LMFDB - Embedded newform 820.2.x.a.273.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.x (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			273.10
Character	$\chi$	$=$	820.273
Dual form			820.2.x.a.817.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.637865 - 0.264212i) q^{3} +(-2.14189 - 0.642112i) q^{5} +(0.168176 - 0.406013i) q^{7} +(-1.78426 - 1.78426i) q^{9} +(1.19622 + 2.88794i) q^{11} +(1.79249 + 0.742475i) q^{13} +(1.19658 + 0.975494i) q^{15} +(-4.05499 + 1.67963i) q^{17} +(0.814358 - 1.96603i) q^{19} +(-0.214547 + 0.214547i) q^{21} +(-2.36438 + 2.36438i) q^{23} +(4.17538 + 2.75067i) q^{25} +(1.45933 + 3.52313i) q^{27} +(1.80369 + 4.35449i) q^{29} +5.50299i q^{31} -2.15817i q^{33} +(-0.620921 + 0.761647i) q^{35} +(-0.0126253 + 0.0126253i) q^{37} +(-0.947197 - 0.947197i) q^{39} +(-1.75818 + 6.15701i) q^{41} +4.32764i q^{43} +(2.67599 + 4.96737i) q^{45} +(1.90172 - 0.787719i) q^{47} +(4.81318 + 4.81318i) q^{49} +3.03032 q^{51} +(-5.24054 + 12.6518i) q^{53} +(-0.707799 - 6.95376i) q^{55} +(-1.03890 + 1.03890i) q^{57} -12.1357i q^{59} +(-6.28769 - 6.28769i) q^{61} +(-1.02450 + 0.424362i) q^{63} +(-3.36257 - 2.74128i) q^{65} +(-8.59787 + 3.56135i) q^{67} +(2.13286 - 0.883458i) q^{69} +(-2.16557 + 0.897008i) q^{71} +1.86878i q^{73} +(-1.93657 - 2.85774i) q^{75} +1.37372 q^{77} +(8.05498 - 3.33648i) q^{79} +4.93711i q^{81} +(0.444700 + 0.444700i) q^{83} +(9.76385 - 0.993828i) q^{85} -3.25413i q^{87} +(6.20741 + 14.9860i) q^{89} +(0.602909 - 0.602909i) q^{91} +(1.45396 - 3.51016i) q^{93} +(-3.00668 + 3.68812i) q^{95} +(-2.87104 - 6.93130i) q^{97} +(3.01846 - 7.28720i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.637865	−	0.264212i	−0.368271	−	0.152543i	0.190870	−	0.981615i	$-0.438869\pi$
$3$	−0.637865	−	0.264212i	−0.368271	−	0.152543i	−0.559141	+	0.829072i	$0.688869\pi$
$4$		0			0
$5$	−2.14189	−	0.642112i	−0.957882	−	0.287161i
$5$	−2.14189	−	0.642112i	−0.957882	−	0.287161i
$6$		0			0
$7$	0.168176	−	0.406013i	0.0635646	−	0.153459i	−0.888905	−	0.458091i	$-0.848534\pi$
$7$	0.168176	−	0.406013i	0.0635646	−	0.153459i	0.952470	+	0.304632i	$0.0985335\pi$
$8$		0			0
$9$	−1.78426	−	1.78426i	−0.594752	−	0.594752i
$10$		0			0
$11$	1.19622	+	2.88794i	0.360675	+	0.870747i	0.995202	+	0.0978456i	$0.0311951\pi$
$11$	1.19622	+	2.88794i	0.360675	+	0.870747i	−0.634526	+	0.772901i	$0.718805\pi$
$12$		0			0
$13$	1.79249	+	0.742475i	0.497148	+	0.205925i	0.617146	−	0.786849i	$-0.288289\pi$
$13$	1.79249	+	0.742475i	0.497148	+	0.205925i	−0.119998	+	0.992774i	$0.538289\pi$
$14$		0			0
$15$	1.19658	+	0.975494i	0.308956	+	0.251872i
$16$		0			0
$17$	−4.05499	+	1.67963i	−0.983479	+	0.407371i	−0.815713	−	0.578456i	$-0.803655\pi$
$17$	−4.05499	+	1.67963i	−0.983479	+	0.407371i	−0.167766	+	0.985827i	$0.553655\pi$
$18$		0			0
$19$	0.814358	−	1.96603i	0.186827	−	0.451039i	−0.802519	−	0.596627i	$-0.796507\pi$
$19$	0.814358	−	1.96603i	0.186827	−	0.451039i	0.989345	+	0.145588i	$0.0465073\pi$
$20$		0			0
$21$	−0.214547	+	0.214547i	−0.0468181	+	0.0468181i
$22$		0			0
$23$	−2.36438	+	2.36438i	−0.493008	+	0.493008i	−0.909253	−	0.416245i	$-0.863346\pi$
$23$	−2.36438	+	2.36438i	−0.493008	+	0.493008i	0.416245	+	0.909253i	$0.363346\pi$
$24$		0			0
$25$	4.17538	+	2.75067i	0.835077	+	0.550133i
$26$		0			0
$27$	1.45933	+	3.52313i	0.280848	+	0.678027i
$28$		0			0
$29$	1.80369	+	4.35449i	0.334937	+	0.808609i	0.998186	+	0.0602099i	$0.0191770\pi$
$29$	1.80369	+	4.35449i	0.334937	+	0.808609i	−0.663249	+	0.748399i	$0.730823\pi$
$30$		0			0
$31$			5.50299i			0.988366i	0.869358	+	0.494183i	$0.164533\pi$
$31$			5.50299i			0.988366i	−0.869358	+	0.494183i	$0.835467\pi$
$32$		0			0
$33$		−	2.15817i		−	0.375690i
$34$		0			0
$35$	−0.620921	+	0.761647i	−0.104955	+	0.128742i
$36$		0			0
$37$	−0.0126253	+	0.0126253i	−0.00207559	+	0.00207559i	−0.708144	−	0.706068i	$-0.750467\pi$
$37$	−0.0126253	+	0.0126253i	−0.00207559	+	0.00207559i	0.706068	+	0.708144i	$0.250467\pi$
$38$		0			0
$39$	−0.947197	−	0.947197i	−0.151673	−	0.151673i
$40$		0			0
$41$	−1.75818	+	6.15701i	−0.274582	+	0.961564i
$41$	−1.75818	+	6.15701i	−0.274582	+	0.961564i
$42$		0			0
$43$			4.32764i			0.659958i	0.943988	+	0.329979i	$0.107042\pi$
$43$			4.32764i			0.659958i	−0.943988	+	0.329979i	$0.892958\pi$
$44$		0			0
$45$	2.67599	+	4.96737i	0.398913	+	0.740492i
$46$		0			0
$47$	1.90172	−	0.787719i	0.277395	−	0.114901i	−0.239649	−	0.970860i	$-0.577032\pi$
$47$	1.90172	−	0.787719i	0.277395	−	0.114901i	0.517044	+	0.855959i	$0.327032\pi$
$48$		0			0
$49$	4.81318	+	4.81318i	0.687598	+	0.687598i
$50$		0			0
$51$	3.03032			0.424329
$52$		0			0
$53$	−5.24054	+	12.6518i	−0.719844	+	1.73786i	−0.0460470	+	0.998939i	$0.514662\pi$
$53$	−5.24054	+	12.6518i	−0.719844	+	1.73786i	−0.673797	+	0.738917i	$0.735338\pi$
$54$		0			0
$55$	−0.707799	−	6.95376i	−0.0954396	−	0.937645i
$56$		0			0
$57$	−1.03890	+	1.03890i	−0.137606	+	0.137606i
$58$		0			0
$59$		−	12.1357i		−	1.57993i	−0.613149	−	0.789967i	$-0.710098\pi$
$59$		−	12.1357i		−	1.57993i	0.613149	−	0.789967i	$-0.289902\pi$
$60$		0			0
$61$	−6.28769	−	6.28769i	−0.805057	−	0.805057i	0.178824	−	0.983881i	$-0.442771\pi$
$61$	−6.28769	−	6.28769i	−0.805057	−	0.805057i	−0.983881	+	0.178824i	$0.942771\pi$
$62$		0			0
$63$	−1.02450	+	0.424362i	−0.129075	+	0.0534646i
$64$		0			0
$65$	−3.36257	−	2.74128i	−0.417075	−	0.340014i
$66$		0			0
$67$	−8.59787	+	3.56135i	−1.05040	+	0.435088i	−0.840033	−	0.542535i	$-0.817465\pi$
$67$	−8.59787	+	3.56135i	−1.05040	+	0.435088i	−0.210363	+	0.977623i	$0.567465\pi$
$68$		0			0
$69$	2.13286	−	0.883458i	0.256766	−	0.106356i
$70$		0			0
$71$	−2.16557	+	0.897008i	−0.257006	+	0.106455i	−0.507467	−	0.861671i	$-0.669418\pi$
$71$	−2.16557	+	0.897008i	−0.257006	+	0.106455i	0.250461	+	0.968127i	$0.419418\pi$
$72$		0			0
$73$			1.86878i			0.218724i	0.994002	+	0.109362i	$0.0348807\pi$
$73$			1.86878i			0.218724i	−0.994002	+	0.109362i	$0.965119\pi$
$74$		0			0
$75$	−1.93657	−	2.85774i	−0.223616	−	0.329984i
$76$		0			0
$77$	1.37372			0.156550
$78$		0			0
$79$	8.05498	−	3.33648i	0.906256	−	0.375384i	0.119634	−	0.992818i	$-0.461828\pi$
$79$	8.05498	−	3.33648i	0.906256	−	0.375384i	0.786622	+	0.617434i	$0.211828\pi$
$80$		0			0
$81$			4.93711i			0.548567i
$82$		0			0
$83$	0.444700	+	0.444700i	0.0488122	+	0.0488122i	0.731092	−	0.682279i	$-0.239011\pi$
$83$	0.444700	+	0.444700i	0.0488122	+	0.0488122i	−0.682279	+	0.731092i	$0.739011\pi$
$84$		0			0
$85$	9.76385	−	0.993828i	1.05904	−	0.107796i
