LMFDB - Embedded newform 572.2.bh.a.57.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

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

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.4
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79433 + 1.30366i) q^{3} +(2.19779 + 1.11983i) q^{5} +(-3.30914 + 0.524116i) q^{7} +(0.593048 - 1.82521i) q^{9} +O(q^{10})$	\(q+(-1.79433 + 1.30366i) q^{3} +(2.19779 + 1.11983i) q^{5} +(-3.30914 + 0.524116i) q^{7} +(0.593048 - 1.82521i) q^{9} +(-0.787561 + 3.22176i) q^{11} +(-0.589942 - 3.55696i) q^{13} +(-5.40343 + 0.855819i) q^{15} +(0.991105 + 3.05031i) q^{17} +(-3.35372 - 0.531176i) q^{19} +(5.25442 - 5.25442i) q^{21} -1.68676i q^{23} +(0.637324 + 0.877201i) q^{25} +(-0.740790 - 2.27992i) q^{27} +(-4.24151 + 5.83794i) q^{29} +(0.222793 + 0.437255i) q^{31} +(-2.78693 - 6.80761i) q^{33} +(-7.85970 - 2.55377i) q^{35} +(-1.32958 - 8.39464i) q^{37} +(5.69561 + 5.61328i) q^{39} +(-9.27682 - 1.46930i) q^{41} -5.16346 q^{43} +(3.34732 - 3.34732i) q^{45} +(5.87874 + 0.931102i) q^{47} +(4.01830 - 1.30562i) q^{49} +(-5.75492 - 4.18120i) q^{51} +(-2.30098 + 7.08168i) q^{53} +(-5.33871 + 6.19881i) q^{55} +(6.71015 - 3.41899i) q^{57} +(0.523074 + 3.30256i) q^{59} +(-2.51372 + 0.816756i) q^{61} +(-1.00585 + 6.35071i) q^{63} +(2.68662 - 8.47807i) q^{65} +(-2.82672 + 2.82672i) q^{67} +(2.19895 + 3.02660i) q^{69} +(-3.48990 - 1.77819i) q^{71} +(-8.97066 + 1.42081i) q^{73} +(-2.28714 - 0.743137i) q^{75} +(0.917572 - 11.0740i) q^{77} +(6.07492 + 1.97386i) q^{79} +(8.95931 + 6.50932i) q^{81} +(3.04634 - 5.97879i) q^{83} +(-1.23758 + 7.81379i) q^{85} -16.0047i q^{87} +(8.01752 + 8.01752i) q^{89} +(3.81646 + 11.4613i) q^{91} +(-0.969794 - 0.494135i) q^{93} +(-6.77593 - 4.92300i) q^{95} +(8.34074 + 16.3696i) q^{97} +(5.41334 + 3.34813i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.79433	+	1.30366i	−1.03596	+	0.752667i	−0.969492	−	0.245122i	$-0.921172\pi$
$3$	−1.79433	+	1.30366i	−1.03596	+	0.752667i	−0.0664648	+	0.997789i	$0.521172\pi$
$4$		0			0
$5$	2.19779	+	1.11983i	0.982880	+	0.500802i	0.870131	−	0.492821i	$-0.164034\pi$
$5$	2.19779	+	1.11983i	0.982880	+	0.500802i	0.112749	+	0.993623i	$0.464034\pi$
$6$		0			0
$7$	−3.30914	+	0.524116i	−1.25074	+	0.198097i	−0.746451	−	0.665440i	$-0.768244\pi$
$7$	−3.30914	+	0.524116i	−1.25074	+	0.198097i	−0.504285	+	0.863537i	$0.668244\pi$
$8$		0			0
$9$	0.593048	−	1.82521i	0.197683	−	0.608405i
$10$		0			0
$11$	−0.787561	+	3.22176i	−0.237459	+	0.971398i
$11$	−0.787561	+	3.22176i	−0.237459	+	0.971398i
$12$		0			0
$13$	−0.589942	−	3.55696i	−0.163620	−	0.986523i
$13$	−0.589942	−	3.55696i	−0.163620	−	0.986523i
$14$		0			0
$15$	−5.40343	+	0.855819i	−1.39516	+	0.220971i
$16$		0			0
$17$	0.991105	+	3.05031i	0.240378	+	0.739808i	0.996362	+	0.0852180i	$0.0271587\pi$
$17$	0.991105	+	3.05031i	0.240378	+	0.739808i	−0.755984	+	0.654590i	$0.772841\pi$
$18$		0			0
$19$	−3.35372	−	0.531176i	−0.769395	−	0.121860i	−0.240617	−	0.970620i	$-0.577350\pi$
$19$	−3.35372	−	0.531176i	−0.769395	−	0.121860i	−0.528778	+	0.848760i	$0.677350\pi$
$20$		0			0
$21$	5.25442	−	5.25442i	1.14661	−	1.14661i
$22$		0			0
$23$		−	1.68676i		−	0.351713i	−0.984416	−	0.175856i	$-0.943731\pi$
$23$		−	1.68676i		−	0.351713i	0.984416	−	0.175856i	$-0.0562694\pi$
$24$		0			0
$25$	0.637324	+	0.877201i	0.127465	+	0.175440i
$26$		0			0
$27$	−0.740790	−	2.27992i	−0.142565	−	0.438770i
$28$		0			0
$29$	−4.24151	+	5.83794i	−0.787628	+	1.08408i	0.206771	+	0.978389i	$0.433704\pi$
$29$	−4.24151	+	5.83794i	−0.787628	+	1.08408i	−0.994399	+	0.105688i	$0.966296\pi$
$30$		0			0
$31$	0.222793	+	0.437255i	0.0400147	+	0.0785333i	0.910148	−	0.414283i	$-0.135968\pi$
$31$	0.222793	+	0.437255i	0.0400147	+	0.0785333i	−0.870133	+	0.492816i	$0.835968\pi$
$32$		0			0
$33$	−2.78693	−	6.80761i	−0.485142	−	1.18505i
$34$		0			0
$35$	−7.85970	−	2.55377i	−1.32853	−	0.431666i
$36$		0			0
$37$	−1.32958	−	8.39464i	−0.218582	−	1.38007i	−0.815959	−	0.578110i	$-0.803790\pi$
$37$	−1.32958	−	8.39464i	−0.218582	−	1.38007i	0.597377	−	0.801961i	$-0.296210\pi$
$38$		0			0
$39$	5.69561	+	5.61328i	0.912027	+	0.898844i
$40$		0			0
$41$	−9.27682	−	1.46930i	−1.44880	−	0.229467i	−0.618059	−	0.786132i	$-0.712081\pi$
$41$	−9.27682	−	1.46930i	−1.44880	−	0.229467i	−0.830737	+	0.556665i	$0.812081\pi$
$42$		0			0
$43$	−5.16346			−0.787420			−0.393710	−	0.919235i	$-0.628809\pi$
$43$	−5.16346			−0.787420			−0.393710	+	0.919235i	$0.628809\pi$
$44$		0			0
$45$	3.34732	−	3.34732i	0.498989	−	0.498989i
$46$		0			0
$47$	5.87874	+	0.931102i	0.857503	+	0.135815i	0.569678	−	0.821868i	$-0.307068\pi$
$47$	5.87874	+	0.931102i	0.857503	+	0.135815i	0.287825	+	0.957683i	$0.407068\pi$
$48$		0			0
$49$	4.01830	−	1.30562i	0.574042	−	0.186518i
$50$		0			0
$51$	−5.75492	−	4.18120i	−0.805850	−	0.585485i
$52$		0			0
$53$	−2.30098	+	7.08168i	−0.316063	+	0.972743i	0.659251	+	0.751923i	$0.270873\pi$
$53$	−2.30098	+	7.08168i	−0.316063	+	0.972743i	−0.975314	+	0.220820i	$0.929127\pi$
$54$		0			0
$55$	−5.33871	+	6.19881i	−0.719872	+	0.835847i
$56$		0			0
$57$	6.71015	−	3.41899i	0.888781	−	0.452856i
$58$		0			0
$59$	0.523074	+	3.30256i	0.0680984	+	0.429956i	0.998058	+	0.0622942i	$0.0198417\pi$
$59$	0.523074	+	3.30256i	0.0680984	+	0.429956i	−0.929959	+	0.367662i	$0.880158\pi$
$60$		0			0
$61$	−2.51372	+	0.816756i	−0.321848	+	0.104575i	−0.465485	−	0.885056i	$-0.654120\pi$
$61$	−2.51372	+	0.816756i	−0.321848	+	0.104575i	0.143637	+	0.989630i	$0.454120\pi$
$62$		0			0
$63$	−1.00585	+	6.35071i	−0.126726	+	0.800114i
$64$		0			0
$65$	2.68662	−	8.47807i	0.333234	−	1.05158i
$66$		0			0
$67$	−2.82672	+	2.82672i	−0.345338	+	0.345338i	−0.858370	−	0.513032i	$-0.828522\pi$
$67$	−2.82672	+	2.82672i	−0.345338	+	0.345338i	0.513032	+	0.858370i	$0.328522\pi$
$68$		0			0
$69$	2.19895	+	3.02660i	0.264723	+	0.364359i
$70$		0			0
$71$	−3.48990	−	1.77819i	−0.414175	−	0.211033i	0.234471	−	0.972123i	$-0.424664\pi$
$71$	−3.48990	−	1.77819i	−0.414175	−	0.211033i	−0.648646	+	0.761090i	$0.724664\pi$
$72$		0			0
$73$	−8.97066	+	1.42081i	−1.04994	+	0.166294i	−0.657476	−	0.753475i	$-0.728376\pi$
$73$	−8.97066	+	1.42081i	−1.04994	+	0.166294i	−0.392460	+	0.919769i	$0.628376\pi$
$74$		0			0
$75$	−2.28714	−	0.743137i	−0.264096	−	0.0858100i
$76$		0			0
$77$	0.917572	−	11.0740i	0.104567	−	1.26200i
$78$		0			0
$79$	6.07492	+	1.97386i	0.683482	+	0.222077i	0.630119	−	0.776498i	$-0.283006\pi$
$79$	6.07492	+	1.97386i	0.683482	+	0.222077i	0.0533631	+	0.998575i	$0.483006\pi$
$80$		0			0
$81$	8.95931	+	6.50932i	0.995479	+	0.723258i
$82$		0			0
$83$	3.04634	−	5.97879i	0.334380	−	0.656257i	−0.661197	−	0.750213i	$-0.729951\pi$
