LMFDB - Embedded newform 896.2.bh.a.753.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(81,896)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("896.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bh (of order $24$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 224)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			753.10
Character	$\chi$	$=$	896.753
Dual form			896.2.bh.a.401.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23586 - 0.162704i) q^{3} +(0.0281519 + 0.213835i) q^{5} +(2.44336 - 1.01488i) q^{7} +(-1.39689 - 0.374296i) q^{9} +O(q^{10})$	\(q+(-1.23586 - 0.162704i) q^{3} +(0.0281519 + 0.213835i) q^{5} +(2.44336 - 1.01488i) q^{7} +(-1.39689 - 0.374296i) q^{9} +(1.29156 + 1.68319i) q^{11} +(3.53590 - 1.46462i) q^{13} -0.268851i q^{15} +(-6.24315 - 3.60448i) q^{17} +(2.81201 + 2.15773i) q^{19} +(-3.18478 + 0.856712i) q^{21} +(-5.02353 - 1.34605i) q^{23} +(4.78470 - 1.28206i) q^{25} +(5.12039 + 2.12094i) q^{27} +(2.56271 + 6.18694i) q^{29} +(2.46695 - 4.27288i) q^{31} +(-1.32232 - 2.29033i) q^{33} +(0.285803 + 0.493906i) q^{35} +(-0.339869 - 2.58156i) q^{37} +(-4.60818 + 1.23476i) q^{39} +(4.31161 - 4.31161i) q^{41} +(4.15699 - 10.0359i) q^{43} +(0.0407125 - 0.309242i) q^{45} +(4.71097 - 2.71988i) q^{47} +(4.94002 - 4.95946i) q^{49} +(7.12921 + 5.47044i) q^{51} +(-3.81048 - 4.96591i) q^{53} +(-0.323565 + 0.323565i) q^{55} +(-3.12418 - 3.12418i) q^{57} +(6.02188 - 4.62075i) q^{59} +(0.501939 - 0.654140i) q^{61} +(-3.79298 + 0.503144i) q^{63} +(0.412729 + 0.714867i) q^{65} +(-4.44474 - 0.585161i) q^{67} +(5.98939 + 2.48089i) q^{69} +(2.53740 + 2.53740i) q^{71} +(3.13587 + 11.7032i) q^{73} +(-6.12182 + 0.805953i) q^{75} +(4.86398 + 2.80186i) q^{77} +(-2.02495 + 1.16910i) q^{79} +(-2.22575 - 1.28504i) q^{81} +(1.12785 - 0.467172i) q^{83} +(0.595009 - 1.43648i) q^{85} +(-2.16052 - 8.06317i) q^{87} +(4.29977 - 16.0470i) q^{89} +(7.15305 - 7.16711i) q^{91} +(-3.74403 + 4.87931i) q^{93} +(-0.382235 + 0.662051i) q^{95} +10.3954 q^{97} +(-1.17415 - 2.83466i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	$ 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) $ 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.23586	−	0.162704i	−0.713526	−	0.0939374i	−0.234980	−	0.972000i	$-0.575503\pi$
$3$	−1.23586	−	0.162704i	−0.713526	−	0.0939374i	−0.478546	+	0.878063i	$0.658836\pi$
$4$		0			0
$5$	0.0281519	+	0.213835i	0.0125899	+	0.0956300i	0.996586	−	0.0825593i	$-0.0263094\pi$
$5$	0.0281519	+	0.213835i	0.0125899	+	0.0956300i	−0.983996	+	0.178189i	$0.942976\pi$
$6$		0			0
$7$	2.44336	−	1.01488i	0.923503	−	0.383590i
$7$	2.44336	−	1.01488i	0.923503	−	0.383590i
$8$		0			0
$9$	−1.39689	−	0.374296i	−0.465631	−	0.124765i
$10$		0			0
$11$	1.29156	+	1.68319i	0.389419	+	0.507500i	0.946388	−	0.323033i	$-0.104702\pi$
$11$	1.29156	+	1.68319i	0.389419	+	0.507500i	−0.556969	+	0.830533i	$0.688036\pi$
$12$		0			0
$13$	3.53590	−	1.46462i	0.980681	−	0.406211i	0.166003	−	0.986125i	$-0.446914\pi$
$13$	3.53590	−	1.46462i	0.980681	−	0.406211i	0.814678	+	0.579914i	$0.196914\pi$
$14$		0			0
$15$		−	0.268851i		−	0.0694171i
$16$		0			0
$17$	−6.24315	−	3.60448i	−1.51419	−	0.874216i	−0.999862	−	0.0166201i	$-0.994709\pi$
$17$	−6.24315	−	3.60448i	−1.51419	−	0.874216i	−0.514324	−	0.857596i	$-0.671957\pi$
$18$		0			0
$19$	2.81201	+	2.15773i	0.645119	+	0.495017i	0.878734	−	0.477312i	$-0.158389\pi$
$19$	2.81201	+	2.15773i	0.645119	+	0.495017i	−0.233615	+	0.972329i	$0.575055\pi$
$20$		0			0
$21$	−3.18478	+	0.856712i	−0.694977	+	0.186950i
$22$		0			0
$23$	−5.02353	−	1.34605i	−1.04748	−	0.280671i	−0.306269	−	0.951945i	$-0.599081\pi$
$23$	−5.02353	−	1.34605i	−1.04748	−	0.280671i	−0.741210	+	0.671274i	$0.765747\pi$
$24$		0			0
$25$	4.78470	−	1.28206i	0.956939	−	0.256411i
$26$		0			0
$27$	5.12039	+	2.12094i	0.985420	+	0.408174i
$28$		0			0
$29$	2.56271	+	6.18694i	0.475884	+	1.14889i	0.961523	+	0.274726i	$0.0885871\pi$
$29$	2.56271	+	6.18694i	0.475884	+	1.14889i	−0.485639	+	0.874160i	$0.661413\pi$
$30$		0			0
$31$	2.46695	−	4.27288i	0.443077	−	0.767432i	−0.554839	−	0.831958i	$-0.687220\pi$
$31$	2.46695	−	4.27288i	0.443077	−	0.767432i	0.997916	+	0.0645260i	$0.0205535\pi$
$32$		0			0
$33$	−1.32232	−	2.29033i	−0.230187	−	0.398696i
$34$		0			0
$35$	0.285803	+	0.493906i	0.0483096	+	0.0834853i
$36$		0			0
$37$	−0.339869	−	2.58156i	−0.0558741	−	0.424406i	−0.996406	−	0.0847015i	$-0.973006\pi$
$37$	−0.339869	−	2.58156i	−0.0558741	−	0.424406i	0.940532	−	0.339704i	$-0.110327\pi$
$38$		0			0
$39$	−4.60818	+	1.23476i	−0.737900	+	0.197720i
$40$		0			0
$41$	4.31161	−	4.31161i	0.673360	−	0.673360i	−0.285129	−	0.958489i	$-0.592036\pi$
$41$	4.31161	−	4.31161i	0.673360	−	0.673360i	0.958489	+	0.285129i	$0.0920365\pi$
$42$		0			0
$43$	4.15699	−	10.0359i	0.633935	−	1.53046i	−0.200700	−	0.979653i	$-0.564322\pi$
$43$	4.15699	−	10.0359i	0.633935	−	1.53046i	0.834635	−	0.550803i	$-0.185678\pi$
$44$		0			0
$45$	0.0407125	−	0.309242i	0.00606906	−	0.0460991i
$46$		0			0
$47$	4.71097	−	2.71988i	0.687165	−	0.396735i	−0.115384	−	0.993321i	$-0.536810\pi$
$47$	4.71097	−	2.71988i	0.687165	−	0.396735i	0.802549	+	0.596586i	$0.203476\pi$
$48$		0			0
$49$	4.94002	−	4.95946i	0.705717	−	0.708494i
$50$		0			0
$51$	7.12921	+	5.47044i	0.998289	+	0.766014i
$52$		0			0
$53$	−3.81048	−	4.96591i	−0.523409	−	0.682120i	0.454597	−	0.890697i	$-0.349783\pi$
$53$	−3.81048	−	4.96591i	−0.523409	−	0.682120i	−0.978006	+	0.208577i	$0.933117\pi$
$54$		0			0
$55$	−0.323565	+	0.323565i	−0.0436295	+	0.0436295i
$56$		0			0
$57$	−3.12418	−	3.12418i	−0.413808	−	0.413808i
$58$		0			0
$59$	6.02188	−	4.62075i	0.783983	−	0.601571i	−0.137271	−	0.990534i	$-0.543833\pi$
$59$	6.02188	−	4.62075i	0.783983	−	0.601571i	0.921254	+	0.388963i	$0.127166\pi$
$60$		0			0
$61$	0.501939	−	0.654140i	0.0642667	−	0.0837540i	−0.760114	−	0.649790i	$-0.774857\pi$
$61$	0.501939	−	0.654140i	0.0642667	−	0.0837540i	0.824381	+	0.566036i	$0.191524\pi$
$62$		0			0
$63$	−3.79298	+	0.503144i	−0.477871	+	0.0633902i
$64$		0			0
$65$	0.412729	+	0.714867i	0.0511927	+	0.0886684i
$66$		0			0
$67$	−4.44474	−	0.585161i	−0.543011	−	0.0714887i	−0.145969	−	0.989289i	$-0.546630\pi$
$67$	−4.44474	−	0.585161i	−0.543011	−	0.0714887i	−0.397042	+	0.917800i	$0.629963\pi$
$68$		0			0
$69$	5.98939	+	2.48089i	0.721038	+	0.298664i
$70$		0			0
$71$	2.53740	+	2.53740i	0.301133	+	0.301133i	0.841457	−	0.540324i	$-0.181698\pi$
$71$	2.53740	+	2.53740i	0.301133	+	0.301133i	−0.540324	+	0.841457i	$0.681698\pi$
$72$		0			0
$73$	3.13587	+	11.7032i	0.367026	+	1.36976i	0.864654	+	0.502369i	$0.167538\pi$
$73$	3.13587	+	11.7032i	0.367026	+	1.36976i	−0.497628	+	0.867391i	$0.665795\pi$
$74$		0			0
$75$	−6.12182	+	0.805953i	−0.706887	+	0.0930635i
$76$		0			0
$77$	4.86398	+	2.80186i	0.554302	+	0.319301i
$78$		0			0
$79$	−2.02495	+	1.16910i	−0.227824	+	0.131534i	−0.609568	−	0.792734i	$-0.708657\pi$
$79$	−2.02495	+	1.16910i	−0.227824	+	0.131534i	0.381744	+	0.924268i	$0.375324\pi$
$80$		0			0
