LMFDB - Embedded newform 220.2.u.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(13,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 2]))

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

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

chi := DirichletCharacter("220.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.u (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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	220.13
Dual form			220.2.u.a.17.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.834729 - 0.132208i) q^{3} +(-2.08639 - 0.804354i) q^{5} +(-0.228981 - 1.44573i) q^{7} +(-2.17388 - 0.706335i) q^{9} +O(q^{10})$	\(q+(-0.834729 - 0.132208i) q^{3} +(-2.08639 - 0.804354i) q^{5} +(-0.228981 - 1.44573i) q^{7} +(-2.17388 - 0.706335i) q^{9} +(-3.21121 - 0.829518i) q^{11} +(0.134489 + 0.263950i) q^{13} +(1.63523 + 0.947255i) q^{15} +(3.43144 - 6.73459i) q^{17} +(-4.63943 + 3.37075i) q^{19} +1.23707i q^{21} +(-5.96043 - 5.96043i) q^{23} +(3.70603 + 3.35639i) q^{25} +(3.98027 + 2.02805i) q^{27} +(6.71592 + 4.87940i) q^{29} +(-0.792277 + 2.43838i) q^{31} +(2.57083 + 1.11697i) q^{33} +(-0.685136 + 3.20054i) q^{35} +(2.12739 - 0.336946i) q^{37} +(-0.0773657 - 0.238107i) q^{39} +(-4.70705 - 6.47870i) q^{41} +(2.62512 - 2.62512i) q^{43} +(3.96741 + 3.22225i) q^{45} +(-1.04991 + 6.62887i) q^{47} +(4.61969 - 1.50103i) q^{49} +(-3.75469 + 5.16789i) q^{51} +(0.739201 - 0.376642i) q^{53} +(6.03261 + 4.31365i) q^{55} +(4.31831 - 2.20029i) q^{57} +(-0.495669 + 0.682230i) q^{59} +(-3.88340 + 1.26179i) q^{61} +(-0.523394 + 3.30458i) q^{63} +(-0.0682875 - 0.658879i) q^{65} +(8.77012 - 8.77012i) q^{67} +(4.18733 + 5.76336i) q^{69} +(-1.44164 - 4.43691i) q^{71} +(-4.17085 + 0.660597i) q^{73} +(-2.64979 - 3.29164i) q^{75} +(-0.463953 + 4.83250i) q^{77} +(-0.875685 + 2.69508i) q^{79} +(2.49330 + 1.81149i) q^{81} +(-9.19653 - 4.68587i) q^{83} +(-12.5763 + 11.2909i) q^{85} +(-4.96087 - 4.96087i) q^{87} -15.6361i q^{89} +(0.350805 - 0.254875i) q^{91} +(0.983710 - 1.93064i) q^{93} +(12.3909 - 3.30094i) q^{95} +(-3.85719 - 7.57015i) q^{97} +(6.39486 + 4.07146i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7}+O(q^{10}) $ 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7	$ 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55} - 120 q^{57} - 40 q^{61} - 50 q^{63} - 72 q^{67} + 4 q^{71} - 20 q^{73} + 20 q^{75} - 36 q^{77} + 100 q^{81} + 40 q^{85} - 8 q^{91} - 14 q^{93} + 50 q^{95} + 6 q^{97}+O(q^{100}) $ 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.834729	−	0.132208i	−0.481931	−	0.0763304i	−0.0892580	−	0.996009i	$-0.528450\pi$
$3$	−0.834729	−	0.132208i	−0.481931	−	0.0763304i	−0.392673	+	0.919678i	$0.628450\pi$
$4$		0			0
$5$	−2.08639	−	0.804354i	−0.933061	−	0.359718i
$5$	−2.08639	−	0.804354i	−0.933061	−	0.359718i
$6$		0			0
$7$	−0.228981	−	1.44573i	−0.0865468	−	0.546435i	−0.992421	−	0.122887i	$-0.960785\pi$
$7$	−0.228981	−	1.44573i	−0.0865468	−	0.546435i	0.905874	−	0.423548i	$-0.139215\pi$
$8$		0			0
$9$	−2.17388	−	0.706335i	−0.724625	−	0.235445i
$10$		0			0
$11$	−3.21121	−	0.829518i	−0.968218	−	0.250109i
$11$	−3.21121	−	0.829518i	−0.968218	−	0.250109i
$12$		0			0
$13$	0.134489	+	0.263950i	0.0373006	+	0.0732065i	0.908905	−	0.417004i	$-0.136920\pi$
$13$	0.134489	+	0.263950i	0.0373006	+	0.0732065i	−0.871604	+	0.490211i	$0.836920\pi$
$14$		0			0
$15$	1.63523	+	0.947255i	0.422214	+	0.244580i
$16$		0			0
$17$	3.43144	−	6.73459i	0.832247	−	1.63338i	0.0598764	−	0.998206i	$-0.480929\pi$
$17$	3.43144	−	6.73459i	0.832247	−	1.63338i	0.772371	−	0.635172i	$-0.219071\pi$
$18$		0			0
$19$	−4.63943	+	3.37075i	−1.06436	+	0.773302i	−0.974890	−	0.222688i	$-0.928517\pi$
$19$	−4.63943	+	3.37075i	−1.06436	+	0.773302i	−0.0894690	+	0.995990i	$0.528517\pi$
$20$		0			0
$21$			1.23707i			0.269950i
$22$		0			0
$23$	−5.96043	−	5.96043i	−1.24284	−	1.24284i	−0.958819	−	0.284017i	$-0.908333\pi$
$23$	−5.96043	−	5.96043i	−1.24284	−	1.24284i	−0.284017	−	0.958819i	$-0.591667\pi$
$24$		0			0
$25$	3.70603	+	3.35639i	0.741206	+	0.671278i
$26$		0			0
$27$	3.98027	+	2.02805i	0.766004	+	0.390299i
$28$		0			0
$29$	6.71592	+	4.87940i	1.24711	+	0.906081i	0.998051	−	0.0624057i	$-0.0198773\pi$
$29$	6.71592	+	4.87940i	1.24711	+	0.906081i	0.249063	+	0.968487i	$0.419877\pi$
$30$		0			0
$31$	−0.792277	+	2.43838i	−0.142297	+	0.437946i	−0.996654	−	0.0817419i	$-0.973952\pi$
$31$	−0.792277	+	2.43838i	−0.142297	+	0.437946i	0.854356	+	0.519688i	$0.173952\pi$
$32$		0			0
$33$	2.57083	+	1.11697i	0.447523	+	0.194440i
$34$		0			0
$35$	−0.685136	+	3.20054i	−0.115809	+	0.540990i
$36$		0			0
$37$	2.12739	−	0.336946i	0.349741	−	0.0553935i	0.0209075	−	0.999781i	$-0.493344\pi$
$37$	2.12739	−	0.336946i	0.349741	−	0.0553935i	0.328834	+	0.944388i	$0.393344\pi$
$38$		0			0
$39$	−0.0773657	−	0.238107i	−0.0123884	−	0.0381277i
$40$		0			0
$41$	−4.70705	−	6.47870i	−0.735117	−	1.01180i	−0.998885	−	0.0472159i	$-0.984965\pi$
$41$	−4.70705	−	6.47870i	−0.735117	−	1.01180i	0.263767	−	0.964586i	$-0.415035\pi$
$42$		0			0
$43$	2.62512	−	2.62512i	0.400327	−	0.400327i	−0.478021	−	0.878348i	$-0.658646\pi$
$43$	2.62512	−	2.62512i	0.400327	−	0.400327i	0.878348	+	0.478021i	$0.158646\pi$
$44$		0			0
$45$	3.96741	+	3.22225i	0.591426	+	0.480345i
$46$		0			0
$47$	−1.04991	+	6.62887i	−0.153145	+	0.966919i	0.784703	+	0.619872i	$0.212816\pi$
$47$	−1.04991	+	6.62887i	−0.153145	+	0.966919i	−0.937848	+	0.347047i	$0.887184\pi$
$48$		0			0
$49$	4.61969	−	1.50103i	0.659956	−	0.214433i
$50$		0			0
$51$	−3.75469	+	5.16789i	−0.525762	+	0.723650i
$52$		0			0
$53$	0.739201	−	0.376642i	0.101537	−	0.0517357i	−0.402484	−	0.915427i	$-0.631853\pi$
$53$	0.739201	−	0.376642i	0.101537	−	0.0517357i	0.504021	+	0.863691i	$0.331853\pi$
$54$		0			0
$55$	6.03261	+	4.31365i	0.813437	+	0.581653i
$56$		0			0
$57$	4.31831	−	2.20029i	0.571974	−	0.291435i
$58$		0			0
$59$	−0.495669	+	0.682230i	−0.0645306	+	0.0888188i	−0.840062	−	0.542490i	$-0.817482\pi$
$59$	−0.495669	+	0.682230i	−0.0645306	+	0.0888188i	0.775532	+	0.631308i	$0.217482\pi$
$60$		0			0
$61$	−3.88340	+	1.26179i	−0.497219	+	0.161556i	−0.546882	−	0.837210i	$-0.684185\pi$
$61$	−3.88340	+	1.26179i	−0.497219	+	0.161556i	0.0496630	+	0.998766i	$0.484185\pi$
$62$		0			0
$63$	−0.523394	+	3.30458i	−0.0659414	+	0.416338i
$64$		0			0
$65$	−0.0682875	−	0.658879i	−0.00847002	−	0.0817239i
$66$		0			0
$67$	8.77012	−	8.77012i	1.07144	−	1.07144i	0.0741974	−	0.997244i	$-0.476361\pi$
$67$	8.77012	−	8.77012i	1.07144	−	1.07144i	0.997244	−	0.0741974i	$-0.0236395\pi$
$68$		0			0
$69$	4.18733	+	5.76336i	0.504095	+	0.693828i
$70$		0			0
$71$	−1.44164	−	4.43691i	−0.171091	−	0.526564i	0.828342	−	0.560222i	$-0.189284\pi$
$71$	−1.44164	−	4.43691i	−0.171091	−	0.526564i	−0.999433	+	0.0336583i	$0.989284\pi$
$72$		0			0
$73$	−4.17085	+	0.660597i	−0.488161	+	0.0773171i	−0.395663	−	0.918396i	$-0.629485\pi$
