LMFDB - Embedded newform 637.2.f.l.295.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$16$
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			295.4
Root			$1.04641 + 1.81243i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.l.393.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.289905 - 0.502131i) q^{2} +(0.946019 - 1.63855i) q^{3} +(0.831910 + 1.44091i) q^{4} +1.47362 q^{5} +(-0.548512 - 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 - 0.502131i) q^{9} +O(q^{10})$	\(q+(0.289905 - 0.502131i) q^{2} +(0.946019 - 1.63855i) q^{3} +(0.831910 + 1.44091i) q^{4} +1.47362 q^{5} +(-0.548512 - 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 - 0.502131i) q^{9} +(0.427209 - 0.739948i) q^{10} +(-0.289905 + 0.502131i) q^{11} +3.14801 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} -0.336180 q^{18} +(0.230479 + 0.399201i) q^{19} +(1.22592 + 2.12335i) q^{20} +(0.168090 + 0.291141i) q^{22} +(-1.18398 + 2.05071i) q^{23} +(2.00965 - 3.48081i) q^{24} -2.82845 q^{25} +(-1.84667 - 0.979879i) q^{26} +4.57909 q^{27} +(3.44550 - 5.96777i) q^{29} +(-0.808297 - 1.40001i) q^{30} +4.44342 q^{31} +(2.73194 + 4.73187i) q^{32} +(0.548512 + 0.950050i) q^{33} +0.693783 q^{34} +(0.482350 - 0.835455i) q^{36} +(-4.58150 + 7.93540i) q^{37} +0.267268 q^{38} +(-6.02605 - 3.19754i) q^{39} +3.13044 q^{40} +(2.00845 - 3.47874i) q^{41} +(-4.02951 - 6.97931i) q^{43} -0.964700 q^{44} +(-0.427209 - 0.739948i) q^{45} +(0.686481 + 1.18902i) q^{46} -11.5193 q^{47} +(1.98280 + 3.43430i) q^{48} +(-0.819983 + 1.42025i) q^{50} +2.26396 q^{51} +(5.08473 - 3.18330i) q^{52} -9.39519 q^{53} +(1.32750 - 2.29930i) q^{54} +(-0.427209 + 0.739948i) q^{55} +0.872150 q^{57} +(-1.99773 - 3.46018i) q^{58} +(-0.120459 - 0.208642i) q^{59} +4.63896 q^{60} +(-3.86355 - 6.69187i) q^{61} +(1.28817 - 2.23118i) q^{62} -1.02385 q^{64} +(-0.189939 - 5.30981i) q^{65} +0.636066 q^{66} +(0.724287 - 1.25450i) q^{67} +(-0.995438 + 1.72415i) q^{68} +(2.24013 + 3.88001i) q^{69} +(6.25725 + 10.8379i) q^{71} +(-0.615852 - 1.06669i) q^{72} -3.69401 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} +16.0793 q^{79} +(-1.54430 + 2.67481i) q^{80} +(5.20163 - 9.00948i) q^{81} +(-1.16452 - 2.01701i) q^{82} -15.4005 q^{83} +(0.881643 + 1.52705i) q^{85} -4.67270 q^{86} +(-6.51901 - 11.2913i) q^{87} +(-0.615852 + 1.06669i) q^{88} +(-1.24553 + 2.15733i) q^{89} -0.495401 q^{90} -3.93984 q^{92} +(4.20356 - 7.28078i) q^{93} +(-3.33950 + 5.78418i) q^{94} +(0.339638 + 0.588270i) q^{95} +10.3379 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} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9	$ 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 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 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 4 * q^16 - 56 * q^18 + 28 * q^22 + 12 * q^23 - 24 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 - 8 * q^37 - 4 * q^39 + 32 * q^43 - 8 * q^44 - 4 * q^46 + 36 * q^50 - 88 * q^51 - 8 * q^53 - 96 * q^57 - 48 * q^58 + 128 * q^60 - 64 * q^64 + 16 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 + 76 * q^74 + 28 * q^78 - 8 * q^79 + 56 * q^81 + 36 * q^85 + 8 * q^86 + 28 * 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.289905	−	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	$0.100949\pi$
$3$	0.946019	−	1.63855i	0.546185	−	0.946019i	−0.452347	−	0.891842i	$-0.649413\pi$
$3$	0.946019	−	1.63855i	0.546185	−	0.946019i	0.998531	−	0.0541772i	$-0.0172536\pi$
$4$	0.831910	+	1.44091i	0.415955	+	0.720455i
$5$	1.47362			0.659022			0.329511	−	0.944152i	$-0.393116\pi$
$5$	1.47362			0.659022			0.329511	+	0.944152i	$0.393116\pi$
$6$	−0.548512	−	0.950050i	−0.223929	−	0.387856i
$7$		0			0
$7$		0			0
$8$	2.12432			0.751061
$9$	−0.289905	−	0.502131i	−0.0966351	−	0.167377i
$10$	0.427209	−	0.739948i	0.135095	−	0.233992i
$11$	−0.289905	+	0.502131i	−0.0874097	+	0.151398i	−0.906415	−	0.422387i	$-0.861192\pi$
$11$	−0.289905	+	0.502131i	−0.0874097	+	0.151398i	0.819006	+	0.573785i	$0.194526\pi$
$12$	3.14801			0.908753
$13$	−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	$0.786981\pi$
$18$	−0.336180			−0.0792384
$19$	0.230479	+	0.399201i	0.0528755	+	0.0915831i	0.891252	−	0.453509i	$-0.149828\pi$
$19$	0.230479	+	0.399201i	0.0528755	+	0.0915831i	−0.838376	+	0.545092i	$0.816495\pi$
$20$	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	$0.246071\pi$
$24$	2.00965	−	3.48081i	0.410218	−	0.710518i
$25$	−2.82845			−0.565690
$26$	−1.84667	−	0.979879i	−0.362161	−	0.192170i
$27$	4.57909			0.881247
$28$		0			0
$29$	3.44550	−	5.96777i	0.639813	−	1.10819i	−0.345661	−	0.938359i	$-0.612345\pi$
$29$	3.44550	−	5.96777i	0.639813	−	1.10819i	0.985474	−	0.169828i	$-0.0543214\pi$
$30$	−0.808297	−	1.40001i	−0.147574	−	0.255606i
$31$	4.44342			0.798061			0.399031	−	0.916938i	$-0.369347\pi$
$31$	4.44342			0.798061			0.399031	+	0.916938i	$0.369347\pi$
$32$	2.73194	+	4.73187i	0.482944	+	0.836484i
$33$	0.548512	+	0.950050i	0.0954837	+	0.165383i
$34$	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	$0.895179\pi$
$38$	0.267268			0.0433566
$39$	−6.02605	−	3.19754i	−0.964940	−	0.512017i
$40$	3.13044			0.494965
$41$	2.00845	−	3.47874i	0.313667	−	0.543288i	−0.665486	−	0.746410i	$-0.731776\pi$
$41$	2.00845	−	3.47874i	0.313667	−	0.543288i	0.979153	+	0.203123i	$0.0651090\pi$
$42$		0			0
$43$	−4.02951	−	6.97931i	−0.614494	−	1.06433i	−0.990473	−	0.137706i	$-0.956027\pi$
$43$	−4.02951	−	6.97931i	−0.614494	−	1.06433i	0.375979	−	0.926628i	$-0.377306\pi$
$44$	−0.964700			−0.145434
$45$	−0.427209	−	0.739948i	−0.0636846	−	0.110305i
$46$	0.686481	+	1.18902i	0.101216	+	0.175312i
$47$	−11.5193			−1.68026			−0.840129	−	0.542386i	$-0.817521\pi$
$47$	−11.5193			−1.68026			−0.840129	+	0.542386i	$0.817521\pi$
$48$	1.98280	+	3.43430i	0.286192	+	0.495699i
$49$		0			0
$50$	−0.819983	+	1.42025i	−0.115963	+	0.200854i
$51$	2.26396			0.317017
$52$	5.08473	−	3.18330i	0.705125	−	0.441444i
$53$	−9.39519			−1.29053			−0.645264	−	0.763959i	$-0.723253\pi$
$53$	−9.39519			−1.29053			−0.645264	+	0.763959i	$0.723253\pi$
$54$	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
$58$	−1.99773	−	3.46018i	−0.262315	−	0.454344i
$59$	−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	$0.838325\pi$
$60$	4.63896			0.598888
$61$	−3.86355	−	6.69187i	−0.494677	−	0.856806i	0.505304	−	0.862941i	$-0.331380\pi$
$61$	−3.86355	−	6.69187i	−0.494677	−	0.856806i	−0.999981	+	0.00613544i	$0.998047\pi$
$62$	1.28817	−	2.23118i	0.163598	−	0.283360i
