LMFDB - Embedded newform 1148.2.ba.a.701.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.10
Character	$\chi$	$=$	1148.701
Dual form			1148.2.ba.a.113.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.304900i q^{3} +(-0.420940 + 1.29552i) q^{5} +(0.587785 - 0.809017i) q^{7} +2.90704 q^{9} +O(q^{10})$	\(q-0.304900i q^{3} +(-0.420940 + 1.29552i) q^{5} +(0.587785 - 0.809017i) q^{7} +2.90704 q^{9} +(-1.66104 + 0.539703i) q^{11} +(-3.66120 - 5.03921i) q^{13} +(0.395004 + 0.128344i) q^{15} +(1.26941 - 0.412455i) q^{17} +(1.99499 - 2.74587i) q^{19} +(-0.246669 - 0.179216i) q^{21} +(2.91110 - 2.11504i) q^{23} +(2.54391 + 1.84826i) q^{25} -1.80105i q^{27} +(5.01259 + 1.62869i) q^{29} +(-0.893181 - 2.74893i) q^{31} +(0.164555 + 0.506449i) q^{33} +(0.800675 + 1.10203i) q^{35} +(-0.584605 + 1.79923i) q^{37} +(-1.53646 + 1.11630i) q^{39} +(3.76696 - 5.17784i) q^{41} +(-2.46586 + 1.79155i) q^{43} +(-1.22369 + 3.76612i) q^{45} +(2.78819 + 3.83762i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-0.125757 - 0.387042i) q^{51} +(3.78028 + 1.22829i) q^{53} -2.37908i q^{55} +(-0.837214 - 0.608272i) q^{57} +(11.2426 - 8.16822i) q^{59} +(-0.00534477 - 0.00388320i) q^{61} +(1.70871 - 2.35184i) q^{63} +(8.06954 - 2.62195i) q^{65} +(-7.38761 - 2.40038i) q^{67} +(-0.644874 - 0.887594i) q^{69} +(-1.97400 + 0.641391i) q^{71} +7.16197 q^{73} +(0.563533 - 0.775637i) q^{75} +(-0.539703 + 1.66104i) q^{77} -14.2442i q^{79} +8.17197 q^{81} -6.99080 q^{83} +1.81816i q^{85} +(0.496588 - 1.52834i) q^{87} +(8.41339 - 11.5800i) q^{89} -6.22881 q^{91} +(-0.838148 + 0.272331i) q^{93} +(2.71755 + 3.74039i) q^{95} +(10.1824 + 3.30846i) q^{97} +(-4.82869 + 1.56894i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	0.304900i		−	0.176034i	−0.996119	−	0.0880170i	$-0.971947\pi$
$3$		−	0.304900i		−	0.176034i	0.996119	−	0.0880170i	$-0.0280530\pi$
$4$		0			0
$5$	−0.420940	+	1.29552i	−0.188250	+	0.579374i	−0.999989	−	0.00464630i	$-0.998521\pi$
$5$	−0.420940	+	1.29552i	−0.188250	+	0.579374i	0.811739	+	0.584020i	$0.198521\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$		0			0
$9$	2.90704			0.969012
$10$		0			0
$11$	−1.66104	+	0.539703i	−0.500821	+	0.162727i	−0.548524	−	0.836135i	$-0.684810\pi$
$11$	−1.66104	+	0.539703i	−0.500821	+	0.162727i	0.0477028	+	0.998862i	$0.484810\pi$
$12$		0			0
$13$	−3.66120	−	5.03921i	−1.01543	−	1.39763i	−0.915356	−	0.402647i	$-0.868090\pi$
$13$	−3.66120	−	5.03921i	−1.01543	−	1.39763i	−0.100079	−	0.994979i	$-0.531910\pi$
$14$		0			0
$15$	0.395004	+	0.128344i	0.101989	+	0.0331384i
$16$		0			0
$17$	1.26941	−	0.412455i	0.307876	−	0.100035i	−0.151004	−	0.988533i	$-0.548251\pi$
$17$	1.26941	−	0.412455i	0.307876	−	0.100035i	0.458880	+	0.888498i	$0.348251\pi$
$18$		0			0
$19$	1.99499	−	2.74587i	0.457682	−	0.629945i	−0.516344	−	0.856381i	$-0.672707\pi$
$19$	1.99499	−	2.74587i	0.457682	−	0.629945i	0.974026	+	0.226436i	$0.0727075\pi$
$20$		0			0
$21$	−0.246669	−	0.179216i	−0.0538276	−	0.0391081i
$22$		0			0
$23$	2.91110	−	2.11504i	0.607006	−	0.441016i	−0.241353	−	0.970437i	$-0.577591\pi$
$23$	2.91110	−	2.11504i	0.607006	−	0.441016i	0.848359	+	0.529422i	$0.177591\pi$
$24$		0			0
$25$	2.54391	+	1.84826i	0.508781	+	0.369651i
$26$		0			0
$27$		−	1.80105i		−	0.346613i
$28$		0			0
$29$	5.01259	+	1.62869i	0.930815	+	0.302440i	0.734896	−	0.678180i	$-0.237231\pi$
$29$	5.01259	+	1.62869i	0.930815	+	0.302440i	0.195919	+	0.980620i	$0.437231\pi$
$30$		0			0
$31$	−0.893181	−	2.74893i	−0.160420	−	0.493722i	0.838250	−	0.545287i	$-0.183579\pi$
$31$	−0.893181	−	2.74893i	−0.160420	−	0.493722i	−0.998670	+	0.0515647i	$0.983579\pi$
$32$		0			0
$33$	0.164555	+	0.506449i	0.0286454	+	0.0881615i
$34$		0			0
$35$	0.800675	+	1.10203i	0.135339	+	0.186278i
$36$		0			0
$37$	−0.584605	+	1.79923i	−0.0961085	+	0.295792i	−0.987541	−	0.157362i	$-0.949701\pi$
$37$	−0.584605	+	1.79923i	−0.0961085	+	0.295792i	0.891432	+	0.453154i	$0.149701\pi$
$38$		0			0
$39$	−1.53646	+	1.11630i	−0.246030	+	0.178751i
$40$		0			0
$41$	3.76696	−	5.17784i	0.588301	−	0.808642i
$41$	3.76696	−	5.17784i	0.588301	−	0.808642i
$42$		0			0
$43$	−2.46586	+	1.79155i	−0.376041	+	0.273209i	−0.759711	−	0.650261i	$-0.774660\pi$
$43$	−2.46586	+	1.79155i	−0.376041	+	0.273209i	0.383671	+	0.923470i	$0.374660\pi$
$44$		0			0
$45$	−1.22369	+	3.76612i	−0.182416	+	0.561420i
$46$		0			0
$47$	2.78819	+	3.83762i	0.406700	+	0.559774i	0.962410	−	0.271602i	$-0.0875535\pi$
$47$	2.78819	+	3.83762i	0.406700	+	0.559774i	−0.555710	+	0.831376i	$0.687554\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$		0			0
$51$	−0.125757	−	0.387042i	−0.0176096	−	0.0541967i
$52$		0			0
$53$	3.78028	+	1.22829i	0.519262	+	0.168718i	0.556910	−	0.830573i	$-0.311987\pi$
$53$	3.78028	+	1.22829i	0.519262	+	0.168718i	−0.0376485	+	0.999291i	$0.511987\pi$
$54$		0			0
$55$		−	2.37908i		−	0.320796i
$56$		0			0
$57$	−0.837214	−	0.608272i	−0.110892	−	0.0805676i
$58$		0			0
$59$	11.2426	−	8.16822i	1.46366	−	1.06341i	0.481270	−	0.876572i	$-0.340176\pi$
$59$	11.2426	−	8.16822i	1.46366	−	1.06341i	0.982391	−	0.186839i	$-0.0598243\pi$
$60$		0			0
$61$	−0.00534477	−	0.00388320i	−0.000684327	−	0.000497193i	0.587443	−	0.809266i	$-0.300135\pi$
$61$	−0.00534477	−	0.00388320i	−0.000684327	−	0.000497193i	−0.588127	+	0.808768i	$0.700135\pi$
$62$		0			0
$63$	1.70871	−	2.35184i	0.215278	−	0.296304i
$64$		0			0
$65$	8.06954	−	2.62195i	1.00090	−	0.325213i
$66$		0			0
$67$	−7.38761	−	2.40038i	−0.902541	−	0.293253i	−0.179255	−	0.983803i	$-0.557369\pi$
$67$	−7.38761	−	2.40038i	−0.902541	−	0.293253i	−0.723285	+	0.690549i	$0.757369\pi$
$68$		0			0
$69$	−0.644874	−	0.887594i	−0.0776338	−	0.106854i
$70$		0			0
$71$	−1.97400	+	0.641391i	−0.234270	+	0.0761191i	−0.423799	−	0.905756i	$-0.639304\pi$
$71$	−1.97400	+	0.641391i	−0.234270	+	0.0761191i	0.189529	+	0.981875i	$0.439304\pi$
$72$		0			0
$73$	7.16197			0.838245			0.419123	−	0.907930i	$-0.362338\pi$
$73$	7.16197			0.838245			0.419123	+	0.907930i	$0.362338\pi$
$74$		0			0
$75$	0.563533	−	0.775637i	0.0650712	−	0.0895628i
$76$		0			0
$77$	−0.539703	+	1.66104i	−0.0615049	+	0.189293i
$78$		0			0
$79$		−	14.2442i		−	1.60260i	−0.598264	−	0.801299i	$-0.704142\pi$
$79$		−	14.2442i		−	1.60260i	0.598264	−	0.801299i	$-0.295858\pi$
$80$		0			0
$81$	8.17197			0.907996
$82$		0			0
$83$	−6.99080			−0.767340			−0.383670	−	0.923470i	$-0.625340\pi$
$83$	−6.99080			−0.767340			−0.383670	+	0.923470i	$0.625340\pi$
$84$		0			0
$85$			1.81816i			0.197207i
$86$		0			0
$87$	0.496588	−	1.52834i	0.0532398	−	0.163855i
