LMFDB - Embedded newform 637.2.g.m.263.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 $ x^16 + 8x^14 + 45x^12 + 124x^10 + 248x^8 + 250x^6 + 177x^4 + 14*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.3
Root			$-1.04641 - 1.81243i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.m.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.289905 - 0.502131i) q^{2} -1.89204 q^{3} +(0.831910 + 1.44091i) q^{4} +(-0.736809 - 1.27619i) q^{5} +(-0.548512 + 0.950050i) q^{6} +2.12432 q^{8} +0.579810 q^{9} +O(q^{10})$	\(q+(0.289905 - 0.502131i) q^{2} -1.89204 q^{3} +(0.831910 + 1.44091i) q^{4} +(-0.736809 - 1.27619i) q^{5} +(-0.548512 + 0.950050i) q^{6} +2.12432 q^{8} +0.579810 q^{9} -0.854419 q^{10} +0.579810 q^{11} +(-1.57401 - 2.72626i) q^{12} +(-0.128893 + 3.60325i) q^{13} +(1.39407 + 2.41460i) q^{15} +(-1.04797 + 1.81513i) q^{16} +(0.598285 + 1.03626i) q^{17} +(0.168090 - 0.291141i) q^{18} -0.460958 q^{19} +(1.22592 - 2.12335i) q^{20} +(0.168090 - 0.291141i) q^{22} +(-1.18398 + 2.05071i) q^{23} -4.01930 q^{24} +(1.41423 - 2.44951i) q^{25} +(1.77193 + 1.10932i) q^{26} +4.57909 q^{27} +(3.44550 + 5.96777i) q^{29} +1.61659 q^{30} +(-2.22171 + 3.84811i) q^{31} +(2.73194 + 4.73187i) q^{32} -1.09702 q^{33} +0.693783 q^{34} +(0.482350 + 0.835455i) q^{36} +(-4.58150 + 7.93540i) q^{37} +(-0.133634 + 0.231461i) q^{38} +(0.243871 - 6.81748i) q^{39} +(-1.56522 - 2.71104i) q^{40} +(2.00845 + 3.47874i) q^{41} +(-4.02951 + 6.97931i) q^{43} +(0.482350 + 0.835455i) q^{44} +(-0.427209 - 0.739948i) q^{45} +(0.686481 + 1.18902i) q^{46} +(5.75964 + 9.97598i) q^{47} +(1.98280 - 3.43430i) q^{48} +(-0.819983 - 1.42025i) q^{50} +(-1.13198 - 1.96064i) q^{51} +(-5.29918 + 2.81185i) q^{52} +(4.69760 - 8.13647i) q^{53} +(1.32750 - 2.29930i) q^{54} +(-0.427209 - 0.739948i) q^{55} +0.872150 q^{57} +3.99547 q^{58} +(-0.120459 - 0.208642i) q^{59} +(-2.31948 + 4.01746i) q^{60} +7.72710 q^{61} +(1.28817 + 2.23118i) q^{62} -1.02385 q^{64} +(4.69340 - 2.49041i) q^{65} +(-0.318033 + 0.550849i) q^{66} -1.44857 q^{67} +(-0.995438 + 1.72415i) q^{68} +(2.24013 - 3.88001i) q^{69} +(6.25725 - 10.8379i) q^{71} +1.23170 q^{72} +(1.84701 - 3.19911i) q^{73} +(2.65640 + 4.60103i) q^{74} +(-2.67577 + 4.63457i) q^{75} +(-0.383476 - 0.664199i) q^{76} +(-3.35257 - 2.09888i) q^{78} +(-8.03967 - 13.9251i) q^{79} +3.08861 q^{80} -10.4033 q^{81} +2.32904 q^{82} -15.4005 q^{83} +(0.881643 - 1.52705i) q^{85} +(2.33635 + 4.04668i) q^{86} +(-6.51901 - 11.2913i) q^{87} +1.23170 q^{88} +(-1.24553 + 2.15733i) q^{89} -0.495401 q^{90} -3.93984 q^{92} +(4.20356 - 7.28078i) q^{93} +6.67900 q^{94} +(0.339638 + 0.588270i) q^{95} +(-5.16894 - 8.95287i) q^{96} +(-7.82275 + 13.5494i) q^{97} +0.336180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 28 q^{18} + 28 q^{22} + 12 q^{23} + 12 q^{25} + 8 q^{29} - 56 q^{30} + 4 q^{36} - 8 q^{37} - 16 q^{39} + 32 q^{43} + 4 q^{44} - 4 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} + 96 q^{58} - 64 q^{60} - 64 q^{64} + 52 q^{65} - 40 q^{67} + 8 q^{71} - 56 q^{72} + 76 q^{74} + 28 q^{78} + 4 q^{79} - 112 q^{81} + 36 q^{85} - 4 q^{86} - 56 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 28 * q^18 + 28 * q^22 + 12 * q^23 + 12 * q^25 + 8 * q^29 - 56 * q^30 + 4 * q^36 - 8 * q^37 - 16 * q^39 + 32 * q^43 + 4 * q^44 - 4 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 + 96 * q^58 - 64 * q^60 - 64 * q^64 + 52 * q^65 - 40 * q^67 + 8 * q^71 - 56 * q^72 + 76 * q^74 + 28 * q^78 + 4 * q^79 - 112 * q^81 + 36 * q^85 - 4 * q^86 - 56 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.289905	−	0.502131i	0.204994	−	0.355060i	−0.745137	−	0.666912i	$-0.767616\pi$
$2$	0.289905	−	0.502131i	0.204994	−	0.355060i	0.950131	+	0.311852i	$0.100949\pi$
$3$	−1.89204			−1.09237			−0.546185	−	0.837665i	$-0.683920\pi$
$3$	−1.89204			−1.09237			−0.546185	+	0.837665i	$0.683920\pi$
$4$	0.831910	+	1.44091i	0.415955	+	0.720455i
$5$	−0.736809	−	1.27619i	−0.329511	−	0.570729i	0.652904	−	0.757441i	$-0.273550\pi$
$5$	−0.736809	−	1.27619i	−0.329511	−	0.570729i	−0.982415	+	0.186711i	$0.940217\pi$
$6$	−0.548512	+	0.950050i	−0.223929	+	0.387856i
$7$		0			0
$7$		0			0
$8$	2.12432			0.751061
$9$	0.579810			0.193270
$10$	−0.854419			−0.270191
$11$	0.579810			0.174819			0.0874097	−	0.996172i	$-0.472141\pi$
$11$	0.579810			0.174819			0.0874097	+	0.996172i	$0.472141\pi$
$12$	−1.57401	−	2.72626i	−0.454376	−	0.787003i
$13$	−0.128893	+	3.60325i	−0.0357485	+	0.999361i
$13$	−0.128893	+	3.60325i	−0.0357485	+	0.999361i
$14$		0			0
$15$	1.39407	+	2.41460i	0.359947	+	0.623447i
$16$	−1.04797	+	1.81513i	−0.261992	+	0.453784i
$17$	0.598285	+	1.03626i	0.145105	+	0.251330i	0.929412	−	0.369043i	$-0.120315\pi$
$17$	0.598285	+	1.03626i	0.145105	+	0.251330i	−0.784307	+	0.620373i	$0.786981\pi$
$18$	0.168090	−	0.291141i	0.0396192	−	0.0686225i
$19$	−0.460958			−0.105751			−0.0528755	−	0.998601i	$-0.516839\pi$
$19$	−0.460958			−0.105751			−0.0528755	+	0.998601i	$0.516839\pi$
$20$	1.22592	−	2.12335i	0.274123	−	0.474796i
$21$		0			0
$22$	0.168090	−	0.291141i	0.0358369	−	0.0620714i
$23$	−1.18398	+	2.05071i	−0.246876	+	0.427602i	−0.962657	−	0.270723i	$-0.912737\pi$
$23$	−1.18398	+	2.05071i	−0.246876	+	0.427602i	0.715781	+	0.698324i	$0.246071\pi$
$24$	−4.01930			−0.820436
$25$	1.41423	−	2.44951i	0.282845	−	0.489902i
$26$	1.77193	+	1.10932i	0.347505	+	0.217556i
$27$	4.57909			0.881247
$28$		0			0
$29$	3.44550	+	5.96777i	0.639813	+	1.10819i	0.985474	+	0.169828i	$0.0543214\pi$
$29$	3.44550	+	5.96777i	0.639813	+	1.10819i	−0.345661	+	0.938359i	$0.612345\pi$
$30$	1.61659			0.295148
$31$	−2.22171	+	3.84811i	−0.399031	+	0.691141i	−0.993607	−	0.112898i	$-0.963987\pi$
$31$	−2.22171	+	3.84811i	−0.399031	+	0.691141i	0.594576	+	0.804040i	$0.297320\pi$
$32$	2.73194	+	4.73187i	0.482944	+	0.836484i
$33$	−1.09702			−0.190967
$34$	0.693783			0.118983
$35$		0			0
$36$	0.482350	+	0.835455i	0.0803917	+	0.139242i
$37$	−4.58150	+	7.93540i	−0.753195	+	1.30457i	0.193072	+	0.981185i	$0.438155\pi$
$37$	−4.58150	+	7.93540i	−0.753195	+	1.30457i	−0.946267	+	0.323387i	$0.895179\pi$
$38$	−0.133634	+	0.231461i	−0.0216783	+	0.0375479i
$39$	0.243871	−	6.81748i	0.0390506	−	1.09167i
$40$	−1.56522	−	2.71104i	−0.247483	−	0.428653i
$41$	2.00845	+	3.47874i	0.313667	+	0.543288i	0.979153	−	0.203123i	$-0.0651090\pi$
$41$	2.00845	+	3.47874i	0.313667	+	0.543288i	−0.665486	+	0.746410i	$0.731776\pi$
$42$		0			0
$43$	−4.02951	+	6.97931i	−0.614494	+	1.06433i	0.375979	+	0.926628i	$0.377306\pi$
$43$	−4.02951	+	6.97931i	−0.614494	+	1.06433i	−0.990473	+	0.137706i	$0.956027\pi$
$44$	0.482350	+	0.835455i	0.0727170	+	0.125950i
$45$	−0.427209	−	0.739948i	−0.0636846	−	0.110305i
$46$	0.686481	+	1.18902i	0.101216	+	0.175312i
$47$	5.75964	+	9.97598i	0.840129	+	1.45515i	0.889785	+	0.456381i	$0.150854\pi$
$47$	5.75964	+	9.97598i	0.840129	+	1.45515i	−0.0496552	+	0.998766i	$0.515812\pi$
$48$	1.98280	−	3.43430i	0.286192	−	0.495699i
$49$		0			0
$50$	−0.819983	−	1.42025i	−0.115963	−	0.200854i
$51$	−1.13198	−	1.96064i	−0.158509	−	0.274545i
$52$	−5.29918	+	2.81185i	−0.734864	+	0.389934i
$53$	4.69760	−	8.13647i	0.645264	−	1.11763i	−0.338976	−	0.940795i	$-0.610081\pi$
$53$	4.69760	−	8.13647i	0.645264	−	1.11763i	0.984240	−	0.176836i	$-0.0565861\pi$
$54$	1.32750	−	2.29930i	0.180650	−	0.312895i
$55$	−0.427209	−	0.739948i	−0.0576049	−	0.0997746i
$56$		0			0
$57$	0.872150			0.115519
$58$	3.99547			0.524631
$59$	−0.120459	−	0.208642i	−0.0156825	−	0.0271629i	0.858078	−	0.513520i	$-0.171659\pi$
$59$	−0.120459	−	0.208642i	−0.0156825	−	0.0271629i	−0.873760	+	0.486357i	$0.838325\pi$
$60$	−2.31948	+	4.01746i	−0.299444	+	0.518652i
$61$	7.72710			0.989354			0.494677	−	0.869077i	$-0.335286\pi$
$61$	7.72710			0.989354			0.494677	+	0.869077i	$0.335286\pi$
$62$	1.28817	+	2.23118i	0.163598	+	0.283360i
$63$		0			0
$64$	−1.02385			−0.127982
$65$	4.69340	−	2.49041i	0.582144	−	0.308897i
$66$	−0.318033	+	0.550849i	−0.0391471	+	0.0678048i
$67$	−1.44857			−0.176971			−0.0884857	−	0.996077i	$-0.528203\pi$
$67$	−1.44857			−0.176971			−0.0884857	+	0.996077i	$0.528203\pi$
$68$	−0.995438	+	1.72415i	−0.120715	+	0.209084i
