LMFDB - Embedded newform 300.2.x.a.53.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(17,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 10, 13]))

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

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

chi := DirichletCharacter("300.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.x (of order $20$, degree $8$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			53.8
Character	$\chi$	$=$	300.53
Dual form			300.2.x.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17077 + 1.27644i) q^{3} +(1.13602 + 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-0.258608 + 2.98883i) q^{9} +O(q^{10})$	\(q+(1.17077 + 1.27644i) q^{3} +(1.13602 + 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-0.258608 + 2.98883i) q^{9} +(-2.76163 - 0.897307i) q^{11} +(0.404807 - 0.794479i) q^{13} +(-1.12840 + 3.70496i) q^{15} +(-3.19333 - 0.505773i) q^{17} +(0.694208 + 0.955496i) q^{19} +(7.36453 + 0.318013i) q^{21} +(2.51796 + 4.94177i) q^{23} +(-2.41891 + 4.37594i) q^{25} +(-4.11784 + 3.16913i) q^{27} +(-6.77941 - 4.92553i) q^{29} +(6.19212 - 4.49884i) q^{31} +(-2.08786 - 4.57559i) q^{33} +(9.21471 + 2.37731i) q^{35} +(-8.57635 - 4.36987i) q^{37} +(1.48804 - 0.413437i) q^{39} +(8.73412 - 2.83789i) q^{41} +(-1.45614 - 1.45614i) q^{43} +(-6.05026 + 2.89730i) q^{45} +(1.10756 + 6.99286i) q^{47} -11.1125i q^{49} +(-3.09305 - 4.66824i) q^{51} +(-2.56331 + 0.405989i) q^{53} +(-1.40906 - 6.33824i) q^{55} +(-0.406879 + 2.00478i) q^{57} +(-3.44583 - 10.6052i) q^{59} +(-2.69549 + 8.29586i) q^{61} +(8.21623 + 9.77272i) q^{63} +(1.99003 - 0.122889i) q^{65} +(0.616819 - 3.89444i) q^{67} +(-3.35994 + 8.99969i) q^{69} +(0.265914 - 0.366000i) q^{71} +(-2.68754 + 1.36937i) q^{73} +(-8.41762 + 2.03561i) q^{75} +(-11.0110 + 5.61041i) q^{77} +(2.07296 - 2.85319i) q^{79} +(-8.86624 - 1.54587i) q^{81} +(2.20859 - 13.9445i) q^{83} +(-2.65357 - 6.72490i) q^{85} +(-1.64996 - 14.4202i) q^{87} +(2.41968 - 7.44701i) q^{89} +(-1.17266 - 3.60908i) q^{91} +(12.9920 + 2.63679i) q^{93} +(-1.05164 + 2.42251i) q^{95} +(-1.51448 + 0.239870i) q^{97} +(3.39608 - 8.02199i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q - 2 * q^3 + 4 * q^7	$ 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) $ 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{20}\right)$

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
$3$	1.17077	+	1.27644i	0.675943	+	0.736954i
$3$	1.17077	+	1.27644i	0.675943	+	0.736954i
$4$		0			0
$5$	1.13602	+	1.92599i	0.508044	+	0.861331i
$5$	1.13602	+	1.92599i	0.508044	+	0.861331i
$6$		0			0
$7$	3.00936	−	3.00936i	1.13743	−	1.13743i	0.148522	−	0.988909i	$-0.452548\pi$
$7$	3.00936	−	3.00936i	1.13743	−	1.13743i	0.988909	−	0.148522i	$-0.0474516\pi$
$8$		0			0
$9$	−0.258608	+	2.98883i	−0.0862027	+	0.996278i
$10$		0			0
$11$	−2.76163	−	0.897307i	−0.832662	−	0.270548i	−0.138496	−	0.990363i	$-0.544227\pi$
$11$	−2.76163	−	0.897307i	−0.832662	−	0.270548i	−0.694166	+	0.719815i	$0.744227\pi$
$12$		0			0
$13$	0.404807	−	0.794479i	0.112273	−	0.220349i	−0.828032	−	0.560681i	$-0.810539\pi$
$13$	0.404807	−	0.794479i	0.112273	−	0.220349i	0.940305	+	0.340332i	$0.110539\pi$
$14$		0			0
$15$	−1.12840	+	3.70496i	−0.291352	+	0.956616i
$16$		0			0
$17$	−3.19333	−	0.505773i	−0.774496	−	0.122668i	−0.243339	−	0.969941i	$-0.578243\pi$
$17$	−3.19333	−	0.505773i	−0.774496	−	0.122668i	−0.531157	+	0.847273i	$0.678243\pi$
$18$		0			0
$19$	0.694208	+	0.955496i	0.159262	+	0.219206i	0.881189	−	0.472763i	$-0.156743\pi$
$19$	0.694208	+	0.955496i	0.159262	+	0.219206i	−0.721927	+	0.691969i	$0.756743\pi$
$20$		0			0
$21$	7.36453	+	0.318013i	1.60707	+	0.0693962i
$22$		0			0
$23$	2.51796	+	4.94177i	0.525030	+	1.03043i	0.989458	+	0.144819i	$0.0462600\pi$
$23$	2.51796	+	4.94177i	0.525030	+	1.03043i	−0.464428	+	0.885611i	$0.653740\pi$
$24$		0			0
$25$	−2.41891	+	4.37594i	−0.483782	+	0.875189i
$26$		0			0
$27$	−4.11784	+	3.16913i	−0.792479	+	0.609899i
$28$		0			0
$29$	−6.77941	−	4.92553i	−1.25890	−	0.914648i	−0.260201	−	0.965554i	$-0.583789\pi$
$29$	−6.77941	−	4.92553i	−1.25890	−	0.914648i	−0.998703	+	0.0509065i	$0.983789\pi$
$30$		0			0
$31$	6.19212	−	4.49884i	1.11214	−	0.808015i	0.129139	−	0.991627i	$-0.458779\pi$
$31$	6.19212	−	4.49884i	1.11214	−	0.808015i	0.982999	+	0.183611i	$0.0587787\pi$
$32$		0			0
$33$	−2.08786	−	4.57559i	−0.363450	−	0.796509i
$34$		0			0
$35$	9.21471	+	2.37731i	1.55757	+	0.401839i
$36$		0			0
$37$	−8.57635	−	4.36987i	−1.40994	−	0.718402i	−0.427335	−	0.904093i	$-0.640548\pi$
$37$	−8.57635	−	4.36987i	−1.40994	−	0.718402i	−0.982608	+	0.185691i	$0.940548\pi$
$38$		0			0
$39$	1.48804	−	0.413437i	0.238277	−	0.0662029i
$40$		0			0
$41$	8.73412	−	2.83789i	1.36404	−	0.443204i	0.466651	−	0.884442i	$-0.345460\pi$
$41$	8.73412	−	2.83789i	1.36404	−	0.443204i	0.897390	+	0.441238i	$0.145460\pi$
$42$		0			0
$43$	−1.45614	−	1.45614i	−0.222059	−	0.222059i	0.587306	−	0.809365i	$-0.300188\pi$
$43$	−1.45614	−	1.45614i	−0.222059	−	0.222059i	−0.809365	+	0.587306i	$0.800188\pi$
$44$		0			0
$45$	−6.05026	+	2.89730i	−0.901920	+	0.431904i
$46$		0			0
$47$	1.10756	+	6.99286i	0.161554	+	1.02001i	0.926603	+	0.376041i	$0.122715\pi$
$47$	1.10756	+	6.99286i	0.161554	+	1.02001i	−0.765049	+	0.643973i	$0.777285\pi$
$48$		0			0
$49$		−	11.1125i		−	1.58750i
$50$		0			0
$51$	−3.09305	−	4.66824i	−0.433114	−	0.653684i
$52$		0			0
$53$	−2.56331	+	0.405989i	−0.352098	+	0.0557668i	−0.329978	−	0.943989i	$-0.607041\pi$
$53$	−2.56331	+	0.405989i	−0.352098	+	0.0557668i	−0.0221195	+	0.999755i	$0.507041\pi$
$54$		0			0
$55$	−1.40906	−	6.33824i	−0.189998	−	0.854648i
$56$		0			0
$57$	−0.406879	+	2.00478i	−0.0538924	+	0.265540i
$58$		0			0
$59$	−3.44583	−	10.6052i	−0.448609	−	1.38068i	−0.878477	−	0.477785i	$-0.841440\pi$
$59$	−3.44583	−	10.6052i	−0.448609	−	1.38068i	0.429867	−	0.902892i	$-0.358560\pi$
$60$		0			0
$61$	−2.69549	+	8.29586i	−0.345122	+	1.06218i	0.616397	+	0.787436i	$0.288592\pi$
$61$	−2.69549	+	8.29586i	−0.345122	+	1.06218i	−0.961519	+	0.274740i	$0.911408\pi$
$62$		0			0
$63$	8.21623	+	9.77272i	1.03515	+	1.23125i
$64$		0			0
$65$	1.99003	−	0.122889i	0.246833	−	0.0152425i
$66$		0			0
$67$	0.616819	−	3.89444i	0.0753564	−	0.475782i	−0.920933	−	0.389720i	$-0.872572\pi$
$67$	0.616819	−	3.89444i	0.0753564	−	0.475782i	0.996290	−	0.0860617i	$-0.0274282\pi$
$68$		0			0
$69$	−3.35994	+	8.99969i	−0.404489	+	1.08343i
$70$		0			0
$71$	0.265914	−	0.366000i	0.0315582	−	0.0434362i	−0.792946	−	0.609292i	$-0.791454\pi$
$71$	0.265914	−	0.366000i	0.0315582	−	0.0434362i	0.824505	+	0.565855i	$0.191454\pi$
$72$		0			0
$73$	−2.68754	+	1.36937i	−0.314553	+	0.160273i	−0.604139	−	0.796879i	$-0.706483\pi$
$73$	−2.68754	+	1.36937i	−0.314553	+	0.160273i	0.289585	+	0.957152i	$0.406483\pi$
$74$		0			0
$75$	−8.41762	+	2.03561i	−0.971983	+	0.235052i
$76$		0			0
$77$	−11.0110	+	5.61041i	−1.25483	+	0.639366i
