LMFDB - Embedded newform 950.2.u.h.149.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, degree $6$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			149.6
Character	$\chi$	$=$	950.149
Dual form			950.2.u.h.899.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 - 0.766044i) q^{2} +(-0.291155 - 0.799943i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.799943 - 0.291155i) q^{6} +(4.37330 - 2.52492i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.74300 - 1.46255i) q^{9} +O(q^{10})$	\(q+(0.642788 - 0.766044i) q^{2} +(-0.291155 - 0.799943i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.799943 - 0.291155i) q^{6} +(4.37330 - 2.52492i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.74300 - 1.46255i) q^{9} +(1.10985 - 1.92232i) q^{11} +(-0.737231 + 0.425641i) q^{12} +(-1.66648 + 4.57862i) q^{13} +(0.876897 - 4.97313i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-2.81261 + 3.35193i) q^{17} -2.27532i q^{18} +(3.62288 - 2.42379i) q^{19} +(-3.29310 - 2.76324i) q^{21} +(-0.759185 - 2.08584i) q^{22} +(4.49168 - 0.792004i) q^{23} +(-0.147823 + 0.838348i) q^{24} +(2.43623 + 4.21968i) q^{26} +(-3.88913 - 2.24539i) q^{27} +(-3.24598 - 3.86841i) q^{28} +(1.48750 - 1.24816i) q^{29} +(3.76171 + 6.51548i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-1.86089 - 0.328125i) q^{33} +(0.759821 + 4.30916i) q^{34} +(-1.74300 - 1.46255i) q^{36} -2.47962i q^{37} +(0.472007 - 4.33327i) q^{38} +4.14784 q^{39} +(-9.83650 + 3.58019i) q^{41} +(-4.23353 + 0.746486i) q^{42} +(-8.29461 - 1.46256i) q^{43} +(-2.08584 - 0.759185i) q^{44} +(2.28048 - 3.94991i) q^{46} +(-3.10005 - 3.69450i) q^{47} +(0.547193 + 0.652119i) q^{48} +(9.25048 - 16.0223i) q^{49} +(3.50026 + 1.27399i) q^{51} +(4.79844 + 0.846095i) q^{52} +(-10.0470 + 1.77156i) q^{53} +(-4.21995 + 1.53594i) q^{54} -5.04985 q^{56} +(-2.99371 - 2.19239i) q^{57} -1.94179i q^{58} +(3.98298 + 3.34212i) q^{59} +(-0.909174 - 5.15618i) q^{61} +(7.40913 + 1.30643i) q^{62} +(3.92982 - 10.7971i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-1.44751 + 1.21461i) q^{66} +(0.949064 + 1.13105i) q^{67} +(3.78941 + 2.18782i) q^{68} +(-1.94133 - 3.36249i) q^{69} +(2.23230 - 12.6600i) q^{71} +(-2.24075 + 0.395105i) q^{72} +(4.54881 + 12.4977i) q^{73} +(-1.89950 - 1.59387i) q^{74} +(-3.01608 - 3.14695i) q^{76} -11.2092i q^{77} +(2.66618 - 3.17743i) q^{78} +(-5.71688 + 2.08077i) q^{79} +(0.521473 - 2.95742i) q^{81} +(-3.58019 + 9.83650i) q^{82} +(-10.8049 + 6.23822i) q^{83} +(-2.14942 + 3.72290i) q^{84} +(-6.45206 + 5.41392i) q^{86} +(-1.43155 - 0.826507i) q^{87} +(-1.92232 + 1.10985i) q^{88} +(5.85651 + 2.13160i) q^{89} +(4.27265 + 24.2314i) q^{91} +(-1.55994 - 4.28591i) q^{92} +(4.11677 - 4.90617i) q^{93} -4.82282 q^{94} +0.851281 q^{96} +(1.26373 - 1.50605i) q^{97} +(-6.32770 - 17.3852i) q^{98} +(-0.877018 - 4.97382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) $ 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	−0.291155	−	0.799943i	−0.168099	−	0.461847i	0.826827	−	0.562456i	$-0.190143\pi$
$3$	−0.291155	−	0.799943i	−0.168099	−	0.461847i	−0.994926	+	0.100608i	$0.967921\pi$
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$		0			0
$5$		0			0
$6$	−0.799943	−	0.291155i	−0.326575	−	0.118864i
$7$	4.37330	−	2.52492i	1.65295	−	0.954331i	0.677100	−	0.735891i	$-0.263236\pi$
$7$	4.37330	−	2.52492i	1.65295	−	0.954331i	0.975850	−	0.218441i	$-0.0700970\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	1.74300	−	1.46255i	0.580999	−	0.487516i
$10$		0			0
$11$	1.10985	−	1.92232i	0.334634	−	0.579602i	−0.648781	−	0.760975i	$-0.724721\pi$
$11$	1.10985	−	1.92232i	0.334634	−	0.579602i	0.983414	+	0.181373i	$0.0580541\pi$
$12$	−0.737231	+	0.425641i	−0.212820	+	0.122872i
$13$	−1.66648	+	4.57862i	−0.462199	+	1.26988i	0.461629	+	0.887073i	$0.347265\pi$
$13$	−1.66648	+	4.57862i	−0.462199	+	1.26988i	−0.923828	+	0.382808i	$0.874957\pi$
$14$	0.876897	−	4.97313i	0.234361	−	1.32912i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−2.81261	+	3.35193i	−0.682157	+	0.812963i	−0.990383	−	0.138350i	$-0.955820\pi$
$17$	−2.81261	+	3.35193i	−0.682157	+	0.812963i	0.308226	+	0.951313i	$0.400265\pi$
$18$		−	2.27532i		−	0.536298i
$19$	3.62288	−	2.42379i	0.831145	−	0.556056i
$19$	3.62288	−	2.42379i	0.831145	−	0.556056i
$20$		0			0
$21$	−3.29310	−	2.76324i	−0.718614	−	0.602989i
$22$	−0.759185	−	2.08584i	−0.161859	−	0.444703i
$23$	4.49168	−	0.792004i	0.936579	−	0.165144i	0.315530	−	0.948916i	$-0.397818\pi$
$23$	4.49168	−	0.792004i	0.936579	−	0.165144i	0.621049	+	0.783771i	$0.286707\pi$
$24$	−0.147823	+	0.838348i	−0.0301743	+	0.171127i
$25$		0			0
$26$	2.43623	+	4.21968i	0.477785	+	0.827548i
$27$	−3.88913	−	2.24539i	−0.748463	−	0.432126i
$28$	−3.24598	−	3.86841i	−0.613432	−	0.731060i
$29$	1.48750	−	1.24816i	0.276222	−	0.231778i	−0.494143	−	0.869380i	$-0.664518\pi$
$29$	1.48750	−	1.24816i	0.276222	−	0.231778i	0.770365	+	0.637603i	$0.220074\pi$
$30$		0			0
$31$	3.76171	+	6.51548i	0.675624	+	1.17021i	0.976286	+	0.216484i	$0.0694590\pi$
$31$	3.76171	+	6.51548i	0.675624	+	1.17021i	−0.300662	+	0.953731i	$0.597208\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	−1.86089	−	0.328125i	−0.323939	−	0.0571192i
$34$	0.759821	+	4.30916i	0.130308	+	0.739015i
$35$		0			0
$36$	−1.74300	−	1.46255i	−0.290499	−	0.243758i
$37$		−	2.47962i		−	0.407648i	−0.979008	−	0.203824i	$-0.934663\pi$
$37$		−	2.47962i		−	0.407648i	0.979008	−	0.203824i	$-0.0653370\pi$
$38$	0.472007	−	4.33327i	0.0765697	−	0.702949i
$39$	4.14784			0.664186
$40$		0			0
$41$	−9.83650	+	3.58019i	−1.53620	+	0.559132i	−0.965131	−	0.261768i	$-0.915695\pi$
$41$	−9.83650	+	3.58019i	−1.53620	+	0.559132i	−0.571072	+	0.820900i	$0.693472\pi$
$42$	−4.23353	+	0.746486i	−0.653248	+	0.115185i
$43$	−8.29461	−	1.46256i	−1.26492	−	0.223039i	−0.499353	−	0.866399i	$-0.666429\pi$
$43$	−8.29461	−	1.46256i	−1.26492	−	0.223039i	−0.765564	+	0.643360i	$0.777540\pi$
$44$	−2.08584	−	0.759185i	−0.314453	−	0.114451i
$45$		0			0
$46$	2.28048	−	3.94991i	0.336239	−	0.582383i
$47$	−3.10005	−	3.69450i	−0.452189	−	0.538898i	0.490998	−	0.871161i	$-0.336632\pi$
$47$	−3.10005	−	3.69450i	−0.452189	−	0.538898i	−0.943187	+	0.332263i	$0.892188\pi$
$48$	0.547193	+	0.652119i	0.0789805	+	0.0941253i
$49$	9.25048	−	16.0223i	1.32150	−	2.28890i
$50$		0			0
$51$	3.50026	+	1.27399i	0.490134	+	0.178394i
$52$	4.79844	+	0.846095i	0.665425	+	0.117332i
$53$	−10.0470	+	1.77156i	−1.38006	+	0.243342i	−0.813925	−	0.580971i	$-0.802673\pi$
$53$	−10.0470	+	1.77156i	−1.38006	+	0.243342i	−0.566135	+	0.824312i	$0.691562\pi$
$54$	−4.21995	+	1.53594i	−0.574263	+	0.209015i
$55$		0			0
$56$	−5.04985			−0.674814
$57$	−2.99371	−	2.19239i	−0.396527	−	0.290390i
$58$		−	1.94179i		−	0.254970i
$59$	3.98298	+	3.34212i	0.518540	+	0.435107i	0.864122	−	0.503282i	$-0.167874\pi$
$59$	3.98298	+	3.34212i	0.518540	+	0.435107i	−0.345582	+	0.938388i	$0.612319\pi$
$60$		0			0
$61$	−0.909174	−	5.15618i	−0.116408	−	0.660181i	−0.986044	−	0.166488i	$-0.946757\pi$
$61$	−0.909174	−	5.15618i	−0.116408	−	0.660181i	0.869636	−	0.493694i	$-0.164354\pi$
$62$	7.40913	+	1.30643i	0.940961	+	0.165917i
$63$	3.92982	−	10.7971i	0.495111	−	1.36031i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$		0			0
$66$	−1.44751	+	1.21461i	−0.178177	+	0.149508i
$67$	0.949064	+	1.13105i	0.115947	+	0.138180i	0.820896	−	0.571078i	$-0.193475\pi$
$67$	0.949064	+	1.13105i	0.115947	+	0.138180i	−0.704949	+	0.709258i	$0.749030\pi$
$68$	3.78941	+	2.18782i	0.459534	+	0.265312i
$69$	−1.94133	−	3.36249i	−0.233709	−	0.404796i
$70$		0			0
$71$	2.23230	−	12.6600i	0.264926	−	1.50247i	−0.504321	−	0.863516i	$-0.668257\pi$
$71$	2.23230	−	12.6600i	0.264926	−	1.50247i	0.769247	−	0.638952i	$-0.220632\pi$
$72$	−2.24075	+	0.395105i	−0.264075	+	0.0465636i
$73$	4.54881	+	12.4977i	0.532398	+	1.46275i	0.856210	+	0.516629i	$0.172813\pi$
$73$	4.54881	+	12.4977i	0.532398	+	1.46275i	−0.323812	+	0.946121i	$0.604965\pi$
$74$	−1.89950	−	1.59387i	−0.220813	−	0.185284i
$75$		0			0
$76$	−3.01608	−	3.14695i	−0.345968	−	0.360980i
$77$		−	11.2092i		−	1.27741i
$78$	2.66618	−	3.17743i	0.301885	−	0.359773i
$79$	−5.71688	+	2.08077i	−0.643199	+	0.234105i	−0.642966	−	0.765895i	$-0.722296\pi$
