LMFDB - Embedded newform 637.2.x.b.215.5

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			215.5
Character	$\chi$	$=$	637.215
Dual form			637.2.x.b.80.6

$q$-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	$-0.893154\pi$
$3$		−	1.14107i		−	0.658797i	0.944191	−	0.329399i	$-0.106846\pi$
$4$	0.993087	+	0.573359i	0.496543	+	0.286679i
$5$	−1.02497	−	3.82526i	−0.458383	−	1.71071i	−0.677948	−	0.735110i	$-0.737131\pi$
$5$	−1.02497	−	3.82526i	−0.458383	−	1.71071i	0.219566	−	0.975598i	$-0.429536\pi$
$6$	−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	−0.991729	−	0.128348i	$-0.959033\pi$
$17$	−1.58621	+	2.74739i	−0.384712	+	0.666341i	0.607017	+	0.794689i	$0.292366\pi$
$18$	0.405947	−	1.51502i	0.0956827	−	0.357093i
$19$	−0.825689	+	0.825689i	−0.189426	+	0.189426i	−0.795448	−	0.606022i	$-0.792764\pi$
$19$	−0.825689	+	0.825689i	−0.189426	+	0.189426i	0.606022	+	0.795448i	$0.292764\pi$
$20$	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	−0.208340	−	0.978056i	$-0.566806\pi$
$31$	−4.88736	−	1.30956i	−0.877796	−	0.235205i	−0.669456	+	0.742852i	$0.733473\pi$
$32$	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	$0.106225\pi$
$41$	1.85922	+	6.93869i	0.290361	+	1.08364i	−0.654472	+	0.756087i	$0.727109\pi$
$42$		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	0.681416	−	0.731896i	$-0.261364\pi$
$47$	11.2261	−	3.00801i	1.63749	−	0.438764i	0.956072	+	0.293132i	$0.0946977\pi$
$48$	−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	−0.274186	−	0.961677i	$-0.588409\pi$
$59$	−0.236582	+	0.0633920i	−0.0308004	+	0.00825293i	0.243386	+	0.969930i	$0.421742\pi$
$60$	−5.00530	−	1.34116i	−0.646181	−	0.173144i
$61$			12.3685i			1.58362i	0.610767	+	0.791811i	$0.290861\pi$
$61$			12.3685i			1.58362i	−0.610767	+	0.791811i	$0.709139\pi$
$62$	−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	$0.176297\pi$
$73$	−1.27338	+	4.75231i	−0.149037	+	0.556216i	−0.999542	+	0.0302484i	$0.990370\pi$
$74$	−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	−0.501602	−	0.865099i	$-0.667256\pi$
$83$	3.31162	−	3.31162i	0.363497	−	0.363497i	0.865099	+	0.501602i	$0.167256\pi$
$84$		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	$0.203518\pi$
$89$	−1.80032	+	6.71890i	−0.190834	+	0.712202i	−0.993306	+	0.115512i	$0.963149\pi$
$90$	−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	−0.661649	−	0.749814i	$-0.730143\pi$
$97$	−15.8523	−	4.24762i	−1.60956	−	0.431280i	−0.947912	+	0.318533i	$0.896810\pi$
$98$		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	$-0.442353\pi$
$101$	3.62029			0.360233			0.180116	+	0.983645i	$0.442353\pi$
$102$	2.36447	−	2.36447i	0.234118	−	0.234118i
$103$	0.795369	−	1.37762i	0.0783700	−	0.135741i	−0.824177	−	0.566333i	$-0.808362\pi$
$103$	0.795369	−	1.37762i	0.0783700	−	0.135741i	0.902547	+	0.430592i	$0.141695\pi$
$104$	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	0.577994	−	0.816041i	$-0.303836\pi$
$131$	1.83447	+	1.05913i	0.160279	+	0.0925369i	−0.417715	+	0.908578i	$0.637169\pi$
$132$	−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	−0.655503	−	0.755193i	$-0.727543\pi$
$139$	−3.88166	+	2.24108i	−0.329238	+	0.190086i	0.326265	+	0.945278i	$0.394210\pi$
$140$		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	0.0681513	−	0.997675i	$-0.478290\pi$
$157$	12.1069	−	6.98994i	0.966239	−	0.557858i	0.898088	+	0.439817i	$0.144957\pi$
$158$	−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	0.185198	−	0.982701i	$-0.440707\pi$
$167$	10.8156	−	2.89803i	0.836935	−	0.224256i	0.651737	+	0.758445i	$0.274041\pi$
$168$		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	$-0.459615\pi$
$173$	3.32856			0.253066			0.126533	+	0.991962i	$0.459615\pi$
$174$	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	$-0.408221\pi$
$181$	7.65115			0.568705			0.284353	+	0.958720i	$0.408221\pi$
$182$		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	−0.712847	−	0.701320i	$-0.752595\pi$
