LMFDB - Embedded newform 290.2.l.b.9.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [290,2,Mod(9,290)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("290.9"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(290, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 290 = 2 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	290.l (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.31566165862$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			9.6
Character	$\chi$	$=$	290.9
Dual form			290.2.l.b.129.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.900969 - 0.433884i) q^{2} +(1.02784 + 1.28888i) q^{3} +(0.623490 - 0.781831i) q^{4} +(2.22995 + 0.165278i) q^{5} +(1.48528 + 0.715272i) q^{6} +(-0.318876 + 0.254295i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.0628256 - 0.275257i) q^{9} +(2.08083 - 0.818630i) q^{10} +(-3.93784 + 0.898786i) q^{11} +1.64853 q^{12} +(-2.77413 + 0.633178i) q^{13} +(-0.176963 + 0.367467i) q^{14} +(2.07902 + 3.04401i) q^{15} +(-0.222521 - 0.974928i) q^{16} +2.77440 q^{17} +(-0.0628256 - 0.275257i) q^{18} +(-2.67198 - 2.13084i) q^{19} +(1.51957 - 1.64040i) q^{20} +(-0.655509 - 0.149616i) q^{21} +(-3.15790 + 2.51834i) q^{22} +(-2.12245 + 4.40731i) q^{23} +(1.48528 - 0.715272i) q^{24} +(4.94537 + 0.737122i) q^{25} +(-2.22468 + 1.77413i) q^{26} +(4.87518 - 2.34776i) q^{27} +0.407857i q^{28} +(-0.926203 - 5.30492i) q^{29} +(3.19388 + 1.84051i) q^{30} +(0.235843 + 0.489733i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(-5.20591 - 4.15158i) q^{33} +(2.49965 - 1.20377i) q^{34} +(-0.753106 + 0.514362i) q^{35} +(-0.176033 - 0.220739i) q^{36} +(-0.842848 + 3.69276i) q^{37} +(-3.33191 - 0.760487i) q^{38} +(-3.66747 - 2.92471i) q^{39} +(0.657345 - 2.13726i) q^{40} +0.945353i q^{41} +(-0.655509 + 0.149616i) q^{42} +(-6.03831 - 2.90790i) q^{43} +(-1.75250 + 3.63911i) q^{44} +(0.185592 - 0.603426i) q^{45} +4.89174i q^{46} +(-0.516365 - 2.26234i) q^{47} +(1.02784 - 1.28888i) q^{48} +(-1.52063 + 6.66232i) q^{49} +(4.77545 - 1.48159i) q^{50} +(2.85165 + 3.57585i) q^{51} +(-1.23461 + 2.56369i) q^{52} +(-1.25951 - 2.61539i) q^{53} +(3.37373 - 4.23052i) q^{54} +(-8.92974 + 1.35341i) q^{55} +(0.176963 + 0.367467i) q^{56} -5.63402i q^{57} +(-3.13620 - 4.37770i) q^{58} -7.18221 q^{59} +(3.67615 + 0.272466i) q^{60} +(10.5175 - 8.38745i) q^{61} +(0.424974 + 0.338906i) q^{62} +(0.0499628 + 0.103749i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-6.29084 + 0.953454i) q^{65} +(-6.49166 - 1.48168i) q^{66} +(-2.34889 - 0.536119i) q^{67} +(1.72981 - 2.16911i) q^{68} +(-7.86202 + 1.79445i) q^{69} +(-0.455352 + 0.790185i) q^{70} +(1.05391 + 4.61747i) q^{71} +(-0.254375 - 0.122501i) q^{72} +(-4.90699 - 2.36308i) q^{73} +(0.842848 + 3.69276i) q^{74} +(4.13301 + 7.13161i) q^{75} +(-3.33191 + 0.760487i) q^{76} +(1.02712 - 1.28797i) q^{77} +(-4.57326 - 1.04382i) q^{78} +(9.62460 + 2.19675i) q^{79} +(-0.335077 - 2.21082i) q^{80} +(7.27377 + 3.50287i) q^{81} +(0.410173 + 0.851734i) q^{82} +(3.24962 + 2.59148i) q^{83} +(-0.525677 + 0.419214i) q^{84} +(6.18677 + 0.458546i) q^{85} -6.70202 q^{86} +(5.88539 - 6.64639i) q^{87} +4.03911i q^{88} +(0.754425 + 1.56658i) q^{89} +(-0.0946042 - 0.624193i) q^{90} +(0.723590 - 0.907353i) q^{91} +(2.12245 + 4.40731i) q^{92} +(-0.388795 + 0.807341i) q^{93} +(-1.44682 - 1.81426i) q^{94} +(-5.60621 - 5.19328i) q^{95} +(0.366833 - 1.60720i) q^{96} +(-9.95427 + 12.4823i) q^{97} +(1.52063 + 6.66232i) q^{98} +1.14038i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 4 q^{3} - 8 q^{4} + 8 q^{5} - 3 q^{6} + 7 q^{7} + 8 q^{8} - 8 q^{9} - q^{10} + 10 q^{12} - 10 q^{15} - 8 q^{16} - 30 q^{17} + 8 q^{18} - 13 q^{20} + 7 q^{21} + 7 q^{23} - 3 q^{24} - 12 q^{25}+ \cdots - 27 q^{98}+O(q^{100}) $ 48 * q + 8 * q^2 - 4 * q^3 - 8 * q^4 + 8 * q^5 - 3 * q^6 + 7 * q^7 + 8 * q^8 - 8 * q^9 - q^10 + 10 * q^12 - 10 * q^15 - 8 * q^16 - 30 * q^17 + 8 * q^18 - 13 * q^20 + 7 * q^21 + 7 * q^23 - 3 * q^24 - 12 * q^25 + 21 * q^26 + 11 * q^27 - 10 * q^29 - 18 * q^30 + 14 * q^31 + 8 * q^32 - 14 * q^33 - 33 * q^34 - q^36 - 44 * q^37 - 28 * q^38 - 14 * q^39 - 8 * q^40 + 7 * q^42 - 8 * q^43 + 14 * q^44 + 25 * q^45 - 6 * q^47 - 4 * q^48 + 27 * q^49 + 5 * q^50 + 24 * q^51 + 77 * q^53 + 10 * q^54 - 32 * q^55 + 10 * q^58 - 24 * q^59 + 4 * q^60 + 56 * q^61 - 8 * q^64 - 34 * q^65 + 42 * q^67 - 2 * q^68 + 28 * q^69 - 30 * q^71 + 22 * q^72 - 29 * q^73 + 44 * q^74 - 32 * q^75 - 28 * q^76 - 30 * q^77 + 14 * q^78 + q^80 - 130 * q^81 - 42 * q^82 - 42 * q^84 + 28 * q^85 - 62 * q^86 + 32 * q^87 + 31 * q^90 - 106 * q^91 - 7 * q^92 - 70 * q^93 + 27 * q^94 + 165 * q^95 + 4 * q^96 - 49 * q^97 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/290\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$e\left(\frac{5}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$2$	0.900969	−	0.433884i	0.637081	−	0.306802i
$3$	1.02784	+	1.28888i	0.593426	+	0.744133i	0.984337	−	0.176296i	$-0.0564115\pi$
$3$	1.02784	+	1.28888i	0.593426	+	0.744133i	−0.390911	+	0.920428i	$0.627840\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	2.22995	+	0.165278i	0.997265	+	0.0739144i
$5$	2.22995	+	0.165278i	0.997265	+	0.0739144i
$6$	1.48528	+	0.715272i	0.606362	+	0.292009i
$7$	−0.318876	+	0.254295i	−0.120524	+	0.0961144i	−0.681897	−	0.731448i	$-0.738845\pi$
$7$	−0.318876	+	0.254295i	−0.120524	+	0.0961144i	0.561373	+	0.827563i	$0.310273\pi$
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	0.0628256	−	0.275257i	0.0209419	−	0.0917522i
$10$	2.08083	−	0.818630i	0.658016	−	0.258873i
$11$	−3.93784	+	0.898786i	−1.18730	+	0.270994i	−0.770163	−	0.637848i	$-0.779825\pi$
$11$	−3.93784	+	0.898786i	−1.18730	+	0.270994i	−0.417141	+	0.908842i	$0.636968\pi$
$12$	1.64853			0.475891
$13$	−2.77413	+	0.633178i	−0.769407	+	0.175612i	−0.589168	−	0.808011i	$-0.700544\pi$
$13$	−2.77413	+	0.633178i	−0.769407	+	0.175612i	−0.180239	+	0.983623i	$0.557687\pi$
$14$	−0.176963	+	0.367467i	−0.0472952	+	0.0982096i
$15$	2.07902	+	3.04401i	0.536801	+	0.785960i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	2.77440			0.672890			0.336445	−	0.941703i	$-0.390775\pi$
$17$	2.77440			0.672890			0.336445	+	0.941703i	$0.390775\pi$
$18$	−0.0628256	−	0.275257i	−0.0148081	−	0.0648786i
$19$	−2.67198	−	2.13084i	−0.612995	−	0.488847i	0.267085	−	0.963673i	$-0.413940\pi$
$19$	−2.67198	−	2.13084i	−0.612995	−	0.488847i	−0.880080	+	0.474826i	$0.842511\pi$
$20$	1.51957	−	1.64040i	0.339786	−	0.366804i
$21$	−0.655509	−	0.149616i	−0.143044	−	0.0326488i
$22$	−3.15790	+	2.51834i	−0.673267	+	0.536913i
$23$	−2.12245	+	4.40731i	−0.442561	+	0.918987i	0.553710	+	0.832709i	$0.313212\pi$
$23$	−2.12245	+	4.40731i	−0.442561	+	0.918987i	−0.996271	+	0.0862778i	$0.972503\pi$
$24$	1.48528	−	0.715272i	0.303181	−	0.146004i
$25$	4.94537	+	0.737122i	0.989073	+	0.147424i
$26$	−2.22468	+	1.77413i	−0.436296	+	0.347935i
$27$	4.87518	−	2.34776i	0.938229	−	0.451827i
$28$			0.407857i			0.0770778i
$29$	−0.926203	−	5.30492i	−0.171992	−	0.985098i
$29$	−0.926203	−	5.30492i	−0.171992	−	0.985098i
$30$	3.19388	+	1.84051i	0.583120	+	0.336029i
$31$	0.235843	+	0.489733i	0.0423586	+	0.0879586i	0.921074	−	0.389387i	$-0.127313\pi$
$31$	0.235843	+	0.489733i	0.0423586	+	0.0879586i	−0.878716	+	0.477346i	$0.841599\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	−5.20591	−	4.15158i	−0.906233	−	0.722696i
$34$	2.49965	−	1.20377i	0.428686	−	0.206444i
$35$	−0.753106	+	0.514362i	−0.127298	+	0.0869430i
$36$	−0.176033	−	0.220739i	−0.0293389	−	0.0367898i
$37$	−0.842848	+	3.69276i	−0.138563	+	0.607086i	0.857188	+	0.515004i	$0.172209\pi$
$37$	−0.842848	+	3.69276i	−0.138563	+	0.607086i	−0.995751	+	0.0920824i	$0.970648\pi$
$38$	−3.33191	−	0.760487i	−0.540507	−	0.123367i
$39$	−3.66747	−	2.92471i	−0.587265	−	0.468328i
$40$	0.657345	−	2.13726i	0.103935	−	0.337931i
$41$			0.945353i			0.147639i	0.997272	+	0.0738197i	$0.0235189\pi$
$41$			0.945353i			0.147639i	−0.997272	+	0.0738197i	$0.976481\pi$
$42$	−0.655509	+	0.149616i	−0.101147	+	0.0230862i
$43$	−6.03831	−	2.90790i	−0.920834	−	0.443450i	−0.0874653	−	0.996168i	$-0.527877\pi$
$43$	−6.03831	−	2.90790i	−0.920834	−	0.443450i	−0.833369	+	0.552717i	$0.813591\pi$
$44$	−1.75250	+	3.63911i	−0.264200	+	0.548617i
$45$	0.185592	−	0.603426i	0.0276664	−	0.0899534i
$46$			4.89174i			0.721248i
$47$	−0.516365	−	2.26234i	−0.0753196	−	0.329997i	0.923204	−	0.384309i	$-0.125560\pi$
$47$	−0.516365	−	2.26234i	−0.0753196	−	0.329997i	−0.998524	+	0.0543126i	$0.982703\pi$
$48$	1.02784	−	1.28888i	0.148357	−	0.186033i
$49$	−1.52063	+	6.66232i	−0.217233	+	0.951760i
$50$	4.77545	−	1.48159i	0.675350	−	0.209529i
$51$	2.85165	+	3.57585i	0.399311	+	0.500720i
$52$	−1.23461	+	2.56369i	−0.171209	+	0.355519i
$53$	−1.25951	−	2.61539i	−0.173006	−	0.359252i	0.796378	−	0.604799i	$-0.206747\pi$
$53$	−1.25951	−	2.61539i	−0.173006	−	0.359252i	−0.969385	+	0.245547i	$0.921032\pi$
$54$	3.37373	−	4.23052i	0.459106	−	0.575701i
$55$	−8.92974	+	1.35341i	−1.20409	+	0.182494i
$56$	0.176963	+	0.367467i	0.0236476	+	0.0491048i
$57$		−	5.63402i		−	0.746245i
$58$	−3.13620	−	4.37770i	−0.411803	−	0.574820i
$59$	−7.18221			−0.935044			−0.467522	−	0.883981i	$-0.654853\pi$
$59$	−7.18221			−0.935044			−0.467522	+	0.883981i	$0.654853\pi$
$60$	3.67615	+	0.272466i	0.474589	+	0.0351752i
$61$	10.5175	−	8.38745i	1.34663	−	1.07390i	0.356421	−	0.934326i	$-0.383997\pi$
$61$	10.5175	−	8.38745i	1.34663	−	1.07390i	0.990211	−	0.139578i	$-0.0445745\pi$
