LMFDB - Embedded newform 756.2.cf.a.659.23

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			659.23
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15796 + 0.811871i) q^{2} +(-1.71844 - 0.216716i) q^{3} +(0.681730 - 1.88022i) q^{4} +(0.0372347 - 0.102301i) q^{5} +(2.16582 - 1.14420i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(0.737087 + 2.73070i) q^{8} +(2.90607 + 0.744826i) q^{9} +(0.0399395 + 0.148691i) q^{10} +(1.44739 - 0.526808i) q^{11} +(-1.57899 + 3.08331i) q^{12} +(-3.59352 + 3.01532i) q^{13} +(1.28135 - 0.598460i) q^{14} +(-0.0861559 + 0.167730i) q^{15} +(-3.07049 - 2.56361i) q^{16} +(1.89301 - 1.09293i) q^{17} +(-3.96981 + 1.49688i) q^{18} +(-5.71979 - 3.30232i) q^{19} +(-0.166966 - 0.139752i) q^{20} +(1.65470 + 0.511827i) q^{21} +(-1.24832 + 1.78512i) q^{22} +(0.158950 + 0.901452i) q^{23} +(-0.674855 - 4.85227i) q^{24} +(3.82114 + 3.20632i) q^{25} +(1.71309 - 6.40909i) q^{26} +(-4.83249 - 1.90973i) q^{27} +(-0.997870 + 1.73328i) q^{28} +(5.10650 - 6.08569i) q^{29} +(-0.0364100 - 0.264171i) q^{30} +(1.99748 - 0.352209i) q^{31} +(5.63682 + 0.475707i) q^{32} +(-2.60142 + 0.591614i) q^{33} +(-1.30471 + 2.80245i) q^{34} +(-0.0544335 + 0.0942816i) q^{35} +(3.38159 - 4.95629i) q^{36} +(2.92633 + 5.06854i) q^{37} +(9.30434 - 0.819787i) q^{38} +(6.82871 - 4.40287i) q^{39} +(0.306799 + 0.0262715i) q^{40} +(6.36935 + 7.59070i) q^{41} +(-2.33161 + 0.750730i) q^{42} +(-0.354332 - 0.973518i) q^{43} +(-0.00378674 - 3.08056i) q^{44} +(0.184403 - 0.269562i) q^{45} +(-0.915921 - 0.914795i) q^{46} +(0.676829 - 3.83849i) q^{47} +(4.72088 + 5.07083i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-7.02784 - 0.610504i) q^{50} +(-3.48988 + 1.46789i) q^{51} +(3.21967 + 8.81225i) q^{52} -5.33962i q^{53} +(7.14627 - 1.71197i) q^{54} -0.167686i q^{55} +(-0.251709 - 2.81720i) q^{56} +(9.11345 + 6.91441i) q^{57} +(-0.972310 + 11.1928i) q^{58} +(13.1469 + 4.78506i) q^{59} +(0.256634 + 0.276339i) q^{60} +(1.31772 - 7.47315i) q^{61} +(-2.02704 + 2.02954i) q^{62} +(-2.73258 - 1.23814i) q^{63} +(-6.91341 + 4.02552i) q^{64} +(0.174668 + 0.479897i) q^{65} +(2.53202 - 2.79708i) q^{66} +(4.10480 + 4.89191i) q^{67} +(-0.764434 - 4.30437i) q^{68} +(-0.0777876 - 1.58354i) q^{69} +(-0.0135129 - 0.153367i) q^{70} +(4.10149 + 7.10399i) q^{71} +(0.108133 + 8.48459i) q^{72} +(-2.00789 + 3.47777i) q^{73} +(-7.50357 - 3.49336i) q^{74} +(-5.87154 - 6.33797i) q^{75} +(-10.1085 + 8.50320i) q^{76} +(-1.51688 + 0.267467i) q^{77} +(-4.33279 + 10.6424i) q^{78} +(8.81797 - 10.5088i) q^{79} +(-0.376590 + 0.218660i) q^{80} +(7.89047 + 4.32903i) q^{81} +(-13.5381 - 3.61861i) q^{82} +(9.78967 + 8.21451i) q^{83} +(2.09041 - 2.76228i) q^{84} +(-0.0413228 - 0.234353i) q^{85} +(1.20067 + 0.839620i) q^{86} +(-10.0941 + 9.35122i) q^{87} +(2.50541 + 3.56408i) q^{88} +(-2.13011 - 1.22982i) q^{89} +(0.00531831 + 0.461853i) q^{90} +(4.06253 - 2.34550i) q^{91} +(1.80329 + 0.315684i) q^{92} +(-3.50887 + 0.172365i) q^{93} +(2.33262 + 4.99430i) q^{94} +(-0.550807 + 0.462182i) q^{95} +(-9.58344 - 2.03906i) q^{96} +(13.3215 - 4.84861i) q^{97} +(-1.36580 + 0.366865i) q^{98} +(4.59860 - 0.452884i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$	−1.15796	+	0.811871i	−0.818799	+	0.574080i
$2$	−1.15796	+	0.811871i	−0.818799	+	0.574080i
$3$	−1.71844	−	0.216716i	−0.992142	−	0.125121i
$3$	−1.71844	−	0.216716i	−0.992142	−	0.125121i
$4$	0.681730	−	1.88022i	0.340865	−	0.940112i
$5$	0.0372347	−	0.102301i	0.0166519	−	0.0457506i	−0.931088	−	0.364794i	$-0.881139\pi$
$5$	0.0372347	−	0.102301i	0.0166519	−	0.0457506i	0.947740	+	0.319043i	$0.103362\pi$
$6$	2.16582	−	1.14420i	0.884194	−	0.467119i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$7$	−0.984808	−	0.173648i	−0.372222	−	0.0656328i
$8$	0.737087	+	2.73070i	0.260600	+	0.965447i
$9$	2.90607	+	0.744826i	0.968690	+	0.248275i
$10$	0.0399395	+	0.148691i	0.0126300	+	0.0470201i
$11$	1.44739	−	0.526808i	0.436405	−	0.158838i	−0.114469	−	0.993427i	$-0.536517\pi$
$11$	1.44739	−	0.526808i	0.436405	−	0.158838i	0.550874	+	0.834588i	$0.314294\pi$
$12$	−1.57899	+	3.08331i	−0.455814	+	0.890075i
$13$	−3.59352	+	3.01532i	−0.996663	+	0.836299i	−0.986519	−	0.163649i	$-0.947673\pi$
$13$	−3.59352	+	3.01532i	−0.996663	+	0.836299i	−0.0101440	+	0.999949i	$0.503229\pi$
$14$	1.28135	−	0.598460i	0.342454	−	0.159945i
$15$	−0.0861559	+	0.167730i	−0.0222454	+	0.0433076i
$16$	−3.07049	−	2.56361i	−0.767622	−	0.640902i
$17$	1.89301	−	1.09293i	0.459123	−	0.265075i	−0.252552	−	0.967583i	$-0.581270\pi$
$17$	1.89301	−	1.09293i	0.459123	−	0.265075i	0.711675	+	0.702508i	$0.247937\pi$
$18$	−3.96981	+	1.49688i	−0.935692	+	0.352817i
$19$	−5.71979	−	3.30232i	−1.31221	−	0.757605i	−0.329749	−	0.944069i	$-0.606964\pi$
$19$	−5.71979	−	3.30232i	−1.31221	−	0.757605i	−0.982462	+	0.186464i	$0.940297\pi$
$20$	−0.166966	−	0.139752i	−0.0373347	−	0.0312494i
$21$	1.65470	+	0.511827i	0.361085	+	0.111690i
$22$	−1.24832	+	1.78512i	−0.266142	+	0.380588i
$23$	0.158950	+	0.901452i	0.0331434	+	0.187966i	0.996885	−	0.0788728i	$-0.0251321\pi$
$23$	0.158950	+	0.901452i	0.0331434	+	0.187966i	−0.963741	+	0.266838i	$0.914021\pi$
$24$	−0.674855	−	4.85227i	−0.137754	−	0.990466i
$25$	3.82114	+	3.20632i	0.764229	+	0.641264i
$26$	1.71309	−	6.40909i	0.335964	−	1.25693i
$27$	−4.83249	−	1.90973i	−0.930013	−	0.367527i
$28$	−0.997870	+	1.73328i	−0.188580	+	0.327559i
$29$	5.10650	−	6.08569i	0.948253	−	1.13008i	−0.0431280	−	0.999070i	$-0.513732\pi$
$29$	5.10650	−	6.08569i	0.948253	−	1.13008i	0.991381	−	0.131014i	$-0.0418232\pi$
$30$	−0.0364100	−	0.264171i	−0.00664752	−	0.0482308i
$31$	1.99748	−	0.352209i	0.358757	−	0.0632586i	0.00863527	−	0.999963i	$-0.497251\pi$
$31$	1.99748	−	0.352209i	0.358757	−	0.0632586i	0.350122	+	0.936704i	$0.386140\pi$
$32$	5.63682	+	0.475707i	0.996458	+	0.0840939i
$33$	−2.60142	+	0.591614i	−0.452850	+	0.102987i
$34$	−1.30471	+	2.80245i	−0.223756	+	0.480616i
$35$	−0.0544335	+	0.0942816i	−0.00920094	+	0.0159365i
$36$	3.38159	−	4.95629i	0.563599	−	0.826049i
$37$	2.92633	+	5.06854i	0.481085	+	0.833264i	0.999764	−	0.0217052i	$-0.00690952\pi$
$37$	2.92633	+	5.06854i	0.481085	+	0.833264i	−0.518679	+	0.854969i	$0.673576\pi$
$38$	9.30434	−	0.819787i	1.50936	−	0.132987i
$39$	6.82871	−	4.40287i	1.09347	−	0.705024i
$40$	0.306799	+	0.0262715i	0.0485093	+	0.00415390i
$41$	6.36935	+	7.59070i	0.994726	+	1.18547i	0.982636	+	0.185541i	$0.0594039\pi$
$41$	6.36935	+	7.59070i	0.994726	+	1.18547i	0.0120896	+	0.999927i	$0.496152\pi$
$42$	−2.33161	+	0.750730i	−0.359775	+	0.115840i
$43$	−0.354332	−	0.973518i	−0.0540351	−	0.148460i	0.909739	−	0.415181i	$-0.136282\pi$
$43$	−0.354332	−	0.973518i	−0.0540351	−	0.148460i	−0.963774	+	0.266721i	$0.914060\pi$
$44$	−0.00378674	−	3.08056i	−0.000570873	−	0.464412i
$45$	0.184403	−	0.269562i	0.0274892	−	0.0401839i
$46$	−0.915921	−	0.914795i	−0.135045	−	0.134879i
$47$	0.676829	−	3.83849i	0.0987256	−	0.559901i	−0.894816	−	0.446435i	$-0.852694\pi$
$47$	0.676829	−	3.83849i	0.0987256	−	0.559901i	0.993542	−	0.113466i	$-0.0361953\pi$
$48$	4.72088	+	5.07083i	0.681400	+	0.731911i
$49$	0.939693	+	0.342020i	0.134242	+	0.0488600i
$50$	−7.02784	−	0.610504i	−0.993887	−	0.0863383i
$51$	−3.48988	+	1.46789i	−0.488681	+	0.205546i
$52$	3.21967	+	8.81225i	0.446488	+	1.22204i
$53$		−	5.33962i		−	0.733453i	−0.930329	−	0.366726i	$-0.880479\pi$
$53$		−	5.33962i		−	0.733453i	0.930329	−	0.366726i	$-0.119521\pi$
$54$	7.14627	−	1.71197i	0.972484	−	0.232970i
$55$		−	0.167686i		−	0.0226108i
$56$	−0.251709	−	2.81720i	−0.0336360	−	0.376465i
$57$	9.11345	+	6.91441i	1.20711	+	0.915836i
$58$	−0.972310	+	11.1928i	−0.127671	+	1.46968i
$59$	13.1469	+	4.78506i	1.71157	+	0.622962i	0.997058	−	0.0766560i	$-0.0244243\pi$
$59$	13.1469	+	4.78506i	1.71157	+	0.622962i	0.714517	+	0.699618i	$0.246647\pi$
$60$	0.256634	+	0.276339i	0.0331313	+	0.0356752i
$61$	1.31772	−	7.47315i	0.168717	−	0.956839i	−0.776433	−	0.630200i	$-0.782973\pi$
$61$	1.31772	−	7.47315i	0.168717	−	0.956839i	0.945149	−	0.326639i	$-0.105916\pi$
$62$	−2.02704	+	2.02954i	−0.257435	+	0.257751i
$63$	−2.73258	−	1.23814i	−0.344273	−	0.155991i
$64$	−6.91341	+	4.02552i	−0.864176	+	0.503190i
$65$	0.174668	+	0.479897i	0.0216649	+	0.0595239i
$66$	2.53202	−	2.79708i	0.311670	−	0.344297i
$67$	4.10480	+	4.89191i	0.501481	+	0.597642i	0.956099	−	0.293045i	$-0.0946685\pi$
$67$	4.10480	+	4.89191i	0.501481	+	0.597642i	−0.454618	+	0.890687i	$0.650224\pi$
$68$	−0.764434	−	4.30437i	−0.0927012	−	0.521982i
$69$	−0.0777876	−	1.58354i	−0.00936453	−	0.190636i
$70$	−0.0135129	−	0.153367i	−0.00161510	−	0.0183309i
$71$	4.10149	+	7.10399i	0.486757	+	0.843088i	0.999884	−	0.0152246i	$-0.00484633\pi$
$71$	4.10149	+	7.10399i	0.486757	+	0.843088i	−0.513127	+	0.858313i	$0.671513\pi$
$72$	0.108133	+	8.48459i	0.0127436	+	0.999919i
$73$	−2.00789	+	3.47777i	−0.235006	+	0.407042i	−0.959274	−	0.282476i	$-0.908844\pi$
$73$	−2.00789	+	3.47777i	−0.235006	+	0.407042i	0.724269	+	0.689518i	$0.242178\pi$
$74$	−7.50357	−	3.49336i	−0.872272	−	0.406095i
$75$	−5.87154	−	6.33797i	−0.677987	−	0.731846i
$76$	−10.1085	+	8.50320i	−1.15952	+	0.975384i
$77$	−1.51688	+	0.267467i	−0.172865	+	0.0304807i
$78$	−4.33279	+	10.6424i	−0.490592	+	1.20501i
$79$	8.81797	−	10.5088i	0.992099	−	1.18234i	0.00887060	−	0.999961i	$-0.497176\pi$
