LMFDB - Embedded newform 460.2.x.a.337.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(17,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 14]))

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

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

chi := DirichletCharacter("460.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			337.6
Character	$\chi$	$=$	460.337
Dual form			460.2.x.a.273.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.346279 - 0.129155i) q^{3} +(2.23551 - 0.0500151i) q^{5} +(2.73872 - 0.595772i) q^{7} +(-2.16402 - 1.87513i) q^{9} +O(q^{10})$	\(q+(-0.346279 - 0.129155i) q^{3} +(2.23551 - 0.0500151i) q^{5} +(2.73872 - 0.595772i) q^{7} +(-2.16402 - 1.87513i) q^{9} +(1.78358 - 0.256440i) q^{11} +(-1.03909 + 4.77664i) q^{13} +(-0.780569 - 0.271409i) q^{15} +(2.53838 - 4.64870i) q^{17} +(-1.01240 - 0.297268i) q^{19} +(-1.02531 - 0.147417i) q^{21} +(-1.23493 - 4.63411i) q^{23} +(4.99500 - 0.223618i) q^{25} +(1.03854 + 1.90194i) q^{27} +(2.32176 + 7.90718i) q^{29} +(1.26614 - 2.77246i) q^{31} +(-0.650737 - 0.141559i) q^{33} +(6.09263 - 1.46883i) q^{35} +(0.259416 + 3.62710i) q^{37} +(0.976746 - 1.51985i) q^{39} +(6.73333 + 7.77068i) q^{41} +(4.20251 - 11.2674i) q^{43} +(-4.93147 - 4.08365i) q^{45} +(-4.87722 - 4.87722i) q^{47} +(0.778212 - 0.355397i) q^{49} +(-1.47939 + 1.28190i) q^{51} +(0.222104 + 1.02100i) q^{53} +(3.97438 - 0.662480i) q^{55} +(0.312179 + 0.233695i) q^{57} +(-0.486060 - 0.756324i) q^{59} +(-7.03820 - 3.21424i) q^{61} +(-7.04380 - 3.84620i) q^{63} +(-2.08400 + 10.7302i) q^{65} +(-2.21900 - 2.96424i) q^{67} +(-0.170890 + 1.76419i) q^{69} +(-2.00088 + 13.9164i) q^{71} +(-9.51592 + 5.19609i) q^{73} +(-1.75854 - 0.567697i) q^{75} +(4.73194 - 1.76492i) q^{77} +(-11.7929 + 7.57885i) q^{79} +(1.10854 + 7.71006i) q^{81} +(-2.76146 + 0.197504i) q^{83} +(5.44207 - 10.5192i) q^{85} +(0.217279 - 3.03796i) q^{87} +(-4.59191 - 10.0549i) q^{89} +13.7009i q^{91} +(-0.796515 + 0.796515i) q^{93} +(-2.27810 - 0.613909i) q^{95} +(-6.02265 - 0.430748i) q^{97} +(-4.34056 - 2.78951i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3}+O(q^{10}) $ 240 * q + 4 * q^3	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{22}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.346279	−	0.129155i	−0.199924	−	0.0745679i	0.247507	−	0.968886i	$-0.420389\pi$
$3$	−0.346279	−	0.129155i	−0.199924	−	0.0745679i	−0.447432	+	0.894318i	$0.647661\pi$
$4$		0			0
$5$	2.23551	−	0.0500151i	0.999750	−	0.0223674i
$5$	2.23551	−	0.0500151i	0.999750	−	0.0223674i
$6$		0			0
$7$	2.73872	−	0.595772i	1.03514	−	0.225181i	0.337271	−	0.941408i	$-0.390496\pi$
$7$	2.73872	−	0.595772i	1.03514	−	0.225181i	0.697867	+	0.716227i	$0.254133\pi$
$8$		0			0
$9$	−2.16402	−	1.87513i	−0.721340	−	0.625045i
$10$		0			0
$11$	1.78358	−	0.256440i	0.537770	−	0.0773196i	0.131922	−	0.991260i	$-0.457885\pi$
$11$	1.78358	−	0.256440i	0.537770	−	0.0773196i	0.405848	+	0.913941i	$0.366976\pi$
$12$		0			0
$13$	−1.03909	+	4.77664i	−0.288193	+	1.32480i	0.574263	+	0.818671i	$0.305289\pi$
$13$	−1.03909	+	4.77664i	−0.288193	+	1.32480i	−0.862456	+	0.506131i	$0.831075\pi$
$14$		0			0
$15$	−0.780569	−	0.271409i	−0.201542	−	0.0700775i
$16$		0			0
$17$	2.53838	−	4.64870i	0.615648	−	1.12748i	−0.364872	−	0.931058i	$-0.618887\pi$
$17$	2.53838	−	4.64870i	0.615648	−	1.12748i	0.980520	−	0.196418i	$-0.0629308\pi$
$18$		0			0
$19$	−1.01240	−	0.297268i	−0.232261	−	0.0681979i	0.163531	−	0.986538i	$-0.447712\pi$
$19$	−1.01240	−	0.297268i	−0.232261	−	0.0681979i	−0.395792	+	0.918340i	$0.629530\pi$
$20$		0			0
$21$	−1.02531	−	0.147417i	−0.223741	−	0.0321690i
$22$		0			0
$23$	−1.23493	−	4.63411i	−0.257500	−	0.966278i
$23$	−1.23493	−	4.63411i	−0.257500	−	0.966278i
$24$		0			0
$25$	4.99500	−	0.223618i	0.998999	−	0.0447236i
$26$		0			0
$27$	1.03854	+	1.90194i	0.199866	+	0.366028i
$28$		0			0
$29$	2.32176	+	7.90718i	0.431139	+	1.46833i	0.833333	+	0.552771i	$0.186430\pi$
$29$	2.32176	+	7.90718i	0.431139	+	1.46833i	−0.402194	+	0.915555i	$0.631752\pi$
$30$		0			0
$31$	1.26614	−	2.77246i	0.227405	−	0.497948i	−0.761193	−	0.648525i	$-0.775386\pi$
$31$	1.26614	−	2.77246i	0.227405	−	0.497948i	0.988598	+	0.150577i	$0.0481133\pi$
$32$		0			0
$33$	−0.650737	−	0.141559i	−0.113279	−	0.0246423i
$34$		0			0
$35$	6.09263	−	1.46883i	1.02984	−	0.248278i
$36$		0			0
$37$	0.259416	+	3.62710i	0.0426477	+	0.596292i	0.973174	+	0.230068i	$0.0738950\pi$
$37$	0.259416	+	3.62710i	0.0426477	+	0.596292i	−0.930527	+	0.366224i	$0.880650\pi$
$38$		0			0
$39$	0.976746	−	1.51985i	0.156404	−	0.243370i
$40$		0			0
$41$	6.73333	+	7.77068i	1.05157	+	1.21358i	0.976302	+	0.216413i	$0.0694356\pi$
$41$	6.73333	+	7.77068i	1.05157	+	1.21358i	0.0752676	+	0.997163i	$0.476019\pi$
$42$		0			0
$43$	4.20251	−	11.2674i	0.640877	−	1.71826i	−0.0534217	−	0.998572i	$-0.517013\pi$
$43$	4.20251	−	11.2674i	0.640877	−	1.71826i	0.694299	−	0.719687i	$-0.255715\pi$
$44$		0			0
$45$	−4.93147	−	4.08365i	−0.735140	−	0.608754i
$46$		0			0
$47$	−4.87722	−	4.87722i	−0.711416	−	0.711416i	0.255416	−	0.966831i	$-0.417788\pi$
$47$	−4.87722	−	4.87722i	−0.711416	−	0.711416i	−0.966831	+	0.255416i	$0.917788\pi$
$48$		0			0
$49$	0.778212	−	0.355397i	0.111173	−	0.0507710i
$50$		0			0
$51$	−1.47939	+	1.28190i	−0.207156	+	0.179502i
$52$		0			0
$53$	0.222104	+	1.02100i	0.0305083	+	0.140245i	0.989882	−	0.141895i	$-0.0453195\pi$
$53$	0.222104	+	1.02100i	0.0305083	+	0.140245i	−0.959373	+	0.282140i	$0.908956\pi$
$54$		0			0
$55$	3.97438	−	0.662480i	0.535906	−	0.0893288i
$56$		0			0
$57$	0.312179	+	0.233695i	0.0413492	+	0.0309536i
$58$		0			0
$59$	−0.486060	−	0.756324i	−0.0632796	−	0.0984650i	0.808172	−	0.588947i	$-0.200457\pi$
$59$	−0.486060	−	0.756324i	−0.0632796	−	0.0984650i	−0.871451	+	0.490482i	$0.836821\pi$
$60$		0			0
$61$	−7.03820	−	3.21424i	−0.901149	−	0.411541i	−0.0897031	−	0.995969i	$-0.528592\pi$
$61$	−7.03820	−	3.21424i	−0.901149	−	0.411541i	−0.811446	+	0.584428i	$0.801319\pi$
$62$		0			0
$63$	−7.04380	−	3.84620i	−0.887435	−	0.484576i
$64$		0			0
$65$	−2.08400	+	10.7302i	−0.258489	+	1.33092i
$66$		0			0
$67$	−2.21900	−	2.96424i	−0.271094	−	0.362139i	0.644248	−	0.764817i	$-0.277171\pi$
$67$	−2.21900	−	2.96424i	−0.271094	−	0.362139i	−0.915342	+	0.402677i	$0.868080\pi$
$68$		0			0
$69$	−0.170890	+	1.76419i	−0.0205728	+	0.212384i
$70$		0			0
$71$	−2.00088	+	13.9164i	−0.237461	+	1.65158i	0.426999	+	0.904252i	$0.359571\pi$
$71$	−2.00088	+	13.9164i	−0.237461	+	1.65158i	−0.664460	+	0.747324i	$0.731338\pi$
$72$		0			0
$73$	−9.51592	+	5.19609i	−1.11375	+	0.608156i	−0.927304	−	0.374308i	$-0.877880\pi$
$73$	−9.51592	+	5.19609i	−1.11375	+	0.608156i	−0.186450	+	0.982464i	$0.559698\pi$
$74$		0			0
$75$	−1.75854	−	0.567697i	−0.203059	−	0.0655520i
$76$		0			0
$77$	4.73194	−	1.76492i	0.539255	−	0.201132i
$78$		0			0
$79$	−11.7929	+	7.57885i	−1.32681	+	0.852687i	−0.995855	−	0.0909603i	$-0.971006\pi$
