LMFDB - Embedded newform 558.2.q.a.185.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [558,2,Mod(185,558)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(558, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("558.185"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 558 = 2 \cdot 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	558.q (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.45565243279$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.7
Character	$\chi$	$=$	558.185
Dual form			558.2.q.a.371.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.296201 - 1.70654i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.42613 - 1.40073i) q^{5} +(1.10979 + 1.32980i) q^{6} +(-0.855855 - 1.48238i) q^{7} +1.00000i q^{8} +(-2.82453 + 1.01095i) q^{9} +2.80145 q^{10} +(0.733565 + 1.27057i) q^{11} +(-1.62600 - 0.596750i) q^{12} +(-3.07658 - 1.77627i) q^{13} +(1.48238 + 0.855855i) q^{14} +(-1.67177 + 4.55517i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.55277 q^{17} +(1.94064 - 2.28778i) q^{18} +7.16077 q^{19} +(-2.42613 + 1.40073i) q^{20} +(-2.27624 + 1.89963i) q^{21} +(-1.27057 - 0.733565i) q^{22} +(-3.83599 + 6.64412i) q^{23} +(1.70654 - 0.296201i) q^{24} +(1.42407 + 2.46656i) q^{25} +3.55253 q^{26} +(2.56186 + 4.52072i) q^{27} -1.71171 q^{28} +(0.755499 + 1.30856i) q^{29} +(-0.829793 - 4.78078i) q^{30} +(-3.18959 - 4.56361i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.95099 - 1.62820i) q^{33} +(1.34474 - 0.776384i) q^{34} +4.79527i q^{35} +(-0.536752 + 2.95159i) q^{36} +10.5948i q^{37} +(-6.20141 + 3.58039i) q^{38} +(-2.11997 + 5.77643i) q^{39} +(1.40073 - 2.42613i) q^{40} +(4.73504 + 2.73378i) q^{41} +(1.02146 - 2.78325i) q^{42} +(3.01033 - 1.73802i) q^{43} +1.46713 q^{44} +(8.26874 + 1.50369i) q^{45} -7.67197i q^{46} +(-8.53055 + 4.92512i) q^{47} +(-1.32980 + 1.10979i) q^{48} +(2.03502 - 3.52477i) q^{49} +(-2.46656 - 1.42407i) q^{50} +(0.459931 + 2.64985i) q^{51} +(-3.07658 + 1.77627i) q^{52} -7.26920 q^{53} +(-4.47899 - 2.63413i) q^{54} -4.11009i q^{55} +(1.48238 - 0.855855i) q^{56} +(-2.12103 - 12.2201i) q^{57} +(-1.30856 - 0.755499i) q^{58} +(-9.52695 - 5.50039i) q^{59} +(3.10901 + 3.72538i) q^{60} +(-0.811064 + 0.468268i) q^{61} +(5.04407 + 2.35740i) q^{62} +(3.91601 + 3.32181i) q^{63} -1.00000 q^{64} +(4.97612 + 8.61890i) q^{65} +(-0.875510 + 2.38556i) q^{66} +(-6.03957 + 10.4608i) q^{67} +(-0.776384 + 1.34474i) q^{68} +(12.4747 + 4.57825i) q^{69} +(-2.39764 - 4.15283i) q^{70} -11.1071i q^{71} +(-1.01095 - 2.82453i) q^{72} +0.138072i q^{73} +(-5.29741 - 9.17538i) q^{74} +(3.78746 - 3.16082i) q^{75} +(3.58039 - 6.20141i) q^{76} +(1.25565 - 2.17485i) q^{77} +(-1.05226 - 6.06252i) q^{78} +(-10.6375 + 6.14158i) q^{79} +2.80145i q^{80} +(6.95594 - 5.71095i) q^{81} -5.46756 q^{82} +(-3.12049 - 5.40484i) q^{83} +(0.507010 + 2.92109i) q^{84} +(3.76721 + 2.17500i) q^{85} +(-1.73802 + 3.01033i) q^{86} +(2.00933 - 1.67688i) q^{87} +(-1.27057 + 0.733565i) q^{88} -1.01069 q^{89} +(-7.91279 + 2.83214i) q^{90} +6.08090i q^{91} +(3.83599 + 6.64412i) q^{92} +(-6.84320 + 6.79490i) q^{93} +(4.92512 - 8.53055i) q^{94} +(-17.3730 - 10.0303i) q^{95} +(0.596750 - 1.62600i) q^{96} +(-5.03375 - 8.71871i) q^{97} +4.07005i q^{98} +(-3.35647 - 2.84717i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) $ 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/558\mathbb{Z}\right)^\times$.

$n$	$127$	$497$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.296201	−	1.70654i	−0.171012	−	0.985269i
$3$	−0.296201	−	1.70654i	−0.171012	−	0.985269i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.42613	−	1.40073i	−1.08500	−	0.626424i	−0.152757	−	0.988264i	$-0.548815\pi$
$5$	−2.42613	−	1.40073i	−1.08500	−	0.626424i	−0.932240	+	0.361840i	$0.882149\pi$
$6$	1.10979	+	1.32980i	0.453068	+	0.542890i
$7$	−0.855855	−	1.48238i	−0.323483	−	0.560289i	0.657721	−	0.753261i	$-0.271520\pi$
$7$	−0.855855	−	1.48238i	−0.323483	−	0.560289i	−0.981204	+	0.192973i	$0.938187\pi$
$8$			1.00000i			0.353553i
$9$	−2.82453	+	1.01095i	−0.941510	+	0.336985i
$10$	2.80145			0.885897
$11$	0.733565	+	1.27057i	0.221178	+	0.383092i	0.955166	−	0.296071i	$-0.0956765\pi$
$11$	0.733565	+	1.27057i	0.221178	+	0.383092i	−0.733988	+	0.679163i	$0.762343\pi$
$12$	−1.62600	−	0.596750i	−0.469387	−	0.172267i
$13$	−3.07658	−	1.77627i	−0.853290	−	0.492647i	0.00846930	−	0.999964i	$-0.497304\pi$
$13$	−3.07658	−	1.77627i	−0.853290	−	0.492647i	−0.861760	+	0.507317i	$0.830637\pi$
$14$	1.48238	+	0.855855i	0.396184	+	0.228737i
$15$	−1.67177	+	4.55517i	−0.431649	+	1.17614i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.55277			−0.376601			−0.188301	−	0.982111i	$-0.560298\pi$
$17$	−1.55277			−0.376601			−0.188301	+	0.982111i	$0.560298\pi$
$18$	1.94064	−	2.28778i	0.457413	−	0.539234i
$19$	7.16077			1.64279			0.821397	−	0.570357i	$-0.193195\pi$
$19$	7.16077			1.64279			0.821397	+	0.570357i	$0.193195\pi$
$20$	−2.42613	+	1.40073i	−0.542499	+	0.313212i
$21$	−2.27624	+	1.89963i	−0.496716	+	0.414533i
$22$	−1.27057	−	0.733565i	−0.270887	−	0.156396i
$23$	−3.83599	+	6.64412i	−0.799859	+	1.38540i	0.119849	+	0.992792i	$0.461759\pi$
$23$	−3.83599	+	6.64412i	−0.799859	+	1.38540i	−0.919708	+	0.392604i	$0.871574\pi$
$24$	1.70654	−	0.296201i	0.348345	−	0.0604618i
$25$	1.42407	+	2.46656i	0.284813	+	0.493311i
$26$	3.55253			0.696709
$27$	2.56186	+	4.52072i	0.493030	+	0.870012i
$28$	−1.71171			−0.323483
$29$	0.755499	+	1.30856i	0.140293	+	0.242994i	0.927607	−	0.373558i	$-0.121862\pi$
$29$	0.755499	+	1.30856i	0.140293	+	0.242994i	−0.787314	+	0.616552i	$0.788529\pi$
$30$	−0.829793	−	4.78078i	−0.151499	−	0.872847i
$31$	−3.18959	−	4.56361i	−0.572868	−	0.819648i
$31$	−3.18959	−	4.56361i	−0.572868	−	0.819648i
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	1.95099	−	1.62820i	0.339624	−	0.283433i
$34$	1.34474	−	0.776384i	0.230620	−	0.133149i
$35$			4.79527i			0.810549i
$36$	−0.536752	+	2.95159i	−0.0894587	+	0.491932i
$37$			10.5948i			1.74178i	0.491480	+	0.870889i	$0.336456\pi$
$37$			10.5948i			1.74178i	−0.491480	+	0.870889i	$0.663544\pi$
$38$	−6.20141	+	3.58039i	−1.00600	+	0.580816i
$39$	−2.11997	+	5.77643i	−0.339468	+	0.924969i
$40$	1.40073	−	2.42613i	0.221474	−	0.383605i
$41$	4.73504	+	2.73378i	0.739489	+	0.426944i	0.821884	−	0.569655i	$-0.192923\pi$
$41$	4.73504	+	2.73378i	0.739489	+	0.426944i	−0.0823943	+	0.996600i	$0.526257\pi$
$42$	1.02146	−	2.78325i	0.157615	−	0.429464i
$43$	3.01033	−	1.73802i	0.459072	−	0.265045i	−0.252582	−	0.967575i	$-0.581280\pi$
$43$	3.01033	−	1.73802i	0.459072	−	0.265045i	0.711654	+	0.702530i	$0.247946\pi$
$44$	1.46713			0.221178
$45$	8.26874	+	1.50369i	1.23263	+	0.224156i
$46$		−	7.67197i		−	1.13117i
$47$	−8.53055	+	4.92512i	−1.24431	+	0.718402i	−0.969968	−	0.243231i	$-0.921793\pi$
$47$	−8.53055	+	4.92512i	−1.24431	+	0.718402i	−0.274340	+	0.961633i	$0.588459\pi$
$48$	−1.32980	+	1.10979i	−0.191941	+	0.160184i
$49$	2.03502	−	3.52477i	0.290718	−	0.503538i
$50$	−2.46656	−	1.42407i	−0.348824	−	0.201393i
$51$	0.459931	+	2.64985i	0.0644032	+	0.371054i
$52$	−3.07658	+	1.77627i	−0.426645	+	0.246324i
$53$	−7.26920			−0.998501			−0.499251	−	0.866458i	$-0.666391\pi$
$53$	−7.26920			−0.998501			−0.499251	+	0.866458i	$0.666391\pi$
$54$	−4.47899	−	2.63413i	−0.609514	−	0.358459i
$55$		−	4.11009i		−	0.554205i
$56$	1.48238	−	0.855855i	0.198092	−	0.114368i
$57$	−2.12103	−	12.2201i	−0.280937	−	1.61859i
$58$	−1.30856	−	0.755499i	−0.171823	−	0.0992018i
$59$	−9.52695	−	5.50039i	−1.24030	−	0.716089i	−0.271147	−	0.962538i	$-0.587403\pi$
$59$	−9.52695	−	5.50039i	−1.24030	−	0.716089i	−0.969156	+	0.246449i	$0.920736\pi$
$60$	3.10901	+	3.72538i	0.401372	+	0.480944i
$61$	−0.811064	+	0.468268i	−0.103846	+	0.0599556i	−0.551024	−	0.834490i	$-0.685763\pi$
$61$	−0.811064	+	0.468268i	−0.103846	+	0.0599556i	0.447177	+	0.894445i	$0.352429\pi$
$62$	5.04407	+	2.35740i	0.640598	+	0.299390i
$63$	3.91601	+	3.32181i	0.493371	+	0.418509i
$64$	−1.00000			−0.125000
$65$	4.97612	+	8.61890i	0.617212	+	1.06904i
$66$	−0.875510	+	2.38556i	−0.107768	+	0.293642i
$67$	−6.03957	+	10.4608i	−0.737851	+	1.27799i	0.215611	+	0.976479i	$0.430826\pi$
$67$	−6.03957	+	10.4608i	−0.737851	+	1.27799i	−0.953461	+	0.301515i	$0.902508\pi$
$68$	−0.776384	+	1.34474i	−0.0941504	+	0.163073i
$69$	12.4747	+	4.57825i	1.50177	+	0.551157i
$70$	−2.39764	−	4.15283i	−0.286572	−	0.496358i
$71$		−	11.1071i		−	1.31817i	−0.752070	−	0.659084i	$-0.770944\pi$
$71$		−	11.1071i		−	1.31817i	0.752070	−	0.659084i	$-0.229056\pi$
$72$	−1.01095	−	2.82453i	−0.119142	−	0.332874i
$73$			0.138072i			0.0161601i	0.999967	+	0.00808004i	$0.00257198\pi$
$73$			0.138072i			0.0161601i	−0.999967	+	0.00808004i	$0.997428\pi$
$74$	−5.29741	−	9.17538i	−0.615811	−	1.06662i
$75$	3.78746	−	3.16082i	0.437338	−	0.364980i
$76$	3.58039	−	6.20141i	0.410699	−	0.711351i
