LMFDB - Embedded newform 920.2.bv.a.617.17

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)

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")

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);

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			617.17
Character	$\chi$	$=$	920.617
Dual form			920.2.bv.a.753.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0448920 + 0.0822135i) q^{3} +(-0.769038 + 2.09966i) q^{5} +(4.17150 + 3.12275i) q^{7} +(1.61718 + 2.51638i) q^{9} +(-3.36211 - 1.53542i) q^{11} +(1.31000 + 1.74996i) q^{13} +(-0.138097 - 0.157483i) q^{15} +(-6.18393 - 0.442284i) q^{17} +(2.05565 - 2.37235i) q^{19} +(-0.443999 + 0.202768i) q^{21} +(-0.466813 + 4.77306i) q^{23} +(-3.81716 - 3.22944i) q^{25} +(-0.559777 + 0.0400361i) q^{27} +(1.75914 - 1.52430i) q^{29} +(-0.693792 - 0.203716i) q^{31} +(0.277164 - 0.207482i) q^{33} +(-9.76475 + 6.35723i) q^{35} +(1.77600 - 8.16416i) q^{37} +(-0.202679 + 0.0291408i) q^{39} +(-4.34358 - 2.79145i) q^{41} +(-0.726651 - 0.396781i) q^{43} +(-6.52722 + 1.46034i) q^{45} +(6.39744 + 6.39744i) q^{47} +(5.67774 + 19.3366i) q^{49} +(0.313971 - 0.488548i) q^{51} +(-6.14168 + 8.20433i) q^{53} +(5.80946 - 5.87849i) q^{55} +(0.102757 + 0.275502i) q^{57} +(1.11563 + 0.160403i) q^{59} +(1.41688 - 4.82546i) q^{61} +(-1.11195 + 15.5471i) q^{63} +(-4.68176 + 1.40478i) q^{65} +(3.47401 + 1.29574i) q^{67} +(-0.371454 - 0.252650i) q^{69} +(5.27911 + 11.5596i) q^{71} +(-0.0898299 - 1.25599i) q^{73} +(0.436864 - 0.168846i) q^{75} +(-9.23029 - 16.9040i) q^{77} +(-0.267327 + 1.85930i) q^{79} +(-3.70596 + 8.11493i) q^{81} +(14.0832 + 3.06361i) q^{83} +(5.68433 - 12.6440i) q^{85} +(0.0463470 + 0.213054i) q^{87} +(-11.9814 + 3.51804i) q^{89} +11.3907i q^{91} +(0.0478939 - 0.0478939i) q^{93} +(3.40025 + 6.14060i) q^{95} +(10.4438 - 2.27190i) q^{97} +(-1.57342 - 10.9434i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.0448920	+	0.0822135i	−0.0259184	+	0.0474660i	−0.890317	−	0.455341i	$-0.849517\pi$
$3$	−0.0448920	+	0.0822135i	−0.0259184	+	0.0474660i	0.864399	+	0.502807i	$0.167699\pi$
$4$		0			0
$5$	−0.769038	+	2.09966i	−0.343924	+	0.938997i
$5$	−0.769038	+	2.09966i	−0.343924	+	0.938997i
$6$		0			0
$7$	4.17150	+	3.12275i	1.57668	+	1.18029i	0.892572	+	0.450906i	$0.148899\pi$
$7$	4.17150	+	3.12275i	1.57668	+	1.18029i	0.684107	+	0.729381i	$0.260192\pi$
$8$		0			0
$9$	1.61718	+	2.51638i	0.539060	+	0.838793i
$10$		0			0
$11$	−3.36211	−	1.53542i	−1.01371	−	0.462947i	−0.161908	−	0.986806i	$-0.551765\pi$
$11$	−3.36211	−	1.53542i	−1.01371	−	0.462947i	−0.851805	+	0.523859i	$0.824492\pi$
$12$		0			0
$13$	1.31000	+	1.74996i	0.363329	+	0.485351i	0.944537	−	0.328404i	$-0.106511\pi$
$13$	1.31000	+	1.74996i	0.363329	+	0.485351i	−0.581208	+	0.813755i	$0.697420\pi$
$14$		0			0
$15$	−0.138097	−	0.157483i	−0.0356565	−	0.0406620i
$16$		0			0
$17$	−6.18393	−	0.442284i	−1.49982	−	0.107270i	−0.702874	−	0.711314i	$-0.748100\pi$
$17$	−6.18393	−	0.442284i	−1.49982	−	0.107270i	−0.796950	+	0.604045i	$0.793555\pi$
$18$		0			0
$19$	2.05565	−	2.37235i	0.471599	−	0.544254i	−0.469257	−	0.883062i	$-0.655478\pi$
$19$	2.05565	−	2.37235i	0.471599	−	0.544254i	0.940856	+	0.338808i	$0.110024\pi$
$20$		0			0
$21$	−0.443999	+	0.202768i	−0.0968885	+	0.0442475i
$22$		0			0
$23$	−0.466813	+	4.77306i	−0.0973372	+	0.995251i
$23$	−0.466813	+	4.77306i	−0.0973372	+	0.995251i
$24$		0			0
$25$	−3.81716	−	3.22944i	−0.763432	−	0.645888i
$26$		0			0
$27$	−0.559777	+	0.0400361i	−0.107729	+	0.00770494i
$28$		0			0
$29$	1.75914	−	1.52430i	0.326664	−	0.283056i	−0.476053	−	0.879417i	$-0.657933\pi$
$29$	1.75914	−	1.52430i	0.326664	−	0.283056i	0.802716	+	0.596361i	$0.203387\pi$
$30$		0			0
$31$	−0.693792	−	0.203716i	−0.124609	−	0.0365884i	0.218834	−	0.975762i	$-0.429775\pi$
$31$	−0.693792	−	0.203716i	−0.124609	−	0.0365884i	−0.343442	+	0.939174i	$0.611593\pi$
$32$		0			0
$33$	0.277164	−	0.207482i	0.0482481	−	0.0361181i
$34$		0			0
$35$	−9.76475	+	6.35723i	−1.65054	+	1.07457i
$36$		0			0
$37$	1.77600	−	8.16416i	0.291973	−	1.34218i	−0.564263	−	0.825595i	$-0.690840\pi$
$37$	1.77600	−	8.16416i	0.291973	−	1.34218i	0.856236	−	0.516584i	$-0.172797\pi$
$38$		0			0
$39$	−0.202679	+	0.0291408i	−0.0324546	+	0.00466626i
$40$		0			0
$41$	−4.34358	−	2.79145i	−0.678354	−	0.435951i	0.155575	−	0.987824i	$-0.450277\pi$
$41$	−4.34358	−	2.79145i	−0.678354	−	0.435951i	−0.833928	+	0.551873i	$0.813913\pi$
$42$		0			0
$43$	−0.726651	−	0.396781i	−0.110813	−	0.0605086i	0.422886	−	0.906183i	$-0.361017\pi$
$43$	−0.726651	−	0.396781i	−0.110813	−	0.0605086i	−0.533700	+	0.845674i	$0.679199\pi$
$44$		0			0
$45$	−6.52722	+	1.46034i	−0.973020	+	0.217694i
$46$		0			0
$47$	6.39744	+	6.39744i	0.933163	+	0.933163i	0.997902	−	0.0647394i	$-0.0206216\pi$
$47$	6.39744	+	6.39744i	0.933163	+	0.933163i	−0.0647394	+	0.997902i	$0.520622\pi$
$48$		0			0
$49$	5.67774	+	19.3366i	0.811106	+	2.76237i
$50$		0			0
$51$	0.313971	−	0.488548i	0.0439647	−	0.0684104i
$52$		0			0
$53$	−6.14168	+	8.20433i	−0.843625	+	1.12695i	0.146836	+	0.989161i	$0.453091\pi$
$53$	−6.14168	+	8.20433i	−0.843625	+	1.12695i	−0.990461	+	0.137790i	$0.956000\pi$
$54$		0			0
$55$	5.80946	−	5.87849i	0.783347	−	0.792655i
$56$		0			0
$57$	0.102757	+	0.275502i	0.0136105	+	0.0364911i
$58$		0			0
$59$	1.11563	+	0.160403i	0.145242	+	0.0208827i	0.214552	−	0.976712i	$-0.431171\pi$
$59$	1.11563	+	0.160403i	0.145242	+	0.0208827i	−0.0693102	+	0.997595i	$0.522080\pi$
$60$		0			0
$61$	1.41688	−	4.82546i	0.181413	−	0.617837i	−0.817696	−	0.575650i	$-0.804749\pi$
$61$	1.41688	−	4.82546i	0.181413	−	0.617837i	0.999110	−	0.0421875i	$-0.0134327\pi$
$62$		0			0
$63$	−1.11195	+	15.5471i	−0.140093	+	1.95875i
$64$		0			0
$65$	−4.68176	+	1.40478i	−0.580701	+	0.174241i
$66$		0			0
$67$	3.47401	+	1.29574i	0.424418	+	0.158300i	0.552592	−	0.833452i	$-0.313639\pi$
$67$	3.47401	+	1.29574i	0.424418	+	0.158300i	−0.128174	+	0.991752i	$0.540912\pi$
$68$		0			0
$69$	−0.371454	−	0.252650i	−0.0447178	−	0.0304155i
$70$		0			0
$71$	5.27911	+	11.5596i	0.626515	+	1.37188i	0.910684	+	0.413103i	$0.135555\pi$
$71$	5.27911	+	11.5596i	0.626515	+	1.37188i	−0.284169	+	0.958774i	$0.591718\pi$
$72$		0			0
$73$	−0.0898299	−	1.25599i	−0.0105138	−	0.147002i	−0.999997	−	0.00235582i	$-0.999250\pi$
$73$	−0.0898299	−	1.25599i	−0.0105138	−	0.147002i	0.989483	−	0.144646i	$-0.0462044\pi$
$74$		0			0
$75$	0.436864	−	0.168846i	0.0504447	−	0.0194967i
$76$		0			0
$77$	−9.23029	−	16.9040i	−1.05189	−	1.92639i
$78$		0			0
$79$	−0.267327	+	1.85930i	−0.0300766	+	0.209187i	−0.999318	−	0.0369245i	$-0.988244\pi$
$79$	−0.267327	+	1.85930i	−0.0300766	+	0.209187i	0.969241	+	0.246112i	$0.0791530\pi$
$80$		0			0
$81$	−3.70596	+	8.11493i	−0.411774	+	0.901658i
$82$		0			0
$83$	14.0832	+	3.06361i	1.54583	+	0.336275i	0.902968	−	0.429708i	$-0.141383\pi$
