LMFDB - Embedded newform 637.2.q.j.589.1

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			589.1
Character	$\chi$	$=$	637.589
Dual form			637.2.q.j.491.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.08022 - 1.20101i) q^{2} +(-0.888571 + 1.53905i) q^{3} +(1.88487 + 3.26470i) q^{4} +0.706642i q^{5} +(3.69684 - 2.13437i) q^{6} -4.25098i q^{8} +(-0.0791164 - 0.137034i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

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	−0.471469	−	0.881882i	$-0.656276\pi$
$2$	−2.08022	−	1.20101i	−1.47094	−	0.849246i	−0.999467	+	0.0326368i	$0.989610\pi$
$3$	−0.888571	+	1.53905i	−0.513017	+	0.888571i	0.486869	+	0.873475i	$0.338139\pi$
$3$	−0.888571	+	1.53905i	−0.513017	+	0.888571i	−0.999886	+	0.0150961i	$0.995195\pi$
$4$	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	0.995151	−	0.0983585i	$-0.0313592\pi$
$11$	4.66830	+	2.69524i	1.40755	+	0.812647i	0.412395	+	0.911005i	$0.364693\pi$
$12$	−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	−0.999838	−	0.0179758i	$-0.994278\pi$
$17$	−2.12541	−	3.68131i	−0.515487	−	0.892849i	0.484352	−	0.874873i	$-0.339056\pi$
$18$			0.380080i			0.0895857i
$19$	2.40306	−	1.38741i	0.551300	−	0.318293i	−0.198346	−	0.980132i	$-0.563557\pi$
$19$	2.40306	−	1.38741i	0.551300	−	0.318293i	0.749646	+	0.661839i	$0.230224\pi$
$20$	−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	−0.267769	−	0.963483i	$-0.586286\pi$
$23$	3.35956	−	5.81893i	0.700517	−	1.21333i	0.968285	−	0.249847i	$-0.0803804\pi$
$24$	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	−0.960016	−	0.279946i	$-0.909683\pi$
$29$	−1.27934	+	2.21588i	−0.237568	+	0.411479i	0.722448	+	0.691425i	$0.243017\pi$
$30$	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	0.399701	−	0.916646i	$-0.369114\pi$
$37$	−1.18180	−	0.682315i	−0.194288	−	0.112172i	−0.593988	+	0.804474i	$0.702447\pi$
$38$	−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	$-0.448094\pi$
$41$	−3.91241	−	2.25883i	−0.611016	−	0.352770i	−0.773363	+	0.633963i	$0.781427\pi$
$42$		0			0
$43$	3.78044	+	6.54792i	0.576512	+	0.998548i	0.995876	+	0.0907300i	$0.0289200\pi$
$43$	3.78044	+	6.54792i	0.576512	+	0.998548i	−0.419363	+	0.907818i	$0.637747\pi$
$44$			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	$-0.533353\pi$
$59$	5.41052	−	3.12376i	0.704389	−	0.406679i	0.808980	+	0.587836i	$0.200020\pi$
$60$		−	4.73406i		−	0.611164i
$61$	6.40224	+	11.0890i	0.819723	+	1.41980i	0.905887	+	0.423521i	$0.139206\pi$
$61$	6.40224	+	11.0890i	0.819723	+	1.41980i	−0.0861637	+	0.996281i	$0.527461\pi$
$62$	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	−0.172236	−	0.985056i	$-0.555099\pi$
$67$	−9.09751	−	5.25245i	−1.11144	−	0.641689i	−0.939201	+	0.343367i	$0.888433\pi$
$68$	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	−0.928650	−	0.370957i	$-0.879030\pi$
$71$	−9.03045	+	5.21373i	−1.07172	+	0.618756i	−0.143067	+	0.989713i	$0.545696\pi$
$72$	−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	$-0.299089\pi$
$89$	1.75452	+	1.01297i	0.185979	+	0.107375i	−0.404120	+	0.914706i	$0.632422\pi$
$90$	−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	$-0.754132\pi$
$97$	−4.62864	+	2.67235i	−0.469968	+	0.271336i	0.246259	+	0.969204i	$0.420799\pi$