$77$	1.25565	−	2.17485i	0.143095	−	0.247847i
$78$	−1.05226	−	6.06252i	−0.119145	−	0.686445i
$79$	−10.6375	+	6.14158i	−1.19681	+	0.690981i	−0.959844	−	0.280535i	$-0.909488\pi$
$79$	−10.6375	+	6.14158i	−1.19681	+	0.690981i	−0.236971	+	0.971517i	$0.576155\pi$
$80$			2.80145i			0.313212i
$81$	6.95594	−	5.71095i	0.772882	−	0.634549i
$82$	−5.46756			−0.603790
$83$	−3.12049	−	5.40484i	−0.342518	−	0.593258i	0.642382	−	0.766385i	$-0.277946\pi$
$83$	−3.12049	−	5.40484i	−0.342518	−	0.593258i	−0.984900	+	0.173126i	$0.944613\pi$
$84$	0.507010	+	2.92109i	0.0553193	+	0.318718i
$85$	3.76721	+	2.17500i	0.408612	+	0.235912i
$86$	−1.73802	+	3.01033i	−0.187415	+	0.324613i
$87$	2.00933	−	1.67688i	0.215423	−	0.179781i
$88$	−1.27057	+	0.733565i	−0.135443	+	0.0781982i
$89$	−1.01069			−0.107133			−0.0535664	−	0.998564i	$-0.517059\pi$
$89$	−1.01069			−0.107133			−0.0535664	+	0.998564i	$0.517059\pi$
$90$	−7.91279	+	2.83214i	−0.834081	+	0.298534i
$91$			6.08090i			0.637452i
$92$	3.83599	+	6.64412i	0.399929	+	0.692698i
$93$	−6.84320	+	6.79490i	−0.709606	+	0.704598i
$94$	4.92512	−	8.53055i	0.507987	−	0.879859i
$95$	−17.3730	−	10.0303i	−1.78243	−	1.02909i
$96$	0.596750	−	1.62600i	0.0609056	−	0.165953i
$97$	−5.03375	−	8.71871i	−0.511100	−	0.885251i	−0.999917	−	0.0128649i	$-0.995905\pi$
$97$	−5.03375	−	8.71871i	−0.511100	−	0.885251i	0.488817	−	0.872386i	$-0.337428\pi$
$98$			4.07005i			0.411137i
$99$	−3.35647	−	2.84717i	−0.337337	−	0.286151i
$100$	2.84813			0.284813
$101$	5.14898	−	2.97276i	0.512343	−	0.295801i	−0.221453	−	0.975171i	$-0.571080\pi$
$101$	5.14898	−	2.97276i	0.512343	−	0.295801i	0.733796	+	0.679370i	$0.237747\pi$
$102$	−1.72324	−	2.06487i	−0.170626	−	0.204453i
$103$	−0.186316	+	0.322708i	−0.0183582	+	0.0317974i	−0.875059	−	0.484017i	$-0.839177\pi$
$103$	−0.186316	+	0.322708i	−0.0183582	+	0.0317974i	0.856700	+	0.515814i	$0.172511\pi$
$104$	1.77627	−	3.07658i	0.174177	−	0.301684i
$105$	8.18331	−	1.42036i	0.798609	−	0.138613i
$106$	6.29531	−	3.63460i	0.611455	−	0.353024i
$107$			4.45522i			0.430702i	0.976537	+	0.215351i	$0.0690896\pi$
$107$			4.45522i			0.430702i	−0.976537	+	0.215351i	$0.930910\pi$
$108$	5.19598	+	0.0417229i	0.499984	+	0.00401479i
$109$	−9.27511			−0.888395			−0.444197	−	0.895929i	$-0.646511\pi$
$109$	−9.27511			−0.888395			−0.444197	+	0.895929i	$0.646511\pi$
$110$	2.05505	+	3.55944i	0.195941	+	0.339380i
$111$	18.0804	−	3.13820i	1.71612	−	0.297864i
$112$	−0.855855	+	1.48238i	−0.0808707	+	0.140072i
$113$	0.738545	+	0.426399i	0.0694764	+	0.0401122i	0.534336	−	0.845272i	$-0.320562\pi$
$113$	0.738545	+	0.426399i	0.0694764	+	0.0401122i	−0.464859	+	0.885385i	$0.653895\pi$
$114$	7.94692	+	9.52242i	0.744298	+	0.891856i
$115$	18.6132	−	10.7463i	1.73569	−	1.00210i
$116$	1.51100			0.140293
$117$	10.4856	+	1.90683i	0.969396	+	0.176286i
$118$	11.0008			1.01270
$119$	1.32894	+	2.30180i	0.121824	+	0.211005i
$120$	−4.55517	−	1.67177i	−0.415828	−	0.152611i
$121$	4.42377	−	7.66219i	0.402161	−	0.696563i
$122$	0.468268	−	0.811064i	0.0423950	−	0.0734303i
$123$	3.26277	−	8.89027i	0.294194	−	0.801608i
$124$	−5.54699	+	0.480466i	−0.498135	+	0.0431471i
$125$			6.02835i			0.539192i
$126$	−5.05227	−	0.918764i	−0.450092	−	0.0818500i
$127$			1.27925i			0.113515i	0.998388	+	0.0567577i	$0.0180762\pi$
$127$			1.27925i			0.113515i	−0.998388	+	0.0567577i	$0.981924\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−3.85765	−	4.62244i	−0.339647	−	0.406983i
$130$	−8.61890	−	4.97612i	−0.755927	−	0.436435i
$131$	−3.33518	−	1.92557i	−0.291396	−	0.168238i	0.347175	−	0.937800i	$-0.387141\pi$
$131$	−3.33518	−	1.92557i	−0.291396	−	0.168238i	−0.638571	+	0.769563i	$0.720474\pi$
$132$	−0.434565	−	2.50371i	−0.0378240	−	0.217920i
$133$	−6.12858	−	10.6150i	−0.531416	−	0.920439i
$134$		−	12.0791i		−	1.04348i
$135$	0.116885	−	14.5563i	0.0100598	−	1.25281i
$136$		−	1.55277i		−	0.133149i
$137$	3.18244	+	5.51214i	0.271894	+	0.470934i	0.969347	−	0.245697i	$-0.0790167\pi$
$137$	3.18244	+	5.51214i	0.271894	+	0.470934i	−0.697453	+	0.716631i	$0.745683\pi$
$138$	−13.0925	+	2.27245i	−1.11451	+	0.193443i
$139$	−12.2227	−	7.05676i	−1.03671	−	0.598546i	−0.117812	−	0.993036i	$-0.537588\pi$
$139$	−12.2227	−	7.05676i	−1.03671	−	0.598546i	−0.918900	+	0.394490i	$0.870921\pi$
$140$	4.15283	+	2.39764i	0.350978	+	0.202637i
$141$	10.9316	+	13.0989i	0.920610	+	1.10312i
$142$	5.55354	+	9.61901i	0.466042	+	0.807209i
$143$		−	5.21202i		−	0.435851i
$144$	2.28778	+	1.94064i	0.190648	+	0.161720i
$145$		−	4.23299i		−	0.351530i
$146$	−0.0690359	−	0.119574i	−0.00571345	−	0.00989599i
$147$	−6.61792	−	2.42880i	−0.545836	−	0.200324i
$148$	9.17538	+	5.29741i	0.754212	+	0.435444i
$149$	3.45276	+	1.99345i	0.282861	+	0.163310i	0.634718	−	0.772744i	$-0.281116\pi$
$149$	3.45276	+	1.99345i	0.282861	+	0.163310i	−0.351857	+	0.936054i	$0.614450\pi$
$150$	−1.69963	+	4.63108i	−0.138774	+	0.378126i
$151$	19.7926	−	11.4273i	1.61070	−	0.929939i	0.621493	−	0.783420i	$-0.286526\pi$
$151$	19.7926	−	11.4273i	1.61070	−	0.929939i	0.989208	−	0.146519i	$-0.0468070\pi$
$152$			7.16077i			0.580816i
$153$	4.38584	−	1.56978i	0.354574	−	0.126909i
$154$			2.51130i			0.202366i
$155$	1.34600	+	15.5396i	0.108114	+	1.24817i
$156$	3.94255	+	4.72417i	0.315656	+	0.378236i
$157$	−3.75070	+	6.49641i	−0.299339	+	0.518470i	−0.975985	−	0.217839i	$-0.930099\pi$
$157$	−3.75070	+	6.49641i	−0.299339	+	0.518470i	0.676646	+	0.736308i	$0.263433\pi$
$158$	6.14158	−	10.6375i	0.488598	−	0.846276i
$159$	2.15314	+	12.4052i	0.170755	+	0.983792i
$160$	−1.40073	−	2.42613i	−0.110737	−	0.191802i
$161$	13.1322			1.03496
$162$	−3.16855	+	8.42379i	−0.248945	+	0.661836i
$163$	−7.62392			−0.597151			−0.298576	−	0.954386i	$-0.596512\pi$
$163$	−7.62392			−0.597151			−0.298576	+	0.954386i	$0.596512\pi$
$164$	4.73504	−	2.73378i	0.369745	−	0.213472i
$165$	−7.01402	+	1.21741i	−0.546041	+	0.0947755i
$166$	5.40484	+	3.12049i	0.419497	+	0.242197i
$167$	9.90418	−	17.1545i	0.766408	−	1.32746i	−0.173090	−	0.984906i	$-0.555375\pi$
$167$	9.90418	−	17.1545i	0.766408	−	1.32746i	0.939499	−	0.342552i	$-0.111291\pi$
$168$	−1.89963	−	2.27624i	−0.146560	−	0.175616i
$169$	−0.189761	−	0.328676i	−0.0145970	−	0.0252827i
$170$	−4.35000			−0.333630
$171$	−20.2258	+	7.23922i	−1.54671	+	0.553597i
$172$		−	3.47603i		−	0.265045i
$173$	21.7443	−	12.5541i	1.65319	−	0.954468i	0.677436	−	0.735582i	$-0.263091\pi$
$173$	21.7443	−	12.5541i	1.65319	−	0.954468i	0.975750	−	0.218886i	$-0.0702422\pi$
$174$	−0.901688	+	2.45689i	−0.0683568	+	0.186256i
$175$	2.43759	−	4.22203i	0.184264	−	0.319155i
$176$	0.733565	−	1.27057i	0.0552945	−	0.0957729i
$177$	−6.56472	+	17.8873i	−0.493434	+	1.34449i
$178$	0.875282	−	0.505344i	0.0656052	−	0.0378772i
$179$	−15.3162			−1.14478			−0.572392	−	0.819980i	$-0.693984\pi$
$179$	−15.3162			−1.14478			−0.572392	+	0.819980i	$0.693984\pi$
$180$	5.43660	−	6.40910i	0.405220	−	0.477706i
$181$			17.1311i			1.27335i	0.771133	+	0.636674i	$0.219690\pi$
$181$			17.1311i			1.27335i	−0.771133	+	0.636674i	$0.780310\pi$
$182$	−3.04045	−	5.26622i	−0.225373	−	0.390358i
$183$	1.03935	+	1.24541i	0.0768312	+	0.0920632i
$184$	−6.64412	−	3.83599i	−0.489811	−	0.282793i
$185$	14.8404	−	25.7044i	1.09109	−	1.88982i
$186$	2.52893	−	9.30615i	0.185430	−	0.682360i
$187$	−1.13906	−	1.97290i	−0.0832960	−	0.144273i
$188$			9.85023i			0.718402i
$189$	4.50886	−	7.66674i	0.327971	−	0.557673i
$190$	20.0606			1.45535
$191$	−1.58477	+	0.914970i	−0.114670	+	0.0662049i	−0.556238	−	0.831023i	$-0.687756\pi$
$191$	−1.58477	+	0.914970i	−0.114670	+	0.0662049i	0.441568	+	0.897228i	$0.354422\pi$
$192$	0.296201	+	1.70654i	0.0213765	+	0.123159i
$193$	−2.95915	+	5.12540i	−0.213004	+	0.368934i	−0.952653	−	0.304059i	$-0.901658\pi$
$193$	−2.95915	+	5.12540i	−0.213004	+	0.368934i	0.739649	+	0.672993i	$0.234991\pi$
$194$	8.71871	+	5.03375i	0.625967	+	0.361402i
$195$	13.2345	−	11.0449i	0.947744	−	0.790939i
$196$	−2.03502	−	3.52477i	−0.145359	−	0.251769i
$197$	−12.4301			−0.885606			−0.442803	−	0.896619i	$-0.646016\pi$
$197$	−12.4301			−0.885606			−0.442803	+	0.896619i	$0.646016\pi$
$198$	4.33037	+	0.787485i	0.307746	+	0.0559641i
$199$			3.47989i			0.246683i	0.992364	+	0.123342i	$0.0393611\pi$
$199$			3.47989i			0.246683i	−0.992364	+	0.123342i	$0.960639\pi$
$200$	−2.46656	+	1.42407i	−0.174412	+	0.100697i
$201$	19.6407	+	7.20823i	1.38535	+	0.508429i
$202$	−2.97276	+	5.14898i	−0.209163	+	0.362281i
$203$	1.29319	−	2.23988i	0.0907645	−	0.157209i
$204$	2.52481	+	0.926615i	0.176772	+	0.0648760i
$205$	−7.65855	−	13.2650i	−0.534896	−	0.926467i
$206$		−	0.372631i		−	0.0259624i
$207$	4.11795	−	22.6445i	0.286217	−	1.57390i
$208$			3.55253i			0.246324i
$209$	5.25289	+	9.09827i	0.363350	+	0.629341i
$210$	−6.37677	+	5.32172i	−0.440039	+	0.367234i
$211$	−6.02815	+	10.4411i	−0.414995	+	0.718792i	−0.995428	−	0.0955160i	$-0.969550\pi$
