LMFDB - Embedded newform 637.2.f.h.393.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$637 = 7^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	637.f (of order $3$ , degree $2$ , 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.100088711424.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 13x^{6} + 130x^{4} - 507x^{2} + 1521$ x^8 - 13x^6 + 130x^4 - 507*x^2 + 1521
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.4
Root			$-1.87694 - 1.08365i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.h.295.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.651388 + 1.12824i) q^{2} +(1.44073 + 2.49541i) q^{3} +(0.151388 - 0.262211i) q^{4} -2.88145 q^{5} +(-1.87694 + 3.25096i) q^{6} +3.00000 q^{8} +(-2.65139 + 4.59234i) q^{9} +(-1.87694 - 3.25096i) q^{10} +(2.95416 + 5.11676i) q^{11} +0.872434 q^{12} +(-3.31767 + 1.41176i) q^{13} +(-4.15139 - 7.19041i) q^{15} +(1.65139 + 2.86029i) q^{16} +(-0.436217 + 0.755550i) q^{17} -6.90833 q^{18} +(1.44073 - 2.49541i) q^{19} +(-0.436217 + 0.755550i) q^{20} +(-3.84861 + 6.66599i) q^{22} +(-3.30278 - 5.72058i) q^{23} +(4.32218 + 7.48624i) q^{24} +3.30278 q^{25} +(-3.75389 - 2.82352i) q^{26} -6.63534 q^{27} +(-0.651388 - 1.12824i) q^{29} +(5.40833 - 9.36750i) q^{30} -0.872434 q^{31} +(0.848612 - 1.46984i) q^{32} +(-8.51229 + 14.7437i) q^{33} -1.13659 q^{34} +(0.802776 + 1.39045i) q^{36} +(-0.697224 - 1.20763i) q^{37} +3.75389 q^{38} +(-8.30278 - 6.24500i) q^{39} -8.64436 q^{40} +(3.75389 + 6.50192i) q^{41} +(-2.75694 + 4.77516i) q^{43} +1.78890 q^{44} +(7.63985 - 13.2326i) q^{45} +(4.30278 - 7.45263i) q^{46} +12.3982 q^{47} +(-4.75840 + 8.24179i) q^{48} +(2.15139 + 3.72631i) q^{50} -2.51388 q^{51} +(-0.132076 + 1.08365i) q^{52} +9.60555 q^{53} +(-4.32218 - 7.48624i) q^{54} +(-8.51229 - 14.7437i) q^{55} +8.30278 q^{57} +(0.848612 - 1.46984i) q^{58} +(3.31767 - 5.74637i) q^{59} -2.51388 q^{60} +(2.88145 - 4.99082i) q^{61} +(-0.568293 - 0.984312i) q^{62} +8.81665 q^{64} +(9.55971 - 4.06792i) q^{65} -22.1792 q^{66} +(-0.500000 - 0.866025i) q^{67} +(0.132076 + 0.228762i) q^{68} +(9.51680 - 16.4836i) q^{69} +(-2.00000 + 3.46410i) q^{71} +(-7.95416 + 13.7770i) q^{72} +5.76291 q^{73} +(0.908327 - 1.57327i) q^{74} +(4.75840 + 8.24179i) q^{75} +(-0.436217 - 0.755550i) q^{76} +(1.63751 - 13.4354i) q^{78} +0.605551 q^{79} +(-4.75840 - 8.24179i) q^{80} +(-1.60555 - 2.78090i) q^{81} +(-4.89047 + 8.47055i) q^{82} +6.63534 q^{83} +(1.25694 - 2.17708i) q^{85} -7.18335 q^{86} +(1.87694 - 3.25096i) q^{87} +(8.86249 + 15.3503i) q^{88} +(4.32218 + 7.48624i) q^{89} +19.9060 q^{90} -2.00000 q^{92} +(-1.25694 - 2.17708i) q^{93} +(8.07607 + 13.9882i) q^{94} +(-4.15139 + 7.19041i) q^{95} +4.89047 q^{96} +(-3.88596 + 6.73069i) q^{97} -31.3305 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} - 14 q^{9} + 2 q^{11} - 26 q^{15} + 6 q^{16} - 12 q^{18} - 38 q^{22} - 12 q^{23} + 12 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} - 52 q^{39} + 14 q^{43} + 72 q^{44}+ \cdots - 92 q^{99}+O(q^{100})$ 8 * q - 2 * q^2 - 6 * q^4 + 24 * q^8 - 14 * q^9 + 2 * q^11 - 26 * q^15 + 6 * q^16 - 12 * q^18 - 38 * q^22 - 12 * q^23 + 12 * q^25 + 2 * q^29 + 14 * q^32 - 8 * q^36 - 20 * q^37 - 52 * q^39 + 14 * q^43 + 72 * q^44 + 20 * q^46 + 10 * q^50 + 52 * q^51 + 48 * q^53 + 52 * q^57 + 14 * q^58 + 52 * q^60 - 16 * q^64 + 26 * q^65 - 4 * q^67 - 16 * q^71 - 42 * q^72 - 36 * q^74 + 78 * q^78 - 24 * q^79 + 16 * q^81 - 26 * q^85 - 144 * q^86 + 6 * q^88 - 16 * q^92 + 26 * q^93 - 26 * q^95 - 92 * q^99

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.651388	+	1.12824i	0.460601	+	0.797784i	0.998991	−	0.0449118i	$-0.0143007\pi$
$2$	0.651388	+	1.12824i	0.460601	+	0.797784i	−0.538390	+	0.842696i	$0.680967\pi$
$3$	1.44073	+	2.49541i	0.831804	+	1.44073i	0.896606	+	0.442829i	$0.146025\pi$
$3$	1.44073	+	2.49541i	0.831804	+	1.44073i	−0.0648022	+	0.997898i	$0.520642\pi$
$4$	0.151388	−	0.262211i	0.0756939	−	0.131106i
$5$	−2.88145			−1.28863			−0.644313	−	0.764762i	$-0.722856\pi$
$5$	−2.88145			−1.28863			−0.644313	+	0.764762i	$0.722856\pi$
$6$	−1.87694	+	3.25096i	−0.766259	+	1.32720i
$7$		0			0
$7$		0			0
$8$	3.00000			1.06066
$9$	−2.65139	+	4.59234i	−0.883796	+	1.53078i
$10$	−1.87694	−	3.25096i	−0.593542	−	1.02804i
$11$	2.95416	+	5.11676i	0.890714	+	1.54276i	0.839021	+	0.544098i	$0.183128\pi$
$11$	2.95416	+	5.11676i	0.890714	+	1.54276i	0.0516924	+	0.998663i	$0.483538\pi$
$12$	0.872434			0.251850
$13$	−3.31767	+	1.41176i	−0.920156	+	0.391551i
$13$	−3.31767	+	1.41176i	−0.920156	+	0.391551i
$14$		0			0
$15$	−4.15139	−	7.19041i	−1.07188	−	1.85656i
$16$	1.65139	+	2.86029i	0.412847	+	0.715072i
$17$	−0.436217	+	0.755550i	−0.105798	+	0.183248i	−0.914064	−	0.405570i	$-0.867073\pi$
$17$	−0.436217	+	0.755550i	−0.105798	+	0.183248i	0.808266	+	0.588818i	$0.200406\pi$
$18$	−6.90833			−1.62831
$19$	1.44073	−	2.49541i	0.330525	−	0.572487i	−0.652090	−	0.758142i	$-0.726107\pi$
$19$	1.44073	−	2.49541i	0.330525	−	0.572487i	0.982615	+	0.185655i	$0.0594407\pi$
$20$	−0.436217	+	0.755550i	−0.0975411	+	0.168946i
$21$		0			0
$22$	−3.84861	+	6.66599i	−0.820527	+	1.42119i
$23$	−3.30278	−	5.72058i	−0.688676	−	1.19282i	−0.972266	−	0.233877i	$-0.924859\pi$
$23$	−3.30278	−	5.72058i	−0.688676	−	1.19282i	0.283590	−	0.958946i	$-0.408475\pi$
$24$	4.32218	+	7.48624i	0.882261	+	1.52812i
$25$	3.30278			0.660555
$26$	−3.75389	−	2.82352i	−0.736198	−	0.553737i
$27$	−6.63534			−1.27697
$28$		0			0
$29$	−0.651388	−	1.12824i	−0.120960	−	0.209508i	0.799187	−	0.601083i	$-0.205264\pi$
$29$	−0.651388	−	1.12824i	−0.120960	−	0.209508i	−0.920146	+	0.391575i	$0.871931\pi$
$30$	5.40833	−	9.36750i	0.987421	−	1.71026i
$31$	−0.872434			−0.156694			−0.0783469	−	0.996926i	$-0.524964\pi$
$31$	−0.872434			−0.156694			−0.0783469	+	0.996926i	$0.524964\pi$
$32$	0.848612	−	1.46984i	0.150015	−	0.259833i
$33$	−8.51229	+	14.7437i	−1.48180	+	2.56655i
$34$	−1.13659			−0.194923
$35$		0			0
$36$	0.802776	+	1.39045i	0.133796	+	0.231741i
$37$	−0.697224	−	1.20763i	−0.114623	−	0.198533i	0.803006	−	0.595971i	$-0.203233\pi$
$37$	−0.697224	−	1.20763i	−0.114623	−	0.198533i	−0.917629	+	0.397438i	$0.869899\pi$
$38$	3.75389			0.608961
$39$	−8.30278	−	6.24500i	−1.32951	−	1.00000i
$40$	−8.64436			−1.36679
$41$	3.75389	+	6.50192i	0.586259	+	1.01543i	0.994717	+	0.102653i	$0.0327331\pi$
$41$	3.75389	+	6.50192i	0.586259	+	1.01543i	−0.408458	+	0.912777i	$0.633934\pi$
$42$		0			0
$43$	−2.75694	+	4.77516i	−0.420429	+	0.728205i	−0.995981	−	0.0895602i	$-0.971454\pi$
$43$	−2.75694	+	4.77516i	−0.420429	+	0.728205i	0.575552	+	0.817765i	$0.304787\pi$
$44$	1.78890			0.269686
$45$	7.63985	−	13.2326i	1.13888	−	1.97260i
$46$	4.30278	−	7.45263i	0.634410	−	1.09883i
$47$	12.3982			1.80847			0.904235	−	0.427035i	$-0.140442\pi$
$47$	12.3982			1.80847			0.904235	+	0.427035i	$0.140442\pi$
$48$	−4.75840	+	8.24179i	−0.686816	+	1.18960i
$49$		0			0
$50$	2.15139	+	3.72631i	0.304252	+	0.526980i
$51$	−2.51388			−0.352013
$52$	−0.132076	+	1.08365i	−0.0183156	+	0.150276i
$53$	9.60555			1.31942			0.659712	−	0.751519i	$-0.270678\pi$
$53$	9.60555			1.31942			0.659712	+	0.751519i	$0.270678\pi$
$54$	−4.32218	−	7.48624i	−0.588174	−	1.01875i
$55$	−8.51229	−	14.7437i	−1.14780	−	1.98804i
$56$		0			0
$57$	8.30278			1.09973
$58$	0.848612	−	1.46984i	0.111428	−	0.192999i
$59$	3.31767	−	5.74637i	0.431924	−	0.748114i	−0.565115	−	0.825012i	$-0.691168\pi$
$59$	3.31767	−	5.74637i	0.431924	−	0.748114i	0.997039	+	0.0768979i	$0.0245016\pi$
$60$	−2.51388			−0.324540
$61$	2.88145	−	4.99082i	0.368932	−	0.639010i	−0.620467	−	0.784233i	$-0.713057\pi$
$61$	2.88145	−	4.99082i	0.368932	−	0.639010i	0.989399	+	0.145223i	$0.0463901\pi$
