LMFDB - Embedded newform 588.2.n.f.263.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(263,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4]))

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

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

chi := DirichletCharacter("588.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.n (of order $6$, degree $2$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			263.7
Character	$\chi$	$=$	588.263
Dual form			588.2.n.f.275.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.300756 + 1.38186i) q^{2} +(0.814407 + 1.52864i) q^{3} +(-1.81909 + 0.831208i) q^{4} +(-0.301907 + 0.174306i) q^{5} +(-1.86743 + 1.58515i) q^{6} +(-1.69572 - 2.26374i) q^{8} +(-1.67348 + 2.48987i) q^{9} +(-0.331667 - 0.364770i) q^{10} +(-1.95188 + 3.38076i) q^{11} +(-2.75210 - 2.10379i) q^{12} -2.93923 q^{13} +(-0.512326 - 0.319551i) q^{15} +(2.61819 - 3.02409i) q^{16} +(-3.38076 - 1.95188i) q^{17} +(-3.94397 - 1.56368i) q^{18} +(4.83098 - 2.78917i) q^{19} +(0.404312 - 0.568026i) q^{20} +(-5.25879 - 1.68045i) q^{22} +(1.09094 + 1.88957i) q^{23} +(2.07945 - 4.43575i) q^{24} +(-2.43923 + 4.22488i) q^{25} +(-0.883993 - 4.06162i) q^{26} +(-5.16901 - 0.530383i) q^{27} +9.75220i q^{29} +(0.287490 - 0.804071i) q^{30} +(2.28553 + 1.31955i) q^{31} +(4.96631 + 2.70846i) q^{32} +(-6.75759 - 0.230411i) q^{33} +(1.68045 - 5.25879i) q^{34} +(0.974616 - 5.92031i) q^{36} +(-0.319551 - 0.553478i) q^{37} +(5.30720 + 5.83689i) q^{38} +(-2.39373 - 4.49303i) q^{39} +(0.906533 + 0.387866i) q^{40} -7.57031i q^{41} -2.51757i q^{43} +(0.740538 - 7.77233i) q^{44} +(0.0712361 - 1.04341i) q^{45} +(-2.28302 + 2.07583i) q^{46} +(2.18189 + 3.77914i) q^{47} +(6.75501 + 1.53943i) q^{48} +(-6.57182 - 2.10003i) q^{50} +(0.230411 - 6.75759i) q^{51} +(5.34674 - 2.44312i) q^{52} +(1.49119 + 0.860938i) q^{53} +(-0.821697 - 7.30238i) q^{54} -1.36090i q^{55} +(8.19802 + 5.11331i) q^{57} +(-13.4762 + 2.93304i) q^{58} +(4.12318 - 7.14155i) q^{59} +(1.19758 + 0.155443i) q^{60} +(7.04795 + 12.2074i) q^{61} +(-1.13605 + 3.55515i) q^{62} +(-2.24908 + 7.67735i) q^{64} +(0.887375 - 0.512326i) q^{65} +(-1.71399 - 9.40736i) q^{66} +(0.553478 + 0.319551i) q^{67} +(7.77233 + 0.740538i) q^{68} +(-2.00000 + 3.20654i) q^{69} +11.9341 q^{71} +(8.47419 - 0.433786i) q^{72} +(-3.93923 + 6.82295i) q^{73} +(0.668724 - 0.608037i) q^{74} +(-8.44485 - 0.287941i) q^{75} +(-6.46962 + 9.08930i) q^{76} +(5.48883 - 4.65912i) q^{78} +(-3.46410 + 2.00000i) q^{79} +(-0.263332 + 1.36936i) q^{80} +(-3.39892 - 8.33351i) q^{81} +(10.4611 - 2.27682i) q^{82} +8.94358 q^{83} +1.36090 q^{85} +(3.47894 - 0.757175i) q^{86} +(-14.9076 + 7.94226i) q^{87} +(10.9630 - 1.31425i) q^{88} +(-9.12760 + 5.26982i) q^{89} +(1.46327 - 0.215373i) q^{90} +(-3.55515 - 2.53050i) q^{92} +(-0.155767 + 4.56840i) q^{93} +(-4.56604 + 4.15167i) q^{94} +(-0.972337 + 1.68414i) q^{95} +(-0.0956677 + 9.79749i) q^{96} -2.00000 q^{97} +(-5.15121 - 10.5176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{4} - 12 q^{6} + 4 q^{9} - 4 q^{10} + 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} - 2 q^{24} + 12 q^{25} - 20 q^{30} + 16 q^{33} + 64 q^{34} - 40 q^{36} + 16 q^{37} - 20 q^{40} - 24 q^{45} + 92 q^{48}+ \cdots - 48 q^{97}+O(q^{100}) $ 24 * q + 4 * q^4 - 12 * q^6 + 4 * q^9 - 4 * q^10 + 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 - 2 * q^24 + 12 * q^25 - 20 * q^30 + 16 * q^33 + 64 * q^34 - 40 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 + 92 * q^48 + 28 * q^52 - 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 + 16 * q^61 + 40 * q^64 + 12 * q^66 - 48 * q^69 + 32 * q^72 - 24 * q^73 - 120 * q^76 + 40 * q^78 - 28 * q^81 - 8 * q^82 + 80 * q^85 + 56 * q^88 - 160 * q^90 - 24 * q^93 + 34 * q^96 - 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.300756	+	1.38186i	0.212667	+	0.977125i
$2$	0.300756	+	1.38186i	0.212667	+	0.977125i
$3$	0.814407	+	1.52864i	0.470198	+	0.882561i
$3$	0.814407	+	1.52864i	0.470198	+	0.882561i
$4$	−1.81909	+	0.831208i	−0.909546	+	0.415604i
$5$	−0.301907	+	0.174306i	−0.135017	+	0.0779520i	−0.565987	−	0.824414i	$-0.691505\pi$
$5$	−0.301907	+	0.174306i	−0.135017	+	0.0779520i	0.430970	+	0.902366i	$0.358171\pi$
$6$	−1.86743	+	1.58515i	−0.762377	+	0.647134i
$7$		0			0
$7$		0			0
$8$	−1.69572	−	2.26374i	−0.599527	−	0.800354i
$9$	−1.67348	+	2.48987i	−0.557827	+	0.829957i
$10$	−0.331667	−	0.364770i	−0.104882	−	0.115350i
$11$	−1.95188	+	3.38076i	−0.588514	+	1.01934i	0.405913	+	0.913912i	$0.366954\pi$
$11$	−1.95188	+	3.38076i	−0.588514	+	1.01934i	−0.994427	+	0.105425i	$0.966380\pi$
$12$	−2.75210	−	2.10379i	−0.794463	−	0.607313i
$13$	−2.93923			−0.815197			−0.407599	−	0.913161i	$-0.633634\pi$
$13$	−2.93923			−0.815197			−0.407599	+	0.913161i	$0.633634\pi$
$14$		0			0
$15$	−0.512326	−	0.319551i	−0.132282	−	0.0825077i
$16$	2.61819	−	3.02409i	0.654547	−	0.756022i
$17$	−3.38076	−	1.95188i	−0.819954	−	0.473401i	0.0304464	−	0.999536i	$-0.490307\pi$
$17$	−3.38076	−	1.95188i	−0.819954	−	0.473401i	−0.850401	+	0.526136i	$0.823640\pi$
$18$	−3.94397	−	1.56368i	−0.929603	−	0.368563i
$19$	4.83098	−	2.78917i	1.10830	−	0.639879i	0.169914	−	0.985459i	$-0.445651\pi$
$19$	4.83098	−	2.78917i	1.10830	−	0.639879i	0.938389	+	0.345580i	$0.112318\pi$
$20$	0.404312	−	0.568026i	0.0904068	−	0.127014i
$21$		0			0
$22$	−5.25879	−	1.68045i	−1.12118	−	0.358273i
$23$	1.09094	+	1.88957i	0.227477	+	0.394003i	0.957060	−	0.289890i	$-0.0936189\pi$
$23$	1.09094	+	1.88957i	0.227477	+	0.394003i	−0.729582	+	0.683893i	$0.760286\pi$
$24$	2.07945	−	4.43575i	0.424465	−	0.905444i
$25$	−2.43923	+	4.22488i	−0.487847	+	0.844976i
$26$	−0.883993	−	4.06162i	−0.173365	−	0.796549i
$27$	−5.16901	−	0.530383i	−0.994777	−	0.102072i
$28$		0			0
$29$			9.75220i			1.81094i	0.424412	+	0.905469i	$0.360481\pi$
$29$			9.75220i			1.81094i	−0.424412	+	0.905469i	$0.639519\pi$
$30$	0.287490	−	0.804071i	0.0524883	−	0.146803i
$31$	2.28553	+	1.31955i	0.410493	+	0.236998i	0.691002	−	0.722853i	$-0.257170\pi$
$31$	2.28553	+	1.31955i	0.410493	+	0.236998i	−0.280508	+	0.959852i	$0.590503\pi$
$32$	4.96631	+	2.70846i	0.877928	+	0.478793i
$33$	−6.75759	−	0.230411i	−1.17635	−	0.0401094i
$34$	1.68045	−	5.25879i	0.288195	−	0.901874i
$35$		0			0
$36$	0.974616	−	5.92031i	0.162436	−	0.986719i
$37$	−0.319551	−	0.553478i	−0.0525338	−	0.0909913i	0.838563	−	0.544805i	$-0.183396\pi$
$37$	−0.319551	−	0.553478i	−0.0525338	−	0.0909913i	−0.891096	+	0.453814i	$0.850063\pi$
$38$	5.30720	+	5.83689i	0.860941	+	0.946869i
$39$	−2.39373	−	4.49303i	−0.383304	−	0.719461i
$40$	0.906533	+	0.387866i	0.143335	+	0.0613270i
$41$		−	7.57031i		−	1.18228i	−0.806567	−	0.591142i	$-0.798677\pi$
$41$		−	7.57031i		−	1.18228i	0.806567	−	0.591142i	$-0.201323\pi$
$42$		0			0
$43$		−	2.51757i		−	0.383926i	−0.981402	−	0.191963i	$-0.938515\pi$
$43$		−	2.51757i		−	0.383926i	0.981402	−	0.191963i	$-0.0614854\pi$
$44$	0.740538	−	7.77233i	0.111640	−	1.17172i
$45$	0.0712361	−	1.04341i	0.0106193	−	0.155542i
$46$	−2.28302	+	2.07583i	−0.336613	+	0.306065i
$47$	2.18189	+	3.77914i	0.318261	+	0.551244i	0.980125	−	0.198379i	$-0.0635678\pi$
$47$	2.18189	+	3.77914i	0.318261	+	0.551244i	−0.661864	+	0.749624i	$0.730235\pi$
$48$	6.75501	+	1.53943i	0.975002	+	0.222197i
$49$		0			0
$50$	−6.57182	−	2.10003i	−0.929396	−	0.296989i
$51$	0.230411	−	6.75759i	0.0322640	−	0.946252i
$52$	5.34674	−	2.44312i	0.741459	−	0.338799i
$53$	1.49119	+	0.860938i	0.204830	+	0.118259i	0.598907	−	0.800819i	$-0.295602\pi$
$53$	1.49119	+	0.860938i	0.204830	+	0.118259i	−0.394076	+	0.919078i	$0.628935\pi$
$54$	−0.821697	−	7.30238i	−0.111819	−	0.993729i
$55$		−	1.36090i		−	0.183504i
$56$		0			0
$57$	8.19802	+	5.11331i	1.08585	+	0.677275i
$58$	−13.4762	+	2.93304i	−1.76951	+	0.385126i
$59$	4.12318	−	7.14155i	0.536792	−	0.929751i	−0.462282	−	0.886733i	$-0.652969\pi$
$59$	4.12318	−	7.14155i	0.536792	−	0.929751i	0.999074	−	0.0430181i	$-0.0136973\pi$
$60$	1.19758	+	0.155443i	0.154607	+	0.0200676i
$61$	7.04795	+	12.2074i	0.902398	+	1.56300i	0.824372	+	0.566048i	$0.191528\pi$
$61$	7.04795	+	12.2074i	0.902398	+	1.56300i	0.0780257	+	0.996951i	$0.475138\pi$
$62$	−1.13605	+	3.55515i	−0.144279	+	0.451505i
$63$		0			0
$64$	−2.24908	+	7.67735i	−0.281135	+	0.959668i
$65$	0.887375	−	0.512326i	0.110065	−	0.0635462i
$66$	−1.71399	−	9.40736i	−0.210978	−	1.15797i
$67$	0.553478	+	0.319551i	0.0676181	+	0.0390393i	0.533428	−	0.845846i	$-0.320904\pi$
$67$	0.553478	+	0.319551i	0.0676181	+	0.0390393i	−0.465810	+	0.884885i	$0.654237\pi$
$68$	7.77233	+	0.740538i	0.942533	+	0.0898034i
$69$	−2.00000	+	3.20654i	−0.240772	+	0.386022i
$70$		0			0
$71$	11.9341			1.41632			0.708158	−	0.706054i	$-0.249526\pi$