$79$	−5.71688	+	2.08077i	−0.643199	+	0.234105i	−0.000232843		1.00000i	$0.500074\pi$
$80$		0			0
$81$	0.521473	−	2.95742i	0.0579415	−	0.328602i
$82$	−3.58019	+	9.83650i	−0.395366	+	1.08626i
$83$	−10.8049	+	6.23822i	−1.18599	+	0.684733i	−0.957393	−	0.288787i	$-0.906748\pi$
$83$	−10.8049	+	6.23822i	−1.18599	+	0.684733i	−0.228599	+	0.973521i	$0.573415\pi$
$84$	−2.14942	+	3.72290i	−0.234521	+	0.406202i
$85$		0			0
$86$	−6.45206	+	5.41392i	−0.695744	+	0.583798i
$87$	−1.43155	−	0.826507i	−0.153478	−	0.0886108i
$88$	−1.92232	+	1.10985i	−0.204920	+	0.118311i
$89$	5.85651	+	2.13160i	0.620789	+	0.225949i	0.633217	−	0.773974i	$-0.281734\pi$
$89$	5.85651	+	2.13160i	0.620789	+	0.225949i	−0.0124282	+	0.999923i	$0.503956\pi$
$90$		0			0
$91$	4.27265	+	24.2314i	0.447896	+	2.54014i
$92$	−1.55994	−	4.28591i	−0.162635	−	0.446837i
$93$	4.11677	−	4.90617i	0.426889	−	0.508746i
$94$	−4.82282			−0.497436
$95$		0			0
$96$	0.851281			0.0868835
$97$	1.26373	−	1.50605i	0.128312	−	0.152917i	−0.698063	−	0.716036i	$-0.745955\pi$
$97$	1.26373	−	1.50605i	0.128312	−	0.152917i	0.826375	+	0.563120i	$0.190399\pi$
$98$	−6.32770	−	17.3852i	−0.639194	−	1.75617i
$99$	−0.877018	−	4.97382i	−0.0881437	−	0.499888i
$100$		0			0
$101$	9.23147	+	3.35998i	0.918565	+	0.334330i	0.757668	−	0.652641i	$-0.226339\pi$
$101$	9.23147	+	3.35998i	0.918565	+	0.334330i	0.160898	+	0.986971i	$0.448561\pi$
$102$	3.22586	−	1.86245i	0.319407	−	0.184410i
$103$	11.5000	+	6.63954i	1.13313	+	0.654213i	0.944720	−	0.327877i	$-0.106333\pi$
$103$	11.5000	+	6.63954i	1.13313	+	0.654213i	0.188410	+	0.982090i	$0.439666\pi$
$104$	3.73253	−	3.13196i	0.366004	−	0.307114i
$105$		0			0
$106$	−5.10099	+	8.83517i	−0.495452	+	0.858148i
$107$	−12.8059	+	7.39351i	−1.23800	+	0.714757i	−0.968684	−	0.248296i	$-0.920130\pi$
$107$	−12.8059	+	7.39351i	−1.23800	+	0.714757i	−0.269312	+	0.963053i	$0.586796\pi$
$108$	−1.53594	+	4.21995i	−0.147796	+	0.406065i
$109$	−1.52425	+	8.64446i	−0.145997	+	0.827989i	0.820565	+	0.571554i	$0.193659\pi$
$109$	−1.52425	+	8.64446i	−0.145997	+	0.827989i	−0.966561	+	0.256435i	$0.917452\pi$
$110$		0			0
$111$	−1.98356	+	0.721956i	−0.188271	+	0.0685250i
$112$	−3.24598	+	3.86841i	−0.306716	+	0.365530i
$113$		−	0.0389940i		−	0.00366825i	−0.999998	−	0.00183412i	$-0.999416\pi$
$113$		−	0.0389940i		−	0.00366825i	0.999998	−	0.00183412i	$-0.000583820\pi$
$114$	−3.60379	+	0.884075i	−0.337526	+	0.0828012i
$115$		0			0
$116$	−1.48750	−	1.24816i	−0.138111	−	0.115889i
$117$	3.79178	+	10.4178i	0.350550	+	0.963129i
$118$	5.12042	−	0.902869i	0.471373	−	0.0831158i
$119$	−3.83698	+	21.7606i	−0.351736	+	1.99479i
$120$		0			0
$121$	3.03645	+	5.25928i	0.276041	+	0.478116i
$122$	−4.53427	−	2.61786i	−0.410514	−	0.237010i
$123$	5.72790	+	6.82624i	0.516467	+	0.615502i
$124$	5.76328	−	4.83597i	0.517558	−	0.434283i
$125$		0			0
$126$	−5.74501	−	9.95065i	−0.511806	−	0.886474i
$127$	−0.0291879	+	0.0801932i	−0.00259001	+	0.00711599i	−0.940981	−	0.338460i	$-0.890094\pi$
$127$	−0.0291879	+	0.0801932i	−0.00259001	+	0.00711599i	0.938391	+	0.345576i	$0.112316\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	1.24505	+	7.06105i	0.109621	+	0.621691i
$130$		0			0
$131$	−0.668494	−	0.560933i	−0.0584066	−	0.0490090i	0.613117	−	0.789992i	$-0.289915\pi$
$131$	−0.668494	−	0.560933i	−0.0584066	−	0.0490090i	−0.671524	+	0.740983i	$0.734360\pi$
$132$			1.88960i			0.164468i
$133$	9.72402	−	19.7474i	0.843179	−	1.71232i
$134$	1.47648			0.127549
$135$		0			0
$136$	4.11175	−	1.49656i	0.352580	−	0.128329i
$137$	11.1440	−	1.96498i	0.952092	−	0.167880i	0.324034	−	0.946046i	$-0.394961\pi$
$137$	11.1440	−	1.96498i	0.952092	−	0.167880i	0.628059	+	0.778166i	$0.283850\pi$
$138$	−3.82368	−	0.674218i	−0.325493	−	0.0573932i
$139$	−0.183382	−	0.0667458i	−0.0155543	−	0.00566130i	0.334231	−	0.942491i	$-0.391523\pi$
$139$	−0.183382	−	0.0667458i	−0.0155543	−	0.00566130i	−0.349786	+	0.936830i	$0.613746\pi$
$140$		0			0
$141$	−2.05279	+	3.55553i	−0.172876	+	0.299430i
$142$	−8.26324	−	9.84775i	−0.693436	−	0.826404i
$143$	6.95204	+	8.28512i	0.581359	+	0.692837i
$144$	−1.13766	+	1.97049i	−0.0948050	+	0.164207i
$145$		0			0
$146$	12.4977	+	4.54881i	1.03432	+	0.376462i
$147$	−15.5102	−	2.73487i	−1.27926	−	0.225569i
$148$	−2.44195	+	0.430582i	−0.200727	+	0.0353936i
$149$	−0.121973	+	0.0443946i	−0.00999244	+	0.00363695i	−0.347012	−	0.937861i	$-0.612804\pi$
$149$	−0.121973	+	0.0443946i	−0.00999244	+	0.00363695i	0.337019	+	0.941498i	$0.390581\pi$
$150$		0			0
$151$	3.54764			0.288703			0.144352	−	0.989526i	$-0.453890\pi$
$151$	3.54764			0.288703			0.144352	+	0.989526i	$0.453890\pi$
$152$	−4.34940	+	0.287627i	−0.352783	+	0.0233297i
$153$			9.95598i			0.804893i
$154$	−8.58674	−	7.20513i	−0.691939	−	0.580606i
$155$		0			0
$156$	−0.720265	−	4.08483i	−0.0576673	−	0.327048i
$157$	4.14861	+	0.731513i	0.331095	+	0.0583811i	0.336725	−	0.941603i	$-0.390681\pi$
$157$	4.14861	+	0.731513i	0.331095	+	0.0583811i	−0.00562936	+	0.999984i	$0.501792\pi$
$158$	−2.08077	+	5.71688i	−0.165537	+	0.454810i
$159$	4.34238	+	7.52122i	0.344373	+	0.596471i
$160$		0			0
$161$	17.6437	−	14.8048i	1.39052	−	1.16678i
$162$	−1.93032	−	2.30046i	−0.151660	−	0.180742i
$163$	19.4128	+	11.2080i	1.52053	+	0.877877i	0.999707	+	0.0242101i	$0.00770708\pi$
$163$	19.4128	+	11.2080i	1.52053	+	0.877877i	0.520820	+	0.853666i	$0.325626\pi$
$164$	5.23389	+	9.06537i	0.408698	+	0.707886i
$165$		0			0
$166$	−2.16651	+	12.2869i	−0.168154	+	0.953647i
$167$	3.73305	−	0.658237i	0.288872	−	0.0509359i	−0.0273344	−	0.999626i	$-0.508702\pi$
$167$	3.73305	−	0.658237i	0.288872	−	0.0509359i	0.316206	+	0.948690i	$0.397591\pi$
$168$	1.47029	+	4.03959i	0.113435	+	0.311661i
$169$	−8.22804	−	6.90415i	−0.632926	−	0.531088i
$170$		0			0
$171$	2.76975	−	9.52329i	0.211808	−	0.728264i
$172$			8.42257i			0.642215i
$173$	−12.5298	+	14.9324i	−0.952624	+	1.13529i	0.0380827	+	0.999275i	$0.487875\pi$
$173$	−12.5298	+	14.9324i	−0.952624	+	1.13529i	−0.990706	+	0.136018i	$0.956569\pi$
$174$	−1.55332	+	0.565364i	−0.117757	+	0.0428601i
$175$		0			0
$176$	−0.385448	+	2.18599i	−0.0290543	+	0.164775i
$177$	1.51384	−	4.15923i	0.113787	−	0.312627i
$178$	5.39739	−	3.11619i	0.404552	−	0.233568i
$179$	4.39396	−	7.61057i	0.328420	−	0.568840i	−0.653778	−	0.756686i	$-0.726817\pi$
$179$	4.39396	−	7.61057i	0.328420	−	0.568840i	0.982199	+	0.187846i	$0.0601505\pi$
$180$		0			0
$181$	7.42429	−	6.22972i	0.551843	−	0.463051i	−0.323721	−	0.946152i	$-0.604934\pi$
$181$	7.42429	−	6.22972i	0.551843	−	0.463051i	0.875565	+	0.483101i	$0.160490\pi$
$182$	21.3087	+	12.3026i	1.57951	+	0.911930i
$183$	−3.85994	+	2.22854i	−0.285335	+	0.164738i
$184$	−4.28591	−	1.55994i	−0.315961	−	0.115000i
$185$		0			0
$186$	−1.11214	−	6.30725i	−0.0815460	−	0.462470i
$187$	3.32192	+	9.12689i	0.242923	+	0.667425i
$188$	−3.10005	+	3.69450i	−0.226094	+	0.269449i
$189$	−22.6778			−1.64956
$190$		0			0
$191$	1.85152			0.133971			0.0669857	−	0.997754i	$-0.478662\pi$
$191$	1.85152			0.133971			0.0669857	+	0.997754i	$0.478662\pi$
$192$	0.547193	−	0.652119i	0.0394903	−	0.0470627i
$193$	0.165699	+	0.455254i	0.0119273	+	0.0327699i	0.945513	−	0.325583i	$-0.105561\pi$
$193$	0.165699	+	0.455254i	0.0119273	+	0.0327699i	−0.933586	+	0.358353i	$0.883338\pi$
$194$	−0.341395	−	1.93615i	−0.0245107	−	0.139007i
$195$		0			0
$196$	−17.3852	−	6.32770i	−1.24180	−	0.451979i
$197$	16.9695	−	9.79734i	1.20903	−	0.698031i	0.246479	−	0.969148i	$-0.420726\pi$
$197$	16.9695	−	9.79734i	1.20903	−	0.698031i	0.962547	+	0.271117i	$0.0873929\pi$
$198$	−4.37390	−	2.52527i	−0.310840	−	0.179463i
$199$	−7.58202	+	6.36207i	−0.537475	+	0.450995i	−0.870673	−	0.491861i	$-0.836317\pi$
$199$	−7.58202	+	6.36207i	−0.537475	+	0.450995i	0.333198	+	0.942857i	$0.391872\pi$
$200$		0			0
$201$	0.628451	−	1.08851i	0.0443275	−	0.0767775i
$202$	8.50776	−	4.91196i	0.598604	−	0.345604i
$203$	3.35377	−	9.21441i	0.235389	−	0.646725i
$204$	0.646822	−	3.66831i	0.0452866	−	0.256833i
$205$		0			0
$206$	12.4783	−	4.54171i	0.869401	−	0.316436i
$207$	6.67063	−	7.94975i	0.463641	−	0.552546i
$208$		−	4.87247i		−	0.337845i
$209$	−0.638449	−	9.65440i	−0.0441624	−	0.667809i
$210$		0			0
$211$	−14.3277	−	12.0224i	−0.986361	−	0.827655i	−0.00132403	−	0.999999i	$-0.500421\pi$
