LMFDB - Embedded newform 588.2.b.d.391.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(391,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.391"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,4,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.15911316233388032.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 35 x^{8} - 56 x^{7} + 84 x^{6} - 112 x^{5} + 140 x^{4} + \cdots + 64 $ x^12 - 4x^11 + 10x^10 - 20x^9 + 35x^8 - 56x^7 + 84x^6 - 112x^5 + 140x^4 - 160x^3 + 160x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			391.8
Root			$0.639847 + 1.26119i$ of defining polynomial
Character	$\chi$	$=$	588.391
Dual form			588.2.b.d.391.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.639847 + 1.26119i) q^{2} +1.00000 q^{3} +(-1.18119 + 1.61393i) q^{4} +3.10455i q^{5} +(0.639847 + 1.26119i) q^{6} +(-2.79126 - 0.457034i) q^{8} +1.00000 q^{9} +(-3.91542 + 1.98644i) q^{10} +5.34455i q^{11} +(-1.18119 + 1.61393i) q^{12} -3.92787i q^{13} +3.10455i q^{15} +(-1.20957 - 3.81273i) q^{16} -5.68178i q^{17} +(0.639847 + 1.26119i) q^{18} +0.170813 q^{19} +(-5.01054 - 3.66707i) q^{20} +(-6.74049 + 3.41969i) q^{22} +6.13153i q^{23} +(-2.79126 - 0.457034i) q^{24} -4.63824 q^{25} +(4.95378 - 2.51324i) q^{26} +1.00000 q^{27} -1.96817 q^{29} +(-3.91542 + 1.98644i) q^{30} -1.53115 q^{31} +(4.03463 - 3.96506i) q^{32} +5.34455i q^{33} +(7.16580 - 3.63547i) q^{34} +(-1.18119 + 1.61393i) q^{36} +8.93993 q^{37} +(0.109294 + 0.215427i) q^{38} -3.92787i q^{39} +(1.41889 - 8.66560i) q^{40} +5.84308i q^{41} +2.38285i q^{43} +(-8.62576 - 6.31294i) q^{44} +3.10455i q^{45} +(-7.73301 + 3.92324i) q^{46} +2.29477 q^{47} +(-1.20957 - 3.81273i) q^{48} +(-2.96776 - 5.84969i) q^{50} -5.68178i q^{51} +(6.33933 + 4.63957i) q^{52} -1.19905 q^{53} +(0.639847 + 1.26119i) q^{54} -16.5924 q^{55} +0.170813 q^{57} +(-1.25933 - 2.48223i) q^{58} +10.9942 q^{59} +(-5.01054 - 3.66707i) q^{60} +6.58977i q^{61} +(-0.979705 - 1.93107i) q^{62} +(7.58224 + 2.55140i) q^{64} +12.1943 q^{65} +(-6.74049 + 3.41969i) q^{66} -9.64794i q^{67} +(9.17002 + 6.71127i) q^{68} +6.13153i q^{69} +2.04649i q^{71} +(-2.79126 - 0.457034i) q^{72} -10.2724i q^{73} +(5.72019 + 11.2749i) q^{74} -4.63824 q^{75} +(-0.201763 + 0.275681i) q^{76} +(4.95378 - 2.51324i) q^{78} +14.3947i q^{79} +(11.8368 - 3.75518i) q^{80} +1.00000 q^{81} +(-7.36922 + 3.73867i) q^{82} +10.9783 q^{83} +17.6394 q^{85} +(-3.00522 + 1.52466i) q^{86} -1.96817 q^{87} +(2.44264 - 14.9180i) q^{88} -5.81871i q^{89} +(-3.91542 + 1.98644i) q^{90} +(-9.89588 - 7.24251i) q^{92} -1.53115 q^{93} +(1.46830 + 2.89414i) q^{94} +0.530298i q^{95} +(4.03463 - 3.96506i) q^{96} -2.32666i q^{97} +5.34455i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 12 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{8} + 12 q^{9} - 4 q^{12} - 4 q^{16} + 4 q^{18} - 24 q^{20} + 4 q^{24} - 12 q^{25} + 24 q^{26} + 12 q^{27} + 32 q^{29} + 16 q^{31} + 4 q^{32} + 32 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) $ 12 * q + 4 * q^2 + 12 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^8 + 12 * q^9 - 4 * q^12 - 4 * q^16 + 4 * q^18 - 24 * q^20 + 4 * q^24 - 12 * q^25 + 24 * q^26 + 12 * q^27 + 32 * q^29 + 16 * q^31 + 4 * q^32 + 32 * q^34 - 4 * q^36 + 32 * q^37 - 24 * q^38 - 32 * q^40 - 24 * q^44 + 24 * q^46 - 4 * q^48 - 28 * q^50 + 32 * q^52 - 32 * q^53 + 4 * q^54 + 16 * q^55 + 16 * q^58 - 16 * q^59 - 24 * q^60 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 4 * q^72 - 32 * q^74 - 12 * q^75 - 32 * q^76 + 24 * q^78 - 16 * q^80 + 12 * q^81 + 32 * q^82 - 16 * q^83 + 16 * q^85 - 24 * q^86 + 32 * q^87 + 24 * q^88 + 16 * q^93 + 4 * q^96

Character values

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

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.639847	+	1.26119i	0.452440	+	0.891795i
$2$	0.639847	+	1.26119i	0.452440	+	0.891795i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.18119	+	1.61393i	−0.590596	+	0.806967i
$5$			3.10455i			1.38840i	0.719783	+	0.694199i	$0.244241\pi$
$5$			3.10455i			1.38840i	−0.719783	+	0.694199i	$0.755759\pi$
$6$	0.639847	+	1.26119i	0.261216	+	0.514878i
$7$		0			0
$7$		0			0
$8$	−2.79126	−	0.457034i	−0.986859	−	0.161586i
$9$	1.00000			0.333333
$10$	−3.91542	+	1.98644i	−1.23817	+	0.628167i
$11$			5.34455i			1.61144i	0.592295	+	0.805721i	$0.298222\pi$
$11$			5.34455i			1.61144i	−0.592295	+	0.805721i	$0.701778\pi$
$12$	−1.18119	+	1.61393i	−0.340981	+	0.465903i
$13$		−	3.92787i		−	1.08939i	−0.838633	−	0.544697i	$-0.816644\pi$
$13$		−	3.92787i		−	1.08939i	0.838633	−	0.544697i	$-0.183356\pi$
$14$		0			0
$15$			3.10455i			0.801592i
$16$	−1.20957	−	3.81273i	−0.302393	−	0.953183i
$17$		−	5.68178i		−	1.37803i	−0.724745	−	0.689017i	$-0.758042\pi$
$17$		−	5.68178i		−	1.37803i	0.724745	−	0.689017i	$-0.241958\pi$
$18$	0.639847	+	1.26119i	0.150813	+	0.297265i
$19$	0.170813			0.0391872			0.0195936	−	0.999808i	$-0.493763\pi$
$19$	0.170813			0.0391872			0.0195936	+	0.999808i	$0.493763\pi$
$20$	−5.01054	−	3.66707i	−1.12039	−	0.819982i
$21$		0			0
$22$	−6.74049	+	3.41969i	−1.43708	+	0.729081i
$23$			6.13153i			1.27851i	0.768994	+	0.639256i	$0.220758\pi$
$23$			6.13153i			1.27851i	−0.768994	+	0.639256i	$0.779242\pi$
$24$	−2.79126	−	0.457034i	−0.569763	−	0.0932917i
$25$	−4.63824			−0.927647
$26$	4.95378	−	2.51324i	0.971517	−	0.492886i
$27$	1.00000			0.192450
$28$		0			0
$29$	−1.96817			−0.365480			−0.182740	−	0.983161i	$-0.558497\pi$
$29$	−1.96817			−0.365480			−0.182740	+	0.983161i	$0.558497\pi$
$30$	−3.91542	+	1.98644i	−0.714855	+	0.362672i
$31$	−1.53115			−0.275003			−0.137502	−	0.990502i	$-0.543907\pi$
$31$	−1.53115			−0.275003			−0.137502	+	0.990502i	$0.543907\pi$
$32$	4.03463	−	3.96506i	0.713229	−	0.700931i
$33$			5.34455i			0.930367i
$34$	7.16580	−	3.63547i	1.22892	−	0.623478i
$35$		0			0
$36$	−1.18119	+	1.61393i	−0.196865	+	0.268989i
$37$	8.93993			1.46972			0.734858	−	0.678221i	$-0.237249\pi$
$37$	8.93993			1.46972			0.734858	+	0.678221i	$0.237249\pi$
$38$	0.109294	+	0.215427i	0.0177299	+	0.0349469i
$39$		−	3.92787i		−	0.628962i
$40$	1.41889	−	8.66560i	0.224345	−	1.37015i
$41$			5.84308i			0.912535i	0.889843	+	0.456268i	$0.150814\pi$
$41$			5.84308i			0.912535i	−0.889843	+	0.456268i	$0.849186\pi$
$42$		0			0
$43$			2.38285i			0.363381i	0.983356	+	0.181691i	$0.0581569\pi$
$43$			2.38285i			0.363381i	−0.983356	+	0.181691i	$0.941843\pi$
$44$	−8.62576	−	6.31294i	−1.30038	−	0.951712i
$45$			3.10455i			0.462799i
$46$	−7.73301	+	3.92324i	−1.14017	+	0.578450i
$47$	2.29477			0.334727			0.167364	−	0.985895i	$-0.446475\pi$
$47$	2.29477			0.334727			0.167364	+	0.985895i	$0.446475\pi$
$48$	−1.20957	−	3.81273i	−0.174587	−	0.550321i
$49$		0			0
$50$	−2.96776	−	5.84969i	−0.419705	−	0.827271i
$51$		−	5.68178i		−	0.795608i
$52$	6.33933	+	4.63957i	0.879106	+	0.643392i
$53$	−1.19905			−0.164702			−0.0823508	−	0.996603i	$-0.526243\pi$
$53$	−1.19905			−0.164702			−0.0823508	+	0.996603i	$0.526243\pi$
$54$	0.639847	+	1.26119i	0.0870721	+	0.171626i
$55$	−16.5924			−2.23732
$56$		0			0
$57$	0.170813			0.0226247
$58$	−1.25933	−	2.48223i	−0.165358	−	0.325933i
$59$	10.9942			1.43133			0.715663	−	0.698446i	$-0.246125\pi$
$59$	10.9942			1.43133			0.715663	+	0.698446i	$0.246125\pi$
$60$	−5.01054	−	3.66707i	−0.646858	−	0.473417i
$61$			6.58977i			0.843734i	0.906658	+	0.421867i	$0.138625\pi$
$61$			6.58977i			0.843734i	−0.906658	+	0.421867i	$0.861375\pi$
$62$	−0.979705	−	1.93107i	−0.124423	−	0.245247i
