LMFDB - Embedded newform 756.2.cf.a.659.67

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			659.67
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.67

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.442552 - 1.34319i) q^{2} +(0.661489 + 1.60076i) q^{3} +(-1.60830 - 1.18886i) q^{4} +(0.851997 - 2.34084i) q^{5} +(2.44286 - 0.180084i) q^{6} +(0.984808 + 0.173648i) q^{7} +(-2.30861 + 1.63411i) q^{8} +(-2.12486 + 2.11777i) q^{9} +(-2.76713 - 2.18033i) q^{10} +(3.41175 - 1.24178i) q^{11} +(0.839206 - 3.36091i) q^{12} +(2.31789 - 1.94494i) q^{13} +(0.669070 - 1.24593i) q^{14} +(4.31071 - 0.184599i) q^{15} +(1.17323 + 3.82407i) q^{16} +(0.475550 - 0.274559i) q^{17} +(1.90420 + 3.79131i) q^{18} +(-0.487855 - 0.281663i) q^{19} +(-4.15319 + 2.75186i) q^{20} +(0.373471 + 1.69131i) q^{21} +(-0.158060 - 5.13217i) q^{22} +(-1.02467 - 5.81118i) q^{23} +(-4.14294 - 2.61459i) 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} +(1.65976 - 5.87178i) q^{30} +(-3.01476 + 0.531583i) q^{31} +(5.65565 + 0.116480i) q^{32} +(4.24462 + 4.63997i) q^{33} +(-0.158328 - 0.760259i) q^{34} +(1.24554 - 2.15733i) q^{35} +(5.93514 - 0.879839i) q^{36} +(-4.41674 - 7.65002i) q^{37} +(-0.594227 + 0.530629i) q^{38} +(4.64665 + 2.42383i) q^{39} +(1.85826 + 6.79635i) q^{40} +(4.71378 + 5.61766i) q^{41} +(2.43702 + 0.246850i) q^{42} +(2.62482 + 7.21164i) q^{43} +(-6.96340 - 2.05894i) q^{44} +(3.14699 + 6.77831i) q^{45} +(-8.25896 - 1.19543i) q^{46} +(0.510683 - 2.89623i) q^{47} +(-5.34534 + 4.40765i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-1.44942 + 0.897421i) q^{50} +(0.754074 + 0.579624i) q^{51} +(-6.04012 + 0.372399i) q^{52} +1.58954i q^{53} +(-4.80937 + 5.55607i) q^{54} -9.04436i q^{55} +(-2.55730 + 1.20840i) q^{56} +(0.128164 - 0.967255i) q^{57} +(-4.25077 - 6.86541i) q^{58} +(3.89118 + 1.41627i) q^{59} +(-7.15237 - 4.82794i) q^{60} +(0.864022 - 4.90011i) q^{61} +(-0.620172 + 4.28464i) q^{62} +(-2.46033 + 1.71662i) q^{63} +(2.65937 - 7.54505i) q^{64} +(-2.57797 - 7.08291i) q^{65} +(8.11081 - 3.64789i) q^{66} +(-3.55255 - 4.23376i) q^{67} +(-1.09124 - 0.123790i) q^{68} +(8.62450 - 5.48428i) q^{69} +(-2.34648 - 2.62772i) q^{70} +(4.92271 + 8.52639i) q^{71} +(1.44482 - 8.36137i) q^{72} +(-5.59592 + 9.69242i) q^{73} +(-12.2300 + 2.54698i) q^{74} +(0.629505 - 1.99073i) q^{75} +(0.449757 + 1.03299i) q^{76} +(3.57555 - 0.630466i) q^{77} +(5.31204 - 5.16864i) 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} +(1.41007 - 3.16413i) q^{84} +(-0.237532 - 1.34711i) q^{85} +(10.8482 - 0.334101i) q^{86} +(9.42940 + 2.98175i) q^{87} +(-5.84721 + 8.44195i) q^{88} +(2.19413 + 1.26678i) q^{89} +(10.4972 - 1.22724i) q^{90} +(2.62042 - 1.51290i) q^{91} +(-5.26070 + 10.5643i) q^{92} +(-2.84517 - 4.47427i) q^{93} +(-3.66417 - 1.96767i) q^{94} +(-1.07498 + 0.902015i) q^{95} +(3.55470 + 9.13040i) q^{96} +(17.3745 - 6.32379i) q^{97} +(0.875259 - 1.11082i) 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 $

$2$	0.442552	−	1.34319i	0.312931	−	0.949776i
$2$	0.442552	−	1.34319i	0.312931	−	0.949776i
$3$	0.661489	+	1.60076i	0.381911	+	0.924199i
$3$	0.661489	+	1.60076i	0.381911	+	0.924199i
$4$	−1.60830	−	1.18886i	−0.804148	−	0.594429i
$5$	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	$-0.0769445\pi$
$6$	2.44286	−	0.180084i	0.997294	−	0.0735189i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$8$	−2.30861	+	1.63411i	−0.816217	+	0.577745i
$9$	−2.12486	+	2.11777i	−0.708288	+	0.705923i
$10$	−2.76713	−	2.18033i	−0.875045	−	0.689482i
$11$	3.41175	−	1.24178i	1.02868	−	0.374409i	0.228103	−	0.973637i	$-0.426748\pi$
$11$	3.41175	−	1.24178i	1.02868	−	0.374409i	0.800579	+	0.599228i	$0.204526\pi$
$12$	0.839206	−	3.36091i	0.242258	−	0.970212i
$13$	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	$0.139947\pi$
$14$	0.669070	−	1.24593i	0.178816	−	0.332989i
$15$	4.31071	−	0.184599i	1.11302	−	0.0476633i
$16$	1.17323	+	3.82407i	0.293308	+	0.956018i
$17$	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	$0.312121\pi$
$18$	1.90420	+	3.79131i	0.448823	+	0.893620i
$19$	−0.487855	−	0.281663i	−0.111922	−	0.0646179i	0.442994	−	0.896524i	$-0.353916\pi$
$19$	−0.487855	−	0.281663i	−0.111922	−	0.0646179i	−0.554916	+	0.831907i	$0.687250\pi$
$20$	−4.15319	+	2.75186i	−0.928682	+	0.615336i
$21$	0.373471	+	1.69131i	0.0814980	+	0.369073i
$22$	−0.158060	−	5.13217i	−0.0336984	−	1.09418i
$23$	−1.02467	−	5.81118i	−0.213658	−	1.21171i	−0.883220	−	0.468959i	$-0.844629\pi$
$23$	−1.02467	−	5.81118i	−0.213658	−	1.21171i	0.669562	−	0.742756i	$-0.266482\pi$
$24$	−4.14294	−	2.61459i	−0.845674	−	0.533700i
$25$	−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	$0.0443621\pi$
$30$	1.65976	−	5.87178i	0.303030	−	1.07204i
$31$	−3.01476	+	0.531583i	−0.541467	+	0.0954752i	−0.437691	−	0.899126i	$-0.644204\pi$
$31$	−3.01476	+	0.531583i	−0.541467	+	0.0954752i	−0.103776	+	0.994601i	$0.533092\pi$
$32$	5.65565	+	0.116480i	0.999788	+	0.0205910i
$33$	4.24462	+	4.63997i	0.738894	+	0.807716i
$34$	−0.158328	−	0.760259i	−0.0271531	−	0.130383i
$35$	1.24554	−	2.15733i	0.210534	−	0.364656i
$36$	5.93514	−	0.879839i	0.989190	−	0.146640i
$37$	−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	$-0.425339\pi$
$38$	−0.594227	+	0.530629i	−0.0963963	+	0.0860794i
$39$	4.64665	+	2.42383i	0.744060	+	0.388124i
$40$	1.85826	+	6.79635i	0.293817	+	1.07460i
$41$	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	$0.583698\pi$
$42$	2.43702	+	0.246850i	0.376040	+	0.0380899i
$43$	2.62482	+	7.21164i	0.400282	+	1.09976i	0.962146	+	0.272535i	$0.0878621\pi$
$43$	2.62482	+	7.21164i	0.400282	+	1.09976i	−0.561864	+	0.827229i	$0.689916\pi$
$44$	−6.96340	−	2.05894i	−1.04977	−	0.310398i
$45$	3.14699	+	6.77831i	0.469125	+	1.01045i
$46$	−8.25896	−	1.19543i	−1.21772	−	0.176256i
$47$	0.510683	−	2.89623i	0.0744908	−	0.422458i	−0.924643	−	0.380836i	$-0.875636\pi$
$47$	0.510683	−	2.89623i	0.0744908	−	0.422458i	0.999133	−	0.0416223i	$-0.0132526\pi$
$48$	−5.34534	+	4.40765i	−0.771533	+	0.636189i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	−1.44942	+	0.897421i	−0.204979	+	0.126914i
$51$	0.754074	+	0.579624i	0.105592	+	0.0811636i
$52$	−6.04012	+	0.372399i	−0.837614	+	0.0516424i
$53$			1.58954i			0.218340i	0.994023	+	0.109170i	$0.0348193\pi$
$53$			1.58954i			0.218340i	−0.994023	+	0.109170i	$0.965181\pi$
$54$	−4.80937	+	5.55607i	−0.654473	+	0.756086i
$55$		−	9.04436i		−	1.21954i
$56$	−2.55730	+	1.20840i	−0.341733	+	0.161479i
$57$	0.128164	−	0.967255i	0.0169758	−	0.128116i
$58$	−4.25077	−	6.86541i	−0.558153	−	0.901472i
$59$	3.89118	+	1.41627i	0.506589	+	0.184383i	0.582655	−	0.812720i	$-0.302014\pi$
$59$	3.89118	+	1.41627i	0.506589	+	0.184383i	−0.0760664	+	0.997103i	$0.524236\pi$
$60$	−7.15237	−	4.82794i	−0.923367	−	0.623284i
$61$	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	$-0.0476359\pi$
$62$	−0.620172	+	4.28464i	−0.0787619	+	0.544149i
$63$	−2.46033	+	1.71662i	−0.309972	+	0.216274i
$64$	2.65937	−	7.54505i	0.332422	−	0.943131i
$65$	−2.57797	−	7.08291i	−0.319758	−	0.878527i
$66$	8.11081	−	3.64789i	0.998372	−	0.449024i
$67$	−3.55255	−	4.23376i	−0.434013	−	0.517237i	0.504063	−	0.863667i	$-0.331838\pi$
$67$	−3.55255	−	4.23376i	−0.434013	−	0.517237i	−0.938076	+	0.346430i	$0.887394\pi$
$68$	−1.09124	−	0.123790i	−0.132332	−	0.0150117i
$69$	8.62450	−	5.48428i	1.03827	−	0.660230i
$70$	−2.34648	−	2.62772i	−0.280458	−	0.314072i
$71$	4.92271	+	8.52639i	0.584218	+	1.01190i	0.994972	+	0.100150i	$0.0319322\pi$
$71$	4.92271	+	8.52639i	0.584218	+	1.01190i	−0.410754	+	0.911746i	$0.634734\pi$
$72$	1.44482	−	8.36137i	0.170273	−	0.985397i
$73$	−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	$0.939355\pi$
$74$	−12.2300	+	2.54698i	−1.42171	+	0.296080i
$75$	0.629505	−	1.99073i	0.0726890	−	0.229870i
$76$	0.449757	+	1.03299i	0.0515907	+	0.118492i
$77$	3.57555	−	0.630466i	0.407472	−	0.0718483i
$78$	5.31204	−	5.16864i	0.601470	−	0.585234i