$211$	−14.3277	−	12.0224i	−0.986361	−	0.827655i	−0.985037	+	0.172344i	$0.944866\pi$
$212$	3.48928	+	9.58672i	0.239645	+	0.658419i
$213$	−10.7772	+	1.90032i	−0.738444	+	0.130208i
$214$	−2.56774	+	14.5624i	−0.175527	+	0.995463i
$215$		0			0
$216$	2.24539	+	3.88913i	0.152779	+	0.264622i
$217$	32.9022	+	18.9961i	2.23355	+	1.28954i
$218$	5.64227	+	6.72420i	0.382143	+	0.455420i
$219$	8.67307	−	7.27757i	0.586072	−	0.491773i
$220$		0			0
$221$	−10.6601	−	18.4638i	−0.717074	−	1.24201i
$222$	−0.721956	+	1.98356i	−0.0484545	+	0.133128i
$223$	3.06534	+	0.540502i	0.205270	+	0.0361947i	0.275338	−	0.961348i	$-0.411210\pi$
$223$	3.06534	+	0.540502i	0.205270	+	0.0361947i	−0.0700673	+	0.997542i	$0.522321\pi$
$224$	0.876897	+	4.97313i	0.0585901	+	0.332281i
$225$		0			0
$226$	−0.0298712	−	0.0250649i	−0.00198700	−	0.00166729i
$227$		−	1.34903i		−	0.0895381i	−0.998997	−	0.0447690i	$-0.985745\pi$
$227$		−	1.34903i		−	0.0895381i	0.998997	−	0.0447690i	$-0.0142552\pi$
$228$	−1.63923	+	3.32894i	−0.108561	+	0.220464i
$229$	−16.0289			−1.05922			−0.529611	−	0.848240i	$-0.677662\pi$
$229$	−16.0289			−1.05922			−0.529611	+	0.848240i	$0.677662\pi$
$230$		0			0
$231$	−8.96671	+	3.26361i	−0.589966	+	0.214730i
$232$	−1.91229	+	0.337189i	−0.125548	+	0.0221376i
$233$	−16.9127	−	2.98216i	−1.10799	−	0.195368i	−0.410426	−	0.911894i	$-0.634620\pi$
$233$	−16.9127	−	2.98216i	−1.10799	−	0.195368i	−0.697560	+	0.716526i	$0.745731\pi$
$234$	10.4178	+	3.79178i	0.681035	+	0.247876i
$235$		0			0
$236$	2.59971	−	4.50282i	0.169227	−	0.293109i
$237$	3.32900	+	3.96734i	0.216242	+	0.257707i
$238$	14.2032	+	16.9267i	0.920659	+	1.09720i
$239$	−13.9049	+	24.0841i	−0.899436	+	1.55787i	−0.0712188	+	0.997461i	$0.522689\pi$
$239$	−13.9049	+	24.0841i	−0.899436	+	1.55787i	−0.828217	+	0.560408i	$0.810644\pi$
$240$		0			0
$241$	6.09195	+	2.21729i	0.392417	+	0.142828i	0.530690	−	0.847566i	$-0.321933\pi$
$241$	6.09195	+	2.21729i	0.392417	+	0.142828i	−0.138273	+	0.990394i	$0.544155\pi$
$242$	5.98063	+	1.05455i	0.384450	+	0.0677889i
$243$	−15.7853	+	2.78337i	−1.01263	+	0.178553i
$244$	−4.91997	+	1.79072i	−0.314969	+	0.114639i
$245$		0			0
$246$	8.91103			0.568146
$247$	5.06017	+	20.6270i	0.321971	+	1.31246i
$248$		−	7.52343i		−	0.477738i
$249$	8.13612	+	6.82702i	0.515606	+	0.432645i
$250$		0			0
$251$	2.10127	+	11.9169i	0.132631	+	0.752189i	0.976480	+	0.215608i	$0.0691732\pi$
$251$	2.10127	+	11.9169i	0.132631	+	0.752189i	−0.843849	+	0.536581i	$0.819716\pi$
$252$	−11.3155	−	1.99522i	−0.712807	−	0.125687i
$253$	3.46262	−	9.51346i	0.217693	−	0.598106i
$254$	0.0426699	+	0.0739064i	0.00267735	+	0.00463730i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−15.2776	−	18.2072i	−0.952992	−	1.13573i	−0.990648	−	0.136440i	$-0.956434\pi$
$257$	−15.2776	−	18.2072i	−0.952992	−	1.13573i	0.0376568	−	0.999291i	$-0.488011\pi$
$258$	6.20938	+	3.58499i	0.386579	+	0.223192i
$259$	−6.26086	−	10.8441i	−0.389031	−	0.673821i
$260$		0			0
$261$	0.767213	−	4.35108i	0.0474893	−	0.269325i
$262$	−0.859400	+	0.151535i	−0.0530939	+	0.00936189i
$263$	5.90950	+	16.2362i	0.364395	+	1.00117i	0.977457	+	0.211133i	$0.0677153\pi$
$263$	5.90950	+	16.2362i	0.364395	+	1.00117i	−0.613062	+	0.790035i	$0.710062\pi$
$264$	1.44751	+	1.21461i	0.0890884	+	0.0747540i
$265$		0			0
$266$	−8.87694	−	20.1424i	−0.544280	−	1.23501i
$267$		−	5.30550i		−	0.324691i
$268$	0.949064	−	1.13105i	0.0579733	−	0.0690899i
$269$	9.95234	−	3.62236i	0.606805	−	0.220859i	−0.0202997	−	0.999794i	$-0.506462\pi$
$269$	9.95234	−	3.62236i	0.606805	−	0.220859i	0.627105	+	0.778935i	$0.284240\pi$
$270$		0			0
$271$	1.78816	−	10.1411i	0.108623	−	0.616030i	−0.881089	−	0.472951i	$-0.843189\pi$
$271$	1.78816	−	10.1411i	0.108623	−	0.616030i	0.989711	−	0.143079i	$-0.0457002\pi$
$272$	1.49656	−	4.11175i	0.0907420	−	0.249312i
$273$	18.1397	−	10.4730i	1.09787	−	0.633854i
$274$	5.65793	−	9.79983i	0.341808	−	0.592029i
$275$		0			0
$276$	−2.97429	+	2.49573i	−0.179031	+	0.150225i
$277$	−6.49560	−	3.75024i	−0.390283	−	0.225330i	0.292000	−	0.956418i	$-0.405679\pi$
$277$	−6.49560	−	3.75024i	−0.390283	−	0.225330i	−0.682283	+	0.731088i	$0.739013\pi$
$278$	−0.169006	+	0.0975758i	−0.0101363	+	0.00585221i
$279$	16.0859	+	5.85477i	0.963035	+	0.350516i
$280$		0			0
$281$	2.03848	+	11.5608i	0.121605	+	0.689659i	0.983266	+	0.182174i	$0.0583135\pi$
$281$	2.03848	+	11.5608i	0.121605	+	0.689659i	−0.861661	+	0.507485i	$0.830575\pi$
$282$	1.40419	+	3.85798i	0.0836183	+	0.229739i
$283$	12.0502	−	14.3608i	0.716309	−	0.853663i	−0.277958	−	0.960593i	$-0.589658\pi$
$283$	12.0502	−	14.3608i	0.716309	−	0.853663i	0.994267	+	0.106930i	$0.0341020\pi$
$284$	−12.8553			−0.762823
$285$		0			0
$286$	10.8155			0.639531
$287$	−33.9782	+	40.4937i	−2.00567	+	2.39026i
$288$	0.778205	+	2.13810i	0.0458562	+	0.125989i
$289$	−0.372684	−	2.11360i	−0.0219226	−	0.124329i
$290$		0			0
$291$	−1.57270	−	0.572415i	−0.0921932	−	0.0335556i
$292$	11.5180	−	6.64991i	0.674039	−	0.389157i
$293$	−15.1789	−	8.76356i	−0.886763	−	0.511973i	−0.0138805	−	0.999904i	$-0.504418\pi$
$293$	−15.1789	−	8.76356i	−0.886763	−	0.511973i	−0.872882	+	0.487931i	$0.837752\pi$
$294$	−12.0648	+	10.1236i	−0.703635	+	0.590420i
$295$		0			0
$296$	−1.23981	+	2.14742i	−0.0720626	+	0.124816i
$297$	−8.63274	+	4.98411i	−0.500922	+	0.289208i
$298$	−0.0443946	+	0.121973i	−0.00257171	+	0.00706572i
$299$	−3.85901	+	21.8855i	−0.223172	+	1.26567i
$300$		0			0
$301$	−39.9677	+	14.5470i	−2.30370	+	0.838477i
$302$	2.28038	−	2.71765i	0.131221	−	0.156383i
$303$		−	8.36292i		−	0.480437i
$304$	−2.57540	+	3.51672i	−0.147710	+	0.201698i
$305$		0			0
$306$	7.62672	+	6.39958i	0.435991	+	0.365840i
$307$	3.87700	+	10.6520i	0.221272	+	0.607940i	0.999807	−	0.0196617i	$-0.00625893\pi$
$307$	3.87700	+	10.6520i	0.221272	+	0.607940i	−0.778535	+	0.627602i	$0.784037\pi$
$308$	−11.0389	+	1.94646i	−0.628999	+	0.110910i
$309$	1.96296	−	11.1325i	0.111669	−	0.633306i
$310$		0			0
$311$	3.53458	+	6.12208i	0.200428	+	0.347151i	0.948666	−	0.316279i	$-0.102433\pi$
$311$	3.53458	+	6.12208i	0.200428	+	0.347151i	−0.748238	+	0.663430i	$0.769100\pi$
$312$	−3.59214	−	2.07392i	−0.203365	−	0.117413i
$313$	7.78494	+	9.27773i	0.440031	+	0.524408i	0.939788	−	0.341757i	$-0.111022\pi$
$313$	7.78494	+	9.27773i	0.440031	+	0.524408i	−0.499758	+	0.866165i	$0.666578\pi$
$314$	3.22705	−	2.70782i	0.182113	−	0.152811i
$315$		0			0
$316$	3.04189	+	5.26870i	0.171119	+	0.296388i
$317$	3.74161	−	10.2800i	0.210150	−	0.577382i	−0.789173	−	0.614171i	$-0.789491\pi$
$317$	3.74161	−	10.2800i	0.210150	−	0.577382i	0.999323	+	0.0367885i	$0.0117128\pi$
$318$	8.55281	+	1.50809i	0.479618	+	0.0845696i
$319$	−0.748462	−	4.24474i	−0.0419058	−	0.237660i
$320$		0			0
$321$	9.64290	+	8.09135i	0.538214	+	0.451615i
$322$		−	23.0322i		−	1.28353i
$323$	−2.06533	+	18.9608i	−0.114918	+	1.05501i
$324$	−3.00304			−0.166836
$325$		0			0
$326$	21.0641	−	7.66671i	1.16663	−	0.424620i
$327$	7.35887	−	1.29757i	0.406946	−	0.0717556i
$328$	10.3088	+	1.81771i	0.569206	+	0.100366i
$329$	−22.8858	−	8.32973i	−1.26173	−	0.459233i
$330$		0			0
$331$	−2.70804	+	4.69047i	−0.148847	+	0.257811i	−0.930802	−	0.365524i	$-0.880890\pi$
$331$	−2.70804	+	4.69047i	−0.148847	+	0.257811i	0.781954	+	0.623336i	$0.214223\pi$
$332$	8.01970	+	9.55750i	0.440138	+	0.524536i
$333$	−3.62657	−	4.32198i	−0.198735	−	0.236843i
$334$	1.89532	−	3.28279i	0.103707	−	0.179626i
$335$		0			0
$336$	4.03959	+	1.47029i	0.220378	+	0.0802109i
$337$	12.7797	+	2.25340i	0.696152	+	0.122750i	0.510516	−	0.859868i	$-0.329454\pi$
$337$	12.7797	+	2.25340i	0.696152	+	0.122750i	0.185636	+	0.982619i	$0.440565\pi$
$338$	−10.5778	+	1.86515i	−0.575355	+	0.101451i
$339$	−0.0311930	+	0.0113533i	−0.00169417	+	0.000616627i
$340$		0			0
$341$	16.6998			0.904346
$342$	−5.51490	−	8.24320i	−0.298212	−	0.445741i
$343$		−	58.0781i		−	3.13592i
$344$	6.45206	+	5.41392i	0.347872	+	0.291899i
$345$		0			0
$346$	3.38491	+	19.1968i	0.181974	+	1.03203i
$347$	−10.8736	−	1.91731i	−0.583727	−	0.102927i	−0.126017	−	0.992028i	$-0.540219\pi$
$347$	−10.8736	−	1.91731i	−0.583727	−	0.102927i	−0.457710	+	0.889101i	$0.651330\pi$
$348$	−0.565364	+	1.55332i	−0.0303067	+	0.0832669i
$349$	−14.3239	−	24.8097i	−0.766740	−	1.32803i	−0.939322	−	0.343038i	$-0.888544\pi$
