LMFDB - Embedded newform 820.2.bg.b.681.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(441,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.441"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bg (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			681.8
Character	$\chi$	$=$	820.681
Dual form			820.2.bg.b.761.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.43298i q^{3} +(-0.809017 - 0.587785i) q^{5} +(-3.30690 + 1.07448i) q^{7} -8.78535 q^{9} +(3.15743 + 4.34583i) q^{11} +(0.256531 + 0.0833521i) q^{13} +(2.01785 - 2.77734i) q^{15} +(-4.15727 - 5.72199i) q^{17} +(4.35396 - 1.41469i) q^{19} +(-3.68866 - 11.3525i) q^{21} +(-0.610350 + 1.87846i) q^{23} +(0.309017 + 0.951057i) q^{25} -19.8610i q^{27} +(2.22301 - 3.05971i) q^{29} +(-7.35345 + 5.34260i) q^{31} +(-14.9191 + 10.8394i) q^{33} +(3.30690 + 1.07448i) q^{35} +(-0.0353143 - 0.0256574i) q^{37} +(-0.286146 + 0.880667i) q^{39} +(6.14835 + 1.78824i) q^{41} +(0.892376 - 2.74645i) q^{43} +(7.10750 + 5.16390i) q^{45} +(-10.4190 - 3.38535i) q^{47} +(4.11798 - 2.99189i) q^{49} +(19.6435 - 14.2718i) q^{51} +(-2.78930 + 3.83915i) q^{53} -5.37174i q^{55} +(4.85659 + 14.9470i) q^{57} +(-2.38781 + 7.34892i) q^{59} +(-0.864716 - 2.66132i) q^{61} +(29.0523 - 9.43966i) q^{63} +(-0.158545 - 0.218219i) q^{65} +(-4.97098 + 6.84197i) q^{67} +(-6.44873 - 2.09532i) q^{69} +(-0.478354 - 0.658398i) q^{71} -8.15541 q^{73} +(-3.26496 + 1.06085i) q^{75} +(-15.1108 - 10.9786i) q^{77} -9.20912i q^{79} +41.8263 q^{81} +4.16410 q^{83} +7.07277i q^{85} +(10.5039 + 7.63155i) q^{87} +(1.91886 - 0.623477i) q^{89} -0.937884 q^{91} +(-18.3410 - 25.2443i) q^{93} +(-4.35396 - 1.41469i) q^{95} +(-2.52047 + 3.46913i) q^{97} +(-27.7391 - 38.1796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{5} - 5 q^{7} - 42 q^{9} + 5 q^{11} + 5 q^{13} - 5 q^{17} - 25 q^{19} - 6 q^{21} - 22 q^{23} - 8 q^{25} + 5 q^{29} - 9 q^{31} + 24 q^{33} + 5 q^{35} - 11 q^{37} + 20 q^{39} + 16 q^{41} + 26 q^{43}+ \cdots - 20 q^{97}+O(q^{100}) $ 32 * q - 8 * q^5 - 5 * q^7 - 42 * q^9 + 5 * q^11 + 5 * q^13 - 5 * q^17 - 25 * q^19 - 6 * q^21 - 22 * q^23 - 8 * q^25 + 5 * q^29 - 9 * q^31 + 24 * q^33 + 5 * q^35 - 11 * q^37 + 20 * q^39 + 16 * q^41 + 26 * q^43 + 13 * q^45 - 25 * q^47 + 33 * q^49 + 29 * q^51 - 35 * q^53 + 27 * q^57 + 10 * q^59 + 32 * q^61 + 90 * q^63 - 5 * q^65 + 30 * q^67 - 10 * q^69 + 45 * q^71 - 80 * q^73 - 5 * q^75 - 78 * q^77 - 20 * q^81 - 10 * q^83 + 27 * q^87 - 60 * q^89 + 14 * q^91 - 80 * q^93 + 25 * q^95 - 20 * q^97

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			3.43298i			1.98203i	0.133745	+	0.991016i	$0.457300\pi$
$3$			3.43298i			1.98203i	−0.133745	+	0.991016i	$0.542700\pi$
$4$		0			0
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−3.30690	+	1.07448i	−1.24989	+	0.406114i	−0.857882	−	0.513847i	$-0.828220\pi$
$7$	−3.30690	+	1.07448i	−1.24989	+	0.406114i	−0.392010	+	0.919961i	$0.628220\pi$
$8$		0			0
$9$	−8.78535			−2.92845
$10$		0			0
$11$	3.15743	+	4.34583i	0.952001	+	1.31032i	0.950633	+	0.310318i	$0.100436\pi$
$11$	3.15743	+	4.34583i	0.952001	+	1.31032i	0.00136834	+	0.999999i	$0.499564\pi$
$12$		0			0
$13$	0.256531	+	0.0833521i	0.0711490	+	0.0231177i	0.344375	−	0.938832i	$-0.388091\pi$
$13$	0.256531	+	0.0833521i	0.0711490	+	0.0231177i	−0.273226	+	0.961950i	$0.588091\pi$
$14$		0			0
$15$	2.01785	−	2.77734i	0.521008	−	0.717106i
$16$		0			0
$17$	−4.15727	−	5.72199i	−1.00829	−	1.38779i	−0.920101	−	0.391682i	$-0.871893\pi$
$17$	−4.15727	−	5.72199i	−1.00829	−	1.38779i	−0.0881848	−	0.996104i	$-0.528107\pi$
$18$		0			0
$19$	4.35396	−	1.41469i	0.998866	−	0.324551i	0.236454	−	0.971643i	$-0.424015\pi$
$19$	4.35396	−	1.41469i	0.998866	−	0.324551i	0.762413	+	0.647091i	$0.224015\pi$
$20$		0			0
$21$	−3.68866	−	11.3525i	−0.804931	−	2.47732i
$22$		0			0
$23$	−0.610350	+	1.87846i	−0.127267	+	0.391687i	−0.994307	−	0.106551i	$-0.966019\pi$
$23$	−0.610350	+	1.87846i	−0.127267	+	0.391687i	0.867040	+	0.498238i	$0.166019\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$		−	19.8610i		−	3.82225i
$28$		0			0
$29$	2.22301	−	3.05971i	0.412803	−	0.568174i	−0.551096	−	0.834442i	$-0.685790\pi$
$29$	2.22301	−	3.05971i	0.412803	−	0.568174i	0.963899	+	0.266267i	$0.0857903\pi$
$30$		0			0
$31$	−7.35345	+	5.34260i	−1.32072	+	0.959559i	−0.320796	+	0.947148i	$0.603950\pi$
$31$	−7.35345	+	5.34260i	−1.32072	+	0.959559i	−0.999923	+	0.0124103i	$0.996050\pi$
$32$		0			0
$33$	−14.9191	+	10.8394i	−2.59709	+	1.88690i
$34$		0			0
$35$	3.30690	+	1.07448i	0.558968	+	0.181620i
$36$		0			0
$37$	−0.0353143	−	0.0256574i	−0.00580564	−	0.00421805i	0.584879	−	0.811121i	$-0.301142\pi$
$37$	−0.0353143	−	0.0256574i	−0.00580564	−	0.00421805i	−0.590684	+	0.806903i	$0.701142\pi$
$38$		0			0
$39$	−0.286146	+	0.880667i	−0.0458200	+	0.141020i
$40$		0			0
$41$	6.14835	+	1.78824i	0.960211	+	0.279277i
$41$	6.14835	+	1.78824i	0.960211	+	0.279277i
$42$		0			0
$43$	0.892376	−	2.74645i	0.136086	−	0.418830i	−0.859671	−	0.510848i	$-0.829332\pi$
$43$	0.892376	−	2.74645i	0.136086	−	0.418830i	0.995757	+	0.0920176i	$0.0293316\pi$
$44$		0			0
$45$	7.10750	+	5.16390i	1.05952	+	0.769788i
$46$		0			0
$47$	−10.4190	−	3.38535i	−1.51977	−	0.493805i	−0.574063	−	0.818811i	$-0.694633\pi$
$47$	−10.4190	−	3.38535i	−1.51977	−	0.493805i	−0.945712	+	0.325007i	$0.894633\pi$
$48$		0			0
$49$	4.11798	−	2.99189i	0.588283	−	0.427413i
$50$		0			0
$51$	19.6435	−	14.2718i	2.75064	−	1.99845i
$52$		0			0
$53$	−2.78930	+	3.83915i	−0.383140	+	0.527347i	−0.956413	−	0.292017i	$-0.905674\pi$
$53$	−2.78930	+	3.83915i	−0.383140	+	0.527347i	0.573273	+	0.819365i	$0.305674\pi$
$54$		0			0
$55$		−	5.37174i		−	0.724326i
$56$		0			0
$57$	4.85659	+	14.9470i	0.643271	+	1.97978i
$58$		0			0
$59$	−2.38781	+	7.34892i	−0.310866	+	0.956748i	0.666556	+	0.745455i	$0.267768\pi$
$59$	−2.38781	+	7.34892i	−0.310866	+	0.956748i	−0.977423	+	0.211294i	$0.932232\pi$
$60$		0			0
$61$	−0.864716	−	2.66132i	−0.110716	−	0.340747i	0.880314	−	0.474392i	$-0.157332\pi$
$61$	−0.864716	−	2.66132i	−0.110716	−	0.340747i	−0.991029	+	0.133644i	$0.957332\pi$
$62$		0			0
$63$	29.0523	−	9.43966i	3.66024	−	1.18929i
$64$		0			0
$65$	−0.158545	−	0.218219i	−0.0196651	−	0.0270667i
$66$		0			0
$67$	−4.97098	+	6.84197i	−0.607302	+	0.835880i	−0.996352	−	0.0853370i	$-0.972803\pi$
$67$	−4.97098	+	6.84197i	−0.607302	+	0.835880i	0.389050	+	0.921217i	$0.372803\pi$
$68$		0			0
$69$	−6.44873	−	2.09532i	−0.776336	−	0.252247i
$70$		0			0
$71$	−0.478354	−	0.658398i	−0.0567702	−	0.0781375i	0.779688	−	0.626168i	$-0.215378\pi$
$71$	−0.478354	−	0.658398i	−0.0567702	−	0.0781375i	−0.836458	+	0.548031i	$0.815378\pi$