$73$	−4.17085	+	0.660597i	−0.488161	+	0.0773171i	−0.0924979	+	0.995713i	$0.529485\pi$
$74$		0			0
$75$	−2.64979	−	3.29164i	−0.305971	−	0.380086i
$76$		0			0
$77$	−0.463953	+	4.83250i	−0.0528723	+	0.550714i
$78$		0			0
$79$	−0.875685	+	2.69508i	−0.0985223	+	0.303220i	−0.988156	−	0.153455i	$-0.950960\pi$
$79$	−0.875685	+	2.69508i	−0.0985223	+	0.303220i	0.889633	+	0.456676i	$0.150960\pi$
$80$		0			0
$81$	2.49330	+	1.81149i	0.277034	+	0.201277i
$82$		0			0
$83$	−9.19653	−	4.68587i	−1.00945	−	0.514341i	−0.130599	−	0.991435i	$-0.541690\pi$
$83$	−9.19653	−	4.68587i	−1.00945	−	0.514341i	−0.878852	+	0.477095i	$0.841690\pi$
$84$		0			0
$85$	−12.5763	+	11.2909i	−1.36409	+	1.22467i
$86$		0			0
$87$	−4.96087	−	4.96087i	−0.531861	−	0.531861i
$88$		0			0
$89$		−	15.6361i		−	1.65742i	−0.559679	−	0.828710i	$-0.689075\pi$
$89$		−	15.6361i		−	1.65742i	0.559679	−	0.828710i	$-0.310925\pi$
$90$		0			0
$91$	0.350805	−	0.254875i	0.0367744	−	0.0267181i
$92$		0			0
$93$	0.983710	−	1.93064i	0.102006	−	0.200198i
$94$		0			0
$95$	12.3909	−	3.30094i	1.27128	−	0.338669i
$96$		0			0
$97$	−3.85719	−	7.57015i	−0.391638	−	0.768633i	0.608043	−	0.793904i	$-0.291955\pi$
$97$	−3.85719	−	7.57015i	−0.391638	−	0.768633i	−0.999681	+	0.0252716i	$0.991955\pi$
$98$		0			0
$99$	6.39486	+	4.07146i	0.642708	+	0.409198i
$100$		0			0
$101$	−4.93782	−	1.60440i	−0.491332	−	0.159643i	0.0528640	−	0.998602i	$-0.483165\pi$
$101$	−4.93782	−	1.60440i	−0.491332	−	0.159643i	−0.544196	+	0.838958i	$0.683165\pi$
$102$		0			0
$103$	−0.834326	−	5.26773i	−0.0822086	−	0.519045i	−0.994087	−	0.108585i	$-0.965368\pi$
$103$	−0.834326	−	5.26773i	−0.0822086	−	0.519045i	0.911879	−	0.410460i	$-0.134632\pi$
$104$		0			0
$105$	0.995040	−	2.58100i	0.0971059	−	0.251880i
$106$		0			0
$107$	−12.4152	−	1.96637i	−1.20022	−	0.190096i	−0.475861	−	0.879521i	$-0.657863\pi$
$107$	−12.4152	−	1.96637i	−1.20022	−	0.190096i	−0.724357	+	0.689425i	$0.757863\pi$
$108$		0			0
$109$	−16.5097			−1.58134			−0.790671	−	0.612241i	$-0.790268\pi$
$109$	−16.5097			−1.58134			−0.790671	+	0.612241i	$0.790268\pi$
$110$		0			0
$111$	−1.82034			−0.172779
$112$		0			0
$113$	3.69327	+	0.584956i	0.347433	+	0.0550280i	0.327713	−	0.944777i	$-0.393722\pi$
$113$	3.69327	+	0.584956i	0.347433	+	0.0550280i	0.0197209	+	0.999806i	$0.493722\pi$
$114$		0			0
$115$	7.64148	+	17.2301i	0.712572	+	1.60671i
$116$		0			0
$117$	−0.105926	−	0.668789i	−0.00979284	−	0.0618295i
$118$		0			0
$119$	−10.5221	−	3.41885i	−0.964563	−	0.313405i
$120$		0			0
$121$	9.62380	+	5.32752i	0.874891	+	0.484320i
$122$		0			0
$123$	3.07257	+	6.03027i	0.277045	+	0.543731i
$124$		0			0
$125$	−5.03249	−	9.98369i	−0.450120	−	0.892968i
$126$		0			0
$127$	3.78852	−	7.43539i	0.336177	−	0.659784i	−0.659598	−	0.751619i	$-0.729273\pi$
$127$	3.78852	−	7.43539i	0.336177	−	0.659784i	0.995774	+	0.0918351i	$0.0292733\pi$
$128$		0			0
$129$	−2.53832	+	1.84420i	−0.223487	+	0.162373i
$130$		0			0
$131$		−	10.5791i		−	0.924303i	−0.886801	−	0.462151i	$-0.847078\pi$
$131$		−	10.5791i		−	0.924303i	0.886801	−	0.462151i	$-0.152922\pi$
$132$		0			0
$133$	5.93553	+	5.93553i	0.514676	+	0.514676i
$134$		0			0
$135$	−6.67313	−	7.43285i	−0.574331	−	0.639718i
$136$		0			0
$137$	10.7094	+	5.45669i	0.914962	+	0.466197i	0.847061	−	0.531495i	$-0.178370\pi$
$137$	10.7094	+	5.45669i	0.914962	+	0.466197i	0.0679012	+	0.997692i	$0.478370\pi$
$138$		0			0
$139$	0.611911	+	0.444579i	0.0519016	+	0.0377087i	0.613434	−	0.789746i	$-0.289788\pi$
$139$	0.611911	+	0.444579i	0.0519016	+	0.0377087i	−0.561532	+	0.827455i	$0.689788\pi$
$140$		0			0
$141$	1.75278	−	5.39450i	0.147611	−	0.454299i
$142$		0			0
$143$	−0.212922	−	0.959161i	−0.0178055	−	0.0802091i
$144$		0			0
$145$	−10.0872	−	15.5823i	−0.837700	−	1.29404i
$146$		0			0
$147$	−4.05464	+	0.642192i	−0.334421	+	0.0529671i
$148$		0			0
$149$	1.14368	+	3.51989i	0.0936941	+	0.288361i	0.986911	−	0.161265i	$-0.0515573\pi$
$149$	1.14368	+	3.51989i	0.0936941	+	0.288361i	−0.893217	+	0.449626i	$0.851557\pi$
$150$		0			0
$151$	2.43710	+	3.35439i	0.198329	+	0.272976i	0.896585	−	0.442872i	$-0.146040\pi$
$151$	2.43710	+	3.35439i	0.198329	+	0.272976i	−0.698256	+	0.715848i	$0.746040\pi$
$152$		0			0
$153$	−12.2164	+	12.2164i	−0.987638	+	0.987638i
$154$		0			0
$155$	3.61432	−	4.45013i	0.290309	−	0.357443i
$156$		0			0
$157$	−1.60690	+	10.1456i	−0.128245	+	0.809705i	0.836779	+	0.547541i	$0.184436\pi$
$157$	−1.60690	+	10.1456i	−0.128245	+	0.809705i	−0.965023	+	0.262164i	$0.915564\pi$
$158$		0			0
$159$	−0.666828	+	0.216665i	−0.0528829	+	0.0171827i
$160$		0			0
$161$	−7.25236	+	9.98201i	−0.571566	+	0.786693i
$162$		0			0
$163$	7.87784	−	4.01396i	0.617040	−	0.314397i	−0.117386	−	0.993086i	$-0.537452\pi$
$163$	7.87784	−	4.01396i	0.617040	−	0.314397i	0.734426	+	0.678689i	$0.237452\pi$
$164$		0			0
$165$	−4.46530	−	4.39829i	−0.347623	−	0.342406i
$166$		0			0
$167$	−8.28987	+	4.22390i	−0.641489	+	0.326855i	−0.744300	−	0.667846i	$-0.767217\pi$
$167$	−8.28987	+	4.22390i	−0.641489	+	0.326855i	0.102810	+	0.994701i	$0.467217\pi$
$168$		0			0
$169$	7.58963	−	10.4462i	0.583817	−	0.803556i
$170$		0			0
$171$	12.4664	−	4.05059i	0.953331	−	0.309756i
$172$		0			0
$173$	−0.309951	+	1.95696i	−0.0235652	+	0.148785i	−0.996665	−	0.0815978i	$-0.973998\pi$
$173$	−0.309951	+	1.95696i	−0.0235652	+	0.148785i	0.973100	+	0.230382i	$0.0739977\pi$
$174$		0			0
$175$	4.00382	−	6.12647i	0.302661	−	0.463118i
$176$		0			0
$177$	0.503946	−	0.503946i	0.0378789	−	0.0378789i
$178$		0			0
$179$	4.88852	+	6.72847i	0.365385	+	0.502909i	0.951639	−	0.307218i	$-0.0993980\pi$
$179$	4.88852	+	6.72847i	0.365385	+	0.502909i	−0.586254	+	0.810127i	$0.699398\pi$
$180$		0			0
$181$	−3.98312	−	12.2588i	−0.296063	−	0.911187i	−0.982862	−	0.184341i	$-0.940985\pi$
$181$	−3.98312	−	12.2588i	−0.296063	−	0.911187i	0.686800	−	0.726847i	$-0.259015\pi$
$182$		0			0
$183$	3.40841	−	0.539839i	0.251957	−	0.0399060i
$184$		0			0
$185$	−4.70959	−	1.00818i	−0.346256	−	0.0741226i
$186$		0			0
$187$	−16.6056	+	18.7798i	−1.21432	+	1.37331i
$188$		0			0
$189$	2.02061	−	6.21879i	0.146978	−	0.452350i
$190$		0			0
$191$	18.5051	+	13.4447i	1.33898	+	0.972825i	0.999481	+	0.0322180i	$0.0102571\pi$
$191$	18.5051	+	13.4447i	1.33898	+	0.972825i	0.339498	+	0.940607i	$0.389743\pi$
$192$		0			0
$193$	−1.51445	−	0.771651i	−0.109013	−	0.0555447i	0.398634	−	0.917110i	$-0.369484\pi$
$193$	−1.51445	−	0.771651i	−0.109013	−	0.0555447i	−0.507647	+	0.861565i	$0.669484\pi$
$194$		0			0
$195$	−0.0301076	+	0.559013i	−0.00215605	+	0.0400318i
$196$		0			0
$197$	10.6799	+	10.6799i	0.760909	+	0.760909i	0.976487	−	0.215577i	$-0.0691634\pi$
$197$	10.6799	+	10.6799i	0.760909	+	0.760909i	−0.215577	+	0.976487i	$0.569163\pi$
$198$		0			0
$199$			8.08438i			0.573086i	0.958067	+	0.286543i	$0.0925062\pi$
$199$			8.08438i			0.573086i	−0.958067	+	0.286543i	$0.907494\pi$
$200$		0			0
