LMFDB - Embedded newform 756.2.cf.a.659.90

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			659.90
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.90

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24593 - 0.669070i) q^{2} +(-0.661489 - 1.60076i) q^{3} +(1.10469 - 1.66723i) q^{4} +(0.851997 - 2.34084i) q^{5} +(-1.89519 - 1.55185i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(0.260874 - 2.81637i) q^{8} +(-2.12486 + 2.11777i) q^{9} +(-0.504658 - 3.48658i) q^{10} +(-3.41175 + 1.24178i) q^{11} +(-3.39958 - 0.665489i) q^{12} +(2.31789 - 1.94494i) q^{13} +(-1.34319 + 0.442552i) q^{14} +(-4.31071 + 0.184599i) q^{15} +(-1.55932 - 3.68355i) q^{16} +(0.475550 - 0.274559i) q^{17} +(-1.23050 + 4.06028i) q^{18} +(0.487855 + 0.281663i) q^{19} +(-2.96153 - 4.00638i) q^{20} +(0.373471 + 1.69131i) q^{21} +(-3.41997 + 3.82987i) q^{22} +(1.02467 + 5.81118i) q^{23} +(-4.68090 + 1.44540i) q^{24} +(-0.923424 - 0.774844i) q^{25} +(1.58663 - 3.97410i) q^{26} +(4.79562 + 2.00052i) q^{27} +(-1.37742 + 1.45007i) q^{28} +(3.67017 - 4.37394i) q^{29} +(-5.24734 + 3.11417i) q^{30} +(3.01476 - 0.531583i) q^{31} +(-4.40736 - 3.54616i) q^{32} +(4.24462 + 4.63997i) q^{33} +(0.408804 - 0.660258i) q^{34} +(-1.24554 + 2.15733i) q^{35} +(1.18349 + 5.88212i) q^{36} +(-4.41674 - 7.65002i) q^{37} +(0.796286 + 0.0245239i) q^{38} +(-4.64665 - 2.42383i) q^{39} +(-6.37042 - 3.01021i) q^{40} +(4.71378 + 5.61766i) q^{41} +(1.59692 + 1.85737i) q^{42} +(-2.62482 - 7.21164i) q^{43} +(-1.69860 + 7.05995i) q^{44} +(3.14699 + 6.77831i) q^{45} +(5.16475 + 6.55476i) q^{46} +(-0.510683 + 2.89623i) q^{47} +(-4.86500 + 4.93272i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-1.66895 - 0.347568i) q^{50} +(-0.754074 - 0.579624i) q^{51} +(-0.682116 - 6.01303i) q^{52} +1.58954i q^{53} +(7.31349 - 0.716098i) q^{54} +9.04436i q^{55} +(-0.745969 + 2.72828i) q^{56} +(0.128164 - 0.967255i) q^{57} +(1.64631 - 7.90522i) q^{58} +(-3.89118 - 1.41627i) q^{59} +(-4.45424 + 7.39088i) q^{60} +(0.864022 - 4.90011i) q^{61} +(3.40052 - 2.67940i) q^{62} +(2.46033 - 1.71662i) q^{63} +(-7.86389 - 1.46944i) q^{64} +(-2.57797 - 7.08291i) q^{65} +(8.39297 + 2.94114i) q^{66} +(3.55255 + 4.23376i) q^{67} +(0.0675824 - 1.09615i) q^{68} +(8.62450 - 5.48428i) q^{69} +(-0.108447 + 3.52124i) q^{70} +(-4.92271 - 8.52639i) q^{71} +(5.41010 + 6.53688i) q^{72} +(-5.59592 + 9.69242i) q^{73} +(-10.6214 - 6.57629i) q^{74} +(-0.629505 + 1.99073i) q^{75} +(1.00853 - 0.502216i) q^{76} +(3.57555 - 0.630466i) q^{77} +(-7.41112 + 0.0890052i) q^{78} +(8.52755 - 10.1627i) q^{79} +(-9.95114 + 0.511746i) q^{80} +(0.0300975 - 8.99995i) q^{81} +(9.63166 + 3.84538i) q^{82} +(0.419295 + 0.351830i) q^{83} +(3.23237 + 1.24571i) q^{84} +(-0.237532 - 1.34711i) q^{85} +(-8.09544 - 7.22902i) q^{86} +(-9.42940 - 2.98175i) q^{87} +(2.60726 + 9.93270i) q^{88} +(2.19413 + 1.26678i) q^{89} +(8.45610 + 6.33975i) q^{90} +(-2.62042 + 1.51290i) q^{91} +(10.8205 + 4.71120i) q^{92} +(-2.84517 - 4.47427i) q^{93} +(1.30150 + 3.95018i) q^{94} +(1.07498 - 0.902015i) q^{95} +(-2.76113 + 9.40086i) q^{96} +(17.3745 - 6.32379i) q^{97} +(1.39963 - 0.202587i) q^{98} +(4.61971 - 9.86391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.24593	−	0.669070i	0.881007	−	0.473104i
$2$	1.24593	−	0.669070i	0.881007	−	0.473104i
$3$	−0.661489	−	1.60076i	−0.381911	−	0.924199i
$3$	−0.661489	−	1.60076i	−0.381911	−	0.924199i
$4$	1.10469	−	1.66723i	0.552345	−	0.833615i
$5$	0.851997	−	2.34084i	0.381025	−	1.04686i	−0.589901	−	0.807476i	$-0.700833\pi$
$5$	0.851997	−	2.34084i	0.381025	−	1.04686i	0.970926	−	0.239381i	$-0.0769445\pi$
$6$	−1.89519	−	1.55185i	−0.773708	−	0.633542i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$8$	0.260874	−	2.81637i	0.0922330	−	0.995737i
$9$	−2.12486	+	2.11777i	−0.708288	+	0.705923i
$10$	−0.504658	−	3.48658i	−0.159587	−	1.10255i
$11$	−3.41175	+	1.24178i	−1.02868	+	0.374409i	−0.800579	−	0.599228i	$-0.795474\pi$
$11$	−3.41175	+	1.24178i	−1.02868	+	0.374409i	−0.228103	+	0.973637i	$0.573252\pi$
$12$	−3.39958	−	0.665489i	−0.981373	−	0.192110i
$13$	2.31789	−	1.94494i	0.642868	−	0.539431i	−0.262029	−	0.965060i	$-0.584392\pi$
$13$	2.31789	−	1.94494i	0.642868	−	0.539431i	0.904898	+	0.425629i	$0.139947\pi$
$14$	−1.34319	+	0.442552i	−0.358981	+	0.118277i
$15$	−4.31071	+	0.184599i	−1.11302	+	0.0476633i
$16$	−1.55932	−	3.68355i	−0.389829	−	0.920887i
$17$	0.475550	−	0.274559i	0.115338	−	0.0665903i	−0.441221	−	0.897398i	$-0.645455\pi$
$17$	0.475550	−	0.274559i	0.115338	−	0.0665903i	0.556559	+	0.830808i	$0.312121\pi$
$18$	−1.23050	+	4.06028i	−0.290031	+	0.957017i
$19$	0.487855	+	0.281663i	0.111922	+	0.0646179i	0.554916	−	0.831907i	$-0.312750\pi$
$19$	0.487855	+	0.281663i	0.111922	+	0.0646179i	−0.442994	+	0.896524i	$0.646084\pi$
$20$	−2.96153	−	4.00638i	−0.662219	−	0.895854i
$21$	0.373471	+	1.69131i	0.0814980	+	0.369073i
$22$	−3.41997	+	3.82987i	−0.729141	+	0.816531i
$23$	1.02467	+	5.81118i	0.213658	+	1.21171i	0.883220	+	0.468959i	$0.155371\pi$
$23$	1.02467	+	5.81118i	0.213658	+	1.21171i	−0.669562	+	0.742756i	$0.733518\pi$
$24$	−4.68090	+	1.44540i	−0.955484	+	0.295041i
$25$	−0.923424	−	0.774844i	−0.184685	−	0.154969i
$26$	1.58663	−	3.97410i	0.311164	−	0.779385i
$27$	4.79562	+	2.00052i	0.922917	+	0.384999i
$28$	−1.37742	+	1.45007i	−0.260308	+	0.274038i
$29$	3.67017	−	4.37394i	0.681533	−	0.812219i	−0.308771	−	0.951136i	$-0.599918\pi$
$29$	3.67017	−	4.37394i	0.681533	−	0.812219i	0.990304	+	0.138917i	$0.0443621\pi$
$30$	−5.24734	+	3.11417i	−0.958030	+	0.568567i
$31$	3.01476	−	0.531583i	0.541467	−	0.0954752i	0.103776	−	0.994601i	$-0.466908\pi$
$31$	3.01476	−	0.531583i	0.541467	−	0.0954752i	0.437691	+	0.899126i	$0.355796\pi$
$32$	−4.40736	−	3.54616i	−0.779118	−	0.626878i
$33$	4.24462	+	4.63997i	0.738894	+	0.807716i
$34$	0.408804	−	0.660258i	0.0701092	−	0.113233i
$35$	−1.24554	+	2.15733i	−0.210534	+	0.364656i
$36$	1.18349	+	5.88212i	0.197249	+	0.980353i
$37$	−4.41674	−	7.65002i	−0.726108	−	1.25766i	−0.958516	−	0.285037i	$-0.907994\pi$
$37$	−4.41674	−	7.65002i	−0.726108	−	1.25766i	0.232409	−	0.972618i	$-0.425339\pi$
$38$	0.796286	+	0.0245239i	0.129175	+	0.00397830i
$39$	−4.64665	−	2.42383i	−0.744060	−	0.388124i
$40$	−6.37042	−	3.01021i	−1.00725	−	0.475955i
$41$	4.71378	+	5.61766i	0.736169	+	0.877332i	0.996094	−	0.0882970i	$-0.0281425\pi$
$41$	4.71378	+	5.61766i	0.736169	+	0.877332i	−0.259926	+	0.965629i	$0.583698\pi$
$42$	1.59692	+	1.85737i	0.246410	+	0.286599i
$43$	−2.62482	−	7.21164i	−0.400282	−	1.09976i	−0.962146	−	0.272535i	$-0.912138\pi$
$43$	−2.62482	−	7.21164i	−0.400282	−	1.09976i	0.561864	−	0.827229i	$-0.310084\pi$
$44$	−1.69860	+	7.05995i	−0.256074	+	1.06433i
$45$	3.14699	+	6.77831i	0.469125	+	1.01045i
$46$	5.16475	+	6.55476i	0.761501	+	0.966446i
$47$	−0.510683	+	2.89623i	−0.0744908	+	0.422458i	0.924643	+	0.380836i	$0.124364\pi$
$47$	−0.510683	+	2.89623i	−0.0744908	+	0.422458i	−0.999133	+	0.0416223i	$0.986747\pi$
$48$	−4.86500	+	4.93272i	−0.702203	+	0.711977i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	−1.66895	−	0.347568i	−0.236025	−	0.0491535i
$51$	−0.754074	−	0.579624i	−0.105592	−	0.0811636i
$52$	−0.682116	−	6.01303i	−0.0945924	−	0.833857i
$53$			1.58954i			0.218340i	0.994023	+	0.109170i	$0.0348193\pi$
$53$			1.58954i			0.218340i	−0.994023	+	0.109170i	$0.965181\pi$
$54$	7.31349	−	0.716098i	0.995241	−	0.0974486i
$55$			9.04436i			1.21954i
$56$	−0.745969	+	2.72828i	−0.0996843	+	0.364582i
$57$	0.128164	−	0.967255i	0.0169758	−	0.128116i
$58$	1.64631	−	7.90522i	0.216171	−	1.03801i
$59$	−3.89118	−	1.41627i	−0.506589	−	0.184383i	0.0760664	−	0.997103i	$-0.475764\pi$
$59$	−3.89118	−	1.41627i	−0.506589	−	0.184383i	−0.582655	+	0.812720i	$0.697986\pi$
$60$	−4.45424	+	7.39088i	−0.575039	+	0.954159i
$61$	0.864022	−	4.90011i	0.110627	−	0.627395i	−0.878196	−	0.478301i	$-0.841253\pi$
$61$	0.864022	−	4.90011i	0.110627	−	0.627395i	0.988823	−	0.149095i	$-0.0476359\pi$
$62$	3.40052	−	2.67940i	0.431866	−	0.340284i
$63$	2.46033	−	1.71662i	0.309972	−	0.216274i
$64$	−7.86389	−	1.46944i	−0.982986	−	0.183680i
$65$	−2.57797	−	7.08291i	−0.319758	−	0.878527i
$66$	8.39297	+	2.94114i	1.03310	+	0.362029i
$67$	3.55255	+	4.23376i	0.434013	+	0.517237i	0.938076	−	0.346430i	$-0.112606\pi$
$67$	3.55255	+	4.23376i	0.434013	+	0.517237i	−0.504063	+	0.863667i	$0.668162\pi$
$68$	0.0675824	−	1.09615i	0.00819558	−	0.132928i
$69$	8.62450	−	5.48428i	1.03827	−	0.660230i
$70$	−0.108447	+	3.52124i	−0.0129618	+	0.420869i
$71$	−4.92271	−	8.52639i	−0.584218	−	1.01190i	−0.994972	−	0.100150i	$-0.968068\pi$
$71$	−4.92271	−	8.52639i	−0.584218	−	1.01190i	0.410754	−	0.911746i	$-0.365266\pi$
$72$	5.41010	+	6.53688i	0.637587	+	0.770378i
$73$	−5.59592	+	9.69242i	−0.654953	+	1.13441i	0.326952	+	0.945041i	$0.393978\pi$
$73$	−5.59592	+	9.69242i	−0.654953	+	1.13441i	−0.981906	+	0.189371i	$0.939355\pi$
$74$	−10.6214	−	6.57629i	−1.23471	−	0.764478i
$75$	−0.629505	+	1.99073i	−0.0726890	+	0.229870i
$76$	1.00853	−	0.502216i	0.115686	−	0.0576081i
$77$	3.57555	−	0.630466i	0.407472	−	0.0718483i
$78$	−7.41112	+	0.0890052i	−0.839144	+	0.0100779i
$79$	8.52755	−	10.1627i	0.959424	−	1.14340i	−0.0301752	−	0.999545i	$-0.509607\pi$
$79$	8.52755	−	10.1627i	0.959424	−	1.14340i	0.989599	−	0.143852i	$-0.0459490\pi$
