LMFDB - Embedded newform 950.2.w.a.113.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.2
Character	$\chi$	$=$	950.113
Dual form			950.2.w.a.227.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(-2.72789 - 1.38993i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.41037 - 1.73518i) q^{5} +(-0.946081 + 2.91174i) q^{6} +(0.545569 - 0.545569i) q^{7} +(0.453990 + 0.891007i) q^{8} +(3.74612 + 5.15610i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(-2.72789 - 1.38993i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.41037 - 1.73518i) q^{5} +(-0.946081 + 2.91174i) q^{6} +(0.545569 - 0.545569i) q^{7} +(0.453990 + 0.891007i) q^{8} +(3.74612 + 5.15610i) q^{9} +(-1.49318 + 1.66445i) q^{10} +(2.07364 + 1.50659i) q^{11} +(3.02389 + 0.478937i) q^{12} +(0.199997 - 1.26273i) q^{13} +(-0.624198 - 0.453506i) q^{14} +(1.43557 + 6.69370i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.51690 + 4.93970i) q^{17} +(4.50659 - 4.50659i) q^{18} +(4.16061 + 1.29975i) q^{19} +(1.87754 + 1.21442i) q^{20} +(-2.24655 + 0.729950i) q^{21} +(1.16365 - 2.28379i) q^{22} +(-0.300522 - 1.89742i) q^{23} -3.06158i q^{24} +(-1.02169 + 4.89450i) q^{25} -1.27847 q^{26} +(-1.61559 - 10.2004i) q^{27} +(-0.350277 + 0.687457i) q^{28} +(1.44466 + 4.44620i) q^{29} +(6.38671 - 2.46502i) q^{30} +(7.41739 + 2.41006i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.56261 - 6.99202i) q^{33} +(4.48515 - 3.25865i) q^{34} +(-1.71612 - 0.177204i) q^{35} +(-5.15610 - 3.74612i) q^{36} +(-5.17761 - 0.820053i) q^{37} +(0.632886 - 4.31271i) q^{38} +(-2.30067 + 3.16660i) q^{39} +(0.905760 - 2.04441i) q^{40} +(-2.44261 - 3.36196i) q^{41} +(1.07240 + 2.10471i) q^{42} +(-5.46001 - 5.46001i) q^{43} +(-2.43771 - 0.792060i) q^{44} +(3.66332 - 13.7722i) q^{45} +(-1.82705 + 0.593644i) q^{46} +(6.30887 + 3.21453i) q^{47} +(-3.02389 + 0.478937i) q^{48} +6.40471i q^{49} +(4.99407 + 0.243445i) q^{50} -16.9733i q^{51} +(0.199997 + 1.26273i) q^{52} +(4.33652 + 2.20957i) q^{53} +(-9.82212 + 3.19140i) q^{54} +(-0.310408 - 5.72299i) q^{55} +(0.733789 + 0.238422i) q^{56} +(-9.54312 - 9.32852i) q^{57} +(4.16547 - 2.12241i) q^{58} +(-1.02939 + 0.747898i) q^{59} +(-3.43377 - 5.92247i) q^{60} +(-4.11298 - 2.98825i) q^{61} +(1.22005 - 7.70309i) q^{62} +(4.85678 + 0.769238i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-2.47313 + 1.43389i) q^{65} +(-6.34862 + 4.61254i) q^{66} +(6.78351 - 3.45637i) q^{67} +(-3.92017 - 3.92017i) q^{68} +(-1.81749 + 5.59366i) q^{69} +(0.0934377 + 1.72271i) q^{70} +(-7.79082 + 2.53139i) q^{71} +(-2.89341 + 5.67864i) q^{72} +(-1.71010 - 10.7971i) q^{73} +5.24215i q^{74} +(9.59007 - 11.9316i) q^{75} +(-4.35862 + 0.0495624i) q^{76} +(1.95326 - 0.309366i) q^{77} +(3.48752 + 1.77698i) q^{78} +(0.660744 + 2.03356i) q^{79} +(-2.16093 - 0.574792i) q^{80} +(-3.86238 + 11.8872i) q^{81} +(-2.93846 + 2.93846i) q^{82} +(10.8409 - 5.52370i) q^{83} +(1.91103 - 1.38845i) q^{84} +(5.02149 - 11.3341i) q^{85} +(-4.53866 + 6.24693i) q^{86} +(2.23904 - 14.1367i) q^{87} +(-0.400966 + 2.53160i) q^{88} +(7.48216 + 5.43610i) q^{89} +(-14.1757 - 1.46377i) q^{90} +(-0.579794 - 0.798018i) q^{91} +(0.872149 + 1.71169i) q^{92} +(-16.8840 - 16.8840i) q^{93} +(2.18803 - 6.73406i) q^{94} +(-3.61271 - 9.05253i) q^{95} +(0.946081 + 2.91174i) q^{96} +(-6.11035 + 11.9922i) q^{97} +(6.32586 - 1.00192i) q^{98} +16.3357i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	−2.72789	−	1.38993i	−1.57495	−	0.802476i	−0.575070	−	0.818104i	$-0.695025\pi$
$3$	−2.72789	−	1.38993i	−1.57495	−	0.802476i	−0.999878	+	0.0156282i	$0.995025\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	−1.41037	−	1.73518i	−0.630738	−	0.775996i
$5$	−1.41037	−	1.73518i	−0.630738	−	0.775996i
$6$	−0.946081	+	2.91174i	−0.386236	+	1.18871i
$7$	0.545569	−	0.545569i	0.206206	−	0.206206i	−0.596447	−	0.802653i	$-0.703421\pi$
$7$	0.545569	−	0.545569i	0.206206	−	0.206206i	0.802653	+	0.596447i	$0.203421\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	3.74612	+	5.15610i	1.24871	+	1.71870i
$10$	−1.49318	+	1.66445i	−0.472187	+	0.526346i
$11$	2.07364	+	1.50659i	0.625226	+	0.454253i	0.854743	−	0.519051i	$-0.173715\pi$
$11$	2.07364	+	1.50659i	0.625226	+	0.454253i	−0.229517	+	0.973305i	$0.573715\pi$
$12$	3.02389	+	0.478937i	0.872922	+	0.138257i
$13$	0.199997	−	1.26273i	0.0554691	−	0.350218i	−0.944307	−	0.329065i	$-0.893266\pi$
$13$	0.199997	−	1.26273i	0.0554691	−	0.350218i	0.999776	−	0.0211527i	$-0.00673361\pi$
$14$	−0.624198	−	0.453506i	−0.166824	−	0.121205i
$15$	1.43557	+	6.69370i	0.370662	+	1.72830i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	2.51690	+	4.93970i	0.610439	+	1.19805i	0.964810	+	0.262948i	$0.0846949\pi$
$17$	2.51690	+	4.93970i	0.610439	+	1.19805i	−0.354371	+	0.935105i	$0.615305\pi$
$18$	4.50659	−	4.50659i	1.06221	−	1.06221i
$19$	4.16061	+	1.29975i	0.954509	+	0.298183i
$19$	4.16061	+	1.29975i	0.954509	+	0.298183i
$20$	1.87754	+	1.21442i	0.419832	+	0.271553i
$21$	−2.24655	+	0.729950i	−0.490238	+	0.159288i
$22$	1.16365	−	2.28379i	0.248091	−	0.486906i
$23$	−0.300522	−	1.89742i	−0.0626632	−	0.395640i	−0.999007	−	0.0445552i	$-0.985813\pi$
$23$	−0.300522	−	1.89742i	−0.0626632	−	0.395640i	0.936344	−	0.351085i	$-0.114187\pi$
$24$		−	3.06158i		−	0.624943i
$25$	−1.02169	+	4.89450i	−0.204338	+	0.978900i
$26$	−1.27847			−0.250728
$27$	−1.61559	−	10.2004i	−0.310921	−	1.96308i
$28$	−0.350277	+	0.687457i	−0.0661961	+	0.129917i
$29$	1.44466	+	4.44620i	0.268266	+	0.825639i	0.990923	+	0.134431i	$0.0429208\pi$
$29$	1.44466	+	4.44620i	0.268266	+	0.825639i	−0.722657	+	0.691207i	$0.757079\pi$
$30$	6.38671	−	2.46502i	1.16605	−	0.450049i
$31$	7.41739	+	2.41006i	1.33220	+	0.432859i	0.886668	−	0.462406i	$-0.153014\pi$
$31$	7.41739	+	2.41006i	1.33220	+	0.432859i	0.445534	+	0.895265i	$0.353014\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.56261	−	6.99202i	−0.620171	−	1.21715i
$34$	4.48515	−	3.25865i	0.769198	−	0.558855i
$35$	−1.71612	−	0.177204i	−0.290077	−	0.0299529i
$36$	−5.15610	−	3.74612i	−0.859349	−	0.624354i
$37$	−5.17761	−	0.820053i	−0.851194	−	0.134816i	−0.284431	−	0.958697i	$-0.591805\pi$
$37$	−5.17761	−	0.820053i	−0.851194	−	0.134816i	−0.566763	+	0.823881i	$0.691805\pi$
$38$	0.632886	−	4.31271i	0.102668	−	0.699614i
$39$	−2.30067	+	3.16660i	−0.368402	+	0.507062i
$40$	0.905760	−	2.04441i	0.143213	−	0.323249i
$41$	−2.44261	−	3.36196i	−0.381472	−	0.525051i	0.574502	−	0.818503i	$-0.305196\pi$
$41$	−2.44261	−	3.36196i	−0.381472	−	0.525051i	−0.955974	+	0.293452i	$0.905196\pi$
$42$	1.07240	+	2.10471i	0.165475	+	0.324763i
$43$	−5.46001	−	5.46001i	−0.832644	−	0.832644i	0.155233	−	0.987878i	$-0.450387\pi$
$43$	−5.46001	−	5.46001i	−0.832644	−	0.832644i	−0.987878	+	0.155233i	$0.950387\pi$
$44$	−2.43771	−	0.792060i	−0.367499	−	0.119408i
$45$	3.66332	−	13.7722i	0.546095	−	2.05304i
$46$	−1.82705	+	0.593644i	−0.269384	+	0.0875281i
$47$	6.30887	+	3.21453i	0.920243	+	0.468887i	0.848894	−	0.528564i	$-0.177269\pi$
$47$	6.30887	+	3.21453i	0.920243	+	0.468887i	0.0713499	+	0.997451i	$0.477269\pi$
$48$	−3.02389	+	0.478937i	−0.436461	+	0.0691286i
$49$			6.40471i			0.914958i
$50$	4.99407	+	0.243445i	0.706268	+	0.0344283i
$51$		−	16.9733i		−	2.37673i
$52$	0.199997	+	1.26273i	0.0277345	+	0.175109i
$53$	4.33652	+	2.20957i	0.595666	+	0.303507i	0.725710	−	0.688001i	$-0.241512\pi$
$53$	4.33652	+	2.20957i	0.595666	+	0.303507i	−0.130043	+	0.991508i	$0.541512\pi$
$54$	−9.82212	+	3.19140i	−1.33662	+	0.434295i
$55$	−0.310408	−	5.72299i	−0.0418554	−	0.771687i
$56$	0.733789	+	0.238422i	0.0980567	+	0.0318605i
$57$	−9.54312	−	9.32852i	−1.26402	−	1.23559i
$58$	4.16547	−	2.12241i	0.546952	−	0.278686i
$59$	−1.02939	+	0.747898i	−0.134016	+	0.0973681i	−0.652773	−	0.757553i	$-0.726395\pi$
$59$	−1.02939	+	0.747898i	−0.134016	+	0.0973681i	0.518758	+	0.854921i	$0.326395\pi$
$60$	−3.43377	−	5.92247i	−0.443298	−	0.764587i
$61$	−4.11298	−	2.98825i	−0.526613	−	0.382606i	0.292477	−	0.956273i	$-0.405521\pi$
$61$	−4.11298	−	2.98825i	−0.526613	−	0.382606i	−0.819089	+	0.573666i	$0.805521\pi$
$62$	1.22005	−	7.70309i	0.154946	−	0.978293i
$63$	4.85678	+	0.769238i	0.611896	+	0.0969148i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	−2.47313	+	1.43389i	−0.306754	+	0.177852i
$66$	−6.34862	+	4.61254i	−0.781461	+	0.567765i
$67$	6.78351	−	3.45637i	0.828738	−	0.422263i	0.0124598	−	0.999922i	$-0.496034\pi$
$67$	6.78351	−	3.45637i	0.828738	−	0.422263i	0.816278	+	0.577659i	$0.196034\pi$
$68$	−3.92017	−	3.92017i	−0.475390	−	0.475390i
$69$	−1.81749	+	5.59366i	−0.218800	+	0.673398i
$70$	0.0934377	+	1.72271i	0.0111679	+	0.205903i
$71$	−7.79082	+	2.53139i	−0.924600	+	0.300421i	−0.732352	−	0.680926i	$-0.761578\pi$
$71$	−7.79082	+	2.53139i	−0.924600	+	0.300421i	−0.192247	+	0.981346i	$0.561578\pi$
$72$	−2.89341	+	5.67864i	−0.340992	+	0.669234i
$73$	−1.71010	−	10.7971i	−0.200152	−	1.26371i	−0.859212	−	0.511619i	$-0.829046\pi$
$73$	−1.71010	−	10.7971i	−0.200152	−	1.26371i	0.659060	−	0.752090i	$-0.270954\pi$
$74$			5.24215i			0.609387i
$75$	9.59007	−	11.9316i	1.10737	−	1.37774i
$76$	−4.35862	+	0.0495624i	−0.499968	+	0.00568520i
$77$	1.95326	−	0.309366i	0.222595	−	0.0352555i
$78$	3.48752	+	1.77698i	0.394884	+	0.201204i
