LMFDB - Embedded newform 637.2.h.f.165.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(165,637)]

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([4, 4]))

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

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

chi := DirichletCharacter("637.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.1
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.f.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.381966 q^{2} +(-0.190983 - 0.330792i) q^{3} -1.85410 q^{4} +(0.190983 + 0.330792i) q^{5} +(-0.0729490 - 0.126351i) q^{6} -1.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +O(q^{10})$	\(q+0.381966 q^{2} +(-0.190983 - 0.330792i) q^{3} -1.85410 q^{4} +(0.190983 + 0.330792i) q^{5} +(-0.0729490 - 0.126351i) q^{6} -1.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +(0.0729490 + 0.126351i) q^{10} +(2.42705 + 4.20378i) q^{11} +(0.354102 + 0.613323i) q^{12} +(2.50000 - 2.59808i) q^{13} +(0.0729490 - 0.126351i) q^{15} +3.14590 q^{16} -7.47214 q^{17} +(0.545085 - 0.944115i) q^{18} +(2.42705 - 4.20378i) q^{19} +(-0.354102 - 0.613323i) q^{20} +(0.927051 + 1.60570i) q^{22} +4.47214 q^{23} +(0.281153 + 0.486971i) q^{24} +(2.42705 - 4.20378i) q^{25} +(0.954915 - 0.992377i) q^{26} -2.23607 q^{27} +(2.04508 - 3.54219i) q^{29} +(0.0278640 - 0.0482619i) q^{30} +(4.35410 - 7.54153i) q^{31} +4.14590 q^{32} +(0.927051 - 1.60570i) q^{33} -2.85410 q^{34} +(-2.64590 + 4.58283i) q^{36} +4.00000 q^{37} +(0.927051 - 1.60570i) q^{38} +(-1.33688 - 0.330792i) q^{39} +(-0.281153 - 0.486971i) q^{40} +(2.61803 - 4.53457i) q^{41} +(3.78115 + 6.54915i) q^{43} +(-4.50000 - 7.79423i) q^{44} +1.09017 q^{45} +1.70820 q^{46} +(1.11803 + 1.93649i) q^{47} +(-0.600813 - 1.04064i) q^{48} +(0.927051 - 1.60570i) q^{50} +(1.42705 + 2.47172i) q^{51} +(-4.63525 + 4.81710i) q^{52} +(-4.11803 + 7.13264i) q^{53} -0.854102 q^{54} +(-0.927051 + 1.60570i) q^{55} -1.85410 q^{57} +(0.781153 - 1.35300i) q^{58} -2.23607 q^{59} +(-0.135255 + 0.234268i) q^{60} +(-3.00000 + 5.19615i) q^{61} +(1.66312 - 2.88061i) q^{62} -4.70820 q^{64} +(1.33688 + 0.330792i) q^{65} +(0.354102 - 0.613323i) q^{66} +(-0.354102 - 0.613323i) q^{67} +13.8541 q^{68} +(-0.854102 - 1.47935i) q^{69} +(-4.09017 - 7.08438i) q^{71} +(-2.10081 + 3.63871i) q^{72} +(-1.00000 + 1.73205i) q^{73} +1.52786 q^{74} -1.85410 q^{75} +(-4.50000 + 7.79423i) q^{76} +(-0.510643 - 0.126351i) q^{78} +(-2.00000 - 3.46410i) q^{79} +(0.600813 + 1.04064i) q^{80} +(-3.85410 - 6.67550i) q^{81} +(1.00000 - 1.73205i) q^{82} +6.70820 q^{83} +(-1.42705 - 2.47172i) q^{85} +(1.44427 + 2.50155i) q^{86} -1.56231 q^{87} +(-3.57295 - 6.18853i) q^{88} -16.0902 q^{89} +0.416408 q^{90} -8.29180 q^{92} -3.32624 q^{93} +(0.427051 + 0.739674i) q^{94} +1.85410 q^{95} +(-0.791796 - 1.37143i) q^{96} +(6.07295 + 10.5187i) q^{97} +13.8541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 3 q^{5} - 7 q^{6} + 12 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 + 3 * q^5 - 7 * q^6 + 12 * q^8 - q^9	$ 4 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 3 q^{5} - 7 q^{6} + 12 q^{8} - q^{9} + 7 q^{10} + 3 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{15} + 26 q^{16} - 12 q^{17} - 9 q^{18} + 3 q^{19} + 12 q^{20} - 3 q^{22} - 19 q^{24} + 3 q^{25} + 15 q^{26} - 3 q^{29} + 18 q^{30} + 4 q^{31} + 30 q^{32} - 3 q^{33} + 2 q^{34} - 24 q^{36} + 16 q^{37} - 3 q^{38} - 21 q^{39} + 19 q^{40} + 6 q^{41} - 5 q^{43} - 18 q^{44} - 18 q^{45} - 20 q^{46} - 27 q^{48} - 3 q^{50} - q^{51} + 15 q^{52} - 12 q^{53} + 10 q^{54} + 3 q^{55} + 6 q^{57} - 17 q^{58} + 33 q^{60} - 12 q^{61} - 9 q^{62} + 8 q^{64} + 21 q^{65} - 12 q^{66} + 12 q^{67} + 42 q^{68} + 10 q^{69} + 6 q^{71} - 33 q^{72} - 4 q^{73} + 24 q^{74} + 6 q^{75} - 18 q^{76} - 49 q^{78} - 8 q^{79} + 27 q^{80} - 2 q^{81} + 4 q^{82} + q^{85} - 30 q^{86} + 34 q^{87} - 21 q^{88} - 42 q^{89} - 52 q^{90} - 60 q^{92} + 18 q^{93} - 5 q^{94} - 6 q^{95} - 30 q^{96} + 31 q^{97} + 42 q^{99}+O(q^{100}) $ 4 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 + 3 * q^5 - 7 * q^6 + 12 * q^8 - q^9 + 7 * q^10 + 3 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^15 + 26 * q^16 - 12 * q^17 - 9 * q^18 + 3 * q^19 + 12 * q^20 - 3 * q^22 - 19 * q^24 + 3 * q^25 + 15 * q^26 - 3 * q^29 + 18 * q^30 + 4 * q^31 + 30 * q^32 - 3 * q^33 + 2 * q^34 - 24 * q^36 + 16 * q^37 - 3 * q^38 - 21 * q^39 + 19 * q^40 + 6 * q^41 - 5 * q^43 - 18 * q^44 - 18 * q^45 - 20 * q^46 - 27 * q^48 - 3 * q^50 - q^51 + 15 * q^52 - 12 * q^53 + 10 * q^54 + 3 * q^55 + 6 * q^57 - 17 * q^58 + 33 * q^60 - 12 * q^61 - 9 * q^62 + 8 * q^64 + 21 * q^65 - 12 * q^66 + 12 * q^67 + 42 * q^68 + 10 * q^69 + 6 * q^71 - 33 * q^72 - 4 * q^73 + 24 * q^74 + 6 * q^75 - 18 * q^76 - 49 * q^78 - 8 * q^79 + 27 * q^80 - 2 * q^81 + 4 * q^82 + q^85 - 30 * q^86 + 34 * q^87 - 21 * q^88 - 42 * q^89 - 52 * q^90 - 60 * q^92 + 18 * q^93 - 5 * q^94 - 6 * q^95 - 30 * q^96 + 31 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.381966			0.270091			0.135045	−	0.990839i	$-0.456882\pi$
$2$	0.381966			0.270091			0.135045	+	0.990839i	$0.456882\pi$
$3$	−0.190983	−	0.330792i	−0.110264	−	0.190983i	0.805613	−	0.592443i	$-0.201836\pi$
$3$	−0.190983	−	0.330792i	−0.110264	−	0.190983i	−0.915877	+	0.401460i	$0.868503\pi$
$4$	−1.85410			−0.927051
$5$	0.190983	+	0.330792i	0.0854102	+	0.147935i	0.905566	−	0.424206i	$-0.139447\pi$
$5$	0.190983	+	0.330792i	0.0854102	+	0.147935i	−0.820156	+	0.572140i	$0.806113\pi$
$6$	−0.0729490	−	0.126351i	−0.0297813	−	0.0515827i
$7$		0			0
$7$		0			0
$8$	−1.47214			−0.520479
$9$	1.42705	−	2.47172i	0.475684	−	0.823908i
$10$	0.0729490	+	0.126351i	0.0230685	+	0.0399558i
$11$	2.42705	+	4.20378i	0.731783	+	1.26749i	0.956120	+	0.292974i	$0.0946451\pi$
$11$	2.42705	+	4.20378i	0.731783	+	1.26749i	−0.224337	+	0.974512i	$0.572022\pi$
$12$	0.354102	+	0.613323i	0.102220	+	0.177051i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$13$	2.50000	−	2.59808i	0.693375	−	0.720577i
$14$		0			0
$15$	0.0729490	−	0.126351i	0.0188354	−	0.0326238i
$16$	3.14590			0.786475
$17$	−7.47214			−1.81226			−0.906130	−	0.423000i	$-0.860977\pi$
$17$	−7.47214			−1.81226			−0.906130	+	0.423000i	$0.860977\pi$
$18$	0.545085	−	0.944115i	0.128478	−	0.222530i
$19$	2.42705	−	4.20378i	0.556804	−	0.964412i	−0.440957	−	0.897528i	$-0.645361\pi$
$19$	2.42705	−	4.20378i	0.556804	−	0.964412i	0.997761	−	0.0668841i	$-0.0213058\pi$
$20$	−0.354102	−	0.613323i	−0.0791796	−	0.137143i
$21$		0			0
$22$	0.927051	+	1.60570i	0.197648	+	0.342336i
$23$	4.47214			0.932505			0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214			0.932505			0.466252	+	0.884652i	$0.345604\pi$
$24$	0.281153	+	0.486971i	0.0573901	+	0.0994026i
$25$	2.42705	−	4.20378i	0.485410	−	0.840755i
$26$	0.954915	−	0.992377i	0.187274	−	0.194621i
$27$	−2.23607			−0.430331
$28$		0			0
$29$	2.04508	−	3.54219i	0.379763	−	0.657768i	−0.611265	−	0.791426i	$-0.709339\pi$
$29$	2.04508	−	3.54219i	0.379763	−	0.657768i	0.991028	+	0.133658i	$0.0426723\pi$
$30$	0.0278640	−	0.0482619i	0.00508726	−	0.00881138i
$31$	4.35410	−	7.54153i	0.782020	−	1.35450i	−0.148744	−	0.988876i	$-0.547523\pi$
$31$	4.35410	−	7.54153i	0.782020	−	1.35450i	0.930763	−	0.365622i	$-0.119144\pi$
$32$	4.14590			0.732898
$33$	0.927051	−	1.60570i	0.161379	−	0.279516i
$34$	−2.85410			−0.489474
$35$		0			0
$36$	−2.64590	+	4.58283i	−0.440983	+	0.763805i
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	0.927051	−	1.60570i	0.150388	−	0.260479i
$39$	−1.33688	−	0.330792i	−0.214072	−	0.0529692i
$40$	−0.281153	−	0.486971i	−0.0444542	−	0.0769969i
$41$	2.61803	−	4.53457i	0.408868	−	0.708181i	−0.585895	−	0.810387i	$-0.699257\pi$
$41$	2.61803	−	4.53457i	0.408868	−	0.708181i	0.994763	+	0.102206i	$0.0325902\pi$
$42$		0			0
$43$	3.78115	+	6.54915i	0.576620	+	0.998736i	0.995864	+	0.0908618i	$0.0289622\pi$
$43$	3.78115	+	6.54915i	0.576620	+	0.998736i	−0.419243	+	0.907874i	$0.637704\pi$
$44$	−4.50000	−	7.79423i	−0.678401	−	1.17502i
$45$	1.09017			0.162513
$46$	1.70820			0.251861
$47$	1.11803	+	1.93649i	0.163082	+	0.282466i	0.935973	−	0.352073i	$-0.114523\pi$
$47$	1.11803	+	1.93649i	0.163082	+	0.282466i	−0.772890	+	0.634539i	$0.781190\pi$
$48$	−0.600813	−	1.04064i	−0.0867199	−	0.150203i
$49$		0			0
$50$	0.927051	−	1.60570i	0.131105	−	0.227080i
$51$	1.42705	+	2.47172i	0.199827	+	0.346111i
$52$	−4.63525	+	4.81710i	−0.642794	+	0.668011i