$83$	3.04634	−	5.97879i	0.334380	−	0.656257i	0.995576	+	0.0939556i	$0.0299512\pi$
$84$		0			0
$85$	−1.23758	+	7.81379i	−0.134235	+	0.847524i
$86$		0			0
$87$		−	16.0047i		−	1.71588i
$88$		0			0
$89$	8.01752	+	8.01752i	0.849856	+	0.849856i	0.990115	−	0.140259i	$-0.0447935\pi$
$89$	8.01752	+	8.01752i	0.849856	+	0.849856i	−0.140259	+	0.990115i	$0.544794\pi$
$90$		0			0
$91$	3.81646	+	11.4613i	0.400073	+	1.20147i
$92$		0			0
$93$	−0.969794	−	0.494135i	−0.100563	−	0.0512394i
$94$		0			0
$95$	−6.77593	−	4.92300i	−0.695195	−	0.505089i
$96$		0			0
$97$	8.34074	+	16.3696i	0.846874	+	1.66208i	0.744781	+	0.667309i	$0.232554\pi$
$97$	8.34074	+	16.3696i	0.846874	+	1.66208i	0.102094	+	0.994775i	$0.467446\pi$
$98$		0			0
$99$	5.41334	+	3.34813i	0.544061	+	0.336499i
$100$		0			0
$101$	−3.24006	+	9.97189i	−0.322398	+	0.992240i	0.650203	+	0.759760i	$0.274684\pi$
$101$	−3.24006	+	9.97189i	−0.322398	+	0.992240i	−0.972601	+	0.232479i	$0.925316\pi$
$102$		0			0
$103$	7.81106	−	10.7510i	0.769647	−	1.05933i	−0.226703	−	0.973964i	$-0.572795\pi$
$103$	7.81106	−	10.7510i	0.769647	−	1.05933i	0.996350	−	0.0853640i	$-0.0272053\pi$
$104$		0			0
$105$	17.4321	−	5.66404i	1.70120	−	0.552754i
$106$		0			0
$107$	7.90472	+	10.8799i	0.764178	+	1.05180i	0.996855	+	0.0792470i	$0.0252516\pi$
$107$	7.90472	+	10.8799i	0.764178	+	1.05180i	−0.232677	+	0.972554i	$0.574748\pi$
$108$		0			0
$109$	11.7447	+	11.7447i	1.12494	+	1.12494i	0.990988	+	0.133951i	$0.0427665\pi$
$109$	11.7447	+	11.7447i	1.12494	+	1.12494i	0.133951	+	0.990988i	$0.457233\pi$
$110$		0			0
$111$	13.3294	+	13.3294i	1.26518	+	1.26518i
$112$		0			0
$113$	11.5430	−	8.38651i	1.08588	−	0.788937i	0.107180	−	0.994240i	$-0.465818\pi$
$113$	11.5430	−	8.38651i	1.08588	−	0.788937i	0.978698	+	0.205303i	$0.0658180\pi$
$114$		0			0
$115$	1.88888	−	3.70713i	0.176139	−	0.345691i
$116$		0			0
$117$	−6.84208	−	1.03268i	−0.632550	−	0.0954712i
$118$		0			0
$119$	−4.87842	−	9.57443i	−0.447204	−	0.877686i
$120$		0			0
$121$	−9.75949	−	5.07467i	−0.887227	−	0.461334i
$122$		0			0
$123$	18.5612	−	9.45738i	1.67360	−	0.852743i
$124$		0			0
$125$	−1.51095	−	9.53973i	−0.135143	−	0.853260i
$126$		0			0
$127$	1.07415	+	3.30588i	0.0953150	+	0.293349i	0.987336	−	0.158645i	$-0.0507126\pi$
$127$	1.07415	+	3.30588i	0.0953150	+	0.293349i	−0.892021	+	0.451995i	$0.850713\pi$
$128$		0			0
$129$	9.26496	−	6.73138i	0.815734	−	0.592665i
$130$		0			0
$131$			14.7380i			1.28767i	0.765166	+	0.643833i	$0.222657\pi$
$131$			14.7380i			1.28767i	−0.765166	+	0.643833i	$0.777343\pi$
$132$		0			0
$133$	11.3763			0.986451
$134$		0			0
$135$	0.925017	−	5.84033i	0.0796128	−	0.502655i
$136$		0			0
$137$	2.99614	−	5.88025i	0.255977	−	0.502384i	−0.726877	−	0.686768i	$-0.759029\pi$
$137$	2.99614	−	5.88025i	0.255977	−	0.502384i	0.982854	+	0.184384i	$0.0590290\pi$
$138$		0			0
$139$	−3.03630	+	4.17911i	−0.257535	+	0.354467i	−0.918132	−	0.396274i	$-0.870303\pi$
$139$	−3.03630	+	4.17911i	−0.257535	+	0.354467i	0.660597	+	0.750741i	$0.270303\pi$
$140$		0			0
$141$	−11.7622	+	5.99316i	−0.990560	+	0.504715i
$142$		0			0
$143$	11.9243	+	0.900673i	0.997160	+	0.0753181i
$144$		0			0
$145$	−15.8594	+	8.08077i	−1.31705	+	0.671072i
$146$		0			0
$147$	−5.50807	+	7.58120i	−0.454298	+	0.625287i
$148$		0			0
$149$	−0.617224	+	1.21137i	−0.0505649	+	0.0992393i	−0.914906	−	0.403666i	$-0.867736\pi$
$149$	−0.617224	+	1.21137i	−0.0505649	+	0.0992393i	0.864341	+	0.502906i	$0.167736\pi$
$150$		0			0
$151$	−1.41635	+	8.94247i	−0.115261	+	0.727728i	0.860591	+	0.509296i	$0.170094\pi$
$151$	−1.41635	+	8.94247i	−0.115261	+	0.727728i	−0.975852	+	0.218432i	$0.929906\pi$
$152$		0			0
$153$	6.15523			0.497621
$154$		0			0
$155$			1.21048i			0.0972283i
$156$		0			0
$157$	−0.433721	+	0.315116i	−0.0346147	+	0.0251490i	−0.604958	−	0.796257i	$-0.706810\pi$
$157$	−0.433721	+	0.315116i	−0.0346147	+	0.0251490i	0.570343	+	0.821406i	$0.306810\pi$
$158$		0			0
$159$	−5.10337	−	15.7066i	−0.404723	−	1.24561i
$160$		0			0
$161$	0.884055	+	5.58170i	0.0696733	+	0.439900i
$162$		0			0
$163$	−22.5472	+	11.4884i	−1.76603	+	0.899839i	−0.822356	+	0.568974i	$0.807341\pi$
$163$	−22.5472	+	11.4884i	−1.76603	+	0.899839i	−0.943678	+	0.330865i	$0.892659\pi$
$164$		0			0
$165$	1.49829	−	18.0826i	0.116641	−	1.40773i
$166$		0			0
$167$	−3.55314	−	6.97343i	−0.274950	−	0.539620i	0.711698	−	0.702485i	$-0.247926\pi$
$167$	−3.55314	−	6.97343i	−0.274950	−	0.539620i	−0.986648	+	0.162865i	$0.947926\pi$
$168$		0			0
$169$	−12.3039	+	4.19680i	−0.946457	+	0.322831i
$170$		0			0
$171$	−2.95843	+	5.80624i	−0.226236	+	0.444014i
$172$		0			0
$173$	−11.2966	+	8.20746i	−0.858864	+	0.624001i	−0.927576	−	0.373635i	$-0.878111\pi$
$173$	−11.2966	+	8.20746i	−0.858864	+	0.624001i	0.0687115	+	0.997637i	$0.478111\pi$
$174$		0			0
$175$	−2.56875	−	2.56875i	−0.194179	−	0.194179i
$176$		0			0
$177$	−5.24397	−	5.24397i	−0.394161	−	0.394161i
$178$		0			0
$179$	−2.39057	−	3.29034i	−0.178680	−	0.245932i	0.710277	−	0.703922i	$-0.248570\pi$
$179$	−2.39057	−	3.29034i	−0.178680	−	0.245932i	−0.888957	+	0.457990i	$0.848570\pi$
$180$		0			0
$181$	18.6232	−	6.05104i	1.38425	−	0.449770i	0.480186	−	0.877167i	$-0.340569\pi$
$181$	18.6232	−	6.05104i	1.38425	−	0.449770i	0.904064	+	0.427396i	$0.140569\pi$
$182$		0			0
$183$	3.44567	−	4.74255i	0.254711	−	0.350580i
$184$		0			0
$185$	6.47842	−	19.9385i	0.476303	−	1.46591i
$186$		0			0
$187$	−10.6079	+	0.790799i	−0.775728	+	0.0578290i
$188$		0			0
$189$	3.64632	+	7.15630i	0.265230	+	0.520544i
$190$		0			0
$191$	−11.9240	−	8.66326i	−0.862787	−	0.626852i	0.0658546	−	0.997829i	$-0.479023\pi$
$191$	−11.9240	−	8.66326i	−0.862787	−	0.626852i	−0.928642	+	0.370978i	$0.879023\pi$
$192$		0			0
$193$	−20.8641	−	10.6308i	−1.50183	−	0.765220i	−0.506545	−	0.862214i	$-0.669077\pi$
$193$	−20.8641	−	10.6308i	−1.50183	−	0.765220i	−0.995285	+	0.0969933i	$0.969077\pi$
$194$		0			0
$195$	6.23182	+	18.7149i	0.446270	+	1.34020i
$196$		0			0
$197$	−1.18796	−	1.18796i	−0.0846383	−	0.0846383i	0.663520	−	0.748158i	$-0.269062\pi$
$197$	−1.18796	−	1.18796i	−0.0846383	−	0.0846383i	−0.748158	+	0.663520i	$0.769062\pi$
$198$		0			0
$199$			24.9852i			1.77116i	0.464491	+	0.885578i	$0.346237\pi$
$199$			24.9852i			1.77116i	−0.464491	+	0.885578i	$0.653763\pi$
$200$		0			0
$201$	1.38699	−	8.75713i	0.0978309	−	0.617680i
$202$		0			0
$203$	10.9760	−	21.5416i	0.770363	−	1.51192i
$204$		0			0
$205$	−18.7431	−	13.6177i	−1.30908	−	0.951099i
$206$		0			0
$207$	−3.07869	−	1.00033i	−0.213984	−	0.0695275i
$208$		0			0
$209$	4.35258	−	10.3865i	0.301074	−	0.718452i
$210$		0			0
$211$	−3.52445	−	1.14516i	−0.242633	−	0.0788363i	0.185176	−	0.982705i	$-0.440714\pi$
$211$	−3.52445	−	1.14516i	−0.242633	−	0.0788363i	−0.427809	+	0.903869i	$0.640714\pi$