$88$		0			0
$89$	8.41339	−	11.5800i	0.891818	−	1.22748i	−0.0811874	−	0.996699i	$-0.525871\pi$
$89$	8.41339	−	11.5800i	0.891818	−	1.22748i	0.973005	−	0.230783i	$-0.0741288\pi$
$90$		0			0
$91$	−6.22881			−0.652957
$92$		0			0
$93$	−0.838148	+	0.272331i	−0.0869119	+	0.0282394i
$94$		0			0
$95$	2.71755	+	3.74039i	0.278815	+	0.383756i
$96$		0			0
$97$	10.1824	+	3.30846i	1.03386	+	0.335923i	0.776317	−	0.630343i	$-0.217086\pi$
$97$	10.1824	+	3.30846i	1.03386	+	0.335923i	0.257548	+	0.966266i	$0.417086\pi$
$98$		0			0
$99$	−4.82869	+	1.56894i	−0.485301	+	0.157684i
$100$		0			0
$101$	−4.35754	+	5.99764i	−0.433591	+	0.596787i	−0.968773	−	0.247950i	$-0.920243\pi$
$101$	−4.35754	+	5.99764i	−0.433591	+	0.596787i	0.535182	+	0.844737i	$0.320243\pi$
$102$		0			0
$103$	−0.513837	−	0.373325i	−0.0506299	−	0.0367848i	0.562182	−	0.827013i	$-0.309962\pi$
$103$	−0.513837	−	0.373325i	−0.0506299	−	0.0367848i	−0.612812	+	0.790228i	$0.709962\pi$
$104$		0			0
$105$	0.336010	−	0.244126i	0.0327912	−	0.0238242i
$106$		0			0
$107$	−0.00186821	−	0.00135734i	−0.000180607	−	0.000131219i	0.587695	−	0.809083i	$-0.300036\pi$
$107$	−0.00186821	−	0.00135734i	−0.000180607	−	0.000131219i	−0.587876	+	0.808951i	$0.700036\pi$
$108$		0			0
$109$			0.358508i			0.0343389i	0.999853	+	0.0171694i	$0.00546547\pi$
$109$			0.358508i			0.0343389i	−0.999853	+	0.0171694i	$0.994535\pi$
$110$		0			0
$111$	0.548585	+	0.178246i	0.0520694	+	0.0169184i
$112$		0			0
$113$	−1.09455	−	3.36867i	−0.102966	−	0.316898i	0.886281	−	0.463147i	$-0.153280\pi$
$113$	−1.09455	−	3.36867i	−0.102966	−	0.316898i	−0.989248	+	0.146249i	$0.953280\pi$
$114$		0			0
$115$	1.51467	+	4.66169i	0.141244	+	0.434704i
$116$		0			0
$117$	−10.6432	−	14.6492i	−0.983968	−	1.35432i
$118$		0			0
$119$	0.412455	−	1.26941i	0.0378097	−	0.116366i
$120$		0			0
$121$	−6.43143	+	4.67271i	−0.584675	+	0.424792i
$122$		0			0
$123$	−1.57872	−	1.14855i	−0.142349	−	0.103561i
$124$		0			0
$125$	−8.97545	+	6.52105i	−0.802789	+	0.583260i
$126$		0			0
$127$	−6.58029	+	20.2520i	−0.583906	+	1.79708i	0.0197134	+	0.999806i	$0.493725\pi$
$127$	−6.58029	+	20.2520i	−0.583906	+	1.79708i	−0.603620	+	0.797273i	$0.706275\pi$
$128$		0			0
$129$	0.546245	+	0.751841i	0.0480942	+	0.0661959i
$130$		0			0
$131$	−4.64085	−	14.2831i	−0.405473	−	1.24792i	−0.920499	−	0.390744i	$-0.872218\pi$
$131$	−4.64085	−	14.2831i	−0.405473	−	1.24792i	0.515026	−	0.857174i	$-0.327782\pi$
$132$		0			0
$133$	−1.04883	−	3.22796i	−0.0909449	−	0.279900i
$134$		0			0
$135$	2.33330	+	0.758135i	0.200819	+	0.0652499i
$136$		0			0
$137$			15.6782i			1.33948i	0.742595	+	0.669741i	$0.233595\pi$
$137$			15.6782i			1.33948i	−0.742595	+	0.669741i	$0.766405\pi$
$138$		0			0
$139$	6.66357	+	4.84136i	0.565196	+	0.410639i	0.833357	−	0.552735i	$-0.186416\pi$
$139$	6.66357	+	4.84136i	0.565196	+	0.410639i	−0.268161	+	0.963374i	$0.586416\pi$
$140$		0			0
$141$	1.17009	−	0.850119i	0.0985393	−	0.0715930i
$142$		0			0
$143$	8.80106	+	6.39435i	0.735982	+	0.534722i
$144$		0			0
$145$	−4.22000	+	5.80833i	−0.350452	+	0.482356i
$146$		0			0
$147$	−0.289977	+	0.0942193i	−0.0239169	+	0.00777107i
$148$		0			0
$149$	−5.31914	−	1.72829i	−0.435761	−	0.141587i	0.0829179	−	0.996556i	$-0.473576\pi$
$149$	−5.31914	−	1.72829i	−0.435761	−	0.141587i	−0.518679	+	0.854969i	$0.673576\pi$
$150$		0			0
$151$	−9.84354	−	13.5485i	−0.801056	−	1.10256i	−0.992642	−	0.121083i	$-0.961363\pi$
$151$	−9.84354	−	13.5485i	−0.801056	−	1.10256i	0.191587	−	0.981476i	$-0.438637\pi$
$152$		0			0
$153$	3.69021	−	1.19902i	0.298336	−	0.0969351i
$154$		0			0
$155$	3.93726			0.316249
$156$		0			0
$157$	−10.4234	+	14.3466i	−0.831882	+	1.14499i	0.155688	+	0.987806i	$0.450241\pi$
$157$	−10.4234	+	14.3466i	−0.831882	+	1.14499i	−0.987570	+	0.157181i	$0.949759\pi$
$158$		0			0
$159$	0.374505	−	1.15261i	0.0297002	−	0.0914078i
$160$		0			0
$161$		−	3.59832i		−	0.283587i
$162$		0			0
$163$	−8.03055			−0.629001			−0.314500	−	0.949257i	$-0.601837\pi$
$163$	−8.03055			−0.629001			−0.314500	+	0.949257i	$0.601837\pi$
$164$		0			0
$165$	−0.725383			−0.0564710
$166$		0			0
$167$		−	11.8793i		−	0.919250i	−0.888113	−	0.459625i	$-0.847984\pi$
$167$		−	11.8793i		−	0.919250i	0.888113	−	0.459625i	$-0.152016\pi$
$168$		0			0
$169$	−7.97204	+	24.5354i	−0.613234	+	1.88734i
$170$		0			0
$171$	5.79950	−	7.98233i	0.443499	−	0.610424i
$172$		0			0
$173$	−12.5516			−0.954282			−0.477141	−	0.878827i	$-0.658327\pi$
$173$	−12.5516			−0.954282			−0.477141	+	0.878827i	$0.658327\pi$
$174$		0			0
$175$	2.99054	−	0.971686i	0.226064	−	0.0734525i
$176$		0			0
$177$	−2.49049	−	3.42786i	−0.187197	−	0.257654i
$178$		0			0
$179$	12.9244	+	4.19939i	0.966014	+	0.313877i	0.749206	−	0.662337i	$-0.230435\pi$
$179$	12.9244	+	4.19939i	0.966014	+	0.313877i	0.216808	+	0.976214i	$0.430435\pi$
$180$		0			0
$181$	10.9217	−	3.54867i	0.811801	−	0.263770i	0.126441	−	0.991974i	$-0.459645\pi$
$181$	10.9217	−	3.54867i	0.811801	−	0.263770i	0.685360	+	0.728204i	$0.259645\pi$
$182$		0			0
$183$	−0.00118399	+	0.00162962i	−8.75229e−5	+	0.000120465i
$184$		0			0
$185$	−2.08485	−	1.51473i	−0.153281	−	0.111366i
$186$		0			0
$187$	−1.88592	+	1.37020i	−0.137912	+	0.100199i
$188$		0			0
$189$	−1.45708	−	1.05863i	−0.105987	−	0.0770043i
$190$		0			0
$191$		−	9.47925i		−	0.685895i	−0.939355	−	0.342947i	$-0.888575\pi$
$191$		−	9.47925i		−	0.685895i	0.939355	−	0.342947i	$-0.111425\pi$
$192$		0			0
$193$	1.58648	+	0.515480i	0.114198	+	0.0371050i	0.365558	−	0.930788i	$-0.380878\pi$
$193$	1.58648	+	0.515480i	0.114198	+	0.0371050i	−0.251361	+	0.967893i	$0.580878\pi$
$194$		0			0
$195$	−0.799433	−	2.46040i	−0.0572486	−	0.176193i
$196$		0			0
$197$	4.00402	+	12.3231i	0.285275	+	0.877985i	0.986316	+	0.164864i	$0.0527187\pi$
$197$	4.00402	+	12.3231i	0.285275	+	0.877985i	−0.701042	+	0.713120i	$0.747281\pi$
$198$		0			0
$199$	−2.42193	−	3.33350i	−0.171686	−	0.236305i	0.714500	−	0.699636i	$-0.246654\pi$
$199$	−2.42193	−	3.33350i	−0.171686	−	0.236305i	−0.886186	+	0.463330i	$0.846654\pi$
$200$		0			0
$201$	−0.731876	+	2.25248i	−0.0516226	+	0.158878i
$202$		0			0
$203$	4.26397	−	3.09795i	0.299272	−	0.217434i
$204$		0			0
$205$	5.12232	+	7.05973i	0.357759	+	0.493073i
$206$		0			0
$207$	8.46267	−	6.14849i	0.588196	−	0.427349i
$208$		0			0
$209$	−1.83179	+	5.63768i	−0.126708	+	0.389967i
$210$		0			0
$211$	0.771638	+	1.06207i	0.0531217	+	0.0731158i	0.834751	−	0.550627i	$-0.185611\pi$
$211$	0.771638	+	1.06207i	0.0531217	+	0.0731158i	−0.781630	+	0.623743i	$0.785611\pi$