$62$	0.424974	+	0.338906i	0.0539718	+	0.0430410i
$63$	0.0499628	+	0.103749i	0.00629472	+	0.0130711i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−6.29084	+	0.953454i	−0.780282	+	0.118261i
$66$	−6.49166	−	1.48168i	−0.799069	−	0.182382i
$67$	−2.34889	−	0.536119i	−0.286963	−	0.0654973i	0.0766166	−	0.997061i	$-0.475588\pi$
$67$	−2.34889	−	0.536119i	−0.286963	−	0.0654973i	−0.363579	+	0.931563i	$0.618445\pi$
$68$	1.72981	−	2.16911i	0.209770	−	0.263043i
$69$	−7.86202	+	1.79445i	−0.946476	+	0.216027i
$70$	−0.455352	+	0.790185i	−0.0544250	+	0.0944451i
$71$	1.05391	+	4.61747i	0.125076	+	0.547993i	0.998172	+	0.0604442i	$0.0192517\pi$
$71$	1.05391	+	4.61747i	0.125076	+	0.547993i	−0.873096	+	0.487549i	$0.837891\pi$
$72$	−0.254375	−	0.122501i	−0.0299784	−	0.0144369i
$73$	−4.90699	−	2.36308i	−0.574320	−	0.276578i	0.124096	−	0.992270i	$-0.460397\pi$
$73$	−4.90699	−	2.36308i	−0.574320	−	0.276578i	−0.698416	+	0.715693i	$0.746111\pi$
$74$	0.842848	+	3.69276i	0.0979791	+	0.429275i
$75$	4.13301	+	7.13161i	0.477239	+	0.823487i
$76$	−3.33191	+	0.760487i	−0.382196	+	0.0872338i
$77$	1.02712	−	1.28797i	0.117052	−	0.146778i
$78$	−4.57326	−	1.04382i	−0.517819	−	0.118189i
$79$	9.62460	+	2.19675i	1.08285	+	0.247154i	0.726478	−	0.687190i	$-0.241156\pi$
$79$	9.62460	+	2.19675i	1.08285	+	0.247154i	0.356374	+	0.934343i	$0.384013\pi$
$80$	−0.335077	−	2.21082i	−0.0374628	−	0.247177i
$81$	7.27377	+	3.50287i	0.808197	+	0.389207i
$82$	0.410173	+	0.851734i	0.0452961	+	0.0940583i
$83$	3.24962	+	2.59148i	0.356692	+	0.284452i	0.785397	−	0.618992i	$-0.212459\pi$
$83$	3.24962	+	2.59148i	0.356692	+	0.284452i	−0.428705	+	0.903444i	$0.641030\pi$
$84$	−0.525677	+	0.419214i	−0.0573561	+	0.0457400i
$85$	6.18677	+	0.458546i	0.671050	+	0.0497363i
$86$	−6.70202			−0.722698
$87$	5.88539	−	6.64639i	0.630980	−	0.712568i
$88$			4.03911i			0.430571i
$89$	0.754425	+	1.56658i	0.0799689	+	0.166057i	0.937119	−	0.349009i	$-0.113482\pi$
$89$	0.754425	+	1.56658i	0.0799689	+	0.166057i	−0.857151	+	0.515066i	$0.827767\pi$
$90$	−0.0946042	−	0.624193i	−0.00997215	−	0.0657957i
$91$	0.723590	−	0.907353i	0.0758528	−	0.0951164i
$92$	2.12245	+	4.40731i	0.221280	+	0.459494i
$93$	−0.388795	+	0.807341i	−0.0403162	+	0.0837174i
$94$	−1.44682	−	1.81426i	−0.149228	−	0.187126i
$95$	−5.60621	−	5.19328i	−0.575185	−	0.532819i
$96$	0.366833	−	1.60720i	0.0374398	−	0.164034i
$97$	−9.95427	+	12.4823i	−1.01070	+	1.26738i	−0.0474251	+	0.998875i	$0.515102\pi$
$97$	−9.95427	+	12.4823i	−1.01070	+	1.26738i	−0.963278	+	0.268507i	$0.913470\pi$
$98$	1.52063	+	6.66232i	0.153607	+	0.672996i
$99$			1.14038i			0.114613i
$100$	3.65969	−	3.40686i	0.365969	−	0.340686i
$101$	5.94387	−	12.3426i	0.591438	−	1.22813i	−0.363574	−	0.931565i	$-0.618444\pi$
$101$	5.94387	−	12.3426i	0.591438	−	1.22813i	0.955012	−	0.296568i	$-0.0958420\pi$
$102$	4.12075	+	1.98445i	0.408015	+	0.196490i
$103$	−13.7133	+	3.12998i	−1.35122	+	0.308406i	−0.836035	−	0.548675i	$-0.815132\pi$
$103$	−13.7133	+	3.12998i	−1.35122	+	0.308406i	−0.515181	+	0.857082i	$0.672275\pi$
$104$			2.84548i			0.279022i
$105$	−1.43702	−	0.441976i	−0.140239	−	0.0431325i
$106$	−2.26955	−	1.80991i	−0.220438	−	0.175794i
$107$	13.3905	+	3.05630i	1.29451	+	0.295464i	0.813662	−	0.581339i	$-0.197471\pi$
$107$	13.3905	+	3.05630i	1.29451	+	0.295464i	0.480851	+	0.876803i	$0.340328\pi$
$108$	1.20407	−	5.27538i	0.115862	−	0.507623i
$109$	12.7912	+	16.0396i	1.22517	+	1.53631i	0.758170	+	0.652057i	$0.226094\pi$
$109$	12.7912	+	16.0396i	1.22517	+	1.53631i	0.467000	+	0.884257i	$0.345335\pi$
$110$	−7.45820	+	5.09385i	−0.711111	+	0.485680i
$111$	−5.62583	+	2.70926i	−0.533980	+	0.257151i
$112$	0.318876	+	0.254295i	0.0301309	+	0.0240286i
$113$	−8.93683	−	11.2064i	−0.840707	−	1.05421i	−0.997778	−	0.0666256i	$-0.978777\pi$
$113$	−8.93683	−	11.2064i	−0.840707	−	1.05421i	0.157071	−	0.987587i	$-0.449795\pi$
$114$	−2.44451	−	5.07608i	−0.228949	−	0.475418i
$115$	−5.46138	+	9.47729i	−0.509277	+	0.883762i
$116$	−4.72503	−	2.58343i	−0.438708	−	0.239865i
$117$			0.803379i			0.0742724i
$118$	−6.47095	+	3.11624i	−0.595699	+	0.286873i
$119$	−0.884688	+	0.705515i	−0.0810992	+	0.0646744i
$120$	3.43032	−	1.34954i	0.313144	−	0.123195i
$121$	4.78811	−	2.30583i	0.435283	−	0.209621i
$122$	5.83679	−	12.1202i	0.528438	−	1.09731i
$123$	−1.21844	+	0.971676i	−0.109863	+	0.0876130i
$124$	0.529934	+	0.120954i	0.0475895	+	0.0108620i
$125$	10.9061	+	2.46110i	0.975471	+	0.220128i
$126$	0.0900299	+	0.0717964i	0.00802050	+	0.00639613i
$127$	1.84159	+	8.06853i	0.163415	+	0.715966i	0.988533	+	0.151006i	$0.0482513\pi$
$127$	1.84159	+	8.06853i	0.163415	+	0.715966i	−0.825118	+	0.564960i	$0.808892\pi$
$128$	−1.00000			−0.0883883
$129$	−2.45853	−	10.7715i	−0.216461	−	0.948378i
$130$	−5.25416	+	3.58852i	−0.460820	+	0.314734i
$131$	8.66725	−	17.9977i	0.757261	−	1.57247i	−0.0613475	−	0.998116i	$-0.519540\pi$
$131$	8.66725	−	17.9977i	0.757261	−	1.57247i	0.818608	−	0.574352i	$-0.194746\pi$
$132$	−6.49166	+	1.48168i	−0.565027	+	0.128964i
$133$	1.39389			0.120866
$134$	−2.34889	+	0.536119i	−0.202913	+	0.0463136i
$135$	11.2594	−	4.42964i	0.969059	−	0.381243i
$136$	0.617362	−	2.70484i	0.0529383	−	0.231938i
$137$	3.04161	−	13.3262i	0.259863	−	1.13853i	−0.661536	−	0.749914i	$-0.730095\pi$
$137$	3.04161	−	13.3262i	0.259863	−	1.13853i	0.921398	−	0.388619i	$-0.127048\pi$
$138$	−6.30485	+	5.02795i	−0.536704	+	0.428008i
$139$	5.15691	+	2.48344i	0.437403	+	0.210642i	0.639609	−	0.768701i	$-0.279096\pi$
$139$	5.15691	+	2.48344i	0.437403	+	0.210642i	−0.202205	+	0.979343i	$0.564811\pi$
$140$	−0.0674096	+	0.909502i	−0.00569715	+	0.0768669i
$141$	2.38514	−	2.99087i	0.200865	−	0.251876i
$142$	2.95298	+	3.70292i	0.247809	+	0.310743i
$143$	10.3550	−	4.98671i	0.865929	−	0.417010i
$144$	−0.282335			−0.0235280
$145$	−1.18860	−	11.9828i	−0.0987082	−	0.995116i
$146$	−5.44635			−0.450743
$147$	−10.1499	+	4.88792i	−0.837147	+	0.403149i
$148$	2.36161	+	2.96136i	0.194123	+	0.243423i
$149$	6.33710	−	7.94647i	0.519155	−	0.651000i	−0.451274	−	0.892385i	$-0.649030\pi$
$149$	6.33710	−	7.94647i	0.519155	−	0.651000i	0.970429	+	0.241385i	$0.0776018\pi$
$150$	6.81800	+	4.63211i	0.556687	+	0.378211i
$151$	12.5734	+	6.05501i	1.02321	+	0.492750i	0.868751	−	0.495250i	$-0.164924\pi$
$151$	12.5734	+	6.05501i	1.02321	+	0.492750i	0.154455	+	0.988000i	$0.450638\pi$
$152$	−2.67198	+	2.13084i	−0.216727	+	0.172834i
$153$	0.174303	−	0.763672i	0.0140916	−	0.0617392i
$154$	0.366576	−	1.60608i	0.0295396	−	0.129421i
$155$	0.444976	+	1.13106i	0.0357413	+	0.0908489i
$156$	−4.57326	+	1.04382i	−0.366154	+	0.0835721i
$157$	21.5036			1.71617			0.858087	−	0.513504i	$-0.171653\pi$
$157$	21.5036			1.71617			0.858087	+	0.513504i	$0.171653\pi$
$158$	9.62460	−	2.19675i	0.765692	−	0.174764i
$159$	2.07634	−	4.31156i	0.164664	−	0.341929i
$160$	−1.26113	−	1.84650i	−0.0997013	−	0.145978i
$161$	−0.443959	−	1.94511i	−0.0349888	−	0.153296i
$162$	8.07328			0.634297
$163$	3.65799	+	16.0267i	0.286516	+	1.25531i	0.889271	+	0.457381i	$0.151213\pi$
$163$	3.65799	+	16.0267i	0.286516	+	1.25531i	−0.602755	+	0.797927i	$0.705930\pi$
$164$	0.739107	+	0.589418i	0.0577145	+	0.0460258i
$165$	−10.9228	−	10.1182i	−0.850336	−	0.787703i
$166$	4.05221	+	0.924890i	0.314512	+	0.0717854i
$167$	−8.36396	+	6.67004i	−0.647223	+	0.516143i	−0.891184	−	0.453642i	$-0.850124\pi$
$167$	−8.36396	+	6.67004i	−0.647223	+	0.516143i	0.243961	+	0.969785i	$0.421553\pi$
$168$	−0.291729	+	0.605781i	−0.0225074	+	0.0467370i
$169$	−4.41769	+	2.12745i	−0.339822	+	0.163650i
$170$	5.77305	−	2.27120i	0.442772	−	0.174193i
$171$	−0.754396	+	0.601611i	−0.0576901	+	0.0460063i
$172$	−6.03831	+	2.90790i	−0.460417	+	0.221725i
$173$			1.56703i			0.119139i	0.998224	+	0.0595694i	$0.0189727\pi$
$173$			1.56703i			0.119139i	−0.998224	+	0.0595694i	$0.981027\pi$
$174$	2.41879	−	8.54176i	0.183368	−	0.647549i
$175$	−1.76440	+	1.02253i	−0.133376	+	0.0772961i
$176$	1.75250	+	3.63911i	0.132100	+	0.274308i
$177$	−7.38219	−	9.25698i	−0.554880	−	0.695797i
$178$	1.35943	+	1.08411i	0.101893	+	0.0812572i
$179$	12.0426	−	5.79942i	0.900107	−	0.433469i	0.0741794	−	0.997245i	$-0.476366\pi$
$179$	12.0426	−	5.79942i	0.900107	−	0.433469i	0.825928	+	0.563776i	$0.190652\pi$
$180$	−0.356063	−	0.521331i	−0.0265393	−	0.0388577i
$181$	−2.98423	−	3.74211i	−0.221816	−	0.278149i	0.658454	−	0.752621i	$-0.271211\pi$
$181$	−2.98423	−	3.74211i	−0.221816	−	0.278149i	−0.880271	+	0.474472i	$0.842639\pi$
$182$	0.258246	−	1.13145i	0.0191425	−	0.0838687i
$183$	21.6208	+	4.93480i	1.59825	+	0.364791i
$184$	3.82452	+	3.04995i	0.281947	+	0.224845i
$185$	−2.48984	+	8.09537i	−0.183057	+	0.595184i
$186$			0.896081i			0.0657038i
$187$	−10.9251	+	2.49359i	−0.798925	+	0.182349i
$188$	−2.09072	−	1.00684i	−0.152481	−	0.0734312i
$189$	−0.957552	+	1.98838i	−0.0696517	+	0.144633i
$190$	−7.30430	−	2.24654i	−0.529910	−	0.162981i
$191$			20.2044i			1.46194i	0.682411	+	0.730968i	$0.260931\pi$
$191$			20.2044i			1.46194i	−0.682411	+	0.730968i	$0.739069\pi$
$192$	−0.366833	−	1.60720i	−0.0264739	−	0.115990i
$193$	9.01059	−	11.2989i	0.648596	−	0.813314i	−0.343452	−	0.939170i	$-0.611596\pi$
$193$	9.01059	−	11.2989i	0.648596	−	0.813314i	0.992049	+	0.125856i	$0.0401677\pi$
$194$	−3.55264	+	15.5651i	−0.255065	+	1.11751i
$195$	−7.69488	−	7.12810i	−0.551042	−	0.510454i
$196$	4.26071	+	5.34276i	0.304337	+	0.381626i
$197$	−0.932101	+	1.93553i	−0.0664095	+	0.137901i	−0.931531	−	0.363661i	$-0.881527\pi$
$197$	−0.932101	+	1.93553i	−0.0664095	+	0.137901i	0.865122	+	0.501562i	$0.167241\pi$