$79$	0.660744	+	2.03356i	0.0743395	+	0.228794i	0.981321	−	0.192377i	$-0.0616195\pi$
$79$	0.660744	+	2.03356i	0.0743395	+	0.228794i	−0.906982	+	0.421170i	$0.861620\pi$
$80$	−2.16093	−	0.574792i	−0.241599	−	0.0642637i
$81$	−3.86238	+	11.8872i	−0.429153	+	1.32080i
$82$	−2.93846	+	2.93846i	−0.324499	+	0.324499i
$83$	10.8409	−	5.52370i	1.18994	−	0.606304i	0.257026	−	0.966405i	$-0.417257\pi$
$83$	10.8409	−	5.52370i	1.18994	−	0.606304i	0.932914	+	0.360100i	$0.117257\pi$
$84$	1.91103	−	1.38845i	0.208511	−	0.151492i
$85$	5.02149	−	11.3341i	0.544657	−	1.22936i
$86$	−4.53866	+	6.24693i	−0.489416	+	0.673623i
$87$	2.23904	−	14.1367i	0.240050	−	1.51561i
$88$	−0.400966	+	2.53160i	−0.0427432	+	0.269870i
$89$	7.48216	+	5.43610i	0.793107	+	0.576226i	0.908884	−	0.417049i	$-0.136936\pi$
$89$	7.48216	+	5.43610i	0.793107	+	0.576226i	−0.115777	+	0.993275i	$0.536936\pi$
$90$	−14.1757	−	1.46377i	−1.49425	−	0.154294i
$91$	−0.579794	−	0.798018i	−0.0607789	−	0.0836550i
$92$	0.872149	+	1.71169i	0.0909279	+	0.178456i
$93$	−16.8840	−	16.8840i	−1.75079	−	1.75079i
$94$	2.18803	−	6.73406i	0.225678	−	0.694565i
$95$	−3.61271	−	9.05253i	−0.370656	−	0.928770i
$96$	0.946081	+	2.91174i	0.0965590	+	0.297178i
$97$	−6.11035	+	11.9922i	−0.620412	+	1.21763i	0.340363	+	0.940294i	$0.389450\pi$
$97$	−6.11035	+	11.9922i	−0.620412	+	1.21763i	−0.960774	+	0.277332i	$0.910550\pi$
$98$	6.32586	−	1.00192i	0.639008	−	0.101209i
$99$			16.3357i			1.64180i
$100$	−0.540797	−	4.97067i	−0.0540797	−	0.497067i
$101$	0.646323			0.0643115			0.0321558	−	0.999483i	$-0.489763\pi$
$101$	0.646323			0.0643115			0.0321558	+	0.999483i	$0.489763\pi$
$102$	−16.7643	+	2.65520i	−1.65991	+	0.262904i
$103$	13.8369	+	7.05024i	1.36339	+	0.694680i	0.974033	−	0.226408i	$-0.0726982\pi$
$103$	13.8369	+	7.05024i	1.36339	+	0.694680i	0.389354	+	0.921088i	$0.372698\pi$
$104$	1.21590	−	0.395069i	0.119228	−	0.0387397i
$105$	4.43508	+	2.86867i	0.432819	+	0.279954i
$106$	1.50398	−	4.62878i	0.146080	−	0.449587i
$107$	8.74787	+	8.74787i	0.845689	+	0.845689i	0.989592	−	0.143903i	$-0.0459654\pi$
$107$	8.74787	+	8.74787i	0.845689	+	0.845689i	−0.143903	+	0.989592i	$0.545965\pi$
$108$	4.68863	+	9.20195i	0.451163	+	0.885458i
$109$	2.64853	−	1.92427i	0.253683	−	0.184312i	−0.453674	−	0.891168i	$-0.649887\pi$
$109$	2.64853	−	1.92427i	0.253683	−	0.184312i	0.707358	+	0.706856i	$0.249887\pi$
$110$	−5.60397	+	1.20186i	−0.534317	+	0.114593i
$111$	12.9841	+	9.43352i	1.23240	+	0.895390i
$112$	0.120697	−	0.762052i	0.0114048	−	0.0720072i
$113$	−2.86686	+	18.1007i	−0.269692	+	1.70277i	0.365828	+	0.930682i	$0.380786\pi$
$113$	−2.86686	+	18.1007i	−0.269692	+	1.70277i	−0.635520	+	0.772085i	$0.719214\pi$
$114$	−7.72080	+	10.8849i	−0.723119	+	1.01947i
$115$	−2.86852	+	3.19753i	−0.267491	+	0.298172i
$116$	−2.74790	−	3.78216i	−0.255136	−	0.351165i
$117$	7.25996	−	3.69914i	0.671184	−	0.341985i
$118$	0.899723	+	0.899723i	0.0828262	+	0.0828262i
$119$	4.06809	+	1.32180i	0.372921	+	0.121170i
$120$	−5.31239	+	4.31797i	−0.484953	+	0.394175i
$121$	−1.36901	−	4.21338i	−0.124456	−	0.383035i
$122$	−2.30805	+	4.52980i	−0.208961	+	0.410109i
$123$	1.99028	+	12.5661i	0.179457	+	1.13305i
$124$	−7.79911			−0.700380
$125$	9.93380	−	5.13026i	0.888506	−	0.458864i
$126$		−	4.91732i		−	0.438069i
$127$	−2.58153	−	16.2991i	−0.229073	−	1.44631i	−0.787273	−	0.616605i	$-0.788508\pi$
$127$	−2.58153	−	16.2991i	−0.229073	−	1.44631i	0.558199	−	0.829707i	$-0.311492\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$	7.30528	+	22.4834i	0.643194	+	1.97955i
$130$	1.80312	+	2.21837i	0.158144	+	0.194564i
$131$	−0.184556	+	0.568006i	−0.0161248	+	0.0496269i	−0.958795	−	0.284098i	$-0.908306\pi$
$131$	−0.184556	+	0.568006i	−0.0161248	+	0.0496269i	0.942670	+	0.333725i	$0.108306\pi$
$132$	5.54890	+	5.54890i	0.482969	+	0.482969i
$133$	2.97900	−	1.56080i	0.258312	−	0.135338i
$134$	−4.47499	−	6.15930i	−0.386580	−	0.532082i
$135$	−15.4210	+	17.1898i	−1.32723	+	1.47946i
$136$	−3.25865	+	4.48515i	−0.279427	+	0.384599i
$137$	−2.72762	+	17.2215i	−0.233037	+	1.47134i	0.542512	+	0.840048i	$0.317473\pi$
$137$	−2.72762	+	17.2215i	−0.233037	+	1.47134i	−0.775549	+	0.631288i	$0.782527\pi$
$138$	5.80911	+	0.920073i	0.494505	+	0.0783218i
$139$	8.63106	−	11.8796i	0.732077	−	1.00762i	−0.266959	−	0.963708i	$-0.586019\pi$
$139$	8.63106	−	11.8796i	0.732077	−	1.00762i	0.999036	−	0.0439095i	$-0.0139813\pi$
$140$	1.68688	−	0.361778i	0.142568	−	0.0305759i
$141$	−12.7419	−	17.5378i	−1.07306	−	1.47695i
$142$	3.71898	+	7.29890i	0.312090	+	0.612510i
$143$	2.31713	−	2.31713i	0.193768	−	0.193768i
$144$	6.06135	+	1.96945i	0.505113	+	0.164121i
$145$	5.67744	−	8.77754i	0.471486	−	0.728935i
$146$	−10.3967	+	3.37809i	−0.860436	+	0.279573i
$147$	8.90209	−	17.4713i	0.734232	−	1.44101i
$148$	5.17761	−	0.820053i	0.425597	−	0.0674079i
$149$			10.0546i			0.823705i	0.911250	+	0.411853i	$0.135118\pi$
$149$			10.0546i			0.823705i	−0.911250	+	0.411853i	$0.864882\pi$
$150$	−13.2849	−	7.60549i	−1.08471	−	0.620986i
$151$		−	17.7302i		−	1.44287i	−0.692484	−	0.721433i	$-0.743484\pi$
$151$		−	17.7302i		−	1.44287i	0.692484	−	0.721433i	$-0.256516\pi$
$152$	0.730790	+	4.29720i	0.0592749	+	0.348549i
$153$	−16.0409	+	31.4821i	−1.29683	+	2.54518i
$154$	−0.611115	−	1.88082i	−0.0492450	−	0.151561i
$155$	−6.27941	−	16.2696i	−0.504375	−	1.30680i
$156$	1.20953	−	3.72257i	0.0968403	−	0.298044i
$157$	11.5008	−	11.5008i	0.917866	−	0.917866i	−0.0790083	−	0.996874i	$-0.525175\pi$
$157$	11.5008	−	11.5008i	0.917866	−	0.917866i	0.996874	+	0.0790083i	$0.0251754\pi$
$158$	1.90516	−	0.970728i	0.151567	−	0.0772270i
$159$	−8.75840	−	12.0549i	−0.694586	−	0.956016i
$160$	−0.229672	+	2.22424i	−0.0181572	+	0.175842i
$161$	−1.19913	−	0.871219i	−0.0945047	−	0.0686617i
$162$	12.3450	+	1.95526i	0.969917	+	0.153620i
$163$	−8.28315	−	1.31192i	−0.648786	−	0.102758i	−0.176637	−	0.984276i	$-0.556522\pi$
$163$	−8.28315	−	1.31192i	−0.648786	−	0.102758i	−0.472150	+	0.881518i	$0.656522\pi$
$164$	3.36196	+	2.44261i	0.262525	+	0.190736i
$165$	−7.10779	+	16.0431i	−0.553341	+	1.24896i
$166$	−7.15157	−	9.84330i	−0.555070	−	0.763988i
$167$	5.42384	−	2.76359i	0.419710	−	0.213853i	−0.231364	−	0.972867i	$-0.574319\pi$
$167$	5.42384	−	2.76359i	0.419710	−	0.213853i	0.651074	+	0.759014i	$0.274319\pi$
$168$	−1.67030	−	1.67030i	−0.128867	−	0.128867i
$169$	10.8092	+	3.51214i	0.831481	+	0.270164i
$170$	−11.9801	−	3.18662i	−0.918831	−	0.244403i
$171$	8.88451	+	26.3215i	0.679415	+	2.01286i
$172$	6.88002	+	3.50555i	0.524597	+	0.267295i
$173$	−16.1689	+	2.56090i	−1.22930	+	0.194701i	−0.737100	−	0.675783i	$-0.763806\pi$
$173$	−16.1689	+	2.56090i	−1.22930	+	0.194701i	−0.492196	+	0.870485i	$0.663806\pi$
$174$	−14.3129			−1.08506
$175$	2.11289	+	3.22769i	0.159719	+	0.243991i
$176$	2.56316			0.193205
$177$	3.84760	−	0.609400i	0.289203	−	0.0458053i
$178$	4.19871	−	8.24043i	0.314707	−	0.617647i
$179$	2.50803	+	7.71894i	0.187459	+	0.576940i	0.999982	−	0.00598911i	$-0.00190640\pi$
$179$	2.50803	+	7.71894i	0.187459	+	0.576940i	−0.812523	+	0.582929i	$0.801906\pi$
$180$	0.771828	+	14.2302i	0.0575287	+	1.06066i
$181$	12.5125	+	4.06556i	0.930047	+	0.302190i	0.734582	−	0.678520i	$-0.237378\pi$
$181$	12.5125	+	4.06556i	0.930047	+	0.302190i	0.195465	+	0.980711i	$0.437378\pi$
$182$	−0.697493	+	0.697493i	−0.0517016	+	0.0517016i
$183$	7.06629	+	13.8684i	0.522355	+	1.02518i
$184$	1.55418	−	1.12918i	0.114576	−	0.0832442i
$185$	5.87942	+	10.1407i	0.432264	+	0.745556i
$186$	−14.0349	+	19.3174i	−1.02909	+	1.41642i
$187$	−2.22294	+	14.0351i	−0.162557	+	1.02635i
$188$	−6.99344	−	1.10765i	−0.510049	−	0.0807838i
$189$	−6.44646	−	4.68363i	−0.468911	−	0.340684i
$190$	−8.37593	+	4.98436i	−0.607654	+	0.361604i
$191$	−7.45687	+	5.41773i	−0.539560	+	0.392013i	−0.823922	−	0.566704i	$-0.808218\pi$
$191$	−7.45687	+	5.41773i	−0.539560	+	0.392013i	0.284361	+	0.958717i	$0.408218\pi$
$192$	2.72789	−	1.38993i	0.196868	−	0.100310i
$193$	0.482365	−	0.482365i	0.0347214	−	0.0347214i	−0.689533	−	0.724254i	$-0.742184\pi$
$193$	0.482365	−	0.482365i	0.0347214	−	0.0347214i	0.724254	+	0.689533i	$0.242184\pi$
$194$	12.8005	+	4.15912i	0.919019	+	0.298607i
$195$	8.73943	−	0.474016i	0.625844	−	0.0339450i
$196$	−1.97916	−	6.09124i	−0.141369	−	0.435089i
$197$	−15.4206	−	7.85719i	−1.09867	−	0.559802i	−0.191897	−	0.981415i	$-0.561464\pi$
$197$	−15.4206	−	7.85719i	−1.09867	−	0.559802i	−0.906776	+	0.421613i	$0.861464\pi$
$198$	16.1346	−	2.55547i	1.14664	−	0.181610i
$199$			3.68043i			0.260899i	0.991455	+	0.130449i	$0.0416420\pi$
$199$			3.68043i			0.260899i	−0.991455	+	0.130449i	$0.958358\pi$
$200$	−4.82487	+	1.31172i	−0.341170	+	0.0927528i
$201$	−23.3088			−1.64407
$202$	−0.101107	−	0.638366i	−0.00711388	−	0.0449152i
$203$	3.21387	+	1.63755i	0.225569	+	0.114933i
$204$	5.24503	+	16.1425i	0.367226	+	1.13020i
$205$	−2.38862	+	8.97999i	−0.166828	+	0.627190i
$206$	4.79887	−	14.7694i	0.334353	−	1.02903i
$207$	8.65750	−	8.65750i	0.601738	−	0.601738i
$208$	−0.580413	−	1.13912i	−0.0402444	−	0.0789840i
$209$	6.66941	+	8.96353i	0.461333	+	0.620020i
$210$	2.13956	−	4.82923i	0.147643	−	0.333249i
$211$	6.79075	−	9.34667i	0.467495	−	0.643451i	−0.508547	−	0.861034i	$-0.669817\pi$
