LMFDB - Embedded newform 792.2.bp.d.667.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [792,2,Mod(19,792)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(792, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("792.19"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 792 = 2^{3} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	792.bp (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.32415184009$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 264)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			667.10
Character	$\chi$	$=$	792.667
Dual form			792.2.bp.d.19.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23741 + 0.684696i) q^{2} +(1.06238 + 1.69450i) q^{4} +(0.409298 + 0.563350i) q^{5} +(-0.510340 - 1.57067i) q^{7} +(0.154385 + 2.82421i) q^{8} +(0.120747 + 0.977341i) q^{10} +(-2.08351 + 2.58050i) q^{11} +(4.92015 + 3.57470i) q^{13} +(0.443927 - 2.29299i) q^{14} +(-1.74269 + 3.60042i) q^{16} +(-2.23176 - 3.07176i) q^{17} +(5.66454 + 1.84052i) q^{19} +(-0.519768 + 1.29205i) q^{20} +(-4.34502 + 1.76658i) q^{22} +8.64584i q^{23} +(1.39525 - 4.29413i) q^{25} +(3.64068 + 7.79219i) q^{26} +(2.11932 - 2.53342i) q^{28} +(-1.33248 - 4.10095i) q^{29} +(-4.09860 + 5.64124i) q^{31} +(-4.62162 + 3.26200i) q^{32} +(-0.658392 - 5.32912i) q^{34} +(0.675953 - 0.930370i) q^{35} +(2.02338 - 0.657436i) q^{37} +(5.74918 + 6.15598i) q^{38} +(-1.52783 + 1.24292i) q^{40} +(-0.736879 - 0.239427i) q^{41} -10.1720i q^{43} +(-6.58615 - 0.789033i) q^{44} +(-5.91977 + 10.6985i) q^{46} +(5.29780 + 1.72136i) q^{47} +(3.45658 - 2.51135i) q^{49} +(4.66667 - 4.35829i) q^{50} +(-0.830261 + 12.1349i) q^{52} +(2.57874 - 3.54933i) q^{53} +(-2.30650 - 0.117551i) q^{55} +(4.35710 - 1.68380i) q^{56} +(1.15908 - 5.98691i) q^{58} +(-3.78102 - 11.6368i) q^{59} +(0.239653 - 0.174118i) q^{61} +(-8.93420 + 4.17425i) q^{62} +(-7.95233 + 0.872033i) q^{64} +4.23488i q^{65} -10.7130 q^{67} +(2.83412 - 7.04512i) q^{68} +(1.47345 - 0.688429i) q^{70} +(-1.14044 - 1.56968i) q^{71} +(-6.90989 + 2.24516i) q^{73} +(2.95390 + 0.571881i) q^{74} +(2.89914 + 11.5539i) q^{76} +(5.11640 + 1.95556i) q^{77} +(-2.76926 - 2.01198i) q^{79} +(-2.74158 + 0.491902i) q^{80} +(-0.747889 - 0.800808i) q^{82} +(1.90883 + 2.62729i) q^{83} +(0.817020 - 2.51453i) q^{85} +(6.96476 - 12.5870i) q^{86} +(-7.60955 - 5.48587i) q^{88} +6.63247 q^{89} +(3.10371 - 9.55222i) q^{91} +(-14.6504 + 9.18519i) q^{92} +(5.37696 + 5.75742i) q^{94} +(1.28163 + 3.94444i) q^{95} +(-3.48568 - 2.53250i) q^{97} +(5.99672 - 0.740872i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{4} - 4 q^{11} + 16 q^{14} + 20 q^{16} - 25 q^{20} + 3 q^{22} - 4 q^{25} - 4 q^{26} - 25 q^{28} - 26 q^{38} - 65 q^{40} + 60 q^{41} + 43 q^{44} - 5 q^{46} - 12 q^{49} + 80 q^{50} - 15 q^{52}+ \cdots - 40 q^{97}+O(q^{100}) $ 48 * q + 4 * q^4 - 4 * q^11 + 16 * q^14 + 20 * q^16 - 25 * q^20 + 3 * q^22 - 4 * q^25 - 4 * q^26 - 25 * q^28 - 26 * q^38 - 65 * q^40 + 60 * q^41 + 43 * q^44 - 5 * q^46 - 12 * q^49 + 80 * q^50 - 15 * q^52 + 14 * q^56 + 73 * q^58 + 8 * q^59 + 45 * q^62 - 38 * q^64 + 8 * q^67 + 55 * q^68 - 40 * q^70 - 60 * q^74 - 35 * q^82 + 100 * q^83 - 81 * q^86 - 18 * q^88 - 96 * q^89 - 20 * q^91 - 59 * q^92 + 35 * q^94 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.23741	+	0.684696i	0.874983	+	0.484153i
$2$	1.23741	+	0.684696i	0.874983	+	0.484153i
$3$		0			0
$3$		0			0
$4$	1.06238	+	1.69450i	0.531191	+	0.847252i
$5$	0.409298	+	0.563350i	0.183044	+	0.251938i	0.890672	−	0.454647i	$-0.150235\pi$
$5$	0.409298	+	0.563350i	0.183044	+	0.251938i	−0.707628	+	0.706585i	$0.750235\pi$
$6$		0			0
$7$	−0.510340	−	1.57067i	−0.192890	−	0.593656i	−0.999995	−	0.00324682i	$-0.998967\pi$
$7$	−0.510340	−	1.57067i	−0.192890	−	0.593656i	0.807104	−	0.590409i	$-0.201033\pi$
$8$	0.154385	+	2.82421i	0.0545835	+	0.998509i
$9$		0			0
$10$	0.120747	+	0.977341i	0.0381835	+	0.309062i
$11$	−2.08351	+	2.58050i	−0.628201	+	0.778051i
$11$	−2.08351	+	2.58050i	−0.628201	+	0.778051i
$12$		0			0
$13$	4.92015	+	3.57470i	1.36460	+	0.991443i	0.998137	+	0.0610124i	$0.0194329\pi$
$13$	4.92015	+	3.57470i	1.36460	+	0.991443i	0.366468	+	0.930431i	$0.380567\pi$
$14$	0.443927	−	2.29299i	0.118644	−	0.612827i
$15$		0			0
$16$	−1.74269	+	3.60042i	−0.435672	+	0.900106i
$17$	−2.23176	−	3.07176i	−0.541282	−	0.745011i	0.447515	−	0.894277i	$-0.352309\pi$
$17$	−2.23176	−	3.07176i	−0.541282	−	0.745011i	−0.988797	+	0.149265i	$0.952309\pi$
$18$		0			0
$19$	5.66454	+	1.84052i	1.29954	+	0.422245i	0.875420	−	0.483364i	$-0.160585\pi$
$19$	5.66454	+	1.84052i	1.29954	+	0.422245i	0.424116	+	0.905608i	$0.360585\pi$
$20$	−0.519768	+	1.29205i	−0.116224	+	0.288911i
$21$		0			0
$22$	−4.34502	+	1.76658i	−0.926362	+	0.376636i
$23$			8.64584i			1.80278i	0.433006	+	0.901391i	$0.357453\pi$
$23$			8.64584i			1.80278i	−0.433006	+	0.901391i	$0.642547\pi$
$24$		0			0
$25$	1.39525	−	4.29413i	0.279049	−	0.858825i
$26$	3.64068	+	7.79219i	0.713996	+	1.52817i
$27$		0			0
$28$	2.11932	−	2.53342i	0.400514	−	0.478771i
$29$	−1.33248	−	4.10095i	−0.247435	−	0.761526i	−0.995226	−	0.0975928i	$-0.968886\pi$
$29$	−1.33248	−	4.10095i	−0.247435	−	0.761526i	0.747791	−	0.663934i	$-0.231114\pi$
$30$		0			0
$31$	−4.09860	+	5.64124i	−0.736131	+	1.01320i	0.262701	+	0.964877i	$0.415387\pi$
$31$	−4.09860	+	5.64124i	−0.736131	+	1.01320i	−0.998832	+	0.0483198i	$0.984613\pi$
$32$	−4.62162	+	3.26200i	−0.816995	+	0.576645i
$33$		0			0
$34$	−0.658392	−	5.32912i	−0.112913	−	0.913936i
$35$	0.675953	−	0.930370i	0.114257	−	0.157261i
$36$		0			0
$37$	2.02338	−	0.657436i	0.332642	−	0.108082i	−0.137934	−	0.990441i	$-0.544046\pi$
$37$	2.02338	−	0.657436i	0.332642	−	0.108082i	0.470576	+	0.882360i	$0.344046\pi$
$38$	5.74918	+	6.15598i	0.932640	+	0.998631i
$39$		0			0
$40$	−1.52783	+	1.24292i	−0.241571	+	0.196522i
$41$	−0.736879	−	0.239427i	−0.115081	−	0.0373921i	0.250910	−	0.968010i	$-0.419270\pi$
$41$	−0.736879	−	0.239427i	−0.115081	−	0.0373921i	−0.365991	+	0.930618i	$0.619270\pi$
$42$		0			0
$43$		−	10.1720i		−	1.55122i	−0.631211	−	0.775611i	$-0.717442\pi$
$43$		−	10.1720i		−	1.55122i	0.631211	−	0.775611i	$-0.282558\pi$
$44$	−6.58615	−	0.789033i	−0.992900	−	0.118951i
$45$		0			0
$46$	−5.91977	+	10.6985i	−0.872823	+	1.57740i
$47$	5.29780	+	1.72136i	0.772764	+	0.251086i	0.668748	−	0.743489i	$-0.266831\pi$
$47$	5.29780	+	1.72136i	0.772764	+	0.251086i	0.104016	+	0.994576i	$0.466831\pi$
$48$		0			0
$49$	3.45658	−	2.51135i	0.493797	−	0.358764i
$50$	4.66667	−	4.35829i	0.659967	−	0.616355i
$51$		0			0
$52$	−0.830261	+	12.1349i	−0.115136	+	1.68281i
$53$	2.57874	−	3.54933i	0.354217	−	0.487538i	−0.594309	−	0.804237i	$-0.702574\pi$
$53$	2.57874	−	3.54933i	0.354217	−	0.487538i	0.948526	+	0.316699i	$0.102574\pi$
$54$		0			0
$55$	−2.30650	−	0.117551i	−0.311009	−	0.0158505i
$56$	4.35710	−	1.68380i	0.582242	−	0.225007i
$57$		0			0
$58$	1.15908	−	5.98691i	0.152194	−	0.786119i
$59$	−3.78102	−	11.6368i	−0.492247	−	1.51498i	−0.821204	−	0.570634i	$-0.806697\pi$
$59$	−3.78102	−	11.6368i	−0.492247	−	1.51498i	0.328958	−	0.944345i	$-0.393303\pi$
$60$		0			0
$61$	0.239653	−	0.174118i	0.0306845	−	0.0222936i	−0.572337	−	0.820018i	$-0.693963\pi$
$61$	0.239653	−	0.174118i	0.0306845	−	0.0222936i	0.603022	+	0.797725i	$0.293963\pi$
$62$	−8.93420	+	4.17425i	−1.13464	+	0.530130i
$63$		0			0
$64$	−7.95233	+	0.872033i	−0.994041	+	0.109004i
$65$			4.23488i			0.525273i
$66$		0			0
$67$	−10.7130			−1.30880			−0.654402	−	0.756147i	$-0.727079\pi$
$67$	−10.7130			−1.30880			−0.654402	+	0.756147i	$0.727079\pi$
$68$	2.83412	−	7.04512i	0.343688	−	0.854346i
$69$		0			0
$70$	1.47345	−	0.688429i	0.176111	−	0.0822830i
$71$	−1.14044	−	1.56968i	−0.135345	−	0.186287i	0.735964	−	0.677020i	$-0.236729\pi$
