LMFDB - Embedded newform 637.2.f.c.393.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.2
Root			$-0.309017 - 0.535233i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.c.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.190983 - 0.330792i) q^{2} +(-0.190983 - 0.330792i) q^{3} +(0.927051 - 1.60570i) q^{4} -0.381966 q^{5} +(-0.0729490 + 0.126351i) q^{6} -1.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +O(q^{10})$	\(q+(-0.190983 - 0.330792i) q^{2} +(-0.190983 - 0.330792i) q^{3} +(0.927051 - 1.60570i) q^{4} -0.381966 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} -0.708204 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} -1.09017 q^{18} +(2.42705 - 4.20378i) q^{19} +(-0.354102 + 0.613323i) q^{20} +(0.927051 - 1.60570i) q^{22} +(-2.23607 - 3.87298i) q^{23} +(0.281153 + 0.486971i) q^{24} -4.85410 q^{25} +(0.381966 - 1.32317i) q^{26} -2.23607 q^{27} +(2.04508 + 3.54219i) q^{29} +(0.0278640 - 0.0482619i) q^{30} -8.70820 q^{31} +(-2.07295 + 3.59045i) q^{32} +(0.927051 - 1.60570i) q^{33} -2.85410 q^{34} +(-2.64590 - 4.58283i) q^{36} +(-2.00000 - 3.46410i) q^{37} -1.85410 q^{38} +(0.381966 - 1.32317i) q^{39} +0.562306 q^{40} +(2.61803 + 4.53457i) q^{41} +(3.78115 - 6.54915i) q^{43} +9.00000 q^{44} +(-0.545085 + 0.944115i) q^{45} +(-0.854102 + 1.47935i) q^{46} -2.23607 q^{47} +(-0.600813 + 1.04064i) q^{48} +(0.927051 + 1.60570i) q^{50} -2.85410 q^{51} +(6.48936 - 1.60570i) q^{52} +8.23607 q^{53} +(0.427051 + 0.739674i) q^{54} +(-0.927051 - 1.60570i) q^{55} -1.85410 q^{57} +(0.781153 - 1.35300i) q^{58} +(1.11803 - 1.93649i) q^{59} +0.270510 q^{60} +(-3.00000 + 5.19615i) q^{61} +(1.66312 + 2.88061i) q^{62} -4.70820 q^{64} +(-0.954915 - 0.992377i) q^{65} -0.708204 q^{66} +(-0.354102 - 0.613323i) q^{67} +(-6.92705 - 11.9980i) q^{68} +(-0.854102 + 1.47935i) q^{69} +(-4.09017 + 7.08438i) q^{71} +(-2.10081 + 3.63871i) q^{72} +2.00000 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} +4.00000 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} -2.88854 q^{86} +(0.781153 - 1.35300i) q^{87} +(-3.57295 - 6.18853i) q^{88} +(8.04508 + 13.9345i) q^{89} +0.416408 q^{90} -8.29180 q^{92} +(1.66312 + 2.88061i) q^{93} +(0.427051 + 0.739674i) q^{94} +(-0.927051 + 1.60570i) q^{95} +1.58359 q^{96} +(6.07295 - 10.5187i) q^{97} +13.8541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 7 * q^6 + 12 * q^8 - q^9	$ 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9} + 7 q^{10} + 3 q^{11} + 24 q^{12} + 10 q^{13} + 7 q^{15} - 13 q^{16} + 6 q^{17} + 18 q^{18} + 3 q^{19} + 12 q^{20} - 3 q^{22} - 19 q^{24} - 6 q^{25} + 6 q^{26} - 3 q^{29} + 18 q^{30} - 8 q^{31} - 15 q^{32} - 3 q^{33} + 2 q^{34} - 24 q^{36} - 8 q^{37} + 6 q^{38} + 6 q^{39} - 38 q^{40} + 6 q^{41} - 5 q^{43} + 36 q^{44} + 9 q^{45} + 10 q^{46} - 27 q^{48} - 3 q^{50} + 2 q^{51} - 21 q^{52} + 24 q^{53} - 5 q^{54} + 3 q^{55} + 6 q^{57} - 17 q^{58} - 66 q^{60} - 12 q^{61} - 9 q^{62} + 8 q^{64} - 15 q^{65} + 24 q^{66} + 12 q^{67} - 21 q^{68} + 10 q^{69} + 6 q^{71} - 33 q^{72} + 8 q^{73} - 12 q^{74} - 3 q^{75} - 18 q^{76} - 49 q^{78} + 16 q^{79} + 27 q^{80} - 2 q^{81} + 4 q^{82} + q^{85} + 60 q^{86} - 17 q^{87} - 21 q^{88} + 21 q^{89} - 52 q^{90} - 60 q^{92} - 9 q^{93} - 5 q^{94} + 3 q^{95} + 60 q^{96} + 31 q^{97} + 42 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 7 * q^6 + 12 * q^8 - q^9 + 7 * q^10 + 3 * q^11 + 24 * q^12 + 10 * q^13 + 7 * q^15 - 13 * q^16 + 6 * q^17 + 18 * q^18 + 3 * q^19 + 12 * q^20 - 3 * q^22 - 19 * q^24 - 6 * q^25 + 6 * q^26 - 3 * q^29 + 18 * q^30 - 8 * q^31 - 15 * q^32 - 3 * q^33 + 2 * q^34 - 24 * q^36 - 8 * q^37 + 6 * q^38 + 6 * q^39 - 38 * q^40 + 6 * q^41 - 5 * q^43 + 36 * q^44 + 9 * q^45 + 10 * q^46 - 27 * q^48 - 3 * q^50 + 2 * q^51 - 21 * q^52 + 24 * q^53 - 5 * q^54 + 3 * q^55 + 6 * q^57 - 17 * q^58 - 66 * q^60 - 12 * q^61 - 9 * q^62 + 8 * q^64 - 15 * q^65 + 24 * q^66 + 12 * q^67 - 21 * q^68 + 10 * q^69 + 6 * q^71 - 33 * q^72 + 8 * q^73 - 12 * q^74 - 3 * q^75 - 18 * q^76 - 49 * q^78 + 16 * q^79 + 27 * q^80 - 2 * q^81 + 4 * q^82 + q^85 + 60 * q^86 - 17 * q^87 - 21 * q^88 + 21 * q^89 - 52 * q^90 - 60 * q^92 - 9 * q^93 - 5 * q^94 + 3 * q^95 + 60 * q^96 + 31 * q^97 + 42 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.190983	−	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	$0.876451\pi$
$3$	−0.190983	−	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	$0.868503\pi$
$4$	0.927051	−	1.60570i	0.463525	−	0.802850i
$5$	−0.381966			−0.170820			−0.0854102	−	0.996346i	$-0.527220\pi$
$5$	−0.381966			−0.170820			−0.0854102	+	0.996346i	$0.527220\pi$
$6$	−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	$0.572022\pi$
$12$	−0.708204			−0.204441
$13$	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	$-0.472356\pi$
$17$	3.73607	−	6.47106i	0.906130	−	1.56946i	0.819394	−	0.573231i	$-0.194310\pi$
$18$	−1.09017			−0.256956
$19$	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
$23$	−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	$0.987729\pi$
$24$	0.281153	+	0.486971i	0.0573901	+	0.0994026i
$25$	−4.85410			−0.970820
$26$	0.381966	−	1.32317i	0.0749097	−	0.259495i
$27$	−2.23607			−0.430331
$28$		0			0
$29$	2.04508	+	3.54219i	0.379763	+	0.657768i	0.991028	−	0.133658i	$-0.0426723\pi$
$29$	2.04508	+	3.54219i	0.379763	+	0.657768i	−0.611265	+	0.791426i	$0.709339\pi$
$30$	0.0278640	−	0.0482619i	0.00508726	−	0.00881138i
$31$	−8.70820			−1.56404			−0.782020	−	0.623254i	$-0.785810\pi$
$31$	−8.70820			−1.56404			−0.782020	+	0.623254i	$0.785810\pi$
$32$	−2.07295	+	3.59045i	−0.366449	+	0.634708i
$33$	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
$37$	−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	$0.939977\pi$
$38$	−1.85410			−0.300775
$39$	0.381966	−	1.32317i	0.0611635	−	0.211877i
$40$	0.562306			0.0889084
$41$	2.61803	+	4.53457i	0.408868	+	0.708181i	0.994763	−	0.102206i	$-0.0325902\pi$