$211$	6.79075	−	9.34667i	0.467495	−	0.643451i	0.976042	+	0.217583i	$0.0698172\pi$
$212$	−4.80707	−	0.761364i	−0.330151	−	0.0522907i
$213$	24.7709	+	3.92333i	1.69728	+	0.268822i
$214$	7.27170	−	10.0086i	0.497083	−	0.684177i
$215$	−1.77344	+	17.1748i	−0.120948	+	1.17131i
$216$	8.35520	−	6.07041i	0.568499	−	0.413039i
$217$	5.36155	−	2.73185i	0.363966	−	0.185450i
$218$	−2.31490	−	2.31490i	−0.156785	−	0.156785i
$219$	−10.3423	+	31.8303i	−0.698868	+	2.15089i
$220$	2.06372	+	5.34696i	0.139136	+	0.360492i
$221$	6.74087	−	2.19024i	0.453440	−	0.147332i
$222$	7.28621	−	14.3000i	0.489019	−	0.959753i
$223$	13.5025	−	2.13859i	0.904198	−	0.143211i	0.313015	−	0.949748i	$-0.398661\pi$
$223$	13.5025	−	2.13859i	0.904198	−	0.143211i	0.591183	+	0.806538i	$0.298661\pi$
$224$	−0.771551			−0.0515514
$225$	−29.0639	+	13.0675i	−1.93759	+	0.871164i
$226$	18.3263			1.21905
$227$	1.20519	+	7.60927i	0.0799913	+	0.505045i	0.994857	+	0.101287i	$0.0322961\pi$
$227$	1.20519	+	7.60927i	0.0799913	+	0.505045i	−0.914866	+	0.403758i	$0.867704\pi$
$228$	11.9587	+	5.92297i	0.791985	+	0.392258i
$229$	−19.4265	+	6.31204i	−1.28374	+	0.417111i	−0.869895	−	0.493237i	$-0.835813\pi$
$229$	−19.4265	+	6.31204i	−1.28374	+	0.417111i	−0.413842	+	0.910349i	$0.635813\pi$
$230$	3.60690	+	2.33300i	0.237832	+	0.153833i
$231$	−5.75828	−	1.87098i	−0.378867	−	0.123101i
$232$	−3.30573	+	3.30573i	−0.217032	+	0.217032i
$233$	12.2853	−	6.25965i	0.804834	−	0.410083i	−0.00263262	−	0.999997i	$-0.500838\pi$
$233$	12.2853	−	6.25965i	0.804834	−	0.410083i	0.807467	+	0.589913i	$0.200838\pi$
$234$	−4.78930	−	6.59191i	−0.313086	−	0.430927i
$235$	−3.32008	−	15.4807i	−0.216578	−	1.00985i
$236$	0.747898	−	1.02939i	0.0486840	−	0.0670078i
$237$	1.02407	−	6.46572i	0.0665204	−	0.419994i
$238$	0.669140	−	4.22478i	0.0433739	−	0.273852i
$239$	8.78612	−	12.0931i	0.568327	−	0.782235i	−0.424028	−	0.905649i	$-0.639384\pi$
$239$	8.78612	−	12.0931i	0.568327	−	0.782235i	0.992355	+	0.123414i	$0.0393843\pi$
$240$	5.09585	+	4.57151i	0.328936	+	0.295090i
$241$	11.4941	+	15.8203i	0.740402	+	1.01908i	0.998595	+	0.0529826i	$0.0168728\pi$
$241$	11.4941	+	15.8203i	0.740402	+	1.01908i	−0.258193	+	0.966093i	$0.583127\pi$
$242$	−3.94735	+	2.01128i	−0.253745	+	0.129290i
$243$	5.15033	−	5.15033i	0.330394	−	0.330394i
$244$	4.83509	+	1.57102i	0.309535	+	0.100574i
$245$	11.1133	−	9.03303i	0.710004	−	0.577099i
$246$	12.1001	−	3.93155i	0.771472	−	0.250666i
$247$	2.47334	−	4.99377i	0.157375	−	0.317746i
$248$	1.22005	+	7.70309i	0.0774732	+	0.489146i
$249$	−37.2502			−2.36064
$250$	−6.62108	−	9.00895i	−0.418754	−	0.569776i
$251$	22.0406			1.39119			0.695596	−	0.718433i	$-0.255140\pi$
$251$	22.0406			1.39119			0.695596	+	0.718433i	$0.255140\pi$
$252$	−4.85678	+	0.769238i	−0.305948	+	0.0484574i
$253$	2.23546	−	4.38733i	0.140542	−	0.275829i
$254$	−15.6946	+	5.09948i	−0.984767	+	0.319970i
$255$	−29.4517	+	23.9387i	−1.84433	+	1.49910i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−12.3119	−	12.3119i	−0.767996	−	0.767996i	0.209757	−	0.977753i	$-0.432733\pi$
$257$	−12.3119	−	12.3119i	−0.767996	−	0.767996i	−0.977753	+	0.209757i	$0.932733\pi$
$258$	21.0637	−	10.7325i	1.31137	−	0.668177i
$259$	−3.27214	+	2.37735i	−0.203321	+	0.147721i
$260$	1.90899	−	2.12795i	0.118391	−	0.131970i
$261$	−17.5132	+	24.1048i	−1.08404	+	1.49205i
$262$	0.589884	+	0.0934284i	0.0364431	+	0.00577202i
$263$	11.6001	+	1.83727i	0.715290	+	0.113291i	0.503464	−	0.864016i	$-0.332059\pi$
$263$	11.6001	+	1.83727i	0.715290	+	0.113291i	0.211827	+	0.977307i	$0.432059\pi$
$264$	4.61254	−	6.34862i	0.283882	−	0.390730i
$265$	−2.28212	−	10.6409i	−0.140189	−	0.653668i
$266$	−2.00760	−	2.69816i	−0.123094	−	0.165435i
$267$	−12.8547	−	25.2288i	−0.786695	−	1.54398i
$268$	−5.38342	+	5.38342i	−0.328845	+	0.328845i
$269$	7.08597	−	21.8084i	0.432039	−	1.32968i	−0.464052	−	0.885808i	$-0.653605\pi$
$269$	7.08597	−	21.8084i	0.432039	−	1.32968i	0.896091	−	0.443871i	$-0.146395\pi$
$270$	19.3905	+	12.5421i	1.18007	+	0.763286i
$271$	−4.61479	−	14.2028i	−0.280328	−	0.862762i	−0.987760	−	0.155980i	$-0.950146\pi$
$271$	−4.61479	−	14.2028i	−0.280328	−	0.862762i	0.707432	−	0.706781i	$-0.249854\pi$
$272$	4.93970	+	2.51690i	0.299513	+	0.152610i
$273$	0.472425	+	2.98278i	0.0285925	+	0.180526i
$274$	17.4362			1.05336
$275$	−9.49261	+	8.61016i	−0.572426	+	0.519212i
$276$		−	5.88153i		−	0.354026i
$277$	−6.18125	+	0.979013i	−0.371395	+	0.0588232i	−0.339342	−	0.940663i	$-0.610204\pi$
$277$	−6.18125	+	0.979013i	−0.371395	+	0.0588232i	−0.0320528	+	0.999486i	$0.510204\pi$
$278$	−13.0836	−	6.66641i	−0.784701	−	0.399825i
$279$	15.3600	+	47.2731i	0.919578	+	2.83017i
$280$	−0.621211	−	1.60952i	−0.0371244	−	0.0961872i
$281$	−15.7572	−	5.11983i	−0.939997	−	0.305424i	−0.201353	−	0.979519i	$-0.564534\pi$
$281$	−15.7572	−	5.11983i	−0.939997	−	0.305424i	−0.738644	+	0.674095i	$0.764534\pi$
$282$	−15.3286	+	15.3286i	−0.912803	+	0.912803i
$283$	−0.740855	+	0.377485i	−0.0440393	+	0.0224391i	−0.475871	−	0.879515i	$-0.657867\pi$
$283$	−0.740855	+	0.377485i	−0.0440393	+	0.0224391i	0.431832	+	0.901954i	$0.357867\pi$
$284$	6.62726	−	4.81499i	0.393256	−	0.285717i
$285$	−2.72730	+	29.7157i	−0.161551	+	1.76021i
$286$	−2.65108	−	1.92612i	−0.156762	−	0.113894i
$287$	−3.16680	−	0.501571i	−0.186930	−	0.0296068i
$288$	0.997001	−	6.29482i	0.0587489	−	0.370926i
$289$	−8.07349	+	11.1122i	−0.474911	+	0.653659i
$290$	−9.55762	−	4.23444i	−0.561243	−	0.248655i
$291$	33.3367	−	24.2205i	1.95423	−	1.41983i
$292$	4.96290	+	9.74024i	0.290432	+	0.570004i
$293$	21.9468	−	21.9468i	1.28215	−	1.28215i	0.342702	−	0.939444i	$-0.388658\pi$
$293$	21.9468	−	21.9468i	1.28215	−	1.28215i	0.939444	−	0.342702i	$-0.111342\pi$
$294$	−18.6488	−	6.05937i	−1.08762	−	0.353390i
$295$	2.74957	+	0.731366i	0.160086	+	0.0425818i
$296$	−1.61991	−	4.98558i	−0.0941555	−	0.289781i
$297$	12.0177	−	23.5861i	0.697338	−	1.36860i
$298$	9.93082	−	1.57289i	0.575277	−	0.0911149i
$299$	−2.45603			−0.142036
$300$	−5.43364	+	14.3111i	−0.313711	+	0.826252i
$301$	−5.95763			−0.343392
$302$	−17.5120	+	2.77362i	−1.00770	+	0.159604i
$303$	−1.76310	−	0.898343i	−0.101287	−	0.0516085i
$304$	4.12998	−	1.39402i	0.236870	−	0.0799527i
$305$	0.615681	+	11.3513i	0.0352538	+	0.649974i
$306$	33.6039	+	10.9186i	1.92101	+	0.624173i
$307$	8.97729	+	8.97729i	0.512361	+	0.512361i	0.915249	−	0.402888i	$-0.131994\pi$
$307$	8.97729	+	8.97729i	0.512361	+	0.512361i	−0.402888	+	0.915249i	$0.631994\pi$
$308$	−1.76206	+	0.897816i	−0.100403	+	0.0511578i
$309$	−27.9461	−	38.4645i	−1.58980	−	2.18817i
$310$	−15.0870	+	8.74723i	−0.856882	+	0.496809i
$311$	14.6459	+	10.6409i	0.830493	+	0.603389i	0.919699	−	0.392625i	$-0.128433\pi$
$311$	14.6459	+	10.6409i	0.830493	+	0.603389i	−0.0892056	+	0.996013i	$0.528433\pi$
$312$	−3.86595	−	0.612306i	−0.218866	−	0.0346650i
$313$	−29.1538	−	4.61751i	−1.64787	−	0.260997i	−0.737668	−	0.675163i	$-0.764073\pi$
$313$	−29.1538	−	4.61751i	−1.64787	−	0.260997i	−0.910201	+	0.414167i	$0.864073\pi$
$314$	−13.1584	−	9.56010i	−0.742569	−	0.539508i
$315$	−5.51510	−	9.51229i	−0.310741	−	0.535957i
$316$	−1.25681	−	1.72985i	−0.0707011	−	0.0973117i
$317$	−11.3264	+	5.77109i	−0.636155	+	0.324137i	−0.742154	−	0.670229i	$-0.766196\pi$
$317$	−11.3264	+	5.77109i	−0.636155	+	0.324137i	0.106000	+	0.994366i	$0.466196\pi$
$318$	−10.5364	+	10.5364i	−0.590850	+	0.590850i
$319$	−3.70289	+	11.3963i	−0.207322	+	0.638071i
$320$	2.23279	−	0.121104i	0.124817	−	0.00676990i
$321$	−11.7043	−	36.0222i	−0.653271	−	2.01056i
$322$	−0.672908	+	1.32066i	−0.0374997	+	0.0735973i
$323$	4.05147	+	23.8235i	0.225430	+	1.32557i
$324$		−	12.4989i		−	0.694384i
$325$	5.97609	+	2.26900i	0.331494	+	0.125862i
$326$			8.38640i			0.464480i
$327$	−9.89950	+	1.56793i	−0.547444	+	0.0867066i
$328$	1.88661	−	3.70268i	0.104171	−	0.204446i
$329$	5.19567	−	1.68818i	0.286447	−	0.0930722i
$330$	16.9575	+	4.51058i	0.933480	+	0.248299i
$331$	−27.4880	−	8.93138i	−1.51088	−	0.490913i	−0.567708	−	0.823230i	$-0.692170\pi$
$331$	−27.4880	−	8.93138i	−1.51088	−	0.490913i	−0.943168	+	0.332317i	$0.892170\pi$
$332$	−8.60336	+	8.60336i	−0.472171	+	0.472171i
$333$	−15.1677	−	29.7683i	−0.831184	−	1.63129i
$334$	−3.57804	−	4.92475i	−0.195782	−	0.269470i
$335$	−15.5647	−	6.89583i	−0.850391	−	0.376759i
$336$	−1.38845	+	1.91103i	−0.0757460	+	0.104255i
$337$	25.9482	+	4.10980i	1.41349	+	0.223875i	0.816023	−	0.578019i	$-0.196174\pi$
$337$	25.9482	+	4.10980i	1.41349	+	0.223875i	0.597467	+	0.801894i	$0.296174\pi$
$338$	1.77796	−	11.2256i	0.0967082	−	0.610592i
$339$	32.9791	−	45.3919i	1.79118	−	2.46535i
$340$	−1.27329	+	12.3311i	−0.0690539	+	0.668748i
$341$	11.7500	+	16.1725i	0.636300	+	0.875792i
$342$	24.6076	−	12.8927i	1.33063	−	0.697158i
$343$	7.31320	+	7.31320i	0.394875	+	0.394875i
$344$	2.38611	−	7.34370i	0.128651	−	0.395946i
$345$	12.2693	−	4.73548i	0.660560	−	0.254950i
$346$	5.05873	+	15.5692i	0.271959	+	0.837005i
$347$	−27.5739	−	14.0496i	−1.48024	−	0.754221i	−0.487346	−	0.873209i	$-0.662035\pi$
$347$	−27.5739	−	14.0496i	−1.48024	−	0.754221i	−0.992896	+	0.118988i	$0.962035\pi$
$348$	2.23904	+	14.1367i	0.120025	+	0.757807i
$349$		−	9.86402i		−	0.528009i	−0.964521	−	0.264004i	$-0.914957\pi$
