LMFDB - Embedded newform 920.2.bv.a.17.9

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			17.9
Character	$\chi$	$=$	920.17
Dual form			920.2.bv.a.433.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.71186 + 0.934747i) q^{3} +(-1.96254 - 1.07164i) q^{5} +(-1.50613 - 2.01195i) q^{7} +(0.434794 - 0.676553i) q^{9} +(-4.24123 + 1.93690i) q^{11} +(2.26863 + 1.69828i) q^{13} +(4.36132 + 2.20316e-5i) q^{15} +(0.101392 + 1.41764i) q^{17} +(-3.21223 - 3.70711i) q^{19} +(4.45894 + 2.03633i) q^{21} +(4.29583 - 2.13210i) q^{23} +(2.70316 + 4.20629i) q^{25} +(0.305527 - 4.27183i) q^{27} +(1.05670 + 0.915636i) q^{29} +(3.73483 - 1.09665i) q^{31} +(5.44988 - 7.28018i) q^{33} +(0.799748 + 5.56257i) q^{35} +(6.14902 - 1.33764i) q^{37} +(-5.47104 - 0.786617i) q^{39} +(4.26137 - 2.73861i) q^{41} +(4.24763 + 7.77896i) q^{43} +(-1.57833 + 0.861821i) q^{45} +(3.58322 + 3.58322i) q^{47} +(0.192605 - 0.655954i) q^{49} +(-1.49870 - 2.33203i) q^{51} +(-1.48283 + 1.11004i) q^{53} +(10.3993 + 0.743823i) q^{55} +(8.96409 + 3.34343i) q^{57} +(-7.19858 + 1.03500i) q^{59} +(2.56930 + 8.75023i) q^{61} +(-2.01605 + 0.144190i) q^{63} +(-2.63234 - 5.76411i) q^{65} +(-2.26999 - 6.08607i) q^{67} +(-5.36089 + 7.66538i) q^{69} +(-6.51918 + 14.2750i) q^{71} +(13.3151 + 0.952316i) q^{73} +(-8.55926 - 4.67382i) q^{75} +(10.2848 + 5.61591i) q^{77} +(-0.712802 - 4.95765i) q^{79} +(4.47231 + 9.79300i) q^{81} +(1.96132 + 9.01603i) q^{83} +(1.32022 - 2.89084i) q^{85} +(-2.66481 - 0.579694i) q^{87} +(0.00355312 + 0.00104329i) q^{89} -7.12219i q^{91} +(-5.36843 + 5.36843i) q^{93} +(2.33144 + 10.7177i) q^{95} +(3.23913 - 14.8900i) q^{97} +(-0.533643 + 3.71157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$1$	$e\left(\frac{7}{22}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.71186	+	0.934747i	−0.988343	+	0.539676i	−0.890236	−	0.455499i	$-0.849461\pi$
$3$	−1.71186	+	0.934747i	−0.988343	+	0.539676i	−0.0981074	+	0.995176i	$0.531279\pi$
$4$		0			0
$5$	−1.96254	−	1.07164i	−0.877677	−	0.479253i
$5$	−1.96254	−	1.07164i	−0.877677	−	0.479253i
$6$		0			0
$7$	−1.50613	−	2.01195i	−0.569262	−	0.760445i	0.419852	−	0.907592i	$-0.362082\pi$
$7$	−1.50613	−	2.01195i	−0.569262	−	0.760445i	−0.989115	+	0.147147i	$0.952991\pi$
$8$		0			0
$9$	0.434794	−	0.676553i	0.144931	−	0.225518i
$10$		0			0
$11$	−4.24123	+	1.93690i	−1.27878	+	0.583998i	−0.934865	−	0.355003i	$-0.884480\pi$
$11$	−4.24123	+	1.93690i	−1.27878	+	0.583998i	−0.343913	+	0.939002i	$0.611752\pi$
$12$		0			0
$13$	2.26863	+	1.69828i	0.629205	+	0.471017i	0.865665	−	0.500624i	$-0.166896\pi$
$13$	2.26863	+	1.69828i	0.629205	+	0.471017i	−0.236460	+	0.971641i	$0.575987\pi$
$14$		0			0
$15$	4.36132		2.20316e-5i	1.12609		5.68854e-6i
$16$		0			0
$17$	0.101392	+	1.41764i	0.0245911	+	0.343828i	0.994821	+	0.101643i	$0.0324098\pi$
$17$	0.101392	+	1.41764i	0.0245911	+	0.343828i	−0.970230	+	0.242186i	$0.922136\pi$
$18$		0			0
$19$	−3.21223	−	3.70711i	−0.736935	−	0.850468i	0.256299	−	0.966598i	$-0.417497\pi$
$19$	−3.21223	−	3.70711i	−0.736935	−	0.850468i	−0.993234	+	0.116129i	$0.962951\pi$
$20$		0			0
$21$	4.45894	+	2.03633i	0.973021	+	0.444364i
$22$		0			0
$23$	4.29583	−	2.13210i	0.895742	−	0.444574i
$23$	4.29583	−	2.13210i	0.895742	−	0.444574i
$24$		0			0
$25$	2.70316	+	4.20629i	0.540632	+	0.841259i
$26$		0			0
$27$	0.305527	−	4.27183i	0.0587987	−	0.822113i
$28$		0			0
$29$	1.05670	+	0.915636i	0.196224	+	0.170029i	0.747431	−	0.664339i	$-0.231287\pi$
$29$	1.05670	+	0.915636i	0.196224	+	0.170029i	−0.551207	+	0.834369i	$0.685832\pi$
$30$		0			0
$31$	3.73483	−	1.09665i	0.670795	−	0.196963i	0.0714382	−	0.997445i	$-0.477241\pi$
$31$	3.73483	−	1.09665i	0.670795	−	0.196963i	0.599357	+	0.800482i	$0.295423\pi$
$32$		0			0
$33$	5.44988	−	7.28018i	0.948702	−	1.26732i
$34$		0			0
$35$	0.799748	+	5.56257i	0.135182	+	0.940246i
$36$		0			0
$37$	6.14902	−	1.33764i	1.01089	−	0.219906i	0.323528	−	0.946219i	$-0.395131\pi$
$37$	6.14902	−	1.33764i	1.01089	−	0.219906i	0.687365	+	0.726312i	$0.258767\pi$
$38$		0			0
$39$	−5.47104	−	0.786617i	−0.876068	−	0.125960i
$40$		0			0
$41$	4.26137	−	2.73861i	0.665514	−	0.427700i	−0.163792	−	0.986495i	$-0.552373\pi$
$41$	4.26137	−	2.73861i	0.665514	−	0.427700i	0.829306	+	0.558795i	$0.188736\pi$
$42$		0			0
$43$	4.24763	+	7.77896i	0.647758	+	1.18628i	0.970799	+	0.239895i	$0.0771130\pi$
$43$	4.24763	+	7.77896i	0.647758	+	1.18628i	−0.323041	+	0.946385i	$0.604705\pi$
$44$		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
$53$	−1.48283	+	1.11004i	−0.203683	+	0.152475i	−0.696250	−	0.717799i	$-0.745149\pi$
$53$	−1.48283	+	1.11004i	−0.203683	+	0.152475i	0.492567	+	0.870274i	$0.336059\pi$
$54$		0			0
$55$	10.3993	+	0.743823i	1.40224	+	0.100297i
$56$		0			0
$57$	8.96409	+	3.34343i	1.18732	+	0.442848i
$58$		0			0
$59$	−7.19858	+	1.03500i	−0.937175	+	0.134745i	−0.593945	−	0.804506i	$-0.702430\pi$
$59$	−7.19858	+	1.03500i	−0.937175	+	0.134745i	−0.343231	+	0.939251i	$0.611521\pi$
$60$		0			0
$61$	2.56930	+	8.75023i	0.328965	+	1.12035i	0.943475	+	0.331443i	$0.107536\pi$
$61$	2.56930	+	8.75023i	0.328965	+	1.12035i	−0.614510	+	0.788909i	$0.710646\pi$
$62$		0			0
$63$	−2.01605	+	0.144190i	−0.253998	+	0.0181663i
$64$		0			0
$65$	−2.63234	−	5.76411i	−0.326502	−	0.714949i
$66$		0			0
$67$	−2.26999	−	6.08607i	−0.277323	−	0.743532i	−0.998699	−	0.0509887i	$-0.983763\pi$
$67$	−2.26999	−	6.08607i	−0.277323	−	0.743532i	0.721376	−	0.692544i	$-0.243510\pi$
$68$		0			0
$69$	−5.36089	+	7.66538i	−0.645375	+	0.922803i
$70$		0			0
$71$	−6.51918	+	14.2750i	−0.773684	+	1.69413i	−0.0553161	+	0.998469i	$0.517617\pi$
$71$	−6.51918	+	14.2750i	−0.773684	+	1.69413i	−0.718368	+	0.695663i	$0.755111\pi$
$72$		0			0
$73$	13.3151	+	0.952316i	1.55842	+	0.111460i	0.823744	−	0.566962i	$-0.191881\pi$
$73$	13.3151	+	0.952316i	1.55842	+	0.111460i	0.734673	+	0.678422i	$0.237336\pi$
$74$		0			0
$75$	−8.55926	−	4.67382i	−0.988338	−	0.539686i
$76$		0			0
$77$	10.2848	+	5.61591i	1.17206	+	0.639992i
$78$		0			0
$79$	−0.712802	−	4.95765i	−0.0801965	−	0.557779i	−0.989818	−	0.142341i	$-0.954537\pi$
$79$	−0.712802	−	4.95765i	−0.0801965	−	0.557779i	0.909621	−	0.415439i	$-0.136372\pi$
$80$		0			0