$212$		0			0
$213$	8.58020	−	1.35897i	0.587905	−	0.0931151i
$214$		0			0
$215$	−11.3482	−	5.78219i	−0.773940	−	0.394342i
$216$		0			0
$217$	−0.966424	−	1.33017i	−0.0656051	−	0.0902977i
$218$		0			0
$219$	14.2441	−	14.2441i	0.962526	−	0.962526i
$220$		0			0
$221$	10.2651	−	5.32482i	0.690507	−	0.358186i
$222$		0			0
$223$	−0.0697219	+	0.440207i	−0.00466893	+	0.0294784i	−0.989913	−	0.141678i	$-0.954750\pi$
$223$	−0.0697219	+	0.440207i	−0.00466893	+	0.0294784i	0.985244	+	0.171156i	$0.0547503\pi$
$224$		0			0
$225$	1.97904	−	0.643030i	0.131936	−	0.0428687i
$226$		0			0
$227$	1.81220	+	11.4418i	0.120280	+	0.759416i	0.971924	+	0.235296i	$0.0756058\pi$
$227$	1.81220	+	11.4418i	0.120280	+	0.759416i	−0.851644	+	0.524120i	$0.824394\pi$
$228$		0			0
$229$	−23.3353	+	11.8899i	−1.54204	+	0.785708i	−0.998556	−	0.0537124i	$-0.982895\pi$
$229$	−23.3353	+	11.8899i	−1.54204	+	0.785708i	−0.543483	+	0.839420i	$0.682895\pi$
$230$		0			0
$231$	12.7903	+	21.0667i	0.841540	+	1.38608i
$232$		0			0
$233$	4.82801	−	14.8591i	0.316293	−	0.973451i	−0.658925	−	0.752208i	$-0.728989\pi$
$233$	4.82801	−	14.8591i	0.316293	−	0.973451i	0.975219	−	0.221243i	$-0.0710113\pi$
$234$		0			0
$235$	11.8776	+	8.62955i	0.774806	+	0.562930i
$236$		0			0
$237$	−13.4737	+	4.37786i	−0.875208	+	0.284372i
$238$		0			0
$239$	20.6663	+	3.27323i	1.33679	+	0.211727i	0.783569	−	0.621304i	$-0.213397\pi$
$239$	20.6663	+	3.27323i	1.33679	+	0.211727i	0.553225	+	0.833032i	$0.313397\pi$
$240$		0			0
$241$	9.78498	−	9.78498i	0.630306	−	0.630306i	−0.317839	−	0.948145i	$-0.602957\pi$
$241$	9.78498	−	9.78498i	0.630306	−	0.630306i	0.948145	+	0.317839i	$0.102957\pi$
$242$		0			0
$243$	−17.3701			−1.11430
$244$		0			0
$245$	10.2934	+	1.63032i	0.657623	+	0.104157i
$246$		0			0
$247$	0.0891234	+	12.2424i	0.00567079	+	0.778965i
$248$		0			0
$249$	2.32814	+	14.6993i	0.147540	+	0.931531i
$250$		0			0
$251$	16.7485	+	5.44191i	1.05715	+	0.343490i	0.785472	−	0.618897i	$-0.212420\pi$
$251$	16.7485	+	5.44191i	1.05715	+	0.343490i	0.271682	+	0.962387i	$0.412420\pi$
$252$		0			0
$253$	5.43432	+	1.32842i	0.341653	+	0.0835173i
$254$		0			0
$255$	−7.96587	−	15.6339i	−0.498842	−	0.979033i
$256$		0			0
$257$	−11.5642	+	15.9167i	−0.721353	+	0.992857i	0.278125	+	0.960545i	$0.410287\pi$
$257$	−11.5642	+	15.9167i	−0.721353	+	0.992857i	−0.999478	+	0.0323122i	$0.989713\pi$
$258$		0			0
$259$	8.79953	+	27.0822i	0.546776	+	1.68280i
$260$		0			0
$261$	8.14006	+	11.2038i	0.503857	+	0.693500i
$262$		0			0
$263$		−	20.9772i		−	1.29351i	−0.762697	−	0.646756i	$-0.776125\pi$
$263$		−	20.9772i		−	1.29351i	0.762697	−	0.646756i	$-0.223875\pi$
$264$		0			0
$265$	−12.9873	+	12.9873i	−0.797805	+	0.797805i
$266$		0			0
$267$	−24.8382	−	3.93398i	−1.52007	−	0.240756i
$268$		0			0
$269$	7.73514	+	23.8063i	0.471620	+	1.45150i	0.850462	+	0.526036i	$0.176322\pi$
$269$	7.73514	+	23.8063i	0.471620	+	1.45150i	−0.378842	+	0.925461i	$0.623678\pi$
$270$		0			0
$271$	−4.12783	+	0.653784i	−0.250748	+	0.0397146i	−0.280543	−	0.959841i	$-0.590515\pi$
$271$	−4.12783	+	0.653784i	−0.250748	+	0.0397146i	0.0297951	+	0.999556i	$0.490515\pi$
$272$		0			0
$273$	−21.7896	−	15.5900i	−1.31876	−	0.943547i
$274$		0			0
$275$	−3.32806	+	1.36246i	−0.200690	+	0.0821592i
$276$		0			0
$277$	−6.34870	+	19.5393i	−0.381456	+	1.17400i	0.557562	+	0.830135i	$0.311737\pi$
$277$	−6.34870	+	19.5393i	−0.381456	+	1.17400i	−0.939018	+	0.343867i	$0.888263\pi$
$278$		0			0
$279$	0.930211	−	0.147331i	0.0556903	−	0.00882047i
$280$		0			0
$281$	−26.1680	−	13.3332i	−1.56105	−	0.795395i	−0.561563	−	0.827434i	$-0.689800\pi$
$281$	−26.1680	−	13.3332i	−1.56105	−	0.795395i	−0.999487	+	0.0320395i	$0.989800\pi$
$282$		0			0
$283$	16.9354	−	12.3043i	1.00671	−	0.731416i	0.0431917	−	0.999067i	$-0.486247\pi$
$283$	16.9354	−	12.3043i	1.00671	−	0.731416i	0.963516	+	0.267651i	$0.0862474\pi$
$284$		0			0
$285$	18.5761			1.10036
$286$		0			0
$287$	31.4684			1.85752
$288$		0			0
$289$	5.43121	−	3.94600i	0.319483	−	0.232118i
$290$		0			0
$291$	−36.3064	−	18.4991i	−2.12832	−	1.08443i
$292$		0			0
$293$	22.6480	−	3.58709i	1.32311	−	0.209560i	0.545396	−	0.838178i	$-0.316379\pi$
$293$	22.6480	−	3.58709i	1.32311	−	0.209560i	0.777714	+	0.628618i	$0.216379\pi$
$294$		0			0
$295$	−2.54869	+	7.84407i	−0.148391	+	0.456699i
$296$		0			0
$297$	7.92877	−	0.591074i	0.460074	−	0.0342976i
$298$		0			0
$299$	−5.99972	+	0.995087i	−0.346973	+	0.0575474i
$300$		0			0
$301$	17.0866	−	2.70625i	0.984855	−	0.155986i
$302$		0			0
$303$	−7.18618	−	22.1168i	−0.412835	−	1.27058i
$304$		0			0
$305$	−6.43924	−	1.01987i	−0.368710	−	0.0583979i
$306$		0			0
$307$	5.38248	−	5.38248i	0.307194	−	0.307194i	−0.536626	−	0.843820i	$-0.680301\pi$
$307$	5.38248	−	5.38248i	0.307194	−	0.307194i	0.843820	+	0.536626i	$0.180301\pi$
$308$		0			0
$309$			29.4738i			1.67671i
$310$		0			0
$311$	−7.24946	−	9.97802i	−0.411079	−	0.565802i	0.552402	−	0.833578i	$-0.313711\pi$
$311$	−7.24946	−	9.97802i	−0.411079	−	0.565802i	−0.963481	+	0.267776i	$0.913711\pi$
$312$		0			0
$313$	3.01233	+	9.27101i	0.170267	+	0.524029i	0.999386	−	0.0350442i	$-0.0111572\pi$
$313$	3.01233	+	9.27101i	0.170267	+	0.524029i	−0.829119	+	0.559073i	$0.811157\pi$
$314$		0			0
$315$	−9.32236	+	12.8311i	−0.525255	+	0.722952i
$316$		0			0
$317$	−4.47472	−	8.78214i	−0.251326	−	0.493254i	0.730531	−	0.682880i	$-0.239273\pi$
$317$	−4.47472	−	8.78214i	−0.251326	−	0.493254i	−0.981857	+	0.189625i	$0.939273\pi$
$318$		0			0
$319$	−15.4680	−	18.2629i	−0.866041	−	1.02252i
$320$		0			0
$321$	−28.3674	−	9.21711i	−1.58331	−	0.514449i
$322$		0			0
$323$	−1.70363	−	10.7563i	−0.0947926	−	0.598497i
$324$		0			0
$325$	2.74419	−	2.78443i	0.152220	−	0.154453i
$326$		0			0
$327$	−36.3850	−	5.76281i	−2.01209	−	0.318684i
$328$		0			0
$329$	−19.9416			−1.09941
$330$		0			0
$331$	7.83666	−	7.83666i	0.430742	−	0.430742i	−0.458139	−	0.888881i	$-0.651484\pi$
$331$	7.83666	−	7.83666i	0.430742	−	0.430742i	0.888881	+	0.458139i	$0.151484\pi$
$332$		0			0
$333$	−16.1105	−	2.55166i	−0.882852	−	0.139830i
$334$		0			0
$335$	−9.37795	+	3.04708i	−0.512372	+	0.166480i
$336$		0			0
$337$	−4.44550	−	3.22985i	−0.242162	−	0.175941i	0.460084	−	0.887875i	$-0.347819\pi$
$337$	−4.44550	−	3.22985i	−0.242162	−	0.175941i	−0.702246	+	0.711934i	$0.747819\pi$
$338$		0			0
$339$	−9.77889	+	30.0963i	−0.531117	+	1.63461i
$340$		0			0
$341$	−1.58419	+	0.373419i	−0.0857889	+	0.0202218i
$342$		0			0
$343$	8.28371	−	4.22076i	0.447279	−	0.227900i
$344$		0			0
$345$	1.44356	+	9.11426i	0.0777185	+	0.490695i
$346$		0			0
$347$	−7.51842	+	2.44288i	−0.403610	+	0.131141i	−0.503785	−	0.863829i	$-0.668060\pi$
$347$	−7.51842	+	2.44288i	−0.403610	+	0.131141i	0.100175	+	0.994970i	$0.468060\pi$
