LMFDB - Embedded newform 588.2.n.g.275.7

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			275.7
Character	$\chi$	$=$	588.275
Dual form			588.2.n.g.263.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.300756 - 1.38186i) q^{2} +(-0.814407 + 1.52864i) q^{3} +(-1.81909 - 0.831208i) q^{4} +(0.301907 + 0.174306i) q^{5} +(1.86743 + 1.58515i) q^{6} +(-1.69572 + 2.26374i) q^{8} +(-1.67348 - 2.48987i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 24 * q + 4 * q^4 + 12 * q^6 + 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.308495\pi$
$5$	0.301907	+	0.174306i	0.135017	+	0.0779520i	−0.430970	+	0.902366i	$0.641829\pi$
$6$	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	−0.994427	−	0.105425i	$-0.966380\pi$
$11$	−1.95188	−	3.38076i	−0.588514	−	1.01934i	0.405913	−	0.913912i	$-0.366954\pi$
$12$	2.75210	−	2.10379i	0.794463	−	0.607313i
$13$	2.93923			0.815197			0.407599	−	0.913161i	$-0.366366\pi$
$13$	2.93923			0.815197			0.407599	+	0.913161i	$0.366366\pi$
$14$		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	$-0.509693\pi$
$17$	3.38076	−	1.95188i	0.819954	−	0.473401i	0.850401	+	0.526136i	$0.176360\pi$
$18$	−3.94397	+	1.56368i	−0.929603	+	0.368563i
$19$	−4.83098	−	2.78917i	−1.10830	−	0.639879i	−0.169914	−	0.985459i	$-0.554349\pi$
$19$	−4.83098	−	2.78917i	−1.10830	−	0.639879i	−0.938389	+	0.345580i	$0.887682\pi$
$20$	−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	−0.729582	−	0.683893i	$-0.760286\pi$
$23$	1.09094	−	1.88957i	0.227477	−	0.394003i	0.957060	+	0.289890i	$0.0936189\pi$
$24$	−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	$-0.639519\pi$
$29$		−	9.75220i		−	1.81094i	0.424412	−	0.905469i	$-0.360481\pi$
$30$	0.287490	+	0.804071i	0.0524883	+	0.146803i
$31$	−2.28553	+	1.31955i	−0.410493	+	0.236998i	−0.691002	−	0.722853i	$-0.742830\pi$
$31$	−2.28553	+	1.31955i	−0.410493	+	0.236998i	0.280508	+	0.959852i	$0.409497\pi$
$32$	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	−0.891096	−	0.453814i	$-0.850063\pi$
$37$	−0.319551	+	0.553478i	−0.0525338	+	0.0909913i	0.838563	+	0.544805i	$0.183396\pi$
$38$	−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	$0.0614854\pi$
$43$			2.51757i			0.383926i	−0.981402	+	0.191963i	$0.938515\pi$
$44$	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	$-0.936432\pi$
$47$	−2.18189	+	3.77914i	−0.318261	+	0.551244i	0.661864	+	0.749624i	$0.269765\pi$
$48$	−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	−0.394076	−	0.919078i	$-0.628935\pi$
$53$	1.49119	−	0.860938i	0.204830	−	0.118259i	0.598907	+	0.800819i	$0.295602\pi$
$54$	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	−0.999074	−	0.0430181i	$-0.986303\pi$
$59$	−4.12318	−	7.14155i	−0.536792	−	0.929751i	0.462282	−	0.886733i	$-0.347031\pi$
$60$	1.19758	−	0.155443i	0.154607	−	0.0200676i
$61$	−7.04795	+	12.2074i	−0.902398	+	1.56300i	−0.0780257	+	0.996951i	$0.524862\pi$
$61$	−7.04795	+	12.2074i	−0.902398	+	1.56300i	−0.824372	+	0.566048i	$0.808472\pi$
$62$	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	−0.465810	−	0.884885i	$-0.654237\pi$
$67$	0.553478	−	0.319551i	0.0676181	−	0.0390393i	0.533428	+	0.845846i	$0.320904\pi$
$68$	−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	$-0.0141386\pi$
$73$	3.93923	+	6.82295i	0.461053	+	0.798566i	−0.537961	+	0.842970i	$0.680805\pi$
$74$	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	0.292306	−	0.956325i	$-0.405577\pi$
$79$	−3.46410	−	2.00000i	−0.389742	−	0.225018i	−0.682048	+	0.731307i	$0.738911\pi$