$83$	14.0832	+	3.06361i	1.54583	+	0.336275i	0.642862	+	0.765982i	$0.277747\pi$
$84$		0			0
$85$	5.68433	−	12.6440i	0.616552	−	1.37144i
$86$		0			0
$87$	0.0463470	+	0.213054i	0.00496892	+	0.0228418i
$88$		0			0
$89$	−11.9814	+	3.51804i	−1.27002	+	0.372912i	−0.846215	−	0.532841i	$-0.821124\pi$
$89$	−11.9814	+	3.51804i	−1.27002	+	0.372912i	−0.423806	+	0.905753i	$0.639306\pi$
$90$		0			0
$91$			11.3907i			1.19407i
$92$		0			0
$93$	0.0478939	−	0.0478939i	0.00496637	−	0.00496637i
$94$		0			0
$95$	3.40025	+	6.14060i	0.348859	+	0.630012i
$96$		0			0
$97$	10.4438	−	2.27190i	1.06040	−	0.230677i	0.351649	−	0.936132i	$-0.385621\pi$
$97$	10.4438	−	2.27190i	1.06040	−	0.230677i	0.708754	+	0.705455i	$0.249257\pi$
$98$		0			0
$99$	−1.57342	−	10.9434i	−0.158135	−	1.09985i
$100$		0			0
$101$	−1.66564	+	1.07044i	−0.165738	+	0.106513i	−0.620880	−	0.783905i	$-0.713225\pi$
$101$	−1.66564	+	1.07044i	−0.165738	+	0.106513i	0.455142	+	0.890419i	$0.349588\pi$
$102$		0			0
$103$	7.17254	−	2.67522i	0.706731	−	0.263597i	0.0297077	−	0.999559i	$-0.490542\pi$
$103$	7.17254	−	2.67522i	0.706731	−	0.263597i	0.677023	+	0.735962i	$0.263270\pi$
$104$		0			0
$105$	−0.0842910	−	1.08818i	−0.00822596	−	0.106196i
$106$		0			0
$107$	15.0652	−	8.22621i	1.45641	−	0.795258i	0.460676	−	0.887568i	$-0.347607\pi$
$107$	15.0652	−	8.22621i	1.45641	−	0.795258i	0.995730	+	0.0923106i	$0.0294253\pi$
$108$		0			0
$109$	−10.7923	−	12.4550i	−1.03372	−	1.19297i	−0.980929	−	0.194365i	$-0.937735\pi$
$109$	−10.7923	−	12.4550i	−1.03372	−	1.19297i	−0.0527863	−	0.998606i	$-0.516810\pi$
$110$		0			0
$111$	0.591476	+	0.512517i	0.0561404	+	0.0486459i
$112$		0			0
$113$	1.24302	−	3.33266i	0.116933	−	0.313510i	−0.865277	−	0.501294i	$-0.832858\pi$
$113$	1.24302	−	3.33266i	0.116933	−	0.313510i	0.982210	+	0.187784i	$0.0601304\pi$
$114$		0			0
$115$	−9.66281	−	4.65081i	−0.901062	−	0.433691i
$116$		0			0
$117$	−2.28505	+	6.12645i	−0.211253	+	0.566391i
$118$		0			0
$119$	−24.4151	−	21.1558i	−2.23813	−	1.93935i
$120$		0			0
$121$	1.74276	+	2.01126i	0.158433	+	0.182841i
$122$		0			0
$123$	0.424487	−	0.231788i	0.0382747	−	0.0208996i
$124$		0			0
$125$	9.71628	−	5.53118i	0.869050	−	0.494724i
$126$		0			0
$127$	−2.90286	+	1.08271i	−0.257587	+	0.0960751i	−0.474940	−	0.880018i	$-0.657530\pi$
$127$	−2.90286	+	1.08271i	−0.257587	+	0.0960751i	0.217353	+	0.976093i	$0.430258\pi$
$128$		0			0
$129$	0.0652416	−	0.0419282i	0.00574420	−	0.00369157i
$130$		0			0
$131$	0.187109	+	1.30137i	0.0163478	+	0.113701i	0.996361	−	0.0852292i	$-0.0271623\pi$
$131$	0.187109	+	1.30137i	0.0163478	+	0.113701i	−0.980014	+	0.198931i	$0.936253\pi$
$132$		0			0
$133$	15.9834	−	3.47697i	1.38594	−	0.301492i
$134$		0			0
$135$	0.346428	−	1.20613i	0.0298158	−	0.103807i
$136$		0			0
$137$	13.6508	−	13.6508i	1.16627	−	1.16627i	0.183188	−	0.983078i	$-0.441358\pi$
$137$	13.6508	−	13.6508i	1.16627	−	1.16627i	0.983078	−	0.183188i	$-0.0586417\pi$
$138$		0			0
$139$			14.1071i			1.19655i	0.801291	+	0.598275i	$0.204147\pi$
$139$			14.1071i			1.19655i	−0.801291	+	0.598275i	$0.795853\pi$
$140$		0			0
$141$	−0.813150	+	0.238762i	−0.0684796	+	0.0201074i
$142$		0			0
$143$	−1.71744	−	7.89495i	−0.143620	−	0.660208i
$144$		0			0
$145$	1.84767	+	4.86584i	0.153441	+	0.404086i
$146$		0			0
$147$	−1.84462	−	0.401272i	−0.152141	−	0.0330963i
$148$		0			0
$149$	4.09582	−	8.96860i	0.335543	−	0.734736i	−0.664377	−	0.747398i	$-0.731303\pi$
$149$	4.09582	−	8.96860i	0.335543	−	0.734736i	0.999920	+	0.0126614i	$0.00403036\pi$
$150$		0			0
$151$	−0.807321	+	5.61504i	−0.0656989	+	0.456946i	0.930243	+	0.366945i	$0.119596\pi$
$151$	−0.807321	+	5.61504i	−0.0656989	+	0.456946i	−0.995942	+	0.0900011i	$0.971313\pi$
$152$		0			0
$153$	−8.88757	−	16.2764i	−0.718518	−	1.31587i
$154$		0			0
$155$	0.961287	−	1.30006i	0.0772124	−	0.104424i
$156$		0			0
$157$	1.00032	+	13.9863i	0.0798340	+	1.11623i	0.866610	+	0.498987i	$0.166294\pi$
$157$	1.00032	+	13.9863i	0.0798340	+	1.11623i	−0.786776	+	0.617239i	$0.788251\pi$
$158$		0			0
$159$	−0.398795	−	0.873238i	−0.0316265	−	0.0692523i
$160$		0			0
$161$	−16.8524	+	18.4531i	−1.32815	+	1.45431i
$162$		0			0
$163$	−19.2743	−	7.18895i	−1.50968	−	0.563082i	−0.547815	−	0.836600i	$-0.684540\pi$
$163$	−19.2743	−	7.18895i	−1.50968	−	0.563082i	−0.961867	+	0.273518i	$0.911813\pi$
$164$		0			0
$165$	0.222493	+	0.741513i	0.0173211	+	0.0577267i
$166$		0			0
$167$	1.45702	−	20.3718i	0.112748	−	1.57642i	−0.554886	−	0.831927i	$-0.687238\pi$
$167$	1.45702	−	20.3718i	0.112748	−	1.57642i	0.667633	−	0.744490i	$-0.267307\pi$
$168$		0			0
$169$	2.31628	−	7.88852i	0.178175	−	0.606809i
$170$		0			0
$171$	9.29408	+	1.33629i	0.710736	+	0.102188i
$172$		0			0
$173$	−1.50556	−	4.03657i	−0.114466	−	0.306895i	0.867066	−	0.498193i	$-0.166003\pi$
$173$	−1.50556	−	4.03657i	−0.114466	−	0.306895i	−0.981532	+	0.191298i	$0.938730\pi$
$174$		0			0
$175$	−5.83856	−	25.3916i	−0.441354	−	1.91943i
$176$		0			0
$177$	−0.0632700	+	0.0845188i	−0.00475566	+	0.00635282i
$178$		0			0
$179$	−8.73930	+	13.5986i	−0.653206	+	1.01641i	0.343797	+	0.939044i	$0.388287\pi$
$179$	−8.73930	+	13.5986i	−0.653206	+	1.01641i	−0.997003	+	0.0773644i	$0.975350\pi$
$180$		0			0
$181$	2.83153	+	9.64330i	0.210466	+	0.716781i	0.995280	+	0.0970491i	$0.0309404\pi$
$181$	2.83153	+	9.64330i	0.210466	+	0.716781i	−0.784814	+	0.619732i	$0.787241\pi$
$182$		0			0
$183$	0.333112	+	0.333112i	0.0246243	+	0.0246243i
$184$		0			0
$185$	15.7762	+	10.0076i	1.15989	+	0.735770i
$186$		0			0
$187$	20.1119	+	10.9820i	1.47073	+	0.803080i
$188$		0			0
$189$	−2.46013	−	1.58103i	−0.178948	−	0.115003i
$190$		0			0
$191$	13.5513	−	1.94839i	0.980541	−	0.140980i	0.366639	−	0.930363i	$-0.380508\pi$
$191$	13.5513	−	1.94839i	0.980541	−	0.140980i	0.613901	+	0.789383i	$0.289599\pi$
$192$		0			0
$193$	−5.21680	+	23.9812i	−0.375513	+	1.72621i	0.270358	+	0.962760i	$0.412858\pi$
$193$	−5.21680	+	23.9812i	−0.375513	+	1.72621i	−0.645871	+	0.763446i	$0.723506\pi$
$194$		0			0
$195$	0.0946819	−	0.447967i	0.00678031	−	0.0320796i
$196$		0			0
$197$	8.46693	−	6.33826i	0.603243	−	0.451582i	−0.253493	−	0.967337i	$-0.581579\pi$
$197$	8.46693	−	6.33826i	0.603243	−	0.451582i	0.856736	+	0.515755i	$0.172488\pi$
$198$		0			0
$199$	4.47558	+	1.31415i	0.317265	+	0.0931575i	0.436488	−	0.899710i	$-0.356222\pi$
$199$	4.47558	+	1.31415i	0.317265	+	0.0931575i	−0.119223	+	0.992868i	$0.538040\pi$
$200$		0			0
$201$	−0.262483	+	0.227443i	−0.0185141	+	0.0160426i
$202$		0			0
$203$	12.0982	−	0.865284i	0.849130	−	0.0607310i
$204$		0			0
$205$	9.20149	−	6.97332i	0.642660	−	0.487038i
$206$		0			0
$207$	−12.7657	+	6.54421i	−0.887281	+	0.454854i
$208$		0			0
$209$	−10.5539	+	4.81979i	−0.730026	+	0.333392i
$210$		0			0
$211$	0.725033	−	0.836732i	0.0499133	−	0.0576030i	−0.730244	−	0.683187i	$-0.760594\pi$
$211$	0.725033	−	0.836732i	0.0499133	−	0.0576030i	0.780157	+	0.625584i	$0.215139\pi$
$212$		0			0