$79$	−8.52755	+	10.1627i	−0.959424	+	1.14340i	0.0301752	+	0.999545i	$0.490393\pi$
$79$	−8.52755	+	10.1627i	−0.959424	+	1.14340i	−0.989599	+	0.143852i	$0.954051\pi$
$80$	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	0.619486	−	0.785008i	$-0.287341\pi$
$83$	−0.419295	−	0.351830i	−0.0460236	−	0.0386184i	−0.665509	+	0.746390i	$0.731786\pi$
$84$	1.41007	−	3.16413i	0.153852	−	0.345234i
$85$	−0.237532	−	1.34711i	−0.0257640	−	0.146115i
$86$	10.8482	−	0.334101i	1.16979	−	0.0360270i
$87$	9.42940	+	2.98175i	1.01094	+	0.319677i
$88$	−5.84721	+	8.44195i	−0.623315	+	0.899915i
$89$	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	$0.623795\pi$
$90$	10.4972	−	1.22724i	1.10651	−	0.129362i
$91$	2.62042	−	1.51290i	0.274694	−	0.158595i
$92$	−5.26070	+	10.5643i	−0.548466	+	1.10140i
$93$	−2.84517	−	4.47427i	−0.295030	−	0.463960i
$94$	−3.66417	−	1.96767i	−0.377930	−	0.202950i
$95$	−1.07498	+	0.902015i	−0.110291	+	0.0925448i
$96$	3.55470	+	9.13040i	0.362800	+	0.931867i
$97$	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	$0.000953912\pi$
$98$	0.875259	−	1.11082i	0.0884145	−	0.112210i
$99$	−4.61971	+	9.86391i	−0.464299	+	0.991360i
$100$	0.563958	+	2.34400i	0.0563958	+	0.234400i
$101$	−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	$0.585151\pi$
$102$	1.11226	−	0.756348i	0.110130	−	0.0748896i
$103$	−4.75510	+	13.0645i	−0.468534	+	1.28729i	0.450383	+	0.892836i	$0.351288\pi$
$103$	−4.75510	+	13.0645i	−0.468534	+	1.28729i	−0.918917	+	0.394451i	$0.870935\pi$
$104$	−2.17287	+	8.27781i	−0.213067	+	0.811706i
$105$	4.27728	+	0.566753i	0.417420	+	0.0553094i
$106$	2.13505	+	0.703454i	0.207374	+	0.0683255i
$107$	−5.71751			−0.552733			−0.276366	−	0.961052i	$-0.589130\pi$
$107$	−5.71751			−0.552733			−0.276366	+	0.961052i	$0.589130\pi$
$108$	5.33444	+	8.91873i	0.513307	+	0.858205i
$109$	−11.8104			−1.13124			−0.565618	−	0.824667i	$-0.691362\pi$
$109$	−11.8104			−1.13124			−0.565618	+	0.824667i	$0.691362\pi$
$110$	−12.1483	−	4.00260i	−1.15829	−	0.381633i
$111$	9.32422	−	12.1305i	0.885016	−	1.15138i
$112$	0.491365	+	3.96971i	0.0464296	+	0.375102i
$113$	−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	$0.779545\pi$
$114$	−1.24248	−	0.600209i	−0.116369	−	0.0562147i
$115$	−14.4761	−	2.55252i	−1.34990	−	0.238024i
$116$	−11.1027	+	2.67127i	−1.03086	+	0.248022i
$117$	−0.806266	+	9.04151i	−0.0745393	+	0.835888i
$118$	3.62437	−	4.59981i	0.333650	−	0.423446i
$119$	0.516002	−	0.187809i	0.0473018	−	0.0172165i
$120$	−9.65011	+	7.47035i	−0.880930	+	0.681946i
$121$	1.67155	−	1.40260i	0.151959	−	0.127509i
$122$	−6.19939	−	3.32910i	−0.561266	−	0.301402i
$123$	−5.87442	+	11.2617i	−0.529678	+	1.01543i
$124$	5.48060	+	2.72918i	0.492173	+	0.245087i
$125$	8.18612	−	4.72626i	0.732189	−	0.422729i
$126$	1.21691	+	4.06437i	0.108411	+	0.362083i
$127$	−4.65729	−	2.68889i	−0.413267	−	0.238600i	0.278925	−	0.960313i	$-0.410022\pi$
$127$	−4.65729	−	2.68889i	−0.413267	−	0.238600i	−0.692193	+	0.721713i	$0.743355\pi$
$128$	−8.95749	−	6.91111i	−0.791738	−	0.610861i
$129$	−9.80781	+	8.97213i	−0.863529	+	0.789952i
$130$	−10.6546	+	0.328137i	−0.934466	+	0.0287795i
$131$	2.59436	+	14.7134i	0.226671	+	1.28551i	0.859466	+	0.511193i	$0.170796\pi$
$131$	2.59436	+	14.7134i	0.226671	+	1.28551i	−0.632795	+	0.774319i	$0.718092\pi$
$132$	−1.31034	−	12.5087i	−0.114050	−	1.08874i
$133$	−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	$0.436805\pi$
$138$	−3.54962	−	14.0114i	−0.302164	−	1.19273i
$139$	−22.8586	+	4.03058i	−1.93884	+	0.341870i	−0.999997	−	0.00247669i	$-0.999212\pi$
$139$	−22.8586	+	4.03058i	−1.93884	+	0.341870i	−0.938843	+	0.344346i	$0.888101\pi$
$140$	−4.56795	+	1.98886i	−0.386063	+	0.168090i
$141$	4.97398	−	1.09834i	0.418884	−	0.0924971i
$142$	13.6311	−	2.83875i	1.14389	−	0.238223i
$143$	5.49289	−	9.51397i	0.459339	−	0.795598i
$144$	−10.5915	−	5.64100i	−0.882622	−	0.470083i
$145$	−7.11172	−	12.3179i	−0.590596	−	1.02294i
$146$	10.5422	+	11.8058i	0.872482	+	0.977052i
$147$	0.0741043	+	1.73046i	0.00611202	+	0.142726i
$148$	−1.99136	+	17.5544i	−0.163689	+	1.44296i
$149$	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	$0.544983\pi$
$150$	−2.39533	−	1.72654i	−0.195578	−	0.140972i
$151$	−2.65495	−	7.29442i	−0.216057	−	0.593611i	0.783559	−	0.621317i	$-0.213402\pi$
$151$	−2.65495	−	7.29442i	−0.216057	−	0.593611i	−0.999616	+	0.0277057i	$0.991180\pi$
$152$	1.58654	−	0.146957i	0.128685	−	0.0119198i
$153$	−0.429027	+	1.59051i	−0.0346847	+	0.128585i
$154$	0.735533	−	5.08164i	0.0592709	−	0.409490i
$155$	−1.32421	+	7.50999i	−0.106363	+	0.603217i
$156$	−4.59160	−	9.42245i	−0.367622	−	0.754400i
$157$	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	$0.202328\pi$
$158$	9.87656	+	15.9516i	0.785737	+	1.26904i
$159$	−2.54447	+	1.05146i	−0.201790	+	0.0833866i
$160$	5.09126	−	13.1398i	0.402500	−	1.03879i
$161$		−	5.90083i		−	0.465050i
$162$	−12.0753	−	4.02337i	−0.948724	−	0.316106i
$163$		−	17.3948i		−	1.36246i	−0.732068	−	0.681231i	$-0.761445\pi$
$163$		−	17.3948i		−	1.36246i	0.732068	−	0.681231i	$-0.238555\pi$
$164$	−0.902547	−	14.6389i	−0.0704771	−	1.14310i
$165$	14.4779	−	5.98275i	1.12710	−	0.465756i
$166$	−0.658133	+	0.407488i	−0.0510810	+	0.0316272i
$167$	0.774686	+	0.281963i	0.0599470	+	0.0218189i	0.371820	−	0.928305i	$-0.378734\pi$
$167$	0.774686	+	0.281963i	0.0599470	+	0.0218189i	−0.311873	+	0.950124i	$0.600956\pi$
$168$	−3.62598	−	3.29428i	−0.279750	−	0.254159i
$169$	−0.667600	+	3.78615i	−0.0513539	+	0.291242i
$170$	−1.91454	−	0.277117i	−0.146839	−	0.0212539i
$171$	1.63312	−	0.434668i	0.124888	−	0.0332399i
$172$	4.35212	−	14.7190i	0.331846	−	1.12231i
$173$	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	$0.580454\pi$
$174$	8.17804	−	11.3459i	0.619975	−	0.860127i
$175$	−0.774844	−	0.923424i	−0.0585727	−	0.0698043i
$176$	8.75142	+	11.5899i	0.659663	+	0.873621i
$177$	0.306859	+	7.16570i	0.0230649	+	0.538607i
$178$	2.67254	−	2.38651i	0.200315	−	0.178876i
$179$	4.95698	+	8.58574i	0.370502	+	0.641728i	0.989643	−	0.143552i	$-0.0458523\pi$
$179$	4.95698	+	8.58574i	0.370502	+	0.641728i	−0.619141	+	0.785280i	$0.712519\pi$
$180$	2.99716	−	14.6428i	0.223395	−	1.09141i
$181$	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	$0.122535\pi$
$182$	−0.872434	−	4.18924i	−0.0646691	−	0.310527i
$183$	8.41545	−	1.85828i	0.622088	−	0.137368i
$184$	11.8617	+	11.7413i	0.874453	+	0.865583i
$185$	−21.6705	+	3.82110i	−1.59325	+	0.280933i
$186$	−7.26891	+	1.84149i	−0.532982	+	0.135025i
$187$	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	0.225414	−	0.974263i	$-0.427627\pi$
$191$	−9.60379	−	8.05853i	−0.694906	−	0.583095i	−0.920319	+	0.391168i	$0.872071\pi$
$192$	13.8370	−	0.733946i	0.998596	−	0.0529680i
$193$	−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	$-0.257989\pi$
$194$	−0.804924	−	26.1357i	−0.0577902	−	1.87644i
$195$	9.63275	−	8.81198i	0.689815	−	0.631039i
$196$	−1.10469	−	1.66723i	−0.0789065	−	0.119088i
$197$	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	$0.644813\pi$
$198$	11.2046	+	10.5704i	0.796276	+	0.751207i
$199$	−2.32094	+	1.34000i	−0.164527	+	0.0949898i	−0.580003	−	0.814615i	$-0.696949\pi$
$199$	−2.32094	+	1.34000i	−0.164527	+	0.0949898i	0.415476	+	0.909604i	$0.363615\pi$
$200$	3.39801	+	0.279840i	0.240275	+	0.0197877i
$201$	4.42727	−	8.48737i	0.312275	−	0.598653i
$202$	−1.24858	+	2.32508i	−0.0878497	+	0.163592i
$203$	4.37394	−	3.67017i	0.306990	−	0.257595i
$204$	−0.523684	−	1.82869i	−0.0366652	−	0.128034i
$205$	17.1662	−	6.24798i	1.19894	−	0.436378i
$206$	15.4437	+	12.1687i	1.07601	+	0.847835i
$207$	14.4840	+	10.1780i	1.00671	+	0.707417i
$208$	10.1570	+	6.58192i	0.704264	+	0.456374i
$209$	−2.01420	−	0.355158i	−0.139325	−	0.0245668i
$210$	2.65417	−	5.49436i	0.183155	−	0.379147i
$211$	−4.39428	+	12.0732i	−0.302515	+	0.831153i	0.691546	+	0.722332i	$0.256930\pi$
$211$	−4.39428	+	12.0732i	−0.302515	+	0.831153i	−0.994061	+	0.108821i	$0.965292\pi$
$212$	1.88974	−	2.55645i	0.129788	−	0.175578i