$72$		0			0
$73$	−8.15541			−0.954518			−0.477259	−	0.878763i	$-0.658370\pi$
$73$	−8.15541			−0.954518			−0.477259	+	0.878763i	$0.658370\pi$
$74$		0			0
$75$	−3.26496	+	1.06085i	−0.377005	+	0.122496i
$76$		0			0
$77$	−15.1108	−	10.9786i	−1.72204	−	1.25113i
$78$		0			0
$79$		−	9.20912i		−	1.03611i	−0.855348	−	0.518053i	$-0.826657\pi$
$79$		−	9.20912i		−	1.03611i	0.855348	−	0.518053i	$-0.173343\pi$
$80$		0			0
$81$	41.8263			4.64736
$82$		0			0
$83$	4.16410			0.457070			0.228535	−	0.973536i	$-0.426607\pi$
$83$	4.16410			0.457070			0.228535	+	0.973536i	$0.426607\pi$
$84$		0			0
$85$			7.07277i			0.767149i
$86$		0			0
$87$	10.5039	+	7.63155i	1.12614	+	0.818188i
$88$		0			0
$89$	1.91886	−	0.623477i	0.203399	−	0.0660884i	−0.205546	−	0.978648i	$-0.565897\pi$
$89$	1.91886	−	0.623477i	0.203399	−	0.0660884i	0.408945	+	0.912559i	$0.365897\pi$
$90$		0			0
$91$	−0.937884			−0.0983170
$92$		0			0
$93$	−18.3410	−	25.2443i	−1.90188	−	2.61771i
$94$		0			0
$95$	−4.35396	−	1.41469i	−0.446707	−	0.145144i
$96$		0			0
$97$	−2.52047	+	3.46913i	−0.255915	+	0.352237i	−0.917572	−	0.397570i	$-0.869854\pi$
$97$	−2.52047	+	3.46913i	−0.255915	+	0.352237i	0.661657	+	0.749807i	$0.269854\pi$
$98$		0			0
$99$	−27.7391	−	38.1796i	−2.78789	−	3.83720i
$100$		0			0
$101$	−8.50468	+	2.76334i	−0.846247	+	0.274962i	−0.699873	−	0.714267i	$-0.746760\pi$
$101$	−8.50468	+	2.76334i	−0.846247	+	0.274962i	−0.146374	+	0.989229i	$0.546760\pi$
$102$		0			0
$103$	−1.16236	−	3.57739i	−0.114531	−	0.352490i	0.877318	−	0.479910i	$-0.159331\pi$
$103$	−1.16236	−	3.57739i	−0.114531	−	0.352490i	−0.991849	+	0.127419i	$0.959331\pi$
$104$		0			0
$105$	−3.68866	+	11.3525i	−0.359976	+	1.10789i
$106$		0			0
$107$	4.56297	+	14.0434i	0.441119	+	1.35762i	0.886684	+	0.462375i	$0.153003\pi$
$107$	4.56297	+	14.0434i	0.441119	+	1.35762i	−0.445565	+	0.895249i	$0.646997\pi$
$108$		0			0
$109$			13.0354i			1.24856i	0.781200	+	0.624280i	$0.214608\pi$
$109$			13.0354i			1.24856i	−0.781200	+	0.624280i	$0.785392\pi$
$110$		0			0
$111$	0.0880812	−	0.121233i	0.00836030	−	0.0115070i
$112$		0			0
$113$	−10.6718	+	7.75350i	−1.00392	+	0.729388i	−0.962924	−	0.269771i	$-0.913052\pi$
$113$	−10.6718	+	7.75350i	−1.00392	+	0.729388i	−0.0409923	+	0.999159i	$0.513052\pi$
$114$		0			0
$115$	1.59792	−	1.16096i	0.149007	−	0.108260i
$116$		0			0
$117$	−2.25372	−	0.732277i	−0.208356	−	0.0676991i
$118$		0			0
$119$	19.8958	+	14.4552i	1.82385	+	1.32510i
$120$		0			0
$121$	−5.51769	+	16.9817i	−0.501608	+	1.54379i
$122$		0			0
$123$	−6.13901	+	21.1072i	−0.553536	+	1.90317i
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	−9.05689	−	6.58022i	−0.803669	−	0.583900i	0.108319	−	0.994116i	$-0.465453\pi$
$127$	−9.05689	−	6.58022i	−0.803669	−	0.583900i	−0.911988	+	0.410216i	$0.865453\pi$
$128$		0			0
$129$	9.42851	+	3.06351i	0.830134	+	0.269727i
$130$		0			0
$131$	4.11049	−	2.98645i	0.359135	−	0.260927i	−0.393556	−	0.919301i	$-0.628755\pi$
$131$	4.11049	−	2.98645i	0.359135	−	0.260927i	0.752691	+	0.658374i	$0.228755\pi$
$132$		0			0
$133$	−12.8781	+	9.35646i	−1.11667	+	0.811308i
$134$		0			0
$135$	−11.6740	+	16.0679i	−1.00474	+	1.38290i
$136$		0			0
$137$			3.20307i			0.273657i	0.990595	+	0.136829i	$0.0436909\pi$
$137$			3.20307i			0.273657i	−0.990595	+	0.136829i	$0.956309\pi$
$138$		0			0
$139$	2.35384	+	7.24438i	0.199650	+	0.614460i	0.999891	+	0.0147809i	$0.00470508\pi$
$139$	2.35384	+	7.24438i	0.199650	+	0.614460i	−0.800241	+	0.599679i	$0.795295\pi$
$140$		0			0
$141$	11.6219	−	35.7684i	0.978736	−	3.01224i
$142$		0			0
$143$	0.447746	+	1.37802i	0.0374424	+	0.115236i
$144$		0			0
$145$	−3.59691	+	1.16871i	−0.298707	+	0.0970558i
$146$		0			0
$147$	10.2711	+	14.1369i	0.847145	+	1.16600i
$148$		0			0
$149$	−1.57402	+	2.16645i	−0.128949	+	0.177483i	−0.868610	−	0.495497i	$-0.834986\pi$
$149$	−1.57402	+	2.16645i	−0.128949	+	0.177483i	0.739661	+	0.672980i	$0.234986\pi$
$150$		0			0
$151$	−9.85419	−	3.20182i	−0.801923	−	0.260561i	−0.120750	−	0.992683i	$-0.538530\pi$
$151$	−9.85419	−	3.20182i	−0.801923	−	0.260561i	−0.681173	+	0.732122i	$0.738530\pi$
$152$		0			0
$153$	36.5230	+	50.2697i	2.95271	+	4.06406i
$154$		0			0
$155$	9.08937			0.730076
$156$		0			0
$157$	6.21351	−	2.01889i	0.495892	−	0.161125i	−0.0503846	−	0.998730i	$-0.516045\pi$
$157$	6.21351	−	2.01889i	0.495892	−	0.161125i	0.546277	+	0.837605i	$0.316045\pi$
$158$		0			0
$159$	−13.1797	−	9.57562i	−1.04522	−	0.759396i
$160$		0			0
$161$		−	6.86771i		−	0.541251i
$162$		0			0
$163$	−6.80919			−0.533337			−0.266668	−	0.963788i	$-0.585923\pi$
$163$	−6.80919			−0.533337			−0.266668	+	0.963788i	$0.585923\pi$
$164$		0			0
$165$	18.4411			1.43564
$166$		0			0
$167$			12.0378i			0.931511i	0.884913	+	0.465756i	$0.154217\pi$
$167$			12.0378i			0.931511i	−0.884913	+	0.465756i	$0.845783\pi$
$168$		0			0
$169$	−10.4584	−	7.59844i	−0.804489	−	0.584496i
$170$		0			0
$171$	−38.2510	+	12.4285i	−2.92513	+	0.950432i
$172$		0			0
$173$	12.9861			0.987318			0.493659	−	0.869656i	$-0.335659\pi$
$173$	12.9861			0.987318			0.493659	+	0.869656i	$0.335659\pi$
$174$		0			0
$175$	−2.04378	−	2.81302i	−0.154495	−	0.212644i
$176$		0			0
$177$	−25.2287	−	8.19730i	−1.89631	−	0.616147i
$178$		0			0
$179$	−8.10112	+	11.1502i	−0.605506	+	0.833408i	−0.996198	−	0.0871137i	$-0.972236\pi$
$179$	−8.10112	+	11.1502i	−0.605506	+	0.833408i	0.390692	+	0.920521i	$0.372236\pi$
$180$		0			0
$181$	−0.708556	−	0.975243i	−0.0526665	−	0.0724893i	0.781871	−	0.623440i	$-0.214265\pi$
$181$	−0.708556	−	0.975243i	−0.0526665	−	0.0724893i	−0.834538	+	0.550950i	$0.814265\pi$
$182$		0			0
$183$	9.13627	−	2.96855i	0.675372	−	0.219442i
$184$		0			0
$185$	0.0134889	+	0.0415145i	0.000991722	+	0.00305221i
$186$		0			0
$187$	11.7405	−	36.1336i	0.858551	−	2.64235i
$188$		0			0
$189$	21.3402	+	65.6783i	1.55227	+	4.77739i
$190$		0			0
$191$			15.5006i			1.12158i	0.827957	+	0.560792i	$0.189503\pi$
$191$			15.5006i			1.12158i	−0.827957	+	0.560792i	$0.810497\pi$
$192$		0			0
$193$	2.70237	−	3.71950i	0.194521	−	0.267735i	−0.700604	−	0.713550i	$-0.747086\pi$
$193$	2.70237	−	3.71950i	0.194521	−	0.267735i	0.895125	+	0.445815i	$0.147086\pi$
$194$		0			0
$195$	0.749140	−	0.544282i	0.0536470	−	0.0389769i
$196$		0			0
$197$	−6.71576	+	4.87929i	−0.478478	+	0.347635i	−0.800736	−	0.599017i	$-0.795558\pi$
$197$	−6.71576	+	4.87929i	−0.478478	+	0.347635i	0.322258	+	0.946652i	$0.395558\pi$
$198$		0			0
$199$	−8.88934	−	2.88832i	−0.630148	−	0.204748i	−0.0235075	−	0.999724i	$-0.507483\pi$
$199$	−8.88934	−	2.88832i	−0.630148	−	0.204748i	−0.606641	+	0.794976i	$0.707483\pi$
$200$		0			0
$201$	−23.4883	−	17.0653i	−1.65674	−	1.20369i
