LMFDB - Embedded newform 756.2.bf.d.271.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(271,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("756.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bf (of order $6$, degree $2$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			271.14
Character	$\chi$	$=$	756.271
Dual form			756.2.bf.d.703.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28874 + 0.582370i) q^{2} +(1.32169 + 1.50104i) q^{4} +(-1.99770 - 1.15337i) q^{5} +(0.0928632 + 2.64412i) q^{7} +(0.829152 + 2.70416i) q^{8} +O(q^{10})$	\(q+(1.28874 + 0.582370i) q^{2} +(1.32169 + 1.50104i) q^{4} +(-1.99770 - 1.15337i) q^{5} +(0.0928632 + 2.64412i) q^{7} +(0.829152 + 2.70416i) q^{8} +(-1.90282 - 2.64979i) q^{10} +(2.38028 - 1.37426i) q^{11} +5.36352i q^{13} +(-1.42018 + 3.46166i) q^{14} +(-0.506264 + 3.96783i) q^{16} +(-1.60656 + 0.927548i) q^{17} +(-1.03158 + 1.78675i) q^{19} +(-0.909078 - 4.52303i) q^{20} +(3.86789 - 0.384853i) q^{22} +(3.19592 + 1.84517i) q^{23} +(0.160525 + 0.278038i) q^{25} +(-3.12355 + 6.91217i) q^{26} +(-3.84620 + 3.63410i) q^{28} +6.56785 q^{29} +(-1.38202 - 2.39374i) q^{31} +(-2.96319 + 4.81866i) q^{32} +(-2.61061 + 0.259755i) q^{34} +(2.86414 - 5.38925i) q^{35} +(-2.63241 + 4.55948i) q^{37} +(-2.36999 + 1.70189i) q^{38} +(1.46251 - 6.35842i) q^{40} +8.65530i q^{41} -3.57467i q^{43} +(5.20882 + 1.75657i) q^{44} +(3.04414 + 4.23915i) q^{46} +(2.54973 - 4.41626i) q^{47} +(-6.98275 + 0.491083i) q^{49} +(0.0449542 + 0.451803i) q^{50} +(-8.05087 + 7.08891i) q^{52} +(-0.523381 - 0.906522i) q^{53} -6.34011 q^{55} +(-7.07314 + 2.44350i) q^{56} +(8.46424 + 3.82492i) q^{58} +(-6.66997 - 11.5527i) q^{59} +(7.62894 + 4.40457i) q^{61} +(-0.387028 - 3.88975i) q^{62} +(-6.62501 + 4.48433i) q^{64} +(6.18612 - 10.7147i) q^{65} +(13.7636 - 7.94642i) q^{67} +(-3.51567 - 1.18559i) q^{68} +(6.82966 - 5.27735i) q^{70} -14.2847i q^{71} +(5.96458 - 3.44365i) q^{73} +(-6.04779 + 4.34293i) q^{74} +(-4.04542 + 0.813085i) q^{76} +(3.85474 + 6.16614i) q^{77} +(3.51577 + 2.02983i) q^{79} +(5.58774 - 7.34261i) q^{80} +(-5.04058 + 11.1544i) q^{82} +0.863684 q^{83} +4.27923 q^{85} +(2.08178 - 4.60681i) q^{86} +(5.68984 + 5.29721i) q^{88} +(-13.9295 - 8.04218i) q^{89} +(-14.1818 + 0.498074i) q^{91} +(1.45435 + 7.23596i) q^{92} +(5.85783 - 4.20652i) q^{94} +(4.12157 - 2.37959i) q^{95} -4.58962i q^{97} +(-9.28493 - 3.43367i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{7}+O(q^{10}) $ 32 * q + 2 * q^7	$ 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) $ 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.28874	+	0.582370i	0.911275	+	0.411797i
$2$	1.28874	+	0.582370i	0.911275	+	0.411797i
$3$		0			0
$3$		0			0
$4$	1.32169	+	1.50104i	0.660846	+	0.750522i
$5$	−1.99770	−	1.15337i	−0.893397	−	0.515803i	−0.0183446	−	0.999832i	$-0.505840\pi$
$5$	−1.99770	−	1.15337i	−0.893397	−	0.515803i	−0.875052	+	0.484029i	$0.839173\pi$
$6$		0			0
$7$	0.0928632	+	2.64412i	0.0350990	+	0.999384i
$7$	0.0928632	+	2.64412i	0.0350990	+	0.999384i
$8$	0.829152	+	2.70416i	0.293149	+	0.956067i
$9$		0			0
$10$	−1.90282	−	2.64979i	−0.601724	−	0.837937i
$11$	2.38028	−	1.37426i	0.717683	−	0.414354i	−0.0962165	−	0.995360i	$-0.530674\pi$
$11$	2.38028	−	1.37426i	0.717683	−	0.414354i	0.813899	+	0.581006i	$0.197341\pi$
$12$		0			0
$13$			5.36352i			1.48757i	0.668418	+	0.743786i	$0.266972\pi$
$13$			5.36352i			1.48757i	−0.668418	+	0.743786i	$0.733028\pi$
$14$	−1.42018	+	3.46166i	−0.379559	+	0.925168i
$15$		0			0
$16$	−0.506264	+	3.96783i	−0.126566	+	0.991958i
$17$	−1.60656	+	0.927548i	−0.389648	+	0.224964i	−0.682008	−	0.731345i	$-0.738893\pi$
$17$	−1.60656	+	0.927548i	−0.389648	+	0.224964i	0.292359	+	0.956308i	$0.405560\pi$
$18$		0			0
$19$	−1.03158	+	1.78675i	−0.236661	+	0.409909i	−0.959754	−	0.280842i	$-0.909386\pi$
$19$	−1.03158	+	1.78675i	−0.236661	+	0.409909i	0.723093	+	0.690750i	$0.242720\pi$
$20$	−0.909078	−	4.52303i	−0.203276	−	1.01138i
$21$		0			0
$22$	3.86789	−	0.384853i	0.824637	−	0.0820510i
$23$	3.19592	+	1.84517i	0.666396	+	0.384744i	0.794710	−	0.606990i	$-0.207623\pi$
$23$	3.19592	+	1.84517i	0.666396	+	0.384744i	−0.128313	+	0.991734i	$0.540956\pi$
$24$		0			0
$25$	0.160525	+	0.278038i	0.0321050	+	0.0556075i
$26$	−3.12355	+	6.91217i	−0.612578	+	1.35559i
$27$		0			0
$28$	−3.84620	+	3.63410i	−0.726864	+	0.686781i
$29$	6.56785			1.21962			0.609810	−	0.792548i	$-0.291246\pi$
$29$	6.56785			1.21962			0.609810	+	0.792548i	$0.291246\pi$
$30$		0			0
$31$	−1.38202	−	2.39374i	−0.248219	−	0.429928i	0.714813	−	0.699316i	$-0.246512\pi$
$31$	−1.38202	−	2.39374i	−0.248219	−	0.429928i	−0.963032	+	0.269388i	$0.913179\pi$
$32$	−2.96319	+	4.81866i	−0.523822	+	0.851828i
$33$		0			0
$34$	−2.61061	+	0.259755i	−0.447716	+	0.0445476i
$35$	2.86414	−	5.38925i	0.484128	−	0.910950i
$36$		0			0
$37$	−2.63241	+	4.55948i	−0.432766	+	0.749573i	−0.997110	−	0.0759665i	$-0.975796\pi$
$37$	−2.63241	+	4.55948i	−0.432766	+	0.749573i	0.564344	+	0.825540i	$0.309129\pi$
$38$	−2.36999	+	1.70189i	−0.384463	+	0.276083i
$39$		0			0
$40$	1.46251	−	6.35842i	0.231243	−	1.00535i
$41$			8.65530i			1.35173i	0.737025	+	0.675865i	$0.236230\pi$
$41$			8.65530i			1.35173i	−0.737025	+	0.675865i	$0.763770\pi$
$42$		0			0
$43$		−	3.57467i		−	0.545132i	−0.962137	−	0.272566i	$-0.912128\pi$
$43$		−	3.57467i		−	0.545132i	0.962137	−	0.272566i	$-0.0878723\pi$
$44$	5.20882	+	1.75657i	0.785259	+	0.264812i
$45$		0			0
$46$	3.04414	+	4.23915i	0.448834	+	0.625028i
$47$	2.54973	−	4.41626i	0.371916	−	0.644178i	−0.617944	−	0.786222i	$-0.712034\pi$
$47$	2.54973	−	4.41626i	0.371916	−	0.644178i	0.989860	+	0.142044i	$0.0453675\pi$
$48$		0			0
$49$	−6.98275	+	0.491083i	−0.997536	+	0.0701548i
$50$	0.0449542	+	0.451803i	0.00635748	+	0.0638946i
$51$		0			0
$52$	−8.05087	+	7.08891i	−1.11646	+	0.983056i
$53$	−0.523381	−	0.906522i	−0.0718919	−	0.124520i	0.827839	−	0.560966i	$-0.189570\pi$
$53$	−0.523381	−	0.906522i	−0.0718919	−	0.124520i	−0.899730	+	0.436446i	$0.856237\pi$
$54$		0			0
$55$	−6.34011			−0.854900
$56$	−7.07314	+	2.44350i	−0.945188	+	0.326526i
$57$		0			0
$58$	8.46424	+	3.82492i	1.11141	+	0.502236i
$59$	−6.66997	−	11.5527i	−0.868357	−	1.50404i	−0.863675	−	0.504049i	$-0.831843\pi$
$59$	−6.66997	−	11.5527i	−0.868357	−	1.50404i	−0.00468155	−	0.999989i	$-0.501490\pi$
$60$		0			0
$61$	7.62894	+	4.40457i	0.976785	+	0.563947i	0.901298	−	0.433199i	$-0.142615\pi$
$61$	7.62894	+	4.40457i	0.976785	+	0.563947i	0.0754874	+	0.997147i	$0.475949\pi$
$62$	−0.387028	−	3.88975i	−0.0491526	−	0.493998i
$63$		0			0
$64$	−6.62501	+	4.48433i	−0.828127	+	0.560541i
$65$	6.18612	−	10.7147i	0.767294	−	1.32899i
$66$		0			0
$67$	13.7636	−	7.94642i	1.68149	−	0.970809i	0.720819	−	0.693123i	$-0.243766\pi$
$67$	13.7636	−	7.94642i	1.68149	−	0.970809i	0.960672	−	0.277686i	$-0.0895675\pi$
$68$	−3.51567	−	1.18559i	−0.426337	−	0.143773i
$69$		0			0
$70$	6.82966	−	5.27735i	0.816301	−	0.630764i
$71$		−	14.2847i		−	1.69528i	−0.530573	−	0.847640i	$-0.678023\pi$
$71$		−	14.2847i		−	1.69528i	0.530573	−	0.847640i	$-0.321977\pi$
$72$		0			0
$73$	5.96458	−	3.44365i	0.698101	−	0.403049i	−0.108539	−	0.994092i	$-0.534617\pi$
$73$	5.96458	−	3.44365i	0.698101	−	0.403049i	0.806640	+	0.591043i	$0.201284\pi$
$74$	−6.04779	+	4.34293i	−0.703042	+	0.504856i
$75$		0			0
$76$	−4.04542	+	0.813085i	−0.464042	+	0.0932672i
$77$	3.85474	+	6.16614i	0.439289	+	0.702697i
$78$		0			0
$79$	3.51577	+	2.02983i	0.395555	+	0.228374i	0.684564	−	0.728952i	$-0.259992\pi$