$213$	−1.18735	−	0.0849209i	−0.0813558	−	0.00581868i
$214$		0			0
$215$	1.39193	−	1.22058i	0.0949288	−	0.0832429i
$216$		0			0
$217$	−2.25800	−	3.01634i	−0.153283	−	0.204762i
$218$		0			0
$219$	0.107292	+	0.0489985i	0.00725010	+	0.00331101i
$220$		0			0
$221$	−7.32699	−	11.4010i	−0.492866	−	0.766915i
$222$		0			0
$223$	2.52333	+	1.88894i	0.168975	+	0.126493i	0.680418	−	0.732824i	$-0.261798\pi$
$223$	2.52333	+	1.88894i	0.168975	+	0.126493i	−0.511443	+	0.859317i	$0.670889\pi$
$224$		0			0
$225$	1.95347	−	14.8280i	0.130231	−	0.988534i
$226$		0			0
$227$	−0.289984	+	0.531065i	−0.0192469	+	0.0352480i	−0.887125	−	0.461528i	$-0.847301\pi$
$227$	−0.289984	+	0.531065i	−0.0192469	+	0.0352480i	0.867879	+	0.496776i	$0.165483\pi$
$228$		0			0
$229$	4.05820			0.268174			0.134087	−	0.990970i	$-0.457190\pi$
$229$	4.05820			0.268174			0.134087	+	0.990970i	$0.457190\pi$
$230$		0			0
$231$	1.80410			0.118701
$232$		0			0
$233$	2.37673	−	4.35266i	0.155705	−	0.285152i	−0.788169	−	0.615459i	$-0.788971\pi$
$233$	2.37673	−	4.35266i	0.155705	−	0.285152i	0.943873	+	0.330307i	$0.107152\pi$
$234$		0			0
$235$	−18.3523	+	8.51259i	−1.19717	+	0.555300i
$236$		0			0
$237$	−0.140859	−	0.105445i	−0.00914974	−	0.00684941i
$238$		0			0
$239$	−8.48775	−	13.2072i	−0.549027	−	0.854302i	0.450228	−	0.892914i	$-0.351343\pi$
$239$	−8.48775	−	13.2072i	−0.549027	−	0.854302i	−0.999254	+	0.0386117i	$0.987706\pi$
$240$		0			0
$241$	−1.35109	−	0.617023i	−0.0870315	−	0.0397460i	0.371424	−	0.928464i	$-0.378870\pi$
$241$	−1.35109	−	0.617023i	−0.0870315	−	0.0397460i	−0.458455	+	0.888718i	$0.651597\pi$
$242$		0			0
$243$	−1.50975	−	2.01678i	−0.0968502	−	0.129377i
$244$		0			0
$245$	−44.9668	−	2.94926i	−2.87282	−	0.188421i
$246$		0			0
$247$	6.84441	+	0.489522i	0.435499	+	0.0311475i
$248$		0			0
$249$	−0.884092	+	1.02030i	−0.0560270	+	0.0646587i
$250$		0			0
$251$	19.3359	−	8.83043i	1.22047	−	0.557372i	0.302172	−	0.953253i	$-0.402288\pi$
$251$	19.3359	−	8.83043i	1.22047	−	0.557372i	0.918302	+	0.395882i	$0.129561\pi$
$252$		0			0
$253$	8.89813	−	15.3308i	0.559421	−	0.963837i
$254$		0			0
$255$	0.784330	+	1.03494i	0.0491167	+	0.0648108i
$256$		0			0
$257$	15.1803	−	1.08572i	0.946921	−	0.0677251i	0.410670	−	0.911784i	$-0.365295\pi$
$257$	15.1803	−	1.08572i	0.946921	−	0.0677251i	0.536251	+	0.844059i	$0.319840\pi$
$258$		0			0
$259$	32.9032	−	28.5108i	2.04450	−	1.77157i
$260$		0			0
$261$	6.68056	+	1.96159i	0.413516	+	0.121419i
$262$		0			0
$263$	9.61917	−	7.20082i	0.593144	−	0.444022i	−0.260065	−	0.965591i	$-0.583744\pi$
$263$	9.61917	−	7.20082i	0.593144	−	0.444022i	0.853209	+	0.521569i	$0.174653\pi$
$264$		0			0
$265$	−12.5031	−	19.2049i	−0.768061	−	1.17975i
$266$		0			0
$267$	0.248636	−	1.14296i	0.0152163	−	0.0699481i
$268$		0			0
$269$	−7.23305	+	1.03996i	−0.441007	+	0.0634073i	−0.359242	−	0.933244i	$-0.616965\pi$
$269$	−7.23305	+	1.03996i	−0.441007	+	0.0634073i	−0.0817650	+	0.996652i	$0.526056\pi$
$270$		0			0
$271$	−5.54876	−	3.56597i	−0.337063	−	0.216617i	0.361149	−	0.932508i	$-0.382385\pi$
$271$	−5.54876	−	3.56597i	−0.337063	−	0.216617i	−0.698212	+	0.715891i	$0.746021\pi$
$272$		0			0
$273$	−0.936474	−	0.511353i	−0.0566780	−	0.0309485i
$274$		0			0
$275$	7.87514	+	16.7187i	0.474889	+	1.00817i
$276$		0			0
$277$	−9.26408	−	9.26408i	−0.556625	−	0.556625i	0.371720	−	0.928345i	$-0.378768\pi$
$277$	−9.26408	−	9.26408i	−0.556625	−	0.556625i	−0.928345	+	0.371720i	$0.878768\pi$
$278$		0			0
$279$	−0.609360	−	2.07529i	−0.0364814	−	0.124244i
$280$		0			0
$281$	3.20148	−	4.98161i	0.190985	−	0.297178i	−0.732535	−	0.680730i	$-0.761663\pi$
$281$	3.20148	−	4.98161i	0.190985	−	0.297178i	0.923519	+	0.383552i	$0.125299\pi$
$282$		0			0
$283$	15.3748	−	20.5383i	0.913934	−	1.22087i	−0.0609454	−	0.998141i	$-0.519412\pi$
$283$	15.3748	−	20.5383i	0.913934	−	1.22087i	0.974880	−	0.222732i	$-0.0714975\pi$
$284$		0			0
$285$	−0.657484	+	0.00388322i	−0.0389460	+	0.000230022i
$286$		0			0
$287$	−9.40227	−	25.2084i	−0.554998	−	1.48801i
$288$		0			0
$289$	21.2185	+	3.05076i	1.24815	+	0.179456i
$290$		0			0
$291$	−0.282060	+	0.960608i	−0.0165347	+	0.0563119i
$292$		0			0
$293$	−1.02432	+	14.3219i	−0.0598417	+	0.836696i	0.875560	+	0.483109i	$0.160493\pi$
$293$	−1.02432	+	14.3219i	−0.0598417	+	0.836696i	−0.935402	+	0.353587i	$0.884962\pi$
$294$		0			0
$295$	−1.19475	+	2.21908i	−0.0695611	+	0.129200i
$296$		0			0
$297$	1.94350	+	0.724889i	0.112773	+	0.0420623i
$298$		0			0
$299$	−8.96417	+	5.43581i	−0.518411	+	0.314361i
$300$		0			0
$301$	−1.79218	−	3.92432i	−0.103299	−	0.226194i
$302$		0			0
$303$	−0.0132310	−	0.184993i	−0.000760098	−	0.0106276i
$304$		0			0
$305$	9.04221	+	6.68595i	0.517755	+	0.382836i
$306$		0			0
$307$	4.93578	+	9.03920i	0.281700	+	0.515895i	0.979768	−	0.200137i	$-0.0641386\pi$
$307$	4.93578	+	9.03920i	0.281700	+	0.515895i	−0.698068	+	0.716031i	$0.745957\pi$
$308$		0			0
$309$	−0.102050	+	0.709775i	−0.00580544	+	0.0403777i
$310$		0			0
$311$	−2.93295	+	6.42227i	−0.166313	+	0.364174i	−0.974377	−	0.224920i	$-0.927788\pi$
$311$	−2.93295	+	6.42227i	−0.166313	+	0.364174i	0.808065	+	0.589094i	$0.200515\pi$
$312$		0			0
$313$	27.8434	+	6.05696i	1.57380	+	0.342360i	0.912923	−	0.408132i	$-0.133820\pi$
$313$	27.8434	+	6.05696i	1.57380	+	0.342360i	0.660880	+	0.750492i	$0.270183\pi$
$314$		0			0
$315$	−31.7886	−	14.2910i	−1.79108	−	0.805209i
$316$		0			0
$317$	4.88851	+	22.4721i	0.274566	+	1.26216i	0.883308	+	0.468793i	$0.155311\pi$
$317$	4.88851	+	22.4721i	0.274566	+	1.26216i	−0.608742	+	0.793368i	$0.708326\pi$
$318$		0			0
$319$	−8.25485	+	2.42384i	−0.462183	+	0.135709i
$320$		0			0
$321$			1.60785i			0.0897416i
$322$		0			0
$323$	−13.7613	+	13.7613i	−0.765697	+	0.765697i
$324$		0			0
$325$	0.650898	−	10.9104i	0.0361053	−	0.605202i
$326$		0			0
$327$	1.50846	−	0.328145i	0.0834178	−	0.0181464i
$328$		0			0
$329$	6.70934	+	46.6645i	0.369898	+	2.57270i
$330$		0			0
$331$	16.4282	−	10.5577i	0.902973	−	0.580306i	−0.00469731	−	0.999989i	$-0.501495\pi$
$331$	16.4282	−	10.5577i	0.902973	−	0.580306i	0.907671	+	0.419683i	$0.137859\pi$
$332$		0			0
$333$	23.4162	−	8.73380i	1.28320	−	0.478609i
$334$		0			0
$335$	−5.39226	+	6.29778i	−0.294611	+	0.344084i
$336$		0			0
$337$	−17.8321	+	9.73706i	−0.971376	+	0.530412i	−0.884869	−	0.465840i	$-0.845752\pi$
$337$	−17.8321	+	9.73706i	−0.971376	+	0.530412i	−0.0865071	+	0.996251i	$0.527571\pi$
$338$		0			0
$339$	0.218188	+	0.251802i	0.0118503	+	0.0136760i
$340$		0			0
$341$	2.01981	+	1.75018i	0.109379	+	0.0947775i
$342$		0			0
$343$	−23.9516	+	64.2167i	−1.29327	+	3.46738i
$344$		0			0
$345$	0.816143	−	0.585630i	0.0439396	−	0.0315292i
$346$		0			0
$347$	6.24949	−	16.7555i	0.335490	−	0.899484i	−0.654208	−	0.756315i	$-0.726998\pi$
$347$	6.24949	−	16.7555i	0.335490	−	0.899484i	0.989698	−	0.143170i	$-0.0457294\pi$
$348$		0			0
