LMFDB - Embedded newform 756.2.cf.a.659.82

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			659.82
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.82

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.971061 - 1.02812i) q^{2} +(-0.935042 - 1.45798i) q^{3} +(-0.114079 - 1.99674i) q^{4} +(-1.06304 + 2.92068i) q^{5} +(-2.40696 - 0.454446i) q^{6} +(0.984808 + 0.173648i) q^{7} +(-2.16368 - 1.82167i) q^{8} +(-1.25139 + 2.72654i) q^{9} +(1.97055 + 3.92910i) q^{10} +(-0.301627 + 0.109783i) q^{11} +(-2.80454 + 2.03336i) q^{12} +(-4.68682 + 3.93271i) q^{13} +(1.13484 - 0.843882i) q^{14} +(5.25228 - 1.18107i) q^{15} +(-3.97397 + 0.455574i) q^{16} +(-4.28094 + 2.47160i) q^{17} +(1.58804 + 3.93422i) q^{18} +(-6.34724 - 3.66458i) q^{19} +(5.95312 + 1.78943i) q^{20} +(-0.667662 - 1.59820i) q^{21} +(-0.180028 + 0.416717i) q^{22} +(1.18706 + 6.73213i) q^{23} +(-0.632827 + 4.85793i) q^{24} +(-3.57010 - 2.99567i) q^{25} +(-0.507877 + 8.63754i) q^{26} +(5.14534 - 0.724928i) q^{27} +(0.234385 - 1.98622i) q^{28} +(4.53340 - 5.40269i) q^{29} +(3.88599 - 6.54688i) q^{30} +(-0.171891 + 0.0303091i) q^{31} +(-3.39058 + 4.52813i) q^{32} +(0.442096 + 0.337113i) q^{33} +(-1.61594 + 6.80141i) q^{34} +(-1.55406 + 2.69172i) q^{35} +(5.58696 + 2.18767i) q^{36} +(1.39294 + 2.41264i) q^{37} +(-9.93121 + 2.96722i) q^{38} +(10.1162 + 3.15603i) q^{39} +(7.62061 - 4.38290i) q^{40} +(2.72121 + 3.24301i) q^{41} +(-2.29148 - 0.865507i) q^{42} +(-2.01222 - 5.52853i) q^{43} +(0.253619 + 0.589748i) q^{44} +(-6.63307 - 6.55334i) q^{45} +(8.07417 + 5.31687i) q^{46} +(0.954507 - 5.41328i) q^{47} +(4.38005 + 5.36798i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-6.54672 + 0.761528i) q^{50} +(7.60639 + 3.93046i) q^{51} +(8.38729 + 8.90974i) q^{52} +1.61946i q^{53} +(4.25112 - 5.99399i) q^{54} -0.997662i q^{55} +(-1.81448 - 2.16972i) q^{56} +(0.592063 + 12.6807i) q^{57} +(-1.15243 - 9.90724i) q^{58} +(-4.65670 - 1.69490i) q^{59} +(-2.95747 - 10.3527i) q^{60} +(0.585773 - 3.32209i) q^{61} +(-0.135755 + 0.206157i) q^{62} +(-1.70584 + 2.46781i) q^{63} +(1.36301 + 7.88303i) q^{64} +(-6.50391 - 17.8694i) q^{65} +(0.775897 - 0.127171i) q^{66} +(-9.54992 - 11.3812i) q^{67} +(5.42352 + 8.26597i) q^{68} +(8.70535 - 8.02553i) q^{69} +(1.25833 + 4.21159i) q^{70} +(1.41743 + 2.45506i) q^{71} +(7.67448 - 3.61973i) q^{72} +(-2.23752 + 3.87551i) q^{73} +(3.83312 + 0.910708i) q^{74} +(-1.02942 + 8.00621i) q^{75} +(-6.59314 + 13.0919i) q^{76} +(-0.316109 + 0.0557385i) q^{77} +(13.0682 - 7.33599i) q^{78} +(-8.71806 + 10.3898i) q^{79} +(2.89391 - 12.0910i) q^{80} +(-5.86803 - 6.82394i) q^{81} +(5.97668 + 0.351422i) q^{82} +(5.07448 + 4.25799i) q^{83} +(-3.11502 + 1.51547i) q^{84} +(-2.66794 - 15.1307i) q^{85} +(-7.63800 - 3.29973i) q^{86} +(-12.1159 - 1.55784i) q^{87} +(0.852614 + 0.311930i) q^{88} +(-0.0619252 - 0.0357525i) q^{89} +(-13.1788 + 0.455923i) q^{90} +(-5.29853 + 3.05911i) q^{91} +(13.3069 - 3.13824i) q^{92} +(0.204915 + 0.222273i) q^{93} +(-4.63864 - 6.23798i) q^{94} +(17.4505 - 14.6427i) q^{95} +(9.77224 + 0.709404i) q^{96} +(2.95549 - 1.07571i) q^{97} +(1.26414 - 0.633998i) q^{98} +(0.0781255 - 0.959781i) 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 $

$2$	0.971061	−	1.02812i	0.686644	−	0.726994i
$2$	0.971061	−	1.02812i	0.686644	−	0.726994i
$3$	−0.935042	−	1.45798i	−0.539847	−	0.841763i
$3$	−0.935042	−	1.45798i	−0.539847	−	0.841763i
$4$	−0.114079	−	1.99674i	−0.0570396	−	0.998372i
$5$	−1.06304	+	2.92068i	−0.475407	+	1.30617i	0.437947	+	0.899001i	$0.355706\pi$
$5$	−1.06304	+	2.92068i	−0.475407	+	1.30617i	−0.913353	+	0.407168i	$0.866516\pi$
$6$	−2.40696	−	0.454446i	−0.982639	−	0.185527i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$7$	0.984808	+	0.173648i	0.372222	+	0.0656328i
$8$	−2.16368	−	1.82167i	−0.764976	−	0.644059i
$9$	−1.25139	+	2.72654i	−0.417131	+	0.908846i
$10$	1.97055	+	3.92910i	0.623141	+	1.24249i
$11$	−0.301627	+	0.109783i	−0.0909440	+	0.0331009i	−0.387091	−	0.922041i	$-0.626520\pi$
$11$	−0.301627	+	0.109783i	−0.0909440	+	0.0331009i	0.296147	+	0.955142i	$0.404298\pi$
$12$	−2.80454	+	2.03336i	−0.809600	+	0.586982i
$13$	−4.68682	+	3.93271i	−1.29989	+	1.09074i	−0.309727	+	0.950826i	$0.600238\pi$
$13$	−4.68682	+	3.93271i	−1.29989	+	1.09074i	−0.990164	+	0.139912i	$0.955318\pi$
$14$	1.13484	−	0.843882i	0.303299	−	0.225537i
$15$	5.25228	−	1.18107i	1.35613	−	0.304951i
$16$	−3.97397	+	0.455574i	−0.993493	+	0.113893i
$17$	−4.28094	+	2.47160i	−1.03828	+	0.599451i	−0.919346	−	0.393451i	$-0.871281\pi$
$17$	−4.28094	+	2.47160i	−1.03828	+	0.599451i	−0.118934	+	0.992902i	$0.537948\pi$
$18$	1.58804	+	3.93422i	0.374305	+	0.927306i
$19$	−6.34724	−	3.66458i	−1.45616	−	0.840713i	−0.457338	−	0.889293i	$-0.651197\pi$
$19$	−6.34724	−	3.66458i	−1.45616	−	0.840713i	−0.998819	+	0.0485799i	$0.984530\pi$
$20$	5.95312	+	1.78943i	1.33116	+	0.400129i
$21$	−0.667662	−	1.59820i	−0.145696	−	0.348755i
$22$	−0.180028	+	0.416717i	−0.0383820	+	0.0888443i
$23$	1.18706	+	6.73213i	0.247518	+	1.40375i	0.814570	+	0.580065i	$0.196973\pi$
$23$	1.18706	+	6.73213i	0.247518	+	1.40375i	−0.567052	+	0.823682i	$0.691916\pi$
$24$	−0.632827	+	4.85793i	−0.129175	+	0.991622i
$25$	−3.57010	−	2.99567i	−0.714021	−	0.599135i
$26$	−0.507877	+	8.63754i	−0.0996029	+	1.69396i
$27$	5.14534	−	0.724928i	0.990220	−	0.139512i
$28$	0.234385	−	1.98622i	0.0442946	−	0.375360i
$29$	4.53340	−	5.40269i	0.841831	−	1.00325i	−0.158044	−	0.987432i	$-0.550519\pi$
$29$	4.53340	−	5.40269i	0.841831	−	1.00325i	0.999875	−	0.0158227i	$-0.00503674\pi$
$30$	3.88599	−	6.54688i	0.709482	−	1.19529i
$31$	−0.171891	+	0.0303091i	−0.0308726	+	0.00544367i	−0.189063	−	0.981965i	$-0.560545\pi$
$31$	−0.171891	+	0.0303091i	−0.0308726	+	0.00544367i	0.158191	+	0.987409i	$0.449434\pi$
$32$	−3.39058	+	4.52813i	−0.599376	+	0.800467i
$33$	0.442096	+	0.337113i	0.0769590	+	0.0586839i
$34$	−1.61594	+	6.80141i	−0.277132	+	1.16643i
$35$	−1.55406	+	2.69172i	−0.262685	+	0.454983i
$36$	5.58696	+	2.18767i	0.931160	+	0.364612i
$37$	1.39294	+	2.41264i	0.228998	+	0.396635i	0.957511	−	0.288396i	$-0.0931219\pi$
$37$	1.39294	+	2.41264i	0.228998	+	0.396635i	−0.728514	+	0.685031i	$0.759789\pi$
$38$	−9.93121	+	2.96722i	−1.61106	+	0.481347i
$39$	10.1162	+	3.15603i	1.61988	+	0.505369i
$40$	7.62061	−	4.38290i	1.20492	−	0.692998i
$41$	2.72121	+	3.24301i	0.424982	+	0.506474i	0.935468	−	0.353413i	$-0.114979\pi$
$41$	2.72121	+	3.24301i	0.424982	+	0.506474i	−0.510486	+	0.859886i	$0.670534\pi$
$42$	−2.29148	−	0.865507i	−0.353584	−	0.133551i
$43$	−2.01222	−	5.52853i	−0.306861	−	0.843092i	−0.993264	−	0.115872i	$-0.963034\pi$
$43$	−2.01222	−	5.52853i	−0.306861	−	0.843092i	0.686404	−	0.727221i	$-0.259188\pi$
$44$	0.253619	+	0.589748i	0.0382344	+	0.0889079i
$45$	−6.63307	−	6.55334i	−0.988800	−	0.976915i
$46$	8.07417	+	5.31687i	1.19047	+	0.783930i
$47$	0.954507	−	5.41328i	0.139229	−	0.789608i	−0.832592	−	0.553887i	$-0.813144\pi$
$47$	0.954507	−	5.41328i	0.139229	−	0.789608i	0.971821	−	0.235721i	$-0.0757451\pi$
$48$	4.38005	+	5.36798i	0.632205	+	0.774801i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	−6.54672	+	0.761528i	−0.925845	+	0.107696i
$51$	7.60639	+	3.93046i	1.06511	+	0.550374i
$52$	8.38729	+	8.90974i	1.16311	+	1.23556i
$53$			1.61946i			0.222450i	0.993795	+	0.111225i	$0.0354774\pi$
$53$			1.61946i			0.222450i	−0.993795	+	0.111225i	$0.964523\pi$
$54$	4.25112	−	5.99399i	0.578504	−	0.815679i
$55$		−	0.997662i		−	0.134525i
$56$	−1.81448	−	2.16972i	−0.242470	−	0.289941i
$57$	0.592063	+	12.6807i	0.0784207	+	1.67960i
$58$	−1.15243	−	9.90724i	−0.151322	−	1.30088i
$59$	−4.65670	−	1.69490i	−0.606250	−	0.220657i	0.0206114	−	0.999788i	$-0.493439\pi$
$59$	−4.65670	−	1.69490i	−0.606250	−	0.220657i	−0.626862	+	0.779130i	$0.715661\pi$
$60$	−2.95747	−	10.3527i	−0.381808	−	1.33653i
$61$	0.585773	−	3.32209i	0.0750006	−	0.425349i	−0.924069	−	0.382225i	$-0.875158\pi$
$61$	0.585773	−	3.32209i	0.0750006	−	0.425349i	0.999070	−	0.0431241i	$-0.0137311\pi$
$62$	−0.135755	+	0.206157i	−0.0172410	+	0.0261820i
$63$	−1.70584	+	2.46781i	−0.214916	+	0.310915i
$64$	1.36301	+	7.88303i	0.170376	+	0.985379i
$65$	−6.50391	−	17.8694i	−0.806711	−	2.21642i
$66$	0.775897	−	0.127171i	0.0955063	−	0.0156537i
$67$	−9.54992	−	11.3812i	−1.16671	−	1.39043i	−0.905069	−	0.425264i	$-0.860181\pi$
$67$	−9.54992	−	11.3812i	−1.16671	−	1.39043i	−0.261640	−	0.965166i	$-0.584263\pi$
$68$	5.42352	+	8.26597i	0.657698	+	1.00240i
$69$	8.70535	−	8.02553i	1.04800	−	0.966160i
$70$	1.25833	+	4.21159i	0.150399	+	0.503381i
$71$	1.41743	+	2.45506i	0.168218	+	0.291362i	0.937793	−	0.347194i	$-0.112865\pi$
$71$	1.41743	+	2.45506i	0.168218	+	0.291362i	−0.769575	+	0.638556i	$0.779532\pi$
$72$	7.67448	−	3.61973i	0.904446	−	0.426589i
$73$	−2.23752	+	3.87551i	−0.261882	+	0.453594i	−0.966742	−	0.255753i	$-0.917677\pi$
$73$	−2.23752	+	3.87551i	−0.261882	+	0.453594i	0.704860	+	0.709347i	$0.251010\pi$
$74$	3.83312	+	0.910708i	0.445591	+	0.105868i
$75$	−1.02942	+	8.00621i	−0.118868	+	0.924478i
$76$	−6.59314	+	13.0919i	−0.756286	+	1.50174i
$77$	−0.316109	+	0.0557385i	−0.0360239	+	0.00635199i
$78$	13.0682	−	7.33599i	1.47968	−	0.830637i
$79$	−8.71806	+	10.3898i	−0.980858	+	1.16894i	0.00476562	+	0.999989i	$0.498483\pi$