$81$	−2.22575	−	1.28504i	−0.247306	−	0.142782i
$82$		0			0
$83$	1.12785	−	0.467172i	0.123798	−	0.0512788i	−0.319925	−	0.947443i	$-0.603658\pi$
$83$	1.12785	−	0.467172i	0.123798	−	0.0512788i	0.443723	+	0.896164i	$0.353658\pi$
$84$		0			0
$85$	0.595009	−	1.43648i	0.0645378	−	0.155808i
$86$		0			0
$87$	−2.16052	−	8.06317i	−0.231632	−	0.864463i
$88$		0			0
$89$	4.29977	−	16.0470i	0.455775	−	1.70098i	−0.230025	−	0.973185i	$-0.573881\pi$
$89$	4.29977	−	16.0470i	0.455775	−	1.70098i	0.685800	−	0.727790i	$-0.259453\pi$
$90$		0			0
$91$	7.15305	−	7.16711i	0.749843	−	0.751317i
$92$		0			0
$93$	−3.74403	+	4.87931i	−0.388237	+	0.505961i
$94$		0			0
$95$	−0.382235	+	0.662051i	−0.0392165	+	0.0679250i
$96$		0			0
$97$	10.3954			1.05549			0.527746	−	0.849402i	$-0.323037\pi$
$97$	10.3954			1.05549			0.527746	+	0.849402i	$0.323037\pi$
$98$		0			0
$99$	−1.17415	−	2.83466i	−0.118007	−	0.284894i
$100$		0			0
$101$	−0.150926	+	0.115809i	−0.0150177	+	0.0115235i	−0.616243	−	0.787556i	$-0.711346\pi$
$101$	−0.150926	+	0.115809i	−0.0150177	+	0.0115235i	0.601225	+	0.799080i	$0.294679\pi$
$102$		0			0
$103$	0.0559668	−	0.208871i	0.00551457	−	0.0205807i	−0.963114	−	0.269095i	$-0.913276\pi$
$103$	0.0559668	−	0.208871i	0.00551457	−	0.0205807i	0.968628	+	0.248514i	$0.0799422\pi$
$104$		0			0
$105$	−0.272853	−	0.656901i	−0.0266277	−	0.0641070i
$106$		0			0
$107$	1.89770	−	0.249836i	0.183457	−	0.0241526i	−0.0382378	−	0.999269i	$-0.512174\pi$
$107$	1.89770	−	0.249836i	0.183457	−	0.0241526i	0.221695	+	0.975116i	$0.428841\pi$
$108$		0			0
$109$	−2.44544	+	18.5750i	−0.234231	+	1.77916i	0.320616	+	0.947209i	$0.396110\pi$
$109$	−2.44544	+	18.5750i	−0.234231	+	1.77916i	−0.554847	+	0.831952i	$0.687223\pi$
$110$		0			0
$111$			3.24575i			0.308073i
$112$		0			0
$113$		−	1.46473i		−	0.137790i	−0.997624	−	0.0688950i	$-0.978053\pi$
$113$		−	1.46473i		−	0.137790i	0.997624	−	0.0688950i	$-0.0219474\pi$
$114$		0			0
$115$	0.146411	−	1.11210i	0.0136529	−	0.103704i
$116$		0			0
$117$	−5.48747	+	0.722439i	−0.507317	+	0.0667895i
$118$		0			0
$119$	−18.9124	−	2.47098i	−1.73370	−	0.226514i
$120$		0			0
$121$	1.68200	−	6.27732i	0.152909	−	0.570665i
$122$		0			0
$123$	−6.03007	+	4.62704i	−0.543713	+	0.417206i
$124$		0			0
$125$	0.821534	+	1.98336i	0.0734802	+	0.177397i
$126$		0			0
$127$	−21.8084			−1.93518			−0.967590	−	0.252526i	$-0.918739\pi$
$127$	−21.8084			−1.93518			−0.967590	+	0.252526i	$0.918739\pi$
$128$		0			0
$129$	−6.77035	+	11.7266i	−0.596096	+	1.03247i
$130$		0			0
$131$	−3.62246	+	4.72088i	−0.316496	+	0.412465i	−0.924327	−	0.381601i	$-0.875373\pi$
$131$	−3.62246	+	4.72088i	−0.316496	+	0.412465i	0.607832	+	0.794066i	$0.292040\pi$
$132$		0			0
$133$	9.06060	+	2.41825i	0.785653	+	0.209689i
$134$		0			0
$135$	−0.309382	+	1.15463i	−0.0266273	+	0.0993746i
$136$		0			0
$137$	0.617217	+	2.30349i	0.0527324	+	0.196800i	0.987267	−	0.159073i	$-0.0508504\pi$
$137$	0.617217	+	2.30349i	0.0527324	+	0.196800i	−0.934534	+	0.355873i	$0.884184\pi$
$138$		0			0
$139$	0.998247	−	2.40998i	0.0846702	−	0.204412i	−0.875874	−	0.482541i	$-0.839714\pi$
$139$	0.998247	−	2.40998i	0.0846702	−	0.204412i	0.960544	+	0.278129i	$0.0897141\pi$
$140$		0			0
$141$	−6.26465	+	2.59490i	−0.527578	+	0.218530i
$142$		0			0
$143$	7.03203	+	4.05995i	0.588048	+	0.339510i
$144$		0			0
$145$	−1.25084	+	0.722173i	−0.103877	+	0.0599732i
$146$		0			0
$147$	−6.91211	+	5.32544i	−0.570101	+	0.439235i
$148$		0			0
$149$	−14.5682	+	1.91794i	−1.19347	+	0.157124i	−0.700972	−	0.713188i	$-0.747250\pi$
$149$	−14.5682	+	1.91794i	−1.19347	+	0.157124i	−0.492501	+	0.870312i	$0.663917\pi$
$150$		0			0
$151$	0.484316	+	1.80749i	0.0394131	+	0.147092i	0.982828	−	0.184522i	$-0.0590737\pi$
$151$	0.484316	+	1.80749i	0.0394131	+	0.147092i	−0.943415	+	0.331614i	$0.892407\pi$
$152$		0			0
$153$	7.37187	+	7.37187i	0.595980	+	0.595980i
$154$		0			0
$155$	0.983141	+	0.407230i	0.0789678	+	0.0327095i
$156$		0			0
$157$	1.78851	+	0.235462i	0.142739	+	0.0187919i	0.201557	−	0.979477i	$-0.435400\pi$
$157$	1.78851	+	0.235462i	0.142739	+	0.0187919i	−0.0588182	+	0.998269i	$0.518733\pi$
$158$		0			0
$159$	3.90125	+	6.75716i	0.309389	+	0.535878i
$160$		0			0
$161$	−13.6404	+	1.80942i	−1.07501	+	0.142602i
$162$		0			0
$163$	−8.36935	+	10.9072i	−0.655538	+	0.854314i	−0.996310	−	0.0858321i	$-0.972645\pi$
$163$	−8.36935	+	10.9072i	−0.655538	+	0.854314i	0.340771	+	0.940146i	$0.389312\pi$
$164$		0			0
$165$	0.452528	−	0.347237i	0.0352292	−	0.0270323i
$166$		0			0
$167$	0.443775	+	0.443775i	0.0343403	+	0.0343403i	0.724068	−	0.689728i	$-0.242270\pi$
$167$	0.443775	+	0.443775i	0.0343403	+	0.0343403i	−0.689728	+	0.724068i	$0.742270\pi$
$168$		0			0
$169$	1.16507	−	1.16507i	0.0896206	−	0.0896206i
$170$		0			0
$171$	−3.12045	−	4.06664i	−0.238626	−	0.310984i
$172$		0			0
$173$	3.25419	+	2.49703i	0.247411	+	0.189845i	0.725021	−	0.688727i	$-0.241830\pi$
$173$	3.25419	+	2.49703i	0.247411	+	0.189845i	−0.477610	+	0.878572i	$0.658497\pi$
$174$		0			0
$175$	10.3896	−	7.98844i	0.785380	−	0.603869i
$176$		0			0
$177$	−8.19404	+	4.73083i	−0.615902	+	0.355591i
$178$		0			0
$179$	−3.29920	+	25.0599i	−0.246594	+	1.87306i	0.202081	+	0.979369i	$0.435230\pi$
$179$	−3.29920	+	25.0599i	−0.246594	+	1.87306i	−0.448675	+	0.893695i	$0.648104\pi$
$180$		0			0
$181$	−1.08379	+	2.61651i	−0.0805578	+	0.194484i	−0.959027	−	0.283316i	$-0.908566\pi$
$181$	−1.08379	+	2.61651i	−0.0805578	+	0.194484i	0.878469	+	0.477800i	$0.158566\pi$
$182$		0			0
$183$	−0.726759	+	0.726759i	−0.0537236	+	0.0537236i
$184$		0			0
$185$	0.542460	−	0.145352i	0.0398825	−	0.0106865i
$186$		0			0
$187$	−1.99635	−	15.1638i	−0.145988	−	1.10889i
$188$		0			0
$189$	14.6635	−	0.0143950i	1.06661	−	0.00104708i
$190$		0			0
$191$	6.61571	+	11.4587i	0.478696	+	0.829125i	0.999702	−	0.0244277i	$-0.00777636\pi$
$191$	6.61571	+	11.4587i	0.478696	+	0.829125i	−0.521006	+	0.853553i	$0.674443\pi$
$192$		0			0
$193$	−1.04305	+	1.80661i	−0.0750803	+	0.130043i	−0.901121	−	0.433567i	$-0.857255\pi$
$193$	−1.04305	+	1.80661i	−0.0750803	+	0.130043i	0.826041	+	0.563610i	$0.190588\pi$
$194$		0			0
$195$	−0.393764	−	0.950631i	−0.0281980	−	0.0680761i
$196$		0			0
$197$	−17.8938	−	7.41186i	−1.27488	−	0.528073i	−0.360437	−	0.932784i	$-0.617372\pi$
$197$	−17.8938	−	7.41186i	−1.27488	−	0.528073i	−0.914445	+	0.404710i	$0.867372\pi$
$198$		0			0
$199$	−16.9330	+	4.53719i	−1.20035	+	0.321633i	−0.802969	−	0.596021i	$-0.796748\pi$
$199$	−16.9330	+	4.53719i	−1.20035	+	0.321633i	−0.397381	+	0.917654i	$0.630081\pi$
$200$		0			0
$201$	5.39787	+	1.44636i	0.380737	+	0.102018i
$202$		0			0
$203$	12.5407	+	12.5161i	0.880182	+	0.878455i
$204$		0			0
$205$	1.04335	+	0.800593i	0.0728710	+	0.0559159i
$206$		0			0
$207$	6.51352	+	3.76058i	0.452721	+	0.261378i
$208$		0			0
$209$			7.51997i			0.520167i
$210$		0			0
$211$	19.7231	−	8.16958i	1.35779	−	0.562417i	0.419343	−	0.907828i	$-0.362260\pi$
$211$	19.7231	−	8.16958i	1.35779	−	0.562417i	0.938452	+	0.345411i	$0.112260\pi$
$212$		0			0