$98$		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	−0.422585	−	0.906323i	$-0.638877\pi$
$101$	5.76467	−	9.98470i	0.573606	−	0.993515i	0.996192	−	0.0871919i	$-0.0277893\pi$
$102$	−15.7146	−	9.07282i	−1.55598	−	0.898343i
$103$	−1.65605			−0.163175			−0.0815877	−	0.996666i	$-0.525999\pi$
$103$	−1.65605			−0.163175			−0.0815877	+	0.996666i	$0.525999\pi$
$104$	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	−0.854707	−	0.519110i	$-0.826263\pi$
$107$	0.229732	−	0.397908i	0.0222091	−	0.0384672i	0.876916	+	0.480643i	$0.159597\pi$
$108$	−9.51903	−	16.4874i	−0.915969	−	1.58650i
$109$			15.5929i			1.49353i	0.665088	+	0.746765i	$0.268394\pi$
$109$			15.5929i			1.49353i	−0.665088	+	0.746765i	$0.731606\pi$
$110$	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	0.824194	−	0.566307i	$-0.191629\pi$
$113$	−0.832761	−	1.44238i	−0.0783396	−	0.135688i	−0.902534	+	0.430619i	$0.858295\pi$
$114$	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	−0.569149	−	0.822234i	$-0.692727\pi$
$127$	4.81769	−	8.34449i	0.427501	−	0.740454i	0.996650	+	0.0817805i	$0.0260607\pi$
$128$	−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	$-0.881401\pi$
$131$	−21.3205			−1.86278			−0.931388	+	0.364027i	$0.881401\pi$
$132$	−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	−0.642430	−	0.766344i	$-0.722074\pi$
$137$	−3.51107	+	2.02712i	−0.299971	+	0.173188i	0.342459	+	0.939533i	$0.388740\pi$
$138$		−	28.6822i		−	2.44159i
$139$	−8.05661	−	13.9545i	−0.683353	−	1.18360i	−0.973952	−	0.226756i	$-0.927188\pi$
$139$	−8.05661	−	13.9545i	−0.683353	−	1.18360i	0.290599	−	0.956845i	$-0.406145\pi$
$140$		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	−0.523424	−	0.852072i	$-0.675346\pi$
$149$	−0.576390	+	0.332779i	−0.0472197	+	0.0272623i	0.476204	+	0.879335i	$0.342012\pi$
$150$	16.6382	−	9.60608i	1.35851	−	0.784333i
$151$		−	3.58885i		−	0.292056i	−0.989280	−	0.146028i	$-0.953351\pi$
$151$		−	3.58885i		−	0.292056i	0.989280	−	0.146028i	$-0.0466490\pi$
$152$	−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	$-0.568923\pi$
$157$	−5.38387			−0.429680			−0.214840	+	0.976649i	$0.568923\pi$
$158$	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	−0.360952	−	0.932584i	$-0.617548\pi$
$163$	3.39879	−	1.96229i	0.266214	−	0.153699i	0.627166	+	0.778886i	$0.284215\pi$
$164$		−	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	$-0.502199\pi$
$167$	−11.3252	−	6.53858i	−0.876367	−	0.505971i	−0.869459	+	0.494005i	$0.835532\pi$
$168$		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	$-0.147625\pi$
$173$	0.786360	+	1.36202i	0.0597859	+	0.103552i	−0.834583	+	0.550882i	$0.814292\pi$
$174$			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	−0.340895	−	0.940101i	$-0.610730\pi$
$179$	8.61218	−	14.9167i	0.643704	−	1.11493i	0.984599	−	0.174827i	$-0.0559367\pi$
$180$	0.365038	+	0.210755i	0.0272084	+	0.0157088i
$181$	23.0795			1.71549			0.857744	−	0.514076i	$-0.171865\pi$
$181$	23.0795			1.71549			0.857744	+	0.514076i	$0.171865\pi$
$182$		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	0.957736	−	0.287649i	$-0.0928737\pi$
$191$	3.17530	+	5.49978i	0.229757	+	0.397950i	−0.727979	+	0.685599i	$0.759540\pi$
$192$	−9.19771	+	15.9309i	−0.663787	+	1.14971i
