LMFDB - Embedded newform 637.2.f.l.393.4

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:	16.0.468066644398978174550016.2
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			393.4
Root			$1.04641 - 1.81243i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.l.295.4

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.289905	+	0.502131i	0.204994	+	0.355060i	0.950131	−	0.311852i	$-0.100949\pi$
$2$	0.289905	+	0.502131i	0.204994	+	0.355060i	−0.745137	+	0.666912i	$0.767616\pi$
$3$	0.946019	+	1.63855i	0.546185	+	0.946019i	0.998531	+	0.0541772i	$0.0172536\pi$
$3$	0.946019	+	1.63855i	0.546185	+	0.946019i	−0.452347	+	0.891842i	$0.649413\pi$
$4$	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	0.819006	−	0.573785i	$-0.194526\pi$
$11$	−0.289905	−	0.502131i	−0.0874097	−	0.151398i	−0.906415	+	0.422387i	$0.861192\pi$
$12$	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	−0.784307	−	0.620373i	$-0.786981\pi$
$17$	0.598285	−	1.03626i	0.145105	−	0.251330i	0.929412	+	0.369043i	$0.120315\pi$
$18$	−0.336180			−0.0792384
$19$	0.230479	−	0.399201i	0.0528755	−	0.0915831i	−0.838376	−	0.545092i	$-0.816495\pi$
$19$	0.230479	−	0.399201i	0.0528755	−	0.0915831i	0.891252	+	0.453509i	$0.149828\pi$
$20$	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	0.715781	−	0.698324i	$-0.246071\pi$
$23$	−1.18398	−	2.05071i	−0.246876	−	0.427602i	−0.962657	+	0.270723i	$0.912737\pi$
$24$	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	0.985474	+	0.169828i	$0.0543214\pi$
$29$	3.44550	+	5.96777i	0.639813	+	1.10819i	−0.345661	+	0.938359i	$0.612345\pi$
$30$	−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	−0.946267	−	0.323387i	$-0.895179\pi$
$37$	−4.58150	−	7.93540i	−0.753195	−	1.30457i	0.193072	−	0.981185i	$-0.438155\pi$
$38$	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	0.979153	−	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	$0.956027\pi$
$44$	−0.964700			−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	−0.873760	−	0.486357i	$-0.838325\pi$
$59$	−0.120459	+	0.208642i	−0.0156825	+	0.0271629i	0.858078	+	0.513520i	$0.171659\pi$
$60$	4.63896			0.598888
$61$	−3.86355	+	6.69187i	−0.494677	+	0.856806i	−0.999981	−	0.00613544i	$-0.998047\pi$
$61$	−3.86355	+	6.69187i	−0.494677	+	0.856806i	0.505304	+	0.862941i	$0.331380\pi$
$62$	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	0.906871	−	0.421408i	$-0.138464\pi$
$67$	0.724287	+	1.25450i	0.0884857	+	0.153262i	−0.818385	+	0.574670i	$0.805131\pi$
$68$	−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	$-0.0997405\pi$
$72$	−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	0.792431	−	0.609961i	$-0.208815\pi$
$89$	−1.24553	−	2.15733i	−0.132026	−	0.228676i	−0.924458	+	0.381285i	$0.875482\pi$
$90$	−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	0.129015	+	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
$100$	−2.35302	+	4.07555i	−0.235302	+	0.407555i
$101$	−7.00682	−	12.1362i	−0.697205	−	1.20759i	−0.969432	−	0.245361i	$-0.921093\pi$
$101$	−7.00682	−	12.1362i	−0.697205	−	1.20759i	0.272227	−	0.962233i	$-0.412240\pi$
$102$	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	0.760881	−	0.648891i	$-0.224767\pi$
$107$	−1.87761	−	3.25212i	−0.181516	−	0.314394i	−0.942397	+	0.334497i	$0.891434\pi$
$108$	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	−0.621860	−	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
$115$	−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	0.886112	−	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
$129$	−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	−0.620341	−	0.784332i	$-0.713006\pi$
$137$	4.31998	−	7.48243i	0.369081	−	0.639267i	0.989422	+	0.145065i	$0.0463391\pi$
$138$	2.59770			0.221131
$139$	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
$142$	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	0.450331	+	0.892861i	$0.351306\pi$
$149$	−6.69011	+	11.5876i	−0.548075	+	0.949294i	−0.998406	+	0.0564323i	$0.982027\pi$