$212$		0			0
$213$	0.195560	+	0.601872i	0.0133996	+	0.0412396i
$214$		0			0
$215$	−1.28301	−	3.94871i	−0.0875008	−	0.269300i
$216$		0			0
$217$	−2.74893	−	0.893181i	−0.186609	−	0.0606331i
$218$		0			0
$219$		−	2.18368i		−	0.147560i
$220$		0			0
$221$	−6.72600	−	4.88672i	−0.452440	−	0.328717i
$222$		0			0
$223$	−6.10117	+	4.43276i	−0.408565	+	0.296840i	−0.773021	−	0.634381i	$-0.781255\pi$
$223$	−6.10117	+	4.43276i	−0.408565	+	0.296840i	0.364456	+	0.931221i	$0.381255\pi$
$224$		0			0
$225$	7.39523	+	5.37295i	0.493015	+	0.358196i
$226$		0			0
$227$	−5.57278	+	7.67027i	−0.369878	+	0.509094i	−0.952868	−	0.303386i	$-0.901883\pi$
$227$	−5.57278	+	7.67027i	−0.369878	+	0.509094i	0.582990	+	0.812480i	$0.301883\pi$
$228$		0			0
$229$	7.18979	−	2.33611i	0.475115	−	0.154374i	−0.0616643	−	0.998097i	$-0.519641\pi$
$229$	7.18979	−	2.33611i	0.475115	−	0.154374i	0.536779	+	0.843723i	$0.319641\pi$
$230$		0			0
$231$	0.506449	+	0.164555i	0.0333219	+	0.0108270i
$232$		0			0
$233$	6.63009	+	9.12554i	0.434352	+	0.597834i	0.968945	−	0.247276i	$-0.0795353\pi$
$233$	6.63009	+	9.12554i	0.434352	+	0.597834i	−0.534594	+	0.845109i	$0.679535\pi$
$234$		0			0
$235$	−6.14537	+	1.99675i	−0.400879	+	0.130254i
$236$		0			0
$237$	−4.34306			−0.282112
$238$		0			0
$239$	−2.07817	+	2.86036i	−0.134426	+	0.185021i	−0.870923	−	0.491419i	$-0.836478\pi$
$239$	−2.07817	+	2.86036i	−0.134426	+	0.185021i	0.736497	+	0.676440i	$0.236478\pi$
$240$		0			0
$241$	−9.33757	+	28.7381i	−0.601486	+	1.85118i	−0.0821367	+	0.996621i	$0.526174\pi$
$241$	−9.33757	+	28.7381i	−0.601486	+	1.85118i	−0.519349	+	0.854562i	$0.673826\pi$
$242$		0			0
$243$		−	7.89480i		−	0.506451i
$244$		0			0
$245$	1.36219			0.0870271
$246$		0			0
$247$	−21.1411			−1.34517
$248$		0			0
$249$			2.13149i			0.135078i
$250$		0			0
$251$	−1.12878	+	3.47404i	−0.0712481	+	0.219279i	−0.980340	−	0.197317i	$-0.936777\pi$
$251$	−1.12878	+	3.47404i	−0.0712481	+	0.219279i	0.909092	+	0.416596i	$0.136777\pi$
$252$		0			0
$253$	−3.69394	+	5.08428i	−0.232236	+	0.319646i
$254$		0			0
$255$	0.554356			0.0347151
$256$		0			0
$257$	0.289332	−	0.0940098i	0.0180481	−	0.00586417i	−0.299979	−	0.953946i	$-0.596980\pi$
$257$	0.289332	−	0.0940098i	0.0180481	−	0.00586417i	0.318027	+	0.948082i	$0.396980\pi$
$258$		0			0
$259$	1.11199	+	1.53052i	0.0690954	+	0.0951017i
$260$		0			0
$261$	14.5718	+	4.73466i	0.901971	+	0.293068i
$262$		0			0
$263$	−13.4049	+	4.35551i	−0.826581	+	0.268572i	−0.691605	−	0.722276i	$-0.743096\pi$
$263$	−13.4049	+	4.35551i	−0.826581	+	0.268572i	−0.134976	+	0.990849i	$0.543096\pi$
$264$		0			0
$265$	−3.18254	+	4.38039i	−0.195502	+	0.269085i
$266$		0			0
$267$	−3.53075	−	2.56524i	−0.216079	−	0.156990i
$268$		0			0
$269$	−12.2365	+	8.89036i	−0.746075	+	0.542055i	−0.894608	−	0.446853i	$-0.852545\pi$
$269$	−12.2365	+	8.89036i	−0.746075	+	0.542055i	0.148533	+	0.988907i	$0.452545\pi$
$270$		0			0
$271$	15.1230	+	10.9875i	0.918655	+	0.667442i	0.943189	−	0.332257i	$-0.107810\pi$
$271$	15.1230	+	10.9875i	0.918655	+	0.667442i	−0.0245336	+	0.999699i	$0.507810\pi$
$272$		0			0
$273$			1.89916i			0.114943i
$274$		0			0
$275$	−5.22303	−	1.69706i	−0.314960	−	0.102337i
$276$		0			0
$277$	−0.302293	−	0.930363i	−0.0181630	−	0.0559001i	0.941564	−	0.336834i	$-0.109356\pi$
$277$	−0.302293	−	0.930363i	−0.0181630	−	0.0559001i	−0.959727	+	0.280933i	$0.909356\pi$
$278$		0			0
$279$	−2.59651	−	7.99123i	−0.155449	−	0.478422i
$280$		0			0
$281$	13.7816	+	18.9688i	0.822142	+	1.13158i	0.989335	+	0.145658i	$0.0465298\pi$
$281$	13.7816	+	18.9688i	0.822142	+	1.13158i	−0.167193	+	0.985924i	$0.553470\pi$
$282$		0			0
$283$	−5.74089	+	17.6687i	−0.341261	+	1.05029i	0.622295	+	0.782783i	$0.286201\pi$
$283$	−5.74089	+	17.6687i	−0.341261	+	1.05029i	−0.963555	+	0.267509i	$0.913799\pi$
$284$		0			0
$285$	1.14044	−	0.828581i	0.0675541	−	0.0490809i
$286$		0			0
$287$	−1.97479	−	6.09099i	−0.116568	−	0.359540i
$288$		0			0
$289$	−12.3120	+	8.94520i	−0.724236	+	0.526188i
$290$		0			0
$291$	1.00875	−	3.10461i	0.0591339	−	0.181995i
$292$		0			0
$293$	−7.93196	−	10.9174i	−0.463390	−	0.637802i	0.511817	−	0.859094i	$-0.328972\pi$
$293$	−7.93196	−	10.9174i	−0.463390	−	0.637802i	−0.975207	+	0.221293i	$0.928972\pi$
$294$		0			0
$295$	5.84963	+	18.0033i	0.340579	+	1.04819i
$296$		0			0
$297$	0.972035	+	2.99162i	0.0564032	+	0.173591i
$298$		0			0
$299$	−21.3162	−	6.92606i	−1.23275	−	0.400545i
$300$		0			0
$301$			3.04797i			0.175682i
$302$		0			0
$303$	1.82868	+	1.32861i	0.105055	+	0.0763268i
$304$		0			0
$305$	0.00728058	−	0.00528965i	0.000416885	−	0.000302885i
$306$		0			0
$307$	−16.4123	−	11.9243i	−0.936702	−	0.680554i	0.0109228	−	0.999940i	$-0.496523\pi$
$307$	−16.4123	−	11.9243i	−0.936702	−	0.680554i	−0.947624	+	0.319387i	$0.896523\pi$
$308$		0			0
$309$	−0.113827	+	0.156669i	−0.00647537	+	0.00891259i
$310$		0			0
$311$	−11.3741	+	3.69566i	−0.644964	+	0.209562i	−0.613193	−	0.789934i	$-0.710115\pi$
$311$	−11.3741	+	3.69566i	−0.644964	+	0.209562i	−0.0317719	+	0.999495i	$0.510115\pi$
$312$		0			0
$313$	−5.20427	−	1.69097i	−0.294163	−	0.0955793i	0.158218	−	0.987404i	$-0.449425\pi$
$313$	−5.20427	−	1.69097i	−0.294163	−	0.0955793i	−0.452381	+	0.891825i	$0.649425\pi$
$314$		0			0
$315$	2.32759	+	3.20365i	0.131145	+	0.180505i
$316$		0			0
$317$	3.54156	−	1.15072i	0.198914	−	0.0646310i	−0.207866	−	0.978157i	$-0.566652\pi$
$317$	3.54156	−	1.15072i	0.198914	−	0.0646310i	0.406780	+	0.913526i	$0.366652\pi$
$318$		0			0
$319$	−9.20510			−0.515387
$320$		0			0
$321$	−0.000413852	0	0.000569618i	−2.30990e−5	0	3.17930e-5i
$322$		0			0
$323$	1.39990	−	4.30846i	0.0778927	−	0.239729i
$324$		0			0
$325$		−	19.5861i		−	1.08644i
$326$		0			0
$327$	0.109309			0.00604481
$328$		0			0
$329$	4.74356			0.261521
$330$		0			0
$331$		−	31.4717i		−	1.72984i	−0.501907	−	0.864922i	$-0.667368\pi$
$331$		−	31.4717i		−	1.72984i	0.501907	−	0.864922i	$-0.332632\pi$
$332$		0			0
$333$	−1.69947	+	5.23043i	−0.0931303	+	0.286626i
$334$		0			0
$335$	6.21948	−	8.56038i	0.339806	−	0.467703i
$336$		0			0
$337$	7.36661			0.401285			0.200642	−	0.979665i	$-0.435697\pi$
$337$	7.36661			0.401285			0.200642	+	0.979665i	$0.435697\pi$
$338$		0			0
$339$	−1.02711	+	0.333727i	−0.0557848	+	0.0181256i
$340$		0			0
$341$	2.96721	+	4.08401i	0.160683	+	0.221162i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$		0			0
$345$	1.42135	−	0.461824i	0.0765228	−	0.0248638i
$346$		0			0
$347$	3.55338	−	4.89081i	0.190756	−	0.262553i	−0.702917	−	0.711272i	$-0.748120\pi$