$349$	3.02435	+	2.62061i	0.161890	+	0.140278i	0.732039	−	0.681263i	$-0.238569\pi$
$349$	3.02435	+	2.62061i	0.161890	+	0.140278i	−0.570149	+	0.821541i	$0.693114\pi$
$350$		0			0
$351$	−0.803371	−	0.927139i	−0.0428807	−	0.0494870i
$352$		0			0
$353$	−7.09691	+	3.87521i	−0.377731	+	0.206257i	−0.656887	−	0.753989i	$-0.728127\pi$
$353$	−7.09691	+	3.87521i	−0.377731	+	0.206257i	0.279156	+	0.960246i	$0.409945\pi$
$354$		0			0
$355$	−28.3312	+	2.19454i	−1.50366	+	0.116474i
$356$		0			0
$357$	2.83534	−	1.05753i	0.150062	−	0.0559703i
$358$		0			0
$359$	−5.37915	+	3.45697i	−0.283901	+	0.182452i	−0.674839	−	0.737965i	$-0.735787\pi$
$359$	−5.37915	+	3.45697i	−0.283901	+	0.182452i	0.390938	+	0.920417i	$0.372151\pi$
$360$		0			0
$361$	1.30165	+	9.05318i	0.0685079	+	0.476483i
$362$		0			0
$363$	−0.243589	+	0.0529894i	−0.0127851	+	0.00278122i
$364$		0			0
$365$	2.70623	+	0.777289i	0.141651	+	0.0406852i
$366$		0			0
$367$	9.22004	−	9.22004i	0.481282	−	0.481282i	−0.424259	−	0.905541i	$-0.639465\pi$
$367$	9.22004	−	9.22004i	0.481282	−	0.481282i	0.905541	+	0.424259i	$0.139465\pi$
$368$		0			0
$369$		−	15.4444i		−	0.804002i
$370$		0			0
$371$	−51.2401	+	15.0454i	−2.66025	+	0.781120i
$372$		0			0
$373$	3.41918	+	15.7177i	0.177038	+	0.813832i	0.976908	+	0.213659i	$0.0685380\pi$
$373$	3.41918	+	15.7177i	0.177038	+	0.813832i	−0.799870	+	0.600173i	$0.795098\pi$
$374$		0			0
$375$	0.0185551	+	1.04712i	0.000958179	+	0.0540728i
$376$		0			0
$377$	4.97193	+	1.08158i	0.256068	+	0.0557041i
$378$		0			0
$379$	−2.89732	+	6.34424i	−0.148825	+	0.325882i	−0.969332	−	0.245755i	$-0.920964\pi$
$379$	−2.89732	+	6.34424i	−0.148825	+	0.325882i	0.820507	+	0.571637i	$0.193691\pi$
$380$		0			0
$381$	0.0413017	−	0.287260i	0.00211595	−	0.0147168i
$382$		0			0
$383$	−3.54900	−	6.49950i	−0.181345	−	0.332109i	0.771155	−	0.636648i	$-0.219679\pi$
$383$	−3.54900	−	6.49950i	−0.181345	−	0.332109i	−0.952500	+	0.304539i	$0.901498\pi$
$384$		0			0
$385$	42.5912	−	6.38065i	2.17065	−	0.325188i
$386$		0			0
$387$	−0.176672	−	2.47020i	−0.00898074	−	0.125567i
$388$		0			0
$389$	−5.34994	−	11.7147i	−0.271253	−	0.593960i	0.724160	−	0.689632i	$-0.242227\pi$
$389$	−5.34994	−	11.7147i	−0.271253	−	0.593960i	−0.995413	+	0.0956713i	$0.969500\pi$
$390$		0			0
$391$	4.99779	−	29.3098i	0.252749	−	1.48226i
$392$		0			0
$393$	−0.115390	−	0.0430383i	−0.00582066	−	0.00217099i
$394$		0			0
$395$	−3.69831	−	1.99117i	−0.186082	−	0.100186i
$396$		0			0
$397$	1.74392	−	24.3832i	0.0875249	−	1.22376i	−0.743965	−	0.668218i	$-0.767057\pi$
$397$	1.74392	−	24.3832i	0.0875249	−	1.22376i	0.831490	−	0.555540i	$-0.187488\pi$
$398$		0			0
$399$	−0.431672	+	1.47014i	−0.0216106	+	0.0735990i
$400$		0			0
$401$	11.6429	+	1.67400i	0.581420	+	0.0835956i	0.426749	−	0.904370i	$-0.359659\pi$
$401$	11.6429	+	1.67400i	0.581420	+	0.0835956i	0.154672	+	0.987966i	$0.450568\pi$
$402$		0			0
$403$	−0.552375	−	1.48097i	−0.0275158	−	0.0737726i
$404$		0			0
$405$	−14.1886	−	14.0220i	−0.705036	−	0.696757i
$406$		0			0
$407$	−18.5065	+	24.7218i	−0.917335	+	1.22542i
$408$		0			0
$409$	−12.2604	+	19.0776i	−0.606238	+	0.943325i	0.393474	+	0.919336i	$0.371273\pi$
$409$	−12.2604	+	19.0776i	−0.606238	+	0.943325i	−0.999712	+	0.0239890i	$0.992363\pi$
$410$		0			0
$411$	0.509469	+	1.73509i	0.0251302	+	0.0855857i
$412$		0			0
$413$	4.15294	+	4.15294i	0.204353	+	0.204353i
$414$		0			0
$415$	−17.2630	+	27.2139i	−0.847410	+	1.33588i
$416$		0			0
$417$	−1.15980	−	0.633296i	−0.0567954	−	0.0310126i
$418$		0			0
$419$	6.67893	+	4.29228i	0.326287	+	0.209692i	0.693520	−	0.720437i	$-0.256059\pi$
$419$	6.67893	+	4.29228i	0.326287	+	0.209692i	−0.367234	+	0.930129i	$0.619695\pi$
$420$		0			0
$421$	−30.5073	+	4.38629i	−1.48684	+	0.213775i	−0.837378	−	0.546624i	$-0.815913\pi$
$421$	−30.5073	+	4.38629i	−1.48684	+	0.213775i	−0.649457	+	0.760398i	$0.725004\pi$
$422$		0			0
$423$	−5.75258	+	26.4442i	−0.279700	+	1.28576i
$424$		0			0
$425$	22.1767	+	21.6589i	1.07573	+	1.05061i
$426$		0			0
$427$	20.9792	−	15.7049i	1.01526	−	0.760011i
$428$		0			0
$429$	0.726171	+	0.213223i	0.0350598	+	0.0102945i
$430$		0			0
$431$	19.7726	−	17.1330i	0.952411	−	0.825269i	−0.0322974	−	0.999478i	$-0.510282\pi$
$431$	19.7726	−	17.1330i	0.952411	−	0.825269i	0.984709	+	0.174209i	$0.0557369\pi$
$432$		0			0
$433$	7.43551	−	0.531798i	0.357328	−	0.0255566i	0.108478	−	0.994099i	$-0.465402\pi$
$433$	7.43551	−	0.531798i	0.357328	−	0.0255566i	0.248849	+	0.968542i	$0.419948\pi$
$434$		0			0
$435$	−0.482984	−	0.0665335i	−0.0231573	−	0.00319004i
$436$		0			0
$437$	10.3637	+	10.9192i	0.495765	+	0.522335i
$438$		0			0
$439$	−18.9660	+	8.66148i	−0.905198	+	0.413390i	−0.812942	−	0.582345i	$-0.802135\pi$
$439$	−18.9660	+	8.66148i	−0.905198	+	0.413390i	−0.0922564	+	0.995735i	$0.529408\pi$
$440$		0			0
$441$	−39.4763	+	45.5581i	−1.87983	+	2.16943i
$442$		0			0
$443$	−30.0075	−	2.14618i	−1.42570	−	0.101968i	−0.662949	−	0.748664i	$-0.730696\pi$
$443$	−30.0075	−	2.14618i	−1.42570	−	0.101968i	−0.762748	+	0.646696i	$0.776150\pi$
$444$		0			0
$445$	1.82742	−	27.8623i	0.0866280	−	1.32080i
$446$		0			0
$447$	0.553470	+	0.739350i	0.0261783	+	0.0349701i
$448$		0			0
$449$	23.6470	+	10.7992i	1.11597	+	0.509647i	0.886063	−	0.463566i	$-0.153430\pi$
$449$	23.6470	+	10.7992i	1.11597	+	0.509647i	0.229908	+	0.973212i	$0.426157\pi$
$450$		0			0
$451$	10.3175	+	16.0544i	0.485833	+	0.755972i
$452$		0			0
$453$	−0.425390	−	0.318443i	−0.0199866	−	0.0149618i
$454$		0			0
$455$	−23.9167	−	8.75992i	−1.12123	−	0.410671i
$456$		0			0
$457$	8.48697	−	15.5427i	0.397004	−	0.727058i	−0.600352	−	0.799736i	$-0.704973\pi$
$457$	8.48697	−	15.5427i	0.397004	−	0.727058i	0.997355	+	0.0726783i	$0.0231546\pi$
$458$		0			0
$459$	3.47933			0.162401
$460$		0			0
$461$	−4.59398			−0.213963			−0.106981	−	0.994261i	$-0.534119\pi$
$461$	−4.59398			−0.213963			−0.106981	+	0.994261i	$0.534119\pi$
$462$		0			0
$463$	11.9013	−	21.7956i	0.553101	−	1.01293i	−0.440258	−	0.897871i	$-0.645113\pi$
$463$	11.9013	−	21.7956i	0.553101	−	1.01293i	0.993359	−	0.115057i	$-0.0367052\pi$
$464$		0			0
$465$	0.0637288	+	0.137393i	0.00295535	+	0.00637146i
$466$		0			0
$467$	−24.5702	−	18.3930i	−1.13697	−	0.851127i	−0.146550	−	0.989203i	$-0.546817\pi$
$467$	−24.5702	−	18.3930i	−1.13697	−	0.851127i	−0.990422	+	0.138077i	$0.955908\pi$
$468$		0			0
$469$	10.4456	+	16.2536i	0.482332	+	0.750523i
$470$		0			0
$471$	−1.19477	−	0.545632i	−0.0550519	−	0.0251414i
$472$		0			0
$473$	1.83385	+	2.44974i	0.0843205	+	0.112639i
$474$		0			0
$475$	−15.5081	+	2.41703i	−0.711560	+	0.110901i
$476$		0			0
$477$	−30.5774	−	2.18694i	−1.40004	−	0.100133i
$478$		0			0
$479$	22.7676	−	26.2752i	1.04028	−	1.20054i	0.0609748	−	0.998139i	$-0.480579\pi$
$479$	22.7676	−	26.2752i	1.04028	−	1.20054i	0.979302	−	0.202404i	$-0.0648755\pi$
$480$		0			0
$481$	16.6135	−	7.58713i	0.757510	−	0.345943i
$482$		0			0