$86$		0			0
$87$		−	3.25413i		−	0.348880i
$88$		0			0
$89$	6.20741	+	14.9860i	0.657984	+	1.58851i	0.800913	+	0.598781i	$0.204348\pi$
$89$	6.20741	+	14.9860i	0.657984	+	1.58851i	−0.142929	+	0.989733i	$0.545652\pi$
$90$		0			0
$91$	0.602909	−	0.602909i	0.0632020	−	0.0632020i
$92$		0			0
$93$	1.45396	−	3.51016i	0.150768	−	0.363987i
$94$		0			0
$95$	−3.00668	+	3.68812i	−0.308479	+	0.378393i
$96$		0			0
$97$	−2.87104	−	6.93130i	−0.291510	−	0.703767i	0.708488	−	0.705722i	$-0.249377\pi$
$97$	−2.87104	−	6.93130i	−0.291510	−	0.703767i	−0.999998	+	0.00195584i	$0.999377\pi$
$98$		0			0
$99$	3.01846	−	7.28720i	0.303366	−	0.732391i
$100$		0			0
$101$	15.3944	+	6.37657i	1.53180	+	0.634493i	0.979913	−	0.199426i	$-0.0639077\pi$
$101$	15.3944	+	6.37657i	1.53180	+	0.634493i	0.551888	+	0.833918i	$0.313908\pi$
$102$		0			0
$103$	−10.4872			−1.03334			−0.516669	−	0.856185i	$-0.672828\pi$
$103$	−10.4872			−1.03334			−0.516669	+	0.856185i	$0.672828\pi$
$104$		0			0
$105$	0.597300	−	0.321773i	0.0582905	−	0.0314019i
$106$		0			0
$107$	−13.3166	−	13.3166i	−1.28737	−	1.28737i	−0.936380	−	0.350987i	$-0.885846\pi$
$107$	−13.3166	−	13.3166i	−1.28737	−	1.28737i	−0.350987	−	0.936380i	$-0.614154\pi$
$108$		0			0
$109$	−3.76907	−	1.56120i	−0.361012	−	0.149536i	0.194803	−	0.980842i	$-0.437593\pi$
$109$	−3.76907	−	1.56120i	−0.361012	−	0.149536i	−0.555814	+	0.831307i	$0.687593\pi$
$110$		0			0
$111$	0.0113890	−	0.00471749i	0.00108100	−	0.000447764i
$112$		0			0
$113$	−3.88371	+	3.88371i	−0.365348	+	0.365348i	−0.865777	−	0.500429i	$-0.833176\pi$
$113$	−3.88371	+	3.88371i	−0.365348	+	0.365348i	0.500429	+	0.865777i	$0.333176\pi$
$114$		0			0
$115$	6.58245	−	3.54605i	0.613816	−	0.330671i
$116$		0			0
$117$	−1.87350	−	4.52303i	−0.173205	−	0.418155i
$118$		0			0
$119$			1.92885i			0.176818i
$120$		0			0
$121$	0.868928	−	0.868928i	0.0789934	−	0.0789934i
$122$		0			0
$123$	2.74824	−	3.46281i	0.247800	−	0.312231i
$124$		0			0
$125$	−7.17698	−	8.57269i	−0.641928	−	0.766765i
$126$		0			0
$127$	5.45426	+	5.45426i	0.483987	+	0.483987i	0.906402	−	0.422415i	$-0.138818\pi$
$127$	5.45426	+	5.45426i	0.483987	+	0.483987i	−0.422415	+	0.906402i	$0.638818\pi$
$128$		0			0
$129$	1.14341	−	2.76045i	0.100672	−	0.243044i
$130$		0			0
$131$	11.6288	−	11.6288i	1.01601	−	1.01601i	0.0161437	−	0.999870i	$-0.494861\pi$
$131$	11.6288	−	11.6288i	1.01601	−	1.01601i	0.999870	−	0.0161437i	$-0.00513892\pi$
$132$		0			0
$133$	−0.661280	−	0.661280i	−0.0573402	−	0.0573402i
$134$		0			0
$135$	−0.863476	−	8.48321i	−0.0743162	−	0.730119i
$136$		0			0
$137$	−16.8836	+	6.99342i	−1.44246	+	0.597488i	−0.960394	−	0.278644i	$-0.910115\pi$
$137$	−16.8836	+	6.99342i	−1.44246	+	0.597488i	−0.482070	+	0.876133i	$0.660115\pi$
$138$		0			0
$139$		−	7.21533i		−	0.611996i	−0.952032	−	0.305998i	$-0.901010\pi$
$139$		−	7.21533i		−	0.611996i	0.952032	−	0.305998i	$-0.0989901\pi$
$140$		0			0
$141$	−1.42117			−0.119684
$142$		0			0
$143$			6.06478i			0.507162i
$144$		0			0
$145$	−1.06723	−	10.4850i	−0.0886288	−	0.870733i
$146$		0			0
$147$	−1.79846	−	4.34186i	−0.148334	−	0.358111i
$148$		0			0
$149$	−3.86029	+	9.31957i	−0.316248	+	0.763489i	0.683199	+	0.730232i	$0.260588\pi$
$149$	−3.86029	+	9.31957i	−0.316248	+	0.763489i	−0.999447	+	0.0332571i	$0.989412\pi$
$150$		0			0
$151$	−0.734324	−	1.77282i	−0.0597585	−	0.144270i	0.891180	−	0.453650i	$-0.149878\pi$
$151$	−0.734324	−	1.77282i	−0.0597585	−	0.144270i	−0.950938	+	0.309380i	$0.899878\pi$
$152$		0			0
$153$	10.2320	+	4.23825i	0.827211	+	0.342642i
$154$		0			0
$155$	3.53354	−	11.7868i	0.283820	−	0.946738i
$156$		0			0
$157$	−7.76327	−	3.21565i	−0.619577	−	0.256637i	0.0507404	−	0.998712i	$-0.483842\pi$
$157$	−7.76327	−	3.21565i	−0.619577	−	0.256637i	−0.670317	+	0.742075i	$0.733842\pi$
$158$		0			0
$159$	6.68551	−	6.68551i	0.530196	−	0.530196i
$160$		0			0
$161$	0.562338	+	1.35760i	0.0443184	+	0.106994i
$162$		0			0
$163$	13.6495	−	13.6495i	1.06911	−	1.06911i	0.0716813	−	0.997428i	$-0.477164\pi$
$163$	13.6495	−	13.6495i	1.06911	−	1.06911i	0.997428	−	0.0716813i	$-0.0228364\pi$
$164$		0			0
$165$	−1.38579	+	4.62257i	−0.107884	+	0.359866i
$166$		0			0
$167$	−5.76385	+	13.9152i	−0.446020	+	1.07679i	0.527780	+	0.849381i	$0.323024\pi$
$167$	−5.76385	+	13.9152i	−0.446020	+	1.07679i	−0.973800	+	0.227406i	$0.926976\pi$
$168$		0			0
$169$	−6.53063	−	6.53063i	−0.502356	−	0.502356i
$170$		0			0
$171$	−4.96093	+	2.05489i	−0.379372	+	0.157141i
$172$		0			0
$173$	4.40027			0.334546			0.167273	−	0.985911i	$-0.446504\pi$
$173$	4.40027			0.334546			0.167273	+	0.985911i	$0.446504\pi$
$174$		0			0
$175$	1.81901	−	1.23266i	0.137504	−	0.0931806i
$176$		0			0
$177$	−3.20640	+	7.74094i	−0.241008	+	0.581845i
$178$		0			0
$179$	−8.17546	−	3.38639i	−0.611063	−	0.253111i	0.0556200	−	0.998452i	$-0.482286\pi$
$179$	−8.17546	−	3.38639i	−0.611063	−	0.253111i	−0.666683	+	0.745341i	$0.732286\pi$
$180$		0			0
$181$	5.91042	+	2.44818i	0.439318	+	0.181972i	0.591369	−	0.806401i	$-0.298588\pi$
$181$	5.91042	+	2.44818i	0.439318	+	0.181972i	−0.152051	+	0.988373i	$0.548588\pi$
$182$		0			0
$183$	2.34941	+	5.67199i	0.173674	+	0.419285i
$184$		0			0
$185$	0.0351489	−	0.0189352i	0.00258420	−	0.00139214i
$186$		0			0
$187$	−9.70135	−	9.70135i	−0.709433	−	0.709433i
$188$		0			0
$189$	1.67586			0.121901
$190$		0			0
$191$	2.01711	−	4.86973i	0.145953	−	0.352361i	−0.833949	−	0.551841i	$-0.813925\pi$
$191$	2.01711	−	4.86973i	0.145953	−	0.352361i	0.979902	+	0.199480i	$0.0639253\pi$
$192$		0			0
$193$	3.59081	+	1.48736i	0.258472	+	0.107063i	0.508157	−	0.861265i	$-0.330327\pi$
$193$	3.59081	+	1.48736i	0.258472	+	0.107063i	−0.249685	+	0.968327i	$0.580327\pi$
$194$		0			0
$195$	1.42059	+	2.63700i	0.101730	+	0.188839i
$196$		0			0
$197$	−11.1945			−0.797574			−0.398787	−	0.917044i	$-0.630569\pi$
$197$	−11.1945			−0.797574			−0.398787	+	0.917044i	$0.630569\pi$
$198$		0			0
$199$	−6.45683	−	2.67451i	−0.457712	−	0.189591i	0.141900	−	0.989881i	$-0.454679\pi$
$199$	−6.45683	−	2.67451i	−0.457712	−	0.189591i	−0.599613	+	0.800290i	$0.704679\pi$
$200$		0			0
$201$	6.42523			0.453201
$202$		0			0
$203$	2.07132			0.145378
$204$		0			0
$205$	7.71932	−	12.0587i	0.539141	−	0.842216i
$206$		0			0
$207$	8.43733			0.586435
$208$		0			0
$209$	6.65194			0.460125
$210$		0			0
$211$	9.37099	+	3.88159i	0.645126	+	0.267220i	0.681164	−	0.732131i	$-0.261474\pi$
$211$	9.37099	+	3.88159i	0.645126	+	0.267220i	−0.0360387	+	0.999350i	$0.511474\pi$
$212$		0			0
$213$	1.61834			0.110887
