LMFDB - Embedded newform 637.2.q.j.491.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.2
Character	$\chi$	$=$	637.491
Dual form			637.2.q.j.589.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08022 + 1.20101i) q^{2} +(0.888571 + 1.53905i) q^{3} +(1.88487 - 3.26470i) q^{4} +0.706642i q^{5} +(-3.69684 - 2.13437i) q^{6} +4.25098i q^{8} +(-0.0791164 + 0.137034i) q^{9} +O(q^{10})$	\(q+(-2.08022 + 1.20101i) q^{2} +(0.888571 + 1.53905i) q^{3} +(1.88487 - 3.26470i) q^{4} +0.706642i q^{5} +(-3.69684 - 2.13437i) q^{6} +4.25098i q^{8} +(-0.0791164 + 0.137034i) q^{9} +(-0.848687 - 1.46997i) q^{10} +(4.66830 - 2.69524i) q^{11} +6.69937 q^{12} +(-0.746990 + 3.52732i) q^{13} +(-1.08756 + 0.627901i) q^{15} +(-1.33575 - 2.31358i) q^{16} +(2.12541 - 3.68131i) q^{17} -0.380080i q^{18} +(-2.40306 - 1.38741i) q^{19} +(2.30697 + 1.33193i) q^{20} +(-6.47406 + 11.2134i) q^{22} +(3.35956 + 5.81893i) q^{23} +(-6.54247 + 3.77730i) q^{24} +4.50066 q^{25} +(-2.68246 - 8.23475i) q^{26} +5.05022 q^{27} +(-1.27934 - 2.21588i) q^{29} +(1.50824 - 2.61234i) q^{30} +8.74418i q^{31} +(-1.80563 - 1.04248i) q^{32} +(8.29623 + 4.78983i) q^{33} +10.2106i q^{34} +(0.298249 + 0.516582i) q^{36} +(-1.18180 + 0.682315i) q^{37} +6.66519 q^{38} +(-6.09248 + 1.98462i) q^{39} -3.00392 q^{40} +(3.91241 - 2.25883i) q^{41} +(3.78044 - 6.54792i) q^{43} -20.3208i q^{44} +(-0.0968337 - 0.0559070i) q^{45} +(-13.9772 - 8.06976i) q^{46} +0.0870907i q^{47} +(2.37381 - 4.11156i) q^{48} +(-9.36235 + 5.40536i) q^{50} +7.55430 q^{51} +(10.1077 + 9.08725i) q^{52} +7.04425 q^{53} +(-10.5056 + 6.06539i) q^{54} +(1.90457 + 3.29882i) q^{55} -4.93124i q^{57} +(5.32262 + 3.07302i) q^{58} +(-5.41052 - 3.12376i) q^{59} +4.73406i q^{60} +(-6.40224 + 11.0890i) q^{61} +(-10.5019 - 18.1898i) q^{62} +10.3511 q^{64} +(-2.49255 - 0.527855i) q^{65} -23.0106 q^{66} +(-9.09751 + 5.25245i) q^{67} +(-8.01224 - 13.8776i) q^{68} +(-5.97041 + 10.3411i) q^{69} +(-9.03045 - 5.21373i) q^{71} +(-0.582527 - 0.336322i) q^{72} +10.1732i q^{73} +(1.63894 - 2.83873i) q^{74} +(3.99915 + 6.92674i) q^{75} +(-9.05893 + 5.23018i) q^{76} +(10.2901 - 11.4456i) q^{78} -10.5270 q^{79} +(1.63487 - 0.943894i) q^{80} +(4.72483 + 8.18365i) q^{81} +(-5.42578 + 9.39773i) q^{82} +3.20483i q^{83} +(2.60137 + 1.50190i) q^{85} +18.1615i q^{86} +(2.27357 - 3.93794i) q^{87} +(11.4574 + 19.8449i) q^{88} +(-1.75452 + 1.01297i) q^{89} +0.268580 q^{90} +25.3294 q^{92} +(-13.4577 + 7.76983i) q^{93} +(-0.104597 - 0.181168i) q^{94} +(0.980401 - 1.69810i) q^{95} -3.70527i q^{96} +(4.62864 + 2.67235i) q^{97} +0.852952i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) $ 32 * q + 20 * q^4 - 28 * q^9	$ 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−2.08022	+	1.20101i	−1.47094	+	0.849246i	−0.999467	−	0.0326368i	$-0.989610\pi$
$2$	−2.08022	+	1.20101i	−1.47094	+	0.849246i	−0.471469	+	0.881882i	$0.656276\pi$
$3$	0.888571	+	1.53905i	0.513017	+	0.888571i	0.999886	+	0.0150961i	$0.00480542\pi$
$3$	0.888571	+	1.53905i	0.513017	+	0.888571i	−0.486869	+	0.873475i	$0.661861\pi$
$4$	1.88487	−	3.26470i	0.942436	−	1.63235i
$5$			0.706642i			0.316020i	0.987438	+	0.158010i	$0.0505078\pi$
$5$			0.706642i			0.316020i	−0.987438	+	0.158010i	$0.949492\pi$
$6$	−3.69684	−	2.13437i	−1.50923	−	0.871354i
$7$		0			0
$7$		0			0
$8$			4.25098i			1.50295i
$9$	−0.0791164	+	0.137034i	−0.0263721	+	0.0456779i
$10$	−0.848687	−	1.46997i	−0.268378	−	0.464845i
$11$	4.66830	−	2.69524i	1.40755	−	0.812647i	0.412395	−	0.911005i	$-0.364693\pi$
$11$	4.66830	−	2.69524i	1.40755	−	0.812647i	0.995151	+	0.0983585i	$0.0313592\pi$
$12$	6.69937			1.93394
$13$	−0.746990	+	3.52732i	−0.207178	+	0.978303i
$13$	−0.746990	+	3.52732i	−0.207178	+	0.978303i
$14$		0			0
$15$	−1.08756	+	0.627901i	−0.280806	+	0.162123i
$16$	−1.33575	−	2.31358i	−0.333936	−	0.578395i
$17$	2.12541	−	3.68131i	0.515487	−	0.892849i	−0.484352	−	0.874873i	$-0.660944\pi$
$17$	2.12541	−	3.68131i	0.515487	−	0.892849i	0.999838	−	0.0179758i	$-0.00572218\pi$
$18$		−	0.380080i		−	0.0895857i
$19$	−2.40306	−	1.38741i	−0.551300	−	0.318293i	0.198346	−	0.980132i	$-0.436443\pi$
$19$	−2.40306	−	1.38741i	−0.551300	−	0.318293i	−0.749646	+	0.661839i	$0.769776\pi$
$20$	2.30697	+	1.33193i	0.515854	+	0.297829i
$21$		0			0
$22$	−6.47406	+	11.2134i	−1.38027	+	2.39070i
$23$	3.35956	+	5.81893i	0.700517	+	1.21333i	0.968285	+	0.249847i	$0.0803804\pi$
$23$	3.35956	+	5.81893i	0.700517	+	1.21333i	−0.267769	+	0.963483i	$0.586286\pi$
$24$	−6.54247	+	3.77730i	−1.33548	+	0.771038i
$25$	4.50066			0.900131
$26$	−2.68246	−	8.23475i	−0.526074	−	1.61497i
$27$	5.05022			0.971916
$28$		0			0
$29$	−1.27934	−	2.21588i	−0.237568	−	0.411479i	0.722448	−	0.691425i	$-0.243017\pi$
$29$	−1.27934	−	2.21588i	−0.237568	−	0.411479i	−0.960016	+	0.279946i	$0.909683\pi$
$30$	1.50824	−	2.61234i	0.275365	−	0.476947i
$31$			8.74418i			1.57050i	0.619178	+	0.785251i	$0.287466\pi$
$31$			8.74418i			1.57050i	−0.619178	+	0.785251i	$0.712534\pi$
$32$	−1.80563	−	1.04248i	−0.319193	−	0.184286i
$33$	8.29623	+	4.78983i	1.44419	+	0.833803i
$34$			10.2106i			1.75110i
$35$		0			0
$36$	0.298249	+	0.516582i	0.0497081	+	0.0860970i
$37$	−1.18180	+	0.682315i	−0.194288	+	0.112172i	−0.593988	−	0.804474i	$-0.702447\pi$
$37$	−1.18180	+	0.682315i	−0.194288	+	0.112172i	0.399701	+	0.916646i	$0.369114\pi$
$38$	6.66519			1.08124
$39$	−6.09248	+	1.98462i	−0.975578	+	0.317794i
$40$	−3.00392			−0.474962
$41$	3.91241	−	2.25883i	0.611016	−	0.352770i	−0.162347	−	0.986734i	$-0.551906\pi$
$41$	3.91241	−	2.25883i	0.611016	−	0.352770i	0.773363	+	0.633963i	$0.218573\pi$
$42$		0			0
$43$	3.78044	−	6.54792i	0.576512	−	0.998548i	−0.419363	−	0.907818i	$-0.637747\pi$
$43$	3.78044	−	6.54792i	0.576512	−	0.998548i	0.995876	−	0.0907300i	$-0.0289200\pi$
$44$		−	20.3208i		−	3.06347i
$45$	−0.0968337	−	0.0559070i	−0.0144351	−	0.00833412i
$46$	−13.9772	−	8.06976i	−2.06083	−	1.18982i
$47$			0.0870907i			0.0127035i	0.999980	+	0.00635175i	$0.00202184\pi$
$47$			0.0870907i			0.0127035i	−0.999980	+	0.00635175i	$0.997978\pi$
$48$	2.37381	−	4.11156i	0.342630	−	0.593452i
$49$		0			0
$50$	−9.36235	+	5.40536i	−1.32404	+	0.764433i
$51$	7.55430			1.05781
$52$	10.1077	+	9.08725i	1.40168	+	1.26017i
$53$	7.04425			0.967602			0.483801	−	0.875178i	$-0.339256\pi$
$53$	7.04425			0.967602			0.483801	+	0.875178i	$0.339256\pi$
$54$	−10.5056	+	6.06539i	−1.42963	+	0.825395i
$55$	1.90457	+	3.29882i	0.256812	+	0.444812i
$56$		0			0
$57$		−	4.93124i		−	0.653159i
$58$	5.32262	+	3.07302i	0.698894	+	0.403507i
$59$	−5.41052	−	3.12376i	−0.704389	−	0.406679i	0.104591	−	0.994515i	$-0.466647\pi$
$59$	−5.41052	−	3.12376i	−0.704389	−	0.406679i	−0.808980	+	0.587836i	$0.799980\pi$
$60$			4.73406i			0.611164i
$61$	−6.40224	+	11.0890i	−0.819723	+	1.41980i	0.0861637	+	0.996281i	$0.472539\pi$
$61$	−6.40224	+	11.0890i	−0.819723	+	1.41980i	−0.905887	+	0.423521i	$0.860794\pi$
$62$	−10.5019	−	18.1898i	−1.33374	−	2.31011i
$63$		0			0
$64$	10.3511			1.29389
$65$	−2.49255	−	0.527855i	−0.309163	−	0.0654723i
$66$	−23.0106			−2.83241
$67$	−9.09751	+	5.25245i	−1.11144	+	0.641689i	−0.939201	−	0.343367i	$-0.888433\pi$
$67$	−9.09751	+	5.25245i	−1.11144	+	0.641689i	−0.172236	+	0.985056i	$0.555099\pi$
$68$	−8.01224	−	13.8776i	−0.971627	−	1.68291i
$69$	−5.97041	+	10.3411i	−0.718753	+	1.24492i
$70$		0			0
$71$	−9.03045	−	5.21373i	−1.07172	−	0.618756i	−0.143067	−	0.989713i	$-0.545696\pi$
$71$	−9.03045	−	5.21373i	−1.07172	−	0.618756i	−0.928650	+	0.370957i	$0.879030\pi$
$72$	−0.582527	−	0.336322i	−0.0686515	−	0.0396360i
$73$			10.1732i			1.19068i	0.803474	+	0.595340i	$0.202983\pi$
$73$			10.1732i			1.19068i	−0.803474	+	0.595340i	$0.797017\pi$
$74$	1.63894	−	2.83873i	0.190523	−	0.329996i
$75$	3.99915	+	6.92674i	0.461782	+	0.799831i
$76$	−9.05893	+	5.23018i	−1.03913	+	0.599942i
$77$		0			0
$78$	10.2901	−	11.4456i	1.16513	−	1.29596i
$79$	−10.5270			−1.18438			−0.592191	−	0.805798i	$-0.701737\pi$
$79$	−10.5270			−1.18438			−0.592191	+	0.805798i	$0.701737\pi$