$71$	−1.14044	−	1.56968i	−0.135345	−	0.186287i	−0.871310	+	0.490733i	$0.836729\pi$
$72$		0			0
$73$	−6.90989	+	2.24516i	−0.808741	+	0.262776i	−0.684064	−	0.729422i	$-0.739789\pi$
$73$	−6.90989	+	2.24516i	−0.808741	+	0.262776i	−0.124677	+	0.992197i	$0.539789\pi$
$74$	2.95390	+	0.571881i	0.343384	+	0.0664798i
$75$		0			0
$76$	2.89914	+	11.5539i	0.332554	+	1.32533i
$77$	5.11640	+	1.95556i	0.583068	+	0.222857i
$78$		0			0
$79$	−2.76926	−	2.01198i	−0.311566	−	0.226366i	0.421002	−	0.907060i	$-0.361678\pi$
$79$	−2.76926	−	2.01198i	−0.311566	−	0.226366i	−0.732568	+	0.680694i	$0.761678\pi$
$80$	−2.74158	+	0.491902i	−0.306518	+	0.0549963i
$81$		0			0
$82$	−0.747889	−	0.800808i	−0.0825906	−	0.0884344i
$83$	1.90883	+	2.62729i	0.209522	+	0.288382i	0.900825	−	0.434183i	$-0.142963\pi$
$83$	1.90883	+	2.62729i	0.209522	+	0.288382i	−0.691303	+	0.722565i	$0.742963\pi$
$84$		0			0
$85$	0.817020	−	2.51453i	0.0886183	−	0.272739i
$86$	6.96476	−	12.5870i	0.751030	−	1.35729i
$87$		0			0
$88$	−7.60955	−	5.48587i	−0.811180	−	0.584796i
$89$	6.63247			0.703040			0.351520	−	0.936180i	$-0.385665\pi$
$89$	6.63247			0.703040			0.351520	+	0.936180i	$0.385665\pi$
$90$		0			0
$91$	3.10371	−	9.55222i	0.325357	−	1.00135i
$92$	−14.6504	+	9.18519i	−1.52741	+	0.957622i
$93$		0			0
$94$	5.37696	+	5.75742i	0.554591	+	0.593832i
$95$	1.28163	+	3.94444i	0.131492	+	0.404691i
$96$		0			0
$97$	−3.48568	−	2.53250i	−0.353917	−	0.257136i	0.396593	−	0.917994i	$-0.370192\pi$
$97$	−3.48568	−	2.53250i	−0.353917	−	0.257136i	−0.750511	+	0.660858i	$0.770192\pi$
$98$	5.99672	−	0.740872i	0.605761	−	0.0748394i
$99$		0			0
$100$	8.75870	−	2.19775i	0.875870	−	0.219775i
$101$	−4.21872	−	3.06508i	−0.419778	−	0.304987i	0.357770	−	0.933810i	$-0.383537\pi$
$101$	−4.21872	−	3.06508i	−0.419778	−	0.304987i	−0.777549	+	0.628823i	$0.783537\pi$
$102$		0			0
$103$	3.29822	−	1.07166i	0.324983	−	0.105593i	−0.141982	−	0.989869i	$-0.545347\pi$
$103$	3.29822	−	1.07166i	0.324983	−	0.105593i	0.466965	+	0.884276i	$0.345347\pi$
$104$	−9.33610	+	14.4474i	−0.915480	+	1.41669i
$105$		0			0
$106$	5.62118	−	2.62634i	0.545977	−	0.255092i
$107$	7.88188	+	2.56098i	0.761970	+	0.247579i	0.664124	−	0.747623i	$-0.268805\pi$
$107$	7.88188	+	2.56098i	0.761970	+	0.247579i	0.0978460	+	0.995202i	$0.468805\pi$
$108$		0			0
$109$	17.7781			1.70284			0.851419	−	0.524487i	$-0.175743\pi$
$109$	17.7781			1.70284			0.851419	+	0.524487i	$0.175743\pi$
$110$	−2.77361	−	1.72471i	−0.264453	−	0.164445i
$111$		0			0
$112$	6.54442	+	0.899739i	0.618390	+	0.0850174i
$113$	2.30521	−	7.09472i	0.216856	−	0.667415i	−0.782160	−	0.623077i	$-0.785882\pi$
$113$	2.30521	−	7.09472i	0.216856	−	0.667415i	0.999017	−	0.0443379i	$-0.0141178\pi$
$114$		0			0
$115$	−4.87063	+	3.53872i	−0.454189	+	0.329988i
$116$	5.53347	−	6.61466i	0.513770	−	0.614156i
$117$		0			0
$118$	3.28898	−	16.9883i	0.302775	−	1.56390i
$119$	−3.68575	+	5.07300i	−0.337872	+	0.465041i
$120$		0			0
$121$	−2.31799	−	10.7530i	−0.210726	−	0.977545i
$122$	0.415768	−	0.0513666i	0.0376419	−	0.00465051i
$123$		0			0
$124$	−13.9134	−	0.951942i	−1.24946	−	0.0854869i
$125$	6.30146	−	2.04747i	0.563619	−	0.183131i
$126$		0			0
$127$	5.14844	−	3.74056i	0.456850	−	0.331921i	−0.335444	−	0.942060i	$-0.608886\pi$
$127$	5.14844	−	3.74056i	0.456850	−	0.331921i	0.792294	+	0.610139i	$0.208886\pi$
$128$	−10.4374	−	4.36586i	−0.922544	−	0.385892i
$129$		0			0
$130$	−2.89961	+	5.24030i	−0.254313	+	0.459605i
$131$			0.239732i			0.0209455i	0.999945	+	0.0104727i	$0.00333363\pi$
$131$			0.239732i			0.0209455i	−0.999945	+	0.0104727i	$0.996666\pi$
$132$		0			0
$133$		−	9.83639i		−	0.852923i
$134$	−13.2564	−	7.33516i	−1.14518	−	0.633662i
$135$		0			0
$136$	8.33075	−	6.77721i	0.714356	−	0.581141i
$137$	2.39415	−	1.73945i	0.204546	−	0.148611i	−0.480797	−	0.876832i	$-0.659652\pi$
$137$	2.39415	−	1.73945i	0.204546	−	0.148611i	0.685343	+	0.728221i	$0.259652\pi$
$138$		0			0
$139$	1.50194	−	0.488010i	0.127393	−	0.0413925i	−0.244627	−	0.969617i	$-0.578665\pi$
$139$	1.50194	−	0.488010i	0.127393	−	0.0413925i	0.372020	+	0.928225i	$0.378665\pi$
$140$	2.29464	+	0.156997i	0.193932	+	0.0132687i
$141$		0			0
$142$	−0.336441	−	2.72320i	−0.0282335	−	0.228526i
$143$	−19.4757	+	5.24855i	−1.62864	+	0.438906i
$144$		0			0
$145$	1.76489	−	2.42916i	0.146566	−	0.201731i
$146$	−10.0876	−	1.95298i	−0.834859	−	0.161630i
$147$		0			0
$148$	3.26363	+	2.73018i	0.268269	+	0.224419i
$149$	14.7822	−	10.7399i	1.21101	−	0.879849i	0.215687	−	0.976463i	$-0.430801\pi$
$149$	14.7822	−	10.7399i	1.21101	−	0.879849i	0.995322	+	0.0966133i	$0.0308010\pi$
$150$		0			0
$151$	−4.68718	+	14.4256i	−0.381437	+	1.17394i	0.557595	+	0.830113i	$0.311724\pi$
$151$	−4.68718	+	14.4256i	−0.381437	+	1.17394i	−0.939032	+	0.343829i	$0.888276\pi$
$152$	−4.32350	+	16.2820i	−0.350682	+	1.32065i
$153$		0			0
$154$	4.99214	+	5.92302i	0.402278	+	0.477290i
$155$	−4.85554			−0.390007
$156$		0			0
$157$	−6.33215	−	2.05744i	−0.505360	−	0.164202i	0.0452308	−	0.998977i	$-0.485598\pi$
$157$	−6.33215	−	2.05744i	−0.505360	−	0.164202i	−0.550591	+	0.834775i	$0.685598\pi$
$158$	−2.04912	−	4.38575i	−0.163019	−	0.348912i
$159$		0			0
$160$	−3.72927	−	1.26846i	−0.294824	−	0.100281i
$161$	13.5797	−	4.41232i	1.07023	−	0.347739i
$162$		0			0
$163$	−0.612537	−	0.445034i	−0.0479776	−	0.0348578i	0.563538	−	0.826090i	$-0.309440\pi$
$163$	−0.612537	−	0.445034i	−0.0479776	−	0.0348578i	−0.611516	+	0.791232i	$0.709440\pi$
$164$	−0.377138	−	1.50301i	−0.0294495	−	0.117365i
$165$		0			0
$166$	0.563125	+	4.55801i	0.0437069	+	0.353770i
$167$	−11.1349	−	8.08998i	−0.861644	−	0.626021i	0.0666874	−	0.997774i	$-0.478757\pi$
$167$	−11.1349	−	8.08998i	−0.861644	−	0.626021i	−0.928332	+	0.371753i	$0.878757\pi$
$168$		0			0
$169$	7.41220	+	22.8124i	0.570169	+	1.75480i
$170$	2.73268	−	2.55210i	0.209587	−	0.195737i
$171$		0			0
$172$	17.2366	−	10.8066i	1.31428	−	0.823996i
$173$	1.35890	−	4.18227i	0.103315	−	0.317972i	−0.886016	−	0.463655i	$-0.846538\pi$
$173$	1.35890	−	4.18227i	0.103315	−	0.317972i	0.989331	+	0.145683i	$0.0465379\pi$
$174$		0			0
$175$	−7.45669			−0.563672
$176$	−5.65999	−	11.9985i	−0.426638	−	0.904422i
$177$		0			0
$178$	8.20710	+	4.54122i	0.615148	+	0.340379i
$179$	5.23266	−	16.1045i	0.391107	−	1.20370i	−0.540845	−	0.841122i	$-0.681895\pi$
$179$	5.23266	−	16.1045i	0.391107	−	1.20370i	0.931952	−	0.362582i	$-0.118105\pi$
$180$		0			0
$181$	−10.7847	−	14.8439i	−0.801620	−	1.10334i	−0.992563	−	0.121734i	$-0.961155\pi$
$181$	−10.7847	−	14.8439i	−0.801620	−	1.10334i	0.190943	−	0.981601i	$-0.438845\pi$
$182$	10.3809	−	9.69495i	0.769486	−	0.718638i
$183$		0			0
$184$	−24.4177	+	1.33479i	−1.80009	+	0.0984021i
$185$	1.19853	+	0.870785i	0.0881178	+	0.0640214i
$186$		0			0
$187$	12.5766	+	0.640964i	0.919691	+	0.0468719i
$188$	2.71144	+	10.8059i	0.197752	+	0.788100i
$189$		0			0
$190$	−1.11484	+	5.75843i	−0.0808792	+	0.417760i
$191$	−23.5927	+	7.66573i	−1.70711	+	0.554673i	−0.989847	−	0.142134i	$-0.954604\pi$
$191$	−23.5927	+	7.66573i	−1.70711	+	0.554673i	−0.717259	+	0.696806i	$0.754604\pi$
$192$		0			0
$193$	0.0138035	+	0.0189988i	0.000993595	+	0.00136757i	0.809514	−	0.587101i	$-0.199731\pi$
$193$	0.0138035	+	0.0189988i	0.000993595	+	0.00136757i	−0.808520	+	0.588469i	$0.799731\pi$
$194$	−2.57924	−	5.52038i	−0.185179	−	0.396340i
$195$		0			0
$196$	7.92770	+	3.18917i	0.566264	+	0.227798i
$197$	−0.183455			−0.0130706			−0.00653530	−	0.999979i	$-0.502080\pi$
$197$	−0.183455			−0.0130706			−0.00653530	+	0.999979i	$0.502080\pi$
$198$		0			0
$199$		−	14.8031i		−	1.04936i	−0.851298	−	0.524682i	$-0.824184\pi$
$199$		−	14.8031i		−	1.04936i	0.851298	−	0.524682i	$-0.175816\pi$
$200$	12.3429	+	3.27752i	0.872776	+	0.231756i
$201$		0			0
$202$	−3.12165	−	6.68131i	−0.219638	−	0.470095i