$202$		0			0
$203$	−4.06369	+	12.5067i	−0.285215	+	0.877802i
$204$		0			0
$205$	−3.92301	−	5.06063i	−0.273995	−	0.353450i
$206$		0			0
$207$	5.36214	−	16.5030i	0.372694	−	1.14704i
$208$		0			0
$209$	19.8953	+	14.4548i	1.37619	+	0.999859i
$210$		0			0
$211$	−12.2972	−	3.99560i	−0.846574	−	0.275069i	−0.146564	−	0.989201i	$-0.546821\pi$
$211$	−12.2972	−	3.99560i	−0.846574	−	0.275069i	−0.700010	+	0.714133i	$0.746821\pi$
$212$		0			0
$213$	2.26027	−	1.64218i	0.154871	−	0.112520i
$214$		0			0
$215$	−2.33627	+	1.69740i	−0.159332	+	0.115762i
$216$		0			0
$217$	18.5766	−	25.5686i	1.26107	−	1.73571i
$218$		0			0
$219$		−	27.9973i		−	1.89188i
$220$		0			0
$221$	−0.589530	−	1.81439i	−0.0396561	−	0.122049i
$222$		0			0
$223$	7.46551	−	22.9765i	0.499928	−	1.53862i	−0.309206	−	0.950995i	$-0.600063\pi$
$223$	7.46551	−	22.9765i	0.499928	−	1.53862i	0.809134	−	0.587624i	$-0.199937\pi$
$224$		0			0
$225$	−2.71482	−	8.35536i	−0.180988	−	0.557024i
$226$		0			0
$227$	12.5602	−	4.08106i	0.833650	−	0.270869i	0.139068	−	0.990283i	$-0.455589\pi$
$227$	12.5602	−	4.08106i	0.833650	−	0.270869i	0.694582	+	0.719413i	$0.255589\pi$
$228$		0			0
$229$	−2.11019	−	2.90443i	−0.139445	−	0.191930i	0.733582	−	0.679600i	$-0.237847\pi$
$229$	−2.11019	−	2.90443i	−0.139445	−	0.191930i	−0.873028	+	0.487670i	$0.837847\pi$
$230$		0			0
$231$	37.6895	−	51.8751i	2.47978	−	3.41313i
$232$		0			0
$233$	9.70309	+	3.15273i	0.635671	+	0.206542i	0.609085	−	0.793105i	$-0.291537\pi$
$233$	9.70309	+	3.15273i	0.635671	+	0.206542i	0.0265853	+	0.999647i	$0.491537\pi$
$234$		0			0
$235$	6.43933	+	8.86297i	0.420055	+	0.578157i
$236$		0			0
$237$	31.6147			2.05360
$238$		0			0
$239$	−3.81170	+	1.23850i	−0.246558	+	0.0801116i	−0.429689	−	0.902977i	$-0.641377\pi$
$239$	−3.81170	+	1.23850i	−0.246558	+	0.0801116i	0.183131	+	0.983089i	$0.441377\pi$
$240$		0			0
$241$	−14.9945	−	10.8941i	−0.965881	−	0.701754i	−0.0113719	−	0.999935i	$-0.503620\pi$
$241$	−14.9945	−	10.8941i	−0.965881	−	0.701754i	−0.954509	+	0.298182i	$0.903620\pi$
$242$		0			0
$243$			84.0058i			5.38898i
$244$		0			0
$245$	−5.09010			−0.325195
$246$		0			0
$247$	1.23484			0.0785712
$248$		0			0
$249$			14.2953i			0.905926i
$250$		0			0
$251$	15.1951	+	11.0399i	0.959104	+	0.696830i	0.952942	−	0.303151i	$-0.0980387\pi$
$251$	15.1951	+	11.0399i	0.959104	+	0.696830i	0.00616145	+	0.999981i	$0.498039\pi$
$252$		0			0
$253$	−10.0906	+	3.27864i	−0.634392	+	0.206127i
$254$		0			0
$255$	−24.2807			−1.52051
$256$		0			0
$257$	5.99666	+	8.25369i	0.374061	+	0.514851i	0.953999	−	0.299810i	$-0.0969231\pi$
$257$	5.99666	+	8.25369i	0.374061	+	0.514851i	−0.579938	+	0.814661i	$0.696923\pi$
$258$		0			0
$259$	0.144349	+	0.0469019i	0.00896943	+	0.00291434i
$260$		0			0
$261$	−19.5299	+	26.8806i	−1.20887	+	1.66387i
$262$		0			0
$263$	8.07721	+	11.1173i	0.498062	+	0.685524i	0.981849	−	0.189662i	$-0.0607392\pi$
$263$	8.07721	+	11.1173i	0.498062	+	0.685524i	−0.483787	+	0.875186i	$0.660739\pi$
$264$		0			0
$265$	4.51319	−	1.46642i	0.277243	−	0.0900817i
$266$		0			0
$267$	2.14038	+	6.58742i	0.130989	+	0.403144i
$268$		0			0
$269$	2.33377	−	7.18260i	0.142292	−	0.437931i	−0.854360	−	0.519681i	$-0.826051\pi$
$269$	2.33377	−	7.18260i	0.142292	−	0.437931i	0.996653	+	0.0817498i	$0.0260509\pi$
$270$		0			0
$271$	2.06623	+	6.35921i	0.125515	+	0.386295i	0.993995	−	0.109430i	$-0.0349025\pi$
$271$	2.06623	+	6.35921i	0.125515	+	0.386295i	−0.868480	+	0.495725i	$0.834903\pi$
$272$		0			0
$273$		−	3.21974i		−	0.194867i
$274$		0			0
$275$	−3.15743	+	4.34583i	−0.190400	+	0.262063i
$276$		0			0
$277$	15.9125	−	11.5611i	0.956090	−	0.694640i	0.00385053	−	0.999993i	$-0.498774\pi$
$277$	15.9125	−	11.5611i	0.956090	−	0.694640i	0.952239	+	0.305353i	$0.0987743\pi$
$278$		0			0
$279$	64.6026	−	46.9366i	3.86766	−	2.81002i
$280$		0			0
$281$	25.1881	+	8.18411i	1.50260	+	0.488223i	0.940774	−	0.339034i	$-0.110100\pi$
$281$	25.1881	+	8.18411i	1.50260	+	0.488223i	0.561823	+	0.827258i	$0.310100\pi$
$282$		0			0
$283$	3.67079	+	2.66699i	0.218206	+	0.158536i	0.691519	−	0.722359i	$-0.256942\pi$
$283$	3.67079	+	2.66699i	0.218206	+	0.158536i	−0.473313	+	0.880894i	$0.656942\pi$
$284$		0			0
$285$	4.85659	−	14.9470i	0.287680	−	0.885387i
$286$		0			0
$287$	−22.2534	+	0.692712i	−1.31358	+	0.0408895i
$288$		0			0
$289$	−10.2050	+	31.4077i	−0.600293	+	1.84751i
$290$		0			0
$291$	−11.9095	−	8.65273i	−0.698145	−	0.507232i
$292$		0			0
$293$	−26.0730	−	8.47164i	−1.52320	−	0.494919i	−0.576519	−	0.817083i	$-0.695590\pi$
$293$	−26.0730	−	8.47164i	−1.52320	−	0.494919i	−0.946684	+	0.322165i	$0.895590\pi$
$294$		0			0
$295$	6.25137	−	4.54188i	0.363969	−	0.264439i
$296$		0			0
$297$	86.3124	−	62.7097i	5.00836	−	3.63878i
$298$		0			0
$299$	−0.313148	+	0.431011i	−0.0181098	+	0.0249260i
$300$		0			0
$301$			10.0411i			0.578759i
$302$		0			0
$303$	−9.48648	−	29.1964i	−0.544984	−	1.67729i
$304$		0			0
$305$	−0.864716	+	2.66132i	−0.0495135	+	0.152387i
$306$		0			0
$307$	7.37797	+	22.7071i	0.421083	+	1.29596i	0.906695	+	0.421786i	$0.138597\pi$
$307$	7.37797	+	22.7071i	0.421083	+	1.29596i	−0.485612	+	0.874174i	$0.661403\pi$
$308$		0			0
$309$	12.2811	−	3.99037i	0.698647	−	0.227004i
$310$		0			0
$311$	−4.27612	−	5.88558i	−0.242477	−	0.333740i	0.670382	−	0.742016i	$-0.266130\pi$
$311$	−4.27612	−	5.88558i	−0.242477	−	0.333740i	−0.912859	+	0.408276i	$0.866130\pi$
$312$		0			0
$313$	−5.70377	+	7.85057i	−0.322396	+	0.443740i	−0.939197	−	0.343379i	$-0.888428\pi$
$313$	−5.70377	+	7.85057i	−0.322396	+	0.443740i	0.616801	+	0.787119i	$0.288428\pi$
$314$		0			0
$315$	−29.0523	−	9.43966i	−1.63691	−	0.531865i
$316$		0			0
$317$	20.0449	+	27.5894i	1.12583	+	1.54958i	0.795749	+	0.605627i	$0.207077\pi$
$317$	20.0449	+	27.5894i	1.12583	+	1.54958i	0.330085	+	0.943951i	$0.392923\pi$
$318$		0			0
$319$	20.3160			1.13748
$320$		0			0
$321$	−48.2106	+	15.6646i	−2.69085	+	0.874312i
$322$		0			0
$323$	−26.1954	−	19.0321i	−1.45755	−	1.05897i
$324$		0			0
$325$			0.269733i			0.0149621i
$326$		0			0
$327$	−44.7501			−2.47469
$328$		0			0
$329$	38.0923			2.10009
$330$		0			0
$331$			8.03934i			0.441882i	0.975287	+	0.220941i	$0.0709128\pi$
$331$			8.03934i			0.441882i	−0.975287	+	0.220941i	$0.929087\pi$
$332$		0			0
$333$	0.310249	+	0.225409i	0.0170015	+	0.0123523i
$334$		0			0
$335$	8.04322	−	2.61340i	0.439448	−	0.142785i
$336$		0			0
$337$	−1.30553			−0.0711166			−0.0355583	−	0.999368i	$-0.511321\pi$
$337$	−1.30553			−0.0711166			−0.0355583	+	0.999368i	$0.511321\pi$
$338$		0			0
$339$	−26.6176	−	36.6360i	−1.44567	−	1.98979i
$340$		0			0
$341$	−46.4360	−	15.0880i	−2.51465	−	0.817060i
$342$		0			0
$343$	3.90340	−	5.37257i	0.210764	−	0.290092i