$63$		0			0
$64$	7.58224	+	2.55140i	0.947780	+	0.318925i
$65$	12.1943			1.51251
$66$	−6.74049	+	3.41969i	−0.829696	+	0.420935i
$67$		−	9.64794i		−	1.17868i	−0.807884	−	0.589342i	$-0.799387\pi$
$67$		−	9.64794i		−	1.17868i	0.807884	−	0.589342i	$-0.200613\pi$
$68$	9.17002	+	6.71127i	1.11203	+	0.813861i
$69$			6.13153i			0.738149i
$70$		0			0
$71$			2.04649i			0.242873i	0.992599	+	0.121437i	$0.0387501\pi$
$71$			2.04649i			0.242873i	−0.992599	+	0.121437i	$0.961250\pi$
$72$	−2.79126	−	0.457034i	−0.328953	−	0.0538620i
$73$		−	10.2724i		−	1.20229i	−0.799138	−	0.601147i	$-0.794711\pi$
$73$		−	10.2724i		−	1.20229i	0.799138	−	0.601147i	$-0.205289\pi$
$74$	5.72019	+	11.2749i	0.664959	+	1.31069i
$75$	−4.63824			−0.535577
$76$	−0.201763	+	0.275681i	−0.0231438	+	0.0316228i
$77$		0			0
$78$	4.95378	−	2.51324i	0.560905	−	0.284568i
$79$			14.3947i			1.61953i	0.586757	+	0.809763i	$0.300404\pi$
$79$			14.3947i			1.61953i	−0.586757	+	0.809763i	$0.699596\pi$
$80$	11.8368	−	3.75518i	1.32340	−	0.419842i
$81$	1.00000			0.111111
$82$	−7.36922	+	3.73867i	−0.813794	+	0.412867i
$83$	10.9783			1.20503			0.602515	−	0.798108i	$-0.294165\pi$
$83$	10.9783			1.20503			0.602515	+	0.798108i	$0.294165\pi$
$84$		0			0
$85$	17.6394			1.91326
$86$	−3.00522	+	1.52466i	−0.324061	+	0.164408i
$87$	−1.96817			−0.211010
$88$	2.44264	−	14.9180i	0.260386	−	1.59027i
$89$		−	5.81871i		−	0.616782i	−0.951260	−	0.308391i	$-0.900209\pi$
$89$		−	5.81871i		−	0.616782i	0.951260	−	0.308391i	$-0.0997905\pi$
$90$	−3.91542	+	1.98644i	−0.412722	+	0.209389i
$91$		0			0
$92$	−9.89588	−	7.24251i	−1.03172	−	0.755084i
$93$	−1.53115			−0.158773
$94$	1.46830	+	2.89414i	0.151444	+	0.298508i
$95$			0.530298i			0.0544074i
$96$	4.03463	−	3.96506i	0.411783	−	0.404683i
$97$		−	2.32666i		−	0.236237i	−0.993000	−	0.118118i	$-0.962314\pi$
$97$		−	2.32666i		−	0.236237i	0.993000	−	0.118118i	$-0.0376862\pi$
$98$		0			0
$99$			5.34455i			0.537148i
$100$	5.47865	−	7.48581i	0.547865	−	0.748581i
$101$		−	7.44428i		−	0.740734i	−0.928886	−	0.370367i	$-0.879232\pi$
$101$		−	7.44428i		−	0.740734i	0.928886	−	0.370367i	$-0.120768\pi$
$102$	7.16580	−	3.63547i	0.709520	−	0.359965i
$103$	−16.2959			−1.60568			−0.802842	−	0.596192i	$-0.796680\pi$
$103$	−16.2959			−1.60568			−0.802842	+	0.596192i	$0.796680\pi$
$104$	−1.79517	+	10.9637i	−0.176031	+	1.07508i
$105$		0			0
$106$	−0.767206	−	1.51222i	−0.0745176	−	0.146880i
$107$		−	16.7392i		−	1.61824i	−0.587645	−	0.809119i	$-0.699945\pi$
$107$		−	16.7392i		−	1.61824i	0.587645	−	0.809119i	$-0.300055\pi$
$108$	−1.18119	+	1.61393i	−0.113660	+	0.155301i
$109$	7.72117			0.739554			0.369777	−	0.929121i	$-0.379434\pi$
$109$	7.72117			0.739554			0.369777	+	0.929121i	$0.379434\pi$
$110$	−10.6166	−	20.9262i	−1.01225	−	1.99523i
$111$	8.93993			0.848541
$112$		0			0
$113$	−0.715845			−0.0673410			−0.0336705	−	0.999433i	$-0.510720\pi$
$113$	−0.715845			−0.0673410			−0.0336705	+	0.999433i	$0.510720\pi$
$114$	0.109294	+	0.215427i	0.0102363	+	0.0201766i
$115$	−19.0356			−1.77508
$116$	2.32478	−	3.17649i	0.215851	−	0.294930i
$117$		−	3.92787i		−	0.363132i
$118$	7.03462	+	13.8658i	0.647589	+	1.27645i
$119$		0			0
$120$	1.41889	−	8.66560i	0.129526	−	0.791058i
$121$	−17.5642			−1.59675
$122$	−8.31095	+	4.21645i	−0.752438	+	0.381739i
$123$			5.84308i			0.526852i
$124$	1.80859	−	2.47118i	0.162416	−	0.221919i
$125$			1.12312i			0.100455i
$126$		0			0
$127$		−	15.4079i		−	1.36723i	−0.729844	−	0.683614i	$-0.760407\pi$
$127$		−	15.4079i		−	1.36723i	0.729844	−	0.683614i	$-0.239593\pi$
$128$	1.63368	+	11.1951i	0.144398	+	0.989520i
$129$			2.38285i			0.209798i
$130$	7.80247	+	15.3793i	0.684322	+	1.34885i
$131$	2.25918			0.197385			0.0986927	−	0.995118i	$-0.468534\pi$
$131$	2.25918			0.197385			0.0986927	+	0.995118i	$0.468534\pi$
$132$	−8.62576	−	6.31294i	−0.750776	−	0.549471i
$133$		0			0
$134$	12.1679	−	6.17321i	1.05114	−	0.533284i
$135$			3.10455i			0.267197i
$136$	−2.59677	+	15.8593i	−0.222671	+	1.35993i
$137$	20.0731			1.71496			0.857479	−	0.514519i	$-0.172030\pi$
$137$	20.0731			1.71496			0.857479	+	0.514519i	$0.172030\pi$
$138$	−7.73301	+	3.92324i	−0.658277	+	0.333968i
$139$	7.98360			0.677160			0.338580	−	0.940938i	$-0.390053\pi$
$139$	7.98360			0.677160			0.338580	+	0.940938i	$0.390053\pi$
$140$		0			0
$141$	2.29477			0.193255
$142$	−2.58100	+	1.30944i	−0.216593	+	0.109886i
$143$	20.9927			1.75550
$144$	−1.20957	−	3.81273i	−0.100798	−	0.317728i
$145$		−	6.11028i		−	0.507431i
$146$	12.9554	−	6.57277i	1.07220	−	0.543966i
$147$		0			0
$148$	−10.5598	+	14.4285i	−0.868008	+	1.18601i
$149$	−5.30170			−0.434332			−0.217166	−	0.976135i	$-0.569681\pi$
$149$	−5.30170			−0.434332			−0.217166	+	0.976135i	$0.569681\pi$
$150$	−2.96776	−	5.84969i	−0.242317	−	0.477625i
$151$			1.52658i			0.124231i	0.998069	+	0.0621155i	$0.0197847\pi$
$151$			1.52658i			0.124231i	−0.998069	+	0.0621155i	$0.980215\pi$
$152$	−0.476783	−	0.0780674i	−0.0386722	−	0.00633210i
$153$		−	5.68178i		−	0.459345i
$154$		0			0
$155$		−	4.75355i		−	0.381814i
$156$	6.33933	+	4.63957i	0.507552	+	0.371463i
$157$			12.4358i			0.992487i	0.868183	+	0.496243i	$0.165288\pi$
$157$			12.4358i			0.992487i	−0.868183	+	0.496243i	$0.834712\pi$
$158$	−18.1544	+	9.21038i	−1.44428	+	0.732738i
$159$	−1.19905			−0.0950905
$160$	12.3097	+	12.5257i	0.973170	+	0.990246i
$161$		0			0
$162$	0.639847	+	1.26119i	0.0502711	+	0.0990883i
$163$			6.22348i			0.487460i	0.969843	+	0.243730i	$0.0783711\pi$
$163$			6.22348i			0.487460i	−0.969843	+	0.243730i	$0.921629\pi$
$164$	−9.43034	−	6.90179i	−0.736386	−	0.538939i
$165$	−16.5924			−1.29172
$166$	7.02446	+	13.8458i	0.545204	+	1.07464i
$167$	−4.14549			−0.320788			−0.160394	−	0.987053i	$-0.551276\pi$
$167$	−4.14549			−0.320788			−0.160394	+	0.987053i	$0.551276\pi$
$168$		0			0
$169$	−2.42816			−0.186781
$170$	11.2865	+	22.2466i	0.865635	+	1.70623i
$171$	0.170813			0.0130624
$172$	−3.84576	−	2.81460i	−0.293237	−	0.214611i
$173$		−	5.54634i		−	0.421681i	−0.977521	−	0.210840i	$-0.932380\pi$
$173$		−	5.54634i		−	0.421681i	0.977521	−	0.210840i	$-0.0676200\pi$
$174$	−1.25933	−	2.48223i	−0.0954693	−	0.188177i
$175$		0			0
$176$	20.3773	−	6.46462i	1.53600	−	0.487289i
$177$	10.9942			0.826376
$178$	7.33849	−	3.72308i	0.550043	−	0.279057i
$179$		−	1.27166i		−	0.0950483i	−0.998870	−	0.0475242i	$-0.984867\pi$
$179$		−	1.27166i		−	0.0950483i	0.998870	−	0.0475242i	$-0.0151331\pi$
$180$	−5.01054	−	3.66707i	−0.373464	−	0.273327i
$181$			0.386679i			0.0287416i	0.999897	+	0.0143708i	$0.00457452\pi$
$181$			0.386679i			0.0287416i	−0.999897	+	0.0143708i	$0.995425\pi$
$182$		0			0
$183$			6.58977i			0.487130i
$184$	2.80232	−	17.1147i	0.206589	−	1.26171i
$185$			27.7545i			2.04055i
$186$	−0.979705	−	1.93107i	−0.0718354	−	0.141593i
$187$	30.3666			2.22062
$188$	−2.71057	+	3.70362i	−0.197689	+	0.270114i
$189$		0			0
$190$	−0.668805	+	0.339309i	−0.0485202	+	0.0246161i
$191$			6.59547i			0.477231i	0.971114	+	0.238616i	$0.0766936\pi$
$191$			6.59547i			0.477231i	−0.971114	+	0.238616i	$0.923306\pi$
$192$	7.58224	+	2.55140i	0.547201	+	0.184131i
$193$	1.95706			0.140872			0.0704362	−	0.997516i	$-0.477561\pi$
$193$	1.95706			0.140872			0.0704362	+	0.997516i	$0.477561\pi$
$194$	2.93436	−	1.48871i	0.210675	−	0.106883i
$195$	12.1943			0.873250
$196$		0			0
$197$	−0.362935			−0.0258580			−0.0129290	−	0.999916i	$-0.504116\pi$
$197$	−0.362935			−0.0258580			−0.0129290	+	0.999916i	$0.504116\pi$
$198$	−6.74049	+	3.41969i	−0.479025	+	0.243027i