$80$	−9.95114	+	0.511746i	−1.11257	+	0.0572149i
$81$	0.0300975	−	8.99995i	0.00334417	−	0.999994i
$82$	9.63166	+	3.84538i	1.06364	+	0.424651i
$83$	0.419295	+	0.351830i	0.0460236	+	0.0386184i	0.665509	−	0.746390i	$-0.268214\pi$
$83$	0.419295	+	0.351830i	0.0460236	+	0.0386184i	−0.619486	+	0.785008i	$0.712659\pi$
$84$	3.23237	+	1.24571i	0.352680	+	0.135918i
$85$	−0.237532	−	1.34711i	−0.0257640	−	0.146115i
$86$	−8.09544	−	7.22902i	−0.872954	−	0.779525i
$87$	−9.42940	−	2.98175i	−1.01094	−	0.319677i
$88$	2.60726	+	9.93270i	0.277935	+	1.05883i
$89$	2.19413	+	1.26678i	0.232577	+	0.134279i	0.611761	−	0.791043i	$-0.290462\pi$
$89$	2.19413	+	1.26678i	0.232577	+	0.134279i	−0.379183	+	0.925322i	$0.623795\pi$
$90$	8.45610	+	6.33975i	0.891351	+	0.668268i
$91$	−2.62042	+	1.51290i	−0.274694	+	0.158595i
$92$	10.8205	+	4.71120i	1.12812	+	0.491176i
$93$	−2.84517	−	4.47427i	−0.295030	−	0.463960i
$94$	1.30150	+	3.95018i	0.134240	+	0.407430i
$95$	1.07498	−	0.902015i	0.110291	−	0.0925448i
$96$	−2.76113	+	9.40086i	−0.281806	+	0.959471i
$97$	17.3745	−	6.32379i	1.76411	−	0.642084i	0.764115	−	0.645080i	$-0.223176\pi$
$97$	17.3745	−	6.32379i	1.76411	−	0.642084i	0.999996	+	0.00299680i	$0.000953912\pi$
$98$	1.39963	−	0.202587i	0.141384	−	0.0204643i
$99$	4.61971	−	9.86391i	0.464299	−	0.991360i
$100$	−2.31194	+	0.683597i	−0.231194	+	0.0683597i
$101$	−1.83779	−	0.324052i	−0.182867	−	0.0322444i	0.0814647	−	0.996676i	$-0.474040\pi$
$101$	−1.83779	−	0.324052i	−0.182867	−	0.0322444i	−0.264332	+	0.964432i	$0.585151\pi$
$102$	−1.32733	−	0.217643i	−0.131426	−	0.0215499i
$103$	4.75510	−	13.0645i	0.468534	−	1.28729i	−0.450383	−	0.892836i	$-0.648712\pi$
$103$	4.75510	−	13.0645i	0.468534	−	1.28729i	0.918917	−	0.394451i	$-0.129065\pi$
$104$	−4.87301	−	7.03544i	−0.477838	−	0.689881i
$105$	4.27728	+	0.566753i	0.417420	+	0.0553094i
$106$	1.06351	+	1.98046i	0.103298	+	0.192359i
$107$	5.71751			0.552733			0.276366	−	0.961052i	$-0.410870\pi$
$107$	5.71751			0.552733			0.276366	+	0.961052i	$0.410870\pi$
$108$	8.63299	−	5.78545i	0.830710	−	0.556705i
$109$	−11.8104			−1.13124			−0.565618	−	0.824667i	$-0.691362\pi$
$109$	−11.8104			−1.13124			−0.565618	+	0.824667i	$0.691362\pi$
$110$	6.05131	+	11.2687i	0.576970	+	1.07442i
$111$	−9.32422	+	12.1305i	−0.885016	+	1.15138i
$112$	0.895987	+	3.89836i	0.0846628	+	0.368360i
$113$	−6.27698	+	17.2459i	−0.590489	+	1.62235i	0.179112	+	0.983829i	$0.442678\pi$
$113$	−6.27698	+	17.2459i	−0.590489	+	1.62235i	−0.769601	+	0.638526i	$0.779545\pi$
$114$	−0.487478	−	1.29088i	−0.0456565	−	0.120902i
$115$	14.4761	+	2.55252i	1.34990	+	0.238024i
$116$	−3.23796	−	10.9509i	−0.300637	−	1.01676i
$117$	−0.806266	+	9.04151i	−0.0745393	+	0.835888i
$118$	−5.79573	+	0.838893i	−0.533540	+	0.0772263i
$119$	−0.516002	+	0.187809i	−0.0473018	+	0.0172165i
$120$	−0.604655	+	12.1887i	−0.0551972	+	1.11267i
$121$	1.67155	−	1.40260i	0.151959	−	0.127509i
$122$	−2.20201	−	6.68330i	−0.199360	−	0.605077i
$123$	5.87442	−	11.2617i	0.529678	−	1.01543i
$124$	2.44410	−	5.61354i	0.219487	−	0.504110i
$125$	8.18612	−	4.72626i	0.732189	−	0.422729i
$126$	1.91686	−	3.78492i	0.170768	−	0.337188i
$127$	4.65729	+	2.68889i	0.413267	+	0.238600i	0.692193	−	0.721713i	$-0.256645\pi$
$127$	4.65729	+	2.68889i	0.413267	+	0.238600i	−0.278925	+	0.960313i	$0.589978\pi$
$128$	−10.7810	+	3.43067i	−0.952917	+	0.303232i
$129$	−9.80781	+	8.97213i	−0.863529	+	0.789952i
$130$	−7.95094	−	7.09998i	−0.697344	−	0.622710i
$131$	−2.59436	−	14.7134i	−0.226671	−	1.28551i	−0.859466	−	0.511193i	$-0.829204\pi$
$131$	−2.59436	−	14.7134i	−0.226671	−	1.28551i	0.632795	−	0.774319i	$-0.281908\pi$
$132$	12.4249	−	1.95103i	1.08145	−	0.169815i
$133$	−0.431533	−	0.362099i	−0.0374186	−	0.0313980i
$134$	7.25892	+	2.89808i	0.627075	+	0.250356i
$135$	8.76874	−	9.52135i	0.754693	−	0.819467i
$136$	−0.649201	−	1.41095i	−0.0556685	−	0.120988i
$137$	−9.39281	+	11.1939i	−0.802482	+	0.956360i	−0.999712	−	0.0239969i	$-0.992361\pi$
$137$	−9.39281	+	11.1939i	−0.802482	+	0.956360i	0.197230	+	0.980357i	$0.436805\pi$
$138$	7.07617	−	12.6034i	0.602363	−	1.07288i
$139$	22.8586	−	4.03058i	1.93884	−	0.341870i	0.938843	−	0.344346i	$-0.111899\pi$
$139$	22.8586	−	4.03058i	1.93884	−	0.341870i	0.999997	+	0.00247669i	$0.000788354\pi$
$140$	2.22084	+	4.45978i	0.187695	+	0.376920i
$141$	4.97398	−	1.09834i	0.418884	−	0.0924971i
$142$	−11.8381	−	7.32965i	−0.993432	−	0.615091i
$143$	−5.49289	+	9.51397i	−0.459339	+	0.795598i
$144$	11.1142	+	4.52476i	0.926187	+	0.377064i
$145$	−7.11172	−	12.3179i	−0.590596	−	1.02294i
$146$	−0.487226	+	15.8202i	−0.0403231	+	1.30929i
$147$	−0.0741043	−	1.73046i	−0.00611202	−	0.142726i
$148$	−17.6335	−	1.08718i	−1.44946	−	0.0893654i
$149$	10.4806	+	12.4902i	0.858600	+	1.02324i	0.999448	+	0.0332087i	$0.0105726\pi$
$149$	10.4806	+	12.4902i	0.858600	+	1.02324i	−0.140848	+	0.990031i	$0.544983\pi$
$150$	0.547618	+	2.90150i	0.0447128	+	0.236906i
$151$	2.65495	+	7.29442i	0.216057	+	0.593611i	0.999616	−	0.0277057i	$-0.00882014\pi$
$151$	2.65495	+	7.29442i	0.216057	+	0.593611i	−0.783559	+	0.621317i	$0.786598\pi$
$152$	0.920536	−	1.30050i	0.0746654	−	0.105485i
$153$	−0.429027	+	1.59051i	−0.0346847	+	0.128585i
$154$	4.03307	−	3.17781i	0.324994	−	0.256075i
$155$	1.32421	−	7.50999i	0.106363	−	0.603217i
$156$	−9.17420	+	5.06945i	−0.734524	+	0.405881i
$157$	22.5883	+	8.22148i	1.80274	+	0.656145i	0.998047	+	0.0624597i	$0.0198945\pi$
$157$	22.5883	+	8.22148i	1.80274	+	0.656145i	0.804697	+	0.593686i	$0.202328\pi$
$158$	3.82516	−	18.3676i	0.304313	−	1.46125i
$159$	2.54447	−	1.05146i	0.201790	−	0.0833866i
$160$	−12.0560	+	7.29561i	−0.953114	+	0.576769i
$161$		−	5.90083i		−	0.465050i
$162$	−5.98410	−	11.2335i	−0.470155	−	0.882584i
$163$			17.3948i			1.36246i	0.732068	+	0.681231i	$0.238555\pi$
$163$			17.3948i			1.36246i	−0.732068	+	0.681231i	$0.761445\pi$
$164$	14.5732	−	1.65318i	1.13798	−	0.129092i
$165$	14.4779	−	5.98275i	1.12710	−	0.465756i
$166$	0.757811	+	0.157819i	0.0588176	+	0.0122491i
$167$	−0.774686	−	0.281963i	−0.0599470	−	0.0218189i	0.311873	−	0.950124i	$-0.399044\pi$
$167$	−0.774686	−	0.281963i	−0.0599470	−	0.0218189i	−0.371820	+	0.928305i	$0.621266\pi$
$168$	4.86078	−	0.610613i	0.375017	−	0.0471098i
$169$	−0.667600	+	3.78615i	−0.0513539	+	0.291242i
$170$	−1.19726	−	1.51948i	−0.0918257	−	0.116539i
$171$	−1.63312	+	0.434668i	−0.124888	+	0.0332399i
$172$	−14.9231	−	3.59044i	−1.13787	−	0.273769i
$173$	7.41640	+	20.3764i	0.563859	+	1.54919i	0.813931	+	0.580962i	$0.197323\pi$
$173$	7.41640	+	20.3764i	0.563859	+	1.54919i	−0.250072	+	0.968227i	$0.580454\pi$
$174$	−13.7434	+	2.59388i	−1.04188	+	0.196641i
$175$	0.774844	+	0.923424i	0.0585727	+	0.0698043i
$176$	9.89415	+	10.6310i	0.745799	+	0.801344i
$177$	0.306859	+	7.16570i	0.0230649	+	0.538607i
$178$	3.58130	+	0.110296i	0.268430	+	0.00826706i
$179$	−4.95698	−	8.58574i	−0.370502	−	0.641728i	0.619141	−	0.785280i	$-0.287481\pi$
$179$	−4.95698	−	8.58574i	−0.370502	−	0.641728i	−0.989643	+	0.143552i	$0.954148\pi$
$180$	14.7775	+	2.24117i	1.10145	+	0.167047i
$181$	1.85930	−	3.22041i	0.138201	−	0.239371i	−0.788615	−	0.614888i	$-0.789201\pi$
$181$	1.85930	−	3.22041i	0.138201	−	0.239371i	0.926816	+	0.375517i	$0.122535\pi$
$182$	−2.25262	+	3.63821i	−0.166976	+	0.269682i
$183$	−8.41545	+	1.85828i	−0.622088	+	0.137368i
$184$	16.6337	−	1.36986i	1.22626	−	0.100987i
$185$	−21.6705	+	3.82110i	−1.59325	+	0.280933i
$186$	−6.53848	−	3.67102i	−0.479425	−	0.269172i
$187$	−1.28152	+	1.52725i	−0.0937139	+	0.111684i
$188$	4.26453	+	4.05086i	0.311023	+	0.295439i
$189$	−4.37537	−	2.80287i	−0.318262	−	0.203879i
$190$	0.735840	−	1.84309i	0.0533834	−	0.133711i
$191$	9.60379	+	8.05853i	0.694906	+	0.583095i	0.920319	−	0.391168i	$-0.127929\pi$
$191$	9.60379	+	8.05853i	0.694906	+	0.583095i	−0.225414	+	0.974263i	$0.572373\pi$
$192$	2.84966	+	13.5602i	0.205656	+	0.978624i
$193$	−2.86570	−	16.2522i	−0.206278	−	1.16986i	−0.895417	−	0.445229i	$-0.853122\pi$
$193$	−2.86570	−	16.2522i	−0.206278	−	1.16986i	0.689139	−	0.724629i	$-0.257989\pi$
$194$	17.4163	−	19.5037i	1.25042	−	1.40029i
$195$	−9.63275	+	8.81198i	−0.689815	+	0.631039i
$196$	1.60830	−	1.18886i	0.114878	−	0.0849184i
$197$	1.66771	+	0.962851i	0.118819	+	0.0686003i	0.558232	−	0.829685i	$-0.311480\pi$
$197$	1.66771	+	0.962851i	0.118819	+	0.0686003i	−0.439413	+	0.898285i	$0.644813\pi$
$198$	−0.843802	−	15.3807i	−0.0599664	−	1.09306i
$199$	2.32094	−	1.34000i	0.164527	−	0.0949898i	−0.415476	−	0.909604i	$-0.636385\pi$
$199$	2.32094	−	1.34000i	0.164527	−	0.0949898i	0.580003	+	0.814615i	$0.303051\pi$
$200$	−2.42315	+	2.39857i	−0.171342	+	0.169604i
$201$	4.42727	−	8.48737i	0.312275	−	0.598653i
$202$	−2.50657	+	0.825863i	−0.176362	+	0.0581075i
$203$	−4.37394	+	3.67017i	−0.306990	+	0.257595i
$204$	−1.79939	+	0.616911i	−0.125982	+	0.0431924i
$205$	17.1662	−	6.24798i	1.19894	−	0.436378i
$206$	−2.81656	−	19.4590i	−0.196239	−	1.35577i
$207$	−14.4840	−	10.1780i	−1.00671	−	0.707417i
$208$	−10.7786	−	5.50529i	−0.747364	−	0.381723i
$209$	−2.01420	−	0.355158i	−0.139325	−	0.0245668i
$210$	5.70840	−	2.15566i	0.393917	−	0.148755i
$211$	4.39428	−	12.0732i	0.302515	−	0.831153i	−0.691546	−	0.722332i	$-0.743070\pi$
$211$	4.39428	−	12.0732i	0.302515	−	0.831153i	0.994061	−	0.108821i	$-0.0347075\pi$