$79$	3.51577	+	2.02983i	0.395555	+	0.228374i	−0.289009	+	0.957326i	$0.593326\pi$
$80$	5.58774	−	7.34261i	0.624728	−	0.820929i
$81$		0			0
$82$	−5.04058	+	11.1544i	−0.556639	+	1.23180i
$83$	0.863684			0.0948016			0.0474008	−	0.998876i	$-0.484906\pi$
$83$	0.863684			0.0948016			0.0474008	+	0.998876i	$0.484906\pi$
$84$		0			0
$85$	4.27923			0.464147
$86$	2.08178	−	4.60681i	0.224484	−	0.496766i
$87$		0			0
$88$	5.68984	+	5.29721i	0.606539	+	0.564685i
$89$	−13.9295	−	8.04218i	−1.47652	−	0.852470i	−0.476872	−	0.878973i	$-0.658230\pi$
$89$	−13.9295	−	8.04218i	−1.47652	−	0.852470i	−0.999649	+	0.0265030i	$0.991563\pi$
$90$		0			0
$91$	−14.1818	+	0.498074i	−1.48666	+	0.0522123i
$92$	1.45435	+	7.23596i	0.151626	+	0.754401i
$93$		0			0
$94$	5.85783	−	4.20652i	0.604189	−	0.433869i
$95$	4.12157	−	2.37959i	0.422864	−	0.244141i
$96$		0			0
$97$		−	4.58962i		−	0.466005i	−0.972476	−	0.233003i	$-0.925145\pi$
$97$		−	4.58962i		−	0.466005i	0.972476	−	0.233003i	$-0.0748551\pi$
$98$	−9.28493	−	3.43367i	−0.937920	−	0.346853i
$99$		0			0
$100$	−0.205182	+	0.608435i	−0.0205182	+	0.0608435i
$101$	10.5165	−	6.07171i	1.04643	−	0.604158i	0.124784	−	0.992184i	$-0.460176\pi$
$101$	10.5165	−	6.07171i	1.04643	−	0.604158i	0.921649	+	0.388026i	$0.126843\pi$
$102$		0			0
$103$	−1.84745	+	3.19987i	−0.182034	+	0.315292i	−0.942573	−	0.334000i	$-0.891601\pi$
$103$	−1.84745	+	3.19987i	−0.182034	+	0.315292i	0.760539	+	0.649292i	$0.224935\pi$
$104$	−14.5038	+	4.44717i	−1.42222	+	0.436081i
$105$		0			0
$106$	−0.146570	−	1.47307i	−0.0142361	−	0.143077i
$107$	2.24809	+	1.29794i	0.217331	+	0.125476i	0.604714	−	0.796443i	$-0.293287\pi$
$107$	2.24809	+	1.29794i	0.217331	+	0.125476i	−0.387383	+	0.921919i	$0.626621\pi$
$108$		0			0
$109$	−3.48300	−	6.03273i	−0.333610	−	0.577830i	0.649606	−	0.760271i	$-0.274934\pi$
$109$	−3.48300	−	6.03273i	−0.333610	−	0.577830i	−0.983217	+	0.182440i	$0.941600\pi$
$110$	−8.17074	−	3.69229i	−0.779050	−	0.352046i
$111$		0			0
$112$	−10.5384	−	0.970157i	−0.995789	−	0.0916712i
$113$	−18.7947			−1.76806			−0.884028	−	0.467434i	$-0.845179\pi$
$113$	−18.7947			−1.76806			−0.884028	+	0.467434i	$0.845179\pi$
$114$		0			0
$115$	−4.25632	−	7.37217i	−0.396904	−	0.687458i
$116$	8.68067	+	9.85863i	0.805980	+	0.915351i
$117$		0			0
$118$	−1.86789	−	18.7728i	−0.171953	−	1.72818i
$119$	−2.60174	−	4.16181i	−0.238501	−	0.381512i
$120$		0			0
$121$	−1.72283	+	2.98403i	−0.156621	+	0.271276i
$122$	7.26662	+	10.1192i	0.657888	+	0.916149i
$123$		0			0
$124$	1.76649	−	5.23826i	0.158636	−	0.470409i
$125$			10.7931i			0.965366i
$126$		0			0
$127$			18.9667i			1.68303i	0.540237	+	0.841513i	$0.318334\pi$
$127$			18.9667i			1.68303i	−0.540237	+	0.841513i	$0.681666\pi$
$128$	−11.1494	+	1.92091i	−0.985481	+	0.169786i
$129$		0			0
$130$	14.2122	−	10.2058i	1.24649	−	0.895108i
$131$	7.00176	−	12.1274i	0.611747	−	1.05958i	−0.379199	−	0.925315i	$-0.623801\pi$
$131$	7.00176	−	12.1274i	0.611747	−	1.05958i	0.990946	−	0.134261i	$-0.0428662\pi$
$132$		0			0
$133$	−4.82018	−	2.56170i	−0.417963	−	0.222128i
$134$	22.3654	−	2.22535i	1.93208	−	0.192241i
$135$		0			0
$136$	−3.84033	−	3.57533i	−0.329305	−	0.306582i
$137$	7.65132	+	13.2525i	0.653696	+	1.13224i	0.982219	+	0.187739i	$0.0601160\pi$
$137$	7.65132	+	13.2525i	0.653696	+	1.13224i	−0.328523	+	0.944496i	$0.606551\pi$
$138$		0			0
$139$	9.05393			0.767945			0.383972	−	0.923345i	$-0.374556\pi$
$139$	9.05393			0.767945			0.383972	+	0.923345i	$0.374556\pi$
$140$	11.8750	−	2.82374i	1.00362	−	0.238649i
$141$		0			0
$142$	8.31896	−	18.4092i	0.698112	−	1.54487i
$143$	7.37086	+	12.7667i	0.616382	+	1.06760i
$144$		0			0
$145$	−13.1206	−	7.57516i	−1.08960	−	0.629083i
$146$	9.69225	−	0.964375i	0.802137	−	0.0798122i
$147$		0			0
$148$	−10.3232	+	2.07485i	−0.848563	+	0.170552i
$149$	9.26510	−	16.0476i	0.759027	−	1.31467i	−0.184321	−	0.982866i	$-0.559008\pi$
$149$	9.26510	−	16.0476i	0.759027	−	1.31467i	0.943347	−	0.331807i	$-0.107658\pi$
$150$		0			0
$151$	7.46473	−	4.30976i	0.607471	−	0.350723i	−0.164504	−	0.986376i	$-0.552602\pi$
$151$	7.46473	−	4.30976i	0.607471	−	0.350723i	0.771975	+	0.635653i	$0.219269\pi$
$152$	−5.68700	−	1.30808i	−0.461277	−	0.106099i
$153$		0			0
$154$	1.37678	+	10.1914i	0.110944	+	0.821249i
$155$			6.37594i			0.512128i
$156$		0			0
$157$	19.8043	−	11.4340i	1.58055	−	0.912534i	0.585777	−	0.810472i	$-0.300790\pi$
$157$	19.8043	−	11.4340i	1.58055	−	0.912534i	0.994778	−	0.102061i	$-0.0325438\pi$
$158$	3.34880	+	4.66340i	0.266416	+	0.371000i
$159$		0			0
$160$	11.4772	−	6.20857i	0.907356	−	0.490831i
$161$	−4.58206	+	8.62176i	−0.361117	+	0.679490i
$162$		0			0
$163$	14.5137	+	8.37950i	1.13680	+	0.656333i	0.945637	−	0.325225i	$-0.105440\pi$
$163$	14.5137	+	8.37950i	1.13680	+	0.656333i	0.191165	+	0.981558i	$0.438773\pi$
$164$	−12.9920	+	11.4396i	−1.01450	+	0.893285i
$165$		0			0
$166$	1.11306	+	0.502983i	0.0863904	+	0.0390391i
$167$	−3.17844			−0.245955			−0.122977	−	0.992409i	$-0.539244\pi$
$167$	−3.17844			−0.245955			−0.122977	+	0.992409i	$0.539244\pi$
$168$		0			0
$169$	−15.7673			−1.21287
$170$	5.51480	+	2.49209i	0.422966	+	0.191135i
$171$		0			0
$172$	5.36574	−	4.72461i	0.409134	−	0.360248i
$173$	9.42422	+	5.44108i	0.716510	+	0.413677i	0.813467	−	0.581611i	$-0.197577\pi$
$173$	9.42422	+	5.44108i	0.716510	+	0.413677i	−0.0969566	+	0.995289i	$0.530911\pi$
$174$		0			0
$175$	−0.720259	+	0.450267i	−0.0544464	+	0.0340370i
$176$	4.24777	+	10.1403i	0.320188	+	0.764354i
$177$		0			0
$178$	−13.2679	−	18.4764i	−0.994472	−	1.38486i
$179$	−12.2098	+	7.04934i	−0.912605	+	0.526893i	−0.881268	−	0.472616i	$-0.843310\pi$
$179$	−12.2098	+	7.04934i	−0.912605	+	0.526893i	−0.0313365	+	0.999509i	$0.509976\pi$
$180$		0			0
$181$			3.05138i			0.226807i	0.993549	+	0.113404i	$0.0361753\pi$
$181$			3.05138i			0.226807i	−0.993549	+	0.113404i	$0.963825\pi$
$182$	−18.5667	−	7.61716i	−1.37625	−	0.564621i
$183$		0			0
$184$	−2.33973	+	10.1722i	−0.172487	+	0.749907i
$185$	10.5175	−	6.07230i	0.773264	−	0.446444i
$186$		0			0
$187$	−2.54938	+	4.41566i	−0.186429	+	0.322905i
$188$	9.99895	−	2.00968i	0.729249	−	0.146571i
$189$		0			0
$190$	6.69742	−	0.666390i	0.485882	−	0.0483450i
$191$	−4.88772	−	2.82193i	−0.353663	−	0.204188i	0.312634	−	0.949874i	$-0.398789\pi$
$191$	−4.88772	−	2.82193i	−0.353663	−	0.204188i	−0.666297	+	0.745686i	$0.732122\pi$
$192$		0			0
$193$	−9.29318	−	16.0963i	−0.668937	−	1.15863i	−0.978202	−	0.207657i	$-0.933416\pi$
$193$	−9.29318	−	16.0963i	−0.668937	−	1.15863i	0.309264	−	0.950976i	$-0.399917\pi$
$194$	2.67285	−	5.91482i	0.191900	−	0.424659i
$195$		0			0
$196$	−9.96618	−	9.83236i	−0.711870	−	0.702311i
$197$	−24.5337			−1.74796			−0.873978	−	0.485966i	$-0.838468\pi$
$197$	−24.5337			−1.74796			−0.873978	+	0.485966i	$0.838468\pi$
$198$		0			0
$199$	−7.44321	−	12.8920i	−0.527635	−	0.913891i	−0.999481	−	0.0322101i	$-0.989745\pi$
$199$	−7.44321	−	12.8920i	−0.527635	−	0.913891i	0.471846	−	0.881681i	$-0.343588\pi$
$200$	−0.618760	+	0.664622i	−0.0437529	+	0.0469959i
$201$		0			0
$202$	17.0890	−	1.70035i	1.20238	−	0.119636i
$203$	0.609912	+	17.3662i	0.0428074	+	1.21887i
$204$		0			0
$205$	9.98276	−	17.2907i	0.697226	−	1.20763i
$206$	−4.24438	+	3.04790i	−0.295720	+	0.212357i
$207$		0			0
$208$	−21.2815	−	2.71536i	−1.47561	−	0.188276i
$209$			5.67063i			0.392246i
$210$		0			0
$211$			2.96827i			0.204344i	0.994767	+	0.102172i	$0.0325792\pi$
$211$			2.96827i			0.204344i	−0.994767	+	0.102172i	$0.967421\pi$