$41$	2.61803	+	4.53457i	0.408868	+	0.708181i	−0.585895	+	0.810387i	$0.699257\pi$
$42$		0			0
$43$	3.78115	−	6.54915i	0.576620	−	0.998736i	−0.419243	−	0.907874i	$-0.637704\pi$
$43$	3.78115	−	6.54915i	0.576620	−	0.998736i	0.995864	−	0.0908618i	$-0.0289622\pi$
$44$	9.00000			1.35680
$45$	−0.545085	+	0.944115i	−0.0812565	+	0.140740i
$46$	−0.854102	+	1.47935i	−0.125930	+	0.218118i
$47$	−2.23607			−0.326164			−0.163082	−	0.986613i	$-0.552144\pi$
$47$	−2.23607			−0.326164			−0.163082	+	0.986613i	$0.552144\pi$
$48$	−0.600813	+	1.04064i	−0.0867199	+	0.150203i
$49$		0			0
$50$	0.927051	+	1.60570i	0.131105	+	0.227080i
$51$	−2.85410			−0.399654
$52$	6.48936	−	1.60570i	0.899912	−	0.222670i
$53$	8.23607			1.13131			0.565655	−	0.824642i	$-0.308623\pi$
$53$	8.23607			1.13131			0.565655	+	0.824642i	$0.308623\pi$
$54$	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
$58$	0.781153	−	1.35300i	0.102570	−	0.177657i
$59$	1.11803	−	1.93649i	0.145556	−	0.252110i	−0.784024	−	0.620730i	$-0.786836\pi$
$59$	1.11803	−	1.93649i	0.145556	−	0.252110i	0.929580	+	0.368620i	$0.120170\pi$
$60$	0.270510			0.0349227
$61$	−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
$65$	−0.954915	−	0.992377i	−0.118443	−	0.123089i
$66$	−0.708204			−0.0871739
$67$	−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	$0.847108\pi$
$68$	−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	−0.999860	−	0.0167615i	$-0.994664\pi$
$71$	−4.09017	+	7.08438i	−0.485414	+	0.840761i	0.514446	+	0.857523i	$0.327998\pi$
$72$	−2.10081	+	3.63871i	−0.247583	+	0.428827i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	−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
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	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
$86$	−2.88854			−0.311480
$87$	0.781153	−	1.35300i	0.0837484	−	0.145056i
$88$	−3.57295	−	6.18853i	−0.380878	−	0.659699i
$89$	8.04508	+	13.9345i	0.852777	+	1.47705i	0.878692	+	0.477389i	$0.158417\pi$
$89$	8.04508	+	13.9345i	0.852777	+	1.47705i	−0.0259145	+	0.999664i	$0.508250\pi$
$90$	0.416408			0.0438932
$91$		0			0
$92$	−8.29180			−0.864479
$93$	1.66312	+	2.88061i	0.172457	+	0.298705i
$94$	0.427051	+	0.739674i	0.0440469	+	0.0762915i
$95$	−0.927051	+	1.60570i	−0.0951134	+	0.164741i
$96$	1.58359			0.161625
$97$	6.07295	−	10.5187i	0.616615	−	1.06801i	−0.373484	−	0.927636i	$-0.621837\pi$
$97$	6.07295	−	10.5187i	0.616615	−	1.06801i	0.990099	−	0.140371i	$-0.0448296\pi$
$98$		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
$103$	−4.70820			−0.463913			−0.231957	−	0.972726i	$-0.574513\pi$
$103$	−4.70820			−0.463913			−0.231957	+	0.972726i	$0.574513\pi$
$104$	−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
$109$	10.7082			1.02566			0.512830	−	0.858490i	$-0.328597\pi$
$109$	10.7082			1.02566			0.512830	+	0.858490i	$0.328597\pi$
$110$	−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	−0.635046	−	0.772475i	$-0.719019\pi$
$113$	3.73607	−	6.47106i	0.351460	−	0.608746i	0.986505	+	0.163728i	$0.0523521\pi$
$114$	0.354102	+	0.613323i	0.0331647	+	0.0574429i
$115$	0.854102	+	1.47935i	0.0796454	+	0.137950i
$116$	7.58359			0.704119
$117$	9.98936	−	2.47172i	0.923516	−	0.228511i
$118$	−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
$122$	2.29180			0.207489
$123$	1.00000	−	1.73205i	0.0901670	−	0.156174i
$124$	−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	0.988027	+	0.154278i	$0.0493053\pi$
$127$	7.07295	+	12.2507i	0.627623	+	1.08707i	−0.360405	+	0.932796i	$0.617361\pi$
$128$	5.04508	+	8.73834i	0.445927	+	0.772368i
$129$	−2.88854			−0.254322
$130$	−0.145898	+	0.505406i	−0.0127961	+	0.0443270i
$131$	−0.326238			−0.0285035			−0.0142518	−	0.999898i	$-0.504537\pi$
$131$	−0.326238			−0.0285035			−0.0142518	+	0.999898i	$0.504537\pi$
$132$	−1.71885	−	2.97713i	−0.149606	−	0.259126i
$133$		0			0
$134$	−0.135255	+	0.234268i	−0.0116842	+	0.0202377i
$135$	0.854102			0.0735094
$136$	−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	$0.161473\pi$
$138$	0.652476			0.0555424
$139$	−7.78115	+	13.4774i	−0.659989	+	1.14313i	0.320629	+	0.947205i	$0.396106\pi$
$139$	−7.78115	+	13.4774i	−0.659989	+	1.14313i	−0.980618	+	0.195929i	$0.937228\pi$
$140$		0			0
$141$	0.427051	+	0.739674i	0.0359642	+	0.0622918i
$142$	3.12461			0.262212
$143$	−4.85410	+	16.8151i	−0.405920	+	1.40615i
$144$	−8.97871			−0.748226
$145$	−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
$149$	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	$0.102952\pi$
$150$	0.354102	−	0.613323i	0.0289123	−	0.0500776i
$151$	−14.7082			−1.19694			−0.598468	−	0.801146i	$-0.704224\pi$
$151$	−14.7082			−1.19694			−0.598468	+	0.801146i	$0.704224\pi$
$152$	−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
$156$	−1.77051	−	1.83997i	−0.141754	−	0.147315i
$157$	−8.14590			−0.650113			−0.325057	−	0.945695i	$-0.605383\pi$
$157$	−8.14590			−0.650113			−0.325057	+	0.945695i	$0.605383\pi$
$158$	−0.763932	−	1.32317i	−0.0607752	−	0.105266i
$159$	−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
$163$	−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	$0.290812\pi$
$164$	9.70820			0.758083
$165$	−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	$-0.0433550\pi$
$167$	4.88197	+	8.45581i	0.377778	+	0.654330i	−0.612961	+	0.790113i	$0.710022\pi$
$168$		0			0
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$	1.09017			0.0836122
$171$	−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
$177$	−0.854102			−0.0641982
$178$	3.07295	−	5.32250i	0.230327	−	0.398939i
$179$	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	$0.724142\pi$
$180$	1.01064	+	1.75049i	0.0753289	+	0.130473i
$181$	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
$184$	3.29180	+	5.70156i	0.242674	+	0.420324i
$185$	0.763932	+	1.32317i	0.0561654	+	0.0972813i
$186$	0.635255	−	1.10029i	0.0465792	−	0.0806775i
$187$	36.2705			2.65236
