LMFDB - Embedded newform 637.2.x.b.80.6

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			80.6
Character	$\chi$	$=$	637.80
Dual form			637.2.x.b.215.5

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

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	0.997488	+	0.0708335i	$0.0225659\pi$
$2$	0.239080	+	0.892257i	0.169055	+	0.630921i	−0.828433	+	0.560088i	$0.810767\pi$
$3$			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	0.219566	+	0.975598i	$0.429536\pi$
$5$	−1.02497	+	3.82526i	−0.458383	+	1.71071i	−0.677948	+	0.735110i	$0.737131\pi$
$6$	−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	0.894997	−	0.446071i	$-0.147177\pi$
$11$	1.48892	+	1.48892i	0.448926	+	0.448926i	−0.446071	+	0.894997i	$0.647177\pi$
$12$	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	$-0.292366\pi$
$17$	−1.58621	−	2.74739i	−0.384712	−	0.666341i	−0.991729	+	0.128348i	$0.959033\pi$
$18$	0.405947	+	1.51502i	0.0956827	+	0.357093i
$19$	−0.825689	−	0.825689i	−0.189426	−	0.189426i	0.606022	−	0.795448i	$-0.292764\pi$
$19$	−0.825689	−	0.825689i	−0.189426	−	0.189426i	−0.795448	+	0.606022i	$0.792764\pi$
$20$	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	0.119464	−	0.992839i	$-0.461882\pi$
$23$	−3.26418	−	1.88457i	−0.680628	−	0.392961i	−0.800092	+	0.599878i	$0.795216\pi$
$24$	−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	0.806596	−	0.591102i	$-0.201307\pi$
$29$	−0.584891	−	1.01306i	−0.108612	−	0.188121i	−0.915208	+	0.402982i	$0.867974\pi$
$30$		−	4.17422i		−	0.762106i
$31$	−4.88736	+	1.30956i	−0.877796	+	0.235205i	−0.669456	−	0.742852i	$-0.733473\pi$
$31$	−4.88736	+	1.30956i	−0.877796	+	0.235205i	−0.208340	+	0.978056i	$0.566806\pi$
$32$	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	−0.592022	−	0.805922i	$-0.701670\pi$
$37$	−4.26868	+	1.14379i	−0.701766	+	0.188038i	−0.109745	+	0.993960i	$0.535003\pi$
$38$	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	−0.654472	−	0.756087i	$-0.727109\pi$
$41$	1.85922	−	6.93869i	0.290361	−	1.08364i	0.944832	−	0.327555i	$-0.106225\pi$
$42$		0			0
$43$	−1.91410	−	1.10511i	−0.291897	−	0.168527i	0.346900	−	0.937902i	$-0.387234\pi$
$43$	−1.91410	−	1.10511i	−0.291897	−	0.168527i	−0.638797	+	0.769375i	$0.720568\pi$
$44$	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	$-0.0946977\pi$
$47$	11.2261	+	3.00801i	1.63749	+	0.438764i	0.681416	+	0.731896i	$0.261364\pi$
$48$	−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	−0.983681	−	0.179921i	$-0.942416\pi$
$53$	−2.44630	+	4.23711i	−0.336025	+	0.582012i	0.647656	+	0.761933i	$0.275749\pi$
$54$	−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	$-0.421742\pi$
$59$	−0.236582	−	0.0633920i	−0.0308004	−	0.00825293i	−0.274186	+	0.961677i	$0.588409\pi$
$60$	−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	−0.104250	−	0.994551i	$-0.533244\pi$
$67$	7.28743	−	7.28743i	0.890301	−	0.890301i	0.994551	+	0.104250i	$0.0332442\pi$
$68$	−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	0.993398	+	0.114722i	$0.0365976\pi$
$71$	1.60477	+	5.98907i	0.190451	+	0.710772i	−0.802947	+	0.596051i	$0.796736\pi$
$72$	3.48993	+	3.48993i	0.411292	+	0.411292i
$73$	−1.27338	−	4.75231i	−0.149037	−	0.556216i	−0.999542	−	0.0302484i	$-0.990370\pi$
$73$	−1.27338	−	4.75231i	−0.149037	−	0.556216i	0.850505	−	0.525967i	$-0.176297\pi$
$74$	−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	0.931855	−	0.362831i	$-0.118190\pi$
