LMFDB - Embedded newform 792.2.bp.d.19.4

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			19.4
Character	$\chi$	$=$	792.19
Dual form			792.2.bp.d.667.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.03357 + 0.965267i) q^{2} +(0.136519 - 1.99534i) q^{4} +(-0.409298 + 0.563350i) q^{5} +(0.510340 - 1.57067i) q^{7} +(1.78493 + 2.19409i) q^{8} +(-0.120747 - 0.977341i) q^{10} +(-2.08351 - 2.58050i) q^{11} +(-4.92015 + 3.57470i) q^{13} +(0.988641 + 2.11600i) q^{14} +(-3.96273 - 0.544803i) q^{16} +(-2.23176 + 3.07176i) q^{17} +(5.66454 - 1.84052i) q^{19} +(1.06820 + 0.893594i) q^{20} +(4.64432 + 0.655979i) q^{22} +8.64584i q^{23} +(1.39525 + 4.29413i) q^{25} +(1.63476 - 8.44395i) q^{26} +(-3.06433 - 1.23273i) q^{28} +(1.33248 - 4.10095i) q^{29} +(4.09860 + 5.64124i) q^{31} +(4.62162 - 3.26200i) q^{32} +(-0.658392 - 5.32912i) q^{34} +(0.675953 + 0.930370i) q^{35} +(-2.02338 - 0.657436i) q^{37} +(-4.07809 + 7.37010i) q^{38} +(-1.96661 + 0.107505i) q^{40} +(-0.736879 + 0.239427i) q^{41} +10.1720i q^{43} +(-5.43341 + 3.80501i) q^{44} +(-8.34554 - 8.93605i) q^{46} +(-5.29780 + 1.72136i) q^{47} +(3.45658 + 2.51135i) q^{49} +(-5.58706 - 3.09148i) q^{50} +(6.46103 + 10.3054i) q^{52} +(-2.57874 - 3.54933i) q^{53} +(2.30650 - 0.117551i) q^{55} +(4.35710 - 1.68380i) q^{56} +(2.58130 + 5.52480i) q^{58} +(-3.78102 + 11.6368i) q^{59} +(-0.239653 - 0.174118i) q^{61} +(-9.68148 - 1.87435i) q^{62} +(-1.62805 + 7.83259i) q^{64} -4.23488i q^{65} -10.7130 q^{67} +(5.82451 + 4.87247i) q^{68} +(-1.59670 - 0.309124i) q^{70} +(1.14044 - 1.56968i) q^{71} +(-6.90989 - 2.24516i) q^{73} +(2.72590 - 1.27360i) q^{74} +(-2.89914 - 11.5539i) q^{76} +(-5.11640 + 1.95556i) q^{77} +(2.76926 - 2.01198i) q^{79} +(1.92885 - 2.00941i) q^{80} +(0.530503 - 0.958748i) q^{82} +(1.90883 - 2.62729i) q^{83} +(-0.817020 - 2.51453i) q^{85} +(-9.81874 - 10.5135i) q^{86} +(1.94294 - 9.17742i) q^{88} +6.63247 q^{89} +(3.10371 + 9.55222i) q^{91} +(17.2513 + 1.18032i) q^{92} +(3.81406 - 6.89293i) q^{94} +(-1.28163 + 3.94444i) q^{95} +(-3.48568 + 2.53250i) q^{97} +(-5.99672 + 0.740872i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/792\mathbb{Z}\right)^\times$.

$n$	$145$	$199$	$353$	$397$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$	$-1$

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 $

$2$	−1.03357	+	0.965267i	−0.730842	+	0.682547i
$2$	−1.03357	+	0.965267i	−0.730842	+	0.682547i
$3$		0			0
$3$		0			0
$4$	0.136519	−	1.99534i	0.0682596	−	0.997668i
$5$	−0.409298	+	0.563350i	−0.183044	+	0.251938i	−0.890672	−	0.454647i	$-0.849765\pi$
$5$	−0.409298	+	0.563350i	−0.183044	+	0.251938i	0.707628	+	0.706585i	$0.249765\pi$
$6$		0			0
$7$	0.510340	−	1.57067i	0.192890	−	0.593656i	−0.807104	−	0.590409i	$-0.798967\pi$
$7$	0.510340	−	1.57067i	0.192890	−	0.593656i	0.999995	−	0.00324682i	$-0.00103350\pi$
$8$	1.78493	+	2.19409i	0.631068	+	0.775728i
$9$		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	−0.366468	+	0.930431i	$0.619433\pi$
$13$	−4.92015	+	3.57470i	−1.36460	+	0.991443i	−0.998137	+	0.0610124i	$0.980567\pi$
$14$	0.988641	+	2.11600i	0.264225	+	0.565525i
$15$		0			0
$16$	−3.96273	−	0.544803i	−0.990681	−	0.136201i
$17$	−2.23176	+	3.07176i	−0.541282	+	0.745011i	−0.988797	−	0.149265i	$-0.952309\pi$
$17$	−2.23176	+	3.07176i	−0.541282	+	0.745011i	0.447515	+	0.894277i	$0.352309\pi$
$18$		0			0
$19$	5.66454	−	1.84052i	1.29954	−	0.422245i	0.424116	−	0.905608i	$-0.360585\pi$
$19$	5.66454	−	1.84052i	1.29954	−	0.422245i	0.875420	+	0.483364i	$0.160585\pi$
$20$	1.06820	+	0.893594i	0.238856	+	0.199814i
$21$		0			0
$22$	4.64432	+	0.655979i	0.990172	+	0.139855i
$23$			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
$26$	1.63476	−	8.44395i	0.320604	−	1.65599i
$27$		0			0
$28$	−3.06433	−	1.23273i	−0.579104	−	0.232963i
$29$	1.33248	−	4.10095i	0.247435	−	0.761526i	−0.747791	−	0.663934i	$-0.768886\pi$
$29$	1.33248	−	4.10095i	0.247435	−	0.761526i	0.995226	−	0.0975928i	$-0.0311143\pi$
$30$		0			0
$31$	4.09860	+	5.64124i	0.736131	+	1.01320i	0.998832	+	0.0483198i	$0.0153867\pi$
$31$	4.09860	+	5.64124i	0.736131	+	1.01320i	−0.262701	+	0.964877i	$0.584613\pi$
$32$	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	$-0.455954\pi$
$37$	−2.02338	−	0.657436i	−0.332642	−	0.108082i	−0.470576	+	0.882360i	$0.655954\pi$
$38$	−4.07809	+	7.37010i	−0.661553	+	1.19559i
$39$		0			0
$40$	−1.96661	+	0.107505i	−0.310948	+	0.0169980i
$41$	−0.736879	+	0.239427i	−0.115081	+	0.0373921i	−0.365991	−	0.930618i	$-0.619270\pi$
$41$	−0.736879	+	0.239427i	−0.115081	+	0.0373921i	0.250910	+	0.968010i	$0.419270\pi$
$42$		0			0
$43$			10.1720i			1.55122i	0.631211	+	0.775611i	$0.282558\pi$
$43$			10.1720i			1.55122i	−0.631211	+	0.775611i	$0.717442\pi$
$44$	−5.43341	+	3.80501i	−0.819117	+	0.573627i
$45$		0			0
$46$	−8.34554	−	8.93605i	−1.23048	−	1.31755i
$47$	−5.29780	+	1.72136i	−0.772764	+	0.251086i	−0.668748	−	0.743489i	$-0.733169\pi$
$47$	−5.29780	+	1.72136i	−0.772764	+	0.251086i	−0.104016	+	0.994576i	$0.533169\pi$
$48$		0			0
$49$	3.45658	+	2.51135i	0.493797	+	0.358764i
$50$	−5.58706	−	3.09148i	−0.790129	−	0.437201i
$51$		0			0
$52$	6.46103	+	10.3054i	0.895983	+	1.42910i
$53$	−2.57874	−	3.54933i	−0.354217	−	0.487538i	0.594309	−	0.804237i	$-0.297426\pi$
$53$	−2.57874	−	3.54933i	−0.354217	−	0.487538i	−0.948526	+	0.316699i	$0.897426\pi$
$54$		0			0
$55$	2.30650	−	0.117551i	0.311009	−	0.0158505i
$56$	4.35710	−	1.68380i	0.582242	−	0.225007i
$57$		0			0
$58$	2.58130	+	5.52480i	0.338942	+	0.725441i
$59$	−3.78102	+	11.6368i	−0.492247	+	1.51498i	0.328958	+	0.944345i	$0.393303\pi$
$59$	−3.78102	+	11.6368i	−0.492247	+	1.51498i	−0.821204	+	0.570634i	$0.806697\pi$
$60$		0			0
$61$	−0.239653	−	0.174118i	−0.0306845	−	0.0222936i	0.572337	−	0.820018i	$-0.306037\pi$
$61$	−0.239653	−	0.174118i	−0.0306845	−	0.0222936i	−0.603022	+	0.797725i	$0.706037\pi$
$62$	−9.68148	−	1.87435i	−1.22955	−	0.238043i
$63$		0			0
$64$	−1.62805	+	7.83259i	−0.203507	+	0.979074i
$65$		−	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	$0.727079\pi$
$68$	5.82451	+	4.87247i	0.706326	+	0.590874i
$69$		0			0
$70$	−1.59670	−	0.309124i	−0.190842	−	0.0369473i
$71$	1.14044	−	1.56968i	0.135345	−	0.186287i	−0.735964	−	0.677020i	$-0.763271\pi$
$71$	1.14044	−	1.56968i	0.135345	−	0.186287i	0.871310	+	0.490733i	$0.163271\pi$
$72$		0			0
$73$	−6.90989	−	2.24516i	−0.808741	−	0.262776i	−0.124677	−	0.992197i	$-0.539789\pi$
$73$	−6.90989	−	2.24516i	−0.808741	−	0.262776i	−0.684064	+	0.729422i	$0.739789\pi$
$74$	2.72590	−	1.27360i	0.316879	−	0.148053i
$75$		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	$-0.638322\pi$
$79$	2.76926	−	2.01198i	0.311566	−	0.226366i	0.732568	+	0.680694i	$0.238322\pi$
$80$	1.92885	−	2.00941i	0.215652	−	0.224659i