$79$	−8.71806	+	10.3898i	−0.980858	+	1.16894i	−0.985624	+	0.168953i	$0.945961\pi$
$80$	2.89391	−	12.0910i	0.323549	−	1.35182i
$81$	−5.86803	−	6.82394i	−0.652004	−	0.758216i
$82$	5.97668	+	0.351422i	0.660014	+	0.0388081i
$83$	5.07448	+	4.25799i	0.556996	+	0.467376i	0.877302	−	0.479939i	$-0.159341\pi$
$83$	5.07448	+	4.25799i	0.556996	+	0.467376i	−0.320306	+	0.947314i	$0.603786\pi$
$84$	−3.11502	+	1.51547i	−0.339877	+	0.165351i
$85$	−2.66794	−	15.1307i	−0.289379	−	1.64115i
$86$	−7.63800	−	3.29973i	−0.823627	−	0.355819i
$87$	−12.1159	−	1.55784i	−1.29896	−	0.167018i
$88$	0.852614	+	0.311930i	0.0908889	+	0.0332519i
$89$	−0.0619252	−	0.0357525i	−0.00656406	−	0.00378976i	0.496714	−	0.867914i	$-0.334540\pi$
$89$	−0.0619252	−	0.0357525i	−0.00656406	−	0.00378976i	−0.503278	+	0.864124i	$0.667873\pi$
$90$	−13.1788	+	0.455923i	−1.38916	+	0.0480585i
$91$	−5.29853	+	3.05911i	−0.555437	+	0.320681i
$92$	13.3069	−	3.13824i	1.38734	−	0.327185i
$93$	0.204915	+	0.222273i	0.0212487	+	0.0230487i
$94$	−4.63864	−	6.23798i	−0.478439	−	0.643399i
$95$	17.4505	−	14.6427i	1.79038	−	1.50231i
$96$	9.77224	+	0.709404i	0.997375	+	0.0724033i
$97$	2.95549	−	1.07571i	0.300084	−	0.109222i	−0.187590	−	0.982247i	$-0.560068\pi$
$97$	2.95549	−	1.07571i	0.300084	−	0.109222i	0.487674	+	0.873026i	$0.337845\pi$
$98$	1.26414	−	0.633998i	0.127697	−	0.0640435i
$99$	0.0781255	−	0.959781i	0.00785191	−	0.0964616i
$100$	−5.57432	+	7.47033i	−0.557432	+	0.747033i
$101$	−3.27304	−	0.577125i	−0.325679	−	0.0574260i	0.00841823	−	0.999965i	$-0.497320\pi$
$101$	−3.27304	−	0.577125i	−0.325679	−	0.0574260i	−0.334097	+	0.942539i	$0.608431\pi$
$102$	11.4273	−	4.00360i	1.13147	−	0.396416i
$103$	−3.51113	+	9.64674i	−0.345961	+	0.950521i	0.637667	+	0.770312i	$0.279900\pi$
$103$	−3.51113	+	9.64674i	−0.345961	+	0.950521i	−0.983628	+	0.180209i	$0.942323\pi$
$104$	17.3049	+	0.0287369i	1.69688	+	0.00281788i
$105$	5.37757	−	0.251080i	0.524797	−	0.0245029i
$106$	1.66501	+	1.57260i	0.161720	+	0.152744i
$107$	8.92005			0.862334			0.431167	−	0.902272i	$-0.358102\pi$
$107$	8.92005			0.862334			0.431167	+	0.902272i	$0.358102\pi$
$108$	−2.03447	−	10.1912i	−0.195767	−	0.980650i
$109$	5.66000			0.542130			0.271065	−	0.962561i	$-0.412624\pi$
$109$	5.66000			0.542130			0.271065	+	0.962561i	$0.412624\pi$
$110$	−1.02572	−	0.968791i	−0.0977986	−	0.0923706i
$111$	2.21512	−	4.28679i	0.210250	−	0.406884i
$112$	−3.99271	−	0.241420i	−0.377275	−	0.0228121i
$113$	−4.01988	+	11.0445i	−0.378159	+	1.03898i	0.593960	+	0.804494i	$0.297564\pi$
$113$	−4.01988	+	11.0445i	−0.378159	+	1.03898i	−0.972119	+	0.234488i	$0.924659\pi$
$114$	13.6122	+	11.7050i	1.27490	+	1.09627i
$115$	−20.9243	−	3.68952i	−1.95120	−	0.344050i
$116$	−11.3050	−	8.43570i	−1.04964	−	0.783235i
$117$	−4.85764	−	17.7002i	−0.449089	−	1.63638i
$118$	−6.26451	+	3.14181i	−0.576695	+	0.289227i
$119$	−4.64509	+	1.69067i	−0.425815	+	0.154984i
$120$	−13.5158	−	7.01247i	−1.23381	−	0.640148i
$121$	−8.34756	+	7.00444i	−0.758869	+	0.636767i
$122$	−2.84669	−	3.82820i	−0.257728	−	0.346589i
$123$	2.18379	−	6.99982i	0.196906	−	0.631152i
$124$	0.0801286	+	0.339765i	0.00719576	+	0.0305118i
$125$	−0.913996	+	0.527696i	−0.0817503	+	0.0471986i
$126$	0.880745	+	4.15022i	0.0784630	+	0.369731i
$127$	−9.50424	−	5.48727i	−0.843365	−	0.486917i	0.0150418	−	0.999887i	$-0.495212\pi$
$127$	−9.50424	−	5.48727i	−0.843365	−	0.486917i	−0.858407	+	0.512970i	$0.828545\pi$
$128$	9.42831	+	6.25356i	0.833352	+	0.552742i
$129$	−6.17895	+	8.10317i	−0.544027	+	0.713445i
$130$	−24.6876	−	10.6654i	−2.16525	−	0.935418i
$131$	3.05643	+	17.3339i	0.267042	+	1.51447i	0.763157	+	0.646213i	$0.223648\pi$
$131$	3.05643	+	17.3339i	0.267042	+	1.51447i	−0.496115	+	0.868257i	$0.665241\pi$
$132$	0.622695	−	0.921210i	0.0541987	−	0.0801810i
$133$	−5.61447	−	4.71110i	−0.486836	−	0.408504i
$134$	−20.9748	−	1.23329i	−1.81195	−	0.106540i
$135$	−3.35242	+	15.7985i	−0.288531	+	1.35972i
$136$	13.7650	+	2.45072i	1.18034	+	0.210148i
$137$	3.65513	−	4.35602i	0.312279	−	0.372160i	−0.586961	−	0.809615i	$-0.699676\pi$
$137$	3.65513	−	4.35602i	0.312279	−	0.372160i	0.899240	+	0.437455i	$0.144120\pi$
$138$	0.202185	−	16.7435i	0.0172111	−	1.42530i
$139$	−9.25901	+	1.63261i	−0.785339	+	0.138476i	−0.551917	−	0.833899i	$-0.686103\pi$
$139$	−9.25901	+	1.63261i	−0.785339	+	0.138476i	−0.233422	+	0.972376i	$0.574992\pi$
$140$	5.55195	+	2.79600i	0.469226	+	0.236305i
$141$	−8.78494	+	3.67000i	−0.739826	+	0.309069i
$142$	3.90052	+	0.926721i	0.327325	+	0.0777687i
$143$	0.981927	−	1.70075i	0.0821129	−	0.142224i
$144$	3.73086	−	11.4053i	0.310905	−	0.950441i
$145$	10.9604	+	18.9839i	0.910208	+	1.57653i
$146$	1.81173	+	6.06381i	0.149940	+	0.501844i
$147$	−0.379995	−	1.68985i	−0.0313414	−	0.139377i
$148$	4.65852	−	3.05657i	0.382928	−	0.251249i
$149$	−10.9631	−	13.0653i	−0.898130	−	1.07035i	−0.997164	−	0.0752656i	$-0.976020\pi$
$149$	−10.9631	−	13.0653i	−0.898130	−	1.07035i	0.0990335	−	0.995084i	$-0.468425\pi$
$150$	7.23175	+	8.83290i	0.590470	+	0.721203i
$151$	−3.44056	−	9.45285i	−0.279989	−	0.769262i	−0.997363	−	0.0725745i	$-0.976878\pi$
$151$	−3.44056	−	9.45285i	−0.279989	−	0.769262i	0.717374	−	0.696688i	$-0.245344\pi$
$152$	7.05772	+	19.4916i	0.572457	+	1.58098i
$153$	−1.38178	−	14.7651i	−0.111710	−	1.19369i
$154$	−0.249655	+	0.379124i	−0.0201178	+	0.0305507i
$155$	0.0942043	−	0.534259i	0.00756667	−	0.0429127i
$156$	5.14773	−	20.5595i	0.412149	−	1.64607i
$157$	−0.863361	−	0.314238i	−0.0689037	−	0.0250789i	0.307338	−	0.951600i	$-0.400562\pi$
$157$	−0.863361	−	0.314238i	−0.0689037	−	0.0250789i	−0.376242	+	0.926521i	$0.622784\pi$
$158$	2.21621	+	19.0524i	0.176312	+	1.51572i
$159$	2.36114	−	1.51426i	0.187250	−	0.120089i
$160$	−9.62089	−	14.7164i	−0.760598	−	1.16343i
$161$			6.83599i			0.538751i
$162$	−12.7141	−	0.593400i	−0.998913	−	0.0466219i
$163$			1.91336i			0.149866i	0.997189	+	0.0749330i	$0.0238743\pi$
$163$			1.91336i			0.149866i	−0.997189	+	0.0749330i	$0.976126\pi$
$164$	6.16503	−	5.80352i	0.481408	−	0.453179i
$165$	−1.45457	+	0.932855i	−0.113238	+	0.0726227i
$166$	9.30538	−	1.08242i	0.722237	−	0.0840122i
$167$	−0.907424	−	0.330275i	−0.0702186	−	0.0255575i	0.306672	−	0.951815i	$-0.400785\pi$
$167$	−0.907424	−	0.330275i	−0.0702186	−	0.0255575i	−0.376891	+	0.926258i	$0.623007\pi$
$168$	−1.46678	+	4.67424i	−0.113165	+	0.360626i
$169$	4.24266	−	24.0613i	0.326359	−	1.85087i
$170$	−18.1469	−	11.9498i	−1.39181	−	0.916510i
$171$	17.9345	−	12.7202i	1.37149	−	0.972736i
$172$	−10.8095	+	4.64858i	−0.824217	+	0.354451i
$173$	3.36152	+	9.23570i	0.255572	+	0.702178i	0.999427	+	0.0338372i	$0.0107728\pi$
$173$	3.36152	+	9.23570i	0.255572	+	0.702178i	−0.743856	+	0.668340i	$0.767005\pi$
$174$	−13.3670	+	10.9439i	−1.01335	+	0.829655i
$175$	−2.99567	−	3.57010i	−0.226452	−	0.269875i
$176$	1.14864	−	0.573689i	0.0865823	−	0.0432435i
$177$	1.88308	+	8.37416i	0.141541	+	0.629440i
$178$	−0.0968913	+	0.0289489i	−0.00726231	+	0.00216981i
$179$	−7.83903	−	13.5776i	−0.585917	−	1.01484i	−0.994760	−	0.102233i	$-0.967401\pi$
$179$	−7.83903	−	13.5776i	−0.585917	−	1.01484i	0.408844	−	0.912604i	$-0.365932\pi$
$180$	−12.3287	+	13.9921i	−0.918924	+	1.04291i
$181$	−3.07807	+	5.33138i	−0.228792	+	0.396279i	−0.957450	−	0.288598i	$-0.906811\pi$
$181$	−3.07807	+	5.33138i	−0.228792	+	0.396279i	0.728659	+	0.684877i	$0.240144\pi$
$182$	−2.00005	+	8.41812i	−0.148254	+	0.623993i
$183$	−5.39125	+	2.25225i	−0.398532	+	0.166491i
$184$	9.69534	−	16.7286i	0.714750	−	1.23325i
$185$	−8.52730	+	1.50359i	−0.626940	+	0.110546i
$186$	0.427510	+	0.00516237i	0.0313465	+	0.000378524i
$187$	1.01991	−	1.21548i	0.0745829	−	0.0888845i
$188$	−10.9178	−	1.28836i	−0.796264	−	0.0939636i
$189$	5.19305	+	0.179564i	0.377739	+	0.0130614i
$190$	1.89098	−	32.1602i	0.137186	−	2.33315i
$191$	4.38710	+	3.68122i	0.317440	+	0.266363i	0.787559	−	0.616239i	$-0.211345\pi$
$191$	4.38710	+	3.68122i	0.317440	+	0.266363i	−0.470119	+	0.882603i	$0.655789\pi$
$192$	10.2188	−	9.35821i	0.737479	−	0.675370i
$193$	3.26298	+	18.5053i	0.234875	+	1.33204i	0.842878	+	0.538105i	$0.180860\pi$
$193$	3.26298	+	18.5053i	0.234875	+	1.33204i	−0.608003	+	0.793935i	$0.708029\pi$
$194$	1.76400	−	4.08319i	0.126648	−	0.293156i
$195$	−19.9717	+	26.1912i	−1.43020	+	1.87559i
$196$	0.575727	−	1.91534i	0.0411234	−	0.136810i
$197$	17.3711	+	10.0292i	1.23764	+	0.714552i	0.968611	−	0.248580i	$-0.0799638\pi$
$197$	17.3711	+	10.0292i	1.23764	+	0.714552i	0.269029	+	0.963132i	$0.413297\pi$
$198$	−0.910909	−	1.01233i	−0.0647355	−	0.0719431i
$199$	20.6668	−	11.9320i	1.46503	−	0.845836i	0.465795	−	0.884893i	$-0.345769\pi$
$199$	20.6668	−	11.9320i	1.46503	−	0.845836i	0.999237	+	0.0390564i	$0.0124352\pi$
$200$	2.26742	+	12.9852i	0.160331	+	0.918195i
$201$	−7.66388	+	24.5654i	−0.540569	+	1.73271i
$202$	−3.77167	+	2.80466i	−0.265374	+	0.197335i
$203$	5.40269	−	4.53340i	0.379195	−	0.318182i
$204$	6.98038	−	15.6364i	0.488725	−	1.09477i
$205$	−12.3646	+	4.50034i	−0.863579	+	0.314317i
$206$	6.50853	+	12.9774i	0.453471	+	0.904182i
$207$	−19.8409	−	5.18798i	−1.37904	−	0.360590i
$208$	16.8337	−	17.7637i	1.16720	−	1.23169i
$209$	2.31681	+	0.408516i	0.160257	+	0.0282577i
$210$	4.96381	−	5.77263i	0.342536	−	0.398349i
$211$	−4.24367	+	11.6594i	−0.292147	+	0.802666i	0.703605	+	0.710591i	$0.251572\pi$