$80$	1.63487	−	0.943894i	0.182784	−	0.105531i
$81$	4.72483	+	8.18365i	0.524981	+	0.909294i
$82$	−5.42578	+	9.39773i	−0.599177	+	1.03781i
$83$			3.20483i			0.351776i	0.984410	+	0.175888i	$0.0562797\pi$
$83$			3.20483i			0.351776i	−0.984410	+	0.175888i	$0.943720\pi$
$84$		0			0
$85$	2.60137	+	1.50190i	0.282158	+	0.162904i
$86$			18.1615i			1.95840i
$87$	2.27357	−	3.93794i	0.243752	−	0.422192i
$88$	11.4574	+	19.8449i	1.22137	+	2.11547i
$89$	−1.75452	+	1.01297i	−0.185979	+	0.107375i	−0.590099	−	0.807331i	$-0.700911\pi$
$89$	−1.75452	+	1.01297i	−0.185979	+	0.107375i	0.404120	+	0.914706i	$0.367578\pi$
$90$	0.268580			0.0283109
$91$		0			0
$92$	25.3294			2.64077
$93$	−13.4577	+	7.76983i	−1.39550	+	0.805694i
$94$	−0.104597	−	0.181168i	−0.0107884	−	0.0186860i
$95$	0.980401	−	1.69810i	0.100587	−	0.174222i
$96$		−	3.70527i		−	0.378168i
$97$	4.62864	+	2.67235i	0.469968	+	0.271336i	0.716226	−	0.697868i	$-0.245868\pi$
$97$	4.62864	+	2.67235i	0.469968	+	0.271336i	−0.246259	+	0.969204i	$0.579201\pi$
$98$		0			0
$99$			0.852952i			0.0857249i
$100$	8.48317	−	14.6933i	0.848317	−	1.46933i
$101$	−5.76467	−	9.98470i	−0.573606	−	0.993515i	−0.996192	−	0.0871919i	$-0.972211\pi$
$101$	−5.76467	−	9.98470i	−0.573606	−	0.993515i	0.422585	−	0.906323i	$-0.361123\pi$
$102$	−15.7146	+	9.07282i	−1.55598	+	0.898343i
$103$	1.65605			0.163175			0.0815877	−	0.996666i	$-0.474001\pi$
$103$	1.65605			0.163175			0.0815877	+	0.996666i	$0.474001\pi$
$104$	−14.9946	−	3.17544i	−1.47034	−	0.311378i
$105$		0			0
$106$	−14.6536	+	8.46024i	−1.42328	+	0.821731i
$107$	0.229732	+	0.397908i	0.0222091	+	0.0384672i	0.876916	−	0.480643i	$-0.159597\pi$
$107$	0.229732	+	0.397908i	0.0222091	+	0.0384672i	−0.854707	+	0.519110i	$0.826263\pi$
$108$	9.51903	−	16.4874i	0.915969	−	1.58650i
$109$		−	15.5929i		−	1.49353i	−0.665088	−	0.746765i	$-0.731606\pi$
$109$		−	15.5929i		−	1.49353i	0.665088	−	0.746765i	$-0.268394\pi$
$110$	−7.92385	−	4.57484i	−0.755510	−	0.436194i
$111$	−2.10023	−	1.21257i	−0.199345	−	0.115092i
$112$		0			0
$113$	−0.832761	+	1.44238i	−0.0783396	+	0.135688i	−0.902534	−	0.430619i	$-0.858295\pi$
$113$	−0.832761	+	1.44238i	−0.0783396	+	0.135688i	0.824194	+	0.566307i	$0.191629\pi$
$114$	5.92249	+	10.2581i	0.554692	+	0.960755i
$115$	−4.11190	+	2.37401i	−0.383436	+	0.221377i
$116$	−9.64558			−0.895570
$117$	−0.424263	−	0.381432i	−0.0392231	−	0.0352634i
$118$	15.0067			1.38148
$119$		0			0
$120$	−2.66920	−	4.62318i	−0.243663	−	0.422037i
$121$	9.02869	−	15.6381i	0.820790	−	1.42165i
$122$		−	30.7567i		−	2.78458i
$123$	6.95291	+	4.01426i	0.626923	+	0.361954i
$124$	28.5471	+	16.4817i	2.56361	+	1.48010i
$125$			6.71356i			0.600479i
$126$		0			0
$127$	4.81769	+	8.34449i	0.427501	+	0.740454i	0.996650	−	0.0817805i	$-0.0260607\pi$
$127$	4.81769	+	8.34449i	0.427501	+	0.740454i	−0.569149	+	0.822234i	$0.692727\pi$
$128$	−17.9213	+	10.3469i	−1.58404	+	0.914544i
$129$	13.4368			1.18304
$130$	5.81902	−	1.89554i	0.510362	−	0.166250i
$131$	21.3205			1.86278			0.931388	−	0.364027i	$-0.118599\pi$
$131$	21.3205			1.86278			0.931388	+	0.364027i	$0.118599\pi$
$132$	31.2747	−	18.0564i	2.72211	−	1.57161i
$133$		0			0
$134$	12.6165	−	21.8525i	1.08990	−	1.88777i
$135$			3.56870i			0.307145i
$136$	15.6492	+	9.03506i	1.34191	+	0.774750i
$137$	−3.51107	−	2.02712i	−0.299971	−	0.173188i	0.342459	−	0.939533i	$-0.388740\pi$
$137$	−3.51107	−	2.02712i	−0.299971	−	0.173188i	−0.642430	+	0.766344i	$0.722074\pi$
$138$		−	28.6822i		−	2.44159i
$139$	8.05661	−	13.9545i	0.683353	−	1.18360i	−0.290599	−	0.956845i	$-0.593855\pi$
$139$	8.05661	−	13.9545i	0.683353	−	1.18360i	0.973952	−	0.226756i	$-0.0728121\pi$
$140$		0			0
$141$	−0.134037	+	0.0773863i	−0.0112880	+	0.00651710i
$142$	25.0471			2.10190
$143$	6.01982	+	18.4799i	0.503403	+	1.54537i
$144$	0.422718			0.0352265
$145$	1.56584	−	0.904036i	0.130036	−	0.0750761i
$146$	−12.2181	−	21.1624i	−1.01118	−	1.75142i
$147$		0			0
$148$			5.14431i			0.422860i
$149$	−0.576390	−	0.332779i	−0.0472197	−	0.0272623i	0.476204	−	0.879335i	$-0.342012\pi$
$149$	−0.576390	−	0.332779i	−0.0472197	−	0.0272623i	−0.523424	+	0.852072i	$0.675346\pi$
$150$	−16.6382	−	9.60608i	−1.35851	−	0.784333i
$151$			3.58885i			0.292056i	0.989280	+	0.146028i	$0.0466490\pi$
$151$			3.58885i			0.292056i	−0.989280	+	0.146028i	$0.953351\pi$
$152$	5.89785	−	10.2154i	0.478378	−	0.828576i
$153$	0.336309	+	0.582504i	0.0271890	+	0.0470927i
$154$		0			0
$155$	−6.17901			−0.496310
$156$	−5.00437	+	23.6308i	−0.400670	+	1.89198i
$157$	5.38387			0.429680			0.214840	−	0.976649i	$-0.431077\pi$
$157$	5.38387			0.429680			0.214840	+	0.976649i	$0.431077\pi$
$158$	21.8985	−	12.6431i	1.74215	−	1.00583i
$159$	6.25931	+	10.8414i	0.496396	+	0.859783i
$160$	0.736661	−	1.27593i	0.0582382	−	0.100871i
$161$		0			0
$162$	−19.6574	−	11.3492i	−1.54443	−	0.891676i
$163$	3.39879	+	1.96229i	0.266214	+	0.153699i	0.627166	−	0.778886i	$-0.284215\pi$
$163$	3.39879	+	1.96229i	0.266214	+	0.153699i	−0.360952	+	0.932584i	$0.617548\pi$
$164$		−	17.0304i		−	1.32985i
$165$	−3.38470	+	5.86246i	−0.263498	+	0.456392i
$166$	−3.84905	−	6.66675i	−0.298744	−	0.517440i
$167$	11.3252	−	6.53858i	0.876367	−	0.505971i	0.00690822	−	0.999976i	$-0.497801\pi$
$167$	11.3252	−	6.53858i	0.876367	−	0.505971i	0.869459	+	0.494005i	$0.164468\pi$
$168$		0			0
$169$	−11.8840	−	5.26975i	−0.914155	−	0.405366i
$170$	−7.21522			−0.553382
$171$	0.380243	−	0.219534i	0.0290779	−	0.0167881i
$172$	−14.2513	−	24.6840i	−1.08665	−	1.88214i
$173$	−0.786360	+	1.36202i	−0.0597859	+	0.103552i	−0.894369	−	0.447330i	$-0.852375\pi$
$173$	−0.786360	+	1.36202i	−0.0597859	+	0.103552i	0.834583	+	0.550882i	$0.185708\pi$
$174$			10.9224i			0.828023i
$175$		0			0
$176$	−12.4713	−	7.20032i	−0.940061	−	0.542745i
$177$		−	11.1027i		−	0.834533i
$178$	2.43319	−	4.21441i	0.182376	−	0.315884i
$179$	8.61218	+	14.9167i	0.643704	+	1.11493i	0.984599	+	0.174827i	$0.0559367\pi$
$179$	8.61218	+	14.9167i	0.643704	+	1.11493i	−0.340895	+	0.940101i	$0.610730\pi$
$180$	−0.365038	+	0.210755i	−0.0272084	+	0.0157088i
$181$	−23.0795			−1.71549			−0.857744	−	0.514076i	$-0.828135\pi$
$181$	−23.0795			−1.71549			−0.857744	+	0.514076i	$0.828135\pi$
$182$		0			0
$183$	−22.7554			−1.68213
$184$	−24.7362	+	14.2814i	−1.82357	+	1.05284i
$185$	−0.482153	−	0.835113i	−0.0354486	−	0.0613987i
$186$	18.6634	−	32.3259i	1.36846	−	2.37025i
$187$		−	22.9140i		−	1.67563i
$188$	0.284325	+	0.164155i	0.0207365	+	0.0119722i
$189$		0			0
$190$			4.70990i			0.341692i
$191$	3.17530	−	5.49978i	0.229757	−	0.397950i	−0.727979	−	0.685599i	$-0.759540\pi$
$191$	3.17530	−	5.49978i	0.229757	−	0.397950i	0.957736	+	0.287649i	$0.0928737\pi$
$192$	9.19771	+	15.9309i	0.663787	+	1.14971i
$193$	−1.71129	+	0.988011i	−0.123181	+	0.0711186i	−0.560324	−	0.828273i	$-0.689324\pi$
$193$	−1.71129	+	0.988011i	−0.123181	+	0.0711186i	0.437143	+	0.899392i	$0.355990\pi$
$194$	−12.8381			−0.921724
$195$	−1.40242	−	4.30520i	−0.100429	−	0.308302i
$196$		0			0
$197$	14.7060	−	8.49053i	1.04776	−	0.604925i	0.125739	−	0.992063i	$-0.459870\pi$
$197$	14.7060	−	8.49053i	1.04776	−	0.604925i	0.922022	+	0.387138i	$0.126536\pi$
$198$	−1.02441	−	1.77433i	−0.0728015	−	0.126096i
$199$	6.15733	−	10.6648i	0.436482	−	0.756009i	−0.560933	−	0.827861i	$-0.689558\pi$
$199$	6.15733	−	10.6648i	0.436482	−	0.756009i	0.997415	+	0.0718521i	$0.0228910\pi$
$200$			19.1322i			1.35285i
$201$	−16.1676	−	9.33434i	−1.14037	−	0.658394i
$202$	23.9835	+	13.8469i	1.68748	+	0.974265i
$203$		0			0
$204$	14.2389	−	24.6625i	0.996922	−	1.72672i
$205$	1.59619	+	2.76467i	0.111482	+	0.193093i
$206$	−3.44494	+	1.98894i	−0.240021	+	0.138576i
$207$	−1.06319			−0.0738965
$208$	9.15853	−	2.98338i	0.635030	−	0.206860i
$209$	−14.9576			−1.03464
$210$		0			0
$211$	3.23809	+	5.60854i	0.222919	+	0.386108i	0.955693	−	0.294365i	$-0.0951080\pi$
$211$	3.23809	+	5.60854i	0.222919	+	0.386108i	−0.732774	+	0.680472i	$0.761775\pi$
$212$	13.2775	−	22.9973i	0.911903	−	1.57946i