$344$		0			0
$345$	3.98553	+	5.48562i	0.214574	+	0.295336i
$346$		0			0
$347$	−1.34198	+	0.436037i	−0.0720415	+	0.0234077i	−0.344816	−	0.938670i	$-0.612059\pi$
$347$	−1.34198	+	0.436037i	−0.0720415	+	0.0234077i	0.272775	+	0.962078i	$0.412059\pi$
$348$		0			0
$349$	1.27229	+	3.91571i	0.0681042	+	0.209603i	0.979317	−	0.202334i	$-0.0648525\pi$
$349$	1.27229	+	3.91571i	0.0681042	+	0.209603i	−0.911213	+	0.411937i	$0.864853\pi$
$350$		0			0
$351$	1.65545	−	5.09496i	0.0883616	−	0.271949i
$352$		0			0
$353$	−2.92220	−	8.99359i	−0.155533	−	0.478681i	0.842682	−	0.538412i	$-0.180976\pi$
$353$	−2.92220	−	8.99359i	−0.155533	−	0.478681i	−0.998214	+	0.0597313i	$0.980976\pi$
$354$		0			0
$355$			0.813825i			0.0431933i
$356$		0			0
$357$	−49.6243	+	68.3020i	−2.62640	+	3.61492i
$358$		0			0
$359$	−15.9754	+	11.6068i	−0.843150	+	0.612585i	−0.923249	−	0.384202i	$-0.874476\pi$
$359$	−15.9754	+	11.6068i	−0.843150	+	0.612585i	0.0800986	+	0.996787i	$0.474476\pi$
$360$		0			0
$361$	1.58429	−	1.15105i	0.0833836	−	0.0605817i
$362$		0			0
$363$	−58.2978	−	18.9421i	−3.05984	−	0.994203i
$364$		0			0
$365$	6.59786	+	4.79363i	0.345348	+	0.250910i
$366$		0			0
$367$	4.26213	−	13.1175i	0.222481	−	0.684727i	−0.776056	−	0.630664i	$-0.782783\pi$
$367$	4.26213	−	13.1175i	0.222481	−	0.684727i	0.998538	−	0.0540632i	$-0.0172172\pi$
$368$		0			0
$369$	−54.0154	−	15.7104i	−2.81193	−	0.817848i
$370$		0			0
$371$	5.09887	−	15.6927i	0.264720	−	0.814726i
$372$		0			0
$373$	0.938099	+	0.681569i	0.0485729	+	0.0352903i	0.611807	−	0.791007i	$-0.290443\pi$
$373$	0.938099	+	0.681569i	0.0485729	+	0.0352903i	−0.563234	+	0.826298i	$0.690443\pi$
$374$		0			0
$375$	3.26496	+	1.06085i	0.168602	+	0.0547820i
$376$		0			0
$377$	0.825306	−	0.599620i	0.0425054	−	0.0308820i
$378$		0			0
$379$	5.43231	−	3.94680i	0.279039	−	0.202734i	−0.439459	−	0.898263i	$-0.644830\pi$
$379$	5.43231	−	3.94680i	0.279039	−	0.202734i	0.718498	+	0.695529i	$0.244830\pi$
$380$		0			0
$381$	22.5897	−	31.0921i	1.15731	−	1.59290i
$382$		0			0
$383$			32.1532i			1.64295i	0.570243	+	0.821476i	$0.306849\pi$
$383$			32.1532i			1.64295i	−0.570243	+	0.821476i	$0.693151\pi$
$384$		0			0
$385$	5.77182	+	17.7638i	0.294159	+	0.905328i
$386$		0			0
$387$	−7.83984	+	24.1285i	−0.398521	+	1.22652i
$388$		0			0
$389$	−5.48000	−	16.8657i	−0.277847	−	0.855125i	−0.988452	−	0.151534i	$-0.951579\pi$
$389$	−5.48000	−	16.8657i	−0.277847	−	0.855125i	0.710605	−	0.703591i	$-0.248421\pi$
$390$		0			0
$391$	13.2859	−	4.31686i	0.671899	−	0.218313i
$392$		0			0
$393$	10.2524	+	14.1112i	0.517165	+	0.711817i
$394$		0			0
$395$	−5.41298	+	7.45033i	−0.272357	+	0.374867i
$396$		0			0
$397$	1.78328	+	0.579424i	0.0895004	+	0.0290805i	0.353425	−	0.935463i	$-0.385017\pi$
$397$	1.78328	+	0.579424i	0.0895004	+	0.0290805i	−0.263924	+	0.964543i	$0.585017\pi$
$398$		0			0
$399$	−32.1205	−	44.2101i	−1.60804	−	2.21327i
$400$		0			0
$401$	3.34927			0.167254			0.0836272	−	0.996497i	$-0.473350\pi$
$401$	3.34927			0.167254			0.0836272	+	0.996497i	$0.473350\pi$
$402$		0			0
$403$	−2.33171	+	0.757618i	−0.116151	+	0.0377396i
$404$		0			0
$405$	−33.8382	−	24.5849i	−1.68143	−	1.22163i
$406$		0			0
$407$		−	0.234481i		−	0.0116228i
$408$		0			0
$409$	20.7198			1.02453			0.512264	−	0.858828i	$-0.328807\pi$
$409$	20.7198			1.02453			0.512264	+	0.858828i	$0.328807\pi$
$410$		0			0
$411$	−10.9961			−0.542397
$412$		0			0
$413$		−	26.8678i		−	1.32208i
$414$		0			0
$415$	−3.36883	−	2.44760i	−0.165369	−	0.120148i
$416$		0			0
$417$	−24.8698	+	8.08069i	−1.21788	+	0.395713i
$418$		0			0
$419$	22.3937			1.09400			0.547001	−	0.837132i	$-0.315769\pi$
$419$	22.3937			1.09400			0.547001	+	0.837132i	$0.315769\pi$
$420$		0			0
$421$	−15.0638	−	20.7336i	−0.734166	−	1.01049i	−0.998933	−	0.0461800i	$-0.985295\pi$
$421$	−15.0638	−	20.7336i	−0.734166	−	1.01049i	0.264768	−	0.964312i	$-0.414705\pi$
$422$		0			0
$423$	91.5350	+	29.7415i	4.45058	+	1.44608i
$424$		0			0
$425$	4.15727	−	5.72199i	0.201657	−	0.277557i
$426$		0			0
$427$	5.71906	+	7.87162i	0.276765	+	0.380934i
$428$		0			0
$429$	−4.73072	+	1.53710i	−0.228401	+	0.0742120i
$430$		0			0
$431$	−3.88103	−	11.9446i	−0.186943	−	0.575351i	0.813034	−	0.582217i	$-0.197815\pi$
$431$	−3.88103	−	11.9446i	−0.186943	−	0.575351i	−0.999976	+	0.00686584i	$0.997815\pi$
$432$		0			0
$433$	7.14245	−	21.9822i	0.343244	−	1.05640i	−0.619273	−	0.785176i	$-0.712572\pi$
$433$	7.14245	−	21.9822i	0.343244	−	1.05640i	0.962517	−	0.271221i	$-0.0874276\pi$
$434$		0			0
$435$	−4.01215	−	12.3481i	−0.192368	−	0.592047i
$436$		0			0
$437$			9.04221i			0.432548i
$438$		0			0
$439$	23.4426	−	32.2659i	1.11885	−	1.53997i	0.311166	−	0.950356i	$-0.399280\pi$
$439$	23.4426	−	32.2659i	1.11885	−	1.53997i	0.807686	−	0.589612i	$-0.200720\pi$
$440$		0			0
$441$	−36.1779	+	26.2848i	−1.72276	+	1.25166i
$442$		0			0
$443$	6.63156	−	4.81811i	0.315075	−	0.228915i	−0.418996	−	0.907988i	$-0.637618\pi$
$443$	6.63156	−	4.81811i	0.315075	−	0.228915i	0.734071	+	0.679073i	$0.237618\pi$
$444$		0			0
$445$	−1.91886	−	0.623477i	−0.0909629	−	0.0295556i
$446$		0			0
$447$	−7.43738	−	5.40357i	−0.351776	−	0.255580i
$448$		0			0
$449$	3.03025	−	9.32614i	0.143006	−	0.440128i	−0.853743	−	0.520695i	$-0.825673\pi$
$449$	3.03025	−	9.32614i	0.143006	−	0.440128i	0.996749	+	0.0805668i	$0.0256730\pi$
$450$		0			0
$451$	11.6416	+	32.3659i	0.548180	+	1.52405i
$452$		0			0
$453$	10.9918	−	33.8292i	0.516439	−	1.58944i
$454$		0			0
$455$	0.758764	+	0.551275i	0.0355714	+	0.0258441i
$456$		0			0
$457$	−32.4871	−	10.5557i	−1.51968	−	0.493774i	−0.573995	−	0.818859i	$-0.694607\pi$
$457$	−32.4871	−	10.5557i	−1.51968	−	0.493774i	−0.945685	+	0.325084i	$0.894607\pi$
$458$		0			0
$459$	−113.644	+	82.5674i	−5.30446	+	3.85392i
$460$		0			0
$461$	−22.8921	+	16.6321i	−1.06619	+	0.774632i	−0.975224	−	0.221222i	$-0.928996\pi$
$461$	−22.8921	+	16.6321i	−1.06619	+	0.774632i	−0.0909663	+	0.995854i	$0.528996\pi$
$462$		0			0
$463$	−13.4318	+	18.4873i	−0.624231	+	0.859180i	−0.997652	−	0.0684820i	$-0.978184\pi$
$463$	−13.4318	+	18.4873i	−0.624231	+	0.859180i	0.373422	+	0.927662i	$0.378184\pi$
$464$		0			0
$465$			31.2036i			1.44703i
$466$		0			0
$467$	11.2362	+	34.5816i	0.519951	+	1.60025i	0.774089	+	0.633077i	$0.218208\pi$
$467$	11.2362	+	34.5816i	0.519951	+	1.60025i	−0.254137	+	0.967168i	$0.581792\pi$
$468$		0			0
$469$	9.08701	−	27.9669i	0.419599	−	1.29139i
$470$		0			0
$471$	6.93081	+	21.3309i	0.319355	+	0.982874i
$472$		0			0
$473$	14.7532	−	4.79362i	0.678354	−	0.220411i
$474$		0			0
$475$	2.69089	+	3.70370i	0.123467	+	0.169937i
$476$		0			0
$477$	24.5050	−	33.7282i	1.12201	−	1.54431i