$193$	−1.71129	−	0.988011i	−0.123181	−	0.0711186i	0.437143	−	0.899392i	$-0.355990\pi$
$193$	−1.71129	−	0.988011i	−0.123181	−	0.0711186i	−0.560324	+	0.828273i	$0.689324\pi$
$194$	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	0.922022	−	0.387138i	$-0.126536\pi$
$197$	14.7060	+	8.49053i	1.04776	+	0.604925i	0.125739	+	0.992063i	$0.459870\pi$
$198$	−1.02441	+	1.77433i	−0.0728015	+	0.126096i
$199$	−6.15733	−	10.6648i	−0.436482	−	0.756009i	0.560933	−	0.827861i	$-0.310442\pi$
$199$	−6.15733	−	10.6648i	−0.436482	−	0.756009i	−0.997415	+	0.0718521i	$0.977109\pi$
$200$		−	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	−0.732774	−	0.680472i	$-0.761775\pi$
$211$	3.23809	−	5.60854i	0.222919	−	0.386108i	0.955693	+	0.294365i	$0.0951080\pi$
$212$	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	$-0.272744\pi$
$223$	4.89368	+	2.82537i	0.327705	+	0.189200i	−0.327117	+	0.944984i	$0.606077\pi$
$224$		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	−0.601285	+	0.799035i	$0.705344\pi$
$227$	−24.0147	+	13.8649i	−1.59391	+	0.920245i	−0.992627	+	0.121211i	$0.961322\pi$
$228$	−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	$-0.869471\pi$
$239$		−	12.3266i		−	0.797345i	0.917093	−	0.398672i	$-0.130529\pi$
$240$	2.90540	−	1.67743i	0.187543	−	0.108278i
$241$	16.7246	−	9.65598i	1.07733	−	0.621996i	0.147154	−	0.989114i	$-0.452989\pi$
$241$	16.7246	−	9.65598i	1.07733	−	0.621996i	0.930175	+	0.367117i	$0.119655\pi$
$242$		−	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	$-0.172865\pi$
$251$	−0.308490	−	0.534320i	−0.0194717	−	0.0337260i	−0.875597	+	0.483042i	$0.839532\pi$
$252$		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	−0.293694	−	0.955900i	$-0.594885\pi$
$257$	10.9170	−	18.9089i	0.680987	−	1.17950i	0.974680	−	0.223604i	$-0.0717821\pi$
$258$	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	−0.837754	−	0.546048i	$-0.816132\pi$
$263$	0.875972	−	1.51723i	0.0540147	−	0.0935563i	0.891768	+	0.452492i	$0.149465\pi$
$264$	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	$-0.0432069\pi$
$269$	6.20308	+	10.7441i	0.378208	+	0.655076i	−0.612593	+	0.790398i	$0.709874\pi$
$270$	−4.28606	+	7.42367i	−0.260841	+	0.451790i
$271$	−9.26425	−	5.34872i	−0.562763	−	0.324911i	0.191491	−	0.981494i	$-0.438668\pi$
$271$	−9.26425	−	5.34872i	−0.562763	−	0.324911i	−0.754254	+	0.656583i	$0.772001\pi$
$272$	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	0.945991	−	0.324194i	$-0.105093\pi$
$277$	3.19944	+	5.54159i	0.192236	+	0.332962i	−0.753755	+	0.657155i	$0.771760\pi$
$278$			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	$0.164271\pi$
$281$			16.5440i			0.986934i	−0.869764	+	0.493467i	$0.835729\pi$
$282$	0.185884	+	0.321961i	0.0110692	+	0.0191725i
$283$	−0.244022	+	0.422659i	−0.0145056	+	0.0251245i	−0.873187	−	0.487385i	$-0.837951\pi$
$283$	−0.244022	+	0.422659i	−0.0145056	+	0.0251245i	0.858681	+	0.512510i	$0.171284\pi$
$284$	−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	$-0.591035\pi$
$293$	6.97836	−	4.02896i	0.407680	−	0.235374i	0.689793	+	0.724007i	$0.257702\pi$
$294$		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	$-0.248752\pi$
$311$	25.0375			1.41975			0.709873	+	0.704330i	$0.248752\pi$
$312$	−8.43658	+	25.8990i	−0.477628	+	1.46624i
