LMFDB - Embedded newform 572.2.n.b.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			53.4
Character	$\chi$	$=$	572.53
Dual form			572.2.n.b.313.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0637055 + 0.0462848i) q^{3} +(-0.454508 - 1.39883i) q^{5} +(1.50470 + 1.09323i) q^{7} +(-0.925135 + 2.84727i) q^{9} +O(q^{10})$	\(q+(-0.0637055 + 0.0462848i) q^{3} +(-0.454508 - 1.39883i) q^{5} +(1.50470 + 1.09323i) q^{7} +(-0.925135 + 2.84727i) q^{9} +(1.73053 + 2.82936i) q^{11} +(-0.309017 + 0.951057i) q^{13} +(0.0936993 + 0.0680765i) q^{15} +(0.0702412 + 0.216180i) q^{17} +(1.31378 - 0.954514i) q^{19} -0.146457 q^{21} +3.95378 q^{23} +(2.29493 - 1.66737i) q^{25} +(-0.145849 - 0.448878i) q^{27} +(6.74550 + 4.90089i) q^{29} +(1.39377 - 4.28958i) q^{31} +(-0.241201 - 0.100148i) q^{33} +(0.845344 - 2.60170i) q^{35} +(5.67796 + 4.12528i) q^{37} +(-0.0243333 - 0.0748903i) q^{39} +(-4.20409 + 3.05445i) q^{41} -0.830272 q^{43} +4.40334 q^{45} +(-4.13705 + 3.00574i) q^{47} +(-1.09415 - 3.36744i) q^{49} +(-0.0144806 - 0.0105208i) q^{51} +(-4.48545 + 13.8048i) q^{53} +(3.17125 - 3.70669i) q^{55} +(-0.0395153 + 0.121616i) q^{57} +(-3.35105 - 2.43468i) q^{59} +(-0.318991 - 0.981754i) q^{61} +(-4.50477 + 3.27290i) q^{63} +1.47082 q^{65} -0.898415 q^{67} +(-0.251877 + 0.183000i) q^{69} +(-1.82363 - 5.61256i) q^{71} +(1.00515 + 0.730283i) q^{73} +(-0.0690262 + 0.212441i) q^{75} +(-0.489204 + 6.14919i) q^{77} +(1.58195 - 4.86875i) q^{79} +(-7.23604 - 5.25729i) q^{81} +(-2.53172 - 7.79184i) q^{83} +(0.270475 - 0.196511i) q^{85} -0.656562 q^{87} +4.23642 q^{89} +(-1.50470 + 1.09323i) q^{91} +(0.109752 + 0.337780i) q^{93} +(-1.93233 - 1.40392i) q^{95} +(3.31236 - 10.1944i) q^{97} +(-9.65693 + 2.30976i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−0.0637055	+	0.0462848i	−0.0367804	+	0.0267225i	−0.606024	−	0.795447i	$-0.707236\pi$
$3$	−0.0637055	+	0.0462848i	−0.0367804	+	0.0267225i	0.569243	+	0.822169i	$0.307236\pi$
$4$		0			0
$5$	−0.454508	−	1.39883i	−0.203262	−	0.625577i	−0.999780	−	0.0209620i	$-0.993327\pi$
$5$	−0.454508	−	1.39883i	−0.203262	−	0.625577i	0.796518	−	0.604615i	$-0.206673\pi$
$6$		0			0
$7$	1.50470	+	1.09323i	0.568723	+	0.413201i	0.834641	−	0.550794i	$-0.185675\pi$
$7$	1.50470	+	1.09323i	0.568723	+	0.413201i	−0.265918	+	0.963996i	$0.585675\pi$
$8$		0			0
$9$	−0.925135	+	2.84727i	−0.308378	+	0.949091i
$10$		0			0
$11$	1.73053	+	2.82936i	0.521775	+	0.853083i
$11$	1.73053	+	2.82936i	0.521775	+	0.853083i
$12$		0			0
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$		0			0
$15$	0.0936993	+	0.0680765i	0.0241930	+	0.0175773i
$16$		0			0
$17$	0.0702412	+	0.216180i	0.0170360	+	0.0524314i	0.959213	−	0.282684i	$-0.0912247\pi$
$17$	0.0702412	+	0.216180i	0.0170360	+	0.0524314i	−0.942177	+	0.335115i	$0.891225\pi$
$18$		0			0
$19$	1.31378	−	0.954514i	0.301401	−	0.218981i	−0.426797	−	0.904347i	$-0.640358\pi$
$19$	1.31378	−	0.954514i	0.301401	−	0.218981i	0.728198	+	0.685367i	$0.240358\pi$
$20$		0			0
$21$	−0.146457			−0.0319596
$22$		0			0
$23$	3.95378			0.824420			0.412210	−	0.911089i	$-0.364757\pi$
$23$	3.95378			0.824420			0.412210	+	0.911089i	$0.364757\pi$
$24$		0			0
$25$	2.29493	−	1.66737i	0.458986	−	0.333473i
$26$		0			0
$27$	−0.145849	−	0.448878i	−0.0280687	−	0.0863865i
$28$		0			0
$29$	6.74550	+	4.90089i	1.25261	+	0.910073i	0.998370	−	0.0570691i	$-0.0181755\pi$
$29$	6.74550	+	4.90089i	1.25261	+	0.910073i	0.254237	+	0.967142i	$0.418176\pi$
$30$		0			0
$31$	1.39377	−	4.28958i	0.250328	−	0.770432i	−0.744386	−	0.667750i	$-0.767258\pi$
$31$	1.39377	−	4.28958i	0.250328	−	0.770432i	0.994714	−	0.102682i	$-0.0327424\pi$
$32$		0			0
$33$	−0.241201	−	0.100148i	−0.0419876	−	0.0174336i
$34$		0			0
$35$	0.845344	−	2.60170i	0.142889	−	0.439768i
$36$		0			0
$37$	5.67796	+	4.12528i	0.933451	+	0.678192i	0.946835	−	0.321719i	$-0.104260\pi$
$37$	5.67796	+	4.12528i	0.933451	+	0.678192i	−0.0133843	+	0.999910i	$0.504260\pi$
$38$		0			0
$39$	−0.0243333	−	0.0748903i	−0.00389645	−	0.0119920i
$40$		0			0
$41$	−4.20409	+	3.05445i	−0.656568	+	0.477025i	−0.865502	−	0.500905i	$-0.833001\pi$
$41$	−4.20409	+	3.05445i	−0.656568	+	0.477025i	0.208934	+	0.977930i	$0.433001\pi$
$42$		0			0
$43$	−0.830272			−0.126615			−0.0633076	−	0.997994i	$-0.520165\pi$
$43$	−0.830272			−0.126615			−0.0633076	+	0.997994i	$0.520165\pi$
$44$		0			0
$45$	4.40334			0.656411
$46$		0			0
$47$	−4.13705	+	3.00574i	−0.603450	+	0.438432i	−0.847102	−	0.531431i	$-0.821655\pi$
$47$	−4.13705	+	3.00574i	−0.603450	+	0.438432i	0.243652	+	0.969863i	$0.421655\pi$
$48$		0			0
$49$	−1.09415	−	3.36744i	−0.156307	−	0.481063i
$50$		0			0
$51$	−0.0144806	−	0.0105208i	−0.00202769	−	0.00147320i
$52$		0			0
$53$	−4.48545	+	13.8048i	−0.616124	+	1.89624i	−0.233352	+	0.972392i	$0.574969\pi$
$53$	−4.48545	+	13.8048i	−0.616124	+	1.89624i	−0.382773	+	0.923843i	$0.625031\pi$
$54$		0			0
$55$	3.17125	−	3.70669i	0.427612	−	0.499810i
$56$		0			0
$57$	−0.0395153	+	0.121616i	−0.00523393	+	0.0161084i
$58$		0			0
$59$	−3.35105	−	2.43468i	−0.436270	−	0.316969i	0.347881	−	0.937539i	$-0.386901\pi$
$59$	−3.35105	−	2.43468i	−0.436270	−	0.316969i	−0.784151	+	0.620570i	$0.786901\pi$
$60$		0			0
$61$	−0.318991	−	0.981754i	−0.0408427	−	0.125701i	0.928556	−	0.371192i	$-0.121051\pi$
$61$	−0.318991	−	0.981754i	−0.0408427	−	0.125701i	−0.969399	+	0.245491i	$0.921051\pi$
$62$		0			0
$63$	−4.50477	+	3.27290i	−0.567547	+	0.412347i
$64$		0			0
$65$	1.47082			0.182433
$66$		0			0
$67$	−0.898415			−0.109759			−0.0548795	−	0.998493i	$-0.517477\pi$
$67$	−0.898415			−0.109759			−0.0548795	+	0.998493i	$0.517477\pi$
$68$		0			0
$69$	−0.251877	+	0.183000i	−0.0303225	+	0.0220306i
$70$		0			0
$71$	−1.82363	−	5.61256i	−0.216425	−	0.666088i	−0.999049	−	0.0435937i	$-0.986119\pi$
$71$	−1.82363	−	5.61256i	−0.216425	−	0.666088i	0.782624	−	0.622495i	$-0.213881\pi$
$72$		0			0
$73$	1.00515	+	0.730283i	0.117644	+	0.0854732i	0.645051	−	0.764139i	$-0.276836\pi$
$73$	1.00515	+	0.730283i	0.117644	+	0.0854732i	−0.527408	+	0.849612i	$0.676836\pi$
$74$		0			0
$75$	−0.0690262	+	0.212441i	−0.00797046	+	0.0245305i
$76$		0			0
$77$	−0.489204	+	6.14919i	−0.0557499	+	0.700766i
$78$		0			0
$79$	1.58195	−	4.86875i	0.177984	−	0.547777i	−0.821774	−	0.569814i	$-0.807015\pi$
$79$	1.58195	−	4.86875i	0.177984	−	0.547777i	0.999757	+	0.0220370i	$0.00701516\pi$
$80$		0			0
$81$	−7.23604	−	5.25729i	−0.804004	−	0.584143i
$82$		0			0
$83$	−2.53172	−	7.79184i	−0.277893	−	0.855266i	−0.988440	−	0.151616i	$-0.951552\pi$
$83$	−2.53172	−	7.79184i	−0.277893	−	0.855266i	0.710547	−	0.703650i	$-0.248448\pi$