$63$		0			0
$64$	−1.02385			−0.127982
$65$	−0.189939	−	5.30981i	−0.0235590	−	0.658600i
$66$	0.636066			0.0782943
$67$	0.724287	−	1.25450i	0.0884857	−	0.153262i	−0.818385	−	0.574670i	$-0.805131\pi$
$67$	0.724287	−	1.25450i	0.0884857	−	0.153262i	0.906871	+	0.421408i	$0.138464\pi$
$68$	−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	0.951308	+	0.308241i	$0.0997405\pi$
$71$	6.25725	+	10.8379i	0.742599	+	1.28622i	−0.208709	+	0.977978i	$0.566926\pi$
$72$	−0.615852	−	1.06669i	−0.0725788	−	0.125710i
$73$	−3.69401			−0.432352			−0.216176	−	0.976354i	$-0.569358\pi$
$73$	−3.69401			−0.432352			−0.216176	+	0.976354i	$0.569358\pi$
$74$	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
$79$	16.0793			1.80907			0.904533	−	0.426403i	$-0.140219\pi$
$79$	16.0793			1.80907			0.904533	+	0.426403i	$0.140219\pi$
$80$	−1.54430	+	2.67481i	−0.172658	+	0.299053i
$81$	5.20163	−	9.00948i	0.577958	−	1.00105i
$82$	−1.16452	−	2.01701i	−0.128600	−	0.222741i
$83$	−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
$86$	−4.67270			−0.503870
$87$	−6.51901	−	11.2913i	−0.698911	−	1.21055i
$88$	−0.615852	+	1.06669i	−0.0656500	+	0.113709i
$89$	−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
$94$	−3.33950	+	5.78418i	−0.344443	+	0.596593i
$95$	0.339638	+	0.588270i	0.0348461	+	0.0603552i
$96$	10.3379			1.05511
$97$	−7.82275	−	13.5494i	−0.794280	−	1.37573i	−0.923295	−	0.384091i	$-0.874515\pi$
$97$	−7.82275	−	13.5494i	−0.794280	−	1.37573i	0.129015	−	0.991643i	$-0.458818\pi$
$98$		0			0
$99$	0.336180			0.0337874
$100$	−2.35302	−	4.07555i	−0.235302	−	0.407555i
$101$	−7.00682	+	12.1362i	−0.697205	+	1.20759i	0.272227	+	0.962233i	$0.412240\pi$
$101$	−7.00682	+	12.1362i	−0.697205	+	1.20759i	−0.969432	+	0.245361i	$0.921093\pi$
$102$	0.656332	−	1.13680i	0.0649866	−	0.112560i
$103$	10.7492			1.05915			0.529576	−	0.848262i	$-0.322351\pi$
$103$	10.7492			1.05915			0.529576	+	0.848262i	$0.322351\pi$
$104$	−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
$109$	−8.20833			−0.786215			−0.393108	−	0.919492i	$-0.628600\pi$
$109$	−8.20833			−0.786215			−0.393108	+	0.919492i	$0.628600\pi$
$110$	0.247700	+	0.429030i	0.0236173	+	0.0409064i
$111$	8.66838	+	15.0141i	0.822766	+	1.42507i
$112$		0			0
$113$	3.90423	+	6.76233i	0.367279	+	0.636146i	0.989139	−	0.146982i	$-0.0469560\pi$
$113$	3.90423	+	6.76233i	0.367279	+	0.636146i	−0.621860	+	0.783129i	$0.713623\pi$
$114$	0.252841	−	0.437933i	0.0236807	−	0.0410162i
$115$	−1.74473	+	3.02196i	−0.162697	+	0.281799i
$116$	11.4654			1.06453
$117$	−1.77193	+	1.10932i	−0.163815	+	0.102557i
$118$	−0.139687			−0.0128593
$119$		0			0
$120$	2.96145	−	5.12939i	0.270342	−	0.468247i
$121$	5.33191	+	9.23514i	0.484719	+	0.839558i
$122$	−4.48026			−0.405623
$123$	−3.80007	−	6.58191i	−0.342641	−	0.593471i
$124$	3.69652	+	6.40257i	0.331958	+	0.574967i
$125$	−11.5361			−1.03182
$126$		0			0
$127$	0.469682	−	0.813513i	0.0416775	−	0.0721876i	−0.844434	−	0.535659i	$-0.820063\pi$
$127$	0.469682	−	0.813513i	0.0416775	−	0.0721876i	0.886112	+	0.463472i	$0.153396\pi$
$128$	−5.76071	+	9.97784i	−0.509179	+	0.881925i
$129$	−15.2480			−1.34251
$130$	−2.72128	−	1.44397i	−0.238672	−	0.126644i
$131$	−1.13717			−0.0993546			−0.0496773	−	0.998765i	$-0.515819\pi$
$131$	−1.13717			−0.0993546			−0.0496773	+	0.998765i	$0.515819\pi$
$132$	−0.912625	+	1.58071i	−0.0794338	+	0.137583i
$133$		0			0
$134$	−0.419949	−	0.727373i	−0.0362781	−	0.0628355i
$135$	6.74783			0.580761
$136$	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	$0.713006\pi$
$138$	2.59770			0.221131
$139$	7.27709	+	12.6043i	0.617235	+	1.06908i	0.989988	+	0.141151i	$0.0450804\pi$
$139$	7.27709	+	12.6043i	0.617235	+	1.06908i	−0.372753	+	0.927930i	$0.621586\pi$
$140$		0			0
$141$	−10.8975	+	18.8749i	−0.917731	+	1.58956i
$142$	7.25604			0.608913
$143$	1.84667	+	0.979879i	0.154426	+	0.0819416i
$144$	1.21525			0.101270
$145$	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
$149$	−6.69011	−	11.5876i	−0.548075	−	0.949294i	−0.998406	−	0.0564323i	$-0.982027\pi$
$149$	−6.69011	−	11.5876i	−0.548075	−	0.949294i	0.450331	−	0.892861i	$-0.351306\pi$
$150$	1.55144	+	2.68717i	0.126675	+	0.219407i
$151$	16.1392			1.31339			0.656693	−	0.754158i	$-0.271955\pi$
$151$	16.1392			1.31339			0.656693	+	0.754158i	$0.271955\pi$
$152$	0.489611	+	0.848032i	0.0397127	+	0.0687845i
$153$	0.346892	−	0.600834i	0.0280445	−	0.0485745i
$154$		0			0
$155$	6.54790			0.525940
$156$	−0.405757	−	11.3431i	−0.0324866	−	0.908172i
$157$	−0.628681			−0.0501742			−0.0250871	−	0.999685i	$-0.507986\pi$
$157$	−0.628681			−0.0501742			−0.0250871	+	0.999685i	$0.507986\pi$
$158$	4.66148	−	8.07393i	0.370848	−	0.642327i
$159$	−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
$163$	5.84207	+	10.1188i	0.457586	+	0.792563i	0.998833	−	0.0483011i	$-0.0153807\pi$
$163$	5.84207	+	10.1188i	0.457586	+	0.792563i	−0.541246	+	0.840864i	$0.682047\pi$
$164$	6.68340			0.521886
$165$	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	0.0245803	+	0.999698i	$0.492175\pi$
$167$	−11.0293	+	19.1033i	−0.853474	+	1.47826i	−0.878054	+	0.478562i	$0.841158\pi$
$168$		0			0
$169$	−12.9668	+	0.928867i	−0.997444	+	0.0714513i
$170$	1.02237			0.0784123
$171$	0.133634	−	0.231461i	0.0102193	−	0.0177003i
$172$	6.70437	−	11.6123i	0.511204	−	0.885431i
$173$	−5.69534	−	9.86463i	−0.433009	−	0.749994i	0.564122	−	0.825692i	$-0.309215\pi$
$173$	−5.69534	−	9.86463i	−0.433009	−	0.749994i	−0.997131	+	0.0756980i	$0.975881\pi$
$174$	−7.55958			−0.573090
$175$		0			0
$176$	−0.607623	−	1.05243i	−0.0458013	−	0.0793302i
$177$	−0.455828			−0.0342621
$178$	0.722173	+	1.25084i	0.0541292	+	0.0937544i
$179$	1.73621	−	3.00721i	0.129771	−	0.224769i	−0.793817	−	0.608157i	$-0.791909\pi$
$179$	1.73621	−	3.00721i	0.129771	−	0.224769i	0.923588	+	0.383387i	$0.125243\pi$
$180$	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
$185$	−6.75138	+	11.6937i	−0.496372	+	0.859741i
$186$	−2.43727	−	4.22147i	−0.178709	−	0.309533i
$187$	−0.693783			−0.0507345
$188$	−9.58300	−	16.5982i	−0.698912	−	1.21055i
$189$		0			0
$190$	0.393851			0.0285730
$191$	−5.95945	−	10.3221i	−0.431211	−	0.746879i	0.565767	−	0.824565i	$-0.308580\pi$
$191$	−5.95945	−	10.3221i	−0.431211	−	0.746879i	−0.996978	+	0.0776864i	$0.975247\pi$
$192$	−0.968585	+	1.67764i	−0.0699016	+	0.121073i
$193$	−7.18970	+	12.4529i	−0.517526	+	0.896381i	0.482267	+	0.876024i	$0.339814\pi$
$193$	−7.18970	+	12.4529i	−0.517526	+	0.896381i	−0.999793	+	0.0203567i	$0.993520\pi$