$214$		0			0
$215$	2.77883	−	9.26932i	0.189514	−	0.632162i
$216$		0			0
$217$	2.23429	+	0.925471i	0.151673	+	0.0628251i
$218$		0			0
$219$	0.493754	−	1.19203i	0.0333648	−	0.0805497i
$220$		0			0
$221$	−8.51562			−0.572823
$222$		0			0
$223$	9.85576	+	9.85576i	0.659990	+	0.659990i	0.955378	−	0.295387i	$-0.0954487\pi$
$223$	9.85576	+	9.85576i	0.659990	+	0.659990i	−0.295387	+	0.955378i	$0.595449\pi$
$224$		0			0
$225$	−2.54206	−	12.3579i	−0.169471	−	0.823857i
$226$		0			0
$227$	−10.0400	−	24.2388i	−0.666381	−	1.60878i	−0.787620	−	0.616162i	$-0.788687\pi$
$227$	−10.0400	−	24.2388i	−0.666381	−	1.60878i	0.121239	−	0.992623i	$-0.461313\pi$
$228$		0			0
$229$	15.5003	+	6.42042i	1.02429	+	0.424273i	0.830647	−	0.556800i	$-0.187971\pi$
$229$	15.5003	+	6.42042i	1.02429	+	0.424273i	0.193639	+	0.981073i	$0.437971\pi$
$230$		0			0
$231$	−0.876246	−	0.362953i	−0.0576528	−	0.0238806i
$232$		0			0
$233$	−7.28855	+	17.5961i	−0.477489	+	1.15276i	0.483294	+	0.875458i	$0.339440\pi$
$233$	−7.28855	+	17.5961i	−0.477489	+	1.15276i	−0.960783	+	0.277302i	$0.910560\pi$
$234$		0			0
$235$	−4.57908	+	0.466089i	−0.298707	+	0.0304043i
$236$		0			0
$237$	−6.01953			−0.391011
$238$		0			0
$239$	−9.63251	+	3.98992i	−0.623075	+	0.258086i	−0.671808	−	0.740726i	$-0.734482\pi$
$239$	−9.63251	+	3.98992i	−0.623075	+	0.258086i	0.0487323	+	0.998812i	$0.484482\pi$
$240$		0			0
$241$	−2.63706	−	2.63706i	−0.169868	−	0.169868i	0.617053	−	0.786921i	$-0.288326\pi$
$241$	−2.63706	−	2.63706i	−0.169868	−	0.169868i	−0.786921	+	0.617053i	$0.788326\pi$
$242$		0			0
$243$	5.68243	−	13.7186i	0.364528	−	0.880049i
$244$		0			0
$245$	−7.21871	−	13.3999i	−0.461186	−	0.856089i
$246$		0			0
$247$	2.91946	−	2.91946i	0.185761	−	0.185761i
$248$		0			0
$249$	−0.166163	−	0.401154i	−0.0105302	−	0.0254221i
$250$		0			0
$251$	1.35640	−	1.35640i	0.0856154	−	0.0856154i	−0.663002	−	0.748618i	$-0.730718\pi$
$251$	1.35640	−	1.35640i	0.0856154	−	0.0856154i	0.748618	+	0.663002i	$0.230718\pi$
$252$		0			0
$253$	−9.65653	−	3.99987i	−0.607101	−	0.251469i
$254$		0			0
$255$	−6.49060	−	1.94580i	−0.406457	−	0.121851i
$256$		0			0
$257$	8.53709	+	3.53618i	0.532529	+	0.220581i	0.632710	−	0.774388i	$-0.281942\pi$
$257$	8.53709	+	3.53618i	0.532529	+	0.220581i	−0.100181	+	0.994969i	$0.531942\pi$
$258$		0			0
$259$	0.00300277	+	0.00724933i	0.000186583	+	0.000450451i
$260$		0			0
$261$	4.55128	−	10.9878i	0.281717	−	0.680126i
$262$		0			0
$263$	5.96221	+	14.3940i	0.367646	+	0.887575i	0.994135	+	0.108145i	$0.0344911\pi$
$263$	5.96221	+	14.3940i	0.367646	+	0.887575i	−0.626490	+	0.779430i	$0.715509\pi$
$264$		0			0
$265$	19.3485	−	23.7337i	1.18857	−	1.45795i
$266$		0			0
$267$		−	11.1991i		−	0.685375i
$268$		0			0
$269$	−16.3914			−0.999402			−0.499701	−	0.866198i	$-0.666557\pi$
$269$	−16.3914			−0.999402			−0.499701	+	0.866198i	$0.666557\pi$
$270$		0			0
$271$			22.3878i			1.35996i	0.733231	+	0.679980i	$0.238011\pi$
$271$			22.3878i			1.35996i	−0.733231	+	0.679980i	$0.761989\pi$
$272$		0			0
$273$	−0.543870	+	0.225278i	−0.0329165	+	0.0136345i
$274$		0			0
$275$	−2.94907	+	15.3487i	−0.177835	+	0.925560i
$276$		0			0
$277$	0.0892857	+	0.0892857i	0.00536466	+	0.00536466i	0.709784	−	0.704419i	$-0.248793\pi$
$277$	0.0892857	+	0.0892857i	0.00536466	+	0.00536466i	−0.704419	+	0.709784i	$0.748793\pi$
$278$		0			0
$279$	9.81875	−	9.81875i	0.587833	−	0.587833i
$280$		0			0
$281$	5.03535	−	12.1564i	0.300384	−	0.725190i	−0.699560	−	0.714574i	$-0.746621\pi$
$281$	5.03535	−	12.1564i	0.300384	−	0.725190i	0.999944	−	0.0106163i	$-0.00337934\pi$
$282$		0			0
$283$	−8.89353	−	8.89353i	−0.528665	−	0.528665i	0.391509	−	0.920174i	$-0.371953\pi$
$283$	−8.89353	−	8.89353i	−0.528665	−	0.528665i	−0.920174	+	0.391509i	$0.871953\pi$
$284$		0			0
$285$	2.89230	−	1.55812i	0.171325	−	0.0922951i
$286$		0			0
$287$	2.20414	+	1.74931i	0.130106	+	0.103258i
$288$		0			0
$289$	1.60096	−	1.60096i	0.0941743	−	0.0941743i
$290$		0			0
$291$			5.17979i			0.303645i
$292$		0			0
$293$	−1.88308	−	4.54615i	−0.110010	−	0.265589i	0.859281	−	0.511504i	$-0.170911\pi$
$293$	−1.88308	−	4.54615i	−0.110010	−	0.265589i	−0.969291	+	0.245915i	$0.920911\pi$
$294$		0			0
$295$	−7.79248	+	25.9933i	−0.453696	+	1.51339i
$296$		0			0
$297$	−8.42891	+	8.42891i	−0.489095	+	0.489095i
$298$		0			0
$299$	−5.99363	+	2.48264i	−0.346621	+	0.143575i
$300$		0			0
$301$	1.75708	+	0.727805i	0.101276	+	0.0419500i
$302$		0			0
$303$	−8.13478	−	8.13478i	−0.467331	−	0.467331i
$304$		0			0
$305$	9.43014	+	17.5050i	0.539968	+	1.00233i
$306$		0			0
$307$	−22.5322			−1.28598			−0.642991	−	0.765874i	$-0.722307\pi$
$307$	−22.5322			−1.28598			−0.642991	+	0.765874i	$0.722307\pi$
$308$		0			0
$309$	6.68944	+	2.77086i	0.380549	+	0.157629i
$310$		0			0
$311$	−8.07417	+	19.4928i	−0.457844	+	1.10533i	0.511424	+	0.859328i	$0.329118\pi$
$311$	−8.07417	+	19.4928i	−0.457844	+	1.10533i	−0.969268	+	0.246006i	$0.920882\pi$
$312$		0			0
$313$	−2.54574	−	6.14596i	−0.143894	−	0.347390i	0.835458	−	0.549554i	$-0.185202\pi$
$313$	−2.54574	−	6.14596i	−0.143894	−	0.347390i	−0.979352	+	0.202164i	$0.935202\pi$
$314$		0			0
$315$	2.46686	−	0.251093i	0.138992	−	0.0141475i
$316$		0			0
$317$	−2.88993	+	6.97690i	−0.162314	+	0.391862i	−0.984022	−	0.178048i	$-0.943022\pi$
$317$	−2.88993	+	6.97690i	−0.162314	+	0.391862i	0.821707	+	0.569910i	$0.193022\pi$
$318$		0			0
$319$	−10.4179	+	10.4179i	−0.583290	+	0.583290i
$320$		0			0
$321$	4.97579	+	12.0126i	0.277722	+	0.670480i
$322$		0			0
$323$			9.34007i			0.519695i
$324$		0			0
$325$	5.44204	+	8.03067i	0.301870	+	0.445461i
$326$		0			0
$327$	1.99167	+	1.99167i	0.110140	+	0.110140i
$328$		0			0
$329$		−	0.904600i		−	0.0498722i
$330$		0			0
$331$	−0.507515	+	0.210220i	−0.0278956	+	0.0115547i	−0.396588	−	0.917997i	$-0.629806\pi$
$331$	−0.507515	+	0.210220i	−0.0278956	+	0.0115547i	0.368692	+	0.929552i	$0.379806\pi$
$332$		0			0
$333$	0.0450537			0.00246893
$334$		0			0
$335$	20.7025	−	2.10723i	1.13110	−	0.115130i
$336$		0			0
$337$			10.5990i			0.577363i	0.957425	+	0.288682i	$0.0932169\pi$
$337$			10.5990i			0.577363i	−0.957425	+	0.288682i	$0.906783\pi$
$338$		0			0
$339$	3.50340	−	1.45116i	0.190279	−	0.0788160i
$340$		0			0
$341$	−15.8923	+	6.58281i	−0.860617	+	0.356479i
$342$		0			0
$343$	5.60577	−	2.32199i	0.302683	−	0.125375i
$344$		0			0
$345$	−5.13562	+	0.522737i	−0.276493	+	0.0281432i
$346$		0			0
$347$	27.6044	−	11.4341i	1.48188	−	0.613815i	0.512348	−	0.858778i	$-0.328776\pi$