$80$	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	$-0.663311\pi$
$83$	−8.94358			−0.981685			−0.490843	+	0.871248i	$0.663311\pi$
$84$		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	$-0.144672\pi$
$89$	9.12760	+	5.26982i	0.967523	+	0.558600i	0.0690430	+	0.997614i	$0.478005\pi$
$90$	−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	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		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	$-0.617455\pi$
$101$	2.68047	−	1.54757i	0.266717	−	0.153989i	0.627395	+	0.778701i	$0.284121\pi$
$102$	9.40736	+	1.71399i	0.931468	+	0.169710i
$103$	6.26948	+	3.61968i	0.617750	+	0.356658i	0.775992	−	0.630742i	$-0.217249\pi$
$103$	6.26948	+	3.61968i	0.617750	+	0.356658i	−0.158243	+	0.987400i	$0.550583\pi$
$104$	−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	−0.466900	−	0.884310i	$-0.654629\pi$
$107$	5.50703	−	9.53846i	0.532385	−	0.922118i	0.999285	−	0.0378077i	$-0.0120374\pi$
$108$	−9.84376	−	3.33171i	−0.947217	−	0.320594i
$109$	−0.699867	−	1.21220i	−0.0670351	−	0.116108i	0.830560	−	0.556929i	$-0.188021\pi$
$109$	−0.699867	−	1.21220i	−0.0670351	−	0.116108i	−0.897595	+	0.440821i	$0.854687\pi$
$110$	−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	$0.136369\pi$
$113$			8.83218i			0.830862i	−0.909625	+	0.415431i	$0.863631\pi$
$114$	−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	$-0.814633\pi$
$127$		−	12.3960i		−	1.09997i	0.835174	−	0.549985i	$-0.185367\pi$
$128$	−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	$-0.855746\pi$
$131$	−0.805238	+	1.39471i	−0.0703540	+	0.121857i	0.828702	+	0.559689i	$0.189080\pi$
$132$	−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	−0.652673	−	0.757640i	$-0.726352\pi$
$137$	−3.77914	+	2.18189i	−0.322874	+	0.186411i	0.329799	+	0.944051i	$0.393019\pi$
$138$	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	0.202999	−	0.979179i	$-0.434931\pi$
$149$	−6.63421	−	3.83026i	−0.543496	−	0.313788i	−0.746495	+	0.665391i	$0.768265\pi$
$150$	2.14195	−	11.7562i	0.174889	−	0.959892i
$151$	10.9458	−	6.31955i	0.890755	−	0.514278i	0.0165658	−	0.999863i	$-0.494727\pi$
$151$	10.9458	−	6.31955i	0.890755	−	0.514278i	0.874189	+	0.485585i	$0.161393\pi$
$152$	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	$-0.163905\pi$
$157$	0.108719	+	0.188307i	0.00867672	+	0.0150285i	−0.861654	+	0.507495i	$0.830571\pi$
$158$	−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	0.667060	−	0.745004i	$-0.267552\pi$
$163$	4.53743	+	2.61968i	0.355399	+	0.205189i	−0.311662	+	0.950193i	$0.600886\pi$
$164$	−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	$-0.353578\pi$
$167$	11.4741			0.887891			0.443945	+	0.896054i	$0.353578\pi$
$168$		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	$-0.631757\pi$
$173$	−18.3642	−	10.6025i	−1.39620	−	0.806097i	−0.993992	+	0.109451i	$0.965091\pi$
$174$	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	0.830177	−	0.557500i	$-0.188239\pi$
$179$	−0.906046	−	1.56932i	−0.0677211	−	0.117296i	−0.897898	+	0.440204i	$0.854906\pi$
$180$	−0.737703	+	1.95726i	−0.0549851	+	0.145886i
$181$	−7.53950			−0.560407			−0.280203	−	0.959941i	$-0.590402\pi$
$181$	−7.53950			−0.560407			−0.280203	+	0.959941i	$0.590402\pi$
$182$		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	−0.894031	−	0.448005i	$-0.852135\pi$
$191$	−0.815830	+	1.41306i	−0.0590314	+	0.102245i	0.834999	+	0.550251i	$0.185468\pi$
$192$	13.5676	+	2.81446i	0.979155	+	0.203116i
$193$	7.57834	+	13.1261i	0.545501	+	0.944835i	0.998575	+	0.0533622i	$0.0169938\pi$