$199$	3.53990	−	6.13129i	0.250937	−	0.434636i	0.963784	+	0.266684i	$0.0859280\pi$
$200$	−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	0.999413	−	0.0342732i	$-0.0109116\pi$
$223$	1.74359	+	6.50716i	0.116759	+	0.435752i	−0.882653	+	0.470025i	$0.844245\pi$
$224$		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	$-0.902859\pi$
$227$	−4.18872	−	15.6325i	−0.278015	−	1.03757i	0.675778	−	0.737105i	$-0.263808\pi$
$228$	0.395455	+	1.47586i	0.0261896	+	0.0977410i
$229$	−18.9495	+	5.07751i	−1.25222	+	0.335531i	−0.823194	−	0.567760i	$-0.807810\pi$
$229$	−18.9495	+	5.07751i	−1.25222	+	0.335531i	−0.429027	+	0.903292i	$0.641143\pi$
$230$	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	−0.939809	−	0.341701i	$-0.888997\pi$
$241$	−24.5725	+	6.58419i	−1.58286	+	0.424125i	−0.643048	+	0.765826i	$0.722330\pi$
$242$	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	0.945292	−	0.326224i	$-0.105776\pi$
$251$	3.01219	+	5.21727i	0.190128	+	0.329311i	−0.755165	+	0.655535i	$0.772443\pi$
$252$		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	$-0.891162\pi$
$257$	−12.2067	−	21.1426i	−0.761434	−	1.31884i	0.180678	−	0.983542i	$-0.442171\pi$
$258$	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	0.590570	−	0.806986i	$-0.298903\pi$
$269$	3.06678	+	1.77061i	0.186985	+	0.107956i	−0.403585	+	0.914942i	$0.632236\pi$
$270$			19.6103i			1.19345i
$271$	−0.195709	+	0.730396i	−0.0118885	+	0.0443684i	−0.971615	−	0.236567i	$-0.923978\pi$
$271$	−0.195709	+	0.730396i	−0.0118885	+	0.0443684i	0.959727	+	0.280935i	$0.0906445\pi$
$272$	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	$-0.499534\pi$
$283$	0.0492199			0.00292582			0.00146291	+	0.999999i	$0.499534\pi$
$284$	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	$0.243335\pi$
$293$	−4.26864	+	15.9308i	−0.249377	+	0.930686i	−0.971133	+	0.238539i	$0.923332\pi$
$294$		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	0.192937	−	0.981211i	$-0.438199\pi$
$307$	−13.8117	−	13.8117i	−0.788274	−	0.788274i	−0.981211	+	0.192937i	$0.938199\pi$
$308$		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	0.922863	−	0.385128i	$-0.125843\pi$
$311$	2.25556	+	3.90675i	0.127901	+	0.221531i	−0.794962	+	0.606659i	$0.792509\pi$
$312$	−5.25912	−	10.7403i	−0.297739	−	0.608052i
$313$	26.8350	+	15.4932i	1.51681	+	0.875728i	0.999805	+	0.0197427i	$0.00628470\pi$
$313$	26.8350	+	15.4932i	1.51681	+	0.875728i	0.517000	+	0.855985i	$0.327049\pi$
$314$	−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	−0.443016	−	0.896514i	$-0.646092\pi$
$349$	−7.06951	+	1.89427i	−0.378422	+	0.101398i	0.0645937	+	0.997912i	$0.479425\pi$
$350$		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	$0.508345\pi$
$353$	−19.2744	+	19.2744i	−1.02587	+	1.02587i	−0.999656	+	0.0262143i	$0.991655\pi$
$354$	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	$-0.772299\pi$
$367$		−	25.1296i		−	1.31175i	0.754867	−	0.655877i	$-0.227701\pi$
$368$	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	$-0.421221\pi$
$383$	23.7683	−	23.7683i	1.21450	−	1.21450i	0.969530	−	0.244974i	$-0.0787795\pi$
$384$	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	0.564550	−	0.825399i	$-0.309050\pi$
$397$	−5.19736	−	5.19736i	−0.260848	−	0.260848i	−0.825399	+	0.564550i	$0.809050\pi$
$398$	−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	0.995936	−	0.0900646i	$-0.0287074\pi$
$409$	1.78773	+	6.67192i	0.0883978	+	0.329905i	−0.907538	+	0.419970i	$0.862041\pi$
$410$	−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	0.292218	−	0.956352i	$-0.405607\pi$
$419$	−7.98102	−	4.60785i	−0.389899	−	0.225108i	−0.682116	+	0.731244i	$0.738940\pi$
$420$		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	$0.0397606\pi$
$433$	12.5684	+	21.7691i	0.604000	+	1.04616i	−0.388209	+	0.921571i	$0.626906\pi$
$434$		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	0.574004	−	0.818853i	$-0.305390\pi$