$213$	−2.72303	−	3.54872i	−0.186579	−	0.243154i
$214$		0			0
$215$	2.26305	+	0.606382i	0.154339	+	0.0413549i
$216$		0			0
$217$	1.69116	−	12.9438i	0.114804	−	0.878686i
$218$		0			0
$219$	−1.97134	−	14.9738i	−0.133211	−	1.01184i
$220$		0			0
$221$	−27.3543	−	3.60126i	−1.84005	−	0.242247i
$222$		0			0
$223$	10.3561			0.693498			0.346749	−	0.937958i	$-0.387286\pi$
$223$	10.3561			0.693498			0.346749	+	0.937958i	$0.387286\pi$
$224$		0			0
$225$	−7.16358			−0.477572
$226$		0			0
$227$	17.6046	+	2.31769i	1.16846	+	0.153830i	0.689686	−	0.724109i	$-0.257749\pi$
$227$	17.6046	+	2.31769i	1.16846	+	0.153830i	0.478772	+	0.877939i	$0.341082\pi$
$228$		0			0
$229$	−1.58151	−	12.0128i	−0.104509	−	0.793826i	−0.960783	−	0.277303i	$-0.910559\pi$
$229$	−1.58151	−	12.0128i	−0.104509	−	0.793826i	0.856273	−	0.516523i	$-0.172774\pi$
$230$		0			0
$231$	−5.55534	−	4.25410i	−0.365514	−	0.279899i
$232$		0			0
$233$	−14.4304	−	3.86660i	−0.945364	−	0.253310i	−0.246970	−	0.969023i	$-0.579435\pi$
$233$	−14.4304	−	3.86660i	−0.945364	−	0.253310i	−0.698394	+	0.715713i	$0.746102\pi$
$234$		0			0
$235$	0.714229	+	0.930801i	0.0465911	+	0.0607188i
$236$		0			0
$237$	2.69277	−	1.11538i	0.174914	−	0.0724519i
$238$		0			0
$239$			25.1348i			1.62584i	0.582379	+	0.812918i	$0.302122\pi$
$239$			25.1348i			1.62584i	−0.582379	+	0.812918i	$0.697878\pi$
$240$		0			0
$241$	−11.2112	−	6.47277i	−0.722175	−	0.416948i	0.0933776	−	0.995631i	$-0.470234\pi$
$241$	−11.2112	−	6.47277i	−0.722175	−	0.416948i	−0.815553	+	0.578683i	$0.803567\pi$
$242$		0			0
$243$	−10.6493	−	8.17149i	−0.683152	−	0.524201i
$244$		0			0
$245$	1.19958	+	0.916732i	0.0766382	+	0.0585678i
$246$		0			0
$247$	13.1032	+	3.51100i	0.833738	+	0.223399i
$248$		0			0
$249$	−1.46988	+	0.393854i	−0.0931501	+	0.0249595i
$250$		0			0
$251$	2.13451	+	0.884142i	0.134729	+	0.0558065i	0.449029	−	0.893517i	$-0.351770\pi$
$251$	2.13451	+	0.884142i	0.134729	+	0.0558065i	−0.314300	+	0.949324i	$0.601770\pi$
$252$		0			0
$253$	−4.22251	−	10.1941i	−0.265467	−	0.640895i
$254$		0			0
$255$	−0.969071	+	1.67848i	−0.0606856	+	0.105110i
$256$		0			0
$257$	−7.31441	−	12.6689i	−0.456261	−	0.790267i	0.542499	−	0.840056i	$-0.317478\pi$
$257$	−7.31441	−	12.6689i	−0.456261	−	0.790267i	−0.998760	+	0.0497898i	$0.984145\pi$
$258$		0			0
$259$	−3.45041	−	5.96275i	−0.214398	−	0.370507i
$260$		0			0
$261$	−1.26409	−	9.60171i	−0.0782451	−	0.594331i
$262$		0			0
$263$	−11.5048	+	3.08270i	−0.709415	+	0.190087i	−0.595444	−	0.803397i	$-0.703024\pi$
$263$	−11.5048	+	3.08270i	−0.709415	+	0.190087i	−0.113971	+	0.993484i	$0.536357\pi$
$264$		0			0
$265$	0.954614	−	0.954614i	0.0586415	−	0.0586415i
$266$		0			0
$267$	−7.92484	+	19.1323i	−0.484992	+	1.17088i
$268$		0			0
$269$	−3.68346	+	27.9787i	−0.224585	+	1.70589i	0.393126	+	0.919485i	$0.371394\pi$
$269$	−3.68346	+	27.9787i	−0.224585	+	1.70589i	−0.617711	+	0.786405i	$0.711940\pi$
$270$		0			0
$271$	23.1368	−	13.3580i	1.40546	−	0.811443i	0.410514	−	0.911854i	$-0.365349\pi$
$271$	23.1368	−	13.3580i	1.40546	−	0.811443i	0.994946	+	0.100412i	$0.0320160\pi$
$272$		0			0
$273$	−10.0063	+	7.69373i	−0.605609	+	0.465646i
$274$		0			0
$275$	8.33764	+	6.39770i	0.502779	+	0.385796i
$276$		0			0
$277$	1.86140	+	2.42582i	0.111840	+	0.145753i	0.845919	−	0.533311i	$-0.179052\pi$
$277$	1.86140	+	2.42582i	0.111840	+	0.145753i	−0.734079	+	0.679064i	$0.762386\pi$
$278$		0			0
$279$	−5.04539	+	5.04539i	−0.302059	+	0.302059i
$280$		0			0
$281$	7.10678	+	7.10678i	0.423955	+	0.423955i	0.886563	−	0.462608i	$-0.153086\pi$
$281$	7.10678	+	7.10678i	0.423955	+	0.423955i	−0.462608	+	0.886563i	$0.653086\pi$
$282$		0			0
$283$	−21.5332	+	16.5230i	−1.28002	+	0.982191i	−0.280264	+	0.959923i	$0.590422\pi$
$283$	−21.5332	+	16.5230i	−1.28002	+	0.982191i	−0.999752	+	0.0222684i	$0.992911\pi$
$284$		0			0
$285$	0.580109	−	0.756013i	0.0343627	−	0.0447823i
$286$		0			0
$287$	6.15903	−	14.9106i	0.363556	−	0.880145i
$288$		0			0
$289$	17.4846	+	30.2842i	1.02851	+	1.78143i
$290$		0			0
$291$	−12.8473	−	1.69138i	−0.753121	−	0.0991502i
$292$		0			0
$293$	12.9251	+	5.35374i	0.755091	+	0.312769i	0.726817	−	0.686831i	$-0.240999\pi$
$293$	12.9251	+	5.35374i	0.755091	+	0.312769i	0.0282738	+	0.999600i	$0.490999\pi$
$294$		0			0
$295$	1.15761	+	1.15761i	0.0673985	+	0.0673985i
$296$		0			0
$297$	3.04334	+	11.3579i	0.176592	+	0.659052i
$298$		0			0
$299$	−19.7341	+	2.59805i	−1.14125	+	0.150249i
$300$		0			0
$301$	−0.0282140	−	28.7401i	−0.00162623	−	1.65655i
$302$		0			0
$303$	0.205366	−	0.118568i	0.0117980	−	0.00681156i
$304$		0			0
$305$	0.154009	+	0.0889170i	0.00881851	+	0.00509137i
$306$		0			0
$307$	−5.63314	+	2.33332i	−0.321500	+	0.133170i	−0.537596	−	0.843202i	$-0.680668\pi$
$307$	−5.63314	+	2.33332i	−0.321500	+	0.133170i	0.216096	+	0.976372i	$0.430668\pi$
$308$		0			0
$309$	−0.103151	+	0.249030i	−0.00586808	+	0.0141668i
$310$		0			0
$311$	−5.11219	−	19.0790i	−0.289886	−	1.08187i	−0.945195	−	0.326508i	$-0.894128\pi$
$311$	−5.11219	−	19.0790i	−0.289886	−	1.08187i	0.655309	−	0.755361i	$-0.272539\pi$
$312$		0			0
$313$	−3.33645	+	12.4518i	−0.188587	+	0.703817i	0.805247	+	0.592939i	$0.202033\pi$
$313$	−3.33645	+	12.4518i	−0.188587	+	0.703817i	−0.993834	+	0.110877i	$0.964634\pi$
$314$		0			0
$315$	−0.214370	−	0.796908i	−0.0120784	−	0.0449007i
$316$		0			0
$317$	8.40379	−	10.9520i	0.472004	−	0.615127i	−0.495308	−	0.868717i	$-0.664945\pi$
$317$	8.40379	−	10.9520i	0.472004	−	0.615127i	0.967312	+	0.253590i	$0.0816114\pi$
$318$		0			0
$319$	−7.10389	+	12.3043i	−0.397742	+	0.688909i
$320$		0			0
$321$	−2.38594			−0.133170
$322$		0			0
$323$	−9.77829	−	23.6069i	−0.544079	−	1.31352i
$324$		0			0
$325$	15.0405	−	11.5410i	0.834295	−	0.640177i
$326$		0			0
$327$	6.04447	−	22.5583i	0.334260	−	1.24747i
$328$		0			0
$329$	8.75023	−	11.4267i	0.482416	−	0.629976i
$330$		0			0
$331$	11.8202	−	1.55616i	0.649699	−	0.0855345i	0.201528	−	0.979483i	$-0.435409\pi$
$331$	11.8202	−	1.55616i	0.649699	−	0.0855345i	0.448170	+	0.893948i	$0.352076\pi$
$332$		0			0
$333$	−0.491508	+	3.73338i	−0.0269345	+	0.204588i
$334$		0			0
$335$		−	0.966914i		−	0.0528282i
$336$		0			0
$337$			6.88603i			0.375106i	0.982254	+	0.187553i	$0.0600556\pi$
$337$			6.88603i			0.375106i	−0.982254	+	0.187553i	$0.939944\pi$
$338$		0			0
$339$	−0.238318	+	1.81020i	−0.0129436	+	0.0983168i
$340$		0			0
$341$	10.3783	−	1.36632i	0.562014	−	0.0739906i
$342$		0			0
$343$	7.03697	−	17.1313i	0.379961	−	0.925003i
$344$		0			0
$345$	−0.361888	+	1.35058i	−0.0194834	+	0.0727130i
$346$		0			0
$347$	15.1597	−	11.6325i	0.813816	−	0.624463i	−0.115684	−	0.993286i	$-0.536906\pi$
$347$	15.1597	−	11.6325i	0.813816	−	0.624463i	0.929500	+	0.368823i	$0.120239\pi$
$348$		0			0
$349$	−6.87406	−	16.5955i	−0.367960	−	0.888334i	−0.994084	−	0.108611i	$-0.965360\pi$
$349$	−6.87406	−	16.5955i	−0.367960	−	0.888334i	0.626124	−	0.779723i	$-0.284640\pi$
$350$		0			0
$351$	21.2115			1.13219
$352$		0			0
$353$	8.34381	−	14.4519i	0.444096	−	0.769197i	−0.553893	−	0.832588i	$-0.686858\pi$