$81$		0			0
$82$	0.530503	−	0.958748i	0.0585843	−	0.105876i
$83$	1.90883	−	2.62729i	0.209522	−	0.288382i	−0.691303	−	0.722565i	$-0.742963\pi$
$83$	1.90883	−	2.62729i	0.209522	−	0.288382i	0.900825	+	0.434183i	$0.142963\pi$
$84$		0			0
$85$	−0.817020	−	2.51453i	−0.0886183	−	0.272739i
$86$	−9.81874	−	10.5135i	−1.05878	−	1.13370i
$87$		0			0
$88$	1.94294	−	9.17742i	0.207118	−	0.978316i
$89$	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
$92$	17.2513	+	1.18032i	1.79858	+	0.123057i
$93$		0			0
$94$	3.81406	−	6.89293i	0.393390	−	0.710952i
$95$	−1.28163	+	3.94444i	−0.131492	+	0.404691i
$96$		0			0
$97$	−3.48568	+	2.53250i	−0.353917	+	0.257136i	−0.750511	−	0.660858i	$-0.770192\pi$
$97$	−3.48568	+	2.53250i	−0.353917	+	0.257136i	0.396593	+	0.917994i	$0.370192\pi$
$98$	−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	$-0.616463\pi$
$101$	4.21872	−	3.06508i	0.419778	−	0.304987i	0.777549	+	0.628823i	$0.216463\pi$
$102$		0			0
$103$	−3.29822	−	1.07166i	−0.324983	−	0.105593i	0.141982	−	0.989869i	$-0.454653\pi$
$103$	−3.29822	−	1.07166i	−0.324983	−	0.105593i	−0.466965	+	0.884276i	$0.654653\pi$
$104$	−16.6253	−	4.41466i	−1.63025	−	0.432893i
$105$		0			0
$106$	6.09135	+	1.17930i	0.591645	+	0.114543i
$107$	7.88188	−	2.56098i	0.761970	−	0.247579i	0.0978460	−	0.995202i	$-0.468805\pi$
$107$	7.88188	−	2.56098i	0.761970	−	0.247579i	0.664124	+	0.747623i	$0.268805\pi$
$108$		0			0
$109$	−17.7781			−1.70284			−0.851419	−	0.524487i	$-0.824257\pi$
$109$	−17.7781			−1.70284			−0.851419	+	0.524487i	$0.824257\pi$
$110$	−2.27046	+	2.34789i	−0.216479	+	0.223862i
$111$		0			0
$112$	−2.87804	+	5.94608i	−0.271949	+	0.561852i
$113$	2.30521	+	7.09472i	0.216856	+	0.667415i	0.999017	+	0.0443379i	$0.0141178\pi$
$113$	2.30521	+	7.09472i	0.216856	+	0.667415i	−0.782160	+	0.623077i	$0.785882\pi$
$114$		0			0
$115$	−4.87063	−	3.53872i	−0.454189	−	0.329988i
$116$	−8.00085	−	3.21860i	−0.742860	−	0.298839i
$117$		0			0
$118$	−7.32466	−	15.6771i	−0.674290	−	1.44319i
$119$	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
$124$	11.8157	−	7.40795i	1.06108	−	0.665253i
$125$	−6.30146	−	2.04747i	−0.563619	−	0.183131i
$126$		0			0
$127$	−5.14844	−	3.74056i	−0.456850	−	0.331921i	0.335444	−	0.942060i	$-0.391114\pi$
$127$	−5.14844	−	3.74056i	−0.456850	−	0.331921i	−0.792294	+	0.610139i	$0.791114\pi$
$128$	−5.87784	−	9.66701i	−0.519533	−	0.854451i
$129$		0			0
$130$	4.08779	+	4.37703i	0.358523	+	0.383891i
$131$		−	0.239732i		−	0.0209455i	−0.999945	−	0.0104727i	$-0.996666\pi$
$131$		−	0.239732i		−	0.0209455i	0.999945	−	0.0104727i	$-0.00333363\pi$
$132$		0			0
$133$		−	9.83639i		−	0.852923i
$134$	11.0726	−	10.3409i	0.956528	−	0.893320i
$135$		0			0
$136$	−10.7233	+	0.586186i	−0.919512	+	0.0502651i
$137$	2.39415	+	1.73945i	0.204546	+	0.148611i	0.685343	−	0.728221i	$-0.259652\pi$
$137$	2.39415	+	1.73945i	0.204546	+	0.148611i	−0.480797	+	0.876832i	$0.659652\pi$
$138$		0			0
$139$	1.50194	+	0.488010i	0.127393	+	0.0413925i	0.372020	−	0.928225i	$-0.378665\pi$
$139$	1.50194	+	0.488010i	0.127393	+	0.0413925i	−0.244627	+	0.969617i	$0.578665\pi$
$140$	1.94868	−	1.22174i	0.164694	−	0.103256i
$141$		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
$146$	9.30900	−	4.34936i	0.770419	−	0.359956i
$147$		0			0
$148$	−1.58804	+	3.94757i	−0.130536	+	0.324488i
$149$	−14.7822	−	10.7399i	−1.21101	−	0.879849i	−0.215687	−	0.976463i	$-0.569199\pi$
$149$	−14.7822	−	10.7399i	−1.21101	−	0.879849i	−0.995322	+	0.0966133i	$0.969199\pi$
$150$		0			0
$151$	4.68718	+	14.4256i	0.381437	+	1.17394i	0.939032	+	0.343829i	$0.111724\pi$
$151$	4.68718	+	14.4256i	0.381437	+	1.17394i	−0.557595	+	0.830113i	$0.688276\pi$
$152$	14.1491	+	9.14331i	1.14764	+	0.741620i
$153$		0			0
$154$	3.40051	−	6.95990i	0.274021	−	0.560845i
$155$	−4.85554			−0.390007
$156$		0			0
$157$	6.33215	−	2.05744i	0.505360	−	0.164202i	−0.0452308	−	0.998977i	$-0.514402\pi$
$157$	6.33215	−	2.05744i	0.505360	−	0.164202i	0.550591	+	0.834775i	$0.314402\pi$
$158$	−0.920110	+	4.75259i	−0.0732000	+	0.378096i
$159$		0			0
$160$	−0.0539720	+	3.93872i	−0.00426686	+	0.311383i
$161$	13.5797	+	4.41232i	1.07023	+	0.347739i
$162$		0			0
$163$	−0.612537	+	0.445034i	−0.0479776	+	0.0348578i	−0.611516	−	0.791232i	$-0.709440\pi$
$163$	−0.612537	+	0.445034i	−0.0479776	+	0.0348578i	0.563538	+	0.826090i	$0.309440\pi$
$164$	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	$-0.521243\pi$
$167$	11.1349	−	8.08998i	0.861644	−	0.626021i	0.928332	+	0.371753i	$0.121243\pi$
$168$		0			0
$169$	7.41220	−	22.8124i	0.570169	−	1.75480i
$170$	3.27164	+	1.81029i	0.250923	+	0.138843i
$171$		0			0
$172$	20.2966	+	1.38868i	1.54760	+	0.105886i
$173$	−1.35890	−	4.18227i	−0.103315	−	0.317972i	0.886016	−	0.463655i	$-0.153462\pi$
$173$	−1.35890	−	4.18227i	−0.103315	−	0.317972i	−0.989331	+	0.145683i	$0.953462\pi$
$174$		0			0
$175$	7.45669			0.563672
$176$	6.85051	+	11.3609i	0.516376	+	0.856362i
$177$		0			0
$178$	−6.85509	+	6.40210i	−0.513811	+	0.479858i
$179$	5.23266	+	16.1045i	0.391107	+	1.20370i	0.931952	+	0.362582i	$0.118105\pi$
$179$	5.23266	+	16.1045i	0.391107	+	1.20370i	−0.540845	+	0.841122i	$0.681895\pi$
$180$		0			0
$181$	10.7847	−	14.8439i	0.801620	−	1.10334i	−0.190943	−	0.981601i	$-0.561155\pi$
$181$	10.7847	−	14.8439i	0.801620	−	1.10334i	0.992563	−	0.121734i	$-0.0388455\pi$
$182$	−12.4283	−	6.87695i	−0.921249	−	0.509754i
$183$		0			0
$184$	−18.9697	+	15.4322i	−1.39847	+	1.13768i
$185$	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
$190$	−2.48279	−	5.31396i	−0.180121	−	0.385515i
$191$	23.5927	+	7.66573i	1.70711	+	0.554673i	0.989847	−	0.142134i	$-0.0453963\pi$
$191$	23.5927	+	7.66573i	1.70711	+	0.554673i	0.717259	+	0.696806i	$0.245396\pi$
$192$		0			0
$193$	0.0138035	−	0.0189988i	0.000993595	−	0.00136757i	−0.808520	−	0.588469i	$-0.799731\pi$
$193$	0.0138035	−	0.0189988i	0.000993595	−	0.00136757i	0.809514	+	0.587101i	$0.199731\pi$
$194$	1.15815	−	5.98212i	0.0831503	−	0.429491i
$195$		0			0
$196$	5.48287	−	6.55418i	0.391634	−	0.468156i
$197$	0.183455			0.0130706			0.00653530	−	0.999979i	$-0.497920\pi$
$197$	0.183455			0.0130706			0.00653530	+	0.999979i	$0.497920\pi$
$198$		0			0
$199$		−	14.8031i		−	1.04936i	−0.851298	−	0.524682i	$-0.824184\pi$
$199$		−	14.8031i		−	1.04936i	0.851298	−	0.524682i	$-0.175816\pi$
$200$	−6.93128	+	10.7260i	−0.490115	+	0.758443i
$201$		0			0
$202$	−1.40171	+	7.24015i	−0.0986237	+	0.509415i
$203$	−5.76120	−	4.18575i	−0.404357	−	0.293782i
$204$		0			0
$205$	0.166722	−	0.513118i	0.0116444	−	0.0358377i
$206$	4.44336	−	2.07603i	0.309583	−	0.144644i
$207$		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	0.509519	−	0.860459i	$-0.329823\pi$
$211$	−6.77305	−	9.32230i	−0.466276	−	0.641774i	−0.975795	+	0.218685i	$0.929823\pi$