$150$	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	−0.541246	−	0.840864i	$-0.682047\pi$
$163$	5.84207	−	10.1188i	0.457586	−	0.792563i	0.998833	+	0.0483011i	$0.0153807\pi$
$164$	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	−0.878054	−	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
$170$	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	−0.997131	−	0.0756980i	$-0.975881\pi$
$173$	−5.69534	+	9.86463i	−0.433009	+	0.749994i	0.564122	+	0.825692i	$0.309215\pi$
$174$	−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	0.923588	−	0.383387i	$-0.125243\pi$
$179$	1.73621	+	3.00721i	0.129771	+	0.224769i	−0.793817	+	0.608157i	$0.791909\pi$
$180$	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	−0.996978	−	0.0776864i	$-0.975247\pi$
$191$	−5.95945	+	10.3221i	−0.431211	+	0.746879i	0.565767	+	0.824565i	$0.308580\pi$
$192$	−0.968585	−	1.67764i	−0.0699016	−	0.121073i
$193$	−7.18970	−	12.4529i	−0.517526	−	0.896381i	−0.999793	−	0.0203567i	$-0.993520\pi$
$193$	−7.18970	−	12.4529i	−0.517526	−	0.896381i	0.482267	−	0.876024i	$-0.339814\pi$
$194$	−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	0.714777	−	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	−0.922381	−	0.386282i	$-0.873759\pi$
$199$	−1.78676	+	3.09476i	−0.126660	+	0.219382i	0.795721	+	0.605664i	$0.207092\pi$
$200$	−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	0.999867	−	0.0162974i	$-0.00518784\pi$
$211$	7.05694	+	12.2230i	0.485820	+	0.841464i	−0.514048	+	0.857762i	$0.671855\pi$
$212$	−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	0.880844	−	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
$226$	4.52743			0.301160
$227$	1.16756	−	2.02228i	0.0774938	−	0.134223i	−0.824674	−	0.565608i	$-0.808642\pi$
$227$	1.16756	−	2.02228i	0.0774938	−	0.134223i	0.902168	+	0.431385i	$0.141975\pi$
$228$	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	0.489110	+	0.872222i	$0.337322\pi$
$241$	−7.92992	+	13.7350i	−0.510811	+	0.884751i	−0.999922	+	0.0125290i	$0.996012\pi$
$242$	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	−0.823952	−	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
$254$	−0.272326	+	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	0.982139	−	0.188155i	$-0.0602508\pi$
$257$	5.26020	+	9.11094i	0.328123	+	0.568325i	−0.654017	+	0.756480i	$0.726917\pi$
$258$	−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	0.705370	+	0.708839i	$0.250781\pi$
$263$	15.6749	+	27.1498i	0.966558	+	1.67413i	0.261188	+	0.965288i	$0.415886\pi$
$264$	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	0.340465	+	0.940257i	$0.389415\pi$
$269$	−10.5633	+	18.2961i	−0.644054	+	1.11553i	−0.984519	+	0.175277i	$0.943918\pi$
$270$	1.95623	+	3.38829i	0.119052	+	0.206205i
$271$	3.26004	+	5.64655i	0.198033	+	0.343004i	0.947891	−	0.318596i	$-0.103211\pi$
$271$	3.26004	+	5.64655i	0.198033	+	0.343004i	−0.749857	+	0.661599i	$0.769878\pi$
$272$	−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	−0.560880	−	0.827897i	$-0.689537\pi$
$277$	7.26548	−	12.5842i	0.436540	−	0.756110i	0.997420	+	0.0717873i	$0.0228703\pi$
$278$	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	0.964866	−	0.262744i	$-0.0846274\pi$
$283$	4.28791	+	7.42688i	0.254890	+	0.441482i	−0.709976	+	0.704226i	$0.751294\pi$
$284$	−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	−0.977557	−	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
$297$	−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	−0.708607	−	0.705604i	$-0.750676\pi$
$331$	4.67148	−	8.09123i	0.256768	−	0.444734i	0.965374	+	0.260869i	$0.0840092\pi$
$332$	−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	−0.246726	−	0.969085i	$-0.579355\pi$
$347$	13.3355	−	23.0978i	0.715889	−	1.23996i	0.962616	−	0.270871i	$-0.0873117\pi$
$348$	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
$352$	−3.16802			−0.168856
$353$	11.2044	+	19.4066i	0.596352	+	1.03291i	0.993355	+	0.115094i	$0.0367170\pi$
$353$	11.2044	+	19.4066i	0.596352	+	1.03291i	−0.397003	+	0.917817i	$0.629950\pi$