$353$	8.34381	−	14.4519i	0.444096	−	0.769197i	0.997989	+	0.0633910i	$0.0201915\pi$
$354$		0			0
$355$	−0.471152	+	0.614017i	−0.0250061	+	0.0325886i
$356$		0			0
$357$	22.9711	+	6.13092i	1.21576	+	0.324483i
$358$		0			0
$359$	−1.85119	+	6.90872i	−0.0977019	+	0.364628i	−0.997415	−	0.0718529i	$-0.977109\pi$
$359$	−1.85119	+	6.90872i	−0.0977019	+	0.364628i	0.899713	+	0.436481i	$0.143775\pi$
$360$		0			0
$361$	−1.66597	−	6.21748i	−0.0876825	−	0.327236i
$362$		0			0
$363$	−3.10007	+	7.48424i	−0.162712	+	0.392821i
$364$		0			0
$365$	−2.41428	+	1.00003i	−0.126369	+	0.0523439i
$366$		0			0
$367$	−6.59509	−	3.80767i	−0.344261	−	0.198759i	0.317894	−	0.948126i	$-0.397024\pi$
$367$	−6.59509	−	3.80767i	−0.344261	−	0.198759i	−0.662155	+	0.749367i	$0.730358\pi$
$368$		0			0
$369$	−7.63668	+	4.40904i	−0.397549	+	0.229525i
$370$		0			0
$371$	−14.3502	−	8.26631i	−0.745025	−	0.429166i
$372$		0			0
$373$	32.3178	−	4.25471i	1.67335	−	0.220301i	0.766647	−	0.642069i	$-0.221924\pi$
$373$	32.3178	−	4.25471i	1.67335	−	0.220301i	0.906704	+	0.421768i	$0.138590\pi$
$374$		0			0
$375$	−0.692602	−	2.58483i	−0.0357658	−	0.133480i
$376$		0			0
$377$	18.1230	+	18.1230i	0.933381	+	0.933381i
$378$		0			0
$379$	−12.9076	−	5.34651i	−0.663020	−	0.274632i	0.0256886	−	0.999670i	$-0.491822\pi$
$379$	−12.9076	−	5.34651i	−0.663020	−	0.274632i	−0.688709	+	0.725038i	$0.741822\pi$
$380$		0			0
$381$	26.9522	+	3.54832i	1.38080	+	0.181786i
$382$		0			0
$383$	−9.79069	−	16.9580i	−0.500281	−	0.866512i	−1.00000		0.000324324i	$-0.999897\pi$
$383$	−9.79069	−	16.9580i	−0.500281	−	0.866512i	0.499719	−	0.866188i	$-0.333437\pi$
$384$		0			0
$385$	−0.462205	+	1.11897i	−0.0235562	+	0.0570279i
$386$		0			0
$387$	−9.56327	+	12.4631i	−0.486128	+	0.633535i
$388$		0			0
$389$	−17.7867	+	13.6482i	−0.901821	+	0.691992i	−0.951787	−	0.306759i	$-0.900755\pi$
$389$	−17.7867	+	13.6482i	−0.901821	+	0.691992i	0.0499661	+	0.998751i	$0.484089\pi$
$390$		0			0
$391$	26.5108	+	26.5108i	1.34071	+	1.34071i
$392$		0			0
$393$	5.24497	−	5.24497i	0.264574	−	0.264574i
$394$		0			0
$395$	−0.307002	−	0.400092i	−0.0154469	−	0.0201308i
$396$		0			0
$397$	26.4656	+	20.3077i	1.32827	+	1.01922i	0.997136	+	0.0756324i	$0.0240976\pi$
$397$	26.4656	+	20.3077i	1.32827	+	1.01922i	0.331133	+	0.943584i	$0.392569\pi$
$398$		0			0
$399$	−10.8042	−	4.46282i	−0.540886	−	0.223421i
$400$		0			0
$401$	9.46637	−	5.46541i	0.472728	−	0.272930i	−0.244653	−	0.969611i	$-0.578674\pi$
$401$	9.46637	−	5.46541i	0.472728	−	0.272930i	0.717381	+	0.696681i	$0.245341\pi$
$402$		0			0
$403$	2.46474	−	18.7216i	0.122778	−	0.932588i
$404$		0			0
$405$	0.212127	−	0.512121i	0.0105407	−	0.0254475i
$406$		0			0
$407$	3.90629	−	3.90629i	0.193628	−	0.193628i
$408$		0			0
$409$	−25.1058	+	6.72708i	−1.24140	+	0.332632i	−0.819009	−	0.573781i	$-0.805476\pi$
$409$	−25.1058	+	6.72708i	−1.24140	+	0.332632i	−0.422392	+	0.906413i	$0.638810\pi$
$410$		0			0
$411$	−0.388008	−	2.94722i	−0.0191390	−	0.145375i
$412$		0			0
$413$	10.0241	−	17.4017i	0.493254	−	0.856281i
$414$		0			0
$415$	0.131649	+	0.228023i	0.00646240	+	0.0111932i
$416$		0			0
$417$	−1.62581	+	2.81599i	−0.0796163	+	0.137900i
$418$		0			0
$419$	10.8125	+	26.1038i	0.528227	+	1.27525i	0.932683	+	0.360696i	$0.117461\pi$
$419$	10.8125	+	26.1038i	0.528227	+	1.27525i	−0.404456	+	0.914558i	$0.632539\pi$
$420$		0			0
$421$	−34.0793	−	14.1161i	−1.66092	−	0.687977i	−0.662776	−	0.748818i	$-0.730622\pi$
$421$	−34.0793	−	14.1161i	−1.66092	−	0.687977i	−0.998147	+	0.0608405i	$0.980622\pi$
$422$		0			0
$423$	−7.59876	+	2.03608i	−0.369464	+	0.0989977i
$424$		0			0
$425$	−34.4927	−	9.24230i	−1.67314	−	0.448317i
$426$		0			0
$427$	0.562542	−	2.10771i	0.0272233	−	0.101999i
$428$		0			0
$429$	−8.03006	−	6.16168i	−0.387695	−	0.297489i
$430$		0			0
$431$	−15.8972	−	9.17826i	−0.765742	−	0.442101i	0.0656118	−	0.997845i	$-0.479100\pi$
$431$	−15.8972	−	9.17826i	−0.765742	−	0.442101i	−0.831353	+	0.555744i	$0.812433\pi$
$432$		0			0
$433$			10.6987i			0.514148i	0.966392	+	0.257074i	$0.0827584\pi$
$433$			10.6987i			0.514148i	−0.966392	+	0.257074i	$0.917242\pi$
$434$		0			0
$435$	1.66337	−	0.688989i	0.0797523	−	0.0330345i
$436$		0			0
$437$	−11.2218	−	14.6245i	−0.536812	−	0.699586i
$438$		0			0
$439$	36.0240	+	9.65259i	1.71933	+	0.460693i	0.977681	−	0.210096i	$-0.0673775\pi$
$439$	36.0240	+	9.65259i	1.71933	+	0.460693i	0.741649	+	0.670788i	$0.234044\pi$
$440$		0			0
$441$	−8.75699	+	5.07880i	−0.416999	+	0.241848i
$442$		0			0
$443$	0.833004	+	6.32729i	0.0395772	+	0.300619i	0.999773	+	0.0212919i	$0.00677794\pi$
$443$	0.833004	+	6.32729i	0.0395772	+	0.300619i	−0.960196	+	0.279327i	$0.909889\pi$
$444$		0			0
$445$	3.55245	+	0.467689i	0.168402	+	0.0221706i
$446$		0			0
$447$	18.3163			0.866334
$448$		0			0
$449$	20.8650			0.984680			0.492340	−	0.870403i	$-0.336142\pi$
$449$	20.8650			0.984680			0.492340	+	0.870403i	$0.336142\pi$
$450$		0			0
$451$	12.8259	+	1.68857i	0.603950	+	0.0795115i
$452$		0			0
$453$	−0.304461	−	2.31261i	−0.0143048	−	0.108656i
$454$		0			0
$455$	1.73395	+	1.32781i	0.0812889	+	0.0622485i
$456$		0			0
$457$	2.30563	+	0.617791i	0.107853	+	0.0288990i	0.312342	−	0.949970i	$-0.398887\pi$
$457$	2.30563	+	0.617791i	0.107853	+	0.0288990i	−0.204489	+	0.978869i	$0.565553\pi$
$458$		0			0
$459$	−24.3225	−	31.6977i	−1.13528	−	1.47952i
$460$		0			0
$461$	−14.7405	+	6.10571i	−0.686533	+	0.284371i	−0.698555	−	0.715556i	$-0.746173\pi$
$461$	−14.7405	+	6.10571i	−0.686533	+	0.284371i	0.0120219	+	0.999928i	$0.496173\pi$
$462$		0			0
$463$			2.04572i			0.0950725i	0.998870	+	0.0475362i	$0.0151370\pi$
$463$			2.04572i			0.0950725i	−0.998870	+	0.0475362i	$0.984863\pi$
$464$		0			0
$465$	−1.14877	−	0.663242i	−0.0532729	−	0.0307571i
$466$		0			0
$467$	−21.1512	−	16.2299i	−0.978762	−	0.751031i	−0.0102375	−	0.999948i	$-0.503259\pi$
$467$	−21.1512	−	16.2299i	−0.978762	−	0.751031i	−0.968525	+	0.248917i	$0.919925\pi$
$468$		0			0
$469$	−11.4540	+	3.08113i	−0.528895	+	0.142274i
$470$		0			0
$471$	−2.17204	−	0.581997i	−0.100082	−	0.0268170i
$472$		0			0
$473$	22.2612	−	5.96488i	1.02357	−	0.274266i
$474$		0			0
$475$	16.2209	+	6.71893i	0.744268	+	0.308286i
$476$		0			0
$477$	3.46411	+	8.36309i	0.158611	+	0.382920i
$478$		0			0
$479$	−3.11186	+	5.38989i	−0.142184	+	0.246270i	−0.928319	−	0.371785i	$-0.878746\pi$
$479$	−3.11186	+	5.38989i	−0.142184	+	0.246270i	0.786135	+	0.618055i	$0.212079\pi$
$480$		0			0
$481$	−4.98273	−	8.63035i	−0.227193	−	0.393510i
$482$		0			0
$483$	17.1520	−	0.0168380i	0.780445	−	0.000766157i
$484$		0			0
$485$	0.292650	+	2.22290i	0.0132886	+	0.100937i
$486$		0			0
$487$	26.9723	−	7.22721i	1.22223	−	0.327496i	0.410682	−	0.911778i	$-0.365291\pi$
$487$	26.9723	−	7.22721i	1.22223	−	0.327496i	0.811551	+	0.584282i	$0.198624\pi$
$488$		0			0
$489$	12.1180	−	12.1180i	0.547995	−	0.547995i
$490$		0			0
$491$	6.95705	−	16.7958i	0.313967	−	0.757984i	−0.685583	−	0.727994i	$-0.740453\pi$
$491$	6.95705	−	16.7958i	0.313967	−	0.757984i	0.999550	−	0.0299894i	$-0.00954734\pi$
