LMFDB - Embedded newform 637.2.x.b.215.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(19,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 5]))

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

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

chi := DirichletCharacter("637.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.x (of order $12$, degree $4$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			215.6
Character	$\chi$	$=$	637.215
Dual form			637.2.x.b.80.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.239080 - 0.892257i) q^{2} +1.14107i q^{3} +(0.993087 + 0.573359i) q^{4} +(1.02497 + 3.82526i) q^{5} +(1.01813 + 0.272807i) q^{6} +(2.05537 - 2.05537i) q^{8} +1.69796 q^{9} +O(q^{10})$	\(q+(0.239080 - 0.892257i) q^{2} +1.14107i q^{3} +(0.993087 + 0.573359i) q^{4} +(1.02497 + 3.82526i) q^{5} +(1.01813 + 0.272807i) q^{6} +(2.05537 - 2.05537i) q^{8} +1.69796 q^{9} +3.65816 q^{10} +(1.48892 - 1.48892i) q^{11} +(-0.654243 + 1.13318i) q^{12} +(-3.41094 - 1.16855i) q^{13} +(-4.36489 + 1.16957i) q^{15} +(-0.195801 - 0.339138i) q^{16} +(1.58621 - 2.74739i) q^{17} +(0.405947 - 1.51502i) q^{18} +(0.825689 - 0.825689i) q^{19} +(-1.17536 + 4.38649i) q^{20} +(-0.972529 - 1.68447i) q^{22} +(-3.26418 + 1.88457i) q^{23} +(2.34532 + 2.34532i) q^{24} +(-9.25190 + 5.34158i) q^{25} +(-1.85813 + 2.76406i) q^{26} +5.36070i q^{27} +(-0.584891 + 1.01306i) q^{29} +4.17422i q^{30} +(4.88736 + 1.30956i) q^{31} +(5.26595 - 1.41101i) q^{32} +(1.69896 + 1.69896i) q^{33} +(-2.07215 - 2.07215i) q^{34} +(1.68622 + 0.973539i) q^{36} +(-4.26868 - 1.14379i) q^{37} +(-0.539321 - 0.934132i) q^{38} +(1.33339 - 3.89212i) q^{39} +(9.96900 + 5.75561i) q^{40} +(-1.85922 - 6.93869i) q^{41} +(-1.91410 + 1.10511i) q^{43} +(2.33231 - 0.624941i) q^{44} +(1.74036 + 6.49513i) q^{45} +(0.901126 + 3.36305i) q^{46} +(-11.2261 + 3.00801i) q^{47} +(0.386980 - 0.223423i) q^{48} +(2.55413 + 9.53214i) q^{50} +(3.13497 + 1.80998i) q^{51} +(-2.71736 - 3.11616i) q^{52} +(-2.44630 - 4.23711i) q^{53} +(4.78313 + 1.28163i) q^{54} +(7.22161 + 4.16940i) q^{55} +(0.942169 + 0.942169i) q^{57} +(0.764076 + 0.764076i) q^{58} +(0.236582 - 0.0633920i) q^{59} +(-5.00530 - 1.34116i) q^{60} -12.3685i q^{61} +(2.33694 - 4.04770i) q^{62} -5.81913i q^{64} +(0.973870 - 14.2454i) q^{65} +(1.92210 - 1.10972i) q^{66} +(7.28743 + 7.28743i) q^{67} +(3.15048 - 1.81893i) q^{68} +(-2.15043 - 3.72465i) q^{69} +(1.60477 - 5.98907i) q^{71} +(3.48993 - 3.48993i) q^{72} +(1.27338 - 4.75231i) q^{73} +(-2.04111 + 3.53530i) q^{74} +(-6.09513 - 10.5571i) q^{75} +(1.29340 - 0.346564i) q^{76} +(-3.15399 - 2.12026i) q^{78} +(1.34840 - 2.33549i) q^{79} +(1.09660 - 1.09660i) q^{80} -1.02306 q^{81} -6.63560 q^{82} +(-3.31162 + 3.31162i) q^{83} +(12.1353 + 3.25165i) q^{85} +(0.528416 + 1.97208i) q^{86} +(-1.15597 - 0.667402i) q^{87} -6.12055i q^{88} +(1.80032 - 6.71890i) q^{89} +6.21141 q^{90} -4.32215 q^{92} +(-1.49431 + 5.57683i) q^{93} +10.7357i q^{94} +(4.00478 + 2.31216i) q^{95} +(1.61006 + 6.00882i) q^{96} +(15.8523 + 4.24762i) q^{97} +(2.52812 - 2.52812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	$ 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) $ 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.239080	−	0.892257i	0.169055	−	0.630921i	−0.828433	−	0.560088i	$-0.810767\pi$
$2$	0.239080	−	0.892257i	0.169055	−	0.630921i	0.997488	−	0.0708335i	$-0.0225659\pi$
$3$			1.14107i			0.658797i	0.944191	+	0.329399i	$0.106846\pi$
$3$			1.14107i			0.658797i	−0.944191	+	0.329399i	$0.893154\pi$
$4$	0.993087	+	0.573359i	0.496543	+	0.286679i
$5$	1.02497	+	3.82526i	0.458383	+	1.71071i	0.677948	+	0.735110i	$0.262869\pi$
$5$	1.02497	+	3.82526i	0.458383	+	1.71071i	−0.219566	+	0.975598i	$0.570464\pi$
$6$	1.01813	+	0.272807i	0.415649	+	0.111373i
$7$		0			0
$7$		0			0
$8$	2.05537	−	2.05537i	0.726682	−	0.726682i
$9$	1.69796			0.565986
$10$	3.65816			1.15681
$11$	1.48892	−	1.48892i	0.448926	−	0.448926i	−0.446071	−	0.894997i	$-0.647177\pi$
$11$	1.48892	−	1.48892i	0.448926	−	0.448926i	0.894997	+	0.446071i	$0.147177\pi$
$12$	−0.654243	+	1.13318i	−0.188864	+	0.327121i
$13$	−3.41094	−	1.16855i	−0.946024	−	0.324097i
$13$	−3.41094	−	1.16855i	−0.946024	−	0.324097i
$14$		0			0
$15$	−4.36489	+	1.16957i	−1.12701	+	0.301981i
$16$	−0.195801	−	0.339138i	−0.0489503	−	0.0847845i
$17$	1.58621	−	2.74739i	0.384712	−	0.666341i	−0.607017	−	0.794689i	$-0.707634\pi$
$17$	1.58621	−	2.74739i	0.384712	−	0.666341i	0.991729	+	0.128348i	$0.0409674\pi$
$18$	0.405947	−	1.51502i	0.0956827	−	0.357093i
$19$	0.825689	−	0.825689i	0.189426	−	0.189426i	−0.606022	−	0.795448i	$-0.707236\pi$
$19$	0.825689	−	0.825689i	0.189426	−	0.189426i	0.795448	+	0.606022i	$0.207236\pi$
$20$	−1.17536	+	4.38649i	−0.262818	+	0.980849i
$21$		0			0
$22$	−0.972529	−	1.68447i	−0.207344	−	0.359130i
$23$	−3.26418	+	1.88457i	−0.680628	+	0.392961i	−0.800092	−	0.599878i	$-0.795216\pi$
$23$	−3.26418	+	1.88457i	−0.680628	+	0.392961i	0.119464	+	0.992839i	$0.461882\pi$
$24$	2.34532	+	2.34532i	0.478736	+	0.478736i
$25$	−9.25190	+	5.34158i	−1.85038	+	1.06832i
$26$	−1.85813	+	2.76406i	−0.364409	+	0.542076i
$27$			5.36070i			1.03167i
$28$		0			0
$29$	−0.584891	+	1.01306i	−0.108612	+	0.188121i	−0.915208	−	0.402982i	$-0.867974\pi$
$29$	−0.584891	+	1.01306i	−0.108612	+	0.188121i	0.806596	+	0.591102i	$0.201307\pi$
$30$			4.17422i			0.762106i
$31$	4.88736	+	1.30956i	0.877796	+	0.235205i	0.669456	−	0.742852i	$-0.266527\pi$
$31$	4.88736	+	1.30956i	0.877796	+	0.235205i	0.208340	+	0.978056i	$0.433194\pi$
$32$	5.26595	−	1.41101i	0.930898	−	0.249433i
$33$	1.69896	+	1.69896i	0.295751	+	0.295751i
$34$	−2.07215	−	2.07215i	−0.355371	−	0.355371i
$35$		0			0
$36$	1.68622	+	0.973539i	0.281037	+	0.162257i
$37$	−4.26868	−	1.14379i	−0.701766	−	0.188038i	−0.109745	−	0.993960i	$-0.535003\pi$
$37$	−4.26868	−	1.14379i	−0.701766	−	0.188038i	−0.592022	+	0.805922i	$0.701670\pi$
$38$	−0.539321	−	0.934132i	−0.0874895	−	0.151536i
$39$	1.33339	−	3.89212i	0.213514	−	0.623238i
$40$	9.96900	+	5.75561i	1.57624	+	0.910041i
$41$	−1.85922	−	6.93869i	−0.290361	−	1.08364i	−0.944832	−	0.327555i	$-0.893775\pi$
$41$	−1.85922	−	6.93869i	−0.290361	−	1.08364i	0.654472	−	0.756087i	$-0.272891\pi$
$42$		0			0
$43$	−1.91410	+	1.10511i	−0.291897	+	0.168527i	−0.638797	−	0.769375i	$-0.720568\pi$
$43$	−1.91410	+	1.10511i	−0.291897	+	0.168527i	0.346900	+	0.937902i	$0.387234\pi$
$44$	2.33231	−	0.624941i	0.351609	−	0.0942134i
$45$	1.74036	+	6.49513i	0.259438	+	0.968236i
$46$	0.901126	+	3.36305i	0.132864	+	0.495854i
$47$	−11.2261	+	3.00801i	−1.63749	+	0.438764i	−0.956072	−	0.293132i	$-0.905302\pi$
$47$	−11.2261	+	3.00801i	−1.63749	+	0.438764i	−0.681416	+	0.731896i	$0.738636\pi$
$48$	0.386980	−	0.223423i	0.0558558	−	0.0322484i
$49$		0			0
$50$	2.55413	+	9.53214i	0.361208	+	1.34805i
$51$	3.13497	+	1.80998i	0.438984	+	0.253447i
$52$	−2.71736	−	3.11616i	−0.376830	−	0.432134i
$53$	−2.44630	−	4.23711i	−0.336025	−	0.582012i	0.647656	−	0.761933i	$-0.275749\pi$
$53$	−2.44630	−	4.23711i	−0.336025	−	0.582012i	−0.983681	+	0.179921i	$0.942416\pi$
$54$	4.78313	+	1.28163i	0.650901	+	0.174408i
$55$	7.22161	+	4.16940i	0.973762	+	0.562202i
$56$		0			0
$57$	0.942169	+	0.942169i	0.124793	+	0.124793i
$58$	0.764076	+	0.764076i	0.100328	+	0.100328i
$59$	0.236582	−	0.0633920i	0.0308004	−	0.00825293i	−0.243386	−	0.969930i	$-0.578258\pi$
$59$	0.236582	−	0.0633920i	0.0308004	−	0.00825293i	0.274186	+	0.961677i	$0.411591\pi$
$60$	−5.00530	−	1.34116i	−0.646181	−	0.173144i
$61$		−	12.3685i		−	1.58362i	−0.610767	−	0.791811i	$-0.709139\pi$
$61$		−	12.3685i		−	1.58362i	0.610767	−	0.791811i	$-0.290861\pi$
$62$	2.33694	−	4.04770i	0.296791	−	0.514058i
$63$		0			0
$64$		−	5.81913i		−	0.727392i
$65$	0.973870	−	14.2454i	0.120794	−	1.76693i
$66$	1.92210	−	1.10972i	0.236594	−	0.136598i
$67$	7.28743	+	7.28743i	0.890301	+	0.890301i	0.994551	−	0.104250i	$-0.0332442\pi$
$67$	7.28743	+	7.28743i	0.890301	+	0.890301i	−0.104250	+	0.994551i	$0.533244\pi$
$68$	3.15048	−	1.81893i	0.382052	−	0.220578i
$69$	−2.15043	−	3.72465i	−0.258881	−	0.448396i
$70$		0			0
$71$	1.60477	−	5.98907i	0.190451	−	0.710772i	−0.802947	−	0.596051i	$-0.796736\pi$
$71$	1.60477	−	5.98907i	0.190451	−	0.710772i	0.993398	−	0.114722i	$-0.0365976\pi$
$72$	3.48993	−	3.48993i	0.411292	−	0.411292i
$73$	1.27338	−	4.75231i	0.149037	−	0.556216i	−0.850505	−	0.525967i	$-0.823703\pi$
$73$	1.27338	−	4.75231i	0.149037	−	0.556216i	0.999542	−	0.0302484i	$-0.00962984\pi$
$74$	−2.04111	+	3.53530i	−0.237274	+	0.410971i
