LMFDB - Embedded newform 637.2.g.b.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (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:	$1$
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			373.2
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	637.373
Dual form			637.2.g.b.263.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190983 - 0.330792i) q^{2} -0.381966 q^{3} +(0.927051 - 1.60570i) q^{4} +(-0.190983 + 0.330792i) q^{5} +(0.0729490 + 0.126351i) q^{6} -1.47214 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+(-0.190983 - 0.330792i) q^{2} -0.381966 q^{3} +(0.927051 - 1.60570i) q^{4} +(-0.190983 + 0.330792i) q^{5} +(0.0729490 + 0.126351i) q^{6} -1.47214 q^{8} -2.85410 q^{9} +0.145898 q^{10} -4.85410 q^{11} +(-0.354102 + 0.613323i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(0.0729490 - 0.126351i) q^{15} +(-1.57295 - 2.72443i) q^{16} +(-3.73607 + 6.47106i) q^{17} +(0.545085 + 0.944115i) q^{18} +4.85410 q^{19} +(0.354102 + 0.613323i) q^{20} +(0.927051 + 1.60570i) q^{22} +(-2.23607 - 3.87298i) q^{23} +0.562306 q^{24} +(2.42705 + 4.20378i) q^{25} +(1.33688 + 0.330792i) q^{26} +2.23607 q^{27} +(2.04508 - 3.54219i) q^{29} -0.0557281 q^{30} +(-4.35410 - 7.54153i) q^{31} +(-2.07295 + 3.59045i) q^{32} +1.85410 q^{33} +2.85410 q^{34} +(-2.64590 + 4.58283i) q^{36} +(-2.00000 - 3.46410i) q^{37} +(-0.927051 - 1.60570i) q^{38} +(0.954915 - 0.992377i) 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} +(0.545085 - 0.944115i) q^{45} +(-0.854102 + 1.47935i) 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} +(1.85410 + 6.42280i) q^{52} +(-4.11803 - 7.13264i) q^{53} +(-0.427051 - 0.739674i) q^{54} +(0.927051 - 1.60570i) q^{55} -1.85410 q^{57} -1.56231 q^{58} +(-1.11803 + 1.93649i) q^{59} +(-0.135255 - 0.234268i) q^{60} -6.00000 q^{61} +(-1.66312 + 2.88061i) q^{62} -4.70820 q^{64} +(-0.381966 - 1.32317i) q^{65} +(-0.354102 - 0.613323i) q^{66} +0.708204 q^{67} +(6.92705 + 11.9980i) q^{68} +(0.854102 + 1.47935i) q^{69} +(-4.09017 - 7.08438i) q^{71} +4.20163 q^{72} +(1.00000 + 1.73205i) q^{73} +(-0.763932 + 1.32317i) q^{74} +(-0.927051 - 1.60570i) q^{75} +(4.50000 - 7.79423i) q^{76} +(-0.510643 - 0.126351i) q^{78} +(-2.00000 + 3.46410i) q^{79} +1.20163 q^{80} +7.70820 q^{81} +2.00000 q^{82} -6.70820 q^{83} +(-1.42705 - 2.47172i) q^{85} +(1.44427 - 2.50155i) q^{86} +(-0.781153 + 1.35300i) q^{87} +7.14590 q^{88} +(-8.04508 - 13.9345i) q^{89} -0.416408 q^{90} -8.29180 q^{92} +(1.66312 + 2.88061i) q^{93} +0.854102 q^{94} +(-0.927051 + 1.60570i) 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 - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 6 * q^3 - 3 * q^4 - 3 * q^5 + 7 * q^6 + 12 * q^8 + 2 * q^9	$ 4 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9} + 14 q^{10} - 6 q^{11} + 12 q^{12} - 10 q^{13} + 7 q^{15} - 13 q^{16} - 6 q^{17} - 9 q^{18} + 6 q^{19} - 12 q^{20} - 3 q^{22} - 38 q^{24} + 3 q^{25} + 21 q^{26} - 3 q^{29} - 36 q^{30} - 4 q^{31} - 15 q^{32} - 6 q^{33} - 2 q^{34} - 24 q^{36} - 8 q^{37} + 3 q^{38} + 15 q^{39} - 19 q^{40} - 6 q^{41} - 5 q^{43} - 18 q^{44} - 9 q^{45} + 10 q^{46} + 27 q^{48} - 3 q^{50} - q^{51} - 6 q^{52} - 12 q^{53} + 5 q^{54} - 3 q^{55} + 6 q^{57} + 34 q^{58} + 33 q^{60} - 24 q^{61} + 9 q^{62} + 8 q^{64} - 6 q^{65} + 12 q^{66} - 24 q^{67} + 21 q^{68} - 10 q^{69} + 6 q^{71} + 66 q^{72} + 4 q^{73} - 12 q^{74} + 3 q^{75} + 18 q^{76} - 49 q^{78} - 8 q^{79} + 54 q^{80} + 4 q^{81} + 8 q^{82} + q^{85} - 30 q^{86} + 17 q^{87} + 42 q^{88} - 21 q^{89} + 52 q^{90} - 60 q^{92} - 9 q^{93} - 10 q^{94} + 3 q^{95} + 30 q^{96} - 31 q^{97} + 42 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 6 * q^3 - 3 * q^4 - 3 * q^5 + 7 * q^6 + 12 * q^8 + 2 * q^9 + 14 * q^10 - 6 * q^11 + 12 * q^12 - 10 * q^13 + 7 * q^15 - 13 * q^16 - 6 * q^17 - 9 * q^18 + 6 * q^19 - 12 * q^20 - 3 * q^22 - 38 * q^24 + 3 * q^25 + 21 * q^26 - 3 * q^29 - 36 * q^30 - 4 * q^31 - 15 * q^32 - 6 * q^33 - 2 * q^34 - 24 * q^36 - 8 * q^37 + 3 * q^38 + 15 * q^39 - 19 * q^40 - 6 * q^41 - 5 * q^43 - 18 * q^44 - 9 * q^45 + 10 * q^46 + 27 * q^48 - 3 * q^50 - q^51 - 6 * q^52 - 12 * q^53 + 5 * q^54 - 3 * q^55 + 6 * q^57 + 34 * q^58 + 33 * q^60 - 24 * q^61 + 9 * q^62 + 8 * q^64 - 6 * q^65 + 12 * q^66 - 24 * q^67 + 21 * q^68 - 10 * q^69 + 6 * q^71 + 66 * q^72 + 4 * q^73 - 12 * q^74 + 3 * q^75 + 18 * q^76 - 49 * q^78 - 8 * q^79 + 54 * q^80 + 4 * q^81 + 8 * q^82 + q^85 - 30 * q^86 + 17 * q^87 + 42 * q^88 - 21 * q^89 + 52 * q^90 - 60 * q^92 - 9 * q^93 - 10 * q^94 + 3 * 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.190983	−	0.330792i	−0.135045	−	0.233905i	0.790569	−	0.612372i	$-0.209785\pi$
$2$	−0.190983	−	0.330792i	−0.135045	−	0.233905i	−0.925615	+	0.378467i	$0.876451\pi$
$3$	−0.381966			−0.220528			−0.110264	−	0.993902i	$-0.535170\pi$
$3$	−0.381966			−0.220528			−0.110264	+	0.993902i	$0.535170\pi$
$4$	0.927051	−	1.60570i	0.463525	−	0.802850i
$5$	−0.190983	+	0.330792i	−0.0854102	+	0.147935i	−0.905566	−	0.424206i	$-0.860553\pi$
$5$	−0.190983	+	0.330792i	−0.0854102	+	0.147935i	0.820156	+	0.572140i	$0.193887\pi$
$6$	0.0729490	+	0.126351i	0.0297813	+	0.0515827i
$7$		0			0
$7$		0			0
$8$	−1.47214			−0.520479
$9$	−2.85410			−0.951367
$10$	0.145898			0.0461370
$11$	−4.85410			−1.46357			−0.731783	−	0.681537i	$-0.761312\pi$
$11$	−4.85410			−1.46357			−0.731783	+	0.681537i	$0.761312\pi$
$12$	−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
$16$	−1.57295	−	2.72443i	−0.393237	−	0.681107i
$17$	−3.73607	+	6.47106i	−0.906130	+	1.56946i	−0.0867359	+	0.996231i	$0.527644\pi$
$17$	−3.73607	+	6.47106i	−0.906130	+	1.56946i	−0.819394	+	0.573231i	$0.805690\pi$
$18$	0.545085	+	0.944115i	0.128478	+	0.222530i
$19$	4.85410			1.11361			0.556804	−	0.830644i	$-0.312028\pi$
$19$	4.85410			1.11361			0.556804	+	0.830644i	$0.312028\pi$
$20$	0.354102	+	0.613323i	0.0791796	+	0.137143i
$21$		0			0
$22$	0.927051	+	1.60570i	0.197648	+	0.342336i
$23$	−2.23607	−	3.87298i	−0.466252	−	0.807573i	0.533005	−	0.846112i	$-0.321063\pi$
$23$	−2.23607	−	3.87298i	−0.466252	−	0.807573i	−0.999257	+	0.0385394i	$0.987729\pi$
$24$	0.562306			0.114780
$25$	2.42705	+	4.20378i	0.485410	+	0.840755i
$26$	1.33688	+	0.330792i	0.262184	+	0.0648737i
$27$	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	$0.0426723\pi$
$30$	−0.0557281			−0.0101745
$31$	−4.35410	−	7.54153i	−0.782020	−	1.35450i	−0.930763	−	0.365622i	$-0.880856\pi$
$31$	−4.35410	−	7.54153i	−0.782020	−	1.35450i	0.148744	−	0.988876i	$-0.452477\pi$
$32$	−2.07295	+	3.59045i	−0.366449	+	0.634708i
$33$	1.85410			0.322758
$34$	2.85410			0.489474
$35$		0			0
$36$	−2.64590	+	4.58283i	−0.440983	+	0.763805i
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$	−0.927051	−	1.60570i	−0.150388	−	0.260479i
$39$	0.954915	−	0.992377i	0.152909	−	0.158907i
$40$	0.281153	−	0.486971i	0.0444542	−	0.0769969i
$41$	−2.61803	+	4.53457i	−0.408868	+	0.708181i	−0.994763	−	0.102206i	$-0.967410\pi$
$41$	−2.61803	+	4.53457i	−0.408868	+	0.708181i	0.585895	+	0.810387i	$0.300743\pi$
$42$		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
$45$	0.545085	−	0.944115i	0.0812565	−	0.140740i
$46$	−0.854102	+	1.47935i	−0.125930	+	0.218118i
$47$	−1.11803	+	1.93649i	−0.163082	+	0.282466i	−0.935973	−	0.352073i	$-0.885477\pi$
$47$	−1.11803	+	1.93649i	−0.163082	+	0.282466i	0.772890	+	0.634539i	$0.218810\pi$