$79$	1.34840	+	2.33549i	0.151707	+	0.262764i	−0.780148	+	0.625595i	$0.784856\pi$
$80$	−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	$-0.167256\pi$
$83$	3.31162	+	3.31162i	0.363497	+	0.363497i	−0.501602	+	0.865099i	$0.667256\pi$
$84$		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	−0.993306	−	0.115512i	$-0.963149\pi$
$89$	−1.80032	−	6.71890i	−0.190834	−	0.712202i	0.802472	−	0.596690i	$-0.203518\pi$
$90$	−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	$-0.896810\pi$
$97$	−15.8523	+	4.24762i	−1.60956	+	0.431280i	−0.661649	+	0.749814i	$0.730143\pi$
$98$		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	0.902547	−	0.430592i	$-0.141695\pi$
$103$	0.795369	+	1.37762i	0.0783700	+	0.135741i	−0.824177	+	0.566333i	$0.808362\pi$
$104$	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	−0.241610	−	0.970373i	$-0.577676\pi$
$107$	7.44322	−	12.8920i	0.719563	−	1.24632i	0.961173	−	0.275946i	$-0.0889911\pi$
$108$	3.07361	+	5.32364i	0.295758	+	0.512268i
$109$	−0.868870	−	3.24267i	−0.0832226	−	0.310591i	0.911749	−	0.410748i	$-0.134732\pi$
$109$	−0.868870	−	3.24267i	−0.0832226	−	0.310591i	−0.994972	+	0.100157i	$0.968066\pi$
$110$	−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	−0.998922	−	0.0464177i	$-0.985219\pi$
$113$	−4.88202	+	8.45591i	−0.459262	+	0.795465i	0.539660	+	0.841883i	$0.318553\pi$
$114$	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	−0.771030	−	0.636799i	$-0.780258\pi$
$127$	−6.81869	+	3.93677i	−0.605061	+	0.349332i	0.165969	+	0.986131i	$0.446925\pi$
$128$	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	$-0.637169\pi$
$131$	1.83447	−	1.05913i	0.160279	−	0.0925369i	0.577994	+	0.816041i	$0.303836\pi$
$132$	−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	0.707760	+	0.706453i	$0.249706\pi$
$137$	−3.02455	+	11.2878i	−0.258405	+	0.964380i	−0.966164	+	0.257927i	$0.916961\pi$
$138$	3.83747	+	1.02825i	0.326668	+	0.0875303i
$139$	−3.88166	−	2.24108i	−0.329238	−	0.190086i	0.326265	−	0.945278i	$-0.394210\pi$
$139$	−3.88166	−	2.24108i	−0.329238	−	0.190086i	−0.655503	+	0.755193i	$0.727543\pi$
$140$		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	−0.562735	−	0.826638i	$-0.690251\pi$
$149$	3.22134	−	3.22134i	0.263903	−	0.263903i	0.826638	+	0.562735i	$0.190251\pi$
$150$	10.8768	+	2.91444i	0.888090	+	0.237963i
$151$	14.6306	−	3.92025i	1.19062	−	0.319026i	0.391489	−	0.920183i	$-0.371960\pi$
$151$	14.6306	−	3.92025i	1.19062	−	0.319026i	0.799131	+	0.601157i	$0.205293\pi$
$152$		−	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	$-0.144957\pi$
$157$	12.1069	+	6.98994i	0.966239	+	0.557858i	0.0681513	+	0.997675i	$0.478290\pi$
$158$	−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	0.933297	+	0.359107i	$0.116919\pi$
$163$	16.5003	+	16.5003i	1.29240	+	1.29240i	0.359107	+	0.933297i	$0.383081\pi$
$164$	−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	$-0.274041\pi$
$167$	10.8156	+	2.89803i	0.836935	+	0.224256i	0.185198	+	0.982701i	$0.440707\pi$
$168$		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	$-0.996960\pi$
$179$		−	0.255535i		−	0.0190996i	0.999954	−	0.00954980i	$-0.00303984\pi$
$180$	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	0.881639	−	0.471924i	$-0.156440\pi$
$193$	5.69196	+	5.69196i	0.409716	+	0.409716i	−0.471924	+	0.881639i	$0.656440\pi$
$194$	−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	0.475536	−	0.879696i	$-0.342254\pi$
$197$	6.28115	+	1.68303i	0.447514	+	0.119911i	−0.0280221	+	0.999607i	$0.508921\pi$