$354$	−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	0.941911	−	0.335863i	$-0.109028\pi$
$367$	3.45002	+	5.97561i	0.180090	+	0.311924i	−0.761821	+	0.647787i	$0.775695\pi$
$368$	−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	−0.948193	−	0.317695i	$-0.897091\pi$
$373$	−3.84264	+	6.65566i	−0.198965	+	0.344617i	0.749228	+	0.662312i	$0.230425\pi$
$374$	−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	0.984004	+	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
$382$	−6.91070			−0.353582
$383$	11.0218	−	19.0904i	0.563189	−	0.975473i	−0.434026	−	0.900900i	$-0.642907\pi$
$383$	11.0218	−	19.0904i	0.563189	−	0.975473i	0.997216	−	0.0745724i	$-0.0237592\pi$
$384$	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	0.358423	+	0.933559i	$0.383315\pi$
$397$	−12.5382	+	21.7168i	−0.629275	+	1.08994i	−0.987698	+	0.156377i	$0.950019\pi$
$398$	−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	0.996975	+	0.0777222i	$0.0247647\pi$
$401$	11.3301	+	19.6243i	0.565797	+	0.979989i	−0.431178	+	0.902267i	$0.641902\pi$
$402$	−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	−0.572400	−	0.819975i	$-0.693987\pi$
$409$	8.57324	−	14.8493i	0.423919	−	0.734250i	0.996319	+	0.0857251i	$0.0273207\pi$
$410$	−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	0.898016	+	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	$0.789205\pi$
$422$	−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	0.998717	−	0.0506447i	$-0.0161276\pi$
$431$	9.45640	+	16.3790i	0.455499	+	0.788947i	−0.543218	+	0.839592i	$0.682794\pi$
$432$	−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
$436$	−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	0.728399	−	0.685153i	$-0.240265\pi$
$439$	−4.80144	−	8.31634i	−0.229160	−	0.396917i	−0.957560	+	0.288236i	$0.906931\pi$
$440$	−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	−0.359720	−	0.933060i	$-0.617128\pi$
$449$	13.3112	−	23.0556i	0.628194	−	1.08806i	0.987914	−	0.155003i	$-0.0495387\pi$
$450$	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	0.884271	−	0.466975i	$-0.154656\pi$
$457$	0.806434	+	1.39678i	0.0377234	+	0.0653388i	−0.846547	+	0.532314i	$0.821323\pi$
$458$	−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	−0.618932	−	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	$0.733847\pi$
$464$	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	−0.880254	−	0.474503i	$-0.842628\pi$
$479$	−18.6263	−	32.2617i	−0.851058	−	1.47408i	0.0291956	−	0.999574i	$-0.490705\pi$
$480$	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	0.450749	+	0.892651i	$0.351157\pi$
$487$	−12.0863	+	20.9341i	−0.547684	+	0.948616i	−0.998433	+	0.0559651i	$0.982176\pi$
$488$	−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	0.789360	−	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
$493$	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	−0.185708	−	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
$506$	−0.796058			−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	−0.983253	−	0.182247i	$-0.941663\pi$
$509$	−14.6524	−	25.3787i	−0.649457	−	1.12489i	0.333796	−	0.942645i	$-0.391670\pi$
$510$	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	0.978021	−	0.208507i	$-0.0668604\pi$
$523$	7.05373	+	12.2174i	0.308438	+	0.534231i	−0.669583	+	0.742737i	$0.733527\pi$
$524$	−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	0.932489	−	0.361199i	$-0.117632\pi$
$557$	3.62124	+	6.27218i	0.153437	+	0.265761i	−0.779052	+	0.626960i	$0.784299\pi$
$558$	−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	−0.983625	−	0.180229i	$-0.942316\pi$
$563$	−7.96606	+	13.7976i	−0.335730	+	0.581501i	0.647895	+	0.761730i	$0.275650\pi$
$564$	−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	0.844392	+	0.535727i	$0.179962\pi$
$569$	21.1379	+	36.6120i	0.886149	+	1.53485i	0.0417571	+	0.999128i	$0.486704\pi$
$570$	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	0.541810	−	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
