LMFDB - Embedded newform 588.2.o.f.31.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [588,2,Mod(19,588)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(588, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("588.19"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [24,-4,12,4,0,-8,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.8
Character	$\chi$	$=$	588.31
Dual form			588.2.o.f.19.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00239545 - 1.41421i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.99999 + 0.00677535i) q^{4} +(-3.15890 + 1.82379i) q^{5} +(-1.22594 - 0.705031i) q^{6} +(0.0143727 + 2.82839i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.58679 + 4.46298i) q^{10} +(5.25694 + 3.03510i) q^{11} +(-0.994127 + 1.73543i) q^{12} +0.483253i q^{13} +3.64758i q^{15} +(3.99991 - 0.0271012i) q^{16} +(2.21053 + 1.27625i) q^{17} +(-1.22355 + 0.709180i) q^{18} +(-0.609546 - 1.05577i) q^{19} +(6.30540 - 3.66896i) q^{20} +(4.27968 - 7.44170i) q^{22} +(-3.00269 + 1.73360i) q^{23} +(2.45664 + 1.40175i) q^{24} +(4.15242 - 7.19220i) q^{25} +(0.683422 - 0.00115761i) q^{26} -1.00000 q^{27} +8.21857 q^{29} +(5.15845 - 0.00873760i) q^{30} +(-3.15625 + 5.46678i) q^{31} +(-0.0479085 - 5.65665i) q^{32} +(5.25694 - 3.03510i) q^{33} +(1.79959 - 3.12921i) q^{34} +(1.00586 + 1.72865i) q^{36} +(-0.595080 - 1.03071i) q^{37} +(-1.49162 + 0.864556i) q^{38} +(0.418509 + 0.241626i) q^{39} +(-5.20379 - 8.90838i) q^{40} +6.59422i q^{41} +3.51184i q^{43} +(-10.5344 - 6.03454i) q^{44} +(3.15890 + 1.82379i) q^{45} +(2.45887 + 4.24228i) q^{46} +(5.83110 + 10.0998i) q^{47} +(1.97648 - 3.47757i) q^{48} +(-10.1812 - 5.85517i) q^{50} +(2.21053 - 1.27625i) q^{51} +(-0.00327421 - 0.966500i) q^{52} +(-1.31391 + 2.27576i) q^{53} +(0.00239545 + 1.41421i) q^{54} -22.1415 q^{55} -1.21909 q^{57} +(-0.0196872 - 11.6228i) q^{58} +(0.580801 - 1.00598i) q^{59} +(-0.0247136 - 7.29512i) q^{60} +(0.180530 - 0.104229i) q^{61} +(7.73874 + 4.45050i) q^{62} +(-7.99959 + 0.0813030i) q^{64} +(-0.881351 - 1.52655i) q^{65} +(-4.30486 - 7.42716i) q^{66} +(1.53820 + 0.888083i) q^{67} +(-4.42968 - 2.53751i) q^{68} +3.46720i q^{69} +9.13166i q^{71} +(2.44227 - 1.42664i) q^{72} +(-5.23883 - 3.02464i) q^{73} +(-1.45621 + 0.844038i) q^{74} +(-4.15242 - 7.19220i) q^{75} +(1.22624 + 2.10739i) q^{76} +(0.340708 - 0.592439i) q^{78} +(-2.75342 + 1.58969i) q^{79} +(-12.5859 + 7.38060i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(9.32562 - 0.0157961i) q^{82} +7.49842 q^{83} -9.31044 q^{85} +(4.96648 - 0.00841243i) q^{86} +(4.10928 - 7.11749i) q^{87} +(-8.50888 + 14.9123i) q^{88} +(10.6411 - 6.14362i) q^{89} +(2.57166 - 4.47172i) q^{90} +(5.99359 - 3.48753i) q^{92} +(3.15625 + 5.46678i) q^{93} +(14.2692 - 8.27060i) q^{94} +(3.85099 + 2.22337i) q^{95} +(-4.92276 - 2.78684i) q^{96} -11.8376i q^{97} -6.07019i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 12 q^{3} + 4 q^{4} - 8 q^{6} + 8 q^{8} - 12 q^{9} - 4 q^{12} + 4 q^{16} - 4 q^{18} + 48 q^{20} + 4 q^{24} + 12 q^{25} + 24 q^{26} - 24 q^{27} + 64 q^{29} + 16 q^{31} - 4 q^{32} - 64 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) $ 24 * q - 4 * q^2 + 12 * q^3 + 4 * q^4 - 8 * q^6 + 8 * q^8 - 12 * q^9 - 4 * q^12 + 4 * q^16 - 4 * q^18 + 48 * q^20 + 4 * q^24 + 12 * q^25 + 24 * q^26 - 24 * q^27 + 64 * q^29 + 16 * q^31 - 4 * q^32 - 64 * q^34 - 8 * q^36 - 32 * q^37 - 24 * q^38 - 32 * q^40 + 24 * q^44 - 24 * q^46 + 8 * q^48 - 56 * q^50 + 32 * q^52 + 32 * q^53 + 4 * q^54 - 32 * q^55 - 16 * q^58 - 16 * q^59 + 24 * q^60 - 16 * q^62 - 8 * q^64 - 8 * q^68 - 4 * q^72 + 32 * q^74 - 12 * q^75 + 64 * q^76 + 48 * q^78 - 16 * q^80 - 12 * q^81 + 32 * q^82 + 32 * q^83 + 32 * 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 $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.00239545	−	1.41421i	−0.00169384	−	0.999999i
$2$	−0.00239545	−	1.41421i	−0.00169384	−	0.999999i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.99999	+	0.00677535i	−0.999994	+	0.00338767i
$5$	−3.15890	+	1.82379i	−1.41270	+	0.815624i	−0.995642	−	0.0932558i	$-0.970273\pi$
$5$	−3.15890	+	1.82379i	−1.41270	+	0.815624i	−0.417059	+	0.908879i	$0.636939\pi$
$6$	−1.22594	−	0.705031i	−0.500488	−	0.287828i
$7$		0			0
$7$		0			0
$8$	0.0143727	+	2.82839i	0.00508150	+	0.999987i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.58679	+	4.46298i	0.818015	+	1.41132i
$11$	5.25694	+	3.03510i	1.58503	+	0.915116i	0.994109	+	0.108385i	$0.0345679\pi$
$11$	5.25694	+	3.03510i	1.58503	+	0.915116i	0.590919	+	0.806731i	$0.298765\pi$
$12$	−0.994127	+	1.73543i	−0.286980	+	0.500975i
$13$			0.483253i			0.134030i	0.997752	+	0.0670151i	$0.0213476\pi$
$13$			0.483253i			0.134030i	−0.997752	+	0.0670151i	$0.978652\pi$
$14$		0			0
$15$			3.64758i			0.941801i
$16$	3.99991	−	0.0271012i	0.999977	−	0.00677531i
$17$	2.21053	+	1.27625i	0.536132	+	0.309536i	0.743510	−	0.668725i	$-0.233160\pi$
$17$	2.21053	+	1.27625i	0.536132	+	0.309536i	−0.207378	+	0.978261i	$0.566493\pi$
$18$	−1.22355	+	0.709180i	−0.288392	+	0.167155i
$19$	−0.609546	−	1.05577i	−0.139840	−	0.242209i	0.787596	−	0.616192i	$-0.211325\pi$
$19$	−0.609546	−	1.05577i	−0.139840	−	0.242209i	−0.927436	+	0.373983i	$0.877992\pi$
$20$	6.30540	−	3.66896i	1.40993	−	0.820405i
$21$		0			0
$22$	4.27968	−	7.44170i	0.912430	−	1.58658i
$23$	−3.00269	+	1.73360i	−0.626103	+	0.361481i	−0.779241	−	0.626724i	$-0.784395\pi$
$23$	−3.00269	+	1.73360i	−0.626103	+	0.361481i	0.153138	+	0.988205i	$0.451062\pi$
$24$	2.45664	+	1.40175i	0.501460	+	0.286131i
$25$	4.15242	−	7.19220i	0.830483	−	1.43844i
$26$	0.683422	−	0.00115761i	0.134030	−	0.000227026i
$27$	−1.00000			−0.192450
$28$		0			0
$29$	8.21857			1.52615			0.763075	−	0.646310i	$-0.223689\pi$
$29$	8.21857			1.52615			0.763075	+	0.646310i	$0.223689\pi$
$30$	5.15845	−	0.00873760i	0.941800	−	0.00159526i
$31$	−3.15625	+	5.46678i	−0.566878	+	0.981862i	0.429994	+	0.902832i	$0.358516\pi$
$31$	−3.15625	+	5.46678i	−0.566878	+	0.981862i	−0.996872	+	0.0790304i	$0.974818\pi$
$32$	−0.0479085	−	5.65665i	−0.00846910	−	0.999964i
$33$	5.25694	−	3.03510i	0.915116	−	0.528343i
$34$	1.79959	−	3.12921i	0.308627	−	0.536655i
$35$		0			0
$36$	1.00586	+	1.72865i	0.167644	+	0.288109i
$37$	−0.595080	−	1.03071i	−0.0978305	−	0.169447i	0.812956	−	0.582325i	$-0.197857\pi$
$37$	−0.595080	−	1.03071i	−0.0978305	−	0.169447i	−0.910786	+	0.412878i	$0.864524\pi$
$38$	−1.49162	+	0.864556i	−0.241972	+	0.140250i
$39$	0.418509	+	0.241626i	0.0670151	+	0.0386912i
$40$	−5.20379	−	8.90838i	−0.822792	−	1.40854i
$41$			6.59422i			1.02984i	0.857237	+	0.514922i	$0.172179\pi$
$41$			6.59422i			1.02984i	−0.857237	+	0.514922i	$0.827821\pi$
$42$		0			0
$43$			3.51184i			0.535550i	0.963481	+	0.267775i	$0.0862884\pi$
$43$			3.51184i			0.535550i	−0.963481	+	0.267775i	$0.913712\pi$
$44$	−10.5344	−	6.03454i	−1.58812	−	0.909741i
$45$	3.15890	+	1.82379i	0.470900	+	0.271875i
$46$	2.45887	+	4.24228i	0.362541	+	0.625490i
$47$	5.83110	+	10.0998i	0.850553	+	1.47320i	0.880710	+	0.473656i	$0.157066\pi$
$47$	5.83110	+	10.0998i	0.850553	+	1.47320i	−0.0301567	+	0.999545i	$0.509601\pi$
$48$	1.97648	−	3.47757i	0.285281	−	0.501944i
$49$		0			0
$50$	−10.1812	−	5.85517i	−1.43984	−	0.828046i
$51$	2.21053	−	1.27625i	0.309536	−	0.178711i
$52$	−0.00327421	−	0.966500i	−0.000454051	−	0.134029i
$53$	−1.31391	+	2.27576i	−0.180479	+	0.312600i	−0.942044	−	0.335490i	$-0.891098\pi$
$53$	−1.31391	+	2.27576i	−0.180479	+	0.312600i	0.761564	+	0.648089i	$0.224432\pi$
$54$	0.00239545	+	1.41421i	0.000325980	+	0.192450i
$55$	−22.1415			−2.98556
$56$		0			0
$57$	−1.21909			−0.161473
$58$	−0.0196872	−	11.6228i	−0.00258505	−	1.52615i
$59$	0.580801	−	1.00598i	0.0756138	−	0.130967i	−0.825739	−	0.564052i	$-0.809242\pi$
$59$	0.580801	−	1.00598i	0.0756138	−	0.130967i	0.901353	+	0.433085i	$0.142575\pi$
$60$	−0.0247136	−	7.29512i	−0.00319052	−	0.941796i
$61$	0.180530	−	0.104229i	0.0231145	−	0.0133451i	−0.488398	−	0.872621i	$-0.662419\pi$
$61$	0.180530	−	0.104229i	0.0231145	−	0.0133451i	0.511513	+	0.859276i	$0.329085\pi$
$62$	7.73874	+	4.45050i	0.982821	+	0.565215i
$63$		0			0
$64$	−7.99959	+	0.0813030i	−0.999948	+	0.0101629i
$65$	−0.881351	−	1.52655i	−0.109318	−	0.189345i
$66$	−4.30486	−	7.42716i	−0.529892	−	0.914220i
$67$	1.53820	+	0.888083i	0.187922	+	0.108497i	0.591009	−	0.806665i	$-0.298730\pi$
$67$	1.53820	+	0.888083i	0.187922	+	0.108497i	−0.403088	+	0.915161i	$0.632063\pi$
$68$	−4.42968	−	2.53751i	−0.537177	−	0.307718i
$69$			3.46720i			0.417402i
$70$		0			0