$193$	7.57834	+	13.1261i	0.545501	+	0.944835i	−0.453075	+	0.891473i	$0.649673\pi$
$194$	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	$0.272924\pi$
$197$			21.2263i			1.51231i	−0.654393	+	0.756155i	$0.727076\pi$
$198$	12.9846	+	10.2815i	0.922774	+	0.730674i
$199$	3.25361	−	1.87847i	0.230642	−	0.133161i	−0.380226	−	0.924894i	$-0.624154\pi$
$199$	3.25361	−	1.87847i	0.230642	−	0.133161i	0.610868	+	0.791732i	$0.290821\pi$
$200$	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	$0.109985\pi$
$211$			9.83963i			0.677388i	−0.940897	+	0.338694i	$0.890015\pi$
$212$	−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	$-0.314891\pi$
$227$	−6.76508	−	11.7175i	−0.449014	−	0.777715i	−0.998322	+	0.0579050i	$0.981558\pi$
$228$	−19.1632	+	2.48732i	−1.26911	+	0.164727i
$229$	7.34809	−	12.7273i	0.485575	−	0.841041i	−0.514287	−	0.857618i	$-0.671944\pi$
$229$	7.34809	−	12.7273i	0.485575	−	0.841041i	0.999863	+	0.0165769i	$0.00527684\pi$
$230$	−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	0.900840	−	0.434151i	$-0.142952\pi$
$233$	14.8869	+	8.59497i	0.975274	+	0.563075i	0.0744343	+	0.997226i	$0.476285\pi$
$234$	−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	−0.992012	−	0.126147i	$-0.959739\pi$
$241$	−9.39604	−	16.2744i	−0.605252	−	1.04833i	0.386759	−	0.922181i	$-0.373594\pi$
$242$	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	$-0.725821\pi$
$251$	−20.6405			−1.30281			−0.651407	+	0.758729i	$0.725821\pi$
$252$		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	$-0.381406\pi$
$257$	−4.17752	−	2.41189i	−0.260587	−	0.150450i	−0.624602	+	0.780943i	$0.714739\pi$
$258$	−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	0.552351	−	0.833612i	$-0.313731\pi$
$263$	−7.22891	−	12.5208i	−0.445754	−	0.772068i	−0.998104	+	0.0615439i	$0.980398\pi$
$264$	−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	$-0.712554\pi$
$269$	−4.08105	+	2.35619i	−0.248826	+	0.143660i	0.370401	+	0.928872i	$0.379220\pi$
$270$	1.52092	−	2.06141i	0.0925605	−	0.125454i
$271$	13.5743	+	7.83712i	0.824580	+	0.476071i	0.851993	−	0.523553i	$-0.175394\pi$
$271$	13.5743	+	7.83712i	0.824580	+	0.476071i	−0.0274135	+	0.999624i	$0.508727\pi$
$272$	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	−0.999924	−	0.0122887i	$-0.996088\pi$
$277$	−8.49815	−	14.7192i	−0.510605	−	0.884393i	0.489320	−	0.872104i	$-0.337245\pi$
$278$	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	$0.0549432\pi$
$281$			5.75822i			0.343507i	−0.985140	+	0.171753i	$0.945057\pi$
$282$	−10.0650	+	3.59868i	−0.599363	+	0.214298i
$283$	−4.83098	+	2.78917i	−0.287172	+	0.165799i	−0.636666	−	0.771140i	$-0.719687\pi$
$283$	−4.83098	+	2.78917i	−0.287172	+	0.165799i	0.349494	+	0.936939i	$0.386354\pi$
$284$	−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	$-0.235657\pi$
$311$	−3.79236	−	6.56857i	−0.215045	−	0.372469i	−0.953287	+	0.302067i	$0.902323\pi$
$312$	−6.11198	−	13.0377i	−0.346023	−	0.738116i
$313$	7.81770	−	13.5407i	0.441883	−	0.765363i	−0.555946	−	0.831218i	$-0.687644\pi$
$313$	7.81770	−	13.5407i	0.441883	−	0.765363i	0.997829	+	0.0658547i	$0.0209774\pi$
$314$	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	0.798262	−	0.602311i	$-0.205753\pi$
$317$	12.0318	+	6.94659i	0.675776	+	0.390159i	−0.122486	+	0.992470i	$0.539087\pi$
$318$	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	0.999875	+	0.0158198i	$0.00503580\pi$
$331$	27.5359	+	15.8979i	1.51351	+	0.873827i	0.513638	+	0.858007i	$0.328298\pi$
$332$	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	0.956845	−	0.290600i	$-0.0938549\pi$