$347$	27.6044	−	11.4341i	1.48188	−	0.613815i	0.969533	+	0.244962i	$0.0787756\pi$
$348$		0			0
$349$	3.21380	+	3.21380i	0.172031	+	0.172031i	0.787871	−	0.615840i	$-0.211183\pi$
$349$	3.21380	+	3.21380i	0.172031	+	0.172031i	−0.615840	+	0.787871i	$0.711183\pi$
$350$		0			0
$351$			7.39870i			0.394914i
$352$		0			0
$353$	5.60431	−	5.60431i	0.298287	−	0.298287i	−0.542055	−	0.840343i	$-0.682354\pi$
$353$	5.60431	−	5.60431i	0.298287	−	0.298287i	0.840343	+	0.542055i	$0.182354\pi$
$354$		0			0
$355$	5.21439	−	0.530755i	0.276751	−	0.0281695i
$356$		0			0
$357$	0.509627	−	1.23035i	0.0269723	−	0.0651169i
$358$		0			0
$359$	2.83601			0.149679			0.0748394	−	0.997196i	$-0.476156\pi$
$359$	2.83601			0.149679			0.0748394	+	0.997196i	$0.476156\pi$
$360$		0			0
$361$	10.2329	+	10.2329i	0.538575	+	0.538575i
$362$		0			0
$363$	−0.783840	+	0.324677i	−0.0411409	+	0.0170411i
$364$		0			0
$365$	1.19996	−	4.00271i	0.0628090	−	0.209512i
$366$		0			0
$367$			24.2208i			1.26432i	0.774840	+	0.632158i	$0.217831\pi$
$367$			24.2208i			1.26432i	−0.774840	+	0.632158i	$0.782169\pi$
$368$		0			0
$369$	14.1227	−	7.84865i	0.735200	−	0.408584i
$370$		0			0
$371$	4.25546	+	4.25546i	0.220932	+	0.220932i
$372$		0			0
$373$	−22.1572	+	22.1572i	−1.14725	+	1.14725i	−0.160164	+	0.987090i	$0.551202\pi$
$373$	−22.1572	+	22.1572i	−1.14725	+	1.14725i	−0.987090	+	0.160164i	$0.948798\pi$
$374$		0			0
$375$	2.31293	+	7.36446i	0.119439	+	0.380299i
$376$		0			0
$377$			9.14459i			0.470970i
$378$		0			0
$379$			3.00889i			0.154556i	0.997010	+	0.0772781i	$0.0246229\pi$
$379$			3.00889i			0.154556i	−0.997010	+	0.0772781i	$0.975377\pi$
$380$		0			0
$381$	−2.03800	−	4.92016i	−0.104410	−	0.252068i
$382$		0			0
$383$	−0.317298	−	0.766025i	−0.0162132	−	0.0391421i	0.915566	−	0.402169i	$-0.131743\pi$
$383$	−0.317298	−	0.766025i	−0.0162132	−	0.0391421i	−0.931779	+	0.363027i	$0.881743\pi$
$384$		0			0
$385$	−2.94235	−	0.882081i	−0.149956	−	0.0449550i
$386$		0			0
$387$	7.72161	−	7.72161i	0.392512	−	0.392512i
$388$		0			0
$389$	−7.05525	+	7.05525i	−0.357715	+	0.357715i	−0.862970	−	0.505255i	$-0.831399\pi$
$389$	−7.05525	+	7.05525i	−0.357715	+	0.357715i	0.505255	+	0.862970i	$0.331399\pi$
$390$		0			0
$391$	5.61626	−	13.5588i	0.284026	−	0.685700i
$392$		0			0
$393$	−10.4901	+	4.34513i	−0.529155	+	0.219183i
$394$		0			0
$395$	−19.3953	+	1.97418i	−0.975882	+	0.0993316i
$396$		0			0
$397$	11.1319	+	4.61100i	0.558696	+	0.231419i	0.644119	−	0.764925i	$-0.277224\pi$
$397$	11.1319	+	4.61100i	0.558696	+	0.231419i	−0.0854231	+	0.996345i	$0.527224\pi$
$398$		0			0
$399$	0.247089	+	0.596526i	0.0123699	+	0.0298636i
$400$		0			0
$401$	−1.65326	−	1.65326i	−0.0825598	−	0.0825598i	0.664621	−	0.747181i	$-0.268593\pi$
$401$	−1.65326	−	1.65326i	−0.0825598	−	0.0825598i	−0.747181	+	0.664621i	$0.768593\pi$
$402$		0			0
$403$	−4.08583	+	9.86407i	−0.203530	+	0.491364i
$404$		0			0
$405$	3.17018	−	10.5747i	0.157527	−	0.525463i
$406$		0			0
$407$	−0.0515639	−	0.0213585i	−0.00255593	−	0.00105870i
$408$		0			0
$409$	13.0459			0.645080			0.322540	−	0.946556i	$-0.395463\pi$
$409$	13.0459			0.645080			0.322540	+	0.946556i	$0.395463\pi$
$410$		0			0
$411$	12.6172			0.622361
$412$		0			0
$413$	−4.92725	−	2.04094i	−0.242454	−	0.100428i
$414$		0			0
$415$	−0.666951	−	1.23805i	−0.0327393	−	0.0607733i
$416$		0			0
$417$	−1.90638	+	4.60240i	−0.0933558	+	0.225381i
$418$		0			0
$419$	0.0309078	+	0.0309078i	0.00150994	+	0.00150994i	0.707861	−	0.706351i	$-0.249660\pi$
$419$	0.0309078	+	0.0309078i	0.00150994	+	0.00150994i	−0.706351	+	0.707861i	$0.749660\pi$
$420$		0			0
$421$	14.9057	+	35.9856i	0.726460	+	1.75383i	0.654045	+	0.756456i	$0.273071\pi$
$421$	14.9057	+	35.9856i	0.726460	+	1.75383i	0.0724158	+	0.997375i	$0.476929\pi$
$422$		0			0
$423$	−4.79865	−	1.98767i	−0.233319	−	0.0966437i
$424$		0			0
$425$	−21.5512	−	4.14082i	−1.04539	−	0.200859i
$426$		0			0
$427$	−3.61033	+	1.49545i	−0.174716	+	0.0723697i
$428$		0			0
$429$	1.60239	−	3.86851i	0.0773641	−	0.186773i
$430$		0			0
$431$	−17.7613	+	17.7613i	−0.855532	+	0.855532i	−0.990808	−	0.135276i	$-0.956808\pi$
$431$	−17.7613	+	17.7613i	−0.855532	+	0.855532i	0.135276	+	0.990808i	$0.456808\pi$
$432$		0			0
$433$	−3.58110	+	3.58110i	−0.172097	+	0.172097i	−0.787900	−	0.615803i	$-0.788832\pi$
$433$	−3.58110	+	3.58110i	−0.172097	+	0.172097i	0.615803	+	0.787900i	$0.288832\pi$
$434$		0			0
$435$	−2.08952	+	6.97000i	−0.100185	+	0.334186i
$436$		0			0
$437$	2.72300	+	6.57391i	0.130259	+	0.314473i
$438$		0			0
$439$	−6.16436	−	14.8821i	−0.294209	−	0.710283i	−0.999998	−	0.00186116i	$-0.999408\pi$
$439$	−6.16436	−	14.8821i	−0.294209	−	0.710283i	0.705790	−	0.708422i	$-0.250592\pi$
$440$		0			0
$441$		−	17.1759i		−	0.817901i
$442$		0			0
$443$			36.4638i			1.73245i	0.499658	+	0.866223i	$0.333459\pi$
$443$			36.4638i			1.73245i	−0.499658	+	0.866223i	$0.666541\pi$
$444$		0			0
$445$	−3.67289	−	36.0842i	−0.174112	−	1.71056i
$446$		0			0
$447$	4.92469	−	4.92469i	0.232930	−	0.232930i
$448$		0			0
$449$	0.594882	+	0.594882i	0.0280742	+	0.0280742i	0.721005	−	0.692930i	$-0.243681\pi$
$449$	0.594882	+	0.594882i	0.0280742	+	0.0280742i	−0.692930	+	0.721005i	$0.743681\pi$
$450$		0			0
$451$	−19.8843	+	2.28765i	−0.936313	+	0.107721i
$452$		0			0
$453$			1.32483i			0.0622461i
$454$		0			0
$455$	−1.67850	+	0.904229i	−0.0786893	+	0.0423909i
$456$		0			0
$457$	−9.62088	+	3.98510i	−0.450046	+	0.186415i	−0.596182	−	0.802849i	$-0.703316\pi$
$457$	−9.62088	+	3.98510i	−0.450046	+	0.186415i	0.146136	+	0.989265i	$0.453316\pi$
$458$		0			0
$459$	−11.8351	−	11.8351i	−0.552417	−	0.552417i
$460$		0			0
$461$	−21.2047			−0.987602			−0.493801	−	0.869575i	$-0.664393\pi$
$461$	−21.2047			−0.987602			−0.493801	+	0.869575i	$0.664393\pi$
$462$		0			0
$463$	5.00277	−	12.0777i	0.232498	−	0.561301i	−0.763972	−	0.645250i	$-0.776753\pi$
$463$	5.00277	−	12.0777i	0.232498	−	0.561301i	0.996470	+	0.0839492i	$0.0267533\pi$
$464$		0			0
$465$	−5.36814	+	6.58478i	−0.248941	+	0.305362i
$466$		0			0
$467$	−3.78983	+	3.78983i	−0.175372	+	0.175372i	−0.789335	−	0.613963i	$-0.789575\pi$
$467$	−3.78983	+	3.78983i	−0.175372	+	0.175372i	0.613963	+	0.789335i	$0.289575\pi$
$468$		0			0
$469$			4.08978i			0.188848i
$470$		0			0
$471$	4.10230	+	4.10230i	0.189024	+	0.189024i
$472$		0			0
$473$	−12.4980	+	5.17682i	−0.574657	+	0.238031i
$474$		0			0
$475$	8.80816	−	5.96892i	0.404146	−	0.273873i
$476$		0			0
$477$	31.9245	−	13.2236i	1.46172	−	0.605465i
$478$		0			0
