LMFDB - Embedded newform 888.2.bo.c.145.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [888,2,Mod(49,888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(888, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 0, 14]))

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

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

chi := DirichletCharacter("888.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 888 = 2^{3} \cdot 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	888.bo (of order $9$, degree $6$, 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:	$7.09071569949$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			145.4
Character	$\chi$	$=$	888.145
Dual form			888.2.bo.c.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{3} +(3.41293 + 1.24220i) q^{5} +(-2.06718 - 0.752391i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{3} +(3.41293 + 1.24220i) q^{5} +(-2.06718 - 0.752391i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-2.44356 + 4.23236i) q^{11} +(1.12113 + 6.35827i) q^{13} +(3.41293 - 1.24220i) q^{15} +(-1.15526 + 6.55178i) q^{17} +(6.22231 - 5.22114i) q^{19} +(-2.06718 + 0.752391i) q^{21} +(1.09992 + 1.90512i) q^{23} +(6.27479 + 5.26518i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(3.05621 - 5.29351i) q^{29} -1.06617 q^{31} +(0.848638 + 4.81287i) q^{33} +(-6.12051 - 5.13572i) q^{35} +(-0.272295 - 6.07666i) q^{37} +(4.94585 + 4.15006i) q^{39} +(-0.391250 - 2.21889i) q^{41} -2.91871 q^{43} +(1.81598 - 3.14537i) q^{45} +(-1.92901 - 3.34114i) q^{47} +(-1.65518 - 1.38886i) q^{49} +(3.32643 + 5.76154i) q^{51} +(0.976516 - 0.355423i) q^{53} +(-13.5971 + 11.4094i) q^{55} +(1.41048 - 7.99925i) q^{57} +(9.96433 - 3.62672i) q^{59} +(-1.27393 - 7.22479i) q^{61} +(-1.09992 + 1.90512i) q^{63} +(-4.07192 + 23.0930i) q^{65} +(-2.25855 - 0.822045i) q^{67} +(2.06718 + 0.752391i) q^{69} +(0.202126 - 0.169604i) q^{71} -3.97412 q^{73} +8.19116 q^{75} +(8.23566 - 6.91054i) q^{77} +(-1.63622 - 0.595534i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-0.645643 + 3.66162i) q^{83} +(-12.0815 + 20.9257i) q^{85} +(-1.06141 - 6.01956i) q^{87} +(12.1081 - 4.40700i) q^{89} +(2.46632 - 13.9872i) q^{91} +(-0.816733 + 0.685321i) q^{93} +(27.7220 - 10.0900i) q^{95} +(4.45903 + 7.72327i) q^{97} +(3.74374 + 3.14137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) $ 24 * q + 3 * q^5 + 15 * q^7	$ 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) $ 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/888\mathbb{Z}\right)^\times$.

$n$	$223$	$409$	$445$	$593$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$3$	0.766044	−	0.642788i	0.442276	−	0.371114i
$4$		0			0
$5$	3.41293	+	1.24220i	1.52631	+	0.555531i	0.962714	−	0.270521i	$-0.0871959\pi$
$5$	3.41293	+	1.24220i	1.52631	+	0.555531i	0.563594	+	0.826052i	$0.309418\pi$
$6$		0			0
$7$	−2.06718	−	0.752391i	−0.781320	−	0.284377i	−0.0795970	−	0.996827i	$-0.525363\pi$
$7$	−2.06718	−	0.752391i	−0.781320	−	0.284377i	−0.701723	+	0.712450i	$0.747586\pi$
$8$		0			0
$9$	0.173648	−	0.984808i	0.0578827	−	0.328269i
$10$		0			0
$11$	−2.44356	+	4.23236i	−0.736760	+	1.27611i	0.217187	+	0.976130i	$0.430312\pi$
$11$	−2.44356	+	4.23236i	−0.736760	+	1.27611i	−0.953947	+	0.299975i	$0.903022\pi$
$12$		0			0
$13$	1.12113	+	6.35827i	0.310947	+	1.76347i	0.594100	+	0.804391i	$0.297508\pi$
$13$	1.12113	+	6.35827i	0.310947	+	1.76347i	−0.283153	+	0.959075i	$0.591380\pi$
$14$		0			0
$15$	3.41293	−	1.24220i	0.881215	−	0.320736i
$16$		0			0
$17$	−1.15526	+	6.55178i	−0.280191	+	1.58904i	0.441784	+	0.897121i	$0.354346\pi$
$17$	−1.15526	+	6.55178i	−0.280191	+	1.58904i	−0.721975	+	0.691919i	$0.756765\pi$
$18$		0			0
$19$	6.22231	−	5.22114i	1.42750	−	1.19781i	0.480322	−	0.877092i	$-0.340520\pi$
$19$	6.22231	−	5.22114i	1.42750	−	1.19781i	0.947174	−	0.320719i	$-0.103925\pi$
$20$		0			0
$21$	−2.06718	+	0.752391i	−0.451095	+	0.164185i
$22$		0			0
$23$	1.09992	+	1.90512i	0.229350	+	0.397245i	0.957616	−	0.288049i	$-0.0930067\pi$
$23$	1.09992	+	1.90512i	0.229350	+	0.397245i	−0.728266	+	0.685295i	$0.759673\pi$
$24$		0			0
$25$	6.27479	+	5.26518i	1.25496	+	1.05304i
$26$		0			0
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$		0			0
$29$	3.05621	−	5.29351i	0.567524	−	0.982980i	−0.429286	−	0.903169i	$-0.641235\pi$
$29$	3.05621	−	5.29351i	0.567524	−	0.982980i	0.996810	−	0.0798117i	$-0.0254319\pi$
$30$		0			0
$31$	−1.06617			−0.191490			−0.0957449	−	0.995406i	$-0.530523\pi$
$31$	−1.06617			−0.191490			−0.0957449	+	0.995406i	$0.530523\pi$
$32$		0			0
$33$	0.848638	+	4.81287i	0.147729	+	0.837812i
$34$		0			0
$35$	−6.12051	−	5.13572i	−1.03456	−	0.868095i
$36$		0			0
$37$	−0.272295	−	6.07666i	−0.0447651	−	0.998998i
$37$	−0.272295	−	6.07666i	−0.0447651	−	0.998998i
$38$		0			0
$39$	4.94585	+	4.15006i	0.791971	+	0.664542i
$40$		0			0
$41$	−0.391250	−	2.21889i	−0.0611029	−	0.346532i	−0.999997	−	0.00232657i	$-0.999259\pi$
$41$	−0.391250	−	2.21889i	−0.0611029	−	0.346532i	0.938894	−	0.344205i	$-0.111852\pi$
$42$		0			0
$43$	−2.91871			−0.445098			−0.222549	−	0.974921i	$-0.571438\pi$
$43$	−2.91871			−0.445098			−0.222549	+	0.974921i	$0.571438\pi$
$44$		0			0
$45$	1.81598	−	3.14537i	0.270711	−	0.468885i
$46$		0			0
$47$	−1.92901	−	3.34114i	−0.281375	−	0.487355i	0.690349	−	0.723477i	$-0.257457\pi$
$47$	−1.92901	−	3.34114i	−0.281375	−	0.487355i	−0.971724	+	0.236121i	$0.924124\pi$
$48$		0			0
$49$	−1.65518	−	1.38886i	−0.236454	−	0.198408i
$50$		0			0
$51$	3.32643	+	5.76154i	0.465793	+	0.806777i
$52$		0			0
$53$	0.976516	−	0.355423i	0.134135	−	0.0488211i	−0.274081	−	0.961707i	$-0.588373\pi$
$53$	0.976516	−	0.355423i	0.134135	−	0.0488211i	0.408215	+	0.912886i	$0.366151\pi$
$54$		0			0
$55$	−13.5971	+	11.4094i	−1.83344	+	1.53844i
$56$		0			0
$57$	1.41048	−	7.99925i	0.186823	−	1.05953i
$58$		0			0
$59$	9.96433	−	3.62672i	1.29725	−	0.472159i	0.401147	−	0.916014i	$-0.368612\pi$
$59$	9.96433	−	3.62672i	1.29725	−	0.472159i	0.896098	+	0.443855i	$0.146390\pi$
$60$		0			0
$61$	−1.27393	−	7.22479i	−0.163109	−	0.925040i	−0.950992	−	0.309214i	$-0.899934\pi$
$61$	−1.27393	−	7.22479i	−0.163109	−	0.925040i	0.787883	−	0.615825i	$-0.211177\pi$
$62$		0			0
$63$	−1.09992	+	1.90512i	−0.138577	+	0.240023i
$64$		0			0
$65$	−4.07192	+	23.0930i	−0.505059	+	2.86433i
$66$		0			0
$67$	−2.25855	−	0.822045i	−0.275926	−	0.100429i	0.200351	−	0.979724i	$-0.435792\pi$
$67$	−2.25855	−	0.822045i	−0.275926	−	0.100429i	−0.476277	+	0.879295i	$0.658014\pi$
$68$		0			0
$69$	2.06718	+	0.752391i	0.248859	+	0.0905773i
$70$		0			0
$71$	0.202126	−	0.169604i	0.0239880	−	0.0201283i	−0.630715	−	0.776015i	$-0.717238\pi$
$71$	0.202126	−	0.169604i	0.0239880	−	0.0201283i	0.654703	+	0.755886i	$0.272794\pi$
$72$		0			0
$73$	−3.97412			−0.465136			−0.232568	−	0.972580i	$-0.574713\pi$
$73$	−3.97412			−0.465136			−0.232568	+	0.972580i	$0.574713\pi$