$201$	−8.48016	+	6.16119i	−0.598144	+	0.434577i
$202$		0			0
$203$	5.51648	−	10.8267i	0.387181	−	0.759885i
$204$		0			0
$205$	4.60956	+	17.3032i	0.321946	+	1.20851i
$206$		0			0
$207$	8.74718	+	17.1673i	0.607971	+	1.19321i
$208$		0			0
$209$	17.6943	−	6.97569i	1.22394	−	0.482519i
$210$		0			0
$211$	18.8288	+	6.11786i	1.29623	+	0.421171i	0.874268	−	0.485443i	$-0.161342\pi$
$211$	18.8288	+	6.11786i	1.29623	+	0.421171i	0.421962	+	0.906614i	$0.361342\pi$
$212$		0			0
$213$	0.616782	+	3.89421i	0.0422612	+	0.266827i
$214$		0			0
$215$	−7.58854	+	3.36549i	−0.517534	+	0.229525i
$216$		0			0
$217$	3.70666	+	0.587077i	0.251624	+	0.0398534i
$218$		0			0
$219$	3.56886			0.241162
$220$		0			0
$221$	2.23909			0.150617
$222$		0			0
$223$	23.2342	+	3.67994i	1.55588	+	0.246427i	0.874325	−	0.485341i	$-0.161304\pi$
$223$	23.2342	+	3.67994i	1.55588	+	0.246427i	0.681554	+	0.731768i	$0.261304\pi$
$224$		0			0
$225$	−5.68571	−	9.91407i	−0.379048	−	0.660938i
$226$		0			0
$227$	−2.82607	−	17.8431i	−0.187573	−	1.18429i	−0.884288	−	0.466941i	$-0.845356\pi$
$227$	−2.82607	−	17.8431i	−0.187573	−	1.18429i	0.696715	−	0.717348i	$-0.254644\pi$
$228$		0			0
$229$	−0.957093	−	0.310978i	−0.0632465	−	0.0205500i	0.277223	−	0.960806i	$-0.410586\pi$
$229$	−0.957093	−	0.310978i	−0.0632465	−	0.0205500i	−0.340469	+	0.940256i	$0.610586\pi$
$230$		0			0
$231$	1.02617	−	3.97249i	0.0675170	−	0.261370i
$232$		0			0
$233$	2.59481	+	5.09261i	0.169992	+	0.333628i	0.960248	−	0.279149i	$-0.0900524\pi$
$233$	2.59481	+	5.09261i	0.169992	+	0.333628i	−0.790256	+	0.612777i	$0.790052\pi$
$234$		0			0
$235$	7.52247	−	12.9859i	0.490712	−	0.847106i
$236$		0			0
$237$	1.08727	−	2.13389i	0.0706259	−	0.138611i
$238$		0			0
$239$	−11.3661	+	8.25792i	−0.735209	+	0.534161i	−0.891207	−	0.453597i	$-0.850141\pi$
$239$	−11.3661	+	8.25792i	−0.735209	+	0.534161i	0.155998	+	0.987757i	$0.450141\pi$
$240$		0			0
$241$			16.9893i			1.09438i	0.837010	+	0.547188i	$0.184302\pi$
$241$			16.9893i			1.09438i	−0.837010	+	0.547188i	$0.815698\pi$
$242$		0			0
$243$	−11.3180	−	11.3180i	−0.726052	−	0.726052i
$244$		0			0
$245$	−10.8458	−	0.584138i	−0.692914	−	0.0373192i
$246$		0			0
$247$	−1.51366	−	0.771249i	−0.0963120	−	0.0490734i
$248$		0			0
$249$	7.05710	+	5.12729i	0.447226	+	0.324929i
$250$		0			0
$251$	−0.854534	+	2.62998i	−0.0539377	+	0.166003i	−0.974397	−	0.224836i	$-0.927815\pi$
$251$	−0.854534	+	2.62998i	−0.0539377	+	0.166003i	0.920459	+	0.390839i	$0.127815\pi$
$252$		0			0
$253$	14.1959	+	24.0845i	0.892491	+	1.51418i
$254$		0			0
$255$	11.9906	−	7.76212i	0.750878	−	0.486083i
$256$		0			0
$257$	−17.4350	+	2.76143i	−1.08756	+	0.172253i	−0.674372	−	0.738391i	$-0.735586\pi$
$257$	−17.4350	+	2.76143i	−1.08756	+	0.172253i	−0.413191	+	0.910644i	$0.635586\pi$
$258$		0			0
$259$	−0.974266	−	2.99848i	−0.0605379	−	0.186317i
$260$		0			0
$261$	−11.1531	−	15.3509i	−0.690358	−	0.950196i
$262$		0			0
$263$	2.88362	−	2.88362i	0.177812	−	0.177812i	−0.612590	−	0.790401i	$-0.709872\pi$
$263$	2.88362	−	2.88362i	0.177812	−	0.177812i	0.790401	+	0.612590i	$0.209872\pi$
$264$		0			0
$265$	−1.84521	+	0.191242i	−0.113351	+	0.0117479i
$266$		0			0
$267$	−2.06721	+	13.0519i	−0.126511	+	0.798762i
$268$		0			0
$269$	−2.43670	+	0.791731i	−0.148568	+	0.0482727i	−0.382357	−	0.924015i	$-0.624888\pi$
$269$	−2.43670	+	0.791731i	−0.148568	+	0.0482727i	0.233789	+	0.972287i	$0.424888\pi$
$270$		0			0
$271$	0.284253	−	0.391241i	0.0172672	−	0.0237662i	−0.800296	−	0.599605i	$-0.795324\pi$
$271$	0.284253	−	0.391241i	0.0172672	−	0.0237662i	0.817563	+	0.575839i	$0.195324\pi$
$272$		0			0
$273$	−0.326524	+	0.166372i	−0.0197621	+	0.0100693i
$274$		0			0
$275$	−9.11667	−	13.8523i	−0.549756	−	0.835325i
$276$		0			0
$277$	−20.7580	+	10.5767i	−1.24723	+	0.635495i	−0.947873	−	0.318647i	$-0.896772\pi$
$277$	−20.7580	+	10.5767i	−1.24723	+	0.635495i	−0.299355	+	0.954142i	$0.596772\pi$
$278$		0			0
$279$	3.44463	−	4.74112i	0.206224	−	0.283843i
$280$		0			0
$281$	17.0251	−	5.53180i	1.01563	−	0.329999i	0.246538	−	0.969133i	$-0.420707\pi$
$281$	17.0251	−	5.53180i	1.01563	−	0.329999i	0.769095	+	0.639134i	$0.220707\pi$
$282$		0			0
$283$	2.93981	−	18.5612i	0.174753	−	1.10335i	−0.731881	−	0.681433i	$-0.761357\pi$
$283$	2.93981	−	18.5612i	0.174753	−	1.10335i	0.906634	−	0.421917i	$-0.138643\pi$
$284$		0			0
$285$	−10.7795	+	1.11721i	−0.638521	+	0.0661776i
$286$		0			0
$287$	−8.28862	+	8.28862i	−0.489262	+	0.489262i
$288$		0			0
$289$	−23.5875	−	32.4654i	−1.38750	−	1.90973i
$290$		0			0
$291$	2.21887	+	6.82898i	0.130072	+	0.400322i
$292$		0			0
$293$	−26.1531	+	4.14224i	−1.52788	+	0.241992i	−0.863094	−	0.505043i	$-0.831477\pi$
$293$	−26.1531	+	4.14224i	−1.52788	+	0.241992i	−0.664785	+	0.747035i	$0.731477\pi$
$294$		0			0
$295$	1.58291	−	1.02470i	0.0921607	−	0.0596605i
$296$		0			0
$297$	−11.0992	−	9.81422i	−0.644041	−	0.569479i
$298$		0			0
$299$	0.771642	−	2.37487i	0.0446252	−	0.137342i
$300$		0			0
$301$	−4.39632	−	3.19411i	−0.253400	−	0.184106i
$302$		0			0
$303$	3.90963	+	1.99206i	0.224602	+	0.114441i
$304$		0			0
$305$	9.11721	+	0.491038i	0.522050	+	0.0281168i
$306$		0			0
$307$	−10.1395	−	10.1395i	−0.578689	−	0.578689i	0.355853	−	0.934542i	$-0.384190\pi$
$307$	−10.1395	−	10.1395i	−0.578689	−	0.578689i	−0.934542	+	0.355853i	$0.884190\pi$
$308$		0			0
$309$			4.50743i			0.256419i
$310$		0			0
$311$	20.0796	−	14.5887i	1.13861	−	0.827250i	0.151686	−	0.988429i	$-0.451530\pi$
$311$	20.0796	−	14.5887i	1.13861	−	0.827250i	0.986925	+	0.161179i	$0.0515296\pi$
$312$		0			0
$313$	−1.06879	+	2.09761i	−0.0604114	+	0.118564i	−0.919238	−	0.393703i	$-0.871194\pi$
$313$	−1.06879	+	2.09761i	−0.0604114	+	0.118564i	0.858827	+	0.512267i	$0.171194\pi$
$314$		0			0
$315$	3.75005	−	6.47364i	0.211291	−	0.364748i
$316$		0			0
$317$	8.30316	+	16.2959i	0.466352	+	0.915268i	0.997678	+	0.0681004i	$0.0216938\pi$
$317$	8.30316	+	16.2959i	0.466352	+	0.915268i	−0.531326	+	0.847167i	$0.678306\pi$
$318$		0			0
$319$	−17.5187	−	21.2398i	−0.980859	−	1.18920i
$320$		0			0
$321$	10.1033	+	3.28277i	0.563912	+	0.183226i
$322$		0			0
$323$	6.78063	+	42.8112i	0.377284	+	2.38208i
$324$		0			0
$325$	−0.387498	+	1.42960i	−0.0214945	+	0.0793002i
$326$		0			0
$327$	13.7811	+	2.18272i	0.762098	+	0.120704i
$328$		0			0
$329$	9.82397			0.541613
$330$		0			0
$331$	−13.6793			−0.751883			−0.375942	−	0.926643i	$-0.622681\pi$
$331$	−13.6793			−0.751883			−0.375942	+	0.926643i	$0.622681\pi$
$332$		0			0
$333$	−4.86268	−	0.770173i	−0.266473	−	0.0422052i
$334$		0			0
$335$	−25.3522	+	11.2436i	−1.38514	+	0.614303i
$336$		0			0
$337$	−4.94300	−	31.2089i	−0.269262	−	1.70005i	−0.637604	−	0.770364i	$-0.720074\pi$
$337$	−4.94300	−	31.2089i	−0.269262	−	1.70005i	0.368342	−	0.929690i	$-0.379926\pi$
$338$		0			0
$339$	−3.00554	−	0.976560i	−0.163239	−	0.0530395i
$340$		0			0
$341$	4.56685	−	7.17295i	0.247309	−	0.388437i
$342$		0			0