$212$	0.668981	−	1.98376i	0.0459458	−	0.136245i
$213$		0			0
$214$	2.14132	+	2.98192i	0.146378	+	0.203840i
$215$	−4.12292	+	7.14110i	−0.281181	+	0.487019i
$216$		0			0
$217$	6.20099	−	3.87653i	0.420950	−	0.263156i
$218$	−0.975393	−	9.80299i	−0.0660620	−	0.663943i
$219$		0			0
$220$	−8.37967	−	9.51678i	−0.564957	−	0.641621i
$221$	−4.97492	−	8.61682i	−0.334649	−	0.579630i
$222$		0			0
$223$	7.35139			0.492285			0.246143	−	0.969234i	$-0.420837\pi$
$223$	7.35139			0.492285			0.246143	+	0.969234i	$0.420837\pi$
$224$	−13.0163	−	7.38755i	−0.869688	−	0.493601i
$225$		0			0
$226$	−24.2214	−	10.9455i	−1.61119	−	0.728081i
$227$	7.50920	+	13.0063i	0.498403	+	0.863260i	0.999998	−	0.00184266i	$-0.000586536\pi$
$227$	7.50920	+	13.0063i	0.498403	+	0.863260i	−0.501595	+	0.865103i	$0.667253\pi$
$228$		0			0
$229$	5.84201	+	3.37289i	0.386051	+	0.222887i	0.680448	−	0.732797i	$-0.261785\pi$
$229$	5.84201	+	3.37289i	0.386051	+	0.222887i	−0.294397	+	0.955683i	$0.595119\pi$
$230$	−1.19196	−	11.9795i	−0.0785955	−	0.789908i
$231$		0			0
$232$	5.44574	+	17.7605i	0.357531	+	1.16604i
$233$	5.12630	−	8.87901i	0.335835	−	0.581683i	−0.647810	−	0.761802i	$-0.724315\pi$
$233$	5.12630	−	8.87901i	0.335835	−	0.581683i	0.983645	+	0.180119i	$0.0576482\pi$
$234$		0			0
$235$	−10.1872	+	5.88156i	−0.664537	+	0.383671i
$236$	8.52551	−	25.2811i	0.554963	−	1.64566i
$237$		0			0
$238$	−0.929253	−	6.87865i	−0.0602345	−	0.445877i
$239$			21.0966i			1.36462i	0.731061	+	0.682312i	$0.239025\pi$
$239$			21.0966i			1.36462i	−0.731061	+	0.682312i	$0.760975\pi$
$240$		0			0
$241$	−16.4313	+	9.48659i	−1.05843	+	0.611085i	−0.924998	−	0.379973i	$-0.875933\pi$
$241$	−16.4313	+	9.48659i	−1.05843	+	0.611085i	−0.133433	+	0.991058i	$0.542600\pi$
$242$	−3.95809	+	2.84231i	−0.254436	+	0.182711i
$243$		0			0
$244$	3.47165	+	17.2729i	0.222250	+	1.10578i
$245$	14.5158	+	7.07266i	0.927381	+	0.451856i
$246$		0			0
$247$	−9.58327	−	5.53290i	−0.609769	−	0.352050i
$248$	5.32715	−	5.72199i	0.338274	−	0.363347i
$249$		0			0
$250$	−6.28559	+	13.9095i	−0.397535	+	0.879714i
$251$	14.4032			0.909123			0.454562	−	0.890715i	$-0.349796\pi$
$251$	14.4032			0.909123			0.454562	+	0.890715i	$0.349796\pi$
$252$		0			0
$253$	10.1429			0.637681
$254$	−11.0456	+	24.4431i	−0.693066	+	1.53370i
$255$		0			0
$256$	−15.4874	−	4.01754i	−0.967962	−	0.251096i
$257$	−7.61935	−	4.39904i	−0.475282	−	0.274404i	0.243166	−	0.969985i	$-0.421814\pi$
$257$	−7.61935	−	4.39904i	−0.475282	−	0.274404i	−0.718448	+	0.695580i	$0.755147\pi$
$258$		0			0
$259$	−12.3003	−	6.53702i	−0.764301	−	0.406190i
$260$	24.2593	−	4.87586i	1.50450	−	0.302388i
$261$		0			0
$262$	16.0861	−	11.5514i	0.993801	−	0.713650i
$263$	9.15975	−	5.28838i	0.564814	−	0.326096i	−0.190261	−	0.981733i	$-0.560934\pi$
$263$	9.15975	−	5.28838i	0.564814	−	0.326096i	0.755076	+	0.655638i	$0.227600\pi$
$264$		0			0
$265$			2.41461i			0.148328i
$266$	−4.72009	−	6.10849i	−0.289407	−	0.374535i
$267$		0			0
$268$	30.1191	+	10.1570i	1.83982	+	0.620441i
$269$	−14.2878	+	8.24909i	−0.871145	+	0.502956i	−0.867729	−	0.497038i	$-0.834421\pi$
$269$	−14.2878	+	8.24909i	−0.871145	+	0.502956i	−0.00341646	+	0.999994i	$0.501087\pi$
$270$		0			0
$271$	13.4568	−	23.3079i	0.817443	−	1.41585i	−0.0901180	−	0.995931i	$-0.528724\pi$
$271$	13.4568	−	23.3079i	0.817443	−	1.41585i	0.907561	−	0.419921i	$-0.137942\pi$
$272$	−2.86701	−	6.84415i	−0.173838	−	0.414988i
$273$		0			0
$274$	2.14271	+	21.5349i	0.129446	+	1.30097i
$275$	0.764191	+	0.441206i	0.0460824	+	0.0266057i
$276$		0			0
$277$	13.7736	+	23.8566i	0.827578	+	1.43341i	0.899933	+	0.436028i	$0.143615\pi$
$277$	13.7736	+	23.8566i	0.827578	+	1.43341i	−0.0723555	+	0.997379i	$0.523052\pi$
$278$	11.6681	+	5.27273i	0.699809	+	0.316238i
$279$		0			0
$280$	16.9482	+	3.27659i	1.01285	+	0.195814i
$281$	2.86077			0.170659			0.0853296	−	0.996353i	$-0.472806\pi$
$281$	2.86077			0.170659			0.0853296	+	0.996353i	$0.472806\pi$
$282$		0			0
$283$	−6.00840	−	10.4069i	−0.357162	−	0.618624i	0.630323	−	0.776333i	$-0.282922\pi$
$283$	−6.00840	−	10.4069i	−0.357162	−	0.618624i	−0.987486	+	0.157709i	$0.949589\pi$
$284$	21.4419	−	18.8799i	1.27234	−	1.12032i
$285$		0			0
$286$	2.06417	+	20.7455i	0.122057	+	1.22671i
$287$	−22.8857	+	0.803759i	−1.35090	+	0.0474444i
$288$		0			0
$289$	−6.77931	+	11.7421i	−0.398783	+	0.690712i
$290$	−12.4974	−	17.4034i	−0.733874	−	1.02196i
$291$		0			0
$292$	13.0524	+	4.40165i	0.763834	+	0.257587i
$293$			13.2285i			0.772816i	0.922328	+	0.386408i	$0.126284\pi$
$293$			13.2285i			0.772816i	−0.922328	+	0.386408i	$0.873716\pi$
$294$		0			0
$295$			30.7718i			1.79160i
$296$	−14.5122	−	3.33799i	−0.843507	−	0.194016i
$297$		0			0
$298$	21.2859	−	15.2855i	1.23306	−	0.885464i
$299$	−9.89659	+	17.1414i	−0.572335	+	0.991313i
$300$		0			0
$301$	9.45186	−	0.331956i	0.544796	−	0.0191336i
$302$	12.1299	−	1.20692i	0.698000	−	0.0694507i
$303$		0			0
$304$	−6.56727	−	4.99771i	−0.376659	−	0.286638i
$305$	−10.1602	−	17.5980i	−0.581771	−	1.00766i
$306$		0			0
$307$	9.67077			0.551940			0.275970	−	0.961166i	$-0.411001\pi$
$307$	9.67077			0.551940			0.275970	+	0.961166i	$0.411001\pi$
$308$	−4.16086	+	13.9359i	−0.237087	+	0.794070i
$309$		0			0
$310$	−3.71315	+	8.21692i	−0.210893	+	0.466689i
$311$	0.524415	+	0.908314i	0.0297369	+	0.0515058i	0.880511	−	0.474026i	$-0.157200\pi$
$311$	0.524415	+	0.908314i	0.0297369	+	0.0515058i	−0.850774	+	0.525532i	$0.823866\pi$
$312$		0			0
$313$	−0.277265	−	0.160079i	−0.0156719	−	0.00904819i	0.492144	−	0.870514i	$-0.336214\pi$
$313$	−0.277265	−	0.160079i	−0.0156719	−	0.00904819i	−0.507815	+	0.861466i	$0.669547\pi$
$314$	32.1814	−	3.20203i	1.81610	−	0.180701i
$315$		0			0
$316$	1.59990	+	7.96014i	0.0900014	+	0.447793i
$317$	5.38699	−	9.33055i	0.302564	−	0.524056i	−0.674152	−	0.738592i	$-0.735491\pi$
$317$	5.38699	−	9.33055i	0.302564	−	0.524056i	0.976716	+	0.214537i	$0.0688242\pi$
$318$		0			0
$319$	15.6333	−	9.02592i	0.875300	−	0.505354i
$320$	18.4069	−	1.31722i	1.02897	−	0.0736351i
$321$		0			0
$322$	−10.9261	+	8.44274i	−0.608889	+	0.470495i
$323$		−	3.82736i		−	0.212960i
$324$		0			0
$325$	−1.49126	+	0.860979i	−0.0827202	+	0.0477585i
$326$	13.8244	+	19.2513i	0.765663	+	1.06623i
$327$		0			0
$328$	−23.4054	+	7.17656i	−1.29234	+	0.396259i
$329$	11.9139	+	6.33168i	0.656835	+	0.349077i
$330$		0			0
$331$	4.29339	+	2.47879i	0.235986	+	0.136247i	0.613331	−	0.789826i	$-0.289829\pi$
$331$	4.29339	+	2.47879i	0.235986	+	0.136247i	−0.377344	+	0.926073i	$0.623163\pi$
$332$	1.14152	+	1.29643i	0.0626492	+	0.0711507i
$333$		0			0
$334$	−4.09617	−	1.85102i	−0.224133	−	0.101284i
$335$	−36.6606			−2.00298
$336$		0			0
$337$	−9.30295			−0.506764			−0.253382	−	0.967366i	$-0.581543\pi$
$337$	−9.30295			−0.506764			−0.253382	+	0.967366i	$0.581543\pi$
$338$	−20.3199	−	9.18241i	−1.10526	−	0.499457i
$339$		0			0
$340$	5.65582	+	6.42331i	0.306730	+	0.348353i
$341$	−6.57922	−	3.79851i	−0.356285	−	0.205701i
$342$		0			0
$343$	−1.94692	−	18.4176i	−0.105124	−	0.994459i
$344$	9.66650	−	2.96394i	0.521183	−	0.159805i
$345$		0			0
$346$	8.97664	+	12.5005i	0.482587	+	0.672031i
$347$	−25.3912	+	14.6596i	−1.36307	+	0.786969i	−0.990031	−	0.140846i	$-0.955018\pi$
$347$	−25.3912	+	14.6596i	−1.36307	+	0.786969i	−0.373039	+	0.927816i	$0.621684\pi$
$348$		0			0
$349$			14.7262i			0.788276i	0.919051	+	0.394138i	$0.128957\pi$
$349$			14.7262i			0.788276i	−0.919051	+	0.394138i	$0.871043\pi$
$350$	−1.19045	+	0.160820i	−0.0636320	+	0.00859620i