$71$			9.13166i			1.08373i	0.840466	+	0.541864i	$0.182281\pi$
$71$			9.13166i			1.08373i	−0.840466	+	0.541864i	$0.817719\pi$
$72$	2.44227	−	1.42664i	0.287824	−	0.168131i
$73$	−5.23883	−	3.02464i	−0.613159	−	0.354007i	0.161042	−	0.986948i	$-0.448515\pi$
$73$	−5.23883	−	3.02464i	−0.613159	−	0.354007i	−0.774201	+	0.632940i	$0.781848\pi$
$74$	−1.45621	+	0.844038i	−0.169281	+	0.0981174i
$75$	−4.15242	−	7.19220i	−0.479480	−	0.830483i
$76$	1.22624	+	2.10739i	0.140659	+	0.241734i
$77$		0			0
$78$	0.340708	−	0.592439i	0.0385776	−	0.0670805i
$79$	−2.75342	+	1.58969i	−0.309784	+	0.178854i	−0.646830	−	0.762634i	$-0.723906\pi$
$79$	−2.75342	+	1.58969i	−0.309784	+	0.178854i	0.337046	+	0.941488i	$0.390572\pi$
$80$	−12.5859	+	7.38060i	−1.40714	+	0.825176i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	9.32562	−	0.0157961i	1.02984	−	0.00174439i
$83$	7.49842			0.823059			0.411529	−	0.911396i	$-0.364995\pi$
$83$	7.49842			0.823059			0.411529	+	0.911396i	$0.364995\pi$
$84$		0			0
$85$	−9.31044			−1.00986
$86$	4.96648	−	0.00841243i	0.535549	−	0.000907136i
$87$	4.10928	−	7.11749i	0.440562	−	0.763075i
$88$	−8.50888	+	14.9123i	−0.907050	+	1.58966i
$89$	10.6411	−	6.14362i	1.12795	−	0.651222i	0.184531	−	0.982827i	$-0.440923\pi$
$89$	10.6411	−	6.14362i	1.12795	−	0.651222i	0.943419	+	0.331604i	$0.107590\pi$
$90$	2.57166	−	4.47172i	0.271076	−	0.471360i
$91$		0			0
$92$	5.99359	−	3.48753i	0.624875	−	0.363600i
$93$	3.15625	+	5.46678i	0.327287	+	0.566878i
$94$	14.2692	−	8.27060i	1.47176	−	0.853047i
$95$	3.85099	+	2.22337i	0.395103	+	0.228113i
$96$	−4.92276	−	2.78684i	−0.502427	−	0.284430i
$97$		−	11.8376i		−	1.20192i	−0.799277	−	0.600962i	$-0.794784\pi$
$97$		−	11.8376i		−	1.20192i	0.799277	−	0.600962i	$-0.205216\pi$
$98$		0			0
$99$		−	6.07019i		−	0.610077i
$100$	−8.25606	+	14.4124i	−0.825606	+	1.44124i
$101$	−4.95940	−	2.86331i	−0.493479	−	0.284910i	0.232538	−	0.972587i	$-0.425297\pi$
$101$	−4.95940	−	2.86331i	−0.493479	−	0.284910i	−0.726016	+	0.687677i	$0.758630\pi$
$102$	−1.81018	−	3.12310i	−0.179235	−	0.309233i
$103$	2.47654	+	4.28949i	0.244020	+	0.422656i	0.961856	−	0.273557i	$-0.0882003\pi$
$103$	2.47654	+	4.28949i	0.244020	+	0.422656i	−0.717835	+	0.696213i	$0.754867\pi$
$104$	−1.36683	+	0.00694562i	−0.134028	+	0.000681074i
$105$		0			0
$106$	3.22155	+	1.85270i	0.312905	+	0.179950i
$107$	−11.8888	+	6.86398i	−1.14933	+	0.663566i	−0.948724	−	0.316107i	$-0.897624\pi$
$107$	−11.8888	+	6.86398i	−1.14933	+	0.663566i	−0.200606	+	0.979672i	$0.564291\pi$
$108$	1.99999	−	0.00677535i	0.192449	−	0.000651958i
$109$	6.82537	−	11.8219i	0.653752	−	1.13233i	−0.328453	−	0.944520i	$-0.606527\pi$
$109$	6.82537	−	11.8219i	0.653752	−	1.13233i	0.982205	−	0.187812i	$-0.0601394\pi$
$110$	0.0530389	+	31.3128i	0.00505706	+	2.98556i
$111$	−1.19016			−0.112965
$112$		0			0
$113$	−7.11968			−0.669764			−0.334882	−	0.942260i	$-0.608696\pi$
$113$	−7.11968			−0.669764			−0.334882	+	0.942260i	$0.608696\pi$
$114$	0.00292028	+	1.72405i	0.000273509	+	0.161473i
$115$	6.32345	−	10.9525i	0.589665	−	1.02133i
$116$	−16.4370	+	0.0556837i	−1.52614	+	0.00517010i
$117$	0.418509	−	0.241626i	0.0386912	−	0.0223384i
$118$	−1.42406	−	0.818966i	−0.131095	−	0.0753919i
$119$		0			0
$120$	−10.3168	+	0.0524254i	−0.941789	+	0.00478576i
$121$	12.9236	+	22.3844i	1.17487	+	2.03494i
$122$	−0.147834	−	0.255058i	−0.0133843	−	0.0230918i
$123$	5.71076	+	3.29711i	0.514922	+	0.297290i
$124$	6.27542	−	10.9549i	0.563549	−	0.983777i
$125$			12.0546i			1.07820i
$126$		0			0
$127$			3.03609i			0.269409i	0.990886	+	0.134705i	$0.0430086\pi$
$127$			3.03609i			0.269409i	−0.990886	+	0.134705i	$0.956991\pi$
$128$	0.134142	+	11.3129i	0.0118566	+	0.999930i
$129$	3.04134	+	1.75592i	0.267775	+	0.154600i
$130$	−2.15675	+	1.25007i	−0.189159	+	0.109639i
$131$	−7.23328	−	12.5284i	−0.631974	−	1.09461i	−0.987148	−	0.159811i	$-0.948911\pi$
$131$	−7.23328	−	12.5284i	−0.631974	−	1.09461i	0.355173	−	0.934800i	$-0.384422\pi$
$132$	−10.4933	+	6.10578i	−0.913321	+	0.531440i
$133$		0			0
$134$	1.25225	−	2.17747i	0.108178	−	0.188105i
$135$	3.15890	−	1.82379i	0.271875	−	0.156967i
$136$	−3.57796	+	6.27058i	−0.306807	+	0.537698i
$137$	−5.78134	+	10.0136i	−0.493933	+	0.855517i	−0.999976	−	0.00699157i	$-0.997774\pi$
$137$	−5.78134	+	10.0136i	−0.493933	+	0.855517i	0.506043	+	0.862508i	$0.331108\pi$
$138$	4.90336	−	0.00830552i	0.417402	−	0.000707013i
$139$	17.6203			1.49453			0.747266	−	0.664525i	$-0.231366\pi$
$139$	17.6203			1.49453			0.747266	+	0.664525i	$0.231366\pi$
$140$		0			0
$141$	11.6622			0.982134
$142$	12.9141	−	0.0218744i	1.08373	−	0.00183566i
$143$	−1.46672	+	2.54043i	−0.122653	+	0.212442i
$144$	−2.02342	−	3.45047i	−0.168619	−	0.287539i
$145$	−25.9616	+	14.9889i	−2.15599	+	1.24476i
$146$	−4.26493	+	7.41606i	−0.352968	+	0.613757i
$147$		0			0
$148$	1.19714	+	2.05737i	0.0984040	+	0.169115i
$149$	−3.05734	−	5.29546i	−0.250467	−	0.433821i	0.713188	−	0.700973i	$-0.247251\pi$
$149$	−3.05734	−	5.29546i	−0.250467	−	0.433821i	−0.963654	+	0.267152i	$0.913917\pi$
$150$	−10.1613	+	5.88962i	−0.829670	+	0.480886i
$151$	−12.3346	−	7.12137i	−1.00377	−	0.579529i	−0.0944112	−	0.995533i	$-0.530097\pi$
$151$	−12.3346	−	7.12137i	−1.00377	−	0.579529i	−0.909363	+	0.416004i	$0.863430\pi$
$152$	2.97736	−	1.73921i	0.241495	−	0.141068i
$153$		−	2.55250i		−	0.206357i
$154$		0			0
$155$		−	23.0253i		−	1.84944i
$156$	−0.838651	−	0.480414i	−0.0671458	−	0.0384639i
$157$	−18.2706	−	10.5485i	−1.45815	−	0.841865i	−0.459232	−	0.888316i	$-0.651875\pi$
$157$	−18.2706	−	10.5485i	−1.45815	−	0.841865i	−0.998921	+	0.0464518i	$0.985209\pi$
$158$	2.25475	+	3.89012i	0.179379	+	0.309481i
$159$	1.31391	+	2.27576i	0.104200	+	0.180479i
$160$	10.4679	+	17.7814i	0.827559	+	1.40574i
$161$		0			0
$162$	1.22594	+	0.705031i	0.0963190	+	0.0553925i
$163$	16.5731	−	9.56851i	1.29811	−	0.749464i	0.318032	−	0.948080i	$-0.396978\pi$
$163$	16.5731	−	9.56851i	1.29811	−	0.749464i	0.980077	+	0.198617i	$0.0636448\pi$
$164$	−0.0446781	−	13.1884i	−0.00348878	−	1.02984i
$165$	−11.0708	+	19.1751i	−0.861857	+	1.49278i
$166$	−0.0179621	−	10.6044i	−0.00139413	−	0.823058i
$167$	−7.69624			−0.595553			−0.297776	−	0.954636i	$-0.596245\pi$
$167$	−7.69624			−0.595553			−0.297776	+	0.954636i	$0.596245\pi$
$168$		0			0
$169$	12.7665			0.982036
$170$	0.0223027	+	13.1669i	0.00171054	+	1.00986i
$171$	−0.609546	+	1.05577i	−0.0466132	+	0.0807364i
$172$	−0.0237939	−	7.02363i	−0.00181427	−	0.535547i
$173$	−0.713055	+	0.411682i	−0.0542125	+	0.0312996i	−0.526861	−	0.849951i	$-0.676631\pi$
$173$	−0.713055	+	0.411682i	−0.0542125	+	0.0312996i	0.472649	+	0.881251i	$0.343298\pi$
$174$	−10.0755	−	5.79435i	−0.763820	−	0.439268i
$175$		0			0
$176$	21.1095	+	11.9976i	1.59119	+	0.904356i
$177$	−0.580801	−	1.00598i	−0.0436557	−	0.0756138i
$178$	−8.71386	−	15.0340i	−0.653132	−	1.12685i
$179$	−8.20383	−	4.73649i	−0.613183	−	0.354022i	0.161027	−	0.986950i	$-0.448519\pi$
$179$	−8.20383	−	4.73649i	−0.613183	−	0.354022i	−0.774210	+	0.632928i	$0.781853\pi$
$180$	−6.33011	−	3.62616i	−0.471819	−	0.270278i
$181$		−	2.06119i		−	0.153207i	−0.997062	−	0.0766034i	$-0.975592\pi$
$181$		−	2.06119i		−	0.153207i	0.997062	−	0.0766034i	$-0.0244075\pi$
$182$		0			0
$183$		−	0.208458i		−	0.0154096i
$184$	−4.94646	−	8.46785i	−0.364658	−	0.624258i
$185$	3.75959	+	2.17060i	0.276411	+	0.159586i
$186$	7.72362	−	4.47669i	0.566323	−	0.328247i
$187$	7.74708	+	13.4183i	0.566522	+	0.981245i
$188$	−11.7306	−	20.1599i	−0.855539	−	1.47031i
$189$		0			0
$190$	3.13509	−	5.45144i	0.227443	−	0.395489i
$191$	−9.40191	+	5.42820i	−0.680298	+	0.392770i	−0.799967	−	0.600043i	$-0.795150\pi$
$191$	−9.40191	+	5.42820i	−0.680298	+	0.392770i	0.119669	+	0.992814i	$0.461817\pi$
$192$	−3.92938	+	6.96850i	−0.283579	+	0.502908i
$193$	−4.85673	+	8.41210i	−0.349595	+	0.605517i	−0.986178	−	0.165692i	$-0.947014\pi$
$193$	−4.85673	+	8.41210i	−0.349595	+	0.605517i	0.636582	+	0.771209i	$0.280348\pi$
$194$	−16.7409	+	0.0283564i	−1.20192	+	0.00203587i
$195$	−1.76270			−0.126230
$196$		0			0
$197$	−15.9300			−1.13496			−0.567481	−	0.823386i	$-0.692082\pi$
$197$	−15.9300			−1.13496			−0.567481	+	0.823386i	$0.692082\pi$
$198$	−8.58454	+	0.0145409i	−0.610077	+	0.00103337i
$199$	−5.02859	+	8.70978i	−0.356467	+	0.617420i	−0.987368	−	0.158444i	$-0.949352\pi$
$199$	−5.02859	+	8.70978i	−0.356467	+	0.617420i	0.630901	+	0.775864i	$0.282686\pi$
$200$	20.4020	+	11.6413i	1.44264	+	0.823163i
$201$	1.53820	−	0.888083i	0.108497	−	0.0626405i
$202$	−4.03745	+	7.02050i	−0.284074	+	0.493961i
$203$		0			0