$75$	−6.09513	−	10.5571i	−0.703804	−	1.21903i
$76$	1.29340	−	0.346564i	0.148363	−	0.0397537i
$77$		0			0
$78$	−3.15399	−	2.12026i	−0.357119	−	0.240072i
$79$	1.34840	−	2.33549i	0.151707	−	0.262764i	−0.780148	−	0.625595i	$-0.784856\pi$
$79$	1.34840	−	2.33549i	0.151707	−	0.262764i	0.931855	+	0.362831i	$0.118190\pi$
$80$	1.09660	−	1.09660i	0.122603	−	0.122603i
$81$	−1.02306			−0.113674
$82$	−6.63560			−0.732779
$83$	−3.31162	+	3.31162i	−0.363497	+	0.363497i	−0.865099	−	0.501602i	$-0.832744\pi$
$83$	−3.31162	+	3.31162i	−0.363497	+	0.363497i	0.501602	+	0.865099i	$0.332744\pi$
$84$		0			0
$85$	12.1353	+	3.25165i	1.31626	+	0.352691i
$86$	0.528416	+	1.97208i	0.0569806	+	0.212654i
$87$	−1.15597	−	0.667402i	−0.123933	−	0.0715530i
$88$		−	6.12055i		−	0.652453i
$89$	1.80032	−	6.71890i	0.190834	−	0.712202i	−0.802472	−	0.596690i	$-0.796482\pi$
$89$	1.80032	−	6.71890i	0.190834	−	0.712202i	0.993306	−	0.115512i	$-0.0368510\pi$
$90$	6.21141			0.654740
$91$		0			0
$92$	−4.32215			−0.450615
$93$	−1.49431	+	5.57683i	−0.154952	+	0.578290i
$94$			10.7357i			1.10730i
$95$	4.00478	+	2.31216i	0.410882	+	0.237223i
$96$	1.61006	+	6.00882i	0.164326	+	0.613273i
$97$	15.8523	+	4.24762i	1.60956	+	0.431280i	0.947912	−	0.318533i	$-0.103190\pi$
$97$	15.8523	+	4.24762i	1.60956	+	0.431280i	0.661649	+	0.749814i	$0.269857\pi$
$98$		0			0
$99$	2.52812	−	2.52812i	0.254086	−	0.254086i
$100$	−12.2506			−1.22506
$101$	−3.62029			−0.360233			−0.180116	−	0.983645i	$-0.557647\pi$
$101$	−3.62029			−0.360233			−0.180116	+	0.983645i	$0.557647\pi$
$102$	2.36447	−	2.36447i	0.234118	−	0.234118i
$103$	−0.795369	+	1.37762i	−0.0783700	+	0.135741i	−0.902547	−	0.430592i	$-0.858305\pi$
$103$	−0.795369	+	1.37762i	−0.0783700	+	0.135741i	0.824177	+	0.566333i	$0.191638\pi$
$104$	−9.41252	+	4.60893i	−0.922973	+	0.451943i
$105$		0			0
$106$	−4.36545	+	1.16972i	−0.424010	+	0.113613i
$107$	7.44322	+	12.8920i	0.719563	+	1.24632i	0.961173	+	0.275946i	$0.0889911\pi$
$107$	7.44322	+	12.8920i	0.719563	+	1.24632i	−0.241610	+	0.970373i	$0.577676\pi$
$108$	−3.07361	+	5.32364i	−0.295758	+	0.512268i
$109$	−0.868870	+	3.24267i	−0.0832226	+	0.310591i	−0.994972	−	0.100157i	$-0.968066\pi$
$109$	−0.868870	+	3.24267i	−0.0832226	+	0.310591i	0.911749	+	0.410748i	$0.134732\pi$
$110$	5.44672	−	5.44672i	0.519324	−	0.519324i
$111$	1.30514	−	4.87086i	0.123879	−	0.462322i
$112$		0			0
$113$	−4.88202	−	8.45591i	−0.459262	−	0.795465i	0.539660	−	0.841883i	$-0.318553\pi$
$113$	−4.88202	−	8.45591i	−0.459262	−	0.795465i	−0.998922	+	0.0464177i	$0.985219\pi$
$114$	1.06591	−	0.615404i	0.0998317	−	0.0576378i
$115$	−10.5547	−	10.5547i	−0.984228	−	0.984228i
$116$	−1.16170	+	0.670705i	−0.107861	+	0.0622734i
$117$	−5.79163	−	1.98414i	−0.535436	−	0.183434i
$118$		−	0.226248i		−	0.0208278i
$119$		0			0
$120$	−6.56755	+	11.3753i	−0.599533	+	1.03842i
$121$			6.56623i			0.596930i
$122$	−11.0359	−	2.95705i	−0.999140	−	0.267719i
$123$	7.91753	−	2.12150i	0.713900	−	0.191289i
$124$	4.10272	+	4.10272i	0.368436	+	0.368436i
$125$	−15.9145	−	15.9145i	−1.42343	−	1.42343i
$126$		0			0
$127$	−6.81869	−	3.93677i	−0.605061	−	0.349332i	0.165969	−	0.986131i	$-0.446925\pi$
$127$	−6.81869	−	3.93677i	−0.605061	−	0.349332i	−0.771030	+	0.636799i	$0.780258\pi$
$128$	5.33974	+	1.43078i	0.471971	+	0.126464i
$129$	−1.26100	−	2.18412i	−0.111025	−	0.192301i
$130$	−12.4778	−	4.27474i	−1.09437	−	0.374919i
$131$	−1.83447	−	1.05913i	−0.160279	−	0.0925369i	0.417715	−	0.908578i	$-0.362831\pi$
$131$	−1.83447	−	1.05913i	−0.160279	−	0.0925369i	−0.577994	+	0.816041i	$0.696164\pi$
$132$	0.713102	+	2.66133i	0.0620676	+	0.231639i
$133$		0			0
$134$	8.24454	−	4.75999i	0.712220	−	0.411200i
$135$	−20.5061	+	5.49458i	−1.76488	+	0.472898i
$136$	−2.38666	−	8.90714i	−0.204654	−	0.763781i
$137$	−3.02455	−	11.2878i	−0.258405	−	0.964380i	−0.966164	−	0.257927i	$-0.916961\pi$
$137$	−3.02455	−	11.2878i	−0.258405	−	0.964380i	0.707760	−	0.706453i	$-0.249706\pi$
$138$	−3.83747	+	1.02825i	−0.326668	+	0.0875303i
$139$	3.88166	−	2.24108i	0.329238	−	0.190086i	−0.326265	−	0.945278i	$-0.605790\pi$
$139$	3.88166	−	2.24108i	0.329238	−	0.190086i	0.655503	+	0.755193i	$0.272457\pi$
$140$		0			0
$141$	−3.43235	−	12.8097i	−0.289056	−	1.07877i
$142$	−4.96013	−	2.86373i	−0.416245	−	0.240319i
$143$	−6.81849	+	3.33874i	−0.570191	+	0.279200i
$144$	−0.332462	−	0.575842i	−0.0277052	−	0.0479868i
$145$	−4.47472	−	1.19900i	−0.371605	−	0.0995713i
$146$	−3.93584	−	2.27236i	−0.325733	−	0.188062i
$147$		0			0
$148$	−3.58337	−	3.58337i	−0.294551	−	0.294551i
$149$	3.22134	+	3.22134i	0.263903	+	0.263903i	0.826638	−	0.562735i	$-0.190251\pi$
$149$	3.22134	+	3.22134i	0.263903	+	0.263903i	−0.562735	+	0.826638i	$0.690251\pi$
$150$	−10.8768	+	2.91444i	−0.888090	+	0.237963i
$151$	14.6306	+	3.92025i	1.19062	+	0.319026i	0.799131	−	0.601157i	$-0.205293\pi$
$151$	14.6306	+	3.92025i	1.19062	+	0.319026i	0.391489	+	0.920183i	$0.371960\pi$
$152$		−	3.39418i		−	0.275305i
$153$	2.69331	−	4.66496i	0.217742	−	0.377140i
$154$		0			0
$155$			20.0377i			1.60947i
$156$	3.55576	−	3.10070i	0.284689	−	0.248255i
$157$	−12.1069	+	6.98994i	−0.966239	+	0.557858i	−0.898088	−	0.439817i	$-0.855043\pi$
$157$	−12.1069	+	6.98994i	−0.966239	+	0.557858i	−0.0681513	+	0.997675i	$0.521710\pi$
$158$	−1.76149	−	1.76149i	−0.140136	−	0.140136i
$159$	4.83484	−	2.79140i	0.383428	−	0.221372i
$160$	10.7949	+	18.6974i	0.853415	+	1.47816i
$161$		0			0
$162$	−0.244594	+	0.912837i	−0.0192171	+	0.0717192i
$163$	16.5003	−	16.5003i	1.29240	−	1.29240i	0.359107	−	0.933297i	$-0.383081\pi$
$163$	16.5003	−	16.5003i	1.29240	−	1.29240i	0.933297	−	0.359107i	$-0.116919\pi$
$164$	2.13200	−	7.95672i	0.166481	−	0.621315i
$165$	−4.75758	+	8.24037i	−0.370377	+	0.641512i
$166$	2.16307	+	3.74655i	0.167887	+	0.290789i
$167$	−10.8156	+	2.89803i	−0.836935	+	0.224256i	−0.651737	−	0.758445i	$-0.725959\pi$
$167$	−10.8156	+	2.89803i	−0.836935	+	0.224256i	−0.185198	+	0.982701i	$0.559293\pi$
$168$		0			0
$169$	10.2690	+	7.97168i	0.789923	+	0.613207i
$170$	5.80261	−	10.0504i	0.445040	−	0.770832i
$171$	1.40198	−	1.40198i	0.107212	−	0.107212i
$172$	−2.53449			−0.193253
$173$	−3.32856			−0.253066			−0.126533	−	0.991962i	$-0.540385\pi$
$173$	−3.32856			−0.253066			−0.126533	+	0.991962i	$0.540385\pi$
$174$	−0.871864	+	0.871864i	−0.0660959	+	0.0660959i
$175$		0			0
$176$	−0.796482	−	0.213417i	−0.0600371	−	0.0160869i
$177$	0.0723347	+	0.269957i	0.00543701	+	0.0202912i
$178$	−5.56457	−	3.21270i	−0.417082	−	0.240802i
$179$			0.255535i			0.0190996i	0.999954	+	0.00954980i	$0.00303984\pi$
$179$			0.255535i			0.0190996i	−0.999954	+	0.00954980i	$0.996960\pi$
$180$	−1.99571	+	7.44808i	−0.148751	+	0.555147i
$181$	−7.65115			−0.568705			−0.284353	−	0.958720i	$-0.591779\pi$
$181$	−7.65115			−0.568705			−0.284353	+	0.958720i	$0.591779\pi$
$182$		0			0
$183$	14.1133			1.04329
$184$	−2.83559	+	10.5826i	−0.209042	+	0.780157i
$185$		−	17.5011i		−	1.28671i
$186$	4.61871	+	2.66661i	0.338660	+	0.195525i
$187$	−1.72891	−	6.45239i	−0.126431	−	0.471845i
$188$	−12.8731	−	3.44934i	−0.938868	−	0.251569i
$189$		0			0
$190$	3.02050	−	3.02050i	0.219130	−	0.219130i
$191$	−14.5107			−1.04996			−0.524978	−	0.851116i	$-0.675927\pi$
$191$	−14.5107			−1.04996			−0.524978	+	0.851116i	$0.675927\pi$
$192$	6.64004			0.479204
$193$	5.69196	−	5.69196i	0.409716	−	0.409716i	−0.471924	−	0.881639i	$-0.656440\pi$
$193$	5.69196	−	5.69196i	0.409716	−	0.409716i	0.881639	+	0.471924i	$0.156440\pi$
$194$	7.57994	−	13.1288i	0.544208	−	0.942596i
$195$	16.2551	+	1.11125i	1.16405	+	0.0795785i
$196$		0			0
$197$	6.28115	−	1.68303i	0.447514	−	0.119911i	−0.0280221	−	0.999607i	$-0.508921\pi$
$197$	6.28115	−	1.68303i	0.447514	−	0.119911i	0.475536	+	0.879696i	$0.342254\pi$
$198$	−1.65131	−	2.86016i	−0.117354	−	0.203263i
$199$	−3.53990	+	6.13129i	−0.250937	+	0.434636i	−0.963784	−	0.266684i	$-0.914072\pi$
$199$	−3.53990	+	6.13129i	−0.250937	+	0.434636i	0.712847	+	0.701320i	$0.247405\pi$
$200$	−8.03712	+	29.9949i	−0.568310	+	2.12096i
$201$	−8.31547	+	8.31547i	−0.586528	+	0.586528i
$202$	−0.865539	+	3.23023i	−0.0608991	+	0.227279i
$203$		0			0
$204$	2.07553	+	3.59493i	0.145316	+	0.251695i
$205$	24.6366	−	14.2240i	1.72070	−	0.993445i
$206$	1.03903	+	1.03903i	0.0723929	+	0.0723929i
$207$	−5.54243	+	3.19993i	−0.385226	+	0.222410i
$208$	0.271568	+	1.38558i	0.0188298	+	0.0960728i
$209$		−	2.45877i		−	0.170077i
$210$		0			0
$211$	−3.81923	+	6.61509i	−0.262926	+	0.455402i	−0.967018	−	0.254707i	$-0.918021\pi$
$211$	−3.81923	+	6.61509i	−0.262926	+	0.455402i	0.704092	+	0.710109i	$0.251354\pi$
$212$		−	5.61043i		−	0.385326i