$79$	−11.7929	+	7.57885i	−1.32681	+	0.852687i	−0.330953	+	0.943647i	$0.607370\pi$
$80$		0			0
$81$	1.10854	+	7.71006i	0.123171	+	0.856673i
$82$		0			0
$83$	−2.76146	+	0.197504i	−0.303110	+	0.0216789i	−0.222066	−	0.975032i	$-0.571280\pi$
$83$	−2.76146	+	0.197504i	−0.303110	+	0.0216789i	−0.0810442	+	0.996711i	$0.525825\pi$
$84$		0			0
$85$	5.44207	−	10.5192i	0.590275	−	1.14096i
$86$		0			0
$87$	0.217279	−	3.03796i	0.0232947	−	0.325703i
$88$		0			0
$89$	−4.59191	−	10.0549i	−0.486742	−	1.06582i	−0.980554	−	0.196248i	$-0.937124\pi$
$89$	−4.59191	−	10.0549i	−0.486742	−	1.06582i	0.493812	−	0.869568i	$-0.335603\pi$
$90$		0			0
$91$			13.7009i			1.43625i
$92$		0			0
$93$	−0.796515	+	0.796515i	−0.0825948	+	0.0825948i
$94$		0			0
$95$	−2.27810	−	0.613909i	−0.233728	−	0.0629857i
$96$		0			0
$97$	−6.02265	−	0.430748i	−0.611507	−	0.0437359i	−0.237849	−	0.971302i	$-0.576442\pi$
$97$	−6.02265	−	0.430748i	−0.611507	−	0.0437359i	−0.373658	+	0.927566i	$0.621897\pi$
$98$		0			0
$99$	−4.34056	−	2.78951i	−0.436243	−	0.280356i
$100$		0			0
$101$	−8.10695	+	9.35592i	−0.806671	+	0.930948i	−0.998727	−	0.0504355i	$-0.983939\pi$
$101$	−8.10695	+	9.35592i	−0.806671	+	0.930948i	0.192056	+	0.981384i	$0.438485\pi$
$102$		0			0
$103$	3.96434	−	5.29574i	0.390618	−	0.521804i	−0.561524	−	0.827460i	$-0.689785\pi$
$103$	3.96434	−	5.29574i	0.390618	−	0.521804i	0.952142	+	0.305656i	$0.0988757\pi$
$104$		0			0
$105$	−2.29946	−	0.278271i	−0.224404	−	0.0271565i
$106$		0			0
$107$	2.43069	+	6.51692i	0.234983	+	0.630015i	0.999900	−	0.0141140i	$-0.00449277\pi$
$107$	2.43069	+	6.51692i	0.234983	+	0.630015i	−0.764917	+	0.644129i	$0.777220\pi$
$108$		0			0
$109$	−12.9058	+	3.78947i	−1.23615	+	0.362966i	−0.833567	−	0.552419i	$-0.813705\pi$
$109$	−12.9058	+	3.78947i	−1.23615	+	0.362966i	−0.402581	+	0.915385i	$0.631887\pi$
$110$		0			0
$111$	0.378630	−	1.28949i	0.0359380	−	0.122393i
$112$		0			0
$113$	6.50047	−	4.86619i	0.611513	−	0.457773i	−0.248089	−	0.968737i	$-0.579802\pi$
$113$	6.50047	−	4.86619i	0.611513	−	0.457773i	0.859602	+	0.510964i	$0.170712\pi$
$114$		0			0
$115$	−2.99247	−	10.2978i	−0.279049	−	0.960277i
$116$		0			0
$117$	11.2055	−	8.38831i	1.03595	−	0.775499i
$118$		0			0
$119$	4.18235	−	14.2438i	0.383395	−	1.30572i
$120$		0			0
$121$	−7.43903	+	2.18430i	−0.676275	+	0.198572i
$122$		0			0
$123$	−1.32799	−	3.56047i	−0.119740	−	0.321037i
$124$		0			0
$125$	11.1552	−	0.749726i	0.997749	−	0.0670575i
$126$		0			0
$127$	−7.75117	+	10.3543i	−0.687805	+	0.918800i	−0.999508	−	0.0313801i	$-0.990010\pi$
$127$	−7.75117	+	10.3543i	−0.687805	+	0.918800i	0.311703	+	0.950180i	$0.399101\pi$
$128$		0			0
$129$	−2.91049	+	3.35888i	−0.256254	+	0.295733i
$130$		0			0
$131$	8.17142	+	5.25145i	0.713940	+	0.458822i	0.846524	−	0.532350i	$-0.178691\pi$
$131$	8.17142	+	5.25145i	0.713940	+	0.458822i	−0.132584	+	0.991172i	$0.542327\pi$
$132$		0			0
$133$	−2.94978	−	0.210973i	−0.255779	−	0.0182937i
$134$		0			0
$135$	2.41678	+	4.19985i	0.208003	+	0.361466i
$136$		0			0
$137$	1.35429	−	1.35429i	0.115705	−	0.115705i	−0.646884	−	0.762589i	$-0.723928\pi$
$137$	1.35429	−	1.35429i	0.115705	−	0.115705i	0.762589	+	0.646884i	$0.223928\pi$
$138$		0			0
$139$			9.07750i			0.769943i	0.922928	+	0.384972i	$0.125789\pi$
$139$			9.07750i			0.769943i	−0.922928	+	0.384972i	$0.874211\pi$
$140$		0			0
$141$	1.05896	+	2.31880i	0.0891805	+	0.195278i
$142$		0			0
$143$	−0.628386	+	8.78599i	−0.0525483	+	0.734721i
$144$		0			0
$145$	5.58578	+	17.5604i	0.463874	+	1.45831i
$146$		0			0
$147$	−0.315380	+	0.0225564i	−0.0260121	+	0.00186042i
$148$		0			0
$149$	−0.442772	−	3.07955i	−0.0362733	−	0.252286i	0.963614	−	0.267298i	$-0.0861307\pi$
$149$	−0.442772	−	3.07955i	−0.0362733	−	0.252286i	−0.999887	+	0.0150112i	$0.995222\pi$
$150$		0			0
$151$	12.6036	−	8.09982i	1.02566	−	0.659154i	0.0842631	−	0.996444i	$-0.473146\pi$
$151$	12.6036	−	8.09982i	1.02566	−	0.659154i	0.941401	+	0.337289i	$0.109510\pi$
$152$		0			0
$153$	−14.2100	+	5.30007i	−1.14881	+	0.428486i
$154$		0			0
$155$	2.69180	−	6.26118i	0.216211	−	0.502910i
$156$		0			0
$157$	−3.76892	+	2.05799i	−0.300793	+	0.164245i	−0.622557	−	0.782575i	$-0.713906\pi$
$157$	−3.76892	+	2.05799i	−0.300793	+	0.164245i	0.321764	+	0.946820i	$0.395724\pi$
$158$		0			0
$159$	0.0549572	−	0.382235i	0.00435839	−	0.0303132i
$160$		0			0
$161$	−6.14299	−	11.9558i	−0.484135	−	0.942248i
$162$		0			0
$163$	−7.88739	−	10.5363i	−0.617788	−	0.825268i	0.377108	−	0.926169i	$-0.376918\pi$
$163$	−7.88739	−	10.5363i	−0.617788	−	0.825268i	−0.994897	+	0.100901i	$0.967828\pi$
$164$		0			0
$165$	−1.46181	−	0.283910i	−0.113802	−	0.0221024i
$166$		0			0
$167$	−17.8215	−	9.73128i	−1.37907	−	0.753029i	−0.393027	−	0.919527i	$-0.628572\pi$
$167$	−17.8215	−	9.73128i	−1.37907	−	0.753029i	−0.986042	+	0.166498i	$0.946754\pi$
$168$		0			0
$169$	−9.91137	−	4.52637i	−0.762413	−	0.348182i
$170$		0			0
$171$	1.63344	+	2.54168i	0.124912	+	0.194367i
$172$		0			0
$173$	6.29422	+	4.71179i	0.478540	+	0.358231i	0.811154	−	0.584832i	$-0.198840\pi$
$173$	6.29422	+	4.71179i	0.478540	+	0.358231i	−0.332614	+	0.943063i	$0.607931\pi$
$174$		0			0
$175$	13.5467	−	3.58831i	1.02403	−	0.271250i
$176$		0			0
$177$	0.0706290	+	0.324676i	0.00530880	+	0.0244042i
$178$		0			0
$179$	1.46278	−	1.26750i	0.109333	−	0.0947377i	−0.598479	−	0.801139i	$-0.704228\pi$
$179$	1.46278	−	1.26750i	0.109333	−	0.0947377i	0.707812	+	0.706401i	$0.249682\pi$
$180$		0			0
$181$	13.0843	−	5.97541i	0.972550	−	0.444149i	0.135201	−	0.990818i	$-0.456832\pi$
$181$	13.0843	−	5.97541i	0.972550	−	0.444149i	0.837348	+	0.546669i	$0.184105\pi$
$182$		0			0
$183$	2.02204	+	2.02204i	0.149474	+	0.149474i
$184$		0			0
$185$	0.761335	+	8.09545i	0.0559745	+	0.595189i
$186$		0			0
$187$	3.33529	−	8.94227i	0.243901	−	0.653924i
$188$		0			0
$189$	3.97738	+	4.59014i	0.289312	+	0.333883i
$190$		0			0
$191$	2.45853	−	3.82554i	0.177893	−	0.276807i	−0.740844	−	0.671677i	$-0.765574\pi$
$191$	2.45853	−	3.82554i	0.177893	−	0.276807i	0.918737	+	0.394871i	$0.129211\pi$
$192$		0			0
$193$	−0.495237	−	6.92431i	−0.0356479	−	0.498423i	−0.983642	−	0.180135i	$-0.942347\pi$
$193$	−0.495237	−	6.92431i	−0.0356479	−	0.498423i	0.947994	−	0.318288i	$-0.103108\pi$
$194$		0			0
$195$	2.10751	−	3.44648i	0.150922	−	0.246808i
$196$		0			0
$197$	25.1222	+	5.46501i	1.78988	+	0.389366i	0.980280	−	0.197611i	$-0.0633183\pi$
$197$	25.1222	+	5.46501i	1.78988	+	0.389366i	0.809604	+	0.586977i	$0.199682\pi$
$198$		0			0
$199$	4.82681	−	10.5692i	0.342163	−	0.749233i	−0.657829	−	0.753167i	$-0.728525\pi$
$199$	4.82681	−	10.5692i	0.342163	−	0.749233i	0.999992	+	0.00393436i	$0.00125235\pi$
$200$		0			0
$201$	0.385546	+	1.31305i	0.0271943	+	0.0926154i
$202$		0			0
$203$	11.0695	+	20.2723i	0.776927	+	1.42284i
$204$		0			0
$205$	15.4411	+	17.0346i	1.07845	+	1.18975i
$206$		0			0
$207$	−6.01717	+	12.3440i	−0.418222	+	0.857965i