$492$		0			0
$493$	6.30132	−	47.8632i	0.283797	−	2.15565i
$494$		0			0
$495$	0.573095	−	0.330877i	0.0257587	−	0.0148718i
$496$		0			0
$497$	8.77493	+	3.62461i	0.393610	+	0.162586i
$498$		0			0
$499$	−3.49724	−	2.68352i	−0.156558	−	0.120131i	0.527512	−	0.849548i	$-0.323125\pi$
$499$	−3.49724	−	2.68352i	−0.156558	−	0.120131i	−0.684070	+	0.729417i	$0.739792\pi$
$500$		0			0
$501$	−0.476241	−	0.620649i	−0.0212769	−	0.0277285i
$502$		0			0
$503$	2.85777	−	2.85777i	0.127422	−	0.127422i	−0.640520	−	0.767942i	$-0.721281\pi$
$503$	2.85777	−	2.85777i	0.127422	−	0.127422i	0.767942	+	0.640520i	$0.221281\pi$
$504$		0			0
$505$	−0.0290129	−	0.0290129i	−0.00129106	−	0.00129106i
$506$		0			0
$507$	−1.62943	+	1.25030i	−0.0723654	+	0.0555279i
$508$		0			0
$509$	−19.6105	+	25.5569i	−0.869220	+	1.13279i	0.120914	+	0.992663i	$0.461417\pi$
$509$	−19.6105	+	25.5569i	−0.869220	+	1.13279i	−0.990134	+	0.140126i	$0.955249\pi$
$510$		0			0
$511$	19.5395	+	25.4127i	0.864376	+	1.12419i
$512$		0			0
$513$	9.82218	+	17.0125i	0.433660	+	0.751121i
$514$		0			0
$515$	0.0462395	+	0.00608755i	0.00203756	+	0.000268249i
$516$		0			0
$517$	10.6625	+	4.41657i	0.468938	+	0.194241i
$518$		0			0
$519$	−3.61545	−	3.61545i	−0.158701	−	0.158701i
$520$		0			0
$521$	9.23441	+	34.4633i	0.404567	+	1.50986i	0.804853	+	0.593474i	$0.202244\pi$
$521$	9.23441	+	34.4633i	0.404567	+	1.50986i	−0.400286	+	0.916390i	$0.631089\pi$
$522$		0			0
$523$	−18.1689	+	2.39198i	−0.794470	+	0.104594i	−0.516826	−	0.856090i	$-0.672887\pi$
$523$	−18.1689	+	2.39198i	−0.794470	+	0.104594i	−0.277644	+	0.960684i	$0.589553\pi$
$524$		0			0
$525$	−14.1399	+	8.18218i	−0.617115	+	0.357100i
$526$		0			0
$527$	−30.8030	+	17.7841i	−1.34180	+	0.774690i
$528$		0			0
$529$	3.50544	+	2.02387i	0.152410	+	0.0879941i
$530$		0			0
$531$	−10.1415	+	4.20073i	−0.440102	+	0.182296i
$532$		0			0
$533$	8.93055	−	21.5602i	0.386825	−	0.933878i
$534$		0			0
$535$	0.106848	+	0.398761i	0.00461943	+	0.0172399i
$536$		0			0
$537$	8.15471	−	30.4338i	0.351902	−	1.31331i
$538$		0			0
$539$	14.7280	+	1.90957i	0.634380	+	0.0822510i
$540$		0			0
$541$	−12.8794	+	16.7847i	−0.553728	+	0.721632i	−0.983420	−	0.181343i	$-0.941956\pi$
$541$	−12.8794	+	16.7847i	−0.553728	+	0.721632i	0.429692	+	0.902976i	$0.358622\pi$
$542$		0			0
$543$	1.76514	−	3.05731i	0.0757493	−	0.131202i
$544$		0			0
$545$	−4.04083			−0.173090
$546$		0			0
$547$	−2.99246	−	7.22444i	−0.127948	−	0.308895i	0.846904	−	0.531746i	$-0.178464\pi$
$547$	−2.99246	−	7.22444i	−0.127948	−	0.308895i	−0.974853	+	0.222851i	$0.928464\pi$
$548$		0			0
$549$	−0.945998	+	0.725890i	−0.0403742	+	0.0309802i
$550$		0			0
$551$	−6.14337	+	22.9274i	−0.261716	+	0.976739i
$552$		0			0
$553$	−3.76117	+	4.91163i	−0.159941	+	0.208864i
$554$		0			0
$555$	−0.694056	+	0.0913742i	−0.0294610	+	0.00387862i
$556$		0			0
$557$	3.26236	−	24.7801i	0.138231	−	1.04997i	−0.771929	−	0.635709i	$-0.780708\pi$
$557$	3.26236	−	24.7801i	0.138231	−	1.04997i	0.910160	−	0.414258i	$-0.135959\pi$
$558$		0			0
$559$		−	41.5742i		−	1.75840i
$560$		0			0
$561$			19.0652i			0.804933i
$562$		0			0
$563$	−0.780096	+	5.92542i	−0.0328771	+	0.249727i	−0.999989	−	0.00462359i	$-0.998528\pi$
$563$	−0.780096	+	5.92542i	−0.0328771	+	0.249727i	0.967112	+	0.254350i	$0.0818616\pi$
$564$		0			0
$565$	0.313211	−	0.0412350i	0.0131769	−	0.00173477i
$566$		0			0
$567$	−6.74249	−	0.880932i	−0.283158	−	0.0369957i
$568$		0			0
$569$	−10.6691	+	39.8176i	−0.447272	+	1.66924i	0.262596	+	0.964906i	$0.415421\pi$
$569$	−10.6691	+	39.8176i	−0.447272	+	1.66924i	−0.709868	+	0.704335i	$0.751245\pi$
$570$		0			0
$571$	−11.1013	+	8.51831i	−0.464574	+	0.356480i	−0.814370	−	0.580346i	$-0.802917\pi$
$571$	−11.1013	+	8.51831i	−0.464574	+	0.356480i	0.349796	+	0.936826i	$0.386251\pi$
$572$		0			0
$573$	−6.31172	−	15.2378i	−0.263676	−	0.636570i
$574$		0			0
$575$	−25.7618			−1.07434
$576$		0			0
$577$	22.6075	−	39.1574i	0.941164	−	1.63014i	0.177908	−	0.984047i	$-0.443067\pi$
$577$	22.6075	−	39.1574i	0.941164	−	1.63014i	0.763256	−	0.646096i	$-0.223600\pi$
$578$		0			0
$579$	1.58301	−	2.06302i	0.0657876	−	0.0857361i
$580$		0			0
$581$	2.28163	−	2.28611i	0.0946579	−	0.0948439i
$582$		0			0
$583$	3.43712	−	12.8275i	0.142351	−	0.531261i
$584$		0			0
$585$	−0.308966	−	1.15308i	−0.0127742	−	0.0476738i
$586$		0			0
$587$	12.3455	−	29.8048i	0.509555	−	1.23017i	−0.434585	−	0.900631i	$-0.643105\pi$
$587$	12.3455	−	29.8048i	0.509555	−	1.23017i	0.944140	−	0.329544i	$-0.106895\pi$
$588$		0			0
$589$	16.1568	−	6.69237i	0.665729	−	0.275754i
$590$		0			0
$591$	20.9084	+	12.0714i	0.860055	+	0.496553i
$592$		0			0
$593$	22.6591	−	13.0822i	0.930498	−	0.537223i	0.0435290	−	0.999052i	$-0.486140\pi$
$593$	22.6591	−	13.0822i	0.930498	−	0.537223i	0.886969	+	0.461829i	$0.152807\pi$
$594$		0			0
$595$	−0.00403839	−	4.11370i	−0.000165558	−	0.168645i
$596$		0			0
$597$	21.6651	−	2.85227i	0.886694	−	0.116735i
$598$		0			0
$599$	9.19109	+	34.3016i	0.375538	+	1.40153i	0.852558	+	0.522633i	$0.175050\pi$
$599$	9.19109	+	34.3016i	0.375538	+	1.40153i	−0.477020	+	0.878893i	$0.658283\pi$
$600$		0			0
$601$	−2.58840	−	2.58840i	−0.105583	−	0.105583i	0.652342	−	0.757925i	$-0.273787\pi$
$601$	−2.58840	−	2.58840i	−0.105583	−	0.105583i	−0.757925	+	0.652342i	$0.773787\pi$
$602$		0			0
$603$	5.98980	+	2.48106i	0.243923	+	0.101036i
$604$		0			0
$605$	1.38966	+	0.182953i	0.0564979	+	0.00743808i
$606$		0			0
$607$	−1.10527	−	1.91438i	−0.0448614	−	0.0777021i	0.842723	−	0.538348i	$-0.180951\pi$
$607$	−1.10527	−	1.91438i	−0.0448614	−	0.0777021i	−0.887584	+	0.460646i	$0.847618\pi$
$608$		0			0
$609$	−13.4621	−	17.5086i	−0.545512	−	0.709482i
$610$		0			0
$611$	12.6739	−	16.5170i	0.512732	−	0.668205i
$612$		0			0
$613$	−13.4056	+	10.2865i	−0.541449	+	0.415468i	−0.842945	−	0.537999i	$-0.819180\pi$
$613$	−13.4056	+	10.2865i	−0.541449	+	0.415468i	0.301497	+	0.953467i	$0.402514\pi$
$614$		0			0
$615$	−1.15918	−	1.15918i	−0.0467427	−	0.0467427i
$616$		0			0
$617$	6.83969	−	6.83969i	0.275356	−	0.275356i	−0.555896	−	0.831252i	$-0.687625\pi$
$617$	6.83969	−	6.83969i	0.275356	−	0.275356i	0.831252	+	0.555896i	$0.187625\pi$
$618$		0			0
$619$	27.1357	+	35.3640i	1.09068	+	1.42140i	0.897924	+	0.440151i	$0.145075\pi$
$619$	27.1357	+	35.3640i	1.09068	+	1.42140i	0.192753	+	0.981247i	$0.438258\pi$
$620$		0			0
$621$	−22.8676	−	17.5469i	−0.917644	−	0.704133i
$622$		0			0
$623$	−5.77992	−	43.5723i	−0.231568	−	1.74569i
$624$		0			0
$625$	21.0482	−	12.1522i	0.841929	−	0.486088i
$626$		0			0
$627$	1.22353	−	9.29365i	0.0488632	−	0.371153i
$628$		0			0
$629$	−7.18334	+	17.3421i	−0.286418	+	0.691475i
$630$		0			0
$631$	−5.38193	+	5.38193i	−0.214251	+	0.214251i	−0.806071	−	0.591819i	$-0.798410\pi$
$631$	−5.38193	+	5.38193i	−0.214251	+	0.214251i	0.591819	+	0.806071i	$0.298410\pi$
$632$		0			0
$633$	−25.7043	+	6.88744i	−1.02165	+	0.273751i
$634$		0			0
$635$	−0.613948	−	4.66340i	−0.0243638	−	0.185061i
$636$		0			0
$637$	10.2037	−	24.7713i	0.404285	−	0.981477i
$638$		0			0