$69$	2.24013	−	3.88001i	0.269680	−	0.467099i
$70$		0			0
$71$	6.25725	−	10.8379i	0.742599	−	1.28622i	−0.208709	−	0.977978i	$-0.566926\pi$
$71$	6.25725	−	10.8379i	0.742599	−	1.28622i	0.951308	−	0.308241i	$-0.0997405\pi$
$72$	1.23170			0.145158
$73$	1.84701	−	3.19911i	0.216176	−	0.374427i	−0.737460	−	0.675391i	$-0.763975\pi$
$73$	1.84701	−	3.19911i	0.216176	−	0.374427i	0.953636	+	0.300963i	$0.0973082\pi$
$74$	2.65640	+	4.60103i	0.308801	+	0.534858i
$75$	−2.67577	+	4.63457i	−0.308971	+	0.535154i
$76$	−0.383476	−	0.664199i	−0.0439877	−	0.0761889i
$77$		0			0
$78$	−3.35257	−	2.09888i	−0.379603	−	0.237651i
$79$	−8.03967	−	13.9251i	−0.904533	−	1.56670i	−0.821542	−	0.570147i	$-0.806886\pi$
$79$	−8.03967	−	13.9251i	−0.904533	−	1.56670i	−0.0829909	−	0.996550i	$-0.526447\pi$
$80$	3.08861			0.345317
$81$	−10.4033			−1.15592
$82$	2.32904			0.257200
$83$	−15.4005			−1.69042			−0.845212	−	0.534431i	$-0.820526\pi$
$83$	−15.4005			−1.69042			−0.845212	+	0.534431i	$0.820526\pi$
$84$		0			0
$85$	0.881643	−	1.52705i	0.0956276	−	0.165632i
$86$	2.33635	+	4.04668i	0.251935	+	0.436364i
$87$	−6.51901	−	11.2913i	−0.698911	−	1.21055i
$88$	1.23170			0.131300
$89$	−1.24553	+	2.15733i	−0.132026	+	0.228676i	−0.924458	−	0.381285i	$-0.875482\pi$
$89$	−1.24553	+	2.15733i	−0.132026	+	0.228676i	0.792431	+	0.609961i	$0.208815\pi$
$90$	−0.495401			−0.0522198
$91$		0			0
$92$	−3.93984			−0.410757
$93$	4.20356	−	7.28078i	0.435889	−	0.754982i
$94$	6.67900			0.688886
$95$	0.339638	+	0.588270i	0.0348461	+	0.0603552i
$96$	−5.16894	−	8.95287i	−0.527553	−	0.913749i
$97$	−7.82275	+	13.5494i	−0.794280	+	1.37573i	0.129015	+	0.991643i	$0.458818\pi$
$97$	−7.82275	+	13.5494i	−0.794280	+	1.37573i	−0.923295	+	0.384091i	$0.874515\pi$
$98$		0			0
$99$	0.336180			0.0337874
$100$	4.70604			0.470604
$101$	14.0136			1.39441			0.697205	−	0.716872i	$-0.254427\pi$
$101$	14.0136			1.39441			0.697205	+	0.716872i	$0.254427\pi$
$102$	−1.31266			−0.129973
$103$	−5.37461	−	9.30910i	−0.529576	−	0.917253i	−0.999405	−	0.0344951i	$-0.989018\pi$
$103$	−5.37461	−	9.30910i	−0.529576	−	0.917253i	0.469829	−	0.882758i	$-0.344316\pi$
$104$	−0.273810	+	7.65445i	−0.0268493	+	0.750581i
$105$		0			0
$106$	−2.72371	−	4.71761i	−0.264551	−	0.458215i
$107$	−1.87761	+	3.25212i	−0.181516	+	0.314394i	−0.942397	−	0.334497i	$-0.891434\pi$
$107$	−1.87761	+	3.25212i	−0.181516	+	0.314394i	0.760881	+	0.648891i	$0.224767\pi$
$108$	3.80939	+	6.59806i	0.366559	+	0.634899i
$109$	4.10417	−	7.10862i	0.393108	−	0.680883i	−0.599750	−	0.800187i	$-0.704733\pi$
$109$	4.10417	−	7.10862i	0.393108	−	0.680883i	0.992858	+	0.119305i	$0.0380666\pi$
$110$	−0.495401			−0.0472346
$111$	8.66838	−	15.0141i	0.822766	−	1.42507i
$112$		0			0
$113$	3.90423	−	6.76233i	0.367279	−	0.636146i	−0.621860	−	0.783129i	$-0.713623\pi$
$113$	3.90423	−	6.76233i	0.367279	−	0.636146i	0.989139	+	0.146982i	$0.0469560\pi$
$114$	0.252841	−	0.437933i	0.0236807	−	0.0410162i
$115$	3.48945			0.325393
$116$	−5.73269	+	9.92930i	−0.532266	+	0.921913i
$117$	−0.0747335	+	2.08920i	−0.00690912	+	0.193147i
$118$	−0.139687			−0.0128593
$119$		0			0
$120$	2.96145	+	5.12939i	0.270342	+	0.468247i
$121$	−10.6638			−0.969438
$122$	2.24013	−	3.88001i	0.202812	−	0.351280i
$123$	−3.80007	−	6.58191i	−0.342641	−	0.593471i
$124$	−7.39305			−0.663915
$125$	−11.5361			−1.03182
$126$		0			0
$127$	0.469682	+	0.813513i	0.0416775	+	0.0721876i	0.886112	−	0.463472i	$-0.153396\pi$
$127$	0.469682	+	0.813513i	0.0416775	+	0.0721876i	−0.844434	+	0.535659i	$0.820063\pi$
$128$	−5.76071	+	9.97784i	−0.509179	+	0.881925i
$129$	7.62398	−	13.2051i	0.671254	−	1.16265i
$130$	0.110129	−	3.07868i	0.00965892	−	0.270018i
$131$	0.568583	+	0.984814i	0.0496773	+	0.0860436i	0.889795	−	0.456361i	$-0.150847\pi$
$131$	0.568583	+	0.984814i	0.0496773	+	0.0860436i	−0.840117	+	0.542404i	$0.817514\pi$
$132$	−0.912625	−	1.58071i	−0.0794338	−	0.137583i
$133$		0			0
$134$	−0.419949	+	0.727373i	−0.0362781	+	0.0628355i
$135$	−3.37391	−	5.84379i	−0.290380	−	0.502954i
$136$	1.27095	+	2.20135i	0.108983	+	0.188764i
$137$	4.31998	+	7.48243i	0.369081	+	0.639267i	0.989422	−	0.145065i	$-0.0463391\pi$
$137$	4.31998	+	7.48243i	0.369081	+	0.639267i	−0.620341	+	0.784332i	$0.713006\pi$
$138$	−1.29885	−	2.24967i	−0.110565	−	0.191505i
$139$	7.27709	−	12.6043i	0.617235	−	1.06908i	−0.372753	−	0.927930i	$-0.621586\pi$
$139$	7.27709	−	12.6043i	0.617235	−	1.06908i	0.989988	−	0.141151i	$-0.0450804\pi$
$140$		0			0
$141$	−10.8975	−	18.8749i	−0.917731	−	1.58956i
$142$	−3.62802	−	6.28391i	−0.304457	−	0.527334i
$143$	−0.0747335	+	2.08920i	−0.00624953	+	0.174708i
$144$	−0.607623	+	1.05243i	−0.0506352	+	0.0877028i
$145$	5.07734	−	8.79422i	0.421650	−	0.730320i
$146$	−1.07091	−	1.85488i	−0.0886295	−	0.153511i
$147$		0			0
$148$	−15.2456			−1.25318
$149$	13.3802			1.09615			0.548075	−	0.836429i	$-0.315361\pi$
$149$	13.3802			1.09615			0.548075	+	0.836429i	$0.315361\pi$
$150$	1.55144	+	2.68717i	0.126675	+	0.219407i
$151$	−8.06958	+	13.9769i	−0.656693	+	1.13743i	0.324774	+	0.945792i	$0.394712\pi$
$151$	−8.06958	+	13.9769i	−0.656693	+	1.13743i	−0.981467	+	0.191634i	$0.938621\pi$
$152$	−0.979223			−0.0794254
$153$	0.346892	+	0.600834i	0.0280445	+	0.0485745i
$154$		0			0
$155$	6.54790			0.525940
$156$	10.0263	−	5.32014i	0.802743	−	0.425952i
$157$	0.314340	−	0.544453i	0.0250871	−	0.0434521i	−0.853209	−	0.521569i	$-0.825347\pi$
$157$	0.314340	−	0.544453i	0.0250871	−	0.0434521i	0.878296	+	0.478117i	$0.158680\pi$
$158$	−9.32297			−0.741695
$159$	−8.88803	+	15.3945i	−0.704867	+	1.22087i
$160$	4.02584	−	6.97296i	0.318271	−	0.551261i
$161$		0			0
$162$	−3.01596	+	5.22379i	−0.236956	+	0.410420i
$163$	−11.6841			−0.915173			−0.457586	−	0.889165i	$-0.651286\pi$
$163$	−11.6841			−0.915173			−0.457586	+	0.889165i	$0.651286\pi$
$164$	−3.34170	+	5.78800i	−0.260943	+	0.451967i
$165$	0.808297	+	1.40001i	0.0629258	+	0.108991i
$166$	−4.46469	+	7.73306i	−0.346527	+	0.600202i
$167$	−11.0293	−	19.1033i	−0.853474	−	1.47826i	−0.878054	−	0.478562i	$-0.841158\pi$
$167$	−11.0293	−	19.1033i	−0.853474	−	1.47826i	0.0245803	−	0.999698i	$-0.492175\pi$
$168$		0			0
$169$	−12.9668	−	0.928867i	−0.997444	−	0.0714513i
$170$	−0.511186	−	0.885399i	−0.0392061	−	0.0679070i
$171$	−0.267268			−0.0204385
$172$	−13.4087			−1.02241
$173$	11.3907			0.866018			0.433009	−	0.901390i	$-0.357452\pi$
$173$	11.3907			0.866018			0.433009	+	0.901390i	$0.357452\pi$
$174$	−7.55958			−0.573090
$175$		0			0
$176$	−0.607623	+	1.05243i	−0.0458013	+	0.0793302i
$177$	0.227914	+	0.394759i	0.0171311	+	0.0296719i
$178$	0.722173	+	1.25084i	0.0541292	+	0.0937544i
$179$	−3.47243			−0.259541			−0.129771	−	0.991544i	$-0.541424\pi$
$179$	−3.47243			−0.259541			−0.129771	+	0.991544i	$0.541424\pi$
$180$	0.710799	−	1.23114i	0.0529799	−	0.0917638i
$181$	21.0992			1.56829			0.784145	−	0.620578i	$-0.213102\pi$
$181$	21.0992			1.56829			0.784145	+	0.620578i	$0.213102\pi$
$182$		0			0
$183$	−14.6200			−1.08074
$184$	−2.51514	+	4.35636i	−0.185419	+	0.321155i
$185$	13.5028			0.992743
$186$	−2.43727	−	4.22147i	−0.178709	−	0.309533i
$187$	0.346892	+	0.600834i	0.0253672	+	0.0439373i
$188$	−9.58300	+	16.5982i	−0.698912	+	1.21055i
$189$		0			0
$190$	0.393851			0.0285730
$191$	11.9189			0.862421			0.431211	−	0.902251i	$-0.358087\pi$
$191$	11.9189			0.862421			0.431211	+	0.902251i	$0.358087\pi$
$192$	1.93717			0.139803
$193$	14.3794			1.03505			0.517526	−	0.855668i	$-0.326853\pi$
$193$	14.3794			1.03505			0.517526	+	0.855668i	$0.326853\pi$
$194$	4.53571	+	7.85608i	0.325645	+	0.564034i
$195$	−8.88009	+	4.71195i	−0.635916	+	0.337430i
$196$		0			0
$197$	−3.48462	−	6.03553i	−0.248269	−	0.430014i	0.714777	−	0.699353i	$-0.246528\pi$
$197$	−3.48462	−	6.03553i	−0.248269	−	0.430014i	−0.963046	+	0.269339i	$0.913195\pi$
$198$	0.0974604	−	0.168806i	0.00692621	−	0.0119965i
$199$	−1.78676	−	3.09476i	−0.126660	−	0.219382i	0.795721	−	0.605664i	$-0.207092\pi$
$199$	−1.78676	−	3.09476i	−0.126660	−	0.219382i	−0.922381	+	0.386282i	$0.873759\pi$
$200$	3.00427	−	5.20355i	0.212434	−	0.367946i
$201$	2.74076			0.193318
$202$	4.06263	−	7.03668i	0.285846	−	0.495099i
$203$		0			0