$211$	−6.02815	+	10.4411i	−0.414995	+	0.718792i	0.580433	+	0.814308i	$0.302883\pi$
$212$	−3.63460	+	6.29531i	−0.249625	+	0.432364i
$213$	−18.9546	+	3.28992i	−1.29875	+	0.225422i
$214$	−2.22761	−	3.85833i	−0.152276	−	0.263750i
$215$	−9.73794			−0.664122
$216$	−4.52072	+	2.56186i	−0.307596	+	0.174312i
$217$	−4.03519	+	8.63399i	−0.273926	+	0.586113i
$218$	8.03248	−	4.63756i	0.544028	−	0.314095i
$219$	0.235624	−	0.0408970i	0.0159220	−	0.00276356i
$220$	−3.55944	−	2.05505i	−0.239978	−	0.138551i
$221$	4.77722	+	2.75813i	0.321350	+	0.185532i
$222$	−14.0890	+	11.7580i	−0.945593	+	0.789144i
$223$	−21.6565	+	12.5034i	−1.45023	+	0.837288i	−0.998494	−	0.0548651i	$-0.982527\pi$
$223$	−21.6565	+	12.5034i	−1.45023	+	0.837288i	−0.451732	+	0.892154i	$0.649194\pi$
$224$		−	1.71171i		−	0.114368i
$225$	−6.51590	−	5.52719i	−0.434393	−	0.368480i
$226$	−0.852798			−0.0567273
$227$	−2.95339	+	1.70514i	−0.196023	+	0.113174i	−0.594799	−	0.803874i	$-0.702768\pi$
$227$	−2.95339	+	1.70514i	−0.196023	+	0.113174i	0.398776	+	0.917048i	$0.369435\pi$
$228$	−11.6434	−	4.27320i	−0.771106	−	0.282999i
$229$	−7.49557	−	4.32757i	−0.495321	−	0.285974i	0.231458	−	0.972845i	$-0.425650\pi$
$229$	−7.49557	−	4.32757i	−0.495321	−	0.285974i	−0.726779	+	0.686871i	$0.758984\pi$
$230$	−10.7463	+	18.6132i	−0.708592	+	1.22732i
$231$	−4.08338	−	1.49862i	−0.268667	−	0.0986019i
$232$	−1.30856	+	0.755499i	−0.0859113	+	0.0496009i
$233$		−	11.0476i		−	0.723749i	−0.932227	−	0.361875i	$-0.882137\pi$
$233$		−	11.0476i		−	0.723749i	0.932227	−	0.361875i	$-0.117863\pi$
$234$	−10.0342	+	3.59145i	−0.655958	+	0.234780i
$235$	27.5949			1.80010
$236$	−9.52695	+	5.50039i	−0.620151	+	0.358045i
$237$	13.6317	+	16.3342i	0.885472	+	1.06102i
$238$	−2.30180	−	1.32894i	−0.149203	−	0.0861426i
$239$	−10.6056	+	18.3695i	−0.686022	+	1.18822i	0.287093	+	0.957903i	$0.407311\pi$
$239$	−10.6056	+	18.3695i	−0.686022	+	1.18822i	−0.973115	+	0.230322i	$0.926022\pi$
$240$	4.78078	−	0.829793i	0.308598	−	0.0535629i
$241$	−1.62450	+	0.937906i	−0.104643	+	0.0604158i	−0.551408	−	0.834236i	$-0.685909\pi$
$241$	−1.62450	+	0.937906i	−0.104643	+	0.0604158i	0.446765	+	0.894651i	$0.352576\pi$
$242$			8.84753i			0.568741i
$243$	−11.8063	−	10.1790i	−0.757374	−	0.652982i
$244$			0.936536i			0.0599556i
$245$	−9.87446	+	5.70102i	−0.630856	+	0.364225i
$246$	1.61949	+	9.33058i	0.103255	+	0.594896i
$247$	−22.0307	−	12.7194i	−1.40178	−	0.809318i
$248$	4.56361	−	3.18959i	0.289789	−	0.202539i
$249$	−8.29927	+	6.92614i	−0.525945	+	0.438926i
$250$	−3.01418	−	5.22070i	−0.190633	−	0.330186i
$251$	−23.3528			−1.47402			−0.737008	−	0.675884i	$-0.763762\pi$
$251$	−23.3528			−1.47402			−0.737008	+	0.675884i	$0.763762\pi$
$252$	4.83478	−	1.73046i	0.304562	−	0.109009i
$253$	−11.2558			−0.707645
$254$	−0.639627	−	1.10787i	−0.0401337	−	0.0695137i
$255$	2.59587	−	7.07312i	0.162559	−	0.442936i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.266405	+	0.153809i	0.0166179	+	0.00959436i	0.508286	−	0.861188i	$-0.330279\pi$
$257$	0.266405	+	0.153809i	0.0166179	+	0.00959436i	−0.491668	+	0.870783i	$0.663613\pi$
$258$	5.65204	+	2.07432i	0.351881	+	0.129142i
$259$	15.7056	−	9.06763i	0.975898	−	0.563435i
$260$	9.95225			0.617212
$261$	−3.45683	−	2.93230i	−0.213972	−	0.181505i
$262$	3.85114			0.237924
$263$	−12.4680	−	21.5952i	−0.768810	−	1.33162i	−0.938209	−	0.346070i	$-0.887516\pi$
$263$	−12.4680	−	21.5952i	−0.768810	−	1.33162i	0.169399	−	0.985548i	$-0.445817\pi$
$264$	1.62820	+	1.95099i	0.100209	+	0.120075i
$265$	17.6360	+	10.1822i	1.08337	+	0.625485i
$266$	10.6150	+	6.12858i	0.650849	+	0.375768i
$267$	0.299367	+	1.72478i	0.0183210	+	0.105555i
$268$	6.03957	+	10.4608i	0.368925	+	0.638997i
$269$	−5.85961			−0.357267			−0.178633	−	0.983916i	$-0.557168\pi$
$269$	−5.85961			−0.357267			−0.178633	+	0.983916i	$0.557168\pi$
$270$	7.17693	+	12.6646i	0.436774	+	0.770741i
$271$			18.2115i			1.10627i	0.833091	+	0.553136i	$0.186569\pi$
$271$			18.2115i			1.10627i	−0.833091	+	0.553136i	$0.813431\pi$
$272$	0.776384	+	1.34474i	0.0470752	+	0.0815366i
$273$	10.3773	−	1.80117i	0.628062	−	0.109012i
$274$	−5.51214	−	3.18244i	−0.333001	−	0.192258i
$275$	−2.08929	+	3.61876i	−0.125989	+	0.218219i
$276$	10.2022	−	8.51425i	0.614101	−	0.512497i
$277$	−9.65869	+	5.57645i	−0.580334	+	0.335056i	−0.761266	−	0.648439i	$-0.775422\pi$
$277$	−9.65869	+	5.57645i	−0.580334	+	0.335056i	0.180932	+	0.983496i	$0.442089\pi$
$278$	14.1135			0.846472
$279$	13.6227	+	9.66551i	0.815570	+	0.578659i
$280$	−4.79527			−0.286572
$281$	−1.20286	+	0.694470i	−0.0717564	+	0.0414286i	−0.535449	−	0.844568i	$-0.679858\pi$
$281$	−1.20286	+	0.694470i	−0.0717564	+	0.0414286i	0.463693	+	0.885996i	$0.346524\pi$
$282$	−16.0165	−	5.87813i	−0.953770	−	0.350038i
$283$	−12.9929	+	22.5044i	−0.772348	+	1.33775i	0.163925	+	0.986473i	$0.447585\pi$
$283$	−12.9929	+	22.5044i	−0.772348	+	1.33775i	−0.936273	+	0.351273i	$0.885749\pi$
$284$	−9.61901	−	5.55354i	−0.570783	−	0.329542i
$285$	−11.9712	+	32.6186i	−0.709110	+	1.93216i
$286$	2.60601	+	4.51374i	0.154097	+	0.266903i
$287$		−	9.35887i		−	0.552437i
$288$	−2.95159	−	0.536752i	−0.173924	−	0.0316284i
$289$	−14.5889			−0.858171
$290$	2.11649	+	3.66587i	0.124285	+	0.215268i
$291$	−13.3878	+	11.1728i	−0.784806	+	0.654959i
$292$	0.119574	+	0.0690359i	0.00699752	+	0.00404002i
$293$	−1.52102	−	0.878162i	−0.0888591	−	0.0513028i	0.454912	−	0.890536i	$-0.349671\pi$
$293$	−1.52102	−	0.878162i	−0.0888591	−	0.0513028i	−0.543771	+	0.839234i	$0.683004\pi$
$294$	6.94568	−	1.20555i	0.405081	−	0.0703092i
$295$	15.4091	+	26.6893i	0.897150	+	1.55391i
$296$	−10.5948			−0.615811
$297$	−3.86460	+	6.57126i	−0.224247	+	0.381303i
$298$	−3.98691			−0.230955
$299$	23.6035	−	13.6275i	1.36502	−	0.788097i
$300$	−0.843620	−	4.86044i	−0.0487064	−	0.280618i
$301$	−5.15282	−	2.97498i	−0.297003	−	0.171475i
$302$	−11.4273	+	19.7926i	−0.657566	+	1.13894i
$303$	−6.59826	−	7.90638i	−0.379060	−	0.454210i
$304$	−3.58039	−	6.20141i	−0.205349	−	0.355675i
$305$	2.62366			0.150230
$306$	−3.01336	+	3.55239i	−0.172262	+	0.203076i
$307$	−19.6057			−1.11895			−0.559477	−	0.828846i	$-0.688998\pi$
$307$	−19.6057			−1.11895			−0.559477	+	0.828846i	$0.688998\pi$
$308$	−1.25565	−	2.17485i	−0.0715473	−	0.123924i
$309$	0.605900	+	0.222368i	0.0344684	+	0.0126501i
$310$	−8.93549	−	12.7847i	−0.507502	−	0.726123i
$311$	−14.9268	−	8.61798i	−0.846420	−	0.488681i	0.0130214	−	0.999915i	$-0.495855\pi$
$311$	−14.9268	−	8.61798i	−0.846420	−	0.488681i	−0.859441	+	0.511234i	$0.829188\pi$
$312$	−5.77643	−	2.11997i	−0.327026	−	0.120020i
$313$	22.5106	−	12.9965i	1.27238	−	0.734607i	0.296942	−	0.954895i	$-0.404033\pi$
$313$	22.5106	−	12.9965i	1.27238	−	0.734607i	0.975435	+	0.220288i	$0.0706998\pi$
$314$		−	7.50140i		−	0.423329i
$315$	−4.84781	−	13.5444i	−0.273143	−	0.763140i
$316$			12.2832i			0.690981i
$317$	16.6768	−	9.62837i	0.936664	−	0.540783i	0.0477510	−	0.998859i	$-0.484795\pi$
$317$	16.6768	−	9.62837i	0.936664	−	0.540783i	0.888913	+	0.458076i	$0.151461\pi$
$318$	−8.06725	−	9.66660i	−0.452389	−	0.542076i
$319$	−1.10841	+	1.91983i	−0.0620593	+	0.107490i
$320$	2.42613	+	1.40073i	0.135625	+	0.0783030i
$321$	7.60299	−	1.31964i	0.424358	−	0.0736551i
$322$	−11.3728	+	6.56610i	−0.633782	+	0.365914i
$323$	−11.1190			−0.618679
$324$	−1.46785	−	8.87949i	−0.0815474	−	0.493305i
$325$		−	10.1181i		−	0.561250i
$326$	6.60251	−	3.81196i	0.365679	−	0.211125i
$327$	2.74730	+	15.8283i	0.151926	+	0.875308i
$328$	−2.73378	+	4.73504i	−0.150948	+	0.261449i
$329$	14.6018	+	8.43037i	0.805025	+	0.464781i
$330$	5.46561	−	4.56132i	0.300872	−	0.251092i
$331$	17.2573	−	9.96350i	0.948546	−	0.547643i	0.0559171	−	0.998435i	$-0.482192\pi$
$331$	17.2573	−	9.96350i	0.948546	−	0.547643i	0.892629	+	0.450792i	$0.148858\pi$
$332$	−6.24097			−0.342518
$333$	−10.7109	−	29.9254i	−0.586953	−	1.63990i
$334$			19.8084i			1.08387i
$335$	29.3055	−	16.9196i	1.60113	−	0.924414i
$336$	2.78325	+	1.02146i	0.151839	+	0.0557254i
$337$	11.4177	+	6.59199i	0.621960	+	0.359089i	0.777632	−	0.628720i	$-0.216421\pi$
$337$	11.4177	+	6.59199i	0.621960	+	0.359089i	−0.155672	+	0.987809i	$0.549754\pi$
$338$	0.328676	+	0.189761i	0.0178776	+	0.0103216i
$339$	0.508908	−	1.38665i	0.0276401	−	0.0753127i
$340$	3.76721	−	2.17500i	0.204306	−	0.117956i
$341$	3.45861	−	7.40030i	0.187294	−	0.400749i
$342$	13.8965	−	16.3823i	0.751435	−	0.885851i
$343$	−18.9487			−1.02313
$344$	1.73802	+	3.01033i	0.0937076	+	0.162306i
$345$	−23.8523	−	28.5810i	−1.28416	−	1.53875i
$346$	−12.5541	+	21.7443i	−0.674911	+	1.16898i
$347$	15.8053	−	27.3756i	0.848474	−	1.46960i	−0.0340955	−	0.999419i	$-0.510855\pi$
$347$	15.8053	−	27.3756i	0.848474	−	1.46960i	0.882570	−	0.470182i	$-0.155812\pi$
$348$	−0.447559	−	2.57857i	−0.0239917	−	0.138226i
$349$	14.7463	+	25.5413i	0.789349	+	1.36719i	0.926366	+	0.376624i	$0.122915\pi$
$349$	14.7463	+	25.5413i	0.789349	+	1.36719i	−0.137017	+	0.990569i	$0.543751\pi$