$84$		0			0
$85$	0.270475	−	0.196511i	0.0293371	−	0.0213147i
$86$		0			0
$87$	−0.656562			−0.0703908
$88$		0			0
$89$	4.23642			0.449060			0.224530	−	0.974467i	$-0.427915\pi$
$89$	4.23642			0.449060			0.224530	+	0.974467i	$0.427915\pi$
$90$		0			0
$91$	−1.50470	+	1.09323i	−0.157735	+	0.114601i
$92$		0			0
$93$	0.109752	+	0.337780i	0.0113807	+	0.0350262i
$94$		0			0
$95$	−1.93233	−	1.40392i	−0.198253	−	0.144039i
$96$		0			0
$97$	3.31236	−	10.1944i	0.336319	−	1.03508i	−0.629750	−	0.776798i	$-0.716843\pi$
$97$	3.31236	−	10.1944i	0.336319	−	1.03508i	0.966069	−	0.258285i	$-0.0831575\pi$
$98$		0			0
$99$	−9.65693	+	2.30976i	−0.970558	+	0.232139i
$100$		0			0
$101$	−0.745601	+	2.29472i	−0.0741900	+	0.228333i	−0.981274	−	0.192616i	$-0.938303\pi$
$101$	−0.745601	+	2.29472i	−0.0741900	+	0.228333i	0.907084	+	0.420949i	$0.138303\pi$
$102$		0			0
$103$	−15.1924	−	11.0379i	−1.49695	−	1.08760i	−0.971575	−	0.236730i	$-0.923924\pi$
$103$	−15.1924	−	11.0379i	−1.49695	−	1.08760i	−0.525377	−	0.850870i	$-0.676076\pi$
$104$		0			0
$105$	0.0665661	+	0.204869i	0.00649618	+	0.0199932i
$106$		0			0
$107$	9.25136	−	6.72150i	0.894362	−	0.649792i	−0.0426493	−	0.999090i	$-0.513580\pi$
$107$	9.25136	−	6.72150i	0.894362	−	0.649792i	0.937012	+	0.349298i	$0.113580\pi$
$108$		0			0
$109$	15.1541			1.45150			0.725748	−	0.687960i	$-0.241494\pi$
$109$	15.1541			1.45150			0.725748	+	0.687960i	$0.241494\pi$
$110$		0			0
$111$	−0.552655			−0.0524557
$112$		0			0
$113$	−5.31386	+	3.86074i	−0.499885	+	0.363188i	−0.808973	−	0.587845i	$-0.799976\pi$
$113$	−5.31386	+	3.86074i	−0.499885	+	0.363188i	0.309088	+	0.951034i	$0.399976\pi$
$114$		0			0
$115$	−1.79702	−	5.53067i	−0.167573	−	0.515738i
$116$		0			0
$117$	−2.42203	−	1.75971i	−0.223917	−	0.162685i
$118$		0			0
$119$	−0.130642	+	0.402076i	−0.0119760	+	0.0368582i
$120$		0			0
$121$	−5.01053	+	9.79258i	−0.455502	+	0.890235i
$122$		0			0
$123$	0.126449	−	0.389171i	0.0114015	−	0.0350903i
$124$		0			0
$125$	−9.32502	−	6.77502i	−0.834055	−	0.605976i
$126$		0			0
$127$	0.315357	+	0.970569i	0.0279834	+	0.0861241i	0.964073	−	0.265638i	$-0.0855826\pi$
$127$	0.315357	+	0.970569i	0.0279834	+	0.0861241i	−0.936089	+	0.351762i	$0.885583\pi$
$128$		0			0
$129$	0.0528929	−	0.0384289i	0.00465696	−	0.00338348i
$130$		0			0
$131$	−12.3720			−1.08095			−0.540474	−	0.841360i	$-0.681755\pi$
$131$	−12.3720			−1.08095			−0.540474	+	0.841360i	$0.681755\pi$
$132$		0			0
$133$	3.02034			0.261897
$134$		0			0
$135$	−0.561615	+	0.408037i	−0.0483361	+	0.0351182i
$136$		0			0
$137$	0.583459	+	1.79570i	0.0498482	+	0.153417i	0.972882	−	0.231302i	$-0.0742984\pi$
$137$	0.583459	+	1.79570i	0.0498482	+	0.153417i	−0.923034	+	0.384719i	$0.874298\pi$
$138$		0			0
$139$	9.20675	+	6.68910i	0.780907	+	0.567362i	0.905251	−	0.424877i	$-0.139683\pi$
$139$	9.20675	+	6.68910i	0.780907	+	0.567362i	−0.124344	+	0.992239i	$0.539683\pi$
$140$		0			0
$141$	0.124433	−	0.382964i	0.0104791	−	0.0322514i
$142$		0			0
$143$	−3.22564	+	0.771513i	−0.269742	+	0.0645172i
$144$		0			0
$145$	3.78964	−	11.6633i	0.314712	−	0.968585i
$146$		0			0
$147$	0.225564	+	0.163882i	0.0186042	+	0.0135168i
$148$		0			0
$149$	−2.73343	−	8.41264i	−0.223932	−	0.689190i	−0.998398	−	0.0565759i	$-0.981982\pi$
$149$	−2.73343	−	8.41264i	−0.223932	−	0.689190i	0.774467	−	0.632615i	$-0.218018\pi$
$150$		0			0
$151$	−0.277105	+	0.201328i	−0.0225505	+	0.0163839i	−0.599003	−	0.800746i	$-0.704436\pi$
$151$	−0.277105	+	0.201328i	−0.0225505	+	0.0163839i	0.576453	+	0.817130i	$0.304436\pi$
$152$		0			0
$153$	−0.680507			−0.0550157
$154$		0			0
$155$	−6.63389			−0.532847
$156$		0			0
$157$	−14.3271	+	10.4092i	−1.14342	+	0.830746i	−0.987593	−	0.157038i	$-0.949806\pi$
$157$	−14.3271	+	10.4092i	−1.14342	+	0.830746i	−0.155831	+	0.987784i	$0.549806\pi$
$158$		0			0
$159$	−0.353204	−	1.08705i	−0.0280109	−	0.0862087i
$160$		0			0
$161$	5.94924	+	4.32238i	0.468866	+	0.340651i
$162$		0			0
$163$	2.80296	−	8.62662i	0.219545	−	0.675689i	−0.779255	−	0.626707i	$-0.784402\pi$
$163$	2.80296	−	8.62662i	0.219545	−	0.675689i	0.998800	−	0.0489820i	$-0.0155977\pi$
$164$		0			0
$165$	−0.0304633	+	0.382917i	−0.00237156	+	0.0298101i
$166$		0			0
$167$	4.35321	−	13.3978i	0.336862	−	1.03675i	−0.628936	−	0.777457i	$-0.716509\pi$
$167$	4.35321	−	13.3978i	0.336862	−	1.03675i	0.965798	−	0.259297i	$-0.0834907\pi$
$168$		0			0
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$		0			0
$171$	1.50234	+	4.62373i	0.114887	+	0.353586i
$172$		0			0
$173$	−20.1385	+	14.6315i	−1.53110	+	1.11241i	−0.575479	+	0.817817i	$0.695184\pi$
$173$	−20.1385	+	14.6315i	−1.53110	+	1.11241i	−0.955623	+	0.294594i	$0.904816\pi$
$174$		0			0
$175$	5.27599			0.398827
$176$		0			0
$177$	0.326169			0.0245164
$178$		0			0
$179$	−13.8074	+	10.0317i	−1.03202	+	0.749804i	−0.968711	−	0.248190i	$-0.920164\pi$
$179$	−13.8074	+	10.0317i	−1.03202	+	0.749804i	−0.0633053	+	0.997994i	$0.520164\pi$
$180$		0			0
$181$	1.99686	+	6.14570i	0.148425	+	0.456807i	0.997436	−	0.0715700i	$-0.0228009\pi$
$181$	1.99686	+	6.14570i	0.148425	+	0.456807i	−0.849010	+	0.528377i	$0.822801\pi$
$182$		0			0
$183$	0.0657618	+	0.0477787i	0.00486125	+	0.00353191i
$184$		0			0
$185$	3.18989	−	9.81749i	0.234526	−	0.721796i
$186$		0			0
$187$	−0.490097	+	0.572844i	−0.0358394	+	0.0418905i
$188$		0			0
$189$	0.271266	−	0.834872i	0.0197317	−	0.0607280i
$190$		0			0
$191$	−9.78015	−	7.10570i	−0.707667	−	0.514150i	0.174753	−	0.984612i	$-0.444087\pi$
$191$	−9.78015	−	7.10570i	−0.707667	−	0.514150i	−0.882420	+	0.470462i	$0.844087\pi$
$192$		0			0
$193$	−6.37921	−	19.6332i	−0.459186	−	1.41323i	−0.866150	−	0.499784i	$-0.833413\pi$
$193$	−6.37921	−	19.6332i	−0.459186	−	1.41323i	0.406964	−	0.913444i	$-0.366587\pi$
$194$		0			0
$195$	−0.0936993	+	0.0680765i	−0.00670994	+	0.00487506i
$196$		0			0
$197$	7.62934			0.543568			0.271784	−	0.962358i	$-0.412386\pi$
$197$	7.62934			0.543568			0.271784	+	0.962358i	$0.412386\pi$
$198$		0			0
$199$	3.30441			0.234243			0.117122	−	0.993118i	$-0.462633\pi$
$199$	3.30441			0.234243			0.117122	+	0.993118i	$0.462633\pi$
$200$		0			0
$201$	0.0572340	−	0.0415829i	0.00403698	−	0.00293304i
$202$		0			0
$203$	4.79215	+	14.7487i	0.336343	+	1.03516i
$204$		0			0
$205$	6.18345	+	4.49254i	0.431871	+	0.313773i
$206$		0			0
$207$	−3.65778	+	11.2575i	−0.254233	+	0.782449i
$208$		0			0
$209$	4.97419	+	2.06533i	0.344072	+	0.142862i
$210$		0			0
$211$	7.84965	−	24.1587i	0.540392	−	1.66316i	−0.191309	−	0.981530i	$-0.561273\pi$
$211$	7.84965	−	24.1587i	0.540392	−	1.66316i	0.731701	−	0.681626i	$-0.238727\pi$
