LMFDB - Embedded newform 920.2.bv.a.617.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [920,2,Mod(17,920)] 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("920.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(920, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([0, 0, 11, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bv (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$720$
Relative dimension:	$36$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			617.9
Character	$\chi$	$=$	920.617
Dual form			920.2.bv.a.753.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.934747 + 1.71186i) q^{3} +(-0.159531 + 2.23037i) q^{5} +(-2.01195 - 1.50613i) q^{7} +(-0.434794 - 0.676553i) q^{9} +(-4.24123 - 1.93690i) q^{11} +(-1.69828 - 2.26863i) q^{13} +(-3.66896 - 2.35793i) q^{15} +(1.41764 + 0.101392i) q^{17} +(3.21223 - 3.70711i) q^{19} +(4.45894 - 2.03633i) q^{21} +(2.13210 - 4.29583i) q^{23} +(-4.94910 - 0.711624i) q^{25} +(-4.27183 + 0.305527i) q^{27} +(-1.05670 + 0.915636i) q^{29} +(3.73483 + 1.09665i) q^{31} +(7.28018 - 5.44988i) q^{33} +(3.68019 - 4.24712i) q^{35} +(-1.33764 + 6.14902i) q^{37} +(5.47104 - 0.786617i) q^{39} +(4.26137 + 2.73861i) q^{41} +(-7.77896 - 4.24763i) q^{43} +(1.57833 - 0.861821i) q^{45} +(3.58322 + 3.58322i) q^{47} +(-0.192605 - 0.655954i) q^{49} +(-1.49870 + 2.33203i) q^{51} +(-1.11004 + 1.48283i) q^{53} +(4.99661 - 9.15051i) q^{55} +(3.34343 + 8.96409i) q^{57} +(7.19858 + 1.03500i) q^{59} +(2.56930 - 8.75023i) q^{61} +(-0.144190 + 2.01605i) q^{63} +(5.33081 - 3.42587i) q^{65} +(-6.08607 - 2.26999i) q^{67} +(5.36089 + 7.66538i) q^{69} +(-6.51918 - 14.2750i) q^{71} +(-0.952316 - 13.3151i) q^{73} +(5.84436 - 7.80698i) q^{75} +(5.61591 + 10.2848i) q^{77} +(0.712802 - 4.95765i) q^{79} +(4.47231 - 9.79300i) q^{81} +(-9.01603 - 1.96132i) q^{83} +(-0.452298 + 3.14569i) q^{85} +(-0.579694 - 2.66481i) q^{87} +(-0.00355312 + 0.00104329i) q^{89} +7.12219i q^{91} +(-5.36843 + 5.36843i) q^{93} +(7.75577 + 7.75585i) q^{95} +(-14.8900 + 3.23913i) q^{97} +(0.533643 + 3.71157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) $ 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{15}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−0.934747	+	1.71186i	−0.539676	+	0.988343i	0.455499	+	0.890236i	$0.349461\pi$
$3$	−0.934747	+	1.71186i	−0.539676	+	0.988343i	−0.995176	+	0.0981074i	$0.968721\pi$
$4$		0			0
$5$	−0.159531	+	2.23037i	−0.0713442	+	0.997452i
$5$	−0.159531	+	2.23037i	−0.0713442	+	0.997452i
$6$		0			0
$7$	−2.01195	−	1.50613i	−0.760445	−	0.569262i	0.147147	−	0.989115i	$-0.452991\pi$
$7$	−2.01195	−	1.50613i	−0.760445	−	0.569262i	−0.907592	+	0.419852i	$0.862082\pi$
$8$		0			0
$9$	−0.434794	−	0.676553i	−0.144931	−	0.225518i
$10$		0			0
$11$	−4.24123	−	1.93690i	−1.27878	−	0.583998i	−0.343913	−	0.939002i	$-0.611752\pi$
$11$	−4.24123	−	1.93690i	−1.27878	−	0.583998i	−0.934865	+	0.355003i	$0.884480\pi$
$12$		0			0
$13$	−1.69828	−	2.26863i	−0.471017	−	0.629205i	0.500624	−	0.865665i	$-0.333104\pi$
$13$	−1.69828	−	2.26863i	−0.471017	−	0.629205i	−0.971641	+	0.236460i	$0.924013\pi$
$14$		0			0
$15$	−3.66896	−	2.35793i	−0.947322	−	0.608814i
$16$		0			0
$17$	1.41764	+	0.101392i	0.343828	+	0.0245911i	0.242186	−	0.970230i	$-0.422136\pi$
$17$	1.41764	+	0.101392i	0.343828	+	0.0245911i	0.101643	+	0.994821i	$0.467590\pi$
$18$		0			0
$19$	3.21223	−	3.70711i	0.736935	−	0.850468i	−0.256299	−	0.966598i	$-0.582503\pi$
$19$	3.21223	−	3.70711i	0.736935	−	0.850468i	0.993234	+	0.116129i	$0.0370487\pi$
$20$		0			0
$21$	4.45894	−	2.03633i	0.973021	−	0.444364i
$22$		0			0
$23$	2.13210	−	4.29583i	0.444574	−	0.895742i
$23$	2.13210	−	4.29583i	0.444574	−	0.895742i
$24$		0			0
$25$	−4.94910	−	0.711624i	−0.989820	−	0.142325i
$26$		0			0
$27$	−4.27183	+	0.305527i	−0.822113	+	0.0587987i
$28$		0			0
$29$	−1.05670	+	0.915636i	−0.196224	+	0.170029i	−0.747431	−	0.664339i	$-0.768713\pi$
$29$	−1.05670	+	0.915636i	−0.196224	+	0.170029i	0.551207	+	0.834369i	$0.314168\pi$
$30$		0			0
$31$	3.73483	+	1.09665i	0.670795	+	0.196963i	0.599357	−	0.800482i	$-0.295423\pi$
$31$	3.73483	+	1.09665i	0.670795	+	0.196963i	0.0714382	+	0.997445i	$0.477241\pi$
$32$		0			0
$33$	7.28018	−	5.44988i	1.26732	−	0.948702i
$34$		0			0
$35$	3.68019	−	4.24712i	0.622065	−	0.717894i
$36$		0			0
$37$	−1.33764	+	6.14902i	−0.219906	+	1.01089i	0.726312	+	0.687365i	$0.241233\pi$
$37$	−1.33764	+	6.14902i	−0.219906	+	1.01089i	−0.946219	+	0.323528i	$0.895131\pi$
$38$		0			0
$39$	5.47104	−	0.786617i	0.876068	−	0.125960i
$40$		0			0
$41$	4.26137	+	2.73861i	0.665514	+	0.427700i	0.829306	−	0.558795i	$-0.188736\pi$
$41$	4.26137	+	2.73861i	0.665514	+	0.427700i	−0.163792	+	0.986495i	$0.552373\pi$
$42$		0			0
$43$	−7.77896	−	4.24763i	−1.18628	−	0.647758i	−0.239895	−	0.970799i	$-0.577113\pi$
$43$	−7.77896	−	4.24763i	−1.18628	−	0.647758i	−0.946385	+	0.323041i	$0.895295\pi$
$44$		0			0
$45$	1.57833	−	0.861821i	0.235283	−	0.128473i
$46$		0			0
$47$	3.58322	+	3.58322i	0.522666	+	0.522666i	0.918376	−	0.395710i	$-0.129501\pi$
$47$	3.58322	+	3.58322i	0.522666	+	0.522666i	−0.395710	+	0.918376i	$0.629501\pi$
$48$		0			0
$49$	−0.192605	−	0.655954i	−0.0275151	−	0.0937077i
$50$		0			0
$51$	−1.49870	+	2.33203i	−0.209860	+	0.326549i
$52$		0			0
$53$	−1.11004	+	1.48283i	−0.152475	+	0.203683i	−0.870274	−	0.492567i	$-0.836059\pi$
$53$	−1.11004	+	1.48283i	−0.152475	+	0.203683i	0.717799	+	0.696250i	$0.245149\pi$
$54$		0			0
$55$	4.99661	−	9.15051i	0.673743	−	1.23385i
$56$		0			0
$57$	3.34343	+	8.96409i	0.442848	+	1.18732i
$58$		0			0
$59$	7.19858	+	1.03500i	0.937175	+	0.134745i	0.593945	−	0.804506i	$-0.297570\pi$
$59$	7.19858	+	1.03500i	0.937175	+	0.134745i	0.343231	+	0.939251i	$0.388479\pi$
$60$		0			0
$61$	2.56930	−	8.75023i	0.328965	−	1.12035i	−0.614510	−	0.788909i	$-0.710646\pi$
$61$	2.56930	−	8.75023i	0.328965	−	1.12035i	0.943475	−	0.331443i	$-0.107536\pi$
$62$		0			0
$63$	−0.144190	+	2.01605i	−0.0181663	+	0.253998i
$64$		0			0
$65$	5.33081	−	3.42587i	0.661206	−	0.424927i
$66$		0			0
$67$	−6.08607	−	2.26999i	−0.743532	−	0.277323i	−0.0509887	−	0.998699i	$-0.516237\pi$
$67$	−6.08607	−	2.26999i	−0.743532	−	0.277323i	−0.692544	+	0.721376i	$0.743510\pi$
$68$		0			0
$69$	5.36089	+	7.66538i	0.645375	+	0.922803i
$70$		0			0
$71$	−6.51918	−	14.2750i	−0.773684	−	1.69413i	−0.718368	−	0.695663i	$-0.755111\pi$
$71$	−6.51918	−	14.2750i	−0.773684	−	1.69413i	−0.0553161	−	0.998469i	$-0.517617\pi$
$72$		0			0
$73$	−0.952316	−	13.3151i	−0.111460	−	1.55842i	−0.678422	−	0.734673i	$-0.737336\pi$
$73$	−0.952316	−	13.3151i	−0.111460	−	1.55842i	0.566962	−	0.823744i	$-0.308119\pi$
$74$		0			0
$75$	5.84436	−	7.80698i	0.674848	−	0.901473i
$76$		0			0
$77$	5.61591	+	10.2848i	0.639992	+	1.17206i
$78$		0			0
$79$	0.712802	−	4.95765i	0.0801965	−	0.557779i	−0.909621	−	0.415439i	$-0.863628\pi$