$199$	−9.86333			−0.699193			−0.349597	−	0.936900i	$-0.613681\pi$
$199$	−9.86333			−0.699193			−0.349597	+	0.936900i	$0.613681\pi$
$200$	12.9465	+	2.11983i	0.915457	+	0.149895i
$201$		−	9.64794i		−	0.680513i
$202$	9.38864	−	4.76320i	0.660583	−	0.335138i
$203$		0			0
$204$	9.17002	+	6.71127i	0.642030	+	0.469883i
$205$	−18.1401			−1.26696
$206$	−10.4269	−	20.5522i	−0.726476	−	1.43194i
$207$			6.13153i			0.426171i
$208$	−14.9759	+	4.75104i	−1.03839	+	0.329425i
$209$			0.912919i			0.0631479i
$210$		0			0
$211$		−	25.7279i		−	1.77118i	−0.464469	−	0.885589i	$-0.653755\pi$
$211$		−	25.7279i		−	1.77118i	0.464469	−	0.885589i	$-0.346245\pi$
$212$	1.41630	−	1.93518i	0.0972721	−	0.132909i
$213$			2.04649i			0.140223i
$214$	21.1113	−	10.7105i	1.44314	−	0.732156i
$215$	−7.39767			−0.504517
$216$	−2.79126	−	0.457034i	−0.189921	−	0.0310972i
$217$		0			0
$218$	4.94037	+	9.73785i	0.334604	+	0.659530i
$219$		−	10.2724i		−	0.694145i
$220$	19.5988	−	26.7791i	1.32135	−	1.80545i
$221$	−22.3173			−1.50122
$222$	5.72019	+	11.2749i	0.383914	+	0.756724i
$223$	−16.2449			−1.08784			−0.543919	−	0.839138i	$-0.683060\pi$
$223$	−16.2449			−1.08784			−0.543919	+	0.839138i	$0.683060\pi$
$224$		0			0
$225$	−4.63824			−0.309216
$226$	−0.458031	−	0.902815i	−0.0304678	−	0.0600544i
$227$	−20.4484			−1.35721			−0.678603	−	0.734506i	$-0.737414\pi$
$227$	−20.4484			−1.35721			−0.678603	+	0.734506i	$0.737414\pi$
$228$	−0.201763	+	0.275681i	−0.0133621	+	0.0182574i
$229$			3.38952i			0.223986i	0.993709	+	0.111993i	$0.0357234\pi$
$229$			3.38952i			0.223986i	−0.993709	+	0.111993i	$0.964277\pi$
$230$	−12.1799	−	24.0075i	−0.803118	−	1.58301i
$231$		0			0
$232$	5.49366	+	0.899520i	0.360677	+	0.0590564i
$233$	1.90437			0.124759			0.0623796	−	0.998052i	$-0.480131\pi$
$233$	1.90437			0.124759			0.0623796	+	0.998052i	$0.480131\pi$
$234$	4.95378	−	2.51324i	0.323839	−	0.164295i
$235$			7.12425i			0.464735i
$236$	−12.9863	+	17.7440i	−0.845335	+	1.15503i
$237$			14.3947i			0.935034i
$238$		0			0
$239$			7.77419i			0.502871i	0.967874	+	0.251435i	$0.0809026\pi$
$239$			7.77419i			0.502871i	−0.967874	+	0.251435i	$0.919097\pi$
$240$	11.8368	−	3.75518i	0.764064	−	0.242396i
$241$		−	12.1107i		−	0.780119i	−0.920790	−	0.390060i	$-0.872454\pi$
$241$		−	12.1107i		−	0.780119i	0.920790	−	0.390060i	$-0.127546\pi$
$242$	−11.2384	−	22.1518i	−0.722433	−	1.42397i
$243$	1.00000			0.0641500
$244$	−10.6355	−	7.78379i	−0.680866	−	0.498306i
$245$		0			0
$246$	−7.36922	+	3.73867i	−0.469844	+	0.238369i
$247$		−	0.670931i		−	0.0426903i
$248$	4.27385	+	0.699790i	0.271390	+	0.0444367i
$249$	10.9783			0.695724
$250$	−1.41646	+	0.718623i	−0.0895849	+	0.0454497i
$251$	−7.89409			−0.498271			−0.249135	−	0.968469i	$-0.580146\pi$
$251$	−7.89409			−0.498271			−0.249135	+	0.968469i	$0.580146\pi$
$252$		0			0
$253$	−32.7703			−2.06025
$254$	19.4322	−	9.85868i	1.21929	−	0.618589i
$255$	17.6394			1.10462
$256$	−13.0739	+	9.22355i	−0.817117	+	0.576472i
$257$		−	3.06316i		−	0.191074i	−0.995426	−	0.0955372i	$-0.969543\pi$
$257$		−	3.06316i		−	0.191074i	0.995426	−	0.0955372i	$-0.0304569\pi$
$258$	−3.00522	+	1.52466i	−0.187097	+	0.0949211i
$259$		0			0
$260$	−14.4038	+	19.6808i	−0.893284	+	1.22055i
$261$	−1.96817			−0.121827
$262$	1.44553	+	2.84925i	0.0893051	+	0.176027i
$263$		−	10.6284i		−	0.655375i	−0.944786	−	0.327687i	$-0.893731\pi$
$263$		−	10.6284i		−	0.655375i	0.944786	−	0.327687i	$-0.106269\pi$
$264$	2.44264	−	14.9180i	0.150334	−	0.918141i
$265$		−	3.72250i		−	0.228671i
$266$		0			0
$267$		−	5.81871i		−	0.356099i
$268$	15.5712	+	11.3961i	0.951159	+	0.696126i
$269$			2.51512i			0.153350i	0.997056	+	0.0766748i	$0.0244303\pi$
$269$			2.51512i			0.153350i	−0.997056	+	0.0766748i	$0.975570\pi$
$270$	−3.91542	+	1.98644i	−0.238285	+	0.120891i
$271$	−0.916212			−0.0556559			−0.0278279	−	0.999613i	$-0.508859\pi$
$271$	−0.916212			−0.0556559			−0.0278279	+	0.999613i	$0.508859\pi$
$272$	−21.6631	+	6.87252i	−1.31352	+	0.416708i
$273$		0			0
$274$	12.8437	+	25.3159i	0.775916	+	1.52939i
$275$		−	24.7893i		−	1.49485i
$276$	−9.89588	−	7.24251i	−0.595662	−	0.435948i
$277$	11.7658			0.706941			0.353470	−	0.935446i	$-0.385002\pi$
$277$	11.7658			0.706941			0.353470	+	0.935446i	$0.385002\pi$
$278$	5.10828	+	10.0688i	0.306374	+	0.603888i
$279$	−1.53115			−0.0916678
$280$		0			0
$281$	−29.8347			−1.77979			−0.889895	−	0.456165i	$-0.849223\pi$
$281$	−29.8347			−1.77979			−0.889895	+	0.456165i	$0.849223\pi$
$282$	1.46830	+	2.89414i	0.0874363	+	0.172344i
$283$	4.82984			0.287104			0.143552	−	0.989643i	$-0.454148\pi$
$283$	4.82984			0.287104			0.143552	+	0.989643i	$0.454148\pi$
$284$	−3.30289	−	2.41729i	−0.195991	−	0.143440i
$285$			0.530298i			0.0314121i
$286$	13.4321	+	26.4757i	0.794258	+	1.56554i
$287$		0			0
$288$	4.03463	−	3.96506i	0.237743	−	0.233644i
$289$	−15.2826			−0.898979
$290$	7.70621	−	3.90964i	0.452524	−	0.229582i
$291$		−	2.32666i		−	0.136391i
$292$	16.5790	+	12.1337i	0.970213	+	0.710070i
$293$		−	22.4276i		−	1.31023i	−0.755528	−	0.655116i	$-0.772620\pi$
$293$		−	22.4276i		−	1.31023i	0.755528	−	0.655116i	$-0.227380\pi$
$294$		0			0
$295$			34.1321i			1.98725i
$296$	−24.9537	−	4.08585i	−1.45040	−	0.237485i
$297$			5.34455i			0.310122i
$298$	−3.39228	−	6.68644i	−0.196509	−	0.387335i
$299$	24.0838			1.39280
$300$	5.47865	−	7.48581i	0.316310	−	0.432193i
$301$		0			0
$302$	−1.92530	+	0.976774i	−0.110788	+	0.0562071i
$303$		−	7.44428i		−	0.427663i
$304$	−0.206611	−	0.651265i	−0.0118499	−	0.0373526i
$305$	−20.4583			−1.17144
$306$	7.16580	−	3.63547i	0.409641	−	0.207826i
$307$	−31.3123			−1.78709			−0.893543	−	0.448978i	$-0.851788\pi$
$307$	−31.3123			−1.78709			−0.893543	+	0.448978i	$0.851788\pi$
$308$		0			0
$309$	−16.2959			−0.927042
$310$	5.99512	−	3.04154i	0.340500	−	0.172748i
$311$	−15.4221			−0.874507			−0.437253	−	0.899338i	$-0.644049\pi$
$311$	−15.4221			−0.874507			−0.437253	+	0.899338i	$0.644049\pi$
$312$	−1.79517	+	10.9637i	−0.101631	+	0.620697i
$313$			6.09799i			0.344679i	0.985038	+	0.172339i	$0.0551326\pi$
$313$			6.09799i			0.344679i	−0.985038	+	0.172339i	$0.944867\pi$
$314$	−15.6839	+	7.95703i	−0.885095	+	0.449041i
$315$		0			0
$316$	−23.2320	−	17.0029i	−1.30690	−	0.956485i
$317$	−29.7110			−1.66874			−0.834369	−	0.551206i	$-0.814168\pi$
$317$	−29.7110			−1.66874			−0.834369	+	0.551206i	$0.814168\pi$
$318$	−0.767206	−	1.51222i	−0.0430228	−	0.0848013i
$319$		−	10.5190i		−	0.588949i
$320$	−7.92095	+	23.5394i	−0.442794	+	1.31590i
$321$		−	16.7392i		−	0.934290i
$322$		0			0
$323$		−	0.970522i		−	0.0540013i
$324$	−1.18119	+	1.61393i	−0.0656218	+	0.0896631i
$325$			18.2184i			1.01057i
$326$	−7.84898	+	3.98207i	−0.434715	+	0.220547i
$327$	7.72117			0.426982
$328$	2.67048	−	16.3095i	0.147453	−	0.900543i
$329$		0			0
$330$	−10.6166	−	20.9262i	−0.584425	−	1.15195i
$331$		−	20.1722i		−	1.10877i	−0.832262	−	0.554383i	$-0.812954\pi$
$331$		−	20.1722i		−	1.10877i	0.832262	−	0.554383i	$-0.187046\pi$
$332$	−12.9675	+	17.7183i	−0.711686	+	0.972420i
$333$	8.93993			0.489905
$334$	−2.65248	−	5.22824i	−0.145137	−	0.286077i
$335$	29.9525			1.63648
$336$		0			0
$337$	14.0021			0.762746			0.381373	−	0.924421i	$-0.375451\pi$
$337$	14.0021			0.762746			0.381373	+	0.924421i	$0.375451\pi$
$338$	−1.55365	−	3.06236i	−0.0845074	−	0.166571i
$339$	−0.715845			−0.0388794
$340$	−20.8355	+	28.4688i	−1.12996	+	1.54394i
$341$		−	8.18333i		−	0.443152i
$342$	0.109294	+	0.215427i	0.00590995	+	0.0116490i