$348$		0			0
$349$	2.79673	−	17.6578i	0.149705	−	0.945203i	−0.792428	−	0.609965i	$-0.791183\pi$
$349$	2.79673	−	17.6578i	0.149705	−	0.945203i	0.942134	−	0.335238i	$-0.108817\pi$
$350$		0			0
$351$	−7.67255	+	3.97998i	−0.409531	+	0.212436i
$352$		0			0
$353$	−6.01326	+	6.01326i	−0.320053	+	0.320053i	−0.848787	−	0.528734i	$-0.822667\pi$
$353$	−6.01326	+	6.01326i	−0.320053	+	0.320053i	0.528734	+	0.848787i	$0.322667\pi$
$354$		0			0
$355$	−5.67879	−	7.81618i	−0.301399	−	0.414840i
$356$		0			0
$357$	21.2353	+	10.8199i	1.12389	+	0.572650i
$358$		0			0
$359$	−8.54252	+	1.35300i	−0.450857	+	0.0714087i	−0.377734	−	0.925914i	$-0.623297\pi$
$359$	−8.54252	+	1.35300i	−0.450857	+	0.0714087i	−0.0731231	+	0.997323i	$0.523297\pi$
$360$		0			0
$361$	−7.10481	−	2.30849i	−0.373937	−	0.121500i
$362$		0			0
$363$	24.1274	−	3.61740i	1.26636	−	0.189864i
$364$		0			0
$365$	−21.3067	−	6.92296i	−1.11524	−	0.362364i
$366$		0			0
$367$	21.5546	+	15.6603i	1.12514	+	0.817462i	0.984980	−	0.172667i	$-0.0552383\pi$
$367$	21.5546	+	15.6603i	1.12514	+	0.817462i	0.140160	+	0.990129i	$0.455238\pi$
$368$		0			0
$369$	−8.18340	+	16.0608i	−0.426011	+	0.836093i
$370$		0			0
$371$	3.90263	−	24.6402i	0.202614	−	1.27926i
$372$		0			0
$373$			16.8212i			0.870967i	0.900197	+	0.435484i	$0.143423\pi$
$373$			16.8212i			0.870967i	−0.900197	+	0.435484i	$0.856577\pi$
$374$		0			0
$375$	15.1477	+	15.1477i	0.782223	+	0.782223i
$376$		0			0
$377$	23.2675	+	11.6428i	1.19834	+	0.599637i
$378$		0			0
$379$	−24.5274	−	12.4973i	−1.25989	−	0.641945i	−0.308877	−	0.951102i	$-0.599953\pi$
$379$	−24.5274	−	12.4973i	−1.25989	−	0.641945i	−0.951011	+	0.309157i	$0.899953\pi$
$380$		0			0
$381$	−6.23711	−	4.53152i	−0.319537	−	0.232157i
$382$		0			0
$383$	−14.9882	−	29.4159i	−0.765860	−	1.50308i	−0.861550	−	0.507673i	$-0.830506\pi$
$383$	−14.9882	−	29.4159i	−0.765860	−	1.50308i	0.0956902	−	0.995411i	$-0.469494\pi$
$384$		0			0
$385$	14.4176	−	23.3108i	0.734791	−	1.18803i
$386$		0			0
$387$	−3.06218	+	9.42442i	−0.155659	+	0.479070i
$388$		0			0
$389$	−12.9170	+	17.7788i	−0.654920	+	0.901420i	−0.999300	−	0.0374103i	$-0.988089\pi$
$389$	−12.9170	+	17.7788i	−0.654920	+	0.901420i	0.344380	+	0.938830i	$0.388089\pi$
$390$		0			0
$391$	5.14512	−	1.67175i	0.260200	−	0.0845441i
$392$		0			0
$393$	−19.2133	−	26.4449i	−0.969183	−	1.33397i
$394$		0			0
$395$	11.1410	+	11.1410i	0.560565	+	0.560565i
$396$		0			0
$397$	2.93899	+	2.93899i	0.147504	+	0.147504i	0.777002	−	0.629498i	$-0.216740\pi$
$397$	2.93899	+	2.93899i	0.147504	+	0.147504i	−0.629498	+	0.777002i	$0.716740\pi$
$398$		0			0
$399$	−20.4128	+	14.8308i	−1.02192	+	0.742469i
$400$		0			0
$401$	−0.299982	+	0.588748i	−0.0149804	+	0.0294006i	−0.898375	−	0.439228i	$-0.855252\pi$
$401$	−0.299982	+	0.588748i	−0.0149804	+	0.0294006i	0.883395	+	0.468629i	$0.155252\pi$
$402$		0			0
$403$	1.42386	−	1.05042i	0.0709278	−	0.0523251i
$404$		0			0
$405$	12.4013	+	24.3390i	0.616227	+	1.20941i
$406$		0			0
$407$	28.0927	+	2.32770i	1.39250	+	0.115380i
$408$		0			0
$409$	13.9080	−	7.08647i	0.687705	−	0.350403i	−0.0749693	−	0.997186i	$-0.523886\pi$
$409$	13.9080	−	7.08647i	0.687705	−	0.350403i	0.762674	+	0.646783i	$0.223886\pi$
$410$		0			0
$411$	2.28977	+	14.4571i	0.112946	+	0.713114i
$412$		0			0
$413$	−3.46185	−	10.6545i	−0.170346	−	0.524272i
$414$		0			0
$415$	13.3904	−	9.72871i	0.657310	−	0.477564i
$416$		0			0
$417$		−	11.4570i		−	0.561051i
$418$		0			0
$419$	23.1507			1.13099			0.565493	−	0.824753i	$-0.308686\pi$
$419$	23.1507			1.13099			0.565493	+	0.824753i	$0.308686\pi$
$420$		0			0
$421$	−4.39496	+	27.7487i	−0.214197	+	1.35239i	0.612824	+	0.790219i	$0.290033\pi$
$421$	−4.39496	+	27.7487i	−0.214197	+	1.35239i	−0.827022	+	0.562170i	$0.809967\pi$
$422$		0			0
$423$	5.18584	−	10.1778i	0.252144	−	0.494861i
$424$		0			0
$425$	−2.04408	+	2.81343i	−0.0991523	+	0.136471i
$426$		0			0
$427$	7.89016	−	4.02024i	0.381831	−	0.194553i
$428$		0			0
$429$	−22.5703	+	13.9291i	−1.08970	+	0.672503i
$430$		0			0
$431$	−0.640906	+	0.326558i	−0.0308713	+	0.0157297i	−0.469358	−	0.883008i	$-0.655515\pi$
$431$	−0.640906	+	0.326558i	−0.0308713	+	0.0157297i	0.438487	+	0.898738i	$0.355515\pi$
$432$		0			0
$433$	10.6300	−	14.6309i	0.510844	−	0.703117i	−0.473217	−	0.880946i	$-0.656907\pi$
$433$	10.6300	−	14.6309i	0.510844	−	0.703117i	0.984061	+	0.177829i	$0.0569074\pi$
$434$		0			0
$435$	17.9225	−	35.1748i	0.859316	−	1.68650i
$436$		0			0
$437$	−0.895965	+	5.65690i	−0.0428598	+	0.270606i
$438$		0			0
$439$	10.2437			0.488906			0.244453	−	0.969661i	$-0.421392\pi$
$439$	10.2437			0.488906			0.244453	+	0.969661i	$0.421392\pi$
$440$		0			0
$441$		−	8.10855i		−	0.386121i
$442$		0			0
$443$	−3.17362	+	2.30577i	−0.150783	+	0.109550i	−0.660619	−	0.750721i	$-0.729706\pi$
$443$	−3.17362	+	2.30577i	−0.150783	+	0.109550i	0.509836	+	0.860272i	$0.329706\pi$
$444$		0			0
$445$	8.64256	+	26.5991i	0.409696	+	1.26092i
$446$		0			0
$447$	−0.471708	−	2.97825i	−0.0223110	−	0.140866i
$448$		0			0
$449$	35.8015	−	18.2418i	1.68958	−	0.860881i	0.700468	−	0.713684i	$-0.252975\pi$
$449$	35.8015	−	18.2418i	1.68958	−	0.860881i	0.989107	−	0.147198i	$-0.0470253\pi$
$450$		0			0
$451$	12.0398	−	28.7305i	0.566933	−	1.35287i
$452$		0			0
$453$	−9.11652	−	17.8922i	−0.428331	−	0.840648i
$454$		0			0
$455$	−4.44690	+	29.4632i	−0.208474	+	1.38126i
$456$		0			0
$457$	14.6781	−	28.8073i	0.686611	−	1.34755i	−0.239722	−	0.970842i	$-0.577056\pi$
$457$	14.6781	−	28.8073i	0.686611	−	1.34755i	0.926332	−	0.376708i	$-0.122944\pi$
$458$		0			0
$459$	6.22024	−	4.51927i	0.290336	−	0.210942i
$460$		0			0
$461$	−7.77956	−	7.77956i	−0.362330	−	0.362330i	0.502340	−	0.864670i	$-0.332473\pi$
$461$	−7.77956	−	7.77956i	−0.362330	−	0.362330i	−0.864670	+	0.502340i	$0.832473\pi$
$462$		0			0
$463$	−11.0773	−	11.0773i	−0.514804	−	0.514804i	0.401191	−	0.915995i	$-0.368596\pi$
$463$	−11.0773	−	11.0773i	−0.514804	−	0.514804i	−0.915995	+	0.401191i	$0.868596\pi$
$464$		0			0
$465$	−1.57805	−	2.17201i	−0.0731805	−	0.100724i
$466$		0			0
$467$	−37.2996	+	12.1194i	−1.72602	+	0.560818i	−0.992865	−	0.119243i	$-0.961953\pi$
$467$	−37.2996	+	12.1194i	−1.72602	+	0.560818i	−0.733156	+	0.680061i	$0.761953\pi$
$468$		0			0
$469$	7.87246	−	10.8355i	0.363517	−	0.500338i
$470$		0			0
$471$	0.367434	−	1.13085i	0.0169305	−	0.0521066i
$472$		0			0
$473$	4.06654	−	16.6354i	0.186980	−	0.764898i
$474$		0			0
$475$	−1.67145	−	3.28041i	−0.0766916	−	0.150516i
$476$		0			0
$477$	11.5610	+	8.39955i	0.529341	+	0.384589i
$478$		0			0
$479$	−13.9011	−	7.08297i	−0.635158	−	0.323629i	0.106595	−	0.994303i	$-0.466005\pi$
$479$	−13.9011	−	7.08297i	−0.635158	−	0.323629i	−0.741753	+	0.670673i	$0.766005\pi$