$349$	−14.3239	−	24.8097i	−0.766740	−	1.32803i	0.172582	−	0.984995i	$-0.444789\pi$
$350$		0			0
$351$	16.7620	−	14.0650i	0.894687	−	0.750732i
$352$	1.42680	+	1.70040i	0.0760487	+	0.0906314i
$353$	−14.9123	−	8.60962i	−0.793701	−	0.458244i	0.0475627	−	0.998868i	$-0.484855\pi$
$353$	−14.9123	−	8.60962i	−0.793701	−	0.458244i	−0.841264	+	0.540625i	$0.818188\pi$
$354$	−2.21308	−	3.83317i	−0.117624	−	0.203731i
$355$		0			0
$356$	1.08224	−	6.13769i	0.0573586	−	0.325297i
$357$	18.5244	−	3.26635i	0.980415	−	0.172874i
$358$	−3.00565	−	8.25795i	−0.158853	−	0.436446i
$359$	9.78292	+	8.20884i	0.516323	+	0.433246i	0.863348	−	0.504610i	$-0.168364\pi$
$359$	9.78292	+	8.20884i	0.516323	+	0.433246i	−0.347025	+	0.937856i	$0.612808\pi$
$360$		0			0
$361$	7.25046	−	17.5622i	0.381603	−	0.924326i
$362$		−	9.69172i		−	0.509386i
$363$	3.32305	−	3.96025i	0.174415	−	0.207859i
$364$	23.1213	−	8.41548i	1.21189	−	0.441091i
$365$		0			0
$366$	−0.773963	+	4.38936i	−0.0404557	+	0.229436i
$367$	8.96147	−	24.6214i	0.467785	−	1.28523i	−0.451724	−	0.892158i	$-0.649191\pi$
$367$	8.96147	−	24.6214i	0.467785	−	1.28523i	0.919509	−	0.393070i	$-0.128587\pi$
$368$	−3.94991	+	2.28048i	−0.205903	+	0.118878i
$369$	−11.9088	+	20.6266i	−0.619946	+	1.07378i
$370$		0			0
$371$	−39.4654	+	33.1154i	−2.04894	+	1.71927i
$372$	−5.54651	−	3.20228i	−0.287573	−	0.166030i
$373$	−3.85144	+	2.22363i	−0.199420	+	0.115135i	−0.596385	−	0.802699i	$-0.703397\pi$
$373$	−3.85144	+	2.22363i	−0.199420	+	0.115135i	0.396965	+	0.917834i	$0.370063\pi$
$374$	9.12689	+	3.32192i	0.471940	+	0.171772i
$375$		0			0
$376$	0.837474	+	4.74955i	0.0431894	+	0.244939i
$377$	3.23597	+	8.89075i	0.166661	+	0.457897i
$378$	−14.5770	+	17.3722i	−0.749759	+	0.893528i
$379$	34.9948			1.79756			0.898782	−	0.438395i	$-0.144453\pi$
$379$	34.9948			1.79756			0.898782	+	0.438395i	$0.144453\pi$
$380$		0			0
$381$	0.0726482			0.00372188
$382$	1.19013	−	1.41835i	0.0608926	−	0.0725690i
$383$	8.37992	+	23.0237i	0.428194	+	1.17645i	0.946908	+	0.321506i	$0.104189\pi$
$383$	8.37992	+	23.0237i	0.428194	+	1.17645i	−0.518714	+	0.854948i	$0.673589\pi$
$384$	−0.147823	−	0.838348i	−0.00754358	−	0.0427818i
$385$		0			0
$386$	0.455254	+	0.165699i	0.0231718	+	0.00843386i
$387$	−16.5965	+	9.58202i	−0.843650	+	0.487082i
$388$	−1.70262	−	0.983007i	−0.0864373	−	0.0499046i
$389$	5.75726	−	4.83092i	0.291905	−	0.244937i	−0.485061	−	0.874481i	$-0.661202\pi$
$389$	5.75726	−	4.83092i	0.291905	−	0.244937i	0.776965	+	0.629543i	$0.216758\pi$
$390$		0			0
$391$	−9.97857	+	17.2834i	−0.504638	+	0.874058i
$392$	−16.0223	+	9.25048i	−0.809248	+	0.467220i
$393$	−0.254079	+	0.698076i	−0.0128166	+	0.0352133i
$394$	3.40258	−	19.2970i	0.171419	−	0.972168i
$395$		0			0
$396$	−4.74596	+	1.72739i	−0.238494	+	0.0868046i
$397$	−1.83378	+	2.18542i	−0.0920350	+	0.109683i	−0.810096	−	0.586297i	$-0.800585\pi$
$397$	−1.83378	+	2.18542i	−0.0920350	+	0.109683i	0.718061	+	0.695980i	$0.245030\pi$
$398$			9.89763i			0.496123i
$399$	−18.6280	−	2.02908i	−0.932568	−	0.101581i
$400$		0			0
$401$	−19.3861	−	16.2669i	−0.968097	−	0.812330i	0.0141541	−	0.999900i	$-0.495494\pi$
$401$	−19.3861	−	16.2669i	−0.968097	−	0.812330i	−0.982251	+	0.187570i	$0.939939\pi$
$402$	−0.429886	−	1.18110i	−0.0214407	−	0.0589080i
$403$	−36.1008	+	6.36554i	−1.79831	+	0.317090i
$404$	1.70591	−	9.67467i	0.0848720	−	0.481333i
$405$		0			0
$406$	−4.90288	−	8.49204i	−0.243326	−	0.421453i
$407$	−4.76664	−	2.75202i	−0.236274	−	0.136413i
$408$	−2.39432	−	2.85344i	−0.118536	−	0.141266i
$409$	12.6896	−	10.6479i	0.627462	−	0.526503i	−0.272677	−	0.962106i	$-0.587909\pi$
$409$	12.6896	−	10.6479i	0.627462	−	0.526503i	0.900139	+	0.435602i	$0.143465\pi$
$410$		0			0
$411$	−4.81649	−	8.34241i	−0.237580	−	0.411501i
$412$	4.54171	−	12.4783i	0.223754	−	0.614760i
$413$	25.8574	+	4.55935i	1.27236	+	0.224351i
$414$	−1.80206	−	10.2200i	−0.0885665	−	0.502286i
$415$		0			0
$416$	−3.73253	−	3.13196i	−0.183002	−	0.153557i
$417$			0.166129i			0.00813536i
$418$	−7.80608	−	5.71665i	−0.381808	−	0.279610i
$419$	−38.3266			−1.87237			−0.936187	−	0.351501i	$-0.885671\pi$
$419$	−38.3266			−1.87237			−0.936187	+	0.351501i	$0.885671\pi$
$420$		0			0
$421$	−9.76019	+	3.55242i	−0.475682	+	0.173134i	−0.568725	−	0.822528i	$-0.692563\pi$
$421$	−9.76019	+	3.55242i	−0.475682	+	0.173134i	0.0930423	+	0.995662i	$0.470341\pi$
$422$	−18.4194	+	3.24783i	−0.896640	+	0.158102i
$423$	−10.8068	−	1.90552i	−0.525442	−	0.0926496i
$424$	9.58672	+	3.48928i	0.465572	+	0.169455i
$425$		0			0
$426$	−5.47175	+	9.47734i	−0.265107	+	0.459179i
$427$	−16.9951	−	20.2539i	−0.822448	−	0.980156i
$428$	9.50491	+	11.3275i	0.459437	+	0.547536i
$429$	4.60350	−	7.97349i	0.222259	−	0.384964i
$430$		0			0
$431$	2.78263	+	1.01279i	0.134034	+	0.0487846i	0.408166	−	0.912908i	$-0.366168\pi$
$431$	2.78263	+	1.01279i	0.134034	+	0.0487846i	−0.274132	+	0.961692i	$0.588391\pi$
$432$	4.42256	+	0.779816i	0.212780	+	0.0375189i
$433$	35.6463	−	6.28540i	1.71305	−	0.302057i	0.770828	−	0.637043i	$-0.219843\pi$
$433$	35.6463	−	6.28540i	1.71305	−	0.302057i	0.942223	+	0.334986i	$0.108732\pi$
$434$	35.7010	−	12.9941i	1.71370	−	0.623736i
$435$		0			0
$436$	8.77781			0.420381
$437$	14.3531	−	13.7562i	0.686603	−	0.658049i
$438$		−	11.3219i		−	0.540981i
$439$	4.90663	+	4.11715i	0.234181	+	0.196501i	0.752325	−	0.658792i	$-0.228932\pi$
$439$	4.90663	+	4.11715i	0.234181	+	0.196501i	−0.518144	+	0.855293i	$0.673377\pi$
$440$		0			0
$441$	−7.30983	−	41.4561i	−0.348087	−	1.97410i
$442$	−20.9963	−	3.70221i	−0.998690	−	0.176096i
$443$	10.4295	−	28.6547i	0.495518	−	1.36143i	−0.400046	−	0.916495i	$-0.631006\pi$
$443$	10.4295	−	28.6547i	0.495518	−	1.36143i	0.895565	−	0.444931i	$-0.146772\pi$
$444$	1.05543	+	1.82806i	0.0500884	+	0.0867557i
$445$		0			0
$446$	2.38441	−	2.00076i	0.112905	−	0.0947387i
$447$	0.0710263	+	0.0846459i	0.00335943	+	0.00400361i
$448$	4.37330	+	2.52492i	0.206619	+	0.119291i
$449$	10.9555	+	18.9754i	0.517020	+	0.895504i	0.999805	+	0.0197655i	$0.00629196\pi$
$449$	10.9555	+	18.9754i	0.517020	+	0.895504i	−0.482785	+	0.875739i	$0.660375\pi$
$450$		0			0
$451$	−4.03479	+	22.8824i	−0.189991	+	1.07749i
$452$	−0.0384016	+	0.00677124i	−0.00180626	+	0.000318492i
$453$	−1.03292	−	2.83791i	−0.0485306	−	0.133337i
$454$	−1.03341	−	0.867138i	−0.0485006	−	0.0406968i
$455$		0			0
$456$	1.49644	+	3.39553i	0.0700770	+	0.159010i
$457$			8.35607i			0.390881i	0.980716	+	0.195440i	$0.0626136\pi$
$457$			8.35607i			0.390881i	−0.980716	+	0.195440i	$0.937386\pi$
$458$	−10.3032	+	12.2789i	−0.481437	+	0.573755i
$459$	18.4650	−	6.72071i	0.861872	−	0.313696i
$460$		0			0
$461$	2.15399	−	12.2159i	0.100321	−	0.568951i	−0.892665	−	0.450721i	$-0.851167\pi$
$461$	2.15399	−	12.2159i	0.100321	−	0.568951i	0.992986	−	0.118230i	$-0.0377219\pi$
$462$	−3.26361	+	8.96671i	−0.151837	+	0.417169i
$463$	13.6745	−	7.89495i	0.635506	−	0.366909i	−0.147376	−	0.989081i	$-0.547083\pi$
$463$	13.6745	−	7.89495i	0.635506	−	0.366909i	0.782881	+	0.622171i	$0.213749\pi$
$464$	−0.970897	+	1.68164i	−0.0450728	+	0.0780683i
$465$		0			0
$466$	−13.1557	+	11.0390i	−0.609427	+	0.511370i
$467$	9.96957	+	5.75594i	0.461337	+	0.266353i	0.712606	−	0.701564i	$-0.247515\pi$
$467$	9.96957	+	5.75594i	0.461337	+	0.266353i	−0.251269	+	0.967917i	$0.580848\pi$
$468$	9.60113	−	5.54321i	0.443812	−	0.256235i
$469$	7.00636	+	2.55010i	0.323523	+	0.117753i
$470$		0			0
$471$	−0.622723	−	3.53164i	−0.0286936	−	0.162729i
$472$	−1.77830	−	4.88585i	−0.0818531	−	0.224890i
$473$	−12.0173	+	14.3217i	−0.552557	+	0.658512i
$474$	5.17900			0.237879
$475$		0			0
$476$	22.0963			1.01278
$477$	−14.9209	+	17.7820i	−0.683180	+	0.814182i
$478$	9.51154	+	26.1327i	0.435048	+	1.19528i
$479$	−2.23499	−	12.6753i	−0.102119	−	0.579148i	−0.992332	−	0.123603i	$-0.960555\pi$
$479$	−2.23499	−	12.6753i	−0.102119	−	0.579148i	0.890212	−	0.455546i	$-0.150556\pi$
$480$		0			0
$481$	11.3533	+	4.13225i	0.517664	+	0.188414i
$482$	5.61437	−	3.24146i	0.255728	−	0.147644i
$483$	−16.9800	−	9.80343i	−0.772619	−	0.446072i
$484$	4.65211	−	3.90358i	0.211459	−	0.177436i
$485$		0			0
$486$	−8.01439	+	13.8813i	−0.363540	+	0.629670i
$487$	−13.3338	+	7.69825i	−0.604210	+	0.348841i	−0.770696	−	0.637203i	$-0.780091\pi$