$343$	−7.87961	−	15.4646i	−0.425459	−	0.835010i
$344$		0			0
$345$	−4.10061	−	15.3927i	−0.220769	−	0.828716i
$346$		0			0
$347$	7.84815	−	15.4029i	0.421311	−	0.826869i	−0.578626	−	0.815593i	$-0.696411\pi$
$347$	7.84815	−	15.4029i	0.421311	−	0.826869i	0.999936	−	0.0112757i	$-0.00358925\pi$
$348$		0			0
$349$	2.47829	−	1.80059i	0.132660	−	0.0963831i	−0.519476	−	0.854485i	$-0.673873\pi$
$349$	2.47829	−	1.80059i	0.132660	−	0.0963831i	0.652136	+	0.758102i	$0.273873\pi$
$350$		0			0
$351$			1.32334i			0.0706349i
$352$		0			0
$353$	15.1192	+	15.1192i	0.804713	+	0.804713i	0.983828	−	0.179115i	$-0.0573235\pi$
$353$	15.1192	+	15.1192i	0.804713	+	0.804713i	−0.179115	+	0.983828i	$0.557323\pi$
$354$		0			0
$355$	−0.561026	+	10.4167i	−0.0297762	+	0.552861i
$356$		0			0
$357$	8.33113	+	4.24493i	0.440930	+	0.224665i
$358$		0			0
$359$	8.61052	+	6.25591i	0.454446	+	0.330174i	0.791349	−	0.611365i	$-0.209379\pi$
$359$	8.61052	+	6.25591i	0.454446	+	0.330174i	−0.336903	+	0.941540i	$0.609379\pi$
$360$		0			0
$361$	4.29109	−	13.2066i	0.225847	−	0.695085i
$362$		0			0
$363$	−7.32892	−	5.71938i	−0.384669	−	0.300190i
$364$		0			0
$365$	9.23336	+	1.97658i	0.483296	+	0.103459i
$366$		0			0
$367$	−18.3687	+	2.90931i	−0.958836	+	0.151865i	−0.616188	−	0.787599i	$-0.711324\pi$
$367$	−18.3687	+	2.90931i	−0.958836	+	0.151865i	−0.342648	+	0.939464i	$0.611324\pi$
$368$		0			0
$369$	5.65641	+	17.4086i	0.294461	+	0.906257i
$370$		0			0
$371$	−0.713786	−	0.982442i	−0.0370579	−	0.0510058i
$372$		0			0
$373$	20.7161	−	20.7161i	1.07264	−	1.07264i	0.0754909	−	0.997146i	$-0.475948\pi$
$373$	20.7161	−	20.7161i	1.07264	−	1.07264i	0.997146	−	0.0754909i	$-0.0240524\pi$
$374$		0			0
$375$	2.88084	+	8.99901i	0.148766	+	0.464707i
$376$		0			0
$377$	−0.384699	+	2.42889i	−0.0198130	+	0.125094i
$378$		0			0
$379$	−7.95463	+	2.58462i	−0.408602	+	0.132763i	−0.506104	−	0.862473i	$-0.668915\pi$
$379$	−7.95463	+	2.58462i	−0.408602	+	0.132763i	0.0975021	+	0.995235i	$0.468915\pi$
$380$		0			0
$381$	−4.14541	+	5.70566i	−0.212376	+	0.292310i
$382$		0			0
$383$	−27.9347	+	14.2335i	−1.42740	+	0.727296i	−0.985485	−	0.169762i	$-0.945700\pi$
$383$	−27.9347	+	14.2335i	−1.42740	+	0.727296i	−0.441913	+	0.897058i	$0.645700\pi$
$384$		0			0
$385$	4.85502	−	9.70928i	0.247435	−	0.494831i
$386$		0			0
$387$	−7.56090	+	3.85247i	−0.384342	+	0.195832i
$388$		0			0
$389$	−3.58343	+	4.93217i	−0.181687	+	0.250071i	−0.890140	−	0.455687i	$-0.849394\pi$
$389$	−3.58343	+	4.93217i	−0.181687	+	0.250071i	0.708453	+	0.705758i	$0.249394\pi$
$390$		0			0
$391$	−60.5940	+	19.6882i	−3.06437	+	0.995674i
$392$		0			0
$393$	−1.39865	+	8.83071i	−0.0705524	+	0.445450i
$394$		0			0
$395$	3.99482	−	4.91863i	0.201001	−	0.247483i
$396$		0			0
$397$	15.9635	−	15.9635i	0.801183	−	0.801183i	−0.182097	−	0.983281i	$-0.558289\pi$
$397$	15.9635	−	15.9635i	0.801183	−	0.801183i	0.983281	+	0.182097i	$0.0582886\pi$
$398$		0			0
$399$	−4.16984	−	5.73929i	−0.208753	−	0.287324i
$400$		0			0
$401$	−6.25493	−	19.2507i	−0.312356	−	0.961334i	−0.976829	−	0.214022i	$-0.931344\pi$
$401$	−6.25493	−	19.2507i	−0.312356	−	0.961334i	0.664472	−	0.747313i	$-0.268656\pi$
$402$		0			0
$403$	−0.750163	+	0.118814i	−0.0373683	+	0.00591855i
$404$		0			0
$405$	−3.74492	−	5.78497i	−0.186086	−	0.287457i
$406$		0			0
$407$	−7.11101	−	0.682706i	−0.352480	−	0.0338405i
$408$		0			0
$409$	−2.33157	+	7.17585i	−0.115289	+	0.354823i	−0.992007	−	0.126181i	$-0.959728\pi$
$409$	−2.33157	+	7.17585i	−0.115289	+	0.354823i	0.876718	+	0.481004i	$0.159728\pi$
$410$		0			0
$411$	−8.21799	−	5.97072i	−0.405364	−	0.294514i
$412$		0			0
$413$	1.09982	+	0.560386i	0.0541186	+	0.0275748i
$414$		0			0
$415$	15.4184	+	17.1738i	0.756861	+	0.843029i
$416$		0			0
$417$	−0.452003	−	0.452003i	−0.0221347	−	0.0221347i
$418$		0			0
$419$			1.67384i			0.0817724i	0.999164	+	0.0408862i	$0.0130181\pi$
$419$			1.67384i			0.0817724i	−0.999164	+	0.0408862i	$0.986982\pi$
$420$		0			0
$421$	16.2255	−	11.7885i	0.790783	−	0.574538i	−0.117412	−	0.993083i	$-0.537460\pi$
$421$	16.2255	−	11.7885i	0.790783	−	0.574538i	0.908196	+	0.418545i	$0.137460\pi$
$422$		0			0
$423$	6.96457	−	13.6687i	0.338629	−	0.664597i
$424$		0			0
$425$	35.3209	−	13.4413i	1.71332	−	0.652000i
$426$		0			0
$427$	2.71344	+	5.32543i	0.131313	+	0.257716i
$428$		0			0
$429$	0.0509236	+	0.828790i	0.00245861	+	0.0400143i
$430$		0			0
$431$	21.9561	+	7.13397i	1.05759	+	0.343631i	0.785642	−	0.618681i	$-0.212333\pi$
$431$	21.9561	+	7.13397i	1.05759	+	0.343631i	0.271946	+	0.962312i	$0.412333\pi$
$432$		0			0
$433$	−1.78393	−	11.2633i	−0.0857301	−	0.541278i	−0.992751	−	0.120192i	$-0.961649\pi$
$433$	−1.78393	−	11.2633i	−0.0857301	−	0.541278i	0.907021	−	0.421086i	$-0.138351\pi$
$434$		0			0
$435$	6.36001	+	14.3406i	0.304939	+	0.687579i
$436$		0			0
$437$	47.7441	+	7.56193i	2.28391	+	0.361736i
$438$		0			0
$439$	22.1936			1.05924			0.529621	−	0.848235i	$-0.322334\pi$
$439$	22.1936			1.05924			0.529621	+	0.848235i	$0.322334\pi$
$440$		0			0
$441$	−11.1029			−0.528708
$442$		0			0
$443$	−15.1124	−	2.39357i	−0.718011	−	0.113722i	−0.213271	−	0.976993i	$-0.568412\pi$
$443$	−15.1124	−	2.39357i	−0.718011	−	0.113722i	−0.504740	+	0.863271i	$0.668412\pi$
$444$		0			0
$445$	−12.5769	+	32.6229i	−0.596204	+	1.54647i
$446$		0			0
$447$	−0.489307	−	3.08936i	−0.0231434	−	0.146122i
$448$		0			0
$449$	14.5971	+	4.74290i	0.688881	+	0.223831i	0.632480	−	0.774577i	$-0.282037\pi$
$449$	14.5971	+	4.74290i	0.688881	+	0.223831i	0.0564019	+	0.998408i	$0.482037\pi$
$450$		0			0
$451$	9.74114	+	24.7091i	0.458693	+	1.16350i
$452$		0			0
$453$	−1.59084	−	3.12221i	−0.0747444	−	0.146694i
$454$		0			0
$455$	−0.936925	+	0.249596i	−0.0439237	+	0.0117013i
$456$		0			0
$457$	−11.5633	+	22.6942i	−0.540906	+	1.06159i	0.445193	+	0.895434i	$0.353135\pi$
$457$	−11.5633	+	22.6942i	−0.540906	+	1.06159i	−0.986100	+	0.166154i	$0.946865\pi$
$458$		0			0
$459$	27.3162	−	19.8464i	1.27501	−	0.926349i
$460$		0			0
$461$			24.4297i			1.13780i	0.822405	+	0.568902i	$0.192632\pi$
$461$			24.4297i			1.13780i	−0.822405	+	0.568902i	$0.807368\pi$
$462$		0			0
$463$	−3.14682	−	3.14682i	−0.146245	−	0.146245i	0.630193	−	0.776438i	$-0.282976\pi$
$463$	−3.14682	−	3.14682i	−0.146245	−	0.146245i	−0.776438	+	0.630193i	$0.782976\pi$
$464$		0			0
$465$	−3.60532	+	3.23681i	−0.167193	+	0.150104i
$466$		0			0
$467$	13.7387	+	7.00019i	0.635749	+	0.323930i	0.741991	−	0.670410i	$-0.233882\pi$
$467$	13.7387	+	7.00019i	0.635749	+	0.323930i	−0.106242	+	0.994340i	$0.533882\pi$
$468$		0			0
$469$	−14.6874	−	10.6710i	−0.678203	−	0.492743i
$470$		0			0
$471$	2.68266	−	8.25636i	0.123610	−	0.380433i
$472$		0			0
$473$	−10.6074	+	6.25223i	−0.487729	+	0.287478i
$474$		0			0
$475$	−28.5074	−	3.07966i	−1.30801	−	0.141304i
$476$		0			0
$477$	−1.87297	+	0.296649i	−0.0857573	+	0.0135826i
$478$		0			0
$479$	8.40471	+	25.8670i	0.384021	+	1.18189i	0.937188	+	0.348824i	$0.113419\pi$