$208$		0			0
$209$	−1.88193	−	0.270581i	−0.130176	−	0.0187164i
$210$		0			0
$211$	−22.0351	−	6.47009i	−1.51696	−	0.445420i	−0.585930	−	0.810362i	$-0.699270\pi$
$211$	−22.0351	−	6.47009i	−1.51696	−	0.445420i	−0.931030	+	0.364942i	$0.881089\pi$
$212$		0			0
$213$	2.49024	−	4.56054i	0.170629	−	0.312483i
$214$		0			0
$215$	8.83122	−	25.3985i	0.602284	−	1.73216i
$216$		0			0
$217$	1.81585	−	8.34731i	0.123268	−	0.566652i
$218$		0			0
$219$	3.96627	−	0.570263i	0.268016	−	0.0385348i
$220$		0			0
$221$	19.5675	+	16.9554i	1.31626	+	1.14054i
$222$		0			0
$223$	−25.4812	+	5.54310i	−1.70635	+	0.371194i	−0.956798	−	0.290753i	$-0.906094\pi$
$223$	−25.4812	+	5.54310i	−1.70635	+	0.371194i	−0.749551	+	0.661946i	$0.769731\pi$
$224$		0			0
$225$	−11.2286	−	8.88238i	−0.748573	−	0.592158i
$226$		0			0
$227$	12.5464	+	4.67956i	0.832733	+	0.310593i	0.729429	−	0.684057i	$-0.239786\pi$
$227$	12.5464	+	4.67956i	0.832733	+	0.310593i	0.103304	+	0.994650i	$0.467059\pi$
$228$		0			0
$229$	6.41339			0.423809			0.211904	−	0.977290i	$-0.432033\pi$
$229$	6.41339			0.423809			0.211904	+	0.977290i	$0.432033\pi$
$230$		0			0
$231$	−1.86652			−0.122808
$232$		0			0
$233$	−3.67708	−	1.37148i	−0.240894	−	0.0898487i	0.226118	−	0.974100i	$-0.427397\pi$
$233$	−3.67708	−	1.37148i	−0.240894	−	0.0898487i	−0.467011	+	0.884251i	$0.654669\pi$
$234$		0			0
$235$	−11.1470	−	10.6591i	−0.727150	−	0.695325i
$236$		0			0
$237$	5.06249	−	1.10128i	0.328844	−	0.0715357i
$238$		0			0
$239$	22.7068	+	19.6756i	1.46878	+	1.27271i	0.888976	+	0.457954i	$0.151418\pi$
$239$	22.7068	+	19.6756i	1.46878	+	1.27271i	0.579807	+	0.814754i	$0.303128\pi$
$240$		0			0
$241$	−11.0402	+	1.58734i	−0.711160	+	0.102249i	−0.488395	−	0.872623i	$-0.662417\pi$
$241$	−11.0402	+	1.58734i	−0.711160	+	0.102249i	−0.222765	+	0.974872i	$0.571508\pi$
$242$		0			0
$243$	1.99382	−	9.16546i	0.127904	−	0.587964i
$244$		0			0
$245$	1.72192	−	0.833416i	0.110010	−	0.0532450i
$246$		0			0
$247$	2.47192	−	4.52699i	0.157285	−	0.288045i
$248$		0			0
$249$	0.981746	+	0.288267i	0.0622156	+	0.0182682i
$250$		0			0
$251$	−15.8595	−	2.28025i	−1.00104	−	0.143928i	−0.377742	−	0.925911i	$-0.623299\pi$
$251$	−15.8595	−	2.28025i	−1.00104	−	0.143928i	−0.623300	+	0.781983i	$0.714209\pi$
$252$		0			0
$253$	−3.39096	−	7.94862i	−0.213188	−	0.499725i
$254$		0			0
$255$	−3.24308	+	2.93969i	−0.203090	+	0.184091i
$256$		0			0
$257$	−7.27438	−	13.3220i	−0.453763	−	0.831006i	0.546214	−	0.837645i	$-0.316068\pi$
$257$	−7.27438	−	13.3220i	−0.453763	−	0.831006i	−0.999978	+	0.00663960i	$0.997887\pi$
$258$		0			0
$259$	2.87139	+	9.77906i	0.178420	+	0.607641i
$260$		0			0
$261$	9.80269	−	21.4649i	0.606771	−	1.32864i
$262$		0			0
$263$	16.4225	+	3.57250i	1.01266	+	0.220290i	0.688130	−	0.725587i	$-0.258432\pi$
$263$	16.4225	+	3.57250i	1.01266	+	0.220290i	0.324525	+	0.945877i	$0.394796\pi$
$264$		0			0
$265$	0.547581	+	2.27134i	0.0336376	+	0.139527i
$266$		0			0
$267$	0.291440	+	4.07487i	0.0178359	+	0.249378i
$268$		0			0
$269$	−7.78876	+	12.1195i	−0.474889	+	0.738942i	−0.993221	−	0.116238i	$-0.962917\pi$
$269$	−7.78876	+	12.1195i	−0.474889	+	0.738942i	0.518332	+	0.855179i	$0.326553\pi$
$270$		0			0
$271$	13.3959	+	15.4597i	0.813743	+	0.939109i	0.999050	−	0.0435713i	$-0.0138736\pi$
$271$	13.3959	+	15.4597i	0.813743	+	0.939109i	−0.185308	+	0.982681i	$0.559328\pi$
$272$		0			0
$273$	1.76955	−	4.74435i	0.107098	−	0.287141i
$274$		0			0
$275$	8.85163	−	1.67976i	0.533774	−	0.101293i
$276$		0			0
$277$	−1.25141	−	1.25141i	−0.0751900	−	0.0751900i	0.668512	−	0.743702i	$-0.266932\pi$
$277$	−1.25141	−	1.25141i	−0.0751900	−	0.0751900i	−0.743702	+	0.668512i	$0.766932\pi$
$278$		0			0
$279$	−7.93868	+	3.62547i	−0.475276	+	0.217051i
$280$		0			0
$281$	−1.23834	+	1.07302i	−0.0738730	+	0.0640113i	−0.691015	−	0.722841i	$-0.742836\pi$
$281$	−1.23834	+	1.07302i	−0.0738730	+	0.0640113i	0.617142	+	0.786852i	$0.288291\pi$
$282$		0			0
$283$	−4.43996	−	20.4101i	−0.263928	−	1.21326i	−0.898004	−	0.439987i	$-0.854983\pi$
$283$	−4.43996	−	20.4101i	−0.263928	−	1.21326i	0.634076	−	0.773271i	$-0.281381\pi$
$284$		0			0
$285$	0.709568	+	0.506813i	0.0420312	+	0.0300210i
$286$		0			0
$287$	23.0702	+	17.2702i	1.36179	+	1.01943i
$288$		0			0
$289$	−5.97613	−	9.29903i	−0.351537	−	0.547002i
$290$		0			0
$291$	2.02988	+	0.927016i	0.118994	+	0.0543427i
$292$		0			0
$293$	13.8875	+	7.58316i	0.811317	+	0.443013i	0.830646	−	0.556800i	$-0.187971\pi$
$293$	13.8875	+	7.58316i	0.811317	+	0.443013i	−0.0193289	+	0.999813i	$0.506153\pi$
$294$		0			0
$295$	−1.12442	−	1.66646i	−0.0654662	−	0.0970249i
$296$		0			0
$297$	2.34004	+	3.12593i	0.135783	+	0.181385i
$298$		0			0
$299$	23.4187	−	1.08353i	1.35434	−	0.0626622i
$300$		0			0
$301$	4.79672	−	33.3619i	0.276478	−	1.92295i
$302$		0			0
$303$	4.01563	−	2.19270i	0.230692	−	0.125967i
$304$		0			0
$305$	−15.8947	−	6.83344i	−0.910129	−	0.391282i
$306$		0			0
$307$	10.4441	−	3.89544i	0.596075	−	0.222324i	−0.0332753	−	0.999446i	$-0.510594\pi$
$307$	10.4441	−	3.89544i	0.596075	−	0.222324i	0.629350	+	0.777122i	$0.283321\pi$
$308$		0			0
$309$	−2.05674	+	1.32179i	−0.117004	+	0.0751938i
$310$		0			0
$311$	1.58760	+	11.0420i	0.0900243	+	0.626133i	0.984020	+	0.178057i	$0.0569813\pi$
$311$	1.58760	+	11.0420i	0.0900243	+	0.626133i	−0.893996	+	0.448075i	$0.852110\pi$
$312$		0			0
$313$	27.5322	−	1.96914i	1.55621	−	0.111303i	0.733473	−	0.679719i	$-0.237898\pi$
$313$	27.5322	−	1.96914i	1.55621	−	0.111303i	0.822741	+	0.568416i	$0.192444\pi$
$314$		0			0
$315$	−15.9388	−	8.24593i	−0.898052	−	0.464605i
$316$		0			0
$317$	−0.396049	+	5.53749i	−0.0222443	+	0.311016i	0.974133	+	0.225975i	$0.0725567\pi$
$317$	−0.396049	+	5.53749i	−0.0222443	+	0.311016i	−0.996377	+	0.0850412i	$0.972898\pi$
$318$		0			0
$319$	6.16876	+	13.5077i	0.345384	+	0.756285i
$320$		0			0
$321$		−	2.57061i		−	0.143478i
$322$		0			0
$323$	−3.95177	+	3.95177i	−0.219882	+	0.219882i
$324$		0			0
$325$	−4.12213	+	24.0917i	−0.228655	+	1.33637i
$326$		0			0
$327$	4.95842	+	0.354633i	0.274201	+	0.0196113i
$328$		0			0
$329$	−16.2630	−	10.4516i	−0.896611	−	0.576217i
$330$		0			0
$331$	−3.32188	+	3.83365i	−0.182587	+	0.210717i	−0.839663	−	0.543108i	$-0.817248\pi$
$331$	−3.32188	+	3.83365i	−0.182587	+	0.210717i	0.657076	+	0.753824i	$0.271793\pi$
$332$		0			0
$333$	6.23993	−	8.33557i	0.341946	−	0.456786i
$334$		0			0
$335$	−5.10885	−	6.51560i	−0.279126	−	0.355985i
$336$		0			0
$337$	−8.02446	−	21.5144i	−0.437120	−	1.17197i	−0.949655	−	0.313298i	$-0.898566\pi$
$337$	−8.02446	−	21.5144i	−0.437120	−	1.17197i	0.512534	−	0.858667i	$-0.328707\pi$
$338$		0			0
$339$	−2.87947	+	0.845490i	−0.156392	+	0.0459207i
$340$		0			0
$341$	1.54729	−	5.26959i	0.0837905	−	0.285364i
$342$		0			0
$343$	−13.7866	+	10.3205i	−0.744405	+	0.557254i
$344$		0			0
$345$	−0.293791	+	3.95241i	−0.0158172	+	0.212791i
$346$		0			0