$212$	−7.43415	+	4.66090i	−0.510580	+	0.320112i
$213$		0			0
$214$	−5.67442	+	10.2551i	−0.387895	+	0.701021i
$215$	−5.73042	−	4.16340i	−0.390812	−	0.283941i
$216$		0			0
$217$	10.9522	−	3.55858i	0.743483	−	0.241572i
$218$	18.3749	−	17.1607i	1.24450	−	1.16227i
$219$		0			0
$220$	0.0803288	−	4.61829i	0.00541577	−	0.311365i
$221$		−	23.0914i		−	1.55330i
$222$		0			0
$223$	9.63345	−	3.13010i	0.645104	−	0.209607i	0.0318497	−	0.999493i	$-0.489860\pi$
$223$	9.63345	−	3.13010i	0.645104	−	0.209607i	0.613254	+	0.789886i	$0.289860\pi$
$224$	−2.76491	−	8.92375i	−0.184738	−	0.596243i
$225$		0			0
$226$	−9.23089	−	5.10772i	−0.614030	−	0.339760i
$227$	8.77003	+	2.84955i	0.582087	+	0.189132i	0.585235	−	0.810863i	$-0.301002\pi$
$227$	8.77003	+	2.84955i	0.582087	+	0.189132i	−0.00314828	+	0.999995i	$0.501002\pi$
$228$		0			0
$229$	15.0976	+	20.7800i	0.997676	+	1.37318i	0.926740	+	0.375703i	$0.122599\pi$
$229$	15.0976	+	20.7800i	0.997676	+	1.37318i	0.0709359	+	0.997481i	$0.477401\pi$
$230$	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	−0.962112	−	0.272654i	$-0.912099\pi$
$233$	−14.1060	−	19.4152i	−0.924112	−	1.27193i	0.0380001	−	0.999278i	$-0.487901\pi$
$234$		0			0
$235$	1.19865	−	3.68907i	0.0781913	−	0.240648i
$236$	22.7031	+	9.13304i	1.47785	+	0.594510i
$237$		0			0
$238$	−8.70626	−	1.68555i	−0.564343	−	0.109258i
$239$	−4.93373	−	15.1845i	−0.319137	−	0.982201i	−0.974018	−	0.226470i	$-0.927282\pi$
$239$	−4.93373	−	15.1845i	−0.319137	−	0.982201i	0.654882	−	0.755731i	$-0.272718\pi$
$240$		0			0
$241$			9.42736i			0.607269i	0.952789	+	0.303635i	$0.0982003\pi$
$241$			9.42736i			0.607269i	−0.952789	+	0.303635i	$0.901800\pi$
$242$	−7.98372	−	13.3514i	−0.513213	−	0.858261i
$243$		0			0
$244$	−0.380142	+	0.454418i	−0.0243361	+	0.0290911i
$245$	−2.82954	+	0.919373i	−0.180773	+	0.0587366i
$246$		0			0
$247$	−21.2911	+	29.3047i	−1.35472	+	1.86461i
$248$	−5.06167	+	19.0619i	−0.321416	+	1.21043i
$249$		0			0
$250$	8.48933	−	3.96639i	0.536912	−	0.250857i
$251$	3.20392	−	2.32778i	0.202229	−	0.146928i	−0.482062	−	0.876137i	$-0.660112\pi$
$251$	3.20392	−	2.32778i	0.202229	−	0.146928i	0.684291	+	0.729209i	$0.260112\pi$
$252$		0			0
$253$	22.3106	−	18.0137i	1.40266	−	1.13251i
$254$	8.93190	−	1.10350i	0.560437	−	0.0692399i
$255$		0			0
$256$	15.4064	+	4.31781i	0.962899	+	0.269863i
$257$	−6.26844	+	19.2923i	−0.391015	+	1.20342i	0.541008	+	0.841018i	$0.318043\pi$
$257$	−6.26844	+	19.2923i	−0.391015	+	1.20342i	−0.932022	+	0.362401i	$0.881957\pi$
$258$		0			0
$259$	−2.06522	+	2.84254i	−0.128327	+	0.176627i
$260$	−8.45001	−	0.578143i	−0.524048	−	0.0358549i
$261$		0			0
$262$	0.231405	+	0.247779i	0.0142963	+	0.0153078i
$263$	−4.86501			−0.299989			−0.149995	−	0.988687i	$-0.547926\pi$
$263$	−4.86501			−0.299989			−0.149995	+	0.988687i	$0.547926\pi$
$264$		0			0
$265$	3.05499			0.187667
$266$	9.49475	+	10.1666i	0.582160	+	0.623352i
$267$		0			0
$268$	−1.46253	+	21.3761i	−0.0893384	+	1.30575i
$269$	−16.9712	+	23.3589i	−1.03475	+	1.42422i	−0.133435	+	0.991058i	$0.542601\pi$
$269$	−16.9712	+	23.3589i	−1.03475	+	1.42422i	−0.901318	+	0.433158i	$0.857399\pi$
$270$		0			0
$271$	−4.51837	+	13.9061i	−0.274472	+	0.844737i	0.714887	+	0.699240i	$0.246478\pi$
$271$	−4.51837	+	13.9061i	−0.274472	+	0.844737i	−0.989359	+	0.145497i	$0.953522\pi$
$272$	10.5174	−	10.9567i	0.637709	−	0.664346i
$273$		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	−0.344556	+	0.938766i	$0.611970\pi$
$277$	−22.3661	+	16.2499i	−1.34385	+	0.976363i	−0.999293	+	0.0375974i	$0.988030\pi$
$278$	−2.02342	+	0.945383i	−0.121356	+	0.0567003i
$279$		0			0
$280$	−0.834785	+	3.14375i	−0.0498880	+	0.187875i
$281$	16.8765	−	23.2286i	1.00677	−	1.38570i	0.0856916	−	0.996322i	$-0.472690\pi$
$281$	16.8765	−	23.2286i	1.00677	−	1.38570i	0.921078	−	0.389378i	$-0.127310\pi$
$282$		0			0
$283$	14.9354	−	4.85281i	0.887818	−	0.288469i	0.170618	−	0.985337i	$-0.445424\pi$
$283$	14.9354	−	4.85281i	0.887818	−	0.288469i	0.717200	+	0.696868i	$0.245424\pi$
$284$	−2.97635	−	2.48985i	−0.176614	−	0.147746i
$285$		0			0
$286$	−25.1957	+	13.3745i	−1.48985	+	0.790852i
$287$			1.27958i			0.0755312i
$288$		0			0
$289$	0.798350	+	2.45707i	0.0469618	+	0.144533i
$290$	−4.16892	−	0.807110i	−0.244807	−	0.0473951i
$291$		0			0
$292$	−5.42317	+	13.4810i	−0.317367	+	0.788918i
$293$	−5.97643	+	18.3936i	−0.349147	+	1.07456i	0.610179	+	0.792264i	$0.291098\pi$
$293$	−5.97643	+	18.3936i	−0.349147	+	1.07456i	−0.959326	+	0.282300i	$0.908902\pi$
$294$		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
$302$	−18.7691	−	10.3855i	−1.08004	−	0.597618i
$303$		0			0
$304$	−23.4497	+	4.20742i	−1.34494	+	0.241312i
$305$	0.196179	−	0.0637424i	0.0112332	−	0.00364988i
$306$		0			0
$307$		−	17.8955i		−	1.02135i	−0.859774	−	0.510675i	$-0.829396\pi$
$307$		−	17.8955i		−	1.02135i	0.859774	−	0.510675i	$-0.170604\pi$
$308$	3.20351	+	10.4759i	0.182537	+	0.596920i
$309$		0			0
$310$	5.01853	−	4.68690i	0.285033	−	0.266198i
$311$	0.940857	−	0.305703i	0.0533511	−	0.0173348i	−0.282220	−	0.959350i	$-0.591071\pi$
$311$	0.940857	−	0.305703i	0.0533511	−	0.0173348i	0.335571	+	0.942015i	$0.391071\pi$
$312$		0			0
$313$	−10.9210	−	7.93456i	−0.617291	−	0.448488i	0.234683	−	0.972072i	$-0.424595\pi$
$313$	−10.9210	−	7.93456i	−0.617291	−	0.448488i	−0.851974	+	0.523584i	$0.824595\pi$
$314$	−4.55872	+	8.23871i	−0.257263	+	0.464938i
$315$		0			0
$316$	−3.63652	−	5.80027i	−0.204570	−	0.326290i
$317$	5.19658	+	7.15248i	0.291869	+	0.401724i	0.929620	−	0.368519i	$-0.120135\pi$
$317$	5.19658	+	7.15248i	0.291869	+	0.401724i	−0.637751	+	0.770243i	$0.720135\pi$
$318$		0			0
$319$	−13.3587	+	5.10589i	−0.747945	+	0.285875i
$320$	−3.74613	−	4.12302i	−0.209415	−	0.230484i
$321$		0			0
$322$	−18.2946	+	8.54763i	−1.01952	+	0.476341i
$323$	−6.98828	+	21.5077i	−0.388839	+	1.19672i
$324$		0			0
$325$	−22.2150	−	16.1402i	−1.23227	−	0.895295i
$326$	0.203521	−	1.05123i	0.0112720	−	0.0582225i
$327$		0			0
$328$	−1.84060	−	1.18942i	−0.101630	−	0.0656747i
$329$			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	$0.419978\pi$
$332$	−4.98172	−	4.16744i	−0.273408	−	0.228718i
$333$		0			0
$334$	−3.69967	+	19.1097i	−0.202437	+	1.04564i
$335$	4.38482	−	6.03518i	0.239568	−	0.329737i
$336$		0			0
$337$	−12.9875	−	4.21989i	−0.707474	−	0.229872i	−0.0668898	−	0.997760i	$-0.521308\pi$
$337$	−12.9875	−	4.21989i	−0.707474	−	0.229872i	−0.640584	+	0.767888i	$0.721308\pi$
$338$	14.3591	+	30.7329i	0.781030	+	1.67165i
$339$		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
$344$	−22.3184	+	18.1564i	−1.20333	+	0.978927i
$345$		0			0
$346$	5.44152	+	3.01095i	0.292538	+	0.161870i
$347$	−1.37075	+	1.88668i	−0.0735859	+	0.101282i	−0.844223	−	0.535991i	$-0.819938\pi$