$343$		0			0
$344$	1.08904	−	6.65115i	0.0587173	−	0.358606i
$345$	−19.0356			−1.02484
$346$	6.99498	−	3.54881i	0.376053	−	0.190785i
$347$			11.9859i			0.643435i	0.946836	+	0.321718i	$0.104260\pi$
$347$			11.9859i			0.643435i	−0.946836	+	0.321718i	$0.895740\pi$
$348$	2.32478	−	3.17649i	0.124621	−	0.170278i
$349$		−	28.8227i		−	1.54284i	−0.636324	−	0.771422i	$-0.719546\pi$
$349$		−	28.8227i		−	1.54284i	0.636324	−	0.771422i	$-0.280454\pi$
$350$		0			0
$351$		−	3.92787i		−	0.209654i
$352$	21.1915	+	21.5633i	1.12951	+	1.14933i
$353$			0.114784i			0.00610936i	0.999995	+	0.00305468i	$0.000972336\pi$
$353$			0.114784i			0.00610936i	−0.999995	+	0.00305468i	$0.999028\pi$
$354$	7.03462	+	13.8658i	0.373886	+	0.736958i
$355$	−6.35342			−0.337204
$356$	9.39102	+	6.87301i	0.497723	+	0.364269i
$357$		0			0
$358$	1.60380	−	0.813668i	0.0847636	−	0.0430037i
$359$			1.97719i			0.104352i	0.998638	+	0.0521760i	$0.0166157\pi$
$359$			1.97719i			0.104352i	−0.998638	+	0.0521760i	$0.983384\pi$
$360$	1.41889	−	8.66560i	0.0747818	−	0.456717i
$361$	−18.9708			−0.998464
$362$	−0.487674	+	0.247415i	−0.0256316	+	0.0130038i
$363$	−17.5642			−0.921883
$364$		0			0
$365$	31.8912			1.66926
$366$	−8.31095	+	4.21645i	−0.434420	+	0.220397i
$367$	26.7789			1.39785			0.698925	−	0.715195i	$-0.253662\pi$
$367$	26.7789			1.39785			0.698925	+	0.715195i	$0.253662\pi$
$368$	23.3779	−	7.41652i	1.21866	−	0.386613i
$369$			5.84308i			0.304178i
$370$	−35.0036	+	17.7586i	−1.81975	+	0.923227i
$371$		0			0
$372$	1.80859	−	2.47118i	0.0937709	−	0.128125i
$373$	23.0396			1.19295			0.596474	−	0.802633i	$-0.296568\pi$
$373$	23.0396			1.19295			0.596474	+	0.802633i	$0.296568\pi$
$374$	19.4300	+	38.2980i	1.00470	+	1.98034i
$375$			1.12312i			0.0579975i
$376$	−6.40531	−	1.04879i	−0.330329	−	0.0540872i
$377$			7.73071i			0.398152i
$378$		0			0
$379$		−	22.3697i		−	1.14906i	−0.818485	−	0.574528i	$-0.805186\pi$
$379$		−	22.3697i		−	1.14906i	0.818485	−	0.574528i	$-0.194814\pi$
$380$	−0.855866	−	0.626383i	−0.0439050	−	0.0321328i
$381$		−	15.4079i		−	0.789370i
$382$	−8.31813	+	4.22009i	−0.425592	+	0.215919i
$383$	−28.7083			−1.46693			−0.733463	−	0.679730i	$-0.762097\pi$
$383$	−28.7083			−1.46693			−0.733463	+	0.679730i	$0.762097\pi$
$384$	1.63368	+	11.1951i	0.0833683	+	0.571299i
$385$		0			0
$386$	1.25222	+	2.46822i	0.0637363	+	0.125629i
$387$			2.38285i			0.121127i
$388$	3.75508	+	2.74823i	0.190635	+	0.139520i
$389$	12.3494			0.626138			0.313069	−	0.949730i	$-0.398643\pi$
$389$	12.3494			0.626138			0.313069	+	0.949730i	$0.398643\pi$
$390$	7.80247	+	15.3793i	0.395093	+	0.778760i
$391$	34.8380			1.76183
$392$		0			0
$393$	2.25918			0.113961
$394$	−0.232223	−	0.457729i	−0.0116992	−	0.0230601i
$395$	−44.6890			−2.24855
$396$	−8.62576	−	6.31294i	−0.433461	−	0.317237i
$397$		−	17.9991i		−	0.903349i	−0.892183	−	0.451674i	$-0.850827\pi$
$397$		−	17.9991i		−	0.903349i	0.892183	−	0.451674i	$-0.149173\pi$
$398$	−6.31102	−	12.4395i	−0.316343	−	0.623537i
$399$		0			0
$400$	5.61028	+	17.6844i	0.280514	+	0.884218i
$401$	−0.0569723			−0.00284506			−0.00142253	−	0.999999i	$-0.500453\pi$
$401$	−0.0569723			−0.00284506			−0.00142253	+	0.999999i	$0.500453\pi$
$402$	12.1679	−	6.17321i	0.606878	−	0.307892i
$403$			6.01418i			0.299587i
$404$	12.0146	+	8.79313i	0.597748	+	0.437474i
$405$			3.10455i			0.154266i
$406$		0			0
$407$			47.7799i			2.36836i
$408$	−2.59677	+	15.8593i	−0.128559	+	0.785153i
$409$		−	35.0224i		−	1.73175i	−0.500265	−	0.865873i	$-0.666764\pi$
$409$		−	35.0224i		−	1.73175i	0.500265	−	0.865873i	$-0.333236\pi$
$410$	−11.6069	−	22.8781i	−0.573224	−	1.12987i
$411$	20.0731			0.990131
$412$	19.2486	−	26.3005i	0.948311	−	1.29574i
$413$		0			0
$414$	−7.73301	+	3.92324i	−0.380057	+	0.192817i
$415$			34.0828i			1.67306i
$416$	−15.5743	−	15.8475i	−0.763591	−	0.776988i
$417$	7.98360			0.390958
$418$	−1.15136	+	0.584128i	−0.0563150	+	0.0285707i
$419$	17.9222			0.875558			0.437779	−	0.899083i	$-0.355765\pi$
$419$	17.9222			0.875558			0.437779	+	0.899083i	$0.355765\pi$
$420$		0			0
$421$	−8.47542			−0.413067			−0.206533	−	0.978440i	$-0.566218\pi$
$421$	−8.47542			−0.413067			−0.206533	+	0.978440i	$0.566218\pi$
$422$	32.4477	−	16.4619i	1.57953	−	0.801352i
$423$	2.29477			0.111576
$424$	3.34685	+	0.548005i	0.162537	+	0.0266135i
$425$			26.3534i			1.27833i
$426$	−2.58100	+	1.30944i	−0.125050	+	0.0634424i
$427$		0			0
$428$	27.0159	+	19.7722i	1.30587	+	0.955725i
$429$	20.9927			1.01354
$430$	−4.73338	−	9.32986i	−0.228264	−	0.449926i
$431$			23.9988i			1.15598i	0.816044	+	0.577990i	$0.196163\pi$
$431$			23.9988i			1.15598i	−0.816044	+	0.577990i	$0.803837\pi$
$432$	−1.20957	−	3.81273i	−0.0581956	−	0.183440i
$433$			12.5505i			0.603137i	0.953445	+	0.301568i	$0.0975102\pi$
$433$			12.5505i			0.603137i	−0.953445	+	0.301568i	$0.902490\pi$
$434$		0			0
$435$		−	6.11028i		−	0.292965i
$436$	−9.12018	+	12.4615i	−0.436777	+	0.596796i
$437$			1.04734i			0.0501013i
$438$	12.9554	−	6.57277i	0.619035	−	0.314059i
$439$	7.15150			0.341323			0.170661	−	0.985330i	$-0.445410\pi$
$439$	7.15150			0.341323			0.170661	+	0.985330i	$0.445410\pi$
$440$	46.3137	+	7.58330i	2.20792	+	0.361520i
$441$		0			0
$442$	−14.2797	−	28.1463i	−0.679214	−	1.33878i
$443$			24.8722i			1.18172i	0.806776	+	0.590858i	$0.201211\pi$
$443$			24.8722i			1.18172i	−0.806776	+	0.590858i	$0.798789\pi$
$444$	−10.5598	+	14.4285i	−0.501145	+	0.684745i
$445$	18.0645			0.856339
$446$	−10.3942	−	20.4879i	−0.492182	−	0.970128i
$447$	−5.30170			−0.250762
$448$		0			0
$449$	−9.93727			−0.468969			−0.234484	−	0.972120i	$-0.575340\pi$
$449$	−9.93727			−0.468969			−0.234484	+	0.972120i	$0.575340\pi$
$450$	−2.96776	−	5.84969i	−0.139902	−	0.275757i
$451$	−31.2286			−1.47050
$452$	0.845550	−	1.15533i	0.0397713	−	0.0543420i
$453$			1.52658i			0.0717248i
$454$	−13.0838	−	25.7892i	−0.614054	−	1.21035i
$455$		0			0
$456$	−0.476783	−	0.0780674i	−0.0223274	−	0.00365584i
$457$	26.0911			1.22049			0.610245	−	0.792213i	$-0.291071\pi$
$457$	26.0911			1.22049			0.610245	+	0.792213i	$0.291071\pi$
$458$	−4.27482	+	2.16877i	−0.199749	+	0.101340i
$459$		−	5.68178i		−	0.265203i
$460$	22.4847	−	30.7223i	1.04836	−	1.43243i
$461$			29.5120i			1.37451i	0.726417	+	0.687254i	$0.241184\pi$
$461$			29.5120i			1.37451i	−0.726417	+	0.687254i	$0.758816\pi$
$462$		0			0
$463$		−	2.80479i		−	0.130350i	−0.997874	−	0.0651748i	$-0.979239\pi$
$463$		−	2.80479i		−	0.130350i	0.997874	−	0.0651748i	$-0.0207605\pi$
$464$	2.38064	+	7.50410i	0.110518	+	0.348369i
$465$		−	4.75355i		−	0.220440i
$466$	1.21850	+	2.40177i	0.0564461	+	0.111260i
$467$	−32.9710			−1.52571			−0.762857	−	0.646567i	$-0.776204\pi$
$467$	−32.9710			−1.52571			−0.762857	+	0.646567i	$0.776204\pi$
$468$	6.33933	+	4.63957i	0.293035	+	0.214464i
$469$		0			0
$470$	−8.98501	+	4.55843i	−0.414448	+	0.210265i
$471$			12.4358i			0.573013i
$472$	−30.6877	−	5.02473i	−1.41252	−	0.231282i
$473$	−12.7353			−0.585568
$474$	−18.1544	+	9.21038i	−0.833858	+	0.423047i
$475$	−0.792271			−0.0363519
$476$		0			0
$477$	−1.19905			−0.0549006
$478$	−9.80472	+	4.97429i	−0.448457	+	0.227519i
$479$	23.9252			1.09317			0.546585	−	0.837403i	$-0.315927\pi$
$479$	23.9252			1.09317			0.546585	+	0.837403i	$0.315927\pi$
$480$	12.3097	+	12.5257i	0.561860	+	0.571719i
$481$		−	35.1149i		−	1.60110i
$482$	15.2739	−	7.74900i	0.695706	−	0.352957i
$483$		0			0
$484$	20.7467	−	28.3475i	0.943033	−	1.28852i
$485$	7.22323			0.327990
$486$	0.639847	+	1.26119i	0.0290240	+	0.0572087i