$479$	8.40471	+	25.8670i	0.384021	+	1.18189i	−0.553167	+	0.833070i	$0.686581\pi$
$480$		0			0
$481$	0.375048	+	0.516209i	0.0171007	+	0.0235371i
$482$		0			0
$483$	7.37345	−	7.37345i	0.335504	−	0.335504i
$484$		0			0
$485$	1.95850	+	18.8968i	0.0889311	+	0.858061i
$486$		0			0
$487$	4.40221	−	27.7944i	0.199483	−	1.25949i	−0.661148	−	0.750256i	$-0.729930\pi$
$487$	4.40221	−	27.7944i	0.199483	−	1.25949i	0.860631	−	0.509230i	$-0.170070\pi$
$488$		0			0
$489$	−7.10654	+	2.30905i	−0.321369	+	0.104419i
$490$		0			0
$491$	−10.9941	+	15.1321i	−0.496156	+	0.682901i	−0.981509	−	0.191418i	$-0.938691\pi$
$491$	−10.9941	+	15.1321i	−0.496156	+	0.682901i	0.485352	+	0.874319i	$0.338691\pi$
$492$		0			0
$493$	55.9060	−	28.4855i	2.51788	−	1.28292i
$494$		0			0
$495$	−10.0673	−	13.6384i	−0.452490	−	0.613000i
$496$		0			0
$497$	−6.08446	+	3.10019i	−0.272925	+	0.139062i
$498$		0			0
$499$	−12.0412	+	16.5732i	−0.539036	+	0.741920i	−0.988474	−	0.151392i	$-0.951624\pi$
$499$	−12.0412	+	16.5732i	−0.539036	+	0.741920i	0.449437	+	0.893312i	$0.351624\pi$
$500$		0			0
$501$	7.47823	−	2.42982i	0.334103	−	0.108557i
$502$		0			0
$503$	5.71229	−	36.0660i	0.254698	−	1.60810i	−0.446263	−	0.894902i	$-0.647245\pi$
$503$	5.71229	−	36.0660i	0.254698	−	1.60810i	0.700961	−	0.713200i	$-0.252755\pi$
$504$		0			0
$505$	9.01171	+	7.31915i	0.401016	+	0.325698i
$506$		0			0
$507$	−7.71636	+	7.71636i	−0.342695	+	0.342695i
$508$		0			0
$509$	0.397850	+	0.547594i	0.0176344	+	0.0242717i	0.817743	−	0.575583i	$-0.195225\pi$
$509$	0.397850	+	0.547594i	0.0176344	+	0.0242717i	−0.800109	+	0.599855i	$0.795225\pi$
$510$		0			0
$511$	1.91009	+	5.87866i	0.0844975	+	0.260057i
$512$		0			0
$513$	−25.3023	+	4.00748i	−1.11712	+	0.176935i
$514$		0			0
$515$	−2.49639	+	11.6616i	−0.110004	+	0.513872i
$516$		0			0
$517$	8.87025	−	20.4158i	0.390113	−	0.897885i
$518$		0			0
$519$	0.517451	−	1.59255i	0.0227136	−	0.0699052i
$520$		0			0
$521$	13.2842	+	9.65151i	0.581990	+	0.422840i	0.839441	−	0.543451i	$-0.182883\pi$
$521$	13.2842	+	9.65151i	0.581990	+	0.422840i	−0.257451	+	0.966291i	$0.582883\pi$
$522$		0			0
$523$	−19.3641	−	9.86649i	−0.846732	−	0.431431i	−0.0238985	−	0.999714i	$-0.507608\pi$
$523$	−19.3641	−	9.86649i	−0.846732	−	0.431431i	−0.822833	+	0.568283i	$0.807608\pi$
$524$		0			0
$525$	−4.15208	+	4.58461i	−0.181211	+	0.200089i
$526$		0			0
$527$	13.7028	+	13.7028i	0.596904	+	0.596904i
$528$		0			0
$529$			48.0535i			2.08928i
$530$		0			0
$531$	1.55941	−	1.13297i	0.0676724	−	0.0491669i
$532$		0			0
$533$	1.07700	−	2.11374i	0.0466502	−	0.0915562i
$534$		0			0
$535$	24.3212	+	14.0888i	1.05150	+	0.609111i
$536$		0			0
$537$	−3.19103	−	6.26275i	−0.137703	−	0.270258i
$538$		0			0
$539$	−16.0799	+	0.988006i	−0.692612	+	0.0425564i
$540$		0			0
$541$	−29.8196	−	9.68896i	−1.28204	−	0.416561i	−0.412744	−	0.910847i	$-0.635429\pi$
$541$	−29.8196	−	9.68896i	−1.28204	−	0.416561i	−0.869299	+	0.494286i	$0.835429\pi$
$542$		0			0
$543$	1.70411	+	10.7594i	0.0731305	+	0.461728i
$544$		0			0
$545$	34.4456	+	13.2796i	1.47549	+	0.568837i
$546$		0			0
$547$	37.7111	+	5.97285i	1.61241	+	0.255381i	0.896576	−	0.442890i	$-0.146047\pi$
$547$	37.7111	+	5.97285i	1.61241	+	0.255381i	0.715834	+	0.698270i	$0.246047\pi$
$548$		0			0
$549$	9.33329			0.398335
$550$		0			0
$551$	−47.6052			−2.02805
$552$		0			0
$553$	4.09688	+	0.648882i	0.174217	+	0.0275933i
$554$		0			0
$555$	3.79794	+	1.46420i	0.161214	+	0.0621518i
$556$		0			0
$557$	−4.58246	−	28.9325i	−0.194165	−	1.22591i	−0.871560	−	0.490289i	$-0.836891\pi$
$557$	−4.58246	−	28.9325i	−0.194165	−	1.22591i	0.677395	−	0.735620i	$-0.263109\pi$
$558$		0			0
$559$	1.04595	+	0.339850i	0.0442390	+	0.0143741i
$560$		0			0
$561$	16.3440	−	13.4806i	0.690044	−	0.569152i
$562$		0			0
$563$	15.9534	+	31.3102i	0.672354	+	1.31957i	0.934990	+	0.354674i	$0.115408\pi$
$563$	15.9534	+	31.3102i	0.672354	+	1.31957i	−0.262636	+	0.964895i	$0.584592\pi$
$564$		0			0
$565$	−7.23508	−	4.19114i	−0.304382	−	0.176323i
$566$		0			0
$567$	2.04801	−	4.01944i	0.0860082	−	0.168801i
$568$		0			0
$569$	8.41044	−	6.11055i	0.352584	−	0.256167i	−0.397368	−	0.917659i	$-0.630076\pi$
$569$	8.41044	−	6.11055i	0.352584	−	0.256167i	0.749952	+	0.661492i	$0.230076\pi$
$570$		0			0
$571$		−	44.5845i		−	1.86580i	−0.360131	−	0.932902i	$-0.617268\pi$
$571$		−	44.5845i		−	1.86580i	0.360131	−	0.932902i	$-0.382732\pi$
$572$		0			0
$573$	−13.6692	−	13.6692i	−0.571039	−	0.571039i
$574$		0			0
$575$	−2.08401	−	42.0951i	−0.0869093	−	1.75549i
$576$		0			0
$577$	2.90672	+	1.48105i	0.121008	+	0.0616569i	0.513447	−	0.858121i	$-0.328368\pi$
$577$	2.90672	+	1.48105i	0.121008	+	0.0616569i	−0.392438	+	0.919778i	$0.628368\pi$
$578$		0			0
$579$	1.16214	+	0.844342i	0.0482968	+	0.0350897i
$580$		0			0
$581$	−4.66867	+	14.3687i	−0.193689	+	0.596114i
$582$		0			0
$583$	−2.68616	+	0.596297i	−0.111250	+	0.0246961i
$584$		0			0
$585$	−0.316941	+	1.48055i	−0.0131039	+	0.0612134i
$586$		0			0
$587$	9.94770	−	1.57556i	0.410585	−	0.0650303i	0.0522747	−	0.998633i	$-0.483353\pi$
$587$	9.94770	−	1.57556i	0.410585	−	0.0650303i	0.358311	+	0.933602i	$0.383353\pi$
$588$		0			0
$589$	−4.54344	−	13.9833i	−0.187209	−	0.576170i
$590$		0			0
$591$	−7.50283	−	10.3268i	−0.308625	−	0.424786i
$592$		0			0
$593$	−24.2434	+	24.2434i	−0.995558	+	0.995558i	−0.999990	−	0.00443249i	$-0.998589\pi$
$593$	−24.2434	+	24.2434i	−0.995558	+	0.995558i	0.00443249	+	0.999990i	$0.498589\pi$
$594$		0			0
$595$	19.2033	+	15.5966i	0.787258	+	0.639397i
$596$		0			0
$597$	1.06882	−	6.74826i	0.0437439	−	0.276188i
$598$		0			0
$599$	−29.0987	+	9.45474i	−1.18894	+	0.386310i	−0.835681	−	0.549215i	$-0.814927\pi$
$599$	−29.0987	+	9.45474i	−1.18894	+	0.386310i	−0.353260	+	0.935525i	$0.614927\pi$
$600$		0			0
$601$	−21.3964	+	29.4496i	−0.872778	+	1.20128i	0.105592	+	0.994410i	$0.466326\pi$
$601$	−21.3964	+	29.4496i	−0.872778	+	1.20128i	−0.978369	+	0.206866i	$0.933674\pi$
$602$		0			0
$603$	−25.2598	+	12.8705i	−1.02866	+	0.524128i
$604$		0			0
$605$	−15.7938	−	18.8562i	−0.642108	−	0.766614i
$606$		0			0
$607$	33.0711	−	16.8506i	1.34231	−	0.683943i	0.372555	−	0.928010i	$-0.378482\pi$
$607$	33.0711	−	16.8506i	1.34231	−	0.683943i	0.969758	+	0.244067i	$0.0784816\pi$
$608$		0			0
$609$	−6.03614	+	8.30804i	−0.244597	+	0.336659i
$610$		0			0
$611$	−1.89089	+	0.614387i	−0.0764972	+	0.0248555i
$612$		0			0
$613$	0.897929	−	5.66930i	0.0362670	−	0.228981i	−0.962897	−	0.269870i	$-0.913019\pi$
$613$	0.897929	−	5.66930i	0.0362670	−	0.228981i	0.999164	+	0.0408895i	$0.0130192\pi$
$614$		0			0
$615$	−1.56011	−	15.0529i	−0.0629098	−	0.606992i
$616$		0			0
$617$	17.2646	−	17.2646i	0.695048	−	0.695048i	−0.268290	−	0.963338i	$-0.586459\pi$
$617$	17.2646	−	17.2646i	0.695048	−	0.695048i	0.963338	+	0.268290i	$0.0864586\pi$
$618$		0			0
$619$	5.30713	+	7.30464i	0.213311	+	0.293598i	0.902243	−	0.431229i	$-0.141920\pi$