$71$	11.9341			1.41632			0.708158	+	0.706054i	$0.249526\pi$
$72$	8.47419	−	0.433786i	0.998692	−	0.0511222i
$73$	−3.93923	+	6.82295i	−0.461053	+	0.798566i	−0.999014	−	0.0444032i	$-0.985861\pi$
$73$	−3.93923	+	6.82295i	−0.461053	+	0.798566i	0.537961	+	0.842970i	$0.319195\pi$
$74$	0.668724	−	0.608037i	0.0777376	−	0.0706829i
$75$	−8.44485	−	0.287941i	−0.975127	−	0.0332485i
$76$	−6.46962	+	9.08930i	−0.742116	+	1.04261i
$77$		0			0
$78$	5.48883	−	4.65912i	0.621487	−	0.527541i
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	0.292306	+	0.956325i	$0.405577\pi$
$80$	−0.263332	+	1.36936i	−0.0294414	+	0.153099i
$81$	−3.39892	−	8.33351i	−0.377657	−	0.925945i
$82$	10.4611	−	2.27682i	1.15524	−	0.251433i
$83$	8.94358			0.981685			0.490843	−	0.871248i	$-0.336689\pi$
$83$	8.94358			0.981685			0.490843	+	0.871248i	$0.336689\pi$
$84$		0			0
$85$	1.36090			0.147610
$86$	3.47894	−	0.757175i	0.375144	−	0.0816483i
$87$	−14.9076	+	7.94226i	−1.59826	+	0.851500i
$88$	10.9630	−	1.31425i	1.16866	−	0.140100i
$89$	−9.12760	+	5.26982i	−0.967523	+	0.558600i	−0.898480	−	0.439014i	$-0.855328\pi$
$89$	−9.12760	+	5.26982i	−0.967523	+	0.558600i	−0.0690430	+	0.997614i	$0.521995\pi$
$90$	1.46327	−	0.215373i	0.154242	−	0.0227023i
$91$		0			0
$92$	−3.55515	−	2.53050i	−0.370650	−	0.263823i
$93$	−0.155767	+	4.56840i	−0.0161523	+	0.473721i
$94$	−4.56604	+	4.15167i	−0.470951	+	0.428212i
$95$	−0.972337	+	1.68414i	−0.0997597	+	0.172789i
$96$	−0.0956677	+	9.79749i	−0.00976404	+	0.999952i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−5.15121	−	10.5176i	−0.517716	−	1.05706i
$100$	0.925439	−	9.71295i	0.0925439	−	0.971295i
$101$	−2.68047	−	1.54757i	−0.266717	−	0.153989i	0.360678	−	0.932690i	$-0.382545\pi$
$101$	−2.68047	−	1.54757i	−0.266717	−	0.153989i	−0.627395	+	0.778701i	$0.715879\pi$
$102$	9.40736	−	1.71399i	0.931468	−	0.169710i
$103$	−6.26948	+	3.61968i	−0.617750	+	0.356658i	−0.775992	−	0.630742i	$-0.782751\pi$
$103$	−6.26948	+	3.61968i	−0.617750	+	0.356658i	0.158243	+	0.987400i	$0.449417\pi$
$104$	4.98412	+	6.65368i	0.488733	+	0.652447i
$105$		0			0
$106$	−0.741214	+	2.31955i	−0.0719931	+	0.225295i
$107$	5.50703	+	9.53846i	0.532385	+	0.922118i	0.999285	+	0.0378077i	$0.0120374\pi$
$107$	5.50703	+	9.53846i	0.532385	+	0.922118i	−0.466900	+	0.884310i	$0.654629\pi$
$108$	9.84376	−	3.33171i	0.947217	−	0.320594i
$109$	−0.699867	+	1.21220i	−0.0670351	+	0.116108i	−0.897595	−	0.440821i	$-0.854687\pi$
$109$	−0.699867	+	1.21220i	−0.0670351	+	0.116108i	0.830560	+	0.556929i	$0.188021\pi$
$110$	1.88058	−	0.409299i	0.179306	−	0.0390251i
$111$	0.585825	−	0.939235i	0.0556040	−	0.0891482i
$112$		0			0
$113$		−	8.83218i		−	0.830862i	−0.909625	−	0.415431i	$-0.863631\pi$
$113$		−	8.83218i		−	0.830862i	0.909625	−	0.415431i	$-0.136369\pi$
$114$	−4.60029	+	12.8664i	−0.430857	+	1.20505i
$115$	−0.658727	−	0.380316i	−0.0614266	−	0.0354646i
$116$	−8.10611	−	17.7401i	−0.752633	−	1.64713i
$117$	4.91876	−	7.31832i	0.454739	−	0.676579i
$118$	11.1087	+	3.54980i	1.02264	+	0.326786i
$119$		0			0
$120$	0.145380	+	1.70164i	0.0132713	+	0.155338i
$121$	−2.11968	−	3.67140i	−0.192699	−	0.333764i
$122$	−14.7493	+	13.4108i	−1.33534	+	1.21415i
$123$	11.5723	−	6.16532i	1.04344	−	0.555908i
$124$	−5.25441	−	0.500634i	−0.471860	−	0.0449582i
$125$		−	3.44375i		−	0.308019i
$126$		0			0
$127$			12.3960i			1.09997i	0.835174	+	0.549985i	$0.185367\pi$
$127$			12.3960i			1.09997i	−0.835174	+	0.549985i	$0.814633\pi$
$128$	−11.2855	−	0.798907i	−0.997504	−	0.0706140i
$129$	3.84846	−	2.05033i	0.338838	−	0.180521i
$130$	0.974848	+	1.07215i	0.0854998	+	0.0940334i
$131$	0.805238	+	1.39471i	0.0703540	+	0.121857i	0.899056	−	0.437833i	$-0.144254\pi$
$131$	0.805238	+	1.39471i	0.0703540	+	0.121857i	−0.828702	+	0.559689i	$0.810920\pi$
$132$	12.4842	−	5.19782i	1.08661	−	0.452412i
$133$		0			0
$134$	−0.275113	+	0.860938i	−0.0237662	+	0.0743737i
$135$	1.65301	−	0.740864i	0.142268	−	0.0637634i
$136$	1.31425	+	10.9630i	0.112696	+	0.940071i
$137$	−3.77914	−	2.18189i	−0.322874	−	0.186411i	0.329799	−	0.944051i	$-0.393019\pi$
$137$	−3.77914	−	2.18189i	−0.322874	−	0.186411i	−0.652673	+	0.757640i	$0.726352\pi$
$138$	−5.03251	−	1.79934i	−0.428396	−	0.153170i
$139$			16.8177i			1.42646i	0.700931	+	0.713230i	$0.252768\pi$
$139$			16.8177i			1.42646i	−0.700931	+	0.713230i	$0.747232\pi$
$140$		0			0
$141$	−4.00000	+	6.41308i	−0.336861	+	0.540079i
$142$	3.58925	+	16.4913i	0.301203	+	1.38392i
$143$	5.73704	−	9.93684i	0.479755	−	0.830961i
$144$	3.14810	+	11.5797i	0.262341	+	0.964975i
$145$	−1.69987	−	2.94426i	−0.141166	−	0.244507i
$146$	−10.6131	−	3.39144i	−0.878350	−	0.280677i
$147$		0			0
$148$	1.04135	+	0.741214i	0.0855982	+	0.0609274i
$149$	−6.63421	+	3.83026i	−0.543496	+	0.313788i	−0.746495	−	0.665391i	$-0.768265\pi$
$149$	−6.63421	+	3.83026i	−0.543496	+	0.313788i	0.202999	+	0.979179i	$0.434931\pi$
$150$	−2.14195	−	11.7562i	−0.174889	−	0.959892i
$151$	10.9458	+	6.31955i	0.890755	+	0.514278i	0.874189	−	0.485585i	$-0.161393\pi$
$151$	10.9458	+	6.31955i	0.890755	+	0.514278i	0.0165658	+	0.999863i	$0.494727\pi$
$152$	−14.5059	−	6.20646i	−1.17659	−	0.503411i
$153$	10.5176	−	5.15121i	0.850295	−	0.416451i
$154$		0			0
$155$	−0.920022			−0.0738980
$156$	8.08907	+	6.18355i	0.647644	+	0.495080i
$157$	−0.108719	+	0.188307i	−0.00867672	+	0.0150285i	−0.870331	−	0.492467i	$-0.836095\pi$
$157$	−0.108719	+	0.188307i	−0.00867672	+	0.0150285i	0.861654	+	0.507495i	$0.169429\pi$
$158$	−3.80558	−	4.18540i	−0.302755	−	0.332973i
$159$	−0.101630	+	2.98064i	−0.00805978	+	0.236381i
$160$	−1.97146	+	0.0479539i	−0.155858	+	0.00379109i
$161$		0			0
$162$	10.4935	−	7.20319i	0.824449	−	0.565936i
$163$	4.53743	−	2.61968i	0.355399	−	0.205189i	−0.311662	−	0.950193i	$-0.600886\pi$
$163$	4.53743	−	2.61968i	0.355399	−	0.205189i	0.667060	+	0.745004i	$0.267552\pi$
$164$	6.29250	+	13.7711i	0.491362	+	1.07534i
$165$	2.08032	−	1.10833i	0.161953	−	0.0862830i
$166$	2.68984	+	12.3588i	0.208772	+	0.959229i
$167$	−11.4741			−0.887891			−0.443945	−	0.896054i	$-0.646422\pi$
$167$	−11.4741			−0.887891			−0.443945	+	0.896054i	$0.646422\pi$
$168$		0			0
$169$	−4.36090			−0.335454
$170$	0.409299	+	1.88058i	0.0313918	+	0.144234i
$171$	−1.13989	+	16.6961i	−0.0871695	+	1.27679i
$172$	2.09263	+	4.57969i	0.159561	+	0.349198i
$173$	18.3642	−	10.6025i	1.39620	−	0.806097i	0.402208	−	0.915548i	$-0.368243\pi$
$173$	18.3642	−	10.6025i	1.39620	−	0.806097i	0.993992	+	0.109451i	$0.0349094\pi$
$174$	−15.4587	−	18.2116i	−1.17192	−	1.38062i
$175$		0			0
$176$	5.11331	+	14.7541i	0.385430	+	1.11213i
$177$	14.2748	+	0.486723i	1.07296	+	0.0365843i
$178$	−10.0274	−	11.0282i	−0.751582	−	0.826595i
$179$	−0.906046	+	1.56932i	−0.0677211	+	0.117296i	−0.897898	−	0.440204i	$-0.854906\pi$
$179$	−0.906046	+	1.56932i	−0.0677211	+	0.117296i	0.830177	+	0.557500i	$0.188239\pi$
$180$	0.737703	+	1.95726i	0.0549851	+	0.145886i
$181$	7.53950			0.560407			0.280203	−	0.959941i	$-0.409598\pi$
$181$	7.53950			0.560407			0.280203	+	0.959941i	$0.409598\pi$
$182$		0			0
$183$	−12.9208	+	20.7156i	−0.955136	+	1.53134i
$184$	2.42757	−	5.67380i	0.178963	−	0.418278i
$185$	0.192949	+	0.111399i	0.0141859	+	0.00819023i
$186$	−6.35976	+	1.15873i	−0.466320	+	0.0849620i
$187$	13.1977	−	7.61968i	0.965110	−	0.557206i
$188$	−7.11030	−	5.06100i	−0.518572	−	0.369111i
$189$		0			0
$190$	−2.61968	−	0.837122i	−0.190052	−	0.0607312i
$191$	−0.815830	−	1.41306i	−0.0590314	−	0.102245i	0.834999	−	0.550251i	$-0.185468\pi$
$191$	−0.815830	−	1.41306i	−0.0590314	−	0.102245i	−0.894031	+	0.448005i	$0.852135\pi$
$192$	−13.5676	+	2.81446i	−0.979155	+	0.203116i
$193$	7.57834	−	13.1261i	0.545501	−	0.944835i	−0.453075	−	0.891473i	$-0.649673\pi$
$193$	7.57834	−	13.1261i	0.545501	−	0.944835i	0.998575	−	0.0533622i	$-0.0169938\pi$
$194$	−0.601512	−	2.76373i	−0.0431861	−	0.198424i
$195$	1.50585	+	0.939235i	0.107836	+	0.0672600i
$196$		0			0
$197$		−	21.2263i		−	1.51231i	−0.654393	−	0.756155i	$-0.727076\pi$
$197$		−	21.2263i		−	1.51231i	0.654393	−	0.756155i	$-0.272924\pi$
$198$	12.9846	−	10.2815i	0.922774	−	0.730674i
$199$	−3.25361	−	1.87847i	−0.230642	−	0.133161i	0.380226	−	0.924894i	$-0.375846\pi$
$199$	−3.25361	−	1.87847i	−0.230642	−	0.133161i	−0.610868	+	0.791732i	$0.709179\pi$
$200$	13.7003	−	1.64240i	0.968758	−	0.116135i
$201$	−0.0377216	+	1.10631i	−0.00266067	+	0.0780333i
$202$	1.33236	−	4.16948i	0.0937447	−	0.293364i
$203$		0			0
$204$	5.19782	+	12.4842i	0.363920	+	0.874068i
$205$	1.31955	+	2.28553i	0.0921614	+	0.159628i
$206$	−6.88749	−	7.57492i	−0.479874	−	0.527769i
$207$	−6.53046	−	0.445852i	−0.453898	−	0.0309888i
$208$	−7.69547	+	8.88850i	−0.533585	+	0.616307i
$209$			21.7765i			1.50631i
$210$		0			0