$347$	−1.37075	+	1.88668i	−0.0735859	+	0.101282i	0.770638	+	0.637274i	$0.219938\pi$
$348$		0			0
$349$	−4.49635	−	13.8383i	−0.240684	−	0.740750i	−0.996316	−	0.0857534i	$-0.972670\pi$
$349$	−4.49635	−	13.8383i	−0.240684	−	0.740750i	0.755632	−	0.654996i	$-0.227330\pi$
$350$	−7.70698	+	7.19769i	−0.411955	+	0.384733i
$351$		0			0
$352$	−18.0468	−	5.12970i	−0.961896	−	0.273414i
$353$	−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
$356$	0.905459	−	13.2340i	0.0479892	−	0.701400i
$357$		0			0
$358$	−20.9534	−	11.5941i	−1.10742	−	0.612768i
$359$	−3.27128	+	10.0680i	−0.172652	+	0.531367i	−0.999518	−	0.0310309i	$-0.990121\pi$
$359$	−3.27128	+	10.0680i	−0.172652	+	0.531367i	0.826867	+	0.562398i	$0.190121\pi$
$360$		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	$-0.161536\pi$
$367$	24.8159	+	8.06317i	1.29538	+	0.420894i	0.421407	+	0.906872i	$0.361536\pi$
$368$	4.71028	−	34.2611i	0.245540	−	1.78598i
$369$		0			0
$370$	−0.398223	+	2.05692i	−0.0207026	+	0.106934i
$371$	−6.89085	+	2.23897i	−0.357755	+	0.116242i
$372$		0			0
$373$	16.7165			0.865549			0.432774	−	0.901502i	$-0.357535\pi$
$373$	16.7165			0.865549			0.432774	+	0.901502i	$0.357535\pi$
$374$	−12.3800	+	12.8022i	−0.640156	+	0.661988i
$375$		0			0
$376$	−13.2330	−	8.55134i	−0.682441	−	0.441002i
$377$	8.10365	+	24.9405i	0.417359	+	1.28450i
$378$		0			0
$379$	−20.2745	−	14.7303i	−1.04143	−	0.756643i	−0.0708660	−	0.997486i	$-0.522576\pi$
$379$	−20.2745	−	14.7303i	−1.04143	−	0.756643i	−0.970564	+	0.240842i	$0.922576\pi$
$380$	7.69552	+	3.09577i	0.394772	+	0.158810i
$381$		0			0
$382$	−31.7841	+	14.8502i	−1.62622	+	0.759802i
$383$	5.14355	+	7.07949i	0.262823	+	0.361745i	0.919950	−	0.392035i	$-0.128229\pi$
$383$	5.14355	+	7.07949i	0.262823	+	0.361745i	−0.657127	+	0.753780i	$0.728229\pi$
$384$		0			0
$385$	0.992468	−	3.68273i	0.0505808	−	0.187689i
$386$	0.00407215	+	0.0329606i	0.000207267	+	0.00167765i
$387$		0			0
$388$	4.57732	+	7.30084i	0.232378	+	0.370644i
$389$	−21.4991	−	6.98549i	−1.09005	−	0.354179i	−0.291784	−	0.956484i	$-0.594249\pi$
$389$	−21.4991	−	6.98549i	−1.09005	−	0.354179i	−0.798265	+	0.602306i	$0.794249\pi$
$390$		0			0
$391$	−26.5579	−	19.2955i	−1.34309	−	0.975814i
$392$	0.659621	+	12.0666i	0.0333159	+	0.609456i
$393$		0			0
$394$	−0.189613	+	0.177083i	−0.00955254	+	0.00892130i
$395$			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	$-0.0222669\pi$
$398$	14.2889	+	15.3000i	0.716240	+	0.766919i
$399$		0			0
$400$	−3.18953	−	17.7766i	−0.159476	−	0.888829i
$401$	−5.19019	−	3.77089i	−0.259186	−	0.188309i	0.450602	−	0.892725i	$-0.351209\pi$
$401$	−5.19019	−	3.77089i	−0.259186	−	0.188309i	−0.709788	+	0.704415i	$0.751209\pi$
$402$		0			0
$403$	−40.3315	−	13.1045i	−2.00905	−	0.652781i
$404$	−5.53992	−	8.83620i	−0.275621	−	0.439617i
$405$		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	−0.979730	−	0.200324i	$-0.935801\pi$
$409$	−17.5440	−	24.1473i	−0.867496	−	1.19401i	0.112234	−	0.993682i	$-0.464199\pi$
$410$	0.322977	+	0.691272i	0.0159507	+	0.0341395i
$411$		0			0
$412$	−2.58858	+	6.43474i	−0.127530	+	0.317017i
$413$	16.3479	+	11.8774i	0.804426	+	0.584450i
$414$		0			0
$415$	0.698800	+	2.15068i	0.0343027	+	0.105573i
$416$	−11.0784	+	32.5704i	−0.543164	+	1.59690i
$417$		0			0
$418$	27.5153	−	4.83215i	1.34582	−	0.236348i
$419$	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	$-0.864851\pi$
$421$	−28.8541	+	9.37526i	−1.40626	+	0.456922i	−0.495051	+	0.868864i	$0.664851\pi$
$422$	15.9989	+	3.09742i	0.778815	+	0.150780i
$423$		0			0
$424$	3.18468	−	11.9933i	0.154662	−	0.582446i
$425$	−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	$-0.914972\pi$
$431$	−21.0004	+	15.2577i	−1.01155	+	0.734937i	−0.0470191	+	0.998894i	$0.514972\pi$
$432$		0			0
$433$	−9.50922	+	29.2664i	−0.456984	+	1.40645i	0.411806	+	0.911271i	$0.364898\pi$
$433$	−9.50922	+	29.2664i	−0.456984	+	1.40645i	−0.868790	+	0.495180i	$0.835102\pi$
$434$	−7.88483	+	14.2498i	−0.378484	+	0.684013i
$435$		0			0
$436$	−2.42706	+	35.4734i	−0.116235	+	1.69887i
$437$	15.9129	+	48.9747i	0.761215	+	2.34278i
$438$		0			0
$439$	13.9098			0.663880			0.331940	−	0.943301i	$-0.392297\pi$
$439$	13.9098			0.663880			0.331940	+	0.943301i	$0.392297\pi$
$440$	4.37486	+	4.85085i	0.208563	+	0.231255i
$441$		0			0
$442$	22.2894	+	23.8665i	1.06020	+	1.13521i
$443$	−2.80215	−	8.62415i	−0.133134	−	0.409746i	0.862161	−	0.506635i	$-0.169111\pi$
$443$	−2.80215	−	8.62415i	−0.133134	−	0.409746i	−0.995295	+	0.0968892i	$0.969111\pi$
$444$		0			0
$445$	−2.71465	+	3.73640i	−0.128687	+	0.177122i
$446$	−6.93543	+	12.5340i	−0.328402	+	0.593503i
$447$		0			0
$448$	11.4715	+	6.55441i	0.541978	+	0.309667i
$449$	14.5319	−	10.5580i	0.685803	−	0.498265i	−0.189475	−	0.981886i	$-0.560679\pi$
$449$	14.5319	−	10.5580i	0.685803	−	0.498265i	0.875278	+	0.483621i	$0.160679\pi$
$450$		0			0
$451$	2.15313	+	1.40267i	0.101387	+	0.0660492i
$452$	14.4711	−	3.63111i	0.680661	−	0.170793i
$453$		0			0
$454$	−11.8150	+	5.52021i	−0.554505	+	0.259076i
$455$	−6.65159	−	2.16123i	−0.311831	−	0.101320i
$456$		0			0
$457$	12.9937	−	17.8843i	0.607820	−	0.836592i	−0.388576	−	0.921417i	$-0.627033\pi$
$457$	12.9937	−	17.8843i	0.607820	−	0.836592i	0.996396	+	0.0848243i	$0.0270329\pi$
$458$	−35.6626	−	6.90435i	−1.66641	−	0.322619i
$459$		0			0
$460$	−7.72587	+	9.23544i	−0.360221	+	0.430605i
$461$	19.6830			0.916730			0.458365	−	0.888764i	$-0.348435\pi$
$461$	19.6830			0.916730			0.458365	+	0.888764i	$0.348435\pi$
$462$		0			0
$463$		−	10.6767i		−	0.496188i	−0.968736	−	0.248094i	$-0.920196\pi$
$463$		−	10.6767i		−	0.496188i	0.968736	−	0.248094i	$-0.0798041\pi$
$464$	−7.51445	+	15.5250i	−0.348850	+	0.720729i
$465$		0			0
$466$	33.3203	+	6.45087i	1.54353	+	0.298831i
$467$	26.3995	+	19.1804i	1.22162	+	0.887562i	0.996234	−	0.0867060i	$-0.0276341\pi$
$467$	26.3995	+	19.1804i	1.22162	+	0.887562i	0.225391	+	0.974268i	$0.427634\pi$
$468$		0			0
$469$	−5.46728	+	16.8266i	−0.252456	+	0.776979i
$470$	2.32205	+	4.96991i	0.107108	+	0.229245i
$471$		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
$476$	10.6255	−	6.66174i	0.487019	−	0.305340i
$477$		0			0
$478$	19.7564	+	10.9318i	0.903637	+	0.500008i
$479$	−12.8754	−	9.35454i	−0.588293	−	0.427420i	0.253411	−	0.967359i	$-0.418447\pi$
$479$	−12.8754	−	9.35454i	−0.588293	−	0.427420i	−0.841704	+	0.539939i	$0.818447\pi$
$480$		0			0
$481$	12.3055	−	3.99829i	0.561082	−	0.182306i
$482$	−9.09992	−	9.74380i	−0.414490	−	0.443818i
$483$		0			0
$484$	21.1394	+	6.09315i	0.960881	+	0.276961i
$485$		−	3.00021i		−	0.136232i
$486$		0			0
$487$	36.0858	−	11.7250i	1.63520	−	0.531310i	0.659744	−	0.751490i	$-0.270665\pi$
$487$	36.0858	−	11.7250i	1.63520	−	0.531310i	0.975459	+	0.220180i	$0.0706645\pi$