$619$	5.30713	+	7.30464i	0.213311	+	0.293598i	−0.688931	+	0.724827i	$0.741920\pi$
$620$		0			0
$621$	−11.6361	−	35.8122i	−0.466940	−	1.43710i
$622$		0			0
$623$	−22.6055	+	3.58037i	−0.905672	+	0.143444i
$624$		0			0
$625$	2.46931	+	24.8778i	0.0987724	+	0.995110i
$626$		0			0
$627$	−15.6922	+	3.48348i	−0.626686	+	0.139117i
$628$		0			0
$629$	5.03083	−	15.4833i	0.200593	−	0.617360i
$630$		0			0
$631$	14.4585	+	10.5047i	0.575585	+	0.418187i	0.837130	−	0.547004i	$-0.184232\pi$
$631$	14.4585	+	10.5047i	0.575585	+	0.418187i	−0.261545	+	0.965191i	$0.584232\pi$
$632$		0			0
$633$	−14.9081	−	7.59608i	−0.592545	−	0.301917i
$634$		0			0
$635$	−13.8850	+	12.4658i	−0.551010	+	0.494690i
$636$		0			0
$637$	1.01749	+	1.01749i	0.0403146	+	0.0403146i
$638$		0			0
$639$			10.6636i			0.421844i
$640$		0			0
$641$	−12.3343	+	8.96143i	−0.487177	+	0.353955i	−0.804098	−	0.594497i	$-0.797351\pi$
$641$	−12.3343	+	8.96143i	−0.487177	+	0.353955i	0.316920	+	0.948452i	$0.397351\pi$
$642$		0			0
$643$	4.80244	−	9.42531i	0.189390	−	0.371698i	−0.776714	−	0.629854i	$-0.783115\pi$
$643$	4.80244	−	9.42531i	0.189390	−	0.371698i	0.966103	+	0.258156i	$0.0831148\pi$
$644$		0			0
$645$	6.77932	−	1.80601i	0.266935	−	0.0711115i
$646$		0			0
$647$	−1.99887	−	3.92300i	−0.0785836	−	0.154229i	0.848371	−	0.529402i	$-0.177583\pi$
$647$	−1.99887	−	3.92300i	−0.0785836	−	0.154229i	−0.926955	+	0.375172i	$0.877583\pi$
$648$		0			0
$649$	2.15762	−	1.77962i	0.0846941	−	0.0698562i
$650$		0			0
$651$	−3.01644	−	0.980100i	−0.118224	−	0.0384131i
$652$		0			0
$653$	−5.30527	−	33.4961i	−0.207611	−	1.31081i	−0.842707	−	0.538372i	$-0.819039\pi$
$653$	−5.30527	−	33.4961i	−0.207611	−	1.31081i	0.635096	−	0.772433i	$-0.280961\pi$
$654$		0			0
$655$	−8.50937	+	22.0722i	−0.332488	+	0.862431i
$656$		0			0
$657$	9.53351	+	1.50996i	0.371938	+	0.0589091i
$658$		0			0
$659$	−22.3584			−0.870962			−0.435481	−	0.900198i	$-0.643422\pi$
$659$	−22.3584			−0.870962			−0.435481	+	0.900198i	$0.643422\pi$
$660$		0			0
$661$	19.3645			0.753194			0.376597	−	0.926377i	$-0.377094\pi$
$661$	19.3645			0.753194			0.376597	+	0.926377i	$0.377094\pi$
$662$		0			0
$663$	−1.86903	−	0.296025i	−0.0725871	−	0.0114967i
$664$		0			0
$665$	−7.60956	−	17.1581i	−0.295086	−	0.665362i
$666$		0			0
$667$	−10.9464	−	69.1131i	−0.423848	−	2.67607i
$668$		0			0
$669$	−18.9078	−	6.14351i	−0.731017	−	0.237522i
$670$		0			0
$671$	13.5171	−	0.830537i	0.521823	−	0.0320625i
$672$		0			0
$673$	2.20467	+	4.32690i	0.0849837	+	0.166790i	0.929587	−	0.368603i	$-0.120164\pi$
$673$	2.20467	+	4.32690i	0.0849837	+	0.166790i	−0.844603	+	0.535393i	$0.820164\pi$
$674$		0			0
$675$	7.94409	+	20.8754i	0.305768	+	0.803493i
$676$		0			0
$677$	5.59274	−	10.9764i	0.214946	−	0.421856i	−0.758207	−	0.652014i	$-0.773924\pi$
$677$	5.59274	−	10.9764i	0.214946	−	0.421856i	0.973153	+	0.230158i	$0.0739243\pi$
$678$		0			0
$679$	−10.0612	+	7.30988i	−0.386113	+	0.280527i
$680$		0			0
$681$			15.2678i			0.585063i
$682$		0			0
$683$	−3.62361	−	3.62361i	−0.138654	−	0.138654i	0.634373	−	0.773027i	$-0.281258\pi$
$683$	−3.62361	−	3.62361i	−0.138654	−	0.138654i	−0.773027	+	0.634373i	$0.781258\pi$
$684$		0			0
$685$	−17.9548	−	19.9989i	−0.686016	−	0.764118i
$686$		0			0
$687$	0.757800	+	0.386118i	0.0289119	+	0.0147313i
$688$		0			0
$689$	0.198829	+	0.144458i	0.00757479	+	0.00550340i
$690$		0			0
$691$	3.92606	−	12.0832i	0.149355	−	0.459666i	−0.848191	−	0.529691i	$-0.822308\pi$
$691$	3.92606	−	12.0832i	0.149355	−	0.459666i	0.997545	+	0.0700250i	$0.0223079\pi$
$692$		0			0
$693$	4.42194	−	10.1775i	0.167976	−	0.386613i
$694$		0			0
$695$	−0.919084	−	1.41976i	−0.0348629	−	0.0538545i
$696$		0			0
$697$	−59.7833	+	9.46875i	−2.26445	+	0.358654i
$698$		0			0
$699$	−1.49268	−	4.59401i	−0.0564585	−	0.173761i
$700$		0			0
$701$	3.86123	+	5.31453i	0.145837	+	0.200727i	0.875686	−	0.482881i	$-0.160410\pi$
$701$	3.86123	+	5.31453i	0.145837	+	0.200727i	−0.729849	+	0.683608i	$0.760410\pi$
$702$		0			0
$703$	−8.73413	+	8.73413i	−0.329414	+	0.329414i
$704$		0			0
$705$	−7.99607	+	9.84517i	−0.301149	+	0.370790i
$706$		0			0
$707$	−1.18886	+	7.50614i	−0.0447115	+	0.282297i
$708$		0			0
$709$	−31.3578	+	10.1888i	−1.17767	+	0.382648i	−0.831500	−	0.555525i	$-0.812517\pi$
$709$	−31.3578	+	10.1888i	−1.17767	+	0.382648i	−0.346168	+	0.938172i	$0.612517\pi$
$710$		0			0
$711$	3.80726	−	5.24025i	0.142783	−	0.196525i
$712$		0			0
$713$	19.2561	−	9.81148i	0.721147	−	0.367443i
$714$		0			0
$715$	−0.327266	+	2.17245i	−0.0122391	+	0.0812449i
$716$		0			0
$717$	10.5793	−	5.39044i	0.395093	−	0.201310i
$718$		0			0
$719$	27.5659	−	37.9411i	1.02803	−	1.41497i	0.121618	−	0.992577i	$-0.461192\pi$
$719$	27.5659	−	37.9411i	1.02803	−	1.41497i	0.906415	−	0.422389i	$-0.138808\pi$
$720$		0			0
$721$	−7.42467	+	2.41242i	−0.276509	+	0.0898433i
$722$		0			0
$723$	2.24612	−	14.1814i	0.0835341	−	0.527414i
$724$		0			0
$725$	8.51222	+	40.6244i	0.316136	+	1.50875i
$726$		0			0
$727$	−6.60329	+	6.60329i	−0.244902	+	0.244902i	−0.818875	−	0.573972i	$-0.805402\pi$
$727$	−6.60329	+	6.60329i	−0.244902	+	0.244902i	0.573972	+	0.818875i	$0.305402\pi$
$728$		0			0
$729$	2.51668	+	3.46392i	0.0932104	+	0.128293i
$730$		0			0
$731$	−8.67114	−	26.6870i	−0.320714	−	0.987056i
$732$		0			0
$733$	−5.19333	+	0.822542i	−0.191820	+	0.0303813i	−0.251605	−	0.967830i	$-0.580958\pi$
$733$	−5.19333	+	0.822542i	−0.191820	+	0.0303813i	0.0597852	+	0.998211i	$0.480958\pi$
$734$		0			0
$735$	8.97610	+	1.92150i	0.331088	+	0.0708757i
$736$		0			0
$737$	−35.4377	+	20.8878i	−1.30537	+	0.769411i
$738$		0			0
$739$	10.7995	−	33.2374i	0.397266	−	1.22266i	−0.529917	−	0.848050i	$-0.677777\pi$
$739$	10.7995	−	33.2374i	0.397266	−	1.22266i	0.927183	−	0.374609i	$-0.122223\pi$
$740$		0			0
$741$	1.16153	+	0.843902i	0.0426699	+	0.0310015i
$742$		0			0
$743$	46.5352	+	23.7109i	1.70721	+	0.869868i	0.983759	+	0.179495i	$0.0574462\pi$
$743$	46.5352	+	23.7109i	1.70721	+	0.869868i	0.723453	+	0.690374i	$0.242554\pi$
$744$		0			0
$745$	0.445074	−	8.26379i	0.0163063	−	0.302762i
$746$		0			0
$747$	16.6823	+	16.6823i	0.610375	+	0.610375i
$748$		0			0
$749$			18.3992i			0.672293i
$750$		0			0
$751$	−12.4792	+	9.06665i	−0.455372	+	0.330847i	−0.791713	−	0.610893i	$-0.790810\pi$
$751$	−12.4792	+	9.06665i	−0.455372	+	0.330847i	0.336341	+	0.941740i	$0.390810\pi$
$752$		0			0
$753$	1.06101	−	2.08235i	0.0386653	−	0.0758850i
$754$		0			0
$755$	−2.38663	−	8.95884i	−0.0868584	−	0.326046i
$756$		0			0
$757$	7.43234	+	14.5868i	0.270133	+	0.530166i	0.985727	−	0.168350i	$-0.0538440\pi$
$757$	7.43234	+	14.5868i	0.270133	+	0.530166i	−0.715594	+	0.698516i	$0.753844\pi$
$758$		0			0
$759$	−8.66560	−	21.9809i	−0.314541	−	0.797855i
$760$		0			0
$761$	−13.4053	−	4.35565i	−0.485943	−	0.157892i	0.0557912	−	0.998442i	$-0.482232\pi$
$761$	−13.4053	−	4.35565i	−0.485943	−	0.157892i	−0.541734	+	0.840550i	$0.682232\pi$
$762$		0			0