$74$		0			0
$75$	8.19116			0.945834
$76$		0			0
$77$	8.23566	−	6.91054i	0.938541	−	0.787529i
$78$		0			0
$79$	−1.63622	−	0.595534i	−0.184089	−	0.0670028i	0.248331	−	0.968675i	$-0.420118\pi$
$79$	−1.63622	−	0.595534i	−0.184089	−	0.0670028i	−0.432420	+	0.901672i	$0.642340\pi$
$80$		0			0
$81$	−0.939693	−	0.342020i	−0.104410	−	0.0380022i
$82$		0			0
$83$	−0.645643	+	3.66162i	−0.0708685	+	0.401915i	0.928652	+	0.370952i	$0.120969\pi$
$83$	−0.645643	+	3.66162i	−0.0708685	+	0.401915i	−0.999521	+	0.0309633i	$0.990143\pi$
$84$		0			0
$85$	−12.0815	+	20.9257i	−1.31042	+	2.26971i
$86$		0			0
$87$	−1.06141	−	6.01956i	−0.113795	−	0.645364i
$88$		0			0
$89$	12.1081	−	4.40700i	1.28346	−	0.467141i	0.391885	−	0.920014i	$-0.371823\pi$
$89$	12.1081	−	4.40700i	1.28346	−	0.467141i	0.891575	+	0.452873i	$0.149601\pi$
$90$		0			0
$91$	2.46632	−	13.9872i	0.258541	−	1.46626i
$92$		0			0
$93$	−0.816733	+	0.685321i	−0.0846913	+	0.0710644i
$94$		0			0
$95$	27.7220	−	10.0900i	2.84422	−	1.03521i
$96$		0			0
$97$	4.45903	+	7.72327i	0.452746	+	0.784180i	0.998556	−	0.0537299i	$-0.0171110\pi$
$97$	4.45903	+	7.72327i	0.452746	+	0.784180i	−0.545809	+	0.837909i	$0.683778\pi$
$98$		0			0
$99$	3.74374	+	3.14137i	0.376261	+	0.315720i
$100$		0			0
$101$	5.63589	+	9.76164i	0.560792	+	0.971320i	0.997428	+	0.0716814i	$0.0228365\pi$
$101$	5.63589	+	9.76164i	0.560792	+	0.971320i	−0.436636	+	0.899638i	$0.643830\pi$
$102$		0			0
$103$	3.61367	−	6.25906i	0.356066	−	0.616724i	−0.631234	−	0.775592i	$-0.717451\pi$
$103$	3.61367	−	6.25906i	0.356066	−	0.616724i	0.987300	+	0.158869i	$0.0507846\pi$
$104$		0			0
$105$	−7.98976			−0.779721
$106$		0			0
$107$	−1.37233	−	7.78285i	−0.132668	−	0.752397i	−0.976455	−	0.215720i	$-0.930790\pi$
$107$	−1.37233	−	7.78285i	−0.132668	−	0.752397i	0.843787	−	0.536677i	$-0.180321\pi$
$108$		0			0
$109$	−7.06304	−	5.92659i	−0.676516	−	0.567665i	0.238470	−	0.971150i	$-0.423354\pi$
$109$	−7.06304	−	5.92659i	−0.676516	−	0.567665i	−0.914986	+	0.403485i	$0.867799\pi$
$110$		0			0
$111$	−4.11460	−	4.47997i	−0.390540	−	0.425220i
$112$		0			0
$113$	1.26266	+	1.05949i	0.118781	+	0.0996688i	0.700243	−	0.713904i	$-0.253075\pi$
$113$	1.26266	+	1.05949i	0.118781	+	0.0996688i	−0.581463	+	0.813573i	$0.697519\pi$
$114$		0			0
$115$	1.38741	+	7.86838i	0.129376	+	0.733730i
$116$		0			0
$117$	6.45635			0.596890
$118$		0			0
$119$	7.31762	−	12.6745i	0.670805	−	1.16187i
$120$		0			0
$121$	−6.44193	−	11.1578i	−0.585630	−	1.01434i
$122$		0			0
$123$	−1.72599	−	1.44828i	−0.155627	−	0.130587i
$124$		0			0
$125$	5.79509	+	10.0374i	0.518329	+	0.897772i
$126$		0			0
$127$	−12.7275	+	4.63245i	−1.12939	+	0.411063i	−0.838070	−	0.545563i	$-0.816316\pi$
$127$	−12.7275	+	4.63245i	−1.12939	+	0.411063i	−0.291317	+	0.956626i	$0.594094\pi$
$128$		0			0
$129$	−2.23586	+	1.87611i	−0.196856	+	0.165182i
$130$		0			0
$131$	−0.219109	+	1.24263i	−0.0191436	+	0.108569i	−0.992882	−	0.119100i	$-0.961999\pi$
$131$	−0.219109	+	1.24263i	−0.0191436	+	0.108569i	0.973739	+	0.227669i	$0.0731103\pi$
$132$		0			0
$133$	−16.7910	+	6.11141i	−1.45596	+	0.529927i
$134$		0			0
$135$	−0.630684	−	3.57679i	−0.0542806	−	0.307841i
$136$		0			0
$137$	5.17425	−	8.96206i	0.442066	−	0.765681i	−0.555777	−	0.831332i	$-0.687579\pi$
$137$	5.17425	−	8.96206i	0.442066	−	0.765681i	0.997843	+	0.0656508i	$0.0209123\pi$
$138$		0			0
$139$	−3.36103	+	19.0613i	−0.285079	+	1.61676i	0.419926	+	0.907558i	$0.362056\pi$
$139$	−3.36103	+	19.0613i	−0.285079	+	1.61676i	−0.705005	+	0.709202i	$0.749055\pi$
$140$		0			0
$141$	−3.62535	−	1.31952i	−0.305310	−	0.111124i
$142$		0			0
$143$	−29.6501	−	10.7917i	−2.47946	−	0.902450i
$144$		0			0
$145$	17.0063	−	14.2699i	1.41229	−	1.18505i
$146$		0			0
$147$	−2.16068			−0.178210
$148$		0			0
$149$	−14.3786			−1.17794			−0.588972	−	0.808154i	$-0.700467\pi$
$149$	−14.3786			−1.17794			−0.588972	+	0.808154i	$0.700467\pi$
$150$		0			0
$151$	−17.7867	+	14.9248i	−1.44746	+	1.21456i	−0.513056	+	0.858355i	$0.671487\pi$
$151$	−17.7867	+	14.9248i	−1.44746	+	1.21456i	−0.934406	+	0.356210i	$0.884069\pi$
$152$		0			0
$153$	6.25164	+	2.27541i	0.505415	+	0.183956i
$154$		0			0
$155$	−3.63876	−	1.32440i	−0.292272	−	0.106378i
$156$		0			0
$157$	−2.80047	+	15.8822i	−0.223502	+	1.26754i	0.642028	+	0.766682i	$0.278093\pi$
$157$	−2.80047	+	15.8822i	−0.223502	+	1.26754i	−0.865529	+	0.500859i	$0.833018\pi$
$158$		0			0
$159$	0.519593	−	0.899962i	0.0412064	−	0.0713716i
$160$		0			0
$161$	−0.840339	−	4.76580i	−0.0662280	−	0.375598i
$162$		0			0
$163$	20.5846	−	7.49217i	1.61231	−	0.586832i	0.630413	−	0.776260i	$-0.282886\pi$
$163$	20.5846	−	7.49217i	1.61231	−	0.586832i	0.981895	+	0.189428i	$0.0606635\pi$
$164$		0			0
$165$	−3.08222	+	17.4802i	−0.239951	+	1.36083i
$166$		0			0
$167$	−7.71540	+	6.47399i	−0.597035	+	0.500972i	−0.890491	−	0.455001i	$-0.849639\pi$
$167$	−7.71540	+	6.47399i	−0.597035	+	0.500972i	0.293456	+	0.955973i	$0.405195\pi$
$168$		0			0
$169$	−26.9546	+	9.81068i	−2.07343	+	0.754668i
$170$		0			0
$171$	−4.06133	−	7.03442i	−0.310577	−	0.537936i
$172$		0			0
$173$	18.6983	+	15.6897i	1.42161	+	1.19287i	0.950473	+	0.310807i	$0.100599\pi$
$173$	18.6983	+	15.6897i	1.42161	+	1.19287i	0.471133	+	0.882062i	$0.343845\pi$
$174$		0			0
$175$	−9.00964	−	15.6052i	−0.681065	−	1.17964i
$176$		0			0
$177$	5.30191	−	9.18317i	0.398516	−	0.690250i
$178$		0			0
$179$	−3.91334			−0.292497			−0.146249	−	0.989248i	$-0.546720\pi$
$179$	−3.91334			−0.292497			−0.146249	+	0.989248i	$0.546720\pi$
$180$		0			0
$181$	−3.36478	−	19.0826i	−0.250102	−	1.41840i	−0.808338	−	0.588719i	$-0.799633\pi$
$181$	−3.36478	−	19.0826i	−0.250102	−	1.41840i	0.558236	−	0.829682i	$-0.311478\pi$
$182$		0			0
$183$	−5.61989	−	4.71565i	−0.415434	−	0.348591i
$184$		0			0
$185$	6.61914	−	21.0775i	0.486649	−	1.54965i
$186$		0			0
$187$	−24.9066	−	20.8991i	−1.82135	−	1.52829i
$188$		0			0
$189$	0.381999	+	2.16642i	0.0277863	+	0.157584i
$190$		0			0
$191$	−6.70722			−0.485317			−0.242659	−	0.970112i	$-0.578019\pi$
$191$	−6.70722			−0.485317			−0.242659	+	0.970112i	$0.578019\pi$
$192$		0			0
$193$	2.97932	−	5.16034i	0.214456	−	0.371450i	−0.738648	−	0.674092i	$-0.764535\pi$
$193$	2.97932	−	5.16034i	0.214456	−	0.371450i	0.953104	+	0.302642i	$0.0978687\pi$
$194$		0			0
$195$	11.7246	+	20.3076i	0.839618	+	1.45426i
$196$		0			0
$197$	−5.16274	−	4.33205i	−0.367830	−	0.308646i	0.440072	−	0.897962i	$-0.354953\pi$
$197$	−5.16274	−	4.33205i	−0.367830	−	0.308646i	−0.807902	+	0.589316i	$0.799397\pi$
$198$		0			0
$199$	−6.99364	−	12.1133i	−0.495766	−	0.858692i	0.504222	−	0.863574i	$-0.331779\pi$
$199$	−6.99364	−	12.1133i	−0.495766	−	0.858692i	−0.999988	+	0.00488204i	$0.998446\pi$
$200$		0			0
$201$	−2.25855	+	0.822045i	−0.159306	+	0.0579826i
$202$		0			0
$203$	−10.3005	+	8.64317i	−0.722955	+	0.606631i
$204$		0			0
$205$	1.42101	−	8.05892i	0.0992473	−	0.562859i