$48$	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
$52$	1.85410	+	6.42280i	0.257118	+	0.890682i
$53$	−4.11803	−	7.13264i	−0.565655	−	0.979744i	−0.996988	−	0.0775512i	$-0.975290\pi$
$53$	−4.11803	−	7.13264i	−0.565655	−	0.979744i	0.431333	−	0.902193i	$-0.358043\pi$
$54$	−0.427051	−	0.739674i	−0.0581143	−	0.100657i
$55$	0.927051	−	1.60570i	0.125004	−	0.216512i
$56$		0			0
$57$	−1.85410			−0.245582
$58$	−1.56231			−0.205141
$59$	−1.11803	+	1.93649i	−0.145556	+	0.252110i	−0.929580	−	0.368620i	$-0.879830\pi$
$59$	−1.11803	+	1.93649i	−0.145556	+	0.252110i	0.784024	+	0.620730i	$0.213164\pi$
$60$	−0.135255	−	0.234268i	−0.0174613	−	0.0302439i
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	−1.66312	+	2.88061i	−0.211216	+	0.365837i
$63$		0			0
$64$	−4.70820			−0.588525
$65$	−0.381966	−	1.32317i	−0.0473771	−	0.164119i
$66$	−0.354102	−	0.613323i	−0.0435869	−	0.0754948i
$67$	0.708204			0.0865209			0.0432604	−	0.999064i	$-0.486225\pi$
$67$	0.708204			0.0865209			0.0432604	+	0.999064i	$0.486225\pi$
$68$	6.92705	+	11.9980i	0.840028	+	1.45497i
$69$	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	$0.994664\pi$
$72$	4.20163			0.495166
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	0.918594	−	0.395203i	$-0.129326\pi$
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	−0.801553	+	0.597924i	$0.795992\pi$
$74$	−0.763932	+	1.32317i	−0.0888053	+	0.153815i
$75$	−0.927051	−	1.60570i	−0.107047	−	0.185410i
$76$	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	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$	1.20163			0.134346
$81$	7.70820			0.856467
$82$	2.00000			0.220863
$83$	−6.70820			−0.736321			−0.368161	−	0.929762i	$-0.620012\pi$
$83$	−6.70820			−0.736321			−0.368161	+	0.929762i	$0.620012\pi$
$84$		0			0
$85$	−1.42705	−	2.47172i	−0.154785	−	0.268096i
$86$	1.44427	−	2.50155i	0.155740	−	0.269749i
$87$	−0.781153	+	1.35300i	−0.0837484	+	0.145056i
$88$	7.14590			0.761755
$89$	−8.04508	−	13.9345i	−0.852777	−	1.47705i	−0.878692	−	0.477389i	$-0.841583\pi$
$89$	−8.04508	−	13.9345i	−0.852777	−	1.47705i	0.0259145	−	0.999664i	$-0.491750\pi$
$90$	−0.416408			−0.0438932
$91$		0			0
$92$	−8.29180			−0.864479
$93$	1.66312	+	2.88061i	0.172457	+	0.298705i
$94$	0.854102			0.0880939
$95$	−0.927051	+	1.60570i	−0.0951134	+	0.164741i
$96$	0.791796	−	1.37143i	0.0808123	−	0.139971i
$97$	−6.07295	−	10.5187i	−0.616615	−	1.06801i	−0.990099	−	0.140371i	$-0.955170\pi$
$97$	−6.07295	−	10.5187i	−0.616615	−	1.06801i	0.373484	−	0.927636i	$-0.378163\pi$
$98$		0			0
$99$	13.8541			1.39239
$100$	9.00000			0.900000
$101$	8.56231			0.851981			0.425991	−	0.904728i	$-0.359926\pi$
$101$	8.56231			0.851981			0.425991	+	0.904728i	$0.359926\pi$
$102$	−1.09017			−0.107943
$103$	−2.35410	+	4.07742i	−0.231957	+	0.401761i	−0.958384	−	0.285483i	$-0.907846\pi$
$103$	−2.35410	+	4.07742i	−0.231957	+	0.401761i	0.726427	+	0.687243i	$0.241179\pi$
$104$	3.68034	−	3.82472i	0.360887	−	0.375045i
$105$		0			0
$106$	−1.57295	+	2.72443i	−0.152778	+	0.264620i
$107$	2.80902	+	4.86536i	0.271558	+	0.470352i	0.969261	−	0.246035i	$-0.0791278\pi$
$107$	2.80902	+	4.86536i	0.271558	+	0.470352i	−0.697703	+	0.716387i	$0.745794\pi$
$108$	2.07295	−	3.59045i	0.199470	−	0.345492i
$109$	−5.35410	−	9.27358i	−0.512830	−	0.888248i	−0.999889	−	0.0148787i	$-0.995264\pi$
$109$	−5.35410	−	9.27358i	−0.512830	−	0.888248i	0.487059	−	0.873369i	$-0.338070\pi$
$110$	−0.708204			−0.0675246
$111$	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	$0.719019\pi$
$114$	0.354102	+	0.613323i	0.0331647	+	0.0574429i
$115$	1.70820			0.159291
$116$	−3.79180	−	6.56758i	−0.352059	−	0.609785i
$117$	7.13525	−	7.41517i	0.659655	−	0.685533i
$118$	0.854102			0.0786265
$119$		0			0
$120$	−0.107391	+	0.186006i	−0.00980340	+	0.0169800i
$121$	12.5623			1.14203
$122$	1.14590	+	1.98475i	0.103745	+	0.179691i
$123$	1.00000	−	1.73205i	0.0901670	−	0.156174i
$124$	−16.1459			−1.44994
$125$	−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	$-0.0493053\pi$
$128$	5.04508	+	8.73834i	0.445927	+	0.772368i
$129$	−1.44427	−	2.50155i	−0.127161	−	0.220249i
$130$	−0.364745	+	0.379054i	−0.0319903	+	0.0332453i
$131$	−0.163119	+	0.282530i	−0.0142518	+	0.0246848i	−0.873063	−	0.487607i	$-0.837870\pi$
$131$	−0.163119	+	0.282530i	−0.0142518	+	0.0246848i	0.858812	+	0.512292i	$0.171203\pi$
$132$	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
$136$	5.50000	−	9.52628i	0.471621	−	0.816872i
$137$	0.190983	−	0.330792i	0.0163168	−	0.0282615i	−0.857752	−	0.514064i	$-0.828139\pi$
$137$	0.190983	−	0.330792i	0.0163168	−	0.0282615i	0.874069	+	0.485803i	$0.161473\pi$
$138$	0.326238	−	0.565061i	0.0277712	−	0.0481012i
$139$	7.78115	+	13.4774i	0.659989	+	1.14313i	0.980618	+	0.195929i	$0.0627723\pi$
$139$	7.78115	+	13.4774i	0.659989	+	1.14313i	−0.320629	+	0.947205i	$0.603894\pi$
$140$		0			0
$141$	0.427051	−	0.739674i	0.0359642	−	0.0622918i
$142$	−1.56231	+	2.70599i	−0.131106	+	0.227082i
$143$	12.1353	−	12.6113i	1.01480	−	1.05461i
$144$	4.48936	+	7.77579i	0.374113	+	0.647983i
$145$	0.781153	+	1.35300i	0.0648712	+	0.112360i
$146$	0.381966	−	0.661585i	0.0316117	−	0.0547531i
$147$		0			0
$148$	−7.41641			−0.609625
$149$	−4.85410			−0.397664			−0.198832	−	0.980034i	$-0.563715\pi$
$149$	−4.85410			−0.397664			−0.198832	+	0.980034i	$0.563715\pi$
$150$	−0.354102	+	0.613323i	−0.0289123	+	0.0500776i
$151$	7.35410	+	12.7377i	0.598468	+	1.03658i	0.993047	+	0.117716i	$0.0375571\pi$
$151$	7.35410	+	12.7377i	0.598468	+	1.03658i	−0.394579	+	0.918862i	$0.629110\pi$
$152$	−7.14590			−0.579609
$153$	10.6631	−	18.4691i	0.862062	−	1.49314i
$154$		0			0
$155$	3.32624			0.267170
$156$	−0.708204	−	2.45329i	−0.0567017	−	0.196420i
$157$	−4.07295	−	7.05455i	−0.325057	−	0.563015i	0.656467	−	0.754355i	$-0.272050\pi$
$157$	−4.07295	−	7.05455i	−0.325057	−	0.563015i	−0.981524	+	0.191340i	$0.938717\pi$
$158$	1.52786			0.121550
$159$	1.57295	+	2.72443i	0.124743	+	0.216061i
$160$	−0.791796	−	1.37143i	−0.0625970	−	0.108421i
$161$		0			0
$162$	−1.47214	−	2.54981i	−0.115662	−	0.200332i
$163$	9.70820			0.760405			0.380203	−	0.924903i	$-0.375854\pi$
$163$	9.70820			0.760405			0.380203	+	0.924903i	$0.375854\pi$
$164$	4.85410	+	8.40755i	0.379042	+	0.656519i
$165$	−0.354102	+	0.613323i	−0.0275668	+	0.0477471i
$166$	1.28115	+	2.21902i	0.0994368	+	0.172230i
$167$	−4.88197	+	8.45581i	−0.377778	+	0.654330i	−0.990739	−	0.135783i	$-0.956645\pi$
$167$	−4.88197	+	8.45581i	−0.377778	+	0.654330i	0.612961	+	0.790113i	$0.289978\pi$
$168$		0			0
$169$	−0.500000	−	12.9904i	−0.0384615	−	0.999260i
$170$	−0.545085	+	0.944115i	−0.0418061	+	0.0724103i
$171$	−13.8541			−1.05945
$172$	14.0213			1.06911
$173$	−9.00000			−0.684257			−0.342129	−	0.939653i	$-0.611148\pi$
$173$	−9.00000			−0.684257			−0.342129	+	0.939653i	$0.611148\pi$
$174$	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
$178$	−3.07295	+	5.32250i	−0.230327	+	0.398939i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$	−1.01064	−	1.75049i	−0.0753289	−	0.130473i
$181$	−3.70820			−0.275629			−0.137814	−	0.990458i	$-0.544008\pi$
$181$	−3.70820			−0.275629			−0.137814	+	0.990458i	$0.544008\pi$
$182$		0			0
$183$	2.29180			0.169414
$184$	3.29180	+	5.70156i	0.242674	+	0.420324i
$185$	1.52786			0.112331
$186$	0.635255	−	1.10029i	0.0465792	−	0.0806775i
$187$	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
$191$	23.6180			1.70894			0.854470	−	0.519500i	$-0.173882\pi$