$347$	−0.0414630	+	0.0310388i	−0.00222585	+	0.00166625i	−0.600390	−	0.799707i	$-0.704988\pi$
$347$	−0.0414630	+	0.0310388i	−0.00222585	+	0.00166625i	0.598164	+	0.801374i	$0.295897\pi$
$348$		0			0
$349$	−3.77903	+	12.8702i	−0.202287	+	0.688926i	0.794385	+	0.607414i	$0.207793\pi$
$349$	−3.77903	+	12.8702i	−0.202287	+	0.688926i	−0.996672	+	0.0815123i	$0.974025\pi$
$350$		0			0
$351$	−10.1640	+	2.98442i	−0.542514	+	0.159297i
$352$		0			0
$353$	−0.0765262	−	0.205175i	−0.00407308	−	0.0109204i	0.934897	−	0.354918i	$-0.115491\pi$
$353$	−0.0765262	−	0.205175i	−0.00407308	−	0.0109204i	−0.938970	+	0.343998i	$0.888219\pi$
$354$		0			0
$355$	−3.77695	+	31.2104i	−0.200460	+	1.65647i
$356$		0			0
$357$	−3.28792	+	4.39215i	−0.174015	+	0.232457i
$358$		0			0
$359$	24.1090	−	27.8233i	1.27243	−	1.46846i	0.457145	−	0.889392i	$-0.348872\pi$
$359$	24.1090	−	27.8233i	1.27243	−	1.46846i	0.815281	−	0.579065i	$-0.196582\pi$
$360$		0			0
$361$	−15.0472	−	9.67027i	−0.791959	−	0.508961i
$362$		0			0
$363$	2.85809	+	0.204415i	0.150011	+	0.0107290i
$364$		0			0
$365$	−21.0130	+	12.0918i	−1.09987	+	0.632916i
$366$		0			0
$367$	−4.06086	+	4.06086i	−0.211975	+	0.211975i	−0.805106	−	0.593131i	$-0.797892\pi$
$367$	−4.06086	+	4.06086i	−0.211975	+	0.211975i	0.593131	+	0.805106i	$0.297892\pi$
$368$		0			0
$369$		−	29.4418i		−	1.53268i
$370$		0			0
$371$	1.21656	+	2.66390i	0.0631607	+	0.138303i
$372$		0			0
$373$	−0.565216	+	7.90276i	−0.0292658	+	0.409189i	0.961611	+	0.274417i	$0.0884848\pi$
$373$	−0.565216	+	7.90276i	−0.0292658	+	0.409189i	−0.990877	+	0.134772i	$0.956970\pi$
$374$		0			0
$375$	−3.95963	−	1.18114i	−0.204475	−	0.0609936i
$376$		0			0
$377$	−40.1823	+	2.87389i	−2.06949	+	0.148013i
$378$		0			0
$379$	3.31146	+	23.0317i	0.170098	+	1.18306i	0.878673	+	0.477425i	$0.158430\pi$
$379$	3.31146	+	23.0317i	0.170098	+	1.18306i	−0.708574	+	0.705636i	$0.750661\pi$
$380$		0			0
$381$	4.02139	−	2.58439i	0.206022	−	0.132402i
$382$		0			0
$383$	−22.1913	+	8.27694i	−1.13392	+	0.422932i	−0.845184	−	0.534476i	$-0.820509\pi$
$383$	−22.1913	+	8.27694i	−1.13392	+	0.422932i	−0.288740	+	0.957407i	$0.593236\pi$
$384$		0			0
$385$	10.4900	−	4.18217i	0.534621	−	0.213143i
$386$		0			0
$387$	−30.2222	+	16.5026i	−1.53628	+	0.838872i
$388$		0			0
$389$	2.61903	−	18.2158i	0.132790	−	0.923576i	−0.809104	−	0.587666i	$-0.800047\pi$
$389$	2.61903	−	18.2158i	0.132790	−	0.923576i	0.941894	−	0.335910i	$-0.109044\pi$
$390$		0			0
$391$	−24.6773	−	6.02233i	−1.24798	−	0.304562i
$392$		0			0
$393$	−2.15134	−	2.87385i	−0.108521	−	0.144967i
$394$		0			0
$395$	−25.9841	+	17.5324i	−1.30740	+	0.882151i
$396$		0			0
$397$	−1.01954	−	0.556714i	−0.0511695	−	0.0279407i	0.453461	−	0.891276i	$-0.350189\pi$
$397$	−1.01954	−	0.556714i	−0.0511695	−	0.0279407i	−0.504630	+	0.863336i	$0.668371\pi$
$398$		0			0
$399$	0.994200	+	0.454036i	0.0497723	+	0.0227302i
$400$		0			0
$401$	11.8571	+	18.4501i	0.592117	+	0.921352i	0.999966	+	0.00830249i	$0.00264279\pi$
$401$	11.8571	+	18.4501i	0.592117	+	0.921352i	−0.407848	+	0.913050i	$0.633721\pi$
$402$		0			0
$403$	11.9274	+	8.92873i	0.594146	+	0.444772i
$404$		0			0
$405$	2.86377	+	17.1805i	0.142302	+	0.853704i
$406$		0			0
$407$	1.39282	+	6.40270i	0.0690397	+	0.317370i
$408$		0			0
$409$	−1.39779	+	1.21119i	−0.0691163	+	0.0598896i	−0.688734	−	0.725014i	$-0.741833\pi$
$409$	−1.39779	+	1.21119i	−0.0691163	+	0.0598896i	0.619618	+	0.784904i	$0.287288\pi$
$410$		0			0
$411$	−0.643876	+	0.294048i	−0.0317601	+	0.0145043i
$412$		0			0
$413$	−1.78178	−	1.78178i	−0.0876755	−	0.0876755i
$414$		0			0
$415$	−6.16340	+	0.579636i	−0.302549	+	0.0284532i
$416$		0			0
$417$	1.17241	−	3.14335i	0.0574131	−	0.153930i
$418$		0			0
$419$	3.34180	+	3.85665i	0.163258	+	0.188410i	0.831484	−	0.555548i	$-0.187492\pi$
$419$	3.34180	+	3.85665i	0.163258	+	0.188410i	−0.668226	+	0.743958i	$0.732946\pi$
$420$		0			0
$421$	19.9438	−	31.0332i	0.972003	−	1.51247i	0.117464	−	0.993077i	$-0.462523\pi$
$421$	19.9438	−	31.0332i	0.972003	−	1.51247i	0.854538	−	0.519388i	$-0.173840\pi$
$422$		0			0
$423$	1.40896	+	19.6998i	0.0685060	+	0.957839i
$424$		0			0
$425$	11.6397	−	23.7879i	0.564607	−	1.15388i
$426$		0			0
$427$	−21.1906	−	4.60973i	−1.02548	−	0.223081i
$428$		0			0
$429$	1.35235	−	2.96124i	0.0652923	−	0.142970i
$430$		0			0
$431$	−7.51696	−	25.6004i	−0.362079	−	1.23313i	−0.916210	−	0.400699i	$-0.868767\pi$
$431$	−7.51696	−	25.6004i	−0.362079	−	1.23313i	0.554131	−	0.832430i	$-0.313051\pi$
$432$		0			0
$433$	9.20200	+	16.8522i	0.442220	+	0.809866i	0.999795	−	0.0202612i	$-0.00644979\pi$
$433$	9.20200	+	16.8522i	0.442220	+	0.809866i	−0.557575	+	0.830127i	$0.688268\pi$
$434$		0			0
$435$	0.333785	−	6.80225i	0.0160038	−	0.326143i
$436$		0			0
$437$	−0.127329	+	5.05868i	−0.00609095	+	0.241989i
$438$		0			0
$439$	−19.1432	−	2.75237i	−0.913654	−	0.131364i	−0.330575	−	0.943780i	$-0.607243\pi$
$439$	−19.1432	−	2.75237i	−0.913654	−	0.131364i	−0.583078	+	0.812416i	$0.698152\pi$
$440$		0			0
$441$	−2.35048	−	0.690164i	−0.111928	−	0.0328650i
$442$		0			0
$443$	−4.02799	+	7.37671i	−0.191376	+	0.350478i	−0.955695	−	0.294360i	$-0.904893\pi$
$443$	−4.02799	+	7.37671i	−0.191376	+	0.350478i	0.764319	+	0.644838i	$0.223075\pi$
$444$		0			0
$445$	−10.7682	−	22.2481i	−0.510460	−	1.05466i
$446$		0			0
$447$	−0.244418	+	1.12357i	−0.0115606	+	0.0531430i
$448$		0			0
$449$	−16.7339	+	2.40597i	−0.789722	+	0.113545i	−0.525362	−	0.850879i	$-0.676070\pi$
$449$	−16.7339	+	2.40597i	−0.789722	+	0.113545i	−0.264361	+	0.964424i	$0.585161\pi$
$450$		0			0
$451$	14.0021	+	12.1329i	0.659335	+	0.571317i
$452$		0			0
$453$	−5.41049	+	1.17698i	−0.254207	+	0.0552993i
$454$		0			0
$455$	0.685253	+	30.6286i	0.0321252	+	1.43589i
$456$		0			0
$457$	16.0613	+	5.99056i	0.751316	+	0.280226i	0.695804	−	0.718232i	$-0.255048\pi$
$457$	16.0613	+	5.99056i	0.751316	+	0.280226i	0.0555119	+	0.998458i	$0.482321\pi$
$458$		0			0
$459$	11.4777			0.535734
$460$		0			0
$461$	16.4854			0.767803			0.383902	−	0.923374i	$-0.374580\pi$
$461$	16.4854			0.767803			0.383902	+	0.923374i	$0.374580\pi$
$462$		0			0
$463$	33.4726	+	12.4846i	1.55560	+	0.580210i	0.972646	−	0.232294i	$-0.0746231\pi$
$463$	33.4726	+	12.4846i	1.55560	+	0.580210i	0.582956	+	0.812503i	$0.301896\pi$
$464$		0			0
$465$	−1.74078	+	1.82045i	−0.0807267	+	0.0844215i
$466$		0			0
$467$	−25.2012	+	5.48218i	−1.16617	+	0.253685i	−0.753658	−	0.657266i	$-0.771713\pi$
$467$	−25.2012	+	5.48218i	−1.16617	+	0.253685i	−0.412514	+	0.910951i	$0.635349\pi$
$468$		0			0
$469$	−7.84323	−	6.79620i	−0.362167	−	0.313819i
$470$		0			0
$471$	1.57090	−	0.225861i	0.0723832	−	0.0104071i
$472$		0			0
$473$	4.60611	−	21.1740i	0.211789	−	0.973580i
$474$		0			0
$475$	−5.12341	−	1.25846i	−0.235078	−	0.0577421i
$476$		0			0
$477$	1.43387	−	2.62593i	0.0656523	−	0.120233i
$478$		0			0
$479$	−5.47981	−	1.60902i	−0.250379	−	0.0735179i	0.154135	−	0.988050i	$-0.450741\pi$