$211$	−4.24367	+	11.6594i	−0.292147	+	0.802666i	−0.995752	+	0.0920753i	$0.970650\pi$
$212$	3.23365	−	0.184747i	0.222088	−	0.0126885i
$213$	2.25407	−	4.36217i	0.154446	−	0.298891i
$214$	8.66192	−	9.17092i	0.592117	−	0.626911i
$215$	18.2861			1.24710
$216$	−12.4534	−	7.80461i	−0.847349	−	0.531037i
$217$	−0.174543			−0.0118487
$218$	5.49621	−	5.81919i	0.372250	−	0.394125i
$219$	7.74258	−	0.361503i	0.523195	−	0.0244281i
$220$	−1.99207	+	0.113812i	−0.134306	+	0.00767323i
$221$	10.3439	−	28.4196i	0.695806	−	1.91171i
$222$	−2.25634	−	6.44015i	−0.151436	−	0.432235i
$223$	28.8561	+	5.08811i	1.93235	+	0.340725i	0.999794	−	0.0203060i	$-0.00646406\pi$
$223$	28.8561	+	5.08811i	1.93235	+	0.340725i	0.932554	+	0.361031i	$0.117575\pi$
$224$	−4.12538	+	3.87057i	−0.275638	+	0.258613i
$225$	12.6354	−	5.98527i	0.842362	−	0.399018i
$226$	7.45160	+	14.8579i	0.495673	+	0.988330i
$227$	21.3803	−	7.78178i	1.41906	−	0.516495i	0.485284	−	0.874357i	$-0.338716\pi$
$227$	21.3803	−	7.78178i	1.41906	−	0.516495i	0.933775	+	0.357862i	$0.116494\pi$
$228$	25.2525	−	2.62880i	1.67239	−	0.174096i
$229$	11.1990	−	9.39706i	0.740049	−	0.620975i	−0.192802	−	0.981238i	$-0.561757\pi$
$229$	11.1990	−	9.39706i	0.740049	−	0.620975i	0.932851	+	0.360263i	$0.117313\pi$
$230$	−24.1121	+	17.9300i	−1.58990	+	1.18227i
$231$	0.376840	+	0.408761i	0.0247943	+	0.0268945i
$232$	−19.6508	+	3.43132i	−1.29014	+	0.225277i
$233$	11.5854	−	6.68885i	0.758986	−	0.438201i	−0.0699455	−	0.997551i	$-0.522283\pi$
$233$	11.5854	−	6.68885i	0.758986	−	0.438201i	0.828932	+	0.559350i	$0.188949\pi$
$234$	−22.9150	−	12.1937i	−1.49800	−	0.797127i
$235$	14.7958	+	8.54235i	0.965171	+	0.557242i
$236$	−2.85305	+	9.49159i	−0.185718	+	0.617850i
$237$	23.2998	+	2.99585i	1.51349	+	0.194601i
$238$	−2.77244	+	6.41748i	−0.179711	+	0.415983i
$239$	−3.43138	−	19.4603i	−0.221957	−	1.25878i	−0.868417	−	0.495834i	$-0.834862\pi$
$239$	−3.43138	−	19.4603i	−0.221957	−	1.25878i	0.646460	−	0.762948i	$-0.276249\pi$
$240$	−20.3343	+	7.08634i	−1.31258	+	0.457421i
$241$	−15.3738	−	12.9001i	−0.990311	−	0.830970i	−0.00469862	−	0.999989i	$-0.501496\pi$
$241$	−15.3738	−	12.9001i	−0.990311	−	0.830970i	−0.985613	+	0.169019i	$0.945940\pi$
$242$	−0.904565	+	15.3841i	−0.0581476	+	0.988925i
$243$	−4.46229	+	14.9361i	−0.286256	+	0.958153i
$244$	−6.70018	−	0.790658i	−0.428935	−	0.0506167i
$245$	−1.99786	+	2.38096i	−0.127639	+	0.152114i
$246$	−5.07609	−	9.04246i	−0.323639	−	0.576526i
$247$	44.1601	−	7.78663i	2.80984	−	0.495451i
$248$	0.427131	+	0.247551i	0.0271228	+	0.0157195i
$249$	1.46320	−	11.3799i	0.0927268	−	0.721170i
$250$	−0.345010	+	1.45213i	−0.0218203	+	0.0918406i
$251$	−5.48963	+	9.50831i	−0.346502	+	0.600159i	−0.985625	−	0.168945i	$-0.945964\pi$
$251$	−5.48963	+	9.50831i	−0.346502	+	0.600159i	0.639123	+	0.769104i	$0.279297\pi$
$252$	5.12220	+	3.12460i	0.322668	+	0.196831i
$253$	−1.09712	−	1.90028i	−0.0689756	−	0.119469i
$254$	−14.8708	+	4.44306i	−0.933077	+	0.278782i
$255$	−19.5655	+	18.0376i	−1.22524	+	1.12956i
$256$	15.5849	−	3.62087i	0.974057	−	0.226305i
$257$	−10.5147	−	12.5309i	−0.655890	−	0.781659i	0.330900	−	0.943666i	$-0.392648\pi$
$257$	−10.5147	−	12.5309i	−0.655890	−	0.781659i	−0.986790	+	0.162007i	$0.948203\pi$
$258$	2.33093	+	14.2214i	0.145117	+	0.885386i
$259$	0.952825	+	2.61787i	0.0592057	+	0.162666i
$260$	−34.9386	+	15.0252i	−2.16680	+	0.931821i
$261$	9.05759	+	19.1214i	0.560651	+	1.18358i
$262$	20.7894	+	13.6899i	1.28437	+	0.845764i
$263$	−4.02834	+	22.8459i	−0.248398	+	1.40874i	0.564068	+	0.825728i	$0.309236\pi$
$263$	−4.02834	+	22.8459i	−0.248398	+	1.40874i	−0.812466	+	0.583008i	$0.801875\pi$
$264$	−0.342442	−	1.53476i	−0.0210759	−	0.0944579i
$265$	−4.72993	−	1.72155i	−0.290557	−	0.105754i
$266$	−10.2956	+	1.19760i	−0.631263	+	0.0734299i
$267$	0.00577631	+	0.123716i	0.000353504	+	0.00757128i
$268$	−21.6358	+	20.3671i	−1.32162	+	1.24412i
$269$			7.71673i			0.470497i	0.971935	+	0.235249i	$0.0755905\pi$
$269$			7.71673i			0.470497i	−0.971935	+	0.235249i	$0.924410\pi$
$270$	12.9874	+	18.7880i	0.790390	+	1.14340i
$271$		−	30.2740i		−	1.83901i	−0.393075	−	0.919507i	$-0.628589\pi$
$271$		−	30.2740i		−	1.83901i	0.393075	−	0.919507i	$-0.371411\pi$
$272$	15.8863	−	11.7723i	0.963250	−	0.713804i
$273$	9.41445	+	4.86474i	0.569789	+	0.294427i
$274$	−0.929169	−	7.98790i	−0.0561332	−	0.482566i
$275$	1.40572	+	0.511639i	0.0847679	+	0.0308530i
$276$	−17.0180	−	16.4668i	−1.02436	−	0.991185i
$277$	−2.37571	+	13.4733i	−0.142742	+	0.809533i	0.826410	+	0.563069i	$0.190380\pi$
$277$	−2.37571	+	13.4733i	−0.142742	+	0.809533i	−0.969152	+	0.246463i	$0.920731\pi$
$278$	−7.31253	+	11.1048i	−0.438577	+	0.666020i
$279$	0.132465	−	0.506597i	0.00793044	−	0.0303291i
$280$	8.26592	−	2.99301i	0.493983	−	0.178867i
$281$	9.45872	+	25.9876i	0.564260	+	1.55029i	0.813328	+	0.581805i	$0.197653\pi$
$281$	9.45872	+	25.9876i	0.564260	+	1.55029i	−0.249069	+	0.968486i	$0.580125\pi$
$282$	−4.75751	+	12.5958i	−0.283305	+	0.750069i
$283$	−12.7347	−	15.1766i	−0.757000	−	0.902157i	0.240654	−	0.970611i	$-0.422638\pi$
$283$	−12.7347	−	15.1766i	−0.757000	−	0.902157i	−0.997654	+	0.0684534i	$0.978194\pi$
$284$	4.74043	−	3.11032i	0.281293	−	0.184563i
$285$	−37.6656	−	11.7509i	−2.23112	−	0.696060i
$286$	−0.795068	−	2.66107i	−0.0470134	−	0.157353i
$287$	2.11673	+	3.66628i	0.124946	+	0.216414i
$288$	−8.10316	−	14.9110i	−0.477484	−	0.878641i
$289$	3.71761	−	6.43909i	0.218683	−	0.378770i
$290$	30.1610	+	7.16592i	1.77111	+	0.420797i
$291$	−4.33186	−	3.30320i	−0.253938	−	0.193637i
$292$	7.99365	+	4.02565i	0.467793	+	0.235583i
$293$	−16.2314	+	2.86203i	−0.948248	+	0.167202i	−0.626323	−	0.779563i	$-0.715441\pi$
$293$	−16.2314	+	2.86203i	−0.948248	+	0.167202i	−0.321925	+	0.946765i	$0.604330\pi$
$294$	−2.10638	−	1.25027i	−0.122846	−	0.0729172i
$295$	9.90052	−	11.7990i	0.576431	−	0.686963i
$296$	1.38117	−	7.75765i	0.0802789	−	0.450904i
$297$	−1.47239	+	0.783530i	−0.0854366	+	0.0454650i
$298$	−24.0786	−	1.41579i	−1.39483	−	0.0820145i
$299$	−32.0391	−	26.8840i	−1.85287	−	1.55474i
$300$	16.1038	+	1.14215i	0.929753	+	0.0659423i
$301$	−1.02163	−	5.79395i	−0.0588858	−	0.333958i
$302$	−13.0597	−	5.64198i	−0.751501	−	0.324660i
$303$	2.21899	+	5.31165i	0.127478	+	0.305146i
$304$	26.8933	+	11.6713i	1.54243	+	0.669396i
$305$	9.08005	+	5.24237i	0.519922	+	0.300177i
$306$	−16.5221	−	12.9172i	−0.944508	−	0.738425i
$307$	−28.0906	+	16.2181i	−1.60322	+	0.925618i	−0.612378	+	0.790565i	$0.709787\pi$
$307$	−28.0906	+	16.2181i	−1.60322	+	0.925618i	−0.990838	+	0.135053i	$0.956880\pi$
$308$	0.147357	+	0.624829i	0.00839643	+	0.0356029i
$309$	17.3478	−	3.90097i	0.986880	−	0.221918i
$310$	−0.457807	−	0.615652i	−0.0260017	−	0.0349667i
$311$	−12.2547	+	10.2829i	−0.694901	+	0.583091i	−0.920318	−	0.391172i	$-0.872070\pi$
$311$	−12.2547	+	10.2829i	−0.694901	+	0.583091i	0.225417	+	0.974262i	$0.427625\pi$
$312$	−16.1389	−	25.2570i	−0.913686	−	1.42990i
$313$	27.1344	−	9.87610i	1.53372	−	0.558230i	0.569194	−	0.822203i	$-0.307255\pi$
$313$	27.1344	−	9.87610i	1.53372	−	0.558230i	0.964530	+	0.263973i	$0.0850329\pi$
$314$	−1.16145	+	0.582499i	−0.0655446	+	0.0328723i
$315$	−5.39432	−	7.60560i	−0.303936	−	0.428527i
$316$	21.7403	+	16.2225i	1.22299	+	0.912586i
$317$	8.97772	+	1.58301i	0.504239	+	0.0889109i	0.419981	−	0.907533i	$-0.362037\pi$
$317$	8.97772	+	1.58301i	0.504239	+	0.0889109i	0.0842582	+	0.996444i	$0.473148\pi$
$318$	0.735957	−	3.89798i	0.0412704	−	0.218588i
$319$	−0.774270	+	2.12729i	−0.0433508	+	0.119105i
$320$	−24.4728	−	4.39907i	−1.36807	−	0.245915i
$321$	−8.34062	−	13.0052i	−0.465528	−	0.725881i
$322$	7.02824	+	6.63816i	0.391669	+	0.369930i
$323$	36.2295			2.01586
$324$	−12.9562	+	12.4954i	−0.719791	+	0.694190i
$325$	28.5136			1.58165
$326$	1.96717	+	1.85799i	0.108952	+	0.102905i
$327$	−5.29234	−	8.25215i	−0.292667	−	0.456345i
$328$	0.0198843	−	11.9740i	0.00109792	−	0.661153i
$329$	1.88001	−	5.16529i	0.103648	−	0.284772i
$330$	−0.453383	+	2.40134i	−0.0249579	+	0.132189i
$331$	−25.9142	−	4.56937i	−1.42437	−	0.251155i	−0.592253	−	0.805752i	$-0.701762\pi$
$331$	−25.9142	−	4.56937i	−1.42437	−	0.251155i	−0.832119	+	0.554597i	$0.812873\pi$
$332$	7.92323	−	10.6182i	0.434844	−	0.582749i
$333$	−8.32127	+	0.778741i	−0.456003	+	0.0426747i
$334$	−1.22073	+	0.612227i	−0.0667953	+	0.0334996i
$335$	43.3927	−	15.7937i	2.37080	−	0.862899i
$336$	3.38136	+	6.04701i	0.184469	+	0.329892i
$337$	−14.4661	+	12.1385i	−0.788020	+	0.661227i	−0.945254	−	0.326334i	$-0.894187\pi$
$337$	−14.4661	+	12.1385i	−0.788020	+	0.661227i	0.157235	+	0.987561i	$0.449742\pi$
$338$	−20.6182	−	27.7270i	−1.12148	−	1.50815i
$339$	19.8614	−	4.46621i	1.07873	−	0.242571i
$340$	−29.9077	+	7.05330i	−1.62197	+	0.382519i
$341$	0.0485196	−	0.0280128i	0.00262749	−	0.00151698i
$342$	4.33760	−	30.7910i	0.234551	−	1.66499i
$343$	0.866025	+	0.500000i	0.0467610	+	0.0269975i
$344$	−5.71737	+	15.6276i	−0.308260	+	0.842582i
$345$	14.1859	+	33.9570i	0.763742	+	1.82818i
$346$	12.7597	+	5.51237i	0.685965	+	0.296347i
$347$	1.22207	+	6.93073i	0.0656044	+	0.372061i	0.999880	+	0.0155086i	$0.00493675\pi$
$347$	1.22207	+	6.93073i	0.0656044	+	0.372061i	−0.934275	+	0.356552i	$0.883952\pi$
$348$	−1.72844	+	24.3701i	−0.0926541	+	1.30637i
$349$	−6.47593	−	5.43395i	−0.346649	−	0.290873i	0.452794	−	0.891615i	$-0.350427\pi$