$204$	1.88341	−	3.26216i	0.131865	−	0.228397i
$205$	2.95969	−	5.12633i	0.206714	−	0.358038i
$206$	−6.23251			−0.434240
$207$	−0.686481	+	1.18902i	−0.0477138	+	0.0826426i
$208$	−6.40530	−	4.01005i	−0.444128	−	0.278047i
$209$	−0.267268			−0.0184873
$210$		0			0
$211$	7.05694	+	12.2230i	0.485820	+	0.841464i	0.999867	−	0.0162974i	$-0.00518784\pi$
$211$	7.05694	+	12.2230i	0.485820	+	0.841464i	−0.514048	+	0.857762i	$0.671855\pi$
$212$	15.6319			1.07360
$213$	−11.8390	+	20.5057i	−0.811192	+	1.40503i
$214$	1.08866	+	1.88561i	0.0744192	+	0.128898i
$215$	11.8759			0.809930
$216$	9.72746			0.661870
$217$		0			0
$218$	−2.37964	−	4.12165i	−0.161169	−	0.279154i
$219$	−3.49461	+	6.05284i	−0.236144	+	0.409013i
$220$	0.710799	−	1.23114i	0.0479221	−	0.0830035i
$221$	−3.81101	+	2.02220i	−0.256356	+	0.136028i
$222$	−5.02602	−	8.70532i	−0.337324	−	0.584263i
$223$	0.454565	+	0.787329i	0.0304399	+	0.0527235i	0.880844	−	0.473407i	$-0.156976\pi$
$223$	0.454565	+	0.787329i	0.0304399	+	0.0527235i	−0.850404	+	0.526130i	$0.823643\pi$
$224$		0			0
$225$	0.819983	−	1.42025i	0.0546655	−	0.0946835i
$226$	−2.26371	−	3.92087i	−0.150580	−	0.260812i
$227$	1.16756	+	2.02228i	0.0774938	+	0.134223i	0.902168	−	0.431385i	$-0.141975\pi$
$227$	1.16756	+	2.02228i	0.0774938	+	0.134223i	−0.824674	+	0.565608i	$0.808642\pi$
$228$	0.725550	+	1.25669i	0.0480508	+	0.0832263i
$229$	8.34036	+	14.4459i	0.551147	+	0.954614i	0.998192	+	0.0601030i	$0.0191429\pi$
$229$	8.34036	+	14.4459i	0.551147	+	0.954614i	−0.447045	+	0.894511i	$0.647524\pi$
$230$	1.01161	−	1.75216i	0.0667036	−	0.115534i
$231$		0			0
$232$	7.31934	+	12.6775i	0.480538	+	0.832317i
$233$	8.26321	+	14.3123i	0.541341	+	0.937630i	0.998827	+	0.0484137i	$0.0154166\pi$
$233$	8.26321	+	14.3123i	0.541341	+	0.937630i	−0.457486	+	0.889217i	$0.651250\pi$
$234$	1.02739	+	0.643196i	0.0671623	+	0.0420470i
$235$	8.48750	−	14.7008i	0.553664	−	0.958973i
$236$	0.200423	−	0.347143i	0.0130464	−	0.0225971i
$237$	15.2114	+	26.3469i	0.988084	+	1.71141i
$238$		0			0
$239$	3.18043			0.205725			0.102862	−	0.994696i	$-0.467200\pi$
$239$	3.18043			0.205725			0.102862	+	0.994696i	$0.467200\pi$
$240$	−5.84377			−0.377213
$241$	−7.92992	−	13.7350i	−0.510811	−	0.884751i	−0.999922	−	0.0125290i	$-0.996012\pi$
$241$	−7.92992	−	13.7350i	−0.510811	−	0.884751i	0.489110	−	0.872222i	$-0.337322\pi$
$242$	−3.09150	+	5.35463i	−0.198729	+	0.344209i
$243$	5.94608			0.381441
$244$	6.42825	+	11.1341i	0.411527	+	0.712785i
$245$		0			0
$246$	−4.40664			−0.280957
$247$	0.0594143	−	1.66095i	0.00378044	−	0.105683i
$248$	−4.71962	+	8.17463i	−0.299696	+	0.519089i
$249$	29.1383			1.84657
$250$	−3.34439	+	5.79265i	−0.211518	+	0.366359i
$251$	1.24788	−	2.16139i	0.0787654	−	0.136426i	−0.823952	−	0.566659i	$-0.808236\pi$
$251$	1.24788	−	2.16139i	0.0787654	−	0.136426i	0.902718	+	0.430234i	$0.141569\pi$
$252$		0			0
$253$	−0.686481	+	1.18902i	−0.0431587	+	0.0747531i
$254$	0.544653			0.0341746
$255$	−1.66810	+	2.88924i	−0.104461	+	0.180931i
$256$	2.31626	+	4.01189i	0.144767	+	0.250743i
$257$	5.26020	−	9.11094i	0.328123	−	0.568325i	−0.654017	−	0.756480i	$-0.726917\pi$
$257$	5.26020	−	9.11094i	0.328123	−	0.568325i	0.982139	+	0.188155i	$0.0602508\pi$
$258$	−4.42046	−	7.65647i	−0.275206	−	0.476671i
$259$		0			0
$260$	7.49294	+	4.69097i	0.464693	+	0.290921i
$261$	1.99773	+	3.46018i	0.123657	+	0.214180i
$262$	0.659340			0.0407342
$263$	−31.3499			−1.93312			−0.966558	−	0.256449i	$-0.917448\pi$
$263$	−31.3499			−1.93312			−0.966558	+	0.256449i	$0.917448\pi$
$264$	−2.33043			−0.143428
$265$	−13.8449			−0.850486
$266$		0			0
$267$	2.35660	−	4.08174i	0.144221	−	0.249799i
$268$	−1.20508	−	2.08727i	−0.0736122	−	0.127500i
$269$	−10.5633	−	18.2961i	−0.644054	−	1.11553i	−0.984519	−	0.175277i	$-0.943918\pi$
$269$	−10.5633	−	18.2961i	−0.644054	−	1.11553i	0.340465	−	0.940257i	$-0.389415\pi$
$270$	−3.91246			−0.238105
$271$	3.26004	−	5.64655i	0.198033	−	0.343004i	−0.749857	−	0.661599i	$-0.769878\pi$
$271$	3.26004	−	5.64655i	0.198033	−	0.343004i	0.947891	+	0.318596i	$0.103211\pi$
$272$	−2.50793			−0.152066
$273$		0			0
$274$	5.00954			0.302638
$275$	0.819983	−	1.42025i	0.0494468	−	0.0856444i
$276$	7.45434			0.448698
$277$	7.26548	+	12.5842i	0.436540	+	0.756110i	0.997420	−	0.0717873i	$-0.0228703\pi$
$277$	7.26548	+	12.5842i	0.436540	+	0.756110i	−0.560880	+	0.827897i	$0.689537\pi$
$278$	−4.21933	−	7.30810i	−0.253059	−	0.438311i
$279$	−1.28817	+	2.23118i	−0.0771207	+	0.133577i
$280$		0			0
$281$	27.1832			1.62161			0.810807	−	0.585314i	$-0.199029\pi$
$281$	27.1832			1.62161			0.810807	+	0.585314i	$0.199029\pi$
$282$	−12.6369			−0.752518
$283$	−8.57582			−0.509780			−0.254890	−	0.966970i	$-0.582039\pi$
$283$	−8.57582			−0.509780			−0.254890	+	0.966970i	$0.582039\pi$
$284$	20.8219			1.23555
$285$	−0.642608	−	1.11303i	−0.0380648	−	0.0659302i
$286$	1.02739	+	0.643196i	0.0607506	+	0.0380330i
$287$		0			0
$288$	1.58401	+	2.74358i	0.0933387	+	0.161667i
$289$	7.78411	−	13.4825i	0.457889	−	0.793087i
$290$	−2.94390	−	5.09898i	−0.172872	−	0.299422i
$291$	14.8009	−	25.6360i	0.867647	−	1.50281i
$292$	6.14617			0.359678
$293$	−5.24356	+	9.08212i	−0.306332	+	0.530583i	−0.977557	−	0.210671i	$-0.932435\pi$
$293$	−5.24356	+	9.08212i	−0.306332	+	0.530583i	0.671225	+	0.741254i	$0.265768\pi$
$294$		0			0
$295$	−0.177511	+	0.307458i	−0.0103351	+	0.0179009i
$296$	−9.73258	+	16.8573i	−0.565695	+	0.979812i
$297$	2.65501			0.154059
$298$	3.87899	−	6.71862i	0.224704	−	0.389199i
$299$	−7.23659	−	4.53048i	−0.418503	−	0.262004i
$300$	−8.90400			−0.514073
$301$		0			0
$302$	4.67882	+	8.10396i	0.269236	+	0.466331i
$303$	−26.5144			−1.52321
$304$	0.483069	−	0.836701i	0.0277059	−	0.0479881i
$305$	−5.69340	−	9.86125i	−0.326003	−	0.564654i
$306$	0.402263			0.0229958
$307$	19.1751			1.09438			0.547190	−	0.837008i	$-0.315697\pi$
$307$	19.1751			1.09438			0.547190	+	0.837008i	$0.315697\pi$
$308$		0			0
$309$	10.1690	+	17.6132i	0.578493	+	1.00198i
$310$	1.89827	−	3.28790i	0.107814	−	0.186740i
$311$	−1.74427	+	3.02117i	−0.0989086	+	0.171315i	−0.911233	−	0.411891i	$-0.864868\pi$
$311$	−1.74427	+	3.02117i	−0.0989086	+	0.171315i	0.812325	+	0.583206i	$0.198202\pi$
$312$	0.518060	−	14.4825i	0.0293294	−	0.819911i
$313$	−10.1607	−	17.5989i	−0.574318	−	0.994748i	−0.996115	−	0.0880579i	$-0.971934\pi$
$313$	−10.1607	−	17.5989i	−0.574318	−	0.994748i	0.421797	−	0.906690i	$-0.361399\pi$
$314$	−0.182258	−	0.315680i	−0.0102854	−	0.0178148i
$315$		0			0
$316$	13.3766	−	23.1689i	0.752490	−	1.30335i
$317$	13.9110	+	24.0946i	0.781320	+	1.35329i	0.931173	+	0.364578i	$0.118787\pi$
$317$	13.9110	+	24.0946i	0.781320	+	1.35329i	−0.149853	+	0.988708i	$0.547880\pi$
$318$	5.15337	+	8.92591i	0.288987	+	0.500540i
$319$	1.99773	+	3.46018i	0.111852	+	0.193733i
$320$	0.754384	+	1.30663i	0.0421714	+	0.0730429i
$321$	3.55252	−	6.15314i	0.198282	−	0.343435i
$322$		0			0
$323$	−0.275784	−	0.477672i	−0.0153450	−	0.0265784i
$324$	−8.65457	−	14.9902i	−0.480809	−	0.832786i
$325$	8.64391	+	5.41153i	0.479478	+	0.300178i
$326$	−3.38729	+	5.86697i	−0.187605	+	0.324941i
$327$	−7.76524	+	13.4498i	−0.429419	+	0.743775i
$328$	4.26660	+	7.38996i	0.235583	+	0.408042i
$329$		0			0
$330$	0.937318			0.0515976
$331$	−9.34295			−0.513535			−0.256768	−	0.966473i	$-0.582657\pi$
$331$	−9.34295			−0.513535			−0.256768	+	0.966473i	$0.582657\pi$
$332$	−12.8118	−	22.1907i	−0.703141	−	1.21788i
$333$	−2.65640	+	4.60103i	−0.145570	+	0.252135i
$334$	−12.7898			−0.699828
$335$	1.06732	+	1.84866i	0.0583140	+	0.101003i
$336$		0			0
$337$	22.9182			1.24844			0.624218	−	0.781250i	$-0.285418\pi$
$337$	22.9182			1.24844			0.624218	+	0.781250i	$0.285418\pi$
$338$	−4.22555	+	6.24173i	−0.229839	+	0.339505i
$339$	−7.38696	+	12.7946i	−0.401205	+	0.694907i
$340$	2.93379			0.159107
$341$	−1.28817	+	2.23118i	−0.0697583	+	0.120825i
$342$	−0.0774824	+	0.134204i	−0.00418977	+	0.00725690i
$343$		0			0
$344$	−8.55996	+	14.8263i	−0.461522	+	0.799380i
$345$	−6.60218			−0.355450
$346$	3.30222	−	5.71961i	0.177528	−	0.307488i
$347$	13.3355	+	23.0978i	0.715889	+	1.23996i	0.962616	+	0.270871i	$0.0873117\pi$