$78$		0			0
$79$	2.07296	−	2.85319i	0.233227	−	0.321009i	−0.676322	−	0.736606i	$-0.736427\pi$
$79$	2.07296	−	2.85319i	0.233227	−	0.321009i	0.909549	+	0.415597i	$0.136427\pi$
$80$		0			0
$81$	−8.86624	−	1.54587i	−0.985138	−	0.171764i
$82$		0			0
$83$	2.20859	−	13.9445i	0.242424	−	1.53060i	−0.503161	−	0.864193i	$-0.667830\pi$
$83$	2.20859	−	13.9445i	0.242424	−	1.53060i	0.745585	−	0.666411i	$-0.232170\pi$
$84$		0			0
$85$	−2.65357	−	6.72490i	−0.287820	−	0.729418i
$86$		0			0
$87$	−1.64996	−	14.4202i	−0.176894	−	1.54600i
$88$		0			0
$89$	2.41968	−	7.44701i	0.256486	−	0.789382i	−0.737048	−	0.675841i	$-0.763781\pi$
$89$	2.41968	−	7.44701i	0.256486	−	0.789382i	0.993533	−	0.113541i	$-0.0362193\pi$
$90$		0			0
$91$	−1.17266	−	3.60908i	−0.122928	−	0.378335i
$92$		0			0
$93$	12.9920	+	2.63679i	1.34721	+	0.273422i
$94$		0			0
$95$	−1.05164	+	2.42251i	−0.107896	+	0.248544i
$96$		0			0
$97$	−1.51448	+	0.239870i	−0.153772	+	0.0243551i	−0.232846	−	0.972514i	$-0.574804\pi$
$97$	−1.51448	+	0.239870i	−0.153772	+	0.0243551i	0.0790736	+	0.996869i	$0.474804\pi$
$98$		0			0
$99$	3.39608	−	8.02199i	0.341319	−	0.806240i
$100$		0			0
$101$		−	4.19521i		−	0.417439i	−0.977976	−	0.208719i	$-0.933070\pi$
$101$		−	4.19521i		−	0.417439i	0.977976	−	0.208719i	$-0.0669296\pi$
$102$		0			0
$103$	2.94153	+	18.5721i	0.289838	+	1.82996i	0.516854	+	0.856074i	$0.327103\pi$
$103$	2.94153	+	18.5721i	0.289838	+	1.82996i	−0.227016	+	0.973891i	$0.572897\pi$
$104$		0			0
$105$	7.75378	+	14.5453i	0.756691	+	1.41948i
$106$		0			0
$107$	−1.62455	−	1.62455i	−0.157051	−	0.157051i	0.624208	−	0.781259i	$-0.285422\pi$
$107$	−1.62455	−	1.62455i	−0.157051	−	0.157051i	−0.781259	+	0.624208i	$0.785422\pi$
$108$		0			0
$109$	−2.44163	+	0.793334i	−0.233866	+	0.0759876i	−0.423605	−	0.905847i	$-0.639236\pi$
$109$	−2.44163	+	0.793334i	−0.233866	+	0.0759876i	0.189740	+	0.981834i	$0.439236\pi$
$110$		0			0
$111$	−4.46303	−	16.0633i	−0.423612	−	1.52466i
$112$		0			0
$113$	4.59551	+	2.34153i	0.432310	+	0.220273i	0.656583	−	0.754253i	$-0.272001\pi$
$113$	4.59551	+	2.34153i	0.432310	+	0.220273i	−0.224274	+	0.974526i	$0.572001\pi$
$114$		0			0
$115$	−6.65736	+	10.4635i	−0.620802	+	0.975729i
$116$		0			0
$117$	2.26988	+	1.41536i	0.209850	+	0.130850i
$118$		0			0
$119$	−11.1319	+	8.08782i	−1.02046	+	0.741409i
$120$		0			0
$121$	−2.07776	−	1.50958i	−0.188888	−	0.137235i
$122$		0			0
$123$	13.8480	+	7.82610i	1.24863	+	0.705655i
$124$		0			0
$125$	−11.1760	+	0.312362i	−0.999610	+	0.0279385i
$126$		0			0
$127$	6.30372	+	12.3717i	0.559364	+	1.09781i	0.981532	+	0.191297i	$0.0612693\pi$
$127$	6.30372	+	12.3717i	0.559364	+	1.09781i	−0.422168	+	0.906518i	$0.638731\pi$
$128$		0			0
$129$	0.153877	−	3.56347i	0.0135481	−	0.313746i
$130$		0			0
$131$	6.21317	+	8.55169i	0.542847	+	0.747165i	0.989020	−	0.147782i	$-0.0472134\pi$
$131$	6.21317	+	8.55169i	0.542847	+	0.747165i	−0.446173	+	0.894947i	$0.647213\pi$
$132$		0			0
$133$	4.96455	+	0.786308i	0.430481	+	0.0681815i
$134$		0			0
$135$	−10.7817	−	4.33074i	−0.927940	−	0.372731i
$136$		0			0
$137$	−9.93006	+	19.4888i	−0.848382	+	1.66504i	−0.106701	+	0.994291i	$0.534029\pi$
$137$	−9.93006	+	19.4888i	−0.848382	+	1.66504i	−0.741681	+	0.670752i	$0.765971\pi$
$138$		0			0
$139$	13.6780	+	4.44425i	1.16015	+	0.376956i	0.824958	−	0.565193i	$-0.191198\pi$
$139$	13.6780	+	4.44425i	1.16015	+	0.376956i	0.335193	+	0.942150i	$0.391198\pi$
$140$		0			0
$141$	−7.62929	+	9.60075i	−0.642502	+	0.808529i
$142$		0			0
$143$	−1.83082	+	1.83082i	−0.153101	+	0.153101i
$144$		0			0
$145$	1.78499	−	18.6526i	0.148235	−	1.54902i
$146$		0			0
$147$	14.1845	−	13.0101i	1.16991	−	1.07306i
$148$		0			0
$149$	19.6307			1.60821			0.804106	−	0.594487i	$-0.202645\pi$
$149$	19.6307			1.60821			0.804106	+	0.594487i	$0.202645\pi$
$150$		0			0
$151$	7.05432			0.574072			0.287036	−	0.957920i	$-0.407330\pi$
$151$	7.05432			0.574072			0.287036	+	0.957920i	$0.407330\pi$
$152$		0			0
$153$	2.33749	−	9.41353i	0.188975	−	0.761038i
$154$		0			0
$155$	15.6991	+	6.81521i	1.26098	+	0.547411i
$156$		0			0
$157$	−12.4751	+	12.4751i	−0.995620	+	0.995620i	−0.999990	−	0.00437087i	$-0.998609\pi$
$157$	−12.4751	+	12.4751i	−0.995620	+	0.995620i	0.00437087	+	0.999990i	$0.498609\pi$
$158$		0			0
$159$	−3.51926	−	2.79660i	−0.279096	−	0.221785i
$160$		0			0
$161$	22.4490	+	7.29412i	1.76923	+	0.574857i
$162$		0			0
$163$	4.70822	−	9.24039i	0.368776	−	0.723764i	−0.629820	−	0.776741i	$-0.716871\pi$
$163$	4.70822	−	9.24039i	0.368776	−	0.723764i	0.998596	+	0.0529778i	$0.0168712\pi$
$164$		0			0
$165$	6.44071	−	9.21919i	0.501409	−	0.717713i
$166$		0			0
$167$	4.64134	+	0.735116i	0.359158	+	0.0568850i	0.333406	−	0.942783i	$-0.391802\pi$
$167$	4.64134	+	0.735116i	0.359158	+	0.0568850i	0.0257518	+	0.999668i	$0.491802\pi$
$168$		0			0
$169$	7.17388	+	9.87400i	0.551837	+	0.759538i
$170$		0			0
$171$	−3.03534	+	1.82777i	−0.232119	+	0.139773i
$172$		0			0
$173$	−5.89408	−	11.5678i	−0.448119	−	0.879483i	−0.998992	−	0.0448938i	$-0.985705\pi$
$173$	−5.89408	−	11.5678i	−0.448119	−	0.879483i	0.550873	−	0.834589i	$-0.314295\pi$
$174$		0			0
$175$	5.88942	+	20.4482i	0.445198	+	1.54574i
$176$		0			0
$177$	9.50263	−	16.8146i	0.714262	−	1.26386i
$178$		0			0
$179$	−9.64168	−	7.00509i	−0.720653	−	0.523585i	0.165940	−	0.986136i	$-0.446934\pi$
$179$	−9.64168	−	7.00509i	−0.720653	−	0.523585i	−0.886593	+	0.462551i	$0.846934\pi$
$180$		0			0
$181$	2.03092	−	1.47555i	0.150957	−	0.109677i	−0.509743	−	0.860327i	$-0.670259\pi$
$181$	2.03092	−	1.47555i	0.150957	−	0.109677i	0.660700	+	0.750650i	$0.270259\pi$
$182$		0			0
$183$	−13.7450	+	6.27188i	−1.01606	+	0.463631i
$184$		0			0
$185$	−1.32658	−	21.4823i	−0.0975320	−	1.57941i
$186$		0			0
$187$	8.36495	+	4.26215i	0.611705	+	0.311679i
$188$		0			0
$189$	−2.85502	+	21.9291i	−0.207672	+	1.59511i
$190$		0			0
$191$	−4.35419	+	1.41476i	−0.315058	+	0.102369i	−0.462278	−	0.886735i	$-0.652968\pi$
$191$	−4.35419	+	1.41476i	−0.315058	+	0.102369i	0.147219	+	0.989104i	$0.452968\pi$
$192$		0			0
$193$	−0.834752	−	0.834752i	−0.0600868	−	0.0600868i	0.676425	−	0.736512i	$-0.263528\pi$
$193$	−0.834752	−	0.834752i	−0.0600868	−	0.0600868i	−0.736512	+	0.676425i	$0.763528\pi$
$194$		0			0
$195$	2.48673	+	2.39629i	0.178078	+	0.171602i
$196$		0			0
$197$	3.31070	+	20.9029i	0.235878	+	1.48927i	0.766819	+	0.641863i	$0.221838\pi$
$197$	3.31070	+	20.9029i	0.235878	+	1.48927i	−0.530941	+	0.847409i	$0.678162\pi$
$198$		0			0
$199$		−	12.1010i		−	0.857815i	−0.903348	−	0.428908i	$-0.858899\pi$
$199$		−	12.1010i		−	0.857815i	0.903348	−	0.428908i	$-0.141101\pi$
$200$		0			0
$201$	5.69318	−	3.77215i	0.401566	−	0.266067i
$202$		0			0
$203$	−35.2244	+	5.57899i	−2.47227	+	0.391569i
$204$		0			0
$205$	15.3879	+	13.5980i	1.07474	+	0.949723i
$206$		0			0
$207$	−15.4213	+	6.24777i	−1.07185	+	0.434250i
$208$		0			0
$209$	−1.05977	−	3.26164i	−0.0733059	−	0.225612i