$349$		−	9.86402i		−	0.528009i	0.964521	−	0.264004i	$-0.0850434\pi$
$350$	2.85743	−	2.59179i	0.152736	−	0.138537i
$351$	−13.2035			−0.704751
$352$	−0.400966	−	2.53160i	−0.0213716	−	0.134935i
$353$	−9.60671	+	18.8542i	−0.511314	+	1.00351i	0.480641	+	0.876917i	$0.340404\pi$
$353$	−9.60671	+	18.8542i	−0.511314	+	1.00351i	−0.991955	+	0.126592i	$0.959596\pi$
$354$	−1.20379	−	3.70490i	−0.0639809	−	0.196913i
$355$	15.3804	+	9.94826i	0.816306	+	0.527999i
$356$	−8.79580	−	2.85793i	−0.466177	−	0.151470i
$357$	−9.26009	−	9.26009i	−0.490096	−	0.490096i
$358$	7.23156	−	3.68466i	0.382200	−	0.194741i
$359$	2.81717	+	3.87750i	0.148685	+	0.204647i	0.876862	−	0.480742i	$-0.159632\pi$
$359$	2.81717	+	3.87750i	0.148685	+	0.204647i	−0.728178	+	0.685388i	$0.759632\pi$
$360$	13.9342	−	2.98842i	0.734399	−	0.157503i
$361$	15.6213	+	10.8155i	0.822174	+	0.569237i
$362$	2.05812	−	12.9944i	0.108172	−	0.682973i
$363$	−2.12179	+	13.3965i	−0.111365	+	0.703133i
$364$	0.798018	+	0.579794i	0.0418275	+	0.0303895i
$365$	−16.3231	+	18.1953i	−0.854389	+	0.952387i
$366$	12.5922	−	9.14878i	0.658206	−	0.478214i
$367$	−2.74510	−	5.38756i	−0.143293	−	0.281229i	0.808194	−	0.588916i	$-0.200445\pi$
$367$	−2.74510	−	5.38756i	−0.143293	−	0.281229i	−0.951488	+	0.307687i	$0.900445\pi$
$368$	−1.35840	−	1.35840i	−0.0708117	−	0.0708117i
$369$	8.18429	−	25.1887i	0.426057	−	1.31127i
$370$	9.09607	−	7.39339i	0.472882	−	0.384364i
$371$	3.57134	−	1.16040i	0.185415	−	0.0602449i
$372$	21.2751	+	10.8402i	1.10306	+	0.562038i
$373$	−4.16996	+	0.660456i	−0.215912	+	0.0341971i	−0.263453	−	0.964672i	$-0.584861\pi$
$373$	−4.16996	+	0.660456i	−0.215912	+	0.0341971i	0.0475411	+	0.998869i	$0.484861\pi$
$374$	14.2100			0.734784
$375$	−34.2290	+	0.187492i	−1.76758	+	0.00968206i
$376$			7.08061i			0.365155i
$377$	5.90327	−	0.934986i	0.304034	−	0.0481542i
$378$	−3.61752	+	7.09978i	−0.186065	+	0.365173i
$379$	−0.168392	−	0.518257i	−0.00864972	−	0.0266211i	0.946639	−	0.322297i	$-0.104455\pi$
$379$	−0.168392	−	0.518257i	−0.00864972	−	0.0266211i	−0.955288	+	0.295676i	$0.904455\pi$
$380$	6.23328	+	7.49308i	0.319760	+	0.384387i
$381$	−15.6125	+	48.0503i	−0.799852	+	2.46169i
$382$	6.51754	+	6.51754i	0.333467	+	0.333467i
$383$	4.01263	+	7.87522i	0.205036	+	0.402405i	0.970510	−	0.241062i	$-0.0774956\pi$
$383$	4.01263	+	7.87522i	0.205036	+	0.402405i	−0.765474	+	0.643467i	$0.777496\pi$
$384$	−1.79955	−	2.47687i	−0.0918330	−	0.126397i
$385$	−3.29163	−	2.95294i	−0.167757	−	0.150496i
$386$	−0.551884	−	0.400968i	−0.0280902	−	0.0204087i
$387$	7.69847	−	48.6062i	0.391335	−	2.47079i
$388$	2.10548	−	13.2935i	0.106890	−	0.674875i
$389$	9.24235	−	12.7210i	0.468606	−	0.644981i	−0.507660	−	0.861558i	$-0.669489\pi$
$389$	9.24235	−	12.7210i	0.468606	−	0.644981i	0.976266	+	0.216577i	$0.0694892\pi$
$390$	−1.83533	−	8.55768i	−0.0929355	−	0.433335i
$391$	8.61631	−	6.26012i	0.435746	−	0.316588i
$392$	−5.70664	+	2.90768i	−0.288229	+	0.146860i
$393$	1.29294	−	1.29294i	0.0652200	−	0.0652200i
$394$	−5.34814	+	16.4599i	−0.269436	+	0.829237i
$395$	2.59670	−	4.01459i	0.130654	−	0.201996i
$396$	−5.04802	−	15.5362i	−0.253673	−	0.780724i
$397$	12.2356	+	6.23434i	0.614086	+	0.312893i	0.733226	−	0.679985i	$-0.238014\pi$
$397$	12.2356	+	6.23434i	0.614086	+	0.312893i	−0.119140	+	0.992877i	$0.538014\pi$
$398$	3.63512	−	0.575746i	0.182212	−	0.0288595i
$399$	−10.2958	+	0.117075i	−0.515434	+	0.00586107i
$400$	2.05035	+	4.56027i	0.102517	+	0.228014i
$401$			26.4760i			1.32215i	0.750321	+	0.661074i	$0.229899\pi$
$401$			26.4760i			1.32215i	−0.750321	+	0.661074i	$0.770101\pi$
$402$	3.64630	+	23.0218i	0.181861	+	1.14822i
$403$	4.52670	−	8.88415i	0.225491	−	0.442551i
$404$	−0.614690	+	0.199725i	−0.0305819	+	0.00993668i
$405$	26.0738	−	10.0634i	1.29562	−	0.500056i
$406$	1.11463	−	3.43047i	0.0553180	−	0.170251i
$407$	−9.50101	−	9.50101i	−0.470948	−	0.470948i
$408$	15.1233	−	7.70570i	0.748715	−	0.381489i
$409$	31.6580	−	23.0009i	1.56539	−	1.13732i	0.633977	−	0.773352i	$-0.281421\pi$
$409$	31.6580	−	23.0009i	1.56539	−	1.13732i	0.931411	−	0.363969i	$-0.118579\pi$
$410$	9.24310	+	0.954429i	0.456484	+	0.0471359i
$411$	31.3774	−	43.1873i	1.54773	−	2.13027i
$412$	−15.3383	−	2.42935i	−0.755663	−	0.119685i
$413$	−0.153575	+	0.969635i	−0.00755694	+	0.0477126i
$414$	−9.90524	−	7.19658i	−0.486816	−	0.353693i
$415$	−24.8743	−	11.0204i	−1.22103	−	0.540968i
$416$	−1.03430	+	0.751465i	−0.0507109	+	0.0368436i
$417$	−40.0564	+	20.4098i	−1.96157	+	0.999471i
$418$	7.80985	−	7.98951i	0.381992	−	0.390779i
$419$	9.42655	+	3.06287i	0.460517	+	0.149631i	0.530082	−	0.847946i	$-0.322161\pi$
$419$	9.42655	+	3.06287i	0.460517	+	0.149631i	−0.0695649	+	0.997577i	$0.522161\pi$
$420$	−5.10448	−	1.35776i	−0.249073	−	0.0662517i
$421$	10.3953	−	3.37763i	0.506634	−	0.164615i	−0.0445368	−	0.999008i	$-0.514181\pi$
$421$	10.3953	−	3.37763i	0.506634	−	0.164615i	0.551171	+	0.834392i	$0.314181\pi$
$422$	−10.2939	−	5.24501i	−0.501099	−	0.255323i
$423$	7.05938	+	44.5712i	0.343239	+	2.16712i
$424$			4.86699i			0.236362i
$425$	−26.7489	+	7.27213i	−1.29751	+	0.352750i
$426$		−	25.0797i		−	1.21512i
$427$	−3.87421	+	0.613615i	−0.187486	+	0.0296949i
$428$	−11.0230	−	5.61648i	−0.532815	−	0.271483i
$429$	−9.54153	+	3.10023i	−0.460669	+	0.149681i
$430$	17.2407	−	0.935117i	0.831422	−	0.0450954i
$431$	−30.9537	−	10.0575i	−1.49099	−	0.484452i	−0.553614	−	0.832773i	$-0.686752\pi$
$431$	−30.9537	−	10.0575i	−1.49099	−	0.484452i	−0.937375	+	0.348322i	$0.886752\pi$
$432$	−7.30271	−	7.30271i	−0.351352	−	0.351352i
$433$	3.08754	+	6.05963i	0.148378	+	0.291207i	0.953218	−	0.302284i	$-0.0977491\pi$
$433$	3.08754	+	6.05963i	0.148378	+	0.291207i	−0.804840	+	0.593491i	$0.797749\pi$
$434$	−3.53694	−	4.86819i	−0.169779	−	0.233680i
$435$	−27.6876	+	16.0529i	−1.32752	+	0.769679i
$436$	−1.92427	+	2.64853i	−0.0921559	+	0.126842i
$437$	1.21582	−	8.28503i	0.0581606	−	0.396327i
$438$	33.0563	+	5.23561i	1.57949	+	0.250167i
$439$	−9.66365	−	7.02105i	−0.461221	−	0.335097i	0.332789	−	0.943001i	$-0.392010\pi$
$439$	−9.66365	−	7.02105i	−0.461221	−	0.335097i	−0.794010	+	0.607905i	$0.792010\pi$
$440$	4.95830	−	2.87476i	0.236377	−	0.137049i
$441$	−33.0233	+	23.9928i	−1.57254	+	1.14252i
$442$	−3.21778	−	6.31525i	−0.153054	−	0.300386i
$443$	−6.64346	−	6.64346i	−0.315640	−	0.315640i	0.531450	−	0.847090i	$-0.321647\pi$
$443$	−6.64346	−	6.64346i	−0.315640	−	0.315640i	−0.847090	+	0.531450i	$0.821647\pi$
$444$	−15.2638	−	4.95950i	−0.724386	−	0.235367i
$445$	−1.12002	−	20.6498i	−0.0530941	−	0.978895i
$446$	−4.22453	−	13.0018i	−0.200037	−	0.615651i
$447$	13.9752	−	27.4279i	0.661004	−	1.29729i
$448$	0.120697	+	0.762052i	0.00570241	+	0.0360036i
$449$	−15.6005			−0.736233			−0.368116	−	0.929780i	$-0.619997\pi$
$449$	−15.6005			−0.736233			−0.368116	+	0.929780i	$0.619997\pi$
$450$	17.4532	+	26.6619i	0.822751	+	1.25685i
$451$		−	10.6515i		−	0.501560i
$452$	−2.86686	−	18.1007i	−0.134846	−	0.851383i
$453$	−24.6438	+	48.3661i	−1.15787	+	2.27244i
$454$	7.32705	−	2.38070i	0.343876	−	0.111732i
$455$	−0.566978	+	2.13155i	−0.0265803	+	0.0999286i
$456$	3.97929	−	12.7380i	0.186347	−	0.596513i
$457$	−15.1917	+	15.1917i	−0.710639	+	0.710639i	−0.966669	−	0.256030i	$-0.917586\pi$
$457$	−15.1917	+	15.1917i	−0.710639	+	0.710639i	0.256030	+	0.966669i	$0.417586\pi$
$458$	9.27330	+	18.1999i	0.433313	+	0.850424i
$459$	46.3208	−	33.6541i	2.16207	−	1.57084i
$460$	1.74003	−	3.92746i	0.0811294	−	0.183119i
$461$	11.3578	+	8.25194i	0.528986	+	0.384331i	0.819978	−	0.572394i	$-0.193985\pi$
$461$	11.3578	+	8.25194i	0.528986	+	0.384331i	−0.290992	+	0.956725i	$0.593985\pi$
$462$	−0.947150	+	5.98007i	−0.0440654	+	0.278218i
$463$	−33.4212	−	5.29340i	−1.55321	−	0.246005i	−0.679952	−	0.733256i	$-0.738000\pi$
$463$	−33.4212	−	5.29340i	−1.55321	−	0.246005i	−0.873262	+	0.487251i	$0.838000\pi$
$464$	3.78216	+	2.74790i	0.175583	+	0.127568i
$465$	−5.48402	+	53.1096i	−0.254315	+	2.46290i
$466$	−8.10442	−	11.1548i	−0.375430	−	0.516735i
$467$	16.8976	+	33.1635i	0.781929	+	1.53462i	0.843873	+	0.536543i	$0.180270\pi$
$467$	16.8976	+	33.1635i	0.781929	+	1.53462i	−0.0619442	+	0.998080i	$0.519730\pi$
$468$	−5.76154	+	5.76154i	−0.266327	+	0.266327i
$469$	1.81518	−	5.58656i	0.0838174	−	0.257964i
$470$	−14.7707	+	5.70092i	−0.681324	+	0.262964i
$471$	−47.3583	+	15.3876i	−2.18216	+	0.709025i
$472$	−1.13372	−	0.577658i	−0.0521836	−	0.0265889i
$473$	−3.09611	−	19.5481i	−0.142359	−	0.898822i
$474$	−6.54631			−0.300682
$475$	−10.6125	+	19.0362i	−0.486934	+	0.873439i
$476$	−4.27745			−0.196056
$477$	4.85239	+	30.6368i	0.222176	+	1.40276i
$478$	−13.3186	−	6.78618i	−0.609180	−	0.310393i
$479$	−17.0351	+	5.53503i	−0.778353	+	0.252902i	−0.671137	−	0.741334i	$-0.734194\pi$
$479$	−17.0351	+	5.53503i	−0.778353	+	0.252902i	−0.107216	+	0.994236i	$0.534194\pi$
$480$	3.71806	−	5.74826i	0.169705	−	0.262371i
$481$	−2.07101	+	6.37391i	−0.0944298	+	0.290625i
$482$	13.8275	−	13.8275i	0.629824	−	0.629824i
$483$	2.06016	+	4.04330i	0.0937407	+	0.183976i
$484$	2.60401	+	3.58412i	0.118364	+	0.162914i
$485$	29.4265	−	6.31098i	1.33619	−	0.286567i
$486$	−5.89261	−	4.28123i	−0.267294	−	0.194201i
$487$	4.72947	+	0.749075i	0.214313	+	0.0339438i	0.262667	−	0.964886i	$-0.415398\pi$