$79$	0.712802	−	4.95765i	0.0801965	−	0.557779i	0.989818	−	0.142341i	$-0.0454628\pi$
$80$		0			0
$81$	4.47231	−	9.79300i	0.496924	−	1.08811i
$82$		0			0
$83$	−9.01603	−	1.96132i	−0.989638	−	0.215283i	−0.311523	−	0.950239i	$-0.600839\pi$
$83$	−9.01603	−	1.96132i	−0.989638	−	0.215283i	−0.678115	+	0.734956i	$0.737203\pi$
$84$		0			0
$85$	−0.452298	+	3.14569i	−0.0490586	+	0.341198i
$86$		0			0
$87$	−0.579694	−	2.66481i	−0.0621497	−	0.285698i
$88$		0			0
$89$	−0.00355312	+	0.00104329i	−0.000376630	+	0.000110588i	−0.281921	−	0.959438i	$-0.590972\pi$
$89$	−0.00355312	+	0.00104329i	−0.000376630	+	0.000110588i	0.281544	+	0.959548i	$0.409153\pi$
$90$		0			0
$91$			7.12219i			0.746608i
$92$		0			0
$93$	−5.36843	+	5.36843i	−0.556680	+	0.556680i
$94$		0			0
$95$	7.75577	+	7.75585i	0.795725	+	0.795733i
$96$		0			0
$97$	−14.8900	+	3.23913i	−1.51185	+	0.328883i	−0.890622	−	0.454744i	$-0.849731\pi$
$97$	−14.8900	+	3.23913i	−1.51185	+	0.328883i	−0.621231	+	0.783628i	$0.713367\pi$
$98$		0			0
$99$	0.533643	+	3.71157i	0.0536331	+	0.373027i
$100$		0			0
$101$	−7.73272	+	4.96952i	−0.769435	+	0.494486i	−0.865512	−	0.500888i	$-0.833007\pi$
$101$	−7.73272	+	4.96952i	−0.769435	+	0.494486i	0.0960774	+	0.995374i	$0.469370\pi$
$102$		0			0
$103$	−1.33867	+	0.499298i	−0.131903	+	0.0491973i	−0.414549	−	0.910027i	$-0.636061\pi$
$103$	−1.33867	+	0.499298i	−0.131903	+	0.0491973i	0.282646	+	0.959224i	$0.408788\pi$
$104$		0			0
$105$	3.83043	+	10.2699i	0.373812	+	1.00224i
$106$		0			0
$107$	−15.4941	+	8.46040i	−1.49787	+	0.817898i	−0.998815	−	0.0486734i	$-0.984501\pi$
$107$	−15.4941	+	8.46040i	−1.49787	+	0.817898i	−0.499053	+	0.866571i	$0.666319\pi$
$108$		0			0
$109$	2.31623	+	2.67307i	0.221855	+	0.256034i	0.855755	−	0.517380i	$-0.173093\pi$
$109$	2.31623	+	2.67307i	0.221855	+	0.256034i	−0.633901	+	0.773414i	$0.718547\pi$
$110$		0			0
$111$	−9.27592	−	8.03763i	−0.880432	−	0.762898i
$112$		0			0
$113$	4.67020	−	12.5213i	0.439335	−	1.17790i	−0.509037	−	0.860745i	$-0.669998\pi$
$113$	4.67020	−	12.5213i	0.439335	−	1.17790i	0.948372	−	0.317159i	$-0.102729\pi$
$114$		0			0
$115$	9.24115	+	5.44069i	0.861742	+	0.507347i
$116$		0			0
$117$	−0.796449	+	2.13536i	−0.0736317	+	0.197414i
$118$		0			0
$119$	−2.69951	−	2.33914i	−0.247464	−	0.214429i
$120$		0			0
$121$	7.03293	+	8.11644i	0.639358	+	0.737858i
$122$		0			0
$123$	−8.67143	+	4.73496i	−0.781876	+	0.426937i
$124$		0			0
$125$	2.37672	−	10.9248i	0.212580	−	0.977144i
$126$		0			0
$127$	−7.08239	+	2.64159i	−0.628460	+	0.234404i	−0.643455	−	0.765484i	$-0.722500\pi$
$127$	−7.08239	+	2.64159i	−0.628460	+	0.234404i	0.0149945	+	0.999888i	$0.495227\pi$
$128$		0			0
$129$	14.5427	−	9.34603i	1.28041	−	0.822872i
$130$		0			0
$131$	0.654229	+	4.55027i	0.0571603	+	0.397559i	0.998236	+	0.0593638i	$0.0189072\pi$
$131$	0.654229	+	4.55027i	0.0571603	+	0.397559i	−0.941076	+	0.338195i	$0.890184\pi$
$132$		0			0
$133$	−12.0462	+	2.62049i	−1.04454	+	0.227225i
$134$		0			0
$135$	4.83766e−5	−	9.57650i	4.16359e−6	−	0.824213i
$136$		0			0
$137$	7.15629	−	7.15629i	0.611403	−	0.611403i	−0.331909	−	0.943312i	$-0.607693\pi$
$137$	7.15629	−	7.15629i	0.611403	−	0.611403i	0.943312	+	0.331909i	$0.107693\pi$
$138$		0			0
$139$		−	2.75673i		−	0.233823i	−0.993142	−	0.116911i	$-0.962701\pi$
$139$		−	2.75673i		−	0.233823i	0.993142	−	0.116911i	$-0.0372993\pi$
$140$		0			0
$141$	−9.48337	+	2.78457i	−0.798644	+	0.234503i
$142$		0			0
$143$	2.80865	+	12.9112i	0.234871	+	1.07969i
$144$		0			0
$145$	−1.87363	−	2.50290i	−0.155597	−	0.207855i
$146$		0			0
$147$	1.30294	+	0.283437i	0.107465	+	0.0233775i
$148$		0			0
$149$	3.69741	−	8.09619i	0.302903	−	0.663266i	−0.695573	−	0.718456i	$-0.744849\pi$
$149$	3.69741	−	8.09619i	0.302903	−	0.663266i	0.998476	+	0.0551902i	$0.0175765\pi$
$150$		0			0
$151$	−2.19453	+	15.2633i	−0.178588	+	1.24211i	0.681446	+	0.731869i	$0.261352\pi$
$151$	−2.19453	+	15.2633i	−0.178588	+	1.24211i	−0.860034	+	0.510238i	$0.829557\pi$
$152$		0			0
$153$	−0.547785	−	1.00319i	−0.0442858	−	0.0811034i
$154$		0			0
$155$	−3.04174	+	8.15510i	−0.244319	+	0.655034i
$156$		0			0
$157$	0.192762	+	2.69516i	0.0153841	+	0.215097i	0.999329	+	0.0366255i	$0.0116609\pi$
$157$	0.192762	+	2.69516i	0.0153841	+	0.215097i	−0.983945	+	0.178472i	$0.942885\pi$
$158$		0			0
$159$	−1.50080	−	3.28630i	−0.119021	−	0.260621i
$160$		0			0
$161$	−10.7597	+	5.43177i	−0.847986	+	0.428084i
$162$		0			0
$163$	−20.2265	−	7.54410i	−1.58426	−	0.590899i	−0.605491	−	0.795852i	$-0.707023\pi$
$163$	−20.2265	−	7.54410i	−1.58426	−	0.590899i	−0.978772	+	0.204953i	$0.934296\pi$
$164$		0			0
$165$	10.9938	+	17.1069i	0.855868	+	1.33177i
$166$		0			0
$167$	−0.858728	+	12.0066i	−0.0664504	+	0.929098i	0.849444	+	0.527679i	$0.176937\pi$
$167$	−0.858728	+	12.0066i	−0.0664504	+	0.929098i	−0.915894	+	0.401419i	$0.868517\pi$
$168$		0			0
$169$	1.39998	−	4.76788i	0.107691	−	0.366760i
$170$		0			0
$171$	−3.90471	−	0.561413i	−0.298601	−	0.0429323i
$172$		0			0
$173$	−3.11676	−	8.35636i	−0.236963	−	0.635322i	0.762975	−	0.646428i	$-0.223738\pi$
$173$	−3.11676	−	8.35636i	−0.236963	−	0.635322i	−0.999938	+	0.0111052i	$0.996465\pi$
$174$		0			0
$175$	8.88554	+	8.88572i	0.671684	+	0.671697i
$176$		0			0
$177$	−8.50063	+	11.3555i	−0.638946	+	0.853532i
$178$		0			0
$179$	−9.15380	+	14.2436i	−0.684187	+	1.06462i	0.309332	+	0.950954i	$0.399894\pi$
$179$	−9.15380	+	14.2436i	−0.684187	+	1.06462i	−0.993519	+	0.113662i	$0.963742\pi$
$180$		0			0
$181$	2.28005	+	7.76512i	0.169474	+	0.577177i	0.999802	+	0.0199013i	$0.00633521\pi$
$181$	2.28005	+	7.76512i	0.169474	+	0.577177i	−0.830327	+	0.557276i	$0.811847\pi$
$182$		0			0
$183$	12.5775	+	12.5775i	0.929758	+	0.929758i
$184$		0			0
$185$	−13.5012	−	3.96439i	−0.992628	−	0.291467i
$186$		0			0
$187$	−5.81615	−	3.17586i	−0.425319	−	0.232242i
$188$		0			0
$189$	9.05486	+	5.81920i	0.658644	+	0.423285i
$190$		0			0
$191$	14.2907	−	2.05470i	1.03404	−	0.148673i	0.395663	−	0.918396i	$-0.370515\pi$
$191$	14.2907	−	2.05470i	1.03404	−	0.148673i	0.638378	+	0.769723i	$0.279606\pi$
$192$		0			0
$193$	−4.93827	+	22.7009i	−0.355464	+	1.63404i	0.358263	+	0.933621i	$0.383369\pi$
$193$	−4.93827	+	22.7009i	−0.355464	+	1.63404i	−0.713728	+	0.700423i	$0.752995\pi$
$194$		0			0
$195$	0.881649	+	12.3279i	0.0631362	+	0.882822i
$196$		0			0
$197$	17.0412	−	12.7569i	1.21413	−	0.908888i	0.216407	−	0.976303i	$-0.430566\pi$
$197$	17.0412	−	12.7569i	1.21413	−	0.908888i	0.997725	+	0.0674151i	$0.0214752\pi$
$198$		0			0
$199$	−18.1890	−	5.34078i	−1.28939	−	0.378598i	−0.436033	−	0.899931i	$-0.643617\pi$
$199$	−18.1890	−	5.34078i	−1.28939	−	0.378598i	−0.853354	+	0.521333i	$0.825435\pi$
$200$		0			0
$201$	9.57484	−	8.29665i	0.675357	−	0.585201i
$202$		0			0
$203$	3.50509	−	0.250689i	0.246009	−	0.0175949i
$204$		0			0
$205$	−6.78794	+	9.06753i	−0.474090	+	0.633304i
$206$		0			0