$198$	−1.65131	+	2.86016i	−0.117354	+	0.203263i
$199$	3.53990	+	6.13129i	0.250937	+	0.434636i	0.963784	−	0.266684i	$-0.0859280\pi$
$199$	3.53990	+	6.13129i	0.250937	+	0.434636i	−0.712847	+	0.701320i	$0.752595\pi$
$200$	−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	0.704092	−	0.710109i	$-0.251354\pi$
$211$	−3.81923	−	6.61509i	−0.262926	−	0.455402i	−0.967018	+	0.254707i	$0.918021\pi$
$212$			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	$-0.844245\pi$
$223$	1.74359	−	6.50716i	0.116759	−	0.435752i	0.999413	+	0.0342732i	$0.0109116\pi$
$224$		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	0.675778	+	0.737105i	$0.263808\pi$
$227$	−4.18872	+	15.6325i	−0.278015	+	1.03757i	−0.953794	+	0.300462i	$0.902859\pi$
$228$	0.395455	−	1.47586i	0.0261896	−	0.0977410i
$229$	−18.9495	−	5.07751i	−1.25222	−	0.335531i	−0.429027	−	0.903292i	$-0.641143\pi$
$229$	−18.9495	−	5.07751i	−1.25222	−	0.335531i	−0.823194	+	0.567760i	$0.807810\pi$
$230$	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	−0.780732	−	0.624866i	$-0.785154\pi$
$233$	−9.61575	+	5.55165i	−0.629949	+	0.363701i	0.150784	+	0.988567i	$0.451820\pi$
$234$	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	−0.182716	+	0.983166i	$0.558489\pi$
$239$	−18.0241	+	18.0241i	−1.16588	+	1.16588i	−0.983166	+	0.182716i	$0.941511\pi$
$240$	1.25130	−	1.25130i	0.0807708	−	0.0807708i
$241$	−24.5725	−	6.58419i	−1.58286	−	0.424125i	−0.643048	−	0.765826i	$-0.722330\pi$
$241$	−24.5725	−	6.58419i	−1.58286	−	0.424125i	−0.939809	+	0.341701i	$0.888997\pi$
$242$	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	$-0.772443\pi$
$251$	3.01219	−	5.21727i	0.190128	−	0.329311i	0.945292	+	0.326224i	$0.105776\pi$
$252$		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	0.180678	+	0.983542i	$0.442171\pi$
$257$	−12.2067	+	21.1426i	−0.761434	+	1.31884i	−0.942112	+	0.335300i	$0.891162\pi$
$258$	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	$-0.632236\pi$
$269$	3.06678	−	1.77061i	0.186985	−	0.107956i	0.590570	+	0.806986i	$0.298903\pi$
$270$		−	19.6103i		−	1.19345i
$271$	−0.195709	−	0.730396i	−0.0118885	−	0.0443684i	0.959727	−	0.280935i	$-0.0906445\pi$
$271$	−0.195709	−	0.730396i	−0.0118885	−	0.0443684i	−0.971615	+	0.236567i	$0.923978\pi$
$272$	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	−0.203530	−	0.979069i	$-0.565242\pi$
$277$	9.03071	−	5.21388i	0.542603	−	0.313272i	0.746133	+	0.665797i	$0.231908\pi$
$278$	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	−0.996313	−	0.0857959i	$-0.972657\pi$
$281$	−18.1394	−	18.1394i	−1.08211	−	1.08211i	−0.0857959	−	0.996313i	$-0.527343\pi$
$282$	−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	−0.971133	−	0.238539i	$-0.923332\pi$
$293$	−4.26864	−	15.9308i	−0.249377	−	0.930686i	0.721756	−	0.692147i	$-0.243335\pi$
$294$		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	$-0.938199\pi$
$307$	−13.8117	+	13.8117i	−0.788274	+	0.788274i	0.192937	+	0.981211i	$0.438199\pi$
$308$		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	$-0.792509\pi$
$311$	2.25556	−	3.90675i	0.127901	−	0.221531i	0.922863	+	0.385128i	$0.125843\pi$
$312$	−5.25912	+	10.7403i	−0.297739	+	0.608052i
$313$	26.8350	−	15.4932i	1.51681	−	0.875728i	0.517000	−	0.855985i	$-0.327049\pi$
$313$	26.8350	−	15.4932i	1.51681	−	0.875728i	0.999805	−	0.0197427i	$-0.00628470\pi$
$314$	−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	0.0886774	−	0.996060i	$-0.471736\pi$