$478$		0			0
$479$	19.0315	+	6.18370i	0.869570	+	0.282541i	0.709620	−	0.704585i	$-0.248867\pi$
$479$	19.0315	+	6.18370i	0.869570	+	0.282541i	0.159950	+	0.987125i	$0.448867\pi$
$480$		0			0
$481$	−0.00692064	−	0.00952545i	−0.000315554	−	0.000434323i
$482$		0			0
$483$	23.5767			1.07278
$484$		0			0
$485$	4.07821	−	1.32509i	0.185182	−	0.0601693i
$486$		0			0
$487$	23.0286	+	16.7313i	1.04353	+	0.758166i	0.970971	−	0.239198i	$-0.0768845\pi$
$487$	23.0286	+	16.7313i	1.04353	+	0.758166i	0.0725558	+	0.997364i	$0.476884\pi$
$488$		0			0
$489$		−	23.3758i		−	1.05709i
$490$		0			0
$491$	−7.23252			−0.326399			−0.163200	−	0.986593i	$-0.552181\pi$
$491$	−7.23252			−0.326399			−0.163200	+	0.986593i	$0.552181\pi$
$492$		0			0
$493$	−26.7493			−1.20473
$494$		0			0
$495$			47.1926i			2.12115i
$496$		0			0
$497$	2.28930	+	1.66328i	0.102689	+	0.0746082i
$498$		0			0
$499$	19.1472	−	6.22129i	0.857145	−	0.278503i	0.152709	−	0.988271i	$-0.451200\pi$
$499$	19.1472	−	6.22129i	0.857145	−	0.278503i	0.704436	+	0.709768i	$0.251200\pi$
$500$		0			0
$501$	−41.3255			−1.84629
$502$		0			0
$503$	1.14294	+	1.57312i	0.0509611	+	0.0701419i	0.833737	−	0.552162i	$-0.186197\pi$
$503$	1.14294	+	1.57312i	0.0509611	+	0.0701419i	−0.782776	+	0.622304i	$0.786197\pi$
$504$		0			0
$505$	8.50468	+	2.76334i	0.378453	+	0.122967i
$506$		0			0
$507$	26.0853	−	35.9033i	1.15849	−	1.59452i
$508$		0			0
$509$	−17.4481	−	24.0153i	−0.773374	−	1.06446i	−0.995982	−	0.0895500i	$-0.971457\pi$
$509$	−17.4481	−	24.0153i	−0.773374	−	1.06446i	0.222608	−	0.974908i	$-0.428543\pi$
$510$		0			0
$511$	26.9691	−	8.76280i	1.19304	−	0.387643i
$512$		0			0
$513$	−28.0971	−	86.4739i	−1.24052	−	3.81791i
$514$		0			0
$515$	−1.16236	+	3.57739i	−0.0512198	+	0.157638i
$516$		0			0
$517$	−18.1852	−	55.9684i	−0.799786	−	2.46149i
$518$		0			0
$519$			44.5811i			1.95690i
$520$		0			0
$521$	10.4626	−	14.4006i	0.458377	−	0.630901i	−0.515795	−	0.856712i	$-0.672503\pi$
$521$	10.4626	−	14.4006i	0.458377	−	0.630901i	0.974171	+	0.225811i	$0.0725032\pi$
$522$		0			0
$523$	−9.20784	+	6.68989i	−0.402631	+	0.292528i	−0.770612	−	0.637305i	$-0.780049\pi$
$523$	−9.20784	+	6.68989i	−0.402631	+	0.292528i	0.367981	+	0.929833i	$0.380049\pi$
$524$		0			0
$525$	9.65704	−	7.01625i	0.421468	−	0.306214i
$526$		0			0
$527$	61.1405	+	19.8658i	2.66332	+	0.865366i
$528$		0			0
$529$	15.4513	+	11.2260i	0.671795	+	0.488088i
$530$		0			0
$531$	20.9777	−	64.5628i	0.910356	−	2.80179i
$532$		0			0
$533$	1.42819	+	0.971219i	0.0618618	+	0.0420682i
$534$		0			0
$535$	4.56297	−	14.0434i	0.197274	−	0.607148i
$536$		0			0
$537$	−38.2785	−	27.8110i	−1.65184	−	1.20013i
$538$		0			0
$539$	26.0045	+	8.44937i	1.12009	+	0.363940i
$540$		0			0
$541$	2.09947	−	1.52535i	0.0902632	−	0.0655801i	−0.541738	−	0.840547i	$-0.682234\pi$
$541$	2.09947	−	1.52535i	0.0902632	−	0.0655801i	0.632002	+	0.774967i	$0.282234\pi$
$542$		0			0
$543$	3.34799	−	2.43246i	0.143676	−	0.104387i
$544$		0			0
$545$	7.66199	−	10.5458i	0.328204	−	0.451734i
$546$		0			0
$547$		−	16.6721i		−	0.712848i	−0.934324	−	0.356424i	$-0.883996\pi$
$547$		−	16.6721i		−	0.712848i	0.934324	−	0.356424i	$-0.116004\pi$
$548$		0			0
$549$	7.59683	+	23.3806i	0.324225	+	0.997862i
$550$		0			0
$551$	5.35036	−	16.4667i	0.227933	−	0.701506i
$552$		0			0
$553$	9.89499	+	30.4536i	0.420778	+	1.29502i
$554$		0			0
$555$	−0.142518	+	0.0463070i	−0.00604957	+	0.00196562i
$556$		0			0
$557$	5.14459	+	7.08092i	0.217983	+	0.300028i	0.903979	−	0.427578i	$-0.140633\pi$
$557$	5.14459	+	7.08092i	0.217983	+	0.300028i	−0.685995	+	0.727606i	$0.740633\pi$
$558$		0			0
$559$	0.457845	−	0.630170i	0.0193648	−	0.0266533i
$560$		0			0
$561$	124.046	+	40.3049i	5.23722	+	1.70167i
$562$		0			0
$563$	−14.1083	−	19.4183i	−0.594592	−	0.818386i	0.400608	−	0.916250i	$-0.368799\pi$
$563$	−14.1083	−	19.4183i	−0.594592	−	0.818386i	−0.995200	+	0.0978641i	$0.968799\pi$
$564$		0			0
$565$	13.1910			0.554952
$566$		0			0
$567$	−138.315	+	44.9414i	−5.80870	+	1.88736i
$568$		0			0
$569$	14.5857	+	10.5971i	0.611465	+	0.444256i	0.849930	−	0.526896i	$-0.176644\pi$
$569$	14.5857	+	10.5971i	0.611465	+	0.444256i	−0.238465	+	0.971151i	$0.576644\pi$
$570$		0			0
$571$		−	21.4414i		−	0.897294i	−0.893709	−	0.448647i	$-0.851906\pi$
$571$		−	21.4414i		−	0.897294i	0.893709	−	0.448647i	$-0.148094\pi$
$572$		0			0
$573$	−53.2132			−2.22302
$574$		0			0
$575$	−1.97513			−0.0823688
$576$		0			0
$577$		−	2.68089i		−	0.111607i	−0.998442	−	0.0558035i	$-0.982228\pi$
$577$		−	2.68089i		−	0.111607i	0.998442	−	0.0558035i	$-0.0177720\pi$
$578$		0			0
$579$	12.7690	+	9.27719i	0.530660	+	0.385547i
$580$		0			0
$581$	−13.7703	+	4.47423i	−0.571287	+	0.185622i
$582$		0			0
$583$	−25.4913			−1.05574
$584$		0			0
$585$	1.39287	+	1.91713i	0.0575883	+	0.0792634i
$586$		0			0
$587$	13.9708	+	4.53940i	0.576638	+	0.187361i	0.582794	−	0.812620i	$-0.301960\pi$
$587$	13.9708	+	4.53940i	0.576638	+	0.187361i	−0.00615591	+	0.999981i	$0.501960\pi$
$588$		0			0
$589$	−24.4585	+	33.6643i	−1.00780	+	1.38711i
$590$		0			0
$591$	−16.7505	−	23.0551i	−0.689023	−	0.948359i
$592$		0			0
$593$	6.71884	−	2.18308i	0.275910	−	0.0896485i	−0.167794	−	0.985822i	$-0.553664\pi$
$593$	6.71884	−	2.18308i	0.275910	−	0.0896485i	0.443704	+	0.896174i	$0.353664\pi$
$594$		0			0
$595$	−7.59953	−	23.3889i	−0.311550	−	0.958853i
$596$		0			0
$597$	9.91554	−	30.5169i	0.405816	−	1.24897i
$598$		0			0
$599$	−2.71734	−	8.36310i	−0.111027	−	0.341707i	0.880070	−	0.474843i	$-0.157495\pi$
$599$	−2.71734	−	8.36310i	−0.111027	−	0.341707i	−0.991098	+	0.133136i	$0.957495\pi$
$600$		0			0
$601$		−	18.1276i		−	0.739439i	−0.929143	−	0.369720i	$-0.879454\pi$
$601$		−	18.1276i		−	0.739439i	0.929143	−	0.369720i	$-0.120546\pi$
$602$		0			0
$603$	43.6718	−	60.1091i	1.77845	−	2.44783i
$604$		0			0
$605$	14.4455	−	10.4953i	0.587293	−	0.426693i
$606$		0			0
$607$	−2.62544	+	1.90749i	−0.106563	+	0.0774228i	−0.639791	−	0.768549i	$-0.720979\pi$
$607$	−2.62544	+	1.90749i	−0.106563	+	0.0774228i	0.533227	+	0.845972i	$0.320979\pi$
$608$		0			0
$609$	−42.9354	−	13.9506i	−1.73983	−	0.565305i
$610$		0			0
$611$	−2.39064	−	1.73690i	−0.0967148	−	0.0702674i
$612$		0			0
$613$	−8.31691	+	25.5968i	−0.335917	+	1.03385i	0.630352	+	0.776309i	$0.282911\pi$
$613$	−8.31691	+	25.5968i	−0.335917	+	1.03385i	−0.966269	+	0.257536i	$0.917089\pi$
$614$		0			0
$615$	17.3730	−	13.4676i	0.700548	−	0.543067i
$616$		0			0
$617$	7.01072	−	21.5768i	0.282241	−	0.868649i	−0.704971	−	0.709236i	$-0.749040\pi$
$617$	7.01072	−	21.5768i	0.282241	−	0.868649i	0.987212	−	0.159412i	$-0.0509600\pi$
$618$		0			0