$79$	8.81797	−	10.5088i	0.992099	−	1.18234i	0.983229	−	0.182377i	$-0.0583792\pi$
$80$	−0.376590	+	0.218660i	−0.0421040	+	0.0244470i
$81$	7.89047	+	4.32903i	0.876719	+	0.481003i
$82$	−13.5381	−	3.61861i	−1.49503	−	0.399609i
$83$	9.78967	+	8.21451i	1.07456	+	0.901659i	0.995457	−	0.0952074i	$-0.0303514\pi$
$83$	9.78967	+	8.21451i	1.07456	+	0.901659i	0.0790984	+	0.996867i	$0.474796\pi$
$84$	2.09041	−	2.76228i	0.228082	−	0.301390i
$85$	−0.0413228	−	0.234353i	−0.00448208	−	0.0254191i
$86$	1.20067	+	0.839620i	0.129472	+	0.0905386i
$87$	−10.0941	+	9.35122i	−1.08220	+	1.00256i
$88$	2.50541	+	3.56408i	0.267077	+	0.379933i
$89$	−2.13011	−	1.22982i	−0.225791	−	0.130361i	0.382838	−	0.923816i	$-0.374947\pi$
$89$	−2.13011	−	1.22982i	−0.225791	−	0.130361i	−0.608629	+	0.793455i	$0.708280\pi$
$90$	0.00531831	+	0.461853i	0.000560600	+	0.0486836i
$91$	4.06253	−	2.34550i	0.425869	−	0.245875i
$92$	1.80329	+	0.315684i	0.188006	+	0.0329123i
$93$	−3.50887	+	0.172365i	−0.363853	+	0.0178734i
$94$	2.33262	+	4.99430i	0.240591	+	0.515123i
$95$	−0.550807	+	0.462182i	−0.0565116	+	0.0474189i
$96$	−9.58344	−	2.03906i	−0.978105	−	0.208111i
$97$	13.3215	−	4.84861i	1.35259	−	0.492302i	0.438834	−	0.898568i	$-0.355391\pi$
$97$	13.3215	−	4.84861i	1.35259	−	0.492302i	0.913755	+	0.406266i	$0.133169\pi$
$98$	−1.36580	+	0.366865i	−0.137967	+	0.0370590i
$99$	4.59860	−	0.452884i	0.462177	−	0.0455166i
$100$	8.63359	−	4.99876i	0.863359	−	0.499876i
$101$	1.35706	+	0.239286i	0.135032	+	0.0238098i	0.240756	−	0.970586i	$-0.422605\pi$
$101$	1.35706	+	0.239286i	0.135032	+	0.0238098i	−0.105724	+	0.994396i	$0.533716\pi$
$102$	2.84940	−	4.53309i	0.282132	−	0.448843i
$103$	−1.61952	+	4.44959i	−0.159576	+	0.438431i	−0.993553	−	0.113368i	$-0.963836\pi$
$103$	−1.61952	+	4.44959i	−0.159576	+	0.438431i	0.833977	+	0.551799i	$0.186058\pi$
$104$	−10.8827	−	7.59025i	−1.06713	−	0.744286i
$105$	0.113973	−	0.150221i	0.0111226	−	0.0146600i
$106$	4.33508	+	6.18305i	0.421060	+	0.600551i
$107$	5.60395			0.541755			0.270877	−	0.962614i	$-0.412686\pi$
$107$	5.60395			0.541755			0.270877	+	0.962614i	$0.412686\pi$
$108$	−6.88517	+	7.78424i	−0.662526	+	0.749039i
$109$	2.24633			0.215159			0.107580	−	0.994196i	$-0.465690\pi$
$109$	2.24633			0.215159			0.107580	+	0.994196i	$0.465690\pi$
$110$	0.136139	+	0.194173i	0.0129804	+	0.0185137i
$111$	−3.93028	−	9.34417i	−0.373046	−	0.886909i
$112$	2.57868	+	3.05785i	0.243662	+	0.288939i
$113$	3.95728	−	10.8725i	0.372269	−	1.02280i	−0.602213	−	0.798336i	$-0.705714\pi$
$113$	3.95728	−	10.8725i	0.372269	−	1.02280i	0.974482	−	0.224466i	$-0.0720637\pi$
$114$	−16.1666	−	0.607642i	−1.51414	−	0.0569109i
$115$	0.0981383	+	0.0173044i	0.00915145	+	0.00161365i
$116$	−7.96121	−	13.7502i	−0.739179	−	1.27667i
$117$	−12.6889	+	6.08618i	−1.17309	+	0.562668i
$118$	−19.1083	+	5.13266i	−1.75907	+	0.472499i
$119$	−2.05404	+	0.747609i	−0.188293	+	0.0685332i
$120$	−0.521523	−	0.111634i	−0.0476083	−	0.0101908i
$121$	−6.60907	+	5.54567i	−0.600825	+	0.504152i
$122$	4.54138	+	9.72341i	0.411157	+	0.880316i
$123$	−9.30033	−	14.4245i	−0.838582	−	1.30061i
$124$	0.699506	−	3.99581i	0.0628175	−	0.358835i
$125$	0.941698	−	0.543690i	0.0842280	−	0.0486291i
$126$	4.16943	−	0.784787i	0.371442	−	0.0699144i
$127$	12.3893	+	7.15298i	1.09938	+	0.634725i	0.936057	−	0.351849i	$-0.114447\pi$
$127$	12.3893	+	7.15298i	1.09938	+	0.634725i	0.163319	+	0.986573i	$0.447780\pi$
$128$	4.73722	−	10.2742i	0.418715	−	0.908118i
$129$	0.397921	+	1.74972i	0.0350350	+	0.154054i
$130$	−0.591873	−	0.413892i	−0.0519107	−	0.0363007i
$131$	−1.25104	−	7.09497i	−0.109303	−	0.619891i	−0.989414	−	0.145122i	$-0.953643\pi$
$131$	−1.25104	−	7.09497i	−0.109303	−	0.619891i	0.880110	−	0.474769i	$-0.157468\pi$
$132$	−0.661099	+	5.29458i	−0.0575413	+	0.460834i
$133$	5.05945	+	4.24539i	0.438710	+	0.368122i
$134$	−8.72478	−	2.33205i	−0.753706	−	0.201459i
$135$	−0.375304	+	0.423262i	−0.0323010	+	0.0364286i
$136$	4.37978	+	4.36366i	0.375563	+	0.374181i
$137$	−4.96639	+	5.91871i	−0.424307	+	0.505669i	−0.935271	−	0.353933i	$-0.884844\pi$
$137$	−4.96639	+	5.91871i	−0.424307	+	0.505669i	0.510964	+	0.859602i	$0.329289\pi$
$138$	1.37570	+	1.77051i	0.117108	+	0.150716i
$139$	−8.91865	+	1.57260i	−0.756470	+	0.133386i	−0.538565	−	0.842584i	$-0.681033\pi$
$139$	−8.91865	+	1.57260i	−0.756470	+	0.133386i	−0.217905	+	0.975970i	$0.569922\pi$
$140$	0.140162	+	0.166622i	0.0118458	+	0.0140821i
$141$	−1.99495	+	6.44953i	−0.168005	+	0.543148i
$142$	−10.5169	−	4.89623i	−0.882556	−	0.410883i
$143$	−3.61274	+	6.25744i	−0.302112	+	0.523273i
$144$	−7.01361	−	9.73700i	−0.584468	−	0.811417i
$145$	−0.432436	−	0.749001i	−0.0359118	−	0.0622011i
$146$	−0.498450	−	5.65726i	−0.0412520	−	0.468198i
$147$	−1.54068	−	0.791387i	−0.127073	−	0.0652725i
$148$	11.5250	−	2.04677i	0.947346	−	0.168244i
$149$	−5.74436	−	6.84586i	−0.470596	−	0.560835i	0.477576	−	0.878590i	$-0.341515\pi$
$149$	−5.74436	−	6.84586i	−0.470596	−	0.560835i	−0.948173	+	0.317755i	$0.897071\pi$
$150$	11.9446	+	2.57216i	0.975273	+	0.210016i
$151$	−5.85864	−	16.0965i	−0.476769	−	1.30991i	−0.912220	−	0.409701i	$-0.865633\pi$
$151$	−5.85864	−	16.0965i	−0.476769	−	1.30991i	0.435451	−	0.900213i	$-0.356589\pi$
$152$	4.80166	−	18.0531i	0.389466	−	1.46430i
$153$	6.31527	−	1.76617i	0.510559	−	0.142786i
$154$	1.53934	−	1.54123i	0.124043	−	0.124196i
$155$	0.0383439	−	0.217459i	0.00307986	−	0.0174667i
$156$	−3.62306	−	15.8411i	−0.290077	−	1.26830i
$157$	−15.9097	−	5.79064i	−1.26973	−	0.462143i	−0.382706	−	0.923870i	$-0.625008\pi$
$157$	−15.9097	−	5.79064i	−1.26973	−	0.462143i	−0.887022	+	0.461727i	$0.847230\pi$
$158$	−1.67900	+	19.3279i	−0.133574	+	1.53764i
$159$	−1.15718	+	9.17581i	−0.0917703	+	0.727689i
$160$	0.258551	−	0.558942i	0.0204402	−	0.0441882i
$161$		−	0.915358i		−	0.0721403i
$162$	−12.6514	+	1.39322i	−0.993991	+	0.109461i
$163$			7.08873i			0.555232i	0.960692	+	0.277616i	$0.0895443\pi$
$163$			7.08873i			0.555232i	−0.960692	+	0.277616i	$0.910456\pi$
$164$	18.6144	−	6.80101i	1.45354	−	0.531070i
$165$	−0.0363402	+	0.288158i	−0.00282908	+	0.0224331i
$166$	−18.0051	−	1.56410i	−1.39747	−	0.121397i
$167$	7.99833	+	2.91115i	0.618929	+	0.225272i	0.632406	−	0.774637i	$-0.282068\pi$
$167$	7.99833	+	2.91115i	0.618929	+	0.225272i	−0.0134764	+	0.999909i	$0.504290\pi$
$168$	−0.177987	+	4.89575i	−0.0137320	+	0.377715i
$169$	1.56379	−	8.86871i	0.120292	−	0.682208i
$170$	0.238114	+	0.237822i	0.0182625	+	0.0182401i
$171$	−14.1625	−	13.8570i	−1.08303	−	1.05967i
$172$	−2.07199	+	0.00254697i	−0.157988	+	0.000194204i
$173$	−5.08942	−	13.9831i	−0.386941	−	1.06311i	−0.968371	−	0.249516i	$-0.919729\pi$
$173$	−5.08942	−	13.9831i	−0.386941	−	1.06311i	0.581429	−	0.813597i	$-0.302494\pi$
$174$	4.09651	−	19.0234i	0.310555	−	1.44216i
$175$	−3.20632	−	3.82114i	−0.242375	−	0.288851i
$176$	−5.79473	−	2.09299i	−0.436794	−	0.157765i
$177$	−21.5551	−	11.0720i	−1.62018	−	0.832220i
$178$	3.46503	−	0.305297i	0.259715	−	0.0228830i
$179$	−0.531463	−	0.920522i	−0.0397234	−	0.0688030i	0.845480	−	0.534007i	$-0.179314\pi$
$179$	−0.531463	−	0.920522i	−0.0397234	−	0.0688030i	−0.885204	+	0.465204i	$0.845981\pi$
$180$	−0.381123	−	0.530488i	−0.0284073	−	0.0395402i
$181$	11.3274	−	19.6196i	0.841956	−	1.45831i	−0.0462833	−	0.998928i	$-0.514738\pi$
$181$	11.3274	−	19.6196i	0.841956	−	1.45831i	0.888239	−	0.459382i	$-0.151929\pi$
$182$	−2.79999	+	6.01424i	−0.207549	+	0.445805i
$183$	−3.88397	+	12.5566i	−0.287111	+	0.928210i
$184$	−2.34443	+	1.09849i	−0.172834	+	0.0809820i
$185$	0.627480	−	0.110642i	0.0461333	−	0.00813454i
$186$	3.92318	−	3.04834i	0.287662	−	0.223515i
$187$	2.16417	−	2.57915i	0.158260	−	0.188606i
$188$	−6.75580	−	3.88940i	−0.492718	−	0.283664i
$189$	4.42745	+	2.71987i	0.322050	+	0.197841i
$190$	0.262579	−	0.982372i	0.0190495	−	0.0712687i
$191$	5.67685	+	4.76345i	0.410763	+	0.344671i	0.824636	−	0.565664i	$-0.191380\pi$
$191$	5.67685	+	4.76345i	0.410763	+	0.344671i	−0.413873	+	0.910334i	$0.635824\pi$
$192$	12.7527	−	5.41937i	0.920344	−	0.391110i
$193$	−3.37566	−	19.1443i	−0.242985	−	1.37804i	−0.825125	−	0.564950i	$-0.808896\pi$
$193$	−3.37566	−	19.1443i	−0.242985	−	1.37804i	0.582140	−	0.813089i	$-0.302216\pi$
$194$	−11.4892	+	16.4298i	−0.824878	+	1.17959i
$195$	−0.196155	−	0.862527i	−0.0140470	−	0.0617668i
$196$	1.28369	−	1.53367i	0.0916922	−	0.109548i
$197$	16.9085	+	9.76211i	1.20468	+	0.695521i	0.961592	−	0.274483i	$-0.0885067\pi$
$197$	16.9085	+	9.76211i	1.20468	+	0.695521i	0.243087	+	0.970005i	$0.421840\pi$
$198$	−4.95730	+	4.25789i	−0.352300	+	0.302595i
$199$	−2.26353	+	1.30685i	−0.160457	+	0.0926401i	−0.578079	−	0.815981i	$-0.696197\pi$
$199$	−2.26353	+	1.30685i	−0.160457	+	0.0926401i	0.417621	+	0.908621i	$0.362864\pi$
$200$	−5.93897	+	12.7977i	−0.419949	+	0.904935i
$201$	−5.99370	−	9.29602i	−0.422763	−	0.655691i
$202$	−1.76568	+	0.824673i	−0.124233	+	0.0580238i
$203$	−6.08569	+	5.10650i	−0.427131	+	0.358406i
$204$	0.380808	+	7.56247i	0.0266619	+	0.529479i
$205$	1.01370	−	0.368957i	0.0707999	−	0.0257691i
$206$	−1.73716	−	6.46727i	−0.121034	−	0.450596i
$207$	−0.209504	+	2.73807i	−0.0145615	+	0.190309i
$208$	18.7640	−	0.0461308i	1.30105	−	0.00319859i
$209$	−10.0185	−	1.76653i	−0.692992	−	0.122193i
$210$	−0.0100160	+	0.266480i	−0.000691170	+	0.0183889i
$211$	−6.96369	+	19.1326i	−0.479400	+	1.31714i	0.430603	+	0.902541i	$0.358301\pi$