$313$	28.3704			1.60359			0.801796	−	0.597598i	$-0.203878\pi$
$313$	28.3704			1.60359			0.801796	+	0.597598i	$0.203878\pi$
$314$	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	$0.328725\pi$
$317$			30.5773i			1.71739i	−0.512485	+	0.858696i	$0.671275\pi$
$318$	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	0.174350	−	0.984684i	$-0.444217\pi$
$331$	20.2727	−	11.7044i	1.11429	−	0.643334i	0.939936	+	0.341350i	$0.110884\pi$
$332$	−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	0.714392	−	0.699746i	$-0.246704\pi$
$347$	−4.63467	−	8.02749i	−0.248802	−	0.430938i	−0.963194	+	0.268808i	$0.913370\pi$
$348$	8.57078	−	14.8450i	0.459442	−	0.795777i
$349$	−13.4954	−	7.79157i	−0.722392	−	0.417073i	0.0932406	−	0.995644i	$-0.470277\pi$
$349$	−13.4954	−	7.79157i	−0.722392	−	0.417073i	−0.815632	+	0.578571i	$0.803611\pi$
$350$		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	$-0.163095\pi$
$353$	16.5863	+	9.57612i	0.882801	+	0.509686i	0.0112204	+	0.999937i	$0.496428\pi$
$354$	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	$0.199123\pi$
$359$			22.1893i			1.17111i	−0.810634	+	0.585553i	$0.800877\pi$
$360$	−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	$-0.709699\pi$
$367$	7.25517	−	12.5663i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$368$	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	0.606622	−	0.794990i	$-0.292524\pi$
$373$	−7.43888	−	12.8845i	−0.385170	−	0.667135i	−0.991793	+	0.127855i	$0.959191\pi$
$374$	−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	0.975439	+	0.220268i	$0.0706931\pi$
$379$	32.1983	+	18.5897i	1.65392	+	0.954889i	0.678477	+	0.734622i	$0.262640\pi$
$380$	−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	$-0.556752\pi$
$383$	11.4736	−	6.62431i	0.586276	−	0.338486i	0.763623	+	0.645662i	$0.223418\pi$
$384$	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	$-0.521204\pi$
$397$	15.2278	−	8.79175i	0.764259	−	0.441245i	0.830823	+	0.556537i	$0.187870\pi$
$398$			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	−0.261701	−	0.965149i	$-0.584283\pi$
$401$	−24.5986	−	14.2020i	−1.22839	−	0.709214i	−0.966694	+	0.255935i	$0.917617\pi$
$402$	−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	$-0.585247\pi$
$409$	8.86247	−	5.11675i	0.438221	−	0.253007i	0.702843	+	0.711345i	$0.251914\pi$
$410$	−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	$-0.931659\pi$
$419$	−6.22291	+	10.7784i	−0.304009	+	0.526559i	0.673031	+	0.739614i	$0.264992\pi$
$420$		0			0
$421$			2.04054i			0.0994498i	0.998763	+	0.0497249i	$0.0158345\pi$
$421$			2.04054i			0.0994498i	−0.998763	+	0.0497249i	$0.984166\pi$
$422$	−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	0.766059	−	0.642771i	$-0.222215\pi$
$431$	12.2992	+	7.10095i	0.592432	+	0.342041i	−0.173626	+	0.984812i	$0.555549\pi$
$432$	6.74581	−	11.6841i	0.324558	−	0.562151i
$433$	8.41174	+	14.5696i	0.404242	+	0.700168i	0.994233	−	0.107242i	$-0.0342019\pi$
$433$	8.41174	+	14.5696i	0.404242	+	0.700168i	−0.589991	+	0.807410i	$0.700869\pi$
$434$		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	−0.405002	−	0.914316i	$-0.632729\pi$
$439$	12.3476	−	21.3867i	0.589320	−	1.02073i	0.994322	−	0.106416i	$-0.0339375\pi$