$194$	−9.07143			−0.651290
$195$	−8.88009	−	4.71195i	−0.635916	−	0.337430i
$196$		0			0
$197$	−3.48462	+	6.03553i	−0.248269	+	0.430014i	−0.963046	−	0.269339i	$-0.913195\pi$
$197$	−3.48462	+	6.03553i	−0.248269	+	0.430014i	0.714777	+	0.699353i	$0.246528\pi$
$198$	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	$0.873759\pi$
$200$	−6.00854			−0.424868
$201$	−1.37038	−	2.37357i	−0.0966591	−	0.167418i
$202$	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
$206$	3.11626	−	5.39751i	0.217120	−	0.376062i
$207$	1.37296			0.0954275
$208$	6.67545	+	3.54213i	0.462859	+	0.245603i
$209$	−0.267268			−0.0184873
$210$		0			0
$211$	7.05694	−	12.2230i	0.485820	−	0.841464i	−0.514048	−	0.857762i	$-0.671855\pi$
$211$	7.05694	−	12.2230i	0.485820	−	0.841464i	0.999867	+	0.0162974i	$0.00518784\pi$
$212$	−7.81595	−	13.5376i	−0.536802	−	0.929768i
$213$	23.6779			1.62238
$214$	1.08866	+	1.88561i	0.0744192	+	0.128898i
$215$	−5.93795	−	10.2848i	−0.404965	−	0.701420i
$216$	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
$220$	−1.42160			−0.0958442
$221$	3.65678	−	2.28933i	0.245982	−	0.153997i
$222$	10.0520			0.674649
$223$	0.454565	−	0.787329i	0.0304399	−	0.0527235i	−0.850404	−	0.526130i	$-0.823643\pi$
$223$	0.454565	−	0.787329i	0.0304399	−	0.0527235i	0.880844	+	0.473407i	$0.156976\pi$
$224$		0			0
$225$	0.819983	+	1.42025i	0.0546655	+	0.0946835i
$226$	4.52743			0.301160
$227$	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
$229$	−16.6807			−1.10229			−0.551147	−	0.834408i	$-0.685810\pi$
$229$	−16.6807			−1.10229			−0.551147	+	0.834408i	$0.685810\pi$
$230$	1.01161	+	1.75216i	0.0667036	+	0.115534i
$231$		0			0
$232$	7.31934	−	12.6775i	0.480538	−	0.832317i
$233$	−16.5264			−1.08268			−0.541341	−	0.840803i	$-0.682083\pi$
$233$	−16.5264			−1.08268			−0.541341	+	0.840803i	$0.682083\pi$
$234$	0.0433313	+	1.21134i	0.00283266	+	0.0791878i
$235$	−16.9750			−1.10733
$236$	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	$0.467200\pi$
$240$	2.92188	+	5.06085i	0.188607	+	0.326676i
$241$	−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	$-0.337322\pi$
$242$	6.18299			0.397458
$243$	−2.97304	−	5.14945i	−0.190720	−	0.330338i
$244$	6.42825	−	11.1341i	0.411527	−	0.712785i
$245$		0			0
$246$	−4.40664			−0.280957
$247$	1.40871	−	0.881927i	0.0896343	−	0.0561157i
$248$	9.43925			0.599393
$249$	−14.5692	+	25.2345i	−0.923284	+	1.59917i
$250$	−3.34439	+	5.79265i	−0.211518	+	0.366359i
$251$	1.24788	+	2.16139i	0.0787654	+	0.136426i	0.902718	−	0.430234i	$-0.141569\pi$
$251$	1.24788	+	2.16139i	0.0787654	+	0.136426i	−0.823952	+	0.566659i	$0.808236\pi$
$252$		0			0
$253$	−0.686481	−	1.18902i	−0.0431587	−	0.0747531i
$254$	−0.272326	−	0.471683i	−0.0170873	−	0.0295960i
$255$	3.33620			0.208921
$256$	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
$261$	−3.99547			−0.247313
$262$	−0.329670	+	0.571006i	−0.0203671	+	0.0352768i
$263$	15.6749	−	27.1498i	0.966558	−	1.67413i	0.261188	−	0.965288i	$-0.415886\pi$
$263$	15.6749	−	27.1498i	0.966558	−	1.67413i	0.705370	−	0.708839i	$-0.250781\pi$
$264$	1.16522	+	2.01821i	0.0717140	+	0.124212i
$265$	−13.8449			−0.850486
$266$		0			0
$267$	2.35660	+	4.08174i	0.144221	+	0.249799i
$268$	2.41017			0.147224
$269$	−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	$-0.389415\pi$
$270$	1.95623	−	3.38829i	0.119052	−	0.206205i
$271$	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
$276$	−3.72717	+	6.45565i	−0.224349	+	0.388584i
$277$	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	$0.689537\pi$
$278$	8.43866			0.506117
$279$	−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	$0.199029\pi$
$282$	6.31846	+	10.9439i	0.376259	+	0.651699i
$283$	4.28791	−	7.42688i	0.254890	−	0.441482i	−0.709976	−	0.704226i	$-0.751294\pi$
$283$	4.28791	−	7.42688i	0.254890	−	0.441482i	0.964866	+	0.262744i	$0.0846274\pi$
$284$	−10.4109	+	18.0323i	−0.617775	+	1.07002i
$285$	1.28522			0.0761296
$286$	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
$291$	−29.6019			−1.73529
$292$	−3.07309	−	5.32274i	−0.179839	−	0.311490i
$293$	−5.24356	−	9.08212i	−0.306332	−	0.530583i	0.671225	−	0.741254i	$-0.265768\pi$
$293$	−5.24356	−	9.08212i	−0.306332	−	0.530583i	−0.977557	+	0.210671i	$0.932435\pi$
$294$		0			0
$295$	−0.177511	−	0.307458i	−0.0103351	−	0.0179009i
$296$	−9.73258	+	16.8573i	−0.565695	+	0.979812i
$297$	−1.32750	+	2.29930i	−0.0770295	+	0.133419i
$298$	−7.75799			−0.449408
$299$	7.54181	+	4.00183i	0.436154	+	0.231432i
$300$	−8.90400			−0.514073
$301$		0			0
$302$	4.67882	−	8.10396i	0.269236	−	0.466331i
$303$	13.2572	+	22.9621i	0.761605	+	1.31914i
$304$	−0.966139			−0.0554118
$305$	−5.69340	−	9.86125i	−0.326003	−	0.564654i
$306$	−0.201131	−	0.348370i	−0.0114979	−	0.0199150i
$307$	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
$311$	3.48854			0.197817			0.0989086	−	0.995097i	$-0.468465\pi$
$311$	3.48854			0.197817			0.0989086	+	0.995097i	$0.468465\pi$
$312$	−12.8013	−	6.79261i	−0.724729	−	0.384556i
$313$	20.3214			1.14864			0.574318	−	0.818632i	$-0.305267\pi$
$313$	20.3214			1.14864			0.574318	+	0.818632i	$0.305267\pi$
$314$	−0.182258	+	0.315680i	−0.0102854	+	0.0178148i
$315$		0			0
$316$	13.3766	+	23.1689i	0.752490	+	1.30335i
$317$	−27.8220			−1.56264			−0.781320	−	0.624131i	$-0.785453\pi$
$317$	−27.8220			−1.56264			−0.781320	+	0.624131i	$0.785453\pi$
$318$	5.15337	+	8.92591i	0.288987	+	0.500540i
$319$	1.99773	+	3.46018i	0.111852	+	0.193733i
$320$	−1.50877			−0.0843427
$321$	3.55252	+	6.15314i	0.198282	+	0.343435i
$322$		0			0
$323$	−0.275784	+	0.477672i	−0.0153450	+	0.0265784i
$324$	17.3091			0.961619
$325$	0.364568	+	10.1916i	0.0202226	+	0.565329i
$326$	6.77459			0.375210
$327$	−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
$331$	4.67148	+	8.09123i	0.256768	+	0.444734i	0.965374	−	0.260869i	$-0.0840092\pi$
$331$	4.67148	+	8.09123i	0.256768	+	0.444734i	−0.708607	+	0.705604i	$0.750676\pi$
$332$	−12.8118	−	22.1907i	−0.703141	−	1.21788i
$333$	5.31281			0.291140
$334$	6.39491	+	11.0763i	0.349914	+	0.606069i
$335$	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	$0.285418\pi$
$338$	−3.29272	+	6.78030i	−0.179100	+	0.368800i
$339$	14.7739			0.802409
$340$	−1.46689	+	2.54074i	−0.0795535	+	0.137791i
$341$	−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
$345$	3.30109	+	5.71766i	0.177725	+	0.307828i
$346$	−6.60444			−0.355057
$347$	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	−0.994636	−	0.103435i	$-0.967017\pi$