$487$	−13.3338	+	7.69825i	−0.604210	+	0.348841i	0.166486	+	0.986044i	$0.446758\pi$
$488$	−1.79072	+	4.91997i	−0.0810622	+	0.222717i
$489$	3.31360	−	18.7924i	0.149846	−	0.849821i
$490$		0			0
$491$	−3.11273	+	1.13294i	−0.140475	+	0.0511289i	−0.411301	−	0.911500i	$-0.634926\pi$
$491$	−3.11273	+	1.13294i	−0.140475	+	0.0511289i	0.270826	+	0.962628i	$0.412703\pi$
$492$	5.72790	−	6.82624i	0.258234	−	0.307751i
$493$			8.49659i			0.382667i
$494$	19.0538	+	9.38246i	0.857271	+	0.422137i
$495$		0			0
$496$	−5.76328	−	4.83597i	−0.258779	−	0.217141i
$497$	−22.2031	−	61.0024i	−0.995943	−	2.73633i
$498$	10.4596	−	1.84431i	0.468706	−	0.0826455i
$499$	−4.48776	+	25.4513i	−0.200900	+	1.13936i	0.702863	+	0.711325i	$0.251905\pi$
$499$	−4.48776	+	25.4513i	−0.200900	+	1.13936i	−0.903763	+	0.428034i	$0.859206\pi$
$500$		0			0
$501$	−1.61345	−	2.79458i	−0.0720836	−	0.124852i
$502$	10.4796	+	6.05037i	0.467725	+	0.270041i
$503$	−26.3263	−	31.3745i	−1.17383	−	1.39892i	−0.899294	−	0.437344i	$-0.855919\pi$
$503$	−26.3263	−	31.3745i	−1.17383	−	1.39892i	−0.274539	−	0.961576i	$-0.588525\pi$
$504$	−8.80187	+	7.38564i	−0.392066	+	0.328983i
$505$		0			0
$506$	−5.06201	−	8.76766i	−0.225034	−	0.389770i
$507$	−3.12728	+	8.59214i	−0.138888	+	0.381590i
$508$	0.0840433	+	0.0148191i	0.00372882	+	0.000657491i
$509$	2.52764	+	14.3350i	0.112036	+	0.635387i	0.988175	+	0.153329i	$0.0489994\pi$
$509$	2.52764	+	14.3350i	0.112036	+	0.635387i	−0.876139	+	0.482058i	$0.839889\pi$
$510$		0			0
$511$	51.4491	+	43.1709i	2.27598	+	1.90977i
$512$		−	1.00000i		−	0.0441942i
$513$	−19.5322	+	1.29167i	−0.862368	+	0.0570287i
$514$	−23.7678			−1.04835
$515$		0			0
$516$	6.73757	−	2.45228i	0.296605	−	0.107955i
$517$	−10.5426	+	1.85895i	−0.463664	+	0.0817564i
$518$	−12.3315	−	2.17437i	−0.541814	−	0.0955365i
$519$	15.5932	+	5.67547i	0.684466	+	0.249125i
$520$		0			0
$521$	−17.9537	+	31.0968i	−0.786568	+	1.36238i	0.141490	+	0.989940i	$0.454811\pi$
$521$	−17.9537	+	31.0968i	−0.786568	+	1.36238i	−0.928058	+	0.372436i	$0.878523\pi$
$522$	−2.83997	−	3.38454i	−0.124302	−	0.148137i
$523$	14.3674	+	17.1224i	0.628244	+	0.748712i	0.982464	−	0.186450i	$-0.0596983\pi$
$523$	14.3674	+	17.1224i	0.628244	+	0.748712i	−0.354221	+	0.935162i	$0.615254\pi$
$524$	−0.436329	+	0.755744i	−0.0190611	+	0.0330148i
$525$		0			0
$526$	16.2362	+	5.90950i	0.707932	+	0.257666i
$527$	−32.4197	−	5.71646i	−1.41222	−	0.249013i
$528$	1.86089	−	0.328125i	0.0809848	−	0.0142798i
$529$	−2.06505	+	0.751616i	−0.0897847	+	0.0326790i
$530$		0			0
$531$	11.8303			0.513393
$532$	−21.1360	−	6.14718i	−0.916362	−	0.266514i
$533$		−	51.0039i		−	2.20923i
$534$	−4.06425	−	3.41031i	−0.175877	−	0.147579i
$535$		0			0
$536$	−0.256388	−	1.45405i	−0.0110743	−	0.0628054i
$537$	−7.36734	−	1.29906i	−0.317924	−	0.0560586i
$538$	3.62236	−	9.95234i	0.156171	−	0.429076i
$539$	−20.5334	−	35.5648i	−0.884435	−	1.53189i
$540$		0			0
$541$	−23.7227	+	19.9057i	−1.01992	+	0.855812i	−0.989617	−	0.143729i	$-0.954091\pi$
$541$	−23.7227	+	19.9057i	−1.01992	+	0.855812i	−0.0302998	+	0.999541i	$0.509646\pi$
$542$	−6.61916	−	7.88840i	−0.284317	−	0.338836i
$543$	−7.14504	−	4.12519i	−0.306623	−	0.177029i
$544$	−2.18782	−	3.78941i	−0.0938019	−	0.162470i
$545$		0			0
$546$	3.63723	−	20.6277i	0.155659	−	0.882786i
$547$	−29.5635	+	5.21283i	−1.26404	+	0.222885i	−0.765191	−	0.643803i	$-0.777356\pi$
$547$	−29.5635	+	5.21283i	−1.26404	+	0.222885i	−0.498851	+	0.866688i	$0.666244\pi$
$548$	−3.87025	−	10.6334i	−0.165329	−	0.454238i
$549$	−9.12585	−	7.65750i	−0.389482	−	0.326814i
$550$		0			0
$551$	2.36375	−	8.12733i	0.100699	−	0.346236i
$552$			3.88267i			0.165257i
$553$	−19.7478	+	23.5345i	−0.839762	+	1.00079i
$554$	−7.04814	+	2.56531i	−0.299447	+	0.108990i
$555$		0			0
$556$	−0.0338877	+	0.192187i	−0.00143716	+	0.00815053i
$557$	−14.9957	+	41.2003i	−0.635388	+	1.74571i	0.0303609	+	0.999539i	$0.490334\pi$
$557$	−14.9957	+	41.2003i	−0.635388	+	1.74571i	−0.665749	+	0.746176i	$0.731888\pi$
$558$	14.8248	−	8.55911i	0.627584	−	0.362336i
$559$	20.5194	−	35.5406i	0.867876	−	1.50321i
$560$		0			0
$561$	6.33380	−	5.31469i	0.267413	−	0.224386i
$562$	10.1664	+	5.86957i	0.428843	+	0.247593i
$563$	15.8490	−	9.15044i	0.667957	−	0.385645i	−0.127345	−	0.991858i	$-0.540646\pi$
$563$	15.8490	−	9.15044i	0.667957	−	0.385645i	0.795302	+	0.606213i	$0.207312\pi$
$564$	3.85798	+	1.40419i	0.162450	+	0.0591271i
$565$		0			0
$566$	−3.25534	−	18.4619i	−0.136832	−	0.776013i
$567$	−5.18671	−	14.2504i	−0.217821	−	0.598459i
$568$	−8.26324	+	9.84775i	−0.346718	+	0.413202i
$569$	31.3182			1.31293			0.656464	−	0.754357i	$-0.272051\pi$
$569$	31.3182			1.31293			0.656464	+	0.754357i	$0.272051\pi$
$570$		0			0
$571$	−3.99941			−0.167370			−0.0836850	−	0.996492i	$-0.526669\pi$
$571$	−3.99941			−0.167370			−0.0836850	+	0.996492i	$0.526669\pi$
$572$	6.95204	−	8.28512i	0.290679	−	0.346418i
$573$	−0.539080	−	1.48111i	−0.0225204	−	0.0618743i
$574$	9.17917	+	52.0576i	0.383131	+	2.17284i
$575$		0			0
$576$	2.13810	+	0.778205i	0.0890876	+	0.0324252i
$577$	28.6263	−	16.5274i	1.19173	−	0.688045i	0.233030	−	0.972469i	$-0.425136\pi$
$577$	28.6263	−	16.5274i	1.19173	−	0.688045i	0.958698	+	0.284425i	$0.0918025\pi$
$578$	−1.85866	−	1.07310i	−0.0773103	−	0.0446351i
$579$	0.315933	−	0.265100i	0.0131297	−	0.0110172i
$580$		0			0
$581$	−31.5020	+	54.5631i	−1.30692	+	2.26366i
$582$	−1.44941	+	0.836815i	−0.0600798	+	0.0346871i
$583$	−7.74519	+	21.2797i	−0.320773	+	0.881316i
$584$	2.30949	−	13.0978i	0.0955674	−	0.541989i
$585$		0			0
$586$	−16.4701	+	5.99463i	−0.680374	+	0.247636i
$587$	3.29993	−	3.93270i	0.136202	−	0.162320i	−0.693632	−	0.720330i	$-0.743990\pi$
$587$	3.29993	−	3.93270i	0.136202	−	0.162320i	0.829834	+	0.558010i	$0.188435\pi$
$588$			15.7495i			0.649499i
$589$	29.4204	+	14.4872i	1.21225	+	0.596933i
$590$		0			0
$591$	−12.7781	−	10.7221i	−0.525619	−	0.441047i
$592$	0.848081	+	2.33008i	0.0348559	+	0.0957659i
$593$	−4.86926	+	0.858582i	−0.199957	+	0.0352577i	−0.272729	−	0.962091i	$-0.587926\pi$
$593$	−4.86926	+	0.858582i	−0.199957	+	0.0352577i	0.0727727	+	0.997349i	$0.476815\pi$
$594$	−1.73096	+	9.81678i	−0.0710223	+	0.402788i
$595$		0			0
$596$	0.0649006	+	0.112411i	0.00265843	+	0.00460454i
$597$	7.29684	+	4.21283i	0.298640	+	0.172420i
$598$	14.2848	+	17.0239i	0.584148	+	0.696160i
$599$	10.2340	−	8.58736i	0.418151	−	0.350870i	−0.409308	−	0.912396i	$-0.634230\pi$
$599$	10.2340	−	8.58736i	0.418151	−	0.350870i	0.827459	+	0.561526i	$0.189786\pi$
$600$		0			0
$601$	−24.2452	−	41.9939i	−0.988983	−	1.71297i	−0.622691	−	0.782468i	$-0.713961\pi$
$601$	−24.2452	−	41.9939i	−0.988983	−	1.71297i	−0.366292	−	0.930500i	$-0.619373\pi$
$602$	−14.5470	+	39.9677i	−0.592893	+	1.62896i
$603$	3.30843	+	0.583366i	0.134730	+	0.0237565i
$604$	−0.616042	−	3.49375i	−0.0250664	−	0.142159i
$605$		0			0
$606$	−6.40637	−	5.37558i	−0.260241	−	0.218368i
$607$		−	31.8211i		−	1.29158i	−0.763517	−	0.645788i	$-0.776529\pi$
$607$		−	31.8211i		−	1.29158i	0.763517	−	0.645788i	$-0.223471\pi$
$608$	1.03852	+	4.23338i	0.0421177	+	0.171686i
$609$	−8.34747			−0.338256
$610$		0			0
$611$	22.0819	−	8.03715i	0.893337	−	0.325148i
$612$	9.80472	−	1.72884i	0.396332	−	0.0698841i
$613$	−34.1851	−	6.02775i	−1.38072	−	0.243458i	−0.566524	−	0.824046i	$-0.691712\pi$
$613$	−34.1851	−	6.02775i	−1.38072	−	0.243458i	−0.814198	+	0.580587i	$0.802823\pi$
$614$	10.6520	+	3.87700i	0.429878	+	0.156463i
$615$		0			0
$616$	−5.60459	+	9.70744i	−0.225816	+	0.391124i
$617$	−9.74759	−	11.6167i	−0.392423	−	0.467672i	0.533271	−	0.845944i	$-0.320963\pi$
$617$	−9.74759	−	11.6167i	−0.392423	−	0.467672i	−0.925694	+	0.378273i	$0.876518\pi$
$618$	−7.26622	−	8.65954i	−0.292290	−	0.348338i
$619$	2.32371	−	4.02478i	0.0933977	−	0.161770i	−0.815541	−	0.578699i	$-0.803561\pi$
$619$	2.32371	−	4.02478i	0.0933977	−	0.161770i	0.908939	+	0.416930i	$0.136894\pi$
$620$		0			0
$621$	−19.2471	−	7.00536i	−0.772358	−	0.281115i
$622$	6.96177	+	1.22755i	0.279142	+	0.0492202i
$623$	30.9944	−	5.46515i	1.24176	−	0.218956i
$624$	−3.89770	+	1.41864i	−0.156033	+	0.0567912i
$625$		0			0
$626$	12.1112			0.484061
$627$	−7.53708	+	3.32165i	−0.301002	+	0.132654i
$628$		−	4.21261i		−	0.168102i
