LMFDB - Embedded newform 820.2.bg.a.701.1

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 = [24] 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.1
Character	$\chi$	$=$	820.701
Dual form			820.2.bg.a.441.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.32495i q^{3} +(-0.309017 + 0.951057i) q^{5} +(-1.65518 + 2.27816i) q^{7} -2.40537 q^{9} +(0.385336 - 0.125203i) q^{11} +(-2.97470 - 4.09432i) q^{13} +(2.21115 + 0.718448i) q^{15} +(-5.17450 + 1.68130i) q^{17} +(-3.53396 + 4.86408i) q^{19} +(5.29661 + 3.84821i) q^{21} +(-5.65628 + 4.10953i) q^{23} +(-0.809017 - 0.587785i) q^{25} -1.38247i q^{27} +(0.857577 + 0.278644i) q^{29} +(-2.83372 - 8.72130i) q^{31} +(-0.291091 - 0.895886i) q^{33} +(-1.65518 - 2.27816i) q^{35} +(-3.19931 + 9.84646i) q^{37} +(-9.51907 + 6.91601i) q^{39} +(3.14992 - 5.57476i) q^{41} +(-1.28772 + 0.935586i) q^{43} +(0.743301 - 2.28765i) q^{45} +(0.958207 + 1.31886i) q^{47} +(-0.287280 - 0.884158i) q^{49} +(3.90893 + 12.0304i) q^{51} +(6.06629 + 1.97106i) q^{53} +0.405167i q^{55} +(11.3087 + 8.21627i) q^{57} +(1.37590 - 0.999652i) q^{59} +(10.4083 + 7.56207i) q^{61} +(3.98133 - 5.47983i) q^{63} +(4.81316 - 1.56389i) q^{65} +(-9.68499 - 3.14684i) q^{67} +(9.55444 + 13.1506i) q^{69} +(-7.93370 + 2.57782i) q^{71} +12.5020 q^{73} +(-1.36657 + 1.88092i) q^{75} +(-0.352568 + 1.08509i) q^{77} -5.50739i q^{79} -10.4303 q^{81} -14.1071 q^{83} -5.44080i q^{85} +(0.647831 - 1.99382i) q^{87} +(4.69327 - 6.45973i) q^{89} +14.2512 q^{91} +(-20.2766 + 6.58825i) q^{93} +(-3.53396 - 4.86408i) q^{95} +(-10.1695 - 3.30427i) q^{97} +(-0.926878 + 0.301161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{5} + 5 q^{7} - 6 q^{9} + 5 q^{11} - 5 q^{13} - 5 q^{17} - 5 q^{19} - 6 q^{21} + 10 q^{23} - 6 q^{25} - 25 q^{29} + 7 q^{31} - 12 q^{33} + 5 q^{35} - 13 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{43}+ \cdots - 60 q^{99}+O(q^{100}) $ 24 * q + 6 * q^5 + 5 * q^7 - 6 * q^9 + 5 * q^11 - 5 * q^13 - 5 * q^17 - 5 * q^19 - 6 * q^21 + 10 * q^23 - 6 * q^25 - 25 * q^29 + 7 * q^31 - 12 * q^33 + 5 * q^35 - 13 * q^37 + 4 * q^39 + 6 * q^41 + 14 * q^43 + q^45 - 35 * q^47 + 23 * q^49 - 27 * q^51 + 35 * q^53 + 9 * q^57 - 14 * q^59 + 22 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 - 55 * q^71 + 8 * q^73 - 5 * q^75 + 6 * q^77 - 28 * q^81 - 82 * q^83 - 27 * q^87 + 50 * q^89 + 70 * q^91 - 80 * q^93 - 5 * q^95 - 20 * q^97 - 60 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$	$1$

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
$3$		−	2.32495i		−	1.34231i	−0.741318	−	0.671154i	$-0.765799\pi$
$3$		−	2.32495i		−	1.34231i	0.741318	−	0.671154i	$-0.234201\pi$
$4$		0			0
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	−1.65518	+	2.27816i	−0.625600	+	0.861065i	−0.997746	−	0.0671096i	$-0.978622\pi$
$7$	−1.65518	+	2.27816i	−0.625600	+	0.861065i	0.372145	+	0.928174i	$0.378622\pi$
$8$		0			0
$9$	−2.40537			−0.801791
$10$		0			0
$11$	0.385336	−	0.125203i	0.116183	−	0.0377502i	−0.250348	−	0.968156i	$-0.580545\pi$
$11$	0.385336	−	0.125203i	0.116183	−	0.0377502i	0.366532	+	0.930406i	$0.380545\pi$
$12$		0			0
$13$	−2.97470	−	4.09432i	−0.825032	−	1.13556i	−0.988827	−	0.149065i	$-0.952374\pi$
$13$	−2.97470	−	4.09432i	−0.825032	−	1.13556i	0.163795	−	0.986494i	$-0.447626\pi$
$14$		0			0
$15$	2.21115	+	0.718448i	0.570918	+	0.185502i
$16$		0			0
$17$	−5.17450	+	1.68130i	−1.25500	+	0.407775i	−0.859711	−	0.510781i	$-0.829356\pi$
$17$	−5.17450	+	1.68130i	−1.25500	+	0.407775i	−0.395291	+	0.918556i	$0.629356\pi$
$18$		0			0
$19$	−3.53396	+	4.86408i	−0.810747	+	1.11590i	0.180461	+	0.983582i	$0.442241\pi$
$19$	−3.53396	+	4.86408i	−0.810747	+	1.11590i	−0.991208	+	0.132315i	$0.957759\pi$
$20$		0			0
$21$	5.29661	+	3.84821i	1.15581	+	0.839748i
$22$		0			0
$23$	−5.65628	+	4.10953i	−1.17942	+	0.856897i	−0.992106	−	0.125404i	$-0.959977\pi$
$23$	−5.65628	+	4.10953i	−1.17942	+	0.856897i	−0.187311	+	0.982301i	$0.559977\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$		0			0
$27$		−	1.38247i		−	0.266057i
$28$		0			0
$29$	0.857577	+	0.278644i	0.159248	+	0.0517428i	0.387556	−	0.921846i	$-0.373319\pi$
$29$	0.857577	+	0.278644i	0.159248	+	0.0517428i	−0.228308	+	0.973589i	$0.573319\pi$
$30$		0			0
$31$	−2.83372	−	8.72130i	−0.508952	−	1.56639i	−0.794024	−	0.607886i	$-0.792018\pi$
$31$	−2.83372	−	8.72130i	−0.508952	−	1.56639i	0.285072	−	0.958506i	$-0.407982\pi$
$32$		0			0
$33$	−0.291091	−	0.895886i	−0.0506725	−	0.155954i
$34$		0			0
$35$	−1.65518	−	2.27816i	−0.279777	−	0.385080i
$36$		0			0
$37$	−3.19931	+	9.84646i	−0.525963	+	1.61875i	0.236441	+	0.971646i	$0.424019\pi$
$37$	−3.19931	+	9.84646i	−0.525963	+	1.61875i	−0.762404	+	0.647102i	$0.775981\pi$
$38$		0			0
$39$	−9.51907	+	6.91601i	−1.52427	+	1.10745i
$40$		0			0
$41$	3.14992	−	5.57476i	0.491935	−	0.870632i
$41$	3.14992	−	5.57476i	0.491935	−	0.870632i
$42$		0			0
$43$	−1.28772	+	0.935586i	−0.196376	+	0.142675i	−0.681628	−	0.731699i	$-0.738728\pi$
$43$	−1.28772	+	0.935586i	−0.196376	+	0.142675i	0.485252	+	0.874374i	$0.338728\pi$
$44$		0			0
$45$	0.743301	−	2.28765i	0.110805	−	0.341022i
$46$		0			0
$47$	0.958207	+	1.31886i	0.139769	+	0.192375i	0.873163	−	0.487428i	$-0.162065\pi$
$47$	0.958207	+	1.31886i	0.139769	+	0.192375i	−0.733394	+	0.679804i	$0.762065\pi$
$48$		0			0
$49$	−0.287280	−	0.884158i	−0.0410400	−	0.126308i
$50$		0			0
$51$	3.90893	+	12.0304i	0.547359	+	1.68460i
$52$		0			0
$53$	6.06629	+	1.97106i	0.833268	+	0.270745i	0.694421	−	0.719569i	$-0.255660\pi$
$53$	6.06629	+	1.97106i	0.833268	+	0.270745i	0.138847	+	0.990314i	$0.455660\pi$
$54$		0			0
$55$			0.405167i			0.0546327i
$56$		0			0
$57$	11.3087	+	8.21627i	1.49788	+	1.08827i
$58$		0			0
$59$	1.37590	−	0.999652i	0.179127	−	0.130144i	−0.494609	−	0.869116i	$-0.664689\pi$
$59$	1.37590	−	0.999652i	0.179127	−	0.130144i	0.673736	+	0.738972i	$0.264689\pi$
$60$		0			0
$61$	10.4083	+	7.56207i	1.33265	+	0.968224i	0.999680	+	0.0252844i	$0.00804912\pi$
$61$	10.4083	+	7.56207i	1.33265	+	0.968224i	0.332965	+	0.942939i	$0.391951\pi$