$188$	−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	$0.764050\pi$
$194$	−4.63932			−0.333084
$195$	−0.145898	+	0.505406i	−0.0104480	+	0.0361928i
$196$		0			0
$197$	−3.89919	−	6.75359i	−0.277806	−	0.481173i	0.693034	−	0.720905i	$-0.256274\pi$
$197$	−3.89919	−	6.75359i	−0.277806	−	0.481173i	−0.970839	+	0.239732i	$0.922940\pi$
$198$	−2.64590	−	4.58283i	−0.188036	−	0.325688i
$199$	1.20820	−	2.09267i	0.0856473	−	0.148345i	−0.820020	−	0.572336i	$-0.806038\pi$
$199$	1.20820	−	2.09267i	0.0856473	−	0.148345i	0.905667	+	0.423990i	$0.139371\pi$
$200$	7.14590			0.505291
$201$	−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
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$	0.899187	+	1.55744i	0.0626493	+	0.108512i
$207$	−12.7639			−0.887155
$208$	3.14590	−	10.8977i	0.218129	−	0.755620i
$209$	23.5623			1.62984
$210$		0			0
$211$	4.35410	+	7.54153i	0.299749	+	0.519180i	0.976078	−	0.217419i	$-0.0697638\pi$
$211$	4.35410	+	7.54153i	0.299749	+	0.519180i	−0.676330	+	0.736599i	$0.736430\pi$
$212$	7.63525	−	13.2246i	0.524391	−	0.908273i
$213$	3.12461			0.214095
$214$	1.07295	−	1.85840i	0.0733453	−	0.127038i
$215$	−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
$219$	−0.381966	−	0.661585i	−0.0258109	−	0.0447057i
$220$	−3.43769			−0.231769
$221$	26.1525	−	6.47106i	1.75921	−	0.435291i
$222$	0.583592			0.0391681
$223$	−6.63525	−	11.4926i	−0.444330	−	0.769601i	0.553676	−	0.832732i	$-0.313225\pi$
$223$	−6.63525	−	11.4926i	−0.444330	−	0.769601i	−0.998005	+	0.0631310i	$0.979891\pi$
$224$		0			0
$225$	−6.92705	+	11.9980i	−0.461803	+	0.799867i
$226$	−2.85410			−0.189852
$227$	−3.73607	+	6.47106i	−0.247972	+	0.429499i	−0.962963	−	0.269634i	$-0.913097\pi$
$227$	−3.73607	+	6.47106i	−0.247972	+	0.429499i	0.714991	+	0.699133i	$0.246431\pi$
$228$	−1.71885	+	2.97713i	−0.113833	+	0.197165i
$229$	−27.1246			−1.79244			−0.896222	−	0.443605i	$-0.853699\pi$
$229$	−27.1246			−1.79244			−0.896222	+	0.443605i	$0.853699\pi$
$230$	0.326238	−	0.565061i	0.0215115	−	0.0372590i
$231$		0			0
$232$	−3.01064	−	5.21459i	−0.197658	−	0.342354i
$233$	0.381966			0.0250234			0.0125117	−	0.999922i	$-0.496017\pi$
$233$	0.381966			0.0250234			0.0125117	+	0.999922i	$0.496017\pi$
$234$	−2.72542	−	2.83234i	−0.178167	−	0.185156i
$235$	0.854102			0.0557155
$236$	−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	$0.619000\pi$
$240$	0.229490	−	0.397489i	0.0148135	−	0.0256578i
$241$	2.21885	−	3.84316i	0.142929	−	0.247559i	−0.785670	−	0.618646i	$-0.787681\pi$
$241$	2.21885	−	3.84316i	0.142929	−	0.247559i	0.928598	+	0.371087i	$0.121015\pi$
$242$	4.79837			0.308451
$243$	−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
$247$	16.9894	−	4.20378i	1.08101	−	0.267480i
$248$	12.8197			0.814049
$249$	−1.28115	−	2.21902i	−0.0811898	−	0.140625i
$250$	−0.718847	−	1.24508i	−0.0454639	−	0.0787457i
$251$	2.61803	−	4.53457i	0.165249	−	0.286219i	−0.771495	−	0.636236i	$-0.780491\pi$
$251$	2.61803	−	4.53457i	0.165249	−	0.286219i	0.936744	+	0.350016i	$0.113824\pi$
$252$		0			0
$253$	10.8541	−	18.7999i	0.682392	−	1.18194i
$254$	2.70163	−	4.67935i	0.169515	−	0.293609i
$255$	1.09017			0.0682691
$256$	−2.78115	+	4.81710i	−0.173822	+	0.301069i
$257$	−12.8713	−	22.2938i	−0.802891	−	1.39065i	−0.917706	−	0.397261i	$-0.869961\pi$
$257$	−12.8713	−	22.2938i	−0.802891	−	1.39065i	0.114815	−	0.993387i	$-0.463373\pi$
$258$	0.551663	+	0.955508i	0.0343450	+	0.0594873i
$259$		0			0
$260$	−2.47871	+	0.613323i	−0.153723	+	0.0380367i
$261$	11.6738			0.722588
$262$	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
$268$	−1.31308			−0.0802093
$269$	6.87132	−	11.9015i	0.418952	−	0.725646i	−0.576882	−	0.816827i	$-0.695731\pi$
$269$	6.87132	−	11.9015i	0.418952	−	0.725646i	0.995834	+	0.0911812i	$0.0290642\pi$
$270$	−0.163119	−	0.282530i	−0.00992710	−	0.0171942i
$271$	9.20820	+	15.9491i	0.559359	+	0.968837i	0.997550	+	0.0699558i	$0.0222858\pi$
$271$	9.20820	+	15.9491i	0.559359	+	0.968837i	−0.438192	+	0.898882i	$0.644381\pi$
$272$	−23.5066			−1.42530
$273$		0			0
$274$	−0.145898			−0.00881402
$275$	−11.7812	−	20.4056i	−0.710430	−	1.23050i
$276$	1.58359	+	2.74286i	0.0953210	+	0.165101i
$277$	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	$0.118672\pi$
$278$	5.94427			0.356514
$279$	−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
$285$	0.708204			0.0419504
$286$	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
$291$	−4.63932			−0.271962
$292$	1.85410	−	3.21140i	0.108503	−	0.187933i
$293$	−5.61803	+	9.73072i	−0.328209	+	0.568475i	−0.982157	−	0.188065i	$-0.939778\pi$
$293$	−5.61803	+	9.73072i	−0.328209	+	0.568475i	0.653947	+	0.756540i	$0.273112\pi$
$294$		0			0
$295$	−0.427051	+	0.739674i	−0.0248639	+	0.0430655i
$296$	2.94427	+	5.09963i	0.171132	+	0.296410i
$297$	−5.42705	−	9.39993i	−0.314909	−	0.545439i
$298$	−1.85410			−0.107405
$299$	4.47214	−	15.4919i	0.258630	−	0.895922i
$300$	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
$304$	−15.2705			−0.875824
$305$	1.14590	−	1.98475i	0.0656139	−	0.113647i
$306$	−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
$310$	−0.635255	−	1.10029i	−0.0360801	−	0.0624925i
$311$	12.3262			0.698957			0.349478	−	0.936944i	$-0.386359\pi$
$311$	12.3262			0.698957			0.349478	+	0.936944i	$0.386359\pi$
$312$	−0.562306	+	1.94788i	−0.0318343	+	0.110277i
$313$	15.1246			0.854894			0.427447	−	0.904041i	$-0.359413\pi$
$313$	15.1246			0.854894			0.427447	+	0.904041i	$0.359413\pi$
$314$	1.55573	+	2.69460i	0.0877948	+	0.152065i
$315$		0			0
$316$	3.70820	−	6.42280i	0.208603	−	0.361311i
$317$	21.7639			1.22238			0.611192	−	0.791482i	$-0.290690\pi$
$317$	21.7639			1.22238			0.611192	+	0.791482i	$0.290690\pi$
$318$	−0.600813	+	1.04064i	−0.0336919	+	0.0583561i
$319$	−9.92705	+	17.1942i	−0.555808	+	0.962688i
$320$	1.79837			0.100532
$321$	1.07295	−	1.85840i	0.0598862	−	0.103726i
$322$		0			0
$323$	−18.1353	−	31.4112i	−1.00907	−	1.74776i
$324$	−14.2918			−0.793989