$191$	23.6180			1.70894			0.854470	+	0.519500i	$0.173882\pi$
$192$	1.79837			0.129786
$193$	−6.00000			−0.431889			−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000			−0.431889			−0.215945	+	0.976406i	$0.569283\pi$
$194$	−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	$0.256274\pi$
$198$	−2.64590	−	4.58283i	−0.188036	−	0.325688i
$199$	−1.20820	+	2.09267i	−0.0856473	+	0.148345i	−0.905667	−	0.423990i	$-0.860629\pi$
$199$	−1.20820	+	2.09267i	−0.0856473	+	0.148345i	0.820020	+	0.572336i	$0.193962\pi$
$200$	−3.57295	−	6.18853i	−0.252646	−	0.437595i
$201$	−0.270510			−0.0190803
$202$	−1.63525	−	2.83234i	−0.115056	−	0.199283i
$203$		0			0
$204$	−2.64590	−	4.58283i	−0.185250	−	0.320862i
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$	1.79837			0.125299
$207$	6.38197	+	11.0539i	0.443577	+	0.768298i
$208$	11.0106	+	2.72443i	0.763451	+	0.188905i
$209$	−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	$0.0697638\pi$
$212$	−15.2705			−1.04878
$213$	1.56231	+	2.70599i	0.107047	+	0.185412i
$214$	1.07295	−	1.85840i	0.0733453	−	0.127038i
$215$	−2.88854			−0.196997
$216$	−3.29180			−0.223978
$217$		0			0
$218$	−2.04508	+	3.54219i	−0.138511	+	0.239907i
$219$	−0.381966	−	0.661585i	−0.0258109	−	0.0447057i
$220$	−1.71885	−	2.97713i	−0.115885	−	0.200718i
$221$	−7.47214	−	25.8842i	−0.502630	−	1.74116i
$222$	0.291796	−	0.505406i	0.0195841	−	0.0339206i
$223$	6.63525	−	11.4926i	0.444330	−	0.769601i	−0.553676	−	0.832732i	$-0.686775\pi$
$223$	6.63525	−	11.4926i	0.444330	−	0.769601i	0.998005	+	0.0631310i	$0.0201086\pi$
$224$		0			0
$225$	−6.92705	−	11.9980i	−0.461803	−	0.799867i
$226$	1.42705	−	2.47172i	0.0949260	−	0.164417i
$227$	3.73607	−	6.47106i	0.247972	−	0.429499i	−0.714991	−	0.699133i	$-0.753569\pi$
$227$	3.73607	−	6.47106i	0.247972	−	0.429499i	0.962963	+	0.269634i	$0.0869027\pi$
$228$	−1.71885	+	2.97713i	−0.113833	+	0.197165i
$229$	−13.5623	+	23.4906i	−0.896222	+	1.55230i	−0.0639380	+	0.997954i	$0.520366\pi$
$229$	−13.5623	+	23.4906i	−0.896222	+	1.55230i	−0.832284	+	0.554349i	$0.812967\pi$
$230$	−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	−0.872213	−	0.489125i	$-0.837316\pi$
$233$	−0.190983	+	0.330792i	−0.0125117	+	0.0216709i	0.859702	+	0.510796i	$0.170649\pi$
$234$	−3.81559	−	0.944115i	−0.249433	−	0.0617187i
$235$	−0.427051	−	0.739674i	−0.0278577	−	0.0482510i
$236$	2.07295	+	3.59045i	0.134937	+	0.233719i
$237$	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	$0.619000\pi$
$240$	−0.458980			−0.0296271
$241$	−2.21885	+	3.84316i	−0.142929	+	0.247559i	−0.928598	−	0.371087i	$-0.878985\pi$
$241$	−2.21885	+	3.84316i	−0.142929	+	0.247559i	0.785670	+	0.618646i	$0.212319\pi$
$242$	−2.39919	−	4.15551i	−0.154226	−	0.267127i
$243$	−9.65248			−0.619207
$244$	−5.56231	+	9.63420i	−0.356090	+	0.616766i
$245$		0			0
$246$	−0.763932			−0.0487065
$247$	−12.1353	+	12.6113i	−0.772148	+	0.802440i
$248$	6.40983	+	11.1022i	0.407025	+	0.704987i
$249$	2.56231			0.162380
$250$	0.718847	+	1.24508i	0.0454639	+	0.0787457i
$251$	−2.61803	−	4.53457i	−0.165249	−	0.286219i	0.771495	−	0.636236i	$-0.219509\pi$
$251$	−2.61803	−	4.53457i	−0.165249	−	0.286219i	−0.936744	+	0.350016i	$0.886176\pi$
$252$		0			0
$253$	10.8541	+	18.7999i	0.682392	+	1.18194i
$254$	−5.40325			−0.339030
$255$	0.545085	+	0.944115i	0.0341345	+	0.0591228i
$256$	−2.78115	+	4.81710i	−0.173822	+	0.301069i
$257$	12.8713	+	22.2938i	0.802891	+	1.39065i	0.917706	+	0.397261i	$0.130039\pi$
$257$	12.8713	+	22.2938i	0.802891	+	1.39065i	−0.114815	+	0.993387i	$0.536627\pi$
$258$	−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
$262$	0.124612			0.00769854
$263$	9.00000			0.554964			0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000			0.554964			0.277482	+	0.960731i	$0.410500\pi$
$264$	−2.72949			−0.167989
$265$	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
$269$	−6.87132	+	11.9015i	−0.418952	+	0.725646i	−0.995834	−	0.0911812i	$-0.970936\pi$
$269$	−6.87132	+	11.9015i	−0.418952	+	0.725646i	0.576882	+	0.816827i	$0.304269\pi$
$270$	0.326238			0.0198542
$271$	−9.20820	−	15.9491i	−0.559359	−	0.968837i	−0.997550	−	0.0699558i	$-0.977714\pi$
$271$	−9.20820	−	15.9491i	−0.559359	−	0.968837i	0.438192	−	0.898882i	$-0.355619\pi$
$272$	23.5066			1.42530
$273$		0			0
$274$	−0.145898			−0.00881402
$275$	−11.7812	−	20.4056i	−0.710430	−	1.23050i
$276$	3.16718			0.190642
$277$	2.50000	−	4.33013i	0.150210	−	0.260172i	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	2.50000	−	4.33013i	0.150210	−	0.260172i	0.931305	+	0.364241i	$0.118672\pi$
$278$	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	$0.520716\pi$
$282$	−0.326238			−0.0194272
$283$	−13.4164			−0.797523			−0.398761	−	0.917055i	$-0.630560\pi$
$283$	−13.4164			−0.797523			−0.398761	+	0.917055i	$0.630560\pi$
$284$	−15.1672			−0.900007
$285$	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
$289$	−19.4164	−	33.6302i	−1.14214	−	1.97825i
$290$	0.298374	−	0.516799i	0.0175211	−	0.0303475i
$291$	2.31966	+	4.01777i	0.135981	+	0.235526i
$292$	3.70820			0.217006
$293$	5.61803	+	9.73072i	0.328209	+	0.568475i	0.982157	−	0.188065i	$-0.0602216\pi$
$293$	5.61803	+	9.73072i	0.328209	+	0.568475i	−0.653947	+	0.756540i	$0.726888\pi$
$294$		0			0
$295$	−0.427051	−	0.739674i	−0.0248639	−	0.0430655i
$296$	2.94427	+	5.09963i	0.171132	+	0.296410i
$297$	−10.8541			−0.629819
$298$	0.927051	+	1.60570i	0.0537026	+	0.0930157i
$299$	15.6525	+	3.87298i	0.905206	+	0.223980i
$300$	−3.43769			−0.198475
$301$		0			0
$302$	2.80902	−	4.86536i	0.161641	−	0.279970i
$303$	−3.27051			−0.187886
$304$	−7.63525	−	13.2246i	−0.437912	−	0.758486i
$305$	1.14590	−	1.98475i	0.0656139	−	0.113647i
$306$	−8.14590			−0.465670
$307$	1.85410			0.105819			0.0529096	−	0.998599i	$-0.483150\pi$
$307$	1.85410			0.105819			0.0529096	+	0.998599i	$0.483150\pi$
$308$		0			0
$309$	0.899187	−	1.55744i	0.0511530	−	0.0885995i
$310$	−0.635255	−	1.10029i	−0.0360801	−	0.0624925i
$311$	6.16312	+	10.6748i	0.349478	+	0.605314i	0.986157	−	0.165815i	$-0.0530255\pi$
$311$	6.16312	+	10.6748i	0.349478	+	0.605314i	−0.636678	+	0.771129i	$0.719692\pi$
$312$	−1.40576	+	1.46091i	−0.0795858	+	0.0827079i
$313$	7.56231	−	13.0983i	0.427447	−	0.740360i	−0.569199	−	0.822200i	$-0.692746\pi$
$313$	7.56231	−	13.0983i	0.427447	−	0.740360i	0.996645	+	0.0818405i	$0.0260798\pi$
$314$	−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	0.379848	+	0.925049i	$0.375976\pi$
$317$	−10.8820	+	18.8481i	−0.611192	+	1.05862i	−0.991040	+	0.133567i	$0.957357\pi$
$318$	0.600813	−	1.04064i	0.0336919	−	0.0583561i
$319$	−9.92705	+	17.1942i	−0.555808	+	0.962688i
$320$	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
$325$	−16.9894	−	4.20378i	−0.942400	−	0.233184i
$326$	−1.85410	−	3.21140i	−0.102689	−	0.177863i
$327$	2.04508	+	3.54219i	0.113093	+	0.195884i
$328$	3.85410	−	6.67550i	0.212807	−	0.368593i
$329$		0			0
$330$	0.270510			0.0148911
$331$	−16.8541			−0.926385			−0.463193	−	0.886258i	$-0.653296\pi$
$331$	−16.8541			−0.926385			−0.463193	+	0.886258i	$0.653296\pi$
$332$	−6.21885	+	10.7714i	−0.341304	+	0.591155i
$333$	5.70820	+	9.88690i	0.312808	+	0.541799i
$334$	3.72949			0.204069
$335$	−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	$0.425077\pi$
$338$	−4.20163	+	2.64634i	−0.228538	+	0.143942i
$339$	−1.42705	−	2.47172i	−0.0775068	−	0.134246i
$340$	−5.29180			−0.286988