$619$	32.5655	+	23.6602i	1.30892	+	0.950984i	1.00000		0.000104725i	$-3.33350e-5\pi$
$619$	32.5655	+	23.6602i	1.30892	+	0.950984i	0.308917	+	0.951089i	$0.400033\pi$
$620$		0			0
$621$	37.3081	+	12.1222i	1.49712	+	0.486445i
$622$		0			0
$623$	−5.67559	+	4.12355i	−0.227388	+	0.165207i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−49.6230	+	68.3002i	−1.98175	+	2.72765i
$628$		0			0
$629$			0.308733i			0.0123100i
$630$		0			0
$631$	11.1467	+	34.3060i	0.443743	+	1.36570i	0.883857	+	0.467758i	$0.154938\pi$
$631$	11.1467	+	34.3060i	0.443743	+	1.36570i	−0.440114	+	0.897942i	$0.645062\pi$
$632$		0			0
$633$	13.7168	−	42.2160i	0.545195	−	1.67794i
$634$		0			0
$635$	3.45942	+	10.6470i	0.137283	+	0.422514i
$636$		0			0
$637$	1.30577	−	0.424271i	0.0517366	−	0.0168102i
$638$		0			0
$639$	4.20251	+	5.78426i	0.166249	+	0.228822i
$640$		0			0
$641$	−20.1874	+	27.7856i	−0.797355	+	1.09747i	0.195798	+	0.980644i	$0.437270\pi$
$641$	−20.1874	+	27.7856i	−0.797355	+	1.09747i	−0.993153	+	0.116821i	$0.962730\pi$
$642$		0			0
$643$	9.76313	+	3.17223i	0.385020	+	0.125101i	0.495130	−	0.868819i	$-0.335120\pi$
$643$	9.76313	+	3.17223i	0.385020	+	0.125101i	−0.110110	+	0.993919i	$0.535120\pi$
$644$		0			0
$645$	−5.82714	−	8.02037i	−0.229443	−	0.315802i
$646$		0			0
$647$	−8.16437			−0.320975			−0.160487	−	0.987038i	$-0.551307\pi$
$647$	−8.16437			−0.320975			−0.160487	+	0.987038i	$0.551307\pi$
$648$		0			0
$649$	−39.4765	+	12.8267i	−1.54959	+	0.503492i
$650$		0			0
$651$	87.7763	+	63.7733i	3.44023	+	2.49947i
$652$		0			0
$653$			17.8885i			0.700030i	0.936744	+	0.350015i	$0.113824\pi$
$653$			17.8885i			0.700030i	−0.936744	+	0.350015i	$0.886176\pi$
$654$		0			0
$655$	−5.08084			−0.198525
$656$		0			0
$657$	71.6481			2.79526
$658$		0			0
$659$		−	19.7388i		−	0.768914i	−0.923143	−	0.384457i	$-0.874389\pi$
$659$		−	19.7388i		−	0.768914i	0.923143	−	0.384457i	$-0.125611\pi$
$660$		0			0
$661$	−4.74924	−	3.45052i	−0.184724	−	0.134210i	0.491580	−	0.870832i	$-0.336419\pi$
$661$	−4.74924	−	3.45052i	−0.184724	−	0.134210i	−0.676304	+	0.736623i	$0.736419\pi$
$662$		0			0
$663$	6.22875	−	2.02384i	0.241905	−	0.0785996i
$664$		0			0
$665$	15.9182			0.617280
$666$		0			0
$667$	4.39075	+	6.04335i	0.170010	+	0.233999i
$668$		0			0
$669$	78.8778	+	25.6290i	3.04959	+	0.990873i
$670$		0			0
$671$	8.83538	−	12.1609i	0.341086	−	0.469464i
$672$		0			0
$673$	−23.4764	−	32.3125i	−0.904949	−	1.24555i	−0.968862	−	0.247599i	$-0.920358\pi$
$673$	−23.4764	−	32.3125i	−0.904949	−	1.24555i	0.0639139	−	0.997955i	$-0.479642\pi$
$674$		0			0
$675$	18.8889	−	6.13738i	0.727035	−	0.236228i
$676$		0			0
$677$	−1.55145	−	4.77486i	−0.0596269	−	0.183513i	0.916806	−	0.399332i	$-0.130758\pi$
$677$	−1.55145	−	4.77486i	−0.0596269	−	0.183513i	−0.976433	+	0.215819i	$0.930758\pi$
$678$		0			0
$679$	4.60745	−	14.1803i	0.176818	−	0.544189i
$680$		0			0
$681$	14.0102	+	43.1189i	0.536872	+	1.65232i
$682$		0			0
$683$			30.2311i			1.15676i	0.815767	+	0.578381i	$0.196315\pi$
$683$			30.2311i			1.15676i	−0.815767	+	0.578381i	$0.803685\pi$
$684$		0			0
$685$	1.88272	−	2.59134i	0.0719350	−	0.0990101i
$686$		0			0
$687$	9.97085	−	7.24425i	0.380412	−	0.276385i
$688$		0			0
$689$	−1.03554	+	0.752367i	−0.0394511	+	0.0286629i
$690$		0			0
$691$	−45.3081	−	14.7215i	−1.72360	−	0.560032i	−0.731101	−	0.682269i	$-0.760993\pi$
$691$	−45.3081	−	14.7215i	−1.72360	−	0.560032i	−0.992501	+	0.122237i	$0.960993\pi$
$692$		0			0
$693$	132.754	+	96.4512i	5.04290	+	3.66388i
$694$		0			0
$695$	2.35384	−	7.24438i	0.0892863	−	0.274795i
$696$		0			0
$697$	−15.3280	−	42.6150i	−0.580590	−	1.61416i
$698$		0			0
$699$	−10.8232	+	33.3105i	−0.409373	+	1.25992i
$700$		0			0
$701$	32.4087	+	23.5463i	1.22406	+	0.889331i	0.996431	−	0.0844166i	$-0.0269027\pi$
$701$	32.4087	+	23.5463i	1.22406	+	0.889331i	0.227629	+	0.973748i	$0.426903\pi$
$702$		0			0
$703$	−0.190054	−	0.0617524i	−0.00716803	−	0.00232904i
$704$		0			0
$705$	−30.4264	+	22.1061i	−1.14592	+	0.832563i
$706$		0			0
$707$	25.1550	−	18.2762i	0.946051	−	0.687346i
$708$		0			0
$709$	−13.1869	+	18.1502i	−0.495245	+	0.681646i	−0.981345	−	0.192257i	$-0.938419\pi$
$709$	−13.1869	+	18.1502i	−0.495245	+	0.681646i	0.486100	+	0.873903i	$0.338419\pi$
$710$		0			0
$711$			80.9053i			3.03419i
$712$		0			0
$713$	−5.54770	−	17.0741i	−0.207763	−	0.639428i
$714$		0			0
$715$	0.447746	−	1.37802i	0.0167448	−	0.0515350i
$716$		0			0
$717$	−4.25173	−	13.0855i	−0.158784	−	0.488686i
$718$		0			0
$719$	19.5530	−	6.35315i	0.729203	−	0.236932i	0.0791942	−	0.996859i	$-0.474765\pi$
$719$	19.5530	−	6.35315i	0.729203	−	0.236932i	0.650009	+	0.759927i	$0.274765\pi$
$720$		0			0
$721$	7.68764	+	10.5811i	0.286303	+	0.394062i
$722$		0			0
$723$	37.3994	−	51.4758i	1.39090	−	1.91441i
$724$		0			0
$725$	3.59691	+	1.16871i	0.133586	+	0.0434047i
$726$		0			0
$727$	−23.4523	−	32.2794i	−0.869799	−	1.19718i	−0.979143	−	0.203172i	$-0.934875\pi$
$727$	−23.4523	−	32.2794i	−0.869799	−	1.19718i	0.109344	−	0.994004i	$-0.465125\pi$
$728$		0			0
$729$	−162.911			−6.03376
$730$		0			0
$731$	−19.4250	+	6.31157i	−0.718460	+	0.233442i
$732$		0			0
$733$	19.4857	+	14.1572i	0.719720	+	0.522907i	0.886295	−	0.463122i	$-0.153271\pi$
$733$	19.4857	+	14.1572i	0.719720	+	0.522907i	−0.166575	+	0.986029i	$0.553271\pi$
$734$		0			0
$735$		−	17.4742i		−	0.644546i
$736$		0			0
$737$	−45.4296			−1.67342
$738$		0			0
$739$	3.57909			0.131659			0.0658294	−	0.997831i	$-0.479031\pi$
$739$	3.57909			0.131659			0.0658294	+	0.997831i	$0.479031\pi$
$740$		0			0
$741$			4.23919i			0.155731i
$742$		0			0
$743$	31.0620	+	22.5679i	1.13956	+	0.827935i	0.987057	−	0.160368i	$-0.0512682\pi$
$743$	31.0620	+	22.5679i	1.13956	+	0.827935i	0.152498	+	0.988304i	$0.451268\pi$
$744$		0			0
$745$	2.54681	−	0.827510i	0.0933081	−	0.0303176i
$746$		0			0
$747$	−36.5831			−1.33850
$748$		0			0
$749$	−30.1786	−	41.5373i	−1.10270	−	1.51774i
$750$		0			0
$751$	−14.4303	−	4.68869i	−0.526569	−	0.171093i	0.0336553	−	0.999433i	$-0.489285\pi$
$751$	−14.4303	−	4.68869i	−0.526569	−	0.171093i	−0.560225	+	0.828341i	$0.689285\pi$
$752$		0			0
$753$	−37.8996	+	52.1643i	−1.38114	+	1.90097i
$754$		0			0
$755$	6.09023	+	8.38248i	0.221646	+	0.305070i
$756$		0			0
$757$	−24.6194	+	7.99934i	−0.894809	+	0.290741i	−0.720093	−	0.693878i	$-0.755901\pi$
$757$	−24.6194	+	7.99934i	−0.894809	+	0.290741i	−0.174716	+	0.984619i	$0.555901\pi$
$758$		0			0
$759$	−11.2555	−	34.6409i	−0.408549	−	1.25739i
$760$		0			0
$761$	0.438199	−	1.34864i	0.0158847	−	0.0488881i	−0.942800	−	0.333359i	$-0.891818\pi$
$761$	0.438199	−	1.34864i	0.0158847	−	0.0488881i	0.958685	+	0.284471i	$0.0918179\pi$
$762$		0			0