$81$	4.47231	+	9.79300i	0.496924	+	1.08811i
$82$		0			0
$83$	1.96132	+	9.01603i	0.215283	+	0.989638i	0.950239	+	0.311523i	$0.100839\pi$
$83$	1.96132	+	9.01603i	0.215283	+	0.989638i	−0.734956	+	0.678115i	$0.762797\pi$
$84$		0			0
$85$	1.32022	−	2.89084i	0.143198	−	0.313555i
$86$		0			0
$87$	−2.66481	−	0.579694i	−0.285698	−	0.0621497i
$88$		0			0
$89$	0.00355312	+	0.00104329i	0.000376630	+	0.000110588i	0.281921	−	0.959438i	$-0.409028\pi$
$89$	0.00355312	+	0.00104329i	0.000376630	+	0.000110588i	−0.281544	+	0.959548i	$0.590847\pi$
$90$		0			0
$91$		−	7.12219i		−	0.746608i
$92$		0			0
$93$	−5.36843	+	5.36843i	−0.556680	+	0.556680i
$94$		0			0
$95$	2.33144	+	10.7177i	0.239201	+	1.09961i
$96$		0			0
$97$	3.23913	−	14.8900i	0.328883	−	1.51185i	−0.454744	−	0.890622i	$-0.650269\pi$
$97$	3.23913	−	14.8900i	0.328883	−	1.51185i	0.783628	−	0.621231i	$-0.213367\pi$
$98$		0			0
$99$	−0.533643	+	3.71157i	−0.0536331	+	0.373027i
$100$		0			0
$101$	−7.73272	−	4.96952i	−0.769435	−	0.494486i	0.0960774	−	0.995374i	$-0.469370\pi$
$101$	−7.73272	−	4.96952i	−0.769435	−	0.494486i	−0.865512	+	0.500888i	$0.833007\pi$
$102$		0			0
$103$	−0.499298	+	1.33867i	−0.0491973	+	0.131903i	−0.959224	−	0.282646i	$-0.908788\pi$
$103$	−0.499298	+	1.33867i	−0.0491973	+	0.131903i	0.910027	+	0.414549i	$0.136061\pi$
$104$		0			0
$105$	−6.56865	−	8.77478i	−0.641035	−	0.856331i
$106$		0			0
$107$	8.46040	−	15.4941i	0.817898	−	1.49787i	−0.0486734	−	0.998815i	$-0.515499\pi$
$107$	8.46040	−	15.4941i	0.817898	−	1.49787i	0.866571	−	0.499053i	$-0.166319\pi$
$108$		0			0
$109$	−2.31623	+	2.67307i	−0.221855	+	0.256034i	−0.855755	−	0.517380i	$-0.826907\pi$
$109$	−2.31623	+	2.67307i	−0.221855	+	0.256034i	0.633901	+	0.773414i	$0.281453\pi$
$110$		0			0
$111$	−9.27592	+	8.03763i	−0.880432	+	0.762898i
$112$		0			0
$113$	12.5213	−	4.67020i	1.17790	−	0.439335i	0.317159	−	0.948372i	$-0.397271\pi$
$113$	12.5213	−	4.67020i	1.17790	−	0.439335i	0.860745	+	0.509037i	$0.169998\pi$
$114$		0			0
$115$	−10.7156	−	0.419250i	−0.999235	−	0.0390952i
$116$		0			0
$117$	2.13536	−	0.796449i	0.197414	−	0.0736317i
$118$		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
$123$	−4.73496	+	8.67143i	−0.426937	+	0.781876i
$124$		0			0
$125$	−0.797427	−	11.1519i	−0.0713241	−	0.997453i
$126$		0			0
$127$	2.64159	−	7.08239i	0.234404	−	0.628460i	−0.765484	−	0.643455i	$-0.777500\pi$
$127$	2.64159	−	7.08239i	0.234404	−	0.628460i	0.999888	+	0.0149945i	$0.00477308\pi$
$128$		0			0
$129$	−14.5427	−	9.34603i	−1.28041	−	0.822872i
$130$		0			0
$131$	0.654229	−	4.55027i	0.0571603	−	0.397559i	−0.941076	−	0.338195i	$-0.890184\pi$
$131$	0.654229	−	4.55027i	0.0571603	−	0.397559i	0.998236	−	0.0593638i	$-0.0189072\pi$
$132$		0			0
$133$	−2.62049	+	12.0462i	−0.227225	+	1.04454i
$134$		0			0
$135$	−5.17748	+	8.05623i	−0.445607	+	0.693370i
$136$		0			0
$137$	−7.15629	+	7.15629i	−0.611403	+	0.611403i	−0.943312	−	0.331909i	$-0.892307\pi$
$137$	−7.15629	+	7.15629i	−0.611403	+	0.611403i	0.331909	+	0.943312i	$0.392307\pi$
$138$		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
$143$	−12.9112	−	2.80865i	−1.07969	−	0.234871i
$144$		0			0
$145$	−1.09259	−	2.92938i	−0.0907343	−	0.243272i
$146$		0			0
$147$	0.283437	+	1.30294i	0.0233775	+	0.107465i
$148$		0			0
$149$	−3.69741	−	8.09619i	−0.302903	−	0.663266i	0.695573	−	0.718456i	$-0.255151\pi$
$149$	−3.69741	−	8.09619i	−0.302903	−	0.663266i	−0.998476	+	0.0551902i	$0.982423\pi$
$150$		0			0
$151$	−2.19453	−	15.2633i	−0.178588	−	1.24211i	−0.860034	−	0.510238i	$-0.829557\pi$
$151$	−2.19453	−	15.2633i	−0.178588	−	1.24211i	0.681446	−	0.731869i	$-0.261352\pi$
$152$		0			0
$153$	1.00319	+	0.547785i	0.0811034	+	0.0442858i
$154$		0			0
$155$	−8.50498	−	1.85019i	−0.683137	−	0.148611i
$156$		0			0
$157$	2.69516	+	0.192762i	0.215097	+	0.0153841i	0.178472	−	0.983945i	$-0.442885\pi$
$157$	2.69516	+	0.192762i	0.215097	+	0.0153841i	0.0366255	+	0.999329i	$0.488339\pi$
$158$		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
$163$	7.54410	+	20.2265i	0.590899	+	1.58426i	0.795852	+	0.605491i	$0.207023\pi$
$163$	7.54410	+	20.2265i	0.590899	+	1.58426i	−0.204953	+	0.978772i	$0.565704\pi$
$164$		0			0
$165$	−18.4974	+	8.44736i	−1.44002	+	0.657626i
$166$		0			0
$167$	12.0066	−	0.858728i	0.929098	−	0.0664504i	0.401419	−	0.915894i	$-0.368517\pi$
$167$	12.0066	−	0.858728i	0.929098	−	0.0664504i	0.527679	+	0.849444i	$0.323063\pi$
$168$		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
$173$	8.35636	+	3.11676i	0.635322	+	0.236963i	0.646428	−	0.762975i	$-0.276262\pi$
$173$	8.35636	+	3.11676i	0.635322	+	0.236963i	−0.0111052	+	0.999938i	$0.503535\pi$
$174$		0			0
$175$	4.39155	−	11.7738i	0.331970	−	0.890018i
$176$		0			0
$177$	11.3555	−	8.50063i	0.853532	−	0.638946i
$178$		0			0
$179$	9.15380	+	14.2436i	0.684187	+	1.06462i	0.993519	+	0.113662i	$0.0362581\pi$
$179$	9.15380	+	14.2436i	0.684187	+	1.06462i	−0.309332	+	0.950954i	$0.600106\pi$
$180$		0			0
$181$	2.28005	−	7.76512i	0.169474	−	0.577177i	−0.830327	−	0.557276i	$-0.811847\pi$
$181$	2.28005	−	7.76512i	0.169474	−	0.577177i	0.999802	−	0.0199013i	$-0.00633521\pi$
$182$		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
$187$	−3.17586	−	5.81615i	−0.232242	−	0.425319i
$188$		0			0
$189$	−9.05486	+	5.81920i	−0.658644	+	0.423285i
$190$		0			0
$191$	14.2907	+	2.05470i	1.03404	+	0.148673i	0.638378	−	0.769723i	$-0.279606\pi$
$191$	14.2907	+	2.05470i	1.03404	+	0.148673i	0.395663	+	0.918396i	$0.370515\pi$
$192$		0			0
$193$	−22.7009	+	4.93827i	−1.63404	+	0.355464i	−0.933621	−	0.358263i	$-0.883369\pi$
$193$	−22.7009	+	4.93827i	−1.63404	+	0.355464i	−0.700423	+	0.713728i	$0.747005\pi$
$194$		0			0
$195$	9.89419	+	7.40677i	0.708537	+	0.530410i
$196$		0			0
$197$	−12.7569	+	17.0412i	−0.908888	+	1.21413i	0.0674151	+	0.997725i	$0.478525\pi$
$197$	−12.7569	+	17.0412i	−0.908888	+	1.21413i	−0.976303	+	0.216407i	$0.930566\pi$
$198$		0			0
$199$	18.1890	−	5.34078i	1.28939	−	0.378598i	0.436033	−	0.899931i	$-0.356383\pi$
$199$	18.1890	−	5.34078i	1.28939	−	0.378598i	0.853354	+	0.521333i	$0.174565\pi$
$200$		0			0
$201$	9.57484	+	8.29665i	0.675357	+	0.585201i
$202$		0			0
$203$	0.250689	−	3.50509i	0.0175949	−	0.246009i