$213$		−	18.5311i		−	1.26973i
$214$	−0.955787	−	0.551824i	−0.0653362	−	0.0377219i
$215$	4.62703	+	2.67142i	0.315561	+	0.182189i
$216$			21.4684i			1.46074i
$217$		0			0
$218$	18.7273	+	32.4367i	1.26837	+	2.19689i
$219$	−15.6570	+	9.03959i	−1.05800	+	0.610839i
$220$	14.3595			0.968118
$221$	11.3975	+	10.2469i	0.766680	+	0.689281i
$222$	5.82526			0.390966
$223$	−4.89368	+	2.82537i	−0.327705	+	0.189200i	−0.654822	−	0.755783i	$-0.727256\pi$
$223$	−4.89368	+	2.82537i	−0.327705	+	0.189200i	0.327117	+	0.944984i	$0.393923\pi$
$224$		0			0
$225$	−0.356076	+	0.616741i	−0.0237384	+	0.0411161i
$226$		−	4.00063i		−	0.266118i
$227$	24.0147	+	13.8649i	1.59391	+	0.920245i	0.992627	+	0.121211i	$0.0386776\pi$
$227$	24.0147	+	13.8649i	1.59391	+	0.920245i	0.601285	+	0.799035i	$0.294656\pi$
$228$	−16.0990	−	9.29476i	−1.06618	−	0.615561i
$229$			5.50360i			0.363688i	0.983327	+	0.181844i	$0.0582066\pi$
$229$			5.50360i			0.363688i	−0.983327	+	0.181844i	$0.941793\pi$
$230$	5.70243	−	9.87690i	0.376007	−	0.651264i
$231$		0			0
$232$	9.41968	−	5.43846i	0.618432	−	0.357052i
$233$	−20.7142			−1.35703			−0.678516	−	0.734586i	$-0.737377\pi$
$233$	−20.7142			−1.35703			−0.678516	+	0.734586i	$0.737377\pi$
$234$	1.34066	+	0.283916i	0.0876420	+	0.0185602i
$235$	−0.0615420			−0.00401455
$236$	−20.3963	+	11.7758i	−1.32768	+	0.766539i
$237$	−9.35400	−	16.2016i	−0.607608	−	1.05241i
$238$		0			0
$239$			12.3266i			0.797345i	0.917093	+	0.398672i	$0.130529\pi$
$239$			12.3266i			0.797345i	−0.917093	+	0.398672i	$0.869471\pi$
$240$	2.90540	+	1.67743i	0.187543	+	0.108278i
$241$	−16.7246	−	9.65598i	−1.07733	−	0.621996i	−0.147154	−	0.989114i	$-0.547011\pi$
$241$	−16.7246	−	9.65598i	−1.07733	−	0.621996i	−0.930175	+	0.367117i	$0.880345\pi$
$242$			43.3743i			2.78821i
$243$	−0.821359	+	1.42264i	−0.0526902	+	0.0912621i
$244$	24.1348	+	41.8027i	1.54507	+	2.67615i
$245$		0			0
$246$	−19.2848			−1.22955
$247$	6.68890	−	7.43999i	0.425605	−	0.473395i
$248$	−37.1714			−2.36038
$249$	−4.93240	+	2.84772i	−0.312578	+	0.180467i
$250$	−8.06309	−	13.9657i	−0.509954	−	0.883267i
$251$	0.308490	−	0.534320i	0.0194717	−	0.0337260i	−0.856125	−	0.516768i	$-0.827135\pi$
$251$	0.308490	−	0.534320i	0.0194717	−	0.0337260i	0.875597	+	0.483042i	$0.160468\pi$
$252$		0			0
$253$	31.3669	+	18.1097i	1.97202	+	1.13855i
$254$	−20.0437	−	11.5722i	−1.25765	−	0.726107i
$255$			5.33818i			0.334290i
$256$	14.5024	−	25.1189i	0.906401	−	1.56993i
$257$	−10.9170	−	18.9089i	−0.680987	−	1.17950i	−0.974680	−	0.223604i	$-0.928218\pi$
$257$	−10.9170	−	18.9089i	−0.680987	−	1.17950i	0.293694	−	0.955900i	$-0.405115\pi$
$258$	−27.9514	+	16.1378i	−1.74018	+	1.00469i
$259$		0			0
$260$	−6.42143	+	7.14249i	−0.398240	+	0.442958i
$261$	0.404868			0.0250607
$262$	−44.3512	+	25.6062i	−2.74003	+	1.58195i
$263$	0.875972	+	1.51723i	0.0540147	+	0.0935563i	0.891768	−	0.452492i	$-0.149465\pi$
$263$	0.875972	+	1.51723i	0.0540147	+	0.0935563i	−0.837754	+	0.546048i	$0.816132\pi$
$264$	−20.3615	+	35.2671i	−1.25316	+	2.17054i
$265$			4.97776i			0.305781i
$266$		0			0
$267$	−3.11804	−	1.80020i	−0.190821	−	0.110170i
$268$			39.6008i			2.41900i
$269$	−6.20308	+	10.7441i	−0.378208	+	0.655076i	−0.990802	−	0.135322i	$-0.956793\pi$
$269$	−6.20308	+	10.7441i	−0.378208	+	0.655076i	0.612593	+	0.790398i	$0.290126\pi$
$270$	−4.28606	−	7.42367i	−0.260841	−	0.451790i
$271$	9.26425	−	5.34872i	0.562763	−	0.324911i	−0.191491	−	0.981494i	$-0.561332\pi$
$271$	9.26425	−	5.34872i	0.562763	−	0.324911i	0.754254	+	0.656583i	$0.227999\pi$
$272$	−11.3560			−0.688559
$273$		0			0
$274$	9.73840			0.588318
$275$	21.0104	−	12.1304i	1.26698	−	0.731489i
$276$	22.5069	+	38.9832i	1.35476	+	2.34651i
$277$	3.19944	−	5.54159i	0.192236	−	0.332962i	−0.753755	−	0.657155i	$-0.771760\pi$
$277$	3.19944	−	5.54159i	0.192236	−	0.332962i	0.945991	+	0.324194i	$0.105093\pi$
$278$			38.7044i			2.32134i
$279$	−1.19825	−	0.691809i	−0.0717372	−	0.0414175i
$280$		0			0
$281$		−	16.5440i		−	0.986934i	−0.869764	−	0.493467i	$-0.835729\pi$
$281$		−	16.5440i		−	0.986934i	0.869764	−	0.493467i	$-0.164271\pi$
$282$	0.185884	−	0.321961i	0.0110692	−	0.0191725i
$283$	0.244022	+	0.422659i	0.0145056	+	0.0251245i	0.873187	−	0.487385i	$-0.162049\pi$
$283$	0.244022	+	0.422659i	0.0145056	+	0.0251245i	−0.858681	+	0.512510i	$0.828716\pi$
$284$	−34.0425	+	19.6544i	−2.02005	+	1.16628i
$285$	3.48462			0.206411
$286$	−34.7172	−	31.2124i	−2.05287	−	1.84563i
$287$		0			0
$288$	0.285710	−	0.164955i	0.0168356	−	0.00972005i
$289$	−0.534703	−	0.926132i	−0.0314531	−	0.0544784i
$290$	−2.17152	+	3.76119i	−0.127516	+	0.220864i
$291$			9.49829i			0.556799i
$292$	33.2123	+	19.1751i	1.94360	+	1.12214i
$293$	−6.97836	−	4.02896i	−0.407680	−	0.235374i	0.282112	−	0.959381i	$-0.408965\pi$
$293$	−6.97836	−	4.02896i	−0.407680	−	0.235374i	−0.689793	+	0.724007i	$0.742298\pi$
$294$		0			0
$295$	2.20738	−	3.82330i	0.128519	−	0.222601i
$296$	−2.90051	−	5.02383i	−0.168589	−	0.292004i
$297$	23.5760	−	13.6116i	1.36802	−	0.789824i
$298$	1.59869			0.0926096
$299$	−23.0348	+	7.50357i	−1.33214	+	0.433943i
$300$	30.1516			1.74080
$301$		0			0
$302$	−4.31026	−	7.46559i	−0.248027	−	0.429596i
$303$	10.2446	−	17.7442i	0.588539	−	1.01938i
$304$			7.41290i			0.425159i
$305$	−7.83595	−	4.52409i	−0.448685	−	0.259049i
$306$	−1.39919	−	0.807824i	−0.0799865	−	0.0461802i
$307$		−	11.4949i		−	0.656049i	−0.944669	−	0.328024i	$-0.893617\pi$
$307$		−	11.4949i		−	0.656049i	0.944669	−	0.328024i	$-0.106383\pi$
$308$		0			0
$309$	1.47152	+	2.54874i	0.0837117	+	0.144993i
$310$	12.8537	−	7.42108i	0.730040	−	0.421489i
$311$	−25.0375			−1.41975			−0.709873	−	0.704330i	$-0.751248\pi$
$311$	−25.0375			−1.41975			−0.709873	+	0.704330i	$0.751248\pi$
$312$	−8.43658	−	25.8990i	−0.477628	−	1.46624i
$313$	−28.3704			−1.60359			−0.801796	−	0.597598i	$-0.796122\pi$
$313$	−28.3704			−1.60359			−0.801796	+	0.597598i	$0.796122\pi$
$314$	−11.1996	+	6.46611i	−0.632032	+	0.364904i
$315$		0			0
$316$	−19.8421	+	34.3675i	−1.11620	+	1.93332i
$317$		−	30.5773i		−	1.71739i	−0.512485	−	0.858696i	$-0.671275\pi$
$317$		−	30.5773i		−	1.71739i	0.512485	−	0.858696i	$-0.328725\pi$
$318$	−26.0415	−	15.0351i	−1.46033	−	0.843124i
$319$	−11.9447	−	6.89628i	−0.668775	−	0.386117i
$320$			7.31454i			0.408895i
$321$	−0.408267	+	0.707139i	−0.0227872	+	0.0394687i
$322$		0			0
$323$	−10.2150	+	5.89761i	−0.568376	+	0.328152i
$324$	35.6228			1.97905
$325$	−3.36195	+	15.8753i	−0.186487	+	0.880602i
$326$	−9.42697			−0.522112
$327$	23.9983	−	13.8554i	1.32711	−	0.766206i
$328$	9.60225	+	16.6316i	0.530196	+	0.918326i
$329$		0			0
$330$		−	16.2603i		−	0.895099i
$331$	20.2727	+	11.7044i	1.11429	+	0.643334i	0.939936	−	0.341350i	$-0.110884\pi$
$331$	20.2727	+	11.7044i	1.11429	+	0.643334i	0.174350	+	0.984684i	$0.444217\pi$
$332$	10.4628	+	6.04070i	0.574221	+	0.331527i
$333$		−	0.215929i		−	0.0118329i
$334$	−15.7059	+	27.2034i	−0.859387	+	1.48850i
$335$	−3.71160	−	6.42868i	−0.202786	−	0.351236i
$336$		0			0
$337$	−14.3821			−0.783442			−0.391721	−	0.920084i	$-0.628120\pi$
$337$	−14.3821			−0.783442			−0.391721	+	0.920084i	$0.628120\pi$
$338$	31.0504	−	3.31063i	1.68892	−	0.180075i
$339$	−2.95987			−0.160758
$340$	9.80650	−	5.66178i	0.531832	−	0.307053i
$341$	23.5677	+	40.8205i	1.27626	+	2.21055i
$342$	−0.527326	+	0.913355i	−0.0285145	+	0.0493886i
$343$		0			0
$344$	27.8351	+	16.0706i	1.50077	+	0.866468i
$345$	−7.30743	−	4.21894i	−0.393419	−	0.227140i
$346$		−	3.77772i		−	0.203092i
$347$	−4.63467	+	8.02749i	−0.248802	+	0.430938i	−0.963194	−	0.268808i	$-0.913370\pi$
$347$	−4.63467	+	8.02749i	−0.248802	+	0.430938i	0.714392	+	0.699746i	$0.246704\pi$
$348$	−8.57078	−	14.8450i	−0.459442	−	0.795777i
$349$	13.4954	−	7.79157i	0.722392	−	0.417073i	−0.0932406	−	0.995644i	$-0.529723\pi$
$349$	13.4954	−	7.79157i	0.722392	−	0.417073i	0.815632	+	0.578571i	$0.196389\pi$
$350$		0			0
$351$	−3.77247	+	17.8138i	−0.201359	+	0.950829i
$352$	−11.2390			−0.599039
$353$	−16.5863	+	9.57612i	−0.882801	+	0.509686i	−0.871581	−	0.490251i	$-0.836905\pi$
