LMFDB - Embedded newform 592.2.w.f.529.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [592,2,Mod(529,592)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("592.529"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(592, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,2,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 28 x^{18} + 320 x^{16} + 1984 x^{14} + 7388 x^{12} + 17136 x^{10} + 24692 x^{8} + 21256 x^{6} + \cdots + 64 $ x^20 + 28x^18 + 320x^16 + 1984x^14 + 7388x^12 + 17136x^10 + 24692x^8 + 21256x^6 + 9956x^4 + 2016*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{18} $
Twist minimal:	no (minimal twist has level 296)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$2.07608i$ of defining polynomial
Character	$\chi$	$=$	592.529
Dual form			592.2.w.f.545.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61426 + 2.79599i) q^{3} +(0.539298 + 0.311364i) q^{5} +(0.278439 - 0.482271i) q^{7} +(-3.71170 - 6.42885i) q^{9} -4.40317 q^{11} +(0.211099 + 0.121878i) q^{13} +(-1.74114 + 1.00525i) q^{15} +(-5.61985 + 3.24462i) q^{17} +(-0.309666 - 0.178786i) q^{19} +(0.898950 + 1.55703i) q^{21} -0.840354i q^{23} +(-2.30611 - 3.99429i) q^{25} +14.2811 q^{27} -0.996730i q^{29} -9.34379i q^{31} +(7.10787 - 12.3112i) q^{33} +(0.300323 - 0.173392i) q^{35} +(2.15231 + 5.68925i) q^{37} +(-0.681538 + 0.393486i) q^{39} +(3.36708 - 5.83196i) q^{41} +1.77846i q^{43} -4.62275i q^{45} -11.5380 q^{47} +(3.34494 + 5.79361i) q^{49} -20.9507i q^{51} +(5.80817 + 10.0600i) q^{53} +(-2.37462 - 1.37099i) q^{55} +(0.999766 - 0.577215i) q^{57} +(0.357898 - 0.206632i) q^{59} +(-12.2063 - 7.04728i) q^{61} -4.13393 q^{63} +(0.0758967 + 0.131457i) q^{65} +(0.0422812 - 0.0732332i) q^{67} +(2.34962 + 1.35655i) q^{69} +(-5.91365 + 10.2428i) q^{71} -9.52922 q^{73} +14.8907 q^{75} +(-1.22602 + 2.12352i) q^{77} +(6.67792 + 3.85550i) q^{79} +(-11.9183 + 20.6431i) q^{81} +(-3.84557 - 6.66072i) q^{83} -4.04103 q^{85} +(2.78685 + 1.60899i) q^{87} +(6.34345 - 3.66239i) q^{89} +(0.117556 - 0.0678712i) q^{91} +(26.1251 + 15.0833i) q^{93} +(-0.111335 - 0.192838i) q^{95} +10.8199i q^{97} +(16.3432 + 28.3073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} + 6 q^{5} + 2 q^{7} - 12 q^{9} - 16 q^{11} - 6 q^{13} + 18 q^{15} - 6 q^{17} + 6 q^{19} + 2 q^{21} + 20 q^{25} + 20 q^{27} - 4 q^{33} + 6 q^{35} + 24 q^{37} - 18 q^{39} + 14 q^{41} + 8 q^{47}+ \cdots + 56 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 + 6 * q^5 + 2 * q^7 - 12 * q^9 - 16 * q^11 - 6 * q^13 + 18 * q^15 - 6 * q^17 + 6 * q^19 + 2 * q^21 + 20 * q^25 + 20 * q^27 - 4 * q^33 + 6 * q^35 + 24 * q^37 - 18 * q^39 + 14 * q^41 + 8 * q^47 + 4 * q^49 + 2 * q^53 - 12 * q^55 - 6 * q^57 + 18 * q^59 - 30 * q^61 - 24 * q^63 + 10 * q^65 + 10 * q^67 - 12 * q^69 + 2 * q^71 - 16 * q^73 + 24 * q^75 + 12 * q^77 + 66 * q^79 - 18 * q^81 - 42 * q^83 - 92 * q^85 - 12 * q^87 - 18 * q^89 - 66 * q^91 + 48 * q^93 - 14 * q^95 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.61426	+	2.79599i	−0.931996	+	1.61426i	−0.152091	+	0.988367i	$0.548601\pi$
$3$	−1.61426	+	2.79599i	−0.931996	+	1.61426i	−0.779905	+	0.625898i	$0.784733\pi$
$4$		0			0
$5$	0.539298	+	0.311364i	0.241181	+	0.139246i	0.615720	−	0.787965i	$-0.288865\pi$
$5$	0.539298	+	0.311364i	0.241181	+	0.139246i	−0.374538	+	0.927211i	$0.622199\pi$
$6$		0			0
$7$	0.278439	−	0.482271i	0.105240	−	0.182281i	−0.808596	−	0.588364i	$-0.799772\pi$
$7$	0.278439	−	0.482271i	0.105240	−	0.182281i	0.913836	+	0.406083i	$0.133106\pi$
$8$		0			0
$9$	−3.71170	−	6.42885i	−1.23723	−	2.14295i
$10$		0			0
$11$	−4.40317			−1.32760			−0.663802	−	0.747908i	$-0.731058\pi$
$11$	−4.40317			−1.32760			−0.663802	+	0.747908i	$0.731058\pi$
$12$		0			0
$13$	0.211099	+	0.121878i	0.0585482	+	0.0338028i	0.528988	−	0.848629i	$-0.322572\pi$
$13$	0.211099	+	0.121878i	0.0585482	+	0.0338028i	−0.470440	+	0.882432i	$0.655905\pi$
$14$		0			0
$15$	−1.74114	+	1.00525i	−0.449560	+	0.259554i
$16$		0			0
$17$	−5.61985	+	3.24462i	−1.36301	+	0.786937i	−0.990024	−	0.140899i	$-0.955001\pi$
$17$	−5.61985	+	3.24462i	−1.36301	+	0.786937i	−0.372990	+	0.927835i	$0.621667\pi$
$18$		0			0
$19$	−0.309666	−	0.178786i	−0.0710423	−	0.0410163i	0.464058	−	0.885805i	$-0.346393\pi$
$19$	−0.309666	−	0.178786i	−0.0710423	−	0.0410163i	−0.535100	+	0.844788i	$0.679726\pi$
$20$		0			0
$21$	0.898950	+	1.55703i	0.196167	+	0.339771i
$22$		0			0
$23$		−	0.840354i		−	0.175226i	−0.996155	−	0.0876129i	$-0.972076\pi$
$23$		−	0.840354i		−	0.175226i	0.996155	−	0.0876129i	$-0.0279239\pi$
$24$		0			0
$25$	−2.30611	−	3.99429i	−0.461221	−	0.798858i
$26$		0			0
$27$	14.2811			2.74839
$28$		0			0
$29$		−	0.996730i		−	0.185088i	−0.995709	−	0.0925441i	$-0.970500\pi$
$29$		−	0.996730i		−	0.185088i	0.995709	−	0.0925441i	$-0.0294999\pi$
$30$		0			0
$31$		−	9.34379i		−	1.67819i	−0.543982	−	0.839097i	$-0.683084\pi$
$31$		−	9.34379i		−	1.67819i	0.543982	−	0.839097i	$-0.316916\pi$
$32$		0			0
$33$	7.10787	−	12.3112i	1.23732	−	2.14310i
$34$		0			0
$35$	0.300323	−	0.173392i	0.0507639	−	0.0293086i
$36$		0			0
$37$	2.15231	+	5.68925i	0.353838	+	0.935307i
$37$	2.15231	+	5.68925i	0.353838	+	0.935307i
$38$		0			0
$39$	−0.681538	+	0.393486i	−0.109133	+	0.0630082i
$40$		0			0
$41$	3.36708	−	5.83196i	0.525850	−	0.910799i	−0.473697	−	0.880688i	$-0.657081\pi$
$41$	3.36708	−	5.83196i	0.525850	−	0.910799i	0.999547	−	0.0301108i	$-0.00958600\pi$
$42$		0			0
$43$			1.77846i			0.271212i	0.990763	+	0.135606i	$0.0432982\pi$
$43$			1.77846i			0.271212i	−0.990763	+	0.135606i	$0.956702\pi$
$44$		0			0
$45$		−	4.62275i		−	0.689119i
$46$		0			0
$47$	−11.5380			−1.68299			−0.841494	−	0.540267i	$-0.818323\pi$
$47$	−11.5380			−1.68299			−0.841494	+	0.540267i	$0.818323\pi$
$48$		0			0
$49$	3.34494	+	5.79361i	0.477849	+	0.827659i
$50$		0			0
$51$		−	20.9507i		−	2.93369i
$52$		0			0
$53$	5.80817	+	10.0600i	0.797814	+	1.38185i	0.921037	+	0.389475i	$0.127343\pi$
$53$	5.80817	+	10.0600i	0.797814	+	1.38185i	−0.123223	+	0.992379i	$0.539323\pi$
$54$		0			0
$55$	−2.37462	−	1.37099i	−0.320193	−	0.184864i
$56$		0			0
$57$	0.999766	−	0.577215i	0.132422	−	0.0764540i
$58$		0			0
$59$	0.357898	−	0.206632i	0.0465943	−	0.0269012i	−0.476522	−	0.879163i	$-0.658103\pi$
$59$	0.357898	−	0.206632i	0.0465943	−	0.0269012i	0.523116	+	0.852261i	$0.324769\pi$
$60$		0			0
$61$	−12.2063	−	7.04728i	−1.56285	−	0.902312i	−0.996967	−	0.0778272i	$-0.975202\pi$
$61$	−12.2063	−	7.04728i	−1.56285	−	0.902312i	−0.565884	−	0.824485i	$-0.691465\pi$
$62$		0			0
$63$	−4.13393			−0.520827
$64$		0			0