$203$	−5.76120	+	4.18575i	−0.404357	+	0.293782i
$204$		0			0
$205$	−0.166722	−	0.513118i	−0.0116444	−	0.0358377i
$206$	4.81501	+	0.932196i	0.335478	+	0.0649491i
$207$		0			0
$208$	−21.4447	+	11.4850i	−1.48692	+	0.796344i
$209$	−16.5516	+	10.7826i	−1.14490	+	0.745850i
$210$		0			0
$211$	−6.77305	+	9.32230i	−0.466276	+	0.641774i	−0.975795	−	0.218685i	$-0.929823\pi$
$211$	−6.77305	+	9.32230i	−0.466276	+	0.641774i	0.509519	+	0.860459i	$0.329823\pi$
$212$	8.75397	+	0.598939i	0.601225	+	0.0411353i
$213$		0			0
$214$	7.99965	+	8.56568i	0.546845	+	0.585538i
$215$	5.73042	−	4.16340i	0.390812	−	0.283941i
$216$		0			0
$217$	10.9522	+	3.55858i	0.743483	+	0.241572i
$218$	21.9989	+	12.1726i	1.48995	+	0.824434i
$219$		0			0
$220$	−2.25120	−	4.03326i	−0.151776	−	0.271922i
$221$		−	23.0914i		−	1.55330i
$222$		0			0
$223$	−9.63345	−	3.13010i	−0.645104	−	0.209607i	−0.0318497	−	0.999493i	$-0.510140\pi$
$223$	−9.63345	−	3.13010i	−0.645104	−	0.209607i	−0.613254	+	0.789886i	$0.710140\pi$
$224$	7.48211	+	5.59429i	0.499919	+	0.373784i
$225$		0			0
$226$	7.71023	−	7.20073i	0.512877	−	0.478985i
$227$	8.77003	−	2.84955i	0.582087	−	0.189132i	−0.00314828	−	0.999995i	$-0.501002\pi$
$227$	8.77003	−	2.84955i	0.582087	−	0.189132i	0.585235	+	0.810863i	$0.301002\pi$
$228$		0			0
$229$	−15.0976	+	20.7800i	−0.997676	+	1.37318i	−0.0709359	+	0.997481i	$0.522599\pi$
$229$	−15.0976	+	20.7800i	−0.997676	+	1.37318i	−0.926740	+	0.375703i	$0.877401\pi$
$230$	−8.44994	+	1.04396i	−0.557172	+	0.0688365i
$231$		0			0
$232$	11.3762	−	4.39632i	0.746885	−	0.288633i
$233$	−14.1060	+	19.4152i	−0.924112	+	1.27193i	0.0380001	+	0.999278i	$0.487901\pi$
$233$	−14.1060	+	19.4152i	−0.924112	+	1.27193i	−0.962112	+	0.272654i	$0.912099\pi$
$234$		0			0
$235$	1.19865	+	3.68907i	0.0781913	+	0.240648i
$236$	15.7017	−	18.7697i	1.02209	−	1.22180i
$237$		0			0
$238$	−8.03426	+	3.75378i	−0.520783	+	0.243321i
$239$	4.93373	−	15.1845i	0.319137	−	0.982201i	−0.654882	−	0.755731i	$-0.727282\pi$
$239$	4.93373	−	15.1845i	0.319137	−	0.982201i	0.974018	−	0.226470i	$-0.0727185\pi$
$240$		0			0
$241$		−	9.42736i		−	0.607269i	−0.952789	−	0.303635i	$-0.901800\pi$
$241$		−	9.42736i		−	0.607269i	0.952789	−	0.303635i	$-0.0982003\pi$
$242$	4.49423	−	14.8930i	0.288900	−	0.957359i
$243$		0			0
$244$	0.549647	+	0.221113i	0.0351876	+	0.0141553i
$245$	2.82954	+	0.919373i	0.180773	+	0.0587366i
$246$		0			0
$247$	21.2911	+	29.3047i	1.35472	+	1.86461i
$248$	−16.5648	−	10.7044i	−1.05187	−	0.679730i
$249$		0			0
$250$	9.19940	+	1.78102i	0.581821	+	0.112642i
$251$	3.20392	+	2.32778i	0.202229	+	0.146928i	0.684291	−	0.729209i	$-0.260112\pi$
$251$	3.20392	+	2.32778i	0.202229	+	0.146928i	−0.482062	+	0.876137i	$0.660112\pi$
$252$		0			0
$253$	−22.3106	−	18.0137i	−1.40266	−	1.13251i
$254$	8.93190	−	1.10350i	0.560437	−	0.0692399i
$255$		0			0
$256$	−9.92608	−	12.5488i	−0.620380	−	0.784301i
$257$	−6.26844	−	19.2923i	−0.391015	−	1.20342i	−0.932022	−	0.362401i	$-0.881957\pi$
$257$	−6.26844	−	19.2923i	−0.391015	−	1.20342i	0.541008	−	0.841018i	$-0.318043\pi$
$258$		0			0
$259$	−2.06522	−	2.84254i	−0.128327	−	0.176627i
$260$	−7.17603	+	4.49907i	−0.445038	+	0.279020i
$261$		0			0
$262$	−0.164143	+	0.296647i	−0.0101408	+	0.0183269i
$263$	4.86501			0.299989			0.149995	−	0.988687i	$-0.452074\pi$
$263$	4.86501			0.299989			0.149995	+	0.988687i	$0.452074\pi$
$264$		0			0
$265$	3.05499			0.187667
$266$	6.73494	−	12.1717i	0.412946	−	0.746294i
$267$		0			0
$268$	−11.3813	−	18.1533i	−0.695225	−	1.10889i
$269$	16.9712	+	23.3589i	1.03475	+	1.42422i	0.901318	+	0.433158i	$0.142601\pi$
$269$	16.9712	+	23.3589i	1.03475	+	1.42422i	0.133435	+	0.991058i	$0.457399\pi$
$270$		0			0
$271$	4.51837	+	13.9061i	0.274472	+	0.844737i	0.989359	+	0.145497i	$0.0464781\pi$
$271$	4.51837	+	13.9061i	0.274472	+	0.844737i	−0.714887	+	0.699240i	$0.753522\pi$
$272$	14.9489	−	2.68218i	0.906410	−	0.162631i
$273$		0			0
$274$	4.15354	−	0.513155i	0.250925	−	0.0310008i
$275$	8.17400	+	12.5473i	0.492911	+	0.756630i
$276$		0			0
$277$	22.3661	+	16.2499i	1.34385	+	0.976363i	0.999293	+	0.0375974i	$0.0119705\pi$
$277$	22.3661	+	16.2499i	1.34385	+	0.976363i	0.344556	+	0.938766i	$0.388030\pi$
$278$	2.19266	+	0.424503i	0.131507	+	0.0254600i
$279$		0			0
$280$	2.73192	+	1.76540i	0.163263	+	0.105503i
$281$	16.8765	+	23.2286i	1.00677	+	1.38570i	0.921078	+	0.389378i	$0.127310\pi$
$281$	16.8765	+	23.2286i	1.00677	+	1.38570i	0.0856916	+	0.996322i	$0.472690\pi$
$282$		0			0
$283$	14.9354	+	4.85281i	0.887818	+	0.288469i	0.717200	−	0.696868i	$-0.245424\pi$
$283$	14.9354	+	4.85281i	0.887818	+	0.288469i	0.170618	+	0.985337i	$0.445424\pi$
$284$	1.44825	−	3.60009i	0.0859378	−	0.213626i
$285$		0			0
$286$	−27.6931	−	6.84031i	−1.63753	−	0.404476i
$287$			1.27958i			0.0755312i
$288$		0			0
$289$	0.798350	−	2.45707i	0.0469618	−	0.144533i
$290$	3.84713	−	1.79746i	0.225911	−	0.105551i
$291$		0			0
$292$	−11.1454	−	9.32361i	−0.652233	−	0.545623i
$293$	5.97643	+	18.3936i	0.349147	+	1.07456i	0.959326	+	0.282300i	$0.0910975\pi$
$293$	5.97643	+	18.3936i	0.349147	+	1.07456i	−0.610179	+	0.792264i	$0.708902\pi$
$294$		0			0
$295$	5.00802	−	6.89294i	0.291578	−	0.401323i
$296$	2.16912	+	5.61296i	0.126077	+	0.326246i
$297$		0			0
$298$	25.6453	−	3.16838i	1.48559	−	0.183539i
$299$	−30.9063	+	42.5388i	−1.78736	+	2.46008i
$300$		0			0
$301$	−15.9769	+	5.19120i	−0.920892	+	0.299216i
$302$	−15.6772	+	14.6412i	−0.902119	+	0.842506i
$303$		0			0
$304$	−16.4982	+	17.1873i	−0.946236	+	0.985759i
$305$	0.196179	+	0.0637424i	0.0112332	+	0.00364988i
$306$		0			0
$307$			17.8955i			1.02135i	0.859774	+	0.510675i	$0.170604\pi$
$307$			17.8955i			1.02135i	−0.859774	+	0.510675i	$0.829396\pi$
$308$	2.12187	+	10.7473i	0.120905	+	0.612385i
$309$		0			0
$310$	−6.00831	−	3.32457i	−0.341249	−	0.188823i
$311$	−0.940857	−	0.305703i	−0.0533511	−	0.0173348i	0.282220	−	0.959350i	$-0.408929\pi$
$311$	−0.940857	−	0.305703i	−0.0533511	−	0.0173348i	−0.335571	+	0.942015i	$0.608929\pi$
$312$		0			0
$313$	−10.9210	+	7.93456i	−0.617291	+	0.448488i	−0.851974	−	0.523584i	$-0.824595\pi$
$313$	−10.9210	+	7.93456i	−0.617291	+	0.448488i	0.234683	+	0.972072i	$0.424595\pi$
$314$	−6.42676	−	6.88150i	−0.362683	−	0.388345i
$315$		0			0
$316$	0.467303	−	6.83001i	0.0262879	−	0.384218i
$317$	−5.19658	+	7.15248i	−0.291869	+	0.401724i	−0.929620	−	0.368519i	$-0.879865\pi$
$317$	−5.19658	+	7.15248i	−0.291869	+	0.401724i	0.637751	+	0.770243i	$0.279865\pi$
$318$		0			0
$319$	13.3587	+	5.10589i	0.747945	+	0.285875i
$320$	−3.74613	−	4.12302i	−0.209415	−	0.230484i
$321$		0			0
$322$	19.8248	+	3.83812i	1.10479	+	0.213890i
$323$	−6.98828	−	21.5077i	−0.388839	−	1.19672i
$324$		0			0
$325$	22.2150	−	16.1402i	1.23227	−	0.895295i
$326$	−0.453248	−	0.970093i	−0.0251031	−	0.0537285i
$327$		0			0
$328$	0.562428	−	2.11807i	0.0310549	−	0.116951i
$329$		−	9.19955i		−	0.507188i
$330$		0			0
$331$	9.05146			0.497513			0.248757	−	0.968566i	$-0.419978\pi$
$331$	9.05146			0.497513			0.248757	+	0.968566i	$0.419978\pi$
$332$	−2.42403	+	6.02571i	−0.133036	+	0.330704i
$333$		0			0
$334$	−8.23929	−	17.6347i	−0.450834	−	0.964926i
$335$	−4.38482	−	6.03518i	−0.239568	−	0.329737i
$336$		0			0
$337$	−12.9875	+	4.21989i	−0.707474	+	0.229872i	−0.640584	−	0.767888i	$-0.721308\pi$
$337$	−12.9875	+	4.21989i	−0.707474	+	0.229872i	−0.0668898	+	0.997760i	$0.521308\pi$
$338$	−6.44761	+	33.3035i	−0.350704	+	1.81147i
$339$		0			0
$340$	5.12887	−	1.28695i	0.278152	−	0.0697945i
$341$	−6.01777	−	22.3300i	−0.325880	−	1.20924i
$342$		0			0
$343$	−15.0611	−	10.9426i	−0.813225	−	0.590842i
$344$	28.7280	−	1.57041i	1.54891	−	0.0846711i
$345$		0			0
$346$	4.54510	−	4.24476i	0.244346	−	0.228200i
$347$	−1.37075	−	1.88668i	−0.0735859	−	0.101282i	0.770638	−	0.637274i	$-0.219938\pi$