$347$	13.3355	+	23.0978i	0.715889	+	1.23996i	−0.246726	+	0.969085i	$0.579355\pi$
$348$	10.8465	−	18.7866i	0.581431	−	1.00707i
$349$	−7.61723	−	13.1934i	−0.407741	−	0.706228i	0.586895	−	0.809663i	$-0.300350\pi$
$349$	−7.61723	−	13.1934i	−0.407741	−	0.706228i	−0.994636	+	0.103435i	$0.967017\pi$
$350$		0			0
$351$	−0.590213	+	16.4996i	−0.0315033	+	0.880683i
$352$	1.58401	+	2.74358i	0.0844280	+	0.146234i
$353$	−22.4089			−1.19270			−0.596352	−	0.802723i	$-0.703384\pi$
$353$	−22.4089			−1.19270			−0.596352	+	0.802723i	$0.703384\pi$
$354$	0.264294			0.0140471
$355$	−18.4416			−0.978778
$356$	−4.14468			−0.219668
$357$		0			0
$358$	−1.00667	+	1.74361i	−0.0532044	+	0.0921528i
$359$	−8.01927	−	13.8898i	−0.423241	−	0.733075i	0.573013	−	0.819546i	$-0.305774\pi$
$359$	−8.01927	−	13.8898i	−0.423241	−	0.733075i	−0.996254	+	0.0864711i	$0.972441\pi$
$360$	−0.907530	−	1.57189i	−0.0478310	−	0.0828457i
$361$	−18.7875			−0.988817
$362$	6.11676	−	10.5945i	0.321490	−	0.556837i
$363$	20.1764			1.05898
$364$		0			0
$365$	−5.44356			−0.284929
$366$	−4.23841	+	7.34114i	−0.221545	+	0.383727i
$367$	−6.90004			−0.360179			−0.180090	−	0.983650i	$-0.557639\pi$
$367$	−6.90004			−0.360179			−0.180090	+	0.983650i	$0.557639\pi$
$368$	−2.48154	−	4.29815i	−0.129359	−	0.224057i
$369$	1.16452	+	2.01701i	0.0606225	+	0.105001i
$370$	3.91452	−	6.78015i	0.203506	−	0.352483i
$371$		0			0
$372$	13.9879			0.725240
$373$	7.68529			0.397929			0.198965	−	0.980007i	$-0.436242\pi$
$373$	7.68529			0.397929			0.198965	+	0.980007i	$0.436242\pi$
$374$	0.402263			0.0208005
$375$	21.8268			1.12713
$376$	12.2353	+	21.1922i	0.630988	+	1.09290i
$377$	−21.9475	+	11.6458i	−1.13035	+	0.599788i
$378$		0			0
$379$	12.5817	+	21.7922i	0.646281	+	1.11939i	0.984004	+	0.178146i	$0.0570098\pi$
$379$	12.5817	+	21.7922i	0.646281	+	1.11939i	−0.337723	+	0.941245i	$0.609657\pi$
$380$	−0.565096	+	0.978775i	−0.0289888	+	0.0502101i
$381$	−0.888656	−	1.53920i	−0.0455272	−	0.0788555i
$382$	3.45535	−	5.98484i	0.176791	−	0.306211i
$383$	−22.0437			−1.12638			−0.563189	−	0.826328i	$-0.690426\pi$
$383$	−22.0437			−1.12638			−0.563189	+	0.826328i	$0.690426\pi$
$384$	10.8995	−	18.8785i	0.556212	−	0.963387i
$385$		0			0
$386$	4.16866	−	7.22033i	0.212179	−	0.367505i
$387$	−2.33635	+	4.04668i	−0.118763	+	0.205704i
$388$	−26.0313			−1.32154
$389$	5.49058	−	9.50996i	0.278383	−	0.482174i	−0.692600	−	0.721322i	$-0.743535\pi$
$389$	5.49058	−	9.50996i	0.278383	−	0.482174i	0.970983	+	0.239148i	$0.0768681\pi$
$390$	−0.208368	+	5.82498i	−0.0105511	+	0.294960i
$391$	−2.83342			−0.143292
$392$		0			0
$393$	−1.07578	−	1.86331i	−0.0542660	−	0.0939914i
$394$	−4.04083			−0.203574
$395$	−11.8474	+	20.5203i	−0.596107	+	1.03249i
$396$	0.279672	+	0.484405i	0.0140540	+	0.0243423i
$397$	25.0764			1.25855			0.629275	−	0.777183i	$-0.283352\pi$
$397$	25.0764			1.25855			0.629275	+	0.777183i	$0.283352\pi$
$398$	−2.07196			−0.103858
$399$		0			0
$400$	2.96413	+	5.13402i	0.148206	+	0.256701i
$401$	11.3301	−	19.6243i	0.565797	−	0.979989i	−0.431178	−	0.902267i	$-0.641902\pi$
$401$	11.3301	−	19.6243i	0.565797	−	0.979989i	0.996975	−	0.0777222i	$-0.0247647\pi$
$402$	0.794560	−	1.37622i	0.0396291	−	0.0686395i
$403$	−13.5793	−	8.50136i	−0.676435	−	0.423483i
$404$	11.6581	+	20.1924i	0.580012	+	1.00461i
$405$	7.66521	+	13.2765i	0.380887	+	0.659716i
$406$		0			0
$407$	−2.65640	+	4.60103i	−0.131673	+	0.228064i
$408$	−2.40468	−	4.16503i	−0.119050	−	0.206200i
$409$	8.57324	+	14.8493i	0.423919	+	0.734250i	0.996319	−	0.0857251i	$-0.0273207\pi$
$409$	8.57324	+	14.8493i	0.423919	+	0.734250i	−0.572400	+	0.819975i	$0.693987\pi$
$410$	−1.71606	−	2.97230i	−0.0847501	−	0.146791i
$411$	−8.17358	−	14.1570i	−0.403173	−	0.698316i
$412$	8.94238	−	15.4887i	0.440560	−	0.763072i
$413$		0			0
$414$	0.398029	+	0.689407i	0.0195621	+	0.0338825i
$415$	11.3472	+	19.6540i	0.557013	+	0.964775i
$416$	−17.4022	+	9.23396i	−0.853213	+	0.452732i
$417$	−13.7685	+	23.8478i	−0.674248	+	1.16783i
$418$	−0.0774824	+	0.134204i	−0.00378979	+	0.00656411i
$419$	16.9902	+	29.4279i	0.830027	+	1.43765i	0.898016	+	0.439963i	$0.145008\pi$
$419$	16.9902	+	29.4279i	0.830027	+	1.43765i	−0.0679891	+	0.997686i	$0.521658\pi$
$420$		0			0
$421$	−32.3623			−1.57724			−0.788621	−	0.614879i	$-0.789205\pi$
$421$	−32.3623			−1.57724			−0.788621	+	0.614879i	$0.789205\pi$
$422$	8.18337			0.398360
$423$	3.33950	+	5.78418i	0.162372	+	0.281236i
$424$	9.97920	−	17.2845i	0.484633	−	0.839409i
$425$	3.38444			0.164169
$426$	6.86435	+	11.8894i	0.332579	+	0.576044i
$427$		0			0
$428$	−6.24802			−0.302009
$429$	0.141399	−	3.95285i	0.00682680	−	0.190845i
$430$	3.44288	−	5.96325i	0.166031	−	0.287574i
$431$	−18.9128			−0.910998			−0.455499	−	0.890236i	$-0.650539\pi$
$431$	−18.9128			−0.910998			−0.455499	+	0.890236i	$0.650539\pi$
$432$	−4.79874	+	8.31167i	−0.230880	+	0.399895i
$433$	−9.57006	+	16.5758i	−0.459908	+	0.796584i	−0.998956	−	0.0456914i	$-0.985451\pi$
$433$	−9.57006	+	16.5758i	−0.459908	+	0.796584i	0.539048	+	0.842275i	$0.318784\pi$
$434$		0			0
$435$	−9.60653	+	16.6390i	−0.460598	+	0.797779i
$436$	13.6572			0.654060
$437$	0.545763	−	0.945289i	0.0261074	−	0.0452193i
$438$	2.02621	+	3.50950i	0.0968161	+	0.167690i
$439$	−4.80144	+	8.31634i	−0.229160	+	0.396917i	−0.957560	−	0.288236i	$-0.906931\pi$
$439$	−4.80144	+	8.31634i	−0.229160	+	0.396917i	0.728399	+	0.685153i	$0.240265\pi$
$440$	−0.907530	−	1.57189i	−0.0432648	−	0.0749368i
$441$		0			0
$442$	−0.0894239	+	2.49987i	−0.00425346	+	0.118907i
$443$	20.1998	+	34.9871i	0.959721	+	1.66229i	0.723175	+	0.690665i	$0.242682\pi$
$443$	20.1998	+	34.9871i	0.959721	+	1.66229i	0.236546	+	0.971620i	$0.423984\pi$
$444$	28.8453			1.36894
$445$	3.67088			0.174016
$446$	0.527123			0.0249600
$447$	−25.3159			−1.19740
$448$		0			0
$449$	13.3112	−	23.0556i	0.628194	−	1.08806i	−0.359720	−	0.933060i	$-0.617128\pi$
$449$	13.3112	−	23.0556i	0.628194	−	1.08806i	0.987914	−	0.155003i	$-0.0495387\pi$
$450$	−0.475435	−	0.823477i	−0.0224122	−	0.0388191i
$451$	1.16452	+	2.01701i	0.0548352	+	0.0949773i
$452$	12.9919			0.611087
$453$	15.2680	−	26.4449i	0.717351	−	1.24249i
$454$	1.35393			0.0635430
$455$		0			0
$456$	1.85273			0.0867619
$457$	0.806434	−	1.39678i	0.0377234	−	0.0653388i	−0.846547	−	0.532314i	$-0.821323\pi$
$457$	0.806434	−	1.39678i	0.0377234	−	0.0653388i	0.884271	+	0.466975i	$0.154656\pi$
$458$	9.67166			0.451927
$459$	2.73960	+	4.74513i	0.127874	+	0.221484i
$460$	2.90291	+	5.02799i	0.135349	+	0.234431i
$461$	7.96032	−	13.7877i	0.370749	−	0.642156i	−0.618932	−	0.785445i	$-0.712434\pi$
$461$	7.96032	−	13.7877i	0.370749	−	0.642156i	0.989681	+	0.143289i	$0.0457677\pi$
$462$		0			0
$463$	−28.8475			−1.34066			−0.670328	−	0.742065i	$-0.733847\pi$
$463$	−28.8475			−1.34066			−0.670328	+	0.742065i	$0.733847\pi$
$464$	−14.4431			−0.670503
$465$	−12.3889			−0.574520
$466$	9.58219			0.443887
$467$	3.72268	+	6.44787i	0.172265	+	0.298372i	0.939211	−	0.343339i	$-0.111558\pi$
$467$	3.72268	+	6.44787i	0.172265	+	0.298372i	−0.766946	+	0.641711i	$0.778225\pi$
$468$	−3.07252	+	1.63034i	−0.142027	+	0.0753626i
$469$		0			0
$470$	−4.92114	−	8.52367i	−0.226995	−	0.393167i
$471$	−0.594744	+	1.03013i	−0.0274044	+	0.0474657i
$472$	−0.255895	−	0.443222i	−0.0117785	−	0.0204010i
$473$	−2.33635	+	4.04668i	−0.107425	+	0.186066i
$474$	17.6394			0.810205
$475$	−0.651899	+	1.12912i	−0.0299112	+	0.0518077i
$476$		0			0
$477$	2.72371	−	4.71761i	0.124710	−	0.216005i
$478$	0.922022	−	1.59699i	0.0421723	−	0.0730446i
$479$	37.2526			1.70212			0.851058	−	0.525071i	$-0.175961\pi$
$479$	37.2526			1.70212			0.851058	+	0.525071i	$0.175961\pi$
$480$	−7.61704	+	13.1931i	−0.347669	+	0.602180i
$481$	−28.0027	−	17.5311i	−1.27681	−	0.799350i
$482$	−9.19570			−0.418853
$483$		0			0
$484$	−8.87134	−	15.3656i	−0.403243	−	0.698437i
$485$	23.0555			1.04690
$486$	1.72380	−	2.98571i	0.0781931	−	0.135434i
$487$	−12.0863	−	20.9341i	−0.547684	−	0.948616i	−0.998433	−	0.0559651i	$-0.982176\pi$
$487$	−12.0863	−	20.9341i	−0.547684	−	0.948616i	0.450749	−	0.892651i	$-0.351157\pi$
$488$	16.4148			0.743065
$489$	22.1069			0.999707
$490$		0			0
$491$	−3.03571	−	5.25800i	−0.137000	−	0.237290i	0.789360	−	0.613931i	$-0.210413\pi$