$317$	−5.92099	−	1.58652i	−0.332556	−	0.0891081i	−0.421233	+	0.906952i	$0.638403\pi$
$318$	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	−0.303139	−	0.952946i	$-0.598035\pi$
$331$	11.8222	−	11.8222i	0.649807	−	0.649807i	0.952946	+	0.303139i	$0.0980348\pi$
$332$	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	$0.110261\pi$
$337$			12.4651i			0.679017i	−0.940603	+	0.339508i	$0.889739\pi$
$338$	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	−0.966815	−	0.255479i	$-0.917767\pi$
$347$	−13.1263	−	22.7355i	−0.704659	−	1.22050i	0.262156	−	0.965026i	$-0.415566\pi$
$348$	0.765322	−	1.32558i	0.0410256	−	0.0710583i
$349$	−7.06951	−	1.89427i	−0.378422	−	0.101398i	0.0645937	−	0.997912i	$-0.479425\pi$
$349$	−7.06951	−	1.89427i	−0.378422	−	0.101398i	−0.443016	+	0.896514i	$0.646092\pi$
$350$		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	−0.999656	−	0.0262143i	$-0.991655\pi$
$353$	−19.2744	−	19.2744i	−1.02587	−	1.02587i	−0.0262143	−	0.999656i	$-0.508345\pi$
$354$	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	0.340969	+	0.940074i	$0.389245\pi$
$359$	−8.04040	+	30.0072i	−0.424356	+	1.58372i	−0.765325	+	0.643644i	$0.777422\pi$
$360$	−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	0.145218	−	0.989400i	$-0.453612\pi$
$379$	−4.35536	−	1.16702i	−0.223720	−	0.0599456i	−0.368938	+	0.929454i	$0.620278\pi$
$380$	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	0.969530	+	0.244974i	$0.0787795\pi$
$383$	23.7683	+	23.7683i	1.21450	+	1.21450i	0.244974	+	0.969530i	$0.421221\pi$
$384$	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	−0.0277136	−	0.999616i	$-0.508823\pi$
$389$	−17.8940	−	10.3311i	−0.907263	−	0.523809i	−0.879550	+	0.475807i	$0.842156\pi$
$390$	−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	$-0.809050\pi$
$397$	−5.19736	+	5.19736i	−0.260848	+	0.260848i	0.564550	+	0.825399i	$0.309050\pi$
$398$	−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	−0.293306	−	0.956019i	$-0.594755\pi$
$401$	−1.38785	+	0.371875i	−0.0693062	+	0.0185705i	0.223999	+	0.974589i	$0.428089\pi$
$402$	−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	$-0.862041\pi$
$409$	1.78773	−	6.67192i	0.0883978	−	0.329905i	0.995936	+	0.0900646i	$0.0287074\pi$
$410$	−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	$-0.738940\pi$
$419$	−7.98102	+	4.60785i	−0.389899	+	0.225108i	0.292218	+	0.956352i	$0.405607\pi$
$420$		0			0
$421$	9.26432	−	9.26432i	0.451515	−	0.451515i	−0.444342	−	0.895857i	$-0.646562\pi$
$421$	9.26432	−	9.26432i	0.451515	−	0.451515i	0.895857	+	0.444342i	$0.146562\pi$
$422$	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	−0.587566	−	0.809176i	$-0.699914\pi$
$431$	4.60076	−	4.60076i	0.221611	−	0.221611i	0.809176	+	0.587566i	$0.199914\pi$
$432$	−1.81802	−	1.04963i	−0.0874694	−	0.0505005i
$433$	12.5684	−	21.7691i	0.604000	−	1.04616i	−0.388209	−	0.921571i	$-0.626906\pi$
$433$	12.5684	−	21.7691i	0.604000	−	1.04616i	0.992209	−	0.124587i	$-0.0397606\pi$
$434$		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	$-0.972056\pi$
$439$	−8.84493	+	15.3199i	−0.422145	+	0.731177i	0.574004	+	0.818853i	$0.305390\pi$
$440$	−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	0.984551	−	0.175099i	$-0.0560245\pi$
$443$	7.16955	+	12.4180i	0.340635	+	0.589998i	−0.643915	+	0.765097i	$0.722691\pi$
$444$	−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	−0.324924	−	0.945740i	$-0.605339\pi$