$210$		0			0
$211$	−6.11917	+	18.8329i	−0.421261	+	1.29651i	0.485269	+	0.874365i	$0.338722\pi$
$211$	−6.11917	+	18.8329i	−0.421261	+	1.29651i	−0.906530	+	0.422142i	$0.861278\pi$
$212$		0			0
$213$	0.778501	−	0.0890762i	0.0533420	−	0.00610340i
$214$		0			0
$215$	1.15031	−	4.45871i	0.0784503	−	0.304082i
$216$		0			0
$217$	5.09569	−	32.1729i	0.345918	−	2.18404i
$218$		0			0
$219$	−4.89441	−	1.82728i	−0.330734	−	0.123476i
$220$		0			0
$221$	−1.69451	+	2.33229i	−0.113985	+	0.156887i
$222$		0			0
$223$	−6.45454	+	3.28875i	−0.432228	+	0.220231i	−0.656548	−	0.754285i	$-0.727984\pi$
$223$	−6.45454	+	3.28875i	−0.432228	+	0.220231i	0.224320	+	0.974516i	$0.427984\pi$
$224$		0			0
$225$	−12.4534	−	8.36137i	−0.830228	−	0.557425i
$226$		0			0
$227$	1.65327	−	0.842383i	0.109731	−	0.0559109i	−0.398263	−	0.917271i	$-0.630387\pi$
$227$	1.65327	−	0.842383i	0.109731	−	0.0559109i	0.507995	+	0.861360i	$0.330387\pi$
$228$		0			0
$229$	−13.9886	+	19.2537i	−0.924394	+	1.27232i	0.0376122	+	0.999292i	$0.488025\pi$
$229$	−13.9886	+	19.2537i	−0.924394	+	1.27232i	−0.962006	+	0.273027i	$0.911975\pi$
$230$		0			0
$231$	−20.0527	−	7.48648i	−1.31937	−	0.492574i
$232$		0			0
$233$	−0.810240	+	5.11565i	−0.0530806	+	0.335138i	0.946830	+	0.321735i	$0.104266\pi$
$233$	−0.810240	+	5.11565i	−0.0530806	+	0.335138i	−0.999910	+	0.0134021i	$0.995734\pi$
$234$		0			0
$235$	−12.2100	+	10.0772i	−0.796493	+	0.657364i
$236$		0			0
$237$	6.06889	−	0.694403i	0.394217	−	0.0451063i
$238$		0			0
$239$	1.51663	−	4.66771i	0.0981026	−	0.301929i	−0.889947	−	0.456064i	$-0.849259\pi$
$239$	1.51663	−	4.66771i	0.0981026	−	0.301929i	0.988050	+	0.154135i	$0.0492590\pi$
$240$		0			0
$241$	1.76890	+	5.44413i	0.113945	+	0.350687i	0.991726	−	0.128376i	$-0.0409765\pi$
$241$	1.76890	+	5.44413i	0.113945	+	0.350687i	−0.877780	+	0.479063i	$0.840976\pi$
$242$		0			0
$243$	−8.40709	−	13.1271i	−0.539315	−	0.842104i
$244$		0			0
$245$	21.4026	−	12.6240i	1.36736	−	0.806520i
$246$		0			0
$247$	1.04014	−	0.164742i	0.0661827	−	0.0104823i
$248$		0			0
$249$	20.3850	−	13.5066i	1.29185	−	0.855945i
$250$		0			0
$251$			20.3411i			1.28392i	0.766738	+	0.641961i	$0.221879\pi$
$251$			20.3411i			1.28392i	−0.766738	+	0.641961i	$0.778121\pi$
$252$		0			0
$253$	−2.51937	−	15.9067i	−0.158392	−	1.00005i
$254$		0			0
$255$	5.47723	−	11.2604i	0.342997	−	0.705155i
$256$		0			0
$257$	−16.9061	−	16.9061i	−1.05458	−	1.05458i	−0.998422	−	0.0561541i	$-0.982116\pi$
$257$	−16.9061	−	16.9061i	−1.05458	−	1.05458i	−0.0561541	−	0.998422i	$-0.517884\pi$
$258$		0			0
$259$	−38.9598	+	12.6588i	−2.42085	+	0.786581i
$260$		0			0
$261$	16.4748	−	18.9887i	1.01976	−	1.17537i
$262$		0			0
$263$	−9.39006	−	4.78447i	−0.579016	−	0.295023i	0.139850	−	0.990173i	$-0.455338\pi$
$263$	−9.39006	−	4.78447i	−0.579016	−	0.295023i	−0.718865	+	0.695150i	$0.755338\pi$
$264$		0			0
$265$	−3.69391	−	4.47571i	−0.226915	−	0.274941i
$266$		0			0
$267$	12.3386	−	5.63014i	0.755108	−	0.344559i
$268$		0			0
$269$	6.24078	−	4.53419i	0.380507	−	0.276454i	−0.381048	−	0.924555i	$-0.624437\pi$
$269$	6.24078	−	4.53419i	0.380507	−	0.276454i	0.761554	+	0.648101i	$0.224437\pi$
$270$		0			0
$271$	−16.4232	−	11.9322i	−0.997641	−	0.724828i	−0.0360598	−	0.999350i	$-0.511481\pi$
$271$	−16.4232	−	11.9322i	−0.997641	−	0.724828i	−0.961581	+	0.274521i	$0.911481\pi$
$272$		0			0
$273$	3.23387	−	5.72223i	0.195723	−	0.346325i
$274$		0			0
$275$	10.6067	−	9.91422i	0.639607	−	0.597850i
$276$		0			0
$277$	8.84515	+	17.3596i	0.531453	+	1.04304i	0.988161	+	0.153419i	$0.0490285\pi$
$277$	8.84515	+	17.3596i	0.531453	+	1.04304i	−0.456708	+	0.889617i	$0.650971\pi$
$278$		0			0
$279$	11.8449	+	19.6707i	0.709138	+	1.17765i
$280$		0			0
$281$	1.43495	+	1.97505i	0.0856022	+	0.117821i	0.849670	−	0.527314i	$-0.176801\pi$
$281$	1.43495	+	1.97505i	0.0856022	+	0.117821i	−0.764068	+	0.645136i	$0.776801\pi$
$282$		0			0
$283$	−8.06450	−	1.27729i	−0.479385	−	0.0759271i	−0.0879343	−	0.996126i	$-0.528027\pi$
$283$	−8.06450	−	1.27729i	−0.479385	−	0.0759271i	−0.391450	+	0.920199i	$0.628027\pi$
$284$		0			0
$285$	−4.32342	+	1.49383i	−0.256097	+	0.0884867i
$286$		0			0
$287$	17.7439	−	34.8244i	1.04739	−	2.05562i
$288$		0			0
$289$	−6.22643	−	2.02309i	−0.366260	−	0.119005i
$290$		0			0
$291$	−2.07929	−	1.65232i	−0.121890	−	0.0968605i
$292$		0			0
$293$	−11.2030	+	11.2030i	−0.654488	+	0.654488i	−0.954070	−	0.299582i	$-0.903153\pi$
$293$	−11.2030	+	11.2030i	−0.654488	+	0.654488i	0.299582	+	0.954070i	$0.403153\pi$
$294$		0			0
$295$	16.5110	−	18.6844i	0.961307	−	1.08785i
$296$		0			0
$297$	14.2156	−	5.05698i	0.824874	−	0.293436i
$298$		0			0
$299$	4.94542			0.286001
$300$		0			0
$301$	−8.76407			−0.505153
$302$		0			0
$303$	5.35494	−	4.91161i	0.307633	−	0.282165i
$304$		0			0
$305$	−19.0399	+	4.23278i	−1.09022	+	0.242368i
$306$		0			0
$307$	−2.43888	+	2.43888i	−0.139194	+	0.139194i	−0.773270	−	0.634076i	$-0.781380\pi$
$307$	−2.43888	+	2.43888i	−0.139194	+	0.139194i	0.634076	+	0.773270i	$0.281380\pi$
$308$		0			0
$309$	−20.2624	+	25.4983i	−1.15269	+	1.45055i
$310$		0			0
$311$	−9.68418	−	3.14658i	−0.549139	−	0.178426i	0.0212893	−	0.999773i	$-0.493223\pi$
$311$	−9.68418	−	3.14658i	−0.549139	−	0.178426i	−0.570429	+	0.821347i	$0.693223\pi$
$312$		0			0
$313$	−1.29485	+	2.54128i	−0.0731892	+	0.143642i	−0.924702	−	0.380692i	$-0.875686\pi$
$313$	−1.29485	+	2.54128i	−0.0731892	+	0.143642i	0.851513	+	0.524334i	$0.175686\pi$
$314$		0			0
$315$	−9.48839	+	26.9264i	−0.534610	+	1.51713i
$316$		0			0
$317$	23.8744	+	3.78133i	1.34092	+	0.212381i	0.785331	−	0.619076i	$-0.212493\pi$
$317$	23.8744	+	3.78133i	1.34092	+	0.212381i	0.555589	+	0.831457i	$0.312493\pi$
$318$		0			0
$319$	14.3025	+	19.6857i	0.800786	+	1.10219i
$320$		0			0
$321$	0.171674	−	3.97561i	0.00958189	−	0.221897i
$322$		0			0
$323$	−1.73357	−	3.40232i	−0.0964584	−	0.189310i
$324$		0			0
$325$	2.49740	+	3.69319i	0.138531	+	0.204861i
$326$		0			0
$327$	−3.87122	−	2.18779i	−0.214079	−	0.120985i
$328$		0			0
$329$	24.3771	+	17.7110i	1.34395	+	0.976439i
$330$		0			0
$331$	6.91086	−	5.02103i	0.379855	−	0.275981i	−0.381431	−	0.924397i	$-0.624568\pi$
$331$	6.91086	−	5.02103i	0.379855	−	0.275981i	0.761286	+	0.648417i	$0.224568\pi$
$332$		0			0
$333$	15.2787	−	24.5032i	0.837269	−	1.34277i
$334$		0			0
$335$	8.20139	−	3.23618i	0.448090	−	0.176811i
$336$		0			0
$337$	−3.29999	−	1.68143i	−0.179762	−	0.0915932i	0.361794	−	0.932258i	$-0.382164\pi$
$337$	−3.29999	−	1.68143i	−0.179762	−	0.0915932i	−0.541556	+	0.840665i	$0.682164\pi$
$338$		0			0
$339$	2.39145	+	8.60729i	0.129886	+	0.467484i
$340$		0			0
$341$	−21.1372	+	6.86788i	−1.14464	+	0.371917i
$342$		0			0
$343$	−12.3760	−	12.3760i	−0.668240	−	0.668240i
$344$		0			0
$345$	−21.1503	+	3.75262i	−1.13869	+	0.202034i
$346$		0			0
$347$	−1.58515	−	10.0082i	−0.0850953	−	0.537270i	−0.993002	−	0.118098i	$-0.962320\pi$