$487$			0.822201i			0.0372575i	0.999826	+	0.0186287i	$0.00593006\pi$
$487$			0.822201i			0.0372575i	−0.999826	+	0.0186287i	$0.994070\pi$
$488$	3.01175	−	18.3938i	0.136336	−	0.832646i
$489$			6.22348i			0.281435i
$490$		0			0
$491$		−	22.6377i		−	1.02163i	−0.859692	−	0.510813i	$-0.829345\pi$
$491$		−	22.6377i		−	1.02163i	0.859692	−	0.510813i	$-0.170655\pi$
$492$	−9.43034	−	6.90179i	−0.425153	−	0.311157i
$493$			11.1827i			0.503643i
$494$	0.846171	−	0.429293i	0.0380710	−	0.0193148i
$495$	−16.5924			−0.745774
$496$	1.85204	+	5.83788i	0.0831591	+	0.262129i
$497$		0			0
$498$	7.02446	+	13.8458i	0.314774	+	0.620443i
$499$		−	29.9874i		−	1.34242i	−0.741267	−	0.671211i	$-0.765775\pi$
$499$		−	29.9874i		−	1.34242i	0.741267	−	0.671211i	$-0.234225\pi$
$500$	−1.81264	−	1.32662i	−0.0810636	−	0.0593281i
$501$	−4.14549			−0.185207
$502$	−5.05101	−	9.95593i	−0.225438	−	0.444355i
$503$	−28.7539			−1.28207			−0.641037	−	0.767510i	$-0.721496\pi$
$503$	−28.7539			−1.28207			−0.641037	+	0.767510i	$0.721496\pi$
$504$		0			0
$505$	23.1112			1.02843
$506$	−20.9679	−	41.3295i	−0.932139	−	1.83732i
$507$	−2.42816			−0.107838
$508$	24.8673	+	18.1997i	1.10331	+	0.807479i
$509$			41.0461i			1.81934i	0.415336	+	0.909668i	$0.363664\pi$
$509$			41.0461i			1.81934i	−0.415336	+	0.909668i	$0.636336\pi$
$510$	11.2865	+	22.2466i	0.499775	+	0.985095i
$511$		0			0
$512$	−19.9979	−	10.5870i	−0.883791	−	0.467882i
$513$	0.170813			0.00754158
$514$	3.86322	−	1.95995i	0.170399	−	0.0864497i
$515$		−	50.5915i		−	2.22933i
$516$	−3.84576	−	2.81460i	−0.169300	−	0.123906i
$517$			12.2645i			0.539394i
$518$		0			0
$519$		−	5.54634i		−	0.243457i
$520$	−34.0374	−	5.57320i	−1.49264	−	0.244401i
$521$			20.4251i			0.894841i	0.894324	+	0.447420i	$0.147657\pi$
$521$			20.4251i			0.894841i	−0.894324	+	0.447420i	$0.852343\pi$
$522$	−1.25933	−	2.48223i	−0.0551192	−	0.108644i
$523$	−1.90741			−0.0834053			−0.0417026	−	0.999130i	$-0.513278\pi$
$523$	−1.90741			−0.0834053			−0.0417026	+	0.999130i	$0.513278\pi$
$524$	−2.66852	+	3.64617i	−0.116575	+	0.159284i
$525$		0			0
$526$	13.4044	−	6.80055i	0.584460	−	0.296518i
$527$			8.69968i			0.378964i
$528$	20.3773	−	6.46462i	0.886810	−	0.281336i
$529$	−14.5956			−0.634592
$530$	4.69477	−	2.38183i	0.203928	−	0.103460i
$531$	10.9942			0.477108
$532$		0			0
$533$	22.9508			0.994111
$534$	7.33849	−	3.72308i	0.317568	−	0.161114i
$535$	51.9676			2.24676
$536$	−4.40944	+	26.9299i	−0.190459	+	1.16319i
$537$		−	1.27166i		−	0.0548762i
$538$	−3.17204	+	1.60929i	−0.136756	+	0.0693815i
$539$		0			0
$540$	−5.01054	−	3.66707i	−0.215619	−	0.157806i
$541$	35.5224			1.52723			0.763614	−	0.645673i	$-0.223423\pi$
$541$	35.5224			1.52723			0.763614	+	0.645673i	$0.223423\pi$
$542$	−0.586235	−	1.15552i	−0.0251810	−	0.0496336i
$543$			0.386679i			0.0165940i
$544$	−22.5286	−	22.9239i	−0.965907	−	0.982854i
$545$			23.9708i			1.02679i
$546$		0			0
$547$		−	9.02584i		−	0.385917i	−0.981207	−	0.192959i	$-0.938192\pi$
$547$		−	9.02584i		−	0.385917i	0.981207	−	0.192959i	$-0.0618083\pi$
$548$	−23.7101	+	32.3966i	−1.01285	+	1.38392i
$549$			6.58977i			0.281245i
$550$	31.2640	−	15.8613i	1.33310	−	0.676330i
$551$	−0.336189			−0.0143221
$552$	2.80232	−	17.1147i	0.119274	−	0.728449i
$553$		0			0
$554$	7.52833	+	14.8389i	0.319848	+	0.630446i
$555$			27.7545i			1.17811i
$556$	−9.43016	+	12.8850i	−0.399928	+	0.546446i
$557$	33.9921			1.44029			0.720145	−	0.693823i	$-0.244075\pi$
$557$	33.9921			1.44029			0.720145	+	0.693823i	$0.244075\pi$
$558$	−0.979705	−	1.93107i	−0.0414742	−	0.0817489i
$559$	9.35952			0.395865
$560$		0			0
$561$	30.3666			1.28208
$562$	−19.0897	−	37.6272i	−0.805249	−	1.58721i
$563$	12.8259			0.540547			0.270274	−	0.962784i	$-0.412886\pi$
$563$	12.8259			0.540547			0.270274	+	0.962784i	$0.412886\pi$
$564$	−2.71057	+	3.70362i	−0.114136	+	0.155950i
$565$		−	2.22238i		−	0.0934961i
$566$	3.09036	+	6.09133i	0.129897	+	0.256038i
$567$		0			0
$568$	0.935313	−	5.71227i	0.0392449	−	0.239681i
$569$	17.6976			0.741923			0.370962	−	0.928648i	$-0.379028\pi$
$569$	17.6976			0.741923			0.370962	+	0.928648i	$0.379028\pi$
$570$	−0.668805	+	0.339309i	−0.0280132	+	0.0142121i
$571$			23.7859i			0.995410i	0.867346	+	0.497705i	$0.165824\pi$
$571$			23.7859i			0.995410i	−0.867346	+	0.497705i	$0.834176\pi$
$572$	−24.7964	+	33.8808i	−1.03679	+	1.41663i
$573$			6.59547i			0.275530i
$574$		0			0
$575$		−	28.4395i		−	1.18601i
$576$	7.58224	+	2.55140i	0.315927	+	0.106308i
$577$			40.5467i			1.68798i	0.536357	+	0.843991i	$0.319800\pi$
$577$			40.5467i			1.68798i	−0.536357	+	0.843991i	$0.680200\pi$
$578$	−9.77855	−	19.2743i	−0.406734	−	0.801704i
$579$	1.95706			0.0813327
$580$	9.86159	+	7.21741i	0.409480	+	0.299687i
$581$		0			0
$582$	2.93436	−	1.48871i	0.121633	−	0.0617089i
$583$		−	6.40836i		−	0.265407i
$584$	−4.69484	+	28.6729i	−0.194274	+	1.18649i
$585$	12.1943			0.504171
$586$	28.2854	−	14.3502i	1.16846	−	0.592801i
$587$	−26.0331			−1.07450			−0.537251	−	0.843422i	$-0.680537\pi$
$587$	−26.0331			−1.07450			−0.537251	+	0.843422i	$0.680537\pi$
$588$		0			0
$589$	−0.261541			−0.0107766
$590$	−43.0470	+	21.8393i	−1.77222	+	0.899111i
$591$	−0.362935			−0.0149291
$592$	−10.8135	−	34.0856i	−0.444432	−	1.40091i
$593$		−	11.2192i		−	0.460719i	−0.973106	−	0.230359i	$-0.926010\pi$
$593$		−	11.2192i		−	0.460719i	0.973106	−	0.230359i	$-0.0739901\pi$
$594$	−6.74049	+	3.41969i	−0.276565	+	0.140312i
$595$		0			0
$596$	6.26232	−	8.55660i	0.256515	−	0.350492i
$597$	−9.86333			−0.403679
$598$	15.4100	+	30.3743i	0.630160	+	1.24210i
$599$		−	17.3998i		−	0.710935i	−0.934689	−	0.355467i	$-0.884322\pi$
$599$		−	17.3998i		−	0.710935i	0.934689	−	0.355467i	$-0.115678\pi$
$600$	12.9465	+	2.11983i	0.528539	+	0.0865417i
$601$			18.1962i			0.742237i	0.928585	+	0.371119i	$0.121026\pi$
$601$			18.1962i			0.742237i	−0.928585	+	0.371119i	$0.878974\pi$
$602$		0			0
$603$		−	9.64794i		−	0.392895i
$604$	−2.46379	−	1.80318i	−0.100250	−	0.0733703i
$605$		−	54.5290i		−	2.21692i
$606$	9.38864	−	4.76320i	0.381388	−	0.193492i
$607$	−5.45708			−0.221496			−0.110748	−	0.993849i	$-0.535325\pi$
$607$	−5.45708			−0.221496			−0.110748	+	0.993849i	$0.535325\pi$
$608$	0.689168	−	0.677284i	0.0279495	−	0.0274675i
$609$		0			0
$610$	−13.0902	−	25.8018i	−0.530006	−	1.04468i
$611$		−	9.01358i		−	0.364650i
$612$	9.17002	+	6.71127i	0.370676	+	0.271287i
$613$	−30.1051			−1.21593			−0.607967	−	0.793962i	$-0.708015\pi$
$613$	−30.1051			−1.21593			−0.607967	+	0.793962i	$0.708015\pi$
$614$	−20.0351	−	39.4907i	−0.808549	−	1.59371i
$615$	−18.1401			−0.731480
$616$		0			0
$617$	38.4324			1.54723			0.773616	−	0.633655i	$-0.218446\pi$
$617$	38.4324			1.54723			0.773616	+	0.633655i	$0.218446\pi$
$618$	−10.4269	−	20.5522i	−0.419431	−	0.826732i
$619$	18.3356			0.736970			0.368485	−	0.929634i	$-0.379877\pi$
$619$	18.3356			0.736970			0.368485	+	0.929634i	$0.379877\pi$
$620$	7.67192	+	5.61485i	0.308112	+	0.225498i
$621$			6.13153i			0.246050i
$622$	−9.86778	−	19.4502i	−0.395662	−	0.779881i
$623$		0			0
$624$	−14.9759	+	4.75104i	−0.599517	+	0.190194i
$625$	−26.6779			−1.06712
$626$	−7.69071	+	3.90178i	−0.307383	+	0.155947i
$627$			0.912919i			0.0364585i
$628$	−20.0706	−	14.6891i	−0.800905	−	0.586159i
$629$		−	50.7948i		−	2.02532i
$630$		0			0
$631$			44.4442i			1.76930i	0.466259	+	0.884648i	$0.345601\pi$
$631$			44.4442i			1.76930i	−0.466259	+	0.884648i	$0.654399\pi$
$632$	6.57885	−	40.1792i	0.261693	−	1.59824i
