6865i		−	1.78785i	0.448215	−	0.893926i	$-0.352060\pi$
$654$		0			0
$655$	−20.9030			−0.816749
$656$		0			0
$657$	−27.1367			−1.05870
$658$		0			0
$659$		−	16.5351i		−	0.644118i	−0.946720	−	0.322059i	$-0.895625\pi$
$659$		−	16.5351i		−	0.644118i	0.946720	−	0.322059i	$-0.104375\pi$
$660$		0			0
$661$	10.9357	+	33.6566i	0.425349	+	1.30909i	0.902660	+	0.430355i	$0.141612\pi$
$661$	10.9357	+	33.6566i	0.425349	+	1.30909i	−0.477311	+	0.878735i	$0.658388\pi$
$662$		0			0
$663$	1.20828	+	1.66305i	0.0469256	+	0.0645875i
$664$		0			0
$665$	23.2950			0.903340
$666$		0			0
$667$	−18.5847	−	6.03852i	−0.719601	−	0.233812i
$668$		0			0
$669$	−0.934548	+	1.28630i	−0.0361317	+	0.0497311i
$670$		0			0
$671$	−56.7171	+	18.4285i	−2.18954	+	0.711425i
$672$		0			0
$673$	−34.3566	−	11.1631i	−1.32435	−	0.430307i	−0.440362	−	0.897820i	$-0.645150\pi$
$673$	−34.3566	−	11.1631i	−1.32435	−	0.430307i	−0.883986	+	0.467513i	$0.845150\pi$
$674$		0			0
$675$	20.6474	+	28.4187i	0.794718	+	1.09384i
$676$		0			0
$677$	23.0289	−	16.7315i	0.885073	−	0.643043i	−0.0495155	−	0.998773i	$-0.515768\pi$
$677$	23.0289	−	16.7315i	0.885073	−	0.643043i	0.934589	+	0.355730i	$0.115768\pi$
$678$		0			0
$679$	−0.795182	−	0.577733i	−0.0305163	−	0.0221714i
$680$		0			0
$681$	9.34002	−	6.78592i	0.357910	−	0.260037i
$682$		0			0
$683$			51.6711i			1.97714i	0.150763	+	0.988570i	$0.451827\pi$
$683$			51.6711i			1.97714i	−0.150763	+	0.988570i	$0.548173\pi$
$684$		0			0
$685$	−27.5163	+	8.94060i	−1.05135	+	0.341603i
$686$		0			0
$687$	7.23324	−	22.2616i	0.275965	−	0.849334i
$688$		0			0
$689$	0.616975	−	1.89885i	0.0235049	−	0.0723405i
$690$		0			0
$691$	−17.1495	+	23.6043i	−0.652398	+	0.897949i	−0.999200	−	0.0399893i	$-0.987268\pi$
$691$	−17.1495	+	23.6043i	−0.652398	+	0.897949i	0.346802	+	0.937938i	$0.387268\pi$
$692$		0			0
$693$	2.59378	+	7.98283i	0.0985295	+	0.303243i
$694$		0			0
$695$	−46.3243	−	33.6566i	−1.75718	−	1.27667i
$696$		0			0
$697$	−16.6967	+	21.9715i	−0.632431	+	0.832230i
$698$		0			0
$699$	−11.1873	−	8.12802i	−0.423141	−	0.307430i
$700$		0			0
$701$	12.6497	+	38.9317i	0.477771	+	1.47043i	0.842183	+	0.539191i	$0.181270\pi$
$701$	12.6497	+	38.9317i	0.477771	+	1.47043i	−0.364412	+	0.931238i	$0.618730\pi$
$702$		0			0
$703$	19.7862	−	27.2333i	0.746250	−	1.02713i
$704$		0			0
$705$	4.43095	−	13.6371i	0.166879	−	0.513602i
$706$		0			0
$707$	−0.0215022	+	0.0661771i	−0.000808675	+	0.00248884i
$708$		0			0
$709$	39.8172	−	12.9374i	1.49537	−	0.485874i	0.556705	−	0.830710i	$-0.312065\pi$