$639$	−2.59473	−	4.49421i	−0.102646	−	0.177788i
$640$		0			0
$641$	1.28693	−	2.22903i	0.0508308	−	0.0880415i	−0.839490	−	0.543374i	$-0.817146\pi$
$641$	1.28693	−	2.22903i	0.0508308	−	0.0880415i	0.890321	+	0.455333i	$0.150480\pi$
$642$		0			0
$643$	−11.0924	−	26.7793i	−0.437440	−	1.05607i	−0.976830	−	0.214018i	$-0.931345\pi$
$643$	−11.0924	−	26.7793i	−0.437440	−	1.05607i	0.539390	−	0.842056i	$-0.318655\pi$
$644$		0			0
$645$	−2.69816	−	1.11761i	−0.106240	−	0.0440060i
$646$		0			0
$647$	−10.8178	+	2.89861i	−0.425291	+	0.113956i	−0.465115	−	0.885250i	$-0.653987\pi$
$647$	−10.8178	+	2.89861i	−0.425291	+	0.113956i	0.0398241	+	0.999207i	$0.487320\pi$
$648$		0			0
$649$	15.5552	+	4.16800i	0.610595	+	0.163608i
$650$		0			0
$651$	−4.19607	+	15.7217i	−0.164457	+	0.616181i
$652$		0			0
$653$	13.4430	+	10.3152i	0.526067	+	0.403665i	0.837363	−	0.546648i	$-0.184096\pi$
$653$	13.4430	+	10.3152i	0.526067	+	0.403665i	−0.311296	+	0.950313i	$0.600763\pi$
$654$		0			0
$655$	−1.11147	−	0.641707i	−0.0434287	−	0.0250736i
$656$		0			0
$657$		−	17.5219i		−	0.683595i
$658$		0			0
$659$	1.75225	−	0.725805i	0.0682579	−	0.0282734i	−0.348293	−	0.937386i	$-0.613239\pi$
$659$	1.75225	−	0.725805i	0.0682579	−	0.0282734i	0.416551	+	0.909112i	$0.363239\pi$
$660$		0			0
$661$	3.00833	+	3.92053i	0.117010	+	0.152491i	0.848186	−	0.529698i	$-0.177695\pi$
$661$	3.00833	+	3.92053i	0.117010	+	0.152491i	−0.731176	+	0.682189i	$0.761028\pi$
$662$		0			0
$663$	33.2202	+	8.90133i	1.29017	+	0.345699i
$664$		0			0
$665$	−0.262033	+	2.00555i	−0.0101612	+	0.0777720i
$666$		0			0
$667$	−4.54594	−	34.5298i	−0.176019	−	1.33700i
$668$		0			0
$669$	−12.7988	−	1.68499i	−0.494829	−	0.0651454i
$670$		0			0
$671$	1.74932			0.0675319
$672$		0			0
$673$	16.2083			0.624784			0.312392	−	0.949953i	$-0.398870\pi$
$673$	16.2083			0.624784			0.312392	+	0.949953i	$0.398870\pi$
$674$		0			0
$675$	27.2187	+	3.58341i	1.04765	+	0.137925i
$676$		0			0
$677$	4.66116	+	35.4051i	0.179143	+	1.36073i	0.810729	+	0.585421i	$0.199071\pi$
$677$	4.66116	+	35.4051i	0.179143	+	1.36073i	−0.631586	+	0.775306i	$0.717596\pi$
$678$		0			0
$679$	25.3997	−	10.5501i	0.974751	−	0.404876i
$680$		0			0
$681$	−21.3798	−	5.72869i	−0.819274	−	0.219524i
$682$		0			0
$683$	11.6723	+	15.2117i	0.446630	+	0.582059i	0.961360	−	0.275293i	$-0.0887748\pi$
$683$	11.6723	+	15.2117i	0.446630	+	0.582059i	−0.514731	+	0.857352i	$0.672108\pi$
$684$		0			0
$685$	−0.475191	+	0.196830i	−0.0181561	+	0.00752050i
$686$		0			0
$687$			15.1034i			0.576232i
$688$		0			0
$689$	−20.7466	−	11.9781i	−0.790382	−	0.456328i
$690$		0			0
$691$	6.45893	+	4.95611i	0.245709	+	0.188539i	0.724273	−	0.689514i	$-0.242176\pi$
$691$	6.45893	+	4.95611i	0.245709	+	0.188539i	−0.478563	+	0.878053i	$0.658842\pi$
$692$		0			0
$693$	−5.74573	−	5.73446i	−0.218262	−	0.217834i
$694$		0			0
$695$	0.543442	+	0.145615i	0.0206139	+	0.00552348i
$696$		0			0
$697$	−42.4591	+	11.3769i	−1.60825	+	0.430931i
$698$		0			0
$699$	17.2048	+	7.12648i	0.650747	+	0.269548i
$700$		0			0
$701$	6.09108	+	14.7052i	0.230057	+	0.555407i	0.996184	−	0.0872829i	$-0.0278184\pi$
$701$	6.09108	+	14.7052i	0.230057	+	0.555407i	−0.766126	+	0.642690i	$0.777818\pi$
$702$		0			0
$703$	4.61460	−	7.99271i	0.174043	−	0.301451i
$704$		0			0
$705$	−0.731243	−	1.26655i	−0.0275402	−	0.0477011i
$706$		0			0
$707$	−0.251233	+	0.436136i	−0.00944857	+	0.0164026i
$708$		0			0
$709$	−1.05364	−	8.00319i	−0.0395703	−	0.300566i	−0.999774	−	0.0212652i	$-0.993231\pi$
$709$	−1.05364	−	8.00319i	−0.0395703	−	0.300566i	0.960204	−	0.279301i	$-0.0901028\pi$
$710$		0			0
$711$	3.26622	−	0.875182i	0.122493	−	0.0328219i
$712$		0			0
$713$	−18.1443	+	18.1443i	−0.679510	+	0.679510i
$714$		0			0
$715$	−0.670194	+	1.61799i	−0.0250638	+	0.0605094i
$716$		0			0
$717$	4.08954	−	31.0632i	0.152727	−	1.16008i
$718$		0			0
$719$	−23.7592	+	13.7174i	−0.886069	+	0.511572i	−0.872655	−	0.488338i	$-0.837603\pi$
$719$	−23.7592	+	13.7174i	−0.886069	+	0.511572i	−0.0134141	+	0.999910i	$0.504270\pi$
$720$		0			0
$721$	−0.0752327	−	0.567146i	−0.00280181	−	0.0211216i
$722$		0			0
$723$	12.8023	+	9.82357i	0.476124	+	0.365342i
$724$		0			0
$725$	20.1938	+	26.3171i	0.749979	+	0.977392i
$726$		0			0
$727$	−37.3364	+	37.3364i	−1.38473	+	1.38473i	−0.548736	+	0.835996i	$0.684891\pi$
$727$	−37.3364	+	37.3364i	−1.38473	+	1.38473i	−0.835996	+	0.548736i	$0.815109\pi$
$728$		0			0
$729$	17.2835	+	17.2835i	0.640129	+	0.640129i
$730$		0			0
$731$	−62.1269	+	47.6716i	−2.29784	+	1.76320i
$732$		0			0
$733$	−15.4846	+	20.1799i	−0.571937	+	0.745362i	−0.986338	−	0.164732i	$-0.947324\pi$
$733$	−15.4846	+	20.1799i	−0.571937	+	0.745362i	0.414402	+	0.910094i	$0.363991\pi$
$734$		0			0
$735$	−1.33336	−	1.32813i	−0.0491816	−	0.0489889i
$736$		0			0
$737$	−4.75569	−	8.23710i	−0.175178	−	0.303417i
$738$		0			0
$739$	−11.4931	−	1.51310i	−0.422781	−	0.0556602i	−0.0838659	−	0.996477i	$-0.526727\pi$
$739$	−11.4931	−	1.51310i	−0.422781	−	0.0556602i	−0.338916	+	0.940817i	$0.610060\pi$
$740$		0			0
$741$	−15.6225	−	6.47106i	−0.573908	−	0.237720i
$742$		0			0
$743$	−1.78374	−	1.78374i	−0.0654392	−	0.0654392i	0.673630	−	0.739069i	$-0.264734\pi$
$743$	−1.78374	−	1.78374i	−0.0654392	−	0.0654392i	−0.739069	+	0.673630i	$0.764734\pi$
$744$		0			0
$745$	−0.820246	−	3.06120i	−0.0300515	−	0.112154i
$746$		0			0
$747$	−1.75035	+	0.230438i	−0.0640420	+	0.00843130i
$748$		0			0
$749$	4.38320	−	2.53638i	0.160159	−	0.0926774i
$750$		0			0
$751$	−21.1263	+	12.1973i	−0.770911	+	0.445085i	−0.833199	−	0.552973i	$-0.813493\pi$
$751$	−21.1263	+	12.1973i	−0.770911	+	0.445085i	0.0622888	+	0.998058i	$0.480160\pi$
$752$		0			0
$753$	−2.49410	−	1.43997i	−0.0908902	−	0.0524755i
$754$		0			0
$755$	−0.372871	+	0.154448i	−0.0135702	+	0.00562095i
$756$		0			0
$757$	−7.21820	+	17.4263i	−0.262350	+	0.633369i	−0.999083	−	0.0428149i	$-0.986367\pi$
$757$	−7.21820	+	17.4263i	−0.262350	+	0.633369i	0.736733	+	0.676184i	$0.236367\pi$
$758$		0			0
$759$	3.55983	+	13.2855i	0.129214	+	0.482232i
$760$		0			0
$761$	6.79304	−	25.3520i	0.246247	−	0.919008i	−0.726505	−	0.687161i	$-0.758857\pi$
$761$	6.79304	−	25.3520i	0.246247	−	0.919008i	0.972752	−	0.231847i	$-0.0744768\pi$
$762$		0			0
$763$	12.8764	+	47.8672i	0.466156	+	1.73291i
$764$		0			0
$765$	−1.36883	+	1.78390i	−0.0494903	+	0.0644970i
$766$		0			0
$767$	14.5251	−	25.1582i	0.524472	−	0.908412i
$768$		0			0
$769$	−22.9189			−0.826475			−0.413238	−	0.910623i	$-0.635602\pi$
$769$	−22.9189			−0.826475			−0.413238	+	0.910623i	$0.635602\pi$
$770$		0			0
$771$	6.97832	+	16.8472i	0.251318	+	0.606736i
$772$		0			0
$773$	−40.9450	+	31.4182i	−1.47269	+	1.13003i	−0.509748	+	0.860324i	$0.670261\pi$
$773$	−40.9450	+	31.4182i	−1.47269	+	1.13003i	−0.962942	+	0.269710i	$0.913072\pi$
$774$		0			0
$775$	6.32553	−	23.6072i	0.227220	−	0.847995i
$776$		0			0
$777$	3.29406	+	7.93054i	0.118174	+	0.284507i
$778$		0			0
$779$	21.4276	−	2.82099i	0.767722	−	0.101073i
$780$		0			0
$781$	−0.993727	+	7.54810i	−0.0355583	+	0.270092i