$480$		0			0
$481$	−29.0750	+	9.68162i	−1.32571	+	0.441444i
$482$		0			0
$483$	−8.86292	−	8.86292i	−0.403277	−	0.403277i
$484$		0			0
$485$			45.3172i			2.05775i
$486$		0			0
$487$	−1.40250	+	8.85505i	−0.0635535	+	0.401261i	0.935320	+	0.353803i	$0.115112\pi$
$487$	−1.40250	+	8.85505i	−0.0635535	+	0.401261i	−0.998873	+	0.0474574i	$0.984888\pi$
$488$		0			0
$489$	25.4802	−	50.0078i	1.15226	−	2.26143i
$490$		0			0
$491$	−23.8885	−	17.3560i	−1.07807	−	0.783266i	−0.100727	−	0.994914i	$-0.532117\pi$
$491$	−23.8885	−	17.3560i	−1.07807	−	0.783266i	−0.977346	+	0.211649i	$0.932117\pi$
$492$		0			0
$493$	−22.0113	−	7.15190i	−0.991338	−	0.322105i
$494$		0			0
$495$	8.14804	+	13.4205i	0.366227	+	0.603206i
$496$		0			0
$497$	12.4805	+	4.05518i	0.559829	+	0.181900i
$498$		0			0
$499$	−31.8222	+	5.04014i	−1.42456	+	0.225628i	−0.820652	−	0.571428i	$-0.806390\pi$
$499$	−31.8222	+	5.04014i	−1.42456	+	0.225628i	−0.603906	+	0.797056i	$0.706390\pi$
$500$		0			0
$501$	15.4665	+	7.88056i	0.690991	+	0.352077i
$502$		0			0
$503$	21.6105	+	29.7443i	0.963564	+	1.32623i	0.945232	+	0.326400i	$0.105836\pi$
$503$	21.6105	+	29.7443i	0.963564	+	1.32623i	0.0183321	+	0.999832i	$0.494164\pi$
$504$		0			0
$505$	−18.2878	+	18.2878i	−0.813795	+	0.813795i
$506$		0			0
$507$	16.6061	−	23.5706i	0.737505	−	1.04681i
$508$		0			0
$509$	−0.942722	+	5.95211i	−0.0417854	+	0.263823i	−0.999733	−	0.0231216i	$-0.992640\pi$
$509$	−0.942722	+	5.95211i	−0.0417854	+	0.263823i	0.957947	+	0.286944i	$0.0926395\pi$
$510$		0			0
$511$	28.9405	−	9.40333i	1.28025	−	0.415979i
$512$		0			0
$513$	1.27336	+	8.03968i	0.0562203	+	0.354961i
$514$		0			0
$515$	29.2063	−	14.8814i	1.28698	−	0.655751i
$516$		0			0
$517$	−7.62966	+	18.2066i	−0.335552	+	0.800726i
$518$		0			0
$519$	9.57011	−	29.4538i	0.420081	−	1.29288i
$520$		0			0
$521$	27.1907	+	19.7552i	1.19125	+	0.865492i	0.993396	−	0.114740i	$-0.0366035\pi$
$521$	27.1907	+	19.7552i	1.19125	+	0.865492i	0.197852	+	0.980232i	$0.436603\pi$
$522$		0			0
$523$	5.85592	−	1.90271i	0.256062	−	0.0831995i	−0.178173	−	0.983999i	$-0.557019\pi$
$523$	5.85592	−	1.90271i	0.256062	−	0.0831995i	0.434235	+	0.900800i	$0.357019\pi$
$524$		0			0
$525$	7.95795	+	1.26041i	0.347313	+	0.0550090i
$526$		0			0
$527$	−1.11295	+	1.11295i	−0.0484809	+	0.0484809i
$528$		0			0
$529$	20.1549			0.876298
$530$		0			0
$531$	6.33808	+	1.00385i	0.275049	+	0.0435635i
$532$		0			0
$533$	0.246527	+	33.8641i	0.0106783	+	1.46682i
$534$		0			0
$535$	5.18925	+	32.7637i	0.224351	+	1.41650i
$536$		0			0
$537$	8.57896	+	2.78747i	0.370209	+	0.120288i
$538$		0			0
$539$	1.04175	+	13.9743i	0.0448715	+	0.601914i
$540$		0			0
$541$	13.9476	+	27.3738i	0.599656	+	1.17689i	0.968875	+	0.247549i	$0.0796250\pi$
$541$	13.9476	+	27.3738i	0.599656	+	1.17689i	−0.369220	+	0.929342i	$0.620375\pi$
$542$		0			0
$543$	−25.5277	+	35.1358i	−1.09550	+	1.50782i
$544$		0			0
$545$	12.6603	+	38.9644i	0.542308	+	1.66905i
$546$		0			0
$547$	10.1096	+	13.9147i	0.432256	+	0.594949i	0.968469	−	0.249133i	$-0.0801457\pi$
$547$	10.1096	+	13.9147i	0.432256	+	0.594949i	−0.536213	+	0.844083i	$0.680146\pi$
$548$		0			0
$549$			5.07245i			0.216487i
$550$		0			0
$551$	17.3258	−	17.3258i	0.738103	−	0.738103i
$552$		0			0
$553$	−21.1373	−	3.34782i	−0.898849	−	0.142364i
$554$		0			0
$555$	14.3686	+	44.2220i	0.609913	+	1.87712i
$556$		0			0
$557$	−10.6669	+	1.68947i	−0.451971	+	0.0715852i	−0.378270	−	0.925695i	$-0.623481\pi$
$557$	−10.6669	+	1.68947i	−0.451971	+	0.0715852i	−0.0737008	+	0.997280i	$0.523481\pi$
$558$		0			0
$559$	3.04614	+	18.3662i	0.128838	+	0.776809i
$560$		0			0
$561$	18.0032	−	15.2480i	0.760095	−	0.643773i
$562$		0			0
$563$	7.28902	−	22.4333i	0.307196	−	0.945451i	−0.671653	−	0.740866i	$-0.734415\pi$
$563$	7.28902	−	22.4333i	0.307196	−	0.945451i	0.978849	−	0.204585i	$-0.0655845\pi$
$564$		0			0
$565$	34.7606	−	5.50554i	1.46239	−	0.231620i
$566$		0			0
$567$	−33.0592	−	16.8445i	−1.38836	−	0.707403i
$568$		0			0
$569$	−9.56976	+	6.95284i	−0.401185	+	0.291478i	−0.770024	−	0.638015i	$-0.779756\pi$
$569$	−9.56976	+	6.95284i	−0.401185	+	0.291478i	0.368838	+	0.929494i	$0.379756\pi$
$570$		0			0
$571$	−2.35392			−0.0985086			−0.0492543	−	0.998786i	$-0.515684\pi$
$571$	−2.35392			−0.0985086			−0.0492543	+	0.998786i	$0.515684\pi$
$572$		0			0
$573$	32.6894			1.36562
$574$		0			0
$575$	1.47962	−	1.07501i	0.0617046	−	0.0448310i
$576$		0			0
$577$	−29.7349	−	15.1507i	−1.23788	−	0.630731i	−0.292363	−	0.956307i	$-0.594442\pi$
$577$	−29.7349	−	15.1507i	−1.23788	−	0.630731i	−0.945516	+	0.325576i	$0.894442\pi$
$578$		0			0
$579$	51.2960	−	8.12448i	2.13179	−	0.337642i
$580$		0			0
$581$	−6.94719	+	21.3813i	−0.288218	+	0.887044i
$582$		0			0
$583$	−21.0033	−	12.9905i	−0.869869	−	0.538010i
$584$		0			0
$585$	−13.8810	−	9.93156i	−0.573909	−	0.410619i
$586$		0			0
$587$	2.59821	−	0.411516i	0.107240	−	0.0169851i	−0.102584	−	0.994724i	$-0.532711\pi$
$587$	2.59821	−	0.411516i	0.107240	−	0.0169851i	0.209824	+	0.977739i	$0.432711\pi$
$588$		0			0
$589$	−0.514924	−	1.58477i	−0.0212171	−	0.0652994i
$590$		0			0
$591$	3.68027	+	0.582898i	0.151386	+	0.0239772i
$592$		0			0
$593$	−14.5536	+	14.5536i	−0.597646	+	0.597646i	−0.939685	−	0.342040i	$-0.888882\pi$
$593$	−14.5536	+	14.5536i	−0.597646	+	0.597646i	0.342040	+	0.939685i	$0.388882\pi$
$594$		0			0
$595$		−	26.5055i		−	1.08662i
$596$		0			0
$597$	−32.5722	−	44.8318i	−1.33309	−	1.83484i
$598$		0			0
$599$	4.07680	+	12.5471i	0.166574	+	0.512661i	0.999149	−	0.0412513i	$-0.0131344\pi$
$599$	4.07680	+	12.5471i	0.166574	+	0.512661i	−0.832575	+	0.553912i	$0.813134\pi$
$600$		0			0
$601$	−9.15095	+	12.5952i	−0.373275	+	0.513769i	−0.953787	−	0.300482i	$-0.902852\pi$
$601$	−9.15095	+	12.5952i	−0.373275	+	0.513769i	0.580512	+	0.814252i	$0.302852\pi$
$602$		0			0
$603$	3.48298	+	6.83574i	0.141838	+	0.278373i
$604$		0			0
$605$	−15.7665	−	22.0820i	−0.641000	−	0.897761i
$606$		0			0
$607$	44.1232	+	14.3365i	1.79091	+	0.581901i	0.999566	−	0.0294740i	$-0.00938322\pi$
$607$	44.1232	+	14.3365i	1.79091	+	0.581901i	0.791341	+	0.611375i	$0.209383\pi$
$608$		0			0
$609$	8.38830	+	52.9616i	0.339911	+	2.14611i
$610$		0			0
$611$	−0.156225	−	21.4598i	−0.00632018	−	0.868169i
$612$		0			0
$613$	−38.3130	−	6.06818i	−1.54745	−	0.245091i	−0.676490	−	0.736452i	$-0.736500\pi$
$613$	−38.3130	−	6.06818i	−1.54745	−	0.245091i	−0.870956	+	0.491361i	$0.836500\pi$
$614$		0			0
$615$	51.3841			2.07201
$616$		0			0
$617$	−13.3622	+	13.3622i	−0.537943	+	0.537943i	−0.922924	−	0.384982i	$-0.874208\pi$
$617$	−13.3622	+	13.3622i	−0.537943	+	0.537943i	0.384982	+	0.922924i	$0.374208\pi$
$618$		0			0