$709$	39.8172	−	12.9374i	1.49537	−	0.485874i	0.938663	+	0.344836i	$0.112065\pi$
$710$		0			0
$711$		−	9.63081i		−	0.361183i
$712$		0			0
$713$	10.3499	−	7.51966i	0.387608	−	0.281614i
$714$		0			0
$715$	−5.71348	−	4.15108i	−0.213672	−	0.155242i
$716$		0			0
$717$	−6.40419	+	4.65292i	−0.239169	+	0.173766i
$718$		0			0
$719$	−9.09406	−	12.5169i	−0.339151	−	0.466802i	0.605042	−	0.796194i	$-0.293156\pi$
$719$	−9.09406	−	12.5169i	−0.339151	−	0.466802i	−0.944193	+	0.329392i	$0.893156\pi$
$720$		0			0
$721$	−17.6083	−	5.72128i	−0.655767	−	0.213071i
$722$		0			0
$723$	0.407932	−	0.132545i	0.0151712	−	0.00492941i
$724$		0			0
$725$	22.3221	−	30.7237i	0.829022	−	1.14105i
$726$		0			0
$727$	−3.96990	−	1.28990i	−0.147235	−	0.0478397i	0.234472	−	0.972123i	$-0.424664\pi$
$727$	−3.96990	−	1.28990i	−0.147235	−	0.0478397i	−0.381708	+	0.924283i	$0.624664\pi$
$728$		0			0
$729$	−20.7305			−0.767795
$730$		0			0
$731$	6.52551	+	8.98160i	0.241355	+	0.332196i
$732$		0			0
$733$	1.30718	+	4.02308i	0.0482817	+	0.148596i	0.972291	−	0.233775i	$-0.0751078\pi$
$733$	1.30718	+	4.02308i	0.0482817	+	0.148596i	−0.924009	+	0.382370i	$0.875108\pi$
$734$		0			0
$735$		−	3.92077i		−	0.144620i
$736$		0			0
$737$	21.1997			0.780903
$738$		0			0
$739$	36.8473			1.35545			0.677725	−	0.735315i	$-0.262966\pi$
$739$	36.8473			1.35545			0.677725	+	0.735315i	$0.262966\pi$
$740$		0			0
$741$		−	3.27403i		−	0.120275i
$742$		0			0
$743$	−6.67553	−	20.5452i	−0.244902	−	0.753730i	−0.995653	−	0.0931444i	$-0.970308\pi$
$743$	−6.67553	−	20.5452i	−0.244902	−	0.753730i	0.750751	−	0.660585i	$-0.229692\pi$
$744$		0			0
$745$	24.1589	+	33.2519i	0.885114	+	1.21825i
$746$		0			0
$747$	−14.8610			−0.543737
$748$		0			0
$749$	8.28304	+	2.69132i	0.302656	+	0.0983389i
$750$		0			0
$751$	−14.1236	+	19.4394i	−0.515377	+	0.709355i	−0.984814	−	0.173610i	$-0.944457\pi$
$751$	−14.1236	+	19.4394i	−0.515377	+	0.709355i	0.469438	+	0.882966i	$0.344457\pi$
$752$		0			0
$753$	1.52475	−	0.495422i	0.0555650	−	0.0180542i
$754$		0			0
$755$	−32.7427	−	10.6387i	−1.19163	−	0.387183i
$756$		0			0
$757$	16.0107	+	22.0368i	0.581918	+	0.800942i	0.993904	−	0.110248i	$-0.0351646\pi$
$757$	16.0107	+	22.0368i	0.581918	+	0.800942i	−0.411986	+	0.911190i	$0.635165\pi$
$758$		0			0
$759$	−15.7987	+	11.4784i	−0.573456	+	0.416640i
$760$		0			0
$761$	−3.60970	−	2.62260i	−0.130852	−	0.0950693i	0.520434	−	0.853902i	$-0.325770\pi$
$761$	−3.60970	−	2.62260i	−0.130852	−	0.0950693i	−0.651286	+	0.758832i	$0.725770\pi$