$347$	−1.37075	−	1.88668i	−0.0735859	−	0.101282i	−0.844223	+	0.535991i	$0.819938\pi$
$348$		0			0
$349$	4.49635	−	13.8383i	0.240684	−	0.740750i	−0.755632	−	0.654996i	$-0.772670\pi$
$349$	4.49635	−	13.8383i	0.240684	−	0.740750i	0.996316	−	0.0857534i	$-0.0273297\pi$
$350$	−9.22700	−	5.10556i	−0.493204	−	0.272904i
$351$		0			0
$352$	1.21159	−	18.7225i	0.0645779	−	0.997913i
$353$	−23.7432			−1.26372			−0.631861	−	0.775082i	$-0.717709\pi$
$353$	−23.7432			−1.26372			−0.631861	+	0.775082i	$0.717709\pi$
$354$		0			0
$355$	0.417501	−	1.28494i	0.0221586	−	0.0681973i
$356$	7.04621	+	11.2387i	0.373449	+	0.595652i
$357$		0			0
$358$	17.5016	−	16.3451i	0.924990	−	0.863865i
$359$	3.27128	+	10.0680i	0.172652	+	0.531367i	0.999518	−	0.0310309i	$-0.00987904\pi$
$359$	3.27128	+	10.0680i	0.172652	+	0.531367i	−0.826867	+	0.562398i	$0.809879\pi$
$360$		0			0
$361$	13.3282	+	9.68351i	0.701484	+	0.509658i
$362$	−3.18159	−	25.7522i	−0.167221	−	1.35351i
$363$		0			0
$364$	19.4836	−	4.88887i	1.02122	−	0.256247i
$365$	−4.09301	−	2.97375i	−0.214238	−	0.155653i
$366$		0			0
$367$	−24.8159	+	8.06317i	−1.29538	+	0.420894i	−0.873971	−	0.485978i	$-0.838464\pi$
$367$	−24.8159	+	8.06317i	−1.29538	+	0.420894i	−0.421407	+	0.906872i	$0.638464\pi$
$368$	−31.1287	−	15.0670i	−1.62269	−	0.785421i
$369$		0			0
$370$	0.886856	+	1.89815i	0.0461055	+	0.0986801i
$371$	−6.89085	−	2.23897i	−0.357755	−	0.116242i
$372$		0			0
$373$	−16.7165			−0.865549			−0.432774	−	0.901502i	$-0.642465\pi$
$373$	−16.7165			−0.865549			−0.432774	+	0.901502i	$0.642465\pi$
$374$	15.1236	+	9.40428i	0.782021	+	0.486284i
$375$		0			0
$376$	−4.04358	+	15.2279i	−0.208532	+	0.785317i
$377$	8.10365	−	24.9405i	0.417359	−	1.28450i
$378$		0			0
$379$	−20.2745	+	14.7303i	−1.04143	+	0.756643i	−0.970564	−	0.240842i	$-0.922576\pi$
$379$	−20.2745	+	14.7303i	−1.04143	+	0.756643i	−0.0708660	+	0.997486i	$0.522576\pi$
$380$	−5.32230	+	6.36223i	−0.273028	+	0.326375i
$381$		0			0
$382$	−34.4426	−	6.66815i	−1.76224	−	0.341172i
$383$	−5.14355	+	7.07949i	−0.262823	+	0.361745i	−0.919950	−	0.392035i	$-0.871771\pi$
$383$	−5.14355	+	7.07949i	−0.262823	+	0.361745i	0.657127	+	0.753780i	$0.271771\pi$
$384$		0			0
$385$	0.992468	+	3.68273i	0.0505808	+	0.187689i
$386$	0.00407215	+	0.0329606i	0.000207267	+	0.00167765i
$387$		0			0
$388$	0.588198	−	8.59698i	0.0298612	−	0.436446i
$389$	21.4991	−	6.98549i	1.09005	−	0.354179i	0.291784	−	0.956484i	$-0.405751\pi$
$389$	21.4991	−	6.98549i	1.09005	−	0.354179i	0.798265	+	0.602306i	$0.205751\pi$
$390$		0			0
$391$	26.5579	−	19.2955i	1.34309	−	0.975814i
$392$	7.62623	+	9.37438i	0.385183	+	0.473478i
$393$		0			0
$394$	−0.227009	−	0.125611i	−0.0114366	−	0.00632817i
$395$		−	2.38356i		−	0.119930i
$396$		0			0
$397$		−	2.78536i		−	0.139793i	−0.997554	−	0.0698965i	$-0.977733\pi$
$397$		−	2.78536i		−	0.139793i	0.997554	−	0.0698965i	$-0.0222669\pi$
$398$	10.1356	−	18.3175i	0.508053	−	0.918175i
$399$		0			0
$400$	13.0292	+	12.5068i	0.651460	+	0.625340i
$401$	−5.19019	+	3.77089i	−0.259186	+	0.188309i	−0.709788	−	0.704415i	$-0.751209\pi$
$401$	−5.19019	+	3.77089i	−0.259186	+	0.188309i	0.450602	+	0.892725i	$0.351209\pi$
$402$		0			0
$403$	−40.3315	+	13.1045i	−2.00905	+	0.652781i
$404$	0.711896	−	10.4049i	0.0354181	−	0.517664i
$405$		0			0
$406$	−9.99495	+	1.23484i	−0.496041	+	0.0612840i
$407$	−2.51921	+	6.59111i	−0.124873	+	0.326709i
$408$		0			0
$409$	−17.5440	+	24.1473i	−0.867496	+	1.19401i	0.112234	+	0.993682i	$0.464199\pi$
$409$	−17.5440	+	24.1473i	−0.867496	+	1.19401i	−0.979730	+	0.200324i	$0.935801\pi$
$410$	0.145026	−	0.749092i	0.00716231	−	0.0369950i
$411$		0			0
$412$	5.31989	+	4.45033i	0.262092	+	0.219252i
$413$	−16.3479	+	11.8774i	−0.804426	+	0.584450i
$414$		0			0
$415$	−0.698800	+	2.15068i	−0.0343027	+	0.105573i
$416$	−34.3997	−	0.471378i	−1.68659	−	0.0231112i
$417$		0			0
$418$	−27.8640	+	2.00975i	−1.36287	+	0.0983001i
$419$	2.52141			0.123179			0.0615895	−	0.998102i	$-0.480383\pi$
$419$	2.52141			0.123179			0.0615895	+	0.998102i	$0.480383\pi$
$420$		0			0
$421$	28.8541	+	9.37526i	1.40626	+	0.456922i	0.911210	−	0.411942i	$-0.135149\pi$
$421$	28.8541	+	9.37526i	1.40626	+	0.456922i	0.495051	+	0.868864i	$0.335149\pi$
$422$	−14.7640	+	6.89806i	−0.718701	+	0.335792i
$423$		0			0
$424$	10.4222	+	6.73494i	0.506146	+	0.327078i
$425$	−16.3044	+	5.29762i	−0.790879	+	0.256972i
$426$		0			0
$427$	−0.395786	−	0.287555i	−0.0191534	−	0.0139158i
$428$	4.03398	+	16.0766i	0.194990	+	0.777092i
$429$		0			0
$430$	9.94156	−	1.22824i	0.479425	−	0.0592311i
$431$	21.0004	+	15.2577i	1.01155	+	0.734937i	0.964534	−	0.263957i	$-0.0850278\pi$
$431$	21.0004	+	15.2577i	1.01155	+	0.734937i	0.0470191	+	0.998894i	$0.485028\pi$
$432$		0			0
$433$	−9.50922	−	29.2664i	−0.456984	−	1.40645i	−0.868790	−	0.495180i	$-0.835102\pi$
$433$	−9.50922	−	29.2664i	−0.456984	−	1.40645i	0.411806	−	0.911271i	$-0.364898\pi$
$434$	11.1158	+	11.9024i	0.533577	+	0.571331i
$435$		0			0
$436$	18.8872	+	30.1251i	0.904532	+	1.44273i
$437$	−15.9129	+	48.9747i	−0.761215	+	2.34278i
$438$		0			0
$439$	−13.9098			−0.663880			−0.331940	−	0.943301i	$-0.607703\pi$
$439$	−13.9098			−0.663880			−0.331940	+	0.943301i	$0.607703\pi$
$440$	−0.0241025	−	6.53219i	−0.00114904	−	0.311410i
$441$		0			0
$442$	15.8106	−	28.5736i	0.752034	−	1.35911i
$443$	−2.80215	+	8.62415i	−0.133134	+	0.409746i	−0.995295	−	0.0968892i	$-0.969111\pi$
$443$	−2.80215	+	8.62415i	−0.133134	+	0.409746i	0.862161	+	0.506635i	$0.169111\pi$
$444$		0			0
$445$	2.71465	+	3.73640i	0.128687	+	0.177122i
$446$	−9.77739	−	10.4692i	−0.462973	−	0.495732i
$447$		0			0
$448$	5.42807	+	12.0454i	0.256452	+	0.569092i
$449$	14.5319	+	10.5580i	0.685803	+	0.498265i	0.875278	−	0.483621i	$-0.160679\pi$
$449$	14.5319	+	10.5580i	0.685803	+	0.498265i	−0.189475	+	0.981886i	$0.560679\pi$
$450$		0			0
$451$	2.15313	−	1.40267i	0.101387	−	0.0660492i
$452$	14.4711	−	3.63111i	0.680661	−	0.170793i
$453$		0			0
$454$	12.8032	+	2.47873i	0.600885	+	0.116332i
$455$	6.65159	−	2.16123i	0.311831	−	0.101320i
$456$		0			0
$457$	12.9937	+	17.8843i	0.607820	+	0.836592i	0.996396	−	0.0848243i	$-0.0270329\pi$
$457$	12.9937	+	17.8843i	0.607820	+	0.836592i	−0.388576	+	0.921417i	$0.627033\pi$
$458$	−32.9100	+	15.3762i	−1.53778	+	0.718484i
$459$		0			0
$460$	−11.1709	−	4.49383i	−0.520844	−	0.209526i
$461$	−19.6830			−0.916730			−0.458365	−	0.888764i	$-0.651565\pi$
$461$	−19.6830			−0.916730			−0.458365	+	0.888764i	$0.651565\pi$
$462$		0			0
$463$		−	10.6767i		−	0.496188i	−0.968736	−	0.248094i	$-0.920196\pi$
$463$		−	10.6767i		−	0.496188i	0.968736	−	0.248094i	$-0.0798041\pi$
$464$	17.0872	+	2.34918i	0.793255	+	0.109058i
$465$		0			0
$466$	−30.7484	+	14.3663i	−1.42439	+	0.665507i
$467$	26.3995	−	19.1804i	1.22162	−	0.887562i	0.225391	−	0.974268i	$-0.427634\pi$
$467$	26.3995	−	19.1804i	1.22162	−	0.887562i	0.996234	+	0.0867060i	$0.0276341\pi$
$468$		0			0
$469$	5.46728	+	16.8266i	0.252456	+	0.776979i
$470$	−1.04266	+	5.38561i	−0.0480945	+	0.248420i
$471$		0			0
$472$	32.2810	−	12.4749i	1.48585	−	0.574206i
$473$	26.2490	+	21.1935i	1.20693	+	0.974480i
$474$		0			0
$475$	15.8069	−	21.7563i	0.725269	−	0.998247i
$476$	−12.5119	−	0.856053i	−0.573481	−	0.0392371i
$477$		0			0
$478$	16.5018	−	15.4113i	0.754775	−	0.704899i
$479$	12.8754	−	9.35454i	0.588293	−	0.427420i	−0.253411	−	0.967359i	$-0.581553\pi$
$479$	12.8754	−	9.35454i	0.588293	−	0.427420i	0.841704	+	0.539939i	$0.181553\pi$
$480$		0			0
$481$	12.3055	+	3.99829i	0.561082	+	0.182306i
$482$	6.45488	−	11.6655i	0.294012	−	0.531351i
$483$		0			0
$484$	15.7584	−	15.3516i	0.716291	−	0.697801i
$485$		−	3.00021i		−	0.136232i
$486$		0			0
$487$	−36.0858	−	11.7250i	−1.63520	−	0.531310i	−0.659744	−	0.751490i	$-0.729335\pi$