$65$	0.0758967	+	0.131457i	0.00941382	+	0.0163052i
$66$		0			0
$67$	0.0422812	−	0.0732332i	0.00516547	−	0.00894685i	−0.863431	−	0.504467i	$-0.831689\pi$
$67$	0.0422812	−	0.0732332i	0.00516547	−	0.00894685i	0.868597	+	0.495520i	$0.165022\pi$
$68$		0			0
$69$	2.34962	+	1.35655i	0.282861	+	0.163310i
$70$		0			0
$71$	−5.91365	+	10.2428i	−0.701822	+	1.21559i	0.266005	+	0.963972i	$0.414296\pi$
$71$	−5.91365	+	10.2428i	−0.701822	+	1.21559i	−0.967826	+	0.251619i	$0.919037\pi$
$72$		0			0
$73$	−9.52922			−1.11531			−0.557656	−	0.830072i	$-0.688299\pi$
$73$	−9.52922			−1.11531			−0.557656	+	0.830072i	$0.688299\pi$
$74$		0			0
$75$	14.8907			1.71942
$76$		0			0
$77$	−1.22602	+	2.12352i	−0.139717	+	0.241998i
$78$		0			0
$79$	6.67792	+	3.85550i	0.751324	+	0.433777i	0.826172	−	0.563418i	$-0.190514\pi$
$79$	6.67792	+	3.85550i	0.751324	+	0.433777i	−0.0748480	+	0.997195i	$0.523847\pi$
$80$		0			0
$81$	−11.9183	+	20.6431i	−1.32426	+	2.29368i
$82$		0			0
$83$	−3.84557	−	6.66072i	−0.422106	−	0.731109i	0.574039	−	0.818828i	$-0.305376\pi$
$83$	−3.84557	−	6.66072i	−0.422106	−	0.731109i	−0.996145	+	0.0877189i	$0.972042\pi$
$84$		0			0
$85$	−4.04103			−0.438311
$86$		0			0
$87$	2.78685	+	1.60899i	0.298781	+	0.172501i
$88$		0			0
$89$	6.34345	−	3.66239i	0.672404	−	0.388213i	−0.124583	−	0.992209i	$-0.539759\pi$
$89$	6.34345	−	3.66239i	0.672404	−	0.388213i	0.796987	+	0.603996i	$0.206426\pi$
$90$		0			0
$91$	0.117556	−	0.0678712i	0.0123233	−	0.00711484i
$92$		0			0
$93$	26.1251	+	15.0833i	2.70905	+	1.56407i
$94$		0			0
$95$	−0.111335	−	0.192838i	−0.0114227	−	0.0197847i
$96$		0			0
$97$			10.8199i			1.09860i	0.835626	+	0.549299i	$0.185105\pi$
$97$			10.8199i			1.09860i	−0.835626	+	0.549299i	$0.814895\pi$
$98$		0			0
$99$	16.3432	+	28.3073i	1.64256	+	2.84499i
$100$		0			0
$101$	−13.7189			−1.36508			−0.682539	−	0.730849i	$-0.739124\pi$
$101$	−13.7189			−1.36508			−0.682539	+	0.730849i	$0.739124\pi$
$102$		0			0
$103$		−	8.18754i		−	0.806742i	−0.915037	−	0.403371i	$-0.867838\pi$
$103$		−	8.18754i		−	0.806742i	0.915037	−	0.403371i	$-0.132162\pi$
$104$		0			0
$105$			1.11960i			0.109262i
$106$		0			0
$107$	0.286432	−	0.496114i	0.0276904	−	0.0479612i	−0.851848	−	0.523789i	$-0.824518\pi$
$107$	0.286432	−	0.496114i	0.0276904	−	0.0479612i	0.879539	+	0.475828i	$0.157851\pi$
$108$		0			0
$109$	−10.0885	+	5.82460i	−0.966303	+	0.557895i	−0.898107	−	0.439777i	$-0.855058\pi$
$109$	−10.0885	+	5.82460i	−0.966303	+	0.557895i	−0.0681958	+	0.997672i	$0.521724\pi$
$110$		0			0
$111$	−19.3815	−	3.16611i	−1.83961	−	0.300514i
$112$		0			0
$113$	−0.463229	+	0.267445i	−0.0435769	+	0.0251592i	−0.521630	−	0.853172i	$-0.674676\pi$
$113$	−0.463229	+	0.267445i	−0.0435769	+	0.0251592i	0.478053	+	0.878331i	$0.341343\pi$
$114$		0			0
$115$	0.261656	−	0.453201i	0.0243995	−	0.0422612i
$116$		0			0
$117$		−	1.80950i		−	0.167288i
$118$		0			0
$119$			3.61372i			0.331269i
$120$		0			0
$121$	8.38787			0.762534
$122$		0			0
$123$	10.8707	+	18.8286i	0.980180	+	1.69772i
$124$		0			0
$125$		−	5.98579i		−	0.535385i
$126$		0			0
$127$	1.27993	+	2.21690i	0.113575	+	0.196718i	0.917209	−	0.398406i	$-0.130436\pi$
$127$	1.27993	+	2.21690i	0.113575	+	0.196718i	−0.803634	+	0.595124i	$0.797103\pi$
$128$		0			0
$129$	−4.97255	−	2.87090i	−0.437808	−	0.252769i
$130$		0			0
$131$	−15.2856	+	8.82515i	−1.33551	+	0.771057i	−0.986138	−	0.165927i	$-0.946938\pi$
$131$	−15.2856	+	8.82515i	−1.33551	+	0.771057i	−0.349372	+	0.936984i	$0.613605\pi$
$132$		0			0
$133$	−0.172447	+	0.0995621i	−0.0149530	+	0.00863313i
$134$		0			0
$135$	7.70174	+	4.44660i	0.662861	+	0.382703i
$136$		0			0
$137$	−5.87002			−0.501509			−0.250755	−	0.968051i	$-0.580679\pi$
$137$	−5.87002			−0.501509			−0.250755	+	0.968051i	$0.580679\pi$
$138$		0			0
$139$	4.64314	+	8.04216i	0.393826	+	0.682127i	0.992951	−	0.118529i	$-0.0378178\pi$
$139$	4.64314	+	8.04216i	0.393826	+	0.682127i	−0.599124	+	0.800656i	$0.704484\pi$
$140$		0			0
$141$	18.6253	−	32.2600i	1.56854	−	2.71679i
$142$		0			0
$143$	−0.929503	−	0.536649i	−0.0777289	−	0.0448768i
$144$		0			0
$145$	0.310346	−	0.537534i	0.0257728	−	0.0446398i
$146$		0			0
$147$	−21.5985			−1.78141
$148$		0			0
$149$	−17.5184			−1.43516			−0.717581	−	0.696475i	$-0.754751\pi$
$149$	−17.5184			−1.43516			−0.717581	+	0.696475i	$0.754751\pi$
$150$		0			0
$151$	−0.729085	+	1.26281i	−0.0593321	+	0.102766i	−0.894166	−	0.447736i	$-0.852230\pi$
$151$	−0.729085	+	1.26281i	−0.0593321	+	0.102766i	0.834834	+	0.550502i	$0.185564\pi$
$152$		0			0
$153$	41.7184	+	24.0861i	3.37273	+	1.94725i
$154$		0			0
$155$	2.90932	−	5.03908i	0.233682	−	0.404749i
$156$		0			0
$157$	−6.80957	−	11.7945i	−0.543463	−	0.941305i	−0.998702	−	0.0509361i	$-0.983780\pi$
$157$	−6.80957	−	11.7945i	−0.543463	−	0.941305i	0.455239	−	0.890369i	$-0.349554\pi$
$158$		0			0
$159$	−37.5037			−2.97424
$160$		0			0
$161$	−0.405278	−	0.233988i	−0.0319404	−	0.0184408i
$162$		0			0
$163$	4.70610	−	2.71707i	0.368610	−	0.212817i	−0.304241	−	0.952595i	$-0.598403\pi$
$163$	4.70610	−	2.71707i	0.368610	−	0.212817i	0.672851	+	0.739778i	$0.265069\pi$
$164$		0			0
$165$	7.66652	−	4.42627i	0.596838	−	0.344584i
$166$		0			0
$167$	16.0783	+	9.28282i	1.24418	+	0.718327i	0.969942	−	0.243336i	$-0.0782417\pi$
$167$	16.0783	+	9.28282i	1.24418	+	0.718327i	0.274236	+	0.961662i	$0.411575\pi$
$168$		0			0
$169$	−6.47029	−	11.2069i	−0.497715	−	0.862067i
$170$		0			0
$171$			2.65440i			0.202987i
$172$		0			0
$173$	10.4147	+	18.0387i	0.791812	+	1.37146i	0.924844	+	0.380347i	$0.124195\pi$
$173$	10.4147	+	18.0387i	0.791812	+	1.37146i	−0.133032	+	0.991112i	$0.542471\pi$
$174$		0			0
$175$	−2.56844			−0.194156
$176$		0			0
$177$			1.33424i			0.100287i
$178$		0			0
$179$			18.0463i			1.34884i	0.738346	+	0.674422i	$0.235607\pi$
$179$			18.0463i			1.34884i	−0.738346	+	0.674422i	$0.764393\pi$
$180$		0			0
$181$	3.10368	−	5.37574i	0.230695	−	0.399575i	−0.727318	−	0.686301i	$-0.759233\pi$
$181$	3.10368	−	5.37574i	0.230695	−	0.399575i	0.958013	+	0.286725i	$0.0925667\pi$
$182$		0			0
$183$	39.4082	−	22.7524i	2.91314	−	1.68190i
$184$		0			0
$185$	−0.610687	+	3.73835i	−0.0448986	+	0.274849i
$186$		0			0
$187$	24.7451	−	14.2866i	1.80954	−	1.04474i
$188$		0			0
$189$	3.97641	−	6.88735i	0.289241	−	0.500981i
$190$		0			0
$191$			19.0987i			1.38194i	0.722885	+	0.690968i	$0.242816\pi$
$191$			19.0987i			1.38194i	−0.722885	+	0.690968i	$0.757184\pi$
$192$		0			0
$193$		−	13.2910i		−	0.956706i	−0.878168	−	0.478353i	$-0.841234\pi$
$193$		−	13.2910i		−	0.956706i	0.878168	−	0.478353i	$-0.158766\pi$
$194$		0			0
$195$	−0.490069			−0.0350946
$196$		0			0