$440$	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	−0.601789	−	0.798655i	$-0.705545\pi$
$449$	−4.47161	+	2.58168i	−0.211028	+	0.121837i	0.390761	+	0.920492i	$0.372212\pi$
$450$			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	0.588994	−	0.808137i	$-0.299524\pi$
$457$	3.92542	+	2.26634i	0.183623	+	0.106015i	−0.405371	+	0.914152i	$0.632858\pi$
$458$	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	0.551756	−	0.834006i	$-0.313958\pi$
$461$	33.2778	−	19.2130i	1.54990	−	0.894837i	0.998148	−	0.0608314i	$-0.0193752\pi$
$462$		0			0
$463$			2.53217i			0.117680i	0.998267	+	0.0588400i	$0.0187402\pi$
$463$			2.53217i			0.117680i	−0.998267	+	0.0588400i	$0.981260\pi$
$464$	−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	$-0.412470\pi$
$467$	11.7357			0.543065			0.271533	+	0.962429i	$0.412470\pi$
$468$	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	$-0.106568\pi$
$479$	24.7786	+	14.3060i	1.13216	+	0.653656i	0.187686	+	0.982229i	$0.439901\pi$
$480$	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	−0.552797	−	0.833316i	$-0.686439\pi$
$487$	−2.37282	+	1.36995i	−0.107523	+	0.0620782i	0.445274	+	0.895394i	$0.353106\pi$
$488$	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	0.00239500	+	0.999997i	$0.499238\pi$
$491$	−19.1633	+	33.1917i	−0.864825	+	1.49792i	−0.867220	+	0.497924i	$0.834096\pi$
$492$	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	$-0.785299\pi$
$499$		−	27.9009i		−	1.24902i	0.781018	−	0.624509i	$-0.214701\pi$
$500$	−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	$-0.183556\pi$
$503$	−1.18942	−	2.06014i	−0.0530336	−	0.0918569i	−0.891323	+	0.453368i	$0.850222\pi$
$504$		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	$-0.530157\pi$
$509$	−22.6522	−	13.0783i	−1.00404	−	0.579684i	−0.909442	+	0.415832i	$0.863490\pi$
$510$	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	$-0.676519\pi$
$521$	−24.0380			−1.05313			−0.526563	+	0.850136i	$0.676519\pi$
$522$	−0.842213	−	0.486252i	−0.0368627	−	0.0212827i
$523$	−5.86969	+	10.1666i	−0.256664	+	0.444554i	−0.965346	−	0.260973i	$-0.915957\pi$
$523$	−5.86969	+	10.1666i	−0.256664	+	0.444554i	0.708682	+	0.705528i	$0.249290\pi$
$524$	−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	$-0.770116\pi$
$541$		−	30.7507i		−	1.32208i	0.750352	−	0.661038i	$-0.229884\pi$
$542$	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	0.649551	−	0.760318i	$-0.274957\pi$
$557$	7.45486	+	4.30406i	0.315872	+	0.182369i	−0.333679	+	0.942687i	$0.608290\pi$
$558$	−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	$-0.200981\pi$
$563$	−2.55291	−	4.42177i	−0.107592	−	0.186355i	−0.914794	+	0.403920i	$0.867647\pi$
$564$		−	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	−0.891602	−	0.452820i	$-0.850418\pi$
$569$	−1.27969	+	2.21650i	−0.0536476	+	0.0929204i	0.837954	+	0.545740i	$0.183751\pi$
$570$	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	$-0.291517\pi$
$587$	5.49704	+	3.17372i	0.226887	+	0.130993i	−0.382248	+	0.924060i	$0.624850\pi$
$588$		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	$-0.731566\pi$
$601$	7.70501	−	13.3455i	0.314294	−	0.544373i	0.979287	+	0.202476i	$0.0648990\pi$
$602$		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	0.991521	+	0.129943i	$0.0414794\pi$