$353$	−16.5863	+	9.57612i	−0.882801	+	0.509686i	−0.0112204	+	0.999937i	$0.503572\pi$
$354$	13.3346	+	23.0961i	0.708724	+	1.22755i
$355$	3.68424	−	6.38129i	0.195539	−	0.338684i
$356$			7.63731i			0.404777i
$357$		0			0
$358$	−35.8304	−	20.6867i	−1.89370	−	1.09333i
$359$		−	22.1893i		−	1.17111i	−0.810634	−	0.585553i	$-0.800877\pi$
$359$		−	22.1893i		−	1.17111i	0.810634	−	0.585553i	$-0.199123\pi$
$360$	0.237659	−	0.411638i	0.0125258	−	0.0216952i
$361$	−5.65020	−	9.78643i	−0.297379	−	0.515075i
$362$	48.0105	−	27.7189i	2.52338	−	1.45687i
$363$	32.0905			1.68432
$364$		0			0
$365$	−7.18879			−0.376279
$366$	47.3362	−	27.3295i	2.47430	−	1.42854i
$367$	−7.25517	−	12.5663i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$367$	−7.25517	−	12.5663i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$368$	8.97503	−	15.5452i	0.467856	−	0.810350i
$369$			0.714843i			0.0372132i
$370$	2.00597	+	1.15814i	0.104285	+	0.0602091i
$371$		0			0
$372$			58.5805i			3.03726i
$373$	−7.43888	+	12.8845i	−0.385170	+	0.667135i	−0.991793	−	0.127855i	$-0.959191\pi$
$373$	−7.43888	+	12.8845i	−0.385170	+	0.667135i	0.606622	+	0.794990i	$0.292524\pi$
$374$	27.5200	+	47.6660i	1.42303	+	2.46475i
$375$	−10.3325	+	5.96548i	−0.533568	+	0.308056i
$376$	−0.370221			−0.0190927
$377$	8.77179	−	2.85741i	0.451770	−	0.147164i
$378$		0			0
$379$	32.1983	−	18.5897i	1.65392	−	0.954889i	0.678477	−	0.734622i	$-0.262640\pi$
$379$	32.1983	−	18.5897i	1.65392	−	0.954889i	0.975439	−	0.220268i	$-0.0706931\pi$
$380$	−3.69586	−	6.40142i	−0.189594	−	0.328386i
$381$	−8.56172	+	14.8293i	−0.438630	+	0.759730i
$382$			15.2543i			0.780479i
$383$	−11.4736	−	6.62431i	−0.586276	−	0.338486i	0.177348	−	0.984148i	$-0.443248\pi$
$383$	−11.4736	−	6.62431i	−0.586276	−	0.338486i	−0.763623	+	0.645662i	$0.776582\pi$
$384$	−31.8488	−	18.3879i	−1.62528	−	0.938353i
$385$		0			0
$386$	2.37323	−	4.11056i	0.120794	−	0.209222i
$387$	0.598190	+	1.03610i	0.0304077	+	0.0526677i
$388$	17.4488	−	10.0741i	0.885829	−	0.511434i
$389$	14.6519			0.742883			0.371441	−	0.928456i	$-0.378864\pi$
$389$	14.6519			0.742883			0.371441	+	0.928456i	$0.378864\pi$
$390$	8.08794	+	7.27144i	0.409549	+	0.368203i
$391$	28.5617			1.44443
$392$		0			0
$393$	18.9447	+	32.8132i	0.955635	+	1.65521i
$394$	−20.3945	+	35.3243i	−1.02746	+	1.77961i
$395$		−	7.43883i		−	0.374288i
$396$	2.78463	+	1.60771i	0.139933	+	0.0807903i
$397$	−15.2278	−	8.79175i	−0.764259	−	0.441245i	0.0665638	−	0.997782i	$-0.478796\pi$
$397$	−15.2278	−	8.79175i	−0.764259	−	0.441245i	−0.830823	+	0.556537i	$0.812130\pi$
$398$			29.5802i			1.48272i
$399$		0			0
$400$	−6.01173	−	10.4126i	−0.300587	−	0.520631i
$401$	−24.5986	+	14.2020i	−1.22839	+	0.709214i	−0.966694	−	0.255935i	$-0.917617\pi$
$401$	−24.5986	+	14.2020i	−1.22839	+	0.709214i	−0.261701	+	0.965149i	$0.584283\pi$
$402$	44.8427			2.23655
$403$	−30.8436	−	6.53182i	−1.53643	−	0.325373i
$404$	−43.4627			−2.16235
$405$	−5.78291	+	3.33876i	−0.287355	+	0.165904i
$406$		0			0
$407$	−3.67801	+	6.37051i	−0.182312	+	0.315774i
$408$			32.1132i			1.58984i
$409$	−8.86247	−	5.11675i	−0.438221	−	0.253007i	0.264622	−	0.964352i	$-0.414753\pi$
$409$	−8.86247	−	5.11675i	−0.438221	−	0.253007i	−0.702843	+	0.711345i	$0.748086\pi$
$410$	−6.64083	−	3.83408i	−0.327967	−	0.189352i
$411$		−	7.20496i		−	0.355394i
$412$	3.12144	−	5.40650i	0.153782	−	0.266359i
$413$		0			0
$414$	2.21166	−	1.27690i	0.108697	−	0.0627563i
$415$	−2.26467			−0.111168
$416$	5.02596	−	5.59032i	0.246418	−	0.274088i
$417$	28.6355			1.40228
$418$	31.1151	−	17.9643i	1.52189	−	0.878664i
$419$	6.22291	+	10.7784i	0.304009	+	0.526559i	0.977040	−	0.213055i	$-0.0683413\pi$
$419$	6.22291	+	10.7784i	0.304009	+	0.526559i	−0.673031	+	0.739614i	$0.735008\pi$
$420$		0			0
$421$		−	2.04054i		−	0.0994498i	−0.998763	−	0.0497249i	$-0.984166\pi$
$421$		−	2.04054i		−	0.0994498i	0.998763	−	0.0497249i	$-0.0158345\pi$
$422$	−13.4719	−	7.77799i	−0.655801	−	0.378627i
$423$	−0.0119344	−	0.00689031i	−0.000580269	−	0.000335018i
$424$			29.9450i			1.45426i
$425$	9.56572	−	16.5683i	0.464006	−	0.803682i
$426$	22.2561	+	38.5487i	1.07831	+	1.86769i
$427$		0			0
$428$	1.73206			0.0837225
$429$	−23.0925	+	25.6855i	−1.11492	+	1.24011i
$430$	−12.8337			−0.618894
$431$	12.2992	−	7.10095i	0.592432	−	0.342041i	−0.173626	−	0.984812i	$-0.555549\pi$
$431$	12.2992	−	7.10095i	0.592432	−	0.342041i	0.766059	+	0.642771i	$0.222215\pi$
$432$	−6.74581	−	11.6841i	−0.324558	−	0.562151i
$433$	−8.41174	+	14.5696i	−0.404242	+	0.700168i	−0.994233	−	0.107242i	$-0.965798\pi$
$433$	−8.41174	+	14.5696i	−0.404242	+	0.700168i	0.589991	+	0.807410i	$0.299131\pi$
$434$		0			0
$435$	2.78271	+	1.60660i	0.133421	+	0.0770306i
$436$	−50.9061	−	29.3907i	−2.43796	−	1.40756i
$437$		−	18.6443i		−	0.891879i
$438$	21.7134	−	37.6087i	1.03750	−	1.79701i
$439$	−12.3476	−	21.3867i	−0.589320	−	1.02073i	−0.994322	−	0.106416i	$-0.966062\pi$
$439$	−12.3476	−	21.3867i	−0.589320	−	1.02073i	0.405002	−	0.914316i	$-0.367271\pi$
$440$	−14.0232	+	8.09630i	−0.668530	+	0.385976i
$441$		0			0
$442$	−36.0160	−	7.62720i	−1.71311	−	0.362789i
$443$	2.95105			0.140208			0.0701042	−	0.997540i	$-0.477667\pi$
$443$	2.95105			0.140208			0.0701042	+	0.997540i	$0.477667\pi$
$444$	−7.91735	+	4.57108i	−0.375741	+	0.216934i
$445$	−0.715810	−	1.23982i	−0.0339326	−	0.0587731i
$446$	6.78661	−	11.7548i	0.321355	−	0.556604i
$447$		−	1.18279i		−	0.0559441i
$448$		0			0
$449$	−4.47161	−	2.58168i	−0.211028	−	0.121837i	0.390761	−	0.920492i	$-0.372212\pi$
$449$	−4.47161	−	2.58168i	−0.211028	−	0.121837i	−0.601789	+	0.798655i	$0.705545\pi$
$450$		−	1.71061i		−	0.0806389i
$451$	12.1762	−	21.0898i	0.573355	−	0.993081i
$452$	3.13930	+	5.43742i	0.147660	+	0.255755i
$453$	−5.52341	+	3.18894i	−0.259513	+	0.149830i
$454$	−66.6078			−3.12606
$455$		0			0
$456$	20.9626			0.981664
$457$	3.92542	−	2.26634i	0.183623	−	0.106015i	−0.405371	−	0.914152i	$-0.632858\pi$
$457$	3.92542	−	2.26634i	0.183623	−	0.106015i	0.588994	+	0.808137i	$0.299524\pi$
$458$	−6.60991	−	11.4487i	−0.308861	−	0.534962i
$459$	10.7338	−	18.5914i	0.501010	−	0.867774i
$460$			17.8988i			0.834536i
$461$	−33.2778	−	19.2130i	−1.54990	−	0.894837i	−0.998148	−	0.0608314i	$-0.980625\pi$
$461$	−33.2778	−	19.2130i	−1.54990	−	0.894837i	−0.551756	−	0.834006i	$-0.686042\pi$
$462$		0			0
$463$		−	2.53217i		−	0.117680i	−0.998267	−	0.0588400i	$-0.981260\pi$
$463$		−	2.53217i		−	0.117680i	0.998267	−	0.0588400i	$-0.0187402\pi$
$464$	−3.41775	+	5.91971i	−0.158665	+	0.274816i
$465$	−5.49049	−	9.50980i	−0.254615	−	0.441006i
$466$	43.0900	−	24.8781i	1.99611	−	1.15245i
$467$	−11.7357			−0.543065			−0.271533	−	0.962429i	$-0.587530\pi$
$467$	−11.7357			−0.543065			−0.271533	+	0.962429i	$0.587530\pi$
$468$	−2.04494	+	0.666138i	−0.0945274	+	0.0307922i
$469$		0			0
$470$	0.128021	−	0.0739128i	0.00590516	−	0.00340934i
$471$	4.78395	+	8.28605i	0.220433	+	0.381801i
$472$	13.2791	−	23.0000i	0.611218	−	1.05866i
$473$		−	40.7569i		−	1.87400i
$474$	38.9167	+	22.4686i	1.78750	+	1.03202i
$475$	−10.8154	−	6.24425i	−0.496243	−	0.286506i
$476$		0			0
$477$	−0.557315	+	0.965299i	−0.0255177	+	0.0441980i
$478$	−14.8045	−	25.6421i	−0.677141	−	1.17284i
$479$	−24.7786	+	14.3060i	−1.13216	+	0.653656i	−0.944478	−	0.328573i	$-0.893432\pi$
$479$	−24.7786	+	14.3060i	−1.13216	+	0.653656i	−0.187686	+	0.982229i	$0.560099\pi$
$480$	2.61830			0.119509
$481$	−1.52395	−	4.67829i	−0.0694861	−	0.213312i
$482$	46.3879			2.11291
$483$		0			0
$484$	−34.0359	−	58.9518i	−1.54708	−	2.67963i
$485$	−1.88839	+	3.27079i	−0.0857475	+	0.148519i
$486$		−	3.94586i		−	0.178988i
$487$	−2.37282	−	1.36995i	−0.107523	−	0.0620782i	0.445274	−	0.895394i	$-0.353106\pi$
$487$	−2.37282	−	1.36995i	−0.107523	−	0.0620782i	−0.552797	+	0.833316i	$0.686439\pi$
$488$	−47.1391	−	27.2158i	−2.13389	−	1.23200i
$489$			6.97455i			0.315400i
$490$		0			0
$491$	−19.1633	−	33.1917i	−0.864825	−	1.49792i	−0.867220	−	0.497924i	$-0.834096\pi$