$211$		−	9.83963i		−	0.677388i	−0.940897	−	0.338694i	$-0.890015\pi$
$211$		−	9.83963i		−	0.677388i	0.940897	−	0.338694i	$-0.109985\pi$
$212$	−3.42823	−	0.326637i	−0.235452	−	0.0224335i
$213$	9.71921	+	18.2429i	0.665949	+	1.24998i
$214$	−11.5246	+	10.4787i	−0.787804	+	0.716310i
$215$	0.438828	+	0.760072i	0.0299278	+	0.0518365i
$216$	7.56454	+	12.6007i	0.514702	+	0.857369i
$217$		0			0
$218$	−1.88559	−	0.602542i	−0.127708	−	0.0408093i
$219$	−13.6380	−	0.465009i	−0.921570	−	0.0314224i
$220$	1.13119	+	2.47560i	0.0762648	+	0.166905i
$221$	9.93684	+	5.73704i	0.668424	+	0.385915i
$222$	1.47408	+	0.527049i	0.0989341	+	0.0353732i
$223$		−	22.9136i		−	1.53441i	−0.641403	−	0.767204i	$-0.721647\pi$
$223$		−	22.9136i		−	1.53441i	0.641403	−	0.767204i	$-0.278353\pi$
$224$		0			0
$225$	−6.43739	−	13.1436i	−0.429159	−	0.876243i
$226$	12.2049	−	2.65633i	0.811855	−	0.176697i
$227$	6.76508	−	11.7175i	0.449014	−	0.777715i	−0.549308	−	0.835620i	$-0.685109\pi$
$227$	6.76508	−	11.7175i	0.449014	−	0.777715i	0.998322	+	0.0579050i	$0.0184421\pi$
$228$	−19.1632	−	2.48732i	−1.26911	−	0.164727i
$229$	−7.34809	−	12.7273i	−0.485575	−	0.841041i	0.514287	−	0.857618i	$-0.328056\pi$
$229$	−7.34809	−	12.7273i	−0.485575	−	0.841041i	−0.999863	+	0.0165769i	$0.994723\pi$
$230$	0.327428	−	1.02465i	0.0215900	−	0.0675636i
$231$		0			0
$232$	22.0765	−	16.5370i	1.44939	−	1.08571i
$233$	14.8869	−	8.59497i	0.975274	−	0.563075i	0.0744343	−	0.997226i	$-0.476285\pi$
$233$	14.8869	−	8.59497i	0.975274	−	0.563075i	0.900840	+	0.434151i	$0.142952\pi$
$234$	11.5923	+	4.59602i	0.757810	+	0.300451i
$235$	−1.31745	−	0.760632i	−0.0859412	−	0.0496182i
$236$	−1.56432	+	16.4184i	−0.101829	+	1.06874i
$237$	−5.87847	−	3.66655i	−0.381848	−	0.238168i
$238$		0			0
$239$	14.5336			0.940102			0.470051	−	0.882639i	$-0.344236\pi$
$239$	14.5336			0.940102			0.470051	+	0.882639i	$0.344236\pi$
$240$	−2.30771	+	0.712675i	−0.148962	+	0.0460030i
$241$	9.39604	−	16.2744i	0.605252	−	1.04833i	−0.386759	−	0.922181i	$-0.626406\pi$
$241$	9.39604	−	16.2744i	0.605252	−	1.04833i	0.992012	−	0.126147i	$-0.0402611\pi$
$242$	4.43586	−	4.03331i	0.285148	−	0.259271i
$243$	9.97083	−	11.9826i	0.639629	−	0.768684i
$244$	−22.9678	−	16.3481i	−1.47036	−	1.04658i
$245$		0			0
$246$	12.0001	+	14.1371i	0.765096	+	0.901346i
$247$	−14.1994	+	8.19802i	−0.903485	+	0.521628i
$248$	−0.888488	−	7.41144i	−0.0564191	−	0.470627i
$249$	7.28371	+	13.6715i	0.461587	+	0.866397i
$250$	4.75879	−	1.03573i	0.300973	−	0.0655053i
$251$	20.6405			1.30281			0.651407	−	0.758729i	$-0.274179\pi$
$251$	20.6405			1.30281			0.651407	+	0.758729i	$0.274179\pi$
$252$		0			0
$253$	−8.51757			−0.535495
$254$	−17.1296	+	3.72819i	−1.07481	+	0.233927i
$255$	1.10833	+	2.08032i	0.0694060	+	0.130275i
$256$	−2.29019	−	15.8352i	−0.143137	−	0.989703i
$257$	4.17752	−	2.41189i	0.260587	−	0.150450i	−0.364016	−	0.931393i	$-0.618594\pi$
$257$	4.17752	−	2.41189i	0.260587	−	0.150450i	0.624602	+	0.780943i	$0.285261\pi$
$258$	3.99072	+	4.70140i	0.248451	+	0.292696i
$259$		0			0
$260$	−1.18837	+	1.66956i	−0.0736994	+	0.103542i
$261$	−24.2817	−	16.3201i	−1.50300	−	1.01019i
$262$	−1.68512	+	1.53220i	−0.104107	+	0.0946595i
$263$	−7.22891	+	12.5208i	−0.445754	+	0.772068i	−0.998104	−	0.0615439i	$-0.980398\pi$
$263$	−7.22891	+	12.5208i	−0.445754	+	0.772068i	0.552351	+	0.833612i	$0.313731\pi$
$264$	10.9374	+	15.6882i	0.673149	+	0.965540i
$265$	−0.600267			−0.0368741
$266$		0			0
$267$	−15.4892	−	9.66103i	−0.947926	−	0.591246i
$268$	−1.27244	−	0.121237i	−0.0777267	−	0.00740571i
$269$	4.08105	+	2.35619i	0.248826	+	0.143660i	0.619226	−	0.785212i	$-0.287446\pi$
$269$	4.08105	+	2.35619i	0.248826	+	0.143660i	−0.370401	+	0.928872i	$0.620780\pi$
$270$	1.52092	+	2.06141i	0.0925605	+	0.125454i
$271$	−13.5743	+	7.83712i	−0.824580	+	0.476071i	−0.851993	−	0.523553i	$-0.824606\pi$
$271$	−13.5743	+	7.83712i	−0.824580	+	0.476071i	0.0274135	+	0.999624i	$0.491273\pi$
$272$	−14.7541	+	5.11331i	−0.894600	+	0.310040i
$273$		0			0
$274$	1.87847	−	5.87847i	0.113483	−	0.355131i
$275$	−9.52220	−	16.4929i	−0.574210	−	0.994561i
$276$	0.972882	−	7.49540i	0.0585606	−	0.451170i
$277$	−8.49815	+	14.7192i	−0.510605	+	0.884393i	0.489320	+	0.872104i	$0.337245\pi$
$277$	−8.49815	+	14.7192i	−0.510605	+	0.884393i	−0.999924	+	0.0122887i	$0.996088\pi$
$278$	−23.2398	+	5.05803i	−1.39383	+	0.303360i
$279$	−7.11030	+	3.48243i	−0.425683	+	0.208488i
$280$		0			0
$281$		−	5.75822i		−	0.343507i	−0.985140	−	0.171753i	$-0.945057\pi$
$281$		−	5.75822i		−	0.343507i	0.985140	−	0.171753i	$-0.0549432\pi$
$282$	−10.0650	−	3.59868i	−0.599363	−	0.214298i
$283$	4.83098	+	2.78917i	0.287172	+	0.165799i	0.636666	−	0.771140i	$-0.280313\pi$
$283$	4.83098	+	2.78917i	0.287172	+	0.165799i	−0.349494	+	0.936939i	$0.613646\pi$
$284$	−21.7092	+	9.91971i	−1.28820	+	0.588626i
$285$	−3.36632	−	0.114780i	−0.199404	−	0.00679899i
$286$	15.4568	+	4.93923i	0.913980	+	0.292063i
$287$		0			0
$288$	−15.0548	+	7.83291i	−0.887110	+	0.461558i
$289$	−0.880316	−	1.52475i	−0.0517833	−	0.0896913i
$290$	3.55731	−	3.23449i	0.208893	−	0.189936i
$291$	−1.62881	−	3.05728i	−0.0954828	−	0.179221i
$292$	1.49453	−	15.6859i	0.0874610	−	0.917948i
$293$			23.7712i			1.38873i	0.719624	+	0.694364i	$0.244314\pi$
$293$			23.7712i			1.38873i	−0.719624	+	0.694364i	$0.755686\pi$
$294$		0			0
$295$			2.87478i			0.167376i
$296$	−0.711065	+	1.66192i	−0.0413298	+	0.0965974i
$297$	11.8824	−	16.4399i	0.689487	−	0.953942i
$298$	−7.28818	−	8.01560i	−0.422193	−	0.464331i
$299$	−3.20654	−	5.55389i	−0.185439	−	0.321190i
$300$	15.6013	−	6.49564i	0.900741	−	0.375026i
$301$		0			0
$302$	−5.44074	+	17.0262i	−0.313080	+	0.979749i
$303$	0.182684	−	5.35783i	0.0104949	−	0.307799i
$304$	4.21373	−	21.9119i	0.241674	−	1.25673i
$305$	−4.25565	−	2.45700i	−0.243678	−	0.140687i
$306$	10.2815	+	12.9846i	0.587754	+	0.742279i
$307$		−	3.69987i		−	0.211163i	−0.994411	−	0.105581i	$-0.966330\pi$
$307$		−	3.69987i		−	0.211163i	0.994411	−	0.105581i	$-0.0336703\pi$
$308$		0			0
$309$	−10.6391	−	6.63588i	−0.605237	−	0.377502i
$310$	−0.276702	−	1.27134i	−0.0157156	−	0.0722075i
$311$	3.79236	−	6.56857i	0.215045	−	0.372469i	−0.738241	−	0.674537i	$-0.764343\pi$
$311$	3.79236	−	6.56857i	0.215045	−	0.372469i	0.953287	+	0.302067i	$0.0976768\pi$
$312$	−6.11198	+	13.0377i	−0.346023	+	0.738116i
$313$	−7.81770	−	13.5407i	−0.441883	−	0.765363i	0.555946	−	0.831218i	$-0.312356\pi$
$313$	−7.81770	−	13.5407i	−0.441883	−	0.765363i	−0.997829	+	0.0658547i	$0.979023\pi$
$314$	−0.292912	−	0.0936004i	−0.0165300	−	0.00528217i
$315$		0			0
$316$	4.63910	−	6.51757i	0.260970	−	0.366642i
$317$	12.0318	−	6.94659i	0.675776	−	0.390159i	−0.122486	−	0.992470i	$-0.539087\pi$
$317$	12.0318	−	6.94659i	0.675776	−	0.390159i	0.798262	+	0.602311i	$0.205753\pi$
$318$	−4.14941	+	0.756009i	−0.232687	+	0.0423949i
$319$	−32.9698	−	19.0351i	−1.84596	−	1.06576i
$320$	−0.659196	−	2.70987i	−0.0368502	−	0.151486i
$321$	−10.0959	+	16.1865i	−0.563499	+	0.903440i
$322$		0			0
$323$	−21.7765			−1.21168
$324$	13.1098	+	12.3342i	0.728323	+	0.685234i
$325$	7.16948	−	12.4179i	0.397691	−	0.688822i
$326$	4.98470	+	5.48222i	0.276077	+	0.303632i
$327$	−2.42300	−	0.0826162i	−0.133992	−	0.00456868i
$328$	−17.1373	+	12.8371i	−0.946247	+	0.708811i
$329$		0			0
$330$	2.15722	+	2.54139i	0.118751	+	0.139899i
$331$	27.5359	−	15.8979i	1.51351	−	0.873827i	0.513638	−	0.858007i	$-0.328298\pi$
$331$	27.5359	−	15.8979i	1.51351	−	0.873827i	0.999875	−	0.0158198i	$-0.00503580\pi$
$332$	−16.2692	+	7.43397i	−0.892888	+	0.407992i
$333$	1.91285	+	0.130595i	0.104824	+	0.00715658i
$334$	−3.45090	−	15.8556i	−0.188825	−	0.867580i
$335$	−0.222798			−0.0121728
$336$		0			0
$337$	−17.1178			−0.932468			−0.466234	−	0.884661i	$-0.654390\pi$
$337$	−17.1178			−0.932468			−0.466234	+	0.884661i	$0.654390\pi$
$338$	−1.31157	−	6.02616i	−0.0713399	−	0.327780i
$339$	13.5012	−	7.19299i	0.733286	−	0.390670i
$340$	−2.47560	+	1.13119i	−0.134258	+	0.0613474i
$341$	−8.92216	+	5.15121i	−0.483162	+	0.278954i
$342$	−23.4146	+	3.44630i	−1.26612	+	0.186354i
$343$		0			0
$344$	−5.69914	+	4.26909i	−0.307277	+	0.230174i
$345$	0.0448946	−	1.31669i	0.00241704	−	0.0708881i
$346$	20.1744	+	22.1880i	1.08458	+	1.19283i
$347$	4.22398	−	7.31616i	0.226755	−	0.392752i	−0.730089	−	0.683352i	$-0.760522\pi$
$347$	4.22398	−	7.31616i	0.226755	−	0.392752i	0.956845	+	0.290600i	$0.0938549\pi$
$348$	20.5166	−	26.8390i	1.09981	−	1.43872i
$349$	17.4956			0.936520			0.468260	−	0.883591i	$-0.344881\pi$
$349$	17.4956			0.936520			0.468260	+	0.883591i	$0.344881\pi$
$350$		0			0
$351$	15.1929	+	1.55892i	0.810939	+	0.0832089i
$352$	−18.8503	+	11.5033i	−1.00472	+	0.613127i
$353$	−7.15990	−	4.13377i	−0.381083	−	0.220018i	0.297206	−	0.954813i	$-0.403945\pi$