$204$	−4.41238	+	2.56746i	−0.308929	+	0.179758i
$205$	−12.0265	−	20.8304i	−0.839965	−	1.45486i
$206$	6.06031	−	3.51262i	0.422242	−	0.244736i
$207$	3.00269	+	1.73360i	0.208701	+	0.120494i
$208$	0.0130967	+	1.93297i	0.000908096	+	0.134027i
$209$		−	7.40013i		−	0.511878i
$210$		0			0
$211$		−	1.03227i		−	0.0710647i	−0.999369	−	0.0355324i	$-0.988687\pi$
$211$		−	1.03227i		−	0.0710647i	0.999369	−	0.0355324i	$-0.0113127\pi$
$212$	2.61239	−	4.56039i	0.179419	−	0.313209i
$213$	7.90825	+	4.56583i	0.541864	+	0.312846i
$214$	9.73559	+	16.7968i	0.665511	+	1.14820i
$215$	−6.40485	−	11.0935i	−0.436807	−	0.756572i
$216$	−0.0143727	−	2.82839i	−0.000977935	−	0.192448i
$217$		0			0
$218$	−16.7350	−	9.62420i	−1.13344	−	0.651833i
$219$	−5.23883	+	3.02464i	−0.354007	+	0.204386i
$220$	44.2828	−	0.150016i	2.98554	−	0.0101141i
$221$	−0.616751	+	1.06824i	−0.0414871	+	0.0718578i
$222$	0.00285097	+	1.68314i	0.000191345	+	0.112965i
$223$	9.57250			0.641022			0.320511	−	0.947245i	$-0.396145\pi$
$223$	9.57250			0.641022			0.320511	+	0.947245i	$0.396145\pi$
$224$		0			0
$225$	−8.30483			−0.553656
$226$	0.0170549	+	10.0687i	0.00113447	+	0.669763i
$227$	−5.57692	+	9.65951i	−0.370153	+	0.641124i	−0.989589	−	0.143923i	$-0.954028\pi$
$227$	−5.57692	+	9.65951i	−0.370153	+	0.641124i	0.619436	+	0.785048i	$0.287362\pi$
$228$	2.43817	−	0.00825978i	0.161472	−	0.000547017i
$229$	8.77151	−	5.06423i	0.579637	−	0.334654i	−0.181352	−	0.983418i	$-0.558047\pi$
$229$	8.77151	−	5.06423i	0.579637	−	0.334654i	0.760989	+	0.648764i	$0.224714\pi$
$230$	−15.5043	−	8.91646i	−1.02233	−	0.587934i
$231$		0			0
$232$	0.118123	+	23.2453i	0.00775513	+	1.52613i
$233$	−6.32072	−	10.9478i	−0.414084	−	0.717215i	0.581248	−	0.813727i	$-0.302565\pi$
$233$	−6.32072	−	10.9478i	−0.414084	−	0.717215i	−0.995332	+	0.0965119i	$0.969231\pi$
$234$	−0.342713	−	0.591282i	−0.0224039	−	0.0386533i
$235$	−36.8397	−	21.2694i	−2.40316	−	1.38746i
$236$	−1.15478	+	2.01588i	−0.0751697	+	0.131222i
$237$			3.17938i			0.206523i
$238$		0			0
$239$			5.46050i			0.353211i	0.984282	+	0.176605i	$0.0565116\pi$
$239$			5.46050i			0.353211i	−0.984282	+	0.176605i	$0.943488\pi$
$240$	0.0988539	+	14.5900i	0.00638099	+	0.941779i
$241$	11.8106	+	6.81887i	0.760790	+	0.439242i	0.829579	−	0.558389i	$-0.188580\pi$
$241$	11.8106	+	6.81887i	0.760790	+	0.439242i	−0.0687894	+	0.997631i	$0.521914\pi$
$242$	31.6253	−	18.3304i	2.03295	−	1.17832i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−0.360351	+	0.209680i	−0.0230691	+	0.0134234i
$245$		0			0
$246$	4.64913	−	8.08412i	0.296418	−	0.515425i
$247$	0.510201	−	0.294565i	0.0324633	−	0.0187427i
$248$	−15.5075	−	8.84852i	−0.984730	−	0.561882i
$249$	3.74921	−	6.49383i	0.237597	−	0.411529i
$250$	17.0478	−	0.0288763i	1.07820	−	0.00182630i
$251$	28.2425			1.78265			0.891324	−	0.453367i	$-0.149777\pi$
$251$	28.2425			1.78265			0.891324	+	0.453367i	$0.149777\pi$
$252$		0			0
$253$	−21.0466			−1.32319
$254$	4.29367	−	0.00727280i	0.269409	−	0.000456336i
$255$	−4.65522	+	8.06307i	−0.291521	+	0.504929i
$256$	15.9985	−	0.216805i	0.999908	−	0.0135503i
$257$	17.4613	−	10.0813i	1.08920	−	0.628852i	0.155840	−	0.987782i	$-0.450192\pi$
$257$	17.4613	−	10.0813i	1.08920	−	0.628852i	0.933364	+	0.358930i	$0.116858\pi$
$258$	2.47595	−	4.30530i	0.154146	−	0.268036i
$259$		0			0
$260$	1.77304	+	3.04710i	0.109959	+	0.188973i
$261$	−4.10928	−	7.11749i	−0.254358	−	0.440562i
$262$	−17.7005	+	10.2594i	−1.09354	+	0.633827i
$263$	10.8326	+	6.25419i	0.667965	+	0.385650i	0.795305	−	0.606209i	$-0.207311\pi$
$263$	10.8326	+	6.25419i	0.667965	+	0.385650i	−0.127340	+	0.991859i	$0.540644\pi$
$264$	8.66000	+	14.8251i	0.532986	+	0.912419i
$265$		−	9.58518i		−	0.588813i
$266$		0			0
$267$		−	12.2872i		−	0.751967i
$268$	−3.08241	−	1.76573i	−0.188288	−	0.107859i
$269$	11.3057	+	6.52738i	0.689324	+	0.397981i	0.803359	−	0.595496i	$-0.203044\pi$
$269$	11.3057	+	6.52738i	0.689324	+	0.397981i	−0.114035	+	0.993477i	$0.536378\pi$
$270$	−2.58679	−	4.46298i	−0.157427	−	0.271608i
$271$	5.14672	+	8.91437i	0.312641	+	0.541510i	0.978933	−	0.204181i	$-0.0654531\pi$
$271$	5.14672	+	8.91437i	0.312641	+	0.541510i	−0.666292	+	0.745691i	$0.732120\pi$
$272$	8.87650	+	5.04497i	0.538217	+	0.305896i
$273$		0			0
$274$	14.1752	+	8.15205i	0.856352	+	0.492483i
$275$	43.6580	−	25.2060i	2.63268	−	1.51998i
$276$	−0.0234915	−	6.93437i	−0.00141402	−	0.417400i
$277$	9.48111	−	16.4218i	0.569665	−	0.986689i	−0.426934	−	0.904283i	$-0.640406\pi$
$277$	9.48111	−	16.4218i	0.569665	−	0.986689i	0.996599	−	0.0824058i	$-0.0262604\pi$
$278$	−0.0422085	−	24.9188i	−0.00253150	−	1.49453i
$279$	6.31249			0.377919
$280$		0			0
$281$	17.5144			1.04482			0.522412	−	0.852693i	$-0.325032\pi$
$281$	17.5144			1.04482			0.522412	+	0.852693i	$0.325032\pi$
$282$	−0.0279362	−	16.4928i	−0.00166358	−	0.982133i
$283$	−9.47095	+	16.4042i	−0.562990	+	0.975127i	0.434244	+	0.900795i	$0.357016\pi$
$283$	−9.47095	+	16.4042i	−0.562990	+	0.975127i	−0.997234	+	0.0743313i	$0.976318\pi$
$284$	−0.0618702	−	18.2632i	−0.00367132	−	1.08372i
$285$	3.85099	−	2.22337i	0.228113	−	0.131701i
$286$	3.59622	+	2.06816i	0.212649	+	0.122293i
$287$		0			0
$288$	−4.87485	+	2.86982i	−0.287253	+	0.169106i
$289$	−5.24238	−	9.08007i	−0.308375	−	0.534122i
$290$	21.2597	+	36.6793i	1.24841	+	2.15388i
$291$	−10.2517	−	5.91879i	−0.600962	−	0.346966i
$292$	10.4981	+	6.01375i	0.614354	+	0.351928i
$293$		−	25.2760i		−	1.47664i	−0.674451	−	0.738320i	$-0.735620\pi$
$293$		−	25.2760i		−	1.47664i	0.674451	−	0.738320i	$-0.264380\pi$
$294$		0			0
$295$			4.23703i			0.246690i
$296$	2.90669	−	1.69793i	0.168948	−	0.0986903i
$297$	−5.25694	−	3.03510i	−0.305039	−	0.176114i
$298$	−7.48158	+	4.33641i	−0.433396	+	0.251201i
$299$	−0.837768	−	1.45106i	−0.0484494	−	0.0839167i
$300$	8.35352	+	14.3562i	0.482290	+	0.828854i
$301$		0			0
$302$	−10.0416	+	17.4608i	−0.577828	+	1.00475i
$303$	−4.95940	+	2.86331i	−0.284910	+	0.164493i
$304$	−2.46674	−	4.20644i	−0.141477	−	0.241256i
$305$	−0.380183	+	0.658497i	−0.0217692	+	0.0377054i
$306$	−3.60977	+	0.00611438i	−0.206357	+	0.000349536i
$307$	10.2457			0.584750			0.292375	−	0.956304i	$-0.405554\pi$
$307$	10.2457			0.584750			0.292375	+	0.956304i	$0.405554\pi$
$308$		0			0
$309$	4.95307			0.281770
$310$	−32.5627	+	0.0551560i	−1.84943	+	0.00313265i
$311$	15.1919	−	26.3131i	0.861451	−	1.49208i	−0.00907691	−	0.999959i	$-0.502889\pi$
$311$	15.1919	−	26.3131i	0.861451	−	1.49208i	0.870528	−	0.492119i	$-0.163777\pi$
$312$	−0.677399	+	1.18718i	−0.0383501	+	0.0672108i
$313$	−14.8277	+	8.56075i	−0.838108	+	0.483882i	−0.856621	−	0.515946i	$-0.827440\pi$
$313$	−14.8277	+	8.56075i	−0.838108	+	0.483882i	0.0185123	+	0.999829i	$0.494107\pi$
$314$	−14.8741	+	25.8638i	−0.839394	+	1.45958i
$315$		0			0
$316$	5.49605	−	3.19802i	0.309177	−	0.179903i
$317$	6.18286	+	10.7090i	0.347264	+	0.601478i	0.985762	−	0.168145i	$-0.0537775\pi$
$317$	6.18286	+	10.7090i	0.347264	+	0.601478i	−0.638499	+	0.769623i	$0.720444\pi$
$318$	3.21526	−	1.86360i	0.180303	−	0.104505i
$319$	43.2045	+	24.9442i	2.41899	+	1.39660i
$320$	25.1216	−	14.8464i	1.40434	−	0.829938i
$321$			13.7280i			0.766220i
$322$		0			0
$323$		−	3.11173i		−	0.173141i
$324$	0.994127	−	1.73543i	0.0552293	−	0.0964127i
$325$	3.47565	+	2.00667i	0.192794	+	0.111310i
$326$	−13.5716	−	23.4150i	−0.751661	−	1.29684i
$327$	−6.82537	−	11.8219i	−0.377444	−	0.653752i
$328$	−18.6510	+	0.0947764i	−1.02983	+	0.00523315i
$329$		0			0
$330$	27.1442	+	15.6105i	1.49424	+	0.859327i
$331$	−6.65278	+	3.84098i	−0.365670	+	0.211120i	−0.671565	−	0.740946i	$-0.734378\pi$
$331$	−6.65278	+	3.84098i	−0.365670	+	0.211120i	0.305895	+	0.952065i	$0.401044\pi$
$332$	−14.9968	+	0.0508044i	−0.823054	+	0.00278826i
$333$	−0.595080	+	1.03071i	−0.0326102	+	0.0564825i
$334$	0.0184360	+	10.8841i	0.00100877	+	0.595552i
$335$	−6.47871			−0.353969
$336$		0			0
$337$	−13.3863			−0.729201			−0.364600	−	0.931164i	$-0.618794\pi$
$337$	−13.3863			−0.729201			−0.364600	+	0.931164i	$0.618794\pi$
$338$	−0.0305815	−	18.0545i	−0.00166341	−	0.982035i
$339$	−3.55984	+	6.16583i	−0.193344	+	0.334882i
$340$	18.6208	−	0.0630815i	1.00985	−	0.00342107i
$341$	−33.1844	+	19.1590i	−1.79704	+	1.03752i
$342$	1.49454	+	0.859498i	0.0808152	+	0.0464763i
$343$		0			0
$344$	−9.93284	+	0.0504744i	−0.535543	+	0.00272140i
$345$	−6.32345	−	10.9525i	−0.340443	−	0.589665i
$346$	0.583914	+	1.00742i	0.0313914	+	0.0541595i
$347$	−27.6076	−	15.9393i	−1.48206	−	0.855666i	−0.482264	−	0.876026i	$-0.660185\pi$
$347$	−27.6076	−	15.9393i	−1.48206	−	0.855666i	−0.999793	+	0.0203606i	$0.993519\pi$