$491$	−19.1633	−	33.1917i	−0.864825	−	1.49792i	0.00239500	−	0.999997i	$-0.499238\pi$
$492$	26.2107	−	15.1328i	1.18167	−	0.682237i
$493$	−10.8765			−0.489852
$494$	−4.97883	+	23.5103i	−0.224008	+	1.05778i
$495$	−0.602732			−0.0270908
$496$	20.2304	−	11.6800i	0.908370	−	0.524448i
$497$		0			0
$498$	6.84031	−	11.8478i	0.306522	−	0.530911i
$499$			27.9009i			1.24902i	0.781018	+	0.624509i	$0.214701\pi$
$499$			27.9009i			1.24902i	−0.781018	+	0.624509i	$0.785299\pi$
$500$	21.9177	+	12.6542i	0.980191	+	0.565913i
$501$	20.1264	+	11.6200i	0.899182	+	0.519143i
$502$			1.48200i			0.0661451i
$503$	1.18942	−	2.06014i	0.0530336	−	0.0918569i	−0.838290	−	0.545225i	$-0.816444\pi$
$503$	1.18942	−	2.06014i	0.0530336	−	0.0918569i	0.891323	+	0.453368i	$0.149778\pi$
$504$		0			0
$505$	7.05561	−	4.07356i	0.313970	−	0.181271i
$506$	−86.9999			−3.86762
$507$	−2.44937	−	22.9726i	−0.108780	−	1.02025i
$508$	36.3230			1.61157
$509$	22.6522	−	13.0783i	1.00404	−	0.579684i	0.0945998	−	0.995515i	$-0.469843\pi$
$509$	22.6522	−	13.0783i	1.00404	−	0.579684i	0.909442	+	0.415832i	$0.136510\pi$
$510$	−6.41123	−	11.1046i	−0.283894	−	0.491719i
$511$		0			0
$512$			28.2829i			1.24994i
$513$	−12.1360	−	7.00672i	−0.535817	−	0.309354i
$514$	45.4197	+	26.2231i	2.00338	+	1.15665i
$515$			1.17023i			0.0515666i
$516$	25.3266	−	43.8670i	1.11494	−	1.93114i
$517$	0.234731	+	0.406566i	0.0103235	+	0.0178807i
$518$		0			0
$519$	−2.79495			−0.122685
$520$	2.24390	−	10.5958i	0.0984015	−	0.464656i
$521$	24.0380			1.05313			0.526563	−	0.850136i	$-0.323481\pi$
$521$	24.0380			1.05313			0.526563	+	0.850136i	$0.323481\pi$
$522$	−0.842213	+	0.486252i	−0.0368627	+	0.0212827i
$523$	5.86969	+	10.1666i	0.256664	+	0.444554i	0.965346	−	0.260973i	$-0.0840434\pi$
$523$	5.86969	+	10.1666i	0.256664	+	0.444554i	−0.708682	+	0.705528i	$0.750710\pi$
$524$	40.1863	−	69.6048i	1.75555	−	3.04070i
$525$		0			0
$526$	−3.64443	−	2.10411i	−0.158905	−	0.0917436i
$527$	32.1901	+	18.5849i	1.40222	+	0.809573i
$528$		−	25.5920i		−	1.11375i
$529$	−11.0733	+	19.1795i	−0.481447	+	0.833891i
$530$	−5.97836	−	10.3548i	−0.259683	−	0.449785i
$531$	0.856121	−	0.494282i	0.0371525	−	0.0214500i
$532$		0			0
$533$	5.04510	+	15.4877i	0.218527	+	0.670845i
$534$	8.64826			0.374247
$535$	−0.281178	+	0.162338i	−0.0121564	+	0.00701850i
$536$	−22.3281	−	38.6733i	−0.964425	−	1.67043i
$537$	−15.3051	+	26.5091i	−0.660462	+	1.14395i
$538$		−	29.8000i		−	1.28477i
$539$		0			0
$540$	11.6507	+	6.72654i	0.501367	+	0.289464i
$541$			30.7507i			1.32208i	0.750352	+	0.661038i	$0.229884\pi$
$541$			30.7507i			1.32208i	−0.750352	+	0.661038i	$0.770116\pi$
$542$	−12.8478	+	22.2530i	−0.551859	+	0.955848i
$543$	−20.5078	−	35.5206i	−0.880074	−	1.52433i
$544$	−7.67540	+	4.43139i	−0.329080	+	0.189994i
$545$	11.0186			0.471985
$546$		0			0
$547$	−26.7184			−1.14240			−0.571199	−	0.820812i	$-0.693522\pi$
$547$	−26.7184			−1.14240			−0.571199	+	0.820812i	$0.693522\pi$
$548$	−13.2359	+	7.64172i	−0.565408	+	0.326438i
$549$	−1.01304	−	1.75464i	−0.0432357	−	0.0748864i
$550$	−29.1375	+	50.4677i	−1.24243	+	2.15195i
$551$			7.09987i			0.302465i
$552$	−43.9597	−	25.3801i	−1.87105	−	1.08025i
$553$		0			0
$554$			15.3703i			0.653021i
$555$	0.856853	−	1.48411i	0.0363714	−	0.0629971i
$556$	−30.3714	−	52.6047i	−1.28803	−	2.23094i
$557$	7.45486	−	4.30406i	0.315872	−	0.182369i	−0.333679	−	0.942687i	$-0.608290\pi$
$557$	7.45486	−	4.30406i	0.315872	−	0.182369i	0.649551	+	0.760318i	$0.274957\pi$
$558$	3.32349			0.140695
$559$	20.2727	+	18.2261i	0.857443	+	0.770881i
$560$		0			0
$561$	35.2657	−	20.3607i	1.48892	−	0.859628i
$562$	19.8696	+	34.4152i	0.838150	+	1.45172i
$563$	2.55291	−	4.42177i	0.107592	−	0.186355i	−0.807202	−	0.590275i	$-0.799019\pi$
$563$	2.55291	−	4.42177i	0.107592	−	0.186355i	0.914794	+	0.403920i	$0.132353\pi$
$564$			0.583453i			0.0245678i
$565$	−1.01925	−	0.588464i	−0.0428801	−	0.0247569i
$566$	−1.01524	−	0.586149i	−0.0426737	−	0.0246377i
$567$		0			0
$568$	22.1635	−	38.3883i	0.929958	−	1.61074i
$569$	−1.27969	−	2.21650i	−0.0536476	−	0.0929204i	0.837954	−	0.545740i	$-0.183751\pi$
$569$	−1.27969	−	2.21650i	−0.0536476	−	0.0929204i	−0.891602	+	0.452820i	$0.850418\pi$
$570$	−7.24877	+	4.18508i	−0.303618	+	0.175294i
$571$	−33.2677			−1.39221			−0.696106	−	0.717939i	$-0.745085\pi$
$571$	−33.2677			−1.39221			−0.696106	+	0.717939i	$0.745085\pi$
$572$	71.6779	+	15.1794i	2.99700	+	0.634684i
$573$	11.2859			0.471476
$574$		0			0
$575$	15.1202	+	26.1890i	0.630557	+	1.09216i
$576$	−0.818944	+	1.41845i	−0.0341227	+	0.0591022i
$577$			40.9053i			1.70291i	0.524428	+	0.851455i	$0.324279\pi$
$577$			40.9053i			1.70291i	−0.524428	+	0.851455i	$0.675721\pi$
$578$	2.22460	+	1.28437i	0.0925310	+	0.0534228i
$579$	−3.04120	−	1.75584i	−0.126388	−	0.0729701i
$580$		−	6.81597i		−	0.283018i
$581$		0			0
$582$	−11.4076	−	19.7585i	−0.472860	−	0.819017i
$583$	32.8847	−	18.9860i	1.36194	−	0.786318i
$584$	−43.2460			−1.78953
$585$	0.269536	−	0.299802i	0.0111439	−	0.0123953i
$586$	19.3554			0.799563
$587$	−5.49704	+	3.17372i	−0.226887	+	0.130993i	−0.609135	−	0.793066i	$-0.708483\pi$
$587$	−5.49704	+	3.17372i	−0.226887	+	0.130993i	0.382248	+	0.924060i	$0.375150\pi$
$588$		0			0
$589$	12.1318	−	21.0128i	0.499880	−	0.865818i
$590$			10.6044i			0.436576i
$591$	26.1347	+	15.0889i	1.07504	+	0.620673i
$592$	3.15718	+	1.82280i	0.129759	+	0.0749166i
$593$		−	38.8012i		−	1.59337i	−0.604392	−	0.796687i	$-0.706584\pi$
$593$		−	38.8012i		−	1.59337i	0.604392	−	0.796687i	$-0.293416\pi$
$594$	−32.6954	+	56.6301i	−1.34151	+	2.32356i
$595$		0			0
$596$	−2.17284	+	1.25449i	−0.0890032	+	0.0513860i
$597$	21.8849			0.895690
$598$	38.9055	−	43.2742i	1.59096	−	1.76961i
$599$	14.7088			0.600987			0.300493	−	0.953784i	$-0.402849\pi$
$599$	14.7088			0.600987			0.300493	+	0.953784i	$0.402849\pi$
$600$	−29.4454	+	17.0003i	−1.20210	+	0.694035i
$601$	−7.70501	−	13.3455i	−0.314294	−	0.544373i	0.664993	−	0.746849i	$-0.268434\pi$
$601$	−7.70501	−	13.3455i	−0.314294	−	0.544373i	−0.979287	+	0.202476i	$0.935101\pi$
$602$		0			0
$603$		−	1.66222i		−	0.0676908i
$604$	11.7165	+	6.76452i	0.476737	+	0.275244i
$605$	11.0506	+	6.38005i	0.449269	+	0.259386i
$606$			49.2158i			1.99926i
$607$	−14.9868	+	25.9579i	−0.608295	+	1.05360i	0.383227	+	0.923654i	$0.374813\pi$
$607$	−14.9868	+	25.9579i	−0.608295	+	1.05360i	−0.991521	+	0.129943i	$0.958521\pi$
$608$	2.89269	+	5.01029i	0.117314	+	0.203194i
$609$		0			0
$610$	21.7340			0.879984
$611$	−0.307197	−	0.0650560i	−0.0124279	−	0.00263188i
$612$	2.53560			0.102496
$613$	−13.1043	+	7.56575i	−0.529276	+	0.305578i	−0.740722	−	0.671812i	$-0.765516\pi$
$613$	−13.1043	+	7.56575i	−0.529276	+	0.305578i	0.211446	+	0.977390i	$0.432183\pi$
$614$	13.8055	+	23.9119i	0.557146	+	0.965006i
$615$	−2.83665	+	4.91322i	−0.114385	+	0.198120i
$616$		0			0
$617$	−30.7475	−	17.7521i	−1.23785	−	0.714673i	−0.269195	−	0.963086i	$-0.586758\pi$
$617$	−30.7475	−	17.7521i	−1.23785	−	0.714673i	−0.968654	+	0.248413i	$0.920091\pi$
$618$	−6.12215	−	3.53463i	−0.246269	−	0.142184i
$619$		−	33.3794i		−	1.34163i	−0.741624	−	0.670815i	$-0.765944\pi$
$619$		−	33.3794i		−	1.34163i	0.741624	−	0.670815i	$-0.234056\pi$
$620$	−11.6466	+	20.1726i	−0.467740	+	0.810150i
$621$	16.9665	+	29.3869i	0.680843	+	1.17926i
$622$	52.0834	−	30.0704i	2.08836	−	1.20571i
$623$		0			0
$624$	12.7296	+	11.4445i	0.509591	+	0.458146i
$625$	17.7592			0.710368
$626$	59.0167	−	34.0733i	2.35878	−	1.36184i
$627$	−13.2909	−	23.0205i	−0.530788	−	0.919351i
$628$	10.1479	−	17.5767i	0.404946	−	0.701387i
$629$			5.80079i			0.231293i
$630$		0			0
$631$	16.8909	+	9.75195i	0.672415	+	0.388219i	0.796991	−	0.603991i	$-0.206424\pi$
$631$	16.8909	+	9.75195i	0.672415	+	0.388219i	−0.124576	+	0.992210i	$0.539757\pi$
$632$		−	44.7502i		−	1.78007i
$633$	−5.75455	+	9.96717i	−0.228723	+	0.396159i
$634$	36.7238	+	63.6075i	1.45849	+	2.52618i
$635$	−5.89657	+	3.40438i	−0.233998	+	0.135099i
$636$	47.1920			1.87129
$637$		0			0