$211$	−6.96369	+	19.1326i	−0.479400	+	1.31714i	−0.910004	+	0.414600i	$0.863921\pi$
$212$	−10.0397	−	3.64017i	−0.689528	−	0.250008i
$213$	−5.50861	−	13.0966i	−0.377444	−	0.897366i
$214$	−6.48914	+	4.54969i	−0.443588	+	0.311010i
$215$	−0.112786			−0.00769192
$216$	1.65293	−	14.6037i	0.112467	−	0.993655i
$217$	−2.02829			−0.137689
$218$	−2.60115	+	1.82373i	−0.176172	+	0.123518i
$219$	4.20413	−	5.54119i	0.284088	−	0.374439i
$220$	−0.315287	−	0.114316i	−0.0212566	−	0.00770721i
$221$	−3.50704	+	9.63551i	−0.235909	+	0.648154i
$222$	12.1374	+	7.62926i	0.814606	+	0.512043i
$223$	−2.87022	−	0.506098i	−0.192204	−	0.0338908i	0.0767172	−	0.997053i	$-0.475556\pi$
$223$	−2.87022	−	0.506098i	−0.192204	−	0.0338908i	−0.268922	+	0.963162i	$0.586667\pi$
$224$	−5.46858	−	1.44730i	−0.365385	−	0.0967020i
$225$	8.71635	+	12.1639i	0.581090	+	0.810925i
$226$	4.24474	+	15.8027i	0.282356	+	1.05118i
$227$	−24.3825	+	8.87450i	−1.61832	+	0.589021i	−0.983062	−	0.183276i	$-0.941330\pi$
$227$	−24.3825	+	8.87450i	−1.61832	+	0.589021i	−0.635262	+	0.772297i	$0.719108\pi$
$228$	19.2136	−	12.4216i	1.27245	−	0.822639i
$229$	−17.1266	+	14.3709i	−1.13176	+	0.949657i	−0.999138	−	0.0415096i	$-0.986783\pi$
$229$	−17.1266	+	14.3709i	−1.13176	+	0.949657i	−0.132620	+	0.991167i	$0.542339\pi$
$230$	−0.127689	+	0.0596379i	−0.00841956	+	0.00393241i
$231$	2.66463	−	0.130894i	0.175320	−	0.00861220i
$232$	20.3821	+	9.45861i	1.33815	+	0.620988i
$233$	13.8380	−	7.98939i	0.906560	−	0.523403i	0.0272371	−	0.999629i	$-0.491329\pi$
$233$	13.8380	−	7.98939i	0.906560	−	0.523403i	0.879323	+	0.476226i	$0.157996\pi$
$234$	9.75200	−	17.3493i	0.637508	−	1.13416i
$235$	−0.367481	−	0.212165i	−0.0239718	−	0.0138401i
$236$	17.9596	−	21.4569i	1.16907	−	1.39673i
$237$	−17.4306	+	16.1478i	−1.13224	+	1.04891i
$238$	1.77153	−	2.53332i	0.114831	−	0.164210i
$239$	1.90343	+	10.7949i	0.123122	+	0.698262i	0.982405	+	0.186761i	$0.0597990\pi$
$239$	1.90343	+	10.7949i	0.123122	+	0.698262i	−0.859283	+	0.511500i	$0.829090\pi$
$240$	0.694534	−	0.294142i	0.0448320	−	0.0189868i
$241$	18.5003	+	15.5236i	1.19171	+	0.999962i	0.999828	+	0.0185436i	$0.00590294\pi$
$241$	18.5003	+	15.5236i	1.19171	+	0.999962i	0.191880	+	0.981418i	$0.438542\pi$
$242$	3.15065	−	11.7874i	0.202532	−	0.757721i
$243$	−12.6211	−	9.14916i	−0.809646	−	0.586919i
$244$	−13.1529	−	7.57228i	−0.842027	−	0.484765i
$245$	0.0699783	−	0.0833969i	0.00447075	−	0.00532803i
$246$	22.4802	+	9.15228i	1.43329	+	0.583528i
$247$	30.5117	−	5.38004i	1.94142	−	0.342324i
$248$	2.43409	+	5.19489i	0.154565	+	0.329876i
$249$	−15.0427	−	16.2377i	−0.953295	−	1.02902i
$250$	−0.649040	+	1.39411i	−0.0410489	+	0.0881711i
$251$	2.29868	−	3.98142i	0.145091	−	0.251305i	−0.784316	−	0.620362i	$-0.786986\pi$
$251$	2.29868	−	3.98142i	0.145091	−	0.251305i	0.929407	+	0.369056i	$0.120319\pi$
$252$	−4.19087	+	4.29379i	−0.264000	+	0.270483i
$253$	0.704955	+	1.22102i	0.0443201	+	0.0767647i
$254$	−20.1536	+	1.77570i	−1.26455	+	0.111417i
$255$	0.0202227	+	0.411677i	0.00126639	+	0.0257802i
$256$	2.85581	+	15.7431i	0.178488	+	0.983942i
$257$	19.9096	+	23.7274i	1.24193	+	1.48007i	0.818880	+	0.573964i	$0.194595\pi$
$257$	19.9096	+	23.7274i	1.24193	+	1.48007i	0.423047	+	0.906108i	$0.360960\pi$
$258$	−1.88132	−	1.70304i	−0.117126	−	0.106027i
$259$	−2.00172	−	5.49969i	−0.124381	−	0.341734i
$260$	1.02139	−	0.00125553i	0.0633439	−	7.78647e-5i
$261$	19.3726	−	13.8820i	1.19913	−	0.859272i
$262$	7.20885	+	7.20000i	0.445364	+	0.444817i
$263$	−3.76224	+	21.3367i	−0.231990	+	1.31568i	0.616872	+	0.787064i	$0.288400\pi$
$263$	−3.76224	+	21.3367i	−0.231990	+	1.31568i	−0.848862	+	0.528615i	$0.822711\pi$
$264$	−3.53299	−	6.66762i	−0.217441	−	0.410364i
$265$	−0.546251	−	0.198819i	−0.0335559	−	0.0122134i
$266$	−9.30534	−	0.808349i	−0.570547	−	0.0495630i
$267$	3.39395	+	2.57500i	0.207706	+	0.157587i
$268$	11.9963	−	4.38299i	0.732788	−	0.267733i
$269$			15.9892i			0.974879i	0.873157	+	0.487440i	$0.162069\pi$
$269$			15.9892i			0.974879i	−0.873157	+	0.487440i	$0.837931\pi$
$270$	0.0909516	−	0.794819i	0.00553514	−	0.0483711i
$271$		−	6.14842i		−	0.373490i	−0.982408	−	0.186745i	$-0.940206\pi$
$271$		−	6.14842i		−	0.373490i	0.982408	−	0.186745i	$-0.0597938\pi$
$272$	−8.61433	−	1.49711i	−0.522320	−	0.0907757i
$273$	−7.48952	+	3.15019i	−0.453286	+	0.190658i
$274$	0.945632	−	10.8857i	0.0571277	−	0.657628i
$275$	7.21980	+	2.62779i	0.435371	+	0.158462i
$276$	−3.03044	−	0.933286i	−0.182411	−	0.0561772i
$277$	0.976978	−	5.54072i	0.0587009	−	0.332909i	−0.941288	−	0.337604i	$-0.890383\pi$
$277$	0.976978	−	5.54072i	0.0587009	−	0.332909i	0.999989	+	0.00469505i	$0.00149449\pi$
$278$	9.05067	−	9.06180i	0.542823	−	0.543491i
$279$	6.06713	+	0.464228i	0.363230	+	0.0277926i
$280$	−0.297577	−	0.0791476i	−0.0177836	−	0.00472997i
$281$	−7.49845	−	20.6018i	−0.447320	−	1.22900i	−0.934583	−	0.355746i	$-0.884227\pi$
$281$	−7.49845	−	20.6018i	−0.447320	−	1.22900i	0.487263	−	0.873256i	$-0.337995\pi$
$282$	−2.92612	−	9.08792i	−0.174248	−	0.541178i
$283$	−6.34531	−	7.56204i	−0.377189	−	0.449517i	0.543736	−	0.839257i	$-0.317009\pi$
$283$	−6.34531	−	7.56204i	−0.377189	−	0.449517i	−0.920925	+	0.389740i	$0.872565\pi$
$284$	16.1532	−	2.86872i	0.958516	−	0.170227i
$285$	1.04669	−	0.674864i	0.0620006	−	0.0399755i
$286$	−0.896845	−	10.1789i	−0.0530316	−	0.601892i
$287$	−4.95448	−	8.58141i	−0.292454	−	0.506544i
$288$	16.0267	+	5.58088i	0.944380	+	0.328857i
$289$	−6.11100	+	10.5846i	−0.359471	+	0.622622i
$290$	1.10883	+	0.516229i	0.0651130	+	0.0303140i
$291$	−23.9429	+	5.44508i	−1.40356	+	0.319196i
$292$	5.17015	+	6.14618i	0.302560	+	0.359678i
$293$	−13.6181	+	2.40125i	−0.795581	+	0.140282i	−0.556642	−	0.830752i	$-0.687911\pi$
$293$	−13.6181	+	2.40125i	−0.795581	+	0.140282i	−0.238938	+	0.971035i	$0.576799\pi$
$294$	2.42655	−	0.334445i	0.141519	−	0.0195052i
$295$	0.979038	−	1.16677i	0.0570018	−	0.0679321i
$296$	−11.6837	+	11.7269i	−0.679101	+	0.681610i
$297$	−8.00056	−	0.218335i	−0.464240	−	0.0126691i
$298$	12.2097	+	3.26353i	0.707288	+	0.189051i
$299$	−3.28936	−	2.76010i	−0.190228	−	0.159621i
$300$	−15.9196	+	6.71904i	−0.919119	+	0.387924i
$301$	0.179899	+	1.02026i	0.0103692	+	0.0588066i
$302$	19.8523	+	13.8826i	1.14237	+	0.798853i
$303$	−2.28016	−	0.705294i	−0.130992	−	0.0405181i
$304$	9.09669	+	24.8031i	0.521731	+	1.42255i
$305$	−0.715450	−	0.413065i	−0.0409665	−	0.0236520i
$306$	−5.87891	+	7.17233i	−0.336075	+	0.410015i
$307$	13.8127	−	7.97477i	0.788333	−	0.455144i	−0.0510424	−	0.998696i	$-0.516254\pi$
$307$	13.8127	−	7.97477i	0.788333	−	0.455144i	0.839375	+	0.543552i	$0.182921\pi$
$308$	−0.531205	+	3.03442i	−0.0302682	+	0.172902i
$309$	3.74734	−	7.29538i	0.213179	−	0.415019i
$310$	0.132148	+	0.282939i	0.00750551	+	0.0160698i
$311$	0.448015	−	0.375929i	0.0254046	−	0.0213170i	−0.629997	−	0.776598i	$-0.716944\pi$
$311$	0.448015	−	0.375929i	0.0254046	−	0.0213170i	0.655402	+	0.755281i	$0.272499\pi$
$312$	17.0563	+	15.4018i	0.965621	+	0.871957i
$313$	−15.5841	+	5.67214i	−0.880863	+	0.320608i	−0.742558	−	0.669782i	$-0.766388\pi$
$313$	−15.5841	+	5.67214i	−0.880863	+	0.320608i	−0.138305	+	0.990390i	$0.544165\pi$
$314$	23.1240	−	6.21128i	1.30496	−	0.350523i
$315$	−0.228411	+	0.233445i	−0.0128695	+	0.0131531i
$316$	−13.7475	−	23.7440i	−0.773359	−	1.33570i
$317$	−30.0089	−	5.29137i	−1.68547	−	0.297193i	−0.752884	−	0.658153i	$-0.771338\pi$
$317$	−30.0089	−	5.29137i	−1.68547	−	0.297193i	−0.932581	+	0.360960i	$0.882449\pi$
$318$	−6.10961	−	11.5647i	−0.342610	−	0.648515i
$319$	4.18512	−	11.4985i	0.234322	−	0.643793i
$320$	0.154398	+	0.857141i	0.00863113	+	0.0479156i
$321$	−9.63006	−	1.21447i	−0.537497	−	0.0677848i
$322$	0.743153	+	1.05995i	0.0414143	+	0.0590685i
$323$	−14.4369			−0.803288
$324$	13.5187	−	11.8846i	0.751040	−	0.660257i
$325$	−23.3994			−1.29797
$326$	−5.75513	−	8.20844i	−0.318747	−	0.454624i
$327$	−3.86018	−	0.486814i	−0.213468	−	0.0269209i
$328$	−16.0331	+	22.9878i	−0.885282	+	1.26929i
$329$	−1.33309	+	3.66264i	−0.0734958	+	0.201928i
$330$	−0.191867	−	0.363178i	−0.0105619	−	0.0199923i
$331$	21.6284	+	3.81368i	1.18881	+	0.209619i	0.732854	−	0.680385i	$-0.238188\pi$
$331$	21.6284	+	3.81368i	1.18881	+	0.209619i	0.455952	+	0.890004i	$0.349299\pi$
$332$	22.1190	−	12.8067i	1.21394	−	0.702859i
$333$	4.72892	+	16.9091i	0.259143	+	0.926615i
$334$	−11.6252	+	3.12262i	−0.636103	+	0.170862i
$335$	0.653290	−	0.237778i	0.0356931	−	0.0129912i
$336$	−3.76861	−	5.81357i	−0.205595	−	0.317156i
$337$	−1.68977	+	1.41788i	−0.0920474	+	0.0772369i	−0.687650	−	0.726042i	$-0.741358\pi$
$337$	−1.68977	+	1.41788i	−0.0920474	+	0.0772369i	0.595603	+	0.803279i	$0.296913\pi$
$338$	5.38945	+	11.5392i	0.293147	+	0.627649i
$339$	−9.15659	+	17.8262i	−0.497318	+	0.968185i
$340$	−0.468807	−	0.0820693i	−0.0254246	−	0.00445083i
$341$	2.70558	−	1.56207i	0.146516	−	0.0845908i
$342$	27.6496	+	4.54775i	1.49512	+	0.245914i
$343$	−0.866025	−	0.500000i	−0.0467610	−	0.0269975i
$344$	2.39721	−	1.68514i	0.129249	−	0.0908566i
$345$	−0.164895	−	0.0510047i	−0.00887763	−	0.00274600i
$346$	17.2458	+	12.0598i	0.927139	+	0.648341i
$347$	4.97090	+	28.1914i	0.266852	+	1.51339i	0.763709	+	0.645561i	$0.223376\pi$
$347$	4.97090	+	28.1914i	0.266852	+	1.51339i	−0.496857	+	0.867833i	$0.665513\pi$
$348$	10.7010	+	25.3541i	0.573633	+	1.35912i