$483$	−0.760557	−	2.21389i	−0.0346065	−	0.100735i
$484$		0			0
$485$	−3.26143	+	23.6755i	−0.148094	+	1.07505i
$486$		0			0
$487$	36.8159	−	2.63312i	1.66829	−	0.119318i	0.795027	−	0.606574i	$-0.207457\pi$
$487$	36.8159	−	2.63312i	1.66829	−	0.119318i	0.873259	+	0.487256i	$0.162002\pi$
$488$		0			0
$489$	1.45629	−	1.26188i	0.0658558	−	0.0570644i
$490$		0			0
$491$	−11.2432	−	3.30129i	−0.507397	−	0.148985i	0.0180074	−	0.999838i	$-0.494268\pi$
$491$	−11.2432	−	3.30129i	−0.507397	−	0.148985i	−0.525404	+	0.850853i	$0.676086\pi$
$492$		0			0
$493$	−11.5526	+	8.64814i	−0.520301	+	0.389493i
$494$		0			0
$495$	24.1874	+	5.11223i	1.08714	+	0.229778i
$496$		0			0
$497$	−14.0760	+	64.7064i	−0.631395	+	2.90248i
$498$		0			0
$499$	−29.6737	+	4.26643i	−1.32838	+	0.190992i	−0.769706	−	0.638399i	$-0.779597\pi$
$499$	−29.6737	+	4.26643i	−1.32838	+	0.190992i	−0.558670	+	0.829390i	$0.688688\pi$
$500$		0			0
$501$	1.60943	+	1.03432i	0.0719040	+	0.0462099i
$502$		0			0
$503$	29.5396	+	16.1298i	1.31711	+	0.719194i	0.975364	−	0.220600i	$-0.0708015\pi$
$503$	29.5396	+	16.1298i	1.31711	+	0.719194i	0.341741	+	0.939794i	$0.388983\pi$
$504$		0			0
$505$	−0.966628	−	4.32050i	−0.0430144	−	0.192260i
$506$		0			0
$507$	0.544560	+	0.544560i	0.0241848	+	0.0241848i
$508$		0			0
$509$	5.85578	+	19.9430i	0.259553	+	0.883956i	0.981411	+	0.191916i	$0.0614700\pi$
$509$	5.85578	+	19.9430i	0.259553	+	0.883956i	−0.721858	+	0.692041i	$0.756712\pi$
$510$		0			0
$511$	3.54740	−	5.51986i	0.156928	−	0.244184i
$512$		0			0
$513$	−1.05573	+	1.41029i	−0.0466115	+	0.0622657i
$514$		0			0
$515$	0.101097	+	17.1172i	0.00445488	+	0.754276i
$516$		0			0
$517$	−11.6861	−	31.3316i	−0.513954	−	1.37796i
$518$		0			0
$519$	0.399448	+	0.0574320i	0.0175338	+	0.00252098i
$520$		0			0
$521$	−6.36709	+	21.6843i	−0.278947	+	0.950007i	0.694192	+	0.719790i	$0.255762\pi$
$521$	−6.36709	+	21.6843i	−0.278947	+	0.950007i	−0.973139	+	0.230217i	$0.926056\pi$
$522$		0			0
$523$	−1.82395	+	25.5022i	−0.0797558	+	1.11513i	0.787184	+	0.616718i	$0.211538\pi$
$523$	−1.82395	+	25.5022i	−0.0797558	+	1.11513i	−0.866940	+	0.498413i	$0.833916\pi$
$524$		0			0
$525$	2.34964	+	0.659872i	0.102547	+	0.0287992i
$526$		0			0
$527$	4.20027	+	1.56662i	0.182966	+	0.0682430i
$528$		0			0
$529$	−22.5642	−	4.45625i	−0.981051	−	0.193750i
$530$		0			0
$531$	1.40053	+	3.06674i	0.0607780	+	0.133085i
$532$		0			0
$533$	−0.805180	−	11.2579i	−0.0348762	−	0.487633i
$534$		0			0
$535$	5.68656	+	37.9581i	0.245851	+	1.64107i
$536$		0			0
$537$	−0.725666	−	1.32896i	−0.0313148	−	0.0573488i
$538$		0			0
$539$	10.6007	−	73.7295i	0.456604	−	3.17575i
$540$		0			0
$541$	15.5497	−	34.0491i	0.668534	−	1.46389i	−0.205816	−	0.978591i	$-0.565985\pi$
$541$	15.5497	−	34.0491i	0.668534	−	1.46389i	0.874350	−	0.485295i	$-0.161288\pi$
$542$		0			0
$543$	−0.919922	−	0.200117i	−0.0394777	−	0.00858784i
$544$		0			0
$545$	34.4510	−	13.0818i	1.47572	−	0.560364i
$546$		0			0
$547$	5.43406	+	24.9800i	0.232344	+	1.06807i	0.934478	+	0.356022i	$0.115867\pi$
$547$	5.43406	+	24.9800i	0.232344	+	1.06807i	−0.702134	+	0.712045i	$0.747769\pi$
$548$		0			0
$549$	14.4341	−	4.23822i	0.616030	−	0.180883i
$550$		0			0
$551$		−	7.30671i		−	0.311276i
$552$		0			0
$553$	−6.92126	+	6.92126i	−0.294322	+	0.294322i
$554$		0			0
$555$	−1.53098	+	0.847754i	−0.0649865	+	0.0359852i
$556$		0			0
$557$	−13.3952	+	2.91394i	−0.567572	+	0.123468i	−0.487189	−	0.873296i	$-0.661978\pi$
$557$	−13.3952	+	2.91394i	−0.567572	+	0.123468i	−0.0803824	+	0.996764i	$0.525614\pi$
$558$		0			0
$559$	−0.257563	−	1.79139i	−0.0108938	−	0.0757678i
$560$		0			0
$561$	−1.80573	+	1.16047i	−0.0762380	+	0.0489952i
$562$		0			0
$563$	−19.3134	+	7.20354i	−0.813964	+	0.303593i	−0.721757	−	0.692147i	$-0.756665\pi$
$563$	−19.3134	+	7.20354i	−0.813964	+	0.303593i	−0.0922075	+	0.995740i	$0.529392\pi$
$564$		0			0
$565$	6.04152	+	5.17285i	0.254169	+	0.217624i
$566$		0			0
$567$	−40.8003	+	22.2786i	−1.71345	+	0.935615i
$568$		0			0
$569$	−5.30428	−	6.12147i	−0.222367	−	0.256625i	0.633594	−	0.773666i	$-0.281579\pi$
$569$	−5.30428	−	6.12147i	−0.222367	−	0.256625i	−0.855961	+	0.517041i	$0.827034\pi$
$570$		0			0
$571$	−16.5118	−	14.3075i	−0.690996	−	0.598752i	0.236925	−	0.971528i	$-0.423860\pi$
$571$	−16.5118	−	14.3075i	−0.690996	−	0.598752i	−0.927921	+	0.372776i	$0.878406\pi$
$572$		0			0
$573$	−0.448163	+	1.20157i	−0.0187223	+	0.0501963i
$574$		0			0
$575$	17.1962	−	16.7120i	0.717132	−	0.696938i
$576$		0			0
$577$	2.59037	−	6.94505i	0.107838	−	0.289126i	−0.871811	−	0.489843i	$-0.837054\pi$
$577$	2.59037	−	6.94505i	0.107838	−	0.289126i	0.979649	+	0.200716i	$0.0643270\pi$
$578$		0			0
$579$	−1.73739	−	1.50546i	−0.0722034	−	0.0625646i
$580$		0			0
$581$	49.1811	+	56.7580i	2.04038	+	2.35472i
$582$		0			0
$583$	33.2461	−	18.1537i	1.37691	−	0.751851i
$584$		0			0
$585$	−11.1062	−	9.50931i	−0.459184	−	0.393161i
$586$		0			0
$587$	22.3765	−	8.34600i	0.923577	−	0.344476i	0.157717	−	0.987484i	$-0.449587\pi$
$587$	22.3765	−	8.34600i	0.923577	−	0.344476i	0.765859	+	0.643008i	$0.222314\pi$
$588$		0			0
$589$	−1.90948	+	1.22715i	−0.0786787	+	0.0505637i
$590$		0			0
$591$	0.140994	+	0.980633i	0.00579971	+	0.0403378i
$592$		0			0
$593$	−45.3434	+	9.86386i	−1.86203	+	0.405060i	−0.995557	−	0.0941617i	$-0.969983\pi$
$593$	−45.3434	+	9.86386i	−1.86203	+	0.405060i	−0.866474	+	0.499222i	$0.833619\pi$
$594$		0			0
$595$	63.1963	−	34.9939i	2.59080	−	1.43461i
$596$		0			0
$597$	−0.308958	+	0.308958i	−0.0126448	+	0.0126448i
$598$		0			0
$599$		−	21.0837i		−	0.861457i	−0.902482	−	0.430729i	$-0.858257\pi$
$599$		−	21.0837i		−	0.861457i	0.902482	−	0.430729i	$-0.141743\pi$
$600$		0			0
$601$	3.89733	−	1.14436i	0.158976	−	0.0466794i	−0.201276	−	0.979534i	$-0.564509\pi$
$601$	3.89733	−	1.14436i	0.158976	−	0.0466794i	0.360252	+	0.932855i	$0.382691\pi$
$602$		0			0
$603$	2.35753	+	10.8374i	0.0960059	+	0.441332i
$604$		0			0
$605$	−5.56321	+	2.11248i	−0.226177	+	0.0858846i
$606$		0			0
$607$	39.2561	+	8.53964i	1.59336	+	0.346613i	0.919759	−	0.392485i	$-0.128384\pi$
$607$	39.2561	+	8.53964i	1.59336	+	0.346613i	0.673598	+	0.739098i	$0.264748\pi$
$608$		0			0
$609$	−0.471976	+	1.03348i	−0.0191254	+	0.0418789i
$610$		0			0
$611$	−2.81459	+	19.5759i	−0.113866	+	0.791956i
$612$		0			0
$613$	−17.4671	−	31.9886i	−0.705489	−	1.29201i	−0.946882	−	0.321580i	$-0.895786\pi$
$613$	−17.4671	−	31.9886i	−0.705489	−	1.29201i	0.241393	−	0.970427i	$-0.422396\pi$
$614$		0			0
$615$	0.160229	+	1.06953i	0.00646104	+	0.0431277i
$616$		0			0
$617$	−2.63934	−	36.9027i	−0.106256	−	1.48565i	−0.718803	−	0.695214i	$-0.755310\pi$
$617$	−2.63934	−	36.9027i	−0.106256	−	1.48565i	0.612547	−	0.790434i	$-0.290145\pi$
$618$		0			0
$619$	9.25412	+	20.2637i	0.371954	+	0.814466i	0.999360	+	0.0357737i	$0.0113896\pi$
$619$	9.25412	+	20.2637i	0.371954	+	0.814466i	−0.627406	+	0.778693i	$0.715883\pi$