$204$		0			0
$205$	−11.2979	+	0.807987i	−0.789082	+	0.0564323i
$206$		0			0
$207$	0.425321	−	3.83338i	0.0295619	−	0.266438i
$208$		0			0
$209$	20.8041	+	9.50090i	1.43905	+	0.657191i
$210$		0			0
$211$	7.53495	+	8.69580i	0.518727	+	0.598643i	0.953312	−	0.301988i	$-0.0976502\pi$
$211$	7.53495	+	8.69580i	0.518727	+	0.598643i	−0.434584	+	0.900631i	$0.643105\pi$
$212$		0			0
$213$	−2.18359	−	30.5306i	−0.149617	−	2.09192i
$214$		0			0
$215$	0.000100115	−	19.8185i	6.82779e−6	−	1.35161i
$216$		0			0
$217$	−7.83152	−	5.86260i	−0.531638	−	0.397979i
$218$		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
$223$	−1.10874	−	1.48110i	−0.0742466	−	0.0991818i	0.761880	−	0.647718i	$-0.224276\pi$
$223$	−1.10874	−	1.48110i	−0.0742466	−	0.0991818i	−0.836127	+	0.548536i	$0.815185\pi$
$224$		0			0
$225$	4.02110		4.06260e-5i	0.268073		2.70840e-6i
$226$		0			0
$227$	−2.56980	+	1.40322i	−0.170563	+	0.0931347i	−0.562263	−	0.826959i	$-0.690069\pi$
$227$	−2.56980	+	1.40322i	−0.170563	+	0.0931347i	0.391699	+	0.920093i	$0.371887\pi$
$228$		0			0
$229$	9.28260			0.613411			0.306706	−	0.951804i	$-0.400773\pi$
$229$	9.28260			0.613411			0.306706	+	0.951804i	$0.400773\pi$
$230$		0			0
$231$	−22.8556			−1.50378
$232$		0			0
$233$	0.417724	−	0.228095i	0.0273660	−	0.0149430i	−0.465508	−	0.885044i	$-0.654128\pi$
$233$	0.417724	−	0.228095i	0.0273660	−	0.0149430i	0.492874	+	0.870101i	$0.335946\pi$
$234$		0			0
$235$	−3.19229	−	10.8722i	−0.208242	−	0.709221i
$236$		0			0
$237$	5.85437	+	7.82052i	0.380282	+	0.507997i
$238$		0			0
$239$	−15.9892	+	24.8796i	−1.03425	+	1.60933i	−0.271722	+	0.962376i	$0.587593\pi$
$239$	−15.9892	+	24.8796i	−1.03425	+	1.60933i	−0.762530	+	0.646952i	$0.776043\pi$
$240$		0			0
$241$	−21.7888	+	9.95062i	−1.40354	+	0.640976i	−0.966076	−	0.258260i	$-0.916851\pi$
$241$	−21.7888	+	9.95062i	−1.40354	+	0.640976i	−0.437465	+	0.899235i	$0.644124\pi$
$242$		0			0
$243$	−6.52443	−	4.88412i	−0.418542	−	0.313317i
$244$		0			0
$245$	−1.08095	+	1.08093i	−0.0690591	+	0.0690584i
$246$		0			0
$247$	−0.991666	−	13.8653i	−0.0630982	−	0.882228i
$248$		0			0
$249$	−11.7852	−	13.6009i	−0.746857	−	0.861919i
$250$		0			0
$251$	−13.2909	−	6.06976i	−0.838915	−	0.383120i	−0.0508459	−	0.998707i	$-0.516192\pi$
$251$	−13.2909	−	6.06976i	−0.838915	−	0.383120i	−0.788069	+	0.615587i	$0.788919\pi$
$252$		0			0
$253$	−14.0899	+	17.3633i	−0.885825	+	1.09162i
$254$		0			0
$255$	0.442170	+	6.18278i	0.0276898	+	0.387181i
$256$		0			0
$257$	0.643264	−	8.99401i	0.0401257	−	0.561031i	−0.937132	−	0.348975i	$-0.886530\pi$
$257$	0.643264	−	8.99401i	0.0401257	−	0.561031i	0.977258	−	0.212055i	$-0.0680157\pi$
$258$		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
$263$	1.94303	−	2.59558i	0.119812	−	0.160051i	−0.736625	−	0.676301i	$-0.763582\pi$
$263$	1.94303	−	2.59558i	0.119812	−	0.160051i	0.856438	+	0.516251i	$0.172673\pi$
$264$		0			0
$265$	4.09969	−	0.589425i	0.251842	−	0.0362081i
$266$		0			0
$267$	−0.00705766	+	0.00153530i	−0.000431922	+	9.39588e-5i
$268$		0			0
$269$	12.5338	+	1.80209i	0.764202	+	0.109876i	0.513384	−	0.858159i	$-0.328392\pi$
$269$	12.5338	+	1.80209i	0.764202	+	0.109876i	0.250817	+	0.968034i	$0.419301\pi$
$270$		0			0
$271$	5.63097	−	3.61880i	0.342057	−	0.219827i	−0.358322	−	0.933598i	$-0.616651\pi$
$271$	5.63097	−	3.61880i	0.342057	−	0.219827i	0.700379	+	0.713771i	$0.253014\pi$
$272$		0			0
$273$	6.65744	+	12.1922i	0.402927	+	0.737905i
$274$		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	0.997323	+	0.0731172i	$0.0232947\pi$
$281$	10.8881	+	16.9422i	0.649530	+	1.01069i	−0.347793	+	0.937571i	$0.613069\pi$
$282$		0			0
$283$	24.9114	−	18.6484i	1.48083	−	1.10853i	0.512550	−	0.858658i	$-0.328701\pi$
$283$	24.9114	−	18.6484i	1.48083	−	1.10853i	0.968278	−	0.249876i	$-0.0803898\pi$
$284$		0			0
$285$	−14.0095	−	16.1679i	−0.829849	−	0.957706i
$286$		0			0
$287$	−11.9281	−	4.44895i	−0.704094	−	0.262614i
$288$		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
$293$	−15.5812	+	1.11439i	−0.910264	+	0.0651034i	−0.518612	−	0.855010i	$-0.673551\pi$
$293$	−15.5812	+	1.11439i	−0.910264	+	0.0651034i	−0.391652	+	0.920113i	$0.628096\pi$
$294$		0			0
$295$	15.2367	+	5.68308i	0.887114	+	0.330882i
$296$		0			0
$297$	6.97830	+	18.7096i	0.404922	+	1.08564i
$298$		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
$303$	17.8826	+	1.27899i	1.02733	+	0.0734759i
$304$		0			0
$305$	4.33476	−	19.9261i	0.248208	−	1.14096i
$306$		0			0
$307$	5.98199	+	3.26642i	0.341410	+	0.186424i	0.640802	−	0.767706i	$-0.278602\pi$
$307$	5.98199	+	3.26642i	0.341410	+	0.186424i	−0.299392	+	0.954130i	$0.596784\pi$
$308$		0			0
$309$	−0.396589	−	2.75834i	−0.0225611	−	0.156916i
$310$		0			0
$311$	11.3674	+	24.8911i	0.644584	+	1.41144i	0.896215	+	0.443619i	$0.146306\pi$
$311$	11.3674	+	24.8911i	0.644584	+	1.41144i	−0.251631	+	0.967823i	$0.580967\pi$
$312$		0			0
$313$	4.71208	+	21.6611i	0.266343	+	1.22436i	0.894784	+	0.446500i	$0.147330\pi$
$313$	4.71208	+	21.6611i	0.266343	+	1.22436i	−0.628441	+	0.777857i	$0.716307\pi$
$314$		0			0
$315$	4.11110	+	1.87750i	0.231634	+	0.105785i
$316$		0			0
$317$	−7.48916	−	1.62917i	−0.420633	−	0.0915031i	−0.00273328	−	0.999996i	$-0.500870\pi$
$317$	−7.48916	−	1.62917i	−0.420633	−	0.0915031i	−0.417900	+	0.908493i	$0.637234\pi$
$318$		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
$325$	−1.01097	+	14.1332i	−0.0560787	+	0.783972i
$326$		0			0
$327$	1.46642	−	6.74101i	0.0810931	−	0.372779i
$328$		0			0
$329$	1.81247	−	12.6060i	0.0999249	−	0.694993i
$330$		0			0
$331$	2.54562	+	1.63597i	0.139920	+	0.0899212i	0.608728	−	0.793379i	$-0.291680\pi$
$331$	2.54562	+	1.63597i	0.139920	+	0.0899212i	−0.468808	+	0.883300i	$0.655316\pi$
$332$		0			0
$333$	1.76858	−	4.74174i	0.0969174	−	0.259846i
$334$		0			0
$335$	−2.06715	+	14.3768i	−0.112940	+	0.785489i
$336$		0			0
$337$	7.74704	−	14.1876i	0.422008	−	0.772850i	−0.577029	−	0.816724i	$-0.695788\pi$
$337$	7.74704	−	14.1876i	0.422008	−	0.772850i	0.999037	+	0.0438736i	$0.0139699\pi$
$338$		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
$343$	−18.0933	+	6.74844i	−0.976944	+	0.364381i
$344$		0			0
$345$	18.7355	−	9.29868i	1.00869	−	0.500624i