$197$	−3.31555	−	5.74270i	−0.236223	−	0.409150i	0.723404	−	0.690425i	$-0.242576\pi$
$197$	−3.31555	−	5.74270i	−0.236223	−	0.409150i	−0.959627	+	0.281274i	$0.909243\pi$
$198$		0			0
$199$		−	14.0446i		−	0.995596i	−0.867293	−	0.497798i	$-0.834142\pi$
$199$		−	14.0446i		−	0.995596i	0.867293	−	0.497798i	$-0.165858\pi$
$200$		0			0
$201$	0.136506	+	0.236435i	0.00962839	+	0.0166769i
$202$		0			0
$203$	−0.480694	−	0.277529i	−0.0337381	−	0.0194787i
$204$		0			0
$205$	3.63172	−	2.09677i	0.253650	−	0.146445i
$206$		0			0
$207$	−5.40251	+	3.11914i	−0.375500	+	0.216795i
$208$		0			0
$209$	1.36351	+	0.787224i	0.0943161	+	0.0544534i
$210$		0			0
$211$	23.8336			1.64077			0.820385	−	0.571811i	$-0.193759\pi$
$211$	23.8336			1.64077			0.820385	+	0.571811i	$0.193759\pi$
$212$		0			0
$213$	−19.0924	−	33.0690i	−1.30819	−	2.26585i
$214$		0			0
$215$	−0.553747	+	0.959118i	−0.0377653	+	0.0654113i
$216$		0			0
$217$	−4.50624	−	2.60168i	−0.305903	−	0.176613i
$218$		0			0
$219$	15.3827	−	26.6436i	1.03947	−	1.80041i
$220$		0			0
$221$	−1.58179			−0.106403
$222$		0			0
$223$	−2.82732			−0.189331			−0.0946655	−	0.995509i	$-0.530178\pi$
$223$	−2.82732			−0.189331			−0.0946655	+	0.995509i	$0.530178\pi$
$224$		0			0
$225$	−17.1191	+	29.6512i	−1.14128	+	1.97675i
$226$		0			0
$227$	−20.3704	−	11.7608i	−1.35203	−	0.780595i	−0.363496	−	0.931596i	$-0.618417\pi$
$227$	−20.3704	−	11.7608i	−1.35203	−	0.780595i	−0.988534	+	0.151001i	$0.951750\pi$
$228$		0			0
$229$	−7.87969	+	13.6480i	−0.520704	+	0.901886i	0.479006	+	0.877812i	$0.340997\pi$
$229$	−7.87969	+	13.6480i	−0.520704	+	0.901886i	−0.999710	+	0.0240745i	$0.992336\pi$
$230$		0			0
$231$	−3.95822	−	6.85585i	−0.260432	−	0.451082i
$232$		0			0
$233$	13.3104			0.871994			0.435997	−	0.899948i	$-0.356396\pi$
$233$	13.3104			0.871994			0.435997	+	0.899948i	$0.356396\pi$
$234$		0			0
$235$	−6.22241	−	3.59251i	−0.405905	−	0.234349i
$236$		0			0
$237$	−21.5598	+	12.4476i	−1.40046	+	0.808557i
$238$		0			0
$239$	−5.62492	+	3.24755i	−0.363846	+	0.210067i	−0.670767	−	0.741669i	$-0.734035\pi$
$239$	−5.62492	+	3.24755i	−0.363846	+	0.210067i	0.306921	+	0.951735i	$0.400701\pi$
$240$		0			0
$241$	3.50787	+	2.02527i	0.225962	+	0.130459i	0.608708	−	0.793395i	$-0.291688\pi$
$241$	3.50787	+	2.02527i	0.225962	+	0.130459i	−0.382746	+	0.923854i	$0.625022\pi$
$242$		0			0
$243$	−17.0570	−	29.5436i	−1.09421	−	1.89522i
$244$		0			0
$245$			4.16597i			0.266154i
$246$		0			0
$247$	−0.0435801	−	0.0754829i	−0.00277293	−	0.00480286i
$248$		0			0
$249$	24.8310			1.57360
$250$		0			0
$251$		−	12.2725i		−	0.774636i	−0.921946	−	0.387318i	$-0.873402\pi$
$251$		−	12.2725i		−	0.774636i	0.921946	−	0.387318i	$-0.126598\pi$
$252$		0			0
$253$			3.70022i			0.232631i
$254$		0			0
$255$	6.52329	−	11.2987i	0.408504	−	0.707550i
$256$		0			0
$257$	−0.296780	+	0.171346i	−0.0185126	+	0.0106883i	−0.509228	−	0.860632i	$-0.670069\pi$
$257$	−0.296780	+	0.171346i	−0.0185126	+	0.0106883i	0.490715	+	0.871320i	$0.336736\pi$
$258$		0			0
$259$	3.34305	+	0.546112i	0.207727	+	0.0339337i
$260$		0			0
$261$	−6.40783	+	3.69956i	−0.396635	+	0.228997i
$262$		0			0
$263$	−6.78573	+	11.7532i	−0.418426	+	0.724735i	−0.995781	−	0.0917580i	$-0.970751\pi$
$263$	−6.78573	+	11.7532i	−0.418426	+	0.724735i	0.577355	+	0.816493i	$0.304085\pi$
$264$		0			0
$265$			7.23381i			0.444370i
$266$		0			0
$267$			23.6483i			1.44725i
$268$		0			0
$269$	−8.00914			−0.488326			−0.244163	−	0.969734i	$-0.578513\pi$
$269$	−8.00914			−0.488326			−0.244163	+	0.969734i	$0.578513\pi$
$270$		0			0
$271$	5.94709	+	10.3007i	0.361260	+	0.625721i	0.988168	−	0.153372i	$-0.0490133\pi$
$271$	5.94709	+	10.3007i	0.361260	+	0.625721i	−0.626908	+	0.779093i	$0.715680\pi$
$272$		0			0
$273$			0.438248i			0.0265240i
$274$		0			0
$275$	10.1542	+	17.5875i	0.612319	+	1.06057i
$276$		0			0
$277$	8.43779	+	4.87156i	0.506978	+	0.292704i	0.731590	−	0.681744i	$-0.238778\pi$
$277$	8.43779	+	4.87156i	0.506978	+	0.292704i	−0.224613	+	0.974448i	$0.572112\pi$
$278$		0			0
$279$	−60.0698	+	34.6813i	−3.59628	+	2.07632i
$280$		0			0
$281$	−12.3336	+	7.12080i	−0.735761	+	0.424792i	−0.820526	−	0.571609i	$-0.806319\pi$
$281$	−12.3336	+	7.12080i	−0.735761	+	0.424792i	0.0847653	+	0.996401i	$0.472986\pi$
$282$		0			0
$283$	−6.02500	−	3.47853i	−0.358149	−	0.206777i	0.310120	−	0.950698i	$-0.399631\pi$
$283$	−6.02500	−	3.47853i	−0.358149	−	0.206777i	−0.668268	+	0.743920i	$0.732964\pi$
$284$		0			0
$285$	0.718895			0.0425837
$286$		0			0
$287$	−1.87506	−	3.24769i	−0.110681	−	0.191705i
$288$		0			0
$289$	12.5552	−	21.7462i	0.738538	−	1.27919i
$290$		0			0
$291$	−30.2524	−	17.4662i	−1.77343	−	1.02389i
$292$		0			0
$293$	3.78613	−	6.55777i	0.221188	−	0.383109i	−0.733981	−	0.679170i	$-0.762340\pi$
$293$	3.78613	−	6.55777i	0.221188	−	0.383109i	0.955169	+	0.296061i	$0.0956732\pi$
$294$		0			0
$295$	0.257351			0.0149836
$296$		0			0
$297$	−62.8819			−3.64878
$298$		0			0
$299$	0.102421	−	0.177398i	0.00592313	−	0.0102592i
$300$		0			0
$301$	0.857699	+	0.495193i	0.0494370	+	0.0285424i
$302$		0			0
$303$	22.1459	−	38.3578i	1.27225	−	2.20360i
$304$		0			0
$305$	−4.38854	−	7.60117i	−0.251287	−	0.435242i
$306$		0			0
$307$	11.6979			0.667635			0.333818	−	0.942638i	$-0.391663\pi$
$307$	11.6979			0.667635			0.333818	+	0.942638i	$0.391663\pi$
$308$		0			0
$309$	22.8923	+	13.2168i	1.30229	+	0.751880i
$310$		0			0
$311$	17.8428	−	10.3016i	1.01177	−	0.584148i	0.100063	−	0.994981i	$-0.468095\pi$
$311$	17.8428	−	10.3016i	1.01177	−	0.584148i	0.911711	+	0.410833i	$0.134762\pi$
$312$		0			0
$313$	13.1698	−	7.60361i	0.744404	−	0.429782i	−0.0792646	−	0.996854i	$-0.525257\pi$
$313$	13.1698	−	7.60361i	0.744404	−	0.429782i	0.823668	+	0.567072i	$0.191924\pi$
$314$		0			0
$315$	−2.22942	−	1.28716i	−0.125614	−	0.0725230i
$316$		0			0
$317$	4.77408	+	8.26895i	0.268139	+	0.464431i	0.968381	−	0.249475i	$-0.0802580\pi$
$317$	4.77408	+	8.26895i	0.268139	+	0.464431i	−0.700242	+	0.713905i	$0.746925\pi$
$318$		0			0
$319$			4.38877i			0.245724i
$320$		0			0
$321$	0.924753	+	1.60172i	0.0516147	+	0.0893992i
$322$		0			0
$323$	2.32037			0.129109
$324$		0			0
$325$		−	1.12425i		−	0.0623623i
$326$		0			0
$327$		−	37.6098i		−	2.07982i
$328$		0			0
$329$	−3.21263	+	5.56444i	−0.177118	+	0.306777i
$330$		0			0
$331$	−27.0009	+	15.5890i	−1.48411	+	0.856849i	−0.999837	−	0.0180703i	$-0.994248\pi$
$331$	−27.0009	+	15.5890i	−1.48411	+	0.856849i	−0.484269	+	0.874919i	$0.660914\pi$
$332$		0			0
$333$	28.5866	−	34.9537i	1.56654	−	1.91545i
$334$		0			0
$335$	0.0456043	−	0.0263296i	0.00249163	−	0.00143854i