$53$	−4.11803	+	7.13264i	−0.565655	+	0.979744i	0.431333	+	0.902193i	$0.358043\pi$
$53$	−4.11803	+	7.13264i	−0.565655	+	0.979744i	−0.996988	+	0.0775512i	$0.975290\pi$
$54$	−0.854102			−0.116229
$55$	−0.927051	+	1.60570i	−0.125004	+	0.216512i
$56$		0			0
$57$	−1.85410			−0.245582
$58$	0.781153	−	1.35300i	0.102570	−	0.177657i
$59$	−2.23607			−0.291111			−0.145556	−	0.989350i	$-0.546497\pi$
$59$	−2.23607			−0.291111			−0.145556	+	0.989350i	$0.546497\pi$
$60$	−0.135255	+	0.234268i	−0.0174613	+	0.0302439i
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$	1.66312	−	2.88061i	0.211216	−	0.365837i
$63$		0			0
$64$	−4.70820			−0.588525
$65$	1.33688	+	0.330792i	0.165820	+	0.0410297i
$66$	0.354102	−	0.613323i	0.0435869	−	0.0754948i
$67$	−0.354102	−	0.613323i	−0.0432604	−	0.0749293i	0.843584	−	0.536997i	$-0.180441\pi$
$67$	−0.354102	−	0.613323i	−0.0432604	−	0.0749293i	−0.886845	+	0.462067i	$0.847108\pi$
$68$	13.8541			1.68006
$69$	−0.854102	−	1.47935i	−0.102822	−	0.178093i
$70$		0			0
$71$	−4.09017	−	7.08438i	−0.485414	−	0.840761i	0.514446	−	0.857523i	$-0.327998\pi$
$71$	−4.09017	−	7.08438i	−0.485414	−	0.840761i	−0.999860	+	0.0167615i	$0.994664\pi$
$72$	−2.10081	+	3.63871i	−0.247583	+	0.428827i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	1.52786			0.177611
$75$	−1.85410			−0.214093
$76$	−4.50000	+	7.79423i	−0.516185	+	0.894059i
$77$		0			0
$78$	−0.510643	−	0.126351i	−0.0578189	−	0.0143065i
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	0.731307	−	0.682048i	$-0.238911\pi$
$79$	−2.00000	−	3.46410i	−0.225018	−	0.389742i	−0.956325	+	0.292306i	$0.905577\pi$
$80$	0.600813	+	1.04064i	0.0671729	+	0.116347i
$81$	−3.85410	−	6.67550i	−0.428234	−	0.741722i
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$	6.70820			0.736321			0.368161	−	0.929762i	$-0.379988\pi$
$83$	6.70820			0.736321			0.368161	+	0.929762i	$0.379988\pi$
$84$		0			0
$85$	−1.42705	−	2.47172i	−0.154785	−	0.268096i
$86$	1.44427	+	2.50155i	0.155740	+	0.269749i
$87$	−1.56231			−0.167497
$88$	−3.57295	−	6.18853i	−0.380878	−	0.659699i
$89$	−16.0902			−1.70555			−0.852777	−	0.522275i	$-0.825084\pi$
$89$	−16.0902			−1.70555			−0.852777	+	0.522275i	$0.825084\pi$
$90$	0.416408			0.0438932
$91$		0			0
$92$	−8.29180			−0.864479
$93$	−3.32624			−0.344915
$94$	0.427051	+	0.739674i	0.0440469	+	0.0762915i
$95$	1.85410			0.190227
$96$	−0.791796	−	1.37143i	−0.0808123	−	0.139971i
$97$	6.07295	+	10.5187i	0.616615	+	1.06801i	0.990099	+	0.140371i	$0.0448296\pi$
$97$	6.07295	+	10.5187i	0.616615	+	1.06801i	−0.373484	+	0.927636i	$0.621837\pi$
$98$		0			0
$99$	13.8541			1.39239
$100$	−4.50000	+	7.79423i	−0.450000	+	0.779423i
$101$	4.28115	+	7.41517i	0.425991	+	0.737837i	0.996512	−	0.0834451i	$-0.0265923\pi$
$101$	4.28115	+	7.41517i	0.425991	+	0.737837i	−0.570522	+	0.821283i	$0.693259\pi$
$102$	0.545085	+	0.944115i	0.0539715	+	0.0934813i
$103$	2.35410	+	4.07742i	0.231957	+	0.401761i	0.958384	−	0.285483i	$-0.0921539\pi$
$103$	2.35410	+	4.07742i	0.231957	+	0.401761i	−0.726427	+	0.687243i	$0.758821\pi$
$104$	−3.68034	+	3.82472i	−0.360887	+	0.375045i
$105$		0			0
$106$	−1.57295	+	2.72443i	−0.152778	+	0.264620i
$107$	−5.61803			−0.543116			−0.271558	−	0.962422i	$-0.587539\pi$
$107$	−5.61803			−0.543116			−0.271558	+	0.962422i	$0.587539\pi$
$108$	4.14590			0.398939
$109$	−5.35410	+	9.27358i	−0.512830	+	0.888248i	0.487059	+	0.873369i	$0.338070\pi$
$109$	−5.35410	+	9.27358i	−0.512830	+	0.888248i	−0.999889	+	0.0148787i	$0.995264\pi$
$110$	−0.354102	+	0.613323i	−0.0337623	+	0.0584780i
$111$	−0.763932	−	1.32317i	−0.0725092	−	0.125590i
$112$		0			0
$113$	3.73607	+	6.47106i	0.351460	+	0.608746i	0.986505	−	0.163728i	$-0.0523521\pi$
$113$	3.73607	+	6.47106i	0.351460	+	0.608746i	−0.635046	+	0.772475i	$0.719019\pi$
$114$	−0.708204			−0.0663294
$115$	0.854102	+	1.47935i	0.0796454	+	0.137950i
$116$	−3.79180	+	6.56758i	−0.352059	+	0.609785i
$117$	−2.85410	−	9.88690i	−0.263862	−	0.914044i
$118$	−0.854102			−0.0786265
$119$		0			0
$120$	−0.107391	+	0.186006i	−0.00980340	+	0.0169800i
$121$	−6.28115	+	10.8793i	−0.571014	+	0.989025i
$122$	−1.14590	+	1.98475i	−0.103745	+	0.179691i
$123$	−2.00000			−0.180334
$124$	−8.07295	+	13.9828i	−0.724972	+	1.25569i
$125$	3.76393			0.336656
$126$		0			0
$127$	7.07295	−	12.2507i	0.627623	−	1.08707i	−0.360405	−	0.932796i	$-0.617361\pi$
$127$	7.07295	−	12.2507i	0.627623	−	1.08707i	0.988027	−	0.154278i	$-0.0493053\pi$
$128$	−10.0902			−0.891853
$129$	1.44427	−	2.50155i	0.127161	−	0.220249i
$130$	0.510643	+	0.126351i	0.0447864	+	0.0110818i
$131$	0.163119	+	0.282530i	0.0142518	+	0.0246848i	0.873063	−	0.487607i	$-0.162130\pi$
$131$	0.163119	+	0.282530i	0.0142518	+	0.0246848i	−0.858812	+	0.512292i	$0.828797\pi$
$132$	−1.71885	+	2.97713i	−0.149606	+	0.259126i
$133$		0			0
$134$	−0.135255	−	0.234268i	−0.0116842	−	0.0202377i
$135$	−0.427051	−	0.739674i	−0.0367547	−	0.0636610i
$136$	11.0000			0.943242
$137$	−0.381966			−0.0326336			−0.0163168	−	0.999867i	$-0.505194\pi$
$137$	−0.381966			−0.0326336			−0.0163168	+	0.999867i	$0.505194\pi$
$138$	−0.326238	−	0.565061i	−0.0277712	−	0.0481012i
$139$	−7.78115	−	13.4774i	−0.659989	−	1.14313i	−0.980618	−	0.195929i	$-0.937228\pi$
$139$	−7.78115	−	13.4774i	−0.659989	−	1.14313i	0.320629	−	0.947205i	$-0.396106\pi$
$140$		0			0
$141$	0.427051	−	0.739674i	0.0359642	−	0.0622918i
$142$	−1.56231	−	2.70599i	−0.131106	−	0.227082i
$143$	16.9894	+	4.20378i	1.42072	+	0.351537i
$144$	4.48936	−	7.77579i	0.374113	−	0.647983i
$145$	1.56231			0.129742
$146$	−0.381966	+	0.661585i	−0.0316117	+	0.0547531i
$147$		0			0
$148$	−7.41641			−0.609625
$149$	2.42705	−	4.20378i	0.198832	−	0.344387i	−0.749318	−	0.662210i	$-0.769619\pi$
$149$	2.42705	−	4.20378i	0.198832	−	0.344387i	0.948150	+	0.317823i	$0.102952\pi$
$150$	−0.708204			−0.0578246
$151$	7.35410	−	12.7377i	0.598468	−	1.03658i	−0.394579	−	0.918862i	$-0.629110\pi$
$151$	7.35410	−	12.7377i	0.598468	−	1.03658i	0.993047	−	0.117716i	$-0.0375571\pi$
$152$	−3.57295	+	6.18853i	−0.289804	+	0.501956i
$153$	−10.6631	+	18.4691i	−0.862062	+	1.49314i
$154$		0			0
$155$	3.32624			0.267170
$156$	2.47871	+	0.613323i	0.198456	+	0.0491051i
$157$	4.07295	−	7.05455i	0.325057	−	0.563015i	−0.656467	−	0.754355i	$-0.727950\pi$
$157$	4.07295	−	7.05455i	0.325057	−	0.563015i	0.981524	+	0.191340i	$0.0612833\pi$
$158$	−0.763932	−	1.32317i	−0.0607752	−	0.105266i
$159$	3.14590			0.249486
$160$	0.791796	+	1.37143i	0.0625970	+	0.108421i
$161$		0			0
$162$	−1.47214	−	2.54981i	−0.115662	−	0.200332i
$163$	−4.85410	+	8.40755i	−0.380203	+	0.658530i	−0.991091	−	0.133186i	$-0.957479\pi$
$163$	−4.85410	+	8.40755i	−0.380203	+	0.658530i	0.610888	+	0.791717i	$0.290812\pi$
$164$	−4.85410	+	8.40755i	−0.379042	+	0.656519i
$165$	0.708204			0.0551336
$166$	2.56231			0.198874
$167$	4.88197	−	8.45581i	0.377778	−	0.654330i	−0.612961	−	0.790113i	$-0.710022\pi$
$167$	4.88197	−	8.45581i	0.377778	−	0.654330i	0.990739	+	0.135783i	$0.0433550\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	−0.545085	−	0.944115i	−0.0418061	−	0.0724103i
$171$	−6.92705	−	11.9980i	−0.529725	−	0.917510i
$172$	−7.01064	−	12.1428i	−0.534557	−	0.925879i
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	−0.984828	−	0.173534i	$-0.944481\pi$
$173$	−4.50000	+	7.79423i	−0.342129	+	0.592584i	0.642699	+	0.766119i	$0.277815\pi$
$174$	−0.596748			−0.0452393
$175$		0			0
$176$	7.63525	+	13.2246i	0.575529	+	0.996845i
$177$	0.427051	+	0.739674i	0.0320991	+	0.0555973i
$178$	−6.14590			−0.460655
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$	−2.02129			−0.150658
$181$	3.70820			0.275629			0.137814	−	0.990458i	$-0.455992\pi$
$181$	3.70820			0.275629			0.137814	+	0.990458i	$0.455992\pi$
$182$		0			0
$183$	2.29180			0.169414
$184$	−6.58359			−0.485349
$185$	0.763932	+	1.32317i	0.0561654	+	0.0972813i
$186$	−1.27051			−0.0931583
$187$	−18.1353	−	31.4112i	−1.32618	−	2.29701i
$188$	−2.07295	−	3.59045i	−0.151185	−	0.261861i
$189$		0			0
$190$	0.708204			0.0513785
$191$	−11.8090	+	20.4538i	−0.854470	+	1.47999i	0.0226649	+	0.999743i	$0.492785\pi$
$191$	−11.8090	+	20.4538i	−0.854470	+	1.47999i	−0.877135	+	0.480243i	$0.840548\pi$
$192$	0.899187	+	1.55744i	0.0648932	+	0.112398i
$193$	3.00000	+	5.19615i	0.215945	+	0.374027i	0.953564	−	0.301189i	$-0.0973836\pi$
$193$	3.00000	+	5.19615i	0.215945	+	0.374027i	−0.737620	+	0.675216i	$0.764050\pi$
$194$	2.31966	+	4.01777i	0.166542	+	0.288459i
$195$	−0.145898	−	0.505406i	−0.0104480	−	0.0361928i
$196$		0			0