$353$	−7.15990	−	4.13377i	−0.381083	−	0.220018i	−0.678289	+	0.734795i	$0.737278\pi$
$354$	3.62065	+	19.8722i	0.192436	+	1.05620i
$355$	−3.60298	+	2.08018i	−0.191226	+	0.110405i
$356$	12.2236	−	17.1732i	0.647850	−	0.910179i
$357$		0			0
$358$	−2.44108	−	0.780049i	−0.129015	−	0.0412269i
$359$	12.5650	+	21.7633i	0.663156	+	1.14862i	0.979782	+	0.200070i	$0.0641169\pi$
$359$	12.5650	+	21.7633i	0.663156	+	1.14862i	−0.316625	+	0.948551i	$0.602550\pi$
$360$	−2.48280	+	1.60806i	−0.130855	+	0.0847524i
$361$	6.05892	−	10.4944i	0.318890	−	0.552334i
$362$	2.26755	+	10.4186i	0.119180	+	0.547587i
$363$	3.88596	−	6.23025i	0.203960	−	0.327003i
$364$		0			0
$365$		−	2.74653i		−	0.143760i
$366$	−32.5121	−	11.6245i	−1.69944	−	0.607622i
$367$	−18.8041	−	10.8565i	−0.981565	−	0.566707i	−0.0788227	−	0.996889i	$-0.525116\pi$
$367$	−18.8041	−	10.8565i	−0.981565	−	0.566707i	−0.902742	+	0.430182i	$0.858449\pi$
$368$	8.57052	+	1.64814i	0.446769	+	0.0859152i
$369$	18.8491	+	12.6688i	0.981245	+	0.659510i
$370$	−0.0959078	+	0.300133i	−0.00498601	+	0.0156032i
$371$		0			0
$372$	−3.51394	−	8.43982i	−0.182189	−	0.437584i
$373$	0.360898	+	0.625094i	0.0186866	+	0.0323662i	0.875217	−	0.483730i	$-0.160718\pi$
$373$	0.360898	+	0.625094i	0.0186866	+	0.0323662i	−0.856531	+	0.516096i	$0.827385\pi$
$374$	14.4986	+	15.9457i	0.749707	+	0.824534i
$375$	5.26426	−	2.80462i	0.271845	−	0.144830i
$376$	4.85514	−	11.3476i	0.250385	−	0.585207i
$377$		−	28.6640i		−	1.47627i
$378$		0			0
$379$		−	18.2745i		−	0.938699i	−0.883013	−	0.469349i	$-0.844489\pi$
$379$		−	18.2745i		−	0.938699i	0.883013	−	0.469349i	$-0.155511\pi$
$380$	0.368902	−	3.87181i	0.0189243	−	0.198620i
$381$	−18.9491	+	10.0954i	−0.970791	+	0.517204i
$382$	1.70729	−	1.55235i	0.0873525	−	0.0794252i
$383$	−1.02465	−	1.77475i	−0.0523573	−	0.0906855i	0.838659	−	0.544657i	$-0.183340\pi$
$383$	−1.02465	−	1.77475i	−0.0523573	−	0.0906855i	−0.891016	+	0.453971i	$0.850007\pi$
$384$	−7.96972	−	17.9021i	−0.406703	−	0.913560i
$385$		0			0
$386$	20.4177	+	6.52448i	1.03923	+	0.332087i
$387$	6.26843	+	4.21311i	0.318642	+	0.214164i
$388$	3.63818	−	1.66242i	0.184701	−	0.0843964i
$389$	9.65328	+	5.57332i	0.489441	+	0.282579i	0.724342	−	0.689440i	$-0.242143\pi$
$389$	9.65328	+	5.57332i	0.489441	+	0.282579i	−0.234902	+	0.972019i	$0.575477\pi$
$390$	−0.845001	+	2.36335i	−0.0427883	+	0.119673i
$391$		−	8.51757i		−	0.430752i
$392$		0			0
$393$	−1.47622	+	2.36678i	−0.0744656	+	0.119389i
$394$	29.3318	−	6.38394i	1.47772	−	0.321618i
$395$	0.697224	−	1.20763i	0.0350811	−	0.0607623i
$396$	18.1128	+	14.8507i	0.910203	+	0.746275i
$397$	−3.98719	−	6.90601i	−0.200111	−	0.346603i	0.748453	−	0.663188i	$-0.230797\pi$
$397$	−3.98719	−	6.90601i	−0.200111	−	0.346603i	−0.948564	+	0.316585i	$0.897464\pi$
$398$	1.61725	−	5.06100i	0.0810652	−	0.253685i
$399$		0			0
$400$	6.39002	+	18.4380i	0.319501	+	0.921899i
$401$	−18.6004	+	10.7390i	−0.928860	+	0.536278i	−0.886451	−	0.462823i	$-0.846837\pi$
$401$	−18.6004	+	10.7390i	−0.928860	+	0.536278i	−0.0424093	+	0.999100i	$0.513503\pi$
$402$	−1.54012	+	0.280605i	−0.0768141	+	0.0139953i
$403$	−6.71771	−	3.87847i	−0.334633	−	0.193200i
$404$	6.16237	+	0.587144i	0.306589	+	0.0292115i
$405$	2.47874	+	1.92349i	0.123169	+	0.0955790i
$406$		0			0
$407$	2.49490			0.123668
$408$	−15.6882	+	10.9374i	−0.776680	+	0.541481i
$409$	−18.4568	+	31.9681i	−0.912630	+	1.58072i	−0.102296	+	0.994754i	$0.532619\pi$
$409$	−18.4568	+	31.9681i	−0.912630	+	1.58072i	−0.810334	+	0.585968i	$0.800714\pi$
$410$	−2.76143	+	2.51083i	−0.136377	+	0.124001i
$411$	0.257562	−	7.55389i	0.0127046	−	0.372606i
$412$	8.39604	−	11.7958i	0.413643	−	0.581136i
$413$		0			0
$414$	−1.34797	−	9.15829i	−0.0662491	−	0.450106i
$415$	−2.70013	+	1.55892i	−0.132544	+	0.0765243i
$416$	−14.5971	−	7.96081i	−0.715684	−	0.390311i
$417$	−25.7082	+	13.6965i	−1.25894	+	0.670719i
$418$	−30.0921	+	6.54942i	−1.47186	+	0.320343i
$419$	−29.5773			−1.44494			−0.722472	−	0.691400i	$-0.756994\pi$
$419$	−29.5773			−1.44494			−0.722472	+	0.691400i	$0.756994\pi$
$420$		0			0
$421$	36.8309			1.79503			0.897515	−	0.440985i	$-0.145371\pi$
$421$	36.8309			1.79503			0.897515	+	0.440985i	$0.145371\pi$
$422$	13.5970	−	2.95933i	0.661893	−	0.144058i
$423$	−13.0609	−	0.891703i	−0.635044	−	0.0433561i
$424$	−0.579692	−	4.83558i	−0.0281523	−	0.234836i
$425$	16.4929	−	9.52220i	0.800024	−	0.461894i
$426$	−22.2861	+	18.9173i	−1.07977	+	0.916546i
$427$		0			0
$428$	−17.9462	−	12.7738i	−0.867464	−	0.617447i
$429$	19.8621	+	0.677232i	0.958953	+	0.0326971i
$430$	−0.918335	+	0.834996i	−0.0442861	+	0.0402671i
$431$	−2.33839	+	4.05022i	−0.112636	+	0.195092i	−0.916832	−	0.399272i	$-0.869263\pi$
$431$	−2.33839	+	4.05022i	−0.112636	+	0.195092i	0.804196	+	0.594364i	$0.202596\pi$
$432$	−15.1374	+	14.2429i	−0.728297	+	0.685262i
$433$	−16.5564			−0.795650			−0.397825	−	0.917461i	$-0.630235\pi$
$433$	−16.5564			−0.795650			−0.397825	+	0.917461i	$0.630235\pi$
$434$		0			0
$435$	3.11632	−	4.99631i	0.149416	−	0.239555i
$436$	0.265527	−	2.78685i	0.0127165	−	0.133466i
$437$	10.5407	+	6.08565i	0.504228	+	0.291116i
$438$	−3.45913	−	18.9857i	−0.165284	−	0.907171i
$439$	−22.9313	+	13.2394i	−1.09445	+	0.631881i	−0.934758	−	0.355286i	$-0.884383\pi$
$439$	−22.9313	+	13.2394i	−1.09445	+	0.631881i	−0.159692	+	0.987167i	$0.551050\pi$
$440$	−3.08073	+	2.30770i	−0.146868	+	0.110015i
$441$		0			0
$442$	−4.93923	+	15.4568i	−0.234935	+	0.735205i
$443$	2.30049	+	3.98457i	0.109300	+	0.189313i	0.915487	−	0.402348i	$-0.131806\pi$
$443$	2.30049	+	3.98457i	0.109300	+	0.189313i	−0.806187	+	0.591661i	$0.798472\pi$
$444$	−0.284969	+	2.19550i	−0.0135240	+	0.104194i
$445$	1.83712	−	3.18199i	0.0870879	−	0.150841i
$446$	31.6635	−	6.89141i	1.49931	−	0.326318i
$447$	−11.2580	−	7.02193i	−0.532487	−	0.332126i
$448$		0			0
$449$			17.0095i			0.802728i	0.915919	+	0.401364i	$0.131464\pi$
$449$			17.0095i			0.802728i	−0.915919	+	0.401364i	$0.868536\pi$
$450$	16.2266	−	12.8486i	0.764930	−	0.605690i
$451$	25.5934	+	14.7764i	1.20515	+	0.695791i
$452$	7.34138	+	16.0665i	0.345309	+	0.755706i
$453$	−0.745995	+	21.8789i	−0.0350499	+	1.02796i
$454$	18.2266	+	5.82431i	0.855415	+	0.273348i
$455$		0			0
$456$	−2.32630	−	27.2290i	−0.108939	−	1.27511i
$457$	7.71559	+	13.3638i	0.360920	+	0.625132i	0.988113	−	0.153732i	$-0.0491293\pi$
$457$	7.71559	+	13.3638i	0.360920	+	0.625132i	−0.627192	+	0.778864i	$0.715796\pi$
$458$	15.3773	−	13.9819i	0.718536	−	0.653329i
$459$	16.4399	+	11.8824i	0.767351	+	0.554623i
$460$	1.51441	+	0.144291i	0.0706095	+	0.00672759i
$461$		−	33.3764i		−	1.55449i	−0.629196	−	0.777247i	$-0.716616\pi$
$461$		−	33.3764i		−	1.55449i	0.629196	−	0.777247i	$-0.283384\pi$
$462$		0			0
$463$			26.4787i			1.23057i	0.788304	+	0.615286i	$0.210959\pi$
$463$			26.4787i			1.23057i	−0.788304	+	0.615286i	$0.789041\pi$
$464$	29.4915	+	25.5331i	1.36911	+	1.18534i
$465$	−0.749273	−	1.40638i	−0.0347467	−	0.0652195i
$466$	16.3544	+	17.9867i	0.757603	+	0.833217i
$467$	−9.29557	−	16.1004i	−0.430148	−	0.745038i	0.566738	−	0.823898i	$-0.308205\pi$
$467$	−9.29557	−	16.1004i	−0.430148	−	0.745038i	−0.996886	+	0.0788602i	$0.974872\pi$
$468$	−2.86462	+	17.4012i	−0.132417	+	0.804371i
$469$		0			0
$470$	0.654857	−	2.04930i	0.0302063	−	0.0945274i
$471$	−0.376395	−	0.0128338i	−0.0173434	−	0.000591350i
$472$	−23.1584	+	2.77624i	−1.06595	+	0.127787i
$473$	8.51130	+	4.91400i	0.391350	+	0.225946i
$474$	3.29868	−	9.22598i	0.151514	−	0.423763i
$475$			27.2137i			1.24865i
$476$		0			0
$477$	−4.63910	+	2.27210i	−0.212410	+	0.104032i
$478$	4.37108	+	20.0835i	0.199928	+	0.918597i
$479$	−20.4388	+	35.4011i	−0.933874	+	1.61752i	−0.157245	+	0.987560i	$0.550261\pi$
$479$	−20.4388	+	35.4011i	−0.933874	+	1.61752i	−0.776629	+	0.629958i	$0.783072\pi$
$480$	−1.67888	−	2.97460i	−0.0766300	−	0.135772i
$481$	0.939235	+	1.62680i	0.0428254	+	0.0741758i
$482$	25.3149	+	8.08941i	1.15306	+	0.368462i
$483$		0			0
$484$	6.90760	+	4.91671i	0.313982	+	0.223487i
$485$	0.603814	−	0.348612i	0.0274178	−	0.0158297i
$486$	19.5571	+	10.1745i	0.887128	+	0.461524i
$487$	18.5599	+	10.7156i	0.841032	+	0.485570i	0.857615	−	0.514293i	$-0.171945\pi$
$487$	18.5599	+	10.7156i	0.841032	+	0.485570i	−0.0165831	+	0.999862i	$0.505279\pi$
$488$	15.6831	−	36.6551i	0.709941	−	1.65930i
$489$	7.69987	+	4.80260i	0.348200	+	0.217181i
$490$		0			0
$491$	1.63166			0.0736358			0.0368179	−	0.999322i	$-0.488278\pi$
$491$	1.63166			0.0736358			0.0368179	+	0.999322i	$0.488278\pi$
$492$	−15.9264	+	20.8343i	−0.718017	+	0.939281i
$493$	19.0351	−	32.9698i	0.857300	−	1.48489i
$494$	−15.5991	−	17.1560i	−0.701837	−	0.771885i
$495$	3.38846	+	2.27744i	0.152300	+	0.102363i
$496$	9.97438	−	3.45681i	0.447863	−	0.155215i