$638$	33.1301			1.31163
$639$	1.42891	−	0.824983i	0.0565269	−	0.0326358i
$640$	−7.31154	−	12.6640i	−0.289014	−	0.500587i
$641$	−4.41475	+	7.64657i	−0.174372	+	0.302022i	−0.939944	−	0.341329i	$-0.889123\pi$
$641$	−4.41475	+	7.64657i	−0.174372	+	0.302022i	0.765572	+	0.643351i	$0.222456\pi$
$642$		−	1.96134i		−	0.0774078i
$643$	18.0992	+	10.4496i	0.713763	+	0.412091i	0.812453	−	0.583027i	$-0.198132\pi$
$643$	18.0992	+	10.4496i	0.713763	+	0.412091i	−0.0986898	+	0.995118i	$0.531465\pi$
$644$		0			0
$645$			9.49498i			0.373865i
$646$	14.1662	−	24.5366i	0.557363	−	0.965381i
$647$	−10.8790	−	18.8430i	−0.427697	−	0.740793i	0.568971	−	0.822358i	$-0.307342\pi$
$647$	−10.8790	−	18.8430i	−0.427697	−	0.740793i	−0.996668	+	0.0815643i	$0.974008\pi$
$648$	−34.7885	+	20.0852i	−1.36662	+	0.789020i
$649$	−33.6772			−1.32195
$650$	−12.0728	−	37.0618i	−0.473536	−	1.45368i
$651$		0			0
$652$	12.8126	−	7.39735i	0.501779	−	0.289702i
$653$	13.3195	+	23.0701i	0.521232	+	0.902801i	0.999695	+	0.0246930i	$0.00786083\pi$
$653$	13.3195	+	23.0701i	0.521232	+	0.902801i	−0.478463	+	0.878108i	$0.658806\pi$
$654$	−33.2811	+	57.6446i	−1.30139	+	2.25408i
$655$			15.0659i			0.588674i
$656$	−10.4520	−	6.03445i	−0.408081	−	0.235606i
$657$	−1.39407	−	0.804865i	−0.0543878	−	0.0314008i
$658$		0			0
$659$	−10.0593	+	17.4232i	−0.391855	+	0.678713i	−0.992694	−	0.120657i	$-0.961500\pi$
$659$	−10.0593	+	17.4232i	−0.391855	+	0.678713i	0.600839	+	0.799370i	$0.294833\pi$
$660$	12.7594	+	22.1000i	0.496661	+	0.860241i
$661$	7.21323	−	4.16456i	0.280562	−	0.161983i	−0.353116	−	0.935580i	$-0.614878\pi$
$661$	7.21323	−	4.16456i	0.280562	−	0.161983i	0.633678	+	0.773597i	$0.281544\pi$
$662$	−56.2288			−2.18539
$663$	−5.64299	+	26.6464i	−0.219155	+	1.03486i
$664$	−13.6237			−0.528701
$665$		0			0
$666$	0.259334	+	0.449180i	0.0100490	+	0.0174054i
$667$	8.59605	−	14.8888i	0.332840	−	0.576496i
$668$		−	49.2976i		−	1.90738i
$669$	−8.69676	−	5.02107i	−0.336236	−	0.194126i
$670$	15.4419	+	8.91537i	0.596572	+	0.344431i
$671$			69.0224i			2.66458i
$672$		0			0
$673$	−16.3774	−	28.3665i	−0.631303	−	1.09345i	−0.987286	−	0.158957i	$-0.949187\pi$
$673$	−16.3774	−	28.3665i	−0.631303	−	1.09345i	0.355982	−	0.934493i	$-0.384146\pi$
$674$	29.9179	−	17.2731i	1.15239	−	0.665335i
$675$	22.7293			0.874852
$676$	−39.6040	+	28.8649i	−1.52323	+	1.11019i
$677$	−47.3896			−1.82133			−0.910666	−	0.413144i	$-0.864431\pi$
$677$	−47.3896			−1.82133			−0.910666	+	0.413144i	$0.864431\pi$
$678$	6.15717	−	3.55485i	0.236465	−	0.136523i
$679$		0			0
$680$	−6.38455	+	11.0584i	−0.244836	+	0.424069i
$681$			49.2798i			1.88840i
$682$	−98.0520	−	56.6104i	−3.75461	−	2.16772i
$683$	12.8486	+	7.41815i	0.491638	+	0.283848i	0.725254	−	0.688482i	$-0.241722\pi$
$683$	12.8486	+	7.41815i	0.491638	+	0.283848i	−0.233616	+	0.972329i	$0.575056\pi$
$684$		−	1.65517i		−	0.0632870i
$685$	1.43245	−	2.48107i	0.0547310	−	0.0947968i
$686$		0			0
$687$	−8.47032	+	4.89034i	−0.323163	+	0.186578i
$688$	−20.1988			−0.770074
$689$	−5.26198	+	24.8473i	−0.200466	+	0.946608i
$690$	20.2681			0.771592
$691$	26.9106	−	15.5369i	1.02373	−	0.591050i	0.108547	−	0.994091i	$-0.465380\pi$
$691$	26.9106	−	15.5369i	1.02373	−	0.591050i	0.915182	+	0.403041i	$0.132047\pi$
$692$	2.96438	+	5.13445i	0.112689	+	0.195183i
$693$		0			0
$694$		−	22.2652i		−	0.845177i
$695$	9.86080	+	5.69314i	0.374041	+	0.215953i
$696$	16.7401	+	9.66491i	0.634532	+	0.366347i
$697$		−	19.2037i		−	0.727394i
$698$	−18.7156	+	32.4163i	−0.708395	+	1.22698i
$699$	−18.4060	−	31.8802i	−0.696180	−	1.20582i
$700$		0			0
$701$	0.358985			0.0135587			0.00677934	−	0.999977i	$-0.497842\pi$
$701$	0.358985			0.0135587			0.00677934	+	0.999977i	$0.497842\pi$
$702$	−13.5470	−	41.5873i	−0.511300	−	1.56961i
$703$	3.78660			0.142814
$704$	48.3222	−	27.8988i	1.82121	−	1.05148i
$705$	−0.0546844	−	0.0947161i	−0.00205953	−	0.00356722i
$706$	23.0021	−	39.8409i	0.865697	−	1.49943i
$707$		0			0
$708$	−36.2471	−	20.9273i	−1.36225	−	0.786494i
$709$	6.93547	+	4.00420i	0.260467	+	0.150381i	0.624548	−	0.780987i	$-0.285283\pi$
$709$	6.93547	+	4.00420i	0.260467	+	0.150381i	−0.364081	+	0.931367i	$0.618617\pi$
$710$			17.6993i			0.664243i
$711$	0.832860	−	1.44256i	0.0312347	−	0.0541001i
$712$	−4.30613	−	7.45844i	−0.161379	−	0.279517i
$713$	−50.8818	+	29.3766i	−1.90554	+	1.10016i
$714$		0			0
$715$	−13.0587	+	4.25386i	−0.488367	+	0.159085i
$716$	64.9314			2.42660
$717$	−18.9713	+	10.9531i	−0.708497	+	0.409051i
$718$	26.6497	+	46.1586i	0.994557	+	1.72262i
$719$	24.0945	−	41.7330i	0.898575	−	1.55638i	0.0692573	−	0.997599i	$-0.477937\pi$
$719$	24.0945	−	41.7330i	0.898575	−	1.55638i	0.829317	−	0.558778i	$-0.188730\pi$
$720$			0.298710i			0.0111323i
$721$		0			0
$722$	23.5073	+	13.5719i	0.874851	+	0.505095i
$723$		−	34.3201i		−	1.27638i
$724$	−43.5020	+	75.3477i	−1.61674	+	2.80027i
$725$	−5.75788	−	9.97294i	−0.213842	−	0.370386i
$726$	−66.7553	+	38.5412i	−2.47752	+	1.43040i
$727$	−13.7547			−0.510135			−0.255068	−	0.966923i	$-0.582098\pi$
$727$	−13.7547			−0.510135			−0.255068	+	0.966923i	$0.582098\pi$
$728$		0			0
$729$	25.4296			0.941839
$730$	14.9543	−	8.63385i	0.553482	−	0.319553i
$731$	−16.0700	−	27.8340i	−0.594369	−	1.02948i
$732$	−42.8910	+	74.2894i	−1.58530	+	2.74581i
$733$		−	48.3294i		−	1.78509i	−0.450961	−	0.892544i	$-0.648918\pi$
$733$		−	48.3294i		−	1.78509i	0.450961	−	0.892544i	$-0.351082\pi$
$734$	30.1847	+	17.4271i	1.11414	+	0.643247i
$735$		0			0
$736$		−	14.0091i		−	0.516383i
$737$	−28.3133	+	49.0400i	−1.04293	+	1.80641i
$738$	−0.858537	−	1.48703i	−0.0316032	−	0.0547383i
$739$	−13.5388	+	7.81663i	−0.498033	+	0.287539i	−0.727901	−	0.685683i	$-0.759504\pi$
$739$	−13.5388	+	7.81663i	−0.498033	+	0.287539i	0.229868	+	0.973222i	$0.426171\pi$
$740$	−3.63518			−0.133632
$741$	17.3941	+	3.68359i	0.638988	+	0.135320i
$742$		0			0
$743$	1.48979	−	0.860131i	0.0546551	−	0.0315551i	−0.472423	−	0.881372i	$-0.656621\pi$
$743$	1.48979	−	0.860131i	0.0546551	−	0.0315551i	0.527079	+	0.849817i	$0.323287\pi$
$744$	−33.0294	−	57.2086i	−1.21092	−	2.09737i
$745$	0.235156	−	0.407301i	0.00861543	−	0.0149224i
$746$		−	35.7368i		−	1.30842i
$747$	−0.439170	−	0.253555i	−0.0160684	−	0.00927709i
$748$	−74.8071	−	43.1899i	−2.73522	−	1.57918i
$749$		0			0
$750$	14.3292	−	24.8190i	0.523230	−	0.906261i
$751$	10.0993	+	17.4925i	0.368529	+	0.638312i	0.989336	−	0.145652i	$-0.0465281\pi$
$751$	10.0993	+	17.4925i	0.368529	+	0.638312i	−0.620806	+	0.783964i	$0.713195\pi$
$752$	0.201491	−	0.116331i	0.00734763	−	0.00424216i
$753$	1.09646			0.0399573
$754$	−14.8155	+	16.4791i	−0.539547	+	0.600133i
$755$	−2.53603			−0.0922955
$756$		0			0
$757$	12.6094	+	21.8401i	0.458296	+	0.793792i	0.998871	−	0.0475040i	$-0.0151267\pi$
$757$	12.6094	+	21.8401i	0.458296	+	0.793792i	−0.540575	+	0.841296i	$0.681793\pi$
$758$	−44.6530	+	77.3413i	−1.62187	+	2.80916i
$759$			64.3669i			2.33637i
$760$	7.21861	+	4.16766i	0.261846	+	0.151177i
$761$	17.5671	+	10.1424i	0.636807	+	0.367661i	0.783383	−	0.621539i	$-0.213492\pi$
$761$	17.5671	+	10.1424i	0.636807	+	0.367661i	−0.146577	+	0.989199i	$0.546825\pi$
$762$		−	41.1310i		−	1.49002i
$763$		0			0
$764$	−11.9701	−	20.7328i	−0.433062	−	0.750085i
$765$	−0.411622	+	0.237650i	−0.0148822	+	0.00859225i
$766$	31.8236			1.14983
$767$	15.0601	−	16.7512i	0.543790	−	0.604851i
$768$	51.5457			1.85999
$769$	−15.3936	+	8.88748i	−0.555106	+	0.320491i	−0.751179	−	0.660099i	$-0.770514\pi$
$769$	−15.3936	+	8.88748i	−0.555106	+	0.320491i	0.196073	+	0.980589i	$0.437181\pi$
$770$		0			0
$771$	19.4011	−	33.6038i	0.698715	−	1.21021i
$772$			7.44910i			0.268099i
$773$	17.2312	+	9.94846i	0.619765	+	0.357821i	0.776777	−	0.629775i	$-0.216853\pi$
$773$	17.2312	+	9.94846i	0.619765	+	0.357821i	−0.157013	+	0.987597i	$0.550186\pi$
$774$	−2.48873	−	1.43687i	−0.0894557	−	0.0516472i
$775$			39.3546i			1.41366i
$776$	−11.3601	+	19.6763i	−0.407804	+	0.706337i
$777$		0			0
$778$	−30.4792	+	17.5972i	−1.09273	+	0.630890i
$779$	−12.5357			−0.449138