$607$	14.9868	+	25.9579i	0.608295	+	1.05360i	−0.383227	+	0.923654i	$0.625187\pi$
$608$	−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	0.211446	−	0.977390i	$-0.432183\pi$
$613$	−13.1043	−	7.56575i	−0.529276	−	0.305578i	−0.740722	+	0.671812i	$0.765516\pi$
$614$	−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	−0.968654	−	0.248413i	$-0.920091\pi$
$617$	−30.7475	+	17.7521i	−1.23785	+	0.714673i	−0.269195	+	0.963086i	$0.586758\pi$
$618$	−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	−0.124576	−	0.992210i	$-0.539757\pi$
$631$	16.8909	−	9.75195i	0.672415	−	0.388219i	0.796991	+	0.603991i	$0.206424\pi$
$632$			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	0.765572	−	0.643351i	$-0.222456\pi$
$641$	−4.41475	−	7.64657i	−0.174372	−	0.302022i	−0.939944	+	0.341329i	$0.889123\pi$
$642$		−	1.96134i		−	0.0774078i
$643$	−18.0992	+	10.4496i	−0.713763	+	0.412091i	−0.812453	−	0.583027i	$-0.801868\pi$
$643$	−18.0992	+	10.4496i	−0.713763	+	0.412091i	0.0986898	+	0.995118i	$0.468535\pi$
$644$		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	$-0.692658\pi$
$647$	10.8790	−	18.8430i	0.427697	−	0.740793i	0.996668	+	0.0815643i	$0.0259916\pi$
$648$	−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	−0.478463	−	0.878108i	$-0.658806\pi$
$653$	13.3195	−	23.0701i	0.521232	−	0.902801i	0.999695	−	0.0246930i	$-0.00786083\pi$
$654$	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	0.600839	−	0.799370i	$-0.294833\pi$
$659$	−10.0593	−	17.4232i	−0.391855	−	0.678713i	−0.992694	+	0.120657i	$0.961500\pi$
$660$	12.7594	−	22.1000i	0.496661	−	0.860241i
$661$	−7.21323	−	4.16456i	−0.280562	−	0.161983i	0.353116	−	0.935580i	$-0.385122\pi$
$661$	−7.21323	−	4.16456i	−0.280562	−	0.161983i	−0.633678	+	0.773597i	$0.718456\pi$
$662$	−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	0.355982	+	0.934493i	$0.384146\pi$
$673$	−16.3774	+	28.3665i	−0.631303	+	1.09345i	−0.987286	+	0.158957i	$0.949187\pi$
$674$	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	$-0.135569\pi$
$677$	47.3896			1.82133			0.910666	+	0.413144i	$0.135569\pi$
$678$	−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	−0.233616	−	0.972329i	$-0.575056\pi$
$683$	12.8486	−	7.41815i	0.491638	−	0.283848i	0.725254	+	0.688482i	$0.241722\pi$
$684$		−	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	$-0.534620\pi$
$691$	−26.9106	−	15.5369i	−1.02373	−	0.591050i	−0.915182	+	0.403041i	$0.867953\pi$
$692$	−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	−0.364081	−	0.931367i	$-0.618617\pi$
$709$	6.93547	−	4.00420i	0.260467	−	0.150381i	0.624548	+	0.780987i	$0.285283\pi$
$710$			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	−0.829317	−	0.558778i	$-0.811270\pi$
$719$	−24.0945	−	41.7330i	−0.898575	−	1.55638i	−0.0692573	−	0.997599i	$-0.522063\pi$
$720$			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	$-0.417902\pi$
$727$	13.7547			0.510135			0.255068	+	0.966923i	$0.417902\pi$
$728$		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	0.229868	−	0.973222i	$-0.426171\pi$
$739$	−13.5388	−	7.81663i	−0.498033	−	0.287539i	−0.727901	+	0.685683i	$0.759504\pi$
$740$	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	0.527079	−	0.849817i	$-0.323287\pi$