$449$	−2.82768	+	0.757676i	−0.133447	+	0.0357569i	0.191477	+	0.981497i	$0.438672\pi$
$450$	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	−0.941202	−	0.337845i	$-0.890302\pi$
$457$	−6.30680	−	23.5373i	−0.295020	−	1.10103i	0.646182	−	0.763183i	$-0.276365\pi$
$458$		−	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	$-0.421938\pi$
$461$	20.1416	−	5.39694i	0.938090	−	0.251360i	0.695301	+	0.718719i	$0.255271\pi$
$462$		0			0
$463$	8.98662	+	8.98662i	0.417644	+	0.417644i	0.884391	−	0.466747i	$-0.154574\pi$
$463$	8.98662	+	8.98662i	0.417644	+	0.417644i	−0.466747	+	0.884391i	$0.654574\pi$
$464$	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	−0.999184	−	0.0403838i	$-0.987142\pi$
$467$	−11.5521	−	20.0088i	−0.534566	−	0.925895i	0.464619	−	0.885511i	$-0.346191\pi$
$468$	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	$-0.668646\pi$
$479$	7.82481	−	7.82481i	0.357525	−	0.357525i	0.862900	+	0.505375i	$0.168646\pi$
$480$	−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	−0.500266	−	0.865872i	$-0.666764\pi$
$487$	−30.1548	−	8.07996i	−1.36644	−	0.366138i	−0.866179	+	0.499734i	$0.833431\pi$
$488$	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	0.00943333	−	0.999956i	$-0.496997\pi$
$491$	19.5025	−	11.2598i	0.880137	−	0.508147i	0.870704	+	0.491808i	$0.163664\pi$
$492$	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	−0.270718	−	0.962659i	$-0.587261\pi$
$499$	−22.0367	−	5.90470i	−0.986496	−	0.264331i	−0.715778	+	0.698328i	$0.753928\pi$
$500$	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	$-0.363939\pi$
$503$	−3.72935	−	2.15314i	−0.166283	−	0.0960037i	−0.580832	+	0.814023i	$0.697273\pi$
$504$		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	$-0.788450\pi$
$509$	−26.1818	+	7.01539i	−1.16049	+	0.310952i	−0.373327	+	0.927700i	$0.621783\pi$
$510$	−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	$-0.234339\pi$
$521$	12.0981	+	6.98482i	0.530026	+	0.306011i	−0.211001	+	0.977486i	$0.567672\pi$
$522$	1.29737	−	1.29737i	0.0567843	−	0.0567843i
$523$	35.9424	+	20.7514i	1.57165	+	0.907394i	0.995967	+	0.0897221i	$0.0285979\pi$
$523$	35.9424	+	20.7514i	1.57165	+	0.907394i	0.575685	+	0.817672i	$0.304735\pi$
$524$	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	−0.991937	−	0.126730i	$-0.959552\pi$
$541$	−1.61721	+	6.03551i	−0.0695292	+	0.259487i	0.922408	+	0.386217i	$0.126218\pi$
$542$	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	0.997203	−	0.0747448i	$-0.0238142\pi$
$557$	21.7708	+	21.7708i	0.922458	+	0.922458i	−0.0747448	+	0.997203i	$0.523814\pi$
$558$	−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	−0.975040	−	0.222030i	$-0.928732\pi$
$563$	−16.1301	−	27.9382i	−0.679804	−	1.17745i	0.295236	−	0.955424i	$-0.404602\pi$
$564$	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	0.417779	−	0.908548i	$-0.362808\pi$
$569$	−3.82034	−	2.20567i	−0.160157	−	0.0924666i	−0.577936	+	0.816082i	$0.696142\pi$
$570$	−3.44661	+	3.44661i	−0.144363	+	0.144363i
$571$	−30.0822	−	17.3680i	−1.25890	−	0.726826i	−0.286039	−	0.958218i	$-0.592339\pi$
$571$	−30.0822	−	17.3680i	−1.25890	−	0.726826i	−0.972861	+	0.231392i	$0.925672\pi$
$572$	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	$-0.334636\pi$
$577$	32.6785	−	8.75618i	1.36042	−	0.364524i	0.863972	+	0.503540i	$0.167969\pi$
$578$	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	0.810349	+	0.585948i	$0.199278\pi$
$587$	−4.46785	+	16.6742i	−0.184408	+	0.688219i	−0.994757	+	0.102271i	$0.967389\pi$