$213$	6.83395	+	1.83115i	0.468255	+	0.125469i
$214$	13.2825	−	3.55904i	0.907975	−	0.243291i
$215$	−6.18921	−	6.18921i	−0.422101	−	0.422101i
$216$	11.0182	+	11.0182i	0.749694	+	0.749694i
$217$		0			0
$218$	2.68556	+	1.55051i	0.181889	+	0.105014i
$219$	5.42272	+	1.45301i	0.366433	+	0.0981855i
$220$	4.78112	+	8.28115i	0.322343	+	0.558315i
$221$	−8.62092	+	7.51763i	−0.579906	+	0.505690i
$222$	−4.03403	−	2.32905i	−0.270746	−	0.156315i
$223$	−1.74359	−	6.50716i	−0.116759	−	0.435752i	0.882653	−	0.470025i	$-0.155755\pi$
$223$	−1.74359	−	6.50716i	−0.116759	−	0.435752i	−0.999413	+	0.0342732i	$0.989088\pi$
$224$		0			0
$225$	−15.7093	+	9.06979i	−1.04729	+	0.604652i
$226$	−8.71204	+	2.33438i	−0.579516	+	0.155281i
$227$	4.18872	+	15.6325i	0.278015	+	1.03757i	0.953794	+	0.300462i	$0.0971409\pi$
$227$	4.18872	+	15.6325i	0.278015	+	1.03757i	−0.675778	+	0.737105i	$0.736192\pi$
$228$	0.395455	+	1.47586i	0.0261896	+	0.0977410i
$229$	18.9495	−	5.07751i	1.25222	−	0.335531i	0.429027	−	0.903292i	$-0.358857\pi$
$229$	18.9495	−	5.07751i	1.25222	−	0.335531i	0.823194	+	0.567760i	$0.192190\pi$
$230$	−11.9409	+	6.89408i	−0.787359	+	0.454582i
$231$		0			0
$232$	0.880046	+	3.28438i	0.0577778	+	0.215630i
$233$	−9.61575	−	5.55165i	−0.629949	−	0.363701i	0.150784	−	0.988567i	$-0.451820\pi$
$233$	−9.61575	−	5.55165i	−0.629949	−	0.363701i	−0.780732	+	0.624866i	$0.785154\pi$
$234$	−3.15503	+	4.69326i	−0.206251	+	0.306808i
$235$	−23.0128	−	39.8594i	−1.50119	−	2.60014i
$236$	0.271293	+	0.0726927i	0.0176597	+	0.00473189i
$237$	2.66496	+	1.53862i	0.173108	+	0.0999439i
$238$		0			0
$239$	−18.0241	−	18.0241i	−1.16588	−	1.16588i	−0.983166	−	0.182716i	$-0.941511\pi$
$239$	−18.0241	−	18.0241i	−1.16588	−	1.16588i	−0.182716	−	0.983166i	$-0.558489\pi$
$240$	1.25130	+	1.25130i	0.0807708	+	0.0807708i
$241$	24.5725	−	6.58419i	1.58286	−	0.424125i	0.643048	−	0.765826i	$-0.277670\pi$
$241$	24.5725	−	6.58419i	1.58286	−	0.424125i	0.939809	+	0.341701i	$0.111003\pi$
$242$	5.85877	+	1.56985i	0.376616	+	0.100914i
$243$			14.9147i			0.956779i
$244$	7.09158	−	12.2830i	0.453992	−	0.786337i
$245$		0			0
$246$		−	7.57168i		−	0.482753i
$247$	−3.78123	+	1.85152i	−0.240594	+	0.117809i
$248$	12.7370	−	7.35368i	0.808797	−	0.466959i
$249$	−3.77879	−	3.77879i	−0.239471	−	0.239471i
$250$	−18.0046	+	10.3950i	−1.13871	+	0.657437i
$251$	−3.01219	−	5.21727i	−0.190128	−	0.329311i	0.755165	−	0.655535i	$-0.227557\pi$
$251$	−3.01219	−	5.21727i	−0.190128	−	0.329311i	−0.945292	+	0.326224i	$0.894224\pi$
$252$		0			0
$253$	−2.05412	+	7.66608i	−0.129141	+	0.481962i
$254$	−5.14282	+	5.14282i	−0.322689	+	0.322689i
$255$	−3.71036	+	13.8472i	−0.232352	+	0.867148i
$256$	8.37238	−	14.5014i	0.523274	−	0.906337i
$257$	12.2067	+	21.1426i	0.761434	+	1.31884i	0.942112	+	0.335300i	$0.108838\pi$
$257$	12.2067	+	21.1426i	0.761434	+	1.31884i	−0.180678	+	0.983542i	$0.557829\pi$
$258$	−2.25028	+	0.602960i	−0.140096	+	0.0375387i
$259$		0			0
$260$	9.13489	−	13.5886i	0.566522	−	0.842728i
$261$	−0.993120	+	1.72014i	−0.0614726	+	0.106474i
$262$	−1.38360	+	1.38360i	−0.0854794	+	0.0854794i
$263$	−15.1408			−0.933624			−0.466812	−	0.884357i	$-0.654597\pi$
$263$	−15.1408			−0.933624			−0.466812	+	0.884357i	$0.654597\pi$
$264$	6.98398			0.429834
$265$	13.7007	−	13.7007i	0.841624	−	0.841624i
$266$		0			0
$267$	7.66674	+	2.05430i	0.469197	+	0.125721i
$268$	3.05874	+	11.4154i	0.186842	+	0.697304i
$269$	−3.06678	−	1.77061i	−0.186985	−	0.107956i	0.403585	−	0.914942i	$-0.367764\pi$
$269$	−3.06678	−	1.77061i	−0.186985	−	0.107956i	−0.590570	+	0.806986i	$0.701097\pi$
$270$			19.6103i			1.19345i
$271$	0.195709	−	0.730396i	0.0118885	−	0.0443684i	−0.959727	−	0.280935i	$-0.909355\pi$
$271$	0.195709	−	0.730396i	0.0118885	−	0.0443684i	0.971615	+	0.236567i	$0.0760221\pi$
$272$	−1.24233			−0.0753271
$273$		0			0
$274$	−10.7947			−0.652133
$275$	−5.82214	+	21.7285i	−0.351088	+	1.31028i
$276$		−	4.93187i		−	0.296864i
$277$	9.03071	+	5.21388i	0.542603	+	0.313272i	0.746133	−	0.665797i	$-0.231908\pi$
$277$	9.03071	+	5.21388i	0.542603	+	0.313272i	−0.203530	+	0.979069i	$0.565242\pi$
$278$	−1.07159	−	3.99923i	−0.0642698	−	0.239858i
$279$	8.29854	+	2.22359i	0.496820	+	0.133123i
$280$		0			0
$281$	−18.1394	+	18.1394i	−1.08211	+	1.08211i	−0.0857959	+	0.996313i	$0.527343\pi$
$281$	−18.1394	+	18.1394i	−1.08211	+	1.08211i	−0.996313	+	0.0857959i	$0.972657\pi$
$282$	−12.2502			−0.729487
$283$	−0.0492199			−0.00292582			−0.00146291	−	0.999999i	$-0.500466\pi$
$283$	−0.0492199			−0.00292582			−0.00146291	+	0.999999i	$0.500466\pi$
$284$	5.02756	−	5.02756i	0.298331	−	0.298331i
$285$	−2.63834	+	4.56974i	−0.156282	+	0.270688i
$286$	1.34885	+	6.88207i	0.0797594	+	0.406945i
$287$		0			0
$288$	8.94137	−	2.39583i	0.526875	−	0.141176i
$289$	3.46789	+	6.00656i	0.203993	+	0.353327i
$290$	−2.13963	+	3.70594i	−0.125643	+	0.217621i
$291$	−4.84683	+	18.0886i	−0.284126	+	1.06037i
$292$	3.98935	−	3.98935i	0.233459	−	0.233459i
$293$	4.26864	−	15.9308i	0.249377	−	0.930686i	−0.721756	−	0.692147i	$-0.756665\pi$
$293$	4.26864	−	15.9308i	0.249377	−	0.930686i	0.971133	−	0.238539i	$-0.0766685\pi$
$294$		0			0
$295$	0.484981	+	0.840012i	0.0282367	+	0.0489074i
$296$	−11.1246	+	6.42279i	−0.646604	+	0.373317i
$297$	7.98166	+	7.98166i	0.463143	+	0.463143i
$298$	3.64443	−	2.10411i	0.211116	−	0.121888i
$299$	13.3361	−	2.61382i	0.771247	−	0.151161i
$300$		−	13.9788i		−	0.807065i
$301$		0			0
$302$	6.99575	−	12.1170i	0.402560	−	0.697255i
$303$		−	4.13101i		−	0.237320i
$304$	−0.441693	−	0.118351i	−0.0253328	−	0.00678791i
$305$	47.3126	−	12.6774i	2.70911	−	0.725905i
$306$	−3.51843	−	3.51843i	−0.201135	−	0.201135i
$307$	13.8117	+	13.8117i	0.788274	+	0.788274i	0.981211	−	0.192937i	$-0.0618012\pi$
$307$	13.8117	+	13.8117i	0.788274	+	0.788274i	−0.192937	+	0.981211i	$0.561801\pi$
$308$		0			0
$309$	−1.57196	−	0.907572i	−0.0894257	−	0.0516300i
$310$	17.8788	+	4.79060i	1.01545	+	0.272088i
$311$	−2.25556	−	3.90675i	−0.127901	−	0.221531i	0.794962	−	0.606659i	$-0.207491\pi$
$311$	−2.25556	−	3.90675i	−0.127901	−	0.221531i	−0.922863	+	0.385128i	$0.874157\pi$
$312$	−5.25912	−	10.7403i	−0.297739	−	0.608052i
$313$	−26.8350	−	15.4932i	−1.51681	−	0.875728i	−0.999805	−	0.0197427i	$-0.993715\pi$
$313$	−26.8350	−	15.4932i	−1.51681	−	0.875728i	−0.517000	−	0.855985i	$-0.672951\pi$
$314$	3.34231	+	12.4737i	0.188617	+	0.703929i
$315$		0			0
$316$	2.67815	−	1.54623i	0.150658	−	0.0869823i
$317$	−5.92099	+	1.58652i	−0.332556	+	0.0891081i	−0.421233	−	0.906952i	$-0.638403\pi$
$317$	−5.92099	+	1.58652i	−0.332556	+	0.0891081i	0.0886774	+	0.996060i	$0.471736\pi$
$318$	−1.33473	−	4.98129i	−0.0748481	−	0.279337i
$319$	0.637511	+	2.37922i	0.0356938	+	0.133211i
$320$	22.2597	−	5.96447i	1.24435	−	0.333424i
$321$	−14.7107	+	8.49323i	−0.821072	+	0.474046i
$322$		0			0
$323$	−0.958777	−	3.57820i	−0.0533478	−	0.199097i
$324$	−1.01599	−	0.586583i	−0.0564440	−	0.0325879i
$325$	37.7995	−	7.40854i	2.09674	−	0.410952i
$326$	−10.7776	−	18.6674i	−0.596918	−	1.03389i
$327$	−3.70011	−	0.991442i	−0.204617	−	0.0548268i
$328$	−18.0829	−	10.4402i	−0.998462	−	0.576462i
$329$		0			0
$330$	6.21509	+	6.21509i	0.342129	+	0.342129i
$331$	11.8222	+	11.8222i	0.649807	+	0.649807i	0.952946	−	0.303139i	$-0.0980348\pi$
$331$	11.8222	+	11.8222i	0.649807	+	0.649807i	−0.303139	+	0.952946i	$0.598035\pi$
$332$	−5.18747	+	1.38998i	−0.284699	+	0.0762849i
$333$	−7.24804	−	1.94211i	−0.397190	−	0.106427i
$334$			10.3431i			0.565952i
$335$	−20.4069	+	35.3457i	−1.11495	+	1.93114i
$336$		0			0
$337$		−	12.4651i		−	0.679017i	−0.940603	−	0.339508i	$-0.889739\pi$
$337$		−	12.4651i		−	0.679017i	0.940603	−	0.339508i	$-0.110261\pi$
$338$	9.56790	−	7.25672i	0.520425	−	0.394713i
$339$	9.64879	−	5.57073i	0.524050	−	0.302561i
$340$	10.1871	+	10.1871i	0.552471	+	0.552471i
$341$	9.22673	−	5.32706i	0.499656	−	0.288476i
$342$	−0.915745	−	1.58612i	−0.0495178	−	0.0857674i
$343$		0			0
$344$	−1.66278	+	6.20557i	−0.0896509	+	0.334582i
$345$	12.0436	−	12.0436i	0.648407	−	0.648407i
$346$	−0.795792	+	2.96994i	−0.0427820	+	0.159665i
$347$	−13.1263	+	22.7355i	−0.704659	+	1.22050i	0.262156	+	0.965026i	$0.415566\pi$
$347$	−13.1263	+	22.7355i	−0.704659	+	1.22050i	−0.966815	+	0.255479i	$0.917767\pi$
$348$	−0.765322	−	1.32558i	−0.0410256	−	0.0710583i
$349$	7.06951	−	1.89427i	0.378422	−	0.101398i	−0.0645937	−	0.997912i	$-0.520575\pi$
$349$	7.06951	−	1.89427i	0.378422	−	0.101398i	0.443016	+	0.896514i	$0.353908\pi$
$350$		0			0
$351$	6.26423	−	18.2850i	0.334360	−	0.975982i
$352$	5.73971	−	9.94146i	0.305927	−	0.529882i