$62$		0			0
$63$	3.98133	−	5.47983i	0.501601	−	0.690394i
$64$		0			0
$65$	4.81316	−	1.56389i	0.596999	−	0.193977i
$66$		0			0
$67$	−9.68499	−	3.14684i	−1.18321	−	0.384448i	−0.349652	−	0.936880i	$-0.613700\pi$
$67$	−9.68499	−	3.14684i	−1.18321	−	0.384448i	−0.833558	+	0.552431i	$0.813700\pi$
$68$		0			0
$69$	9.55444	+	13.1506i	1.15022	+	1.58314i
$70$		0			0
$71$	−7.93370	+	2.57782i	−0.941557	+	0.305931i	−0.739280	−	0.673398i	$-0.764834\pi$
$71$	−7.93370	+	2.57782i	−0.941557	+	0.305931i	−0.202277	+	0.979328i	$0.564834\pi$
$72$		0			0
$73$	12.5020			1.46325			0.731626	−	0.681706i	$-0.238762\pi$
$73$	12.5020			1.46325			0.731626	+	0.681706i	$0.238762\pi$
$74$		0			0
$75$	−1.36657	+	1.88092i	−0.157798	+	0.217190i
$76$		0			0
$77$	−0.352568	+	1.08509i	−0.0401789	+	0.123658i
$78$		0			0
$79$		−	5.50739i		−	0.619630i	−0.950797	−	0.309815i	$-0.899733\pi$
$79$		−	5.50739i		−	0.619630i	0.950797	−	0.309815i	$-0.100267\pi$
$80$		0			0
$81$	−10.4303			−1.15892
$82$		0			0
$83$	−14.1071			−1.54846			−0.774229	−	0.632905i	$-0.781862\pi$
$83$	−14.1071			−1.54846			−0.774229	+	0.632905i	$0.781862\pi$
$84$		0			0
$85$		−	5.44080i		−	0.590137i
$86$		0			0
$87$	0.647831	−	1.99382i	0.0694548	−	0.213760i
$88$		0			0
$89$	4.69327	−	6.45973i	0.497485	−	0.684730i	−0.484261	−	0.874923i	$-0.660912\pi$
$89$	4.69327	−	6.45973i	0.497485	−	0.684730i	0.981747	+	0.190194i	$0.0609116\pi$
$90$		0			0
$91$	14.2512			1.49393
$92$		0			0
$93$	−20.2766	+	6.58825i	−2.10258	+	0.683170i
$94$		0			0
$95$	−3.53396	−	4.86408i	−0.362577	−	0.499044i
$96$		0			0
$97$	−10.1695	−	3.30427i	−1.03256	−	0.335498i	−0.256756	−	0.966476i	$-0.582654\pi$
$97$	−10.1695	−	3.30427i	−1.03256	−	0.335498i	−0.775800	+	0.630978i	$0.782654\pi$
$98$		0			0
$99$	−0.926878	+	0.301161i	−0.0931547	+	0.0302678i
$100$		0			0
$101$	4.84588	−	6.66978i	0.482183	−	0.663668i	−0.496740	−	0.867900i	$-0.665470\pi$
$101$	4.84588	−	6.66978i	0.482183	−	0.663668i	0.978923	+	0.204232i	$0.0654696\pi$
$102$		0			0
$103$	−0.447482	−	0.325115i	−0.0440917	−	0.0320345i	0.565521	−	0.824734i	$-0.308675\pi$
$103$	−0.447482	−	0.325115i	−0.0440917	−	0.0320345i	−0.609613	+	0.792699i	$0.708675\pi$
$104$		0			0
$105$	−5.29661	+	3.84821i	−0.516896	+	0.375547i
$106$		0			0
$107$	2.58966	+	1.88150i	0.250352	+	0.181892i	0.705883	−	0.708329i	$-0.250550\pi$
$107$	2.58966	+	1.88150i	0.250352	+	0.181892i	−0.455531	+	0.890220i	$0.650550\pi$
$108$		0			0
$109$			6.05732i			0.580186i	0.956998	+	0.290093i	$0.0936862\pi$
$109$			6.05732i			0.580186i	−0.956998	+	0.290093i	$0.906314\pi$
$110$		0			0
$111$	22.8925	+	7.43822i	2.17286	+	0.706004i
$112$		0			0
$113$	−4.58613	−	14.1146i	−0.431427	−	1.32779i	−0.896704	−	0.442630i	$-0.854046\pi$
$113$	−4.58613	−	14.1146i	−0.431427	−	1.32779i	0.465278	−	0.885165i	$-0.345954\pi$
$114$		0			0
$115$	−2.16051	−	6.64936i	−0.201468	−	0.620056i
$116$		0			0
$117$	7.15525	+	9.84836i	0.661503	+	0.910481i
$118$		0			0
$119$	4.73448	−	14.5712i	0.434009	−	1.33574i
$120$		0			0
$121$	−8.76638	+	6.36915i	−0.796944	+	0.579013i
$122$		0			0
$123$	−12.9610	−	7.32340i	−1.16866	−	0.660329i
$124$		0			0
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	−0.324433	+	0.998501i	−0.0287887	+	0.0886027i	−0.964419	−	0.264380i	$-0.914833\pi$
$127$	−0.324433	+	0.998501i	−0.0287887	+	0.0886027i	0.935630	+	0.352983i	$0.114833\pi$
$128$		0			0
$129$	2.17519	+	2.99389i	0.191514	+	0.263597i
$130$		0			0
$131$	1.30645	+	4.02083i	0.114145	+	0.351302i	0.991768	−	0.128050i	$-0.0408718\pi$
$131$	1.30645	+	4.02083i	0.114145	+	0.351302i	−0.877623	+	0.479352i	$0.840872\pi$
$132$		0			0
$133$	−5.23182	−	16.1019i	−0.453656	−	1.39621i
$134$		0			0
$135$	1.31481	+	0.427208i	0.113161	+	0.0367682i
$136$		0			0
$137$		−	21.4792i		−	1.83509i	−0.397633	−	0.917545i	$-0.630168\pi$
$137$		−	21.4792i		−	1.83509i	0.397633	−	0.917545i	$-0.369832\pi$
$138$		0			0
$139$	−18.6449	−	13.5463i	−1.58144	−	1.14899i	−0.915018	−	0.403414i	$-0.867823\pi$
$139$	−18.6449	−	13.5463i	−1.58144	−	1.14899i	−0.666425	−	0.745572i	$-0.732177\pi$
$140$		0			0
$141$	3.06628	−	2.22778i	0.258227	−	0.187613i
$142$		0			0
$143$	−1.65888	−	1.20525i	−0.138723	−	0.100788i
$144$		0			0
$145$	−0.530012	+	0.729498i	−0.0440151	+	0.0605815i
$146$		0			0
$147$	−2.05562	+	0.667911i	−0.169545	+	0.0550884i
$148$		0			0
$149$	15.3930	+	5.00148i	1.26104	+	0.409737i	0.861865	−	0.507137i	$-0.169296\pi$
$149$	15.3930	+	5.00148i	1.26104	+	0.409737i	0.399176	+	0.916874i	$0.369296\pi$
$150$		0			0
$151$	2.70210	+	3.71912i	0.219894	+	0.302658i	0.904685	−	0.426082i	$-0.140106\pi$
$151$	2.70210	+	3.71912i	0.219894	+	0.302658i	−0.684791	+	0.728740i	$0.740106\pi$
$152$		0			0
$153$	12.4466	−	4.04415i	1.00625	−	0.326950i
$154$		0			0
$155$	9.17012			0.736562
$156$		0			0
$157$	−6.29764	+	8.66796i	−0.502606	+	0.691778i	−0.982651	−	0.185466i	$-0.940621\pi$
$157$	−6.29764	+	8.66796i	−0.502606	+	0.691778i	0.480044	+	0.877244i	$0.340621\pi$
$158$		0			0
$159$	4.58260	−	14.1038i	0.363424	−	1.11850i
$160$		0			0
$161$		−	19.6880i		−	1.55163i
$162$		0			0
$163$	−3.65736			−0.286466			−0.143233	−	0.989689i	$-0.545750\pi$
$163$	−3.65736			−0.286466			−0.143233	+	0.989689i	$0.545750\pi$
$164$		0			0
$165$	0.941991			0.0733339
$166$		0			0
$167$			10.6890i			0.827139i	0.910473	+	0.413570i	$0.135718\pi$
$167$			10.6890i			0.827139i	−0.910473	+	0.413570i	$0.864282\pi$
$168$		0			0
$169$	−3.89740	+	11.9950i	−0.299800	+	0.922689i
$170$		0			0
$171$	8.50050	−	11.6999i	0.650049	−	0.894716i
$172$		0			0
$173$	14.7704			1.12297			0.561486	−	0.827486i	$-0.310230\pi$
$173$	14.7704			1.12297			0.561486	+	0.827486i	$0.310230\pi$
$174$		0			0
$175$	2.67814	−	0.870181i	0.202448	−	0.0657795i
$176$		0			0
$177$	−2.32414	−	3.19890i	−0.174693	−	0.240444i
$178$		0			0
$179$	−9.38842	−	3.05048i	−0.701723	−	0.228004i	−0.0636420	−	0.997973i	$-0.520272\pi$
$179$	−9.38842	−	3.05048i	−0.701723	−	0.228004i	−0.638081	+	0.769969i	$0.720272\pi$
$180$		0			0
$181$	−12.3848	+	4.02405i	−0.920551	+	0.299105i	−0.730693	−	0.682706i	$-0.760803\pi$