$325$	−12.1353	−	12.6113i	−0.673143	−	0.699551i
$326$	3.70820			0.205378
$327$	−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
$331$	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	$0.0133705\pi$
$332$	6.21885	−	10.7714i	0.341304	−	0.591155i
$333$	−11.4164			−0.625615
$334$	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	$0.425077\pi$
$338$	4.39261	−	2.31555i	0.238926	−	0.125949i
$339$	−2.85410			−0.155014
$340$	2.64590	+	4.58283i	0.143494	+	0.248539i
$341$	−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
$345$	0.326238	−	0.565061i	0.0175641	−	0.0304218i
$346$	3.43769			0.184812
$347$	−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	$-0.104144\pi$
$349$	3.64590	+	6.31488i	0.195160	+	0.338028i	−0.751793	+	0.659400i	$0.770811\pi$
$350$		0			0
$351$	−5.59017	−	5.80948i	−0.298381	−	0.310087i
$352$	−20.1246			−1.07265
$353$	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
$359$	−10.9098			−0.575799			−0.287899	−	0.957661i	$-0.592957\pi$
$359$	−10.9098			−0.575799			−0.287899	+	0.957661i	$0.592957\pi$
$360$	0.802439	−	1.38987i	0.0422923	−	0.0732523i
$361$	−2.28115	−	3.95107i	−0.120061	−	0.207951i
$362$	−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
$367$	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	$0.602462\pi$
$368$	−7.03444	+	12.1840i	−0.366696	+	0.635135i
$369$	14.9443			0.777968
$370$	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
$376$	3.29180			0.169761
$377$	−4.09017	+	14.1688i	−0.210654	+	0.729728i
$378$		0			0
$379$	6.42705	+	11.1320i	0.330135	+	0.571811i	0.982538	−	0.186061i	$-0.0595722\pi$
$379$	6.42705	+	11.1320i	0.330135	+	0.571811i	−0.652403	+	0.757872i	$0.726239\pi$
$380$	1.71885	+	2.97713i	0.0881750	+	0.152724i
$381$	2.70163	−	4.67935i	0.138408	−	0.239731i
$382$	9.02129			0.461569
$383$	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
$387$	−10.7918	−	18.6919i	−0.548578	−	0.950165i
$388$	−11.2599	−	19.5027i	−0.571633	−	0.990098i
$389$	23.8885			1.21120			0.605599	−	0.795770i	$-0.292934\pi$
$389$	23.8885			1.21120			0.605599	+	0.795770i	$0.292934\pi$
$390$	0.195048	−	0.0482619i	0.00987666	−	0.00244384i
$391$	−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
$395$	−1.52786			−0.0768752
$396$	12.8435	−	22.2455i	0.645408	−	1.11788i
$397$	−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
$401$	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	$0.662744\pi$
$402$	0.103326			0.00515341
$403$	−21.7705	−	22.6246i	−1.08447	−	1.12701i
$404$	15.8754			0.789830
$405$	1.47214	+	2.54981i	0.0731510	+	0.126701i
$406$		0			0
$407$	9.70820	−	16.8151i	0.481218	−	0.833494i
$408$	4.20163			0.208011
$409$	17.2812	−	29.9318i	0.854498	−	1.48003i	−0.0226119	−	0.999744i	$-0.507198\pi$
$409$	17.2812	−	29.9318i	0.854498	−	1.48003i	0.877110	−	0.480290i	$-0.159468\pi$
$410$	−0.381966	+	0.661585i	−0.0188640	+	0.0326733i
$411$	−0.145898			−0.00719662
$412$	−4.36475	+	7.55996i	−0.215036	+	0.372453i
$413$		0			0
$414$	2.43769	+	4.22221i	0.119806	+	0.207510i
$415$	−2.56231			−0.125779
$416$	−14.5106	+	3.59045i	−0.711443	+	0.176036i
$417$	5.94427			0.291092
$418$	−4.50000	−	7.79423i	−0.220102	−	0.381228i
$419$	2.97214	+	5.14789i	0.145198	+	0.251491i	0.929447	−	0.368956i	$-0.120285\pi$
$419$	2.97214	+	5.14789i	0.145198	+	0.251491i	−0.784249	+	0.620447i	$0.786951\pi$
$420$		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
$423$	−3.19098	+	5.52694i	−0.155151	+	0.268729i
$424$	−12.1246			−0.588823
$425$	−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
$429$	6.48936	−	1.60570i	0.313309	−	0.0775239i
$430$	1.10333			0.0532071
$431$	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	$0.700753\pi$
$432$	3.51722	+	6.09201i	0.169222	+	0.293102i
$433$	0.500000	−	0.866025i	0.0240285	−	0.0416185i	−0.853761	−	0.520665i	$-0.825684\pi$
$433$	0.500000	−	0.866025i	0.0240285	−	0.0416185i	0.877790	+	0.479046i	$0.159017\pi$
$434$		0			0
$435$	−0.298374	+	0.516799i	−0.0143059	+	0.0247786i
$436$	9.92705	−	17.1942i	0.475420	−	0.823451i
$437$	−21.7082			−1.03844
$438$	−0.145898	+	0.252703i	−0.00697128	+	0.0120746i
$439$	4.07295	+	7.05455i	0.194391	+	0.336696i	0.946701	−	0.322114i	$-0.104394\pi$
$439$	4.07295	+	7.05455i	0.194391	+	0.336696i	−0.752310	+	0.658810i	$0.771060\pi$
$440$	1.36475	+	2.36381i	0.0650617	+	0.112690i
$441$		0			0
$442$	−7.13525	−	7.41517i	−0.339389	−	0.352704i
$443$	−0.763932			−0.0362955			−0.0181478	−	0.999835i	$-0.505777\pi$
$443$	−0.763932			−0.0362955			−0.0181478	+	0.999835i	$0.505777\pi$
$444$	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	0.305540	+	0.952179i	$0.401163\pi$
$449$	−14.2361	+	24.6576i	−0.671842	+	1.16366i	−0.977381	+	0.211484i	$0.932170\pi$
$450$	5.29180			0.249458
$451$	−12.7082	+	22.0113i	−0.598406	+	1.03647i
$452$	−6.92705	−	11.9980i	−0.325821	−	0.564339i
$453$	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	$0.747295\pi$
$458$	5.18034	+	8.97261i	0.242061	+	0.419263i
$459$	−8.35410	+	14.4697i	−0.389936	+	0.675389i
$460$	3.16718			0.147671
$461$	19.6074	−	33.9610i	0.913207	−	1.58172i	0.103702	−	0.994608i	$-0.466931\pi$
$461$	19.6074	−	33.9610i	0.913207	−	1.58172i	0.809505	−	0.587113i	$-0.199736\pi$
$462$		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
$467$	−33.6525			−1.55725			−0.778625	−	0.627489i	$-0.784083\pi$
$467$	−33.6525			−1.55725			−0.778625	+	0.627489i	$0.784083\pi$
$468$	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
$473$	36.7082			1.68785
$474$	−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
$478$	2.15654	+	3.73524i	0.0986379	+	0.170846i
$479$	−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	$-0.334112\pi$
$480$	−0.604878			−0.0276088
$481$	4.00000	−	13.8564i	0.182384	−	0.631798i
$482$	−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
$486$	3.68692			0.167242
$487$	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	$0.0409752\pi$