$62$	−0.568293	−	0.984312i	−0.0721733	−	0.125008i
$63$		0			0
$64$	8.81665			1.10208
$65$	9.55971	−	4.06792i	1.18574	−	0.504563i
$66$	−22.1792			−2.73007
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i	0.833866	−	0.551967i	$-0.186123\pi$
$67$	−0.500000	−	0.866025i	−0.0610847	−	0.105802i	−0.894951	+	0.446165i	$0.852789\pi$
$68$	0.132076	+	0.228762i	0.0160166	+	0.0277415i
$69$	9.51680	−	16.4836i	1.14569	−	1.98439i
$70$		0			0
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	−0.959955	−	0.280155i	$-0.909614\pi$
$71$	−2.00000	+	3.46410i	−0.237356	+	0.411113i	0.722599	+	0.691268i	$0.242948\pi$
$72$	−7.95416	+	13.7770i	−0.937407	+	1.62364i
$73$	5.76291			0.674497			0.337249	−	0.941416i	$-0.390504\pi$
$73$	5.76291			0.674497			0.337249	+	0.941416i	$0.390504\pi$
$74$	0.908327	−	1.57327i	0.105591	−	0.182889i
$75$	4.75840	+	8.24179i	0.549452	+	0.951680i
$76$	−0.436217	−	0.755550i	−0.0500375	−	0.0866675i
$77$		0			0
$78$	1.63751	−	13.4354i	0.185411	−	1.52126i
$79$	0.605551			0.0681298			0.0340649	−	0.999420i	$-0.489155\pi$
$79$	0.605551			0.0681298			0.0340649	+	0.999420i	$0.489155\pi$
$80$	−4.75840	−	8.24179i	−0.532005	−	0.921460i
$81$	−1.60555	−	2.78090i	−0.178395	−	0.308988i
$82$	−4.89047	+	8.47055i	−0.540062	+	0.935416i
$83$	6.63534			0.728323			0.364162	−	0.931336i	$-0.381356\pi$
$83$	6.63534			0.728323			0.364162	+	0.931336i	$0.381356\pi$
$84$		0			0
$85$	1.25694	−	2.17708i	0.136334	−	0.236138i
$86$	−7.18335			−0.774600
$87$	1.87694	−	3.25096i	0.201230	−	0.348540i
$88$	8.86249	+	15.3503i	0.944745	+	1.63635i
$89$	4.32218	+	7.48624i	0.458150	+	0.793539i	0.998863	−	0.0476677i	$-0.0151788\pi$
$89$	4.32218	+	7.48624i	0.458150	+	0.793539i	−0.540713	+	0.841207i	$0.681846\pi$
$90$	19.9060			2.09828
$91$		0			0
$92$	−2.00000			−0.208514
$93$	−1.25694	−	2.17708i	−0.130339	−	0.225753i
$94$	8.07607	+	13.9882i	0.832983	+	1.44277i
$95$	−4.15139	+	7.19041i	−0.425923	+	0.737721i
$96$	4.89047			0.499132
$97$	−3.88596	+	6.73069i	−0.394560	+	0.683398i	−0.993045	−	0.117736i	$-0.962436\pi$
$97$	−3.88596	+	6.73069i	−0.394560	+	0.683398i	0.598485	+	0.801134i	$0.295770\pi$
$98$		0			0
$99$	−31.3305			−3.14884
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−4.32218	−	7.48624i	−0.430073	−	0.744908i	0.566806	−	0.823851i	$-0.308179\pi$
$101$	−4.32218	−	7.48624i	−0.430073	−	0.744908i	−0.996879	+	0.0789429i	$0.974846\pi$
$102$	−1.63751	−	2.83625i	−0.162138	−	0.280831i
$103$	−4.89047			−0.481873			−0.240936	−	0.970541i	$-0.577455\pi$
$103$	−4.89047			−0.481873			−0.240936	+	0.970541i	$0.577455\pi$
$104$	−9.95301	+	4.23527i	−0.975973	+	0.415303i
$105$		0			0
$106$	6.25694	+	10.8373i	0.607728	+	1.05262i
$107$	−4.65139	−	8.05644i	−0.449667	−	0.778845i	0.548698	−	0.836021i	$-0.315124\pi$
$107$	−4.65139	−	8.05644i	−0.449667	−	0.778845i	−0.998364	+	0.0571755i	$0.981791\pi$
$108$	−1.00451	+	1.73986i	−0.0966590	+	0.167418i
$109$	−6.21110			−0.594916			−0.297458	−	0.954735i	$-0.596139\pi$
$109$	−6.21110			−0.594916			−0.297458	+	0.954735i	$0.596139\pi$
$110$	11.0896	−	19.2077i	1.05735	−	1.83139i
$111$	2.00902	−	3.47972i	0.190688	−	0.330281i
$112$		0			0
$113$	7.40833	−	12.8316i	0.696917	−	1.20710i	−0.272613	−	0.962124i	$-0.587888\pi$
$113$	7.40833	−	12.8316i	0.696917	−	1.20710i	0.969530	−	0.244972i	$-0.0787786\pi$
$114$	5.40833	+	9.36750i	0.506536	+	0.877346i
$115$	9.51680	+	16.4836i	0.887446	+	1.53710i
$116$	−0.394449			−0.0366236
$117$	2.31316	−	18.9790i	0.213852	−	1.75461i
$118$	8.64436			0.795778
$119$		0			0
$120$	−12.4542	−	21.5712i	−1.13690	−	1.96918i
$121$	−11.9542	+	20.7052i	−1.08674	+	1.88229i
$122$	7.50778			0.679722
$123$	−10.8167	+	18.7350i	−0.975305	+	1.68928i
$124$	−0.132076	+	0.228762i	−0.0118608	+	0.0205434i
$125$	4.89047			0.437417
$126$		0			0
$127$	1.45416	+	2.51868i	0.129036	+	0.223497i	0.923303	−	0.384071i	$-0.125478\pi$
$127$	1.45416	+	2.51868i	0.129036	+	0.223497i	−0.794267	+	0.607569i	$0.792145\pi$
$128$	4.04584	+	7.00759i	0.357605	+	0.619390i
$129$	−15.8880			−1.39886
$130$	10.8167	+	8.13583i	0.948683	+	0.713560i
$131$	−17.0246			−1.48744			−0.743722	−	0.668489i	$-0.766941\pi$
$131$	−17.0246			−1.48744			−0.743722	+	0.668489i	$0.766941\pi$
$132$	2.57731	+	4.46404i	0.224326	+	0.388544i
$133$		0			0
$134$	0.651388	−	1.12824i	0.0562713	−	0.0974648i
$135$	19.1194			1.64554
$136$	−1.30865	+	2.26665i	−0.112216	+	0.194364i
$137$	−1.34861	+	2.33586i	−0.115220	+	0.199566i	−0.917868	−	0.396887i	$-0.870091\pi$
$137$	−1.34861	+	2.33586i	−0.115220	+	0.199566i	0.802648	+	0.596453i	$0.203424\pi$
$138$	24.7965			2.11082
$139$	8.51229	−	14.7437i	0.722003	−	1.25055i	−0.238193	−	0.971218i	$-0.576555\pi$
$139$	8.51229	−	14.7437i	0.722003	−	1.25055i	0.960196	−	0.279327i	$-0.0901115\pi$
$140$		0			0
$141$	17.8625	+	30.9387i	1.50429	+	2.60551i
$142$	−5.21110			−0.437306
$143$	−17.0246	−	12.8052i	−1.42367	−	1.07082i
$144$	−17.5139			−1.45949
$145$	1.87694	+	3.25096i	0.155872	+	0.269978i
$146$	3.75389	+	6.50192i	0.310674	+	0.538103i
$147$		0			0
$148$	−0.422205			−0.0347050
$149$	−0.256939	+	0.445032i	−0.0210493	+	0.0364584i	−0.876358	−	0.481660i	$-0.840034\pi$
$149$	−0.256939	+	0.445032i	−0.0210493	+	0.0364584i	0.855309	+	0.518118i	$0.173367\pi$
$150$	−6.19912	+	10.7372i	−0.506156	+	0.876689i
$151$	−6.21110			−0.505452			−0.252726	−	0.967538i	$-0.581327\pi$
$151$	−6.21110			−0.505452			−0.252726	+	0.967538i	$0.581327\pi$
$152$	4.32218	−	7.48624i	0.350575	−	0.607214i
$153$	−2.31316	−	4.00651i	−0.187008	−	0.323907i
$154$		0			0
$155$	2.51388			0.201920
$156$	−2.89445	+	1.23167i	−0.231741	+	0.0986122i
$157$	−9.51680			−0.759523			−0.379761	−	0.925084i	$-0.623994\pi$
$157$	−9.51680			−0.759523			−0.379761	+	0.925084i	$0.623994\pi$
$158$	0.394449	+	0.683205i	0.0313807	+	0.0543529i
$159$	13.8390	+	23.9698i	1.09750	+	1.90093i
$160$	−2.44524	+	4.23527i	−0.193313	+	0.334828i
$161$		0			0
$162$	2.09167	−	3.62288i	0.164337	−	0.284641i
$163$	8.60555	−	14.9053i	0.674039	−	1.16747i	−0.302710	−	0.953083i	$-0.597891\pi$
$163$	8.60555	−	14.9053i	0.674039	−	1.16747i	0.976749	−	0.214387i	$-0.0687753\pi$
$164$	2.27317			0.177505
$165$	24.5278	−	42.4833i	1.90948	−	3.30732i
$166$	4.32218	+	7.48624i	0.335466	+	0.581045i
$167$	2.44524	+	4.23527i	0.189218	+	0.327735i	0.944990	−	0.327100i	$-0.106071\pi$
$167$	2.44524	+	4.23527i	0.189218	+	0.327735i	−0.755772	+	0.654835i	$0.772738\pi$
$168$		0			0
$169$	9.01388	−	9.36750i	0.693375	−	0.720577i
$170$	3.27502			0.251183
$171$	7.63985	+	13.2326i	0.584234	+	1.01192i
$172$	0.834734	+	1.44580i	0.0636479	+	0.110241i
$173$	11.9620	−	20.7188i	0.909456	−	1.57522i	0.0946356	−	0.995512i	$-0.469831\pi$
$173$	11.9620	−	20.7188i	0.909456	−	1.57522i	0.814821	−	0.579713i	$-0.196835\pi$
$174$	4.89047			0.370746
$175$		0			0
$176$	−9.75694	+	16.8995i	−0.735457	+	1.27385i
$177$	19.1194			1.43710
$178$	−5.63083	+	9.75289i	−0.422049	+	0.731010i
$179$	−7.19722	−	12.4660i	−0.537946	−	0.931749i	−0.999014	−	0.0443850i	$-0.985867\pi$
$179$	−7.19722	−	12.4660i	−0.537946	−	0.931749i	0.461069	−	0.887364i	$-0.347466\pi$
$180$	−2.31316	−	4.00651i	−0.172413	−	0.298628i
$181$	−9.25264			−0.687744			−0.343872	−	0.939017i	$-0.611739\pi$
$181$	−9.25264			−0.687744			−0.343872	+	0.939017i	$0.611739\pi$
$182$		0			0
$183$	16.6056			1.22752
$184$	−9.90833	−	17.1617i	−0.730452	−	1.26518i
$185$	2.00902	+	3.47972i	0.147706	+	0.255834i
$186$	1.63751	−	2.83625i	0.120068	−	0.207964i
$187$	−5.15463			−0.376944
$188$	1.87694	−	3.25096i	0.136890	−	0.237101i
$189$		0			0
$190$	−10.8167			−0.784723
$191$	−9.65139	+	16.7167i	−0.698350	+	1.20958i	0.270688	+	0.962667i	$0.412749\pi$
$191$	−9.65139	+	16.7167i	−0.698350	+	1.20958i	−0.969038	+	0.246911i	$0.920585\pi$