$743$	1.48979	+	0.860131i	0.0546551	+	0.0315551i	−0.472423	+	0.881372i	$0.656621\pi$
$744$	−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	−0.620806	−	0.783964i	$-0.713195\pi$
$751$	10.0993	−	17.4925i	0.368529	−	0.638312i	0.989336	+	0.145652i	$0.0465281\pi$
$752$	−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	−0.540575	−	0.841296i	$-0.681793\pi$
$757$	12.6094	−	21.8401i	0.458296	−	0.793792i	0.998871	+	0.0475040i	$0.0151267\pi$
$758$	−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	$-0.786508\pi$
$761$	−17.5671	+	10.1424i	−0.636807	+	0.367661i	0.146577	+	0.989199i	$0.453175\pi$
$762$		−	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	$-0.229486\pi$
$769$	15.3936	+	8.88748i	0.555106	+	0.320491i	−0.196073	+	0.980589i	$0.562819\pi$
$770$		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	$-0.783147\pi$
$773$	−17.2312	+	9.94846i	−0.619765	+	0.357821i	0.157013	+	0.987597i	$0.449814\pi$
$774$	−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	$-0.662601\pi$
$787$	0.620594	−	0.358300i	0.0221218	−	0.0127720i	0.511020	+	0.859569i	$0.329268\pi$
$788$			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	$-0.120117\pi$
$797$	4.11380	+	7.12530i	0.145718	+	0.252391i	−0.783923	+	0.620859i	$0.786784\pi$
$798$		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	−0.881365	−	0.472436i	$-0.843375\pi$
$809$	−0.897101	+	1.55382i	−0.0315404	+	0.0546295i	0.849824	+	0.527066i	$0.176708\pi$
$810$	−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	0.336133	−	0.941815i	$-0.390881\pi$
$821$	−8.92361	−	5.15205i	−0.311436	−	0.179808i	−0.647569	+	0.762007i	$0.724214\pi$
$822$	−8.65326	+	14.9879i	−0.301817	+	0.522762i
$823$	16.1496	+	27.9719i	0.562940	+	0.975040i	0.997238	+	0.0742711i	$0.0236630\pi$
$823$	16.1496	+	27.9719i	0.562940	+	0.975040i	−0.434298	+	0.900769i	$0.643004\pi$
$824$			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	$0.0513632\pi$
$827$			9.24057i			0.321326i	−0.987009	+	0.160663i	$0.948637\pi$
$828$	−2.00397	−	3.47098i	−0.0696427	−	0.120625i
$829$	19.5014	−	33.7774i	0.677311	−	1.17314i	−0.298477	−	0.954417i	$-0.596479\pi$
$829$	19.5014	−	33.7774i	0.677311	−	1.17314i	0.975788	−	0.218720i	$-0.0701880\pi$
$830$	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	$-0.681182\pi$
$839$	−2.28694	+	1.32036i	−0.0789538	+	0.0455840i	0.460003	+	0.887917i	$0.347848\pi$
$840$		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	$-0.222164\pi$
$857$	44.8581			1.53232			0.766162	+	0.642647i	$0.222164\pi$
$858$	17.1887	+	81.1659i	0.586813	+	2.77096i
$859$	14.6058			0.498344			0.249172	−	0.968459i	$-0.419842\pi$
$859$	14.6058			0.498344			0.249172	+	0.968459i	$0.419842\pi$
$860$	−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	$0.147911\pi$
$863$			26.3294i			0.896264i	−0.893967	+	0.448132i	$0.852089\pi$
$864$	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	−0.481098	−	0.876667i	$-0.659762\pi$
$877$	1.11257	−	0.642341i	0.0375687	−	0.0216903i	0.518667	+	0.854977i	$0.326429\pi$
$878$	−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	$-0.833803\pi$
$881$	−0.0438196	+	0.0758978i	−0.00147632	+	0.00255706i	0.865286	+	0.501278i	$0.167137\pi$
$882$		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	$-0.829262\pi$