$346$		0			0
$347$	−1.41015	+	0.525958i	−0.0757007	+	0.0282349i	−0.387029	−	0.922067i	$-0.626499\pi$
$347$	−1.41015	+	0.525958i	−0.0757007	+	0.0282349i	0.311329	+	0.950302i	$0.399226\pi$
$348$		0			0
$349$	12.8199	−	11.1085i	0.686236	−	0.594627i	−0.240361	−	0.970684i	$-0.577266\pi$
$349$	12.8199	−	11.1085i	0.686236	−	0.594627i	0.926597	+	0.376057i	$0.122720\pi$
$350$		0			0
$351$	7.94787	−	9.17233i	0.424226	−	0.489583i
$352$		0			0
$353$	9.32334	−	17.0744i	0.496231	−	0.908780i	−0.502784	−	0.864412i	$-0.667691\pi$
$353$	9.32334	−	17.0744i	0.496231	−	0.908780i	0.999015	−	0.0443678i	$-0.0141274\pi$
$354$		0			0
$355$	28.0919	−	21.0291i	1.49096	−	1.11611i
$356$		0			0
$357$	−2.43468	+	6.52764i	−0.128857	+	0.345479i
$358$		0			0
$359$	−7.27262	−	4.67383i	−0.383834	−	0.246675i	0.334467	−	0.942407i	$-0.391444\pi$
$359$	−7.27262	−	4.67383i	−0.383834	−	0.246675i	−0.718301	+	0.695732i	$0.755080\pi$
$360$		0			0
$361$	−0.720259	+	5.00951i	−0.0379083	+	0.263658i
$362$		0			0
$363$	−4.45259	+	20.4682i	−0.233700	+	1.07430i
$364$		0			0
$365$	−25.1110	−	16.1380i	−1.31437	−	0.844703i
$366$		0			0
$367$	18.0897	−	18.0897i	0.944276	−	0.944276i	−0.0542509	−	0.998527i	$-0.517277\pi$
$367$	18.0897	−	18.0897i	0.944276	−	0.944276i	0.998527	+	0.0542509i	$0.0172771\pi$
$368$		0			0
$369$		−	4.07378i		−	0.212072i
$370$		0			0
$371$	4.46667	+	1.31153i	0.231898	+	0.0680913i
$372$		0			0
$373$	−21.0638	−	4.58214i	−1.09064	−	0.237254i	−0.368935	−	0.929455i	$-0.620278\pi$
$373$	−21.0638	−	4.58214i	−1.09064	−	0.237254i	−0.721705	+	0.692201i	$0.756641\pi$
$374$		0			0
$375$	11.7893	+	18.3451i	0.608795	+	0.947334i
$376$		0			0
$377$	0.842260	+	3.87181i	0.0433786	+	0.199408i
$378$		0			0
$379$	−3.35290	−	7.34183i	−0.172227	−	0.377125i	0.803760	−	0.594954i	$-0.202830\pi$
$379$	−3.35290	−	7.34183i	−0.172227	−	0.377125i	−0.975987	+	0.217829i	$0.930102\pi$
$380$		0			0
$381$	2.09820	+	14.5933i	0.107494	+	0.747637i
$382$		0			0
$383$	12.6618	+	6.91387i	0.646989	+	0.353282i	0.769002	−	0.639246i	$-0.220753\pi$
$383$	12.6618	+	6.91387i	0.646989	+	0.353282i	−0.122014	+	0.992528i	$0.538935\pi$
$384$		0			0
$385$	−14.1661	−	22.0431i	−0.721970	−	1.12342i
$386$		0			0
$387$	7.10972	+	0.508498i	0.361408	+	0.0258484i
$388$		0			0
$389$	−7.66853	+	16.7917i	−0.388810	+	0.851375i	0.609473	+	0.792807i	$0.291381\pi$
$389$	−7.66853	+	16.7917i	−0.388810	+	0.851375i	−0.998283	+	0.0585687i	$0.981346\pi$
$390$		0			0
$391$	3.45812	+	5.87376i	0.174884	+	0.297049i
$392$		0			0
$393$	3.13340	+	8.40096i	0.158059	+	0.423773i
$394$		0			0
$395$	−3.91392	+	10.4935i	−0.196931	+	0.527984i
$396$		0			0
$397$	7.00243	−	0.500824i	0.351442	−	0.0251356i	0.105498	−	0.994420i	$-0.466356\pi$
$397$	7.00243	−	0.500824i	0.351442	−	0.0251356i	0.245944	+	0.969284i	$0.420902\pi$
$398$		0			0
$399$	−6.77423	−	23.0709i	−0.339136	−	1.15499i
$400$		0			0
$401$	−16.9558	+	2.43787i	−0.846730	+	0.121741i	−0.552005	−	0.833841i	$-0.686137\pi$
$401$	−16.9558	+	2.43787i	−0.846730	+	0.121741i	−0.294725	+	0.955582i	$0.595228\pi$
$402$		0			0
$403$	10.3354	+	3.85489i	0.514841	+	0.192026i
$404$		0			0
$405$	1.71749	−	24.0119i	0.0853427	−	1.19316i
$406$		0			0
$407$	−23.4885	+	17.5833i	−1.16428	+	0.871571i
$408$		0			0
$409$	3.47028	+	5.39986i	0.171594	+	0.267006i	0.916390	−	0.400287i	$-0.131089\pi$
$409$	3.47028	+	5.39986i	0.171594	+	0.267006i	−0.744796	+	0.667293i	$0.767453\pi$
$410$		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
$417$	2.57684	+	4.71913i	0.126189	+	0.231097i
$418$		0			0
$419$	−11.6813	+	7.50714i	−0.570670	+	0.366748i	−0.793928	−	0.608012i	$-0.791967\pi$
$419$	−11.6813	+	7.50714i	−0.570670	+	0.366748i	0.223257	+	0.974760i	$0.428331\pi$
$420$		0			0
$421$	−6.96130	−	1.00088i	−0.339273	−	0.0487801i	−0.0294274	−	0.999567i	$-0.509368\pi$
$421$	−6.96130	−	1.00088i	−0.339273	−	0.0487801i	−0.309846	+	0.950787i	$0.600277\pi$
$422$		0			0
$423$	3.98220	−	0.866274i	0.193621	−	0.0421197i
$424$		0			0
$425$	−5.68894	+	4.25859i	−0.275954	+	0.206572i
$426$		0			0
$427$	13.7353	−	18.3482i	0.664699	−	0.887934i
$428$		0			0
$429$	24.7275	−	7.26065i	1.19386	−	0.350548i
$430$		0			0
$431$	−13.4737	−	11.6751i	−0.649008	−	0.562368i	0.266917	−	0.963720i	$-0.413995\pi$
$431$	−13.4737	−	11.6751i	−0.649008	−	0.562368i	−0.915924	+	0.401351i	$0.868541\pi$
$432$		0			0
$433$	2.17781	−	30.4497i	0.104659	−	1.46332i	−0.625596	−	0.780147i	$-0.715144\pi$
$433$	2.17781	−	30.4497i	0.104659	−	1.46332i	0.730255	−	0.683175i	$-0.239401\pi$
$434$		0			0
$435$	4.60858	+	3.99340i	0.220965	+	0.191469i
$436$		0			0
$437$	−21.7031	−	9.07630i	−1.03820	−	0.434178i
$438$		0			0
$439$	26.2480	+	11.9870i	1.25275	+	0.572110i	0.927608	−	0.373556i	$-0.121862\pi$
$439$	26.2480	+	11.9870i	1.25275	+	0.572110i	0.325139	+	0.945666i	$0.394589\pi$
$440$		0			0
$441$	−0.360044	−	0.415513i	−0.0171449	−	0.0197863i
$442$		0			0
$443$	−1.47646	−	20.6436i	−0.0701486	−	0.980806i	−0.903645	−	0.428281i	$-0.859119\pi$
$443$	−1.47646	−	20.6436i	−0.0701486	−	0.980806i	0.833497	−	0.552524i	$-0.186335\pi$
$444$		0			0
$445$	−0.00585512	−	0.00585518i	−0.000277559	−	0.000277562i
$446$		0			0
$447$	13.8973	+	10.4034i	0.657321	+	0.492065i
$448$		0			0
$449$	29.7488	−	13.5858i	1.40393	−	0.641156i	0.437771	−	0.899086i	$-0.355768\pi$
$449$	29.7488	−	13.5858i	1.40393	−	0.641156i	0.966163	+	0.257931i	$0.0830406\pi$
$450$		0			0
$451$	−12.7690	+	19.8689i	−0.601268	+	0.935592i
$452$		0			0
$453$	18.0240	+	24.0773i	0.846842	+	1.13125i
$454$		0			0
$455$	−7.63244	+	13.9776i	−0.357815	+	0.655281i
$456$		0			0
$457$	−11.0409	+	6.02878i	−0.516471	+	0.282015i	−0.716271	−	0.697822i	$-0.754153\pi$
$457$	−11.0409	+	6.02878i	−0.516471	+	0.282015i	0.199800	+	0.979837i	$0.435971\pi$
$458$		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
$463$	−4.90931	+	2.68068i	−0.228155	+	0.124582i	−0.589261	−	0.807943i	$-0.700581\pi$
$463$	−4.90931	+	2.68068i	−0.228155	+	0.124582i	0.361106	+	0.932525i	$0.382399\pi$
$464$		0			0
$465$	16.2888	−	4.78274i	0.755375	−	0.221794i
$466$		0			0
$467$	−3.59285	−	4.79948i	−0.166257	−	0.222093i	0.709673	−	0.704531i	$-0.248843\pi$