$207$	−3.83338	+	0.425321i	−0.266438	+	0.0295619i
$208$		0			0
$209$	−20.8041	+	9.50090i	−1.43905	+	0.657191i
$210$		0			0
$211$	7.53495	−	8.69580i	0.518727	−	0.598643i	−0.434584	−	0.900631i	$-0.643105\pi$
$211$	7.53495	−	8.69580i	0.518727	−	0.598643i	0.953312	+	0.301988i	$0.0976502\pi$
$212$		0			0
$213$	30.5306	+	2.18359i	2.09192	+	0.149617i
$214$		0			0
$215$	10.7148	−	16.6723i	0.730741	−	1.13704i
$216$		0			0
$217$	−5.86260	−	7.83152i	−0.397979	−	0.531638i
$218$		0			0
$219$	23.6838	+	10.8160i	1.60040	+	0.730880i
$220$		0			0
$221$	−2.17752	−	3.38829i	−0.146476	−	0.227921i
$222$		0			0
$223$	1.48110	+	1.10874i	0.0991818	+	0.0742466i	0.647718	−	0.761880i	$-0.275724\pi$
$223$	1.48110	+	1.10874i	0.0991818	+	0.0742466i	−0.548536	+	0.836127i	$0.684815\pi$
$224$		0			0
$225$	1.67039	+	3.65774i	0.111359	+	0.243849i
$226$		0			0
$227$	1.40322	−	2.56980i	0.0931347	−	0.170563i	−0.826959	−	0.562263i	$-0.809931\pi$
$227$	1.40322	−	2.56980i	0.0931347	−	0.170563i	0.920093	+	0.391699i	$0.128113\pi$
$228$		0			0
$229$	−9.28260			−0.613411			−0.306706	−	0.951804i	$-0.599227\pi$
$229$	−9.28260			−0.613411			−0.306706	+	0.951804i	$0.599227\pi$
$230$		0			0
$231$	−22.8556			−1.50378
$232$		0			0
$233$	0.228095	−	0.417724i	0.0149430	−	0.0273660i	−0.870101	−	0.492874i	$-0.835946\pi$
$233$	0.228095	−	0.417724i	0.0149430	−	0.0273660i	0.885044	+	0.465508i	$0.154128\pi$
$234$		0			0
$235$	−8.56353	+	7.42027i	−0.558623	+	0.484045i
$236$		0			0
$237$	7.82052	+	5.85437i	0.507997	+	0.380282i
$238$		0			0
$239$	15.9892	+	24.8796i	1.03425	+	1.60933i	0.762530	+	0.646952i	$0.223957\pi$
$239$	15.9892	+	24.8796i	1.03425	+	1.60933i	0.271722	+	0.962376i	$0.412407\pi$
$240$		0			0
$241$	−21.7888	−	9.95062i	−1.40354	−	0.640976i	−0.437465	−	0.899235i	$-0.644124\pi$
$241$	−21.7888	−	9.95062i	−1.40354	−	0.640976i	−0.966076	+	0.258260i	$0.916851\pi$
$242$		0			0
$243$	4.88412	+	6.52443i	0.313317	+	0.418542i
$244$		0			0
$245$	1.49375	−	0.324937i	0.0954319	−	0.0207594i
$246$		0			0
$247$	−13.8653	−	0.991666i	−0.882228	−	0.0630982i
$248$		0			0
$249$	11.7852	−	13.6009i	0.746857	−	0.861919i
$250$		0			0
$251$	−13.2909	+	6.06976i	−0.838915	+	0.383120i	−0.788069	−	0.615587i	$-0.788919\pi$
$251$	−13.2909	+	6.06976i	−0.838915	+	0.383120i	−0.0508459	+	0.998707i	$0.516192\pi$
$252$		0			0
$253$	−17.3633	+	14.0899i	−1.09162	+	0.885825i
$254$		0			0
$255$	−4.96220	−	3.71469i	−0.310745	−	0.232623i
$256$		0			0
$257$	−8.99401	+	0.643264i	−0.561031	+	0.0401257i	−0.348975	−	0.937132i	$-0.613470\pi$
$257$	−8.99401	+	0.643264i	−0.561031	+	0.0401257i	−0.212055	+	0.977258i	$0.568016\pi$
$258$		0			0
$259$	11.9525	−	10.3569i	0.742690	−	0.643545i
$260$		0			0
$261$	1.07892	+	0.316800i	0.0667837	+	0.0196095i
$262$		0			0
$263$	2.59558	−	1.94303i	0.160051	−	0.119812i	−0.516251	−	0.856438i	$-0.672673\pi$
$263$	2.59558	−	1.94303i	0.160051	−	0.119812i	0.676301	+	0.736625i	$0.263582\pi$
$264$		0			0
$265$	−3.13018	−	2.71235i	−0.192286	−	0.166618i
$266$		0			0
$267$	0.00153530	−	0.00705766i	9.39588e−5	−	0.000431922i
$268$		0			0
$269$	−12.5338	+	1.80209i	−0.764202	+	0.109876i	−0.513384	−	0.858159i	$-0.671608\pi$
$269$	−12.5338	+	1.80209i	−0.764202	+	0.109876i	−0.250817	+	0.968034i	$0.580699\pi$
$270$		0			0
$271$	5.63097	+	3.61880i	0.342057	+	0.219827i	0.700379	−	0.713771i	$-0.253014\pi$
$271$	5.63097	+	3.61880i	0.342057	+	0.219827i	−0.358322	+	0.933598i	$0.616651\pi$
$272$		0			0
$273$	−12.1922	−	6.65744i	−0.737905	−	0.402927i
$274$		0			0
$275$	19.6119	+	12.6041i	1.18264	+	0.760055i
$276$		0			0
$277$	19.8907	+	19.8907i	1.19511	+	1.19511i	0.975612	+	0.219502i	$0.0704432\pi$
$277$	19.8907	+	19.8907i	1.19511	+	1.19511i	0.219502	+	0.975612i	$0.429557\pi$
$278$		0			0
$279$	−0.881944	−	3.00363i	−0.0528006	−	0.179822i
$280$		0			0
$281$	10.8881	−	16.9422i	0.649530	−	1.01069i	−0.347793	−	0.937571i	$-0.613069\pi$
$281$	10.8881	−	16.9422i	0.649530	−	1.01069i	0.997323	−	0.0731172i	$-0.0232947\pi$
$282$		0			0
$283$	18.6484	−	24.9114i	1.10853	−	1.48083i	0.249876	−	0.968278i	$-0.419610\pi$
$283$	18.6484	−	24.9114i	1.10853	−	1.48083i	0.858658	−	0.512550i	$-0.171299\pi$
$284$		0			0
$285$	−20.5266	+	6.02705i	−1.21589	+	0.357011i
$286$		0			0
$287$	−4.44895	−	11.9281i	−0.262614	−	0.704094i
$288$		0			0
$289$	−14.8275	−	2.13188i	−0.872208	−	0.125405i
$290$		0			0
$291$	8.37347	−	28.5174i	0.490861	−	1.67172i
$292$		0			0
$293$	−1.11439	+	15.5812i	−0.0651034	+	0.910264i	0.855010	+	0.518612i	$0.173551\pi$
$293$	−1.11439	+	15.5812i	−0.0651034	+	0.910264i	−0.920113	+	0.391652i	$0.871904\pi$
$294$		0			0
$295$	−3.45683	+	15.8904i	−0.201264	+	0.925174i
$296$		0			0
$297$	18.7096	+	6.97830i	1.08564	+	0.404922i
$298$		0			0
$299$	−13.3665	+	2.45855i	−0.773007	+	0.142182i
$300$		0			0
$301$	9.25340	+	20.2621i	0.533357	+	1.16789i
$302$		0			0
$303$	−1.27899	−	17.8826i	−0.0734759	−	1.02733i
$304$		0			0
$305$	19.1064	+	7.12642i	1.09403	+	0.408057i
$306$		0			0
$307$	3.26642	+	5.98199i	0.186424	+	0.341410i	0.954130	−	0.299392i	$-0.0967837\pi$
$307$	3.26642	+	5.98199i	0.186424	+	0.341410i	−0.767706	+	0.640802i	$0.778602\pi$
$308$		0			0
$309$	0.396589	−	2.75834i	0.0225611	−	0.156916i
$310$		0			0
$311$	11.3674	−	24.8911i	0.644584	−	1.41144i	−0.251631	−	0.967823i	$-0.580967\pi$
$311$	11.3674	−	24.8911i	0.644584	−	1.41144i	0.896215	−	0.443619i	$-0.146306\pi$
$312$		0			0
$313$	−21.6611	−	4.71208i	−1.22436	−	0.266343i	−0.446500	−	0.894784i	$-0.647330\pi$
$313$	−21.6611	−	4.71208i	−1.22436	−	0.266343i	−0.777857	+	0.628441i	$0.783693\pi$
$314$		0			0
$315$	−4.47352	−	0.643219i	−0.252055	−	0.0362413i
$316$		0			0
$317$	−1.62917	−	7.48916i	−0.0915031	−	0.420633i	−0.999996	−	0.00273328i	$-0.999130\pi$
$317$	−1.62917	−	7.48916i	−0.0915031	−	0.420633i	0.908493	−	0.417900i	$-0.137234\pi$
$318$		0			0
$319$	6.25520	−	1.83669i	0.350224	−	0.102835i
$320$		0			0
$321$		−	34.4320i		−	1.92181i
$322$		0			0
$323$	4.92965	−	4.92965i	0.274293	−	0.274293i
$324$		0			0
$325$	6.79053	+	12.4362i	0.376671	+	0.689837i
$326$		0			0
$327$	−6.74101	+	1.46642i	−0.372779	+	0.0810931i
$328$		0			0
$329$	−1.81247	−	12.6060i	−0.0999249	−	0.694993i
$330$		0			0
$331$	2.54562	−	1.63597i	0.139920	−	0.0899212i	−0.468808	−	0.883300i	$-0.655316\pi$
$331$	2.54562	−	1.63597i	0.139920	−	0.0899212i	0.608728	+	0.793379i	$0.291680\pi$
$332$		0			0
$333$	4.74174	−	1.76858i	0.259846	−	0.0969174i
$334$		0			0
$335$	6.03383	−	13.2121i	0.329663	−	0.721852i
$336$		0			0
$337$	−14.1876	+	7.74704i	−0.772850	+	0.422008i	−0.816724	−	0.577029i	$-0.804212\pi$
$337$	−14.1876	+	7.74704i	−0.772850	+	0.422008i	0.0438736	+	0.999037i	$0.486030\pi$
$338$		0			0
$339$	17.0693	+	19.6990i	0.927075	+	1.06990i
$340$		0			0
$341$	−13.7162	−	11.8851i	−0.742772	−	0.643615i
$342$		0			0
$343$	−6.74844	+	18.0933i	−0.364381	+	0.976944i
$344$		0			0
$345$	−17.9518	+	10.7339i	−0.966495	+	0.577894i