$488$	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	0.652631	−	0.757676i	$-0.273665\pi$
$491$	−7.30902	−	12.6596i	−0.329851	−	0.571319i	−0.982482	+	0.186357i	$0.940332\pi$
$492$	−1.85410	−	3.21140i	−0.0835894	−	0.144781i
$493$	30.5623			1.37646
$494$	−4.63525	−	4.81710i	−0.208550	−	0.216731i
$495$	−5.29180			−0.237849
$496$	13.6976	+	23.7249i	0.615039	+	1.06528i
$497$		0			0
$498$	−0.489357	+	0.847591i	−0.0219286	+	0.0379815i
$499$	8.14590			0.364660			0.182330	−	0.983237i	$-0.441636\pi$
$499$	8.14590			0.364660			0.182330	+	0.983237i	$0.441636\pi$
$500$	3.48936	−	6.04374i	0.156049	−	0.270284i
$501$	1.86475	−	3.22983i	0.0833107	−	0.144298i
$502$	−2.00000			−0.0892644
$503$	12.1910	−	21.1154i	0.543569	−	0.941489i	−0.455126	−	0.890427i	$-0.650406\pi$
$503$	12.1910	−	21.1154i	0.543569	−	0.941489i	0.998695	−	0.0510624i	$-0.0162607\pi$
$504$		0			0
$505$	−1.63525	−	2.83234i	−0.0727679	−	0.126038i
$506$	−8.29180			−0.368615
$507$	4.39261	−	2.31555i	0.195083	−	0.102837i
$508$	26.2279			1.16368
$509$	15.2984	+	26.4976i	0.678089	+	1.17448i	0.975556	+	0.219752i	$0.0705247\pi$
$509$	15.2984	+	26.4976i	0.678089	+	1.17448i	−0.297467	+	0.954732i	$0.596142\pi$
$510$	−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
$514$	−4.91641	+	8.51547i	−0.216853	+	0.375601i
$515$	1.79837			0.0792458
$516$	−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
$520$	1.40576	+	1.46091i	0.0616469	+	0.0640653i
$521$	12.6525			0.554315			0.277158	−	0.960824i	$-0.410608\pi$
$521$	12.6525			0.554315			0.277158	+	0.960824i	$0.410608\pi$
$522$	−2.22949	−	3.86159i	−0.0975821	−	0.169017i
$523$	−19.5623	−	33.8829i	−0.855400	−	1.48160i	−0.876274	−	0.481814i	$-0.839978\pi$
$523$	−19.5623	−	33.8829i	−0.855400	−	1.48160i	0.0208736	−	0.999782i	$-0.493355\pi$
$524$	−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
$528$	−5.83282			−0.253841
$529$	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
$534$	−2.34752			−0.101587
$535$	−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
$541$	1.72949			0.0743566			0.0371783	−	0.999309i	$-0.488163\pi$
$541$	1.72949			0.0743566			0.0371783	+	0.999309i	$0.488163\pi$
$542$	3.51722	−	6.09201i	0.151078	−	0.261674i
$543$	−0.708204	−	1.22665i	−0.0303919	−	0.0526404i
$544$	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
$549$	8.56231	+	14.8303i	0.365430	+	0.632944i
$550$	−4.50000	+	7.79423i	−0.191881	+	0.332347i
$551$	19.8541			0.845813
$552$	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	$0.965045\pi$
$558$	9.49342			0.401889
$559$	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	$0.473057\pi$
$563$	−19.4721	+	33.7267i	−0.820653	+	1.42141i	−0.905197	+	0.424992i	$0.860277\pi$
$564$	1.58359			0.0666813
$565$	−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
$569$	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	$0.813676\pi$
$570$	−0.135255	−	0.234268i	−0.00566521	−	0.00981242i
$571$	−35.6869			−1.49345			−0.746726	−	0.665132i	$-0.768375\pi$
$571$	−35.6869			−1.49345			−0.746726	+	0.665132i	$0.768375\pi$
$572$	22.5000	+	23.3827i	0.940772	+	0.977679i
$573$	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
$577$	−9.83282			−0.409345			−0.204673	−	0.978830i	$-0.565613\pi$
$577$	−9.83282			−0.409345			−0.204673	+	0.978830i	$0.565613\pi$
$578$	−7.41641	+	12.8456i	−0.308482	+	0.534306i
$579$	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
$583$	19.9894	+	34.6226i	0.827875	+	1.43392i
$584$	−2.94427			−0.121835
$585$	−3.81559	+	0.944115i	−0.157755	+	0.0390343i
$586$	4.29180			0.177292
$587$	−15.5451	−	26.9249i	−0.641614	−	1.11131i	−0.985072	−	0.172141i	$-0.944932\pi$
$587$	−15.5451	−	26.9249i	−0.641614	−	1.11131i	0.343458	−	0.939168i	$-0.388402\pi$
$588$		0			0
$589$	−21.1353	+	36.6073i	−0.870863	+	1.50838i
$590$	0.326238			0.0134310
$591$	−1.48936	+	2.57964i	−0.0612640	+	0.106112i
$592$	−6.29180	+	10.8977i	−0.258591	+	0.447893i
$593$	−19.2016			−0.788516			−0.394258	−	0.919000i	$-0.628998\pi$
$593$	−19.2016			−0.788516			−0.394258	+	0.919000i	$0.628998\pi$
$594$	−2.07295	+	3.59045i	−0.0850541	+	0.147318i
$595$		0			0
$596$	−4.50000	−	7.79423i	−0.184327	−	0.319264i
$597$	−0.922986			−0.0377753
$598$	−5.97871	+	1.47935i	−0.244488	+	0.0604950i
$599$	−8.50658			−0.347569			−0.173785	−	0.984784i	$-0.555600\pi$
$599$	−8.50658			−0.347569			−0.173785	+	0.984784i	$0.555600\pi$
$600$	−1.36475	−	2.36381i	−0.0557155	−	0.0965021i
$601$	−16.6976	−	28.9210i	−0.681108	−	1.17971i	−0.974643	−	0.223765i	$-0.928165\pi$
$601$	−16.6976	−	28.9210i	−0.681108	−	1.17971i	0.293535	−	0.955948i	$-0.405168\pi$
$602$		0			0
$603$	−2.02129			−0.0823131
$604$	−13.6353	+	23.6170i	−0.554811	+	0.960960i
$605$	2.39919	−	4.15551i	0.0975408	−	0.168946i
$606$	−1.24922			−0.0507462
$607$	−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
$611$	−5.59017	−	5.80948i	−0.226154	−	0.235026i
$612$	−39.5410			−1.59835
$613$	−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	$0.927510\pi$
$614$	0.354102	+	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	−0.988159	−	0.153431i	$-0.950968\pi$
$617$	−8.97214	+	15.5402i	−0.361205	+	0.625625i	0.626955	+	0.779056i	$0.284301\pi$
$618$	0.343459	−	0.594888i	0.0138159	−	0.0239299i
$619$	17.4164			0.700025			0.350012	−	0.936745i	$-0.386177\pi$
$619$	17.4164			0.700025			0.350012	+	0.936745i	$0.386177\pi$
$620$	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
$625$	22.8328			0.913313
$626$	−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	−0.145360	−	0.989379i	$-0.546434\pi$
$631$	19.6976	−	34.1172i	0.784148	−	1.35818i	0.929507	−	0.368804i	$-0.120233\pi$
$632$	−5.88854			−0.234234
$633$	1.66312	−	2.88061i	0.0661030	−	0.114494i
$634$	−4.15654	−	7.19934i	−0.165077	−	0.285922i
$635$	−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
$640$	−1.92705	−	3.33775i	−0.0761734	−	0.131936i
$641$	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	$0.106633\pi$
$642$	−0.819660			−0.0323494