$206$		0			0
$207$	2.06718	−	0.752391i	0.143679	−	0.0522948i
$208$		0			0
$209$	6.89319	+	39.0932i	0.476812	+	2.70414i
$210$		0			0
$211$	8.59552	−	14.8879i	0.591740	−	1.02492i	−0.402258	−	0.915526i	$-0.631775\pi$
$211$	8.59552	−	14.8879i	0.591740	−	1.02492i	0.993998	−	0.109397i	$-0.0348920\pi$
$212$		0			0
$213$	0.0458183	−	0.259849i	0.00313942	−	0.0178045i
$214$		0			0
$215$	−9.96134	−	3.62563i	−0.679358	−	0.247266i
$216$		0			0
$217$	2.20396	+	0.802177i	0.149615	+	0.0544553i
$218$		0			0
$219$	−3.04436	+	2.55452i	−0.205718	+	0.172618i
$220$		0			0
$221$	−42.9532			−2.88934
$222$		0			0
$223$	19.2617			1.28986			0.644929	−	0.764243i	$-0.276887\pi$
$223$	19.2617			1.28986			0.644929	+	0.764243i	$0.276887\pi$
$224$		0			0
$225$	6.27479	−	5.26518i	0.418320	−	0.351012i
$226$		0			0
$227$	8.55494	+	3.11374i	0.567811	+	0.206666i	0.609943	−	0.792446i	$-0.291193\pi$
$227$	8.55494	+	3.11374i	0.567811	+	0.206666i	−0.0421311	+	0.999112i	$0.513415\pi$
$228$		0			0
$229$	−17.4863	−	6.36449i	−1.15553	−	0.420577i	−0.308029	−	0.951377i	$-0.599669\pi$
$229$	−17.4863	−	6.36449i	−1.15553	−	0.420577i	−0.847497	+	0.530800i	$0.821892\pi$
$230$		0			0
$231$	1.86687	−	10.5876i	0.122831	−	0.696610i
$232$		0			0
$233$	13.7155	−	23.7560i	0.898535	−	1.55631i	0.0691674	−	0.997605i	$-0.477966\pi$
$233$	13.7155	−	23.7560i	0.898535	−	1.55631i	0.829368	−	0.558703i	$-0.188701\pi$
$234$		0			0
$235$	−2.43319	−	13.7993i	−0.158724	−	0.900167i
$236$		0			0
$237$	−1.63622	+	0.595534i	−0.106284	+	0.0386841i
$238$		0			0
$239$	3.35142	−	19.0068i	0.216785	−	1.22945i	−0.660997	−	0.750389i	$-0.729866\pi$
$239$	3.35142	−	19.0068i	0.216785	−	1.22945i	0.877782	−	0.479061i	$-0.159023\pi$
$240$		0			0
$241$	11.0506	−	9.27252i	0.711829	−	0.597296i	−0.213282	−	0.976991i	$-0.568415\pi$
$241$	11.0506	−	9.27252i	0.711829	−	0.597296i	0.925112	+	0.379695i	$0.123971\pi$
$242$		0			0
$243$	−0.939693	+	0.342020i	−0.0602813	+	0.0219406i
$244$		0			0
$245$	−3.92376	−	6.79615i	−0.250680	−	0.434190i
$246$		0			0
$247$	40.1734	+	33.7095i	2.55618	+	2.14489i
$248$		0			0
$249$	1.85905	+	3.21998i	0.117813	+	0.204058i
$250$		0			0
$251$	0.572856	−	0.992215i	0.0361583	−	0.0626281i	−0.847380	−	0.530987i	$-0.821821\pi$
$251$	0.572856	−	0.992215i	0.0361583	−	0.0626281i	0.883538	+	0.468359i	$0.155155\pi$
$252$		0			0
$253$	−10.7509			−0.675903
$254$		0			0
$255$	4.19585	+	23.7958i	0.262754	+	1.49015i
$256$		0			0
$257$	9.43410	+	7.91615i	0.588483	+	0.493796i	0.887721	−	0.460383i	$-0.152288\pi$
$257$	9.43410	+	7.91615i	0.588483	+	0.493796i	−0.299237	+	0.954179i	$0.596732\pi$
$258$		0			0
$259$	−4.00915	+	12.7664i	−0.249116	+	0.793267i
$260$		0			0
$261$	−4.68239	−	3.92899i	−0.289832	−	0.243198i
$262$		0			0
$263$	−2.44577	−	13.8707i	−0.150813	−	0.855302i	−0.962515	−	0.271230i	$-0.912570\pi$
$263$	−2.44577	−	13.8707i	−0.150813	−	0.855302i	0.811702	−	0.584072i	$-0.198542\pi$
$264$		0			0
$265$	3.77429			0.231853
$266$		0			0
$267$	6.44261	−	11.1589i	0.394281	−	0.682915i
$268$		0			0
$269$	3.64306	+	6.30997i	0.222121	+	0.384725i	0.955452	−	0.295147i	$-0.0953686\pi$
$269$	3.64306	+	6.30997i	0.222121	+	0.384725i	−0.733331	+	0.679872i	$0.762035\pi$
$270$		0			0
$271$	7.96738	+	6.68543i	0.483984	+	0.406111i	0.851864	−	0.523762i	$-0.175472\pi$
$271$	7.96738	+	6.68543i	0.483984	+	0.406111i	−0.367880	+	0.929873i	$0.619916\pi$
$272$		0			0
$273$	−7.10149	−	12.3001i	−0.429802	−	0.744438i
$274$		0			0
$275$	−37.6170	+	13.6915i	−2.26839	+	0.825626i
$276$		0			0
$277$	5.48212	−	4.60004i	0.329389	−	0.276390i	−0.463062	−	0.886326i	$-0.653249\pi$
$277$	5.48212	−	4.60004i	0.329389	−	0.276390i	0.792451	+	0.609936i	$0.208805\pi$
$278$		0			0
$279$	−0.185138	+	1.04997i	−0.0110839	+	0.0628602i
$280$		0			0
$281$	13.0389	−	4.74578i	0.777837	−	0.283109i	0.0775663	−	0.996987i	$-0.475285\pi$
$281$	13.0389	−	4.74578i	0.777837	−	0.283109i	0.700270	+	0.713878i	$0.253063\pi$
$282$		0			0
$283$	1.15507	+	6.55070i	0.0686615	+	0.389399i	0.999700	+	0.0244787i	$0.00779261\pi$
$283$	1.15507	+	6.55070i	0.0686615	+	0.389399i	−0.931039	+	0.364920i	$0.881096\pi$
$284$		0			0
$285$	14.7506	−	25.5488i	0.873749	−	1.51338i
$286$		0			0
$287$	−0.860689	+	4.88121i	−0.0508049	+	0.288129i
$288$		0			0
$289$	−25.6164	−	9.32362i	−1.50685	−	0.548448i
$290$		0			0
$291$	8.38024	+	3.05016i	0.491258	+	0.178803i
$292$		0			0
$293$	11.9408	−	10.0195i	0.697590	−	0.585347i	−0.223497	−	0.974705i	$-0.571747\pi$
$293$	11.9408	−	10.0195i	0.697590	−	0.585347i	0.921087	+	0.389357i	$0.127303\pi$
$294$		0			0
$295$	38.5127			2.24229
$296$		0			0
$297$	4.88711			0.283579
$298$		0			0
$299$	−10.8801	+	9.12950i	−0.629213	+	0.527973i
$300$		0			0
$301$	6.03349	+	2.19601i	0.347764	+	0.126576i
$302$		0			0
$303$	10.5920	+	3.85517i	0.608495	+	0.221474i
$304$		0			0
$305$	4.62685	−	26.2402i	0.264933	−	1.50251i
$306$		0			0
$307$	−1.66067	+	2.87636i	−0.0947794	+	0.164163i	−0.909517	−	0.415668i	$-0.863548\pi$
$307$	−1.66067	+	2.87636i	−0.0947794	+	0.164163i	0.814737	+	0.579831i	$0.196881\pi$
$308$		0			0
$309$	−1.25502	−	7.11754i	−0.0713953	−	0.404903i
$310$		0			0
$311$	−9.42838	+	3.43165i	−0.534635	+	0.194591i	−0.595207	−	0.803573i	$-0.702930\pi$
$311$	−9.42838	+	3.43165i	−0.534635	+	0.194591i	0.0605720	+	0.998164i	$0.480708\pi$
$312$		0			0
$313$	−1.83599	+	10.4124i	−0.103776	+	0.588545i	0.887926	+	0.459987i	$0.152146\pi$
$313$	−1.83599	+	10.4124i	−0.103776	+	0.588545i	−0.991702	+	0.128558i	$0.958965\pi$
$314$		0			0
$315$	−6.12051	+	5.13572i	−0.344852	+	0.289365i
$316$		0			0
$317$	−20.9878	+	7.63895i	−1.17879	+	0.429046i	−0.855776	−	0.517346i	$-0.826920\pi$
$317$	−20.9878	+	7.63895i	−1.17879	+	0.429046i	−0.323019	+	0.946393i	$0.604698\pi$
$318$		0			0
$319$	14.9360	+	25.8700i	0.836258	+	1.44844i
$320$		0			0
$321$	−6.05399	−	5.07990i	−0.337901	−	0.283532i
$322$		0			0
$323$	27.0194	+	46.7990i	1.50340	+	2.60396i
$324$		0			0
$325$	−26.4425	+	45.7998i	−1.46677	+	2.54052i
$326$		0			0
$327$	−9.22014			−0.509875
$328$		0			0
$329$	1.47376	+	8.35810i	0.0812510	+	0.460797i
$330$		0			0
$331$	−16.8461	−	14.1355i	−0.925944	−	0.776960i	0.0491404	−	0.998792i	$-0.484352\pi$
$331$	−16.8461	−	14.1355i	−0.925944	−	0.776960i	−0.975085	+	0.221832i	$0.928796\pi$
$332$		0			0
$333$	−6.03163	−	0.787043i	−0.330531	−	0.0431297i
$334$		0			0
$335$	−6.68712	−	5.61116i	−0.365357	−	0.306571i
$336$		0			0
$337$	−1.37651	−	7.80660i	−0.0749835	−	0.425253i	−0.999072	−	0.0430738i	$-0.986285\pi$
$337$	−1.37651	−	7.80660i	−0.0749835	−	0.425253i	0.924088	−	0.382179i	$-0.124826\pi$
$338$		0			0
$339$	1.64828			0.0895223
$340$		0			0
$341$	2.60525	−	4.51242i	0.141082	−	0.244361i
$342$		0			0
$343$	10.0760	+	17.4522i	0.544055	+	0.942331i
$344$		0			0
$345$	6.12051	+	5.13572i	0.329517	+	0.276498i
$346$		0			0
$347$	−8.20839	−	14.2174i	−0.440650	−	0.763227i	0.557088	−	0.830453i	$-0.311919\pi$