$192$	12.7024	+	22.0012i	0.916716	+	1.58780i
$193$	0.908327	+	1.57327i	0.0653828	+	0.113246i	0.896864	−	0.442307i	$-0.145840\pi$
$193$	0.908327	+	1.57327i	0.0653828	+	0.113246i	−0.831481	+	0.555553i	$0.812506\pi$
$194$	−10.1251			−0.726938
$195$	23.9241	+	17.9947i	1.71324	+	1.28863i
$196$		0			0
$197$	5.95416	+	10.3129i	0.424217	+	0.734765i	0.996347	−	0.0853980i	$-0.0272162\pi$
$197$	5.95416	+	10.3129i	0.424217	+	0.734765i	−0.572130	+	0.820163i	$0.693883\pi$
$198$	−20.4083	−	35.3483i	−1.45036	−	2.51209i
$199$	0.436217	−	0.755550i	0.0309226	−	0.0535595i	−0.850150	−	0.526541i	$-0.823489\pi$
$199$	0.436217	−	0.755550i	0.0309226	−	0.0535595i	0.881073	+	0.472981i	$0.156822\pi$
$200$	9.90833			0.700625
$201$	1.44073	−	2.49541i	0.101621	−	0.176013i
$202$	5.63083	−	9.75289i	0.396184	−	0.686211i
$203$		0			0
$204$	−0.380571	+	0.659168i	−0.0266453	+	0.0461510i
$205$	−10.8167	−	18.7350i	−0.755468	−	1.30851i
$206$	−3.18559	−	5.51761i	−0.221951	−	0.384430i
$207$	35.0278			2.43460
$208$	−9.51680	−	7.15813i	−0.659871	−	0.496327i
$209$	17.0246			1.17761
$210$		0			0
$211$	−7.50000	−	12.9904i	−0.516321	−	0.894295i	−0.999820	−	0.0189499i	$-0.993968\pi$
$211$	−7.50000	−	12.9904i	−0.516321	−	0.894295i	0.483499	−	0.875345i	$-0.339366\pi$
$212$	1.45416	−	2.51868i	0.0998724	−	0.172984i
$213$	−11.5258			−0.789736
$214$	6.05971	−	10.4957i	0.414234	−	0.717474i
$215$	7.94399	−	13.7594i	0.541776	−	0.938383i
$216$	−19.9060			−1.35443
$217$		0			0
$218$	−4.04584	−	7.00759i	−0.274019	−	0.474614i
$219$	8.30278	+	14.3808i	0.561050	+	0.971766i
$220$	−5.15463			−0.347525
$221$	0.380571	−	3.12250i	0.0255999	−	0.210042i
$222$	5.23460			0.351324
$223$	−6.76742	−	11.7215i	−0.453180	−	0.784930i	0.545402	−	0.838175i	$-0.316377\pi$
$223$	−6.76742	−	11.7215i	−0.453180	−	0.784930i	−0.998582	+	0.0532444i	$0.983044\pi$
$224$		0			0
$225$	−8.75694	+	15.1675i	−0.583796	+	1.01116i
$226$	19.3028			1.28400
$227$	13.7069	−	23.7410i	0.909759	−	1.57575i	0.0953602	−	0.995443i	$-0.469600\pi$
$227$	13.7069	−	23.7410i	0.909759	−	1.57575i	0.814399	−	0.580306i	$-0.197067\pi$
$228$	1.25694	−	2.17708i	0.0832428	−	0.144181i
$229$	−20.7785			−1.37308			−0.686540	−	0.727092i	$-0.740871\pi$
$229$	−20.7785			−1.37308			−0.686540	+	0.727092i	$0.740871\pi$
$230$	−12.3982	+	21.4744i	−0.817516	+	1.41598i
$231$		0			0
$232$	−1.95416	−	3.38471i	−0.128297	−	0.222217i
$233$	−23.9083			−1.56629			−0.783143	−	0.621841i	$-0.786385\pi$
$233$	−23.9083			−1.56629			−0.783143	+	0.621841i	$0.786385\pi$
$234$	22.9196	−	9.75289i	1.49830	−	0.637566i
$235$	−35.7250			−2.33044
$236$	−1.00451	−	1.73986i	−0.0653880	−	0.113255i
$237$	0.872434	+	1.51110i	0.0566707	+	0.0981565i
$238$		0			0
$239$	11.6056			0.750701			0.375350	−	0.926883i	$-0.377522\pi$
$239$	11.6056			0.750701			0.375350	+	0.926883i	$0.377522\pi$
$240$	13.7111	−	23.7483i	0.885048	−	1.53295i
$241$	−1.00451	+	1.73986i	−0.0647062	+	0.112074i	−0.896564	−	0.442915i	$-0.853944\pi$
$241$	−1.00451	+	1.73986i	−0.0647062	+	0.112074i	0.831857	+	0.554989i	$0.187278\pi$
$242$	−31.1472			−2.00222
$243$	−5.32669	+	9.22610i	−0.341707	+	0.591854i
$244$	−0.872434	−	1.51110i	−0.0558519	−	0.0967383i
$245$		0			0
$246$	−28.1833			−1.79690
$247$	−1.25694	+	10.3129i	−0.0799771	+	0.656195i
$248$	−2.61730			−0.166199
$249$	9.55971	+	16.5579i	0.605822	+	1.04932i
$250$	3.18559	+	5.51761i	0.201475	+	0.348964i
$251$	−11.2617	+	19.5058i	−0.710830	+	1.23119i	0.253716	+	0.967279i	$0.418347\pi$
$251$	−11.2617	+	19.5058i	−0.710830	+	1.23119i	−0.964546	+	0.263915i	$0.914986\pi$
$252$		0			0
$253$	19.5139	−	33.7990i	1.22683	−	2.12493i
$254$	−1.89445	+	3.28128i	−0.118868	+	0.205886i
$255$	7.24362			0.453613
$256$	3.54584	−	6.14157i	0.221615	−	0.383848i
$257$	−11.3937	−	19.7345i	−0.710722	−	1.23101i	−0.964587	−	0.263767i	$-0.915035\pi$
$257$	−11.3937	−	19.7345i	−0.710722	−	1.23101i	0.253865	−	0.967240i	$-0.418298\pi$
$258$	−10.3492	−	17.9254i	−0.644316	−	1.11599i
$259$		0			0
$260$	0.380571	−	3.12250i	0.0236020	−	0.193649i
$261$	6.90833			0.427615
$262$	−11.0896	−	19.2077i	−0.685118	−	1.18666i
$263$	6.71110	+	11.6240i	0.413824	+	0.716765i	0.995304	−	0.0967960i	$-0.0308594\pi$
$263$	6.71110	+	11.6240i	0.413824	+	0.716765i	−0.581480	+	0.813561i	$0.697526\pi$
$264$	−25.5369	+	44.2311i	−1.57168	+	2.72224i
$265$	−27.6780			−1.70024
$266$		0			0
$267$	−12.4542	+	21.5712i	−0.762182	+	1.32014i
$268$	−0.302776			−0.0184950
$269$	4.75840	−	8.24179i	0.290125	−	0.502511i	−0.683714	−	0.729750i	$-0.739637\pi$
$269$	4.75840	−	8.24179i	0.290125	−	0.502511i	0.973839	+	0.227239i	$0.0729699\pi$
$270$	12.4542	+	21.5712i	0.757936	+	1.31278i
$271$	14.8435	+	25.7097i	0.901678	+	1.56175i	0.825316	+	0.564671i	$0.190997\pi$
$271$	14.8435	+	25.7097i	0.901678	+	1.56175i	0.0763615	+	0.997080i	$0.475670\pi$
$272$	−2.88145			−0.174714
$273$		0			0
$274$	−3.51388			−0.212281
$275$	9.75694	+	16.8995i	0.588366	+	1.01908i
$276$	−2.88145	−	4.99082i	−0.173443	−	0.300412i
$277$	−7.10555	+	12.3072i	−0.426931	+	0.739467i	−0.996599	−	0.0824088i	$-0.973739\pi$
$277$	−7.10555	+	12.3072i	−0.426931	+	0.739467i	0.569667	+	0.821875i	$0.307072\pi$
$278$	22.1792			1.33022
$279$	2.31316	−	4.00651i	0.138485	−	0.239864i
$280$		0			0
$281$	2.18335			0.130248			0.0651238	−	0.997877i	$-0.479256\pi$
$281$	2.18335			0.130248			0.0651238	+	0.997877i	$0.479256\pi$
$282$	−23.2708	+	40.3062i	−1.38576	+	2.40020i
$283$	2.00902	+	3.47972i	0.119424	+	0.206848i	0.919539	−	0.392998i	$-0.128562\pi$
$283$	2.00902	+	3.47972i	0.119424	+	0.206848i	−0.800116	+	0.599846i	$0.795229\pi$
$284$	0.605551	+	1.04885i	0.0359329	+	0.0622375i
$285$	−23.9241			−1.41714
$286$	3.35766	−	27.5489i	0.198543	−	1.62900i
$287$		0			0
$288$	4.50000	+	7.79423i	0.265165	+	0.459279i
$289$	8.11943	+	14.0633i	0.477613	+	0.827251i
$290$	−2.44524	+	4.23527i	−0.143589	+	0.248704i
$291$	−22.3944			−1.31279
$292$	0.872434	−	1.51110i	0.0510553	−	0.0884304i
$293$	1.74487	−	3.02220i	0.101936	−	0.176559i	−0.810546	−	0.585675i	$-0.800830\pi$
$293$	1.74487	−	3.02220i	0.101936	−	0.176559i	0.912482	+	0.409116i	$0.134163\pi$
$294$		0			0
$295$	−9.55971	+	16.5579i	−0.556588	+	0.964039i
$296$	−2.09167	−	3.62288i	−0.121576	−	0.210576i
$297$	−19.6019	−	33.9515i	−1.13742	−	1.97006i
$298$	−0.669468			−0.0387812
$299$	19.0336	+	14.3163i	1.10074	+	0.827931i
$300$	2.88145			0.166361
$301$		0			0
$302$	−4.04584	−	7.00759i	−0.232812	−	0.403242i
$303$	12.4542	−	21.5712i	0.715473	−	1.23924i
$304$	9.51680			0.545826
$305$	−8.30278	+	14.3808i	−0.475416	+	0.823444i
$306$	3.01353	−	5.21959i	0.172272	−	0.298384i
$307$	−15.2797			−0.872059			−0.436029	−	0.899932i	$-0.643616\pi$
$307$	−15.2797			−0.872059			−0.436029	+	0.899932i	$0.643616\pi$
$308$		0			0
$309$	−7.04584	−	12.2037i	−0.400824	−	0.694247i
$310$	1.63751	+	2.83625i	0.0930043	+	0.161088i
$311$	17.0246			0.965375			0.482687	−	0.875793i	$-0.339661\pi$
$311$	17.0246			0.965375			0.482687	+	0.875793i	$0.339661\pi$
$312$	−24.9083	−	18.7350i	−1.41016	−	1.06066i
$313$	−13.2707			−0.750103			−0.375052	−	0.927004i	$-0.622375\pi$
$313$	−13.2707			−0.750103			−0.375052	+	0.927004i	$0.622375\pi$
$314$	−6.19912	−	10.7372i	−0.349837	−	0.605935i
$315$		0			0
$316$	0.0916731	−	0.158782i	0.00515701	−	0.00893221i
$317$	8.21110			0.461181			0.230591	−	0.973051i	$-0.425934\pi$
$317$	8.21110			0.461181			0.230591	+	0.973051i	$0.425934\pi$
$318$	−18.0291	+	31.2273i	−1.01102	+	1.75114i
$319$	3.84861	−	6.66599i	0.215481	−	0.373224i
$320$	−25.4048			−1.42017
$321$	13.4028	−	23.2143i	0.748069	−	1.29569i
$322$		0			0
$323$	1.25694	+	2.17708i	0.0699380	+	0.121136i
$324$	−0.972244			−0.0540135
$325$	−10.9575	+	4.66272i	−0.607814	+	0.258641i