$643$	−3.50000	+	6.06218i	−0.138027	+	0.239069i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$	−3.50000	+	6.06218i	−0.138027	+	0.239069i	0.788723	+	0.614749i	$0.210743\pi$
$644$		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
$649$	10.8541			0.426061
$650$	−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
$655$	0.124612			0.00486899
$656$	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	−0.958266	−	0.285877i	$-0.907715\pi$
$659$	−5.94427	+	10.2958i	−0.231556	+	0.401067i	0.726710	+	0.686944i	$0.241048\pi$
$660$	0.656541	+	1.13716i	0.0255558	+	0.0442640i
$661$	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	$0.715912\pi$
$662$	−6.43769			−0.250208
$663$	−7.13525	−	7.41517i	−0.277110	−	0.287982i
$664$	−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
$668$	18.1033			0.700439
$669$	−2.53444	+	4.38978i	−0.0979872	+	0.169719i
$670$	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	−0.922826	−	0.385216i	$-0.874127\pi$
$673$	−20.6246	−	35.7229i	−0.795020	−	1.37702i	0.127806	−	0.991799i	$-0.459207\pi$
$674$	−1.63525	−	2.83234i	−0.0629877	−	0.109098i
$675$	10.8541			0.417775
$676$	20.3951	+	12.8456i	0.784428	+	0.494061i
$677$	−1.25735			−0.0483240			−0.0241620	−	0.999708i	$-0.507692\pi$
$677$	−1.25735			−0.0483240			−0.0241620	+	0.999708i	$0.507692\pi$
$678$	0.545085	+	0.944115i	0.0209339	+	0.0362585i
$679$		0			0
$680$	2.10081	−	3.63871i	0.0805625	−	0.139538i
$681$	2.85410			0.109369
$682$	−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	$0.121006\pi$
$684$	−25.6869			−0.982164
$685$	−0.0729490	+	0.126351i	−0.00278724	+	0.00482764i
$686$		0			0
$687$	5.18034	+	8.97261i	0.197642	+	0.342326i
$688$	−23.7902			−0.906995
$689$	20.5902	+	21.3979i	0.784423	+	0.815196i
$690$	−0.249224			−0.00948778
$691$	0.427051	+	0.739674i	0.0162458	+	0.0281385i	0.874034	−	0.485865i	$-0.161495\pi$
$691$	0.427051	+	0.739674i	0.0162458	+	0.0281385i	−0.857788	+	0.514003i	$0.828162\pi$
$692$	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
$696$	−1.14996	+	1.99179i	−0.0435892	+	0.0754988i
$697$	39.1246			1.48195
$698$	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	$0.459229\pi$
$702$	−0.854102	+	2.95870i	−0.0322360	+	0.111669i
$703$	−19.4164			−0.732304
$704$	−11.4271	−	19.7922i	−0.430673	−	0.745948i
$705$	−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
$709$	−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	$0.187229\pi$
$710$	−1.19350			−0.0447911
$711$	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
$716$	16.6869			0.623619
$717$	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
$723$	−1.69505			−0.0630395
$724$	3.43769	−	5.95426i	0.127761	−	0.221288i
$725$	−9.92705	−	17.1942i	−0.368681	−	0.638575i
$726$	−0.916408	−	1.58726i	−0.0340111	−	0.0589089i
$727$	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
$730$	0.145898	+	0.252703i	0.00539993	+	0.00935295i
$731$	−28.2533	−	48.9361i	−1.04499	−	1.80997i
$732$	2.12461	−	3.67994i	0.0785279	−	0.136014i
$733$	−1.27051			−0.0469274			−0.0234637	−	0.999725i	$-0.507469\pi$
$733$	−1.27051			−0.0469274			−0.0234637	+	0.999725i	$0.507469\pi$
$734$	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	$0.499536\pi$
$740$	2.83282			0.104136
$741$	−4.63525	−	4.81710i	−0.170280	−	0.176961i
$742$		0			0
$743$	−11.8369	−	20.5021i	−0.434253	−	0.752148i	0.562981	−	0.826470i	$-0.309654\pi$
$743$	−11.8369	−	20.5021i	−0.434253	−	0.752148i	−0.997234	+	0.0743213i	$0.976321\pi$
$744$	−2.44834	−	4.24064i	−0.0897604	−	0.155470i
$745$	−0.927051	+	1.60570i	−0.0339645	+	0.0588283i
$746$	−0.167184			−0.00612105
$747$	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
$751$	−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	$0.887559\pi$
$752$	3.51722	+	6.09201i	0.128260	+	0.222153i
$753$	−2.00000			−0.0728841
$754$	5.46807	−	1.35300i	0.199135	−	0.0492732i
$755$	5.61803			0.204461
$756$		0			0
$757$	−14.0000	−	24.2487i	−0.508839	−	0.881334i	−0.999948	−	0.0102362i	$-0.996742\pi$
$757$	−14.0000	−	24.2487i	−0.508839	−	0.881334i	0.491109	−	0.871098i	$-0.336592\pi$
$758$	2.45492	−	4.25204i	0.0891665	−	0.154441i
$759$	−8.29180			−0.300973
$760$	1.36475	−	2.36381i	0.0495045	−	0.0857443i
$761$	−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
$765$	4.07295	+	7.05455i	0.147258	+	0.255058i
$766$	−9.54102			−0.344731
$767$	7.82624	−	1.93649i	0.282589	−	0.0699227i
$768$	2.12461			0.0766653
$769$	4.20820	+	7.28882i	0.151752	+	0.262842i	0.931872	−	0.362788i	$-0.118175\pi$
$769$	4.20820	+	7.28882i	0.151752	+	0.262842i	−0.780120	+	0.625630i	$0.784842\pi$
$770$		0			0
$771$	−4.91641	+	8.51547i	−0.177060	+	0.306677i
$772$	11.1246			0.400384
$773$	−9.68034	+	16.7668i	−0.348178	+	0.603061i	−0.985926	−	0.167184i	$-0.946533\pi$
$773$	−9.68034	+	16.7668i	−0.348178	+	0.603061i	0.637748	+	0.770245i	$0.279866\pi$
$774$	−4.12210	+	7.13969i	−0.148166	+	0.256631i
$775$	42.2705			1.51840
$776$	−8.94021	+	15.4849i	−0.320935	+	0.555875i
$777$		0			0
$778$	−4.56231	−	7.90215i	−0.163567	−	0.283306i
$779$	25.4164			0.910637
$780$	0.676275	+	0.702805i	0.0242145	+	0.0251645i
$781$	−39.7082			−1.42087
$782$	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
$786$	0.0237987	−	0.0412206i	0.000848873	−	0.00147029i
$787$	14.7082	−	25.4754i	0.524291	−	0.908098i	−0.475309	−	0.879819i	$-0.657664\pi$
$787$	14.7082	−	25.4754i	0.524291	−	0.908098i	0.999600	−	0.0282796i	$-0.00900287\pi$
$788$	−14.4590			−0.515080
$789$	−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
$793$	−21.0000	+	5.19615i	−0.745732	+	0.184521i
$794$	9.70820			0.344531
$795$	0.600813	+	1.04064i	0.0213086	+	0.0369077i
$796$	−2.24013	−	3.88002i	−0.0793994	−	0.137524i
$797$	7.09017	−	12.2805i	0.251147	−	0.434999i	−0.712695	−	0.701474i	$-0.752526\pi$
$797$	7.09017	−	12.2805i	0.251147	−	0.434999i	0.963842	+	0.266475i	$0.0858590\pi$
$798$		0			0
$799$	−8.35410	+	14.4697i	−0.295547	+	0.511902i