$347$	4.22398	+	7.31616i	0.226755	+	0.392752i	−0.730089	+	0.683352i	$0.760522\pi$
$348$	−20.5166	−	26.8390i	−1.09981	−	1.43872i
$349$	−17.4956			−0.936520			−0.468260	−	0.883591i	$-0.655119\pi$
$349$	−17.4956			−0.936520			−0.468260	+	0.883591i	$0.655119\pi$
$350$		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	$-0.596055\pi$
$353$	7.15990	−	4.13377i	0.381083	−	0.220018i	0.678289	+	0.734795i	$0.262722\pi$
$354$	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	−0.316625	−	0.948551i	$-0.602550\pi$
$359$	12.5650	−	21.7633i	0.663156	−	1.14862i	0.979782	−	0.200070i	$-0.0641169\pi$
$360$	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	$-0.474884\pi$
$367$	18.8041	−	10.8565i	0.981565	−	0.566707i	0.902742	+	0.430182i	$0.141551\pi$
$368$	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	−0.856531	−	0.516096i	$-0.827385\pi$
$373$	0.360898	−	0.625094i	0.0186866	−	0.0323662i	0.875217	+	0.483730i	$0.160718\pi$
$374$	−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	$0.155511\pi$
$379$			18.2745i			0.938699i	−0.883013	+	0.469349i	$0.844489\pi$
$380$	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	$-0.816660\pi$
$383$	1.02465	−	1.77475i	0.0523573	−	0.0906855i	0.891016	+	0.453971i	$0.149993\pi$
$384$	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	−0.234902	−	0.972019i	$-0.575477\pi$
$389$	9.65328	−	5.57332i	0.489441	−	0.282579i	0.724342	+	0.689440i	$0.242143\pi$
$390$	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	$-0.769203\pi$
$397$	3.98719	−	6.90601i	0.200111	−	0.346603i	0.948564	+	0.316585i	$0.102536\pi$
$398$	−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	−0.0424093	−	0.999100i	$-0.513503\pi$
$401$	−18.6004	−	10.7390i	−0.928860	−	0.536278i	−0.886451	+	0.462823i	$0.846837\pi$
$402$	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	0.810334	+	0.585968i	$0.199286\pi$
$409$	18.4568	+	31.9681i	0.912630	+	1.58072i	0.102296	+	0.994754i	$0.467381\pi$
$410$	−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	$-0.243006\pi$
$419$	29.5773			1.44494			0.722472	+	0.691400i	$0.243006\pi$
$420$		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	0.804196	−	0.594364i	$-0.202596\pi$
$431$	−2.33839	−	4.05022i	−0.112636	−	0.195092i	−0.916832	+	0.399272i	$0.869263\pi$
$432$	15.1374	+	14.2429i	0.728297	+	0.685262i
$433$	16.5564			0.795650			0.397825	−	0.917461i	$-0.369765\pi$
$433$	16.5564			0.795650			0.397825	+	0.917461i	$0.369765\pi$
$434$		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	$-0.115617\pi$
$439$	22.9313	+	13.2394i	1.09445	+	0.631881i	0.159692	+	0.987167i	$0.448950\pi$
$440$	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	−0.806187	−	0.591661i	$-0.798472\pi$
$443$	2.30049	−	3.98457i	0.109300	−	0.189313i	0.915487	+	0.402348i	$0.131806\pi$
$444$	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	$-0.868536\pi$
$449$		−	17.0095i		−	0.802728i	0.915919	−	0.401364i	$-0.131464\pi$
$450$	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	−0.627192	−	0.778864i	$-0.715796\pi$
$457$	7.71559	−	13.3638i	0.360920	−	0.625132i	0.988113	+	0.153732i	$0.0491293\pi$
$458$	−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	$-0.789041\pi$
$463$		−	26.4787i		−	1.23057i	0.788304	−	0.615286i	$-0.210959\pi$
$464$	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	$-0.691795\pi$
$467$	9.29557	−	16.1004i	0.430148	−	0.745038i	0.996886	+	0.0788602i	$0.0251281\pi$
$468$	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	0.776629	+	0.629958i	$0.216928\pi$