$479$	−6.53738	+	2.70787i	−0.298700	+	0.123726i	−0.527000	−	0.849865i	$-0.676683\pi$
$479$	−6.53738	+	2.70787i	−0.298700	+	0.123726i	0.228300	+	0.973591i	$0.426683\pi$
$480$		0			0
$481$	−0.0320048	+	0.0132568i	−0.00145929	+	0.000604459i
$482$		0			0
$483$		−	1.01454i		−	0.0461633i
$484$		0			0
$485$	1.69878	+	16.6896i	0.0771374	+	0.757836i
$486$		0			0
$487$	41.5271			1.88177			0.940887	−	0.338720i	$-0.109994\pi$
$487$	41.5271			1.88177			0.940887	+	0.338720i	$0.109994\pi$
$488$		0			0
$489$	−12.3129	+	5.10016i	−0.556807	+	0.230637i
$490$		0			0
$491$		−	17.5416i		−	0.791639i	−0.918328	−	0.395820i	$-0.870461\pi$
$491$		−	17.5416i		−	0.791639i	0.918328	−	0.395820i	$-0.129539\pi$
$492$		0			0
$493$	−14.6279	−	14.6279i	−0.658807	−	0.658807i
$494$		0			0
$495$	−11.1444	+	13.6702i	−0.500903	+	0.614429i
$496$		0			0
$497$			1.03010i			0.0462065i
$498$		0			0
$499$	4.83152	+	11.6643i	0.216288	+	0.522166i	0.994366	−	0.106002i	$-0.0338050\pi$
$499$	4.83152	+	11.6643i	0.216288	+	0.522166i	−0.778078	+	0.628168i	$0.783805\pi$
$500$		0			0
$501$	7.35311	−	7.35311i	0.328513	−	0.328513i
$502$		0			0
$503$	3.19128	−	7.70444i	0.142292	−	0.343524i	−0.836627	−	0.547774i	$-0.815475\pi$
$503$	3.19128	−	7.70444i	0.142292	−	0.343524i	0.978919	+	0.204250i	$0.0654755\pi$
$504$		0			0
$505$	−28.8787	−	23.5429i	−1.28508	−	1.04764i
$506$		0			0
$507$	2.44019	+	5.89113i	0.108372	+	0.261634i
$508$		0			0
$509$	11.9012	−	28.7322i	0.527514	−	1.27353i	−0.405634	−	0.914036i	$-0.632949\pi$
$509$	11.9012	−	28.7322i	0.527514	−	1.27353i	0.933147	−	0.359495i	$-0.117051\pi$
$510$		0			0
$511$	0.758747	+	0.314283i	0.0335650	+	0.0139031i
$512$		0			0
$513$	8.11502			0.358287
$514$		0			0
$515$	22.4625	+	6.73398i	0.989816	+	0.296735i
$516$		0			0
$517$	4.54977	+	4.54977i	0.200099	+	0.200099i
$518$		0			0
$519$	−2.80678	−	1.16261i	−0.123204	−	0.0510327i
$520$		0			0
$521$	11.7454	−	4.86512i	0.514577	−	0.213145i	−0.110256	−	0.993903i	$-0.535167\pi$
$521$	11.7454	−	4.86512i	0.514577	−	0.213145i	0.624833	+	0.780759i	$0.285167\pi$
$522$		0			0
$523$	28.5810	−	28.5810i	1.24976	−	1.24976i	0.293933	−	0.955826i	$-0.405036\pi$
$523$	28.5810	−	28.5810i	1.24976	−	1.24976i	0.955826	−	0.293933i	$-0.0949643\pi$
$524$		0			0
$525$	−1.48597	+	0.305669i	−0.0648528	+	0.0133405i
$526$		0			0
$527$	−9.24300	−	22.3146i	−0.402631	−	0.972038i
$528$		0			0
$529$			11.8194i			0.513886i
$530$		0			0
$531$	−21.6532	+	21.6532i	−0.939669	+	0.939669i
$532$		0			0
$533$	−7.72295	+	9.73100i	−0.334518	+	0.421496i
$534$		0			0
$535$	19.9720	+	37.0735i	0.863464	+	1.60283i
$536$		0			0
$537$	4.32012	+	4.32012i	0.186427	+	0.186427i
$538$		0			0
$539$	−8.14254	+	19.6578i	−0.350724	+	0.846723i
$540$		0			0
$541$	9.24860	−	9.24860i	0.397629	−	0.397629i	−0.479767	−	0.877396i	$-0.659279\pi$
$541$	9.24860	−	9.24860i	0.397629	−	0.397629i	0.877396	+	0.479767i	$0.159279\pi$
$542$		0			0
$543$	−3.12321	−	3.12321i	−0.134030	−	0.134030i
$544$		0			0
$545$	7.07047	+	5.76409i	0.302866	+	0.246906i
$546$		0			0
$547$	−36.9122	+	15.2895i	−1.57825	+	0.653734i	−0.988136	−	0.153584i	$-0.950918\pi$
$547$	−36.9122	+	15.2895i	−1.57825	+	0.653734i	−0.590117	+	0.807318i	$0.700918\pi$
$548$		0			0
$549$			22.4377i			0.957619i
$550$		0			0
$551$	10.0299			0.427289
$552$		0			0
$553$		−	3.83154i		−	0.162934i
$554$		0			0
$555$	−0.0274232	+	0.00279131i	−0.00116405	+	0.000118485i
$556$		0			0
$557$	−6.09753	−	14.7207i	−0.258361	−	0.623738i	0.740470	−	0.672090i	$-0.234603\pi$
$557$	−6.09753	−	14.7207i	−0.258361	−	0.623738i	−0.998830	+	0.0483517i	$0.984603\pi$
$558$		0			0
$559$	−3.21316	+	7.75726i	−0.135902	+	0.328097i
$560$		0			0
$561$	3.62494	+	8.75137i	0.153045	+	0.369483i
$562$		0			0
$563$	35.0595	+	14.5221i	1.47758	+	0.612034i	0.968573	−	0.248729i	$-0.0800128\pi$
$563$	35.0595	+	14.5221i	1.47758	+	0.612034i	0.509007	+	0.860763i	$0.330013\pi$
$564$		0			0
$565$	10.8122	−	5.82469i	0.454874	−	0.245047i
$566$		0			0
$567$	2.00453	+	0.830303i	0.0841823	+	0.0348695i
$568$		0			0
$569$	7.55847	−	7.55847i	0.316868	−	0.316868i	−0.530695	−	0.847563i	$-0.678069\pi$
$569$	7.55847	−	7.55847i	0.316868	−	0.316868i	0.847563	+	0.530695i	$0.178069\pi$
$570$		0			0
$571$	−2.05414	−	4.95914i	−0.0859633	−	0.207534i	0.875052	−	0.484029i	$-0.160827\pi$
$571$	−2.05414	−	4.95914i	−0.0859633	−	0.207534i	−0.961015	+	0.276495i	$0.910827\pi$
$572$		0			0
$573$	−2.57329	+	2.57329i	−0.107501	+	0.107501i
$574$		0			0
$575$	−16.3758	+	3.36858i	−0.682920	+	0.140479i
$576$		0			0
$577$	2.18694	−	5.27973i	0.0910433	−	0.219798i	−0.871798	−	0.489865i	$-0.837046\pi$
$577$	2.18694	−	5.27973i	0.0910433	−	0.219798i	0.962841	+	0.270067i	$0.0870459\pi$
$578$		0			0
$579$	−1.89747	−	1.89747i	−0.0788562	−	0.0788562i
$580$		0			0
$581$	0.255342	−	0.105766i	0.0105934	−	0.00438792i
$582$		0			0
$583$	−42.8065			−1.77286
$584$		0			0
$585$	1.10854	+	10.8908i	0.0458325	+	0.450281i
$586$		0			0
$587$	−14.7454	+	35.5986i	−0.608610	+	1.46931i	0.255903	+	0.966702i	$0.417627\pi$
$587$	−14.7454	+	35.5986i	−0.608610	+	1.46931i	−0.864513	+	0.502611i	$0.832373\pi$
$588$		0			0
$589$	10.8191	+	4.48140i	0.445792	+	0.184653i
$590$		0			0
$591$	7.14057	+	2.95772i	0.293724	+	0.121664i
$592$		0			0
$593$	5.23223	+	12.6317i	0.214862	+	0.518723i	0.994158	−	0.107933i	$-0.0344232\pi$
$593$	5.23223	+	12.6317i	0.214862	+	0.518723i	−0.779296	+	0.626656i	$0.784423\pi$
$594$		0			0
$595$	1.23854	−	4.13139i	0.0507752	−	0.169370i
$596$		0			0
$597$	3.41195	+	3.41195i	0.139642	+	0.139642i
$598$		0			0
$599$	−26.5128			−1.08328			−0.541641	−	0.840610i	$-0.682197\pi$
$599$	−26.5128			−1.08328			−0.541641	+	0.840610i	$0.682197\pi$
$600$		0			0
$601$	12.8800	−	31.0950i	0.525385	−	1.26839i	−0.409133	−	0.912475i	$-0.634169\pi$
$601$	12.8800	−	31.0950i	0.525385	−	1.26839i	0.934518	−	0.355917i	$-0.115831\pi$
$602$		0			0
$603$	21.6952	+	8.98643i	0.883496	+	0.365956i
$604$		0			0
$605$	−2.41910	+	1.30320i	−0.0983502	+	0.0529825i
$606$		0			0
$607$	38.8891			1.57846			0.789230	−	0.614098i	$-0.210480\pi$
$607$	38.8891			1.57846			0.789230	+	0.614098i	$0.210480\pi$
$608$		0			0
$609$	−1.32122	−	0.547268i	−0.0535386	−	0.0221764i
$610$		0			0
$611$	3.99368			0.161567
$612$		0			0
$613$	−3.57635			−0.144447			−0.0722237	−	0.997388i	$-0.523010\pi$
$613$	−3.57635			−0.144447			−0.0722237	+	0.997388i	$0.523010\pi$
$614$		0			0
$615$	−8.10994	+	5.65228i	−0.327024	+	0.227922i
$616$		0			0
$617$	12.2844			0.494551			0.247276	−	0.968945i	$-0.420465\pi$
$617$	12.2844			0.494551			0.247276	+	0.968945i	$0.420465\pi$