$349$	−6.47593	−	5.43395i	−0.346649	−	0.290873i	−0.799443	+	0.600742i	$0.794872\pi$
$350$	−6.57949	−	0.386866i	−0.351689	−	0.0206789i
$351$	−21.2643	+	23.6327i	−1.13501	+	1.26142i
$352$	0.525580	−	1.73804i	0.0280135	−	0.0926376i
$353$	−0.883981	+	1.05349i	−0.0470495	+	0.0560715i	−0.789056	−	0.614321i	$-0.789430\pi$
$353$	−0.883981	+	1.05349i	−0.0470495	+	0.0560715i	0.742006	+	0.670393i	$0.233874\pi$
$354$	10.4383	+	6.19578i	0.554788	+	0.329302i
$355$	−8.67724	+	1.53003i	−0.460540	+	0.0812057i
$356$	−0.0643243	+	0.127727i	−0.00340918	+	0.00676954i
$357$	6.80832	+	5.19158i	0.360334	+	0.274768i
$358$	−21.5716	−	5.12519i	−1.14010	−	0.270875i
$359$	−11.4970	+	19.9134i	−0.606790	+	1.05099i	0.384976	+	0.922927i	$0.374210\pi$
$359$	−11.4970	+	19.9134i	−0.606790	+	1.05099i	−0.991766	+	0.128065i	$0.959124\pi$
$360$	2.41378	+	26.2626i	0.127218	+	1.38416i
$361$	17.3583	+	30.0655i	0.913596	+	1.58240i
$362$	2.49232	+	8.34174i	0.130994	+	0.438432i
$363$	18.0176	+	5.62111i	0.945680	+	0.295032i
$364$	6.71270	+	10.2308i	0.351841	+	0.536241i
$365$	−8.94054	−	10.6549i	−0.467969	−	0.557704i
$366$	−2.91964	+	7.72994i	−0.152612	+	0.404050i
$367$	−3.31981	−	9.12110i	−0.173293	−	0.476118i	0.822392	−	0.568922i	$-0.192639\pi$
$367$	−3.31981	−	9.12110i	−0.173293	−	0.476118i	−0.995684	+	0.0928040i	$0.970417\pi$
$368$	−7.78431	−	26.2125i	−0.405785	−	1.36642i
$369$	−12.2475	+	3.36121i	−0.637580	+	0.174977i
$370$	−6.73465	+	10.2272i	−0.350118	+	0.531687i
$371$	−0.281216	+	1.59486i	−0.0146000	+	0.0828009i
$372$	0.420446	−	0.434520i	0.0217991	−	0.0225288i
$373$	−1.58603	−	0.577268i	−0.0821216	−	0.0298898i	0.300633	−	0.953740i	$-0.402802\pi$
$373$	−1.58603	−	0.577268i	−0.0821216	−	0.0298898i	−0.382754	+	0.923850i	$0.625024\pi$
$374$	−0.259270	−	2.22889i	−0.0134065	−	0.115253i
$375$	1.62399	+	0.839168i	0.0838627	+	0.0433344i
$376$	−11.9265	+	9.97380i	−0.615061	+	0.514359i
$377$			43.1500i			2.22234i
$378$	5.22738	−	5.16473i	0.268868	−	0.265645i
$379$		−	10.3436i		−	0.531313i	−0.964068	−	0.265656i	$-0.914411\pi$
$379$		−	10.3436i		−	0.531313i	0.964068	−	0.265656i	$-0.0855887\pi$
$380$	−31.2284	−	33.1737i	−1.60198	−	1.70177i
$381$	0.886544	+	18.9878i	0.0454190	+	0.972774i
$382$	8.04489	−	0.935799i	0.411613	−	0.0478797i
$383$	12.7799	+	4.65151i	0.653023	+	0.237681i	0.647221	−	0.762302i	$-0.275931\pi$
$383$	12.7799	+	4.65151i	0.653023	+	0.237681i	0.00580206	+	0.999983i	$0.498153\pi$
$384$	0.301689	−	19.5936i	0.0153955	−	0.999881i
$385$	0.173242	−	0.982505i	0.00882924	−	0.0500731i
$386$	22.1943	+	14.6150i	1.12966	+	0.743885i
$387$	17.5918	+	1.43196i	0.894242	+	0.0727908i
$388$	−2.48507	−	5.77863i	−0.126161	−	0.293366i
$389$	−0.408818	−	1.12322i	−0.0207279	−	0.0569494i	0.928897	−	0.370338i	$-0.120758\pi$
$389$	−0.408818	−	1.12322i	−0.0207279	−	0.0569494i	−0.949625	+	0.313388i	$0.898536\pi$
$390$	7.53404	+	45.9666i	0.381501	+	2.32761i
$391$	−21.7209	−	25.8859i	−1.09847	−	1.30911i
$392$	−1.41014	−	2.45183i	−0.0712230	−	0.123836i
$393$	22.4145	−	20.6641i	1.13066	−	1.04237i
$394$	27.1797	−	8.12068i	1.36929	−	0.409114i
$395$	−21.0776	−	36.5075i	−1.06053	−	1.83689i
$396$	−1.92535	−	0.0465057i	−0.0967524	−	0.00233700i
$397$	9.42987	−	16.3330i	0.473271	−	0.819730i	−0.526260	−	0.850323i	$-0.676406\pi$
$397$	9.42987	−	16.3330i	0.473271	−	0.819730i	0.999532	+	0.0305932i	$0.00973963\pi$
$398$	7.80118	−	32.8348i	0.391038	−	1.64586i
$399$	−1.61891	+	12.5908i	−0.0810467	+	0.630330i
$400$	15.5522	+	10.2783i	0.777612	+	0.513914i
$401$	38.2672	−	6.74754i	1.91097	−	0.336956i	0.913428	−	0.407001i	$-0.133425\pi$
$401$	38.2672	−	6.74754i	1.91097	−	0.336956i	0.997544	+	0.0700451i	$0.0223143\pi$
$402$	17.8142	+	31.7340i	0.888492	+	1.58275i
$403$	0.686427	−	0.818052i	0.0341934	−	0.0407501i
$404$	−0.778985	+	6.60125i	−0.0387559	+	0.328425i
$405$	26.1685	−	9.88453i	1.30032	−	0.491166i
$406$	0.585451	−	9.95685i	0.0290554	−	0.494150i
$407$	−0.685015	−	0.574796i	−0.0339550	−	0.0284916i
$408$	−9.29778	−	22.3606i	−0.460309	−	1.10701i
$409$	5.55613	+	31.5104i	0.274733	+	1.55809i	0.739809	+	0.672817i	$0.234916\pi$
$409$	5.55613	+	31.5104i	0.274733	+	1.55809i	−0.465076	+	0.885271i	$0.653973\pi$
$410$	−7.37985	+	17.0824i	−0.364465	+	0.843641i
$411$	−9.76868	−	1.25604i	−0.481854	−	0.0619559i
$412$	19.6626	+	5.91033i	0.968707	+	0.291181i
$413$	−4.29164	−	2.47778i	−0.211178	−	0.121923i
$414$	−24.6006	+	15.3611i	−1.20905	+	0.754955i
$415$	−17.8306	+	10.2945i	−0.875271	+	0.505338i
$416$	−1.91675	−	34.5567i	−0.0939763	−	1.69428i
$417$	11.0379	+	11.9729i	0.540527	+	0.586313i
$418$	2.66977	−	1.98528i	0.130583	−	0.0971030i
$419$	−11.4604	+	9.61640i	−0.559876	+	0.469792i	−0.878269	−	0.478167i	$-0.841301\pi$
$419$	−11.4604	+	9.61640i	−0.559876	+	0.469792i	0.318393	+	0.947959i	$0.396857\pi$
$420$	−1.11481	−	10.7090i	−0.0543972	−	0.522545i
$421$	−34.5862	+	12.5883i	−1.68563	+	0.613518i	−0.994064	−	0.108797i	$-0.965300\pi$
$421$	−34.5862	+	12.5883i	−1.68563	+	0.613518i	−0.691564	+	0.722315i	$0.743078\pi$
$422$	7.86644	+	15.6850i	0.382932	+	0.763535i
$423$	13.5651	+	9.37664i	0.659556	+	0.455908i
$424$	2.95013	−	3.50399i	0.143271	−	0.170169i
$425$	22.6875	+	4.00042i	1.10051	+	0.194049i
$426$	−2.29601	−	6.55339i	−0.111242	−	0.317513i
$427$	1.15375	−	3.16990i	0.0558338	−	0.153402i
$428$	−1.01759	−	17.8111i	−0.0491872	−	0.860930i
$429$	−3.39779	+	0.158644i	−0.164047	+	0.00765939i
$430$	17.7570	−	18.8004i	0.856317	−	0.906637i
$431$	−10.7137			−0.516061			−0.258030	−	0.966137i	$-0.583073\pi$
$431$	−10.7137			−0.516061			−0.258030	+	0.966137i	$0.583073\pi$
$432$	−20.1172	+	5.22492i	−0.967887	+	0.251384i
$433$	31.5845			1.51786			0.758928	−	0.651174i	$-0.225723\pi$
$433$	31.5845			1.51786			0.758928	+	0.651174i	$0.225723\pi$
$434$	−0.169492	+	0.179452i	−0.00813587	+	0.00861396i
$435$	17.4297	−	33.7307i	0.835689	−	1.61726i
$436$	−0.645689	−	11.3016i	−0.0309229	−	0.541247i
$437$	17.1359	−	47.0806i	0.819722	−	2.25217i
$438$	7.14685	−	8.31137i	0.341490	−	0.397133i
$439$	7.48288	+	1.31943i	0.357138	+	0.0629731i	0.349339	−	0.936996i	$-0.386406\pi$
$439$	7.48288	+	1.31943i	0.357138	+	0.0629731i	0.00779947	+	0.999970i	$0.497517\pi$
$440$	−1.81741	+	2.15862i	−0.0866418	+	0.102908i
$441$	−2.10846	+	2.13411i	−0.100403	+	0.101624i
$442$	−19.1744	−	38.2320i	−0.912031	−	1.81851i
$443$	17.9102	−	6.51879i	0.850941	−	0.309717i	0.120517	−	0.992711i	$-0.461545\pi$
$443$	17.9102	−	6.51879i	0.850941	−	0.309717i	0.730424	+	0.682994i	$0.239323\pi$
$444$	−8.81232	−	3.93399i	−0.418214	−	0.186699i
$445$	0.170251	−	0.142857i	0.00807067	−	0.00677209i
$446$	33.2523	−	24.7268i	1.57454	−	1.17085i
$447$	−8.79794	+	28.2005i	−0.416128	+	1.33384i
$448$	−0.0265699	+	7.99996i	−0.00125531	+	0.377962i
$449$	−27.6828	+	15.9827i	−1.30643	+	0.754270i	−0.981499	−	0.191466i	$-0.938676\pi$
$449$	−27.6828	+	15.9827i	−1.30643	+	0.754270i	−0.324935	+	0.945736i	$0.605342\pi$
$450$	6.11618	−	18.8028i	0.288319	−	0.886375i
$451$	−1.17682	−	0.679437i	−0.0554143	−	0.0319935i
$452$	22.5117	+	6.76672i	1.05886	+	0.318280i
$453$	−10.5650	+	13.8551i	−0.496386	+	0.650968i
$454$	12.7609	−	29.5382i	0.598900	−	1.38629i
$455$	−3.30212	−	18.7273i	−0.154806	−	0.877948i
$456$	21.8190	−	28.5154i	1.02177	−	1.33536i
$457$	8.37411	+	7.02671i	0.391724	+	0.328696i	0.817284	−	0.576234i	$-0.195478\pi$
$457$	8.37411	+	7.02671i	0.391724	+	0.328696i	−0.425560	+	0.904930i	$0.639923\pi$
$458$	1.21355	−	20.6391i	0.0567056	−	0.964400i
$459$	−20.2351	+	15.8206i	−0.944495	+	0.738441i
$460$	−4.98000	+	42.2014i	−0.232194	+	1.96765i
$461$	−23.4368	+	27.9309i	−1.09156	+	1.30087i	−0.141113	+	0.989993i	$0.545068\pi$
$461$	−23.4368	+	27.9309i	−1.09156	+	1.30087i	−0.950449	+	0.310880i	$0.899376\pi$
$462$	0.786192	+	0.00949362i	0.0365770	+	0.000441683i
$463$	−7.97768	+	1.40668i	−0.370754	+	0.0653739i	−0.355921	−	0.934516i	$-0.615833\pi$
$463$	−7.97768	+	1.40668i	−0.370754	+	0.0653739i	−0.0148330	+	0.999890i	$0.504722\pi$
$464$	−15.5543	+	23.5354i	−0.722089	+	1.09261i
$465$	−0.867023	+	0.362207i	−0.0402072	+	0.0167970i
$466$	4.37319	−	18.4065i	0.202584	−	0.852666i
$467$	3.22911	−	5.59298i	0.149425	−	0.258812i	−0.781590	−	0.623793i	$-0.785591\pi$
$467$	3.22911	−	5.59298i	0.149425	−	0.258812i	0.931015	+	0.364980i	$0.118924\pi$
$468$	−34.7886	+	11.7187i	−1.60810	+	0.541696i
$469$	−7.42852	−	12.8666i	−0.343017	−	0.594123i
$470$	23.1502	−	6.91676i	1.06784	−	0.319046i
$471$	0.349128	+	1.55259i	0.0160870	+	0.0715394i
$472$	6.98804	+	12.1502i	0.321651	+	0.559258i
$473$	1.21388	+	1.44665i	0.0558143	+	0.0665169i
$474$	25.7057	−	21.0460i	1.18070	−	0.966673i
$475$	11.6824	+	32.0972i	0.536027	+	1.47272i
$476$	3.90575	+	9.08218i	0.179020	+	0.416281i
$477$	−4.41552	−	2.02658i	−0.202173	−	0.0927908i
$478$	−23.3397	−	15.3693i	−1.06753	−	0.702974i
$479$	−0.0904697	+	0.513079i	−0.00413367	+	0.0234432i	−0.986805	−	0.161914i	$-0.948233\pi$
$479$	−0.0904697	+	0.513079i	−0.00413367	+	0.0234432i	0.982671	+	0.185357i	$0.0593443\pi$
$480$	−12.4602	+	27.7875i	−0.568730	+	1.26832i
$481$	−16.0167	−	5.82959i	−0.730297	−	0.265806i
$482$	−28.1918	+	3.27933i	−1.28410	+	0.149369i
$483$	9.96671	−	6.39194i	0.453501	−	0.290843i
$484$	14.9383	+	15.8689i	0.679016	+	0.721313i
$485$			9.77556i			0.443885i