$763$	−14.0062	−	43.1067i	−0.507059	−	1.56057i
$764$		0			0
$765$		−	62.1367i		−	2.24656i
$766$		0			0
$767$	−1.22510	+	1.68620i	−0.0442357	+	0.0608852i
$768$		0			0
$769$	−2.57470	+	1.87063i	−0.0928460	+	0.0674566i	−0.633240	−	0.773956i	$-0.718275\pi$
$769$	−2.57470	+	1.87063i	−0.0928460	+	0.0674566i	0.540394	+	0.841412i	$0.318275\pi$
$770$		0			0
$771$	−28.3348	+	20.5864i	−1.02045	+	0.741401i
$772$		0			0
$773$	−10.9393	−	3.55440i	−0.393459	−	0.127843i	0.105604	−	0.994408i	$-0.466322\pi$
$773$	−10.9393	−	3.55440i	−0.393459	−	0.127843i	−0.499063	+	0.866566i	$0.666322\pi$
$774$		0			0
$775$	−7.35345	−	5.34260i	−0.264144	−	0.191912i
$776$		0			0
$777$	−0.161013	+	0.495548i	−0.00577632	+	0.0177777i
$778$		0			0
$779$	29.2995	−	0.912044i	1.04976	−	0.0326774i
$780$		0			0
$781$	1.35092	−	4.15769i	0.0483396	−	0.148774i
$782$		0			0
$783$	−60.7689	−	44.1512i	−2.17170	−	1.57783i
$784$		0			0
$785$	−6.21351	−	2.01889i	−0.221770	−	0.0720573i
$786$		0			0
$787$	−27.3143	+	19.8450i	−0.973650	+	0.707398i	−0.956281	−	0.292451i	$-0.905529\pi$
$787$	−27.3143	+	19.8450i	−0.973650	+	0.707398i	−0.0173698	+	0.999849i	$0.505529\pi$
$788$		0			0
$789$	−38.1656	+	27.7289i	−1.35873	+	0.987175i
$790$		0			0
$791$	26.9596	−	37.1067i	0.958572	−	1.31936i
$792$		0			0
$793$		−	0.754789i		−	0.0268033i
$794$		0			0
$795$	5.03420	+	15.4937i	0.178545	+	0.549504i
$796$		0			0
$797$	−9.86373	+	30.3575i	−0.349391	+	1.07532i	0.609799	+	0.792556i	$0.291250\pi$
$797$	−9.86373	+	30.3575i	−0.349391	+	1.07532i	−0.959191	+	0.282760i	$0.908750\pi$
$798$		0			0
$799$	23.9438	+	73.6915i	0.847071	+	2.60702i
$800$		0			0
$801$	−16.8579	+	5.47746i	−0.595644	+	0.193537i
$802$		0			0
$803$	−25.7501	−	35.4420i	−0.908702	−	1.25072i
$804$		0			0
$805$	−4.03674	+	5.55609i	−0.142276	+	0.195826i
$806$		0			0
$807$	24.6577	+	8.01178i	0.867993	+	0.282028i
$808$		0			0
$809$	−3.95238	−	5.43998i	−0.138958	−	0.191260i	0.733866	−	0.679294i	$-0.237714\pi$
$809$	−3.95238	−	5.43998i	−0.138958	−	0.191260i	−0.872824	+	0.488035i	$0.837714\pi$
$810$		0			0
$811$	−2.59100			−0.0909822			−0.0454911	−	0.998965i	$-0.514485\pi$
$811$	−2.59100			−0.0909822			−0.0454911	+	0.998965i	$0.514485\pi$
$812$		0			0
$813$	−21.8310	+	7.09334i	−0.765648	+	0.248774i
$814$		0			0
$815$	5.50875	+	4.00234i	0.192963	+	0.140196i
$816$		0			0
$817$		−	13.2204i		−	0.462522i
$818$		0			0
$819$	8.23964			0.287916
$820$		0			0
$821$	22.2207			0.775508			0.387754	−	0.921763i	$-0.373251\pi$
$821$	22.2207			0.775508			0.387754	+	0.921763i	$0.373251\pi$
$822$		0			0
$823$			44.9090i			1.56543i	0.622381	+	0.782714i	$0.286165\pi$
$823$			44.9090i			1.56543i	−0.622381	+	0.782714i	$0.713835\pi$
$824$		0			0
$825$	−14.9191	−	10.8394i	−0.519418	−	0.377379i
$826$		0			0
$827$	19.5226	−	6.34329i	0.678869	−	0.220578i	0.0507686	−	0.998710i	$-0.483833\pi$
$827$	19.5226	−	6.34329i	0.678869	−	0.220578i	0.628100	+	0.778133i	$0.283833\pi$
$828$		0			0
$829$	4.20342			0.145991			0.0729955	−	0.997332i	$-0.476744\pi$
$829$	4.20342			0.145991			0.0729955	+	0.997332i	$0.476744\pi$
$830$		0			0
$831$	39.6891	+	54.6273i	1.37680	+	1.89500i
$832$		0			0
$833$	−34.2391	−	11.1250i	−1.18631	−	0.385457i
$834$		0			0
$835$	7.07563	−	9.73877i	0.244862	−	0.337024i
$836$		0			0
$837$	106.109	+	146.047i	3.66767	+	5.04811i
$838$		0			0
$839$	−41.5876	+	13.5126i	−1.43576	+	0.466508i	−0.920574	−	0.390568i	$-0.872279\pi$
$839$	−41.5876	+	13.5126i	−1.43576	+	0.466508i	−0.515190	+	0.857076i	$0.672279\pi$
$840$		0			0
$841$	4.54143	+	13.9771i	0.156601	+	0.481968i
$842$		0			0
$843$	−28.0959	+	86.4703i	−0.967674	+	2.97819i
$844$		0			0
$845$	3.99474	+	12.2945i	0.137423	+	0.422945i
$846$		0			0
$847$		−	62.0854i		−	2.13328i
$848$		0			0
$849$	−9.15571	+	12.6018i	−0.314223	+	0.432491i
$850$		0			0
$851$	0.0697506	−	0.0506768i	0.00239102	−	0.00173718i
$852$		0			0
$853$	31.7524	−	23.0694i	1.08718	−	0.789883i	0.108259	−	0.994123i	$-0.465472\pi$
$853$	31.7524	−	23.0694i	1.08718	−	0.789883i	0.978921	+	0.204240i	$0.0654723\pi$
$854$		0			0
$855$	38.2510	+	12.4285i	1.30816	+	0.425046i
$856$		0			0
$857$	−10.8884	−	7.91085i	−0.371939	−	0.270230i	0.386075	−	0.922467i	$-0.373830\pi$
$857$	−10.8884	−	7.91085i	−0.371939	−	0.270230i	−0.758015	+	0.652238i	$0.773830\pi$
$858$		0			0
$859$	4.47937	−	13.7861i	0.152834	−	0.470375i	−0.845101	−	0.534607i	$-0.820460\pi$
$859$	4.47937	−	13.7861i	0.152834	−	0.470375i	0.997935	+	0.0642317i	$0.0204597\pi$
$860$		0			0
$861$	−2.37807	−	76.3955i	−0.0810443	−	2.60355i
$862$		0			0
$863$	14.0546	−	43.2557i	0.478425	−	1.47244i	−0.362858	−	0.931844i	$-0.618199\pi$
$863$	14.0546	−	43.2557i	0.478425	−	1.47244i	0.841283	−	0.540595i	$-0.181801\pi$
$864$		0			0
$865$	−10.5060	−	7.63306i	−0.357215	−	0.259532i
$866$		0			0
$867$	−107.822	−	35.0335i	−3.66183	−	1.18980i
$868$		0			0
$869$	40.0213	−	29.0771i	1.35763	−	0.986375i
$870$		0			0
$871$	−1.84551	+	1.34084i	−0.0625326	+	0.0454326i
$872$		0			0
$873$	22.1432	−	30.4775i	0.749435	−	1.03151i
$874$		0			0
$875$			3.47708i			0.117547i
$876$		0			0
$877$	6.23618	+	19.1930i	0.210581	+	0.648101i	0.999438	+	0.0335246i	$0.0106732\pi$
$877$	6.23618	+	19.1930i	0.210581	+	0.648101i	−0.788857	+	0.614577i	$0.789327\pi$
$878$		0			0
$879$	29.0830	−	89.5082i	0.980944	−	3.01904i
$880$		0			0
$881$	15.7860	+	48.5842i	0.531843	+	1.63684i	0.750373	+	0.661014i	$0.229874\pi$
$881$	15.7860	+	48.5842i	0.531843	+	1.63684i	−0.218531	+	0.975830i	$0.570126\pi$
$882$		0			0
$883$	−28.1342	+	9.14135i	−0.946791	+	0.307631i	−0.741411	−	0.671051i	$-0.765843\pi$
$883$	−28.1342	+	9.14135i	−0.946791	+	0.307631i	−0.205380	+	0.978682i	$0.565843\pi$
$884$		0			0
$885$	15.5922	+	21.4608i	0.524126	+	0.721397i
$886$		0			0
$887$	−28.3643	+	39.0400i	−0.952378	+	1.31084i	−0.00191555	+	0.999998i	$0.500610\pi$
$887$	−28.3643	+	39.0400i	−0.952378	+	1.31084i	−0.950463	+	0.310838i	$0.899390\pi$
$888$		0			0
$889$	37.0205	+	12.0287i	1.24163	+	0.403430i
$890$		0			0
$891$	132.064	+	181.770i	4.42430	+	6.08952i
$892$		0			0
$893$	−50.1533			−1.67832
$894$		0			0
$895$	13.1079	−	4.25901i	0.438148	−	0.142363i
$896$		0			0
$897$	−1.47965	−	1.07503i	−0.0494042	−	0.0358942i
$898$		0			0
$899$			34.3761i			1.14651i
$900$		0			0
$901$	33.5634			1.11816
$902$		0			0
$903$	−34.4708			−1.14712
$904$		0			0
$905$			1.20547i			0.0400711i
$906$		0			0
$907$	−1.08309	−	0.786913i	−0.0359635	−	0.0261290i	0.569658	−	0.821882i	$-0.307076\pi$
$907$	−1.08309	−	0.786913i	−0.0359635	−	0.0261290i	−0.605622	+	0.795753i	$0.707076\pi$
$908$		0			0
$909$	74.7165	−	24.2769i	2.47819	−	0.805213i
$910$		0			0
$911$	−47.0315			−1.55822			−0.779112	−	0.626885i	$-0.784330\pi$