$618$		0			0
$619$	27.7804			1.11659			0.558295	−	0.829642i	$-0.311456\pi$
$619$	27.7804			1.11659			0.558295	+	0.829642i	$0.311456\pi$
$620$		0			0
$621$	−11.7804	−	4.87962i	−0.472733	−	0.195812i
$622$		0			0
$623$	7.12845			0.285595
$624$		0			0
$625$	9.86766	+	22.9702i	0.394707	+	0.918807i
$626$		0			0
$627$	−4.24304	−	1.75753i	−0.169451	−	0.0701888i
$628$		0			0
$629$	0.0299897	−	0.0724015i	0.00119577	−	0.00288684i
$630$		0			0
$631$	−38.8717			−1.54746			−0.773728	−	0.633518i	$-0.781610\pi$
$631$	−38.8717			−1.54746			−0.773728	+	0.633518i	$0.781610\pi$
$632$		0			0
$633$	−4.95186	−	4.95186i	−0.196819	−	0.196819i
$634$		0			0
$635$	−8.18018	−	15.1847i	−0.324620	−	0.602585i
$636$		0			0
$637$	5.05393	+	12.2013i	0.200244	+	0.483432i
$638$		0			0
$639$	5.46443	+	2.26344i	0.216169	+	0.0895403i
$640$		0			0
$641$	−33.0923	−	13.7073i	−1.30707	−	0.541404i	−0.383039	−	0.923732i	$-0.625123\pi$
$641$	−33.0923	−	13.7073i	−1.30707	−	0.541404i	−0.924027	+	0.382328i	$0.875123\pi$
$642$		0			0
$643$	10.3797	−	25.0588i	0.409335	−	0.988221i	−0.575979	−	0.817465i	$-0.695379\pi$
$643$	10.3797	−	25.0588i	0.409335	−	0.988221i	0.985313	−	0.170757i	$-0.0546212\pi$
$644$		0			0
$645$	−4.22159	+	5.17837i	−0.166225	+	0.203898i
$646$		0			0
$647$	−23.6754			−0.930775			−0.465388	−	0.885107i	$-0.654085\pi$
$647$	−23.6754			−0.930775			−0.465388	+	0.885107i	$0.654085\pi$
$648$		0			0
$649$	35.0472	−	14.5170i	1.37572	−	0.569843i
$650$		0			0
$651$	−1.18065	−	1.18065i	−0.0462734	−	0.0462734i
$652$		0			0
$653$	7.32319	−	17.6797i	0.286579	−	0.691862i	−0.713382	−	0.700776i	$-0.752837\pi$
$653$	7.32319	−	17.6797i	0.286579	−	0.691862i	0.999960	+	0.00891373i	$0.00283736\pi$
$654$		0			0
$655$	−32.3746	+	17.4406i	−1.26498	+	0.681462i
$656$		0			0
$657$	3.33438	−	3.33438i	0.130086	−	0.130086i
$658$		0			0
$659$	−12.2728	−	29.6293i	−0.478082	−	1.15419i	−0.960507	−	0.278255i	$-0.910244\pi$
$659$	−12.2728	−	29.6293i	−0.478082	−	1.15419i	0.482425	−	0.875937i	$-0.339756\pi$
$660$		0			0
$661$	11.0238	−	11.0238i	0.428775	−	0.428775i	−0.459436	−	0.888211i	$-0.651948\pi$
$661$	11.0238	−	11.0238i	0.428775	−	0.428775i	0.888211	+	0.459436i	$0.151948\pi$
$662$		0			0
$663$	5.43182	+	2.24993i	0.210954	+	0.0873801i
$664$		0			0
$665$	0.991773	+	1.84100i	0.0384593	+	0.0713911i
$666$		0			0
$667$	−14.5603	−	6.03107i	−0.563777	−	0.233524i
$668$		0			0
$669$	−3.68263	−	8.89065i	−0.142379	−	0.343733i
$670$		0			0
$671$	10.6370	−	25.6800i	0.410637	−	0.991365i
$672$		0			0
$673$	−17.0648	−	41.1981i	−0.657800	−	1.58807i	−0.801195	−	0.598404i	$-0.795802\pi$
$673$	−17.0648	−	41.1981i	−0.657800	−	1.58807i	0.143395	−	0.989666i	$-0.454198\pi$
$674$		0			0
$675$	−3.59770	+	18.7246i	−0.138476	+	0.720709i
$676$		0			0
$677$			29.5570i			1.13597i	0.823040	+	0.567983i	$0.192276\pi$
$677$			29.5570i			1.13597i	−0.823040	+	0.567983i	$0.807724\pi$
$678$		0			0
$679$	−3.29704			−0.126529
$680$		0			0
$681$			18.1138i			0.694121i
$682$		0			0
$683$	29.1178	−	12.0610i	1.11416	−	0.461502i	0.251794	−	0.967781i	$-0.418980\pi$
$683$	29.1178	−	12.0610i	1.11416	−	0.461502i	0.862370	+	0.506279i	$0.168980\pi$
$684$		0			0
$685$	40.6534	−	4.13797i	1.55329	−	0.158104i
$686$		0			0
$687$	−8.19072	−	8.19072i	−0.312495	−	0.312495i
$688$		0			0
$689$	−18.7873	+	18.7873i	−0.715738	+	0.715738i
$690$		0			0
$691$	17.0029	−	41.0486i	0.646820	−	1.56156i	−0.170488	−	0.985360i	$-0.554534\pi$
$691$	17.0029	−	41.0486i	0.646820	−	1.56156i	0.817308	−	0.576201i	$-0.195466\pi$
$692$		0			0
$693$	−2.45107	−	2.45107i	−0.0931083	−	0.0931083i
$694$		0			0
$695$	−4.63305	+	15.4544i	−0.175742	+	0.586220i
$696$		0			0
$697$	−3.21211	−	27.9197i	−0.121667	−	1.05753i
$698$		0			0
$699$	9.29822	−	9.29822i	0.351691	−	0.351691i
$700$		0			0
$701$			15.0696i			0.569169i	0.958651	+	0.284585i	$0.0918557\pi$
$701$			15.0696i			0.569169i	−0.958651	+	0.284585i	$0.908144\pi$
$702$		0			0
$703$	0.0145403	+	0.0351034i	0.000548398	+	0.00132395i
$704$		0			0
$705$	3.04398	+	0.912549i	0.114643	+	0.0343686i
$706$		0			0
$707$	5.17794	−	5.17794i	0.194737	−	0.194737i
$708$		0			0
$709$	−28.9790	+	12.0035i	−1.08833	+	0.450800i	−0.853424	−	0.521218i	$-0.825478\pi$
$709$	−28.9790	+	12.0035i	−1.08833	+	0.450800i	−0.234905	+	0.972018i	$0.575478\pi$
$710$		0			0
$711$	−20.3253	−	8.41901i	−0.762258	−	0.315738i
$712$		0			0
$713$	−13.0112	−	13.0112i	−0.487272	−	0.487272i
$714$		0			0
$715$	3.89427	−	12.9901i	0.145637	−	0.485802i
$716$		0			0
$717$	7.19843			0.268830
$718$		0			0
$719$	−2.22581	−	0.921963i	−0.0830089	−	0.0343834i	0.340793	−	0.940138i	$-0.389305\pi$
$719$	−2.22581	−	0.921963i	−0.0830089	−	0.0343834i	−0.423802	+	0.905755i	$0.639305\pi$
$720$		0			0
$721$	−1.76370	+	4.25795i	−0.0656837	+	0.158574i
$722$		0			0
$723$	0.985343	+	2.37883i	0.0366453	+	0.0884696i
$724$		0			0
$725$	−4.44666	+	23.1430i	−0.165145	+	0.859510i
$726$		0			0
$727$	4.80468	−	11.5995i	0.178196	−	0.430203i	−0.809392	−	0.587268i	$-0.800203\pi$
$727$	4.80468	−	11.5995i	0.178196	−	0.430203i	0.987588	+	0.157066i	$0.0502034\pi$
$728$		0			0
$729$	3.22393	−	3.22393i	0.119405	−	0.119405i
$730$		0			0
$731$	−7.26884	−	17.5485i	−0.268848	−	0.649055i
$732$		0			0
$733$		−	18.4110i		−	0.680025i	−0.940421	−	0.340012i	$-0.889569\pi$
$733$		−	18.4110i		−	0.680025i	0.940421	−	0.340012i	$-0.110431\pi$
$734$		0			0
$735$	1.06414	+	10.4546i	0.0392513	+	0.385624i
$736$		0			0
$737$	−20.5699	−	20.5699i	−0.757704	−	0.757704i
$738$		0			0
$739$			22.9210i			0.843161i	0.906791	+	0.421580i	$0.138524\pi$
$739$			22.9210i			0.843161i	−0.906791	+	0.421580i	$0.861476\pi$
$740$		0			0
$741$	−2.63358	+	1.09086i	−0.0967470	+	0.0400739i
$742$		0			0
$743$	45.6996			1.67656			0.838279	−	0.545242i	$-0.183562\pi$
$743$	45.6996			1.67656			0.838279	+	0.545242i	$0.183562\pi$
$744$		0			0
$745$	14.2525	−	17.4828i	0.522172	−	0.640519i
$746$		0			0
$747$		−	1.58692i		−	0.0580623i
$748$		0			0
$749$	−7.64626	+	3.16719i	−0.279388	+	0.115726i
$750$		0			0
$751$	22.3986	−	9.27781i	0.817337	−	0.338552i	0.0654600	−	0.997855i	$-0.479149\pi$
$751$	22.3986	−	9.27781i	0.817337	−	0.338552i	0.751877	+	0.659303i	$0.229149\pi$
$752$		0			0
$753$	−1.22358	+	0.506824i	−0.0445898	+	0.0184697i
$754$		0			0
$755$	0.434495	+	4.26869i	0.0158129	+	0.155354i
$756$		0			0
$757$	15.7922	−	6.54132i	0.573976	−	0.237748i	−0.0767642	−	0.997049i	$-0.524459\pi$
$757$	15.7922	−	6.54132i	0.573976	−	0.237748i	0.650740	+	0.759301i	$0.274459\pi$