$588$		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	$-0.243981\pi$
$593$	24.2880	+	6.50794i	0.997387	+	0.267249i	0.277037	+	0.960859i	$0.410648\pi$
$594$	−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	−0.856936	−	0.515423i	$-0.827635\pi$
$599$	0.438119	−	0.758845i	0.0179011	−	0.0310056i	0.874837	+	0.484417i	$0.160968\pi$
$600$	34.2263	−	9.17092i	1.39728	−	0.374401i
$601$	19.6980	−	11.3726i	0.803496	−	0.463899i	−0.0411960	−	0.999151i	$-0.513117\pi$
$601$	19.6980	−	11.3726i	0.803496	−	0.463899i	0.844692	+	0.535252i	$0.179783\pi$
$602$		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	0.452071	−	0.891982i	$-0.350685\pi$
$613$	33.2772	−	33.2772i	1.34405	−	1.34405i	0.891982	−	0.452071i	$-0.149315\pi$
$614$	−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	0.917673	−	0.397336i	$-0.130065\pi$
$617$	−1.88092	−	7.01970i	−0.0757231	−	0.282602i	−0.993396	+	0.114734i	$0.963399\pi$
$618$	−1.18561	−	1.18561i	−0.0476923	−	0.0476923i
$619$	5.34817	+	19.9596i	0.214961	+	0.802246i	0.986180	+	0.165676i	$0.0529806\pi$
$619$	5.34817	+	19.9596i	0.214961	+	0.802246i	−0.771219	+	0.636570i	$0.780353\pi$
$620$	−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	−0.142109	−	0.989851i	$-0.545388\pi$
$631$	5.77115	−	1.54637i	0.229746	−	0.0615602i	0.371855	+	0.928291i	$0.378722\pi$
$632$	−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	−0.830253	−	0.557387i	$-0.811804\pi$
$641$	−19.3092	+	11.1482i	−0.762667	+	0.440326i	0.0675854	+	0.997713i	$0.478470\pi$
$642$	−4.06112	+	15.1563i	−0.160280	+	0.598171i
$643$	−19.2524	+	5.15868i	−0.759242	+	0.203438i	−0.617614	−	0.786481i	$-0.711901\pi$
$643$	−19.2524	+	5.15868i	−0.759242	+	0.203438i	−0.141629	+	0.989920i	$0.545234\pi$
$644$		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	0.336067	+	0.941838i	$0.390903\pi$
$653$	−16.5493	+	28.6642i	−0.647623	+	1.12172i	−0.983689	+	0.179877i	$0.942430\pi$
$654$	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	0.119797	−	0.992798i	$-0.461776\pi$
$659$	23.6093	−	40.8925i	0.919687	−	1.59295i	0.799890	−	0.600147i	$-0.204891\pi$
$660$	−9.44937	−	5.45560i	−0.367816	−	0.212359i
$661$	11.7411	−	11.7411i	0.456675	−	0.456675i	−0.440888	−	0.897562i	$-0.645336\pi$
$661$	11.7411	−	11.7411i	0.456675	−	0.456675i	0.897562	+	0.440888i	$0.145336\pi$
$662$	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	−0.867615	−	0.497237i	$-0.834348\pi$
$673$	−22.5906	+	13.0427i	−0.870802	+	0.502758i	−0.00318750	+	0.999995i	$0.501015\pi$
$674$	−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	$-0.788706\pi$
$677$	−16.8583	+	9.73314i	−0.647917	+	0.374075i	0.139741	+	0.990188i	$0.455373\pi$
$678$	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	−0.784502	−	0.620127i	$-0.787081\pi$
$683$	5.35648	−	19.9907i	0.204960	−	0.764921i	0.989462	−	0.144794i	$-0.0462521\pi$
$684$	−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	$-0.496791\pi$
$691$	13.6373	−	3.65409i	0.518786	−	0.139008i	0.508705	+	0.860941i	$0.330124\pi$
$692$	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	$0.168970\pi$
$701$			26.8075i			1.01251i	−0.862385	+	0.506253i	$0.831030\pi$
$702$	−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	0.213706	−	0.976898i	$-0.431447\pi$
$709$	−20.3216	−	20.3216i	−0.763192	−	0.763192i	−0.976898	+	0.213706i	$0.931447\pi$
$710$	−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	−0.989684	−	0.143269i	$-0.954239\pi$