$351$		0			0
$352$	−0.431140	+	15.5420i	−0.0229798	+	0.828390i
$353$	7.89544	−	4.55844i	0.420232	−	0.242621i	−0.274945	−	0.961460i	$-0.588660\pi$
$353$	7.89544	−	4.55844i	0.420232	−	0.242621i	0.695177	+	0.718839i	$0.255326\pi$
$354$		0			0
$355$	−16.4755	+	28.5364i	−0.874430	+	1.51456i
$356$	−6.33879	−	31.5380i	−0.335955	−	1.67151i
$357$		0			0
$358$	−19.8406	+	1.97413i	−1.04861	+	0.104336i
$359$	−6.00520	−	3.46711i	−0.316943	−	0.182987i	0.333086	−	0.942896i	$-0.391910\pi$
$359$	−6.00520	−	3.46711i	−0.316943	−	0.182987i	−0.650029	+	0.759909i	$0.725243\pi$
$360$		0			0
$361$	7.37168	+	12.7681i	0.387983	+	0.672007i
$362$	−1.77703	+	3.93243i	−0.0933986	+	0.206684i
$363$		0			0
$364$	−19.4916	−	20.6292i	−1.02164	−	1.08126i
$365$	−15.8872			−0.831575
$366$		0			0
$367$	−12.8762	−	22.3023i	−0.672134	−	1.16417i	−0.977298	−	0.211870i	$-0.932045\pi$
$367$	−12.8762	−	22.3023i	−0.672134	−	1.16417i	0.305164	−	0.952300i	$-0.401289\pi$
$368$	−8.93930	+	11.7468i	−0.465993	+	0.612342i
$369$		0			0
$370$	17.0907	−	1.70051i	0.888501	−	0.0884054i
$371$	2.34835	−	1.46806i	0.121920	−	0.0762181i
$372$		0			0
$373$	−7.79633	+	13.5036i	−0.403679	+	0.699192i	−0.994167	−	0.107855i	$-0.965602\pi$
$373$	−7.79633	+	13.5036i	−0.403679	+	0.699192i	0.590488	+	0.807046i	$0.298935\pi$
$374$	−5.85703	+	4.20594i	−0.302860	+	0.217484i
$375$		0			0
$376$	14.0564	+	3.23314i	0.724904	+	0.166736i
$377$			35.2268i			1.81427i
$378$		0			0
$379$		−	0.782076i		−	0.0401726i	−0.999798	−	0.0200863i	$-0.993606\pi$
$379$		−	0.782076i		−	0.0401726i	0.999798	−	0.0200863i	$-0.00639409\pi$
$380$	9.01931	+	3.04157i	0.462681	+	0.156029i
$381$		0			0
$382$	−4.65559	−	6.48319i	−0.238201	−	0.331709i
$383$	−0.192955	+	0.334208i	−0.00985954	+	0.0170772i	−0.870913	−	0.491437i	$-0.836472\pi$
$383$	−0.192955	+	0.334208i	−0.00985954	+	0.0170772i	0.861054	+	0.508514i	$0.169805\pi$
$384$		0			0
$385$	−0.588763	−	16.7640i	−0.0300062	−	0.854374i
$386$	−2.60250	−	26.1559i	−0.132464	−	1.33130i
$387$		0			0
$388$	6.88922	−	6.06606i	0.349747	−	0.307958i
$389$	−13.8479	−	23.9852i	−0.702115	−	1.21610i	−0.967722	−	0.252018i	$-0.918906\pi$
$389$	−13.8479	−	23.9852i	−0.702115	−	1.21610i	0.265607	−	0.964081i	$-0.414428\pi$
$390$		0			0
$391$	−6.84593			−0.346214
$392$	−7.11773	−	18.4753i	−0.359500	−	0.933145i
$393$		0			0
$394$	−31.6175	−	14.2877i	−1.59287	−	0.719804i
$395$	−4.68229	−	8.10997i	−0.235592	−	0.408057i
$396$		0			0
$397$	1.93255	+	1.11576i	0.0969921	+	0.0559984i	0.547711	−	0.836667i	$-0.315499\pi$
$397$	1.93255	+	1.11576i	0.0969921	+	0.0559984i	−0.450719	+	0.892666i	$0.648832\pi$
$398$	−2.08443	−	20.9491i	−0.104483	−	1.05009i
$399$		0			0
$400$	−1.18448	+	0.496176i	−0.0592238	+	0.0248088i
$401$	6.49805	−	11.2550i	0.324497	−	0.562046i	−0.656913	−	0.753966i	$-0.728138\pi$
$401$	6.49805	−	11.2550i	0.324497	−	0.562046i	0.981410	+	0.191921i	$0.0614716\pi$
$402$		0			0
$403$	12.8388	−	7.41251i	0.639548	−	0.369243i
$404$	23.0135	+	7.76082i	1.14496	+	0.386115i
$405$		0			0
$406$	−9.32753	+	22.7357i	−0.462917	+	1.12835i
$407$			14.4705i			0.717274i
$408$		0			0
$409$	−23.4826	+	13.5577i	−1.16114	+	0.670385i	−0.951577	−	0.307411i	$-0.900538\pi$
$409$	−23.4826	+	13.5577i	−1.16114	+	0.670385i	−0.209563	+	0.977795i	$0.567204\pi$
$410$	22.9347	−	16.4695i	1.13266	−	0.813369i
$411$		0			0
$412$	−7.24490	+	1.45614i	−0.356930	+	0.0717390i
$413$	29.9274	−	18.7090i	1.47263	−	0.920612i
$414$		0			0
$415$	−1.72538	−	0.996147i	−0.0846955	−	0.0488989i
$416$	−25.8450	−	15.8931i	−1.26715	−	0.779223i
$417$		0			0
$418$	−3.30240	+	7.30796i	−0.161526	+	0.357444i
$419$	−6.62682			−0.323741			−0.161871	−	0.986812i	$-0.551753\pi$
$419$	−6.62682			−0.323741			−0.161871	+	0.986812i	$0.551753\pi$
$420$		0			0
$421$	7.27401			0.354514			0.177257	−	0.984165i	$-0.443278\pi$
$421$	7.27401			0.354514			0.177257	+	0.984165i	$0.443278\pi$
$422$	−1.72863	+	3.82532i	−0.0841484	+	0.186214i
$423$		0			0
$424$	2.01742	−	2.16695i	0.0979747	−	0.105236i
$425$	−0.515787	−	0.297790i	−0.0250193	−	0.0144449i
$426$		0			0
$427$	−10.9378	+	20.5809i	−0.529316	+	0.995978i
$428$	1.02303	+	5.08996i	0.0494498	+	0.246033i
$429$		0			0
$430$	−9.47212	+	6.80195i	−0.456786	+	0.328019i
$431$	17.3520	−	10.0182i	0.835816	−	0.482559i	−0.0200237	−	0.999800i	$-0.506374\pi$
$431$	17.3520	−	10.0182i	0.835816	−	0.482559i	0.855840	+	0.517241i	$0.173041\pi$
$432$		0			0
$433$		−	20.4234i		−	0.981486i	−0.871304	−	0.490743i	$-0.836725\pi$
$433$		−	20.4234i		−	0.981486i	0.871304	−	0.490743i	$-0.163275\pi$
$434$	10.2490	−	1.38456i	0.491969	−	0.0664612i
$435$		0			0
$436$	4.45194	−	13.2015i	0.213209	−	0.632239i
$437$	−6.59371	+	3.80688i	−0.315420	+	0.182108i
$438$		0			0
$439$	−12.5430	+	21.7251i	−0.598646	+	1.03688i	0.394376	+	0.918949i	$0.370961\pi$
$439$	−12.5430	+	21.7251i	−0.598646	+	1.03688i	−0.993021	+	0.117935i	$0.962372\pi$
$440$	−5.25691	−	17.1447i	−0.250614	−	0.817342i
$441$		0			0
$442$	−1.39320	−	14.0021i	−0.0662677	−	0.666010i
$443$	10.1283	+	5.84760i	0.481212	+	0.277828i	0.720922	−	0.693017i	$-0.243719\pi$
$443$	10.1283	+	5.84760i	0.481212	+	0.277828i	−0.239709	+	0.970845i	$0.577052\pi$
$444$		0			0
$445$	18.5512	+	32.1317i	0.879413	+	1.52319i
$446$	9.47401	+	4.28122i	0.448608	+	0.202722i
$447$		0			0
$448$	−12.4723	−	17.1009i	−0.589262	−	0.807942i
$449$	−10.7574			−0.507671			−0.253836	−	0.967247i	$-0.581692\pi$
$449$	−10.7574			−0.507671			−0.253836	+	0.967247i	$0.581692\pi$
$450$		0			0
$451$	11.8946	+	20.6021i	0.560095	+	0.970114i
$452$	−24.8408	−	28.2117i	−1.16841	−	1.32696i
$453$		0			0
$454$	2.10291	+	21.1349i	0.0986945	+	0.991909i
$455$	28.9054	+	15.3619i	1.35510	+	0.720175i
$456$		0			0
$457$	11.9148	−	20.6371i	0.557351	−	0.965361i	−0.440365	−	0.897819i	$-0.645151\pi$
$457$	11.9148	−	20.6371i	0.557351	−	0.965361i	0.997716	−	0.0675419i	$-0.0215156\pi$
$458$	5.56456	+	7.74898i	0.260015	+	0.362086i
$459$		0			0
$460$	5.44040	−	16.1327i	0.253660	−	0.752189i
$461$			29.7366i			1.38497i	0.721431	+	0.692486i	$0.243485\pi$
$461$			29.7366i			1.38497i	−0.721431	+	0.692486i	$0.756515\pi$
$462$		0			0
$463$			13.8275i			0.642616i	0.946975	+	0.321308i	$0.104122\pi$
$463$			13.8275i			0.642616i	−0.946975	+	0.321308i	$0.895878\pi$
$464$	−3.32507	+	26.0601i	−0.154362	+	1.20981i
$465$		0			0
$466$	11.7773	−	8.45732i	0.545574	−	0.391778i
$467$	−12.1071	+	20.9701i	−0.560249	+	0.970380i	0.437225	+	0.899352i	$0.355961\pi$
$467$	−12.1071	+	20.9701i	−0.560249	+	0.970380i	−0.997474	+	0.0710282i	$0.977372\pi$
$468$		0			0
$469$	22.2894	+	35.6547i	1.02923	+	1.64638i
$470$	−16.5538	+	1.64710i	−0.763571	+	0.0759750i
$471$		0			0
$472$	25.7101	−	27.6157i	1.18340	−	1.27111i
$473$	−4.91252	−	8.50873i	−0.225878	−	0.391232i
$474$		0			0
$475$	−0.662379			−0.0303920
$476$	2.80835	−	9.40595i	0.128721	−	0.431121i
$477$		0			0
$478$	−12.2860	+	27.1879i	−0.561949	+	1.24355i
$479$	7.83399	+	13.5689i	0.357944	+	0.619978i	0.987617	−	0.156883i	$-0.0501445\pi$
$479$	7.83399	+	13.5689i	0.357944	+	0.619978i	−0.629673	+	0.776860i	$0.716811\pi$
$480$		0			0
$481$	−24.4548	−	14.1190i	−1.11504	−	0.643771i
$482$	−26.7003	+	2.65667i	−1.21617	+	0.121008i
$483$		0			0
$484$	−6.75621	+	1.35792i	−0.307101	+	0.0617238i
$485$	−5.29353	+	9.16866i	−0.240367	+	0.416328i
$486$		0			0
$487$	16.9537	−	9.78823i	0.768246	−	0.443547i	−0.0640024	−	0.997950i	$-0.520387\pi$
$487$	16.9537	−	9.78823i	0.768246	−	0.443547i	0.832249	+	0.554403i	$0.187053\pi$