$590$	−0.205846			−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	0.940538	−	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
$604$	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	−0.554768	−	0.832005i	$-0.687193\pi$
$607$	10.9181	−	18.9107i	0.443153	−	0.767564i	0.997922	+	0.0644411i	$0.0205265\pi$
$608$	−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	0.694543	+	0.719451i	$0.255607\pi$
$613$	24.0244	+	41.6114i	0.970334	+	1.68067i	0.275791	+	0.961218i	$0.411060\pi$
$614$	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	$0.0590739\pi$
$618$	−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	−0.719634	−	0.694353i	$-0.755691\pi$
$631$	6.06667	−	10.5078i	0.241510	−	0.418308i	0.961145	+	0.276045i	$0.0890239\pi$
$632$	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	−0.862005	−	0.506900i	$-0.830791\pi$
$641$	0.202177	−	0.350182i	0.00798553	−	0.0138313i	0.869991	+	0.493068i	$0.164125\pi$
$642$	4.11957			0.162587
$643$	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
$646$	0.159902	−	0.276959i	0.00629128	−	0.0108968i
$647$	−17.4045	−	30.1455i	−0.684242	−	1.18514i	−0.973675	−	0.227943i	$-0.926800\pi$
$647$	−17.4045	−	30.1455i	−0.684242	−	1.18514i	0.289433	−	0.957198i	$-0.406533\pi$
$648$	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	0.999959	−	0.00910088i	$-0.00289694\pi$
$653$	12.5750	+	21.7805i	0.492098	+	0.852338i	−0.507861	+	0.861439i	$0.669564\pi$
$654$	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	−0.938053	−	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
$661$	9.50000	+	16.4545i	0.369507	+	0.640005i	0.989489	−	0.144612i	$-0.0461932\pi$
$661$	9.50000	+	16.4545i	0.369507	+	0.640005i	−0.619982	+	0.784616i	$0.712860\pi$
$662$	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	0.871452	−	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
$675$	−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	−0.543517	−	0.839398i	$-0.682908\pi$
$683$	11.8958	−	20.6042i	0.455181	−	0.788397i	0.998699	+	0.0510006i	$0.0162411\pi$
$684$	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	0.968188	+	0.250222i	$0.0805037\pi$
$691$	18.4217	+	31.9073i	0.700793	+	1.21381i	−0.267395	+	0.963587i	$0.586163\pi$
$692$	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	−0.945031	−	0.326981i	$-0.893969\pi$
$709$	−5.04160	+	8.73231i	−0.189341	+	0.327949i	0.755689	+	0.654930i	$0.227302\pi$
$710$	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	−0.799013	−	0.601314i	$-0.794644\pi$
$719$	3.25113	−	5.63113i	0.121247	−	0.210006i	0.920260	+	0.391308i	$0.127977\pi$
$720$	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	0.614638	−	0.788809i	$-0.289302\pi$
$739$	−10.2162	−	17.6950i	−0.375810	−	0.650922i	−0.990448	+	0.137887i	$0.955969\pi$
$740$	−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	0.757893	−	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
$746$	−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	0.994529	−	0.104461i	$-0.0333116\pi$
$751$	11.1481	+	19.3090i	0.406799	+	0.704597i	−0.587730	+	0.809057i	$0.699978\pi$
$752$	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	0.551451	−	0.834207i	$-0.314074\pi$
$757$	−12.2909	−	21.2884i	−0.446720	−	0.773741i	−0.998170	+	0.0604666i	$0.980741\pi$
$758$	−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	0.347136	+	0.937815i	$0.387154\pi$
$761$	−17.6167	+	30.5130i	−0.638603	+	1.10609i	−0.985739	+	0.168279i	$0.946179\pi$
$762$	−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	0.937256	−	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
$772$	−23.9247			−0.861070
$773$	−3.16336	+	5.47909i	−0.113778	+	0.197069i	−0.917291	−	0.398218i	$-0.869629\pi$
$773$	−3.16336	+	5.47909i	−0.113778	+	0.197069i	0.803513	+	0.595288i	$0.202962\pi$
$774$	1.35464	−	2.34630i	0.0486915	−	0.0843362i
$775$	−12.5680			−0.451456
$776$	−16.6180	+	28.7833i	−0.596553	+	1.03326i

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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