$733$	−1.65037	+	6.15927i	−0.0609579	+	0.227498i	0.928726	+	0.370767i	$0.120905\pi$
$734$	−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	0.954099	−	0.299490i	$-0.0968165\pi$
$739$	17.7953	+	17.7953i	0.654609	+	0.654609i	−0.299490	+	0.954099i	$0.596817\pi$
$740$	−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	−0.207547	−	0.978225i	$-0.566548\pi$
$743$	−23.8890	−	6.40103i	−0.876401	−	0.234831i	−0.668854	+	0.743394i	$0.733215\pi$
$744$	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	0.258646	−	0.965972i	$-0.416724\pi$
$751$	−12.2932	−	7.09751i	−0.448587	−	0.258992i	−0.707233	+	0.706980i	$0.750057\pi$
$752$	−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	0.548852	−	0.835920i	$-0.315065\pi$
$757$	−12.3674	−	21.4210i	−0.449502	−	0.778559i	−0.998354	+	0.0573601i	$0.981732\pi$
$758$		−	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	$-0.682496\pi$
$761$	8.21162	−	8.21162i	0.297671	−	0.297671i	0.840101	+	0.542430i	$0.182496\pi$
$762$	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	0.576899	+	0.816815i	$0.304263\pi$
$769$	−9.18218	+	34.2684i	−0.331118	+	1.23575i	−0.908017	+	0.418933i	$0.862404\pi$
$770$		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	0.806655	+	0.591023i	$0.201276\pi$
$773$	−5.21138	+	19.4491i	−0.187440	+	0.699536i	−0.994095	+	0.108513i	$0.965391\pi$
$774$	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	$-0.498078\pi$
$787$	−13.7104	−	3.67369i	−0.488723	−	0.130953i	−0.494762	+	0.869029i	$0.664745\pi$
$788$	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	$-0.828954\pi$
$797$	0.388404	−	0.672735i	0.0137580	−	0.0238295i	0.872822	+	0.488038i	$0.162287\pi$
$798$		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	0.977716	+	0.209930i	$0.0673237\pi$
$811$	33.8219	+	33.8219i	1.18765	+	1.18765i	0.209930	+	0.977716i	$0.432676\pi$
$812$		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	0.990972	+	0.134069i	$0.0428045\pi$
$821$	5.72488	+	21.3655i	0.199800	+	0.745663i	−0.791172	+	0.611593i	$0.790529\pi$
$822$		−	12.3175i		−	0.429623i
$823$	−12.7603	+	7.36718i	−0.444797	+	0.256804i	−0.705630	−	0.708580i	$-0.749336\pi$
$823$	−12.7603	+	7.36718i	−0.444797	+	0.256804i	0.260833	+	0.965384i	$0.416003\pi$
$824$	−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	0.596901	−	0.802315i	$-0.296399\pi$
$827$	−5.90723	−	5.90723i	−0.205415	−	0.205415i	−0.802315	+	0.596901i	$0.796399\pi$
$828$	−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	0.979576	−	0.201073i	$-0.0644429\pi$
$839$	0.889290	+	3.31888i	0.0307017	+	0.114580i	−0.948875	+	0.315654i	$0.897776\pi$
$840$		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	$-0.644993\pi$
$853$	13.3798	−	13.3798i	0.458117	−	0.458117i	0.898037	+	0.439920i	$0.144993\pi$
$854$		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	$-0.940326\pi$
$857$	−9.65574	+	16.7242i	−0.329834	+	0.571289i	0.652645	+	0.757664i	$0.273659\pi$
$858$	−7.85293	−	1.53914i	−0.268095	−	0.0525453i
$859$	−49.4177	+	28.5313i	−1.68611	+	0.973477i	−0.728662	+	0.684873i	$0.759858\pi$
$859$	−49.4177	+	28.5313i	−1.68611	+	0.973477i	−0.957449	+	0.288604i	$0.906809\pi$
$860$	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	0.409974	−	0.912097i	$-0.365538\pi$
$863$	9.07665	+	2.43208i	0.308973	+	0.0827890i	−0.101001	+	0.994886i	$0.532205\pi$
$864$	−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	−0.869861	−	0.493297i	$-0.835791\pi$