$353$	19.2744	−	19.2744i	1.02587	−	1.02587i	0.0262143	−	0.999656i	$-0.491655\pi$
$353$	19.2744	−	19.2744i	1.02587	−	1.02587i	0.999656	−	0.0262143i	$-0.00834524\pi$
$354$	0.258165			0.0137213
$355$	24.5546			1.30322
$356$	5.64022	−	5.64022i	0.298931	−	0.298931i
$357$		0			0
$358$	0.228003	+	0.0610933i	0.0120503	+	0.00322888i
$359$	−8.04040	−	30.0072i	−0.424356	−	1.58372i	−0.765325	−	0.643644i	$-0.777422\pi$
$359$	−8.04040	−	30.0072i	−0.424356	−	1.58372i	0.340969	−	0.940074i	$-0.389245\pi$
$360$	16.9269	+	9.77278i	0.892128	+	0.515071i
$361$			17.6365i			0.928236i
$362$	−1.82923	+	6.82679i	−0.0961424	+	0.358808i
$363$	−7.49254			−0.393256
$364$		0			0
$365$	19.4840			1.01984
$366$	3.37420	−	12.5927i	0.176372	−	0.658231i
$367$			25.1296i			1.31175i	0.754867	+	0.655877i	$0.227701\pi$
$367$			25.1296i			1.31175i	−0.754867	+	0.655877i	$0.772299\pi$
$368$	1.27826	+	0.738004i	0.0666339	+	0.0384711i
$369$	−3.15687	−	11.7816i	−0.164340	−	0.613326i
$370$	−15.6155	−	4.18417i	−0.811813	−	0.217525i
$371$		0			0
$372$	−4.68150	+	4.68150i	−0.242724	+	0.242724i
$373$	−3.10820			−0.160937			−0.0804683	−	0.996757i	$-0.525642\pi$
$373$	−3.10820			−0.160937			−0.0804683	+	0.996757i	$0.525642\pi$
$374$	−6.17054			−0.319071
$375$	18.1595	−	18.1595i	0.937755	−	0.937755i
$376$	−16.8911	+	29.2562i	−0.871091	+	1.50877i
$377$	3.17884	−	2.77202i	0.163718	−	0.142766i
$378$		0			0
$379$	−4.35536	+	1.16702i	−0.223720	+	0.0599456i	−0.368938	−	0.929454i	$-0.620278\pi$
$379$	−4.35536	+	1.16702i	−0.223720	+	0.0599456i	0.145218	+	0.989400i	$0.453612\pi$
$380$	2.65140	+	4.59235i	0.136014	+	0.235583i
$381$	4.49213	−	7.78060i	0.230139	−	0.398612i
$382$	−3.46921	+	12.9473i	−0.177500	+	0.662440i
$383$	−23.7683	+	23.7683i	−1.21450	+	1.21450i	−0.244974	+	0.969530i	$0.578779\pi$
$383$	−23.7683	+	23.7683i	−1.21450	+	1.21450i	−0.969530	+	0.244974i	$0.921221\pi$
$384$	−1.63262	+	6.09302i	−0.0833143	+	0.310933i
$385$		0			0
$386$	−3.71786	−	6.43952i	−0.189234	−	0.327763i
$387$	−3.25006	+	1.87642i	−0.165210	+	0.0953839i
$388$	13.3073	+	13.3073i	0.675577	+	0.675577i
$389$	−17.8940	+	10.3311i	−0.907263	+	0.523809i	−0.879550	−	0.475807i	$-0.842156\pi$
$389$	−17.8940	+	10.3311i	−0.907263	+	0.523809i	−0.0277136	+	0.999616i	$0.508823\pi$
$390$	4.87778	−	14.2380i	0.246996	−	0.720970i
$391$			11.9573i			0.604707i
$392$		0			0
$393$	1.20855	−	2.09326i	0.0609631	−	0.105591i
$394$		−	6.00678i		−	0.302617i
$395$	10.3159	+	2.76415i	0.519051	+	0.139079i
$396$	3.96017	−	1.06112i	0.199006	−	0.0533235i
$397$	5.19736	+	5.19736i	0.260848	+	0.260848i	0.825399	−	0.564550i	$-0.190950\pi$
$397$	5.19736	+	5.19736i	0.260848	+	0.260848i	−0.564550	+	0.825399i	$0.690950\pi$
$398$	4.62437	+	4.62437i	0.231799	+	0.231799i
$399$		0			0
$400$	3.62307	+	2.09178i	0.181153	+	0.104589i
$401$	−1.38785	−	0.371875i	−0.0693062	−	0.0185705i	0.223999	−	0.974589i	$-0.428089\pi$
$401$	−1.38785	−	0.371875i	−0.0693062	−	0.0185705i	−0.293306	+	0.956019i	$0.594755\pi$
$402$	5.43148	+	9.40760i	0.270898	+	0.469208i
$403$	−15.1402	−	10.1780i	−0.754187	−	0.507000i
$404$	−3.59527	−	2.07573i	−0.178871	−	0.103271i
$405$	−1.04862	−	3.91348i	−0.0521061	−	0.194463i
$406$		0			0
$407$	−8.05873	+	4.65271i	−0.399457	+	0.230626i
$408$	10.1637	−	2.72335i	0.503177	−	0.134826i
$409$	−1.78773	−	6.67192i	−0.0883978	−	0.329905i	0.907538	−	0.419970i	$-0.137959\pi$
$409$	−1.78773	−	6.67192i	−0.0883978	−	0.329905i	−0.995936	+	0.0900646i	$0.971293\pi$
$410$	−6.80132	−	25.3829i	−0.335893	−	1.25357i
$411$	12.8802	−	3.45123i	0.635331	−	0.170236i
$412$	−1.57974	+	0.912063i	−0.0778282	+	0.0449341i
$413$		0			0
$414$	1.53007	+	5.71031i	0.0751990	+	0.280647i
$415$	−16.0621	−	9.27346i	−0.788458	−	0.455216i
$416$	−19.6107	−	1.34066i	−0.961492	−	0.0657310i
$417$	2.55723	+	4.42925i	0.125228	+	0.216901i
$418$	−2.19385	−	0.587842i	−0.107305	−	0.0287523i
$419$	7.98102	+	4.60785i	0.389899	+	0.225108i	0.682116	−	0.731244i	$-0.261060\pi$
$419$	7.98102	+	4.60785i	0.389899	+	0.225108i	−0.292218	+	0.956352i	$0.594393\pi$
$420$		0			0
$421$	9.26432	+	9.26432i	0.451515	+	0.451515i	0.895857	−	0.444342i	$-0.146562\pi$
$421$	9.26432	+	9.26432i	0.451515	+	0.451515i	−0.444342	+	0.895857i	$0.646562\pi$
$422$	4.98927	+	4.98927i	0.242874	+	0.242874i
$423$	−19.0614	+	5.10748i	−0.926795	+	0.248334i
$424$	−13.7369	−	3.68078i	−0.667120	−	0.178754i
$425$			33.8915i			1.64398i
$426$	3.26772	−	5.65985i	0.158321	−	0.274221i
$427$		0			0
$428$			17.0705i			0.825136i
$429$	−3.80974	−	7.78038i	−0.183936	−	0.375640i
$430$	−7.00209	+	4.04266i	−0.337671	+	0.194954i
$431$	4.60076	+	4.60076i	0.221611	+	0.221611i	0.809176	−	0.587566i	$-0.199914\pi$
$431$	4.60076	+	4.60076i	0.221611	+	0.221611i	−0.587566	+	0.809176i	$0.699914\pi$
$432$	1.81802	−	1.04963i	0.0874694	−	0.0505005i
$433$	−12.5684	−	21.7691i	−0.604000	−	1.04616i	−0.992209	−	0.124587i	$-0.960239\pi$
$433$	−12.5684	−	21.7691i	−0.604000	−	1.04616i	0.388209	−	0.921571i	$-0.373094\pi$
$434$		0			0
$435$	1.36814	−	5.10597i	0.0655973	−	0.244812i
$436$	−2.72207	+	2.72207i	−0.130364	+	0.130364i
$437$	−1.13912	+	4.25126i	−0.0544916	+	0.203365i
$438$	2.59292	−	4.49107i	0.123895	−	0.214592i
$439$	8.84493	+	15.3199i	0.422145	+	0.731177i	0.996149	−	0.0876754i	$-0.0279438\pi$
$439$	8.84493	+	15.3199i	0.422145	+	0.731177i	−0.574004	+	0.818853i	$0.694610\pi$
$440$	23.4127	−	6.27341i	1.11616	−	0.299073i
$441$		0			0
$442$	4.64657	+	9.48939i	0.221015	+	0.451364i
$443$	7.16955	−	12.4180i	0.340635	−	0.589998i	−0.643915	−	0.765097i	$-0.722691\pi$
$443$	7.16955	−	12.4180i	0.340635	−	0.589998i	0.984551	+	0.175099i	$0.0560245\pi$
$444$	4.08887	−	4.08887i	0.194049	−	0.194049i
$445$	27.5468			1.30584
$446$	−6.22292			−0.294664
$447$	−3.67578	+	3.67578i	−0.173858	+	0.173858i
$448$		0			0
$449$	−2.82768	−	0.757676i	−0.133447	−	0.0357569i	0.191477	−	0.981497i	$-0.438672\pi$
$449$	−2.82768	−	0.757676i	−0.133447	−	0.0357569i	−0.324924	+	0.945740i	$0.605339\pi$
$450$	4.33680	+	16.1852i	0.204439	+	0.762976i
$451$	−13.0994	−	7.56293i	−0.616826	−	0.356124i
$452$		−	11.1966i		−	0.526644i
$453$	−4.47329	+	16.6945i	−0.210173	+	0.784378i
$454$	14.9497			0.701623
$455$		0			0
$456$	3.87300			0.181370
$457$	−6.30680	+	23.5373i	−0.295020	+	1.10103i	0.646182	+	0.763183i	$0.276365\pi$
$457$	−6.30680	+	23.5373i	−0.295020	+	1.10103i	−0.941202	+	0.337845i	$0.890302\pi$
$458$		−	18.1218i		−	0.846776i
$459$	14.7280	+	8.50319i	0.687442	+	0.396895i
$460$	−4.43009	−	16.5333i	−0.206554	−	0.770870i
$461$	−20.1416	−	5.39694i	−0.938090	−	0.251360i	−0.242789	−	0.970079i	$-0.578062\pi$
$461$	−20.1416	−	5.39694i	−0.938090	−	0.251360i	−0.695301	+	0.718719i	$0.744729\pi$
$462$		0			0
$463$	8.98662	−	8.98662i	0.417644	−	0.417644i	−0.466747	−	0.884391i	$-0.654574\pi$
$463$	8.98662	−	8.98662i	0.417644	−	0.417644i	0.884391	+	0.466747i	$0.154574\pi$
$464$	0.458090			0.0212663
$465$	−22.8644			−1.06031
$466$	−7.25243	+	7.25243i	−0.335963	+	0.335963i
$467$	11.5521	−	20.0088i	0.534566	−	0.925895i	−0.464619	−	0.885511i	$-0.653809\pi$
$467$	11.5521	−	20.0088i	0.534566	−	0.925895i	0.999184	−	0.0403838i	$-0.0128581\pi$
$468$	−4.61396	−	5.29111i	−0.213281	−	0.244582i
$469$		0			0
$470$	−41.0668	+	11.0038i	−1.89427	+	0.507568i
$471$	−7.97602	−	13.8149i	−0.367516	−	0.636556i
$472$	0.355969	−	0.616557i	0.0163848	−	0.0283793i
$473$	−1.20453	+	4.49535i	−0.0553842	+	0.206697i
$474$	2.00998	−	2.00998i	0.0923215	−	0.0923215i
$475$	−3.22870	+	12.0497i	−0.148143	+	0.552877i
$476$		0			0
$477$	−4.15371	−	7.19444i	−0.190185	−	0.329411i
$478$	−20.3913	+	11.7729i	−0.932678	+	0.538482i
$479$	−7.82481	−	7.82481i	−0.357525	−	0.357525i	0.505375	−	0.862900i	$-0.331354\pi$
$479$	−7.82481	−	7.82481i	−0.357525	−	0.357525i	−0.862900	+	0.505375i	$0.831354\pi$
$480$	−21.3350	+	12.3178i	−0.973807	+	0.562227i
$481$	13.2236	+	8.88955i	0.602945	+	0.405328i
$482$		−	23.4992i		−	1.07036i
$483$		0			0
$484$	−3.76481	+	6.52084i	−0.171128	+	0.296402i
$485$			64.9930i			2.95118i
$486$	13.3078	+	3.56580i	0.603652	+	0.161748i
$487$	−30.1548	+	8.07996i	−1.36644	+	0.366138i	−0.866179	−	0.499734i	$-0.833431\pi$
$487$	−30.1548	+	8.07996i	−1.36644	+	0.366138i	−0.500266	+	0.865872i	$0.666764\pi$
$488$	−25.4217	−	25.4217i	−1.15079	−	1.15079i
$489$	18.8280	+	18.8280i	0.851432	+	0.851432i
$490$		0			0
$491$	19.5025	+	11.2598i	0.880137	+	0.508147i	0.870704	−	0.491808i	$-0.163664\pi$
$491$	19.5025	+	11.2598i	0.880137	+	0.508147i	0.00943333	+	0.999956i	$0.496997\pi$
$492$	9.07918	+	2.43276i	0.409321	+	0.109677i
$493$	1.85552	+	3.21385i	0.0835683	+	0.144745i
$494$	0.748014	+	3.81649i	0.0336547	+	0.171712i