$467$	−3.59285	−	4.79948i	−0.166257	−	0.222093i	−0.875930	+	0.482437i	$0.839752\pi$
$468$		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
$473$	−33.0823	−	24.7651i	−1.52112	−	1.13870i
$474$		0			0
$475$	6.91002	−	23.5325i	0.317053	−	1.07974i
$476$		0			0
$477$	0.106270	+	1.48585i	0.00486578	+	0.0680325i
$478$		0			0
$479$	10.3604	+	11.9565i	0.473378	+	0.546307i	0.941348	−	0.337437i	$-0.109560\pi$
$479$	10.3604	+	11.9565i	0.473378	+	0.546307i	−0.467970	+	0.883744i	$0.655015\pi$
$480$		0			0
$481$	16.2215	+	7.40813i	0.739639	+	0.337782i
$482$		0			0
$483$	23.4965	−	0.759194i	1.06913	−	0.0345445i
$484$		0			0
$485$	−22.3137	+	25.7511i	−1.01321	+	1.16930i
$486$		0			0
$487$	−2.10827	+	29.4774i	−0.0955346	+	1.33575i	0.693080	+	0.720861i	$0.256253\pi$
$487$	−2.10827	+	29.4774i	−0.0955346	+	1.33575i	−0.788615	+	0.614888i	$0.789201\pi$
$488$		0			0
$489$	−31.8211	−	27.5732i	−1.43900	−	1.24690i
$490$		0			0
$491$	14.3242	−	4.20597i	0.646443	−	0.189813i	0.0579554	−	0.998319i	$-0.481542\pi$
$491$	14.3242	−	4.20597i	0.646443	−	0.189813i	0.588487	+	0.808506i	$0.299724\pi$
$492$		0			0
$493$	−1.19090	+	1.59086i	−0.0536355	+	0.0716486i
$494$		0			0
$495$	5.02478	−	6.71224i	0.225847	−	0.301693i
$496$		0			0
$497$	38.5393	−	8.38371i	1.72872	−	0.376061i
$498$		0			0
$499$	15.3568	+	2.20797i	0.687464	+	0.0988424i	0.477190	−	0.878800i	$-0.341655\pi$
$499$	15.3568	+	2.20797i	0.687464	+	0.0988424i	0.210274	+	0.977642i	$0.432564\pi$
$500$		0			0
$501$	−19.7509	+	12.6931i	−0.882406	+	0.567088i
$502$		0			0
$503$	−5.07222	−	9.28907i	−0.226159	−	0.414179i	0.739818	−	0.672807i	$-0.234912\pi$
$503$	−5.07222	−	9.28907i	−0.226159	−	0.414179i	−0.965977	+	0.258628i	$0.916730\pi$
$504$		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	0.136340	−	0.990662i	$-0.456466\pi$
$509$	12.5718	−	42.8157i	0.557236	−	1.89777i	0.420896	−	0.907109i	$-0.361716\pi$
$510$		0			0
$511$	−18.1382	−	28.2236i	−0.802388	−	1.24854i
$512$		0			0
$513$	−16.8175	+	12.5894i	−0.742512	+	0.555838i
$514$		0			0
$515$	2.41447	−	2.09213i	0.106394	−	0.0921903i
$516$		0			0
$517$	−22.1376	−	8.25689i	−0.973609	−	0.363138i
$518$		0			0
$519$	−17.2183	+	2.47562i	−0.755800	+	0.108668i
$520$		0			0
$521$	12.5745	+	42.8249i	0.550900	+	1.87619i	0.476946	+	0.878933i	$0.341744\pi$
$521$	12.5745	+	42.8249i	0.550900	+	1.87619i	0.0739543	+	0.997262i	$0.476438\pi$
$522$		0			0
$523$	40.6039	−	2.90405i	1.77548	−	0.126985i	0.855215	−	0.518273i	$-0.173425\pi$
$523$	40.6039	−	2.90405i	1.77548	−	0.126985i	0.920268	+	0.391288i	$0.127970\pi$
$524$		0			0
$525$	3.48783	+	24.2602i	0.152222	+	1.05880i
$526$		0			0
$527$	1.93333	+	5.18346i	0.0842171	+	0.225795i
$528$		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
$533$	14.3184	+	1.02407i	0.620199	+	0.0443575i
$534$		0			0
$535$	−33.2080	+	21.3413i	−1.43571	+	0.922663i
$536$		0			0
$537$	−28.9842	−	15.8266i	−1.25076	−	0.682967i
$538$		0			0
$539$	0.453636	+	3.15511i	0.0195395	+	0.135900i
$540$		0			0
$541$	−3.44131	−	7.53543i	−0.147954	−	0.323973i	0.821116	−	0.570762i	$-0.193352\pi$
$541$	−3.44131	−	7.53543i	−0.147954	−	0.323973i	−0.969069	+	0.246788i	$0.920625\pi$
$542$		0			0
$543$	3.35530	+	15.4241i	0.143990	+	0.661911i
$544$		0			0
$545$	7.41028	−	2.76385i	0.317422	−	0.118390i
$546$		0			0
$547$	15.6837	+	3.41178i	0.670586	+	0.145877i	0.534953	−	0.844882i	$-0.320329\pi$
$547$	15.6837	+	3.41178i	0.670586	+	0.145877i	0.135633	+	0.990759i	$0.456693\pi$
$548$		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
$555$	26.8179	−	5.83373i	1.13836	−	0.247628i
$556$		0			0
$557$	−3.56519	+	16.3889i	−0.151062	+	0.694421i	0.837848	+	0.545904i	$0.183814\pi$
$557$	−3.56519	+	16.3889i	−0.151062	+	0.694421i	−0.988910	+	0.148517i	$0.952550\pi$
$558$		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
$563$	10.8848	−	29.1833i	0.458741	−	1.22993i	−0.477519	−	0.878622i	$-0.658464\pi$
$563$	10.8848	−	29.1833i	0.458741	−	1.22993i	0.936259	−	0.351310i	$-0.114264\pi$
$564$		0			0
$565$	−29.5784	−	4.25288i	−1.24437	−	0.178920i
$566$		0			0
$567$	12.9671	−	23.7476i	0.544569	−	0.997304i
$568$		0			0
$569$	−2.84620	+	3.28468i	−0.119319	+	0.137701i	−0.812266	−	0.583287i	$-0.801766\pi$
$569$	−2.84620	+	3.28468i	−0.119319	+	0.137701i	0.692947	+	0.720988i	$0.256312\pi$
$570$		0			0
$571$	12.3574	−	10.7077i	0.517141	−	0.448105i	−0.356769	−	0.934192i	$-0.616122\pi$
$571$	12.3574	−	10.7077i	0.517141	−	0.448105i	0.873910	+	0.486087i	$0.161576\pi$
$572$		0			0
$573$	−26.3843	+	9.84085i	−1.10222	+	0.411107i
$574$		0			0
$575$	20.5806	+	12.3061i	0.858269	+	0.513200i
$576$		0			0
$577$	−30.9105	+	11.5290i	−1.28682	+	0.479960i	−0.897448	−	0.441120i	$-0.854581\pi$
$577$	−30.9105	+	11.5290i	−1.28682	+	0.479960i	−0.389373	+	0.921080i	$0.627308\pi$
$578$		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
$583$	4.13900	−	7.58001i	0.171420	−	0.313932i
$584$		0			0
$585$	−5.04425	−	0.725280i	−0.208554	−	0.0299866i
$586$		0			0
$587$	14.8437	−	39.7975i	0.612665	−	1.64262i	−0.144585	−	0.989492i	$-0.546185\pi$
$587$	14.8437	−	39.7975i	0.612665	−	1.64262i	0.757250	−	0.653125i	$-0.226542\pi$
$588$		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
$593$	−2.18383	+	10.0389i	−0.0896791	+	0.412248i	−0.999999	−	0.00165816i	$-0.999472\pi$
$593$	−2.18383	+	10.0389i	−0.0896791	+	0.412248i	0.910320	+	0.413906i	$0.135836\pi$
$594$		0			0
$595$	−7.80463	+	1.69775i	−0.319959	+	0.0696011i
$596$		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	0.597496	−	0.801872i	$-0.296163\pi$
$601$	16.3423	+	4.79853i	0.666616	+	0.195736i	0.0691204	+	0.997608i	$0.477981\pi$
$602$		0			0
$603$	−5.10453	−	1.11042i	−0.207873	−	0.0452199i
$604$		0			0
$605$	−22.5004	+	8.39208i	−0.914770	+	0.341186i
$606$		0			0
$607$	5.51036	+	25.3307i	0.223659	+	1.02814i	0.942821	+	0.333300i	$0.108162\pi$
$607$	5.51036	+	25.3307i	0.223659	+	1.02814i	−0.719162	+	0.694842i	$0.755474\pi$
$608$		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
$613$	23.3530	+	12.7517i	0.943221	+	0.515037i	0.875793	−	0.482687i	$-0.160339\pi$
$613$	23.3530	+	12.7517i	0.943221	+	0.515037i	0.0674276	+	0.997724i	$0.478521\pi$
$614$		0			0
$615$	18.5852	−	11.9439i	0.749429	−	0.481624i
$616$		0			0