$336$		0			0
$337$	5.39361	−	9.34201i	0.293809	−	0.508892i	−0.680898	−	0.732378i	$-0.738410\pi$
$337$	5.39361	−	9.34201i	0.293809	−	0.508892i	0.974707	+	0.223486i	$0.0717438\pi$
$338$		0			0
$339$		−	1.72691i		−	0.0937929i
$340$		0			0
$341$			41.1422i			2.22798i
$342$		0			0
$343$	7.62361			0.411636
$344$		0			0
$345$	0.844763	+	1.46317i	0.0454805	+	0.0787745i
$346$		0			0
$347$		−	0.764409i		−	0.0410356i	−0.999789	−	0.0205178i	$-0.993469\pi$
$347$		−	0.764409i		−	0.0410356i	0.999789	−	0.0205178i	$-0.00653148\pi$
$348$		0			0
$349$	13.2111	+	22.8823i	0.707173	+	1.22486i	0.965902	+	0.258910i	$0.0833631\pi$
$349$	13.2111	+	22.8823i	0.707173	+	1.22486i	−0.258729	+	0.965950i	$0.583304\pi$
$350$		0			0
$351$	3.01471	+	1.74055i	0.160913	+	0.0929034i
$352$		0			0
$353$	−0.656786	+	0.379195i	−0.0349572	+	0.0201825i	−0.517377	−	0.855758i	$-0.673091\pi$
$353$	−0.656786	+	0.379195i	−0.0349572	+	0.0201825i	0.482420	+	0.875940i	$0.339758\pi$
$354$		0			0
$355$	−6.37844	+	3.68259i	−0.338532	+	0.195452i
$356$		0			0
$357$	−10.1039	−	5.83350i	−0.534756	−	0.308742i
$358$		0			0
$359$	−1.79946			−0.0949719			−0.0474860	−	0.998872i	$-0.515121\pi$
$359$	−1.79946			−0.0949719			−0.0474860	+	0.998872i	$0.515121\pi$
$360$		0			0
$361$	−9.43607	−	16.3438i	−0.496635	−	0.860198i
$362$		0			0
$363$	−13.5402	+	23.4524i	−0.710678	+	1.23093i
$364$		0			0
$365$	−5.13909	−	2.96705i	−0.268992	−	0.155303i
$366$		0			0
$367$	9.63461	−	16.6876i	0.502923	−	0.871087i	−0.497072	−	0.867709i	$-0.665591\pi$
$367$	9.63461	−	16.6876i	0.502923	−	0.871087i	0.999994	−	0.00337799i	$-0.00107525\pi$
$368$		0			0
$369$	−49.9904			−2.60240
$370$		0			0
$371$	6.46890			0.335848
$372$		0			0
$373$	1.39281	−	2.41242i	0.0721172	−	0.124911i	−0.827712	−	0.561153i	$-0.810358\pi$
$373$	1.39281	−	2.41242i	0.0721172	−	0.124911i	0.899829	+	0.436243i	$0.143691\pi$
$374$		0			0
$375$	16.7362	+	9.66264i	0.864253	+	0.498977i
$376$		0			0
$377$	0.121479	−	0.210408i	0.00625651	−	0.0108366i
$378$		0			0
$379$	−14.2716	−	24.7191i	−0.733081	−	1.26973i	−0.955560	−	0.294796i	$-0.904748\pi$
$379$	−14.2716	−	24.7191i	−0.733081	−	1.26973i	0.222480	−	0.974937i	$-0.428585\pi$
$380$		0			0
$381$	−8.26455			−0.423406
$382$		0			0
$383$	20.0941	+	11.6013i	1.02676	+	0.592801i	0.916055	−	0.401052i	$-0.131355\pi$
$383$	20.0941	+	11.6013i	1.02676	+	0.592801i	0.110706	+	0.993853i	$0.464689\pi$
$384$		0			0
$385$	−1.32237	+	0.763473i	−0.0673944	+	0.0389102i
$386$		0			0
$387$	11.4334	−	6.60110i	0.581194	−	0.335553i
$388$		0			0
$389$	−10.4727	−	6.04641i	−0.530986	−	0.306565i	0.210432	−	0.977609i	$-0.432513\pi$
$389$	−10.4727	−	6.04641i	−0.530986	−	0.306565i	−0.741418	+	0.671043i	$0.765846\pi$
$390$		0			0
$391$	2.72663	+	4.72266i	0.137892	+	0.238835i
$392$		0			0
$393$		−	56.9845i		−	2.87449i
$394$		0			0
$395$	2.40092	+	4.15852i	0.120804	+	0.209238i
$396$		0			0
$397$	−4.57948			−0.229837			−0.114919	−	0.993375i	$-0.536661\pi$
$397$	−4.57948			−0.229837			−0.114919	+	0.993375i	$0.536661\pi$
$398$		0			0
$399$		−	0.642878i		−	0.0321842i
$400$		0			0
$401$		−	19.6468i		−	0.981116i	−0.871408	−	0.490558i	$-0.836793\pi$
$401$		−	19.6468i		−	0.981116i	0.871408	−	0.490558i	$-0.163207\pi$
$402$		0			0
$403$	1.13880	−	1.97246i	0.0567277	−	0.0982553i
$404$		0			0
$405$	−12.8550	+	7.42186i	−0.638772	+	0.368795i
$406$		0			0
$407$	−9.47700	−	25.0507i	−0.469757	−	1.24172i
$408$		0			0
$409$	27.1868	−	15.6963i	1.34430	−	0.776132i	0.356864	−	0.934156i	$-0.383846\pi$
$409$	27.1868	−	15.6963i	1.34430	−	0.776132i	0.987435	+	0.158024i	$0.0505125\pi$
$410$		0			0
$411$	9.47576	−	16.4125i	0.467405	−	0.809569i
$412$		0			0
$413$		−	0.230138i		−	0.0113244i
$414$		0			0
$415$		−	4.78948i		−	0.235106i
$416$		0			0
$417$	−29.9810			−1.46818
$418$		0			0
$419$	−4.68134	−	8.10832i	−0.228698	−	0.396117i	0.728724	−	0.684807i	$-0.240114\pi$
$419$	−4.68134	−	8.10832i	−0.228698	−	0.396117i	−0.957423	+	0.288690i	$0.906780\pi$
$420$		0			0
$421$			22.6491i			1.10385i	0.833893	+	0.551926i	$0.186107\pi$
$421$			22.6491i			1.10385i	−0.833893	+	0.551926i	$0.813893\pi$
$422$		0			0
$423$	42.8255	+	74.1759i	2.08225	+	3.60656i
$424$		0			0
$425$	25.9199	+	14.9649i	1.25730	+	0.725903i
$426$		0			0
$427$	−6.79740	+	3.92448i	−0.328949	+	0.189919i
$428$		0			0
$429$	3.00093	−	1.73259i	0.144886	−	0.0836500i
$430$		0			0
$431$	9.13478	+	5.27397i	0.440007	+	0.254038i	0.703601	−	0.710596i	$-0.251574\pi$
$431$	9.13478	+	5.27397i	0.440007	+	0.254038i	−0.263594	+	0.964634i	$0.584908\pi$
$432$		0			0
$433$	10.7984			0.518937			0.259469	−	0.965752i	$-0.416453\pi$
$433$	10.7984			0.518937			0.259469	+	0.965752i	$0.416453\pi$
$434$		0			0
$435$	1.00196	+	1.73545i	0.0480403	+	0.0832082i
$436$		0			0
$437$	−0.150243	+	0.260229i	−0.00718712	+	0.0124485i
$438$		0			0
$439$	−18.1902	−	10.5021i	−0.868170	−	0.501238i	−0.00143027	−	0.999999i	$-0.500455\pi$
$439$	−18.1902	−	10.5021i	−0.868170	−	0.501238i	−0.866740	+	0.498761i	$0.833789\pi$
$440$		0			0
$441$	24.8308	−	43.0083i	1.18242	−	2.04801i
$442$		0			0
$443$	−2.51855			−0.119660			−0.0598300	−	0.998209i	$-0.519056\pi$
$443$	−2.51855			−0.119660			−0.0598300	+	0.998209i	$0.519056\pi$
$444$		0			0
$445$	4.56134			0.216228
$446$		0			0
$447$	28.2793	−	48.9812i	1.33756	−	2.31673i
$448$		0			0
$449$	10.4622	+	6.04035i	0.493741	+	0.285062i	0.726125	−	0.687562i	$-0.241319\pi$
$449$	10.4622	+	6.04035i	0.493741	+	0.285062i	−0.232384	+	0.972624i	$0.574653\pi$
$450$		0			0
$451$	−14.8258	+	25.6791i	−0.698121	+	1.20918i
$452$		0			0
$453$	−2.35387	−	4.07703i	−0.110595	−	0.191555i
$454$		0			0
$455$	0.0845305			0.00396285
$456$		0			0
$457$	22.3387	+	12.8972i	1.04496	+	0.603307i	0.921234	−	0.389010i	$-0.127183\pi$
$457$	22.3387	+	12.8972i	1.04496	+	0.603307i	0.123724	+	0.992317i	$0.460516\pi$
$458$		0			0
$459$	−80.2574	+	46.3367i	−3.74610	+	2.16281i
$460$		0			0
$461$	18.6937	−	10.7928i	0.870653	−	0.502672i	0.00308800	−	0.999995i	$-0.499017\pi$
$461$	18.6937	−	10.7928i	0.870653	−	0.502672i	0.867565	+	0.497323i	$0.165684\pi$
$462$		0			0
$463$	9.51536	+	5.49370i	0.442216	+	0.255314i	0.704537	−	0.709667i	$-0.251155\pi$
$463$	9.51536	+	5.49370i	0.442216	+	0.255314i	−0.262321	+	0.964981i	$0.584488\pi$
$464$		0			0
$465$	9.39281	+	16.2688i	0.435581	+	0.754448i
$466$		0			0
$467$		−	24.8812i		−	1.15136i	−0.817674	−	0.575681i	$-0.804737\pi$
$467$		−	24.8812i		−	1.15136i	0.817674	−	0.575681i	$-0.195263\pi$
$468$		0			0
$469$	−0.0235455	−	0.0407820i	−0.00108723	−	0.00188314i
$470$		0			0
$471$	43.9698			2.02602
$472$		0			0
$473$		−	7.83085i		−	0.360063i