$479$	−5.47981	−	1.60902i	−0.250379	−	0.0735179i	−0.404514	+	0.914532i	$0.632559\pi$
$480$		0			0
$481$	−17.5949	−	2.52977i	−0.802260	−	0.115348i
$482$		0			0
$483$	0.583035	+	4.93344i	0.0265290	+	0.224479i
$484$		0			0
$485$	−13.4852	−	0.661718i	−0.612332	−	0.0300471i
$486$		0			0
$487$	−9.79202	−	17.9328i	−0.443719	−	0.812611i	0.556110	−	0.831109i	$-0.312293\pi$
$487$	−9.79202	−	17.9328i	−0.443719	−	0.812611i	−0.999829	+	0.0184981i	$0.994112\pi$
$488$		0			0
$489$	1.37042	+	4.66721i	0.0619723	+	0.211058i
$490$		0			0
$491$	11.6783	−	25.5719i	0.527034	−	1.15404i	−0.439674	−	0.898158i	$-0.644906\pi$
$491$	11.6783	−	25.5719i	0.527034	−	1.15404i	0.966707	−	0.255885i	$-0.0823668\pi$
$492$		0			0
$493$	42.6516	+	9.27828i	1.92093	+	0.417873i
$494$		0			0
$495$	−9.84289	−	6.01888i	−0.442405	−	0.270529i
$496$		0			0
$497$	2.81117	+	39.3052i	0.126098	+	1.76308i
$498$		0			0
$499$	13.2840	−	20.6704i	0.594676	−	0.925333i	−0.405262	−	0.914200i	$-0.632820\pi$
$499$	13.2840	−	20.6704i	0.594676	−	0.925333i	0.999938	−	0.0111328i	$-0.00354376\pi$
$500$		0			0
$501$	4.91437	+	5.67148i	0.219558	+	0.253383i
$502$		0			0
$503$	7.93626	−	21.2779i	0.353860	−	0.948736i	−0.631061	−	0.775733i	$-0.717380\pi$
$503$	7.93626	−	21.2779i	0.353860	−	0.948736i	0.984921	−	0.173003i	$-0.0553470\pi$
$504$		0			0
$505$	−17.6552	+	21.3207i	−0.785647	+	0.948759i
$506$		0			0
$507$	2.84749	+	2.84749i	0.126462	+	0.126462i
$508$		0			0
$509$	22.8685	−	10.4437i	1.01363	−	0.462909i	0.161853	−	0.986815i	$-0.448253\pi$
$509$	22.8685	−	10.4437i	1.01363	−	0.462909i	0.851776	+	0.523906i	$0.175526\pi$
$510$		0			0
$511$	−22.9658	+	19.8999i	−1.01595	+	0.880321i
$512$		0			0
$513$	−0.486030	−	2.23424i	−0.0214588	−	0.0986443i
$514$		0			0
$515$	8.59745	−	12.0369i	0.378849	−	0.530411i
$516$		0			0
$517$	−9.94963	−	7.44820i	−0.437584	−	0.327571i
$518$		0			0
$519$	−1.57100	−	2.44453i	−0.0689593	−	0.107303i
$520$		0			0
$521$	−27.9954	−	12.7851i	−1.22650	−	0.560124i	−0.306437	−	0.951891i	$-0.599137\pi$
$521$	−27.9954	−	12.7851i	−1.22650	−	0.560124i	−0.920065	+	0.391767i	$0.871864\pi$
$522$		0			0
$523$	22.3107	+	12.1826i	0.975579	+	0.532707i	0.886206	−	0.463292i	$-0.153332\pi$
$523$	22.3107	+	12.1826i	0.975579	+	0.532707i	0.0893734	+	0.995998i	$0.471514\pi$
$524$		0			0
$525$	−5.15438	−	0.507070i	−0.224955	−	0.0221304i
$526$		0			0
$527$	−9.67437	−	12.9235i	−0.421422	−	0.562954i
$528$		0			0
$529$	−19.9499	+	11.4456i	−0.867387	+	0.497634i
$530$		0			0
$531$	−0.366366	+	2.54813i	−0.0158989	+	0.110579i
$532$		0			0
$533$	−44.1143	+	24.0882i	−1.91080	+	1.04338i
$534$		0			0
$535$	5.75977	+	14.4471i	0.249016	+	0.624601i
$536$		0			0
$537$	−0.670234	+	0.249984i	−0.0289227	+	0.0107876i
$538$		0			0
$539$	1.29686	−	0.833444i	0.0558599	−	0.0358990i
$540$		0			0
$541$	−4.48061	−	31.1633i	−0.192636	−	1.33981i	−0.824995	−	0.565139i	$-0.808822\pi$
$541$	−4.48061	−	31.1633i	−0.192636	−	1.33981i	0.632359	−	0.774675i	$-0.282087\pi$
$542$		0			0
$543$	−5.30258	+	0.379248i	−0.227556	+	0.0162751i
$544$		0			0
$545$	−28.6614	+	9.11688i	−1.22772	+	0.390524i
$546$		0			0
$547$	−0.0574578	+	0.803365i	−0.00245672	+	0.0343494i	−0.998533	−	0.0541539i	$-0.982754\pi$
$547$	−0.0574578	+	0.803365i	−0.00245672	+	0.0343494i	0.996076	+	0.0885033i	$0.0282084\pi$
$548$		0			0
$549$	9.20368	+	20.1532i	0.392803	+	0.860120i
$550$		0			0
$551$		−	8.69541i		−	0.370437i
$552$		0			0
$553$	−27.7822	+	27.7822i	−1.18142	+	1.18142i
$554$		0			0
$555$	0.781936	−	2.90161i	0.0331913	−	0.123167i
$556$		0			0
$557$	−4.75069	−	0.339776i	−0.201293	−	0.0143968i	−0.0296716	−	0.999560i	$-0.509446\pi$
$557$	−4.75069	−	0.339776i	−0.201293	−	0.0143968i	−0.171622	+	0.985163i	$0.554901\pi$
$558$		0			0
$559$	49.4534	+	31.7818i	2.09166	+	1.34423i
$560$		0			0
$561$	−2.30988	+	2.66575i	−0.0975234	+	0.112548i
$562$		0			0
$563$	9.24602	−	12.3512i	0.389673	−	0.520542i	−0.562214	−	0.826992i	$-0.690050\pi$
$563$	9.24602	−	12.3512i	0.389673	−	0.520542i	0.951887	+	0.306450i	$0.0991411\pi$
$564$		0			0
$565$	14.2885	−	11.2035i	0.601121	−	0.471337i
$566$		0			0
$567$	7.62941	+	20.4552i	0.320405	+	0.859040i
$568$		0			0
$569$	−6.11606	+	1.79584i	−0.256398	+	0.0752854i	−0.407406	−	0.913247i	$-0.633567\pi$
$569$	−6.11606	+	1.79584i	−0.256398	+	0.0752854i	0.151007	+	0.988533i	$0.451748\pi$
$570$		0			0
$571$	−9.51627	+	32.4094i	−0.398243	+	1.35629i	0.479660	+	0.877455i	$0.340760\pi$
$571$	−9.51627	+	32.4094i	−0.398243	+	1.35629i	−0.877903	+	0.478838i	$0.841058\pi$
$572$		0			0
$573$	−1.34543	+	1.00717i	−0.0562060	+	0.0420753i
$574$		0			0
$575$	−7.20473	−	22.8712i	−0.300458	−	0.953795i
$576$		0			0
$577$	16.5059	−	12.3562i	0.687150	−	0.514394i	−0.197704	−	0.980262i	$-0.563349\pi$
$577$	16.5059	−	12.3562i	0.687150	−	0.514394i	0.884855	+	0.465867i	$0.154258\pi$
$578$		0			0
$579$	−0.722822	+	2.46171i	−0.0300395	+	0.102305i
$580$		0			0
$581$	−7.44521	+	2.18611i	−0.308879	+	0.0906951i
$582$		0			0
$583$	0.657965	+	1.76407i	0.0272501	+	0.0730604i
$584$		0			0
$585$	24.6304	−	19.3126i	1.01834	−	0.798477i
$586$		0			0
$587$	5.74900	−	7.67977i	0.237287	−	0.316978i	−0.666052	−	0.745905i	$-0.732017\pi$
$587$	5.74900	−	7.67977i	0.237287	−	0.316978i	0.903339	+	0.428927i	$0.141108\pi$
$588$		0			0
$589$	−2.10600	+	2.43046i	−0.0867763	+	0.100145i
$590$		0			0
$591$	−7.99346	−	5.13709i	−0.328807	−	0.211312i
$592$		0			0
$593$	18.5731	+	1.32837i	0.762705	+	0.0545497i	0.447272	−	0.894398i	$-0.352396\pi$
$593$	18.5731	+	1.32837i	0.762705	+	0.0545497i	0.315433	+	0.948948i	$0.397850\pi$
$594$		0			0
$595$	8.63727	−	32.0513i	0.354094	−	1.31397i
$596$		0			0
$597$	−3.03650	+	3.03650i	−0.124275	+	0.124275i
$598$		0			0
$599$		−	35.0945i		−	1.43392i	−0.697112	−	0.716962i	$-0.745532\pi$
$599$		−	35.0945i		−	1.43392i	0.697112	−	0.716962i	$-0.254468\pi$
$600$		0			0
$601$	1.90977	+	4.18181i	0.0779012	+	0.170580i	0.944575	−	0.328295i	$-0.106474\pi$
$601$	1.90977	+	4.18181i	0.0779012	+	0.170580i	−0.866674	+	0.498875i	$0.833747\pi$
$602$		0			0
$603$	−0.756382	+	10.5756i	−0.0308022	+	0.430672i
$604$		0			0
$605$	−16.5208	+	5.25507i	−0.671664	+	0.213649i
$606$		0			0
$607$	−14.9440	+	1.06882i	−0.606559	+	0.0433820i	−0.371241	−	0.928536i	$-0.621068\pi$
$607$	−14.9440	+	1.06882i	−0.606559	+	0.0433820i	−0.235318	+	0.971918i	$0.575613\pi$
$608$		0			0
$609$	−1.21486	−	8.44956i	−0.0492287	−	0.342393i
$610$		0			0
$611$	28.3646	−	18.2288i	1.14751	−	0.737460i
$612$		0			0
$613$	28.0785	−	10.4727i	1.13408	−	0.422989i	0.288839	−	0.957378i	$-0.406731\pi$
$613$	28.0785	−	10.4727i	1.13408	−	0.422989i	0.845239	+	0.534388i	$0.179458\pi$
$614$		0			0
$615$	−3.14680	−	7.89304i	−0.126891	−	0.318278i
$616$		0			0
$617$	13.3752	−	7.30339i	0.538464	−	0.294023i	−0.186912	−	0.982377i	$-0.559848\pi$
$617$	13.3752	−	7.30339i	0.538464	−	0.294023i	0.725376	+	0.688353i	$0.241666\pi$
$618$		0			0