$350$			4.87518i			0.260589i
$351$	0.148222	−	18.4589i	0.00791150	−	0.985263i
$352$			1.46713i			0.0781982i
$353$	−2.19529	−	3.80236i	−0.116844	−	0.202379i	0.801672	−	0.597765i	$-0.203944\pi$
$353$	−2.19529	−	3.80236i	−0.116844	−	0.202379i	−0.918515	+	0.395386i	$0.870611\pi$
$354$	−3.25844	−	18.7732i	−0.173184	−	0.997785i
$355$	−15.5580	+	26.9472i	−0.825731	+	1.43021i
$356$	−0.505344	+	0.875282i	−0.0267832	+	0.0463899i
$357$	3.53447	−	2.94969i	0.187064	−	0.156114i
$358$	13.2642	−	7.65808i	0.701034	−	0.404742i
$359$			15.9884i			0.843836i	0.906634	+	0.421918i	$0.138643\pi$
$359$			15.9884i			0.843836i	−0.906634	+	0.421918i	$0.861357\pi$
$360$	−1.50369	+	8.26874i	−0.0792512	+	0.435801i
$361$	32.2767			1.69877
$362$	−8.56557	−	14.8360i	−0.450196	−	0.779763i
$363$	−14.3861	−	5.27977i	−0.755076	−	0.277116i
$364$	5.26622	+	3.04045i	0.276025	+	0.159363i
$365$	0.193401	−	0.334980i	0.0101231	−	0.0175336i
$366$	−1.52281	−	0.558878i	−0.0795986	−	0.0292130i
$367$	26.6166	−	15.3671i	1.38937	−	0.802155i	0.396129	−	0.918195i	$-0.370353\pi$
$367$	26.6166	−	15.3671i	1.38937	−	0.802155i	0.993245	+	0.116040i	$0.0370201\pi$
$368$	7.67197			0.399929
$369$	−16.1380	−	2.93472i	−0.840110	−	0.152776i
$370$			29.6809i			1.54304i
$371$	6.22138	+	10.7757i	0.322998	+	0.559449i
$372$	2.46296	+	9.32383i	0.127698	+	0.483418i
$373$	−13.4906	+	23.3664i	−0.698516	+	1.20987i	0.270465	+	0.962730i	$0.412823\pi$
$373$	−13.4906	+	23.3664i	−0.698516	+	1.20987i	−0.968981	+	0.247136i	$0.920511\pi$
$374$	1.97290	+	1.13906i	0.102016	+	0.0588991i
$375$	10.2876	−	1.78560i	0.531249	−	0.0922081i
$376$	−4.92512	−	8.53055i	−0.253993	−	0.439930i
$377$		−	5.36787i		−	0.276459i
$378$	−0.0714175	+	8.89402i	−0.00367332	+	0.457459i
$379$	19.1216			0.982211			0.491106	−	0.871100i	$-0.336593\pi$
$379$	19.1216			0.982211			0.491106	+	0.871100i	$0.336593\pi$
$380$	−17.3730	+	10.0303i	−0.891214	+	0.514543i
$381$	2.18309	−	0.378916i	0.111843	−	0.0194125i
$382$	0.914970	−	1.58477i	0.0468139	−	0.0810841i
$383$	−0.976928	+	1.69209i	−0.0499187	+	0.0864617i	−0.889905	−	0.456146i	$-0.849230\pi$
$383$	−0.976928	+	1.69209i	−0.0499187	+	0.0864617i	0.839986	+	0.542607i	$0.182563\pi$
$384$	−1.10979	−	1.32980i	−0.0566335	−	0.0678612i
$385$	−6.09274	+	3.51764i	−0.310515	+	0.179276i
$386$		−	5.91830i		−	0.301234i
$387$	−6.74572	+	7.95239i	−0.342904	+	0.404243i
$388$	−10.0675			−0.511100
$389$	−15.7084	−	27.2077i	−0.796447	−	1.37949i	−0.921916	−	0.387389i	$-0.873377\pi$
$389$	−15.7084	−	27.2077i	−0.796447	−	1.37949i	0.125470	−	0.992097i	$-0.459956\pi$
$390$	−5.93901	+	16.1824i	−0.300733	+	0.819427i
$391$	5.95640	−	10.3168i	0.301228	−	0.521742i
$392$	3.52477	+	2.03502i	0.178028	+	0.102784i
$393$	−2.29817	+	6.26196i	−0.115927	+	0.315874i
$394$	10.7648	−	6.21503i	0.542320	−	0.313109i
$395$	34.4107			1.73139
$396$	−4.14395	+	1.48320i	−0.208241	+	0.0745337i
$397$	18.7186			0.939458			0.469729	−	0.882811i	$-0.344352\pi$
$397$	18.7186			0.939458			0.469729	+	0.882811i	$0.344352\pi$
$398$	−1.73995	−	3.01368i	−0.0872157	−	0.151062i
$399$	−16.2996	+	13.6028i	−0.816002	+	0.680993i
$400$	1.42407	−	2.46656i	0.0712033	−	0.123328i
$401$	1.80742	−	3.13054i	0.0902583	−	0.156332i	−0.817361	−	0.576125i	$-0.804564\pi$
$401$	1.80742	−	3.13054i	0.0902583	−	0.156332i	0.907620	+	0.419793i	$0.137897\pi$
$402$	−20.6135	+	3.57785i	−1.02811	+	0.178447i
$403$	1.70687	+	19.7059i	0.0850253	+	0.981619i
$404$		−	5.94553i		−	0.295801i
$405$	−24.8755	+	4.11212i	−1.23607	+	0.204333i
$406$			2.58639i			0.128360i
$407$	−13.4615	+	7.77198i	−0.667260	+	0.385243i
$408$	−2.64985	+	0.459931i	−0.131187	+	0.0227700i
$409$	3.08139	+	1.77904i	0.152365	+	0.0879679i	0.574244	−	0.818684i	$-0.305296\pi$
$409$	3.08139	+	1.77904i	0.152365	+	0.0879679i	−0.421879	+	0.906652i	$0.638629\pi$
$410$	13.2650	+	7.65855i	0.655111	+	0.378229i
$411$	8.46403	−	7.06364i	0.417500	−	0.348424i
$412$	0.186316	+	0.322708i	0.00917911	+	0.0158987i
$413$			18.8301i			0.926570i
$414$	7.75602	+	21.6697i	0.381188	+	1.06501i
$415$			17.4838i			0.858245i
$416$	−1.77627	−	3.07658i	−0.0870886	−	0.150842i
$417$	−8.42225	+	22.9486i	−0.412439	+	1.12380i
$418$	−9.09827	−	5.25289i	−0.445011	−	0.256927i
$419$	29.1162	+	16.8102i	1.42242	+	0.821233i	0.996505	−	0.0835308i	$-0.0266197\pi$
$419$	29.1162	+	16.8102i	1.42242	+	0.821233i	0.425913	+	0.904764i	$0.359953\pi$
$420$	2.86158	−	7.79713i	0.139631	−	0.380461i
$421$	3.44737	+	5.97103i	0.168015	+	0.291010i	0.937722	−	0.347387i	$-0.112931\pi$
$421$	3.44737	+	5.97103i	0.168015	+	0.291010i	−0.769707	+	0.638397i	$0.779598\pi$
$422$		−	12.0563i		−	0.586891i
$423$	19.1157	−	22.5351i	0.929438	−	1.09570i
$424$		−	7.26920i		−	0.353024i
$425$	−2.21124	−	3.82999i	−0.107261	−	0.185782i
$426$	14.7702	−	12.3265i	0.715619	−	0.597219i
$427$	1.38831	+	0.801539i	0.0671848	+	0.0387892i
$428$	3.85833	+	2.22761i	0.186500	+	0.107676i
$429$	−8.89450	+	1.54381i	−0.429431	+	0.0745356i
$430$	8.43331	−	4.86897i	0.406690	−	0.234803i
$431$			1.48642i			0.0715984i	0.999359	+	0.0357992i	$0.0113977\pi$
$431$			1.48642i			0.0715984i	−0.999359	+	0.0357992i	$0.988602\pi$
$432$	2.63413	−	4.47899i	0.126734	−	0.215496i
$433$		−	16.5728i		−	0.796440i	−0.917290	−	0.398220i	$-0.869628\pi$
$433$		−	16.5728i		−	0.796440i	0.917290	−	0.398220i	$-0.130372\pi$
$434$	−0.822419	−	9.49485i	−0.0394774	−	0.455767i
$435$	−7.22374	+	1.25381i	−0.346352	+	0.0601158i
$436$	−4.63756	+	8.03248i	−0.222099	+	0.384686i
$437$	−27.4686	+	47.5771i	−1.31400	+	2.27592i
$438$	−0.183608	+	0.153230i	−0.00877314	+	0.00732161i
$439$	−17.8947	−	30.9945i	−0.854065	−	1.47928i	−0.877509	−	0.479559i	$-0.840796\pi$
$439$	−17.8947	−	30.9945i	−0.854065	−	1.47928i	0.0234440	−	0.999725i	$-0.492537\pi$
$440$	4.11009			0.195941
$441$	−2.18461	+	12.0131i	−0.104029	+	0.572054i
$442$	−5.51626			−0.262381
$443$	−16.1237	+	9.30903i	−0.766061	+	0.442286i	−0.831468	−	0.555573i	$-0.812499\pi$
$443$	−16.1237	+	9.30903i	−0.766061	+	0.442286i	0.0654066	+	0.997859i	$0.479166\pi$
$444$	6.32246	−	17.2272i	0.300051	−	0.817568i
$445$	2.45206	+	1.41570i	0.116239	+	0.0671105i
$446$	12.5034	−	21.6565i	0.592052	−	1.02546i
$447$	2.37919	−	6.48273i	0.112532	−	0.306622i
$448$	0.855855	+	1.48238i	0.0404353	+	0.0700361i
$449$	37.5508			1.77213			0.886065	−	0.463560i	$-0.153428\pi$
$449$	37.5508			1.77213			0.886065	+	0.463560i	$0.153428\pi$
$450$	8.40653	+	1.52874i	0.396288	+	0.0720656i
$451$			8.02161i			0.377723i
$452$	0.738545	−	0.426399i	0.0347382	−	0.0200561i
$453$	−25.3637	−	30.3921i	−1.19169	−	1.42794i
$454$	1.70514	−	2.95339i	0.0800262	−	0.138609i
$455$	8.51768	−	14.7531i	0.399315	−	0.691634i
$456$	12.2201	−	2.12103i	0.572260	−	0.0993262i
$457$	−15.3789	+	8.87898i	−0.719392	+	0.415341i	−0.814529	−	0.580123i	$-0.803005\pi$
$457$	−15.3789	+	8.87898i	−0.719392	+	0.415341i	0.0951366	+	0.995464i	$0.469671\pi$
$458$	8.65514			0.404428
$459$	−3.97797	−	7.01962i	−0.185676	−	0.327648i
$460$		−	21.4927i		−	1.00210i
$461$	16.6185	+	28.7841i	0.774000	+	1.34061i	0.935355	+	0.353711i	$0.115080\pi$
$461$	16.6185	+	28.7841i	0.774000	+	1.34061i	−0.161355	+	0.986896i	$0.551586\pi$
$462$	4.28562	−	0.743849i	0.199385	−	0.0346070i
$463$	−13.2832	−	7.66907i	−0.617323	−	0.356412i	0.158503	−	0.987359i	$-0.449333\pi$
$463$	−13.2832	−	7.66907i	−0.617323	−	0.356412i	−0.775826	+	0.630947i	$0.782667\pi$
$464$	0.755499	−	1.30856i	0.0350731	−	0.0607485i
$465$	26.1203	−	6.89986i	1.21130	−	0.319973i
$466$	5.52378	+	9.56746i	0.255884	+	0.443204i
$467$		−	7.95169i		−	0.367960i	−0.982930	−	0.183980i	$-0.941102\pi$
$467$		−	7.95169i		−	0.367960i	0.982930	−	0.183980i	$-0.0588982\pi$
$468$	6.89417	−	8.12740i	0.318683	−	0.375689i
$469$	20.6760			0.954728
$470$	−23.8979	+	13.7975i	−1.10233	+	0.636430i
$471$	12.1973	+	4.47647i	0.562022	+	0.206265i
$472$	5.50039	−	9.52695i	0.253176	−	0.438513i
$473$	4.41655	+	2.54989i	0.203073	+	0.117244i
$474$	−19.9725	−	7.32998i	−0.917365	−	0.336677i
$475$	10.1974	+	17.6625i	0.467890	+	0.810409i
$476$	2.65789			0.121824
$477$	20.5321	−	7.34883i	0.940099	−	0.336480i
$478$		−	21.2113i		−	0.970181i
$479$	0.289339	−	0.167050i	0.0132202	−	0.00763271i	−0.493375	−	0.869817i	$-0.664237\pi$
$479$	0.289339	−	0.167050i	0.0132202	−	0.00763271i	0.506596	+	0.862184i	$0.330904\pi$
$480$	−3.72538	+	3.10901i	−0.170040	+	0.141906i
$481$	18.8192	−	32.5958i	0.858082	−	1.48624i
$482$	0.937906	−	1.62450i	0.0427204	−	0.0739940i
$483$	−3.88977	−	22.4106i	−0.176991	−	1.01972i
$484$	−4.42377	−	7.66219i	−0.201080	−	0.348281i
$485$			28.2036i			1.28066i
$486$	15.3140	+	2.91211i	0.694659	+	0.132096i
$487$		−	26.5619i		−	1.20363i	−0.798634	−	0.601817i	$-0.794444\pi$
$487$		−	26.5619i		−	1.20363i	0.798634	−	0.601817i	$-0.205556\pi$
$488$	−0.468268	−	0.811064i	−0.0211975	−	0.0367151i
$489$	2.25821	+	13.0105i	0.102120	+	0.588355i
$490$	5.70102	−	9.87446i	0.257546	−	0.446083i