$486$	11.0230	+	19.0917i	0.500015	+	0.866017i
$487$			20.7223i			0.939015i	0.882928	+	0.469508i	$0.155569\pi$
$487$			20.7223i			0.939015i	−0.882928	+	0.469508i	$0.844431\pi$
$488$	−7.31918	+	6.12084i	−0.331324	+	0.277077i
$489$	2.78964	−	1.78907i	0.126152	−	0.0809047i
$490$	0.507876	+	4.36611i	0.0229435	+	0.197241i
$491$	−10.0199	−	3.64695i	−0.452193	−	0.164585i	0.105876	−	0.994379i	$-0.466235\pi$
$491$	−10.0199	−	3.64695i	−0.452193	−	0.164585i	−0.558069	+	0.829795i	$0.688457\pi$
$492$	−14.2260	−	3.56194i	−0.641356	−	0.160585i
$493$	−6.05389	+	34.3333i	−0.272654	+	1.54630i
$494$	34.8766	−	52.9634i	1.56917	−	2.38294i
$495$	2.72016	+	1.24847i	0.122262	+	0.0561144i
$496$	0.669283	−	0.198756i	0.0300517	−	0.00892443i
$497$	0.969580	+	2.66390i	0.0434916	+	0.119492i
$498$	−10.2791	−	12.5549i	−0.460616	−	0.562599i
$499$	24.0264	+	28.6336i	1.07557	+	1.28181i	0.957383	+	0.288823i	$0.0932639\pi$
$499$	24.0264	+	28.6336i	1.07557	+	1.28181i	0.118187	+	0.992991i	$0.462292\pi$
$500$	1.15794	+	1.76482i	0.0517847	+	0.0789250i
$501$	0.366946	+	1.63182i	0.0163939	+	0.0729045i
$502$	4.44496	+	14.8772i	0.198388	+	0.664001i
$503$	−2.75526	−	4.77225i	−0.122851	−	0.212784i	0.798040	−	0.602605i	$-0.205870\pi$
$503$	−2.75526	−	4.77225i	−0.122851	−	0.212784i	−0.920891	+	0.389820i	$0.872537\pi$
$504$	8.18644	−	2.23208i	0.364653	−	0.0994246i
$505$	5.16497	−	8.94599i	0.229838	−	0.398091i
$506$	−3.01910	−	0.717304i	−0.134215	−	0.0318881i
$507$	−39.0479	+	16.3127i	−1.73418	+	0.724471i
$508$	−9.87245	+	19.6035i	−0.438019	+	0.869765i
$509$	25.2839	−	4.45823i	1.12069	−	0.197607i	0.417545	−	0.908656i	$-0.362891\pi$
$509$	25.2839	−	4.45823i	1.12069	−	0.197607i	0.703143	+	0.711049i	$0.251780\pi$
$510$	−0.454416	+	37.6314i	−0.0201219	+	1.66635i
$511$	−2.87651	+	3.42809i	−0.127249	+	0.151650i
$512$	11.4112	−	19.5393i	0.504308	−	0.863524i
$513$	−35.3153	−	14.2542i	−1.55921	−	0.629339i
$514$	−23.0938	−	1.35789i	−1.01862	−	0.0598939i
$515$	−24.4426	−	20.5098i	−1.07707	−	0.903768i
$516$	16.8849	+	11.4134i	0.743314	+	0.502446i
$517$	0.306383	+	1.73758i	0.0134747	+	0.0764188i
$518$	3.61674	+	1.56249i	0.158911	+	0.0686517i
$519$	10.3223	−	13.5368i	0.453098	−	0.594199i
$520$	−18.4797	+	50.5115i	−0.810391	+	2.21508i
$521$	−8.83379	−	5.10019i	−0.387015	−	0.223443i	0.293851	−	0.955851i	$-0.405063\pi$
$521$	−8.83379	−	5.10019i	−0.387015	−	0.223443i	−0.680866	+	0.732408i	$0.738396\pi$
$522$	28.4546	+	9.25570i	1.24543	+	0.405111i
$523$	−18.6365	+	10.7598i	−0.814918	+	0.470493i	−0.848661	−	0.528937i	$-0.822591\pi$
$523$	−18.6365	+	10.7598i	−0.814918	+	0.470493i	0.0337426	+	0.999431i	$0.489257\pi$
$524$	34.2627	−	8.08035i	1.49677	−	0.352992i
$525$	−2.40405	+	7.70582i	−0.104921	+	0.336310i
$526$	19.5766	+	26.3264i	0.853581	+	1.14788i
$527$	0.660943	−	0.554597i	0.0287911	−	0.0241586i
$528$	−1.91046	−	1.13827i	−0.0831419	−	0.0495369i
$529$	−22.2996	+	8.11638i	−0.969547	+	0.352886i
$530$	−6.36302	+	3.19122i	−0.276392	+	0.138618i
$531$	10.4486	−	10.5757i	0.453429	−	0.458946i
$532$	−8.76636	+	11.7481i	−0.380070	+	0.509344i
$533$	−25.5077	−	4.49769i	−1.10486	−	0.194817i
$534$	0.132804	+	0.114197i	0.00574700	+	0.00494178i
$535$	−9.48239	+	26.0526i	−0.409959	+	1.12635i
$536$	−0.0697826	+	42.0220i	−0.00301415	+	1.81507i
$537$	−12.4660	+	24.1248i	−0.537948	+	1.04106i
$538$	7.93376	+	7.49342i	0.342049	+	0.323064i
$539$	−0.320985			−0.0138258
$540$	31.9280	+	4.89165i	1.37396	+	0.210503i
$541$	16.0287			0.689126			0.344563	−	0.938763i	$-0.388027\pi$
$541$	16.0287			0.689126			0.344563	+	0.938763i	$0.388027\pi$
$542$	−31.1254	−	29.3979i	−1.33695	−	1.26275i
$543$	10.6512	−	0.497305i	0.457085	−	0.0213414i
$544$	3.32316	−	27.7648i	0.142479	−	1.19041i
$545$	−6.01682	+	16.5311i	−0.257732	+	0.708113i
$546$	14.1436	−	4.95527i	0.605289	−	0.212066i
$547$	14.6780	+	2.58814i	0.627588	+	0.110661i	0.478391	−	0.878147i	$-0.341220\pi$
$547$	14.6780	+	2.58814i	0.627588	+	0.110661i	0.149197	+	0.988808i	$0.452331\pi$
$548$	−9.11483	−	6.80144i	−0.389366	−	0.290543i
$549$	8.32476	+	5.75437i	0.355292	+	0.245590i
$550$	1.89106	−	0.948418i	0.0806353	−	0.0404407i
$551$	−48.5732	+	17.6792i	−2.06929	+	0.753159i
$552$	−33.4555	+	1.50637i	−1.42396	+	0.0641153i
$553$	−10.3898	+	8.71806i	−0.441818	+	0.370730i
$554$	11.5453	+	15.5259i	0.490512	+	0.659634i
$555$	10.1656	+	11.0267i	0.431505	+	0.468057i
$556$	4.31617	+	18.3016i	0.183046	+	0.776161i
$557$	−33.3926	+	19.2793i	−1.41489	+	0.816888i	−0.995844	−	0.0910760i	$-0.970969\pi$
$557$	−33.3926	+	19.2793i	−1.41489	+	0.816888i	−0.419048	+	0.907964i	$0.637636\pi$
$558$	−0.392213	−	0.628126i	−0.0166037	−	0.0265907i
$559$	31.1730	+	17.9977i	1.31848	+	0.761223i
$560$	4.94953	−	11.4048i	0.209156	−	0.481940i
$561$	−2.72579	−	0.350478i	−0.115083	−	0.0147972i
$562$	35.9035	+	15.5108i	1.51450	+	0.654285i
$563$	−2.62423	−	14.8828i	−0.110598	−	0.627234i	−0.988836	−	0.149009i	$-0.952392\pi$
$563$	−2.62423	−	14.8828i	−0.110598	−	0.627234i	0.878237	−	0.478225i	$-0.158720\pi$
$564$	8.33022	+	17.1226i	0.350766	+	0.720992i
$565$	−27.9843	−	23.4816i	−1.17731	−	0.987878i
$566$	−27.9697	−	1.64458i	−1.17565	−	0.0691270i
$567$	−4.59392	−	7.73924i	−0.192926	−	0.325018i
$568$	1.40546	−	7.89406i	0.0589717	−	0.331227i
$569$	−3.48263	+	4.15043i	−0.145999	+	0.173995i	−0.834088	−	0.551631i	$-0.814006\pi$
$569$	−3.48263	+	4.15043i	−0.145999	+	0.173995i	0.688089	+	0.725627i	$0.258450\pi$
$570$	−48.6570	+	27.3141i	−2.03802	+	1.14406i
$571$	18.2828	−	3.22375i	0.765110	−	0.134910i	0.222544	−	0.974923i	$-0.428564\pi$
$571$	18.2828	−	3.22375i	0.765110	−	0.134910i	0.542566	+	0.840013i	$0.317453\pi$
$572$	−3.50798	−	1.76664i	−0.146676	−	0.0738668i
$573$	1.26500	−	9.83838i	0.0528462	−	0.411004i
$574$	5.82486	+	1.38392i	0.243125	+	0.0577638i
$575$	15.9294	−	27.5905i	0.664300	−	1.15060i
$576$	−23.1991	−	6.14846i	−0.966628	−	0.256186i
$577$	4.92635	+	8.53270i	0.205087	+	0.355221i	0.950160	−	0.311762i	$-0.100919\pi$
$577$	4.92635	+	8.53270i	0.205087	+	0.355221i	−0.745074	+	0.666982i	$0.767586\pi$
$578$	−3.01016	−	10.0749i	−0.125206	−	0.419061i
$579$	23.9293	−	22.0606i	0.994466	−	0.916806i
$580$	36.6556	−	24.0507i	1.52204	−	0.998651i
$581$	4.25799	+	5.07448i	0.176651	+	0.210525i
$582$	−7.60260	+	1.24609i	−0.315138	+	0.0516519i
$583$	−0.177790	−	0.488473i	−0.00736330	−	0.0202305i
$584$	11.9012	−	4.30931i	0.492475	−	0.178321i
$585$	56.8604	+	4.62840i	2.35089	+	0.191361i
$586$	−12.8192	+	19.4671i	−0.529555	+	0.804179i
$587$	−8.27017	+	46.9024i	−0.341346	+	1.93587i	0.0108397	+	0.999941i	$0.496550\pi$
$587$	−8.27017	+	46.9024i	−0.341346	+	1.93587i	−0.352186	+	0.935930i	$0.614562\pi$
$588$	−3.33085	+	0.951529i	−0.137362	+	0.0392404i
$589$	1.20211	+	0.437531i	0.0495319	+	0.0180281i
$590$	−2.51681	−	21.6365i	−0.103615	−	0.890761i
$591$	−1.62036	−	34.7044i	−0.0666526	−	1.42755i
$592$	−6.63463	−	8.95317i	−0.272682	−	0.367973i
$593$		−	9.35689i		−	0.384242i	−0.981371	−	0.192121i	$-0.938463\pi$
$593$		−	9.35689i		−	0.384242i	0.981371	−	0.192121i	$-0.0615365\pi$
$594$	−0.624213	+	2.27465i	−0.0256118	+	0.0933302i
$595$		−	15.3641i		−	0.629866i
$596$	−24.8374	+	23.3809i	−1.01738	+	0.957720i
$597$	−36.7209	−	18.9748i	−1.50289	−	0.776588i
$598$	−58.7519	+	6.83415i	−2.40255	+	0.279469i
$599$	−7.42752	−	2.70340i	−0.303480	−	0.110458i	0.185791	−	0.982589i	$-0.440515\pi$
$599$	−7.42752	−	2.70340i	−0.303480	−	0.110458i	−0.489272	+	0.872131i	$0.662737\pi$
$600$	16.8120	−	15.4476i	0.686349	−	0.630645i
$601$	4.01751	−	22.7844i	0.163877	−	0.929395i	−0.786337	−	0.617798i	$-0.788025\pi$
$601$	4.01751	−	22.7844i	0.163877	−	0.929395i	0.950214	−	0.311597i	$-0.100864\pi$
$602$	−6.94897	−	4.57592i	−0.283219	−	0.186501i
$603$	42.9819	−	11.7959i	1.75036	−	0.480368i
$604$	−18.4824	+	7.94829i	−0.752040	+	0.323411i
$605$	−11.5839	−	31.8266i	−0.470954	−	1.29393i
$606$	7.61581	+	2.87654i	0.309371	+	0.116851i
$607$	0.159390	+	0.189953i	0.00646943	+	0.00770996i	0.769269	−	0.638924i	$-0.220620\pi$
$607$	0.159390	+	0.189953i	0.00646943	+	0.00770996i	−0.762800	+	0.646634i	$0.776176\pi$
$608$	38.1146	−	16.3160i	1.54575	−	0.661703i
$609$	−11.6613	−	3.63808i	−0.472541	−	0.147423i
$610$	14.2071	−	4.24476i	0.575229	−	0.171865i
$611$	16.8153	+	29.1249i	0.680273	+	1.17827i
$612$	−29.3245	+	4.44345i	−1.18537	+	0.179616i
$613$	11.3019	−	19.5754i	0.456479	−	0.790644i	−0.542293	−	0.840189i	$-0.682444\pi$
$613$	11.3019	−	19.5754i	0.456479	−	0.790644i	0.998772	+	0.0495452i	$0.0157772\pi$
$614$	−10.6035	+	44.6295i	−0.427921	+	1.80110i
$615$	18.1228	+	13.8193i	0.730781	+	0.557246i
$616$	0.785495	+	0.455246i	0.0316485	+	0.0183424i
$617$	33.2569	−	5.86409i	1.33887	−	0.236079i	0.542077	−	0.840329i	$-0.317638\pi$
$617$	33.2569	−	5.86409i	1.33887	−	0.236079i	0.796795	+	0.604250i	$0.206527\pi$
$618$	12.8351	−	21.6237i	0.516302	−	0.869834i
$619$	−2.06000	+	2.45501i	−0.0827983	+	0.0986752i	−0.805853	−	0.592115i	$-0.798293\pi$
$619$	−2.06000	+	2.45501i	−0.0827983	+	0.0986752i	0.723055	+	0.690791i	$0.242737\pi$
$620$	−1.07753	−	0.127154i	−0.0432745	−	0.00510663i
$621$	10.9881	+	33.7786i	0.440938	+	1.35549i
$622$	−1.32795	+	22.5847i	−0.0532461	+	0.905564i
$623$	−0.0547761	−	0.0459626i	−0.00219456	−	0.00184145i
$624$	−41.6392	−	7.93330i	−1.66690	−	0.317586i
$625$	−4.61600	−	26.1786i	−0.184640	−	1.04715i