$326$	22.4222			1.24185
$327$	−8.94850	−	15.4993i	−0.494853	−	0.857111i
$328$	11.2617	+	19.5058i	0.621821	+	1.07703i
$329$		0			0
$330$	63.9083			3.51804
$331$	−0.348612	+	0.603814i	−0.0191615	+	0.0331886i	−0.875447	−	0.483314i	$-0.839433\pi$
$331$	−0.348612	+	0.603814i	−0.0191615	+	0.0331886i	0.856286	+	0.516503i	$0.172766\pi$
$332$	1.00451	−	1.73986i	0.0551296	−	0.0954873i
$333$	7.39445			0.405213
$334$	−3.18559	+	5.51761i	−0.174308	+	0.301910i
$335$	1.44073	+	2.49541i	0.0787153	+	0.136339i
$336$		0			0
$337$	−7.11943			−0.387820			−0.193910	−	0.981019i	$-0.562117\pi$
$337$	−7.11943			−0.387820			−0.193910	+	0.981019i	$0.562117\pi$
$338$	16.4403	+	4.06792i	0.894234	+	0.221265i
$339$	42.6935			2.31879
$340$	−0.380571	−	0.659168i	−0.0206393	−	0.0357484i
$341$	−2.57731	−	4.46404i	−0.139569	−	0.241741i
$342$	−9.95301	+	17.2391i	−0.538197	+	0.932185i
$343$		0			0
$344$	−8.27082	+	14.3255i	−0.445933	+	0.772378i
$345$	−27.4222	+	47.4967i	−1.47636	+	2.55713i
$346$	31.1677			1.67559
$347$	−0.394449	+	0.683205i	−0.0211751	+	0.0366764i	−0.876419	−	0.481550i	$-0.840074\pi$
$347$	−0.394449	+	0.683205i	−0.0211751	+	0.0366764i	0.855244	+	0.518226i	$0.173407\pi$
$348$	−0.568293	−	0.984312i	−0.0304637	−	0.0527647i
$349$	11.9620	+	20.7188i	0.640313	+	1.10905i	0.985363	+	0.170470i	$0.0545286\pi$
$349$	11.9620	+	20.7188i	0.640313	+	1.10905i	−0.345050	+	0.938584i	$0.612138\pi$
$350$		0			0
$351$	22.0139	−	9.36750i	1.17501	−	0.500000i
$352$	10.0278			0.534481
$353$	3.18559	+	5.51761i	0.169552	+	0.293673i	0.938262	−	0.345924i	$-0.112435\pi$
$353$	3.18559	+	5.51761i	0.169552	+	0.293673i	−0.768710	+	0.639597i	$0.779101\pi$
$354$	12.4542	+	21.5712i	0.661931	+	1.14650i
$355$	5.76291	−	9.98165i	0.305863	−	0.529771i
$356$	2.61730			0.138717
$357$		0			0
$358$	9.37637	−	16.2403i	0.495556	−	0.858329i
$359$	−22.9083			−1.20906			−0.604528	−	0.796584i	$-0.706638\pi$
$359$	−22.9083			−1.20906			−0.604528	+	0.796584i	$0.706638\pi$
$360$	22.9196	−	39.6978i	1.20797	−	2.09226i
$361$	5.34861	+	9.26407i	0.281506	+	0.487583i
$362$	−6.02706	−	10.4392i	−0.316775	−	0.548671i
$363$	−68.8907			−3.61583
$364$		0			0
$365$	−16.6056			−0.869174
$366$	10.8167	+	18.7350i	0.565396	+	0.979294i
$367$	−14.1431	−	24.4966i	−0.738265	−	1.27871i	−0.953276	−	0.302100i	$-0.902312\pi$
$367$	−14.1431	−	24.4966i	−0.738265	−	1.27871i	0.215011	−	0.976612i	$-0.431021\pi$
$368$	10.9083	−	18.8938i	0.568636	−	0.984906i
$369$	−39.8120			−2.07253
$370$	−2.61730	+	4.53330i	−0.136067	+	0.235675i
$371$		0			0
$372$	−0.761141			−0.0394633
$373$	8.15139	−	14.1186i	0.422063	−	0.731034i	−0.574078	−	0.818800i	$-0.694639\pi$
$373$	8.15139	−	14.1186i	0.422063	−	0.731034i	0.996141	+	0.0877661i	$0.0279728\pi$
$374$	−3.35766	−	5.81564i	−0.173620	−	0.300719i
$375$	7.04584	+	12.2037i	0.363845	+	0.630199i
$376$	37.1947			1.91817
$377$	3.75389	+	2.82352i	0.193335	+	0.145418i
$378$		0			0
$379$	−6.55971	−	11.3618i	−0.336950	−	0.583614i	0.646908	−	0.762568i	$-0.276062\pi$
$379$	−6.55971	−	11.3618i	−0.336950	−	0.583614i	−0.983857	+	0.178954i	$0.942729\pi$
$380$	1.25694	+	2.17708i	0.0644796	+	0.111682i
$381$	−4.19010	+	7.25747i	−0.214666	+	0.371812i
$382$	−25.1472			−1.28664
$383$	−9.64887	+	16.7123i	−0.493034	+	0.853960i	−0.999968	−	0.00802473i	$-0.997446\pi$
$383$	−9.64887	+	16.7123i	−0.493034	+	0.853960i	0.506934	+	0.861985i	$0.330779\pi$
$384$	−11.6579	+	20.1921i	−0.594914	+	1.03042i
$385$		0			0
$386$	−1.18335	+	2.04962i	−0.0602307	+	0.104323i
$387$	−14.6194	−	25.3216i	−0.743147	−	1.28717i
$388$	1.17658	+	2.03789i	0.0597316	+	0.103458i
$389$	−7.02776			−0.356321			−0.178161	−	0.984001i	$-0.557015\pi$
$389$	−7.02776			−0.356321			−0.178161	+	0.984001i	$0.557015\pi$
$390$	−4.71841	+	38.7135i	−0.238926	+	1.96034i
$391$	5.76291			0.291443
$392$		0			0
$393$	−24.5278	−	42.4833i	−1.23726	−	2.14300i
$394$	−7.75694	+	13.4354i	−0.390789	+	0.676866i
$395$	−1.74487			−0.0877938
$396$	−4.74306	+	8.21522i	−0.238348	+	0.412830i
$397$	2.88145	−	4.99082i	0.144616	−	0.250482i	−0.784614	−	0.619985i	$-0.787139\pi$
$397$	2.88145	−	4.99082i	0.144616	−	0.250482i	0.929230	+	0.369503i	$0.120472\pi$
$398$	1.13659			0.0569719
$399$		0			0
$400$	5.45416	+	9.44689i	0.272708	+	0.472344i
$401$	−7.55971	−	13.0938i	−0.377514	−	0.653874i	0.613186	−	0.789939i	$-0.289888\pi$
$401$	−7.55971	−	13.0938i	−0.377514	−	0.653874i	−0.990700	+	0.136065i	$0.956554\pi$
$402$	3.75389			0.187227
$403$	2.89445	−	1.23167i	0.144183	−	0.0613536i
$404$	−2.61730			−0.130216
$405$	4.62632	+	8.01302i	0.229884	+	0.398170i
$406$		0			0
$407$	4.11943	−	7.13506i	0.204193	−	0.353672i
$408$	−7.54163			−0.373367
$409$	−8.07607	+	13.9882i	−0.399336	+	0.691670i	−0.993644	−	0.112567i	$-0.964093\pi$
$409$	−8.07607	+	13.9882i	−0.399336	+	0.691670i	0.594308	+	0.804237i	$0.297426\pi$
$410$	14.0917	−	24.4075i	0.695938	−	1.20540i
$411$	−7.77193			−0.383361
$412$	−0.740358	+	1.28234i	−0.0364748	+	0.0631763i
$413$		0			0
$414$	22.8167	+	39.5196i	1.12138	+	1.94228i
$415$	−19.1194			−0.938536
$416$	−0.740358	+	6.07448i	−0.0362990	+	0.297826i
$417$	49.0555			2.40226
$418$	11.0896	+	19.2077i	0.542410	+	0.939482i
$419$	4.19010	+	7.25747i	0.204700	+	0.354551i	0.950037	−	0.312137i	$-0.101045\pi$
$419$	4.19010	+	7.25747i	0.204700	+	0.354551i	−0.745337	+	0.666688i	$0.767711\pi$
$420$		0			0
$421$	−31.0278			−1.51220			−0.756100	−	0.654456i	$-0.772898\pi$
$421$	−31.0278			−1.51220			−0.756100	+	0.654456i	$0.772898\pi$
$422$	9.77082	−	16.9236i	0.475636	−	0.823826i
$423$	−32.8726	+	56.9370i	−1.59832	+	2.76837i
$424$	28.8167			1.39946
$425$	−1.44073	+	2.49541i	−0.0698855	+	0.121045i
$426$	−7.50778	−	13.0038i	−0.363753	−	0.630039i
$427$		0			0
$428$	−2.81665			−0.136148
$429$	7.42641	−	60.9321i	0.358550	−	2.94183i
$430$	20.6985			0.998169
$431$	−12.9680	−	22.4613i	−0.624649	−	1.08192i	−0.988609	−	0.150509i	$-0.951909\pi$
$431$	−12.9680	−	22.4613i	−0.624649	−	1.08192i	0.363960	−	0.931415i	$-0.381424\pi$
$432$	−10.9575	−	18.9790i	−0.527194	−	0.913127i
$433$	−4.19010	+	7.25747i	−0.201364	+	0.348772i	−0.948968	−	0.315372i	$-0.897871\pi$
$433$	−4.19010	+	7.25747i	−0.201364	+	0.348772i	0.747604	+	0.664144i	$0.231204\pi$
$434$		0			0
$435$	−5.40833	+	9.36750i	−0.259309	+	0.449137i
$436$	−0.940285	+	1.62862i	−0.0450315	+	0.0779968i
$437$	−19.0336			−0.910500
$438$	−10.8167	+	18.7350i	−0.516840	+	0.895193i
$439$	−7.63985	−	13.2326i	−0.364630	−	0.631558i	0.624087	−	0.781355i	$-0.285471\pi$
$439$	−7.63985	−	13.2326i	−0.364630	−	0.631558i	−0.988717	+	0.149797i	$0.952138\pi$
$440$	−25.5369	−	44.2311i	−1.21742	−	2.10864i
$441$		0			0
$442$	3.77082	−	1.60458i	0.179359	−	0.0763223i
$443$	30.2389			1.43669			0.718346	−	0.695686i	$-0.244900\pi$
$443$	30.2389			1.43669			0.718346	+	0.695686i	$0.244900\pi$
$444$	−0.608282	−	1.05358i	−0.0288678	−	0.0500005i
$445$	−12.4542	−	21.5712i	−0.590384	−	1.02258i
$446$	8.81643	−	15.2705i	0.417470	−	0.723079i
$447$	−1.48072			−0.0700355
$448$		0			0
$449$	−4.21110	+	7.29384i	−0.198734	+	0.344218i	−0.948118	−	0.317918i	$-0.897016\pi$
$449$	−4.21110	+	7.29384i	−0.198734	+	0.344218i	0.749384	+	0.662136i	$0.230350\pi$
$450$	−22.8167			−1.07559
$451$	−22.1792	+	38.4155i	−1.04438	+	1.80891i
$452$	−2.24306	−	3.88510i	−0.105505	−	0.182740i
$453$	−8.94850	−	15.4993i	−0.420437	−	0.728219i
$454$	35.7140			1.67614
$455$		0			0
$456$	24.9083			1.16644
$457$	−6.69722	−	11.5999i	−0.313283	−	0.542622i	0.665788	−	0.746141i	$-0.268095\pi$
$457$	−6.69722	−	11.5999i	−0.313283	−	0.542622i	−0.979071	+	0.203519i	$0.934762\pi$
$458$	−13.5348	−	23.4430i	−0.632441	−	1.09542i
$459$	2.89445	−	5.01333i	0.135101	−	0.234002i
$460$	5.76291			0.268697