$487$	−36.0858	−	11.7250i	−1.63520	−	0.531310i	−0.975459	+	0.220180i	$0.929335\pi$
$488$	0.528746	+	0.649950i	0.0239352	+	0.0294218i
$489$		0			0
$490$	2.87182	+	3.07502i	0.129735	+	0.138915i
$491$	−0.524914	+	0.170555i	−0.0236890	+	0.00769703i	−0.320838	−	0.947134i	$-0.603964\pi$
$491$	−0.524914	+	0.170555i	−0.0236890	+	0.00769703i	0.297149	+	0.954831i	$0.403964\pi$
$492$		0			0
$493$	−9.62334	+	13.2454i	−0.433414	+	0.596543i
$494$	6.28108	+	50.8399i	0.282599	+	2.28740i
$495$		0			0
$496$	−13.1683	−	24.5876i	−0.591273	−	1.10402i
$497$	−1.88343	+	2.59232i	−0.0844835	+	0.116282i
$498$		0			0
$499$	0.743321	+	2.28771i	0.0332756	+	0.102412i	0.966315	−	0.257363i	$-0.0828536\pi$
$499$	0.743321	+	2.28771i	0.0332756	+	0.102412i	−0.933039	+	0.359775i	$0.882854\pi$
$500$	10.1640	+	8.50265i	0.454548	+	0.380250i
$501$		0			0
$502$	2.37074	+	5.07413i	0.105811	+	0.226470i
$503$	−0.451670	+	1.39010i	−0.0201390	+	0.0619814i	−0.960621	−	0.277862i	$-0.910374\pi$
$503$	−0.451670	+	1.39010i	−0.0201390	+	0.0619814i	0.940482	+	0.339844i	$0.110374\pi$
$504$		0			0
$505$		−	3.63114i		−	0.161584i
$506$	−15.2735	−	37.5663i	−0.678992	−	1.67003i
$507$		0			0
$508$	11.8080	+	4.75015i	0.523896	+	0.210754i
$509$	−38.7738	−	12.5984i	−1.71862	−	0.558413i	−0.726889	−	0.686755i	$-0.759035\pi$
$509$	−38.7738	−	12.5984i	−1.71862	−	0.558413i	−0.991730	+	0.128342i	$0.959035\pi$
$510$		0			0
$511$	7.05278	+	9.70732i	0.311997	+	0.429427i
$512$	−3.69053	−	22.3244i	−0.163100	−	0.986610i
$513$		0			0
$514$	5.45270	−	28.1645i	0.240508	−	1.24228i
$515$	1.95367	+	1.41942i	0.0860890	+	0.0625473i
$516$		0			0
$517$	−15.4800	+	10.0845i	−0.680809	+	0.443517i
$518$	−0.609261	−	4.93145i	−0.0267694	−	0.216675i
$519$		0			0
$520$	−11.9602	+	0.653804i	−0.524490	+	0.0286712i
$521$	0.971088	+	2.98870i	0.0425441	+	0.130937i	0.970073	−	0.242815i	$-0.0780709\pi$
$521$	0.971088	+	2.98870i	0.0425441	+	0.130937i	−0.927528	+	0.373753i	$0.878071\pi$
$522$		0			0
$523$	2.82713	+	3.89121i	0.123622	+	0.170151i	0.866342	−	0.499451i	$-0.166465\pi$
$523$	2.82713	+	3.89121i	0.123622	+	0.170151i	−0.742720	+	0.669602i	$0.766465\pi$
$524$	−0.406226	+	0.254687i	−0.0177461	+	0.0111260i
$525$		0			0
$526$	6.02003	+	3.33105i	0.262486	+	0.145241i
$527$	26.4757			1.15330
$528$		0			0
$529$	−51.7505			−2.25002
$530$	3.78028	+	2.09174i	0.164205	+	0.0908594i
$531$		0			0
$532$	16.6678	−	10.4500i	0.722641	−	0.453065i
$533$	−2.76968	−	3.81214i	−0.119968	−	0.165122i
$534$		0			0
$535$	1.78331	+	5.48846i	0.0770991	+	0.237287i
$536$	−1.65393	−	30.2558i	−0.0714390	−	1.30685i
$537$		0			0
$538$	5.00667	+	40.5247i	0.215853	+	1.74714i
$539$	−0.721261	+	14.1521i	−0.0310669	+	0.609575i
$540$		0			0
$541$	12.8453	+	9.33268i	0.552264	+	0.401243i	0.828620	−	0.559812i	$-0.189127\pi$
$541$	12.8453	+	9.33268i	0.552264	+	0.401243i	−0.276355	+	0.961056i	$0.589127\pi$
$542$	−3.93038	+	20.3013i	−0.168824	+	0.872017i
$543$		0			0
$544$	20.3344	+	6.91650i	0.871832	+	0.296542i
$545$	7.27656	+	10.0153i	0.311693	+	0.429009i
$546$		0			0
$547$	2.96072	+	0.961995i	0.126591	+	0.0411319i	0.371627	−	0.928382i	$-0.378800\pi$
$547$	2.96072	+	0.961995i	0.126591	+	0.0411319i	−0.245036	+	0.969514i	$0.578800\pi$
$548$	5.49100	+	2.20893i	0.234564	+	0.0943609i
$549$		0			0
$550$	1.52353	+	21.1229i	0.0649637	+	0.900683i
$551$		−	25.6824i		−	1.09411i
$552$		0			0
$553$	−1.74689	+	5.37637i	−0.0742852	+	0.228626i
$554$	16.5498	+	35.4219i	0.703136	+	1.50493i
$555$		0			0
$556$	2.42257	+	2.02659i	0.102740	+	0.0859466i
$557$	−1.84128	−	5.66686i	−0.0780174	−	0.240113i	0.904440	−	0.426601i	$-0.140289\pi$
$557$	−1.84128	−	5.66686i	−0.0780174	−	0.240113i	−0.982457	+	0.186489i	$0.940289\pi$
$558$		0			0
$559$	36.3620	−	50.0480i	1.53795	−	2.11681i
$560$	2.17175	+	4.05506i	0.0917732	+	0.171358i
$561$		0			0
$562$	4.97874	+	40.2986i	0.210016	+	1.69989i
$563$	11.7180	−	16.1284i	0.493853	−	0.679730i	−0.487240	−	0.873268i	$-0.661996\pi$
$563$	11.7180	−	16.1284i	0.493853	−	0.679730i	0.981093	+	0.193538i	$0.0619963\pi$
$564$		0			0
$565$	4.94033	−	1.60521i	0.207841	−	0.0675317i
$566$	15.1586	+	16.2311i	0.637162	+	0.682246i
$567$		0			0
$568$	4.25705	−	3.46318i	0.178622	−	0.145312i
$569$	10.2471	+	3.32949i	0.429582	+	0.139580i	0.515824	−	0.856695i	$-0.327486\pi$
$569$	10.2471	+	3.32949i	0.429582	+	0.139580i	−0.0862422	+	0.996274i	$0.527486\pi$
$570$		0			0
$571$		−	31.9637i		−	1.33764i	−0.743424	−	0.668820i	$-0.766800\pi$
$571$		−	31.9637i		−	1.33764i	0.743424	−	0.668820i	$-0.233200\pi$
$572$	−29.5843	−	27.4257i	−1.23698	−	1.14673i
$573$		0			0
$574$	−0.876123	+	1.58337i	−0.0365687	+	0.0660885i
$575$	37.1263	+	12.0631i	1.54827	+	0.503065i
$576$		0			0
$577$	−0.0764768	+	0.0555637i	−0.00318377	+	0.00231315i	−0.589376	−	0.807859i	$-0.700626\pi$
$577$	−0.0764768	+	0.0555637i	−0.00318377	+	0.00231315i	0.586192	+	0.810172i	$0.300626\pi$
$578$	2.67023	−	2.49378i	0.111067	−	0.103728i
$579$		0			0
$580$	5.99121	+	0.409913i	0.248771	+	0.0170207i
$581$	3.15243	−	4.33895i	0.130785	−	0.180010i
$582$		0			0
$583$	3.78623	+	14.0495i	0.156810	+	0.581871i
$584$	−7.40758	−	19.1684i	−0.306528	−	0.793192i
$585$		0			0
$586$	−5.19869	+	26.8525i	−0.214756	+	1.10927i
$587$	1.27747	+	3.93166i	0.0527270	+	0.162277i	0.973953	−	0.226752i	$-0.0728106\pi$
$587$	1.27747	+	3.93166i	0.0527270	+	0.162277i	−0.921226	+	0.389029i	$0.872811\pi$
$588$		0			0
$589$	−33.5995	+	24.4115i	−1.38444	+	1.00586i
$590$	10.9166	−	5.10045i	0.449428	−	0.209982i
$591$		0			0
$592$	−1.15907	+	8.43073i	−0.0476376	+	0.346501i
$593$		−	35.7489i		−	1.46803i	−0.679133	−	0.734015i	$-0.737644\pi$
$593$		−	35.7489i		−	1.46803i	0.679133	−	0.734015i	$-0.262356\pi$
$594$		0			0
$595$	−4.36644			−0.179007
$596$	33.9032	+	13.6387i	1.38873	+	0.558661i
$597$		0			0
$598$	−67.3700	+	31.4767i	−2.75496	+	1.28718i
$599$	7.34693	+	10.1122i	0.300187	+	0.413172i	0.932290	−	0.361713i	$-0.117808\pi$
$599$	7.34693	+	10.1122i	0.300187	+	0.413172i	−0.632102	+	0.774885i	$0.717808\pi$
$600$		0			0
$601$	21.8025	−	7.08405i	0.889341	−	0.288964i	0.171510	−	0.985182i	$-0.445135\pi$
$601$	21.8025	−	7.08405i	0.889341	−	0.288964i	0.717830	+	0.696218i	$0.245135\pi$
$602$	−23.3244	−	4.51565i	−0.950632	−	0.184044i
$603$		0			0
$604$	−29.4239	+	7.38311i	−1.19724	+	0.300415i
$605$	5.10895	−	5.70702i	0.207709	−	0.232023i
$606$		0			0
$607$	−23.1519	−	16.8209i	−0.939708	−	0.682738i	0.00864207	−	0.999963i	$-0.497249\pi$
$607$	−23.1519	−	16.8209i	−0.939708	−	0.682738i	−0.948350	+	0.317225i	$0.897249\pi$
$608$	−32.1831	+	9.97154i	−1.30520	+	0.404399i
$609$		0			0
$610$	0.199110	+	0.213199i	0.00806174	+	0.00863217i
$611$	19.9126	+	27.4074i	0.805579	+	1.10878i
$612$		0			0
$613$	−4.21216	+	12.9637i	−0.170128	+	0.523599i	−0.999378	−	0.0352789i	$-0.988768\pi$
$613$	−4.21216	+	12.9637i	−0.170128	+	0.523599i	0.829250	+	0.558878i	$0.188768\pi$
$614$	−12.2530	+	22.1441i	−0.494490	+	0.893664i
$615$		0			0
$616$	−4.73302	+	14.7517i	−0.190699	+	0.594363i
$617$	−14.0298			−0.564819			−0.282410	−	0.959294i	$-0.591134\pi$
$617$	−14.0298			−0.564819			−0.282410	+	0.959294i	$0.591134\pi$
$618$		0			0
$619$	−7.23719	+	22.2738i	−0.290887	+	0.895259i	0.693685	+	0.720279i	$0.255986\pi$
$619$	−7.23719	+	22.2738i	−0.290887	+	0.895259i	−0.984572	+	0.174980i	$0.944014\pi$
$620$	−5.15844	−	8.22774i	−0.207168	−	0.330434i
$621$		0			0
$622$	−0.954915	−	1.02248i	−0.0382886	−	0.0409978i
$623$	−3.38481	−	10.4174i	−0.135610	−	0.417364i
$624$		0			0
$625$	−14.5314	−	10.5577i	−0.581256	−	0.422307i
$626$	−18.9465	+	2.34077i	−0.757256	+	0.0935561i
$627$		0			0
$628$	−3.24082	−	12.9156i	−0.129323	−	0.515390i
$629$	−6.53520	−	4.74810i	−0.260575	−	0.189319i
$630$		0			0