$495$	12.2620	+	7.07946i	0.551135	+	0.318198i
$496$	−0.512829	−	1.91390i	−0.0230267	−	0.0859368i
$497$		0			0
$498$	−4.27508	+	2.46822i	−0.191571	+	0.110604i
$499$	−22.0367	+	5.90470i	−0.986496	+	0.264331i	−0.715778	−	0.698328i	$-0.753928\pi$
$499$	−22.0367	+	5.90470i	−0.986496	+	0.264331i	−0.270718	+	0.962659i	$0.587261\pi$
$500$	−6.67975	−	24.9292i	−0.298728	−	1.11487i
$501$	−3.30686	−	12.3414i	−0.147739	−	0.551371i
$502$	−5.37530	+	1.44031i	−0.239911	+	0.0642841i
$503$	3.72935	−	2.15314i	0.166283	−	0.0960037i	−0.414549	−	0.910027i	$-0.636061\pi$
$503$	3.72935	−	2.15314i	0.166283	−	0.0960037i	0.580832	+	0.814023i	$0.302727\pi$
$504$		0			0
$505$	−3.71071	−	13.8486i	−0.165124	−	0.616253i
$506$	6.34901	+	3.66561i	0.282248	+	0.162956i
$507$	−9.09625	+	11.7176i	−0.403979	+	0.520399i
$508$	−4.51437	−	7.81911i	−0.200293	−	0.346917i
$509$	26.1818	+	7.01539i	1.16049	+	0.310952i	0.787161	−	0.616748i	$-0.211550\pi$
$509$	26.1818	+	7.01539i	1.16049	+	0.310952i	0.373327	+	0.927700i	$0.378217\pi$
$510$	11.4682	+	6.62119i	0.507822	+	0.293191i
$511$		0			0
$512$	−3.11938	−	3.11938i	−0.137858	−	0.137858i
$513$	4.42627	+	4.42627i	0.195425	+	0.195425i
$514$	21.7831	−	5.83675i	0.960809	−	0.257448i
$515$	−6.08498	−	1.63047i	−0.268136	−	0.0718469i
$516$		−	2.89203i		−	0.127314i
$517$	−12.2360	+	21.1934i	−0.538139	+	0.932084i
$518$		0			0
$519$		−	3.79813i		−	0.166719i
$520$	−27.2779	−	31.2813i	−1.19622	−	1.37177i
$521$	−12.0981	+	6.98482i	−0.530026	+	0.306011i	−0.741027	−	0.671475i	$-0.765661\pi$
$521$	−12.0981	+	6.98482i	−0.530026	+	0.306011i	0.211001	+	0.977486i	$0.432328\pi$
$522$	1.29737	+	1.29737i	0.0567843	+	0.0567843i
$523$	−35.9424	+	20.7514i	−1.57165	+	0.907394i	−0.575685	+	0.817672i	$0.695265\pi$
$523$	−35.9424	+	20.7514i	−1.57165	+	0.907394i	−0.995967	+	0.0897221i	$0.971402\pi$
$524$	−1.21453	−	2.10362i	−0.0530569	−	0.0918972i
$525$		0			0
$526$	−3.61986	+	13.5095i	−0.157834	+	0.589043i
$527$	11.3503	−	11.3503i	0.494425	−	0.494425i
$528$	0.243523	−	0.908842i	0.0105980	−	0.0395523i
$529$	−4.39677	+	7.61543i	−0.191164	+	0.331106i
$530$	−8.94896	−	15.5001i	−0.388718	−	0.673279i
$531$	0.401707	−	0.107637i	0.0174326	−	0.00467105i
$532$		0			0
$533$	−1.76652	+	25.8400i	−0.0765163	+	1.11926i
$534$	3.66592	−	6.34956i	0.158640	−	0.274773i
$535$	−41.6862	+	41.6862i	−1.80225	+	1.80225i
$536$	29.9567			1.29393
$537$	−0.291584			−0.0125828
$538$	−2.31304	+	2.31304i	−0.0997223	+	0.0997223i
$539$		0			0
$540$	−23.5147	−	6.30074i	−1.01191	−	0.271141i
$541$	−1.61721	−	6.03551i	−0.0695292	−	0.259487i	0.922408	−	0.386217i	$-0.126218\pi$
$541$	−1.61721	−	6.03551i	−0.0695292	−	0.259487i	−0.991937	+	0.126730i	$0.959552\pi$
$542$	−0.604911	−	0.349246i	−0.0259832	−	0.0150014i
$543$		−	8.73050i		−	0.374661i
$544$	4.47630	−	16.7058i	0.191920	−	0.716255i
$545$	−13.2946			−0.569478
$546$		0			0
$547$	−25.9633			−1.11011			−0.555055	−	0.831814i	$-0.687303\pi$
$547$	−25.9633			−1.11011			−0.555055	+	0.831814i	$0.687303\pi$
$548$	3.46831	−	12.9439i	0.148159	−	0.552936i
$549$		−	21.0012i		−	0.896308i
$550$	17.9955	+	10.3897i	0.767330	+	0.443018i
$551$	0.353535	+	1.31941i	0.0150611	+	0.0562088i
$552$	−12.0755	−	3.23561i	−0.513965	−	0.137717i
$553$		0			0
$554$	6.81118	−	6.81118i	0.289379	−	0.289379i
$555$	19.9700			0.847681
$556$	5.13976			0.217975
$557$	21.7708	−	21.7708i	0.922458	−	0.922458i	−0.0747448	−	0.997203i	$-0.523814\pi$
$557$	21.7708	−	21.7708i	0.922458	−	0.922458i	0.997203	+	0.0747448i	$0.0238142\pi$
$558$	3.96802	−	6.87282i	0.167980	−	0.290950i
$559$	7.82024	−	1.53273i	0.330761	−	0.0648276i
$560$		0			0
$561$	7.36263	−	1.97281i	0.310850	−	0.0832921i
$562$	11.8483	+	20.5218i	0.499790	+	0.865661i
$563$	16.1301	−	27.9382i	0.679804	−	1.17745i	−0.295236	−	0.955424i	$-0.595398\pi$
$563$	16.1301	−	27.9382i	0.679804	−	1.17745i	0.975040	−	0.222030i	$-0.0712683\pi$
$564$	3.93594	−	14.6891i	0.165733	−	0.618524i
$565$	27.3421	−	27.3421i	1.15029	−	1.15029i
$566$	−0.0117675	+	0.0439168i	−0.000494624	+	0.00184596i
$567$		0			0
$568$	−9.01135	−	15.6081i	−0.378108	−	0.654902i
$569$	−3.82034	+	2.20567i	−0.160157	+	0.0924666i	−0.577936	−	0.816082i	$-0.696142\pi$
$569$	−3.82034	+	2.20567i	−0.160157	+	0.0924666i	0.417779	+	0.908548i	$0.362808\pi$
$570$	3.44661	+	3.44661i	0.144363	+	0.144363i
$571$	−30.0822	+	17.3680i	−1.25890	+	0.726826i	−0.972861	−	0.231392i	$-0.925672\pi$
$571$	−30.0822	+	17.3680i	−1.25890	+	0.726826i	−0.286039	+	0.958218i	$0.592339\pi$
$572$	−8.68565	−	0.593782i	−0.363165	−	0.0248273i
$573$		−	16.5577i		−	0.691709i
$574$		0			0
$575$	20.1332	−	34.8717i	0.839613	−	1.45425i
$576$		−	9.88065i		−	0.411694i
$577$	−32.6785	−	8.75618i	−1.36042	−	0.364524i	−0.496452	−	0.868064i	$-0.665364\pi$
$577$	−32.6785	−	8.75618i	−1.36042	−	0.364524i	−0.863972	+	0.503540i	$0.832031\pi$
$578$	6.18850	−	1.65820i	0.257408	−	0.0689721i
$579$	6.49492	+	6.49492i	0.269920	+	0.269920i
$580$	−3.75633	−	3.75633i	−0.155973	−	0.155973i
$581$		0			0
$582$	14.9809	+	8.64925i	0.620980	+	0.358523i
$583$	−9.95106	−	2.66638i	−0.412131	−	0.110430i
$584$	−7.15047	−	12.3850i	−0.295889	−	0.512494i
$585$	1.65359	−	24.1882i	0.0683675	−	1.00006i
$586$	−13.1938	−	7.61745i	−0.545031	−	0.314674i
$587$	4.46785	+	16.6742i	0.184408	+	0.688219i	0.994757	+	0.102271i	$0.0326109\pi$
$587$	4.46785	+	16.6742i	0.184408	+	0.688219i	−0.810349	+	0.585948i	$0.800722\pi$
$588$		0			0
$589$	5.11673	−	2.95415i	0.210831	−	0.121723i
$590$	0.865456	−	0.231898i	0.0356303	−	0.00954710i
$591$	1.92046	+	7.16724i	0.0789970	+	0.294821i
$592$	0.447911	+	1.67163i	0.0184090	+	0.0687034i
$593$	−24.2880	+	6.50794i	−0.997387	+	0.267249i	−0.720351	−	0.693610i	$-0.756019\pi$
$593$	−24.2880	+	6.50794i	−0.997387	+	0.267249i	−0.277037	+	0.960859i	$0.589352\pi$
$594$	9.02994	−	5.21344i	0.370503	−	0.213910i
$595$		0			0
$596$	1.35209	+	5.04606i	0.0553837	+	0.206695i
$597$	−6.99624	−	4.03928i	−0.286337	−	0.165317i
$598$	0.856196	−	12.5242i	0.0350125	−	0.512151i
$599$	0.438119	+	0.758845i	0.0179011	+	0.0310056i	0.874837	−	0.484417i	$-0.160968\pi$
$599$	0.438119	+	0.758845i	0.0179011	+	0.0310056i	−0.856936	+	0.515423i	$0.827635\pi$
$600$	−34.2263	−	9.17092i	−1.39728	−	0.374401i
$601$	−19.6980	−	11.3726i	−0.803496	−	0.463899i	0.0411960	−	0.999151i	$-0.486883\pi$
$601$	−19.6980	−	11.3726i	−0.803496	−	0.463899i	−0.844692	+	0.535252i	$0.820217\pi$
$602$		0			0
$603$	12.3737	+	12.3737i	0.503898	+	0.503898i
$604$	12.2817	+	12.2817i	0.499737	+	0.499737i
$605$	−25.1175	+	6.73022i	−1.02117	+	0.273622i
$606$	−3.68593	−	0.987641i	−0.149730	−	0.0401202i
$607$		−	30.8708i		−	1.25301i	−0.779418	−	0.626504i	$-0.784485\pi$
$607$		−	30.8708i		−	1.25301i	0.779418	−	0.626504i	$-0.215515\pi$
$608$	3.18298	−	5.51309i	0.129087	−	0.223585i
$609$		0			0
$610$		−	45.2459i		−	1.83195i
$611$	41.8064	+	2.85803i	1.69130	+	0.115624i
$612$	5.34939	−	3.08847i	0.216236	−	0.124844i
$613$	33.2772	+	33.2772i	1.34405	+	1.34405i	0.891982	+	0.452071i	$0.149315\pi$
$613$	33.2772	+	33.2772i	1.34405	+	1.34405i	0.452071	+	0.891982i	$0.350685\pi$
$614$	15.6257	−	9.02148i	0.630601	−	0.364077i
$615$	16.2305	+	28.1121i	0.654479	+	1.13359i
$616$		0			0
$617$	−1.88092	+	7.01970i	−0.0757231	+	0.282602i	−0.993396	−	0.114734i	$-0.963399\pi$
$617$	−1.88092	+	7.01970i	−0.0757231	+	0.282602i	0.917673	+	0.397336i	$0.130065\pi$
$618$	−1.18561	+	1.18561i	−0.0476923	+	0.0476923i
$619$	−5.34817	+	19.9596i	−0.214961	+	0.802246i	0.771219	+	0.636570i	$0.219647\pi$
$619$	−5.34817	+	19.9596i	−0.214961	+	0.802246i	−0.986180	+	0.165676i	$0.947019\pi$
$620$	−11.4888	+	19.8992i	−0.461401	+	0.799170i
$621$	−10.1026	−	17.4983i	−0.405405	−	0.702182i
$622$	−4.02508	+	1.07852i	−0.161391	+	0.0432446i
$623$		0			0
$624$	−1.58105	+	0.309878i	−0.0632925	+	0.0124050i
$625$	17.8571	−	30.9295i	0.714285	−	1.23718i
$626$	−20.2396	+	20.2396i	−0.808939	+	0.808939i
$627$	2.80563			0.112046
$628$	−16.0310			−0.639706
$629$	−9.91345	+	9.91345i	−0.395275	+	0.395275i
$630$		0			0
$631$	5.77115	+	1.54637i	0.229746	+	0.0615602i	0.371855	−	0.928291i	$-0.378722\pi$
$631$	5.77115	+	1.54637i	0.229746	+	0.0615602i	−0.142109	+	0.989851i	$0.545388\pi$
$632$	−2.02884	−	7.57174i	−0.0807030	−	0.301188i
$633$	−7.54829	−	4.35801i	−0.300018	−	0.173215i
$634$			5.66235i			0.224881i
$635$	8.07018	−	30.1183i	0.320255	−	1.19521i
$636$	6.40189			0.253852
$637$		0			0
$638$	2.27530			0.0900798
$639$	2.72483	−	10.1692i	0.107793	−	0.402287i
$640$			21.8924i			0.865373i
$641$	−19.3092	−	11.1482i	−0.762667	−	0.440326i	0.0675854	−	0.997713i	$-0.478470\pi$