$461$	−6.33120	+	10.9660i	−0.294873	+	0.510736i	−0.974955	−	0.222400i	$-0.928611\pi$
$461$	−6.33120	+	10.9660i	−0.294873	+	0.510736i	0.680082	+	0.733136i	$0.261944\pi$
$462$		0			0
$463$	−28.2111			−1.31108			−0.655541	−	0.755160i	$-0.727559\pi$
$463$	−28.2111			−1.31108			−0.655541	+	0.755160i	$0.727559\pi$
$464$	2.15139	−	3.72631i	0.0998757	−	0.172990i
$465$	3.62181	+	6.27316i	0.167958	+	0.290911i
$466$	−15.5736	−	26.9743i	−0.721433	−	1.24956i
$467$	14.1431			0.654465			0.327233	−	0.944944i	$-0.393884\pi$
$467$	14.1431			0.654465			0.327233	+	0.944944i	$0.393884\pi$
$468$	−4.62632	−	3.47972i	−0.213852	−	0.160850i
$469$		0			0
$470$	−23.2708	−	40.3062i	−1.07340	−	1.85919i
$471$	−13.7111	−	23.7483i	−0.631774	−	1.09427i
$472$	9.95301	−	17.2391i	0.458125	−	0.793495i
$473$	−32.5778			−1.49793
$474$	−1.13659	+	1.96862i	−0.0522051	+	0.0904219i
$475$	4.75840	−	8.24179i	0.218330	−	0.378159i
$476$		0			0
$477$	−25.4680	+	44.1119i	−1.16610	+	2.01975i
$478$	7.55971	+	13.0938i	0.345773	+	0.598897i
$479$	−0.568293	−	0.984312i	−0.0259660	−	0.0449744i	0.852750	−	0.522319i	$-0.174933\pi$
$479$	−0.568293	−	0.984312i	−0.0259660	−	0.0449744i	−0.878716	+	0.477344i	$0.841599\pi$
$480$	−14.0917			−0.643194
$481$	4.01804	+	3.02220i	0.183207	+	0.137800i
$482$	−2.61730			−0.119215
$483$		0			0
$484$	3.61943	+	6.26904i	0.164520	+	0.284956i
$485$	11.1972	−	19.3942i	0.508440	−	0.880644i
$486$	−13.8790			−0.629563
$487$	13.8486	−	23.9865i	0.627541	−	1.08693i	−0.360503	−	0.932758i	$-0.617395\pi$
$487$	13.8486	−	23.9865i	0.627541	−	1.08693i	0.988044	−	0.154174i	$-0.0492717\pi$
$488$	8.64436	−	14.9725i	0.391312	−	0.677772i
$489$	49.5930			2.24267
$490$		0			0
$491$	6.36249	+	11.0202i	0.287135	+	0.497333i	0.973125	−	0.230279i	$-0.0739638\pi$
$491$	6.36249	+	11.0202i	0.287135	+	0.497333i	−0.685990	+	0.727611i	$0.740630\pi$
$492$	3.27502	+	5.67250i	0.147649	+	0.255736i
$493$	1.13659			0.0511892
$494$	−12.4542	+	5.29958i	−0.560339	+	0.238439i
$495$	90.2775			4.05767
$496$	−1.44073	−	2.49541i	−0.0646905	−	0.112047i
$497$		0			0
$498$	−12.4542	+	21.5712i	−0.558084	+	0.966631i
$499$	31.3305			1.40255			0.701274	−	0.712892i	$-0.252615\pi$
$499$	31.3305			1.40255			0.701274	+	0.712892i	$0.252615\pi$
$500$	0.740358	−	1.28234i	0.0331098	−	0.0573479i
$501$	−7.04584	+	12.2037i	−0.314785	+	0.545223i
$502$	−29.3428			−1.30964
$503$	−12.9665	+	22.4587i	−0.578150	+	1.00138i	0.417542	+	0.908658i	$0.362892\pi$
$503$	−12.9665	+	22.4587i	−0.578150	+	1.00138i	−0.995692	+	0.0927268i	$0.970442\pi$
$504$		0			0
$505$	12.4542	+	21.5712i	0.554203	+	0.959908i
$506$	50.8444			2.26031
$507$	36.3623	+	8.99734i	1.61491	+	0.399586i
$508$	0.880571			0.0390690
$509$	−1.30865	−	2.26665i	−0.0580049	−	0.100467i	0.835565	−	0.549392i	$-0.185141\pi$
$509$	−1.30865	−	2.26665i	−0.0580049	−	0.100467i	−0.893570	+	0.448924i	$0.851807\pi$
$510$	4.71841	+	8.17252i	0.208935	+	0.361885i
$511$		0			0
$512$	25.4222			1.12351
$513$	−9.55971	+	16.5579i	−0.422072	+	0.731050i
$514$	14.8435	−	25.7097i	0.654718	−	1.13400i
$515$	14.0917			0.620953
$516$	−2.40525	+	4.16601i	−0.105885	+	0.183398i
$517$	36.6265	+	63.4389i	1.61083	+	2.79004i
$518$		0			0
$519$	68.9361			3.02596
$520$	28.6791	−	12.2037i	1.25766	−	0.535170i
$521$	28.8145			1.26239			0.631194	−	0.775625i	$-0.282565\pi$
$521$	28.8145			1.26239			0.631194	+	0.775625i	$0.282565\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	−4.62632	−	8.01302i	−0.202295	−	0.350385i	0.746973	−	0.664855i	$-0.231507\pi$
$523$	−4.62632	−	8.01302i	−0.202295	−	0.350385i	−0.949267	+	0.314470i	$0.898173\pi$
$524$	−2.57731	+	4.46404i	−0.112590	+	0.195012i
$525$		0			0
$526$	−8.74306	+	15.1434i	−0.381216	+	0.660285i
$527$	0.380571	−	0.659168i	0.0165779	−	0.0287138i
$528$	−56.2283			−2.44702
$529$	−10.3167	+	17.8690i	−0.448550	+	0.776912i
$530$	−18.0291	−	31.2273i	−0.783133	−	1.35643i
$531$	17.5929	+	30.4717i	0.763465	+	1.32236i
$532$		0			0
$533$	−21.6333	−	16.2717i	−0.937043	−	0.704804i
$534$	−32.4500			−1.40425
$535$	13.4028	+	23.2143i	0.579452	+	1.00364i
$536$	−1.50000	−	2.59808i	−0.0647901	−	0.112220i
$537$	20.7385	−	35.9201i	0.894931	−	1.55007i
$538$	12.3982			0.534526
$539$		0			0
$540$	2.89445	−	5.01333i	0.124557	−	0.215739i
$541$	−18.9361			−0.814126			−0.407063	−	0.913400i	$-0.633447\pi$
$541$	−18.9361			−0.814126			−0.407063	+	0.913400i	$0.633447\pi$
$542$	−19.3377	+	33.4939i	−0.830627	+	1.43869i
$543$	−13.3305	−	23.0892i	−0.572068	−	0.990851i
$544$	0.740358	+	1.28234i	0.0317426	+	0.0549798i
$545$	17.8970			0.766623
$546$		0			0
$547$	29.0000			1.23995			0.619975	−	0.784621i	$-0.287143\pi$
$547$	29.0000			1.23995			0.619975	+	0.784621i	$0.287143\pi$
$548$	0.408327	+	0.707243i	0.0174429	+	0.0302119i
$549$	15.2797	+	26.4652i	0.652122	+	1.12951i
$550$	−12.7111	+	22.0163i	−0.542003	+	0.938777i
$551$	−3.75389			−0.159921
$552$	28.5504	−	49.4507i	1.21519	−	2.10476i
$553$		0			0
$554$	−18.5139			−0.786579
$555$	−5.78890	+	10.0267i	−0.245725	+	0.425608i
$556$	−2.57731	−	4.46404i	−0.109302	−	0.189317i
$557$	−8.45416	−	14.6430i	−0.358214	−	0.620446i	0.629448	−	0.777042i	$-0.283281\pi$
$557$	−8.45416	−	14.6430i	−0.358214	−	0.620446i	−0.987663	+	0.156597i	$0.949948\pi$
$558$	6.02706			0.255146
$559$	2.40525	−	19.7345i	0.101731	−	0.834682i
$560$		0			0
$561$	−7.42641	−	12.8629i	−0.313543	−	0.543073i
$562$	1.42221	+	2.46333i	0.0599921	+	0.103909i
$563$	−9.51680	+	16.4836i	−0.401085	+	0.694700i	−0.993857	−	0.110671i	$-0.964700\pi$
$563$	−9.51680	+	16.4836i	−0.401085	+	0.694700i	0.592772	+	0.805370i	$0.298034\pi$
$564$	10.8167			0.455463
$565$	−21.3468	+	36.9737i	−0.898065	+	1.55549i
$566$	−2.61730	+	4.53330i	−0.110013	+	0.190549i
$567$		0			0
$568$	−6.00000	+	10.3923i	−0.251754	+	0.436051i
$569$	13.6972	+	23.7243i	0.574218	+	0.994574i	0.996126	+	0.0879356i	$0.0280270\pi$
$569$	13.6972	+	23.7243i	0.574218	+	0.994574i	−0.421909	+	0.906638i	$0.638640\pi$
$570$	−15.5838	−	26.9920i	−0.652735	−	1.13057i
$571$	21.7250			0.909162			0.454581	−	0.890705i	$-0.349789\pi$
$571$	21.7250			0.909162			0.454581	+	0.890705i	$0.349789\pi$
$572$	−5.93497	+	2.52549i	−0.248154	+	0.105596i
$573$	−55.6201			−2.32356
$574$		0			0
$575$	−10.9083	−	18.8938i	−0.454909	−	0.787925i
$576$	−23.3764	+	40.4891i	−0.974015	+	1.68704i
$577$	−33.7050			−1.40316			−0.701579	−	0.712592i	$-0.747521\pi$
$577$	−33.7050			−1.40316			−0.701579	+	0.712592i	$0.747521\pi$
$578$	−10.5778	+	18.3213i	−0.439978	+	0.762065i
$579$	−2.61730	+	4.53330i	−0.108771	+	0.188398i
$580$	1.13659			0.0471942
$581$		0			0
$582$	−14.5875	−	25.2662i	−0.604670	−	1.04732i
$583$	28.3764	+	49.1493i	1.17523	+	2.03556i
$584$	17.2887			0.715412
$585$	−6.66527	+	54.6871i	−0.275575	+	2.26103i
$586$	4.54634			0.187808
$587$	−14.2752	−	24.7254i	−0.589200	−	1.02052i	−0.994337	−	0.106269i	$-0.966110\pi$
$587$	−14.2752	−	24.7254i	−0.589200	−	1.02052i	0.405137	−	0.914256i	$-0.367224\pi$
$588$		0			0
$589$	−1.25694	+	2.17708i	−0.0517913	+	0.0897051i
$590$	−24.9083			−1.02546
$591$	−17.1566	+	29.7162i	−0.705730	+	1.22236i
$592$	2.30278	−	3.98852i	0.0946435	−	0.163927i
$593$	22.7875			0.935770			0.467885	−	0.883789i	$-0.345016\pi$
$593$	22.7875			0.935770			0.467885	+	0.883789i	$0.345016\pi$
$594$	25.5369	−	44.2311i	1.04779	−	1.81483i
$595$		0			0
$596$	0.0777949	+	0.134745i	0.00318660	+	0.00551936i
$597$	2.51388			0.102886
$598$	−3.75389	+	30.7998i	−0.153508	+	1.25950i
$599$	7.51388			0.307009			0.153504	−	0.988148i	$-0.450944\pi$
$599$	7.51388			0.307009			0.153504	+	0.988148i	$0.450944\pi$
$600$	14.2752	+	24.7254i	0.582782	+	1.00941i
$601$	−14.7114	−	25.4809i	−0.600091	−	1.03939i	−0.992807	−	0.119728i	$-0.961798\pi$