$212$		0			0
$213$	0.375951	+	0.273145i	0.0257598	+	0.0187156i
$214$		0			0
$215$	0.377365	+	1.16141i	0.0257361	+	0.0792075i
$216$		0			0
$217$	6.78669	−	4.93082i	0.460711	−	0.334726i
$218$		0			0
$219$	−0.0978345			−0.00661104
$220$		0			0
$221$	−0.227305			−0.0152902
$222$		0			0
$223$	−9.85712	+	7.16162i	−0.660082	+	0.479577i	−0.866691	−	0.498846i	$-0.833757\pi$
$223$	−9.85712	+	7.16162i	−0.660082	+	0.479577i	0.206609	+	0.978424i	$0.433757\pi$
$224$		0			0
$225$	2.62432	+	8.07683i	0.174955	+	0.538456i
$226$		0			0
$227$	6.08902	+	4.42394i	0.404143	+	0.293627i	0.771226	−	0.636561i	$-0.219644\pi$
$227$	6.08902	+	4.42394i	0.404143	+	0.293627i	−0.367084	+	0.930188i	$0.619644\pi$
$228$		0			0
$229$	−5.21732	+	16.0573i	−0.344771	+	1.06109i	0.616936	+	0.787013i	$0.288374\pi$
$229$	−5.21732	+	16.0573i	−0.344771	+	1.06109i	−0.961707	+	0.274081i	$0.911626\pi$
$230$		0			0
$231$	−0.253449	−	0.414380i	−0.0166757	−	0.0272642i
$232$		0			0
$233$	−1.13846	+	3.50383i	−0.0745832	+	0.229543i	−0.981397	−	0.191987i	$-0.938507\pi$
$233$	−1.13846	+	3.50383i	−0.0745832	+	0.229543i	0.906814	+	0.421530i	$0.138507\pi$
$234$		0			0
$235$	6.08485	+	4.42090i	0.396932	+	0.288388i
$236$		0			0
$237$	0.124570	+	0.383387i	0.00809168	+	0.0249036i
$238$		0			0
$239$	21.3249	−	15.4934i	1.37939	−	1.00219i	0.382457	−	0.923973i	$-0.375078\pi$
$239$	21.3249	−	15.4934i	1.37939	−	1.00219i	0.996937	−	0.0782143i	$-0.0249218\pi$
$240$		0			0
$241$	22.0055			1.41750			0.708748	−	0.705461i	$-0.249260\pi$
$241$	22.0055			1.41750			0.708748	+	0.705461i	$0.249260\pi$
$242$		0			0
$243$	2.12024			0.136014
$244$		0			0
$245$	−4.21318	+	3.06106i	−0.269170	+	0.195564i
$246$		0			0
$247$	0.501818	+	1.54444i	0.0319299	+	0.0982702i
$248$		0			0
$249$	0.521928	+	0.379203i	0.0330759	+	0.0240310i
$250$		0			0
$251$	5.67184	−	17.4561i	0.358003	−	1.10182i	−0.596245	−	0.802803i	$-0.703341\pi$
$251$	5.67184	−	17.4561i	0.358003	−	1.10182i	0.954248	−	0.299017i	$-0.0966588\pi$
$252$		0			0
$253$	6.84214	+	11.1867i	0.430161	+	0.703299i
$254$		0			0
$255$	−0.00813525	+	0.0250377i	−0.000509449	+	0.00156792i
$256$		0			0
$257$	−11.4498	−	8.31875i	−0.714218	−	0.518910i	0.170314	−	0.985390i	$-0.445522\pi$
$257$	−11.4498	−	8.31875i	−0.714218	−	0.518910i	−0.884532	+	0.466480i	$0.845522\pi$
$258$		0			0
$259$	4.03375	+	12.4146i	0.250645	+	0.771406i
$260$		0			0
$261$	−20.1947	+	14.6723i	−1.25002	+	0.908192i
$262$		0			0
$263$	20.3289			1.25353			0.626766	−	0.779208i	$-0.284378\pi$
$263$	20.3289			1.25353			0.626766	+	0.779208i	$0.284378\pi$
$264$		0			0
$265$	21.3493			1.31148
$266$		0			0
$267$	−0.269883	+	0.196082i	−0.0165166	+	0.0120000i
$268$		0			0
$269$	2.34701	+	7.22335i	0.143100	+	0.440416i	0.996762	−	0.0804117i	$-0.0256235\pi$
$269$	2.34701	+	7.22335i	0.143100	+	0.440416i	−0.853662	+	0.520827i	$0.825624\pi$
$270$		0			0
$271$	9.23748	+	6.71142i	0.561137	+	0.407690i	0.831875	−	0.554963i	$-0.187268\pi$
$271$	9.23748	+	6.71142i	0.561137	+	0.407690i	−0.270738	+	0.962653i	$0.587268\pi$
$272$		0			0
$273$	0.0452578	−	0.139289i	0.00273913	−	0.00843017i
$274$		0			0
$275$	8.68902	+	3.60775i	0.523968	+	0.217556i
$276$		0			0
$277$	0.564827	−	1.73836i	0.0339372	−	0.104448i	−0.932653	−	0.360775i	$-0.882512\pi$
$277$	0.564827	−	1.73836i	0.0339372	−	0.104448i	0.966590	+	0.256327i	$0.0825123\pi$
$278$		0			0
$279$	10.9242	+	7.93689i	0.654014	+	0.475169i
$280$		0			0
$281$	−1.21526	−	3.74017i	−0.0724961	−	0.223120i	0.908243	−	0.418444i	$-0.137424\pi$
$281$	−1.21526	−	3.74017i	−0.0724961	−	0.223120i	−0.980739	+	0.195324i	$0.937424\pi$
$282$		0			0
$283$	13.8070	−	10.0314i	0.820740	−	0.596302i	−0.0961847	−	0.995364i	$-0.530664\pi$
$283$	13.8070	−	10.0314i	0.820740	−	0.596302i	0.916924	+	0.399061i	$0.130664\pi$
$284$		0			0
$285$	0.188080			0.0111409
$286$		0			0
$287$	−9.66509			−0.570512
$288$		0			0
$289$	13.7115	−	9.96198i	0.806558	−	0.585999i
$290$		0			0
$291$	0.260829	+	0.802751i	0.0152901	+	0.0470581i
$292$		0			0
$293$	−11.3576	−	8.25181i	−0.663520	−	0.482076i	0.204330	−	0.978902i	$-0.434499\pi$
$293$	−11.3576	−	8.25181i	−0.663520	−	0.482076i	−0.867850	+	0.496826i	$0.834499\pi$
$294$		0			0
$295$	−1.88263	+	5.79414i	−0.109611	+	0.337348i
$296$		0			0
$297$	1.01764	−	1.18946i	0.0590494	−	0.0690192i
$298$		0			0
$299$	−1.22178	+	3.76027i	−0.0706576	+	0.217462i
$300$		0			0
$301$	−1.24931	−	0.907676i	−0.0720090	−	0.0523176i
$302$		0			0
$303$	−0.0587118	−	0.180696i	−0.00337291	−	0.0103807i
$304$		0			0
$305$	−1.22833	+	0.892430i	−0.0703337	+	0.0511004i
$306$		0			0
$307$	−26.8898			−1.53468			−0.767340	−	0.641240i	$-0.778420\pi$
$307$	−26.8898			−1.53468			−0.767340	+	0.641240i	$0.778420\pi$
$308$		0			0
$309$	1.47873			0.0841219
$310$		0			0
$311$	−20.4522	+	14.8594i	−1.15974	+	0.842601i	−0.989745	−	0.142844i	$-0.954375\pi$
$311$	−20.4522	+	14.8594i	−1.15974	+	0.842601i	−0.169995	+	0.985445i	$0.554375\pi$
$312$		0			0
$313$	−4.82446	−	14.8482i	−0.272695	−	0.839268i	−0.989820	−	0.142324i	$-0.954543\pi$
$313$	−4.82446	−	14.8482i	−0.272695	−	0.839268i	0.717125	−	0.696944i	$-0.245457\pi$
$314$		0			0
$315$	6.62569	+	4.81385i	0.373316	+	0.271230i
$316$		0			0
$317$	0.946778	−	2.91388i	0.0531764	−	0.163660i	−0.920941	−	0.389701i	$-0.872578\pi$
$317$	0.946778	−	2.91388i	0.0531764	−	0.163660i	0.974118	+	0.226041i	$0.0725783\pi$
$318$		0			0
$319$	−2.19308	+	27.5666i	−0.122789	+	1.54343i
$320$		0			0
$321$	−0.278259	+	0.856394i	−0.0155309	+	0.0477992i
$322$		0			0
$323$	0.298629	+	0.216966i	0.0166161	+	0.0120723i
$324$		0			0
$325$	0.876586	+	2.69785i	0.0486242	+	0.149650i
$326$		0			0
$327$	−0.965398	+	0.701403i	−0.0533866	+	0.0387877i
$328$		0			0
$329$	−9.51097			−0.524357
$330$		0			0
$331$	22.4435			1.23361			0.616804	−	0.787117i	$-0.288427\pi$
$331$	22.4435			1.23361			0.616804	+	0.787117i	$0.288427\pi$
$332$		0			0
$333$	−16.9987	+	12.3503i	−0.931522	+	0.676790i
$334$		0			0
$335$	0.408337	+	1.25673i	0.0223098	+	0.0686626i
$336$		0			0
$337$	6.35800	+	4.61936i	0.346343	+	0.251633i	0.747333	−	0.664450i	$-0.231334\pi$
$337$	6.35800	+	4.61936i	0.346343	+	0.251633i	−0.400991	+	0.916082i	$0.631334\pi$
$338$		0			0
$339$	0.159828	−	0.491901i	0.00868069	−	0.0267164i
$340$		0			0
$341$	14.5487	−	3.47978i	0.787858	−	0.188441i
$342$		0			0
$343$	6.05822	−	18.6453i	0.327113	−	1.00675i
$344$		0			0
$345$	0.370466	+	0.269159i	0.0199452	+	0.0144911i
$346$		0			0
$347$	2.56937	+	7.90772i	0.137931	+	0.424509i	0.996034	−	0.0889686i	$-0.0283571\pi$
$347$	2.56937	+	7.90772i	0.137931	+	0.424509i	−0.858103	+	0.513477i	$0.828357\pi$