$197$	−3.89919	+	6.75359i	−0.277806	+	0.481173i	−0.970839	−	0.239732i	$-0.922940\pi$
$197$	−3.89919	+	6.75359i	−0.277806	+	0.481173i	0.693034	+	0.720905i	$0.256274\pi$
$198$	5.29180			0.376072
$199$	−2.41641			−0.171295			−0.0856473	−	0.996326i	$-0.527296\pi$
$199$	−2.41641			−0.171295			−0.0856473	+	0.996326i	$0.527296\pi$
$200$	−3.57295	+	6.18853i	−0.252646	+	0.437595i
$201$	−0.135255	+	0.234268i	−0.00954015	+	0.0165240i
$202$	1.63525	+	2.83234i	0.115056	+	0.199283i
$203$		0			0
$204$	−2.64590	−	4.58283i	−0.185250	−	0.320862i
$205$	2.00000			0.139686
$206$	0.899187	+	1.55744i	0.0626493	+	0.108512i
$207$	6.38197	−	11.0539i	0.443577	−	0.768298i
$208$	7.86475	−	8.17328i	0.545322	−	0.566715i
$209$	23.5623			1.62984
$210$		0			0
$211$	4.35410	−	7.54153i	0.299749	−	0.519180i	−0.676330	−	0.736599i	$-0.736430\pi$
$211$	4.35410	−	7.54153i	0.299749	−	0.519180i	0.976078	+	0.217419i	$0.0697638\pi$
$212$	7.63525	−	13.2246i	0.524391	−	0.908273i
$213$	−1.56231	+	2.70599i	−0.107047	+	0.185412i
$214$	−2.14590			−0.146691
$215$	−1.44427	+	2.50155i	−0.0984985	+	0.170604i
$216$	3.29180			0.223978
$217$		0			0
$218$	−2.04508	+	3.54219i	−0.138511	+	0.239907i
$219$	0.763932			0.0516217
$220$	1.71885	−	2.97713i	0.115885	−	0.200718i
$221$	−18.6803	+	19.4132i	−1.25658	+	1.30587i
$222$	−0.291796	−	0.505406i	−0.0195841	−	0.0339206i
$223$	−6.63525	+	11.4926i	−0.444330	+	0.769601i	−0.998005	−	0.0631310i	$-0.979891\pi$
$223$	−6.63525	+	11.4926i	−0.444330	+	0.769601i	0.553676	+	0.832732i	$0.313225\pi$
$224$		0			0
$225$	−6.92705	−	11.9980i	−0.461803	−	0.799867i
$226$	1.42705	+	2.47172i	0.0949260	+	0.164417i
$227$	7.47214			0.495943			0.247972	−	0.968767i	$-0.420236\pi$
$227$	7.47214			0.495943			0.247972	+	0.968767i	$0.420236\pi$
$228$	3.43769			0.227667
$229$	13.5623	+	23.4906i	0.896222	+	1.55230i	0.832284	+	0.554349i	$0.187033\pi$
$229$	13.5623	+	23.4906i	0.896222	+	1.55230i	0.0639380	+	0.997954i	$0.479634\pi$
$230$	0.326238	+	0.565061i	0.0215115	+	0.0372590i
$231$		0			0
$232$	−3.01064	+	5.21459i	−0.197658	+	0.342354i
$233$	−0.190983	−	0.330792i	−0.0125117	−	0.0216709i	0.859702	−	0.510796i	$-0.170649\pi$
$233$	−0.190983	−	0.330792i	−0.0125117	−	0.0216709i	−0.872213	+	0.489125i	$0.837316\pi$
$234$	−1.09017	−	3.77646i	−0.0712666	−	0.246875i
$235$	−0.427051	+	0.739674i	−0.0278577	+	0.0482510i
$236$	4.14590			0.269875
$237$	−0.763932	+	1.32317i	−0.0496227	+	0.0859491i
$238$		0			0
$239$	−11.2918			−0.730406			−0.365203	−	0.930928i	$-0.619000\pi$
$239$	−11.2918			−0.730406			−0.365203	+	0.930928i	$0.619000\pi$
$240$	0.229490	−	0.397489i	0.0148135	−	0.0256578i
$241$	−4.43769			−0.285857			−0.142929	−	0.989733i	$-0.545652\pi$
$241$	−4.43769			−0.285857			−0.142929	+	0.989733i	$0.545652\pi$
$242$	−2.39919	+	4.15551i	−0.154226	+	0.267127i
$243$	−4.82624	+	8.35929i	−0.309603	+	0.536249i
$244$	5.56231	−	9.63420i	0.356090	−	0.616766i
$245$		0			0
$246$	−0.763932			−0.0487065
$247$	−4.85410	−	16.8151i	−0.308859	−	1.06992i
$248$	−6.40983	+	11.1022i	−0.407025	+	0.704987i
$249$	−1.28115	−	2.21902i	−0.0811898	−	0.140625i
$250$	1.43769			0.0909278
$251$	2.61803	+	4.53457i	0.165249	+	0.286219i	0.936744	−	0.350016i	$-0.113824\pi$
$251$	2.61803	+	4.53457i	0.165249	+	0.286219i	−0.771495	+	0.636236i	$0.780491\pi$
$252$		0			0
$253$	10.8541	+	18.7999i	0.682392	+	1.18194i
$254$	2.70163	−	4.67935i	0.169515	−	0.293609i
$255$	−0.545085	+	0.944115i	−0.0341345	+	0.0591228i
$256$	5.56231			0.347644
$257$	25.7426			1.60578			0.802891	−	0.596126i	$-0.203294\pi$
$257$	25.7426			1.60578			0.802891	+	0.596126i	$0.203294\pi$
$258$	0.551663	−	0.955508i	0.0343450	−	0.0594873i
$259$		0			0
$260$	−2.47871	−	0.613323i	−0.153723	−	0.0380367i
$261$	−5.83688	−	10.1098i	−0.361294	−	0.625779i
$262$	0.0623059	+	0.107917i	0.00384927	+	0.00666713i
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$	−1.36475	+	2.36381i	−0.0839943	+	0.145482i
$265$	−3.14590			−0.193251
$266$		0			0
$267$	3.07295	+	5.32250i	0.188061	+	0.325732i
$268$	0.656541	+	1.13716i	0.0401046	+	0.0694633i
$269$	−13.7426			−0.837904			−0.418952	−	0.908008i	$-0.637602\pi$
$269$	−13.7426			−0.837904			−0.418952	+	0.908008i	$0.637602\pi$
$270$	−0.163119	−	0.282530i	−0.00992710	−	0.0171942i
$271$	−18.4164			−1.11872			−0.559359	−	0.828926i	$-0.688952\pi$
$271$	−18.4164			−1.11872			−0.559359	+	0.828926i	$0.688952\pi$
$272$	−23.5066			−1.42530
$273$		0			0
$274$	−0.145898			−0.00881402
$275$	23.5623			1.42086
$276$	1.58359	+	2.74286i	0.0953210	+	0.165101i
$277$	−5.00000			−0.300421			−0.150210	−	0.988654i	$-0.547995\pi$
$277$	−5.00000			−0.300421			−0.150210	+	0.988654i	$0.547995\pi$
$278$	−2.97214	−	5.14789i	−0.178257	−	0.308750i
$279$	−12.4271	−	21.5243i	−0.743988	−	1.28863i
$280$		0			0
$281$	−2.18034			−0.130068			−0.0650341	−	0.997883i	$-0.520716\pi$
$281$	−2.18034			−0.130068			−0.0650341	+	0.997883i	$0.520716\pi$
$282$	0.163119	−	0.282530i	0.00971359	−	0.0168244i
$283$	−6.70820	−	11.6190i	−0.398761	−	0.690675i	0.594812	−	0.803865i	$-0.297226\pi$
$283$	−6.70820	−	11.6190i	−0.398761	−	0.690675i	−0.993573	+	0.113190i	$0.963893\pi$
$284$	7.58359	+	13.1352i	0.450003	+	0.779429i
$285$	−0.354102	−	0.613323i	−0.0209752	−	0.0363301i
$286$	6.48936	+	1.60570i	0.383724	+	0.0949470i
$287$		0			0
$288$	5.91641	−	10.2475i	0.348628	−	0.603841i
$289$	38.8328			2.28428
$290$	0.596748			0.0350422
$291$	2.31966	−	4.01777i	0.135981	−	0.235526i
$292$	1.85410	−	3.21140i	0.108503	−	0.187933i
$293$	−5.61803	−	9.73072i	−0.328209	−	0.568475i	0.653947	−	0.756540i	$-0.273112\pi$
$293$	−5.61803	−	9.73072i	−0.328209	−	0.568475i	−0.982157	+	0.188065i	$0.939778\pi$
$294$		0			0
$295$	−0.427051	−	0.739674i	−0.0248639	−	0.0430655i
$296$	−5.88854			−0.342265
$297$	−5.42705	−	9.39993i	−0.314909	−	0.545439i
$298$	0.927051	−	1.60570i	0.0537026	−	0.0930157i
$299$	11.1803	−	11.6190i	0.646576	−	0.671941i
$300$	3.43769			0.198475
$301$		0			0
$302$	2.80902	−	4.86536i	0.161641	−	0.279970i
$303$	1.63525	−	2.83234i	0.0939429	−	0.162714i
$304$	7.63525	−	13.2246i	0.437912	−	0.758486i
$305$	−2.29180			−0.131228
$306$	−4.07295	+	7.05455i	−0.232835	+	0.403282i
$307$	−1.85410			−0.105819			−0.0529096	−	0.998599i	$-0.516850\pi$
$307$	−1.85410			−0.105819			−0.0529096	+	0.998599i	$0.516850\pi$
$308$		0			0
$309$	0.899187	−	1.55744i	0.0511530	−	0.0885995i
$310$	1.27051			0.0721601
$311$	−6.16312	+	10.6748i	−0.349478	+	0.605314i	−0.986157	−	0.165815i	$-0.946975\pi$
$311$	−6.16312	+	10.6748i	−0.349478	+	0.605314i	0.636678	+	0.771129i	$0.280308\pi$
$312$	1.96807	+	0.486971i	0.111420	+	0.0275693i
$313$	−7.56231	−	13.0983i	−0.427447	−	0.740360i	0.569199	−	0.822200i	$-0.307254\pi$
$313$	−7.56231	−	13.0983i	−0.427447	−	0.740360i	−0.996645	+	0.0818405i	$0.973920\pi$
$314$	1.55573	−	2.69460i	0.0877948	−	0.152065i
$315$		0			0
$316$	3.70820	+	6.42280i	0.208603	+	0.361311i
$317$	−10.8820	−	18.8481i	−0.611192	−	1.05862i	−0.991040	−	0.133567i	$-0.957357\pi$
$317$	−10.8820	−	18.8481i	−0.611192	−	1.05862i	0.379848	−	0.925049i	$-0.375976\pi$
$318$	1.20163			0.0673838
$319$	19.8541			1.11162
$320$	−0.899187	−	1.55744i	−0.0502661	−	0.0870634i
$321$	1.07295	+	1.85840i	0.0598862	+	0.103726i
$322$		0			0
$323$	−18.1353	+	31.4112i	−1.00907	+	1.74776i
$324$	7.14590	+	12.3771i	0.396994	+	0.687614i
$325$	−4.85410	−	16.8151i	−0.269257	−	0.932734i
$326$	−1.85410	+	3.21140i	−0.102689	+	0.177863i
$327$	4.09017			0.226187
$328$	−3.85410	+	6.67550i	−0.212807	+	0.368593i
$329$		0			0
$330$	0.270510			0.0148911
$331$	8.42705	−	14.5961i	0.463193	−	0.802273i	−0.535925	−	0.844265i	$-0.680037\pi$
$331$	8.42705	−	14.5961i	0.463193	−	0.802273i	0.999118	+	0.0419923i	$0.0133705\pi$
$332$	−12.4377			−0.682607
$333$	5.70820	−	9.88690i	0.312808	−	0.541799i
$334$	1.86475	−	3.22983i	0.102034	−	0.176729i
$335$	0.135255	−	0.234268i	0.00738977	−	0.0127994i
$336$		0			0
$337$	8.56231			0.466419			0.233209	−	0.972427i	$-0.425077\pi$
$337$	8.56231			0.466419			0.233209	+	0.972427i	$0.425077\pi$
$338$	−0.190983	−	4.96188i	−0.0103881	−	0.269891i
$339$	1.42705	−	2.47172i	0.0775068	−	0.134246i
$340$	2.64590	+	4.58283i	0.143494	+	0.248539i
$341$	42.2705			2.28908
$342$	−2.64590	−	4.58283i	−0.143074	−	0.247811i
$343$		0			0
$344$	−5.56637	−	9.64124i	−0.300119	−	0.519821i
$345$	0.326238	−	0.565061i	0.0175641	−	0.0304218i
$346$	−1.71885	+	2.97713i	−0.0924058	+	0.160052i
$347$	35.2361			1.89157			0.945786	−	0.324792i	$-0.105294\pi$