$601$	−14.7114	−	25.4809i	−0.600091	−	1.03939i	0.392716	−	0.919660i	$-0.371536\pi$
$602$		0			0
$603$	5.30278			0.215946
$604$	−0.940285	+	1.62862i	−0.0382597	+	0.0662677i
$605$	34.4454	−	59.6611i	1.40040	−	2.42557i
$606$	32.4500			1.31819
$607$	10.2172	−	17.6966i	0.414702	−	0.718285i	−0.580695	−	0.814121i	$-0.697219\pi$
$607$	10.2172	−	17.6966i	0.414702	−	0.718285i	0.995397	+	0.0958363i	$0.0305525\pi$
$608$	−2.44524	−	4.23527i	−0.0991674	−	0.171763i
$609$		0			0
$610$	−21.6333			−0.875907
$611$	−41.1333	+	17.5033i	−1.66408	+	0.708109i
$612$	−1.40074			−0.0566215
$613$	−10.5458	−	18.2659i	−0.425942	−	0.737754i	0.570566	−	0.821252i	$-0.306724\pi$
$613$	−10.5458	−	18.2659i	−0.425942	−	0.737754i	−0.996508	+	0.0834983i	$0.973391\pi$
$614$	−9.95301	−	17.2391i	−0.401671	−	0.695714i
$615$	31.1677	−	53.9840i	1.25680	−	2.17685i
$616$		0			0
$617$	20.9222	−	36.2383i	0.842296	−	1.45890i	−0.0456524	−	0.998957i	$-0.514537\pi$
$617$	20.9222	−	36.2383i	0.842296	−	1.45890i	0.887949	−	0.459943i	$-0.152130\pi$
$618$	9.17914	−	15.8987i	0.369239	−	0.639541i
$619$	−22.5233			−0.905289			−0.452644	−	0.891691i	$-0.649519\pi$
$619$	−22.5233			−0.905289			−0.452644	+	0.891691i	$0.649519\pi$
$620$	0.380571	−	0.659168i	0.0152841	−	0.0264728i
$621$	21.9150	+	37.9580i	0.879420	+	1.52320i
$622$	11.0896	+	19.2077i	0.444652	+	0.770160i
$623$		0			0
$624$	4.15139	−	34.0612i	0.166189	−	1.36354i
$625$	−30.6056			−1.22422
$626$	−8.64436	−	14.9725i	−0.345498	−	0.598420i
$627$	24.5278	+	42.4833i	0.979544	+	1.69662i
$628$	−1.44073	+	2.49541i	−0.0574913	+	0.0995778i
$629$	1.21656			0.0485076
$630$		0			0
$631$	−6.04584	+	10.4717i	−0.240681	+	0.416872i	−0.960908	−	0.276866i	$-0.910704\pi$
$631$	−6.04584	+	10.4717i	−0.240681	+	0.416872i	0.720227	+	0.693738i	$0.244037\pi$
$632$	1.81665			0.0722626
$633$	21.6109	−	37.4312i	0.858956	−	1.48776i
$634$	5.34861	+	9.26407i	0.212421	+	0.367923i
$635$	−4.19010	−	7.25747i	−0.166279	−	0.288004i
$636$	8.38021			0.332297
$637$		0			0
$638$	10.0278			0.397003
$639$	−10.6056	−	18.3694i	−0.419549	−	0.726680i
$640$	−11.6579	−	20.1921i	−0.460819	−	0.798161i
$641$	−1.75694	+	3.04311i	−0.0693949	+	0.120196i	−0.898635	−	0.438697i	$-0.855440\pi$
$641$	−1.75694	+	3.04311i	−0.0693949	+	0.120196i	0.829240	+	0.558892i	$0.188774\pi$
$642$	34.9216			1.37824
$643$	−4.19010	+	7.25747i	−0.165242	+	0.286207i	−0.936741	−	0.350023i	$-0.886174\pi$
$643$	−4.19010	+	7.25747i	−0.165242	+	0.286207i	0.771499	+	0.636230i	$0.219507\pi$
$644$		0			0
$645$	45.7805			1.80261
$646$	−1.63751	+	2.83625i	−0.0644270	+	0.111591i
$647$	−1.13659	−	1.96862i	−0.0446838	−	0.0773946i	0.842819	−	0.538198i	$-0.180895\pi$
$647$	−1.13659	−	1.96862i	−0.0446838	−	0.0773946i	−0.887502	+	0.460803i	$0.847561\pi$
$648$	−4.81665	−	8.34269i	−0.189216	−	0.327732i
$649$	39.2038			1.53888
$650$	−12.3982	−	9.32544i	−0.486299	−	0.365774i
$651$		0			0
$652$	−2.60555	−	4.51295i	−0.102041	−	0.176741i
$653$	−10.8764	−	18.8384i	−0.425625	−	0.737204i	0.570853	−	0.821052i	$-0.306612\pi$
$653$	−10.8764	−	18.8384i	−0.425625	−	0.737204i	−0.996479	+	0.0838475i	$0.973279\pi$
$654$	11.6579	−	20.1921i	0.455860	−	0.789572i
$655$	49.0555			1.91676
$656$	−12.3982	+	21.4744i	−0.484070	+	0.838434i
$657$	−15.2797	+	26.4652i	−0.596118	+	1.03251i
$658$		0			0
$659$	−11.8167	+	20.4670i	−0.460311	+	0.797283i	−0.998976	−	0.0452373i	$-0.985596\pi$
$659$	−11.8167	+	20.4670i	−0.460311	+	0.797283i	0.538665	+	0.842520i	$0.318929\pi$
$660$	−7.42641	−	12.8629i	−0.289073	−	0.500688i
$661$	−4.89047	−	8.47055i	−0.190217	−	0.329466i	0.755105	−	0.655604i	$-0.227586\pi$
$661$	−4.89047	−	8.47055i	−0.190217	−	0.329466i	−0.945322	+	0.326138i	$0.894253\pi$
$662$	−0.908327			−0.0353031
$663$	8.34022	−	3.54899i	0.323907	−	0.137831i
$664$	19.9060			0.772504
$665$		0			0
$666$	4.81665	+	8.34269i	0.186642	+	0.323273i
$667$	−4.30278	+	7.45263i	−0.166604	+	0.288567i
$668$	1.48072			0.0572906
$669$	19.5000	−	33.7750i	0.753914	−	1.30582i
$670$	−1.87694	+	3.25096i	−0.0725127	+	0.125596i
$671$	34.0491			1.31445
$672$		0			0
$673$	−6.10555	−	10.5751i	−0.235352	−	0.407641i	0.724023	−	0.689776i	$-0.242291\pi$
$673$	−6.10555	−	10.5751i	−0.235352	−	0.407641i	−0.959375	+	0.282135i	$0.908958\pi$
$674$	−4.63751	−	8.03240i	−0.178630	−	0.309397i
$675$	−21.9150			−0.843510
$676$	−1.09167	−	3.78167i	−0.0419874	−	0.145449i
$677$	−6.37119			−0.244865			−0.122432	−	0.992477i	$-0.539069\pi$
$677$	−6.37119			−0.244865			−0.122432	+	0.992477i	$0.539069\pi$
$678$	27.8100	+	48.1684i	1.06804	+	1.84990i
$679$		0			0
$680$	3.77082	−	6.53125i	0.144604	−	0.250462i
$681$	78.9916			3.02696
$682$	3.35766	−	5.81564i	0.128571	−	0.222692i
$683$	−1.80278	+	3.12250i	−0.0689813	+	0.119479i	−0.898453	−	0.439069i	$-0.855308\pi$
$683$	−1.80278	+	3.12250i	−0.0689813	+	0.119479i	0.829472	+	0.558549i	$0.188642\pi$
$684$	4.62632			0.176892
$685$	3.88596	−	6.73069i	0.148475	−	0.257166i
$686$		0			0
$687$	−29.9361	−	51.8508i	−1.14213	−	1.97823i
$688$	−18.2111			−0.694292
$689$	−31.8681	+	13.5607i	−1.21408	+	0.516622i
$690$	−71.4500			−2.72005
$691$	16.4563	+	28.5031i	0.626026	+	1.08431i	0.988341	+	0.152254i	$0.0486531\pi$
$691$	16.4563	+	28.5031i	0.626026	+	1.08431i	−0.362315	+	0.932056i	$0.618014\pi$
$692$	−3.62181	−	6.27316i	−0.137681	−	0.238470i
$693$		0			0
$694$	−1.02776			−0.0390131
$695$	−24.5278	+	42.4833i	−0.930391	+	1.61148i
$696$	5.63083	−	9.75289i	0.213436	−	0.369682i
$697$	−6.55004			−0.248100
$698$	−15.5838	+	26.9920i	−0.589857	+	1.02166i
$699$	−34.4454	−	59.6611i	−1.30284	−	2.25659i
$700$		0			0
$701$	−27.0278			−1.02082			−0.510412	−	0.859930i	$-0.670507\pi$
$701$	−27.0278			−1.02082			−0.510412	+	0.859930i	$0.670507\pi$
$702$	24.9083	+	18.7350i	0.940104	+	0.707107i
$703$	−4.01804			−0.151543
$704$	26.0458	+	45.1127i	0.981639	+	1.70025i
$705$	−51.4699	−	89.1486i	−1.93847	−	3.35753i
$706$	−4.15012	+	7.18821i	−0.156192	+	0.270532i
$707$		0			0
$708$	2.89445	−	5.01333i	0.108780	−	0.188413i
$709$	−0.137510	+	0.238174i	−0.00516428	+	0.00894480i	−0.868596	−	0.495521i	$-0.834977\pi$
$709$	−0.137510	+	0.238174i	−0.00516428	+	0.00894480i	0.863432	+	0.504466i	$0.168311\pi$
$710$	15.0156			0.563524
$711$	−1.60555	+	2.78090i	−0.0602129	+	0.104292i
$712$	12.9665	+	22.4587i	0.485942	+	0.841676i
$713$	2.88145	+	4.99082i	0.107911	+	0.186908i
$714$		0			0
$715$	49.0555	+	36.8975i	1.83457	+	1.37989i
$716$	−4.35829			−0.162877
$717$	16.7204	+	28.9606i	0.624436	+	1.08155i
$718$	−14.9222	−	25.8460i	−0.556892	−	0.964565i
$719$	10.8254	−	18.7502i	0.403721	−	0.699265i	−0.590451	−	0.807074i	$-0.701050\pi$
$719$	10.8254	−	18.7502i	0.403721	−	0.699265i	0.994172	+	0.107808i	$0.0343833\pi$
$720$	50.4654			1.88074
$721$		0			0
$722$	−6.96804	+	12.0690i	−0.259324	+	0.449162i
$723$	−5.78890			−0.215291
$724$	−1.40074	+	2.42615i	−0.0520580	+	0.0901671i
$725$	−2.15139	−	3.72631i	−0.0799005	−	0.138392i
$726$	−44.8746	−	77.7251i	−1.66545	−	2.88465i
$727$	23.3958			0.867701			0.433850	−	0.900985i	$-0.357155\pi$
$727$	23.3958			0.867701			0.433850	+	0.900985i	$0.357155\pi$
$728$		0			0
$729$	−40.3305			−1.49372
$730$	−10.8167	−	18.7350i	−0.400342	−	0.693413i
$731$	−2.40525	−	4.16601i	−0.0889613	−	0.154085i
$732$	2.51388	−	4.35416i	0.0929156	−	0.160935i
$733$	40.0762			1.48025			0.740124	−	0.672470i	$-0.234767\pi$
$733$	40.0762			1.48025			0.740124	+	0.672470i	$0.234767\pi$
$734$	18.4253	−	31.9136i	0.680091	−	1.17795i
$735$		0			0
$736$	−11.2111			−0.413247
$737$	2.95416	−	5.11676i	0.108818	−	0.188478i
$738$	−25.9331	−	44.9174i	−0.954610	−	1.65343i
$739$	9.39445	+	16.2717i	0.345580	+	0.598563i	0.985459	−	0.169913i	$-0.0543487\pi$
$739$	9.39445	+	16.2717i	0.345580	+	0.598563i	−0.639879	+	0.768476i	$0.721015\pi$