$349$	−7.61723	+	13.1934i	−0.407741	+	0.706228i	0.586895	+	0.809663i	$0.300350\pi$
$350$		0			0
$351$	−0.590213	−	16.4996i	−0.0315033	−	0.880683i
$352$	−3.16802			−0.168856
$353$	11.2044	−	19.4066i	0.596352	−	1.03291i	−0.397003	−	0.917817i	$-0.629950\pi$
$353$	11.2044	−	19.4066i	0.596352	−	1.03291i	0.993355	−	0.115094i	$-0.0367170\pi$
$354$	−0.132147	+	0.228885i	−0.00702353	+	0.0121651i
$355$	9.22079	+	15.9709i	0.489389	+	0.847646i
$356$	−4.14468			−0.219668
$357$		0			0
$358$	−1.00667	−	1.74361i	−0.0532044	−	0.0921528i
$359$	16.0385			0.846482			0.423241	−	0.906017i	$-0.360892\pi$
$359$	16.0385			0.846482			0.423241	+	0.906017i	$0.360892\pi$
$360$	−0.907530	−	1.57189i	−0.0478310	−	0.0828457i
$361$	9.39376	−	16.2705i	0.494408	−	0.856340i
$362$	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
$367$	3.45002	−	5.97561i	0.180090	−	0.311924i	−0.761821	−	0.647787i	$-0.775695\pi$
$367$	3.45002	−	5.97561i	0.180090	−	0.311924i	0.941911	+	0.335863i	$0.109028\pi$
$368$	−2.48154	−	4.29815i	−0.129359	−	0.224057i
$369$	−2.32904			−0.121245
$370$	3.91452	+	6.78015i	0.203506	+	0.352483i
$371$		0			0
$372$	13.9879			0.725240
$373$	−3.84264	−	6.65566i	−0.198965	−	0.344617i	0.749228	−	0.662312i	$-0.230425\pi$
$373$	−3.84264	−	6.65566i	−0.198965	−	0.344617i	−0.948193	+	0.317695i	$0.897091\pi$
$374$	−0.201131	+	0.348370i	−0.0104003	+	0.0180138i
$375$	−10.9134	+	18.9026i	−0.563566	+	0.976125i
$376$	−24.4706			−1.26198
$377$	−21.9475	−	11.6458i	−1.13035	−	0.599788i
$378$		0			0
$379$	12.5817	−	21.7922i	0.646281	−	1.11939i	−0.337723	−	0.941245i	$-0.609657\pi$
$379$	12.5817	−	21.7922i	0.646281	−	1.11939i	0.984004	−	0.178146i	$-0.0570098\pi$
$380$	−0.565096	+	0.978775i	−0.0289888	+	0.0502101i
$381$	−0.888656	−	1.53920i	−0.0455272	−	0.0788555i
$382$	−6.91070			−0.353582
$383$	11.0218	+	19.0904i	0.563189	+	0.975473i	0.997216	+	0.0745724i	$0.0237592\pi$
$383$	11.0218	+	19.0904i	0.563189	+	0.975473i	−0.434026	+	0.900900i	$0.642907\pi$
$384$	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
$388$	13.0156	−	22.5438i	0.660769	−	1.14449i
$389$	−10.9812			−0.556767			−0.278383	−	0.960470i	$-0.589799\pi$
$389$	−10.9812			−0.556767			−0.278383	+	0.960470i	$0.589799\pi$
$390$	−4.94040	+	3.09294i	−0.250167	+	0.156617i
$391$	−2.83342			−0.143292
$392$		0			0
$393$	−1.07578	+	1.86331i	−0.0542660	+	0.0939914i
$394$	2.02042	+	3.49946i	0.101787	+	0.176300i
$395$	23.6948			1.19221
$396$	0.279672	+	0.484405i	0.0140540	+	0.0243423i
$397$	−12.5382	−	21.7168i	−0.629275	−	1.08994i	−0.987698	−	0.156377i	$-0.950019\pi$
$397$	−12.5382	−	21.7168i	−0.629275	−	1.08994i	0.358423	−	0.933559i	$-0.383315\pi$
$398$	−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	$-0.0247647\pi$
$402$	−1.58912			−0.0792581
$403$	−0.572726	−	16.0107i	−0.0285295	−	0.797551i
$404$	−23.3162			−1.16002
$405$	7.66521	−	13.2765i	0.380887	−	0.659716i
$406$		0			0
$407$	−2.65640	−	4.60103i	−0.131673	−	0.228064i
$408$	4.80937			0.238099
$409$	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
$411$	16.3472			0.806345
$412$	8.94238	+	15.4887i	0.440560	+	0.763072i
$413$		0			0
$414$	0.398029	−	0.689407i	0.0195621	−	0.0338825i
$415$	−22.6944			−1.11403
$416$	16.6979	−	10.4538i	0.818684	−	0.512538i
$417$	27.5371			1.34850
$418$	−0.0774824	+	0.134204i	−0.00378979	+	0.00656411i
$419$	16.9902	−	29.4279i	0.830027	−	1.43765i	−0.0679891	−	0.997686i	$-0.521658\pi$
$419$	16.9902	−	29.4279i	0.830027	−	1.43765i	0.898016	−	0.439963i	$-0.145008\pi$
$420$		0			0
$421$	−32.3623			−1.57724			−0.788621	−	0.614879i	$-0.789205\pi$
$421$	−32.3623			−1.57724			−0.788621	+	0.614879i	$0.789205\pi$
$422$	−4.09169	−	7.08701i	−0.199180	−	0.344990i
$423$	3.33950	+	5.78418i	0.162372	+	0.281236i
$424$	−19.9584			−0.969266
$425$	−1.69222	−	2.93101i	−0.0820847	−	0.142175i
$426$	6.86435	−	11.8894i	0.332579	−	0.576044i
$427$		0			0
$428$	−6.24802			−0.302009
$429$	3.35257	−	2.09888i	0.161863	−	0.101335i
$430$	−6.88577			−0.332061
$431$	9.45640	−	16.3790i	0.455499	−	0.788947i	−0.543218	−	0.839592i	$-0.682794\pi$
$431$	9.45640	−	16.3790i	0.455499	−	0.788947i	0.998717	+	0.0506447i	$0.0161276\pi$
$432$	−4.79874	+	8.31167i	−0.230880	+	0.399895i
$433$	−9.57006	−	16.5758i	−0.459908	−	0.796584i	0.539048	−	0.842275i	$-0.318784\pi$
$433$	−9.57006	−	16.5758i	−0.459908	−	0.796584i	−0.998956	+	0.0456914i	$0.985451\pi$
$434$		0			0
$435$	−9.60653	−	16.6390i	−0.460598	−	0.797779i
$436$	−6.82859	−	11.8275i	−0.327030	−	0.566433i
$437$	−1.09153			−0.0522148
$438$	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
$443$	−40.3996			−1.91944			−0.959721	−	0.280955i	$-0.909349\pi$
$443$	−40.3996			−1.91944			−0.959721	+	0.280955i	$0.909349\pi$
$444$	−14.4226	+	24.9807i	−0.684468	+	1.18553i
$445$	−1.83544	+	3.17907i	−0.0870081	+	0.150703i
$446$	−0.263561	−	0.456502i	−0.0124800	−	0.0216160i
$447$	−25.3159			−1.19740
$448$		0			0
$449$	13.3112	+	23.0556i	0.628194	+	1.08806i	0.987914	+	0.155003i	$0.0495387\pi$
$449$	13.3112	+	23.0556i	0.628194	+	1.08806i	−0.359720	+	0.933060i	$0.617128\pi$
$450$	0.950869			0.0448244
$451$	1.16452	+	2.01701i	0.0548352	+	0.0949773i
$452$	−6.49594	+	11.2513i	−0.305543	+	0.529217i
$453$	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	$0.154656\pi$
$458$	−4.83583	+	8.37590i	−0.225963	+	0.391380i
$459$	2.73960	+	4.74513i	0.127874	+	0.221484i
$460$	−5.80582			−0.270698
$461$	7.96032	+	13.7877i	0.370749	+	0.642156i	0.989681	−	0.143289i	$-0.0457677\pi$
$461$	7.96032	+	13.7877i	0.370749	+	0.642156i	−0.618932	+	0.785445i	$0.712434\pi$
$462$		0			0
$463$	−28.8475			−1.34066			−0.670328	−	0.742065i	$-0.733847\pi$
$463$	−28.8475			−1.34066			−0.670328	+	0.742065i	$0.733847\pi$
$464$	7.22154	+	12.5081i	0.335252	+	0.580673i
$465$	6.19444	−	10.7291i	0.287260	−	0.497549i
$466$	−4.79110	+	8.29842i	−0.221943	+	0.384417i
$467$	−7.44536			−0.344530			−0.172265	−	0.985051i	$-0.555109\pi$
$467$	−7.44536			−0.344530			−0.172265	+	0.985051i	$0.555109\pi$
$468$	−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
$473$	4.67270			0.214851
$474$	−8.81971	−	15.2762i	−0.405103	−	0.701658i
$475$	−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
$479$	−18.6263	+	32.2617i	−0.851058	+	1.47408i	0.0291956	+	0.999574i	$0.490705\pi$
$479$	−18.6263	+	32.2617i	−0.851058	+	1.47408i	−0.880254	+	0.474503i	$0.842628\pi$
$480$	15.2341			0.695338
$481$	29.1837	+	15.4855i	1.33066	+	0.706077i
$482$	−9.19570			−0.418853
$483$		0			0
$484$	−8.87134	+	15.3656i	−0.403243	+	0.698437i