$491$	−0.293876	+	0.509009i	−0.0132625	+	0.0229712i	−0.872580	−	0.488470i	$-0.837555\pi$
$491$	−0.293876	+	0.509009i	−0.0132625	+	0.0229712i	0.859318	+	0.511442i	$0.170888\pi$
$492$	−6.06781	−	7.27077i	−0.273558	−	0.327792i
$493$	−1.17311	−	2.03189i	−0.0528344	−	0.0915118i
$494$	25.4389			1.14455
$495$	4.15512	+	11.6091i	0.186759	+	0.521789i
$496$	−2.35740	+	5.04407i	−0.105850	+	0.226486i
$497$	−16.4650	+	9.50604i	−0.738554	+	0.426404i
$498$	3.72430	−	10.1478i	0.166890	−	0.454736i
$499$	24.6683	+	14.2422i	1.10430	+	0.637571i	0.937348	−	0.348394i	$-0.113273\pi$
$499$	24.6683	+	14.2422i	1.10430	+	0.637571i	0.166956	+	0.985964i	$0.446606\pi$
$500$	5.22070	+	3.01418i	0.233477	+	0.134798i
$501$	−32.2085	−	11.8206i	−1.43897	−	0.528108i
$502$	20.2241	−	11.6764i	0.902647	−	0.521144i
$503$			1.68247i			0.0750177i	0.999296	+	0.0375088i	$0.0119422\pi$
$503$			1.68247i			0.0750177i	−0.999296	+	0.0375088i	$0.988058\pi$
$504$	−3.32181	+	3.91601i	−0.147965	+	0.174433i
$505$	−16.6561			−0.741187
$506$	9.74779	−	5.62789i	0.433342	−	0.250190i
$507$	−0.504690	+	0.421188i	−0.0224141	+	0.0187056i
$508$	1.10787	+	0.639627i	0.0491536	+	0.0283788i
$509$	3.73041	−	6.46126i	0.165347	−	0.286390i	−0.771431	−	0.636313i	$-0.780459\pi$
$509$	3.73041	−	6.46126i	0.165347	−	0.286390i	0.936779	+	0.349923i	$0.113792\pi$
$510$	1.28848	+	7.42344i	0.0570546	+	0.328715i
$511$	0.204675	−	0.118169i	0.00905431	−	0.00522751i
$512$		−	1.00000i		−	0.0441942i
$513$	18.3449	+	32.3718i	0.809947	+	1.42925i
$514$	−0.307619			−0.0135685
$515$	0.904051	−	0.521954i	0.0398373	−	0.0230001i
$516$	−5.93198	+	1.02960i	−0.261141	+	0.0453258i
$517$	−12.5154	−	7.22578i	−0.550427	−	0.317789i
$518$	−9.06763	+	15.7056i	−0.398409	+	0.690064i
$519$	−27.8646	−	33.3889i	−1.22312	−	1.46561i
$520$	−8.61890	+	4.97612i	−0.377964	+	0.218217i
$521$		−	5.59532i		−	0.245136i	−0.992460	−	0.122568i	$-0.960887\pi$
$521$		−	5.59532i		−	0.245136i	0.992460	−	0.122568i	$-0.0391129\pi$
$522$	4.45985	+	0.811031i	0.195202	+	0.0354979i
$523$		−	1.73661i		−	0.0759367i	−0.999279	−	0.0379684i	$-0.987911\pi$
$523$		−	1.73661i		−	0.0759367i	0.999279	−	0.0379684i	$-0.0120886\pi$
$524$	−3.33518	+	1.92557i	−0.145698	+	0.0841188i
$525$	−7.92706	−	2.90927i	−0.345965	−	0.126971i
$526$	21.5952	+	12.4680i	0.941596	+	0.543630i
$527$	4.95270	+	7.08622i	0.215743	+	0.308681i
$528$	−2.38556	−	0.875510i	−0.103818	−	0.0381017i
$529$	−17.9296	−	31.0550i	−0.779548	−	1.35022i
$530$	−20.3643			−0.884569
$531$	32.4698	+	5.90469i	1.40907	+	0.256242i
$532$	−12.2572			−0.531416
$533$	−9.71183	−	16.8214i	−0.420666	−	0.728615i
$534$	−1.12165	−	1.34402i	−0.0485384	−	0.0581613i
$535$	6.24054	−	10.8089i	0.269802	−	0.467311i
$536$	−10.4608	−	6.03957i	−0.451839	−	0.260870i
$537$	4.53666	+	26.1376i	0.195771	+	1.12792i
$538$	5.07457	−	2.92980i	0.218780	−	0.126313i
$539$	5.97129			0.257202
$540$	−12.5477	−	7.37938i	−0.539966	−	0.317558i
$541$	−8.04805			−0.346013			−0.173006	−	0.984921i	$-0.555348\pi$
$541$	−8.04805			−0.346013			−0.173006	+	0.984921i	$0.555348\pi$
$542$	−9.10576	−	15.7716i	−0.391126	−	0.677450i
$543$	29.2349	−	5.07426i	1.25459	−	0.217757i
$544$	−1.34474	−	0.776384i	−0.0576551	−	0.0332872i
$545$	22.5026	+	12.9919i	0.963906	+	0.556511i
$546$	−8.08640	+	6.74850i	−0.346066	+	0.288809i
$547$	6.72268	+	11.6440i	0.287441	+	0.497863i	0.973198	−	0.229968i	$-0.0738621\pi$
$547$	6.72268	+	11.6440i	0.287441	+	0.497863i	−0.685757	+	0.727831i	$0.740529\pi$
$548$	6.36487			0.271894
$549$	1.81748	−	2.14259i	0.0775680	−	0.0914433i
$550$		−	4.17858i		−	0.178175i
$551$	5.40996	+	9.37032i	0.230472	+	0.399189i
$552$	−4.57825	+	12.4747i	−0.194863	+	0.530957i
$553$	18.2084	+	10.5126i	0.774298	+	0.447041i
$554$	5.57645	−	9.65869i	0.236920	−	0.410358i
$555$	−48.2612	−	17.7121i	−2.04858	−	0.751836i
$556$	−12.2227	+	7.05676i	−0.518356	+	0.299273i
$557$	0.933781			0.0395656			0.0197828	−	0.999804i	$-0.493703\pi$
$557$	0.933781			0.0395656			0.0197828	+	0.999804i	$0.493703\pi$
$558$	−16.6304	−	1.55922i	−0.704019	−	0.0660071i
$559$	−12.3487			−0.522295
$560$	4.15283	−	2.39764i	0.175489	−	0.101319i
$561$	−3.02944	+	2.52821i	−0.127903	+	0.106741i
$562$	0.694470	−	1.20286i	0.0292944	−	0.0507394i
$563$	−10.9266	−	6.30846i	−0.460500	−	0.265870i	0.251754	−	0.967791i	$-0.418992\pi$
$563$	−10.9266	−	6.30846i	−0.460500	−	0.265870i	−0.712254	+	0.701921i	$0.752326\pi$
$564$	16.8098	−	2.91765i	0.707819	−	0.122855i
$565$	−1.19454	−	2.06900i	−0.0502545	−	0.0870434i
$566$		−	25.9858i		−	1.09227i
$567$	−14.4191	−	5.42364i	−0.605545	−	0.227771i
$568$	11.1071			0.466042
$569$	−21.0010	−	36.3748i	−0.880407	−	1.52491i	−0.850889	−	0.525346i	$-0.823936\pi$
$569$	−21.0010	−	36.3748i	−0.880407	−	1.52491i	−0.0295185	−	0.999564i	$-0.509397\pi$
$570$	−5.94196	−	34.2341i	−0.248881	−	1.43391i
$571$	22.8546	+	13.1951i	0.956435	+	0.552198i	0.895074	−	0.445917i	$-0.147123\pi$
$571$	22.8546	+	13.1951i	0.956435	+	0.552198i	0.0613612	+	0.998116i	$0.480456\pi$
$572$	−4.51374	−	2.60601i	−0.188729	−	0.108963i
$573$	2.03084	+	2.43346i	0.0848396	+	0.101659i
$574$	4.67943	+	8.10502i	0.195316	+	0.338297i
$575$	−21.8508			−0.911242
$576$	2.82453	−	1.01095i	0.117689	−	0.0421231i
$577$	11.6642			0.485586			0.242793	−	0.970078i	$-0.421936\pi$
$577$	11.6642			0.485586			0.242793	+	0.970078i	$0.421936\pi$
$578$	12.6344	−	7.29446i	0.525520	−	0.303409i
$579$	9.62318	+	3.53175i	0.399926	+	0.146774i
$580$	−3.66587	−	2.11649i	−0.152217	−	0.0878826i
$581$	−5.34137	+	9.25152i	−0.221597	+	0.383818i
$582$	6.00779	−	16.3698i	0.249031	−	0.678550i
$583$	−5.33243	−	9.23603i	−0.220847	−	0.382517i
$584$	−0.138072			−0.00571345
$585$	−22.7685	−	19.3137i	−0.941363	−	0.798523i
$586$	1.75632			0.0725531
$587$	15.8654	+	27.4797i	0.654835	+	1.13421i	0.981935	+	0.189217i	$0.0605951\pi$
$587$	15.8654	+	27.4797i	0.654835	+	1.13421i	−0.327101	+	0.944990i	$0.606072\pi$
$588$	−5.41236	+	4.51688i	−0.223202	+	0.186273i
$589$	−22.8400	−	32.6789i	−0.941104	−	1.34651i
$590$	−26.6893	−	15.4091i	−1.09878	−	0.634381i
$591$	3.68180	+	21.2124i	0.151449	+	0.872560i
$592$	9.17538	−	5.29741i	0.377106	−	0.217722i
$593$		−	14.9623i		−	0.614426i	−0.951641	−	0.307213i	$-0.900604\pi$
$593$		−	14.9623i		−	0.614426i	0.951641	−	0.307213i	$-0.0993964\pi$
$594$	0.0612129	−	7.62318i	0.00251159	−	0.312783i
$595$		−	7.44594i		−	0.305254i
$596$	3.45276	−	1.99345i	0.141431	−	0.0816550i
$597$	5.93857	−	1.03075i	0.243049	−	0.0421857i
$598$	−13.6275	+	23.6035i	−0.557268	+	0.965217i
$599$	−32.4012	−	18.7068i	−1.32388	−	0.764341i	−0.339532	−	0.940594i	$-0.610269\pi$
$599$	−32.4012	−	18.7068i	−1.32388	−	0.764341i	−0.984345	+	0.176254i	$0.943602\pi$
$600$	3.16082	+	3.78746i	0.129040	+	0.154622i
$601$	−29.9367	+	17.2840i	−1.22115	+	0.705028i	−0.965162	−	0.261653i	$-0.915732\pi$
$601$	−29.9367	+	17.2840i	−1.22115	+	0.705028i	−0.255983	+	0.966681i	$0.582399\pi$
$602$	5.94996			0.242502
$603$	6.48350	−	35.6527i	0.264029	−	1.45189i
$604$		−	22.8546i		−	0.929939i
$605$	−21.4653	+	12.3930i	−0.872687	+	0.503846i
$606$	9.66745	+	3.54800i	0.392713	+	0.144128i
$607$	6.70104	−	11.6065i	0.271987	−	0.471095i	−0.697384	−	0.716698i	$-0.745653\pi$
$607$	6.70104	−	11.6065i	0.271987	−	0.471095i	0.969371	+	0.245603i	$0.0789859\pi$
$608$	6.20141	+	3.58039i	0.251500	+	0.145204i
$609$	−4.20548	−	1.54343i	−0.170415	−	0.0625429i
$610$	−2.27216	+	1.31183i	−0.0919969	+	0.0531144i
$611$	34.9933			1.41568
$612$	0.833452	−	4.58314i	0.0336903	−	0.185262i
$613$		−	22.6537i		−	0.914975i	−0.889216	−	0.457488i	$-0.848749\pi$
$613$		−	22.6537i		−	0.914975i	0.889216	−	0.457488i	$-0.151251\pi$
$614$	16.9790	−	9.80284i	0.685217	−	0.395610i
$615$	−20.3687	+	16.9987i	−0.821346	+	0.685453i
$616$	2.17485	+	1.25565i	0.0876272	+	0.0505916i
$617$	−19.6767	−	11.3604i	−0.792155	−	0.457351i	0.0485657	−	0.998820i	$-0.484535\pi$
$617$	−19.6767	−	11.3604i	−0.792155	−	0.457351i	−0.840721	+	0.541469i	$0.817868\pi$
$618$	−0.635909	+	0.110374i	−0.0255800	+	0.00443988i
$619$	−29.8488	+	17.2332i	−1.19973	+	0.692662i	−0.960494	−	0.278300i	$-0.910229\pi$
$619$	−29.8488	+	17.2332i	−1.19973	+	0.692662i	−0.239232	+	0.970962i	$0.576896\pi$
$620$	14.1307	+	6.60415i	0.567504	+	0.265229i
$621$	−39.8635	−	0.320097i	−1.59967	−	0.0128450i
$622$	17.2360			0.691099
$623$	0.865003	+	1.49823i	0.0346556	+	0.0600253i
$624$	6.06252	−	1.05226i	0.242695	−	0.0421242i
$625$	15.5644	−	26.9583i	0.622576	−	1.07833i
$626$	−12.9965	+	22.5106i	−0.519446	+	0.899706i
$627$	13.9706	−	11.6592i	0.557933	−	0.465622i
$628$	3.75070	+	6.49641i	0.149669	+	0.259235i
$629$		−	16.4513i		−	0.655956i
$630$	10.9705	+	9.30589i	0.437076	+	0.370755i
$631$		−	22.1803i		−	0.882983i	−0.897265	−	0.441492i	$-0.854449\pi$
$631$		−	22.1803i		−	0.882983i	0.897265	−	0.441492i	$-0.145551\pi$
$632$	−6.14158	−	10.6375i	−0.244299	−	0.423138i
$633$	19.6036	+	7.19460i	0.779172	+	0.285960i