$479$	20.4388	+	35.4011i	0.933874	+	1.61752i	0.157245	+	0.987560i	$0.449739\pi$
$480$	−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	−0.0165831	−	0.999862i	$-0.505279\pi$
$487$	18.5599	−	10.7156i	0.841032	−	0.485570i	0.857615	+	0.514293i	$0.171945\pi$
$488$	−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	0.317844	−	0.948143i	$-0.397041\pi$
$499$	−7.69218	−	4.44108i	−0.344349	−	0.198810i	−0.662194	+	0.749333i	$0.730374\pi$
$500$	−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	$-0.783757\pi$
$503$	−34.8967			−1.55597			−0.777983	+	0.628286i	$0.783757\pi$
$504$		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	$-0.156718\pi$
$509$	20.5865	+	11.8856i	0.912479	+	0.526820i	0.0312508	+	0.999512i	$0.490051\pi$
$510$	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	$-0.706728\pi$
$521$	−4.96256	+	2.86513i	−0.217414	+	0.125524i	0.387338	+	0.921938i	$0.373394\pi$
$522$	15.2493	+	38.4624i	0.667444	+	1.68345i
$523$	−4.17225	−	2.40885i	−0.182440	−	0.105332i	0.405999	−	0.913874i	$-0.366924\pi$
$523$	−4.17225	−	2.40885i	−0.182440	−	0.105332i	−0.588439	+	0.808542i	$0.700257\pi$
$524$	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	−0.707124	−	0.707089i	$-0.750008\pi$
$541$	6.01942	−	10.4259i	0.258795	−	0.448246i	0.965919	+	0.258843i	$0.0833413\pi$
$542$	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	$0.272298\pi$
$547$			35.3097i			1.50973i	−0.655879	+	0.754866i	$0.727702\pi$
$548$	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	−0.976237	−	0.216706i	$-0.930469\pi$
$557$	−30.1308	+	17.3960i	−1.27668	+	0.737093i	−0.300445	+	0.953799i	$0.597135\pi$
$558$	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	$-0.0793027\pi$
$563$	6.43088	+	11.1386i	0.271029	+	0.469436i	−0.698096	+	0.716004i	$0.745969\pi$
$564$	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	0.187349	−	0.982293i	$-0.440010\pi$
$569$	−13.5887	−	7.84543i	−0.569667	−	0.328897i	−0.757016	+	0.653396i	$0.773344\pi$
$570$	0.853831	−	4.68631i	0.0357630	−	0.196288i
$571$	36.4003	−	21.0157i	1.52331	−	0.879481i	0.523685	−	0.851912i	$-0.324557\pi$
$571$	36.4003	−	21.0157i	1.52331	−	0.879481i	0.999620	−	0.0275690i	$-0.00877659\pi$
$572$	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	0.914612	+	0.404332i	$0.132496\pi$
$577$	19.3960	+	33.5949i	0.807468	+	1.39858i	−0.107145	+	0.994243i	$0.534171\pi$
$578$	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	$-0.546641\pi$
$587$	−7.07471			−0.292004			−0.146002	+	0.989284i	$0.546641\pi$
$588$		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	$-0.210088\pi$
$593$	15.9258	+	9.19477i	0.653994	+	0.377584i	−0.135991	+	0.990710i	$0.543422\pi$
$594$	−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	0.935752	+	0.352658i	$0.114722\pi$
$599$	18.9258	+	32.7804i	0.773287	+	1.33937i	−0.162466	+	0.986714i	$0.551945\pi$
$600$	−13.6683	+	19.6052i	−0.558005	+	0.800381i
$601$	−21.9488			−0.895308			−0.447654	−	0.894207i	$-0.647740\pi$
$601$	−21.9488			−0.895308			−0.447654	+	0.894207i	$0.647740\pi$
$602$		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	$-0.509338\pi$
$607$	−22.4114	−	12.9392i	−0.909651	−	0.525187i	−0.880319	+	0.474382i	$0.842671\pi$
$608$	−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	0.966452	−	0.256849i	$-0.0826843\pi$
$613$	6.45681	+	11.1835i	0.260788	+	0.451698i	−0.705664	+	0.708547i	$0.749351\pi$
$614$	−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	$-0.821149\pi$
$617$		−	26.4677i		−	1.06555i	0.846257	−	0.532775i	$-0.178851\pi$