$439$	−8.84493	−	15.3199i	−0.422145	−	0.731177i	−0.996149	+	0.0876754i	$0.972056\pi$
$440$	−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	0.695301	−	0.718719i	$-0.255271\pi$
$461$	20.1416	+	5.39694i	0.938090	+	0.251360i	0.242789	+	0.970079i	$0.421938\pi$
$462$		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	$0.346191\pi$
$467$	−11.5521	+	20.0088i	−0.534566	+	0.925895i	−0.999184	+	0.0403838i	$0.987142\pi$
$468$	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	0.862900	−	0.505375i	$-0.168646\pi$
$479$	7.82481	+	7.82481i	0.357525	+	0.357525i	−0.505375	+	0.862900i	$0.668646\pi$
$480$	−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	−0.580832	−	0.814023i	$-0.697273\pi$
$503$	−3.72935	+	2.15314i	−0.166283	+	0.0960037i	0.414549	+	0.910027i	$0.363939\pi$
$504$		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	−0.373327	−	0.927700i	$-0.621783\pi$
$509$	−26.1818	−	7.01539i	−1.16049	−	0.310952i	−0.787161	+	0.616748i	$0.788450\pi$
$510$	−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	−0.211001	−	0.977486i	$-0.567672\pi$
$521$	12.0981	−	6.98482i	0.530026	−	0.306011i	0.741027	+	0.671475i	$0.234339\pi$
$522$	1.29737	+	1.29737i	0.0567843	+	0.0567843i
$523$	35.9424	−	20.7514i	1.57165	−	0.907394i	0.575685	−	0.817672i	$-0.304735\pi$
$523$	35.9424	−	20.7514i	1.57165	−	0.907394i	0.995967	−	0.0897221i	$-0.0285979\pi$
$524$	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	$0.404602\pi$
$563$	−16.1301	+	27.9382i	−0.679804	+	1.17745i	−0.975040	+	0.222030i	$0.928732\pi$
$564$	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	0.863972	−	0.503540i	$-0.167969\pi$
$577$	32.6785	+	8.75618i	1.36042	+	0.364524i	0.496452	+	0.868064i	$0.334636\pi$
$578$	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	$-0.967389\pi$
$587$	−4.46785	−	16.6742i	−0.184408	−	0.688219i	0.810349	−	0.585948i	$-0.199278\pi$
$588$		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	0.277037	−	0.960859i	$-0.410648\pi$
$593$	24.2880	−	6.50794i	0.997387	−	0.267249i	0.720351	+	0.693610i	$0.243981\pi$
$594$	−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	0.844692	−	0.535252i	$-0.179783\pi$
$601$	19.6980	+	11.3726i	0.803496	+	0.463899i	−0.0411960	+	0.999151i	$0.513117\pi$
$602$		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	$0.215515\pi$
$607$			30.8708i			1.25301i	−0.779418	+	0.626504i	$0.784485\pi$
$608$	−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	$-0.780353\pi$
$619$	5.34817	−	19.9596i	0.214961	−	0.802246i	0.986180	−	0.165676i	$-0.0529806\pi$
$620$	−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	−0.141629	−	0.989920i	$-0.545234\pi$
$643$	−19.2524	−	5.15868i	−0.759242	−	0.203438i	−0.617614	+	0.786481i	$0.711901\pi$
$644$		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	$-0.594385\pi$
$647$	−14.8646			−0.584389			−0.292195	+	0.956359i	$0.594385\pi$
$648$	−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	0.897562	−	0.440888i	$-0.145336\pi$
$661$	11.7411	+	11.7411i	0.456675	+	0.456675i	−0.440888	+	0.897562i	$0.645336\pi$
$662$	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	0.139741	−	0.990188i	$-0.455373\pi$
$677$	−16.8583	−	9.73314i	−0.647917	−	0.374075i	−0.787658	+	0.616113i	$0.788706\pi$
$678$	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	0.508705	−	0.860941i	$-0.330124\pi$
$691$	13.6373	+	3.65409i	0.518786	+	0.139008i	0.0100808	+	0.999949i	$0.496791\pi$
$692$	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	$-0.482689\pi$
$719$	2.91511			0.108715			0.0543577	+	0.998522i	$0.482689\pi$
$720$	−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	$-0.661469\pi$
$727$	−26.1967			−0.971584			−0.485792	+	0.874075i	$0.661469\pi$
$728$		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	0.928726	−	0.370767i	$-0.120905\pi$
$733$	−1.65037	−	6.15927i	−0.0609579	−	0.227498i	−0.989684	+	0.143269i	$0.954239\pi$