$487$	4.72947	+	0.749075i	0.214313	+	0.0339438i	−0.0483547	+	0.998830i	$0.515398\pi$
$488$	0.795300	−	5.02133i	0.0360015	−	0.227305i
$489$	20.7720	+	15.0918i	0.939344	+	0.682473i
$490$	−10.6603	−	9.56341i	−0.481584	−	0.432031i
$491$	27.1377	−	19.7167i	1.22471	−	0.889801i	0.228224	−	0.973609i	$-0.426708\pi$
$491$	27.1377	−	19.7167i	1.22471	−	0.889801i	0.996482	+	0.0838076i	$0.0267081\pi$
$492$	−5.77601	−	11.3361i	−0.260403	−	0.511069i
$493$	−18.3268	+	18.3268i	−0.825399	+	0.825399i
$494$	−5.31921	−	1.66169i	−0.239322	−	0.0747630i
$495$	28.3454	−	23.0395i	1.27403	−	1.03555i
$496$	7.41739	−	2.41006i	0.333051	−	0.108215i
$497$	−2.86938	+	5.63148i	−0.128709	+	0.252606i
$498$	5.82722	+	36.7916i	0.261124	+	1.64867i
$499$			23.4023i			1.04763i	0.851831	+	0.523816i	$0.175492\pi$
$499$			23.4023i			1.04763i	−0.851831	+	0.523816i	$0.824508\pi$
$500$	−7.86227	+	7.94888i	−0.351611	+	0.355485i
$501$	−18.6368			−0.832633
$502$	−3.44792	−	21.7693i	−0.153888	−	0.971611i
$503$	7.14715	−	14.0271i	0.318676	−	0.625436i	−0.674988	−	0.737828i	$-0.735851\pi$
$503$	7.14715	−	14.0271i	0.318676	−	0.625436i	0.993664	+	0.112392i	$0.0358513\pi$
$504$	1.51953	+	4.67665i	0.0676854	+	0.208314i
$505$	−0.911557	−	1.12149i	−0.0405637	−	0.0499055i
$506$	−4.68302	−	1.52161i	−0.208186	−	0.0676436i
$507$	−24.6048	−	24.6048i	−1.09274	−	1.09274i
$508$	7.49188	+	14.7036i	0.332398	+	0.652368i
$509$	17.9161	−	13.0168i	0.794118	−	0.576960i	−0.115065	−	0.993358i	$-0.536708\pi$
$509$	17.9161	−	13.0168i	0.794118	−	0.576960i	0.909183	+	0.416398i	$0.136708\pi$
$510$	28.2512	+	25.3442i	1.25098	+	1.12226i
$511$	−6.82356	−	4.95761i	−0.301857	−	0.219312i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	6.53618	−	44.5399i	0.288580	−	1.96648i
$514$	−10.2343	+	14.0863i	−0.451417	+	0.621322i
$515$	−7.28173	−	33.9529i	−0.320871	−	1.49614i
$516$	−13.8955	−	19.1255i	−0.611714	−	0.841952i
$517$	8.23935	+	16.1706i	0.362366	+	0.711184i
$518$	2.85995	+	2.85995i	0.125659	+	0.125659i
$519$	47.6663	+	15.4877i	2.09232	+	0.679836i
$520$	−2.40038	−	1.55260i	−0.105264	−	0.0680861i
$521$	−22.9731	+	7.46440i	−1.00647	+	0.327021i	−0.765447	−	0.643499i	$-0.777482\pi$
$521$	−22.9731	+	7.46440i	−1.00647	+	0.327021i	−0.241021	+	0.970520i	$0.577482\pi$
$522$	26.5477	+	13.5267i	1.16196	+	0.592049i
$523$	−5.36716	+	0.850075i	−0.234690	+	0.0371712i	−0.272671	−	0.962107i	$-0.587907\pi$
$523$	−5.36716	+	0.850075i	−0.234690	+	0.0371712i	0.0379817	+	0.999278i	$0.487907\pi$
$524$		−	0.597237i		−	0.0260904i
$525$	−1.27745	−	11.7416i	−0.0557526	−	0.512443i
$526$		−	11.7447i		−	0.512091i
$527$	6.76390	+	42.7056i	0.294640	+	1.86028i
$528$	−6.99202	−	3.56261i	−0.304288	−	0.155043i
$529$	18.3644	−	5.96696i	0.798452	−	0.259433i
$530$	−10.1529	+	3.91863i	−0.441015	+	0.170214i
$531$	−7.71247	−	2.50593i	−0.334693	−	0.108748i
$532$	−2.35089	+	2.40497i	−0.101924	+	0.104269i
$533$	−4.73376	+	2.41197i	−0.205042	+	0.104474i
$534$	−22.9072	+	16.6431i	−0.991293	+	0.720217i
$535$	2.84136	−	27.5169i	0.122842	−	1.18966i
$536$	6.15930	+	4.47499i	0.266041	+	0.193290i
$537$	3.88713	−	24.5424i	0.167742	−	1.05908i
$538$	−22.6484	−	3.58715i	−0.976440	−	0.154653i
$539$	−9.64925	+	13.2811i	−0.415623	+	0.572056i
$540$	9.35431	−	21.1138i	0.402546	−	0.908593i
$541$	19.0676	−	13.8534i	0.819779	−	0.595604i	−0.0968704	−	0.995297i	$-0.530883\pi$
$541$	19.0676	−	13.8534i	0.819779	−	0.595604i	0.916649	+	0.399693i	$0.130883\pi$
$542$	−13.3061	+	6.77978i	−0.571545	+	0.291217i
$543$	−28.4819	−	28.4819i	−1.22227	−	1.22227i
$544$	1.71318	−	5.27261i	0.0734518	−	0.226061i
$545$	−7.07437	−	1.88174i	−0.303033	−	0.0806047i
$546$	2.87215	−	0.933218i	0.122917	−	0.0399381i
$547$	−10.0788	+	19.7807i	−0.430938	+	0.845764i	0.568791	+	0.822482i	$0.307411\pi$
$547$	−10.0788	+	19.7807i	−0.430938	+	0.845764i	−0.999729	+	0.0232814i	$0.992589\pi$
$548$	−2.72762	−	17.2215i	−0.116518	−	0.735668i
$549$		−	32.4013i		−	1.38285i
$550$	9.98913	+	8.02882i	0.425938	+	0.342350i
$551$	0.231705	+	20.3766i	0.00987096	+	0.868072i
$552$	−5.80911	+	0.920073i	−0.247252	+	0.0391609i
$553$	1.46993	+	0.748967i	0.0625078	+	0.0318493i
$554$	1.93392	+	5.95199i	0.0821644	+	0.252876i
$555$	−1.94363	−	35.8346i	−0.0825023	−	1.52109i
$556$	−4.53762	+	13.9653i	−0.192438	+	0.592263i
$557$	−11.7026	+	11.7026i	−0.495856	+	0.495856i	−0.910145	−	0.414289i	$-0.864030\pi$
$557$	−11.7026	+	11.7026i	−0.495856	+	0.495856i	0.414289	+	0.910145i	$0.364030\pi$
$558$	44.2883	−	22.5660i	1.87487	−	0.955296i
$559$	−7.98650	+	5.80253i	−0.337793	+	0.245421i
$560$	−1.49253	+	0.865347i	−0.0630707	+	0.0365676i
$561$	25.5717	−	35.1965i	1.07964	−	1.48600i
$562$	−2.59183	+	16.3641i	−0.109330	+	0.690280i
$563$	1.58259	−	9.99211i	0.0666984	−	0.421117i	−0.931634	−	0.363397i	$-0.881617\pi$
$563$	1.58259	−	9.99211i	0.0666984	−	0.421117i	0.998333	−	0.0577202i	$-0.0183831\pi$
$564$	17.5378	+	12.7419i	0.738473	+	0.536532i
$565$	35.4512	−	20.5542i	1.49144	−	0.864721i
$566$	0.488733	+	0.672683i	0.0205430	+	0.0282750i
$567$	4.37808	+	8.59247i	0.183862	+	0.360850i
$568$	−5.79244	−	5.79244i	−0.243045	−	0.243045i
$569$	12.3824	−	38.1090i	0.519096	−	1.59761i	−0.256608	−	0.966516i	$-0.582605\pi$
$569$	12.3824	−	38.1090i	0.519096	−	1.59761i	0.775704	−	0.631097i	$-0.217395\pi$
$570$	29.7765	−	1.95484i	1.24720	−	0.0818793i
$571$	−0.140060	−	0.431060i	−0.00586133	−	0.0180393i	0.948083	−	0.318023i	$-0.103019\pi$
$571$	−0.140060	−	0.431060i	−0.00586133	−	0.0180393i	−0.953944	+	0.299983i	$0.903019\pi$
$572$	−1.48769	+	2.91976i	−0.0622035	+	0.122081i
$573$	27.8718	−	4.41446i	1.16436	−	0.184417i
$574$			3.20627i			0.133827i
$575$	9.59398	+	0.467675i	0.400097	+	0.0195034i
$576$	−6.37329			−0.265554
$577$	−3.49883	+	0.554161i	−0.145658	+	0.0230700i	−0.228838	−	0.973465i	$-0.573493\pi$
$577$	−3.49883	+	0.554161i	−0.145658	+	0.0230700i	0.0831795	+	0.996535i	$0.473493\pi$
$578$	12.2384	+	6.23576i	0.509049	+	0.259373i
$579$	−1.98629	+	0.645385i	−0.0825474	+	0.0268213i
$580$	−2.68716	+	10.1024i	−0.111578	+	0.419478i
$581$	2.90088	−	8.92800i	0.120349	−	0.370396i
$582$	−29.1373	−	29.1373i	−1.20778	−	1.20778i
$583$	5.66347	+	11.1152i	0.234557	+	0.460344i
$584$	8.84395	−	6.42551i	0.365965	−	0.265889i
$585$	−16.6579	−	7.38017i	−0.688720	−	0.305133i
$586$	−25.1098	−	18.2434i	−1.03728	−	0.753627i
$587$	−4.43975	+	28.0315i	−0.183248	+	1.15698i	0.708924	+	0.705285i	$0.249181\pi$
$587$	−4.43975	+	28.0315i	−0.183248	+	1.15698i	−0.892172	+	0.451697i	$0.850819\pi$
$588$	−3.06745	+	19.3671i	−0.126500	+	0.798687i
$589$	27.7284	+	19.6681i	1.14253	+	0.810408i
$590$	0.292235	−	2.83013i	0.0120311	−	0.116514i
$591$	31.1448	+	42.8671i	1.28113	+	1.76332i
$592$	−4.67079	+	2.37989i	−0.191968	+	0.0978127i
$593$	−25.5040	−	25.5040i	−1.04732	−	1.04732i	−0.998823	−	0.0485018i	$-0.984555\pi$
$593$	−25.5040	−	25.5040i	−1.04732	−	1.04732i	−0.0485018	−	0.998823i	$-0.515445\pi$
$594$	−25.1757	−	8.18007i	−1.03297	−	0.335632i
$595$	−3.44397	−	8.92310i	−0.141189	−	0.365812i
$596$	−3.10704	−	9.56250i	−0.127269	−	0.391695i
$597$	5.11554	−	10.0398i	0.209365	−	0.410902i
$598$	0.384208	+	2.42580i	0.0157114	+	0.0991981i
$599$	15.4544			0.631451			0.315726	−	0.948851i	$-0.397752\pi$
$599$	15.4544			0.631451			0.315726	+	0.948851i	$0.397752\pi$
$600$	14.9849	+	3.12799i	0.611757	+	0.127700i
$601$		−	22.4302i		−	0.914946i	−0.889224	−	0.457473i	$-0.848755\pi$
$601$		−	22.4302i		−	0.914946i	0.889224	−	0.457473i	$-0.151245\pi$
$602$	0.931979	+	5.88428i	0.0379846	+	0.239825i
$603$	43.2332	+	22.0284i	1.76059	+	0.897067i
$604$	5.47895	+	16.8625i	0.222935	+	0.686124i
$605$	−5.38016	+	8.31793i	−0.218735	+	0.338172i
$606$	−0.611474	+	1.88192i	−0.0248394	+	0.0764479i
$607$	19.3479	+	19.3479i	0.785307	+	0.785307i	0.980721	−	0.195414i	$-0.0626050\pi$
$607$	19.3479	+	19.3479i	0.785307	+	0.785307i	−0.195414	+	0.980721i	$0.562605\pi$
$608$	−2.02293	−	3.86106i	−0.0820407	−	0.156586i
$609$	−6.49101	−	8.93410i	−0.263029	−	0.362028i
$610$	11.1152	−	2.38384i	0.450043	−	0.0965187i
$611$	5.32083	−	7.32350i	0.215258	−	0.296277i
$612$	5.52733	−	34.8982i	0.223429	−	1.41068i
$613$	47.2753	+	7.48768i	1.90943	+	0.302424i	0.994799	−	0.101859i	$-0.0324791\pi$
$613$	47.2753	+	7.48768i	1.90943	+	0.302424i	0.914634	+	0.404283i	$0.132479\pi$
$614$	7.46241	−	10.2711i	0.301158	−	0.414509i
$615$	18.9974	−	21.1764i	0.766051	−	0.853916i
$616$	1.16241	+	1.59992i	0.0468348	+	0.0644626i
$617$	5.35749	+	10.5147i	0.215685	+	0.423305i	0.973346	−	0.229343i	$-0.0736579\pi$
$617$	5.35749	+	10.5147i	0.215685	+	0.423305i	−0.757661	+	0.652648i	$0.773658\pi$
$618$	−33.6192	+	33.6192i	−1.35236	+	1.35236i
$619$	34.8186	+	11.3133i	1.39948	+	0.454718i	0.909022	−	0.416747i	$-0.136830\pi$
$619$	34.8186	+	11.3133i	1.39948	+	0.454718i	0.490457	+	0.871466i	$0.336830\pi$
$620$	10.9997	+	13.5328i	0.441757	+	0.543492i
$621$	−18.8690	+	6.13092i	−0.757188	+	0.246025i
$622$	8.21874	−	16.1302i	0.329542	−	0.646762i
$623$	7.04780	−	1.11626i	0.282364	−	0.0447221i
$624$			3.91414i			0.156691i
$625$	−22.9123	−	10.0013i	−0.916492	−	0.400054i
$626$			29.5172i			1.17974i
$627$	−5.73475	−	33.7215i	−0.229024	−	1.34671i
$628$	−7.38398	+	14.4919i	−0.294653	+	0.578289i