$348$		0			0
$349$	22.9864	−	16.7006i	1.23044	−	0.893963i	0.233512	−	0.972354i	$-0.424978\pi$
$349$	22.9864	−	16.7006i	1.23044	−	0.893963i	0.996923	+	0.0783904i	$0.0249781\pi$
$350$		0			0
$351$	0.471978			0.0251923
$352$		0			0
$353$	8.45822			0.450185			0.225093	−	0.974337i	$-0.427732\pi$
$353$	8.45822			0.450185			0.225093	+	0.974337i	$0.427732\pi$
$354$		0			0
$355$	−7.02217	+	5.10191i	−0.372698	+	0.270781i
$356$		0			0
$357$	−0.0102873	−	0.0316612i	−0.000544464	−	0.00167569i
$358$		0			0
$359$	26.5011	+	19.2541i	1.39867	+	1.01619i	0.994850	+	0.101358i	$0.0323186\pi$
$359$	26.5011	+	19.2541i	1.39867	+	1.01619i	0.403822	+	0.914837i	$0.367681\pi$
$360$		0			0
$361$	−5.05641	+	15.5620i	−0.266127	+	0.819055i
$362$		0			0
$363$	−0.134049	−	0.855752i	−0.00703576	−	0.0449154i
$364$		0			0
$365$	0.564695	−	1.73795i	0.0295575	−	0.0909687i
$366$		0			0
$367$	−5.12683	−	3.72486i	−0.267618	−	0.194436i	0.445880	−	0.895093i	$-0.352891\pi$
$367$	−5.12683	−	3.72486i	−0.267618	−	0.194436i	−0.713499	+	0.700656i	$0.752891\pi$
$368$		0			0
$369$	−4.80750	−	14.7960i	−0.250268	−	0.770247i
$370$		0			0
$371$	−21.8410	+	15.8684i	−1.13393	+	0.823849i
$372$		0			0
$373$	−12.0415			−0.623485			−0.311742	−	0.950167i	$-0.600913\pi$
$373$	−12.0415			−0.623485			−0.311742	+	0.950167i	$0.600913\pi$
$374$		0			0
$375$	0.907635			0.0468701
$376$		0			0
$377$	−6.74550	+	4.90089i	−0.347411	+	0.252409i
$378$		0			0
$379$	−9.02953	−	27.7900i	−0.463816	−	1.42748i	−0.860466	−	0.509509i	$-0.829827\pi$
$379$	−9.02953	−	27.7900i	−0.463816	−	1.42748i	0.396650	−	0.917970i	$-0.370173\pi$
$380$		0			0
$381$	−0.0650125	−	0.0472344i	−0.00333069	−	0.00241989i
$382$		0			0
$383$	−2.03744	+	6.27058i	−0.104108	+	0.320412i	−0.989520	−	0.144395i	$-0.953876\pi$
$383$	−2.03744	+	6.27058i	−0.104108	+	0.320412i	0.885412	+	0.464807i	$0.153876\pi$
$384$		0			0
$385$	8.82404	−	2.11054i	0.449714	−	0.107563i
$386$		0			0
$387$	0.768113	−	2.36401i	0.0390454	−	0.120169i
$388$		0			0
$389$	9.25961	+	6.72750i	0.469481	+	0.341098i	0.797239	−	0.603664i	$-0.206293\pi$
$389$	9.25961	+	6.72750i	0.469481	+	0.341098i	−0.327758	+	0.944762i	$0.606293\pi$
$390$		0			0
$391$	0.277718	+	0.854729i	0.0140448	+	0.0432255i
$392$		0			0
$393$	0.788166	−	0.572636i	0.0397577	−	0.0288857i
$394$		0			0
$395$	−7.52957			−0.378854
$396$		0			0
$397$	13.9006			0.697649			0.348825	−	0.937188i	$-0.386581\pi$
$397$	13.9006			0.697649			0.348825	+	0.937188i	$0.386581\pi$
$398$		0			0
$399$	−0.192412	+	0.139796i	−0.00963266	+	0.00699854i
$400$		0			0
$401$	6.07128	+	18.6855i	0.303185	+	0.933109i	0.980348	+	0.197275i	$0.0632093\pi$
$401$	6.07128	+	18.6855i	0.303185	+	0.933109i	−0.677163	+	0.735833i	$0.736791\pi$
$402$		0			0
$403$	3.64894	+	2.65111i	0.181767	+	0.132061i
$404$		0			0
$405$	−4.06523	+	12.5115i	−0.202003	+	0.621700i
$406$		0			0
$407$	−1.84600	+	23.2039i	−0.0915030	+	1.15017i
$408$		0			0
$409$	12.4677	−	38.3715i	0.616486	−	1.89735i	0.240981	−	0.970530i	$-0.422531\pi$
$409$	12.4677	−	38.3715i	0.616486	−	1.89735i	0.375505	−	0.926820i	$-0.377469\pi$
$410$		0			0
$411$	−0.120283	−	0.0873908i	−0.00593313	−	0.00431067i
$412$		0			0
$413$	−2.38066	−	7.32692i	−0.117145	−	0.360534i
$414$		0			0
$415$	−9.74879	+	7.08291i	−0.478549	+	0.347686i
$416$		0			0
$417$	−0.896124			−0.0438834
$418$		0			0
$419$	17.1111			0.835932			0.417966	−	0.908463i	$-0.362743\pi$
$419$	17.1111			0.835932			0.417966	+	0.908463i	$0.362743\pi$
$420$		0			0
$421$	6.33282	−	4.60107i	0.308643	−	0.224242i	−0.422671	−	0.906283i	$-0.638907\pi$
$421$	6.33282	−	4.60107i	0.308643	−	0.224242i	0.731314	+	0.682041i	$0.238907\pi$
$422$		0			0
$423$	−4.73084	−	14.5600i	−0.230021	−	0.707932i
$424$		0			0
$425$	0.521651	+	0.379001i	0.0253038	+	0.0183843i
$426$		0			0
$427$	0.593295	−	1.82597i	0.0287116	−	0.0883651i
$428$		0			0
$429$	0.169782	−	0.198448i	0.00819715	−	0.00958115i
$430$		0			0
$431$	−4.36299	+	13.4279i	−0.210158	+	0.646799i	0.789304	+	0.614002i	$0.210441\pi$
$431$	−4.36299	+	13.4279i	−0.210158	+	0.646799i	−0.999462	+	0.0327969i	$0.989559\pi$
$432$		0			0
$433$	−13.3610	−	9.70735i	−0.642089	−	0.466505i	0.218478	−	0.975842i	$-0.429891\pi$
$433$	−13.3610	−	9.70735i	−0.642089	−	0.466505i	−0.860567	+	0.509337i	$0.829891\pi$
$434$		0			0
$435$	0.298413	+	0.918420i	0.0143078	+	0.0440349i
$436$		0			0
$437$	5.19438	−	3.77394i	0.248481	−	0.180532i
$438$		0			0
$439$	32.2430			1.53887			0.769437	−	0.638722i	$-0.220537\pi$
$439$	32.2430			1.53887			0.769437	+	0.638722i	$0.220537\pi$
$440$		0			0
$441$	10.6003			0.504774
$442$		0			0
$443$	−14.6192	+	10.6215i	−0.694578	+	0.504641i	−0.878162	−	0.478364i	$-0.841230\pi$
$443$	−14.6192	+	10.6215i	−0.694578	+	0.504641i	0.183584	+	0.983004i	$0.441230\pi$
$444$		0			0
$445$	−1.92549	−	5.92604i	−0.0912768	−	0.280921i
$446$		0			0
$447$	0.563512	+	0.409415i	0.0266532	+	0.0193647i
$448$		0			0
$449$	7.30583	−	22.4850i	0.344783	−	1.06113i	−0.616916	−	0.787029i	$-0.711618\pi$
$449$	7.30583	−	22.4850i	0.344783	−	1.06113i	0.961700	−	0.274105i	$-0.0883816\pi$
$450$		0			0
$451$	−15.9174	−	6.60905i	−0.749523	−	0.311208i
$452$		0			0
$453$	0.00833466	−	0.0256514i	0.000391596	−	0.00120521i
$454$		0			0
$455$	2.21314	+	1.60794i	0.103754	+	0.0753814i
$456$		0			0
$457$	−5.35548	−	16.4825i	−0.250519	−	0.771017i	−0.994680	−	0.103017i	$-0.967150\pi$
$457$	−5.35548	−	16.4825i	−0.250519	−	0.771017i	0.744161	−	0.668000i	$-0.232850\pi$
$458$		0			0
$459$	0.0867939	−	0.0630594i	0.00405119	−	0.00294336i
$460$		0			0
$461$	−15.8687			−0.739079			−0.369540	−	0.929215i	$-0.620485\pi$
$461$	−15.8687			−0.739079			−0.369540	+	0.929215i	$0.620485\pi$
$462$		0			0
$463$	−34.7822			−1.61647			−0.808233	−	0.588863i	$-0.799576\pi$
$463$	−34.7822			−1.61647			−0.808233	+	0.588863i	$0.799576\pi$
$464$		0			0
$465$	0.422615	−	0.307048i	0.0195983	−	0.0142390i
$466$		0			0
$467$	−2.92397	−	8.99905i	−0.135305	−	0.416427i	0.860332	−	0.509734i	$-0.170256\pi$
$467$	−2.92397	−	8.99905i	−0.135305	−	0.416427i	−0.995637	+	0.0933073i	$0.970256\pi$
$468$		0			0
$469$	−1.35184	−	0.982172i	−0.0624224	−	0.0453525i
$470$		0			0
$471$	0.430924	−	1.32625i	0.0198559	−	0.0611103i
$472$		0			0
$473$	−1.43681	−	2.34914i	−0.0660646	−	0.108013i
$474$		0			0
$475$	1.42350	−	4.38109i	0.0653148	−	0.201018i
$476$		0			0
$477$	−35.1564	−	25.5426i	−1.60970	−	1.16952i
$478$		0			0
$479$	−4.04176	−	12.4393i	−0.184673	−	0.568364i	0.815270	−	0.579081i	$-0.196589\pi$
$479$	−4.04176	−	12.4393i	−0.184673	−	0.568364i	−0.999943	+	0.0107169i	$0.996589\pi$