$641$	−19.3092	−	11.1482i	−0.762667	−	0.440326i	−0.830253	+	0.557387i	$0.811804\pi$
$642$	4.06112	+	15.1563i	0.160280	+	0.598171i
$643$	19.2524	+	5.15868i	0.759242	+	0.203438i	0.617614	−	0.786481i	$-0.288099\pi$
$643$	19.2524	+	5.15868i	0.759242	+	0.203438i	0.141629	+	0.989920i	$0.454766\pi$
$644$		0			0
$645$	7.06233	−	7.06233i	0.278079	−	0.278079i
$646$	−3.42190			−0.134633
$647$	14.8646			0.584389			0.292195	−	0.956359i	$-0.405615\pi$
$647$	14.8646			0.584389			0.292195	+	0.956359i	$0.405615\pi$
$648$	−2.10277	+	2.10277i	−0.0826047	+	0.0826047i
$649$	0.257866	−	0.446638i	0.0101221	−	0.0175321i
$650$	2.42678	−	35.4981i	0.0951861	−	1.39235i
$651$		0			0
$652$	25.8468	−	6.92564i	1.01224	−	0.271229i
$653$	−16.5493	−	28.6642i	−0.647623	−	1.12172i	−0.983689	−	0.179877i	$-0.942430\pi$
$653$	−16.5493	−	28.6642i	−0.647623	−	1.12172i	0.336067	−	0.941838i	$-0.390903\pi$
$654$	−1.76924	+	3.06442i	−0.0691828	+	0.119828i
$655$	2.17117	−	8.10292i	0.0848346	−	0.316607i
$656$	−1.98914	+	1.98914i	−0.0776627	+	0.0776627i
$657$	2.16214	−	8.06922i	0.0843531	−	0.314810i
$658$		0			0
$659$	23.6093	+	40.8925i	0.919687	+	1.59295i	0.799890	+	0.600147i	$0.204891\pi$
$659$	23.6093	+	40.8925i	0.919687	+	1.59295i	0.119797	+	0.992798i	$0.461776\pi$
$660$	−9.44937	+	5.45560i	−0.367816	+	0.212359i
$661$	−11.7411	−	11.7411i	−0.456675	−	0.456675i	0.440888	−	0.897562i	$-0.354664\pi$
$661$	−11.7411	−	11.7411i	−0.456675	−	0.456675i	−0.897562	+	0.440888i	$0.854664\pi$
$662$	13.3749	−	7.72200i	0.519830	−	0.300124i
$663$	−8.57814	−	9.83707i	−0.333147	−	0.382040i
$664$			13.6132i			0.528293i
$665$		0			0
$666$	−3.46572	+	6.00280i	−0.134294	+	0.232604i
$667$		−	4.40908i		−	0.170720i
$668$	−12.4024	−	3.32322i	−0.479864	−	0.128579i
$669$	7.42513	−	1.98956i	0.287072	−	0.0769207i
$670$	26.6586	+	26.6586i	1.02991	+	1.02991i
$671$	−18.4157	−	18.4157i	−0.710929	−	0.710929i
$672$		0			0
$673$	−22.5906	−	13.0427i	−0.870802	−	0.502758i	−0.00318750	−	0.999995i	$-0.501015\pi$
$673$	−22.5906	−	13.0427i	−0.870802	−	0.502758i	−0.867615	+	0.497237i	$0.834348\pi$
$674$	−11.1221	−	2.98015i	−0.428406	−	0.114791i
$675$	−28.6346	−	49.5967i	−1.10215	−	1.90898i
$676$	5.62737	+	13.8044i	0.216437	+	0.530938i
$677$	16.8583	+	9.73314i	0.647917	+	0.374075i	0.787658	−	0.616113i	$-0.211294\pi$
$677$	16.8583	+	9.73314i	0.647917	+	0.374075i	−0.139741	+	0.990188i	$0.544627\pi$
$678$	−2.66370	−	9.94105i	−0.102299	−	0.381784i
$679$		0			0
$680$	31.6258	−	18.2592i	1.21280	−	0.700208i
$681$	−17.8378	+	4.77963i	−0.683546	+	0.183156i
$682$	−2.54718	−	9.50621i	−0.0975366	−	0.364012i
$683$	5.35648	+	19.9907i	0.204960	+	0.764921i	0.989462	+	0.144794i	$0.0462521\pi$
$683$	5.35648	+	19.9907i	0.204960	+	0.764921i	−0.784502	+	0.620127i	$0.787081\pi$
$684$	2.19613	−	0.588452i	0.0839712	−	0.0225000i
$685$	40.0786	−	23.1394i	1.53132	−	0.884110i
$686$		0			0
$687$	5.79380	+	21.6228i	0.221047	+	0.824960i
$688$	0.749566	+	0.432762i	0.0285769	+	0.0164989i
$689$	3.39290	+	17.3111i	0.129259	+	0.659502i
$690$	−7.86663	−	13.6254i	−0.299477	−	0.518710i
$691$	−13.6373	−	3.65409i	−0.518786	−	0.139008i	−0.0100808	−	0.999949i	$-0.503209\pi$
$691$	−13.6373	−	3.65409i	−0.518786	−	0.139008i	−0.508705	+	0.860941i	$0.669876\pi$
$692$	−3.30555	−	1.90846i	−0.125658	−	0.0725488i
$693$		0			0
$694$	17.1477	+	17.1477i	0.650916	+	0.650916i
$695$	12.5513	+	12.5513i	0.476098	+	0.476098i
$696$	−3.74770	+	1.00419i	−0.142056	+	0.0380639i
$697$	−22.0124	−	5.89821i	−0.833779	−	0.223411i
$698$		−	6.76071i		−	0.255896i
$699$	6.33483	−	10.9722i	0.239605	−	0.415008i
$700$		0			0
$701$		−	26.8075i		−	1.01251i	−0.862385	−	0.506253i	$-0.831030\pi$
$701$		−	26.8075i		−	1.01251i	0.862385	−	0.506253i	$-0.168970\pi$
$702$	−14.8173	−	9.96088i	−0.559243	−	0.375949i
$703$	−4.46901	+	2.58019i	−0.168552	+	0.0973135i
$704$	−8.66423	−	8.66423i	−0.326545	−	0.326545i
$705$	45.4824	−	26.2593i	1.71297	−	0.988981i
$706$	−12.5896	−	21.8058i	−0.473815	−	0.820672i
$707$		0			0
$708$	−0.0829475	+	0.309564i	−0.00311736	+	0.0116341i
$709$	−20.3216	+	20.3216i	−0.763192	+	0.763192i	−0.976898	−	0.213706i	$-0.931447\pi$
$709$	−20.3216	+	20.3216i	−0.763192	+	0.763192i	0.213706	+	0.976898i	$0.431447\pi$
$710$	5.87050	−	21.9090i	0.220316	−	0.822231i
$711$	2.28952	−	3.96557i	0.0858638	−	0.148720i
$712$	−10.1095	−	17.5101i	−0.378869	−	0.656220i
$713$	−18.4212	+	4.93594i	−0.689879	+	0.184852i
$714$		0			0
$715$	−19.7603	−	22.6603i	−0.738994	−	0.847449i
$716$	−0.146513	+	0.253769i	−0.00547547	+	0.00948378i
$717$	20.5668	−	20.5668i	0.768080	−	0.768080i
$718$	−28.6964			−1.07094
$719$	−2.91511			−0.108715			−0.0543577	−	0.998522i	$-0.517311\pi$
$719$	−2.91511			−0.108715			−0.0543577	+	0.998522i	$0.517311\pi$
$720$	1.86198	−	1.86198i	0.0693918	−	0.0693918i
$721$		0			0
$722$	15.7363	+	4.21652i	0.585644	+	0.156923i
$723$	7.51303	+	28.0390i	0.279413	+	1.04278i
$724$	−7.59825	−	4.38685i	−0.282387	−	0.163036i
$725$		−	12.4970i		−	0.464126i
$726$	−1.79131	+	6.68527i	−0.0664818	+	0.248114i
$727$	26.1967			0.971584			0.485792	−	0.874075i	$-0.338531\pi$
$727$	26.1967			0.971584			0.485792	+	0.874075i	$0.338531\pi$
$728$		0			0
$729$	−20.0879			−0.743998
$730$	4.65822	−	17.3847i	0.172409	−	0.643437i
$731$			7.01171i			0.259337i
$732$	14.0157	+	8.09199i	0.518037	+	0.299089i
$733$	1.65037	+	6.15927i	0.0609579	+	0.227498i	0.989684	−	0.143269i	$-0.0457615\pi$
$733$	1.65037	+	6.15927i	0.0609579	+	0.227498i	−0.928726	+	0.370767i	$0.879095\pi$
$734$	22.4221	+	6.00798i	0.827614	+	0.221758i
$735$		0			0
$736$	−14.5299	+	14.5299i	−0.535577	+	0.535577i
$737$	21.7008			0.799359
$738$	−11.2670			−0.414743
$739$	17.7953	−	17.7953i	0.654609	−	0.654609i	−0.299490	−	0.954099i	$-0.596817\pi$
$739$	17.7953	−	17.7953i	0.654609	−	0.654609i	0.954099	+	0.299490i	$0.0968165\pi$
$740$	10.0344	−	17.3802i	0.368873	−	0.638907i
$741$	−2.11271	−	4.31465i	−0.0776124	−	0.158503i
$742$		0			0
$743$	−23.8890	+	6.40103i	−0.876401	+	0.234831i	−0.668854	−	0.743394i	$-0.733215\pi$
$743$	−23.8890	+	6.40103i	−0.876401	+	0.234831i	−0.207547	+	0.978225i	$0.566548\pi$
$744$	8.39107	+	14.5338i	0.307632	+	0.532834i
$745$	−9.02067	+	15.6243i	−0.330492	+	0.572429i
$746$	−0.743108	+	2.77332i	−0.0272071	+	0.101538i
$747$	−5.62298	+	5.62298i	−0.205734	+	0.205734i
$748$	1.98257	−	7.39907i	0.0724901	−	0.270537i
$749$		0			0
$750$	−11.8614	−	20.5446i	−0.433118	−	0.750182i
$751$	−12.2932	+	7.09751i	−0.448587	+	0.258992i	−0.707233	−	0.706980i	$-0.750057\pi$
$751$	−12.2932	+	7.09751i	−0.448587	+	0.258992i	0.258646	+	0.965972i	$0.416724\pi$
$752$	3.21821	+	3.21821i	0.117356	+	0.117356i
$753$	5.95327	−	3.43712i	0.216949	−	0.125256i
$754$	−1.71336	−	3.49907i	−0.0623967	−	0.127429i
$755$			59.9839i			2.18304i
$756$		0			0
$757$	−12.3674	+	21.4210i	−0.449502	+	0.778559i	−0.998354	−	0.0573601i	$-0.981732\pi$
$757$	−12.3674	+	21.4210i	−0.449502	+	0.778559i	0.548852	+	0.835920i	$0.315065\pi$
$758$			4.16511i			0.151284i
$759$	−8.74753	−	2.34389i	−0.317515	−	0.0850780i
$760$	12.9836	−	3.47895i	0.470966	−	0.126195i
$761$	−8.21162	−	8.21162i	−0.297671	−	0.297671i	0.542430	−	0.840101i	$-0.317504\pi$
$761$	−8.21162	−	8.21162i	−0.297671	−	0.297671i	−0.840101	+	0.542430i	$0.817504\pi$
$762$	−5.86832	−	5.86832i	−0.212587	−	0.212587i
$763$		0			0
$764$	−14.4104	−	8.31983i	−0.521349	−	0.301001i
$765$	20.6052	+	5.52116i	0.744984	+	0.199618i
$766$	15.5249	+	26.8900i	0.560938	+	0.971574i
$767$	−0.881044	−	0.0602313i	−0.0318126	−	0.00217483i
$768$	16.5471	+	9.55348i	0.597092	+	0.344731i
$769$	9.18218	+	34.2684i	0.331118	+	1.23575i	0.908017	+	0.418933i	$0.137596\pi$
$769$	9.18218	+	34.2684i	0.331118	+	1.23575i	−0.576899	+	0.816815i	$0.695737\pi$
$770$		0			0
$771$	−24.1252	+	13.9287i	−0.868850	+	0.501631i
$772$	8.91614	−	2.38907i	0.320899	−	0.0859846i
$773$	5.21138	+	19.4491i	0.187440	+	0.699536i	0.994095	+	0.108513i	$0.0346090\pi$
$773$	5.21138	+	19.4491i	0.187440	+	0.699536i	−0.806655	+	0.591023i	$0.798724\pi$
$774$	0.897229	+	3.34850i	0.0322502	+	0.120359i
$775$	−52.2125	+	13.9903i	−1.87553	+	0.502547i
$776$	41.3128	−	23.8519i	1.48304	−	0.856234i
$777$		0			0
$778$	4.93992	+	18.4360i	0.177105	+	0.660964i
$779$	−7.26433	−	4.19406i	−0.260272	−	0.150268i
$780$	15.5055	+	10.4236i	0.555187	+	0.373223i
$781$	−6.52788	−	11.3066i	−0.233586	−	0.404583i
$782$	10.6690	+	2.85875i	0.381522	+	0.102229i
$783$	−5.43072	−	3.13543i	−0.194078	−	0.112051i
$784$		0			0
$785$	−39.1476	−	39.1476i	−1.39724	−	1.39724i
$786$	−1.57879	−	1.57879i	−0.0563136	−	0.0563136i