$631$	−16.4648	+	5.34974i	−0.655453	+	0.212970i	−0.617817	−	0.786322i	$-0.711983\pi$
$631$	−16.4648	+	5.34974i	−0.655453	+	0.212970i	−0.0376362	+	0.999292i	$0.511983\pi$
$632$	5.25473	−	8.13158i	0.209022	−	0.323457i
$633$		0			0
$634$	−11.3276	+	5.29250i	−0.449876	+	0.210192i
$635$	4.21449	+	1.36937i	0.167247	+	0.0543418i
$636$		0			0
$637$	25.9842			1.02953
$638$	13.0343	+	15.4648i	0.516032	+	0.612256i
$639$		0			0
$640$	−1.81249	−	7.66685i	−0.0716451	−	0.303059i
$641$	0.223394	−	0.687535i	0.00882352	−	0.0271560i	−0.946548	−	0.322564i	$-0.895455\pi$
$641$	0.223394	−	0.687535i	0.00882352	−	0.0271560i	0.955371	+	0.295407i	$0.0954554\pi$
$642$		0			0
$643$	3.53380	−	2.56746i	0.139359	−	0.101251i	−0.515921	−	0.856636i	$-0.672550\pi$
$643$	3.53380	−	2.56746i	0.139359	−	0.101251i	0.655281	+	0.755385i	$0.272550\pi$
$644$	21.9035	+	18.3233i	0.863121	+	0.722040i
$645$		0			0
$646$	6.07886	−	31.3988i	0.239170	−	1.23537i
$647$	19.5634	−	26.9267i	0.769115	−	1.05860i	−0.227286	−	0.973828i	$-0.572985\pi$
$647$	19.5634	−	26.9267i	0.769115	−	1.05860i	0.996401	−	0.0847680i	$-0.0270149\pi$
$648$		0			0
$649$	37.9065	+	14.4884i	1.48796	+	0.568719i
$650$	38.5403	−	4.76151i	1.51167	−	0.186762i
$651$		0			0
$652$	0.103364	−	1.51074i	0.00404804	−	0.0591653i
$653$	14.5362	−	4.72309i	0.568845	−	0.184829i	−0.0104521	−	0.999945i	$-0.503327\pi$
$653$	14.5362	−	4.72309i	0.568845	−	0.184829i	0.579297	+	0.815116i	$0.303327\pi$
$654$		0			0
$655$	−0.135053	+	0.0981217i	−0.00527695	+	0.00383393i
$656$	2.14619	−	2.23583i	0.0837945	−	0.0872945i
$657$		0			0
$658$	6.29890	−	11.3836i	0.245557	−	0.443781i
$659$		−	31.0396i		−	1.20913i	−0.796556	−	0.604565i	$-0.793347\pi$
$659$		−	31.0396i		−	1.20913i	0.796556	−	0.604565i	$-0.206653\pi$
$660$		0			0
$661$		−	30.3454i		−	1.18030i	−0.807294	−	0.590149i	$-0.799069\pi$
$661$		−	30.3454i		−	1.18030i	0.807294	−	0.590149i	$-0.200931\pi$
$662$	11.2004	+	6.19750i	0.435316	+	0.240873i
$663$		0			0
$664$	−7.12531	+	5.79656i	−0.276516	+	0.224950i
$665$	5.54133	−	4.02601i	0.214884	−	0.156122i
$666$		0			0
$667$	35.4561	−	11.5204i	1.37287	−	0.446071i
$668$	1.87898	−	27.4628i	0.0726999	−	1.06257i
$669$		0			0
$670$	−1.29356	−	10.4703i	−0.0499747	−	0.404502i
$671$	−0.0500069	+	0.981203i	−0.00193049	+	0.0378789i
$672$		0			0
$673$	8.88632	−	12.2310i	0.342543	−	0.471469i	−0.602639	−	0.798014i	$-0.705884\pi$
$673$	8.88632	−	12.2310i	0.342543	−	0.471469i	0.945182	+	0.326544i	$0.105884\pi$
$674$	−18.9602	−	3.67074i	−0.730321	−	0.141391i
$675$		0			0
$676$	−30.7811	+	36.7955i	−1.18389	+	1.41521i
$677$	−29.0399	+	21.0987i	−1.11609	+	0.810890i	−0.983613	−	0.180295i	$-0.942295\pi$
$677$	−29.0399	+	21.0987i	−1.11609	+	0.810890i	−0.132482	+	0.991185i	$0.542295\pi$
$678$		0			0
$679$	−2.19882	+	6.76728i	−0.0843830	+	0.259704i
$680$	7.22770	+	1.91923i	0.277170	+	0.0735991i
$681$		0			0
$682$	7.84282	−	31.7518i	0.300317	−	1.21584i
$683$	−16.5721			−0.634112			−0.317056	−	0.948407i	$-0.602694\pi$
$683$	−16.5721			−0.634112			−0.317056	+	0.948407i	$0.602694\pi$
$684$		0			0
$685$	1.95984	+	0.636790i	0.0748816	+	0.0243305i
$686$	−11.1445	−	23.8528i	−0.425500	−	0.910703i
$687$		0			0
$688$	36.6237	+	17.7267i	1.39626	+	0.675824i
$689$	25.3756	−	8.24503i	0.966733	−	0.314111i
$690$		0			0
$691$	17.4532	+	12.6805i	0.663949	+	0.482387i	0.867994	−	0.496574i	$-0.165409\pi$
$691$	17.4532	+	12.6805i	0.663949	+	0.482387i	−0.204045	+	0.978961i	$0.565409\pi$
$692$	8.53054	−	2.14050i	0.324283	−	0.0813697i
$693$		0			0
$694$	−0.404385	−	3.27315i	−0.0153503	−	0.124247i
$695$	0.889662	+	0.646377i	0.0337468	+	0.0245185i
$696$		0			0
$697$	0.909080	+	2.79786i	0.0344338	+	0.105976i
$698$	15.0389	−	14.0451i	0.569231	−	0.531615i
$699$		0			0
$700$	−7.92185	−	12.6354i	−0.299418	−	0.477573i
$701$	−10.2401	+	31.5157i	−0.386762	+	1.19033i	0.548432	+	0.836195i	$0.315225\pi$
$701$	−10.2401	+	31.5157i	−0.386762	+	1.19033i	−0.935194	+	0.354135i	$0.884775\pi$
$702$		0			0
$703$	12.6716			0.477917
$704$	14.3185	−	22.3379i	0.539647	−	0.841891i
$705$		0			0
$706$	−29.3801	−	16.2569i	−1.10573	−	0.611835i
$707$	−2.66123	+	8.19043i	−0.100086	+	0.308033i
$708$		0			0
$709$	−11.7145	−	16.1236i	−0.439946	−	0.605534i	0.530254	−	0.847839i	$-0.322097\pi$
$709$	−11.7145	−	16.1236i	−0.439946	−	0.605534i	−0.970200	+	0.242305i	$0.922097\pi$
$710$	1.39641	−	1.30413i	0.0524064	−	0.0489433i
$711$		0			0
$712$	1.02396	+	18.7315i	0.0383744	+	0.701992i
$713$	−48.7733	−	35.4359i	−1.82657	−	1.32708i
$714$		0			0
$715$	−10.9281	−	8.82342i	−0.408689	−	0.329977i
$716$	32.8482	−	8.24234i	1.22759	−	0.308031i
$717$		0			0
$718$	−2.84557	+	14.6981i	−0.106196	+	0.548527i
$719$	−8.25695	+	2.68285i	−0.307932	+	0.100053i	−0.458907	−	0.888484i	$-0.651759\pi$
$719$	−8.25695	+	2.68285i	−0.307932	+	0.100053i	0.150974	+	0.988538i	$0.451759\pi$
$720$		0			0
$721$	−3.36642	−	4.63348i	−0.125372	−	0.172560i
$722$	9.86223	+	21.1083i	0.367034	+	0.785568i
$723$		0			0
$724$	13.6955	−	34.0446i	0.508990	−	1.26526i
$725$	−19.4691			−0.723065
$726$		0			0
$727$			8.14327i			0.302017i	0.988532	+	0.151009i	$0.0482521\pi$
$727$			8.14327i			0.302017i	−0.988532	+	0.151009i	$0.951748\pi$
$728$	27.4567	+	7.29080i	1.01761	+	0.270215i
$729$		0			0
$730$	−3.02863	−	6.48222i	−0.112095	−	0.239918i
$731$	−31.2461	+	22.7016i	−1.15568	+	0.839649i
$732$		0			0
$733$	0.185339	+	0.570415i	0.00684566	+	0.0210688i	0.954421	−	0.298464i	$-0.0964742\pi$
$733$	0.185339	+	0.570415i	0.00684566	+	0.0210688i	−0.947575	+	0.319532i	$0.896474\pi$
$734$	−36.2283	−	7.01387i	−1.33721	−	0.258887i
$735$		0			0
$736$	−28.2027	−	39.9578i	−1.03957	−	1.47286i
$737$	22.3207	−	27.6450i	0.822192	−	1.01832i
$738$		0			0
$739$	3.55308	−	4.89040i	0.130702	−	0.179896i	−0.738650	−	0.674089i	$-0.764536\pi$
$739$	3.55308	−	4.89040i	0.130702	−	0.179896i	0.869352	+	0.494193i	$0.164536\pi$
$740$	−0.202249	+	2.95602i	−0.00743481	+	0.108666i
$741$		0			0
$742$	−6.99381	−	7.48867i	−0.256751	−	0.274918i
$743$	−14.7479	+	10.7149i	−0.541046	+	0.393093i	−0.824473	−	0.565901i	$-0.808529\pi$
$743$	−14.7479	+	10.7149i	−0.541046	+	0.393093i	0.283427	+	0.958994i	$0.408529\pi$
$744$		0			0
$745$	12.1007	+	3.93175i	0.443335	+	0.144048i
$746$	−20.6852	−	11.4457i	−0.757341	−	0.419058i
$747$		0			0
$748$	12.2750	+	21.9920i	0.448819	+	0.804108i
$749$		−	13.6868i		−	0.500103i
$750$		0			0
$751$	48.5455	+	15.7734i	1.77145	+	0.575579i	0.998280	−	0.0586211i	$-0.0186704\pi$
$751$	48.5455	+	15.7734i	1.77145	+	0.575579i	0.773169	+	0.634200i	$0.218670\pi$
$752$	−15.4300	+	16.0745i	−0.562676	+	0.586178i
$753$		0			0
$754$	27.1042	−	25.3131i	0.987077	−	0.921850i
$755$	−10.0451	+	3.26386i	−0.365580	+	0.118784i
$756$		0			0
$757$	−4.99944	+	6.88113i	−0.181708	+	0.250099i	−0.890148	−	0.455672i	$-0.849399\pi$
$757$	−4.99944	+	6.88113i	−0.181708	+	0.250099i	0.708440	+	0.705771i	$0.249399\pi$
$758$	−35.1737	+	4.34557i	−1.27757	+	0.157838i
$759$		0			0
$760$	−10.9421	+	4.22855i	−0.396911	+	0.153386i
$761$	−20.9441	+	28.8271i	−0.759224	+	1.04498i	0.238054	+	0.971252i	$0.423490\pi$
$761$	−20.9441	+	28.8271i	−0.759224	+	1.04498i	−0.997278	+	0.0737302i	$0.976510\pi$
$762$		0			0
$763$	−9.07290	−	27.9235i	−0.328461	−	1.01090i
$764$	−38.0541	−	31.8340i	−1.37675	−	1.15171i
$765$		0			0
$766$	−11.2120	+	5.23848i	−0.405106	+	0.189274i
$767$	22.9948	−	70.7707i	0.830294	−	2.55538i
$768$		0			0
$769$		−	45.0073i		−	1.62300i	−0.584350	−	0.811502i	$-0.698651\pi$
$769$		−	45.0073i		−	1.62300i	0.584350	−	0.811502i	$-0.301349\pi$
$770$	−1.29346	+	5.23660i	−0.0466131	+	0.188714i
$771$		0			0
$772$	−0.0175290	+	0.0435740i	−0.000630884	+	0.00156826i
$773$	−27.7270	−	9.00903i	−0.997269	−	0.324032i	−0.235495	−	0.971875i	$-0.575671\pi$
$773$	−27.7270	−	9.00903i	−0.997269	−	0.324032i	−0.761774	+	0.647843i	$0.775671\pi$