$347$	−8.20839	−	14.2174i	−0.440650	−	0.763227i	−0.997738	+	0.0672259i	$0.978585\pi$
$348$		0			0
$349$	5.22418	−	1.90144i	0.279644	−	0.101782i	−0.198391	−	0.980123i	$-0.563572\pi$
$349$	5.22418	−	1.90144i	0.279644	−	0.101782i	0.478035	+	0.878341i	$0.341349\pi$
$350$		0			0
$351$	4.94585	−	4.15006i	0.263990	−	0.221514i
$352$		0			0
$353$	3.82748	−	21.7067i	0.203716	−	1.15533i	−0.695731	−	0.718303i	$-0.744919\pi$
$353$	3.82748	−	21.7067i	0.203716	−	1.15533i	0.899447	−	0.437030i	$-0.143970\pi$
$354$		0			0
$355$	0.900526	−	0.327765i	0.0477950	−	0.0173959i
$356$		0			0
$357$	−2.54138	−	14.4129i	−0.134504	−	0.762812i
$358$		0			0
$359$	−2.45554	+	4.25312i	−0.129598	+	0.224471i	−0.923521	−	0.383548i	$-0.874702\pi$
$359$	−2.45554	+	4.25312i	−0.129598	+	0.224471i	0.793923	+	0.608019i	$0.208035\pi$
$360$		0			0
$361$	8.15755	−	46.2638i	0.429345	−	2.43494i
$362$		0			0
$363$	−12.1069	−	4.40654i	−0.635446	−	0.231283i
$364$		0			0
$365$	−13.5634	−	4.93668i	−0.709941	−	0.258397i
$366$		0			0
$367$	−21.3837	+	17.9431i	−1.11622	+	0.936621i	−0.998407	−	0.0564144i	$-0.982033\pi$
$367$	−21.3837	+	17.9431i	−1.11622	+	0.936621i	−0.117814	+	0.993036i	$0.537589\pi$
$368$		0			0
$369$	−2.25312			−0.117293
$370$		0			0
$371$	−2.28605			−0.118686
$372$		0			0
$373$	8.41769	−	7.06328i	0.435851	−	0.365723i	−0.398303	−	0.917254i	$-0.630401\pi$
$373$	8.41769	−	7.06328i	0.435851	−	0.365723i	0.834154	+	0.551531i	$0.185956\pi$
$374$		0			0
$375$	10.8912	+	3.96408i	0.562420	+	0.204704i
$376$		0			0
$377$	37.0840	+	13.4975i	1.90992	+	0.695155i
$378$		0			0
$379$	2.47423	−	14.0320i	0.127092	−	0.720777i	−0.852951	−	0.521992i	$-0.825189\pi$
$379$	2.47423	−	14.0320i	0.127092	−	0.720777i	0.980043	−	0.198785i	$-0.0636997\pi$
$380$		0			0
$381$	−6.77219	+	11.7298i	−0.346950	+	0.600934i
$382$		0			0
$383$	−5.77161	−	32.7324i	−0.294916	−	1.67255i	−0.667545	−	0.744569i	$-0.732655\pi$
$383$	−5.77161	−	32.7324i	−0.294916	−	1.67255i	0.372630	−	0.927980i	$-0.378456\pi$
$384$		0			0
$385$	36.6920	−	13.3548i	1.87000	−	0.680624i
$386$		0			0
$387$	−0.506828	+	2.87436i	−0.0257635	+	0.146112i
$388$		0			0
$389$	−12.6307	+	10.5984i	−0.640401	+	0.537360i	−0.904141	−	0.427234i	$-0.859488\pi$
$389$	−12.6307	+	10.5984i	−0.640401	+	0.537360i	0.263740	+	0.964594i	$0.415044\pi$
$390$		0			0
$391$	−13.7526	+	5.00555i	−0.695501	+	0.253142i
$392$		0			0
$393$	0.630899	+	1.09275i	0.0318247	+	0.0551219i
$394$		0			0
$395$	−4.84452	−	4.06503i	−0.243754	−	0.204534i
$396$		0			0
$397$	−16.9196	−	29.3055i	−0.849168	−	1.47080i	−0.881951	−	0.471340i	$-0.843770\pi$
$397$	−16.9196	−	29.3055i	−0.849168	−	1.47080i	0.0327831	−	0.999462i	$-0.489563\pi$
$398$		0			0
$399$	−8.93429	+	15.4746i	−0.447274	+	0.774701i
$400$		0			0
$401$	37.5546			1.87539			0.937693	−	0.347464i	$-0.112957\pi$
$401$	37.5546			1.87539			0.937693	+	0.347464i	$0.112957\pi$
$402$		0			0
$403$	−1.19532	−	6.77899i	−0.0595431	−	0.337686i
$404$		0			0
$405$	−2.78225	−	2.33458i	−0.138251	−	0.116006i
$406$		0			0
$407$	26.3840	+	13.6962i	1.30781	+	0.678896i
$408$		0			0
$409$	−2.09781	−	1.76027i	−0.103730	−	0.0870399i	0.589448	−	0.807807i	$-0.299345\pi$
$409$	−2.09781	−	1.76027i	−0.103730	−	0.0870399i	−0.693178	+	0.720767i	$0.743790\pi$
$410$		0			0
$411$	−1.79700	−	10.1913i	−0.0886394	−	0.502699i
$412$		0			0
$413$	−23.3268			−1.14783
$414$		0			0
$415$	−6.75202	+	11.6948i	−0.331444	+	0.574077i
$416$		0			0
$417$	9.67769	+	16.7622i	0.473918	+	0.820851i
$418$		0			0
$419$	21.4576	+	18.0051i	1.04827	+	0.879605i	0.992911	−	0.118862i	$-0.0379246\pi$
$419$	21.4576	+	18.0051i	1.04827	+	0.879605i	0.0553611	+	0.998466i	$0.482369\pi$
$420$		0			0
$421$	−16.2035	−	28.0653i	−0.789711	−	1.36782i	−0.926144	−	0.377171i	$-0.876897\pi$
$421$	−16.2035	−	28.0653i	−0.789711	−	1.36782i	0.136432	−	0.990649i	$-0.456436\pi$
$422$		0			0
$423$	−3.62535	+	1.31952i	−0.176271	+	0.0641572i
$424$		0			0
$425$	−41.7453	+	35.0284i	−2.02494	+	1.69913i
$426$		0			0
$427$	−2.80244	+	15.8934i	−0.135620	+	0.769137i
$428$		0			0
$429$	−29.6501	+	10.7917i	−1.43152	+	0.521030i
$430$		0			0
$431$	6.91890	+	39.2390i	0.333272	+	1.89008i	0.443671	+	0.896190i	$0.353676\pi$
$431$	6.91890	+	39.2390i	0.333272	+	1.89008i	−0.110400	+	0.993887i	$0.535213\pi$
$432$		0			0
$433$	−9.20021	+	15.9352i	−0.442134	+	0.765798i	−0.997848	−	0.0655753i	$-0.979112\pi$
$433$	−9.20021	+	15.9352i	−0.442134	+	0.765798i	0.555714	+	0.831374i	$0.312445\pi$
$434$		0			0
$435$	3.85501	−	21.8628i	0.184833	−	1.04824i
$436$		0			0
$437$	16.7910	+	6.11141i	0.803221	+	0.292349i
$438$		0			0
$439$	−6.70502	−	2.44043i	−0.320013	−	0.116475i	0.177019	−	0.984207i	$-0.443355\pi$
$439$	−6.70502	−	2.44043i	−0.320013	−	0.116475i	−0.497032	+	0.867732i	$0.665577\pi$
$440$		0			0
$441$	−1.65518	+	1.38886i	−0.0788180	+	0.0661361i
$442$		0			0
$443$	−19.8367			−0.942471			−0.471236	−	0.882007i	$-0.656192\pi$
$443$	−19.8367			−0.942471			−0.471236	+	0.882007i	$0.656192\pi$
$444$		0			0
$445$	46.7986			2.21847
$446$		0			0
$447$	−11.0147	+	9.24241i	−0.520976	+	0.437151i
$448$		0			0
$449$	−7.71814	−	2.80917i	−0.364242	−	0.132573i	0.153414	−	0.988162i	$-0.450973\pi$
$449$	−7.71814	−	2.80917i	−0.364242	−	0.132573i	−0.517656	+	0.855589i	$0.673195\pi$
$450$		0			0
$451$	10.3472	+	3.76607i	0.487230	+	0.177337i
$452$		0			0
$453$	−4.03192	+	22.8662i	−0.189436	+	1.07435i
$454$		0			0
$455$	25.7924	−	44.6737i	1.20916	−	2.09433i
$456$		0			0
$457$	1.48206	+	8.40520i	0.0693280	+	0.393179i	0.999651	+	0.0264362i	$0.00841589\pi$
$457$	1.48206	+	8.40520i	0.0693280	+	0.393179i	−0.930322	+	0.366743i	$0.880473\pi$
$458$		0			0
$459$	6.25164	−	2.27541i	0.291801	−	0.106207i
$460$		0			0
$461$	−3.91313	+	22.1925i	−0.182253	+	1.03361i	0.747182	+	0.664619i	$0.231406\pi$
$461$	−3.91313	+	22.1925i	−0.182253	+	1.03361i	−0.929435	+	0.368987i	$0.879705\pi$
$462$		0			0
$463$	−25.3799	+	21.2962i	−1.17950	+	0.989720i	−0.179520	+	0.983754i	$0.557455\pi$
$463$	−25.3799	+	21.2962i	−1.17950	+	0.989720i	−0.999982	+	0.00596571i	$0.998101\pi$
$464$		0			0
$465$	−3.63876	+	1.32440i	−0.168744	+	0.0614176i
$466$		0			0
$467$	12.0844	+	20.9307i	0.559197	+	0.968558i	0.997564	+	0.0697618i	$0.0222239\pi$
$467$	12.0844	+	20.9307i	0.559197	+	0.968558i	−0.438366	+	0.898796i	$0.644443\pi$
$468$		0			0
$469$	4.05033	+	3.39863i	0.187027	+	0.156934i
$470$		0			0
$471$	8.06362	+	13.9666i	0.371552	+	0.643547i
$472$		0			0
$473$	7.13202	−	12.3530i	0.327931	−	0.567993i
$474$		0			0
$475$	66.5339			3.05279
$476$		0			0
$477$	−0.180453	−	1.02340i	−0.00826237	−	0.0468582i
$478$		0			0
$479$	12.8790	+	10.8068i	0.588458	+	0.493775i	0.887712	−	0.460399i	$-0.152294\pi$
$479$	12.8790	+	10.8068i	0.588458	+	0.493775i	−0.299254	+	0.954173i	$0.596738\pi$
$480$		0			0
$481$	38.3318	−	8.54408i	1.74778	−	0.389577i
$482$		0			0