$491$	−3.03571	−	5.25800i	−0.137000	−	0.237290i	−0.926360	+	0.376640i	$0.877079\pi$
$492$	6.32263	−	10.9511i	0.285046	−	0.493714i
$493$	−4.12277	+	7.14086i	−0.185680	+	0.321608i
$494$	−0.816787	−	0.511350i	−0.0367490	−	0.0230067i
$495$	−0.247700	−	0.429030i	−0.0111333	−	0.0192835i
$496$	−4.65656	−	8.06540i	−0.209086	−	0.362147i
$497$		0			0
$498$	8.44736	−	14.6313i	0.378535	−	0.655642i
$499$	1.25782	+	2.17861i	0.0563079	+	0.0975281i	0.892805	−	0.450443i	$-0.148734\pi$
$499$	1.25782	+	2.17861i	0.0563079	+	0.0975281i	−0.836497	+	0.547971i	$0.815400\pi$
$500$	−9.59703	−	16.6225i	−0.429192	−	0.743383i
$501$	20.8679	+	36.1442i	0.932308	+	1.61481i
$502$	−0.723533	−	1.25320i	−0.0322929	−	0.0559329i
$503$	17.0026	−	29.4493i	0.758107	−	1.31308i	−0.185708	−	0.982605i	$-0.559458\pi$
$503$	17.0026	−	29.4493i	0.758107	−	1.31308i	0.943815	−	0.330474i	$-0.107209\pi$
$504$		0			0
$505$	−10.3254	−	17.8841i	−0.459473	−	0.795831i
$506$	0.398029	+	0.689407i	0.0176946	+	0.0306479i
$507$	24.5336	+	1.75745i	1.08958	+	0.0780512i
$508$	−0.781466	+	1.35354i	−0.0346719	+	0.0600536i
$509$	−14.6524	+	25.3787i	−0.649457	+	1.12489i	0.333796	+	0.942645i	$0.391670\pi$
$509$	−14.6524	+	25.3787i	−0.649457	+	1.12489i	−0.983253	+	0.182247i	$0.941663\pi$
$510$	0.967183	+	1.67521i	0.0428276	+	0.0741795i
$511$		0			0
$512$	−20.3568			−0.899654
$513$	−2.11077			−0.0931927
$514$	−3.04992	−	5.28262i	−0.134526	−	0.233006i
$515$	−7.92012	+	13.7180i	−0.349002	+	0.604489i
$516$	25.3699			1.11685
$517$	3.33950	+	5.78418i	0.146871	+	0.254388i
$518$		0			0
$519$	−21.5516			−0.946011
$520$	9.97028	−	5.29043i	0.437226	−	0.232001i
$521$	4.57386	−	7.92216i	0.200385	−	0.347076i	−0.748268	−	0.663397i	$-0.769114\pi$
$521$	4.57386	−	7.92216i	0.200385	−	0.347076i	0.948652	+	0.316321i	$0.102448\pi$
$522$	2.31661			0.101395
$523$	7.05373	−	12.2174i	0.308438	−	0.534231i	−0.669583	−	0.742737i	$-0.733527\pi$
$523$	7.05373	−	12.2174i	0.308438	−	0.534231i	0.978021	+	0.208507i	$0.0668604\pi$
$524$	−0.946019	+	1.63855i	−0.0413270	+	0.0715805i
$525$		0			0
$526$	−9.08849	+	15.7417i	−0.396277	+	0.686372i
$527$	−5.31686			−0.231606
$528$	1.14965	−	1.99125i	0.0500319	−	0.0866578i
$529$	8.69640	+	15.0626i	0.378104	+	0.654896i
$530$	−4.01371	+	6.95196i	−0.174345	+	0.301974i
$531$	−0.0698437	−	0.120973i	−0.00303096	−	0.00524977i
$532$		0			0
$533$	−12.7936	+	6.78856i	−0.554154	+	0.294045i
$534$	−1.36638	−	2.36664i	−0.0591290	−	0.102414i
$535$	5.53376			0.239246
$536$	−3.07724			−0.132916
$537$	6.56997			0.283515
$538$	−12.2494			−0.528109
$539$		0			0
$540$	5.61359	−	9.72302i	0.241570	−	0.418412i
$541$	−3.90147	−	6.75754i	−0.167737	−	0.290529i	0.769887	−	0.638181i	$-0.220313\pi$
$541$	−3.90147	−	6.75754i	−0.167737	−	0.290529i	−0.937624	+	0.347651i	$0.886979\pi$
$542$	−1.89020	−	3.27393i	−0.0811912	−	0.140627i
$543$	−39.9205			−1.71315
$544$	−3.26896	+	5.66200i	−0.140155	+	0.242756i
$545$	−12.0959			−0.518133
$546$		0			0
$547$	6.99390			0.299038			0.149519	−	0.988759i	$-0.452228\pi$
$547$	6.99390			0.299038			0.149519	+	0.988759i	$0.452228\pi$
$548$	−7.18767	+	12.4494i	−0.307042	+	0.531813i
$549$	4.48026			0.191213
$550$	−0.475435	−	0.823477i	−0.0202726	−	0.0351132i
$551$	−1.58823	−	2.75089i	−0.0676608	−	0.117192i
$552$	4.75875	−	8.24240i	0.202546	−	0.350820i
$553$		0			0
$554$	8.42520			0.357952
$555$	−25.5478			−1.08444
$556$	24.2155			1.02697
$557$	−7.24249			−0.306874			−0.153437	−	0.988158i	$-0.549034\pi$
$557$	−7.24249			−0.306874			−0.153437	+	0.988158i	$0.549034\pi$
$558$	0.746894	+	1.29366i	0.0316186	+	0.0547650i
$559$	−24.6288	−	15.4189i	−1.04169	−	0.652149i
$560$		0			0
$561$	−0.656332	−	1.13680i	−0.0277104	−	0.0479958i
$562$	7.88055	−	13.6495i	0.332421	−	0.575770i
$563$	−7.96606	−	13.7976i	−0.335730	−	0.581501i	0.647895	−	0.761730i	$-0.275650\pi$
$563$	−7.96606	−	13.7976i	−0.335730	−	0.581501i	−0.983625	+	0.180229i	$0.942316\pi$
$564$	18.1314	−	31.4045i	0.763470	−	1.32237i
$565$	−11.5067			−0.484090
$566$	−2.48618	+	4.30618i	−0.104502	+	0.181002i
$567$		0			0
$568$	13.2924	−	23.0231i	0.557737	−	0.966029i
$569$	21.1379	−	36.6120i	0.886149	−	1.53485i	0.0417571	−	0.999128i	$-0.486704\pi$
$569$	21.1379	−	36.6120i	0.886149	−	1.53485i	0.844392	−	0.535727i	$-0.179962\pi$
$570$	−0.745181			−0.0312122
$571$	−6.81247	+	11.7995i	−0.285093	+	0.493795i	−0.972632	−	0.232352i	$-0.925358\pi$
$571$	−6.81247	+	11.7995i	−0.285093	+	0.493795i	0.687539	+	0.726148i	$0.258691\pi$
$572$	−3.07252	+	1.63034i	−0.128469	+	0.0681680i
$573$	−22.5510			−0.942082
$574$		0			0
$575$	3.34882	+	5.80032i	0.139655	+	0.241890i
$576$	−0.593641			−0.0247350
$577$	−13.1925	+	22.8500i	−0.549209	+	0.951258i	0.449120	+	0.893472i	$0.351738\pi$
$577$	−13.1925	+	22.8500i	−0.549209	+	0.951258i	−0.998329	+	0.0577867i	$0.981596\pi$
$578$	−4.51331	−	7.81728i	−0.187729	−	0.325156i
$579$	−27.2064			−1.13066
$580$	16.8956			0.701550
$581$		0			0
$582$	−8.58174	−	14.8640i	−0.355725	−	0.616133i
$583$	2.72371	−	4.71761i	0.112805	−	0.195384i
$584$	3.92364	−	6.79594i	0.162361	−	0.281218i
$585$	2.72128	−	1.44397i	0.112511	−	0.0597007i
$586$	3.04027	+	5.26591i	0.125592	+	0.217533i
$587$	−11.0720	−	19.1773i	−0.456990	−	0.791530i	0.541810	−	0.840501i	$-0.317739\pi$
$587$	−11.0720	−	19.1773i	−0.456990	−	0.791530i	−0.998800	+	0.0489708i	$0.984406\pi$
$588$		0			0
$589$	1.02411	−	1.77382i	0.0421979	−	0.0730889i
$590$	0.102923	+	0.178268i	0.00423727	+	0.00733916i
$591$	6.59303	+	11.4195i	0.271201	+	0.469734i
$592$	−9.60254	−	16.6321i	−0.394662	−	0.683575i
$593$	−13.0419	−	22.5893i	−0.535568	−	0.927630i	−0.999136	−	0.0415689i	$-0.986764\pi$
$593$	−13.0419	−	22.5893i	−0.535568	−	0.927630i	0.463568	−	0.886061i	$-0.346569\pi$
$594$	0.769700	−	1.33316i	0.0315812	−	0.0547002i
$595$		0			0
$596$	11.1311	+	19.2797i	0.455949	+	0.789727i
$597$	3.38062	+	5.85540i	0.138360	+	0.239646i
$598$	−4.37282	+	2.32031i	−0.178818	+	0.0948843i
$599$	8.42202	−	14.5874i	0.344114	−	0.596024i	−0.641078	−	0.767476i	$-0.721512\pi$
$599$	8.42202	−	14.5874i	0.344114	−	0.596024i	0.985192	+	0.171452i	$0.0548458\pi$
$600$	−5.68420	+	9.84532i	−0.232056	+	0.401933i
$601$	4.31691	+	7.47710i	0.176090	+	0.304997i	0.940538	−	0.339688i	$-0.110322\pi$
$601$	4.31691	+	7.47710i	0.176090	+	0.304997i	−0.764448	+	0.644686i	$0.776988\pi$
$602$		0			0
$603$	−0.839898			−0.0342033
$604$	−26.8526			−1.09262
$605$	7.85719	+	13.6091i	0.319440	+	0.553287i
$606$	−7.68665	+	13.3137i	−0.312249	+	0.540831i
$607$	−21.8363			−0.886306			−0.443153	−	0.896446i	$-0.646140\pi$
$607$	−21.8363			−0.886306			−0.443153	+	0.896446i	$0.646140\pi$
$608$	−1.25931	−	2.18119i	−0.0510718	−	0.0884590i
$609$		0			0
$610$	−6.60218			−0.267315
$611$	−36.6883	+	19.4676i	−1.48425	+	0.787573i
$612$	−0.577165	+	0.999680i	−0.0233305	+	0.0404096i
$613$	−48.0487			−1.94067			−0.970334	−	0.241767i	$-0.922273\pi$
$613$	−48.0487			−1.94067			−0.970334	+	0.241767i	$0.922273\pi$
$614$	5.55896	−	9.62840i	0.224341	−	0.388571i
$615$	−5.59985	+	9.69922i	−0.225808	+	0.391110i
$616$		0			0
$617$	8.23709	−	14.2671i	0.331613	−	0.574370i	−0.651215	−	0.758893i	$-0.725741\pi$
$617$	8.23709	−	14.2671i	0.331613	−	0.574370i	0.982828	+	0.184523i	$0.0590739\pi$
$618$	11.7922			0.474350
$619$	21.0267	−	36.4192i	0.845133	−	1.46381i	−0.0403733	−	0.999185i	$-0.512855\pi$
$619$	21.0267	−	36.4192i	0.845133	−	1.46381i	0.885506	−	0.464628i	$-0.153812\pi$
$620$	5.44726	+	9.43493i	0.218767	+	0.378916i
$621$	−5.42153	+	9.39037i	−0.217559	+	0.376823i
$622$	1.01135	+	1.75170i	0.0405513	+	0.0702370i
$623$		0			0
$624$	12.1191	+	7.58716i	0.485151	+	0.303730i
$625$	1.42880	+	2.47475i	0.0571519	+	0.0989900i
$626$	−11.7826			−0.470927
$627$	0.505682			0.0201950
$628$	1.04601			0.0417404
$629$	−10.9642			−0.437170
$630$		0			0
$631$	6.06667	−	10.5078i	0.241510	−	0.418308i	−0.719634	−	0.694353i	$-0.755691\pi$
$631$	6.06667	−	10.5078i	0.241510	−	0.418308i	0.961145	+	0.276045i	$0.0890239\pi$
$632$	−17.0788	−	29.5814i	−0.679360	−	1.17669i
$633$	−13.3520	−	23.1263i	−0.530694	−	0.919190i
$634$	16.1315			0.640663
$635$	0.692131	−	1.19881i	0.0274664	−	0.0475732i