$181$	−12.3848	+	4.02405i	−0.920551	+	0.299105i	−0.189858	+	0.981811i	$0.560803\pi$
$182$		0			0
$183$	17.5814	−	24.1987i	1.29965	−	1.78882i
$184$		0			0
$185$	−8.37590	−	6.08545i	−0.615808	−	0.447411i
$186$		0			0
$187$	−1.78342	+	1.29573i	−0.130417	+	0.0947532i
$188$		0			0
$189$	3.14950	+	2.28825i	0.229093	+	0.166446i
$190$		0			0
$191$			7.77636i			0.562677i	0.959609	+	0.281339i	$0.0907784\pi$
$191$			7.77636i			0.562677i	−0.959609	+	0.281339i	$0.909222\pi$
$192$		0			0
$193$	−20.2129	−	6.56758i	−1.45496	−	0.472745i	−0.528433	−	0.848975i	$-0.677220\pi$
$193$	−20.2129	−	6.56758i	−1.45496	−	0.472745i	−0.926526	+	0.376230i	$0.877220\pi$
$194$		0			0
$195$	−3.63596	−	11.1903i	−0.260376	−	0.801356i
$196$		0			0
$197$	−0.491778	−	1.51354i	−0.0350378	−	0.107835i	0.932008	−	0.362438i	$-0.118055\pi$
$197$	−0.491778	−	1.51354i	−0.0350378	−	0.107835i	−0.967046	+	0.254602i	$0.918055\pi$
$198$		0			0
$199$	6.59415	+	9.07607i	0.467447	+	0.643386i	0.976032	−	0.217626i	$-0.0698313\pi$
$199$	6.59415	+	9.07607i	0.467447	+	0.643386i	−0.508585	+	0.861012i	$0.669831\pi$
$200$		0			0
$201$	−7.31624	+	22.5171i	−0.516048	+	1.58823i
$202$		0			0
$203$	−2.05424	+	1.49249i	−0.144179	+	0.104753i
$204$		0			0
$205$	4.32854	+	4.71845i	0.302318	+	0.329551i
$206$		0			0
$207$	13.6055	−	9.88496i	0.945646	−	0.687052i
$208$		0			0
$209$	−0.752765	+	2.31677i	−0.0520698	+	0.160254i
$210$		0			0
$211$	−0.987209	−	1.35878i	−0.0679622	−	0.0935420i	0.773683	−	0.633573i	$-0.218412\pi$
$211$	−0.987209	−	1.35878i	−0.0679622	−	0.0935420i	−0.841645	+	0.540031i	$0.818412\pi$
$212$		0			0
$213$	5.99328	+	18.4454i	0.410653	+	1.26386i
$214$		0			0
$215$	−0.491866	−	1.51381i	−0.0335450	−	0.103241i
$216$		0			0
$217$	24.5589	+	7.97966i	1.66717	+	0.541695i
$218$		0			0
$219$		−	29.0665i		−	1.96414i
$220$		0			0
$221$	22.2763	+	16.1847i	1.49847	+	1.08870i
$222$		0			0
$223$	0.557215	−	0.404841i	0.0373139	−	0.0271101i	−0.568972	−	0.822357i	$-0.692659\pi$
$223$	0.557215	−	0.404841i	0.0373139	−	0.0271101i	0.606286	+	0.795247i	$0.292659\pi$
$224$		0			0
$225$	1.94599	+	1.41384i	0.129733	+	0.0942562i
$226$		0			0
$227$	16.7380	−	23.0379i	1.11094	−	1.52908i	0.290914	−	0.956749i	$-0.406041\pi$
$227$	16.7380	−	23.0379i	1.11094	−	1.52908i	0.820025	−	0.572328i	$-0.193959\pi$
$228$		0			0
$229$	6.77124	−	2.20011i	0.447456	−	0.145387i	−0.0766171	−	0.997061i	$-0.524412\pi$
$229$	6.77124	−	2.20011i	0.447456	−	0.145387i	0.524073	+	0.851673i	$0.324412\pi$
$230$		0			0
$231$	2.52278	+	0.819702i	0.165987	+	0.0539325i
$232$		0			0
$233$	−8.65265	−	11.9094i	−0.566854	−	0.780208i	0.425324	−	0.905041i	$-0.360160\pi$
$233$	−8.65265	−	11.9094i	−0.566854	−	0.780208i	−0.992178	+	0.124834i	$0.960160\pi$
$234$		0			0
$235$	−1.55041	+	0.503759i	−0.101138	+	0.0328616i
$236$		0			0
$237$	−12.8044			−0.831734
$238$		0			0
$239$	5.35759	−	7.37409i	0.346554	−	0.476991i	−0.599787	−	0.800159i	$-0.704748\pi$
$239$	5.35759	−	7.37409i	0.346554	−	0.476991i	0.946341	+	0.323169i	$0.104748\pi$
$240$		0			0
$241$	−5.09803	+	15.6901i	−0.328393	+	1.01069i	0.641493	+	0.767129i	$0.278315\pi$
$241$	−5.09803	+	15.6901i	−0.328393	+	1.01069i	−0.969886	+	0.243560i	$0.921685\pi$
$242$		0			0
$243$			20.1025i			1.28957i
$244$		0			0
$245$	0.929658			0.0593937
$246$		0			0
$247$	30.4276			1.93606
$248$		0			0
$249$			32.7983i			2.07851i
$250$		0			0
$251$	−5.27292	+	16.2284i	−0.332824	+	1.02433i	0.634961	+	0.772545i	$0.281016\pi$
$251$	−5.27292	+	16.2284i	−0.332824	+	1.02433i	−0.967784	+	0.251781i	$0.918984\pi$
$252$		0			0
$253$	−1.66505	+	2.29174i	−0.104680	+	0.144080i
$254$		0			0
$255$	−12.6496			−0.792146
$256$		0			0
$257$	23.6610	−	7.68792i	1.47593	−	0.479560i	0.543038	−	0.839708i	$-0.317274\pi$
$257$	23.6610	−	7.68792i	1.47593	−	0.479560i	0.932895	+	0.360149i	$0.117274\pi$
$258$		0			0
$259$	−17.1364	−	23.5862i	−1.06480	−	1.46558i
$260$		0			0
$261$	−2.06279	−	0.670242i	−0.127684	−	0.0414869i
$262$		0			0
$263$	5.11255	−	1.66117i	0.315253	−	0.102432i	−0.147117	−	0.989119i	$-0.546999\pi$
$263$	5.11255	−	1.66117i	0.315253	−	0.102432i	0.462370	+	0.886687i	$0.346999\pi$
$264$		0			0
$265$	−3.74917	+	5.16029i	−0.230310	+	0.316994i
$266$		0			0
$267$	−15.0185	−	10.9116i	−0.919118	−	0.667778i
$268$		0			0
$269$	10.8808	−	7.90538i	0.663416	−	0.482000i	−0.204399	−	0.978888i	$-0.565524\pi$
$269$	10.8808	−	7.90538i	0.663416	−	0.482000i	0.867815	+	0.496888i	$0.165524\pi$
$270$		0			0
$271$	−15.4527	−	11.2270i	−0.938682	−	0.681992i	0.00942112	−	0.999956i	$-0.497001\pi$
$271$	−15.4527	−	11.2270i	−0.938682	−	0.681992i	−0.948103	+	0.317963i	$0.897001\pi$
$272$		0			0
$273$		−	33.1332i		−	2.00531i
$274$		0			0
$275$	−0.385336	−	0.125203i	−0.0232367	−	0.00755005i
$276$		0			0
$277$	8.56714	+	26.3670i	0.514750	+	1.58424i	0.783737	+	0.621093i	$0.213311\pi$
$277$	8.56714	+	26.3670i	0.514750	+	1.58424i	−0.268987	+	0.963144i	$0.586689\pi$
$278$		0			0
$279$	6.81616	+	20.9780i	0.408073	+	1.25592i
$280$		0			0
$281$	1.80539	+	2.48490i	0.107700	+	0.148237i	0.859465	−	0.511195i	$-0.170797\pi$
$281$	1.80539	+	2.48490i	0.107700	+	0.148237i	−0.751764	+	0.659432i	$0.770797\pi$
$282$		0			0
$283$	−2.04009	+	6.27875i	−0.121271	+	0.373233i	−0.993203	−	0.116393i	$-0.962867\pi$
$283$	−2.04009	+	6.27875i	−0.121271	+	0.373233i	0.871932	+	0.489626i	$0.162867\pi$
$284$		0			0
$285$	−11.3087	+	8.21627i	−0.669871	+	0.486690i
$286$		0			0
$287$	7.48653	+	16.4033i	0.441916	+	0.968256i
$288$		0			0
$289$	10.1954	−	7.40742i	0.599732	−	0.435731i
$290$		0			0
$291$	−7.68225	+	23.6435i	−0.450342	+	1.38601i
$292$		0			0
$293$	−10.4051	−	14.3214i	−0.607874	−	0.836667i	0.388527	−	0.921438i	$-0.372984\pi$
$293$	−10.4051	−	14.3214i	−0.607874	−	0.836667i	−0.996400	+	0.0847708i	$0.972984\pi$
$294$		0			0
$295$	0.525548	+	1.61747i	0.0305986	+	0.0941728i
$296$		0			0
$297$	−0.173091	−	0.532718i	−0.0100437	−	0.0309114i
$298$		0			0
$299$	33.6514	+	10.9340i	1.94611	+	0.632331i
$300$		0			0
$301$		−	4.48221i		−	0.258350i
$302$		0			0
$303$	−15.5069	−	11.2664i	−0.890847	−	0.647238i
$304$		0			0