$618$	5.97010	+	16.6976i	0.240153	+	0.671675i
$619$	29.7384	−	17.1695i	1.19529	−	0.690100i	0.235787	−	0.971805i	$-0.424233\pi$
$619$	29.7384	−	17.1695i	1.19529	−	0.690100i	0.959501	+	0.281705i	$0.0908999\pi$
$620$	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	$-0.813677\pi$
$631$		−	27.7569i		−	1.10499i	0.833517	−	0.552493i	$-0.186323\pi$
$632$	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	−0.376156	−	0.926556i	$-0.622754\pi$
$641$	6.03040	−	3.48165i	0.238186	−	0.137517i	0.614343	+	0.789039i	$0.289421\pi$
$642$	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	0.997971	+	0.0636677i	$0.0202798\pi$
$647$	14.0948	+	24.4129i	0.554123	+	0.959770i	−0.443848	+	0.896102i	$0.646387\pi$
$648$	−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	0.672496	−	0.740101i	$-0.265222\pi$
$653$	9.39867	+	5.42633i	0.367799	+	0.212349i	−0.304698	+	0.952449i	$0.598555\pi$
$654$	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	$-0.183682\pi$
$661$	−1.37371	−	2.37933i	−0.0534311	−	0.0925454i	−0.891504	+	0.453013i	$0.850349\pi$
$662$	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	$-0.201229\pi$
$677$	18.1712	+	10.4911i	0.698376	+	0.403208i	−0.108366	+	0.994111i	$0.534562\pi$
$678$	−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	0.976754	−	0.214363i	$-0.0687675\pi$
$683$	7.91172	+	13.7035i	0.302734	+	0.524350i	−0.674021	+	0.738713i	$0.735434\pi$
$684$	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	$-0.487022\pi$
$691$	−21.1390	−	12.2046i	−0.804167	−	0.464286i	−0.844926	+	0.534883i	$0.820356\pi$
$692$	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	$-0.867061\pi$
$701$		−	21.4779i		−	0.811209i	0.914049	−	0.405605i	$-0.132939\pi$
$702$	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	−0.132283	−	0.991212i	$-0.542231\pi$
$709$	21.0959	−	36.5392i	0.792273	−	1.37226i	0.924556	−	0.381046i	$-0.124436\pi$
$710$	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	$-0.717683\pi$
$719$	9.52940	−	16.5054i	0.355387	−	0.615548i	0.987184	+	0.159586i	$0.0510158\pi$
$720$	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	$-0.988869\pi$
$733$	−12.7090	+	22.0126i	−0.469417	+	0.813054i	0.529972	+	0.848015i	$0.322203\pi$
$734$	−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	−0.823007	−	0.568031i	$-0.807705\pi$
$739$	−20.1868	+	11.6548i	−0.742582	+	0.428730i	0.0804256	+	0.996761i	$0.474372\pi$
$740$	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	0.999671	+	0.0256461i	$0.00816430\pi$
$751$	41.7017	+	24.0765i	1.52172	+	0.878564i	0.522046	+	0.852918i	$0.325169\pi$
$752$	−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	$-0.499753\pi$
$761$	−23.8583	−	13.7746i	−0.864861	−	0.499328i	−0.865637	+	0.500672i	$0.833086\pi$
$762$	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	$-0.466451\pi$
$769$	5.83461			0.210401			0.105201	+	0.994451i	$0.466451\pi$
$770$		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	$-0.339945\pi$
$773$	41.1952	−	23.7841i	1.48169	−	0.855454i	0.999784	+	0.0207689i	$0.00661143\pi$
$774$	−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	−0.507059	+	0.861911i	$0.669267\pi$
$787$	−42.2774	+	24.4089i	−1.50703	+	0.870082i	−0.999967	+	0.00817024i	$0.997399\pi$
$788$	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	−0.0373853	−	0.999301i	$-0.511903\pi$
$809$	23.0201	−	13.2906i	0.809342	−	0.467274i	0.846727	+	0.532027i	$0.178570\pi$
$810$	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	−0.0173172	−	0.999850i	$-0.505513\pi$