$633$		−	25.7279i		−	1.02259i
$634$	−19.0105	−	37.4712i	−0.755004	−	1.48817i
$635$	47.8345			1.89826
$636$	1.41630	−	1.93518i	0.0561601	−	0.0767350i
$637$		0			0
$638$	13.2664	−	6.73053i	0.525222	−	0.266464i
$639$			2.04649i			0.0809577i
$640$	−34.7559	+	5.07184i	−1.37385	+	0.200482i
$641$	0.827523			0.0326852			0.0163426	−	0.999866i	$-0.494798\pi$
$641$	0.827523			0.0326852			0.0163426	+	0.999866i	$0.494798\pi$
$642$	21.1113	−	10.7105i	0.833195	−	0.422710i
$643$	50.0469			1.97366			0.986829	−	0.161764i	$-0.0517183\pi$
$643$	50.0469			1.97366			0.986829	+	0.161764i	$0.0517183\pi$
$644$		0			0
$645$	−7.39767			−0.291283
$646$	1.22401	−	0.620986i	0.0481581	−	0.0244324i
$647$	17.3220			0.680998			0.340499	−	0.940245i	$-0.389404\pi$
$647$	17.3220			0.680998			0.340499	+	0.940245i	$0.389404\pi$
$648$	−2.79126	−	0.457034i	−0.109651	−	0.0179540i
$649$			58.7592i			2.30650i
$650$	−22.9768	+	11.6570i	−0.901225	+	0.457224i
$651$		0			0
$652$	−10.0443	−	7.35112i	−0.393365	−	0.287892i
$653$	6.96007			0.272368			0.136184	−	0.990684i	$-0.456516\pi$
$653$	6.96007			0.272368			0.136184	+	0.990684i	$0.456516\pi$
$654$	4.94037	+	9.73785i	0.193184	+	0.380780i
$655$			7.01374i			0.274049i
$656$	22.2781	−	7.06762i	0.869813	−	0.275944i
$657$		−	10.2724i		−	0.400765i
$658$		0			0
$659$		−	20.5979i		−	0.802381i	−0.915995	−	0.401191i	$-0.868596\pi$
$659$		−	20.5979i		−	0.802381i	0.915995	−	0.401191i	$-0.131404\pi$
$660$	19.5988	−	26.7791i	0.762884	−	1.04238i
$661$		−	43.7552i		−	1.70188i	−0.525262	−	0.850940i	$-0.676033\pi$
$661$		−	43.7552i		−	1.70188i	0.525262	−	0.850940i	$-0.323967\pi$
$662$	25.4410	−	12.9071i	0.988792	−	0.501650i
$663$	−22.3173			−0.866732
$664$	−30.6434	−	5.01748i	−1.18919	−	0.194716i
$665$		0			0
$666$	5.72019	+	11.2749i	0.221653	+	0.436895i
$667$		−	12.0679i		−	0.467270i
$668$	4.89662	−	6.69055i	0.189456	−	0.258865i
$669$	−16.2449			−0.628064
$670$	19.1650	+	37.7758i	0.740410	+	1.45941i
$671$	−35.2194			−1.35963
$672$		0			0
$673$	5.42765			0.209220			0.104610	−	0.994513i	$-0.466641\pi$
$673$	5.42765			0.209220			0.104610	+	0.994513i	$0.466641\pi$
$674$	8.95923	+	17.6593i	0.345097	+	0.680213i
$675$	−4.63824			−0.178526
$676$	2.86812	−	3.91889i	0.110312	−	0.150726i
$677$		−	33.9056i		−	1.30310i	−0.758607	−	0.651549i	$-0.774120\pi$
$677$		−	33.9056i		−	1.30310i	0.758607	−	0.651549i	$-0.225880\pi$
$678$	−0.458031	−	0.902815i	−0.0175906	−	0.0346724i
$679$		0			0
$680$	−49.2361	−	8.06180i	−1.88812	−	0.309156i
$681$	−20.4484			−0.783583
$682$	10.3207	−	5.23608i	0.395201	−	0.200500i
$683$			5.89787i			0.225676i	0.993613	+	0.112838i	$0.0359941\pi$
$683$			5.89787i			0.225676i	−0.993613	+	0.112838i	$0.964006\pi$
$684$	−0.201763	+	0.275681i	−0.00771460	+	0.0105409i
$685$			62.3179i			2.38104i
$686$		0			0
$687$			3.38952i			0.129318i
$688$	9.08517	−	2.88223i	0.346369	−	0.109884i
$689$			4.70970i			0.179425i
$690$	−12.1799	−	24.0075i	−0.463681	−	0.913951i
$691$	−43.3271			−1.64824			−0.824119	−	0.566416i	$-0.808329\pi$
$691$	−43.3271			−1.64824			−0.824119	+	0.566416i	$0.808329\pi$
$692$	8.95144	+	6.55129i	0.340283	+	0.249043i
$693$		0			0
$694$	−15.1164	+	7.66913i	−0.573812	+	0.291116i
$695$			24.7855i			0.940167i
$696$	5.49366	+	0.899520i	0.208237	+	0.0340962i
$697$	33.1991			1.25750
$698$	36.3509	−	18.4421i	1.37590	−	0.698045i
$699$	1.90437			0.0720298
$700$		0			0
$701$	28.9345			1.09284			0.546420	−	0.837511i	$-0.315990\pi$
$701$	28.9345			1.09284			0.546420	+	0.837511i	$0.315990\pi$
$702$	4.95378	−	2.51324i	0.186968	−	0.0948559i
$703$	1.52706			0.0575941
$704$	−13.6361	+	40.5237i	−0.513929	+	1.52729i
$705$			7.12425i			0.268315i
$706$	−0.144765	+	0.0734444i	−0.00544829	+	0.00276412i
$707$		0			0
$708$	−12.9863	+	17.7440i	−0.488054	+	0.666859i
$709$	16.7583			0.629373			0.314686	−	0.949196i	$-0.398101\pi$
$709$	16.7583			0.629373			0.314686	+	0.949196i	$0.398101\pi$
$710$	−4.06521	−	8.01286i	−0.152565	−	0.300717i
$711$			14.3947i			0.539842i
$712$	−2.65935	+	16.2415i	−0.0996633	+	0.608677i
$713$		−	9.38831i		−	0.351595i
$714$		0			0
$715$			65.1729i			2.43733i
$716$	2.05238	+	1.50207i	0.0767009	+	0.0561352i
$717$			7.77419i			0.290333i
$718$	−2.49361	+	1.26510i	−0.0930605	+	0.0472130i
$719$	−30.8239			−1.14954			−0.574768	−	0.818316i	$-0.694908\pi$
$719$	−30.8239			−1.14954			−0.574768	+	0.818316i	$0.694908\pi$
$720$	11.8368	−	3.75518i	0.441132	−	0.139947i
$721$		0			0
$722$	−12.1384	−	23.9258i	−0.451745	−	0.890425i
$723$		−	12.1107i		−	0.450402i
$724$	−0.624074	−	0.456742i	−0.0231935	−	0.0169747i
$725$	9.12883			0.339036
$726$	−11.2384	−	22.1518i	−0.417097	−	0.822130i
$727$	20.6890			0.767313			0.383657	−	0.923476i	$-0.374665\pi$
$727$	20.6890			0.767313			0.383657	+	0.923476i	$0.374665\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	20.4055	+	40.2208i	0.755241	+	1.48864i
$731$	13.5388			0.500752
$732$	−10.6355	−	7.78379i	−0.393098	−	0.287697i
$733$			25.2113i			0.931201i	0.884995	+	0.465601i	$0.154162\pi$
$733$			25.2113i			0.931201i	−0.884995	+	0.465601i	$0.845838\pi$
$734$	17.1344	+	33.7733i	0.632443	+	1.24660i
$735$		0			0
$736$	24.3119	+	24.7385i	0.896148	+	0.911872i
$737$	51.5639			1.89938
$738$	−7.36922	+	3.73867i	−0.271265	+	0.137622i
$739$		−	29.1040i		−	1.07061i	−0.844659	−	0.535305i	$-0.820197\pi$
$739$		−	29.1040i		−	1.07061i	0.844659	−	0.535305i	$-0.179803\pi$
$740$	−44.7939	−	32.7834i	−1.64666	−	1.20514i
$741$		−	0.670931i		−	0.0246473i
$742$		0			0
$743$			4.72777i			0.173445i	0.996233	+	0.0867226i	$0.0276394\pi$
$743$			4.72777i			0.173445i	−0.996233	+	0.0867226i	$0.972361\pi$
$744$	4.27385	+	0.699790i	0.156687	+	0.0256555i
$745$		−	16.4594i		−	0.603026i
$746$	14.7418	+	29.0573i	0.539737	+	1.06386i
$747$	10.9783			0.401677
$748$	−35.8687	+	49.0097i	−1.31149	+	1.79197i
$749$		0			0
$750$	−1.41646	+	0.718623i	−0.0517219	+	0.0262404i
$751$			7.35651i			0.268443i	0.990951	+	0.134221i	$0.0428533\pi$
$751$			7.35651i			0.268443i	−0.990951	+	0.134221i	$0.957147\pi$
$752$	−2.77570	−	8.74937i	−0.101219	−	0.319057i
$753$	−7.89409			−0.287677
$754$	−9.74988	+	4.94647i	−0.355070	+	0.180140i
$755$	−4.73933			−0.172482
$756$		0			0
$757$	6.36602			0.231377			0.115688	−	0.993286i	$-0.463093\pi$
$757$	6.36602			0.231377			0.115688	+	0.993286i	$0.463093\pi$
$758$	28.2125	−	14.3132i	1.02472	−	0.519879i
$759$	−32.7703			−1.18948
$760$	0.242364	−	1.48020i	0.00879147	−	0.0536924i
$761$			2.01702i			0.0731167i	0.999332	+	0.0365584i	$0.0116395\pi$
$761$			2.01702i			0.0731167i	−0.999332	+	0.0365584i	$0.988361\pi$
$762$	19.4322	−	9.85868i	0.703956	−	0.357142i
$763$		0			0
$764$	−10.6447	−	7.79051i	−0.385110	−	0.281851i
$765$	17.6394			0.637753
$766$	−18.3689	−	36.2066i	−0.663696	−	1.30820i
$767$		−	43.1839i		−	1.55928i
$768$	−13.0739	+	9.22355i	−0.471763	+	0.332826i
$769$		−	52.1122i		−	1.87922i	−0.342253	−	0.939608i	$-0.611190\pi$
$769$		−	52.1122i		−	1.87922i	0.342253	−	0.939608i	$-0.388810\pi$
$770$		0			0
$771$		−	3.06316i		−	0.110317i
$772$	−2.31167	+	3.15857i	−0.0831987	+	0.113679i
$773$		−	25.2185i		−	0.907045i	−0.891245	−	0.453523i	$-0.850167\pi$
$773$		−	25.2185i		−	0.907045i	0.891245	−	0.453523i	$-0.149833\pi$
$774$	−3.00522	+	1.52466i	−0.108020	+	0.0548027i
$775$	7.10186			0.255106
$776$	−1.06336	+	6.49431i	−0.0381725	+	0.233132i
$777$		0			0
$778$	7.90171	+	15.5749i	0.283290	+	0.558387i
$779$			0.998073i			0.0357597i
$780$	−14.4038	+	19.6808i	−0.515738	+	0.704684i
$781$	−10.9375			−0.391376