$213$	−10.3924	+	13.5202i	−0.712074	+	0.926388i
$214$	−2.53030	+	7.67968i	−0.172967	+	0.524972i
$215$	19.1177			1.30381
$216$	14.3403	−	3.21815i	0.975732	−	0.218967i
$217$	−3.06127			−0.207812
$218$	−5.22673	+	15.8636i	−0.353999	+	1.07442i
$219$	−19.2169	−	2.54630i	−1.29856	−	0.172063i
$220$	−10.7525	+	14.5460i	−0.724931	+	0.980692i
$221$	0.568273	−	1.56132i	0.0382262	−	0.105026i
$222$	−12.1671	−	17.8926i	−0.816604	−	1.20087i
$223$	−4.46070	−	0.786542i	−0.298710	−	0.0526707i	0.0222843	−	0.999752i	$-0.492906\pi$
$223$	−4.46070	−	0.786542i	−0.298710	−	0.0526707i	−0.320995	+	0.947081i	$0.604017\pi$
$224$	5.54951	+	1.09680i	0.370792	+	0.0732834i
$225$	3.60309	−	0.309160i	0.240206	−	0.0206107i
$226$	20.3865	+	16.0633i	1.35609	+	1.06852i
$227$	28.1863	−	10.2590i	1.87079	−	0.680912i	0.902725	−	0.430218i	$-0.141563\pi$
$227$	28.1863	−	10.2590i	1.87079	−	0.680912i	0.968066	−	0.250695i	$-0.0806590\pi$
$228$	−1.35606	+	1.40326i	−0.0898070	+	0.0929334i
$229$	−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	$0.278674\pi$
$230$	−9.83492	+	18.3144i	−0.648495	+	1.20762i
$231$	3.37441	+	5.30655i	0.222020	+	0.349145i
$232$	−1.32550	+	16.0952i	−0.0870236	+	1.05670i
$233$	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	$0.324634\pi$
$234$	11.7876	+	5.08430i	0.770581	+	0.332371i
$235$	−6.34451	−	3.66301i	−0.413870	−	0.238948i
$236$	−4.57442	−	6.90385i	−0.297770	−	0.449402i
$237$	−21.9090	−	6.92802i	−1.42314	−	0.450023i
$238$	−0.0239053	−	0.776202i	−0.00154955	−	0.0503137i
$239$	−1.16205	−	6.59029i	−0.0751665	−	0.426290i	−0.999049	−	0.0436129i	$-0.986113\pi$
$239$	−1.16205	−	6.59029i	−0.0751665	−	0.426290i	0.923882	−	0.382677i	$-0.124998\pi$
$240$	5.76339	+	16.2679i	0.372025	+	1.05009i
$241$	−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
$246$	12.5268	+	12.8743i	0.798677	+	0.820835i
$247$	−1.67861	+	0.295985i	−0.106808	+	0.0188331i
$248$	6.09124	−	6.15367i	0.386794	−	0.390758i
$249$	0.285837	−	0.903922i	0.0181142	−	0.0572837i
$250$	−2.72546	−	13.0871i	−0.172373	−	0.827700i
$251$	2.31558	−	4.01070i	0.146158	−	0.253153i	−0.783646	−	0.621207i	$-0.786642\pi$
$251$	2.31558	−	4.01070i	0.146158	−	0.253153i	0.929804	+	0.368054i	$0.119976\pi$
$252$	5.99775	+	0.164154i	0.377823	+	0.0103407i
$253$	−10.7121	−	18.5539i	−0.673464	−	1.16647i
$254$	−5.67276	+	5.06563i	−0.355941	+	0.317846i
$255$	1.99928	−	1.27133i	0.125200	−	0.0796139i
$256$	−13.2471	+	8.97305i	−0.827941	+	0.560816i
$257$	−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	$0.840848\pi$
$258$	7.71077	+	17.1443i	0.480052	+	1.06736i
$259$	−3.02123	−	8.30076i	−0.187730	−	0.515784i
$260$	−4.27444	+	14.4563i	−0.265090	+	0.896539i
$261$	1.46438	+	17.0666i	0.0906430	+	1.05640i
$262$	20.9109	+	3.02671i	1.29188	+	0.186991i
$263$	1.18499	−	6.72041i	0.0730696	−	0.414398i	−0.926229	−	0.376960i	$-0.876969\pi$
$263$	1.18499	−	6.72041i	0.0730696	−	0.414398i	0.999299	−	0.0374378i	$-0.0119196\pi$
$264$	−17.3814	−	3.77572i	−1.06975	−	0.232380i
$265$	3.72087	+	1.35429i	0.228571	+	0.0831931i
$266$	−0.677342	+	0.419381i	−0.0415305	+	0.0257139i
$267$	−0.576421	+	4.35024i	−0.0352764	+	0.266230i
$268$	0.680207	+	11.0326i	0.0415502	+	0.673925i
$269$		−	10.2533i		−	0.625153i	−0.949893	−	0.312577i	$-0.898808\pi$
$269$		−	10.2533i		−	0.625153i	0.949893	−	0.312577i	$-0.101192\pi$
$270$	8.90832	+	15.9917i	0.542143	+	0.973226i
$271$		−	15.8317i		−	0.961707i	−0.876801	−	0.480854i	$-0.840327\pi$
$271$		−	15.8317i		−	0.961707i	0.876801	−	0.480854i	$-0.159673\pi$
$272$	1.60786	+	1.49642i	0.0974911	+	0.0907336i
$273$	4.15516	+	3.19389i	0.251482	+	0.193303i
$274$	10.8787	+	17.5702i	0.657206	+	1.06145i
$275$	−4.11267	−	1.49689i	−0.248004	−	0.0902659i
$276$	−20.3908	−	1.43296i	−1.22738	−	0.0862540i
$277$	−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	$0.830553\pi$
$278$	−4.70228	+	32.4871i	−0.282024	+	1.94844i
$279$	5.28018	−	7.51411i	0.316116	−	0.449858i
$280$	0.649857	+	7.01578i	0.0388364	+	0.419273i
$281$	−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	$-0.543120\pi$
$282$	0.725964	−	7.16705i	0.0432305	−	0.426791i
$283$	9.34788	+	11.1404i	0.555674	+	0.662226i	0.968625	−	0.248527i	$-0.0799465\pi$
$283$	9.34788	+	11.1404i	0.555674	+	0.662226i	−0.412951	+	0.910753i	$0.635502\pi$
$284$	2.21949	−	19.5654i	0.131702	−	1.16099i
$285$	−2.15500	−	1.12411i	−0.127651	−	0.0665866i
$286$	−10.3481	−	11.5884i	−0.611898	−	0.685236i
$287$	3.66667	+	6.35086i	0.216437	+	0.374879i
$288$	−12.2642	+	11.7299i	−0.722674	+	0.691189i
$289$	−8.34923	+	14.4613i	−0.491131	+	0.850665i
$290$	−19.6925	+	4.10107i	−1.15638	+	0.240823i
$291$	21.6159	+	23.6292i	1.26715	+	1.38517i
$292$	20.5228	−	8.93553i	1.20101	−	0.522912i
$293$	−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	$0.610066\pi$
$294$	2.35713	+	0.666284i	0.137471	+	0.0388585i
$295$	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
$300$	−3.37913	+	2.45329i	−0.195094	+	0.141641i
$301$	1.33266	+	7.55787i	0.0768131	+	0.435629i
$302$	−10.9727	+	0.337936i	−0.631409	+	0.0194460i
$303$	−0.696948	−	3.15622i	−0.0400386	−	0.181320i
$304$	0.504733	−	2.19605i	0.0289484	−	0.125952i
$305$	−10.7343	−	6.19742i	−0.614641	−	0.354863i
$306$	1.94648	+	1.28014i	0.111273	+	0.0731809i
$307$	−7.57863	+	4.37552i	−0.432535	+	0.249724i	−0.700426	−	0.713725i	$-0.747007\pi$
$307$	−7.57863	+	4.37552i	−0.432535	+	0.249724i	0.267891	+	0.963449i	$0.413673\pi$
$308$	−6.50008	−	3.23685i	−0.370376	−	0.184436i
$309$	−24.0586	+	1.03027i	−1.36865	+	0.0586101i
$310$	9.50127	+	5.10222i	0.539636	+	0.289787i
$311$	14.3907	−	12.0753i	0.816024	−	0.684725i	−0.136014	−	0.990707i	$-0.543429\pi$
$311$	14.3907	−	12.0753i	0.816024	−	0.684725i	0.952037	+	0.305982i	$0.0989847\pi$
$312$	−14.6881	+	1.99745i	−0.831551	+	0.113083i
$313$	−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	$0.389027\pi$
$314$	21.0395	−	26.7019i	1.18733	−	1.50687i
$315$	1.92214	+	7.22180i	0.108300	+	0.406902i
$316$	25.7969	−	6.20664i	1.45119	−	0.349151i
$317$	−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	$0.603762\pi$
$318$	0.286251	+	3.88303i	0.0160521	+	0.217750i
$319$	7.09025	−	19.4803i	0.396978	−	1.09069i
$320$	−15.3960	−	12.6535i	−0.860662	−	0.707354i
$321$	−3.78207	−	9.15237i	−0.211095	−	0.510835i
$322$	−7.92591	−	2.61142i	−0.441693	−	0.145529i
$323$	−0.309332			−0.0172117
$324$	−10.7481	+	14.4388i	−0.597115	+	0.802156i
$325$	−3.64743			−0.202323
$326$	−23.3644	−	7.69808i	−1.29403	−	0.426357i
$327$	−7.81248	−	18.9057i	−0.432031	−	1.04549i
$328$	−20.0622	−	5.26617i	−1.10775	−	0.290776i
$329$	1.00585	−	2.76355i	0.0554543	−	0.152359i
$330$	−1.62874	−	22.0941i	−0.0896593	−	1.21624i
$331$	−20.7763	−	3.66342i	−1.14197	−	0.201360i	−0.429502	−	0.903066i	$-0.641311\pi$
$331$	−20.7763	−	3.66342i	−1.14197	−	0.201360i	−0.712467	+	0.701706i	$0.752422\pi$
$332$	0.256074	+	1.06433i	0.0140539	+	0.0584126i
$333$	25.5860	+	6.90161i	1.40210	+	0.378206i
$334$	0.721566	−	0.915764i	0.0394824	−	0.0501084i
$335$	−12.9373	+	4.70881i	−0.706842	+	0.257270i
$336$	−6.02951	+	3.41247i	−0.328937	+	0.186166i
$337$	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	$0.162751\pi$
$338$	4.79005	+	2.57228i	0.260545	+	0.139913i
$339$	−31.7586	+	1.36001i	−1.72489	+	0.0738657i
$340$	−1.21950	+	2.44895i	−0.0661368	+	0.132813i
$341$	−9.62550	+	5.55729i	−0.521250	+	0.300944i
$342$	0.138901	−	2.38595i	0.00751089	−	0.129017i
$343$	0.866025	+	0.500000i	0.0467610	+	0.0269975i
$344$	−17.8443	−	12.3596i	−0.962100	−	0.666386i
$345$	−5.48979	−	24.8612i	−0.295560	−	1.33848i
$346$	30.6514	−	0.943997i	1.64783	−	0.0507496i
$347$	−2.62751	−	14.9013i	−0.141052	−	0.799945i	−0.970453	−	0.241291i	$-0.922429\pi$
$347$	−2.62751	−	14.9013i	−0.141052	−	0.799945i	0.829401	−	0.558654i	$-0.188682\pi$
$348$	−11.6204	−	16.0057i	−0.622918	−	0.857998i
$349$	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	$-0.0197766\pi$
$354$	9.76066	+	2.75902i	0.518773	+	0.146640i