$617$	−35.4655	−	2.53654i	−1.42779	−	0.102117i	−0.664071	−	0.747670i	$-0.731173\pi$
$617$	−35.4655	−	2.53654i	−1.42779	−	0.102117i	−0.763716	+	0.645553i	$0.776627\pi$
$618$		0			0
$619$	−12.5295	+	27.4358i	−0.503604	+	1.10274i	0.471678	+	0.881771i	$0.343649\pi$
$619$	−12.5295	+	27.4358i	−0.503604	+	1.10274i	−0.975281	+	0.220967i	$0.929079\pi$
$620$		0			0
$621$	−7.79548	−	19.0024i	−0.312822	−	0.762542i
$622$		0			0
$623$	−0.00325240	−	0.00872002i	−0.000130305	−	0.000349360i
$624$		0			0
$625$	−10.3858	+	22.7406i	−0.415433	+	0.909624i
$626$		0			0
$627$	−44.4946	+	3.18232i	−1.77694	+	0.127090i
$628$		0			0
$629$	2.51975	+	8.58148i	0.100469	+	0.342166i
$630$		0			0
$631$	31.0040	−	4.45771i	1.23425	−	0.177459i	0.505857	−	0.862617i	$-0.331176\pi$
$631$	31.0040	−	4.45771i	1.23425	−	0.177459i	0.728394	+	0.685159i	$0.240267\pi$
$632$		0			0
$633$	−21.0272	−	7.84272i	−0.835755	−	0.311720i
$634$		0			0
$635$	−12.7740	+	11.0687i	−0.506922	+	0.439246i
$636$		0			0
$637$	1.55094	−	1.16102i	0.0614505	−	0.0460013i
$638$		0			0
$639$	6.82330	+	10.6173i	0.269926	+	0.420013i
$640$		0			0
$641$	6.71934	−	22.8840i	0.265398	−	0.903862i	−0.713696	−	0.700455i	$-0.752980\pi$
$641$	6.71934	−	22.8840i	0.265398	−	0.903862i	0.979094	−	0.203407i	$-0.0652014\pi$
$642$		0			0
$643$	19.1680	+	19.1680i	0.755913	+	0.755913i	0.975576	−	0.219663i	$-0.0704957\pi$
$643$	19.1680	+	19.1680i	0.755913	+	0.755913i	−0.219663	+	0.975576i	$0.570496\pi$
$644$		0			0
$645$	18.5251	+	33.9266i	0.729425	+	1.33586i
$646$		0			0
$647$	22.6931	+	41.5593i	0.892157	+	1.63386i	0.766926	+	0.641735i	$0.221785\pi$
$647$	22.6931	+	41.5593i	0.892157	+	1.63386i	0.125230	+	0.992128i	$0.460033\pi$
$648$		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
$653$	−22.1639	+	4.82145i	−0.867339	+	0.188678i	−0.624153	−	0.781302i	$-0.714556\pi$
$653$	−22.1639	+	4.82145i	−0.867339	+	0.188678i	−0.243185	+	0.969980i	$0.578192\pi$
$654$		0			0
$655$	−6.16022	+	8.22900i	−0.240700	+	0.321534i
$656$		0			0
$657$	6.43363	−	8.59432i	0.251000	−	0.335297i
$658$		0			0
$659$	−29.8294	+	8.75869i	−1.16199	+	0.341190i	−0.805204	−	0.592997i	$-0.797944\pi$
$659$	−29.8294	+	8.75869i	−1.16199	+	0.341190i	−0.356783	+	0.934187i	$0.616126\pi$
$660$		0			0
$661$	−3.60466	−	3.12346i	−0.140205	−	0.121488i	0.581935	−	0.813235i	$-0.302296\pi$
$661$	−3.60466	−	3.12346i	−0.140205	−	0.121488i	−0.722140	+	0.691747i	$0.756841\pi$
$662$		0			0
$663$	0.560422	−	7.83572i	0.0217650	−	0.304314i
$664$		0			0
$665$	18.0521	−	20.8330i	0.700029	−	0.807868i
$666$		0			0
$667$	6.49163	+	1.68042i	0.251357	+	0.0650662i
$668$		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
$673$	−2.11852	−	29.6208i	−0.0816629	−	1.14180i	−0.858747	−	0.512400i	$-0.828757\pi$
$673$	−2.11852	−	29.6208i	−0.0816629	−	1.14180i	0.777084	−	0.629397i	$-0.216698\pi$
$674$		0			0
$675$	18.7945	−	10.2623i	0.723399	−	0.394996i
$676$		0			0
$677$	2.21406	+	1.65742i	0.0850931	+	0.0636999i	0.640977	−	0.767560i	$-0.278529\pi$
$677$	2.21406	+	1.65742i	0.0850931	+	0.0636999i	−0.555884	+	0.831260i	$0.687620\pi$
$678$		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
$683$	2.48748	+	3.32288i	0.0951806	+	0.127146i	0.845603	−	0.533812i	$-0.179241\pi$
$683$	2.48748	+	3.32288i	0.0951806	+	0.127146i	−0.750423	+	0.660958i	$0.770150\pi$
$684$		0			0
$685$	21.7135	−	6.37555i	0.829631	−	0.243597i
$686$		0			0
$687$	−15.8905	+	8.67688i	−0.606261	+	0.331044i
$688$		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
$693$	8.27122	−	4.51643i	0.314198	−	0.171565i
$694$		0			0
$695$	−2.95423	+	5.41020i	−0.112060	+	0.205221i
$696$		0			0
$697$	4.31444	+	5.76341i	0.163421	+	0.218305i
$698$		0			0
$699$	−0.501875	+	0.780932i	−0.0189826	+	0.0295376i
$700$		0			0
$701$	21.4174	−	9.78099i	0.808923	−	0.369423i	0.0323711	−	0.999476i	$-0.489694\pi$
$701$	21.4174	−	9.78099i	0.808923	−	0.369423i	0.776552	+	0.630053i	$0.216967\pi$
$702$		0			0
$703$	−24.7108	−	18.4983i	−0.931986	−	0.697676i
$704$		0			0
$705$	15.6275	+	15.6276i	0.588565	+	0.588571i
$706$		0			0
$707$	1.64804	+	23.0426i	0.0619808	+	0.866605i
$708$		0			0
$709$	21.9733	+	25.3586i	0.825226	+	0.952362i	0.999477	−	0.0323393i	$-0.0102957\pi$
$709$	21.9733	+	25.3586i	0.825226	+	0.952362i	−0.174251	+	0.984701i	$0.555750\pi$
$710$		0			0
$711$	−3.66404	−	1.67331i	−0.137412	−	0.0627540i
$712$		0			0
$713$	13.7060	−	12.6740i	0.513295	−	0.474646i
$714$		0			0
$715$	22.3289	+	19.3483i	0.835053	+	0.723585i
$716$		0			0
$717$	4.11507	−	57.5363i	0.153680	−	2.14873i
$718$		0			0
$719$	19.5013	+	16.8980i	0.727277	+	0.630189i	0.937710	−	0.347419i	$-0.112942\pi$
$719$	19.5013	+	16.8980i	0.727277	+	0.630189i	−0.210433	+	0.977608i	$0.567487\pi$
$720$		0			0
$721$	3.44534	−	1.01164i	0.128311	−	0.0376756i
$722$		0			0
$723$	27.9981	−	37.4011i	1.04126	−	1.39096i
$724$		0			0
$725$	−0.995003	+	6.91990i	−0.0369535	+	0.256999i
$726$		0			0
$727$	−43.8066	+	9.52954i	−1.62470	+	0.353431i	−0.930482	−	0.366337i	$-0.880612\pi$
$727$	−43.8066	+	9.52954i	−1.62470	+	0.353431i	−0.694214	+	0.719768i	$0.744248\pi$
$728$		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
$733$	19.9128	+	36.4675i	0.735495	+	1.34696i	0.930549	+	0.366166i	$0.119330\pi$
$733$	19.9128	+	36.4675i	0.735495	+	1.34696i	−0.195054	+	0.980792i	$0.562488\pi$
$734$		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	0.808178	+	0.588938i	$0.200454\pi$
$739$	−5.16801	+	17.6006i	−0.190108	+	0.647450i	−0.998287	+	0.0585120i	$0.981364\pi$
$740$		0			0
$741$	14.6581	+	22.8085i	0.538480	+	0.837892i
$742$		0			0
$743$	−2.05289	+	1.53677i	−0.0753132	+	0.0563788i	−0.636271	−	0.771466i	$-0.719524\pi$
$743$	−2.05289	+	1.53677i	−0.0753132	+	0.0563788i	0.560958	+	0.827844i	$0.310433\pi$
$744$		0			0
$745$	−1.41990	+	19.8514i	−0.0520212	+	0.727300i
$746$		0			0
$747$	6.95259	+	2.59318i	0.254382	+	0.0948796i
$748$		0			0
$749$	−43.9157	+	6.31412i	−1.60464	+	0.230713i
$750$		0			0
$751$	−0.372917	−	1.27004i	−0.0136079	−	0.0463443i	0.952409	−	0.304823i	$-0.0985972\pi$
$751$	−0.372917	−	1.27004i	−0.0136079	−	0.0463443i	−0.966017	+	0.258478i	$0.916779\pi$
$752$		0			0
$753$	28.4259	−	2.03306i	1.03590	−	0.0740888i
$754$		0			0