$305$	−10.4083	+	7.56207i	−0.595977	+	0.433003i
$306$		0			0
$307$	12.7161	+	9.23882i	0.725748	+	0.527287i	0.888216	−	0.459427i	$-0.151945\pi$
$307$	12.7161	+	9.23882i	0.725748	+	0.527287i	−0.162467	+	0.986714i	$0.551945\pi$
$308$		0			0
$309$	−0.755875	+	1.04037i	−0.0430002	+	0.0591847i
$310$		0			0
$311$	−9.37608	+	3.04647i	−0.531669	+	0.172750i	−0.562534	−	0.826774i	$-0.690174\pi$
$311$	−9.37608	+	3.04647i	−0.531669	+	0.172750i	0.0308655	+	0.999524i	$0.490174\pi$
$312$		0			0
$313$	−0.0354736	−	0.0115261i	−0.00200508	−	0.000651491i	0.308014	−	0.951382i	$-0.400336\pi$
$313$	−0.0354736	−	0.0115261i	−0.00200508	−	0.000651491i	−0.310019	+	0.950730i	$0.600336\pi$
$314$		0			0
$315$	3.98133	+	5.47983i	0.224323	+	0.308754i
$316$		0			0
$317$	−31.4583	+	10.2214i	−1.76688	+	0.574092i	−0.997875	−	0.0651563i	$-0.979245\pi$
$317$	−31.4583	+	10.2214i	−1.76688	+	0.574092i	−0.769000	+	0.639249i	$0.779245\pi$
$318$		0			0
$319$	0.365343			0.0204553
$320$		0			0
$321$	4.37439	−	6.02083i	0.244154	−	0.336050i
$322$		0			0
$323$	10.1085	−	31.1109i	0.562454	−	1.73105i
$324$		0			0
$325$			5.06085i			0.280726i
$326$		0			0
$327$	14.0829			0.778788
$328$		0			0
$329$	−4.59058			−0.253087
$330$		0			0
$331$			16.2440i			0.892852i	0.894820	+	0.446426i	$0.147303\pi$
$331$			16.2440i			0.892852i	−0.894820	+	0.446426i	$0.852697\pi$
$332$		0			0
$333$	7.69553	−	23.6844i	0.421712	−	1.29790i
$334$		0			0
$335$	5.98565	−	8.23855i	0.327031	−	0.450120i
$336$		0			0
$337$	25.0946			1.36699			0.683496	−	0.729954i	$-0.260459\pi$
$337$	25.0946			1.36699			0.683496	+	0.729954i	$0.260459\pi$
$338$		0			0
$339$	−32.8158	+	10.6625i	−1.78231	+	0.579107i
$340$		0			0
$341$	−2.18387	−	3.00584i	−0.118263	−	0.162776i
$342$		0			0
$343$	−16.2572	−	5.28230i	−0.877808	−	0.285217i
$344$		0			0
$345$	−15.4594	+	5.02307i	−0.832306	+	0.270433i
$346$		0			0
$347$	13.1802	−	18.1410i	0.707549	−	0.973858i	−0.292297	−	0.956328i	$-0.594420\pi$
$347$	13.1802	−	18.1410i	0.707549	−	0.973858i	0.999846	−	0.0175305i	$-0.00558042\pi$
$348$		0			0
$349$	−15.0584	−	10.9406i	−0.806058	−	0.585636i	0.106627	−	0.994299i	$-0.465995\pi$
$349$	−15.0584	−	10.9406i	−0.806058	−	0.585636i	−0.912685	+	0.408663i	$0.865995\pi$
$350$		0			0
$351$	−5.66029	+	4.11244i	−0.302124	+	0.219506i
$352$		0			0
$353$	9.55008	+	6.93854i	0.508300	+	0.369301i	0.812178	−	0.583410i	$-0.198282\pi$
$353$	9.55008	+	6.93854i	0.508300	+	0.369301i	−0.303879	+	0.952711i	$0.598282\pi$
$354$		0			0
$355$		−	8.34199i		−	0.442747i
$356$		0			0
$357$	−33.8773	−	11.0074i	−1.79298	−	0.582574i
$358$		0			0
$359$	4.09571	+	12.6053i	0.216163	+	0.665282i	0.999069	+	0.0431415i	$0.0137366\pi$
$359$	4.09571	+	12.6053i	0.216163	+	0.665282i	−0.782906	+	0.622140i	$0.786263\pi$
$360$		0			0
$361$	−5.29908	−	16.3089i	−0.278899	−	0.858362i
$362$		0			0
$363$	14.8079	+	20.3814i	0.777214	+	1.06974i
$364$		0			0
$365$	−3.86334	+	11.8901i	−0.202216	+	0.622358i
$366$		0			0
$367$	−2.42973	+	1.76530i	−0.126831	+	0.0921479i	−0.649392	−	0.760454i	$-0.724977\pi$
$367$	−2.42973	+	1.76530i	−0.126831	+	0.0921479i	0.522561	+	0.852602i	$0.324977\pi$
$368$		0			0
$369$	−7.57674	+	13.4094i	−0.394429	+	0.698065i
$370$		0			0
$371$	−14.5312	+	10.5575i	−0.754422	+	0.548120i
$372$		0			0
$373$	−1.33725	+	4.11563i	−0.0692401	+	0.213099i	−0.979689	−	0.200522i	$-0.935736\pi$
$373$	−1.33725	+	4.11563i	−0.0692401	+	0.213099i	0.910449	+	0.413621i	$0.135736\pi$
$374$		0			0
$375$	−1.36657	−	1.88092i	−0.0705693	−	0.0971303i
$376$		0			0
$377$	−1.41017	−	4.34007i	−0.0726277	−	0.223525i
$378$		0			0
$379$	3.86555	+	11.8969i	0.198560	+	0.611105i	0.999917	+	0.0129178i	$0.00411199\pi$
$379$	3.86555	+	11.8969i	0.198560	+	0.611105i	−0.801357	+	0.598187i	$0.795888\pi$
$380$		0			0
$381$	2.32146	+	0.754288i	0.118932	+	0.0386434i
$382$		0			0
$383$			14.4084i			0.736235i	0.929779	+	0.368118i	$0.119998\pi$
$383$			14.4084i			0.736235i	−0.929779	+	0.368118i	$0.880002\pi$
$384$		0			0
$385$	−0.923036	−	0.670625i	−0.0470423	−	0.0341782i
$386$		0			0
$387$	3.09746	−	2.25043i	0.157452	−	0.114396i
$388$		0			0
$389$	12.5266	+	9.10113i	0.635125	+	0.461446i	0.858172	−	0.513362i	$-0.171600\pi$
$389$	12.5266	+	9.10113i	0.635125	+	0.461446i	−0.223047	+	0.974808i	$0.571600\pi$
$390$		0			0
$391$	22.3591	−	30.7747i	1.13075	−	1.55634i
$392$		0			0
$393$	9.34822	−	3.03742i	0.471555	−	0.153218i
$394$		0			0
$395$	5.23784	+	1.70188i	0.263544	+	0.0856307i
$396$		0			0
$397$	0.216285	+	0.297690i	0.0108550	+	0.0149407i	0.814410	−	0.580290i	$-0.197061\pi$
$397$	0.216285	+	0.297690i	0.0108550	+	0.0149407i	−0.803555	+	0.595231i	$0.797061\pi$
$398$		0			0
$399$	−37.4360	+	12.1637i	−1.87414	+	0.608947i
$400$		0			0
$401$	−9.76709			−0.487745			−0.243873	−	0.969807i	$-0.578418\pi$
$401$	−9.76709			−0.487745			−0.243873	+	0.969807i	$0.578418\pi$
$402$		0			0
$403$	−27.2783	+	37.5454i	−1.35883	+	1.87027i
$404$		0			0
$405$	3.22314	−	9.91980i	0.160159	−	0.492919i
$406$		0			0
$407$			4.19476i			0.207927i
$408$		0			0
$409$	14.9991			0.741658			0.370829	−	0.928701i	$-0.379074\pi$
$409$	14.9991			0.741658			0.370829	+	0.928701i	$0.379074\pi$
$410$		0			0
$411$	−49.9379			−2.46326
$412$		0			0
$413$			4.78914i			0.235658i
$414$		0			0
$415$	4.35934	−	13.4167i	0.213992	−	0.658599i
$416$		0			0
$417$	−31.4945	+	43.3485i	−1.54229	+	2.12278i
$418$		0			0
$419$	15.9163			0.777563			0.388781	−	0.921330i	$-0.372896\pi$
$419$	15.9163			0.777563			0.388781	+	0.921330i	$0.372896\pi$
$420$		0			0
$421$	−34.3441	+	11.1591i	−1.67383	+	0.543861i	−0.983699	−	0.179823i	$-0.942447\pi$
$421$	−34.3441	+	11.1591i	−1.67383	+	0.543861i	−0.690132	+	0.723684i	$0.742447\pi$
$422$		0			0
$423$	−2.30485	−	3.17235i	−0.112065	−	0.154245i
$424$		0			0
$425$	5.17450	+	1.68130i	0.251000	+	0.0815549i
$426$		0			0
$427$	−34.4553	+	11.1952i	−1.66741	+	0.541773i
$428$		0			0
$429$	−2.80214	+	3.85681i	−0.135288	+	0.186208i
$430$		0			0
$431$	−6.56033	−	4.76636i	−0.316000	−	0.229587i	0.418467	−	0.908232i	$-0.362568\pi$