$355$	24.1531	−	4.25884i	1.28191	−	0.226036i
$356$	−2.02279	−	4.64587i	−0.107208	−	0.246231i
$357$	0.641967	+	0.701762i	0.0339765	+	0.0371412i
$358$	13.7260	−	2.85851i	0.725440	−	0.151077i
$359$	11.8564	−	20.5360i	0.625759	−	1.08385i	−0.362634	−	0.931932i	$-0.618123\pi$
$359$	11.8564	−	20.5360i	0.625759	−	1.08385i	0.988394	−	0.151915i	$-0.0485441\pi$
$360$	−18.3417	−	10.5060i	−0.966691	−	0.553712i
$361$	−9.34133	−	16.1797i	−0.491649	−	0.851561i
$362$	−3.50277	−	3.92259i	−0.184101	−	0.206167i
$363$	3.35093	+	1.74795i	0.175878	+	0.0917434i
$364$	−6.01303	−	0.682116i	−0.315168	−	0.0357526i
$365$	17.9207	+	21.3571i	0.938014	+	1.11788i
$366$	1.22826	−	12.1259i	0.0642019	−	0.633831i
$367$	5.49134	+	15.0873i	0.286645	+	0.787552i	0.996530	+	0.0832338i	$0.0265248\pi$
$367$	5.49134	+	15.0873i	0.286645	+	0.787552i	−0.709885	+	0.704318i	$0.751253\pi$
$368$	21.0202	−	10.7363i	1.09575	−	0.559667i
$369$	−21.9131	−	1.95407i	−1.14075	−	0.101725i
$370$	−4.45789	+	30.7986i	−0.231754	+	1.60114i
$371$	−0.276021	+	1.56539i	−0.0143303	+	0.0812712i
$372$	−0.743400	+	10.5785i	−0.0385435	+	0.548467i
$373$	−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	$0.805808\pi$
$374$	−1.48425	−	2.39720i	−0.0767486	−	0.123957i
$375$	12.9806	+	9.97764i	0.670317	+	0.515243i
$376$	3.55378	+	7.52078i	0.183272	+	0.387854i
$377$		−	17.2766i		−	0.889790i
$378$	−5.70111	+	4.63652i	−0.293233	+	0.238477i
$379$		−	15.8400i		−	0.813645i	−0.913507	−	0.406823i	$-0.866637\pi$
$379$		−	15.8400i		−	0.813645i	0.913507	−	0.406823i	$-0.133363\pi$
$380$	2.80125	−	0.172709i	0.143701	−	0.00885978i
$381$	1.22352	−	9.23386i	0.0626826	−	0.473065i
$382$	−15.0743	+	9.33335i	−0.771267	+	0.477536i
$383$	−20.0545	−	7.29924i	−1.02474	−	0.372974i	−0.225663	−	0.974206i	$-0.572455\pi$
$383$	−20.0545	−	7.29924i	−1.02474	−	0.372974i	−0.799075	+	0.601232i	$0.794677\pi$
$384$	5.13774	−	18.9104i	0.262184	−	0.965018i
$385$	1.57054	−	8.90696i	0.0800420	−	0.453941i
$386$	−23.0979	−	3.34327i	−1.17565	−	0.170168i
$387$	−20.8500	−	9.76498i	−1.05986	−	0.496382i
$388$	−35.4614	−	10.4853i	−1.80028	−	0.532308i
$389$	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	$0.567372\pi$
$390$	−7.57314	−	16.8383i	−0.383481	−	0.852642i
$391$	−2.08279	−	2.48218i	−0.105331	−	0.125529i
$392$	−2.72828	+	0.745969i	−0.137799	+	0.0376771i
$393$	−21.8364	+	13.8857i	−1.10150	+	0.700440i
$394$	2.03133	−	1.81393i	0.102337	−	0.0913844i
$395$	16.5239	+	28.6203i	0.831409	+	1.44004i
$396$	19.1567	−	10.3719i	0.962658	−	0.521208i
$397$	−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	$0.186260\pi$
$398$	0.772727	+	3.71047i	0.0387333	+	0.185989i
$399$	0.294179	−	0.930305i	0.0147274	−	0.0465735i
$400$	1.87967	−	4.44031i	0.0939835	−	0.222016i
$401$	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	$0.392869\pi$
$402$	−9.44082	−	9.70274i	−0.470865	−	0.483929i
$403$	−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
$408$	−2.68803	−	0.105887i	−0.133077	−	0.00524216i
$409$	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	$0.666487\pi$
$410$	−0.795275	−	25.8224i	−0.0392758	−	1.27528i
$411$	−24.1320	−	7.63098i	−1.19034	−	0.376408i
$412$	23.1795	−	15.3585i	1.14197	−	0.756659i
$413$	3.58613	+	2.07045i	0.176462	+	0.101880i
$414$	20.0808	−	14.9505i	0.986918	−	0.734775i
$415$	−1.18082	+	0.681745i	−0.0579640	+	0.0334655i
$416$	13.3358	−	10.7299i	0.653839	−	0.526079i
$417$	−21.5727	−	33.9249i	−1.05642	−	1.66131i
$418$	−1.36843	+	2.54827i	−0.0669322	+	0.124640i
$419$	−25.1656	+	21.1165i	−1.22942	+	1.03161i	−0.231145	+	0.972919i	$0.574247\pi$
$419$	−25.1656	+	21.1165i	−1.22942	+	1.03161i	−0.998276	+	0.0586878i	$0.981308\pi$
$420$	−6.20534	−	5.99659i	−0.302790	−	0.292603i
$421$	−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	$0.723935\pi$
$422$	14.2718	+	11.2454i	0.694743	+	0.547415i
$423$	5.04841	+	7.23560i	0.245462	+	0.351807i
$424$	−2.59749	−	3.66963i	−0.126145	−	0.178213i
$425$	−0.651875	−	0.114943i	−0.0316206	−	0.00557556i
$426$	13.5610	+	19.9423i	0.657031	+	0.966206i
$427$	1.70179	−	4.67563i	0.0823555	−	0.226270i
$428$	9.19546	+	6.79731i	0.444479	+	0.328561i
$429$	18.8631	+	2.49942i	0.910718	+	0.120673i
$430$	8.46055	−	25.6786i	0.408004	−	1.23833i
$431$	−15.7135			−0.756890			−0.378445	−	0.925624i	$-0.623541\pi$
$431$	−15.7135			−0.756890			−0.378445	+	0.925624i	$0.623541\pi$
$432$	2.02374	−	20.6859i	0.0973674	−	0.995249i
$433$	−22.7396			−1.09280			−0.546398	−	0.837526i	$-0.684001\pi$
$433$	−22.7396			−1.09280			−0.546398	+	0.837526i	$0.684001\pi$
$434$	−1.35477	+	4.11185i	−0.0650310	+	0.197375i
$435$	15.0136	−	19.5323i	0.719848	−	0.936502i
$436$	18.9947	+	14.0409i	0.909681	+	0.672439i
$437$	−1.13691	+	3.12362i	−0.0543856	+	0.149423i
$438$	−11.9246	+	24.6850i	−0.569780	+	1.17949i
$439$	22.4308	+	3.95516i	1.07057	+	0.188770i	0.681040	−	0.732246i	$-0.261528\pi$
$439$	22.4308	+	3.95516i	1.07057	+	0.188770i	0.389526	+	0.921016i	$0.372639\pi$
$440$	14.7795	+	20.8799i	0.704584	+	0.995411i
$441$	−2.72104	+	1.26331i	−0.129573	+	0.0601575i
$442$	−1.84565	−	1.45426i	−0.0877886	−	0.0691721i
$443$	26.1511	−	9.51823i	1.24248	−	0.452225i	0.364624	−	0.931155i	$-0.381197\pi$
$443$	26.1511	−	9.51823i	1.24248	−	0.452225i	0.877853	+	0.478930i	$0.158975\pi$
$444$	−29.4176	+	8.42434i	−1.39610	+	0.399801i
$445$	4.83473	−	4.05682i	0.229188	−	0.192312i
$446$	−3.03056	+	5.64346i	−0.143501	+	0.267226i
$447$	−13.0611	+	25.0390i	−0.617769	+	1.18430i
$448$	3.92916	−	6.96862i	0.185635	−	0.329237i
$449$	−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	$0.346438\pi$
$450$	1.17930	−	4.97644i	0.0555925	−	0.234592i
$451$	23.0581	+	13.3126i	1.08576	+	0.626866i
$452$	30.5981	−	20.2740i	1.43921	−	0.953609i
$453$	9.92039	−	9.07512i	0.466101	−	0.426386i
$454$	−1.30581	−	42.3996i	−0.0612849	−	1.98991i
$455$	−1.30887	−	7.42297i	−0.0613608	−	0.347994i
$456$	1.28472	+	2.44245i	0.0601625	+	0.114378i
$457$	−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	$0.334792\pi$
$462$	8.62104	−	2.18404i	0.401087	−	0.101611i
$463$	27.3719	−	4.82641i	1.27208	−	0.224302i	0.503467	−	0.864014i	$-0.332057\pi$
$463$	27.3719	−	4.82641i	1.27208	−	0.224302i	0.768615	+	0.639712i	$0.220946\pi$
$464$	21.0322	+	8.90334i	0.976396	+	0.413327i
$465$	−12.8976	+	2.84803i	−0.598114	+	0.132074i
$466$	−0.240534	−	1.15499i	−0.0111425	−	0.0535040i
$467$	7.82023	−	13.5450i	0.361877	−	0.626789i	−0.626393	−	0.779508i	$-0.715469\pi$
$467$	7.82023	−	13.5450i	0.361877	−	0.626789i	0.988270	+	0.152718i	$0.0488027\pi$
$468$	12.0458	−	13.5829i	0.556817	−	0.627869i
$469$	−2.76339	−	4.78634i	−0.127602	−	0.221013i
$470$	−7.72787	+	6.90079i	−0.356460	+	0.318310i
$471$	1.78132	+	41.5969i	0.0820788	+	1.91668i
$472$	−11.2976	+	3.08899i	−0.520013	+	0.142182i
$473$	17.9105	+	21.3449i	0.823524	+	0.981438i
$474$	−19.0015	+	26.3618i	−0.872766	+	1.21084i
$475$	0.232252	+	0.638106i	0.0106564	+	0.0292783i
$476$	−1.05316	−	0.311400i	−0.0482716	−	0.0142730i
$477$	−3.36628	−	3.37756i	−0.154132	−	0.154648i
$478$	−9.36625	−	1.35570i	−0.428402	−	0.0620083i
$479$	2.31588	−	13.1340i	0.105815	−	0.600109i	−0.885076	−	0.465446i	$-0.845894\pi$
$479$	2.31588	−	13.1340i	0.105815	−	0.600109i	0.990892	−	0.134663i	$-0.0429950\pi$
$480$	24.4014	−	0.541915i	1.11377	−	0.0247349i
$481$	−25.1164	−	9.14162i	−1.14521	−	0.416822i
$482$	−1.41826	+	0.878123i	−0.0645998	+	0.0399974i
$483$	9.44581	−	3.90333i	0.429799	−	0.177608i
$484$	−4.35583	+	0.268555i	−0.197992	+	0.0122070i
$485$		−	46.0588i		−	2.09142i
$486$	−1.54722	−	21.9910i	−0.0701834	−	0.997534i
$487$			27.9244i			1.26537i	0.774408	+	0.632687i	$0.218048\pi$
$487$			27.9244i			1.26537i	−0.774408	+	0.632687i	$0.781952\pi$
$488$	6.01263	+	12.7244i	0.272179	+	0.576005i
$489$	27.8448	−	11.5064i	1.25919	−	0.520339i
$490$	−1.85454	−	2.99526i	−0.0837794	−	0.135312i
$491$	6.46025	+	2.35134i	0.291547	+	0.106114i	0.483653	−	0.875260i	$-0.339310\pi$
$491$	6.46025	+	2.35134i	0.291547	+	0.106114i	−0.192106	+	0.981374i	$0.561532\pi$