$483$	−3.70713	−	3.11065i	−0.168680	−	0.141540i
$484$		0			0
$485$	5.62448	+	31.8980i	0.255395	+	1.44841i
$486$		0			0
$487$	5.25701			0.238218			0.119109	−	0.992881i	$-0.461996\pi$
$487$	5.25701			0.238218			0.119109	+	0.992881i	$0.461996\pi$
$488$		0			0
$489$	10.9528	−	18.9708i	0.495303	−	0.857891i
$490$		0			0
$491$	−3.43003	−	5.94099i	−0.154795	−	0.268113i	0.778189	−	0.628030i	$-0.216138\pi$
$491$	−3.43003	−	5.94099i	−0.154795	−	0.268113i	−0.932984	+	0.359917i	$0.882805\pi$
$492$		0			0
$493$	31.1512	+	26.1390i	1.40298	+	1.17724i
$494$		0			0
$495$	8.87491	+	15.3718i	0.398897	+	0.690911i
$496$		0			0
$497$	−0.545440	+	0.198524i	−0.0244663	+	0.00890501i
$498$		0			0
$499$	−9.98370	+	8.37732i	−0.446932	+	0.375020i	−0.838296	−	0.545216i	$-0.816448\pi$
$499$	−9.98370	+	8.37732i	−0.446932	+	0.375020i	0.391364	+	0.920236i	$0.372003\pi$
$500$		0			0
$501$	−1.74894	+	9.91872i	−0.0781368	+	0.443136i
$502$		0			0
$503$	7.89385	−	2.87313i	0.351970	−	0.128106i	−0.159984	−	0.987120i	$-0.551144\pi$
$503$	7.89385	−	2.87313i	0.351970	−	0.128106i	0.511953	+	0.859013i	$0.328922\pi$
$504$		0			0
$505$	7.10893	+	40.3167i	0.316343	+	1.79407i
$506$		0			0
$507$	−14.3423	+	24.8415i	−0.636962	+	1.10325i
$508$		0			0
$509$	0.741657	−	4.20614i	0.0328734	−	0.186434i	−0.963949	−	0.266086i	$-0.914270\pi$
$509$	0.741657	−	4.20614i	0.0328734	−	0.186434i	0.996823	+	0.0796515i	$0.0253807\pi$
$510$		0			0
$511$	8.21522	+	2.99010i	0.363420	+	0.132274i
$512$		0			0
$513$	−7.63280	−	2.77811i	−0.336996	−	0.122657i
$514$		0			0
$515$	20.1082	−	16.8728i	0.886075	−	0.743505i
$516$		0			0
$517$	18.8546			0.829223
$518$		0			0
$519$	24.4089			1.07143
$520$		0			0
$521$	23.7822	−	19.9556i	1.04192	−	0.874272i	0.0496959	−	0.998764i	$-0.484175\pi$
$521$	23.7822	−	19.9556i	1.04192	−	0.874272i	0.992221	+	0.124493i	$0.0397303\pi$
$522$		0			0
$523$	18.6125	+	6.77441i	0.813869	+	0.296224i	0.715221	−	0.698898i	$-0.246326\pi$
$523$	18.6125	+	6.77441i	0.813869	+	0.296224i	0.0986481	+	0.995122i	$0.468548\pi$
$524$		0			0
$525$	−16.9326	−	6.16296i	−0.738999	−	0.268974i
$526$		0			0
$527$	1.23170	−	6.98531i	0.0536536	−	0.304285i
$528$		0			0
$529$	9.08034	−	15.7276i	0.394797	−	0.683809i
$530$		0			0
$531$	−1.84133	−	10.4427i	−0.0799071	−	0.453176i
$532$		0			0
$533$	13.6696	−	4.97534i	0.592098	−	0.215506i
$534$		0			0
$535$	4.98424	−	28.2670i	0.215488	−	1.22209i
$536$		0			0
$537$	−2.99780	+	2.51545i	−0.129364	+	0.108550i
$538$		0			0
$539$	9.92267	−	3.61156i	0.427400	−	0.155561i
$540$		0			0
$541$	17.0233	+	29.4852i	0.731889	+	1.26767i	0.956075	+	0.293123i	$0.0946944\pi$
$541$	17.0233	+	29.4852i	0.731889	+	1.26767i	−0.224186	+	0.974546i	$0.571972\pi$
$542$		0			0
$543$	−14.8437	−	12.4553i	−0.637002	−	0.534508i
$544$		0			0
$545$	−16.7436	−	29.0008i	−0.717217	−	1.24226i
$546$		0			0
$547$	−1.99846	+	3.46144i	−0.0854482	+	0.148001i	−0.905582	−	0.424171i	$-0.860566\pi$
$547$	−1.99846	+	3.46144i	−0.0854482	+	0.148001i	0.820134	+	0.572172i	$0.193899\pi$
$548$		0			0
$549$	−7.33624			−0.313103
$550$		0			0
$551$	−8.62147	−	48.8948i	−0.367287	−	2.08299i
$552$		0			0
$553$	2.93428	+	2.46215i	0.124778	+	0.104701i
$554$		0			0
$555$	−8.47779	−	20.4010i	−0.359862	−	0.865974i
$556$		0			0
$557$	1.79053	+	1.50243i	0.0758672	+	0.0636601i	0.679933	−	0.733275i	$-0.262009\pi$
$557$	1.79053	+	1.50243i	0.0758672	+	0.0636601i	−0.604065	+	0.796935i	$0.706453\pi$
$558$		0			0
$559$	−3.27226	−	18.5579i	−0.138402	−	0.784916i
$560$		0			0
$561$	−32.5132			−1.37271
$562$		0			0
$563$	−18.7609	+	32.4949i	−0.790679	+	1.36950i	0.134868	+	0.990864i	$0.456939\pi$
$563$	−18.7609	+	32.4949i	−0.790679	+	1.36950i	−0.925547	+	0.378632i	$0.876394\pi$
$564$		0			0
$565$	2.99325	+	5.18445i	0.125927	+	0.218112i
$566$		0			0
$567$	1.68518	+	1.41403i	0.0707709	+	0.0593838i
$568$		0			0
$569$	15.9880	+	27.6920i	0.670251	+	1.16091i	0.977833	+	0.209388i	$0.0671471\pi$
$569$	15.9880	+	27.6920i	0.670251	+	1.16091i	−0.307581	+	0.951522i	$0.599520\pi$
$570$		0			0
$571$	−26.6929	+	9.71542i	−1.11706	+	0.406578i	−0.833580	−	0.552399i	$-0.813712\pi$
$571$	−26.6929	+	9.71542i	−1.11706	+	0.406578i	−0.283483	+	0.958977i	$0.591490\pi$
$572$		0			0
$573$	−5.13803	+	4.31132i	−0.214644	+	0.180108i
$574$		0			0
$575$	−3.12902	+	17.7455i	−0.130489	+	0.740040i
$576$		0			0
$577$	−13.6246	+	4.95894i	−0.567198	+	0.206443i	−0.609671	−	0.792654i	$-0.708699\pi$
$577$	−13.6246	+	4.95894i	−0.567198	+	0.206443i	0.0424729	+	0.999098i	$0.486476\pi$
$578$		0			0
$579$	−1.03471	−	5.86812i	−0.0430010	−	0.243871i
$580$		0			0
$581$	4.08963	−	7.08345i	0.169667	−	0.293871i
$582$		0			0
$583$	−0.881893	+	5.00147i	−0.0365243	+	0.207140i
$584$		0			0
$585$	22.0351	+	8.02011i	0.911039	+	0.331591i
$586$		0			0
$587$	28.9515	+	10.5375i	1.19496	+	0.434928i	0.861461	−	0.507824i	$-0.169550\pi$
$587$	28.9515	+	10.5375i	1.19496	+	0.434928i	0.333495	+	0.942752i	$0.391772\pi$
$588$		0			0
$589$	−6.63404	+	5.56662i	−0.273351	+	0.229369i
$590$		0			0
$591$	−6.73948			−0.277225
$592$		0			0
$593$	−26.3795			−1.08328			−0.541639	−	0.840611i	$-0.682196\pi$
$593$	−26.3795			−1.08328			−0.541639	+	0.840611i	$0.682196\pi$
$594$		0			0
$595$	40.7189	−	34.1672i	1.66931	−	1.40072i
$596$		0			0
$597$	−13.1437	−	4.78393i	−0.537938	−	0.195793i
$598$		0			0
$599$	−36.1244	−	13.1482i	−1.47600	−	0.537221i	−0.526280	−	0.850311i	$-0.676414\pi$
$599$	−36.1244	−	13.1482i	−1.47600	−	0.537221i	−0.949724	+	0.313090i	$0.898636\pi$
$600$		0			0
$601$	4.35857	−	24.7187i	0.177790	−	1.00829i	−0.757085	−	0.653317i	$-0.773377\pi$
$601$	4.35857	−	24.7187i	0.177790	−	1.00829i	0.934874	−	0.354978i	$-0.115512\pi$
$602$		0			0
$603$	−1.20175	+	2.08149i	−0.0489390	+	0.0847648i
$604$		0			0
$605$	−8.12564	−	46.0828i	−0.330354	−	1.87353i
$606$		0			0
$607$	7.62601	−	2.77564i	0.309530	−	0.112660i	−0.182584	−	0.983190i	$-0.558446\pi$
$607$	7.62601	−	2.77564i	0.309530	−	0.112660i	0.492115	+	0.870530i	$0.336224\pi$
$608$		0			0
$609$	−2.33494	+	13.2421i	−0.0946165	+	0.536597i
$610$		0			0
$611$	19.0812	−	16.0110i	0.771942	−	0.647737i
$612$		0			0
$613$	−18.5369	+	6.74687i	−0.748697	+	0.272503i	−0.688057	−	0.725656i	$-0.741536\pi$
$613$	−18.5369	+	6.74687i	−0.748697	+	0.272503i	−0.0606396	+	0.998160i	$0.519314\pi$
$614$		0			0
$615$	−4.09162	−	7.08690i	−0.164990	−	0.285771i
$616$		0			0
$617$	−27.9677	−	23.4677i	−1.12594	−	0.944773i	−0.127047	−	0.991897i	$-0.540550\pi$
$617$	−27.9677	−	23.4677i	−1.12594	−	0.944773i	−0.998889	+	0.0471240i	$0.984994\pi$
$618$		0			0
$619$	16.9513	+	29.3606i	0.681331	+	1.18010i	0.974575	+	0.224063i	$0.0719321\pi$
$619$	16.9513	+	29.3606i	0.681331	+	1.18010i	−0.293243	+	0.956038i	$0.594735\pi$
$620$		0			0
$621$	1.09992	−	1.90512i	0.0441384	−	0.0764499i
$622$		0			0
$623$	−28.3455			−1.13564
$624$		0			0
$625$	0.197841	+	1.12201i	0.00791365	+	0.0448805i
$626$		0			0