$636$	−29.5762			−1.17277
$637$		0			0
$638$	2.31661			0.0917157
$639$	3.62802	−	6.28391i	0.143522	−	0.248588i
$640$	16.9782			0.671121
$641$	0.202177	+	0.350182i	0.00798553	+	0.0138313i	0.869991	−	0.493068i	$-0.164125\pi$
$641$	0.202177	+	0.350182i	0.00798553	+	0.0138313i	−0.862005	+	0.506900i	$0.830791\pi$
$642$	−2.05979	−	3.56765i	−0.0812933	−	0.140804i
$643$	14.1741	−	24.5503i	0.558973	−	0.968169i	−0.438610	−	0.898678i	$-0.644529\pi$
$643$	14.1741	−	24.5503i	0.558973	−	0.968169i	0.997583	−	0.0694914i	$-0.0221377\pi$
$644$		0			0
$645$	−22.4697			−0.884742
$646$	−0.319805			−0.0125826
$647$	34.8090			1.36848			0.684242	−	0.729255i	$-0.260133\pi$
$647$	34.8090			1.36848			0.684242	+	0.729255i	$0.260133\pi$
$648$	−22.0998			−0.868164
$649$	−0.0698437	−	0.120973i	−0.00274160	−	0.00474860i
$650$	5.22321	−	2.77154i	0.204871	−	0.108709i
$651$		0			0
$652$	−9.72016	−	16.8358i	−0.380671	−	0.659341i
$653$	12.5750	−	21.7805i	0.492098	−	0.852338i	−0.507861	−	0.861439i	$-0.669564\pi$
$653$	12.5750	−	21.7805i	0.492098	−	0.852338i	0.999959	+	0.00910088i	$0.00289694\pi$
$654$	4.50237	+	7.79833i	0.176056	+	0.304939i
$655$	0.837873	−	1.45124i	0.0327384	−	0.0567046i
$656$	−8.41917			−0.328713
$657$	1.07091	−	1.85488i	0.0417803	−	0.0723657i
$658$		0			0
$659$	−4.33723	+	7.51230i	−0.168954	+	0.292638i	−0.938053	−	0.346493i	$-0.887372\pi$
$659$	−4.33723	+	7.51230i	−0.168954	+	0.292638i	0.769098	+	0.639131i	$0.220706\pi$
$660$	−1.34486	+	2.32937i	−0.0523486	+	0.0906704i
$661$	−19.0000			−0.739014			−0.369507	−	0.929228i	$-0.620473\pi$
$661$	−19.0000			−0.739014			−0.369507	+	0.929228i	$0.620473\pi$
$662$	−2.70857	+	4.69138i	−0.105272	+	0.182336i
$663$	7.21058	−	3.82608i	0.280036	−	0.148593i
$664$	−32.7156			−1.26961
$665$		0			0
$666$	1.54021	+	2.66772i	0.0596819	+	0.103372i
$667$	−16.3175			−0.631817
$668$	18.3508	−	31.7845i	0.710013	−	1.22978i
$669$	−0.860054	−	1.48966i	−0.0332516	−	0.0575935i
$670$	1.23769			0.0478161
$671$	4.48026			0.172958
$672$		0			0
$673$	0.284273	+	0.492376i	0.0109579	+	0.0189797i	0.871452	−	0.490480i	$-0.163179\pi$
$673$	0.284273	+	0.492376i	0.0109579	+	0.0189797i	−0.860494	+	0.509460i	$0.829845\pi$
$674$	6.64412	−	11.5079i	0.255922	−	0.443269i
$675$	6.47587	−	11.2165i	0.249256	−	0.431725i
$676$	−9.44877	−	19.4567i	−0.363414	−	0.748334i
$677$	13.8398	+	23.9713i	0.531908	+	0.921292i	0.999306	+	0.0372449i	$0.0118581\pi$
$677$	13.8398	+	23.9713i	0.531908	+	0.921292i	−0.467398	+	0.884047i	$0.654809\pi$
$678$	4.28304	+	7.41844i	0.164489	+	0.284903i
$679$		0			0
$680$	1.87289	−	3.24394i	0.0718221	−	0.124400i
$681$	−2.20907	−	3.82622i	−0.0846518	−	0.146621i
$682$	0.746894	+	1.29366i	0.0286001	+	0.0495368i
$683$	11.8958	+	20.6042i	0.455181	+	0.788397i	0.998699	−	0.0510006i	$-0.0162411\pi$
$683$	11.8958	+	20.6042i	0.455181	+	0.788397i	−0.543517	+	0.839398i	$0.682908\pi$
$684$	−0.222343	−	0.385110i	−0.00850150	−	0.0147250i
$685$	6.36600	−	11.0262i	0.243232	−	0.421291i
$686$		0			0
$687$	−15.7803	−	27.3323i	−0.602056	−	1.04279i
$688$	−8.44559	−	14.6282i	−0.321985	−	0.557694i
$689$	28.7122	+	17.9753i	1.09385	+	0.684806i
$690$	−1.91401	+	3.31516i	−0.0728650	+	0.126206i
$691$	18.4217	−	31.9073i	0.700793	−	1.21381i	−0.267395	−	0.963587i	$-0.586163\pi$
$691$	18.4217	−	31.9073i	0.700793	−	1.21381i	0.968188	−	0.250222i	$-0.0805037\pi$
$692$	9.47603	+	16.4130i	0.360224	+	0.623927i
$693$		0			0
$694$	15.4642			0.587012
$695$	−21.4473			−0.813542
$696$	−13.8485	−	23.9863i	−0.524925	−	0.909197i
$697$	−2.40325	+	4.16255i	−0.0910296	+	0.157668i
$698$	−8.83310			−0.334338
$699$	−15.6343	−	27.0794i	−0.591344	−	1.02424i
$700$		0			0
$701$	2.34987			0.0887533			0.0443767	−	0.999015i	$-0.485870\pi$
$701$	2.34987			0.0887533			0.0443767	+	0.999015i	$0.485870\pi$
$702$	8.11385	+	5.07968i	0.306237	+	0.191720i
$703$	2.11188	−	3.65788i	0.0796511	−	0.137960i
$704$	−0.593641			−0.0223737
$705$	−16.0587	+	27.8145i	−0.604805	+	1.04755i
$706$	−6.49645	+	11.2522i	−0.244497	+	0.423481i
$707$		0			0
$708$	−0.379208	+	0.656807i	−0.0142515	+	0.0246843i
$709$	10.0832			0.378683			0.189341	−	0.981911i	$-0.439365\pi$
$709$	10.0832			0.378683			0.189341	+	0.981911i	$0.439365\pi$
$710$	−5.34631	+	9.26008i	−0.200643	+	0.347525i
$711$	−4.66148	−	8.07393i	−0.174819	−	0.302796i
$712$	−2.64591	+	4.58285i	−0.0991597	+	0.171750i
$713$	−5.26090	−	9.11214i	−0.197022	−	0.341252i
$714$		0			0
$715$	2.72128	−	1.44397i	0.101770	−	0.0540013i
$716$	−2.88875	−	5.00346i	−0.107958	−	0.186988i
$717$	−6.01749			−0.224727
$718$	−9.29931			−0.347047
$719$	−6.50227			−0.242494			−0.121247	−	0.992622i	$-0.538689\pi$
$719$	−6.50227			−0.242494			−0.121247	+	0.992622i	$0.538689\pi$
$720$	1.79081			0.0667394
$721$		0			0
$722$	−5.44660	+	9.43379i	−0.202701	+	0.351089i
$723$	15.0037	+	25.9872i	0.557994	+	0.966474i
$724$	17.5526	+	30.4020i	0.652338	+	1.12988i
$725$	19.4908			0.723872
$726$	5.84923	−	10.1312i	0.217085	−	0.376003i
$727$	3.12636			0.115950			0.0579750	−	0.998318i	$-0.481536\pi$
$727$	3.12636			0.115950			0.0579750	+	0.998318i	$0.481536\pi$
$728$		0			0
$729$	19.9595			0.739242
$730$	−1.57812	+	2.73338i	−0.0584087	+	0.101167i
$731$	−9.64317			−0.356665
$732$	−12.1625	−	21.0661i	−0.449539	−	0.778625i
$733$	−3.83220	−	6.63756i	−0.141545	−	0.245164i	0.786533	−	0.617548i	$-0.211874\pi$
$733$	−3.83220	−	6.63756i	−0.141545	−	0.245164i	−0.928079	+	0.372384i	$0.878540\pi$
$734$	−2.00036	+	3.46472i	−0.0738346	+	0.127885i
$735$		0			0
$736$	−12.9382			−0.476909
$737$	−0.839898			−0.0309381
$738$	1.35040			0.0497090
$739$	20.4325			0.751620			0.375810	−	0.926697i	$-0.377365\pi$
$739$	20.4325			0.751620			0.375810	+	0.926697i	$0.377365\pi$
$740$	11.2331	+	19.4563i	0.412936	+	0.715227i
$741$	−0.112414	+	3.14257i	−0.00412964	+	0.115445i
$742$		0			0
$743$	−5.07080	−	8.78288i	−0.186030	−	0.322213i	0.757893	−	0.652378i	$-0.226229\pi$
$743$	−5.07080	−	8.78288i	−0.186030	−	0.322213i	−0.943923	+	0.330166i	$0.892895\pi$
$744$	8.92971	−	15.4667i	0.327379	−	0.567037i
$745$	−9.85866	−	17.0757i	−0.361193	−	0.625605i
$746$	2.22801	−	3.85902i	0.0815731	−	0.141289i
$747$	−8.92937			−0.326709
$748$	−0.577165	+	0.999680i	−0.0211033	+	0.0365519i
$749$		0			0
$750$	6.32771	−	10.9599i	0.231055	−	0.400200i
$751$	11.1481	−	19.3090i	0.406799	−	0.704597i	−0.587730	−	0.809057i	$-0.699978\pi$
$751$	11.1481	−	19.3090i	0.406799	−	0.704597i	0.994529	+	0.104461i	$0.0333116\pi$
$752$	−24.1437			−0.880429
$753$	−2.36104	+	4.08943i	−0.0860409	+	0.149027i
$754$	−0.514988	+	14.3967i	−0.0187548	+	0.524295i
$755$	23.7829			0.865550
$756$		0			0
$757$	−12.2909	−	21.2884i	−0.446720	−	0.773741i	0.551451	−	0.834207i	$-0.314074\pi$
$757$	−12.2909	−	21.2884i	−0.446720	−	0.773741i	−0.998170	+	0.0604666i	$0.980741\pi$
$758$	14.5901			0.529935
$759$	1.29885	−	2.24967i	0.0471452	−	0.0816580i
$760$	0.721500	+	1.24967i	0.0261715	+	0.0453304i
$761$	35.2333			1.27721			0.638603	−	0.769536i	$-0.279512\pi$
$761$	35.2333			1.27721			0.638603	+	0.769536i	$0.279512\pi$
$762$	−1.03050			−0.0373312
$763$		0			0
$764$	9.91545	+	17.1741i	0.358728	+	0.621336i
$765$	0.511186	−	0.885399i	0.0184820	−	0.0320117i
$766$	−6.39057	+	11.0688i	−0.230901	+	0.399932i
$767$	0.767315	−	0.407153i	0.0277061	−	0.0147014i
$768$	−4.38246	−	7.59065i	−0.158138	−	0.273904i
$769$	4.62257	+	8.00653i	0.166694	+	0.288723i	0.937256	−	0.348643i	$-0.113357\pi$
$769$	4.62257	+	8.00653i	0.166694	+	0.288723i	−0.770561	+	0.637366i	$0.780024\pi$
$770$		0			0
$771$	−9.95251	+	17.2383i	−0.358431	+	0.620821i
$772$	11.9624	+	20.7194i	0.430535	+	0.745708i
$773$	−3.16336	−	5.47909i	−0.113778	−	0.197069i	0.803513	−	0.595288i	$-0.202962\pi$
$773$	−3.16336	−	5.47909i	−0.113778	−	0.197069i	−0.917291	+	0.398218i	$0.869629\pi$
$774$	1.35464	+	2.34630i	0.0486915	+	0.0843362i
$775$	6.28400	+	10.8842i	0.225728	+	0.390972i
$776$	−16.6180	+	28.7833i	−0.596553	+	1.03326i
$777$		0			0
$778$	−3.18349	−	5.51397i	−0.114134	−	0.197686i
$779$	−0.925812	−	1.60355i	−0.0331706	−	0.0574532i
$780$	−14.1769	−	8.87549i	−0.507616	−	0.317793i
$781$	3.62802	−	6.28391i	0.129821	−	0.224856i
$782$	−0.821423	+	1.42275i	−0.0293740	+	0.0508773i