$347$	−1.58515	−	10.0082i	−0.0850953	−	0.537270i	0.907907	−	0.419172i	$-0.137680\pi$
$348$		0			0
$349$		−	10.8302i		−	0.579729i	−0.957068	−	0.289864i	$-0.906390\pi$
$349$		−	10.8302i		−	0.579729i	0.957068	−	0.289864i	$-0.0936102\pi$
$350$		0			0
$351$	0.850874	+	4.55443i	0.0454163	+	0.243097i
$352$		0			0
$353$	13.1776	−	2.08713i	0.701375	−	0.111087i	0.204445	−	0.978878i	$-0.434461\pi$
$353$	13.1776	−	2.08713i	0.701375	−	0.111087i	0.496929	+	0.867791i	$0.334461\pi$
$354$		0			0
$355$	1.00700	+	0.0963659i	0.0534459	+	0.00511457i
$356$		0			0
$357$	−23.3565	−	4.74031i	−1.23616	−	0.250884i
$358$		0			0
$359$	−10.0379	−	30.8935i	−0.529781	−	1.63050i	−0.754663	−	0.656113i	$-0.772200\pi$
$359$	−10.0379	−	30.8935i	−0.529781	−	1.63050i	0.224882	−	0.974386i	$-0.427800\pi$
$360$		0			0
$361$	5.44028	−	16.7434i	0.286330	−	0.881234i
$362$		0			0
$363$	−0.505681	−	4.41951i	−0.0265414	−	0.231964i
$364$		0			0
$365$	−5.69051	−	3.62056i	−0.297855	−	0.189509i
$366$		0			0
$367$	−1.65984	+	10.4798i	−0.0866430	+	0.547042i	0.905738	+	0.423837i	$0.139317\pi$
$367$	−1.65984	+	10.4798i	−0.0866430	+	0.547042i	−0.992381	+	0.123205i	$0.960683\pi$
$368$		0			0
$369$	6.22326	+	26.8387i	0.323970	+	1.39717i
$370$		0			0
$371$	−6.49216	+	8.93569i	−0.337056	+	0.463918i
$372$		0			0
$373$	14.2945	−	7.28340i	0.740140	−	0.377120i	−0.0429097	−	0.999079i	$-0.513663\pi$
$373$	14.2945	−	7.28340i	0.740140	−	0.377120i	0.783050	+	0.621959i	$0.213663\pi$
$374$		0			0
$375$	−13.4832	−	13.8998i	−0.696268	−	0.717782i
$376$		0			0
$377$	−6.65759	+	3.39221i	−0.342883	+	0.174708i
$378$		0			0
$379$	18.2024	−	25.0535i	0.934995	−	1.28691i	−0.0228835	−	0.999738i	$-0.507285\pi$
$379$	18.2024	−	25.0535i	0.934995	−	1.28691i	0.957879	−	0.287173i	$-0.0927153\pi$
$380$		0			0
$381$	−8.41163	+	22.5308i	−0.430941	+	1.15429i
$382$		0			0
$383$	−4.80077	+	30.3108i	−0.245308	+	1.54881i	0.490391	+	0.871503i	$0.336854\pi$
$383$	−4.80077	+	30.3108i	−0.245308	+	1.54881i	−0.735698	+	0.677309i	$0.763146\pi$
$384$		0			0
$385$	−23.3144	−	14.8337i	−1.18821	−	0.755994i
$386$		0			0
$387$	4.72872	−	3.97558i	0.240374	−	0.202090i
$388$		0			0
$389$	−7.88532	+	24.2685i	−0.399802	+	1.23046i	0.525357	+	0.850882i	$0.323932\pi$
$389$	−7.88532	+	24.2685i	−0.399802	+	1.23046i	−0.925159	+	0.379581i	$0.876068\pi$
$390$		0			0
$391$	−5.54125	−	17.0542i	−0.280233	−	0.862468i
$392$		0			0
$393$	−3.64157	+	17.9428i	−0.183693	+	0.905094i
$394$		0			0
$395$	7.85016	+	0.751231i	0.394984	+	0.0377985i
$396$		0			0
$397$	8.20587	−	1.29968i	0.411841	−	0.0652292i	0.0529236	−	0.998599i	$-0.483146\pi$
$397$	8.20587	−	1.29968i	0.411841	−	0.0652292i	0.358917	+	0.933369i	$0.383146\pi$
$398$		0			0
$399$	4.80866	+	7.25755i	0.240734	+	0.363332i
$400$		0			0
$401$			17.6021i			0.879008i	0.898241	+	0.439504i	$0.144846\pi$
$401$			17.6021i			0.879008i	−0.898241	+	0.439504i	$0.855154\pi$
$402$		0			0
$403$	−1.06762	−	6.74067i	−0.0531818	−	0.335777i
$404$		0			0
$405$	−7.09490	−	18.8325i	−0.352549	−	0.935794i
$406$		0			0
$407$	19.7636	+	19.7636i	0.979644	+	0.979644i
$408$		0			0
$409$	−14.6004	+	4.74394i	−0.721941	+	0.234573i	−0.646865	−	0.762605i	$-0.723920\pi$
$409$	−14.6004	+	4.74394i	−0.721941	+	0.234573i	−0.0750765	+	0.997178i	$0.523920\pi$
$410$		0			0
$411$	−36.5022	+	10.1417i	−1.80052	+	0.500255i
$412$		0			0
$413$	−42.2846	−	21.5451i	−2.08069	−	1.06016i
$414$		0			0
$415$	29.3660	−	11.5875i	1.44152	−	0.568807i
$416$		0			0
$417$	10.3409	+	22.6623i	0.506397	+	1.10978i
$418$		0			0
$419$	7.27149	−	5.28305i	0.355236	−	0.258094i	−0.395827	−	0.918325i	$-0.629542\pi$
$419$	7.27149	−	5.28305i	0.355236	−	0.258094i	0.751062	+	0.660232i	$0.229542\pi$
$420$		0			0
$421$	22.8808	+	16.6239i	1.11514	+	0.810199i	0.983466	−	0.181093i	$-0.0579636\pi$
$421$	22.8808	+	16.6239i	1.11514	+	0.810199i	0.131678	+	0.991293i	$0.457964\pi$
$422$		0			0
$423$	−21.1869	+	1.50190i	−1.03014	+	0.0730250i
$424$		0			0
$425$	9.93760	−	12.7504i	0.482045	−	0.618485i
$426$		0			0
$427$	16.8535	+	33.0769i	0.815599	+	1.60070i
$428$		0			0
$429$	−4.48040	−	0.193471i	−0.216316	−	0.00934088i
$430$		0			0
$431$	18.6234	+	25.6329i	0.897059	+	1.23470i	0.971397	+	0.237462i	$0.0763156\pi$
$431$	18.6234	+	25.6329i	0.897059	+	1.23470i	−0.0743381	+	0.997233i	$0.523684\pi$
$432$		0			0
$433$	8.79670	+	1.39326i	0.422743	+	0.0669559i	0.364182	−	0.931328i	$-0.381349\pi$
$433$	8.79670	+	1.39326i	0.422743	+	0.0669559i	0.0585611	+	0.998284i	$0.481349\pi$
$434$		0			0
$435$	25.8988	−	19.5594i	1.24175	−	0.937803i
$436$		0			0
$437$	−2.97385	+	5.83651i	−0.142259	+	0.279198i
$438$		0			0
$439$	35.2858	+	11.4651i	1.68410	+	0.547198i	0.985700	−	0.168509i	$-0.0538953\pi$
$439$	35.2858	+	11.4651i	1.68410	+	0.547198i	0.698401	+	0.715707i	$0.253895\pi$
$440$		0			0
$441$	33.2134	+	2.87378i	1.58159	+	0.136847i
$442$		0			0
$443$	0.101009	−	0.101009i	0.00479907	−	0.00479907i	−0.704703	−	0.709502i	$-0.748920\pi$
$443$	0.101009	−	0.101009i	0.00479907	−	0.00479907i	0.709502	+	0.704703i	$0.248920\pi$
$444$		0			0
$445$	17.0917	−	3.79968i	0.810225	−	0.180122i
$446$		0			0
$447$	22.9830	+	25.0575i	1.08706	+	1.18518i
$448$		0			0
$449$	5.09561			0.240477			0.120238	−	0.992745i	$-0.461634\pi$
$449$	5.09561			0.240477			0.120238	+	0.992745i	$0.461634\pi$
$450$		0			0
$451$	−26.6669			−1.25569
$452$		0			0
$453$	8.25897	+	9.00443i	0.388040	+	0.423065i
$454$		0			0
$455$	5.61891	−	6.35854i	0.263418	−	0.298093i
$456$		0			0
$457$	9.17964	−	9.17964i	0.429406	−	0.429406i	−0.459020	−	0.888426i	$-0.651799\pi$
$457$	9.17964	−	9.17964i	0.429406	−	0.429406i	0.888426	+	0.459020i	$0.151799\pi$
$458$		0			0
$459$	14.7525	−	8.03737i	0.688587	−	0.375152i
$460$		0			0
$461$	−2.89432	−	0.940423i	−0.134802	−	0.0437999i	0.240839	−	0.970565i	$-0.422577\pi$
$461$	−2.89432	−	0.940423i	−0.134802	−	0.0437999i	−0.375641	+	0.926765i	$0.622577\pi$
$462$		0			0
$463$	3.81952	−	7.49623i	0.177508	−	0.348380i	−0.785060	−	0.619420i	$-0.787368\pi$
$463$	3.81952	−	7.49623i	0.177508	−	0.348380i	0.962568	+	0.271041i	$0.0873678\pi$
$464$		0			0
$465$	9.68080	+	28.0180i	0.448936	+	1.29931i
$466$		0			0
$467$	3.67547	+	0.582137i	0.170080	+	0.0269381i	0.240894	−	0.970551i	$-0.422559\pi$
$467$	3.67547	+	0.582137i	0.170080	+	0.0269381i	−0.0708133	+	0.997490i	$0.522559\pi$
$468$		0			0
$469$	−9.86354	−	13.5760i	−0.455456	−	0.626882i
$470$		0			0
$471$	−30.5291	−	1.31830i	−1.40671	−	0.0607441i
$472$		0			0
$473$	2.71470	+	5.32791i	0.124822	+	0.244977i
$474$		0			0
$475$	−5.86042	+	0.726559i	−0.268895	+	0.0333368i
$476$		0			0
$477$	−0.550539	−	7.76630i	−0.0252074	−	0.355594i
$478$		0			0
$479$	−19.2357	−	13.9755i	−0.878900	−	0.638558i	0.0540606	−	0.998538i	$-0.482784\pi$
$479$	−19.2357	−	13.9755i	−0.878900	−	0.638558i	−0.932960	+	0.359980i	$0.882784\pi$
$480$		0			0
$481$	−6.94354	+	5.04478i	−0.316598	+	0.230022i
$482$		0			0
$483$	16.9720	+	37.1946i	0.772254	+	1.69241i