$800$	10.0623	−	17.4284i	0.355756	−	0.616188i
$801$	45.9230			1.62261
$802$	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
$807$	−5.24922			−0.184781
$808$	−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
$814$	−7.41641			−0.259945
$815$	1.85410	−	3.21140i	0.0649464	−	0.112490i
$816$	4.48936	+	7.77579i	0.157159	+	0.272207i
$817$	−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	$-0.392715\pi$
$822$	0.0278640	+	0.0482619i	0.000971870	+	0.00168333i
$823$	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	$0.101959\pi$
$824$	6.93112			0.241457
$825$	−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
$831$	−1.90983			−0.0662513
$832$	−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
$837$	19.4721			0.673055
$838$	1.13525	−	1.96632i	0.0392167	−	0.0679254i
$839$	−14.3713	+	24.8919i	−0.496153	+	0.859362i	−0.999990	−	0.00443626i	$-0.998588\pi$
$839$	−14.3713	+	24.8919i	−0.496153	+	0.859362i	0.503837	+	0.863799i	$0.331921\pi$
$840$		0			0
$841$	6.13525	−	10.6266i	0.211561	−	0.366434i
$842$	4.85410	+	8.40755i	0.167283	+	0.289743i
$843$	0.416408	+	0.721240i	0.0143418	+	0.0248408i
$844$	16.1459			0.555765
$845$	0.190983	−	4.96188i	0.00657002	−	0.170694i
$846$	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
$850$	13.8541			0.475192
$851$	−8.94427	+	15.4919i	−0.306606	+	0.531057i
$852$	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
$856$	−4.13525	−	7.16247i	−0.141340	−	0.244808i
$857$	−29.4508			−1.00602			−0.503011	−	0.864280i	$-0.667774\pi$
$857$	−29.4508			−1.00602			−0.503011	+	0.864280i	$0.667774\pi$
$858$	−1.77051	−	1.83997i	−0.0604442	−	0.0628155i
$859$	−36.2492			−1.23681			−0.618404	−	0.785861i	$-0.712220\pi$
$859$	−36.2492			−1.23681			−0.618404	+	0.785861i	$0.712220\pi$
$860$	2.67783	+	4.63813i	0.0913132	+	0.158159i
$861$		0			0
$862$	3.20820	−	5.55677i	0.109272	−	0.189264i
$863$	−23.8885			−0.813175			−0.406588	−	0.913612i	$-0.633281\pi$
$863$	−23.8885			−0.813175			−0.406588	+	0.913612i	$0.633281\pi$
$864$	4.63525	−	8.02850i	0.157695	−	0.273135i
$865$	1.71885	−	2.97713i	0.0584426	−	0.101225i
$866$	−0.381966			−0.0129797
$867$	−7.41641	+	12.8456i	−0.251874	+	0.436259i
$868$		0			0
$869$	9.70820	+	16.8151i	0.329328	+	0.570413i
$870$	0.227937			0.00772780
$871$	0.708204	−	2.45329i	0.0239966	−	0.0831266i
$872$	−15.7639			−0.533834
$873$	−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
$877$	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	$0.0978340\pi$
$878$	1.55573	−	2.69460i	0.0525033	−	0.0909383i
$879$	4.29180			0.144759
$880$	−2.91641	+	5.05137i	−0.0983121	+	0.170282i
$881$	6.29837	+	10.9091i	0.212198	+	0.367537i	0.952402	−	0.304845i	$-0.0986046\pi$
$881$	6.29837	+	10.9091i	0.212198	+	0.367537i	−0.740204	+	0.672382i	$0.765271\pi$
$882$		0			0
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	13.8541	−	47.9920i	0.465964	−	1.61415i
$885$	0.326238			0.0109664
$886$	0.145898	+	0.252703i	0.00490154	+	0.00848972i
$887$	11.6738	+	20.2195i	0.391967	+	0.678906i	0.992709	−	0.120537i	$-0.0384616\pi$
$887$	11.6738	+	20.2195i	0.391967	+	0.678906i	−0.600742	+	0.799443i	$0.705128\pi$
$888$	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
$892$	−24.6049			−0.823832
$893$	−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
$898$	10.8754			0.362916
$899$	−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
$905$	−1.41641			−0.0470830
$906$	1.07295	−	1.85840i	0.0356463	−	0.0617413i
$907$	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	$0.702880\pi$
$908$	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
$913$	16.2812	+	28.1998i	0.538828	+	0.933277i
$914$	2.18034	−	3.77646i	0.0721192	−	0.124914i
$915$	−0.875388			−0.0289394
$916$	−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
$922$	−14.9787			−0.493298
$923$	−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
$928$	−16.9574			−0.556655
$929$	−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
$933$	−2.35410	−	4.07742i	−0.0770698	−	0.133489i
$934$	6.42705	+	11.1320i	0.210300	+	0.364249i
$935$	−13.8541			−0.453078
$936$	−14.7057	+	3.63871i	−0.480671	+	0.118935i
$937$	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
$941$	−51.6525			−1.68382			−0.841911	−	0.539616i	$-0.818569\pi$
$941$	−51.6525			−1.68382			−0.841911	+	0.539616i	$0.818569\pi$
$942$	0.594235	−	1.02925i	0.0193612	−	0.0335346i
$943$	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
$947$	−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	$-0.434333\pi$
$948$	−2.83282			−0.0920056
$949$	5.00000	+	5.19615i	0.162307	+	0.168674i
$950$	9.00000			0.291999
$951$	−4.15654	−	7.19934i	−0.134785	−	0.233455i
$952$		0			0
$953$	22.3885	−	38.7781i	0.725236	−	1.25615i	−0.233641	−	0.972323i	$-0.575064\pi$
$953$	22.3885	−	38.7781i	0.725236	−	1.25615i	0.958877	−	0.283823i	$-0.0916027\pi$
$954$	−8.97871			−0.290697
$955$	4.51064	−	7.81266i	0.145961	−	0.252812i
$956$	−10.4681	+	18.1312i	−0.338562	+	0.586406i
$957$	7.58359			0.245143
$958$	−4.19756	+	7.27039i	−0.135617	+	0.234896i
$959$		0			0
$960$	−0.343459	−	0.594888i	−0.0110851	−	0.0191999i
$961$	44.8328			1.44622
$962$	−5.34752	+	1.32317i	−0.172411	+	0.0426607i
$963$	16.0344			0.516703
$964$	−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	$0.715749\pi$
$968$	9.24671	−	16.0158i	0.297201	−	0.514766i
$969$	−6.92705	+	11.9980i	−0.222529	+	0.385431i
$970$	1.77206			0.0568975
$971$	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
$975$	−1.85410	+	6.42280i	−0.0593788	+	0.205694i
$976$	18.8754			0.604186
$977$	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	$0.665400\pi$
$978$	−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
$982$	−2.79180	+	4.83553i	−0.0890898	+	0.154308i
$983$	−20.6180			−0.657613			−0.328807	−	0.944397i	$-0.606646\pi$
$983$	−20.6180			−0.657613			−0.328807	+	0.944397i	$0.606646\pi$
$984$	−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
$989$	−33.8197			−1.07540