$782$		0			0
$783$			37.1149i			1.32638i
$784$		0			0
$785$			0.389075i			0.0138867i
$786$		0			0
$787$	4.76589	−	36.2005i	0.169886	−	1.29041i	−0.667835	−	0.744309i	$-0.732779\pi$
$787$	4.76589	−	36.2005i	0.169886	−	1.29041i	0.837721	−	0.546099i	$-0.183888\pi$
$788$		0			0
$789$	14.7199	−	1.93791i	0.524042	−	0.0689915i
$790$		0			0
$791$	−1.48653	−	3.57886i	−0.0528549	−	0.127250i
$792$		0			0
$793$	0.816741	−	3.04812i	0.0290033	−	0.108242i
$794$		0			0
$795$	−1.33509	+	1.02445i	−0.0473508	+	0.0363336i
$796$		0			0
$797$	7.73109	+	18.6645i	0.273849	+	0.661130i	0.999641	−	0.0267837i	$-0.00852655\pi$
$797$	7.73109	+	18.6645i	0.273849	+	0.661130i	−0.725792	+	0.687914i	$0.758527\pi$
$798$		0			0
$799$	−39.2150			−1.38733
$800$		0			0
$801$	−12.0126	+	20.8065i	−0.424446	+	0.735162i
$802$		0			0
$803$	−15.6486	+	20.3936i	−0.552227	+	0.719676i
$804$		0			0
$805$	−0.770920	−	2.86586i	−0.0271714	−	0.101008i
$806$		0			0
$807$	9.10451	−	33.9785i	0.320494	−	1.19610i
$808$		0			0
$809$	−12.0352	−	44.9160i	−0.423135	−	1.57916i	−0.767962	−	0.640496i	$-0.778729\pi$
$809$	−12.0352	−	44.9160i	−0.423135	−	1.57916i	0.344827	−	0.938666i	$-0.387938\pi$
$810$		0			0
$811$	−0.761002	+	1.83722i	−0.0267224	+	0.0645136i	−0.936677	−	0.350193i	$-0.886116\pi$
$811$	−0.761002	+	1.83722i	−0.0267224	+	0.0645136i	0.909955	+	0.414707i	$0.136116\pi$
$812$		0			0
$813$	−30.7673	+	12.7442i	−1.07906	+	0.446960i
$814$		0			0
$815$	−2.56795	−	1.48260i	−0.0899512	−	0.0519334i
$816$		0			0
$817$	33.3442	−	19.2513i	1.16657	−	0.673517i
$818$		0			0
$819$	−12.6747	+	7.33433i	−0.442889	+	0.256282i
$820$		0			0
$821$	−15.8910	+	2.09209i	−0.554601	+	0.0730146i	−0.402617	−	0.915368i	$-0.631899\pi$
$821$	−15.8910	+	2.09209i	−0.554601	+	0.0730146i	−0.151984	+	0.988383i	$0.548566\pi$
$822$		0			0
$823$	7.58865	+	28.3212i	0.264524	+	0.987215i	0.962541	+	0.271135i	$0.0873990\pi$
$823$	7.58865	+	28.3212i	0.264524	+	0.987215i	−0.698018	+	0.716080i	$0.745934\pi$
$824$		0			0
$825$	−9.26325	−	9.26325i	−0.322505	−	0.322505i
$826$		0			0
$827$	−7.29696	−	3.02250i	−0.253740	−	0.105103i	0.252188	−	0.967678i	$-0.418850\pi$
$827$	−7.29696	−	3.02250i	−0.253740	−	0.105103i	−0.505928	+	0.862576i	$0.668850\pi$
$828$		0			0
$829$	39.0302	+	5.13842i	1.35558	+	0.178465i	0.773049	−	0.634347i	$-0.218731\pi$
$829$	39.0302	+	5.13842i	1.35558	+	0.178465i	0.582526	+	0.812812i	$0.302064\pi$
$830$		0			0
$831$	−1.90574	−	3.30084i	−0.0661094	−	0.114505i
$832$		0			0
$833$	−48.7176	+	13.1564i	−1.68796	+	0.455842i
$834$		0			0
$835$	−0.0824015	+	0.107388i	−0.00285162	+	0.00371631i
$836$		0			0
$837$	21.6942	−	16.6466i	0.749863	−	0.575390i
$838$		0			0
$839$	−31.2997	−	31.2997i	−1.08059	−	1.08059i	−0.996455	−	0.0841319i	$-0.973188\pi$
$839$	−31.2997	−	31.2997i	−1.08059	−	1.08059i	−0.0841319	−	0.996455i	$-0.526812\pi$
$840$		0			0
$841$	−11.2046	+	11.2046i	−0.386366	+	0.386366i
$842$		0			0
$843$	−7.62670	−	9.93931i	−0.262678	−	0.342328i
$844$		0			0
$845$	0.281932	+	0.216334i	0.00969874	+	0.00744211i
$846$		0			0
$847$	−2.26101	−	17.0448i	−0.0776894	−	0.585666i
$848$		0			0
$849$	29.3005	−	16.9166i	1.00559	−	0.580577i
$850$		0			0
$851$	−1.76757	+	13.4260i	−0.0605915	+	0.460238i
$852$		0			0
$853$	−13.0830	+	31.5851i	−0.447953	+	1.08145i	0.525135	+	0.851019i	$0.324015\pi$
$853$	−13.0830	+	31.5851i	−0.447953	+	1.08145i	−0.973088	+	0.230435i	$0.925985\pi$
$854$		0			0
$855$	0.781745	−	0.781745i	0.0267351	−	0.0267351i
$856$		0			0
$857$	24.6533	−	6.60584i	0.842142	−	0.225651i	0.188138	−	0.982143i	$-0.439755\pi$
$857$	24.6533	−	6.60584i	0.842142	−	0.225651i	0.654004	+	0.756491i	$0.273088\pi$
$858$		0			0
$859$	7.22325	+	54.8661i	0.246454	+	1.87201i	0.450124	+	0.892966i	$0.351380\pi$
$859$	7.22325	+	54.8661i	0.246454	+	1.87201i	−0.203670	+	0.979040i	$0.565287\pi$
$860$		0			0
$861$	−10.0377	+	17.4253i	−0.342085	+	0.593854i
$862$		0			0
$863$	−12.3555	−	21.4003i	−0.420586	−	0.728476i	0.575411	−	0.817864i	$-0.304842\pi$
$863$	−12.3555	−	21.4003i	−0.420586	−	0.728476i	−0.995997	+	0.0893882i	$0.971509\pi$
$864$		0			0
$865$	−0.442340	+	0.766156i	−0.0150400	+	0.0260501i
$866$		0			0
$867$	−16.6812	−	40.2720i	−0.566523	−	1.36771i
$868$		0			0
$869$	−4.58315	−	1.89840i	−0.155473	−	0.0643989i
$870$		0			0
$871$	−16.5732	+	4.44076i	−0.561560	+	0.150470i
$872$		0			0
$873$	−14.5213	−	3.89096i	−0.491470	−	0.131689i
$874$		0			0
$875$	4.02018	+	4.01230i	0.135907	+	0.135640i
$876$		0			0
$877$	−21.8639	−	16.7767i	−0.738290	−	0.566510i	0.169703	−	0.985495i	$-0.445719\pi$
$877$	−21.8639	−	16.7767i	−0.738290	−	0.566510i	−0.907993	+	0.418985i	$0.862386\pi$
$878$		0			0
$879$	−15.1025	−	8.71945i	−0.509396	−	0.294100i
$880$		0			0
$881$			26.8351i			0.904096i	0.891994	+	0.452048i	$0.149306\pi$
$881$			26.8351i			0.904096i	−0.891994	+	0.452048i	$0.850694\pi$
$882$		0			0
$883$	−8.17897	+	3.38784i	−0.275244	+	0.114010i	−0.516036	−	0.856567i	$-0.672593\pi$
$883$	−8.17897	+	3.38784i	−0.275244	+	0.114010i	0.240792	+	0.970577i	$0.422593\pi$
$884$		0			0
$885$	−1.24230	−	1.61899i	−0.0417593	−	0.0544218i
$886$		0			0
$887$	−25.4214	−	6.81164i	−0.853566	−	0.228712i	−0.194598	−	0.980883i	$-0.562340\pi$
$887$	−25.4214	−	6.81164i	−0.853566	−	0.228712i	−0.658968	+	0.752171i	$0.729007\pi$
$888$		0			0
$889$	−53.2857	+	22.1330i	−1.78715	+	0.742316i
$890$		0			0
$891$	−0.711722	−	5.40607i	−0.0238436	−	0.181110i
$892$		0			0
$893$	19.1160	+	2.51668i	0.639694	+	0.0842173i
$894$		0			0
$895$	−5.45157			−0.182226
$896$		0			0
$897$	24.8114			0.828428
$898$		0			0
$899$	32.7581	+	4.31269i	1.09254	+	0.143836i
$900$		0			0
$901$	5.88983	+	44.7377i	0.196219	+	1.49043i
$902$		0			0
$903$	−4.64127	+	35.5234i	−0.154452	+	1.18215i
$904$		0			0
$905$	−0.590013	−	0.158093i	−0.0196127	−	0.00525521i
$906$		0			0
$907$	4.67424	+	6.09159i	0.155206	+	0.202268i	0.864484	−	0.502661i	$-0.167646\pi$
$907$	4.67424	+	6.09159i	0.155206	+	0.202268i	−0.709278	+	0.704929i	$0.750979\pi$
$908$		0			0
$909$	0.254174	−	0.105282i	0.00843042	−	0.00349199i
$910$		0			0
$911$			13.0632i			0.432802i	0.976305	+	0.216401i	$0.0694318\pi$
$911$			13.0632i			0.432802i	−0.976305	+	0.216401i	$0.930568\pi$
$912$		0			0
$913$	2.24303	+	1.29501i	0.0742333	+	0.0428586i
$914$		0			0
$915$	−0.175866	−	0.134947i	−0.00581397	−	0.00446121i
$916$		0			0
$917$	−4.05983	+	15.2112i	−0.134067	+	0.502318i
$918$		0			0
$919$	−2.14116	−	0.573723i	−0.0706305	−	0.0189254i	0.223331	−	0.974743i	$-0.428307\pi$
$919$	−2.14116	−	0.573723i	−0.0706305	−	0.0189254i	−0.293961	+	0.955817i	$0.594974\pi$
$920$		0			0
$921$	7.34143	−	1.96713i	0.241908	−	0.0648191i
$922$		0			0
$923$	12.6883	+	5.25566i	0.417640	+	0.172992i
$924$		0			0
$925$	−4.93587	−	11.9162i	−0.162290	−	0.391804i
$926$		0			0
$927$	−0.156359	+	0.270822i	−0.00513551	+	0.00889496i
$928$		0			0
$929$	−16.4138	−	28.4296i	−0.538521	−	0.932745i	−0.998984	−	0.0450664i	$-0.985650\pi$
$929$	−16.4138	−	28.4296i	−0.538521	−	0.932745i	0.460463	−	0.887679i	$-0.347683\pi$
$930$		0			0