$474$		0			0
$475$			1.64920i			0.0756703i
$476$		0			0
$477$	43.1164	−	74.6797i	1.97416	−	3.41935i
$478$		0			0
$479$	−23.8814	+	13.7879i	−1.09117	+	0.629986i	−0.933887	−	0.357568i	$-0.883606\pi$
$479$	−23.8814	+	13.7879i	−1.09117	+	0.629986i	−0.157281	+	0.987554i	$0.550273\pi$
$480$		0			0
$481$	−0.239043	+	1.46331i	−0.0108994	+	0.0667213i
$482$		0			0
$483$	1.30845	−	0.755436i	0.0595367	−	0.0343735i
$484$		0			0
$485$	−3.36893	+	5.83516i	−0.152975	+	0.264961i
$486$		0			0
$487$		−	7.49345i		−	0.339561i	−0.985482	−	0.169780i	$-0.945694\pi$
$487$		−	7.49345i		−	0.339561i	0.985482	−	0.169780i	$-0.0543058\pi$
$488$		0			0
$489$			17.5443i			0.793379i
$490$		0			0
$491$	1.03405			0.0466661			0.0233331	−	0.999728i	$-0.492572\pi$
$491$	1.03405			0.0466661			0.0233331	+	0.999728i	$0.492572\pi$
$492$		0			0
$493$	3.23401	+	5.60148i	0.145653	+	0.252278i
$494$		0			0
$495$			20.3547i			0.914878i
$496$		0			0
$497$	3.29319	+	5.70397i	0.147720	+	0.255858i
$498$		0			0
$499$	32.0161	+	18.4845i	1.43324	+	0.827480i	0.997366	−	0.0725293i	$-0.0231071\pi$
$499$	32.0161	+	18.4845i	1.43324	+	0.827480i	0.435871	+	0.900009i	$0.356440\pi$
$500$		0			0
$501$	−51.9093	+	29.9699i	−2.31914	+	1.33895i
$502$		0			0
$503$	−18.1279	+	10.4662i	−0.808283	+	0.466663i	−0.846359	−	0.532612i	$-0.821210\pi$
$503$	−18.1279	+	10.4662i	−0.808283	+	0.466663i	0.0380760	+	0.999275i	$0.487877\pi$
$504$		0			0
$505$	−7.39855	−	4.27156i	−0.329231	−	0.190082i
$506$		0			0
$507$	41.7790			1.85547
$508$		0			0
$509$	13.0860	+	22.6656i	0.580027	+	1.00464i	0.995475	+	0.0950196i	$0.0302914\pi$
$509$	13.0860	+	22.6656i	0.580027	+	1.00464i	−0.415448	+	0.909617i	$0.636375\pi$
$510$		0			0
$511$	−2.65331	+	4.59567i	−0.117376	+	0.203301i
$512$		0			0
$513$	−4.42236	−	2.55325i	−0.195252	−	0.112729i
$514$		0			0
$515$	2.54930	−	4.41552i	0.112336	−	0.194571i
$516$		0			0
$517$	50.8036			2.23434
$518$		0			0
$519$	−67.2480			−2.95186
$520$		0			0
$521$	11.6448	−	20.1694i	0.510168	−	0.883636i	−0.489763	−	0.871856i	$-0.662917\pi$
$521$	11.6448	−	20.1694i	0.510168	−	0.883636i	0.999931	−	0.0117807i	$-0.00375000\pi$
$522$		0			0
$523$	7.52851	+	4.34659i	0.329199	+	0.190063i	0.655485	−	0.755208i	$-0.272464\pi$
$523$	7.52851	+	4.34659i	0.329199	+	0.190063i	−0.326287	+	0.945271i	$0.605797\pi$
$524$		0			0
$525$	4.14615	−	7.18133i	0.180953	−	0.313419i
$526$		0			0
$527$	30.3171	+	52.5107i	1.32063	+	2.28740i
$528$		0			0
$529$	22.2938			0.969296
$530$		0			0
$531$	−2.65682	−	1.53391i	−0.115296	−	0.0665662i
$532$		0			0
$533$	1.42157	−	0.820746i	0.0615752	−	0.0355504i
$534$		0			0
$535$	0.308944	−	0.178369i	0.0133568	−	0.00771155i
$536$		0			0
$537$	−50.4573	−	29.1315i	−2.17739	−	1.25712i
$538$		0			0
$539$	−14.7283	−	25.5102i	−0.634395	−	1.09880i
$540$		0			0
$541$			2.39581i			0.103004i	0.998673	+	0.0515019i	$0.0164008\pi$
$541$			2.39581i			0.103004i	−0.998673	+	0.0515019i	$0.983599\pi$
$542$		0			0
$543$	10.0203	+	17.3557i	0.430014	+	0.744805i
$544$		0			0
$545$	−7.25427			−0.310739
$546$		0			0
$547$			45.2864i			1.93630i	0.250362	+	0.968152i	$0.419450\pi$
$547$			45.2864i			1.93630i	−0.250362	+	0.968152i	$0.580550\pi$
$548$		0			0
$549$			104.630i			4.46548i
$550$		0			0
$551$	−0.178201	+	0.308654i	−0.00759163	+	0.0131491i
$552$		0			0
$553$	3.71879	−	2.14704i	0.158139	−	0.0913016i
$554$		0			0
$555$	−9.46657	−	7.74216i	−0.401834	−	0.328636i
$556$		0			0
$557$	−29.1161	+	16.8102i	−1.23369	+	0.712271i	−0.967797	−	0.251732i	$-0.919000\pi$
$557$	−29.1161	+	16.8102i	−1.23369	+	0.712271i	−0.265893	+	0.964003i	$0.585667\pi$
$558$		0			0
$559$	−0.216755	+	0.375430i	−0.00916775	+	0.0158790i
$560$		0			0
$561$			92.2495i			3.89478i
$562$		0			0
$563$		−	17.8580i		−	0.752627i	−0.926492	−	0.376313i	$-0.877192\pi$
$563$		−	17.8580i		−	0.752627i	0.926492	−	0.376313i	$-0.122808\pi$
$564$		0			0
$565$	−0.333091			−0.0140133
$566$		0			0
$567$	6.63706	+	11.4957i	0.278730	+	0.482775i
$568$		0			0
$569$			10.4276i			0.437149i	0.975820	+	0.218575i	$0.0701407\pi$
$569$			10.4276i			0.437149i	−0.975820	+	0.218575i	$0.929859\pi$
$570$		0			0
$571$	−18.3170	−	31.7259i	−0.766541	−	1.32769i	−0.939428	−	0.342746i	$-0.888643\pi$
$571$	−18.3170	−	31.7259i	−0.766541	−	1.32769i	0.172887	−	0.984942i	$-0.444690\pi$
$572$		0			0
$573$	−53.3998	−	30.8304i	−2.23081	−	1.28796i
$574$		0			0
$575$	−3.35662	+	1.93794i	−0.139981	+	0.0808179i
$576$		0			0
$577$	−25.7296	+	14.8550i	−1.07114	+	0.618421i	−0.928492	−	0.371353i	$-0.878894\pi$
$577$	−25.7296	+	14.8550i	−1.07114	+	0.618421i	−0.142644	+	0.989774i	$0.545561\pi$
$578$		0			0
$579$	37.1614	+	21.4552i	1.54438	+	0.891646i
$580$		0			0
$581$	−4.28303			−0.177690
$582$		0			0
$583$	−25.5743	−	44.2961i	−1.05918	−	1.83456i
$584$		0			0
$585$	0.563411	−	0.975857i	0.0232942	−	0.0403467i
$586$		0			0
$587$	−18.3392	−	10.5882i	−0.756941	−	0.437020i	0.0712553	−	0.997458i	$-0.477300\pi$
$587$	−18.3392	−	10.5882i	−0.756941	−	0.437020i	−0.828196	+	0.560438i	$0.810633\pi$
$588$		0			0
$589$	−1.67054	+	2.89345i	−0.0688333	+	0.119223i
$590$		0			0
$591$	21.4087			0.880636
$592$		0			0
$593$	−17.1280			−0.703364			−0.351682	−	0.936120i	$-0.614390\pi$
$593$	−17.1280			−0.703364			−0.351682	+	0.936120i	$0.614390\pi$
$594$		0			0
$595$	−1.12518	+	1.94887i	−0.0461280	+	0.0798960i
$596$		0			0
$597$	39.2685	+	22.6717i	1.60715	+	0.927891i
$598$		0			0
$599$	8.59578	−	14.8883i	0.351214	−	0.608321i	−0.635248	−	0.772308i	$-0.719102\pi$
$599$	8.59578	−	14.8883i	0.351214	−	0.608321i	0.986462	+	0.163987i	$0.0524356\pi$
$600$		0			0
$601$	−14.1946	−	24.5858i	−0.579011	−	1.00288i	−0.995593	−	0.0937786i	$-0.970105\pi$
$601$	−14.1946	−	24.5858i	−0.579011	−	1.00288i	0.416582	−	0.909098i	$-0.363228\pi$
$602$		0			0
$603$	−0.627740			−0.0255635
$604$		0			0
$605$	4.52356	+	2.61168i	0.183909	+	0.106180i
$606$		0			0
$607$	−25.0454	+	14.4599i	−1.01656	+	0.586911i	−0.913106	−	0.407723i	$-0.866323\pi$
$607$	−25.0454	+	14.4599i	−1.01656	+	0.586911i	−0.103454	+	0.994634i	$0.532990\pi$
$608$		0			0
$609$	1.55194	−	0.896010i	0.0628876	−	0.0363082i
$610$		0			0
$611$	−2.43565	−	1.40622i	−0.0985359	−	0.0568897i
$612$		0			0
$613$	3.55272	+	6.15349i	0.143493	+	0.248537i	0.928810	−	0.370557i	$-0.120833\pi$
$613$	3.55272	+	6.15349i	0.143493	+	0.248537i	−0.785317	+	0.619094i	$0.787500\pi$
$614$		0			0
$615$			13.5390i			0.545945i
$616$		0			0
$617$	−1.78768	−	3.09635i	−0.0719693	−	0.124654i	0.827795	−	0.561031i	$-0.189595\pi$
$617$	−1.78768	−	3.09635i	−0.0719693	−	0.124654i	−0.899764	+	0.436376i	$0.856262\pi$
$618$		0			0