$347$	3.55338	−	4.89081i	0.190756	−	0.262553i	0.893673	+	0.448719i	$0.148120\pi$
$348$		0			0
$349$	−26.0309	−	18.9126i	−1.39340	−	1.01237i	−0.995482	−	0.0949482i	$-0.969731\pi$
$349$	−26.0309	−	18.9126i	−1.39340	−	1.01237i	−0.397922	−	0.917419i	$-0.630269\pi$
$350$		0			0
$351$	−9.07590	+	6.59403i	−0.484436	+	0.351963i
$352$		0			0
$353$	−4.66229	−	3.38736i	−0.248149	−	0.180291i	0.456757	−	0.889591i	$-0.349011\pi$
$353$	−4.66229	−	3.38736i	−0.248149	−	0.180291i	−0.704906	+	0.709301i	$0.749011\pi$
$354$		0			0
$355$		−	2.82734i		−	0.150060i
$356$		0			0
$357$	−0.387042	−	0.125757i	−0.0204844	−	0.00665579i
$358$		0			0
$359$	−5.60427	−	17.2482i	−0.295782	−	0.910324i	−0.982958	−	0.183832i	$-0.941150\pi$
$359$	−5.60427	−	17.2482i	−0.295782	−	0.910324i	0.687175	−	0.726492i	$-0.258850\pi$
$360$		0			0
$361$	2.31152	+	7.11413i	0.121659	+	0.374428i
$362$		0			0
$363$	1.42471	+	1.96094i	0.0747778	+	0.102923i
$364$		0			0
$365$	−3.01476	+	9.27847i	−0.157800	+	0.485657i
$366$		0			0
$367$	−11.4485	+	8.31784i	−0.597608	+	0.434188i	−0.845029	−	0.534720i	$-0.820417\pi$
$367$	−11.4485	+	8.31784i	−0.597608	+	0.434188i	0.247421	+	0.968908i	$0.420417\pi$
$368$		0			0
$369$	10.9507	−	15.0522i	0.570070	−	0.783584i
$370$		0			0
$371$	3.21570	−	2.33634i	0.166951	−	0.121297i
$372$		0			0
$373$	3.76037	−	11.5732i	0.194704	−	0.599238i	−0.805276	−	0.592901i	$-0.797983\pi$
$373$	3.76037	−	11.5732i	0.194704	−	0.599238i	0.999980	−	0.00633771i	$-0.00201737\pi$
$374$		0			0
$375$	1.98827	+	2.73661i	0.102674	+	0.141318i
$376$		0			0
$377$	−10.1448	−	31.2225i	−0.522484	−	1.60804i
$378$		0			0
$379$	6.63217	+	20.4117i	0.340672	+	1.04848i	0.963860	+	0.266408i	$0.0858369\pi$
$379$	6.63217	+	20.4117i	0.340672	+	1.04848i	−0.623189	+	0.782072i	$0.714163\pi$
$380$		0			0
$381$	6.17485	+	2.00633i	0.316347	+	0.102787i
$382$		0			0
$383$		−	4.87601i		−	0.249153i	−0.992210	−	0.124576i	$-0.960243\pi$
$383$		−	4.87601i		−	0.249153i	0.992210	−	0.124576i	$-0.0397572\pi$
$384$		0			0
$385$	−1.92472	−	1.39839i	−0.0980928	−	0.0712686i
$386$		0			0
$387$	−7.16835	+	5.20811i	−0.364388	+	0.264743i
$388$		0			0
$389$	20.4976	+	14.8924i	1.03927	+	0.755073i	0.970143	−	0.242535i	$-0.0779789\pi$
$389$	20.4976	+	14.8924i	1.03927	+	0.755073i	0.0691262	+	0.997608i	$0.477979\pi$
$390$		0			0
$391$	2.82301	−	3.88554i	0.142766	−	0.196500i
$392$		0			0
$393$	−4.35491	+	1.41500i	−0.219676	+	0.0713771i
$394$		0			0
$395$	18.4536	+	5.99595i	0.928503	+	0.301689i
$396$		0			0
$397$	1.84939	+	2.54547i	0.0928182	+	0.127753i	0.852900	−	0.522074i	$-0.174841\pi$
$397$	1.84939	+	2.54547i	0.0928182	+	0.127753i	−0.760082	+	0.649827i	$0.774841\pi$
$398$		0			0
$399$	−0.984204	+	0.319787i	−0.0492718	+	0.0160094i
$400$		0			0
$401$	21.3830			1.06782			0.533909	−	0.845542i	$-0.320723\pi$
$401$	21.3830			1.06782			0.533909	+	0.845542i	$0.320723\pi$
$402$		0			0
$403$	−10.5823	+	14.5653i	−0.527143	+	0.725550i
$404$		0			0
$405$	−3.43990	+	10.5869i	−0.170930	+	0.526069i
$406$		0			0
$407$		−	3.30410i		−	0.163778i
$408$		0			0
$409$	−8.40686			−0.415692			−0.207846	−	0.978162i	$-0.566645\pi$
$409$	−8.40686			−0.415692			−0.207846	+	0.978162i	$0.566645\pi$
$410$		0			0
$411$	4.78029			0.235794
$412$		0			0
$413$		−	13.8966i		−	0.683807i
$414$		0			0
$415$	2.94270	−	9.05671i	0.144452	−	0.444577i
$416$		0			0
$417$	1.47613	−	2.03172i	0.0722865	−	0.0994938i
$418$		0			0
$419$	10.5515			0.515477			0.257738	−	0.966215i	$-0.417023\pi$
$419$	10.5515			0.515477			0.257738	+	0.966215i	$0.417023\pi$
$420$		0			0
$421$	−4.29222	+	1.39463i	−0.209190	+	0.0679699i	−0.411737	−	0.911303i	$-0.635078\pi$
$421$	−4.29222	+	1.39463i	−0.209190	+	0.0679699i	0.202548	+	0.979272i	$0.435078\pi$
$422$		0			0
$423$	8.10537	+	11.1561i	0.394097	+	0.542428i
$424$		0			0
$425$	3.99157	+	1.29694i	0.193620	+	0.0629108i
$426$		0			0
$427$	−0.00628315	+	0.00204152i	−0.000304063	+	9.87960e-5i
$428$		0			0
$429$	1.94964	−	2.68344i	0.0941293	−	0.129558i
$430$		0			0
$431$	−3.08384	−	2.24054i	−0.148543	−	0.107923i	0.511031	−	0.859562i	$-0.329264\pi$
$431$	−3.08384	−	2.24054i	−0.148543	−	0.107923i	−0.659575	+	0.751639i	$0.729264\pi$
$432$		0			0
$433$	27.8317	−	20.2209i	1.33751	−	0.971756i	0.337976	−	0.941155i	$-0.390258\pi$
$433$	27.8317	−	20.2209i	1.33751	−	0.971756i	0.999532	−	0.0306012i	$-0.00974218\pi$
$434$		0			0
$435$	1.77096	+	1.28668i	0.0849110	+	0.0616915i
$436$		0			0
$437$		−	12.2130i		−	0.584225i
$438$		0			0
$439$	−27.1009	−	8.80561i	−1.29345	−	0.420269i	−0.420155	−	0.907452i	$-0.638024\pi$
$439$	−27.1009	−	8.80561i	−1.29345	−	0.420269i	−0.873300	+	0.487183i	$0.838024\pi$
$440$		0			0
$441$	−0.898324	−	2.76476i	−0.0427773	−	0.131655i
$442$		0			0
$443$	11.2211	+	34.5349i	0.533130	+	1.64080i	0.747656	+	0.664086i	$0.231179\pi$
$443$	11.2211	+	34.5349i	0.533130	+	1.64080i	−0.214527	+	0.976718i	$0.568821\pi$
$444$		0			0
$445$	11.4606	+	15.7742i	0.543286	+	0.747769i
$446$		0			0
$447$	−0.526957	+	1.62181i	−0.0249242	+	0.0767088i
$448$		0			0
$449$	−23.1445	+	16.8155i	−1.09226	+	0.793572i	−0.979779	−	0.200082i	$-0.935879\pi$
$449$	−23.1445	+	16.8155i	−1.09226	+	0.793572i	−0.112479	+	0.993654i	$0.535879\pi$
$450$		0			0
$451$	−3.46256	+	10.6336i	−0.163046	+	0.500717i
$452$		0			0
$453$	−4.13093	+	3.00129i	−0.194088	+	0.141013i
$454$		0			0
$455$	2.62195	−	8.06954i	0.122919	−	0.378306i
$456$		0			0
$457$	−5.26117	−	7.24138i	−0.246107	−	0.338738i	0.668036	−	0.744129i	$-0.267135\pi$
$457$	−5.26117	−	7.24138i	−0.246107	−	0.338738i	−0.914143	+	0.405391i	$0.867135\pi$
$458$		0			0
$459$	−0.742854	−	2.28627i	−0.0346735	−	0.106714i
$460$		0			0
$461$	1.11097	+	3.41922i	0.0517431	+	0.159249i	0.973589	−	0.228308i	$-0.0733192\pi$
$461$	1.11097	+	3.41922i	0.0517431	+	0.159249i	−0.921846	+	0.387557i	$0.873319\pi$
$462$		0			0
$463$	39.5953	+	12.8653i	1.84015	+	0.597902i	0.998306	+	0.0581835i	$0.0185308\pi$
$463$	39.5953	+	12.8653i	1.84015	+	0.597902i	0.841846	+	0.539718i	$0.181469\pi$
$464$		0			0
$465$		−	1.20047i		−	0.0556705i
$466$		0			0
$467$	−15.1387	−	10.9989i	−0.700533	−	0.508967i	0.179573	−	0.983745i	$-0.442529\pi$
$467$	−15.1387	−	10.9989i	−0.700533	−	0.508967i	−0.880106	+	0.474777i	$0.842529\pi$
$468$		0			0
$469$	−6.28428	+	4.56580i	−0.290181	+	0.210829i
$470$		0			0
$471$	4.37429	+	3.17811i	0.201557	+	0.146440i
$472$		0			0
$473$	3.12898	−	4.30667i	0.143871	−	0.198021i
$474$		0			0
$475$	10.1501	−	3.29798i	0.465720	−	0.151321i
$476$		0			0
$477$	10.9894	+	3.57068i	0.503171	+	0.163490i
$478$		0			0