$762$		0			0
$763$	−9.91006	+	7.20008i	−0.358768	+	0.260660i
$764$		0			0
$765$		−	24.3565i		−	0.880611i
$766$		0			0
$767$	−1.34277	+	0.436291i	−0.0484845	+	0.0157536i
$768$		0			0
$769$	15.4993	−	47.7021i	0.558920	−	1.72018i	−0.126439	−	0.991974i	$-0.540355\pi$
$769$	15.4993	−	47.7021i	0.558920	−	1.72018i	0.685359	−	0.728205i	$-0.259645\pi$
$770$		0			0
$771$	2.01294	−	6.19520i	0.0724943	−	0.223115i
$772$		0			0
$773$	−7.75841	+	10.6785i	−0.279051	+	0.384080i	−0.925419	−	0.378945i	$-0.876287\pi$
$773$	−7.75841	+	10.6785i	−0.279051	+	0.384080i	0.646369	+	0.763025i	$0.276287\pi$
$774$		0			0
$775$	7.68299	+	23.6458i	0.275981	+	0.849383i
$776$		0			0
$777$	−4.58364	−	3.33021i	−0.164437	−	0.119471i
$778$		0			0
$779$	42.0831	−	12.6799i	1.50778	−	0.454306i
$780$		0			0
$781$	14.9570	+	10.8669i	0.535205	+	0.388849i
$782$		0			0
$783$	9.70505	+	29.8691i	0.346830	+	1.06743i
$784$		0			0
$785$	7.79198	−	10.7247i	0.278108	−	0.382782i
$786$		0			0
$787$	4.96943	−	15.2943i	0.177141	−	0.545184i	−0.822584	−	0.568644i	$-0.807468\pi$
$787$	4.96943	−	15.2943i	0.177141	−	0.545184i	0.999725	+	0.0234597i	$0.00746815\pi$
$788$		0			0
$789$	9.39699	−	28.9210i	0.334542	−	1.02961i
$790$		0			0
$791$	−3.12691	+	1.01600i	−0.111180	+	0.0361246i
$792$		0			0
$793$			4.88481i			0.173465i
$794$		0			0
$795$	15.3395	−	11.1448i	0.544037	−	0.395266i
$796$		0			0
$797$	5.90392	+	4.28945i	0.209127	+	0.151940i	0.687419	−	0.726261i	$-0.258744\pi$
$797$	5.90392	+	4.28945i	0.209127	+	0.151940i	−0.478291	+	0.878201i	$0.658744\pi$
$798$		0			0
$799$	−12.7512	+	9.26428i	−0.451105	+	0.327747i
$800$		0			0
$801$	7.58770	+	10.4436i	0.268098	+	0.369005i
$802$		0			0
$803$	78.1159	+	25.3814i	2.75665	+	0.895690i
$804$		0			0
$805$	−10.8240	+	3.51694i	−0.381496	+	0.123956i
$806$		0			0
$807$	−3.47973	+	4.78944i	−0.122492	+	0.168596i
$808$		0			0
$809$	42.6321	+	13.8520i	1.49887	+	0.487011i	0.939687	−	0.342035i	$-0.111116\pi$
$809$	42.6321	+	13.8520i	1.49887	+	0.487011i	0.559179	+	0.829047i	$0.311116\pi$
$810$		0			0
$811$	43.8416			1.53949			0.769743	−	0.638354i	$-0.220385\pi$
$811$	43.8416			1.53949			0.769743	+	0.638354i	$0.220385\pi$
$812$		0			0
$813$	19.9764	+	27.4952i	0.700604	+	0.964299i
$814$		0			0
$815$	−6.12081	−	18.8379i	−0.214403	−	0.659863i
$816$		0			0
$817$		−	17.6820i		−	0.618614i
$818$		0			0
$819$	0.687528			0.0240242
$820$		0			0
$821$	28.5083			0.994947			0.497473	−	0.867479i	$-0.334261\pi$
$821$	28.5083			0.994947			0.497473	+	0.867479i	$0.334261\pi$
$822$		0			0