$619$	−19.0006			−0.763700			−0.381850	−	0.924224i	$-0.624713\pi$
$619$	−19.0006			−0.763700			−0.381850	+	0.924224i	$0.624713\pi$
$620$		0			0
$621$		−	12.0011i		−	0.481589i
$622$		0			0
$623$		−	4.07902i		−	0.163422i
$624$		0			0
$625$	−9.66677	+	16.7433i	−0.386671	+	0.669734i
$626$		0			0
$627$	−4.40214	+	2.54157i	−0.175804	+	0.101501i
$628$		0			0
$629$	−30.5551	−	24.9893i	−1.21831	−	0.996388i
$630$		0			0
$631$	−35.3370	+	20.4018i	−1.40674	+	0.812183i	−0.995072	−	0.0991504i	$-0.968388\pi$
$631$	−35.3370	+	20.4018i	−1.40674	+	0.812183i	−0.411669	+	0.911333i	$0.635054\pi$
$632$		0			0
$633$	−38.4737	+	66.6384i	−1.52919	+	2.64864i
$634$		0			0
$635$			1.59409i			0.0632595i
$636$		0			0
$637$			1.63070i			0.0646106i
$638$		0			0
$639$	87.7988			3.47327
$640$		0			0
$641$	7.86693	+	13.6259i	0.310725	+	0.538191i	0.978520	−	0.206154i	$-0.0660949\pi$
$641$	7.86693	+	13.6259i	0.310725	+	0.538191i	−0.667795	+	0.744346i	$0.732762\pi$
$642$		0			0
$643$		−	9.87544i		−	0.389449i	−0.980858	−	0.194725i	$-0.937619\pi$
$643$		−	9.87544i		−	0.389449i	0.980858	−	0.194725i	$-0.0623813\pi$
$644$		0			0
$645$	−1.78779	−	3.09654i	−0.0703941	−	0.121926i
$646$		0			0
$647$	34.1370	+	19.7090i	1.34207	+	0.774842i	0.987110	−	0.160042i	$-0.0511629\pi$
$647$	34.1370	+	19.7090i	1.34207	+	0.774842i	0.354955	+	0.934883i	$0.384496\pi$
$648$		0			0
$649$	−1.57588	+	0.909836i	−0.0618588	+	0.0357142i
$650$		0			0
$651$	14.5485	−	8.39959i	0.570201	−	0.329206i
$652$		0			0
$653$	−12.9570	−	7.48075i	−0.507048	−	0.292744i	0.224571	−	0.974458i	$-0.427902\pi$
$653$	−12.9570	−	7.48075i	−0.507048	−	0.292744i	−0.731619	+	0.681713i	$0.761235\pi$
$654$		0			0
$655$	−10.9913			−0.429467
$656$		0			0
$657$	35.3696	+	61.2620i	1.37990	+	2.39006i
$658$		0			0
$659$	13.8932	−	24.0636i	0.541200	−	0.937387i	−0.457635	−	0.889140i	$-0.651303\pi$
$659$	13.8932	−	24.0636i	0.541200	−	0.937387i	0.998835	−	0.0482465i	$-0.0153633\pi$
$660$		0			0
$661$	−13.4620	−	7.77230i	−0.523612	−	0.302308i	0.214799	−	0.976658i	$-0.431090\pi$
$661$	−13.4620	−	7.77230i	−0.523612	−	0.302308i	−0.738411	+	0.674351i	$0.764424\pi$
$662$		0			0
$663$	2.55343	−	4.42267i	0.0991669	−	0.171762i
$664$		0			0
$665$	−0.124000			−0.00480852
$666$		0			0
$667$	−0.837606			−0.0324322
$668$		0			0
$669$	4.56403	−	7.90514i	0.176456	−	0.305630i
$670$		0			0
$671$	53.7462	+	31.0304i	2.07485	+	1.19791i
$672$		0			0
$673$	8.62708	−	14.9425i	0.332550	−	0.575993i	−0.650461	−	0.759539i	$-0.725424\pi$
$673$	8.62708	−	14.9425i	0.332550	−	0.575993i	0.983011	+	0.183547i	$0.0587578\pi$
$674$		0			0
$675$	−32.9336	−	57.0427i	−1.26762	−	2.19558i
$676$		0			0
$677$	−3.38410			−0.130062			−0.0650308	−	0.997883i	$-0.520715\pi$
$677$	−3.38410			−0.130062			−0.0650308	+	0.997883i	$0.520715\pi$
$678$		0			0
$679$	5.21814	+	3.01269i	0.200254	+	0.115617i
$680$		0			0
$681$	65.7664	−	37.9702i	2.52017	−	1.45502i
$682$		0			0
$683$	10.3844	−	5.99541i	0.397346	−	0.229408i	−0.287992	−	0.957633i	$-0.592988\pi$
$683$	10.3844	−	5.99541i	0.397346	−	0.229408i	0.685338	+	0.728225i	$0.259654\pi$
$684$		0			0
$685$	−3.16569	−	1.82771i	−0.120955	−	0.0698332i
$686$		0			0
$687$	−25.4398	−	44.0630i	−0.970588	−	1.68111i
$688$		0			0
$689$			2.83155i			0.107873i
$690$		0			0
$691$	9.68904	+	16.7819i	0.368589	+	0.638414i	0.989345	−	0.145589i	$-0.0465078\pi$
$691$	9.68904	+	16.7819i	0.368589	+	0.638414i	−0.620757	+	0.784003i	$0.713174\pi$
$692$		0			0
$693$	18.2024			0.691452
$694$		0			0
$695$			5.78282i			0.219355i
$696$		0			0
$697$			43.6996i			1.65524i
$698$		0			0
$699$	−21.4865	+	37.2157i	−0.812695	+	1.40763i
$700$		0			0
$701$	39.0366	−	22.5378i	1.47439	−	0.851240i	0.474806	−	0.880090i	$-0.342518\pi$
$701$	39.0366	−	22.5378i	1.47439	−	0.851240i	0.999584	+	0.0288507i	$0.00918474\pi$
$702$		0			0
$703$	0.350658	−	2.14657i	0.0132253	−	0.0809595i
$704$		0			0
$705$	20.0892	−	11.5985i	0.756604	−	0.436825i
$706$		0			0
$707$	−3.81987	+	6.61622i	−0.143661	+	0.248828i
$708$		0			0
$709$		−	37.7864i		−	1.41910i	−0.704657	−	0.709548i	$-0.748899\pi$
$709$		−	37.7864i		−	1.41910i	0.704657	−	0.709548i	$-0.251101\pi$
$710$		0			0
$711$		−	57.2418i		−	2.14673i
$712$		0			0
$713$	−7.85209			−0.294063
$714$		0			0
$715$	−0.334186	−	0.578827i	−0.0124978	−	0.0216469i
$716$		0			0
$717$		−	20.9696i		−	0.783125i
$718$		0			0
$719$	−17.7702	−	30.7789i	−0.662718	−	1.14786i	−0.979899	−	0.199496i	$-0.936070\pi$
$719$	−17.7702	−	30.7789i	−0.662718	−	1.14786i	0.317181	−	0.948365i	$-0.397264\pi$
$720$		0			0
$721$	−3.94861	−	2.27973i	−0.147054	−	0.0849017i
$722$		0			0
$723$	−11.3253	+	6.53864i	−0.421191	+	0.243175i
$724$		0			0
$725$	−3.98123	+	2.29857i	−0.147859	+	0.0853666i
$726$		0			0
$727$	17.8900	+	10.3288i	0.663504	+	0.383074i	0.793611	−	0.608426i	$-0.208199\pi$
$727$	17.8900	+	10.3288i	0.663504	+	0.383074i	−0.130107	+	0.991500i	$0.541532\pi$
$728$		0			0
$729$	38.6283			1.43068
$730$		0			0
$731$	−5.77043	−	9.99467i	−0.213427	−	0.369666i
$732$		0			0
$733$	−1.15118	+	1.99390i	−0.0425197	+	0.0736462i	−0.886502	−	0.462725i	$-0.846872\pi$
$733$	−1.15118	+	1.99390i	−0.0425197	+	0.0736462i	0.843982	+	0.536371i	$0.180205\pi$
$734$		0			0
$735$	−11.6480	−	6.72498i	−0.429643	−	0.248055i
$736$		0			0
$737$	−0.186171	+	0.322458i	−0.00685770	+	0.0118779i
$738$		0			0
$739$	−20.8269			−0.766131			−0.383066	−	0.923721i	$-0.625132\pi$
$739$	−20.8269			−0.766131			−0.383066	+	0.923721i	$0.625132\pi$
$740$		0			0
$741$	0.281399			0.0103375
$742$		0			0
$743$	1.19119	−	2.06321i	0.0437006	−	0.0756917i	−0.843348	−	0.537368i	$-0.819419\pi$
$743$	1.19119	−	2.06321i	0.0437006	−	0.0756917i	0.887048	+	0.461676i	$0.152752\pi$
$744$		0			0
$745$	−9.44762	−	5.45459i	−0.346134	−	0.199841i
$746$		0			0
$747$	−28.5472	+	49.4451i	−1.04449	+	1.80910i
$748$		0			0
$749$	−0.159508	−	0.276275i	−0.00582828	−	0.0100949i
$750$		0			0
$751$	17.0259			0.621283			0.310641	−	0.950527i	$-0.399456\pi$
$751$	17.0259			0.621283			0.310641	+	0.950527i	$0.399456\pi$
$752$		0			0
$753$	34.3139	+	19.8111i	1.25047	+	0.721957i
$754$		0			0
$755$	−0.786388	+	0.454021i	−0.0286196	+	0.0165235i
$756$		0			0
$757$	15.8422	−	9.14648i	0.575793	−	0.332434i	−0.183667	−	0.982989i	$-0.558797\pi$
$757$	15.8422	−	9.14648i	0.575793	−	0.332434i	0.759460	+	0.650554i	$0.225463\pi$
$758$		0			0
$759$	−10.3458	−	5.97313i	−0.375527	−	0.216811i
$760$		0			0
$761$	−7.66771	−	13.2809i	−0.277954	−	0.481431i	0.692922	−	0.721013i	$-0.256323\pi$
$761$	−7.66771	−	13.2809i	−0.277954	−	0.481431i	−0.970876	+	0.239582i	$0.922990\pi$
$762$		0			0
$763$			6.48719i			0.234852i