$780$	−16.6985	−	3.53630i	−0.597904	−	0.126620i
$781$	−56.2091			−2.01132
$782$	−59.4146	+	34.3030i	−2.12466	+	1.22667i
$783$	−6.46096	−	11.1907i	−0.230896	−	0.399923i
$784$		0			0
$785$			3.80447i			0.135787i
$786$	−78.8184	−	45.5058i	−2.81136	−	1.62314i
$787$	−0.620594	−	0.358300i	−0.0221218	−	0.0127720i	0.488898	−	0.872341i	$-0.337399\pi$
$787$	−0.620594	−	0.358300i	−0.0221218	−	0.0127720i	−0.511020	+	0.859569i	$0.670732\pi$
$788$		−	64.0143i		−	2.28041i
$789$	−1.55673	+	2.69633i	−0.0554209	+	0.0959919i
$790$	8.93415	+	15.4744i	0.317863	+	0.550554i
$791$		0			0
$792$	−3.62588			−0.128840
$793$	−34.3321	−	30.8661i	−1.21917	−	1.09609i
$794$	42.2361			1.49890
$795$	−7.66102	+	4.42309i	−0.271708	+	0.156871i
$796$	−23.2116	−	40.2036i	−0.822713	−	1.42498i
$797$	−4.11380	+	7.12530i	−0.145718	+	0.252391i	−0.929641	−	0.368467i	$-0.879883\pi$
$797$	−4.11380	+	7.12530i	−0.145718	+	0.252391i	0.783923	+	0.620859i	$0.213216\pi$
$798$		0			0
$799$	0.320608	+	0.185103i	0.0113423	+	0.00654848i
$800$	−8.12652	−	4.69185i	−0.287316	−	0.165882i
$801$		−	0.320571i		−	0.0113268i
$802$	34.1136	−	59.0865i	1.20459	−	2.08642i
$803$	27.4192	+	47.4915i	0.967603	+	1.67594i
$804$	−60.9476	+	35.1881i	−2.14946	+	1.24099i
$805$		0			0
$806$	72.0062	−	23.4560i	2.53631	−	0.826201i
$807$	−22.0475			−0.776109
$808$	42.4448	−	24.5055i	1.49320	−	0.862101i
$809$	−0.897101	−	1.55382i	−0.0315404	−	0.0546295i	0.849824	−	0.527066i	$-0.176708\pi$
$809$	−0.897101	−	1.55382i	−0.0315404	−	0.0546295i	−0.881365	+	0.472436i	$0.843375\pi$
$810$	8.01981	−	13.8907i	0.281787	−	0.488070i
$811$		−	8.58932i		−	0.301612i	−0.988563	−	0.150806i	$-0.951813\pi$
$811$		−	8.58932i		−	0.301612i	0.988563	−	0.150806i	$-0.0481869\pi$
$812$		0			0
$813$	16.4639	+	9.50543i	0.577414	+	0.333370i
$814$		−	17.6694i		−	0.619312i
$815$	−1.38664	+	2.40173i	−0.0485718	+	0.0841289i
$816$	−10.0906	−	17.4775i	−0.353242	−	0.611833i
$817$	−18.1693	+	10.4900i	−0.635662	+	0.367000i
$818$	24.5812			0.859460
$819$		0			0
$820$	12.0344			0.420260
$821$	−8.92361	+	5.15205i	−0.311436	+	0.179808i	−0.647569	−	0.762007i	$-0.724214\pi$
$821$	−8.92361	+	5.15205i	−0.311436	+	0.179808i	0.336133	+	0.941815i	$0.390881\pi$
$822$	8.65326	+	14.9879i	0.301817	+	0.522762i
$823$	16.1496	−	27.9719i	0.562940	−	0.975040i	−0.434298	−	0.900769i	$-0.643004\pi$
$823$	16.1496	−	27.9719i	0.562940	−	0.975040i	0.997238	−	0.0742711i	$-0.0236630\pi$
$824$			7.03983i			0.245244i
$825$	37.3385	+	21.5574i	1.29996	+	0.750532i
$826$		0			0
$827$		−	9.24057i		−	0.321326i	−0.987009	−	0.160663i	$-0.948637\pi$
$827$		−	9.24057i		−	0.321326i	0.987009	−	0.160663i	$-0.0513632\pi$
$828$	−2.00397	+	3.47098i	−0.0696427	+	0.120625i
$829$	−19.5014	−	33.7774i	−0.677311	−	1.17314i	−0.975788	−	0.218720i	$-0.929812\pi$
$829$	−19.5014	−	33.7774i	−0.677311	−	1.17314i	0.298477	−	0.954417i	$-0.403521\pi$
$830$	4.71101	−	2.71990i	0.163521	−	0.0944091i
$831$	11.3717			0.394480
$832$	−7.73219	+	36.5118i	−0.268065	+	1.26582i
$833$		0			0
$834$	−59.5680	+	34.3916i	−2.06267	+	1.19088i
$835$	4.62044	+	8.00283i	0.159897	+	0.276949i
$836$	−28.1932	+	48.8321i	−0.975082	+	1.68889i
$837$			44.1601i			1.52640i
$838$	−25.8900	−	14.9476i	−0.894356	−	0.516357i
$839$	2.28694	+	1.32036i	0.0789538	+	0.0455840i	0.538957	−	0.842333i	$-0.318818\pi$
$839$	2.28694	+	1.32036i	0.0789538	+	0.0455840i	−0.460003	+	0.887917i	$0.652152\pi$
$840$		0			0
$841$	11.2266	−	19.4450i	0.387123	−	0.670517i
$842$	2.45072	+	4.24477i	0.0844573	+	0.146284i
$843$	25.4621	−	14.7005i	0.876961	−	0.506314i
$844$	24.4136			0.840349
$845$	3.72383	−	8.39774i	0.128104	−	0.288891i
$846$	0.0331014			0.00113805
$847$		0			0
$848$	−9.40932	−	16.2974i	−0.323117	−	0.559656i
$849$	−0.433662	+	0.751125i	−0.0148833	+	0.0257786i
$850$			45.9543i			1.57622i
$851$	−7.94069	−	4.58456i	−0.272203	−	0.157157i
$852$	−60.4983	−	34.9287i	−2.07264	−	1.19664i
$853$		−	23.6875i		−	0.811046i	−0.914085	−	0.405523i	$-0.867089\pi$
$853$		−	23.6875i		−	0.811046i	0.914085	−	0.405523i	$-0.132911\pi$
$854$		0			0
$855$	0.155132	+	0.268696i	0.00530539	+	0.00918920i
$856$	−1.69150	+	0.976588i	−0.0578143	+	0.0333791i
$857$	−44.8581			−1.53232			−0.766162	−	0.642647i	$-0.777836\pi$
$857$	−44.8581			−1.53232			−0.766162	+	0.642647i	$0.777836\pi$
$858$	17.1887	−	81.1659i	0.586813	−	2.77096i
$859$	−14.6058			−0.498344			−0.249172	−	0.968459i	$-0.580158\pi$
$859$	−14.6058			−0.498344			−0.249172	+	0.968459i	$0.580158\pi$
$860$	17.4427	−	10.0706i	0.594793	−	0.343404i
$861$		0			0
$862$	−17.0567	+	29.5431i	−0.580954	+	1.00624i
$863$		−	26.3294i		−	0.896264i	−0.893967	−	0.448132i	$-0.852089\pi$
$863$		−	26.3294i		−	0.896264i	0.893967	−	0.448132i	$-0.147911\pi$
$864$	−9.11884	−	5.26476i	−0.310229	−	0.179111i
$865$	−0.962457	−	0.555675i	−0.0327245	−	0.0188935i
$866$		−	40.4105i		−	1.37320i
$867$	0.950243	−	1.64587i	0.0322719	−	0.0558966i
$868$		0			0
$869$	−49.1433	+	28.3729i	−1.66707	+	0.962484i
$870$	−7.71820			−0.261672
$871$	−11.7313	−	36.0134i	−0.397501	−	1.22027i
$872$	66.2852			2.24470
$873$	−0.732404	+	0.422853i	−0.0247881	+	0.0143114i
$874$	22.3921	+	38.7843i	0.757424	+	1.31190i
$875$		0			0
$876$			68.1539i			2.30271i
$877$	1.11257	+	0.642341i	0.0375687	+	0.0216903i	0.518667	−	0.854977i	$-0.326429\pi$
$877$	1.11257	+	0.642341i	0.0375687	+	0.0216903i	−0.481098	+	0.876667i	$0.659762\pi$
$878$	51.3715	+	29.6594i	1.73370	+	1.00095i
$879$		−	14.3201i		−	0.483004i
$880$	5.08805	−	8.81276i	0.171518	−	0.297078i
$881$	0.0438196	+	0.0758978i	0.00147632	+	0.00255706i	0.866763	−	0.498721i	$-0.166197\pi$
$881$	0.0438196	+	0.0758978i	0.00147632	+	0.00255706i	−0.865286	+	0.501278i	$0.832863\pi$
$882$		0			0
$883$	4.38547			0.147583			0.0737914	−	0.997274i	$-0.476490\pi$
$883$	4.38547			0.147583			0.0737914	+	0.997274i	$0.476490\pi$
$884$	54.9359	−	17.8953i	1.84769	−	0.601885i
$885$	7.84566			0.263729
$886$	−6.13882	+	3.54425i	−0.206238	+	0.119071i
$887$	−0.380897	−	0.659733i	−0.0127893	−	0.0221517i	0.859560	−	0.511035i	$-0.170738\pi$
$887$	−0.380897	−	0.659733i	−0.0127893	−	0.0221517i	−0.872349	+	0.488883i	$0.837404\pi$
$888$	5.15462	−	8.92806i	0.172978	−	0.299606i
$889$		0			0
$890$	2.97808	+	1.71940i	0.0998255	+	0.0576343i
$891$	44.1139	+	25.4691i	1.47787	+	0.853249i
$892$			21.3018i			0.713238i
$893$	0.120830	−	0.209284i	0.00404344	−	0.00700344i
$894$	1.42055	+	2.46046i	0.0475103	+	0.0822902i
$895$	−10.5408	+	6.08572i	−0.352340	+	0.203423i
$896$		0			0
$897$	−32.0164	−	28.7843i	−1.06900	−	0.961078i
$898$	12.4026			0.413879
$899$	19.3761	−	11.1868i	0.646229	−	0.373101i
$900$	1.34232	+	2.32496i	0.0447438	+	0.0774986i
$901$	14.9719	−	25.9321i	0.498786	−	0.863922i
$902$			58.4952i			1.94768i
$903$		0			0
$904$	−6.13155	−	3.54005i	−0.203932	−	0.117740i
$905$		−	16.3090i		−	0.542128i
$906$	7.65994	−	13.2674i	0.254484	−	0.440780i
$907$	24.9934	+	43.2899i	0.829893	+	1.43742i	0.898122	+	0.439747i	$0.144932\pi$
$907$	24.9934	+	43.2899i	0.829893	+	1.43742i	−0.0682293	+	0.997670i	$0.521735\pi$
$908$	90.5293	−	52.2671i	3.00432	−	1.73455i
$909$	1.82432			0.0605089
$910$		0			0
$911$	−16.2985			−0.539994			−0.269997	−	0.962861i	$-0.587023\pi$
$911$	−16.2985			−0.539994			−0.269997	+	0.962861i	$0.587023\pi$
$912$	−11.4088	+	6.58688i	−0.377784	+	0.218114i
$913$	8.63781	+	14.9611i	0.285870	+	0.495141i
$914$	−5.44382	+	9.42897i	−0.180065	+	0.311882i
$915$		−	16.0799i		−	0.531585i
$916$	17.9676	+	10.3736i	0.593666	+	0.342753i
$917$		0			0
$918$			51.5657i			1.70192i
$919$	−3.75013	+	6.49542i	−0.123705	+	0.214264i	−0.921226	−	0.389028i	$-0.872811\pi$
$919$	−3.75013	+	6.49542i	−0.123705	+	0.214264i	0.797521	+	0.603291i	$0.206144\pi$
$920$	−10.0919	−	17.4796i	−0.332719	−	0.576285i
$921$	17.6912	−	10.2140i	0.582946	−	0.336564i
$922$	92.3002			3.03975
$923$	25.1362	−	27.9587i	0.827367	−	0.920271i
$924$		0			0
$925$	−5.31890	+	3.07087i	−0.174884	+	0.100970i
$926$	3.04118	+	5.26747i	0.0999392	+	0.173100i