$346$		0			0
$347$	0.525958	−	1.41015i	0.0282349	−	0.0757007i	−0.922067	−	0.387029i	$-0.873501\pi$
$347$	0.525958	−	1.41015i	0.0282349	−	0.0757007i	0.950302	+	0.311329i	$0.100774\pi$
$348$		0			0
$349$	−12.8199	−	11.1085i	−0.686236	−	0.594627i	0.240361	−	0.970684i	$-0.422734\pi$
$349$	−12.8199	−	11.1085i	−0.686236	−	0.594627i	−0.926597	+	0.376057i	$0.877280\pi$
$350$		0			0
$351$	7.94787	+	9.17233i	0.424226	+	0.489583i
$352$		0			0
$353$	17.0744	−	9.32334i	0.908780	−	0.496231i	0.0443678	−	0.999015i	$-0.485873\pi$
$353$	17.0744	−	9.32334i	0.908780	−	0.496231i	0.864412	+	0.502784i	$0.167691\pi$
$354$		0			0
$355$	32.8786	−	12.2629i	1.74501	−	0.650846i
$356$		0			0
$357$	6.52764	−	2.43468i	0.345479	−	0.128857i
$358$		0			0
$359$	7.27262	−	4.67383i	0.383834	−	0.246675i	−0.334467	−	0.942407i	$-0.608556\pi$
$359$	7.27262	−	4.67383i	0.383834	−	0.246675i	0.718301	+	0.695732i	$0.244920\pi$
$360$		0			0
$361$	−0.720259	−	5.00951i	−0.0379083	−	0.263658i
$362$		0			0
$363$	−20.4682	+	4.45259i	−1.07430	+	0.233700i
$364$		0			0
$365$	29.8496		0.000150788i	1.56240		7.89260e-6i
$366$		0			0
$367$	−18.0897	+	18.0897i	−0.944276	+	0.944276i	−0.998527	−	0.0542509i	$-0.982723\pi$
$367$	−18.0897	+	18.0897i	−0.944276	+	0.944276i	0.0542509	+	0.998527i	$0.482723\pi$
$368$		0			0
$369$		−	4.07378i		−	0.212072i
$370$		0			0
$371$	4.46667	−	1.31153i	0.231898	−	0.0680913i
$372$		0			0
$373$	4.58214	+	21.0638i	0.237254	+	1.09064i	0.929455	+	0.368935i	$0.120278\pi$
$373$	4.58214	+	21.0638i	0.237254	+	1.09064i	−0.692201	+	0.721705i	$0.743359\pi$
$374$		0			0
$375$	16.4801	+	14.2805i	0.851029	+	0.737443i
$376$		0			0
$377$	3.87181	+	0.842260i	0.199408	+	0.0433786i
$378$		0			0
$379$	3.35290	−	7.34183i	0.172227	−	0.377125i	−0.803760	−	0.594954i	$-0.797170\pi$
$379$	3.35290	−	7.34183i	0.172227	−	0.377125i	0.975987	+	0.217829i	$0.0698976\pi$
$380$		0			0
$381$	2.09820	−	14.5933i	0.107494	−	0.747637i
$382$		0			0
$383$	−6.91387	−	12.6618i	−0.353282	−	0.646989i	0.639246	−	0.769002i	$-0.279247\pi$
$383$	−6.91387	−	12.6618i	−0.353282	−	0.646989i	−0.992528	+	0.122014i	$0.961065\pi$
$384$		0			0
$385$	−23.8348	+	10.8848i	−1.21473	+	0.554742i
$386$		0			0
$387$	0.508498	+	7.10972i	0.0258484	+	0.361408i
$388$		0			0
$389$	7.66853	+	16.7917i	0.388810	+	0.851375i	0.998283	+	0.0585687i	$0.0186537\pi$
$389$	7.66853	+	16.7917i	0.388810	+	0.851375i	−0.609473	+	0.792807i	$0.708619\pi$
$390$		0			0
$391$	3.45812	−	5.87376i	0.174884	−	0.297049i
$392$		0			0
$393$	−8.40096	−	3.13340i	−0.423773	−	0.158059i
$394$		0			0
$395$	10.9437	+	2.38071i	0.550636	+	0.119786i
$396$		0			0
$397$	−0.500824	+	7.00243i	−0.0251356	+	0.351442i	0.969284	+	0.245944i	$0.0790981\pi$
$397$	−0.500824	+	7.00243i	−0.0251356	+	0.351442i	−0.994420	+	0.105498i	$0.966356\pi$
$398$		0			0
$399$	6.77423	−	23.0709i	0.339136	−	1.15499i
$400$		0			0
$401$	−16.9558	−	2.43787i	−0.846730	−	0.121741i	−0.294725	−	0.955582i	$-0.595228\pi$
$401$	−16.9558	−	2.43787i	−0.846730	−	0.121741i	−0.552005	+	0.833841i	$0.686137\pi$
$402$		0			0
$403$	−3.85489	−	10.3354i	−0.192026	−	0.514841i
$404$		0			0
$405$	21.1285	+	11.5372i	1.04989	+	0.573288i
$406$		0			0
$407$	17.5833	−	23.4885i	0.871571	−	1.16428i
$408$		0			0
$409$	−3.47028	+	5.39986i	−0.171594	+	0.267006i	−0.916390	−	0.400287i	$-0.868911\pi$
$409$	−3.47028	+	5.39986i	−0.171594	+	0.267006i	0.744796	+	0.667293i	$0.232547\pi$
$410$		0			0
$411$	5.56125	+	18.9399i	0.274316	+	0.934236i
$412$		0			0
$413$	−12.9243	−	12.9243i	−0.635965	−	0.635965i
$414$		0			0
$415$	5.81280	−	19.7962i	0.285339	−	0.971757i
$416$		0			0
$417$	4.71913	+	2.57684i	0.231097	+	0.126189i
$418$		0			0
$419$	11.6813	+	7.50714i	0.570670	+	0.366748i	0.793928	−	0.608012i	$-0.208033\pi$
$419$	11.6813	+	7.50714i	0.570670	+	0.366748i	−0.223257	+	0.974760i	$0.571669\pi$
$420$		0			0
$421$	−6.96130	+	1.00088i	−0.339273	+	0.0487801i	−0.309846	−	0.950787i	$-0.600277\pi$
$421$	−6.96130	+	1.00088i	−0.339273	+	0.0487801i	−0.0294274	+	0.999567i	$0.509368\pi$
$422$		0			0
$423$	0.866274	−	3.98220i	0.0421197	−	0.193621i
$424$		0			0
$425$	−6.94389	−	1.51062i	−0.336828	−	0.0732760i
$426$		0			0
$427$	−18.3482	+	13.7353i	−0.887934	+	0.664699i
$428$		0			0
$429$	−24.7275	−	7.26065i	−1.19386	−	0.350548i
$430$		0			0
$431$	−13.4737	+	11.6751i	−0.649008	+	0.562368i	−0.915924	−	0.401351i	$-0.868541\pi$
$431$	−13.4737	+	11.6751i	−0.649008	+	0.562368i	0.266917	+	0.963720i	$0.413995\pi$
$432$		0			0
$433$	30.4497	−	2.17781i	1.46332	−	0.104659i	0.683175	−	0.730255i	$-0.260599\pi$
$433$	30.4497	−	2.17781i	1.46332	−	0.104659i	0.780147	+	0.625596i	$0.215144\pi$
$434$		0			0
$435$	6.03599	−	0.867814i	0.289404	−	0.0416085i
$436$		0			0
$437$	−9.07630	−	21.7031i	−0.434178	−	1.03820i
$438$		0			0
$439$	−26.2480	+	11.9870i	−1.25275	+	0.572110i	−0.927608	−	0.373556i	$-0.878138\pi$
$439$	−26.2480	+	11.9870i	−1.25275	+	0.572110i	−0.325139	+	0.945666i	$0.605411\pi$
$440$		0			0
$441$	−0.360044	+	0.415513i	−0.0171449	+	0.0197863i
$442$		0			0
$443$	20.6436	+	1.47646i	0.980806	+	0.0701486i	0.552524	−	0.833497i	$-0.313665\pi$
$443$	20.6436	+	1.47646i	0.980806	+	0.0701486i	0.428281	+	0.903645i	$0.359119\pi$
$444$		0			0
$445$	−0.00176009	−	0.00809120i	−8.34363e−5	−	0.000383560i
$446$		0			0
$447$	10.4034	+	13.8973i	0.492065	+	0.657321i
$448$		0			0
$449$	−29.7488	−	13.5858i	−1.40393	−	0.641156i	−0.437771	−	0.899086i	$-0.644232\pi$
$449$	−29.7488	−	13.5858i	−1.40393	−	0.641156i	−0.966163	+	0.257931i	$0.916959\pi$
$450$		0			0
$451$	−12.7690	−	19.8689i	−0.601268	−	0.935592i
$452$		0			0
$453$	−24.0773	−	18.0240i	−1.13125	−	0.846842i
$454$		0			0
$455$	−15.8851	−	1.13621i	−0.744706	−	0.0532662i
$456$		0			0
$457$	6.02878	−	11.0409i	0.282015	−	0.516471i	−0.697822	−	0.716271i	$-0.745847\pi$
$457$	6.02878	−	11.0409i	0.282015	−	0.516471i	0.979837	+	0.199800i	$0.0640292\pi$
$458$		0			0
$459$	−6.08689			−0.284112
$460$		0			0
$461$	28.5574			1.33005			0.665025	−	0.746821i	$-0.268421\pi$
$461$	28.5574			1.33005			0.665025	+	0.746821i	$0.268421\pi$
$462$		0			0
$463$	−2.68068	+	4.90931i	−0.124582	+	0.228155i	−0.932525	−	0.361106i	$-0.882399\pi$
$463$	−2.68068	+	4.90931i	−0.124582	+	0.228155i	0.807943	+	0.589261i	$0.200581\pi$
$464$		0			0
$465$	−11.1171	−	12.8300i	−0.515545	−	0.594977i
$466$		0			0
$467$	−4.79948	−	3.59285i	−0.222093	−	0.166257i	0.482437	−	0.875930i	$-0.339752\pi$
$467$	−4.79948	−	3.59285i	−0.222093	−	0.166257i	−0.704531	+	0.709673i	$0.748843\pi$
$468$		0			0
$469$	8.82598	+	13.7335i	0.407546	+	0.634154i
$470$		0			0
$471$	−4.79393	−	2.18931i	−0.220893	−	0.100878i
$472$		0			0
$473$	24.7651	+	33.0823i	1.13870	+	1.52112i
$474$		0			0
$475$	−18.5357	+	16.0609i	−0.850476	+	0.736926i
$476$		0			0
$477$	1.48585	+	0.106270i	0.0680325	+	0.00486578i
$478$		0			0
$479$	−10.3604	+	11.9565i	−0.473378	+	0.546307i	−0.941348	−	0.337437i	$-0.890440\pi$