$198$	0.494794	+	1.02745i	0.0351635	+	0.0730177i
$199$	−13.6676	+	17.1386i	−0.968870	+	1.21492i	0.00775440	+	0.999970i	$0.497532\pi$
$199$	−13.6676	+	17.1386i	−0.968870	+	1.21492i	−0.976624	+	0.214954i	$0.931040\pi$
$200$	1.81909	−	4.65735i	0.128629	−	0.329324i
$201$	−1.72330	−	3.57847i	−0.121552	−	0.252406i
$202$		−	13.6992i		−	0.963875i
$203$	1.64436	+	1.45608i	0.115411	+	0.102197i
$204$	4.57369			0.320222
$205$	−0.156246	+	2.10809i	−0.0109127	+	0.147235i
$206$	−10.9972	+	8.77001i	−0.766215	+	0.611036i
$207$	1.07980	+	0.861110i	0.0750511	+	0.0598513i
$208$	1.23461	+	2.56369i	0.0856045	+	0.177760i
$209$	12.4370	+	5.98935i	0.860286	+	0.414292i
$210$	−1.48648	+	0.225295i	−0.102577	+	0.0155468i
$211$	−10.4051	−	2.37490i	−0.716317	−	0.163495i	−0.151197	−	0.988504i	$-0.548313\pi$
$211$	−10.4051	−	2.37490i	−0.716317	−	0.163495i	−0.565120	+	0.825009i	$0.691170\pi$
$212$	−2.83008	−	0.645948i	−0.194371	−	0.0443639i
$213$	−4.86809	+	6.10440i	−0.333556	+	0.418266i
$214$	13.3905	−	3.05630i	0.915358	−	0.208925i
$215$	−12.9845	−	7.48247i	−0.885538	−	0.510300i
$216$	−1.20407	−	5.27538i	−0.0819266	−	0.358944i
$217$	−0.199741	−	0.0961902i	−0.0135593	−	0.00652981i
$218$	18.4837	+	8.90130i	1.25188	+	0.602872i
$219$	−1.99790	−	8.75338i	−0.135006	−	0.591498i
$220$	−4.50946	+	7.82539i	−0.304028	+	0.527588i
$221$	−7.69655	+	1.75669i	−0.517726	+	0.118168i
$222$	−3.89319	+	4.88191i	−0.261294	+	0.327652i
$223$	19.4854	+	4.44743i	1.30484	+	0.297822i	0.817773	−	0.575542i	$-0.195209\pi$
$223$	19.4854	+	4.44743i	1.30484	+	0.297822i	0.487070	+	0.873363i	$0.338066\pi$
$224$	0.397631	+	0.0907567i	0.0265679	+	0.00606394i
$225$	0.513593	−	1.31494i	0.0342395	−	0.0876624i
$226$	−12.9141	−	6.21910i	−0.859033	−	0.413689i
$227$	−4.86923	−	10.1111i	−0.323182	−	0.671095i	0.674562	−	0.738218i	$-0.264332\pi$
$227$	−4.86923	−	10.1111i	−0.323182	−	0.671095i	−0.997745	+	0.0671229i	$0.978618\pi$
$228$	−4.40486	−	3.51276i	−0.291719	−	0.232638i
$229$	−14.0267	+	11.1859i	−0.926912	+	0.739187i	−0.965591	−	0.260064i	$-0.916256\pi$
$229$	−14.0267	+	11.1859i	−0.926912	+	0.739187i	0.0386796	+	0.999252i	$0.487685\pi$
$230$	−0.808495	+	10.9083i	−0.0533106	+	0.719275i
$231$	2.71576			0.178684
$232$	−5.37801	−	0.277474i	−0.353084	−	0.0182171i
$233$		−	5.12605i		−	0.335818i	−0.985802	−	0.167909i	$-0.946298\pi$
$233$		−	5.12605i		−	0.335818i	0.985802	−	0.167909i	$-0.0537016\pi$
$234$	0.348573	+	0.723820i	0.0227869	+	0.0473176i
$235$	−0.777554	−	5.13026i	−0.0507221	−	0.334661i
$236$	−4.47803	+	5.61528i	−0.291495	+	0.365523i
$237$	7.06125	+	14.6628i	0.458677	+	0.952453i
$238$	−0.490965	+	1.01950i	−0.0318245	+	0.0660843i
$239$	−9.21900	−	11.5603i	−0.596327	−	0.747771i	0.388473	−	0.921460i	$-0.373003\pi$
$239$	−9.21900	−	11.5603i	−0.596327	−	0.747771i	−0.984801	+	0.173689i	$0.944431\pi$
$240$	2.50506	−	2.70425i	0.161701	−	0.174559i
$241$	−2.03145	+	8.90037i	−0.130857	+	0.573323i	0.866403	+	0.499346i	$0.166426\pi$
$241$	−2.03145	+	8.90037i	−0.130857	+	0.573323i	−0.997260	+	0.0739772i	$0.976431\pi$
$242$	3.31348	−	4.15497i	0.212998	−	0.267092i
$243$	−0.650662	−	2.85074i	−0.0417400	−	0.182875i
$244$		−	13.4524i		−	0.861203i
$245$	−4.49206	+	14.6053i	−0.286987	+	0.933100i
$246$	−0.676185	+	1.40411i	−0.0431120	+	0.0895229i
$247$	8.76164	+	4.21938i	0.557490	+	0.268473i
$248$	0.529934	−	0.120954i	0.0336508	−	0.00768059i
$249$			6.85199i			0.434227i
$250$	10.8939	−	2.51460i	0.688990	−	0.159037i
$251$	1.20195	+	0.958525i	0.0758665	+	0.0605016i	0.660689	−	0.750660i	$-0.270264\pi$
$251$	1.20195	+	0.958525i	0.0758665	+	0.0605016i	−0.584822	+	0.811161i	$0.698836\pi$
$252$	0.112265	+	0.0256239i	0.00707206	+	0.00161415i
$253$	4.39663	−	19.2629i	0.276414	−	1.21105i
$254$	5.16002	+	6.47046i	0.323768	+	0.405992i
$255$	5.76803	+	8.44530i	0.361208	+	0.528865i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−21.5247	−	17.1654i	−1.34268	−	1.07075i	−0.990891	−	0.134667i	$-0.957004\pi$
$257$	−21.5247	−	17.1654i	−1.34268	−	1.07075i	−0.351784	−	0.936081i	$-0.614425\pi$
$258$	−6.88863	−	8.63807i	−0.428868	−	0.537783i
$259$	−0.670286	−	1.39186i	−0.0416495	−	0.0864862i
$260$	−3.17683	+	5.51284i	−0.197019	+	0.341892i
$261$	−1.51840	−	0.0783407i	−0.0939868	−	0.00484917i
$262$		−	19.9760i		−	1.23412i
$263$	−8.01312	+	3.85892i	−0.494110	+	0.237951i	−0.664308	−	0.747459i	$-0.731274\pi$
$263$	−8.01312	+	3.85892i	−0.494110	+	0.237951i	0.170198	+	0.985410i	$0.445559\pi$
$264$	−5.20591	+	4.15158i	−0.320402	+	0.255512i
$265$	−2.37637	−	6.04036i	−0.145979	−	0.371056i
$266$	1.25585	−	0.604787i	0.0770012	−	0.0370818i
$267$	−1.24369	+	2.58256i	−0.0761129	+	0.158050i
$268$	−1.88366	+	1.50217i	−0.115063	+	0.0917597i
$269$	12.1595	+	2.77533i	0.741377	+	0.169215i	0.576497	−	0.817099i	$-0.304419\pi$
$269$	12.1595	+	2.77533i	0.741377	+	0.169215i	0.164880	+	0.986314i	$0.447276\pi$
$270$	8.22246	−	8.87626i	0.500403	−	0.540192i
$271$	9.38217	+	7.48203i	0.569926	+	0.454501i	0.865563	−	0.500799i	$-0.166961\pi$
$271$	9.38217	+	7.48203i	0.569926	+	0.454501i	−0.295637	+	0.955300i	$0.595532\pi$
$272$	−0.617362	−	2.70484i	−0.0374330	−	0.164005i
$273$	1.91320			0.115792
$274$	−3.04161	−	13.3262i	−0.183751	−	0.805064i
$275$	−20.1366	+	1.54216i	−1.21428	+	0.0929957i
$276$	−3.49893	+	7.26560i	−0.210611	+	0.437338i
$277$	−12.5502	+	2.86449i	−0.754066	+	0.172111i	−0.582241	−	0.813017i	$-0.697824\pi$
$277$	−12.5502	+	2.86449i	−0.754066	+	0.172111i	−0.171826	+	0.985127i	$0.554967\pi$
$278$	5.72374			0.343287
$279$	0.149619	−	0.0341496i	0.00895747	−	0.00204448i
$280$	0.333884	+	0.848681i	0.0199534	+	0.0507184i
$281$	0.389980	−	1.70862i	0.0232643	−	0.101927i	−0.961963	−	0.273180i	$-0.911924\pi$
$281$	0.389980	−	1.70862i	0.0232643	−	0.101927i	0.985227	+	0.171253i	$0.0547815\pi$
$282$	0.851245	−	3.72955i	0.0506909	−	0.222091i
$283$	−3.19736	+	2.54981i	−0.190063	+	0.151570i	−0.713898	−	0.700249i	$-0.753072\pi$
$283$	−3.19736	+	2.54981i	−0.190063	+	0.151570i	0.523835	+	0.851820i	$0.324501\pi$
$284$	4.26718	+	2.05497i	0.253211	+	0.121940i
$285$	0.931178	−	12.5636i	0.0551582	−	0.744203i
$286$	7.16589	−	8.98574i	0.423728	−	0.531338i
$287$	−0.240398	−	0.301450i	−0.0141903	−	0.0177940i
$288$	−0.254375	+	0.122501i	−0.0149892	+	0.00721843i
$289$	−9.30272			−0.547219
$290$	−6.27003	−	10.2804i	−0.368189	−	0.603686i
$291$	−26.3195			−1.54288
$292$	−4.90699	+	2.36308i	−0.287160	+	0.138289i
$293$	−5.67822	−	7.12027i	−0.331725	−	0.415970i	0.587797	−	0.809009i	$-0.299995\pi$
$293$	−5.67822	−	7.12027i	−0.331725	−	0.415970i	−0.919522	+	0.393038i	$0.871424\pi$
$294$	−7.02393	+	8.80773i	−0.409644	+	0.513677i
$295$	−16.0160	−	1.18706i	−0.932486	−	0.0691132i
$296$	3.41262	+	1.64343i	0.198355	+	0.0955226i
$297$	−17.0875	+	13.6269i	−0.991520	+	0.790711i
$298$	2.26168	−	9.90908i	0.131016	−	0.574018i
$299$	3.09735	−	13.5704i	0.179124	−	0.784794i
$300$	8.15261	+	1.21517i	0.470691	+	0.0701579i
$301$	2.66493	−	0.608254i	0.153604	−	0.0350592i
$302$	13.9554			0.803042
$303$	22.0174	−	5.02534i	1.26487	−	0.288698i
$304$	−1.48284	+	3.07915i	−0.0850467	+	0.176601i
$305$	24.8398	−	16.9653i	1.42233	−	0.971430i
$306$	−0.174303	−	0.763672i	−0.00996424	−	0.0436562i
$307$	−24.7008			−1.40975			−0.704875	−	0.709331i	$-0.748997\pi$
$307$	−24.7008			−1.40975			−0.704875	+	0.709331i	$0.748997\pi$
$308$	−0.366576	−	1.60608i	−0.0208876	−	0.0915147i
$309$	−18.1293	−	14.4577i	−1.03134	−	0.822468i
$310$	0.891658	+	0.825982i	0.0506428	+	0.0469126i
$311$	−5.19546	−	1.18583i	−0.294608	−	0.0672422i	0.0726626	−	0.997357i	$-0.476850\pi$
$311$	−5.19546	−	1.18583i	−0.294608	−	0.0672422i	−0.367270	+	0.930114i	$0.619708\pi$
$312$	−3.66747	+	2.92471i	−0.207629	+	0.165579i
$313$	−11.0207	+	22.8847i	−0.622927	+	1.29352i	0.315789	+	0.948829i	$0.397731\pi$
$313$	−11.0207	+	22.8847i	−0.622927	+	1.29352i	−0.938716	+	0.344692i	$0.887984\pi$
$314$	19.3741	−	9.33006i	1.09334	−	0.526526i
$315$	0.0942673	+	0.239613i	0.00531136	+	0.0135006i
$316$	7.71833	−	6.15516i	0.434190	−	0.346255i
$317$	14.5623	−	7.01281i	0.817898	−	0.393879i	0.0223354	−	0.999751i	$-0.492890\pi$
$317$	14.5623	−	7.01281i	0.817898	−	0.393879i	0.795562	+	0.605872i	$0.207176\pi$
$318$		−	4.78547i		−	0.268356i
$319$	8.41523	+	20.0575i	0.471162	+	1.12300i
$320$	−1.93741	−	1.11645i	−0.108304	−	0.0624114i
$321$	9.82419	+	20.4001i	0.548333	+	1.13863i
$322$	−1.24394	−	1.55986i	−0.0693223	−	0.0869274i
$323$	−7.41315	−	5.91179i	−0.412479	−	0.328941i
$324$	7.27377	−	3.50287i	0.404099	−	0.194604i
$325$	−14.1858	+	1.08642i	−0.786889	+	0.0602639i
$326$	10.2495	+	12.8524i	0.567665	+	0.711829i
$327$	−7.52574	+	32.9724i	−0.416174	+	1.82338i
$328$	0.921651	+	0.210361i	0.0508897	+	0.0116152i
$329$	0.739958	+	0.590097i	0.0407952	+	0.0325331i
$330$	−14.2312	−	4.37700i	−0.783402	−	0.240946i
$331$		−	26.7918i		−	1.47261i	−0.676649	−	0.736306i	$-0.736568\pi$
$331$		−	26.7918i		−	1.47261i	0.676649	−	0.736306i	$-0.263432\pi$
$332$	4.05221	−	0.924890i	0.222394	−	0.0507599i
$333$	0.963505	+	0.463999i	0.0527997	+	0.0254270i
$334$	−4.64165	+	9.63848i	−0.253980	+	0.527394i
$335$	−5.14930	−	1.58374i	−0.281336	−	0.0865288i
$336$			0.672366i			0.0366806i
$337$	3.69780	+	16.2011i	0.201432	+	0.882532i	0.970066	+	0.242842i	$0.0780798\pi$
$337$	3.69780	+	16.2011i	0.201432	+	0.882532i	−0.768634	+	0.639689i	$0.779063\pi$
$338$	−3.05713	+	3.83352i	−0.166286	+	0.208516i
$339$	5.25803	−	23.0369i	0.285577	−	1.25119i
$340$	4.21590	−	4.55112i	0.228639	−	0.246819i