$212$	2.65013	+	1.75595i	0.182012	+	0.120599i
$213$	−10.3924	+	13.5202i	−0.712074	+	0.926388i
$214$	7.12363	−	3.82542i	0.486961	−	0.261500i
$215$	−19.1177			−1.30381
$216$	6.88525	−	12.9844i	0.468482	−	0.883473i
$217$	−3.06127			−0.207812
$218$	−14.7150	+	7.90202i	−0.996626	+	0.535192i
$219$	19.2169	+	2.54630i	1.29856	+	0.172063i
$220$	15.0790	+	9.99122i	1.01663	+	0.673608i
$221$	0.568273	−	1.56132i	0.0382262	−	0.105026i
$222$	−3.50115	+	21.3524i	−0.234982	+	1.43308i
$223$	4.46070	+	0.786542i	0.298710	+	0.0526707i	0.320995	−	0.947081i	$-0.395983\pi$
$223$	4.46070	+	0.786542i	0.298710	+	0.0526707i	−0.0222843	+	0.999752i	$0.507094\pi$
$224$	3.72461	+	4.25761i	0.248861	+	0.284474i
$225$	3.60309	−	0.309160i	0.240206	−	0.0206107i
$226$	3.71800	+	25.6869i	0.247318	+	1.70867i
$227$	−28.1863	+	10.2590i	−1.87079	+	0.680912i	−0.902725	+	0.430218i	$0.858437\pi$
$227$	−28.1863	+	10.2590i	−1.87079	+	0.680912i	−0.968066	+	0.250695i	$0.919341\pi$
$228$	−1.47106	−	1.28220i	−0.0974231	−	0.0849156i
$229$	−0.0652466	+	0.0547484i	−0.00431162	+	0.00361788i	−0.644941	−	0.764232i	$-0.723118\pi$
$229$	−0.0652466	+	0.0547484i	−0.00431162	+	0.00361788i	0.640629	+	0.767850i	$0.278674\pi$
$230$	19.7440	−	6.50524i	1.30188	−	0.428943i
$231$	−3.37441	−	5.30655i	−0.222020	−	0.349145i
$232$	−11.3612	−	11.4776i	−0.745898	−	0.753541i
$233$	0.722460	−	0.417113i	0.0473299	−	0.0273259i	−0.476148	−	0.879365i	$-0.657967\pi$
$233$	0.722460	−	0.417113i	0.0473299	−	0.0273259i	0.523478	+	0.852039i	$0.324634\pi$
$234$	5.04485	+	11.8046i	0.329792	+	0.771688i
$235$	6.34451	+	3.66301i	0.413870	+	0.238948i
$236$	−6.65981	+	4.92295i	−0.433517	+	0.320457i
$237$	−21.9090	−	6.92802i	−1.42314	−	0.450023i
$238$	−0.517246	+	0.579239i	−0.0335281	+	0.0375465i
$239$	1.16205	+	6.59029i	0.0751665	+	0.426290i	0.999049	+	0.0436129i	$0.0138868\pi$
$239$	1.16205	+	6.59029i	0.0751665	+	0.426290i	−0.923882	+	0.382677i	$0.875002\pi$
$240$	7.40175	+	15.5909i	0.477781	+	1.00639i
$241$	−0.903567	−	0.758183i	−0.0582039	−	0.0488388i	0.613222	−	0.789911i	$-0.289873\pi$
$241$	−0.903567	−	0.758183i	−0.0582039	−	0.0488388i	−0.671426	+	0.741072i	$0.734318\pi$
$242$	1.14420	−	2.86592i	0.0735519	−	0.184228i
$243$	−14.4267	+	5.90519i	−0.925471	+	0.378818i
$244$	−7.21514	−	6.85363i	−0.461902	−	0.438759i
$245$	1.60123	−	1.90827i	0.102299	−	0.121915i
$246$	−0.215714	−	17.9616i	−0.0137534	−	1.14519i
$247$	1.67861	−	0.295985i	0.106808	−	0.0188331i
$248$	−0.710663	−	8.62936i	−0.0451271	−	0.547965i
$249$	0.285837	−	0.903922i	0.0181142	−	0.0572837i
$250$	7.03715	−	11.3657i	0.445068	−	0.718829i
$251$	−2.31558	+	4.01070i	−0.146158	+	0.253153i	−0.929804	−	0.368054i	$-0.880024\pi$
$251$	−2.31558	+	4.01070i	−0.146158	+	0.253153i	0.783646	+	0.621207i	$0.213358\pi$
$252$	−0.144095	−	5.99827i	−0.00907715	−	0.377855i
$253$	−10.7121	−	18.5539i	−0.673464	−	1.16647i
$254$	7.60171	+	0.234116i	0.476974	+	0.0146898i
$255$	−1.99928	+	1.27133i	−0.125200	+	0.0796139i
$256$	−11.1371	+	11.4876i	−0.696066	+	0.717978i
$257$	−4.05686	−	4.83478i	−0.253060	−	0.301585i	0.624526	−	0.781004i	$-0.285292\pi$
$257$	−4.05686	−	4.83478i	−0.253060	−	0.301585i	−0.877586	+	0.479419i	$0.840848\pi$
$258$	−6.21688	+	17.7408i	−0.387046	+	1.10449i
$259$	3.02123	+	8.30076i	0.187730	+	0.515784i
$260$	−14.6567	−	3.52636i	−0.908971	−	0.218695i
$261$	1.46438	+	17.0666i	0.0906430	+	1.05640i
$262$	−13.0767	−	16.5960i	−0.807879	−	1.02531i
$263$	−1.18499	+	6.72041i	−0.0730696	+	0.414398i	0.926229	+	0.376960i	$0.123031\pi$
$263$	−1.18499	+	6.72041i	−0.0730696	+	0.414398i	−0.999299	+	0.0374378i	$0.988080\pi$
$264$	14.1752	−	10.7440i	0.872423	−	0.661246i
$265$	3.72087	+	1.35429i	0.228571	+	0.0831931i
$266$	−0.779930	−	0.162425i	−0.0478206	−	0.00995891i
$267$	0.576421	−	4.35024i	0.0352764	−	0.266230i
$268$	10.9831	−	1.24592i	0.670902	−	0.0761068i
$269$		−	10.2533i		−	0.625153i	−0.949893	−	0.312577i	$-0.898808\pi$
$269$		−	10.2533i		−	0.625153i	0.949893	−	0.312577i	$-0.101192\pi$
$270$	4.55480	−	17.7299i	0.277197	−	1.07900i
$271$			15.8317i			0.961707i	0.876801	+	0.480854i	$0.159673\pi$
$271$			15.8317i			0.961707i	−0.876801	+	0.480854i	$0.840327\pi$
$272$	−1.75289	−	1.32359i	−0.106284	−	0.0802542i
$273$	4.15516	+	3.19389i	0.251482	+	0.193303i
$274$	−4.21328	+	20.2313i	−0.254534	+	1.22222i
$275$	4.11267	+	1.49689i	0.248004	+	0.0902659i
$276$	0.383840	−	20.4375i	0.0231045	−	1.23019i
$277$	−3.75395	+	21.2897i	−0.225553	+	1.27917i	0.636072	+	0.771630i	$0.280558\pi$
$277$	−3.75395	+	21.2897i	−0.225553	+	1.27917i	−0.861625	+	0.507545i	$0.830553\pi$
$278$	25.7835	−	20.3158i	1.54639	−	1.21846i
$279$	−5.28018	+	7.51411i	−0.316116	+	0.449858i
$280$	5.75092	+	4.07069i	0.343683	+	0.243270i
$281$	−11.2060	−	30.7883i	−0.668495	−	1.83667i	−0.533444	−	0.845835i	$-0.679103\pi$
$281$	−11.2060	−	30.7883i	−0.668495	−	1.83667i	−0.135050	−	0.990839i	$-0.543120\pi$
$282$	5.46237	−	4.69640i	0.325279	−	0.279666i
$283$	−9.34788	−	11.1404i	−0.555674	−	0.662226i	0.412951	−	0.910753i	$-0.364498\pi$
$283$	−9.34788	−	11.1404i	−0.555674	−	0.662226i	−0.968625	+	0.248527i	$0.920054\pi$
$284$	−19.6535	−	1.21172i	−1.16622	−	0.0719024i
$285$	−2.15500	−	1.12411i	−0.127651	−	0.0665866i
$286$	−0.478256	+	15.5289i	−0.0282799	+	0.918242i
$287$	−3.66667	−	6.35086i	−0.216437	−	0.374879i
$288$	16.8750	−	1.79867i	0.994367	−	0.105987i
$289$	−8.34923	+	14.4613i	−0.491131	+	0.850665i
$290$	−17.1022	−	10.5890i	−1.00428	−	0.621806i
$291$	−21.6159	−	23.6292i	−1.26715	−	1.38517i
$292$	9.97774	+	20.0368i	0.583903	+	1.17257i
$293$	−16.7612	+	2.95545i	−0.979200	+	0.172659i	−0.640268	−	0.768152i	$-0.721177\pi$
$293$	−16.7612	+	2.95545i	−0.979200	+	0.172659i	−0.338932	+	0.940811i	$0.610066\pi$
$294$	−1.25013	−	2.10646i	−0.0729091	−	0.122851i
$295$	−6.63055	+	7.90198i	−0.386046	+	0.460071i
$296$	−22.6975	+	10.4435i	−1.31927	+	0.607015i
$297$	−18.8456	−	0.870181i	−1.09353	−	0.0504930i
$298$	21.4149	+	8.54975i	1.24053	+	0.495274i
$299$	13.6775	+	11.4768i	0.790990	+	0.663719i
$300$	2.62360	+	3.24867i	0.151474	+	0.187562i
$301$	1.33266	+	7.55787i	0.0768131	+	0.435629i
$302$	8.18836	+	7.31200i	0.471187	+	0.420758i
$303$	0.696948	+	3.15622i	0.0400386	+	0.181320i
$304$	0.276799	−	2.23624i	0.0158755	−	0.128257i
$305$	−10.7343	−	6.19742i	−0.614641	−	0.354863i
$306$	0.529623	+	2.26871i	0.0302765	+	0.129694i
$307$	7.57863	−	4.37552i	0.432535	−	0.249724i	−0.267891	−	0.963449i	$-0.586327\pi$
$307$	7.57863	−	4.37552i	0.432535	−	0.249724i	0.700426	+	0.713725i	$0.252993\pi$
$308$	2.89874	−	6.65774i	0.165171	−	0.379360i
$309$	−24.0586	+	1.03027i	−1.36865	+	0.0586101i
$310$	−3.37483	−	10.2429i	−0.191677	−	0.581759i
$311$	−14.3907	+	12.0753i	−0.816024	+	0.684725i	−0.952037	−	0.305982i	$-0.901015\pi$
$311$	−14.3907	+	12.0753i	−0.816024	+	0.684725i	0.136014	+	0.990707i	$0.456571\pi$
$312$	−8.03860	+	12.4544i	−0.455096	+	0.705090i
$313$	−0.0144270	+	0.00525100i	−0.000815463	+	0.000296804i	−0.342428	−	0.939544i	$-0.611249\pi$
$313$	−0.0144270	+	0.00525100i	−0.000815463	+	0.000296804i	0.341612	+	0.939841i	$0.389027\pi$
$314$	33.6442	−	4.86977i	1.89865	−	0.274817i
$315$	−1.92214	−	7.22180i	−0.108300	−	0.406902i
$316$	−7.52333	−	25.4441i	−0.423220	−	1.43134i
$317$	−5.29064	−	0.932883i	−0.297152	−	0.0523960i	0.0230845	−	0.999734i	$-0.492651\pi$
$317$	−5.29064	−	0.932883i	−0.297152	−	0.0523960i	−0.320237	+	0.947338i	$0.603762\pi$
$318$	2.46674	−	3.01248i	0.138328	−	0.168932i
$319$	−7.09025	+	19.4803i	−0.396978	+	1.09069i
$320$	−10.1397	+	17.1562i	−0.566828	+	0.959059i
$321$	−3.78207	−	9.15237i	−0.211095	−	0.510835i
$322$	−3.94807	−	7.35203i	−0.220017	−	0.409712i
$323$	0.309332			0.0172117
$324$	−14.9717	−	9.99234i	−0.831764	−	0.555130i
$325$	−3.64743			−0.202323
$326$	11.6383	+	21.6727i	0.644586	+	1.20034i
$327$	7.81248	+	18.9057i	0.432031	+	1.04549i
$328$	17.0511	−	11.8102i	0.941491	−	0.652112i
$329$	1.00585	−	2.76355i	0.0554543	−	0.152359i
$330$	14.0355	−	17.1408i	0.772631	−	0.943569i
$331$	20.7763	+	3.66342i	1.14197	+	0.201360i	0.712467	−	0.701706i	$-0.247578\pi$
$331$	20.7763	+	3.66342i	1.14197	+	0.201360i	0.429502	+	0.903066i	$0.358689\pi$
$332$	1.04977	−	0.310398i	0.0576138	−	0.0170353i
$333$	25.5860	+	6.90161i	1.40210	+	0.378206i
$334$	−1.15386	+	0.167013i	−0.0631363	+	0.00913855i
$335$	12.9373	−	4.70881i	0.706842	−	0.257270i
$336$	5.64765	−	4.01298i	0.308105	−	0.218926i
$337$	9.94386	−	8.34389i	0.541676	−	0.454520i	−0.330434	−	0.943829i	$-0.607195\pi$
$337$	9.94386	−	8.34389i	0.541676	−	0.454520i	0.872111	+	0.489309i	$0.162751\pi$
$338$	1.70141	+	5.16395i	0.0925448	+	0.280882i
$339$	31.7586	−	1.36001i	1.72489	−	0.0738657i
$340$	−2.50835	−	1.09212i	−0.136034	−	0.0592285i
$341$	−9.62550	+	5.55729i	−0.521250	+	0.300944i
$342$	−1.74394	+	1.63424i	−0.0943012	+	0.0883696i
$343$	−0.866025	−	0.500000i	−0.0467610	−	0.0269975i
$344$	−20.9954	+	5.51114i	−1.13200	+	0.297141i
$345$	−5.48979	−	24.8612i	−0.295560	−	1.33848i
$346$	22.8736	+	20.4255i	1.22969	+	1.09808i
$347$	2.62751	+	14.9013i	0.141052	+	0.799945i	0.970453	+	0.241291i	$0.0775709\pi$
$347$	2.62751	+	14.9013i	0.141052	+	0.799945i	−0.829401	+	0.558654i	$0.811318\pi$
$348$	−15.3878	+	12.4271i	−0.824874	+	0.666161i