$479$	−10.3604	+	11.9565i	−0.473378	+	0.546307i	0.467970	+	0.883744i	$0.344985\pi$
$480$		0			0
$481$	16.2215	−	7.40813i	0.739639	−	0.337782i
$482$		0			0
$483$	0.759194	−	23.4965i	0.0345445	−	1.06913i
$484$		0			0
$485$	−4.84904	−	33.7270i	−0.220183	−	1.53146i
$486$		0			0
$487$	29.4774	−	2.10827i	1.33575	−	0.0955346i	0.614888	−	0.788615i	$-0.289201\pi$
$487$	29.4774	−	2.10827i	1.33575	−	0.0955346i	0.720861	+	0.693080i	$0.243747\pi$
$488$		0			0
$489$	31.8211	−	27.5732i	1.43900	−	1.24690i
$490$		0			0
$491$	14.3242	+	4.20597i	0.646443	+	0.189813i	0.588487	−	0.808506i	$-0.299724\pi$
$491$	14.3242	+	4.20597i	0.646443	+	0.189813i	0.0579554	+	0.998319i	$0.481542\pi$
$492$		0			0
$493$	−1.59086	+	1.19090i	−0.0716486	+	0.0536355i
$494$		0			0
$495$	−8.36330	+	0.598113i	−0.375903	+	0.0268832i
$496$		0			0
$497$	−8.38371	+	38.5393i	−0.376061	+	1.72872i
$498$		0			0
$499$	−15.3568	+	2.20797i	−0.687464	+	0.0988424i	−0.477190	−	0.878800i	$-0.658345\pi$
$499$	−15.3568	+	2.20797i	−0.687464	+	0.0988424i	−0.210274	+	0.977642i	$0.567436\pi$
$500$		0			0
$501$	−19.7509	−	12.6931i	−0.882406	−	0.567088i
$502$		0			0
$503$	9.28907	+	5.07222i	0.414179	+	0.226159i	0.672807	−	0.739818i	$-0.265088\pi$
$503$	9.28907	+	5.07222i	0.414179	+	0.226159i	−0.258628	+	0.965977i	$0.583270\pi$
$504$		0			0
$505$	−9.85026	−	18.0396i	−0.438331	−	0.802752i
$506$		0			0
$507$	6.85333	+	6.85333i	0.304367	+	0.304367i
$508$		0			0
$509$	−12.5718	−	42.8157i	−0.557236	−	1.89777i	−0.420896	−	0.907109i	$-0.638284\pi$
$509$	−12.5718	−	42.8157i	−0.557236	−	1.89777i	−0.136340	−	0.990662i	$-0.543534\pi$
$510$		0			0
$511$	−18.1382	+	28.2236i	−0.802388	+	1.24854i
$512$		0			0
$513$	−12.5894	+	16.8175i	−0.555838	+	0.742512i
$514$		0			0
$515$	−0.900061	−	3.06538i	−0.0396614	−	0.135077i
$516$		0			0
$517$	−8.25689	−	22.1376i	−0.363138	−	0.973609i
$518$		0			0
$519$	17.2183	+	2.47562i	0.755800	+	0.108668i
$520$		0			0
$521$	12.5745	−	42.8249i	0.550900	−	1.87619i	0.0739543	−	0.997262i	$-0.476438\pi$
$521$	12.5745	−	42.8249i	0.550900	−	1.87619i	0.476946	−	0.878933i	$-0.341744\pi$
$522$		0			0
$523$	2.90405	−	40.6039i	0.126985	−	1.77548i	−0.391288	−	0.920268i	$-0.627970\pi$
$523$	2.90405	−	40.6039i	0.126985	−	1.77548i	0.518273	−	0.855215i	$-0.326575\pi$
$524$		0			0
$525$	−23.5168	+	6.90491i	−1.02636	+	0.301355i
$526$		0			0
$527$	5.18346	+	1.93333i	0.225795	+	0.0842171i
$528$		0			0
$529$	−13.9083	−	18.3183i	−0.604708	−	0.796447i
$530$		0			0
$531$	−2.42967	−	5.32023i	−0.105439	−	0.230879i
$532$		0			0
$533$	−1.02407	−	14.3184i	−0.0443575	−	0.620199i
$534$		0			0
$535$	−16.3980	−	35.9072i	−0.708949	−	1.55240i
$536$		0			0
$537$	−15.8266	−	28.9842i	−0.682967	−	1.25076i
$538$		0			0
$539$	−0.453636	+	3.15511i	−0.0195395	+	0.135900i
$540$		0			0
$541$	−3.44131	+	7.53543i	−0.147954	+	0.323973i	−0.969069	−	0.246788i	$-0.920625\pi$
$541$	−3.44131	+	7.53543i	−0.147954	+	0.323973i	0.821116	+	0.570762i	$0.193352\pi$
$542$		0			0
$543$	−15.4241	−	3.35530i	−0.661911	−	0.143990i
$544$		0			0
$545$	−6.33145	+	4.73961i	−0.271209	+	0.203023i
$546$		0			0
$547$	3.41178	+	15.6837i	0.145877	+	0.670586i	0.990759	+	0.135633i	$0.0433069\pi$
$547$	3.41178	+	15.6837i	0.145877	+	0.670586i	−0.844882	+	0.534953i	$0.820329\pi$
$548$		0			0
$549$	−7.03711	+	2.06628i	−0.300337	+	0.0881868i
$550$		0			0
$551$			6.85853i			0.292183i
$552$		0			0
$553$	−8.90097	+	8.90097i	−0.378508	+	0.378508i
$554$		0			0
$555$	19.4067	−	19.4065i	0.823768	−	0.823760i
$556$		0			0
$557$	16.3889	−	3.56519i	0.694421	−	0.151062i	0.148517	−	0.988910i	$-0.452550\pi$
$557$	16.3889	−	3.56519i	0.694421	−	0.151062i	0.545904	+	0.837848i	$0.316186\pi$
$558$		0			0
$559$	3.57451	+	24.8612i	0.151186	+	1.05152i
$560$		0			0
$561$	10.8732	−	6.98781i	0.459069	−	0.295026i
$562$		0			0
$563$	29.1833	−	10.8848i	1.22993	−	0.458741i	0.351310	−	0.936259i	$-0.385736\pi$
$563$	29.1833	−	10.8848i	1.22993	−	0.458741i	0.878622	+	0.477519i	$0.158464\pi$
$564$		0			0
$565$	27.1821	+	12.4138i	1.14356	+	0.522253i
$566$		0			0
$567$	−23.7476	+	12.9671i	−0.997304	+	0.544569i
$568$		0			0
$569$	2.84620	+	3.28468i	0.119319	+	0.137701i	0.812266	−	0.583287i	$-0.198234\pi$
$569$	2.84620	+	3.28468i	0.119319	+	0.137701i	−0.692947	+	0.720988i	$0.743688\pi$
$570$		0			0
$571$	12.3574	+	10.7077i	0.517141	+	0.448105i	0.873910	−	0.486087i	$-0.161576\pi$
$571$	12.3574	+	10.7077i	0.517141	+	0.448105i	−0.356769	+	0.934192i	$0.616122\pi$
$572$		0			0
$573$	−9.84085	+	26.3843i	−0.411107	+	1.10222i
$574$		0			0
$575$	−13.6090	+	19.7432i	−0.567535	+	0.823350i
$576$		0			0
$577$	11.5290	−	30.9105i	0.479960	−	1.28682i	−0.441120	−	0.897448i	$-0.645419\pi$
$577$	11.5290	−	30.9105i	0.479960	−	1.28682i	0.921080	−	0.389373i	$-0.127308\pi$
$578$		0			0
$579$	−34.2447	−	29.6732i	−1.42316	−	1.23318i
$580$		0			0
$581$	15.1858	+	17.5253i	0.630013	+	0.727074i
$582$		0			0
$583$	7.58001	−	4.13900i	0.313932	−	0.171420i
$584$		0			0
$585$	−4.63559	−	2.11703i	−0.191658	−	0.0875285i
$586$		0			0
$587$	−39.7975	+	14.8437i	−1.64262	+	0.612665i	−0.989492	−	0.144585i	$-0.953815\pi$
$587$	−39.7975	+	14.8437i	−1.64262	+	0.612665i	−0.653125	+	0.757250i	$0.726542\pi$
$588$		0			0
$589$	16.0625	−	10.3227i	0.661844	−	0.425341i
$590$		0			0
$591$	5.90879	+	41.0965i	0.243055	+	1.69049i
$592$		0			0
$593$	−10.0389	+	2.18383i	−0.412248	+	0.0896791i	−0.413906	−	0.910320i	$-0.635836\pi$
$593$	−10.0389	+	2.18383i	−0.412248	+	0.0896791i	0.00165816	+	0.999999i	$0.499472\pi$
$594$		0			0
$595$	5.64780	−	5.64774i	0.231537	−	0.231535i
$596$		0			0
$597$	26.1448	−	26.1448i	1.07004	−	1.07004i
$598$		0			0
$599$			27.6923i			1.13148i	0.824585	+	0.565738i	$0.191409\pi$
$599$			27.6923i			1.13148i	−0.824585	+	0.565738i	$0.808591\pi$
$600$		0			0
$601$	16.3423	−	4.79853i	0.666616	−	0.195736i	0.0691204	−	0.997608i	$-0.477981\pi$
$601$	16.3423	−	4.79853i	0.666616	−	0.195736i	0.597496	+	0.801872i	$0.296163\pi$
$602$		0			0
$603$	1.11042	+	5.10453i	0.0452199	+	0.207873i
$604$		0			0
$605$	−19.2246	+	14.3912i	−0.781592	+	0.585087i
$606$		0			0
$607$	25.3307	+	5.51036i	1.02814	+	0.223659i	0.694842	−	0.719162i	$-0.255474\pi$
$607$	25.3307	+	5.51036i	1.02814	+	0.223659i	0.333300	+	0.942821i	$0.391838\pi$
$608$		0			0
$609$	−2.84723	+	6.23456i	−0.115375	+	0.252637i
$610$		0			0
$611$	2.04371	−	14.2143i	0.0826795	−	0.575049i
$612$		0			0
$613$	−12.7517	−	23.3530i	−0.515037	−	0.943221i	−0.997724	−	0.0674276i	$-0.978521\pi$
$613$	−12.7517	−	23.3530i	−0.515037	−	0.943221i	0.482687	−	0.875793i	$-0.339661\pi$
$614$		0			0
$615$	−9.17735	−	20.0959i	−0.370066	−	0.810343i
$616$		0			0
$617$	−2.53654	−	35.4655i	−0.102117	−	1.42779i	−0.747670	−	0.664071i	$-0.768827\pi$
$617$	−2.53654	−	35.4655i	−0.102117	−	1.42779i	0.645553	−	0.763716i	$-0.276627\pi$
$618$		0			0