$341$	21.1353	+	36.6073i	1.14454	+	1.98240i
$342$	2.64590	+	4.58283i	0.143074	+	0.247811i
$343$		0			0
$344$	−5.56637	−	9.64124i	−0.300119	−	0.519821i
$345$	−0.652476			−0.0351281
$346$	1.71885	+	2.97713i	0.0924058	+	0.160052i
$347$	−17.6180	+	30.5153i	−0.945786	+	1.63815i	−0.191615	+	0.981470i	$0.561373\pi$
$347$	−17.6180	+	30.5153i	−0.945786	+	1.63815i	−0.754171	+	0.656679i	$0.771961\pi$
$348$	1.44834	+	2.50859i	0.0776390	+	0.134475i
$349$	−3.64590	+	6.31488i	−0.195160	+	0.338028i	−0.946953	−	0.321372i	$-0.895856\pi$
$349$	−3.64590	+	6.31488i	−0.195160	+	0.338028i	0.751793	+	0.659400i	$0.229189\pi$
$350$		0			0
$351$	−5.59017	+	5.80948i	−0.298381	+	0.310087i
$352$	10.0623	−	17.4284i	0.536323	−	0.928938i
$353$	28.8541			1.53575			0.767874	−	0.640600i	$-0.221314\pi$
$353$	28.8541			1.53575			0.767874	+	0.640600i	$0.221314\pi$
$354$	−0.326238			−0.0173393
$355$	3.12461			0.165837
$356$	−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	−0.685409	−	0.728159i	$-0.740376\pi$
$359$	5.45492	−	9.44819i	0.287899	−	0.498656i	0.973308	+	0.229502i	$0.0737098\pi$
$360$	−0.802439	+	1.38987i	−0.0422923	+	0.0732523i
$361$	4.56231			0.240121
$362$	0.708204	+	1.22665i	0.0372224	+	0.0644710i
$363$	−4.79837			−0.251849
$364$		0			0
$365$	−0.763932			−0.0399860
$366$	−0.437694	−	0.758108i	−0.0228786	−	0.0396270i
$367$	25.4164			1.32673			0.663363	−	0.748298i	$-0.269129\pi$
$367$	25.4164			1.32673			0.663363	+	0.748298i	$0.269129\pi$
$368$	−7.03444	+	12.1840i	−0.366696	+	0.635135i
$369$	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
$373$	−0.437694			−0.0226629			−0.0113315	−	0.999936i	$-0.503607\pi$
$373$	−0.437694			−0.0226629			−0.0113315	+	0.999936i	$0.503607\pi$
$374$	−13.8541			−0.716379
$375$	1.43769			0.0742422
$376$	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	$0.0595722\pi$
$380$	1.71885	+	2.97713i	0.0881750	+	0.152724i
$381$	−2.70163	+	4.67935i	−0.138408	+	0.239731i
$382$	−4.51064	−	7.81266i	−0.230785	−	0.399731i
$383$	24.9787			1.27635			0.638176	−	0.769890i	$-0.279689\pi$
$383$	24.9787			1.27635			0.638176	+	0.769890i	$0.279689\pi$
$384$	−1.92705	−	3.33775i	−0.0983394	−	0.170329i
$385$		0			0
$386$	1.14590	+	1.98475i	0.0583247	+	0.101021i
$387$	−10.7918	−	18.6919i	−0.548578	−	0.950165i
$388$	−22.5197			−1.14327
$389$	−11.9443	−	20.6881i	−0.605599	−	1.04893i	−0.991957	−	0.126579i	$-0.959600\pi$
$389$	−11.9443	−	20.6881i	−0.605599	−	1.04893i	0.386358	−	0.922349i	$-0.373733\pi$
$390$	0.139320	−	0.144786i	0.00705475	−	0.00733152i
$391$	33.4164			1.68994
$392$		0			0
$393$	0.0623059	−	0.107917i	0.00314292	−	0.00544369i
$394$	2.97871			0.150065
$395$	−0.763932	−	1.32317i	−0.0384376	−	0.0665759i
$396$	12.8435	−	22.2455i	0.645408	−	1.11788i
$397$	−25.4164			−1.27561			−0.637806	−	0.770197i	$-0.720158\pi$
$397$	−25.4164			−1.27561			−0.637806	+	0.770197i	$0.720158\pi$
$398$	0.922986			0.0462651
$399$		0			0
$400$	7.63525	−	13.2246i	0.381763	−	0.661232i
$401$	10.2254	+	17.7110i	0.510633	+	0.884443i	0.999924	+	0.0123222i	$0.00392237\pi$
$401$	10.2254	+	17.7110i	0.510633	+	0.884443i	−0.489291	+	0.872121i	$0.662744\pi$
$402$	0.0516628	+	0.0894826i	0.00257671	+	0.00446298i
$403$	30.4787	+	7.54153i	1.51825	+	0.375670i
$404$	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
$409$	−17.2812	+	29.9318i	−0.854498	+	1.48003i	0.0226119	+	0.999744i	$0.492802\pi$
$409$	−17.2812	+	29.9318i	−0.854498	+	1.48003i	−0.877110	+	0.480290i	$0.840532\pi$
$410$	−0.381966	+	0.661585i	−0.0188640	+	0.0326733i
$411$	−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
$416$	−4.14590	−	14.3618i	−0.203269	−	0.704146i
$417$	−2.97214	−	5.14789i	−0.145546	−	0.252093i
$418$	4.50000	+	7.79423i	0.220102	+	0.381228i
$419$	−2.97214	+	5.14789i	−0.145198	+	0.251491i	−0.929447	−	0.368956i	$-0.879715\pi$
$419$	−2.97214	+	5.14789i	−0.145198	+	0.251491i	0.784249	+	0.620447i	$0.213049\pi$
$420$		0			0
$421$	−25.4164			−1.23872			−0.619360	−	0.785107i	$-0.712608\pi$
$421$	−25.4164			−1.23872			−0.619360	+	0.785107i	$0.712608\pi$
$422$	−3.32624			−0.161919
$423$	3.19098	−	5.52694i	0.155151	−	0.268729i
$424$	6.06231	+	10.5002i	0.294412	+	0.509936i
$425$	−36.2705			−1.75938
$426$	0.596748	−	1.03360i	0.0289125	−	0.0500780i
$427$		0			0
$428$	10.4164			0.503496
$429$	−4.63525	+	4.81710i	−0.223792	+	0.232572i
$430$	0.551663	+	0.955508i	0.0266035	+	0.0460787i
$431$	−16.7984			−0.809149			−0.404575	−	0.914505i	$-0.632580\pi$
$431$	−16.7984			−0.809149			−0.404575	+	0.914505i	$0.632580\pi$
$432$	−3.51722	−	6.09201i	−0.169222	−	0.293102i
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	0.853761	−	0.520665i	$-0.174316\pi$
$433$	−0.500000	−	0.866025i	−0.0240285	−	0.0416185i	−0.877790	+	0.479046i	$0.840983\pi$
$434$		0			0
$435$	−0.298374	−	0.516799i	−0.0143059	−	0.0247786i
$436$	−19.8541			−0.950839
$437$	−10.8541	−	18.7999i	−0.519222	−	0.899319i
$438$	−0.145898	+	0.252703i	−0.00697128	+	0.0120746i
$439$	−4.07295	−	7.05455i	−0.194391	−	0.336696i	0.752310	−	0.658810i	$-0.228940\pi$
$439$	−4.07295	−	7.05455i	−0.194391	−	0.336696i	−0.946701	+	0.322114i	$0.895606\pi$
$440$	−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	−0.856809	−	0.515634i	$-0.827556\pi$
$443$	0.381966	−	0.661585i	0.0181478	−	0.0314328i	0.874957	+	0.484201i	$0.160890\pi$
$444$	2.83282			0.134439
$445$	6.14590			0.291344
$446$	−5.06888			−0.240019
$447$	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
$451$	12.7082	−	22.0113i	0.598406	−	1.03647i
$452$	13.8541			0.651642
$453$	−2.80902	−	4.86536i	−0.131979	−	0.228595i
$454$	−2.85410			−0.133950
$455$		0			0
$456$	2.72949			0.127820
$457$	5.70820	+	9.88690i	0.267019	+	0.462490i	0.968090	−	0.250601i	$-0.0806282\pi$
$457$	5.70820	+	9.88690i	0.267019	+	0.462490i	−0.701072	+	0.713091i	$0.747295\pi$
$458$	10.3607			0.484123
$459$	−8.35410	+	14.4697i	−0.389936	+	0.675389i
$460$	1.58359	−	2.74286i	0.0738354	−	0.127887i
$461$	−19.6074	−	33.9610i	−0.913207	−	1.58172i	−0.809505	−	0.587113i	$-0.800264\pi$
$461$	−19.6074	−	33.9610i	−0.913207	−	1.58172i	−0.103702	−	0.994608i	$-0.533069\pi$
$462$		0			0
$463$	−6.70820			−0.311757			−0.155878	−	0.987776i	$-0.549821\pi$
$463$	−6.70820			−0.311757			−0.155878	+	0.987776i	$0.549821\pi$
$464$	−12.8673			−0.597347
$465$	−1.27051			−0.0589185
$466$	0.145898			0.00675860
$467$	−16.8262	+	29.1439i	−0.778625	+	1.34862i	0.154109	+	0.988054i	$0.450749\pi$
$467$	−16.8262	+	29.1439i	−0.778625	+	1.34862i	−0.932734	+	0.360565i	$0.882584\pi$
$468$	−5.29180	−	18.3313i	−0.244613	−	0.847366i
$469$		0			0
$470$	−0.163119	+	0.282530i	−0.00752412	+	0.0130322i
$471$	1.55573	+	2.69460i	0.0716842	+	0.124161i
$472$	1.64590	−	2.85078i	0.0757586	−	0.131218i
$473$	−18.3541	−	31.7902i	−0.843923	−	1.46172i
$474$	−0.583592			−0.0268053
$475$	11.7812	+	20.4056i	0.540556	+	0.936271i
$476$		0			0
$477$	11.7533	+	20.3573i	0.538146	+	0.932096i
$478$	2.15654	+	3.73524i	0.0986379	+	0.170846i
$479$	−21.9787			−1.00423			−0.502117	−	0.864800i	$-0.667445\pi$
$479$	−21.9787			−1.00423			−0.502117	+	0.864800i	$0.667445\pi$
$480$	0.302439	+	0.523840i	0.0138044	+	0.0239099i
$481$	14.0000	+	3.46410i	0.638345	+	0.157949i
$482$	1.69505			0.0772073
$483$		0			0
$484$	11.6459	−	20.1713i	0.529359	−	0.916877i
$485$	4.63932			0.210661
$486$	1.84346	+	3.19296i	0.0836210	+	0.144836i
$487$	8.48936	−	14.7040i	0.384689	−	0.666302i	−0.607037	−	0.794674i	$-0.707642\pi$