$627$	30.4091	+	25.5163i	1.21442	+	1.01902i
$628$		0			0
$629$	40.1275	+	5.23608i	1.59999	+	0.208776i
$630$		0			0
$631$	3.30172	+	2.77047i	0.131439	+	0.110291i	0.706137	−	0.708075i	$-0.250436\pi$
$631$	3.30172	+	2.77047i	0.131439	+	0.110291i	−0.574698	+	0.818365i	$0.694881\pi$
$632$		0			0
$633$	−2.98519	−	16.9299i	−0.118651	−	0.672902i
$634$		0			0
$635$	−49.1927			−1.95215
$636$		0			0
$637$	6.97506	−	12.0812i	0.276362	−	0.478673i
$638$		0			0
$639$	−0.131929	−	0.228507i	−0.00521902	−	0.00903960i
$640$		0			0
$641$	−7.69310	−	6.45528i	−0.303859	−	0.254968i	0.478089	−	0.878311i	$-0.341330\pi$
$641$	−7.69310	−	6.45528i	−0.303859	−	0.254968i	−0.781948	+	0.623343i	$0.785774\pi$
$642$		0			0
$643$	0.915522	+	1.58573i	0.0361047	+	0.0625351i	0.883513	−	0.468406i	$-0.155172\pi$
$643$	0.915522	+	1.58573i	0.0361047	+	0.0625351i	−0.847408	+	0.530942i	$0.821838\pi$
$644$		0			0
$645$	−9.96134	+	3.62563i	−0.392227	+	0.142759i
$646$		0			0
$647$	2.97773	−	2.49861i	0.117067	−	0.0982306i	−0.582375	−	0.812920i	$-0.697876\pi$
$647$	2.97773	−	2.49861i	0.117067	−	0.0982306i	0.699442	+	0.714690i	$0.253432\pi$
$648$		0			0
$649$	−8.99880	+	51.0347i	−0.353234	+	2.00329i
$650$		0			0
$651$	2.20396	−	0.802177i	0.0863801	−	0.0314398i
$652$		0			0
$653$	−1.15323	−	6.54029i	−0.0451293	−	0.255941i	0.953893	−	0.300146i	$-0.0970356\pi$
$653$	−1.15323	−	6.54029i	−0.0451293	−	0.255941i	−0.999022	+	0.0442053i	$0.985924\pi$
$654$		0			0
$655$	−2.29140	+	3.96883i	−0.0895325	+	0.155075i
$656$		0			0
$657$	−0.690099	+	3.91375i	−0.0269233	+	0.152690i
$658$		0			0
$659$	−30.6783	−	11.1660i	−1.19506	−	0.434965i	−0.333559	−	0.942729i	$-0.608250\pi$
$659$	−30.6783	−	11.1660i	−1.19506	−	0.434965i	−0.861496	+	0.507765i	$0.830472\pi$
$660$		0			0
$661$	−23.6835	−	8.62010i	−0.921183	−	0.335283i	−0.162474	−	0.986713i	$-0.551947\pi$
$661$	−23.6835	−	8.62010i	−0.921183	−	0.335283i	−0.758709	+	0.651430i	$0.774170\pi$
$662$		0			0
$663$	−32.9040	+	27.6098i	−1.27789	+	1.07227i
$664$		0			0
$665$	−64.8980			−2.51664
$666$		0			0
$667$	13.4464			0.520646
$668$		0			0
$669$	14.7553	−	12.3812i	0.570473	−	0.478684i
$670$		0			0
$671$	33.6908	+	12.2625i	1.30062	+	0.473387i
$672$		0			0
$673$	24.9513	+	9.08154i	0.961803	+	0.350068i	0.774740	−	0.632280i	$-0.217881\pi$
$673$	24.9513	+	9.08154i	0.961803	+	0.350068i	0.187063	+	0.982348i	$0.440103\pi$
$674$		0			0
$675$	1.42238	−	8.06672i	0.0547474	−	0.310488i
$676$		0			0
$677$	−16.9309	+	29.3252i	−0.650709	+	1.12706i	0.332243	+	0.943194i	$0.392195\pi$
$677$	−16.9309	+	29.3252i	−0.650709	+	1.12706i	−0.982951	+	0.183866i	$0.941139\pi$
$678$		0			0
$679$	−3.40669	−	19.3203i	−0.130737	−	0.741446i
$680$		0			0
$681$	8.55494	−	3.11374i	0.327826	−	0.119319i
$682$		0			0
$683$	−3.33698	+	18.9250i	−0.127686	+	0.724144i	0.851990	+	0.523558i	$0.175396\pi$
$683$	−3.33698	+	18.9250i	−0.127686	+	0.724144i	−0.979676	+	0.200586i	$0.935715\pi$
$684$		0			0
$685$	28.7921	−	24.1594i	1.10009	−	0.923084i
$686$		0			0
$687$	−17.4863	+	6.36449i	−0.667143	+	0.242820i
$688$		0			0
$689$	3.35468	+	5.81047i	0.127803	+	0.221361i
$690$		0			0
$691$	−5.39200	−	4.52443i	−0.205121	−	0.172117i	0.534440	−	0.845206i	$-0.320523\pi$
$691$	−5.39200	−	4.52443i	−0.205121	−	0.172117i	−0.739561	+	0.673089i	$0.764967\pi$
$692$		0			0
$693$	−5.37545	−	9.31054i	−0.204196	−	0.353678i
$694$		0			0
$695$	−35.1490	+	60.8799i	−1.33328	+	2.30931i
$696$		0			0
$697$	14.9897			0.567774
$698$		0			0
$699$	−4.76336	−	27.0143i	−0.180167	−	1.02178i
$700$		0			0
$701$	−9.10742	−	7.64204i	−0.343983	−	0.288636i	0.454386	−	0.890805i	$-0.349859\pi$
$701$	−9.10742	−	7.64204i	−0.343983	−	0.288636i	−0.798368	+	0.602169i	$0.794303\pi$
$702$		0			0
$703$	−33.4214	−	36.3892i	−1.26051	−	1.37245i
$704$		0			0
$705$	−10.7340	−	9.00685i	−0.404264	−	0.339218i
$706$		0			0
$707$	−4.30581	−	24.4194i	−0.161937	−	0.918388i
$708$		0			0
$709$	18.6221			0.699369			0.349685	−	0.936867i	$-0.386289\pi$
$709$	18.6221			0.699369			0.349685	+	0.936867i	$0.386289\pi$
$710$		0			0
$711$	−0.870613	+	1.50795i	−0.0326505	+	0.0565524i
$712$		0			0
$713$	−1.17270	−	2.03118i	−0.0439181	−	0.0760684i
$714$		0			0
$715$	−87.7880	−	73.6629i	−3.28308	−	2.75484i
$716$		0			0
$717$	−9.65002	−	16.7143i	−0.360387	−	0.624208i
$718$		0			0
$719$	23.2987	−	8.48004i	0.868895	−	0.316252i	0.131176	−	0.991359i	$-0.458125\pi$
$719$	23.2987	−	8.48004i	0.868895	−	0.316252i	0.737720	+	0.675107i	$0.235903\pi$
$720$		0			0
$721$	−12.1794	+	10.2197i	−0.453583	+	0.380602i
$722$		0			0
$723$	2.50496	−	14.2063i	0.0931604	−	0.528339i
$724$		0			0
$725$	47.0484	−	17.1242i	1.74733	−	0.635977i
$726$		0			0
$727$	−6.03056	−	34.2010i	−0.223661	−	1.26844i	−0.865229	−	0.501378i	$-0.832827\pi$
$727$	−6.03056	−	34.2010i	−0.223661	−	1.26844i	0.641568	−	0.767067i	$-0.278284\pi$
$728$		0			0
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$		0			0
$731$	3.37185	−	19.1227i	0.124712	−	0.707279i
$732$		0			0
$733$	−6.97572	−	2.53896i	−0.257654	−	0.0937785i	0.209964	−	0.977709i	$-0.432665\pi$
$733$	−6.97572	−	2.53896i	−0.257654	−	0.0937785i	−0.467618	+	0.883931i	$0.654888\pi$
$734$		0			0
$735$	−7.37425	−	2.68401i	−0.272003	−	0.0990011i
$736$		0			0
$737$	8.99808	−	7.55029i	0.331449	−	0.278118i
$738$		0			0
$739$	7.89275			0.290340			0.145170	−	0.989407i	$-0.453627\pi$
$739$	7.89275			0.290340			0.145170	+	0.989407i	$0.453627\pi$
$740$		0			0
$741$	52.4427			1.92653
$742$		0			0
$743$	33.7563	−	28.3249i	1.23840	−	1.03914i	0.240749	−	0.970587i	$-0.422607\pi$
$743$	33.7563	−	28.3249i	1.23840	−	1.03914i	0.997648	−	0.0685511i	$-0.0218376\pi$
$744$		0			0
$745$	−49.0733	−	17.8612i	−1.79790	−	0.654384i
$746$		0			0
$747$	3.49388	+	1.27167i	0.127834	+	0.0465279i
$748$		0			0
$749$	−3.01891	+	17.1211i	−0.110308	+	0.625591i
$750$		0			0
$751$	18.7985	−	32.5600i	0.685967	−	1.18813i	−0.287165	−	0.957881i	$-0.592713\pi$
$751$	18.7985	−	32.5600i	0.685967	−	1.18813i	0.973132	−	0.230249i	$-0.0739540\pi$
$752$		0			0
$753$	−0.198951	−	1.12831i	−0.00725017	−	0.0411177i
$754$		0			0
$755$	−79.2445	+	28.8426i	−2.88400	+	1.04969i
$756$		0			0
$757$	3.49245	−	19.8067i	0.126935	−	0.719886i	−0.853204	−	0.521577i	$-0.825344\pi$
$757$	3.49245	−	19.8067i	0.126935	−	0.719886i	0.980140	−	0.198309i	$-0.0635449\pi$
$758$		0			0
$759$	−8.23566	+	6.91054i	−0.298936	+	0.250837i
$760$		0			0
$761$	−28.8248	+	10.4914i	−1.04490	+	0.380311i	−0.806735	−	0.590914i	$-0.798767\pi$
$761$	−28.8248	+	10.4914i	−1.04490	+	0.380311i	−0.238163	+	0.971225i	$0.576545\pi$
$762$		0			0
$763$	10.1414	+	17.5655i	0.367145	+	0.635914i
$764$		0			0
$765$	18.5099	+	15.5316i	0.669226	+	0.561547i
$766$		0			0
$767$	34.2310	+	59.2898i	1.23601	+	2.14083i
$768$		0			0
$769$	−5.88128	+	10.1867i	−0.212085	+	0.367341i	−0.952367	−	0.304955i	$-0.901359\pi$
$769$	−5.88128	+	10.1867i	−0.212085	+	0.367341i	0.740282	+	0.672296i	$0.234692\pi$