$488$	−0.0457332	−	0.836609i	−0.00207025	−	0.0378715i
$489$		0			0
$490$	2.03708	−	3.68149i	0.0920257	−	0.166313i
$491$	−0.524914	−	0.170555i	−0.0236890	−	0.00769703i	0.297149	−	0.954831i	$-0.403964\pi$
$491$	−0.524914	−	0.170555i	−0.0236890	−	0.00769703i	−0.320838	+	0.947134i	$0.603964\pi$
$492$		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	−0.933039	−	0.359775i	$-0.882854\pi$
$499$	0.743321	−	2.28771i	0.0332756	−	0.102412i	0.966315	+	0.257363i	$0.0828536\pi$
$500$	−4.94565	+	12.2940i	−0.221176	+	0.549804i
$501$		0			0
$502$	−1.06453	+	5.49855i	−0.0475123	+	0.245412i
$503$	0.451670	+	1.39010i	0.0201390	+	0.0619814i	0.960621	−	0.277862i	$-0.0896259\pi$
$503$	0.451670	+	1.39010i	0.0201390	+	0.0619814i	−0.940482	+	0.339844i	$0.889626\pi$
$504$		0			0
$505$			3.63114i			0.161584i
$506$	−5.67149	+	40.1540i	−0.252128	+	1.78506i
$507$		0			0
$508$	−8.16653	+	9.76221i	−0.362331	+	0.433128i
$509$	38.7738	−	12.5984i	1.71862	−	0.558413i	0.726889	−	0.686755i	$-0.240965\pi$
$509$	38.7738	−	12.5984i	1.71862	−	0.558413i	0.991730	+	0.128342i	$0.0409655\pi$
$510$		0			0
$511$	−7.05278	+	9.70732i	−0.311997	+	0.429427i
$512$	−20.0914	+	10.4085i	−0.887921	+	0.459996i
$513$		0			0
$514$	−12.1433	−	25.9906i	−0.535620	−	1.14639i
$515$	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
$520$	9.29171	−	7.55897i	0.407469	−	0.331483i
$521$	0.971088	−	2.98870i	0.0425441	−	0.130937i	−0.927528	−	0.373753i	$-0.878071\pi$
$521$	0.971088	−	2.98870i	0.0425441	−	0.130937i	0.970073	+	0.242815i	$0.0780709\pi$
$522$		0			0
$523$	2.82713	−	3.89121i	0.123622	−	0.170151i	−0.742720	−	0.669602i	$-0.766465\pi$
$523$	2.82713	−	3.89121i	0.123622	−	0.170151i	0.866342	+	0.499451i	$0.166465\pi$
$524$	−0.478345	−	0.0327280i	−0.0208966	−	0.00142973i
$525$		0			0
$526$	5.02831	−	4.69603i	0.219245	−	0.204757i
$527$	−26.4757			−1.15330
$528$		0			0
$529$	−51.7505			−2.25002
$530$	−3.15753	+	2.94888i	−0.137155	+	0.128091i
$531$		0			0
$532$	−19.6269	−	1.34286i	−0.850934	−	0.0582202i
$533$	2.76968	−	3.81214i	0.119968	−	0.165122i
$534$		0			0
$535$	−1.78331	+	5.48846i	−0.0770991	+	0.237287i
$536$	−19.1220	−	23.5053i	−0.825944	−	1.01528i
$537$		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	$-0.810873\pi$
$541$	−12.8453	+	9.33268i	−0.552264	+	0.401243i	0.276355	+	0.961056i	$0.410873\pi$
$542$	−8.75309	−	18.7343i	−0.375977	−	0.804709i
$543$		0			0
$544$	−0.294291	+	21.4765i	−0.0126176	+	0.920798i
$545$	7.27656	−	10.0153i	0.311693	−	0.429009i
$546$		0			0
$547$	2.96072	−	0.961995i	0.126591	−	0.0411319i	−0.245036	−	0.969514i	$-0.578800\pi$
$547$	2.96072	−	0.961995i	0.126591	−	0.0411319i	0.371627	+	0.928382i	$0.378800\pi$
$548$	3.79763	−	4.53966i	0.162227	−	0.193925i
$549$		0			0
$550$	3.66311	+	20.8585i	0.156196	+	0.889411i
$551$		−	25.6824i		−	1.09411i
$552$		0			0
$553$	−1.74689	−	5.37637i	−0.0742852	−	0.228626i
$554$	7.43134	−	38.3846i	0.315727	−	1.63081i
$555$		0			0
$556$	1.17879	−	2.93025i	0.0499917	−	0.124270i
$557$	1.84128	−	5.66686i	0.0780174	−	0.240113i	−0.904440	−	0.426601i	$-0.859711\pi$
$557$	1.84128	−	5.66686i	0.0780174	−	0.240113i	0.982457	+	0.186489i	$0.0597107\pi$
$558$		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	0.981093	−	0.193538i	$-0.0619963\pi$
$563$	11.7180	+	16.1284i	0.493853	+	0.679730i	−0.487240	+	0.873268i	$0.661996\pi$
$564$		0			0
$565$	−4.94033	−	1.60521i	−0.207841	−	0.0675317i
$566$	−10.7525	+	19.4324i	−0.451960	+	0.816803i
$567$		0			0
$568$	5.47963	−	0.299544i	0.229920	−	0.0125686i
$569$	10.2471	−	3.32949i	0.429582	−	0.139580i	−0.0862422	−	0.996274i	$-0.527486\pi$
$569$	10.2471	−	3.32949i	0.429582	−	0.139580i	0.515824	+	0.856695i	$0.327486\pi$
$570$		0			0
$571$			31.9637i			1.33764i	0.743424	+	0.668820i	$0.233200\pi$
$571$			31.9637i			1.33764i	−0.743424	+	0.668820i	$0.766800\pi$
$572$	13.1314	−	38.1440i	0.549052	−	1.59488i
$573$		0			0
$574$	−1.23514	−	1.32253i	−0.0515536	−	0.0552013i
$575$	−37.1263	+	12.0631i	−1.54827	+	0.503065i
$576$		0			0
$577$	−0.0764768	−	0.0555637i	−0.00318377	−	0.00231315i	0.586192	−	0.810172i	$-0.300626\pi$
$577$	−0.0764768	−	0.0555637i	−0.00318377	−	0.00231315i	−0.589376	+	0.807859i	$0.700626\pi$
$578$	−3.19688	−	1.76892i	−0.132973	−	0.0735775i
$579$		0			0
$580$	5.08793	−	3.18992i	0.211265	−	0.132454i
$581$	−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
$586$	−11.5777	−	24.7798i	−0.478269	−	1.02365i
$587$	1.27747	−	3.93166i	0.0527270	−	0.162277i	−0.921226	−	0.389029i	$-0.872811\pi$
$587$	1.27747	−	3.93166i	0.0527270	−	0.162277i	0.973953	+	0.226752i	$0.0728106\pi$
$588$		0			0
$589$	33.5995	+	24.4115i	1.38444	+	1.00586i
$590$	11.8296	+	2.29024i	0.487019	+	0.0942878i
$591$		0			0
$592$	7.65993	+	3.70758i	0.314821	+	0.152381i
$593$			35.7489i			1.46803i	0.679133	+	0.734015i	$0.262356\pi$
$593$			35.7489i			1.46803i	−0.679133	+	0.734015i	$0.737644\pi$
$594$		0			0
$595$	−4.36644			−0.179007
$596$	−23.4478	+	28.0293i	−0.960460	+	1.14813i
$597$		0			0
$598$	73.0050	+	14.1339i	2.98540	+	0.577978i
$599$	−7.34693	+	10.1122i	−0.300187	+	0.413172i	−0.932290	−	0.361713i	$-0.882192\pi$
$599$	−7.34693	+	10.1122i	−0.300187	+	0.413172i	0.632102	+	0.774885i	$0.282192\pi$
$600$		0			0
$601$	21.8025	+	7.08405i	0.889341	+	0.288964i	0.717830	−	0.696218i	$-0.245135\pi$
$601$	21.8025	+	7.08405i	0.889341	+	0.288964i	0.171510	+	0.985182i	$0.445135\pi$
$602$	−21.5241	+	10.0565i	−0.877255	+	0.409872i
$603$		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	$-0.502751\pi$
$607$	23.1519	−	16.8209i	0.939708	−	0.682738i	0.948350	+	0.317225i	$0.102751\pi$
$608$	20.1756	−	26.9839i	0.818228	−	1.09434i
$609$		0			0
$610$	−0.141236	+	0.255247i	−0.00571846	+	0.0103347i
$611$	19.9126	−	27.4074i	0.805579	−	1.10878i
$612$		0			0
$613$	4.21216	+	12.9637i	0.170128	+	0.523599i	0.999378	−	0.0352789i	$-0.0112320\pi$
$613$	4.21216	+	12.9637i	0.170128	+	0.523599i	−0.829250	+	0.558878i	$0.811232\pi$
$614$	17.2739	+	18.4962i	0.697119	+	0.746445i
$615$		0			0
$616$	−13.4231	−	7.73531i	−0.540832	−	0.311664i
$617$	−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	−0.984572	−	0.174980i	$-0.944014\pi$
$619$	−7.23719	−	22.2738i	−0.290887	−	0.895259i	0.693685	−	0.720279i	$-0.255986\pi$
$620$	−0.662875	+	9.68844i	−0.0266217	+	0.389097i
$621$		0			0
$622$	−0.677353	+	1.22414i	−0.0271594	+	0.0490836i
$623$	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	$-0.288017\pi$
$631$	16.4648	+	5.34974i	0.655453	+	0.212970i	0.0376362	+	0.999292i	$0.488017\pi$
$632$	9.35739	+	2.48475i	0.372217	+	0.0988379i
$633$		0			0
$634$	−12.2751	−	2.37648i	−0.487505	−	0.0943819i
$635$	4.21449	−	1.36937i	0.167247	−	0.0543418i
$636$		0			0
$637$	−25.9842			−1.02953
$638$	8.87859	−	18.1720i	0.351507	−	0.719437i