$492$	22.8363	−	11.1282i	1.02954	−	0.501699i
$493$	0.544445	−	3.08770i	0.0245206	−	0.139063i
$494$	−0.345311	+	2.38568i	−0.0155363	+	0.107337i
$495$	19.1539	+	19.2180i	0.860903	+	0.863787i
$496$	−5.56983	−	10.9050i	−0.250093	−	0.489648i
$497$	3.36733	+	9.25167i	0.151046	+	0.414994i
$498$	−1.08764	−	0.783964i	−0.0487382	−	0.0351302i
$499$	−23.1878	−	27.6341i	−1.03803	−	1.23707i	−0.970939	−	0.239327i	$-0.923073\pi$
$499$	−23.1878	−	27.6341i	−1.03803	−	1.23707i	−0.0670890	−	0.997747i	$-0.521371\pi$
$500$	−18.7846	−	2.13091i	−0.840071	−	0.0952973i
$501$	0.0610918	+	1.42660i	0.00272938	+	0.0637358i
$502$	−4.36236	−	4.88520i	−0.194702	−	0.218037i
$503$	−18.6089	−	32.2316i	−0.829730	−	1.43714i	−0.898250	−	0.439485i	$-0.855161\pi$
$503$	−18.6089	−	32.2316i	−0.829730	−	1.43714i	0.0685195	−	0.997650i	$-0.478172\pi$
$504$	2.87480	−	7.98345i	0.128054	−	0.355611i
$505$	−2.32435	+	4.02588i	−0.103432	+	0.179150i
$506$	−29.6620	+	6.17728i	−1.31864	+	0.274613i
$507$	−6.50232	+	1.43583i	−0.288778	+	0.0637674i
$508$	4.29359	+	9.86138i	0.190497	+	0.437528i
$509$	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	$0.209745\pi$
$510$	−0.822851	−	3.24803i	−0.0364364	−	0.143825i
$511$	−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
$516$	26.4404	−	2.76974i	1.16398	−	0.121931i
$517$	−1.85414	−	10.5154i	−0.0815451	−	0.462465i
$518$	−12.4865	+	0.384557i	−0.548626	+	0.0168965i
$519$	−27.7119	+	25.3506i	−1.21642	+	1.11277i
$520$	17.5258	+	12.1390i	0.768557	+	0.532331i
$521$	−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	$0.896237\pi$
$522$	23.5717	+	5.58591i	1.03170	+	0.244489i
$523$	18.6358	−	10.7594i	0.814886	−	0.470474i	−0.0337640	−	0.999430i	$-0.510749\pi$
$523$	18.6358	−	10.7594i	0.814886	−	0.470474i	0.848650	+	0.528955i	$0.177416\pi$
$524$	13.3196	−	26.7478i	0.581869	−	1.16848i
$525$	0.965628	−	1.85117i	0.0421435	−	0.0807919i
$526$	−8.50234	−	4.56579i	−0.370720	−	0.199078i
$527$	−1.28772	+	1.08052i	−0.0560939	+	0.0470684i
$528$	−12.7637	+	21.6755i	−0.555467	+	0.943305i
$529$	−11.1069	+	4.04259i	−0.482910	+	0.175765i
$530$	3.46573	−	4.39848i	0.150542	−	0.191058i
$531$	−11.2676	+	5.23124i	−0.488971	+	0.227016i
$532$	0.263548	+	1.09539i	0.0114263	+	0.0474913i
$533$	21.8521	+	3.85311i	0.946519	+	0.166897i
$534$	5.58809	+	2.69945i	0.241820	+	0.116816i
$535$	−4.87131	+	13.3838i	−0.210605	+	0.578632i
$536$	15.1199	+	3.96886i	0.653080	+	0.171429i
$537$	−10.4647	+	13.6143i	−0.451586	+	0.587501i
$538$	−13.7720	−	4.53760i	−0.593755	−	0.195630i
$539$	3.63071			0.156386
$540$	25.4223	−	4.88836i	1.09400	−	0.210361i
$541$	24.3595			1.04730			0.523649	−	0.851934i	$-0.324571\pi$
$541$	24.3595			1.04730			0.523649	+	0.851934i	$0.324571\pi$
$542$	−21.2649	−	7.00635i	−0.913406	−	0.300948i
$543$	6.38501	+	0.846034i	0.274007	+	0.0363068i
$544$	2.72153	−	1.49742i	0.116685	−	0.0642013i
$545$	−10.0625	+	27.6464i	−0.431029	+	1.18424i
$546$	6.12887	−	4.16769i	0.262291	−	0.178361i
$547$	11.3225	+	1.99646i	0.484115	+	0.0853625i	0.410378	−	0.911915i	$-0.365397\pi$
$547$	11.3225	+	1.99646i	0.484115	+	0.0853625i	0.0737361	+	0.997278i	$0.476508\pi$
$548$	28.4144	−	6.83641i	1.21380	−	0.292037i
$549$	8.54138	+	12.2419i	0.364537	+	0.522471i
$550$	−3.83067	+	4.86163i	−0.163340	+	0.207301i
$551$	−3.02248	+	1.10009i	−0.128762	+	0.0468656i
$552$	−10.9487	+	26.7544i	−0.466008	+	1.13874i
$553$	−10.1627	+	8.52755i	−0.432163	+	0.362628i
$554$	26.9347	+	14.4640i	1.14435	+	0.614519i
$555$	−20.4515	−	32.1617i	−0.868118	−	1.36519i
$556$	41.5552	+	20.6932i	1.76233	+	0.877589i
$557$	−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	$0.546800\pi$
$558$	−7.75609	−	10.4176i	−0.328342	−	0.441014i
$559$	20.1103	+	11.6107i	0.850575	+	0.491080i
$560$	9.71110	+	2.23197i	0.410369	+	0.0943179i
$561$	3.29248	+	1.04114i	0.139008	+	0.0439570i
$562$	−46.3136	+	1.42636i	−1.95362	+	0.0601673i
$563$	4.92281	+	27.9187i	0.207472	+	1.17663i	0.893502	+	0.449058i	$0.148241\pi$
$563$	4.92281	+	27.9187i	0.207472	+	1.17663i	−0.686031	+	0.727573i	$0.740648\pi$
$564$	−9.30540	−	4.14689i	−0.391828	−	0.174616i
$565$	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	$-0.0575293\pi$
$570$	−2.46359	+	2.39708i	−0.103188	+	0.100403i
$571$	4.89103	−	0.862420i	0.204683	−	0.0360911i	−0.0703665	−	0.997521i	$-0.522417\pi$
$571$	4.89103	−	0.862420i	0.204683	−	0.0360911i	0.275049	+	0.961430i	$0.411306\pi$
$572$	−20.1450	+	8.77101i	−0.842303	+	0.366734i
$573$	6.54698	−	20.7040i	0.273504	−	0.864921i
$574$	10.1531	−	2.11444i	0.423781	−	0.0882548i
$575$	−3.55656	+	6.16014i	−0.148319	+	0.256896i
$576$	10.3279	+	21.6641i	0.430328	+	0.902673i
$577$	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	$0.807886\pi$
$578$	15.7292	+	17.6144i	0.654250	+	0.732664i
$579$	24.1202	−	15.3379i	1.00240	−	0.637423i
$580$	−3.20644	+	28.2656i	−0.133140	+	1.17367i
$581$	−0.351830	−	0.419295i	−0.0145964	−	0.0173953i
$582$	41.3046	−	18.5770i	1.71213	−	0.770041i
$583$	1.97385	+	5.42312i	0.0817487	+	0.224603i
$584$	−2.91966	−	31.5204i	−0.120817	−	1.30432i
$585$	20.4778	+	9.59068i	0.846654	+	0.396526i
$586$	−3.44798	+	23.8213i	−0.142435	+	0.984051i
$587$	3.42835	−	19.4432i	0.141503	−	0.802505i	−0.828605	−	0.559834i	$-0.810865\pi$
$587$	3.42835	−	19.4432i	0.141503	−	0.802505i	0.970108	−	0.242672i	$-0.0780238\pi$
$588$	1.93810	−	2.87120i	0.0799257	−	0.118406i
$589$	1.62049	+	0.589811i	0.0667712	+	0.0243027i
$590$	−7.67947	−	12.4031i	−0.316159	−	0.510627i
$591$	−0.438123	+	3.30651i	−0.0180220	+	0.136012i
$592$	24.0724	−	25.8652i	0.989368	−	1.06305i
$593$		−	11.3018i		−	0.464109i	−0.972703	−	0.232054i	$-0.925455\pi$
$593$		−	11.3018i		−	0.464109i	0.972703	−	0.232054i	$-0.0745447\pi$
$594$	−9.50898	+	24.9281i	−0.390158	+	1.02281i
$595$		−	1.36789i		−	0.0560781i
$596$	−2.00671	−	32.5479i	−0.0821981	−	1.33321i
$597$	−3.68029	−	2.82888i	−0.150624	−	0.115778i
$598$	−21.4684	+	13.2923i	−0.877910	+	0.543564i
$599$	−23.0144	−	8.37655i	−0.940342	−	0.342256i	−0.174041	−	0.984738i	$-0.555683\pi$
$599$	−23.0144	−	8.37655i	−0.940342	−	0.342256i	−0.766301	+	0.642482i	$0.777905\pi$
$600$	1.79979	+	5.62450i	0.0734760	+	0.229619i
$601$	−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	$0.0951867\pi$
$602$	10.7414	+	1.55474i	0.437787	+	0.0633666i
$603$	16.5148	+	1.47269i	0.672536	+	0.0599726i
$604$	−4.40208	+	14.8879i	−0.179118	+	0.605782i
$605$	−1.85910	−	5.10784i	−0.0755832	−	0.207663i
$606$	−4.54782	−	0.460658i	−0.184743	−	0.0187129i
$607$	0.0408195	+	0.0486467i	0.00165681	+	0.00197451i	0.766872	−	0.641800i	$-0.221812\pi$
$607$	0.0408195	+	0.0486467i	0.00165681	+	0.00197451i	−0.765215	+	0.643774i	$0.777368\pi$
$608$	−2.72633	−	1.64981i	−0.110567	−	0.0669088i
$609$	8.76837	+	4.57384i	0.355312	+	0.185342i
$610$	−13.0748	+	11.6754i	−0.529381	+	0.472724i
$611$	−4.44929	−	7.70640i	−0.179999	−	0.311768i
$612$	2.58089	−	2.04795i	0.104326	−	0.0827836i
$613$	−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	$0.966004\pi$
$614$	2.52321	+	12.1159i	0.101828	+	0.488958i
$615$	21.3568	+	23.3460i	0.861188	+	0.941401i
$616$	−7.22431	+	7.29834i	−0.291076	+	0.294059i
$617$	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	$0.291962\pi$
$618$	−9.26334	+	32.7712i	−0.372626	+	1.31825i
$619$	−15.4711	+	18.4377i	−0.621835	+	0.741074i	−0.981385	−	0.192052i	$-0.938486\pi$
$619$	−15.4711	+	18.4377i	−0.621835	+	0.741074i	0.359550	+	0.933126i	$0.382930\pi$
$620$	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
$624$	−3.81731	+	20.6128i	−0.152815	+	0.825174i
$625$	−5.13549	−	29.1248i	−0.205420	−	1.16499i
$626$	0.000668374		0.0217020i	2.67136e−5		0.000867386i
$627$	−0.763849	−	3.45919i	−0.0305052	−	0.138147i
$628$	−26.5545	−	40.0769i	−1.05964	−	1.59924i
$629$	−4.20076	−	2.42531i	−0.167495	−	0.0967035i
$630$	10.5509	+	0.614230i	0.420356	+	0.0244715i
$631$	−1.68101	+	0.970532i	−0.0669200	+	0.0386363i	−0.533087	−	0.846061i	$-0.678968\pi$