$877$	−11.1516	+	11.1516i	−0.376563	+	0.376563i	0.493297	+	0.869861i	$0.335791\pi$
$878$	−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	−0.974891	−	0.222681i	$-0.928519\pi$
$881$	−20.1922	−	34.9739i	−0.680293	−	1.17830i	0.294599	−	0.955621i	$-0.404814\pi$
$882$		0			0
$883$		−	29.9282i		−	1.00716i	−0.863947	−	0.503582i	$-0.832015\pi$
$883$		−	29.9282i		−	1.00716i	0.863947	−	0.503582i	$-0.167985\pi$
$884$	−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	$-0.199645\pi$
$887$	21.0340	+	12.1440i	0.706254	+	0.407756i	−0.103418	+	0.994638i	$0.532978\pi$
$888$	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	$0.144280\pi$
$907$			26.3763i			0.875811i	−0.899021	+	0.437906i	$0.855720\pi$
$908$	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	−0.998374	−	0.0569949i	$-0.981848\pi$
$929$	−32.1671	−	32.1671i	−1.05537	−	1.05537i	−0.0569949	−	0.998374i	$-0.518152\pi$
$930$	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	$-0.598763\pi$
$941$	−2.87139	+	0.769386i	−0.0936046	+	0.0250813i	0.211713	+	0.977332i	$0.432096\pi$
$942$	−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	−0.701426	−	0.712742i	$-0.747453\pi$
$947$	−29.3119	+	7.85409i	−0.952508	+	0.255224i	−0.251082	+	0.967966i	$0.580786\pi$
$948$	−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	0.654935	−	0.755685i	$-0.272696\pi$
$953$	10.1244	+	5.84531i	0.327961	+	0.189348i	−0.326975	+	0.945033i	$0.606029\pi$
$954$	−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	−0.905141	−	0.425112i	$-0.860235\pi$
$967$	−14.9273	+	14.9273i	−0.480028	+	0.480028i	0.425112	+	0.905141i	$0.360235\pi$
$968$	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	−0.302787	+	0.953058i	$0.597917\pi$
$977$	−39.2539	+	39.2539i	−1.25585	+	1.25585i	−0.953058	+	0.302787i	$0.902083\pi$
$978$	−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	0.996003	+	0.0893237i	$0.0284705\pi$
$983$	5.58397	+	20.8396i	0.178101	+	0.664682i	−0.817902	+	0.575358i	$0.804863\pi$
$984$	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	$-0.485745\pi$
$997$	29.4379	−	16.9960i	0.932308	−	0.538268i	0.887541	+	0.460729i	$0.152412\pi$
$998$		−	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.80.6		32
7.2	even	3		637.2.bb.b.509.5		32
7.3	odd	6		91.2.bc.a.41.3	yes	32
7.4	even	3		91.2.bc.a.41.4	yes	32
7.5	odd	6		637.2.bb.b.509.6		32
7.6	odd	2	inner	637.2.x.b.80.5		32
13.7	odd	12		637.2.bb.b.423.6		32
21.11	odd	6		819.2.fm.g.496.6		32
21.17	even	6		819.2.fm.g.496.5		32
91.20	even	12		637.2.bb.b.423.5		32
91.33	even	12	inner	637.2.x.b.215.5		32
91.46	odd	12		91.2.bc.a.20.3	✓	32
91.59	even	12		91.2.bc.a.20.4	yes	32
91.72	odd	12	inner	637.2.x.b.215.6		32
273.59	odd	12		819.2.fm.g.748.6		32
273.137	even	12		819.2.fm.g.748.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bc.a.20.3	✓	32	91.46	odd	12
91.2.bc.a.20.4	yes	32	91.59	even	12
91.2.bc.a.41.3	yes	32	7.3	odd	6
91.2.bc.a.41.4	yes	32	7.4	even	3
637.2.x.b.80.5		32	7.6	odd	2	inner
637.2.x.b.80.6		32	1.1	even	1	trivial
637.2.x.b.215.5		32	91.33	even	12	inner
637.2.x.b.215.6		32	91.72	odd	12	inner
637.2.bb.b.423.5		32	91.20	even	12
637.2.bb.b.423.6		32	13.7	odd	12
637.2.bb.b.509.5		32	7.2	even	3
637.2.bb.b.509.6		32	7.5	odd	6
819.2.fm.g.496.5		32	21.17	even	6
819.2.fm.g.496.6		32	21.11	odd	6
819.2.fm.g.748.5		32	273.137	even	12
819.2.fm.g.748.6		32	273.59	odd	12

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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