$774$		0			0
$775$	18.5056	+	25.4708i	0.664743	+	0.914940i
$776$	6.61417	−	10.2353i	0.237435	−	0.367425i
$777$		0			0
$778$	31.3863	+	6.07644i	1.12525	+	0.217851i
$779$	−3.73341	−	2.71248i	−0.133763	−	0.0971848i
$780$		0			0
$781$	6.42669	+	0.327535i	0.229965	+	0.0117201i
$782$	46.0747	−	5.69235i	1.64763	−	0.203558i
$783$		0			0
$784$	3.01819	+	16.8216i	0.107792	+	0.600773i
$785$	−1.43268	−	4.40932i	−0.0511344	−	0.157375i
$786$		0			0
$787$	16.0741	+	22.1241i	0.572980	+	0.788639i	0.992904	−	0.118920i	$-0.0379432\pi$
$787$	16.0741	+	22.1241i	0.572980	+	0.788639i	−0.419924	+	0.907559i	$0.637943\pi$
$788$	−0.194899	−	0.310865i	−0.00694299	−	0.0110741i
$789$		0			0
$790$	1.63201	−	2.94945i	0.0580645	−	0.104937i
$791$	−12.3199			−0.438044
$792$		0			0
$793$	1.80155			0.0639749
$794$	1.90712	−	3.44664i	0.0676813	−	0.122317i
$795$		0			0
$796$	25.0839	−	15.7265i	0.889075	−	0.557413i
$797$	−0.554736	−	0.763529i	−0.0196498	−	0.0270456i	0.799079	−	0.601226i	$-0.205321\pi$
$797$	−0.554736	−	0.763529i	−0.0196498	−	0.0270456i	−0.818729	+	0.574180i	$0.805321\pi$
$798$		0			0
$799$	−6.53584	−	20.1152i	−0.231221	−	0.711626i
$800$	7.55913	+	24.3971i	0.267256	+	0.862568i
$801$		0			0
$802$	−9.00432	+	1.11245i	−0.317954	+	0.0392820i
$803$	8.60317	−	22.5088i	0.303599	−	0.794318i
$804$		0			0
$805$	8.04383	+	5.84418i	0.283508	+	0.205980i
$806$	−58.8793	−	11.3991i	−2.07394	−	0.401518i
$807$		0			0
$808$	8.00512	−	12.3877i	0.281619	−	0.435799i
$809$	−11.5315	−	15.8717i	−0.405424	−	0.558019i	0.556671	−	0.830733i	$-0.312079\pi$
$809$	−11.5315	−	15.8717i	−0.405424	−	0.558019i	−0.962095	+	0.272714i	$0.912079\pi$
$810$		0			0
$811$	−18.2649	−	5.93462i	−0.641367	−	0.208393i	−0.0297632	−	0.999557i	$-0.509475\pi$
$811$	−18.2649	−	5.93462i	−0.641367	−	0.208393i	−0.611604	+	0.791164i	$0.709475\pi$
$812$	−13.2134	−	5.31550i	−0.463698	−	0.186537i
$813$		0			0
$814$	−7.63022	+	6.43103i	−0.267439	+	0.225408i
$815$		−	0.527224i		−	0.0184679i
$816$		0			0
$817$	18.7219	−	57.6200i	0.654995	−	2.01587i
$818$	−38.2427	+	17.8678i	−1.33713	+	0.624734i
$819$		0			0
$820$	0.692357	−	0.827638i	0.0241782	−	0.0289024i
$821$	4.88277	+	15.0276i	0.170410	+	0.524467i	0.999394	−	0.0348046i	$-0.0110809\pi$
$821$	4.88277	+	15.0276i	0.170410	+	0.524467i	−0.828984	+	0.559272i	$0.811081\pi$
$822$		0			0
$823$	23.2795	−	32.0414i	0.811471	−	1.11689i	−0.179623	−	0.983735i	$-0.557488\pi$
$823$	23.2795	−	32.0414i	0.811471	−	1.11689i	0.991095	−	0.133159i	$-0.0425122\pi$
$824$	3.53578	+	9.14941i	0.123175	+	0.318735i
$825$		0			0
$826$	−28.3615	+	3.50396i	−0.986823	+	0.121918i
$827$	23.2594	−	32.0138i	0.808807	−	1.11323i	−0.182699	−	0.983169i	$-0.558484\pi$
$827$	23.2594	−	32.0138i	0.808807	−	1.11323i	0.991506	−	0.130058i	$-0.0415165\pi$
$828$		0			0
$829$	14.5137	−	4.71578i	0.504081	−	0.163786i	−0.0459279	−	0.998945i	$-0.514624\pi$
$829$	14.5137	−	4.71578i	0.504081	−	0.163786i	0.550009	+	0.835159i	$0.314624\pi$
$830$	−2.33727	+	2.18282i	−0.0811278	+	0.0757668i
$831$		0			0
$832$	−42.2439	−	24.1367i	−1.46454	−	0.836788i
$833$	−15.4285	−	5.01303i	−0.534567	−	0.173691i
$834$		0			0
$835$		−	9.58406i		−	0.331670i
$836$	−35.8553	−	16.5915i	−1.24008	−	0.573828i
$837$		0			0
$838$	3.12003	+	1.72640i	0.107780	+	0.0596376i
$839$	13.3878	+	4.34995i	0.462197	+	0.150177i	0.530854	−	0.847463i	$-0.321871\pi$
$839$	13.3878	+	4.34995i	0.462197	+	0.150177i	−0.0686565	+	0.997640i	$0.521871\pi$
$840$		0			0
$841$	8.41924	−	6.11693i	0.290318	−	0.210929i
$842$	29.2852	+	31.3573i	1.00923	+	1.08065i
$843$		0			0
$844$	−22.9922	−	1.57311i	−0.791426	−	0.0541487i
$845$	−9.81757	+	13.5127i	−0.337735	+	0.464852i
$846$		0			0
$847$	−15.7064	+	9.12847i	−0.539678	+	0.313658i
$848$	8.28515	+	15.4699i	0.284513	+	0.531240i
$849$		0			0
$850$	−23.8025	−	4.60821i	−0.816420	−	0.158060i
$851$	5.68409	+	17.4938i	0.194848	+	0.599681i
$852$		0			0
$853$	−15.7626	+	11.4522i	−0.539702	+	0.392117i	−0.823974	−	0.566627i	$-0.808248\pi$
$853$	−15.7626	+	11.4522i	−0.539702	+	0.392117i	0.284272	+	0.958744i	$0.408248\pi$
$854$	−0.292863	−	0.626818i	−0.0100216	−	0.0214493i
$855$		0			0
$856$	−6.01589	+	22.6555i	−0.205619	+	0.774348i
$857$			22.1714i			0.757359i	0.925528	+	0.378680i	$0.123622\pi$
$857$			22.1714i			0.757359i	−0.925528	+	0.378680i	$0.876378\pi$
$858$		0			0
$859$	−2.34314			−0.0799470			−0.0399735	−	0.999201i	$-0.512727\pi$
$859$	−2.34314			−0.0799470			−0.0399735	+	0.999201i	$0.512727\pi$
$860$	13.1428	+	5.28711i	0.448165	+	0.180289i
$861$		0			0
$862$	15.5393	+	33.2589i	0.529270	+	1.13280i
$863$	−29.5571	−	40.6819i	−1.00614	−	1.38483i	−0.921484	−	0.388416i	$-0.873022\pi$
$863$	−29.5571	−	40.6819i	−1.00614	−	1.38483i	−0.0846518	−	0.996411i	$-0.526978\pi$
$864$		0			0
$865$	2.91228	−	0.946256i	0.0990204	−	0.0321737i
$866$	8.27174	−	42.7255i	0.281085	−	1.45187i
$867$		0			0
$868$	5.60538	+	22.3391i	0.190259	+	0.758238i
$869$	10.9617	−	2.95409i	0.371850	−	0.100211i
$870$		0			0
$871$	−52.7097	−	38.2958i	−1.78600	−	1.29760i
$872$	2.74469	+	50.2092i	0.0929468	+	1.70030i
$873$		0			0
$874$	−53.2236	+	49.7065i	−1.80031	+	1.68135i
$875$	−6.43177	−	8.85257i	−0.217434	−	0.299272i
$876$		0			0
$877$	8.48419	−	26.1117i	0.286491	−	0.881728i	−0.699457	−	0.714675i	$-0.746575\pi$
$877$	8.48419	−	26.1117i	0.286491	−	0.881728i	0.985948	−	0.167053i	$-0.0534252\pi$
$878$	−17.2122	−	9.52401i	−0.580884	−	0.321420i
$879$		0			0
$880$	4.44274	−	8.09953i	0.149765	−	0.273035i
$881$	−15.6647			−0.527756			−0.263878	−	0.964556i	$-0.585002\pi$
$881$	−15.6647			−0.527756			−0.263878	+	0.964556i	$0.585002\pi$
$882$		0			0
$883$	14.0543	−	43.2547i	0.472965	−	1.45564i	−0.375717	−	0.926735i	$-0.622603\pi$
$883$	14.0543	−	43.2547i	0.472965	−	1.45564i	0.848682	−	0.528903i	$-0.177397\pi$
$884$	39.1285	−	24.5319i	1.31603	−	0.825097i
$885$		0			0
$886$	−9.37234	+	8.75301i	−0.314870	+	0.294063i
$887$	−11.7143	−	36.0529i	−0.393327	−	1.21054i	−0.930257	−	0.366909i	$-0.880416\pi$
$887$	−11.7143	−	36.0529i	−0.393327	−	1.21054i	0.536930	−	0.843627i	$-0.319584\pi$
$888$		0			0
$889$	−8.50263	−	6.17752i	−0.285169	−	0.207187i
$890$	0.800849	+	6.48218i	0.0268445	+	0.217283i
$891$		0			0
$892$	−4.93044	−	19.6493i	−0.165084	−	0.657907i
$893$	26.8414	+	19.5014i	0.898214	+	0.652591i
$894$		0			0
$895$	11.2142	−	3.64370i	0.374848	−	0.121796i
$896$	−1.53069	+	18.6217i	−0.0511368	+	0.622108i
$897$		0			0
$898$	10.7529	+	23.0146i	0.358829	+	0.768007i
$899$	28.5957	+	9.29131i	0.953721	+	0.309883i
$900$		0			0
$901$	−16.6578			−0.554953
$902$	3.62472	−	0.261441i	0.120690	−	0.00870503i
$903$		0			0
$904$	20.3929	+	5.41509i	0.678257	+	0.180103i
$905$	3.94814	−	12.1511i	0.131241	−	0.403917i
$906$		0			0
$907$	24.3629	−	17.7007i	0.808957	−	0.587742i	−0.104571	−	0.994517i	$-0.533347\pi$
$907$	24.3629	−	17.7007i	0.808957	−	0.587742i	0.913528	+	0.406776i	$0.133347\pi$
$908$	14.1457	+	11.8335i	0.469442	+	0.392709i
$909$		0			0
$910$	9.71055	+	1.87998i	0.321901	+	0.0623207i
$911$	−21.2777	+	29.2863i	−0.704963	+	0.970298i	0.294928	+	0.955519i	$0.404704\pi$
$911$	−21.2777	+	29.2863i	−0.704963	+	0.970298i	−0.999891	+	0.0147785i	$0.995296\pi$
$912$		0			0
$913$	−10.7568	−	0.548218i	−0.355998	−	0.0181434i
$914$	3.83327	+	31.0270i	0.126793	+	1.02628i
$915$		0			0
$916$	−51.2513	−	3.50657i	−1.69339	−	0.115860i
$917$	0.376538	−	0.122345i	0.0124344	−	0.00404018i
$918$		0			0
$919$	22.9541	−	16.6771i	0.757184	−	0.550127i	−0.140861	−	0.990029i	$-0.544987\pi$
$919$	22.9541	−	16.6771i	0.757184	−	0.550127i	0.898045	+	0.439903i	$0.144987\pi$
$920$	−10.7461	−	13.2094i	−0.354287	−	0.435500i
$921$		0			0
$922$	−24.3560	−	13.4769i	−0.802123	−	0.443838i
$923$		−	11.7998i		−	0.388395i
$924$		0			0
$925$		−	9.60594i		−	0.315841i