$487$	8.48936	−	14.7040i	0.384689	−	0.666302i	0.991726	+	0.128372i	$0.0409752\pi$
$488$	8.83282			0.399843
$489$	−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	$0.273665\pi$
$492$	−1.85410	−	3.21140i	−0.0835894	−	0.144781i
$493$	15.2812	+	26.4677i	0.688229	+	1.19205i
$494$	6.48936	+	1.60570i	0.291970	+	0.0722438i
$495$	−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	−0.942674	−	0.333716i	$-0.891697\pi$
$499$	−4.07295	+	7.05455i	−0.182330	+	0.315805i	0.760343	+	0.649521i	$0.225031\pi$
$500$	−3.48936	+	6.04374i	−0.156049	+	0.270284i
$501$	1.86475	−	3.22983i	0.0833107	−	0.144298i
$502$	−1.00000	+	1.73205i	−0.0446322	+	0.0773052i
$503$	−12.1910	−	21.1154i	−0.543569	−	0.941489i	−0.998695	−	0.0510624i	$-0.983739\pi$
$503$	−12.1910	−	21.1154i	−0.543569	−	0.941489i	0.455126	−	0.890427i	$-0.349594\pi$
$504$		0			0
$505$	−1.63525	+	2.83234i	−0.0727679	+	0.126038i
$506$	4.14590	−	7.18091i	0.184308	−	0.319230i
$507$	0.190983	+	4.96188i	0.00848185	+	0.220365i
$508$	−13.1140	−	22.7141i	−0.581838	−	1.00777i
$509$	−15.2984	−	26.4976i	−0.678089	−	1.17448i	−0.975556	−	0.219752i	$-0.929475\pi$
$509$	−15.2984	−	26.4976i	−0.678089	−	1.17448i	0.297467	−	0.954732i	$-0.403858\pi$
$510$	0.208204	−	0.360620i	0.00921943	−	0.0159685i
$511$		0			0
$512$	22.3050			0.985749
$513$	10.8541			0.479220
$514$	4.91641	−	8.51547i	0.216853	−	0.375601i
$515$	−0.899187	−	1.55744i	−0.0396229	−	0.0686289i
$516$	−5.35565			−0.235770
$517$	5.42705	−	9.39993i	0.238681	−	0.413408i
$518$		0			0
$519$	3.43769			0.150898
$520$	0.562306	+	1.94788i	0.0246587	+	0.0854204i
$521$	6.32624	+	10.9574i	0.277158	+	0.480051i	0.970677	−	0.240387i	$-0.0772743\pi$
$521$	6.32624	+	10.9574i	0.277158	+	0.480051i	−0.693520	+	0.720438i	$0.743941\pi$
$522$	4.45898			0.195164
$523$	19.5623	+	33.8829i	0.855400	+	1.48160i	0.876274	+	0.481814i	$0.160022\pi$
$523$	19.5623	+	33.8829i	0.855400	+	1.48160i	−0.0208736	+	0.999782i	$0.506645\pi$
$524$	0.302439	+	0.523840i	0.0132121	+	0.0228841i
$525$		0			0
$526$	−1.71885	−	2.97713i	−0.0749453	−	0.129809i
$527$	65.0689			2.83445
$528$	−2.91641	−	5.05137i	−0.126920	−	0.219833i
$529$	1.50000	−	2.59808i	0.0652174	−	0.112960i
$530$	−0.600813	−	1.04064i	−0.0260977	−	0.0452025i
$531$	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
$535$	−2.14590			−0.0927753
$536$	−1.04257			−0.0450323
$537$	3.43769			0.148347
$538$	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	−0.884016	−	0.467457i	$-0.845170\pi$
$541$	−0.864745	+	1.49778i	−0.0371783	+	0.0643947i	0.846838	+	0.531852i	$0.178504\pi$
$542$	−3.51722	+	6.09201i	−0.151078	+	0.261674i
$543$	1.41641			0.0607839
$544$	−15.4894	−	26.8284i	−0.664101	−	1.15026i
$545$	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	$0.520429\pi$
$548$	−0.354102	−	0.613323i	−0.0151265	−	0.0261998i
$549$	17.1246			0.730861
$550$	−4.50000	+	7.79423i	−0.191881	+	0.332347i
$551$	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
$555$	−0.583592			−0.0247721
$556$	28.8541			1.22369
$557$	18.9787			0.804154			0.402077	−	0.915606i	$-0.368288\pi$
$557$	18.9787			0.804154			0.402077	+	0.915606i	$0.368288\pi$
$558$	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
$562$	0.416408	+	0.721240i	0.0175651	+	0.0304237i
$563$	19.4721	−	33.7267i	0.820653	−	1.42141i	−0.0845442	−	0.996420i	$-0.526943\pi$
$563$	19.4721	−	33.7267i	0.820653	−	1.42141i	0.905197	−	0.424992i	$-0.139723\pi$
$564$	−0.791796	−	1.37143i	−0.0333406	−	0.0577477i
$565$	−2.85410			−0.120073
$566$	2.56231	+	4.43804i	0.107702	+	0.186545i
$567$		0			0
$568$	6.02129	+	10.4292i	0.252648	+	0.437598i
$569$	1.47214	+	2.54981i	0.0617151	+	0.106894i	0.895232	−	0.445600i	$-0.147010\pi$
$569$	1.47214	+	2.54981i	0.0617151	+	0.106894i	−0.833517	+	0.552494i	$0.813676\pi$
$570$	−0.270510			−0.0113304
$571$	17.8435	+	30.9058i	0.746726	+	1.29337i	0.949384	+	0.314117i	$0.101708\pi$
$571$	17.8435	+	30.9058i	0.746726	+	1.29337i	−0.202659	+	0.979249i	$0.564958\pi$
$572$	−9.00000	−	31.1769i	−0.376309	−	1.30357i
$573$	−9.02129			−0.376870
$574$		0			0
$575$	10.8541	−	18.7999i	0.452647	−	0.784008i
$576$	13.4377			0.559904
$577$	−4.91641	−	8.51547i	−0.204673	−	0.354504i	0.745356	−	0.666667i	$-0.232280\pi$
$577$	−4.91641	−	8.51547i	−0.204673	−	0.354504i	−0.950028	+	0.312163i	$0.898946\pi$
$578$	−7.41641	+	12.8456i	−0.308482	+	0.534306i
$579$	2.29180			0.0952438
$580$	2.89667			0.120278
$581$		0			0
$582$	0.886031	−	1.53465i	0.0367272	−	0.0636133i
$583$	19.9894	+	34.6226i	0.827875	+	1.43392i
$584$	−1.47214	−	2.54981i	−0.0609174	−	0.105512i
$585$	1.09017	+	3.77646i	0.0450730	+	0.156137i
$586$	2.14590	−	3.71680i	0.0886462	−	0.153540i
$587$	15.5451	−	26.9249i	0.641614	−	1.11131i	−0.343458	−	0.939168i	$-0.611598\pi$
$587$	15.5451	−	26.9249i	0.641614	−	1.11131i	0.985072	−	0.172141i	$-0.0550683\pi$
$588$		0			0
$589$	−21.1353	−	36.6073i	−0.870863	−	1.50838i
$590$	−0.163119	+	0.282530i	−0.00671550	+	0.0116316i
$591$	1.48936	−	2.57964i	0.0612640	−	0.106112i
$592$	−6.29180	+	10.8977i	−0.258591	+	0.447893i
$593$	−9.60081	+	16.6291i	−0.394258	+	0.682875i	−0.993006	−	0.118062i	$-0.962332\pi$
$593$	−9.60081	+	16.6291i	−0.394258	+	0.682875i	0.598748	+	0.800937i	$0.295665\pi$
$594$	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
$598$	−1.70820	−	5.91739i	−0.0698537	−	0.241980i
$599$	4.25329	+	7.36691i	0.173785	+	0.301004i	0.939740	−	0.341890i	$-0.111067\pi$
$599$	4.25329	+	7.36691i	0.173785	+	0.301004i	−0.765955	+	0.642894i	$0.777734\pi$
$600$	1.36475	+	2.36381i	0.0557155	+	0.0965021i
$601$	16.6976	−	28.9210i	0.681108	−	1.17971i	−0.293535	−	0.955948i	$-0.594832\pi$
$601$	16.6976	−	28.9210i	0.681108	−	1.17971i	0.974643	−	0.223765i	$-0.0718348\pi$
$602$		0			0
$603$	−2.02129			−0.0823131
$604$	27.2705			1.10962
$605$	−2.39919	+	4.15551i	−0.0975408	+	0.168946i
$606$	0.624612	+	1.08186i	0.0253731	+	0.0439475i
$607$	−23.0000			−0.933541			−0.466771	−	0.884378i	$-0.654583\pi$
$607$	−23.0000			−0.933541			−0.466771	+	0.884378i	$0.654583\pi$
$608$	−10.0623	+	17.4284i	−0.408080	+	0.706816i
$609$		0			0
$610$	−0.875388			−0.0354434
$611$	−2.23607	−	7.74597i	−0.0904616	−	0.313368i
$612$	−19.7705	−	34.2435i	−0.799175	−	1.38421i
$613$	14.4377			0.583133			0.291566	−	0.956551i	$-0.405824\pi$
$613$	14.4377			0.583133			0.291566	+	0.956551i	$0.405824\pi$
$614$	−0.354102	−	0.613323i	−0.0142904	−	0.0247517i
$615$	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	$0.950968\pi$
$618$	−0.686918			−0.0276319
$619$	8.70820	+	15.0831i	0.350012	+	0.606239i	0.986251	−	0.165253i	$-0.0528441\pi$
$619$	8.70820	+	15.0831i	0.350012	+	0.606239i	−0.636239	+	0.771492i	$0.719511\pi$
$620$	3.08359	−	5.34094i	0.123840	−	0.214497i
$621$	−5.00000	−	8.66025i	−0.200643	−	0.347524i
$622$	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
$626$	−5.77709			−0.230899
$627$	9.00000			0.359425
$628$	−15.1033			−0.602688
$629$	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
$633$	−1.66312	+	2.88061i	−0.0661030	+	0.114494i
$634$	8.31308			0.330155
$635$	2.70163	+	4.67935i	0.107211	+	0.185694i
$636$	5.83282			0.231286
$637$		0			0
$638$	7.58359			0.300237
$639$	11.6738	+	20.2195i	0.461807	+	0.799873i
$640$	−3.85410			−0.152347
$641$	4.74671	−	8.22154i	0.187484	−	0.324731i	−0.756927	−	0.653500i	$-0.773300\pi$
$641$	4.74671	−	8.22154i	0.187484	−	0.324731i	0.944411	+	0.328768i	$0.106633\pi$