$823$			37.7141i			1.31463i	0.753615	+	0.657316i	$0.228308\pi$
$823$			37.7141i			1.31463i	−0.753615	+	0.657316i	$0.771692\pi$
$824$		0			0
$825$	−11.7277	−	36.0942i	−0.408307	−	1.25664i
$826$		0			0
$827$	28.7140	+	39.5215i	0.998485	+	1.37430i	0.926250	+	0.376909i	$0.123013\pi$
$827$	28.7140	+	39.5215i	0.998485	+	1.37430i	0.0722347	+	0.997388i	$0.476987\pi$
$828$		0			0
$829$	47.3630			1.64499			0.822493	−	0.568775i	$-0.192582\pi$
$829$	47.3630			1.64499			0.822493	+	0.568775i	$0.192582\pi$
$830$		0			0
$831$	−35.2494	−	11.4532i	−1.22279	−	0.397308i
$832$		0			0
$833$	−2.53320	+	3.48665i	−0.0877701	+	0.120805i
$834$		0			0
$835$	−43.8064	+	14.2335i	−1.51598	+	0.492572i
$836$		0			0
$837$	−19.5548	−	6.35374i	−0.675913	−	0.219617i
$838$		0			0
$839$	−21.6343	−	29.7771i	−0.746900	−	1.02802i	−0.998192	−	0.0601085i	$-0.980855\pi$
$839$	−21.6343	−	29.7771i	−0.746900	−	1.02802i	0.251292	−	0.967911i	$-0.419145\pi$
$840$		0			0
$841$	4.00755	−	2.91165i	0.138191	−	0.100402i
$842$		0			0
$843$	−29.3828	−	21.3478i	−1.01200	−	0.735258i
$844$		0			0
$845$	35.2246	−	25.5922i	1.21176	−	0.880397i
$846$		0			0
$847$		−	14.4054i		−	0.494976i
$848$		0			0
$849$	−1.52738	+	0.496277i	−0.0524196	+	0.0170322i
$850$		0			0
$851$	−5.08213	+	15.6412i	−0.174213	+	0.536173i
$852$		0			0
$853$	5.03889	−	15.5081i	0.172528	−	0.530987i	−0.826984	−	0.562226i	$-0.809945\pi$
$853$	5.03889	−	15.5081i	0.172528	−	0.530987i	0.999512	+	0.0312386i	$0.00994518\pi$
$854$		0			0
$855$	−22.8018	+	31.3839i	−0.779804	+	1.07331i
$856$		0			0
$857$	−8.17343	−	25.1552i	−0.279199	−	0.859286i	−0.988078	−	0.153956i	$-0.950799\pi$
$857$	−8.17343	−	25.1552i	−0.279199	−	0.859286i	0.708879	−	0.705330i	$-0.249201\pi$
$858$		0			0
$859$	25.1388	+	18.2644i	0.857723	+	0.623173i	0.927265	−	0.374407i	$-0.122154\pi$
$859$	25.1388	+	18.2644i	0.857723	+	0.623173i	−0.0695413	+	0.997579i	$0.522154\pi$
$860$		0			0
$861$	−2.13416	−	7.08300i	−0.0727319	−	0.241388i
$862$		0			0
$863$	−0.673959	−	0.489660i	−0.0229418	−	0.0166682i	0.576255	−	0.817270i	$-0.304513\pi$
$863$	−0.673959	−	0.489660i	−0.0229418	−	0.0166682i	−0.599197	+	0.800602i	$0.704513\pi$
$864$		0			0
$865$	−19.4694	−	59.9208i	−0.661981	−	2.03737i
$866$		0			0
$867$	1.06871	−	1.47095i	0.0362953	−	0.0499562i
$868$		0			0
$869$	−9.00784	+	27.7233i	−0.305570	+	0.940447i
$870$		0			0
$871$	0.536602	−	1.65149i	0.0181821	−	0.0559587i
$872$		0			0
$873$	1.55669	−	0.505800i	0.0526860	−	0.0171187i
$874$		0			0
$875$		−	5.14959i		−	0.174088i