$349$	−13.0018	−	10.9098i	−0.695972	−	0.583990i	0.224652	−	0.974439i	$-0.427875\pi$
$349$	−13.0018	−	10.9098i	−0.695972	−	0.583990i	−0.920625	+	0.390449i	$0.872320\pi$
$350$	6.81506	+	1.82160i	0.364280	+	0.0973686i
$351$	23.1241	−	7.70885i	1.23427	−	0.411468i
$352$	8.40929	−	2.28098i	0.448217	−	0.121577i
$353$	2.11244	−	2.51750i	0.112434	−	0.133993i	−0.706892	−	0.707321i	$-0.749903\pi$
$353$	2.11244	−	2.51750i	0.112434	−	0.133993i	0.819326	+	0.573328i	$0.194348\pi$
$354$	33.9489	−	4.67908i	1.80436	−	0.248690i
$355$	0.879466	−	0.155074i	0.0466772	−	0.00823045i
$356$	−3.76450	+	3.16668i	−0.199518	+	0.167834i
$357$	3.69176	−	0.839578i	0.195389	−	0.0444352i
$358$	1.36276	+	0.634445i	0.0720239	+	0.0335314i
$359$	−8.01609	+	13.8843i	−0.423073	+	0.732784i	−0.996238	−	0.0866559i	$-0.972382\pi$
$359$	−8.01609	+	13.8843i	−0.423073	+	0.732784i	0.573165	+	0.819440i	$0.305715\pi$
$360$	0.872013	+	0.304859i	0.0459591	+	0.0160675i
$361$	12.3107	+	21.3227i	0.647931	+	1.12225i
$362$	2.81196	+	31.9150i	0.147794	+	1.67741i
$363$	12.5591	−	8.09761i	0.659183	−	0.425014i
$364$	−1.64052	−	9.23747i	−0.0859869	−	0.484175i
$365$	0.281018	+	0.334904i	0.0147091	+	0.0175297i
$366$	−5.69687	−	17.6933i	−0.297780	−	0.924843i
$367$	8.83472	+	24.2732i	0.461168	+	1.26705i	0.924608	+	0.380921i	$0.124393\pi$
$367$	8.83472	+	24.2732i	0.461168	+	1.26705i	−0.463439	+	0.886129i	$0.653385\pi$
$368$	1.82292	−	3.17538i	0.0950260	−	0.165528i
$369$	12.8560	+	26.8032i	0.669258	+	1.39532i
$370$	−0.636769	+	0.637552i	−0.0331040	+	0.0331447i
$371$	−0.927215	+	5.25850i	−0.0481386	+	0.273008i
$372$	−2.06801	+	6.71497i	−0.107222	+	0.348155i
$373$	−25.3110	−	9.21246i	−1.31056	−	0.477003i	−0.410135	−	0.912025i	$-0.634519\pi$
$373$	−25.3110	−	9.21246i	−1.31056	−	0.477003i	−0.900420	+	0.435021i	$0.856741\pi$
$374$	−0.412071	+	4.74357i	−0.0213077	+	0.245284i
$375$	−1.73608	+	0.730217i	−0.0896506	+	0.0377082i
$376$	10.9806	−	0.981085i	0.566282	−	0.0505956i
$377$			37.2667i			1.91933i
$378$	−7.33498	+	0.445029i	−0.377271	+	0.0228898i
$379$		−	36.1545i		−	1.85713i	−0.371165	−	0.928567i	$-0.621042\pi$
$379$		−	36.1545i		−	1.85713i	0.371165	−	0.928567i	$-0.378958\pi$
$380$	0.493505	+	1.35072i	0.0253163	+	0.0692907i
$381$	−19.7402	−	14.9769i	−1.01132	−	0.767292i
$382$	−10.4409	−	0.906991i	−0.534201	−	0.0464057i
$383$	−19.3687	−	7.04961i	−0.989692	−	0.360218i	−0.204091	−	0.978952i	$-0.565424\pi$
$383$	−19.3687	−	7.04961i	−0.989692	−	0.360218i	−0.785601	+	0.618734i	$0.787646\pi$
$384$	−10.3672	+	16.6289i	−0.529049	+	0.848591i
$385$	−0.0291183	+	0.165138i	−0.00148401	+	0.00841623i
$386$	19.4516	+	19.4277i	0.990060	+	0.988844i
$387$	−0.304611	−	3.09303i	−0.0154842	−	0.157227i
$388$	−0.0348523	−	28.3528i	−0.00176936	−	1.43939i
$389$	2.32971	+	6.40083i	0.118121	+	0.324535i	0.984637	−	0.174615i	$-0.0558680\pi$
$389$	2.32971	+	6.40083i	0.118121	+	0.324535i	−0.866516	+	0.499150i	$0.833646\pi$
$390$	0.927400	+	0.839516i	0.0469607	+	0.0425105i
$391$	1.28612	+	1.53274i	0.0650419	+	0.0775139i
$392$	−0.241318	+	2.81811i	−0.0121884	+	0.142336i
$393$	0.612236	+	12.4634i	0.0308832	+	0.628696i
$394$	−27.5049	+	2.42340i	−1.38567	+	0.122089i
$395$	−0.746736	−	1.29339i	−0.0375724	−	0.0650773i
$396$	2.28348	−	8.95514i	0.114749	−	0.450013i
$397$	−0.298016	+	0.516178i	−0.0149570	+	0.0259062i	−0.873407	−	0.486991i	$-0.838094\pi$
$397$	−0.298016	+	0.516178i	−0.0149570	+	0.0259062i	0.858450	+	0.512897i	$0.171428\pi$
$398$	1.56008	−	3.35097i	0.0781996	−	0.167969i
$399$	−7.77432	−	8.39190i	−0.389203	−	0.420121i
$400$	−3.51303	−	19.6409i	−0.175651	−	0.982044i
$401$	14.9651	−	2.63876i	0.747323	−	0.131773i	0.212998	−	0.977053i	$-0.431677\pi$
$401$	14.9651	−	2.63876i	0.747323	−	0.131773i	0.534325	+	0.845279i	$0.320566\pi$
$402$	14.4876	+	5.89829i	0.722577	+	0.294180i
$403$	−6.11594	+	7.28869i	−0.304657	+	0.363076i
$404$	1.37506	−	2.38844i	0.0684116	−	0.118830i
$405$	0.736665	−	0.646017i	0.0366052	−	0.0321008i
$406$	2.90114	−	10.8539i	0.143981	−	0.538670i
$407$	6.90569	+	5.79456i	0.342302	+	0.287226i
$408$	−6.58071	−	8.44785i	−0.325794	−	0.418231i
$409$	3.10531	+	17.6111i	0.153548	+	0.870811i	0.960102	+	0.279651i	$0.0902188\pi$
$409$	3.10531	+	17.6111i	0.153548	+	0.870811i	−0.806554	+	0.591160i	$0.798670\pi$
$410$	−0.874277	+	1.25023i	−0.0431774	+	0.0617445i
$411$	9.81711	−	9.09465i	0.484242	−	0.448606i
$412$	7.26215	+	6.07847i	0.357781	+	0.299465i
$413$	−12.1162	−	6.99529i	−0.596199	−	0.344216i
$414$	−1.98036	−	3.34066i	−0.0973296	−	0.164184i
$415$	1.20487	−	0.695633i	0.0591448	−	0.0341473i
$416$	−21.6904	+	15.2873i	−1.06346	+	0.749524i
$417$	15.6670	−	0.769604i	0.767215	−	0.0376877i
$418$	13.0352	−	6.08815i	0.637570	−	0.297781i
$419$	6.76864	−	5.67956i	0.330670	−	0.277465i	−0.462303	−	0.886722i	$-0.652977\pi$
$419$	6.76864	−	5.67956i	0.330670	−	0.277465i	0.792973	+	0.609257i	$0.208532\pi$
$420$	−0.204750	−	0.316705i	−0.00999076	−	0.0154536i
$421$	27.6731	−	10.0722i	1.34870	−	0.490888i	0.436160	−	0.899869i	$-0.356338\pi$
$421$	27.6731	−	10.0722i	1.34870	−	0.490888i	0.912543	+	0.408982i	$0.134116\pi$
$422$	−7.46954	−	27.8083i	−0.363612	−	1.35369i
$423$	4.82591	−	10.6508i	0.234644	−	0.517859i
$424$	14.5809	−	3.93576i	0.708110	−	0.191138i
$425$	10.7378	+	1.89336i	0.520858	+	0.0918413i
$426$	17.0115	+	10.6930i	0.824211	+	0.518080i
$427$	−2.59540	+	7.13080i	−0.125600	+	0.345084i
$428$	3.82038	−	10.5367i	0.184665	−	0.509310i
$429$	7.56435	−	9.97010i	0.365210	−	0.481361i
$430$	0.130601	−	0.0915675i	0.00629814	−	0.00441578i
$431$	16.7569			0.807151			0.403576	−	0.914946i	$-0.367767\pi$
$431$	16.7569			0.807151			0.403576	+	0.914946i	$0.367767\pi$
$432$	9.94230	+	18.2524i	0.478349	+	0.878170i
$433$	9.71729			0.466983			0.233492	−	0.972359i	$-0.424985\pi$
$433$	9.71729			0.466983			0.233492	+	0.972359i	$0.424985\pi$
$434$	2.34867	−	1.64671i	0.112740	−	0.0790446i
$435$	0.580794	+	1.38083i	0.0278470	+	0.0662056i
$436$	1.53139	−	4.22360i	0.0733402	−	0.202274i
$437$	2.06772	−	5.68102i	0.0989126	−	0.271760i
$438$	−0.369461	+	9.82967i	−0.0176535	+	0.469680i
$439$	−14.8748	−	2.62282i	−0.709934	−	0.125181i	−0.192991	−	0.981200i	$-0.561819\pi$
$439$	−14.8748	−	2.62282i	−0.709934	−	0.125181i	−0.516943	+	0.856020i	$0.672930\pi$
$440$	0.457899	−	0.123599i	0.0218295	−	0.00589235i
$441$	2.47607	+	1.69384i	0.117908	+	0.0806591i
$442$	−3.76179	−	14.0048i	−0.178930	−	0.666139i
$443$	3.44677	−	1.25452i	0.163761	−	0.0596042i	−0.258839	−	0.965921i	$-0.583340\pi$
$443$	3.44677	−	1.25452i	0.163761	−	0.0596042i	0.422600	+	0.906316i	$0.361118\pi$
$444$	−20.2485	+	1.01961i	−0.960952	+	0.0483887i
$445$	−0.205126	+	0.172122i	−0.00972393	+	0.00815934i
$446$	3.73448	−	1.74421i	0.176833	−	0.0825909i
$447$	8.38773	+	13.0091i	0.396726	+	0.615309i
$448$	7.50740	−	2.76386i	0.354691	−	0.130580i
$449$	−20.1880	+	11.6555i	−0.952729	+	0.550058i	−0.893928	−	0.448211i	$-0.852061\pi$
$449$	−20.1880	+	11.6555i	−0.952729	+	0.550058i	−0.0588013	+	0.998270i	$0.518728\pi$
$450$	−19.9687	−	7.00868i	−0.941332	−	0.330392i
$451$	13.2178	+	7.63129i	0.622401	+	0.359344i
$452$	−17.7450	−	14.8527i	−0.834655	−	0.698612i
$453$	6.57936	+	28.9305i	0.309125	+	1.35927i
$454$	21.0289	−	30.0717i	0.986937	−	1.41134i
$455$	−0.0886813	−	0.502937i	−0.00415744	−	0.0235780i
$456$	−12.1638	+	29.9826i	−0.569620	+	1.40406i
$457$	−16.5150	−	13.8577i	−0.772539	−	0.648237i	0.168819	−	0.985647i	$-0.446005\pi$
$457$	−16.5150	−	13.8577i	−0.772539	−	0.648237i	−0.941358	+	0.337410i	$0.890449\pi$
$458$	8.16453	−	30.5455i	0.381503	−	1.42730i
$459$	−11.2352	+	1.66644i	−0.524413	+	0.0777826i
$460$	0.0994400	−	0.172725i	0.00463641	−	0.00805335i
$461$	7.55961	−	9.00920i	0.352086	−	0.419600i	−0.560712	−	0.828011i	$-0.689472\pi$
$461$	7.55961	−	9.00920i	0.352086	−	0.419600i	0.912798	+	0.408411i	$0.133917\pi$
$462$	−2.97926	+	2.31491i	−0.138608	+	0.107699i
$463$	27.5568	−	4.85901i	1.28067	−	0.225817i	0.508407	−	0.861117i	$-0.330235\pi$
$463$	27.5568	−	4.85901i	1.28067	−	0.225817i	0.772266	+	0.635300i	$0.219123\pi$
$464$	−31.2808	+	5.59497i	−1.45217	+	0.259740i
$465$	−0.113018	+	0.365381i	−0.00524111	+	0.0169441i
$466$	−9.53749	+	20.4861i	−0.441816	+	0.948999i
$467$	18.3116	−	31.7166i	0.847358	−	1.46767i	−0.0361989	−	0.999345i	$-0.511525\pi$
$467$	18.3116	−	31.7166i	0.847358	−	1.46767i	0.883557	−	0.468323i	$-0.155142\pi$
$468$	2.79299	+	28.0071i	0.129106	+	1.29463i
$469$	−3.19297	−	5.53038i	−0.147438	−	0.255369i
$470$	0.597779	−	0.0526691i	0.0275735	−	0.00242944i
$471$	26.0849	+	13.3987i	1.20193	+	0.617381i
$472$	−3.37618	+	39.4271i	−0.155401	+	1.81478i
$473$	−1.02571	−	1.22240i	−0.0471623	−	0.0562059i
$474$	7.07391	−	32.8499i	0.324915	−	1.50885i
$475$	−11.2678	−	30.9581i	−0.517004	−	1.42046i
$476$	0.00537388	+	4.37172i	0.000246312	+	0.200378i
$477$	3.97708	−	15.5173i	0.182098	−	0.710488i
$478$	−10.9681	−	10.9547i	−0.501670	−	0.501054i
$479$	6.87445	−	38.9869i	0.314101	−	1.78136i	−0.263112	−	0.964765i	$-0.584749\pi$
$479$	6.87445	−	38.9869i	0.314101	−	1.78136i	0.577214	−	0.816593i	$-0.304140\pi$
$480$	−0.565435	+	0.904476i	−0.0258085	+	0.0412835i
$481$	−25.7991	−	9.39010i	−1.17634	−	0.428152i
$482$	−34.0257	−	2.95579i	−1.54983	−	0.134633i
$483$	−0.198373	+	1.57299i	−0.00902626	+	0.0715734i
$484$	5.92151	+	16.2072i	0.269159	+	0.736690i
$485$		−	1.54334i		−	0.0700795i
$486$	22.0427	+	0.347609i	0.999876	+	0.0157678i