$770$		0			0
$771$	12.3153			0.443526
$772$		0			0
$773$	0.659211	+	3.73857i	0.0237102	+	0.134467i	0.994365	−	0.106010i	$-0.0338074\pi$
$773$	0.659211	+	3.73857i	0.0237102	+	0.134467i	−0.970655	+	0.240477i	$0.922696\pi$
$774$		0			0
$775$	−6.69000	−	5.61357i	−0.240312	−	0.201645i
$776$		0			0
$777$	5.13491	+	12.3567i	0.184214	+	0.443293i
$778$		0			0
$779$	−14.0196	−	11.7638i	−0.502304	−	0.421483i
$780$		0			0
$781$	0.223919	+	1.26991i	0.00801246	+	0.0454409i
$782$		0			0
$783$	−6.11242			−0.218440
$784$		0			0
$785$	−29.2868	+	50.7262i	−1.04529	+	1.81050i
$786$		0			0
$787$	19.3332	+	33.4862i	0.689156	+	1.19365i	0.972111	+	0.234520i	$0.0753517\pi$
$787$	19.3332	+	33.4862i	0.689156	+	1.19365i	−0.282956	+	0.959133i	$0.591315\pi$
$788$		0			0
$789$	−10.7895	−	9.05344i	−0.384115	−	0.322311i
$790$		0			0
$791$	−1.81298	−	3.14017i	−0.0644621	−	0.111652i
$792$		0			0
$793$	44.5089	−	16.1999i	1.58056	−	0.575276i
$794$		0			0
$795$	2.89127	−	2.42607i	0.102543	−	0.0860437i
$796$		0			0
$797$	−0.297515	+	1.68729i	−0.0105385	+	0.0597670i	−0.989624	−	0.143685i	$-0.954105\pi$
$797$	−0.297515	+	1.68729i	−0.0105385	+	0.0597670i	0.979085	+	0.203452i	$0.0652160\pi$
$798$		0			0
$799$	24.1189	−	8.77857i	0.853266	−	0.310563i
$800$		0			0
$801$	−2.23749	−	12.6895i	−0.0790580	−	0.448360i
$802$		0			0
$803$	9.71099	−	16.8199i	0.342694	−	0.593563i
$804$		0			0
$805$	3.05208	−	17.3092i	0.107572	−	0.610070i
$806$		0			0
$807$	6.84671	+	2.49200i	0.241016	+	0.0877226i
$808$		0			0
$809$	−21.5705	−	7.85101i	−0.758378	−	0.276027i	−0.0662511	−	0.997803i	$-0.521104\pi$
$809$	−21.5705	−	7.85101i	−0.758378	−	0.276027i	−0.692127	+	0.721776i	$0.743326\pi$
$810$		0			0
$811$	−20.8433	+	17.4896i	−0.731906	+	0.614142i	−0.930651	−	0.365909i	$-0.880758\pi$
$811$	−20.8433	+	17.4896i	−0.731906	+	0.614142i	0.198744	+	0.980051i	$0.436314\pi$
$812$		0			0
$813$	10.4007			0.364768
$814$		0			0
$815$	79.5605			2.78688
$816$		0			0
$817$	−18.1611	+	15.2390i	−0.635376	+	0.533144i
$818$		0			0
$819$	−13.3464	−	4.85771i	−0.466362	−	0.169742i
$820$		0			0
$821$	−41.6474	−	15.1584i	−1.45350	−	0.529032i	−0.509936	−	0.860212i	$-0.670331\pi$
$821$	−41.6474	−	15.1584i	−1.45350	−	0.529032i	−0.943568	+	0.331180i	$0.892553\pi$
$822$		0			0
$823$	−1.34748	+	7.64193i	−0.0469701	+	0.266381i	−0.999245	−	0.0388623i	$-0.987627\pi$
$823$	−1.34748	+	7.64193i	−0.0469701	+	0.266381i	0.952274	+	0.305243i	$0.0987377\pi$
$824$		0			0
$825$	−20.0156	+	34.6680i	−0.696852	+	1.20698i
$826$		0			0
$827$	8.01303	+	45.4442i	0.278640	+	1.58025i	0.727155	+	0.686473i	$0.240842\pi$
$827$	8.01303	+	45.4442i	0.278640	+	1.58025i	−0.448515	+	0.893775i	$0.648047\pi$
$828$		0			0
$829$	−26.8112	+	9.75849i	−0.931193	+	0.338926i	−0.762682	−	0.646773i	$-0.776118\pi$
$829$	−26.8112	+	9.75849i	−0.931193	+	0.338926i	−0.168511	+	0.985700i	$0.553896\pi$
$830$		0			0
$831$	1.24270	−	7.04768i	0.0431086	−	0.244481i
$832$		0			0
$833$	11.0116	−	9.23987i	0.381531	−	0.320143i
$834$		0			0
$835$	−34.3741	+	12.5112i	−1.18957	+	0.432966i
$836$		0			0
$837$	0.533085	+	0.923330i	0.0184261	+	0.0319150i
$838$		0			0
$839$	22.4406	+	18.8299i	0.774734	+	0.650079i	0.941917	−	0.335847i	$-0.109023\pi$
$839$	22.4406	+	18.8299i	0.774734	+	0.650079i	−0.167183	+	0.985926i	$0.553467\pi$
$840$		0			0
$841$	−4.18084	−	7.24143i	−0.144167	−	0.249704i
$842$		0			0
$843$	6.93786	−	12.0167i	0.238953	−	0.413878i
$844$		0			0
$845$	−104.181			−3.58394
$846$		0			0
$847$	4.92162	+	27.9119i	0.169109	+	0.959065i
$848$		0			0
$849$	5.09554	+	4.27567i	0.174879	+	0.146741i
$850$		0			0
$851$	11.2773	−	7.20262i	0.386580	−	0.246903i
$852$		0			0
$853$	11.5682	+	9.70688i	0.396088	+	0.332357i	0.818979	−	0.573823i	$-0.194540\pi$
$853$	11.5682	+	9.70688i	0.396088	+	0.332357i	−0.422891	+	0.906180i	$0.638985\pi$
$854$		0			0
$855$	−5.12283	−	29.0530i	−0.175197	−	0.993591i
$856$		0			0
$857$	−11.2116			−0.382980			−0.191490	−	0.981495i	$-0.561332\pi$
$857$	−11.2116			−0.382980			−0.191490	+	0.981495i	$0.561332\pi$
$858$		0			0
$859$	25.7018	−	44.5168i	0.876933	−	1.51889i	0.0222431	−	0.999753i	$-0.492919\pi$
$859$	25.7018	−	44.5168i	0.876933	−	1.51889i	0.854690	−	0.519139i	$-0.173747\pi$
$860$		0			0
$861$	2.47826	+	4.29246i	0.0844587	+	0.146287i
$862$		0			0
$863$	−3.44831	−	2.89348i	−0.117382	−	0.0984952i	0.582207	−	0.813040i	$-0.302189\pi$
$863$	−3.44831	−	2.89348i	−0.117382	−	0.0984952i	−0.699589	+	0.714545i	$0.746634\pi$
$864$		0			0
$865$	44.3261	+	76.7751i	1.50713	+	2.61043i
$866$		0			0
$867$	−25.6164	+	9.32362i	−0.869980	+	0.316647i
$868$		0			0
$869$	6.51870	−	5.46984i	0.221132	−	0.185552i
$870$		0			0
$871$	2.69464	−	15.2821i	0.0913045	−	0.517814i
$872$		0			0
$873$	8.38024	−	3.05016i	0.283628	−	0.103232i
$874$		0			0
$875$	−4.42744	−	25.1093i	−0.149675	−	0.848848i
$876$		0			0
$877$	−8.01881	+	13.8890i	−0.270776	+	0.468998i	−0.969061	−	0.246822i	$-0.920614\pi$
$877$	−8.01881	+	13.8890i	−0.270776	+	0.468998i	0.698285	+	0.715820i	$0.253947\pi$
$878$		0			0
$879$	2.70676	−	15.3508i	0.0912968	−	0.517770i
$880$		0			0
$881$	26.7833	+	9.74833i	0.902353	+	0.328429i	0.751195	−	0.660080i	$-0.229478\pi$
$881$	26.7833	+	9.74833i	0.902353	+	0.328429i	0.151157	+	0.988510i	$0.451700\pi$
$882$		0			0
$883$	51.6652	+	18.8046i	1.73867	+	0.632826i	0.999186	−	0.0403441i	$-0.0128454\pi$
$883$	51.6652	+	18.8046i	1.73867	+	0.632826i	0.739488	+	0.673170i	$0.235068\pi$
$884$		0			0
$885$	29.5024	−	24.7555i	0.991713	−	0.832146i
$886$		0			0
$887$	−15.1126			−0.507432			−0.253716	−	0.967279i	$-0.581653\pi$
$887$	−15.1126			−0.507432			−0.253716	+	0.967279i	$0.581653\pi$
$888$		0			0
$889$	29.7955			0.999310
$890$		0			0
$891$	3.74374	−	3.14137i	0.125420	−	0.105240i
$892$		0			0
$893$	−29.4475	−	10.7180i	−0.985421	−	0.358664i
$894$		0			0
$895$	−13.3560	−	4.86118i	−0.446441	−	0.162491i
$896$		0			0
$897$	−2.46632	+	13.9872i	−0.0823481	+	0.467019i
$898$		0			0
$899$	−3.25844	+	5.64378i	−0.108675	+	0.188231i
$900$		0			0
$901$	1.20053	+	6.80852i	0.0399953	+	0.226825i
$902$		0			0
$903$	6.03349	−	2.19601i	0.200782	−	0.0730786i
$904$		0			0
$905$	12.2208	−	69.3074i	0.406232	−	2.30386i
$906$		0			0
$907$	11.2355	−	9.42773i	0.373070	−	0.313043i	−0.436905	−	0.899508i	$-0.643925\pi$
$907$	11.2355	−	9.42773i	0.373070	−	0.313043i	0.809974	+	0.586465i	$0.199481\pi$
$908$		0			0
$909$	10.5920	−	3.85517i	0.351315	−	0.127868i
$910$		0			0
$911$	3.04012	+	5.26565i	0.100724	+	0.174459i	0.911983	−	0.410228i	$-0.134551\pi$
$911$	3.04012	+	5.26565i	0.100724	+	0.174459i	−0.811259	+	0.584687i	$0.801218\pi$
$912$		0			0
$913$	−13.9197	−	11.6800i	−0.460673	−	0.386551i
$914$		0			0
$915$	−13.3225	−	23.0752i	−0.440428	−	0.762843i
$916$		0			0
$917$	1.38788	−	2.40388i	0.0458319	−	0.0793831i
$918$		0			0
$919$	8.73521			0.288148			0.144074	−	0.989567i	$-0.453980\pi$