$484$		0			0
$485$	−2.18247	−	2.64439i	−0.0991010	−	0.120075i
$486$		0			0
$487$	−36.1675	−	18.4282i	−1.63890	−	0.835063i	−0.997707	−	0.0676872i	$-0.978438\pi$
$487$	−36.1675	−	18.4282i	−1.63890	−	0.835063i	−0.641197	−	0.767376i	$-0.721562\pi$
$488$		0			0
$489$	17.3071	−	4.80859i	0.782652	−	0.217452i
$490$		0			0
$491$	22.0112	−	7.15186i	0.993350	−	0.322759i	0.233145	−	0.972442i	$-0.425098\pi$
$491$	22.0112	−	7.15186i	0.993350	−	0.322759i	0.760205	+	0.649683i	$0.225098\pi$
$492$		0			0
$493$	19.1577	+	19.1577i	0.862818	+	0.862818i
$494$		0			0
$495$	19.3083	−	2.57232i	0.867845	−	0.115617i
$496$		0			0
$497$	−0.301193	−	1.90166i	−0.0135103	−	0.0853010i
$498$		0			0
$499$		−	35.2669i		−	1.57876i	−0.613904	−	0.789381i	$-0.710402\pi$
$499$		−	35.2669i		−	1.57876i	0.613904	−	0.789381i	$-0.289598\pi$
$500$		0			0
$501$	4.49560	+	6.78505i	0.200848	+	0.303134i
$502$		0			0
$503$	25.0737	−	3.97129i	1.11798	−	0.177071i	0.430021	−	0.902819i	$-0.358506\pi$
$503$	25.0737	−	3.97129i	1.11798	−	0.177071i	0.687961	+	0.725748i	$0.258506\pi$
$504$		0			0
$505$	8.07995	−	4.76585i	0.359553	−	0.212078i
$506$		0			0
$507$	−4.20464	+	20.7172i	−0.186735	+	0.920083i
$508$		0			0
$509$	−1.80435	−	5.55322i	−0.0799765	−	0.246142i	0.903072	−	0.429490i	$-0.141307\pi$
$509$	−1.80435	−	5.55322i	−0.0799765	−	0.246142i	−0.983048	+	0.183348i	$0.941307\pi$
$510$		0			0
$511$	−3.96685	+	12.2087i	−0.175483	+	0.540082i
$512$		0			0
$513$	−5.88673	−	1.73454i	−0.259905	−	0.0765820i
$514$		0			0
$515$	−32.4281	+	26.7637i	−1.42895	+	1.17935i
$516$		0			0
$517$	3.21608	−	20.3055i	0.141443	−	0.893035i
$518$		0			0
$519$	7.86501	−	21.0666i	0.345236	−	0.924723i
$520$		0			0
$521$	5.69171	−	7.83396i	0.249358	−	0.343212i	−0.665928	−	0.746016i	$-0.731964\pi$
$521$	5.69171	−	7.83396i	0.249358	−	0.343212i	0.915286	+	0.402804i	$0.131964\pi$
$522$		0			0
$523$	−0.993315	+	0.506119i	−0.0434346	+	0.0221310i	−0.475573	−	0.879676i	$-0.657759\pi$
$523$	−0.993315	+	0.506119i	−0.0434346	+	0.0221310i	0.432138	+	0.901807i	$0.357759\pi$
$524$		0			0
$525$	−19.2057	+	31.4575i	−0.838207	+	1.37292i
$526$		0			0
$527$	−22.0489	+	11.2345i	−0.960464	+	0.489381i
$528$		0			0
$529$	−4.56191	+	6.27893i	−0.198344	+	0.272997i
$530$		0			0
$531$	32.5882	−	7.55643i	1.41421	−	0.327921i
$532$		0			0
$533$	1.28099	−	8.08788i	0.0554860	−	0.350325i
$534$		0			0
$535$	1.28335	−	4.97439i	0.0554840	−	0.215062i
$536$		0			0
$537$	−2.34657	−	20.5084i	−0.101262	−	0.885002i
$538$		0			0
$539$	−9.97132	+	30.6886i	−0.429495	+	1.32185i
$540$		0			0
$541$	−9.75500	−	30.0228i	−0.419400	−	1.29078i	−0.908255	−	0.418417i	$-0.862585\pi$
$541$	−9.75500	−	30.0228i	−0.419400	−	1.29078i	0.488855	−	0.872365i	$-0.337415\pi$
$542$		0			0
$543$	4.26120	+	0.864828i	0.182865	+	0.0371133i
$544$		0			0
$545$	−4.30170	−	3.80132i	−0.184265	−	0.162831i
$546$		0			0
$547$	−30.7784	+	4.87482i	−1.31599	+	0.208432i	−0.774660	−	0.632378i	$-0.782079\pi$
$547$	−30.7784	+	4.87482i	−1.31599	+	0.208432i	−0.541330	+	0.840810i	$0.682079\pi$
$548$		0			0
$549$	−24.0978	−	10.2017i	−1.02847	−	0.435399i
$550$		0			0
$551$		−	9.89704i		−	0.421628i
$552$		0			0
$553$	−2.34798	−	14.8246i	−0.0998463	−	0.630405i
$554$		0			0
$555$	25.8678	−	26.8440i	1.09803	−	1.13947i
$556$		0			0
$557$	11.9164	+	11.9164i	0.504915	+	0.504915i	0.912961	−	0.408046i	$-0.133790\pi$
$557$	11.9164	+	11.9164i	0.504915	+	0.504915i	−0.408046	+	0.912961i	$0.633790\pi$
$558$		0			0
$559$	−1.74632	+	0.567415i	−0.0738616	+	0.0239991i
$560$		0			0
$561$	4.35301	+	15.6674i	0.183784	+	0.661476i
$562$		0			0
$563$	16.5294	+	8.42215i	0.696631	+	0.354951i	0.766179	−	0.642627i	$-0.222156\pi$
$563$	16.5294	+	8.42215i	0.696631	+	0.354951i	−0.0695477	+	0.997579i	$0.522156\pi$
$564$		0			0
$565$	0.710828	+	11.5110i	0.0299047	+	0.484270i
$566$		0			0
$567$	−31.3338	+	22.0296i	−1.31590	+	0.925157i
$568$		0			0
$569$	1.23297	−	0.895803i	0.0516887	−	0.0375540i	−0.561641	−	0.827381i	$-0.689830\pi$
$569$	1.23297	−	0.895803i	0.0516887	−	0.0375540i	0.613330	+	0.789827i	$0.289830\pi$
$570$		0			0
$571$	24.3901	+	17.7205i	1.02070	+	0.741579i	0.966425	−	0.256948i	$-0.0827168\pi$
$571$	24.3901	+	17.7205i	1.02070	+	0.741579i	0.0542700	+	0.998526i	$0.482717\pi$
$572$		0			0
$573$	−6.90361	−	3.90152i	−0.288402	−	0.162988i
$574$		0			0
$575$	−27.7156	−	0.935252i	−1.15582	−	0.0390027i
$576$		0			0
$577$	16.3743	+	32.1363i	0.681669	+	1.33785i	0.929419	+	0.369027i	$0.120309\pi$
$577$	16.3743	+	32.1363i	0.681669	+	1.33785i	−0.247749	+	0.968824i	$0.579691\pi$
$578$		0			0
$579$	0.0882122	−	2.04281i	0.00366598	−	0.0848964i
$580$		0			0
$581$	−35.3175	−	48.6103i	−1.46522	−	2.01670i
$582$		0			0
$583$	7.44321	+	1.17889i	0.308266	+	0.0488245i
$584$		0			0
$585$	−0.147344	+	5.97965i	−0.00609194	+	0.247228i
$586$		0			0
$587$	7.58856	−	14.8934i	0.313213	−	0.614716i	−0.679709	−	0.733482i	$-0.737894\pi$
$587$	7.58856	−	14.8934i	0.313213	−	0.614716i	0.992922	+	0.118766i	$0.0378939\pi$
$588$		0			0
$589$	8.59724	+	2.79341i	0.354243	+	0.115101i
$590$		0			0
$591$	−22.8053	+	28.6984i	−0.938085	+	1.18049i
$592$		0			0
$593$	17.3573	−	17.3573i	0.712780	−	0.712780i	−0.254336	−	0.967116i	$-0.581857\pi$
$593$	17.3573	−	17.3573i	0.712780	−	0.712780i	0.967116	+	0.254336i	$0.0818568\pi$
$594$		0			0
$595$	−28.2232	−	12.2521i	−1.15704	−	0.502287i
$596$		0			0
$597$	15.4462	−	14.1674i	0.632170	−	0.579834i
$598$		0			0
$599$	14.4303			0.589605			0.294802	−	0.955558i	$-0.404746\pi$
$599$	14.4303			0.589605			0.294802	+	0.955558i	$0.404746\pi$
$600$		0			0
$601$	−40.6930			−1.65990			−0.829951	−	0.557837i	$-0.811632\pi$
$601$	−40.6930			−1.65990			−0.829951	+	0.557837i	$0.811632\pi$
$602$		0			0
$603$	11.4803	+	2.85070i	0.467515	+	0.116090i
$604$		0			0
$605$	0.547065	−	5.71668i	0.0222413	−	0.232416i
$606$		0			0
$607$	31.1483	−	31.1483i	1.26427	−	1.26427i	0.315266	−	0.949003i	$-0.397906\pi$
$607$	31.1483	−	31.1483i	1.26427	−	1.26427i	0.949003	−	0.315266i	$-0.102094\pi$
$608$		0			0
$609$	−48.3608	−	38.4302i	−1.95968	−	1.55727i
$610$		0			0
$611$	6.00403	+	1.95083i	0.242897	+	0.0789221i
$612$		0			0
$613$	−16.5958	+	32.5711i	−0.670299	+	1.31554i	0.265878	+	0.964007i	$0.414338\pi$
$613$	−16.5958	+	32.5711i	−0.670299	+	1.31554i	−0.936177	+	0.351529i	$0.885662\pi$
$614$		0			0
$615$	0.658644	+	35.5618i	0.0265591	+	1.43399i
$616$		0			0
$617$	−34.4877	−	5.46232i	−1.38842	−	0.219905i	−0.582936	−	0.812518i	$-0.698096\pi$
$617$	−34.4877	−	5.46232i	−1.38842	−	0.219905i	−0.805487	+	0.592613i	$0.798096\pi$
$618$		0			0
$619$	3.48931	+	4.80263i	0.140247	+	0.193034i	0.873363	−	0.487070i	$-0.161934\pi$
$619$	3.48931	+	4.80263i	0.140247	+	0.193034i	−0.733115	+	0.680104i	$0.761934\pi$
$620$		0			0
$621$	−26.0297	−	12.3697i	−1.04453	−	0.496379i
$622$		0			0
$623$	−15.1291	−	29.6924i	−0.606133	−	1.18960i
$624$		0			0
$625$	−13.2978	−	21.1700i	−0.531910	−	0.846801i