$487$		−	20.6005i		−	0.933500i	−0.884389	−	0.466750i	$-0.845425\pi$
$487$		−	20.6005i		−	0.933500i	0.884389	−	0.466750i	$-0.154575\pi$
$488$	21.3782	−	1.91008i	0.967745	−	0.0864651i
$489$	1.53624	−	12.1815i	0.0694711	−	0.550869i
$490$	−0.0133243	+	0.153383i	−0.000601932	+	0.00692916i
$491$	13.3265	+	4.85044i	0.601416	+	0.218897i	0.624743	−	0.780830i	$-0.285204\pi$
$491$	13.3265	+	4.85044i	0.601416	+	0.218897i	−0.0233272	+	0.999728i	$0.507426\pi$
$492$	−33.4616	+	7.65309i	−1.50857	+	0.345028i
$493$	3.01543	−	17.1013i	0.135808	−	0.770205i
$494$	−30.9634	+	31.0015i	−1.39311	+	1.39482i
$495$	0.124897	−	0.487307i	0.00561369	−	0.0219028i
$496$	−7.03615	−	4.03929i	−0.315933	−	0.181370i
$497$	−2.80558	−	7.70828i	−0.125848	−	0.345763i
$498$	30.6018	+	6.58980i	1.37130	+	0.295296i
$499$	8.30376	+	9.89603i	0.371727	+	0.443007i	0.919185	−	0.393826i	$-0.128849\pi$
$499$	8.30376	+	9.89603i	0.371727	+	0.443007i	−0.547458	+	0.836833i	$0.684404\pi$
$500$	−0.380275	−	2.14125i	−0.0170064	−	0.0957598i
$501$	−13.1138	−	6.73600i	−0.585879	−	0.300942i
$502$	0.570636	+	6.47655i	0.0254687	+	0.289063i
$503$	0.237733	+	0.411766i	0.0106000	+	0.0183598i	0.871277	−	0.490792i	$-0.163293\pi$
$503$	0.237733	+	0.411766i	0.0106000	+	0.0183598i	−0.860677	+	0.509152i	$0.829959\pi$
$504$	1.36684	−	8.37447i	0.0608841	−	0.373029i
$505$	0.0750089	−	0.129919i	0.00333785	−	0.00578133i
$506$	−1.80762	−	0.841553i	−0.0803584	−	0.0374116i
$507$	−4.60927	+	14.9014i	−0.204705	+	0.661796i
$508$	21.8954	−	18.4183i	0.971451	−	0.817181i
$509$	15.3208	−	2.70147i	0.679081	−	0.119740i	0.176540	−	0.984293i	$-0.443510\pi$
$509$	15.3208	−	2.70147i	0.679081	−	0.119740i	0.502541	+	0.864553i	$0.332398\pi$
$510$	−0.357646	−	0.460286i	−0.0158368	−	0.0203818i
$511$	2.58129	−	3.07627i	0.114190	−	0.136086i
$512$	−16.0883	−	15.9113i	−0.711007	−	0.703185i
$513$	21.3343	+	26.8817i	0.941932	+	1.18686i
$514$	−42.3180	−	11.3112i	−1.86657	−	0.498916i
$515$	0.394897	+	0.331358i	0.0174013	+	0.0146014i
$516$	3.56114	+	0.444656i	0.156771	+	0.0195749i
$517$	−1.04251	−	5.91235i	−0.0458494	−	0.260025i
$518$	6.78295	+	4.74327i	0.298026	+	0.208407i
$519$	5.71551	+	25.1320i	0.250883	+	1.10317i
$520$	−1.18171	+	0.830691i	−0.0518213	+	0.0364282i
$521$	30.6943	+	17.7214i	1.34474	+	0.776387i	0.987499	−	0.157625i	$-0.0503836\pi$
$521$	30.6943	+	17.7214i	1.34474	+	0.776387i	0.357242	+	0.934012i	$0.383717\pi$
$522$	−11.1623	+	31.8028i	−0.488559	+	1.39197i
$523$	−12.6938	+	7.32879i	−0.555063	+	0.320466i	−0.751162	−	0.660118i	$-0.770506\pi$
$523$	−12.6938	+	7.32879i	−0.555063	+	0.320466i	0.196099	+	0.980584i	$0.437173\pi$
$524$	−14.1930	−	2.48463i	−0.620025	−	0.108541i
$525$	4.68176	+	7.26126i	0.204329	+	0.316907i
$526$	−12.9662	−	27.7615i	−0.565352	−	1.21046i
$527$	3.39631	−	2.84984i	0.147945	−	0.124141i
$528$	9.50431	+	4.85249i	0.413622	+	0.211177i
$529$	20.8256	−	7.57989i	0.905460	−	0.329560i
$530$	0.793950	−	0.213261i	0.0344870	−	0.00926349i
$531$	34.6416	+	23.6978i	1.50332	+	1.02840i
$532$	11.4315	−	6.61870i	0.495617	−	0.286957i
$533$	−45.7768	−	8.07168i	−1.98281	−	0.349623i
$534$	−6.02061	−	0.226292i	−0.260537	−	0.00979263i
$535$	0.208662	−	0.573293i	0.00902122	−	0.0247856i
$536$	−10.3327	+	14.8147i	−0.446306	+	0.639899i
$537$	0.713796	+	1.69704i	0.0308026	+	0.0732326i
$538$	−12.9812	−	18.5148i	−0.559658	−	0.798230i
$539$	1.54028			0.0663446
$540$	0.539973	+	0.994207i	0.0232367	+	0.0427839i
$541$	10.9794			0.472041			0.236020	−	0.971748i	$-0.424157\pi$
$541$	10.9794			0.472041			0.236020	+	0.971748i	$0.424157\pi$
$542$	4.99172	+	7.11960i	0.214413	+	0.305813i
$543$	−23.7172	+	31.2602i	−1.01780	+	1.34150i
$544$	11.1905	−	5.26013i	0.479788	−	0.225526i
$545$	0.0836413	−	0.229803i	0.00358280	−	0.00984366i
$546$	6.11499	−	9.72831i	0.261697	−	0.416333i
$547$	−7.85474	−	1.38500i	−0.335845	−	0.0592185i	0.00318290	−	0.999995i	$-0.498987\pi$
$547$	−7.85474	−	1.38500i	−0.335845	−	0.0592185i	−0.339027	+	0.940776i	$0.610098\pi$
$548$	7.74277	+	13.3729i	0.330755	+	0.571261i
$549$	9.39558	−	20.7360i	0.400994	−	0.884992i
$550$	−10.4937	+	2.81868i	−0.447451	+	0.120189i
$551$	−49.3050	+	17.9456i	−2.10046	+	0.764506i
$552$	4.26682	−	1.37962i	0.181608	−	0.0587205i
$553$	−10.5088	+	8.81797i	−0.446882	+	0.374978i
$554$	3.36705	+	7.20909i	0.143052	+	0.306285i
$555$	−1.10226	+	0.0541462i	−0.0467885	+	0.00229838i
$556$	−3.12327	+	17.8412i	−0.132456	+	0.756633i
$557$	−23.0301	+	13.2965i	−0.975819	+	0.563389i	−0.901005	−	0.433808i	$-0.857169\pi$
$557$	−23.0301	+	13.2965i	−0.975819	+	0.563389i	−0.0748135	+	0.997198i	$0.523836\pi$
$558$	−7.40238	+	4.38818i	−0.313368	+	0.185766i
$559$	4.20876	+	2.42993i	0.178012	+	0.102775i
$560$	0.408839	−	0.149944i	0.0172766	−	0.00633630i
$561$	−4.27793	+	3.96311i	−0.180614	+	0.167323i
$562$	25.4089	+	17.7683i	1.07181	+	0.749508i
$563$	−2.98341	−	16.9197i	−0.125736	−	0.713082i	−0.980868	−	0.194673i	$-0.937635\pi$
$563$	−2.98341	−	16.9197i	−0.125736	−	0.713082i	0.855133	−	0.518409i	$-0.173476\pi$
$564$	10.7665	+	8.14779i	0.453353	+	0.343084i
$565$	−0.964928	−	0.809671i	−0.0405948	−	0.0340631i
$566$	13.4870	+	3.60495i	0.566901	+	0.151527i
$567$	−7.01887	−	5.63343i	−0.294765	−	0.236582i
$568$	−16.3757	+	16.4362i	−0.687108	+	0.689647i
$569$	21.8177	−	26.0013i	0.914646	−	1.09003i	−0.0809901	−	0.996715i	$-0.525808\pi$
$569$	21.8177	−	26.0013i	0.914646	−	1.09003i	0.995636	−	0.0933180i	$-0.0297473\pi$
$570$	−0.664121	+	1.63124i	−0.0278170	+	0.0683252i
$571$	7.52233	−	1.32639i	0.314800	−	0.0555077i	−0.0140161	−	0.999902i	$-0.504462\pi$
$571$	7.52233	−	1.32639i	0.314800	−	0.0555077i	0.328816	+	0.944394i	$0.393351\pi$
$572$	9.30249	+	11.0586i	0.388956	+	0.462385i
$573$	−8.72302	−	9.41596i	−0.364409	−	0.393357i
$574$	12.7041	+	5.91450i	0.530258	+	0.246867i
$575$	−2.28297	+	3.95422i	−0.0952065	+	0.164902i
$576$	−23.0891	+	6.54916i	−0.962048	+	0.272882i
$577$	11.1833	+	19.3700i	0.465566	+	0.806383i	0.999227	−	0.0393151i	$-0.0125176\pi$
$577$	11.1833	+	19.3700i	0.465566	+	0.806383i	−0.533661	+	0.845698i	$0.679184\pi$
$578$	−1.51703	−	17.2178i	−0.0631001	−	0.716167i
$579$	1.65199	+	33.6299i	0.0686545	+	1.39761i
$580$	−1.70309	+	0.302460i	−0.0707171	+	0.0125590i
$581$	−8.21451	−	9.78967i	−0.340795	−	0.406144i
$582$	23.3041	−	25.7437i	0.965988	−	1.06711i
$583$	−2.81295	−	7.72852i	−0.116500	−	0.320082i
$584$	−10.9767	−	2.91952i	−0.454220	−	0.120811i
$585$	0.150158	+	1.52471i	0.00620827	+	0.0630390i
$586$	13.8197	−	13.8367i	0.570888	−	0.571590i
$587$	0.309297	−	1.75411i	0.0127660	−	0.0723998i	−0.977759	−	0.209731i	$-0.932741\pi$
$587$	0.309297	−	1.75411i	0.0127660	−	0.0723998i	0.990525	+	0.137331i	$0.0438524\pi$
$588$	−2.53832	+	2.35732i	−0.104678	+	0.0972142i
$589$	−12.5883	−	4.58175i	−0.518690	−	0.188788i
$590$	−0.186415	+	2.14593i	−0.00767459	+	0.0883463i
$591$	−26.9406	−	20.4399i	−1.10819	−	0.840786i
$592$	4.00852	−	23.0649i	0.164749	−	0.947960i
$593$		−	18.6090i		−	0.764179i	−0.924125	−	0.382089i	$-0.875205\pi$
$593$		−	18.6090i		−	0.764179i	0.924125	−	0.382089i	$-0.124795\pi$
$594$	9.44157	−	6.24261i	0.387392	−	0.256137i
$595$			0.237968i			0.00975575i
$596$	−16.7879	+	6.13366i	−0.687657	+	0.251245i
$597$	4.17295	−	1.75520i	0.170788	−	0.0718355i
$598$	6.04978	+	0.525540i	0.247394	+	0.0214909i
$599$	−25.0862	−	9.13064i	−1.02500	−	0.373068i	−0.225823	−	0.974168i	$-0.572507\pi$
$599$	−25.0862	−	9.13064i	−1.02500	−	0.373068i	−0.799173	+	0.601100i	$0.794729\pi$
$600$	12.9792	−	20.7050i	0.529875	−	0.845280i
$601$	4.10854	−	23.3007i	0.167591	−	0.950455i	−0.778762	−	0.627320i	$-0.784152\pi$
$601$	4.10854	−	23.3007i	0.167591	−	0.950455i	0.946353	−	0.323135i	$-0.104737\pi$
$602$	−1.03663	−	1.03536i	−0.0422500	−	0.0421981i
$603$	8.28521	+	17.2736i	0.337400	+	0.703435i
$604$	−34.2590	+	0.0421125i	−1.39398	+	0.00171353i
$605$	0.321243	+	0.882609i	0.0130604	+	0.0358832i
$606$	3.21294	−	1.03450i	0.130517	−	0.0420237i
$607$	−22.3365	−	26.6196i	−0.906611	−	1.08046i	−0.996424	−	0.0844978i	$-0.973071\pi$
$607$	−22.3365	−	26.6196i	−0.906611	−	1.08046i	0.0898131	−	0.995959i	$-0.471373\pi$
$608$	−30.6705	−	21.3355i	−1.24385	−	0.865270i
$609$	11.5645	−	7.45634i	0.468619	−	0.302146i
$610$	1.16382	−	0.102542i	0.0471215	−	0.00415179i
$611$	9.14207	+	15.8345i	0.369848	+	0.640596i
$612$	0.984510	−	13.0782i	0.0397965	−	0.528654i
$613$	10.0774	−	17.4545i	0.407021	−	0.704981i	−0.587533	−	0.809200i	$-0.699901\pi$
$613$	10.0774	−	17.4545i	0.407021	−	0.704981i	0.994554	+	0.104219i	$0.0332343\pi$
$614$	−9.52004	+	20.4486i	−0.384197	+	0.825238i
$615$	−1.82194	+	0.414345i	−0.0734678	+	0.0167080i
$616$	−1.84845	−	3.94500i	−0.0744760	−	0.158948i
$617$	5.32587	−	0.939095i	0.214412	−	0.0378065i	−0.0654105	−	0.997858i	$-0.520836\pi$
$617$	5.32587	−	0.939095i	0.214412	−	0.0378065i	0.279822	+	0.960052i	$0.409725\pi$
$618$	1.58365	+	11.4901i	0.0637037	+	0.462199i
$619$	−0.992098	+	1.18234i	−0.0398758	+	0.0475221i	−0.785614	−	0.618717i	$-0.787653\pi$
$619$	−0.992098	+	1.18234i	−0.0398758	+	0.0475221i	0.745738	+	0.666239i	$0.232097\pi$
$620$	−0.382732	−	0.220343i	−0.0153709	−	0.00884920i
$621$	0.953403	−	4.65981i	0.0382588	−	0.186992i
$622$	−0.213576	+	0.799041i	−0.00856362	+	0.0320386i
$623$	1.88419	+	1.58103i	0.0754886	+	0.0633425i
$624$	−32.2547	−	3.98717i	−1.29122	−	0.159615i
$625$	4.31036	+	24.4453i	0.172414	+	0.977810i