$349$	25.4343	+	21.3419i	1.36146	+	1.14240i	0.975527	+	0.219879i	$0.0705663\pi$
$349$	25.4343	+	21.3419i	1.36146	+	1.14240i	0.385937	+	0.922525i	$0.373878\pi$
$350$	1.58324	+	0.632097i	0.0846276	+	0.0337870i
$351$	15.0066	−	4.69022i	0.800994	−	0.250346i
$352$	19.4403	+	6.62565i	1.03617	+	0.353148i
$353$	16.6446	−	19.8363i	0.885904	−	1.05578i	−0.112167	−	0.993689i	$-0.535779\pi$
$353$	16.6446	−	19.8363i	0.885904	−	1.05578i	0.998071	−	0.0620899i	$-0.0197766\pi$
$354$	5.17668	+	8.72266i	0.275137	+	0.463604i
$355$	−24.1531	+	4.25884i	−1.28191	+	0.226036i
$356$	4.53586	−	2.25872i	0.240400	−	0.119712i
$357$	0.641967	+	0.701762i	0.0339765	+	0.0371412i
$358$	−11.9205	−	7.38068i	−0.630019	−	0.390081i
$359$	−11.8564	+	20.5360i	−0.625759	+	1.08385i	0.362634	+	0.931932i	$0.381877\pi$
$359$	−11.8564	+	20.5360i	−0.625759	+	1.08385i	−0.988394	+	0.151915i	$0.951456\pi$
$360$	19.9112	−	7.09480i	1.04941	−	0.373929i
$361$	−9.34133	−	16.1797i	−0.491649	−	0.851561i
$362$	0.161886	−	5.25641i	0.00850854	−	0.276271i
$363$	−3.35093	−	1.74795i	−0.175878	−	0.0917434i
$364$	−0.372399	+	6.04012i	−0.0195190	+	0.316589i
$365$	17.9207	+	21.3571i	0.938014	+	1.11788i
$366$	−9.24175	+	7.94581i	−0.483074	+	0.415334i
$367$	−5.49134	−	15.0873i	−0.286645	−	0.787552i	−0.996530	−	0.0832338i	$-0.973475\pi$
$367$	−5.49134	−	15.0873i	−0.286645	−	0.787552i	0.709885	−	0.704318i	$-0.248747\pi$
$368$	19.8080	−	12.8359i	1.03256	−	0.669117i
$369$	−21.9131	−	1.95407i	−1.14075	−	0.101725i
$370$	−24.4434	+	19.2599i	−1.27075	+	1.00128i
$371$	0.276021	−	1.56539i	0.0143303	−	0.0812712i
$372$	−10.6027	−	0.199131i	−0.549723	−	0.0103245i
$373$	−20.8426	−	7.58610i	−1.07919	−	0.392793i	−0.259585	−	0.965720i	$-0.583586\pi$
$373$	−20.8426	−	7.58610i	−1.07919	−	0.392793i	−0.819607	+	0.572927i	$0.805808\pi$
$374$	−0.574844	+	2.76028i	−0.0297245	+	0.142731i
$375$	−12.9806	−	9.97764i	−0.670317	−	0.515243i
$376$	8.02363	+	2.19382i	0.413787	+	0.113138i
$377$		−	17.2766i		−	0.889790i
$378$	−7.32674	−	0.564756i	−0.376847	−	0.0290479i
$379$			15.8400i			0.813645i	0.913507	+	0.406823i	$0.133363\pi$
$379$			15.8400i			0.813645i	−0.913507	+	0.406823i	$0.866637\pi$
$380$	−0.316348	−	2.78869i	−0.0162283	−	0.143057i
$381$	1.22352	−	9.23386i	0.0626826	−	0.473065i
$382$	17.3574	+	3.61477i	0.888081	+	0.184948i
$383$	20.0545	+	7.29924i	1.02474	+	0.372974i	0.799075	−	0.601232i	$-0.205323\pi$
$383$	20.0545	+	7.29924i	1.02474	+	0.372974i	0.225663	+	0.974206i	$0.427545\pi$
$384$	12.6232	+	14.9885i	0.644176	+	0.764878i
$385$	1.57054	−	8.90696i	0.0800420	−	0.453941i
$386$	−14.4443	−	18.3318i	−0.735197	−	0.933062i
$387$	20.8500	+	9.76498i	1.05986	+	0.496382i
$388$	8.65019	−	35.9531i	0.439147	−	1.82524i
$389$	11.4255	+	31.3912i	0.579294	+	1.59160i	0.789373	+	0.613914i	$0.210406\pi$
$389$	11.4255	+	31.3912i	0.579294	+	1.59160i	−0.210079	+	0.977684i	$0.567372\pi$
$390$	−6.10591	+	17.4241i	−0.309185	+	0.882304i
$391$	2.08279	+	2.48218i	0.105331	+	0.125529i
$392$	1.20840	−	2.55730i	0.0610333	−	0.129163i
$393$	−21.8364	+	13.8857i	−1.10150	+	0.700440i
$394$	2.72206	+	0.0838336i	0.137136	+	0.00422348i
$395$	−16.5239	−	28.6203i	−0.831409	−	1.44004i
$396$	−11.3421	−	18.5987i	−0.569960	−	0.934620i
$397$	−1.22572	+	2.12300i	−0.0615169	+	0.106550i	−0.895144	−	0.445778i	$-0.852927\pi$
$397$	−1.22572	+	2.12300i	−0.0615169	+	0.106550i	0.833627	+	0.552328i	$0.186260\pi$
$398$	1.99518	−	3.22242i	0.100009	−	0.161525i
$399$	−0.294179	+	0.930305i	−0.0147274	+	0.0465735i
$400$	−1.41427	+	4.60970i	−0.0707133	+	0.230485i
$401$	6.36276	−	1.12193i	0.317741	−	0.0560264i	−0.0125031	−	0.999922i	$-0.503980\pi$
$401$	6.36276	−	1.12193i	0.317741	−	0.0560264i	0.330244	+	0.943895i	$0.392869\pi$
$402$	−0.162573	−	13.5368i	−0.00810840	−	0.675156i
$403$	5.95399	−	7.09569i	0.296590	−	0.353462i
$404$	−2.57046	+	2.70604i	−0.127885	+	0.134631i
$405$	−21.0418	−	7.73838i	−1.04558	−	0.384523i
$406$	−2.99402	+	7.49925i	−0.148591	+	0.372181i
$407$	24.5684	+	20.6154i	1.21781	+	1.02187i
$408$	−1.82915	+	1.97254i	−0.0905566	+	0.0976555i
$409$	5.38296	+	30.5283i	0.266170	+	1.50953i	0.765682	+	0.643220i	$0.222402\pi$
$409$	5.38296	+	30.5283i	0.266170	+	1.50953i	−0.499511	+	0.866307i	$0.666487\pi$
$410$	17.2076	−	19.2699i	0.849821	−	0.951675i
$411$	24.1320	+	7.63098i	1.19034	+	0.376408i
$412$	−16.5287	−	22.3601i	−0.814310	−	1.10160i
$413$	3.58613	+	2.07045i	0.176462	+	0.101880i
$414$	−24.8559	−	2.99021i	−1.22160	−	0.146961i
$415$	1.18082	−	0.681745i	0.0579640	−	0.0334655i
$416$	−17.1129	+	0.352446i	−0.839027	+	0.0172801i
$417$	−21.5727	−	33.9249i	−1.05642	−	1.66131i
$418$	−2.74718	+	0.905139i	−0.134369	+	0.0442718i
$419$	25.1656	−	21.1165i	1.22942	−	1.03161i	0.231145	−	0.972919i	$-0.425753\pi$
$419$	25.1656	−	21.1165i	1.22942	−	1.03161i	0.998276	−	0.0586878i	$-0.0186916\pi$
$420$	5.66998	−	6.50513i	0.276667	−	0.317418i
$421$	−33.4987	+	12.1925i	−1.63263	+	0.594228i	−0.985728	−	0.168347i	$-0.946157\pi$
$421$	−33.4987	+	12.1925i	−1.63263	+	0.594228i	−0.646900	+	0.762575i	$0.723935\pi$
$422$	−2.60284	−	17.9825i	−0.126704	−	0.875372i
$423$	−5.04841	−	7.23560i	−0.245462	−	0.351807i
$424$	4.47674	+	0.414671i	0.217410	+	0.0201382i
$425$	−0.651875	−	0.114943i	−0.0316206	−	0.00557556i
$426$	−3.90224	+	23.7985i	−0.189064	+	1.15304i
$427$	−1.70179	+	4.67563i	−0.0823555	+	0.226270i
$428$	6.31608	−	9.53242i	0.305299	−	0.460767i
$429$	18.8631	+	2.49942i	0.910718	+	0.120673i
$430$	−23.8193	+	12.7910i	−1.14867	+	0.616839i
$431$	15.7135			0.756890			0.378445	−	0.925624i	$-0.376459\pi$
$431$	15.7135			0.756890			0.378445	+	0.925624i	$0.376459\pi$
$432$	−0.108894	−	20.7843i	−0.00523918	−	0.999986i
$433$	−22.7396			−1.09280			−0.546398	−	0.837526i	$-0.684001\pi$
$433$	−22.7396			−1.09280			−0.546398	+	0.837526i	$0.684001\pi$
$434$	−3.81413	+	2.04820i	−0.183084	+	0.0983168i
$435$	−15.0136	+	19.5323i	−0.719848	+	0.936502i
$436$	−13.0469	+	19.6907i	−0.624833	+	0.943016i
$437$	−1.13691	+	3.12362i	−0.0543856	+	0.149423i
$438$	25.6466	−	9.68493i	1.22544	−	0.462764i
$439$	−22.4308	−	3.95516i	−1.07057	−	0.188770i	−0.389526	−	0.921016i	$-0.627361\pi$
$439$	−22.4308	−	3.95516i	−1.07057	−	0.188770i	−0.681040	+	0.732246i	$0.738472\pi$
$440$	25.4723	+	2.35944i	1.21434	+	0.112482i
$441$	−2.72104	+	1.26331i	−0.129573	+	0.0601575i
$442$	−0.336601	−	2.32551i	−0.0160105	−	0.110613i
$443$	−26.1511	+	9.51823i	−1.24248	+	0.452225i	−0.877853	−	0.478930i	$-0.841025\pi$
$443$	−26.1511	+	9.51823i	−1.24248	+	0.452225i	−0.364624	+	0.931155i	$0.618803\pi$
$444$	9.92405	+	28.9461i	0.470974	+	1.37372i
$445$	4.83473	−	4.05682i	0.229188	−	0.192312i
$446$	6.08398	−	2.00454i	0.288085	−	0.0949179i
$447$	13.0611	−	25.0390i	0.617769	−	1.18430i
$448$	7.48925	+	2.81266i	0.353834	+	0.132886i
$449$	−1.51052	+	0.872098i	−0.0712858	+	0.0411569i	−0.535219	−	0.844713i	$-0.679771\pi$
$449$	−1.51052	+	0.872098i	−0.0712858	+	0.0411569i	0.463933	+	0.885870i	$0.346438\pi$
$450$	4.28236	−	2.79591i	0.201872	−	0.131801i
$451$	−23.0581	−	13.3126i	−1.08576	−	0.626866i
$452$	21.8187	+	29.5165i	1.02627	+	1.38834i
$453$	9.92039	−	9.07512i	0.466101	−	0.426386i
$454$	−28.2542	+	31.6406i	−1.32604	+	1.48497i
$455$	1.30887	+	7.42297i	0.0613608	+	0.347994i
$456$	−2.69071	−	0.613290i	−0.126004	−	0.0287200i
$457$	−7.19602	−	6.03818i	−0.336615	−	0.282454i	0.458773	−	0.888553i	$-0.348289\pi$
$457$	−7.19602	−	6.03818i	−0.336615	−	0.282454i	−0.795389	+	0.606099i	$0.792733\pi$
$458$	−0.0446623	+	0.111867i	−0.00208693	+	0.00522722i
$459$	2.82982	−	0.365334i	0.132084	−	0.0170523i
$460$	20.2472	−	21.3152i	0.944032	−	0.993827i
$461$	−9.55937	+	11.3924i	−0.445224	+	0.530598i	−0.941250	−	0.337710i	$-0.890348\pi$
$461$	−9.55937	+	11.3924i	−0.445224	+	0.530598i	0.496026	+	0.868308i	$0.334792\pi$
$462$	−7.75474	−	4.35388i	−0.360783	−	0.202561i
$463$	−27.3719	+	4.82641i	−1.27208	+	0.224302i	−0.768615	−	0.639712i	$-0.779054\pi$
$463$	−27.3719	+	4.82641i	−1.27208	+	0.224302i	−0.503467	+	0.864014i	$0.667943\pi$
$464$	−21.8346	−	6.69888i	−1.01364	−	0.310988i
$465$	−12.8976	+	2.84803i	−0.598114	+	0.132074i
$466$	0.621058	−	1.00307i	0.0287700	−	0.0464663i
$467$	−7.82023	+	13.5450i	−0.361877	+	0.626789i	−0.988270	−	0.152718i	$-0.951197\pi$
$467$	−7.82023	+	13.5450i	−0.361877	+	0.626789i	0.626393	+	0.779508i	$0.284531\pi$
$468$	14.1836	+	11.3323i	0.655638	+	0.523836i
$469$	−2.76339	−	4.78634i	−0.127602	−	0.221013i
$470$	10.3556	+	0.318931i	0.477670	+	0.0147112i
$471$	−1.78132	−	41.5969i	−0.0820788	−	1.91668i
$472$	−5.00386	+	10.5895i	−0.230321	+	0.487423i
$473$	17.9105	+	21.3449i	0.823524	+	0.981438i
$474$	−31.9324	+	6.02681i	−1.46670	+	0.276820i
$475$	−0.232252	−	0.638106i	−0.0106564	−	0.0292783i
$476$	−0.256901	+	1.06777i	−0.0117750	+	0.0489410i
$477$	−3.36628	−	3.37756i	−0.154132	−	0.154648i
$478$	5.85719	+	7.43356i	0.267902	+	0.340003i
$479$	−2.31588	+	13.1340i	−0.105815	+	0.600109i	0.885076	+	0.465446i	$0.154106\pi$
$479$	−2.31588	+	13.1340i	−0.105815	+	0.600109i	−0.990892	+	0.134663i	$0.957005\pi$
$480$	19.6535	+	14.4729i	0.897054	+	0.660593i
$481$	−25.1164	−	9.14162i	−1.14521	−	0.416822i
$482$	−1.63306	−	0.340094i	−0.0743838	−	0.0154909i
$483$	−9.44581	+	3.90333i	−0.429799	+	0.177608i
$484$	−0.491907	−	4.33629i	−0.0223594	−	0.197104i
$485$		−	46.0588i		−	2.09142i