$734$	−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	0.840101	−	0.542430i	$-0.182496\pi$
$761$	8.21162	+	8.21162i	0.297671	+	0.297671i	−0.542430	+	0.840101i	$0.682496\pi$
$762$	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	$-0.862404\pi$
$769$	−9.18218	−	34.2684i	−0.331118	−	1.23575i	0.576899	−	0.816815i	$-0.304263\pi$
$770$		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	$-0.965391\pi$
$773$	−5.21138	−	19.4491i	−0.187440	−	0.699536i	0.806655	−	0.591023i	$-0.201276\pi$
$774$	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	−0.494762	−	0.869029i	$-0.664745\pi$
$787$	−13.7104	+	3.67369i	−0.488723	+	0.130953i	0.00603826	+	0.999982i	$0.498078\pi$
$788$	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	0.872822	−	0.488038i	$-0.162287\pi$
$797$	0.388404	+	0.672735i	0.0137580	+	0.0238295i	−0.859064	+	0.511867i	$0.828954\pi$
$798$		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	$-0.432676\pi$
$811$	33.8219	−	33.8219i	1.18765	−	1.18765i	0.977716	−	0.209930i	$-0.0673237\pi$
$812$		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	$-0.802725\pi$
$829$	−46.8750			−1.62804			−0.814018	+	0.580839i	$0.802725\pi$
$830$	−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	−0.948875	−	0.315654i	$-0.897776\pi$
$839$	0.889290	−	3.31888i	0.0307017	−	0.114580i	0.979576	+	0.201073i	$0.0644429\pi$
$840$		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	0.898037	−	0.439920i	$-0.144993\pi$
$853$	13.3798	+	13.3798i	0.458117	+	0.458117i	−0.439920	+	0.898037i	$0.644993\pi$
$854$		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	0.652645	−	0.757664i	$-0.273659\pi$
$857$	−9.65574	−	16.7242i	−0.329834	−	0.571289i	−0.982479	+	0.186375i	$0.940326\pi$
$858$	−7.85293	+	1.53914i	−0.268095	+	0.0525453i
$859$	−49.4177	−	28.5313i	−1.68611	−	0.973477i	−0.957449	−	0.288604i	$-0.906809\pi$
$859$	−49.4177	−	28.5313i	−1.68611	−	0.973477i	−0.728662	−	0.684873i	$-0.759858\pi$
$860$	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	$0.404814\pi$
$881$	−20.1922	+	34.9739i	−0.680293	+	1.17830i	−0.974891	+	0.222681i	$0.928519\pi$
$882$		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	−0.103418	−	0.994638i	$-0.532978\pi$
$887$	21.0340	−	12.1440i	0.706254	−	0.407756i	0.809673	+	0.586882i	$0.199645\pi$
$888$	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	$0.518152\pi$
$929$	−32.1671	+	32.1671i	−1.05537	+	1.05537i	−0.998374	+	0.0569949i	$0.981848\pi$
$930$	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	$0.263561\pi$
$937$			45.0942i			1.47316i	−0.676348	+	0.736582i	$0.736439\pi$
$938$		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	0.211713	−	0.977332i	$-0.432096\pi$
$941$	−2.87139	−	0.769386i	−0.0936046	−	0.0250813i	−0.305317	+	0.952251i	$0.598763\pi$
$942$	−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	$0.0302466\pi$
$971$			5.91305i			0.189759i	−0.995489	+	0.0948795i	$0.969753\pi$
$972$	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	$-0.804863\pi$
$983$	5.58397	−	20.8396i	0.178101	−	0.664682i	0.996003	−	0.0893237i	$-0.0284705\pi$
$984$	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	0.887541	−	0.460729i	$-0.152412\pi$
$997$	29.4379	+	16.9960i	0.932308	+	0.538268i	0.0447672	+	0.998997i	$0.485745\pi$
$998$			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.215.5		32
7.2	even	3		91.2.bc.a.20.4	yes	32
7.3	odd	6		637.2.bb.b.423.6		32
7.4	even	3		637.2.bb.b.423.5		32
7.5	odd	6		91.2.bc.a.20.3	✓	32
7.6	odd	2	inner	637.2.x.b.215.6		32
13.2	odd	12		637.2.bb.b.509.6		32
21.2	odd	6		819.2.fm.g.748.6		32
21.5	even	6		819.2.fm.g.748.5		32
91.2	odd	12		91.2.bc.a.41.3	yes	32
91.41	even	12		637.2.bb.b.509.5		32
91.54	even	12		91.2.bc.a.41.4	yes	32
91.67	odd	12	inner	637.2.x.b.80.5		32
91.80	even	12	inner	637.2.x.b.80.6		32
273.2	even	12		819.2.fm.g.496.5		32
273.236	odd	12		819.2.fm.g.496.6		32

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