$347$	35.2361			1.89157			0.945786	+	0.324792i	$0.105294\pi$
$348$	2.89667			0.155278
$349$	3.64590	−	6.31488i	0.195160	−	0.338028i	−0.751793	−	0.659400i	$-0.770811\pi$
$349$	3.64590	−	6.31488i	0.195160	−	0.338028i	0.946953	+	0.321372i	$0.104144\pi$
$350$		0			0
$351$	−5.59017	+	5.80948i	−0.298381	+	0.310087i
$352$	10.0623	+	17.4284i	0.536323	+	0.928938i
$353$	14.4271	+	24.9884i	0.767874	+	1.33000i	0.938713	+	0.344699i	$0.112019\pi$
$353$	14.4271	+	24.9884i	0.767874	+	1.33000i	−0.170839	+	0.985299i	$0.554648\pi$
$354$	0.163119	+	0.282530i	0.00866967	+	0.0150163i
$355$	1.56231	−	2.70599i	0.0829186	−	0.143619i
$356$	29.8328			1.58114
$357$		0			0
$358$	1.71885	+	2.97713i	0.0908439	+	0.157346i
$359$	5.45492	+	9.44819i	0.287899	+	0.498656i	0.973308	−	0.229502i	$-0.0737098\pi$
$359$	5.45492	+	9.44819i	0.287899	+	0.498656i	−0.685409	+	0.728159i	$0.740376\pi$
$360$	−1.60488			−0.0845845
$361$	−2.28115	−	3.95107i	−0.120061	−	0.207951i
$362$	1.41641			0.0744447
$363$	4.79837			0.251849
$364$		0			0
$365$	−0.763932			−0.0399860
$366$	0.875388			0.0457573
$367$	12.7082	+	22.0113i	0.663363	+	1.14898i	0.979726	+	0.200340i	$0.0642047\pi$
$367$	12.7082	+	22.0113i	0.663363	+	1.14898i	−0.316364	+	0.948638i	$0.602462\pi$
$368$	14.0689			0.733391
$369$	−7.47214	−	12.9421i	−0.388984	−	0.673740i
$370$	0.291796	+	0.505406i	0.0151698	+	0.0262748i
$371$		0			0
$372$	6.16718			0.319754
$373$	0.218847	−	0.379054i	0.0113315	−	0.0196267i	−0.860304	−	0.509781i	$-0.829726\pi$
$373$	0.218847	−	0.379054i	0.0113315	−	0.0196267i	0.871636	+	0.490155i	$0.163060\pi$
$374$	−6.92705	−	11.9980i	−0.358189	−	0.620402i
$375$	−0.718847	−	1.24508i	−0.0371211	−	0.0642956i
$376$	−1.64590	−	2.85078i	−0.0848807	−	0.147018i
$377$	−4.09017	−	14.1688i	−0.210654	−	0.729728i
$378$		0			0
$379$	6.42705	−	11.1320i	0.330135	−	0.571811i	−0.652403	−	0.757872i	$-0.726239\pi$
$379$	6.42705	−	11.1320i	0.330135	−	0.571811i	0.982538	+	0.186061i	$0.0595722\pi$
$380$	−3.43769			−0.176350
$381$	−5.40325			−0.276817
$382$	−4.51064	+	7.81266i	−0.230785	+	0.399731i
$383$	12.4894	−	21.6322i	0.638176	−	1.10535i	−0.347656	−	0.937622i	$-0.613022\pi$
$383$	12.4894	−	21.6322i	0.638176	−	1.10535i	0.985833	−	0.167732i	$-0.0536443\pi$
$384$	1.92705	+	3.33775i	0.0983394	+	0.170329i
$385$		0			0
$386$	1.14590	+	1.98475i	0.0583247	+	0.101021i
$387$	21.5836			1.09716
$388$	−11.2599	−	19.5027i	−0.571633	−	0.990098i
$389$	−11.9443	+	20.6881i	−0.605599	+	1.04893i	0.386358	+	0.922349i	$0.373733\pi$
$389$	−11.9443	+	20.6881i	−0.605599	+	1.04893i	−0.991957	+	0.126579i	$0.959600\pi$
$390$	−0.0557281	−	0.193048i	−0.00282190	−	0.00977535i
$391$	−33.4164			−1.68994
$392$		0			0
$393$	0.0623059	−	0.107917i	0.00314292	−	0.00544369i
$394$	−1.48936	+	2.57964i	−0.0750327	+	0.129960i
$395$	0.763932	−	1.32317i	0.0384376	−	0.0665759i
$396$	−25.6869			−1.29082
$397$	−12.7082	+	22.0113i	−0.637806	+	1.10471i	0.348107	+	0.937455i	$0.386825\pi$
$397$	−12.7082	+	22.0113i	−0.637806	+	1.10471i	−0.985913	+	0.167258i	$0.946509\pi$
$398$	−0.922986			−0.0462651
$399$		0			0
$400$	7.63525	−	13.2246i	0.381763	−	0.661232i
$401$	−20.4508			−1.02127			−0.510633	−	0.859799i	$-0.670589\pi$
$401$	−20.4508			−1.02127			−0.510633	+	0.859799i	$0.670589\pi$
$402$	−0.0516628	+	0.0894826i	−0.00257671	+	0.00446298i
$403$	−8.70820	−	30.1661i	−0.433787	−	1.50268i
$404$	−7.93769	−	13.7485i	−0.394915	−	0.684013i
$405$	1.47214	−	2.54981i	0.0731510	−	0.126701i
$406$		0			0
$407$	9.70820	+	16.8151i	0.481218	+	0.833494i
$408$	−2.10081	−	3.63871i	−0.104006	−	0.180143i
$409$	−34.5623			−1.70900			−0.854498	−	0.519455i	$-0.826135\pi$
$409$	−34.5623			−1.70900			−0.854498	+	0.519455i	$0.826135\pi$
$410$	0.763932			0.0377279
$411$	0.0729490	+	0.126351i	0.00359831	+	0.00623246i
$412$	−4.36475	−	7.55996i	−0.215036	−	0.372453i
$413$		0			0
$414$	2.43769	−	4.22221i	0.119806	−	0.207510i
$415$	1.28115	+	2.21902i	0.0628893	+	0.108928i
$416$	10.3647	−	10.7714i	0.508173	−	0.528109i
$417$	−2.97214	+	5.14789i	−0.145546	+	0.252093i
$418$	9.00000			0.440204
$419$	2.97214	−	5.14789i	0.145198	−	0.251491i	−0.784249	−	0.620447i	$-0.786951\pi$
$419$	2.97214	−	5.14789i	0.145198	−	0.251491i	0.929447	+	0.368956i	$0.120285\pi$
$420$		0			0
$421$	−25.4164			−1.23872			−0.619360	−	0.785107i	$-0.712608\pi$
$421$	−25.4164			−1.23872			−0.619360	+	0.785107i	$0.712608\pi$
$422$	1.66312	−	2.88061i	0.0809594	−	0.140226i
$423$	6.38197			0.310302
$424$	6.06231	−	10.5002i	0.294412	−	0.509936i
$425$	−18.1353	+	31.4112i	−0.879689	+	1.52367i
$426$	−0.596748	+	1.03360i	−0.0289125	+	0.0500780i
$427$		0			0
$428$	10.4164			0.503496
$429$	−1.85410	−	6.42280i	−0.0895169	−	0.310096i
$430$	−0.551663	+	0.955508i	−0.0266035	+	0.0460787i
$431$	8.39919	+	14.5478i	0.404575	+	0.700744i	0.994272	−	0.106881i	$-0.0340863\pi$
$431$	8.39919	+	14.5478i	0.404575	+	0.700744i	−0.589697	+	0.807624i	$0.700753\pi$
$432$	−7.03444			−0.338445
$433$	0.500000	+	0.866025i	0.0240285	+	0.0416185i	0.877790	−	0.479046i	$-0.159017\pi$
$433$	0.500000	+	0.866025i	0.0240285	+	0.0416185i	−0.853761	+	0.520665i	$0.825684\pi$
$434$		0			0
$435$	−0.298374	−	0.516799i	−0.0143059	−	0.0247786i
$436$	9.92705	−	17.1942i	0.475420	−	0.823451i
$437$	10.8541	−	18.7999i	0.519222	−	0.899319i
$438$	0.291796			0.0139426
$439$	−8.14590			−0.388783			−0.194391	−	0.980924i	$-0.562273\pi$
$439$	−8.14590			−0.388783			−0.194391	+	0.980924i	$0.562273\pi$
$440$	1.36475	−	2.36381i	0.0650617	−	0.112690i
$441$		0			0
$442$	−7.13525	+	7.41517i	−0.339389	+	0.352704i
$443$	0.381966	+	0.661585i	0.0181478	+	0.0314328i	0.874957	−	0.484201i	$-0.160890\pi$
$443$	0.381966	+	0.661585i	0.0181478	+	0.0314328i	−0.856809	+	0.515634i	$0.827556\pi$
$444$	1.41641	+	2.45329i	0.0672197	+	0.116428i
$445$	−3.07295	−	5.32250i	−0.145672	−	0.252311i
$446$	−2.53444	+	4.38978i	−0.120009	+	0.207862i
$447$	−1.85410			−0.0876960
$448$		0			0
$449$	−14.2361	−	24.6576i	−0.671842	−	1.16366i	−0.977381	−	0.211484i	$-0.932170\pi$
$449$	−14.2361	−	24.6576i	−0.671842	−	1.16366i	0.305540	−	0.952179i	$-0.401163\pi$
$450$	−2.64590	−	4.58283i	−0.124729	−	0.216037i
$451$	25.4164			1.19681
$452$	−6.92705	−	11.9980i	−0.325821	−	0.564339i
$453$	−5.61803			−0.263958
$454$	2.85410			0.133950
$455$		0			0
$456$	2.72949			0.127820
$457$	−11.4164			−0.534037			−0.267019	−	0.963691i	$-0.586038\pi$
$457$	−11.4164			−0.534037			−0.267019	+	0.963691i	$0.586038\pi$
$458$	5.18034	+	8.97261i	0.242061	+	0.419263i
$459$	16.7082			0.779872
$460$	−1.58359	−	2.74286i	−0.0738354	−	0.127887i
$461$	19.6074	+	33.9610i	0.913207	+	1.58172i	0.809505	+	0.587113i	$0.199736\pi$
$461$	19.6074	+	33.9610i	0.913207	+	1.58172i	0.103702	+	0.994608i	$0.466931\pi$
$462$		0			0
$463$	−6.70820			−0.311757			−0.155878	−	0.987776i	$-0.549821\pi$
$463$	−6.70820			−0.311757			−0.155878	+	0.987776i	$0.549821\pi$
$464$	6.43363	−	11.1434i	0.298674	−	0.517318i
$465$	−0.635255	−	1.10029i	−0.0294592	−	0.0510249i
$466$	−0.0729490	−	0.126351i	−0.00337930	−	0.00585312i
$467$	16.8262	+	29.1439i	0.778625	+	1.34862i	0.932734	+	0.360565i	$0.117416\pi$
$467$	16.8262	+	29.1439i	0.778625	+	1.34862i	−0.154109	+	0.988054i	$0.549251\pi$
$468$	5.29180	+	18.3313i	0.244613	+	0.847366i
$469$		0			0
$470$	−0.163119	+	0.282530i	−0.00752412	+	0.0130322i
$471$	−3.11146			−0.143368
$472$	3.29180			0.151517
$473$	−18.3541	+	31.7902i	−0.843923	+	1.46172i
$474$	−0.291796	+	0.505406i	−0.0134026	+	0.0232140i
$475$	−11.7812	−	20.4056i	−0.540556	−	0.936271i
$476$		0			0
$477$	11.7533	+	20.3573i	0.538146	+	0.932096i
$478$	−4.31308			−0.197276
$479$	−10.9894	−	19.0341i	−0.502117	−	0.869691i	−0.999997	−	0.00244569i	$-0.999222\pi$
$479$	−10.9894	−	19.0341i	−0.502117	−	0.869691i	0.497880	−	0.867246i	$-0.334112\pi$
$480$	0.302439	−	0.523840i	0.0138044	−	0.0239099i
$481$	10.0000	−	10.3923i	0.455961	−	0.473848i
$482$	−1.69505			−0.0772073
$483$		0			0
$484$	11.6459	−	20.1713i	0.529359	−	0.916877i
$485$	−2.31966	+	4.01777i	−0.105330	+	0.182438i
$486$	−1.84346	+	3.19296i	−0.0836210	+	0.144836i
$487$	−16.9787			−0.769379			−0.384689	−	0.923046i	$-0.625691\pi$
$487$	−16.9787			−0.769379			−0.384689	+	0.923046i	$0.625691\pi$
$488$	4.41641	−	7.64944i	0.199921	−	0.346274i
$489$	3.70820			0.167691
$490$		0			0
$491$	−7.30902	+	12.6596i	−0.329851	+	0.571319i	−0.982482	−	0.186357i	$-0.940332\pi$
$491$	−7.30902	+	12.6596i	−0.329851	+	0.571319i	0.652631	+	0.757676i	$0.273665\pi$
$492$	3.70820			0.167179