$480$		0			0
$481$	−5.67796	+	4.12528i	−0.258893	+	0.188097i
$482$		0			0
$483$	−0.579060			−0.0263481
$484$		0			0
$485$	−15.7657			−0.715885
$486$		0			0
$487$	12.2188	−	8.87747i	0.553686	−	0.402276i	−0.275457	−	0.961313i	$-0.588829\pi$
$487$	12.2188	−	8.87747i	0.553686	−	0.402276i	0.829143	+	0.559037i	$0.188829\pi$
$488$		0			0
$489$	0.220717	+	0.679298i	0.00998118	+	0.0307189i
$490$		0			0
$491$	−15.7971	−	11.4772i	−0.712911	−	0.517960i	0.171200	−	0.985236i	$-0.445235\pi$
$491$	−15.7971	−	11.4772i	−0.712911	−	0.517960i	−0.884111	+	0.467276i	$0.845235\pi$
$492$		0			0
$493$	−0.585664	+	1.80249i	−0.0263770	+	0.0811800i
$494$		0			0
$495$	7.62011	+	12.4586i	0.342498	+	0.559973i
$496$		0			0
$497$	3.39179	−	10.4389i	0.152143	−	0.468247i
$498$		0			0
$499$	3.64226	+	2.64626i	0.163050	+	0.118463i	0.666318	−	0.745667i	$-0.267869\pi$
$499$	3.64226	+	2.64626i	0.163050	+	0.118463i	−0.503268	+	0.864130i	$0.667869\pi$
$500$		0			0
$501$	0.342791	+	1.05500i	0.0153148	+	0.0471340i
$502$		0			0
$503$	15.8140	−	11.4895i	0.705110	−	0.512292i	−0.176483	−	0.984304i	$-0.556472\pi$
$503$	15.8140	−	11.4895i	0.705110	−	0.512292i	0.881592	+	0.472012i	$0.156472\pi$
$504$		0			0
$505$	3.54881			0.157920
$506$		0			0
$507$	0.0787443			0.00349716
$508$		0			0
$509$	−23.5326	+	17.0974i	−1.04306	+	0.757831i	−0.970881	−	0.239561i	$-0.922997\pi$
$509$	−23.5326	+	17.0974i	−1.04306	+	0.757831i	−0.0721832	+	0.997391i	$0.522997\pi$
$510$		0			0
$511$	0.714080	+	2.19771i	0.0315890	+	0.0972211i
$512$		0			0
$513$	−0.620073	−	0.450510i	−0.0273769	−	0.0198905i
$514$		0			0
$515$	−8.53514	+	26.2685i	−0.376103	+	1.15753i
$516$		0			0
$517$	−15.6636	−	6.50366i	−0.688884	−	0.286030i
$518$		0			0
$519$	0.605719	−	1.86421i	0.0265881	−	0.0818298i
$520$		0			0
$521$	−21.9874	−	15.9748i	−0.963285	−	0.699868i	−0.00937380	−	0.999956i	$-0.502984\pi$
$521$	−21.9874	−	15.9748i	−0.963285	−	0.699868i	−0.953911	+	0.300088i	$0.902984\pi$
$522$		0			0
$523$	9.88166	+	30.4126i	0.432095	+	1.32985i	0.896035	+	0.443984i	$0.146435\pi$
$523$	9.88166	+	30.4126i	0.432095	+	1.32985i	−0.463940	+	0.885867i	$0.653565\pi$
$524$		0			0
$525$	−0.336110	+	0.244198i	−0.0146690	+	0.0106577i
$526$		0			0
$527$	1.02522			0.0446594
$528$		0			0
$529$	−7.36764			−0.320332
$530$		0			0
$531$	10.0324	−	7.28895i	0.435368	−	0.316313i
$532$		0			0
$533$	−1.60582	−	4.94220i	−0.0695557	−	0.214071i
$534$		0			0
$535$	−13.6071	−	9.88612i	−0.588285	−	0.427414i
$536$		0			0
$537$	0.415296	−	1.27815i	0.0179213	−	0.0551562i
$538$		0			0
$539$	7.63423	−	8.92319i	0.328830	−	0.384349i
$540$		0			0
$541$	−4.86142	+	14.9619i	−0.209009	+	0.643263i	0.790516	+	0.612441i	$0.209812\pi$
$541$	−4.86142	+	14.9619i	−0.209009	+	0.643263i	−0.999525	+	0.0308218i	$0.990188\pi$
$542$		0			0
$543$	−0.411664	−	0.299091i	−0.0176662	−	0.0128352i
$544$		0			0
$545$	−6.88765	−	21.1980i	−0.295034	−	0.908023i
$546$		0			0
$547$	−17.9761	+	13.0604i	−0.768602	+	0.558422i	−0.901537	−	0.432703i	$-0.857560\pi$
$547$	−17.9761	+	13.0604i	−0.768602	+	0.558422i	0.132935	+	0.991125i	$0.457560\pi$
$548$		0			0
$549$	3.09043			0.131896
$550$		0			0
$551$	13.5400			0.576825
$552$		0			0
$553$	7.70301	−	5.59657i	0.327565	−	0.237990i
$554$		0			0
$555$	0.251186	+	0.773072i	0.0106623	+	0.0328151i
$556$		0			0
$557$	3.64434	+	2.64777i	0.154416	+	0.112190i	0.662310	−	0.749230i	$-0.269576\pi$
$557$	3.64434	+	2.64777i	0.154416	+	0.112190i	−0.507895	+	0.861419i	$0.669576\pi$
$558$		0			0
$559$	0.256568	−	0.789635i	0.0108517	−	0.0333980i
$560$		0			0
$561$	0.00470790	−	0.0591774i	0.000198768	−	0.00249847i
$562$		0			0
$563$	−3.62655	+	11.1614i	−0.152841	+	0.470395i	−0.997936	−	0.0642208i	$-0.979544\pi$
$563$	−3.62655	+	11.1614i	−0.152841	+	0.470395i	0.845095	+	0.534616i	$0.179544\pi$
$564$		0			0
$565$	7.81572	+	5.67845i	0.328810	+	0.238894i
$566$		0			0
$567$	−5.14064	−	15.8213i	−0.215887	−	0.664431i
$568$		0			0
$569$	−1.84286	+	1.33891i	−0.0772565	+	0.0561301i	−0.625743	−	0.780029i	$-0.715204\pi$
$569$	−1.84286	+	1.33891i	−0.0772565	+	0.0561301i	0.548487	+	0.836159i	$0.315204\pi$
$570$		0			0
$571$	−18.5798			−0.777539			−0.388769	−	0.921335i	$-0.627100\pi$
$571$	−18.5798			−0.777539			−0.388769	+	0.921335i	$0.627100\pi$
$572$		0			0
$573$	0.951935			0.0397677
$574$		0			0
$575$	9.07365	−	6.59239i	0.378397	−	0.274922i
$576$		0			0
$577$	−4.58700	−	14.1173i	−0.190959	−	0.587712i	0.809041	−	0.587752i	$-0.199987\pi$
$577$	−4.58700	−	14.1173i	−0.190959	−	0.587712i	−1.00000		4.05252e-5i	$0.999987\pi$
$578$		0			0
$579$	1.31511	+	0.955482i	0.0546540	+	0.0397085i
$580$		0			0
$581$	4.70878	−	14.4921i	0.195353	−	0.601234i
$582$		0			0
$583$	−46.8209	+	11.1987i	−1.93912	+	0.463802i
$584$		0			0
$585$	−1.36071	+	4.18782i	−0.0562583	+	0.173145i
$586$		0			0
$587$	25.1085	+	18.2424i	1.03634	+	0.752945i	0.969568	−	0.244823i	$-0.0787298\pi$
$587$	25.1085	+	18.2424i	1.03634	+	0.752945i	0.0667725	+	0.997768i	$0.478730\pi$
$588$		0			0
$589$	−2.26337	−	6.96593i	−0.0932604	−	0.287026i
$590$		0			0
$591$	−0.486031	+	0.353122i	−0.0199926	+	0.0145255i
$592$		0			0
$593$	−34.2425			−1.40617			−0.703086	−	0.711104i	$-0.748195\pi$
$593$	−34.2425			−1.40617			−0.703086	+	0.711104i	$0.748195\pi$
$594$		0			0
$595$	0.621815			0.0254919
$596$		0			0
$597$	−0.210509	+	0.152944i	−0.00861556	+	0.00625957i
$598$		0			0
$599$	3.40213	+	10.4707i	0.139007	+	0.427820i	0.996192	−	0.0871892i	$-0.0277885\pi$
$599$	3.40213	+	10.4707i	0.139007	+	0.427820i	−0.857185	+	0.515009i	$0.827788\pi$
$600$		0			0
$601$	−9.22992	−	6.70593i	−0.376496	−	0.273541i	0.383403	−	0.923581i	$-0.374752\pi$
$601$	−9.22992	−	6.70593i	−0.376496	−	0.273541i	−0.759900	+	0.650040i	$0.774752\pi$
$602$		0			0
$603$	0.831155	−	2.55803i	0.0338473	−	0.104171i
$604$		0			0
$605$	15.9755	+	2.55808i	0.649496	+	0.104001i
$606$		0			0
$607$	−7.46723	+	22.9818i	−0.303086	+	0.932802i	0.677299	+	0.735708i	$0.263150\pi$
$607$	−7.46723	+	22.9818i	−0.303086	+	0.932802i	−0.980385	+	0.197094i	$0.936850\pi$
$608$		0			0
$609$	−0.987928	−	0.717772i	−0.0400329	−	0.0290856i
$610$		0			0
$611$	−1.58021	−	4.86339i	−0.0639285	−	0.196752i
$612$		0			0
$613$	−10.2829	+	7.47098i	−0.415324	+	0.301750i	−0.775753	−	0.631036i	$-0.782630\pi$
$613$	−10.2829	+	7.47098i	−0.415324	+	0.301750i	0.360430	+	0.932786i	$0.382630\pi$
$614$		0			0
$615$	−0.601856			−0.0242692
$616$		0			0
$617$	−9.31402			−0.374968			−0.187484	−	0.982268i	$-0.560033\pi$
$617$	−9.31402			−0.374968			−0.187484	+	0.982268i	$0.560033\pi$
$618$		0			0