$619$	12.5295	+	27.4358i	0.503604	+	1.10274i	0.975281	+	0.220967i	$0.0709213\pi$
$619$	12.5295	+	27.4358i	0.503604	+	1.10274i	−0.471678	+	0.881771i	$0.656351\pi$
$620$		0			0
$621$	−7.79548	+	19.0024i	−0.312822	+	0.762542i
$622$		0			0
$623$	0.00872002	+	0.00325240i	0.000349360	+	0.000130305i
$624$		0			0
$625$	23.9872	+	7.04380i	0.959487	+	0.281752i
$626$		0			0
$627$	3.18232	−	44.4946i	0.127090	−	1.77694i
$628$		0			0
$629$	−2.51975	+	8.58148i	−0.100469	+	0.342166i
$630$		0			0
$631$	31.0040	+	4.45771i	1.23425	+	0.177459i	0.728394	−	0.685159i	$-0.240267\pi$
$631$	31.0040	+	4.45771i	1.23425	+	0.177459i	0.505857	+	0.862617i	$0.331176\pi$
$632$		0			0
$633$	7.84272	+	21.0272i	0.311720	+	0.835755i
$634$		0			0
$635$	−4.76188	−	16.2178i	−0.188969	−	0.643582i
$636$		0			0
$637$	−1.16102	+	1.55094i	−0.0460013	+	0.0614505i
$638$		0			0
$639$	−6.82330	+	10.6173i	−0.269926	+	0.420013i
$640$		0			0
$641$	6.71934	+	22.8840i	0.265398	+	0.903862i	0.979094	+	0.203407i	$0.0652014\pi$
$641$	6.71934	+	22.8840i	0.265398	+	0.903862i	−0.713696	+	0.700455i	$0.752980\pi$
$642$		0			0
$643$	−19.1680	−	19.1680i	−0.755913	−	0.755913i	0.219663	−	0.975576i	$-0.429504\pi$
$643$	−19.1680	−	19.1680i	−0.755913	−	0.755913i	−0.975576	+	0.219663i	$0.929504\pi$
$644$		0			0
$645$	18.5251	+	33.9266i	0.729425	+	1.33586i
$646$		0			0
$647$	41.5593	+	22.6931i	1.63386	+	0.892157i	0.992128	+	0.125230i	$0.0399669\pi$
$647$	41.5593	+	22.6931i	1.63386	+	0.892157i	0.641735	+	0.766926i	$0.278215\pi$
$648$		0			0
$649$	−28.5261	−	18.3326i	−1.11975	−	0.719618i
$650$		0			0
$651$	18.8865	−	2.71547i	0.740221	−	0.106428i
$652$		0			0
$653$	−4.82145	+	22.1639i	−0.188678	+	0.867339i	0.781302	+	0.624153i	$0.214556\pi$
$653$	−4.82145	+	22.1639i	−0.188678	+	0.867339i	−0.969980	+	0.243185i	$0.921808\pi$
$654$		0			0
$655$	−10.2531	+	0.733267i	−0.400624	+	0.0286511i
$656$		0			0
$657$	−8.59432	+	6.43363i	−0.335297	+	0.251000i
$658$		0			0
$659$	29.8294	+	8.75869i	1.16199	+	0.341190i	0.805204	−	0.592997i	$-0.202056\pi$
$659$	29.8294	+	8.75869i	1.16199	+	0.341190i	0.356783	+	0.934187i	$0.383874\pi$
$660$		0			0
$661$	−3.60466	+	3.12346i	−0.140205	+	0.121488i	−0.722140	−	0.691747i	$-0.756841\pi$
$661$	−3.60466	+	3.12346i	−0.140205	+	0.121488i	0.581935	+	0.813235i	$0.302296\pi$
$662$		0			0
$663$	7.83572	−	0.560422i	0.304314	−	0.0217650i
$664$		0			0
$665$	−3.92293	−	27.2855i	−0.152125	−	1.05809i
$666$		0			0
$667$	1.68042	+	6.49163i	0.0650662	+	0.251357i
$668$		0			0
$669$	−3.28246	+	1.49905i	−0.126907	+	0.0579566i
$670$		0			0
$671$	−27.8453	+	32.1352i	−1.07496	+	1.24057i
$672$		0			0
$673$	29.6208	+	2.11852i	1.14180	+	0.0816629i	0.629397	−	0.777084i	$-0.283302\pi$
$673$	29.6208	+	2.11852i	1.14180	+	0.0816629i	0.512400	+	0.858747i	$0.328757\pi$
$674$		0			0
$675$	21.3591	+	1.52785i	0.822113	+	0.0588070i
$676$		0			0
$677$	1.65742	+	2.21406i	0.0636999	+	0.0850931i	0.831260	−	0.555884i	$-0.187620\pi$
$677$	1.65742	+	2.21406i	0.0636999	+	0.0850931i	−0.767560	+	0.640977i	$0.778529\pi$
$678$		0			0
$679$	34.8365	+	15.9093i	1.33690	+	0.610543i
$680$		0			0
$681$	3.08749	+	4.80422i	0.118313	+	0.184098i
$682$		0			0
$683$	−3.32288	−	2.48748i	−0.127146	−	0.0951806i	0.533812	−	0.845603i	$-0.320759\pi$
$683$	−3.32288	−	2.48748i	−0.127146	−	0.0951806i	−0.660958	+	0.750423i	$0.729850\pi$
$684$		0			0
$685$	14.8195	+	17.1028i	0.566225	+	0.653465i
$686$		0			0
$687$	8.67688	−	15.8905i	0.331044	−	0.606261i
$688$		0			0
$689$	5.24915			0.199977
$690$		0			0
$691$	−37.9093			−1.44214			−0.721069	−	0.692864i	$-0.756349\pi$
$691$	−37.9093			−1.44214			−0.721069	+	0.692864i	$0.756349\pi$
$692$		0			0
$693$	4.51643	−	8.27122i	0.171565	−	0.314198i
$694$		0			0
$695$	6.14852	+	0.439782i	0.233227	+	0.0166819i
$696$		0			0
$697$	5.76341	+	4.31444i	0.218305	+	0.163421i
$698$		0			0
$699$	0.501875	+	0.780932i	0.0189826	+	0.0295376i
$700$		0			0
$701$	21.4174	+	9.78099i	0.808923	+	0.369423i	0.776552	−	0.630053i	$-0.216967\pi$
$701$	21.4174	+	9.78099i	0.808923	+	0.369423i	0.0323711	+	0.999476i	$0.489694\pi$
$702$		0			0
$703$	18.4983	+	24.7108i	0.697676	+	0.931986i
$704$		0			0
$705$	−4.69773	−	21.5956i	−0.176927	−	0.813339i
$706$		0			0
$707$	23.0426	+	1.64804i	0.866605	+	0.0619808i
$708$		0			0
$709$	−21.9733	+	25.3586i	−0.825226	+	0.952362i	−0.999477	−	0.0323393i	$-0.989704\pi$
$709$	−21.9733	+	25.3586i	−0.825226	+	0.952362i	0.174251	+	0.984701i	$0.444250\pi$
$710$		0			0
$711$	−3.66404	+	1.67331i	−0.137412	+	0.0627540i
$712$		0			0
$713$	12.6740	−	13.7060i	0.474646	−	0.513295i
$714$		0			0
$715$	−29.2448	+	4.20461i	−1.09369	+	0.157244i
$716$		0			0
$717$	−57.5363	+	4.11507i	−2.14873	+	0.153680i
$718$		0			0
$719$	−19.5013	+	16.8980i	−0.727277	+	0.630189i	−0.937710	−	0.347419i	$-0.887058\pi$
$719$	−19.5013	+	16.8980i	−0.727277	+	0.630189i	0.210433	+	0.977608i	$0.432513\pi$
$720$		0			0
$721$	3.44534	+	1.01164i	0.128311	+	0.0376756i
$722$		0			0
$723$	37.4011	−	27.9981i	1.39096	−	1.04126i
$724$		0			0
$725$	5.88130	−	3.77960i	0.218426	−	0.140371i
$726$		0			0
$727$	9.52954	−	43.8066i	0.353431	−	1.62470i	−0.366337	−	0.930482i	$-0.619388\pi$
$727$	9.52954	−	43.8066i	0.353431	−	1.62470i	0.719768	−	0.694214i	$-0.244248\pi$
$728$		0			0
$729$	16.2346	−	2.33418i	0.601281	−	0.0864512i
$730$		0			0
$731$	−10.5971	−	6.81034i	−0.391948	−	0.251889i
$732$		0			0
$733$	−36.4675	−	19.9128i	−1.34696	−	0.735495i	−0.366166	−	0.930549i	$-0.619330\pi$
$733$	−36.4675	−	19.9128i	−1.34696	−	0.735495i	−0.980792	+	0.195054i	$0.937512\pi$
$734$		0			0
$735$	−0.840028	+	2.86082i	−0.0309849	+	0.105523i
$736$		0			0
$737$	21.4157	+	21.4157i	0.788856	+	0.788856i
$738$		0			0
$739$	5.16801	+	17.6006i	0.190108	+	0.647450i	0.998287	+	0.0585120i	$0.0186356\pi$
$739$	5.16801	+	17.6006i	0.190108	+	0.647450i	−0.808178	+	0.588938i	$0.799546\pi$
$740$		0			0
$741$	14.6581	−	22.8085i	0.538480	−	0.837892i
$742$		0			0
$743$	−1.53677	+	2.05289i	−0.0563788	+	0.0753132i	−0.827844	−	0.560958i	$-0.810433\pi$
$743$	−1.53677	+	2.05289i	−0.0563788	+	0.0753132i	0.771466	+	0.636271i	$0.219524\pi$
$744$		0			0
$745$	17.4676	+	9.53817i	0.639965	+	0.349452i
$746$		0			0
$747$	2.59318	+	6.95259i	0.0948796	+	0.254382i
$748$		0			0
$749$	43.9157	+	6.31412i	1.60464	+	0.230713i
$750$		0			0
$751$	−0.372917	+	1.27004i	−0.0136079	+	0.0463443i	−0.966017	−	0.258478i	$-0.916779\pi$
$751$	−0.372917	+	1.27004i	−0.0136079	+	0.0463443i	0.952409	+	0.304823i	$0.0985972\pi$
$752$		0			0
$753$	2.03306	−	28.4259i	0.0740888	−	1.03590i
$754$		0			0
$755$	−33.6926	−	7.32956i	−1.22620	−	0.266750i
$756$		0			0
$757$	17.3650	+	6.47682i	0.631143	+	0.235404i	0.644618	−	0.764505i	$-0.277017\pi$
$757$	17.3650	+	6.47682i	0.631143	+	0.235404i	−0.0134747	+	0.999909i	$0.504289\pi$
$758$		0			0
$759$	−7.88964	−	42.8941i	−0.286376	−	1.55696i
$760$		0			0