$758$		0			0
$759$	5.10275	+	5.10275i	0.185218	+	0.185218i
$760$		0			0
$761$			3.59028i			0.130148i	0.997880	+	0.0650739i	$0.0207283\pi$
$761$			3.59028i			0.130148i	−0.997880	+	0.0650739i	$0.979272\pi$
$762$		0			0
$763$	−1.26774	+	1.26774i	−0.0458951	+	0.0458951i
$764$		0			0
$765$	−19.1945	−	15.6480i	−0.693977	−	0.565754i
$766$		0			0
$767$	9.01045	−	21.7532i	0.325349	−	0.785461i
$768$		0			0
$769$	−21.9885			−0.792925			−0.396463	−	0.918051i	$-0.629762\pi$
$769$	−21.9885			−0.792925			−0.396463	+	0.918051i	$0.629762\pi$
$770$		0			0
$771$	−4.51121	−	4.51121i	−0.162467	−	0.162467i
$772$		0			0
$773$	27.5281	−	11.4025i	0.990117	−	0.410120i	0.171953	−	0.985105i	$-0.444992\pi$
$773$	27.5281	−	11.4025i	0.990117	−	0.410120i	0.818164	+	0.574985i	$0.194992\pi$
$774$		0			0
$775$	−15.1369	+	22.9771i	−0.543733	+	0.825362i
$776$		0			0
$777$		−	0.00541746i		−	0.000194350i
$778$		0			0
$779$	10.6731	+	8.47065i	0.382404	+	0.303493i
$780$		0			0
$781$	−5.18101	−	5.18101i	−0.185391	−	0.185391i
$782$		0			0
$783$	−12.7093	+	12.7093i	−0.454192	+	0.454192i
$784$		0			0
$785$	14.5633	+	11.8725i	0.519785	+	0.423746i
$786$		0			0
$787$		−	29.7477i		−	1.06039i	−0.847875	−	0.530196i	$-0.822118\pi$
$787$		−	29.7477i		−	1.06039i	0.847875	−	0.530196i	$-0.177882\pi$
$788$		0			0
$789$		−	10.7567i		−	0.382950i
$790$		0			0
$791$	0.923688	+	2.22998i	0.0328426	+	0.0792890i
$792$		0			0
$793$	−6.60219	−	15.9391i	−0.234451	−	0.566014i
$794$		0			0
$795$	−18.6125	+	10.0268i	−0.660117	+	0.355613i
$796$		0			0
$797$	31.5824	−	31.5824i	1.11870	−	1.11870i	0.126773	−	0.991932i	$-0.459538\pi$
$797$	31.5824	−	31.5824i	1.11870	−	1.11870i	0.991932	−	0.126773i	$-0.0404621\pi$
$798$		0			0
$799$	−6.38839	+	6.38839i	−0.226005	+	0.226005i
$800$		0			0
$801$	15.6633	−	37.8145i	0.553435	−	1.33611i
$802$		0			0
$803$	−5.39691	+	2.23547i	−0.190453	+	0.0788882i
$804$		0			0
$805$	−0.332732	−	3.26892i	−0.0117273	−	0.115214i
$806$		0			0
$807$	10.4555	+	4.33081i	0.368051	+	0.152452i
$808$		0			0
$809$	−4.74737	−	11.4612i	−0.166909	−	0.402953i	0.818189	−	0.574950i	$-0.194978\pi$
$809$	−4.74737	−	11.4612i	−0.166909	−	0.402953i	−0.985098	+	0.171996i	$0.944978\pi$
$810$		0			0
$811$	−28.9469	−	28.9469i	−1.01646	−	1.01646i	−0.999862	−	0.0165993i	$-0.994716\pi$
$811$	−28.9469	−	28.9469i	−1.01646	−	1.01646i	−0.0165993	−	0.999862i	$-0.505284\pi$
$812$		0			0
$813$	5.91512	−	14.2804i	0.207452	−	0.500834i
$814$		0			0
$815$	−38.0001	+	20.4712i	−1.33109	+	0.717074i
$816$		0			0
$817$	8.50828	+	3.52425i	0.297667	+	0.123298i
$818$		0			0
$819$	−2.15149			−0.0751791
$820$		0			0
$821$	9.91600			0.346071			0.173035	−	0.984916i	$-0.444642\pi$
$821$	9.91600			0.346071			0.173035	+	0.984916i	$0.444642\pi$
$822$		0			0
$823$	−14.9048	−	6.17377i	−0.519549	−	0.215204i	0.107470	−	0.994208i	$-0.465725\pi$
$823$	−14.9048	−	6.17377i	−0.519549	−	0.215204i	−0.627019	+	0.779004i	$0.715725\pi$
$824$		0			0
$825$	5.93641	−	9.01120i	0.206679	−	0.313730i
$826$		0			0
$827$	12.3321	−	29.7724i	0.428831	−	1.03529i	−0.550828	−	0.834619i	$-0.685688\pi$
$827$	12.3321	−	29.7724i	0.428831	−	1.03529i	0.979659	−	0.200670i	$-0.0643120\pi$
$828$		0			0
$829$	4.97528	+	4.97528i	0.172799	+	0.172799i	0.788208	−	0.615409i	$-0.211009\pi$
$829$	4.97528	+	4.97528i	0.172799	+	0.172799i	−0.615409	+	0.788208i	$0.711009\pi$
$830$		0			0
$831$	−0.0333618	−	0.0805426i	−0.00115731	−	0.00279399i
$832$		0			0
$833$	−27.6018	−	11.4330i	−0.956345	−	0.396131i
$834$		0			0
$835$	21.2806	−	26.1037i	0.736446	−	0.903356i
$836$		0			0
$837$	−19.3878	+	8.03067i	−0.670139	+	0.277581i
$838$		0			0
$839$	11.4347	−	27.6057i	0.394768	−	0.953055i	−0.594117	−	0.804378i	$-0.702499\pi$
$839$	11.4347	−	27.6057i	0.394768	−	0.953055i	0.988886	−	0.148677i	$-0.0475014\pi$
$840$		0			0
$841$	4.79780	−	4.79780i	0.165441	−	0.165441i
$842$		0			0
$843$	−6.42374	+	6.42374i	−0.221245	+	0.221245i
$844$		0			0
$845$	9.79449	+	18.1813i	0.336941	+	0.625455i
$846$		0			0
$847$	−0.206663	−	0.498929i	−0.00710103	−	0.0171434i
$848$		0			0
$849$	3.32309	+	8.02265i	0.114048	+	0.275337i
$850$		0			0
$851$		−	0.0597022i		−	0.00204657i
$852$		0			0
$853$		−	17.7973i		−	0.609369i	−0.952453	−	0.304684i	$-0.901449\pi$
$853$		−	17.7973i		−	0.609369i	0.952453	−	0.304684i	$-0.0985510\pi$
$854$		0			0
$855$	11.9452	−	1.21586i	0.408519	−	0.0415817i
$856$		0			0
$857$	21.7356	−	21.7356i	0.742475	−	0.742475i	−0.230579	−	0.973054i	$-0.574062\pi$
$857$	21.7356	−	21.7356i	0.742475	−	0.742475i	0.973054	+	0.230579i	$0.0740619\pi$
$858$		0			0
$859$	4.82290	+	4.82290i	0.164555	+	0.164555i	0.784581	−	0.620026i	$-0.212878\pi$
$859$	4.82290	+	4.82290i	0.164555	+	0.164555i	−0.620026	+	0.784581i	$0.712878\pi$
$860$		0			0
$861$	−0.943758	−	1.69818i	−0.0321632	−	0.0578739i
$862$		0			0
$863$			26.8228i			0.913057i	0.889709	+	0.456529i	$0.150907\pi$
$863$			26.8228i			0.913057i	−0.889709	+	0.456529i	$0.849093\pi$
$864$		0			0
$865$	−9.42490	−	2.82547i	−0.320456	−	0.0960688i
$866$		0			0
$867$	−1.44419	+	0.598204i	−0.0490473	+	0.0203161i
$868$		0			0
$869$	19.2711	+	19.2711i	0.653728	+	0.653728i
$870$		0			0
$871$	−18.0558			−0.611798
$872$		0			0
$873$	−7.24455	+	17.4899i	−0.245191	+	0.591943i
$874$		0			0
$875$	−4.68762	+	1.47222i	−0.158470	+	0.0497703i
$876$		0			0
$877$	−20.0017	+	20.0017i	−0.675411	+	0.675411i	−0.958958	−	0.283547i	$-0.908489\pi$
$877$	−20.0017	+	20.0017i	−0.675411	+	0.675411i	0.283547	+	0.958958i	$0.408489\pi$
$878$		0			0
$879$			3.39736i			0.114590i
$880$		0			0
$881$	−36.1967	−	36.1967i	−1.21950	−	1.21950i	−0.967808	−	0.251690i	$-0.919014\pi$
$881$	−36.1967	−	36.1967i	−1.21950	−	1.21950i	−0.251690	−	0.967808i	$-0.580986\pi$
$882$		0			0
$883$	25.5553	−	10.5854i	0.860005	−	0.356226i	0.0912957	−	0.995824i	$-0.470899\pi$
$883$	25.5553	−	10.5854i	0.860005	−	0.356226i	0.768710	+	0.639598i	$0.220899\pi$
$884$		0			0
$885$	11.8383	−	14.5214i	0.397940	−	0.488131i
$886$		0			0
$887$	22.2352	−	9.21013i	0.746585	−	0.309246i	0.0232379	−	0.999730i	$-0.492602\pi$
$887$	22.2352	−	9.21013i	0.746585	−	0.309246i	0.723348	+	0.690484i	$0.242602\pi$
$888$		0			0
$889$	3.13178	−	1.29722i	0.105036	−	0.0435075i
$890$		0			0
$891$	−14.2581	+	5.90588i	−0.477663	+	0.197855i
$892$		0			0
$893$		−	4.38034i		−	0.146582i
$894$		0			0
$895$	15.3365	+	12.5028i	0.512643	+	0.417924i
$896$		0			0
$897$	4.47907			0.149552
$898$		0			0
$899$	−23.9627	+	9.92568i	−0.799201	+	0.331040i
$900$		0			0
$901$		−	60.1050i		−	2.00239i