$620$		0			0
$621$	0.0702169	−	2.69054i	0.00281771	−	0.107968i
$622$		0			0
$623$	−60.9662	−	22.7392i	−2.44256	−	0.911027i
$624$		0			0
$625$	4.14142	+	24.6546i	0.165657	+	0.986183i
$626$		0			0
$627$	0.0775321	−	1.08404i	0.00309633	−	0.0432924i
$628$		0			0
$629$	−14.5936	+	49.7011i	−0.581884	+	1.98171i
$630$		0			0
$631$	−16.2403	−	2.33500i	−0.646515	−	0.0929548i	−0.188746	−	0.982026i	$-0.560442\pi$
$631$	−16.2403	−	2.33500i	−0.646515	−	0.0929548i	−0.457769	+	0.889071i	$0.651351\pi$
$632$		0			0
$633$	0.0362426	+	0.0971701i	0.00144051	+	0.00386216i
$634$		0			0
$635$	−0.0409161	−	6.92768i	−0.00162370	−	0.274916i
$636$		0			0
$637$	−26.4004	+	35.2668i	−1.04602	+	1.39732i
$638$		0			0
$639$	−20.5512	+	31.9783i	−0.812992	+	1.26504i
$640$		0			0
$641$	−13.0786	−	44.5416i	−0.516573	−	1.75929i	−0.641503	−	0.767121i	$-0.721689\pi$
$641$	−13.0786	−	44.5416i	−0.516573	−	1.75929i	0.124930	−	0.992166i	$-0.460129\pi$
$642$		0			0
$643$	−2.82024	−	2.82024i	−0.111220	−	0.111220i	0.649307	−	0.760526i	$-0.275059\pi$
$643$	−2.82024	−	2.82024i	−0.111220	−	0.111220i	−0.760526	+	0.649307i	$0.775059\pi$
$644$		0			0
$645$	0.0378618	+	0.169230i	0.00149081	+	0.00666341i
$646$		0			0
$647$	7.54383	+	4.11924i	0.296578	+	0.161944i	0.620648	−	0.784089i	$-0.286869\pi$
$647$	7.54383	+	4.11924i	0.296578	+	0.161944i	−0.324070	+	0.946033i	$0.605051\pi$
$648$		0			0
$649$	−3.50457	−	2.25225i	−0.137566	−	0.0884085i
$650$		0			0
$651$	0.349350	−	0.0502289i	0.0136921	−	0.00196863i
$652$		0			0
$653$	1.05815	−	4.86422i	0.0414085	−	0.190352i	−0.951796	−	0.306730i	$-0.900765\pi$
$653$	1.05815	−	4.86422i	0.0414085	−	0.190352i	0.993205	+	0.116379i	$0.0371286\pi$
$654$		0			0
$655$	−2.87633	−	0.607939i	−0.112388	−	0.0237541i
$656$		0			0
$657$	3.01527	−	2.25720i	0.117637	−	0.0880618i
$658$		0			0
$659$	−16.1318	−	4.73672i	−0.628405	−	0.184516i	−0.0480038	−	0.998847i	$-0.515286\pi$
$659$	−16.1318	−	4.73672i	−0.628405	−	0.184516i	−0.580401	+	0.814331i	$0.697104\pi$
$660$		0			0
$661$	8.96638	−	7.76941i	0.348752	−	0.302195i	−0.462815	−	0.886455i	$-0.653161\pi$
$661$	8.96638	−	7.76941i	0.348752	−	0.302195i	0.811567	+	0.584260i	$0.198615\pi$
$662$		0			0
$663$	1.26624	−	0.0905633i	0.0491767	−	0.00351719i
$664$		0			0
$665$	−4.99137	+	36.2336i	−0.193557	+	1.40508i
$666$		0			0
$667$	6.45439	+	9.10803i	0.249915	+	0.352664i
$668$		0			0
$669$	−0.268574	+	0.122654i	−0.0103837	+	0.00474207i
$670$		0			0
$671$	−12.1728	+	14.0482i	−0.469927	+	0.542325i
$672$		0			0
$673$	−11.3673	−	0.813003i	−0.438176	−	0.0313390i	−0.149491	−	0.988763i	$-0.547764\pi$
$673$	−11.3673	−	0.813003i	−0.438176	−	0.0313390i	−0.288685	+	0.957424i	$0.593218\pi$
$674$		0			0
$675$	2.26605	+	1.65494i	0.0872205	+	0.0636988i
$676$		0			0
$677$	−27.2666	−	36.4239i	−1.04794	−	1.39988i	−0.912489	−	0.409101i	$-0.865842\pi$
$677$	−27.2666	−	36.4239i	−1.04794	−	1.39988i	−0.135452	−	0.990784i	$-0.543248\pi$
$678$		0			0
$679$	50.6607	+	23.1360i	1.94418	+	0.887877i
$680$		0			0
$681$	−0.0306428	−	0.0476811i	−0.00117424	−	0.00182715i
$682$		0			0
$683$	24.7237	+	18.5080i	0.946028	+	0.708188i	0.956492	−	0.291758i	$-0.0942401\pi$
$683$	24.7237	+	18.5080i	0.946028	+	0.708188i	−0.0104644	+	0.999945i	$0.503331\pi$
$684$		0			0
$685$	18.1641	+	39.1600i	0.694013	+	1.49623i
$686$		0			0
$687$	−0.182181	+	0.333639i	−0.00695063	+	0.0127291i
$688$		0			0
$689$	−22.4028			−0.853480
$690$		0			0
$691$	−2.37208			−0.0902382			−0.0451191	−	0.998982i	$-0.514367\pi$
$691$	−2.37208			−0.0902382			−0.0451191	+	0.998982i	$0.514367\pi$
$692$		0			0
$693$	27.6099	−	50.5637i	1.04881	−	1.92076i
$694$		0			0
$695$	−29.6202	−	10.8489i	−1.12356	−	0.411522i
$696$		0			0
$697$	25.6258	+	19.1833i	0.970647	+	0.726617i
$698$		0			0
$699$	0.251151	+	0.390799i	0.00949941	+	0.0147814i
$700$		0			0
$701$	−46.3864	−	21.1839i	−1.75199	−	0.800106i	−0.987919	−	0.154973i	$-0.950471\pi$
$701$	−46.3864	−	21.1839i	−1.75199	−	0.800106i	−0.764070	−	0.645133i	$-0.776802\pi$
$702$		0			0
$703$	−15.7174	−	20.9960i	−0.592792	−	0.791877i
$704$		0			0
$705$	0.124023	−	1.89096i	0.00467099	−	0.0712176i
$706$		0			0
$707$	−10.2910	−	0.736024i	−0.387032	−	0.0276810i
$708$		0			0
$709$	18.0763	−	20.8612i	0.678871	−	0.783459i	−0.306866	−	0.951753i	$-0.599280\pi$
$709$	18.0763	−	20.8612i	0.678871	−	0.783459i	0.985737	+	0.168294i	$0.0538257\pi$
$710$		0			0
$711$	−5.11101	+	2.33412i	−0.191678	+	0.0875363i
$712$		0			0
$713$	1.29622	−	3.21641i	0.0485438	−	0.120456i
$714$		0			0
$715$	17.8975	+	2.46547i	0.669328	+	0.0922034i
$716$		0			0
$717$	1.46684	−	0.104911i	0.0547802	−	0.00391796i
$718$		0			0
$719$	4.52564	−	3.92149i	0.168778	−	0.146247i	−0.566376	−	0.824147i	$-0.691655\pi$
$719$	4.52564	−	3.92149i	0.168778	−	0.146247i	0.735154	+	0.677900i	$0.237110\pi$
$720$		0			0
$721$	38.2743	+	11.2383i	1.42541	+	0.418538i
$722$		0			0
$723$	0.111381	−	0.0833787i	0.00414230	−	0.00310089i
$724$		0			0
$725$	−11.6375	+	0.137472i	−0.432208	+	0.00510557i
$726$		0			0
$727$	−2.98785	+	13.7349i	−0.110813	+	0.509401i	0.887962	+	0.459917i	$0.152121\pi$
$727$	−2.98785	+	13.7349i	−0.110813	+	0.509401i	−0.998775	+	0.0494831i	$0.984243\pi$
$728$		0			0
$729$	−26.2573	+	3.77523i	−0.972494	+	0.139823i
$730$		0			0
$731$	4.31807	+	2.77506i	0.159710	+	0.102639i
$732$		0			0
$733$	−6.81559	−	3.72159i	−0.251740	−	0.137460i	0.348425	−	0.937337i	$-0.386717\pi$
$733$	−6.81559	−	3.72159i	−0.251740	−	0.137460i	−0.600165	+	0.799876i	$0.704898\pi$
$734$		0			0
$735$	2.26112	−	3.56448i	0.0834025	−	0.131478i
$736$		0			0
$737$	−9.69049	−	9.69049i	−0.356954	−	0.356954i
$738$		0			0
$739$	−0.354436	−	1.20710i	−0.0130381	−	0.0444038i	0.952717	−	0.303859i	$-0.0982752\pi$
$739$	−0.354436	−	1.20710i	−0.0130381	−	0.0444038i	−0.965755	+	0.259455i	$0.916457\pi$
$740$		0			0
$741$	−0.347504	+	0.540728i	−0.0127659	+	0.0198641i
$742$		0			0
$743$	−2.85694	+	3.81643i	−0.104811	+	0.140011i	−0.849880	−	0.526976i	$-0.823326\pi$
$743$	−2.85694	+	3.81643i	−0.104811	+	0.140011i	0.745069	+	0.666987i	$0.232417\pi$
$744$		0			0
$745$	15.6812	+	15.4970i	0.574514	+	0.567767i
$746$		0			0
$747$	15.0658	+	40.3930i	0.551229	+	1.47790i
$748$		0			0
$749$	88.5328	+	12.7291i	3.23492	+	0.465111i
$750$		0			0
$751$	−5.37467	+	18.3044i	−0.196124	+	0.667938i	0.801433	+	0.598085i	$0.204071\pi$
$751$	−5.37467	+	18.3044i	−0.196124	+	0.667938i	−0.997557	+	0.0698536i	$0.977747\pi$
$752$		0			0
$753$	−0.142048	+	1.98609i	−0.00517652	+	0.0723772i
$754$		0			0
$755$	−11.1688	−	6.01328i	−0.406475	−	0.218846i
$756$		0			0
$757$	−7.89292	−	2.94391i	−0.286873	−	0.106998i	0.201908	−	0.979404i	$-0.435286\pi$
$757$	−7.89292	−	2.94391i	−0.286873	−	0.106998i	−0.488781	+	0.872406i	$0.662558\pi$
$758$		0			0
$759$	0.860942	+	1.41978i	0.0312502	+	0.0515346i
$760$		0			0
$761$	2.69497	+	5.90117i	0.0976927	+	0.213917i	0.952168	−	0.305575i	$-0.0988486\pi$