$876$		0			0
$877$	−45.1121	+	32.7758i	−1.52333	+	1.10676i	−0.563518	+	0.826104i	$0.690552\pi$
$877$	−45.1121	+	32.7758i	−1.52333	+	1.10676i	−0.959808	+	0.280657i	$0.909448\pi$
$878$		0			0
$879$	−11.9949	−	8.71481i	−0.404578	−	0.293943i
$880$		0			0
$881$	−41.9270	+	30.4617i	−1.41256	+	1.02628i	−0.419611	+	0.907704i	$0.637833\pi$
$881$	−41.9270	+	30.4617i	−1.41256	+	1.02628i	−0.992945	+	0.118577i	$0.962167\pi$
$882$		0			0
$883$	24.3207	+	33.4745i	0.818455	+	1.12651i	0.989963	+	0.141324i	$0.0451360\pi$
$883$	24.3207	+	33.4745i	0.818455	+	1.12651i	−0.171508	+	0.985183i	$0.554864\pi$
$884$		0			0
$885$	−12.7517	−	4.14329i	−0.428645	−	0.139275i
$886$		0			0
$887$	−19.8496	+	6.44954i	−0.666485	+	0.216554i	−0.622669	−	0.782485i	$-0.713952\pi$
$887$	−19.8496	+	6.44954i	−0.666485	+	0.216554i	−0.0438164	+	0.999040i	$0.513952\pi$
$888$		0			0
$889$	−11.1299	+	15.3190i	−0.373285	+	0.513783i
$890$		0			0
$891$	5.90100	+	1.91735i	0.197691	+	0.0642337i
$892$		0			0
$893$	25.1031			0.840044
$894$		0			0
$895$	43.3905	+	59.7219i	1.45038	+	1.99628i
$896$		0			0
$897$	0.494294	+	1.52128i	0.0165040	+	0.0507941i
$898$		0			0
$899$			22.2289i			0.741374i
$900$		0			0
$901$	−20.8417			−0.694336
$902$		0			0
$903$	−2.97605			−0.0990368
$904$		0			0
$905$			61.1815i			2.03374i
$906$		0			0
$907$	6.32287	+	19.4598i	0.209947	+	0.646152i	0.999474	+	0.0324352i	$0.0103263\pi$
$907$	6.32287	+	19.4598i	0.209947	+	0.646152i	−0.789526	+	0.613717i	$0.789674\pi$
$908$		0			0
$909$	−0.0681095	−	0.0937446i	−0.00225905	−	0.00310931i
$910$		0			0
$911$	21.0535			0.697534			0.348767	−	0.937209i	$-0.386600\pi$
$911$	21.0535			0.697534			0.348767	+	0.937209i	$0.386600\pi$
$912$		0			0
$913$	42.7790	+	13.8997i	1.41578	+	0.460015i
$914$		0			0
$915$	−27.2669	+	37.5296i	−0.901415	+	1.24069i
$916$		0			0
$917$	−5.85786	+	1.90333i	−0.193443	+	0.0628536i
$918$		0			0
$919$	33.5944	+	10.9155i	1.10818	+	0.360069i	0.805245	−	0.592943i	$-0.202034\pi$
$919$	33.5944	+	10.9155i	1.10818	+	0.360069i	0.302933	+	0.953012i	$0.402034\pi$
$920$		0			0
$921$	−15.9441	−	21.9451i	−0.525374	−	0.723116i
$922$		0			0
$923$	1.22514	−	0.890116i	0.0403260	−	0.0292985i
$924$		0			0
$925$	−25.8577	−	18.7867i	−0.850195	−	0.617703i
$926$		0			0
$927$	24.9434	−	18.1224i	0.819249	−	0.595219i
$928$		0			0
$929$		−	5.68947i		−	0.186665i	−0.995635	−	0.0933327i	$-0.970248\pi$
$929$		−	5.68947i		−	0.186665i	0.995635	−	0.0933327i	$-0.0297520\pi$
$930$		0			0
$931$	6.52817	−	2.12113i	0.213952	−	0.0695173i