$619$	21.8220	−	15.8546i	0.877099	−	0.637250i	−0.0553836	−	0.998465i	$-0.517638\pi$
$619$	21.8220	−	15.8546i	0.877099	−	0.637250i	0.932482	+	0.361216i	$0.117638\pi$
$620$		0			0
$621$	−0.576655	−	1.77476i	−0.0231404	−	0.0712188i
$622$		0			0
$623$	6.37454	+	4.63137i	0.255390	+	0.185552i
$624$		0			0
$625$	−0.855891	+	2.63416i	−0.0342356	+	0.105366i
$626$		0			0
$627$	−0.412477	+	0.0986567i	−0.0164727	+	0.00393997i
$628$		0			0
$629$	−0.492977	+	1.51723i	−0.0196563	+	0.0604959i
$630$		0			0
$631$	−31.7683	−	23.0810i	−1.26468	−	0.918840i	−0.265698	−	0.964056i	$-0.585602\pi$
$631$	−31.7683	−	23.0810i	−1.26468	−	0.918840i	−0.998977	+	0.0452159i	$0.985602\pi$
$632$		0			0
$633$	0.618115	+	1.90236i	0.0245679	+	0.0756122i
$634$		0			0
$635$	1.21433	−	0.882263i	0.0481892	−	0.0350115i
$636$		0			0
$637$	3.54074			0.140289
$638$		0			0
$639$	17.6676			0.698919
$640$		0			0
$641$	4.71609	−	3.42644i	0.186274	−	0.135336i	−0.490740	−	0.871306i	$-0.663273\pi$
$641$	4.71609	−	3.42644i	0.186274	−	0.135336i	0.677014	+	0.735970i	$0.263273\pi$
$642$		0			0
$643$	−10.2064	−	31.4121i	−0.402502	−	1.23877i	−0.922963	−	0.384888i	$-0.874240\pi$
$643$	−10.2064	−	31.4121i	−0.402502	−	1.23877i	0.520461	−	0.853885i	$-0.325760\pi$
$644$		0			0
$645$	−0.0777959	−	0.0565220i	−0.00306321	−	0.00222555i
$646$		0			0
$647$	8.20960	−	25.2666i	0.322753	−	0.993331i	−0.649692	−	0.760198i	$-0.725102\pi$
$647$	8.20960	−	25.2666i	0.322753	−	0.993331i	0.972445	−	0.233133i	$-0.0748979\pi$
$648$		0			0
$649$	1.08949	−	13.6946i	0.0427660	−	0.537561i
$650$		0			0
$651$	−0.204128	+	0.628241i	−0.00800040	+	0.0246227i
$652$		0			0
$653$	−28.4759	−	20.6890i	−1.11435	−	0.809622i	−0.131006	−	0.991382i	$-0.541821\pi$
$653$	−28.4759	−	20.6890i	−1.11435	−	0.809622i	−0.983343	+	0.181760i	$0.941821\pi$
$654$		0			0
$655$	5.62319	+	17.3064i	0.219716	+	0.676216i
$656$		0			0
$657$	−3.00921	+	2.18632i	−0.117401	+	0.0852965i
$658$		0			0
$659$	38.6546			1.50577			0.752884	−	0.658153i	$-0.228662\pi$
$659$	38.6546			1.50577			0.752884	+	0.658153i	$0.228662\pi$
$660$		0			0
$661$	27.4090			1.06609			0.533043	−	0.846088i	$-0.321048\pi$
$661$	27.4090			1.06609			0.533043	+	0.846088i	$0.321048\pi$
$662$		0			0
$663$	0.0144806	−	0.0105208i	0.000562380	−	0.000408593i
$664$		0			0
$665$	−1.37277	−	4.22495i	−0.0532337	−	0.163836i
$666$		0			0
$667$	26.6702	+	19.3770i	1.03267	+	0.750282i
$668$		0			0
$669$	0.296479	−	0.912469i	0.0114625	−	0.0352781i
$670$		0			0
$671$	2.22571	−	2.60150i	0.0859226	−	0.100430i
$672$		0			0
$673$	−10.6687	+	32.8350i	−0.411249	+	1.26570i	0.504314	+	0.863520i	$0.331746\pi$
$673$	−10.6687	+	32.8350i	−0.411249	+	1.26570i	−0.915563	+	0.402175i	$0.868254\pi$
$674$		0			0
$675$	−1.08316	−	0.786960i	−0.0416907	−	0.0302901i
$676$		0			0
$677$	12.9555	+	39.8730i	0.497921	+	1.53244i	0.812355	+	0.583163i	$0.198185\pi$
$677$	12.9555	+	39.8730i	0.497921	+	1.53244i	−0.314434	+	0.949279i	$0.601815\pi$
$678$		0			0
$679$	16.1289	−	11.7183i	0.618970	−	0.449708i
$680$		0			0
$681$	−0.592665			−0.0227110
$682$		0			0
$683$	−29.7781			−1.13943			−0.569715	−	0.821843i	$-0.692946\pi$
$683$	−29.7781			−1.13943			−0.569715	+	0.821843i	$0.692946\pi$
$684$		0			0
$685$	2.24670	−	1.63232i	0.0858419	−	0.0623678i
$686$		0			0
$687$	−0.410835	−	1.26442i	−0.0156743	−	0.0482406i
$688$		0			0
$689$	−11.7431	−	8.53184i	−0.447375	−	0.325037i
$690$		0			0
$691$	0.0331122	−	0.101909i	0.00125965	−	0.00387679i	−0.950425	−	0.310955i	$-0.899351\pi$
$691$	0.0331122	−	0.101909i	0.00125965	−	0.00387679i	0.951684	+	0.307078i	$0.0993512\pi$
$692$		0			0
$693$	−17.0558	−	7.08173i	−0.647898	−	0.269013i
$694$		0			0
$695$	5.17238	−	15.9189i	0.196200	−	0.603840i
$696$		0			0
$697$	−0.955612	−	0.694293i	−0.0361964	−	0.0262982i
$698$		0			0
$699$	−0.0896475	−	0.275907i	−0.00339078	−	0.0104357i
$700$		0			0
$701$	9.31044	−	6.76443i	0.351650	−	0.255489i	−0.397911	−	0.917424i	$-0.630265\pi$
$701$	9.31044	−	6.76443i	0.351650	−	0.255489i	0.749561	+	0.661935i	$0.230265\pi$
$702$		0			0
$703$	11.3972			0.429854
$704$		0			0
$705$	−0.592259			−0.0223057
$706$		0			0
$707$	−3.63056	+	2.63776i	−0.136541	+	0.0992030i
$708$		0			0
$709$	8.00655	+	24.6416i	0.300692	+	0.925436i	0.981250	+	0.192741i	$0.0617377\pi$
$709$	8.00655	+	24.6416i	0.300692	+	0.925436i	−0.680557	+	0.732695i	$0.738262\pi$
$710$		0			0
$711$	12.3991	+	9.00850i	0.465004	+	0.337845i
$712$		0			0
$713$	5.51066	−	16.9601i	0.206376	−	0.635159i
$714$		0			0
$715$	2.54530	+	4.16147i	0.0951887	+	0.155630i
$716$		0			0
$717$	−0.641403	+	1.97404i	−0.0239536	+	0.0737217i
$718$		0			0
$719$	7.47766	+	5.43284i	0.278870	+	0.202611i	0.718424	−	0.695605i	$-0.244864\pi$
$719$	7.47766	+	5.43284i	0.278870	+	0.202611i	−0.439555	+	0.898216i	$0.644864\pi$
$720$		0			0
$721$	−10.7930	−	33.2175i	−0.401953	−	1.23708i
$722$		0			0
$723$	−1.40187	+	1.01852i	−0.0521361	+	0.0378791i
$724$		0			0
$725$	23.6520			0.878415
$726$		0			0
$727$	−34.6267			−1.28423			−0.642117	−	0.766606i	$-0.721944\pi$
$727$	−34.6267			−1.28423			−0.642117	+	0.766606i	$0.721944\pi$
$728$		0			0
$729$	21.5730	−	15.6737i	0.799001	−	0.580508i
$730$		0			0
$731$	−0.0583193	−	0.179488i	−0.00215702	−	0.00663862i
$732$		0			0
$733$	6.20548	+	4.50854i	0.229205	+	0.166527i	0.696460	−	0.717595i	$-0.254757\pi$
$733$	6.20548	+	4.50854i	0.229205	+	0.166527i	−0.467256	+	0.884122i	$0.654757\pi$
$734$		0			0
$735$	0.126723	−	0.390012i	0.00467424	−	0.0143858i
$736$		0			0
$737$	−1.55474	−	2.54194i	−0.0572694	−	0.0936335i
$738$		0			0
$739$	−10.9816	+	33.7980i	−0.403966	+	1.24328i	0.517790	+	0.855508i	$0.326755\pi$
$739$	−10.9816	+	33.7980i	−0.403966	+	1.24328i	−0.921756	+	0.387772i	$0.873245\pi$
$740$		0			0
$741$	−0.103452	−	0.0751626i	−0.00380042	−	0.00276117i
$742$		0			0
$743$	−1.99126	−	6.12845i	−0.0730521	−	0.224831i	0.907863	−	0.419266i	$-0.137713\pi$
$743$	−1.99126	−	6.12845i	−0.0730521	−	0.224831i	−0.980915	+	0.194435i	$0.937713\pi$
$744$		0			0
$745$	−10.5255	+	7.64723i	−0.385625	+	0.280173i
$746$		0			0
$747$	24.5277			0.897421
$748$		0			0
$749$	21.2686			0.777139
$750$		0			0
$751$	−34.0572	+	24.7440i	−1.24276	+	0.902920i	−0.997779	−	0.0666067i	$-0.978783\pi$
$751$	−34.0572	+	24.7440i	−1.24276	+	0.902920i	−0.244984	+	0.969527i	$0.578783\pi$
$752$		0			0
$753$	0.446625	+	1.37457i	0.0162759	+	0.0500921i
$754$		0			0
$755$	0.407571	+	0.296117i	0.0148330	+	0.0107768i
$756$		0			0
$757$	−6.20496	+	19.0969i	−0.225523	+	0.694088i	0.772715	+	0.634753i	$0.218898\pi$
$757$	−6.20496	+	19.0969i	−0.225523	+	0.694088i	−0.998238	+	0.0593354i	$0.981102\pi$
$758$		0			0