$348$	−8.17030	+	14.2627i	−0.437974	+	0.764563i
$349$		−	9.51634i		−	0.509398i	−0.967020	−	0.254699i	$-0.918024\pi$
$349$		−	9.51634i		−	0.509398i	0.967020	−	0.254699i	$-0.0819764\pi$
$350$		0			0
$351$		−	0.483253i		−	0.0257941i
$352$	16.9166	−	29.8821i	0.901659	−	1.59272i
$353$	12.2392	+	7.06628i	0.651425	+	0.376100i	0.789002	−	0.614391i	$-0.210598\pi$
$353$	12.2392	+	7.06628i	0.651425	+	0.376100i	−0.137577	+	0.990491i	$0.543931\pi$
$354$	−1.42127	+	0.823785i	−0.0755398	+	0.0437837i
$355$	−16.6542	−	28.8460i	−0.883915	−	1.53099i
$356$	−21.2404	+	12.3593i	−1.12574	+	0.655040i
$357$		0			0
$358$	−6.67874	+	11.6133i	−0.352982	+	0.613782i
$359$	19.4557	−	11.2328i	1.02684	−	0.592843i	0.110759	−	0.993847i	$-0.464672\pi$
$359$	19.4557	−	11.2328i	1.02684	−	0.592843i	0.916076	+	0.401004i	$0.131339\pi$
$360$	−5.11299	+	8.96081i	−0.269478	+	0.472276i
$361$	8.75691	−	15.1674i	0.460890	−	0.798285i
$362$	−2.91495	+	0.00493747i	−0.153207	+	0.000259508i
$363$	25.8472			1.35663
$364$		0			0
$365$	22.0652			1.15495
$366$	−0.294803		0.000499351i	−0.0154096		2.61015e-5i
$367$	5.99956	−	10.3915i	0.313174	−	0.542434i	−0.665873	−	0.746065i	$-0.731941\pi$
$367$	5.99956	−	10.3915i	0.313174	−	0.542434i	0.979048	+	0.203631i	$0.0652742\pi$
$368$	−11.9635	+	7.01562i	−0.623640	+	0.365715i
$369$	5.71076	−	3.29711i	0.297290	−	0.171641i
$370$	3.06068	−	5.32206i	0.159117	−	0.276680i
$371$		0			0
$372$	−6.34949	−	10.9121i	−0.329206	−	0.565766i
$373$	−2.81380	−	4.87365i	−0.145693	−	0.252348i	0.783938	−	0.620839i	$-0.213208\pi$
$373$	−2.81380	−	4.87365i	−0.145693	−	0.252348i	−0.929631	+	0.368491i	$0.879875\pi$
$374$	18.9578	−	10.9881i	0.980284	−	0.568184i
$375$	10.4396	+	6.02732i	0.539100	+	0.311250i
$376$	−28.4823	+	16.6378i	−1.46886	+	0.858028i
$377$			3.97165i			0.204550i
$378$		0			0
$379$		−	21.3356i		−	1.09594i	−0.836500	−	0.547968i	$-0.815402\pi$
$379$		−	21.3356i		−	1.09594i	0.836500	−	0.547968i	$-0.184598\pi$
$380$	−7.71699	−	4.42062i	−0.395873	−	0.226773i
$381$	2.62933	+	1.51804i	0.134705	+	0.0777718i
$382$	7.69914	+	13.2833i	0.393922	+	0.679632i
$383$	−3.77595	−	6.54013i	−0.192942	−	0.334185i	0.753282	−	0.657698i	$-0.228470\pi$
$383$	−3.77595	−	6.54013i	−0.192942	−	0.334185i	−0.946224	+	0.323513i	$0.895136\pi$
$384$	9.86434	+	5.54029i	0.503388	+	0.282727i
$385$		0			0
$386$	11.9081	+	6.84829i	0.606108	+	0.348569i
$387$	3.04134	−	1.75592i	0.154600	−	0.0892583i
$388$	0.0802038	+	23.6750i	0.00407173	+	1.20192i
$389$	1.32531	−	2.29550i	0.0671957	−	0.116386i	−0.830470	−	0.557063i	$-0.811928\pi$
$389$	1.32531	−	2.29550i	0.0671957	−	0.116386i	0.897666	+	0.440677i	$0.145261\pi$
$390$	0.00422247	+	2.49283i	0.000213813	+	0.126230i
$391$	−8.85003			−0.447565
$392$		0			0
$393$	−14.4666			−0.729741
$394$	0.0381594	+	22.5283i	0.00192244	+	1.13496i
$395$	5.79852	−	10.0433i	0.291755	−	0.505335i
$396$	0.0411277	+	12.1403i	0.00206674	+	0.610074i
$397$	16.1515	−	9.32508i	0.810621	−	0.468012i	−0.0365505	−	0.999332i	$-0.511637\pi$
$397$	16.1515	−	9.32508i	0.810621	−	0.468012i	0.847171	+	0.531320i	$0.178304\pi$
$398$	12.3295	+	7.09063i	0.618023	+	0.355421i
$399$		0			0
$400$	16.4144	−	28.8807i	0.820718	−	1.44403i
$401$	11.9242	+	20.6533i	0.595464	+	1.03137i	0.993481	+	0.113996i	$0.0363652\pi$
$401$	11.9242	+	20.6533i	0.595464	+	1.03137i	−0.398017	+	0.917378i	$0.630302\pi$
$402$	−1.25962	−	2.17322i	−0.0628242	−	0.108390i
$403$	−2.64184	−	1.52526i	−0.131599	−	0.0759788i
$404$	9.93814	+	5.69299i	0.494441	+	0.283237i
$405$		−	3.64758i		−	0.181250i
$406$		0			0
$407$		−	7.22450i		−	0.358105i
$408$	3.64150	+	6.23389i	0.180281	+	0.308624i
$409$	−15.0922	−	8.71346i	−0.746259	−	0.430853i	0.0780817	−	0.996947i	$-0.475121\pi$
$409$	−15.0922	−	8.71346i	−0.746259	−	0.430853i	−0.824341	+	0.566094i	$0.808454\pi$
$410$	−29.4299	+	17.0579i	−1.45344	+	0.842428i
$411$	5.78134	+	10.0136i	0.285172	+	0.493933i
$412$	−4.98211	−	8.56215i	−0.245451	−	0.421827i
$413$		0			0
$414$	2.44449	−	4.25059i	0.120140	−	0.208905i
$415$	−23.6867	+	13.6755i	−1.16274	+	0.671306i
$416$	2.73359	−	0.0231519i	0.134025	−	0.00113512i
$417$	8.81014	−	15.2596i	0.431434	−	0.747266i
$418$	−10.4653	+	0.0177266i	−0.511877	+	0.000867039i
$419$	−26.6148			−1.30022			−0.650109	−	0.759841i	$-0.725277\pi$
$419$	−26.6148			−1.30022			−0.650109	+	0.759841i	$0.725277\pi$
$420$		0			0
$421$	17.2196			0.839234			0.419617	−	0.907701i	$-0.362164\pi$
$421$	17.2196			0.839234			0.419617	+	0.907701i	$0.362164\pi$
$422$	−1.45985	+	0.00247276i	−0.0710646	+	0.000120372i
$423$	5.83110	−	10.0998i	0.283518	−	0.491067i
$424$	−6.45562	−	3.68354i	−0.313513	−	0.178889i
$425$	18.3581	−	10.5990i	0.890497	−	0.514129i
$426$	6.43811	−	11.1949i	0.311927	−	0.542394i
$427$		0			0
$428$	23.7309	−	13.8084i	1.14707	−	0.667455i
$429$	1.46672	+	2.54043i	0.0708138	+	0.122653i
$430$	−15.6732	+	9.08439i	−0.755831	+	0.438088i
$431$	17.0459	+	9.84148i	0.821074	+	0.474047i	0.850787	−	0.525511i	$-0.176126\pi$
$431$	17.0459	+	9.84148i	0.821074	+	0.474047i	−0.0297126	+	0.999558i	$0.509459\pi$
$432$	−3.99991	+	0.0271012i	−0.192446	+	0.00130391i
$433$		−	6.43311i		−	0.309156i	−0.987981	−	0.154578i	$-0.950598\pi$
$433$		−	6.43311i		−	0.309156i	0.987981	−	0.154578i	$-0.0494017\pi$
$434$		0			0
$435$			29.9779i			1.43733i
$436$	−13.5706	+	23.6899i	−0.649912	+	1.13454i
$437$	3.66055	+	2.11342i	0.175108	+	0.101099i
$438$	4.29003	+	7.40157i	0.204986	+	0.353661i
$439$	−3.47675	−	6.02190i	−0.165936	−	0.287410i	0.771051	−	0.636773i	$-0.219731\pi$
$439$	−3.47675	−	6.02190i	−0.165936	−	0.287410i	−0.936987	+	0.349363i	$0.886398\pi$
$440$	−0.318232	−	62.6248i	−0.0151711	−	2.98552i
$441$		0			0
$442$	1.51220	+	0.869657i	0.0719280	+	0.0413654i
$443$	−6.74126	+	3.89207i	−0.320287	+	0.184918i	−0.651520	−	0.758631i	$-0.725868\pi$
$443$	−6.74126	+	3.89207i	−0.320287	+	0.184918i	0.331234	+	0.943549i	$0.392535\pi$
$444$	2.38031	−	0.00806375i	0.112964	−	0.000382688i
$445$	−22.4093	+	38.8141i	−1.06230	+	1.83996i
$446$	−0.0229305	−	13.5375i	−0.00108579	−	0.641021i
$447$	−6.11467			−0.289214
$448$		0			0
$449$	−13.4404			−0.634290			−0.317145	−	0.948377i	$-0.602724\pi$
$449$	−13.4404			−0.634290			−0.317145	+	0.948377i	$0.602724\pi$
$450$	0.0198938	+	11.7448i	0.000937804	+	0.553655i
$451$	−20.0141	+	34.6654i	−0.942427	+	1.63233i
$452$	14.2393	−	0.0482384i	0.669760	−	0.00226894i
$453$	−12.3346	+	7.12137i	−0.579529	+	0.334591i
$454$	13.6740	+	7.86381i	0.641750	+	0.369067i
$455$		0			0
$456$	−0.0175216	−	3.44807i	−0.000820524	−	0.161471i
$457$	0.581825	+	1.00775i	0.0272166	+	0.0471406i	0.879313	−	0.476244i	$-0.158002\pi$
$457$	0.581825	+	1.00775i	0.0272166	+	0.0471406i	−0.852096	+	0.523385i	$0.824669\pi$
$458$	−7.18291	−	12.3926i	−0.335635	−	0.579070i
$459$	−2.21053	−	1.27625i	−0.103179	−	0.0595702i
$460$	−12.5726	+	21.9478i	−0.586201	+	1.02332i
$461$		−	21.4211i		−	0.997678i	−0.866695	−	0.498839i	$-0.833760\pi$
$461$		−	21.4211i		−	0.997678i	0.866695	−	0.498839i	$-0.166240\pi$
$462$		0			0
$463$			14.4408i			0.671119i	0.942019	+	0.335560i	$0.108925\pi$
$463$			14.4408i			0.671119i	−0.942019	+	0.335560i	$0.891075\pi$
$464$	32.8735	−	0.222733i	1.52611	−	0.0103401i
$465$	−19.9405	−	11.5127i	−0.924719	−	0.533887i
$466$	−15.4674	+	8.96506i	−0.716512	+	0.415298i
$467$	14.8830	+	25.7780i	0.688701	+	1.19287i	0.972258	+	0.233910i	$0.0751521\pi$
$467$	14.8830	+	25.7780i	0.688701	+	1.19287i	−0.283557	+	0.958955i	$0.591515\pi$
$468$	−0.835376	+	0.486085i	−0.0386153	+	0.0224693i
$469$		0			0
$470$	−29.9912	+	52.1500i	−1.38339	+	2.40550i
$471$	−18.2706	+	10.5485i	−0.841865	+	0.486051i
$472$	2.85364	+	1.62827i	0.131350	+	0.0749474i
$473$	−10.6588	+	18.4615i	−0.490090	+	0.848861i
$474$	4.49632	−	0.00761605i	0.206523	−	0.000349817i
$475$	−10.1244			−0.464538
$476$		0			0
$477$	2.62782			0.120320
$478$	7.72231	−	0.0130804i	0.353210	−	0.000598282i
$479$	−14.1776	+	24.5563i	−0.647790	+	1.12201i	0.335859	+	0.941912i	$0.390973\pi$
$479$	−14.1776	+	24.5563i	−0.647790	+	1.12201i	−0.983649	+	0.180094i	$0.942360\pi$
$480$	20.6331	−	0.174750i	0.941767	−	0.00797621i
$481$	0.498093	−	0.287574i	0.0227111	−	0.0131122i
$482$	9.61504	−	16.7191i	0.437953	−	0.761533i
$483$		0			0
$484$	−25.9988	−	44.6809i	−1.18176	−	2.03095i
$485$	21.5893	+	37.3937i	0.980318	+	1.69796i
$486$	1.22355	−	0.709180i	0.0555011	−	0.0321691i
$487$	−8.28601	−	4.78393i	−0.375475	−	0.216781i	0.300373	−	0.953822i	$-0.402889\pi$
$487$	−8.28601	−	4.78393i	−0.375475	−	0.216781i	−0.675848	+	0.737041i	$0.736222\pi$
$488$	0.297395	+	0.509111i	0.0134624	+	0.0230464i