$341$	−1.36888	−	1.71652i	−0.0741288	−	0.0929546i
$342$	−0.418658	+	0.869353i	−0.0226384	+	0.0470092i
$343$	−2.44804	−	5.08340i	−0.132182	−	0.274478i
$344$	−4.17864	+	5.23985i	−0.225297	+	0.282514i
$345$	−17.8285	+	2.70213i	−0.959854	+	0.145478i
$346$	0.679907	+	1.41184i	0.0365520	+	0.0759010i
$347$		−	29.4690i		−	1.58198i	−0.611831	−	0.790988i	$-0.709567\pi$
$347$		−	29.4690i		−	1.58198i	0.611831	−	0.790988i	$-0.290433\pi$
$348$	−1.52688	−	8.74534i	−0.0818492	−	0.468799i
$349$	−29.3953			−1.57350			−0.786748	−	0.617274i	$-0.788237\pi$
$349$	−29.3953			−1.57350			−0.786748	+	0.617274i	$0.788237\pi$
$350$	−1.14601	+	1.68681i	−0.0612569	+	0.0901640i
$351$	−12.0379	+	9.59987i	−0.642533	+	0.512403i
$352$	3.15790	+	2.51834i	0.168317	+	0.134228i
$353$	15.0525	+	31.2568i	0.801163	+	1.66363i	0.746742	+	0.665114i	$0.231617\pi$
$353$	15.0525	+	31.2568i	0.801163	+	1.66363i	0.0544207	+	0.998518i	$0.482669\pi$
$354$	−10.6676	−	5.13723i	−0.566975	−	0.273041i
$355$	1.58700	+	10.4709i	0.0842291	+	0.555739i
$356$	1.69518	+	0.386913i	0.0898442	+	0.0205064i
$357$	−1.81864	−	0.415093i	−0.0962527	−	0.0219691i
$358$	8.33375	−	10.4502i	0.440452	−	0.552309i
$359$	−6.18107	+	1.41079i	−0.326224	+	0.0744586i	−0.382497	−	0.923957i	$-0.624936\pi$
$359$	−6.18107	+	1.41079i	−0.326224	+	0.0744586i	0.0562723	+	0.998415i	$0.482078\pi$
$360$	−0.546998	−	0.315213i	−0.0288293	−	0.0166132i
$361$	−1.62886	−	7.13651i	−0.0857296	−	0.375606i
$362$	−4.31234	−	2.07671i	−0.226652	−	0.109150i
$363$	7.89337	+	3.80125i	0.414294	+	0.199514i
$364$	−0.258246	−	1.13145i	−0.0135358	−	0.0593041i
$365$	−10.5518	−	6.08057i	−0.552305	−	0.318272i
$366$	21.6208	−	4.93480i	1.13014	−	0.257946i
$367$	20.4628	−	25.6595i	1.06815	−	1.33941i	0.130647	−	0.991429i	$-0.458294\pi$
$367$	20.4628	−	25.6595i	1.06815	−	1.33941i	0.937500	−	0.347985i	$-0.113134\pi$
$368$	4.76910	+	1.08852i	0.248606	+	0.0567428i
$369$	0.260215	+	0.0593923i	0.0135462	+	0.00309184i
$370$	1.26918	+	8.37398i	0.0659816	+	0.435343i
$371$	1.06671	+	0.513698i	0.0553806	+	0.0266699i
$372$	0.388795	+	0.807341i	0.0201581	+	0.0418587i
$373$	9.85212	+	7.85680i	0.510123	+	0.406810i	0.844439	−	0.535651i	$-0.179934\pi$
$373$	9.85212	+	7.85680i	0.510123	+	0.406810i	−0.334316	+	0.942461i	$0.608505\pi$
$374$	−8.76128	+	6.98689i	−0.453035	+	0.361283i
$375$	8.03771	+	16.5862i	0.415066	+	0.856510i
$376$	−2.32052			−0.119672
$377$	5.92837	+	14.1301i	0.305327	+	0.727737i
$378$			2.20693i			0.113512i
$379$	−9.66872	−	20.0773i	−0.496649	−	1.03130i	−0.987140	−	0.159856i	$-0.948897\pi$
$379$	−9.66872	−	20.0773i	−0.496649	−	1.03130i	0.490492	−	0.871446i	$-0.336817\pi$
$380$	−7.55569	+	1.14516i	−0.387599	+	0.0587454i
$381$	−8.50646	+	10.6668i	−0.435799	+	0.546475i
$382$	8.76635	+	18.2035i	0.448525	+	0.931372i
$383$	−5.65195	+	11.7364i	−0.288801	+	0.599702i	−0.994009	−	0.109299i	$-0.965139\pi$
$383$	−5.65195	+	11.7364i	−0.288801	+	0.599702i	0.705208	+	0.709001i	$0.250854\pi$
$384$	−1.02784	−	1.28888i	−0.0524520	−	0.0657727i
$385$	2.50331	−	2.70236i	0.127581	−	0.137725i
$386$	3.21584	−	14.0895i	0.163682	−	0.717138i
$387$	−1.17978	+	1.47940i	−0.0599715	+	0.0752019i
$388$	3.55264	+	15.5651i	0.180358	+	0.790199i
$389$			12.4664i			0.632073i	0.948747	+	0.316037i	$0.102352\pi$
$389$			12.4664i			0.632073i	−0.948747	+	0.316037i	$0.897648\pi$
$390$	−10.0256	−	3.08352i	−0.507667	−	0.156140i
$391$	−5.88852	+	12.2276i	−0.297795	+	0.618378i
$392$	6.15691	+	2.96501i	0.310971	+	0.149756i
$393$	32.1054	−	7.32785i	1.61950	−	0.369641i
$394$			2.14827i			0.108229i
$395$	21.0993	+	6.48938i	1.06162	+	0.326516i
$396$	0.891588	+	0.711018i	0.0448040	+	0.0357300i
$397$	11.4895	+	2.62241i	0.576643	+	0.131615i	0.500889	−	0.865511i	$-0.333006\pi$
$397$	11.4895	+	2.62241i	0.576643	+	0.131615i	0.0757541	+	0.997127i	$0.475864\pi$
$398$	−4.87791	+	21.3715i	−0.244507	+	1.07126i
$399$	1.43270	+	1.79655i	0.0717248	+	0.0899401i
$400$	−0.381807	−	4.98540i	−0.0190903	−	0.249270i
$401$	−9.39029	+	4.52212i	−0.468928	+	0.225824i	−0.653399	−	0.757014i	$-0.726657\pi$
$401$	−9.39029	+	4.52212i	−0.468928	+	0.225824i	0.184470	+	0.982838i	$0.440943\pi$
$402$	−3.10528	−	2.47638i	−0.154877	−	0.123511i
$403$	−0.964348	−	1.20925i	−0.0480376	−	0.0602372i
$404$	−5.94387	−	12.3426i	−0.295719	−	0.614066i
$405$	15.6412	+	9.01341i	0.777218	+	0.447880i
$406$	2.11328	+	0.598423i	0.104880	+	0.0296992i
$407$		−	15.2990i		−	0.758345i
$408$	4.12075	−	1.98445i	0.204008	−	0.0982449i
$409$	−7.95469	+	6.34365i	−0.393334	+	0.313674i	−0.800109	−	0.599855i	$-0.795225\pi$
$409$	−7.95469	+	6.34365i	−0.393334	+	0.313674i	0.406775	+	0.913529i	$0.366653\pi$
$410$	0.773894	+	1.96712i	0.0382199	+	0.0971490i
$411$	20.3021	−	9.77698i	1.00143	−	0.482263i
$412$	−6.10301	+	12.6730i	−0.300674	+	0.624356i
$413$	2.29023	−	1.82640i	0.112695	−	0.0898712i
$414$	1.34649	+	0.307326i	0.0661761	+	0.0151043i
$415$	6.81817	+	6.31597i	0.334691	+	0.310039i
$416$	2.22468	+	1.77413i	0.109074	+	0.0869837i
$417$	2.09966	+	9.19920i	0.102821	+	0.450487i
$418$	13.8040			0.675178
$419$	−3.45860	−	15.1531i	−0.168963	−	0.740277i	−0.986414	−	0.164278i	$-0.947470\pi$
$419$	−3.45860	−	15.1531i	−0.168963	−	0.740277i	0.817451	−	0.575999i	$-0.195387\pi$
$420$	−1.24152	+	0.847943i	−0.0605800	+	0.0413754i
$421$	9.86219	−	20.4791i	0.480654	−	0.998088i	−0.509806	−	0.860289i	$-0.670283\pi$
$421$	9.86219	−	20.4791i	0.480654	−	0.998088i	0.990460	−	0.137799i	$-0.0440028\pi$
$422$	−10.4051	+	2.37490i	−0.506513	+	0.115608i
$423$	−0.655166			−0.0318553
$424$	−2.83008	+	0.645948i	−0.137441	+	0.0313700i
$425$	13.7204	+	2.04507i	0.665538	+	0.0992004i
$426$	−1.73740	+	7.61206i	−0.0841774	+	0.368805i
$427$	−1.22090	+	5.34911i	−0.0590834	+	0.258861i
$428$	10.7384	−	8.56357i	0.519059	−	0.413936i
$429$	17.0706	+	8.22076i	0.824176	+	0.396902i
$430$	−14.9452	−	1.10769i	−0.720721	−	0.0534178i
$431$	9.79032	−	12.2767i	0.471583	−	0.591346i	−0.487975	−	0.872858i	$-0.662264\pi$
$431$	9.79032	−	12.2767i	0.471583	−	0.591346i	0.959558	+	0.281511i	$0.0908357\pi$
$432$	−3.37373	−	4.23052i	−0.162319	−	0.203541i
$433$	11.5309	−	5.55299i	0.554140	−	0.266860i	−0.135788	−	0.990738i	$-0.543357\pi$
$433$	11.5309	−	5.55299i	0.554140	−	0.266860i	0.689928	+	0.723878i	$0.257642\pi$
$434$	−0.221696			−0.0106417
$435$	14.2226	−	13.8484i	0.681923	−	0.663980i
$436$	20.5154			0.982510
$437$	15.0624	−	7.25367i	0.720532	−	0.346990i
$438$	−5.59799	−	7.01966i	−0.267483	−	0.335412i
$439$	18.7778	−	23.5466i	0.896216	−	1.12382i	−0.0955077	−	0.995429i	$-0.530447\pi$
$439$	18.7778	−	23.5466i	0.896216	−	1.12382i	0.991724	−	0.128391i	$-0.0409811\pi$
$440$	−0.667574	+	9.00702i	−0.0318254	+	0.429393i
$441$	1.73831	+	0.837128i	0.0827768	+	0.0398632i
$442$	−6.17216	+	4.92213i	−0.293580	+	0.234122i
$443$	1.67459	−	7.33688i	0.0795624	−	0.348586i	−0.919441	−	0.393229i	$-0.871358\pi$
$443$	1.67459	−	7.33688i	0.0795624	−	0.348586i	0.999003	+	0.0446433i	$0.0142151\pi$
$444$	−1.38946	+	6.08764i	−0.0659411	+	0.288907i
$445$	1.42341	+	3.61808i	0.0674761	+	0.171514i
$446$	19.4854	−	4.44743i	0.922663	−	0.210592i
$447$	16.7556			0.792511
$448$	0.397631	−	0.0907567i	0.0187863	−	0.00428785i
$449$	−8.52994	+	17.7126i	−0.402553	+	0.835909i	0.596883	+	0.802328i	$0.296406\pi$
$449$	−8.52994	+	17.7126i	−0.402553	+	0.835909i	−0.999436	+	0.0335813i	$0.989309\pi$
$450$	−0.107798	−	1.40756i	−0.00508163	−	0.0663528i
$451$	−0.849671	−	3.72265i	−0.0400094	−	0.175293i
$452$	−14.3336			−0.674194
$453$	5.11930	+	22.4291i	0.240526	+	1.05381i
$454$	−8.77405	−	6.99707i	−0.411787	−	0.328389i
$455$	1.76354	−	1.90376i	0.0826758	−	0.0892496i
$456$	−5.49277	−	1.25369i	−0.257222	−	0.0587093i
$457$	−9.38027	+	7.48052i	−0.438791	+	0.349924i	−0.817833	−	0.575455i	$-0.804825\pi$
$457$	−9.38027	+	7.48052i	−0.438791	+	0.349924i	0.379043	+	0.925379i	$0.376253\pi$
$458$	−7.78424	+	16.1641i	−0.363734	+	0.755301i
$459$	13.5257	−	6.51363i	0.631325	−	0.304030i
$460$	4.00453	+	10.1789i	0.186712	+	0.474593i
$461$	1.16005	−	0.925108i	0.0540288	−	0.0430866i	−0.596103	−	0.802908i	$-0.703285\pi$
$461$	1.16005	−	0.925108i	0.0540288	−	0.0430866i	0.650132	+	0.759821i	$0.274714\pi$
$462$	2.44682	−	1.17832i	0.113836	−	0.0548206i
$463$		−	31.1920i		−	1.44961i	−0.688952	−	0.724807i	$-0.741929\pi$
$463$		−	31.1920i		−	1.44961i	0.688952	−	0.724807i	$-0.258071\pi$
$464$	−4.96581	+	2.08344i	−0.230532	+	0.0967211i
$465$	−1.00043	+	1.73607i	−0.0463938	+	0.0805084i
$466$	−2.22411	−	4.61841i	−0.103030	−	0.213944i
$467$	−10.9665	−	13.7516i	−0.507471	−	0.636349i	0.460425	−	0.887699i	$-0.347697\pi$
$467$	−10.9665	−	13.7516i	−0.507471	−	0.636349i	−0.967896	+	0.251350i	$0.919126\pi$
$468$	0.628107	+	0.500899i	0.0290343	+	0.0231540i
$469$	0.885336	−	0.426355i	0.0408810	−	0.0196873i
$470$	−2.92649	−	4.28484i	−0.134989	−	0.197645i
$471$	22.1023	+	27.7155i	1.01842	+	1.27706i
$472$	−1.59819	+	7.00214i	−0.0735627	+	0.322299i
$473$	26.3915	+	6.02369i	1.21348	+	0.276969i
$474$	12.7239	+	10.1470i	0.584429	+	0.466067i
$475$	−11.6433	−	12.5073i	−0.534229	−	0.573876i
$476$			1.13156i			0.0518649i
$477$	−0.799033	+	0.182374i	−0.0365852	+	0.00835034i
$478$	−13.3218	−	6.41546i	−0.609327	−	0.293436i
$479$	12.3346	−	25.6130i	0.563580	−	1.17029i	−0.403303	−	0.915066i	$-0.632138\pi$
$479$	12.3346	−	25.6130i	0.563580	−	1.17029i	0.966883	−	0.255220i	$-0.0821477\pi$
$480$	1.08365	−	3.52335i	0.0494619	−	0.160818i
$481$		−	10.7779i		−	0.491429i
$482$	2.03145	+	8.90037i	0.0925301	+	0.405401i
$483$	2.05069	−	2.57148i	0.0933094	−	0.117006i