$761$	21.0927	+	46.1866i	0.764610	+	1.67426i	0.738172	+	0.674613i	$0.235689\pi$
$761$	21.0927	+	46.1866i	0.764610	+	1.67426i	0.0264384	+	0.999650i	$0.491583\pi$
$762$		0			0
$763$	−0.634153	−	8.86661i	−0.0229579	−	0.320993i
$764$		0			0
$765$	2.32488	−	1.06172i	0.0840563	−	0.0383867i
$766$		0			0
$767$	−9.87715	−	18.0886i	−0.356643	−	0.653143i
$768$		0			0
$769$	6.75619	−	46.9903i	0.243634	−	1.69451i	−0.389946	−	0.920838i	$-0.627506\pi$
$769$	6.75619	−	46.9903i	0.243634	−	1.69451i	0.633581	−	0.773677i	$-0.281585\pi$
$770$		0			0
$771$	7.30594	−	15.9978i	0.263117	−	0.576146i
$772$		0			0
$773$	−1.00517	−	0.218661i	−0.0361534	−	0.00786469i	0.194452	−	0.980912i	$-0.437707\pi$
$773$	−1.00517	−	0.218661i	−0.0361534	−	0.00786469i	−0.230606	+	0.973047i	$0.574071\pi$
$774$		0			0
$775$	−17.7036	−	8.08520i	−0.635934	−	0.290429i
$776$		0			0
$777$	6.55699	+	30.1420i	0.235231	+	1.08134i
$778$		0			0
$779$	23.8408	−	7.00029i	0.854186	−	0.250812i
$780$		0			0
$781$			73.1706i			2.61825i
$782$		0			0
$783$	4.23429	−	4.23429i	0.151321	−	0.151321i
$784$		0			0
$785$	−6.04196		3.05216e-5i	−0.215647		1.08936e-6i
$786$		0			0
$787$	−33.7810	+	7.34861i	−1.20416	+	0.261949i	−0.769502	−	0.638645i	$-0.779495\pi$
$787$	−33.7810	+	7.34861i	−1.20416	+	0.261949i	−0.434661	+	0.900594i	$0.643132\pi$
$788$		0			0
$789$	0.899983	+	6.25952i	0.0320402	+	0.222845i
$790$		0			0
$791$	−28.2548	+	18.1583i	−1.00463	+	0.645634i
$792$		0			0
$793$	−24.2144	+	9.03151i	−0.859880	+	0.320718i
$794$		0			0
$795$	7.56909	−	2.82308i	0.268448	−	0.100124i
$796$		0			0
$797$	−15.4895	+	8.45789i	−0.548665	+	0.299594i	−0.729569	−	0.683907i	$-0.760279\pi$
$797$	−15.4895	+	8.45789i	−0.548665	+	0.299594i	0.180904	+	0.983501i	$0.442098\pi$
$798$		0			0
$799$	4.71640	+	5.44302i	0.166854	+	0.192560i
$800$		0			0
$801$	0.00225072	+	0.00195026i	7.95252e−5	+	6.89089e-5i
$802$		0			0
$803$	−21.7511	+	58.3170i	−0.767580	+	2.05796i
$804$		0			0
$805$	−10.3984	−	24.8647i	−0.366494	−	0.876367i
$806$		0			0
$807$	8.63103	−	23.1407i	0.303827	−	0.814591i
$808$		0			0
$809$	19.8829	+	17.2286i	0.699046	+	0.605727i	0.930140	−	0.367205i	$-0.119685\pi$
$809$	19.8829	+	17.2286i	0.699046	+	0.605727i	−0.231094	+	0.972931i	$0.574231\pi$
$810$		0			0
$811$	−17.3545	−	20.0281i	−0.609397	−	0.703282i	0.364260	−	0.931297i	$-0.381322\pi$
$811$	−17.3545	−	20.0281i	−0.609397	−	0.703282i	−0.973658	+	0.228015i	$0.926776\pi$
$812$		0			0
$813$	−11.4584	+	6.25677i	−0.401864	+	0.219435i
$814$		0			0
$815$	20.0529	−	43.9091i	0.702422	−	1.53807i
$816$		0			0
$817$	−40.7342	+	15.1931i	−1.42511	+	0.531538i
$818$		0			0
$819$	4.81854	−	3.09669i	0.168373	−	0.108207i
$820$		0			0
$821$	0.458276	+	3.18738i	0.0159939	+	0.111240i	0.996254	−	0.0864699i	$-0.0275586\pi$
$821$	0.458276	+	3.18738i	0.0159939	+	0.111240i	−0.980261	+	0.197710i	$0.936650\pi$
$822$		0			0
$823$	−36.8961	+	8.02626i	−1.28612	+	0.279778i	−0.803106	−	0.595836i	$-0.796821\pi$
$823$	−36.8961	+	8.02626i	−1.28612	+	0.279778i	−0.483012	+	0.875614i	$0.660457\pi$
$824$		0			0
$825$	−39.9086	+	21.7912i	−1.38944	+	0.758673i
$826$		0			0
$827$	−23.1852	+	23.1852i	−0.806230	+	0.806230i	−0.984061	−	0.177831i	$-0.943092\pi$
$827$	−23.1852	+	23.1852i	−0.806230	+	0.806230i	0.177831	+	0.984061i	$0.443092\pi$
$828$		0			0
$829$		−	10.6628i		−	0.370333i	−0.982707	−	0.185166i	$-0.940718\pi$
$829$		−	10.6628i		−	0.370333i	0.982707	−	0.185166i	$-0.0592824\pi$
$830$		0			0
$831$	−52.6428	+	15.4573i	−1.82616	+	0.536208i
$832$		0			0
$833$	−0.206537	−	0.949435i	−0.00715608	−	0.0328960i
$834$		0			0
$835$	−26.6421	−	3.83070i	−0.921989	−	0.132567i
$836$		0			0
$837$	−16.2896	−	3.54359i	−0.563051	−	0.122484i
$838$		0			0
$839$	−3.79858	+	8.31772i	−0.131141	+	0.287160i	−0.963800	−	0.266628i	$-0.914091\pi$
$839$	−3.79858	+	8.31772i	−0.131141	+	0.287160i	0.832658	+	0.553787i	$0.186818\pi$
$840$		0			0
$841$	−3.84890	+	26.7697i	−0.132721	+	0.923094i
$842$		0			0
$843$	18.8251	+	34.4756i	0.648371	+	1.18740i
$844$		0			0
$845$	10.4108	+	3.88309i	0.358143	+	0.133582i
$846$		0			0
$847$	−1.92552	−	26.9223i	−0.0661618	−	0.925063i
$848$		0			0
$849$	25.2133	+	55.2093i	0.865317	+	1.89478i
$850$		0			0
$851$	23.5632	+	18.8566i	0.807735	+	0.646396i
$852$		0			0
$853$	31.7824	+	11.8542i	1.08821	+	0.405881i	0.828605	−	0.559834i	$-0.189135\pi$
$853$	31.7824	+	11.8542i	1.08821	+	0.405881i	0.259605	+	0.965715i	$0.416408\pi$
$854$		0			0
$855$	1.87508	−	8.61939i	0.0641263	−	0.294777i
$856$		0			0
$857$	−1.48521	+	20.7659i	−0.0507338	+	0.709351i	0.906897	+	0.421352i	$0.138444\pi$
$857$	−1.48521	+	20.7659i	−0.0507338	+	0.709351i	−0.957631	+	0.287999i	$0.907010\pi$
$858$		0			0
$859$	9.91196	−	33.7570i	0.338192	−	1.15178i	−0.598355	−	0.801231i	$-0.704179\pi$
$859$	9.91196	−	33.7570i	0.338192	−	1.15178i	0.936546	−	0.350544i	$-0.114003\pi$
$860$		0			0
$861$	24.5779	+	3.53377i	0.837613	+	0.120431i
$862$		0			0
$863$	7.90788	+	21.2019i	0.269187	+	0.721719i	0.999264	+	0.0383543i	$0.0122116\pi$
$863$	7.90788	+	21.2019i	0.269187	+	0.721719i	−0.730077	+	0.683365i	$0.760516\pi$
$864$		0			0
$865$	19.1350	−	5.61844i	0.650609	−	0.191033i
$866$		0			0
$867$	17.5095	−	23.3899i	0.594653	−	0.794363i
$868$		0			0
$869$	−12.6256	+	19.6459i	−0.428296	+	0.666441i
$870$		0			0
$871$	5.18607	+	17.6621i	0.175723	+	0.598458i
$872$		0			0
$873$	8.66554	+	8.66554i	0.293284	+	0.293284i
$874$		0			0
$875$	−21.2360	+	18.4005i	−0.717906	+	0.622050i
$876$		0			0
$877$	24.0343	+	13.1237i	0.811582	+	0.443157i	0.830741	−	0.556659i	$-0.187917\pi$
$877$	24.0343	+	13.1237i	0.811582	+	0.443157i	−0.0191589	+	0.999816i	$0.506099\pi$
$878$		0			0
$879$	−25.6312	−	16.4722i	−0.864519	−	0.555592i
$880$		0			0
$881$	−53.2287	+	7.65313i	−1.79332	+	0.257841i	−0.956935	−	0.290301i	$-0.906245\pi$
$881$	−53.2287	+	7.65313i	−1.79332	+	0.257841i	−0.836386	+	0.548141i	$0.815336\pi$
$882$		0			0
$883$	−3.93431	+	18.0857i	−0.132400	+	0.608633i	0.862351	+	0.506310i	$0.168991\pi$
$883$	−3.93431	+	18.0857i	−0.132400	+	0.608633i	−0.994751	+	0.102323i	$0.967373\pi$
$884$		0			0
$885$	−23.9709	−	20.7711i	−0.805772	−	0.698213i
$886$		0			0
$887$	8.09800	−	6.06209i	0.271904	−	0.203545i	−0.454620	−	0.890685i	$-0.650225\pi$
$887$	8.09800	−	6.06209i	0.271904	−	0.203545i	0.726525	+	0.687140i	$0.241134\pi$
$888$		0			0
$889$	18.2280	+	5.35222i	0.611347	+	0.179508i
$890$		0			0
$891$	−37.9362	+	32.8719i	−1.27091	+	1.10125i
$892$		0			0
$893$	24.7935	−	1.77326i	0.829682	−	0.0593400i
$894$		0			0
$895$	−30.3082	−	22.6886i	−1.01309	−	0.758398i
$896$		0			0
$897$	8.28565	−	25.1798i	0.276650	−	0.840729i
$898$		0			0
$899$	−4.95072	+	2.26092i	−0.165116	+	0.0754059i
$900$		0			0
$901$	−1.72398	+	1.98958i	−0.0574340	+	0.0662824i
$902$		0			0
$903$	−43.3355	−	3.09942i	−1.44212	−	0.103142i
$904$		0			0
$905$	−17.6828	+	3.84657i	−0.587797	+	0.127864i
$906$		0			0