$639$		0			0
$640$	7.85170	+	0.645403i	0.310366	+	0.0255118i
$641$	0.223394	+	0.687535i	0.00882352	+	0.0271560i	0.955371	−	0.295407i	$-0.0954554\pi$
$641$	0.223394	+	0.687535i	0.00882352	+	0.0271560i	−0.946548	+	0.322564i	$0.895455\pi$
$642$		0			0
$643$	3.53380	+	2.56746i	0.139359	+	0.101251i	0.655281	−	0.755385i	$-0.272550\pi$
$643$	3.53380	+	2.56746i	0.139359	+	0.101251i	−0.515921	+	0.856636i	$0.672550\pi$
$644$	10.6579	−	26.4937i	0.419982	−	1.04400i
$645$		0			0
$646$	−13.5378	−	28.9752i	−0.532639	−	1.14002i
$647$	−19.5634	−	26.9267i	−0.769115	−	1.05860i	−0.996401	−	0.0847680i	$-0.972985\pi$
$647$	−19.5634	−	26.9267i	−0.769115	−	1.05860i	0.227286	−	0.973828i	$-0.427015\pi$
$648$		0			0
$649$	37.9065	−	14.4884i	1.48796	−	0.568719i
$650$	38.5403	−	4.76151i	1.51167	−	0.186762i
$651$		0			0
$652$	0.804369	+	1.28297i	0.0315015	+	0.0502451i
$653$	−14.5362	−	4.72309i	−0.568845	−	0.184829i	0.0104521	−	0.999945i	$-0.496673\pi$
$653$	−14.5362	−	4.72309i	−0.568845	−	0.184829i	−0.579297	+	0.815116i	$0.696673\pi$
$654$		0			0
$655$	0.135053	+	0.0981217i	0.00527695	+	0.00383393i
$656$	3.05049	−	0.547328i	0.119102	−	0.0213696i
$657$		0			0
$658$	−8.88002	−	9.50835i	−0.346179	−	0.370674i
$659$			31.0396i			1.20913i	0.796556	+	0.604565i	$0.206653\pi$
$659$			31.0396i			1.20913i	−0.796556	+	0.604565i	$0.793347\pi$
$660$		0			0
$661$		−	30.3454i		−	1.18030i	−0.807294	−	0.590149i	$-0.799069\pi$
$661$		−	30.3454i		−	1.18030i	0.807294	−	0.590149i	$-0.200931\pi$
$662$	−9.35529	+	8.73708i	−0.363604	+	0.339576i
$663$		0			0
$664$	9.17163	−	0.501367i	0.355928	−	0.0194568i
$665$	5.54133	+	4.02601i	0.214884	+	0.156122i
$666$		0			0
$667$	35.4561	+	11.5204i	1.37287	+	0.446071i
$668$	−14.6221	−	23.3223i	−0.565746	−	0.902367i
$669$		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	0.945182	−	0.326544i	$-0.105884\pi$
$673$	8.88632	+	12.2310i	0.342543	+	0.471469i	−0.602639	+	0.798014i	$0.705884\pi$
$674$	17.4968	−	8.17486i	0.673950	−	0.314884i
$675$		0			0
$676$	−44.5065	−	17.9041i	−1.71179	−	0.688621i
$677$	29.0399	+	21.0987i	1.11609	+	0.810890i	0.983613	−	0.180295i	$-0.0577053\pi$
$677$	29.0399	+	21.0987i	1.11609	+	0.810890i	0.132482	+	0.991185i	$0.457705\pi$
$678$		0			0
$679$	2.19882	+	6.76728i	0.0843830	+	0.259704i
$680$	4.05878	−	6.28087i	0.155647	−	0.240860i
$681$		0			0
$682$	15.3347	+	28.8883i	0.587195	+	1.10619i
$683$	−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
$686$	−5.00420	+	25.8479i	−0.191061	+	0.986876i
$687$		0			0
$688$	5.54176	−	40.3090i	0.211278	−	1.53677i
$689$	25.3756	+	8.24503i	0.966733	+	0.314111i
$690$		0			0
$691$	17.4532	−	12.6805i	0.663949	−	0.482387i	−0.204045	−	0.978961i	$-0.565409\pi$
$691$	17.4532	−	12.6805i	0.663949	−	0.482387i	0.867994	+	0.496574i	$0.165409\pi$
$692$	−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
$698$	18.0050	+	9.96267i	0.681498	+	0.377093i
$699$		0			0
$700$	1.01798	−	14.8786i	0.0384760	−	0.562358i
$701$	10.2401	+	31.5157i	0.386762	+	1.19033i	0.935194	+	0.354135i	$0.115225\pi$
$701$	10.2401	+	31.5157i	0.386762	+	1.19033i	−0.548432	+	0.836195i	$0.684775\pi$
$702$		0			0
$703$	−12.6716			−0.477917
$704$	23.6041	−	12.1181i	0.889612	−	0.456717i
$705$		0			0
$706$	24.5401	−	22.9185i	0.923580	−	0.862549i
$707$	−2.66123	−	8.19043i	−0.100086	−	0.308033i
$708$		0			0
$709$	11.7145	−	16.1236i	0.439946	−	0.605534i	−0.530254	−	0.847839i	$-0.677903\pi$
$709$	11.7145	−	16.1236i	0.439946	−	0.605534i	0.970200	+	0.242305i	$0.0779035\pi$
$710$	−1.67182	−	0.925066i	−0.0627423	−	0.0347171i
$711$		0			0
$712$	11.8385	+	14.5522i	0.443666	+	0.545368i
$713$	−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
$718$	−6.33719	−	13.5636i	−0.236502	−	0.506188i
$719$	8.25695	+	2.68285i	0.307932	+	0.100053i	0.458907	−	0.888484i	$-0.348241\pi$
$719$	8.25695	+	2.68285i	0.307932	+	0.100053i	−0.150974	+	0.988538i	$0.548241\pi$
$720$		0			0
$721$	−3.36642	+	4.63348i	−0.125372	+	0.172560i
$722$	−4.42841	+	22.8738i	−0.164808	+	0.851275i
$723$		0			0
$724$	−28.1462	−	23.5455i	−1.04604	−	0.875063i
$725$	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	$0.951748\pi$
$728$	−15.4185	+	23.8599i	−0.571449	+	0.884305i
$729$		0			0
$730$	−1.35994	+	7.02441i	−0.0503336	+	0.259985i
$731$	−31.2461	−	22.7016i	−1.15568	−	0.839649i
$732$		0			0
$733$	−0.185339	+	0.570415i	−0.00684566	+	0.0210688i	−0.954421	−	0.298464i	$-0.903526\pi$
$733$	−0.185339	+	0.570415i	−0.00684566	+	0.0210688i	0.947575	+	0.319532i	$0.103526\pi$
$734$	−33.4320	+	15.6201i	−1.23400	+	0.576549i
$735$		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	0.869352	−	0.494193i	$-0.164536\pi$
$739$	3.55308	+	4.89040i	0.130702	+	0.179896i	−0.738650	+	0.674089i	$0.764536\pi$
$740$	−1.57388	−	2.51035i	−0.0578571	−	0.0922824i
$741$		0			0
$742$	4.96094	−	8.96563i	0.182122	−	0.329139i
$743$	14.7479	+	10.7149i	0.541046	+	0.393093i	0.824473	−	0.565901i	$-0.191471\pi$
$743$	14.7479	+	10.7149i	0.541046	+	0.393093i	−0.283427	+	0.958994i	$0.591471\pi$
$744$		0			0
$745$	12.1007	−	3.93175i	0.443335	−	0.144048i
$746$	−17.2776	+	16.1359i	−0.632579	+	0.590778i
$747$		0			0
$748$	0.438006	−	25.1820i	0.0160151	−	0.920745i
$749$		−	13.6868i		−	0.500103i
$750$		0			0
$751$	−48.5455	+	15.7734i	−1.77145	+	0.575579i	−0.998280	−	0.0586211i	$-0.981330\pi$
$751$	−48.5455	+	15.7734i	−1.77145	+	0.575579i	−0.773169	+	0.634200i	$0.781330\pi$
$752$	21.9315	−	3.93502i	0.799761	−	0.143495i
$753$		0			0
$754$	−32.4499	−	17.9555i	−1.18176	−	0.653899i
$755$	−10.0451	−	3.26386i	−0.365580	−	0.118784i
$756$		0			0
$757$	4.99944	+	6.88113i	0.181708	+	0.250099i	0.890148	−	0.455672i	$-0.150601\pi$
$757$	4.99944	+	6.88113i	0.181708	+	0.250099i	−0.708440	+	0.705771i	$0.750601\pi$
$758$	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	−0.997278	−	0.0737302i	$-0.976510\pi$
$761$	−20.9441	−	28.8271i	−0.759224	−	1.04498i	0.238054	−	0.971252i	$-0.423490\pi$
$762$		0			0
$763$	−9.07290	+	27.9235i	−0.328461	+	1.01090i
$764$	18.5166	−	46.0288i	0.669905	−	1.66526i
$765$		0			0
$766$	−12.1498	−	2.35222i	−0.438990	−	0.0849893i
$767$	−22.9948	−	70.7707i	−0.830294	−	2.55538i
$768$		0			0
$769$			45.0073i			1.62300i	0.584350	+	0.811502i	$0.301349\pi$
$769$			45.0073i			1.62300i	−0.584350	+	0.811502i	$0.698651\pi$
$770$	2.52904	+	4.76435i	0.0911403	+	0.171695i
$771$		0			0
$772$	−0.0360246	−	0.0301362i	−0.00129655	−	0.00108463i
$773$	27.7270	−	9.00903i	0.997269	−	0.324032i	0.235495	−	0.971875i	$-0.424329\pi$
$773$	27.7270	−	9.00903i	0.997269	−	0.324032i	0.761774	+	0.647843i	$0.224329\pi$
$774$		0			0
$775$	−18.5056	+	25.4708i	−0.664743	+	0.914940i
$776$	−11.7782	−	3.12757i	−0.422814	−	0.112273i
$777$		0			0
$778$	28.9636	−	13.5324i	1.03840	−	0.485161i