$493$	−15.2812	+	26.4677i	−0.688229	+	1.19205i
$494$	−1.85410	−	6.42280i	−0.0834200	−	0.288975i
$495$	2.64590	+	4.58283i	0.118924	+	0.205983i
$496$	13.6976	−	23.7249i	0.615039	−	1.06528i
$497$		0			0
$498$	−0.489357	−	0.847591i	−0.0219286	−	0.0379815i
$499$	−4.07295	−	7.05455i	−0.182330	−	0.315805i	0.760343	−	0.649521i	$-0.225031\pi$
$499$	−4.07295	−	7.05455i	−0.182330	−	0.315805i	−0.942674	+	0.333716i	$0.891697\pi$
$500$	−6.97871			−0.312098
$501$	−3.72949			−0.166621
$502$	1.00000	+	1.73205i	0.0446322	+	0.0773052i
$503$	12.1910	+	21.1154i	0.543569	+	0.941489i	0.998695	+	0.0510624i	$0.0162607\pi$
$503$	12.1910	+	21.1154i	0.543569	+	0.941489i	−0.455126	+	0.890427i	$0.650406\pi$
$504$		0			0
$505$	−1.63525	+	2.83234i	−0.0727679	+	0.126038i
$506$	4.14590	+	7.18091i	0.184308	+	0.319230i
$507$	−4.20163	+	2.64634i	−0.186601	+	0.117528i
$508$	−13.1140	+	22.7141i	−0.581838	+	1.00777i
$509$	−30.5967			−1.35618			−0.678089	−	0.734980i	$-0.737191\pi$
$509$	−30.5967			−1.35618			−0.678089	+	0.734980i	$0.737191\pi$
$510$	−0.208204	+	0.360620i	−0.00921943	+	0.0159685i
$511$		0			0
$512$	22.3050			0.985749
$513$	−5.42705	+	9.39993i	−0.239610	+	0.415017i
$514$	9.83282			0.433707
$515$	−0.899187	+	1.55744i	−0.0396229	+	0.0686289i
$516$	−2.67783	+	4.63813i	−0.117885	+	0.204182i
$517$	−5.42705	+	9.39993i	−0.238681	+	0.413408i
$518$		0			0
$519$	3.43769			0.150898
$520$	−1.96807	−	0.486971i	−0.0863056	−	0.0213551i
$521$	−6.32624	+	10.9574i	−0.277158	+	0.480051i	−0.970677	−	0.240387i	$-0.922726\pi$
$521$	−6.32624	+	10.9574i	−0.277158	+	0.480051i	0.693520	+	0.720438i	$0.256059\pi$
$522$	−2.22949	−	3.86159i	−0.0975821	−	0.169017i
$523$	39.1246			1.71080			0.855400	−	0.517968i	$-0.173311\pi$
$523$	39.1246			1.71080			0.855400	+	0.517968i	$0.173311\pi$
$524$	−0.302439	−	0.523840i	−0.0132121	−	0.0228841i
$525$		0			0
$526$	−1.71885	−	2.97713i	−0.0749453	−	0.129809i
$527$	−32.5344	+	56.3513i	−1.41722	+	2.45470i
$528$	2.91641	−	5.05137i	0.126920	−	0.219833i
$529$	−3.00000			−0.130435
$530$	−1.20163			−0.0521953
$531$	−3.19098	+	5.52694i	−0.138477	+	0.239849i
$532$		0			0
$533$	−5.23607	−	18.1383i	−0.226799	−	0.785656i
$534$	1.17376	+	2.03302i	0.0507937	+	0.0879772i
$535$	−1.07295	−	1.85840i	−0.0463876	−	0.0803457i
$536$	0.521286	+	0.902894i	0.0225161	+	0.0389991i
$537$	1.71885	−	2.97713i	0.0741737	−	0.128473i
$538$	−5.24922			−0.226310
$539$		0			0
$540$	0.791796	+	1.37143i	0.0340735	+	0.0590170i
$541$	−0.864745	−	1.49778i	−0.0371783	−	0.0643947i	0.846838	−	0.531852i	$-0.178504\pi$
$541$	−0.864745	−	1.49778i	−0.0371783	−	0.0643947i	−0.884016	+	0.467457i	$0.845170\pi$
$542$	−7.03444			−0.302155
$543$	−0.708204	−	1.22665i	−0.0303919	−	0.0526404i
$544$	−30.9787			−1.32820
$545$	−4.09017			−0.175204
$546$		0			0
$547$	−3.00000			−0.128271			−0.0641354	−	0.997941i	$-0.520429\pi$
$547$	−3.00000			−0.128271			−0.0641354	+	0.997941i	$0.520429\pi$
$548$	0.708204			0.0302530
$549$	8.56231	+	14.8303i	0.365430	+	0.632944i
$550$	9.00000			0.383761
$551$	−9.92705	−	17.1942i	−0.422907	−	0.732496i
$552$	1.25735	+	2.17780i	0.0535165	+	0.0926934i
$553$		0			0
$554$	−1.90983			−0.0811409
$555$	0.291796	−	0.505406i	0.0123861	−	0.0214533i
$556$	14.4271	+	24.9884i	0.611843	+	1.05974i
$557$	−9.48936	−	16.4360i	−0.402077	−	0.696418i	0.591899	−	0.806012i	$-0.298378\pi$
$557$	−9.48936	−	16.4360i	−0.402077	−	0.696418i	−0.993976	+	0.109594i	$0.965045\pi$
$558$	−4.74671	−	8.22154i	−0.200944	−	0.348046i
$559$	26.4681	+	6.54915i	1.11948	+	0.276999i
$560$		0			0
$561$	−6.92705	+	11.9980i	−0.292460	+	0.506556i
$562$	−0.832816			−0.0351302
$563$	38.9443			1.64131			0.820653	−	0.571427i	$-0.193610\pi$
$563$	38.9443			1.64131			0.820653	+	0.571427i	$0.193610\pi$
$564$	−0.791796	+	1.37143i	−0.0333406	+	0.0577477i
$565$	−1.42705	+	2.47172i	−0.0600365	+	0.103986i
$566$	−2.56231	−	4.43804i	−0.107702	−	0.186545i
$567$		0			0
$568$	6.02129	+	10.4292i	0.252648	+	0.437598i
$569$	−2.94427			−0.123430			−0.0617151	−	0.998094i	$-0.519657\pi$
$569$	−2.94427			−0.123430			−0.0617151	+	0.998094i	$0.519657\pi$
$570$	−0.135255	−	0.234268i	−0.00566521	−	0.00981242i
$571$	17.8435	−	30.9058i	0.746726	−	1.29337i	−0.202659	−	0.979249i	$-0.564958\pi$
$571$	17.8435	−	30.9058i	0.746726	−	1.29337i	0.949384	−	0.314117i	$-0.101708\pi$
$572$	−31.5000	−	7.79423i	−1.31708	−	0.325893i
$573$	9.02129			0.376870
$574$		0			0
$575$	10.8541	−	18.7999i	0.452647	−	0.784008i
$576$	−6.71885	+	11.6374i	−0.279952	+	0.484891i
$577$	4.91641	−	8.51547i	0.204673	−	0.354504i	−0.745356	−	0.666667i	$-0.767720\pi$
$577$	4.91641	−	8.51547i	0.204673	−	0.354504i	0.950028	+	0.312163i	$0.101054\pi$
$578$	14.8328			0.616964
$579$	1.14590	−	1.98475i	0.0476219	−	0.0824835i
$580$	−2.89667			−0.120278
$581$		0			0
$582$	0.886031	−	1.53465i	0.0367272	−	0.0636133i
$583$	−39.9787			−1.65575
$584$	1.47214	−	2.54981i	0.0609174	−	0.105512i
$585$	2.72542	−	2.83234i	0.112682	−	0.117103i
$586$	−2.14590	−	3.71680i	−0.0886462	−	0.153540i
$587$	−15.5451	+	26.9249i	−0.641614	+	1.11131i	0.343458	+	0.939168i	$0.388402\pi$
$587$	−15.5451	+	26.9249i	−0.641614	+	1.11131i	−0.985072	+	0.172141i	$0.944932\pi$
$588$		0			0
$589$	−21.1353	−	36.6073i	−0.870863	−	1.50838i
$590$	−0.163119	−	0.282530i	−0.00671550	−	0.0116316i
$591$	2.97871			0.122528
$592$	12.5836			0.517182
$593$	9.60081	+	16.6291i	0.394258	+	0.682875i	0.993006	−	0.118062i	$-0.0376683\pi$
$593$	9.60081	+	16.6291i	0.394258	+	0.682875i	−0.598748	+	0.800937i	$0.704335\pi$
$594$	−2.07295	−	3.59045i	−0.0850541	−	0.147318i
$595$		0			0
$596$	−4.50000	+	7.79423i	−0.184327	+	0.319264i
$597$	0.461493	+	0.799329i	0.0188876	+	0.0327144i
$598$	4.27051	−	4.43804i	0.174634	−	0.181485i
$599$	4.25329	−	7.36691i	0.173785	−	0.301004i	−0.765955	−	0.642894i	$-0.777734\pi$
$599$	4.25329	−	7.36691i	0.173785	−	0.301004i	0.939740	+	0.341890i	$0.111067\pi$
$600$	2.72949			0.111431
$601$	−16.6976	+	28.9210i	−0.681108	+	1.17971i	0.293535	+	0.955948i	$0.405168\pi$
$601$	−16.6976	+	28.9210i	−0.681108	+	1.17971i	−0.974643	+	0.223765i	$0.928165\pi$
$602$		0			0
$603$	−2.02129			−0.0823131
$604$	−13.6353	+	23.6170i	−0.554811	+	0.960960i
$605$	−4.79837			−0.195082
$606$	0.624612	−	1.08186i	0.0253731	−	0.0439475i
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	−0.999279	−	0.0379540i	$-0.987916\pi$
$607$	−11.5000	+	19.9186i	−0.466771	+	0.808470i	0.532509	+	0.846424i	$0.321249\pi$
$608$	10.0623	−	17.4284i	0.408080	−	0.706816i
$609$		0			0
$610$	−0.875388			−0.0354434
$611$	7.82624	+	1.93649i	0.316616	+	0.0783421i
$612$	19.7705	−	34.2435i	0.799175	−	1.38421i
$613$	−7.21885	−	12.5034i	−0.291566	−	0.505008i	0.682614	−	0.730779i	$-0.260843\pi$
$613$	−7.21885	−	12.5034i	−0.291566	−	0.505008i	−0.974180	+	0.225771i	$0.927510\pi$
$614$	−0.708204			−0.0285808
$615$	−0.381966	−	0.661585i	−0.0154024	−	0.0266777i
$616$		0			0
$617$	−8.97214	−	15.5402i	−0.361205	−	0.625625i	0.626955	−	0.779056i	$-0.284301\pi$
$617$	−8.97214	−	15.5402i	−0.361205	−	0.625625i	−0.988159	+	0.153431i	$0.950968\pi$
$618$	0.343459	−	0.594888i	0.0138159	−	0.0239299i
$619$	−8.70820	+	15.0831i	−0.350012	+	0.606239i	−0.986251	−	0.165253i	$-0.947156\pi$
$619$	−8.70820	+	15.0831i	−0.350012	+	0.606239i	0.636239	+	0.771492i	$0.280489\pi$
$620$	−6.16718			−0.247680
$621$	−10.0000			−0.401286
$622$	−2.35410	+	4.07742i	−0.0943909	+	0.163490i
$623$		0			0
$624$	−4.20569	−	1.04064i	−0.168362	−	0.0416589i
$625$	−11.4164	−	19.7738i	−0.456656	−	0.790952i
$626$	−2.88854	−	5.00310i	−0.115449	−	0.199964i
$627$	−4.50000	−	7.79423i	−0.179713	−	0.311272i
$628$	−7.55166	+	13.0799i	−0.301344	+	0.521943i
$629$	−29.8885			−1.19173
$630$		0			0
$631$	19.6976	+	34.1172i	0.784148	+	1.35818i	0.929507	+	0.368804i	$0.120233\pi$
$631$	19.6976	+	34.1172i	0.784148	+	1.35818i	−0.145360	+	0.989379i	$0.546434\pi$
$632$	2.94427	+	5.09963i	0.117117	+	0.202852i
$633$	−3.32624			−0.132206
$634$	−4.15654	−	7.19934i	−0.165077	−	0.285922i
$635$	5.40325			0.214422
$636$	−5.83282			−0.231286
$637$		0			0
$638$	7.58359			0.300237
$639$	−23.3475			−0.923614
$640$	−1.92705	−	3.33775i	−0.0761734	−	0.131936i
$641$	−9.49342			−0.374968			−0.187484	−	0.982268i	$-0.560033\pi$
$641$	−9.49342			−0.374968			−0.187484	+	0.982268i	$0.560033\pi$
$642$	0.409830	+	0.709846i	0.0161747	+	0.0280154i
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	0.788723	−	0.614749i	$-0.210743\pi$
$643$	−3.50000	−	6.06218i	−0.138027	−	0.239069i	−0.926750	+	0.375680i	$0.877409\pi$