$821$	−25.5549	−	14.7541i	−0.891871	−	0.514922i	−0.874554	+	0.484928i	$0.838846\pi$
$822$	−10.5159	−	1.91596i	−0.366784	−	0.0668269i
$823$	−10.4596	+	6.03884i	−0.364598	+	0.210501i	−0.671096	−	0.741371i	$-0.734176\pi$
$823$	−10.4596	+	6.03884i	−0.364598	+	0.210501i	0.306498	+	0.951871i	$0.400843\pi$
$824$	−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	$-0.180514\pi$
$829$	−1.25218	−	2.16884i	−0.0434900	−	0.0753269i	−0.886951	+	0.461863i	$0.847181\pi$
$830$	−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	$-0.490954\pi$
$839$	1.64607			0.0568288			0.0284144	+	0.999596i	$0.490954\pi$
$840$		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	$-0.416594\pi$
$853$	15.1311			0.518077			0.259039	+	0.965867i	$0.416594\pi$
$854$		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	$-0.981534\pi$
$857$	−42.3681	+	24.4612i	−1.44727	+	0.835579i	−0.448947	+	0.893558i	$0.648201\pi$
$858$	5.03782	−	27.6504i	0.171988	−	0.943971i
$859$	13.9058	+	8.02854i	0.474461	+	0.273930i	0.718105	−	0.695935i	$-0.245010\pi$
$859$	13.9058	+	8.02854i	0.474461	+	0.273930i	−0.243644	+	0.969865i	$0.578343\pi$
$860$	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	−0.710871	−	0.703322i	$-0.751699\pi$
$863$	7.45171	−	12.9067i	0.253659	−	0.439350i	0.964530	+	0.263972i	$0.0850325\pi$
$864$	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	−0.948707	−	0.316157i	$-0.897607\pi$
$877$	−5.93923	+	10.2871i	−0.200554	+	0.347369i	0.748153	+	0.663526i	$0.230941\pi$
$878$	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	$0.175411\pi$
$883$			31.1178i			1.04720i	−0.851965	+	0.523599i	$0.824589\pi$
$884$	−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	0.222855	−	0.974852i	$-0.428462\pi$
$887$	28.4624	−	49.2983i	0.955674	−	1.65528i	0.732819	−	0.680424i	$-0.238204\pi$
$888$	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	−0.400421	−	0.916331i	$-0.631136\pi$
$907$	5.81050	−	3.35469i	0.192934	−	0.111391i	0.593356	+	0.804940i	$0.297803\pi$
$908$	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	0.236532	−	0.971624i	$-0.423989\pi$
$919$	−14.7529	−	8.51757i	−0.486652	−	0.280969i	−0.723185	+	0.690655i	$0.757322\pi$
$920$	−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	$-0.207880\pi$
$929$	20.2721	+	11.7041i	0.665105	+	0.383999i	−0.129114	+	0.991630i	$0.541213\pi$
$930$	−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	$-0.208136\pi$
$937$	48.5929			1.58746			0.793730	+	0.608270i	$0.208136\pi$
$938$		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	$-0.590122\pi$
$941$	12.6540	−	7.30579i	0.412509	−	0.238162i	0.691867	+	0.722025i	$0.256788\pi$
$942$	−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	−0.489338	−	0.872094i	$-0.662762\pi$
$947$	15.7125	−	27.2148i	0.510587	−	0.884362i	0.999925	−	0.0122681i	$-0.00390516\pi$
$948$	−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	$0.0728708\pi$
$953$			14.0113i			0.453872i	−0.973910	+	0.226936i	$0.927129\pi$
$954$	−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	$-0.803583\pi$
$967$		−	35.9876i		−	1.15728i	0.815582	−	0.578641i	$-0.196417\pi$
$968$	−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	0.157659	+	0.987494i	$0.449605\pi$
$971$	−24.1922	+	41.9022i	−0.776365	+	1.34470i	−0.934024	+	0.357210i	$0.883728\pi$
$972$	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	−0.920672	−	0.390338i	$-0.872358\pi$
$977$	−32.6000	+	18.8216i	−1.04296	+	0.602156i	−0.122293	+	0.992494i	$0.539025\pi$
$978$	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	$-0.193883\pi$