$634$	−9.62837	+	16.6768i	−0.382391	+	0.662321i
$635$	1.79188	−	3.10363i	0.0711087	−	0.123164i
$636$	11.8197	+	4.33790i	0.468683	+	0.172009i
$637$	−12.5218	+	7.22949i	−0.496133	+	0.286443i
$638$		−	2.21683i		−	0.0877651i
$639$	11.2288	+	31.3723i	0.444203	+	1.24107i
$640$	−2.80145			−0.110737
$641$	4.64820	+	8.05092i	0.183593	+	0.317992i	0.943101	−	0.332505i	$-0.107894\pi$
$641$	4.64820	+	8.05092i	0.183593	+	0.317992i	−0.759509	+	0.650497i	$0.774560\pi$
$642$	−5.92456	+	4.94434i	−0.233824	+	0.195137i
$643$	31.8796	+	18.4057i	1.25721	+	0.725849i	0.972531	−	0.232775i	$-0.0747804\pi$
$643$	31.8796	+	18.4057i	1.25721	+	0.725849i	0.284677	+	0.958624i	$0.408114\pi$
$644$	6.56610	−	11.3728i	0.258740	−	0.448152i
$645$	2.88439	+	16.6181i	0.113573	+	0.654339i
$646$	9.62935	−	5.55951i	0.378862	−	0.218736i
$647$	−0.908098			−0.0357010			−0.0178505	−	0.999841i	$-0.505682\pi$
$647$	−0.908098			−0.0357010			−0.0178505	+	0.999841i	$0.505682\pi$
$648$	5.71095	+	6.95594i	0.224347	+	0.273255i
$649$		−	16.1395i		−	0.633533i
$650$	5.05904	+	8.76252i	0.198432	+	0.343694i
$651$	15.9294	+	4.32880i	0.624324	+	0.169659i
$652$	−3.81196	+	6.60251i	−0.149288	+	0.258574i
$653$	20.6816	+	11.9405i	0.809335	+	0.467270i	0.846725	−	0.532031i	$-0.178571\pi$
$653$	20.6816	+	11.9405i	0.809335	+	0.467270i	−0.0373900	+	0.999301i	$0.511904\pi$
$654$	−10.2934	−	12.3341i	−0.402503	−	0.482300i
$655$	5.39439	+	9.34335i	0.210776	+	0.365075i
$656$		−	5.46756i		−	0.213472i
$657$	−0.139584	−	0.389988i	−0.00544570	−	0.0152149i
$658$	−16.8607			−0.657300
$659$	−28.4514	+	16.4264i	−1.10831	+	0.639883i	−0.938391	−	0.345575i	$-0.887684\pi$
$659$	−28.4514	+	16.4264i	−1.10831	+	0.639883i	−0.169919	+	0.985458i	$0.554351\pi$
$660$	−2.45270	+	6.68303i	−0.0954712	+	0.260136i
$661$	12.3834	−	21.4487i	0.481659	−	0.834258i	−0.518120	−	0.855308i	$-0.673368\pi$
$661$	12.3834	−	21.4487i	0.481659	−	0.834258i	0.999778	+	0.0210506i	$0.00670112\pi$
$662$	−9.96350	+	17.2573i	−0.387242	+	0.670723i
$663$	3.29183	−	8.96945i	0.127844	−	0.348345i
$664$	5.40484	−	3.12049i	0.209749	−	0.121098i
$665$			34.3379i			1.33157i
$666$	24.2386	+	20.5607i	0.939226	+	0.796711i
$667$	−11.5923			−0.448857
$668$	−9.90418	−	17.1545i	−0.383204	−	0.663729i
$669$	27.7521	+	33.2541i	1.07296	+	1.28568i
$670$	−16.9196	+	29.3055i	−0.653660	+	1.13217i
$671$	−1.18994	−	0.687009i	−0.0459369	−	0.0265217i
$672$	−2.92109	+	0.507010i	−0.112684	+	0.0195583i
$673$	−7.04262	+	4.06606i	−0.271473	+	0.156735i	−0.629557	−	0.776954i	$-0.716764\pi$
$673$	−7.04262	+	4.06606i	−0.271473	+	0.156735i	0.358084	+	0.933689i	$0.383430\pi$
$674$	−13.1840			−0.507828
$675$	−7.50234	+	12.7568i	−0.288765	+	0.491008i
$676$	−0.379522			−0.0145970
$677$	−25.5772	−	44.3010i	−0.983012	−	1.70263i	−0.650456	−	0.759544i	$-0.725422\pi$
$677$	−25.5772	−	44.3010i	−0.983012	−	1.70263i	−0.332556	−	0.943084i	$-0.607911\pi$
$678$	0.252600	+	1.45533i	0.00970103	+	0.0558916i
$679$	−8.61632	+	14.9239i	−0.330664	+	0.572727i
$680$	−2.17500	+	3.76721i	−0.0834075	+	0.144466i
$681$	3.78468	+	4.53500i	0.145029	+	0.173782i
$682$	0.704906	+	8.13816i	0.0269922	+	0.311626i
$683$			37.0300i			1.41691i	0.705755	+	0.708456i	$0.250608\pi$
$683$			37.0300i			1.41691i	−0.705755	+	0.708456i	$0.749392\pi$
$684$	−3.84356	+	21.1357i	−0.146962	+	0.808143i
$685$		−	17.8309i		−	0.681283i
$686$	16.4101	−	9.47436i	0.626539	−	0.361733i
$687$	−5.16496	+	14.0733i	−0.197055	+	0.536930i
$688$	−3.01033	−	1.73802i	−0.114768	−	0.0662613i
$689$	22.3643	+	12.9120i	0.852012	+	0.491909i
$690$	34.9472	+	12.8258i	1.33042	+	0.488268i
$691$	18.9242	+	32.7776i	0.719909	+	1.24692i	0.961035	+	0.276425i	$0.0891498\pi$
$691$	18.9242	+	32.7776i	0.719909	+	1.24692i	−0.241127	+	0.970494i	$0.577517\pi$
$692$		−	25.1081i		−	0.954468i
$693$	−1.34795	+	7.41233i	−0.0512042	+	0.281571i
$694$			31.6106i			1.19992i
$695$	19.7692	+	34.2412i	0.749887	+	1.29884i
$696$	1.67688	+	2.00933i	0.0635621	+	0.0761634i
$697$	−7.35242	−	4.24492i	−0.278493	−	0.160788i
$698$	−25.5413	−	14.7463i	−0.966751	−	0.558154i
$699$	−18.8531	+	3.27230i	−0.713088	+	0.123770i
$700$	−2.43759	−	4.22203i	−0.0921322	−	0.159578i
$701$		−	11.1960i		−	0.422866i	−0.977392	−	0.211433i	$-0.932187\pi$
$701$		−	11.1960i		−	0.422866i	0.977392	−	0.211433i	$-0.0678130\pi$
$702$	9.10109	+	16.0600i	0.343498	+	0.606145i
$703$			75.8671i			2.86138i
$704$	−0.733565	−	1.27057i	−0.0276473	−	0.0478864i
$705$	−8.17365	−	47.0918i	−0.307837	−	1.77358i
$706$	3.80236	+	2.19529i	0.143104	+	0.0826210i
$707$	−8.81356	−	5.08851i	−0.331468	−	0.191373i
$708$	12.2085	+	14.6289i	0.458823	+	0.549786i
$709$	−14.6470	+	8.45643i	−0.550078	+	0.317588i	−0.749154	−	0.662396i	$-0.769540\pi$
$709$	−14.6470	+	8.45643i	−0.550078	+	0.317588i	0.199075	+	0.979984i	$0.436206\pi$
$710$		−	31.1159i		−	1.16776i
$711$	23.8371	−	28.1011i	0.893963	−	1.05387i
$712$		−	1.01069i		−	0.0378772i
$713$	42.5564	−	3.68612i	1.59375	−	0.138046i
$714$	−1.58610	+	4.32174i	−0.0593581	+	0.161737i
$715$	−7.30061	+	12.6450i	−0.273027	+	0.472897i
$716$	−7.65808	+	13.2642i	−0.286196	+	0.495706i
$717$	34.4896	+	12.6578i	1.28804	+	0.472716i
$718$	−7.99421	−	13.8464i	−0.298341	−	0.516742i
$719$	−19.5121			−0.727680			−0.363840	−	0.931461i	$-0.618535\pi$
$719$	−19.5121			−0.727680			−0.363840	+	0.931461i	$0.618535\pi$
$720$	−2.83214	−	7.91279i	−0.105548	−	0.294892i
$721$	0.637837			0.0237543
$722$	−27.9524	+	16.1383i	−1.04028	+	0.600607i
$723$	2.08175	+	2.49446i	0.0774211	+	0.0927700i
$724$	14.8360	+	8.56557i	0.551376	+	0.318337i
$725$	−2.15176	+	3.72696i	−0.0799144	+	0.138416i
$726$	15.0986	−	2.62065i	0.560363	−	0.0972613i
$727$	−21.7893	−	37.7402i	−0.808121	−	1.39971i	−0.914164	−	0.405345i	$-0.867151\pi$
$727$	−21.7893	−	37.7402i	−0.808121	−	1.39971i	0.106043	−	0.994362i	$-0.466182\pi$
$728$	−6.08090			−0.225373
$729$	−13.8738	+	23.1629i	−0.513843	+	0.857884i
$730$			0.386801i			0.0143162i
$731$	−4.67435	+	2.69874i	−0.172887	+	0.0998164i
$732$	1.59823	−	0.277403i	0.0590724	−	0.0102531i
$733$	7.07522	−	12.2546i	0.261329	−	0.452635i	−0.705266	−	0.708943i	$-0.749173\pi$
$733$	7.07522	−	12.2546i	0.261329	−	0.452635i	0.966595	+	0.256307i	$0.0825059\pi$
$734$	−15.3671	+	26.6166i	−0.567209	+	0.982435i
$735$	12.6538	+	15.1625i	0.466743	+	0.559276i
$736$	−6.64412	+	3.83599i	−0.244906	+	0.141396i
$737$	−17.7217			−0.652785
$738$	15.4433	−	5.52745i	0.568475	−	0.203468i
$739$		−	9.47332i		−	0.348482i	−0.984703	−	0.174241i	$-0.944253\pi$
$739$		−	9.47332i		−	0.348482i	0.984703	−	0.174241i	$-0.0557471\pi$
$740$	−14.8404	−	25.7044i	−0.545545	−	0.944912i
$741$	−15.1807	+	41.3637i	−0.557676	+	1.51953i
$742$	−10.7757	−	6.22138i	−0.395590	−	0.228394i
$743$	0.971636	−	1.68292i	0.0356459	−	0.0617404i	−0.847652	−	0.530552i	$-0.821984\pi$
$743$	0.971636	−	1.68292i	0.0356459	−	0.0617404i	0.883298	+	0.468812i	$0.155318\pi$
$744$	−6.79490	−	6.84320i	−0.249113	−	0.250884i
$745$	−5.58457	−	9.67275i	−0.204603	−	0.354382i
$746$		−	26.9812i		−	0.987851i
$747$	14.2780	+	12.1115i	0.522403	+	0.443135i
$748$	−2.27811			−0.0832960
$749$	6.60435	−	3.81302i	0.241318	−	0.139325i
$750$	−8.01652	+	6.69018i	−0.292722	+	0.244291i
$751$	2.74754	−	4.75887i	0.100259	−	0.173654i	−0.811532	−	0.584308i	$-0.801366\pi$
$751$	2.74754	−	4.75887i	0.100259	−	0.173654i	0.911791	+	0.410654i	$0.134700\pi$
$752$	8.53055	+	4.92512i	0.311077	+	0.179600i
$753$	6.91713	+	39.8524i	0.252074	+	1.45230i
$754$	2.68393	+	4.64871i	0.0977431	+	0.169296i
$755$	−64.0259			−2.33014
$756$	−4.38516	−	7.73816i	−0.159487	−	0.281434i
$757$		−	1.41065i		−	0.0512710i	−0.999671	−	0.0256355i	$-0.991839\pi$
$757$		−	1.41065i		−	0.0512710i	0.999671	−	0.0256355i	$-0.00816093\pi$
$758$	−16.5598	+	9.56081i	−0.601479	+	0.347264i
$759$	3.33397	+	19.2084i	0.121015	+	0.697220i
$760$	10.0303	−	17.3730i	0.363837	−	0.630184i
$761$	−2.55571	+	4.42662i	−0.0926445	+	0.160465i	−0.908623	−	0.417617i	$-0.862865\pi$
$761$	−2.55571	+	4.42662i	−0.0926445	+	0.160465i	0.815979	+	0.578082i	$0.196199\pi$
$762$	−1.70115	+	1.41970i	−0.0616263	+	0.0514302i
$763$	7.93815	+	13.7493i	0.287380	+	0.497757i
$764$			1.82994i			0.0662049i
$765$	−12.8394	−	2.33487i	−0.464211	−	0.0844176i
$766$		−	1.95386i		−	0.0705957i
$767$	19.5403	+	33.8448i	0.705559	+	1.22206i
$768$	1.62600	+	0.596750i	0.0586734	+	0.0215334i
$769$	−0.0607588	+	0.105237i	−0.00219102	+	0.00379496i	−0.867119	−	0.498101i	$-0.834031\pi$
$769$	−0.0607588	+	0.105237i	−0.00219102	+	0.00379496i	0.864928	+	0.501896i	$0.167364\pi$
$770$	3.51764	−	6.09274i	0.126767	−	0.219567i
$771$	0.183572	−	0.500189i	0.00661117	−	0.0180139i
$772$	2.95915	+	5.12540i	0.106502	+	0.184467i
$773$	48.3540			1.73917			0.869585	−	0.493782i	$-0.164386\pi$
$773$	48.3540			1.73917			0.869585	+	0.493782i	$0.164386\pi$
$774$	1.86577	−	10.2598i	0.0670637	−	0.368782i
$775$	6.71419	−	14.3662i	0.241181	−	0.516049i