$631$	−1.68101	+	0.970532i	−0.0669200	+	0.0386363i	0.466167	+	0.884697i	$0.345635\pi$
$632$	3.07977	−	37.3967i	0.122507	−	1.48756i
$633$	−22.2331	+	0.952094i	−0.883685	+	0.0378423i
$634$	−3.59442	+	6.69347i	−0.142753	+	0.265832i
$635$	−10.2623	+	8.61105i	−0.407245	+	0.341719i
$636$	5.34231	+	1.33395i	0.211836	+	0.0528947i
$637$	2.84332	−	1.03488i	0.112656	−	0.0410036i
$638$	−23.0279	−	18.1446i	−0.911682	−	0.718350i
$639$	−28.5170	−	7.69224i	−1.12812	−	0.304300i
$640$	−23.8096	+	15.0798i	−0.941156	+	0.596083i
$641$	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	$0.422539\pi$
$642$	−13.9671	+	1.02963i	−0.551237	+	0.0406363i
$643$	−9.60776	+	26.3971i	−0.378893	+	1.04100i	0.592923	+	0.805259i	$0.297974\pi$
$643$	−9.60776	+	26.3971i	−0.378893	+	1.04100i	−0.971816	+	0.235741i	$0.924248\pi$
$644$	−7.01525	+	9.49028i	−0.276439	+	0.373969i
$645$	12.6461	+	30.6028i	0.497940	+	1.20498i
$646$	−0.136896	+	0.415491i	−0.00538609	+	0.0163473i
$647$	9.07554			0.356796			0.178398	−	0.983958i	$-0.442909\pi$
$647$	9.07554			0.356796			0.178398	+	0.983958i	$0.442909\pi$
$648$	14.6374	+	20.8266i	0.575012	+	0.818145i
$649$	15.0344			0.590153
$650$	−1.61418	+	4.89917i	−0.0633132	+	0.192161i
$651$	−2.02499	−	4.90035i	−0.0793658	−	0.192060i
$652$	−20.6799	+	27.9759i	−0.809887	+	1.09562i
$653$	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	$-0.144500\pi$
$654$	−28.8513	+	2.12687i	−1.12817	+	0.0831672i
$655$	36.6521	+	6.46275i	1.43211	+	0.252520i
$656$	−15.9520	+	24.6167i	−0.622821	+	0.961119i
$657$	−8.63575	−	32.4460i	−0.336913	−	1.26584i
$658$	−3.26682	−	2.57406i	−0.127354	−	0.100347i
$659$	−22.3941	+	8.15079i	−0.872351	+	0.317510i	−0.739119	−	0.673575i	$-0.764758\pi$
$659$	−22.3941	+	8.15079i	−0.872351	+	0.317510i	−0.133232	+	0.991085i	$0.542536\pi$
$660$	−30.3973	−	7.59008i	−1.18321	−	0.295444i
$661$	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	$-0.0528711\pi$
$662$	−14.1152	+	26.2852i	−0.548604	+	1.02160i
$663$	2.87520	−	0.123126i	0.111664	−	0.00478180i
$664$	1.54292	+	0.127066i	0.0598768	+	0.00493110i
$665$	−1.21528	+	0.701643i	−0.0471266	+	0.0272086i
$666$	20.5933	−	31.3124i	0.797973	−	1.21333i
$667$	−29.1784	−	16.8462i	−1.12979	−	0.652286i
$668$	−0.910710	−	1.37447i	−0.0352364	−	0.0531799i
$669$	−1.69164	−	7.66080i	−0.0654026	−	0.296184i
$670$	0.599361	+	19.4611i	0.0231553	+	0.751849i
$671$	−3.13701	−	17.7909i	−0.121103	−	0.686810i
$672$	1.91522	+	9.60895i	0.0738811	+	0.370673i
$673$	−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	$-0.0176549\pi$
$678$	−12.2281	+	43.2596i	−0.469617	+	1.66138i
$679$	18.2086	−	3.21067i	0.698783	−	0.123214i
$680$	2.74970	+	2.72180i	0.105446	+	0.104376i
$681$	35.0671	+	38.3333i	1.34377	+	1.46894i
$682$	3.20469	+	15.3882i	0.122714	+	0.589245i
$683$	19.7570	−	34.2201i	0.755979	−	1.30939i	−0.188906	−	0.981995i	$-0.560494\pi$
$683$	19.7570	−	34.2201i	0.755979	−	1.30939i	0.944886	−	0.327400i	$-0.106172\pi$
$684$	−3.14330	−	1.24248i	−0.120187	−	0.0475072i
$685$	18.2005	+	31.5243i	0.695407	+	1.20448i
$686$	1.05485	−	0.941957i	0.0402745	−	0.0359641i
$687$	−0.130799	−	0.0682287i	−0.00499029	−	0.00260309i
$688$	−24.4983	+	18.4984i	−0.933989	+	0.705246i
$689$	3.09157	+	3.68439i	0.117779	+	0.140364i
$690$	−35.8227	−	3.62855i	−1.36375	−	0.138137i
$691$	14.0564	+	38.6198i	0.534732	+	1.46917i	0.853379	+	0.521292i	$0.174550\pi$
$691$	14.0564	+	38.6198i	0.534732	+	1.46917i	−0.318646	+	0.947874i	$0.603228\pi$
$692$	12.2969	−	41.5883i	0.467457	−	1.58095i
$693$	−6.26238	+	8.91185i	−0.237888	+	0.338533i
$694$	−21.1781	−	3.06538i	−0.803908	−	0.116360i
$695$	−10.0405	+	56.9424i	−0.380857	+	2.15995i
$696$	−26.6413	+	8.52497i	−1.00984	+	0.323138i
$697$	3.78402	+	1.37727i	0.143330	+	0.0521678i
$698$	39.9221	−	24.7180i	1.51107	−	0.935592i
$699$	1.14560	+	0.880570i	0.0433304	+	0.0333062i
$700$	0.148359	+	2.40632i	0.00560746	+	0.0909503i
$701$			2.91498i			0.110097i	0.998484	+	0.0550486i	$0.0175314\pi$
$701$			2.91498i			0.110097i	−0.998484	+	0.0550486i	$0.982469\pi$
$702$	−0.341366	+	22.2324i	−0.0128840	+	0.839106i
$703$			4.97613i			0.187678i
$704$	−0.296133	−	29.0442i	−0.0111609	−	1.09464i
$705$	1.66677	−	12.5791i	0.0627741	−	0.473756i
$706$	−19.2777	−	31.1354i	−0.725527	−	1.17180i
$707$	−1.75360	−	0.638257i	−0.0659508	−	0.0240041i
$708$	8.02548	−	11.8894i	0.301616	−	0.446830i
$709$	−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	$0.791832\pi$
$710$	4.96857	−	34.3268i	0.186467	−	1.28826i
$711$	−3.40246	−	39.6538i	−0.127602	−	1.48713i
$712$	−7.13546	+	0.660942i	−0.267413	+	0.0247699i
$713$	6.17825	+	16.9746i	0.231377	+	0.635704i
$714$	1.22670	−	0.551716i	0.0459081	−	0.0206474i
$715$	−17.5908	−	20.9639i	−0.657858	−	0.784005i
$716$	2.23494	−	19.7016i	0.0835235	−	0.736282i
$717$	9.78079	−	6.21956i	0.365270	−	0.232274i
$718$	−22.3365	−	25.0136i	−0.833592	−	0.933501i
$719$	−11.7507	−	20.3527i	−0.438226	−	0.759029i	0.559327	−	0.828947i	$-0.311060\pi$
$719$	−11.7507	−	20.3527i	−0.438226	−	0.759029i	−0.997553	+	0.0699179i	$0.977726\pi$
$720$	−22.2286	+	19.9868i	−0.828411	+	0.744866i
$721$	−6.95149	+	12.0403i	−0.258887	+	0.448406i
$722$	−25.8663	+	5.38681i	−0.962644	+	0.200476i
$723$	0.615969	−	1.94792i	0.0229081	−	0.0724440i
$724$	−6.81892	+	2.96892i	−0.253423	+	0.110339i
$725$	−6.77824	+	1.19519i	−0.251737	+	0.0443881i
$726$	3.83078	−	3.72736i	0.142173	−	0.138335i
$727$	1.03813	−	1.23720i	0.0385022	−	0.0458852i	−0.746450	−	0.665442i	$-0.768243\pi$
$727$	1.03813	−	1.23720i	0.0385022	−	0.0458852i	0.784952	+	0.619557i	$0.212688\pi$
$728$	−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
$732$	−15.7438	−	7.01611i	−0.581906	−	0.259323i
$733$	−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	$0.957423\pi$
$734$	22.6953	−	0.698965i	0.837698	−	0.0257993i
$735$	4.11388	+	1.30088i	0.151743	+	0.0479838i
$736$	−5.11828	−	32.9854i	−0.188662	−	1.21586i
$737$	−17.3778	−	10.0331i	−0.640120	−	0.369573i
$738$	−12.3223	+	28.5685i	−0.453592	+	1.05162i
$739$	4.17900	−	2.41275i	0.153727	−	0.0887543i	−0.421163	−	0.906985i	$-0.638378\pi$
$739$	4.17900	−	2.41275i	0.153727	−	0.0887543i	0.574890	+	0.818231i	$0.305045\pi$
$740$	39.3954	+	19.6177i	1.44820	+	0.721163i
$741$	−1.58419	−	2.49127i	−0.0581965	−	0.0915190i
$742$	1.98046	+	1.06351i	0.0727050	+	0.0390429i
$743$	−16.7351	+	14.0425i	−0.613953	+	0.515168i	−0.895896	−	0.444263i	$-0.853465\pi$
$743$	−16.7351	+	14.0425i	−0.613953	+	0.515168i	0.281943	+	0.959431i	$0.409021\pi$
$744$	13.8798	+	5.68003i	0.508859	+	0.208240i
$745$	38.1671	−	13.8917i	1.39833	−	0.508952i
$746$	−19.4135	+	24.6383i	−0.710778	+	0.902072i
$747$	1.63604	−	0.140379i	0.0598596	−	0.00513619i
$748$	−3.87675	+	0.932733i	−0.141748	+	0.0341041i
$749$	−5.63065	−	0.992836i	−0.205740	−	0.0362774i
$750$	19.1464	−	13.0198i	0.699129	−	0.475415i
$751$	−8.66801	+	23.8152i	−0.316300	+	0.869027i	0.675049	+	0.737773i	$0.264123\pi$
$751$	−8.66801	+	23.8152i	−0.316300	+	0.869027i	−0.991349	+	0.131254i	$0.958100\pi$
$752$	11.6745	−	1.44506i	0.425726	−	0.0526959i
$753$	7.95191	+	1.05365i	0.289784	+	0.0383972i
$754$	−23.2057	−	7.64579i	−0.845101	−	0.278443i
$755$	−19.3371			−0.703749
$756$	3.70468	+	9.70955i	0.134738	+	0.353133i
$757$	−49.2601			−1.79039			−0.895194	−	0.445676i	$-0.852963\pi$
$757$	−49.2601			−1.79039			−0.895194	+	0.445676i	$0.852963\pi$
$758$	−21.2760	−	7.01001i	−0.772780	−	0.254615i
$759$	22.6144	−	29.4207i	0.820850	−	1.06790i
$760$	1.00772	−	3.83904i	0.0365538	−	0.139256i
$761$	−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	$0.207577\pi$
$762$	−11.8613	−	5.72987i	−0.429691	−	0.207571i
$763$	−11.6310	−	2.05086i	−0.421071	−	0.0742462i
$764$	5.86528	+	24.3780i	0.212198	+	0.881967i
$765$	3.35760	+	2.35939i	0.121394	+	0.0853040i
$766$	−18.6794	+	23.7066i	−0.674914	+	0.856556i
$767$	11.7739	−	4.28536i	0.425132	−	0.154735i
$768$	−23.1265	−	15.2698i	−0.834505	−	0.551001i
$769$	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	$0.200765\pi$