$902$		0			0
$903$	−0.928483	−	0.928483i	−0.0308980	−	0.0308980i
$904$		0			0
$905$	−11.0875	−	9.03888i	−0.368560	−	0.300462i
$906$		0			0
$907$			20.7839i			0.690116i	0.938581	+	0.345058i	$0.112141\pi$
$907$			20.7839i			0.690116i	−0.938581	+	0.345058i	$0.887859\pi$
$908$		0			0
$909$	−16.0901	−	38.8450i	−0.533676	−	1.28841i
$910$		0			0
$911$	−15.3593	+	15.3593i	−0.508878	+	0.508878i	−0.914182	−	0.405304i	$-0.867166\pi$
$911$	−15.3593	+	15.3593i	−0.508878	+	0.508878i	0.405304	+	0.914182i	$0.367166\pi$
$912$		0			0
$913$	−0.752306	+	1.81623i	−0.0248977	+	0.0601084i
$914$		0			0
$915$	−1.39013	−	13.6574i	−0.0459564	−	0.451498i
$916$		0			0
$917$	−2.76576	−	6.67713i	−0.0913334	−	0.220498i
$918$		0			0
$919$	−18.4524	+	44.5479i	−0.608687	+	1.46950i	0.255742	+	0.966745i	$0.417680\pi$
$919$	−18.4524	+	44.5479i	−0.608687	+	1.46950i	−0.864429	+	0.502755i	$0.832320\pi$
$920$		0			0
$921$	14.3725	+	5.95329i	0.473590	+	0.196168i
$922$		0			0
$923$	−4.54777			−0.149692
$924$		0			0
$925$	−0.0874437	+	0.0179875i	−0.00287513	+	0.000591426i
$926$		0			0
$927$	18.7119	+	18.7119i	0.614580	+	0.614580i
$928$		0			0
$929$	−7.47775	−	3.09738i	−0.245337	−	0.101622i	0.256627	−	0.966511i	$-0.417389\pi$
$929$	−7.47775	−	3.09738i	−0.245337	−	0.101622i	−0.501964	+	0.864889i	$0.667389\pi$
$930$		0			0
$931$	13.3825	−	5.54323i	0.438595	−	0.181672i
$932$		0			0
$933$	10.3005	−	10.3005i	0.337222	−	0.337222i
$934$		0			0
$935$	14.5499	+	27.0086i	0.475832	+	0.883275i
$936$		0			0
$937$	−0.843767	−	2.03703i	−0.0275647	−	0.0665470i	0.909498	−	0.415709i	$-0.136466\pi$
$937$	−0.843767	−	2.03703i	−0.0275647	−	0.0665470i	−0.937062	+	0.349162i	$0.886466\pi$
$938$		0			0
$939$			4.59290i			0.149884i
$940$		0			0
$941$	−34.7556	+	34.7556i	−1.13300	+	1.13300i	−0.143325	+	0.989676i	$0.545779\pi$
$941$	−34.7556	+	34.7556i	−1.13300	+	1.13300i	−0.989676	+	0.143325i	$0.954221\pi$
$942$		0			0
$943$	−10.4005	−	18.7145i	−0.338688	−	0.609430i
$944$		0			0
$945$	−3.58951	−	1.07609i	−0.116767	−	0.0350052i
$946$		0			0
$947$	11.1861	+	11.1861i	0.363498	+	0.363498i	0.865099	−	0.501601i	$-0.167255\pi$
$947$	11.1861	+	11.1861i	0.363498	+	0.363498i	−0.501601	+	0.865099i	$0.667255\pi$
$948$		0			0
$949$	−1.38752	+	3.34977i	−0.0450408	+	0.108738i
$950$		0			0
$951$	3.68677	−	3.68677i	0.119552	−	0.119552i
$952$		0			0
$953$	−33.1071	−	33.1071i	−1.07244	−	1.07244i	−0.997162	−	0.0752810i	$-0.976015\pi$
$953$	−33.1071	−	33.1071i	−1.07244	−	1.07244i	−0.0752810	−	0.997162i	$-0.523985\pi$
$954$		0			0
$955$	−7.44734	+	9.13522i	−0.240990	+	0.295609i
$956$		0			0
$957$	9.39774	−	3.89267i	0.303786	−	0.125832i
$958$		0			0
$959$			8.03109i			0.259338i
$960$		0			0
$961$	0.717106			0.0231325
$962$		0			0
$963$			47.5206i			1.53133i
$964$		0			0
$965$	−6.73606	−	5.49146i	−0.216841	−	0.176777i
$966$		0			0
$967$	5.26445	+	12.7095i	0.169293	+	0.408710i	0.985642	−	0.168849i	$-0.0540051\pi$
$967$	5.26445	+	12.7095i	0.169293	+	0.408710i	−0.816349	+	0.577560i	$0.804005\pi$
$968$		0			0
$969$	2.46776	−	5.95770i	0.0792759	−	0.191389i
$970$		0			0
$971$	−14.6957	−	35.4785i	−0.471606	−	1.13856i	−0.963453	−	0.267877i	$-0.913678\pi$
$971$	−14.6957	−	35.4785i	−0.471606	−	1.13856i	0.491847	−	0.870682i	$-0.336322\pi$
$972$		0			0
$973$	−2.92952	−	1.21345i	−0.0939160	−	0.0389013i
$974$		0			0
$975$	−1.34949	−	6.56034i	−0.0432182	−	0.210099i
$976$		0			0
$977$	27.3693	+	11.3367i	0.875621	+	0.362694i	0.774797	−	0.632210i	$-0.217852\pi$
$977$	27.3693	+	11.3367i	0.875621	+	0.362694i	0.100824	+	0.994904i	$0.467852\pi$
$978$		0			0
$979$	−35.8532	+	35.8532i	−1.14587	+	1.14587i
$980$		0			0
$981$	3.93941	+	9.51057i	0.125776	+	0.303649i
$982$		0			0
$983$	30.3986	−	30.3986i	0.969564	−	0.969564i	−0.0299866	−	0.999550i	$-0.509546\pi$
$983$	30.3986	−	30.3986i	0.969564	−	0.969564i	0.999550	+	0.0299866i	$0.00954648\pi$
$984$		0			0
$985$	23.9774	+	7.18812i	0.763982	+	0.229032i
$986$		0			0
$987$	−0.239006	+	0.577012i	−0.00760766	+	0.0183665i
$988$		0			0
$989$	−10.2322	−	10.2322i	−0.325365	−	0.325365i
$990$		0			0
$991$	−14.6254	+	6.05805i	−0.464592	+	0.192440i	−0.602685	−	0.797979i	$-0.705903\pi$
$991$	−14.6254	+	6.05805i	−0.464592	+	0.192440i	0.138093	+	0.990419i	$0.455903\pi$
$992$		0			0
$993$	0.379269			0.0120357
$994$		0			0
$995$	12.1125	+	9.87450i	0.383991	+	0.313043i
$996$		0			0
$997$	−19.3818	+	46.7917i	−0.613826	+	1.48191i	0.244939	+	0.969538i	$0.421232\pi$
$997$	−19.3818	+	46.7917i	−0.613826	+	1.48191i	−0.858765	+	0.512369i	$0.828768\pi$
$998$		0			0
$999$	−0.0629052	−	0.0260562i	−0.00199023	−	0.000824382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.273.10	✓	84
5.2	odd	4		820.2.y.a.437.10	yes	84
41.38	odd	8		820.2.y.a.653.10	yes	84
205.202	even	8	inner	820.2.x.a.817.10	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.10	✓	84	1.1	even	1	trivial
820.2.x.a.817.10	yes	84	205.202	even	8	inner
820.2.y.a.437.10	yes	84	5.2	odd	4
820.2.y.a.653.10	yes	84	41.38	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.637865 - 0.264212i) q^{3} +(-2.14189 - 0.642112i) q^{5} +(0.168176 - 0.406013i) q^{7} +(-1.78426 - 1.78426i) q^{9} +(1.19622 + 2.88794i) q^{11} +(1.79249 + 0.742475i) q^{13} +(1.19658 + 0.975494i) q^{15} +(-4.05499 + 1.67963i) q^{17} +(0.814358 - 1.96603i) q^{19} +(-0.214547 + 0.214547i) q^{21} +(-2.36438 + 2.36438i) q^{23} +(4.17538 + 2.75067i) q^{25} +(1.45933 + 3.52313i) q^{27} +(1.80369 + 4.35449i) q^{29} +5.50299i q^{31} -2.15817i q^{33} +(-0.620921 + 0.761647i) q^{35} +(-0.0126253 + 0.0126253i) q^{37} +(-0.947197 - 0.947197i) q^{39} +(-1.75818 + 6.15701i) q^{41} +4.32764i q^{43} +(2.67599 + 4.96737i) q^{45} +(1.90172 - 0.787719i) q^{47} +(4.81318 + 4.81318i) q^{49} +3.03032 q^{51} +(-5.24054 + 12.6518i) q^{53} +(-0.707799 - 6.95376i) q^{55} +(-1.03890 + 1.03890i) q^{57} -12.1357i q^{59} +(-6.28769 - 6.28769i) q^{61} +(-1.02450 + 0.424362i) q^{63} +(-3.36257 - 2.74128i) q^{65} +(-8.59787 + 3.56135i) q^{67} +(2.13286 - 0.883458i) q^{69} +(-2.16557 + 0.897008i) q^{71} +1.86878i q^{73} +(-1.93657 - 2.85774i) q^{75} +1.37372 q^{77} +(8.05498 - 3.33648i) q^{79} +4.93711i q^{81} +(0.444700 + 0.444700i) q^{83} +(9.76385 - 0.993828i) q^{85} -3.25413i q^{87} +(6.20741 + 14.9860i) q^{89} +(0.602909 - 0.602909i) q^{91} +(1.45396 - 3.51016i) q^{93} +(-3.00668 + 3.68812i) q^{95} +(-2.87104 - 6.93130i) q^{97} +(3.01846 - 7.28720i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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