$486$	−14.0237	+	17.0099i	−0.636126	+	0.771585i
$487$		−	27.9244i		−	1.26537i	−0.774408	−	0.632687i	$-0.781952\pi$
$487$		−	27.9244i		−	1.26537i	0.774408	−	0.632687i	$-0.218048\pi$
$488$	−13.5751	−	3.71172i	−0.614518	−	0.168022i
$489$	27.8448	−	11.5064i	1.25919	−	0.520339i
$490$	0.718256	−	3.44891i	0.0324475	−	0.155806i
$491$	−6.46025	−	2.35134i	−0.291547	−	0.106114i	0.192106	−	0.981374i	$-0.438468\pi$
$491$	−6.46025	−	2.35134i	−0.291547	−	0.106114i	−0.483653	+	0.875260i	$0.660690\pi$
$492$	−12.2864	−	22.2346i	−0.553912	−	1.00242i
$493$	0.544445	−	3.08770i	0.0245206	−	0.139063i
$494$	1.89340	−	1.49189i	0.0851883	−	0.0671232i
$495$	−19.1539	−	19.2180i	−0.860903	−	0.863787i
$496$	−6.65908	−	10.2761i	−0.299002	−	0.461411i
$497$	3.36733	+	9.25167i	0.151046	+	0.414994i
$498$	−0.248654	−	1.31747i	−0.0111425	−	0.0590372i
$499$	23.1878	+	27.6341i	1.03803	+	1.23707i	0.970939	+	0.239327i	$0.0769267\pi$
$499$	23.1878	+	27.6341i	1.03803	+	1.23707i	0.0670890	+	0.997747i	$0.478629\pi$
$500$	1.16336	−	18.8692i	0.0520272	−	0.843856i
$501$	0.0610918	+	1.42660i	0.00272938	+	0.0637358i
$502$	−0.201613	+	6.54635i	−0.00899844	+	0.292178i
$503$	18.6089	+	32.2316i	0.829730	+	1.43714i	0.898250	+	0.439485i	$0.144839\pi$
$503$	18.6089	+	32.2316i	0.829730	+	1.43714i	−0.0685195	+	0.997650i	$0.521828\pi$
$504$	−4.19280	−	7.37702i	−0.186762	−	0.328599i
$505$	−2.32435	+	4.02588i	−0.103432	+	0.179150i
$506$	−25.7604	−	15.9497i	−1.14519	−	0.709052i
$507$	6.50232	−	1.43583i	0.288778	−	0.0637674i
$508$	9.62785	−	4.79439i	0.427167	−	0.212716i
$509$	29.8753	−	5.26783i	1.32420	−	0.233492i	0.533555	−	0.845766i	$-0.320856\pi$
$509$	29.8753	−	5.26783i	1.32420	−	0.233492i	0.790646	+	0.612273i	$0.209745\pi$
$510$	−1.64035	+	2.92165i	−0.0726360	+	0.129373i
$511$	7.19398	−	8.57345i	0.318243	−	0.379267i
$512$	−6.18997	+	21.7643i	−0.273561	+	0.961855i
$513$	1.77609	+	2.32671i	0.0784164	+	0.102727i
$514$	−8.28937	−	3.30948i	−0.365629	−	0.145975i
$515$	−26.5307	−	22.2619i	−1.16908	−	0.980976i
$516$	4.12402	+	26.2633i	0.181550	+	1.15618i
$517$	−1.85414	−	10.5154i	−0.0815451	−	0.462465i
$518$	9.31803	+	8.32076i	0.409411	+	0.365593i
$519$	27.7119	−	25.3506i	1.21642	−	1.11277i
$520$	−20.6206	+	5.41277i	−0.904275	+	0.237366i
$521$	−26.1048	−	15.0716i	−1.14367	−	0.660299i	−0.196334	−	0.980537i	$-0.562904\pi$
$521$	−26.1048	−	15.0716i	−1.14367	−	0.660299i	−0.947337	+	0.320238i	$0.896237\pi$
$522$	13.2433	+	20.2840i	0.579642	+	0.887808i
$523$	−18.6358	+	10.7594i	−0.814886	+	0.470474i	−0.848650	−	0.528955i	$-0.822584\pi$
$523$	−18.6358	+	10.7594i	−0.814886	+	0.470474i	0.0337640	+	0.999430i	$0.489251\pi$
$524$	−27.3965	−	11.9283i	−1.19682	−	0.521091i
$525$	0.965628	−	1.85117i	0.0421435	−	0.0807919i
$526$	3.02001	+	9.16601i	0.131679	+	0.399657i
$527$	1.28772	−	1.08052i	0.0560939	−	0.0470684i
$528$	10.4729	−	22.8705i	0.455772	−	0.995309i
$529$	−11.1069	+	4.04259i	−0.482910	+	0.175765i
$530$	5.54206	−	0.802175i	0.240732	−	0.0348442i
$531$	11.2676	−	5.23124i	0.488971	−	0.227016i
$532$	−1.08041	+	0.319458i	−0.0468418	+	0.0138502i
$533$	21.8521	+	3.85311i	0.946519	+	0.166897i
$534$	−2.19244	−	5.80577i	−0.0948760	−	0.251240i
$535$	4.87131	−	13.3838i	0.210605	−	0.578632i
$536$	12.8506	−	8.90082i	0.555062	−	0.384457i
$537$	−10.4647	+	13.6143i	−0.451586	+	0.587501i
$538$	−6.86016	−	12.7749i	−0.295762	−	0.550764i
$539$	−3.63071			−0.156386
$540$	−6.18754	−	25.1377i	−0.266269	−	1.08175i
$541$	24.3595			1.04730			0.523649	−	0.851934i	$-0.324571\pi$
$541$	24.3595			1.04730			0.523649	+	0.851934i	$0.324571\pi$
$542$	10.5925	+	19.7252i	0.454988	+	0.847271i
$543$	−6.38501	−	0.846034i	−0.274007	−	0.0363068i
$544$	−3.06955	−	0.476296i	−0.131606	−	0.0204210i
$545$	−10.0625	+	27.6464i	−0.431029	+	1.18424i
$546$	7.31399	+	1.19927i	0.313010	+	0.0513242i
$547$	−11.3225	−	1.99646i	−0.484115	−	0.0853625i	−0.0737361	−	0.997278i	$-0.523492\pi$
$547$	−11.3225	−	1.99646i	−0.484115	−	0.0853625i	−0.410378	+	0.911915i	$0.634603\pi$
$548$	8.28669	+	28.0258i	0.353990	+	1.19720i
$549$	8.54138	+	12.2419i	0.364537	+	0.522471i
$550$	6.12564	−	0.886644i	0.261198	−	0.0378066i
$551$	3.02248	−	1.10009i	0.128762	−	0.0468656i
$552$	−13.1959	−	25.7205i	−0.561653	−	1.09474i
$553$	−10.1627	+	8.52755i	−0.432163	+	0.362628i
$554$	9.56714	+	29.0372i	0.406469	+	1.23367i
$555$	20.4515	+	32.1617i	0.868118	+	1.36519i
$556$	18.5317	−	42.5631i	0.785921	−	1.80508i
$557$	−25.4046	+	14.6674i	−1.07643	+	0.621476i	−0.929931	−	0.367735i	$-0.880133\pi$
$557$	−25.4046	+	14.6674i	−1.07643	+	0.621476i	−0.146497	+	0.989211i	$0.546800\pi$
$558$	−1.55128	+	12.8949i	−0.0656709	+	0.545884i
$559$	−20.1103	−	11.6107i	−0.850575	−	0.491080i
$560$	9.88883	+	1.22403i	0.417879	+	0.0517246i
$561$	3.29248	+	1.04114i	0.139008	+	0.0439570i
$562$	−34.5614	−	30.8625i	−1.45789	−	1.30185i
$563$	−4.92281	−	27.9187i	−0.207472	−	1.17663i	−0.893502	−	0.449058i	$-0.851759\pi$
$563$	−4.92281	−	27.9187i	−0.207472	−	1.17663i	0.686031	−	0.727573i	$-0.259352\pi$
$564$	3.66351	−	9.50610i	0.154262	−	0.400279i
$565$	35.0219	+	29.3869i	1.47338	+	1.23631i
$566$	−19.1005	−	7.62575i	−0.802854	−	0.320534i
$567$	−1.59247	+	8.85799i	−0.0668772	+	0.372001i
$568$	−25.2977	+	11.6399i	−1.06147	+	0.488398i
$569$	23.6131	−	28.1410i	0.989913	−	1.17973i	0.00620072	−	0.999981i	$-0.498026\pi$
$569$	23.6131	−	28.1410i	0.989913	−	1.17973i	0.983712	−	0.179751i	$-0.0575293\pi$
$570$	−3.43709	+	0.0412783i	−0.143964	+	0.00172896i
$571$	−4.89103	+	0.862420i	−0.204683	+	0.0360911i	−0.275049	−	0.961430i	$-0.588694\pi$
$571$	−4.89103	+	0.862420i	−0.204683	+	0.0360911i	0.0703665	+	0.997521i	$0.477583\pi$
$572$	9.79404	+	19.6679i	0.409509	+	0.822357i
$573$	6.54698	−	20.7040i	0.273504	−	0.864921i
$574$	−8.81759	−	5.45947i	−0.368039	−	0.227874i
$575$	3.55656	−	6.16014i	0.148319	−	0.256896i
$576$	19.8216	−	13.5316i	0.825901	−	0.563815i
$577$	1.91829	+	3.32257i	0.0798594	+	0.138321i	0.903189	−	0.429243i	$-0.141220\pi$
$577$	1.91829	+	3.32257i	0.0798594	+	0.138321i	−0.823330	+	0.567563i	$0.807886\pi$
$578$	−0.726952	+	23.6040i	−0.0302372	+	0.981797i
$579$	−24.1202	+	15.3379i	−1.00240	+	0.637423i
$580$	−28.3930	−	1.75054i	−1.17895	−	0.0726874i
$581$	−0.351830	−	0.419295i	−0.0145964	−	0.0173953i
$582$	−42.7415	−	14.9779i	−1.77169	−	0.620852i
$583$	−1.97385	−	5.42312i	−0.0817487	−	0.224603i
$584$	25.8376	+	18.2887i	1.06917	+	0.756792i
$585$	20.4778	+	9.59068i	0.846654	+	0.396526i
$586$	−18.9059	+	14.8967i	−0.780996	+	0.615377i
$587$	−3.42835	+	19.4432i	−0.141503	+	0.802505i	0.828605	+	0.559834i	$0.189135\pi$
$587$	−3.42835	+	19.4432i	−0.141503	+	0.802505i	−0.970108	+	0.242672i	$0.921976\pi$
$588$	−2.96695	−	1.78808i	−0.122355	−	0.0737391i
$589$	1.62049	+	0.589811i	0.0667712	+	0.0243027i
$590$	−2.97423	+	14.2816i	−0.122447	+	0.587966i
$591$	0.438123	−	3.30651i	0.0180220	−	0.136012i
$592$	−21.2921	+	28.1981i	−0.875101	+	1.15893i
$593$		−	11.3018i		−	0.464109i	−0.972703	−	0.232054i	$-0.925455\pi$
$593$		−	11.3018i		−	0.464109i	0.972703	−	0.232054i	$-0.0745447\pi$
$594$	−24.0626	+	11.5249i	−0.987300	+	0.472871i
$595$			1.36789i			0.0560781i
$596$	32.4019	−	3.67566i	1.32723	−	0.150561i
$597$	−3.68029	−	2.82888i	−0.150624	−	0.115778i
$598$	24.7200	+	5.14808i	1.01088	+	0.210521i
$599$	23.0144	+	8.37655i	0.940342	+	0.342256i	0.766301	−	0.642482i	$-0.222095\pi$
$599$	23.0144	+	8.37655i	0.940342	+	0.342256i	0.174041	+	0.984738i	$0.444317\pi$
$600$	5.44241	+	2.29225i	0.222186	+	0.0935807i
$601$	−1.05731	+	5.99629i	−0.0431285	+	0.244594i	−0.998749	−	0.0500071i	$-0.984076\pi$
$601$	−1.05731	+	5.99629i	−0.0431285	+	0.244594i	0.955620	+	0.294601i	$0.0951867\pi$
$602$	6.71715	+	8.52495i	0.273770	+	0.347451i
$603$	−16.5148	−	1.47269i	−0.672536	−	0.0599726i
$604$	15.0944	+	3.63166i	0.614182	+	0.147770i
$605$	−1.85910	−	5.10784i	−0.0755832	−	0.207663i
$606$	2.98008	+	3.46612i	0.121057	+	0.140802i
$607$	−0.0408195	−	0.0486467i	−0.00165681	−	0.00197451i	0.765215	−	0.643774i	$-0.222632\pi$
$607$	−0.0408195	−	0.0486467i	−0.00165681	−	0.00197451i	−0.766872	+	0.641800i	$0.778188\pi$
$608$	−1.15133	−	2.97140i	−0.0466925	−	0.120506i
$609$	8.76837	+	4.57384i	0.355312	+	0.185342i
$610$	−17.5207	−	0.539598i	−0.709390	−	0.0218477i
$611$	4.44929	+	7.70640i	0.179999	+	0.311768i
$612$	2.17780	+	2.47230i	0.0880323	+	0.0999370i
$613$	−14.5945	+	25.2785i	−0.589468	+	1.02099i	0.404834	+	0.914390i	$0.367329\pi$
$613$	−14.5945	+	25.2785i	−0.589468	+	1.02099i	−0.994302	+	0.106598i	$0.966004\pi$
$614$	6.51492	−	10.5222i	0.262921	−	0.424643i
$615$	−21.3568	−	23.3460i	−0.861188	−	0.941401i
$616$	−0.842857	−	10.2345i	−0.0339597	−	0.412362i
$617$	22.5504	−	3.97624i	0.907845	−	0.160078i	0.299820	−	0.953996i	$-0.403073\pi$
$617$	22.5504	−	3.97624i	0.907845	−	0.160078i	0.608025	+	0.793918i	$0.291962\pi$
$618$	−29.2861	+	17.3806i	−1.17806	+	0.699149i
$619$	15.4711	−	18.4377i	0.621835	−	0.741074i	−0.359550	−	0.933126i	$-0.617070\pi$
$619$	15.4711	−	18.4377i	0.621835	−	0.741074i	0.981385	+	0.192052i	$0.0615141\pi$
$620$	−11.0580	−	10.5040i	−0.444101	−	0.421850i
$621$	−6.71144	+	29.9181i	−0.269321	+	1.20057i
$622$	−9.85067	+	24.6734i	−0.394976	+	0.989311i
$623$	−1.94082	−	1.62854i	−0.0777574	−	0.0652462i
$624$	−1.68270	+	20.8957i	−0.0673619	+	0.836497i
$625$	−5.13549	−	29.1248i	−0.205420	−	1.16499i