$431$	−6.56033	−	4.76636i	−0.316000	−	0.229587i	−0.734467	+	0.678645i	$0.762568\pi$
$432$		0			0
$433$	−19.2638	+	13.9960i	−0.925759	+	0.672603i	−0.944951	−	0.327212i	$-0.893891\pi$
$433$	−19.2638	+	13.9960i	−0.925759	+	0.672603i	0.0191916	+	0.999816i	$0.493891\pi$
$434$		0			0
$435$	1.69604	+	1.23225i	0.0813191	+	0.0590818i
$436$		0			0
$437$		−	42.0356i		−	2.01083i
$438$		0			0
$439$	−3.86662	−	1.25634i	−0.184543	−	0.0599618i	0.215287	−	0.976551i	$-0.430931\pi$
$439$	−3.86662	−	1.25634i	−0.184543	−	0.0599618i	−0.399831	+	0.916589i	$0.630931\pi$
$440$		0			0
$441$	0.691016	+	2.12673i	0.0329055	+	0.101273i
$442$		0			0
$443$	−0.880783	−	2.71077i	−0.0418473	−	0.128793i	0.927950	−	0.372704i	$-0.121569\pi$
$443$	−0.880783	−	2.71077i	−0.0418473	−	0.128793i	−0.969798	+	0.243911i	$0.921569\pi$
$444$		0			0
$445$	4.69327	+	6.45973i	0.222482	+	0.306220i
$446$		0			0
$447$	11.6282	−	35.7878i	0.549994	−	1.69271i
$448$		0			0
$449$	8.18631	−	5.94770i	0.386336	−	0.280690i	−0.377616	−	0.925962i	$-0.623256\pi$
$449$	8.18631	−	5.94770i	0.386336	−	0.280690i	0.763952	+	0.645273i	$0.223256\pi$
$450$		0			0
$451$	0.515800	−	2.54254i	0.0242881	−	0.119724i
$452$		0			0
$453$	8.64676	−	6.28224i	0.406260	−	0.295165i
$454$		0			0
$455$	−4.40386	+	13.5537i	−0.206456	+	0.635407i
$456$		0			0
$457$	−20.3206	−	27.9689i	−0.950559	−	1.30833i	−0.951279	−	0.308332i	$-0.900229\pi$
$457$	−20.3206	−	27.9689i	−0.950559	−	1.30833i	0.000720312	−	1.00000i	$-0.499771\pi$
$458$		0			0
$459$	2.32435	+	7.15362i	0.108491	+	0.333902i
$460$		0			0
$461$	6.07680	+	18.7025i	0.283025	+	0.871061i	0.986984	+	0.160820i	$0.0514140\pi$
$461$	6.07680	+	18.7025i	0.283025	+	0.871061i	−0.703959	+	0.710241i	$0.748586\pi$
$462$		0			0
$463$	26.2768	+	8.53784i	1.22119	+	0.396787i	0.847514	−	0.530774i	$-0.178099\pi$
$463$	26.2768	+	8.53784i	1.22119	+	0.396787i	0.373672	+	0.927561i	$0.378099\pi$
$464$		0			0
$465$		−	21.3200i		−	0.988693i
$466$		0			0
$467$	−15.2598	−	11.0869i	−0.706141	−	0.513042i	0.175785	−	0.984429i	$-0.443754\pi$
$467$	−15.2598	−	11.0869i	−0.706141	−	0.513042i	−0.881926	+	0.471387i	$0.843754\pi$
$468$		0			0
$469$	23.1995	−	16.8554i	1.07125	−	0.778310i
$470$		0			0
$471$	20.1525	+	14.6417i	0.928580	+	0.674653i
$472$		0			0
$473$	−0.379068	+	0.521743i	−0.0174296	+	0.0239897i
$474$		0			0
$475$	5.71807	−	1.85791i	0.262363	−	0.0852469i
$476$		0			0
$477$	−14.5917	−	4.74112i	−0.668107	−	0.217081i
$478$		0			0
$479$	−25.1229	−	34.5787i	−1.14789	−	1.57994i	−0.748464	−	0.663176i	$-0.769208\pi$
$479$	−25.1229	−	34.5787i	−1.14789	−	1.57994i	−0.399430	−	0.916764i	$-0.630792\pi$
$480$		0			0
$481$	49.8315	−	16.1912i	2.27212	−	0.738257i
$482$		0			0
$483$	−45.7735			−2.08276
$484$		0			0
$485$	6.28510	−	8.65069i	0.285392	−	0.392808i
$486$		0			0
$487$	−8.42293	+	25.9231i	−0.381680	+	1.17469i	0.557181	+	0.830391i	$0.311883\pi$
$487$	−8.42293	+	25.9231i	−0.381680	+	1.17469i	−0.938860	+	0.344298i	$0.888117\pi$
$488$		0			0
$489$			8.50316i			0.384526i
$490$		0			0
$491$	−3.69878			−0.166924			−0.0834619	−	0.996511i	$-0.526598\pi$
$491$	−3.69878			−0.166924			−0.0834619	+	0.996511i	$0.526598\pi$
$492$		0			0
$493$	−4.90602			−0.220956
$494$		0			0
$495$		−	0.974577i		−	0.0438040i
$496$		0			0
$497$	7.25904	−	22.3410i	0.325612	−	1.00213i
$498$		0			0
$499$	−16.7812	+	23.0973i	−0.751228	+	1.03398i	0.246665	+	0.969101i	$0.420665\pi$
$499$	−16.7812	+	23.0973i	−0.751228	+	1.03398i	−0.997893	+	0.0648760i	$0.979335\pi$
$500$		0			0
$501$	24.8513			1.11028
$502$		0			0
$503$	20.7450	−	6.74044i	0.924972	−	0.300542i	0.192467	−	0.981303i	$-0.438351\pi$
$503$	20.7450	−	6.74044i	0.924972	−	0.300542i	0.732505	+	0.680762i	$0.238351\pi$
$504$		0			0
$505$	4.84588	+	6.66978i	0.215639	+	0.296801i
$506$		0			0
$507$	27.8876	+	9.06124i	1.23853	+	0.402424i
$508$		0			0
$509$	−28.3138	+	9.19972i	−1.25499	+	0.407770i	−0.859706	−	0.510790i	$-0.829353\pi$
$509$	−28.3138	+	9.19972i	−1.25499	+	0.407770i	−0.395282	+	0.918560i	$0.629353\pi$
$510$		0			0
$511$	−20.6931	+	28.4817i	−0.915411	+	1.25996i
$512$		0			0
$513$	6.72447	+	4.88561i	0.296893	+	0.215705i
$514$		0			0
$515$	0.447482	−	0.325115i	0.0197184	−	0.0143263i
$516$		0			0
$517$	0.534358	+	0.388234i	0.0235010	+	0.0170745i
$518$		0			0
$519$		−	34.3403i		−	1.50737i
$520$		0			0
$521$	23.8783	+	7.75852i	1.04613	+	0.339907i	0.781147	−	0.624347i	$-0.214635\pi$
$521$	23.8783	+	7.75852i	1.04613	+	0.339907i	0.264979	+	0.964254i	$0.414635\pi$
$522$		0			0
$523$	13.0386	+	40.1287i	0.570139	+	1.75471i	0.652165	+	0.758077i	$0.273861\pi$
$523$	13.0386	+	40.1287i	0.570139	+	1.75471i	−0.0820265	+	0.996630i	$0.526139\pi$
$524$		0			0
$525$	−2.02312	−	6.22653i	−0.0882964	−	0.271748i
$526$		0			0
$527$	29.3262	+	40.3641i	1.27747	+	1.75829i
$528$		0			0
$529$	7.99792	−	24.6151i	0.347736	−	1.07022i
$530$		0			0
$531$	−3.30956	+	2.40454i	−0.143623	+	0.104348i
$532$		0			0
$533$	−32.1949	+	3.68645i	−1.39452	+	0.159678i
$534$		0			0
$535$	−2.58966	+	1.88150i	−0.111961	+	0.0813444i
$536$		0			0
$537$	−7.09220	+	21.8276i	−0.306051	+	0.941929i
$538$		0			0
$539$	−0.221399	−	0.304730i	−0.00953633	−	0.0131256i
$540$		0			0
$541$	6.71264	+	20.6594i	0.288599	+	0.888216i	0.985297	+	0.170851i	$0.0546518\pi$
$541$	6.71264	+	20.6594i	0.288599	+	0.888216i	−0.696698	+	0.717365i	$0.745348\pi$
$542$		0			0
$543$	9.35570	+	28.7939i	0.401491	+	1.23566i
$544$		0			0
$545$	−5.76085	−	1.87181i	−0.246768	−	0.0801797i
$546$		0			0
$547$			32.7600i			1.40072i	0.713791	+	0.700359i	$0.246977\pi$
$547$			32.7600i			1.40072i	−0.713791	+	0.700359i	$0.753023\pi$
$548$		0			0
$549$	−25.0358	−	18.1896i	−1.06850	−	0.776313i
$550$		0			0
$551$	−4.38599	+	3.18661i	−0.186849	+	0.135754i
$552$		0			0
$553$	12.5467	+	9.11574i	0.533541	+	0.387641i
$554$		0			0
$555$	−14.1483	+	19.4735i	−0.600563	+	0.826604i
$556$		0			0
$557$	−39.2807	+	12.7631i	−1.66437	+	0.540788i	−0.981782	−	0.190011i	$-0.939148\pi$
$557$	−39.2807	+	12.7631i	−1.66437	+	0.540788i	−0.682593	+	0.730799i	$0.739148\pi$
$558$		0			0
$559$	7.66117	+	2.48926i	0.324033	+	0.105285i