$619$	34.4012	+	5.44862i	1.38270	+	0.218998i	0.803072	−	0.595882i	$-0.203197\pi$
$619$	34.4012	+	5.44862i	1.38270	+	0.218998i	0.579629	+	0.814880i	$0.303197\pi$
$620$		0			0
$621$	−3.84566	+	1.24953i	−0.154321	+	0.0501420i
$622$		0			0
$623$	−30.7332	−	22.3290i	−1.23130	−	0.894592i
$624$		0			0
$625$	9.03743	−	27.8143i	0.361497	−	1.11257i
$626$		0			0
$627$	5.73052	+	24.3112i	0.228855	+	0.970894i
$628$		0			0
$629$	24.2885	−	12.3756i	0.968445	−	0.493447i
$630$		0			0
$631$	−0.910273	−	5.74724i	−0.0362374	−	0.228794i	0.962922	−	0.269779i	$-0.0869505\pi$
$631$	−0.910273	−	5.74724i	−0.0362374	−	0.228794i	−0.999160	+	0.0409847i	$0.986950\pi$
$632$		0			0
$633$	7.81693	−	2.53987i	0.310695	−	0.100951i
$634$		0			0
$635$	−1.34128	+	8.46848i	−0.0532269	+	0.336061i
$636$		0			0
$637$	−7.01461	−	13.5227i	−0.277929	−	0.535788i
$638$		0			0
$639$	−5.31527	+	5.31527i	−0.210269	+	0.210269i
$640$		0			0
$641$	−9.82375	−	13.5212i	−0.388015	−	0.534056i	0.569671	−	0.821873i	$-0.307071\pi$
$641$	−9.82375	−	13.5212i	−0.388015	−	0.534056i	−0.957686	+	0.287817i	$0.907071\pi$
$642$		0			0
$643$	1.10231	+	0.561657i	0.0434710	+	0.0221496i	0.475591	−	0.879667i	$-0.342234\pi$
$643$	1.10231	+	0.561657i	0.0434710	+	0.0221496i	−0.432120	+	0.901816i	$0.642234\pi$
$644$		0			0
$645$	27.9004	−	4.41899i	1.09858	−	0.173997i
$646$		0			0
$647$	44.2540	+	14.3790i	1.73980	+	0.565296i	0.994808	−	0.101773i	$-0.0324516\pi$
$647$	44.2540	+	14.3790i	1.73980	+	0.565296i	0.744996	+	0.667069i	$0.232452\pi$
$648$		0			0
$649$	−11.0520	−	0.915748i	−0.433829	−	0.0359463i
$650$		0			0
$651$	3.46817	+	1.12688i	0.135928	+	0.0441657i
$652$		0			0
$653$	6.03777	+	4.38669i	0.236276	+	0.171665i	0.699623	−	0.714513i	$-0.253351\pi$
$653$	6.03777	+	4.38669i	0.236276	+	0.171665i	−0.463347	+	0.886177i	$0.653351\pi$
$654$		0			0
$655$	−16.5040	+	32.3910i	−0.644866	+	1.26562i
$656$		0			0
$657$	−2.72674	+	17.2160i	−0.106380	+	0.671660i
$658$		0			0
$659$		−	37.8887i		−	1.47594i	−0.674836	−	0.737968i	$-0.735786\pi$
$659$		−	37.8887i		−	1.47594i	0.674836	−	0.737968i	$-0.264214\pi$
$660$		0			0
$661$	1.28970	+	1.28970i	0.0501636	+	0.0501636i	0.731744	−	0.681580i	$-0.238707\pi$
$661$	1.28970	+	1.28970i	0.0501636	+	0.0501636i	−0.681580	+	0.731744i	$0.738707\pi$
$662$		0			0
$663$	−11.4773	+	22.9367i	−0.445741	+	0.890788i
$664$		0			0
$665$	25.0027	+	12.7395i	0.969563	+	0.494017i
$666$		0			0
$667$	9.84717	+	7.15439i	0.381284	+	0.277019i
$668$		0			0
$669$	−0.448775	−	0.880770i	−0.0173506	−	0.0340525i
$670$		0			0
$671$	−0.651687	−	8.74184i	−0.0251581	−	0.337475i
$672$		0			0
$673$	−0.714700	+	2.19962i	−0.0275497	+	0.0847892i	−0.963886	−	0.266315i	$-0.914194\pi$
$673$	−0.714700	+	2.19962i	−0.0275497	+	0.0847892i	0.936336	+	0.351104i	$0.114194\pi$
$674$		0			0
$675$	1.52782	−	2.10287i	0.0588059	−	0.0809394i
$676$		0			0
$677$	−10.7600	+	3.49614i	−0.413541	+	0.134368i	−0.508396	−	0.861124i	$-0.669761\pi$
$677$	−10.7600	+	3.49614i	−0.413541	+	0.134368i	0.0948549	+	0.995491i	$0.469761\pi$
$678$		0			0
$679$	−36.1803	−	49.7978i	−1.38847	−	1.91107i
$680$		0			0
$681$	−18.1678	−	18.1678i	−0.696192	−	0.696192i
$682$		0			0
$683$	0.462070	+	0.462070i	0.0176806	+	0.0176806i	0.715892	−	0.698211i	$-0.246020\pi$
$683$	0.462070	+	0.462070i	0.0176806	+	0.0176806i	−0.698211	+	0.715892i	$0.746020\pi$
$684$		0			0
$685$	13.1697	−	9.56838i	0.503190	−	0.365589i
$686$		0			0
$687$	26.3708	−	51.7557i	1.00611	−	1.97460i
$688$		0			0
$689$	26.5467	+	4.00671i	1.01135	+	0.152643i
$690$		0			0
$691$	−9.80113	−	19.2358i	−0.372853	−	0.731764i	0.625992	−	0.779830i	$-0.284694\pi$
$691$	−9.80113	−	19.2358i	−0.372853	−	0.731764i	−0.998844	+	0.0480655i	$0.984694\pi$
$692$		0			0
$693$	−19.6683	−	8.24219i	−0.747137	−	0.313095i
$694$		0			0
$695$	−11.3530	+	5.78465i	−0.430644	+	0.219424i
$696$		0			0
$697$	−4.71247	−	29.7534i	−0.178498	−	1.12699i
$698$		0			0
$699$	10.7081	+	32.9562i	0.405018	+	1.24652i
$700$		0			0
$701$	14.5669	−	10.5835i	0.550185	−	0.399733i	−0.277668	−	0.960677i	$-0.589562\pi$
$701$	14.5669	−	10.5835i	0.550185	−	0.399733i	0.827854	+	0.560944i	$0.189562\pi$
$702$		0			0
$703$			28.8595i			1.08846i
$704$		0			0
$705$	−32.5622			−1.22636
$706$		0			0
$707$	5.49539	−	34.6965i	0.206675	−	1.30490i
$708$		0			0
$709$	1.74141	−	3.41771i	0.0654000	−	0.128355i	−0.855992	−	0.516989i	$-0.827053\pi$
$709$	1.74141	−	3.41771i	0.0654000	−	0.128355i	0.921392	+	0.388634i	$0.127053\pi$
$710$		0			0
$711$	7.20544	−	9.91744i	0.270225	−	0.371933i
$712$		0			0
$713$	0.737542	−	0.375797i	0.0276212	−	0.0140737i
$714$		0			0
$715$	25.1985	+	15.3326i	0.942369	+	0.573408i
$716$		0			0
$717$	−41.3494	+	21.0686i	−1.54422	+	0.786820i
$718$		0			0
$719$	−13.4416	+	18.5008i	−0.501287	+	0.689963i	−0.982420	−	0.186685i	$-0.940226\pi$
$719$	−13.4416	+	18.5008i	−0.501287	+	0.689963i	0.481132	+	0.876648i	$0.340226\pi$
$720$		0			0
$721$	−20.2131	+	39.6704i	−0.752775	+	1.47740i
$722$		0			0
$723$	−4.80122	+	30.3137i	−0.178559	+	1.12738i
$724$		0			0
$725$	−7.82426			−0.290586
$726$		0			0
$727$			33.4585i			1.24091i	0.784243	+	0.620454i	$0.213052\pi$
$727$			33.4585i			1.24091i	−0.784243	+	0.620454i	$0.786948\pi$
$728$		0			0
$729$	4.28985	−	3.11676i	0.158883	−	0.115436i
$730$		0			0
$731$	−5.11753	−	15.7501i	−0.189279	−	0.582540i
$732$		0			0
$733$	−7.03084	−	44.3909i	−0.259690	−	1.63962i	−0.680701	−	0.732562i	$-0.738325\pi$
$733$	−7.03084	−	44.3909i	−0.259690	−	1.63962i	0.421011	−	0.907056i	$-0.361675\pi$
$734$		0			0
$735$	−20.5952	+	10.4938i	−0.759665	+	0.387069i
$736$		0			0
$737$	−6.88079	−	11.3332i	−0.253457	−	0.417464i
$738$		0			0
$739$	−16.9117	−	33.1912i	−0.622109	−	1.22096i	−0.960060	−	0.279793i	$-0.909734\pi$
$739$	−16.9117	−	33.1912i	−0.622109	−	1.22096i	0.337952	−	0.941163i	$-0.390266\pi$
$740$		0			0
$741$	−16.1198	−	21.8507i	−0.592176	−	0.802706i
$742$		0			0
$743$	−4.76244	+	9.34682i	−0.174717	+	0.342902i	−0.961714	−	0.274055i	$-0.911635\pi$
$743$	−4.76244	+	9.34682i	−0.174717	+	0.342902i	0.786997	+	0.616957i	$0.211635\pi$
$744$		0			0
$745$	−2.71305	+	1.97115i	−0.0993985	+	0.0722173i
$746$		0			0
$747$	−9.10594	−	9.10594i	−0.333169	−	0.333169i
$748$		0			0
$749$	−31.8601	−	31.8601i	−1.16414	−	1.16414i
$750$		0			0
$751$	12.0899	+	16.6403i	0.441167	+	0.607214i	0.970471	−	0.241218i	$-0.0775469\pi$
$751$	12.0899	+	16.6403i	0.441167	+	0.607214i	−0.529304	+	0.848432i	$0.677547\pi$
$752$		0			0
$753$	−37.1467	+	12.0697i	−1.35370	+	0.439844i
$754$		0			0
$755$	−13.1269	+	18.0676i	−0.477735	+	0.657546i
$756$		0			0
$757$	−2.98299	+	9.18070i	−0.108419	+	0.333678i	−0.990518	−	0.137386i	$-0.956130\pi$
$757$	−2.98299	+	9.18070i	−0.108419	+	0.333678i	0.882099	+	0.471064i	$0.156130\pi$