$626$	−0.0144618	+	0.0161951i	−0.000578009	+	0.000647285i
$627$	0.763849	+	3.45919i	0.0305052	+	0.138147i
$628$	38.6602	−	28.5778i	1.54271	−	1.14038i
$629$	−4.20076	−	2.42531i	−0.167495	−	0.0967035i
$630$	−7.22674	−	7.71182i	−0.287920	−	0.307246i
$631$	1.68101	−	0.970532i	0.0669200	−	0.0386363i	−0.466167	−	0.884697i	$-0.654365\pi$
$631$	1.68101	−	0.970532i	0.0669200	−	0.0386363i	0.533087	+	0.846061i	$0.321032\pi$
$632$	−26.3974	−	26.6679i	−1.05003	−	1.06079i
$633$	−22.2331	+	0.952094i	−0.883685	+	0.0378423i
$634$	−7.21595	+	2.37750i	−0.286582	+	0.0944227i
$635$	10.2623	−	8.61105i	0.407245	−	0.341719i
$636$	1.05782	−	5.40377i	0.0419454	−	0.214273i
$637$	2.84332	−	1.03488i	0.112656	−	0.0410036i
$638$	4.19972	+	29.0150i	0.166269	+	1.14871i
$639$	28.5170	+	7.69224i	1.12812	+	0.304300i
$640$	−1.15473	+	28.1596i	−0.0456448	+	1.11311i
$641$	20.2372	+	3.56837i	0.799322	+	0.140942i	0.558367	−	0.829594i	$-0.311428\pi$
$641$	20.2372	+	3.56837i	0.799322	+	0.140942i	0.240955	+	0.970536i	$0.422539\pi$
$642$	−10.8358	−	8.87275i	−0.427654	−	0.350180i
$643$	9.60776	−	26.3971i	0.378893	−	1.04100i	−0.592923	−	0.805259i	$-0.702026\pi$
$643$	9.60776	−	26.3971i	0.378893	−	1.04100i	0.971816	−	0.235741i	$-0.0757516\pi$
$644$	−9.83804	−	6.51859i	−0.387673	−	0.256868i
$645$	12.6461	+	30.6028i	0.497940	+	1.20498i
$646$	0.385407	−	0.206965i	0.0151636	−	0.00814293i
$647$	−9.07554			−0.356796			−0.178398	−	0.983958i	$-0.557091\pi$
$647$	−9.07554			−0.356796			−0.178398	+	0.983958i	$0.557091\pi$
$648$	−25.3393	−	2.43262i	−0.995423	−	0.0955624i
$649$	15.0344			0.590153
$650$	−4.54445	+	2.44038i	−0.178248	+	0.0957198i
$651$	2.02499	+	4.90035i	0.0793658	+	0.192060i
$652$	29.0011	+	19.2158i	1.13577	+	0.752550i
$653$	12.5761	−	34.5525i	0.492140	−	1.35214i	−0.406578	−	0.913616i	$-0.633278\pi$
$653$	12.5761	−	34.5525i	0.492140	−	1.35214i	0.898718	−	0.438528i	$-0.144500\pi$
$654$	22.3831	+	18.3281i	0.875247	+	0.716685i
$655$	−36.6521	−	6.46275i	−1.43211	−	0.252520i
$656$	13.3427	−	26.1232i	0.520943	−	1.01994i
$657$	−8.63575	−	32.4460i	−0.336913	−	1.26584i
$658$	−0.595788	−	4.11618i	−0.0232262	−	0.160465i
$659$	22.3941	−	8.15079i	0.872351	−	0.317510i	0.133232	−	0.991085i	$-0.457464\pi$
$659$	22.3941	−	8.15079i	0.872351	−	0.317510i	0.739119	+	0.673575i	$0.235242\pi$
$660$	6.01892	−	30.7470i	0.234286	−	1.19683i
$661$	33.9453	−	28.4835i	1.32032	−	1.10788i	0.334083	−	0.942544i	$-0.391573\pi$
$661$	33.9453	−	28.4835i	1.32032	−	1.10788i	0.986237	−	0.165337i	$-0.0528711\pi$
$662$	28.3369	−	9.33643i	1.10135	−	0.362870i
$663$	−2.87520	+	0.123126i	−0.111664	+	0.00478180i
$664$	1.10027	−	1.08911i	0.0426986	−	0.0422655i
$665$	−1.21528	+	0.701643i	−0.0471266	+	0.0272086i
$666$	36.4960	−	8.51987i	1.41419	−	0.330138i
$667$	29.1784	+	16.8462i	1.12979	+	0.652286i
$668$	−1.32588	+	0.980099i	−0.0513000	+	0.0379212i
$669$	−1.69164	−	7.66080i	−0.0654026	−	0.296184i
$670$	12.9685	−	14.5228i	0.501018	−	0.561066i
$671$	3.13701	+	17.7909i	0.121103	+	0.686810i
$672$	4.35162	−	8.77858i	0.167867	−	0.338641i
$673$	−19.6838	−	16.5166i	−0.758753	−	0.636669i	0.179049	−	0.983840i	$-0.442698\pi$
$673$	−19.6838	−	16.5166i	−0.758753	−	0.636669i	−0.937802	+	0.347171i	$0.887142\pi$
$674$	6.80672	−	17.0490i	0.262185	−	0.656705i
$675$	−2.87830	−	5.56318i	−0.110786	−	0.214127i
$676$	5.57489	+	5.29557i	0.214419	+	0.203676i
$677$	22.8885	−	27.2774i	0.879675	−	1.04836i	−0.118787	−	0.992920i	$-0.537901\pi$
$677$	22.8885	−	27.2774i	0.879675	−	1.04836i	0.998462	−	0.0554361i	$-0.0176549\pi$
$678$	38.6591	−	22.9432i	1.48470	−	0.881130i
$679$	−18.2086	+	3.21067i	−0.698783	+	0.123214i
$680$	−3.85593	+	0.317552i	−0.147868	+	0.0121776i
$681$	35.0671	+	38.3333i	1.34377	+	1.46894i
$682$	−8.27450	+	13.3641i	−0.316847	+	0.511739i
$683$	−19.7570	+	34.2201i	−0.755979	+	1.30939i	0.188906	+	0.981995i	$0.439506\pi$
$683$	−19.7570	+	34.2201i	−0.755979	+	1.30939i	−0.944886	+	0.327400i	$0.893828\pi$
$684$	−1.07940	+	3.20297i	−0.0412720	+	0.122468i
$685$	18.2005	+	31.5243i	0.695407	+	1.20448i
$686$	−1.41354	−	0.0435341i	−0.0539693	−	0.00166214i
$687$	0.130799	+	0.0682287i	0.00499029	+	0.00260309i
$688$	−22.4715	+	20.9139i	−0.856717	+	0.797335i
$689$	3.09157	+	3.68439i	0.117779	+	0.140364i
$690$	−23.4738	−	27.3023i	−0.893631	−	1.03938i
$691$	−14.0564	−	38.6198i	−0.534732	−	1.46917i	−0.853379	−	0.521292i	$-0.825450\pi$
$691$	−14.0564	−	38.6198i	−0.534732	−	1.46917i	0.318646	−	0.947874i	$-0.396772\pi$
$692$	42.1650	+	10.1448i	1.60287	+	0.385646i
$693$	−6.26238	+	8.91185i	−0.237888	+	0.338533i
$694$	13.2437	+	16.8081i	0.502725	+	0.638025i
$695$	10.0405	−	56.9424i	0.380857	−	2.15995i
$696$	−10.8576	+	25.7788i	−0.411556	+	0.977144i
$697$	3.78402	+	1.37727i	0.143330	+	0.0521678i
$698$	45.9685	+	9.57321i	1.73993	+	0.362351i
$699$	−1.14560	−	0.880570i	−0.0433304	−	0.0333062i
$700$	2.39552	−	0.271747i	0.0905423	−	0.0102711i
$701$			2.91498i			0.110097i	0.998484	+	0.0550486i	$0.0175314\pi$
$701$			2.91498i			0.110097i	−0.998484	+	0.0550486i	$0.982469\pi$
$702$	15.5591	−	15.8842i	0.587242	−	0.599510i
$703$		−	4.97613i		−	0.187678i
$704$	28.6543	−	4.75183i	1.07995	−	0.179091i
$705$	1.66677	−	12.5791i	0.0627741	−	0.473756i
$706$	7.46619	−	35.8511i	0.280994	−	1.34927i
$707$	1.75360	+	0.638257i	0.0659508	+	0.0240041i
$708$	12.2859	+	7.40427i	0.461731	+	0.278270i
$709$	−6.81471	+	38.6481i	−0.255932	+	1.45146i	0.537738	+	0.843112i	$0.319279\pi$
$709$	−6.81471	+	38.6481i	−0.255932	+	1.45146i	−0.793670	+	0.608349i	$0.791832\pi$
$710$	−27.2436	+	21.4663i	−1.02243	+	0.805616i
$711$	3.40246	+	39.6538i	0.127602	+	1.48713i
$712$	4.14012	−	5.84902i	0.155158	−	0.219201i
$713$	6.17825	+	16.9746i	0.231377	+	0.635704i
$714$	1.26938	+	0.444826i	0.0475052	+	0.0166472i
$715$	17.5908	+	20.9639i	0.657858	+	0.784005i
$716$	−19.7903	−	1.22016i	−0.739600	−	0.0455994i
$717$	9.78079	−	6.21956i	0.365270	−	0.232274i
$718$	−1.03232	+	33.5192i	−0.0385258	+	1.25093i
$719$	11.7507	+	20.3527i	0.438226	+	0.759029i	0.997553	−	0.0699179i	$-0.0222737\pi$
$719$	11.7507	+	20.3527i	0.438226	+	0.759029i	−0.559327	+	0.828947i	$0.688940\pi$
$720$	20.0611	−	22.1616i	0.747632	−	0.825915i
$721$	−6.95149	+	12.0403i	−0.258887	+	0.448406i
$722$	−22.4640	−	13.9087i	−0.836023	−	0.517630i
$723$	−0.615969	+	1.94792i	−0.0229081	+	0.0724440i
$724$	−3.31521	−	6.65744i	−0.123209	−	0.247422i
$725$	−6.77824	+	1.19519i	−0.251737	+	0.0443881i
$726$	−5.34453	+	0.0641860i	−0.198354	+	0.00238217i
$727$	−1.03813	+	1.23720i	−0.0385022	+	0.0458852i	−0.784952	−	0.619557i	$-0.787312\pi$
$727$	−1.03813	+	1.23720i	−0.0385022	+	0.0458852i	0.746450	+	0.665442i	$0.231757\pi$
$728$	3.57728	+	7.77474i	0.132583	+	0.288151i
$729$	18.9959	+	19.1874i	0.703551	+	0.710645i
$730$	36.6174	+	14.6192i	1.35527	+	0.541083i
$731$	−3.22825	−	2.70883i	−0.119401	−	0.100190i
$732$	−6.19828	+	16.0833i	−0.229095	+	0.594456i
$733$	−0.383263	−	2.17359i	−0.0141561	−	0.0802835i	0.976911	−	0.213646i	$-0.0685338\pi$
$733$	−0.383263	−	2.17359i	−0.0141561	−	0.0802835i	−0.991067	+	0.133362i	$0.957423\pi$
$734$	−16.9363	−	15.1237i	−0.625130	−	0.558225i
$735$	−4.11388	−	1.30088i	−0.151743	−	0.0479838i
$736$	16.0913	−	29.2456i	0.593132	−	1.07801i
$737$	−17.3778	−	10.0331i	−0.640120	−	0.369573i
$738$	−28.6096	+	12.2267i	−1.05313	+	0.450072i
$739$	−4.17900	+	2.41275i	−0.153727	+	0.0887543i	−0.574890	−	0.818231i	$-0.694955\pi$
$739$	−4.17900	+	2.41275i	−0.153727	+	0.0887543i	0.421163	+	0.906985i	$0.361622\pi$
$740$	−17.5686	+	40.3509i	−0.645834	+	1.48333i
$741$	−1.58419	−	2.49127i	−0.0581965	−	0.0915190i
$742$	−0.703454	−	2.13505i	−0.0258246	−	0.0783802i
$743$	16.7351	−	14.0425i	0.613953	−	0.515168i	−0.281943	−	0.959431i	$-0.590979\pi$
$743$	16.7351	−	14.0425i	0.613953	−	0.515168i	0.895896	+	0.444263i	$0.146535\pi$
$744$	−13.3434	+	6.84583i	−0.489194	+	0.250980i
$745$	38.1671	−	13.8917i	1.39833	−	0.508952i
$746$	−31.0441	+	4.49343i	−1.13661	+	0.164516i
$747$	−1.63604	+	0.140379i	−0.0598596	+	0.00513619i
$748$	1.13060	+	3.82373i	0.0413390	+	0.139809i
$749$	−5.63065	−	0.992836i	−0.205740	−	0.0362774i
$750$	−22.8487	−	3.74651i	−0.834317	−	0.136803i
$751$	8.66801	−	23.8152i	0.316300	−	0.869027i	−0.675049	−	0.737773i	$-0.735877\pi$
$751$	8.66801	−	23.8152i	0.316300	−	0.869027i	0.991349	−	0.131254i	$-0.0419004\pi$
$752$	11.4647	−	2.63501i	0.418075	−	0.0960891i
$753$	7.95191	+	1.05365i	0.289784	+	0.0383972i
$754$	−11.5593	−	21.5255i	−0.420963	−	0.783911i
$755$	19.3371			0.703749
$756$	−9.50647	+	4.19845i	−0.345747	+	0.152696i
$757$	−49.2601			−1.79039			−0.895194	−	0.445676i	$-0.852963\pi$
$757$	−49.2601			−1.79039			−0.895194	+	0.445676i	$0.852963\pi$
$758$	10.5981	+	19.7355i	0.384939	+	0.716827i
$759$	−22.6144	+	29.4207i	−0.820850	+	1.06790i
$760$	−2.25997	−	3.26285i	−0.0819779	−	0.118356i
$761$	−5.63156	+	15.4726i	−0.204144	+	0.560880i	−0.998942	−	0.0459938i	$-0.985355\pi$
$761$	−5.63156	+	15.4726i	−0.204144	+	0.560880i	0.794798	+	0.606874i	$0.207577\pi$
$762$	−4.65369	−	12.3234i	−0.168585	−	0.446429i
$763$	11.6310	+	2.05086i	0.421071	+	0.0742462i
$764$	24.0446	−	7.10954i	0.869905	−	0.257214i
$765$	3.35760	+	2.35939i	0.121394	+	0.0853040i
$766$	29.8702	−	4.32351i	1.07926	−	0.156215i
$767$	−11.7739	+	4.28536i	−0.425132	+	0.154735i