$776$	8.71871	−	5.03375i	0.312984	−	0.180701i
$777$	−20.1262	−	24.1163i	−0.722025	−	0.865168i
$778$	27.2077	+	15.7084i	0.975444	+	0.563173i
$779$	33.9066	+	19.5760i	1.21483	+	0.701382i
$780$	−2.94786	−	16.9839i	−0.105550	−	0.608120i
$781$	14.1123	−	8.14775i	0.504979	−	0.291550i
$782$			11.9128i			0.426001i
$783$	−3.98016	+	6.76775i	−0.142239	+	0.241860i
$784$	−4.07005			−0.145359
$785$	18.1994	−	10.5074i	0.649563	−	0.375026i
$786$	−1.14071	−	6.57210i	−0.0406878	−	0.234419i
$787$	−27.9505	−	16.1372i	−0.996326	−	0.575229i	−0.0891668	−	0.996017i	$-0.528420\pi$
$787$	−27.9505	−	16.1372i	−0.996326	−	0.575229i	−0.907159	+	0.420788i	$0.861754\pi$
$788$	−6.21503	+	10.7648i	−0.221401	+	0.383478i
$789$	−33.1600	+	27.6736i	−1.18053	+	0.985206i
$790$	−29.8005	+	17.2053i	−1.06025	+	0.612138i
$791$		−	1.45974i		−	0.0519025i
$792$	2.84717	−	3.35647i	0.101170	−	0.119267i
$793$	3.32707			0.118148
$794$	−16.2108	+	9.35928i	−0.575298	+	0.332148i
$795$	12.1524	−	33.1125i	0.431002	−	1.17438i
$796$	3.01368	+	1.73995i	0.106817	+	0.0616708i
$797$	22.9770	−	39.7974i	0.813888	−	1.40969i	−0.0962361	−	0.995359i	$-0.530680\pi$
$797$	22.9770	−	39.7974i	0.813888	−	1.40969i	0.910124	−	0.414336i	$-0.135986\pi$
$798$	7.31447	−	19.9302i	0.258929	−	0.705522i
$799$	13.2460	−	7.64756i	0.468608	−	0.270551i
$800$			2.84813i			0.100697i
$801$	2.85472	−	1.02176i	0.100867	−	0.0361021i
$802$			3.61484i			0.127644i
$803$	−0.175430	+	0.101285i	−0.00619079	+	0.00357425i
$804$	16.0629	−	13.4052i	0.566494	−	0.472767i
$805$	−31.8604	−	18.3946i	−1.12293	−	0.648325i
$806$	−11.3311	−	16.2124i	−0.399122	−	0.571056i
$807$	1.73562	+	9.99963i	0.0610967	+	0.352004i
$808$	2.97276	+	5.14898i	0.104581	+	0.181140i
$809$	−39.8147			−1.39981			−0.699906	−	0.714235i	$-0.746775\pi$
$809$	−39.8147			−1.39981			−0.699906	+	0.714235i	$0.746775\pi$
$810$	19.4867	−	15.9989i	0.684694	−	0.562145i
$811$	30.5818			1.07387			0.536936	−	0.843623i	$-0.319582\pi$
$811$	30.5818			1.07387			0.536936	+	0.843623i	$0.319582\pi$
$812$	−1.29319	−	2.23988i	−0.0453822	−	0.0786043i
$813$	31.0786	−	5.39427i	1.08997	−	0.189185i
$814$	7.77198	−	13.4615i	0.272408	−	0.471824i
$815$	18.4966	+	10.6790i	0.647908	+	0.374070i
$816$	2.06487	−	1.72324i	0.0722851	−	0.0603254i
$817$	21.5563	−	12.4455i	0.754160	−	0.435415i
$818$	−3.55808			−0.124405
$819$	−6.14752	−	17.1757i	−0.214812	−	0.600167i
$820$	−15.3171			−0.534896
$821$	12.0397	+	20.8533i	0.420187	+	0.727786i	0.995957	−	0.0898259i	$-0.0286311\pi$
$821$	12.0397	+	20.8533i	0.420187	+	0.727786i	−0.575770	+	0.817612i	$0.695298\pi$
$822$	−3.79824	+	10.3493i	−0.132479	+	0.360974i
$823$	0.553517	+	0.319573i	0.0192944	+	0.0111396i	0.509616	−	0.860402i	$-0.329787\pi$
$823$	0.553517	+	0.319573i	0.0192944	+	0.0111396i	−0.490322	+	0.871541i	$0.663121\pi$
$824$	−0.322708	−	0.186316i	−0.0112421	−	0.00649061i
$825$	6.79439	+	2.49357i	0.236550	+	0.0868149i
$826$	−9.41506	−	16.3074i	−0.327592	−	0.567406i
$827$	−25.0098			−0.869675			−0.434838	−	0.900509i	$-0.643194\pi$
$827$	−25.0098			−0.869675			−0.434838	+	0.900509i	$0.643194\pi$
$828$	−17.5518	−	14.8885i	−0.609966	−	0.517412i
$829$			25.9309i			0.900617i	0.892873	+	0.450308i	$0.148686\pi$
$829$			25.9309i			0.900617i	−0.892873	+	0.450308i	$0.851314\pi$
$830$	−8.74189	−	15.1414i	−0.303436	−	0.525566i
$831$	12.3773	+	14.8311i	0.429364	+	0.514487i
$832$	3.07658	+	1.77627i	0.106661	+	0.0615809i
$833$	−3.15992	+	5.47314i	−0.109485	+	0.189633i
$834$	−4.18044	−	24.0852i	−0.144757	−	0.834003i
$835$	−48.0576	+	27.7461i	−1.66310	+	0.960193i
$836$	10.5058			0.363350
$837$	12.4595	−	26.1106i	0.430662	−	0.902513i
$838$	−33.6205			−1.16140
$839$	−40.3348	+	23.2873i	−1.39251	+	0.803966i	−0.993593	−	0.113020i	$-0.963948\pi$
$839$	−40.3348	+	23.2873i	−1.39251	+	0.803966i	−0.398918	+	0.916987i	$0.630614\pi$
$840$	1.42036	+	8.18331i	0.0490072	+	0.282351i
$841$	13.3584	−	23.1375i	0.460636	−	0.797845i
$842$	−5.97103	−	3.44737i	−0.205775	−	0.118804i
$843$	1.54142	+	1.84702i	0.0530895	+	0.0636146i
$844$	6.02815	+	10.4411i	0.207497	+	0.359396i
$845$			1.06321i			0.0365756i
$846$	−5.28713	+	29.0739i	−0.181775	+	0.999580i
$847$	−15.1444			−0.520368
$848$	3.63460	+	6.29531i	0.124813	+	0.216182i
$849$	42.2530	+	15.5070i	1.45012	+	0.532200i
$850$	3.82999	+	2.21124i	0.131368	+	0.0758451i
$851$	−70.3933	−	40.6416i	−2.41305	−	1.39318i
$852$	−6.62815	+	18.0601i	−0.227077	+	0.618730i
$853$	−21.9940	−	38.0947i	−0.753061	−	1.30434i	−0.946333	−	0.323194i	$-0.895243\pi$
$853$	−21.9940	−	38.0947i	−0.753061	−	1.30434i	0.193272	−	0.981145i	$-0.438090\pi$
$854$	−1.60308			−0.0548562
$855$	59.2106	+	10.7676i	2.02496	+	0.368243i
$856$	−4.45522			−0.152276
$857$	32.2115	−	18.5973i	1.10033	−	0.635273i	0.164019	−	0.986457i	$-0.447554\pi$
$857$	32.2115	−	18.5973i	1.10033	−	0.635273i	0.936306	+	0.351184i	$0.114221\pi$
$858$	6.93096	−	5.78423i	0.236619	−	0.197470i
$859$	−36.5777	−	21.1182i	−1.24802	−	0.720542i	−0.277302	−	0.960783i	$-0.589440\pi$
$859$	−36.5777	−	21.1182i	−1.24802	−	0.720542i	−0.970713	+	0.240241i	$0.922774\pi$
$860$	−4.86897	+	8.43331i	−0.166031	+	0.287573i
$861$	−15.9712	+	2.77211i	−0.544299	+	0.0944731i
$862$	−0.743210	−	1.28728i	−0.0253138	−	0.0438449i
$863$	38.2498			1.30204			0.651019	−	0.759062i	$-0.274342\pi$
$863$	38.2498			1.30204			0.651019	+	0.759062i	$0.274342\pi$
$864$	−0.0417229	+	5.19598i	−0.00141944	+	0.176771i
$865$	−70.3392			−2.39160
$866$	8.28642	+	14.3525i	0.281584	+	0.487718i
$867$	4.32125	+	24.8965i	0.146757	+	0.845530i
$868$	5.45966	+	7.81157i	0.185313	+	0.265142i
$869$	−15.6066	−	9.01048i	−0.529418	−	0.305660i
$870$	5.62904	−	4.69771i	0.190842	−	0.159267i
$871$	37.1625	−	21.4558i	1.25920	−	0.727000i
$872$		−	9.27511i		−	0.314095i
$873$	23.0322	+	19.5374i	0.779522	+	0.661240i
$874$		−	54.9373i		−	1.85828i
$875$	8.93633	−	5.15939i	0.302103	−	0.174419i
$876$	0.0823944	−	0.224505i	0.00278385	−	0.00758533i
$877$	22.6974	−	39.3131i	0.766437	−	1.32751i	−0.173046	−	0.984914i	$-0.555361\pi$
$877$	22.6974	−	39.3131i	0.766437	−	1.32751i	0.939483	−	0.342594i	$-0.111306\pi$
$878$	30.9945	+	17.8947i	1.04601	+	0.603915i
$879$	−1.04809	+	2.85579i	−0.0353511	+	0.0963234i
$880$	−3.55944	+	2.05505i	−0.119989	+	0.0692756i
$881$	28.3421			0.954870			0.477435	−	0.878667i	$-0.341567\pi$
$881$	28.3421			0.954870			0.477435	+	0.878667i	$0.341567\pi$
$882$	−4.11464	−	11.4960i	−0.138547	−	0.387090i
$883$		−	30.2606i		−	1.01835i	−0.860663	−	0.509176i	$-0.829950\pi$
$883$		−	30.2606i		−	1.01835i	0.860663	−	0.509176i	$-0.170050\pi$
$884$	4.77722	−	2.75813i	0.160675	−	0.0927659i
$885$	40.9820	−	34.2015i	1.37760	−	1.14967i
$886$	9.30903	−	16.1237i	0.312743	−	0.541687i
$887$	9.66606	+	5.58070i	0.324554	+	0.187382i	0.653421	−	0.756995i	$-0.273333\pi$
$887$	9.66606	+	5.58070i	0.324554	+	0.187382i	−0.328866	+	0.944376i	$0.606667\pi$
$888$	3.13820	+	18.0804i	0.105311	+	0.606740i
$889$	1.89634	−	1.09486i	0.0636014	−	0.0367203i
$890$	−2.83140			−0.0949086
$891$	12.3588	+	4.64867i	0.414035	+	0.155736i
$892$			25.0068i			0.837288i
$893$	−61.0853	+	35.2676i	−2.04414	+	1.18019i
$894$	1.18093	+	6.80380i	0.0394961	+	0.227553i
$895$	37.1590	+	21.4537i	1.24209	+	0.717119i
$896$	−1.48238	−	0.855855i	−0.0495230	−	0.0285921i
$897$	−30.2471	−	36.2437i	−1.00992	−	1.21014i
$898$	−32.5199	+	18.7754i	−1.08520	+	0.626543i
$899$	3.56203	−	7.62158i	0.118800	−	0.254194i
$900$	−8.04464	+	2.87933i	−0.268155	+	0.0959778i
$901$	11.2874			0.376037
$902$	−4.01080	−	6.94692i	−0.133545	−	0.231307i
$903$	−3.55064	+	9.67466i	−0.118158	+	0.321953i
$904$	−0.426399	+	0.738545i	−0.0141818	+	0.0245636i
$905$	23.9960	−	41.5623i	0.797655	−	1.38158i
$906$	37.1616	+	13.6385i	1.23461	+	0.453108i
$907$	−21.7875	−	37.7371i	−0.723443	−	1.25304i	−0.959612	−	0.281328i	$-0.909225\pi$
$907$	−21.7875	−	37.7371i	−0.723443	−	1.25304i	0.236169	−	0.971712i	$-0.424108\pi$
$908$			3.41028i			0.113174i
$909$	−11.5381	+	13.6021i	−0.382695	+	0.451152i
$910$			17.0354i			0.564717i
$911$	15.0062	+	25.9915i	0.497178	+	0.861137i	0.999995	−	0.00325559i	$-0.00103629\pi$
$911$	15.0062	+	25.9915i	0.497178	+	0.861137i	−0.502817	+	0.864393i	$0.667703\pi$
$912$	−9.52242	+	7.94692i	−0.315319	+	0.263149i
$913$	4.57816	−	7.92960i	0.151515	−	0.262431i
$914$	8.87898	−	15.3789i	0.293691	−	0.508687i
$915$	−0.777131	−	4.47737i	−0.0256911	−	0.148017i
$916$	−7.49557	+	4.32757i	−0.247661	+	0.142987i
$917$			6.59203i			0.217688i
$918$	6.95484	+	4.09018i	0.229544	+	0.134996i
$919$	7.79709			0.257202			0.128601	−	0.991696i	$-0.458951\pi$
$919$	7.79709			0.257202			0.128601	+	0.991696i	$0.458951\pi$
$920$	10.7463	+	18.6132i	0.354296	+	0.613659i
$921$	5.80722	+	33.4578i	0.191354	+	1.10247i
$922$	−28.7841	−	16.6185i	−0.947953	−	0.547301i
$923$	−19.7291	+	34.1718i	−0.649392	+	1.12478i
$924$	−3.33953	+	2.78700i	−0.109863	+	0.0916857i