$560$		0			0
$561$	3.01250	+	4.14636i	0.127188	+	0.175059i
$562$		0			0
$563$	−4.57254	+	1.48571i	−0.192710	+	0.0626151i	−0.403782	−	0.914855i	$-0.632304\pi$
$563$	−4.57254	+	1.48571i	−0.192710	+	0.0626151i	0.211072	+	0.977470i	$0.432304\pi$
$564$		0			0
$565$	14.8410			0.624366
$566$		0			0
$567$	17.2640	−	23.7619i	0.725022	−	0.997907i
$568$		0			0
$569$	1.55126	−	4.77429i	0.0650322	−	0.200148i	−0.913261	−	0.407376i	$-0.866444\pi$
$569$	1.55126	−	4.77429i	0.0650322	−	0.200148i	0.978293	+	0.207227i	$0.0664440\pi$
$570$		0			0
$571$		−	24.4013i		−	1.02116i	−0.859830	−	0.510581i	$-0.829430\pi$
$571$		−	24.4013i		−	1.02116i	0.859830	−	0.510581i	$-0.170570\pi$
$572$		0			0
$573$	18.0796			0.755286
$574$		0			0
$575$	6.99155			0.291568
$576$		0			0
$577$			6.17215i			0.256950i	0.991713	+	0.128475i	$0.0410082\pi$
$577$			6.17215i			0.256950i	−0.991713	+	0.128475i	$0.958992\pi$
$578$		0			0
$579$	−15.2693	+	46.9940i	−0.634570	+	1.95300i
$580$		0			0
$581$	23.3499	−	32.1384i	0.968716	−	1.33332i
$582$		0			0
$583$	2.58434			0.107033
$584$		0			0
$585$	−11.5774	+	3.76174i	−0.478668	+	0.155529i
$586$		0			0
$587$	−14.7932	−	20.3611i	−0.610581	−	0.840392i	0.386044	−	0.922480i	$-0.373841\pi$
$587$	−14.7932	−	20.3611i	−0.610581	−	0.840392i	−0.996625	+	0.0820880i	$0.973841\pi$
$588$		0			0
$589$	52.4354	+	17.0373i	2.16056	+	0.702009i
$590$		0			0
$591$	−3.51889	+	1.14336i	−0.144748	+	0.0470315i
$592$		0			0
$593$	−2.85396	+	3.92814i	−0.117198	+	0.161309i	−0.863586	−	0.504202i	$-0.831787\pi$
$593$	−2.85396	+	3.92814i	−0.117198	+	0.161309i	0.746388	+	0.665512i	$0.231787\pi$
$594$		0			0
$595$	12.3950	+	9.00551i	0.508146	+	0.369190i
$596$		0			0
$597$	21.1014	−	15.3311i	0.863622	−	0.627458i
$598$		0			0
$599$	10.0339	+	7.29005i	0.409973	+	0.297863i	0.773591	−	0.633685i	$-0.218459\pi$
$599$	10.0339	+	7.29005i	0.409973	+	0.297863i	−0.363618	+	0.931548i	$0.618459\pi$
$600$		0			0
$601$		−	26.2292i		−	1.06991i	−0.844880	−	0.534955i	$-0.820329\pi$
$601$		−	26.2292i		−	1.06991i	0.844880	−	0.534955i	$-0.179671\pi$
$602$		0			0
$603$	23.2960	+	7.56934i	0.948687	+	0.308247i
$604$		0			0
$605$	−3.34846	−	10.3055i	−0.136134	−	0.418978i
$606$		0			0
$607$	12.1184	+	37.2966i	0.491871	+	1.51382i	0.821776	+	0.569810i	$0.192983\pi$
$607$	12.1184	+	37.2966i	0.491871	+	1.51382i	−0.329905	+	0.944014i	$0.607017\pi$
$608$		0			0
$609$	3.46997	+	4.77600i	0.140610	+	0.193533i
$610$		0			0
$611$	2.54945	−	7.84641i	0.103140	−	0.317432i
$612$		0			0
$613$	−18.1605	+	13.1944i	−0.733496	+	0.532916i	−0.890667	−	0.454655i	$-0.849762\pi$
$613$	−18.1605	+	13.1944i	−0.733496	+	0.532916i	0.157171	+	0.987571i	$0.449762\pi$
$614$		0			0
$615$	10.9701	−	10.0636i	0.442359	−	0.405804i
$616$		0			0
$617$	7.76290	−	5.64007i	0.312522	−	0.227061i	−0.420456	−	0.907313i	$-0.638130\pi$
$617$	7.76290	−	5.64007i	0.312522	−	0.227061i	0.732978	+	0.680252i	$0.238130\pi$
$618$		0			0
$619$	7.06024	−	21.7292i	0.283775	−	0.873370i	−0.702988	−	0.711202i	$-0.748151\pi$
$619$	7.06024	−	21.7292i	0.283775	−	0.873370i	0.986763	−	0.162168i	$-0.0518488\pi$
$620$		0			0
$621$	5.68132	+	7.81967i	0.227984	+	0.313793i
$622$		0			0
$623$	6.94810	+	21.3841i	0.278370	+	0.856734i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$		0			0
$627$	5.38637	+	1.75014i	0.215111	+	0.0698938i
$628$		0			0
$629$		−	56.3295i		−	2.24601i
$630$		0			0
$631$	−1.59850	−	1.16138i	−0.0636352	−	0.0462336i	0.555513	−	0.831508i	$-0.312522\pi$
$631$	−1.59850	−	1.16138i	−0.0636352	−	0.0462336i	−0.619148	+	0.785274i	$0.712522\pi$
$632$		0			0
$633$	−3.15908	+	2.29521i	−0.125562	+	0.0912263i
$634$		0			0
$635$	−0.849376	−	0.617108i	−0.0337065	−	0.0244892i
$636$		0			0
$637$	−2.76545	+	3.80632i	−0.109571	+	0.150812i
$638$		0			0
$639$	19.0835	−	6.20061i	0.754932	−	0.245292i
$640$		0			0
$641$	2.86950	+	0.932358i	0.113339	+	0.0368259i	0.365137	−	0.930954i	$-0.381022\pi$
$641$	2.86950	+	0.932358i	0.113339	+	0.0368259i	−0.251799	+	0.967780i	$0.581022\pi$
$642$		0			0
$643$	−11.9916	−	16.5050i	−0.472902	−	0.650894i	0.504220	−	0.863576i	$-0.331780\pi$
$643$	−11.9916	−	16.5050i	−0.472902	−	0.650894i	−0.977122	+	0.212682i	$0.931780\pi$
$644$		0			0
$645$	−3.51952	+	1.14356i	−0.138581	+	0.0450277i
$646$		0			0
$647$	1.04860			0.0412249			0.0206124	−	0.999788i	$-0.493438\pi$
$647$	1.04860			0.0412249			0.0206124	+	0.999788i	$0.493438\pi$
$648$		0			0
$649$	0.405026	−	0.557470i	0.0158986	−	0.0218826i
$650$		0			0
$651$	18.5523	−	57.0981i	0.727122	−	2.23785i
$652$		0			0
$653$		−	16.5195i		−	0.646459i	−0.946321	−	0.323229i	$-0.895231\pi$
$653$		−	16.5195i		−	0.646459i	0.946321	−	0.323229i	$-0.104769\pi$
$654$		0			0
$655$	−4.22776			−0.165192
$656$		0			0
$657$	−30.0721			−1.17322
$658$		0			0
$659$			30.3738i			1.18320i	0.806233	+	0.591598i	$0.201503\pi$
$659$			30.3738i			1.18320i	−0.806233	+	0.591598i	$0.798497\pi$
$660$		0			0
$661$	0.921102	−	2.83486i	0.0358267	−	0.110263i	−0.931544	−	0.363629i	$-0.881538\pi$
$661$	0.921102	−	2.83486i	0.0358267	−	0.110263i	0.967371	+	0.253366i	$0.0815376\pi$
$662$		0			0
$663$	37.6286	−	51.7913i	1.46137	−	2.01141i
$664$		0			0
$665$	16.9305			0.656538
$666$		0			0
$667$	−5.99579	+	1.94815i	−0.232158	+	0.0754327i
$668$		0			0
$669$	−0.941233	−	1.29550i	−0.0363902	−	0.0500867i
$670$		0			0
$671$	4.95749	+	1.61079i	0.191382	+	0.0621837i
$672$		0			0
$673$	−10.8983	+	3.54107i	−0.420098	+	0.136498i	−0.511435	−	0.859322i	$-0.670886\pi$
$673$	−10.8983	+	3.54107i	−0.420098	+	0.136498i	0.0913369	+	0.995820i	$0.470886\pi$
$674$		0			0
$675$	−0.812598	+	1.11845i	−0.0312769	+	0.0430490i
$676$		0			0
$677$	−14.7150	−	10.6911i	−0.565542	−	0.410891i	0.267941	−	0.963435i	$-0.413657\pi$
$677$	−14.7150	−	10.6911i	−0.565542	−	0.410891i	−0.833483	+	0.552545i	$0.813657\pi$
$678$		0			0
$679$	24.3601	−	17.6986i	0.934853	−	0.679210i
$680$		0			0
$681$	−53.5618	−	38.9149i	−2.05249	−	1.49122i
$682$		0			0
$683$			37.5823i			1.43805i	0.694985	+	0.719024i	$0.255411\pi$
$683$			37.5823i			1.43805i	−0.694985	+	0.719024i	$0.744589\pi$