$497$		0			0
$498$	−16.7015	+	14.1769i	−0.748414	+	0.635282i
$499$	−7.69218	+	4.44108i	−0.344349	+	0.198810i	−0.662194	−	0.749333i	$-0.730374\pi$
$499$	−7.69218	+	4.44108i	−0.344349	+	0.198810i	0.317844	+	0.948143i	$0.397041\pi$
$500$	2.86247	+	6.26450i	0.128014	+	0.280157i
$501$	−9.34457	−	17.5397i	−0.417485	−	0.783618i
$502$	6.20775	+	28.5223i	0.277065	+	1.27301i
$503$	34.8967			1.55597			0.777983	−	0.628286i	$-0.216243\pi$
$503$	34.8967			1.55597			0.777983	+	0.628286i	$0.216243\pi$
$504$		0			0
$505$	1.07900			0.0480150
$506$	−2.56171	−	11.7701i	−0.113882	−	0.523246i
$507$	−3.55155	−	6.66624i	−0.157730	−	0.296058i
$508$	−10.3037	−	22.5495i	−0.457152	−	1.00047i
$509$	−20.5865	+	11.8856i	−0.912479	+	0.526820i	−0.881228	−	0.472692i	$-0.843282\pi$
$509$	−20.5865	+	11.8856i	−0.912479	+	0.526820i	−0.0312508	+	0.999512i	$0.509949\pi$
$510$	−2.54139	+	2.15722i	−0.112535	+	0.0955235i
$511$		0			0
$512$	21.1934	−	7.92728i	0.936623	−	0.350340i
$513$	−26.4507	+	11.8550i	−1.16783	+	0.523410i
$514$	4.58932	+	5.04737i	0.202426	+	0.222630i
$515$	1.26186	−	2.18561i	0.0556044	−	0.0963097i
$516$	−5.29645	+	6.92861i	−0.233163	+	0.305015i
$517$	−17.0351			−0.749205
$518$		0			0
$519$	31.1634	+	19.4374i	1.36792	+	0.853207i
$520$	−2.66451	−	1.14003i	−0.116847	−	0.0499936i
$521$	4.96256	+	2.86513i	0.217414	+	0.125524i	0.604752	−	0.796414i	$-0.293272\pi$
$521$	4.96256	+	2.86513i	0.217414	+	0.125524i	−0.387338	+	0.921938i	$0.626606\pi$
$522$	15.2493	−	38.4624i	0.667444	−	1.68345i
$523$	4.17225	−	2.40885i	0.182440	−	0.105332i	−0.405999	−	0.913874i	$-0.633076\pi$
$523$	4.17225	−	2.40885i	0.182440	−	0.105332i	0.588439	+	0.808542i	$0.299743\pi$
$524$	−2.62410	−	1.86779i	−0.114634	−	0.0815948i
$525$		0			0
$526$	−19.4762	−	6.22364i	−0.849204	−	0.271364i
$527$	−5.15121	−	8.92216i	−0.224390	−	0.388656i
$528$	−18.3894	+	19.8323i	−0.800297	+	0.863089i
$529$	9.11968	−	15.7958i	0.396508	−	0.686772i
$530$	−0.180534	−	0.829486i	−0.00784189	−	0.0360306i
$531$	10.8815	+	22.2174i	0.472216	+	0.964155i
$532$		0			0
$533$			22.2509i			0.963795i
$534$	8.69174	−	24.3096i	0.376128	−	1.05198i
$535$	−3.32522	−	1.91982i	−0.143762	−	0.0830009i
$536$	−0.215162	−	1.79480i	−0.00929358	−	0.0775236i
$537$	−3.13681	−	0.106955i	−0.135363	−	0.00461544i
$538$	−2.02854	+	6.34809i	−0.0874564	+	0.273685i
$539$		0			0
$540$	−2.39116	+	2.72169i	−0.102899	+	0.117123i
$541$	6.01942	+	10.4259i	0.258795	+	0.448246i	0.965919	−	0.258843i	$-0.0833413\pi$
$541$	6.01942	+	10.4259i	0.258795	+	0.448246i	−0.707124	+	0.707089i	$0.750008\pi$
$542$	−14.9124	−	16.4008i	−0.640542	−	0.704473i
$543$	6.14022	+	11.5252i	0.263502	+	0.494593i
$544$	−11.5033	−	18.8503i	−0.493200	−	0.808200i
$545$		−	0.487964i		−	0.0209021i
$546$		0			0
$547$		−	35.3097i		−	1.50973i	−0.655879	−	0.754866i	$-0.727702\pi$
$547$		−	35.3097i		−	1.50973i	0.655879	−	0.754866i	$-0.272298\pi$
$548$	8.68820	+	0.827802i	0.371142	+	0.0353619i
$549$	−42.1895	−	2.88039i	−1.80060	−	0.122932i
$550$	19.9271	−	18.1187i	0.849695	−	0.772585i
$551$	27.2005	+	47.1127i	1.15878	+	2.00707i
$552$	10.6502	−	0.909900i	0.453304	−	0.0387279i
$553$		0			0
$554$	−22.8958	−	7.31638i	−0.972751	−	0.310843i
$555$	−0.0131502	+	0.385674i	−0.000558194	+	0.0163710i
$556$	−13.9790	−	30.5929i	−0.592842	−	1.29743i
$557$	−30.1308	−	17.3960i	−1.27668	−	0.737093i	−0.300445	−	0.953799i	$-0.597135\pi$
$557$	−30.1308	−	17.3960i	−1.27668	−	0.737093i	−0.976237	+	0.216706i	$0.930469\pi$
$558$	−6.95071	−	8.77810i	−0.294247	−	0.371607i
$559$			7.39973i			0.312975i
$560$		0			0
$561$	22.3960	+	13.9690i	0.945562	+	0.589771i
$562$	7.95707	−	1.73182i	0.335649	−	0.0730525i
$563$	−6.43088	+	11.1386i	−0.271029	+	0.469436i	−0.969126	−	0.246567i	$-0.920697\pi$
$563$	−6.43088	+	11.1386i	−0.271029	+	0.469436i	0.698096	+	0.716004i	$0.254031\pi$
$564$	1.94576	−	14.9908i	0.0819314	−	0.631227i
$565$	1.53950	+	2.66649i	0.0647673	+	0.112180i
$566$	−2.40130	+	7.51461i	−0.100934	+	0.315863i
$567$		0			0
$568$	−20.2369	−	27.0157i	−0.849120	−	1.13355i
$569$	−13.5887	+	7.84543i	−0.569667	+	0.328897i	−0.757016	−	0.653396i	$-0.773344\pi$
$569$	−13.5887	+	7.84543i	−0.569667	+	0.328897i	0.187349	+	0.982293i	$0.440010\pi$
$570$	−0.853831	−	4.68631i	−0.0357630	−	0.196288i
$571$	36.4003	+	21.0157i	1.52331	+	0.879481i	0.999620	+	0.0275690i	$0.00877659\pi$
$571$	36.4003	+	21.0157i	1.52331	+	0.879481i	0.523685	+	0.851912i	$0.324557\pi$
$572$	−2.17662	+	22.8447i	−0.0910089	+	0.955185i
$573$	1.49564	−	2.39792i	0.0624813	−	0.100174i
$574$		0			0
$575$	−10.6443			−0.443897
$576$	−15.3518	−	18.4478i	−0.639659	−	0.768659i
$577$	−19.3960	+	33.5949i	−0.807468	+	1.39858i	0.107145	+	0.994243i	$0.465829\pi$
$577$	−19.3960	+	33.5949i	−0.807468	+	1.39858i	−0.914612	+	0.404332i	$0.867504\pi$
$578$	1.84224	−	1.67505i	0.0766270	−	0.0696731i
$579$	26.2369	+	0.894589i	1.09037	+	0.0371778i
$580$	5.53950	+	3.94293i	0.230015	+	0.163721i
$581$		0			0
$582$	3.73487	−	3.17029i	0.154815	−	0.131413i
$583$	−5.82125	+	3.36090i	−0.241091	+	0.139194i
$584$	22.1253	−	2.65239i	0.915550	−	0.109757i
$585$	−0.209380	+	3.06682i	−0.00865678	+	0.126797i
$586$	−32.8485	+	7.14933i	−1.35696	+	0.295336i
$587$	7.07471			0.292004			0.146002	−	0.989284i	$-0.453359\pi$
$587$	7.07471			0.292004			0.146002	+	0.989284i	$0.453359\pi$
$588$		0			0
$589$	14.7218			0.606601
$590$	−3.97255	+	0.864607i	−0.163547	+	0.0355953i
$591$	32.4473	−	17.2868i	1.33471	−	0.711085i
$592$	−2.51041	−	0.482760i	−0.103177	−	0.0198413i
$593$	−15.9258	+	9.19477i	−0.653994	+	0.377584i	−0.789985	−	0.613126i	$-0.789912\pi$
$593$	−15.9258	+	9.19477i	−0.653994	+	0.377584i	0.135991	+	0.990710i	$0.456578\pi$
$594$	26.2915	+	11.4754i	1.07875	+	0.470843i
$595$		0			0
$596$	8.88449	−	12.4820i	0.363923	−	0.511283i
$597$	0.221745	−	6.50343i	0.00907542	−	0.266168i
$598$	6.71033	−	6.10137i	0.274406	−	0.249503i
$599$	18.9258	−	32.7804i	0.773287	−	1.33937i	−0.162466	−	0.986714i	$-0.551945\pi$
$599$	18.9258	−	32.7804i	0.773287	−	1.33937i	0.935752	−	0.352658i	$-0.114722\pi$
$600$	13.6683	+	19.6052i	0.558005	+	0.800381i
$601$	21.9488			0.895308			0.447654	−	0.894207i	$-0.352260\pi$
$601$	21.9488			0.895308			0.447654	+	0.894207i	$0.352260\pi$
$602$		0			0
$603$	−1.72188	+	0.843327i	−0.0701202	+	0.0343429i
$604$	−25.1642	−	2.39762i	−1.02392	−	0.0975577i
$605$	1.27989	+	0.738947i	0.0520351	+	0.0300425i
$606$	7.45873	−	1.35896i	0.302990	−	0.0552038i
$607$	22.4114	−	12.9392i	0.909651	−	0.525187i	0.0293323	−	0.999570i	$-0.490662\pi$
$607$	22.4114	−	12.9392i	0.909651	−	0.525187i	0.880319	+	0.474382i	$0.157329\pi$
$608$	31.5465	−	0.767338i	1.27938	−	0.0311197i
$609$		0			0
$610$	2.11533	−	6.61968i	0.0856470	−	0.268023i
$611$	−6.41308	−	11.1078i	−0.259445	−	0.449373i
$612$	−14.8507	+	18.1128i	−0.600304	+	0.732167i
$613$	6.45681	−	11.1835i	0.260788	−	0.451698i	−0.705664	−	0.708547i	$-0.749351\pi$
$613$	6.45681	−	11.1835i	0.260788	−	0.451698i	0.966452	+	0.256849i	$0.0826843\pi$
$614$	5.11271	−	1.11276i	0.206332	−	0.0449073i
$615$	−2.41910	+	3.87847i	−0.0975475	+	0.156395i
$616$		0			0
$617$			26.4677i			1.06555i	0.846257	+	0.532775i	$0.178851\pi$
$617$			26.4677i			1.06555i	−0.846257	+	0.532775i	$0.821149\pi$
$618$	5.97010	−	16.6976i	0.240153	−	0.671675i
$619$	−29.7384	−	17.1695i	−1.19529	−	0.690100i	−0.235787	−	0.971805i	$-0.575767\pi$
$619$	−29.7384	−	17.1695i	−1.19529	−	0.690100i	−0.959501	+	0.281705i	$0.909100\pi$
$620$	1.67360	−	0.764730i	0.0672136	−	0.0307123i
$621$	−4.63691	−	10.3458i	−0.186073	−	0.415164i
$622$	10.2174	+	3.26499i	0.409682	+	0.130914i
$623$		0			0
$624$	−19.8546	−	4.52474i	−0.794819	−	0.181135i
$625$	−11.5959	−	20.0847i	−0.463836	−	0.803388i
$626$	16.3601	−	14.8754i	0.653882	−	0.594542i
$627$	−33.2884	+	17.7349i	−1.32941	+	0.708265i
$628$	0.0412477	−	0.432916i	0.00164596	−	0.0172752i
$629$			2.49490i			0.0994782i
$630$		0			0
$631$			27.7569i			1.10499i	0.833517	+	0.552493i	$0.186323\pi$
$631$			27.7569i			1.10499i	−0.833517	+	0.552493i	$0.813677\pi$
$632$	10.4016	+	4.45040i	0.413755	+	0.177028i
$633$	15.0413	−	8.01347i	0.597836	−	0.318507i
$634$	13.2179	+	14.5371i	0.524949	+	0.577343i
$635$	−2.16070	−	3.74245i	−0.0857449	−	0.148515i
$636$	−2.29266	−	5.50654i	−0.0909099	−	0.218349i
$637$		0			0
$638$	16.3881	−	51.2847i	0.648810	−	2.03038i
$639$	−19.9715	+	29.7143i	−0.790060	+	1.17548i
$640$	3.54641	−	1.72593i	0.140184	−	0.0682233i
$641$	6.03040	+	3.48165i	0.238186	+	0.137517i	0.614343	−	0.789039i	$-0.289421\pi$
$641$	6.03040	+	3.48165i	0.238186	+	0.137517i	−0.376156	+	0.926556i	$0.622754\pi$
$642$	−25.4039	−	9.08298i	−1.00261	−	0.358477i
$643$		−	9.74373i		−	0.384255i	−0.981370	−	0.192128i	$-0.938461\pi$