$485$	−11.5277	−	19.9666i	−0.523448	−	0.906638i
$486$	−3.44760			−0.156386
$487$	−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	$-0.351157\pi$
$488$	−8.20742	−	14.2157i	−0.371533	−	0.643513i
$489$	22.1069			0.999707
$490$		0			0
$491$	−3.03571	+	5.25800i	−0.137000	+	0.237290i	−0.926360	−	0.376640i	$-0.877079\pi$
$491$	−3.03571	+	5.25800i	−0.137000	+	0.237290i	0.789360	+	0.613931i	$0.210413\pi$
$492$	6.32263	−	10.9511i	0.285046	−	0.493714i
$493$	8.24555			0.371361
$494$	−0.0344490	−	0.963033i	−0.00154993	−	0.0433289i
$495$	0.495401			0.0222666
$496$	−4.65656	+	8.06540i	−0.209086	+	0.362147i
$497$		0			0
$498$	8.44736	+	14.6313i	0.378535	+	0.655642i
$499$	−2.51565			−0.112616			−0.0563079	−	0.998413i	$-0.517933\pi$
$499$	−2.51565			−0.112616			−0.0563079	+	0.998413i	$0.517933\pi$
$500$	−9.59703	−	16.6225i	−0.429192	−	0.743383i
$501$	20.8679	+	36.1442i	0.932308	+	1.61481i
$502$	1.44707			0.0645858
$503$	17.0026	+	29.4493i	0.758107	+	1.31308i	0.943815	+	0.330474i	$0.107209\pi$
$503$	17.0026	+	29.4493i	0.758107	+	1.31308i	−0.185708	+	0.982605i	$0.559458\pi$
$504$		0			0
$505$	−10.3254	+	17.8841i	−0.459473	+	0.795831i
$506$	−0.796058			−0.0353891
$507$	−10.7448	+	22.1255i	−0.477194	+	0.982627i
$508$	1.56293			0.0693439
$509$	−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
$513$	1.05538	+	1.82798i	0.0465964	+	0.0807073i
$514$	−3.04992	−	5.28262i	−0.134526	−	0.233006i
$515$	15.8402			0.698004
$516$	−12.6849	−	21.9709i	−0.558423	−	0.967217i
$517$	3.33950	−	5.78418i	0.146871	−	0.254388i
$518$		0			0
$519$	−21.5516			−0.946011
$520$	−0.403492	−	11.2797i	−0.0176943	−	0.494649i
$521$	−9.14772			−0.400769			−0.200385	−	0.979717i	$-0.564219\pi$
$521$	−9.14772			−0.400769			−0.200385	+	0.979717i	$0.564219\pi$
$522$	−1.15831	+	2.00625i	−0.0506977	+	0.0878111i
$523$	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
$527$	2.65843	+	4.60453i	0.115803	+	0.200577i
$528$	−2.29929			−0.100064
$529$	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
$534$	2.73276			0.118258
$535$	−2.76688	+	4.79238i	−0.119623	+	0.207193i
$536$	1.53862	−	2.66496i	0.0664582	−	0.115109i
$537$	−3.28498	−	5.68976i	−0.141758	−	0.245531i
$538$	−12.2494			−0.528109
$539$		0			0
$540$	5.61359	+	9.72302i	0.241570	+	0.418412i
$541$	7.80293			0.335474			0.167737	−	0.985832i	$-0.446354\pi$
$541$	7.80293			0.335474			0.167737	+	0.985832i	$0.446354\pi$
$542$	−1.89020	−	3.27393i	−0.0811912	−	0.140627i
$543$	19.9602	−	34.5721i	0.856576	−	1.48363i
$544$	−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
$549$	−2.24013	+	3.88001i	−0.0956063	+	0.165595i
$550$	−0.475435	−	0.823477i	−0.0202726	−	0.0351132i
$551$	3.17646			0.135322
$552$	4.75875	+	8.24240i	0.202546	+	0.350820i
$553$		0			0
$554$	8.42520			0.357952
$555$	12.7739	+	22.1250i	0.542221	+	0.939154i
$556$	−12.1078	+	20.9713i	−0.513484	+	0.889380i
$557$	3.62124	−	6.27218i	0.153437	−	0.265761i	−0.779052	−	0.626960i	$-0.784299\pi$
$557$	3.62124	−	6.27218i	0.153437	−	0.265761i	0.932489	+	0.361199i	$0.117632\pi$
$558$	−1.49379			−0.0632371
$559$	−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	$0.942316\pi$
$564$	−36.2628			−1.52694
$565$	5.75334	+	9.96509i	0.242045	+	0.419234i
$566$	−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	$-0.179962\pi$
$570$	0.372591	−	0.645346i	0.0156061	−	0.0270306i
$571$	13.6249			0.570186			0.285093	−	0.958500i	$-0.407976\pi$
$571$	13.6249			0.570186			0.285093	+	0.958500i	$0.407976\pi$
$572$	0.124343	+	3.47605i	0.00519905	+	0.145341i
$573$	−22.5510			−0.942082
$574$		0			0
$575$	3.34882	−	5.80032i	0.139655	−	0.241890i
$576$	0.296821	+	0.514108i	0.0123675	+	0.0214212i
$577$	26.3849			1.09842			0.549209	−	0.835685i	$-0.314929\pi$
$577$	26.3849			1.09842			0.549209	+	0.835685i	$0.314929\pi$
$578$	−4.51331	−	7.81728i	−0.187729	−	0.325156i
$579$	13.6032	+	23.5614i	0.565329	+	0.979179i
$580$	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
$584$	−7.84727			−0.324722
$585$	−2.61115	+	1.63471i	−0.107958	+	0.0675871i
$586$	−6.08054			−0.251185
$587$	−11.0720	+	19.1773i	−0.456990	+	0.791530i	−0.998800	−	0.0489708i	$-0.984406\pi$
$587$	−11.0720	+	19.1773i	−0.456990	+	0.791530i	0.541810	+	0.840501i	$0.317739\pi$
$588$		0			0
$589$	1.02411	+	1.77382i	0.0421979	+	0.0730889i
$590$	−0.205846			−0.00847453
$591$	6.59303	+	11.4195i	0.271201	+	0.469734i
$592$	−9.60254	−	16.6321i	−0.394662	−	0.683575i
$593$	26.0838			1.07114			0.535568	−	0.844492i	$-0.320098\pi$
$593$	26.0838			1.07114			0.535568	+	0.844492i	$0.320098\pi$
$594$	0.769700	+	1.33316i	0.0315812	+	0.0547002i
$595$		0			0
$596$	11.1311	−	19.2797i	0.455949	−	0.789727i
$597$	−6.76124			−0.276719
$598$	4.19585	−	2.62682i	0.171581	−	0.107419i
$599$	−16.8440			−0.688229			−0.344114	−	0.938928i	$-0.611821\pi$
$599$	−16.8440			−0.688229			−0.344114	+	0.938928i	$0.611821\pi$
$600$	−5.68420	+	9.84532i	−0.232056	+	0.401933i
$601$	4.31691	−	7.47710i	0.176090	−	0.304997i	−0.764448	−	0.644686i	$-0.776988\pi$
$601$	4.31691	−	7.47710i	0.176090	−	0.304997i	0.940538	+	0.339688i	$0.110322\pi$
$602$		0			0
$603$	−0.839898			−0.0342033
$604$	13.4263	+	23.2551i	0.546309	+	0.946235i
$605$	7.85719	+	13.6091i	0.319440	+	0.553287i
$606$	15.3733			0.624498
$607$	10.9181	+	18.9107i	0.443153	+	0.767564i	0.997922	−	0.0644411i	$-0.0205265\pi$
$607$	10.9181	+	18.9107i	0.443153	+	0.767564i	−0.554768	+	0.832005i	$0.687193\pi$
$608$	−1.25931	+	2.18119i	−0.0510718	+	0.0884590i
$609$		0			0
$610$	−6.60218			−0.267315
$611$	1.48475	+	41.5068i	0.0600668	+	1.67918i
$612$	1.15433			0.0466610
$613$	24.0244	−	41.6114i	0.970334	−	1.68067i	0.275791	−	0.961218i	$-0.411060\pi$
$613$	24.0244	−	41.6114i	0.970334	−	1.68067i	0.694543	−	0.719451i	$-0.255607\pi$
$614$	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	0.982828	−	0.184523i	$-0.0590739\pi$
$617$	8.23709	+	14.2671i	0.331613	+	0.574370i	−0.651215	+	0.758893i	$0.725741\pi$
$618$	−5.89608	−	10.2123i	−0.237175	−	0.410799i
$619$	−42.0533			−1.69027			−0.845133	−	0.534557i	$-0.820479\pi$
$619$	−42.0533			−1.69027			−0.845133	+	0.534557i	$0.820479\pi$
$620$	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
$625$	−2.85760			−0.114304
$626$	5.89129	−	10.2040i	0.235463	−	0.407835i
$627$	−0.252841	+	0.437933i	−0.0100975	+	0.0174894i
$628$	−0.523006	−	0.905872i	−0.0208702	−	0.0361482i
$629$	−10.9642			−0.437170
$630$		0			0
$631$	6.06667	+	10.5078i	0.241510	+	0.418308i	0.961145	−	0.276045i	$-0.0890239\pi$