$684$		0			0
$685$	20.4279	+	6.63743i	0.780510	+	0.253603i
$686$		0			0
$687$	−5.11513	−	15.7428i	−0.195154	−	0.600624i
$688$		0			0
$689$	−9.97522	−	30.7006i	−0.380026	−	1.16960i
$690$		0			0
$691$	−3.70830	−	5.10404i	−0.141070	−	0.194167i	0.732636	−	0.680621i	$-0.238290\pi$
$691$	−3.70830	−	5.10404i	−0.141070	−	0.194167i	−0.873706	+	0.486454i	$0.838290\pi$
$692$		0			0
$693$	0.848059	−	2.61006i	0.0322151	−	0.0991478i
$694$		0			0
$695$	18.6449	−	13.5463i	0.707243	−	0.513842i
$696$		0			0
$697$	−6.92644	+	34.1426i	−0.262358	+	1.29324i
$698$		0			0
$699$	−27.6886	+	20.1170i	−1.04728	+	0.760893i
$700$		0			0
$701$	0.637975	−	1.96348i	0.0240960	−	0.0741598i	−0.938285	−	0.345862i	$-0.887587\pi$
$701$	0.637975	−	1.96348i	0.0240960	−	0.0741598i	0.962381	+	0.271702i	$0.0875866\pi$
$702$		0			0
$703$	−36.5877	−	50.3587i	−1.37993	−	1.89931i
$704$		0			0
$705$	1.17121	+	3.60462i	0.0441104	+	0.135758i
$706$		0			0
$707$	7.17404	+	22.0794i	0.269807	+	0.830382i
$708$		0			0
$709$	−14.5949	−	4.74217i	−0.548122	−	0.178096i	0.0218475	−	0.999761i	$-0.493045\pi$
$709$	−14.5949	−	4.74217i	−0.548122	−	0.178096i	−0.569970	+	0.821666i	$0.693045\pi$
$710$		0			0
$711$			13.2473i			0.496814i
$712$		0			0
$713$	51.8688	+	37.6849i	1.94250	+	1.41131i
$714$		0			0
$715$	1.65888	−	1.20525i	0.0620386	−	0.0450737i
$716$		0			0
$717$	−17.1444	−	12.4561i	−0.640268	−	0.465182i
$718$		0			0
$719$	−10.4061	+	14.3227i	−0.388081	+	0.534147i	−0.957703	−	0.287760i	$-0.907090\pi$
$719$	−10.4061	+	14.3227i	−0.388081	+	0.534147i	0.569622	+	0.821907i	$0.307090\pi$
$720$		0			0
$721$	1.48133	−	0.481313i	0.0551676	−	0.0179250i
$722$		0			0
$723$	36.4787	+	11.8526i	1.35666	+	0.440804i
$724$		0			0
$725$	−0.530012	−	0.729498i	−0.0196841	−	0.0270929i
$726$		0			0
$727$	1.92943	−	0.626910i	0.0715586	−	0.0232508i	−0.273019	−	0.962009i	$-0.588022\pi$
$727$	1.92943	−	0.626910i	0.0715586	−	0.0232508i	0.344578	+	0.938758i	$0.388022\pi$
$728$		0			0
$729$	15.4462			0.572083
$730$		0			0
$731$	5.09033	−	7.00624i	0.188273	−	0.259135i
$732$		0			0
$733$	−1.46928	+	4.52199i	−0.0542692	+	0.167023i	−0.974517	−	0.224312i	$-0.927987\pi$
$733$	−1.46928	+	4.52199i	−0.0542692	+	0.167023i	0.920248	+	0.391335i	$0.127987\pi$
$734$		0			0
$735$		−	2.16141i		−	0.0797246i
$736$		0			0
$737$	−4.12598			−0.151982
$738$		0			0
$739$	−49.9496			−1.83743			−0.918713	−	0.394926i	$-0.870770\pi$
$739$	−49.9496			−1.83743			−0.918713	+	0.394926i	$0.870770\pi$
$740$		0			0
$741$		−	70.7424i		−	2.59879i
$742$		0			0
$743$	−2.07778	+	6.39474i	−0.0762263	+	0.234600i	−0.981908	−	0.189357i	$-0.939360\pi$
$743$	−2.07778	+	6.39474i	−0.0762263	+	0.234600i	0.905682	+	0.423958i	$0.139360\pi$
$744$		0			0
$745$	−9.51338	+	13.0940i	−0.348543	+	0.479729i
$746$		0			0
$747$	33.9329			1.24154
$748$		0			0
$749$	−8.57273	+	2.78545i	−0.313241	+	0.101778i
$750$		0			0
$751$	−27.9581	−	38.4810i	−1.02020	−	1.40419i	−0.912061	−	0.410055i	$-0.865510\pi$
$751$	−27.9581	−	38.4810i	−1.02020	−	1.40419i	−0.108143	−	0.994135i	$-0.534490\pi$
$752$		0			0
$753$	37.7301	+	12.2592i	1.37496	+	0.446752i
$754$		0			0
$755$	−4.37209	+	1.42058i	−0.159117	+	0.0517002i
$756$		0			0
$757$	15.8440	−	21.8074i	0.575860	−	0.792603i	−0.417374	−	0.908735i	$-0.637050\pi$
$757$	15.8440	−	21.8074i	0.575860	−	0.792603i	0.993234	+	0.116132i	$0.0370495\pi$
$758$		0			0
$759$	5.32817	+	3.87114i	0.193400	+	0.140513i
$760$		0			0
$761$	−34.3567	+	24.9616i	−1.24543	+	0.904857i	−0.997948	−	0.0640359i	$-0.979603\pi$
$761$	−34.3567	+	24.9616i	−1.24543	+	0.904857i	−0.247481	+	0.968893i	$0.579603\pi$
$762$		0			0
$763$	−13.7996	−	10.0260i	−0.499578	−	0.362964i
$764$		0			0
$765$			13.0871i			0.473167i
$766$		0			0
$767$	−8.18578	−	2.65972i	−0.295571	−	0.0960370i
$768$		0			0
$769$	−0.424876	−	1.30763i	−0.0153214	−	0.0471545i	0.943104	−	0.332499i	$-0.107892\pi$
$769$	−0.424876	−	1.30763i	−0.0153214	−	0.0471545i	−0.958425	+	0.285345i	$0.907892\pi$
$770$		0			0
$771$	−17.8740	−	55.0105i	−0.643717	−	1.98116i
$772$		0			0
$773$	15.0643	+	20.7342i	0.541825	+	0.745758i	0.988875	−	0.148751i	$-0.0475254\pi$
$773$	15.0643	+	20.7342i	0.541825	+	0.745758i	−0.447050	+	0.894509i	$0.647525\pi$
$774$		0			0
$775$	−2.83372	+	8.72130i	−0.101790	+	0.313278i
$776$		0			0
$777$	−54.8367	+	39.8412i	−1.96726	+	1.42930i
$778$		0			0
$779$	15.9844	+	35.0225i	0.572701	+	1.25481i
$780$		0			0
$781$	−2.73439	+	1.98665i	−0.0978443	+	0.0710880i
$782$		0			0
$783$	0.385218	−	1.18558i	0.0137666	−	0.0423691i
$784$		0			0
$785$	−6.29764	−	8.66796i	−0.224772	−	0.309373i
$786$		0			0
$787$	1.26430	+	3.89110i	0.0450673	+	0.138703i	0.971058	−	0.238843i	$-0.0767681\pi$
$787$	1.26430	+	3.89110i	0.0450673	+	0.138703i	−0.925991	+	0.377546i	$0.876768\pi$
$788$		0			0
$789$	−3.86213	−	11.8864i	−0.137495	−	0.423167i
$790$		0			0
$791$	39.7464	+	12.9144i	1.41322	+	0.459182i
$792$		0			0
$793$		−	65.1097i		−	2.31211i
$794$		0			0
$795$	11.9974	+	8.71662i	0.425504	+	0.309147i
$796$		0			0
$797$	30.4676	−	22.1360i	1.07922	−	0.784096i	0.101670	−	0.994818i	$-0.467581\pi$
$797$	30.4676	−	22.1360i	1.07922	−	0.784096i	0.977546	+	0.210722i	$0.0675814\pi$
$798$		0			0
$799$	−7.17564	−	5.21341i	−0.253856	−	0.184437i
$800$		0			0
$801$	−11.2891	+	15.5381i	−0.398879	+	0.549010i
$802$		0			0
$803$	4.81749	−	1.56530i	0.170005	−	0.0552381i
$804$		0			0
$805$	18.7244	+	6.08392i	0.659947	+	0.214430i
$806$		0			0
$807$	−18.3796	−	25.2973i	−0.646992	−	0.890508i
$808$		0			0
$809$	33.6932	−	10.9476i	1.18459	−	0.384897i	0.350520	−	0.936555i	$-0.386005\pi$
$809$	33.6932	−	10.9476i	1.18459	−	0.384897i	0.834070	+	0.551659i	$0.186005\pi$
$810$		0			0
$811$	42.3997			1.48885			0.744427	−	0.667704i	$-0.232723\pi$
$811$	42.3997			1.48885			0.744427	+	0.667704i	$0.232723\pi$
$812$		0			0
$813$	−26.1022	+	35.9266i	−0.915444	+	1.26000i
$814$		0			0
$815$	1.13019	−	3.47835i	0.0395887	−	0.121841i
$816$		0			0
$817$		−	9.56992i		−	0.334809i
$818$		0			0
$819$	−34.2794			−1.19782
$820$		0			0
$821$	14.6675			0.511898			0.255949	−	0.966690i	$-0.417612\pi$