$770$	−11.2687	−	6.05131i	−0.406094	−	0.218074i
$771$	5.05575	−	9.69221i	0.182078	−	0.349056i
$772$	−14.7127	+	29.5452i	−0.529520	+	1.06336i
$773$	−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	$0.385179\pi$
$774$	−22.3434	+	23.6839i	−0.803116	+	0.851300i
$775$	3.19579	+	1.84509i	0.114796	+	0.0662777i
$776$	−29.7771	+	42.9910i	−1.06894	+	1.54329i
$777$	11.2890	−	10.3271i	0.404991	−	0.370484i
$778$	47.2206	−	1.45429i	1.69294	−	0.0521389i
$779$	−0.717351	−	4.06830i	−0.0257018	−	0.145762i
$780$	−25.9685	+	2.72031i	−0.929822	+	0.0974026i
$781$	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
$786$	8.98731	+	35.4755i	0.320567	+	1.26537i
$787$	52.5231	−	9.26124i	1.87225	−	0.330127i	0.882200	−	0.470875i	$-0.156062\pi$
$787$	52.5231	−	9.26124i	1.87225	−	0.330127i	0.990046	+	0.140748i	$0.0449506\pi$
$788$	−1.53747	−	3.53122i	−0.0547702	−	0.125794i
$789$	11.5416	−	2.54859i	0.410893	−	0.0907324i
$790$	45.7550	−	9.52875i	1.62789	−	0.339018i
$791$	−9.17633	+	15.8939i	−0.326273	+	0.565121i
$792$	−5.45359	−	30.3211i	−0.193785	−	1.07741i
$793$	−7.52774	−	13.0384i	−0.267318	−	0.463008i
$794$	2.30914	+	2.58590i	0.0819484	+	0.0917702i
$795$	0.293428	+	6.85206i	0.0104068	+	0.243018i
$796$	5.32583	+	0.604160i	0.188769	+	0.0214139i
$797$	−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	$0.801186\pi$
$798$	−1.11938	−	0.806846i	−0.0396257	−	0.0285620i
$799$	−0.552330	−	1.51751i	−0.0195400	−	0.0536858i
$800$	−5.13231	−	4.48981i	−0.181455	−	0.158739i
$801$	−7.34499	+	1.95493i	−0.259522	+	0.0690739i
$802$	1.30890	−	9.04288i	0.0462187	−	0.319315i
$803$	−7.05608	+	40.0170i	−0.249004	+	1.41217i
$804$	−17.2106	+	8.38681i	−0.606972	+	0.295780i
$805$	−13.8129	−	5.02749i	−0.486841	−	0.177196i
$806$	6.89589	+	11.1375i	0.242897	+	0.392303i
$807$	16.4130	−	6.78243i	0.577766	−	0.238753i
$808$	4.77228	−	2.25504i	0.167888	−	0.0793320i
$809$			13.1967i			0.463972i	0.972719	+	0.231986i	$0.0745223\pi$
$809$			13.1967i			0.463972i	−0.972719	+	0.231986i	$0.925478\pi$
$810$	−19.7062	+	24.8384i	−0.692405	+	0.872734i
$811$		−	16.5670i		−	0.581745i	−0.956762	−	0.290873i	$-0.906054\pi$
$811$		−	16.5670i		−	0.581745i	0.956762	−	0.290873i	$-0.0939456\pi$
$812$	−11.3979	+	0.702727i	−0.399988	+	0.0246609i
$813$	25.3428	−	10.4725i	0.888809	−	0.367287i
$814$	−38.5631	+	23.8766i	−1.35163	+	0.836875i
$815$	−40.7184	−	14.8203i	−1.42630	−	0.519132i
$816$	−1.33182	+	3.56367i	−0.0466230	+	0.124753i
$817$	0.750720	−	4.25755i	0.0262644	−	0.148953i
$818$	43.3874	+	6.28003i	1.51701	+	0.219576i
$819$	−2.36406	+	8.76414i	−0.0826069	+	0.306244i
$820$	−35.0363	−	10.3596i	−1.22352	−	0.361772i
$821$	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	$0.733976\pi$
$822$	−20.9295	+	29.0367i	−0.729999	+	1.01277i
$823$	−25.2646	−	30.1092i	−0.880670	−	1.04954i	−0.998403	−	0.0564960i	$-0.982007\pi$
$823$	−25.2646	−	30.1092i	−0.880670	−	1.04954i	0.117733	−	0.993045i	$-0.462437\pi$
$824$	−10.3712	−	37.9313i	−0.361298	−	1.32140i
$825$	−0.324326	−	7.57358i	−0.0112916	−	0.263678i
$826$	4.36805	−	3.90056i	0.151984	−	0.135718i
$827$	5.32231	+	9.21851i	0.185075	+	0.320559i	0.943602	−	0.331083i	$-0.107414\pi$
$827$	5.32231	+	9.21851i	0.185075	+	0.320559i	−0.758527	+	0.651642i	$0.774081\pi$
$828$	−11.1945	−	33.5886i	−0.389034	−	1.16729i
$829$	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	$0.0517879\pi$
$830$	0.393138	+	1.88776i	0.0136460	+	0.0655252i
$831$	−36.5629	+	8.07374i	−1.26835	+	0.280075i
$832$	−8.51055	−	22.6610i	−0.295050	−	0.785627i
$833$	0.540776	−	0.0953533i	0.0187368	−	0.00330380i
$834$	−55.1145	+	13.9626i	−1.90846	+	0.483486i
$835$	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	0.573424	−	0.819259i	$-0.305615\pi$
$839$	−3.87598	−	3.25233i	−0.133814	−	0.112283i	−0.707238	+	0.706975i	$0.750059\pi$
$840$	−10.8007	+	5.68113i	−0.372660	+	0.196018i
$841$	−0.625385	−	3.54673i	−0.0215650	−	0.122301i
$842$	1.55193	+	50.3908i	0.0534830	+	1.73658i
$843$	41.8720	−	38.3042i	1.44215	−	1.31927i
$844$	21.4206	−	14.1931i	0.737328	−	0.488546i
$845$	8.29398	+	4.78853i	0.285322	+	0.164731i
$846$	11.9529	−	3.57883i	0.410951	−	0.123043i
$847$	1.88971	−	1.09103i	0.0649313	−	0.0374881i
$848$	−6.07852	+	1.86490i	−0.208737	+	0.0640410i
$849$	−11.6495	+	22.3329i	−0.399811	+	0.766464i
$850$	−0.442878	+	0.824721i	−0.0151906	+	0.0282877i
$851$	−39.9300	+	33.5052i	−1.36878	+	1.14854i
$852$	32.7876	−	9.38941i	1.12328	−	0.321676i
$853$	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	$0.258232\pi$
$854$	−5.52711	−	4.35503i	−0.189134	−	0.149026i
$855$	0.373925	−	4.19322i	0.0127880	−	0.143405i
$856$	13.1995	−	9.34304i	0.451150	−	0.319339i
$857$	−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	$0.560865\pi$
$858$	11.7051	−	24.2305i	0.399604	−	0.827215i
$859$	−10.0504	+	27.6131i	−0.342914	+	0.942148i	0.641631	+	0.767014i	$0.278258\pi$
$859$	−10.0504	+	27.6131i	−0.342914	+	0.942148i	−0.984545	+	0.175134i	$0.943964\pi$
$860$	−30.7468	−	22.7282i	−1.04846	−	0.775024i
$861$	−7.74074	+	10.0705i	−0.263804	+	0.343201i
$862$	−6.95402	+	21.1061i	−0.236855	+	0.718876i
$863$	−23.7496			−0.808444			−0.404222	−	0.914661i	$-0.632458\pi$
$863$	−23.7496			−0.808444			−0.404222	+	0.914661i	$0.632458\pi$
$864$	−26.8893	−	11.8728i	−0.914794	−	0.403922i
$865$	54.0167			1.83662
$866$	−10.0634	+	30.5435i	−0.341970	+	1.03791i
$867$	−28.6720	−	3.79913i	−0.973752	−	0.129025i
$868$	4.92342	+	3.63941i	0.167112	+	0.123530i
$869$	−16.4740	+	45.2620i	−0.558843	+	1.53541i
$870$	−19.5912	−	28.8101i	−0.664204	−	0.976755i
$871$	−16.4689	−	2.90391i	−0.558026	−	0.0983951i
$872$	27.2657	−	19.2996i	0.923334	−	0.653566i
$873$	−23.5261	+	50.2323i	−0.796236	+	1.70011i
$874$	3.69247	+	2.90944i	0.124900	+	0.0984133i
$875$	8.88246	−	3.23295i	0.300282	−	0.109294i
$876$	27.8792	+	26.9413i	0.941953	+	0.910264i
$877$	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	$0.192718\pi$
$878$	15.2393	−	28.3784i	0.514302	−	0.957726i
$879$	−15.8183	−	24.8757i	−0.533539	−	0.839035i
$880$	34.5863	−	10.6111i	1.16590	−	0.357701i
$881$	−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	$0.557573\pi$
$882$	0.492655	+	4.21394i	0.0165886	+	0.141891i
$883$	−29.5182	−	17.0423i	−0.993366	−	0.573520i	−0.0870873	−	0.996201i	$-0.527756\pi$
$883$	−29.5182	−	17.0423i	−0.993366	−	0.573520i	−0.906279	+	0.422680i	$0.861089\pi$
$884$	−2.77014	+	1.83546i	−0.0931698	+	0.0617333i
$885$	17.0352	+	5.38685i	0.572633	+	0.181077i
$886$	−1.21153	−	39.3381i	−0.0407021	−	1.32159i
$887$	9.36825	+	53.1300i	0.314555	+	1.78393i	0.574704	+	0.818361i	$0.305117\pi$
$887$	9.36825	+	53.1300i	0.314555	+	1.78393i	−0.260150	+	0.965568i	$0.583772\pi$
$888$	−1.70336	+	43.2415i	−0.0571611	+	1.45109i
$889$	−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
$894$	27.8518	+	28.6245i	0.931504	+	0.957348i
$895$	24.3212	−	4.28848i	0.812968	−	0.143348i
$896$	−7.62130	−	8.36156i	−0.254610	−	0.279340i
$897$	9.32406	−	29.4861i	0.311321	−	0.984514i
$898$	0.502908	+	2.41486i	0.0167822	+	0.0805848i
$899$	−8.73956	+	15.1374i	−0.291481	+	0.504859i
$900$	−6.16239	−	3.78635i	−0.205413	−	0.126212i
$901$	0.436423	+	0.755907i	0.0145394	+	0.0251829i
$902$	28.0857	−	25.0798i	0.935152	−	0.835067i
$903$	−11.2168	+	7.13271i	−0.373272	+	0.237362i
$904$	−13.6905	−	50.0713i	−0.455340	−	1.66535i
$905$	−5.95435	−	7.09612i	−0.197929	−	0.235883i
$906$	−7.79928	−	17.3411i	−0.259114	−	0.576121i
$907$	−7.77481	−	21.3611i	−0.258158	−	0.709284i	−0.999281	−	0.0379147i	$-0.987928\pi$
$907$	−7.77481	−	21.3611i	−0.258158	−	0.709284i	0.741123	−	0.671370i	$-0.234294\pi$
$908$	−57.5284	−	17.0101i	−1.90915	−	0.564498i
$909$	4.59132	−	3.20345i	0.152284	−	0.106252i
$910$	−10.5497	−	1.52699i	−0.349718	−	0.0506193i
$911$	−8.74450	+	49.5925i	−0.289718	+	1.64307i	0.398210	+	0.917294i	$0.369632\pi$
$911$	−8.74450	+	49.5925i	−0.289718	+	1.64307i	−0.687928	+	0.725779i	$0.741479\pi$
$912$	3.84922	−	0.644705i	0.127460	−	0.0213483i