$629$	−8.98072	−	27.6398i	−0.358085	−	1.10207i
$630$	−8.53242	+	6.93525i	−0.339940	+	0.276307i
$631$	−3.40475	+	10.4787i	−0.135541	+	0.417152i	−0.995674	−	0.0929182i	$-0.970381\pi$
$631$	−3.40475	+	10.4787i	−0.135541	+	0.417152i	0.860133	+	0.510070i	$0.170381\pi$
$632$	−1.51194	+	1.51194i	−0.0601419	+	0.0601419i
$633$	−31.5156	+	16.0580i	−1.25263	+	0.638249i
$634$	7.47188	+	10.2842i	0.296746	+	0.408436i
$635$	−24.6410	+	27.4672i	−0.977846	+	1.09000i
$636$	12.0549	+	8.75840i	0.478008	+	0.347293i
$637$	8.08741	+	1.28092i	0.320435	+	0.0507519i
$638$	11.8353	+	1.87452i	0.468563	+	0.0742131i
$639$	−42.2374	−	30.6873i	−1.67089	−	1.21397i
$640$	−0.468897	−	2.18635i	−0.0185348	−	0.0864232i
$641$	13.6522	+	18.7907i	0.539230	+	0.742186i	0.988502	−	0.151209i	$-0.0483166\pi$
$641$	13.6522	+	18.7907i	0.539230	+	0.742186i	−0.449272	+	0.893395i	$0.648317\pi$
$642$	−33.7477	+	17.1953i	−1.33192	+	0.678645i
$643$	−32.6943	−	32.6943i	−1.28934	−	1.28934i	−0.935188	−	0.354150i	$-0.884770\pi$
$643$	−32.6943	−	32.6943i	−1.28934	−	1.28934i	−0.354150	−	0.935188i	$-0.615230\pi$
$644$	1.40966	+	0.458027i	0.0555485	+	0.0180488i
$645$	28.7095	−	44.3859i	1.13043	−	1.74769i
$646$	22.8964	−	7.72840i	0.900847	−	0.304070i
$647$	18.7252	+	9.54095i	0.736162	+	0.375093i	0.781522	−	0.623877i	$-0.214444\pi$
$647$	18.7252	+	9.54095i	0.736162	+	0.375093i	−0.0453601	+	0.998971i	$0.514444\pi$
$648$	−12.3450	+	1.95526i	−0.484959	+	0.0768099i
$649$	−3.26136			−0.128020
$650$	1.30620	−	6.25747i	0.0512334	−	0.245438i
$651$	−18.4228			−0.722046
$652$	8.28315	−	1.31192i	0.324393	−	0.0513788i
$653$	−13.0163	+	25.5460i	−0.509368	+	0.999692i	0.482911	+	0.875669i	$0.339579\pi$
$653$	−13.0163	+	25.5460i	−0.509368	+	0.999692i	−0.992279	+	0.124022i	$0.960421\pi$
$654$	3.09725	+	9.53235i	0.121112	+	0.372744i
$655$	1.24588	−	0.480862i	0.0486807	−	0.0187888i
$656$	−3.95223	−	1.28416i	−0.154309	−	0.0501379i
$657$	49.2648	−	49.2648i	1.92200	−	1.92200i
$658$	−2.48018	−	4.86762i	−0.0966873	−	0.189759i
$659$	−37.6914	+	27.3844i	−1.46825	+	1.06675i	−0.487133	+	0.873328i	$0.661957\pi$
$659$	−37.6914	+	27.3844i	−1.46825	+	1.06675i	−0.981117	+	0.193417i	$0.938043\pi$
$660$	1.80231	−	17.4543i	0.0701548	−	0.679409i
$661$	15.8162	−	21.7692i	0.615180	−	0.846723i	−0.381811	−	0.924241i	$-0.624699\pi$
$661$	15.8162	−	21.7692i	0.615180	−	0.846723i	0.996991	+	0.0775176i	$0.0246994\pi$
$662$	−4.52136	+	28.5467i	−0.175728	+	1.10950i
$663$	−21.4326	−	3.39460i	−0.832375	−	0.131835i
$664$	9.84330	+	7.15157i	0.381994	+	0.277535i
$665$	−6.90977	−	2.96780i	−0.267949	−	0.115086i
$666$	−27.0290	+	19.6377i	−1.04735	+	0.760947i
$667$	8.00217	−	4.07731i	0.309845	−	0.157874i
$668$	−4.30439	+	4.30439i	−0.166542	+	0.166542i
$669$	−39.8060	−	12.9337i	−1.53899	−	0.500047i
$670$	−4.37607	+	16.4518i	−0.169062	+	0.635589i
$671$	−4.02677	−	12.3931i	−0.155452	−	0.478431i
$672$	2.10471	+	1.07240i	0.0811908	+	0.0413688i
$673$	26.3942	−	4.18043i	1.01742	−	0.161144i	0.374621	−	0.927178i	$-0.377773\pi$
$673$	26.3942	−	4.18043i	1.01742	−	0.161144i	0.642800	+	0.766034i	$0.277773\pi$
$674$		−	26.2717i		−	1.01195i
$675$	51.5767	+	2.51420i	1.98519	+	0.0967715i
$676$	−11.3655			−0.437135
$677$	2.40834	+	15.2057i	0.0925601	+	0.584402i	0.989756	+	0.142769i	$0.0456006\pi$
$677$	2.40834	+	15.2057i	0.0925601	+	0.584402i	−0.897196	+	0.441633i	$0.854399\pi$
$678$	−49.9921	−	25.4722i	−1.91993	−	0.978256i
$679$	3.20897	+	9.87621i	0.123149	+	0.379014i
$680$	12.3785	−	0.671393i	0.474692	−	0.0257468i
$681$	7.28872	−	22.4324i	0.279304	−	0.859610i
$682$	14.1353	−	14.1353i	0.541269	−	0.541269i
$683$	7.94003	+	15.5832i	0.303817	+	0.596274i	0.991555	−	0.129685i	$-0.0413965\pi$
$683$	7.94003	+	15.5832i	0.303817	+	0.596274i	−0.687739	+	0.725958i	$0.741396\pi$
$684$	−16.5835	−	22.2878i	−0.634085	−	0.852195i
$685$	33.7294	−	19.5559i	1.28874	−	0.747192i
$686$	6.07912	−	8.36719i	0.232102	−	0.319461i
$687$	61.7665	+	9.78286i	2.35654	+	0.373239i
$688$	−7.62656	−	1.20793i	−0.290760	−	0.0460518i
$689$	3.65737	−	5.03394i	0.139335	−	0.191778i
$690$	−6.59653	−	11.3775i	−0.251126	−	0.433134i
$691$	−37.9351	+	27.5615i	−1.44312	+	1.04849i	−0.455741	+	0.890112i	$0.650626\pi$
$691$	−37.9351	+	27.5615i	−1.44312	+	1.04849i	−0.987379	+	0.158376i	$0.949374\pi$
$692$	14.5861	−	7.43201i	0.554482	−	0.282523i
$693$	8.91228	+	8.91228i	0.338549	+	0.338549i
$694$	−9.56310	+	29.4322i	−0.363010	+	1.11723i
$695$	−32.7863	+	1.77829i	−1.24366	+	0.0674544i
$696$	13.6124	−	4.42294i	0.515977	−	0.167651i
$697$	10.4593	−	20.5275i	0.396174	−	0.777535i
$698$	−9.74258	+	1.54307i	−0.368762	+	0.0584062i
$699$	−42.2133			−1.59665
$700$	−3.00689	−	2.41680i	−0.113650	−	0.0913465i
$701$	−17.1665			−0.648371			−0.324186	−	0.945993i	$-0.605090\pi$
$701$	−17.1665			−0.648371			−0.324186	+	0.945993i	$0.605090\pi$
$702$	2.06548	+	13.0409i	0.0779566	+	0.492199i
$703$	−20.4761	−	10.1415i	−0.772272	−	0.382494i
$704$	−2.43771	+	0.792060i	−0.0918746	+	0.0298519i
$705$	−12.4603	+	46.8443i	−0.469281	+	1.76426i
$706$	20.1249	+	6.53899i	0.757412	+	0.246098i
$707$	0.352614	−	0.352614i	0.0132614	−	0.0132614i
$708$	−3.47097	+	1.76855i	−0.130447	+	0.0664660i
$709$	30.4838	+	41.9573i	1.14484	+	1.57574i	0.756185	+	0.654358i	$0.227061\pi$
$709$	30.4838	+	41.9573i	1.14484	+	1.57574i	0.388657	+	0.921382i	$0.372939\pi$
$710$	7.41975	−	16.7473i	0.278458	−	0.628514i
$711$	−8.01001	+	11.0248i	−0.300399	+	0.413463i
$712$	−1.44678	+	9.13459i	−0.0542203	+	0.342333i
$713$	2.34380	−	14.7982i	0.0877762	−	0.554197i
$714$	−7.69749	+	10.5947i	−0.288071	+	0.396496i
$715$	−7.28866	−	0.752617i	−0.272580	−	0.0281463i
$716$	−4.77056	−	6.56612i	−0.178284	−	0.245387i
$717$	−40.7761	+	20.7764i	−1.52281	+	0.775911i
$718$	3.38906	−	3.38906i	0.126479	−	0.126479i
$719$	41.5078	+	13.4867i	1.54798	+	0.502969i	0.953564	−	0.301190i	$-0.0973838\pi$
$719$	41.5078	+	13.4867i	1.54798	+	0.502969i	0.594415	+	0.804159i	$0.297384\pi$
$720$	−5.13142	−	13.2952i	−0.191237	−	0.495483i
$721$	11.3954	−	3.70258i	0.424385	−	0.137891i
$722$	8.23863	−	17.1209i	0.306610	−	0.637174i
$723$	−9.36560	−	59.1321i	−0.348311	−	2.19915i
$724$	−13.1564			−0.488954
$725$	−23.2379	+	2.52823i	−0.863035	+	0.0938962i
$726$	13.5635			0.503387
$727$	3.34296	−	0.529473i	0.123984	−	0.0196371i	−0.0941343	−	0.995560i	$-0.530008\pi$
$727$	3.34296	−	0.529473i	0.123984	−	0.0196371i	0.218118	+	0.975922i	$0.430008\pi$
$728$	0.447818	−	0.878893i	0.0165972	−	0.0325739i
$729$	14.4534	−	4.69619i	0.535310	−	0.173933i
$730$	20.5248	+	13.2757i	0.759657	+	0.491357i
$731$	13.2285	−	40.7132i	0.489274	−	1.50583i
$732$	−11.0060	−	11.0060i	−0.406793	−	0.406793i
$733$	−5.21961	+	2.65952i	−0.192791	+	0.0982318i	−0.547721	−	0.836661i	$-0.684505\pi$
$733$	−5.21961	+	2.65952i	−0.192791	+	0.0982318i	0.354930	+	0.934893i	$0.384505\pi$
$734$	−4.89181	+	3.55411i	−0.180560	+	0.131184i
$735$	−42.8712	+	9.19439i	−1.58133	+	0.339140i
$736$	−1.12918	+	1.55418i	−0.0416221	+	0.0572879i
$737$	19.2739	+	3.05268i	0.709963	+	0.112447i
$738$	−26.1589	−	4.14316i	−0.962921	−	0.152512i
$739$	−15.1230	+	20.8150i	−0.556307	+	0.765691i	−0.990851	−	0.134959i	$-0.956910\pi$
$739$	−15.1230	+	20.8150i	−0.556307	+	0.765691i	0.434544	+	0.900651i	$0.356910\pi$
$740$	−8.72530	−	7.82750i	−0.320748	−	0.287745i
$741$	−13.6880	+	10.1847i	−0.502841	+	0.374144i
$742$	−1.70479	−	3.34584i	−0.0625849	−	0.122830i
$743$	−4.45178	+	4.45178i	−0.163320	+	0.163320i	−0.784036	−	0.620716i	$-0.786842\pi$
$743$	−4.45178	+	4.45178i	−0.163320	+	0.163320i	0.620716	+	0.784036i	$0.286842\pi$
$744$	7.37859	−	22.7090i	0.270512	−	0.832551i
$745$	17.4465	−	14.1808i	0.639192	−	0.519543i
$746$	1.30465	+	4.01530i	0.0477666	+	0.147011i
$747$	69.0919	+	35.2041i	2.52794	+	1.28805i
$748$	−2.22294	−	14.0351i	−0.0812787	−	0.513174i
$749$	9.54514			0.348772
$750$	5.53978	+	33.7783i	0.202284	+	1.23341i
$751$			17.7991i			0.649497i	0.945800	+	0.324749i	$0.105280\pi$
$751$			17.7991i			0.649497i	−0.945800	+	0.324749i	$0.894720\pi$
$752$	6.99344	−	1.10765i	0.255024	−	0.0403919i
$753$	−60.1244	−	30.6349i	−2.19106	−	1.11640i
$754$	−1.84695	−	5.68433i	−0.0672620	−	0.207011i
$755$	−30.7651	+	25.0063i	−1.11966	+	0.910071i
$756$	7.57827	+	2.46233i	0.275619	+	0.0895541i
$757$	27.3251	−	27.3251i	0.993147	−	0.993147i	−0.00682960	−	0.999977i	$-0.502174\pi$
$757$	27.3251	−	27.3251i	0.993147	−	0.993147i	0.999977	+	0.00682960i	$0.00217395\pi$
$758$	−0.485534	+	0.247392i	−0.0176354	+	0.00898569i
$759$	−12.1962	+	8.86103i	−0.442693	+	0.321635i
$760$	6.42573	−	7.32871i	0.233086	−	0.265840i
$761$	−11.4723	−	8.33509i	−0.415870	−	0.302147i	0.360104	−	0.932912i	$-0.382741\pi$
$761$	−11.4723	−	8.33509i	−0.415870	−	0.302147i	−0.775974	+	0.630765i	$0.782741\pi$
$762$	49.9011	+	7.90355i	1.80772	+	0.286315i
$763$	0.395134	−	2.49478i	0.0143048	−	0.0903171i
$764$	5.41773	−	7.45687i	0.196007	−	0.269780i
$765$	77.2508	−	16.5676i	2.79301	−	0.599005i
$766$	7.15055	−	5.19518i	0.258360	−	0.187709i
$767$	0.738517	+	1.44942i	0.0266663	+	0.0523356i
$768$	−2.16487	+	2.16487i	−0.0781179	+	0.0781179i
$769$	2.91993	+	0.948744i	0.105295	+	0.0342126i	0.361191	−	0.932492i	$-0.382370\pi$