$644$		0			0
$645$	1.10333			0.0434434
$646$	−6.92705	+	11.9980i	−0.272541	+	0.472055i
$647$	14.6180	+	25.3192i	0.574694	+	0.995400i	0.996075	+	0.0885157i	$0.0282123\pi$
$647$	14.6180	+	25.3192i	0.574694	+	0.995400i	−0.421381	+	0.906884i	$0.638454\pi$
$648$	5.67376	+	9.82724i	0.222886	+	0.386051i
$649$	−5.42705	−	9.39993i	−0.213030	−	0.368979i
$650$	−1.85410	−	6.42280i	−0.0727239	−	0.251923i
$651$		0			0
$652$	9.00000	−	15.5885i	0.352467	−	0.610491i
$653$	−2.61803			−0.102452			−0.0512258	−	0.998687i	$-0.516313\pi$
$653$	−2.61803			−0.102452			−0.0512258	+	0.998687i	$0.516313\pi$
$654$	1.56231			0.0610910
$655$	−0.0623059	+	0.107917i	−0.00243449	+	0.00421667i
$656$	8.23607	−	14.2653i	0.321564	−	0.556966i
$657$	2.85410	+	4.94345i	0.111349	+	0.192862i
$658$		0			0
$659$	−5.94427	−	10.2958i	−0.231556	−	0.401067i	0.726710	−	0.686944i	$-0.241048\pi$
$659$	−5.94427	−	10.2958i	−0.231556	−	0.401067i	−0.958266	+	0.285877i	$0.907715\pi$
$660$	−1.31308			−0.0511117
$661$	9.27051	+	16.0570i	0.360581	+	0.624545i	0.988057	−	0.154092i	$-0.0492451\pi$
$661$	9.27051	+	16.0570i	0.360581	+	0.624545i	−0.627476	+	0.778636i	$0.715912\pi$
$662$	3.21885	−	5.57521i	0.125104	−	0.216687i
$663$	9.98936	+	2.47172i	0.387954	+	0.0959938i
$664$	−9.87539			−0.383239
$665$		0			0
$666$	2.18034	−	3.77646i	0.0844865	−	0.146335i
$667$	9.14590	−	15.8412i	0.354131	−	0.613372i
$668$	−9.05166	+	15.6779i	−0.350219	+	0.606598i
$669$	5.06888			0.195974
$670$	0.0516628	−	0.0894826i	0.00199591	−	0.00345701i
$671$	−29.1246			−1.12434
$672$		0			0
$673$	−20.6246	+	35.7229i	−0.795020	+	1.37702i	0.127806	+	0.991799i	$0.459207\pi$
$673$	−20.6246	+	35.7229i	−0.795020	+	1.37702i	−0.922826	+	0.385216i	$0.874127\pi$
$674$	3.27051			0.125975
$675$	−5.42705	+	9.39993i	−0.208887	+	0.361803i
$676$	0.927051	+	24.0855i	0.0356558	+	0.926365i
$677$	0.628677	+	1.08890i	0.0241620	+	0.0418499i	0.877854	−	0.478929i	$-0.158975\pi$
$677$	0.628677	+	1.08890i	0.0241620	+	0.0418499i	−0.853692	+	0.520779i	$0.825642\pi$
$678$	0.545085	−	0.944115i	0.0209339	−	0.0362585i
$679$		0			0
$680$	2.10081	+	3.63871i	0.0805625	+	0.139538i
$681$	−1.42705	−	2.47172i	−0.0546847	−	0.0947167i
$682$	16.1459			0.618258
$683$	−7.47214			−0.285913			−0.142957	−	0.989729i	$-0.545661\pi$
$683$	−7.47214			−0.285913			−0.142957	+	0.989729i	$0.545661\pi$
$684$	12.8435	+	22.2455i	0.491082	+	0.850579i
$685$	−0.0729490	−	0.126351i	−0.00278724	−	0.00482764i
$686$		0			0
$687$	5.18034	−	8.97261i	0.197642	−	0.342326i
$688$	11.8951	+	20.6030i	0.453497	+	0.785480i
$689$	8.23607	+	28.5306i	0.313769	+	1.08693i
$690$	0.124612	−	0.215834i	0.00474389	−	0.00821666i
$691$	−0.854102			−0.0324916			−0.0162458	−	0.999868i	$-0.505171\pi$
$691$	−0.854102			−0.0324916			−0.0162458	+	0.999868i	$0.505171\pi$
$692$	8.34346	−	14.4513i	0.317171	−	0.549356i
$693$		0			0
$694$	13.4590			0.510896
$695$	2.97214	−	5.14789i	0.112740	−	0.195271i
$696$	2.29993			0.0871785
$697$	−19.5623	+	33.8829i	−0.740975	+	1.28341i
$698$	1.39261	−	2.41207i	0.0527110	−	0.0912982i
$699$	−0.0729490	+	0.126351i	−0.00275919	+	0.00477905i
$700$		0			0
$701$	6.76393			0.255470			0.127735	−	0.991808i	$-0.459229\pi$
$701$	6.76393			0.255470			0.127735	+	0.991808i	$0.459229\pi$
$702$	−2.13525	+	2.21902i	−0.0805900	+	0.0837516i
$703$	9.70820	−	16.8151i	0.366152	−	0.634194i
$704$	−11.4271	−	19.7922i	−0.430673	−	0.745948i
$705$	0.326238			0.0122868
$706$	5.51064	+	9.54471i	0.207396	+	0.359220i
$707$		0			0
$708$	−0.791796	−	1.37143i	−0.0297575	−	0.0515415i
$709$	−1.71885	+	2.97713i	−0.0645527	+	0.111808i	−0.896495	−	0.443053i	$-0.853895\pi$
$709$	−1.71885	+	2.97713i	−0.0645527	+	0.111808i	0.831943	+	0.554861i	$0.187229\pi$
$710$	0.596748	−	1.03360i	0.0223955	−	0.0387902i
$711$	−11.4164			−0.428149
$712$	23.6869			0.887705
$713$	19.4721	−	33.7267i	0.729237	−	1.26308i
$714$		0			0
$715$	1.85410	+	6.42280i	0.0693395	+	0.240199i
$716$	−8.34346	−	14.4513i	−0.311810	−	0.540070i
$717$	2.15654	+	3.73524i	0.0805375	+	0.139495i
$718$	2.08359	+	3.60889i	0.0777590	+	0.134682i
$719$	−16.0623	+	27.8207i	−0.599023	+	1.03754i	0.393943	+	0.919135i	$0.371111\pi$
$719$	−16.0623	+	27.8207i	−0.599023	+	1.03754i	−0.992966	+	0.118403i	$0.962222\pi$
$720$	3.42956			0.127812
$721$		0			0
$722$	−0.871323	−	1.50918i	−0.0324273	−	0.0561657i
$723$	0.847524	+	1.46795i	0.0315198	+	0.0545938i
$724$	−6.87539			−0.255522
$725$	−9.92705	−	17.1942i	−0.368681	−	0.638575i
$726$	1.83282			0.0680222
$727$	17.2918			0.641317			0.320659	−	0.947195i	$-0.396096\pi$
$727$	17.2918			0.641317			0.320659	+	0.947195i	$0.396096\pi$
$728$		0			0
$729$	−19.4377			−0.719915
$730$	−0.291796			−0.0107999
$731$	−28.2533	−	48.9361i	−1.04499	−	1.80997i
$732$	−4.24922			−0.157056
$733$	0.635255	+	1.10029i	0.0234637	+	0.0406403i	0.877519	−	0.479542i	$-0.159197\pi$
$733$	0.635255	+	1.10029i	0.0234637	+	0.0406403i	−0.854055	+	0.520182i	$0.825864\pi$
$734$	4.85410	+	8.40755i	0.179168	+	0.310328i
$735$		0			0
$736$	18.5410			0.683431
$737$	1.71885	−	2.97713i	0.0633145	−	0.109664i
$738$	−2.85410	−	4.94345i	−0.105061	−	0.181971i
$739$	23.5623	+	40.8111i	0.866753	+	1.50126i	0.865296	+	0.501262i	$0.167131\pi$
$739$	23.5623	+	40.8111i	0.866753	+	1.50126i	0.00145790	+	0.999999i	$0.499536\pi$
$740$	−1.41641	−	2.45329i	−0.0520682	−	0.0901847i
$741$	−4.63525	+	4.81710i	−0.170280	+	0.176961i
$742$		0			0
$743$	−11.8369	+	20.5021i	−0.434253	+	0.752148i	−0.997234	−	0.0743213i	$-0.976321\pi$
$743$	−11.8369	+	20.5021i	−0.434253	+	0.752148i	0.562981	+	0.826470i	$0.309654\pi$
$744$	4.89667			0.179521
$745$	1.85410			0.0679290
$746$	0.0835921	−	0.144786i	0.00306053	−	0.00530099i
$747$	9.57295	−	16.5808i	0.350256	−	0.606661i
$748$	33.6246	+	58.2395i	1.22944	+	2.12945i
$749$		0			0
$750$	−0.274575	−	0.475578i	−0.0100261	−	0.0173657i
$751$	9.29180			0.339062			0.169531	−	0.985525i	$-0.445775\pi$
$751$	9.29180			0.339062			0.169531	+	0.985525i	$0.445775\pi$
$752$	3.51722	+	6.09201i	0.128260	+	0.222153i
$753$	1.00000	−	1.73205i	0.0364420	−	0.0631194i
$754$	−1.56231	−	5.41199i	−0.0568958	−	0.197093i
$755$	5.61803			0.204461
$756$		0			0
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	0.491109	+	0.871098i	$0.336592\pi$
$757$	−14.0000	+	24.2487i	−0.508839	+	0.881334i	−0.999948	+	0.0102362i	$0.996742\pi$
$758$	2.45492	−	4.25204i	0.0891665	−	0.154441i
$759$	4.14590	−	7.18091i	0.150487	−	0.260650i
$760$	−2.72949			−0.0990090
$761$	−11.0729	+	19.1789i	−0.401394	+	0.695235i	−0.993894	−	0.110335i	$-0.964808\pi$
$761$	−11.0729	+	19.1789i	−0.401394	+	0.695235i	0.592500	+	0.805570i	$0.298141\pi$
$762$	−2.06386			−0.0747657
$763$		0			0
$764$	21.8951	−	37.9235i	0.792138	−	1.37202i
$765$	−8.14590			−0.294516
$766$	4.77051	−	8.26277i	0.172366	−	0.298546i
$767$	−5.59017	+	5.80948i	−0.201849	+	0.209768i
$768$	−1.06231	−	1.83997i	−0.0383327	−	0.0663941i
$769$	4.20820	−	7.28882i	0.151752	−	0.262842i	−0.780120	−	0.625630i	$-0.784842\pi$
$769$	4.20820	−	7.28882i	0.151752	−	0.262842i	0.931872	+	0.362788i	$0.118175\pi$
$770$		0			0
$771$	−4.91641	−	8.51547i	−0.177060	−	0.306677i
$772$	−5.56231	−	9.63420i	−0.200192	−	0.346742i
$773$	19.3607			0.696355			0.348178	−	0.937429i	$-0.386801\pi$
$773$	19.3607			0.696355			0.348178	+	0.937429i	$0.386801\pi$
$774$	8.24420			0.296332
$775$	−21.1353	−	36.6073i	−0.759201	−	1.31497i
$776$	−8.94021	−	15.4849i	−0.320935	−	0.555875i
$777$		0			0
$778$	−4.56231	+	7.90215i	−0.163567	+	0.283306i
$779$	−12.7082	−	22.0113i	−0.455319	−	0.788635i
$780$	0.270510	+	0.937074i	0.00968581	+	0.0335526i
$781$	19.8541	−	34.3883i	0.710436	−	1.23051i
$782$	−12.7639			−0.456437
$783$	−4.57295	+	7.92058i	−0.163424	+	0.283058i
$784$		0			0
$785$	3.11146			0.111053
$786$	0.0237987	−	0.0412206i	0.000848873	−	0.00147029i
$787$	−29.4164			−1.04858			−0.524291	−	0.851539i	$-0.675670\pi$
$787$	−29.4164			−1.04858			−0.524291	+	0.851539i	$0.675670\pi$
$788$	7.22949	−	12.5218i	0.257540	−	0.446072i
$789$	−1.71885	+	2.97713i	−0.0611926	+	0.105989i
$790$	0.291796	−	0.505406i	0.0103816	−	0.0179815i
$791$		0			0
$792$	−20.3951			−0.724709
$793$	6.00000	+	20.7846i	0.213066	+	0.738083i
$794$	−4.85410	+	8.40755i	−0.172266	+	0.298373i
$795$	0.600813	+	1.04064i	0.0213086	+	0.0369077i
$796$	4.48027			0.158799
$797$	7.09017	+	12.2805i	0.251147	+	0.434999i	0.963842	−	0.266475i	$-0.0858590\pi$
$797$	7.09017	+	12.2805i	0.251147	+	0.434999i	−0.712695	+	0.701474i	$0.752526\pi$
$798$		0			0