$643$		−	9.74373i		−	0.384255i	0.981370	−	0.192128i	$-0.0615387\pi$
$644$		0			0
$645$	−0.804492	+	1.28982i	−0.0316768	+	0.0507865i
$646$	−6.54942	−	30.0921i	−0.257683	−	1.18396i
$647$	−14.0948	+	24.4129i	−0.554123	+	0.959770i	0.443848	+	0.896102i	$0.353613\pi$
$647$	−14.0948	+	24.4129i	−0.554123	+	0.959770i	−0.997971	+	0.0636677i	$0.979720\pi$
$648$	−13.1013	+	21.8256i	−0.514669	+	0.857389i
$649$	16.0959	+	27.8789i	0.631820	+	1.09434i
$650$	19.3161	+	6.17248i	0.757641	+	0.242105i
$651$		0			0
$652$	−6.07649	+	8.53699i	−0.237974	+	0.334334i
$653$	9.39867	−	5.42633i	0.367799	−	0.212349i	−0.304698	−	0.952449i	$-0.598555\pi$
$653$	9.39867	−	5.42633i	0.367799	−	0.212349i	0.672496	+	0.740101i	$0.265222\pi$
$654$	−0.614569	−	3.37310i	−0.0240315	−	0.131899i
$655$	−0.486214	−	0.280716i	−0.0189979	−	0.0109685i
$656$	−22.8933	−	19.8205i	−0.893832	−	0.773860i
$657$	−10.3960	−	21.2263i	−0.405588	−	0.828116i
$658$		0			0
$659$	−19.2248			−0.748893			−0.374446	−	0.927249i	$-0.622167\pi$
$659$	−19.2248			−0.748893			−0.374446	+	0.927249i	$0.622167\pi$
$660$	−2.86305	+	3.74533i	−0.111444	+	0.145787i
$661$	1.37371	−	2.37933i	0.0534311	−	0.0925454i	−0.838073	−	0.545558i	$-0.816318\pi$
$661$	1.37371	−	2.37933i	0.0534311	−	0.0925454i	0.891504	+	0.453013i	$0.149651\pi$
$662$	30.2503	+	33.2695i	1.17571	+	1.29306i
$663$	−0.677232	+	19.8621i	−0.0263015	+	0.771382i
$664$	−15.1658	−	20.2460i	−0.588547	−	0.785696i
$665$		0			0
$666$	0.394837	+	2.68258i	0.0152996	+	0.103948i
$667$	−18.4275	+	10.6391i	−0.713514	+	0.411948i
$668$	20.8724	−	9.53734i	0.807577	−	0.369011i
$669$	35.0267	−	18.6610i	1.35421	−	0.721476i
$670$	−0.0670080	−	0.307877i	−0.00258875	−	0.0118943i
$671$	−55.0271			−2.12430
$672$		0			0
$673$	31.3097			1.20690			0.603449	−	0.797401i	$-0.293793\pi$
$673$	31.3097			1.20690			0.603449	+	0.797401i	$0.293793\pi$
$674$	−5.14830	−	23.6545i	−0.198305	−	0.911138i
$675$	14.8492	−	20.5447i	0.571547	−	0.790767i
$676$	7.93287	−	3.62481i	0.305110	−	0.139416i
$677$	−18.1712	+	10.4911i	−0.698376	+	0.403208i	−0.806742	−	0.590903i	$-0.798771\pi$
$677$	−18.1712	+	10.4911i	−0.698376	+	0.403208i	0.108366	+	0.994111i	$0.465438\pi$
$678$	14.0003	+	16.4935i	0.537678	+	0.633429i
$679$		0			0
$680$	−2.30770	−	3.08073i	−0.0884963	−	0.118140i
$681$	23.4213	+	0.798587i	0.897506	+	0.0306019i
$682$	−9.80167	−	10.7800i	−0.375325	−	0.412786i
$683$	7.91172	−	13.7035i	0.302734	−	0.524350i	−0.674021	−	0.738713i	$-0.735434\pi$
$683$	7.91172	−	13.7035i	0.302734	−	0.524350i	0.976754	+	0.214363i	$0.0687675\pi$
$684$	−11.8044	−	31.3193i	−0.451353	−	1.19752i
$685$	1.52126			0.0581245
$686$		0			0
$687$	13.4711	−	21.5978i	0.513953	−	0.824006i
$688$	−7.61335	−	6.59147i	−0.290256	−	0.251298i
$689$	−4.38295	−	2.53050i	−0.166977	−	0.0964043i
$690$	1.83298	−	0.333964i	0.0697805	−	0.0127138i
$691$	21.1390	−	12.2046i	0.804167	−	0.464286i	−0.0407593	−	0.999169i	$-0.512978\pi$
$691$	21.1390	−	12.2046i	0.804167	−	0.464286i	0.844926	+	0.534883i	$0.179644\pi$
$692$	−24.5931	+	34.5514i	−0.934891	+	1.31345i
$693$		0			0
$694$	11.3803	+	3.63659i	0.431991	+	0.138043i
$695$	−2.93143	−	5.07738i	−0.111195	−	0.192596i
$696$	43.2584	+	20.2792i	1.63970	+	0.768680i
$697$	−14.7764	+	25.5934i	−0.559694	+	0.969419i
$698$	5.26192	+	24.1766i	0.199167	+	0.915097i
$699$	25.2626	+	15.7569i	0.955520	+	0.595982i
$700$		0			0
$701$			21.4779i			0.811209i	0.914049	+	0.405605i	$0.132939\pi$
$701$			21.4779i			0.811209i	−0.914049	+	0.405605i	$0.867061\pi$
$702$	2.41516	+	21.4634i	0.0911543	+	0.810085i
$703$	−3.08749	−	1.78256i	−0.116447	−	0.0672306i
$704$	−21.5653	−	22.5889i	−0.812774	−	0.851350i
$705$	0.0897892	−	2.63338i	0.00338166	−	0.0991787i
$706$	3.55892	−	11.1373i	0.133942	−	0.419156i
$707$		0			0
$708$	−26.3718	+	10.9799i	−0.991111	+	0.412651i
$709$	21.0959	+	36.5392i	0.792273	+	1.37226i	0.924556	+	0.381046i	$0.124436\pi$
$709$	21.0959	+	36.5392i	0.792273	+	1.37226i	−0.132283	+	0.991212i	$0.542231\pi$
$710$	−3.95815	−	4.35320i	−0.148547	−	0.163373i
$711$	0.817369	−	11.9721i	0.0306537	−	0.448990i
$712$	27.4074	+	11.7264i	1.02713	+	0.439466i
$713$			5.75822i			0.215647i
$714$		0			0
$715$			4.00000i			0.149592i
$716$	0.343751	−	3.60784i	0.0128466	−	0.134831i
$717$	11.8363	+	22.2167i	0.442034	+	0.829697i
$718$	−26.2948	+	23.9086i	−0.981314	+	0.892260i
$719$	−9.52940	−	16.5054i	−0.355387	−	0.615548i	0.631797	−	0.775134i	$-0.282317\pi$
$719$	−9.52940	−	16.5054i	−0.355387	−	0.615548i	−0.987184	+	0.159586i	$0.948984\pi$
$720$	−2.96884	−	2.94726i	−0.110642	−	0.109838i
$721$		0			0
$722$	16.3240	+	5.21635i	0.607517	+	0.194133i
$723$	32.5299	+	1.10916i	1.20980	+	0.0412501i
$724$	−13.7150	+	6.26689i	−0.509716	+	0.232907i
$725$	−41.2019	−	23.7879i	−1.53020	−	0.883461i
$726$	9.77808	+	3.49608i	0.362899	+	0.129752i
$727$		−	3.72549i		−	0.138171i	−0.997611	−	0.0690854i	$-0.977992\pi$
$727$		−	3.72549i		−	0.138171i	0.997611	−	0.0690854i	$-0.0220081\pi$
$728$		0			0
$729$	26.4374	+	5.48311i	0.979163	+	0.203078i
$730$	3.79533	−	0.826036i	0.140471	−	0.0305729i
$731$	−4.91400	+	8.51130i	−0.181751	+	0.314802i
$732$	6.28523	−	48.4235i	0.232309	−	1.78978i
$733$	12.7090	+	22.0126i	0.469417	+	0.813054i	0.999389	−	0.0349611i	$-0.0111307\pi$
$733$	12.7090	+	22.0126i	0.469417	+	0.813054i	−0.529972	+	0.848015i	$0.677797\pi$
$734$	9.34681	−	29.2498i	0.344997	−	1.07963i
$735$		0			0
$736$	0.300133	+	12.3390i	0.0110631	+	0.454820i
$737$	−2.16065	+	1.24745i	−0.0795885	+	0.0459504i
$738$	−11.8375	+	29.8571i	−0.435746	+	1.09906i
$739$	−20.1868	−	11.6548i	−0.742582	−	0.428730i	0.0804256	−	0.996761i	$-0.474372\pi$
$739$	−20.1868	−	11.6548i	−0.742582	−	0.428730i	−0.823007	+	0.568031i	$0.807705\pi$
$740$	−0.443588	−	0.0422645i	−0.0163066	−	0.00155368i
$741$	−24.0959	−	15.0292i	−0.885185	−	0.552113i
$742$		0			0
$743$	33.8576			1.24211			0.621057	−	0.783765i	$-0.286703\pi$
$743$	33.8576			1.24211			0.621057	+	0.783765i	$0.286703\pi$
$744$	10.6058	−	7.39411i	0.388829	−	0.271081i
$745$	1.33528	−	2.31277i	0.0489207	−	0.0847332i
$746$	−0.755252	+	0.686713i	−0.0276518	+	0.0251424i
$747$	−14.9669	+	22.2684i	−0.547611	+	0.814757i
$748$	−17.6742	+	24.8309i	−0.646234	+	0.907908i
$749$		0			0
$750$	5.45885	+	6.43098i	0.199329	+	0.234826i
$751$	41.7017	−	24.0765i	1.52172	−	0.878564i	0.522046	−	0.852918i	$-0.325169\pi$
$751$	41.7017	−	24.0765i	1.52172	−	0.878564i	0.999671	−	0.0256461i	$-0.00816430\pi$
$752$	17.1410	+	3.29628i	0.625069	+	0.120203i
$753$	16.8097	+	31.5518i	0.612581	+	1.14981i
$754$	39.6097	−	8.62088i	1.44250	−	0.313954i
$755$	−4.40614			−0.160356
$756$		0			0
$757$	−11.3923			−0.414062			−0.207031	−	0.978334i	$-0.566380\pi$
$757$	−11.3923			−0.414062			−0.207031	+	0.978334i	$0.566380\pi$
$758$	25.2529	−	5.49617i	0.917226	−	0.199630i
$759$	−6.93677	−	13.0203i	−0.251789	−	0.472607i
$760$	5.46127	−	0.654700i	0.198101	−	0.0237485i
$761$	23.8583	−	13.7746i	0.864861	−	0.499328i	−0.000776011	−	1.00000i	$-0.500247\pi$
$761$	23.8583	−	13.7746i	0.864861	−	0.499328i	0.865637	+	0.500672i	$0.166914\pi$
$762$	−19.6496	−	23.1488i	−0.711828	−	0.838592i
$763$		0			0
$764$	2.65862	+	1.89236i	0.0961853	+	0.0684632i
$765$	−2.27744	+	3.38846i	−0.0823410	+	0.122510i
$766$	2.14429	−	1.94970i	0.0774764	−	0.0704454i
$767$	−12.1190	+	20.9907i	−0.437591	+	0.757930i
$768$	22.3412	−	16.3972i	0.806170	−	0.591684i
$769$	−5.83461			−0.210401			−0.105201	−	0.994451i	$-0.533549\pi$
$769$	−5.83461			−0.210401			−0.105201	+	0.994451i	$0.533549\pi$
$770$		0			0
$771$	7.08912	+	4.42166i	0.255308	+	0.159242i
$772$	−2.87520	+	30.1767i	−0.103481	+	1.08608i
$773$	−41.1952	−	23.7841i	−1.48169	−	0.855454i	−0.481906	−	0.876223i	$-0.660055\pi$
$773$	−41.1952	−	23.7841i	−1.48169	−	0.855454i	−0.999784	+	0.0207689i	$0.993389\pi$
$774$	−3.93667	+	9.92923i	−0.141501	+	0.356899i
$775$	−11.1499	+	6.43739i	−0.400516	+	0.231238i
$776$	3.39144	+	4.52749i	0.121745	+	0.162527i
$777$		0			0
$778$	−4.79829	+	15.0157i	−0.172027	+	0.538340i
$779$	−21.1149	−	36.5720i	−0.756519	−	1.31033i
$780$	−3.51997	−	0.456882i	−0.126035	−	0.0163590i
$781$	−23.2939	+	40.3463i	−0.833522	+	1.44370i
$782$	11.7701	−	2.56171i	0.420899	−	0.0916067i
$783$	5.17240	−	50.4093i	0.184846	−	1.80148i
$784$		0			0
$785$		−	0.0758015i		−	0.00270547i
$786$	−3.71456	−	1.32811i	−0.132494	−	0.0473723i
$787$	42.2774	+	24.4089i	1.50703	+	0.870082i	0.999967	+	0.00817024i	$0.00260070\pi$
$787$	42.2774	+	24.4089i	1.50703	+	0.870082i	0.507059	+	0.861911i	$0.330733\pi$
$788$	17.6435	+	38.6125i	0.628522	+	1.37551i
$789$	−25.0271	−	0.853341i	−0.890989	−	0.0303797i
$790$	1.87847	+	0.600267i	0.0668330	+	0.0213565i
$791$		0			0
$792$	−15.0741	+	29.4959i	−0.535634	+	1.04809i
$793$	−20.7156	−	35.8805i	−0.735632	−	1.27415i