$983$	−2.67750	−	4.63756i	−0.0853989	−	0.147915i	−0.905561	+	0.424216i	$0.860550\pi$
$984$	−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	−0.994779	−	0.102057i	$-0.967458\pi$
$991$	−44.1913	+	25.5139i	−1.40378	+	0.810475i	−0.409005	+	0.912532i	$0.634124\pi$
$992$	−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	−0.877571	−	0.479446i	$-0.840838\pi$
$997$	−26.9653	−	46.7052i	−0.853998	−	1.47917i	0.0235729	−	0.999722i	$-0.492496\pi$
$998$	−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.g.275.7		24
3.2	odd	2	inner	588.2.n.g.275.6		24
4.3	odd	2	inner	588.2.n.g.275.3		24
7.2	even	3		588.2.e.c.491.2		12
7.3	odd	6		588.2.n.f.263.10		24
7.4	even	3	inner	588.2.n.g.263.10		24
7.5	odd	6		84.2.e.a.71.2	yes	12
7.6	odd	2		588.2.n.f.275.7		24
12.11	even	2	inner	588.2.n.g.275.10		24
21.2	odd	6		588.2.e.c.491.11		12
21.5	even	6		84.2.e.a.71.11	yes	12
21.11	odd	6	inner	588.2.n.g.263.3		24
21.17	even	6		588.2.n.f.263.3		24
21.20	even	2		588.2.n.f.275.6		24
28.3	even	6		588.2.n.f.263.6		24
28.11	odd	6	inner	588.2.n.g.263.6		24
28.19	even	6		84.2.e.a.71.12	yes	12
28.23	odd	6		588.2.e.c.491.12		12
28.27	even	2		588.2.n.f.275.3		24
56.5	odd	6		1344.2.h.h.575.3		12
56.19	even	6		1344.2.h.h.575.10		12
84.11	even	6	inner	588.2.n.g.263.7		24
84.23	even	6		588.2.e.c.491.1		12
84.47	odd	6		84.2.e.a.71.1	✓	12
84.59	odd	6		588.2.n.f.263.7		24
84.83	odd	2		588.2.n.f.275.10		24
168.5	even	6		1344.2.h.h.575.9		12
168.131	odd	6		1344.2.h.h.575.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.1	✓	12	84.47	odd	6
84.2.e.a.71.2	yes	12	7.5	odd	6
84.2.e.a.71.11	yes	12	21.5	even	6
84.2.e.a.71.12	yes	12	28.19	even	6
588.2.e.c.491.1		12	84.23	even	6
588.2.e.c.491.2		12	7.2	even	3
588.2.e.c.491.11		12	21.2	odd	6
588.2.e.c.491.12		12	28.23	odd	6
588.2.n.f.263.3		24	21.17	even	6
588.2.n.f.263.6		24	28.3	even	6
588.2.n.f.263.7		24	84.59	odd	6
588.2.n.f.263.10		24	7.3	odd	6
588.2.n.f.275.3		24	28.27	even	2
588.2.n.f.275.6		24	21.20	even	2
588.2.n.f.275.7		24	7.6	odd	2
588.2.n.f.275.10		24	84.83	odd	2
588.2.n.g.263.3		24	21.11	odd	6	inner
588.2.n.g.263.6		24	28.11	odd	6	inner
588.2.n.g.263.7		24	84.11	even	6	inner
588.2.n.g.263.10		24	7.4	even	3	inner
588.2.n.g.275.3		24	4.3	odd	2	inner
588.2.n.g.275.6		24	3.2	odd	2	inner
588.2.n.g.275.7		24	1.1	even	1	trivial
588.2.n.g.275.10		24	12.11	even	2	inner
1344.2.h.h.575.3		12	56.5	odd	6
1344.2.h.h.575.4		12	168.131	odd	6
1344.2.h.h.575.9		12	168.5	even	6
1344.2.h.h.575.10		12	56.19	even	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)

\(f(q)\)	\(=\)	\(q+(0.300756 - 1.38186i) q^{2} +(-0.814407 + 1.52864i) q^{3} +(-1.81909 - 0.831208i) q^{4} +(0.301907 + 0.174306i) q^{5} +(1.86743 + 1.58515i) q^{6} +(-1.69572 + 2.26374i) q^{8} +(-1.67348 - 2.48987i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{4} + 12 q^{6} + 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^4 + 12 * q^6 + 4 * q^9	\( 24 q + 4 q^{4} + 12 q^{6} + 4 q^{9} + 4 q^{10} - 6 q^{12} - 4 q^{16} + 8 q^{18} - 32 q^{22} + 2 q^{24} + 12 q^{25} - 20 q^{30} - 16 q^{33} - 64 q^{34} - 40 q^{36} + 16 q^{37} + 20 q^{40} + 24 q^{45} - 92 q^{48} - 28 q^{52} + 10 q^{54} + 32 q^{57} + 32 q^{58} - 28 q^{60} - 16 q^{61} + 40 q^{64} - 12 q^{66} + 48 q^{69} + 32 q^{72} + 24 q^{73} + 120 q^{76} + 40 q^{78} - 28 q^{81} + 8 q^{82} + 80 q^{85} + 56 q^{88} + 160 q^{90} - 24 q^{93} - 34 q^{96} + 48 q^{97}+O(q^{100}) \) 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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