$484$	1.18257	−	5.18116i	0.0537530	−	0.235507i
$485$	−24.2606	+	26.1896i	−1.10162	+	1.18921i
$486$	−1.82311	−	2.28611i	−0.0826981	−	0.103700i
$487$	16.5442	−	34.3544i	0.749689	−	1.55675i	−0.0788960	−	0.996883i	$-0.525139\pi$
$487$	16.5442	−	34.3544i	0.749689	−	1.55675i	0.828585	−	0.559863i	$-0.189146\pi$
$488$	−5.83679	−	12.1202i	−0.264219	−	0.548657i
$489$	−16.8966	+	21.1876i	−0.764090	+	0.958138i
$490$	2.28980	+	15.1080i	0.103443	+	0.682509i
$491$	−9.20001	−	19.1040i	−0.415191	−	0.862153i	−0.998745	−	0.0500786i	$-0.984053\pi$
$491$	−9.20001	−	19.1040i	−0.415191	−	0.862153i	0.583554	−	0.812074i	$-0.301661\pi$
$492$			1.55845i			0.0702602i
$493$	−2.56966	−	14.7180i	−0.115731	−	0.662863i
$494$	9.72469			0.437534
$495$	−0.188480	+	2.54300i	−0.00847154	+	0.114299i
$496$	0.424974	−	0.338906i	0.0190819	−	0.0152173i
$497$	−1.51026	−	1.20440i	−0.0677446	−	0.0540245i
$498$	2.97297	+	6.17343i	0.133222	+	0.276638i
$499$	28.3399	+	13.6478i	1.26867	+	0.610959i	0.942454	−	0.334337i	$-0.108512\pi$
$499$	28.3399	+	13.6478i	1.26867	+	0.610959i	0.326215	+	0.945296i	$0.394227\pi$
$500$	8.72401	−	6.99226i	0.390150	−	0.312703i
$501$	−17.1937	−	3.92435i	−0.768158	−	0.175327i
$502$	1.49881	+	0.342094i	0.0668952	+	0.0152684i
$503$	−19.5269	+	24.4859i	−0.870660	+	1.09177i	0.124374	+	0.992235i	$0.460308\pi$
$503$	−19.5269	+	24.4859i	−0.870660	+	1.09177i	−0.995034	+	0.0995373i	$0.968264\pi$
$504$	0.112265	−	0.0256239i	0.00500070	−	0.00114138i
$505$	15.2945	−	26.5410i	0.680596	−	1.18106i
$506$	−4.39663	−	19.2629i	−0.195454	−	0.856341i
$507$	−7.28271	−	3.50717i	−0.323436	−	0.155759i
$508$	7.45644	+	3.59083i	0.330826	+	0.159317i
$509$	9.24194	+	40.4916i	0.409642	+	1.79476i	0.585865	+	0.810408i	$0.300755\pi$
$509$	9.24194	+	40.4916i	0.409642	+	1.79476i	−0.176223	+	0.984350i	$0.556388\pi$
$510$	8.86109	+	5.10629i	0.392376	+	0.226110i
$511$	2.16564	−	0.494293i	0.0958022	−	0.0218662i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	−18.0291	−	4.11502i	−0.796004	−	0.181683i
$514$	−26.8409	−	6.12626i	−1.18390	−	0.270218i
$515$	−31.0974	+	4.71320i	−1.37032	+	0.207688i
$516$	−9.95437	−	4.79377i	−0.438217	−	0.211034i
$517$	4.06673	+	8.44464i	0.178854	+	0.371395i
$518$	−1.20781	−	0.963199i	−0.0530683	−	0.0423205i
$519$	−2.01970	+	1.61066i	−0.0886550	+	0.0707000i
$520$	−0.470294	+	6.34528i	−0.0206237	+	0.278259i
$521$	20.7337			0.908359			0.454179	−	0.890910i	$-0.349932\pi$
$521$	20.7337			0.908359			0.454179	+	0.890910i	$0.349932\pi$
$522$	−1.40203	+	0.588228i	−0.0613650	+	0.0257460i
$523$		−	10.5864i		−	0.462913i	−0.972845	−	0.231456i	$-0.925651\pi$
$523$		−	10.5864i		−	0.462913i	0.972845	−	0.231456i	$-0.0743490\pi$
$524$	−8.66725	−	17.9977i	−0.378630	−	0.786234i
$525$	−3.13145	−	1.22309i	−0.136668	−	0.0533802i
$526$	−5.54525	+	6.95353i	−0.241784	+	0.303188i
$527$	0.654322	+	1.35871i	0.0285027	+	0.0591865i
$528$	−2.88906	+	5.99920i	−0.125730	+	0.261082i
$529$	−0.579317	−	0.726440i	−0.0251877	−	0.0315844i
$530$	−4.76185	−	4.41111i	−0.206842	−	0.191606i
$531$	−0.451226	+	1.97695i	−0.0195816	+	0.0857924i
$532$	0.869077	−	1.08979i	0.0376793	−	0.0472483i
$533$	−0.598577	−	2.62254i	−0.0259272	−	0.113595i
$534$			2.86642i			0.124042i
$535$	29.3551	+	9.02856i	1.26913	+	0.390339i
$536$	−1.04535	+	2.17070i	−0.0451524	+	0.0937600i
$537$	19.8527	+	9.56053i	0.856705	+	0.412568i
$538$	12.1595	−	2.77533i	0.524233	−	0.119653i
$539$		−	27.6019i		−	1.18890i
$540$	3.55692	−	11.5648i	0.153065	−	0.497671i
$541$	15.4090	+	12.2882i	0.662484	+	0.528313i	0.896008	−	0.444038i	$-0.146454\pi$
$541$	15.4090	+	12.2882i	0.662484	+	0.528313i	−0.233524	+	0.972351i	$0.575026\pi$
$542$	11.6994	+	2.67031i	0.502531	+	0.114699i
$543$	1.75579	−	7.69261i	0.0753481	−	0.330121i
$544$	−1.72981	−	2.16911i	−0.0741649	−	0.0929999i
$545$	25.8727	+	37.8816i	1.10826	+	1.62267i
$546$	1.72374	−	0.830108i	0.0737691	−	0.0355253i
$547$	−3.67336	−	2.92941i	−0.157062	−	0.125252i	0.541806	−	0.840504i	$-0.317741\pi$
$547$	−3.67336	−	2.92941i	−0.157062	−	0.125252i	−0.698867	+	0.715251i	$0.746312\pi$
$548$	−8.52242	−	10.6868i	−0.364060	−	0.456516i
$549$	−1.64793	−	3.42197i	−0.0703321	−	0.146046i
$550$	−17.4733	+	10.1264i	−0.745065	+	0.431790i
$551$	−8.82911	+	16.1482i	−0.376133	+	0.687938i
$552$			8.06421i			0.343235i
$553$	−3.62767	+	1.74699i	−0.154264	+	0.0742898i
$554$	−10.0645	+	8.02613i	−0.427598	+	0.340998i
$555$	−12.9931	+	5.11168i	−0.551526	+	0.216979i
$556$	5.15691	−	2.48344i	0.218702	−	0.105321i
$557$	7.53911	−	15.6551i	0.319442	−	0.663329i	−0.677980	−	0.735080i	$-0.737144\pi$
$557$	7.53911	−	15.6551i	0.319442	−	0.663329i	0.997423	+	0.0717512i	$0.0228588\pi$
$558$	0.119985	−	0.0956851i	0.00507938	−	0.00405067i
$559$	18.5923	+	4.24357i	0.786371	+	0.179484i
$560$	0.669048	+	0.619768i	0.0282724	+	0.0261900i
$561$	−14.4433	−	11.5181i	−0.609795	−	0.486295i
$562$	−0.389980	−	1.70862i	−0.0164503	−	0.0720736i
$563$	−42.8562			−1.80617			−0.903087	−	0.429458i	$-0.858705\pi$
$563$	−42.8562			−1.80617			−0.903087	+	0.429458i	$0.858705\pi$
$564$	−0.851245	−	3.72955i	−0.0358439	−	0.157042i
$565$	−18.0765	−	26.4669i	−0.760486	−	1.11347i
$566$	−1.77440	+	3.68458i	−0.0745836	+	0.154874i
$567$	−3.21019	+	0.732705i	−0.134815	+	0.0307707i
$568$	4.73622			0.198727
$569$	−37.0103	+	8.44735i	−1.55155	+	0.354132i	−0.910547	−	0.413406i	$-0.864339\pi$
$569$	−37.0103	+	8.44735i	−1.55155	+	0.354132i	−0.641005	+	0.767537i	$0.721482\pi$
$570$	−4.61218	−	11.7234i	−0.193183	−	0.491041i
$571$	4.05313	−	17.7579i	0.169618	−	0.743146i	−0.816533	−	0.577299i	$-0.804107\pi$
$571$	4.05313	−	17.7579i	0.169618	−	0.743146i	0.986151	−	0.165848i	$-0.0530360\pi$
$572$	2.55748	−	11.2050i	0.106933	−	0.468506i
$573$	−26.0409	+	20.7669i	−1.08787	+	0.867551i
$574$	−0.347386	−	0.167292i	−0.0144996	−	0.00698264i
$575$	−13.7450	+	20.2313i	−0.573206	+	0.843702i
$576$	−0.176033	+	0.220739i	−0.00733472	+	0.00919745i
$577$	−16.1247	−	20.2197i	−0.671280	−	0.841758i	0.323239	−	0.946317i	$-0.395228\pi$
$577$	−16.1247	−	20.2197i	−0.671280	−	0.841758i	−0.994519	+	0.104559i	$0.966657\pi$
$578$	−8.38146	+	4.03630i	−0.348623	+	0.167888i
$579$	23.8244			0.990108
$580$	−10.1096	−	6.54186i	−0.419778	−	0.271636i
$581$	−1.69522			−0.0703297
$582$	−23.7131	+	11.4196i	−0.982938	+	0.473358i
$583$	7.31041	+	9.16696i	0.302766	+	0.379657i
$584$	−3.39574	+	4.25812i	−0.140517	+	0.176202i
$585$	−0.132781	+	1.79150i	−0.00548980	+	0.0740693i
$586$	−8.20527	−	3.95145i	−0.338957	−	0.163233i
$587$	−15.0968	+	12.0393i	−0.623113	+	0.496916i	−0.883403	−	0.468614i	$-0.844753\pi$
$587$	−15.0968	+	12.0393i	−0.623113	+	0.496916i	0.260290	+	0.965531i	$0.416182\pi$
$588$	−2.50681	+	10.9831i	−0.103379	+	0.452934i
$589$	0.413372	−	1.81110i	0.0170327	−	0.0746251i
$590$	−14.9449	+	5.87957i	−0.615274	+	0.242058i
$591$	−3.45271	+	0.788059i	−0.142026	+	0.0324164i
$592$	3.78773			0.155675
$593$	−0.396646	+	0.0905319i	−0.0162883	+	0.00371770i	−0.230657	−	0.973035i	$-0.574088\pi$
$593$	−0.396646	+	0.0905319i	−0.0162883	+	0.00371770i	0.214369	+	0.976753i	$0.431230\pi$
$594$	−9.48287	+	19.6914i	−0.389087	+	0.807947i
$595$	−2.08942	+	1.42704i	−0.0856577	+	0.0585031i
$596$	−2.26168	−	9.90908i	−0.0926421	−	0.405892i
$597$	−36.1377			−1.47902
$598$	−3.09735	−	13.5704i	−0.126660	−	0.554933i
$599$	−12.9284	−	10.3100i	−0.528238	−	0.421256i	0.322716	−	0.946496i	$-0.395404\pi$
$599$	−12.9284	−	10.3100i	−0.528238	−	0.421256i	−0.850954	+	0.525240i	$0.823976\pi$
$600$	7.87249	−	2.44245i	0.321393	−	0.0997127i
$601$	−47.2595	−	10.7867i	−1.92775	−	0.439997i	−0.997286	−	0.0736224i	$-0.976544\pi$
$601$	−47.2595	−	10.7867i	−1.92775	−	0.439997i	−0.930467	−	0.366375i	$-0.880599\pi$
$602$	2.13711	−	1.70429i	0.0871021	−	0.0694616i
$603$	−0.295141	+	0.612866i	−0.0120191	+	0.0249578i
$604$	12.5734	−	6.05501i	0.511603	−	0.246375i
$605$	11.0584	−	4.35053i	0.449586	−	0.176874i
$606$	17.6566	−	14.0807i	0.717251	−	0.571988i
$607$	−26.8041	+	12.9082i	−1.08795	+	0.523927i	−0.889849	−	0.456255i	$-0.849190\pi$
$607$	−26.8041	+	12.9082i	−1.08795	+	0.523927i	−0.198097	+	0.980182i	$0.563476\pi$
$608$			3.41760i			0.138602i
$609$	−0.186564	+	3.61599i	−0.00755996	+	0.146527i
$610$	15.0190	−	26.0628i	0.608100	−	1.05525i
$611$	2.86493	+	5.94909i	0.115903	+	0.240675i
$612$	−0.488386	−	0.612417i	−0.0197419	−	0.0247555i
$613$	4.79678	+	3.82531i	0.193740	+	0.154503i	0.715556	−	0.698556i	$-0.246174\pi$
$613$	4.79678	+	3.82531i	0.193740	+	0.154503i	−0.521815	+	0.853058i	$0.674745\pi$
$614$	−22.2547	+	10.7173i	−0.898126	+	0.432515i
$615$	−2.87766	+	1.96541i	−0.116039	+	0.0792529i
$616$	−1.02712	−	1.28797i	−0.0413840	−	0.0518939i
$617$	7.84996	−	34.3929i	0.316027	−	1.38461i	−0.528427	−	0.848979i	$-0.677218\pi$
$617$	7.84996	−	34.3929i	0.316027	−	1.38461i	0.844454	−	0.535628i	$-0.179925\pi$
$618$	−22.6069	−	5.15988i	−0.909383	−	0.207561i
$619$	−17.0443	−	13.5924i	−0.685070	−	0.546325i	0.217931	−	0.975964i	$-0.430069\pi$
$619$	−17.0443	−	13.5924i	−0.685070	−	0.546325i	−0.903001	+	0.429639i	$0.858641\pi$
$620$	1.16174	+	0.357308i	0.0466564	+	0.0143498i
$621$			26.4694i			1.06218i
$622$	−5.19546	+	1.18583i	−0.208319	+	0.0475474i
$623$	−0.638940	−	0.307697i	−0.0255986	−	0.0123276i
$624$	−2.03529	+	4.22632i	−0.0814768	+	0.169188i
$625$	23.9133	+	7.29068i	0.956532	+	0.291627i
$626$			25.4001i			1.01519i
$627$	5.06378	+	22.1859i	0.202228	+	0.886019i
$628$	13.4073	−	16.8122i	0.535008	−	0.670879i
$629$	−2.33840	+	10.2452i	−0.0932380	+	0.408502i