$769$	2.91993	+	0.948744i	0.105295	+	0.0342126i	−0.255895	+	0.966704i	$0.582370\pi$
$770$	−2.40166	+	3.71305i	−0.0865496	+	0.133809i
$771$	16.4729	+	50.6982i	0.593255	+	1.82585i
$772$	−0.309697	+	0.607815i	−0.0111462	+	0.0218757i
$773$	−6.83823	+	1.08307i	−0.245954	+	0.0389553i	−0.278194	−	0.960525i	$-0.589736\pi$
$773$	−6.83823	+	1.08307i	−0.245954	+	0.0389553i	0.0322401	+	0.999480i	$0.489736\pi$
$774$	−49.2121			−1.76889
$775$	−19.3743	+	33.8421i	−0.695946	+	1.21564i
$776$	−13.4592			−0.483157
$777$	12.2304	−	1.93710i	0.438762	−	0.0694931i
$778$	−14.0102	−	7.13856i	−0.502291	−	0.255930i
$779$	−5.79303	−	17.1626i	−0.207557	−	0.614914i
$780$	−8.16521	+	3.15145i	−0.292362	+	0.112840i
$781$	−19.9691	−	6.48836i	−0.714551	−	0.232172i
$782$	−7.53093	−	7.53093i	−0.269306	−	0.269306i
$783$	43.0192	−	21.9194i	1.53738	−	0.783335i
$784$	3.76459	+	5.18152i	0.134450	+	0.185054i
$785$	−36.1764	−	3.73553i	−1.29119	−	0.133327i
$786$	−1.47928	−	1.07476i	−0.0527641	−	0.0383354i
$787$	−24.9542	−	3.95236i	−0.889521	−	0.140886i	−0.305084	−	0.952325i	$-0.598685\pi$
$787$	−24.9542	−	3.95236i	−0.889521	−	0.140886i	−0.584437	+	0.811439i	$0.698685\pi$
$788$	17.0939	+	2.70740i	0.608944	+	0.0964473i
$789$	−29.0900	−	21.1351i	−1.03563	−	0.752430i
$790$	−4.37138	−	1.93671i	−0.155527	−	0.0689049i
$791$	8.31109	+	11.4392i	0.295508	+	0.406732i
$792$	−14.5553	+	7.41627i	−0.517199	+	0.263526i
$793$	−4.59593	+	4.59593i	−0.163206	+	0.163206i
$794$	4.24352	−	13.0602i	0.150597	−	0.463489i
$795$	−8.56480	+	32.1993i	−0.303762	+	1.14199i
$796$	−1.13731	−	3.50030i	−0.0403111	−	0.124065i
$797$	−17.6678	+	34.6750i	−0.625825	+	1.22825i	0.332644	+	0.943052i	$0.392059\pi$
$797$	−17.6678	+	34.6750i	−0.625825	+	1.22825i	−0.958469	+	0.285198i	$0.907941\pi$
$798$	1.72625	+	10.1507i	0.0611085	+	0.359331i
$799$			39.2546i			1.38873i
$800$	4.18338	−	2.73849i	0.147905	−	0.0968202i
$801$			58.9430i			2.08265i
$802$	26.1500	−	4.14176i	0.923390	−	0.146251i
$803$	12.7207	−	24.9658i	0.448904	−	0.881023i
$804$	22.1680	−	7.20281i	0.781804	−	0.254023i
$805$	0.179501	+	3.30945i	0.00632657	+	0.116643i
$806$	−9.48290	−	3.08118i	−0.334021	−	0.108530i
$807$	−49.6418	+	49.6418i	−1.74747	+	1.74747i
$808$	0.293424	+	0.575878i	0.0103226	+	0.0202593i
$809$	−17.8408	−	24.5558i	−0.627249	−	0.863334i	0.370606	−	0.928790i	$-0.379150\pi$
$809$	−17.8408	−	24.5558i	−0.627249	−	0.863334i	−0.997855	+	0.0654558i	$0.979150\pi$
$810$	−14.0184	−	24.1785i	−0.492556	−	0.849545i
$811$	19.4500	−	26.7706i	0.682981	−	0.940042i	−0.316984	−	0.948431i	$-0.602670\pi$
$811$	19.4500	−	26.7706i	0.682981	−	0.940042i	0.999965	+	0.00838876i	$0.00267026\pi$
$812$	−3.56260	−	0.564261i	−0.125023	−	0.0198017i
$813$	−7.15233	+	45.1580i	−0.250843	+	1.58376i
$814$	−7.89775	+	10.8703i	−0.276816	+	0.381005i
$815$	9.40592	+	16.2230i	0.329475	+	0.568268i
$816$	−9.97664	−	13.7317i	−0.349252	−	0.480704i
$817$	−15.6203	−	29.8136i	−0.546486	−	1.04305i
$818$	−27.6701	−	27.6701i	−0.967463	−	0.967463i
$819$	1.94268	−	5.97895i	0.0678826	−	0.208921i
$820$	−0.503260	−	9.27860i	−0.0175746	−	0.324023i
$821$	8.46686	+	26.0583i	0.295495	+	0.909442i	0.983055	+	0.183313i	$0.0586822\pi$
$821$	8.46686	+	26.0583i	0.295495	+	0.909442i	−0.687559	+	0.726128i	$0.741318\pi$
$822$	−47.5641	−	24.2351i	−1.65899	−	0.845296i
$823$	−0.713148	−	4.50264i	−0.0248588	−	0.156952i	0.972136	−	0.234416i	$-0.0753178\pi$
$823$	−0.713148	−	4.50264i	−0.0248588	−	0.156952i	−0.996995	+	0.0774638i	$0.975318\pi$
$824$			15.5295i			0.540995i
$825$	37.8623	−	10.2935i	1.31820	−	0.358374i
$826$	0.981722			0.0341585
$827$	−0.419495	−	2.64859i	−0.0145873	−	0.0921004i	0.979321	−	0.202315i	$-0.0648463\pi$
$827$	−0.419495	−	2.64859i	−0.0145873	−	0.0921004i	−0.993908	+	0.110214i	$0.964846\pi$
$828$	−5.55846	+	10.9091i	−0.193170	+	0.379117i
$829$	6.75583	+	20.7923i	0.234640	+	0.722147i	0.997169	+	0.0751932i	$0.0239573\pi$
$829$	6.75583	+	20.7923i	0.234640	+	0.722147i	−0.762529	+	0.646954i	$0.776043\pi$
$830$	−6.99349	+	26.2920i	−0.242748	+	0.912608i
$831$	18.2225	+	5.92086i	0.632132	+	0.205392i
$832$	0.904014	+	0.904014i	0.0313410	+	0.0313410i
$833$	−31.6373	+	16.1200i	−1.09617	+	0.558526i
$834$	26.4247	+	36.3705i	0.915013	+	1.25941i
$835$	−12.4450	−	5.51365i	−0.430676	−	0.190808i
$836$	−9.11287	−	6.46386i	−0.315175	−	0.223557i
$837$	12.6002	−	79.5543i	0.435525	−	2.74980i
$838$	1.55053	−	9.78963i	0.0535620	−	0.338177i
$839$	−40.2852	−	29.2689i	−1.39080	−	1.01048i	−0.995777	−	0.0918041i	$-0.970737\pi$
$839$	−40.2852	−	29.2689i	−1.39080	−	1.01048i	−0.395023	−	0.918671i	$-0.629263\pi$
$840$	−0.542524	+	5.25403i	−0.0187188	+	0.181281i
$841$	5.77984	−	4.19930i	0.199305	−	0.144803i
$842$	−4.96222	−	9.73891i	−0.171009	−	0.335625i
$843$	35.8678	+	35.8678i	1.23535	+	1.23535i
$844$	−3.57011	+	10.9877i	−0.122888	+	0.378211i
$845$	−9.15089	−	23.7094i	−0.314800	−	0.815628i
$846$	42.9181	−	13.9449i	1.47555	−	0.479437i
$847$	−3.04558	−	1.55180i	−0.104647	−	0.0533205i
$848$	4.80707	−	0.761364i	0.165075	−	0.0261454i
$849$	2.54565			0.0873664
$850$	11.3670	+	25.2819i	0.389886	+	0.867163i
$851$			10.0706i			0.345214i
$852$	−24.7709	+	3.92333i	−0.848638	+	0.134411i
$853$	10.4021	−	20.4153i	0.356161	−	0.699006i	−0.641517	−	0.767109i	$-0.721695\pi$
$853$	10.4021	−	20.4153i	0.356161	−	0.699006i	0.997678	+	0.0681030i	$0.0216946\pi$
$854$	1.21212	+	3.73052i	0.0414779	+	0.127656i
$855$	33.1421	−	52.5394i	1.13343	−	1.79681i
$856$	−3.82296	+	11.7659i	−0.130666	+	0.402149i
$857$	23.5535	+	23.5535i	0.804571	+	0.804571i	0.983806	−	0.179236i	$-0.0573624\pi$
$857$	23.5535	+	23.5535i	0.804571	+	0.804571i	−0.179236	+	0.983806i	$0.557362\pi$
$858$	4.55469	+	8.93907i	0.155494	+	0.305175i
$859$	−4.06901	−	5.60052i	−0.138833	−	0.191087i	0.733939	−	0.679215i	$-0.237680\pi$
$859$	−4.06901	−	5.60052i	−0.138833	−	0.191087i	−0.872772	+	0.488128i	$0.837680\pi$
$860$	−3.62065	−	16.8822i	−0.123463	−	0.575678i
$861$	7.94152	+	5.76986i	0.270646	+	0.196636i
$862$	−5.09142	+	32.1460i	−0.173415	+	1.09490i
$863$	2.08804	−	13.1833i	0.0710776	−	0.448766i	−0.926324	−	0.376727i	$-0.877049\pi$
$863$	2.08804	−	13.1833i	0.0710776	−	0.448766i	0.997402	−	0.0720391i	$-0.0229506\pi$
$864$	−6.07041	+	8.35520i	−0.206519	+	0.284250i
$865$	27.2478	+	24.4440i	0.926451	+	0.831123i
$866$	5.50203	−	3.99746i	0.186967	−	0.135839i
$867$	37.4688	−	19.0913i	1.27251	−	0.648374i
$868$	−4.25495	+	4.25495i	−0.144422	+	0.144422i
$869$	−1.69359	+	5.21234i	−0.0574512	+	0.176817i
$870$	20.1866	+	24.8355i	0.684389	+	0.842002i
$871$	−3.00778	−	9.25700i	−0.101915	−	0.313661i
$872$	2.91695	+	1.48626i	0.0987803	+	0.0503311i
$873$	−84.7232	+	13.4188i	−2.86745	+	0.454159i
$874$	−8.37323	+	0.0952131i	−0.283229	+	0.00322063i
$875$	2.62067	−	8.21849i	0.0885947	−	0.277836i
$876$		−	33.4684i		−	1.13079i
$877$	0.942970	+	5.95368i	0.0318418	+	0.201041i	0.998481	−	0.0551015i	$-0.0175482\pi$
$877$	0.942970	+	5.95368i	0.0318418	+	0.201041i	−0.966639	+	0.256143i	$0.917548\pi$
$878$	−5.42288	+	10.6430i	−0.183013	+	0.359184i
$879$	−90.3730	+	29.3640i	−3.04821	+	0.990422i
$880$	−3.61501	−	4.44754i	−0.121862	−	0.149927i
$881$	−16.0571	+	49.4188i	−0.540979	+	1.66496i	0.189384	+	0.981903i	$0.439351\pi$
$881$	−16.0571	+	49.4188i	−0.540979	+	1.66496i	−0.730363	+	0.683059i	$0.760649\pi$
$882$	28.8634	+	28.8634i	0.971882	+	0.971882i
$883$	−10.0943	+	5.14332i	−0.339701	+	0.173086i	−0.615516	−	0.788124i	$-0.711052\pi$
$883$	−10.0943	+	5.14332i	−0.339701	+	0.173086i	0.275815	+	0.961211i	$0.411052\pi$
$884$	−5.73413	+	4.16609i	−0.192860	+	0.140121i
$885$	−6.48397	−	5.81679i	−0.217956	−	0.195529i
$886$	−5.52240	+	7.60093i	−0.185529	+	0.255358i
$887$	25.2325	+	3.99644i	0.847226	+	0.134187i	0.564929	−	0.825140i	$-0.308904\pi$
$887$	25.2325	+	3.99644i	0.847226	+	0.134187i	0.282297	+	0.959327i	$0.408904\pi$
$888$	−2.51066	+	15.8517i	−0.0842522	+	0.531947i
$889$	−10.3007	−	7.48389i	−0.345474	−	0.251002i
$890$	−20.2204	+	4.33658i	−0.677789	+	0.145362i
$891$	−25.9182	+	18.8307i	−0.868294	+	0.630852i
$892$	−12.1808	+	6.20644i	−0.407844	+	0.207807i
$893$	22.0706	+	21.5744i	0.738566	+	0.721958i
$894$	−29.2764	−	9.51247i	−0.979148	−	0.318145i
$895$	9.85647	−	15.2385i	0.329465	−	0.509366i
$896$	0.733789	−	0.238422i	0.0245142	−	0.00796514i
$897$	6.69979	+	3.41371i	0.223699	+	0.113981i
$898$	2.44046	+	15.4084i	0.0814390	+	0.514186i
$899$			36.4609i			1.21604i
$900$	23.6033	−	21.4091i	0.786778	−	0.713638i
$901$			26.9824i			0.898913i
$902$	−10.5204	+	1.66626i	−0.350290	+	0.0554805i
$903$	16.2518	+	8.28069i	0.540825	+	0.275564i
$904$	−17.4293	+	5.66313i	−0.579691	+	0.188353i
$905$	−10.5928	−	27.4454i	−0.352118	−	0.912315i
$906$	51.6258	+	16.7742i	1.71515	+	0.557287i
$907$	−24.2633	−	24.2633i	−0.805651	−	0.805651i	0.178321	−	0.983972i	$-0.442933\pi$
$907$	−24.2633	−	24.2633i	−0.805651	−	0.805651i	−0.983972	+	0.178321i	$0.942933\pi$
$908$	−3.49760	−	6.86442i	−0.116072	−	0.227804i
$909$	2.42121	+	3.33250i	0.0803063	+	0.110532i
$910$	2.19400	+	0.226549i	0.0727304	+	0.00751004i
$911$	−0.502797	+	0.692041i	−0.0166584	+	0.0229283i	−0.817265	−	0.576262i	$-0.804511\pi$
$911$	−0.502797	+	0.692041i	−0.0166584	+	0.0229283i	0.800607	+	0.599190i	$0.204511\pi$
$912$	−13.2037	−	1.93763i	−0.437219	−	0.0641614i