$783$	15.7772	+	27.3270i	0.563833	+	0.976587i
$784$		0			0
$785$	−0.926435			−0.0330659
$786$	−1.24750			−0.0444968
$787$	23.0029	+	39.8421i	0.819963	+	1.42022i	0.905708	+	0.423901i	$0.139340\pi$
$787$	23.0029	+	39.8421i	0.819963	+	1.42022i	−0.0857450	+	0.996317i	$0.527327\pi$
$788$	5.79777	−	10.0420i	0.206537	−	0.357733i
$789$	59.3152			2.11168
$790$	6.86924	+	11.8979i	0.244397	+	0.423307i
$791$		0			0
$792$	0.714154			0.0253764
$793$	−0.995970	+	27.8427i	−0.0353679	+	0.988722i
$794$	7.26979	−	12.5916i	0.257995	−	0.446861i
$795$	26.1951			0.929045
$796$	2.97285	−	5.14912i	0.105370	−	0.182506i
$797$	12.3745	−	21.4333i	0.438327	−	0.759205i	−0.559233	−	0.829010i	$-0.688904\pi$
$797$	12.3745	−	21.4333i	0.438327	−	0.759205i	0.997561	+	0.0698051i	$0.0222377\pi$
$798$		0			0
$799$	−6.89181	+	11.9370i	−0.243815	+	0.422299i
$800$	15.4543			0.546394
$801$	−0.722173	+	1.25084i	−0.0255167	+	0.0441963i
$802$	−6.56930	−	11.3784i	−0.231970	−	0.401784i
$803$	1.07091	−	1.85488i	0.0377917	−	0.0654572i
$804$	2.28006	+	3.94919i	0.0804117	+	0.139277i
$805$		0			0
$806$	−8.20551	+	4.35401i	−0.289027	+	0.153363i
$807$	19.9861	+	34.6170i	0.703545	+	1.21858i
$808$	29.7695			1.04729
$809$	30.0348			1.05597			0.527983	−	0.849255i	$-0.322948\pi$
$809$	30.0348			1.05597			0.527983	+	0.849255i	$0.322948\pi$
$810$	8.88873			0.312318
$811$	13.4160			0.471101			0.235550	−	0.971862i	$-0.424311\pi$
$811$	13.4160			0.471101			0.235550	+	0.971862i	$0.424311\pi$
$812$		0			0
$813$	−6.16812	+	10.6835i	−0.216325	+	0.374686i
$814$	1.54021	+	2.66772i	0.0539843	+	0.0935036i
$815$	8.60898	+	14.9112i	0.301559	+	0.522316i
$816$	4.74511			0.166112
$817$	1.85743	−	3.21717i	0.0649833	−	0.112554i
$818$	9.94171			0.347604
$819$		0			0
$820$	9.84878			0.343934
$821$	−5.07528	+	8.79064i	−0.177128	+	0.306796i	−0.940896	−	0.338696i	$-0.890014\pi$
$821$	−5.07528	+	8.79064i	−0.177128	+	0.306796i	0.763767	+	0.645492i	$0.223347\pi$
$822$	−9.47825			−0.330592
$823$	24.0217	+	41.6068i	0.837344	+	1.45032i	0.892108	+	0.451823i	$0.149226\pi$
$823$	24.0217	+	41.6068i	0.837344	+	1.45032i	−0.0547635	+	0.998499i	$0.517440\pi$
$824$	−11.4174	−	19.7755i	−0.397744	−	0.688913i
$825$	−1.55144	+	2.68717i	−0.0540142	+	0.0935553i
$826$		0			0
$827$	8.41781			0.292716			0.146358	−	0.989232i	$-0.453245\pi$
$827$	8.41781			0.292716			0.146358	+	0.989232i	$0.453245\pi$
$828$	−2.28436			−0.0793871
$829$	−56.1642			−1.95066			−0.975331	−	0.220745i	$-0.929151\pi$
$829$	−56.1642			−1.95066			−0.975331	+	0.220745i	$0.929151\pi$
$830$	13.1585			0.456737
$831$	−13.7466	−	23.8098i	−0.476863	−	0.825951i
$832$	0.131968	−	3.68920i	0.00457516	−	0.127900i
$833$		0			0
$834$	7.98314	+	13.8272i	0.276434	+	0.478797i
$835$	−16.2530	+	28.1510i	−0.562458	+	0.974205i
$836$	−0.222343	−	0.385110i	−0.00768990	−	0.0133193i
$837$	−10.1734	+	17.6209i	−0.351645	+	0.609066i
$838$	19.7022			0.680602
$839$	13.0690	−	22.6362i	0.451192	−	0.781488i	−0.547268	−	0.836957i	$-0.684332\pi$
$839$	13.0690	−	22.6362i	0.451192	−	0.781488i	0.998460	+	0.0554692i	$0.0176655\pi$
$840$		0			0
$841$	−9.24289	+	16.0092i	−0.318720	+	0.552040i
$842$	−9.38200	+	16.2501i	−0.323325	+	0.560016i
$843$	−51.4316			−1.77140
$844$	−11.7415	+	20.3368i	−0.404158	+	0.700023i
$845$	8.36862	+	17.2325i	0.287889	+	0.592815i
$846$	3.87255			0.133141
$847$		0			0
$848$	9.84586	+	17.0535i	0.338108	+	0.585621i
$849$	16.2258			0.556868
$850$	0.981166	−	1.69943i	0.0336537	−	0.0582900i
$851$	−10.8488	−	18.7906i	−0.371891	−	0.644135i
$852$	−39.3958			−1.34968
$853$	9.56236			0.327409			0.163705	−	0.986509i	$-0.447656\pi$
$853$	9.56236			0.327409			0.163705	+	0.986509i	$0.447656\pi$
$854$		0			0
$855$	0.196926	+	0.341085i	0.00673471	+	0.0116649i
$856$	−3.98865	+	6.90855i	−0.136329	+	0.236129i
$857$	−2.83687	+	4.91361i	−0.0969058	+	0.167846i	−0.910402	−	0.413724i	$-0.864228\pi$
$857$	−2.83687	+	4.91361i	−0.0969058	+	0.167846i	0.813497	+	0.581570i	$0.197561\pi$
$858$	−1.94385	−	1.21695i	−0.0663620	−	0.0415460i
$859$	13.2675	+	22.9801i	0.452683	+	0.784070i	0.998552	−	0.0538010i	$-0.0171337\pi$
$859$	13.2675	+	22.9801i	0.452683	+	0.784070i	−0.545869	+	0.837871i	$0.683800\pi$
$860$	9.87968	+	17.1121i	0.336894	+	0.583518i
$861$		0			0
$862$	−5.48292	+	9.49669i	−0.186749	+	0.323459i
$863$	−9.52402	−	16.4961i	−0.324202	−	0.561533i	0.657149	−	0.753761i	$-0.271762\pi$
$863$	−9.52402	−	16.4961i	−0.324202	−	0.561533i	−0.981350	+	0.192227i	$0.938429\pi$
$864$	12.5098	+	21.6676i	0.425593	+	0.737148i
$865$	−8.39276	−	14.5367i	−0.285362	−	0.494262i
$866$	5.54882	+	9.61084i	0.188557	+	0.326590i
$867$	−14.7278	+	25.5094i	−0.500184	+	0.866343i
$868$		0			0
$869$	−4.66148	−	8.07393i	−0.158130	−	0.273889i
$870$	5.56997	+	9.64746i	0.188840	+	0.327080i
$871$	0.186711	−	5.21957i	0.00632647	−	0.176858i
$872$	8.71856	−	15.1010i	0.295248	−	0.511384i
$873$	−4.53571	+	7.85608i	−0.153511	+	0.265888i
$874$	−0.316439	−	0.548089i	−0.0107037	−	0.0185394i
$875$		0			0
$876$	−11.6288			−0.392901
$877$	26.5171			0.895420			0.447710	−	0.894179i	$-0.352240\pi$
$877$	26.5171			0.895420			0.447710	+	0.894179i	$0.352240\pi$
$878$	2.78393	+	4.82190i	0.0939530	+	0.162731i
$879$	9.92102	−	17.1837i	0.334628	−	0.579592i
$880$	1.79081			0.0603681
$881$	2.02357	+	3.50492i	0.0681757	+	0.118084i	0.898098	−	0.439795i	$-0.144949\pi$
$881$	2.02357	+	3.50492i	0.0681757	+	0.118084i	−0.829923	+	0.557879i	$0.811615\pi$
$882$		0			0
$883$	44.7968			1.50753			0.753766	−	0.657142i	$-0.228235\pi$
$883$	44.7968			1.50753			0.753766	+	0.657142i	$0.228235\pi$
$884$	−6.08423	−	3.80904i	−0.204635	−	0.128112i
$885$	0.335858	−	0.581723i	0.0112897	−	0.0195544i
$886$	23.4241			0.786948
$887$	25.0533	−	43.3936i	0.841207	−	1.45701i	−0.0476683	−	0.998863i	$-0.515179\pi$
$887$	25.0533	−	43.3936i	0.841207	−	1.45701i	0.888875	−	0.458150i	$-0.151488\pi$
$888$	18.4144	−	31.8947i	0.617948	−	1.07032i
$889$		0			0
$890$	1.06421	−	1.84326i	0.0356723	−	0.0617862i
$891$	−6.03191			−0.202077
$892$	−0.756314	+	1.30997i	−0.0253233	+	0.0438612i
$893$	−2.65495	−	4.59851i	−0.0888445	−	0.153883i
$894$	−7.33921	+	12.7119i	−0.245460	+	0.425149i
$895$	2.55851	+	4.43148i	0.0855217	+	0.148128i
$896$		0			0
$897$	13.6919	+	8.57184i	0.457160	+	0.286205i
$898$	−7.71796	−	13.3679i	−0.257552	−	0.446093i
$899$	−30.6196			−1.02122
$900$	2.72861			0.0909536
$901$	11.2420			0.374525
$902$	1.35040			0.0449635
$903$		0			0
$904$	8.29384	−	14.3654i	0.275849	−	0.477785i
$905$	−15.5461	−	26.9266i	−0.516769	−	0.895069i
$906$	−8.85252	−	15.3330i	−0.294105	−	0.509405i
$907$	5.55577			0.184476			0.0922382	−	0.995737i	$-0.470598\pi$
$907$	5.55577			0.184476			0.0922382	+	0.995737i	$0.470598\pi$
$908$	−1.94261	+	3.36470i	−0.0644679	+	0.111662i
$909$	8.12526			0.269498
$910$		0			0
$911$	−14.5845			−0.483205			−0.241603	−	0.970375i	$-0.577673\pi$
$911$	−14.5845			−0.483205			−0.241603	+	0.970375i	$0.577673\pi$
$912$	−0.913986	+	1.58307i	−0.0302651	+	0.0524207i
$913$	−8.92937			−0.295519
$914$	−0.467579	−	0.809870i	−0.0154661	−	0.0267881i
$915$	10.7721	+	18.6579i	0.356116	+	0.616810i
$916$	−13.8769	+	24.0354i	−0.458504	+	0.794153i
$917$		0			0
$918$	3.17690			0.104853
$919$	−7.01646			−0.231452			−0.115726	−	0.993281i	$-0.536919\pi$
$919$	−7.01646			−0.231452			−0.115726	+	0.993281i	$0.536919\pi$
$920$	7.41272			0.244390
$921$	−36.2800			−1.19547
$922$	−4.61548	−	7.99424i	−0.152003	−	0.263276i
$923$	38.2450	+	23.9433i	1.25885	+	0.788105i
$924$		0			0
$925$	12.9586	+	22.4449i	0.426075	+	0.737984i
$926$	−8.36304	+	14.4852i	−0.274826	+	0.476013i
$927$	−3.11626	−	5.39751i	−0.102351	−	0.177278i
$928$	−18.8258	+	32.6072i	−0.617987	+	1.07039i
$929$	−59.6196			−1.95606			−0.978028	−	0.208475i	$-0.933150\pi$
$929$	−59.6196			−1.95606			−0.978028	+	0.208475i	$0.933150\pi$
$930$	−3.59160	+	6.22083i	−0.117773	+	0.203989i
$931$		0			0
$932$	−13.7485	+	23.8131i	−0.450347	+	0.780024i
$933$	3.30023	−	5.71617i	0.108045	−	0.187139i
$934$	4.31690			0.141253
$935$	0.511186	−	0.885399i	0.0167176	−	0.0289557i
$936$	−0.158758	+	4.43813i	−0.00518917	+	0.145065i
$937$	−14.5256			−0.474531			−0.237266	−	0.971445i	$-0.576251\pi$