$931$	24.5925	−	3.28680i	0.805988	−	0.107721i
$932$		0			0
$933$	3.21374	+	24.4108i	0.105213	+	0.799172i
$934$		0			0
$935$	3.18635	−	0.853780i	0.104205	−	0.0279216i
$936$		0			0
$937$	16.3925	−	16.3925i	0.535520	−	0.535520i	−0.386690	−	0.922210i	$-0.626382\pi$
$937$	16.3925	−	16.3925i	0.535520	−	0.535520i	0.922210	+	0.386690i	$0.126382\pi$
$938$		0			0
$939$	6.14935	−	14.8458i	0.200676	−	0.484476i
$940$		0			0
$941$	−1.01540	+	7.71275i	−0.0331012	+	0.251428i	−0.999993	−	0.00375849i	$-0.998804\pi$
$941$	−1.01540	+	7.71275i	−0.0331012	+	0.251428i	0.966892	+	0.255187i	$0.0821370\pi$
$942$		0			0
$943$	−27.4631	+	15.8559i	−0.894323	+	0.516338i
$944$		0			0
$945$	0.415883	+	3.13516i	0.0135287	+	0.101987i
$946$		0			0
$947$	17.6136	+	13.5154i	0.572365	+	0.439191i	0.853957	−	0.520343i	$-0.174196\pi$
$947$	17.6136	+	13.5154i	0.572365	+	0.439191i	−0.281592	+	0.959534i	$0.590863\pi$
$948$		0			0
$949$	28.2288	+	36.7885i	0.916347	+	1.19421i
$950$		0			0
$951$	−12.1679	+	12.1679i	−0.394570	+	0.394570i
$952$		0			0
$953$	−9.12055	−	9.12055i	−0.295443	−	0.295443i	0.543783	−	0.839226i	$-0.316992\pi$
$953$	−9.12055	−	9.12055i	−0.295443	−	0.295443i	−0.839226	+	0.543783i	$0.816992\pi$
$954$		0			0
$955$	−2.26404	+	1.73726i	−0.0732625	+	0.0562163i
$956$		0			0
$957$	10.7814	−	14.0506i	0.348513	−	0.454191i
$958$		0			0
$959$	3.84586	+	5.00184i	0.124189	+	0.161518i
$960$		0			0
$961$	3.32834	+	5.76485i	0.107366	+	0.185963i
$962$		0			0
$963$	−2.74439	−	0.361306i	−0.0884368	−	0.0116429i
$964$		0			0
$965$	−0.415681	−	0.172181i	−0.0133813	−	0.00554270i
$966$		0			0
$967$	29.1918	+	29.1918i	0.938746	+	0.938746i	0.998229	−	0.0594832i	$-0.0189453\pi$
$967$	29.1918	+	29.1918i	0.938746	+	0.938746i	−0.0594832	+	0.998229i	$0.518945\pi$
$968$		0			0
$969$	8.24368	+	30.7658i	0.264825	+	0.988341i
$970$		0			0
$971$	32.4996	−	4.27866i	1.04296	−	0.137309i	0.410469	−	0.911874i	$-0.365365\pi$
$971$	32.4996	−	4.27866i	1.04296	−	0.137309i	0.632493	+	0.774566i	$0.282032\pi$
$972$		0			0
$973$	−0.00677521	−	6.90156i	−0.000217203	−	0.221254i
$974$		0			0
$975$	−20.4657	+	11.8159i	−0.655428	+	0.378411i
$976$		0			0
$977$	35.3440	+	20.4059i	1.13076	+	0.652842i	0.944125	−	0.329588i	$-0.106910\pi$
$977$	35.3440	+	20.4059i	1.13076	+	0.652842i	0.186631	+	0.982430i	$0.440243\pi$
$978$		0			0
$979$	32.5635	−	13.4882i	1.04073	−	0.431086i
$980$		0			0
$981$	10.3686	−	25.0320i	0.331043	−	0.799209i
$982$		0			0
$983$	−14.7764	−	55.1464i	−0.471295	−	1.75890i	−0.635127	−	0.772408i	$-0.719052\pi$
$983$	−14.7764	−	55.1464i	−0.471295	−	1.75890i	0.163833	−	0.986488i	$-0.447614\pi$
$984$		0			0
$985$	1.08117	−	4.03499i	0.0344490	−	0.128565i
$986$		0			0
$987$	−12.6733	+	12.6982i	−0.403394	+	0.404187i
$988$		0			0
$989$	−34.3916	+	44.8200i	−1.09359	+	1.42519i
$990$		0			0
$991$	−5.91906	+	10.2521i	−0.188025	+	0.325669i	−0.944592	−	0.328248i	$-0.893542\pi$
$991$	−5.91906	+	10.2521i	−0.188025	+	0.325669i	0.756567	+	0.653917i	$0.226875\pi$
$992$		0			0
$993$	−14.8614			−0.471612
$994$		0			0
$995$	−1.44691	−	3.49315i	−0.0458701	−	0.110740i
$996$		0			0
$997$	1.12328	−	0.861923i	0.0355746	−	0.0272974i	−0.590821	−	0.806803i	$-0.701196\pi$
$997$	1.12328	−	0.861923i	0.0355746	−	0.0272974i	0.626396	+	0.779505i	$0.284529\pi$
$998$		0			0
$999$	3.73506	−	13.9394i	0.118172	−	0.441024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bh.a.753.10		240
4.3	odd	2		224.2.bd.a.165.29	yes	240
7.2	even	3	inner	896.2.bh.a.625.21		240
28.23	odd	6		224.2.bd.a.37.11	✓	240
32.13	even	8	inner	896.2.bh.a.529.21		240
32.19	odd	8		224.2.bd.a.109.11	yes	240
224.51	odd	24		224.2.bd.a.205.29	yes	240
224.205	even	24	inner	896.2.bh.a.401.10		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.11	✓	240	28.23	odd	6
224.2.bd.a.109.11	yes	240	32.19	odd	8
224.2.bd.a.165.29	yes	240	4.3	odd	2
224.2.bd.a.205.29	yes	240	224.51	odd	24
896.2.bh.a.401.10		240	224.205	even	24	inner
896.2.bh.a.529.21		240	32.13	even	8	inner
896.2.bh.a.625.21		240	7.2	even	3	inner
896.2.bh.a.753.10		240	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bh (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23586 - 0.162704i) q^{3} +(0.0281519 + 0.213835i) q^{5} +(2.44336 - 1.01488i) q^{7} +(-1.39689 - 0.374296i) q^{9} +O(q^{10})\)	\(q+(-1.23586 - 0.162704i) q^{3} +(0.0281519 + 0.213835i) q^{5} +(2.44336 - 1.01488i) q^{7} +(-1.39689 - 0.374296i) q^{9} +(1.29156 + 1.68319i) q^{11} +(3.53590 - 1.46462i) q^{13} -0.268851i q^{15} +(-6.24315 - 3.60448i) q^{17} +(2.81201 + 2.15773i) q^{19} +(-3.18478 + 0.856712i) q^{21} +(-5.02353 - 1.34605i) q^{23} +(4.78470 - 1.28206i) q^{25} +(5.12039 + 2.12094i) q^{27} +(2.56271 + 6.18694i) q^{29} +(2.46695 - 4.27288i) q^{31} +(-1.32232 - 2.29033i) q^{33} +(0.285803 + 0.493906i) q^{35} +(-0.339869 - 2.58156i) q^{37} +(-4.60818 + 1.23476i) q^{39} +(4.31161 - 4.31161i) q^{41} +(4.15699 - 10.0359i) q^{43} +(0.0407125 - 0.309242i) q^{45} +(4.71097 - 2.71988i) q^{47} +(4.94002 - 4.95946i) q^{49} +(7.12921 + 5.47044i) q^{51} +(-3.81048 - 4.96591i) q^{53} +(-0.323565 + 0.323565i) q^{55} +(-3.12418 - 3.12418i) q^{57} +(6.02188 - 4.62075i) q^{59} +(0.501939 - 0.654140i) q^{61} +(-3.79298 + 0.503144i) q^{63} +(0.412729 + 0.714867i) q^{65} +(-4.44474 - 0.585161i) q^{67} +(5.98939 + 2.48089i) q^{69} +(2.53740 + 2.53740i) q^{71} +(3.13587 + 11.7032i) q^{73} +(-6.12182 + 0.805953i) q^{75} +(4.86398 + 2.80186i) q^{77} +(-2.02495 + 1.16910i) q^{79} +(-2.22575 - 1.28504i) q^{81} +(1.12785 - 0.467172i) q^{83} +(0.595009 - 1.43648i) q^{85} +(-2.16052 - 8.06317i) q^{87} +(4.29977 - 16.0470i) q^{89} +(7.15305 - 7.16711i) q^{91} +(-3.74403 + 4.87931i) q^{93} +(-0.382235 + 0.662051i) q^{95} +10.3954 q^{97} +(-1.17415 - 2.83466i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9}+O(q^{10}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9	\( 240 q + 4 q^{3} - 4 q^{5} + 8 q^{7} - 4 q^{9} + 4 q^{11} - 16 q^{13} + 4 q^{19} - 8 q^{21} + 12 q^{23} - 4 q^{25} + 16 q^{27} - 16 q^{29} + 56 q^{31} - 8 q^{33} + 32 q^{35} - 4 q^{37} + 4 q^{39} - 16 q^{41} + 8 q^{45} + 28 q^{51} - 20 q^{53} + 16 q^{55} - 16 q^{57} + 36 q^{59} - 4 q^{61} + 16 q^{63} - 8 q^{65} - 36 q^{67} - 16 q^{69} - 48 q^{71} - 4 q^{73} - 16 q^{75} - 8 q^{77} + 96 q^{83} - 56 q^{85} + 4 q^{87} - 4 q^{89} + 56 q^{91} + 20 q^{93} + 8 q^{95} - 32 q^{97} - 8 q^{99}+O(q^{100}) \) 240 * q + 4 * q^3 - 4 * q^5 + 8 * q^7 - 4 * q^9 + 4 * q^11 - 16 * q^13 + 4 * q^19 - 8 * q^21 + 12 * q^23 - 4 * q^25 + 16 * q^27 - 16 * q^29 + 56 * q^31 - 8 * q^33 + 32 * q^35 - 4 * q^37 + 4 * q^39 - 16 * q^41 + 8 * q^45 + 28 * q^51 - 20 * q^53 + 16 * q^55 - 16 * q^57 + 36 * q^59 - 4 * q^61 + 16 * q^63 - 8 * q^65 - 36 * q^67 - 16 * q^69 - 48 * q^71 - 4 * q^73 - 16 * q^75 - 8 * q^77 + 96 * q^83 - 56 * q^85 + 4 * q^87 - 4 * q^89 + 56 * q^91 + 20 * q^93 + 8 * q^95 - 32 * q^97 - 8 * q^99

Introduction

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Groups

Database

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