$761$	2.69497	+	5.90117i	0.0976927	+	0.213917i	−0.854475	+	0.519492i	$0.826121\pi$
$762$		0			0
$763$	−6.12635	−	85.6576i	−0.221789	−	3.10101i
$764$		0			0
$765$	41.0098	−	6.14374i	1.48271	−	0.222127i
$766$		0			0
$767$	1.18077	+	2.16243i	0.0426353	+	0.0780807i
$768$		0			0
$769$	5.20768	−	36.2202i	0.187794	−	1.30613i	−0.649910	−	0.760011i	$-0.725194\pi$
$769$	5.20768	−	36.2202i	0.187794	−	1.30613i	0.837704	−	0.546124i	$-0.183897\pi$
$770$		0			0
$771$	−0.592213	+	1.29677i	−0.0213280	+	0.0467019i
$772$		0			0
$773$	37.7653	+	8.21535i	1.35833	+	0.295486i	0.831989	−	0.554791i	$-0.187202\pi$
$773$	37.7653	+	8.21535i	1.35833	+	0.295486i	0.526336	+	0.850277i	$0.323566\pi$
$774$		0			0
$775$	1.99043	+	3.01818i	0.0714983	+	0.108416i
$776$		0			0
$777$	0.866882	+	3.98499i	0.0310992	+	0.142961i
$778$		0			0
$779$	−15.5512	+	4.56624i	−0.557179	+	0.163602i
$780$		0			0
$781$		−	46.9704i		−	1.68073i
$782$		0			0
$783$	−0.923698	+	0.923698i	−0.0330103	+	0.0330103i
$784$		0			0
$785$	−30.1357	−	8.65565i	−1.07559	−	0.308933i
$786$		0			0
$787$	−39.8085	+	8.65982i	−1.41902	+	0.308689i	−0.855667	−	0.517527i	$-0.826853\pi$
$787$	−39.8085	+	8.65982i	−1.41902	+	0.308689i	−0.563354	+	0.826216i	$0.690489\pi$
$788$		0			0
$789$	0.160181	+	1.11409i	0.00570261	+	0.0396625i
$790$		0			0
$791$	15.5923	−	10.0205i	0.554398	−	0.356290i
$792$		0			0
$793$	10.3005	−	3.84188i	0.365781	−	0.136429i
$794$		0			0
$795$	2.14019	−	0.165780i	0.0759048	−	0.00587961i
$796$		0			0
$797$	−1.66276	+	0.907934i	−0.0588979	+	0.0321607i	−0.508428	−	0.861104i	$-0.669773\pi$
$797$	−1.66276	+	0.907934i	−0.0588979	+	0.0321607i	0.449530	+	0.893265i	$0.351591\pi$
$798$		0			0
$799$	−36.7319	−	42.3908i	−1.29948	−	1.49968i
$800$		0			0
$801$	−28.2287	−	24.4603i	−0.997413	−	0.864263i
$802$		0			0
$803$	−1.62645	+	4.36069i	−0.0573962	+	0.153885i
$804$		0			0
$805$	−25.7851	−	49.5754i	−0.908806	−	1.74730i
$806$		0			0
$807$	0.239208	−	0.641341i	0.00842051	−	0.0225763i
$808$		0			0
$809$	−14.3327	−	12.4194i	−0.503912	−	0.436643i	0.365440	−	0.930835i	$-0.380918\pi$
$809$	−14.3327	−	12.4194i	−0.503912	−	0.436643i	−0.869353	+	0.494192i	$0.835464\pi$
$810$		0			0
$811$	−25.9379	−	29.9339i	−0.910802	−	1.05112i	−0.998488	−	0.0549733i	$-0.982493\pi$
$811$	−25.9379	−	29.9339i	−0.910802	−	1.05112i	0.0876859	−	0.996148i	$-0.472053\pi$
$812$		0			0
$813$	0.542266	−	0.296100i	0.0190181	−	0.0103847i
$814$		0			0
$815$	29.9171	−	34.9410i	1.04795	−	1.22393i
$816$		0			0
$817$	−2.43504	+	0.908224i	−0.0851914	+	0.0317747i
$818$		0			0
$819$	−28.6634	+	18.4209i	−1.00158	+	0.643677i
$820$		0			0
$821$	1.55883	+	10.8419i	0.0544035	+	0.378385i	0.998774	+	0.0495014i	$0.0157632\pi$
$821$	1.55883	+	10.8419i	0.0544035	+	0.378385i	−0.944371	+	0.328883i	$0.893328\pi$
$822$		0			0
$823$	4.66453	−	1.01471i	0.162595	−	0.0353704i	−0.130531	−	0.991444i	$-0.541668\pi$
$823$	4.66453	−	1.01471i	0.162595	−	0.0353704i	0.293126	+	0.956074i	$0.405304\pi$
$824$		0			0
$825$	−1.72803	−	0.103091i	−0.0601623	−	0.00358918i
$826$		0			0
$827$	−30.5587	+	30.5587i	−1.06263	+	1.06263i	−0.0647275	+	0.997903i	$0.520618\pi$
$827$	−30.5587	+	30.5587i	−1.06263	+	1.06263i	−0.997903	+	0.0647275i	$0.979382\pi$
$828$		0			0
$829$			9.00927i			0.312905i	0.987686	+	0.156452i	$0.0500058\pi$
$829$			9.00927i			0.312905i	−0.987686	+	0.156452i	$0.949994\pi$
$830$		0			0
$831$	1.17752	−	0.345750i	0.0408476	−	0.0119939i
$832$		0			0
$833$	−26.5585	−	122.088i	−0.920198	−	4.23008i
$834$		0			0
$835$	41.6534	+	18.7259i	1.44147	+	0.648038i
$836$		0			0
$837$	0.396525	+	0.0862588i	0.0137059	+	0.00298154i
$838$		0			0
$839$	5.77968	−	12.6557i	0.199537	−	0.436924i	−0.783240	−	0.621719i	$-0.786435\pi$
$839$	5.77968	−	12.6557i	0.199537	−	0.436924i	0.982777	+	0.184794i	$0.0591619\pi$
$840$		0			0
$841$	−3.35606	+	23.3419i	−0.115726	+	0.804894i
$842$		0			0
$843$	0.265835	+	0.486840i	0.00915583	+	0.0167676i
$844$		0			0
$845$	14.7819	+	10.9300i	0.508513	+	0.376002i
$846$		0			0
$847$	0.989296	+	13.8322i	0.0339926	+	0.475279i
$848$		0			0
$849$	0.998320	+	2.18602i	0.0342623	+	0.0750239i
$850$		0			0
$851$	38.1389	+	12.2881i	1.30739	+	0.421231i
$852$		0			0
$853$	38.9357	+	14.5223i	1.33313	+	0.497232i	0.912157	−	0.409840i	$-0.134416\pi$
$853$	38.9357	+	14.5223i	1.33313	+	0.497232i	0.420974	+	0.907073i	$0.361688\pi$
$854$		0			0
$855$	−9.95325	+	18.4868i	−0.340394	+	0.632234i
$856$		0			0
$857$	3.58062	−	50.0636i	0.122312	−	1.71014i	−0.452427	−	0.891801i	$-0.649442\pi$
$857$	3.58062	−	50.0636i	0.122312	−	1.71014i	0.574738	−	0.818337i	$-0.305104\pi$
$858$		0			0
$859$	6.21934	−	21.1811i	0.212201	−	0.722690i	−0.782751	−	0.622335i	$-0.786184\pi$
$859$	6.21934	−	21.1811i	0.212201	−	0.722690i	0.994952	−	0.100355i	$-0.0319978\pi$
$860$		0			0
$861$	2.49456	+	0.358664i	0.0850144	+	0.0122232i
$862$		0			0
$863$	−1.79314	−	4.80760i	−0.0610393	−	0.163653i	0.902850	−	0.429955i	$-0.141471\pi$
$863$	−1.79314	−	4.80760i	−0.0610393	−	0.163653i	−0.963889	+	0.266303i	$0.914198\pi$
$864$		0			0
$865$	9.63326	−	0.0568957i	0.327541	−	0.00193451i
$866$		0			0
$867$	−1.20335	+	1.60749i	−0.0408680	+	0.0545933i
$868$		0			0
$869$	3.75359	−	5.84069i	0.127332	−	0.198132i
$870$		0			0
$871$	2.28347	+	7.77679i	0.0773725	+	0.263507i
$872$		0			0
$873$	22.6064	+	22.6064i	0.765110	+	0.765110i
$874$		0			0
$875$	57.8039	+	7.26814i	1.95413	+	0.245708i
$876$		0			0
$877$	−33.0839	−	18.0652i	−1.11716	−	0.610017i	−0.188920	−	0.981992i	$-0.560499\pi$
$877$	−33.0839	−	18.0652i	−1.11716	−	0.610017i	−0.928243	+	0.371976i	$0.878680\pi$
$878$		0			0
$879$	−1.13147	−	0.727153i	−0.0381636	−	0.0245263i
$880$		0			0
$881$	−3.51891	+	0.505942i	−0.118555	+	0.0170456i	−0.201337	−	0.979522i	$-0.564529\pi$
$881$	−3.51891	+	0.505942i	−0.118555	+	0.0170456i	0.0827819	+	0.996568i	$0.473620\pi$
$882$		0			0
$883$	−4.17274	+	19.1818i	−0.140424	+	0.645519i	0.852091	+	0.523394i	$0.175334\pi$
$883$	−4.17274	+	19.1818i	−0.140424	+	0.645519i	−0.992515	+	0.122125i	$0.961029\pi$
$884$		0			0
$885$	−0.128804	−	0.197844i	−0.00432970	−	0.00665045i
$886$		0			0
$887$	13.3501	−	9.99376i	0.448252	−	0.335558i	−0.351186	−	0.936306i	$-0.614221\pi$
$887$	13.3501	−	9.99376i	0.448252	−	0.335558i	0.799438	+	0.600748i	$0.205131\pi$
$888$		0			0
$889$	−15.4903	−	4.54837i	−0.519529	−	0.152547i
$890$		0			0
$891$	24.9197	−	21.5930i	0.834840	−	0.723393i
$892$		0			0
$893$	28.3279	−	2.02605i	0.947956	−	0.0677991i
$894$		0			0
$895$	−21.8316	−	28.8074i	−0.729751	−	0.962926i
$896$		0			0
$897$	−0.0444777	−	0.981001i	−0.00148507	−	0.0327547i
$898$		0			0
$899$	−1.53100	+	0.699184i	−0.0510617	+	0.0233191i
$900$		0			0
$901$	41.6084	−	48.0187i	1.38618	−	1.59973i
$902$		0			0
$903$	0.403087	+	0.0288293i	0.0134139	+	0.000959380i
$904$		0			0
$905$	−22.4252	−	1.47081i	−0.745439	−	0.0488915i
$906$		0			0