$626$	16.1953	−	37.4878i	0.647293	−	1.49831i
$627$	−1.57071	−	3.75984i	−0.0627281	−	0.150153i
$628$	−0.528961	+	1.75976i	−0.0211078	+	0.0702220i
$629$	−11.9262	−	6.88557i	−0.475527	−	0.274546i
$630$	−13.0577	−	1.83947i	−0.520232	−	0.0732864i
$631$	24.2722	−	14.0136i	0.966262	−	0.557872i	0.0681675	−	0.997674i	$-0.478285\pi$
$631$	24.2722	−	14.0136i	0.966262	−	0.557872i	0.898095	+	0.439802i	$0.144951\pi$
$632$	37.7899	−	6.59869i	1.50320	−	0.262482i
$633$	20.9671	−	4.71485i	0.833369	−	0.187398i
$634$	10.3455	−	7.69301i	0.410870	−	0.305528i
$635$	26.1300	−	21.9257i	1.03694	−	0.870093i
$636$	−3.29295	−	4.54184i	−0.130574	−	0.180096i
$637$	−5.74924	+	2.09255i	−0.227793	+	0.0829099i
$638$	1.43525	+	2.86178i	0.0568223	+	0.113299i
$639$	−8.46759	+	0.792434i	−0.334973	+	0.0313482i
$640$	−28.2874	+	20.8893i	−1.11816	+	0.825722i
$641$	−32.7116	−	5.76793i	−1.29203	−	0.227820i	−0.514949	−	0.857221i	$-0.672189\pi$
$641$	−32.7116	−	5.76793i	−1.29203	−	0.227820i	−0.777080	+	0.629401i	$0.783300\pi$
$642$	−21.4703	−	4.05368i	−0.847363	−	0.159986i
$643$	−3.17264	+	8.71676i	−0.125117	+	0.343756i	−0.986398	−	0.164372i	$-0.947440\pi$
$643$	−3.17264	+	8.71676i	−0.125117	+	0.343756i	0.861282	+	0.508128i	$0.169662\pi$
$644$	13.6497	−	0.779844i	0.537874	−	0.0307301i
$645$	−17.0983	−	26.6608i	−0.673245	−	1.04977i
$646$	35.1811	−	37.2485i	1.38418	−	1.46552i
$647$	−30.0339			−1.18075			−0.590377	−	0.807128i	$-0.701021\pi$
$647$	−30.0339			−1.18075			−0.590377	+	0.807128i	$0.701021\pi$
$648$	0.265544	+	25.4545i	0.0104315	+	0.999946i
$649$	1.59066			0.0624388
$650$	27.6884	−	29.3155i	1.08603	−	1.14985i
$651$	0.163205	+	0.254479i	0.00639651	+	0.00997384i
$652$	3.82049	−	0.218275i	0.149622	−	0.00854829i
$653$	9.35707	−	25.7083i	0.366171	−	1.00605i	−0.610634	−	0.791913i	$-0.709085\pi$
$653$	9.35707	−	25.7083i	0.366171	−	1.00605i	0.976805	−	0.214132i	$-0.0686924\pi$
$654$	−13.6234	−	2.57216i	−0.532718	−	0.100580i
$655$	−53.8759	−	9.49978i	−2.10511	−	0.371187i
$656$	−12.2914	−	11.6479i	−0.479900	−	0.454775i
$657$	−7.76670	−	10.9505i	−0.303008	−	0.427219i
$658$	−3.48495	−	6.94870i	−0.135858	−	0.270889i
$659$	3.43774	−	1.25124i	0.133915	−	0.0487412i	−0.274193	−	0.961675i	$-0.588411\pi$
$659$	3.43774	−	1.25124i	0.133915	−	0.0487412i	0.408108	+	0.912933i	$0.366189\pi$
$660$	2.02861	+	2.79798i	0.0789635	+	0.108911i
$661$	18.9121	−	15.8691i	0.735594	−	0.617236i	−0.196057	−	0.980593i	$-0.562814\pi$
$661$	18.9121	−	15.8691i	0.735594	−	0.617236i	0.931650	+	0.363356i	$0.118369\pi$
$662$	−29.8622	+	22.2059i	−1.16063	+	0.863056i
$663$	−51.1071	+	11.4924i	−1.98484	+	0.446327i
$664$	−3.22287	−	18.4570i	−0.125072	−	0.716270i
$665$	19.7280	−	11.3900i	0.765020	−	0.441685i
$666$	−7.27982	+	9.31150i	−0.282087	+	0.360813i
$667$	41.7530	+	24.1061i	1.61668	+	0.933393i
$668$	−0.555957	+	1.84957i	−0.0215106	+	0.0715620i
$669$	−19.5633	−	46.8291i	−0.756362	−	1.81052i
$670$	25.8991	−	59.9497i	1.00057	−	2.31606i
$671$	0.188024	+	1.06634i	0.00725860	+	0.0411656i
$672$	9.50059	+	2.39556i	0.366493	+	0.0924107i
$673$	−9.33180	−	7.83031i	−0.359714	−	0.301836i	0.444962	−	0.895549i	$-0.353217\pi$
$673$	−9.33180	−	7.83031i	−0.359714	−	0.301836i	−0.804677	+	0.593713i	$0.797661\pi$
$674$	−1.56759	+	26.6602i	−0.0603813	+	1.02691i
$675$	−20.5410	−	12.8257i	−0.790625	−	0.493661i
$676$	−48.5283	−	5.72661i	−1.86647	−	0.220254i
$677$	−17.6608	+	21.0473i	−0.678760	+	0.808915i	−0.989948	−	0.141434i	$-0.954829\pi$
$677$	−17.6608	+	21.0473i	−0.678760	+	0.808915i	0.311188	+	0.950349i	$0.399273\pi$
$678$	14.6949	−	24.7570i	0.564353	−	0.950787i
$679$	3.09738	−	0.546152i	0.118867	−	0.0209594i
$680$	−21.7906	+	37.5980i	−0.835630	+	1.44182i
$681$	−31.3371	−	23.8956i	−1.20084	−	0.915683i
$682$	0.0183149	−	0.0770864i	0.000701313	−	0.00295179i
$683$	−9.28030	+	16.0740i	−0.355101	+	0.615053i	−0.987135	−	0.159887i	$-0.948887\pi$
$683$	−9.28030	+	16.0740i	−0.355101	+	0.615053i	0.632034	+	0.774940i	$0.282220\pi$
$684$	−27.4449	−	34.3595i	−1.04938	−	1.31377i
$685$	8.83699	+	15.3061i	0.337644	+	0.584817i
$686$	1.35503	−	0.404851i	0.0517351	−	0.0154573i
$687$	−24.1722	−	7.54120i	−0.922227	−	0.287715i
$688$	10.5152	+	21.0535i	0.400886	+	0.802657i
$689$	−6.36887	−	7.59012i	−0.242635	−	0.289161i
$690$	48.6874	+	18.3895i	1.85350	+	0.700077i
$691$	5.10019	+	14.0127i	0.194021	+	0.533067i	0.998111	−	0.0614402i	$-0.0195694\pi$
$691$	5.10019	+	14.0127i	0.194021	+	0.533067i	−0.804090	+	0.594507i	$0.797347\pi$
$692$	18.0579	−	7.76570i	0.686457	−	0.295208i
$693$	0.243603	−	0.931633i	0.00925370	−	0.0353898i
$694$	8.31236	+	5.47372i	0.315533	+	0.207780i
$695$	5.07436	−	28.7781i	0.192482	−	1.09162i
$696$	23.3771	+	25.4419i	0.886106	+	0.964373i
$697$	−19.6648	−	7.15739i	−0.744856	−	0.271105i
$698$	−11.8753	+	1.38136i	−0.449487	+	0.0522853i
$699$	−20.5850	−	10.6369i	−0.778598	−	0.402325i
$700$	−6.78684	+	6.38887i	−0.256518	+	0.241476i
$701$			0.316437i			0.0119517i	0.999982	+	0.00597583i	$0.00190218\pi$
$701$			0.316437i			0.0119517i	−0.999982	+	0.00597583i	$0.998098\pi$
$702$	3.64839	+	44.8112i	0.137700	+	1.69129i
$703$		−	20.4181i		−	0.770085i
$704$	−1.27655	−	2.22810i	−0.0481117	−	0.0839747i
$705$	−1.38013	−	29.5594i	−0.0519788	−	1.11327i
$706$	0.224716	+	1.93184i	0.00845730	+	0.0727059i
$707$	−3.12309	−	1.13671i	−0.117456	−	0.0427505i
$708$	16.5062	−	4.71535i	0.620342	−	0.177214i
$709$	5.82065	−	33.0106i	0.218599	−	1.23974i	−0.655951	−	0.754803i	$-0.727732\pi$
$709$	5.82065	−	33.0106i	0.218599	−	1.23974i	0.874550	−	0.484935i	$-0.161157\pi$
$710$	−6.85307	+	10.4070i	−0.257191	+	0.390569i
$711$	−17.4184	−	36.7718i	−0.653242	−	1.37905i
$712$	0.0688568	+	0.190165i	0.00258052	+	0.00712672i
$713$	−0.408089	−	1.12122i	−0.0152831	−	0.0419899i
$714$	11.9489	−	1.95845i	0.447176	−	0.0732932i
$715$	3.92351	+	4.67586i	0.146731	+	0.174867i
$716$	−26.2167	+	17.2015i	−0.979765	+	0.642849i
$717$	−25.1642	+	23.1991i	−0.939773	+	0.866385i
$718$	9.30917	+	31.1576i	0.347415	+	1.16279i
$719$	−6.30453	−	10.9198i	−0.235119	−	0.407239i	0.724188	−	0.689603i	$-0.242215\pi$
$719$	−6.30453	−	10.9198i	−0.235119	−	0.407239i	−0.959307	+	0.282364i	$0.908881\pi$
$720$	29.3452	+	23.0210i	1.09363	+	0.857940i
$721$	−5.13292	+	8.89048i	−0.191160	+	0.331099i
$722$	47.7671	+	11.3489i	1.77771	+	0.422364i
$723$	−4.43296	+	34.4768i	−0.164864	+	1.28220i
$724$	10.9965	+	5.53793i	0.408684	+	0.205815i
$725$	−32.3694	+	5.70760i	−1.20217	+	0.211975i
$726$	23.2754	−	13.0659i	0.863832	−	0.484922i
$727$	22.7683	−	27.1342i	0.844428	−	1.00635i	−0.155401	−	0.987851i	$-0.549667\pi$
$727$	22.7683	−	27.1342i	0.844428	−	1.00635i	0.999829	−	0.0184985i	$-0.00588860\pi$
$728$	17.0370	+	3.03326i	0.631433	+	0.112420i
$729$	25.9490	−	7.45999i	0.961073	−	0.276296i
$730$	−19.6364	−	1.15460i	−0.726776	−	0.0427335i
$731$	22.2785	+	18.6939i	0.823999	+	0.691418i
$732$	5.11219	+	10.5080i	0.188952	+	0.388387i
$733$	−0.297850	−	1.68919i	−0.0110013	−	0.0623917i	0.978813	−	0.204757i	$-0.0656404\pi$
$733$	−0.297850	−	1.68919i	−0.0110013	−	0.0623917i	−0.989814	+	0.142365i	$0.954529\pi$
$734$	−12.6014	−	5.44397i	−0.465125	−	0.200941i
$735$	5.33947	+	0.686540i	0.196949	+	0.0253234i
$736$	−34.5088	−	17.4507i	−1.27201	−	0.643242i
$737$	4.12998	+	2.38444i	0.152130	+	0.0878321i
$738$	−8.43734	+	15.8559i	−0.310583	+	0.583664i
$739$	−0.0528659	+	0.0305221i	−0.00194470	+	0.00112277i	−0.500972	−	0.865463i	$-0.667024\pi$
$739$	−0.0528659	+	0.0305221i	−0.00194470	+	0.00112277i	0.499027	+	0.866586i	$0.333691\pi$
$740$	3.97508	+	16.8553i	0.146127	+	0.619613i
$741$	−52.6443	−	57.1036i	−1.93394	−	2.09775i
$742$	1.36663	+	1.83783i	0.0501707	+	0.0674688i
$743$	−33.3193	+	27.9582i	−1.22237	+	1.02569i	−0.223668	+	0.974665i	$0.571803\pi$
$743$	−33.3193	+	27.9582i	−1.22237	+	1.02569i	−0.998698	+	0.0510207i	$0.983753\pi$
$744$	−0.0384620	−	0.854217i	−0.00141009	−	0.0313171i
$745$	49.8137	−	18.1307i	1.82503	−	0.664258i
$746$	−2.13364	+	1.07007i	−0.0781180	+	0.0391782i
$747$	−17.9598	+	8.50735i	−0.657113	+	0.311267i
$748$	−2.54335	−	1.89783i	−0.0929940	−	0.0693916i
$749$	8.78454	+	1.54895i	0.320980	+	0.0565974i
$750$	2.43977	−	0.854784i	0.0890877	−	0.0312123i
$751$	8.35114	−	22.9446i	0.304737	−	0.837259i	−0.688923	−	0.724834i	$-0.741916\pi$
$751$	8.35114	−	22.9446i	0.304737	−	0.837259i	0.993660	−	0.112424i	$-0.0358616\pi$
$752$	−1.32704	+	21.9471i	−0.0483921	+	0.800327i
$753$	18.9959	−	0.886924i	0.692250	−	0.0323213i
$754$	44.3636	+	41.9013i	1.61563	+	1.52596i
$755$	31.2662			1.13789
$756$	−0.233876	−	10.3897i	−0.00850597	−	0.377869i
$757$	−7.52508			−0.273504			−0.136752	−	0.990605i	$-0.543666\pi$
$757$	−7.52508			−0.273504			−0.136752	+	0.990605i	$0.543666\pi$
$758$	−10.6345	−	10.0442i	−0.386261	−	0.364823i
$759$	−1.74470	+	3.37642i	−0.0633286	+	0.122556i
$760$	−64.4314	−	0.106996i	−2.33717	−	0.00388115i
$761$	14.3003	−	39.2897i	0.518385	−	1.42425i	−0.353914	−	0.935278i	$-0.615150\pi$
$761$	14.3003	−	39.2897i	0.518385	−	1.42425i	0.872299	−	0.488973i	$-0.162628\pi$
$762$	20.3827	+	17.5268i	0.738387	+	0.634930i
$763$	5.57402	+	0.982849i	0.201793	+	0.0355815i
$764$	6.84997	−	9.17987i	0.247823	−	0.332116i
$765$	44.5930	+	11.6601i	1.61226	+	0.421574i
$766$	17.1924	−	8.62244i	0.621187	−	0.311542i
$767$	28.4907	−	10.3698i	1.02874	−	0.374430i