$479$	−16.2719	−	22.3963i	−0.743481	−	1.02331i	−0.998411	−	0.0563548i	$-0.982052\pi$
$479$	−16.2719	−	22.3963i	−0.743481	−	1.02331i	0.254929	−	0.966960i	$-0.417948\pi$
$480$		0			0
$481$	11.2071	−	3.64140i	0.510998	−	0.166033i
$482$		0			0
$483$	−1.09713			−0.0499210
$484$		0			0
$485$	−8.57234	+	11.7988i	−0.389250	+	0.535756i
$486$		0			0
$487$	−2.26211	+	6.96206i	−0.102506	+	0.315481i	−0.989137	−	0.146996i	$-0.953039\pi$
$487$	−2.26211	+	6.96206i	−0.102506	+	0.315481i	0.886631	+	0.462478i	$0.153039\pi$
$488$		0			0
$489$			2.44851i			0.110726i
$490$		0			0
$491$	37.0346			1.67135			0.835674	−	0.549226i	$-0.185078\pi$
$491$	37.0346			1.67135			0.835674	+	0.549226i	$0.185078\pi$
$492$		0			0
$493$	7.03478			0.316830
$494$		0			0
$495$		−	6.91609i		−	0.310855i
$496$		0			0
$497$	−0.641391	+	1.97400i	−0.0287703	+	0.0885459i
$498$		0			0
$499$	−10.7527	+	14.7999i	−0.481359	+	0.662534i	−0.978765	−	0.204984i	$-0.934286\pi$
$499$	−10.7527	+	14.7999i	−0.481359	+	0.662534i	0.497406	+	0.867518i	$0.334286\pi$
$500$		0			0
$501$	−3.62201			−0.161819
$502$		0			0
$503$	3.16317	−	1.02777i	0.141039	−	0.0458262i	−0.237647	−	0.971352i	$-0.576376\pi$
$503$	3.16317	−	1.02777i	0.141039	−	0.0458262i	0.378686	+	0.925525i	$0.376376\pi$
$504$		0			0
$505$	−5.93579	−	8.16991i	−0.264139	−	0.363556i
$506$		0			0
$507$	7.48085	+	2.43067i	0.332236	+	0.107950i
$508$		0			0
$509$	33.8651	−	11.0035i	1.50105	−	0.487719i	0.560723	−	0.828003i	$-0.310523\pi$
$509$	33.8651	−	11.0035i	1.50105	−	0.487719i	0.940323	+	0.340284i	$0.110523\pi$
$510$		0			0
$511$	4.20970	−	5.79416i	0.186226	−	0.256318i
$512$		0			0
$513$	−4.94545	−	3.59308i	−0.218347	−	0.158639i
$514$		0			0
$515$	0.699944	−	0.508539i	0.0308432	−	0.0224089i
$516$		0			0
$517$	−6.70246	−	4.86962i	−0.294774	−	0.214166i
$518$		0			0
$519$			3.82699i			0.167986i
$520$		0			0
$521$	29.2063	+	9.48971i	1.27955	+	0.415752i	0.868422	−	0.495825i	$-0.165134\pi$
$521$	29.2063	+	9.48971i	1.27955	+	0.415752i	0.411130	+	0.911577i	$0.365134\pi$
$522$		0			0
$523$	1.21648	+	3.74395i	0.0531930	+	0.163711i	0.974124	−	0.226015i	$-0.0725697\pi$
$523$	1.21648	+	3.74395i	0.0531930	+	0.163711i	−0.920931	+	0.389726i	$0.872570\pi$
$524$		0			0
$525$	−0.296267	−	0.911816i	−0.0129301	−	0.0397949i
$526$		0			0
$527$	−2.26762	−	3.12111i	−0.0987790	−	0.135958i
$528$		0			0
$529$	−3.10628	+	9.56014i	−0.135056	+	0.415658i
$530$		0			0
$531$	32.6826	−	23.7453i	1.41830	−	1.03046i
$532$		0			0
$533$	−39.8838	−	0.0254083i	−1.72756	−	0.00110055i
$534$		0			0
$535$	0.00254486	−	0.00184895i	0.000110024	−	7.99371e-5i
$536$		0			0
$537$	1.28039	−	3.94064i	0.0552530	−	0.170051i
$538$		0			0
$539$	1.02658	+	1.41296i	0.0442178	+	0.0608605i
$540$		0			0
$541$	−10.2293	−	31.4826i	−0.439793	−	1.35354i	−0.888094	−	0.459661i	$-0.847971\pi$
$541$	−10.2293	−	31.4826i	−0.439793	−	1.35354i	0.448301	−	0.893882i	$-0.352029\pi$
$542$		0			0
$543$	−1.08199	−	3.33002i	−0.0464325	−	0.142905i
$544$		0			0
$545$	−0.464454	−	0.150910i	−0.0198950	−	0.00646429i
$546$		0			0
$547$		−	40.7582i		−	1.74269i	−0.490668	−	0.871346i	$-0.663247\pi$
$547$		−	40.7582i		−	1.74269i	0.490668	−	0.871346i	$-0.336753\pi$
$548$		0			0
$549$	−0.0155374	−	0.0112886i	−0.000663121	−	0.000481786i
$550$		0			0
$551$	14.4722	−	10.5147i	0.616538	−	0.447941i
$552$		0			0
$553$	−11.5238	−	8.37254i	−0.490042	−	0.356036i
$554$		0			0
$555$	−0.461843	+	0.635672i	−0.0196041	+	0.0269828i
$556$		0			0
$557$	−19.9626	+	6.48625i	−0.845844	+	0.274831i	−0.699704	−	0.714433i	$-0.746685\pi$
$557$	−19.9626	+	6.48625i	−0.845844	+	0.274831i	−0.146140	+	0.989264i	$0.546685\pi$
$558$		0			0
$559$	18.0560	+	5.86676i	0.763689	+	0.248138i
$560$		0			0
$561$	0.417775	+	0.575018i	0.0176385	+	0.0242773i
$562$		0			0
$563$	−4.08245	+	1.32647i	−0.172055	+	0.0559040i	−0.393778	−	0.919206i	$-0.628832\pi$
$563$	−4.08245	+	1.32647i	−0.172055	+	0.0559040i	0.221723	+	0.975110i	$0.428832\pi$
$564$		0			0
$565$	4.82492			0.202986
$566$		0			0
$567$	4.80336	−	6.61126i	0.201722	−	0.277647i
$568$		0			0
$569$	6.71404	−	20.6637i	0.281467	−	0.866267i	−0.705968	−	0.708243i	$-0.749488\pi$
$569$	6.71404	−	20.6637i	0.281467	−	0.866267i	0.987435	−	0.158023i	$-0.0505121\pi$
$570$		0			0
$571$			40.4748i			1.69382i	0.531739	+	0.846908i	$0.321539\pi$
$571$			40.4748i			1.69382i	−0.531739	+	0.846908i	$0.678461\pi$
$572$		0			0
$573$	−2.89022			−0.120741
$574$		0			0
$575$	11.3147			0.471855
$576$		0			0
$577$		−	11.0980i		−	0.462017i	−0.972952	−	0.231009i	$-0.925797\pi$
$577$		−	11.0980i		−	0.462017i	0.972952	−	0.231009i	$-0.0742026\pi$
$578$		0			0
$579$	0.157170	−	0.483719i	0.00653175	−	0.0201027i
$580$		0			0
$581$	−4.10909	+	5.65568i	−0.170474	+	0.234637i
$582$		0			0
$583$	−6.94209			−0.287512
$584$		0			0
$585$	23.4584	−	7.62211i	0.969887	−	0.315135i
$586$		0			0
$587$	15.9989	+	22.0206i	0.660346	+	0.908888i	0.999493	−	0.0318454i	$-0.0101384\pi$
$587$	15.9989	+	22.0206i	0.660346	+	0.908888i	−0.339147	+	0.940733i	$0.610138\pi$
$588$		0			0
$589$	−9.33007	−	3.03152i	−0.384439	−	0.124912i
$590$		0			0
$591$	3.75731	−	1.22082i	0.154555	−	0.0502180i
$592$		0			0
$593$	13.8639	−	19.0820i	0.569322	−	0.783605i	−0.423152	−	0.906059i	$-0.639076\pi$
$593$	13.8639	−	19.0820i	0.569322	−	0.783605i	0.992474	+	0.122454i	$0.0390764\pi$
$594$		0			0
$595$	1.47092	+	1.06869i	0.0603019	+	0.0438119i
$596$		0			0
$597$	−1.01638	+	0.738445i	−0.0415978	+	0.0302226i
$598$		0			0
$599$	−13.8266	−	10.0456i	−0.564939	−	0.410452i	0.268325	−	0.963329i	$-0.413530\pi$
$599$	−13.8266	−	10.0456i	−0.564939	−	0.410452i	−0.833263	+	0.552877i	$0.813530\pi$
$600$		0			0
$601$			2.20274i			0.0898516i	0.998990	+	0.0449258i	$0.0143051\pi$
$601$			2.20274i			0.0898516i	−0.998990	+	0.0449258i	$0.985695\pi$
$602$		0			0
$603$	−21.4761	−	6.97800i	−0.874573	−	0.284166i
$604$		0			0
$605$	−3.34634	−	10.2990i	−0.136048	−	0.418712i
$606$		0			0
$607$	11.1705	+	34.3792i	0.453395	+	1.39541i	0.873009	+	0.487705i	$0.162166\pi$
$607$	11.1705	+	34.3792i	0.453395	+	1.39541i	−0.419613	+	0.907703i	$0.637834\pi$
$608$		0			0
$609$	−0.944566	−	1.30008i	−0.0382757	−	0.0526820i
$610$		0			0
$611$	9.13043	−	28.1006i	0.369378	−	1.13683i
$612$		0			0
$613$	20.2963	−	14.7461i	0.819759	−	0.595589i	−0.0968848	−	0.995296i	$-0.530888\pi$
$613$	20.2963	−	14.7461i	0.819759	−	0.595589i	0.916643	+	0.399706i	$0.130888\pi$
$614$		0			0
$615$	2.15251	−	1.56180i	0.0867976	−	0.0629777i
$616$		0			0
$617$	37.6480	−	27.3529i	1.51565	−	1.10119i	0.552061	−	0.833804i	$-0.313842\pi$