$925$	−26.1327	+	15.0877i	−0.859238	+	0.496082i
$926$	15.3381			0.504042
$927$	0.200011	−	1.09986i	0.00656921	−	0.0361240i
$928$			1.51100i			0.0496009i
$929$	2.51238	+	4.35156i	0.0824284	+	0.142770i	0.904293	−	0.426913i	$-0.140399\pi$
$929$	2.51238	+	4.35156i	0.0824284	+	0.142770i	−0.821864	+	0.569684i	$0.807066\pi$
$930$	−19.1709	+	19.0356i	−0.628638	+	0.624201i
$931$	14.5724	−	25.2401i	0.477590	−	0.827209i
$932$	−9.56746	−	5.52378i	−0.313393	−	0.180937i
$933$	−10.2856	+	28.0257i	−0.336734	+	0.917521i
$934$	3.97584	+	6.88637i	0.130094	+	0.225329i
$935$			6.38202i			0.208714i
$936$	−1.90683	+	10.4856i	−0.0623267	+	0.342733i
$937$	43.6734			1.42675			0.713373	−	0.700784i	$-0.247166\pi$
$937$	43.6734			1.42675			0.713373	+	0.700784i	$0.247166\pi$
$938$	−17.9059	+	10.3380i	−0.584649	+	0.337547i
$939$	−28.8467	−	34.5656i	−0.941377	−	1.12801i
$940$	13.7975	−	23.8979i	0.450024	−	0.779464i
$941$	−20.0254	+	34.6850i	−0.652810	+	1.13070i	0.329628	+	0.944111i	$0.393077\pi$
$941$	−20.0254	+	34.6850i	−0.652810	+	1.13070i	−0.982438	+	0.186589i	$0.940257\pi$
$942$	−12.8014	+	2.22192i	−0.417093	+	0.0723941i
$943$	−36.3271	+	20.9735i	−1.18297	+	0.682990i
$944$			11.0008i			0.358045i
$945$	−21.6781	+	12.2848i	−0.705188	+	0.399625i
$946$	−5.09979			−0.165808
$947$	−11.7628	−	20.3738i	−0.382241	−	0.662061i	0.609141	−	0.793062i	$-0.291514\pi$
$947$	−11.7628	−	20.3738i	−0.382241	−	0.662061i	−0.991382	+	0.131001i	$0.958181\pi$
$948$	20.9616	−	3.63828i	0.680802	−	0.118166i
$949$	0.245252	−	0.424789i	0.00796122	−	0.0137892i
$950$	−17.6625	−	10.1974i	−0.573046	−	0.330848i
$951$	−21.3709	−	25.6077i	−0.692997	−	0.830386i
$952$	−2.30180	+	1.32894i	−0.0746017	+	0.0430713i
$953$	−21.2533			−0.688463			−0.344232	−	0.938885i	$-0.611861\pi$
$953$	−21.2533			−0.688463			−0.344232	+	0.938885i	$0.611861\pi$
$954$	−14.1069	+	16.6303i	−0.456727	+	0.538426i
$955$	5.12649			0.165889
$956$	10.6056	+	18.3695i	0.343011	+	0.594112i
$957$	3.60457	+	1.32289i	0.116519	+	0.0427631i
$958$	−0.167050	+	0.289339i	−0.00539714	+	0.00934812i
$959$	5.44741	−	9.43519i	0.175906	−	0.304678i
$960$	1.67177	−	4.55517i	0.0539561	−	0.147018i
$961$	−10.6530	+	29.1121i	−0.343645	+	0.939100i
$962$			37.6384i			1.21351i
$963$	−4.50403	−	12.5839i	−0.145140	−	0.405511i
$964$			1.87581i			0.0604158i
$965$	14.3586	−	8.28992i	0.462218	−	0.266862i
$966$	14.5739	+	17.4632i	0.468908	+	0.561870i
$967$	−1.99596	−	1.15237i	−0.0641858	−	0.0370577i	0.467564	−	0.883959i	$-0.345132\pi$
$967$	−1.99596	−	1.15237i	−0.0641858	−	0.0370577i	−0.531749	+	0.846902i	$0.678465\pi$
$968$	7.66219	+	4.42377i	0.246272	+	0.142185i
$969$	3.29346	+	18.9750i	0.105801	+	0.609565i
$970$	−14.1018	−	24.4251i	−0.452782	−	0.784241i
$971$			31.8838i			1.02320i	0.859224	+	0.511600i	$0.170947\pi$
$971$			31.8838i			1.02320i	−0.859224	+	0.511600i	$0.829053\pi$
$972$	−14.7184	+	5.13506i	−0.472093	+	0.164707i
$973$			24.1582i			0.774478i
$974$	13.2809	+	23.0033i	0.425549	+	0.737072i
$975$	−17.2669	+	2.99699i	−0.552983	+	0.0959803i
$976$	0.811064	+	0.468268i	0.0259615	+	0.0149889i
$977$	−7.76184	−	4.48130i	−0.248323	−	0.143369i	0.370673	−	0.928763i	$-0.379127\pi$
$977$	−7.76184	−	4.48130i	−0.248323	−	0.143369i	−0.618996	+	0.785394i	$0.712460\pi$
$978$	−8.46091	−	10.1383i	−0.270550	−	0.324187i
$979$	−0.741405	−	1.28415i	−0.0236954	−	0.0410417i
$980$			11.4020i			0.364225i
$981$	26.1978	−	9.37672i	0.836432	−	0.299376i
$982$		−	0.587753i		−	0.0187559i
$983$	0.172770	+	0.299246i	0.00551050	+	0.00954446i	0.868768	−	0.495220i	$-0.164913\pi$
$983$	0.172770	+	0.299246i	0.00551050	+	0.00954446i	−0.863257	+	0.504765i	$0.831579\pi$
$984$	8.89027	+	3.26277i	0.283411	+	0.104013i
$985$	30.1569	+	17.4111i	0.960880	+	0.554764i
$986$	2.03189	+	1.17311i	0.0647086	+	0.0373596i
$987$	10.0617	−	27.4156i	0.320266	−	0.872649i
$988$	−22.0307	+	12.7194i	−0.700890	+	0.404659i
$989$			26.6680i			0.847994i
$990$	−9.40298	−	7.97620i	−0.298846	−	0.253500i
$991$		−	23.9983i		−	0.762333i	−0.924507	−	0.381166i	$-0.875523\pi$
$991$		−	23.9983i		−	0.762333i	0.924507	−	0.381166i	$-0.124477\pi$
$992$	−0.480466	−	5.54699i	−0.0152548	−	0.176117i
$993$	−22.1147	−	26.4990i	−0.701788	−	0.840920i
$994$	9.50604	−	16.4650i	0.301513	−	0.522237i
$995$	4.87438	−	8.44267i	0.154528	−	0.267651i
$996$	1.84858	+	10.6504i	0.0585746	+	0.337472i
$997$	12.7281	+	22.0457i	0.403102	+	0.698194i	0.994099	−	0.108481i	$-0.0345985\pi$
$997$	12.7281	+	22.0457i	0.403102	+	0.698194i	−0.590996	+	0.806674i	$0.701265\pi$
$998$	−28.4845			−0.901661
$999$	−47.8962	+	27.1424i	−1.51537	+	0.858749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	558.2.q.a.185.7	✓	64
3.2	odd	2		1674.2.q.a.557.24		64
9.2	odd	6	inner	558.2.q.a.371.10	yes	64
9.7	even	3		1674.2.q.a.1115.27		64
31.30	odd	2	inner	558.2.q.a.185.10	yes	64
93.92	even	2		1674.2.q.a.557.27		64
279.61	odd	6		1674.2.q.a.1115.24		64
279.92	even	6	inner	558.2.q.a.371.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
558.2.q.a.185.7	✓	64	1.1	even	1	trivial
558.2.q.a.185.10	yes	64	31.30	odd	2	inner
558.2.q.a.371.7	yes	64	279.92	even	6	inner
558.2.q.a.371.10	yes	64	9.2	odd	6	inner
1674.2.q.a.557.24		64	3.2	odd	2
1674.2.q.a.557.27		64	93.92	even	2
1674.2.q.a.1115.24		64	279.61	odd	6
1674.2.q.a.1115.27		64	9.7	even	3

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:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.296201 - 1.70654i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.42613 - 1.40073i) q^{5} +(1.10979 + 1.32980i) q^{6} +(-0.855855 - 1.48238i) q^{7} +1.00000i q^{8} +(-2.82453 + 1.01095i) q^{9} +2.80145 q^{10} +(0.733565 + 1.27057i) q^{11} +(-1.62600 - 0.596750i) q^{12} +(-3.07658 - 1.77627i) q^{13} +(1.48238 + 0.855855i) q^{14} +(-1.67177 + 4.55517i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.55277 q^{17} +(1.94064 - 2.28778i) q^{18} +7.16077 q^{19} +(-2.42613 + 1.40073i) q^{20} +(-2.27624 + 1.89963i) q^{21} +(-1.27057 - 0.733565i) q^{22} +(-3.83599 + 6.64412i) q^{23} +(1.70654 - 0.296201i) q^{24} +(1.42407 + 2.46656i) q^{25} +3.55253 q^{26} +(2.56186 + 4.52072i) q^{27} -1.71171 q^{28} +(0.755499 + 1.30856i) q^{29} +(-0.829793 - 4.78078i) q^{30} +(-3.18959 - 4.56361i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.95099 - 1.62820i) q^{33} +(1.34474 - 0.776384i) q^{34} +4.79527i q^{35} +(-0.536752 + 2.95159i) q^{36} +10.5948i q^{37} +(-6.20141 + 3.58039i) q^{38} +(-2.11997 + 5.77643i) q^{39} +(1.40073 - 2.42613i) q^{40} +(4.73504 + 2.73378i) q^{41} +(1.02146 - 2.78325i) q^{42} +(3.01033 - 1.73802i) q^{43} +1.46713 q^{44} +(8.26874 + 1.50369i) q^{45} -7.67197i q^{46} +(-8.53055 + 4.92512i) q^{47} +(-1.32980 + 1.10979i) q^{48} +(2.03502 - 3.52477i) q^{49} +(-2.46656 - 1.42407i) q^{50} +(0.459931 + 2.64985i) q^{51} +(-3.07658 + 1.77627i) q^{52} -7.26920 q^{53} +(-4.47899 - 2.63413i) q^{54} -4.11009i q^{55} +(1.48238 - 0.855855i) q^{56} +(-2.12103 - 12.2201i) q^{57} +(-1.30856 - 0.755499i) q^{58} +(-9.52695 - 5.50039i) q^{59} +(3.10901 + 3.72538i) q^{60} +(-0.811064 + 0.468268i) q^{61} +(5.04407 + 2.35740i) q^{62} +(3.91601 + 3.32181i) q^{63} -1.00000 q^{64} +(4.97612 + 8.61890i) q^{65} +(-0.875510 + 2.38556i) q^{66} +(-6.03957 + 10.4608i) q^{67} +(-0.776384 + 1.34474i) q^{68} +(12.4747 + 4.57825i) q^{69} +(-2.39764 - 4.15283i) q^{70} -11.1071i q^{71} +(-1.01095 - 2.82453i) q^{72} +0.138072i q^{73} +(-5.29741 - 9.17538i) q^{74} +(3.78746 - 3.16082i) q^{75} +(3.58039 - 6.20141i) q^{76} +(1.25565 - 2.17485i) q^{77} +(-1.05226 - 6.06252i) q^{78} +(-10.6375 + 6.14158i) q^{79} +2.80145i q^{80} +(6.95594 - 5.71095i) q^{81} -5.46756 q^{82} +(-3.12049 - 5.40484i) q^{83} +(0.507010 + 2.92109i) q^{84} +(3.76721 + 2.17500i) q^{85} +(-1.73802 + 3.01033i) q^{86} +(2.00933 - 1.67688i) q^{87} +(-1.27057 + 0.733565i) q^{88} -1.01069 q^{89} +(-7.91279 + 2.83214i) q^{90} +6.08090i q^{91} +(3.83599 + 6.64412i) q^{92} +(-6.84320 + 6.79490i) q^{93} +(4.92512 - 8.53055i) q^{94} +(-17.3730 - 10.0303i) q^{95} +(0.596750 - 1.62600i) q^{96} +(-5.03375 - 8.71871i) q^{97} +4.07005i q^{98} +(-3.35647 - 2.84717i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} + 12 q^{5} - 4 q^{7} - 4 q^{9} - 32 q^{16} + 8 q^{18} - 8 q^{19} + 12 q^{20} + 44 q^{25} - 8 q^{28} + 8 q^{31} - 36 q^{33} - 8 q^{36} + 36 q^{38} - 8 q^{39} + 24 q^{41} - 8 q^{45} - 48 q^{47}+ \cdots - 16 q^{97}+O(q^{100}) \) 64 * q + 32 * q^4 + 12 * q^5 - 4 * q^7 - 4 * q^9 - 32 * q^16 + 8 * q^18 - 8 * q^19 + 12 * q^20 + 44 * q^25 - 8 * q^28 + 8 * q^31 - 36 * q^33 - 8 * q^36 + 36 * q^38 - 8 * q^39 + 24 * q^41 - 8 * q^45 - 48 * q^47 - 36 * q^49 - 32 * q^51 - 12 * q^59 - 52 * q^63 - 64 * q^64 - 16 * q^66 + 16 * q^67 + 112 * q^69 - 12 * q^70 - 8 * q^72 - 4 * q^76 - 28 * q^78 + 60 * q^81 + 44 * q^87 + 56 * q^90 - 64 * q^93 - 180 * q^95 - 16 * q^97

Introduction

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