$768$	−19.8517	−	19.3368i	−0.716336	−	0.697755i
$769$	17.5998	−	14.7680i	0.634666	−	0.532548i	−0.267709	−	0.963500i	$-0.586267\pi$
$769$	17.5998	−	14.7680i	0.634666	−	0.532548i	0.902375	+	0.430952i	$0.141822\pi$
$770$	−0.841908	−	1.13219i	−0.0303403	−	0.0408012i
$771$	−8.43813	+	27.0472i	−0.303892	+	0.974080i
$772$	36.5781	−	8.62641i	1.31647	−	0.310471i
$773$	29.4762	−	17.0181i	1.06018	−	0.612098i	0.134701	−	0.990886i	$-0.456993\pi$
$773$	29.4762	−	17.0181i	1.06018	−	0.612098i	0.925483	+	0.378789i	$0.123659\pi$
$774$	18.5550	−	16.6961i	0.666945	−	0.600127i
$775$	0.704466	+	0.406723i	0.0253052	+	0.0146099i
$776$	−8.35431	−	3.05644i	−0.299902	−	0.109720i
$777$	2.92586	−	3.83701i	0.104965	−	0.137652i
$778$	−1.55180	−	0.670398i	−0.0556346	−	0.0240349i
$779$	−5.38790	−	30.5563i	−0.193042	−	1.09479i
$780$	54.5754	+	36.8904i	1.95411	+	1.32089i
$781$	−0.697061	−	0.584903i	−0.0249428	−	0.0209295i
$782$	−47.7062	−	2.80507i	−1.70597	−	0.100309i
$783$	19.4093	−	31.0851i	0.693631	−	1.11089i
$784$	−3.89013	−	0.931079i	−0.138933	−	0.0332528i
$785$	1.83558	−	2.18756i	0.0655146	−	0.0780772i
$786$	0.520586	−	43.1111i	0.0185687	−	1.53772i
$787$	−11.1153	+	1.95993i	−0.396218	+	0.0698639i	−0.368207	−	0.929744i	$-0.620028\pi$
$787$	−11.1153	+	1.95993i	−0.396218	+	0.0698639i	−0.0280106	+	0.999608i	$0.508917\pi$
$788$	18.0441	−	35.8298i	0.642794	−	1.27638i
$789$	37.0754	−	15.4886i	1.31992	−	0.551409i
$790$	−58.0018	−	13.7806i	−2.06361	−	0.490292i
$791$	−5.87668	+	10.1787i	−0.208951	+	0.361913i
$792$	−1.91745	+	1.93434i	−0.0681335	+	0.0687337i
$793$	10.3194	+	17.8737i	0.366452	+	0.634714i
$794$	−7.63538	−	25.5554i	−0.270970	−	0.906928i
$795$	1.91270	+	8.50585i	0.0678364	+	0.301671i
$796$	−26.1828	−	39.9051i	−0.928024	−	1.41440i
$797$	−24.7129	−	29.4517i	−0.875377	−	1.04323i	−0.998705	−	0.0508673i	$-0.983801\pi$
$797$	−24.7129	−	29.4517i	−0.875377	−	1.04323i	0.123329	−	0.992366i	$-0.460643\pi$
$798$	11.3729	+	13.8909i	0.402596	+	0.491733i
$799$	9.29328	+	25.5331i	0.328773	+	0.903295i
$800$	25.6695	−	6.00880i	0.907555	−	0.212443i
$801$	0.174973	−	0.124101i	0.00618238	−	0.00438490i
$802$	30.2225	−	45.8957i	1.06719	−	1.62063i
$803$	0.249432	−	1.41460i	0.00880228	−	0.0499202i
$804$	49.9252	+	12.5004i	1.76072	+	0.440855i
$805$	−19.9657	−	7.26694i	−0.703700	−	0.256126i
$806$	−0.174496	−	1.50011i	−0.00614636	−	0.0528391i
$807$	11.2508	−	7.21547i	0.396048	−	0.253997i
$808$	6.03047	+	7.21111i	0.212151	+	0.253686i
$809$		−	14.8423i		−	0.521828i	−0.965362	−	0.260914i	$-0.915976\pi$
$809$		−	14.8423i		−	0.521828i	0.965362	−	0.260914i	$-0.0840239\pi$
$810$	15.2487	−	36.5030i	0.535786	−	1.28258i
$811$		−	14.7640i		−	0.518433i	−0.965819	−	0.259217i	$-0.916536\pi$
$811$		−	14.7640i		−	0.518433i	0.965819	−	0.259217i	$-0.0834643\pi$
$812$	−9.66837	−	10.2706i	−0.339293	−	0.360428i
$813$	−44.1388	+	28.3074i	−1.54801	+	0.992785i
$814$	−1.25615	+	0.146119i	−0.0440282	+	0.00512145i
$815$	−5.58832	−	2.03398i	−0.195750	−	0.0712473i
$816$	−32.0182	−	12.1542i	−1.12086	−	0.425484i
$817$	−7.48770	+	42.4648i	−0.261961	+	1.48566i
$818$	37.7919	+	24.8861i	1.32136	+	0.870123i
$819$	−1.71024	−	18.2748i	−0.0597604	−	0.638573i
$820$	10.3966	+	24.1755i	0.363064	+	0.844245i
$821$	5.91204	+	16.2432i	0.206332	+	0.566892i	0.999090	−	0.0426439i	$-0.0135781\pi$
$821$	5.91204	+	16.2432i	0.206332	+	0.566892i	−0.792759	+	0.609536i	$0.791356\pi$
$822$	−10.7774	+	8.82373i	−0.375903	+	0.307763i
$823$	6.74610	+	8.03969i	0.235154	+	0.280246i	0.870697	−	0.491820i	$-0.163668\pi$
$823$	6.74610	+	8.03969i	0.235154	+	0.280246i	−0.635543	+	0.772066i	$0.719224\pi$
$824$	25.1702	−	14.4763i	0.876844	−	0.504306i
$825$	−0.568446	−	2.52790i	−0.0197908	−	0.0880104i
$826$	−6.71491	+	2.00626i	−0.233641	+	0.0698068i
$827$	−4.38626	−	7.59722i	−0.152525	−	0.264181i	0.779630	−	0.626240i	$-0.215407\pi$
$827$	−4.38626	−	7.59722i	−0.152525	−	0.264181i	−0.932155	+	0.362059i	$0.882074\pi$
$828$	−8.09564	+	40.2090i	−0.281343	+	1.39736i
$829$	−6.39834	+	11.0822i	−0.222223	+	0.384902i	−0.955483	−	0.295047i	$-0.904665\pi$
$829$	−6.39834	+	11.0822i	−0.222223	+	0.384902i	0.733259	+	0.679949i	$0.237998\pi$
$830$	−6.73059	+	28.3287i	−0.233622	+	0.983304i
$831$	21.8652	−	9.13439i	0.758494	−	0.316868i
$832$	−37.3899	−	31.5860i	−1.29626	−	1.09505i
$833$	−4.86810	+	0.858378i	−0.168670	+	0.0297410i
$834$	23.0280	+	0.278074i	0.797396	+	0.00962891i
$835$	1.92926	−	2.29920i	0.0667647	−	0.0795671i
$836$	0.551403	−	4.67268i	0.0190707	−	0.161608i
$837$	−0.862466	+	0.280559i	−0.0298112	+	0.00969754i
$838$	−1.24188	+	21.1208i	−0.0429000	+	0.729606i
$839$	−37.5100	−	31.4746i	−1.29499	−	1.08662i	−0.990988	−	0.133952i	$-0.957233\pi$
$839$	−37.5100	−	31.4746i	−1.29499	−	1.08662i	−0.304001	−	0.952672i	$-0.598322\pi$
$840$	−12.0927	−	9.25292i	−0.417239	−	0.319256i
$841$	−3.60160	−	20.4257i	−0.124193	−	0.704334i
$842$	−20.6429	+	47.7830i	−0.711403	+	1.64671i
$843$	29.0450	−	38.0901i	1.00036	−	1.31189i
$844$	23.7649	+	7.14344i	0.818023	+	0.245887i
$845$	65.7654	+	37.9697i	2.26240	+	1.30620i
$846$	22.8129	−	4.84127i	0.784322	−	0.166446i
$847$	−9.43705	+	5.44848i	−0.324261	+	0.187212i
$848$	−0.737784	−	6.43569i	−0.0253356	−	0.221002i
$849$	−10.2197	+	32.7577i	−0.350739	+	1.12424i
$850$	26.1439	−	19.4409i	0.896728	−	0.666818i
$851$	−14.5887	+	12.2414i	−0.500095	+	0.419629i
$852$	−8.96727	−	4.00316i	−0.307214	−	0.137146i
$853$	−25.9121	+	9.43125i	−0.887215	+	0.322920i	−0.745118	−	0.666933i	$-0.767607\pi$
$853$	−25.9121	+	9.43125i	−0.887215	+	0.322920i	−0.142097	+	0.989853i	$0.545385\pi$
$854$	−2.13869	−	4.26436i	−0.0731844	−	0.145923i
$855$	18.0865	+	65.9031i	0.618544	+	2.25384i
$856$	−19.3001	−	16.2494i	−0.659665	−	0.555394i
$857$	−25.4874	−	4.49412i	−0.870634	−	0.153516i	−0.279555	−	0.960130i	$-0.590187\pi$
$857$	−25.4874	−	4.49412i	−0.870634	−	0.153516i	−0.591079	+	0.806613i	$0.701298\pi$
$858$	−3.13636	+	3.64741i	−0.107074	+	0.124520i
$859$	−3.12453	+	8.58457i	−0.106608	+	0.292902i	−0.981514	−	0.191390i	$-0.938700\pi$
$859$	−3.12453	+	8.58457i	−0.106608	+	0.292902i	0.874907	+	0.484292i	$0.160923\pi$
$860$	−2.08607	−	36.5127i	−0.0711343	−	1.24507i
$861$	3.36612	−	6.51426i	0.114717	−	0.222005i
$862$	−10.4037	+	11.0150i	−0.354350	+	0.375173i
$863$	−2.68034			−0.0912398			−0.0456199	−	0.998959i	$-0.514526\pi$
$863$	−2.68034			−0.0912398			−0.0456199	+	0.998959i	$0.514526\pi$
$864$	−14.1631	+	25.7567i	−0.481840	+	0.876259i
$865$	−30.5480			−1.03866
$866$	30.6705	−	32.4728i	1.04223	−	1.10347i
$867$	−12.8642	+	0.600630i	−0.436890	+	0.0203985i
$868$	0.0199117	+	0.348517i	0.000675847	+	0.0118295i
$869$	1.48898	−	4.09094i	0.0505102	−	0.138776i
$870$	−17.7540	−	50.6745i	−0.601919	−	1.71803i
$871$	89.5176	+	15.7844i	3.03319	+	0.534833i
$872$	−12.2464	−	10.3107i	−0.414716	−	0.349164i
$873$	−0.765511	+	9.40438i	−0.0259086	+	0.318290i
$874$	−31.7646	−	63.3360i	−1.07445	−	2.14237i
$875$	−0.991744	+	0.360965i	−0.0335271	+	0.0122029i
$876$	−1.60509	−	15.4187i	−0.0542311	−	0.520950i
$877$	−2.30039	+	1.93026i	−0.0776787	+	0.0651802i	−0.680800	−	0.732469i	$-0.738368\pi$
$877$	−2.30039	+	1.93026i	−0.0776787	+	0.0651802i	0.603122	+	0.797649i	$0.293923\pi$
$878$	8.62288	−	6.41208i	0.291008	−	0.216397i
$879$	19.3498	+	20.9889i	0.652653	+	0.707937i
$880$	0.454508	+	3.96468i	0.0153215	+	0.133649i
$881$	−19.5575	+	11.2915i	−0.658908	+	0.380420i	−0.791861	−	0.610702i	$-0.790887\pi$
$881$	−19.5575	+	11.2915i	−0.658908	+	0.380420i	0.132953	+	0.991122i	$0.457554\pi$
$882$	0.146687	+	4.24010i	0.00493922	+	0.142772i
$883$	4.19051	+	2.41939i	0.141022	+	0.0814191i	0.568851	−	0.822441i	$-0.307388\pi$
$883$	4.19051	+	2.41939i	0.141022	+	0.0814191i	−0.427829	+	0.903860i	$0.640721\pi$
$884$	−57.9267	−	17.4120i	−1.94829	−	0.585630i
$885$	−26.4601	−	3.40219i	−0.889445	−	0.114363i
$886$	10.6898	−	24.7441i	0.359131	−	0.831294i
$887$	2.38014	+	13.4984i	0.0799173	+	0.453233i	0.998338	+	0.0576285i	$0.0183539\pi$
$887$	2.38014	+	13.4984i	0.0799173	+	0.453233i	−0.918421	+	0.395605i	$0.870535\pi$
$888$	−12.6019	+	5.24002i	−0.422893	+	0.175843i
$889$	−8.40699	−	7.05430i	−0.281961	−	0.236594i
$890$	0.0184489	−	0.313762i	0.000618407	−	0.0105173i
$891$	2.51911	+	1.41407i	0.0843935	+	0.0473733i
$892$	6.86777	−	58.1987i	0.229950	−	1.94864i
$893$	−25.8959	+	30.8615i	−0.866573	+	1.03274i
$894$	20.4503	+	36.4298i	0.683959	+	1.21839i
$895$	47.9891	−	8.46177i	1.60410	−	0.282846i
$896$	8.19915	+	7.79577i	0.273914	+	0.260438i
$897$	−9.23832	+	71.8498i	−0.308459	+	2.39900i
$898$	−10.4495	+	43.9816i	−0.348706	+	1.46768i
$899$	−0.615501	+	1.06608i	−0.0205281	+	0.0355557i
$900$	−13.3925	−	24.5469i	−0.446416	−	0.818230i
$901$	−4.00266	−	6.93281i	−0.133348	−	0.230965i
$902$	−1.84131	+	0.550142i	−0.0613090	+	0.0183177i
$903$	−7.49218	+	6.90710i	−0.249324	+	0.229854i
$904$	28.8173	−	16.5739i	0.958448	−	0.551240i
$905$	−12.2992	−	14.6576i	−0.408838	−	0.487234i
$906$	3.98549	+	24.3162i	0.132409	+	0.807853i
$907$	−12.6972	−	34.8852i	−0.421603	−	1.15834i	−0.950789	−	0.309839i	$-0.899725\pi$
$907$	−12.6972	−	34.8852i	−0.421603	−	1.15834i	0.529186	−	0.848506i	$-0.322497\pi$
$908$	−17.9773	−	41.8032i	−0.596597	−	1.38729i
$909$	5.66941	−	8.20185i	0.188042	−	0.272038i
$910$	−22.4605	−	14.7903i	−0.744559	−	0.490295i