$794$	8.34399	−	7.58678i	0.296117	−	0.269245i
$795$	−0.488861	−	0.917592i	−0.0173381	−	0.0325436i
$796$	7.48000	+	0.712686i	0.265122	+	0.0252605i
$797$			12.7292i			0.450890i	0.974256	+	0.225445i	$0.0723837\pi$
$797$			12.7292i			0.450890i	−0.974256	+	0.225445i	$0.927616\pi$
$798$		0			0
$799$		−	17.0351i		−	0.602660i
$800$	−23.5569	+	14.3755i	−0.832863	+	0.508250i
$801$	2.15369	−	31.5455i	0.0760970	−	1.11461i
$802$	−20.4340	−	22.4734i	−0.721548	−	0.793564i
$803$	−15.3778	−	26.6352i	−0.542672	−	0.939936i
$804$	−0.850958	−	2.04384i	−0.0300110	−	0.0720807i
$805$		0			0
$806$	3.33912	−	10.4494i	0.117616	−	0.368065i
$807$	−0.278138	+	8.15735i	−0.00979093	+	0.287152i
$808$	1.04202	+	8.69214i	0.0366581	+	0.305789i
$809$	23.0201	+	13.2906i	0.809342	+	0.467274i	0.846727	−	0.532027i	$-0.178570\pi$
$809$	23.0201	+	13.2906i	0.809342	+	0.467274i	−0.0373853	+	0.999301i	$0.511903\pi$
$810$	−1.91251	+	4.00378i	−0.0671986	+	0.140678i
$811$			4.13977i			0.145367i	0.997355	+	0.0726835i	$0.0231563\pi$
$811$			4.13977i			0.145367i	−0.997355	+	0.0726835i	$0.976844\pi$
$812$		0			0
$813$	−23.0351	−	14.3676i	−0.807878	−	0.503894i
$814$	0.750357	+	3.44761i	0.0263000	+	0.120839i
$815$	−0.913253	+	1.58180i	−0.0319899	+	0.0554081i
$816$	−19.8323	−	18.3894i	−0.694268	−	0.643758i
$817$	−7.02193	−	12.1623i	−0.245666	−	0.425506i
$818$	−49.7266	−	15.8902i	−1.73865	−	0.555587i
$819$		0			0
$820$	−4.30013	−	3.06077i	−0.150167	−	0.106887i
$821$	−25.5549	+	14.7541i	−0.891871	+	0.514922i	−0.874554	−	0.484928i	$-0.838846\pi$
$821$	−25.5549	+	14.7541i	−0.891871	+	0.514922i	−0.0173172	+	0.999850i	$0.505513\pi$
$822$	10.5159	−	1.91596i	0.366784	−	0.0668269i
$823$	−10.4596	−	6.03884i	−0.364598	−	0.210501i	0.306498	−	0.951871i	$-0.400843\pi$
$823$	−10.4596	−	6.03884i	−0.364598	−	0.210501i	−0.671096	+	0.741371i	$0.734176\pi$
$824$	18.8253	+	8.05453i	0.655811	+	0.280593i
$825$	17.4568	−	27.9880i	0.607768	−	0.974416i
$826$		0			0
$827$	−11.9341			−0.414989			−0.207494	−	0.978236i	$-0.566531\pi$
$827$	−11.9341			−0.414989			−0.207494	+	0.978236i	$0.566531\pi$
$828$	12.2501	−	4.61712i	0.425720	−	0.160456i
$829$	1.25218	−	2.16884i	0.0434900	−	0.0753269i	−0.843461	−	0.537190i	$-0.819486\pi$
$829$	1.25218	−	2.16884i	0.0434900	−	0.0753269i	0.886951	+	0.461863i	$0.152819\pi$
$830$	−2.96629	−	3.26235i	−0.102962	−	0.113238i
$831$	−29.4214	−	1.00317i	−1.02062	−	0.0347996i
$832$	6.61057	−	22.5655i	0.229180	−	0.782319i
$833$		0			0
$834$	−26.6585	−	31.4059i	−0.923110	−	1.08750i
$835$	3.46410	−	2.00000i	0.119880	−	0.0692129i
$836$	−18.1008	−	39.6135i	−0.626029	−	1.37006i
$837$	−11.1141	−	8.03298i	−0.384158	−	0.277660i
$838$	−8.89555	−	40.8717i	−0.307292	−	1.41189i
$839$	−1.64607			−0.0568288			−0.0284144	−	0.999596i	$-0.509046\pi$
$839$	−1.64607			−0.0568288			−0.0284144	+	0.999596i	$0.509046\pi$
$840$		0			0
$841$	−66.1054			−2.27950
$842$	11.0771	+	50.8953i	0.381743	+	1.75397i
$843$	8.80225	−	4.68954i	0.303166	−	0.161516i
$844$	8.17878	+	17.8992i	0.281525	+	0.616116i
$845$	1.31658	−	0.760131i	0.0452919	−	0.0261493i
$846$	−2.69594	−	18.3166i	−0.0926884	−	0.629737i
$847$		0			0
$848$	6.50776	−	2.25539i	0.223477	−	0.0774503i
$849$	−0.329249	+	9.65635i	−0.0112998	+	0.331405i
$850$	18.1187	+	19.9271i	0.621467	+	0.683494i
$851$	0.697224	−	1.20763i	0.0239005	−	0.0413969i
$852$	−32.8438	−	25.1069i	−1.12521	−	0.860147i
$853$	−15.1311			−0.518077			−0.259039	−	0.965867i	$-0.583406\pi$
$853$	−15.1311			−0.518077			−0.259039	+	0.965867i	$0.583406\pi$
$854$		0			0
$855$	−2.56610	−	5.23937i	−0.0877587	−	0.179183i
$856$	12.2543	−	28.6411i	0.418842	−	0.978931i
$857$	42.3681	+	24.4612i	1.44727	+	0.835579i	0.998318	−	0.0579792i	$-0.0184657\pi$
$857$	42.3681	+	24.4612i	1.44727	+	0.835579i	0.448947	+	0.893558i	$0.351799\pi$
$858$	5.03782	+	27.6504i	0.171988	+	0.943971i
$859$	−13.9058	+	8.02854i	−0.474461	+	0.273930i	−0.718105	−	0.695935i	$-0.754990\pi$
$859$	−13.9058	+	8.02854i	−0.474461	+	0.273930i	0.243644	+	0.969865i	$0.421657\pi$
$860$	−1.43005	−	1.01788i	−0.0487641	−	0.0347095i
$861$		0			0
$862$	−6.30013	−	2.01321i	−0.214583	−	0.0685703i
$863$	7.45171	+	12.9067i	0.253659	+	0.439350i	0.964530	−	0.263972i	$-0.0850325\pi$
$863$	7.45171	+	12.9067i	0.253659	+	0.439350i	−0.710871	+	0.703322i	$0.751699\pi$
$864$	−24.2344	−	16.6341i	−0.824471	−	0.565904i
$865$	−3.69617	+	6.40196i	−0.125674	+	0.217673i
$866$	−4.97944	−	22.8787i	−0.169208	−	0.777449i
$867$	1.61386	−	2.58746i	0.0548096	−	0.0878746i
$868$		0			0
$869$		−	15.6151i		−	0.529704i
$870$	7.84147	+	2.80366i	0.265851	+	0.0950531i
$871$	−1.62680	−	0.939235i	−0.0551221	−	0.0318248i
$872$	3.93090	−	0.471239i	0.133117	−	0.0159582i
$873$	3.34696	−	4.97974i	0.113278	−	0.168539i
$874$	−5.23937	+	16.3960i	−0.177224	+	0.554604i
$875$		0			0
$876$	25.1953	−	10.4901i	0.851269	−	0.354428i
$877$	−5.93923	−	10.2871i	−0.200554	−	0.347369i	0.748153	−	0.663526i	$-0.230941\pi$
$877$	−5.93923	−	10.2871i	−0.200554	−	0.347369i	−0.948707	+	0.316157i	$0.897607\pi$
$878$	−25.1917	−	27.7060i	−0.850179	−	0.935033i
$879$	−36.3376	+	19.3594i	−1.22564	+	0.652977i
$880$	−4.11547	−	3.56309i	−0.138733	−	0.120112i
$881$			36.4995i			1.22970i	0.788644	+	0.614850i	$0.210783\pi$
$881$			36.4995i			1.22970i	−0.788644	+	0.614850i	$0.789217\pi$
$882$		0			0
$883$		−	31.1178i		−	1.04720i	−0.851965	−	0.523599i	$-0.824589\pi$
$883$		−	31.1178i		−	1.04720i	0.851965	−	0.523599i	$-0.175411\pi$
$884$	−22.8447	−	2.17662i	−0.768350	−	0.0732075i
$885$	−4.39450	+	2.34124i	−0.147720	+	0.0786999i
$886$	−4.81424	+	4.37735i	−0.161738	+	0.147060i
$887$	−28.4624	−	49.2983i	−0.955674	−	1.65528i	−0.732819	−	0.680424i	$-0.761796\pi$
$887$	−28.4624	−	49.2983i	−0.955674	−	1.65528i	−0.222855	−	0.974852i	$-0.571538\pi$
$888$	−3.11958	+	0.266521i	−0.104686	+	0.00894386i
$889$		0			0
$890$	4.94960	+	1.58165i	0.165911	+	0.0530170i
$891$	34.8079	+	4.77510i	1.16611	+	0.159972i
$892$	19.0460	+	41.6820i	0.637706	+	1.39562i
$893$	21.0813	+	12.1713i	0.705459	+	0.407297i
$894$	6.31742	−	17.6690i	0.211286	−	0.590939i
$895$		−	0.631717i		−	0.0211160i
$896$		0			0
$897$	5.87847	−	9.42477i	0.196276	−	0.314684i
$898$	−23.5048	+	5.11571i	−0.784365	+	0.170714i
$899$	−12.8685	+	22.2889i	−0.429189	+	0.743378i
$900$	22.6353	+	18.5587i	0.754510	+	0.618622i
$901$	−3.36090	−	5.82125i	−0.111968	−	0.193934i
$902$	−12.7215	+	39.8107i	−0.423581	+	1.32555i
$903$		0			0
$904$	−19.9938	+	14.9769i	−0.664984	+	0.498124i
$905$	−2.27623	+	1.31418i	−0.0756643	+	0.0436848i
$906$	−30.4579	+	5.54934i	−1.01190	+	0.184364i
$907$	5.81050	+	3.35469i	0.192934	+	0.111391i	0.593356	−	0.804940i	$-0.297803\pi$
$907$	5.81050	+	3.35469i	0.192934	+	0.111391i	−0.400421	+	0.916331i	$0.631136\pi$
$908$	−2.56665	+	26.9383i	−0.0851773	+	0.893979i
$909$	8.33897	−	4.08419i	0.276586	−	0.135464i
$910$		0			0
$911$	−50.1275			−1.66080			−0.830399	−	0.557169i	$-0.811888\pi$
$911$	−50.1275			−1.66080			−0.830399	+	0.557169i	$0.811888\pi$
$912$	36.9271	−	11.4039i	1.22278	−	0.377621i
$913$	−17.4568	+	30.2361i	−0.577736	+	1.00067i
$914$	−16.1464	+	14.6811i	−0.534076	+	0.485609i
$915$	0.290038	−	8.50636i	0.00958836	−	0.281211i
$916$	23.9458	+	17.0443i	0.791193	+	0.563158i
$917$		0			0
$918$	−11.4754	+	26.2915i	−0.378746	+	0.867747i
$919$	−14.7529	+	8.51757i	−0.486652	+	0.280969i	−0.723185	−	0.690655i	$-0.757322\pi$
$919$	−14.7529	+	8.51757i	−0.486652	+	0.280969i	0.236532	+	0.971624i	$0.423989\pi$
$920$	0.256077	+	2.13610i	0.00844260	+	0.0704250i
$921$	5.65577	−	3.01320i	0.186364	−	0.0992883i
$922$	46.1216	−	10.0382i	1.51893	−	0.330589i
$923$	−35.0771			−1.15458
$924$		0			0
$925$	3.11784			0.102514
$926$	−36.5900	+	7.96364i	−1.20242	+	0.261702i
$927$	1.47931	−	21.6677i	0.0485869	−	0.711659i
$928$	−26.4135	+	48.4324i	−0.867065	+	1.58987i
$929$	−20.2721	+	11.7041i	−0.665105	+	0.383999i	−0.794219	−	0.607631i	$-0.792120\pi$
$929$	−20.2721	+	11.7041i	−0.665105	+	0.383999i	0.129114	+	0.991630i	$0.458787\pi$
$930$	1.71808	−	1.45837i	0.0563381	−	0.0478219i
$931$		0			0
$932$	−19.9365	+	28.0092i	−0.653040	+	0.917470i
$933$	13.1295	+	0.447672i	0.429841	+	0.0146561i
$934$	19.4529	−	17.6875i	0.636517	−	0.578753i
$935$	−2.65631	+	4.60087i	−0.0868707	+	0.150464i
$936$	−24.9076	+	1.27500i	−0.814131	+	0.0416746i
$937$	−48.5929			−1.58746			−0.793730	−	0.608270i	$-0.791864\pi$
$937$	−48.5929			−1.58746			−0.793730	+	0.608270i	$0.791864\pi$
$938$		0			0
$939$	14.3320	−	22.9781i	0.467707	−	0.749861i
$940$	3.02881	+	0.288582i	0.0987889	+	0.00941249i
$941$	−12.6540	−	7.30579i	−0.412509	−	0.238162i	0.279358	−	0.960187i	$-0.409878\pi$
$941$	−12.6540	−	7.30579i	−0.412509	−	0.238162i	−0.691867	+	0.722025i	$0.743212\pi$
$942$	−0.0954686	−	0.523986i	−0.00311054	−	0.0170724i