$763$	3.78041	+	23.8686i	0.136860	+	0.864100i
$764$		0			0
$765$	35.3145	−	15.6619i	1.27680	−	0.566255i
$766$		0			0
$767$	−0.246737	−	0.0390792i	−0.00890914	−	0.00141107i
$768$		0			0
$769$	−4.97963			−0.179570			−0.0897850	−	0.995961i	$-0.528618\pi$
$769$	−4.97963			−0.179570			−0.0897850	+	0.995961i	$0.528618\pi$
$770$		0			0
$771$	14.9186			0.537279
$772$		0			0
$773$	−20.0917	−	3.18221i	−0.722647	−	0.114456i	−0.215733	−	0.976452i	$-0.569214\pi$
$773$	−20.0917	−	3.18221i	−0.722647	−	0.114456i	−0.506914	+	0.861996i	$0.669214\pi$
$774$		0			0
$775$	−11.1204	+	6.37751i	−0.399455	+	0.229087i
$776$		0			0
$777$	0.416824	+	2.63173i	0.0149535	+	0.0944126i
$778$		0			0
$779$	43.6761	+	14.1912i	1.56486	+	0.508453i
$780$		0			0
$781$	0.948914	+	15.4437i	0.0339548	+	0.552620i
$782$		0			0
$783$	16.8355	+	33.0416i	0.601652	+	1.18081i
$784$		0			0
$785$	11.5133	−	19.8751i	0.410926	−	0.709373i
$786$		0			0
$787$	2.41237	−	4.73454i	0.0859917	−	0.168768i	−0.844006	−	0.536334i	$-0.819809\pi$
$787$	2.41237	−	4.73454i	0.0859917	−	0.168768i	0.929998	+	0.367566i	$0.119809\pi$
$788$		0			0
$789$	−2.78828	+	2.02580i	−0.0992654	+	0.0721205i
$790$		0			0
$791$		−	5.47342i		−	0.194612i
$792$		0			0
$793$	−0.855326	−	0.855326i	−0.0303735	−	0.0303735i
$794$		0			0
$795$	1.56554	+	0.0843173i	0.0555239	+	0.00299043i
$796$		0			0
$797$	35.1948	+	17.9327i	1.24667	+	0.635208i	0.947732	−	0.319066i	$-0.103369\pi$
$797$	35.1948	+	17.9327i	1.24667	+	0.635208i	0.298933	+	0.954274i	$0.403369\pi$
$798$		0			0
$799$	41.0400	+	29.8173i	1.45189	+	1.05486i
$800$		0			0
$801$	−11.0443	+	33.9909i	−0.390231	+	1.20101i
$802$		0			0
$803$	13.9415	+	1.33848i	0.491984	+	0.0472338i
$804$		0			0
$805$	23.1603	−	14.9929i	0.816293	−	0.528430i
$806$		0			0
$807$	2.13865	−	0.338730i	0.0752842	−	0.0119238i
$808$		0			0
$809$	8.94301	+	27.5237i	0.314419	+	0.967683i	0.975993	+	0.217803i	$0.0698890\pi$
$809$	8.94301	+	27.5237i	0.314419	+	0.967683i	−0.661573	+	0.749880i	$0.730111\pi$
$810$		0			0
$811$	1.60859	+	2.21403i	0.0564852	+	0.0777453i	0.836325	−	0.548234i	$-0.184700\pi$
$811$	1.60859	+	2.21403i	0.0564852	+	0.0777453i	−0.779840	+	0.625979i	$0.784700\pi$
$812$		0			0
$813$	−0.289000	+	0.289000i	−0.0101357	+	0.0101357i
$814$		0			0
$815$	−19.6649	+	2.03811i	−0.688830	+	0.0713917i
$816$		0			0
$817$	−3.33046	+	21.0277i	−0.116518	+	0.735665i
$818$		0			0
$819$	−0.942634	+	0.306280i	−0.0329383	+	0.0107023i
$820$		0			0
$821$	15.2748	−	21.0240i	0.533096	−	0.733743i	−0.454502	−	0.890745i	$-0.650183\pi$
$821$	15.2748	−	21.0240i	0.533096	−	0.733743i	0.987598	+	0.157002i	$0.0501829\pi$
$822$		0			0
$823$	9.58273	−	4.88264i	0.334033	−	0.170198i	−0.278927	−	0.960312i	$-0.589979\pi$
$823$	9.58273	−	4.88264i	0.334033	−	0.170198i	0.612960	+	0.790114i	$0.289979\pi$
$824$		0			0
$825$	5.77856	+	12.7682i	0.201184	+	0.444532i
$826$		0			0
$827$	−32.3953	+	16.5062i	−1.12649	+	0.573977i	−0.915021	−	0.403407i	$-0.867826\pi$
$827$	−32.3953	+	16.5062i	−1.12649	+	0.573977i	−0.211473	+	0.977384i	$0.567826\pi$
$828$		0			0
$829$	18.6173	−	25.6245i	0.646604	−	0.889974i	−0.352342	−	0.935871i	$-0.614615\pi$
$829$	18.6173	−	25.6245i	0.646604	−	0.889974i	0.998946	+	0.0458969i	$0.0146146\pi$
$830$		0			0
$831$	18.7257	−	6.08433i	0.649586	−	0.211063i
$832$		0			0
$833$	5.74340	−	36.2624i	0.198997	−	1.25642i
$834$		0			0
$835$	20.6934	−	2.14470i	0.716125	−	0.0742205i
$836$		0			0
$837$	−8.09864	+	8.09864i	−0.279930	+	0.279930i
$838$		0			0
$839$	−6.75378	−	9.29577i	−0.233166	−	0.320926i	0.676361	−	0.736570i	$-0.263556\pi$
$839$	−6.75378	−	9.29577i	−0.233166	−	0.320926i	−0.909527	+	0.415645i	$0.863556\pi$
$840$		0			0
$841$	12.3335	+	37.9586i	0.425293	+	1.30892i
$842$		0			0
$843$	−14.9427	+	2.36669i	−0.514654	+	0.0815132i
$844$		0			0
$845$	−24.2374	+	15.6901i	−0.833791	+	0.539757i
$846$		0			0
$847$	5.49850	−	15.1333i	0.188931	−	0.519987i
$848$		0			0
$849$	−4.90789	+	15.1049i	−0.168438	+	0.518400i
$850$		0			0
$851$	−14.6885	−	10.6718i	−0.503516	−	0.365826i
$852$		0			0
$853$	−33.5651	−	17.1023i	−1.14925	−	0.585571i	−0.227659	−	0.973741i	$-0.573107\pi$
$853$	−33.5651	−	17.1023i	−1.14925	−	0.585571i	−0.921588	+	0.388170i	$0.873107\pi$
$854$		0			0
$855$	−29.2679	−	1.57632i	−1.00094	−	0.0539091i
$856$		0			0
$857$	−38.5292	−	38.5292i	−1.31613	−	1.31613i	−0.916810	−	0.399323i	$-0.869245\pi$
$857$	−38.5292	−	38.5292i	−1.31613	−	1.31613i	−0.399323	−	0.916810i	$-0.630755\pi$
$858$		0			0
$859$		−	13.1305i		−	0.448007i	−0.974588	−	0.224004i	$-0.928087\pi$
$859$		−	13.1305i		−	0.448007i	0.974588	−	0.224004i	$-0.0719127\pi$
$860$		0			0
$861$	8.01458	−	5.82293i	0.273136	−	0.198445i
$862$		0			0
$863$	2.96508	−	5.81929i	0.100932	−	0.198091i	−0.835018	−	0.550222i	$-0.814543\pi$
$863$	2.96508	−	5.81929i	0.100932	−	0.198091i	0.935951	+	0.352131i	$0.114543\pi$
$864$		0			0
$865$	2.22076	−	3.83366i	0.0755082	−	0.130348i
$866$		0			0
$867$	15.3970	+	30.2183i	0.522909	+	1.02627i
$868$		0			0
$869$	5.04763	−	7.92809i	0.171229	−	0.268942i
$870$		0			0
$871$	3.49436	+	1.13539i	0.118402	+	0.0384711i
$872$		0			0
$873$	3.03798	+	19.1810i	0.102820	+	0.649180i
$874$		0			0
$875$	−13.2814	+	9.56171i	−0.448993	+	0.323245i
$876$		0			0
$877$	10.2502	+	1.62347i	0.346125	+	0.0548208i	0.327077	−	0.944998i	$-0.393936\pi$
$877$	10.2502	+	1.62347i	0.346125	+	0.0548208i	0.0190480	+	0.999819i	$0.493936\pi$
$878$		0			0
$879$	22.3784			0.754804
$880$		0			0
$881$	2.81394			0.0948039			0.0474020	−	0.998876i	$-0.484906\pi$
$881$	2.81394			0.0948039			0.0474020	+	0.998876i	$0.484906\pi$
$882$		0			0
$883$	39.1108	+	6.19453i	1.31618	+	0.208463i	0.774742	−	0.632277i	$-0.217880\pi$
$883$	39.1108	+	6.19453i	1.31618	+	0.208463i	0.541439	+	0.840740i	$0.317880\pi$
$884$		0			0
$885$	−1.45678	+	0.646075i	−0.0489690	+	0.0217176i
$886$		0			0
$887$	5.24874	+	33.1393i	0.176236	+	1.11271i	0.904205	+	0.427098i	$0.140464\pi$
$887$	5.24874	+	33.1393i	0.176236	+	1.11271i	−0.727970	+	0.685609i	$0.759536\pi$
$888$		0			0
$889$	−11.6171	−	3.77461i	−0.389624	−	0.126597i
$890$		0			0
$891$	−6.50386	−	7.88532i	−0.217888	−	0.264168i
$892$		0			0
$893$	−17.4732	−	34.2932i	−0.584719	−	1.14758i
$894$		0			0
$895$	−4.78728	−	17.9703i	−0.160021	−	0.600681i
$896$		0			0
$897$	−0.958089	+	1.88036i	−0.0319897	+	0.0627832i
$898$		0			0
$899$	−17.2187	+	12.5101i	−0.574275	+	0.417236i
$900$		0			0
$901$		−	6.27064i		−	0.208905i
$902$		0			0
$903$	3.24745	+	3.24745i	0.108068	+	0.108068i
$904$		0			0
$905$	−1.55007	+	28.7804i	−0.0515259	+	0.956693i
$906$		0			0
$907$	35.7325	+	18.2066i	1.18648	+	0.604541i	0.931972	−	0.362530i	$-0.118087\pi$
$907$	35.7325	+	18.2066i	1.18648	+	0.604541i	0.254507	+	0.967071i	$0.418087\pi$
$908$		0			0
$909$	9.60097	+	6.97551i	0.318444	+	0.231363i
$910$		0			0
$911$	7.63301	−	23.4920i	0.252893	−	0.778325i	−0.741344	−	0.671125i	$-0.765811\pi$