$782$	22.2910	+	43.9373i	0.797124	+	1.57119i
$783$	−1.96817			−0.0703366
$784$		0			0
$785$	−38.6077			−1.37797
$786$	1.44553	+	2.84925i	0.0515603	+	0.101629i
$787$	23.4850			0.837148			0.418574	−	0.908183i	$-0.362530\pi$
$787$	23.4850			0.837148			0.418574	+	0.908183i	$0.362530\pi$
$788$	0.428696	−	0.585753i	0.0152717	−	0.0208666i
$789$		−	10.6284i		−	0.378381i
$790$	−28.5941	−	56.3612i	−1.01733	−	2.00524i
$791$		0			0
$792$	2.44264	−	14.9180i	0.0867955	−	0.530089i
$793$	25.8838			0.919160
$794$	22.7002	−	11.5167i	0.805602	−	0.408711i
$795$		−	3.72250i		−	0.132023i
$796$	11.6505	−	15.9188i	0.412941	−	0.564226i
$797$		−	44.2469i		−	1.56730i	−0.621200	−	0.783652i	$-0.713354\pi$
$797$		−	44.2469i		−	1.56730i	0.621200	−	0.783652i	$-0.286646\pi$
$798$		0			0
$799$		−	13.0384i		−	0.461266i
$800$	−18.7136	+	18.3909i	−0.661625	+	0.650216i
$801$		−	5.81871i		−	0.205594i
$802$	−0.0364535	−	0.0718528i	−0.00128722	−	0.00253721i
$803$	54.9014			1.93743
$804$	15.5712	+	11.3961i	0.549152	+	0.401908i
$805$		0			0
$806$	−7.58501	+	3.84815i	−0.267170	+	0.135545i
$807$			2.51512i			0.0885364i
$808$	−3.40229	+	20.7789i	−0.119692	+	0.731000i
$809$	−29.9743			−1.05384			−0.526920	−	0.849915i	$-0.676653\pi$
$809$	−29.9743			−1.05384			−0.526920	+	0.849915i	$0.676653\pi$
$810$	−3.91542	+	1.98644i	−0.137574	+	0.0697963i
$811$	8.74124			0.306946			0.153473	−	0.988153i	$-0.450954\pi$
$811$	8.74124			0.306946			0.153473	+	0.988153i	$0.450954\pi$
$812$		0			0
$813$	−0.916212			−0.0321329
$814$	−60.2595	+	30.5718i	−2.11209	+	1.07154i
$815$	−19.3211			−0.676789
$816$	−21.6631	+	6.87252i	−0.758361	+	0.240586i
$817$			0.407022i			0.0142399i
$818$	44.1698	−	22.4090i	1.54436	−	0.783511i
$819$		0			0
$820$	21.4270	−	29.2770i	0.748262	−	1.02240i
$821$	−48.0127			−1.67566			−0.837828	−	0.545935i	$-0.816175\pi$
$821$	−48.0127			−1.67566			−0.837828	+	0.545935i	$0.816175\pi$
$822$	12.8437	+	25.3159i	0.447975	+	0.882994i
$823$			20.1297i			0.701676i	0.936436	+	0.350838i	$0.114103\pi$
$823$			20.1297i			0.701676i	−0.936436	+	0.350838i	$0.885897\pi$
$824$	45.4861	+	7.44779i	1.58458	+	0.259456i
$825$		−	24.7893i		−	0.863052i
$826$		0			0
$827$			24.4464i			0.850084i	0.905174	+	0.425042i	$0.139741\pi$
$827$			24.4464i			0.850084i	−0.905174	+	0.425042i	$0.860259\pi$
$828$	−9.89588	−	7.24251i	−0.343906	−	0.251695i
$829$			10.8168i			0.375682i	0.982199	+	0.187841i	$0.0601490\pi$
$829$			10.8168i			0.375682i	−0.982199	+	0.187841i	$0.939851\pi$
$830$	−42.9849	+	21.8078i	−1.49203	+	0.756959i
$831$	11.7658			0.408152
$832$	10.0216	−	29.7820i	0.347435	−	1.03251i
$833$		0			0
$834$	5.10828	+	10.0688i	0.176885	+	0.348655i
$835$		−	12.8699i		−	0.445381i
$836$	−1.47339	−	1.07833i	−0.0509583	−	0.0372949i
$837$	−1.53115			−0.0529244
$838$	11.4675	+	22.6033i	0.396137	+	0.780818i
$839$	−10.6831			−0.368821			−0.184410	−	0.982849i	$-0.559038\pi$
$839$	−10.6831			−0.368821			−0.184410	+	0.982849i	$0.559038\pi$
$840$		0			0
$841$	−25.1263			−0.866425
$842$	−5.42297	−	10.6891i	−0.186888	−	0.368371i
$843$	−29.8347			−1.02756
$844$	41.5231	+	30.3895i	1.42928	+	1.04605i
$845$		−	7.53834i		−	0.259327i
$846$	1.46830	+	2.89414i	0.0504814	+	0.0995027i
$847$		0			0
$848$	1.45033	+	4.57164i	0.0498046	+	0.156991i
$849$	4.82984			0.165760
$850$	−33.2366	+	16.8622i	−1.14001	+	0.578368i
$851$			54.8154i			1.87905i
$852$	−3.30289	−	2.41729i	−0.113155	−	0.0828150i
$853$			47.6336i			1.63094i	0.578796	+	0.815472i	$0.303523\pi$
$853$			47.6336i			1.63094i	−0.578796	+	0.815472i	$0.696477\pi$
$854$		0			0
$855$			0.530298i			0.0181358i
$856$	−7.65037	+	46.7234i	−0.261484	+	1.59697i
$857$			17.9251i			0.612311i	0.951981	+	0.306156i	$0.0990428\pi$
$857$			17.9251i			0.612311i	−0.951981	+	0.306156i	$0.900957\pi$
$858$	13.4321	+	26.4757i	0.458565	+	0.903867i
$859$	19.2616			0.657199			0.328599	−	0.944469i	$-0.393423\pi$
$859$	19.2616			0.657199			0.328599	+	0.944469i	$0.393423\pi$
$860$	8.73807	−	11.9394i	0.297966	−	0.407129i
$861$		0			0
$862$	−30.2670	+	15.3555i	−1.03090	+	0.523012i
$863$			7.57076i			0.257712i	0.991663	+	0.128856i	$0.0411305\pi$
$863$			7.57076i			0.257712i	−0.991663	+	0.128856i	$0.958870\pi$
$864$	4.03463	−	3.96506i	0.137261	−	0.134894i
$865$	17.2189			0.585460
$866$	−15.8285	+	8.03038i	−0.537874	+	0.272883i
$867$	−15.2826			−0.519026
$868$		0			0
$869$	−76.9330			−2.60977
$870$	7.70621	−	3.90964i	0.261265	−	0.132549i
$871$	−37.8959			−1.28405
$872$	−21.5518	−	3.52884i	−0.729835	−	0.119501i
$873$		−	2.32666i		−	0.0787455i
$874$	−1.32090	+	0.670140i	−0.0446801	+	0.0226678i
$875$		0			0
$876$	16.5790	+	12.1337i	0.560152	+	0.409959i
$877$	−23.0973			−0.779939			−0.389969	−	0.920828i	$-0.627514\pi$
$877$	−23.0973			−0.779939			−0.389969	+	0.920828i	$0.627514\pi$
$878$	4.57587	+	9.01939i	0.154428	+	0.304390i
$879$		−	22.4276i		−	0.756463i
$880$	20.0697	+	63.2625i	0.676551	+	2.13258i
$881$			26.0108i			0.876325i	0.898896	+	0.438163i	$0.144371\pi$
$881$			26.0108i			0.876325i	−0.898896	+	0.438163i	$0.855629\pi$
$882$		0			0
$883$		−	13.5662i		−	0.456539i	−0.973598	−	0.228270i	$-0.926693\pi$
$883$		−	13.5662i		−	0.456539i	0.973598	−	0.228270i	$-0.0733068\pi$
$884$	26.3610	−	36.0187i	0.886617	−	1.21144i
$885$			34.1321i			1.14734i
$886$	−31.3686	+	15.9144i	−1.05385	+	0.534656i
$887$	1.15898			0.0389147			0.0194573	−	0.999811i	$-0.493806\pi$
$887$	1.15898			0.0389147			0.0194573	+	0.999811i	$0.493806\pi$
$888$	−24.9537	−	4.08585i	−0.837390	−	0.137112i
$889$		0			0
$890$	11.5585	+	22.7827i	0.387442	+	0.763678i
$891$			5.34455i			0.179049i
$892$	19.1883	−	26.2182i	0.642473	−	0.877850i
$893$	0.391977			0.0131170
$894$	−3.39228	−	6.68644i	−0.113455	−	0.223628i
$895$	3.94793			0.131965
$896$		0			0
$897$	24.0838			0.804136
$898$	−6.35833	−	12.5328i	−0.212180	−	0.418224i
$899$	3.01357			0.100508
$900$	5.47865	−	7.48581i	0.182622	−	0.249527i
$901$			6.81272i			0.226965i
$902$	−19.9815	−	39.3852i	−0.665312	−	1.31138i
$903$		0			0
$904$	1.99811	+	0.327166i	0.0664561	+	0.0108814i
$905$	−1.20046			−0.0399047
$906$	−1.92530	+	0.976774i	−0.0639638	+	0.0324512i
$907$			37.1328i			1.23298i	0.787364	+	0.616488i	$0.211445\pi$
$907$			37.1328i			1.23298i	−0.787364	+	0.616488i	$0.788555\pi$
$908$	24.1534	−	33.0023i	0.801560	−	1.09522i
$909$		−	7.44428i		−	0.246911i
$910$		0			0
$911$		−	27.9490i		−	0.925992i	−0.886360	−	0.462996i	$-0.846774\pi$
$911$		−	27.9490i		−	0.925992i	0.886360	−	0.462996i	$-0.153226\pi$
$912$	−0.206611	−	0.651265i	−0.00684156	−	0.0215655i
$913$			58.6743i			1.94184i
$914$	16.6943	+	32.9058i	0.552198	+	1.08843i
$915$	−20.4583			−0.676330
$916$	−5.47046	−	4.00367i	−0.180749	−	0.132285i
$917$		0			0
$918$	7.16580	−	3.63547i	0.236507	−	0.119988i
$919$			8.62097i			0.284380i	0.989839	+	0.142190i	$0.0454143\pi$
$919$			8.62097i			0.284380i	−0.989839	+	0.142190i	$0.954586\pi$
$920$	53.1334	+	8.69993i	1.75176	+	0.286828i
$921$	−31.3123			−1.03177
$922$	−37.2201	+	18.8831i	−1.22578	+	0.621883i
$923$	8.03833			0.264585
$924$		0			0
$925$	−41.4655			−1.36338
$926$	3.53737	−	1.79464i	0.116245	−	0.0589754i
$927$	−16.2959			−0.535228
$928$	−7.94084	+	7.80391i	−0.260671	+	0.256176i
$929$			22.7403i			0.746086i	0.927814	+	0.373043i	$0.121686\pi$
$929$			22.7403i			0.746086i	−0.927814	+	0.373043i	$0.878314\pi$
$930$	5.99512	−	3.04154i	0.196588	−	0.0997361i
$931$		0			0
$932$	−2.24942	+	3.07353i	−0.0736823	+	0.100677i
$933$	−15.4221			−0.504897
$934$	−21.0964	−	41.5826i	−0.690294	−	1.36062i