$907$	−16.8680	−	22.5329i	−0.560091	−	0.748194i	0.427710	−	0.903916i	$-0.359321\pi$
$907$	−16.8680	−	22.5329i	−0.560091	−	0.748194i	−0.987801	+	0.155722i	$0.950230\pi$
$908$		0			0
$909$	6.72429	+	3.07088i	0.223031	+	0.101855i
$910$		0			0
$911$	−28.5939	−	44.4929i	−0.947357	−	1.47412i	−0.879207	−	0.476441i	$-0.841927\pi$
$911$	−28.5939	−	44.4929i	−0.947357	−	1.47412i	−0.0681501	−	0.997675i	$-0.521710\pi$
$912$		0			0
$913$	34.4401	+	25.7816i	1.13980	+	0.853245i
$914$		0			0
$915$	−30.0591	+	26.0461i	−0.993722	+	0.861056i
$916$		0			0
$917$	5.53700	−	10.1403i	0.182848	−	0.334861i
$918$		0			0
$919$	27.8551			0.918854			0.459427	−	0.888216i	$-0.348055\pi$
$919$	27.8551			0.918854			0.459427	+	0.888216i	$0.348055\pi$
$920$		0			0
$921$	−13.2936			−0.438039
$922$		0			0
$923$	−21.3134	+	39.0325i	−0.701538	+	1.28477i
$924$		0			0
$925$	10.9959	−	29.4802i	0.361543	−	0.969304i
$926$		0			0
$927$	0.919848	+	0.688590i	0.0302118	+	0.0226163i
$928$		0			0
$929$	4.49750	+	6.99825i	0.147558	+	0.229605i	0.907162	−	0.420780i	$-0.138244\pi$
$929$	4.49750	+	6.99825i	0.147558	+	0.229605i	−0.759604	+	0.650386i	$0.774607\pi$
$930$		0			0
$931$	−3.05038	−	1.39306i	−0.0999722	−	0.0456558i
$932$		0			0
$933$	31.9844	+	42.7262i	1.04712	+	1.39879i
$934$		0			0
$935$	8.01119	−	12.4655i	0.261994	−	0.407666i
$936$		0			0
$937$	−1.30023	−	0.0929942i	−0.0424766	−	0.00303799i	0.0500847	−	0.998745i	$-0.484051\pi$
$937$	−1.30023	−	0.0929942i	−0.0424766	−	0.00303799i	−0.0925613	+	0.995707i	$0.529505\pi$
$938$		0			0
$939$	28.3141	−	32.6762i	0.923995	−	1.06635i
$940$		0			0
$941$	−20.1623	+	9.20783i	−0.657273	+	0.300167i	−0.715993	−	0.698108i	$-0.754026\pi$
$941$	−20.1623	+	9.20783i	−0.657273	+	0.300167i	0.0587193	+	0.998275i	$0.481298\pi$
$942$		0			0
$943$	20.8503	−	12.4671i	0.678979	−	0.405985i
$944$		0			0
$945$	−14.4235	+	19.2673i	−0.469197	+	0.626767i
$946$		0			0
$947$	−42.2225	+	3.01981i	−1.37205	+	0.0981306i	−0.737810	−	0.675009i	$-0.764140\pi$
$947$	−42.2225	+	3.01981i	−1.37205	+	0.0981306i	−0.634236	+	0.773140i	$0.718685\pi$
$948$		0			0
$949$	−28.5898	+	24.7732i	−0.928064	+	0.804172i
$950$		0			0
$951$	14.3433	+	4.21156i	0.465112	+	0.136569i
$952$		0			0
$953$	−20.2697	+	15.1737i	−0.656599	+	0.491524i	−0.874866	−	0.484365i	$-0.839051\pi$
$953$	−20.2697	+	15.1737i	−0.656599	+	0.491524i	0.218267	+	0.975889i	$0.429960\pi$
$954$		0			0
$955$	2.30292	+	32.2014i	0.0745209	+	1.04201i
$956$		0			0
$957$	−2.70287	+	12.4249i	−0.0873713	+	0.401639i
$958$		0			0
$959$	−25.1764	+	3.61981i	−0.812987	+	0.116890i
$960$		0			0
$961$	−13.3325	−	8.56830i	−0.430082	−	0.276397i
$962$		0			0
$963$	12.4606	+	6.80403i	0.401539	+	0.219257i
$964$		0			0
$965$	−49.8435	−	14.6356i	−1.60452	−	0.471138i
$966$		0			0
$967$	−21.1246	−	21.1246i	−0.679322	−	0.679322i	0.280525	−	0.959847i	$-0.409491\pi$
$967$	−21.1246	−	21.1246i	−0.679322	−	0.679322i	−0.959847	+	0.280525i	$0.909491\pi$
$968$		0			0
$969$	3.83090	+	13.0468i	0.123066	+	0.419125i
$970$		0			0
$971$	7.32887	−	11.4039i	0.235195	−	0.365970i	−0.703514	−	0.710681i	$-0.748387\pi$
$971$	7.32887	−	11.4039i	0.235195	−	0.365970i	0.938709	+	0.344711i	$0.112023\pi$
$972$		0			0
$973$	−4.15198	+	5.54639i	−0.133106	+	0.177809i
$974$		0			0
$975$	−27.6365		0.000279217i	−0.885076		8.94210e-6i
$976$		0			0
$977$	6.22378	+	16.6866i	0.199116	+	0.533851i	0.997681	−	0.0680570i	$-0.0216800\pi$
$977$	6.22378	+	16.6866i	0.199116	+	0.533851i	−0.798565	+	0.601908i	$0.794407\pi$
$978$		0			0
$979$	0.0170903	+	0.00245722i	0.000546209	+	7.85330e-5i
$980$		0			0
$981$	0.801391	−	2.72929i	0.0255865	−	0.0871395i
$982$		0			0
$983$	1.16056	−	16.2268i	0.0370163	−	0.517555i	−0.944791	−	0.327674i	$-0.893735\pi$
$983$	1.16056	−	16.2268i	0.0370163	−	0.517555i	0.981807	−	0.189881i	$-0.0608102\pi$
$984$		0			0
$985$	25.7339	+	40.0432i	0.819951	+	1.27588i
$986$		0			0
$987$	23.2740	+	8.68074i	0.740819	+	0.276311i
$988$		0			0
$989$	−34.8326	+	24.3607i	−1.10761	+	0.774625i
$990$		0			0
$991$	11.1861	+	24.4942i	0.355338	+	0.778082i	0.999908	+	0.0135372i	$0.00430914\pi$
$991$	11.1861	+	24.4942i	0.355338	+	0.778082i	−0.644570	+	0.764545i	$0.722964\pi$
$992$		0			0
$993$	0.421045	+	5.88697i	0.0133614	+	0.186817i
$994$		0			0
$995$	14.8136	−	39.7163i	0.469624	−	1.25909i
$996$		0			0
$997$	−3.16280	−	5.79223i	−0.100167	−	0.183442i	0.822790	−	0.568346i	$-0.192416\pi$
$997$	−3.16280	−	5.79223i	−0.100167	−	0.183442i	−0.922957	+	0.384904i	$0.874235\pi$
$998$		0			0
$999$	3.83547	−	26.6763i	0.121349	−	0.843999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.617.9	yes	720
5.3	odd	4	inner	920.2.bv.a.433.9	yes	720
23.17	odd	22	inner	920.2.bv.a.17.9	✓	720
115.63	even	44	inner	920.2.bv.a.753.9	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.9	✓	720	23.17	odd	22	inner
920.2.bv.a.433.9	yes	720	5.3	odd	4	inner
920.2.bv.a.617.9	yes	720	1.1	even	1	trivial
920.2.bv.a.753.9	yes	720	115.63	even	44	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bv (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.934747 + 1.71186i) q^{3} +(-0.159531 + 2.23037i) q^{5} +(-2.01195 - 1.50613i) q^{7} +(-0.434794 - 0.676553i) q^{9} +(-4.24123 - 1.93690i) q^{11} +(-1.69828 - 2.26863i) q^{13} +(-3.66896 - 2.35793i) q^{15} +(1.41764 + 0.101392i) q^{17} +(3.21223 - 3.70711i) q^{19} +(4.45894 - 2.03633i) q^{21} +(2.13210 - 4.29583i) q^{23} +(-4.94910 - 0.711624i) q^{25} +(-4.27183 + 0.305527i) q^{27} +(-1.05670 + 0.915636i) q^{29} +(3.73483 + 1.09665i) q^{31} +(7.28018 - 5.44988i) q^{33} +(3.68019 - 4.24712i) q^{35} +(-1.33764 + 6.14902i) q^{37} +(5.47104 - 0.786617i) q^{39} +(4.26137 + 2.73861i) q^{41} +(-7.77896 - 4.24763i) q^{43} +(1.57833 - 0.861821i) q^{45} +(3.58322 + 3.58322i) q^{47} +(-0.192605 - 0.655954i) q^{49} +(-1.49870 + 2.33203i) q^{51} +(-1.11004 + 1.48283i) q^{53} +(4.99661 - 9.15051i) q^{55} +(3.34343 + 8.96409i) q^{57} +(7.19858 + 1.03500i) q^{59} +(2.56930 - 8.75023i) q^{61} +(-0.144190 + 2.01605i) q^{63} +(5.33081 - 3.42587i) q^{65} +(-6.08607 - 2.26999i) q^{67} +(5.36089 + 7.66538i) q^{69} +(-6.51918 - 14.2750i) q^{71} +(-0.952316 - 13.3151i) q^{73} +(5.84436 - 7.80698i) q^{75} +(5.61591 + 10.2848i) q^{77} +(0.712802 - 4.95765i) q^{79} +(4.47231 - 9.79300i) q^{81} +(-9.01603 - 1.96132i) q^{83} +(-0.452298 + 3.14569i) q^{85} +(-0.579694 - 2.66481i) q^{87} +(-0.00355312 + 0.00104329i) q^{89} +7.12219i q^{91} +(-5.36843 + 5.36843i) q^{93} +(7.75577 + 7.75585i) q^{95} +(-14.8900 + 3.23913i) q^{97} +(0.533643 + 3.71157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 720 * q - 20 * q^23 + 16 * q^25 - 24 * q^27 - 16 * q^31 + 88 * q^37 - 32 * q^41 + 56 * q^47 - 40 * q^55 + 88 * q^57 + 16 * q^73 - 140 * q^75 - 48 * q^77 + 40 * q^81 - 92 * q^85 - 88 * q^87 + 72 * q^93 - 248 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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