$764$		0			0
$765$	14.9991	+	25.9792i	0.542293	+	0.939279i
$766$		0			0
$767$	0.100736			0.00363735
$768$		0			0
$769$		−	33.2742i		−	1.19990i	−0.800038	−	0.599950i	$-0.795187\pi$
$769$		−	33.2742i		−	1.19990i	0.800038	−	0.599950i	$-0.204813\pi$
$770$		0			0
$771$		−	1.10639i		−	0.0398457i
$772$		0			0
$773$	−6.75699	+	11.7034i	−0.243032	+	0.420944i	−0.961576	−	0.274537i	$-0.911475\pi$
$773$	−6.75699	+	11.7034i	−0.243032	+	0.420944i	0.718545	+	0.695481i	$0.244809\pi$
$774$		0			0
$775$	−37.3218	+	21.5478i	−1.34064	+	0.774018i
$776$		0			0
$777$	−6.92349	+	8.46556i	−0.248379	+	0.303700i
$778$		0			0
$779$	−2.08534	+	1.20397i	−0.0747152	+	0.0431368i
$780$		0			0
$781$	26.0388	−	45.1005i	0.931742	−	1.61382i
$782$		0			0
$783$		−	14.2344i		−	0.508695i
$784$		0			0
$785$		−	8.48101i		−	0.302700i
$786$		0			0
$787$	23.4178			0.834754			0.417377	−	0.908733i	$-0.362949\pi$
$787$	23.4178			0.834754			0.417377	+	0.908733i	$0.362949\pi$
$788$		0			0
$789$	−21.9079	−	37.9456i	−0.779943	−	1.35090i
$790$		0			0
$791$			0.297869i			0.0105910i
$792$		0			0
$793$	−1.71782	−	2.97534i	−0.0610014	−	0.105658i
$794$		0			0
$795$	−20.2257	−	11.6773i	−0.717330	−	0.414151i
$796$		0			0
$797$	−32.4334	+	18.7254i	−1.14885	+	0.663288i	−0.948606	−	0.316459i	$-0.897506\pi$
$797$	−32.4334	+	18.7254i	−1.14885	+	0.663288i	−0.200242	+	0.979746i	$0.564173\pi$
$798$		0			0
$799$	64.8417	−	37.4364i	2.29394	−	1.32440i
$800$		0			0
$801$	−47.0899	−	27.1874i	−1.66384	−	0.960619i
$802$		0			0
$803$	41.9588			1.48069
$804$		0			0
$805$	−0.145711	−	0.252378i	−0.00513562	−	0.00889516i
$806$		0			0
$807$	12.9289	−	22.3935i	0.455118	−	0.788287i
$808$		0			0
$809$	34.5682	+	19.9580i	1.21535	+	0.701685i	0.963921	−	0.266190i	$-0.0857649\pi$
$809$	34.5682	+	19.9580i	1.21535	+	0.701685i	0.251433	+	0.967875i	$0.419098\pi$
$810$		0			0
$811$	−19.5104	+	33.7930i	−0.685104	+	1.18663i	0.288301	+	0.957540i	$0.406910\pi$
$811$	−19.5104	+	33.7930i	−0.685104	+	1.18663i	−0.973404	+	0.229094i	$0.926424\pi$
$812$		0			0
$813$	−38.4007			−1.34677
$814$		0			0
$815$	3.38399			0.118536
$816$		0			0
$817$	0.317963	−	0.550728i	0.0111241	−	0.0192675i
$818$		0			0
$819$	−0.872668	−	0.503835i	−0.0304935	−	0.0176054i
$820$		0			0
$821$	18.8031	−	32.5679i	0.656233	−	1.13663i	−0.325350	−	0.945594i	$-0.605482\pi$
$821$	18.8031	−	32.5679i	0.656233	−	1.13663i	0.981583	−	0.191035i	$-0.0611845\pi$
$822$		0			0
$823$	−12.1504	−	21.0451i	−0.423537	−	0.733588i	0.572746	−	0.819733i	$-0.305878\pi$
$823$	−12.1504	−	21.0451i	−0.423537	−	0.733588i	−0.996283	+	0.0861456i	$0.972545\pi$
$824$		0			0
$825$	−65.5660			−2.28272
$826$		0			0
$827$	−19.4912	−	11.2533i	−0.677776	−	0.391314i	0.121240	−	0.992623i	$-0.461313\pi$
$827$	−19.4912	−	11.2533i	−0.677776	−	0.391314i	−0.799017	+	0.601309i	$0.794646\pi$
$828$		0			0
$829$	−27.7690	+	16.0324i	−0.964457	+	0.556830i	−0.897542	−	0.440929i	$-0.854649\pi$
$829$	−27.7690	+	16.0324i	−0.964457	+	0.556830i	−0.0669154	+	0.997759i	$0.521316\pi$
$830$		0			0
$831$	−27.2417	+	15.7280i	−0.945002	+	0.545597i
$832$		0			0
$833$	−37.5962	−	21.7062i	−1.30263	−	0.752074i
$834$		0			0
$835$	5.78067	+	10.0124i	0.200048	+	0.346494i
$836$		0			0
$837$		−	133.439i		−	4.61233i
$838$		0			0
$839$	−17.5787	−	30.4472i	−0.606884	−	1.05115i	−0.991751	−	0.128182i	$-0.959086\pi$
$839$	−17.5787	−	30.4472i	−0.606884	−	1.05115i	0.384866	−	0.922972i	$-0.374248\pi$
$840$		0			0
$841$	28.0065			0.965742
$842$		0			0
$843$		−	45.9794i		−	1.58362i
$844$		0			0
$845$		−	8.05845i		−	0.277219i
$846$		0			0
$847$	2.33551	−	4.04523i	0.0802492	−	0.138996i
$848$		0			0
$849$	19.4519	−	11.2305i	0.667587	−	0.385431i
$850$		0			0
$851$	4.78098	−	1.80871i	0.163890	−	0.0620016i
$852$		0			0
$853$	−26.1260	+	15.0839i	−0.894538	+	0.516462i	−0.875424	−	0.483355i	$-0.839418\pi$
$853$	−26.1260	+	15.0839i	−0.894538	+	0.516462i	−0.0191142	+	0.999817i	$0.506085\pi$
$854$		0			0
$855$	−0.826483	+	1.43151i	−0.0282651	+	0.0489566i
$856$		0			0
$857$			41.5860i			1.42055i	0.703923	+	0.710276i	$0.251430\pi$
$857$			41.5860i			1.42055i	−0.703923	+	0.710276i	$0.748570\pi$
$858$		0			0
$859$		−	6.18916i		−	0.211171i	−0.994410	−	0.105586i	$-0.966328\pi$
$859$		−	6.18916i		−	0.211171i	0.994410	−	0.105586i	$-0.0336717\pi$
$860$		0			0
$861$	12.1074			0.412617
$862$		0			0
$863$	4.42067	+	7.65683i	0.150481	+	0.260641i	0.931405	−	0.363986i	$-0.118584\pi$
$863$	4.42067	+	7.65683i	0.150481	+	0.260641i	−0.780923	+	0.624627i	$0.785251\pi$
$864$		0			0
$865$			12.9710i			0.441027i
$866$		0			0
$867$	40.5347	+	70.2081i	1.37663	+	2.38439i
$868$		0			0
$869$	−29.4040	−	16.9764i	−0.997461	−	0.575885i
$870$		0			0
$871$	0.0178510	−	0.0103063i	0.000604858	−	0.000349215i
$872$		0			0
$873$	69.5597	−	40.1603i	2.35424	−	1.35922i
$874$		0			0
$875$	−2.88677	−	1.66668i	−0.0975907	−	0.0563440i
$876$		0			0
$877$	−20.6596			−0.697626			−0.348813	−	0.937192i	$-0.613415\pi$
$877$	−20.6596			−0.697626			−0.348813	+	0.937192i	$0.613415\pi$
$878$		0			0
$879$	12.2236	+	21.1720i	0.412293	+	0.714112i
$880$		0			0
$881$	22.3841	−	38.7703i	0.754138	−	1.30621i	−0.191663	−	0.981461i	$-0.561388\pi$
$881$	22.3841	−	38.7703i	0.754138	−	1.30621i	0.945802	−	0.324745i	$-0.105279\pi$
$882$		0			0
$883$	−22.8082	−	13.1683i	−0.767556	−	0.443149i	0.0644458	−	0.997921i	$-0.479472\pi$
$883$	−22.8082	−	13.1683i	−0.767556	−	0.443149i	−0.832002	+	0.554772i	$0.812805\pi$
$884$		0			0
$885$	−0.415433	+	0.719551i	−0.0139646	+	0.0241874i
$886$		0			0
$887$	−24.8590			−0.834683			−0.417341	−	0.908750i	$-0.637038\pi$
$887$	−24.8590			−0.834683			−0.417341	+	0.908750i	$0.637038\pi$
$888$		0			0
$889$	1.42553			0.0478106
$890$		0			0
$891$	52.4783	−	90.8951i	1.75809	−	3.04510i
$892$		0			0
$893$	3.57292	+	2.06283i	0.119563	+	0.0690299i
$894$		0			0
$895$	−5.61896	+	9.73233i	−0.187821	+	0.325316i
$896$		0			0
$897$	0.330668	+	0.572733i	0.0110407	+	0.0191230i
$898$		0			0
$899$	−9.31323			−0.310614
$900$		0			0
$901$	−65.2821	−	37.6906i	−2.17486	−	1.25566i
$902$		0			0
$903$	−2.76911	+	1.59874i	−0.0921501	+	0.0532029i
$904$		0			0
$905$	3.34762	−	1.93275i	0.111279	−	0.0642467i
$906$		0			0
$907$	22.0998	+	12.7593i	0.733810	+	0.423666i	0.819815	−	0.572629i	$-0.194076\pi$
$907$	22.0998	+	12.7593i	0.733810	+	0.423666i	−0.0860041	+	0.996295i	$0.527410\pi$
$908$		0			0
$909$	50.9203	+	88.1966i	1.68892	+	2.92530i
$910$		0			0
$911$			31.0298i			1.02806i	0.857771	+	0.514032i	$0.171849\pi$
$911$			31.0298i			1.02806i	−0.857771	+	0.514032i	$0.828151\pi$
$912$		0			0
$913$	16.9327	+	29.3282i	0.560390	+	0.970623i