$990$	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
$996$	−4.75078			−0.150534
$997$	24.5000	−	42.4352i	0.775923	−	1.34394i	−0.158352	−	0.987383i	$-0.550618\pi$
$997$	24.5000	−	42.4352i	0.775923	−	1.34394i	0.934274	−	0.356555i	$-0.116049\pi$
$998$	−1.55573	−	2.69460i	−0.0492457	−	0.0852961i
$999$	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.f.c.393.2		4
7.2	even	3		637.2.g.c.263.2		4
7.3	odd	6		637.2.h.g.471.1		4
7.4	even	3		637.2.h.f.471.1		4
7.5	odd	6		637.2.g.b.263.2		4
7.6	odd	2		91.2.f.a.29.2	yes	4
13.3	even	3		8281.2.a.bb.1.1		2
13.9	even	3	inner	637.2.f.c.295.2		4
13.10	even	6		8281.2.a.n.1.2		2
21.20	even	2		819.2.o.c.757.1		4
28.27	even	2		1456.2.s.h.1121.2		4
91.9	even	3		637.2.h.f.165.1		4
91.41	even	12		1183.2.c.c.337.2		4
91.48	odd	6		91.2.f.a.22.2	✓	4
91.55	odd	6		1183.2.a.g.1.1		2
91.61	odd	6		637.2.h.g.165.1		4
91.62	odd	6		1183.2.a.c.1.2		2
91.74	even	3		637.2.g.c.373.2		4
91.76	even	12		1183.2.c.c.337.3		4
91.87	odd	6		637.2.g.b.373.2		4
273.230	even	6		819.2.o.c.568.1		4
364.139	even	6		1456.2.s.h.113.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.2	✓	4	91.48	odd	6
91.2.f.a.29.2	yes	4	7.6	odd	2
637.2.f.c.295.2		4	13.9	even	3	inner
637.2.f.c.393.2		4	1.1	even	1	trivial
637.2.g.b.263.2		4	7.5	odd	6
637.2.g.b.373.2		4	91.87	odd	6
637.2.g.c.263.2		4	7.2	even	3
637.2.g.c.373.2		4	91.74	even	3
637.2.h.f.165.1		4	91.9	even	3
637.2.h.f.471.1		4	7.4	even	3
637.2.h.g.165.1		4	91.61	odd	6
637.2.h.g.471.1		4	7.3	odd	6
819.2.o.c.568.1		4	273.230	even	6
819.2.o.c.757.1		4	21.20	even	2
1183.2.a.c.1.2		2	91.62	odd	6
1183.2.a.g.1.1		2	91.55	odd	6
1183.2.c.c.337.2		4	91.41	even	12
1183.2.c.c.337.3		4	91.76	even	12
1456.2.s.h.113.2		4	364.139	even	6
1456.2.s.h.1121.2		4	28.27	even	2
8281.2.a.n.1.2		2	13.10	even	6
8281.2.a.bb.1.1		2	13.3	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 - 0.330792i) q^{2} +(-0.190983 - 0.330792i) q^{3} +(0.927051 - 1.60570i) q^{4} -0.381966 q^{5} +(-0.0729490 + 0.126351i) q^{6} -1.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +O(q^{10})\)	\(q+(-0.190983 - 0.330792i) q^{2} +(-0.190983 - 0.330792i) q^{3} +(0.927051 - 1.60570i) q^{4} -0.381966 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} -0.708204 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} -1.09017 q^{18} +(2.42705 - 4.20378i) q^{19} +(-0.354102 + 0.613323i) q^{20} +(0.927051 - 1.60570i) q^{22} +(-2.23607 - 3.87298i) q^{23} +(0.281153 + 0.486971i) q^{24} -4.85410 q^{25} +(0.381966 - 1.32317i) q^{26} -2.23607 q^{27} +(2.04508 + 3.54219i) q^{29} +(0.0278640 - 0.0482619i) q^{30} -8.70820 q^{31} +(-2.07295 + 3.59045i) q^{32} +(0.927051 - 1.60570i) q^{33} -2.85410 q^{34} +(-2.64590 - 4.58283i) q^{36} +(-2.00000 - 3.46410i) q^{37} -1.85410 q^{38} +(0.381966 - 1.32317i) q^{39} +0.562306 q^{40} +(2.61803 + 4.53457i) q^{41} +(3.78115 - 6.54915i) q^{43} +9.00000 q^{44} +(-0.545085 + 0.944115i) q^{45} +(-0.854102 + 1.47935i) q^{46} -2.23607 q^{47} +(-0.600813 + 1.04064i) q^{48} +(0.927051 + 1.60570i) q^{50} -2.85410 q^{51} +(6.48936 - 1.60570i) q^{52} +8.23607 q^{53} +(0.427051 + 0.739674i) q^{54} +(-0.927051 - 1.60570i) q^{55} -1.85410 q^{57} +(0.781153 - 1.35300i) q^{58} +(1.11803 - 1.93649i) q^{59} +0.270510 q^{60} +(-3.00000 + 5.19615i) q^{61} +(1.66312 + 2.88061i) q^{62} -4.70820 q^{64} +(-0.954915 - 0.992377i) q^{65} -0.708204 q^{66} +(-0.354102 - 0.613323i) q^{67} +(-6.92705 - 11.9980i) q^{68} +(-0.854102 + 1.47935i) q^{69} +(-4.09017 + 7.08438i) q^{71} +(-2.10081 + 3.63871i) q^{72} +2.00000 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} +4.00000 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} -2.88854 q^{86} +(0.781153 - 1.35300i) q^{87} +(-3.57295 - 6.18853i) q^{88} +(8.04508 + 13.9345i) q^{89} +0.416408 q^{90} -8.29180 q^{92} +(1.66312 + 2.88061i) q^{93} +(0.427051 + 0.739674i) q^{94} +(-0.927051 + 1.60570i) q^{95} +1.58359 q^{96} +(6.07295 - 10.5187i) q^{97} +13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 7 * q^6 + 12 * q^8 - q^9	\( 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9} + 7 q^{10} + 3 q^{11} + 24 q^{12} + 10 q^{13} + 7 q^{15} - 13 q^{16} + 6 q^{17} + 18 q^{18} + 3 q^{19} + 12 q^{20} - 3 q^{22} - 19 q^{24} - 6 q^{25} + 6 q^{26} - 3 q^{29} + 18 q^{30} - 8 q^{31} - 15 q^{32} - 3 q^{33} + 2 q^{34} - 24 q^{36} - 8 q^{37} + 6 q^{38} + 6 q^{39} - 38 q^{40} + 6 q^{41} - 5 q^{43} + 36 q^{44} + 9 q^{45} + 10 q^{46} - 27 q^{48} - 3 q^{50} + 2 q^{51} - 21 q^{52} + 24 q^{53} - 5 q^{54} + 3 q^{55} + 6 q^{57} - 17 q^{58} - 66 q^{60} - 12 q^{61} - 9 q^{62} + 8 q^{64} - 15 q^{65} + 24 q^{66} + 12 q^{67} - 21 q^{68} + 10 q^{69} + 6 q^{71} - 33 q^{72} + 8 q^{73} - 12 q^{74} - 3 q^{75} - 18 q^{76} - 49 q^{78} + 16 q^{79} + 27 q^{80} - 2 q^{81} + 4 q^{82} + q^{85} + 60 q^{86} - 17 q^{87} - 21 q^{88} + 21 q^{89} - 52 q^{90} - 60 q^{92} - 9 q^{93} - 5 q^{94} + 3 q^{95} + 60 q^{96} + 31 q^{97} + 42 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 6 * q^5 - 7 * q^6 + 12 * q^8 - q^9 + 7 * q^10 + 3 * q^11 + 24 * q^12 + 10 * q^13 + 7 * q^15 - 13 * q^16 + 6 * q^17 + 18 * q^18 + 3 * q^19 + 12 * q^20 - 3 * q^22 - 19 * q^24 - 6 * q^25 + 6 * q^26 - 3 * q^29 + 18 * q^30 - 8 * q^31 - 15 * q^32 - 3 * q^33 + 2 * q^34 - 24 * q^36 - 8 * q^37 + 6 * q^38 + 6 * q^39 - 38 * q^40 + 6 * q^41 - 5 * q^43 + 36 * q^44 + 9 * q^45 + 10 * q^46 - 27 * q^48 - 3 * q^50 + 2 * q^51 - 21 * q^52 + 24 * q^53 - 5 * q^54 + 3 * q^55 + 6 * q^57 - 17 * q^58 - 66 * q^60 - 12 * q^61 - 9 * q^62 + 8 * q^64 - 15 * q^65 + 24 * q^66 + 12 * q^67 - 21 * q^68 + 10 * q^69 + 6 * q^71 - 33 * q^72 + 8 * q^73 - 12 * q^74 - 3 * q^75 - 18 * q^76 - 49 * q^78 + 16 * q^79 + 27 * q^80 - 2 * q^81 + 4 * q^82 + q^85 + 60 * q^86 - 17 * q^87 - 21 * q^88 + 21 * q^89 - 52 * q^90 - 60 * q^92 - 9 * q^93 - 5 * q^94 + 3 * q^95 + 60 * q^96 + 31 * q^97 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more