$626$	13.4406	−	19.2203i	0.537196	−	0.768199i
$627$	16.8333	+	5.20683i	0.672257	+	0.207941i
$628$	−21.7338	+	25.9661i	−0.867273	+	1.03616i
$629$	11.0791	+	6.39655i	0.441754	+	0.255047i
$630$	0.0749624	−	0.455760i	0.00298657	−	0.0181579i
$631$	−35.9719	+	20.7684i	−1.43202	+	0.826777i	−0.997275	−	0.0737765i	$-0.976495\pi$
$631$	−35.9719	+	20.7684i	−1.43202	+	0.826777i	−0.434745	+	0.900554i	$0.643162\pi$
$632$	35.1961	+	16.3333i	1.40003	+	0.649702i
$633$	16.1130	−	31.3690i	0.640435	−	1.24681i
$634$	39.0449	−	18.2362i	1.55067	−	0.724250i
$635$	1.19307	−	1.00111i	0.0473457	−	0.0397278i
$636$	16.4637	+	8.43118i	0.652828	+	0.334318i
$637$	−4.40810	+	1.60442i	−0.174655	+	0.0635694i
$638$	4.48913	+	16.7126i	0.177726	+	0.661657i
$639$	6.62798	+	23.6996i	0.262199	+	0.937540i
$640$	−0.874675	−	0.867181i	−0.0345746	−	0.0342783i
$641$	−42.7284	−	7.53418i	−1.68767	−	0.297582i	−0.754310	−	0.656518i	$-0.772028\pi$
$641$	−42.7284	−	7.53418i	−1.68767	−	0.297582i	−0.933362	+	0.358936i	$0.883140\pi$
$642$	12.1372	−	6.41207i	0.479016	−	0.253064i
$643$	−6.03680	+	16.5860i	−0.238068	+	0.654087i	0.761911	+	0.647682i	$0.224261\pi$
$643$	−6.03680	+	16.5860i	−0.238068	+	0.654087i	−0.999979	+	0.00640580i	$0.997961\pi$
$644$	−1.72108	−	0.624027i	−0.0678200	−	0.0245901i
$645$	0.193815	+	0.0244424i	0.00763148	+	0.000962420i
$646$	16.7173	−	11.7209i	0.657732	−	0.461151i
$647$	−16.0164			−0.629670			−0.314835	−	0.949146i	$-0.601949\pi$
$647$	−16.0164			−0.629670			−0.314835	+	0.949146i	$0.601949\pi$
$648$	−6.00530	+	24.7373i	−0.235911	+	0.971775i
$649$	21.5495			0.845890
$650$	27.0955	−	18.9973i	1.06277	−	0.745136i
$651$	3.48549	+	0.439562i	0.136607	+	0.0172278i
$652$	13.3284	+	4.83259i	0.521980	+	0.189259i
$653$	−1.43506	+	3.94279i	−0.0561581	+	0.154293i	−0.964600	−	0.263719i	$-0.915051\pi$
$653$	−1.43506	+	3.94279i	−0.0561581	+	0.154293i	0.908441	+	0.418012i	$0.137273\pi$
$654$	4.86515	−	2.57026i	0.190242	−	0.100505i
$655$	−0.772408	−	0.136196i	−0.0301805	−	0.00532163i
$656$	−0.0974435	−	39.6357i	−0.00380453	−	1.54751i
$657$	−8.42540	+	8.61110i	−0.328706	+	0.335951i
$658$	−1.42993	−	5.32348i	−0.0557445	−	0.207531i
$659$	10.3124	−	3.75339i	0.401713	−	0.146211i	−0.133259	−	0.991081i	$-0.542544\pi$
$659$	10.3124	−	3.75339i	0.401713	−	0.146211i	0.534972	+	0.844870i	$0.320322\pi$
$660$	0.517028	+	0.264773i	0.0201253	+	0.0103063i
$661$	−25.0995	+	21.0610i	−0.976258	+	0.819178i	−0.983521	−	0.180796i	$-0.942133\pi$
$661$	−25.0995	+	21.0610i	−0.976258	+	0.819178i	0.00726275	+	0.999974i	$0.497688\pi$
$662$	−28.1410	+	13.1434i	−1.09373	+	0.510834i
$663$	8.11480	−	15.7980i	0.315153	−	0.613544i
$664$	−15.2155	+	32.7874i	−0.590475	+	1.27240i
$665$	0.622696	−	0.359514i	0.0241471	−	0.0139414i
$666$	−19.2039	−	15.7408i	−0.744137	−	0.609943i
$667$	6.29763	+	3.63594i	0.243845	+	0.140784i
$668$	10.9263	−	13.0540i	0.422752	−	0.505076i
$669$	4.82263	+	1.49172i	0.186453	+	0.0576733i
$670$	−0.563437	+	0.805725i	−0.0217675	+	0.0311279i
$671$	−2.02966	−	11.5108i	−0.0783541	−	0.444368i
$672$	9.08376	+	3.67223i	0.350414	+	0.141659i
$673$	−9.59434	−	8.05061i	−0.369835	−	0.310328i	0.438862	−	0.898555i	$-0.355382\pi$
$673$	−9.59434	−	8.05061i	−0.369835	−	0.310328i	−0.808696	+	0.588227i	$0.799826\pi$
$674$	0.805539	−	3.01372i	0.0310282	−	0.116084i
$675$	−12.3424	−	22.7918i	−0.475060	−	0.877259i
$676$	−15.6091	−	8.98634i	−0.600349	−	0.345629i
$677$	0.402170	−	0.479287i	0.0154566	−	0.0184205i	−0.758261	−	0.651951i	$-0.773951\pi$
$677$	0.402170	−	0.479287i	0.0154566	−	0.0184205i	0.773717	+	0.633531i	$0.218395\pi$
$678$	−3.86963	−	28.0759i	−0.148612	−	1.07825i
$679$	−13.9610	+	2.46171i	−0.535775	+	0.0944716i
$680$	0.609488	−	0.285578i	0.0233728	−	0.0109514i
$681$	43.8231	−	9.96623i	1.67930	−	0.381907i
$682$	−1.86475	+	4.00539i	−0.0714050	+	0.153374i
$683$	13.3675	−	23.1531i	0.511492	−	0.885929i	−0.488420	−	0.872609i	$-0.662426\pi$
$683$	13.3675	−	23.1531i	0.511492	−	0.885929i	0.999911	−	0.0133206i	$-0.00424019\pi$
$684$	−35.7093	+	17.1818i	−1.36538	+	0.656964i
$685$	0.420571	+	0.728450i	0.0160692	+	0.0278326i
$686$	1.40876	−	0.124123i	0.0537866	−	0.00473903i
$687$	32.5454	−	20.9840i	1.24169	−	0.800588i
$688$	−1.40775	+	3.89754i	−0.0536699	+	0.148592i
$689$	16.1007	+	19.1880i	0.613386	+	0.731005i
$690$	0.232350	−	0.0748119i	0.00884542	−	0.00284804i
$691$	7.78679	+	21.3940i	0.296223	+	0.813867i	0.995123	+	0.0986468i	$0.0314514\pi$
$691$	7.78679	+	21.3940i	0.296223	+	0.813867i	−0.698899	+	0.715220i	$0.746326\pi$
$692$	−29.7609	+	0.0365832i	−1.13134	+	0.00139069i
$693$	−4.60738	−	0.352535i	−0.175020	−	0.0133917i
$694$	−28.6439	−	28.6087i	−1.08731	−	1.08597i
$695$	−0.171204	+	0.970946i	−0.00649414	+	0.0368301i
$696$	−32.9756	−	20.6712i	−1.24994	−	0.783539i
$697$	20.3534	+	7.40803i	0.770939	+	0.280599i
$698$	23.9129	+	2.07730i	0.905118	+	0.0786271i
$699$	−25.5113	+	10.7304i	−0.964924	+	0.405860i
$700$	−9.37045	+	3.42362i	−0.354170	+	0.129400i
$701$			9.69791i			0.366285i	0.983086	+	0.183142i	$0.0586270\pi$
$701$			9.69791i			0.366285i	−0.983086	+	0.183142i	$0.941373\pi$
$702$	−20.5181	+	27.7003i	−0.774405	+	1.04548i
$703$		−	38.6547i		−	1.45789i
$704$	−7.88573	+	9.46854i	−0.297205	+	0.356859i
$705$	0.585515	+	0.444232i	0.0220518	+	0.0167308i
$706$	−0.402222	+	4.63019i	−0.0151378	+	0.174259i
$707$	−1.29489	−	0.471301i	−0.0486993	−	0.0177251i
$708$	−35.5125	+	32.9803i	−1.33464	+	1.23948i
$709$	−5.11585	+	29.0134i	−0.192130	+	1.08962i	0.724318	+	0.689466i	$0.242155\pi$
$709$	−5.11585	+	29.0134i	−0.192130	+	1.08962i	−0.916447	+	0.400155i	$0.868956\pi$
$710$	−0.892484	+	0.893582i	−0.0334943	+	0.0335355i
$711$	33.4529	−	23.9716i	1.25458	−	0.899005i
$712$	1.78819	−	6.72317i	0.0670152	−	0.251962i
$713$	0.634999	+	1.74464i	0.0237809	+	0.0653374i
$714$	−3.59327	+	3.96943i	−0.134475	+	0.148552i
$715$	0.505626	+	0.602582i	0.0189094	+	0.0225353i
$716$	−2.09310	+	0.371724i	−0.0782229	+	0.0138920i
$717$	−0.931505	−	18.9628i	−0.0347877	−	0.708179i
$718$	−1.98996	−	22.5854i	−0.0742645	−	0.842881i
$719$	−4.18118	−	7.24202i	−0.155932	−	0.270082i	0.777466	−	0.628925i	$-0.216505\pi$
$719$	−4.18118	−	7.24202i	−0.155932	−	0.270082i	−0.933398	+	0.358843i	$0.883171\pi$
$720$	−1.25726	+	0.354948i	−0.0468553	+	0.0132281i
$721$	2.36758	−	4.10076i	0.0881732	−	0.152720i
$722$	−31.5666	−	14.6961i	−1.17479	−	0.546933i
$723$	−28.4274	−	30.6856i	−1.05723	−	1.14121i
$724$	−29.1670	−	34.6732i	−1.08398	−	1.28862i
$725$	39.0253	−	6.88121i	1.44936	−	0.255562i
$726$	−7.96871	+	19.5731i	−0.295747	+	0.726425i
$727$	20.0332	−	23.8746i	0.742990	−	0.885461i	−0.253656	−	0.967294i	$-0.581633\pi$
$727$	20.0332	−	23.8746i	0.742990	−	0.885461i	0.996646	+	0.0818338i	$0.0260777\pi$
$728$	9.39929	+	9.36469i	0.348361	+	0.347079i
$729$	19.7059	+	18.4575i	0.729847	+	0.683610i
$730$	−0.597305	−	0.159654i	−0.0221073	−	0.00590906i
$731$	−1.73474	−	1.45562i	−0.0641618	−	0.0538381i
$732$	20.9614	+	15.8629i	0.774756	+	0.586311i
$733$	0.508394	+	2.88325i	0.0187780	+	0.106495i	0.992756	−	0.120147i	$-0.0383365\pi$
$733$	0.508394	+	2.88325i	0.0187780	+	0.106495i	−0.973978	+	0.226642i	$0.927225\pi$
$734$	−29.9369	−	20.9347i	−1.10499	−	0.772712i
$735$	−0.138327	+	0.128147i	−0.00510227	+	0.00472678i
$736$	0.467146	+	5.15693i	0.0172192	+	0.190087i
$737$	8.51835	+	4.91807i	0.313777	+	0.181159i
$738$	−36.6475	−	20.5995i	−1.34901	−	0.758277i
$739$	−29.2977	+	16.9151i	−1.07774	+	0.622231i	−0.930285	−	0.366839i	$-0.880440\pi$
$739$	−29.2977	+	16.9151i	−1.07774	+	0.622231i	−0.147451	+	0.989069i	$0.547107\pi$
$740$	0.219741	−	1.25523i	0.00807783	−	0.0461432i
$741$	−53.5985	+	2.63290i	−1.96899	+	0.0967222i
$742$	−3.19555	−	6.84189i	−0.117312	−	0.251174i
$743$	−1.22486	+	1.02778i	−0.0449357	+	0.0377055i	−0.664979	−	0.746862i	$-0.731559\pi$
$743$	−1.22486	+	1.02778i	−0.0449357	+	0.0377055i	0.620043	+	0.784568i	$0.287115\pi$
$744$	−3.05702	−	9.45461i	−0.112076	−	0.346623i
$745$	−0.914231	+	0.332753i	−0.0334948	+	0.0121911i
$746$	36.7884	−	9.88167i	1.34692	−	0.361794i
$747$	22.3311	+	31.1635i	0.817051	+	1.14021i
$748$	−3.37401	−	5.82740i	−0.123366	−	0.213071i
$749$	−5.51882	−	0.973116i	−0.201653	−	0.0355569i
$750$	1.41746	−	2.25503i	0.0517584	−	0.0823421i
$751$	−18.0388	+	49.5612i	−0.658245	+	1.80851i	−0.0735007	+	0.997295i	$0.523417\pi$
$751$	−18.0388	+	49.5612i	−0.658245	+	1.80851i	−0.584744	+	0.811218i	$0.698805\pi$
$752$	−11.9186	+	10.0509i	−0.434626	+	0.366519i
$753$	−4.81297	+	6.34368i	−0.175395	+	0.231176i
$754$	−30.2558	−	43.1533i	−1.10185	−	1.57155i
$755$	−1.86484			−0.0678684
$756$	8.13229	−	6.47039i	0.295768	−	0.235326i
$757$	−33.7023			−1.22493			−0.612466	−	0.790497i	$-0.709822\pi$
$757$	−33.7023			−1.22493			−0.612466	+	0.790497i	$0.709822\pi$
$758$	29.3528	+	41.8654i	1.06614	+	1.52062i
$759$	−0.946809	−	2.25102i	−0.0343670	−	0.0817068i
$760$	−1.66807	−	1.16342i	−0.0605073	−	0.0422016i
$761$	11.4170	−	31.3680i	0.413866	−	1.13709i	−0.541251	−	0.840861i	$-0.682049\pi$
$761$	11.4170	−	31.3680i	0.413866	−	1.13709i	0.955117	−	0.296227i	$-0.0957286\pi$
$762$	35.0176	+	1.31618i	1.26855	+	0.0476802i
$763$	−2.21220	−	0.390071i	−0.0800870	−	0.0141215i
$764$	12.8264	−	7.42638i	0.464044	−	0.268677i
$765$	0.0544654	−	0.711824i	0.00196920	−	0.0257361i
$766$	28.1514	−	7.56171i	1.01715	−	0.273216i
$767$	−61.6719	+	22.4468i	−2.22684	+	0.810505i