$631$	6.06667	+	10.5078i	0.241510	+	0.418308i	−0.719634	+	0.694353i	$0.755691\pi$
$632$	34.1577			1.35872
$633$	−13.3520	−	23.1263i	−0.530694	−	0.919190i
$634$	−8.06575	+	13.9703i	−0.320332	+	0.554831i
$635$	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
$640$	−8.48908	+	14.7035i	−0.335560	+	0.581207i
$641$	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	$0.830791\pi$
$642$	4.11957			0.162587
$643$	14.1741	+	24.5503i	0.558973	+	0.968169i	0.997583	+	0.0694914i	$0.0221377\pi$
$643$	14.1741	+	24.5503i	0.558973	+	0.968169i	−0.438610	+	0.898678i	$0.644529\pi$
$644$		0			0
$645$	−22.4697			−0.884742
$646$	0.159902	+	0.276959i	0.00629128	+	0.0108968i
$647$	−17.4045	+	30.1455i	−0.684242	+	1.18514i	0.289433	+	0.957198i	$0.406533\pi$
$647$	−17.4045	+	30.1455i	−0.684242	+	1.18514i	−0.973675	+	0.227943i	$0.926800\pi$
$648$	11.0499	−	19.1390i	0.434082	−	0.751852i
$649$	0.139687			0.00548321
$650$	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
$655$	−1.67575			−0.0654768
$656$	4.20959	+	7.29122i	0.164357	+	0.284674i
$657$	1.07091	+	1.85488i	0.0417803	+	0.0723657i
$658$		0			0
$659$	−4.33723	−	7.51230i	−0.168954	−	0.292638i	0.769098	−	0.639131i	$-0.220706\pi$
$659$	−4.33723	−	7.51230i	−0.168954	−	0.292638i	−0.938053	+	0.346493i	$0.887372\pi$
$660$	−1.34486	+	2.32937i	−0.0523486	+	0.0906704i
$661$	9.50000	−	16.4545i	0.369507	−	0.640005i	−0.619982	−	0.784616i	$-0.712860\pi$
$661$	9.50000	−	16.4545i	0.369507	−	0.640005i	0.989489	+	0.144612i	$0.0461932\pi$
$662$	5.41714			0.210543
$663$	−0.291808	−	8.15759i	−0.0113329	−	0.316815i
$664$	−32.7156			−1.26961
$665$		0			0
$666$	1.54021	−	2.66772i	0.0596819	−	0.103372i
$667$	8.15877	+	14.1314i	0.315909	+	0.547170i
$668$	−36.7016			−1.42003
$669$	−0.860054	−	1.48966i	−0.0332516	−	0.0575935i
$670$	−0.618844	−	1.07187i	−0.0239080	−	0.0414099i
$671$	4.48026			0.172958
$672$		0			0
$673$	0.284273	−	0.492376i	0.0109579	−	0.0189797i	−0.860494	−	0.509460i	$-0.829845\pi$
$673$	0.284273	−	0.492376i	0.0109579	−	0.0189797i	0.871452	+	0.490480i	$0.163179\pi$
$674$	6.64412	−	11.5079i	0.255922	−	0.443269i
$675$	−12.9517			−0.498513
$676$	−12.1256	−	17.9112i	−0.466369	−	0.688893i
$677$	−27.6797			−1.06382			−0.531908	−	0.846802i	$-0.678525\pi$
$677$	−27.6797			−1.06382			−0.531908	+	0.846802i	$0.678525\pi$
$678$	4.28304	−	7.41844i	0.164489	−	0.284903i
$679$		0			0
$680$	1.87289	+	3.24394i	0.0718221	+	0.124400i
$681$	4.41814			0.169304
$682$	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	$0.682908\pi$
$684$	0.444686			0.0170030
$685$	6.36600	+	11.0262i	0.243232	+	0.421291i
$686$		0			0
$687$	−15.7803	+	27.3323i	−0.602056	+	1.04279i
$688$	16.8912			0.643970
$689$	1.21098	+	33.8532i	0.0461345	+	1.28970i
$690$	3.82801			0.145730
$691$	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
$695$	10.7236	+	18.5739i	0.406771	+	0.704548i
$696$	−13.8485	−	23.9863i	−0.524925	−	0.909197i
$697$	4.80650			0.182059
$698$	4.41655	+	7.64969i	0.167169	+	0.289545i
$699$	−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	$0.485870\pi$
$702$	−8.45606	−	4.48696i	−0.319153	−	0.169349i
$703$	−4.22376			−0.159302
$704$	0.296821	−	0.514108i	0.0111868	−	0.0193762i
$705$	−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
$709$	−5.04160	−	8.73231i	−0.189341	−	0.327949i	0.755689	−	0.654930i	$-0.227302\pi$
$709$	−5.04160	−	8.73231i	−0.189341	−	0.327949i	−0.945031	+	0.326981i	$0.893969\pi$
$710$	10.6926			0.401287
$711$	−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
$716$	5.77749			0.215915
$717$	3.00875	−	5.21130i	0.112364	−	0.194620i
$718$	4.64966	−	8.05344i	0.173524	−	0.300552i
$719$	3.25113	+	5.63113i	0.121247	+	0.210006i	0.920260	−	0.391308i	$-0.127977\pi$
$719$	3.25113	+	5.63113i	0.121247	+	0.210006i	−0.799013	+	0.601314i	$0.794644\pi$
$720$	1.79081			0.0667394
$721$		0			0
$722$	−5.44660	−	9.43379i	−0.202701	−	0.351089i
$723$	−30.0074			−1.11599
$724$	17.5526	+	30.4020i	0.652338	+	1.12988i
$725$	−9.74542	+	16.8796i	−0.361936	+	0.626891i
$726$	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
$731$	4.82158	−	8.35123i	0.178333	−	0.308881i
$732$	−12.1625	−	21.0661i	−0.449539	−	0.778625i
$733$	7.66440			0.283091			0.141545	−	0.989932i	$-0.454793\pi$
$733$	7.66440			0.283091			0.141545	+	0.989932i	$0.454793\pi$
$734$	−2.00036	−	3.46472i	−0.0738346	−	0.127885i
$735$		0			0
$736$	−12.9382			−0.476909
$737$	0.419949	+	0.727373i	0.0154690	+	0.0267931i
$738$	−0.675201	+	1.16948i	−0.0248545	+	0.0430493i
$739$	−10.2162	+	17.6950i	−0.375810	+	0.650922i	−0.990448	−	0.137887i	$-0.955969\pi$
$739$	−10.2162	+	17.6950i	−0.375810	+	0.650922i	0.614638	+	0.788809i	$0.289302\pi$
$740$	−22.4662			−0.825873
$741$	−0.112414	−	3.14257i	−0.00412964	−	0.115445i
$742$		0			0
$743$	−5.07080	+	8.78288i	−0.186030	+	0.322213i	−0.943923	−	0.330166i	$-0.892895\pi$
$743$	−5.07080	+	8.78288i	−0.186030	+	0.322213i	0.757893	+	0.652378i	$0.226229\pi$
$744$	8.92971	−	15.4667i	0.327379	−	0.567037i
$745$	−9.85866	−	17.0757i	−0.361193	−	0.625605i
$746$	−4.45601			−0.163146
$747$	4.46469	+	7.73306i	0.163354	+	0.282938i
$748$	−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	$0.0333116\pi$
$752$	12.0718	−	20.9090i	0.440214	−	0.762474i
$753$	4.72207			0.172082
$754$	−12.2104	+	7.64432i	−0.444676	+	0.278390i
$755$	23.7829			0.865550
$756$		0			0
$757$	−12.2909	+	21.2884i	−0.446720	+	0.773741i	−0.998170	−	0.0604666i	$-0.980741\pi$
$757$	−12.2909	+	21.2884i	−0.446720	+	0.773741i	0.551451	+	0.834207i	$0.314074\pi$
$758$	−7.29503	−	12.6354i	−0.264967	−	0.458937i
$759$	−2.59770			−0.0942905
$760$	0.721500	+	1.24967i	0.0261715	+	0.0453304i
$761$	−17.6167	−	30.5130i	−0.638603	−	1.10609i	−0.985739	−	0.168279i	$-0.946179\pi$
$761$	−17.6167	−	30.5130i	−0.638603	−	1.10609i	0.347136	−	0.937815i	$-0.387154\pi$
$762$	−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
$766$	12.7811			0.461802
$767$	−0.736262	+	0.460938i	−0.0265849	+	0.0166435i
$768$	8.76493			0.316277
$769$	4.62257	−	8.00653i	0.166694	−	0.288723i	−0.770561	−	0.637366i	$-0.780024\pi$
$769$	4.62257	−	8.00653i	0.166694	−	0.288723i	0.937256	+	0.348643i	$0.113357\pi$
$770$		0			0
$771$	−9.95251	−	17.2383i	−0.358431	−	0.620821i
$772$	−23.9247			−0.861070
$773$	−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
$775$	−12.5680			−0.451456
$776$	−16.6180	−	28.7833i	−0.596553	−	1.03326i
$777$		0			0
$778$	−3.18349	+	5.51397i	−0.114134	+	0.197686i
$779$	1.85162			0.0663413
$780$	−0.597930	−	16.7153i	−0.0214093	−	0.598505i