$932$		0			0
$933$	−4.35103	+	13.3911i	−0.142446	+	0.438404i
$934$		0			0
$935$	−22.7810	+	70.1127i	−0.745018	+	2.29293i
$936$		0			0
$937$	0.748614	−	1.03038i	0.0244562	−	0.0336610i	−0.796614	−	0.604489i	$-0.793378\pi$
$937$	0.748614	−	1.03038i	0.0244562	−	0.0336610i	0.821070	+	0.570828i	$0.193378\pi$
$938$		0			0
$939$	−9.54377	−	29.3727i	−0.311449	−	0.958542i
$940$		0			0
$941$	−0.987921	−	0.717766i	−0.0322053	−	0.0233985i	0.571566	−	0.820556i	$-0.306336\pi$
$941$	−0.987921	−	0.717766i	−0.0322053	−	0.0233985i	−0.603771	+	0.797157i	$0.706336\pi$
$942$		0			0
$943$	−17.6396	+	12.2452i	−0.574423	+	0.398758i
$944$		0			0
$945$	14.7981	+	10.7515i	0.481384	+	0.349746i
$946$		0			0
$947$	−15.6281	−	48.0984i	−0.507845	−	1.56299i	−0.795934	−	0.605383i	$-0.793020\pi$
$947$	−15.6281	−	48.0984i	−0.507845	−	1.56299i	0.288089	−	0.957604i	$-0.406980\pi$
$948$		0			0
$949$	3.95450	−	5.44290i	0.128368	−	0.176684i
$950$		0			0
$951$	−2.87394	+	8.84506i	−0.0931937	+	0.286821i
$952$		0			0
$953$	−5.13279	+	15.7971i	−0.166267	+	0.511719i	−0.999127	−	0.0417651i	$-0.986702\pi$
$953$	−5.13279	+	15.7971i	−0.166267	+	0.511719i	0.832860	+	0.553484i	$0.186702\pi$
$954$		0			0
$955$	−18.5878	+	6.03954i	−0.601487	+	0.195435i
$956$		0			0
$957$		−	33.9313i		−	1.09684i
$958$		0			0
$959$	−6.89708	+	5.01102i	−0.222718	+	0.161814i
$960$		0			0
$961$	13.3060	+	9.66737i	0.429226	+	0.311851i
$962$		0			0
$963$	−11.7335	+	8.52491i	−0.378108	+	0.274711i
$964$		0			0
$965$	20.1294	+	27.7057i	0.647988	+	0.891878i
$966$		0			0
$967$	30.8346	+	10.0188i	0.991572	+	0.322181i	0.759493	−	0.650515i	$-0.225447\pi$
$967$	30.8346	+	10.0188i	0.991572	+	0.322181i	0.232079	+	0.972697i	$0.425447\pi$
$968$		0			0
$969$	−32.5040	+	10.5612i	−1.04418	+	0.339274i
$970$		0			0
$971$	16.3727	−	22.5351i	0.525425	−	0.723185i	−0.461000	−	0.887400i	$-0.652509\pi$
$971$	16.3727	−	22.5351i	0.525425	−	0.723185i	0.986425	+	0.164215i	$0.0525091\pi$
$972$		0			0
$973$	−16.0465	−	5.21383i	−0.514428	−	0.167148i
$974$		0			0
$975$	−3.10864			−0.0995563
$976$		0			0
$977$	6.79274	+	9.34940i	0.217319	+	0.299114i	0.903733	−	0.428097i	$-0.140816\pi$
$977$	6.79274	+	9.34940i	0.217319	+	0.299114i	−0.686414	+	0.727211i	$0.740816\pi$
$978$		0			0
$979$	−12.0739	−	37.1598i	−0.385885	−	1.18763i
$980$		0			0
$981$		−	20.3989i		−	0.651286i
$982$		0			0
$983$	−21.1481			−0.674519			−0.337259	−	0.941412i	$-0.609500\pi$
$983$	−21.1481			−0.674519			−0.337259	+	0.941412i	$0.609500\pi$
$984$		0			0
$985$	−51.2566			−1.63317