$758$		0			0
$759$	−11.4828	+	4.70086i	−0.416798	+	0.170631i
$760$		0			0
$761$	−17.4040	−	34.1573i	−0.630895	−	1.23820i	−0.956234	−	0.292604i	$-0.905478\pi$
$761$	−17.4040	−	34.1573i	−0.630895	−	1.23820i	0.325339	−	0.945598i	$-0.394522\pi$
$762$		0			0
$763$	−45.0204	−	32.7093i	−1.62985	−	1.18415i
$764$		0			0
$765$	13.5279	+	6.89281i	0.489102	+	0.249210i
$766$		0			0
$767$	11.4385	−	3.80887i	0.413020	−	0.137530i
$768$		0			0
$769$	11.5214	+	11.5214i	0.415473	+	0.415473i	0.883640	−	0.468167i	$-0.155085\pi$
$769$	11.5214	+	11.5214i	0.415473	+	0.415473i	−0.468167	+	0.883640i	$0.655085\pi$
$770$		0			0
$771$		−	43.6355i		−	1.57150i
$772$		0			0
$773$	−5.55260	+	35.0577i	−0.199713	+	1.26094i	0.660431	+	0.750887i	$0.270374\pi$
$773$	−5.55260	+	35.0577i	−0.199713	+	1.26094i	−0.860144	+	0.510052i	$0.829626\pi$
$774$		0			0
$775$	−0.241570	+	0.474107i	−0.00867744	+	0.0170304i
$776$		0			0
$777$	−51.0951	−	37.1228i	−1.83303	−	1.33177i
$778$		0			0
$779$	30.3314	+	9.85526i	1.08673	+	0.353101i
$780$		0			0
$781$	8.47743	−	9.84320i	0.303346	−	0.352217i
$782$		0			0
$783$	16.4521	+	5.34560i	0.587949	+	0.191036i
$784$		0			0
$785$	−1.30610	+	0.206866i	−0.0466168	+	0.00738337i
$786$		0			0
$787$	−27.1046	−	13.8105i	−0.966174	−	0.492290i	−0.101616	−	0.994824i	$-0.532401\pi$
$787$	−27.1046	−	13.8105i	−0.966174	−	0.492290i	−0.864558	+	0.502533i	$0.832401\pi$
$788$		0			0
$789$	27.3471	+	37.6401i	0.973583	+	1.34002i
$790$		0			0
$791$	−33.8020	+	33.8020i	−1.20186	+	1.20186i
$792$		0			0
$793$	4.38811	+	8.45935i	0.155827	+	0.300400i
$794$		0			0
$795$	6.37253	−	40.2345i	0.226010	−	1.42697i
$796$		0			0
$797$	−8.89737	+	2.89093i	−0.315161	+	0.102402i	−0.462326	−	0.886710i	$-0.652985\pi$
$797$	−8.89737	+	2.89093i	−0.315161	+	0.102402i	0.147165	+	0.989112i	$0.452985\pi$
$798$		0			0
$799$	2.98631	+	18.8548i	0.105648	+	0.667035i
$800$		0			0
$801$	19.3885	−	9.87892i	0.685058	−	0.349055i
$802$		0			0
$803$	2.48743	−	30.0203i	0.0877793	−	1.05939i
$804$		0			0
$805$	−4.30759	+	13.2574i	−0.151822	+	0.467261i
$806$		0			0
$807$	−44.9147	−	32.6324i	−1.58107	−	1.14872i
$808$		0			0
$809$	−1.20371	+	0.391108i	−0.0423200	+	0.0137506i	−0.330101	−	0.943946i	$-0.607083\pi$
$809$	−1.20371	+	0.391108i	−0.0423200	+	0.0137506i	0.287780	+	0.957696i	$0.407083\pi$
$810$		0			0
$811$	21.2736	+	3.36942i	0.747019	+	0.118316i	0.518327	−	0.855183i	$-0.326555\pi$
$811$	21.2736	+	3.36942i	0.747019	+	0.118316i	0.228692	+	0.973499i	$0.426555\pi$
$812$		0			0
$813$	6.55438	−	6.55438i	0.229872	−	0.229872i
$814$		0			0
$815$	−62.4190			−2.18644
$816$		0			0
$817$	17.3168	+	2.74271i	0.605838	+	0.0959552i
$818$		0			0
$819$	23.1826	−	0.168767i	0.810066	−	0.00589720i
$820$		0			0
$821$	3.20139	+	20.2128i	0.111729	+	0.705430i	0.978426	+	0.206596i	$0.0662385\pi$
$821$	3.20139	+	20.2128i	0.111729	+	0.705430i	−0.866697	+	0.498835i	$0.833762\pi$
$822$		0			0
$823$	2.15786	+	0.701133i	0.0752184	+	0.0244399i	0.346384	−	0.938093i	$-0.387409\pi$
$823$	2.15786	+	0.701133i	0.0752184	+	0.0244399i	−0.271166	+	0.962533i	$0.587409\pi$
$824$		0			0
$825$	4.19547	−	6.78335i	0.146068	−	0.236166i
$826$		0			0
$827$	12.7105	+	24.9458i	0.441988	+	0.867451i	0.999310	+	0.0371539i	$0.0118292\pi$
$827$	12.7105	+	24.9458i	0.441988	+	0.867451i	−0.557321	+	0.830297i	$0.688171\pi$
$828$		0			0
$829$	20.5522	−	28.2877i	0.713808	−	0.982472i	−0.285899	−	0.958260i	$-0.592292\pi$
$829$	20.5522	−	28.2877i	0.713808	−	0.982472i	0.999707	−	0.0242124i	$-0.00770780\pi$
$830$		0			0
$831$	−14.0809	−	43.3365i	−0.488460	−	1.50333i
$832$		0			0
$833$	7.96510	+	10.9630i	0.275975	+	0.379846i
$834$		0			0
$835$		−	19.3050i		−	0.668077i
$836$		0			0
$837$	0.831863	−	0.831863i	0.0287534	−	0.0287534i
$838$		0			0
$839$	32.7531	+	5.18759i	1.13076	+	0.179095i	0.693651	−	0.720311i	$-0.256001\pi$
$839$	32.7531	+	5.18759i	1.13076	+	0.179095i	0.437113	+	0.899407i	$0.356001\pi$
$840$		0			0
$841$	−7.12960	−	21.9427i	−0.245848	−	0.756644i
$842$		0			0
$843$	64.3359	−	10.1898i	2.21585	−	0.350956i
$844$		0			0
$845$	−31.7411	−	4.55463i	−1.09193	−	0.156684i
$846$		0			0
$847$	34.9552	+	11.6777i	1.20108	+	0.401250i
$848$		0			0
$849$	−14.3472	+	44.1560i	−0.492393	+	1.51543i
$850$		0			0
$851$	−14.1597	+	2.24268i	−0.485389	+	0.0768780i
$852$		0			0
$853$	−9.64690	−	4.91534i	−0.330303	−	0.168298i	0.280972	−	0.959716i	$-0.409343\pi$
$853$	−9.64690	−	4.91534i	−0.330303	−	0.168298i	−0.611275	+	0.791418i	$0.709343\pi$
$854$		0			0
$855$	−13.0040	+	9.44794i	−0.444727	+	0.323113i
$856$		0			0
$857$	40.9238			1.39793			0.698965	−	0.715156i	$-0.253644\pi$
$857$	40.9238			1.39793			0.698965	+	0.715156i	$0.253644\pi$
$858$		0			0
$859$	−24.4983			−0.835871			−0.417935	−	0.908477i	$-0.637246\pi$
$859$	−24.4983			−0.835871			−0.417935	+	0.908477i	$0.637246\pi$
$860$		0			0
$861$	−56.4647	+	41.0240i	−1.92431	+	1.39809i
$862$		0			0
$863$	−33.3741	−	17.0049i	−1.13607	−	0.578855i	−0.218263	−	0.975890i	$-0.570039\pi$
$863$	−33.3741	−	17.0049i	−1.13607	−	0.578855i	−0.917804	+	0.397035i	$0.870039\pi$
$864$		0			0
$865$	−34.0184	+	5.38799i	−1.15666	+	0.183197i
$866$		0			0
$867$	−4.60115	+	14.1609i	−0.156263	+	0.480928i
$868$		0			0
$869$	−11.1437	+	18.0174i	−0.378024	+	0.611199i
$870$		0			0
$871$	11.7221	+	8.38692i	0.397189	+	0.284180i
$872$		0			0
$873$	34.8245	−	5.51567i	1.17863	−	0.186677i
$874$		0			0
$875$	9.99985	+	30.7764i	0.338057	+	1.04043i
$876$		0			0
$877$	11.7714	+	1.86440i	0.397491	+	0.0629563i	0.351980	−	0.936008i	$-0.385508\pi$
$877$	11.7714	+	1.86440i	0.397491	+	0.0629563i	0.0455107	+	0.998964i	$0.485508\pi$
$878$		0			0
$879$	−35.9616	+	35.9616i	−1.21296	+	1.21296i
$880$		0			0
$881$		−	37.2387i		−	1.25460i	−0.778777	−	0.627301i	$-0.784160\pi$
$881$		−	37.2387i		−	1.25460i	0.778777	−	0.627301i	$-0.215840\pi$
$882$		0			0
$883$	13.2476	+	18.2337i	0.445816	+	0.613613i	0.971492	−	0.237071i	$-0.0761875\pi$
$883$	13.2476	+	18.2337i	0.445816	+	0.613613i	−0.525676	+	0.850685i	$0.676188\pi$
$884$		0			0
$885$	−5.65278	−	17.3975i	−0.190016	−	0.584810i
$886$		0			0
$887$	−12.8719	+	17.7166i	−0.432195	+	0.594866i	−0.968455	−	0.249187i	$-0.919837\pi$
$887$	−12.8719	+	17.7166i	−0.432195	+	0.594866i	0.536260	+	0.844053i	$0.319837\pi$
$888$		0			0
$889$	−5.28716	−	10.3766i	−0.177326	−	0.348021i
$890$		0			0
$891$	−28.0275	+	23.7383i	−0.938956	+	0.795262i
$892$		0			0
$893$	−19.2211	−	6.24530i	−0.643208	−	0.208991i
$894$		0			0
$895$	−1.56935	−	9.90850i	−0.0524577	−	0.331205i
$896$		0			0
$897$	9.46823	−	9.60710i	0.316135	−	0.320772i
$898$		0			0
$899$	−3.49764	−	0.553972i	−0.116653	−	0.0184760i
$900$		0			0
$901$	−23.8818			−0.795618
$902$		0			0
$903$	−27.1310	+	27.1310i	−0.902863	+	0.902863i