$781$	−7.25604			−0.259641
$782$	−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
$786$	0.623749	+	1.08036i	0.0222484	+	0.0385353i
$787$	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	$0.527327\pi$
$788$	−11.5955			−0.413074
$789$	−29.6576	−	51.3684i	−1.05584	−	1.82876i
$790$	6.86924	−	11.8979i	0.244397	−	0.423307i
$791$		0			0
$792$	0.714154			0.0253764
$793$	−23.6145	+	14.7839i	−0.838574	+	0.524990i
$794$	−14.5396			−0.515990
$795$	−13.0976	+	22.6856i	−0.464523	+	0.804577i
$796$	2.97285	−	5.14912i	0.105370	−	0.182506i
$797$	12.3745	+	21.4333i	0.438327	+	0.759205i	0.997561	−	0.0698051i	$-0.0222377\pi$
$797$	12.3745	+	21.4333i	0.438327	+	0.759205i	−0.559233	+	0.829010i	$0.688904\pi$
$798$		0			0
$799$	−6.89181	−	11.9370i	−0.243815	−	0.422299i
$800$	−7.72717	−	13.3839i	−0.273197	−	0.473191i
$801$	1.44435			0.0510335
$802$	−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
$807$	−39.9722			−1.40709
$808$	−14.8847	+	25.7811i	−0.523643	+	0.906977i
$809$	−15.0174	+	26.0109i	−0.527983	+	0.914494i	0.471485	+	0.881874i	$0.343718\pi$
$809$	−15.0174	+	26.0109i	−0.527983	+	0.914494i	−0.999468	+	0.0326194i	$0.989615\pi$
$810$	−4.44437	−	7.69787i	−0.156159	−	0.270475i
$811$	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
$814$	−3.08042			−0.107969
$815$	8.60898	+	14.9112i	0.301559	+	0.522316i
$816$	−2.37255	+	4.10938i	−0.0830560	+	0.143857i
$817$	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	$0.223347\pi$
$822$	4.73912	−	8.20840i	0.165296	−	0.286301i
$823$	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	$0.517440\pi$
$824$	22.8348			0.795488
$825$	−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	$0.453245\pi$
$828$	1.14218	+	1.97832i	0.0396935	+	0.0687512i
$829$	28.0821	−	48.6396i	0.975331	−	1.68932i	0.296495	−	0.955034i	$-0.404182\pi$
$829$	28.0821	−	48.6396i	0.975331	−	1.68932i	0.678837	−	0.734289i	$-0.262484\pi$
$830$	−6.57924	+	11.3956i	−0.228369	+	0.395546i
$831$	27.4931			0.953726
$832$	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
$837$	20.3468			0.703289
$838$	−9.85111	−	17.0626i	−0.340301	−	0.589419i
$839$	13.0690	+	22.6362i	0.451192	+	0.781488i	0.998460	−	0.0554692i	$-0.0176655\pi$
$839$	13.0690	+	22.6362i	0.451192	+	0.781488i	−0.547268	+	0.836957i	$0.684332\pi$
$840$		0			0
$841$	−9.24289	−	16.0092i	−0.318720	−	0.552040i
$842$	−9.38200	+	16.2501i	−0.323325	+	0.560016i
$843$	25.7158	−	44.5411i	0.885700	−	1.53408i
$844$	23.4829			0.808316
$845$	−19.1081	+	1.36879i	−0.657337	+	0.0470880i
$846$	3.87255			0.133141
$847$		0			0
$848$	9.84586	−	17.0535i	0.338108	−	0.585621i
$849$	−8.11290	−	14.0519i	−0.278434	−	0.482262i
$850$	−1.96233			−0.0673075
$851$	−10.8488	−	18.7906i	−0.371891	−	0.644135i
$852$	19.6979	+	34.1178i	0.674839	+	1.16886i
$853$	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
$857$	5.67375			0.193812			0.0969058	−	0.995294i	$-0.469105\pi$
$857$	5.67375			0.193812			0.0969058	+	0.995294i	$0.469105\pi$
$858$	−0.0819845	−	2.29190i	−0.00279890	−	0.0782442i
$859$	−26.5351			−0.905366			−0.452683	−	0.891672i	$-0.649533\pi$
$859$	−26.5351			−0.905366			−0.452683	+	0.891672i	$0.649533\pi$
$860$	9.87968	−	17.1121i	0.336894	−	0.583518i
$861$		0			0
$862$	−5.48292	−	9.49669i	−0.186749	−	0.323459i
$863$	19.0480			0.648403			0.324202	−	0.945988i	$-0.394904\pi$
$863$	19.0480			0.648403			0.324202	+	0.945988i	$0.394904\pi$
$864$	12.5098	+	21.6676i	0.425593	+	0.737148i
$865$	−8.39276	−	14.5367i	−0.285362	−	0.494262i
$866$	−11.0976			−0.377113
$867$	−14.7278	−	25.5094i	−0.500184	−	0.866343i
$868$		0			0
$869$	−4.66148	+	8.07393i	−0.158130	+	0.273889i
$870$	−11.1399			−0.377679
$871$	−4.61364	−	2.44809i	−0.156327	−	0.0829503i
$872$	−17.4371			−0.590496
$873$	−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
$877$	−13.2586	−	22.9645i	−0.447710	−	0.775456i	0.550527	−	0.834818i	$-0.314427\pi$
$877$	−13.2586	−	22.9645i	−0.447710	−	0.775456i	−0.998237	+	0.0593613i	$0.981094\pi$
$878$	2.78393	+	4.82190i	0.0939530	+	0.162731i
$879$	−19.8420			−0.669256
$880$	−0.895404	−	1.55088i	−0.0301840	−	0.0522803i
$881$	2.02357	−	3.50492i	0.0681757	−	0.118084i	−0.829923	−	0.557879i	$-0.811615\pi$
$881$	2.02357	−	3.50492i	0.0681757	−	0.118084i	0.898098	+	0.439795i	$0.144949\pi$
$882$		0			0
$883$	44.7968			1.50753			0.753766	−	0.657142i	$-0.228235\pi$
$883$	44.7968			1.50753			0.753766	+	0.657142i	$0.228235\pi$
$884$	6.34084	+	3.36458i	0.213265	+	0.113163i
$885$	−0.671716			−0.0225795
$886$	−11.7120	+	20.2859i	−0.393474	+	0.681517i
$887$	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
$891$	3.01596	+	5.22379i	0.101038	+	0.175004i
$892$	1.51263			0.0506465
$893$	−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
$898$	15.4359			0.515103
$899$	15.3098	−	26.5173i	0.510610	−	0.884402i
$900$	−1.36430	+	2.36304i	−0.0454768	+	0.0787681i
$901$	−5.62100	−	9.73586i	−0.187263	−	0.324348i
$902$	1.35040			0.0449635
$903$		0			0
$904$	8.29384	+	14.3654i	0.275849	+	0.477785i
$905$	31.0921			1.03354
$906$	−8.85252	−	15.3330i	−0.294105	−	0.509405i
$907$	−2.77789	+	4.81144i	−0.0922382	+	0.159761i	−0.908453	−	0.417988i	$-0.862735\pi$
$907$	−2.77789	+	4.81144i	−0.0922382	+	0.159761i	0.816214	+	0.577749i	$0.196069\pi$
$908$	−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
$913$	4.46469	−	7.73306i	0.147760	−	0.255927i
$914$	−0.467579	−	0.809870i	−0.0154661	−	0.0267881i
$915$	−21.5443			−0.712231
$916$	−13.8769	−	24.0354i	−0.458504	−	0.794153i
$917$		0			0
$918$	3.17690			0.104853
$919$	3.50823	+	6.07643i	0.115726	+	0.200443i	0.918070	−	0.396419i	$-0.129747\pi$
$919$	3.50823	+	6.07643i	0.115726	+	0.200443i	−0.802344	+	0.596862i	$0.796414\pi$
$920$	−3.70636	+	6.41960i	−0.122195	+	0.211648i
$921$	18.1400	−	31.4194i	0.597734	−	1.03531i
$922$	9.23095			0.304005
$923$	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
$928$	37.6516			1.23597
$929$	29.8098	+	51.6321i	0.978028	+	1.69399i	0.669558	+	0.742760i	$0.266483\pi$
$929$	29.8098	+	51.6321i	0.978028	+	1.69399i	0.308469	+	0.951234i	$0.400183\pi$
$930$	−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
$934$	−2.15845	+	3.73854i	−0.0706266	+	0.122329i
$935$	−1.02237			−0.0334351
$936$	−3.76416	+	2.35655i	−0.123035	+	0.0770264i
$937$	−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
$940$	−14.1217	−	24.4595i	−0.460598	−	0.797779i
$941$	30.2459			0.985988			0.492994	−	0.870033i	$-0.335902\pi$
$941$	30.2459			0.985988			0.492994	+	0.870033i	$0.335902\pi$