$642$	−0.409830	+	0.709846i	−0.0161747	+	0.0280154i
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	0.926750	−	0.375680i	$-0.122591\pi$
$643$	3.50000	+	6.06218i	0.138027	+	0.239069i	−0.788723	+	0.614749i	$0.789257\pi$
$644$		0			0
$645$	1.10333			0.0434434
$646$	13.8541			0.545082
$647$	29.2361			1.14939			0.574694	−	0.818368i	$-0.305121\pi$
$647$	29.2361			1.14939			0.574694	+	0.818368i	$0.305121\pi$
$648$	−11.3475			−0.445773
$649$	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
$653$	1.30902	+	2.26728i	0.0512258	+	0.0887257i	0.890501	−	0.454981i	$-0.150354\pi$
$653$	1.30902	+	2.26728i	0.0512258	+	0.0887257i	−0.839275	+	0.543706i	$0.817021\pi$
$654$	0.781153	−	1.35300i	0.0305455	−	0.0529064i
$655$	−0.0623059	−	0.107917i	−0.00243449	−	0.00421667i
$656$	16.4721			0.643129
$657$	−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	$0.907715\pi$
$660$	0.656541	+	1.13716i	0.0255558	+	0.0442640i
$661$	18.5410			0.721162			0.360581	−	0.932728i	$-0.382578\pi$
$661$	18.5410			0.721162			0.360581	+	0.932728i	$0.382578\pi$
$662$	3.21885	+	5.57521i	0.125104	+	0.216687i
$663$	2.85410	+	9.88690i	0.110844	+	0.383975i
$664$	9.87539			0.383239
$665$		0			0
$666$	2.18034	−	3.77646i	0.0844865	−	0.146335i
$667$	−18.2918			−0.708261
$668$	9.05166	+	15.6779i	0.350219	+	0.606598i
$669$	−2.53444	+	4.38978i	−0.0979872	+	0.169719i
$670$	0.103326			0.00399181
$671$	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	$0.874127\pi$
$674$	−1.63525	−	2.83234i	−0.0629877	−	0.109098i
$675$	5.42705	+	9.39993i	0.208887	+	0.361803i
$676$	−21.3222	−	11.2399i	−0.820084	−	0.432304i
$677$	−0.628677	+	1.08890i	−0.0241620	+	0.0418499i	−0.877854	−	0.478929i	$-0.841025\pi$
$677$	−0.628677	+	1.08890i	−0.0241620	+	0.0418499i	0.853692	+	0.520779i	$0.174358\pi$
$678$	−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
$682$	8.07295	−	13.9828i	0.309129	−	0.535427i
$683$	3.73607	−	6.47106i	0.142957	−	0.247608i	−0.785652	−	0.618669i	$-0.787672\pi$
$683$	3.73607	−	6.47106i	0.142957	−	0.247608i	0.928609	+	0.371060i	$0.121006\pi$
$684$	−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
$689$	28.8262	+	7.13264i	1.09819	+	0.271732i
$690$	0.124612	+	0.215834i	0.00474389	+	0.00821666i
$691$	−0.427051	−	0.739674i	−0.0162458	−	0.0281385i	0.857788	−	0.514003i	$-0.171838\pi$
$691$	−0.427051	−	0.739674i	−0.0162458	−	0.0281385i	−0.874034	+	0.485865i	$0.838505\pi$
$692$	−8.34346	+	14.4513i	−0.317171	+	0.549356i
$693$		0			0
$694$	13.4590			0.510896
$695$	−5.94427			−0.225479
$696$	1.14996	−	1.99179i	0.0435892	−	0.0754988i
$697$	−19.5623	−	33.8829i	−0.740975	−	1.28341i
$698$	2.78522			0.105422
$699$	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	$0.459229\pi$
$702$	2.98936	+	0.739674i	0.112826	+	0.0279172i
$703$	−9.70820	−	16.8151i	−0.366152	−	0.634194i
$704$	22.8541			0.861346
$705$	0.163119	+	0.282530i	0.00614342	+	0.0106407i
$706$	−5.51064	−	9.54471i	−0.207396	−	0.359220i
$707$		0			0
$708$	−0.791796	−	1.37143i	−0.0297575	−	0.0515415i
$709$	3.43769			0.129105			0.0645527	−	0.997914i	$-0.479438\pi$
$709$	3.43769			0.129105			0.0645527	+	0.997914i	$0.479438\pi$
$710$	−0.596748	−	1.03360i	−0.0223955	−	0.0387902i
$711$	5.70820	−	9.88690i	0.214074	−	0.370788i
$712$	11.8435	+	20.5135i	0.443852	+	0.768775i
$713$	−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
$717$	4.31308			0.161075
$718$	−4.16718			−0.155518
$719$	−32.1246			−1.19805			−0.599023	−	0.800732i	$-0.704444\pi$
$719$	−32.1246			−1.19805			−0.599023	+	0.800732i	$0.704444\pi$
$720$	−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
$724$	−3.43769	+	5.95426i	−0.127761	+	0.221288i
$725$	19.8541			0.737363
$726$	0.916408	+	1.58726i	0.0340111	+	0.0589089i
$727$	−17.2918			−0.641317			−0.320659	−	0.947195i	$-0.603904\pi$
$727$	−17.2918			−0.641317			−0.320659	+	0.947195i	$0.603904\pi$
$728$		0			0
$729$	−19.4377			−0.719915
$730$	0.145898	+	0.252703i	0.00539993	+	0.00935295i
$731$	−56.5066			−2.08997
$732$	2.12461	−	3.67994i	0.0785279	−	0.136014i
$733$	−0.635255	+	1.10029i	−0.0234637	+	0.0406403i	−0.877519	−	0.479542i	$-0.840803\pi$
$733$	−0.635255	+	1.10029i	−0.0234637	+	0.0406403i	0.854055	+	0.520182i	$0.174136\pi$
$734$	−4.85410	−	8.40755i	−0.179168	−	0.310328i
$735$		0			0
$736$	18.5410			0.683431
$737$	−3.43769			−0.126629
$738$	−5.70820			−0.210122
$739$	−47.1246			−1.73351			−0.866753	−	0.498737i	$-0.833797\pi$
$739$	−47.1246			−1.73351			−0.866753	+	0.498737i	$0.833797\pi$
$740$	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	$0.309654\pi$
$744$	−2.44834	−	4.24064i	−0.0897604	−	0.155470i
$745$	0.927051	−	1.60570i	0.0339645	−	0.0588283i
$746$	0.0835921	+	0.144786i	0.00306053	+	0.00530099i
$747$	19.1459			0.700512
$748$	−33.6246	−	58.2395i	−1.22944	−	2.12945i
$749$		0			0
$750$	−0.274575	−	0.475578i	−0.0100261	−	0.0173657i
$751$	−4.64590	−	8.04693i	−0.169531	−	0.293637i	0.768724	−	0.639581i	$-0.220892\pi$
$751$	−4.64590	−	8.04693i	−0.169531	−	0.293637i	−0.938255	+	0.345944i	$0.887559\pi$
$752$	7.03444			0.256520
$753$	1.00000	+	1.73205i	0.0364420	+	0.0631194i
$754$	3.90576	−	4.05899i	0.142240	−	0.147820i
$755$	−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	$0.996742\pi$
$758$	−4.90983			−0.178333
$759$	−4.14590	−	7.18091i	−0.150487	−	0.260650i
$760$	1.36475	−	2.36381i	0.0495045	−	0.0857443i
$761$	−22.1459			−0.802788			−0.401394	−	0.915905i	$-0.631474\pi$
$761$	−22.1459			−0.802788			−0.401394	+	0.915905i	$0.631474\pi$
$762$	2.06386			0.0747657
$763$		0			0
$764$	21.8951	−	37.9235i	0.792138	−	1.37202i
$765$	4.07295	+	7.05455i	0.147258	+	0.255058i
$766$	−4.77051	−	8.26277i	−0.172366	−	0.298546i
$767$	−2.23607	−	7.74597i	−0.0807397	−	0.279691i
$768$	1.06231	−	1.83997i	0.0383327	−	0.0663941i
$769$	−4.20820	+	7.28882i	−0.151752	+	0.262842i	−0.931872	−	0.362788i	$-0.881825\pi$
$769$	−4.20820	+	7.28882i	−0.151752	+	0.262842i	0.780120	+	0.625630i	$0.215158\pi$
$770$		0			0
$771$	−4.91641	−	8.51547i	−0.177060	−	0.306677i
$772$	−5.56231	+	9.63420i	−0.200192	+	0.346742i
$773$	9.68034	−	16.7668i	0.348178	−	0.603061i	−0.637748	−	0.770245i	$-0.720134\pi$
$773$	9.68034	−	16.7668i	0.348178	−	0.603061i	0.985926	+	0.167184i	$0.0534673\pi$
$774$	−4.12210	+	7.13969i	−0.148166	+	0.256631i
$775$	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
$780$	0.946784	+	0.234268i	0.0339003	+	0.00838815i
$781$	19.8541	+	34.3883i	0.710436	+	1.23051i
$782$	−6.38197	−	11.0539i	−0.228219	−	0.395286i
$783$	4.57295	−	7.92058i	0.163424	−	0.283058i
$784$		0			0
$785$	3.11146			0.111053
$786$	−0.0475975			−0.00169775
$787$	−14.7082	+	25.4754i	−0.524291	+	0.908098i	0.475309	+	0.879819i	$0.342336\pi$
$787$	−14.7082	+	25.4754i	−0.524291	+	0.908098i	−0.999600	+	0.0282796i	$0.990997\pi$
$788$	7.22949	+	12.5218i	0.257540	+	0.446072i
$789$	−3.43769			−0.122385
$790$	−0.291796	+	0.505406i	−0.0103816	+	0.0179815i
$791$		0			0
$792$	−20.3951			−0.724709
$793$	15.0000	−	15.5885i	0.532666	−	0.553562i
$794$	4.85410	+	8.40755i	0.172266	+	0.298373i
$795$	−1.20163			−0.0426173
$796$	2.24013	+	3.88002i	0.0793994	+	0.137524i
$797$	−7.09017	−	12.2805i	−0.251147	−	0.434999i	0.712695	−	0.701474i	$-0.247474\pi$
$797$	−7.09017	−	12.2805i	−0.251147	−	0.434999i	−0.963842	+	0.266475i	$0.914141\pi$
$798$		0			0
$799$	−8.35410	−	14.4697i	−0.295547	−	0.511902i
$800$	−20.1246			−0.711512