$911$	7.63301	−	23.4920i	0.252893	−	0.778325i	0.994237	−	0.107200i	$-0.0341885\pi$
$912$		0			0
$913$	25.6450	+	22.6760i	0.848727	+	0.750467i
$914$		0			0
$915$	−7.54548	−	1.61525i	−0.249446	−	0.0533986i
$916$		0			0
$917$	−15.2946	+	2.42242i	−0.505071	+	0.0799955i
$918$		0			0
$919$	−14.4328	−	44.4197i	−0.476095	−	1.46527i	−0.844475	−	0.535594i	$-0.820088\pi$
$919$	−14.4328	−	44.4197i	−0.476095	−	1.46527i	0.368380	−	0.929675i	$-0.379912\pi$
$920$		0			0
$921$	7.12318	+	9.80421i	0.234717	+	0.323060i
$922$		0			0
$923$	0.977236	−	0.977236i	0.0321661	−	0.0321661i
$924$		0			0
$925$	9.01510	+	5.89162i	0.296415	+	0.193715i
$926$		0			0
$927$	−1.90706	+	12.0407i	−0.0626361	+	0.395469i
$928$		0			0
$929$	44.1182	−	14.3349i	1.44747	−	0.470312i	0.523254	−	0.852177i	$-0.324718\pi$
$929$	44.1182	−	14.3349i	1.44747	−	0.470312i	0.924218	+	0.381864i	$0.124718\pi$
$930$		0			0
$931$	−16.3732	+	22.5357i	−0.536609	+	0.738578i
$932$		0			0
$933$	−18.6898	+	9.52293i	−0.611877	+	0.311767i
$934$		0			0
$935$	49.7512	−	25.8251i	1.62704	−	0.844571i
$936$		0			0
$937$	−50.0611	+	25.5074i	−1.63542	+	0.833290i	−0.637395	+	0.770537i	$0.719988\pi$
$937$	−50.0611	+	25.5074i	−1.63542	+	0.833290i	−0.998029	+	0.0627527i	$0.980012\pi$
$938$		0			0
$939$	1.16947	−	1.60963i	0.0381641	−	0.0525284i
$940$		0			0
$941$	−34.9147	+	11.3445i	−1.13819	+	0.369819i	−0.816682	−	0.577088i	$-0.804189\pi$
$941$	−34.9147	+	11.3445i	−1.13819	+	0.369819i	−0.321506	+	0.946908i	$0.604189\pi$
$942$		0			0
$943$	−10.5598	+	66.6719i	−0.343874	+	2.17114i
$944$		0			0
$945$	−9.21788	+	11.3495i	−0.299858	+	0.369200i
$946$		0			0
$947$	12.8812	−	12.8812i	0.418582	−	0.418582i	−0.466133	−	0.884715i	$-0.654353\pi$
$947$	12.8812	−	12.8812i	0.418582	−	0.418582i	0.884715	+	0.466133i	$0.154353\pi$
$948$		0			0
$949$	−0.735299	−	1.01205i	−0.0238688	−	0.0328526i
$950$		0			0
$951$	−4.77645	−	14.7004i	−0.154887	−	0.476693i
$952$		0			0
$953$	−0.630156	+	0.0998069i	−0.0204127	+	0.00323306i	−0.166632	−	0.986019i	$-0.553289\pi$
$953$	−0.630156	+	0.0998069i	−0.0204127	+	0.00323306i	0.146220	+	0.989252i	$0.453289\pi$
$954$		0			0
$955$	−27.7944	−	42.9355i	−0.899406	−	1.38936i
$956$		0			0
$957$	11.8153	+	20.0456i	0.381934	+	0.647981i
$958$		0			0
$959$	5.43666	−	16.7323i	0.175559	−	0.540315i
$960$		0			0
$961$	19.7615	+	14.3576i	0.637469	+	0.463148i
$962$		0			0
$963$	25.6001	+	13.0439i	0.824951	+	0.420334i
$964$		0			0
$965$	2.53905	+	2.82812i	0.0817349	+	0.0910403i
$966$		0			0
$967$	−10.3036	−	10.3036i	−0.331340	−	0.331340i	0.521755	−	0.853095i	$-0.325278\pi$
$967$	−10.3036	−	10.3036i	−0.331340	−	0.331340i	−0.853095	+	0.521755i	$0.825278\pi$
$968$		0			0
$969$		−	36.6322i		−	1.17680i
$970$		0			0
$971$	31.2434	−	22.6996i	1.00265	−	0.728466i	0.0399933	−	0.999200i	$-0.487266\pi$
$971$	31.2434	−	22.6996i	1.00265	−	0.728466i	0.962654	+	0.270734i	$0.0872663\pi$
$972$		0			0
$973$	0.502626	−	0.986459i	0.0161134	−	0.0316244i
$974$		0			0
$975$	0.512461	−	1.14210i	0.0164119	−	0.0365765i
$976$		0			0
$977$	−21.7547	−	42.6959i	−0.695993	−	1.36596i	−0.920210	−	0.391424i	$-0.871982\pi$
$977$	−21.7547	−	42.6959i	−0.695993	−	1.36596i	0.224217	−	0.974539i	$-0.428018\pi$
$978$		0			0
$979$	−12.9704	+	50.2108i	−0.414536	+	1.60474i
$980$		0			0
$981$	35.8900	+	11.6614i	1.14588	+	0.372319i
$982$		0			0
$983$	1.77684	+	11.2185i	0.0566725	+	0.357816i	0.999686	+	0.0250612i	$0.00797807\pi$
$983$	1.77684	+	11.2185i	0.0566725	+	0.357816i	−0.943013	+	0.332755i	$0.892022\pi$
$984$		0			0
$985$	−13.6920	−	30.8728i	−0.436262	−	0.983688i
$986$		0			0
$987$	−8.20035	−	1.29881i	−0.261020	−	0.0413415i
$988$		0			0
$989$	−31.2937			−0.995081
$990$		0			0
$991$	32.0668			1.01863			0.509317	−	0.860579i	$-0.329898\pi$
$991$	32.0668			1.01863			0.509317	+	0.860579i	$0.329898\pi$
$992$		0			0
$993$	11.4185	+	1.80852i	0.362356	+	0.0573915i
$994$		0			0
$995$	6.50270	−	16.8671i	0.206149	−	0.534724i
$996$		0			0
$997$	4.34985	+	27.4639i	0.137761	+	0.869790i	0.955670	+	0.294441i	$0.0951335\pi$
$997$	4.34985	+	27.4639i	0.137761	+	0.869790i	−0.817908	+	0.575348i	$0.804866\pi$
$998$		0			0
$999$	9.15095	+	2.97332i	0.289523	+	0.0940718i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.u.a.13.2	✓	48
4.3	odd	2		880.2.cm.b.673.5		48
5.2	odd	4	inner	220.2.u.a.57.2	yes	48
11.6	odd	10	inner	220.2.u.a.193.2	yes	48
20.7	even	4		880.2.cm.b.497.5		48
44.39	even	10		880.2.cm.b.193.5		48
55.17	even	20	inner	220.2.u.a.17.2	yes	48
220.127	odd	20		880.2.cm.b.17.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.13.2	✓	48	1.1	even	1	trivial
220.2.u.a.17.2	yes	48	55.17	even	20	inner
220.2.u.a.57.2	yes	48	5.2	odd	4	inner
220.2.u.a.193.2	yes	48	11.6	odd	10	inner
880.2.cm.b.17.5		48	220.127	odd	20
880.2.cm.b.193.5		48	44.39	even	10
880.2.cm.b.497.5		48	20.7	even	4
880.2.cm.b.673.5		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.834729 - 0.132208i) q^{3} +(-2.08639 - 0.804354i) q^{5} +(-0.228981 - 1.44573i) q^{7} +(-2.17388 - 0.706335i) q^{9} +O(q^{10})\)	\(q+(-0.834729 - 0.132208i) q^{3} +(-2.08639 - 0.804354i) q^{5} +(-0.228981 - 1.44573i) q^{7} +(-2.17388 - 0.706335i) q^{9} +(-3.21121 - 0.829518i) q^{11} +(0.134489 + 0.263950i) q^{13} +(1.63523 + 0.947255i) q^{15} +(3.43144 - 6.73459i) q^{17} +(-4.63943 + 3.37075i) q^{19} +1.23707i q^{21} +(-5.96043 - 5.96043i) q^{23} +(3.70603 + 3.35639i) q^{25} +(3.98027 + 2.02805i) q^{27} +(6.71592 + 4.87940i) q^{29} +(-0.792277 + 2.43838i) q^{31} +(2.57083 + 1.11697i) q^{33} +(-0.685136 + 3.20054i) q^{35} +(2.12739 - 0.336946i) q^{37} +(-0.0773657 - 0.238107i) q^{39} +(-4.70705 - 6.47870i) q^{41} +(2.62512 - 2.62512i) q^{43} +(3.96741 + 3.22225i) q^{45} +(-1.04991 + 6.62887i) q^{47} +(4.61969 - 1.50103i) q^{49} +(-3.75469 + 5.16789i) q^{51} +(0.739201 - 0.376642i) q^{53} +(6.03261 + 4.31365i) q^{55} +(4.31831 - 2.20029i) q^{57} +(-0.495669 + 0.682230i) q^{59} +(-3.88340 + 1.26179i) q^{61} +(-0.523394 + 3.30458i) q^{63} +(-0.0682875 - 0.658879i) q^{65} +(8.77012 - 8.77012i) q^{67} +(4.18733 + 5.76336i) q^{69} +(-1.44164 - 4.43691i) q^{71} +(-4.17085 + 0.660597i) q^{73} +(-2.64979 - 3.29164i) q^{75} +(-0.463953 + 4.83250i) q^{77} +(-0.875685 + 2.69508i) q^{79} +(2.49330 + 1.81149i) q^{81} +(-9.19653 - 4.68587i) q^{83} +(-12.5763 + 11.2909i) q^{85} +(-4.96087 - 4.96087i) q^{87} -15.6361i q^{89} +(0.350805 - 0.254875i) q^{91} +(0.983710 - 1.93064i) q^{93} +(12.3909 - 3.30094i) q^{95} +(-3.85719 - 7.57015i) q^{97} +(6.39486 + 4.07146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7}+O(q^{10}) \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55} - 120 q^{57} - 40 q^{61} - 50 q^{63} - 72 q^{67} + 4 q^{71} - 20 q^{73} + 20 q^{75} - 36 q^{77} + 100 q^{81} + 40 q^{85} - 8 q^{91} - 14 q^{93} + 50 q^{95} + 6 q^{97}+O(q^{100}) \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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