$629$	8.31153	+	6.97420i	0.331402	+	0.278080i
$630$		0			0
$631$	5.37475	+	30.4817i	0.213965	+	1.21346i	0.882693	+	0.469950i	$0.155728\pi$
$631$	5.37475	+	30.4817i	0.213965	+	1.21346i	−0.668728	+	0.743507i	$0.733161\pi$
$632$	5.99135	+	1.05644i	0.238323	+	0.0420228i
$633$	−5.44563	+	14.9617i	−0.216444	+	0.594676i
$634$	−5.46987	−	9.47410i	−0.217236	−	0.376265i
$635$		0			0
$636$	6.65291	−	5.58245i	0.263805	−	0.221359i
$637$	57.9443	+	69.0553i	2.29584	+	2.73607i
$638$	−3.73276	−	2.15511i	−0.147781	−	0.0853216i
$639$	−14.6250	−	25.3312i	−0.578555	−	1.00209i
$640$		0			0
$641$	8.35103	−	47.3611i	0.329846	−	1.87065i	−0.143321	−	0.989676i	$-0.545778\pi$
$641$	8.35103	−	47.3611i	0.329846	−	1.87065i	0.473167	−	0.880973i	$-0.343111\pi$
$642$	12.3967	−	2.18587i	0.489258	−	0.0862693i
$643$	−9.93113	−	27.2856i	−0.391646	−	1.07604i	−0.966250	−	0.257606i	$-0.917066\pi$
$643$	−9.93113	−	27.2856i	−0.391646	−	1.07604i	0.574605	−	0.818431i	$-0.305156\pi$
$644$	−17.6437	−	14.8048i	−0.695258	−	0.583391i
$645$		0			0
$646$	13.1973	+	13.7699i	0.519239	+	0.541770i
$647$		−	40.5552i		−	1.59439i	−0.603723	−	0.797194i	$-0.706317\pi$
$647$		−	40.5552i		−	1.59439i	0.603723	−	0.797194i	$-0.293683\pi$
$648$	−1.93032	+	2.30046i	−0.0758301	+	0.0903708i
$649$	10.8452	−	3.94732i	0.425710	−	0.154946i
$650$		0			0
$651$	5.61613	−	31.8507i	0.220114	−	1.24833i
$652$	7.66671	−	21.0641i	0.300251	−	0.824934i
$653$	20.6575	−	11.9266i	0.808391	−	0.466725i	−0.0380061	−	0.999278i	$-0.512101\pi$
$653$	20.6575	−	11.9266i	0.808391	−	0.466725i	0.846397	+	0.532553i	$0.178767\pi$
$654$	3.73619	−	6.47128i	0.146097	−	0.253047i
$655$		0			0
$656$	8.01879	−	6.72856i	0.313081	−	0.262706i
$657$	26.2071	+	15.1307i	1.02244	+	0.590304i
$658$	−21.0916	+	12.1773i	−0.822237	+	0.474719i
$659$	−39.5190	−	14.3837i	−1.53944	−	0.560310i	−0.573529	−	0.819185i	$-0.694426\pi$
$659$	−39.5190	−	14.3837i	−1.53944	−	0.560310i	−0.965911	+	0.258875i	$0.916648\pi$
$660$		0			0
$661$	1.33225	+	7.55554i	0.0518184	+	0.293877i	0.999693	−	0.0247661i	$-0.00788411\pi$
$661$	1.33225	+	7.55554i	0.0518184	+	0.293877i	−0.947875	+	0.318643i	$0.896773\pi$
$662$	1.85241	+	5.08945i	0.0719959	+	0.197807i
$663$	−11.6662	+	13.9033i	−0.453079	+	0.539959i
$664$	12.4764			0.484179
$665$		0			0
$666$	−5.64194			−0.218621
$667$	5.69282	−	6.78444i	0.220427	−	0.262695i
$668$	−1.29647	−	3.56203i	−0.0501621	−	0.137819i
$669$	−0.460119	−	2.60947i	−0.0177892	−	0.100888i
$670$		0			0
$671$	−10.9209	−	3.97488i	−0.421597	−	0.153449i
$672$	3.72290	−	2.14942i	0.143614	−	0.0829157i
$673$	10.5879	+	6.11296i	0.408135	+	0.235637i	0.689988	−	0.723821i	$-0.257616\pi$
$673$	10.5879	+	6.11296i	0.408135	+	0.235637i	−0.281853	+	0.959458i	$0.590949\pi$
$674$	9.94081	−	8.34133i	0.382906	−	0.321296i
$675$		0			0
$676$	−5.37047	+	9.30193i	−0.206557	+	0.357767i
$677$	−8.95818	+	5.17201i	−0.344291	+	0.198776i	−0.662168	−	0.749356i	$-0.730363\pi$
$677$	−8.95818	+	5.17201i	−0.344291	+	0.198776i	0.317877	+	0.948132i	$0.397030\pi$
$678$	−0.0113533	+	0.0311930i	−0.000436021	+	0.00119796i
$679$	1.72399	−	9.77724i	0.0661607	−	0.375216i
$680$		0			0
$681$	−1.07914	+	0.392776i	−0.0413529	+	0.0150512i
$682$	10.7344	−	12.7928i	0.411043	−	0.489862i
$683$		−	20.3440i		−	0.778443i	−0.921144	−	0.389221i	$-0.872744\pi$
$683$		−	20.3440i		−	0.778443i	0.921144	−	0.389221i	$-0.127256\pi$
$684$	−9.85957	−	1.07397i	−0.376990	−	0.0410642i
$685$		0			0
$686$	−44.4904	−	37.3319i	−1.69865	−	1.42534i
$687$	4.66691	+	12.8222i	0.178054	+	0.489199i
$688$	8.29461	−	1.46256i	0.316229	−	0.0557597i
$689$	8.63185	−	48.9536i	0.328847	−	1.86498i
$690$		0			0
$691$	14.7919	+	25.6203i	0.562709	+	0.974641i	0.997259	+	0.0739930i	$0.0235742\pi$
$691$	14.7919	+	25.6203i	0.562709	+	0.974641i	−0.434550	+	0.900648i	$0.643092\pi$
$692$	16.8814	+	9.74646i	0.641733	+	0.370505i
$693$	−16.3940	−	19.5376i	−0.622756	−	0.742171i
$694$	−8.45818	+	7.09726i	−0.321068	+	0.269408i
$695$		0			0
$696$	0.826507	+	1.43155i	0.0313287	+	0.0542628i
$697$	15.6656	−	43.0410i	0.593378	−	1.63029i
$698$	−28.2126	−	4.97463i	−1.06786	−	0.188293i
$699$	2.53866	+	14.3974i	0.0960209	+	0.544561i
$700$		0			0
$701$	−2.79045	−	2.34146i	−0.105394	−	0.0884359i	0.588568	−	0.808448i	$-0.299692\pi$
$701$	−2.79045	−	2.34146i	−0.105394	−	0.0884359i	−0.693962	+	0.720012i	$0.744136\pi$
$702$		−	21.8812i		−	0.825852i
$703$	−6.01009	−	8.98337i	−0.226675	−	0.338814i
$704$	2.21971			0.0836584
$705$		0			0
$706$	−16.1808	+	5.88932i	−0.608972	+	0.221648i
$707$	48.8556	−	8.61456i	1.83740	−	0.323984i
$708$	−4.35892	−	0.768595i	−0.163818	−	0.0288856i
$709$	−38.1690	−	13.8924i	−1.43347	−	0.521739i	−0.495544	−	0.868583i	$-0.665031\pi$
$709$	−38.1690	−	13.8924i	−1.43347	−	0.521739i	−0.937923	+	0.346843i	$0.887254\pi$
$710$		0			0
$711$	−6.92127	+	11.9880i	−0.259568	+	0.449585i
$712$	−4.00609	−	4.77427i	−0.150135	−	0.178923i
$713$	22.0567	+	26.2861i	0.826029	+	0.984424i
$714$	9.40508	−	16.2901i	0.351976	−	0.609641i
$715$		0			0
$716$	−8.25795	−	3.00565i	−0.308614	−	0.112326i
$717$	23.3144	+	4.11095i	0.870691	+	0.153526i
$718$	12.5767	−	2.21761i	0.469357	−	0.0827604i
$719$	−29.1532	+	10.6109i	−1.08723	+	0.395720i	−0.822595	−	0.568628i	$-0.807475\pi$
$719$	−29.1532	+	10.6109i	−1.08723	+	0.395720i	−0.264638	+	0.964348i	$0.585252\pi$
$720$		0			0
$721$	67.0573			2.49735
$722$	−8.79292	−	16.8429i	−0.327238	−	0.626829i
$723$		−	5.51878i		−	0.205246i
$724$	−7.42429	−	6.22972i	−0.275922	−	0.231526i
$725$		0			0
$726$	−0.897716	−	5.09120i	−0.0333174	−	0.188952i
$727$	6.18292	+	1.09022i	0.229312	+	0.0404339i	0.287123	−	0.957894i	$-0.407301\pi$
$727$	6.18292	+	1.09022i	0.229312	+	0.0404339i	−0.0578114	+	0.998328i	$0.518412\pi$
$728$	8.41548	−	23.1213i	0.311898	−	0.856934i
$729$	2.31793	+	4.01478i	0.0858494	+	0.148695i
$730$		0			0
$731$	28.2319	−	23.6894i	1.04419	−	0.876183i
$732$	2.86495	+	3.41432i	0.105892	+	0.126197i
$733$	−23.2546	−	13.4260i	−0.858927	−	0.495902i	0.00472555	−	0.999989i	$-0.498496\pi$
$733$	−23.2546	−	13.4260i	−0.858927	−	0.495902i	−0.863653	+	0.504087i	$0.831829\pi$
$734$	−13.1008	−	22.6912i	−0.483559	−	0.837548i
$735$		0			0
$736$	−0.792004	+	4.49168i	−0.0291936	+	0.165565i
$737$	3.22757	−	0.569107i	0.118889	−	0.0209633i
$738$	8.14609	+	22.3812i	0.299862	+	0.823863i
$739$	29.5975	+	24.8353i	1.08876	+	0.913581i	0.996619	−	0.0821650i	$-0.0261835\pi$
$739$	29.5975	+	24.8353i	1.08876	+	0.913581i	0.0921443	+	0.995746i	$0.470628\pi$
$740$		0			0
$741$	15.0271	−	10.0535i	0.552035	−	0.369325i
$742$			51.5184i			1.89130i
$743$	1.11058	−	1.32354i	0.0407432	−	0.0485559i	−0.745288	−	0.666743i	$-0.767688\pi$
$743$	1.11058	−	1.32354i	0.0407432	−	0.0485559i	0.786031	+	0.618187i	$0.212132\pi$
$744$	−6.01831	+	2.19049i	−0.220642	+	0.0803071i
$745$		0			0
$746$	−0.772258	+	4.37969i	−0.0282744	+	0.160352i
$747$	−9.70923	+	26.6759i	−0.355242	+	0.976020i
$748$	8.41139	−	4.85632i	0.307551	−	0.177565i
$749$	−37.3361	+	64.6680i	−1.36423	+	2.36292i
$750$		0			0
$751$	13.6370	−	11.4428i	0.497622	−	0.417555i	−0.359126	−	0.933289i	$-0.616925\pi$
$751$	13.6370	−	11.4428i	0.497622	−	0.417555i	0.856749	+	0.515734i	$0.172481\pi$
$752$	4.17669	+	2.41141i	0.152308	+	0.0879351i
$753$	8.92105	−	5.15057i	0.325101	−	0.187697i
$754$	8.89075	+	3.23597i	0.323782	+	0.117847i
$755$		0			0
$756$	3.93795	+	22.3332i	0.143222	+	0.812252i
$757$	−0.0128671	−	0.0353520i	−0.000467662	−	0.00128489i	0.939459	−	0.342663i	$-0.111329\pi$
$757$	−0.0128671	−	0.0353520i	−0.000467662	−	0.00128489i	−0.939926	+	0.341378i	$0.889107\pi$
$758$	22.4943	−	26.8076i	0.817028	−	0.973696i
$759$	−8.61838			−0.312828
$760$		0			0
$761$	−11.8171			−0.428370			−0.214185	−	0.976793i	$-0.568709\pi$
$761$	−11.8171			−0.428370			−0.214185	+	0.976793i	$0.568709\pi$
$762$	0.0466973	−	0.0556517i	0.00169167	−	0.00201605i
$763$	15.1606	+	41.6534i	0.548851	+	1.50795i
$764$	−0.321513	−	1.82339i	−0.0116319	−	0.0659680i
$765$		0			0
$766$	23.0237	+	8.37992i	0.831878	+	0.302779i
$767$	−21.9399	+	12.6670i	−0.792203	+	0.457379i
$768$	−0.737231	−	0.425641i	−0.0266025	−	0.0153590i
$769$	−33.4794	+	28.0926i	−1.20730	+	1.01304i	−0.207908	+	0.978148i	$0.566665\pi$
$769$	−33.4794	+	28.0926i	−1.20730	+	1.01304i	−0.999391	+	0.0348957i	$0.988890\pi$