$801$	22.9615	+	39.7705i	0.811304	+	1.40522i
$802$	3.90576	−	6.76498i	0.137917	−	0.238880i
$803$	−4.85410	−	8.40755i	−0.171298	−	0.296696i
$804$	−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
$808$	−12.6049			−0.443438
$809$	22.4164			0.788119			0.394059	−	0.919085i	$-0.371070\pi$
$809$	22.4164			0.788119			0.394059	+	0.919085i	$0.371070\pi$
$810$	1.12461			0.0395148
$811$	5.72949			0.201190			0.100595	−	0.994927i	$-0.467925\pi$
$811$	5.72949			0.201190			0.100595	+	0.994927i	$0.467925\pi$
$812$		0			0
$813$	3.51722	+	6.09201i	0.123354	+	0.213656i
$814$	3.70820	−	6.42280i	0.129972	−	0.225119i
$815$	−1.85410	+	3.21140i	−0.0649464	+	0.112490i
$816$	−8.97871			−0.314318
$817$	18.3541	+	31.7902i	0.642129	+	1.11220i
$818$	13.2016			0.461584
$819$		0			0
$820$	−3.70820			−0.129496
$821$	−18.6803	−	32.3553i	−0.651948	−	1.12921i	−0.982650	−	0.185472i	$-0.940619\pi$
$821$	−18.6803	−	32.3553i	−0.651948	−	1.12921i	0.330701	−	0.943736i	$-0.392715\pi$
$822$	0.0557281			0.00194374
$823$	5.79180	−	10.0317i	0.201889	−	0.349683i	−0.747248	−	0.664545i	$-0.768625\pi$
$823$	5.79180	−	10.0317i	0.201889	−	0.349683i	0.949137	+	0.314863i	$0.101959\pi$
$824$	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	$0.681053\pi$
$828$	23.6656			0.822438
$829$	−12.5623			−0.436307			−0.218153	−	0.975914i	$-0.570003\pi$
$829$	−12.5623			−0.436307			−0.218153	+	0.975914i	$0.570003\pi$
$830$	−0.978714			−0.0339717
$831$	−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
$835$	−1.86475	−	3.22983i	−0.0645322	−	0.111773i
$836$	−21.8435	+	37.8340i	−0.755472	+	1.30852i
$837$	−9.73607	−	16.8634i	−0.336528	−	0.582883i
$838$	2.27051			0.0784335
$839$	14.3713	+	24.8919i	0.496153	+	0.859362i	0.999990	−	0.00443626i	$-0.00141211\pi$
$839$	14.3713	+	24.8919i	0.496153	+	0.859362i	−0.503837	+	0.863799i	$0.668079\pi$
$840$		0			0
$841$	6.13525	+	10.6266i	0.211561	+	0.366434i
$842$	4.85410	+	8.40755i	0.167283	+	0.289743i
$843$	0.832816			0.0286837
$844$	−8.07295	−	13.9828i	−0.277882	−	0.481306i
$845$	4.39261	+	2.31555i	0.151110	+	0.0796572i
$846$	−2.43769			−0.0838096
$847$		0			0
$848$	−12.9549	+	22.4386i	−0.444874	+	0.770544i
$849$	5.12461			0.175876
$850$	6.92705	+	11.9980i	0.237596	+	0.411528i
$851$	−8.94427	+	15.4919i	−0.306606	+	0.531057i
$852$	5.79335			0.198477
$853$	−26.1246			−0.894490			−0.447245	−	0.894412i	$-0.647595\pi$
$853$	−26.1246			−0.894490			−0.447245	+	0.894412i	$0.647595\pi$
$854$		0			0
$855$	2.64590	−	4.58283i	0.0904878	−	0.156729i
$856$	−4.13525	−	7.16247i	−0.141340	−	0.244808i
$857$	−14.7254	−	25.5052i	−0.503011	−	0.871240i	−0.999994	−	0.00348022i	$-0.998892\pi$
$857$	−14.7254	−	25.5052i	−0.503011	−	0.871240i	0.496983	−	0.867760i	$-0.334441\pi$
$858$	2.47871	+	0.613323i	0.0846219	+	0.0209385i
$859$	−18.1246	+	31.3927i	−0.618404	+	1.07111i	0.371373	+	0.928484i	$0.378887\pi$
$859$	−18.1246	+	31.3927i	−0.618404	+	1.07111i	−0.989777	+	0.142623i	$0.954446\pi$
$860$	−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	−0.587917	−	0.808921i	$-0.700052\pi$
$863$	11.9443	−	20.6881i	0.406588	−	0.704231i	0.994505	+	0.104691i	$0.0333852\pi$
$864$	−4.63525	+	8.02850i	−0.157695	+	0.273135i
$865$	1.71885	−	2.97713i	0.0584426	−	0.101225i
$866$	−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
$871$	−1.77051	+	1.83997i	−0.0599914	+	0.0623449i
$872$	7.88197	+	13.6520i	0.266917	+	0.462314i
$873$	17.3328	+	30.0213i	0.586627	+	1.01607i
$874$	−4.14590	+	7.18091i	−0.140237	+	0.242898i
$875$		0			0
$876$	−1.41641			−0.0478560
$877$	−12.7082			−0.429126			−0.214563	−	0.976710i	$-0.568833\pi$
$877$	−12.7082			−0.429126			−0.214563	+	0.976710i	$0.568833\pi$
$878$	−1.55573	+	2.69460i	−0.0525033	+	0.0909383i
$879$	−2.14590	−	3.71680i	−0.0723793	−	0.125365i
$880$	−5.83282			−0.196624
$881$	−6.29837	+	10.9091i	−0.212198	+	0.367537i	−0.952402	−	0.304845i	$-0.901395\pi$
$881$	−6.29837	+	10.9091i	−0.212198	+	0.367537i	0.740204	+	0.672382i	$0.234729\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	−48.4894	−	11.9980i	−1.63087	−	0.403537i
$885$	0.163119	+	0.282530i	0.00548318	+	0.00949715i
$886$	−0.291796			−0.00980308
$887$	−11.6738	−	20.2195i	−0.391967	−	0.678906i	0.600742	−	0.799443i	$-0.294872\pi$
$887$	−11.6738	−	20.2195i	−0.391967	−	0.678906i	−0.992709	+	0.120537i	$0.961538\pi$
$888$	−1.12461	−	1.94788i	−0.0377395	−	0.0653667i
$889$		0			0
$890$	−1.17376	−	2.03302i	−0.0393446	−	0.0681468i
$891$	−37.4164			−1.25350
$892$	−12.3024	−	21.3084i	−0.411916	−	0.713460i
$893$	−5.42705	+	9.39993i	−0.181609	+	0.314557i
$894$	−0.354102	−	0.613323i	−0.0118429	−	0.0205126i
$895$	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
$899$	−35.6180			−1.18793
$900$	−25.6869			−0.856231
$901$	61.5410			2.05023
$902$	−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
$906$	−1.07295	+	1.85840i	−0.0356463	+	0.0617413i
$907$	−24.0000			−0.796907			−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000			−0.796907			−0.398453	+	0.917189i	$0.630453\pi$
$908$	−6.92705	−	11.9980i	−0.229882	−	0.398168i
$909$	−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	$0.285380\pi$
$912$	2.91641	+	5.05137i	0.0965719	+	0.167267i
$913$	32.5623			1.07766
$914$	2.18034	−	3.77646i	0.0721192	−	0.124914i
$915$	−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
$919$	−30.0000			−0.989609			−0.494804	−	0.869004i	$-0.664760\pi$
$919$	−30.0000			−0.989609			−0.494804	+	0.869004i	$0.664760\pi$
$920$	−2.51471			−0.0829075
$921$	−0.708204			−0.0233361
$922$	−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
$926$	1.28115	+	2.21902i	0.0421013	+	0.0729216i
$927$	6.71885	−	11.6374i	0.220676	−	0.382222i
$928$	8.47871	+	14.6856i	0.278327	+	0.482077i
$929$	−47.0689			−1.54428			−0.772140	−	0.635452i	$-0.780814\pi$
$929$	−47.0689			−1.54428			−0.772140	+	0.635452i	$0.780814\pi$
$930$	0.242646	+	0.420275i	0.00795667	+	0.0137814i
$931$		0			0
$932$	0.354102	+	0.613323i	0.0115990	+	0.0200900i
$933$	−2.35410	−	4.07742i	−0.0770698	−	0.133489i
$934$	12.8541			0.420599
$935$	6.92705	+	11.9980i	0.226539	+	0.392377i
$936$	−10.5041	+	10.9161i	−0.343336	+	0.356805i
$937$	−56.1246			−1.83351			−0.916756	−	0.399449i	$-0.869202\pi$
$937$	−56.1246			−1.83351			−0.916756	+	0.399449i	$0.869202\pi$
$938$		0			0
$939$	−2.88854	+	5.00310i	−0.0942641	+	0.163270i
$940$	−1.58359			−0.0516511
$941$	−25.8262	−	44.7324i	−0.841911	−	1.45823i	−0.888277	−	0.459309i	$-0.848097\pi$
$941$	−25.8262	−	44.7324i	−0.841911	−	1.45823i	0.0463655	−	0.998925i	$-0.485236\pi$
$942$	0.594235	−	1.02925i	0.0193612	−	0.0335346i
$943$	23.4164			0.762543
$944$	7.03444			0.228952
$945$		0			0
$946$	−7.01064	+	12.1428i	−0.227936	+	0.394796i
$947$	−22.9336	−	39.7222i	−0.745243	−	1.29080i	−0.950081	−	0.312003i	$-0.899000\pi$
$947$	−22.9336	−	39.7222i	−0.745243	−	1.29080i	0.204838	−	0.978796i	$-0.434333\pi$
$948$	−1.41641	−	2.45329i	−0.0460028	−	0.0796792i
$949$	−7.00000	−	1.73205i	−0.227230	−	0.0562247i
$950$	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
$955$	−4.51064	+	7.81266i	−0.145961	+	0.252812i
$956$	−10.4681	+	18.1312i	−0.338562	+	0.586406i
$957$	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
$962$	−1.52786	−	5.29268i	−0.0492603	−	0.170643i
$963$	−8.01722	−	13.8862i	−0.258351	−	0.447478i
$964$	4.11397	+	7.12560i	0.132502	+	0.229500i
$965$	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	$0.715749\pi$