$740$	1.21656			0.0447218
$741$	−27.5459	+	11.7215i	−1.01192	+	0.430600i
$742$		0			0
$743$	18.8486	+	32.6468i	0.691489	+	1.19769i	0.971350	+	0.237653i	$0.0763781\pi$
$743$	18.8486	+	32.6468i	0.691489	+	1.19769i	−0.279862	+	0.960040i	$0.590289\pi$
$744$	−3.77082	−	6.53125i	−0.138245	−	0.239447i
$745$	0.740358	−	1.28234i	0.0271246	−	0.0469812i
$746$	21.2389			0.777610
$747$	−17.5929	+	30.4717i	−0.643689	+	1.11490i
$748$	−0.780347	+	1.35160i	−0.0285323	+	0.0494194i
$749$		0			0
$750$	−9.17914	+	15.8987i	−0.335175	+	0.580540i
$751$	2.19722	+	3.80570i	0.0801779	+	0.138872i	0.903326	−	0.428954i	$-0.141118\pi$
$751$	2.19722	+	3.80570i	0.0801779	+	0.138872i	−0.823148	+	0.567826i	$0.807785\pi$
$752$	20.4743	+	35.4626i	0.746622	+	1.29319i
$753$	−64.8999			−2.36508
$754$	−0.740358	+	6.07448i	−0.0269623	+	0.221219i
$755$	17.8970			0.651339
$756$		0			0
$757$	22.1194	+	38.3120i	0.803944	+	1.39247i	0.917001	+	0.398884i	$0.130602\pi$
$757$	22.1194	+	38.3120i	0.803944	+	1.39247i	−0.113057	+	0.993588i	$0.536064\pi$
$758$	8.54584	−	14.8018i	0.310399	−	0.537626i
$759$	112.457			4.08192
$760$	−12.4542	+	21.5712i	−0.451760	+	0.782471i
$761$	−2.14110	+	3.70849i	−0.0776147	+	0.134433i	−0.902220	−	0.431275i	$-0.858064\pi$
$761$	−2.14110	+	3.70849i	−0.0776147	+	0.134433i	0.824606	+	0.565708i	$0.191397\pi$
$762$	−10.9175			−0.395500
$763$		0			0
$764$	2.92221	+	5.06141i	0.105722	+	0.183115i
$765$	6.66527	+	11.5446i	0.240983	+	0.417395i
$766$	−25.1406			−0.908368
$767$	−2.89445	+	23.7483i	−0.104512	+	0.857502i
$768$	20.4343			0.737360
$769$	−15.4518	−	26.7632i	−0.557205	−	0.965107i	−0.997728	−	0.0673662i	$-0.978540\pi$
$769$	−15.4518	−	26.7632i	−0.557205	−	0.965107i	0.440523	−	0.897741i	$-0.354793\pi$
$770$		0			0
$771$	32.8305	−	56.8641i	1.18236	−	2.04791i
$772$	0.550039			0.0197963
$773$	−17.4608	+	30.2430i	−0.628021	+	1.08776i	0.359927	+	0.932980i	$0.382801\pi$
$773$	−17.4608	+	30.2430i	−0.628021	+	1.08776i	−0.987948	+	0.154784i	$0.950532\pi$
$774$	19.0458	−	32.9884i	0.684588	−	1.18574i
$775$	−2.88145			−0.103505
$776$	−11.6579	+	20.1921i	−0.418494	+	0.724853i
$777$		0			0
$778$	−4.57779	−	7.92897i	−0.164122	−	0.284267i
$779$	21.6333			0.775094
$780$	8.34022	−	3.54899i	0.298628	−	0.127074i
$781$	−23.6333			−0.845666
$782$	3.75389	+	6.50192i	0.134239	+	0.232508i
$783$	4.32218	+	7.48624i	0.154462	+	0.267536i
$784$		0			0
$785$	27.4222			0.978740
$786$	31.9542	−	55.3462i	1.13977	−	1.97413i
$787$	20.7785	−	35.9893i	0.740672	−	1.28288i	−0.211518	−	0.977374i	$-0.567841\pi$
$787$	20.7785	−	35.9893i	0.740672	−	1.28288i	0.952190	−	0.305507i	$-0.0988261\pi$
$788$	3.60555			0.128442
$789$	−19.3377	+	33.4939i	−0.688441	+	1.19242i
$790$	−1.13659	−	1.96862i	−0.0404379	−	0.0700405i
$791$		0			0
$792$	−93.9916			−3.33985
$793$	−2.51388	+	20.6258i	−0.0892704	+	0.732445i
$794$	7.50778			0.266441
$795$	−39.8764	−	69.0679i	−1.41427	−	2.44959i
$796$	−0.132076	−	0.228762i	−0.00468131	−	0.00810826i
$797$	17.2887	−	29.9449i	0.612398	−	1.06070i	−0.378437	−	0.925627i	$-0.623538\pi$
$797$	17.2887	−	29.9449i	0.612398	−	1.06070i	0.990835	−	0.135077i	$-0.0431283\pi$
$798$		0			0
$799$	−5.40833	+	9.36750i	−0.191333	+	0.331398i
$800$	2.80278	−	4.85455i	0.0990931	−	0.171634i
$801$	−45.8391			−1.61965
$802$	9.84861	−	17.0583i	0.347767	−	0.602349i
$803$	17.0246	+	29.4874i	0.600784	+	1.04059i
$804$	−0.436217	−	0.755550i	−0.0153842	−	0.0266462i
$805$		0			0
$806$	3.27502	+	2.46333i	0.115358	+	0.0867672i
$807$	27.4222			0.965307
$808$	−12.9665	−	22.4587i	−0.456161	−	0.790095i
$809$	8.01388	+	13.8804i	0.281753	+	0.488010i	0.971817	−	0.235738i	$-0.0757508\pi$
$809$	8.01388	+	13.8804i	0.281753	+	0.488010i	−0.690064	+	0.723749i	$0.742417\pi$
$810$	−6.02706	+	10.4392i	−0.211769	+	0.366795i
$811$	−21.9150			−0.769541			−0.384771	−	0.923012i	$-0.625719\pi$
$811$	−21.9150			−0.769541			−0.384771	+	0.923012i	$0.625719\pi$
$812$		0			0
$813$	−42.7708	+	74.0812i	−1.50004	+	2.59814i
$814$	10.7334			0.376205
$815$	−24.7965	+	42.9488i	−0.868583	+	1.50443i
$816$	−4.15139	−	7.19041i	−0.145328	−	0.251715i
$817$	7.94399	+	13.7594i	0.277925	+	0.481380i
$818$	−21.0426			−0.735738
$819$		0			0
$820$	−6.55004			−0.228737
$821$	−0.922205	−	1.59731i	−0.0321852	−	0.0557464i	0.849484	−	0.527614i	$-0.176913\pi$
$821$	−0.922205	−	1.59731i	−0.0321852	−	0.0557464i	−0.881669	+	0.471868i	$0.843580\pi$
$822$	−5.06254	−	8.76857i	−0.176576	−	0.305839i
$823$	22.1333	−	38.3360i	0.771519	−	1.33631i	−0.165212	−	0.986258i	$-0.552831\pi$
$823$	22.1333	−	38.3360i	0.771519	−	1.33631i	0.936731	−	0.350051i	$-0.113836\pi$
$824$	−14.6714			−0.511103
$825$	−28.1142	+	48.6952i	−0.978810	+	1.69535i
$826$		0			0
$827$	51.7527			1.79962			0.899809	−	0.436283i	$-0.143705\pi$
$827$	51.7527			1.79962			0.899809	+	0.436283i	$0.143705\pi$
$828$	5.30278	−	9.18468i	0.184284	−	0.319190i
$829$	−7.81192	−	13.5306i	−0.271319	−	0.469938i	0.697881	−	0.716214i	$-0.254127\pi$
$829$	−7.81192	−	13.5306i	−0.271319	−	0.469938i	−0.969200	+	0.246276i	$0.920793\pi$
$830$	−12.4542	−	21.5712i	−0.432290	−	0.748749i
$831$	−40.9486			−1.42049
$832$	−29.2508	+	12.4470i	−1.01409	+	0.431521i
$833$		0			0
$834$	31.9542	+	55.3462i	1.10648	+	1.91648i
$835$	−7.04584	−	12.2037i	−0.243831	−	0.422328i
$836$	2.57731	−	4.46404i	0.0891382	−	0.154392i
$837$	5.78890			0.200094
$838$	−5.45877	+	9.45486i	−0.188570	+	0.326613i
$839$	−11.8300	+	20.4901i	−0.408415	+	0.707396i	−0.994712	−	0.102700i	$-0.967252\pi$
$839$	−11.8300	+	20.4901i	−0.408415	+	0.707396i	0.586297	+	0.810096i	$0.300585\pi$
$840$		0			0
$841$	13.6514	−	23.6449i	0.470738	−	0.815341i
$842$	−20.2111	−	35.0067i	−0.696521	−	1.20641i
$843$	3.14561	+	5.44835i	0.108340	+	0.187651i
$844$	−4.54163			−0.156330
$845$	−25.9731	+	26.9920i	−0.893501	+	0.928553i
$846$	−85.6512			−2.94475
$847$		0			0
$848$	15.8625	+	27.4746i	0.544720	+	0.943483i
$849$	−5.78890	+	10.0267i	−0.198674	+	0.344114i
$850$	−3.75389			−0.128757
$851$	−4.60555	+	7.97705i	−0.157876	+	0.273450i
$852$	−1.74487	+	3.02220i	−0.0597782	+	0.103539i
$853$	14.1431			0.484251			0.242126	−	0.970245i	$-0.422155\pi$
$853$	14.1431			0.484251			0.242126	+	0.970245i	$0.422155\pi$
$854$		0			0
$855$	−22.0139	−	38.1292i	−0.752859	−	1.30399i
$856$	−13.9542	−	24.1693i	−0.476943	−	0.826090i
$857$	47.5840			1.62544			0.812719	−	0.582656i	$-0.197987\pi$
$857$	47.5840			1.62544			0.812719	+	0.582656i	$0.197987\pi$
$858$	73.5833	−	31.3117i	2.51209	−	1.06896i
$859$	−24.7965			−0.846046			−0.423023	−	0.906119i	$-0.639031\pi$
$859$	−24.7965			−0.846046			−0.423023	+	0.906119i	$0.639031\pi$
$860$	−2.40525	−	4.16601i	−0.0820183	−	0.142060i
$861$		0			0
$862$	16.8944	−	29.2620i	0.575427	−	0.996669i
$863$	−11.8167			−0.402244			−0.201122	−	0.979566i	$-0.564459\pi$
$863$	−11.8167			−0.402244			−0.201122	+	0.979566i	$0.564459\pi$
$864$	−5.63083	+	9.75289i	−0.191565	+	0.331800i
$865$	−34.4680	+	59.7004i	−1.17195	+	2.02987i
$866$	−10.9175			−0.370993
$867$	−23.3958	+	40.5226i	−0.794562	+	1.37622i
$868$		0			0
$869$	1.78890	+	3.09846i	0.0606842	+	0.105108i
$870$	−14.0917			−0.477752
$871$	2.88145	+	2.16731i	0.0976343	+	0.0734364i
$872$	−18.6333			−0.631003
$873$	−20.6064	−	35.6913i	−0.697421	−	1.20797i
$874$	−12.3982	−	21.4744i	−0.419377	−	0.726382i
$875$		0			0
$876$	5.02776			0.169872
$877$	19.1972	−	33.2506i	0.648244	−	1.12279i	−0.335298	−	0.942112i	$-0.608837\pi$
$877$	19.1972	−	33.2506i	0.648244	−	1.12279i	0.983542	−	0.180680i	$-0.0578297\pi$
$878$	9.95301	−	17.2391i	0.335898	−	0.581792i
$879$	10.0555			0.339164
$880$	28.1142	−	48.6952i	0.947728	−	1.64151i
$881$	17.7249	+	30.7005i	0.597168	+	1.03433i	0.993237	+	0.116105i	$0.0370409\pi$