$914$		0			0
$915$	28.3370			0.936793
$916$		0			0
$917$			9.82908i			0.324585i
$918$		0			0
$919$		−	4.80421i		−	0.158476i	−0.996856	−	0.0792381i	$-0.974751\pi$
$919$		−	4.80421i		−	0.158476i	0.996856	−	0.0792381i	$-0.0252487\pi$
$920$		0			0
$921$	−18.8835	+	32.7072i	−0.622233	+	1.07774i
$922$		0			0
$923$	−2.49673	+	1.44149i	−0.0821808	+	0.0474471i
$924$		0			0
$925$	17.7611	−	21.7170i	0.583980	−	0.714050i
$926$		0			0
$927$	−52.6364	+	30.3897i	−1.72881	+	0.998128i
$928$		0			0
$929$	−6.80623	+	11.7887i	−0.223305	+	0.386776i	−0.955810	−	0.293986i	$-0.905018\pi$
$929$	−6.80623	+	11.7887i	−0.223305	+	0.386776i	0.732505	+	0.680762i	$0.238351\pi$
$930$		0			0
$931$		−	2.39211i		−	0.0783984i
$932$		0			0
$933$			66.5178i			2.17769i
$934$		0			0
$935$	17.7933			0.581904
$936$		0			0
$937$	15.8190	+	27.3993i	0.516783	+	0.895095i	0.999810	+	0.0194895i	$0.00620411\pi$
$937$	15.8190	+	27.3993i	0.516783	+	0.895095i	−0.483027	+	0.875606i	$0.660463\pi$
$938$		0			0
$939$			49.0970i			1.60222i
$940$		0			0
$941$	−19.3567	−	33.5269i	−0.631012	−	1.09294i	−0.987345	−	0.158586i	$-0.949307\pi$
$941$	−19.3567	−	33.5269i	−0.631012	−	1.09294i	0.356333	−	0.934359i	$-0.384027\pi$
$942$		0			0
$943$	−4.90091	−	2.82954i	−0.159596	−	0.0921425i
$944$		0			0
$945$	4.28894	−	2.47622i	0.139519	−	0.0805514i
$946$		0			0
$947$	−4.07971	+	2.35542i	−0.132573	+	0.0765409i	−0.564820	−	0.825214i	$-0.691054\pi$
$947$	−4.07971	+	2.35542i	−0.132573	+	0.0765409i	0.432247	+	0.901755i	$0.357721\pi$
$948$		0			0
$949$	−2.01161	−	1.16140i	−0.0652995	−	0.0377007i
$950$		0			0
$951$	−30.8265			−0.999618
$952$		0			0
$953$	−29.4117	−	50.9426i	−0.952739	−	1.65019i	−0.739460	−	0.673200i	$-0.764919\pi$
$953$	−29.4117	−	50.9426i	−0.952739	−	1.65019i	−0.213278	−	0.976992i	$-0.568414\pi$
$954$		0			0
$955$	−5.94665	+	10.2999i	−0.192429	+	0.333297i
$956$		0			0
$957$	−12.2709	−	7.08463i	−0.396663	−	0.229014i
$958$		0			0
$959$	−1.63444	+	2.83094i	−0.0527790	+	0.0914158i
$960$		0			0
$961$	−56.3063			−1.81633
$962$		0			0
$963$	−4.25259			−0.137038
$964$		0			0
$965$	4.13833	−	7.16779i	0.133218	−	0.230739i
$966$		0			0
$967$	−0.198986	−	0.114885i	−0.00639897	−	0.00369445i	0.496797	−	0.867867i	$-0.334509\pi$
$967$	−0.198986	−	0.114885i	−0.00639897	−	0.00369445i	−0.503196	+	0.864172i	$0.667843\pi$
$968$		0			0
$969$	−3.74569	+	6.48773i	−0.120329	+	0.208416i
$970$		0			0
$971$	−5.07700	−	8.79362i	−0.162929	−	0.282201i	0.772989	−	0.634419i	$-0.218761\pi$
$971$	−5.07700	−	8.79362i	−0.162929	−	0.282201i	−0.935918	+	0.352219i	$0.885427\pi$
$972$		0			0
$973$	5.17134			0.165785
$974$		0			0
$975$	3.14340	+	1.81484i	0.100669	+	0.0581214i
$976$		0			0
$977$	−7.19534	+	4.15423i	−0.230199	+	0.132906i	−0.610664	−	0.791890i	$-0.709097\pi$
$977$	−7.19534	+	4.15423i	−0.230199	+	0.132906i	0.380465	+	0.924795i	$0.375764\pi$
$978$		0			0
$979$	−27.9313	+	16.1261i	−0.892687	+	0.515393i
$980$		0			0
$981$	74.8909	+	43.2383i	2.39108	+	1.38049i
$982$		0			0
$983$	9.17432	+	15.8904i	0.292615	+	0.506824i	0.974427	−	0.224703i	$-0.0721412\pi$
$983$	9.17432	+	15.8904i	0.292615	+	0.506824i	−0.681812	+	0.731527i	$0.738808\pi$
$984$		0			0
$985$		−	4.12937i		−	0.131573i
$986$		0			0
$987$	−10.3721	−	17.9649i	−0.330146	−	0.571830i
$988$		0			0
$989$	1.49453			0.0475234
$990$		0			0
$991$		−	17.3646i		−	0.551604i	−0.961214	−	0.275802i	$-0.911057\pi$
$991$		−	17.3646i		−	0.551604i	0.961214	−	0.275802i	$-0.0889435\pi$
$992$		0			0
$993$		−	100.659i		−	3.19432i
$994$		0			0
$995$	4.37298	−	7.57422i	0.138633	−	0.240119i
$996$		0			0
$997$	−19.8363	+	11.4525i	−0.628223	+	0.362705i	−0.780064	−	0.625700i	$-0.784813\pi$
$997$	−19.8363	+	11.4525i	−0.628223	+	0.362705i	0.151840	+	0.988405i	$0.451480\pi$
$998$		0			0
$999$	30.7373	+	81.2485i	0.972486	+	2.57059i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.w.f.529.1		20
4.3	odd	2		296.2.o.a.233.10	✓	20
12.11	even	2		2664.2.cq.c.2305.5		20
37.27	even	6	inner	592.2.w.f.545.1		20
148.27	odd	6		296.2.o.a.249.10	yes	20
444.323	even	6		2664.2.cq.c.1729.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
296.2.o.a.233.10	✓	20	4.3	odd	2
296.2.o.a.249.10	yes	20	148.27	odd	6
592.2.w.f.529.1		20	1.1	even	1	trivial
592.2.w.f.545.1		20	37.27	even	6	inner
2664.2.cq.c.1729.5		20	444.323	even	6
2664.2.cq.c.2305.5		20	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61426 + 2.79599i) q^{3} +(0.539298 + 0.311364i) q^{5} +(0.278439 - 0.482271i) q^{7} +(-3.71170 - 6.42885i) q^{9} -4.40317 q^{11} +(0.211099 + 0.121878i) q^{13} +(-1.74114 + 1.00525i) q^{15} +(-5.61985 + 3.24462i) q^{17} +(-0.309666 - 0.178786i) q^{19} +(0.898950 + 1.55703i) q^{21} -0.840354i q^{23} +(-2.30611 - 3.99429i) q^{25} +14.2811 q^{27} -0.996730i q^{29} -9.34379i q^{31} +(7.10787 - 12.3112i) q^{33} +(0.300323 - 0.173392i) q^{35} +(2.15231 + 5.68925i) q^{37} +(-0.681538 + 0.393486i) q^{39} +(3.36708 - 5.83196i) q^{41} +1.77846i q^{43} -4.62275i q^{45} -11.5380 q^{47} +(3.34494 + 5.79361i) q^{49} -20.9507i q^{51} +(5.80817 + 10.0600i) q^{53} +(-2.37462 - 1.37099i) q^{55} +(0.999766 - 0.577215i) q^{57} +(0.357898 - 0.206632i) q^{59} +(-12.2063 - 7.04728i) q^{61} -4.13393 q^{63} +(0.0758967 + 0.131457i) q^{65} +(0.0422812 - 0.0732332i) q^{67} +(2.34962 + 1.35655i) q^{69} +(-5.91365 + 10.2428i) q^{71} -9.52922 q^{73} +14.8907 q^{75} +(-1.22602 + 2.12352i) q^{77} +(6.67792 + 3.85550i) q^{79} +(-11.9183 + 20.6431i) q^{81} +(-3.84557 - 6.66072i) q^{83} -4.04103 q^{85} +(2.78685 + 1.60899i) q^{87} +(6.34345 - 3.66239i) q^{89} +(0.117556 - 0.0678712i) q^{91} +(26.1251 + 15.0833i) q^{93} +(-0.111335 - 0.192838i) q^{95} +10.8199i q^{97} +(16.3432 + 28.3073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} + 6 q^{5} + 2 q^{7} - 12 q^{9} - 16 q^{11} - 6 q^{13} + 18 q^{15} - 6 q^{17} + 6 q^{19} + 2 q^{21} + 20 q^{25} + 20 q^{27} - 4 q^{33} + 6 q^{35} + 24 q^{37} - 18 q^{39} + 14 q^{41} + 8 q^{47}+ \cdots + 56 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 + 6 * q^5 + 2 * q^7 - 12 * q^9 - 16 * q^11 - 6 * q^13 + 18 * q^15 - 6 * q^17 + 6 * q^19 + 2 * q^21 + 20 * q^25 + 20 * q^27 - 4 * q^33 + 6 * q^35 + 24 * q^37 - 18 * q^39 + 14 * q^41 + 8 * q^47 + 4 * q^49 + 2 * q^53 - 12 * q^55 - 6 * q^57 + 18 * q^59 - 30 * q^61 - 24 * q^63 + 10 * q^65 + 10 * q^67 - 12 * q^69 + 2 * q^71 - 16 * q^73 + 24 * q^75 + 12 * q^77 + 66 * q^79 - 18 * q^81 - 42 * q^83 - 92 * q^85 - 12 * q^87 - 18 * q^89 - 66 * q^91 + 48 * q^93 - 14 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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