$943$	14.3046	−	8.25879i	0.465823	−	0.268943i
$944$	−10.8014	−	31.1668i	−0.351556	−	1.01439i
$945$		0			0
$946$	−4.23065	+	13.2394i	−0.137550	+	0.430449i
$947$	15.7125	+	27.2148i	0.510587	+	0.884362i	0.999925	+	0.0122681i	$0.00390516\pi$
$947$	15.7125	+	27.2148i	0.510587	+	0.884362i	−0.489338	+	0.872094i	$0.662762\pi$
$948$	13.7411	+	1.78356i	0.446291	+	0.0579273i
$949$	11.5783	−	20.0543i	0.375849	−	0.650989i
$950$	−37.6057	+	8.18470i	−1.22009	+	0.265547i
$951$	20.4177	+	12.7350i	0.662088	+	0.412961i
$952$		0			0
$953$		−	14.0113i		−	0.453872i	−0.973910	−	0.226936i	$-0.927129\pi$
$953$		−	14.0113i		−	0.453872i	0.973910	−	0.226936i	$-0.0728708\pi$
$954$	−4.53497	−	5.72725i	−0.146825	−	0.185427i
$955$	0.492609	+	0.284408i	0.0159405	+	0.00920323i
$956$	−26.4380	+	12.0805i	−0.855065	+	0.390710i
$957$	2.24701	−	65.9014i	0.0726357	−	2.13029i
$958$	−55.0666	−	17.5966i	−1.77912	−	0.568520i
$959$		0			0
$960$	3.60556	−	3.21461i	0.116369	−	0.103751i
$961$	−12.0176	−	20.8150i	−0.387664	−	0.671453i
$962$	−1.96554	+	1.78717i	−0.0633715	+	0.0576205i
$963$	−32.9655	−	2.25064i	−1.06230	−	0.0725258i
$964$	−3.56483	+	37.4147i	−0.114815	+	1.20505i
$965$			5.28380i			0.170091i
$966$		0			0
$967$			35.9876i			1.15728i	0.815582	+	0.578641i	$0.196417\pi$
$967$			35.9876i			1.15728i	−0.815582	+	0.578641i	$0.803583\pi$
$968$	−4.71672	+	11.0241i	−0.151601	+	0.354328i
$969$	−17.7349	−	33.2884i	−0.569728	−	1.06938i
$970$	0.663335	+	0.729540i	0.0212984	+	0.0234241i
$971$	24.1922	+	41.9022i	0.776365	+	1.34470i	0.934024	+	0.357210i	$0.116272\pi$
$971$	24.1922	+	41.9022i	0.776365	+	1.34470i	−0.157659	+	0.987494i	$0.550395\pi$
$972$	−8.17783	+	30.0853i	−0.262304	+	0.964985i
$973$		0			0
$974$	−9.22546	+	28.8701i	−0.295603	+	0.925057i
$975$	24.8214	+	0.846326i	0.794921	+	0.0271041i
$976$	55.3691	+	10.6477i	1.77232	+	0.340824i
$977$	−32.6000	−	18.8216i	−1.04296	−	0.602156i	−0.122293	−	0.992494i	$-0.539025\pi$
$977$	−32.6000	−	18.8216i	−1.04296	−	0.602156i	−0.920672	+	0.390338i	$0.872358\pi$
$978$	−4.32076	+	12.0846i	−0.138163	+	0.386422i
$979$		−	41.1443i		−	1.31498i
$980$		0			0
$981$	−1.84702	−	3.77118i	−0.0589708	−	0.120405i
$982$	0.490732	+	2.25473i	0.0156599	+	0.0719514i
$983$	2.67750	−	4.63756i	0.0853989	−	0.147915i	−0.820162	−	0.572131i	$-0.806117\pi$
$983$	2.67750	−	4.63756i	0.0853989	−	0.147915i	0.905561	+	0.424216i	$0.139450\pi$
$984$	−33.5800	−	15.7421i	−1.07049	−	0.501838i
$985$	3.69987	+	6.40836i	0.117888	+	0.204187i
$986$	51.2847	+	16.3881i	1.63324	+	0.521903i
$987$		0			0
$988$	19.0157	−	26.7156i	0.604971	−	0.849936i
$989$	4.75713	−	2.74653i	0.151268	−	0.0873345i
$990$	−2.12801	+	5.36734i	−0.0676325	+	0.170585i
$991$	−44.1913	−	25.5139i	−1.40378	−	0.810475i	−0.409005	−	0.912532i	$-0.634124\pi$
$991$	−44.1913	−	25.5139i	−1.40378	−	0.810475i	−0.994779	+	0.102057i	$0.967458\pi$
$992$	7.77669	+	12.7436i	0.246910	+	0.404609i
$993$	46.7276	+	29.1452i	1.48286	+	0.924895i
$994$		0			0
$995$	1.30971			0.0415207
$996$	−24.6136	−	18.8155i	−0.779912	−	0.596190i
$997$	26.9653	−	46.7052i	0.853998	−	1.47917i	−0.0235729	−	0.999722i	$-0.507504\pi$
$997$	26.9653	−	46.7052i	0.853998	−	1.47917i	0.877571	−	0.479446i	$-0.159162\pi$
$998$	−8.45044	−	9.29385i	−0.267494	−	0.294192i
$999$	1.35821	+	3.03042i	0.0429718	+	0.0958783i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.n.f.263.7		24
3.2	odd	2	inner	588.2.n.f.263.6		24
4.3	odd	2	inner	588.2.n.f.263.3		24
7.2	even	3	inner	588.2.n.f.275.10		24
7.3	odd	6		588.2.e.c.491.1		12
7.4	even	3		84.2.e.a.71.1	✓	12
7.5	odd	6		588.2.n.g.275.10		24
7.6	odd	2		588.2.n.g.263.7		24
12.11	even	2	inner	588.2.n.f.263.10		24
21.2	odd	6	inner	588.2.n.f.275.3		24
21.5	even	6		588.2.n.g.275.3		24
21.11	odd	6		84.2.e.a.71.12	yes	12
21.17	even	6		588.2.e.c.491.12		12
21.20	even	2		588.2.n.g.263.6		24
28.3	even	6		588.2.e.c.491.11		12
28.11	odd	6		84.2.e.a.71.11	yes	12
28.19	even	6		588.2.n.g.275.6		24
28.23	odd	6	inner	588.2.n.f.275.6		24
28.27	even	2		588.2.n.g.263.3		24
56.11	odd	6		1344.2.h.h.575.9		12
56.53	even	6		1344.2.h.h.575.4		12
84.11	even	6		84.2.e.a.71.2	yes	12
84.23	even	6	inner	588.2.n.f.275.7		24
84.47	odd	6		588.2.n.g.275.7		24
84.59	odd	6		588.2.e.c.491.2		12
84.83	odd	2		588.2.n.g.263.10		24
168.11	even	6		1344.2.h.h.575.3		12
168.53	odd	6		1344.2.h.h.575.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.1	✓	12	7.4	even	3
84.2.e.a.71.2	yes	12	84.11	even	6
84.2.e.a.71.11	yes	12	28.11	odd	6
84.2.e.a.71.12	yes	12	21.11	odd	6
588.2.e.c.491.1		12	7.3	odd	6
588.2.e.c.491.2		12	84.59	odd	6
588.2.e.c.491.11		12	28.3	even	6
588.2.e.c.491.12		12	21.17	even	6
588.2.n.f.263.3		24	4.3	odd	2	inner
588.2.n.f.263.6		24	3.2	odd	2	inner
588.2.n.f.263.7		24	1.1	even	1	trivial
588.2.n.f.263.10		24	12.11	even	2	inner
588.2.n.f.275.3		24	21.2	odd	6	inner
588.2.n.f.275.6		24	28.23	odd	6	inner
588.2.n.f.275.7		24	84.23	even	6	inner
588.2.n.f.275.10		24	7.2	even	3	inner
588.2.n.g.263.3		24	28.27	even	2
588.2.n.g.263.6		24	21.20	even	2
588.2.n.g.263.7		24	7.6	odd	2
588.2.n.g.263.10		24	84.83	odd	2
588.2.n.g.275.3		24	21.5	even	6
588.2.n.g.275.6		24	28.19	even	6
588.2.n.g.275.7		24	84.47	odd	6
588.2.n.g.275.10		24	7.5	odd	6
1344.2.h.h.575.3		12	168.11	even	6
1344.2.h.h.575.4		12	56.53	even	6
1344.2.h.h.575.9		12	56.11	odd	6
1344.2.h.h.575.10		12	168.53	odd	6

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.300756 + 1.38186i) q^{2} +(0.814407 + 1.52864i) q^{3} +(-1.81909 + 0.831208i) q^{4} +(-0.301907 + 0.174306i) q^{5} +(-1.86743 + 1.58515i) q^{6} +(-1.69572 - 2.26374i) q^{8} +(-1.67348 + 2.48987i) q^{9} +(-0.331667 - 0.364770i) q^{10} +(-1.95188 + 3.38076i) q^{11} +(-2.75210 - 2.10379i) q^{12} -2.93923 q^{13} +(-0.512326 - 0.319551i) q^{15} +(2.61819 - 3.02409i) q^{16} +(-3.38076 - 1.95188i) q^{17} +(-3.94397 - 1.56368i) q^{18} +(4.83098 - 2.78917i) q^{19} +(0.404312 - 0.568026i) q^{20} +(-5.25879 - 1.68045i) q^{22} +(1.09094 + 1.88957i) q^{23} +(2.07945 - 4.43575i) q^{24} +(-2.43923 + 4.22488i) q^{25} +(-0.883993 - 4.06162i) q^{26} +(-5.16901 - 0.530383i) q^{27} +9.75220i q^{29} +(0.287490 - 0.804071i) q^{30} +(2.28553 + 1.31955i) q^{31} +(4.96631 + 2.70846i) q^{32} +(-6.75759 - 0.230411i) q^{33} +(1.68045 - 5.25879i) q^{34} +(0.974616 - 5.92031i) q^{36} +(-0.319551 - 0.553478i) q^{37} +(5.30720 + 5.83689i) q^{38} +(-2.39373 - 4.49303i) q^{39} +(0.906533 + 0.387866i) q^{40} -7.57031i q^{41} -2.51757i q^{43} +(0.740538 - 7.77233i) q^{44} +(0.0712361 - 1.04341i) q^{45} +(-2.28302 + 2.07583i) q^{46} +(2.18189 + 3.77914i) q^{47} +(6.75501 + 1.53943i) q^{48} +(-6.57182 - 2.10003i) q^{50} +(0.230411 - 6.75759i) q^{51} +(5.34674 - 2.44312i) q^{52} +(1.49119 + 0.860938i) q^{53} +(-0.821697 - 7.30238i) q^{54} -1.36090i q^{55} +(8.19802 + 5.11331i) q^{57} +(-13.4762 + 2.93304i) q^{58} +(4.12318 - 7.14155i) q^{59} +(1.19758 + 0.155443i) q^{60} +(7.04795 + 12.2074i) q^{61} +(-1.13605 + 3.55515i) q^{62} +(-2.24908 + 7.67735i) q^{64} +(0.887375 - 0.512326i) q^{65} +(-1.71399 - 9.40736i) q^{66} +(0.553478 + 0.319551i) q^{67} +(7.77233 + 0.740538i) q^{68} +(-2.00000 + 3.20654i) q^{69} +11.9341 q^{71} +(8.47419 - 0.433786i) q^{72} +(-3.93923 + 6.82295i) q^{73} +(0.668724 - 0.608037i) q^{74} +(-8.44485 - 0.287941i) q^{75} +(-6.46962 + 9.08930i) q^{76} +(5.48883 - 4.65912i) q^{78} +(-3.46410 + 2.00000i) q^{79} +(-0.263332 + 1.36936i) q^{80} +(-3.39892 - 8.33351i) q^{81} +(10.4611 - 2.27682i) q^{82} +8.94358 q^{83} +1.36090 q^{85} +(3.47894 - 0.757175i) q^{86} +(-14.9076 + 7.94226i) q^{87} +(10.9630 - 1.31425i) q^{88} +(-9.12760 + 5.26982i) q^{89} +(1.46327 - 0.215373i) q^{90} +(-3.55515 - 2.53050i) q^{92} +(-0.155767 + 4.56840i) q^{93} +(-4.56604 + 4.15167i) q^{94} +(-0.972337 + 1.68414i) q^{95} +(-0.0956677 + 9.79749i) q^{96} -2.00000 q^{97} +(-5.15121 - 10.5176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} - 12 q^{6} + 4 q^{9} - 4 q^{10} + 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} - 2 q^{24} + 12 q^{25} - 20 q^{30} + 16 q^{33} + 64 q^{34} - 40 q^{36} + 16 q^{37} - 20 q^{40} - 24 q^{45} + 92 q^{48}+ \cdots - 48 q^{97}+O(q^{100}) \) 24 * q + 4 * q^4 - 12 * q^6 + 4 * q^9 - 4 * q^10 + 6 * q^12 - 4 * q^16 + 8 * q^18 - 32 * q^22 - 2 * q^24 + 12 * q^25 - 20 * q^30 + 16 * q^33 + 64 * q^34 - 40 * q^36 + 16 * q^37 - 20 * q^40 - 24 * q^45 + 92 * q^48 + 28 * q^52 - 10 * q^54 + 32 * q^57 + 32 * q^58 - 28 * q^60 + 16 * q^61 + 40 * q^64 + 12 * q^66 - 48 * q^69 + 32 * q^72 - 24 * q^73 - 120 * q^76 + 40 * q^78 - 28 * q^81 - 8 * q^82 + 80 * q^85 + 56 * q^88 - 160 * q^90 - 24 * q^93 + 34 * q^96 - 48 * q^97

Introduction

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