$881$	17.7249	+	30.7005i	0.597168	+	1.03433i	−0.396069	+	0.918221i	$0.629626\pi$
$882$		0			0
$883$	−31.6056			−1.06361			−0.531806	−	0.846866i	$-0.678486\pi$
$883$	−31.6056			−1.06361			−0.531806	+	0.846866i	$0.678486\pi$
$884$	−0.761141	−	0.572498i	−0.0255999	−	0.0192552i
$885$	−55.0918			−1.85189
$886$	19.6972	+	34.1166i	0.661741	+	1.14617i
$887$	23.0516	+	39.9266i	0.773998	+	1.34060i	0.935356	+	0.353708i	$0.115079\pi$
$887$	23.0516	+	39.9266i	0.773998	+	1.34060i	−0.161358	+	0.986896i	$0.551587\pi$
$888$	6.02706	−	10.4392i	0.202255	−	0.350316i
$889$		0			0
$890$	16.2250	−	28.1025i	0.543863	−	0.941998i
$891$	9.48612	−	16.4304i	0.317797	−	0.550441i
$892$	−4.09802			−0.137212
$893$	17.8625	−	30.9387i	0.597745	−	1.03533i
$894$	−0.964521	−	1.67060i	−0.0322584	−	0.0558732i
$895$	20.7385	+	35.9201i	0.693211	+	1.20068i
$896$		0			0
$897$	−8.30278	+	68.1225i	−0.277222	+	2.27454i
$898$	−10.9722			−0.366149
$899$	0.568293	+	0.984312i	0.0189536	+	0.0328286i
$900$	2.65139	+	4.59234i	0.0883796	+	0.153078i
$901$	−4.19010	+	7.25747i	−0.139593	+	0.241782i
$902$	−57.7890			−1.92416
$903$		0			0
$904$	22.2250	−	38.4948i	0.739192	−	1.28032i
$905$	26.6611			0.886244
$906$	11.6579	−	20.1921i	0.387307	−	0.670836i
$907$	−9.42221	−	16.3197i	−0.312859	−	0.541888i	0.666121	−	0.745844i	$-0.267953\pi$
$907$	−9.42221	−	16.3197i	−0.312859	−	0.541888i	−0.978980	+	0.203956i	$0.934620\pi$
$908$	−4.15012	−	7.18821i	−0.137726	−	0.238549i
$909$	45.8391			1.52039
$910$		0			0
$911$	−10.9361			−0.362329			−0.181164	−	0.983453i	$-0.557987\pi$
$911$	−10.9361			−0.362329			−0.181164	+	0.983453i	$0.557987\pi$
$912$	13.7111	+	23.7483i	0.454020	+	0.786386i
$913$	19.6019	+	33.9515i	0.648728	+	1.12363i
$914$	8.72498	−	15.1121i	0.288597	−	0.499864i
$915$	−47.8481			−1.58181
$916$	−3.14561	+	5.44835i	−0.103934	+	0.180019i
$917$		0			0
$918$	7.54163			0.248911
$919$	5.72498	−	9.91596i	0.188850	−	0.327097i	−0.756017	−	0.654552i	$-0.772857\pi$
$919$	5.72498	−	9.91596i	0.188850	−	0.327097i	0.944867	+	0.327454i	$0.106191\pi$
$920$	28.5504	+	49.4507i	0.941278	+	1.63034i
$921$	−22.0139	−	38.1292i	−0.725382	−	1.25640i
$922$	−16.4963			−0.543276
$923$	1.74487	−	14.3163i	0.0574330	−	0.471226i
$924$		0			0
$925$	−2.30278	−	3.98852i	−0.0757148	−	0.131142i
$926$	−18.3764	−	31.8288i	−0.603885	−	1.04596i
$927$	12.9665	−	22.4587i	0.425877	−	0.737641i
$928$	−2.21110			−0.0725830
$929$	4.19010	−	7.25747i	0.137473	−	0.238110i	−0.789067	−	0.614308i	$-0.789435\pi$
$929$	4.19010	−	7.25747i	0.137473	−	0.238110i	0.926539	+	0.376198i	$0.122769\pi$
$930$	−4.71841	+	8.17252i	−0.154723	+	0.267988i
$931$		0			0
$932$	−3.61943	+	6.26904i	−0.118558	+	0.205349i
$933$	24.5278	+	42.4833i	0.803003	+	1.39084i
$934$	9.21265	+	15.9568i	0.301447	+	0.522122i
$935$	14.8528			0.485739
$936$	6.93948	−	56.9370i	0.226824	−	1.86104i
$937$	−46.4474			−1.51737			−0.758685	−	0.651458i	$-0.774158\pi$
$937$	−46.4474			−1.51737			−0.758685	+	0.651458i	$0.774158\pi$
$938$		0			0
$939$	−19.1194	−	33.1158i	−0.623939	−	1.08069i
$940$	−5.40833	+	9.36750i	−0.176400	+	0.305534i
$941$	−44.7025			−1.45726			−0.728630	−	0.684907i	$-0.759843\pi$
$941$	−44.7025			−1.45726			−0.728630	+	0.684907i	$0.759843\pi$
$942$	17.8625	−	30.9387i	0.581991	−	1.00804i
$943$	24.7965	−	42.9488i	0.807485	−	1.39861i
$944$	21.9150			0.713274
$945$		0			0
$946$	−21.2208	−	36.7555i	−0.689947	−	1.19502i
$947$	−26.5597	−	46.0028i	−0.863075	−	1.49489i	−0.868946	−	0.494907i	$-0.835202\pi$
$947$	−26.5597	−	46.0028i	−0.863075	−	1.49489i	0.00587143	−	0.999983i	$-0.498131\pi$
$948$	0.528304			0.0171585
$949$	−19.1194	+	8.13583i	−0.620643	+	0.264100i
$950$	12.3982			0.402252
$951$	11.8300	+	20.4901i	0.383613	+	0.664437i
$952$		0			0
$953$	−20.8028	+	36.0315i	−0.673868	+	1.16717i	0.302930	+	0.953013i	$0.402035\pi$
$953$	−20.8028	+	36.0315i	−0.673868	+	1.16717i	−0.976798	+	0.214161i	$0.931298\pi$
$954$	−66.3583			−2.14843
$955$	27.8100	−	48.1684i	0.899911	−	1.55869i
$956$	1.75694	−	3.04311i	0.0568235	−	0.0984211i
$957$	22.1792			0.716952
$958$	0.740358	−	1.28234i	0.0239199	−	0.0414305i
$959$		0			0
$960$	−36.6013	−	63.3954i	−1.18130	−	2.04608i
$961$	−30.2389			−0.975447
$962$	−0.792455	+	6.50192i	−0.0255498	+	0.209630i
$963$	49.3305			1.58965
$964$	0.304141	+	0.526788i	0.00979573	+	0.0169667i
$965$	−2.61730	−	4.53330i	−0.0842539	−	0.145932i
$966$		0			0
$967$	22.4500			0.721942			0.360971	−	0.932577i	$-0.382445\pi$
$967$	22.4500			0.721942			0.360971	+	0.932577i	$0.382445\pi$
$968$	−35.8625	+	62.1157i	−1.15266	+	1.99647i
$969$	−3.62181	+	6.27316i	−0.116349	+	0.201523i
$970$	29.1749			0.936751
$971$	5.06254	−	8.76857i	0.162465	−	0.281397i	−0.773287	−	0.634056i	$-0.781389\pi$
$971$	5.06254	−	8.76857i	0.162465	−	0.281397i	0.935752	+	0.352659i	$0.114722\pi$
$972$	1.61279	+	2.79344i	0.0517303	+	0.0895996i
$973$		0			0
$974$	36.0833			1.15618
$975$	−27.4222	−	20.6258i	−0.878213	−	0.660555i
$976$	19.0336			0.609250
$977$	20.0139	+	34.6651i	0.640301	+	1.10903i	0.985366	+	0.170454i	$0.0545236\pi$
$977$	20.0139	+	34.6651i	0.640301	+	1.10903i	−0.345065	+	0.938579i	$0.612143\pi$
$978$	32.3043	+	55.9526i	1.03298	+	1.78917i
$979$	−25.5369	+	44.2311i	−0.816161	+	1.41363i
$980$		0			0
$981$	16.4680	−	28.5235i	0.525784	−	0.910685i
$982$	−8.28890	+	14.3568i	−0.264509	+	0.458144i
$983$	13.0065			0.414844			0.207422	−	0.978252i	$-0.433493\pi$
$983$	13.0065			0.414844			0.207422	+	0.978252i	$0.433493\pi$
$984$	−32.4500	+	56.2050i	−1.03447	+	1.79175i
$985$	−17.1566	−	29.7162i	−0.546656	−	0.946836i
$986$	0.740358	+	1.28234i	0.0235778	+	0.0408380i
$987$		0			0
$988$	2.51388	+	1.89083i	0.0799771	+	0.0601554i
$989$	36.4222			1.15816
$990$	58.8056	+	101.854i	1.86897	+	3.23714i
$991$	23.1653	+	40.1234i	0.735869	+	1.27456i	0.954341	+	0.298719i	$0.0965594\pi$
$991$	23.1653	+	40.1234i	0.735869	+	1.27456i	−0.218472	+	0.975843i	$0.570107\pi$
$992$	−0.740358	+	1.28234i	−0.0235064	+	0.0407143i
$993$	−2.00902			−0.0637543
$994$		0			0
$995$	−1.25694	+	2.17708i	−0.0398476	+	0.0690182i
$996$	5.78890			0.183428
$997$	−22.0871	+	38.2560i	−0.699506	+	1.21158i	0.269132	+	0.963103i	$0.413263\pi$
$997$	−22.0871	+	38.2560i	−0.699506	+	1.21158i	−0.968638	+	0.248476i	$0.920070\pi$
$998$	20.4083	+	35.3483i	0.646014	+	1.11893i
$999$	4.62632	+	8.01302i	0.146370	+	0.253521i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.h.393.4	yes	8
7.2	even	3		637.2.g.i.263.3		8
7.3	odd	6		637.2.h.j.471.1		8
7.4	even	3		637.2.h.j.471.2		8
7.5	odd	6		637.2.g.i.263.4		8
7.6	odd	2	inner	637.2.f.h.393.3	yes	8
13.3	even	3		8281.2.a.bu.1.1		4
13.9	even	3	inner	637.2.f.h.295.4	yes	8
13.10	even	6		8281.2.a.bo.1.3		4
91.9	even	3		637.2.h.j.165.2		8
91.48	odd	6	inner	637.2.f.h.295.3	✓	8
91.55	odd	6		8281.2.a.bu.1.2		4
91.61	odd	6		637.2.h.j.165.1		8
91.62	odd	6		8281.2.a.bo.1.4		4
91.74	even	3		637.2.g.i.373.3		8
91.87	odd	6		637.2.g.i.373.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.h.295.3	✓	8	91.48	odd	6	inner
637.2.f.h.295.4	yes	8	13.9	even	3	inner
637.2.f.h.393.3	yes	8	7.6	odd	2	inner
637.2.f.h.393.4	yes	8	1.1	even	1	trivial
637.2.g.i.263.3		8	7.2	even	3
637.2.g.i.263.4		8	7.5	odd	6
637.2.g.i.373.3		8	91.74	even	3
637.2.g.i.373.4		8	91.87	odd	6
637.2.h.j.165.1		8	91.61	odd	6
637.2.h.j.165.2		8	91.9	even	3
637.2.h.j.471.1		8	7.3	odd	6
637.2.h.j.471.2		8	7.4	even	3
8281.2.a.bo.1.3		4	13.10	even	6
8281.2.a.bo.1.4		4	91.62	odd	6
8281.2.a.bu.1.1		4	13.3	even	3
8281.2.a.bu.1.2		4	91.55	odd	6

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	637.2.f.h.393.4

Level	$637$
Weight	$2$
Character	637.393
Analytic conductor	$5.086$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$