$799$	−8.35410	−	14.4697i	−0.295547	−	0.511902i
$800$	10.0623	−	17.4284i	0.355756	−	0.616188i
$801$	−22.9615	+	39.7705i	−0.811304	+	1.40522i
$802$	−7.81153			−0.275835
$803$	−9.70820			−0.342595
$804$	0.250776	−	0.434357i	0.00884420	−	0.0153186i
$805$		0			0
$806$	−3.32624	−	11.5224i	−0.117162	−	0.405860i
$807$	2.62461	+	4.54596i	0.0923907	+	0.160025i
$808$	−6.30244	−	10.9161i	−0.221719	−	0.384029i
$809$	−11.2082	−	19.4132i	−0.394059	−	0.682531i	0.598921	−	0.800808i	$-0.295596\pi$
$809$	−11.2082	−	19.4132i	−0.394059	−	0.682531i	−0.992981	+	0.118277i	$0.962263\pi$
$810$	0.562306	−	0.973942i	0.0197574	−	0.0342208i
$811$	−5.72949			−0.201190			−0.100595	−	0.994927i	$-0.532075\pi$
$811$	−5.72949			−0.201190			−0.100595	+	0.994927i	$0.532075\pi$
$812$		0			0
$813$	3.51722	+	6.09201i	0.123354	+	0.213656i
$814$	3.70820	+	6.42280i	0.129972	+	0.225119i
$815$	−3.70820			−0.129893
$816$	4.48936	+	7.77579i	0.157159	+	0.272207i
$817$	36.7082			1.28426
$818$	−13.2016			−0.461584
$819$		0			0
$820$	−3.70820			−0.129496
$821$	37.3607			1.30390			0.651948	−	0.758263i	$-0.273952\pi$
$821$	37.3607			1.30390			0.651948	+	0.758263i	$0.273952\pi$
$822$	0.0278640	+	0.0482619i	0.000971870	+	0.00168333i
$823$	−11.5836			−0.403779			−0.201889	−	0.979408i	$-0.564708\pi$
$823$	−11.5836			−0.403779			−0.201889	+	0.979408i	$0.564708\pi$
$824$	−3.46556	−	6.00252i	−0.120728	−	0.209108i
$825$	−4.50000	−	7.79423i	−0.156670	−	0.271360i
$826$		0			0
$827$	−30.9787			−1.07724			−0.538618	−	0.842550i	$-0.681053\pi$
$827$	−30.9787			−1.07724			−0.538618	+	0.842550i	$0.681053\pi$
$828$	−11.8328	+	20.4950i	−0.411219	+	0.712252i
$829$	−6.28115	−	10.8793i	−0.218153	−	0.377853i	0.736090	−	0.676884i	$-0.236670\pi$
$829$	−6.28115	−	10.8793i	−0.218153	−	0.377853i	−0.954243	+	0.299031i	$0.903337\pi$
$830$	0.489357	+	0.847591i	0.0169858	+	0.0294203i
$831$	0.954915	+	1.65396i	0.0331256	+	0.0573753i
$832$	−11.7705	+	12.2323i	−0.408069	+	0.424078i
$833$		0			0
$834$	−1.13525	+	1.96632i	−0.0393107	+	0.0680881i
$835$	3.72949			0.129064
$836$	−43.6869			−1.51094
$837$	−9.73607	+	16.8634i	−0.336528	+	0.582883i
$838$	1.13525	−	1.96632i	0.0392167	−	0.0679254i
$839$	−14.3713	−	24.8919i	−0.496153	−	0.859362i	0.503837	−	0.863799i	$-0.331921\pi$
$839$	−14.3713	−	24.8919i	−0.496153	−	0.859362i	−0.999990	+	0.00443626i	$0.998588\pi$
$840$		0			0
$841$	6.13525	+	10.6266i	0.211561	+	0.366434i
$842$	−9.70820			−0.334567
$843$	0.416408	+	0.721240i	0.0143418	+	0.0248408i
$844$	−8.07295	+	13.9828i	−0.277882	+	0.481306i
$845$	4.20163	−	2.64634i	0.144540	−	0.0910368i
$846$	2.43769			0.0838096
$847$		0			0
$848$	−12.9549	+	22.4386i	−0.444874	+	0.770544i
$849$	−2.56231	+	4.43804i	−0.0879381	+	0.152313i
$850$	−6.92705	+	11.9980i	−0.237596	+	0.411528i
$851$	17.8885			0.613211
$852$	2.89667	−	5.01719i	0.0992384	−	0.171886i
$853$	26.1246			0.894490			0.447245	−	0.894412i	$-0.352405\pi$
$853$	26.1246			0.894490			0.447245	+	0.894412i	$0.352405\pi$
$854$		0			0
$855$	2.64590	−	4.58283i	0.0904878	−	0.156729i
$856$	8.27051			0.282680
$857$	14.7254	−	25.5052i	0.503011	−	0.871240i	−0.496983	−	0.867760i	$-0.665559\pi$
$857$	14.7254	−	25.5052i	0.503011	−	0.871240i	0.999994	−	0.00348022i	$-0.00110779\pi$
$858$	−0.708204	−	2.45329i	−0.0241777	−	0.0837540i
$859$	18.1246	+	31.3927i	0.618404	+	1.07111i	0.989777	+	0.142623i	$0.0455537\pi$
$859$	18.1246	+	31.3927i	0.618404	+	1.07111i	−0.371373	+	0.928484i	$0.621113\pi$
$860$	2.67783	−	4.63813i	0.0913132	−	0.158159i
$861$		0			0
$862$	3.20820	+	5.55677i	0.109272	+	0.189264i
$863$	11.9443	+	20.6881i	0.406588	+	0.704231i	0.994505	−	0.104691i	$-0.0333852\pi$
$863$	11.9443	+	20.6881i	0.406588	+	0.704231i	−0.587917	+	0.808921i	$0.700052\pi$
$864$	−9.27051			−0.315389
$865$	−3.43769			−0.116885
$866$	0.190983	+	0.330792i	0.00648987	+	0.0112408i
$867$	−7.41641	−	12.8456i	−0.251874	−	0.436259i
$868$		0			0
$869$	9.70820	−	16.8151i	0.329328	−	0.570413i
$870$	−0.113969	−	0.197400i	−0.00386390	−	0.00669247i
$871$	−2.47871	−	0.613323i	−0.0839880	−	0.0207816i
$872$	7.88197	−	13.6520i	0.266917	−	0.462314i
$873$	34.6656			1.17325
$874$	4.14590	−	7.18091i	0.140237	−	0.242898i
$875$		0			0
$876$	−1.41641			−0.0478560
$877$	6.35410	−	11.0056i	0.214563	−	0.371634i	−0.738574	−	0.674172i	$-0.764501\pi$
$877$	6.35410	−	11.0056i	0.214563	−	0.371634i	0.953137	+	0.302538i	$0.0978340\pi$
$878$	−3.11146			−0.105007
$879$	−2.14590	+	3.71680i	−0.0723793	+	0.125365i
$880$	−2.91641	+	5.05137i	−0.0983121	+	0.170282i
$881$	6.29837	−	10.9091i	0.212198	−	0.367537i	−0.740204	−	0.672382i	$-0.765271\pi$
$881$	6.29837	−	10.9091i	0.212198	−	0.367537i	0.952402	+	0.304845i	$0.0986046\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	34.6353	−	35.9940i	1.16491	−	1.21061i
$885$	−0.163119	+	0.282530i	−0.00548318	+	0.00949715i
$886$	0.145898	+	0.252703i	0.00490154	+	0.00848972i
$887$	−23.3475			−0.783933			−0.391967	−	0.919979i	$-0.628205\pi$
$887$	−23.3475			−0.783933			−0.391967	+	0.919979i	$0.628205\pi$
$888$	1.12461	+	1.94788i	0.0377395	+	0.0653667i
$889$		0			0
$890$	−1.17376	−	2.03302i	−0.0393446	−	0.0681468i
$891$	18.7082	−	32.4036i	0.626748	−	1.08556i
$892$	12.3024	−	21.3084i	0.411916	−	0.713460i
$893$	10.8541			0.363219
$894$	−0.708204			−0.0236859
$895$	−1.71885	+	2.97713i	−0.0574547	+	0.0995145i
$896$		0			0
$897$	−5.97871	−	1.47935i	−0.199623	−	0.0493940i
$898$	−5.43769	−	9.41836i	−0.181458	−	0.314295i
$899$	−17.8090	−	30.8461i	−0.593964	−	1.02878i
$900$	12.8435	+	22.2455i	0.428115	+	0.741517i
$901$	30.7705	−	53.2961i	1.02511	−	1.77555i
$902$	9.70820			0.323248
$903$		0			0
$904$	−5.50000	−	9.52628i	−0.182927	−	0.316839i
$905$	0.708204	+	1.22665i	0.0235415	+	0.0407751i
$906$	−2.14590			−0.0712927
$907$	12.0000	+	20.7846i	0.398453	+	0.690142i	0.993535	−	0.113523i	$-0.0362137\pi$
$907$	12.0000	+	20.7846i	0.398453	+	0.690142i	−0.595082	+	0.803665i	$0.702880\pi$
$908$	−13.8541			−0.459765
$909$	24.4377			0.810547
$910$		0			0
$911$	37.6869			1.24862			0.624312	−	0.781175i	$-0.285380\pi$
$911$	37.6869			1.24862			0.624312	+	0.781175i	$0.285380\pi$
$912$	−5.83282			−0.193144
$913$	16.2812	+	28.1998i	0.538828	+	0.933277i
$914$	−4.36068			−0.144238
$915$	0.437694	+	0.758108i	0.0144697	+	0.0250623i
$916$	−25.1459	−	43.5540i	−0.830844	−	1.43906i
$917$		0			0
$918$	6.38197			0.210636
$919$	15.0000	−	25.9808i	0.494804	−	0.857026i	−0.505178	−	0.863015i	$-0.668573\pi$
$919$	15.0000	−	25.9808i	0.494804	−	0.857026i	0.999982	+	0.00598907i	$0.00190639\pi$
$920$	−1.25735	−	2.17780i	−0.0414537	−	0.0718000i
$921$	0.354102	+	0.613323i	0.0116681	+	0.0202097i
$922$	7.48936	+	12.9719i	0.246649	+	0.427208i
$923$	−28.6312	−	7.08438i	−0.942407	−	0.233185i
$924$		0			0
$925$	9.70820	−	16.8151i	0.319204	−	0.552877i
$926$	−2.56231			−0.0842026
$927$	13.4377			0.441352
$928$	8.47871	−	14.6856i	0.278327	−	0.482077i
$929$	−23.5344	+	40.7628i	−0.772140	+	1.33739i	0.164248	+	0.986419i	$0.447480\pi$
$929$	−23.5344	+	40.7628i	−0.772140	+	1.33739i	−0.936388	+	0.350967i	$0.885853\pi$
$930$	−0.242646	−	0.420275i	−0.00795667	−	0.0137814i
$931$		0			0
$932$	0.354102	+	0.613323i	0.0115990	+	0.0200900i
$933$	4.70820			0.154140
$934$	6.42705	+	11.1320i	0.210300	+	0.364249i
$935$	6.92705	−	11.9980i	0.226539	−	0.392377i
$936$	4.20163	+	14.5549i	0.137334	+	0.475740i
$937$	56.1246			1.83351			0.916756	−	0.399449i	$-0.130798\pi$
$937$	56.1246			1.83351			0.916756	+	0.399449i	$0.130798\pi$
$938$		0			0
$939$	−2.88854	+	5.00310i	−0.0942641	+	0.163270i
$940$	0.791796	−	1.37143i	0.0258255	−	0.0447311i
$941$	25.8262	−	44.7324i	0.841911	−	1.45823i	−0.0463655	−	0.998925i	$-0.514764\pi$
$941$	25.8262	−	44.7324i	0.841911	−	1.45823i	0.888277	−	0.459309i	$-0.151903\pi$
$942$	−1.18847			−0.0387225
$943$	11.7082	−	20.2792i	0.381272	−	0.660382i
$944$	−7.03444			−0.228952
$945$		0			0
$946$	−7.01064	+	12.1428i	−0.227936	+	0.394796i
$947$	45.8673			1.49049			0.745243	−	0.666793i	$-0.232334\pi$
$947$	45.8673			1.49049			0.745243	+	0.666793i	$0.232334\pi$
$948$	1.41641	−	2.45329i	0.0460028	−	0.0796792i
$949$	2.00000	+	6.92820i	0.0649227	+	0.224899i
$950$	−4.50000	−	7.79423i	−0.145999	−	0.252878i
$951$	−4.15654	+	7.19934i	−0.134785	+	0.233455i
$952$		0			0
$953$	22.3885	+	38.7781i	0.725236	+	1.25615i	0.958877	+	0.283823i	$0.0916027\pi$
$953$	22.3885	+	38.7781i	0.725236	+	1.25615i	−0.233641	+	0.972323i	$0.575064\pi$
$954$	4.48936	+	7.77579i	0.145348	+	0.251751i
$955$	−9.02129			−0.291922