$488$	−5.58513	+	24.2820i	−0.252827	+	1.09919i
$489$		0			0
$490$	14.5882	+	17.5684i	0.659027	+	0.793658i
$491$		−	15.2930i		−	0.690163i	−0.938573	−	0.345082i	$-0.887851\pi$
$491$		−	15.2930i		−	0.690163i	0.938573	−	0.345082i	$-0.112149\pi$
$492$		0			0
$493$	−10.5517	+	6.09200i	−0.475222	+	0.274370i
$494$	−9.12813	−	12.7115i	−0.410694	−	0.571916i
$495$		0			0
$496$	10.1976	−	4.27178i	0.457886	−	0.191808i
$497$	37.7704	−	1.32652i	1.69423	−	0.0595026i
$498$		0			0
$499$	−10.1324	−	5.84995i	−0.453589	−	0.261880i	0.255756	−	0.966741i	$-0.417676\pi$
$499$	−10.1324	−	5.84995i	−0.453589	−	0.261880i	−0.709345	+	0.704862i	$0.751009\pi$
$500$	−16.2009	+	14.2652i	−0.724528	+	0.637958i
$501$		0			0
$502$	18.5620	+	8.38800i	0.828462	+	0.374375i
$503$	13.7872			0.614743			0.307371	−	0.951590i	$-0.400551\pi$
$503$	13.7872			0.614743			0.307371	+	0.951590i	$0.400551\pi$
$504$		0			0
$505$	−28.0117			−1.24651
$506$	13.0716	+	5.90694i	0.581103	+	0.262596i
$507$		0			0
$508$	−28.4699	+	25.0682i	−1.26315	+	1.11222i
$509$	9.22551	+	5.32635i	0.408914	+	0.236086i	0.690323	−	0.723501i	$-0.257468\pi$
$509$	9.22551	+	5.32635i	0.408914	+	0.236086i	−0.281409	+	0.959588i	$0.590802\pi$
$510$		0			0
$511$	9.65932	+	15.4513i	0.427303	+	0.683524i
$512$	−17.6195	−	14.1969i	−0.778679	−	0.627422i
$513$		0			0
$514$	−7.25749	−	10.1065i	−0.320114	−	0.445778i
$515$	7.38127	−	4.26158i	0.325257	−	0.187788i
$516$		0			0
$517$		−	14.0159i		−	0.616420i
$518$	−12.0449	−	15.5878i	−0.529221	−	0.684889i
$519$		0			0
$520$	34.1035	+	7.84420i	1.49554	+	0.343991i
$521$	13.6109	−	7.85827i	0.596305	−	0.344277i	−0.171282	−	0.985222i	$-0.554791\pi$
$521$	13.6109	−	7.85827i	0.596305	−	0.344277i	0.767587	+	0.640945i	$0.221457\pi$
$522$		0			0
$523$	4.47228	−	7.74622i	0.195559	−	0.338718i	−0.751525	−	0.659705i	$-0.770681\pi$
$523$	4.47228	−	7.74622i	0.195559	−	0.338718i	0.947084	+	0.320987i	$0.104014\pi$
$524$	27.4579	−	5.51874i	1.19951	−	0.241087i
$525$		0			0
$526$	14.8843	−	1.48098i	0.648987	−	0.0645739i
$527$	4.44061	+	2.56379i	0.193436	+	0.111680i
$528$		0			0
$529$	−4.69071	−	8.12455i	−0.203944	−	0.353241i
$530$	−1.40619	+	3.11180i	−0.0610811	+	0.135168i
$531$		0			0
$532$	−2.52557	−	10.6211i	−0.109497	−	0.460482i
$533$	−46.4228			−2.01080
$534$		0			0
$535$	−2.99401	−	5.18577i	−0.129442	−	0.224200i
$536$	32.9005	+	30.6302i	1.42109	+	1.32303i
$537$		0			0
$538$	−23.2173	+	2.31011i	−1.00097	+	0.0995959i
$539$	−15.9461	+	10.7650i	−0.686845	+	0.463682i
$540$		0			0
$541$	−6.30754	+	10.9250i	−0.271182	+	0.469701i	−0.969165	−	0.246413i	$-0.920748\pi$
$541$	−6.30754	+	10.9250i	−0.271182	+	0.469701i	0.697983	+	0.716115i	$0.254081\pi$
$542$	30.9161	−	22.2009i	1.32796	−	0.953610i
$543$		0			0
$544$	0.290996	−	10.4900i	0.0124763	−	0.449754i
$545$			16.0687i			0.688309i
$546$		0			0
$547$		−	35.7372i		−	1.52801i	−0.645210	−	0.764005i	$-0.723230\pi$
$547$		−	35.7372i		−	1.52801i	0.645210	−	0.764005i	$-0.276770\pi$
$548$	−9.77986	+	29.0006i	−0.417775	+	1.23885i
$549$		0			0
$550$	0.727897	+	1.01364i	0.0310376	+	0.0432218i
$551$	−6.77527	+	11.7351i	−0.288636	+	0.499932i
$552$		0			0
$553$	−5.04063	+	9.48462i	−0.214350	+	0.403327i
$554$	3.85723	+	38.7663i	0.163878	+	1.64702i
$555$		0			0
$556$	11.9665	+	13.5903i	0.507493	+	0.576359i
$557$	−4.85967	−	8.41720i	−0.205911	−	0.356648i	0.744512	−	0.667610i	$-0.232682\pi$
$557$	−4.85967	−	8.41720i	−0.205911	−	0.356648i	−0.950423	+	0.310961i	$0.899349\pi$
$558$		0			0
$559$	19.1728			0.810924
$560$	19.9337	+	14.0928i	0.842351	+	0.595530i
$561$		0			0
$562$	3.68678	+	1.66602i	0.155518	+	0.0702770i
$563$	−20.5178	−	35.5379i	−0.864722	−	1.49774i	−0.867323	−	0.497746i	$-0.834161\pi$
$563$	−20.5178	−	35.5379i	−0.864722	−	1.49774i	0.00260096	−	0.999997i	$-0.499172\pi$
$564$		0			0
$565$	37.5461	+	21.6772i	1.57958	+	0.911968i
$566$	−1.68262	−	16.9108i	−0.0707258	−	0.710815i
$567$		0			0
$568$	38.6281	−	11.8442i	1.62080	−	0.496970i
$569$	2.64355	−	4.57876i	0.110823	−	0.191951i	−0.805279	−	0.592896i	$-0.797985\pi$
$569$	2.64355	−	4.57876i	0.110823	−	0.191951i	0.916102	+	0.400944i	$0.131318\pi$
$570$		0			0
$571$	−18.7270	+	10.8121i	−0.783702	+	0.452471i	−0.837741	−	0.546068i	$-0.816124\pi$
$571$	−18.7270	+	10.8121i	−0.783702	+	0.452471i	0.0540384	+	0.998539i	$0.482791\pi$
$572$	−9.42137	+	27.9376i	−0.393927	+	1.16813i
$573$		0			0
$574$	−29.9617	−	12.2921i	−1.25058	−	0.513061i
$575$			1.18478i			0.0494089i
$576$		0			0
$577$	26.8001	−	15.4731i	1.11570	−	0.644152i	0.175404	−	0.984497i	$-0.443877\pi$
$577$	26.8001	−	15.4731i	1.11570	−	0.644152i	0.940301	+	0.340344i	$0.110544\pi$
$578$	−15.5750	+	11.1844i	−0.647834	+	0.465211i
$579$		0			0
$580$	−5.97069	−	29.7066i	−0.247919	−	1.23350i
$581$	0.0802045	+	2.28368i	0.00332744	+	0.0947432i
$582$		0			0
$583$	−2.49159	−	1.43852i	−0.103191	−	0.0595774i
$584$	14.2577	+	13.2739i	0.589989	+	0.549277i
$585$		0			0
$586$	−7.70387	+	17.0481i	−0.318244	+	0.704248i
$587$	6.03776			0.249205			0.124602	−	0.992207i	$-0.460234\pi$
$587$	6.03776			0.249205			0.124602	+	0.992207i	$0.460234\pi$
$588$		0			0
$589$	5.70268			0.234975
$590$	−17.9206	+	39.6568i	−0.737778	+	1.63264i
$591$		0			0
$592$	−16.7585	−	12.7533i	−0.688772	−	0.524157i
$593$	12.2226	+	7.05674i	0.501923	+	0.289785i	0.729507	−	0.683973i	$-0.239749\pi$
$593$	12.2226	+	7.05674i	0.501923	+	0.289785i	−0.227584	+	0.973758i	$0.573083\pi$
$594$		0			0
$595$	0.397383	+	11.3148i	0.0162911	+	0.463861i
$596$	36.3338	−	7.30269i	1.48829	−	0.299130i
$597$		0			0
$598$	−22.7367	+	16.3273i	−0.929775	+	0.667673i
$599$	−30.8515	+	17.8121i	−1.26056	+	0.727783i	−0.973182	−	0.230035i	$-0.926116\pi$
$599$	−30.8515	+	17.8121i	−1.26056	+	0.727783i	−0.287375	+	0.957818i	$0.592783\pi$
$600$		0			0
$601$			1.19147i			0.0486011i	0.999705	+	0.0243005i	$0.00773586\pi$
$601$			1.19147i			0.0486011i	−0.999705	+	0.0243005i	$0.992264\pi$
$602$	12.3743	+	5.07667i	0.504339	+	0.206910i
$603$		0			0
$604$	16.3352	+	5.50870i	0.664670	+	0.224146i
$605$	6.88339	−	3.97413i	0.279849	−	0.161571i
$606$		0			0
$607$	5.40294	−	9.35817i	0.219299	−	0.379836i	−0.735295	−	0.677747i	$-0.762956\pi$
$607$	5.40294	−	9.35817i	0.219299	−	0.379836i	0.954594	+	0.297911i	$0.0962898\pi$
$608$	−5.55298	−	10.2653i	−0.225203	−	0.416314i
$609$		0			0
$610$	−2.84531	−	28.5962i	−0.115203	−	1.15783i
$611$	23.6867	+	13.6755i	0.958261	+	0.553252i
$612$		0			0
$613$	−0.0664000	−	0.115008i	−0.00268187	−	0.00464514i	0.864681	−	0.502321i	$-0.167520\pi$
$613$	−0.0664000	−	0.115008i	−0.00268187	−	0.00464514i	−0.867363	+	0.497676i	$0.834187\pi$
$614$	12.4631	+	5.63196i	0.502969	+	0.227287i
$615$		0			0
$616$	−13.4781	+	15.5365i	−0.543048	+	0.625985i
$617$	−11.7441			−0.472800			−0.236400	−	0.971656i	$-0.575968\pi$
$617$	−11.7441			−0.472800			−0.236400	+	0.971656i	$0.575968\pi$
$618$		0			0
$619$	−0.551064	−	0.954471i	−0.0221491	−	0.0383634i	0.854738	−	0.519059i	$-0.173718\pi$
$619$	−0.551064	−	0.954471i	−0.0221491	−	0.0383634i	−0.876888	+	0.480696i	$0.840384\pi$
$620$	−9.57056	+	8.42702i	−0.384363	+	0.338437i
$621$		0			0
$622$	0.146860	+	1.47598i	0.00588853	+	0.0591815i
$623$	19.9710	−	37.5780i	0.800120	−	1.50553i
$624$		0			0
$625$	13.2511	−	22.9516i	0.530044	−	0.918062i
$626$	−0.264096	−	0.367770i	−0.0105554	−	0.0146991i
$627$		0			0
$628$	43.3381	+	14.6149i	1.72938	+	0.583197i
$629$		−	9.76677i		−	0.389427i
$630$		0			0
$631$		−	22.8240i		−	0.908610i	−0.890846	−	0.454305i	$-0.849888\pi$