$619$	−3.20626	+	22.3000i	−0.128870	+	0.896314i	0.818119	+	0.575049i	$0.195017\pi$
$619$	−3.20626	+	22.3000i	−0.128870	+	0.896314i	−0.946989	+	0.321265i	$0.895892\pi$
$620$		0			0
$621$	7.53126	−	7.16144i	0.302219	−	0.287379i
$622$		0			0
$623$	−18.5664	−	24.8018i	−0.743846	−	0.993662i
$624$		0			0
$625$	24.9000	−	2.23394i	0.996000	−	0.0893578i
$626$		0			0
$627$	0.616726	+	0.336758i	0.0246297	+	0.0134488i
$628$		0			0
$629$	17.5198	+	8.00103i	0.698560	+	0.319022i
$630$		0			0
$631$	−1.49106	−	2.32014i	−0.0593582	−	0.0923632i	0.810306	−	0.586007i	$-0.199301\pi$
$631$	−1.49106	−	2.32014i	−0.0593582	−	0.0923632i	−0.869664	+	0.493644i	$0.835665\pi$
$632$		0			0
$633$	6.79465	+	5.08641i	0.270063	+	0.202167i
$634$		0			0
$635$	−16.8099	+	23.5349i	−0.667082	+	0.933954i
$636$		0			0
$637$	0.888970	+	4.08653i	0.0352223	+	0.161914i
$638$		0			0
$639$	30.4251	−	26.3635i	1.20360	−	1.04292i
$640$		0			0
$641$	14.9434	−	6.82443i	0.590229	−	0.269549i	−0.0978301	−	0.995203i	$-0.531190\pi$
$641$	14.9434	−	6.82443i	0.590229	−	0.269549i	0.688059	+	0.725655i	$0.258463\pi$
$642$		0			0
$643$	−20.4405	−	20.4405i	−0.806094	−	0.806094i	0.177947	−	0.984040i	$-0.443055\pi$
$643$	−20.4405	−	20.4405i	−0.806094	−	0.806094i	−0.984040	+	0.177947i	$0.943055\pi$
$644$		0			0
$645$	−6.33842	+	7.65437i	−0.249575	+	0.301391i
$646$		0			0
$647$	−3.55398	+	9.52859i	−0.139721	+	0.374607i	−0.987898	−	0.155106i	$-0.950428\pi$
$647$	−3.55398	+	9.52859i	−0.139721	+	0.374607i	0.848176	+	0.529714i	$0.177701\pi$
$648$		0			0
$649$	−1.06088	−	1.22432i	−0.0416431	−	0.0480587i
$650$		0			0
$651$	−1.70689	+	2.65597i	−0.0668983	+	0.104096i
$652$		0			0
$653$	1.25129	+	17.4953i	0.0489668	+	0.684645i	0.961354	+	0.275316i	$0.0887825\pi$
$653$	1.25129	+	17.4953i	0.0489668	+	0.684645i	−0.912387	+	0.409329i	$0.865763\pi$
$654$		0			0
$655$	18.5299	+	11.3310i	0.724024	+	0.442738i
$656$		0			0
$657$	30.3360	+	6.59920i	1.18352	+	0.257459i
$658$		0			0
$659$	−2.53094	+	5.54199i	−0.0985914	+	0.215885i	−0.952500	−	0.304537i	$-0.901498\pi$
$659$	−2.53094	+	5.54199i	−0.0985914	+	0.215885i	0.853909	+	0.520422i	$0.174225\pi$
$660$		0			0
$661$	−12.7674	−	43.4819i	−0.496596	−	1.69125i	−0.701668	−	0.712504i	$-0.747561\pi$
$661$	−12.7674	−	43.4819i	−0.496596	−	1.69125i	0.205072	−	0.978747i	$-0.434257\pi$
$662$		0			0
$663$	−4.58595	−	8.39855i	−0.178104	−	0.326172i
$664$		0			0
$665$	−6.60482	−	0.324098i	−0.256124	−	0.0125680i
$666$		0			0
$667$	33.7755	−	20.5241i	1.30779	−	0.794695i
$668$		0			0
$669$	9.53954	+	1.37158i	0.368820	+	0.0530283i
$670$		0			0
$671$	−13.3774	−	3.92797i	−0.516431	−	0.151638i
$672$		0			0
$673$	2.39552	−	4.38708i	0.0923407	−	0.169109i	−0.827426	−	0.561574i	$-0.810196\pi$
$673$	2.39552	−	4.38708i	0.0923407	−	0.169109i	0.919767	+	0.392465i	$0.128378\pi$
$674$		0			0
$675$	5.61279	+	9.26793i	0.216036	+	0.356723i
$676$		0			0
$677$	−3.34684	+	15.3852i	−0.128630	+	0.591301i	0.867032	+	0.498252i	$0.166025\pi$
$677$	−3.34684	+	15.3852i	−0.128630	+	0.591301i	−0.995662	+	0.0930482i	$0.970339\pi$
$678$		0			0
$679$	−16.7510	+	2.40842i	−0.642843	+	0.0924269i
$680$		0			0
$681$	−3.74016	−	3.24087i	−0.143323	−	0.124190i
$682$		0			0
$683$	33.4958	−	7.28657i	1.28168	−	0.278813i	0.480374	−	0.877064i	$-0.340501\pi$
$683$	33.4958	−	7.28657i	1.28168	−	0.278813i	0.801309	+	0.598251i	$0.204137\pi$
$684$		0			0
$685$	2.95979	−	3.09526i	0.113088	−	0.118264i
$686$		0			0
$687$	−2.22082	−	0.828324i	−0.0847297	−	0.0316025i
$688$		0			0
$689$	−5.10772			−0.194589
$690$		0			0
$691$	44.1976			1.68136			0.840678	−	0.541536i	$-0.182157\pi$
$691$	44.1976			1.68136			0.840678	+	0.541536i	$0.182157\pi$
$692$		0			0
$693$	−13.5495	−	5.05370i	−0.514703	−	0.191974i
$694$		0			0
$695$	0.454012	+	20.2928i	0.0172216	+	0.769751i
$696$		0			0
$697$	53.2153	−	11.5763i	2.01567	−	0.438483i
$698$		0			0
$699$	1.09616	+	0.949830i	0.0414607	+	0.0359259i
$700$		0			0
$701$	24.2745	−	3.49014i	0.916835	−	0.131821i	0.332285	−	0.943179i	$-0.392180\pi$
$701$	24.2745	−	3.49014i	0.916835	−	0.131821i	0.584550	+	0.811358i	$0.301271\pi$
$702$		0			0
$703$	0.815588	−	3.74920i	0.0307605	−	0.141404i
$704$		0			0
$705$	2.48329	+	5.13073i	0.0935261	+	0.193234i
$706$		0			0
$707$	−16.6287	+	30.4531i	−0.625385	+	1.14531i
$708$		0			0
$709$	5.74213	+	1.68604i	0.215650	+	0.0633206i	0.387773	−	0.921755i	$-0.373244\pi$
$709$	5.74213	+	1.68604i	0.215650	+	0.0633206i	−0.172123	+	0.985075i	$0.555063\pi$
$710$		0			0
$711$	39.7315	+	5.71252i	1.49005	+	0.214236i
$712$		0			0
$713$	−14.4115	−	2.44364i	−0.539713	−	0.0915150i
$714$		0			0
$715$	−0.965331	+	19.6726i	−0.0361013	+	0.735713i
$716$		0			0
$717$	−5.32169	−	9.74595i	−0.198742	−	0.363969i
$718$		0			0
$719$	12.4880	+	42.5304i	0.465726	+	1.58612i	0.772942	+	0.634476i	$0.218784\pi$
$719$	12.4880	+	42.5304i	0.465726	+	1.58612i	−0.307217	+	0.951640i	$0.599398\pi$
$720$		0			0
$721$	7.70216	−	16.8654i	0.286843	−	0.628099i
$722$		0			0
$723$	4.02799	+	0.876236i	0.149803	+	0.0325876i
$724$		0			0
$725$	13.3654	+	38.9771i	0.496377	+	1.44757i
$726$		0			0
$727$	−0.0364675	−	0.509882i	−0.00135250	−	0.0189105i	0.996731	−	0.0807912i	$-0.0257447\pi$
$727$	−0.0364675	−	0.509882i	−0.00135250	−	0.0189105i	−0.998084	+	0.0618807i	$0.980290\pi$
$728$		0			0
$729$	10.7595	−	16.7421i	0.398501	−	0.620080i
$730$		0			0
$731$	−41.7111	−	48.1371i	−1.54274	−	1.78042i
$732$		0			0
$733$	3.90303	−	10.4644i	0.144162	−	0.386512i	−0.844722	−	0.535206i	$-0.820234\pi$
$733$	3.90303	−	10.4644i	0.144162	−	0.386512i	0.988883	+	0.148694i	$0.0475068\pi$
$734$		0			0
$735$	−0.703906	+	0.0661988i	−0.0259640	+	0.00244178i
$736$		0			0
$737$	−4.71792	−	4.71792i	−0.173787	−	0.173787i
$738$		0			0
$739$	8.74222	−	3.99244i	0.321588	−	0.146864i	−0.248079	−	0.968740i	$-0.579799\pi$
$739$	8.74222	−	3.99244i	0.321588	−	0.146864i	0.569667	+	0.821875i	$0.307072\pi$
$740$		0			0
$741$	−1.44066	+	1.24834i	−0.0529239	+	0.0458589i
$742$		0			0
$743$	−5.01501	−	23.0536i	−0.183983	−	0.845756i	−0.972895	−	0.231249i	$-0.925719\pi$
$743$	−5.01501	−	23.0536i	−0.183983	−	0.845756i	0.788912	−	0.614507i	$-0.210645\pi$
$744$		0			0
$745$	−1.14385	−	6.86221i	−0.0419072	−	0.251412i
$746$		0			0
$747$	6.34621	+	4.75072i	0.232196	+	0.173820i
$748$		0			0
$749$	10.5396	+	16.3999i	0.385107	+	0.599239i
$750$		0			0
$751$	−2.26519	−	1.03448i	−0.0826579	−	0.0377486i	0.373657	−	0.927567i	$-0.378104\pi$
$751$	−2.26519	−	1.03448i	−0.0826579	−	0.0377486i	−0.456315	+	0.889818i	$0.650831\pi$
$752$		0			0
$753$	5.19730	+	2.83794i	0.189400	+	0.103420i
$754$		0			0
$755$	27.7703	−	18.7376i	1.01066	−	0.681931i
$756$		0			0
$757$	0.291836	+	0.389847i	0.0106069	+	0.0141692i	0.805813	−	0.592170i	$-0.201728\pi$
$757$	0.291836	+	0.389847i	0.0106069	+	0.0141692i	−0.795206	+	0.606339i	$0.792638\pi$
$758$		0			0
$759$	0.147613	+	3.19040i	0.00535801	+	0.115804i
$760$		0			0
$761$	−0.660261	+	4.59221i	−0.0239344	+	0.166468i	−0.998283	−	0.0585770i	$-0.981344\pi$