$489$		−	19.1370i		−	0.865406i
$490$		0			0
$491$			17.7521i			0.801141i	0.916266	+	0.400571i	$0.131188\pi$
$491$			17.7521i			0.801141i	−0.916266	+	0.400571i	$0.868812\pi$
$492$	−11.4438	−	6.55549i	−0.515926	−	0.295544i
$493$	18.1674	+	10.4889i	0.818217	+	0.472398i
$494$	−0.417799	−	0.720827i	−0.0187977	−	0.0324315i
$495$	11.0708	+	19.1751i	0.497593	+	0.861857i
$496$	−12.4765	+	21.9521i	−0.560213	+	0.985681i
$497$		0			0
$498$	−9.19262	−	5.28662i	−0.411931	−	0.236899i
$499$	8.14160	−	4.70056i	0.364468	−	0.210426i	−0.306571	−	0.951848i	$-0.599182\pi$
$499$	8.14160	−	4.70056i	0.364468	−	0.210426i	0.671039	+	0.741422i	$0.265848\pi$
$500$	−0.0816744	−	24.1092i	−0.00365259	−	1.07819i
$501$	−3.84812	+	6.66514i	−0.171921	+	0.297776i
$502$	−0.0676534	−	39.9408i	−0.00301952	−	1.78265i
$503$	−40.9278			−1.82488			−0.912440	−	0.409211i	$-0.865804\pi$
$503$	−40.9278			−1.82488			−0.912440	+	0.409211i	$0.865804\pi$
$504$		0			0
$505$	20.8883			0.929517
$506$	0.0504161	+	29.7643i	0.00224127	+	1.32319i
$507$	6.38323	−	11.0561i	0.283489	−	0.491018i
$508$	−0.0205706	−	6.07214i	−0.000912671	−	0.269408i
$509$	−12.4798	+	7.20520i	−0.553156	+	0.319365i	−0.750394	−	0.660991i	$-0.770136\pi$
$509$	−12.4798	+	7.20520i	−0.553156	+	0.319365i	0.197238	+	0.980356i	$0.436803\pi$
$510$	11.4140	+	6.56415i	0.505422	+	0.290665i
$511$		0			0
$512$	−0.344932	−	22.6248i	−0.0152440	−	0.999884i
$513$	0.609546	+	1.05577i	0.0269121	+	0.0466132i
$514$	−14.2989	−	24.6698i	−0.630696	−	1.08814i
$515$	−15.6462	−	9.03336i	−0.689456	−	0.398058i
$516$	−6.09454	−	3.49121i	−0.268297	−	0.153692i
$517$			70.7918i			3.11342i
$518$		0			0
$519$			0.823365i			0.0361417i
$520$	4.30500	−	2.51475i	0.188787	−	0.110279i
$521$	9.18855	+	5.30501i	0.402558	+	0.232417i	0.687587	−	0.726102i	$-0.258670\pi$
$521$	9.18855	+	5.30501i	0.402558	+	0.232417i	−0.285029	+	0.958519i	$0.592003\pi$
$522$	−10.0558	+	5.82845i	−0.440130	+	0.255104i
$523$	18.1358	+	31.4121i	0.793022	+	1.37355i	0.924088	+	0.382181i	$0.124827\pi$
$523$	18.1358	+	31.4121i	0.793022	+	1.37355i	−0.131066	+	0.991374i	$0.541840\pi$
$524$	14.5514	+	25.0077i	0.635679	+	1.09246i
$525$		0			0
$526$	8.81880	−	15.3345i	0.384518	−	0.668618i
$527$	−13.9539	+	8.05631i	−0.607843	+	0.350938i
$528$	20.9450	−	12.2826i	0.911515	−	0.534531i
$529$	−5.48925	+	9.50766i	−0.238663	+	0.413377i
$530$	−13.5555	+	0.0229608i	−0.588812	+	0.000997355i
$531$	−1.16160			−0.0504092
$532$		0			0
$533$	−3.18667			−0.138030
$534$	−17.3767	+	0.0294335i	−0.751965	+	0.00127371i
$535$	25.0369	−	43.3652i	1.08244	−	1.87484i
$536$	−2.48974	+	4.36341i	−0.107540	+	0.188471i
$537$	−8.20383	+	4.73649i	−0.354022	+	0.204394i
$538$	9.20401	−	16.0044i	0.396813	−	0.689997i
$539$		0			0
$540$	−6.30540	+	3.66896i	−0.271341	+	0.157887i
$541$	11.8173	+	20.4682i	0.508065	+	0.879995i	0.999956	+	0.00933811i	$0.00297245\pi$
$541$	11.8173	+	20.4682i	0.508065	+	0.879995i	−0.491891	+	0.870657i	$0.663694\pi$
$542$	12.5945	−	7.29990i	0.540979	−	0.313558i
$543$	−1.78504	−	1.03059i	−0.0766034	−	0.0442270i
$544$	7.11339	−	12.5653i	0.304984	−	0.538734i
$545$			49.7922i			2.13286i
$546$		0			0
$547$		−	40.9096i		−	1.74917i	−0.484875	−	0.874583i	$-0.661135\pi$
$547$		−	40.9096i		−	1.74917i	0.484875	−	0.874583i	$-0.338865\pi$
$548$	11.4948	−	20.0662i	0.491032	−	0.857185i
$549$	−0.180530	−	0.104229i	−0.00770482	−	0.00444838i
$550$	−35.7512	−	61.6813i	−1.52443	−	2.63010i
$551$	−5.00960	−	8.67688i	−0.213416	−	0.369647i
$552$	−9.80661	+	0.0498329i	−0.417397	+	0.00212103i
$553$		0			0
$554$	−23.2466	−	13.3690i	−0.987652	−	0.567993i
$555$	3.75959	−	2.17060i	0.159586	−	0.0921369i
$556$	−35.2404	+	0.119384i	−1.49452	+	0.00506299i
$557$	19.1391	−	33.1498i	0.810948	−	1.40460i	−0.101254	−	0.994861i	$-0.532285\pi$
$557$	19.1391	−	33.1498i	0.810948	−	1.40460i	0.912202	−	0.409742i	$-0.134381\pi$
$558$	−0.0151213	−	8.92720i	−0.000640134	−	0.377918i
$559$	−1.69710			−0.0717799
$560$		0			0
$561$	15.4942			0.654164
$562$	−0.0419550	−	24.7691i	−0.00176976	−	1.04482i
$563$	2.28008	−	3.94921i	0.0960939	−	0.166439i	−0.813971	−	0.580906i	$-0.802698\pi$
$563$	2.28008	−	3.94921i	0.0960939	−	0.166439i	0.910065	+	0.414466i	$0.136032\pi$
$564$	−23.3243	+	0.0790155i	−0.982129	+	0.00332715i
$565$	22.4903	−	12.9848i	0.946176	−	0.546275i
$566$	23.2216	+	13.3546i	0.976079	+	0.561337i
$567$		0			0
$568$	−25.8279	+	0.131246i	−1.08371	+	0.00550697i
$569$	−21.9078	−	37.9455i	−0.918425	−	1.59076i	−0.801808	−	0.597581i	$-0.796129\pi$
$569$	−21.9078	−	37.9455i	−0.918425	−	1.59076i	−0.116616	−	0.993177i	$-0.537205\pi$
$570$	−3.15354	−	5.44078i	−0.132087	−	0.227889i
$571$	7.32046	+	4.22647i	0.306352	+	0.176872i	0.645293	−	0.763935i	$-0.276735\pi$
$571$	7.32046	+	4.22647i	0.306352	+	0.176872i	−0.338941	+	0.940808i	$0.610069\pi$
$572$	2.91621	−	5.09077i	0.121933	−	0.212856i
$573$			10.8564i			0.453532i
$574$		0			0
$575$			28.7945i			1.20082i
$576$	4.07020	+	6.88719i	0.169592	+	0.286966i
$577$	−21.8371	−	12.6076i	−0.909089	−	0.524863i	−0.0289511	−	0.999581i	$-0.509217\pi$
$577$	−21.8371	−	12.6076i	−0.909089	−	0.524863i	−0.880138	+	0.474718i	$0.842550\pi$
$578$	−12.8286	+	7.43558i	−0.533598	+	0.309279i
$579$	4.85673	+	8.41210i	0.201839	+	0.349595i
$580$	51.8214	−	30.1536i	2.15176	−	1.25206i
$581$		0			0
$582$	−8.34587	+	14.5122i	−0.345947	+	0.601549i
$583$	−13.8143	+	7.97569i	−0.572130	+	0.330319i
$584$	8.47957	−	14.8609i	0.350887	−	0.614950i
$585$	−0.881351	+	1.52655i	−0.0364394	+	0.0631149i
$586$	−35.7456	+	0.0605474i	−1.47664	+	0.00250119i
$587$	3.61615			0.149254			0.0746272	−	0.997212i	$-0.476223\pi$
$587$	3.61615			0.149254			0.0746272	+	0.997212i	$0.476223\pi$
$588$		0			0
$589$	7.69551			0.317088
$590$	5.99206	−	0.0101496i	0.246689	−	0.000417853i
$591$	−7.96498	+	13.7957i	−0.327635	+	0.567481i
$592$	−2.40820	−	4.10661i	−0.0989763	−	0.168781i
$593$	7.35701	−	4.24757i	0.302116	−	0.174427i	−0.341277	−	0.939963i	$-0.610859\pi$
$593$	7.35701	−	4.24757i	0.302116	−	0.174427i	0.643393	+	0.765536i	$0.277526\pi$
$594$	−4.27968	+	7.44170i	−0.175597	+	0.305337i
$595$		0			0
$596$	6.15052	+	10.5702i	0.251935	+	0.432970i
$597$	5.02859	+	8.70978i	0.205807	+	0.356467i
$598$	−2.05009	+	1.18826i	−0.0838346	+	0.0485914i
$599$	16.0128	+	9.24497i	0.654264	+	0.377739i	0.790088	−	0.612994i	$-0.210035\pi$
$599$	16.0128	+	9.24497i	0.654264	+	0.377739i	−0.135824	+	0.990733i	$0.543368\pi$
$600$	20.2827	−	11.8480i	0.828036	−	0.483694i
$601$			31.5493i			1.28692i	0.765479	+	0.643461i	$0.222502\pi$
$601$			31.5493i			1.28692i	−0.765479	+	0.643461i	$0.777498\pi$
$602$		0			0
$603$		−	1.77617i		−	0.0723311i
$604$	24.7173	+	14.1591i	1.00573	+	0.576125i
$605$	−81.6488	−	47.1399i	−3.31949	−	1.91651i
$606$	4.06121	+	7.00678i	0.164975	+	0.284631i
$607$	−7.76045	−	13.4415i	−0.314987	−	0.545573i	0.664448	−	0.747335i	$-0.268667\pi$
$607$	−7.76045	−	13.4415i	−0.314987	−	0.545573i	−0.979435	+	0.201761i	$0.935333\pi$
$608$	−5.94289	+	3.49857i	−0.241016	+	0.141886i
$609$		0			0
$610$	0.932164	+	0.536082i	0.0377422	+	0.0217053i
$611$	−4.88074	+	2.81789i	−0.197453	+	0.114000i
$612$	0.0172941	+	5.10497i	0.000699071	+	0.206356i
$613$	2.77406	−	4.80481i	0.112043	−	0.194064i	−0.804551	−	0.593884i	$-0.797594\pi$
$613$	2.77406	−	4.80481i	0.112043	−	0.194064i	0.916594	+	0.399820i	$0.130927\pi$
$614$	−0.0245430	−	14.4895i	−0.000990474	−	0.584750i
$615$	−24.0529			−0.969908
$616$		0			0
$617$	−32.3633			−1.30290			−0.651448	−	0.758693i	$-0.725838\pi$
$617$	−32.3633			−1.30290			−0.651448	+	0.758693i	$0.725838\pi$
$618$	−0.0118648	−	7.00469i	−0.000477274	−	0.281770i
$619$	1.04453	−	1.80918i	0.0419832	−	0.0727171i	−0.844270	−	0.535918i	$-0.819966\pi$
$619$	1.04453	−	1.80918i	0.0419832	−	0.0727171i	0.886253	+	0.463201i	$0.153299\pi$
$620$	0.156005	+	46.0504i	0.00626529	+	1.84943i
$621$	3.00269	−	1.73360i	0.120494	−	0.0695670i
$622$	−37.2486	−	21.4215i	−1.49353	−	0.858923i
$623$		0			0
$624$	1.68055	+	0.955141i	0.0672757	+	0.0382362i
$625$	−1.22305	−	2.11839i	−0.0489220	−	0.0847354i
$626$	12.1422	+	20.9489i	0.485301	+	0.837288i
$627$	−6.40870	−	3.70006i	−0.255939	−	0.147766i
$628$	36.6125	+	20.9732i	1.46100	+	0.836920i
$629$		−	3.03788i		−	0.121128i
$630$		0			0
$631$			37.2258i			1.48194i	0.671541	+	0.740968i	$0.265633\pi$
$631$			37.2258i			1.48194i	−0.671541	+	0.740968i	$0.734367\pi$
$632$	−4.53584	−	7.76491i	−0.180426	−	0.308872i
$633$	−0.893976	−	0.516137i	−0.0355324	−	0.0205146i
$634$	15.1300	−	8.76952i	0.600889	−	0.348282i
$635$	−5.53719	−	9.59069i	−0.219737	−	0.380595i