$626$		0			0
$627$	2.92255	−	5.17136i	0.116715	−	0.206524i
$628$		0			0
$629$	25.1769	+	18.2921i	1.00387	+	0.729354i
$630$		0			0
$631$	21.9450	−	15.9440i	0.873616	−	0.634719i	−0.0579392	−	0.998320i	$-0.518453\pi$
$631$	21.9450	−	15.9440i	0.873616	−	0.634719i	0.931555	+	0.363601i	$0.118453\pi$
$632$		0			0
$633$	−31.2032	+	14.2381i	−1.24021	+	0.565915i
$634$		0			0
$635$	−16.6667	+	26.1955i	−0.661400	+	1.03954i
$636$		0			0
$637$	−8.82864	−	4.49842i	−0.349804	−	0.178234i
$638$		0			0
$639$	1.02514	+	0.889424i	0.0405541	+	0.0351851i
$640$		0			0
$641$	6.43772	−	2.09174i	0.254275	−	0.0826188i	−0.179106	−	0.983830i	$-0.557321\pi$
$641$	6.43772	−	2.09174i	0.254275	−	0.0826188i	0.433381	+	0.901211i	$0.357321\pi$
$642$		0			0
$643$	−1.88726	−	1.88726i	−0.0744264	−	0.0744264i	0.668914	−	0.743340i	$-0.266760\pi$
$643$	−1.88726	−	1.88726i	−0.0744264	−	0.0744264i	−0.743340	+	0.668914i	$0.766760\pi$
$644$		0			0
$645$	7.03803	−	3.75181i	0.277122	−	0.147727i
$646$		0			0
$647$	−1.80177	−	11.3759i	−0.0708349	−	0.447234i	−0.997459	−	0.0712445i	$-0.977303\pi$
$647$	−1.80177	−	11.3759i	−0.0708349	−	0.447234i	0.926624	−	0.375989i	$-0.122697\pi$
$648$		0			0
$649$			32.3795i			1.27101i
$650$		0			0
$651$	47.0328	−	31.1627i	1.84336	−	1.22136i
$652$		0			0
$653$	41.2088	−	6.52683i	1.61262	−	0.255414i	0.715965	−	0.698136i	$-0.245987\pi$
$653$	41.2088	−	6.52683i	1.61262	−	0.255414i	0.896659	+	0.442722i	$0.145987\pi$
$654$		0			0
$655$	−9.41222	+	21.6814i	−0.367766	+	0.847164i
$656$		0			0
$657$	−3.39780	−	8.38675i	−0.132561	−	0.327198i
$658$		0			0
$659$	−0.104879	−	0.322784i	−0.00408550	−	0.0125739i	0.948993	−	0.315297i	$-0.102104\pi$
$659$	−0.104879	−	0.322784i	−0.00408550	−	0.0125739i	−0.953078	+	0.302723i	$0.902104\pi$
$660$		0			0
$661$	4.25007	−	13.0804i	0.165308	−	0.508767i	−0.833750	−	0.552141i	$-0.813811\pi$
$661$	4.25007	−	13.0804i	0.165308	−	0.508767i	0.999059	+	0.0433745i	$0.0138109\pi$
$662$		0			0
$663$	−4.96091	+	0.567628i	−0.192666	+	0.0220448i
$664$		0			0
$665$	4.12542	+	10.4550i	0.159977	+	0.405426i
$666$		0			0
$667$	7.27057	−	45.9045i	0.281517	−	1.77743i
$668$		0			0
$669$	−11.7547	−	4.38848i	−0.454461	−	0.169668i
$670$		0			0
$671$	14.8879	−	20.4914i	0.574739	−	0.791061i
$672$		0			0
$673$	−8.28693	+	4.22240i	−0.319438	+	0.162762i	−0.606356	−	0.795193i	$-0.707369\pi$
$673$	−8.28693	+	4.22240i	−0.319438	+	0.162762i	0.286918	+	0.957955i	$0.407369\pi$
$674$		0			0
$675$	−3.90724	−	25.6853i	−0.150390	−	0.988627i
$676$		0			0
$677$	−3.29687	+	1.67984i	−0.126709	+	0.0645615i	−0.516196	−	0.856470i	$-0.672652\pi$
$677$	−3.29687	+	1.67984i	−0.126709	+	0.0645615i	0.389487	+	0.921032i	$0.372652\pi$
$678$		0			0
$679$	−3.83576	+	5.27948i	−0.147203	+	0.202608i
$680$		0			0
$681$	3.01085	+	1.12407i	0.115376	+	0.0430744i
$682$		0			0
$683$	1.53600	−	9.69792i	0.0587734	−	0.371081i	−0.940718	−	0.339190i	$-0.889847\pi$
$683$	1.53600	−	9.69792i	0.0587734	−	0.371081i	0.999491	−	0.0318908i	$-0.0101529\pi$
$684$		0			0
$685$	−48.8161	+	3.01451i	−1.86517	+	0.115178i
$686$		0			0
$687$	−40.9536	+	4.68592i	−1.56248	+	0.178779i
$688$		0			0
$689$	−0.715098	+	2.20084i	−0.0272430	+	0.0838455i
$690$		0			0
$691$	−5.28572	−	16.2678i	−0.201078	−	0.618855i	−0.999852	−	0.0172234i	$-0.994517\pi$
$691$	−5.28572	−	16.2678i	−0.201078	−	0.618855i	0.798773	−	0.601632i	$-0.205483\pi$
$692$		0			0
$693$	−13.9210	−	34.3611i	−0.528816	−	1.30527i
$694$		0			0
$695$	6.97889	+	31.3925i	0.264725	+	1.19078i
$696$		0			0
$697$	−29.3262	+	4.64482i	−1.11081	+	0.175935i
$698$		0			0
$699$	−7.47844	+	4.95501i	−0.282860	+	0.187416i
$700$		0			0
$701$		−	33.4650i		−	1.26396i	−0.774986	−	0.631979i	$-0.782243\pi$
$701$		−	33.4650i		−	1.26396i	0.774986	−	0.631979i	$-0.217757\pi$
$702$		0			0
$703$	−1.77838	−	11.2283i	−0.0670730	−	0.423482i
$704$		0			0
$705$	−27.1580	−	3.78730i	−1.02283	−	0.142638i
$706$		0			0
$707$	−12.6249	−	12.6249i	−0.474808	−	0.474808i
$708$		0			0
$709$	12.9358	−	4.20308i	0.485813	−	0.157850i	−0.0558616	−	0.998439i	$-0.517791\pi$
$709$	12.9358	−	4.20308i	0.485813	−	0.157850i	0.541674	+	0.840588i	$0.317791\pi$
$710$		0			0
$711$	7.99162	+	6.93360i	0.299709	+	0.260030i
$712$		0			0
$713$	37.8237	+	19.2721i	1.41651	+	0.721748i
$714$		0			0
$715$	−5.60600	−	1.44630i	−0.209652	−	0.0540884i
$716$		0			0
$717$	7.73368	−	3.52891i	0.288819	−	0.131789i
$718$		0			0
$719$	−29.7221	+	21.5944i	−1.10845	+	0.805335i	−0.982419	−	0.186692i	$-0.940223\pi$
$719$	−29.7221	+	21.5944i	−1.10845	+	0.805335i	−0.126030	+	0.992026i	$0.540223\pi$
$720$		0			0
$721$	64.7423	+	47.0380i	2.41113	+	1.75179i
$722$		0			0
$723$	−4.87814	+	8.63171i	−0.181420	+	0.321017i
$724$		0			0
$725$	37.9526	−	17.7519i	1.40952	−	0.659289i
$726$		0			0
$727$	−4.12344	−	8.09270i	−0.152930	−	0.300142i	0.801813	−	0.597576i	$-0.203869\pi$
$727$	−4.12344	−	8.09270i	−0.152930	−	0.300142i	−0.954742	+	0.297434i	$0.903869\pi$
$728$		0			0
$729$	6.91324	−	26.0999i	0.256046	−	0.966665i
$730$		0			0
$731$	3.91344	+	5.38639i	0.144744	+	0.199223i
$732$		0			0
$733$	−9.91162	−	1.56985i	−0.366094	−	0.0579836i	−0.0293225	−	0.999570i	$-0.509335\pi$
$733$	−9.91162	−	1.56985i	−0.366094	−	0.0579836i	−0.336771	+	0.941586i	$0.609335\pi$
$734$		0			0
$735$	41.1713	+	12.5394i	1.51863	+	0.462522i
$736$		0			0
$737$	−5.19793	+	10.2015i	−0.191468	+	0.375778i
$738$		0			0
$739$	−47.6656	−	15.4875i	−1.75341	−	0.569717i	−0.756924	−	0.653503i	$-0.773299\pi$
$739$	−47.6656	−	15.4875i	−1.75341	−	0.569717i	−0.996484	+	0.0837861i	$0.973299\pi$
$740$		0			0
$741$	1.42805	+	1.13481i	0.0524607	+	0.0416881i
$742$		0			0
$743$	−0.668282	+	0.668282i	−0.0245169	+	0.0245169i	−0.719259	−	0.694742i	$-0.755519\pi$
$743$	−0.668282	+	0.668282i	−0.0245169	+	0.0245169i	0.694742	+	0.719259i	$0.255519\pi$
$744$		0			0
$745$	22.3009	+	37.8087i	0.817043	+	1.38520i
$746$		0			0
$747$	41.1065	+	10.2072i	1.50401	+	0.373464i
$748$		0			0
$749$	−9.77769			−0.357269
$750$		0			0
$751$	16.7359			0.610702			0.305351	−	0.952240i	$-0.401226\pi$
$751$	16.7359			0.610702			0.305351	+	0.952240i	$0.401226\pi$
$752$		0			0
$753$	−25.9643	+	23.8147i	−0.946191	+	0.867857i
$754$		0			0
$755$	8.01386	+	13.5866i	0.291654	+	0.494466i
$756$		0			0
$757$	−14.6049	+	14.6049i	−0.530826	+	0.530826i	−0.920818	−	0.389992i	$-0.872478\pi$
$757$	−14.6049	+	14.6049i	−0.530826	+	0.530826i	0.389992	+	0.920818i	$0.372478\pi$
$758$		0			0
$759$	17.3544	−	21.8389i	0.629924	−	0.792701i
$760$		0			0
$761$	−21.2600	−	6.90779i	−0.770674	−	0.250407i	−0.102821	−	0.994700i	$-0.532787\pi$
$761$	−21.2600	−	6.90779i	−0.770674	−	0.250407i	−0.667854	+	0.744293i	$0.732787\pi$
$762$		0			0
$763$	−4.96032	+	9.73517i	−0.179575	+	0.352437i
$764$		0			0
$765$	20.7858	−	6.19197i	0.751514	−	0.223871i
$766$		0			0
$767$	−9.82050	−	1.55541i	−0.354598	−	0.0561627i
$768$		0			0
$769$	−2.03314	−	2.79838i	−0.0733169	−	0.100912i	0.770784	−	0.637097i	$-0.219865\pi$