$761$	−0.660261	+	4.59221i	−0.0239344	+	0.166468i	0.974348	+	0.225045i	$0.0722528\pi$
$762$		0			0
$763$	−33.0876	+	18.0672i	−1.19785	+	0.654076i
$764$		0			0
$765$	−31.5016	+	12.5591i	−1.13894	+	0.454074i
$766$		0			0
$767$	4.11775	−	1.53584i	0.148683	−	0.0554560i
$768$		0			0
$769$	−9.47678	+	6.09036i	−0.341742	+	0.219624i	−0.700242	−	0.713906i	$-0.746925\pi$
$769$	−9.47678	+	6.09036i	−0.341742	+	0.219624i	0.358500	+	0.933530i	$0.383288\pi$
$770$		0			0
$771$	0.798353	+	5.55267i	0.0287520	+	0.199974i
$772$		0			0
$773$	−8.70288	+	0.622442i	−0.313021	+	0.0223877i	−0.226966	−	0.973903i	$-0.572881\pi$
$773$	−8.70288	+	0.622442i	−0.313021	+	0.0223877i	−0.0860548	+	0.996290i	$0.527426\pi$
$774$		0			0
$775$	5.70439	−	14.1315i	0.204908	−	0.507620i
$776$		0			0
$777$	0.268716	−	3.75714i	0.00964013	−	0.134787i
$778$		0			0
$779$	−4.50686	−	9.86864i	−0.161475	−	0.353581i
$780$		0			0
$781$			25.3342i			0.906528i
$782$		0			0
$783$	−12.6277	+	12.6277i	−0.451278	+	0.451278i
$784$		0			0
$785$	−8.32253	+	4.78915i	−0.297044	+	0.170932i
$786$		0			0
$787$	−13.5149	−	0.966608i	−0.481756	−	0.0344559i	−0.171650	−	0.985158i	$-0.554910\pi$
$787$	−13.5149	−	0.966608i	−0.481756	−	0.0344559i	−0.310106	+	0.950702i	$0.600364\pi$
$788$		0			0
$789$	−5.22536	−	3.35814i	−0.186028	−	0.119553i
$790$		0			0
$791$	14.9038	−	17.1999i	0.529919	−	0.611559i
$792$		0			0
$793$	22.6666	−	30.2790i	0.804915	−	1.07524i
$794$		0			0
$795$	0.103740	−	0.857239i	0.00367927	−	0.0304031i
$796$		0			0
$797$	−0.453070	−	1.21473i	−0.0160486	−	0.0430279i	0.928678	−	0.370886i	$-0.120946\pi$
$797$	−0.453070	−	1.21473i	−0.0160486	−	0.0430279i	−0.944727	+	0.327858i	$0.893673\pi$
$798$		0			0
$799$	−35.0530	+	10.2925i	−1.24008	+	0.364122i
$800$		0			0
$801$	−8.91727	+	30.3694i	−0.315076	+	1.07305i
$802$		0			0
$803$	−15.6399	+	11.7079i	−0.551921	+	0.413163i
$804$		0			0
$805$	−14.3307	−	26.4200i	−0.505090	−	0.931183i
$806$		0			0
$807$	4.26239	−	3.19078i	0.150043	−	0.112321i
$808$		0			0
$809$	4.70265	−	16.0158i	0.165336	−	0.563084i	−0.834589	−	0.550873i	$-0.814295\pi$
$809$	4.70265	−	16.0158i	0.165336	−	0.563084i	0.999925	−	0.0122112i	$-0.00388703\pi$
$810$		0			0
$811$	−46.0855	+	13.5319i	−1.61828	+	0.475170i	−0.960556	−	0.278087i	$-0.910300\pi$
$811$	−46.0855	+	13.5319i	−1.61828	+	0.475170i	−0.657726	+	0.753258i	$0.728481\pi$
$812$		0			0
$813$	−2.64202	−	7.08352i	−0.0926595	−	0.248430i
$814$		0			0
$815$	−18.1593	−	23.1596i	−0.636093	−	0.811244i
$816$		0			0
$817$	−7.60405	+	10.1578i	−0.266032	+	0.355377i
$818$		0			0
$819$	25.6911	−	29.6491i	0.897720	−	1.03602i
$820$		0			0
$821$	−14.5467	−	9.34857i	−0.507682	−	0.326267i	0.261601	−	0.965176i	$-0.415750\pi$
$821$	−14.5467	−	9.34857i	−0.507682	−	0.326267i	−0.769282	+	0.638909i	$0.779386\pi$
$822$		0			0
$823$	34.8254	+	2.49076i	1.21394	+	0.0868226i	0.663580	−	0.748106i	$-0.269036\pi$
$823$	34.8254	+	2.49076i	1.21394	+	0.0868226i	0.550359	+	0.834928i	$0.314491\pi$
$824$		0			0
$825$	−3.28208	−	0.561571i	−0.114268	−	0.0195514i
$826$		0			0
$827$	14.6344	−	14.6344i	0.508887	−	0.508887i	−0.405298	−	0.914185i	$-0.632832\pi$
$827$	14.6344	−	14.6344i	0.508887	−	0.508887i	0.914185	+	0.405298i	$0.132832\pi$
$828$		0			0
$829$			2.31849i			0.0805245i	0.999189	+	0.0402622i	$0.0128193\pi$
$829$			2.31849i			0.0805245i	−0.999189	+	0.0402622i	$0.987181\pi$
$830$		0			0
$831$	0.271711	+	0.594964i	0.00942554	+	0.0206391i
$832$		0			0
$833$	0.323263	−	4.51981i	0.0112004	−	0.156602i
$834$		0			0
$835$	−40.3268	−	20.8630i	−1.39557	−	0.721994i
$836$		0			0
$837$	6.58797	−	0.471181i	0.227713	−	0.0162864i
$838$		0			0
$839$	0.891721	+	6.20206i	0.0307856	+	0.214119i	0.999407	−	0.0344205i	$-0.0109586\pi$
$839$	0.891721	+	6.20206i	0.0307856	+	0.214119i	−0.968622	+	0.248539i	$0.920049\pi$
$840$		0			0
$841$	−32.7365	+	21.0385i	−1.12885	+	0.725465i
$842$		0			0
$843$	0.567397	−	0.211628i	0.0195422	−	0.00728886i
$844$		0			0
$845$	−22.3833	−	9.62302i	−0.770010	−	0.331042i
$846$		0			0
$847$	−19.0721	+	10.4141i	−0.655324	+	0.357834i
$848$		0			0
$849$	−1.09862	+	7.64105i	−0.0377044	+	0.262240i
$850$		0			0
$851$	16.4880	−	5.68137i	0.565202	−	0.194755i
$852$		0			0
$853$	28.0661	+	37.4920i	0.960966	+	1.28370i	0.958912	+	0.283703i	$0.0915629\pi$
$853$	28.0661	+	37.4920i	0.960966	+	1.28370i	0.00205389	+	0.999998i	$0.499346\pi$
$854$		0			0
$855$	3.77869	+	5.60025i	0.129228	+	0.191525i
$856$		0			0
$857$	13.7069	+	7.48454i	0.468219	+	0.255667i	0.695995	−	0.718047i	$-0.254964\pi$
$857$	13.7069	+	7.48454i	0.468219	+	0.255667i	−0.227776	+	0.973714i	$0.573145\pi$
$858$		0			0
$859$	−39.1911	−	17.8980i	−1.33718	−	0.610671i	−0.386918	−	0.922114i	$-0.626461\pi$
$859$	−39.1911	−	17.8980i	−1.33718	−	0.610671i	−0.950265	+	0.311443i	$0.899188\pi$
$860$		0			0
$861$	−5.75821	−	8.95995i	−0.196239	−	0.305354i
$862$		0			0
$863$	−2.02509	−	1.51597i	−0.0689350	−	0.0516041i	0.564254	−	0.825601i	$-0.309164\pi$
$863$	−2.02509	−	1.51597i	−0.0689350	−	0.0516041i	−0.633189	+	0.773997i	$0.718255\pi$
$864$		0			0
$865$	14.3064	+	10.2184i	0.486433	+	0.347438i
$866$		0			0
$867$	0.868387	+	3.99191i	0.0294920	+	0.135572i
$868$		0			0
$869$	−19.0901	+	16.5417i	−0.647587	+	0.561137i
$870$		0			0
$871$	16.4649	−	7.51925i	0.557890	−	0.254780i
$872$		0			0
$873$	12.2254	+	12.2254i	0.413768	+	0.413768i
$874$		0			0
$875$	30.1042	−	8.69923i	1.01771	−	0.294087i
$876$		0			0
$877$	13.0295	−	34.9335i	0.439976	−	1.17962i	−0.508021	−	0.861345i	$-0.669623\pi$
$877$	13.0295	−	34.9335i	0.439976	−	1.17962i	0.947998	−	0.318278i	$-0.103104\pi$
$878$		0			0
$879$	−3.82955	−	4.41954i	−0.129168	−	0.149067i
$880$		0			0
$881$	−26.9854	+	41.9901i	−0.909161	+	1.41468i	0.000805510		1.00000i	$0.499744\pi$
$881$	−26.9854	+	41.9901i	−0.909161	+	1.41468i	−0.909966	+	0.414682i	$0.863893\pi$
$882$		0			0
$883$	2.35681	+	32.9525i	0.0793130	+	1.10894i	0.868796	+	0.495169i	$0.164894\pi$
$883$	2.35681	+	32.9525i	0.0793130	+	1.10894i	−0.789483	+	0.613772i	$0.789651\pi$
$884$		0			0
$885$	0.174130	+	0.722284i	0.00585333	+	0.0242793i
$886$		0			0
$887$	21.4727	+	4.67110i	0.720983	+	0.156840i	0.558062	−	0.829799i	$-0.311545\pi$
$887$	21.4727	+	4.67110i	0.720983	+	0.156840i	0.162920	+	0.986639i	$0.447909\pi$
$888$		0			0
$889$	−15.0594	+	32.9756i	−0.505077	+	1.10596i
$890$		0			0
$891$	3.95434	+	13.4672i	0.132475	+	0.451169i
$892$		0			0
$893$	3.48786	+	6.38754i	0.116717	+	0.213751i
$894$		0			0
$895$	3.20666	−	2.90668i	0.107187	−	0.0971595i
$896$		0			0
$897$	−8.24934	−	2.64944i	−0.275437	−	0.0884624i
$898$		0			0
$899$	24.8620	+	3.57461i	0.829193	+	0.119220i
$900$		0			0
$901$	5.31009	+	1.55918i	0.176905	+	0.0519439i
$902$		0			0
$903$	−5.96987	+	10.9330i	−0.198665	+	0.363828i
$904$		0			0
$905$	28.9512	−	14.0125i	0.962372	−	0.465791i
$906$		0			0
$907$	−6.73448	+	30.9579i	−0.223615	+	1.02794i	0.719246	+	0.694755i	$0.244487\pi$