$968$	−18.4934			−0.594401
$969$	6.92705	−	11.9980i	0.222529	−	0.385431i
$970$	−0.886031	−	1.53465i	−0.0284488	−	0.0492747i
$971$	58.4164			1.87467			0.937336	−	0.348427i	$-0.113284\pi$
$971$	58.4164			1.87467			0.937336	+	0.348427i	$0.113284\pi$
$972$	−8.94834	+	15.4990i	−0.287018	+	0.497130i
$973$		0			0
$974$	−6.48529			−0.207802
$975$	6.48936	+	1.60570i	0.207826	+	0.0514235i
$976$	9.43769	+	16.3466i	0.302093	+	0.523241i
$977$	−31.4721			−1.00688			−0.503441	−	0.864029i	$-0.667933\pi$
$977$	−31.4721			−1.00688			−0.503441	+	0.864029i	$0.667933\pi$
$978$	0.708204	+	1.22665i	0.0226459	+	0.0392238i
$979$	39.0517	+	67.6395i	1.24810	+	2.16177i
$980$		0			0
$981$	15.2812	+	26.4677i	0.487890	+	0.845050i
$982$	5.58359			0.178180
$983$	−10.3090	−	17.8557i	−0.328807	−	0.569510i	0.653469	−	0.756953i	$-0.273313\pi$
$983$	−10.3090	−	17.8557i	−0.328807	−	0.569510i	−0.982275	+	0.187444i	$0.939980\pi$
$984$	−1.47214	+	2.54981i	−0.0469300	+	0.0812851i
$985$	−1.48936	−	2.57964i	−0.0474549	−	0.0821942i
$986$	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
$990$	2.02129			0.0642407
$991$	−22.8541			−0.725984			−0.362992	−	0.931792i	$-0.618245\pi$
$991$	−22.8541			−0.725984			−0.362992	+	0.931792i	$0.618245\pi$
$992$	36.1033			1.14628
$993$	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
$997$	−24.5000	+	42.4352i	−0.775923	+	1.34394i	0.158352	+	0.987383i	$0.449382\pi$
$997$	−24.5000	+	42.4352i	−0.775923	+	1.34394i	−0.934274	+	0.356555i	$0.883951\pi$
$998$	3.11146			0.0984914
$999$	−4.47214	−	7.74597i	−0.141492	−	0.245072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.b.373.2		4
7.2	even	3		91.2.f.a.22.2	✓	4
7.3	odd	6		637.2.h.f.165.1		4
7.4	even	3		637.2.h.g.165.1		4
7.5	odd	6		637.2.f.c.295.2		4
7.6	odd	2		637.2.g.c.373.2		4
13.3	even	3		637.2.h.g.471.1		4
21.2	odd	6		819.2.o.c.568.1		4
28.23	odd	6		1456.2.s.h.113.2		4
91.3	odd	6		637.2.g.c.263.2		4
91.9	even	3		1183.2.a.g.1.1		2
91.16	even	3		91.2.f.a.29.2	yes	4
91.30	even	6		1183.2.a.c.1.2		2
91.55	odd	6		637.2.h.f.471.1		4
91.58	odd	12		1183.2.c.c.337.2		4
91.61	odd	6		8281.2.a.bb.1.1		2
91.68	odd	6		637.2.f.c.393.2		4
91.72	odd	12		1183.2.c.c.337.3		4
91.81	even	3	inner	637.2.g.b.263.2		4
91.82	odd	6		8281.2.a.n.1.2		2
273.107	odd	6		819.2.o.c.757.1		4
364.107	odd	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	7.2	even	3
91.2.f.a.29.2	yes	4	91.16	even	3
637.2.f.c.295.2		4	7.5	odd	6
637.2.f.c.393.2		4	91.68	odd	6
637.2.g.b.263.2		4	91.81	even	3	inner
637.2.g.b.373.2		4	1.1	even	1	trivial
637.2.g.c.263.2		4	91.3	odd	6
637.2.g.c.373.2		4	7.6	odd	2
637.2.h.f.165.1		4	7.3	odd	6
637.2.h.f.471.1		4	91.55	odd	6
637.2.h.g.165.1		4	7.4	even	3
637.2.h.g.471.1		4	13.3	even	3
819.2.o.c.568.1		4	21.2	odd	6
819.2.o.c.757.1		4	273.107	odd	6
1183.2.a.c.1.2		2	91.30	even	6
1183.2.a.g.1.1		2	91.9	even	3
1183.2.c.c.337.2		4	91.58	odd	12
1183.2.c.c.337.3		4	91.72	odd	12
1456.2.s.h.113.2		4	28.23	odd	6
1456.2.s.h.1121.2		4	364.107	odd	6
8281.2.a.n.1.2		2	91.82	odd	6
8281.2.a.bb.1.1		2	91.61	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.190983 - 0.330792i) q^{2} -0.381966 q^{3} +(0.927051 - 1.60570i) q^{4} +(-0.190983 + 0.330792i) q^{5} +(0.0729490 + 0.126351i) q^{6} -1.47214 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+(-0.190983 - 0.330792i) q^{2} -0.381966 q^{3} +(0.927051 - 1.60570i) q^{4} +(-0.190983 + 0.330792i) q^{5} +(0.0729490 + 0.126351i) q^{6} -1.47214 q^{8} -2.85410 q^{9} +0.145898 q^{10} -4.85410 q^{11} +(-0.354102 + 0.613323i) q^{12} +(-2.50000 + 2.59808i) q^{13} +(0.0729490 - 0.126351i) q^{15} +(-1.57295 - 2.72443i) q^{16} +(-3.73607 + 6.47106i) q^{17} +(0.545085 + 0.944115i) q^{18} +4.85410 q^{19} +(0.354102 + 0.613323i) q^{20} +(0.927051 + 1.60570i) q^{22} +(-2.23607 - 3.87298i) q^{23} +0.562306 q^{24} +(2.42705 + 4.20378i) q^{25} +(1.33688 + 0.330792i) q^{26} +2.23607 q^{27} +(2.04508 - 3.54219i) q^{29} -0.0557281 q^{30} +(-4.35410 - 7.54153i) q^{31} +(-2.07295 + 3.59045i) q^{32} +1.85410 q^{33} +2.85410 q^{34} +(-2.64590 + 4.58283i) q^{36} +(-2.00000 - 3.46410i) q^{37} +(-0.927051 - 1.60570i) q^{38} +(0.954915 - 0.992377i) 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} +(0.545085 - 0.944115i) q^{45} +(-0.854102 + 1.47935i) 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} +(1.85410 + 6.42280i) q^{52} +(-4.11803 - 7.13264i) q^{53} +(-0.427051 - 0.739674i) q^{54} +(0.927051 - 1.60570i) q^{55} -1.85410 q^{57} -1.56231 q^{58} +(-1.11803 + 1.93649i) q^{59} +(-0.135255 - 0.234268i) q^{60} -6.00000 q^{61} +(-1.66312 + 2.88061i) q^{62} -4.70820 q^{64} +(-0.381966 - 1.32317i) q^{65} +(-0.354102 - 0.613323i) q^{66} +0.708204 q^{67} +(6.92705 + 11.9980i) q^{68} +(0.854102 + 1.47935i) q^{69} +(-4.09017 - 7.08438i) q^{71} +4.20163 q^{72} +(1.00000 + 1.73205i) q^{73} +(-0.763932 + 1.32317i) q^{74} +(-0.927051 - 1.60570i) q^{75} +(4.50000 - 7.79423i) q^{76} +(-0.510643 - 0.126351i) q^{78} +(-2.00000 + 3.46410i) q^{79} +1.20163 q^{80} +7.70820 q^{81} +2.00000 q^{82} -6.70820 q^{83} +(-1.42705 - 2.47172i) q^{85} +(1.44427 - 2.50155i) q^{86} +(-0.781153 + 1.35300i) q^{87} +7.14590 q^{88} +(-8.04508 - 13.9345i) q^{89} -0.416408 q^{90} -8.29180 q^{92} +(1.66312 + 2.88061i) q^{93} +0.854102 q^{94} +(-0.927051 + 1.60570i) q^{95} +(0.791796 - 1.37143i) q^{96} +(-6.07295 - 10.5187i) q^{97} +13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 6 * q^3 - 3 * q^4 - 3 * q^5 + 7 * q^6 + 12 * q^8 + 2 * q^9	\( 4 q - 3 q^{2} - 6 q^{3} - 3 q^{4} - 3 q^{5} + 7 q^{6} + 12 q^{8} + 2 q^{9} + 14 q^{10} - 6 q^{11} + 12 q^{12} - 10 q^{13} + 7 q^{15} - 13 q^{16} - 6 q^{17} - 9 q^{18} + 6 q^{19} - 12 q^{20} - 3 q^{22} - 38 q^{24} + 3 q^{25} + 21 q^{26} - 3 q^{29} - 36 q^{30} - 4 q^{31} - 15 q^{32} - 6 q^{33} - 2 q^{34} - 24 q^{36} - 8 q^{37} + 3 q^{38} + 15 q^{39} - 19 q^{40} - 6 q^{41} - 5 q^{43} - 18 q^{44} - 9 q^{45} + 10 q^{46} + 27 q^{48} - 3 q^{50} - q^{51} - 6 q^{52} - 12 q^{53} + 5 q^{54} - 3 q^{55} + 6 q^{57} + 34 q^{58} + 33 q^{60} - 24 q^{61} + 9 q^{62} + 8 q^{64} - 6 q^{65} + 12 q^{66} - 24 q^{67} + 21 q^{68} - 10 q^{69} + 6 q^{71} + 66 q^{72} + 4 q^{73} - 12 q^{74} + 3 q^{75} + 18 q^{76} - 49 q^{78} - 8 q^{79} + 54 q^{80} + 4 q^{81} + 8 q^{82} + q^{85} - 30 q^{86} + 17 q^{87} + 42 q^{88} - 21 q^{89} + 52 q^{90} - 60 q^{92} - 9 q^{93} - 10 q^{94} + 3 q^{95} + 30 q^{96} - 31 q^{97} + 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 6 * q^3 - 3 * q^4 - 3 * q^5 + 7 * q^6 + 12 * q^8 + 2 * q^9 + 14 * q^10 - 6 * q^11 + 12 * q^12 - 10 * q^13 + 7 * q^15 - 13 * q^16 - 6 * q^17 - 9 * q^18 + 6 * q^19 - 12 * q^20 - 3 * q^22 - 38 * q^24 + 3 * q^25 + 21 * q^26 - 3 * q^29 - 36 * q^30 - 4 * q^31 - 15 * q^32 - 6 * q^33 - 2 * q^34 - 24 * q^36 - 8 * q^37 + 3 * q^38 + 15 * q^39 - 19 * q^40 - 6 * q^41 - 5 * q^43 - 18 * q^44 - 9 * q^45 + 10 * q^46 + 27 * q^48 - 3 * q^50 - q^51 - 6 * q^52 - 12 * q^53 + 5 * q^54 - 3 * q^55 + 6 * q^57 + 34 * q^58 + 33 * q^60 - 24 * q^61 + 9 * q^62 + 8 * q^64 - 6 * q^65 + 12 * q^66 - 24 * q^67 + 21 * q^68 - 10 * q^69 + 6 * q^71 + 66 * q^72 + 4 * q^73 - 12 * q^74 + 3 * q^75 + 18 * q^76 - 49 * q^78 - 8 * q^79 + 54 * q^80 + 4 * q^81 + 8 * q^82 + q^85 - 30 * q^86 + 17 * q^87 + 42 * q^88 - 21 * q^89 + 52 * q^90 - 60 * q^92 - 9 * q^93 - 10 * q^94 + 3 * q^95 + 30 * q^96 - 31 * q^97 + 42 * q^99

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