$904$		0			0
$905$	47.7059	+	7.55587i	1.58580	+	0.251166i
$906$		0			0
$907$	−28.0777	+	9.12298i	−0.932303	+	0.302924i	−0.735504	−	0.677520i	$-0.763055\pi$
$907$	−28.0777	+	9.12298i	−0.932303	+	0.302924i	−0.196799	+	0.980444i	$0.563055\pi$
$908$		0			0
$909$	16.2793	+	11.8276i	0.539951	+	0.392297i
$910$		0			0
$911$	−2.30376	+	7.09023i	−0.0763268	+	0.234910i	−0.981939	−	0.189196i	$-0.939412\pi$
$911$	−2.30376	+	7.09023i	−0.0763268	+	0.234910i	0.905612	+	0.424106i	$0.139412\pi$
$912$		0			0
$913$	16.8630	+	14.5233i	0.558085	+	0.480650i
$914$		0			0
$915$	12.8837	−	6.56457i	0.425922	−	0.217018i
$916$		0			0
$917$	−7.72442	−	48.7701i	−0.255083	−	1.61053i
$918$		0			0
$919$	34.2991	−	11.1444i	1.13142	−	0.367621i	0.317306	−	0.948323i	$-0.397222\pi$
$919$	34.2991	−	11.1444i	1.13142	−	0.367621i	0.814116	+	0.580702i	$0.197222\pi$
$920$		0			0
$921$	−2.64104	+	16.6748i	−0.0870251	+	0.549455i
$922$		0			0
$923$	−4.26613	+	13.4625i	−0.140421	+	0.443123i
$924$		0			0
$925$	6.51642	−	6.51642i	0.214258	−	0.214258i
$926$		0			0
$927$	−14.9905	−	20.6327i	−0.492354	−	0.677668i
$928$		0			0
$929$	26.0040	+	13.2497i	0.853164	+	0.434709i	0.825160	−	0.564899i	$-0.191085\pi$
$929$	26.0040	+	13.2497i	0.853164	+	0.434709i	0.0280039	+	0.999608i	$0.491085\pi$
$930$		0			0
$931$	−14.1697	+	2.24427i	−0.464395	+	0.0735529i
$932$		0			0
$933$	26.0158	+	8.45306i	0.851721	+	0.276741i
$934$		0			0
$935$	−24.1995	−	10.1410i	−0.791408	−	0.331647i
$936$		0			0
$937$	−46.1165	−	14.9842i	−1.50656	−	0.489511i	−0.564637	−	0.825339i	$-0.690984\pi$
$937$	−46.1165	−	14.9842i	−1.50656	−	0.489511i	−0.941923	+	0.335828i	$0.890984\pi$
$938$		0			0
$939$	−17.4913	−	12.7082i	−0.570809	−	0.414717i
$940$		0			0
$941$	−10.1705	+	19.9608i	−0.331550	+	0.650703i	−0.995256	−	0.0972900i	$-0.968983\pi$
$941$	−10.1705	+	19.9608i	−0.331550	+	0.650703i	0.663706	+	0.747993i	$0.268983\pi$
$942$		0			0
$943$	−2.47836	+	15.6477i	−0.0807064	+	0.509560i
$944$		0			0
$945$			19.8113i			0.644460i
$946$		0			0
$947$	−35.7263	−	35.7263i	−1.16095	−	1.16095i	−0.984268	−	0.176681i	$-0.943464\pi$
$947$	−35.7263	−	35.7263i	−1.16095	−	1.16095i	−0.176681	−	0.984268i	$-0.556536\pi$
$948$		0			0
$949$	10.3459	+	31.0701i	0.335844	+	1.00858i
$950$		0			0
$951$	19.4780	+	9.92456i	0.631619	+	0.321826i
$952$		0			0
$953$	−17.6529	−	12.8256i	−0.571833	−	0.415461i	0.263938	−	0.964540i	$-0.414979\pi$
$953$	−17.6529	−	12.8256i	−0.571833	−	0.415461i	−0.835771	+	0.549079i	$0.814979\pi$
$954$		0			0
$955$	−16.5049	−	32.3928i	−0.534088	−	1.04821i
$956$		0			0
$957$	51.5632	+	12.6047i	1.66680	+	0.407450i
$958$		0			0
$959$	−6.83270	+	21.0289i	−0.220639	+	0.679058i
$960$		0			0
$961$	18.0798	−	24.8847i	0.583219	−	0.802732i
$962$		0			0
$963$	24.5461	−	7.97550i	0.790986	−	0.257007i
$964$		0			0
$965$	−33.9502	−	46.7284i	−1.09289	−	1.50424i
$966$		0			0
$967$	23.7822	+	23.7822i	0.764786	+	0.764786i	0.977183	−	0.212398i	$-0.0681272\pi$
$967$	23.7822	+	23.7822i	0.764786	+	0.764786i	−0.212398	+	0.977183i	$0.568127\pi$
$968$		0			0
$969$	17.0794	+	17.0794i	0.548670	+	0.548670i
$970$		0			0
$971$	10.9263	−	7.93842i	0.350642	−	0.254756i	−0.398497	−	0.917170i	$-0.630468\pi$
$971$	10.9263	−	7.93842i	0.350642	−	0.254756i	0.749138	+	0.662414i	$0.230468\pi$
$972$		0			0
$973$	7.85719	−	15.4206i	0.251890	−	0.494362i
$974$		0			0
$975$	−1.29403	+	8.57367i	−0.0414421	+	0.274577i
$976$		0			0
$977$	16.1494	+	31.6949i	0.516664	+	1.01401i	0.991025	+	0.133679i	$0.0426791\pi$
$977$	16.1494	+	31.6949i	0.516664	+	1.01401i	−0.474361	+	0.880330i	$0.657321\pi$
$978$		0			0
$979$	−32.1448	+	19.5163i	−1.02735	+	0.623742i
$980$		0			0
$981$	28.4018	−	14.4714i	0.906799	−	0.462037i
$982$		0			0
$983$	1.03457	+	6.53201i	0.0329976	+	0.208339i	0.998679	−	0.0513927i	$-0.0163660\pi$
$983$	1.03457	+	6.53201i	0.0329976	+	0.208339i	−0.965681	+	0.259731i	$0.916366\pi$
$984$		0			0
$985$	−1.28057	−	3.94118i	−0.0408022	−	0.125576i
$986$		0			0
$987$	35.7818	−	25.9970i	1.13895	−	0.827493i
$988$		0			0
$989$			8.70950i			0.276946i
$990$		0			0
$991$	54.4729			1.73039			0.865195	−	0.501436i	$-0.167195\pi$
$991$	54.4729			1.73039			0.865195	+	0.501436i	$0.167195\pi$
$992$		0			0
$993$	−3.84524	+	24.2779i	−0.122025	+	0.770435i
$994$		0			0
$995$	−27.9792	+	54.9122i	−0.886999	+	1.74083i
$996$		0			0
$997$	16.4217	−	22.6026i	0.520081	−	0.715830i	−0.465497	−	0.885049i	$-0.654124\pi$
$997$	16.4217	−	22.6026i	0.520081	−	0.715830i	0.985578	+	0.169219i	$0.0541245\pi$
$998$		0			0
$999$	−18.1542	+	9.25000i	−0.574372	+	0.292657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.4	✓	112
11.6	odd	10	inner	572.2.bh.a.369.4	yes	112
13.8	odd	4	inner	572.2.bh.a.541.4	yes	112
143.138	even	20	inner	572.2.bh.a.281.4	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.4	✓	112	1.1	even	1	trivial
572.2.bh.a.281.4	yes	112	143.138	even	20	inner
572.2.bh.a.369.4	yes	112	11.6	odd	10	inner
572.2.bh.a.541.4	yes	112	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79433 + 1.30366i) q^{3} +(2.19779 + 1.11983i) q^{5} +(-3.30914 + 0.524116i) q^{7} +(0.593048 - 1.82521i) q^{9} +O(q^{10})\)	\(q+(-1.79433 + 1.30366i) q^{3} +(2.19779 + 1.11983i) q^{5} +(-3.30914 + 0.524116i) q^{7} +(0.593048 - 1.82521i) q^{9} +(-0.787561 + 3.22176i) q^{11} +(-0.589942 - 3.55696i) q^{13} +(-5.40343 + 0.855819i) q^{15} +(0.991105 + 3.05031i) q^{17} +(-3.35372 - 0.531176i) q^{19} +(5.25442 - 5.25442i) q^{21} -1.68676i q^{23} +(0.637324 + 0.877201i) q^{25} +(-0.740790 - 2.27992i) q^{27} +(-4.24151 + 5.83794i) q^{29} +(0.222793 + 0.437255i) q^{31} +(-2.78693 - 6.80761i) q^{33} +(-7.85970 - 2.55377i) q^{35} +(-1.32958 - 8.39464i) q^{37} +(5.69561 + 5.61328i) q^{39} +(-9.27682 - 1.46930i) q^{41} -5.16346 q^{43} +(3.34732 - 3.34732i) q^{45} +(5.87874 + 0.931102i) q^{47} +(4.01830 - 1.30562i) q^{49} +(-5.75492 - 4.18120i) q^{51} +(-2.30098 + 7.08168i) q^{53} +(-5.33871 + 6.19881i) q^{55} +(6.71015 - 3.41899i) q^{57} +(0.523074 + 3.30256i) q^{59} +(-2.51372 + 0.816756i) q^{61} +(-1.00585 + 6.35071i) q^{63} +(2.68662 - 8.47807i) q^{65} +(-2.82672 + 2.82672i) q^{67} +(2.19895 + 3.02660i) q^{69} +(-3.48990 - 1.77819i) q^{71} +(-8.97066 + 1.42081i) q^{73} +(-2.28714 - 0.743137i) q^{75} +(0.917572 - 11.0740i) q^{77} +(6.07492 + 1.97386i) q^{79} +(8.95931 + 6.50932i) q^{81} +(3.04634 - 5.97879i) q^{83} +(-1.23758 + 7.81379i) q^{85} -16.0047i q^{87} +(8.01752 + 8.01752i) q^{89} +(3.81646 + 11.4613i) q^{91} +(-0.969794 - 0.494135i) q^{93} +(-6.77593 - 4.92300i) q^{95} +(8.34074 + 16.3696i) q^{97} +(5.41334 + 3.34813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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