$787$	13.7104	−	3.67369i	0.488723	−	0.130953i	−0.00603826	−	0.999982i	$-0.501922\pi$
$787$	13.7104	−	3.67369i	0.488723	−	0.130953i	0.494762	+	0.869029i	$0.335255\pi$
$788$	7.20271	+	1.92996i	0.256586	+	0.0687520i
$789$		−	17.2768i		−	0.615069i
$790$	4.93266	−	8.54362i	0.175496	−	0.303968i
$791$		0			0
$792$		−	10.3924i		−	0.369279i
$793$	−14.4532	+	42.1881i	−0.513247	+	1.49814i
$794$	5.87997	−	3.39480i	0.208672	−	0.120477i
$795$	15.6334	+	15.6334i	0.554460	+	0.554460i
$796$	−7.03086	+	4.05927i	−0.249202	+	0.143877i
$797$	−0.388404	−	0.672735i	−0.0137580	−	0.0238295i	0.859064	−	0.511867i	$-0.171046\pi$
$797$	−0.388404	−	0.672735i	−0.0137580	−	0.0238295i	−0.872822	+	0.488038i	$0.837713\pi$
$798$		0			0
$799$	−9.54267	+	35.6137i	−0.337595	+	1.25992i
$800$	−41.1830	+	41.1830i	−1.45604	+	1.45604i
$801$	3.05687	−	11.4084i	0.108009	−	0.403096i
$802$	−0.663616	+	1.14942i	−0.0234331	+	0.0405873i
$803$	−5.17985	−	8.97176i	−0.182793	−	0.316607i
$804$	−13.0257	+	3.49023i	−0.459382	+	0.123091i
$805$		0			0
$806$	−12.7011	+	11.0756i	−0.447376	+	0.390122i
$807$	2.02039	−	3.49941i	0.0711210	−	0.123185i
$808$	−7.44103	+	7.44103i	−0.261775	+	0.261775i
$809$	−32.2608			−1.13423			−0.567115	−	0.823639i	$-0.691940\pi$
$809$	−32.2608			−1.13423			−0.567115	+	0.823639i	$0.691940\pi$
$810$	−3.74254			−0.131499
$811$	−33.8219	+	33.8219i	−1.18765	+	1.18765i	−0.209930	+	0.977716i	$0.567324\pi$
$811$	−33.8219	+	33.8219i	−1.18765	+	1.18765i	−0.977716	+	0.209930i	$0.932676\pi$
$812$		0			0
$813$	0.833434	+	0.223318i	0.0292298	+	0.00783210i
$814$	2.22474	+	8.30283i	0.0779770	+	0.291014i
$815$	80.0303	+	46.2055i	2.80334	+	1.61851i
$816$		−	1.41758i		−	0.0496253i
$817$	−0.667976	+	2.49292i	−0.0233695	+	0.0872163i
$818$	−6.38048			−0.223088
$819$		0			0
$820$	32.6217			1.13920
$821$	5.72488	−	21.3655i	0.199800	−	0.745663i	−0.791172	−	0.611593i	$-0.790529\pi$
$821$	5.72488	−	21.3655i	0.199800	−	0.745663i	0.990972	−	0.134069i	$-0.0428045\pi$
$822$		−	12.3175i		−	0.429623i
$823$	−12.7603	−	7.36718i	−0.444797	−	0.256804i	0.260833	−	0.965384i	$-0.416003\pi$
$823$	−12.7603	−	7.36718i	−0.444797	−	0.256804i	−0.705630	+	0.708580i	$0.749336\pi$
$824$	1.19674	+	4.46628i	0.0416903	+	0.155590i
$825$	−24.7938	−	6.64347i	−0.863209	−	0.231296i
$826$		0			0
$827$	−5.90723	+	5.90723i	−0.205415	+	0.205415i	−0.802315	−	0.596901i	$-0.796399\pi$
$827$	−5.90723	+	5.90723i	−0.205415	+	0.205415i	0.596901	+	0.802315i	$0.296399\pi$
$828$	−7.33882			−0.255042
$829$	46.8750			1.62804			0.814018	−	0.580839i	$-0.197275\pi$
$829$	46.8750			1.62804			0.814018	+	0.580839i	$0.197275\pi$
$830$	−12.1144	+	12.1144i	−0.420498	+	0.420498i
$831$	−5.94941	+	10.3047i	−0.206383	+	0.357465i
$832$	−6.79993	+	19.8487i	−0.235745	+	0.688130i
$833$		0			0
$834$	4.56341	−	1.22276i	0.158018	−	0.0423408i
$835$	−22.1714	−	38.4020i	−0.767273	−	1.32896i
$836$	1.40976	−	2.44177i	0.0487575	−	0.0844504i
$837$	−7.02019	+	26.1997i	−0.242653	+	0.905594i
$838$	6.01948	−	6.01948i	0.207940	−	0.207940i
$839$	−0.889290	+	3.31888i	−0.0307017	+	0.114580i	−0.979576	−	0.201073i	$-0.935557\pi$
$839$	−0.889290	+	3.31888i	−0.0307017	+	0.114580i	0.948875	+	0.315654i	$0.102224\pi$
$840$		0			0
$841$	13.8158	+	23.9297i	0.476407	+	0.825161i
$842$	10.4811	−	6.05125i	0.361201	−	0.208540i
$843$	−20.6984	−	20.6984i	−0.712890	−	0.712890i
$844$	−7.58565	+	4.37958i	−0.261109	+	0.150751i
$845$	−19.9683	+	47.4523i	−0.686930	+	1.63241i
$846$			18.2287i			0.626717i
$847$		0			0
$848$	−0.957977	+	1.65926i	−0.0328971	+	0.0569794i
$849$		−	0.0561634i		−	0.00192752i
$850$	30.2399	+	8.10276i	1.03722	+	0.277922i
$851$	16.0893	−	4.31111i	0.551533	−	0.147783i
$852$	5.73680	+	5.73680i	0.196540	+	0.196540i
$853$	−13.3798	−	13.3798i	−0.458117	−	0.458117i	0.439920	−	0.898037i	$-0.355007\pi$
$853$	−13.3798	−	13.3798i	−0.458117	−	0.458117i	−0.898037	+	0.439920i	$0.855007\pi$
$854$		0			0
$855$	6.79995	+	3.92595i	0.232553	+	0.134265i
$856$	41.7964	+	11.1993i	1.42857	+	0.382784i
$857$	9.65574	+	16.7242i	0.329834	+	0.571289i	0.982479	−	0.186375i	$-0.0596740\pi$
$857$	9.65574	+	16.7242i	0.329834	+	0.571289i	−0.652645	+	0.757664i	$0.726341\pi$
$858$	−7.85293	+	1.53914i	−0.268095	+	0.0525453i
$859$	49.4177	+	28.5313i	1.68611	+	0.973477i	0.957449	+	0.288604i	$0.0931910\pi$
$859$	49.4177	+	28.5313i	1.68611	+	0.973477i	0.728662	+	0.684873i	$0.240142\pi$
$860$	−2.59779	−	9.69507i	−0.0885837	−	0.330599i
$861$		0			0
$862$	5.20501	−	3.00511i	0.177283	−	0.102355i
$863$	9.07665	−	2.43208i	0.308973	−	0.0827890i	−0.101001	−	0.994886i	$-0.532205\pi$
$863$	9.07665	−	2.43208i	0.308973	−	0.0827890i	0.409974	+	0.912097i	$0.365538\pi$
$864$	7.56399	+	28.2292i	0.257332	+	0.960377i
$865$	−3.41169	−	12.7326i	−0.116001	−	0.432922i
$866$	−22.4285	+	6.00971i	−0.762153	+	0.204218i
$867$	−6.85391	+	3.95710i	−0.232771	+	0.134390i
$868$		0			0
$869$	−1.46971	−	5.48502i	−0.0498564	−	0.186067i
$870$	−4.22874	−	2.44147i	−0.143368	−	0.0827735i
$871$	−16.3413	−	33.3727i	−0.553703	−	1.13079i
$872$	4.87902	+	8.45071i	0.165224	+	0.286177i
$873$	26.9166	+	7.21228i	0.910989	+	0.244099i
$874$	3.52088	+	2.03278i	0.119096	+	0.0687598i
$875$		0			0
$876$	4.55213	+	4.55213i	0.153802	+	0.153802i
$877$	−11.1516	−	11.1516i	−0.376563	−	0.376563i	0.493297	−	0.869861i	$-0.335791\pi$
$877$	−11.1516	−	11.1516i	−0.376563	−	0.376563i	−0.869861	+	0.493297i	$0.835791\pi$
$878$	15.7839	−	4.22928i	0.532681	−	0.142731i
$879$	18.1781	+	4.87082i	0.613134	+	0.164289i
$880$		−	3.26549i		−	0.110080i
$881$	20.1922	−	34.9739i	0.680293	−	1.17830i	−0.294599	−	0.955621i	$-0.595186\pi$
$881$	20.1922	−	34.9739i	0.680293	−	1.17830i	0.974891	−	0.222681i	$-0.0714807\pi$
$882$		0			0
$883$			29.9282i			1.00716i	0.863947	+	0.503582i	$0.167985\pi$
$883$			29.9282i			1.00716i	−0.863947	+	0.503582i	$0.832015\pi$
$884$	−12.8716	+	2.52278i	−0.432919	+	0.0848502i
$885$	−0.958513	+	0.553398i	−0.0322201	+	0.0186023i
$886$	−9.36597	−	9.36597i	−0.314656	−	0.314656i
$887$	−21.0340	+	12.1440i	−0.706254	+	0.407756i	−0.809673	−	0.586882i	$-0.800355\pi$
$887$	−21.0340	+	12.1440i	−0.706254	+	0.407756i	0.103418	+	0.994638i	$0.467022\pi$
$888$	−7.32886	−	12.6940i	−0.245940	−	0.425981i
$889$		0			0
$890$	6.58588	−	24.5788i	0.220759	−	0.823885i
$891$	−1.52326	+	1.52326i	−0.0510312	+	0.0510312i
$892$	1.99940	−	7.46188i	0.0669450	−	0.249842i
$893$	−6.78554	+	11.7529i	−0.227070	+	0.393296i
$894$	2.40094	+	4.15855i	0.0802994	+	0.139083i
$895$	−0.977489	+	0.261917i	−0.0326738	+	0.00875493i
$896$		0			0
$897$	2.98255	+	15.2174i	0.0995844	+	0.508096i
$898$	−1.35208	+	2.34188i	−0.0451196	+	0.0781495i
$899$	−4.18524	+	4.18524i	−0.139586	+	0.139586i
$900$	−20.8010			−0.693366
$901$	−15.5213			−0.517091
$902$	−9.87987	+	9.87987i	−0.328964	+	0.328964i
$903$		0			0
$904$	−27.4143	−	7.34565i	−0.911787	−	0.244313i
$905$	−7.84223	−	29.2676i	−0.260685	−	0.972888i
$906$	13.8263	+	7.98265i	0.459350	+	0.265206i
$907$		−	26.3763i		−	0.875811i	−0.899021	−	0.437906i	$-0.855720\pi$
$907$		−	26.3763i		−	0.875811i	0.899021	−	0.437906i	$-0.144280\pi$
$908$	−4.80328	+	17.9261i	−0.159403	+	0.594898i
$909$	−6.14711			−0.203887
$910$		0			0
$911$	49.3906			1.63638			0.818192	−	0.574945i	$-0.194977\pi$
$911$	49.3906			1.63638			0.818192	+	0.574945i	$0.194977\pi$
$912$	0.135047	−	0.504003i	0.00447186	−	0.0166892i
$913$			9.86146i			0.326367i
$914$	19.4935	+	11.2546i	0.644787	+	0.372268i
$915$	14.4658	+	53.9870i	0.478224	+	1.78476i
$916$	21.7298	+	5.82247i	0.717972	+	0.192380i
$917$		0			0
$918$	11.1082	−	11.1082i	0.366625	−	0.366625i
$919$	51.0587			1.68427			0.842135	−	0.539267i	$-0.181299\pi$
$919$	51.0587			1.68427			0.842135	+	0.539267i	$0.181299\pi$
$920$	−43.3874			−1.43044
$921$	−15.7601	+	15.7601i	−0.519313	+	0.519313i
$922$	−9.63091	+	16.6812i	−0.317177	+	0.549367i
$923$	−12.4723	+	18.5531i	−0.410530	+	0.610683i
$924$		0			0
$925$	45.6030	−	12.2193i	1.49942	−	0.401768i
$926$	−5.86986	−	10.1669i	−0.192896	−	0.334105i
$927$	−1.35050	+	2.33914i	−0.0443563	+	0.0768274i
$928$	−1.65057	+	6.16002i	−0.0541827	+	0.202213i
$929$	32.1671	−	32.1671i	1.05537	−	1.05537i	0.0569949	−	0.998374i	$-0.481848\pi$
$929$	32.1671	−	32.1671i	1.05537	−	1.05537i	0.998374	−	0.0569949i	$-0.0181519\pi$
$930$	−5.46642	+	20.4009i	−0.179251	+	0.668973i
$931$		0			0
$932$	−6.36618	−	11.0265i	−0.208531	−	0.361187i
$933$	4.45787	−	2.57375i	0.145944	−	0.0842609i
$934$	−15.0911	−	15.0911i	−0.493796	−	0.493796i
$935$	22.9100	−	13.2271i	0.749235	−	0.432571i
$936$	−15.9821	+	7.82577i	−0.522390	+	0.255793i
$937$		−	45.0942i		−	1.47316i	−0.676348	−	0.736582i	$-0.736439\pi$