$630$	0.188896	+	0.174982i	0.00752579	+	0.00697147i
$631$	23.5002	+	29.4683i	0.935526	+	1.17311i	0.984689	+	0.174322i	$0.0557735\pi$
$631$	23.5002	+	29.4683i	0.935526	+	1.17311i	−0.0491622	+	0.998791i	$0.515655\pi$
$632$	4.28335	−	8.89447i	0.170382	−	0.353803i
$633$	−7.63388	−	15.8519i	−0.303419	−	0.630057i
$634$	10.0774	−	12.6367i	0.400224	−	0.501866i
$635$	2.77311	+	18.2968i	0.110047	+	0.726086i
$636$	−2.07634	−	4.31156i	−0.0823322	−	0.170964i
$637$		−	19.4450i		−	0.770439i
$638$	16.2845	+	14.4199i	0.644708	+	0.570890i
$639$	1.33720			0.0528989
$640$	−2.22995	−	0.165278i	−0.0881466	−	0.00653317i
$641$	−1.31064	+	1.04520i	−0.0517670	+	0.0412828i	−0.649032	−	0.760762i	$-0.724826\pi$
$641$	−1.31064	+	1.04520i	−0.0517670	+	0.0412828i	0.597265	+	0.802044i	$0.296254\pi$
$642$	17.7026	+	14.1173i	0.698665	+	0.557167i
$643$	−4.94290	−	10.2640i	−0.194929	−	0.404774i	0.780479	−	0.625182i	$-0.214975\pi$
$643$	−4.94290	−	10.2640i	−0.194929	−	0.404774i	−0.975408	+	0.220408i	$0.929261\pi$
$644$	−1.79755	−	0.865655i	−0.0708335	−	0.0341116i
$645$	−3.70210	−	24.4263i	−0.145770	−	0.961783i
$646$	−9.24404	−	2.10989i	−0.363702	−	0.0830126i
$647$	32.7490	+	7.47474i	1.28749	+	0.293862i	0.810860	−	0.585240i	$-0.199000\pi$
$647$	32.7490	+	7.47474i	1.28749	+	0.293862i	0.476634	+	0.879102i	$0.341857\pi$
$648$	5.03361	−	6.31194i	0.197739	−	0.247957i
$649$	28.2824	−	6.45527i	1.11018	−	0.253392i
$650$	−12.3096	+	7.13384i	−0.482823	+	0.279812i
$651$	−0.0813254	−	0.356310i	−0.00318739	−	0.0139649i
$652$	14.8109	+	7.13255i	0.580040	+	0.279332i
$653$	−36.0675	−	17.3692i	−1.41143	−	0.679709i	−0.435986	−	0.899953i	$-0.643600\pi$
$653$	−36.0675	−	17.3692i	−1.41143	−	0.679709i	−0.975445	+	0.220244i	$0.929315\pi$
$654$	7.52574	+	32.9724i	0.294280	+	1.28932i
$655$	22.3022	−	38.7016i	0.871418	−	1.51219i
$656$	0.921651	−	0.210361i	0.0359844	−	0.00821321i
$657$	−0.958738	+	1.20222i	−0.0374039	+	0.0469031i
$658$	0.922713	+	0.210603i	0.0359711	+	0.00821017i
$659$	36.8628	+	8.41370i	1.43597	+	0.327751i	0.868520	−	0.495654i	$-0.165072\pi$
$659$	36.8628	+	8.41370i	1.43597	+	0.327751i	0.567453	+	0.823406i	$0.307929\pi$
$660$	−14.7210	+	2.23115i	−0.573014	+	0.0868473i
$661$	−25.8698	−	12.4582i	−1.00622	−	0.484570i	−0.143175	−	0.989697i	$-0.545731\pi$
$661$	−25.8698	−	12.4582i	−1.00622	−	0.484570i	−0.863045	+	0.505128i	$0.831445\pi$
$662$	−11.6245	−	24.1386i	−0.451800	−	0.938173i
$663$	−10.1750	−	8.11430i	−0.395165	−	0.315133i
$664$	3.24962	−	2.59148i	0.126110	−	0.100569i
$665$	3.10831	+	0.230379i	0.120535	+	0.00893371i
$666$	1.06941			0.0414388
$667$	25.3462	+	7.17735i	0.981410	+	0.277908i
$668$			10.6979i			0.413915i
$669$	14.2958	+	29.6856i	0.552708	+	1.14771i
$670$	−5.32652	+	0.807300i	−0.205781	+	0.0311887i
$671$	−33.8778	+	42.4815i	−1.30784	+	1.63998i
$672$	0.291729	+	0.605781i	0.0112537	+	0.0233685i
$673$	1.70122	−	3.53261i	0.0655770	−	0.136172i	−0.865604	−	0.500729i	$-0.833065\pi$
$673$	1.70122	−	3.53261i	0.0655770	−	0.136172i	0.931181	+	0.364557i	$0.118780\pi$
$674$	10.3610	+	12.9923i	0.399091	+	0.500445i
$675$	25.8401	−	8.01695i	0.994588	−	0.308572i
$676$	−1.09108	+	4.78033i	−0.0419645	+	0.183859i
$677$	12.9302	−	16.2140i	0.496949	−	0.623155i	−0.468589	−	0.883416i	$-0.655237\pi$
$677$	12.9302	−	16.2140i	0.496949	−	0.623155i	0.965538	+	0.260262i	$0.0838089\pi$
$678$	−5.25803	−	23.0369i	−0.201933	−	0.884728i
$679$		−	6.51161i		−	0.249892i
$680$	1.82374	−	5.92962i	0.0699371	−	0.227391i
$681$	8.02709	−	16.6684i	0.307599	−	0.638736i
$682$	−1.97808	−	0.952595i	−0.0757447	−	0.0364767i
$683$	−23.7030	+	5.41005i	−0.906970	+	0.207010i	−0.650468	−	0.759534i	$-0.725427\pi$
$683$	−23.7030	+	5.41005i	−0.906970	+	0.207010i	−0.256502	+	0.966544i	$0.582570\pi$
$684$			0.964908i			0.0368942i
$685$	8.98517	−	29.2140i	0.343306	−	1.11621i
$686$	−4.41121	−	3.51783i	−0.168421	−	0.134311i
$687$	−28.8346	−	6.58130i	−1.10011	−	0.251092i
$688$	−1.49134	+	6.53399i	−0.0568568	+	0.249106i
$689$	5.15005	+	6.45795i	0.196201	+	0.246028i
$690$	−14.8905	+	10.1700i	−0.566872	+	0.387167i
$691$	−37.3957	+	18.0088i	−1.42260	+	0.685087i	−0.977605	−	0.210447i	$-0.932508\pi$
$691$	−37.3957	+	18.0088i	−1.42260	+	0.685087i	−0.444992	+	0.895534i	$0.646794\pi$
$692$	1.22515	+	0.977024i	0.0465732	+	0.0371409i
$693$	−0.289994	−	0.363641i	−0.0110159	−	0.0138136i
$694$	−12.7861	−	26.5506i	−0.485354	−	1.00785i
$695$	11.0892	+	6.39027i	0.420637	+	0.242397i
$696$	−5.17013	−	7.21679i	−0.195973	−	0.273552i
$697$			2.62279i			0.0993451i
$698$	−26.4843	+	12.7542i	−1.00244	+	0.482752i
$699$	6.60684	−	5.26878i	0.249894	−	0.199283i
$700$	−0.300640	+	2.01700i	−0.0113631	+	0.0762355i
$701$	−25.4692	+	12.2653i	−0.961957	+	0.463254i	−0.847863	−	0.530216i	$-0.822111\pi$
$701$	−25.4692	+	12.2653i	−0.961957	+	0.463254i	−0.114094	+	0.993470i	$0.536397\pi$
$702$	−6.68051	+	13.8722i	−0.252139	+	0.523573i
$703$	10.1207	−	8.07102i	0.381711	−	0.304404i
$704$	3.93784	+	0.898786i	0.148413	+	0.0338743i
$705$	5.81306	−	6.27528i	0.218933	−	0.236341i
$706$	27.1236	+	21.6304i	1.02081	+	0.814070i
$707$	1.24330	+	5.44724i	0.0467590	+	0.204865i
$708$	−11.8401			−0.444979
$709$	6.45621	+	28.2865i	0.242468	+	1.06232i	0.938762	+	0.344566i	$0.111974\pi$
$709$	6.45621	+	28.2865i	0.242468	+	1.06232i	−0.696294	+	0.717757i	$0.745169\pi$
$710$	5.97300	+	8.74540i	0.224163	+	0.328209i
$711$	1.20934	−	2.51122i	0.0453539	−	0.0941782i
$712$	1.69518	−	0.386913i	0.0635294	−	0.0145002i
$713$	−2.65897			−0.0995791
$714$	−1.81864	+	0.415093i	−0.0680610	+	0.0155345i
$715$	23.9154	−	9.40867i	0.894384	−	0.351864i
$716$	2.97428	−	13.0312i	0.111154	−	0.486998i
$717$	5.42404	−	23.7643i	0.202565	−	0.887493i
$718$	−4.95683	+	3.95294i	−0.184987	+	0.147522i
$719$	8.82786	+	4.25127i	0.329224	+	0.158546i	0.591192	−	0.806531i	$-0.298657\pi$
$719$	8.82786	+	4.25127i	0.329224	+	0.158546i	−0.261969	+	0.965076i	$0.584372\pi$
$720$	−0.629594	−	0.0466637i	−0.0234636	−	0.00173905i
$721$	3.57691	−	4.48531i	0.133211	−	0.167042i
$722$	−4.56397	−	5.72304i	−0.169853	−	0.212989i
$723$	−13.5595	+	6.52990i	−0.504283	+	0.242850i
$724$	−4.78634			−0.177883
$725$	−0.670043	−	26.9175i	−0.0248848	−	0.999690i
$726$	8.76098			0.325150
$727$	−28.1247	+	13.5441i	−1.04309	+	0.502324i	−0.875341	−	0.483506i	$-0.839363\pi$
$727$	−28.1247	+	13.5441i	−1.04309	+	0.502324i	−0.167746	+	0.985830i	$0.553649\pi$
$728$	−0.723590	−	0.907353i	−0.0268180	−	0.0336287i
$729$	18.1063	−	22.7046i	0.670603	−	0.840910i
$730$	−12.1451	−	0.900159i	−0.449510	−	0.0333164i
$731$	−16.7527	−	8.06767i	−0.619620	−	0.298393i
$732$	17.3385	−	13.8270i	0.640850	−	0.511061i
$733$	4.95352	−	21.7028i	0.182962	−	0.801611i	−0.797248	−	0.603652i	$-0.793712\pi$
$733$	4.95352	−	21.7028i	0.182962	−	0.801611i	0.980210	−	0.197959i	$-0.0634312\pi$
$734$	7.30307	−	31.9969i	0.269561	−	1.18103i
$735$	−23.4416	+	9.22228i	−0.864656	+	0.340169i
$736$	4.76910	−	1.08852i	0.175791	−	0.0401232i
$737$	9.73141			0.358461
$738$	0.260215	−	0.0593923i	0.00957864	−	0.00218626i
$739$	−10.6179	+	22.0482i	−0.390585	+	0.811057i	0.609252	+	0.792977i	$0.291470\pi$
$739$	−10.6179	+	22.0482i	−0.390585	+	0.811057i	−0.999837	+	0.0180805i	$0.994244\pi$
$740$	4.77683	+	6.99402i	0.175600	+	0.257105i
$741$	3.56734	+	15.6295i	0.131050	+	0.574165i
$742$	1.18395			0.0434643
$743$	−5.30040	−	23.2226i	−0.194453	−	0.851954i	−0.974169	−	0.225821i	$-0.927494\pi$
$743$	−5.30040	−	23.2226i	−0.194453	−	0.851954i	0.779716	−	0.626133i	$-0.215363\pi$
$744$	0.700584	+	0.558697i	0.0256847	+	0.0204828i
$745$	15.4448	−	16.6729i	0.565853	−	0.610846i
$746$	12.2854	+	2.80406i	0.449800	+	0.102664i
$747$	0.917482	−	0.731668i	0.0335689	−	0.0267703i
$748$	−4.86214	+	10.0963i	−0.177778	+	0.369159i
$749$	−5.04712	+	2.43056i	−0.184418	+	0.0888109i
$750$	14.4382	+	11.4563i	0.527209	+	0.418323i
$751$	−9.46367	+	7.54703i	−0.345334	+	0.275395i	−0.780762	−	0.624829i	$-0.785169\pi$
$751$	−9.46367	+	7.54703i	−0.345334	+	0.275395i	0.435427	+	0.900224i	$0.356597\pi$
$752$	−2.09072	+	1.00684i	−0.0762407	+	0.0367156i
$753$			2.53438i			0.0923580i
$754$	11.4721	+	10.1586i	0.417789	+	0.369953i
$755$	27.0372	+	15.5805i	0.983986	+	0.567032i
$756$	0.957552	+	1.98838i	0.0348258	+	0.0723166i
$757$	21.0841	+	26.4386i	0.766315	+	0.960929i	0.999935	−	0.0113990i	$-0.00362850\pi$
$757$	21.0841	+	26.4386i	0.766315	+	0.960929i	−0.233620	+	0.972328i	$0.575057\pi$
$758$	−17.4224	−	13.8939i	−0.632811	−	0.504650i
$759$	29.3465	−	14.1326i	1.06521	−	0.512979i
$760$	−6.31057	+	4.31004i	−0.228909	+	0.156342i
$761$	7.04630	+	8.83578i	0.255428	+	0.320297i	0.892968	−	0.450121i	$-0.148619\pi$
$761$	7.04630	+	8.83578i	0.255428	+	0.320297i	−0.637539	+	0.770418i	$0.720048\pi$
$762$	−3.03592	+	13.3012i	−0.109980	+	0.481853i
$763$	−8.15757	−	1.86191i	−0.295324	−	0.0674057i
$764$	15.7964	+	12.5972i	0.571494	+	0.455751i
$765$	0.514905	−	1.67414i	0.0186164	−	0.0605287i
$766$			13.0264i			0.470663i
$767$	19.9244	−	4.54762i	0.719429	−	0.164205i
$768$	−1.48528	−	0.715272i	−0.0535953	−	0.0258102i
$769$	−5.31009	+	11.0265i	−0.191487	+	0.397626i	−0.974503	−	0.224375i	$-0.927966\pi$
$769$	−5.31009	+	11.0265i	−0.191487	+	0.397626i	0.783016	+	0.622001i	$0.213680\pi$
$770$	1.08290	−	3.52089i	0.0390249	−	0.126884i
$771$		−	45.3860i		−	1.63454i
$772$	−3.21584	−	14.0895i	−0.115741	−	0.507093i
$773$	−17.2170	+	21.5895i	−0.619254	+	0.776520i	−0.988239	−	0.152915i	$-0.951134\pi$
$773$	−17.2170	+	21.5895i	−0.619254	+	0.776520i	0.368985	+	0.929435i	$0.379705\pi$