$636$	−2.64322	−	4.54259i	−0.104811	−	0.180125i
$637$		0			0
$638$	35.1728	−	61.1601i	1.39250	−	2.42135i
$639$	7.90825	−	4.56583i	0.312846	−	0.180621i
$640$	−21.0561	−	35.4917i	−0.832316	−	1.40293i
$641$	5.78071	−	10.0125i	0.228324	−	0.395469i	−0.728987	−	0.684527i	$-0.760009\pi$
$641$	5.78071	−	10.0125i	0.228324	−	0.395469i	0.957312	+	0.289058i	$0.0933420\pi$
$642$	19.4142	−	0.0328846i	0.766218	−	0.00129785i
$643$	5.82948			0.229892			0.114946	−	0.993372i	$-0.463330\pi$
$643$	5.82948			0.229892			0.114946	+	0.993372i	$0.463330\pi$
$644$		0			0
$645$	−12.8097			−0.504381
$646$	−4.40064	+	0.00745400i	−0.173141	+	0.000293274i
$647$	23.1386	−	40.0772i	0.909671	−	1.57560i	0.0951507	−	0.995463i	$-0.469667\pi$
$647$	23.1386	−	40.0772i	0.909671	−	1.57560i	0.814521	−	0.580134i	$-0.197000\pi$
$648$	−2.45664	−	1.40175i	−0.0965061	−	0.0550659i
$649$	6.10647	−	3.52557i	0.239700	−	0.138391i
$650$	2.82953	−	4.92011i	0.110983	−	0.192983i
$651$		0			0
$652$	−33.0813	+	19.2492i	−1.29556	+	0.753857i
$653$	−11.7881	−	20.4175i	−0.461303	−	0.798999i	0.537724	−	0.843121i	$-0.319284\pi$
$653$	−11.7881	−	20.4175i	−0.461303	−	0.798999i	−0.999026	+	0.0441218i	$0.985951\pi$
$654$	−16.7023	+	9.68084i	−0.653112	+	0.378551i
$655$	45.6983	+	26.3839i	1.78558	+	1.03091i
$656$	0.178712	+	26.3763i	0.00697751	+	1.02982i
$657$			6.04928i			0.236005i
$658$		0			0
$659$			20.7935i			0.810001i	0.914316	+	0.405001i	$0.132729\pi$
$659$			20.7935i			0.810001i	−0.914316	+	0.405001i	$0.867271\pi$
$660$	22.0115	−	38.4250i	0.856795	−	1.49569i
$661$	28.8226	+	16.6407i	1.12107	+	0.647249i	0.941674	−	0.336528i	$-0.109253\pi$
$661$	28.8226	+	16.6407i	1.12107	+	0.647249i	0.179395	+	0.983777i	$0.442586\pi$
$662$	5.44790	+	9.39923i	0.211739	+	0.365312i
$663$	0.616751	+	1.06824i	0.0239526	+	0.0414871i
$664$	0.107772	+	21.2085i	0.00418237	+	0.823048i
$665$		0			0
$666$	1.45907	+	0.839100i	0.0565376	+	0.0325144i
$667$	−24.6778	+	14.2477i	−0.955528	+	0.551674i
$668$	15.3924	−	0.0521447i	0.595550	−	0.00201754i
$669$	4.78625	−	8.29003i	0.185047	−	0.320511i
$670$	0.0155194	+	9.16226i	0.000599568	+	0.353969i
$671$	1.26538			0.0488494
$672$		0			0
$673$	−13.1796			−0.508037			−0.254019	−	0.967199i	$-0.581752\pi$
$673$	−13.1796			−0.508037			−0.254019	+	0.967199i	$0.581752\pi$
$674$	0.0320663	+	18.9311i	0.00123515	+	0.729200i
$675$	−4.15242	+	7.19220i	−0.159827	+	0.276828i
$676$	−25.5328	+	0.0864973i	−0.982030	+	0.00332682i
$677$	38.0749	−	21.9825i	1.46334	−	0.844858i	0.464173	−	0.885745i	$-0.346352\pi$
$677$	38.0749	−	21.9825i	1.46334	−	0.844858i	0.999164	+	0.0408865i	$0.0130182\pi$
$678$	8.72831	+	5.01960i	0.335209	+	0.192777i
$679$		0			0
$680$	−0.133816	−	26.3336i	−0.00513160	−	1.00985i
$681$	5.57692	+	9.65951i	0.213708	+	0.370153i
$682$	27.1744	+	46.8839i	1.04056	+	1.79528i
$683$	10.3341	+	5.96637i	0.395422	+	0.228297i	0.684507	−	0.729007i	$-0.260018\pi$
$683$	10.3341	+	5.96637i	0.395422	+	0.228297i	−0.289085	+	0.957303i	$0.593351\pi$
$684$	1.21193	−	2.11565i	0.0463394	−	0.0808938i
$685$		−	42.1758i		−	1.61145i
$686$		0			0
$687$		−	10.1285i		−	0.386425i
$688$	0.0951751	+	14.0470i	0.00362852	+	0.535538i
$689$	−1.09977	−	0.634951i	−0.0418978	−	0.0241897i
$690$	−15.4741	+	8.96893i	−0.589087	+	0.341441i
$691$	−18.6375	−	32.2811i	−0.709003	−	1.22803i	−0.965227	−	0.261412i	$-0.915812\pi$
$691$	−18.6375	−	32.2811i	−0.709003	−	1.22803i	0.256224	−	0.966617i	$-0.417522\pi$
$692$	1.42331	−	0.828191i	0.0541062	−	0.0314831i
$693$		0			0
$694$	−22.4754	+	39.0812i	−0.853154	+	1.48350i
$695$	−55.6606	+	32.1357i	−2.11133	+	1.21898i
$696$	20.1901	+	11.5204i	0.765304	+	0.436678i
$697$	−8.41586	+	14.5767i	−0.318773	+	0.552132i
$698$	−13.4581	+	0.0227959i	−0.509397	+	0.000862839i
$699$	−12.6414			−0.478143
$700$		0			0
$701$	−30.9151			−1.16765			−0.583823	−	0.811881i	$-0.698444\pi$
$701$	−30.9151			−1.16765			−0.583823	+	0.811881i	$0.698444\pi$
$702$	−0.683422	+	0.00115761i	−0.0257941	+	4.36911e-5i
$703$	−0.725457	+	1.25653i	−0.0273611	+	0.0473909i
$704$	−42.3001	−	23.8521i	−1.59425	−	0.898960i
$705$	−36.8397	+	21.2694i	−1.38746	+	0.801052i
$706$	9.96390	−	17.3257i	0.374996	−	0.652061i
$707$		0			0
$708$	1.16841	+	2.00801i	0.0439116	+	0.0754655i
$709$	4.32776	+	7.49590i	0.162532	+	0.281514i	0.935776	−	0.352594i	$-0.114700\pi$
$709$	4.32776	+	7.49590i	0.162532	+	0.281514i	−0.773244	+	0.634109i	$0.781367\pi$
$710$	−40.7544	+	23.6217i	−1.52949	+	0.886507i
$711$	2.75342	+	1.58969i	0.103261	+	0.0596180i
$712$	17.5295	+	30.0088i	0.656945	+	1.12463i
$713$		−	21.8867i		−	0.819663i
$714$		0			0
$715$		−	10.6999i		−	0.400155i
$716$	16.4397	+	9.41733i	0.614379	+	0.351942i
$717$	4.72894	+	2.73025i	0.176605	+	0.101963i
$718$	−15.9321	−	27.4876i	−0.594582	−	1.02583i
$719$	13.8268	+	23.9487i	0.515653	+	0.893137i	0.999835	+	0.0181697i	$0.00578391\pi$
$719$	13.8268	+	23.9487i	0.515653	+	0.893137i	−0.484182	+	0.874967i	$0.660883\pi$
$720$	12.6847	+	7.20938i	0.472732	+	0.268678i
$721$		0			0
$722$	−21.4709	−	12.3478i	−0.799064	−	0.459537i
$723$	11.8106	−	6.81887i	0.439242	−	0.253597i
$724$	0.0139653	+	4.12235i	0.000519015	+	0.153206i
$725$	34.1269	−	59.1096i	1.26744	−	2.19527i
$726$	−0.0619158	−	36.5535i	−0.00229791	−	1.35663i
$727$	−31.3975			−1.16447			−0.582235	−	0.813021i	$-0.697822\pi$
$727$	−31.3975			−1.16447			−0.582235	+	0.813021i	$0.697822\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−0.0528562	−	31.2049i	−0.00195629	−	1.15494i
$731$	−4.48198	+	7.76301i	−0.165772	+	0.287125i
$732$	0.00141237	+	0.416913i	5.22029e−5	+	0.0154096i
$733$	16.8834	−	9.74763i	0.623602	−	0.360037i	−0.154668	−	0.987966i	$-0.549431\pi$
$733$	16.8834	−	9.74763i	0.623602	−	0.360037i	0.778270	+	0.627930i	$0.216097\pi$
$734$	−14.7102	−	8.45975i	−0.542964	−	0.312255i
$735$		0			0
$736$	9.95023	+	16.9021i	0.366771	+	0.623019i
$737$	5.39083	+	9.33720i	0.198574	+	0.343940i
$738$	−4.67649	−	8.06832i	−0.172144	−	0.296999i
$739$	34.2166	+	19.7550i	1.25868	+	0.726698i	0.972818	−	0.231573i	$-0.0743871\pi$
$739$	34.2166	+	19.7550i	1.25868	+	0.726698i	0.285861	+	0.958271i	$0.407720\pi$
$740$	−7.53384	−	4.31570i	−0.276950	−	0.158648i
$741$		−	0.589130i		−	0.0216422i
$742$		0			0
$743$		−	10.9193i		−	0.400590i	−0.979736	−	0.200295i	$-0.935810\pi$
$743$		−	10.9193i		−	0.400590i	0.979736	−	0.200295i	$-0.0641901\pi$
$744$	−15.4168	+	9.00567i	−0.565208	+	0.330164i
$745$	19.3156	+	11.1519i	0.707670	+	0.408573i
$746$	−6.88563	+	3.99099i	−0.252101	+	0.146120i
$747$	−3.74921	−	6.49383i	−0.137176	−	0.237597i
$748$	−15.5850	−	26.7840i	−0.569843	−	0.979321i
$749$		0			0
$750$	8.49890	−	14.7783i	0.310336	−	0.539627i
$751$	26.2548	−	15.1582i	0.958050	−	0.553130i	0.0624774	−	0.998046i	$-0.480100\pi$
$751$	26.2548	−	15.1582i	0.958050	−	0.553130i	0.895572	+	0.444916i	$0.146767\pi$
$752$	23.5976	+	40.2401i	0.860515	+	1.46740i
$753$	14.1212	−	24.4587i	0.514606	−	0.891324i
$754$	5.61675	−	0.00951388i	0.204550	−	0.000346475i
$755$	51.9515			1.89071
$756$		0			0
$757$	18.4211			0.669526			0.334763	−	0.942302i	$-0.391344\pi$
$757$	18.4211			0.669526			0.334763	+	0.942302i	$0.391344\pi$
$758$	−30.1730	+	0.0511083i	−1.09593	+	0.00185634i
$759$	−10.5233	+	18.2269i	−0.381971	+	0.661594i
$760$	−6.23320	+	10.9241i	−0.226102	+	0.396257i
$761$	−29.0996	+	16.8007i	−1.05486	+	0.609023i	−0.924006	−	0.382379i	$-0.875105\pi$
$761$	−29.0996	+	16.8007i	−1.05486	+	0.609023i	−0.130853	+	0.991402i	$0.541772\pi$
$762$	2.14054	−	3.72206i	0.0775435	−	0.134836i
$763$		0			0
$764$	18.7669	−	10.9200i	0.678964	−	0.395073i
$765$	4.65522	+	8.06307i	0.168310	+	0.291521i
$766$	−9.24008	+	5.35565i	−0.333858	+	0.193508i
$767$	0.486141	+	0.280674i	0.0175535	+	0.0101345i
$768$	7.81151	−	13.9635i	0.281873	−	0.503866i
$769$		−	0.776682i		−	0.0280079i	−0.999902	−	0.0140039i	$-0.995542\pi$
$769$		−	0.776682i		−	0.0280079i	0.999902	−	0.0140039i	$-0.00445774\pi$
$770$		0			0
$771$		−	20.1625i		−	0.726136i
$772$	9.65641	−	16.8570i	0.347542	−	0.606697i
$773$	17.6333	+	10.1806i	0.634225	+	0.366170i	0.782387	−	0.622793i	$-0.214002\pi$
$773$	17.6333	+	10.1806i	0.634225	+	0.366170i	−0.148161	+	0.988963i	$0.547335\pi$
$774$	−2.49052	−	4.29689i	−0.0895201	−	0.154449i
$775$	26.2121	+	45.4007i	0.941566	+	1.63084i
$776$	33.4813	−	0.170138i	1.20191	−	0.00610758i
$777$		0			0
$778$	−3.24949	−	1.86876i	−0.116500	−	0.0669984i
$779$	6.96194	−	4.01948i	0.249438	−	0.144013i
$780$	3.52538	−	0.0119429i	0.126229	−	0.000427625i
$781$	−27.7155	+	48.0046i	−0.991738	+	1.71774i
$782$	0.0211998	+	12.5158i	0.000758104	+	0.447564i