$617$	37.6480	−	27.3529i	1.51565	−	1.10119i	0.963591	−	0.267381i	$-0.0861583\pi$
$618$		0			0
$619$	−6.77254	+	20.8437i	−0.272211	+	0.837780i	0.717733	+	0.696319i	$0.245180\pi$
$619$	−6.77254	+	20.8437i	−0.272211	+	0.837780i	−0.989944	+	0.141461i	$0.954820\pi$
$620$		0			0
$621$	−3.80930	−	5.24305i	−0.152862	−	0.210396i
$622$		0			0
$623$	−4.42318	−	13.6132i	−0.177211	−	0.545400i
$624$		0			0
$625$	0.188410	+	0.579868i	0.00753642	+	0.0231947i
$626$		0			0
$627$	1.71893	+	0.558514i	0.0686474	+	0.0223049i
$628$		0			0
$629$			2.52508i			0.100681i
$630$		0			0
$631$	6.54436	+	4.75475i	0.260527	+	0.189284i	0.710379	−	0.703819i	$-0.248523\pi$
$631$	6.54436	+	4.75475i	0.260527	+	0.189284i	−0.449852	+	0.893103i	$0.648523\pi$
$632$		0			0
$633$	0.323825	−	0.235272i	0.0128709	−	0.00935123i
$634$		0			0
$635$	−23.4670	−	17.0498i	−0.931260	−	0.676600i
$636$		0			0
$637$	−3.66120	+	5.03921i	−0.145062	+	0.199661i
$638$		0			0
$639$	−5.73848	+	1.86455i	−0.227011	+	0.0737603i
$640$		0			0
$641$	36.8141	+	11.9616i	1.45407	+	0.472456i	0.926253	−	0.376903i	$-0.123011\pi$
$641$	36.8141	+	11.9616i	1.45407	+	0.472456i	0.527816	+	0.849359i	$0.323011\pi$
$642$		0			0
$643$	2.83101	+	3.89655i	0.111644	+	0.153665i	0.861182	−	0.508296i	$-0.169724\pi$
$643$	2.83101	+	3.89655i	0.111644	+	0.153665i	−0.749538	+	0.661961i	$0.769724\pi$
$644$		0			0
$645$	−1.20396	+	0.391191i	−0.0474059	+	0.0154031i
$646$		0			0
$647$	20.9467			0.823500			0.411750	−	0.911297i	$-0.364918\pi$
$647$	20.9467			0.823500			0.411750	+	0.911297i	$0.364918\pi$
$648$		0			0
$649$	−14.2659	+	19.6354i	−0.559986	+	0.770755i
$650$		0			0
$651$	−0.272331	+	0.838148i	−0.0106735	+	0.0328496i
$652$		0			0
$653$			8.39614i			0.328566i	0.986413	+	0.164283i	$0.0525311\pi$
$653$			8.39614i			0.328566i	−0.986413	+	0.164283i	$0.947469\pi$
$654$		0			0
$655$	20.4575			0.799341
$656$		0			0
$657$	20.8201			0.812270
$658$		0			0
$659$			31.4971i			1.22695i	0.789714	+	0.613476i	$0.210229\pi$
$659$			31.4971i			1.22695i	−0.789714	+	0.613476i	$0.789771\pi$
$660$		0			0
$661$	−3.78362	+	11.6448i	−0.147166	+	0.452930i	−0.997283	−	0.0736636i	$-0.976531\pi$
$661$	−3.78362	+	11.6448i	−0.147166	+	0.452930i	0.850117	+	0.526593i	$0.176531\pi$
$662$		0			0
$663$	−1.48996	+	2.05076i	−0.0578653	+	0.0796448i
$664$		0			0
$665$	4.62338			0.179287
$666$		0			0
$667$	18.0369	−	5.86054i	0.698391	−	0.226921i
$668$		0			0
$669$	1.35155	+	1.86025i	0.0522539	+	0.0719213i
$670$		0			0
$671$	0.0109736	+	0.00356555i	0.000423632	+	0.000137646i
$672$		0			0
$673$	−19.5233	+	6.34350i	−0.752567	+	0.244524i	−0.660086	−	0.751190i	$-0.729480\pi$
$673$	−19.5233	+	6.34350i	−0.752567	+	0.244524i	−0.0924818	+	0.995714i	$0.529480\pi$
$674$		0			0
$675$	3.32881	−	4.58171i	0.128126	−	0.176350i
$676$		0			0
$677$	−3.35299	−	2.43609i	−0.128866	−	0.0936264i	0.521485	−	0.853260i	$-0.325378\pi$
$677$	−3.35299	−	2.43609i	−0.128866	−	0.0936264i	−0.650351	+	0.759634i	$0.725378\pi$
$678$		0			0
$679$	8.66165	−	6.29306i	0.332404	−	0.241505i
$680$		0			0
$681$	2.33866	+	1.69914i	0.0896178	+	0.0651112i
$682$		0			0
$683$		−	43.9663i		−	1.68233i	−0.540782	−	0.841163i	$-0.681872\pi$
$683$		−	43.9663i		−	1.68233i	0.540782	−	0.841163i	$-0.318128\pi$
$684$		0			0
$685$	−20.3115	−	6.59959i	−0.776061	−	0.252157i
$686$		0			0
$687$	−0.712278	−	2.19217i	−0.0271751	−	0.0836364i
$688$		0			0
$689$	−7.65077	−	23.5467i	−0.291471	−	0.897056i
$690$		0			0
$691$	−6.85511	−	9.43525i	−0.260781	−	0.358934i	0.658470	−	0.752607i	$-0.271204\pi$
$691$	−6.85511	−	9.43525i	−0.260781	−	0.358934i	−0.919250	+	0.393673i	$0.871204\pi$
$692$		0			0
$693$	−1.56894	+	4.82869i	−0.0595990	+	0.183427i
$694$		0			0
$695$	−9.07704	+	6.59485i	−0.344312	+	0.250157i
$696$		0			0
$697$	2.64618	−	8.12648i	0.100231	−	0.307812i
$698$		0			0
$699$	2.78238	−	2.02151i	0.105239	−	0.0764607i
$700$		0			0
$701$	1.90017	−	5.84812i	0.0717683	−	0.220880i	−0.908738	−	0.417367i	$-0.862953\pi$
$701$	1.90017	−	5.84812i	0.0717683	−	0.220880i	0.980507	+	0.196486i	$0.0629531\pi$
$702$		0			0
$703$	3.77417	+	5.19469i	0.142345	+	0.195922i
$704$		0			0
$705$	0.608809	+	1.87372i	0.0229291	+	0.0705684i
$706$		0			0
$707$	2.29089	+	7.05064i	0.0861579	+	0.265167i
$708$		0			0
$709$	−43.5449	−	14.1486i	−1.63536	−	0.531361i	−0.659866	−	0.751383i	$-0.729387\pi$
$709$	−43.5449	−	14.1486i	−1.63536	−	0.531361i	−0.975495	+	0.220022i	$0.929387\pi$
$710$		0			0
$711$		−	41.4084i		−	1.55294i
$712$		0			0
$713$	−8.41422	−	6.11329i	−0.315115	−	0.228944i
$714$		0			0
$715$	−11.9887	+	8.71031i	−0.448352	+	0.325747i
$716$		0			0
$717$	0.872123	+	0.633635i	0.0325700	+	0.0236635i
$718$		0			0
$719$	12.2056	−	16.7996i	0.455192	−	0.626518i	−0.518311	−	0.855192i	$-0.673439\pi$
$719$	12.2056	−	16.7996i	0.455192	−	0.626518i	0.973503	+	0.228674i	$0.0734391\pi$
$720$		0			0
$721$	−0.604052	+	0.196268i	−0.0224961	+	0.00730942i
$722$		0			0
$723$	8.76224	+	2.84702i	0.325871	+	0.105882i
$724$		0			0
$725$	9.74133	+	13.4078i	0.361784	+	0.497953i
$726$		0			0
$727$	−15.8818	+	5.16032i	−0.589025	+	0.191386i	−0.588340	−	0.808614i	$-0.700218\pi$
$727$	−15.8818	+	5.16032i	−0.589025	+	0.191386i	−0.000685263		1.00000i	$0.500218\pi$
$728$		0			0
$729$	22.1088			0.818844
$730$		0			0
$731$	−2.39124	+	3.29127i	−0.0884434	+	0.121732i
$732$		0			0
$733$	5.70851	−	17.5690i	0.210849	−	0.648925i	−0.788574	−	0.614940i	$-0.789180\pi$
$733$	5.70851	−	17.5690i	0.210849	−	0.648925i	0.999422	−	0.0339850i	$-0.0108198\pi$
$734$		0			0
$735$		−	0.415331i		−	0.0153197i
$736$		0			0
$737$	13.5666			0.499731
$738$		0			0
$739$	−4.80997			−0.176937			−0.0884687	−	0.996079i	$-0.528197\pi$
$739$	−4.80997			−0.176937			−0.0884687	+	0.996079i	$0.528197\pi$
$740$		0			0
$741$			6.44591i			0.236796i
$742$		0			0
$743$	−15.6615	+	48.2011i	−0.574564	+	1.76833i	0.0630952	+	0.998008i	$0.479903\pi$
$743$	−15.6615	+	48.2011i	−0.574564	+	1.76833i	−0.637659	+	0.770319i	$0.720097\pi$
$744$		0			0
$745$	4.47808	−	6.16354i	0.164064	−	0.225815i
$746$		0			0
$747$	−20.3225			−0.743562
$748$		0			0
$749$	−0.00219622		0.000713594i	−8.02480e−5		2.60742e-5i
$750$		0			0
$751$	12.7475	+	17.5454i	0.465162	+	0.640240i	0.975569	−	0.219693i	$-0.0705054\pi$
$751$	12.7475	+	17.5454i	0.465162	+	0.640240i	−0.510408	+	0.859933i	$0.670505\pi$
$752$		0			0
$753$	1.05923	+	0.344166i	0.0386006	+	0.0125421i
$754$		0			0
$755$	21.6958	−	7.04940i	0.789592	−	0.256554i
$756$		0			0
$757$	−28.2308	+	38.8564i	−1.02607	+	1.41226i	−0.118206	+	0.992989i	$0.537714\pi$