$919$	8.73521			0.288148			0.144074	+	0.989567i	$0.453980\pi$
$920$		0			0
$921$	0.576744	+	3.27088i	0.0190044	+	0.107779i
$922$		0			0
$923$	1.30500	+	1.09502i	0.0429546	+	0.0360432i
$924$		0			0
$925$	30.2861	−	39.5635i	0.995802	−	1.30084i
$926$		0			0
$927$	−5.53647	−	4.64565i	−0.181841	−	0.152583i
$928$		0			0
$929$	6.69025	+	37.9423i	0.219500	+	1.24485i	0.872924	+	0.487855i	$0.162221\pi$
$929$	6.69025	+	37.9423i	0.219500	+	1.24485i	−0.653424	+	0.756992i	$0.726668\pi$
$930$		0			0
$931$	−17.5505			−0.575193
$932$		0			0
$933$	−5.01674	+	8.68924i	−0.164241	+	0.284473i
$934$		0			0
$935$	−59.0434	−	102.266i	−1.93093	−	3.34446i
$936$		0			0
$937$	−39.5448	−	33.1820i	−1.29187	−	1.08401i	−0.991489	−	0.130189i	$-0.958442\pi$
$937$	−39.5448	−	33.1820i	−1.29187	−	1.08401i	−0.300382	−	0.953819i	$-0.597114\pi$
$938$		0			0
$939$	5.28653	+	9.15654i	0.172519	+	0.298812i
$940$		0			0
$941$	36.2861	−	13.2071i	1.18289	−	0.430538i	0.325670	−	0.945484i	$-0.394410\pi$
$941$	36.2861	−	13.2071i	1.18289	−	0.430538i	0.857223	+	0.514946i	$0.172188\pi$
$942$		0			0
$943$	3.79691	−	3.18598i	0.123644	−	0.103750i
$944$		0			0
$945$	−1.38741	+	7.86838i	−0.0451324	+	0.255958i
$946$		0			0
$947$	−25.1243	+	9.14450i	−0.816430	+	0.297156i	−0.716277	−	0.697816i	$-0.754155\pi$
$947$	−25.1243	+	9.14450i	−0.816430	+	0.297156i	−0.100153	+	0.994972i	$0.531933\pi$
$948$		0			0
$949$	−4.45553	−	25.2685i	−0.144632	−	0.820252i
$950$		0			0
$951$	−11.1674	+	19.3425i	−0.362128	+	0.627224i
$952$		0			0
$953$	−0.255895	+	1.45125i	−0.00828926	+	0.0470107i	−0.988672	−	0.150093i	$-0.952043\pi$
$953$	−0.255895	+	1.45125i	−0.00828926	+	0.0470107i	0.980383	+	0.197104i	$0.0631537\pi$
$954$		0			0
$955$	−22.8913	−	8.33174i	−0.740744	−	0.269609i
$956$		0			0
$957$	28.0706	+	10.2169i	0.907393	+	0.330264i
$958$		0			0
$959$	−17.4391	+	14.6331i	−0.563137	+	0.472528i
$960$		0			0
$961$	−29.8633			−0.963332
$962$		0			0
$963$	−7.90292			−0.254668
$964$		0			0
$965$	16.5784	−	13.9110i	0.533678	−	0.447809i
$966$		0			0
$967$	−18.8950	−	6.87720i	−0.607621	−	0.221156i	0.0198412	−	0.999803i	$-0.493684\pi$
$967$	−18.8950	−	6.87720i	−0.607621	−	0.221156i	−0.627462	+	0.778647i	$0.715906\pi$
$968$		0			0
$969$	50.7799	+	18.4824i	1.63128	+	0.593739i
$970$		0			0
$971$	5.11781	−	29.0246i	0.164238	−	0.931443i	−0.785608	−	0.618725i	$-0.787650\pi$
$971$	5.11781	−	29.0246i	0.164238	−	0.931443i	0.949846	−	0.312718i	$-0.101239\pi$
$972$		0			0
$973$	21.2894	−	36.8744i	0.682507	−	1.18214i
$974$		0			0
$975$	9.18339	+	52.0816i	0.294104	+	1.66795i
$976$		0			0
$977$	−28.6686	+	10.4345i	−0.917191	+	0.333830i	−0.757120	−	0.653275i	$-0.773394\pi$
$977$	−28.6686	+	10.4345i	−0.917191	+	0.333830i	−0.160070	+	0.987106i	$0.551172\pi$
$978$		0			0
$979$	−10.9349	+	62.0148i	−0.349480	+	1.98200i
$980$		0			0
$981$	−7.06304	+	5.92659i	−0.225505	+	0.189222i
$982$		0			0
$983$	−8.56221	+	3.11639i	−0.273092	+	0.0993974i	−0.474936	−	0.880020i	$-0.657529\pi$
$983$	−8.56221	+	3.11639i	−0.273092	+	0.0993974i	0.201844	+	0.979418i	$0.435307\pi$
$984$		0			0
$985$	−12.2388	−	21.1982i	−0.389960	−	0.675430i
$986$		0			0
$987$	6.50145	+	5.45536i	0.206943	+	0.173646i
$988$		0			0
$989$	−3.21035	−	5.56049i	−0.102083	−	0.176813i
$990$		0			0
$991$	−4.26455	+	7.38641i	−0.135468	+	0.234637i	−0.925776	−	0.378072i	$-0.876587\pi$
$991$	−4.26455	+	7.38641i	−0.135468	+	0.234637i	0.790308	+	0.612709i	$0.209920\pi$
$992$		0			0
$993$	−21.9910			−0.697863
$994$		0			0
$995$	−8.82155	−	50.0295i	−0.279662	−	1.58604i
$996$		0			0
$997$	−25.7364	−	21.5954i	−0.815079	−	0.683932i	0.136735	−	0.990608i	$-0.456339\pi$
$997$	−25.7364	−	21.5954i	−0.815079	−	0.683932i	−0.951814	+	0.306675i	$0.900783\pi$
$998$		0			0
$999$	−5.12640	+	3.27415i	−0.162192	+	0.103589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	888.2.bo.c.145.4	yes	24
37.12	even	9	inner	888.2.bo.c.49.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
888.2.bo.c.49.4	✓	24	37.12	even	9	inner
888.2.bo.c.145.4	yes	24	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:	\( N \)	\(=\)	\( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	888.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{3} +(3.41293 + 1.24220i) q^{5} +(-2.06718 - 0.752391i) q^{7} +(0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{3} +(3.41293 + 1.24220i) q^{5} +(-2.06718 - 0.752391i) q^{7} +(0.173648 - 0.984808i) q^{9} +(-2.44356 + 4.23236i) q^{11} +(1.12113 + 6.35827i) q^{13} +(3.41293 - 1.24220i) q^{15} +(-1.15526 + 6.55178i) q^{17} +(6.22231 - 5.22114i) q^{19} +(-2.06718 + 0.752391i) q^{21} +(1.09992 + 1.90512i) q^{23} +(6.27479 + 5.26518i) q^{25} +(-0.500000 - 0.866025i) q^{27} +(3.05621 - 5.29351i) q^{29} -1.06617 q^{31} +(0.848638 + 4.81287i) q^{33} +(-6.12051 - 5.13572i) q^{35} +(-0.272295 - 6.07666i) q^{37} +(4.94585 + 4.15006i) q^{39} +(-0.391250 - 2.21889i) q^{41} -2.91871 q^{43} +(1.81598 - 3.14537i) q^{45} +(-1.92901 - 3.34114i) q^{47} +(-1.65518 - 1.38886i) q^{49} +(3.32643 + 5.76154i) q^{51} +(0.976516 - 0.355423i) q^{53} +(-13.5971 + 11.4094i) q^{55} +(1.41048 - 7.99925i) q^{57} +(9.96433 - 3.62672i) q^{59} +(-1.27393 - 7.22479i) q^{61} +(-1.09992 + 1.90512i) q^{63} +(-4.07192 + 23.0930i) q^{65} +(-2.25855 - 0.822045i) q^{67} +(2.06718 + 0.752391i) q^{69} +(0.202126 - 0.169604i) q^{71} -3.97412 q^{73} +8.19116 q^{75} +(8.23566 - 6.91054i) q^{77} +(-1.63622 - 0.595534i) q^{79} +(-0.939693 - 0.342020i) q^{81} +(-0.645643 + 3.66162i) q^{83} +(-12.0815 + 20.9257i) q^{85} +(-1.06141 - 6.01956i) q^{87} +(12.1081 - 4.40700i) q^{89} +(2.46632 - 13.9872i) q^{91} +(-0.816733 + 0.685321i) q^{93} +(27.7220 - 10.0900i) q^{95} +(4.45903 + 7.72327i) q^{97} +(3.74374 + 3.14137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{5} + 15 q^{7}+O(q^{10}) \) 24 * q + 3 * q^5 + 15 * q^7	\( 24 q + 3 q^{5} + 15 q^{7} + 12 q^{13} + 3 q^{15} + 3 q^{17} + 9 q^{19} + 15 q^{21} + 27 q^{25} - 12 q^{27} - 6 q^{29} - 30 q^{31} + 9 q^{33} + 15 q^{35} + 9 q^{37} + 3 q^{39} + 15 q^{41} - 54 q^{43} + 6 q^{45} - 12 q^{47} + 27 q^{49} + 18 q^{51} + 39 q^{53} - 6 q^{55} - 3 q^{59} + 12 q^{61} + 36 q^{65} + 48 q^{67} - 15 q^{69} + 33 q^{71} - 48 q^{73} + 60 q^{75} + 36 q^{77} + 18 q^{79} - 42 q^{83} + 15 q^{87} + 36 q^{89} - 36 q^{91} - 18 q^{93} + 27 q^{95} + 9 q^{97}+O(q^{100}) \) 24 * q + 3 * q^5 + 15 * q^7 + 12 * q^13 + 3 * q^15 + 3 * q^17 + 9 * q^19 + 15 * q^21 + 27 * q^25 - 12 * q^27 - 6 * q^29 - 30 * q^31 + 9 * q^33 + 15 * q^35 + 9 * q^37 + 3 * q^39 + 15 * q^41 - 54 * q^43 + 6 * q^45 - 12 * q^47 + 27 * q^49 + 18 * q^51 + 39 * q^53 - 6 * q^55 - 3 * q^59 + 12 * q^61 + 36 * q^65 + 48 * q^67 - 15 * q^69 + 33 * q^71 - 48 * q^73 + 60 * q^75 + 36 * q^77 + 18 * q^79 - 42 * q^83 + 15 * q^87 + 36 * q^89 - 36 * q^91 - 18 * q^93 + 27 * q^95 + 9 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more