$783$	−8.21857			−0.293708
$784$		0			0
$785$	76.9532			2.74658
$786$	0.0346539	+	20.4588i	0.00123606	+	0.729740i
$787$	24.3908	−	42.2461i	0.869437	−	1.50591i	0.00686444	−	0.999976i	$-0.497815\pi$
$787$	24.3908	−	42.2461i	0.869437	−	1.50591i	0.862573	−	0.505933i	$-0.168852\pi$
$788$	31.8597	−	0.107931i	1.13496	−	0.00384488i
$789$	10.8326	−	6.25419i	0.385650	−	0.222655i
$790$	−14.2173	−	8.17628i	−0.505828	−	0.290899i
$791$		0			0
$792$	17.1689	−	0.0872448i	0.610070	−	0.00310011i
$793$	0.0503689	+	0.0872415i	0.00178865	+	0.00309804i
$794$	−13.2263	−	22.8193i	−0.469385	−	0.809827i
$795$	−8.30101	−	4.79259i	−0.294407	−	0.169976i
$796$	9.99811	−	17.4535i	0.354374	−	0.618624i
$797$		−	5.84706i		−	0.207113i	−0.994624	−	0.103557i	$-0.966978\pi$
$797$		−	5.84706i		−	0.207113i	0.994624	−	0.103557i	$-0.0330223\pi$
$798$		0			0
$799$			29.7677i			1.05311i
$800$	−40.8827	−	23.1442i	−1.44542	−	0.818271i
$801$	−10.6411	−	6.14362i	−0.375983	−	0.217074i
$802$	29.1795	−	16.9128i	1.03036	−	0.597210i
$803$	−18.3601	−	31.8007i	−0.647915	−	1.12222i
$804$	−3.07037	+	1.78658i	−0.108284	+	0.0630077i
$805$		0			0
$806$	−2.15072	+	3.73977i	−0.0757558	+	0.131728i
$807$	11.3057	−	6.52738i	0.397981	−	0.229775i
$808$	8.02728	−	14.0683i	0.282399	−	0.494920i
$809$	−12.5937	+	21.8130i	−0.442772	+	0.766903i	−0.997894	−	0.0648654i	$-0.979338\pi$
$809$	−12.5937	+	21.8130i	−0.442772	+	0.766903i	0.555122	+	0.831769i	$0.312672\pi$
$810$	−5.15845	+	0.00873760i	−0.181249	+	0.000307008i
$811$	−12.4012			−0.435465			−0.217733	−	0.976008i	$-0.569866\pi$
$811$	−12.4012			−0.435465			−0.217733	+	0.976008i	$0.569866\pi$
$812$		0			0
$813$	10.2934			0.361006
$814$	−10.2170	+	0.0173059i	−0.358105	+	0.000606573i
$815$	−34.9019	+	60.4519i	−1.22256	+	2.11754i
$816$	8.80732	−	5.16479i	0.308318	−	0.180804i
$817$	3.70767	−	2.14063i	0.129715	−	0.0748910i
$818$	−12.2865	+	21.3644i	−0.429588	+	0.746988i
$819$		0			0
$820$	24.1939	+	41.5792i	0.844889	+	1.45201i
$821$	−7.13932	−	12.3657i	−0.249164	−	0.431564i	0.714130	−	0.700013i	$-0.246822\pi$
$821$	−7.13932	−	12.3657i	−0.249164	−	0.431564i	−0.963294	+	0.268448i	$0.913489\pi$
$822$	14.1475	−	8.20002i	0.493449	−	0.286009i
$823$	−12.2752	−	7.08709i	−0.427887	−	0.247040i	0.270559	−	0.962703i	$-0.412791\pi$
$823$	−12.2752	−	7.08709i	−0.427887	−	0.247040i	−0.698446	+	0.715663i	$0.746125\pi$
$824$	−12.0968	+	7.06626i	−0.421410	+	0.246165i
$825$		−	50.4119i		−	1.75512i
$826$		0			0
$827$		−	25.5816i		−	0.889559i	−0.895640	−	0.444779i	$-0.853282\pi$
$827$		−	25.5816i		−	0.889559i	0.895640	−	0.444779i	$-0.146718\pi$
$828$	−6.01708	−	3.44684i	−0.209108	−	0.119786i
$829$	35.2159	+	20.3319i	1.22310	+	0.706156i	0.965577	−	0.260117i	$-0.0837611\pi$
$829$	35.2159	+	20.3319i	1.22310	+	0.706156i	0.257521	+	0.966273i	$0.417094\pi$
$830$	19.3969	+	33.4653i	0.673275	+	1.16160i
$831$	−9.48111	−	16.4218i	−0.328896	−	0.569665i
$832$	−0.0392899	−	3.86582i	−0.00136213	−	0.134023i
$833$		0			0
$834$	−21.6014	−	12.4228i	−0.747996	−	0.430168i
$835$	24.3116	−	14.0363i	0.841338	−	0.485747i
$836$	0.0501385	+	14.8002i	0.00173407	+	0.511875i
$837$	3.15625	−	5.46678i	0.109096	−	0.188959i
$838$	0.0637545	+	37.6390i	0.00220236	+	1.30022i
$839$	−24.4293			−0.843394			−0.421697	−	0.906737i	$-0.638565\pi$
$839$	−24.4293			−0.843394			−0.421697	+	0.906737i	$0.638565\pi$
$840$		0			0
$841$	38.5449			1.32913
$842$	−0.0412488	−	24.3522i	−0.00142153	−	0.839233i
$843$	8.75722	−	15.1679i	0.301615	−	0.522412i
$844$	0.00699402	+	2.06454i	0.000240744	+	0.0710643i
$845$	−40.3279	+	23.2833i	−1.38732	+	0.800972i
$846$	−14.2972	−	8.22221i	−0.491547	−	0.282686i
$847$		0			0
$848$	−5.19384	+	9.13844i	−0.178357	+	0.313815i
$849$	9.47095	+	16.4042i	0.325042	+	0.562990i
$850$	−15.0333	−	25.9368i	−0.515636	−	0.889625i
$851$	3.57368	+	2.06326i	0.122504	+	0.0707277i
$852$	−15.8473	−	9.07803i	−0.542921	−	0.311008i
$853$			21.6039i			0.739705i	0.929091	+	0.369852i	$0.120592\pi$
$853$			21.6039i			0.739705i	−0.929091	+	0.369852i	$0.879408\pi$
$854$		0			0
$855$		−	4.44674i		−	0.152075i
$856$	−19.5849	−	33.5274i	−0.669397	−	1.14594i
$857$	−2.05943	−	1.18901i	−0.0703487	−	0.0406159i	0.464413	−	0.885619i	$-0.346265\pi$
$857$	−2.05943	−	1.18901i	−0.0703487	−	0.0406159i	−0.534762	+	0.845003i	$0.679599\pi$
$858$	3.58919	−	2.08034i	0.122533	−	0.0710215i
$859$	−20.9336	−	36.2580i	−0.714244	−	1.23711i	−0.963250	−	0.268605i	$-0.913437\pi$
$859$	−20.9336	−	36.2580i	−0.714244	−	1.23711i	0.249007	−	0.968502i	$-0.419896\pi$
$860$	12.8848	+	22.1435i	0.439368	+	0.755088i
$861$		0			0
$862$	13.8771	−	24.1301i	0.472656	−	0.821876i
$863$	34.4456	−	19.8872i	1.17254	−	0.676967i	0.218263	−	0.975890i	$-0.429961\pi$
$863$	34.4456	−	19.8872i	1.17254	−	0.676967i	0.954277	+	0.298923i	$0.0966275\pi$
$864$	0.0479085	+	5.65665i	0.00162988	+	0.192443i
$865$	1.50164	−	2.60092i	0.0510574	−	0.0884341i
$866$	−9.09778	+	0.0154102i	−0.309155	+	0.000523660i
$867$	−10.4848			−0.356081
$868$		0			0
$869$	−19.2995			−0.654689
$870$	42.3951	−	0.0718106i	1.43733	−	0.00243461i
$871$	−0.429168	+	0.743342i	−0.0145418	+	0.0251872i
$872$	33.5350	+	19.1349i	1.13564	+	0.647990i
$873$	−10.2517	+	5.91879i	−0.346966	+	0.200321i
$874$	2.98006	−	5.18186i	0.100802	−	0.175279i
$875$		0			0
$876$	10.4571	−	6.08474i	0.353313	−	0.205584i
$877$	−13.3590	−	23.1385i	−0.451102	−	0.781331i	0.547353	−	0.836902i	$-0.315635\pi$
$877$	−13.3590	−	23.1385i	−0.451102	−	0.781331i	−0.998455	+	0.0555709i	$0.982302\pi$
$878$	−8.50792	+	4.93128i	−0.287128	+	0.166423i
$879$	−21.8897	−	12.6380i	−0.738320	−	0.426269i
$880$	−88.5640	+	0.600062i	−2.98549	+	0.0202281i
$881$			39.2357i			1.32188i	0.750437	+	0.660942i	$0.229843\pi$
$881$			39.2357i			1.32188i	−0.750437	+	0.660942i	$0.770157\pi$
$882$		0			0
$883$			57.7837i			1.94458i	0.233783	+	0.972289i	$0.424889\pi$
$883$			57.7837i			1.94458i	−0.233783	+	0.972289i	$0.575111\pi$
$884$	1.22626	−	2.14065i	0.0412435	−	0.0719980i
$885$	3.66938	+	2.11852i	0.123345	+	0.0712132i
$886$	5.52035	+	9.52424i	0.185460	+	0.319973i
$887$	24.9877	+	43.2800i	0.839005	+	1.45320i	0.890727	+	0.454538i	$0.150196\pi$
$887$	24.9877	+	43.2800i	0.839005	+	1.45320i	−0.0517223	+	0.998662i	$0.516471\pi$
$888$	−0.0171057	−	3.36624i	−0.000574031	−	0.112963i
$889$		0			0
$890$	54.9450	+	31.5986i	1.84176	+	1.05919i
$891$	−5.25694	+	3.03510i	−0.176114	+	0.101680i
$892$	−19.1449	+	0.0648570i	−0.641018	+	0.00217157i
$893$	7.10865	−	12.3125i	0.237882	−	0.412023i
$894$	0.0146474	+	8.64744i	0.000489883	+	0.289214i
$895$	34.5534			1.15499
$896$		0			0
$897$	−1.67554			−0.0559445
$898$	0.0321957	+	19.0075i	0.00107439	+	0.634289i
$899$	−25.9398	+	44.9291i	−0.865141	+	1.49847i
$900$	16.6096	−	0.0562682i	0.553652	−	0.00187561i
$901$	−5.80887	+	3.35375i	−0.193522	+	0.111730i
$902$	49.0722	+	28.2211i	1.63392	+	0.939660i
$903$		0			0
$904$	−0.102329	−	20.1372i	−0.00340340	−	0.669755i
$905$	3.75917	+	6.51107i	0.124959	+	0.216435i
$906$	10.1007	+	17.4266i	0.335572	+	0.578962i
$907$	−13.4055	−	7.73965i	−0.445121	−	0.256991i	0.260646	−	0.965434i	$-0.416064\pi$
$907$	−13.4055	−	7.73965i	−0.445121	−	0.256991i	−0.705768	+	0.708444i	$0.749398\pi$
$908$	11.0883	−	19.3567i	0.367979	−	0.642375i
$909$			5.72662i			0.189940i
$910$		0			0
$911$		−	2.22992i		−	0.0738807i	−0.999317	−	0.0369403i	$-0.988239\pi$
$911$		−	2.22992i		−	0.0738807i	0.999317	−	0.0369403i	$-0.0117612\pi$
$912$	−4.87626	+	0.0330389i	−0.161469	+	0.00109403i
$913$	39.4188	+	22.7584i	1.30457	+	0.753194i
$914$	1.42378	−	0.825238i	0.0470944	−	0.0272964i
$915$	0.380183	+	0.658497i	0.0125685	+	0.0217692i
$916$	−17.5086	+	10.1878i	−0.578500	+	0.336616i
$917$		0			0
$918$	−1.79959	+	3.12921i	−0.0593953	+	0.103279i
$919$	26.1682	−	15.1082i	0.863211	−	0.498375i	−0.00187547	−	0.999998i	$-0.500597\pi$
$919$	26.1682	−	15.1082i	0.863211	−	0.498375i	0.865086	+	0.501623i	$0.167264\pi$
$920$	31.0689	+	17.7278i	1.02431	+	0.584467i
$921$	5.12283	−	8.87300i	0.168803	−	0.292375i
$922$	−30.2939	+	0.0513131i	−0.997677	+	0.00168991i
$923$	−4.41290			−0.145252
$924$		0			0
$925$	−9.88408			−0.324986
$926$	20.4223	−	0.0345921i	0.671118	−	0.00113677i
$927$	2.47654	−	4.28949i	0.0813401	−	0.140885i
$928$	−0.393739	−	46.4896i	−0.0129251	−	1.52610i
$929$	2.41731	−	1.39564i	0.0793095	−	0.0457894i	−0.459821	−	0.888012i	$-0.652086\pi$
$929$	2.41731	−	1.39564i	0.0793095	−	0.0457894i	0.539130	+	0.842222i	$0.318753\pi$
$930$	−16.2336	+	28.2277i	−0.532320	+	0.925622i
$931$		0			0
$932$	12.7155	+	21.8527i	0.416511	+	0.715808i