$757$	−28.2308	+	38.8564i	−1.02607	+	1.41226i	−0.907861	+	0.419271i	$0.862286\pi$
$758$		0			0
$759$	1.55020	+	1.12628i	0.0562685	+	0.0408815i
$760$		0			0
$761$	35.6279	−	25.8852i	1.29151	−	0.938337i	0.291675	−	0.956517i	$-0.405787\pi$
$761$	35.6279	−	25.8852i	1.29151	−	0.938337i	0.999835	+	0.0181803i	$0.00578730\pi$
$762$		0			0
$763$	0.290039	+	0.210726i	0.0105001	+	0.00762879i
$764$		0			0
$765$			5.28545i			0.191096i
$766$		0			0
$767$	−82.3228	−	26.7483i	−2.97250	−	0.965825i
$768$		0			0
$769$	0.737876	+	2.27095i	0.0266085	+	0.0818925i	0.963479	−	0.267784i	$-0.0862914\pi$
$769$	0.737876	+	2.27095i	0.0266085	+	0.0818925i	−0.936870	+	0.349677i	$0.886291\pi$
$770$		0			0
$771$	−0.0286636	−	0.0882175i	−0.00103229	−	0.00317707i
$772$		0			0
$773$	16.7091	+	22.9981i	0.600984	+	0.827184i	0.995798	−	0.0915776i	$-0.0291909\pi$
$773$	16.7091	+	22.9981i	0.600984	+	0.827184i	−0.394814	+	0.918761i	$0.629191\pi$
$774$		0			0
$775$	2.80855	−	8.64384i	0.100886	−	0.310496i
$776$		0			0
$777$	0.466655	−	0.339044i	0.0167411	−	0.0121631i
$778$		0			0
$779$	−6.70260	−	20.6733i	−0.240146	−	0.740698i
$780$		0			0
$781$	2.93272	−	2.13075i	0.104941	−	0.0762441i
$782$		0			0
$783$	2.93336	−	9.02796i	0.104830	−	0.322633i
$784$		0			0
$785$	−14.1987	−	19.5428i	−0.506774	−	0.697514i
$786$		0			0
$787$	5.92971	+	18.2498i	0.211371	+	0.650534i	0.999391	+	0.0348843i	$0.0111063\pi$
$787$	5.92971	+	18.2498i	0.211371	+	0.650534i	−0.788020	+	0.615649i	$0.788894\pi$
$788$		0			0
$789$	1.32800	+	4.08715i	0.0472779	+	0.145506i
$790$		0			0
$791$	−3.36867	−	1.09455i	−0.119776	−	0.0389176i
$792$		0			0
$793$			0.0411506i			0.00146130i
$794$		0			0
$795$	1.33558	+	0.970357i	0.0473682	+	0.0344150i
$796$		0			0
$797$	−30.7617	+	22.3497i	−1.08963	+	0.791666i	−0.979337	−	0.202233i	$-0.935180\pi$
$797$	−30.7617	+	22.3497i	−1.08963	+	0.791666i	−0.110297	+	0.993899i	$0.535180\pi$
$798$		0			0
$799$	5.12219	+	3.72149i	0.181210	+	0.131657i
$800$		0			0
$801$	24.4580	−	33.6636i	0.864182	−	1.18944i
$802$		0			0
$803$	−11.8963	+	3.86534i	−0.419811	+	0.136405i
$804$		0			0
$805$	4.66169	+	1.51467i	0.164303	+	0.0533852i
$806$		0			0
$807$	2.71067	+	3.73092i	0.0954201	+	0.131335i
$808$		0			0
$809$	−9.05232	+	2.94128i	−0.318263	+	0.103410i	−0.463792	−	0.885944i	$-0.653511\pi$
$809$	−9.05232	+	2.94128i	−0.318263	+	0.103410i	0.145529	+	0.989354i	$0.453511\pi$
$810$		0			0
$811$	−15.7722			−0.553836			−0.276918	−	0.960894i	$-0.589313\pi$
$811$	−15.7722			−0.553836			−0.276918	+	0.960894i	$0.589313\pi$
$812$		0			0
$813$	3.35008	−	4.61099i	0.117493	−	0.161715i
$814$		0			0
$815$	3.38038	−	10.4037i	0.118409	−	0.364427i
$816$		0			0
$817$			10.3451i			0.361928i
$818$		0			0
$819$	−18.1074			−0.632723
$820$		0			0
$821$	29.8544			1.04193			0.520963	−	0.853580i	$-0.325573\pi$
$821$	29.8544			1.04193			0.520963	+	0.853580i	$0.325573\pi$
$822$		0			0
$823$			9.00148i			0.313772i	0.987617	+	0.156886i	$0.0501455\pi$
$823$			9.00148i			0.313772i	−0.987617	+	0.156886i	$0.949855\pi$
$824$		0			0
$825$	−0.517435	+	1.59250i	−0.0180148	+	0.0554437i
$826$		0			0
$827$	8.02296	−	11.0427i	0.278986	−	0.383991i	−0.646412	−	0.762989i	$-0.723731\pi$
$827$	8.02296	−	11.0427i	0.278986	−	0.383991i	0.925398	+	0.378998i	$0.123731\pi$
$828$		0			0
$829$	−25.1564			−0.873717			−0.436858	−	0.899530i	$-0.643909\pi$
$829$	−25.1564			−0.873717			−0.436858	+	0.899530i	$0.643909\pi$
$830$		0			0
$831$	−0.283668	+	0.0921692i	−0.00984032	+	0.00319731i
$832$		0			0
$833$	−0.784536	−	1.07982i	−0.0271826	−	0.0374136i
$834$		0			0
$835$	15.3899	+	5.00048i	0.532589	+	0.173049i
$836$		0			0
$837$	−4.95097	+	1.60867i	−0.171131	+	0.0556037i
$838$		0			0
$839$	−7.51830	+	10.3481i	−0.259561	+	0.357254i	−0.918831	−	0.394652i	$-0.870865\pi$
$839$	−7.51830	+	10.3481i	−0.259561	+	0.357254i	0.659270	+	0.751906i	$0.270865\pi$
$840$		0			0
$841$	−0.988020	−	0.717839i	−0.0340697	−	0.0247531i
$842$		0			0
$843$	5.78358	−	4.20201i	0.199197	−	0.144725i
$844$		0			0
$845$	−28.4303	−	20.6559i	−0.978034	−	0.710583i
$846$		0			0
$847$			7.94968i			0.273154i
$848$		0			0
$849$	5.38717	+	1.75040i	0.184887	+	0.0600735i
$850$		0			0
$851$	2.10359	+	6.47420i	0.0721103	+	0.221933i
$852$		0			0
$853$	−2.45864	−	7.56693i	−0.0841824	−	0.259087i	0.900101	−	0.435680i	$-0.143492\pi$
$853$	−2.45864	−	7.56693i	−0.0841824	−	0.259087i	−0.984284	+	0.176594i	$0.943492\pi$
$854$		0			0
$855$	7.90002	+	10.8734i	0.270175	+	0.371864i
$856$		0			0
$857$	0.528922	−	1.62785i	0.0180676	−	0.0556064i	−0.941616	−	0.336688i	$-0.890693\pi$
$857$	0.528922	−	1.62785i	0.0180676	−	0.0556064i	0.959684	+	0.281082i	$0.0906932\pi$
$858$		0			0
$859$	2.32604	−	1.68997i	0.0793635	−	0.0576610i	−0.547396	−	0.836874i	$-0.684381\pi$
$859$	2.32604	−	1.68997i	0.0793635	−	0.0576610i	0.626760	+	0.779213i	$0.284381\pi$
$860$		0			0
$861$	−1.85714	+	0.602115i	−0.0632913	+	0.0205200i
$862$		0			0
$863$	−7.07572	+	5.14081i	−0.240860	+	0.174995i	−0.701666	−	0.712506i	$-0.747560\pi$
$863$	−7.07572	+	5.14081i	−0.240860	+	0.174995i	0.460806	+	0.887501i	$0.347560\pi$
$864$		0			0
$865$	5.28348	−	16.2609i	0.179644	−	0.552886i
$866$		0			0
$867$	2.72739	+	3.75393i	0.0926271	+	0.127490i
$868$		0			0
$869$	7.68764	+	23.6601i	0.260785	+	0.802615i
$870$		0			0
$871$	14.9515	+	46.0160i	0.506613	+	1.55919i
$872$		0			0
$873$	29.6006	+	9.61781i	1.00183	+	0.325513i
$874$		0			0
$875$			11.0943i			0.375055i
$876$		0			0
$877$	−3.90522	−	2.83731i	−0.131870	−	0.0958091i	0.519895	−	0.854230i	$-0.325971\pi$
$877$	−3.90522	−	2.83731i	−0.131870	−	0.0958091i	−0.651765	+	0.758421i	$0.725971\pi$
$878$		0			0
$879$	−3.32872	+	2.41845i	−0.112275	+	0.0815724i
$880$		0			0
$881$	−31.8476	−	23.1386i	−1.07297	−	0.779559i	−0.0965275	−	0.995330i	$-0.530774\pi$
$881$	−31.8476	−	23.1386i	−1.07297	−	0.779559i	−0.976444	+	0.215771i	$0.930774\pi$
$882$		0			0
$883$	23.3780	−	32.1771i	0.786734	−	1.08285i	−0.207773	−	0.978177i	$-0.566622\pi$
$883$	23.3780	−	32.1771i	0.786734	−	1.08285i	0.994507	−	0.104669i	$-0.0333783\pi$
$884$		0			0
$885$	5.48921	−	1.78355i	0.184518	−	0.0599535i
$886$		0			0
$887$	33.2070	+	10.7896i	1.11498	+	0.362280i	0.807850	−	0.589388i	$-0.200631\pi$
$887$	33.2070	+	10.7896i	1.11498	+	0.362280i	0.307131	+	0.951667i	$0.400631\pi$
$888$		0			0
$889$	12.5165	+	17.2274i	0.419788	+	0.577789i
$890$		0			0
$891$	−13.5739	+	4.41044i	−0.454744	+	0.147755i
$892$		0			0
$893$	16.1000			0.538766
$894$		0			0
$895$	−10.8808	+	14.9761i	−0.363704	+	0.500596i