$986$		0			0
$987$		−	4.22511i		−	0.134487i
$988$		0			0
$989$	2.66952	+	8.21594i	0.0848858	+	0.261252i
$990$		0			0
$991$	3.13119	+	4.30971i	0.0994655	+	0.136903i	0.855849	−	0.517226i	$-0.173035\pi$
$991$	3.13119	+	4.30971i	0.0994655	+	0.136903i	−0.756383	+	0.654129i	$0.773035\pi$
$992$		0			0
$993$	18.9023			0.599845
$994$		0			0
$995$	−11.6529	−	3.78627i	−0.369423	−	0.120033i
$996$		0			0
$997$	21.6314	−	29.7730i	0.685073	−	0.942921i	−0.314908	−	0.949122i	$-0.601974\pi$
$997$	21.6314	−	29.7730i	0.685073	−	0.942921i	0.999981	+	0.00620068i	$0.00197375\pi$
$998$		0			0
$999$	25.1384	−	8.16796i	0.795343	−	0.258423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.7	✓	80
41.4	even	10	inner	1148.2.ba.a.701.14	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.7	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.14	yes	80	41.4	even	10	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-1.15530i q^{3} +(-1.04872 - 3.22763i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.66528 q^{9} +O(q^{10})\)	\(q-1.15530i q^{3} +(-1.04872 - 3.22763i) q^{5} +(-0.587785 - 0.809017i) q^{7} +1.66528 q^{9} +(-4.79368 - 1.55756i) q^{11} +(-0.242673 + 0.334011i) q^{13} +(-3.72888 + 1.21159i) q^{15} +(4.09880 + 1.33178i) q^{17} +(-4.03463 - 5.55319i) q^{19} +(-0.934658 + 0.679068i) q^{21} +(2.71308 + 1.97117i) q^{23} +(-5.27268 + 3.83082i) q^{25} -5.38980i q^{27} +(-5.54178 + 1.80063i) q^{29} +(1.17885 - 3.62811i) q^{31} +(-1.79945 + 5.53814i) q^{33} +(-1.99478 + 2.74558i) q^{35} +(1.51545 + 4.66407i) q^{37} +(0.385883 + 0.280360i) q^{39} +(-2.10916 + 6.04578i) q^{41} +(2.08403 + 1.51413i) q^{43} +(-1.74641 - 5.37491i) q^{45} +(-2.14962 + 2.95870i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(1.53861 - 4.73534i) q^{51} +(-4.59927 + 1.49439i) q^{53} +17.1057i q^{55} +(-6.41561 + 4.66121i) q^{57} +(2.76662 + 2.01006i) q^{59} +(9.57199 - 6.95446i) q^{61} +(-0.978828 - 1.34724i) q^{63} +(1.33256 + 0.432974i) q^{65} +(-4.00013 + 1.29972i) q^{67} +(2.27729 - 3.13442i) q^{69} +(-3.48844 - 1.13346i) q^{71} -16.2956 q^{73} +(4.42575 + 6.09152i) q^{75} +(1.55756 + 4.79368i) q^{77} -5.78329i q^{79} -1.23099 q^{81} -8.92404 q^{83} -14.6261i q^{85} +(2.08027 + 6.40242i) q^{87} +(4.55641 + 6.27135i) q^{89} +0.412860 q^{91} +(-4.19156 - 1.36192i) q^{93} +(-13.6924 + 18.8460i) q^{95} +(0.934792 - 0.303732i) q^{97} +(-7.98283 - 2.59378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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