$907$	−15.1354	−	20.2185i	−0.502561	−	0.671343i	0.475487	−	0.879723i	$-0.342272\pi$
$907$	−15.1354	−	20.2185i	−0.502561	−	0.671343i	−0.978048	+	0.208380i	$0.933181\pi$
$908$		0			0
$909$	−5.38729	−	2.46029i	−0.178685	−	0.0816028i
$910$		0			0
$911$	−3.60786	−	5.61394i	−0.119534	−	0.185998i	0.776330	−	0.630326i	$-0.217079\pi$
$911$	−3.60786	−	5.61394i	−0.119534	−	0.185998i	−0.895864	+	0.444328i	$0.853442\pi$
$912$		0			0
$913$	−42.6452	−	31.9238i	−1.41135	−	1.05652i
$914$		0			0
$915$	−0.955598	+	0.443246i	−0.0315911	+	0.0146533i
$916$		0			0
$917$	−3.28333	+	6.01297i	−0.108425	+	0.198566i
$918$		0			0
$919$	9.30621			0.306984			0.153492	−	0.988150i	$-0.450948\pi$
$919$	9.30621			0.306984			0.153492	+	0.988150i	$0.450948\pi$
$920$		0			0
$921$	−0.964722			−0.0317887
$922$		0			0
$923$	−13.3132	+	24.3814i	−0.438210	+	0.802523i
$924$		0			0
$925$	−33.1450	+	25.4284i	−1.08980	+	0.836081i
$926$		0			0
$927$	18.3311	+	13.7225i	0.602073	+	0.450707i
$928$		0			0
$929$	13.9736	+	21.7433i	0.458458	+	0.713374i	0.991122	−	0.132952i	$-0.0424457\pi$
$929$	13.9736	+	21.7433i	0.458458	+	0.713374i	−0.532665	+	0.846326i	$0.678809\pi$
$930$		0			0
$931$	57.5446	+	26.2798i	1.88595	+	0.861284i
$932$		0			0
$933$	−0.396332	−	0.529437i	−0.0129753	−	0.0173330i
$934$		0			0
$935$	−38.5252	+	33.7827i	−1.25991	+	1.10481i
$936$		0			0
$937$	−3.91723	−	0.280166i	−0.127970	−	0.00915262i	0.00720707	−	0.999974i	$-0.497706\pi$
$937$	−3.91723	−	0.280166i	−0.127970	−	0.00915262i	−0.135177	+	0.990821i	$0.543160\pi$
$938$		0			0
$939$	−1.74791	+	2.01720i	−0.0570409	+	0.0658287i
$940$		0			0
$941$	10.6775	−	4.87624i	0.348076	−	0.158961i	−0.233703	−	0.972308i	$-0.575084\pi$
$941$	10.6775	−	4.87624i	0.348076	−	0.158961i	0.581778	+	0.813347i	$0.302357\pi$
$942$		0			0
$943$	15.3514	−	19.4291i	0.499910	−	0.632698i
$944$		0			0
$945$	5.21157	−	3.94958i	0.169532	−	0.128480i
$946$		0			0
$947$	6.98129	−	0.499312i	0.226861	−	0.0162255i	0.0425543	−	0.999094i	$-0.486450\pi$
$947$	6.98129	−	0.499312i	0.226861	−	0.0162255i	0.184307	+	0.982869i	$0.440996\pi$
$948$		0			0
$949$	2.08025	−	1.80254i	0.0675276	−	0.0585130i
$950$		0			0
$951$	−2.06697	−	0.606917i	−0.0670261	−	0.0196806i
$952$		0			0
$953$	8.51151	−	6.37164i	0.275715	−	0.206398i	−0.452468	−	0.891781i	$-0.649456\pi$
$953$	8.51151	−	6.37164i	0.275715	−	0.206398i	0.728183	+	0.685383i	$0.240365\pi$
$954$		0			0
$955$	−6.33054	+	29.9516i	−0.204852	+	0.969212i
$956$		0			0
$957$	0.171304	−	0.787472i	0.00553747	−	0.0254553i
$958$		0			0
$959$	99.5722	−	14.3163i	3.21536	−	0.462298i
$960$		0			0
$961$	−25.6390	−	16.4772i	−0.827065	−	0.531522i
$962$		0			0
$963$	45.0634	+	24.6065i	1.45215	+	0.792932i
$964$		0			0
$965$	−46.3405	−	29.3960i	−1.49175	−	0.946290i
$966$		0			0
$967$	−28.4658	−	28.4658i	−0.915397	−	0.915397i	0.0812932	−	0.996690i	$-0.474095\pi$
$967$	−28.4658	−	28.4658i	−0.915397	−	0.915397i	−0.996690	+	0.0812932i	$0.974095\pi$
$968$		0			0
$969$	−0.513591	−	1.74913i	−0.0164989	−	0.0561902i
$970$		0			0
$971$	31.8548	−	49.5670i	1.02227	−	1.59068i	0.237015	−	0.971506i	$-0.423831\pi$
$971$	31.8548	−	49.5670i	1.02227	−	1.59068i	0.785253	−	0.619175i	$-0.212533\pi$
$972$		0			0
$973$	−44.0529	+	58.8478i	−1.41227	+	1.88657i
$974$		0			0
$975$	0.867766	+	0.543304i	0.0277907	+	0.0173996i
$976$		0			0
$977$	17.4786	+	46.8619i	0.559190	+	1.49925i	0.841681	+	0.539976i	$0.181567\pi$
$977$	17.4786	+	46.8619i	0.559190	+	1.49925i	−0.282491	+	0.959270i	$0.591161\pi$
$978$		0			0
$979$	45.6843	+	6.56840i	1.46008	+	0.209927i
$980$		0			0
$981$	13.8884	−	47.2995i	0.443422	−	1.51016i
$982$		0			0
$983$	1.77546	−	24.8242i	0.0566284	−	0.791769i	−0.887211	−	0.461364i	$-0.847360\pi$
$983$	1.77546	−	24.8242i	0.0566284	−	0.791769i	0.943839	−	0.330405i	$-0.107185\pi$
$984$		0			0
$985$	6.79681	+	22.6520i	0.216565	+	0.721754i
$986$		0			0
$987$	−4.13765	−	1.54326i	−0.131703	−	0.0491226i
$988$		0			0
$989$	2.23307	−	3.28312i	0.0710075	−	0.104397i
$990$		0			0
$991$	19.2444	+	42.1394i	0.611320	+	1.33860i	0.921668	+	0.387980i	$0.126827\pi$
$991$	19.2444	+	42.1394i	0.611320	+	1.33860i	−0.310348	+	0.950623i	$0.600446\pi$
$992$		0			0
$993$	0.130496	+	1.82457i	0.00414117	+	0.0579011i
$994$		0			0
$995$	−6.20116	+	8.38657i	−0.196590	+	0.265872i
$996$		0			0
$997$	12.0199	+	22.0128i	0.380673	+	0.697151i	0.995827	−	0.0912559i	$-0.0290881\pi$
$997$	12.0199	+	22.0128i	0.380673	+	0.697151i	−0.615154	+	0.788407i	$0.710906\pi$
$998$		0			0
$999$	−0.667306	+	4.64121i	−0.0211126	+	0.146842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bv.a.617.17	yes	720
5.3	odd	4	inner	920.2.bv.a.433.17	yes	720
23.17	odd	22	inner	920.2.bv.a.17.17	✓	720
115.63	even	44	inner	920.2.bv.a.753.17	yes	720

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bv.a.17.17	✓	720	23.17	odd	22	inner
920.2.bv.a.433.17	yes	720	5.3	odd	4	inner
920.2.bv.a.617.17	yes	720	1.1	even	1	trivial
920.2.bv.a.753.17	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)

\(f(q)\)	\(=\)	\(q+(-0.0448920 + 0.0822135i) q^{3} +(-0.769038 + 2.09966i) q^{5} +(4.17150 + 3.12275i) q^{7} +(1.61718 + 2.51638i) q^{9} +(-3.36211 - 1.53542i) q^{11} +(1.31000 + 1.74996i) q^{13} +(-0.138097 - 0.157483i) q^{15} +(-6.18393 - 0.442284i) q^{17} +(2.05565 - 2.37235i) q^{19} +(-0.443999 + 0.202768i) q^{21} +(-0.466813 + 4.77306i) q^{23} +(-3.81716 - 3.22944i) q^{25} +(-0.559777 + 0.0400361i) q^{27} +(1.75914 - 1.52430i) q^{29} +(-0.693792 - 0.203716i) q^{31} +(0.277164 - 0.207482i) q^{33} +(-9.76475 + 6.35723i) q^{35} +(1.77600 - 8.16416i) q^{37} +(-0.202679 + 0.0291408i) q^{39} +(-4.34358 - 2.79145i) q^{41} +(-0.726651 - 0.396781i) q^{43} +(-6.52722 + 1.46034i) q^{45} +(6.39744 + 6.39744i) q^{47} +(5.67774 + 19.3366i) q^{49} +(0.313971 - 0.488548i) q^{51} +(-6.14168 + 8.20433i) q^{53} +(5.80946 - 5.87849i) q^{55} +(0.102757 + 0.275502i) q^{57} +(1.11563 + 0.160403i) q^{59} +(1.41688 - 4.82546i) q^{61} +(-1.11195 + 15.5471i) q^{63} +(-4.68176 + 1.40478i) q^{65} +(3.47401 + 1.29574i) q^{67} +(-0.371454 - 0.252650i) q^{69} +(5.27911 + 11.5596i) q^{71} +(-0.0898299 - 1.25599i) q^{73} +(0.436864 - 0.168846i) q^{75} +(-9.23029 - 16.9040i) q^{77} +(-0.267327 + 1.85930i) q^{79} +(-3.70596 + 8.11493i) q^{81} +(14.0832 + 3.06361i) q^{83} +(5.68433 - 12.6440i) q^{85} +(0.0463470 + 0.213054i) q^{87} +(-11.9814 + 3.51804i) q^{89} +11.3907i q^{91} +(0.0478939 - 0.0478939i) q^{93} +(3.40025 + 6.14060i) q^{95} +(10.4438 - 2.27190i) q^{97} +(-1.57342 - 10.9434i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 720 q - 20 q^{23} + 16 q^{25} - 24 q^{27} - 16 q^{31} + 88 q^{37} - 32 q^{41} + 56 q^{47} - 40 q^{55} + 88 q^{57} + 16 q^{73} - 140 q^{75} - 48 q^{77} + 40 q^{81} - 92 q^{85} - 88 q^{87} + 72 q^{93} - 248 q^{95}+O(q^{100}) \) 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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