$631$		−	22.8240i		−	0.908610i	0.890846	−	0.454305i	$-0.150112\pi$
$632$	−2.57389	+	11.1903i	−0.102384	+	0.445125i
$633$		0			0
$634$	12.3763	−	8.88741i	0.491524	−	0.352964i
$635$	21.8757	−	37.8898i	0.868109	−	1.50361i
$636$		0			0
$637$	−2.63393	−	37.4521i	−0.104360	−	1.48391i
$638$	25.4037	−	2.52766i	1.00574	−	0.100071i
$639$		0			0
$640$	24.4887	+	9.02203i	0.968002	+	0.356627i
$641$	−10.1429	−	17.5680i	−0.400621	−	0.693896i	0.593180	−	0.805070i	$-0.297872\pi$
$641$	−10.1429	−	17.5680i	−0.400621	−	0.693896i	−0.993801	+	0.111174i	$0.964539\pi$
$642$		0			0
$643$	−21.0851			−0.831514			−0.415757	−	0.909476i	$-0.636483\pi$
$643$	−21.0851			−0.831514			−0.415757	+	0.909476i	$0.636483\pi$
$644$	−18.9977	+	4.51743i	−0.748615	+	0.178012i
$645$		0			0
$646$	2.22894	−	4.93247i	0.0876965	−	0.194065i
$647$	7.48119	+	12.9578i	0.294116	+	0.509423i	0.974779	−	0.223173i	$-0.0716415\pi$
$647$	7.48119	+	12.9578i	0.294116	+	0.509423i	−0.680663	+	0.732597i	$0.738308\pi$
$648$		0			0
$649$	−31.7529	−	18.3325i	−1.24641	−	0.719615i
$650$	−2.42325	+	0.241112i	−0.0950478	+	0.00945721i
$651$		0			0
$652$	6.60466	+	32.8608i	0.258658	+	1.28693i
$653$	−21.2644	+	36.8310i	−0.832140	+	1.44131i	0.0641976	+	0.997937i	$0.479551\pi$
$653$	−21.2644	+	36.8310i	−0.832140	+	1.44131i	−0.896338	+	0.443372i	$0.853782\pi$
$654$		0			0
$655$	−27.9748	+	16.1512i	−1.09306	+	0.631081i
$656$	−34.3428	−	4.38187i	−1.34086	−	0.171083i
$657$		0			0
$658$	11.6665	+	15.0982i	0.454808	+	0.588588i
$659$		−	35.8548i		−	1.39671i	−0.715754	−	0.698353i	$-0.753917\pi$
$659$		−	35.8548i		−	1.39671i	0.715754	−	0.698353i	$-0.246083\pi$
$660$		0			0
$661$	4.19758	−	2.42348i	0.163267	−	0.0942623i	−0.416140	−	0.909300i	$-0.636617\pi$
$661$	4.19758	−	2.42348i	0.163267	−	0.0942623i	0.579407	+	0.815038i	$0.303284\pi$
$662$	4.08949	+	5.69486i	0.158942	+	0.221337i
$663$		0			0
$664$	0.716125	+	2.33554i	0.0277910	+	0.0906367i
$665$	6.67466	+	10.6770i	0.258832	+	0.414034i
$666$		0			0
$667$	20.9904	+	12.1188i	0.812750	+	0.469241i
$668$	−4.20091	−	4.77097i	−0.162538	−	0.184594i
$669$		0			0
$670$	−47.2460	−	21.3500i	−1.82527	−	0.824824i
$671$	24.2121			0.934696
$672$		0			0
$673$	−0.356589			−0.0137455			−0.00687274	−	0.999976i	$-0.502188\pi$
$673$	−0.356589			−0.0137455			−0.00687274	+	0.999976i	$0.502188\pi$
$674$	−11.9891	−	5.41776i	−0.461802	−	0.208684i
$675$		0			0
$676$	−20.8395	−	23.6674i	−0.801520	−	0.910286i
$677$	−14.3710	−	8.29712i	−0.552324	−	0.318884i	0.197735	−	0.980256i	$-0.436641\pi$
$677$	−14.3710	−	8.29712i	−0.552324	−	0.318884i	−0.750059	+	0.661371i	$0.769975\pi$
$678$		0			0
$679$	12.1355	−	0.426207i	0.465718	−	0.0163563i
$680$	3.54813	+	11.5717i	0.136065	+	0.443756i
$681$		0			0
$682$	−6.26675	−	8.72683i	−0.239966	−	0.334167i
$683$	24.6555	−	14.2348i	0.943415	−	0.544681i	0.0523857	−	0.998627i	$-0.483317\pi$
$683$	24.6555	−	14.2348i	0.943415	−	0.544681i	0.891029	+	0.453946i	$0.149984\pi$
$684$		0			0
$685$		−	35.2992i		−	1.34871i
$686$	8.21680	−	24.8693i	0.313719	−	0.949516i
$687$		0			0
$688$	14.1837	+	1.80973i	0.540748	+	0.0689952i
$689$	4.86215	−	2.80716i	0.185233	−	0.106944i
$690$		0			0
$691$	15.6520	−	27.1100i	0.595429	−	1.03131i	−0.398057	−	0.917361i	$-0.630315\pi$
$691$	15.6520	−	27.1100i	0.595429	−	1.03131i	0.993486	−	0.113953i	$-0.0363513\pi$
$692$	4.28862	+	21.3376i	0.163029	+	0.811134i
$693$		0			0
$694$	−41.2599	+	4.10534i	−1.56620	+	0.155837i
$695$	−18.0870	−	10.4425i	−0.686079	−	0.396108i
$696$		0			0
$697$	−8.02821	−	13.9053i	−0.304090	−	0.526699i
$698$	−8.57610	+	18.9782i	−0.324610	+	0.718337i
$699$		0			0
$700$	−1.62783	−	0.486025i	−0.0615262	−	0.0183700i
$701$	−11.9142			−0.449993			−0.224996	−	0.974360i	$-0.572237\pi$
$701$	−11.9142			−0.449993			−0.224996	+	0.974360i	$0.572237\pi$
$702$		0			0
$703$	−5.43110	−	9.40694i	−0.204838	−	0.354789i
$704$	−9.60680	+	19.7784i	−0.362070	+	0.745428i
$705$		0			0
$706$	12.8299	−	1.27656i	0.482858	−	0.0480441i
$707$	17.0309	+	27.2431i	0.640515	+	1.02458i
$708$		0			0
$709$	2.24316	−	3.88527i	0.0842437	−	0.145914i	−0.820825	−	0.571180i	$-0.806486\pi$
$709$	2.24316	−	3.88527i	0.0842437	−	0.145914i	0.905069	+	0.425265i	$0.139819\pi$
$710$	−37.8514	+	27.1811i	−1.42054	+	1.02009i
$711$		0			0
$712$	10.1977	−	44.3358i	0.382177	−	1.66155i
$713$		−	10.2003i		−	0.382003i
$714$		0			0
$715$		−	34.0053i		−	1.27173i
$716$	−26.7190	−	9.01042i	−0.998535	−	0.336735i
$717$		0			0
$718$	−5.72000	−	7.96544i	−0.213468	−	0.297268i
$719$	−5.53725	+	9.59080i	−0.206505	+	0.357677i	−0.950611	−	0.310385i	$-0.899542\pi$
$719$	−5.53725	+	9.59080i	−0.206505	+	0.357677i	0.744106	+	0.668061i	$0.232876\pi$
$720$		0			0
$721$	−8.63240	−	4.58772i	−0.321487	−	0.170856i
$722$	2.06440	+	20.7478i	0.0768289	+	0.772154i
$723$		0			0
$724$	−4.58025	+	4.03298i	−0.170224	+	0.149884i
$725$	1.05431	+	1.82611i	0.0391559	+	0.0678200i
$726$		0			0
$727$	−13.2445			−0.491210			−0.245605	−	0.969370i	$-0.578987\pi$
$727$	−13.2445			−0.491210			−0.245605	+	0.969370i	$0.578987\pi$
$728$	−13.1057	−	37.9369i	−0.485731	−	1.40604i
$729$		0			0
$730$	−20.4745	−	9.25223i	−0.757794	−	0.342440i
$731$	3.31568	+	5.74293i	0.122635	+	0.212410i
$732$		0			0
$733$	−17.0079	−	9.81954i	−0.628203	−	0.362693i	0.151853	−	0.988403i	$-0.451476\pi$
$733$	−17.0079	−	9.81954i	−0.628203	−	0.362693i	−0.780056	+	0.625710i	$0.784809\pi$
$734$	−3.60592	−	36.2405i	−0.133097	−	1.33766i
$735$		0			0
$736$	−18.3614	+	9.93251i	−0.676809	+	0.366117i
$737$	21.8408	−	37.8295i	0.804518	−	1.39347i
$738$		0			0
$739$	23.9451	−	13.8247i	0.880836	−	0.508551i	0.00990226	−	0.999951i	$-0.496848\pi$
$739$	23.9451	−	13.8247i	0.880836	−	0.508551i	0.870934	+	0.491400i	$0.163515\pi$
$740$	23.0157	+	7.76156i	0.846074	+	0.285321i
$741$		0			0
$742$	3.88137	−	0.524342i	0.142489	−	0.0192492i
$743$		−	34.5688i		−	1.26821i	−0.773248	−	0.634104i	$-0.781369\pi$
$743$		−	34.5688i		−	1.26821i	0.773248	−	0.634104i	$-0.218631\pi$
$744$		0			0
$745$	−37.0177	+	21.3722i	−1.35622	+	0.783016i
$746$	−17.9115	+	12.8623i	−0.655788	+	0.470922i
$747$		0			0
$748$	−9.99759	+	2.00940i	−0.365548	+	0.0734711i
$749$	−3.22314	+	6.06476i	−0.117771	+	0.221602i
$750$		0			0
$751$	12.2614	+	7.07912i	0.447425	+	0.258321i	0.706742	−	0.707471i	$-0.250164\pi$
$751$	12.2614	+	7.07912i	0.447425	+	0.258321i	−0.259317	+	0.965792i	$0.583498\pi$
$752$	16.2321	+	12.3527i	0.591925	+	0.450456i
$753$		0			0
$754$	−20.5150	+	45.3981i	−0.747112	+	1.65330i
$755$	−19.8830			−0.723616
$756$		0			0
$757$	49.6992			1.80635			0.903174	−	0.429275i	$-0.141231\pi$
$757$	49.6992			1.80635			0.903174	+	0.429275i	$0.141231\pi$
$758$	0.455457	−	1.00789i	0.0165430	−	0.0366083i
$759$		0			0
$760$	9.85221	+	9.17236i	0.357377	+	0.332717i
$761$	38.7958	+	22.3988i	1.40635	+	0.811955i	0.995034	−	0.0995388i	$-0.0317367\pi$
$761$	38.7958	+	22.3988i	1.40635	+	0.811955i	0.411314	+	0.911494i	$0.365070\pi$
$762$		0			0
$763$	15.6278	−	9.76968i	0.565765	−	0.353686i
$764$	−2.22422	−	11.0664i	−0.0804696	−	0.400368i
$765$		0			0
$766$	−0.443301	+	0.318335i	−0.0160171	+	0.0115019i
$767$	61.9633	−	35.7745i	2.23736	−	1.29174i
$768$		0			0
$769$		−	24.6680i		−	0.889550i	−0.895642	−	0.444775i	$-0.853284\pi$
$769$		−	24.6680i		−	0.889550i	0.895642	−	0.444775i	$-0.146716\pi$
$770$	9.00409	−	21.9473i	0.324485	−	0.790926i
$771$		0			0
$772$	11.8785	−	35.2237i	0.427515	−	1.26773i
$773$	29.6113	−	17.0961i	1.06505	−	0.614904i	0.138222	−	0.990401i	$-0.455861\pi$