$911$	−7.32014	+	41.5146i	−0.242527	+	1.37544i	0.583640	+	0.812013i	$0.301628\pi$
$911$	−7.32014	+	41.5146i	−0.242527	+	1.37544i	−0.826167	+	0.563426i	$0.809483\pi$
$912$	−8.12982	−	50.1229i	−0.269205	−	1.65974i
$913$	−1.99806	−	0.727234i	−0.0661261	−	0.0240679i
$914$	15.3561	−	1.78626i	0.507935	−	0.0590841i
$915$	−0.846976	−	18.1403i	−0.0280002	−	0.599701i
$916$	−20.0411	−	21.2895i	−0.662176	−	0.703424i
$917$			17.6013i			0.581246i
$918$	−3.38403	+	36.1670i	−0.111690	+	1.19369i
$919$			23.7830i			0.784528i	0.919853	+	0.392264i	$0.128308\pi$
$919$			23.7830i			0.784528i	−0.919853	+	0.392264i	$0.871692\pi$
$920$	38.5524	+	46.1002i	1.27103	+	1.51988i
$921$	49.9116	+	25.7908i	1.64464	+	0.849837i
$922$	5.95786	+	51.2186i	0.196212	+	1.68680i
$923$	−16.2983	−	5.93209i	−0.536465	−	0.195257i
$924$	0.773202	−	0.799084i	0.0254365	−	0.0262879i
$925$	2.25455	−	12.7862i	0.0741290	−	0.420406i
$926$	−6.30057	+	9.56801i	−0.207050	+	0.314424i
$927$	−21.9084	−	21.6451i	−0.719567	−	0.710918i
$928$	9.09321	+	38.8461i	0.298499	+	1.27519i
$929$	−16.7361	−	45.9820i	−0.549093	−	1.50862i	−0.834937	−	0.550346i	$-0.814496\pi$
$929$	−16.7361	−	45.9820i	−0.549093	−	1.50862i	0.285844	−	0.958276i	$-0.407726\pi$
$930$	−0.469538	+	1.24313i	−0.0153968	+	0.0407639i
$931$	−4.71110	−	5.61447i	−0.154400	−	0.184007i
$932$	−14.6776	−	22.3701i	−0.480780	−	0.732756i
$933$	26.4509	+	8.25211i	0.865964	+	0.270162i
$934$	−2.61462	−	8.75106i	−0.0855529	−	0.286343i
$935$	2.46582	+	4.27093i	0.0806409	+	0.139674i
$936$	−21.7336	+	47.1465i	−0.710384	+	1.54103i
$937$	−1.05333	+	1.82441i	−0.0344106	+	0.0596010i	−0.882718	−	0.469903i	$-0.844289\pi$
$937$	−1.05333	+	1.82441i	−0.0344106	+	0.0596010i	0.848307	+	0.529504i	$0.177622\pi$
$938$	−20.4420	−	4.85679i	−0.667455	−	0.158580i
$939$	−39.7709	−	30.3267i	−1.29787	−	0.989674i
$940$	15.3690	−	30.5179i	0.501282	−	0.995384i
$941$	−18.4296	+	3.24964i	−0.600789	+	0.105935i	−0.465767	−	0.884907i	$-0.654222\pi$
$941$	−18.4296	+	3.24964i	−0.600789	+	0.105935i	−0.135022	+	0.990843i	$0.543110\pi$
$942$	1.93528	+	1.14871i	0.0630547	+	0.0374270i
$943$	−18.6022	+	22.1692i	−0.605770	+	0.721928i
$944$	19.2777	+	4.61401i	0.627437	+	0.150173i
$945$	−6.04487	+	14.9764i	−0.196640	+	0.487181i
$946$	2.66608	+	0.156763i	0.0866819	+	0.00509679i
$947$	11.3710	+	9.54144i	0.369509	+	0.310055i	0.808567	−	0.588403i	$-0.200243\pi$
$947$	11.3710	+	9.54144i	0.369509	+	0.310055i	−0.439058	+	0.898459i	$0.644688\pi$
$948$	3.32392	−	46.8655i	0.107956	−	1.52212i
$949$	−4.75437	−	26.9633i	−0.154333	−	0.875267i
$950$	44.3443	+	19.1574i	1.43872	+	0.621547i
$951$	−6.08655	−	14.5695i	−0.197370	−	0.472448i
$952$	13.1303	+	4.80376i	0.425557	+	0.155691i
$953$	35.0929	+	20.2609i	1.13677	+	0.656314i	0.945629	−	0.325248i	$-0.105448\pi$
$953$	35.0929	+	20.2609i	1.13677	+	0.656314i	0.191141	+	0.981563i	$0.438781\pi$
$954$	−6.37132	+	2.57177i	−0.206279	+	0.0832642i
$955$	−15.4153	+	8.90005i	−0.498828	+	0.287999i
$956$	−38.4658	+	9.07159i	−1.24407	+	0.293396i
$957$	3.82552	−	0.860238i	0.123661	−	0.0278075i
$958$	0.439657	+	0.591245i	0.0142047	+	0.0191023i
$959$	4.35602	−	3.65513i	0.140663	−	0.118030i
$960$	16.4693	+	39.7940i	0.531545	+	1.28435i
$961$	−29.1018	+	10.5922i	−0.938769	+	0.341684i
$962$	−21.5467	+	10.8062i	−0.694694	+	0.348407i
$963$	−11.1625	+	24.3209i	−0.359706	+	0.783729i
$964$	−24.0044	+	32.1691i	−0.773130	+	1.03610i
$965$	−57.5168	−	10.1418i	−1.85153	−	0.326475i
$966$	3.10658	−	16.4540i	0.0999527	−	0.529398i
$967$	−12.1724	+	33.4433i	−0.391437	+	1.07546i	0.574908	+	0.818218i	$0.305038\pi$
$967$	−12.1724	+	33.4433i	−0.391437	+	1.07546i	−0.966346	+	0.257247i	$0.917185\pi$
$968$	30.8212	+	0.0511824i	0.990632	+	0.00164506i
$969$	−33.8761	−	52.8218i	−1.08826	−	1.69688i
$970$	10.0505	+	9.49267i	0.322702	+	0.304791i
$971$	−28.4639			−0.913449			−0.456724	−	0.889608i	$-0.650977\pi$
$971$	−28.4639			−0.913449			−0.456724	+	0.889608i	$0.650977\pi$
$972$	30.3327	+	7.20615i	0.972921	+	0.231137i
$973$	−9.40184			−0.301409
$974$	21.3051	+	20.1226i	0.682658	+	0.644769i
$975$	−26.6614	−	41.5721i	−0.853848	−	1.33137i
$976$	−0.814392	+	13.4687i	−0.0260680	+	0.431124i
$977$	−9.92190	+	27.2602i	−0.317430	+	0.872131i	0.673673	+	0.739030i	$0.264716\pi$
$977$	−9.92190	+	27.2602i	−0.317430	+	0.872131i	−0.991102	+	0.133101i	$0.957507\pi$
$978$	0.869518	−	4.60539i	0.0278041	−	0.147264i
$979$	0.0226034	+	0.00398558i	0.000722407	+	0.000127380i
$980$	4.98209	+	3.71760i	0.159147	+	0.118755i
$981$	−7.08289	+	15.4322i	−0.226139	+	0.492713i
$982$	−13.4795	+	6.76031i	−0.430147	+	0.215730i
$983$	−9.33866	+	3.39899i	−0.297857	+	0.108411i	−0.486626	−	0.873610i	$-0.661772\pi$
$983$	−9.33866	+	3.39899i	−0.297857	+	0.108411i	0.188769	+	0.982022i	$0.439550\pi$
$984$	−17.4764	+	11.1672i	−0.557127	+	0.355997i
$985$	−47.7584	+	40.0740i	−1.52171	+	1.27687i
$986$	29.4202	+	39.5639i	0.936931	+	1.25997i
$987$	−9.28877	+	2.08875i	−0.295665	+	0.0664857i
$988$	−20.5856	−	87.2882i	−0.654917	−	2.77701i
$989$	34.8302	−	20.1092i	1.10753	−	0.639435i
$990$	3.92502	−	1.58433i	0.124745	−	0.0503533i
$991$	20.0759	+	11.5908i	0.637732	+	0.368195i	0.783740	−	0.621089i	$-0.213309\pi$
$991$	20.0759	+	11.5908i	0.637732	+	0.368195i	−0.146008	+	0.989283i	$0.546643\pi$
$992$	0.445568	−	0.881111i	0.0141468	−	0.0279753i
$993$	17.5688	+	42.0548i	0.557530	+	1.33457i
$994$	3.68034	+	1.58996i	0.116733	+	0.0504305i
$995$	12.8799	+	73.0454i	0.408319	+	2.31569i
$996$	−22.8896	−	1.62344i	−0.725285	−	0.0514406i
$997$	11.8782	+	9.96698i	0.376186	+	0.315657i	0.811203	−	0.584765i	$-0.198813\pi$
$997$	11.8782	+	9.96698i	0.376186	+	0.315657i	−0.435017	+	0.900422i	$0.643258\pi$
$998$	52.7700	+	3.10281i	1.67040	+	0.0982178i
$999$	8.91612	+	11.4041i	0.282094	+	0.360808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.82	yes	648
4.3	odd	2	inner	756.2.cf.a.659.75	yes	648
27.5	odd	18	inner	756.2.cf.a.491.75	✓	648
108.59	even	18	inner	756.2.cf.a.491.82	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.75	✓	648	27.5	odd	18	inner
756.2.cf.a.491.82	yes	648	108.59	even	18	inner
756.2.cf.a.659.75	yes	648	4.3	odd	2	inner
756.2.cf.a.659.82	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+(0.971061 - 1.02812i) q^{2} +(-0.935042 - 1.45798i) q^{3} +(-0.114079 - 1.99674i) q^{4} +(-1.06304 + 2.92068i) q^{5} +(-2.40696 - 0.454446i) q^{6} +(0.984808 + 0.173648i) q^{7} +(-2.16368 - 1.82167i) q^{8} +(-1.25139 + 2.72654i) q^{9} +(1.97055 + 3.92910i) q^{10} +(-0.301627 + 0.109783i) q^{11} +(-2.80454 + 2.03336i) q^{12} +(-4.68682 + 3.93271i) q^{13} +(1.13484 - 0.843882i) q^{14} +(5.25228 - 1.18107i) q^{15} +(-3.97397 + 0.455574i) q^{16} +(-4.28094 + 2.47160i) q^{17} +(1.58804 + 3.93422i) q^{18} +(-6.34724 - 3.66458i) q^{19} +(5.95312 + 1.78943i) q^{20} +(-0.667662 - 1.59820i) q^{21} +(-0.180028 + 0.416717i) q^{22} +(1.18706 + 6.73213i) q^{23} +(-0.632827 + 4.85793i) q^{24} +(-3.57010 - 2.99567i) q^{25} +(-0.507877 + 8.63754i) q^{26} +(5.14534 - 0.724928i) q^{27} +(0.234385 - 1.98622i) q^{28} +(4.53340 - 5.40269i) q^{29} +(3.88599 - 6.54688i) q^{30} +(-0.171891 + 0.0303091i) q^{31} +(-3.39058 + 4.52813i) q^{32} +(0.442096 + 0.337113i) q^{33} +(-1.61594 + 6.80141i) q^{34} +(-1.55406 + 2.69172i) q^{35} +(5.58696 + 2.18767i) q^{36} +(1.39294 + 2.41264i) q^{37} +(-9.93121 + 2.96722i) q^{38} +(10.1162 + 3.15603i) q^{39} +(7.62061 - 4.38290i) q^{40} +(2.72121 + 3.24301i) q^{41} +(-2.29148 - 0.865507i) q^{42} +(-2.01222 - 5.52853i) q^{43} +(0.253619 + 0.589748i) q^{44} +(-6.63307 - 6.55334i) q^{45} +(8.07417 + 5.31687i) q^{46} +(0.954507 - 5.41328i) q^{47} +(4.38005 + 5.36798i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-6.54672 + 0.761528i) q^{50} +(7.60639 + 3.93046i) q^{51} +(8.38729 + 8.90974i) q^{52} +1.61946i q^{53} +(4.25112 - 5.99399i) q^{54} -0.997662i q^{55} +(-1.81448 - 2.16972i) q^{56} +(0.592063 + 12.6807i) q^{57} +(-1.15243 - 9.90724i) q^{58} +(-4.65670 - 1.69490i) q^{59} +(-2.95747 - 10.3527i) q^{60} +(0.585773 - 3.32209i) q^{61} +(-0.135755 + 0.206157i) q^{62} +(-1.70584 + 2.46781i) q^{63} +(1.36301 + 7.88303i) q^{64} +(-6.50391 - 17.8694i) q^{65} +(0.775897 - 0.127171i) q^{66} +(-9.54992 - 11.3812i) q^{67} +(5.42352 + 8.26597i) q^{68} +(8.70535 - 8.02553i) q^{69} +(1.25833 + 4.21159i) q^{70} +(1.41743 + 2.45506i) q^{71} +(7.67448 - 3.61973i) q^{72} +(-2.23752 + 3.87551i) q^{73} +(3.83312 + 0.910708i) q^{74} +(-1.02942 + 8.00621i) q^{75} +(-6.59314 + 13.0919i) q^{76} +(-0.316109 + 0.0557385i) q^{77} +(13.0682 - 7.33599i) q^{78} +(-8.71806 + 10.3898i) q^{79} +(2.89391 - 12.0910i) q^{80} +(-5.86803 - 6.82394i) q^{81} +(5.97668 + 0.351422i) q^{82} +(5.07448 + 4.25799i) q^{83} +(-3.11502 + 1.51547i) q^{84} +(-2.66794 - 15.1307i) q^{85} +(-7.63800 - 3.29973i) q^{86} +(-12.1159 - 1.55784i) q^{87} +(0.852614 + 0.311930i) q^{88} +(-0.0619252 - 0.0357525i) q^{89} +(-13.1788 + 0.455923i) q^{90} +(-5.29853 + 3.05911i) q^{91} +(13.3069 - 3.13824i) q^{92} +(0.204915 + 0.222273i) q^{93} +(-4.63864 - 6.23798i) q^{94} +(17.4505 - 14.6427i) q^{95} +(9.77224 + 0.709404i) q^{96} +(2.95549 - 1.07571i) q^{97} +(1.26414 - 0.633998i) q^{98} +(0.0781255 - 0.959781i) 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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