$770$		0			0
$771$	−10.1165	+	17.5223i	−0.364338	+	0.631051i
$772$	0.419565	−	0.242236i	0.0151005	−	0.00871826i
$773$	−5.96385	+	16.3855i	−0.214505	+	0.589347i	−0.999547	−	0.0300952i	$-0.990419\pi$
$773$	−5.96385	+	16.3855i	−0.214505	+	0.589347i	0.785042	+	0.619442i	$0.212641\pi$
$774$	−3.32780	+	18.8729i	−0.119615	+	0.678372i
$775$		0			0
$776$	−1.84745	+	0.672416i	−0.0663195	+	0.0241383i
$777$	−6.85180	+	8.16565i	−0.245807	+	0.292941i
$778$		−	7.51557i		−	0.269446i
$779$	−26.9588	+	36.8122i	−0.965898	+	1.31893i
$780$		0			0
$781$	−21.8591	−	18.3420i	−0.782181	−	0.656328i
$782$	6.82574	+	18.7536i	0.244088	+	0.670626i
$783$	−8.58770	+	1.51424i	−0.306899	+	0.0541146i
$784$	−3.21266	+	18.2199i	−0.114738	+	0.650710i
$785$		0			0
$786$	0.371438	+	0.643350i	0.0132488	+	0.0229475i
$787$	25.8430	+	14.9205i	0.921203	+	0.531857i	0.884019	−	0.467452i	$-0.154828\pi$
$787$	25.8430	+	14.9205i	0.921203	+	0.531857i	0.0371843	+	0.999308i	$0.488161\pi$
$788$	−12.5952	−	15.0104i	−0.448686	−	0.534723i
$789$	11.2675	−	9.45452i	0.401132	−	0.336590i
$790$		0			0
$791$	−0.0984569	−	0.170532i	−0.00350072	−	0.00606343i
$792$	−1.72739	+	4.74596i	−0.0613801	+	0.168640i
$793$	25.1233	+	4.42992i	0.892156	+	0.157311i
$794$	0.495394	+	2.80952i	0.0175809	+	0.0997062i
$795$		0			0
$796$	7.58202	+	6.36207i	0.268738	+	0.225498i
$797$		−	8.25156i		−	0.292285i	−0.989264	−	0.146143i	$-0.953314\pi$
$797$		−	8.25156i		−	0.292285i	0.989264	−	0.146143i	$-0.0466859\pi$
$798$	−13.5282	+	12.9656i	−0.478894	+	0.458978i
$799$	21.1029			0.746567
$800$		0			0
$801$	13.3254	−	4.85007i	0.470831	−	0.171369i
$802$	−24.9223	+	4.39448i	−0.880038	+	0.155174i
$803$	29.0732	+	5.12639i	1.02597	+	0.180906i
$804$	−1.18110	−	0.429886i	−0.0416542	−	0.0151609i
$805$		0			0
$806$	−18.3288	+	31.7465i	−0.645606	+	1.11822i
$807$	−5.79535	−	6.90663i	−0.204006	−	0.243125i
$808$	−6.31469	−	7.52556i	−0.222150	−	0.264748i
$809$	17.2942	−	29.9544i	0.608030	−	1.05314i	−0.383534	−	0.923527i	$-0.625293\pi$
$809$	17.2942	−	29.9544i	0.608030	−	1.05314i	0.991565	−	0.129613i	$-0.0413734\pi$
$810$		0			0
$811$	−15.0518	−	5.47841i	−0.528541	−	0.192373i	0.0639460	−	0.997953i	$-0.479631\pi$
$811$	−15.0518	−	5.47841i	−0.528541	−	0.192373i	−0.592487	+	0.805580i	$0.701854\pi$
$812$	−9.65680	−	1.70275i	−0.338887	−	0.0597549i
$813$	−8.63296	+	1.52222i	−0.302771	+	0.0533867i
$814$	−5.17211	+	1.88249i	−0.181282	+	0.0659813i
$815$		0			0
$816$	−3.72490			−0.130397
$817$	−33.5953	+	14.8057i	−1.17535	+	0.517987i
$818$		−	16.5651i		−	0.579187i
$819$	42.8868	+	35.9863i	1.49859	+	1.25746i
$820$		0			0
$821$	−5.38408	−	30.5347i	−0.187906	−	1.06567i	−0.922165	−	0.386797i	$-0.873581\pi$
$821$	−5.38408	−	30.5347i	−0.187906	−	1.06567i	0.734259	−	0.678870i	$-0.237530\pi$
$822$	−9.48664	−	1.67275i	−0.330885	−	0.0583439i
$823$	−12.4645	+	34.2461i	−0.434487	+	1.19374i	0.508544	+	0.861036i	$0.330184\pi$
$823$	−12.4645	+	34.2461i	−0.434487	+	1.19374i	−0.943031	+	0.332706i	$0.892038\pi$
$824$	−6.63954	−	11.5000i	−0.231299	−	0.400622i
$825$		0			0
$826$	20.1135	−	16.8772i	0.699837	−	0.587233i
$827$	14.1368	+	16.8476i	0.491585	+	0.585849i	0.953620	−	0.301013i	$-0.0973248\pi$
$827$	14.1368	+	16.8476i	0.491585	+	0.585849i	−0.462035	+	0.886862i	$0.652880\pi$
$828$	−8.98732	−	5.18883i	−0.312331	−	0.180324i
$829$	14.1054	+	24.4313i	0.489902	+	0.848536i	0.999932	−	0.0116207i	$-0.00369908\pi$
$829$	14.1054	+	24.4313i	0.489902	+	0.848536i	−0.510030	+	0.860157i	$0.670366\pi$
$830$		0			0
$831$	−1.10875	+	6.28801i	−0.0384620	+	0.218129i
$832$	−4.79844	+	0.846095i	−0.166356	+	0.0293331i
$833$	27.6877	+	76.0714i	0.959323	+	2.63572i
$834$	0.127262	+	0.106786i	0.00440672	+	0.00369768i
$835$		0			0
$836$	−9.39686	+	2.30522i	−0.324997	+	0.0797276i
$837$		−	33.7861i		−	1.16782i
$838$	−24.6358	+	29.3598i	−0.851031	+	1.01422i
$839$	−31.7659	+	11.5618i	−1.09668	+	0.399159i	−0.826091	−	0.563537i	$-0.809440\pi$
$839$	−31.7659	+	11.5618i	−1.09668	+	0.399159i	−0.270588	+	0.962695i	$0.587218\pi$
$840$		0			0
$841$	−4.38105	+	24.8461i	−0.151071	+	0.856763i
$842$	−3.55242	+	9.76019i	−0.122424	+	0.336358i
$843$	8.65445	−	4.99665i	0.298075	−	0.172094i
$844$	−9.35175	+	16.1977i	−0.321901	+	0.557548i
$845$		0			0
$846$	−8.40616	+	7.05361i	−0.289010	+	0.242508i
$847$	26.5586	+	15.3336i	0.912563	+	0.526869i
$848$	8.83517	−	5.10099i	0.303401	−	0.175169i
$849$	−14.9963	−	5.45821i	−0.514672	−	0.187325i
$850$		0			0
$851$	−1.96387	−	11.1377i	−0.0673206	−	0.381794i
$852$	3.74289	+	10.2835i	0.128229	+	0.352308i
$853$	15.9550	−	19.0144i	0.546287	−	0.651040i	−0.420298	−	0.907386i	$-0.638074\pi$
$853$	15.9550	−	19.0144i	0.546287	−	0.651040i	0.966585	+	0.256346i	$0.0825188\pi$
$854$	−26.4396			−0.904745
$855$		0			0
$856$	14.7870			0.505410
$857$	−23.1366	+	27.5731i	−0.790332	+	0.941881i	−0.999351	−	0.0360308i	$-0.988529\pi$
$857$	−23.1366	+	27.5731i	−0.790332	+	0.941881i	0.209019	+	0.977912i	$0.432973\pi$
$858$	−3.14898	−	8.65175i	−0.107504	−	0.295366i
$859$	1.04772	+	5.94193i	0.0357479	+	0.202736i	0.997451	−	0.0713578i	$-0.0227332\pi$
$859$	1.04772	+	5.94193i	0.0357479	+	0.202736i	−0.961703	+	0.274094i	$0.911622\pi$
$860$		0			0
$861$	42.2855	+	15.3907i	1.44109	+	0.524513i
$862$	2.56448	−	1.48061i	0.0873467	−	0.0504296i
$863$	4.68002	+	2.70201i	0.159310	+	0.0919775i	0.577535	−	0.816366i	$-0.304015\pi$
$863$	4.68002	+	2.70201i	0.159310	+	0.0919775i	−0.418226	+	0.908343i	$0.637348\pi$
$864$	3.44014	−	2.88662i	0.117036	−	0.0982048i
$865$		0			0
$866$	18.0981	−	31.3468i	0.614998	−	1.06521i
$867$	−1.58225	+	0.913510i	−0.0537359	+	0.0310244i
$868$	12.9941	−	35.7010i	0.441048	−	1.21177i
$869$	−2.34498	+	13.2990i	−0.0795480	+	0.451139i
$870$		0			0
$871$	−6.76025	+	2.46053i	−0.229062	+	0.0833719i
$872$	5.64227	−	6.72420i	0.191071	−	0.227710i
$873$		−	4.47331i		−	0.151399i
$874$	−1.31186	−	19.8375i	−0.0443743	−	0.671012i
$875$		0			0
$876$	−8.67307	−	7.27757i	−0.293036	−	0.245886i
$877$	−9.54107	−	26.2139i	−0.322179	−	0.885180i	−0.990026	−	0.140881i	$-0.955006\pi$
$877$	−9.54107	−	26.2139i	−0.322179	−	0.885180i	0.667847	−	0.744298i	$-0.267216\pi$
$878$	6.30785	−	1.11224i	0.212879	−	0.0375364i
$879$	−2.59092	+	14.6938i	−0.0873895	+	0.495611i
$880$		0			0
$881$	24.2475	+	41.9980i	0.816920	+	1.41495i	0.907941	+	0.419098i	$0.137654\pi$
$881$	24.2475	+	41.9980i	0.816920	+	1.41495i	−0.0910206	+	0.995849i	$0.529013\pi$
$882$	−36.4559	−	21.0478i	−1.22753	−	0.708716i
$883$	24.8997	+	29.6743i	0.837940	+	0.998618i	0.999930	+	0.0118259i	$0.00376439\pi$
$883$	24.8997	+	29.6743i	0.837940	+	0.998618i	−0.161990	+	0.986792i	$0.551791\pi$
$884$	−16.3322	+	13.7043i	−0.549311	+	0.460926i
$885$		0			0
$886$	−15.2468	−	26.4083i	−0.512228	−	0.887205i
$887$	−0.787669	+	2.16410i	−0.0264473	+	0.0726635i	−0.952214	−	0.305433i	$-0.901199\pi$
$887$	−0.787669	+	2.16410i	−0.0264473	+	0.0726635i	0.925766	+	0.378096i	$0.123421\pi$
$888$	2.07879	+	0.366546i	0.0697596	+	0.0123005i
$889$	0.0748342	+	0.424406i	0.00250986	+	0.0142341i
$890$		0			0
$891$	−5.10636	−	4.28475i	−0.171070	−	0.143544i
$892$		−	3.11263i		−	0.104219i
$893$	−20.1858	−	5.87082i	−0.675492	−	0.196460i
$894$	0.110497			0.00369558
$895$		0			0
$896$	4.74530	−	1.72715i	0.158529	−	0.0577000i
$897$	18.6308	−	3.28510i	0.622063	−	0.109686i
$898$	21.5780	+	3.80479i	0.720068	+	0.126967i
$899$	13.7279	+	4.99656i	0.457852	+	0.166645i
$900$		0			0
$901$	22.3201	−	38.6595i	0.743590	−	1.28794i
$902$	14.9354	+	17.7994i	0.497296	+	0.592654i
$903$	23.2736	+	27.7364i	0.774497	+	0.923009i
$904$	−0.0194970	+	0.0337698i	−0.000648461	+	0.00112317i
$905$		0			0
$906$	−2.83791	−	1.03292i	−0.0942833	−	0.0343163i
$907$	−3.38910	−	0.597590i	−0.112533	−	0.0198427i	0.117098	−	0.993120i	$-0.462641\pi$
$907$	−3.38910	−	0.597590i	−0.112533	−	0.0198427i	−0.229631	+	0.973278i	$0.573752\pi$
$908$	−1.32853	+	0.234256i	−0.0440889	+	0.00777406i
$909$	21.0045	−	7.64503i	0.696677	−	0.253570i
$910$		0			0
$911$	−13.5169			−0.447834			−0.223917	−	0.974608i	$-0.571885\pi$
$911$	−13.5169			−0.447834			−0.223917	+	0.974608i	$0.571885\pi$
$912$	3.56301	+	1.03627i	0.117983	+	0.0343142i
$913$			27.6940i			0.916539i
$914$	6.40112	+	5.37118i	0.211730	+	0.177663i