$779$	−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
$784$	−12.3293	−	11.8349i	−0.440331	−	0.422676i
$785$	−1.43268	+	4.40932i	−0.0511344	+	0.157375i
$786$		0			0
$787$	16.0741	−	22.1241i	0.572980	−	0.788639i	−0.419924	−	0.907559i	$-0.637943\pi$
$787$	16.0741	−	22.1241i	0.572980	−	0.788639i	0.992904	+	0.118920i	$0.0379432\pi$
$788$	0.0250451	−	0.366053i	0.000892193	−	0.0130401i
$789$		0			0
$790$	−2.30077	−	2.46357i	−0.0818578	−	0.0876498i
$791$	12.3199			0.438044
$792$		0			0
$793$	1.80155			0.0639749
$794$	2.68861	+	2.87885i	0.0954153	+	0.102167i
$795$		0			0
$796$	−29.5371	−	2.02091i	−1.04692	−	0.0716291i
$797$	0.554736	−	0.763529i	0.0196498	−	0.0270456i	−0.799079	−	0.601226i	$-0.794679\pi$
$797$	0.554736	−	0.763529i	0.0196498	−	0.0270456i	0.818729	+	0.574180i	$0.194679\pi$
$798$		0			0
$799$	6.53584	−	20.1152i	0.231221	−	0.711626i
$800$	20.4557	+	15.2945i	0.723219	+	0.540743i
$801$		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
$806$	54.3346	−	25.3863i	1.91386	−	0.894194i
$807$		0			0
$808$	14.2552	+	3.78529i	0.501495	+	0.133166i
$809$	−11.5315	+	15.8717i	−0.405424	+	0.558019i	−0.962095	−	0.272714i	$-0.912079\pi$
$809$	−11.5315	+	15.8717i	−0.405424	+	0.558019i	0.556671	+	0.830733i	$0.312079\pi$
$810$		0			0
$811$	−18.2649	+	5.93462i	−0.641367	+	0.208393i	−0.611604	−	0.791164i	$-0.709475\pi$
$811$	−18.2649	+	5.93462i	−0.641367	+	0.208393i	−0.0297632	+	0.999557i	$0.509475\pi$
$812$	−9.13850	+	10.9241i	−0.320698	+	0.383360i
$813$		0			0
$814$	−8.96596	−	4.38064i	−0.314257	−	0.153541i
$815$		−	0.527224i		−	0.0184679i
$816$		0			0
$817$	18.7219	+	57.6200i	0.654995	+	2.01587i
$818$	41.4415	+	8.02314i	1.44897	+	0.280523i
$819$		0			0
$820$	−1.00108	−	0.402717i	−0.0349593	−	0.0140635i
$821$	−4.88277	+	15.0276i	−0.170410	+	0.524467i	−0.999394	−	0.0348046i	$-0.988919\pi$
$821$	−4.88277	+	15.0276i	−0.170410	+	0.524467i	0.828984	+	0.559272i	$0.188919\pi$
$822$		0			0
$823$	−23.2795	−	32.0414i	−0.811471	−	1.11689i	−0.991095	−	0.133159i	$-0.957488\pi$
$823$	−23.2795	−	32.0414i	−0.811471	−	1.11689i	0.179623	−	0.983735i	$-0.442512\pi$
$824$	−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	0.991506	+	0.130058i	$0.0415165\pi$
$827$	23.2594	+	32.0138i	0.808807	+	1.11323i	−0.182699	+	0.983169i	$0.558484\pi$
$828$		0			0
$829$	−14.5137	−	4.71578i	−0.504081	−	0.163786i	0.0459279	−	0.998945i	$-0.485376\pi$
$829$	−14.5137	−	4.71578i	−0.504081	−	0.163786i	−0.550009	+	0.835159i	$0.685376\pi$
$830$	−2.79824	−	1.54835i	−0.0971283	−	0.0537439i
$831$		0			0
$832$	−19.9889	−	44.3573i	−0.692990	−	1.53781i
$833$	−15.4285	+	5.01303i	−0.534567	+	0.173691i
$834$		0			0
$835$			9.58406i			0.331670i
$836$	−23.7746	+	31.5539i	−0.822260	+	1.09132i
$837$		0			0
$838$	−2.60605	+	2.43384i	−0.0900244	+	0.0840755i
$839$	−13.3878	+	4.34995i	−0.462197	+	0.150177i	−0.530854	−	0.847463i	$-0.678129\pi$
$839$	−13.3878	+	4.34995i	−0.462197	+	0.150177i	0.0686565	+	0.997640i	$0.478129\pi$
$840$		0			0
$841$	8.41924	+	6.11693i	0.290318	+	0.210929i
$842$	20.7730	−	37.5418i	0.715884	−	1.29378i
$843$		0			0
$844$	−19.5258	+	12.2418i	−0.672105	+	0.421381i
$845$	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
$850$	21.9653	−	10.2627i	0.753403	−	0.352006i
$851$	5.68409	−	17.4938i	0.194848	−	0.599681i
$852$		0			0
$853$	15.7626	+	11.4522i	0.539702	+	0.392117i	0.823974	−	0.566627i	$-0.191752\pi$
$853$	15.7626	+	11.4522i	0.539702	+	0.392117i	−0.284272	+	0.958744i	$0.591752\pi$
$854$	0.131503	−	0.679247i	0.00449996	−	0.0232434i
$855$		0			0
$856$	19.6876	+	12.7224i	0.672909	+	0.434842i
$857$		−	22.1714i		−	0.757359i	−0.925528	−	0.378680i	$-0.876378\pi$
$857$		−	22.1714i		−	0.757359i	0.925528	−	0.378680i	$-0.123622\pi$
$858$		0			0
$859$	−2.34314			−0.0799470			−0.0399735	−	0.999201i	$-0.512727\pi$
$859$	−2.34314			−0.0799470			−0.0399735	+	0.999201i	$0.512727\pi$
$860$	−9.08968	+	10.8657i	−0.309956	+	0.370518i
$861$		0			0
$862$	6.97757	−	36.0408i	0.237657	−	1.22755i
$863$	29.5571	−	40.6819i	1.00614	−	1.38483i	0.0846518	−	0.996411i	$-0.473022\pi$
$863$	29.5571	−	40.6819i	1.00614	−	1.38483i	0.921484	−	0.388416i	$-0.126978\pi$
$864$		0			0
$865$	2.91228	+	0.946256i	0.0990204	+	0.0321737i
$866$	−18.4214	−	39.4277i	−0.625986	−	1.33981i
$867$		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
$872$	−31.7327	−	39.0068i	−1.07461	−	1.32094i
$873$		0			0
$874$	−63.7207	−	35.2585i	−2.15538	−	1.19264i
$875$	−6.43177	+	8.85257i	−0.217434	+	0.299272i
$876$		0			0
$877$	−8.48419	−	26.1117i	−0.286491	−	0.881728i	−0.985948	−	0.167053i	$-0.946575\pi$
$877$	−8.48419	−	26.1117i	−0.286491	−	0.881728i	0.699457	−	0.714675i	$-0.253425\pi$
$878$	−14.3767	+	13.4267i	−0.485191	+	0.453129i
$879$		0			0
$880$	−9.20407	−	0.790768i	−0.310269	−	0.0266568i
$881$	−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	0.848682	+	0.528903i	$0.177397\pi$
$883$	14.0543	+	43.2547i	0.472965	+	1.45564i	−0.375717	+	0.926735i	$0.622603\pi$
$884$	−46.0751	−	3.15242i	−1.54967	−	0.106027i
$885$		0			0
$886$	11.2208	+	6.20880i	0.376971	+	0.208589i
$887$	11.7143	−	36.0529i	0.393327	−	1.21054i	−0.536930	−	0.843627i	$-0.680416\pi$
$887$	11.7143	−	36.0529i	0.393327	−	1.21054i	0.930257	−	0.366909i	$-0.119584\pi$
$888$		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
$896$	−18.1833	+	4.29866i	−0.607462	+	0.143608i
$897$		0			0
$898$	−4.82835	+	24.9396i	−0.161124	+	0.832245i
$899$	28.5957	−	9.29131i	0.953721	−	0.309883i
$900$		0			0
$901$	16.6578			0.554953
$902$	−3.57936	+	0.628596i	−0.119180	+	0.0209300i
$903$		0			0
$904$	−11.4518	+	17.7214i	−0.380881	+	0.589406i
$905$	3.94814	+	12.1511i	0.131241	+	0.403917i
$906$		0			0
$907$	24.3629	+	17.7007i	0.808957	+	0.587742i	0.913528	−	0.406776i	$-0.133347\pi$
$907$	24.3629	+	17.7007i	0.808957	+	0.587742i	−0.104571	+	0.994517i	$0.533347\pi$
$908$	6.88309	−	17.1101i	0.228423	−	0.567819i
$909$		0			0
$910$	8.96102	−	4.18678i	0.297055	−	0.138790i
$911$	21.2777	+	29.2863i	0.704963	+	0.970298i	0.999891	+	0.0147785i	$0.00470432\pi$
$911$	21.2777	+	29.2863i	0.704963	+	0.970298i	−0.294928	+	0.955519i	$0.595296\pi$
$912$		0			0
$913$	−10.7568	+	0.548218i	−0.355998	+	0.0181434i
$914$	3.83327	+	31.0270i	0.126793	+	1.02628i
$915$		0			0
$916$	43.5242	−	27.2879i	1.43808	−	0.901616i
$917$	−0.376538	−	0.122345i	−0.0124344	−	0.00404018i
$918$		0			0
$919$	−22.9541	−	16.6771i	−0.757184	−	0.550127i	0.140861	−	0.990029i	$-0.455013\pi$
$919$	−22.9541	−	16.6771i	−0.757184	−	0.550127i	−0.898045	+	0.439903i	$0.855013\pi$
$920$	−0.929467	−	17.0030i	−0.0306436	−	0.560571i
$921$		0			0
$922$	−20.3437	+	18.9994i	−0.669985	+	0.625711i
$923$			11.7998i			0.388395i
$924$		0			0
$925$		−	9.60594i		−	0.315841i
$926$	10.3059	+	11.0351i	0.338671	+	0.362635i
$927$		0			0