$956$	20.9361			0.677123
$957$	−3.79180	−	6.56758i	−0.122571	−	0.212300i
$958$	−4.19756	−	7.27039i	−0.135617	−	0.234896i
$959$		0			0
$960$	−0.343459	+	0.594888i	−0.0110851	+	0.0191999i
$961$	−22.4164	−	38.8264i	−0.723110	−	1.25246i
$962$	3.81966	−	3.96951i	0.123151	−	0.127982i
$963$	−8.01722	+	13.8862i	−0.258351	+	0.447478i
$964$	8.22794			0.265004
$965$	−1.14590	+	1.98475i	−0.0368878	+	0.0638915i
$966$		0			0
$967$	−39.0000			−1.25416			−0.627078	−	0.778957i	$-0.715749\pi$
$967$	−39.0000			−1.25416			−0.627078	+	0.778957i	$0.715749\pi$
$968$	9.24671	−	16.0158i	0.297201	−	0.514766i
$969$	13.8541			0.445058
$970$	−0.886031	+	1.53465i	−0.0284488	+	0.0492747i
$971$	29.2082	−	50.5901i	0.937336	−	1.62351i	0.166921	−	0.985970i	$-0.446617\pi$
$971$	29.2082	−	50.5901i	0.937336	−	1.62351i	0.770415	−	0.637543i	$-0.220049\pi$
$972$	8.94834	−	15.4990i	0.287018	−	0.497130i
$973$		0			0
$974$	−6.48529			−0.207802
$975$	−4.63525	+	4.81710i	−0.148447	+	0.154271i
$976$	−9.43769	+	16.3466i	−0.302093	+	0.523241i
$977$	15.7361	+	27.2557i	0.503441	+	0.871986i	0.999992	+	0.00397838i	$0.00126636\pi$
$977$	15.7361	+	27.2557i	0.503441	+	0.871986i	−0.496551	+	0.868008i	$0.665400\pi$
$978$	1.41641			0.0452917
$979$	−39.0517	−	67.6395i	−1.24810	−	2.16177i
$980$		0			0
$981$	15.2812	+	26.4677i	0.487890	+	0.845050i
$982$	−2.79180	+	4.83553i	−0.0890898	+	0.154308i
$983$	10.3090	−	17.8557i	0.328807	−	0.569510i	−0.653469	−	0.756953i	$-0.726687\pi$
$983$	10.3090	−	17.8557i	0.328807	−	0.569510i	0.982275	+	0.187444i	$0.0600202\pi$
$984$	2.94427			0.0938600
$985$	−2.97871			−0.0949097
$986$	−5.83688	+	10.1098i	−0.185884	+	0.321961i
$987$		0			0
$988$	9.00000	+	31.1769i	0.286328	+	0.991870i
$989$	16.9098	+	29.2887i	0.537701	+	0.931326i
$990$	1.01064	+	1.75049i	0.0321203	+	0.0556341i
$991$	11.4271	+	19.7922i	0.362992	+	0.628721i	0.988452	−	0.151536i	$-0.0484218\pi$
$991$	11.4271	+	19.7922i	0.362992	+	0.628721i	−0.625460	+	0.780257i	$0.715088\pi$
$992$	18.0517	−	31.2664i	0.573141	−	0.992709i
$993$	−6.43769			−0.204294
$994$		0			0
$995$	−0.461493	−	0.799329i	−0.0146303	−	0.0253404i
$996$	2.37539	+	4.11429i	0.0752671	+	0.130366i
$997$	−49.0000			−1.55185			−0.775923	−	0.630828i	$-0.782715\pi$
$997$	−49.0000			−1.55185			−0.775923	+	0.630828i	$0.782715\pi$
$998$	−1.55573	−	2.69460i	−0.0492457	−	0.0852961i
$999$	−8.94427			−0.282984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.f.165.1		4
7.2	even	3		637.2.g.c.373.2		4
7.3	odd	6		91.2.f.a.22.2	✓	4
7.4	even	3		637.2.f.c.295.2		4
7.5	odd	6		637.2.g.b.373.2		4
7.6	odd	2		637.2.h.g.165.1		4
13.3	even	3		637.2.g.c.263.2		4
21.17	even	6		819.2.o.c.568.1		4
28.3	even	6		1456.2.s.h.113.2		4
91.3	odd	6		91.2.f.a.29.2	yes	4
91.4	even	6		8281.2.a.n.1.2		2
91.16	even	3	inner	637.2.h.f.471.1		4
91.17	odd	6		1183.2.a.c.1.2		2
91.45	even	12		1183.2.c.c.337.2		4
91.55	odd	6		637.2.g.b.263.2		4
91.59	even	12		1183.2.c.c.337.3		4
91.68	odd	6		637.2.h.g.471.1		4
91.74	even	3		8281.2.a.bb.1.1		2
91.81	even	3		637.2.f.c.393.2		4
91.87	odd	6		1183.2.a.g.1.1		2
273.185	even	6		819.2.o.c.757.1		4
364.3	even	6		1456.2.s.h.1121.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.2	✓	4	7.3	odd	6
91.2.f.a.29.2	yes	4	91.3	odd	6
637.2.f.c.295.2		4	7.4	even	3
637.2.f.c.393.2		4	91.81	even	3
637.2.g.b.263.2		4	91.55	odd	6
637.2.g.b.373.2		4	7.5	odd	6
637.2.g.c.263.2		4	13.3	even	3
637.2.g.c.373.2		4	7.2	even	3
637.2.h.f.165.1		4	1.1	even	1	trivial
637.2.h.f.471.1		4	91.16	even	3	inner
637.2.h.g.165.1		4	7.6	odd	2
637.2.h.g.471.1		4	91.68	odd	6
819.2.o.c.568.1		4	21.17	even	6
819.2.o.c.757.1		4	273.185	even	6
1183.2.a.c.1.2		2	91.17	odd	6
1183.2.a.g.1.1		2	91.87	odd	6
1183.2.c.c.337.2		4	91.45	even	12
1183.2.c.c.337.3		4	91.59	even	12
1456.2.s.h.113.2		4	28.3	even	6
1456.2.s.h.1121.2		4	364.3	even	6
8281.2.a.n.1.2		2	91.4	even	6
8281.2.a.bb.1.1		2	91.74	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.381966 q^{2} +(-0.190983 - 0.330792i) q^{3} -1.85410 q^{4} +(0.190983 + 0.330792i) q^{5} +(-0.0729490 - 0.126351i) q^{6} -1.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +O(q^{10})\)	\(q+0.381966 q^{2} +(-0.190983 - 0.330792i) q^{3} -1.85410 q^{4} +(0.190983 + 0.330792i) q^{5} +(-0.0729490 - 0.126351i) q^{6} -1.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +(0.0729490 + 0.126351i) q^{10} +(2.42705 + 4.20378i) q^{11} +(0.354102 + 0.613323i) q^{12} +(2.50000 - 2.59808i) q^{13} +(0.0729490 - 0.126351i) q^{15} +3.14590 q^{16} -7.47214 q^{17} +(0.545085 - 0.944115i) q^{18} +(2.42705 - 4.20378i) q^{19} +(-0.354102 - 0.613323i) q^{20} +(0.927051 + 1.60570i) q^{22} +4.47214 q^{23} +(0.281153 + 0.486971i) q^{24} +(2.42705 - 4.20378i) q^{25} +(0.954915 - 0.992377i) q^{26} -2.23607 q^{27} +(2.04508 - 3.54219i) q^{29} +(0.0278640 - 0.0482619i) q^{30} +(4.35410 - 7.54153i) q^{31} +4.14590 q^{32} +(0.927051 - 1.60570i) q^{33} -2.85410 q^{34} +(-2.64590 + 4.58283i) q^{36} +4.00000 q^{37} +(0.927051 - 1.60570i) q^{38} +(-1.33688 - 0.330792i) q^{39} +(-0.281153 - 0.486971i) q^{40} +(2.61803 - 4.53457i) q^{41} +(3.78115 + 6.54915i) q^{43} +(-4.50000 - 7.79423i) q^{44} +1.09017 q^{45} +1.70820 q^{46} +(1.11803 + 1.93649i) q^{47} +(-0.600813 - 1.04064i) q^{48} +(0.927051 - 1.60570i) q^{50} +(1.42705 + 2.47172i) q^{51} +(-4.63525 + 4.81710i) q^{52} +(-4.11803 + 7.13264i) q^{53} -0.854102 q^{54} +(-0.927051 + 1.60570i) q^{55} -1.85410 q^{57} +(0.781153 - 1.35300i) q^{58} -2.23607 q^{59} +(-0.135255 + 0.234268i) q^{60} +(-3.00000 + 5.19615i) q^{61} +(1.66312 - 2.88061i) q^{62} -4.70820 q^{64} +(1.33688 + 0.330792i) q^{65} +(0.354102 - 0.613323i) q^{66} +(-0.354102 - 0.613323i) q^{67} +13.8541 q^{68} +(-0.854102 - 1.47935i) q^{69} +(-4.09017 - 7.08438i) q^{71} +(-2.10081 + 3.63871i) q^{72} +(-1.00000 + 1.73205i) q^{73} +1.52786 q^{74} -1.85410 q^{75} +(-4.50000 + 7.79423i) q^{76} +(-0.510643 - 0.126351i) q^{78} +(-2.00000 - 3.46410i) q^{79} +(0.600813 + 1.04064i) q^{80} +(-3.85410 - 6.67550i) q^{81} +(1.00000 - 1.73205i) q^{82} +6.70820 q^{83} +(-1.42705 - 2.47172i) q^{85} +(1.44427 + 2.50155i) q^{86} -1.56231 q^{87} +(-3.57295 - 6.18853i) q^{88} -16.0902 q^{89} +0.416408 q^{90} -8.29180 q^{92} -3.32624 q^{93} +(0.427051 + 0.739674i) q^{94} +1.85410 q^{95} +(-0.791796 - 1.37143i) q^{96} +(6.07295 + 10.5187i) q^{97} +13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 3 q^{5} - 7 q^{6} + 12 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 + 3 * q^5 - 7 * q^6 + 12 * q^8 - q^9	\( 4 q + 6 q^{2} - 3 q^{3} + 6 q^{4} + 3 q^{5} - 7 q^{6} + 12 q^{8} - q^{9} + 7 q^{10} + 3 q^{11} - 12 q^{12} + 10 q^{13} + 7 q^{15} + 26 q^{16} - 12 q^{17} - 9 q^{18} + 3 q^{19} + 12 q^{20} - 3 q^{22} - 19 q^{24} + 3 q^{25} + 15 q^{26} - 3 q^{29} + 18 q^{30} + 4 q^{31} + 30 q^{32} - 3 q^{33} + 2 q^{34} - 24 q^{36} + 16 q^{37} - 3 q^{38} - 21 q^{39} + 19 q^{40} + 6 q^{41} - 5 q^{43} - 18 q^{44} - 18 q^{45} - 20 q^{46} - 27 q^{48} - 3 q^{50} - q^{51} + 15 q^{52} - 12 q^{53} + 10 q^{54} + 3 q^{55} + 6 q^{57} - 17 q^{58} + 33 q^{60} - 12 q^{61} - 9 q^{62} + 8 q^{64} + 21 q^{65} - 12 q^{66} + 12 q^{67} + 42 q^{68} + 10 q^{69} + 6 q^{71} - 33 q^{72} - 4 q^{73} + 24 q^{74} + 6 q^{75} - 18 q^{76} - 49 q^{78} - 8 q^{79} + 27 q^{80} - 2 q^{81} + 4 q^{82} + q^{85} - 30 q^{86} + 34 q^{87} - 21 q^{88} - 42 q^{89} - 52 q^{90} - 60 q^{92} + 18 q^{93} - 5 q^{94} - 6 q^{95} - 30 q^{96} + 31 q^{97} + 42 q^{99}+O(q^{100}) \) 4 * q + 6 * q^2 - 3 * q^3 + 6 * q^4 + 3 * q^5 - 7 * q^6 + 12 * q^8 - q^9 + 7 * q^10 + 3 * q^11 - 12 * q^12 + 10 * q^13 + 7 * q^15 + 26 * q^16 - 12 * q^17 - 9 * q^18 + 3 * q^19 + 12 * q^20 - 3 * q^22 - 19 * q^24 + 3 * q^25 + 15 * q^26 - 3 * q^29 + 18 * q^30 + 4 * q^31 + 30 * q^32 - 3 * q^33 + 2 * q^34 - 24 * q^36 + 16 * q^37 - 3 * q^38 - 21 * q^39 + 19 * q^40 + 6 * q^41 - 5 * q^43 - 18 * q^44 - 18 * q^45 - 20 * q^46 - 27 * q^48 - 3 * q^50 - q^51 + 15 * q^52 - 12 * q^53 + 10 * q^54 + 3 * q^55 + 6 * q^57 - 17 * q^58 + 33 * q^60 - 12 * q^61 - 9 * q^62 + 8 * q^64 + 21 * q^65 - 12 * q^66 + 12 * q^67 + 42 * q^68 + 10 * q^69 + 6 * q^71 - 33 * q^72 - 4 * q^73 + 24 * q^74 + 6 * q^75 - 18 * q^76 - 49 * q^78 - 8 * q^79 + 27 * q^80 - 2 * q^81 + 4 * q^82 + q^85 - 30 * q^86 + 34 * q^87 - 21 * q^88 - 42 * q^89 - 52 * q^90 - 60 * q^92 + 18 * q^93 - 5 * q^94 - 6 * q^95 - 30 * q^96 + 31 * q^97 + 42 * q^99

Introduction

L-functions

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