$933$	−15.1919	−	26.3131i	−0.497359	−	0.861451i
$934$	36.4199	−	21.1094i	1.19170	−	0.690721i
$935$	−48.9444	−	28.2581i	−1.60065	−	0.924138i
$936$	0.689429	+	1.18023i	0.0225347	+	0.0385772i
$937$			13.5645i			0.443133i	0.975145	+	0.221566i	$0.0711169\pi$
$937$			13.5645i			0.443133i	−0.975145	+	0.221566i	$0.928883\pi$
$938$		0			0
$939$			17.1215i			0.558739i
$940$	73.8230	+	42.2889i	2.40784	+	1.37931i
$941$	22.7548	+	13.1375i	0.741787	+	0.428271i	0.822719	−	0.568449i	$-0.192456\pi$
$941$	22.7548	+	13.1375i	0.741787	+	0.428271i	−0.0809319	+	0.996720i	$0.525790\pi$
$942$	14.9616	+	25.8132i	0.487476	+	0.841040i
$943$	−11.4317	−	19.8004i	−0.372269	−	0.644789i
$944$	2.29589	−	4.03956i	0.0747248	−	0.131476i
$945$		0			0
$946$	26.1340	+	15.0295i	0.849690	+	0.488652i
$947$	−7.80904	+	4.50855i	−0.253760	+	0.146508i	−0.621485	−	0.783426i	$-0.713470\pi$
$947$	−7.80904	+	4.50855i	−0.253760	+	0.146508i	0.367725	+	0.929935i	$0.380137\pi$
$948$	−0.0215414	−	6.35873i	−0.000699633	−	0.206522i
$949$	1.46167	−	2.53168i	0.0474477	−	0.0821818i
$950$	0.0242524	+	14.3180i	0.000786852	+	0.464537i
$951$	12.3657			0.400986
$952$		0			0
$953$	5.49448			0.177984			0.0889918	−	0.996032i	$-0.471636\pi$
$953$	5.49448			0.177984			0.0889918	+	0.996032i	$0.471636\pi$
$954$	−0.00629482	−	3.71629i	−0.000203802	−	0.120319i
$955$	19.7998	−	34.2942i	0.640706	−	1.10973i
$956$	−0.0369968	−	10.9209i	−0.00119656	−	0.353209i
$957$	43.2045	−	24.9442i	1.39660	−	0.806330i
$958$	34.7618	+	19.9913i	1.12310	+	0.645889i
$959$		0			0
$960$	−0.296559	−	29.1791i	−0.00957140	−	0.941752i
$961$	−4.42377	−	7.66220i	−0.142702	−	0.247168i
$962$	−0.407883	−	0.703719i	−0.0131507	−	0.0226888i
$963$	11.8888	+	6.86398i	0.383110	+	0.221189i
$964$	−23.6673	−	13.5576i	−0.762273	−	0.436662i
$965$		−	35.4306i		−	1.14055i
$966$		0			0
$967$		−	45.1993i		−	1.45351i	−0.686896	−	0.726756i	$-0.741027\pi$
$967$		−	45.1993i		−	1.45351i	0.686896	−	0.726756i	$-0.258973\pi$
$968$	−63.1260	+	36.8748i	−2.02895	+	1.18520i
$969$	−2.69484	−	1.55587i	−0.0865707	−	0.0499816i
$970$	52.8309	−	30.6214i	1.69630	−	0.983193i
$971$	20.5279	+	35.5554i	0.658772	+	1.14103i	0.980934	+	0.194342i	$0.0622572\pi$
$971$	20.5279	+	35.5554i	0.658772	+	1.14103i	−0.322162	+	0.946685i	$0.604409\pi$
$972$	−1.00586	−	1.72865i	−0.0322630	−	0.0554466i
$973$		0			0
$974$	−6.74564	+	11.7296i	−0.216144	+	0.375842i
$975$	3.47565	−	2.00667i	0.111310	−	0.0642648i
$976$	0.719278	−	0.421799i	0.0230235	−	0.0135014i
$977$	−28.6096	+	49.5532i	−0.915301	+	1.58535i	−0.108842	+	0.994059i	$0.534714\pi$
$977$	−28.6096	+	49.5532i	−0.915301	+	1.58535i	−0.806459	+	0.591289i	$0.798619\pi$
$978$	−27.0638	+	0.0458418i	−0.865405	+	0.00146586i
$979$	74.5859			2.38378
$980$		0			0
$981$	−13.6507			−0.435835
$982$	25.1052	−	0.0425243i	0.801140	−	0.00135700i
$983$	−26.1872	+	45.3575i	−0.835241	+	1.44668i	0.0585929	+	0.998282i	$0.481339\pi$
$983$	−26.1872	+	45.3575i	−0.835241	+	1.44668i	−0.893834	+	0.448398i	$0.851995\pi$
$984$	−9.24343	+	16.1996i	−0.294670	+	0.516426i
$985$	50.3211	−	29.0529i	1.60336	−	0.925702i
$986$	14.7901	−	25.7176i	0.471011	−	0.819016i
$987$		0			0
$988$	−1.01840	+	0.592583i	−0.0323997	+	0.0188526i
$989$	−6.08812	−	10.5449i	−0.193591	−	0.335310i
$990$	27.0911	−	15.7023i	0.861013	−	0.499053i
$991$	−51.5895	−	29.7852i	−1.63879	−	0.946158i	−0.981249	−	0.192743i	$-0.938262\pi$
$991$	−51.5895	−	29.7852i	−1.63879	−	0.946158i	−0.657545	−	0.753415i	$-0.728405\pi$
$992$	31.0749	+	17.5919i	0.986628	+	0.558543i
$993$			7.68197i			0.243780i
$994$		0			0
$995$		−	36.6844i		−	1.16297i
$996$	−7.45438	+	13.0130i	−0.236201	+	0.412332i
$997$	−28.0159	−	16.1750i	−0.887274	−	0.512268i	−0.0142239	−	0.999899i	$-0.504528\pi$
$997$	−28.0159	−	16.1750i	−0.887274	−	0.512268i	−0.873050	+	0.487631i	$0.837861\pi$
$998$	−6.66708	−	11.5027i	−0.211043	−	0.364111i
$999$	0.595080	+	1.03071i	0.0188275	+	0.0326102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.o.f.31.8		24
4.3	odd	2		588.2.o.e.31.3		24
7.2	even	3	inner	588.2.o.f.19.3		24
7.3	odd	6		588.2.b.d.391.10	yes	12
7.4	even	3		588.2.b.c.391.10	yes	12
7.5	odd	6		588.2.o.e.19.3		24
7.6	odd	2		588.2.o.e.31.8		24
21.11	odd	6		1764.2.b.l.1567.3		12
21.17	even	6		1764.2.b.m.1567.3		12
28.3	even	6		588.2.b.c.391.9	✓	12
28.11	odd	6		588.2.b.d.391.9	yes	12
28.19	even	6	inner	588.2.o.f.19.8		24
28.23	odd	6		588.2.o.e.19.8		24
28.27	even	2	inner	588.2.o.f.31.3		24
84.11	even	6		1764.2.b.m.1567.4		12
84.59	odd	6		1764.2.b.l.1567.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.9	✓	12	28.3	even	6
588.2.b.c.391.10	yes	12	7.4	even	3
588.2.b.d.391.9	yes	12	28.11	odd	6
588.2.b.d.391.10	yes	12	7.3	odd	6
588.2.o.e.19.3		24	7.5	odd	6
588.2.o.e.19.8		24	28.23	odd	6
588.2.o.e.31.3		24	4.3	odd	2
588.2.o.e.31.8		24	7.6	odd	2
588.2.o.f.19.3		24	7.2	even	3	inner
588.2.o.f.19.8		24	28.19	even	6	inner
588.2.o.f.31.3		24	28.27	even	2	inner
588.2.o.f.31.8		24	1.1	even	1	trivial
1764.2.b.l.1567.3		12	21.11	odd	6
1764.2.b.l.1567.4		12	84.59	odd	6
1764.2.b.m.1567.3		12	21.17	even	6
1764.2.b.m.1567.4		12	84.11	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.00239545 - 1.41421i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.99999 + 0.00677535i) q^{4} +(-3.15890 + 1.82379i) q^{5} +(-1.22594 - 0.705031i) q^{6} +(0.0143727 + 2.82839i) q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.58679 + 4.46298i) q^{10} +(5.25694 + 3.03510i) q^{11} +(-0.994127 + 1.73543i) q^{12} +0.483253i q^{13} +3.64758i q^{15} +(3.99991 - 0.0271012i) q^{16} +(2.21053 + 1.27625i) q^{17} +(-1.22355 + 0.709180i) q^{18} +(-0.609546 - 1.05577i) q^{19} +(6.30540 - 3.66896i) q^{20} +(4.27968 - 7.44170i) q^{22} +(-3.00269 + 1.73360i) q^{23} +(2.45664 + 1.40175i) q^{24} +(4.15242 - 7.19220i) q^{25} +(0.683422 - 0.00115761i) q^{26} -1.00000 q^{27} +8.21857 q^{29} +(5.15845 - 0.00873760i) q^{30} +(-3.15625 + 5.46678i) q^{31} +(-0.0479085 - 5.65665i) q^{32} +(5.25694 - 3.03510i) q^{33} +(1.79959 - 3.12921i) q^{34} +(1.00586 + 1.72865i) q^{36} +(-0.595080 - 1.03071i) q^{37} +(-1.49162 + 0.864556i) q^{38} +(0.418509 + 0.241626i) q^{39} +(-5.20379 - 8.90838i) q^{40} +6.59422i q^{41} +3.51184i q^{43} +(-10.5344 - 6.03454i) q^{44} +(3.15890 + 1.82379i) q^{45} +(2.45887 + 4.24228i) q^{46} +(5.83110 + 10.0998i) q^{47} +(1.97648 - 3.47757i) q^{48} +(-10.1812 - 5.85517i) q^{50} +(2.21053 - 1.27625i) q^{51} +(-0.00327421 - 0.966500i) q^{52} +(-1.31391 + 2.27576i) q^{53} +(0.00239545 + 1.41421i) q^{54} -22.1415 q^{55} -1.21909 q^{57} +(-0.0196872 - 11.6228i) q^{58} +(0.580801 - 1.00598i) q^{59} +(-0.0247136 - 7.29512i) q^{60} +(0.180530 - 0.104229i) q^{61} +(7.73874 + 4.45050i) q^{62} +(-7.99959 + 0.0813030i) q^{64} +(-0.881351 - 1.52655i) q^{65} +(-4.30486 - 7.42716i) q^{66} +(1.53820 + 0.888083i) q^{67} +(-4.42968 - 2.53751i) q^{68} +3.46720i q^{69} +9.13166i q^{71} +(2.44227 - 1.42664i) q^{72} +(-5.23883 - 3.02464i) q^{73} +(-1.45621 + 0.844038i) q^{74} +(-4.15242 - 7.19220i) q^{75} +(1.22624 + 2.10739i) q^{76} +(0.340708 - 0.592439i) q^{78} +(-2.75342 + 1.58969i) q^{79} +(-12.5859 + 7.38060i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(9.32562 - 0.0157961i) q^{82} +7.49842 q^{83} -9.31044 q^{85} +(4.96648 - 0.00841243i) q^{86} +(4.10928 - 7.11749i) q^{87} +(-8.50888 + 14.9123i) q^{88} +(10.6411 - 6.14362i) q^{89} +(2.57166 - 4.47172i) q^{90} +(5.99359 - 3.48753i) q^{92} +(3.15625 + 5.46678i) q^{93} +(14.2692 - 8.27060i) q^{94} +(3.85099 + 2.22337i) q^{95} +(-4.92276 - 2.78684i) q^{96} -11.8376i q^{97} -6.07019i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 12 q^{3} + 4 q^{4} - 8 q^{6} + 8 q^{8} - 12 q^{9} - 4 q^{12} + 4 q^{16} - 4 q^{18} + 48 q^{20} + 4 q^{24} + 12 q^{25} + 24 q^{26} - 24 q^{27} + 64 q^{29} + 16 q^{31} - 4 q^{32} - 64 q^{34}+ \cdots + 4 q^{96}+O(q^{100}) \) 24 * q - 4 * q^2 + 12 * q^3 + 4 * q^4 - 8 * q^6 + 8 * q^8 - 12 * q^9 - 4 * q^12 + 4 * q^16 - 4 * q^18 + 48 * q^20 + 4 * q^24 + 12 * q^25 + 24 * q^26 - 24 * q^27 + 64 * q^29 + 16 * q^31 - 4 * q^32 - 64 * q^34 - 8 * q^36 - 32 * q^37 - 24 * q^38 - 32 * q^40 + 24 * q^44 - 24 * q^46 + 8 * q^48 - 56 * q^50 + 32 * q^52 + 32 * q^53 + 4 * q^54 - 32 * q^55 - 16 * q^58 - 16 * q^59 + 24 * q^60 - 16 * q^62 - 8 * q^64 - 8 * q^68 - 4 * q^72 + 32 * q^74 - 12 * q^75 + 64 * q^76 + 48 * q^78 - 16 * q^80 - 12 * q^81 + 32 * q^82 + 32 * q^83 + 32 * q^85 + 24 * q^86 + 32 * q^87 - 24 * q^88 - 16 * q^93 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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