$928$	−7.21907	−	23.2996i	−0.236978	−	0.764845i
$929$	−17.2036	−	12.4992i	−0.564433	−	0.410084i	0.268646	−	0.963239i	$-0.413424\pi$
$929$	−17.2036	−	12.4992i	−0.564433	−	0.410084i	−0.833079	+	0.553155i	$0.813424\pi$
$930$		0			0
$931$	24.2021	+	7.86374i	0.793192	+	0.257724i
$932$	−40.6655	+	25.4956i	−1.33204	+	0.835135i
$933$		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	−0.988421	−	0.151738i	$-0.951513\pi$
$937$	−25.3238	−	34.8552i	−0.827293	−	1.13867i	0.161128	−	0.986934i	$-0.448487\pi$
$938$	−10.5913	−	22.6688i	−0.345819	−	0.740161i
$939$		0			0
$940$	−7.19728	−	2.89534i	−0.234750	−	0.0944355i
$941$	7.65773	+	5.56367i	0.249635	+	0.181370i	0.705565	−	0.708645i	$-0.250693\pi$
$941$	7.65773	+	5.56367i	0.249635	+	0.181370i	−0.455930	+	0.890016i	$0.650693\pi$
$942$		0			0
$943$	−2.07004	−	6.37094i	−0.0674099	−	0.207466i
$944$	21.3229	−	44.0534i	0.694001	−	1.43382i
$945$		0			0
$946$	−6.67265	+	47.2422i	−0.216947	+	1.53598i
$947$	−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
$950$	−37.3381	−	7.22872i	−1.21141	−	0.234531i
$951$		0			0
$952$	−4.55181	+	17.1418i	−0.147525	+	0.555569i
$953$	37.3273	+	12.1284i	1.20915	+	0.392876i	0.843119	−	0.537727i	$-0.180717\pi$
$953$	37.3273	+	12.1284i	1.20915	+	0.392876i	0.366030	+	0.930603i	$0.380717\pi$
$954$		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
$962$	−8.85911	+	16.0106i	−0.285629	+	0.516202i
$963$		0			0
$964$	18.8107	+	1.28701i	0.605853	+	0.0414520i
$965$	0.00505327	+	0.0155524i	0.000162670	+	0.000500648i
$966$		0			0
$967$	−35.8221			−1.15196			−0.575980	−	0.817464i	$-0.695379\pi$
$967$	−35.8221			−1.15196			−0.575980	+	0.817464i	$0.695379\pi$
$968$	−27.7305	+	14.1075i	−0.891291	+	0.453431i
$969$		0			0
$970$	2.89600	+	3.10091i	0.0929849	+	0.0995643i
$971$	9.05079	+	27.8555i	0.290454	+	0.893924i	0.984711	+	0.174197i	$0.0557330\pi$
$971$	9.05079	+	27.8555i	0.290454	+	0.893924i	−0.694257	+	0.719727i	$0.744267\pi$
$972$		0			0
$973$	1.53300	−	2.11000i	0.0491458	−	0.0676434i
$974$	−25.9793	+	46.9510i	−0.832431	+	1.50441i
$975$		0			0
$976$	0.854820	+	0.820547i	0.0273621	+	0.0262651i
$977$	19.3774	−	14.0785i	0.619939	−	0.450412i	−0.232961	−	0.972486i	$-0.574841\pi$
$977$	19.3774	−	14.0785i	0.619939	−	0.450412i	0.852900	+	0.522074i	$0.174841\pi$
$978$		0			0
$979$	−13.8188	−	17.1151i	−0.441651	−	0.547001i
$980$	1.44817	+	5.77139i	0.0462601	+	0.184360i
$981$		0			0
$982$	0.707164	−	0.330402i	0.0225665	−	0.0105436i
$983$	−15.5566	−	5.05465i	−0.496179	−	0.161218i	0.0502286	−	0.998738i	$-0.484005\pi$
$983$	−15.5566	−	5.05465i	−0.496179	−	0.161218i	−0.546408	+	0.837519i	$0.684005\pi$
$984$		0			0
$985$	−0.0750876	+	0.103349i	−0.00239249	+	0.00329298i
$986$	−22.7317	−	4.40090i	−0.723925	−	0.140153i
$987$		0			0
$988$	55.5660	+	46.4835i	1.76779	+	1.47884i
$989$	−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	$0.662591\pi$
$992$	37.3439	+	12.7020i	1.18567	+	0.403290i
$993$		0			0
$994$	4.44894	+	0.861322i	0.141112	+	0.0273195i
$995$	8.33932	+	6.05887i	0.264374	+	0.192079i
$996$		0			0
$997$	2.82716	−	8.70110i	0.0895370	−	0.275567i	−0.896254	−	0.443540i	$-0.853722\pi$
$997$	2.82716	−	8.70110i	0.0895370	−	0.275567i	0.985791	+	0.167974i	$0.0537223\pi$
$998$	1.43998	+	3.08200i	0.0455817	+	0.0975590i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	792.2.bp.d.19.4		48
3.2	odd	2		264.2.z.b.19.9	yes	48
8.3	odd	2	inner	792.2.bp.d.19.10		48
11.7	odd	10	inner	792.2.bp.d.667.10		48
12.11	even	2		1056.2.bp.a.943.7		48
24.5	odd	2		1056.2.bp.a.943.6		48
24.11	even	2		264.2.z.b.19.3	✓	48
33.29	even	10		264.2.z.b.139.3	yes	48
88.51	even	10	inner	792.2.bp.d.667.4		48
132.95	odd	10		1056.2.bp.a.271.6		48
264.29	even	10		1056.2.bp.a.271.7		48
264.227	odd	10		264.2.z.b.139.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
264.2.z.b.19.3	✓	48	24.11	even	2
264.2.z.b.19.9	yes	48	3.2	odd	2
264.2.z.b.139.3	yes	48	33.29	even	10
264.2.z.b.139.9	yes	48	264.227	odd	10
792.2.bp.d.19.4		48	1.1	even	1	trivial
792.2.bp.d.19.10		48	8.3	odd	2	inner
792.2.bp.d.667.4		48	88.51	even	10	inner
792.2.bp.d.667.10		48	11.7	odd	10	inner
1056.2.bp.a.271.6		48	132.95	odd	10
1056.2.bp.a.271.7		48	264.29	even	10
1056.2.bp.a.943.6		48	24.5	odd	2
1056.2.bp.a.943.7		48	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q+(-1.03357 + 0.965267i) q^{2} +(0.136519 - 1.99534i) q^{4} +(-0.409298 + 0.563350i) q^{5} +(0.510340 - 1.57067i) q^{7} +(1.78493 + 2.19409i) q^{8} +(-0.120747 - 0.977341i) q^{10} +(-2.08351 - 2.58050i) q^{11} +(-4.92015 + 3.57470i) q^{13} +(0.988641 + 2.11600i) q^{14} +(-3.96273 - 0.544803i) q^{16} +(-2.23176 + 3.07176i) q^{17} +(5.66454 - 1.84052i) q^{19} +(1.06820 + 0.893594i) q^{20} +(4.64432 + 0.655979i) q^{22} +8.64584i q^{23} +(1.39525 + 4.29413i) q^{25} +(1.63476 - 8.44395i) q^{26} +(-3.06433 - 1.23273i) q^{28} +(1.33248 - 4.10095i) q^{29} +(4.09860 + 5.64124i) q^{31} +(4.62162 - 3.26200i) q^{32} +(-0.658392 - 5.32912i) q^{34} +(0.675953 + 0.930370i) q^{35} +(-2.02338 - 0.657436i) q^{37} +(-4.07809 + 7.37010i) q^{38} +(-1.96661 + 0.107505i) q^{40} +(-0.736879 + 0.239427i) q^{41} +10.1720i q^{43} +(-5.43341 + 3.80501i) q^{44} +(-8.34554 - 8.93605i) q^{46} +(-5.29780 + 1.72136i) q^{47} +(3.45658 + 2.51135i) q^{49} +(-5.58706 - 3.09148i) q^{50} +(6.46103 + 10.3054i) q^{52} +(-2.57874 - 3.54933i) q^{53} +(2.30650 - 0.117551i) q^{55} +(4.35710 - 1.68380i) q^{56} +(2.58130 + 5.52480i) q^{58} +(-3.78102 + 11.6368i) q^{59} +(-0.239653 - 0.174118i) q^{61} +(-9.68148 - 1.87435i) q^{62} +(-1.62805 + 7.83259i) q^{64} -4.23488i q^{65} -10.7130 q^{67} +(5.82451 + 4.87247i) q^{68} +(-1.59670 - 0.309124i) q^{70} +(1.14044 - 1.56968i) q^{71} +(-6.90989 - 2.24516i) q^{73} +(2.72590 - 1.27360i) q^{74} +(-2.89914 - 11.5539i) q^{76} +(-5.11640 + 1.95556i) q^{77} +(2.76926 - 2.01198i) q^{79} +(1.92885 - 2.00941i) q^{80} +(0.530503 - 0.958748i) q^{82} +(1.90883 - 2.62729i) q^{83} +(-0.817020 - 2.51453i) q^{85} +(-9.81874 - 10.5135i) q^{86} +(1.94294 - 9.17742i) q^{88} +6.63247 q^{89} +(3.10371 + 9.55222i) q^{91} +(17.2513 + 1.18032i) q^{92} +(3.81406 - 6.89293i) q^{94} +(-1.28163 + 3.94444i) q^{95} +(-3.48568 + 2.53250i) q^{97} +(-5.99672 + 0.740872i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{4} - 4 q^{11} + 16 q^{14} + 20 q^{16} - 25 q^{20} + 3 q^{22} - 4 q^{25} - 4 q^{26} - 25 q^{28} - 26 q^{38} - 65 q^{40} + 60 q^{41} + 43 q^{44} - 5 q^{46} - 12 q^{49} + 80 q^{50} - 15 q^{52}+ \cdots - 40 q^{97}+O(q^{100}) \) 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

Varieties

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Representations

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Database

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