$759$	−0.953653	−	0.395965i	−0.0346154	−	0.0143726i
$760$		0			0
$761$	5.34335	−	16.4451i	0.193696	−	0.596136i	−0.806293	−	0.591516i	$-0.798530\pi$
$761$	5.34335	−	16.4451i	0.193696	−	0.596136i	0.999989	−	0.00461947i	$-0.00147043\pi$
$762$		0			0
$763$	22.8023	+	16.5668i	0.825499	+	0.599760i
$764$		0			0
$765$	0.309296	+	0.951915i	0.0111826	+	0.0344166i
$766$		0			0
$767$	3.35105	−	2.43468i	0.120999	−	0.0879113i
$768$		0			0
$769$	32.1312			1.15868			0.579340	−	0.815086i	$-0.303311\pi$
$769$	32.1312			1.15868			0.579340	+	0.815086i	$0.303311\pi$
$770$		0			0
$771$	1.11445			0.0401358
$772$		0			0
$773$	−7.67215	+	5.57414i	−0.275948	+	0.200488i	−0.717148	−	0.696921i	$-0.754553\pi$
$773$	−7.67215	+	5.57414i	−0.275948	+	0.200488i	0.441200	+	0.897409i	$0.354553\pi$
$774$		0			0
$775$	−3.95370	−	12.1682i	−0.142021	−	0.437096i
$776$		0			0
$777$	−0.831579	−	0.604178i	−0.0298327	−	0.0216748i
$778$		0			0
$779$	−2.60772	+	8.02573i	−0.0934311	+	0.287551i
$780$		0			0
$781$	12.7241	−	14.8724i	0.455304	−	0.532177i
$782$		0			0
$783$	1.21607	−	3.74269i	0.0434590	−	0.133753i
$784$		0			0
$785$	21.0725	+	15.3101i	0.752110	+	0.546440i
$786$		0			0
$787$	16.4549	+	50.6431i	0.586555	+	1.80523i	0.592933	+	0.805251i	$0.297970\pi$
$787$	16.4549	+	50.6431i	0.586555	+	1.80523i	−0.00637833	+	0.999980i	$0.502030\pi$
$788$		0			0
$789$	−1.29506	+	0.940917i	−0.0461054	+	0.0334975i
$790$		0			0
$791$	−12.2164			−0.434366
$792$		0			0
$793$	1.03228			0.0366573
$794$		0			0
$795$	−1.36007	+	0.988146i	−0.0482366	+	0.0350459i
$796$		0			0
$797$	8.44621	+	25.9947i	0.299180	+	0.920781i	0.981785	+	0.189994i	$0.0608469\pi$
$797$	8.44621	+	25.9947i	0.299180	+	0.920781i	−0.682605	+	0.730787i	$0.739153\pi$
$798$		0			0
$799$	−0.940373	−	0.683221i	−0.0332680	−	0.0241706i
$800$		0			0
$801$	−3.91926	+	12.0622i	−0.138480	+	0.426198i
$802$		0			0
$803$	−0.326791	+	4.10770i	−0.0115322	+	0.144958i
$804$		0			0
$805$	3.34230	−	10.2865i	0.117801	−	0.362553i
$806$		0			0
$807$	−0.483849	−	0.351537i	−0.0170323	−	0.0123747i
$808$		0			0
$809$	3.31971	+	10.2170i	0.116715	+	0.359212i	0.992301	−	0.123851i	$-0.0395244\pi$
$809$	3.31971	+	10.2170i	0.116715	+	0.359212i	−0.875586	+	0.483062i	$0.839524\pi$
$810$		0			0
$811$	−9.16595	+	6.65945i	−0.321860	+	0.233845i	−0.736969	−	0.675927i	$-0.763744\pi$
$811$	−9.16595	+	6.65945i	−0.321860	+	0.233845i	0.415109	+	0.909772i	$0.363744\pi$
$812$		0			0
$813$	−0.899115			−0.0315333
$814$		0			0
$815$	−13.3412			−0.467320
$816$		0			0
$817$	−1.09079	+	0.792506i	−0.0381620	+	0.0277263i
$818$		0			0
$819$	−1.72067	−	5.29567i	−0.0601250	−	0.185046i
$820$		0			0
$821$	−13.9792	−	10.1565i	−0.487879	−	0.354465i	0.316489	−	0.948596i	$-0.397496\pi$
$821$	−13.9792	−	10.1565i	−0.487879	−	0.354465i	−0.804368	+	0.594131i	$0.797496\pi$
$822$		0			0
$823$	−0.436380	+	1.34304i	−0.0152113	+	0.0468154i	−0.958374	−	0.285516i	$-0.907835\pi$
$823$	−0.436380	+	1.34304i	−0.0152113	+	0.0468154i	0.943163	+	0.332331i	$0.107835\pi$
$824$		0			0
$825$	−0.720523	+	0.172336i	−0.0250854	+	0.00599995i
$826$		0			0
$827$	12.1153	−	37.2872i	0.421292	−	1.29660i	−0.485209	−	0.874398i	$-0.661256\pi$
$827$	12.1153	−	37.2872i	0.421292	−	1.29660i	0.906500	−	0.422205i	$-0.138744\pi$
$828$		0			0
$829$	25.3589	+	18.4243i	0.880750	+	0.639902i	0.933450	−	0.358708i	$-0.116783\pi$
$829$	25.3589	+	18.4243i	0.880750	+	0.639902i	−0.0526999	+	0.998610i	$0.516783\pi$
$830$		0			0
$831$	0.0444770	+	0.136886i	0.00154289	+	0.00474852i
$832$		0			0
$833$	0.651120	−	0.473066i	0.0225600	−	0.0163908i
$834$		0			0
$835$	−20.7199			−0.717040
$836$		0			0
$837$	−2.12878			−0.0735813
$838$		0			0
$839$	24.7305	−	17.9677i	0.853790	−	0.620315i	−0.0723981	−	0.997376i	$-0.523065\pi$
$839$	24.7305	−	17.9677i	0.853790	−	0.620315i	0.926189	+	0.377061i	$0.123065\pi$
$840$		0			0
$841$	12.5215	+	38.5373i	0.431777	+	1.32887i
$842$		0			0
$843$	0.250531	+	0.182022i	0.00862876	+	0.00626916i
$844$		0			0
$845$	−0.454508	+	1.39883i	−0.0156356	+	0.0481213i
$846$		0			0
$847$	−18.2448	+	9.25724i	−0.626900	+	0.318082i
$848$		0			0
$849$	−0.415282	+	1.27811i	−0.0142524	+	0.0438645i
$850$		0			0
$851$	22.4494	+	16.3104i	0.769556	+	0.559115i
$852$		0			0
$853$	1.77728	+	5.46989i	0.0608528	+	0.187286i	0.976862	−	0.213873i	$-0.0686077\pi$
$853$	1.77728	+	5.46989i	0.0608528	+	0.187286i	−0.916009	+	0.401158i	$0.868608\pi$
$854$		0			0
$855$	5.78500	−	4.20305i	0.197843	−	0.143741i
$856$		0			0
$857$	3.29195			0.112451			0.0562254	−	0.998418i	$-0.482093\pi$
$857$	3.29195			0.112451			0.0562254	+	0.998418i	$0.482093\pi$
$858$		0			0
$859$	−34.1761			−1.16607			−0.583037	−	0.812446i	$-0.698136\pi$
$859$	−34.1761			−1.16607			−0.583037	+	0.812446i	$0.698136\pi$
$860$		0			0
$861$	0.615720	−	0.447347i	0.0209837	−	0.0152455i
$862$		0			0
$863$	2.55019	+	7.84868i	0.0868095	+	0.267172i	0.985033	−	0.172367i	$-0.0551416\pi$
$863$	2.55019	+	7.84868i	0.0868095	+	0.267172i	−0.898223	+	0.439540i	$0.855142\pi$
$864$		0			0
$865$	29.6201	+	21.5202i	1.00711	+	0.731710i
$866$		0			0
$867$	−0.412410	+	1.26927i	−0.0140062	+	0.0431065i
$868$		0			0
$869$	16.5131	−	3.94961i	0.560167	−	0.133981i
$870$		0			0
$871$	0.277626	−	0.854444i	0.00940699	−	0.0289517i
$872$		0			0
$873$	25.9618	+	18.8624i	0.878675	+	0.638395i
$874$		0			0
$875$	−6.62470	−	20.3887i	−0.223956	−	0.689265i
$876$		0			0
$877$	−26.9326	+	19.5677i	−0.909450	+	0.660754i	−0.940876	−	0.338752i	$-0.889995\pi$
$877$	−26.9326	+	19.5677i	−0.909450	+	0.660754i	0.0314258	+	0.999506i	$0.489995\pi$
$878$		0			0
$879$	1.10548			0.0372868
$880$		0			0
$881$	8.12321			0.273678			0.136839	−	0.990593i	$-0.456306\pi$
$881$	8.12321			0.273678			0.136839	+	0.990593i	$0.456306\pi$
$882$		0			0
$883$	7.28498	−	5.29285i	0.245159	−	0.178118i	−0.458420	−	0.888736i	$-0.651584\pi$
$883$	7.28498	−	5.29285i	0.245159	−	0.178118i	0.703579	+	0.710617i	$0.251584\pi$
$884$		0			0
$885$	−0.148247	−	0.456256i	−0.00498325	−	0.0153369i
$886$		0			0
$887$	9.88949	+	7.18513i	0.332056	+	0.241253i	0.741303	−	0.671171i	$-0.234208\pi$
$887$	9.88949	+	7.18513i	0.332056	+	0.241253i	−0.409246	+	0.912424i	$0.634208\pi$
$888$		0			0
$889$	−0.586536	+	1.80517i	−0.0196718	+	0.0605435i
$890$		0			0
$891$	2.35256	−	29.5712i	0.0788138	−	0.990674i
$892$		0			0
$893$	−2.56613	+	7.89774i	−0.0858723	+	0.264288i
$894$		0			0
$895$	20.3082	+	14.7548i	0.678830	+	0.493199i
$896$		0			0
$897$	−0.0962086	−	0.296100i	−0.00321231	−	0.00988648i
$898$		0			0
$899$	30.4245	−	22.1047i	1.01471	−	0.737232i
$900$		0			0
$901$	−3.29939			−0.109919