$937$	−14.5256			−0.474531			−0.237266	+	0.971445i	$0.576251\pi$
$938$		0			0
$939$	19.2245	+	33.2978i	0.627367	+	1.08663i
$940$	28.2433			0.921196
$941$	−15.1230	+	26.1937i	−0.492994	+	0.853891i	−0.999967	−	0.00807086i	$-0.997431\pi$
$941$	−15.1230	+	26.1937i	−0.492994	+	0.853891i	0.506973	+	0.861962i	$0.330764\pi$
$942$	0.344839	+	0.597278i	0.0112355	+	0.0194604i
$943$	−9.51183			−0.309748
$944$	0.504951			0.0164348
$945$		0			0
$946$	1.35464	+	2.34630i	0.0440431	+	0.0762849i
$947$	−7.76388	+	13.4474i	−0.252292	+	0.436983i	−0.964157	−	0.265334i	$-0.914518\pi$
$947$	−7.76388	+	13.4474i	−0.252292	+	0.436983i	0.711864	+	0.702317i	$0.247851\pi$
$948$	−25.3090	+	43.8364i	−0.821997	+	1.42374i
$949$	11.2891	+	7.06756i	0.366460	+	0.229423i
$950$	0.377978	+	0.654677i	0.0122632	+	0.0212405i
$951$	−26.3202	−	45.5879i	−0.853490	−	1.47829i
$952$		0			0
$953$	−10.8527	+	18.7974i	−0.351554	+	0.608909i	−0.986522	−	0.163629i	$-0.947680\pi$
$953$	−10.8527	+	18.7974i	−0.351554	+	0.608909i	0.634968	+	0.772538i	$0.281013\pi$
$954$	−1.57924	−	2.73532i	−0.0511297	−	0.0885593i
$955$	−8.78195	−	15.2108i	−0.284177	−	0.492209i
$956$	2.64583	+	4.58271i	0.0855722	+	0.148215i
$957$	−3.77979	−	6.54679i	−0.122183	−	0.211628i
$958$	10.7997	−	18.7057i	0.348924	−	0.604353i
$959$		0			0
$960$	−1.42732	−	2.47220i	−0.0460667	−	0.0797899i
$961$	5.62802	+	9.74801i	0.181549	+	0.314452i
$962$	−16.9210	+	8.97864i	−0.545556	+	0.289483i
$963$	−1.08866	+	1.88561i	−0.0350816	+	0.0607630i
$964$	13.1940	−	22.8526i	0.424949	−	0.736033i
$965$	−10.5949	−	18.3508i	−0.341061	−	0.590735i
$966$		0			0
$967$	22.7524			0.731667			0.365833	−	0.930680i	$-0.380784\pi$
$967$	22.7524			0.731667			0.365833	+	0.930680i	$0.380784\pi$
$968$	−22.6534			−0.728107
$969$	0.521794	+	0.903774i	0.0167624	+	0.0290334i
$970$	6.68390	−	11.5769i	0.214607	−	0.371711i
$971$	−53.0128			−1.70126			−0.850632	−	0.525762i	$-0.823780\pi$
$971$	−53.0128			−1.70126			−0.850632	+	0.525762i	$0.823780\pi$
$972$	4.94660	+	8.56776i	0.158662	+	0.274811i
$973$		0			0
$974$	−14.0156			−0.449087
$975$	−16.3546	−	10.2388i	−0.523767	−	0.327905i
$976$	−8.09776	+	14.0257i	−0.259203	+	0.448953i
$977$	−4.64588			−0.148635			−0.0743174	−	0.997235i	$-0.523678\pi$
$977$	−4.64588			−0.148635			−0.0743174	+	0.997235i	$0.523678\pi$
$978$	6.40889	−	11.1005i	0.204934	−	0.354956i
$979$	−0.722173	+	1.25084i	−0.0230807	+	0.0399770i
$980$		0			0
$981$	2.37964	−	4.12165i	0.0759760	−	0.131594i
$982$	−3.52027			−0.112336
$983$	−3.91896	+	6.78783i	−0.124995	+	0.216498i	−0.921731	−	0.387830i	$-0.873225\pi$
$983$	−3.91896	+	6.78783i	−0.124995	+	0.216498i	0.796736	+	0.604328i	$0.206558\pi$
$984$	−8.07256	−	13.9821i	−0.257344	−	0.445733i
$985$	−5.13499	+	8.89406i	−0.163614	+	0.283388i
$986$	2.39043	+	4.14034i	0.0761267	+	0.131855i
$987$		0			0
$988$	2.44270	−	1.29615i	0.0777127	−	0.0412359i
$989$	−9.54167	−	16.5267i	−0.303408	−	0.525517i
$990$	−0.287239			−0.00912904
$991$	−17.7501			−0.563852			−0.281926	−	0.959436i	$-0.590973\pi$
$991$	−17.7501			−0.563852			−0.281926	+	0.959436i	$0.590973\pi$
$992$	−24.2783			−0.770838
$993$	17.6772			0.560970
$994$		0			0
$995$	−2.63300	+	4.56049i	−0.0834717	+	0.144577i
$996$	24.2405	+	41.9857i	0.768089	+	1.33037i
$997$	17.6602	+	30.5883i	0.559303	+	0.968741i	0.997555	+	0.0698887i	$0.0222644\pi$
$997$	17.6602	+	30.5883i	0.559303	+	0.968741i	−0.438252	+	0.898852i	$0.644402\pi$
$998$	1.45860			0.0461711
$999$	−20.9791	+	36.3369i	−0.663750	+	1.14965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.m.263.3		16
7.2	even	3		637.2.h.m.471.6		16
7.3	odd	6		637.2.f.l.393.3	yes	16
7.4	even	3		637.2.f.l.393.4	yes	16
7.5	odd	6		637.2.h.m.471.5		16
7.6	odd	2	inner	637.2.g.m.263.4		16
13.9	even	3		637.2.h.m.165.6		16
91.3	odd	6		8281.2.a.ci.1.6		8
91.9	even	3	inner	637.2.g.m.373.3		16
91.10	odd	6		8281.2.a.cl.1.4		8
91.48	odd	6		637.2.h.m.165.5		16
91.61	odd	6	inner	637.2.g.m.373.4		16
91.74	even	3		637.2.f.l.295.4	yes	16
91.81	even	3		8281.2.a.ci.1.5		8
91.87	odd	6		637.2.f.l.295.3	✓	16
91.88	even	6		8281.2.a.cl.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.3	✓	16	91.87	odd	6
637.2.f.l.295.4	yes	16	91.74	even	3
637.2.f.l.393.3	yes	16	7.3	odd	6
637.2.f.l.393.4	yes	16	7.4	even	3
637.2.g.m.263.3		16	1.1	even	1	trivial
637.2.g.m.263.4		16	7.6	odd	2	inner
637.2.g.m.373.3		16	91.9	even	3	inner
637.2.g.m.373.4		16	91.61	odd	6	inner
637.2.h.m.165.5		16	91.48	odd	6
637.2.h.m.165.6		16	13.9	even	3
637.2.h.m.471.5		16	7.5	odd	6
637.2.h.m.471.6		16	7.2	even	3
8281.2.a.ci.1.5		8	91.81	even	3
8281.2.a.ci.1.6		8	91.3	odd	6
8281.2.a.cl.1.3		8	91.88	even	6
8281.2.a.cl.1.4		8	91.10	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.289905 - 0.502131i) q^{2} -1.89204 q^{3} +(0.831910 + 1.44091i) q^{4} +(-0.736809 - 1.27619i) q^{5} +(-0.548512 + 0.950050i) q^{6} +2.12432 q^{8} +0.579810 q^{9} +O(q^{10})\)	\(q+(0.289905 - 0.502131i) q^{2} -1.89204 q^{3} +(0.831910 + 1.44091i) q^{4} +(-0.736809 - 1.27619i) q^{5} +(-0.548512 + 0.950050i) q^{6} +2.12432 q^{8} +0.579810 q^{9} -0.854419 q^{10} +0.579810 q^{11} +(-1.57401 - 2.72626i) q^{12} +(-0.128893 + 3.60325i) q^{13} +(1.39407 + 2.41460i) q^{15} +(-1.04797 + 1.81513i) q^{16} +(0.598285 + 1.03626i) q^{17} +(0.168090 - 0.291141i) q^{18} -0.460958 q^{19} +(1.22592 - 2.12335i) q^{20} +(0.168090 - 0.291141i) q^{22} +(-1.18398 + 2.05071i) q^{23} -4.01930 q^{24} +(1.41423 - 2.44951i) q^{25} +(1.77193 + 1.10932i) q^{26} +4.57909 q^{27} +(3.44550 + 5.96777i) q^{29} +1.61659 q^{30} +(-2.22171 + 3.84811i) q^{31} +(2.73194 + 4.73187i) q^{32} -1.09702 q^{33} +0.693783 q^{34} +(0.482350 + 0.835455i) q^{36} +(-4.58150 + 7.93540i) q^{37} +(-0.133634 + 0.231461i) q^{38} +(0.243871 - 6.81748i) q^{39} +(-1.56522 - 2.71104i) q^{40} +(2.00845 + 3.47874i) q^{41} +(-4.02951 + 6.97931i) q^{43} +(0.482350 + 0.835455i) q^{44} +(-0.427209 - 0.739948i) q^{45} +(0.686481 + 1.18902i) q^{46} +(5.75964 + 9.97598i) q^{47} +(1.98280 - 3.43430i) q^{48} +(-0.819983 - 1.42025i) q^{50} +(-1.13198 - 1.96064i) q^{51} +(-5.29918 + 2.81185i) q^{52} +(4.69760 - 8.13647i) q^{53} +(1.32750 - 2.29930i) q^{54} +(-0.427209 - 0.739948i) q^{55} +0.872150 q^{57} +3.99547 q^{58} +(-0.120459 - 0.208642i) q^{59} +(-2.31948 + 4.01746i) q^{60} +7.72710 q^{61} +(1.28817 + 2.23118i) q^{62} -1.02385 q^{64} +(4.69340 - 2.49041i) q^{65} +(-0.318033 + 0.550849i) q^{66} -1.44857 q^{67} +(-0.995438 + 1.72415i) q^{68} +(2.24013 - 3.88001i) q^{69} +(6.25725 - 10.8379i) q^{71} +1.23170 q^{72} +(1.84701 - 3.19911i) q^{73} +(2.65640 + 4.60103i) q^{74} +(-2.67577 + 4.63457i) q^{75} +(-0.383476 - 0.664199i) q^{76} +(-3.35257 - 2.09888i) q^{78} +(-8.03967 - 13.9251i) q^{79} +3.08861 q^{80} -10.4033 q^{81} +2.32904 q^{82} -15.4005 q^{83} +(0.881643 - 1.52705i) q^{85} +(2.33635 + 4.04668i) q^{86} +(-6.51901 - 11.2913i) q^{87} +1.23170 q^{88} +(-1.24553 + 2.15733i) q^{89} -0.495401 q^{90} -3.93984 q^{92} +(4.20356 - 7.28078i) q^{93} +6.67900 q^{94} +(0.339638 + 0.588270i) q^{95} +(-5.16894 - 8.95287i) q^{96} +(-7.82275 + 13.5494i) q^{97} +0.336180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} + 8 q^{9} + 8 q^{11} - 8 q^{15} - 4 q^{16} + 28 q^{18} + 28 q^{22} + 12 q^{23} + 12 q^{25} + 8 q^{29} - 56 q^{30} + 4 q^{36} - 8 q^{37} - 16 q^{39} + 32 q^{43} + 4 q^{44} - 4 q^{46} + 36 q^{50} + 44 q^{51} + 4 q^{53} - 96 q^{57} + 96 q^{58} - 64 q^{60} - 64 q^{64} + 52 q^{65} - 40 q^{67} + 8 q^{71} - 56 q^{72} + 76 q^{74} + 28 q^{78} + 4 q^{79} - 112 q^{81} + 36 q^{85} - 4 q^{86} - 56 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 + 8 * q^9 + 8 * q^11 - 8 * q^15 - 4 * q^16 + 28 * q^18 + 28 * q^22 + 12 * q^23 + 12 * q^25 + 8 * q^29 - 56 * q^30 + 4 * q^36 - 8 * q^37 - 16 * q^39 + 32 * q^43 + 4 * q^44 - 4 * q^46 + 36 * q^50 + 44 * q^51 + 4 * q^53 - 96 * q^57 + 96 * q^58 - 64 * q^60 - 64 * q^64 + 52 * q^65 - 40 * q^67 + 8 * q^71 - 56 * q^72 + 76 * q^74 + 28 * q^78 + 4 * q^79 - 112 * q^81 + 36 * q^85 - 4 * q^86 - 56 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Introduction

L-functions

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