$915$		0			0
$916$	2.78340	+	15.7854i	0.0919660	+	0.521565i
$917$	−4.33984	−	0.765231i	−0.143314	−	0.0252701i
$918$	6.72071	−	18.4650i	0.221816	−	0.609435i
$919$	−1.47338	−	2.55196i	−0.0486022	−	0.0841815i	0.840701	−	0.541500i	$-0.182143\pi$
$919$	−1.47338	−	2.55196i	−0.0486022	−	0.0841815i	−0.889303	+	0.457318i	$0.848810\pi$
$920$		0			0
$921$	7.39215	−	6.20275i	0.243580	−	0.204388i
$922$	−7.97336	−	9.50227i	−0.262588	−	0.312941i
$923$	54.2453	+	31.3186i	1.78551	+	1.03086i
$924$	4.77109	+	8.26376i	0.156957	+	0.271858i
$925$		0			0
$926$	2.74189	−	15.5500i	0.0901040	−	0.511005i
$927$	29.7551	−	5.24663i	0.977287	−	0.172322i
$928$	0.664133	+	1.82469i	0.0218012	+	0.0598984i
$929$	24.4020	+	20.4757i	0.800603	+	0.671786i	0.948345	−	0.317240i	$-0.102756\pi$
$929$	24.4020	+	20.4757i	0.800603	+	0.671786i	−0.147742	+	0.989026i	$0.547200\pi$
$930$		0			0
$931$	−5.32138	−	80.4680i	−0.174401	−	2.63723i
$932$			17.1736i			0.562539i
$933$	3.86820	−	4.60994i	0.126639	−	0.150923i
$934$	10.8176	−	3.93729i	0.353963	−	0.128832i
$935$		0			0
$936$	1.92514	−	10.9180i	0.0629251	−	0.356866i
$937$	1.02970	−	2.82907i	0.0336387	−	0.0924216i	−0.921736	−	0.387817i	$-0.873229\pi$
$937$	1.02970	−	2.82907i	0.0336387	−	0.0924216i	0.955375	+	0.295396i	$0.0954514\pi$
$938$	6.45709	−	3.72800i	0.210832	−	0.121724i
$939$	5.15502	−	8.92876i	0.168228	−	0.291379i
$940$		0			0
$941$	−26.3537	+	22.1134i	−0.859106	+	0.720875i	−0.961775	−	0.273840i	$-0.911706\pi$
$941$	−26.3537	+	22.1134i	−0.859106	+	0.720875i	0.102670	+	0.994716i	$0.467262\pi$
$942$	−3.10567	−	1.79306i	−0.101188	−	0.0584210i
$943$	−41.3468	+	23.8716i	−1.34644	+	0.777366i
$944$	−4.88585	−	1.77830i	−0.159021	−	0.0578789i
$945$		0			0
$946$	3.24647	+	18.4116i	0.105552	+	0.598613i
$947$	4.03368	+	11.0825i	0.131077	+	0.360131i	0.987818	−	0.155616i	$-0.0497364\pi$
$947$	4.03368	+	11.0825i	0.131077	+	0.360131i	−0.856740	+	0.515748i	$0.827514\pi$
$948$	3.32900	−	3.96734i	0.108121	−	0.128853i
$949$	−64.8030			−2.10359
$950$		0			0
$951$	−9.31280			−0.301988
$952$	14.2032	−	16.9267i	0.460329	−	0.548599i
$953$	−3.10917	−	8.54236i	−0.100716	−	0.276714i	0.879093	−	0.476650i	$-0.158149\pi$
$953$	−3.10917	−	8.54236i	−0.100716	−	0.276714i	−0.979809	+	0.199935i	$0.935927\pi$
$954$	4.03086	+	22.8601i	0.130504	+	0.740124i
$955$		0			0
$956$	26.1327	+	9.51154i	0.845193	+	0.307625i
$957$	−3.17763	+	1.83460i	−0.102718	+	0.0593043i
$958$	−11.1465	−	6.43541i	−0.360126	−	0.207919i
$959$	43.7744	−	36.7311i	1.41355	−	1.18611i
$960$		0			0
$961$	−12.8010	+	22.1720i	−0.412935	+	0.715225i
$962$	10.4632	−	6.04094i	0.337348	−	0.194768i
$963$	−11.5073	+	31.6161i	−0.370819	+	1.01882i
$964$	1.12575	−	6.38443i	0.0362579	−	0.205629i
$965$		0			0
$966$	−18.4244	+	6.70594i	−0.592796	+	0.215760i
$967$	3.27990	−	3.90883i	0.105474	−	0.125700i	−0.710725	−	0.703470i	$-0.751633\pi$
$967$	3.27990	−	3.90883i	0.105474	−	0.125700i	0.816199	+	0.577771i	$0.196077\pi$
$968$		−	6.07290i		−	0.195190i
$969$	15.7689	−	3.86839i	0.506570	−	0.124271i
$970$		0			0
$971$	−2.03318	−	1.70604i	−0.0652479	−	0.0547495i	0.609580	−	0.792724i	$-0.291338\pi$
$971$	−2.03318	−	1.70604i	−0.0652479	−	0.0547495i	−0.674828	+	0.737975i	$0.735782\pi$
$972$	5.48216	+	15.0621i	0.175841	+	0.483118i
$973$	−0.970514	+	0.171128i	−0.0311132	+	0.00548610i
$974$	−2.67357	+	15.1626i	−0.0856668	+	0.485841i
$975$		0			0
$976$	2.61786	+	4.53427i	0.0837957	+	0.145138i
$977$	−28.3946	−	16.3936i	−0.908422	−	0.524478i	−0.0284992	−	0.999594i	$-0.509073\pi$
$977$	−28.3946	−	16.3936i	−0.908422	−	0.524478i	−0.879923	+	0.475116i	$0.842406\pi$
$978$	−12.2659	−	14.6179i	−0.392219	−	0.467428i
$979$	10.5975	−	8.89235i	0.338697	−	0.284201i
$980$		0			0
$981$	9.98617	+	17.2966i	0.318834	+	0.552236i
$982$	−1.13294	+	3.11273i	−0.0361536	+	0.0993311i
$983$	−34.0096	−	5.99682i	−1.08474	−	0.191269i	−0.397429	−	0.917633i	$-0.630098\pi$
$983$	−34.0096	−	5.99682i	−1.08474	−	0.191269i	−0.687310	+	0.726364i	$0.741209\pi$
$984$	−1.54738	−	8.77565i	−0.0493288	−	0.279757i
$985$		0			0
$986$	6.50877	+	5.46150i	0.207281	+	0.173930i
$987$			20.7325i			0.659924i
$988$	19.4349	−	8.56513i	0.618307	−	0.272493i
$989$	−38.4151			−1.22153
$990$		0			0
$991$	−9.49996	+	3.45770i	−0.301776	+	0.109838i	−0.488470	−	0.872581i	$-0.662445\pi$
$991$	−9.49996	+	3.45770i	−0.301776	+	0.109838i	0.186694	+	0.982418i	$0.440223\pi$
$992$	−7.40913	+	1.30643i	−0.235240	+	0.0414792i
$993$	4.54056	+	0.800624i	0.144090	+	0.0254070i
$994$	−61.0024	−	22.2031i	−1.93488	−	0.704238i
$995$		0			0
$996$	5.31048	−	9.19801i	0.168269	−	0.291450i
$997$	6.03242	+	7.18916i	0.191049	+	0.227683i	0.853063	−	0.521809i	$-0.174742\pi$
$997$	6.03242	+	7.18916i	0.191049	+	0.227683i	−0.662014	+	0.749492i	$0.730298\pi$
$998$	16.6122	+	19.7976i	0.525850	+	0.626683i
$999$	−5.56772	+	9.64358i	−0.176155	+	0.305109i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.h.149.6		48
5.2	odd	4		950.2.l.k.301.2	yes	24
5.3	odd	4		950.2.l.j.301.3	yes	24
5.4	even	2	inner	950.2.u.h.149.3		48
19.6	even	9	inner	950.2.u.h.899.3		48
95.44	even	18	inner	950.2.u.h.899.6		48
95.63	odd	36		950.2.l.j.101.3	✓	24
95.82	odd	36		950.2.l.k.101.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.101.3	✓	24	95.63	odd	36
950.2.l.j.301.3	yes	24	5.3	odd	4
950.2.l.k.101.2	yes	24	95.82	odd	36
950.2.l.k.301.2	yes	24	5.2	odd	4
950.2.u.h.149.3		48	5.4	even	2	inner
950.2.u.h.149.6		48	1.1	even	1	trivial
950.2.u.h.899.3		48	19.6	even	9	inner
950.2.u.h.899.6		48	95.44	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(-0.291155 - 0.799943i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.799943 - 0.291155i) q^{6} +(4.37330 - 2.52492i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.74300 - 1.46255i) q^{9} +O(q^{10})\)	\(q+(0.642788 - 0.766044i) q^{2} +(-0.291155 - 0.799943i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-0.799943 - 0.291155i) q^{6} +(4.37330 - 2.52492i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.74300 - 1.46255i) q^{9} +(1.10985 - 1.92232i) q^{11} +(-0.737231 + 0.425641i) q^{12} +(-1.66648 + 4.57862i) q^{13} +(0.876897 - 4.97313i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-2.81261 + 3.35193i) q^{17} -2.27532i q^{18} +(3.62288 - 2.42379i) q^{19} +(-3.29310 - 2.76324i) q^{21} +(-0.759185 - 2.08584i) q^{22} +(4.49168 - 0.792004i) q^{23} +(-0.147823 + 0.838348i) q^{24} +(2.43623 + 4.21968i) q^{26} +(-3.88913 - 2.24539i) q^{27} +(-3.24598 - 3.86841i) q^{28} +(1.48750 - 1.24816i) q^{29} +(3.76171 + 6.51548i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(-1.86089 - 0.328125i) q^{33} +(0.759821 + 4.30916i) q^{34} +(-1.74300 - 1.46255i) q^{36} -2.47962i q^{37} +(0.472007 - 4.33327i) q^{38} +4.14784 q^{39} +(-9.83650 + 3.58019i) q^{41} +(-4.23353 + 0.746486i) q^{42} +(-8.29461 - 1.46256i) q^{43} +(-2.08584 - 0.759185i) q^{44} +(2.28048 - 3.94991i) q^{46} +(-3.10005 - 3.69450i) q^{47} +(0.547193 + 0.652119i) q^{48} +(9.25048 - 16.0223i) q^{49} +(3.50026 + 1.27399i) q^{51} +(4.79844 + 0.846095i) q^{52} +(-10.0470 + 1.77156i) q^{53} +(-4.21995 + 1.53594i) q^{54} -5.04985 q^{56} +(-2.99371 - 2.19239i) q^{57} -1.94179i q^{58} +(3.98298 + 3.34212i) q^{59} +(-0.909174 - 5.15618i) q^{61} +(7.40913 + 1.30643i) q^{62} +(3.92982 - 10.7971i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-1.44751 + 1.21461i) q^{66} +(0.949064 + 1.13105i) q^{67} +(3.78941 + 2.18782i) q^{68} +(-1.94133 - 3.36249i) q^{69} +(2.23230 - 12.6600i) q^{71} +(-2.24075 + 0.395105i) q^{72} +(4.54881 + 12.4977i) q^{73} +(-1.89950 - 1.59387i) q^{74} +(-3.01608 - 3.14695i) q^{76} -11.2092i q^{77} +(2.66618 - 3.17743i) q^{78} +(-5.71688 + 2.08077i) q^{79} +(0.521473 - 2.95742i) q^{81} +(-3.58019 + 9.83650i) q^{82} +(-10.8049 + 6.23822i) q^{83} +(-2.14942 + 3.72290i) q^{84} +(-6.45206 + 5.41392i) q^{86} +(-1.43155 - 0.826507i) q^{87} +(-1.92232 + 1.10985i) q^{88} +(5.85651 + 2.13160i) q^{89} +(4.27265 + 24.2314i) q^{91} +(-1.55994 - 4.28591i) q^{92} +(4.11677 - 4.90617i) q^{93} -4.82282 q^{94} +0.851281 q^{96} +(1.26373 - 1.50605i) q^{97} +(-6.32770 - 17.3852i) q^{98} +(-0.877018 - 4.97382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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