$926$	7.31029	−	13.2115i	0.240231	−	0.434156i
$927$		0			0
$928$	19.5355	+	14.6065i	0.641284	+	0.479481i
$929$	−17.2036	+	12.4992i	−0.564433	+	0.410084i	−0.833079	−	0.553155i	$-0.813424\pi$
$929$	−17.2036	+	12.4992i	−0.564433	+	0.410084i	0.268646	+	0.963239i	$0.413424\pi$
$930$		0			0
$931$	24.2021	−	7.86374i	0.793192	−	0.257724i
$932$	−47.8850	−	3.27625i	−1.56853	−	0.107317i
$933$		0			0
$934$	45.7999	−	5.65840i	1.49862	−	0.185148i
$935$	4.78648	+	7.34737i	0.156535	+	0.240285i
$936$		0			0
$937$	−25.3238	+	34.8552i	−0.827293	+	1.13867i	0.161128	+	0.986934i	$0.448487\pi$
$937$	−25.3238	+	34.8552i	−0.827293	+	1.13867i	−0.988421	+	0.151738i	$0.951513\pi$
$938$	−4.75580	+	24.5648i	−0.155282	+	0.802071i
$939$		0			0
$940$	−4.97771	+	5.95032i	−0.162355	+	0.194078i
$941$	−7.65773	+	5.56367i	−0.249635	+	0.181370i	−0.705565	−	0.708645i	$-0.749307\pi$
$941$	−7.65773	+	5.56367i	−0.249635	+	0.181370i	0.455930	+	0.890016i	$0.349307\pi$
$942$		0			0
$943$	2.07004	−	6.37094i	0.0674099	−	0.207466i
$944$	48.4864	+	6.66601i	1.57810	+	0.216960i
$945$		0			0
$946$	17.9697	+	44.1978i	0.584246	+	1.43699i
$947$	−58.1103			−1.88833			−0.944166	−	0.329471i	$-0.893130\pi$
$947$	−58.1103			−1.88833			−0.944166	+	0.329471i	$0.893130\pi$
$948$		0			0
$949$	−42.0235	−	13.6542i	−1.36414	−	0.443236i
$950$	34.4561	−	16.0986i	1.11790	−	0.522308i
$951$		0			0
$952$	−14.8962	−	9.62613i	−0.482790	−	0.311985i
$953$	37.3273	−	12.1284i	1.20915	−	0.392876i	0.366030	−	0.930603i	$-0.380717\pi$
$953$	37.3273	−	12.1284i	1.20915	−	0.392876i	0.843119	+	0.537727i	$0.180717\pi$
$954$		0			0
$955$	−13.9749	−	10.1534i	−0.452218	−	0.328556i
$956$	30.9716	−	7.77148i	1.00169	−	0.251348i
$957$		0			0
$958$	22.3372	−	2.75968i	0.721684	−	0.0891612i
$959$	−3.95392	−	2.87269i	−0.127679	−	0.0927641i
$960$		0			0
$961$	−5.44555	−	16.7597i	−0.175663	−	0.540635i
$962$	12.4893	+	13.3731i	0.402673	+	0.431165i
$963$		0			0
$964$	15.9747	−	10.0155i	0.514510	−	0.322576i
$965$	−0.00505327	+	0.0155524i	−0.000162670	+	0.000500648i
$966$		0			0
$967$	35.8221			1.15196			0.575980	−	0.817464i	$-0.304621\pi$
$967$	35.8221			1.15196			0.575980	+	0.817464i	$0.304621\pi$
$968$	30.0109	−	8.20659i	0.964586	−	0.263770i
$969$		0			0
$970$	2.05423	−	3.71249i	0.0659573	−	0.119201i
$971$	9.05079	−	27.8555i	0.290454	−	0.893924i	−0.694257	−	0.719727i	$-0.744267\pi$
$971$	9.05079	−	27.8555i	0.290454	−	0.893924i	0.984711	−	0.174197i	$-0.0557330\pi$
$972$		0			0
$973$	−1.53300	−	2.11000i	−0.0491458	−	0.0676434i
$974$	−36.6250	−	39.2165i	−1.17354	−	1.25658i
$975$		0			0
$976$	0.209259	+	1.16629i	0.00669820	+	0.0373319i
$977$	19.3774	+	14.0785i	0.619939	+	0.450412i	0.852900	−	0.522074i	$-0.174841\pi$
$977$	19.3774	+	14.0785i	0.619939	+	0.450412i	−0.232961	+	0.972486i	$0.574841\pi$
$978$		0			0
$979$	−13.8188	+	17.1151i	−0.441651	+	0.547001i
$980$	1.44817	+	5.77139i	0.0462601	+	0.184360i
$981$		0			0
$982$	−0.766314	−	0.148360i	−0.0244540	−	0.00473435i
$983$	15.5566	−	5.05465i	0.496179	−	0.161218i	−0.0502286	−	0.998738i	$-0.515995\pi$
$983$	15.5566	−	5.05465i	0.496179	−	0.161218i	0.546408	+	0.837519i	$0.315995\pi$
$984$		0			0
$985$	−0.0750876	−	0.103349i	−0.00239249	−	0.00329298i
$986$	−20.9771	+	9.80096i	−0.668048	+	0.312126i
$987$		0			0
$988$	−27.0376	+	67.2106i	−0.860181	+	2.13825i
$989$	87.9459			2.79652
$990$		0			0
$991$			54.9239i			1.74471i	0.488870	+	0.872357i	$0.337409\pi$
$991$			54.9239i			1.74471i	−0.488870	+	0.872357i	$0.662591\pi$
$992$	0.540462	−	39.4413i	0.0171597	−	1.25226i
$993$		0			0
$994$	−4.10554	+	1.91820i	−0.130220	+	0.0608415i
$995$	8.33932	−	6.05887i	0.264374	−	0.192079i
$996$		0			0
$997$	−2.82716	−	8.70110i	−0.0895370	−	0.275567i	0.896254	−	0.443540i	$-0.146278\pi$
$997$	−2.82716	−	8.70110i	−0.0895370	−	0.275567i	−0.985791	+	0.167974i	$0.946278\pi$
$998$	−0.646589	+	3.33979i	−0.0204674	+	0.105719i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.bp.d.667.10		48
3.2	odd	2		264.2.z.b.139.3	yes	48
8.3	odd	2	inner	792.2.bp.d.667.4		48
11.8	odd	10	inner	792.2.bp.d.19.4		48
12.11	even	2		1056.2.bp.a.271.6		48
24.5	odd	2		1056.2.bp.a.271.7		48
24.11	even	2		264.2.z.b.139.9	yes	48
33.8	even	10		264.2.z.b.19.9	yes	48
88.19	even	10	inner	792.2.bp.d.19.10		48
132.107	odd	10		1056.2.bp.a.943.7		48
264.107	odd	10		264.2.z.b.19.3	✓	48
264.173	even	10		1056.2.bp.a.943.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.z.b.19.3	✓	48	264.107	odd	10
264.2.z.b.19.9	yes	48	33.8	even	10
264.2.z.b.139.3	yes	48	3.2	odd	2
264.2.z.b.139.9	yes	48	24.11	even	2
792.2.bp.d.19.4		48	11.8	odd	10	inner
792.2.bp.d.19.10		48	88.19	even	10	inner
792.2.bp.d.667.4		48	8.3	odd	2	inner
792.2.bp.d.667.10		48	1.1	even	1	trivial
1056.2.bp.a.271.6		48	12.11	even	2
1056.2.bp.a.271.7		48	24.5	odd	2
1056.2.bp.a.943.6		48	264.173	even	10
1056.2.bp.a.943.7		48	132.107	odd	10

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:	\( N \)	\(=\)	\( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	792.bp (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23741 + 0.684696i) q^{2} +(1.06238 + 1.69450i) q^{4} +(0.409298 + 0.563350i) q^{5} +(-0.510340 - 1.57067i) q^{7} +(0.154385 + 2.82421i) q^{8} +(0.120747 + 0.977341i) q^{10} +(-2.08351 + 2.58050i) q^{11} +(4.92015 + 3.57470i) q^{13} +(0.443927 - 2.29299i) q^{14} +(-1.74269 + 3.60042i) q^{16} +(-2.23176 - 3.07176i) q^{17} +(5.66454 + 1.84052i) q^{19} +(-0.519768 + 1.29205i) q^{20} +(-4.34502 + 1.76658i) q^{22} +8.64584i q^{23} +(1.39525 - 4.29413i) q^{25} +(3.64068 + 7.79219i) q^{26} +(2.11932 - 2.53342i) q^{28} +(-1.33248 - 4.10095i) q^{29} +(-4.09860 + 5.64124i) q^{31} +(-4.62162 + 3.26200i) q^{32} +(-0.658392 - 5.32912i) q^{34} +(0.675953 - 0.930370i) q^{35} +(2.02338 - 0.657436i) q^{37} +(5.74918 + 6.15598i) q^{38} +(-1.52783 + 1.24292i) q^{40} +(-0.736879 - 0.239427i) q^{41} -10.1720i q^{43} +(-6.58615 - 0.789033i) q^{44} +(-5.91977 + 10.6985i) q^{46} +(5.29780 + 1.72136i) q^{47} +(3.45658 - 2.51135i) q^{49} +(4.66667 - 4.35829i) q^{50} +(-0.830261 + 12.1349i) q^{52} +(2.57874 - 3.54933i) q^{53} +(-2.30650 - 0.117551i) q^{55} +(4.35710 - 1.68380i) q^{56} +(1.15908 - 5.98691i) q^{58} +(-3.78102 - 11.6368i) q^{59} +(0.239653 - 0.174118i) q^{61} +(-8.93420 + 4.17425i) q^{62} +(-7.95233 + 0.872033i) q^{64} +4.23488i q^{65} -10.7130 q^{67} +(2.83412 - 7.04512i) q^{68} +(1.47345 - 0.688429i) q^{70} +(-1.14044 - 1.56968i) q^{71} +(-6.90989 + 2.24516i) q^{73} +(2.95390 + 0.571881i) q^{74} +(2.89914 + 11.5539i) q^{76} +(5.11640 + 1.95556i) q^{77} +(-2.76926 - 2.01198i) q^{79} +(-2.74158 + 0.491902i) q^{80} +(-0.747889 - 0.800808i) q^{82} +(1.90883 + 2.62729i) q^{83} +(0.817020 - 2.51453i) q^{85} +(6.96476 - 12.5870i) q^{86} +(-7.60955 - 5.48587i) q^{88} +6.63247 q^{89} +(3.10371 - 9.55222i) q^{91} +(-14.6504 + 9.18519i) q^{92} +(5.37696 + 5.75742i) q^{94} +(1.28163 + 3.94444i) q^{95} +(-3.48568 - 2.53250i) q^{97} +(5.99672 - 0.740872i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4} - 4 q^{11} + 16 q^{14} + 20 q^{16} - 25 q^{20} + 3 q^{22} - 4 q^{25} - 4 q^{26} - 25 q^{28} - 26 q^{38} - 65 q^{40} + 60 q^{41} + 43 q^{44} - 5 q^{46} - 12 q^{49} + 80 q^{50} - 15 q^{52}+ \cdots - 40 q^{97}+O(q^{100}) \) 48 * q + 4 * q^4 - 4 * q^11 + 16 * q^14 + 20 * q^16 - 25 * q^20 + 3 * q^22 - 4 * q^25 - 4 * q^26 - 25 * q^28 - 26 * q^38 - 65 * q^40 + 60 * q^41 + 43 * q^44 - 5 * q^46 - 12 * q^49 + 80 * q^50 - 15 * q^52 + 14 * q^56 + 73 * q^58 + 8 * q^59 + 45 * q^62 - 38 * q^64 + 8 * q^67 + 55 * q^68 - 40 * q^70 - 60 * q^74 - 35 * q^82 + 100 * q^83 - 81 * q^86 - 18 * q^88 - 96 * q^89 - 20 * q^91 - 59 * q^92 + 35 * q^94 - 40 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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