$907$	−6.73448	+	30.9579i	−0.223615	+	1.02794i	−0.942861	+	0.333186i	$0.891876\pi$
$908$		0			0
$909$	35.0872	−	5.04478i	1.16377	−	0.167325i
$910$		0			0
$911$	40.4318	+	35.0343i	1.33956	+	1.16074i	0.973120	+	0.230299i	$0.0739704\pi$
$911$	40.4318	+	35.0343i	1.33956	+	1.16074i	0.366444	+	0.930440i	$0.380575\pi$
$912$		0			0
$913$	−4.87465	+	1.06041i	−0.161327	+	0.0350946i
$914$		0			0
$915$	4.62143	+	4.41916i	0.152780	+	0.146093i
$916$		0			0
$917$	25.5079	+	9.51395i	0.842345	+	0.314178i
$918$		0			0
$919$	−19.8127			−0.653560			−0.326780	−	0.945100i	$-0.605964\pi$
$919$	−19.8127			−0.653560			−0.326780	+	0.945100i	$0.605964\pi$
$920$		0			0
$921$	−4.11968			−0.135748
$922$		0			0
$923$	−64.3947	−	24.0180i	−2.11958	−	0.790561i
$924$		0			0
$925$	2.10687	+	18.0594i	0.0692733	+	0.593788i
$926$		0			0
$927$	−18.5091	+	4.02642i	−0.607920	+	0.132245i
$928$		0			0
$929$	−28.6021	−	24.7839i	−0.938406	−	0.813133i	0.0441648	−	0.999024i	$-0.485937\pi$
$929$	−28.6021	−	24.7839i	−0.938406	−	0.813133i	−0.982570	+	0.185891i	$0.940483\pi$
$930$		0			0
$931$	−0.893510	+	0.128467i	−0.0292836	+	0.00421035i
$932$		0			0
$933$	0.876379	−	4.02865i	0.0286914	−	0.131892i
$934$		0			0
$935$	7.00883	−	20.1573i	0.229213	−	0.659215i
$936$		0			0
$937$	−7.86151	+	14.3973i	−0.256824	+	0.470339i	−0.973998	−	0.226555i	$-0.927254\pi$
$937$	−7.86151	+	14.3973i	−0.256824	+	0.470339i	0.717174	+	0.696894i	$0.245435\pi$
$938$		0			0
$939$	−9.78816	−	2.87406i	−0.319425	−	0.0937915i
$940$		0			0
$941$	−14.6748	−	2.10992i	−0.478386	−	0.0687815i	−0.101096	−	0.994877i	$-0.532235\pi$
$941$	−14.6748	−	2.10992i	−0.478386	−	0.0687815i	−0.377290	+	0.926095i	$0.623144\pi$
$942$		0			0
$943$	27.6950	−	40.7992i	0.901873	−	1.32860i
$944$		0			0
$945$	9.12103	+	10.0624i	0.296707	+	0.327329i
$946$		0			0
$947$	−6.81890	−	12.4879i	−0.221584	−	0.405802i	0.743112	−	0.669168i	$-0.233349\pi$
$947$	−6.81890	−	12.4879i	−0.221584	−	0.405802i	−0.964696	+	0.263366i	$0.915167\pi$
$948$		0			0
$949$	−14.9319	−	50.8534i	−0.484710	−	1.65077i
$950$		0			0
$951$	0.852340	−	1.86636i	0.0276390	−	0.0605210i
$952$		0			0
$953$	−32.4283	−	7.05434i	−1.05045	−	0.228512i	−0.345980	−	0.938242i	$-0.612454\pi$
$953$	−32.4283	−	7.05434i	−1.05045	−	0.228512i	−0.704475	+	0.709729i	$0.748817\pi$
$954$		0			0
$955$	5.30473	−	8.67500i	0.171657	−	0.280716i
$956$		0			0
$957$	−0.391520	−	5.47416i	−0.0126560	−	0.176954i
$958$		0			0
$959$	2.90217	−	4.51587i	0.0937160	−	0.145825i
$960$		0			0
$961$	14.2173	+	16.4076i	0.458622	+	0.529278i
$962$		0			0
$963$	6.96005	−	18.6606i	0.224285	−	0.601330i
$964$		0			0
$965$	−1.45343	−	15.4546i	−0.0467874	−	0.497501i
$966$		0			0
$967$	−32.0256	−	32.0256i	−1.02987	−	1.02987i	−0.999540	−	0.0303327i	$-0.990343\pi$
$967$	−32.0256	−	32.0256i	−1.02987	−	1.02987i	−0.0303327	−	0.999540i	$-0.509657\pi$
$968$		0			0
$969$	1.87881	−	0.858022i	0.0603560	−	0.0275636i
$970$		0			0
$971$	−1.19662	+	1.03688i	−0.0384013	+	0.0332749i	−0.673850	−	0.738868i	$-0.735361\pi$
$971$	−1.19662	+	1.03688i	−0.0384013	+	0.0332749i	0.635449	+	0.772143i	$0.280815\pi$
$972$		0			0
$973$	5.40812	+	24.8607i	0.173376	+	0.796998i
$974$		0			0
$975$	4.53898	−	7.81004i	0.145364	−	0.250122i
$976$		0			0
$977$	−43.1150	−	32.2755i	−1.37937	−	1.03259i	−0.993949	−	0.109846i	$-0.964964\pi$
$977$	−43.1150	−	32.2755i	−1.37937	−	1.03259i	−0.385424	−	0.922740i	$-0.625945\pi$
$978$		0			0
$979$	−10.7685	−	16.7562i	−0.344164	−	0.535529i
$980$		0			0
$981$	35.0341	+	15.9995i	1.11855	+	0.510826i
$982$		0			0
$983$	1.17077	+	0.639289i	0.0373418	+	0.0203901i	0.497811	−	0.867285i	$-0.334137\pi$
$983$	1.17077	+	0.639289i	0.0373418	+	0.0203901i	−0.460470	+	0.887675i	$0.652319\pi$
$984$		0			0
$985$	56.4343	+	10.9606i	1.79815	+	0.349233i
$986$		0			0
$987$	4.28167	+	5.71964i	0.136287	+	0.182058i
$988$		0			0
$989$	−57.4040	−	5.56051i	−1.82534	−	0.176814i
$990$		0			0
$991$	−0.0908562	+	0.631919i	−0.00288614	+	0.0200736i	−0.991214	−	0.132271i	$-0.957773\pi$
$991$	−0.0908562	+	0.631919i	−0.00288614	+	0.0200736i	0.988327	+	0.152344i	$0.0486823\pi$
$992$		0			0
$993$	1.64543	−	0.898475i	0.0522163	−	0.0285122i
$994$		0			0
$995$	10.2617	−	23.8690i	0.325319	−	0.756699i
$996$		0			0
$997$	−38.8496	+	14.4901i	−1.23038	+	0.458908i	−0.878773	−	0.477241i	$-0.841637\pi$
$997$	−38.8496	+	14.4901i	−1.23038	+	0.458908i	−0.351606	+	0.936148i	$0.614364\pi$
$998$		0			0
$999$	−6.62911	+	4.26027i	−0.209736	+	0.134789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.337.6	yes	240
5.3	odd	4	inner	460.2.x.a.153.7	✓	240
23.20	odd	22	inner	460.2.x.a.457.7	yes	240
115.43	even	44	inner	460.2.x.a.273.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.153.7	✓	240	5.3	odd	4	inner
460.2.x.a.273.6	yes	240	115.43	even	44	inner
460.2.x.a.337.6	yes	240	1.1	even	1	trivial
460.2.x.a.457.7	yes	240	23.20	odd	22	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.346279 - 0.129155i) q^{3} +(2.23551 - 0.0500151i) q^{5} +(2.73872 - 0.595772i) q^{7} +(-2.16402 - 1.87513i) q^{9} +O(q^{10})\)	\(q+(-0.346279 - 0.129155i) q^{3} +(2.23551 - 0.0500151i) q^{5} +(2.73872 - 0.595772i) q^{7} +(-2.16402 - 1.87513i) q^{9} +(1.78358 - 0.256440i) q^{11} +(-1.03909 + 4.77664i) q^{13} +(-0.780569 - 0.271409i) q^{15} +(2.53838 - 4.64870i) q^{17} +(-1.01240 - 0.297268i) q^{19} +(-1.02531 - 0.147417i) q^{21} +(-1.23493 - 4.63411i) q^{23} +(4.99500 - 0.223618i) q^{25} +(1.03854 + 1.90194i) q^{27} +(2.32176 + 7.90718i) q^{29} +(1.26614 - 2.77246i) q^{31} +(-0.650737 - 0.141559i) q^{33} +(6.09263 - 1.46883i) q^{35} +(0.259416 + 3.62710i) q^{37} +(0.976746 - 1.51985i) q^{39} +(6.73333 + 7.77068i) q^{41} +(4.20251 - 11.2674i) q^{43} +(-4.93147 - 4.08365i) q^{45} +(-4.87722 - 4.87722i) q^{47} +(0.778212 - 0.355397i) q^{49} +(-1.47939 + 1.28190i) q^{51} +(0.222104 + 1.02100i) q^{53} +(3.97438 - 0.662480i) q^{55} +(0.312179 + 0.233695i) q^{57} +(-0.486060 - 0.756324i) q^{59} +(-7.03820 - 3.21424i) q^{61} +(-7.04380 - 3.84620i) q^{63} +(-2.08400 + 10.7302i) q^{65} +(-2.21900 - 2.96424i) q^{67} +(-0.170890 + 1.76419i) q^{69} +(-2.00088 + 13.9164i) q^{71} +(-9.51592 + 5.19609i) q^{73} +(-1.75854 - 0.567697i) q^{75} +(4.73194 - 1.76492i) q^{77} +(-11.7929 + 7.57885i) q^{79} +(1.10854 + 7.71006i) q^{81} +(-2.76146 + 0.197504i) q^{83} +(5.44207 - 10.5192i) q^{85} +(0.217279 - 3.03796i) q^{87} +(-4.59191 - 10.0549i) q^{89} +13.7009i q^{91} +(-0.796515 + 0.796515i) q^{93} +(-2.27810 - 0.613909i) q^{95} +(-6.02265 - 0.430748i) q^{97} +(-4.34056 - 2.78951i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3}+O(q^{10}) \) 240 * q + 4 * q^3	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75} + 36 q^{77} + 200 q^{81} - 28 q^{85} + 16 q^{87} - 88 q^{93} - 86 q^{95} - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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