$937$		−	45.0942i		−	1.47316i	0.676348	−	0.736582i	$-0.263561\pi$
$938$		0			0
$939$	17.6788	−	30.6207i	0.576927	−	0.999267i
$940$		−	52.7785i		−	1.72144i
$941$	2.87139	+	0.769386i	0.0936046	+	0.0250813i	0.305317	−	0.952251i	$-0.401237\pi$
$941$	2.87139	+	0.769386i	0.0936046	+	0.0250813i	−0.211713	+	0.977332i	$0.567904\pi$
$942$	−14.2333	+	3.81381i	−0.463747	+	0.124261i
$943$	19.1453	+	19.1453i	0.623456	+	0.623456i
$944$	−0.0678217	−	0.0678217i	−0.00220741	−	0.00220741i
$945$		0			0
$946$	3.72303	+	2.14949i	0.121046	+	0.0698861i
$947$	−29.3119	−	7.85409i	−0.952508	−	0.255224i	−0.251082	−	0.967966i	$-0.580786\pi$
$947$	−29.3119	−	7.85409i	−0.952508	−	0.255224i	−0.701426	+	0.712742i	$0.747453\pi$
$948$	1.76436	+	3.05596i	0.0573037	+	0.0992530i
$949$	−9.89671	+	14.7218i	−0.321261	+	0.477891i
$950$	9.97949	+	5.76166i	0.323777	+	0.186933i
$951$	−1.81034	−	6.75627i	−0.0587042	−	0.219087i
$952$		0			0
$953$	10.1244	−	5.84531i	0.327961	−	0.189348i	−0.326975	−	0.945033i	$-0.606029\pi$
$953$	10.1244	−	5.84531i	0.327961	−	0.189348i	0.654935	+	0.755685i	$0.272696\pi$
$954$	−7.41236	+	1.98614i	−0.239984	+	0.0643035i
$955$	−14.8731	−	55.5071i	−0.481282	−	1.79617i
$956$	−7.56522	−	28.2338i	−0.244677	−	0.913145i
$957$	−2.71486	+	0.727445i	−0.0877590	+	0.0235150i
$958$	−8.85250	+	5.11099i	−0.286011	+	0.165129i
$959$		0			0
$960$	6.80588	+	25.3999i	0.219659	+	0.819777i
$961$	−4.67543	−	2.69936i	−0.150820	−	0.0870762i
$962$	11.0933	−	9.67357i	0.357661	−	0.311888i
$963$	12.6383	+	21.8901i	0.407263	+	0.705399i
$964$	28.1778	+	7.55021i	0.907545	+	0.243176i
$965$	27.6073	+	15.9391i	0.888711	+	0.513097i
$966$		0			0
$967$	−14.9273	−	14.9273i	−0.480028	−	0.480028i	0.425112	−	0.905141i	$-0.360235\pi$
$967$	−14.9273	−	14.9273i	−0.480028	−	0.480028i	−0.905141	+	0.425112i	$0.860235\pi$
$968$	13.4960	+	13.4960i	0.433778	+	0.433778i
$969$	4.08298	−	1.09403i	0.131164	−	0.0351454i
$970$	57.9904	+	15.5385i	1.86196	+	0.498911i
$971$		−	5.91305i		−	0.189759i	−0.995489	−	0.0948795i	$-0.969753\pi$
$971$		−	5.91305i		−	0.189759i	0.995489	−	0.0948795i	$-0.0302466\pi$
$972$	−8.55149	+	14.8116i	−0.274289	+	0.475083i
$973$		0			0
$974$			28.8376i			0.924016i
$975$	8.45366	+	43.1319i	0.270734	+	1.38133i
$976$	−4.19462	+	2.42176i	−0.134266	+	0.0775188i
$977$	−39.2539	−	39.2539i	−1.25585	−	1.25585i	−0.953058	−	0.302787i	$-0.902083\pi$
$977$	−39.2539	−	39.2539i	−1.25585	−	1.25585i	−0.302787	−	0.953058i	$-0.597917\pi$
$978$	21.3008	−	12.2980i	0.681125	−	0.393248i
$979$	−7.32337	−	12.6844i	−0.234056	−	0.405397i
$980$		0			0
$981$	−1.47530	+	5.50591i	−0.0471028	+	0.175790i
$982$	14.7093	−	14.7093i	0.469392	−	0.469392i
$983$	−5.58397	+	20.8396i	−0.178101	+	0.664682i	0.817902	+	0.575358i	$0.195137\pi$
$983$	−5.58397	+	20.8396i	−0.178101	+	0.664682i	−0.996003	+	0.0893237i	$0.971529\pi$
$984$	11.9130	−	20.6339i	0.379772	−	0.657784i
$985$	12.8760	+	22.3020i	0.410265	+	0.710600i
$986$	3.31120	−	0.887233i	0.105450	−	0.0282553i
$987$		0			0
$988$	−4.81667	−	0.329285i	−0.153239	−	0.0104759i
$989$	4.16530	−	7.21451i	0.132449	−	0.229408i
$990$	9.24829	−	9.24829i	0.293930	−	0.293930i
$991$	54.7204			1.73825			0.869125	−	0.494592i	$-0.164683\pi$
$991$	54.7204			1.73825			0.869125	+	0.494592i	$0.164683\pi$
$992$	27.5844			0.875807
$993$	−13.4900	+	13.4900i	−0.428091	+	0.428091i
$994$		0			0
$995$	−27.0821	−	7.25662i	−0.858560	−	0.230050i
$996$	−1.58606	−	5.91926i	−0.0502563	−	0.187559i
$997$	−29.4379	−	16.9960i	−0.932308	−	0.538268i	−0.0447672	−	0.998997i	$-0.514255\pi$
$997$	−29.4379	−	16.9960i	−0.932308	−	0.538268i	−0.887541	+	0.460729i	$0.847588\pi$
$998$			21.0741i			0.667088i
$999$	6.13151	−	22.8831i	0.193992	−	0.723990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.x.b.215.6		32
7.2	even	3		91.2.bc.a.20.3	✓	32
7.3	odd	6		637.2.bb.b.423.5		32
7.4	even	3		637.2.bb.b.423.6		32
7.5	odd	6		91.2.bc.a.20.4	yes	32
7.6	odd	2	inner	637.2.x.b.215.5		32
13.2	odd	12		637.2.bb.b.509.5		32
21.2	odd	6		819.2.fm.g.748.5		32
21.5	even	6		819.2.fm.g.748.6		32
91.2	odd	12		91.2.bc.a.41.4	yes	32
91.41	even	12		637.2.bb.b.509.6		32
91.54	even	12		91.2.bc.a.41.3	yes	32
91.67	odd	12	inner	637.2.x.b.80.6		32
91.80	even	12	inner	637.2.x.b.80.5		32
273.2	even	12		819.2.fm.g.496.6		32
273.236	odd	12		819.2.fm.g.496.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.3	✓	32	7.2	even	3
91.2.bc.a.20.4	yes	32	7.5	odd	6
91.2.bc.a.41.3	yes	32	91.54	even	12
91.2.bc.a.41.4	yes	32	91.2	odd	12
637.2.x.b.80.5		32	91.80	even	12	inner
637.2.x.b.80.6		32	91.67	odd	12	inner
637.2.x.b.215.5		32	7.6	odd	2	inner
637.2.x.b.215.6		32	1.1	even	1	trivial
637.2.bb.b.423.5		32	7.3	odd	6
637.2.bb.b.423.6		32	7.4	even	3
637.2.bb.b.509.5		32	13.2	odd	12
637.2.bb.b.509.6		32	91.41	even	12
819.2.fm.g.496.5		32	273.236	odd	12
819.2.fm.g.496.6		32	273.2	even	12
819.2.fm.g.748.5		32	21.2	odd	6
819.2.fm.g.748.6		32	21.5	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.239080 - 0.892257i) q^{2} +1.14107i q^{3} +(0.993087 + 0.573359i) q^{4} +(1.02497 + 3.82526i) q^{5} +(1.01813 + 0.272807i) q^{6} +(2.05537 - 2.05537i) q^{8} +1.69796 q^{9} +O(q^{10})\)	\(q+(0.239080 - 0.892257i) q^{2} +1.14107i q^{3} +(0.993087 + 0.573359i) q^{4} +(1.02497 + 3.82526i) q^{5} +(1.01813 + 0.272807i) q^{6} +(2.05537 - 2.05537i) q^{8} +1.69796 q^{9} +3.65816 q^{10} +(1.48892 - 1.48892i) q^{11} +(-0.654243 + 1.13318i) q^{12} +(-3.41094 - 1.16855i) q^{13} +(-4.36489 + 1.16957i) q^{15} +(-0.195801 - 0.339138i) q^{16} +(1.58621 - 2.74739i) q^{17} +(0.405947 - 1.51502i) q^{18} +(0.825689 - 0.825689i) q^{19} +(-1.17536 + 4.38649i) q^{20} +(-0.972529 - 1.68447i) q^{22} +(-3.26418 + 1.88457i) q^{23} +(2.34532 + 2.34532i) q^{24} +(-9.25190 + 5.34158i) q^{25} +(-1.85813 + 2.76406i) q^{26} +5.36070i q^{27} +(-0.584891 + 1.01306i) q^{29} +4.17422i q^{30} +(4.88736 + 1.30956i) q^{31} +(5.26595 - 1.41101i) q^{32} +(1.69896 + 1.69896i) q^{33} +(-2.07215 - 2.07215i) q^{34} +(1.68622 + 0.973539i) q^{36} +(-4.26868 - 1.14379i) q^{37} +(-0.539321 - 0.934132i) q^{38} +(1.33339 - 3.89212i) q^{39} +(9.96900 + 5.75561i) q^{40} +(-1.85922 - 6.93869i) q^{41} +(-1.91410 + 1.10511i) q^{43} +(2.33231 - 0.624941i) q^{44} +(1.74036 + 6.49513i) q^{45} +(0.901126 + 3.36305i) q^{46} +(-11.2261 + 3.00801i) q^{47} +(0.386980 - 0.223423i) q^{48} +(2.55413 + 9.53214i) q^{50} +(3.13497 + 1.80998i) q^{51} +(-2.71736 - 3.11616i) q^{52} +(-2.44630 - 4.23711i) q^{53} +(4.78313 + 1.28163i) q^{54} +(7.22161 + 4.16940i) q^{55} +(0.942169 + 0.942169i) q^{57} +(0.764076 + 0.764076i) q^{58} +(0.236582 - 0.0633920i) q^{59} +(-5.00530 - 1.34116i) q^{60} -12.3685i q^{61} +(2.33694 - 4.04770i) q^{62} -5.81913i q^{64} +(0.973870 - 14.2454i) q^{65} +(1.92210 - 1.10972i) q^{66} +(7.28743 + 7.28743i) q^{67} +(3.15048 - 1.81893i) q^{68} +(-2.15043 - 3.72465i) q^{69} +(1.60477 - 5.98907i) q^{71} +(3.48993 - 3.48993i) q^{72} +(1.27338 - 4.75231i) q^{73} +(-2.04111 + 3.53530i) q^{74} +(-6.09513 - 10.5571i) q^{75} +(1.29340 - 0.346564i) q^{76} +(-3.15399 - 2.12026i) q^{78} +(1.34840 - 2.33549i) q^{79} +(1.09660 - 1.09660i) q^{80} -1.02306 q^{81} -6.63560 q^{82} +(-3.31162 + 3.31162i) q^{83} +(12.1353 + 3.25165i) q^{85} +(0.528416 + 1.97208i) q^{86} +(-1.15597 - 0.667402i) q^{87} -6.12055i q^{88} +(1.80032 - 6.71890i) q^{89} +6.21141 q^{90} -4.32215 q^{92} +(-1.49431 + 5.57683i) q^{93} +10.7357i q^{94} +(4.00478 + 2.31216i) q^{95} +(1.61006 + 6.00882i) q^{96} +(15.8523 + 4.24762i) q^{97} +(2.52812 - 2.52812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9	\( 32 q + 4 q^{2} + 12 q^{4} - 16 q^{8} - 16 q^{9} + 20 q^{11} - 8 q^{15} + 12 q^{16} - 64 q^{18} + 4 q^{22} + 12 q^{23} + 4 q^{29} + 64 q^{32} + 4 q^{37} + 36 q^{39} - 48 q^{43} - 84 q^{44} - 108 q^{46} - 44 q^{50} + 12 q^{51} - 36 q^{53} - 92 q^{57} + 44 q^{58} + 28 q^{60} + 28 q^{65} + 64 q^{67} + 84 q^{71} + 4 q^{72} - 24 q^{74} + 148 q^{78} + 40 q^{79} - 56 q^{81} + 36 q^{85} + 108 q^{86} + 24 q^{92} - 24 q^{93} + 84 q^{95} - 60 q^{99}+O(q^{100}) \) 32 * q + 4 * q^2 + 12 * q^4 - 16 * q^8 - 16 * q^9 + 20 * q^11 - 8 * q^15 + 12 * q^16 - 64 * q^18 + 4 * q^22 + 12 * q^23 + 4 * q^29 + 64 * q^32 + 4 * q^37 + 36 * q^39 - 48 * q^43 - 84 * q^44 - 108 * q^46 - 44 * q^50 + 12 * q^51 - 36 * q^53 - 92 * q^57 + 44 * q^58 + 28 * q^60 + 28 * q^65 + 64 * q^67 + 84 * q^71 + 4 * q^72 - 24 * q^74 + 148 * q^78 + 40 * q^79 - 56 * q^81 + 36 * q^85 + 108 * q^86 + 24 * q^92 - 24 * q^93 + 84 * q^95 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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