$768$	−1.49577	−	27.6724i	−0.0539740	−	0.998542i
$769$	9.27191	−	7.78006i	0.334354	−	0.280556i	−0.460117	−	0.887858i	$-0.652193\pi$
$769$	9.27191	−	7.78006i	0.334354	−	0.280556i	0.794471	+	0.607302i	$0.207748\pi$
$770$	−0.100353	−	0.214863i	−0.00361648	−	0.00774314i
$771$	−29.0714	−	45.0888i	−1.04698	−	1.62383i
$772$	−38.2969	−	6.70425i	−1.37834	−	0.241291i
$773$	−1.08695	+	0.627551i	−0.0390949	+	0.0225714i	−0.519420	−	0.854519i	$-0.673852\pi$
$773$	−1.08695	+	0.627551i	−0.0390949	+	0.0225714i	0.480325	+	0.877090i	$0.340519\pi$
$774$	2.86386	+	3.33429i	0.102939	+	0.119848i
$775$	8.76193	+	5.05870i	0.314738	+	0.181714i
$776$	23.0592	+	32.8030i	0.827776	+	1.17756i
$777$	2.24797	+	9.88469i	0.0806456	+	0.354611i
$778$	−7.89436	−	5.52046i	−0.283027	−	0.197918i
$779$	−11.3644	−	64.4509i	−0.407173	−	2.30919i
$780$	−1.75547	−	0.219194i	−0.0628559	−	0.00784839i
$781$	9.67889	+	8.12156i	0.346338	+	0.290612i
$782$	−2.73366	−	0.730681i	−0.0977554	−	0.0261291i
$783$	−36.2991	+	19.6570i	−1.29722	+	0.702483i
$784$	−2.00851	−	3.45917i	−0.0717325	−	0.123542i
$785$	−1.18478	+	1.41197i	−0.0422867	+	0.0503953i
$786$	−10.8276	−	13.9350i	−0.386209	−	0.497046i
$787$	13.4432	−	2.37039i	0.479197	−	0.0844954i	0.0711681	−	0.997464i	$-0.477327\pi$
$787$	13.4432	−	2.37039i	0.479197	−	0.0844954i	0.408029	+	0.912969i	$0.366216\pi$
$788$	29.8820	−	25.1366i	1.06450	−	0.895454i
$789$	11.0892	−	35.8505i	0.394785	−	1.27631i
$790$	1.91475	+	0.891431i	0.0681238	+	0.0317157i
$791$	−5.78515	+	10.0202i	−0.205696	+	0.356277i
$792$	4.62626	+	12.2236i	0.164387	+	0.434345i
$793$	17.7987	+	30.8283i	0.632050	+	1.09474i
$794$	−0.0739810	−	0.839662i	−0.00262549	−	0.0297985i
$795$	0.895612	+	0.460040i	0.0317641	+	0.0163159i
$796$	0.914055	+	5.14686i	0.0323978	+	0.182426i
$797$	15.3386	+	18.2799i	0.543322	+	0.647506i	0.965929	−	0.258807i	$-0.0833294\pi$
$797$	15.3386	+	18.2799i	0.543322	+	0.647506i	−0.422607	+	0.906313i	$0.638885\pi$
$798$	15.8155	+	3.40571i	0.559862	+	0.120561i
$799$	−2.91396	−	8.00603i	−0.103088	−	0.283233i
$800$	20.0138	+	19.8912i	0.707595	+	0.703259i
$801$	−5.27425	−	5.16050i	−0.186356	−	0.182337i
$802$	−15.1867	+	15.2053i	−0.536259	+	0.536919i
$803$	−1.07409	+	6.09146i	−0.0379038	+	0.214963i
$804$	−21.5647	+	4.93212i	−0.760528	+	0.173942i
$805$	−0.0936425	−	0.0340831i	−0.00330046	−	0.00120127i
$806$	1.16451	−	13.4054i	0.0410183	−	0.472183i
$807$	3.46511	−	27.4765i	0.121978	−	0.967218i
$808$	0.346852	+	3.88208i	0.0122022	+	0.136571i
$809$			17.0535i			0.599569i	0.954007	+	0.299784i	$0.0969147\pi$
$809$			17.0535i			0.599569i	−0.954007	+	0.299784i	$0.903085\pi$
$810$	−0.328544	+	1.34614i	−0.0115439	+	0.0472984i
$811$			15.5476i			0.545951i	0.962021	+	0.272976i	$0.0880079\pi$
$811$			15.5476i			0.545951i	−0.962021	+	0.272976i	$0.911992\pi$
$812$	5.45257	+	14.9237i	0.191348	+	0.523719i
$813$	−1.33246	+	10.5657i	−0.0467314	+	0.370555i
$814$	−12.7009	−	1.10332i	−0.445167	−	0.0386714i
$815$	0.725187	+	0.263947i	0.0254022	+	0.00924565i
$816$	14.4787	+	4.43955i	0.506858	+	0.155415i
$817$	−1.18817	+	6.73844i	−0.0415687	+	0.235748i
$818$	−17.8937	−	17.8718i	−0.625640	−	0.624871i
$819$	13.5530	−	3.79031i	0.473579	−	0.132444i
$820$	−0.00265210	−	2.15751i	−9.26152e−5	−	0.0753437i
$821$	−7.42180	−	20.3912i	−0.259022	−	0.711658i	−0.999228	−	0.0392781i	$-0.987494\pi$
$821$	−7.42180	−	20.3912i	−0.259022	−	0.711658i	0.740206	−	0.672380i	$-0.234728\pi$
$822$	−3.98411	+	18.5014i	−0.138962	+	0.645312i
$823$	−19.8954	−	23.7105i	−0.693511	−	0.826495i	0.298264	−	0.954483i	$-0.403592\pi$
$823$	−19.8954	−	23.7105i	−0.693511	−	0.826495i	−0.991776	+	0.127989i	$0.959148\pi$
$824$	−13.3442	−	1.14268i	−0.464867	−	0.0398071i
$825$	−11.8373	−	6.08035i	−0.412122	−	0.211691i
$826$	19.7093	−	1.73655i	0.685775	−	0.0604223i
$827$	−1.40574	−	2.43481i	−0.0488824	−	0.0846668i	0.840549	−	0.541736i	$-0.182233\pi$
$827$	−1.40574	−	2.43481i	−0.0488824	−	0.0846668i	−0.889431	+	0.457069i	$0.848899\pi$
$828$	5.00536	+	2.26054i	0.173948	+	0.0785592i
$829$	2.40826	−	4.17123i	0.0836424	−	0.144873i	−0.821170	−	0.570684i	$-0.806678\pi$
$829$	2.40826	−	4.17123i	0.0836424	−	0.144873i	0.904812	+	0.425812i	$0.140011\pi$
$830$	−0.830425	+	1.78371i	−0.0288245	+	0.0619136i
$831$	−2.87964	+	9.30966i	−0.0998935	+	0.322949i
$832$	12.7052	−	35.3119i	0.440474	−	1.22422i
$833$	2.15265	−	0.379571i	0.0745851	−	0.0131514i
$834$	−17.5169	+	13.6107i	−0.606559	+	0.471301i
$835$	0.595631	−	0.709845i	0.0206126	−	0.0245652i
$836$	−10.1514	+	17.6327i	−0.351092	+	0.609839i
$837$	−10.3254	−	2.11259i	−0.356898	−	0.0730218i
$838$	−3.22672	+	12.0720i	−0.111465	+	0.417019i
$839$	17.6527	+	14.8124i	0.609438	+	0.511379i	0.894464	−	0.447141i	$-0.147558\pi$
$839$	17.6527	+	14.8124i	0.609438	+	0.511379i	−0.285026	+	0.958520i	$0.592002\pi$
$840$	0.494215	+	0.200500i	0.0170520	+	0.00691790i
$841$	−5.92346	−	33.5936i	−0.204257	−	1.15840i
$842$	−23.8669	+	34.1301i	−0.822508	+	1.17620i
$843$	8.42089	+	37.0280i	0.290031	+	1.27531i
$844$	31.2262	+	26.1366i	1.07485	+	0.899657i
$845$	−0.849055	−	0.490202i	−0.0292084	−	0.0168635i
$846$	3.05887	+	16.2512i	0.105166	+	0.558727i
$847$	7.47166	−	4.31377i	0.256729	−	0.148223i
$848$	−13.6887	+	16.3952i	−0.470072	+	0.563015i
$849$	9.26522	+	14.3700i	0.317981	+	0.493179i
$850$	−13.9710	+	6.52525i	−0.479202	+	0.223814i
$851$	−4.10391	+	3.44359i	−0.140680	+	0.118045i
$852$	−28.3800	+	1.42907i	−0.972282	+	0.0489593i
$853$	40.5794	−	14.7697i	1.38941	−	0.505705i	0.464395	−	0.885628i	$-0.346272\pi$
$853$	40.5794	−	14.7697i	1.38941	−	0.505705i	0.925018	+	0.379924i	$0.124050\pi$
$854$	−2.78393	−	10.3643i	−0.0952642	−	0.354659i
$855$	−1.94493	+	0.932878i	−0.0665152	+	0.0319037i
$856$	4.13060	+	15.3027i	0.141181	+	0.523035i
$857$	−6.07011	−	1.07032i	−0.207351	−	0.0365616i	0.0690077	−	0.997616i	$-0.478017\pi$
$857$	−6.07011	−	1.07032i	−0.207351	−	0.0365616i	−0.276359	+	0.961055i	$0.589128\pi$
$858$	−0.664759	+	17.6862i	−0.0226945	+	0.603798i
$859$	−8.48355	+	23.3084i	−0.289455	+	0.795271i	0.706688	+	0.707525i	$0.250188\pi$
$859$	−8.48355	+	23.3084i	−0.289455	+	0.795271i	−0.996143	+	0.0877455i	$0.972034\pi$
$860$	−0.0768894	+	0.212063i	−0.00262191	+	0.00723127i
$861$	6.65424	+	15.8203i	0.226776	+	0.539156i
$862$	−19.4038	+	13.6044i	−0.660895	+	0.463369i
$863$	39.7716			1.35384			0.676921	−	0.736055i	$-0.263314\pi$
$863$	39.7716			1.35384			0.676921	+	0.736055i	$0.263314\pi$
$864$	−26.3314	−	13.0636i	−0.895812	−	0.444434i
$865$	−1.61999			−0.0550813
$866$	−11.2522	+	7.88919i	−0.382365	+	0.268086i
$867$	12.7952	−	16.8646i	0.434549	−	0.572751i
$868$	−1.38274	+	3.81364i	−0.0469334	+	0.129443i
$869$	7.22692	−	19.8558i	0.245156	−	0.673562i
$870$	−1.79359	−	1.12741i	−0.0608084	−	0.0382228i
$871$	−29.5013	−	5.20188i	−0.999615	−	0.176259i
$872$	1.65574	+	6.13404i	0.0560704	+	0.207725i
$873$	42.3244	−	4.16824i	1.43247	−	0.141074i
$874$	2.21793	+	8.25711i	0.0750224	+	0.279301i
$875$	−1.02180	+	0.371906i	−0.0345432	+	0.0125727i
$876$	−7.55261	−	11.6823i	−0.255179	−	0.394708i
$877$	1.37224	−	1.15145i	0.0463373	−	0.0388816i	−0.619325	−	0.785135i	$-0.712594\pi$
$877$	1.37224	−	1.15145i	0.0463373	−	0.0388816i	0.665662	+	0.746253i	$0.268149\pi$
$878$	19.3538	−	9.03929i	0.653157	−	0.305061i
$879$	23.9223	−	1.17513i	0.806881	−	0.0396362i
$880$	−0.429881	+	0.514878i	−0.0144913	+	0.0173565i
$881$	−10.0204	+	5.78529i	−0.337596	+	0.194911i	−0.659209	−	0.751960i	$-0.729109\pi$
$881$	−10.0204	+	5.78529i	−0.337596	+	0.194911i	0.321612	+	0.946871i	$0.395775\pi$
$882$	−4.24236	+	0.0488515i	−0.142848	+	0.00164492i
$883$	−2.53017	−	1.46079i	−0.0851470	−	0.0491596i	0.456822	−	0.889558i	$-0.348988\pi$
$883$	−2.53017	−	1.46079i	−0.0851470	−	0.0491596i	−0.541969	+	0.840399i	$0.682321\pi$
$884$	15.7261	+	13.1628i	0.528925	+	0.442714i
$885$	−1.93528	+	1.79285i	−0.0650536	+	0.0602661i
$886$	−2.97271	+	4.25102i	−0.0998700	+	0.142816i
$887$	0.347362	+	1.96999i	0.0116633	+	0.0661457i	0.990084	−	0.140477i	$-0.0448637\pi$
$887$	0.347362	+	1.96999i	0.0116633	+	0.0661457i	−0.978421	+	0.206623i	$0.933753\pi$
$888$	22.6191	−	17.6199i	0.759048	−	0.591284i
$889$	−10.9590	−	9.19570i	−0.367553	−	0.308414i
$890$	0.0977871	−	0.365846i	0.00327783	−	0.0122632i
$891$	13.7012	+	2.10904i	0.459006	+	0.0706556i
$892$	−2.90829	+	5.05164i	−0.0973769	+	0.169141i
$893$	−16.5472	+	19.7202i	−0.553732	+	0.659913i
$894$	−20.2743	−	8.25421i	−0.678075	−	0.276062i
$895$	−0.113960	+	0.0200942i	−0.00380925	+	0.000671673i
$896$	−6.44934	+	9.29548i	−0.215457	+	0.310540i
$897$	5.05440	+	5.45592i	0.168762	+	0.182168i
$898$	13.9140	−	29.8866i	0.464316	−	0.997330i
$899$	8.05667	−	13.9546i	0.268705	−	0.465411i
$900$	28.8130	−	8.09623i	0.960434	−	0.269874i
$901$	−5.83583	−	10.1080i	−0.194420	−	0.336745i
$902$	−21.5013	+	1.89443i	−0.715914	+	0.0630777i
$903$	−0.0880395	−	1.79224i	−0.00292977	−	0.0596419i
$904$	32.6064	+	2.79212i	1.08447	+	0.0928646i
$905$	−1.58534	−	1.88933i	−0.0526984	−	0.0628036i
$906$	−31.1065	−	28.1587i	−1.03344	−	0.935509i
$907$	19.2121	+	52.7849i	0.637928	+	1.75269i	0.658138	+	0.752897i	$0.271344\pi$
$907$	19.2121	+	52.7849i	0.637928	+	1.75269i	−0.0202105	+	0.999796i	$0.506434\pi$
$908$	0.0637908	+	51.8946i	0.00211697	+	1.72218i
$909$	3.76547	+	1.70615i	0.124893	+	0.0565895i
$910$	0.511009	+	0.510381i	0.0169398	+	0.0169190i