$913$	30.8020	+	4.87855i	1.01940	+	0.161457i
$914$	17.3812	+	12.6282i	0.574919	+	0.417703i
$915$	14.0980	−	31.8208i	0.466065	−	1.05196i
$916$	16.5251	−	12.0062i	0.546006	−	0.396697i
$917$	0.209198	+	0.410575i	0.00690833	+	0.0135584i
$918$	−40.4859	−	40.4859i	−1.33623	−	1.33623i
$919$	−19.6529	−	6.38562i	−0.648289	−	0.210642i	−0.0336297	−	0.999434i	$-0.510707\pi$
$919$	−19.6529	−	6.38562i	−0.648289	−	0.210642i	−0.614660	+	0.788792i	$0.710707\pi$
$920$	−4.15130	−	1.10422i	−0.136864	−	0.0364050i
$921$	−12.0113	−	36.9669i	−0.395784	−	1.21810i
$922$	6.37359	−	12.5089i	0.209903	−	0.411958i
$923$	1.63832	+	10.3440i	0.0539260	+	0.340476i
$924$	6.05461			0.199182
$925$	9.30367	−	24.5040i	0.305903	−	0.805686i
$926$			33.8378i			1.11198i
$927$	15.4829	+	97.7553i	0.508526	+	3.21070i
$928$	2.12241	−	4.16547i	0.0696715	−	0.136738i
$929$	50.0672	−	16.2678i	1.64265	−	0.533730i	0.665523	−	0.746377i	$-0.268209\pi$
$929$	50.0672	−	16.2678i	1.64265	−	0.533730i	0.977129	+	0.212647i	$0.0682086\pi$
$930$	53.3136	−	2.89167i	1.74822	−	0.0948214i
$931$	−8.32452	+	26.6475i	−0.272825	+	0.873336i
$932$	−9.74964	+	9.74964i	−0.319360	+	0.319360i
$933$	−25.1624	−	49.3839i	−0.823779	−	1.61676i
$934$	30.1118	−	21.8775i	0.985288	−	0.715854i
$935$	27.4886	−	15.9375i	0.898972	−	0.521213i
$936$	6.59191	+	4.78930i	0.215463	+	0.156543i
$937$	−8.49460	+	53.6328i	−0.277507	+	1.75211i	0.317380	+	0.948298i	$0.397197\pi$
$937$	−8.49460	+	53.6328i	−0.277507	+	1.75211i	−0.594887	+	0.803809i	$0.702803\pi$
$938$	−5.80174	−	0.918906i	−0.189434	−	0.0300033i
$939$	73.1103	+	53.1177i	2.38586	+	1.73343i
$940$	7.94139	+	13.6971i	0.259019	+	0.446749i
$941$	18.1749	+	25.0157i	0.592486	+	0.815487i	0.994995	−	0.0999289i	$-0.0318615\pi$
$941$	18.1749	+	25.0157i	0.592486	+	0.815487i	−0.402508	+	0.915416i	$0.631862\pi$
$942$	22.6067	+	44.3681i	0.736565	+	1.44559i
$943$	−5.64501	+	5.64501i	−0.183827	+	0.183827i
$944$	−0.393193	+	1.21012i	−0.0127974	+	0.0393862i
$945$	0.964986	+	17.7914i	0.0313910	+	0.578755i
$946$	−18.8231	+	6.11599i	−0.611991	+	0.198848i
$947$	16.7590	+	8.53916i	0.544596	+	0.277485i	0.704568	−	0.709636i	$-0.251141\pi$
$947$	16.7590	+	8.53916i	0.544596	+	0.277485i	−0.159973	+	0.987121i	$0.551141\pi$
$948$	1.02407	+	6.46572i	0.0332602	+	0.209997i
$949$	−13.9759			−0.453676
$950$	20.4619	+	7.50392i	0.663873	+	0.243459i
$951$	38.9186			1.26202
$952$	0.669140	+	4.22478i	0.0216869	+	0.136926i
$953$	48.2573	+	24.5883i	1.56321	+	0.796494i	0.999564	−	0.0295237i	$-0.00939905\pi$
$953$	48.2573	+	24.5883i	1.56321	+	0.796494i	0.563644	+	0.826018i	$0.309399\pi$
$954$	29.5005	−	9.58530i	0.955115	−	0.310336i
$955$	19.9177	+	5.29798i	0.644522	+	0.171438i
$956$	−4.61914	+	14.2162i	−0.149394	+	0.459786i
$957$	25.9411	−	25.9411i	0.838558	−	0.838558i
$958$	8.13176	+	15.9595i	0.262725	+	0.515628i
$959$	7.90744	+	10.8837i	0.255344	+	0.351451i
$960$	−6.25912	−	2.77306i	−0.202012	−	0.0895000i
$961$	24.1298	+	17.5313i	0.778380	+	0.565526i
$962$	6.61941	+	1.04841i	0.213418	+	0.0338022i
$963$	−12.3343	+	77.8755i	−0.397466	+	2.50950i
$964$	−15.8203	−	11.4941i	−0.509538	−	0.370201i
$965$	−1.51730	−	0.156675i	−0.0488437	−	0.00504353i
$966$	3.67124	−	2.66731i	0.118120	−	0.0858193i
$967$	27.2297	+	53.4414i	0.875649	+	1.71856i	0.673477	+	0.739208i	$0.264800\pi$
$967$	27.2297	+	53.4414i	0.875649	+	1.71856i	0.202172	+	0.979350i	$0.435200\pi$
$968$	3.13263	−	3.13263i	0.100687	−	0.100687i
$969$	22.0610	−	70.6191i	0.708702	−	2.26861i
$970$	−10.8366	−	28.0770i	−0.347942	−	0.901498i
$971$	−3.58982	+	1.16640i	−0.115203	+	0.0374316i	−0.366051	−	0.930595i	$-0.619290\pi$
$971$	−3.58982	+	1.16640i	−0.115203	+	0.0374316i	0.250848	+	0.968026i	$0.419290\pi$
$972$	−3.30672	+	6.48980i	−0.106063	+	0.208160i
$973$	−1.77232	−	11.1900i	−0.0568180	−	0.358735i
$974$		−	4.78842i		−	0.153431i
$975$	−13.1484	−	14.4959i	−0.421085	−	0.464242i
$976$	−5.08392			−0.162732
$977$	7.08858	+	44.7555i	0.226784	+	1.43186i	0.793814	+	0.608160i	$0.208092\pi$
$977$	7.08858	+	44.7555i	0.226784	+	1.43186i	−0.567031	+	0.823697i	$0.691908\pi$
$978$	11.6565	−	22.8772i	0.372734	−	0.731531i
$979$	7.32533	+	22.5450i	0.234119	+	0.720543i
$980$	−7.77803	+	12.0251i	−0.248460	+	0.384129i
$981$	19.8435	+	6.44753i	0.633553	+	0.205854i
$982$	−23.7192	−	23.7192i	−0.756910	−	0.756910i
$983$	−8.51525	−	16.7121i	−0.271594	−	0.533034i	0.714415	−	0.699722i	$-0.246693\pi$
$983$	−8.51525	−	16.7121i	−0.271594	−	0.533034i	−0.986010	+	0.166688i	$0.946693\pi$
$984$	−10.2929	+	7.47825i	−0.328127	+	0.238398i
$985$	8.11519	+	37.8391i	0.258571	+	1.20565i
$986$	20.9681	+	15.2342i	0.667762	+	0.485157i
$987$	−16.5197	−	2.61646i	−0.525827	−	0.0832828i
$988$	−0.809125	+	5.51366i	−0.0257417	+	0.175413i
$989$	−8.71910	+	12.0008i	−0.277251	+	0.381604i
$990$	−27.1901	−	24.3923i	−0.864157	−	0.775238i
$991$	−6.16266	−	8.48217i	−0.195763	−	0.269445i	0.699839	−	0.714301i	$-0.253255\pi$
$991$	−6.16266	−	8.48217i	−0.195763	−	0.269445i	−0.895602	+	0.444855i	$0.853255\pi$
$992$	−3.54072	−	6.94905i	−0.112418	−	0.220633i
$993$	62.5702	+	62.5702i	1.98560	+	1.98560i
$994$	6.01101	+	1.95310i	0.190658	+	0.0619485i
$995$	6.38620	−	5.19078i	0.202456	−	0.164559i
$996$	35.4271	−	11.5110i	1.12255	−	0.364739i
$997$	−15.2353	−	7.76275i	−0.482505	−	0.245849i	0.195779	−	0.980648i	$-0.437276\pi$
$997$	−15.2353	−	7.76275i	−0.482505	−	0.245849i	−0.678285	+	0.734799i	$0.737276\pi$
$998$	23.1142	−	3.66093i	0.731668	−	0.115885i
$999$			54.1388i			1.71287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.113.2	✓	400
19.18	odd	2	inner	950.2.w.a.113.49	yes	400
25.2	odd	20	inner	950.2.w.a.227.49	yes	400
475.227	even	20	inner	950.2.w.a.227.2	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.113.2	✓	400	1.1	even	1	trivial
950.2.w.a.113.49	yes	400	19.18	odd	2	inner
950.2.w.a.227.2	yes	400	475.227	even	20	inner
950.2.w.a.227.49	yes	400	25.2	odd	20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-2.72789 - 1.38993i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.41037 - 1.73518i) q^{5} +(-0.946081 + 2.91174i) q^{6} +(0.545569 - 0.545569i) q^{7} +(0.453990 + 0.891007i) q^{8} +(3.74612 + 5.15610i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(-2.72789 - 1.38993i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-1.41037 - 1.73518i) q^{5} +(-0.946081 + 2.91174i) q^{6} +(0.545569 - 0.545569i) q^{7} +(0.453990 + 0.891007i) q^{8} +(3.74612 + 5.15610i) q^{9} +(-1.49318 + 1.66445i) q^{10} +(2.07364 + 1.50659i) q^{11} +(3.02389 + 0.478937i) q^{12} +(0.199997 - 1.26273i) q^{13} +(-0.624198 - 0.453506i) q^{14} +(1.43557 + 6.69370i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.51690 + 4.93970i) q^{17} +(4.50659 - 4.50659i) q^{18} +(4.16061 + 1.29975i) q^{19} +(1.87754 + 1.21442i) q^{20} +(-2.24655 + 0.729950i) q^{21} +(1.16365 - 2.28379i) q^{22} +(-0.300522 - 1.89742i) q^{23} -3.06158i q^{24} +(-1.02169 + 4.89450i) q^{25} -1.27847 q^{26} +(-1.61559 - 10.2004i) q^{27} +(-0.350277 + 0.687457i) q^{28} +(1.44466 + 4.44620i) q^{29} +(6.38671 - 2.46502i) q^{30} +(7.41739 + 2.41006i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.56261 - 6.99202i) q^{33} +(4.48515 - 3.25865i) q^{34} +(-1.71612 - 0.177204i) q^{35} +(-5.15610 - 3.74612i) q^{36} +(-5.17761 - 0.820053i) q^{37} +(0.632886 - 4.31271i) q^{38} +(-2.30067 + 3.16660i) q^{39} +(0.905760 - 2.04441i) q^{40} +(-2.44261 - 3.36196i) q^{41} +(1.07240 + 2.10471i) q^{42} +(-5.46001 - 5.46001i) q^{43} +(-2.43771 - 0.792060i) q^{44} +(3.66332 - 13.7722i) q^{45} +(-1.82705 + 0.593644i) q^{46} +(6.30887 + 3.21453i) q^{47} +(-3.02389 + 0.478937i) q^{48} +6.40471i q^{49} +(4.99407 + 0.243445i) q^{50} -16.9733i q^{51} +(0.199997 + 1.26273i) q^{52} +(4.33652 + 2.20957i) q^{53} +(-9.82212 + 3.19140i) q^{54} +(-0.310408 - 5.72299i) q^{55} +(0.733789 + 0.238422i) q^{56} +(-9.54312 - 9.32852i) q^{57} +(4.16547 - 2.12241i) q^{58} +(-1.02939 + 0.747898i) q^{59} +(-3.43377 - 5.92247i) q^{60} +(-4.11298 - 2.98825i) q^{61} +(1.22005 - 7.70309i) q^{62} +(4.85678 + 0.769238i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-2.47313 + 1.43389i) q^{65} +(-6.34862 + 4.61254i) q^{66} +(6.78351 - 3.45637i) q^{67} +(-3.92017 - 3.92017i) q^{68} +(-1.81749 + 5.59366i) q^{69} +(0.0934377 + 1.72271i) q^{70} +(-7.79082 + 2.53139i) q^{71} +(-2.89341 + 5.67864i) q^{72} +(-1.71010 - 10.7971i) q^{73} +5.24215i q^{74} +(9.59007 - 11.9316i) q^{75} +(-4.35862 + 0.0495624i) q^{76} +(1.95326 - 0.309366i) q^{77} +(3.48752 + 1.77698i) q^{78} +(0.660744 + 2.03356i) q^{79} +(-2.16093 - 0.574792i) q^{80} +(-3.86238 + 11.8872i) q^{81} +(-2.93846 + 2.93846i) q^{82} +(10.8409 - 5.52370i) q^{83} +(1.91103 - 1.38845i) q^{84} +(5.02149 - 11.3341i) q^{85} +(-4.53866 + 6.24693i) q^{86} +(2.23904 - 14.1367i) q^{87} +(-0.400966 + 2.53160i) q^{88} +(7.48216 + 5.43610i) q^{89} +(-14.1757 - 1.46377i) q^{90} +(-0.579794 - 0.798018i) q^{91} +(0.872149 + 1.71169i) q^{92} +(-16.8840 - 16.8840i) q^{93} +(2.18803 - 6.73406i) q^{94} +(-3.61271 - 9.05253i) q^{95} +(0.946081 + 2.91174i) q^{96} +(-6.11035 + 11.9922i) q^{97} +(6.32586 - 1.00192i) q^{98} +16.3357i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more