$927$	−0.131021	+	0.226934i	−0.00430328	+	0.00745350i
$928$			5.33476i			0.175122i
$929$	−0.562197	−	0.324584i	−0.0184451	−	0.0106493i	0.490749	−	0.871301i	$-0.336723\pi$
$929$	−0.562197	−	0.324584i	−0.0184451	−	0.0106493i	−0.509194	+	0.860652i	$0.670056\pi$
$930$	22.8428	+	13.1883i	0.749045	+	0.432462i
$931$		0			0
$932$	−39.0436	+	67.6255i	−1.27892	+	2.21515i
$933$	−22.2476	−	38.5339i	−0.728353	−	1.26154i
$934$	24.4129	−	14.0948i	0.798815	−	0.461196i
$935$	16.1920			0.529534
$936$	1.62146	−	1.80353i	0.0529991	−	0.0589503i
$937$	−50.1982			−1.63990			−0.819951	−	0.572433i	$-0.806000\pi$
$937$	−50.1982			−1.63990			−0.819951	+	0.572433i	$0.806000\pi$
$938$		0			0
$939$	−25.2091	−	43.6635i	−0.822669	−	1.42490i
$940$	−0.115999	+	0.200916i	−0.00378346	+	0.00655315i
$941$		−	14.5390i		−	0.473957i	−0.971515	−	0.236978i	$-0.923843\pi$
$941$		−	14.5390i		−	0.473957i	0.971515	−	0.236978i	$-0.0761570\pi$
$942$	−19.9033	−	11.4912i	−0.648486	−	0.374403i
$943$	26.2880	+	15.1774i	0.856054	+	0.494243i
$944$			16.6902i			0.543220i
$945$		0			0
$946$	48.9496	+	84.7832i	1.59149	+	2.75654i
$947$	8.17967	−	4.72254i	0.265804	−	0.153462i	−0.361175	−	0.932498i	$-0.617624\pi$
$947$	8.17967	−	4.72254i	0.265804	−	0.153462i	0.626979	+	0.779036i	$0.284291\pi$
$948$	−70.5244			−2.29053
$949$	−35.8841	−	7.59927i	−1.16485	−	0.246683i
$950$	29.9977			0.973255
$951$	47.0600	−	27.1701i	1.52602	−	0.881051i
$952$		0			0
$953$	−11.0874	+	19.2040i	−0.359158	+	0.622079i	−0.987820	−	0.155599i	$-0.950269\pi$
$953$	−11.0874	+	19.2040i	−0.359158	+	0.622079i	0.628663	+	0.777678i	$0.283603\pi$
$954$		−	2.67738i		−	0.0866833i
$955$	3.88637	+	2.24380i	0.125760	+	0.0726076i
$956$	40.2428	+	23.2342i	1.30154	+	0.751447i
$957$		−	24.5113i		−	0.792338i
$958$	34.3633	−	59.5190i	1.11023	−	1.92297i
$959$		0			0
$960$	−11.2574	+	6.49948i	−0.363332	+	0.209770i
$961$	−45.4608			−1.46648
$962$	8.78884	+	7.90158i	0.283364	+	0.254757i
$963$	−0.0727024			−0.00234280
$964$	−63.0476	+	36.4006i	−2.03063	+	1.17238i
$965$	−0.698170	−	1.20927i	−0.0224749	−	0.0389277i
$966$		0			0
$967$		−	11.4753i		−	0.369022i	−0.982830	−	0.184511i	$-0.940930\pi$
$967$		−	11.4753i		−	0.369022i	0.982830	−	0.184511i	$-0.0590702\pi$
$968$	66.4775	+	38.3808i	2.13667	+	1.23360i
$969$	−18.1534	−	10.4809i	−0.583172	−	0.336695i
$970$		−	9.07195i		−	0.291283i
$971$	8.40453	−	14.5571i	0.269714	−	0.467159i	−0.699074	−	0.715050i	$-0.746404\pi$
$971$	8.40453	−	14.5571i	0.269714	−	0.467159i	0.968788	+	0.247891i	$0.0797374\pi$
$972$	3.09631	+	5.36297i	0.0993143	+	0.172017i
$973$		0			0
$974$	6.58130			0.210879
$975$	−27.4202	+	8.93210i	−0.878148	+	0.286056i
$976$	34.2070			1.09494
$977$	−4.21546	+	2.43380i	−0.134864	+	0.0778640i	−0.565914	−	0.824464i	$-0.691477\pi$
$977$	−4.21546	+	2.43380i	−0.134864	+	0.0778640i	0.431050	+	0.902328i	$0.358143\pi$
$978$	−8.37653	−	14.5086i	−0.267852	−	0.463933i
$979$	−5.46043	+	9.45773i	−0.174516	+	0.302271i
$980$		0			0
$981$	2.13675	+	1.23366i	0.0682213	+	0.0393876i
$982$	79.7275	+	46.0307i	2.54421	+	1.46890i
$983$			36.6352i			1.16848i	0.811580	+	0.584241i	$0.198608\pi$
$983$			36.6352i			1.16848i	−0.811580	+	0.584241i	$0.801392\pi$
$984$	−17.0646	+	29.5567i	−0.543998	+	0.942233i
$985$	5.99976	+	10.3919i	0.191168	+	0.331113i
$986$	22.6255	−	13.0628i	0.720541	−	0.416005i
$987$		0			0
$988$	−11.6816	−	35.8607i	−0.371641	−	1.14088i
$989$	50.8025			1.61543
$990$	1.25381	−	0.723890i	0.0398488	−	0.0230067i
$991$	−17.8509	−	30.9187i	−0.567054	−	0.982166i	−0.996855	−	0.0792424i	$-0.974750\pi$
$991$	−17.8509	−	30.9187i	−0.567054	−	0.982166i	0.429802	−	0.902923i	$-0.358583\pi$
$992$	9.11565	−	15.7888i	0.289422	−	0.501294i
$993$			41.6009i			1.32016i
$994$		0			0
$995$	7.53620	+	4.35103i	0.238914	+	0.137937i
$996$			21.4704i			0.680315i
$997$	18.9178	−	32.7665i	0.599131	−	1.03773i	−0.393818	−	0.919188i	$-0.628846\pi$
$997$	18.9178	−	32.7665i	0.599131	−	1.03773i	0.992950	−	0.118538i	$-0.0378206\pi$
$998$	−33.5094	−	58.0400i	−1.06072	−	1.83723i
$999$	−5.96838	+	3.44584i	−0.188831	+	0.109022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.j.491.2	yes	32
7.2	even	3		637.2.u.j.361.15		32
7.3	odd	6		637.2.k.j.569.1		32
7.4	even	3		637.2.k.j.569.2		32
7.5	odd	6		637.2.u.j.361.16		32
7.6	odd	2	inner	637.2.q.j.491.1	✓	32
13.2	odd	12		8281.2.a.cx.1.3		32
13.4	even	6	inner	637.2.q.j.589.2	yes	32
13.11	odd	12		8281.2.a.cx.1.29		32
91.4	even	6		637.2.u.j.30.15		32
91.17	odd	6		637.2.u.j.30.16		32
91.30	even	6		637.2.k.j.459.16		32
91.41	even	12		8281.2.a.cx.1.4		32
91.69	odd	6	inner	637.2.q.j.589.1	yes	32
91.76	even	12		8281.2.a.cx.1.30		32
91.82	odd	6		637.2.k.j.459.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.j.459.15		32	91.82	odd	6
637.2.k.j.459.16		32	91.30	even	6
637.2.k.j.569.1		32	7.3	odd	6
637.2.k.j.569.2		32	7.4	even	3
637.2.q.j.491.1	✓	32	7.6	odd	2	inner
637.2.q.j.491.2	yes	32	1.1	even	1	trivial
637.2.q.j.589.1	yes	32	91.69	odd	6	inner
637.2.q.j.589.2	yes	32	13.4	even	6	inner
637.2.u.j.30.15		32	91.4	even	6
637.2.u.j.30.16		32	91.17	odd	6
637.2.u.j.361.15		32	7.2	even	3
637.2.u.j.361.16		32	7.5	odd	6
8281.2.a.cx.1.3		32	13.2	odd	12
8281.2.a.cx.1.4		32	91.41	even	12
8281.2.a.cx.1.29		32	13.11	odd	12
8281.2.a.cx.1.30		32	91.76	even	12

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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.08022 + 1.20101i) q^{2} +(0.888571 + 1.53905i) q^{3} +(1.88487 - 3.26470i) q^{4} +0.706642i q^{5} +(-3.69684 - 2.13437i) q^{6} +4.25098i q^{8} +(-0.0791164 + 0.137034i) q^{9} +O(q^{10})\)	\(q+(-2.08022 + 1.20101i) q^{2} +(0.888571 + 1.53905i) q^{3} +(1.88487 - 3.26470i) q^{4} +0.706642i q^{5} +(-3.69684 - 2.13437i) q^{6} +4.25098i q^{8} +(-0.0791164 + 0.137034i) q^{9} +(-0.848687 - 1.46997i) q^{10} +(4.66830 - 2.69524i) q^{11} +6.69937 q^{12} +(-0.746990 + 3.52732i) q^{13} +(-1.08756 + 0.627901i) q^{15} +(-1.33575 - 2.31358i) q^{16} +(2.12541 - 3.68131i) q^{17} -0.380080i q^{18} +(-2.40306 - 1.38741i) q^{19} +(2.30697 + 1.33193i) q^{20} +(-6.47406 + 11.2134i) q^{22} +(3.35956 + 5.81893i) q^{23} +(-6.54247 + 3.77730i) q^{24} +4.50066 q^{25} +(-2.68246 - 8.23475i) q^{26} +5.05022 q^{27} +(-1.27934 - 2.21588i) q^{29} +(1.50824 - 2.61234i) q^{30} +8.74418i q^{31} +(-1.80563 - 1.04248i) q^{32} +(8.29623 + 4.78983i) q^{33} +10.2106i q^{34} +(0.298249 + 0.516582i) q^{36} +(-1.18180 + 0.682315i) q^{37} +6.66519 q^{38} +(-6.09248 + 1.98462i) q^{39} -3.00392 q^{40} +(3.91241 - 2.25883i) q^{41} +(3.78044 - 6.54792i) q^{43} -20.3208i q^{44} +(-0.0968337 - 0.0559070i) q^{45} +(-13.9772 - 8.06976i) q^{46} +0.0870907i q^{47} +(2.37381 - 4.11156i) q^{48} +(-9.36235 + 5.40536i) q^{50} +7.55430 q^{51} +(10.1077 + 9.08725i) q^{52} +7.04425 q^{53} +(-10.5056 + 6.06539i) q^{54} +(1.90457 + 3.29882i) q^{55} -4.93124i q^{57} +(5.32262 + 3.07302i) q^{58} +(-5.41052 - 3.12376i) q^{59} +4.73406i q^{60} +(-6.40224 + 11.0890i) q^{61} +(-10.5019 - 18.1898i) q^{62} +10.3511 q^{64} +(-2.49255 - 0.527855i) q^{65} -23.0106 q^{66} +(-9.09751 + 5.25245i) q^{67} +(-8.01224 - 13.8776i) q^{68} +(-5.97041 + 10.3411i) q^{69} +(-9.03045 - 5.21373i) q^{71} +(-0.582527 - 0.336322i) q^{72} +10.1732i q^{73} +(1.63894 - 2.83873i) q^{74} +(3.99915 + 6.92674i) q^{75} +(-9.05893 + 5.23018i) q^{76} +(10.2901 - 11.4456i) q^{78} -10.5270 q^{79} +(1.63487 - 0.943894i) q^{80} +(4.72483 + 8.18365i) q^{81} +(-5.42578 + 9.39773i) q^{82} +3.20483i q^{83} +(2.60137 + 1.50190i) q^{85} +18.1615i q^{86} +(2.27357 - 3.93794i) q^{87} +(11.4574 + 19.8449i) q^{88} +(-1.75452 + 1.01297i) q^{89} +0.268580 q^{90} +25.3294 q^{92} +(-13.4577 + 7.76983i) q^{93} +(-0.104597 - 0.181168i) q^{94} +(0.980401 - 1.69810i) q^{95} -3.70527i q^{96} +(4.62864 + 2.67235i) q^{97} +0.852952i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) \) 32 * q + 20 * q^4 - 28 * q^9	\( 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Introduction

L-functions

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