$769$	−2.03314	−	2.79838i	−0.0733169	−	0.100912i	−0.844101	+	0.536185i	$0.819865\pi$
$770$		0			0
$771$	1.78655	−	41.3729i	0.0643411	−	1.49001i
$772$		0			0
$773$	15.1556	+	29.7445i	0.545109	+	1.06984i	0.985124	+	0.171846i	$0.0549731\pi$
$773$	15.1556	+	29.7445i	0.545109	+	1.06984i	−0.440015	+	0.897990i	$0.645027\pi$
$774$		0			0
$775$	4.70849	+	37.9787i	0.169134	+	1.36423i
$776$		0			0
$777$	−61.7711	−	34.9094i	−2.21603	−	1.25237i
$778$		0			0
$779$	8.77489	+	6.37533i	0.314393	+	0.228420i
$780$		0			0
$781$	−1.06277	+	0.772148i	−0.0380289	+	0.0276296i
$782$		0			0
$783$	43.5262	−	1.20227i	1.55550	−	0.0429658i
$784$		0			0
$785$	−38.1989	−	9.85497i	−1.36338	−	0.351739i
$786$		0			0
$787$	18.0985	+	9.22165i	0.645142	+	0.328716i	0.745766	−	0.666208i	$-0.232084\pi$
$787$	18.0985	+	9.22165i	0.645142	+	0.328716i	−0.100624	+	0.994925i	$0.532084\pi$
$788$		0			0
$789$	−4.88647	−	17.5874i	−0.173963	−	0.626127i
$790$		0			0
$791$	20.8761	−	6.78304i	0.742267	−	0.241177i
$792$		0			0
$793$	5.49973	+	5.49973i	0.195301	+	0.195301i
$794$		0			0
$795$	1.38828	−	9.95508i	0.0492371	−	0.353070i
$796$		0			0
$797$	5.53887	+	34.9710i	0.196197	+	1.23874i	0.867456	+	0.497515i	$0.165754\pi$
$797$	5.53887	+	34.9710i	0.196197	+	1.23874i	−0.671259	+	0.741223i	$0.734246\pi$
$798$		0			0
$799$		−	22.8907i		−	0.809814i
$800$		0			0
$801$	21.6321	+	9.15788i	0.764334	+	0.323578i
$802$		0			0
$803$	8.65074	−	1.37014i	0.305278	−	0.0483513i
$804$		0			0
$805$	11.4541	+	51.5229i	0.403704	+	1.81594i
$806$		0			0
$807$	13.0941	+	2.65751i	0.460935	+	0.0935487i
$808$		0			0
$809$	−9.11568	−	28.0552i	−0.320490	−	0.986367i	−0.973435	−	0.228962i	$-0.926467\pi$
$809$	−9.11568	−	28.0552i	−0.320490	−	0.986367i	0.652945	−	0.757405i	$-0.273533\pi$
$810$		0			0
$811$	−8.95372	+	27.5567i	−0.314408	+	0.967647i	0.661590	+	0.749866i	$0.269882\pi$
$811$	−8.95372	+	27.5567i	−0.314408	+	0.967647i	−0.975998	+	0.217781i	$0.930118\pi$
$812$		0			0
$813$	−3.99705	−	34.9331i	−0.140183	−	1.22516i
$814$		0			0
$815$	23.1456	−	1.42929i	0.810754	−	0.0500659i
$816$		0			0
$817$	0.380470	−	2.40219i	0.0133110	−	0.0840421i
$818$		0			0
$819$	11.0902	−	2.57155i	0.387523	−	0.0898574i
$820$		0			0
$821$	−9.77536	+	13.4546i	−0.341162	+	0.469570i	−0.944781	−	0.327704i	$-0.893725\pi$
$821$	−9.77536	+	13.4546i	−0.341162	+	0.469570i	0.603618	+	0.797274i	$0.293725\pi$
$822$		0			0
$823$	−8.42788	+	4.29422i	−0.293777	+	0.149687i	−0.594667	−	0.803972i	$-0.702716\pi$
$823$	−8.42788	+	4.29422i	−0.293777	+	0.149687i	0.300890	+	0.953659i	$0.402716\pi$
$824$		0			0
$825$	25.0729	+	1.93158i	0.872926	+	0.0672490i
$826$		0			0
$827$	21.1902	−	10.7969i	0.736856	−	0.375447i	−0.0449332	−	0.998990i	$-0.514307\pi$
$827$	21.1902	−	10.7969i	0.736856	−	0.375447i	0.781789	+	0.623543i	$0.214307\pi$
$828$		0			0
$829$	13.0582	−	17.9730i	0.453529	−	0.624230i	−0.519622	−	0.854396i	$-0.673927\pi$
$829$	13.0582	−	17.9730i	0.453529	−	0.624230i	0.973151	+	0.230167i	$0.0739272\pi$
$830$		0			0
$831$	−11.8029	+	31.6143i	−0.409438	+	1.09669i
$832$		0			0
$833$	−5.62040	+	35.4858i	−0.194735	+	1.22951i
$834$		0			0
$835$	3.85683	+	9.77430i	0.133471	+	0.338254i
$836$		0			0
$837$	−11.2408	+	38.1491i	−0.388538	+	1.31863i
$838$		0			0
$839$	6.41219	−	19.7347i	0.221373	−	0.681317i	−0.777266	−	0.629172i	$-0.783394\pi$
$839$	6.41219	−	19.7347i	0.221373	−	0.681317i	0.998640	−	0.0521452i	$-0.0166059\pi$
$840$		0			0
$841$	12.7381	+	39.2037i	0.439244	+	1.35185i
$842$		0			0
$843$	−0.841033	+	4.14396i	−0.0289667	+	0.142725i
$844$		0			0
$845$	−10.8676	+	25.0339i	−0.373856	+	0.861193i
$846$		0			0
$847$	−10.7956	+	1.70986i	−0.370942	+	0.0587514i
$848$		0			0
$849$	−7.81126	−	11.7893i	−0.268082	−	0.404607i
$850$		0			0
$851$		−	53.3855i		−	1.83003i
$852$		0			0
$853$	0.650084	+	4.10447i	0.0222584	+	0.140534i	0.996315	−	0.0857709i	$-0.0273353\pi$
$853$	0.650084	+	4.10447i	0.0222584	+	0.140534i	−0.974056	+	0.226305i	$0.927335\pi$
$854$		0			0
$855$	−6.96850	−	3.76967i	−0.238318	−	0.128920i
$856$		0			0
$857$	−32.3548	−	32.3548i	−1.10522	−	1.10522i	−0.993770	−	0.111449i	$-0.964451\pi$
$857$	−32.3548	−	32.3548i	−1.10522	−	1.10522i	−0.111449	−	0.993770i	$-0.535549\pi$
$858$		0			0
$859$	−14.1040	+	4.58268i	−0.481224	+	0.156359i	−0.539576	−	0.841937i	$-0.681415\pi$
$859$	−14.1040	+	4.58268i	−0.481224	+	0.156359i	0.0583522	+	0.998296i	$0.481415\pi$
$860$		0			0
$861$	65.2252	−	18.1222i	2.22287	−	0.617602i
$862$		0			0
$863$	16.0284	+	8.16685i	0.545612	+	0.278003i	0.704993	−	0.709214i	$-0.250950\pi$
$863$	16.0284	+	8.16685i	0.545612	+	0.278003i	−0.159382	+	0.987217i	$0.550950\pi$
$864$		0			0
$865$	15.5837	−	24.4932i	0.529862	−	0.832795i
$866$		0			0
$867$	−4.70734	−	10.3162i	−0.159870	−	0.350358i
$868$		0			0
$869$	−8.28494	+	6.01936i	−0.281047	+	0.204193i
$870$		0			0
$871$	−2.84436	−	2.06655i	−0.0963774	−	0.0700223i
$872$		0			0
$873$	−0.325275	−	4.58856i	−0.0110089	−	0.155299i
$874$		0			0
$875$	−32.6925	+	34.5725i	−1.10521	+	1.16877i
$876$		0			0
$877$	3.95637	+	7.76482i	0.133597	+	0.262199i	0.948108	−	0.317950i	$-0.102994\pi$
$877$	3.95637	+	7.76482i	0.133597	+	0.262199i	−0.814510	+	0.580149i	$0.802994\pi$
$878$		0			0
$879$	−27.4162	−	1.18388i	−0.924724	−	0.0399312i
$880$		0			0
$881$	−13.8523	−	19.0660i	−0.466695	−	0.642350i	0.509185	−	0.860657i	$-0.329947\pi$
$881$	−13.8523	−	19.0660i	−0.466695	−	0.642350i	−0.975880	+	0.218307i	$0.929947\pi$
$882$		0			0
$883$	−18.5572	−	2.93918i	−0.624501	−	0.0989112i	−0.163839	−	0.986487i	$-0.552388\pi$
$883$	−18.5572	−	2.93918i	−0.624501	−	0.0989112i	−0.460662	+	0.887576i	$0.652388\pi$
$884$		0			0
$885$	43.1800	−	0.799742i	1.45148	−	0.0268830i
$886$		0			0
$887$	−2.28429	+	4.48316i	−0.0766988	+	0.150530i	−0.926171	−	0.377103i	$-0.876920\pi$
$887$	−2.28429	+	4.48316i	−0.0766988	+	0.150530i	0.849473	+	0.527633i	$0.176920\pi$
$888$		0			0
$889$	56.2012	+	18.2609i	1.88493	+	0.612450i
$890$		0			0
$891$	23.0981	+	12.2249i	0.773817	+	0.409549i
$892$		0			0
$893$	−5.91277	+	5.91277i	−0.197863	+	0.197863i
$894$		0			0
$895$	2.53861	−	26.5278i	0.0848563	−	0.886725i
$896$		0			0
$897$	5.78994	+	6.31254i	0.193320	+	0.210770i
$898$		0			0
$899$	−64.1381			−2.13913
$900$		0			0
$901$	8.39083			0.279539
$902$		0			0
$903$	−10.2607	−	11.1868i	−0.341454	−	0.372274i
$904$		0			0
$905$	5.14908	+	2.23529i	0.171161	+	0.0743035i
$906$		0			0
$907$	−2.29109	+	2.29109i	−0.0760744	+	0.0760744i	−0.744120	−	0.668046i	$-0.767131\pi$
$907$	−2.29109	+	2.29109i	−0.0760744	+	0.0760744i	0.668046	+	0.744120i	$0.267131\pi$
$908$		0			0
$909$	12.5388	+	1.08492i	0.415885	+	0.0359844i
$910$		0			0
$911$	7.00575	+	2.27631i	0.232111	+	0.0754174i	0.422763	−	0.906240i	$-0.361060\pi$
$911$	7.00575	+	2.27631i	0.232111	+	0.0754174i	−0.190652	+	0.981658i	$0.561060\pi$
$912$		0			0
$913$	−18.6118	+	36.5276i	−0.615959	+	1.20889i
$914$		0			0