$896$		0			0
$897$	−2.11176	+	6.49932i	−0.0705095	+	0.217006i
$898$		0			0
$899$		−	15.2340i		−	0.508081i
$900$		0			0
$901$	5.30533			0.176746
$902$		0			0
$903$	0.929327			0.0309261
$904$		0			0
$905$			15.6430i			0.519991i
$906$		0			0
$907$	−9.38560	+	28.8859i	−0.311644	+	0.959141i	0.665470	+	0.746425i	$0.268231\pi$
$907$	−9.38560	+	28.8859i	−0.311644	+	0.959141i	−0.977114	+	0.212717i	$0.931769\pi$
$908$		0			0
$909$	−12.6675	+	17.4353i	−0.420155	+	0.578294i
$910$		0			0
$911$	38.2202			1.26629			0.633146	−	0.774032i	$-0.281763\pi$
$911$	38.2202			1.26629			0.633146	+	0.774032i	$0.281763\pi$
$912$		0			0
$913$	11.6120	−	3.77296i	0.384300	−	0.124867i
$914$		0			0
$915$	−0.00161281	−	0.00221985i	−5.33180e−5	−	7.33860e-5i
$916$		0			0
$917$	−14.2831	−	4.64085i	−0.471669	−	0.153254i
$918$		0			0
$919$	23.6990	−	7.70029i	0.781759	−	0.254009i	0.109168	−	0.994023i	$-0.465181\pi$
$919$	23.6990	−	7.70029i	0.781759	−	0.254009i	0.672591	+	0.740014i	$0.265181\pi$
$920$		0			0
$921$	−3.63571	+	5.00412i	−0.119801	+	0.164891i
$922$		0			0
$923$	10.4593	+	7.59913i	0.344272	+	0.250129i
$924$		0			0
$925$	−4.81262	+	3.49657i	−0.158238	+	0.114967i
$926$		0			0
$927$	−1.49374	−	1.08527i	−0.0490610	−	0.0356449i
$928$		0			0
$929$			30.9103i			1.01414i	0.861906	+	0.507068i	$0.169271\pi$
$929$			30.9103i			1.01414i	−0.861906	+	0.507068i	$0.830729\pi$
$930$		0			0
$931$	−3.22796	−	1.04883i	−0.105792	−	0.0343739i
$932$		0			0
$933$	1.12681	+	3.46795i	0.0368900	+	0.113536i
$934$		0			0
$935$	−0.981265	−	3.02002i	−0.0320908	−	0.0987653i
$936$		0			0
$937$	−24.7821	−	34.1097i	−0.809597	−	1.11431i	−0.991385	−	0.130977i	$-0.958189\pi$
$937$	−24.7821	−	34.1097i	−0.809597	−	1.11431i	0.181789	−	0.983338i	$-0.441811\pi$
$938$		0			0
$939$	−0.515577	+	1.58678i	−0.0168252	+	0.0517827i
$940$		0			0
$941$	−38.0549	+	27.6485i	−1.24056	+	0.901316i	−0.997635	−	0.0687304i	$-0.978105\pi$
$941$	−38.0549	+	27.6485i	−1.24056	+	0.901316i	−0.242920	+	0.970046i	$0.578105\pi$
$942$		0			0
$943$	0.0146781	−	23.0405i	0.000477984	−	0.750300i
$944$		0			0
$945$	1.98482	−	1.44206i	0.0645663	−	0.0469102i
$946$		0			0
$947$	−2.97015	+	9.14117i	−0.0965168	+	0.297048i	−0.987646	−	0.156701i	$-0.949914\pi$
$947$	−2.97015	+	9.14117i	−0.0965168	+	0.297048i	0.891129	+	0.453750i	$0.149914\pi$
$948$		0			0
$949$	−26.2214	−	36.0907i	−0.851183	−	1.17155i
$950$		0			0
$951$	−0.350855	−	1.07982i	−0.0113773	−	0.0350156i
$952$		0			0
$953$	0.402927	+	1.24008i	0.0130521	+	0.0401702i	0.957370	−	0.288863i	$-0.0932772\pi$
$953$	0.402927	+	1.24008i	0.0130521	+	0.0401702i	−0.944318	+	0.329033i	$0.893277\pi$
$954$		0			0
$955$	12.2805	+	3.99019i	0.397389	+	0.129120i
$956$		0			0
$957$			2.80664i			0.0907256i
$958$		0			0
$959$	12.6840	+	9.21544i	0.409586	+	0.297582i
$960$		0			0
$961$	18.3207	−	13.3108i	0.590990	−	0.429380i
$962$		0			0
$963$	−0.00543096	−	0.00394583i	−0.000175010	−	0.000127152i
$964$		0			0
$965$	−1.33563	+	1.83833i	−0.0429954	+	0.0591780i
$966$		0			0
$967$	−44.1539	+	14.3465i	−1.41989	+	0.461351i	−0.915568	−	0.402162i	$-0.868259\pi$
$967$	−44.1539	+	14.3465i	−1.41989	+	0.461351i	−0.504325	+	0.863514i	$0.668259\pi$
$968$		0			0
$969$	−1.31365	−	0.426831i	−0.0422005	−	0.0137118i
$970$		0			0
$971$	21.6218	+	29.7599i	0.693877	+	0.955040i	0.999995	+	0.00304637i	$0.000969693\pi$
$971$	21.6218	+	29.7599i	0.693877	+	0.955040i	−0.306118	+	0.951993i	$0.599030\pi$
$972$		0			0
$973$	7.83349	−	2.54526i	0.251130	−	0.0815972i
$974$		0			0
$975$	−5.97181			−0.191251
$976$		0			0
$977$	−11.5213	+	15.8576i	−0.368598	+	0.507331i	−0.952519	−	0.304479i	$-0.901518\pi$
$977$	−11.5213	+	15.8576i	−0.368598	+	0.507331i	0.583921	+	0.811810i	$0.301518\pi$
$978$		0			0
$979$	−7.72516	+	23.7756i	−0.246897	+	0.759871i
$980$		0			0
$981$			1.04220i			0.0332748i
$982$		0			0
$983$	−7.39366			−0.235821			−0.117911	−	0.993024i	$-0.537620\pi$
$983$	−7.39366			−0.235821			−0.117911	+	0.993024i	$0.537620\pi$
$984$		0			0
$985$	−17.6503			−0.562384
$986$		0			0
$987$		−	1.44631i		−	0.0460365i
$988$		0			0
$989$	−3.38917	+	10.4308i	−0.107769	+	0.331679i
$990$		0			0
$991$	−34.8753	+	48.0017i	−1.10785	+	1.52482i	−0.283301	+	0.959031i	$0.591430\pi$
$991$	−34.8753	+	48.0017i	−1.10785	+	1.52482i	−0.824548	+	0.565792i	$0.808570\pi$
$992$		0			0
$993$	−9.59573			−0.304511
$994$		0			0
$995$	5.33809	−	1.73445i	0.169229	−	0.0549858i
$996$		0			0
$997$	−19.4054	−	26.7092i	−0.614574	−	0.845889i	0.382370	−	0.924009i	$-0.375108\pi$
$997$	−19.4054	−	26.7092i	−0.614574	−	0.845889i	−0.996944	+	0.0781206i	$0.975108\pi$
$998$		0			0
$999$	3.24051	+	1.05291i	0.102525	+	0.0333125i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.701.10	yes	80
41.31	even	10	inner	1148.2.ba.a.113.11	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.11	✓	80	41.31	even	10	inner
1148.2.ba.a.701.10	yes	80	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.304900i q^{3} +(-0.420940 + 1.29552i) q^{5} +(0.587785 - 0.809017i) q^{7} +2.90704 q^{9} +O(q^{10})\)	\(q-0.304900i q^{3} +(-0.420940 + 1.29552i) q^{5} +(0.587785 - 0.809017i) q^{7} +2.90704 q^{9} +(-1.66104 + 0.539703i) q^{11} +(-3.66120 - 5.03921i) q^{13} +(0.395004 + 0.128344i) q^{15} +(1.26941 - 0.412455i) q^{17} +(1.99499 - 2.74587i) q^{19} +(-0.246669 - 0.179216i) q^{21} +(2.91110 - 2.11504i) q^{23} +(2.54391 + 1.84826i) q^{25} -1.80105i q^{27} +(5.01259 + 1.62869i) q^{29} +(-0.893181 - 2.74893i) q^{31} +(0.164555 + 0.506449i) q^{33} +(0.800675 + 1.10203i) q^{35} +(-0.584605 + 1.79923i) q^{37} +(-1.53646 + 1.11630i) q^{39} +(3.76696 - 5.17784i) q^{41} +(-2.46586 + 1.79155i) q^{43} +(-1.22369 + 3.76612i) q^{45} +(2.78819 + 3.83762i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-0.125757 - 0.387042i) q^{51} +(3.78028 + 1.22829i) q^{53} -2.37908i q^{55} +(-0.837214 - 0.608272i) q^{57} +(11.2426 - 8.16822i) q^{59} +(-0.00534477 - 0.00388320i) q^{61} +(1.70871 - 2.35184i) q^{63} +(8.06954 - 2.62195i) q^{65} +(-7.38761 - 2.40038i) q^{67} +(-0.644874 - 0.887594i) q^{69} +(-1.97400 + 0.641391i) q^{71} +7.16197 q^{73} +(0.563533 - 0.775637i) q^{75} +(-0.539703 + 1.66104i) q^{77} -14.2442i q^{79} +8.17197 q^{81} -6.99080 q^{83} +1.81816i q^{85} +(0.496588 - 1.52834i) q^{87} +(8.41339 - 11.5800i) q^{89} -6.22881 q^{91} +(-0.838148 + 0.272331i) q^{93} +(2.71755 + 3.74039i) q^{95} +(10.1824 + 3.30846i) q^{97} +(-4.82869 + 1.56894i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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