$768$	25.7560	+	10.2288i	0.929390	+	0.369100i
$769$	10.1793	−	8.54142i	0.367074	−	0.308012i	−0.440529	−	0.897738i	$-0.645209\pi$
$769$	10.1793	−	8.54142i	0.367074	−	0.308012i	0.807603	+	0.589727i	$0.200765\pi$
$770$	−4.00260	−	12.1483i	−0.144244	−	0.437793i
$771$	−5.05575	+	9.69221i	−0.182078	+	0.349056i
$772$	−30.2619	−	13.1759i	−1.08915	−	0.474209i
$773$	−7.80887	+	4.50846i	−0.280866	+	0.162158i	−0.633815	−	0.773484i	$-0.718512\pi$
$773$	−7.80887	+	4.50846i	−0.280866	+	0.162158i	0.352950	+	0.935642i	$0.385179\pi$
$774$	32.5111	−	1.78360i	1.16859	−	0.0641101i
$775$	−3.19579	−	1.84509i	−0.114796	−	0.0662777i
$776$	−13.2776	−	50.5827i	−0.476638	−	1.81581i
$777$	11.2890	−	10.3271i	0.404991	−	0.370484i
$778$	35.2383	+	31.4669i	1.26335	+	1.12814i
$779$	0.717351	+	4.06830i	0.0257018	+	0.145762i
$780$	4.05040	+	25.7945i	0.145028	+	0.923592i
$781$	27.3829	+	22.9770i	0.979838	+	0.822182i
$782$	4.25577	+	1.69909i	0.152186	+	0.0607592i
$783$	26.3508	−	13.6335i	0.941702	−	0.487221i
$784$	−0.205432	−	3.99472i	−0.00733685	−	0.142669i
$785$	38.4904	−	45.8710i	1.37378	−	1.63721i
$786$	−17.9162	+	31.9107i	−0.639049	+	1.13822i
$787$	−52.5231	+	9.26124i	−1.87225	+	0.330127i	−0.990046	−	0.140748i	$-0.955049\pi$
$787$	−52.5231	+	9.26124i	−1.87225	+	0.330127i	−0.882200	+	0.470875i	$0.843938\pi$
$788$	3.44759	−	1.71680i	0.122815	−	0.0611585i
$789$	11.5416	−	2.54859i	0.410893	−	0.0907324i
$790$	−39.7366	−	24.6032i	−1.41377	−	0.875344i
$791$	9.17633	−	15.8939i	0.326273	−	0.565121i
$792$	−26.5753	−	15.5841i	−0.944311	−	0.553756i
$793$	−7.52774	−	13.0384i	−0.267318	−	0.463008i
$794$	−0.106721	+	3.46520i	−0.00378738	+	0.122975i
$795$	−0.293428	−	6.85206i	−0.0104068	−	0.243018i
$796$	0.329839	−	5.34983i	0.0116908	−	0.189620i
$797$	−2.66663	−	3.17796i	−0.0944568	−	0.112569i	0.716746	−	0.697335i	$-0.245631\pi$
$797$	−2.66663	−	3.17796i	−0.0944568	−	0.112569i	−0.811202	+	0.584766i	$0.801186\pi$
$798$	0.255912	+	1.35592i	0.00905918	+	0.0479991i
$799$	0.552330	+	1.51751i	0.0195400	+	0.0536858i
$800$	1.32214	+	6.68962i	0.0467446	+	0.236514i
$801$	−7.34499	+	1.95493i	−0.259522	+	0.0690739i
$802$	7.17692	−	5.65498i	0.253426	−	0.199684i
$803$	7.05608	−	40.0170i	0.249004	−	1.41217i
$804$	−9.25964	−	16.7572i	−0.326562	−	0.590981i
$805$	−13.8129	−	5.02749i	−0.486841	−	0.177196i
$806$	2.67075	−	12.8244i	0.0940732	−	0.451720i
$807$	−16.4130	+	6.78243i	−0.577766	+	0.238753i
$808$	−1.39208	+	5.09136i	−0.0489733	+	0.179113i
$809$			13.1967i			0.463972i	0.972719	+	0.231986i	$0.0745223\pi$
$809$			13.1967i			0.463972i	−0.972719	+	0.231986i	$0.925478\pi$
$810$	−31.3942	+	4.43696i	−1.10308	+	0.155899i
$811$			16.5670i			0.581745i	0.956762	+	0.290873i	$0.0939456\pi$
$811$			16.5670i			0.581745i	−0.956762	+	0.290873i	$0.906054\pi$
$812$	1.28717	+	11.3468i	0.0451709	+	0.398193i
$813$	25.3428	−	10.4725i	0.888809	−	0.367287i
$814$	44.4037	+	9.24733i	1.55635	+	0.324119i
$815$	40.7184	+	14.8203i	1.42630	+	0.519132i
$816$	−0.959231	+	3.68149i	−0.0335798	+	0.128878i
$817$	0.750720	−	4.25755i	0.0262644	−	0.148953i
$818$	27.1324	+	34.4346i	0.948661	+	1.20398i
$819$	2.36406	−	8.76414i	0.0826069	−	0.306244i
$820$	8.54650	−	35.5221i	0.298457	−	1.24049i
$821$	9.16662	+	25.1851i	0.319917	+	0.878965i	0.990547	+	0.137173i	$0.0438017\pi$
$821$	9.16662	+	25.1851i	0.319917	+	0.878965i	−0.670630	+	0.741792i	$0.733976\pi$
$822$	35.1725	−	6.63832i	1.22678	−	0.231538i
$823$	25.2646	+	30.1092i	0.880670	+	1.04954i	0.998403	+	0.0564960i	$0.0179928\pi$
$823$	25.2646	+	30.1092i	0.880670	+	1.04954i	−0.117733	+	0.993045i	$0.537563\pi$
$824$	−35.5541	−	16.8003i	−1.23859	−	0.585267i
$825$	−0.324326	−	7.57358i	−0.0112916	−	0.263678i
$826$	5.85335	+	0.180271i	0.203664	+	0.00627242i
$827$	−5.32231	−	9.21851i	−0.185075	−	0.320559i	0.758527	−	0.651642i	$-0.225919\pi$
$827$	−5.32231	−	9.21851i	−0.185075	−	0.320559i	−0.943602	+	0.331083i	$0.892586\pi$
$828$	−32.9694	+	12.9047i	−1.14576	+	0.448470i
$829$	10.1671	−	17.6100i	0.353118	−	0.611619i	−0.633676	−	0.773599i	$-0.718455\pi$
$829$	10.1671	−	17.6100i	0.353118	−	0.611619i	0.986794	+	0.161980i	$0.0517879\pi$
$830$	1.01508	−	1.63946i	0.0352340	−	0.0569064i
$831$	36.5629	−	8.07374i	1.26835	−	0.280075i
$832$	−21.0856	+	11.8888i	−0.731013	+	0.412171i
$833$	0.540776	−	0.0953533i	0.0187368	−	0.00330380i
$834$	−49.5763	−	27.8345i	−1.71669	−	0.963829i
$835$	−1.32006	+	1.57319i	−0.0456826	+	0.0544423i
$836$	−2.81720	+	2.96580i	−0.0974349	+	0.102574i
$837$	15.5211	+	3.48180i	0.536487	+	0.120349i
$838$	17.2263	−	43.1472i	0.595071	−	1.49050i
$839$	3.87598	+	3.25233i	0.133814	+	0.112283i	0.707238	−	0.706975i	$-0.249941\pi$
$839$	3.87598	+	3.25233i	0.133814	+	0.112283i	−0.573424	+	0.819259i	$0.694385\pi$
$840$	2.71202	−	11.8986i	0.0935735	−	0.410539i
$841$	−0.625385	−	3.54673i	−0.0215650	−	0.122301i
$842$	−33.5795	+	37.6041i	−1.15722	+	1.29592i
$843$	−41.8720	+	38.3042i	−1.44215	+	1.31927i
$844$	−15.2745	−	20.6634i	−0.525769	−	0.711264i
$845$	8.29398	+	4.78853i	0.285322	+	0.164731i
$846$	−11.1311	−	5.63732i	−0.382695	−	0.193815i
$847$	−1.88971	+	1.09103i	−0.0649313	+	0.0374881i
$848$	5.85515	−	2.47860i	0.201067	−	0.0851155i
$849$	−11.6495	+	22.3329i	−0.399811	+	0.766464i
$850$	−0.889096	+	0.292939i	−0.0304957	+	0.0100477i
$851$	39.9300	−	33.5052i	1.36878	−	1.14854i
$852$	11.0609	+	32.2621i	0.378941	+	1.10528i
$853$	21.9032	−	7.97212i	0.749952	−	0.272960i	0.0613664	−	0.998115i	$-0.480454\pi$
$853$	21.9032	−	7.97212i	0.749952	−	0.272960i	0.688586	+	0.725155i	$0.258232\pi$
$854$	1.00801	+	6.96414i	0.0344934	+	0.238308i
$855$	−0.373925	+	4.19322i	−0.0127880	+	0.143405i
$856$	1.49155	−	16.1026i	0.0509802	−	0.550377i
$857$	−0.961708	−	0.169575i	−0.0328513	−	0.00579257i	0.157198	−	0.987567i	$-0.449754\pi$
$857$	−0.961708	−	0.169575i	−0.0328513	−	0.00579257i	−0.190050	+	0.981774i	$0.560865\pi$
$858$	25.1744	−	9.50662i	0.859439	−	0.324551i
$859$	10.0504	−	27.6131i	0.342914	−	0.942148i	−0.641631	−	0.767014i	$-0.721742\pi$
$859$	10.0504	−	27.6131i	0.342914	−	0.942148i	0.984545	−	0.175134i	$-0.0560359\pi$
$860$	−21.1191	+	31.8735i	−0.720155	+	1.08688i
$861$	−7.74074	+	10.0705i	−0.263804	+	0.343201i
$862$	19.5779	−	10.5134i	0.666825	−	0.358088i
$863$	23.7496			0.808444			0.404222	−	0.914661i	$-0.367542\pi$
$863$	23.7496			0.808444			0.404222	+	0.914661i	$0.367542\pi$
$864$	−14.0418	−	25.8230i	−0.477713	−	0.878516i
$865$	54.0167			1.83662
$866$	−28.3320	+	15.2144i	−0.962760	+	0.517006i
$867$	28.6720	+	3.79913i	0.973752	+	0.129025i
$868$	−3.38175	+	5.10384i	−0.114784	+	0.173236i
$869$	−16.4740	+	45.2620i	−0.558843	+	1.53541i
$870$	−5.63747	+	34.3811i	−0.191128	+	1.16563i
$871$	16.4689	+	2.90391i	0.558026	+	0.0983951i
$872$	−3.08104	+	33.2626i	−0.104337	+	1.12641i
$873$	−23.5261	+	50.2323i	−0.796236	+	1.70011i
$874$	0.673416	+	4.65249i	0.0227786	+	0.157373i
$875$	−8.88246	+	3.23295i	−0.300282	+	0.109294i
$876$	25.4740	−	29.2261i	0.860686	−	0.987459i
$877$	11.9806	−	10.0529i	0.404556	−	0.339463i	−0.417695	−	0.908587i	$-0.637162\pi$
$877$	11.9806	−	10.0529i	0.404556	−	0.339463i	0.822252	+	0.569124i	$0.192718\pi$
$878$	−30.5936	+	10.0799i	−1.03248	+	0.340182i
$879$	15.8183	+	24.8757i	0.533539	+	0.839035i
$880$	33.3153	−	14.1030i	1.12306	−	0.475413i
$881$	−33.2947	+	19.2227i	−1.12173	+	0.647629i	−0.941841	−	0.336058i	$-0.890906\pi$
$881$	−33.2947	+	19.2227i	−1.12173	+	0.647629i	−0.179886	+	0.983688i	$0.557573\pi$
$882$	−2.54499	+	3.39456i	−0.0856942	+	0.114301i
$883$	29.5182	+	17.0423i	0.993366	+	0.573520i	0.906279	−	0.422680i	$-0.138911\pi$
$883$	29.5182	+	17.0423i	0.993366	+	0.573520i	0.0870873	+	0.996201i	$0.472244\pi$
$884$	−1.97531	−	2.67221i	−0.0664369	−	0.0898763i
$885$	17.0352	+	5.38685i	0.572633	+	0.181077i
$886$	−26.2141	+	29.3560i	−0.880681	+	0.986234i
$887$	−9.36825	−	53.1300i	−0.314555	−	1.78393i	−0.574704	−	0.818361i	$-0.694883\pi$
$887$	−9.36825	−	53.1300i	−0.314555	−	1.78393i	0.260150	−	0.965568i	$-0.416228\pi$
$888$	31.7317	+	29.4250i	1.06485	+	0.987439i
$889$	−4.11961	−	3.45676i	−0.138167	−	0.115936i
$890$	3.30945	−	8.28930i	0.110933	−	0.277858i
$891$	11.0732	+	30.7430i	0.370967	+	1.02993i
$892$	6.23904	−	6.56813i	0.208898	−	0.219917i
$893$	−1.06490	+	1.26910i	−0.0356355	+	0.0424687i
$894$	−0.479614	−	39.9357i	−0.0160407	−	1.33565i
$895$	−24.3212	+	4.28848i	−0.812968	+	0.143348i
$896$	11.2130	−	1.50645i	0.374599	−	0.0503269i
$897$	9.32406	−	29.4861i	0.311321	−	0.984514i
$898$	−1.29851	+	2.09722i	−0.0433318	+	0.0699851i
$899$	8.73956	−	15.1374i	0.291481	−	0.504859i
$900$	3.46486	−	6.34871i	0.115495	−	0.211624i
$901$	0.436423	+	0.755907i	0.0145394	+	0.0251829i
$902$	−37.6359	−	1.15910i	−1.25314	−	0.0385939i
$903$	11.2168	−	7.13271i	0.373272	−	0.237362i
$904$	46.9332	+	22.1773i	1.56098	+	0.737606i
$905$	−5.95435	−	7.09612i	−0.197929	−	0.235883i
$906$	6.28824	−	17.9444i	0.208913	−	0.596163i
$907$	7.77481	+	21.3611i	0.258158	+	0.709284i	0.999281	+	0.0379147i	$0.0120715\pi$
$907$	7.77481	+	21.3611i	0.258158	+	0.709284i	−0.741123	+	0.671370i	$0.765706\pi$
$908$	−14.0331	+	58.3261i	−0.465704	+	1.93562i
$909$	4.59132	−	3.20345i	0.152284	−	0.106252i
$910$	6.59725	+	8.37278i	0.218697	+	0.277555i
$911$	8.74450	−	49.5925i	0.289718	−	1.64307i	−0.398210	−	0.917294i	$-0.630368\pi$