$773$	29.6113	−	17.0961i	1.06505	−	0.614904i	0.926824	+	0.375497i	$0.122528\pi$
$774$		0			0
$775$	0.443699	−	0.768509i	0.0159381	−	0.0276057i
$776$	12.4111	−	3.80549i	0.445532	−	0.136609i
$777$		0			0
$778$	−3.87802	−	38.9753i	−0.139034	−	1.39733i
$779$	−15.4649	−	8.92864i	−0.554086	−	0.319902i
$780$		0			0
$781$	−19.6308	−	34.0016i	−0.702446	−	1.21667i
$782$	−8.82261	−	3.98686i	−0.315496	−	0.142570i
$783$		0			0
$784$	1.58658	−	27.9550i	0.0566635	−	0.998393i
$785$	−52.7506			−1.88275
$786$		0			0
$787$	19.3736	+	33.5561i	0.690595	+	1.19615i	0.971643	+	0.236451i	$0.0759844\pi$
$787$	19.3736	+	33.5561i	0.690595	+	1.19615i	−0.281049	+	0.959694i	$0.590682\pi$
$788$	−32.4260	−	36.8262i	−1.15513	−	1.31188i
$789$		0			0
$790$	−1.31125	−	13.1785i	−0.0466522	−	0.468868i
$791$	−1.74534	−	49.6955i	−0.0620570	−	1.76697i
$792$		0			0
$793$	−23.6240	+	40.9179i	−0.838912	+	1.45304i
$794$	1.84077	+	2.56338i	0.0653265	+	0.0909711i
$795$		0			0
$796$	9.51386	−	28.2119i	0.337210	−	0.999943i
$797$		−	21.5702i		−	0.764057i	−0.924151	−	0.382028i	$-0.875226\pi$
$797$		−	21.5702i		−	0.764057i	0.924151	−	0.382028i	$-0.124774\pi$
$798$		0			0
$799$			9.45999i			0.334670i
$800$	−1.81544	−	0.0503608i	−0.0641854	−	0.00178052i
$801$		0			0
$802$	14.9288	−	10.7204i	0.527155	−	0.378551i
$803$	9.46492	−	16.3937i	0.334010	−	0.578522i
$804$		0			0
$805$	19.0976	−	11.9388i	0.673104	−	0.420789i
$806$	20.8627	−	2.07583i	0.734858	−	0.0731180i
$807$		0			0
$808$	25.1387	+	23.4040i	0.884377	+	0.823351i
$809$	13.0502	+	22.6036i	0.458821	+	0.794702i	0.998899	−	0.0469133i	$-0.0149384\pi$
$809$	13.0502	+	22.6036i	0.458821	+	0.794702i	−0.540078	+	0.841615i	$0.681605\pi$
$810$		0			0
$811$	−41.6937			−1.46406			−0.732032	−	0.681270i	$-0.761428\pi$
$811$	−41.6937			−1.46406			−0.732032	+	0.681270i	$0.761428\pi$
$812$	−25.2613	+	23.8683i	−0.886498	+	0.837611i
$813$		0			0
$814$	−8.42716	+	18.6486i	−0.295372	+	0.653634i
$815$	−19.3293	−	33.4794i	−0.677077	−	1.17273i
$816$		0			0
$817$	6.38705	+	3.68756i	0.223454	+	0.129011i
$818$	−38.1585	+	3.79675i	−1.33418	+	0.132750i
$819$		0			0
$820$	39.1482	−	7.86834i	1.36711	−	0.274774i
$821$	7.99602	−	13.8495i	0.279063	−	0.483351i	−0.692089	−	0.721812i	$-0.743309\pi$
$821$	7.99602	−	13.8495i	0.279063	−	0.483351i	0.971152	+	0.238461i	$0.0766428\pi$
$822$		0			0
$823$	−27.1732	+	15.6884i	−0.947197	+	0.546864i	−0.892209	−	0.451623i	$-0.850845\pi$
$823$	−27.1732	+	15.6884i	−0.947197	+	0.546864i	−0.0549879	+	0.998487i	$0.517512\pi$
$824$	−10.1848	−	2.34262i	−0.354804	−	0.0816090i
$825$		0			0
$826$	49.4642	−	6.68223i	1.72108	−	0.232505i
$827$		−	16.7628i		−	0.582900i	−0.956586	−	0.291450i	$-0.905862\pi$
$827$		−	16.7628i		−	0.582900i	0.956586	−	0.291450i	$-0.0941378\pi$
$828$		0			0
$829$	15.0512	−	8.68980i	0.522749	−	0.301809i	−0.215310	−	0.976546i	$-0.569076\pi$
$829$	15.0512	−	8.68980i	0.522749	−	0.301809i	0.738059	+	0.674737i	$0.235743\pi$
$830$	−1.64343	−	2.28858i	−0.0570444	−	0.0794378i
$831$		0			0
$832$	−24.0518	−	35.5334i	−0.833845	−	1.23190i
$833$	10.7627	−	7.26580i	0.372906	−	0.251745i
$834$		0			0
$835$	6.34955	+	3.66591i	0.219735	+	0.126864i
$836$	−8.51187	+	7.49482i	−0.294389	+	0.259214i
$837$		0			0
$838$	−8.54024	−	3.85926i	−0.295018	−	0.133316i
$839$	−42.4474			−1.46545			−0.732724	−	0.680526i	$-0.761751\pi$
$839$	−42.4474			−1.46545			−0.732724	+	0.680526i	$0.761751\pi$
$840$		0			0
$841$	14.1367			0.487471
$842$	9.37430	+	4.23616i	0.323060	+	0.145988i
$843$		0			0
$844$	−4.45550	+	3.92314i	−0.153365	+	0.135040i
$845$	31.4983	+	18.1856i	1.08357	+	0.625602i
$846$		0			0
$847$	−8.05013	−	4.27827i	−0.276606	−	0.147003i
$848$	3.86190	−	1.61775i	0.132618	−	0.0555537i
$849$		0			0
$850$	−0.491290	−	0.684151i	−0.0168511	−	0.0234662i
$851$	−16.8260	+	9.71449i	−0.576788	+	0.333009i
$852$		0			0
$853$			52.9713i			1.81370i	0.421449	+	0.906852i	$0.361521\pi$
$853$			52.9713i			1.81370i	−0.421449	+	0.906852i	$0.638479\pi$
$854$	−26.0816	+	20.1535i	−0.892493	+	0.689639i
$855$		0			0
$856$	−1.64583	+	7.15540i	−0.0562532	+	0.244567i
$857$	−36.9073	+	21.3084i	−1.26073	+	0.727882i	−0.973215	−	0.229895i	$-0.926162\pi$
$857$	−36.9073	+	21.3084i	−1.26073	+	0.727882i	−0.287513	+	0.957777i	$0.592828\pi$
$858$		0			0
$859$	14.6290	−	25.3382i	0.499136	−	0.864529i	−0.500863	−	0.865526i	$-0.666984\pi$
$859$	14.6290	−	25.3382i	0.499136	−	0.864529i	1.00000		0.000997369i	$0.000317472\pi$
$860$	−16.1683	+	3.24966i	−0.551336	+	0.110812i
$861$		0			0
$862$	28.1965	−	2.80553i	0.960375	−	0.0955569i
$863$	−20.5035	−	11.8377i	−0.697947	−	0.402960i	0.108635	−	0.994082i	$-0.465352\pi$
$863$	−20.5035	−	11.8377i	−0.697947	−	0.402960i	−0.806583	+	0.591122i	$0.798685\pi$
$864$		0			0
$865$	−12.5512	−	21.7392i	−0.426752	−	0.739156i
$866$	11.8940	−	26.3204i	0.404173	−	0.894404i
$867$		0			0
$868$	14.0146	+	4.18438i	0.475687	+	0.142027i
$869$	11.1580			0.378511
$870$		0			0
$871$	42.6207	+	73.8213i	1.44415	+	2.50134i
$872$	13.4256	−	14.4206i	0.454647	−	0.488344i
$873$		0			0
$874$	−10.7146	+	1.06610i	−0.362426	+	0.0360612i
$875$	−28.5383	+	1.00228i	−0.964771	+	0.0338834i
$876$		0			0
$877$	8.08300	−	14.0002i	0.272943	−	0.472752i	−0.696671	−	0.717391i	$-0.745336\pi$
$877$	8.08300	−	14.0002i	0.272943	−	0.472752i	0.969614	+	0.244639i	$0.0786695\pi$
$878$	−28.8167	+	20.6933i	−0.972517	+	0.698367i
$879$		0			0
$880$	3.20977	−	25.1565i	0.108201	−	0.848025i
$881$			15.7701i			0.531307i	0.964069	+	0.265653i	$0.0855877\pi$
$881$			15.7701i			0.531307i	−0.964069	+	0.265653i	$0.914412\pi$
$882$		0			0
$883$			20.2738i			0.682267i	0.940015	+	0.341134i	$0.110811\pi$
$883$			20.2738i			0.682267i	−0.940015	+	0.341134i	$0.889189\pi$
$884$	6.35891	−	18.8563i	0.213873	−	0.634208i
$885$		0			0
$886$	9.64732	+	13.4345i	0.324108	+	0.451340i
$887$	9.96636	−	17.2622i	0.334638	−	0.579609i	−0.648778	−	0.760978i	$-0.724719\pi$
$887$	9.96636	−	17.2622i	0.334638	−	0.579609i	0.983415	+	0.181369i	$0.0580528\pi$
$888$		0			0
$889$	−50.1503	+	1.76131i	−1.68199	+	0.0590725i
$890$	5.19517	+	52.2130i	0.174142	+	1.75018i
$891$		0			0
$892$	9.71627	+	11.0348i	0.325325	+	0.369471i
$893$	5.26050	+	9.11146i	0.176036	+	0.304903i
$894$		0			0
$895$	32.5220			1.08709
$896$	−6.11450	−	29.3021i	−0.204271	−	0.978914i
$897$		0			0
$898$	−13.8634	−	6.26476i	−0.462628	−	0.209058i
$899$	−9.07693	−	15.7217i	−0.302732	−	0.524348i
$900$		0			0
$901$	1.68169	+	0.970922i	0.0560251	+	0.0323461i
$902$	3.33102	+	33.4777i	0.110911	+	1.11469i
$903$		0			0
$904$	−15.5837	−	50.8240i	−0.518305	−	1.69038i
$905$	3.51937	−	6.09572i	0.116988	−	0.202629i
$906$		0			0
$907$	4.55137	−	2.62774i	0.151126	−	0.0872525i	−0.422530	−	0.906349i	$-0.638858\pi$
$907$	4.55137	−	2.62774i	0.151126	−	0.0872525i	0.573656	+	0.819096i	$0.305525\pi$
$908$	−9.59821	+	28.4620i	−0.318528	+	0.944544i
$909$		0			0
$910$	28.3052	+	36.6310i	0.938307	+	1.21431i
$911$			8.12247i			0.269109i	0.990906	+	0.134555i	$0.0429604\pi$
$911$			8.12247i			0.269109i	−0.990906	+	0.134555i	$0.957040\pi$
$912$		0			0
$913$	2.05581	−	1.18692i	0.0680375	−	0.0392815i
$914$	27.3735	−	19.6569i	0.905434	−	0.650194i
$915$		0			0
$916$	2.65849	+	13.2270i	0.0878389	+	0.437033i
$917$	32.7165	+	17.3873i	1.08040	+	0.574180i
$918$		0			0
$919$	−49.1351	−	28.3682i	−1.62082	−	0.935780i	−0.986701	−	0.162543i	$-0.948030\pi$
$919$	−49.1351	−	28.3682i	−1.62082	−	0.935780i	−0.634117	−	0.773237i	$-0.718636\pi$
$920$	16.4064	−	17.6224i	0.540904	−	0.580995i
$921$		0			0