$755$	−12.0499	+	32.3066i	−0.438541	+	1.17576i
$756$		0			0
$757$	6.47682	+	17.3650i	0.235404	+	0.631143i	0.999909	−	0.0134747i	$-0.00428926\pi$
$757$	6.47682	+	17.3650i	0.235404	+	0.631143i	−0.764505	+	0.644618i	$0.777017\pi$
$758$		0			0
$759$	7.88964	−	42.8941i	0.286376	−	1.55696i
$760$		0			0
$761$	21.0927	−	46.1866i	0.764610	−	1.67426i	0.0264384	−	0.999650i	$-0.491583\pi$
$761$	21.0927	−	46.1866i	0.764610	−	1.67426i	0.738172	−	0.674613i	$-0.235689\pi$
$762$		0			0
$763$	8.86661	+	0.634153i	0.320993	+	0.0229579i
$764$		0			0
$765$	−1.38178	−	2.15012i	−0.0499584	−	0.0777377i
$766$		0			0
$767$	−18.0886	−	9.87715i	−0.653143	−	0.356643i
$768$		0			0
$769$	−6.75619	−	46.9903i	−0.243634	−	1.69451i	−0.633581	−	0.773677i	$-0.718415\pi$
$769$	−6.75619	−	46.9903i	−0.243634	−	1.69451i	0.389946	−	0.920838i	$-0.372494\pi$
$770$		0			0
$771$	7.30594	+	15.9978i	0.263117	+	0.576146i
$772$		0			0
$773$	0.218661	+	1.00517i	0.00786469	+	0.0361534i	0.980912	−	0.194452i	$-0.0622929\pi$
$773$	0.218661	+	1.00517i	0.00786469	+	0.0361534i	−0.973047	+	0.230606i	$0.925929\pi$
$774$		0			0
$775$	14.7087	+	12.7454i	0.528351	+	0.457828i
$776$		0			0
$777$	30.1420	+	6.55699i	1.08134	+	0.235231i
$778$		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
$785$	−5.08281	−	3.26656i	−0.181413	−	0.116588i
$786$		0			0
$787$	7.34861	−	33.7810i	0.261949	−	1.20416i	−0.638645	−	0.769502i	$-0.720505\pi$
$787$	7.34861	−	33.7810i	0.261949	−	1.20416i	0.900594	−	0.434661i	$-0.143132\pi$
$788$		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
$793$	−9.03151	+	24.2144i	−0.320718	+	0.859880i
$794$		0			0
$795$	−6.46713	+	4.84118i	−0.229366	+	0.171699i
$796$		0			0
$797$	8.45789	−	15.4895i	0.299594	−	0.548665i	−0.683907	−	0.729569i	$-0.739721\pi$
$797$	8.45789	−	15.4895i	0.299594	−	0.548665i	0.983501	+	0.180904i	$0.0579024\pi$
$798$		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
$803$	−58.3170	+	21.7511i	−2.05796	+	0.767580i
$804$		0			0
$805$	15.2955	+	22.1907i	0.539097	+	0.782119i
$806$		0			0
$807$	−23.1407	+	8.63103i	−0.814591	+	0.303827i
$808$		0			0
$809$	−19.8829	+	17.2286i	−0.699046	+	0.605727i	−0.930140	−	0.367205i	$-0.880315\pi$
$809$	−19.8829	+	17.2286i	−0.699046	+	0.605727i	0.231094	+	0.972931i	$0.425769\pi$
$810$		0			0
$811$	−17.3545	+	20.0281i	−0.609397	+	0.703282i	−0.973658	−	0.228015i	$-0.926776\pi$
$811$	−17.3545	+	20.0281i	−0.609397	+	0.703282i	0.364260	+	0.931297i	$0.381322\pi$
$812$		0			0
$813$	−6.25677	+	11.4584i	−0.219435	+	0.401864i
$814$		0			0
$815$	6.86997	−	47.7800i	0.240645	−	1.67366i
$816$		0			0
$817$	15.1931	−	40.7342i	0.531538	−	1.42511i
$818$		0			0
$819$	−4.81854	−	3.09669i	−0.168373	−	0.108207i
$820$		0			0
$821$	0.458276	−	3.18738i	0.0159939	−	0.111240i	−0.980261	−	0.197710i	$-0.936650\pi$
$821$	0.458276	−	3.18738i	0.0159939	−	0.111240i	0.996254	+	0.0864699i	$0.0275586\pi$
$822$		0			0
$823$	−8.02626	+	36.8961i	−0.279778	+	1.28612i	0.595836	+	0.803106i	$0.296821\pi$
$823$	−8.02626	+	36.8961i	−0.279778	+	1.28612i	−0.875614	+	0.483012i	$0.839543\pi$
$824$		0			0
$825$	45.3545	+	3.24428i	1.57904	+	0.112951i
$826$		0			0
$827$	23.1852	−	23.1852i	0.806230	−	0.806230i	−0.177831	−	0.984061i	$-0.556908\pi$
$827$	23.1852	−	23.1852i	0.806230	−	0.806230i	0.984061	+	0.177831i	$0.0569081\pi$
$828$		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
$833$	0.949435	+	0.206537i	0.0328960	+	0.00715608i
$834$		0			0
$835$	−24.4837	−	11.1815i	−0.847294	−	0.386951i
$836$		0			0
$837$	−3.54359	−	16.2896i	−0.122484	−	0.563051i
$838$		0			0
$839$	3.79858	+	8.31772i	0.131141	+	0.287160i	0.963800	−	0.266628i	$-0.0859094\pi$
$839$	3.79858	+	8.31772i	0.131141	+	0.287160i	−0.832658	+	0.553787i	$0.813182\pi$
$840$		0			0
$841$	−3.84890	−	26.7697i	−0.132721	−	0.923094i
$842$		0			0
$843$	−34.4756	−	18.8251i	−1.18740	−	0.648371i
$844$		0			0
$845$	−2.36195	+	10.8575i	−0.0812537	+	0.373508i
$846$		0			0
$847$	−26.9223	−	1.92552i	−0.925063	−	0.0661618i
$848$		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
$853$	−11.8542	−	31.7824i	−0.405881	−	1.08821i	−0.965715	−	0.259605i	$-0.916408\pi$
$853$	−11.8542	−	31.7824i	−0.405881	−	1.08821i	0.559834	−	0.828605i	$-0.310865\pi$
$854$		0			0
$855$	8.26480	+	3.08266i	0.282650	+	0.105425i
$856$		0			0
$857$	20.7659	−	1.48521i	0.709351	−	0.0507338i	0.287999	−	0.957631i	$-0.407010\pi$
$857$	20.7659	−	1.48521i	0.709351	−	0.0507338i	0.421352	+	0.906897i	$0.361556\pi$
$858$		0			0
$859$	−9.91196	−	33.7570i	−0.338192	−	1.15178i	−0.936546	−	0.350544i	$-0.885997\pi$
$859$	−9.91196	−	33.7570i	−0.338192	−	1.15178i	0.598355	−	0.801231i	$-0.295821\pi$
$860$		0			0
$861$	24.5779	−	3.53377i	0.837613	−	0.120431i
$862$		0			0
$863$	−21.2019	−	7.90788i	−0.721719	−	0.269187i	−0.0383543	−	0.999264i	$-0.512212\pi$
$863$	−21.2019	−	7.90788i	−0.721719	−	0.269187i	−0.683365	+	0.730077i	$0.739484\pi$
$864$		0			0
$865$	−13.0597	−	15.0718i	−0.444042	−	0.512457i
$866$		0			0
$867$	−23.3899	+	17.5095i	−0.794363	+	0.594653i
$868$		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
$877$	13.1237	+	24.0343i	0.443157	+	0.811582i	0.999816	−	0.0191589i	$-0.00609885\pi$
$877$	13.1237	+	24.0343i	0.443157	+	0.811582i	−0.556659	+	0.830741i	$0.687917\pi$
$878$		0			0
$879$	25.6312	−	16.4722i	0.864519	−	0.555592i
$880$		0			0
$881$	−53.2287	−	7.65313i	−1.79332	−	0.257841i	−0.836386	−	0.548141i	$-0.815336\pi$
$881$	−53.2287	−	7.65313i	−1.79332	−	0.257841i	−0.956935	+	0.290301i	$0.906245\pi$
$882$		0			0
$883$	−18.0857	+	3.93431i	−0.608633	+	0.132400i	−0.506310	−	0.862351i	$-0.668991\pi$
$883$	−18.0857	+	3.93431i	−0.608633	+	0.132400i	−0.102323	+	0.994751i	$0.532627\pi$
$884$		0			0
$885$	−31.3953	+	4.51380i	−1.05534	+	0.151730i
$886$		0			0
$887$	−6.06209	+	8.09800i	−0.203545	+	0.271904i	−0.890685	−	0.454620i	$-0.849775\pi$
$887$	−6.06209	+	8.09800i	−0.203545	+	0.271904i	0.687140	+	0.726525i	$0.258866\pi$
$888$		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
$893$	1.77326	−	24.7935i	0.0593400	−	0.829682i
$894$		0			0
$895$	−2.70069	−	37.7633i	−0.0902742	−	1.26229i
$896$		0			0
$897$	−25.1798	+	8.28565i	−0.840729	+	0.276650i
$898$		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