$913$	−1.86742	−	0.679686i	−0.0618027	−	0.0224943i
$914$	−11.2950	+	6.99338i	−0.373605	+	0.231321i
$915$	2.82000	−	21.2825i	0.0932262	−	0.703577i
$916$	0.170024	−	0.0104827i	0.00561775	−	0.000346358i
$917$			14.9403i			0.493374i
$918$	−0.761628	+	3.96265i	−0.0251375	+	0.130787i
$919$			20.3505i			0.671300i	0.941987	+	0.335650i	$0.108956\pi$
$919$			20.3505i			0.671300i	−0.941987	+	0.335650i	$0.891044\pi$
$920$	37.5907	−	17.7627i	1.23933	−	0.585619i
$921$	−12.0173	−	9.23721i	−0.395985	−	0.304376i
$922$	11.0716	+	17.8817i	0.364624	+	0.588904i
$923$	27.9937	+	10.1889i	0.921423	+	0.335371i
$924$	0.881683	−	12.5462i	0.0290053	−	0.412740i
$925$	−1.84905	+	10.4865i	−0.0607965	+	0.344794i
$926$	5.63073	−	38.9015i	0.185037	−	1.27838i
$927$	−17.5637	−	37.8306i	−0.576869	−	1.24252i
$928$	21.2667	−	24.3100i	0.698113	−	0.798014i
$929$	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	$0.709579\pi$
$930$	−1.88244	+	18.5843i	−0.0617277	+	0.609404i
$931$	−0.362099	−	0.431533i	−0.0118673	−	0.0141429i
$932$	−1.65782	−	0.188062i	−0.0543036	−	0.00616018i
$933$	28.8489	+	15.0485i	0.944471	+	0.492664i
$934$	−14.7326	−	16.4984i	−0.482067	−	0.539844i
$935$	−2.48321	−	4.30105i	−0.0812097	−	0.140659i
$936$	−12.9135	−	22.1909i	−0.422090	−	0.725331i
$937$	−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	$0.296421\pi$
$938$	−7.65189	+	1.59355i	−0.249843	+	0.0520312i
$939$	−0.0179489	−	0.0196207i	−0.000585740	−	0.000640297i
$940$	5.84906	+	13.4339i	0.190775	+	0.438166i
$941$	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	$0.325816\pi$
$942$	56.6607	+	16.0161i	1.84611	+	0.521834i
$943$	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	0.992699	−	0.120621i	$-0.0384884\pi$
$947$	32.1979	+	27.0172i	1.04629	+	0.877942i	0.0535923	+	0.998563i	$0.482933\pi$
$948$	26.9997	+	37.1890i	0.876909	+	1.20784i
$949$	5.88046	+	33.3498i	0.190888	+	1.08258i
$950$	0.959878	−	0.0295621i	0.0311426	−	0.000959123i
$951$	−2.00638	−	9.08614i	−0.0650614	−	0.294638i
$952$	−0.884347	+	1.27678i	−0.0286619	+	0.0413808i
$953$	−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	$0.785305\pi$
$954$	−6.02645	+	3.02680i	−0.195113	+	0.0979963i
$955$	−27.0462	+	15.6151i	−0.875193	+	0.505293i
$956$	−5.96601	+	11.9806i	−0.192954	+	0.387482i
$957$	35.8734	−	1.53622i	1.15962	−	0.0496589i
$958$	−16.6165	−	8.92314i	−0.536856	−	0.288294i
$959$	−11.1939	+	9.39281i	−0.361470	+	0.303310i
$960$	10.0710	−	33.0155i	0.325040	−	1.06557i
$961$	−20.3243	+	7.39743i	−0.655622	+	0.238627i
$962$	−23.3942	+	29.6904i	−0.754260	+	0.957256i
$963$	12.1489	−	12.1084i	0.391494	−	0.390187i
$964$	0.551831	+	2.29359i	0.0177733	+	0.0738717i
$965$	−40.4854	−	7.13867i	−1.30327	−	0.229802i
$966$	−1.06264	−	14.4149i	−0.0341900	−	0.463792i
$967$	0.421349	−	1.15765i	0.0135497	−	0.0372274i	−0.932733	−	0.360567i	$-0.882583\pi$
$967$	0.421349	−	1.15765i	0.0135497	−	0.0372274i	0.946283	+	0.323339i	$0.104806\pi$
$968$	−1.56696	+	5.96954i	−0.0503640	+	0.191868i
$969$	−0.204620	−	0.495167i	−0.00657334	−	0.0159071i
$970$	−61.8655	−	20.3834i	−1.98638	−	0.654471i
$971$	50.7457			1.62851			0.814254	−	0.580509i	$-0.197146\pi$
$971$	50.7457			1.62851			0.814254	+	0.580509i	$0.197146\pi$
$972$	−30.2228	−	7.65397i	−0.969396	−	0.245501i
$973$	−23.2112			−0.744117
$974$	37.5076	+	12.3580i	1.20182	+	0.395975i
$975$	−2.41273	−	5.83866i	−0.0772693	−	0.186987i
$976$	19.7521	−	2.44489i	0.632249	−	0.0782590i
$977$	−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	$0.206112\pi$
$978$	−3.13251	−	42.4930i	−0.100167	−	1.35878i
$979$	9.05889	+	1.59733i	0.289523	+	0.0510508i
$980$	−4.84392	+	1.16543i	−0.154733	+	0.0372283i
$981$	25.0956	−	25.0118i	0.801241	−	0.798566i
$982$	6.01727	−	7.63672i	0.192019	−	0.243698i
$983$	19.4584	−	7.08229i	0.620628	−	0.225890i	−0.0125191	−	0.999922i	$-0.503985\pi$
$983$	19.4584	−	7.08229i	0.620628	−	0.225890i	0.633147	+	0.774032i	$0.281763\pi$
$984$	−4.84102	−	35.5982i	−0.154326	−	1.13483i
$985$	3.67476	−	3.08349i	0.117088	−	0.0982483i
$986$	−3.90641	−	2.09776i	−0.124406	−	0.0668063i
$987$	5.08914	−	0.217934i	0.161989	−	0.00693691i
$988$	3.05159	+	1.51960i	0.0970841	+	0.0483450i
$989$	39.2186	−	22.6428i	1.24708	−	0.720000i
$990$	34.2900	−	17.2222i	1.08981	−	0.547359i
$991$	7.95615	+	4.59349i	0.252735	+	0.145917i	0.621016	−	0.783798i	$-0.286720\pi$
$991$	7.95615	+	4.59349i	0.252735	+	0.145917i	−0.368281	+	0.929715i	$0.620053\pi$
$992$	−17.1124	+	2.65529i	−0.543318	+	0.0843056i
$993$	−7.87903	−	35.6812i	−0.250034	−	1.13231i
$994$	13.9169	−	0.428611i	0.441418	−	0.0135947i
$995$	1.15929	+	6.57463i	0.0367518	+	0.208430i
$996$	−1.53434	+	1.11395i	−0.0486176	+	0.0352970i
$997$	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.659.67	yes	648
4.3	odd	2	inner	756.2.cf.a.659.90	yes	648
27.5	odd	18	inner	756.2.cf.a.491.90	yes	648
108.59	even	18	inner	756.2.cf.a.491.67	✓	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.67	✓	648	108.59	even	18	inner
756.2.cf.a.491.90	yes	648	27.5	odd	18	inner
756.2.cf.a.659.67	yes	648	1.1	even	1	trivial
756.2.cf.a.659.90	yes	648	4.3	odd	2	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.442552 - 1.34319i) q^{2} +(0.661489 + 1.60076i) q^{3} +(-1.60830 - 1.18886i) q^{4} +(0.851997 - 2.34084i) q^{5} +(2.44286 - 0.180084i) q^{6} +(0.984808 + 0.173648i) q^{7} +(-2.30861 + 1.63411i) q^{8} +(-2.12486 + 2.11777i) q^{9} +(-2.76713 - 2.18033i) q^{10} +(3.41175 - 1.24178i) q^{11} +(0.839206 - 3.36091i) q^{12} +(2.31789 - 1.94494i) q^{13} +(0.669070 - 1.24593i) q^{14} +(4.31071 - 0.184599i) q^{15} +(1.17323 + 3.82407i) q^{16} +(0.475550 - 0.274559i) q^{17} +(1.90420 + 3.79131i) q^{18} +(-0.487855 - 0.281663i) q^{19} +(-4.15319 + 2.75186i) q^{20} +(0.373471 + 1.69131i) q^{21} +(-0.158060 - 5.13217i) q^{22} +(-1.02467 - 5.81118i) q^{23} +(-4.14294 - 2.61459i) 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} +(1.65976 - 5.87178i) q^{30} +(-3.01476 + 0.531583i) q^{31} +(5.65565 + 0.116480i) q^{32} +(4.24462 + 4.63997i) q^{33} +(-0.158328 - 0.760259i) q^{34} +(1.24554 - 2.15733i) q^{35} +(5.93514 - 0.879839i) q^{36} +(-4.41674 - 7.65002i) q^{37} +(-0.594227 + 0.530629i) q^{38} +(4.64665 + 2.42383i) q^{39} +(1.85826 + 6.79635i) q^{40} +(4.71378 + 5.61766i) q^{41} +(2.43702 + 0.246850i) q^{42} +(2.62482 + 7.21164i) q^{43} +(-6.96340 - 2.05894i) q^{44} +(3.14699 + 6.77831i) q^{45} +(-8.25896 - 1.19543i) q^{46} +(0.510683 - 2.89623i) q^{47} +(-5.34534 + 4.40765i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-1.44942 + 0.897421i) q^{50} +(0.754074 + 0.579624i) q^{51} +(-6.04012 + 0.372399i) q^{52} +1.58954i q^{53} +(-4.80937 + 5.55607i) q^{54} -9.04436i q^{55} +(-2.55730 + 1.20840i) q^{56} +(0.128164 - 0.967255i) q^{57} +(-4.25077 - 6.86541i) q^{58} +(3.89118 + 1.41627i) q^{59} +(-7.15237 - 4.82794i) q^{60} +(0.864022 - 4.90011i) q^{61} +(-0.620172 + 4.28464i) q^{62} +(-2.46033 + 1.71662i) q^{63} +(2.65937 - 7.54505i) q^{64} +(-2.57797 - 7.08291i) q^{65} +(8.11081 - 3.64789i) q^{66} +(-3.55255 - 4.23376i) q^{67} +(-1.09124 - 0.123790i) q^{68} +(8.62450 - 5.48428i) q^{69} +(-2.34648 - 2.62772i) q^{70} +(4.92271 + 8.52639i) q^{71} +(1.44482 - 8.36137i) q^{72} +(-5.59592 + 9.69242i) q^{73} +(-12.2300 + 2.54698i) q^{74} +(0.629505 - 1.99073i) q^{75} +(0.449757 + 1.03299i) q^{76} +(3.57555 - 0.630466i) q^{77} +(5.31204 - 5.16864i) 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} +(1.41007 - 3.16413i) q^{84} +(-0.237532 - 1.34711i) q^{85} +(10.8482 - 0.334101i) q^{86} +(9.42940 + 2.98175i) q^{87} +(-5.84721 + 8.44195i) q^{88} +(2.19413 + 1.26678i) q^{89} +(10.4972 - 1.22724i) q^{90} +(2.62042 - 1.51290i) q^{91} +(-5.26070 + 10.5643i) q^{92} +(-2.84517 - 4.47427i) q^{93} +(-3.66417 - 1.96767i) q^{94} +(-1.07498 + 0.902015i) q^{95} +(3.55470 + 9.13040i) q^{96} +(17.3745 - 6.32379i) q^{97} +(0.875259 - 1.11082i) 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

Related objects

Downloads

Learn more