$922$	−17.3177	+	38.3227i	−0.570328	+	1.26209i
$923$	76.6161			2.52185
$924$		0			0
$925$	−1.69028			−0.0555759
$926$	−8.05269	+	17.8200i	−0.264628	+	0.585600i
$927$		0			0
$928$	−19.4618	+	31.6483i	−0.638864	+	1.03891i
$929$	−16.5057	−	9.52958i	−0.541535	−	0.312655i	0.204166	−	0.978936i	$-0.434552\pi$
$929$	−16.5057	−	9.52958i	−0.541535	−	0.312655i	−0.745701	+	0.666281i	$0.767885\pi$
$930$		0			0
$931$	6.32583	−	12.9830i	0.207321	−	0.425502i
$932$	20.1032	−	4.04051i	0.658501	−	0.132351i
$933$		0			0
$934$	−27.8152	+	19.9742i	−0.910142	+	0.653575i
$935$	10.1858	−	5.88076i	0.333110	−	0.192321i
$936$		0			0
$937$			19.7495i			0.645189i	0.946537	+	0.322595i	$0.104555\pi$
$937$			19.7495i			0.645189i	−0.946537	+	0.322595i	$0.895445\pi$
$938$	7.96102	+	58.9302i	0.259936	+	1.92414i
$939$		0			0
$940$	−22.2928	−	7.51777i	−0.727110	−	0.245203i
$941$	25.9551	−	14.9852i	0.846112	−	0.488503i	−0.0132248	−	0.999913i	$-0.504210\pi$
$941$	25.9551	−	14.9852i	0.846112	−	0.488503i	0.859337	+	0.511409i	$0.170876\pi$
$942$		0			0
$943$	−15.9705	+	27.6617i	−0.520070	+	0.900788i
$944$	49.2161	−	20.6166i	1.60185	−	0.671014i
$945$		0			0
$946$	−1.37572	−	13.8264i	−0.0447286	−	0.449536i
$947$	−13.8730	−	8.00958i	−0.450812	−	0.260276i	0.257361	−	0.966315i	$-0.417147\pi$
$947$	−13.8730	−	8.00958i	−0.450812	−	0.260276i	−0.708173	+	0.706039i	$0.750480\pi$
$948$		0			0
$949$	18.4701	+	31.9911i	0.599564	+	1.03848i
$950$	−0.853633	−	0.385749i	−0.0276955	−	0.0125154i
$951$		0			0
$952$	9.09697	−	10.4863i	0.294835	−	0.339863i
$953$	32.1002			1.03983			0.519914	−	0.854219i	$-0.325964\pi$
$953$	32.1002			1.03983			0.519914	+	0.854219i	$0.325964\pi$
$954$		0			0
$955$	6.50945	+	11.2747i	0.210641	+	0.364841i
$956$	−31.6669	+	27.8832i	−1.02418	+	0.901806i
$957$		0			0
$958$	2.19386	+	22.0490i	0.0708806	+	0.712371i
$959$	−34.3306	+	21.4617i	−1.10859	+	0.693034i
$960$		0			0
$961$	11.6800	−	20.2304i	0.376775	−	0.652593i
$962$	−23.2934	−	32.4374i	−0.751009	−	1.04583i
$963$		0			0
$964$	−35.9569	−	12.1257i	−1.15809	−	0.390542i
$965$			42.8739i			1.38016i
$966$		0			0
$967$			13.1511i			0.422910i	0.977388	+	0.211455i	$0.0678202\pi$
$967$			13.1511i			0.422910i	−0.977388	+	0.211455i	$0.932180\pi$
$968$	−9.49780	−	2.18461i	−0.305271	−	0.0702159i
$969$		0			0
$970$	−12.1615	+	8.73321i	−0.390483	+	0.280407i
$971$	26.2200	−	45.4144i	0.841441	−	1.45742i	−0.0472354	−	0.998884i	$-0.515041\pi$
$971$	26.2200	−	45.4144i	0.841441	−	1.45742i	0.888676	−	0.458535i	$-0.151626\pi$
$972$		0			0
$973$	0.840777	+	23.9397i	0.0269541	+	0.767471i
$974$	27.5493	−	2.74114i	0.882735	−	0.0878318i
$975$		0			0
$976$	−21.3389	+	28.0405i	−0.683040	+	0.897554i
$977$	−15.8361	−	27.4290i	−0.506643	−	0.877532i	−0.999970	−	0.00768790i	$-0.997553\pi$
$977$	−15.8361	−	27.4290i	−0.506643	−	0.877532i	0.493327	−	0.869844i	$-0.335780\pi$
$978$		0			0
$979$	−44.2081			−1.41290
$980$	8.56905	+	31.1368i	0.273728	+	0.994627i
$981$		0			0
$982$	8.90617	−	19.7087i	0.284207	−	0.628929i
$983$	26.4679	+	45.8438i	0.844195	+	1.46219i	0.886318	+	0.463076i	$0.153254\pi$
$983$	26.4679	+	45.8438i	0.844195	+	1.46219i	−0.0421232	+	0.999112i	$0.513412\pi$
$984$		0			0
$985$	49.0109	+	28.2965i	1.56162	+	0.901600i
$986$	−17.1461	+	1.70603i	−0.546043	+	0.0543311i
$987$		0			0
$988$	−4.36099	−	21.6977i	−0.138742	−	0.690295i
$989$	6.59587	−	11.4244i	0.209736	−	0.363274i
$990$		0			0
$991$	−48.3895	+	27.9377i	−1.53714	+	0.887470i	−0.538138	+	0.842856i	$0.680872\pi$
$991$	−48.3895	+	27.9377i	−1.53714	+	0.887470i	−0.999004	+	0.0446134i	$0.985794\pi$
$992$	15.6298	+	0.433576i	0.496247	+	0.0137661i
$993$		0			0
$994$	49.4487	+	20.2868i	1.56842	+	0.643458i
$995$			34.3391i			1.08862i
$996$		0			0
$997$	27.0045	−	15.5910i	0.855240	−	0.493773i	−0.00717513	−	0.999974i	$-0.502284\pi$
$997$	27.0045	−	15.5910i	0.855240	−	0.493773i	0.862416	+	0.506201i	$0.168951\pi$
$998$	−9.65120	−	13.4399i	−0.305503	−	0.425432i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bf.d.271.14	yes	32
3.2	odd	2	inner	756.2.bf.d.271.3	yes	32
4.3	odd	2		756.2.bf.a.271.3	✓	32
7.3	odd	6		756.2.bf.a.703.3	yes	32
12.11	even	2		756.2.bf.a.271.14	yes	32
21.17	even	6		756.2.bf.a.703.14	yes	32
28.3	even	6	inner	756.2.bf.d.703.14	yes	32
84.59	odd	6	inner	756.2.bf.d.703.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bf.a.271.3	✓	32	4.3	odd	2
756.2.bf.a.271.14	yes	32	12.11	even	2
756.2.bf.a.703.3	yes	32	7.3	odd	6
756.2.bf.a.703.14	yes	32	21.17	even	6
756.2.bf.d.271.3	yes	32	3.2	odd	2	inner
756.2.bf.d.271.14	yes	32	1.1	even	1	trivial
756.2.bf.d.703.3	yes	32	84.59	odd	6	inner
756.2.bf.d.703.14	yes	32	28.3	even	6	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28874 + 0.582370i) q^{2} +(1.32169 + 1.50104i) q^{4} +(-1.99770 - 1.15337i) q^{5} +(0.0928632 + 2.64412i) q^{7} +(0.829152 + 2.70416i) q^{8} +O(q^{10})\)	\(q+(1.28874 + 0.582370i) q^{2} +(1.32169 + 1.50104i) q^{4} +(-1.99770 - 1.15337i) q^{5} +(0.0928632 + 2.64412i) q^{7} +(0.829152 + 2.70416i) q^{8} +(-1.90282 - 2.64979i) q^{10} +(2.38028 - 1.37426i) q^{11} +5.36352i q^{13} +(-1.42018 + 3.46166i) q^{14} +(-0.506264 + 3.96783i) q^{16} +(-1.60656 + 0.927548i) q^{17} +(-1.03158 + 1.78675i) q^{19} +(-0.909078 - 4.52303i) q^{20} +(3.86789 - 0.384853i) q^{22} +(3.19592 + 1.84517i) q^{23} +(0.160525 + 0.278038i) q^{25} +(-3.12355 + 6.91217i) q^{26} +(-3.84620 + 3.63410i) q^{28} +6.56785 q^{29} +(-1.38202 - 2.39374i) q^{31} +(-2.96319 + 4.81866i) q^{32} +(-2.61061 + 0.259755i) q^{34} +(2.86414 - 5.38925i) q^{35} +(-2.63241 + 4.55948i) q^{37} +(-2.36999 + 1.70189i) q^{38} +(1.46251 - 6.35842i) q^{40} +8.65530i q^{41} -3.57467i q^{43} +(5.20882 + 1.75657i) q^{44} +(3.04414 + 4.23915i) q^{46} +(2.54973 - 4.41626i) q^{47} +(-6.98275 + 0.491083i) q^{49} +(0.0449542 + 0.451803i) q^{50} +(-8.05087 + 7.08891i) q^{52} +(-0.523381 - 0.906522i) q^{53} -6.34011 q^{55} +(-7.07314 + 2.44350i) q^{56} +(8.46424 + 3.82492i) q^{58} +(-6.66997 - 11.5527i) q^{59} +(7.62894 + 4.40457i) q^{61} +(-0.387028 - 3.88975i) q^{62} +(-6.62501 + 4.48433i) q^{64} +(6.18612 - 10.7147i) q^{65} +(13.7636 - 7.94642i) q^{67} +(-3.51567 - 1.18559i) q^{68} +(6.82966 - 5.27735i) q^{70} -14.2847i q^{71} +(5.96458 - 3.44365i) q^{73} +(-6.04779 + 4.34293i) q^{74} +(-4.04542 + 0.813085i) q^{76} +(3.85474 + 6.16614i) q^{77} +(3.51577 + 2.02983i) q^{79} +(5.58774 - 7.34261i) q^{80} +(-5.04058 + 11.1544i) q^{82} +0.863684 q^{83} +4.27923 q^{85} +(2.08178 - 4.60681i) q^{86} +(5.68984 + 5.29721i) q^{88} +(-13.9295 - 8.04218i) q^{89} +(-14.1818 + 0.498074i) q^{91} +(1.45435 + 7.23596i) q^{92} +(5.85783 - 4.20652i) q^{94} +(4.12157 - 2.37959i) q^{95} -4.58962i q^{97} +(-9.28493 - 3.43367i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{7}+O(q^{10}) \) 32 * q + 2 * q^7	\( 32 q + 2 q^{7} + 4 q^{10} + 20 q^{16} - 6 q^{19} + 20 q^{22} + 20 q^{25} - 24 q^{28} + 8 q^{34} - 2 q^{37} + 52 q^{40} + 24 q^{46} - 10 q^{49} + 16 q^{52} + 16 q^{55} - 80 q^{58} + 48 q^{64} + 42 q^{67} + 32 q^{70} - 18 q^{73} - 40 q^{76} - 6 q^{79} + 8 q^{82} - 8 q^{85} - 80 q^{88} + 8 q^{91} - 8 q^{94}+O(q^{100}) \) 32 * q + 2 * q^7 + 4 * q^10 + 20 * q^16 - 6 * q^19 + 20 * q^22 + 20 * q^25 - 24 * q^28 + 8 * q^34 - 2 * q^37 + 52 * q^40 + 24 * q^46 - 10 * q^49 + 16 * q^52 + 16 * q^55 - 80 * q^58 + 48 * q^64 + 42 * q^67 + 32 * q^70 - 18 * q^73 - 40 * q^76 - 6 * q^79 + 8 * q^82 - 8 * q^85 - 80 * q^88 + 8 * q^91 - 8 * q^94

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