$935$			94.2746i			3.08311i
$936$	−1.79517	+	10.9637i	−0.0586770	+	0.358360i
$937$			0.364981i			0.0119234i	0.999982	+	0.00596171i	$0.00189768\pi$
$937$			0.364981i			0.0119234i	−0.999982	+	0.00596171i	$0.998102\pi$
$938$		0			0
$939$			6.09799i			0.199000i
$940$	−11.4981	−	8.41510i	−0.375026	−	0.274470i
$941$		−	18.7799i		−	0.612207i	−0.951998	−	0.306104i	$-0.900975\pi$
$941$		−	18.7799i		−	0.612207i	0.951998	−	0.306104i	$-0.0990254\pi$
$942$	−15.6839	+	7.95703i	−0.511010	+	0.259254i
$943$	−35.8270			−1.16669
$944$	−13.2983	−	41.9180i	−0.432823	−	1.36432i
$945$		0			0
$946$	−8.14861	−	16.0616i	−0.264934	−	0.522206i
$947$			4.20227i			0.136555i	0.997666	+	0.0682776i	$0.0217504\pi$
$947$			4.20227i			0.136555i	−0.997666	+	0.0682776i	$0.978250\pi$
$948$	−23.2320	−	17.0029i	−0.754542	−	0.552227i
$949$	−40.3487			−1.30977
$950$	−0.506932	−	0.999203i	−0.0164471	−	0.0324184i
$951$	−29.7110			−0.963446
$952$		0			0
$953$	−24.9457			−0.808072			−0.404036	−	0.914743i	$-0.632393\pi$
$953$	−24.9457			−0.808072			−0.404036	+	0.914743i	$0.632393\pi$
$954$	−0.767206	−	1.51222i	−0.0248392	−	0.0489600i
$955$	−20.4760			−0.662587
$956$	−12.5470	−	9.18281i	−0.405800	−	0.296993i
$957$		−	10.5190i		−	0.340030i
$958$	15.3085	+	30.1742i	0.494594	+	0.974884i
$959$		0			0
$960$	−7.92095	+	23.5394i	−0.255648	+	0.759732i
$961$	−28.6556			−0.924373
$962$	44.2865	−	22.4682i	1.42785	−	0.724402i
$963$		−	16.7392i		−	0.539413i
$964$	19.5459	+	14.3051i	0.629531	+	0.460735i
$965$			6.07580i			0.195587i
$966$		0			0
$967$			45.6476i			1.46793i	0.679188	+	0.733964i	$0.262332\pi$
$967$			45.6476i			1.46793i	−0.679188	+	0.733964i	$0.737668\pi$
$968$	49.0263	+	8.02745i	1.57576	+	0.258012i
$969$		−	0.970522i		−	0.0311777i
$970$	4.62176	+	9.10986i	0.148396	+	0.292500i
$971$	−50.6854			−1.62657			−0.813286	−	0.581864i	$-0.802324\pi$
$971$	−50.6854			−1.62657			−0.813286	+	0.581864i	$0.802324\pi$
$972$	−1.18119	+	1.61393i	−0.0378867	+	0.0517670i
$973$		0			0
$974$	−1.03695	+	0.526083i	−0.0332260	+	0.0168568i
$975$			18.2184i			0.583455i
$976$	25.1251	−	7.97080i	0.804233	−	0.255139i
$977$	30.6897			0.981850			0.490925	−	0.871202i	$-0.336659\pi$
$977$	30.6897			0.981850			0.490925	+	0.871202i	$0.336659\pi$
$978$	−7.84898	+	3.98207i	−0.250983	+	0.127333i
$979$	31.0984			0.993909
$980$		0			0
$981$	7.72117			0.246518
$982$	28.5504	−	14.4847i	0.911080	−	0.462224i
$983$	−24.6949			−0.787646			−0.393823	−	0.919186i	$-0.628848\pi$
$983$	−24.6949			−0.787646			−0.393823	+	0.919186i	$0.628848\pi$
$984$	2.67048	−	16.3095i	0.0851319	−	0.519929i
$985$		−	1.12675i		−	0.0359012i
$986$	−14.1035	+	7.15522i	−0.449147	+	0.227868i
$987$		0			0
$988$	1.08284	+	0.792498i	0.0344497	+	0.0252127i
$989$	−14.6105			−0.464587
$990$	−10.6166	−	20.9262i	−0.337418	−	0.665078i
$991$		−	58.9597i		−	1.87292i	−0.350778	−	0.936459i	$-0.614083\pi$
$991$		−	58.9597i		−	1.87292i	0.350778	−	0.936459i	$-0.385917\pi$
$992$	−6.17765	+	6.07113i	−0.196141	+	0.192758i
$993$		−	20.1722i		−	0.640147i
$994$		0			0
$995$		−	30.6212i		−	0.970758i
$996$	−12.9675	+	17.7183i	−0.410892	+	0.561427i
$997$			25.6594i			0.812640i	0.913731	+	0.406320i	$0.133188\pi$
$997$			25.6594i			0.812640i	−0.913731	+	0.406320i	$0.866812\pi$
$998$	37.8198	−	19.1874i	1.19716	−	0.607365i
$999$	8.93993			0.282847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.b.d.391.8	yes	12
3.2	odd	2		1764.2.b.m.1567.5		12
4.3	odd	2		588.2.b.c.391.7	✓	12
7.2	even	3		588.2.o.e.31.9		24
7.3	odd	6		588.2.o.f.19.1		24
7.4	even	3		588.2.o.e.19.1		24
7.5	odd	6		588.2.o.f.31.9		24
7.6	odd	2		588.2.b.c.391.8	yes	12
12.11	even	2		1764.2.b.l.1567.6		12
21.20	even	2		1764.2.b.l.1567.5		12
28.3	even	6		588.2.o.e.19.9		24
28.11	odd	6		588.2.o.f.19.9		24
28.19	even	6		588.2.o.e.31.1		24
28.23	odd	6		588.2.o.f.31.1		24
28.27	even	2	inner	588.2.b.d.391.7	yes	12
84.83	odd	2		1764.2.b.m.1567.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.7	✓	12	4.3	odd	2
588.2.b.c.391.8	yes	12	7.6	odd	2
588.2.b.d.391.7	yes	12	28.27	even	2	inner
588.2.b.d.391.8	yes	12	1.1	even	1	trivial
588.2.o.e.19.1		24	7.4	even	3
588.2.o.e.19.9		24	28.3	even	6
588.2.o.e.31.1		24	28.19	even	6
588.2.o.e.31.9		24	7.2	even	3
588.2.o.f.19.1		24	7.3	odd	6
588.2.o.f.19.9		24	28.11	odd	6
588.2.o.f.31.1		24	28.23	odd	6
588.2.o.f.31.9		24	7.5	odd	6
1764.2.b.l.1567.5		12	21.20	even	2
1764.2.b.l.1567.6		12	12.11	even	2
1764.2.b.m.1567.5		12	3.2	odd	2
1764.2.b.m.1567.6		12	84.83	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.639847 + 1.26119i) q^{2} +1.00000 q^{3} +(-1.18119 + 1.61393i) q^{4} +3.10455i q^{5} +(0.639847 + 1.26119i) q^{6} +(-2.79126 - 0.457034i) q^{8} +1.00000 q^{9} +(-3.91542 + 1.98644i) q^{10} +5.34455i q^{11} +(-1.18119 + 1.61393i) q^{12} -3.92787i q^{13} +3.10455i q^{15} +(-1.20957 - 3.81273i) q^{16} -5.68178i q^{17} +(0.639847 + 1.26119i) q^{18} +0.170813 q^{19} +(-5.01054 - 3.66707i) q^{20} +(-6.74049 + 3.41969i) q^{22} +6.13153i q^{23} +(-2.79126 - 0.457034i) q^{24} -4.63824 q^{25} +(4.95378 - 2.51324i) q^{26} +1.00000 q^{27} -1.96817 q^{29} +(-3.91542 + 1.98644i) q^{30} -1.53115 q^{31} +(4.03463 - 3.96506i) q^{32} +5.34455i q^{33} +(7.16580 - 3.63547i) q^{34} +(-1.18119 + 1.61393i) q^{36} +8.93993 q^{37} +(0.109294 + 0.215427i) q^{38} -3.92787i q^{39} +(1.41889 - 8.66560i) q^{40} +5.84308i q^{41} +2.38285i q^{43} +(-8.62576 - 6.31294i) q^{44} +3.10455i q^{45} +(-7.73301 + 3.92324i) q^{46} +2.29477 q^{47} +(-1.20957 - 3.81273i) q^{48} +(-2.96776 - 5.84969i) q^{50} -5.68178i q^{51} +(6.33933 + 4.63957i) q^{52} -1.19905 q^{53} +(0.639847 + 1.26119i) q^{54} -16.5924 q^{55} +0.170813 q^{57} +(-1.25933 - 2.48223i) q^{58} +10.9942 q^{59} +(-5.01054 - 3.66707i) q^{60} +6.58977i q^{61} +(-0.979705 - 1.93107i) q^{62} +(7.58224 + 2.55140i) q^{64} +12.1943 q^{65} +(-6.74049 + 3.41969i) q^{66} -9.64794i q^{67} +(9.17002 + 6.71127i) q^{68} +6.13153i q^{69} +2.04649i q^{71} +(-2.79126 - 0.457034i) q^{72} -10.2724i q^{73} +(5.72019 + 11.2749i) q^{74} -4.63824 q^{75} +(-0.201763 + 0.275681i) q^{76} +(4.95378 - 2.51324i) q^{78} +14.3947i q^{79} +(11.8368 - 3.75518i) q^{80} +1.00000 q^{81} +(-7.36922 + 3.73867i) q^{82} +10.9783 q^{83} +17.6394 q^{85} +(-3.00522 + 1.52466i) q^{86} -1.96817 q^{87} +(2.44264 - 14.9180i) q^{88} -5.81871i q^{89} +(-3.91542 + 1.98644i) q^{90} +(-9.89588 - 7.24251i) q^{92} -1.53115 q^{93} +(1.46830 + 2.89414i) q^{94} +0.530298i q^{95} +(4.03463 - 3.96506i) q^{96} -2.32666i q^{97} +5.34455i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 12 q^{3} - 4 q^{4} + 4 q^{6} + 4 q^{8} + 12 q^{9} - 4 q^{12} - 4 q^{16} + 4 q^{18} - 24 q^{20} + 4 q^{24} - 12 q^{25} + 24 q^{26} + 12 q^{27} + 32 q^{29} + 16 q^{31} + 4 q^{32} + 32 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) \) 12 * q + 4 * q^2 + 12 * q^3 - 4 * q^4 + 4 * q^6 + 4 * q^8 + 12 * q^9 - 4 * q^12 - 4 * q^16 + 4 * q^18 - 24 * q^20 + 4 * q^24 - 12 * q^25 + 24 * q^26 + 12 * q^27 + 32 * q^29 + 16 * q^31 + 4 * q^32 + 32 * q^34 - 4 * q^36 + 32 * q^37 - 24 * q^38 - 32 * q^40 - 24 * q^44 + 24 * q^46 - 4 * q^48 - 28 * q^50 + 32 * q^52 - 32 * q^53 + 4 * q^54 + 16 * q^55 + 16 * q^58 - 16 * q^59 - 24 * q^60 + 8 * q^62 - 4 * q^64 - 8 * q^68 + 4 * q^72 - 32 * q^74 - 12 * q^75 - 32 * q^76 + 24 * q^78 - 16 * q^80 + 12 * q^81 + 32 * q^82 - 16 * q^83 + 16 * q^85 - 24 * q^86 + 32 * q^87 + 24 * q^88 + 16 * q^93 + 4 * q^96

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