$915$	−27.6942	−	19.3477i	−0.915542	−	0.639616i
$916$		0			0
$917$	44.4328	+	7.03746i	1.46730	+	0.232397i
$918$		0			0
$919$	5.55147	+	7.64094i	0.183126	+	0.252052i	0.890704	−	0.454584i	$-0.150212\pi$
$919$	5.55147	+	7.64094i	0.183126	+	0.252052i	−0.707578	+	0.706636i	$0.750212\pi$
$920$		0			0
$921$	−5.96844	−	0.257728i	−0.196667	−	0.00849242i
$922$		0			0
$923$	−0.183135	−	0.359423i	−0.00602797	−	0.0118305i
$924$		0			0
$925$	39.8677	−	26.9593i	1.31084	−	0.886417i
$926$		0			0
$927$	−56.2696	+	3.98885i	−1.84814	+	0.131011i
$928$		0			0
$929$	−33.3251	−	24.2121i	−1.09336	−	0.794374i	−0.113398	−	0.993550i	$-0.536174\pi$
$929$	−33.3251	−	24.2121i	−1.09336	−	0.794374i	−0.979964	+	0.199176i	$0.936174\pi$
$930$		0			0
$931$	10.6179	−	7.71439i	0.347989	−	0.252829i
$932$		0			0
$933$	−7.32149	−	16.0452i	−0.239695	−	0.525296i
$934$		0			0
$935$	1.29388	+	20.9527i	0.0423143	+	0.685228i
$936$		0			0
$937$	22.1064	+	11.2638i	0.722184	+	0.367971i	0.776130	−	0.630573i	$-0.217180\pi$
$937$	22.1064	+	11.2638i	0.722184	+	0.367971i	−0.0539460	+	0.998544i	$0.517180\pi$
$938$		0			0
$939$	−4.75977	+	1.32245i	−0.155329	+	0.0431566i
$940$		0			0
$941$	−52.3488	+	17.0091i	−1.70652	+	0.554482i	−0.989748	−	0.142825i	$-0.954382\pi$
$941$	−52.3488	+	17.0091i	−1.70652	+	0.554482i	−0.716773	+	0.697307i	$0.754382\pi$
$942$		0			0
$943$	36.0163	+	36.0163i	1.17285	+	1.17285i
$944$		0			0
$945$	−45.4787	+	19.4132i	−1.47942	+	0.631512i
$946$		0			0
$947$	−4.52336	−	28.5594i	−0.146989	−	0.928055i	−0.945393	−	0.325932i	$-0.894322\pi$
$947$	−4.52336	−	28.5594i	−0.146989	−	0.928055i	0.798404	−	0.602123i	$-0.205678\pi$
$948$		0			0
$949$			2.68953i			0.0873058i
$950$		0			0
$951$	23.1247	+	34.9013i	0.749870	+	1.13175i
$952$		0			0
$953$	2.50232	−	0.396328i	0.0810580	−	0.0128383i	−0.115774	−	0.993276i	$-0.536935\pi$
$953$	2.50232	−	0.396328i	0.0810580	−	0.0128383i	0.196832	+	0.980437i	$0.436935\pi$
$954$		0			0
$955$	−7.67129	−	6.77895i	−0.248237	−	0.219362i
$956$		0			0
$957$	−8.38275	+	41.3037i	−0.270976	+	1.33516i
$958$		0			0
$959$	28.7658	+	88.5320i	0.928896	+	2.85885i
$960$		0			0
$961$	8.52328	−	26.2320i	0.274945	−	0.846192i
$962$		0			0
$963$	5.27562	−	4.43538i	0.170005	−	0.142928i
$964$		0			0
$965$	0.659431	−	2.55602i	0.0212278	−	0.0822814i
$966$		0			0
$967$	−1.85714	+	11.7255i	−0.0597217	+	0.377068i	0.939667	+	0.342092i	$0.111135\pi$
$967$	−1.85714	+	11.7255i	−0.0597217	+	0.377068i	−0.999388	+	0.0349758i	$0.988865\pi$
$968$		0			0
$969$	2.31326	−	6.19613i	0.0743126	−	0.199048i
$970$		0			0
$971$	−8.55440	+	11.7741i	−0.274524	+	0.377849i	−0.923910	−	0.382609i	$-0.875026\pi$
$971$	−8.55440	+	11.7741i	−0.274524	+	0.377849i	0.649387	+	0.760458i	$0.275026\pi$
$972$		0			0
$973$	54.5363	−	27.7876i	1.74835	−	0.890831i
$974$		0			0
$975$	−1.79026	+	7.51165i	−0.0573342	+	0.240565i
$976$		0			0
$977$	10.6092	−	5.40565i	0.339418	−	0.172942i	−0.275971	−	0.961166i	$-0.588999\pi$
$977$	10.6092	−	5.40565i	0.339418	−	0.172942i	0.615388	+	0.788224i	$0.288999\pi$
$978$		0			0
$979$	−13.3645	+	18.3947i	−0.427132	+	0.587896i
$980$		0			0
$981$	−1.73972	−	7.50279i	−0.0555448	−	0.239545i
$982$		0			0
$983$	1.03511	−	6.53546i	0.0330150	−	0.208449i	−0.965666	−	0.259785i	$-0.916348\pi$
$983$	1.03511	−	6.53546i	0.0330150	−	0.208449i	0.998681	+	0.0513367i	$0.0163482\pi$
$984$		0			0
$985$	−36.4979	+	30.1226i	−1.16292	+	0.959785i
$986$		0			0
$987$	5.93284	+	51.8514i	0.188845	+	1.65045i
$988$		0			0
$989$	3.52940	−	10.8624i	0.112228	−	0.345403i
$990$		0			0
$991$	4.94416	+	15.2165i	0.157056	+	0.483369i	0.998363	−	0.0571879i	$-0.0182134\pi$
$991$	4.94416	+	15.2165i	0.157056	+	0.483369i	−0.841307	+	0.540557i	$0.818213\pi$
$992$		0			0
$993$	14.5001	+	2.94285i	0.460146	+	0.0933885i
$994$		0			0
$995$	23.3064	−	13.7470i	0.738863	−	0.435808i
$996$		0			0
$997$	−30.2523	+	4.79149i	−0.958099	+	0.151748i	−0.615852	−	0.787862i	$-0.711188\pi$
$997$	−30.2523	+	4.79149i	−0.958099	+	0.151748i	−0.342247	+	0.939610i	$0.611188\pi$
$998$		0			0
$999$	49.1647	−	9.18513i	1.55550	−	0.290605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.x.a.53.8	yes	80
3.2	odd	2	inner	300.2.x.a.53.4	yes	80
25.17	odd	20	inner	300.2.x.a.17.4	✓	80
75.17	even	20	inner	300.2.x.a.17.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.x.a.17.4	✓	80	25.17	odd	20	inner
300.2.x.a.17.8	yes	80	75.17	even	20	inner
300.2.x.a.53.4	yes	80	3.2	odd	2	inner
300.2.x.a.53.8	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.x (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17077 + 1.27644i) q^{3} +(1.13602 + 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-0.258608 + 2.98883i) q^{9} +O(q^{10})\)	\(q+(1.17077 + 1.27644i) q^{3} +(1.13602 + 1.92599i) q^{5} +(3.00936 - 3.00936i) q^{7} +(-0.258608 + 2.98883i) q^{9} +(-2.76163 - 0.897307i) q^{11} +(0.404807 - 0.794479i) q^{13} +(-1.12840 + 3.70496i) q^{15} +(-3.19333 - 0.505773i) q^{17} +(0.694208 + 0.955496i) q^{19} +(7.36453 + 0.318013i) q^{21} +(2.51796 + 4.94177i) q^{23} +(-2.41891 + 4.37594i) q^{25} +(-4.11784 + 3.16913i) q^{27} +(-6.77941 - 4.92553i) q^{29} +(6.19212 - 4.49884i) q^{31} +(-2.08786 - 4.57559i) q^{33} +(9.21471 + 2.37731i) q^{35} +(-8.57635 - 4.36987i) q^{37} +(1.48804 - 0.413437i) q^{39} +(8.73412 - 2.83789i) q^{41} +(-1.45614 - 1.45614i) q^{43} +(-6.05026 + 2.89730i) q^{45} +(1.10756 + 6.99286i) q^{47} -11.1125i q^{49} +(-3.09305 - 4.66824i) q^{51} +(-2.56331 + 0.405989i) q^{53} +(-1.40906 - 6.33824i) q^{55} +(-0.406879 + 2.00478i) q^{57} +(-3.44583 - 10.6052i) q^{59} +(-2.69549 + 8.29586i) q^{61} +(8.21623 + 9.77272i) q^{63} +(1.99003 - 0.122889i) q^{65} +(0.616819 - 3.89444i) q^{67} +(-3.35994 + 8.99969i) q^{69} +(0.265914 - 0.366000i) q^{71} +(-2.68754 + 1.36937i) q^{73} +(-8.41762 + 2.03561i) q^{75} +(-11.0110 + 5.61041i) q^{77} +(2.07296 - 2.85319i) q^{79} +(-8.86624 - 1.54587i) q^{81} +(2.20859 - 13.9445i) q^{83} +(-2.65357 - 6.72490i) q^{85} +(-1.64996 - 14.4202i) q^{87} +(2.41968 - 7.44701i) q^{89} +(-1.17266 - 3.60908i) q^{91} +(12.9920 + 2.63679i) q^{93} +(-1.05164 + 2.42251i) q^{95} +(-1.51448 + 0.239870i) q^{97} +(3.39608 - 8.02199i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q - 2 * q^3 + 4 * q^7	\( 80 q - 2 q^{3} + 4 q^{7} + 12 q^{13} + 10 q^{15} + 20 q^{19} + 40 q^{25} - 14 q^{27} - 20 q^{33} + 12 q^{37} - 40 q^{39} + 12 q^{43} - 60 q^{45} - 76 q^{57} - 98 q^{63} - 36 q^{67} - 70 q^{69} - 44 q^{73} - 90 q^{75} - 40 q^{79} + 20 q^{81} - 100 q^{85} - 70 q^{87} - 18 q^{93} - 56 q^{97}+O(q^{100}) \) 80 * q - 2 * q^3 + 4 * q^7 + 12 * q^13 + 10 * q^15 + 20 * q^19 + 40 * q^25 - 14 * q^27 - 20 * q^33 + 12 * q^37 - 40 * q^39 + 12 * q^43 - 60 * q^45 - 76 * q^57 - 98 * q^63 - 36 * q^67 - 70 * q^69 - 44 * q^73 - 90 * q^75 - 40 * q^79 + 20 * q^81 - 100 * q^85 - 70 * q^87 - 18 * q^93 - 56 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more