$902$		0			0
$903$	0.121599			0.00404658
$904$		0			0
$905$	7.68922	−	5.58654i	0.255598	−	0.185703i
$906$		0			0
$907$	−5.25696	−	16.1793i	−0.174555	−	0.537224i	0.825058	−	0.565048i	$-0.191142\pi$
$907$	−5.25696	−	16.1793i	−0.174555	−	0.537224i	−0.999613	+	0.0278239i	$0.991142\pi$
$908$		0			0
$909$	−5.84392	−	4.24586i	−0.193831	−	0.140826i
$910$		0			0
$911$	−3.16231	+	9.73259i	−0.104772	+	0.322455i	−0.989677	−	0.143317i	$-0.954223\pi$
$911$	−3.16231	+	9.73259i	−0.104772	+	0.322455i	0.884905	+	0.465772i	$0.154223\pi$
$912$		0			0
$913$	17.6647	−	20.6472i	0.584616	−	0.683322i
$914$		0			0
$915$	0.0369452	−	0.113705i	0.00122137	−	0.00375899i
$916$		0			0
$917$	−18.6162	−	13.5254i	−0.614760	−	0.446649i
$918$		0			0
$919$	1.21040	+	3.72524i	0.0399275	+	0.122884i	0.969033	−	0.246929i	$-0.0794216\pi$
$919$	1.21040	+	3.72524i	0.0399275	+	0.122884i	−0.929106	+	0.369814i	$0.879422\pi$
$920$		0			0
$921$	1.71303	−	1.24459i	0.0564461	−	0.0410105i
$922$		0			0
$923$	5.90139			0.194247
$924$		0			0
$925$	19.9089			0.654600
$926$		0			0
$927$	45.4830	−	33.0454i	1.49386	−	1.08535i
$928$		0			0
$929$	15.9690	+	49.1475i	0.523926	+	1.61248i	0.766430	+	0.642328i	$0.222031\pi$
$929$	15.9690	+	49.1475i	0.523926	+	1.61248i	−0.242504	+	0.970150i	$0.577969\pi$
$930$		0			0
$931$	−4.65174	−	3.37968i	−0.152454	−	0.110765i
$932$		0			0
$933$	0.615156	−	1.89325i	0.0201393	−	0.0619824i
$934$		0			0
$935$	1.02407	+	0.425201i	0.0334905	+	0.0139055i
$936$		0			0
$937$	6.65871	−	20.4934i	0.217531	−	0.669490i	−0.781434	−	0.623988i	$-0.785511\pi$
$937$	6.65871	−	20.4934i	0.217531	−	0.669490i	0.998964	−	0.0455018i	$-0.0144887\pi$
$938$		0			0
$939$	0.994589	+	0.722611i	0.0324572	+	0.0235815i
$940$		0			0
$941$	−10.9962	−	33.8429i	−0.358467	−	1.10325i	−0.953972	−	0.299896i	$-0.903048\pi$
$941$	−10.9962	−	33.8429i	−0.358467	−	1.10325i	0.595505	−	0.803352i	$-0.296952\pi$
$942$		0			0
$943$	−16.6220	+	12.0766i	−0.541288	+	0.393269i
$944$		0			0
$945$	−1.29114			−0.0420007
$946$		0			0
$947$	−12.5460			−0.407691			−0.203846	−	0.979003i	$-0.565344\pi$
$947$	−12.5460			−0.407691			−0.203846	+	0.979003i	$0.565344\pi$
$948$		0			0
$949$	−1.00515	+	0.730283i	−0.0326285	+	0.0237060i
$950$		0			0
$951$	0.0745535	+	0.229452i	0.00241756	+	0.00744049i
$952$		0			0
$953$	−30.6246	−	22.2501i	−0.992028	−	0.720751i	−0.0316641	−	0.999499i	$-0.510081\pi$
$953$	−30.6246	−	22.2501i	−0.992028	−	0.720751i	−0.960364	+	0.278748i	$0.910081\pi$
$954$		0			0
$955$	−5.49452	+	16.9104i	−0.177798	+	0.547207i
$956$		0			0
$957$	−1.13620	−	1.85765i	−0.0367282	−	0.0600493i
$958$		0			0
$959$	−1.08518	+	3.33984i	−0.0350423	+	0.107849i
$960$		0			0
$961$	8.62160	+	6.26396i	0.278116	+	0.202063i
$962$		0			0
$963$	10.5792	+	32.5594i	0.340910	+	1.04921i
$964$		0			0
$965$	−24.5641	+	17.8469i	−0.790747	+	0.574512i
$966$		0			0
$967$	16.4503			0.529007			0.264504	−	0.964385i	$-0.414792\pi$
$967$	16.4503			0.529007			0.264504	+	0.964385i	$0.414792\pi$
$968$		0			0
$969$	−0.0290665			−0.000933751
$970$		0			0
$971$	0.376052	−	0.273218i	0.0120681	−	0.00876798i	−0.581735	−	0.813378i	$-0.697626\pi$
$971$	0.376052	−	0.273218i	0.0120681	−	0.00876798i	0.593803	+	0.804611i	$0.297626\pi$
$972$		0			0
$973$	6.54068	+	20.1301i	0.209685	+	0.645343i
$974$		0			0
$975$	−0.180713	−	0.131296i	−0.00578744	−	0.00420482i
$976$		0			0
$977$	−2.49040	+	7.66466i	−0.0796749	+	0.245214i	−0.982958	−	0.183831i	$-0.941150\pi$
$977$	−2.49040	+	7.66466i	−0.0796749	+	0.245214i	0.903283	+	0.429046i	$0.141150\pi$
$978$		0			0
$979$	7.33126	+	11.9863i	0.234308	+	0.383085i
$980$		0			0
$981$	−14.0196	+	43.1478i	−0.447610	+	1.37760i
$982$		0			0
$983$	17.8081	+	12.9383i	0.567990	+	0.412669i	0.834375	−	0.551198i	$-0.185829\pi$
$983$	17.8081	+	12.9383i	0.567990	+	0.412669i	−0.266384	+	0.963867i	$0.585829\pi$
$984$		0			0
$985$	−3.46760	−	10.6722i	−0.110487	−	0.340043i
$986$		0			0
$987$	0.605901	−	0.440213i	0.0192860	−	0.0140121i
$988$		0			0
$989$	−3.28271			−0.104384
$990$		0			0
$991$	−41.1071			−1.30581			−0.652905	−	0.757439i	$-0.726450\pi$
$991$	−41.1071			−1.30581			−0.652905	+	0.757439i	$0.726450\pi$
$992$		0			0
$993$	−1.42978	+	1.03879i	−0.0453726	+	0.0329651i
$994$		0			0
$995$	−1.50188	−	4.62231i	−0.0476128	−	0.146537i
$996$		0			0
$997$	−7.34814	−	5.33873i	−0.232718	−	0.169079i	0.465315	−	0.885145i	$-0.345941\pi$
$997$	−7.34814	−	5.33873i	−0.232718	−	0.169079i	−0.698033	+	0.716066i	$0.745941\pi$
$998$		0			0
$999$	1.02362	−	3.15038i	0.0323859	−	0.0996736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.53.4	✓	28
11.4	even	5		6292.2.a.z.1.7		14
11.5	even	5	inner	572.2.n.b.313.4	yes	28
11.7	odd	10		6292.2.a.y.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.53.4	✓	28	1.1	even	1	trivial
572.2.n.b.313.4	yes	28	11.5	even	5	inner
6292.2.a.y.1.7		14	11.7	odd	10
6292.2.a.z.1.7		14	11.4	even	5

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0637055 + 0.0462848i) q^{3} +(-0.454508 - 1.39883i) q^{5} +(1.50470 + 1.09323i) q^{7} +(-0.925135 + 2.84727i) q^{9} +O(q^{10})\)	\(q+(-0.0637055 + 0.0462848i) q^{3} +(-0.454508 - 1.39883i) q^{5} +(1.50470 + 1.09323i) q^{7} +(-0.925135 + 2.84727i) q^{9} +(1.73053 + 2.82936i) q^{11} +(-0.309017 + 0.951057i) q^{13} +(0.0936993 + 0.0680765i) q^{15} +(0.0702412 + 0.216180i) q^{17} +(1.31378 - 0.954514i) q^{19} -0.146457 q^{21} +3.95378 q^{23} +(2.29493 - 1.66737i) q^{25} +(-0.145849 - 0.448878i) q^{27} +(6.74550 + 4.90089i) q^{29} +(1.39377 - 4.28958i) q^{31} +(-0.241201 - 0.100148i) q^{33} +(0.845344 - 2.60170i) q^{35} +(5.67796 + 4.12528i) q^{37} +(-0.0243333 - 0.0748903i) q^{39} +(-4.20409 + 3.05445i) q^{41} -0.830272 q^{43} +4.40334 q^{45} +(-4.13705 + 3.00574i) q^{47} +(-1.09415 - 3.36744i) q^{49} +(-0.0144806 - 0.0105208i) q^{51} +(-4.48545 + 13.8048i) q^{53} +(3.17125 - 3.70669i) q^{55} +(-0.0395153 + 0.121616i) q^{57} +(-3.35105 - 2.43468i) q^{59} +(-0.318991 - 0.981754i) q^{61} +(-4.50477 + 3.27290i) q^{63} +1.47082 q^{65} -0.898415 q^{67} +(-0.251877 + 0.183000i) q^{69} +(-1.82363 - 5.61256i) q^{71} +(1.00515 + 0.730283i) q^{73} +(-0.0690262 + 0.212441i) q^{75} +(-0.489204 + 6.14919i) q^{77} +(1.58195 - 4.86875i) q^{79} +(-7.23604 - 5.25729i) q^{81} +(-2.53172 - 7.79184i) q^{83} +(0.270475 - 0.196511i) q^{85} -0.656562 q^{87} +4.23642 q^{89} +(-1.50470 + 1.09323i) q^{91} +(0.109752 + 0.337780i) q^{93} +(-1.93233 - 1.40392i) q^{95} +(3.31236 - 10.1944i) q^{97} +(-9.65693 + 2.30976i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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