$911$	8.74450	−	49.5925i	0.289718	−	1.64307i	0.687928	−	0.725779i	$-0.258521\pi$
$912$	−3.76278	+	1.03616i	−0.124598	+	0.0343106i
$913$	−1.86742	−	0.679686i	−0.0618027	−	0.0224943i
$914$	−13.0057	−	2.70851i	−0.430191	−	0.0895896i
$915$	−2.82000	+	21.2825i	−0.0932262	+	0.703577i
$916$	0.0192009	+	0.169261i	0.000634417	+	0.00559255i
$917$			14.9403i			0.493374i
$918$	3.28132	−	2.34853i	0.108300	−	0.0775129i
$919$		−	20.3505i		−	0.671300i	−0.941987	−	0.335650i	$-0.891044\pi$
$919$		−	20.3505i		−	0.671300i	0.941987	−	0.335650i	$-0.108956\pi$
$920$	10.9653	−	40.1041i	0.361515	−	1.32219i
$921$	−12.0173	−	9.23721i	−0.395985	−	0.304376i
$922$	−4.28800	+	20.5901i	−0.141218	+	0.678098i
$923$	−27.9937	−	10.1889i	−0.921423	−	0.335371i
$924$	−12.5749	−	0.236172i	−0.413685	−	0.00776950i
$925$	−1.84905	+	10.4865i	−0.0607965	+	0.344794i
$926$	−30.8744	+	24.3271i	−1.01459	+	0.799439i
$927$	17.5637	+	37.8306i	0.576869	+	1.24252i
$928$	−31.6864	+	6.26250i	−1.04016	+	0.205577i
$929$	11.1334	+	30.5887i	0.365274	+	1.00358i	0.977136	+	0.212618i	$0.0681988\pi$
$929$	11.1334	+	30.5887i	0.365274	+	1.00358i	−0.611861	+	0.790965i	$0.709579\pi$
$930$	−14.1640	+	12.1779i	−0.464457	+	0.399328i
$931$	0.362099	+	0.431533i	0.0118673	+	0.0141429i
$932$	0.102672	−	1.66529i	0.00336313	−	0.0545483i
$933$	28.8489	+	15.0485i	0.944471	+	0.492664i
$934$	−0.680893	+	22.1085i	−0.0222795	+	0.723411i
$935$	2.48321	+	4.30105i	0.0812097	+	0.140659i
$936$	25.2539	+	4.62944i	0.825450	+	0.151318i
$937$	−12.1352	+	21.0187i	−0.396439	+	0.686652i	−0.993284	−	0.115704i	$-0.963087\pi$
$937$	−12.1352	+	21.0187i	−0.396439	+	0.686652i	0.596845	+	0.802357i	$0.296421\pi$
$938$	−6.64539	−	4.11455i	−0.216980	−	0.134345i
$939$	0.0179489	+	0.0196207i	0.000585740	+	0.000640297i
$940$	13.1158	−	6.53128i	0.427790	−	0.213027i
$941$	21.9996	−	3.87913i	0.717167	−	0.126456i	0.196856	−	0.980432i	$-0.436927\pi$
$941$	21.9996	−	3.87913i	0.717167	−	0.126456i	0.520312	+	0.853976i	$0.325816\pi$
$942$	−30.0506	−	50.6351i	−0.979103	−	1.64978i
$943$	−27.8152	+	33.1489i	−0.905787	+	1.07948i
$944$	0.850675	+	16.5418i	0.0276871	+	0.538389i
$945$	−10.2889	+	7.85402i	−0.334698	+	0.255491i
$946$	36.5964	+	14.6109i	1.18985	+	0.475041i
$947$	−32.1979	−	27.0172i	−1.04629	−	0.877942i	−0.0535923	−	0.998563i	$-0.517067\pi$
$947$	−32.1979	−	27.0172i	−1.04629	−	0.877942i	−0.992699	+	0.120621i	$0.961512\pi$
$948$	−35.7532	+	28.8740i	−1.16121	+	0.937784i
$949$	5.88046	+	33.3498i	0.190888	+	1.08258i
$950$	−0.716307	−	0.639644i	−0.0232401	−	0.0207528i
$951$	2.00638	+	9.08614i	0.0650614	+	0.294638i
$952$	0.394329	+	1.50225i	0.0127803	+	0.0486881i
$953$	−19.4706	−	11.2414i	−0.630715	−	0.364143i	0.150314	−	0.988638i	$-0.451972\pi$
$953$	−19.4706	−	11.2414i	−0.630715	−	0.364143i	−0.781029	+	0.624495i	$0.785305\pi$
$954$	−6.45399	−	1.95593i	−0.208955	−	0.0633255i
$955$	27.0462	−	15.6151i	0.875193	−	0.505293i
$956$	12.2712	+	5.34283i	0.396880	+	0.172799i
$957$	35.8734	−	1.53622i	1.15962	−	0.0496589i
$958$	5.90215	+	17.9136i	0.190690	+	0.578761i
$959$	11.1939	−	9.39281i	0.361470	−	0.303310i
$960$	34.1702	+	4.88266i	1.10284	+	0.157587i
$961$	−20.3243	+	7.39743i	−0.655622	+	0.238627i
$962$	−37.4097	+	5.41480i	−1.20614	+	0.174580i
$963$	−12.1489	+	12.1084i	−0.391494	+	0.390187i
$964$	−2.26223	+	0.668897i	−0.0728614	+	0.0215437i
$965$	−40.4854	−	7.13867i	−1.30327	−	0.229802i
$966$	−9.15722	+	11.1832i	−0.294629	+	0.359813i
$967$	−0.421349	+	1.15765i	−0.0135497	+	0.0372274i	−0.946283	−	0.323339i	$-0.895194\pi$
$967$	−0.421349	+	1.15765i	−0.0135497	+	0.0372274i	0.932733	+	0.360567i	$0.117417\pi$
$968$	−3.51416	−	5.07360i	−0.112950	−	0.163072i
$969$	−0.204620	−	0.495167i	−0.00657334	−	0.0159071i
$970$	−30.8165	−	57.3861i	−0.989459	−	1.84256i
$971$	−50.7457			−1.62851			−0.814254	−	0.580509i	$-0.802854\pi$
$971$	−50.7457			−1.62851			−0.814254	+	0.580509i	$0.802854\pi$
$972$	−6.09169	+	30.5760i	−0.195391	+	0.980725i
$973$	−23.2112			−0.744117
$974$	−18.6834	−	34.7918i	−0.598653	−	1.11480i
$975$	2.41273	+	5.83866i	0.0772693	+	0.186987i
$976$	−19.3971	+	4.45817i	−0.620886	+	0.142702i
$977$	−6.28697	+	17.2733i	−0.201138	+	0.552622i	−0.998720	−	0.0505893i	$-0.983890\pi$
$977$	−6.28697	+	17.2733i	−0.201138	+	0.552622i	0.797582	+	0.603211i	$0.206112\pi$
$978$	26.9941	−	32.9664i	0.863177	−	1.05415i
$979$	−9.05889	−	1.59733i	−0.289523	−	0.0510508i
$980$	−1.41267	−	4.77767i	−0.0451260	−	0.152617i
$981$	25.0956	−	25.0118i	0.801241	−	0.798566i
$982$	−9.62223	+	1.39275i	−0.307058	+	0.0444445i
$983$	−19.4584	+	7.08229i	−0.620628	+	0.225890i	−0.633147	−	0.774032i	$-0.718237\pi$
$983$	−19.4584	+	7.08229i	−0.620628	+	0.225890i	0.0125191	+	0.999922i	$0.496015\pi$
$984$	−30.1845	−	19.4824i	−0.962247	−	0.621077i
$985$	3.67476	−	3.08349i	0.117088	−	0.0982483i
$986$	−1.38755	−	4.21134i	−0.0441885	−	0.134116i
$987$	−5.08914	+	0.217934i	−0.161989	+	0.00693691i
$988$	1.36087	−	3.12561i	0.0432952	−	0.0994389i
$989$	39.2186	−	22.6428i	1.24708	−	0.720000i
$990$	−36.7226	−	11.1291i	−1.16712	−	0.353705i
$991$	−7.95615	−	4.59349i	−0.252735	−	0.145917i	0.368281	−	0.929715i	$-0.379947\pi$
$991$	−7.95615	−	4.59349i	−0.252735	−	0.145917i	−0.621016	+	0.783798i	$0.713280\pi$
$992$	−15.1722	−	8.34793i	−0.481718	−	0.265047i
$993$	−7.87903	−	35.6812i	−0.250034	−	1.13231i
$994$	10.3855	+	9.27397i	0.329408	+	0.294152i
$995$	−1.15929	−	6.57463i	−0.0367518	−	0.208430i
$996$	−1.19129	−	1.47511i	−0.0377473	−	0.0467406i
$997$	44.6750	+	37.4868i	1.41487	+	1.18722i	0.954021	+	0.299739i	$0.0968996\pi$
$997$	44.6750	+	37.4868i	1.41487	+	1.18722i	0.460849	+	0.887478i	$0.347545\pi$
$998$	47.3796	+	18.9160i	1.49977	+	0.598775i
$999$	−5.87701	−	45.5223i	−0.185940	−	1.44026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.90	yes	648
4.3	odd	2	inner	756.2.cf.a.659.67	yes	648
27.5	odd	18	inner	756.2.cf.a.491.67	✓	648
108.59	even	18	inner	756.2.cf.a.491.90	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.67	✓	648	27.5	odd	18	inner
756.2.cf.a.491.90	yes	648	108.59	even	18	inner
756.2.cf.a.659.67	yes	648	4.3	odd	2	inner
756.2.cf.a.659.90	yes	648	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24593 - 0.669070i) q^{2} +(-0.661489 - 1.60076i) q^{3} +(1.10469 - 1.66723i) q^{4} +(0.851997 - 2.34084i) q^{5} +(-1.89519 - 1.55185i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(0.260874 - 2.81637i) q^{8} +(-2.12486 + 2.11777i) q^{9} +(-0.504658 - 3.48658i) q^{10} +(-3.41175 + 1.24178i) q^{11} +(-3.39958 - 0.665489i) q^{12} +(2.31789 - 1.94494i) q^{13} +(-1.34319 + 0.442552i) q^{14} +(-4.31071 + 0.184599i) q^{15} +(-1.55932 - 3.68355i) q^{16} +(0.475550 - 0.274559i) q^{17} +(-1.23050 + 4.06028i) q^{18} +(0.487855 + 0.281663i) q^{19} +(-2.96153 - 4.00638i) q^{20} +(0.373471 + 1.69131i) q^{21} +(-3.41997 + 3.82987i) q^{22} +(1.02467 + 5.81118i) q^{23} +(-4.68090 + 1.44540i) q^{24} +(-0.923424 - 0.774844i) q^{25} +(1.58663 - 3.97410i) q^{26} +(4.79562 + 2.00052i) q^{27} +(-1.37742 + 1.45007i) q^{28} +(3.67017 - 4.37394i) q^{29} +(-5.24734 + 3.11417i) q^{30} +(3.01476 - 0.531583i) q^{31} +(-4.40736 - 3.54616i) q^{32} +(4.24462 + 4.63997i) q^{33} +(0.408804 - 0.660258i) q^{34} +(-1.24554 + 2.15733i) q^{35} +(1.18349 + 5.88212i) q^{36} +(-4.41674 - 7.65002i) q^{37} +(0.796286 + 0.0245239i) q^{38} +(-4.64665 - 2.42383i) q^{39} +(-6.37042 - 3.01021i) q^{40} +(4.71378 + 5.61766i) q^{41} +(1.59692 + 1.85737i) q^{42} +(-2.62482 - 7.21164i) q^{43} +(-1.69860 + 7.05995i) q^{44} +(3.14699 + 6.77831i) q^{45} +(5.16475 + 6.55476i) q^{46} +(-0.510683 + 2.89623i) q^{47} +(-4.86500 + 4.93272i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-1.66895 - 0.347568i) q^{50} +(-0.754074 - 0.579624i) q^{51} +(-0.682116 - 6.01303i) q^{52} +1.58954i q^{53} +(7.31349 - 0.716098i) q^{54} +9.04436i q^{55} +(-0.745969 + 2.72828i) q^{56} +(0.128164 - 0.967255i) q^{57} +(1.64631 - 7.90522i) q^{58} +(-3.89118 - 1.41627i) q^{59} +(-4.45424 + 7.39088i) q^{60} +(0.864022 - 4.90011i) q^{61} +(3.40052 - 2.67940i) q^{62} +(2.46033 - 1.71662i) q^{63} +(-7.86389 - 1.46944i) q^{64} +(-2.57797 - 7.08291i) q^{65} +(8.39297 + 2.94114i) q^{66} +(3.55255 + 4.23376i) q^{67} +(0.0675824 - 1.09615i) q^{68} +(8.62450 - 5.48428i) q^{69} +(-0.108447 + 3.52124i) q^{70} +(-4.92271 - 8.52639i) q^{71} +(5.41010 + 6.53688i) q^{72} +(-5.59592 + 9.69242i) q^{73} +(-10.6214 - 6.57629i) q^{74} +(-0.629505 + 1.99073i) q^{75} +(1.00853 - 0.502216i) q^{76} +(3.57555 - 0.630466i) q^{77} +(-7.41112 + 0.0890052i) q^{78} +(8.52755 - 10.1627i) q^{79} +(-9.95114 + 0.511746i) q^{80} +(0.0300975 - 8.99995i) q^{81} +(9.63166 + 3.84538i) q^{82} +(0.419295 + 0.351830i) q^{83} +(3.23237 + 1.24571i) q^{84} +(-0.237532 - 1.34711i) q^{85} +(-8.09544 - 7.22902i) q^{86} +(-9.42940 - 2.98175i) q^{87} +(2.60726 + 9.93270i) q^{88} +(2.19413 + 1.26678i) q^{89} +(8.45610 + 6.33975i) q^{90} +(-2.62042 + 1.51290i) q^{91} +(10.8205 + 4.71120i) q^{92} +(-2.84517 - 4.47427i) q^{93} +(1.30150 + 3.95018i) q^{94} +(1.07498 - 0.902015i) q^{95} +(-2.76113 + 9.40086i) q^{96} +(17.3745 - 6.32379i) q^{97} +(1.39963 - 0.202587i) q^{98} +(4.61971 - 9.86391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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