$911$	5.48420	−	31.1025i	0.181700	−	1.03047i	−0.748423	−	0.663222i	$-0.769189\pi$
$911$	5.48420	−	31.1025i	0.181700	−	1.03047i	0.930123	−	0.367249i	$-0.119700\pi$
$912$	−10.2569	−	44.5940i	−0.339640	−	1.47665i
$913$	18.4970	+	6.73234i	0.612160	+	0.222808i
$914$	30.3743	+	2.63860i	1.00469	+	0.0872771i
$915$	1.13994	+	0.864877i	0.0376852	+	0.0285919i
$916$	15.3449	+	41.9989i	0.507008	+	1.38768i
$917$			7.20443i			0.237911i
$918$	11.6569	−	11.0512i	0.384735	−	0.364743i
$919$			21.6347i			0.713662i	0.934169	+	0.356831i	$0.116143\pi$
$919$			21.6347i			0.713662i	−0.934169	+	0.356831i	$0.883857\pi$
$920$	0.0250833	+	0.280741i	0.000826973	+	0.00925575i
$921$	−25.4646	+	10.7107i	−0.839086	+	0.352931i
$922$	−1.43940	+	16.5697i	−0.0474041	+	0.545694i
$923$	−36.1596	−	13.1610i	−1.19021	−	0.433200i
$924$	1.57045	−	5.09934i	0.0516640	−	0.167756i
$925$	−5.06947	+	28.7504i	−0.166683	+	0.945306i
$926$	−27.9647	+	27.9991i	−0.918977	+	0.920107i
$927$	−8.02060	+	11.7246i	−0.263431	+	0.385085i
$928$	31.6794	−	31.8747i	1.03993	−	1.04634i
$929$	19.2174	+	52.7993i	0.630501	+	1.73229i	0.679691	+	0.733499i	$0.262114\pi$
$929$	19.2174	+	52.7993i	0.630501	+	1.73229i	−0.0491894	+	0.998789i	$0.515664\pi$
$930$	−0.165771	−	0.514851i	−0.00543586	−	0.0168826i
$931$	−4.24539	−	5.05945i	−0.139137	−	0.165817i
$932$	−5.58806	−	31.4652i	−0.183043	−	1.03068i
$933$	−0.851357	+	0.548920i	−0.0278722	+	0.0179708i
$934$	4.54576	+	51.5931i	0.148742	+	1.68818i
$935$	−0.183269	−	0.317431i	−0.00599354	−	0.0103811i
$936$	−25.9723	−	30.1635i	−0.848932	−	0.985924i
$937$	12.9985	−	22.5140i	0.424641	−	0.735500i	−0.571746	−	0.820431i	$-0.693734\pi$
$937$	12.9985	−	22.5140i	0.424641	−	0.735500i	0.996387	+	0.0849307i	$0.0270669\pi$
$938$	8.18728	+	3.81167i	0.267324	+	0.124455i
$939$	28.0095	−	6.36991i	0.914056	−	0.207874i
$940$	−0.649442	+	0.546308i	−0.0211824	+	0.0178186i
$941$	56.3869	−	9.94252i	1.83816	−	0.324117i	0.856704	−	0.515809i	$-0.172509\pi$
$941$	56.3869	−	9.94252i	1.83816	−	0.324117i	0.981455	+	0.191692i	$0.0613974\pi$
$942$	−41.0832	+	5.66239i	−1.33856	+	0.184490i
$943$	−5.83024	+	6.94821i	−0.189859	+	0.226265i
$944$	−28.1002	−	48.3959i	−0.914585	−	1.57515i
$945$	0.443101	−	0.351661i	0.0144141	−	0.0114395i
$946$	2.18016	+	0.582737i	0.0708832	+	0.0189464i
$947$	39.4893	+	33.1355i	1.28323	+	1.07676i	0.992790	+	0.119866i	$0.0382464\pi$
$947$	39.4893	+	33.1355i	1.28323	+	1.07676i	0.290441	+	0.956893i	$0.406198\pi$
$948$	18.4786	+	43.7819i	0.600157	+	1.42197i
$949$	−3.27119	−	18.5519i	−0.106187	−	0.602219i
$950$	38.1817	+	26.7002i	1.23878	+	0.866267i
$951$	50.4217	+	15.5963i	1.63504	+	0.505744i
$952$	−3.55550	−	5.05790i	−0.115234	−	0.163928i
$953$	0.136594	+	0.0788626i	0.00442472	+	0.00255461i	0.502211	−	0.864745i	$-0.332520\pi$
$953$	0.136594	+	0.0788626i	0.00442472	+	0.00255461i	−0.497786	+	0.867300i	$0.665854\pi$
$954$	7.99275	+	21.1972i	0.258775	+	0.686286i
$955$	0.698684	−	0.403385i	0.0226089	−	0.0130532i
$956$	21.5944	+	3.78031i	0.698412	+	0.122264i
$957$	−9.68378	+	18.8525i	−0.313032	+	0.609415i
$958$	23.6921	+	50.7264i	0.765456	+	1.63889i
$959$	5.91871	−	4.96639i	0.191125	−	0.160373i
$960$	−0.0795683	−	1.50640i	−0.00256806	−	0.0486190i
$961$	−25.2646	+	9.19557i	−0.814988	+	0.296631i
$962$	37.4978	−	10.0722i	1.20898	−	0.324741i
$963$	16.2855	+	4.17397i	0.524792	+	0.134504i
$964$	41.8000	−	24.2018i	1.34629	−	0.779488i
$965$	−2.08418	−	0.367498i	−0.0670922	−	0.0118302i
$966$	−1.04736	−	1.98251i	−0.0336982	−	0.0637861i
$967$	3.28077	−	9.01383i	0.105502	−	0.289865i	−0.875697	−	0.482860i	$-0.839598\pi$
$967$	3.28077	−	9.01383i	0.105502	−	0.289865i	0.981200	+	0.192995i	$0.0618201\pi$
$968$	−20.0150	−	13.9597i	−0.643307	−	0.448683i
$969$	24.8089	+	3.12869i	0.796975	+	0.100508i
$970$	1.25300	+	1.78712i	0.0402312	+	0.0573811i
$971$	24.3849			0.782548			0.391274	−	0.920274i	$-0.372035\pi$
$971$	24.3849			0.782548			0.391274	+	0.920274i	$0.372035\pi$
$972$	−25.8067	+	17.4933i	−0.827750	+	0.561098i
$973$	9.05623			0.290330
$974$	16.7250	+	23.8546i	0.535903	+	0.764349i
$975$	40.2105	+	5.07102i	1.28777	+	0.162403i
$976$	−23.2043	+	19.5681i	−0.742751	+	0.626360i
$977$	0.437696	−	1.20256i	0.0140031	−	0.0384733i	−0.932494	−	0.361185i	$-0.882372\pi$
$977$	0.437696	−	1.20256i	0.0140031	−	0.0384733i	0.946497	+	0.322712i	$0.104594\pi$
$978$	8.11095	+	15.3529i	0.259360	+	0.490933i
$979$	−3.73098	−	0.657873i	−0.119243	−	0.0210257i
$980$	−0.109099	−	0.188429i	−0.00348503	−	0.00601915i
$981$	6.52798	+	1.67312i	0.208422	+	0.0534187i
$982$	−19.3694	+	5.20279i	−0.618103	+	0.166028i
$983$	18.9617	−	6.90149i	0.604784	−	0.220123i	−0.0214357	−	0.999770i	$-0.506824\pi$
$983$	18.9617	−	6.90149i	0.604784	−	0.220123i	0.626219	+	0.779647i	$0.284601\pi$
$984$	32.5338	−	36.0285i	1.03714	−	1.14855i
$985$	1.62826	−	1.36627i	0.0518807	−	0.0435331i
$986$	10.3923	+	22.2507i	0.330960	+	0.708608i
$987$	3.08459	−	6.00512i	0.0981836	−	0.191145i
$988$	10.6851	−	61.0367i	0.339937	−	1.94183i
$989$	0.821258	−	0.474154i	0.0261145	−	0.0150772i
$990$	0.251005	+	0.665680i	0.00797747	+	0.0211567i
$991$	−31.2682	−	18.0527i	−0.993266	−	0.573463i	−0.0870174	−	0.996207i	$-0.527734\pi$
$991$	−31.2682	−	18.0527i	−0.993266	−	0.573463i	−0.906249	+	0.422744i	$0.861067\pi$
$992$	11.4270	−	1.03512i	0.362806	−	0.0328652i
$993$	−36.3407	−	11.2408i	−1.15324	−	0.356716i
$994$	9.50688	+	6.64808i	0.301540	+	0.210864i
$995$	0.0494108	+	0.280223i	0.00156643	+	0.00888365i
$996$	−40.7856	+	17.2140i	−1.29234	+	0.545447i
$997$	31.2649	+	26.2344i	0.990170	+	0.830851i	0.985592	−	0.169139i	$-0.0540985\pi$
$997$	31.2649	+	26.2344i	0.990170	+	0.830851i	0.00457737	+	0.999990i	$0.498543\pi$
$998$	−17.6497	−	4.71760i	−0.558692	−	0.149333i
$999$	−4.46189	−	30.0822i	−0.141168	−	0.951758i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.659.23	yes	648
4.3	odd	2	inner	756.2.cf.a.659.39	yes	648
27.5	odd	18	inner	756.2.cf.a.491.39	yes	648
108.59	even	18	inner	756.2.cf.a.491.23	✓	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.23	✓	648	108.59	even	18	inner
756.2.cf.a.491.39	yes	648	27.5	odd	18	inner
756.2.cf.a.659.23	yes	648	1.1	even	1	trivial
756.2.cf.a.659.39	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+(-1.15796 + 0.811871i) q^{2} +(-1.71844 - 0.216716i) q^{3} +(0.681730 - 1.88022i) q^{4} +(0.0372347 - 0.102301i) q^{5} +(2.16582 - 1.14420i) q^{6} +(-0.984808 - 0.173648i) q^{7} +(0.737087 + 2.73070i) q^{8} +(2.90607 + 0.744826i) q^{9} +(0.0399395 + 0.148691i) q^{10} +(1.44739 - 0.526808i) q^{11} +(-1.57899 + 3.08331i) q^{12} +(-3.59352 + 3.01532i) q^{13} +(1.28135 - 0.598460i) q^{14} +(-0.0861559 + 0.167730i) q^{15} +(-3.07049 - 2.56361i) q^{16} +(1.89301 - 1.09293i) q^{17} +(-3.96981 + 1.49688i) q^{18} +(-5.71979 - 3.30232i) q^{19} +(-0.166966 - 0.139752i) q^{20} +(1.65470 + 0.511827i) q^{21} +(-1.24832 + 1.78512i) q^{22} +(0.158950 + 0.901452i) q^{23} +(-0.674855 - 4.85227i) q^{24} +(3.82114 + 3.20632i) q^{25} +(1.71309 - 6.40909i) q^{26} +(-4.83249 - 1.90973i) q^{27} +(-0.997870 + 1.73328i) q^{28} +(5.10650 - 6.08569i) q^{29} +(-0.0364100 - 0.264171i) q^{30} +(1.99748 - 0.352209i) q^{31} +(5.63682 + 0.475707i) q^{32} +(-2.60142 + 0.591614i) q^{33} +(-1.30471 + 2.80245i) q^{34} +(-0.0544335 + 0.0942816i) q^{35} +(3.38159 - 4.95629i) q^{36} +(2.92633 + 5.06854i) q^{37} +(9.30434 - 0.819787i) q^{38} +(6.82871 - 4.40287i) q^{39} +(0.306799 + 0.0262715i) q^{40} +(6.36935 + 7.59070i) q^{41} +(-2.33161 + 0.750730i) q^{42} +(-0.354332 - 0.973518i) q^{43} +(-0.00378674 - 3.08056i) q^{44} +(0.184403 - 0.269562i) q^{45} +(-0.915921 - 0.914795i) q^{46} +(0.676829 - 3.83849i) q^{47} +(4.72088 + 5.07083i) q^{48} +(0.939693 + 0.342020i) q^{49} +(-7.02784 - 0.610504i) q^{50} +(-3.48988 + 1.46789i) q^{51} +(3.21967 + 8.81225i) q^{52} -5.33962i q^{53} +(7.14627 - 1.71197i) q^{54} -0.167686i q^{55} +(-0.251709 - 2.81720i) q^{56} +(9.11345 + 6.91441i) q^{57} +(-0.972310 + 11.1928i) q^{58} +(13.1469 + 4.78506i) q^{59} +(0.256634 + 0.276339i) q^{60} +(1.31772 - 7.47315i) q^{61} +(-2.02704 + 2.02954i) q^{62} +(-2.73258 - 1.23814i) q^{63} +(-6.91341 + 4.02552i) q^{64} +(0.174668 + 0.479897i) q^{65} +(2.53202 - 2.79708i) q^{66} +(4.10480 + 4.89191i) q^{67} +(-0.764434 - 4.30437i) q^{68} +(-0.0777876 - 1.58354i) q^{69} +(-0.0135129 - 0.153367i) q^{70} +(4.10149 + 7.10399i) q^{71} +(0.108133 + 8.48459i) q^{72} +(-2.00789 + 3.47777i) q^{73} +(-7.50357 - 3.49336i) q^{74} +(-5.87154 - 6.33797i) q^{75} +(-10.1085 + 8.50320i) q^{76} +(-1.51688 + 0.267467i) q^{77} +(-4.33279 + 10.6424i) q^{78} +(8.81797 - 10.5088i) q^{79} +(-0.376590 + 0.218660i) q^{80} +(7.89047 + 4.32903i) q^{81} +(-13.5381 - 3.61861i) q^{82} +(9.78967 + 8.21451i) q^{83} +(2.09041 - 2.76228i) q^{84} +(-0.0413228 - 0.234353i) q^{85} +(1.20067 + 0.839620i) q^{86} +(-10.0941 + 9.35122i) q^{87} +(2.50541 + 3.56408i) q^{88} +(-2.13011 - 1.22982i) q^{89} +(0.00531831 + 0.461853i) q^{90} +(4.06253 - 2.34550i) q^{91} +(1.80329 + 0.315684i) q^{92} +(-3.50887 + 0.172365i) q^{93} +(2.33262 + 4.99430i) q^{94} +(-0.550807 + 0.462182i) q^{95} +(-9.58344 - 2.03906i) q^{96} +(13.3215 - 4.84861i) q^{97} +(-1.36580 + 0.366865i) q^{98} +(4.59860 - 0.452884i) 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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