$903$	3.09942	+	43.3355i	0.103142	+	1.44212i
$904$		0			0
$905$	−12.7961	+	12.7960i	−0.425358	+	0.425354i
$906$		0			0
$907$	−22.5329	−	16.8680i	−0.748194	−	0.560091i	0.155722	−	0.987801i	$-0.450230\pi$
$907$	−22.5329	−	16.8680i	−0.748194	−	0.560091i	−0.903916	+	0.427710i	$0.859321\pi$
$908$		0			0
$909$	−6.72429	+	3.07088i	−0.223031	+	0.101855i
$910$		0			0
$911$	−28.5939	+	44.4929i	−0.947357	+	1.47412i	−0.0681501	+	0.997675i	$0.521710\pi$
$911$	−28.5939	+	44.4929i	−0.947357	+	1.47412i	−0.879207	+	0.476441i	$0.841927\pi$
$912$		0			0
$913$	−25.7816	−	34.4401i	−0.853245	−	1.13980i
$914$		0			0
$915$	11.2053	+	38.1626i	0.370437	+	1.26162i
$916$		0			0
$917$	−10.1403	+	5.53700i	−0.334861	+	0.182848i
$918$		0			0
$919$	−27.8551			−0.918854			−0.459427	−	0.888216i	$-0.651945\pi$
$919$	−27.8551			−0.918854			−0.459427	+	0.888216i	$0.651945\pi$
$920$		0			0
$921$	−13.2936			−0.438039
$922$		0			0
$923$	−39.0325	+	21.3134i	−1.28477	+	0.701538i
$924$		0			0
$925$	22.2483	+	22.2488i	0.731520	+	0.731535i
$926$		0			0
$927$	0.688590	+	0.919848i	0.0226163	+	0.0302118i
$928$		0			0
$929$	−4.49750	+	6.99825i	−0.147558	+	0.229605i	−0.907162	−	0.420780i	$-0.861756\pi$
$929$	−4.49750	+	6.99825i	−0.147558	+	0.229605i	0.759604	+	0.650386i	$0.225393\pi$
$930$		0			0
$931$	−3.05038	+	1.39306i	−0.0999722	+	0.0456558i
$932$		0			0
$933$	−42.7262	−	31.9844i	−1.39879	−	1.04712i
$934$		0			0
$935$	−7.48537e−5		14.8178i	−2.44798e−6		0.484595i
$936$		0			0
$937$	−0.0929942	−	1.30023i	−0.00303799	−	0.0424766i	0.995707	−	0.0925613i	$-0.0295054\pi$
$937$	−0.0929942	−	1.30023i	−0.00303799	−	0.0424766i	−0.998745	+	0.0500847i	$0.984051\pi$
$938$		0			0
$939$	−28.3141	−	32.6762i	−0.923995	−	1.06635i
$940$		0			0
$941$	−20.1623	−	9.20783i	−0.657273	−	0.300167i	0.0587193	−	0.998275i	$-0.481298\pi$
$941$	−20.1623	−	9.20783i	−0.657273	−	0.300167i	−0.715993	+	0.698108i	$0.754026\pi$
$942$		0			0
$943$	12.4671	−	20.8503i	0.405985	−	0.678979i
$944$		0			0
$945$	24.0067	−	1.71687i	0.780937	−	0.0558498i
$946$		0			0
$947$	3.01981	−	42.2225i	0.0981306	−	1.37205i	−0.675009	−	0.737810i	$-0.735860\pi$
$947$	3.01981	−	42.2225i	0.0981306	−	1.37205i	0.773140	−	0.634236i	$-0.218685\pi$
$948$		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
$953$	−15.1737	+	20.2697i	−0.491524	+	0.656599i	−0.975889	−	0.218267i	$-0.929960\pi$
$953$	−15.1737	+	20.2697i	−0.491524	+	0.656599i	0.484365	+	0.874866i	$0.339051\pi$
$954$		0			0
$955$	−25.8443	−	19.3470i	−0.836301	−	0.626054i
$956$		0			0
$957$	12.4249	−	2.70287i	0.401639	−	0.0873713i
$958$		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
$963$	−6.80403	−	12.4606i	−0.219257	−	0.401539i
$964$		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	0.938709	−	0.344711i	$-0.112023\pi$
$971$	7.32887	+	11.4039i	0.235195	+	0.365970i	−0.703514	+	0.710681i	$0.748387\pi$
$972$		0			0
$973$	−5.54639	+	4.15198i	−0.177809	+	0.133106i
$974$		0			0
$975$	−11.4804	−	25.1392i	−0.367666	−	0.805097i
$976$		0			0
$977$	16.6866	+	6.22378i	0.533851	+	0.199116i	0.601908	−	0.798565i	$-0.294407\pi$
$977$	16.6866	+	6.22378i	0.533851	+	0.199116i	−0.0680570	+	0.997681i	$0.521680\pi$
$978$		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
$983$	16.2268	−	1.16056i	0.517555	−	0.0370163i	0.189881	−	0.981807i	$-0.439190\pi$
$983$	16.2268	−	1.16056i	0.517555	−	0.0370163i	0.327674	+	0.944791i	$0.393735\pi$
$984$		0			0
$985$	43.2979	−	19.7732i	1.37959	−	0.630028i
$986$		0			0
$987$	8.68074	+	23.2740i	0.276311	+	0.740819i
$988$		0			0
$989$	34.8326	+	24.3607i	1.10761	+	0.774625i
$990$		0			0
$991$	11.1861	−	24.4942i	0.355338	−	0.778082i	−0.644570	−	0.764545i	$-0.722964\pi$
$991$	11.1861	−	24.4942i	0.355338	−	0.778082i	0.999908	−	0.0135372i	$-0.00430914\pi$
$992$		0			0
$993$	−5.88697	−	0.421045i	−0.186817	−	0.0133614i
$994$		0			0
$995$	−41.4202	−	9.01063i	−1.31311	−	0.285656i
$996$		0			0
$997$	−5.79223	−	3.16280i	−0.183442	−	0.100167i	0.384904	−	0.922957i	$-0.374235\pi$
$997$	−5.79223	−	3.16280i	−0.183442	−	0.100167i	−0.568346	+	0.822790i	$0.692416\pi$
$998$		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.17.9	✓	720
5.3	odd	4	inner	920.2.bv.a.753.9	yes	720
23.19	odd	22	inner	920.2.bv.a.617.9	yes	720
115.88	even	44	inner	920.2.bv.a.433.9	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.9	✓	720	1.1	even	1	trivial
920.2.bv.a.433.9	yes	720	115.88	even	44	inner
920.2.bv.a.617.9	yes	720	23.19	odd	22	inner
920.2.bv.a.753.9	yes	720	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(-1.71186 + 0.934747i) q^{3} +(-1.96254 - 1.07164i) q^{5} +(-1.50613 - 2.01195i) q^{7} +(0.434794 - 0.676553i) q^{9} +(-4.24123 + 1.93690i) q^{11} +(2.26863 + 1.69828i) q^{13} +(4.36132 + 2.20316e-5i) q^{15} +(0.101392 + 1.41764i) q^{17} +(-3.21223 - 3.70711i) q^{19} +(4.45894 + 2.03633i) q^{21} +(4.29583 - 2.13210i) q^{23} +(2.70316 + 4.20629i) q^{25} +(0.305527 - 4.27183i) q^{27} +(1.05670 + 0.915636i) q^{29} +(3.73483 - 1.09665i) q^{31} +(5.44988 - 7.28018i) q^{33} +(0.799748 + 5.56257i) q^{35} +(6.14902 - 1.33764i) q^{37} +(-5.47104 - 0.786617i) q^{39} +(4.26137 - 2.73861i) q^{41} +(4.24763 + 7.77896i) q^{43} +(-1.57833 + 0.861821i) q^{45} +(3.58322 + 3.58322i) q^{47} +(0.192605 - 0.655954i) q^{49} +(-1.49870 - 2.33203i) q^{51} +(-1.48283 + 1.11004i) q^{53} +(10.3993 + 0.743823i) q^{55} +(8.96409 + 3.34343i) q^{57} +(-7.19858 + 1.03500i) q^{59} +(2.56930 + 8.75023i) q^{61} +(-2.01605 + 0.144190i) q^{63} +(-2.63234 - 5.76411i) q^{65} +(-2.26999 - 6.08607i) q^{67} +(-5.36089 + 7.66538i) q^{69} +(-6.51918 + 14.2750i) q^{71} +(13.3151 + 0.952316i) q^{73} +(-8.55926 - 4.67382i) q^{75} +(10.2848 + 5.61591i) q^{77} +(-0.712802 - 4.95765i) q^{79} +(4.47231 + 9.79300i) q^{81} +(1.96132 + 9.01603i) q^{83} +(1.32022 - 2.89084i) q^{85} +(-2.66481 - 0.579694i) q^{87} +(0.00355312 + 0.00104329i) q^{89} -7.12219i q^{91} +(-5.36843 + 5.36843i) q^{93} +(2.33144 + 10.7177i) q^{95} +(3.23913 - 14.8900i) q^{97} +(-0.533643 + 3.71157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 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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