$774$	−0.421058	+	1.84478i	−0.0151346	+	0.0663091i
$775$	0.805337	+	2.59575i	0.0289285	+	0.0932422i
$776$	9.95427	+	12.4823i	0.357337	+	0.448087i
$777$	1.10499	−	2.29453i	0.0396413	−	0.0823159i
$778$	5.40898	+	11.2319i	0.193921	+	0.402682i
$779$	2.01439	−	2.52597i	0.0721731	−	0.0905022i
$780$	−10.3707	+	1.57180i	−0.371329	+	0.0562795i
$781$	−8.30024	−	17.2356i	−0.297006	−	0.616739i
$782$			13.5716i			0.485321i
$783$	−16.9701	−	23.6879i	−0.606462	−	0.846537i
$784$	6.83365			0.244059
$785$	47.9520	+	3.55406i	1.71148	+	0.126850i
$786$	25.7465	−	20.5322i	0.918349	−	0.732359i
$787$	37.0968	+	29.5837i	1.32236	+	1.05455i	0.993930	+	0.110018i	$0.0350910\pi$
$787$	37.0968	+	29.5837i	1.32236	+	1.05455i	0.328430	+	0.944528i	$0.393480\pi$
$788$	0.932101	+	1.93553i	0.0332047	+	0.0689504i
$789$	−13.2099	−	6.36155i	−0.470285	−	0.226477i
$790$	21.8255	−	3.30792i	0.776515	−	0.117690i
$791$	5.69948	+	1.30087i	0.202650	+	0.0462536i
$792$	1.11179	+	0.253759i	0.0395058	+	0.00901694i
$793$	−23.8663	+	29.9274i	−0.847517	+	1.06275i
$794$	11.4895	−	2.62241i	0.407748	−	0.0930659i
$795$	5.34274	−	9.27140i	0.189487	−	0.328823i
$796$	4.87791	+	21.3715i	0.172893	+	0.757493i
$797$	33.2783	+	16.0260i	1.17878	+	0.567669i	0.917555	−	0.397609i	$-0.130160\pi$
$797$	33.2783	+	16.0260i	1.17878	+	0.567669i	0.261223	+	0.965279i	$0.415874\pi$
$798$	2.07032	+	0.997011i	0.0732884	+	0.0352938i
$799$	−1.43260	−	6.27664i	−0.0506818	−	0.222052i
$800$	−2.50708	−	4.32603i	−0.0886387	−	0.152948i
$801$	0.478609	−	0.109239i	0.0169108	−	0.00385978i
$802$	−6.49828	+	8.14858i	−0.229462	+	0.287737i
$803$	21.4468	+	4.89510i	0.756843	+	0.172744i
$804$	−3.87223	−	0.883810i	−0.136563	−	0.0311696i
$805$	−0.668523	−	4.41088i	−0.0235623	−	0.155463i
$806$	−1.39352	−	0.671085i	−0.0490848	−	0.0236380i
$807$	8.92102	+	18.5247i	0.314035	+	0.652100i
$808$	−10.7105	−	8.54133i	−0.376794	−	0.300483i
$809$	1.81605	−	1.44825i	0.0638489	−	0.0509178i	−0.591045	−	0.806638i	$-0.701285\pi$
$809$	1.81605	−	1.44825i	0.0638489	−	0.0509178i	0.654894	+	0.755721i	$0.272713\pi$
$810$	18.0030	+	1.33433i	0.632562	+	0.0468837i
$811$	1.62511			0.0570652			0.0285326	−	0.999593i	$-0.490917\pi$
$811$	1.62511			0.0570652			0.0285326	+	0.999593i	$0.490917\pi$
$812$	2.16365	−	0.377759i	0.0759292	−	0.0132567i
$813$			19.7828i			0.693813i
$814$	−6.63801	−	13.7840i	−0.232662	−	0.483128i
$815$	5.50828	+	36.3433i	0.192947	+	1.27305i
$816$	2.85165	−	3.57585i	0.0998277	−	0.125180i
$817$	9.93802	+	20.6365i	0.347687	+	0.721980i
$818$	−4.41452	+	9.16685i	−0.154350	+	0.320511i
$819$	−0.204295	−	0.256178i	−0.00713865	−	0.00895158i
$820$	1.55075	+	1.43653i	0.0541547	+	0.0501659i
$821$	−6.76536	+	29.6410i	−0.236113	+	1.03448i	0.708351	+	0.705861i	$0.249440\pi$
$821$	−6.76536	+	29.6410i	−0.236113	+	1.03448i	−0.944463	+	0.328617i	$0.893418\pi$
$822$	14.0495	−	17.6175i	0.490032	−	0.614481i
$823$	−4.55300	−	19.9480i	−0.158708	−	0.695344i	−0.990182	−	0.139781i	$-0.955360\pi$
$823$	−4.55300	−	19.9480i	−0.158708	−	0.695344i	0.831475	−	0.555563i	$-0.187497\pi$
$824$			14.0660i			0.490013i
$825$	−22.6849	−	24.3685i	−0.789788	−	0.848401i
$826$	1.27098	−	2.63922i	0.0442231	−	0.0918303i
$827$	38.3176	+	18.4528i	1.33243	+	0.641666i	0.958315	−	0.285714i	$-0.0922309\pi$
$827$	38.3176	+	18.4528i	1.33243	+	0.641666i	0.374119	+	0.927381i	$0.377945\pi$
$828$	1.34649	−	0.307326i	0.0467936	−	0.0106803i
$829$		−	42.8026i		−	1.48660i	−0.668961	−	0.743298i	$-0.733261\pi$
$829$		−	42.8026i		−	1.48660i	0.668961	−	0.743298i	$-0.266739\pi$
$830$	8.88336	+	2.73220i	0.308346	+	0.0948360i
$831$	−16.5916	−	13.2314i	−0.575556	−	0.458991i
$832$	2.77413	+	0.633178i	0.0961758	+	0.0219515i
$833$	−4.21883	+	18.4839i	−0.146174	+	0.640430i
$834$	5.88311	+	7.37719i	0.203716	+	0.255451i
$835$	−19.7536	+	13.4915i	−0.683603	+	0.466892i
$836$	12.4370	−	5.98935i	0.430143	−	0.207146i
$837$	2.29955	+	1.83383i	0.0794842	+	0.0633865i
$838$	−9.69077	−	12.1518i	−0.334762	−	0.419778i
$839$	−12.5943	−	26.1523i	−0.434802	−	0.902876i	−0.997112	−	0.0759492i	$-0.975801\pi$
$839$	−12.5943	−	26.1523i	−0.434802	−	0.902876i	0.562309	−	0.826927i	$-0.309913\pi$
$840$	−0.750663	+	1.30265i	−0.0259003	+	0.0449456i
$841$	−27.2843	+	9.82686i	−0.940838	+	0.338857i
$842$		−	22.7300i		−	0.783329i
$843$	2.60303	−	1.25355i	0.0896532	−	0.0431747i
$844$	−8.34425	+	6.65431i	−0.287221	+	0.229051i
$845$	−10.2028	+	4.01396i	−0.350988	+	0.138084i
$846$	−0.590284	+	0.284266i	−0.0202944	+	0.00977326i
$847$	−0.940451	+	1.95287i	−0.0323143	+	0.0671013i
$848$	−2.26955	+	1.80991i	−0.0779367	+	0.0621524i
$849$	−6.57277	−	1.50019i	−0.225577	−	0.0514865i
$850$	13.2490	−	4.11052i	0.454437	−	0.140990i
$851$	−14.4862	−	11.5524i	−0.496582	−	0.396011i
$852$	1.73740	+	7.61206i	0.0595224	+	0.260785i
$853$	10.3975			0.356003			0.178002	−	0.984030i	$-0.443037\pi$
$853$	10.3975			0.356003			0.178002	+	0.984030i	$0.443037\pi$
$854$	1.22090	+	5.34911i	0.0417783	+	0.183043i
$855$	−1.78170	+	1.21688i	−0.0609328	+	0.0416163i
$856$	5.95935	−	12.3747i	0.203686	−	0.422959i
$857$	−56.1004	+	12.8045i	−1.91635	+	0.437395i	−0.917103	+	0.398649i	$0.869479\pi$
$857$	−56.1004	+	12.8045i	−1.91635	+	0.437395i	−0.999249	+	0.0387457i	$0.987664\pi$
$858$	18.9469			0.646837
$859$	−18.8407	+	4.30028i	−0.642838	+	0.146724i	−0.531499	−	0.847059i	$-0.678371\pi$
$859$	−18.8407	+	4.30028i	−0.642838	+	0.146724i	−0.111339	+	0.993782i	$0.535514\pi$
$860$	−13.9458	+	5.48647i	−0.475546	+	0.187087i
$861$	0.141440	−	0.619687i	0.00482025	−	0.0211189i
$862$	3.49412	−	15.3088i	0.119010	−	0.521418i
$863$	−21.8369	+	17.4144i	−0.743338	+	0.592792i	−0.920202	−	0.391443i	$-0.871976\pi$
$863$	−21.8369	+	17.4144i	−0.743338	+	0.592792i	0.176864	+	0.984235i	$0.443405\pi$
$864$	−4.87518	−	2.34776i	−0.165857	−	0.0798725i
$865$	−0.258994	+	3.49439i	−0.00880606	+	0.118813i
$866$	7.97963	−	10.0061i	0.271159	−	0.340023i
$867$	−9.56174	−	11.9900i	−0.324734	−	0.407203i
$868$	−0.199741	+	0.0961902i	−0.00677965	+	0.00326491i
$869$	−39.8745			−1.35265
$870$	6.80555	−	18.6479i	0.230730	−	0.632225i
$871$	6.85560			0.232293
$872$	18.4837	−	8.90130i	0.625939	−	0.301436i
$873$	2.81044	+	3.52418i	0.0951191	+	0.119276i
$874$	10.4235	−	13.0707i	0.352580	−	0.442122i
$875$	−4.10353	+	1.98858i	−0.138725	+	0.0672262i
$876$	−8.08934	−	3.89562i	−0.273313	−	0.131621i
$877$	−13.0006	+	10.3677i	−0.439000	+	0.350091i	−0.817914	−	0.575341i	$-0.804869\pi$
$877$	−13.0006	+	10.3677i	−0.439000	+	0.350091i	0.378913	+	0.925432i	$0.376298\pi$
$878$	6.70172	−	29.3622i	0.226172	−	0.990925i
$879$	3.34081	−	14.6371i	0.112683	−	0.493695i
$880$	3.30653	+	8.40469i	0.111463	+	0.283322i
$881$	36.9973	−	8.44440i	1.24647	−	0.284499i	0.452120	−	0.891957i	$-0.350668\pi$
$881$	36.9973	−	8.44440i	1.24647	−	0.284499i	0.794352	+	0.607458i	$0.207811\pi$
$882$	1.92938			0.0649657
$883$	33.9670	−	7.75274i	1.14308	−	0.260901i	0.391267	−	0.920277i	$-0.372037\pi$
$883$	33.9670	−	7.75274i	1.14308	−	0.260901i	0.751813	+	0.659376i	$0.229180\pi$
$884$	−3.42529	+	7.11269i	−0.115205	+	0.239226i
$885$	−14.9320	−	21.8627i	−0.501932	−	0.734907i
$886$	−1.67459	−	7.33688i	−0.0562591	−	0.246487i
$887$	−21.6603			−0.727282			−0.363641	−	0.931539i	$-0.618466\pi$
$887$	−21.6603			−0.727282			−0.363641	+	0.931539i	$0.618466\pi$
$888$	1.38946	+	6.08764i	0.0466274	+	0.204288i
$889$	−2.63902	−	2.10455i	−0.0885099	−	0.0705843i
$890$	2.85228	+	2.64219i	0.0956085	+	0.0885663i
$891$	−31.7913	−	7.25615i	−1.06505	−	0.243090i
$892$	15.6261	−	12.4614i	0.523201	−	0.417239i
$893$	−3.44096	+	7.14523i	−0.115147	+	0.239106i
$894$	15.0962	−	7.26996i	0.504894	−	0.243144i
$895$	27.8130	−	10.9420i	0.929684	−	0.365752i
$896$	0.318876	−	0.254295i	0.0106529	−	0.00849539i
$897$	20.6741	−	9.95612i	0.690288	−	0.332425i
$898$			19.6595i			0.656046i
$899$	2.37955	−	1.70472i	0.0793625	−	0.0568556i
$900$	−0.707838	−	1.22139i	−0.0235946	−	0.0407131i
$901$	−3.49437	−	7.25613i	−0.116414	−	0.241737i
$902$	−2.38072	−	2.98533i	−0.0792694	−	0.0994007i
$903$	3.52310	+	2.80958i	0.117241	+	0.0934969i
$904$	−12.9141	+	6.21910i	−0.429517	+	0.206844i
$905$	−6.03621	−	8.83795i	−0.200650	−	0.293783i
$906$	14.3440	+	17.9868i	0.476546	+	0.597570i
$907$	−7.47104	+	32.7328i	−0.248072	+	1.08687i	0.685384	+	0.728181i	$0.259634\pi$
$907$	−7.47104	+	32.7328i	−0.248072	+	1.08687i	−0.933456	+	0.358692i	$0.883223\pi$
$908$	−10.9411	−	2.49723i	−0.363092	−	0.0828734i
$909$	−3.02395	−	2.41152i	−0.100298	−	0.0799851i
$910$	0.762880	−	2.48040i	0.0252892	−	0.0822244i
$911$			20.7779i			0.688401i	0.938896	+	0.344200i	$0.111850\pi$
$911$			20.7779i			0.688401i	−0.938896	+	0.344200i	$0.888150\pi$
$912$	−5.49277	+	1.25369i	−0.181884	+	0.0415138i
$913$	−15.1257	−	7.28414i	−0.500586	−	0.241070i
$914$	−5.20566	+	10.8097i	−0.172188	+	0.357552i
$915$	47.3976	+	14.5778i	1.56692	+	0.481927i
$916$			17.9408i			0.592782i
$917$	1.81295	+	7.94307i	0.0598690	+	0.262303i
$918$	9.36007	−	11.7372i	0.308928	−	0.387384i
$919$	−4.93327	+	21.6141i	−0.162733	+	0.712982i	0.826046	+	0.563602i	$0.190585\pi$
$919$	−4.93327	+	21.6141i	−0.162733	+	0.712982i	−0.988780	+	0.149380i	$0.952272\pi$
$920$	8.02440	+	7.43335i	0.264557	+	0.245070i
$921$	−25.3886	−	31.8363i	−0.836583	−	1.04904i
$922$	0.643778	−	1.33682i	0.0212017	−	0.0440258i
$923$	−5.84736	−	12.1422i	−0.192468	−	0.399665i
$924$	1.69325	−	2.12327i	0.0557038	−	0.0698504i
$925$	−6.89021	+	17.6408i	−0.226549	+	0.580025i
$926$	−13.5337	−	28.1030i	−0.444745	−	0.923522i
$927$			3.97133i			0.130436i