$911$	−47.0315			−1.55822			−0.779112	+	0.626885i	$0.784330\pi$
$912$		0			0
$913$	13.1479	+	18.0965i	0.435131	+	0.598906i
$914$		0			0
$915$	−9.13627	−	2.96855i	−0.302036	−	0.0981373i
$916$		0			0
$917$	−10.3841	+	14.2925i	−0.342914	+	0.471980i
$918$		0			0
$919$	27.3000	+	37.5752i	0.900543	+	1.23949i	0.970295	+	0.241927i	$0.0777793\pi$
$919$	27.3000	+	37.5752i	0.900543	+	1.23949i	−0.0697517	+	0.997564i	$0.522221\pi$
$920$		0			0
$921$	−77.9529	+	25.3284i	−2.56863	+	0.834600i
$922$		0			0
$923$	−0.0678340	−	0.208772i	−0.00223278	−	0.00687180i
$924$		0			0
$925$	0.0134889	−	0.0415145i	0.000443512	−	0.00136499i
$926$		0			0
$927$	10.2118	+	31.4286i	0.335398	+	1.03225i
$928$		0			0
$929$			45.1578i			1.48158i	0.671737	+	0.740790i	$0.265549\pi$
$929$			45.1578i			1.48158i	−0.671737	+	0.740790i	$0.734451\pi$
$930$		0			0
$931$	13.6969	−	18.8522i	0.448899	−	0.617856i
$932$		0			0
$933$	20.2051	−	14.6798i	0.661484	−	0.480596i
$934$		0			0
$935$	−30.7370	+	22.3318i	−1.00521	+	0.730327i
$936$		0			0
$937$	2.43673	+	0.791742i	0.0796045	+	0.0258651i	0.348549	−	0.937291i	$-0.386675\pi$
$937$	2.43673	+	0.791742i	0.0796045	+	0.0258651i	−0.268944	+	0.963156i	$0.586675\pi$
$938$		0			0
$939$	−26.9508	−	19.5809i	−0.879507	−	0.638999i
$940$		0			0
$941$	6.47579	−	19.9304i	0.211105	−	0.649713i	−0.788303	−	0.615288i	$-0.789040\pi$
$941$	6.47579	−	19.9304i	0.211105	−	0.649713i	0.999407	−	0.0344257i	$-0.0109602\pi$
$942$		0			0
$943$	−7.11180	+	10.4580i	−0.231592	+	0.340559i
$944$		0			0
$945$	21.3402	−	65.6783i	0.694196	−	2.13652i
$946$		0			0
$947$	−8.27045	−	6.00884i	−0.268754	−	0.195261i	0.445244	−	0.895409i	$-0.353117\pi$
$947$	−8.27045	−	6.00884i	−0.268754	−	0.195261i	−0.713997	+	0.700149i	$0.753117\pi$
$948$		0			0
$949$	−2.09212	−	0.679770i	−0.0679130	−	0.0220663i
$950$		0			0
$951$	−94.7140	+	68.8138i	−3.07131	+	2.23144i
$952$		0			0
$953$	9.29587	−	6.75384i	0.301123	−	0.218778i	−0.426955	−	0.904273i	$-0.640414\pi$
$953$	9.29587	−	6.75384i	0.301123	−	0.218778i	0.728078	+	0.685494i	$0.240414\pi$
$954$		0			0
$955$	9.11102	−	12.5402i	0.294826	−	0.405793i
$956$		0			0
$957$			69.7444i			2.25452i
$958$		0			0
$959$	−3.44163	−	10.5923i	−0.111136	−	0.342042i
$960$		0			0
$961$	15.9504	−	49.0903i	0.514529	−	1.58356i
$962$		0			0
$963$	−40.0873	−	123.376i	−1.29179	−	3.97573i
$964$		0			0
$965$	−4.37253	+	1.42072i	−0.140757	+	0.0457346i
$966$		0			0
$967$	29.2783	+	40.2981i	0.941526	+	1.29590i	0.955190	+	0.295992i	$0.0956503\pi$
$967$	29.2783	+	40.2981i	0.941526	+	1.29590i	−0.0136647	+	0.999907i	$0.504350\pi$
$968$		0			0
$969$	65.3367	−	89.9282i	2.09892	−	2.88891i
$970$		0			0
$971$	−41.5403	−	13.4973i	−1.33309	−	0.433148i	−0.446121	−	0.894973i	$-0.647195\pi$
$971$	−41.5403	−	13.4973i	−1.33309	−	0.433148i	−0.886971	+	0.461825i	$0.847195\pi$
$972$		0			0
$973$	−15.5678	−	21.4273i	−0.499082	−	0.686927i
$974$		0			0
$975$	−0.925988			−0.0296554
$976$		0			0
$977$	13.8359	−	4.49556i	0.442650	−	0.143826i	−0.0792080	−	0.996858i	$-0.525239\pi$
$977$	13.8359	−	4.49556i	0.442650	−	0.143826i	0.521858	+	0.853032i	$0.325239\pi$
$978$		0			0
$979$	8.76821	+	6.37048i	0.280233	+	0.203601i
$980$		0			0
$981$		−	114.520i		−	3.65635i
$982$		0			0
$983$	12.2384			0.390343			0.195172	−	0.980769i	$-0.437474\pi$
$983$	12.2384			0.390343			0.195172	+	0.980769i	$0.437474\pi$
$984$		0			0
$985$	8.30114			0.264496
$986$		0			0
$987$			130.770i			4.16245i
$988$		0			0
$989$	4.61445	+	3.35260i	0.146731	+	0.106606i
$990$		0			0
$991$	−7.04352	+	2.28858i	−0.223745	+	0.0726991i	−0.418744	−	0.908104i	$-0.637530\pi$
$991$	−7.04352	+	2.28858i	−0.223745	+	0.0726991i	0.194999	+	0.980803i	$0.437530\pi$
$992$		0			0
$993$	−27.5989			−0.875824
$994$		0			0
$995$	5.49391	+	7.56172i	0.174169	+	0.239723i
$996$		0			0
$997$	−42.6042	−	13.8429i	−1.34929	−	0.438410i	−0.456835	−	0.889551i	$-0.651017\pi$
$997$	−42.6042	−	13.8429i	−1.34929	−	0.438410i	−0.892453	+	0.451141i	$0.851017\pi$
$998$		0			0
$999$	−0.509580	+	0.701377i	−0.0161224	+	0.0221906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bg.b.681.8	✓	32
41.23	even	10	inner	820.2.bg.b.761.1	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bg.b.681.8	✓	32	1.1	even	1	trivial
820.2.bg.b.761.1	yes	32	41.23	even	10	inner

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.bg (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+3.43298i q^{3} +(-0.809017 - 0.587785i) q^{5} +(-3.30690 + 1.07448i) q^{7} -8.78535 q^{9} +(3.15743 + 4.34583i) q^{11} +(0.256531 + 0.0833521i) q^{13} +(2.01785 - 2.77734i) q^{15} +(-4.15727 - 5.72199i) q^{17} +(4.35396 - 1.41469i) q^{19} +(-3.68866 - 11.3525i) q^{21} +(-0.610350 + 1.87846i) q^{23} +(0.309017 + 0.951057i) q^{25} -19.8610i q^{27} +(2.22301 - 3.05971i) q^{29} +(-7.35345 + 5.34260i) q^{31} +(-14.9191 + 10.8394i) q^{33} +(3.30690 + 1.07448i) q^{35} +(-0.0353143 - 0.0256574i) q^{37} +(-0.286146 + 0.880667i) q^{39} +(6.14835 + 1.78824i) q^{41} +(0.892376 - 2.74645i) q^{43} +(7.10750 + 5.16390i) q^{45} +(-10.4190 - 3.38535i) q^{47} +(4.11798 - 2.99189i) q^{49} +(19.6435 - 14.2718i) q^{51} +(-2.78930 + 3.83915i) q^{53} -5.37174i q^{55} +(4.85659 + 14.9470i) q^{57} +(-2.38781 + 7.34892i) q^{59} +(-0.864716 - 2.66132i) q^{61} +(29.0523 - 9.43966i) q^{63} +(-0.158545 - 0.218219i) q^{65} +(-4.97098 + 6.84197i) q^{67} +(-6.44873 - 2.09532i) q^{69} +(-0.478354 - 0.658398i) q^{71} -8.15541 q^{73} +(-3.26496 + 1.06085i) q^{75} +(-15.1108 - 10.9786i) q^{77} -9.20912i q^{79} +41.8263 q^{81} +4.16410 q^{83} +7.07277i q^{85} +(10.5039 + 7.63155i) q^{87} +(1.91886 - 0.623477i) q^{89} -0.937884 q^{91} +(-18.3410 - 25.2443i) q^{93} +(-4.35396 - 1.41469i) q^{95} +(-2.52047 + 3.46913i) q^{97} +(-27.7391 - 38.1796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{5} - 5 q^{7} - 42 q^{9} + 5 q^{11} + 5 q^{13} - 5 q^{17} - 25 q^{19} - 6 q^{21} - 22 q^{23} - 8 q^{25} + 5 q^{29} - 9 q^{31} + 24 q^{33} + 5 q^{35} - 11 q^{37} + 20 q^{39} + 16 q^{41} + 26 q^{43}+ \cdots - 20 q^{97}+O(q^{100}) \) 32 * q - 8 * q^5 - 5 * q^7 - 42 * q^9 + 5 * q^11 + 5 * q^13 - 5 * q^17 - 25 * q^19 - 6 * q^21 - 22 * q^23 - 8 * q^25 + 5 * q^29 - 9 * q^31 + 24 * q^33 + 5 * q^35 - 11 * q^37 + 20 * q^39 + 16 * q^41 + 26 * q^43 + 13 * q^45 - 25 * q^47 + 33 * q^49 + 29 * q^51 - 35 * q^53 + 27 * q^57 + 10 * q^59 + 32 * q^61 + 90 * q^63 - 5 * q^65 + 30 * q^67 - 10 * q^69 + 45 * q^71 - 80 * q^73 - 5 * q^75 - 78 * q^77 - 20 * q^81 - 10 * q^83 + 27 * q^87 - 60 * q^89 + 14 * q^91 - 80 * q^93 + 25 * q^95 - 20 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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