$887$	0.380897	−	0.659733i	0.0127893	−	0.0221517i	0.872349	+	0.488883i	$0.162596\pi$
$888$	−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	−0.0682293	−	0.997670i	$-0.521735\pi$
$907$	24.9934	−	43.2899i	0.829893	−	1.43742i	0.898122	−	0.439747i	$-0.144932\pi$
$908$	−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	0.797521	−	0.603291i	$-0.206144\pi$
$919$	−3.75013	−	6.49542i	−0.123705	−	0.214264i	−0.921226	+	0.389028i	$0.872811\pi$
$920$	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	$-0.663277\pi$
$929$	0.562197	−	0.324584i	0.0184451	−	0.0106493i	0.509194	+	0.860652i	$0.329944\pi$
$930$	−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	$-0.194000\pi$
$937$	50.1982			1.63990			0.819951	+	0.572433i	$0.194000\pi$
$938$		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	0.626979	−	0.779036i	$-0.284291\pi$
$947$	8.17967	+	4.72254i	0.265804	+	0.153462i	−0.361175	+	0.932498i	$0.617624\pi$
$948$	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	0.628663	−	0.777678i	$-0.283603\pi$
$953$	−11.0874	−	19.2040i	−0.359158	−	0.622079i	−0.987820	+	0.155599i	$0.950269\pi$
$954$			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	$0.0590702\pi$
$967$			11.4753i			0.369022i	−0.982830	+	0.184511i	$0.940930\pi$
$968$	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	$-0.253596\pi$
$971$	−8.40453	−	14.5571i	−0.269714	−	0.467159i	−0.968788	+	0.247891i	$0.920263\pi$
$972$	−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	0.431050	−	0.902328i	$-0.358143\pi$
$977$	−4.21546	−	2.43380i	−0.134864	−	0.0778640i	−0.565914	+	0.824464i	$0.691477\pi$
$978$	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	0.429802	+	0.902923i	$0.358583\pi$
$991$	−17.8509	+	30.9187i	−0.567054	+	0.982166i	−0.996855	+	0.0792424i	$0.974750\pi$
$992$	−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	−0.992950	−	0.118538i	$-0.962179\pi$
$997$	−18.9178	−	32.7665i	−0.599131	−	1.03773i	0.393818	−	0.919188i	$-0.371154\pi$
$998$	−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.589.1	yes	32
7.2	even	3		637.2.k.j.459.15		32
7.3	odd	6		637.2.u.j.30.15		32
7.4	even	3		637.2.u.j.30.16		32
7.5	odd	6		637.2.k.j.459.16		32
7.6	odd	2	inner	637.2.q.j.589.2	yes	32
13.6	odd	12		8281.2.a.cx.1.30		32
13.7	odd	12		8281.2.a.cx.1.4		32
13.10	even	6	inner	637.2.q.j.491.1	✓	32
91.6	even	12		8281.2.a.cx.1.29		32
91.10	odd	6		637.2.k.j.569.2		32
91.20	even	12		8281.2.a.cx.1.3		32
91.23	even	6		637.2.u.j.361.16		32
91.62	odd	6	inner	637.2.q.j.491.2	yes	32
91.75	odd	6		637.2.u.j.361.15		32
91.88	even	6		637.2.k.j.569.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.j.459.15		32	7.2	even	3
637.2.k.j.459.16		32	7.5	odd	6
637.2.k.j.569.1		32	91.88	even	6
637.2.k.j.569.2		32	91.10	odd	6
637.2.q.j.491.1	✓	32	13.10	even	6	inner
637.2.q.j.491.2	yes	32	91.62	odd	6	inner
637.2.q.j.589.1	yes	32	1.1	even	1	trivial
637.2.q.j.589.2	yes	32	7.6	odd	2	inner
637.2.u.j.30.15		32	7.3	odd	6
637.2.u.j.30.16		32	7.4	even	3
637.2.u.j.361.15		32	91.75	odd	6
637.2.u.j.361.16		32	91.23	even	6
8281.2.a.cx.1.3		32	91.20	even	12
8281.2.a.cx.1.4		32	13.7	odd	12
8281.2.a.cx.1.29		32	91.6	even	12
8281.2.a.cx.1.30		32	13.6	odd	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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