$928$	−3.57007	+	4.03170i	−0.117193	+	0.132347i
$929$	−1.92934			−0.0632996			−0.0316498	−	0.999499i	$-0.510076\pi$
$929$	−1.92934			−0.0632996			−0.0316498	+	0.999499i	$0.510076\pi$
$930$	−0.148102	+	1.99822i	−0.00485646	+	0.0655241i
$931$	18.2594	−	14.5614i	0.598428	−	0.477230i
$932$	−4.00770	−	3.19604i	−0.131277	−	0.104690i
$933$	−3.81174	−	7.91515i	−0.124791	−	0.259130i
$934$	−15.8471	−	7.63157i	−0.518534	−	0.249713i
$935$	−24.7747	+	3.75491i	−0.810218	+	0.122799i
$936$	0.783237	+	0.178769i	0.0256009	+	0.00584324i
$937$	−16.6072	−	3.79048i	−0.542533	−	0.123830i	−0.0575330	−	0.998344i	$-0.518323\pi$
$937$	−16.6072	−	3.79048i	−0.542533	−	0.123830i	−0.485000	+	0.874514i	$0.661181\pi$
$938$	0.612671	−	0.768266i	0.0200044	−	0.0250848i
$939$	−40.8231	+	9.31761i	−1.33221	+	0.304069i
$940$	−4.49580	−	2.59075i	−0.146637	−	0.0845009i
$941$	6.12224	+	26.8233i	0.199579	+	0.874415i	0.971188	+	0.238316i	$0.0765955\pi$
$941$	6.12224	+	26.8233i	0.199579	+	0.874415i	−0.771608	+	0.636098i	$0.780547\pi$
$942$	31.9388	+	15.3809i	1.04062	+	0.501138i
$943$	−4.16646	−	2.00646i	−0.135679	−	0.0653394i
$944$	1.59819	+	7.00214i	0.0520167	+	0.227900i
$945$	−2.46393	+	4.27572i	−0.0801516	+	0.139089i
$946$	26.3915	−	6.02369i	0.858062	−	0.195847i
$947$	−6.54463	+	8.20671i	−0.212672	+	0.266682i	−0.876713	−	0.481014i	$-0.840269\pi$
$947$	−6.54463	+	8.20671i	−0.212672	+	0.266682i	0.664041	+	0.747696i	$0.268840\pi$
$948$	15.8665	+	3.62142i	0.515319	+	0.117618i
$949$	15.1089	+	3.44851i	0.490456	+	0.111943i
$950$	−15.9169	−	6.21691i	−0.516414	−	0.201703i
$951$	24.0064	+	11.5609i	0.778460	+	0.374887i
$952$	0.490965	+	1.01950i	0.0159123	+	0.0330421i
$953$	43.0450	+	34.3272i	1.39436	+	1.11197i	0.979354	+	0.202151i	$0.0647931\pi$
$953$	43.0450	+	34.3272i	1.39436	+	1.11197i	0.415009	+	0.909817i	$0.363778\pi$
$954$	−0.640775	+	0.511001i	−0.0207458	+	0.0165443i
$955$	−3.33933	+	45.0548i	−0.108058	+	1.45794i
$956$	−14.7861			−0.478217
$957$	−17.2020	+	31.4621i	−0.556063	+	1.01703i
$958$		−	28.4282i		−	0.918475i
$959$	2.41888	+	5.02286i	0.0781098	+	0.162197i
$960$	−0.552386	−	3.64461i	−0.0178282	−	0.117629i
$961$	19.1440	−	24.0058i	0.617547	−	0.774380i
$962$	−4.67635	−	9.71054i	−0.150772	−	0.313080i
$963$	1.68254	−	3.49382i	0.0542190	−	0.112587i
$964$	5.69200	+	7.13754i	0.183327	+	0.229885i
$965$	21.9606	−	23.7068i	0.706938	−	0.763149i
$966$	0.731881	−	3.20658i	0.0235479	−	0.103170i
$967$	28.4200	−	35.6375i	0.913925	−	1.14603i	−0.0749365	−	0.997188i	$-0.523875\pi$
$967$	28.4200	−	35.6375i	0.913925	−	1.14603i	0.988862	−	0.148838i	$-0.0475532\pi$
$968$	−1.18257	−	5.18116i	−0.0380091	−	0.166529i
$969$		−	15.6310i		−	0.502141i
$970$	−10.4948	+	34.1223i	−0.336967	+	1.09560i
$971$	11.4390	−	23.7534i	0.367096	−	0.762282i	−0.632832	−	0.774289i	$-0.718108\pi$
$971$	11.4390	−	23.7534i	0.367096	−	0.762282i	0.999928	+	0.0120070i	$0.00382203\pi$
$972$	−2.63448	−	1.26870i	−0.0845009	−	0.0406935i
$973$	−2.27594	+	0.519468i	−0.0729632	+	0.0166534i
$974$		−	38.1305i		−	1.22178i
$975$	−15.9811	−	17.1671i	−0.511805	−	0.549788i
$976$	−10.5175	−	8.38745i	−0.336658	−	0.268476i
$977$	−31.4021	−	7.16733i	−1.00464	−	0.229303i	−0.311611	−	0.950210i	$-0.600868\pi$
$977$	−31.4021	−	7.16733i	−1.00464	−	0.229303i	−0.693032	+	0.720907i	$0.743726\pi$
$978$	−6.03032	+	26.4206i	−0.192828	+	0.844836i
$979$	−4.37882	−	5.49087i	−0.139948	−	0.175489i
$980$	8.61814	+	12.6183i	0.275296	+	0.403077i
$981$	5.21862	−	2.51315i	0.166618	−	0.0802388i
$982$	−16.5779	−	13.2204i	−0.529020	−	0.421880i
$983$	14.3461	+	17.9895i	0.457570	+	0.573775i	0.956079	−	0.293110i	$-0.0946901\pi$
$983$	14.3461	+	17.9895i	0.457570	+	0.573775i	−0.498508	+	0.866885i	$0.666119\pi$
$984$	0.676185	+	1.40411i	0.0215560	+	0.0447615i
$985$	−2.39844	+	4.16208i	−0.0764207	+	0.132615i
$986$	−8.70106	−	12.1455i	−0.277098	−	0.386791i
$987$			1.56024i			0.0496630i
$988$	8.76164	−	4.21938i	0.278745	−	0.134237i
$989$	25.6320	−	20.4408i	0.815051	−	0.649981i
$990$	0.933552	+	2.37294i	0.0296702	+	0.0754171i
$991$	38.5132	−	18.5470i	1.22341	−	0.589165i	0.293153	−	0.956066i	$-0.405295\pi$
$991$	38.5132	−	18.5470i	1.22341	−	0.589165i	0.930260	+	0.366901i	$0.119581\pi$
$992$	0.235843	−	0.489733i	0.00748802	−	0.0155490i
$993$	34.5313	−	27.5378i	1.09582	−	0.873886i
$994$	−1.88327	−	0.429844i	−0.0597337	−	0.0136338i
$995$	−33.3107	+	35.9593i	−1.05602	+	1.13999i
$996$	5.35710	+	4.27215i	0.169746	+	0.135368i
$997$	1.49534	+	6.55153i	0.0473580	+	0.207489i	0.993071	−	0.117513i	$-0.0374922\pi$
$997$	1.49534	+	6.55153i	0.0473580	+	0.207489i	−0.945713	+	0.325002i	$0.894635\pi$
$998$	31.4549			0.995688
$999$	4.56069	+	19.9817i	0.144294	+	0.632192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	290.2.l.b.9.6	yes	48
5.4	even	2		290.2.l.a.9.3	✓	48
29.13	even	14		290.2.l.a.129.3	yes	48
145.129	even	14	inner	290.2.l.b.129.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.l.a.9.3	✓	48	5.4	even	2
290.2.l.a.129.3	yes	48	29.13	even	14
290.2.l.b.9.6	yes	48	1.1	even	1	trivial
290.2.l.b.129.6	yes	48	145.129	even	14	inner

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:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.l (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(1.02784 + 1.28888i) q^{3} +(0.623490 - 0.781831i) q^{4} +(2.22995 + 0.165278i) q^{5} +(1.48528 + 0.715272i) q^{6} +(-0.318876 + 0.254295i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.0628256 - 0.275257i) q^{9} +(2.08083 - 0.818630i) q^{10} +(-3.93784 + 0.898786i) q^{11} +1.64853 q^{12} +(-2.77413 + 0.633178i) q^{13} +(-0.176963 + 0.367467i) q^{14} +(2.07902 + 3.04401i) q^{15} +(-0.222521 - 0.974928i) q^{16} +2.77440 q^{17} +(-0.0628256 - 0.275257i) q^{18} +(-2.67198 - 2.13084i) q^{19} +(1.51957 - 1.64040i) q^{20} +(-0.655509 - 0.149616i) q^{21} +(-3.15790 + 2.51834i) q^{22} +(-2.12245 + 4.40731i) q^{23} +(1.48528 - 0.715272i) q^{24} +(4.94537 + 0.737122i) q^{25} +(-2.22468 + 1.77413i) q^{26} +(4.87518 - 2.34776i) q^{27} +0.407857i q^{28} +(-0.926203 - 5.30492i) q^{29} +(3.19388 + 1.84051i) q^{30} +(0.235843 + 0.489733i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(-5.20591 - 4.15158i) q^{33} +(2.49965 - 1.20377i) q^{34} +(-0.753106 + 0.514362i) q^{35} +(-0.176033 - 0.220739i) q^{36} +(-0.842848 + 3.69276i) q^{37} +(-3.33191 - 0.760487i) q^{38} +(-3.66747 - 2.92471i) q^{39} +(0.657345 - 2.13726i) q^{40} +0.945353i q^{41} +(-0.655509 + 0.149616i) q^{42} +(-6.03831 - 2.90790i) q^{43} +(-1.75250 + 3.63911i) q^{44} +(0.185592 - 0.603426i) q^{45} +4.89174i q^{46} +(-0.516365 - 2.26234i) q^{47} +(1.02784 - 1.28888i) q^{48} +(-1.52063 + 6.66232i) q^{49} +(4.77545 - 1.48159i) q^{50} +(2.85165 + 3.57585i) q^{51} +(-1.23461 + 2.56369i) q^{52} +(-1.25951 - 2.61539i) q^{53} +(3.37373 - 4.23052i) q^{54} +(-8.92974 + 1.35341i) q^{55} +(0.176963 + 0.367467i) q^{56} -5.63402i q^{57} +(-3.13620 - 4.37770i) q^{58} -7.18221 q^{59} +(3.67615 + 0.272466i) q^{60} +(10.5175 - 8.38745i) q^{61} +(0.424974 + 0.338906i) q^{62} +(0.0499628 + 0.103749i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-6.29084 + 0.953454i) q^{65} +(-6.49166 - 1.48168i) q^{66} +(-2.34889 - 0.536119i) q^{67} +(1.72981 - 2.16911i) q^{68} +(-7.86202 + 1.79445i) q^{69} +(-0.455352 + 0.790185i) q^{70} +(1.05391 + 4.61747i) q^{71} +(-0.254375 - 0.122501i) q^{72} +(-4.90699 - 2.36308i) q^{73} +(0.842848 + 3.69276i) q^{74} +(4.13301 + 7.13161i) q^{75} +(-3.33191 + 0.760487i) q^{76} +(1.02712 - 1.28797i) q^{77} +(-4.57326 - 1.04382i) q^{78} +(9.62460 + 2.19675i) q^{79} +(-0.335077 - 2.21082i) q^{80} +(7.27377 + 3.50287i) q^{81} +(0.410173 + 0.851734i) q^{82} +(3.24962 + 2.59148i) q^{83} +(-0.525677 + 0.419214i) q^{84} +(6.18677 + 0.458546i) q^{85} -6.70202 q^{86} +(5.88539 - 6.64639i) q^{87} +4.03911i q^{88} +(0.754425 + 1.56658i) q^{89} +(-0.0946042 - 0.624193i) q^{90} +(0.723590 - 0.907353i) q^{91} +(2.12245 + 4.40731i) q^{92} +(-0.388795 + 0.807341i) q^{93} +(-1.44682 - 1.81426i) q^{94} +(-5.60621 - 5.19328i) q^{95} +(0.366833 - 1.60720i) q^{96} +(-9.95427 + 12.4823i) q^{97} +(1.52063 + 6.66232i) q^{98} +1.14038i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 4 q^{3} - 8 q^{4} + 8 q^{5} - 3 q^{6} + 7 q^{7} + 8 q^{8} - 8 q^{9} - q^{10} + 10 q^{12} - 10 q^{15} - 8 q^{16} - 30 q^{17} + 8 q^{18} - 13 q^{20} + 7 q^{21} + 7 q^{23} - 3 q^{24} - 12 q^{25}+ \cdots - 27 q^{98}+O(q^{100}) \) 48 * q + 8 * q^2 - 4 * q^3 - 8 * q^4 + 8 * q^5 - 3 * q^6 + 7 * q^7 + 8 * q^8 - 8 * q^9 - q^10 + 10 * q^12 - 10 * q^15 - 8 * q^16 - 30 * q^17 + 8 * q^18 - 13 * q^20 + 7 * q^21 + 7 * q^23 - 3 * q^24 - 12 * q^25 + 21 * q^26 + 11 * q^27 - 10 * q^29 - 18 * q^30 + 14 * q^31 + 8 * q^32 - 14 * q^33 - 33 * q^34 - q^36 - 44 * q^37 - 28 * q^38 - 14 * q^39 - 8 * q^40 + 7 * q^42 - 8 * q^43 + 14 * q^44 + 25 * q^45 - 6 * q^47 - 4 * q^48 + 27 * q^49 + 5 * q^50 + 24 * q^51 + 77 * q^53 + 10 * q^54 - 32 * q^55 + 10 * q^58 - 24 * q^59 + 4 * q^60 + 56 * q^61 - 8 * q^64 - 34 * q^65 + 42 * q^67 - 2 * q^68 + 28 * q^69 - 30 * q^71 + 22 * q^72 - 29 * q^73 + 44 * q^74 - 32 * q^75 - 28 * q^76 - 30 * q^77 + 14 * q^78 + q^80 - 130 * q^81 - 42 * q^82 - 42 * q^84 + 28 * q^85 - 62 * q^86 + 32 * q^87 + 31 * q^90 - 106 * q^91 - 7 * q^92 - 70 * q^93 + 27 * q^94 + 165 * q^95 + 4 * q^96 - 49 * q^97 - 27 * q^98

Introduction

L-functions

Modular forms

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Database

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