$942$	0.344839	+	0.597278i	0.0112355	+	0.0194604i
$943$	4.75591	+	8.23749i	0.154874	+	0.268249i
$944$	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	$0.247851\pi$
$948$	50.6179			1.64399
$949$	0.476133	+	13.3104i	0.0154559	+	0.432075i
$950$	−0.755955			−0.0245264
$951$	−26.3202	+	45.5879i	−0.853490	+	1.47829i
$952$		0			0
$953$	−10.8527	−	18.7974i	−0.351554	−	0.608909i	0.634968	−	0.772538i	$-0.281013\pi$
$953$	−10.8527	−	18.7974i	−0.351554	−	0.608909i	−0.986522	+	0.163629i	$0.947680\pi$
$954$	3.15848			0.102259
$955$	−8.78195	−	15.2108i	−0.284177	−	0.492209i
$956$	2.64583	+	4.58271i	0.0855722	+	0.148215i
$957$	7.55958			0.244367
$958$	10.7997	+	18.7057i	0.348924	+	0.604353i
$959$		0			0
$960$	−1.42732	+	2.47220i	−0.0460667	+	0.0797899i
$961$	−11.2560			−0.363098
$962$	16.2362	−	10.1647i	0.523477	−	0.327724i
$963$	2.17732			0.0701631
$964$	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	$0.380784\pi$
$968$	11.3267	+	19.6184i	0.364054	+	0.630559i
$969$	0.521794	+	0.903774i	0.0167624	+	0.0290334i
$970$	−13.3678			−0.429214
$971$	26.5064	+	45.9105i	0.850632	+	1.47334i	0.880639	+	0.473787i	$0.157114\pi$
$971$	26.5064	+	45.9105i	0.850632	+	1.47334i	−0.0300076	+	0.999550i	$0.509553\pi$
$972$	4.94660	−	8.56776i	0.158662	−	0.274811i
$973$		0			0
$974$	−14.0156			−0.449087
$975$	17.0444	+	9.04410i	0.545857	+	0.289643i
$976$	16.1955			0.518406
$977$	2.32294	−	4.02345i	0.0743174	−	0.128722i	−0.826472	−	0.562978i	$-0.809656\pi$
$977$	2.32294	−	4.02345i	0.0743174	−	0.128722i	0.900789	+	0.434257i	$0.142989\pi$
$978$	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
$982$	1.76014	+	3.04865i	0.0561682	+	0.0972862i
$983$	7.83791			0.249991			0.124995	−	0.992157i	$-0.460108\pi$
$983$	7.83791			0.249991			0.124995	+	0.992157i	$0.460108\pi$
$984$	−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
$989$	19.0833			0.606815
$990$	0.143619	−	0.248756i	0.00456452	−	0.00790598i
$991$	8.87507	−	15.3721i	0.281926	−	0.488310i	−0.689933	−	0.723873i	$-0.742360\pi$
$991$	8.87507	−	15.3721i	0.281926	−	0.488310i	0.971859	+	0.235563i	$0.0756935\pi$
$992$	12.1392	+	21.0257i	0.385419	+	0.667565i
$993$	17.6772			0.560970
$994$		0			0
$995$	−2.63300	−	4.56049i	−0.0834717	−	0.144577i
$996$	−48.4810			−1.53618
$997$	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	$0.644402\pi$
$998$	−0.729299	+	1.26318i	−0.0230855	+	0.0399853i
$999$	−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.f.l.295.4	yes	16
7.2	even	3		637.2.h.m.165.6		16
7.3	odd	6		637.2.g.m.373.4		16
7.4	even	3		637.2.g.m.373.3		16
7.5	odd	6		637.2.h.m.165.5		16
7.6	odd	2	inner	637.2.f.l.295.3	✓	16
13.3	even	3	inner	637.2.f.l.393.4	yes	16
13.4	even	6		8281.2.a.cl.1.3		8
13.9	even	3		8281.2.a.ci.1.5		8
91.3	odd	6		637.2.h.m.471.5		16
91.16	even	3		637.2.g.m.263.3		16
91.48	odd	6		8281.2.a.ci.1.6		8
91.55	odd	6	inner	637.2.f.l.393.3	yes	16
91.68	odd	6		637.2.g.m.263.4		16
91.69	odd	6		8281.2.a.cl.1.4		8
91.81	even	3		637.2.h.m.471.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.l.295.3	✓	16	7.6	odd	2	inner
637.2.f.l.295.4	yes	16	1.1	even	1	trivial
637.2.f.l.393.3	yes	16	91.55	odd	6	inner
637.2.f.l.393.4	yes	16	13.3	even	3	inner
637.2.g.m.263.3		16	91.16	even	3
637.2.g.m.263.4		16	91.68	odd	6
637.2.g.m.373.3		16	7.4	even	3
637.2.g.m.373.4		16	7.3	odd	6
637.2.h.m.165.5		16	7.5	odd	6
637.2.h.m.165.6		16	7.2	even	3
637.2.h.m.471.5		16	91.3	odd	6
637.2.h.m.471.6		16	91.81	even	3
8281.2.a.ci.1.5		8	13.9	even	3
8281.2.a.ci.1.6		8	91.48	odd	6
8281.2.a.cl.1.3		8	13.4	even	6
8281.2.a.cl.1.4		8	91.69	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.289905 - 0.502131i) q^{2} +(0.946019 - 1.63855i) q^{3} +(0.831910 + 1.44091i) q^{4} +1.47362 q^{5} +(-0.548512 - 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 - 0.502131i) q^{9} +O(q^{10})\)	\(q+(0.289905 - 0.502131i) q^{2} +(0.946019 - 1.63855i) q^{3} +(0.831910 + 1.44091i) q^{4} +1.47362 q^{5} +(-0.548512 - 0.950050i) q^{6} +2.12432 q^{8} +(-0.289905 - 0.502131i) q^{9} +(0.427209 - 0.739948i) q^{10} +(-0.289905 + 0.502131i) q^{11} +3.14801 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} -0.336180 q^{18} +(0.230479 + 0.399201i) q^{19} +(1.22592 + 2.12335i) q^{20} +(0.168090 + 0.291141i) q^{22} +(-1.18398 + 2.05071i) q^{23} +(2.00965 - 3.48081i) q^{24} -2.82845 q^{25} +(-1.84667 - 0.979879i) q^{26} +4.57909 q^{27} +(3.44550 - 5.96777i) q^{29} +(-0.808297 - 1.40001i) q^{30} +4.44342 q^{31} +(2.73194 + 4.73187i) q^{32} +(0.548512 + 0.950050i) q^{33} +0.693783 q^{34} +(0.482350 - 0.835455i) q^{36} +(-4.58150 + 7.93540i) q^{37} +0.267268 q^{38} +(-6.02605 - 3.19754i) q^{39} +3.13044 q^{40} +(2.00845 - 3.47874i) q^{41} +(-4.02951 - 6.97931i) q^{43} -0.964700 q^{44} +(-0.427209 - 0.739948i) q^{45} +(0.686481 + 1.18902i) q^{46} -11.5193 q^{47} +(1.98280 + 3.43430i) q^{48} +(-0.819983 + 1.42025i) q^{50} +2.26396 q^{51} +(5.08473 - 3.18330i) q^{52} -9.39519 q^{53} +(1.32750 - 2.29930i) q^{54} +(-0.427209 + 0.739948i) q^{55} +0.872150 q^{57} +(-1.99773 - 3.46018i) q^{58} +(-0.120459 - 0.208642i) q^{59} +4.63896 q^{60} +(-3.86355 - 6.69187i) q^{61} +(1.28817 - 2.23118i) q^{62} -1.02385 q^{64} +(-0.189939 - 5.30981i) q^{65} +0.636066 q^{66} +(0.724287 - 1.25450i) q^{67} +(-0.995438 + 1.72415i) q^{68} +(2.24013 + 3.88001i) q^{69} +(6.25725 + 10.8379i) q^{71} +(-0.615852 - 1.06669i) q^{72} -3.69401 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} +16.0793 q^{79} +(-1.54430 + 2.67481i) q^{80} +(5.20163 - 9.00948i) q^{81} +(-1.16452 - 2.01701i) q^{82} -15.4005 q^{83} +(0.881643 + 1.52705i) q^{85} -4.67270 q^{86} +(-6.51901 - 11.2913i) q^{87} +(-0.615852 + 1.06669i) q^{88} +(-1.24553 + 2.15733i) q^{89} -0.495401 q^{90} -3.93984 q^{92} +(4.20356 - 7.28078i) q^{93} +(-3.33950 + 5.78418i) q^{94} +(0.339638 + 0.588270i) q^{95} +10.3379 q^{96} +(-7.82275 - 13.5494i) q^{97} +0.336180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 12 * q^4 + 24 * q^8 - 4 * q^9 - 4 * q^11 - 8 * q^15 - 4 * q^16 - 56 * q^18 + 28 * q^22 + 12 * q^23 - 24 * q^25 + 8 * q^29 + 28 * q^30 + 4 * q^36 - 8 * q^37 - 4 * q^39 + 32 * q^43 - 8 * q^44 - 4 * q^46 + 36 * q^50 - 88 * q^51 - 8 * q^53 - 96 * q^57 - 48 * q^58 + 128 * q^60 - 64 * q^64 + 16 * q^65 + 20 * q^67 + 8 * q^71 + 28 * q^72 + 76 * q^74 + 28 * q^78 - 8 * q^79 + 56 * q^81 + 36 * q^85 + 8 * q^86 + 28 * q^88 - 160 * q^92 + 8 * q^93 + 52 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

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