$821$	14.6675			0.511898			0.255949	+	0.966690i	$0.417612\pi$
$822$		0			0
$823$		−	6.71194i		−	0.233964i	−0.993134	−	0.116982i	$-0.962678\pi$
$823$		−	6.71194i		−	0.233964i	0.993134	−	0.116982i	$-0.0373219\pi$
$824$		0			0
$825$	−0.291091	+	0.895886i	−0.0101345	+	0.0311908i
$826$		0			0
$827$	28.1028	−	38.6803i	0.977232	−	1.34504i	0.0389243	−	0.999242i	$-0.487607\pi$
$827$	28.1028	−	38.6803i	0.977232	−	1.34504i	0.938308	−	0.345802i	$-0.112393\pi$
$828$		0			0
$829$	7.39404			0.256806			0.128403	−	0.991722i	$-0.459015\pi$
$829$	7.39404			0.256806			0.128403	+	0.991722i	$0.459015\pi$
$830$		0			0
$831$	61.3017	−	19.9181i	2.12653	−	0.690953i
$832$		0			0
$833$	2.97307	+	4.09207i	0.103011	+	0.141782i
$834$		0			0
$835$	−10.1658	−	3.30308i	−0.351803	−	0.114308i
$836$		0			0
$837$	−12.0570	+	3.91755i	−0.416750	+	0.135410i
$838$		0			0
$839$	−13.3186	+	18.3315i	−0.459808	+	0.632872i	−0.974469	−	0.224522i	$-0.927918\pi$
$839$	−13.3186	+	18.3315i	−0.459808	+	0.632872i	0.514661	+	0.857394i	$0.327918\pi$
$840$		0			0
$841$	−22.8037	−	16.5679i	−0.786334	−	0.571305i
$842$		0			0
$843$	5.77727	−	4.19743i	0.198980	−	0.144567i
$844$		0			0
$845$	−10.2035	−	7.41329i	−0.351012	−	0.255025i
$846$		0			0
$847$		−	30.5133i		−	1.04845i
$848$		0			0
$849$	14.5978	+	4.74310i	0.500994	+	0.162783i
$850$		0			0
$851$	−22.3681	−	68.8420i	−0.766770	−	2.35987i
$852$		0			0
$853$	2.47707	+	7.62362i	0.0848131	+	0.261028i	0.984465	−	0.175579i	$-0.0561799\pi$
$853$	2.47707	+	7.62362i	0.0848131	+	0.261028i	−0.899652	+	0.436607i	$0.856180\pi$
$854$		0			0
$855$	8.50050	+	11.6999i	0.290711	+	0.400129i
$856$		0			0
$857$	−11.1936	+	34.4503i	−0.382366	+	1.17680i	0.556008	+	0.831177i	$0.312332\pi$
$857$	−11.1936	+	34.4503i	−0.382366	+	1.17680i	−0.938373	+	0.345623i	$0.887668\pi$
$858$		0			0
$859$	16.3393	−	11.8712i	0.557491	−	0.405041i	−0.273049	−	0.962000i	$-0.588032\pi$
$859$	16.3393	−	11.8712i	0.557491	−	0.405041i	0.830540	+	0.556959i	$0.188032\pi$
$860$		0			0
$861$	38.1368	−	17.4058i	1.29970	−	0.593187i
$862$		0			0
$863$	−23.6435	+	17.1780i	−0.804832	+	0.584745i	−0.912328	−	0.409461i	$-0.865717\pi$
$863$	−23.6435	+	17.1780i	−0.804832	+	0.584745i	0.107495	+	0.994206i	$0.465717\pi$
$864$		0			0
$865$	−4.56430	+	14.0475i	−0.155191	+	0.477628i
$866$		0			0
$867$	−17.2218	−	23.7038i	−0.584885	−	0.805025i
$868$		0			0
$869$	−0.689544	−	2.12220i	−0.0233912	−	0.0719906i
$870$		0			0
$871$	15.9257	+	49.0143i	0.539623	+	1.66079i
$872$		0			0
$873$	24.4614	+	7.94801i	0.827895	+	0.268999i
$874$		0			0
$875$			2.81596i			0.0951970i
$876$		0			0
$877$	−15.5810	−	11.3203i	−0.526134	−	0.382259i	0.292776	−	0.956181i	$-0.405421\pi$
$877$	−15.5810	−	11.3203i	−0.526134	−	0.382259i	−0.818910	+	0.573923i	$0.805421\pi$
$878$		0			0
$879$	−33.2965	+	24.1914i	−1.12306	+	0.815954i
$880$		0			0
$881$	−28.9917	−	21.0637i	−0.976756	−	0.709655i	−0.0197747	−	0.999804i	$-0.506295\pi$
$881$	−28.9917	−	21.0637i	−0.976756	−	0.709655i	−0.956981	+	0.290150i	$0.906295\pi$
$882$		0			0
$883$	13.3058	−	18.3139i	0.447777	−	0.616313i	−0.524141	−	0.851632i	$-0.675613\pi$
$883$	13.3058	−	18.3139i	0.447777	−	0.616313i	0.971918	+	0.235319i	$0.0756135\pi$
$884$		0			0
$885$	3.76053	−	1.22187i	0.126409	−	0.0410727i
$886$		0			0
$887$	−38.0461	−	12.3619i	−1.27746	−	0.415073i	−0.409777	−	0.912186i	$-0.634394\pi$
$887$	−38.0461	−	12.3619i	−1.27746	−	0.415073i	−0.867686	+	0.497113i	$0.834394\pi$
$888$		0			0
$889$	−1.73775	−	2.39181i	−0.0582824	−	0.0802188i
$890$		0			0
$891$	−4.01917	+	1.30591i	−0.134647	+	0.0437496i
$892$		0			0
$893$	−9.80130			−0.327988
$894$		0			0
$895$	5.80236	−	7.98626i	0.193952	−	0.266951i
$896$		0			0
$897$	25.4210	−	78.2378i	0.848783	−	2.61228i
$898$		0			0
$899$		−	8.26878i		−	0.275779i
$900$		0			0
$901$	−34.7039			−1.15616
$902$		0			0
$903$	−10.4209			−0.346786
$904$		0			0
$905$		−	13.0221i		−	0.432869i
$906$		0			0
$907$	2.67591	−	8.23561i	0.0888522	−	0.273459i	−0.896751	−	0.442536i	$-0.854079\pi$
$907$	2.67591	−	8.23561i	0.0888522	−	0.273459i	0.985603	+	0.169077i	$0.0540788\pi$
$908$		0			0
$909$	−11.6561	+	16.0433i	−0.386610	+	0.532123i
$910$		0			0
$911$	30.1434			0.998696			0.499348	−	0.866401i	$-0.333573\pi$
$911$	30.1434			0.998696			0.499348	+	0.866401i	$0.333573\pi$
$912$		0			0
$913$	−5.43599	+	1.76626i	−0.179905	+	0.0584547i
$914$		0			0
$915$	17.5814	+	24.1987i	0.581223	+	0.799985i
$916$		0			0
$917$	−11.3225	−	3.67891i	−0.373903	−	0.121488i
$918$		0			0
$919$	12.5886	−	4.09029i	0.415260	−	0.134926i	−0.0939329	−	0.995579i	$-0.529944\pi$
$919$	12.5886	−	4.09029i	0.415260	−	0.134926i	0.509193	+	0.860652i	$0.329944\pi$
$920$		0			0
$921$	21.4797	−	29.5643i	0.707782	−	0.974178i
$922$		0			0
$923$	34.1547	+	24.8149i	1.12422	+	0.816792i
$924$		0			0
$925$	8.37590	−	6.08545i	0.275398	−	0.200088i
$926$		0			0
$927$	1.07636	+	0.782023i	0.0353524	+	0.0256850i
$928$		0			0
$929$			13.7716i			0.451830i	0.974147	+	0.225915i	$0.0725372\pi$
$929$			13.7716i			0.451830i	−0.974147	+	0.225915i	$0.927463\pi$
$930$		0			0
$931$	5.31585	+	1.72723i	0.174220	+	0.0566075i
$932$		0			0
$933$	7.08289	+	21.7989i	0.231883	+	0.713664i
$934$		0			0
$935$	−0.681206	−	2.09654i	−0.0222778	−	0.0685641i
$936$		0			0
$937$	−3.95603	−	5.44501i	−0.129238	−	0.177881i	0.739494	−	0.673163i	$-0.235065\pi$
$937$	−3.95603	−	5.44501i	−0.129238	−	0.177881i	−0.868732	+	0.495282i	$0.835065\pi$
$938$		0			0
$939$	−0.0267975	+	0.0824741i	−0.000874502	+	0.00269144i
$940$		0			0
$941$	19.7534	−	14.3517i	0.643943	−	0.467852i	−0.217260	−	0.976114i	$-0.569712\pi$
$941$	19.7534	−	14.3517i	0.643943	−	0.467852i	0.861202	+	0.508262i	$0.169712\pi$
$942$		0			0
$943$	5.09281	+	44.4772i	0.165845	+	1.44838i
$944$		0			0
$945$	−3.14950	+	2.28825i	−0.102453	+	0.0744367i
$946$		0			0
$947$	−1.56232	+	4.80834i	−0.0507687	+	0.156250i	−0.973227	−	0.229848i	$-0.926177\pi$
$947$	−1.56232	+	4.80834i	−0.0507687	+	0.156250i	0.922458	+	0.386098i	$0.126177\pi$
$948$		0			0
$949$	−37.1897	−	51.1873i	−1.20723	−	1.66161i
$950$		0			0
$951$	23.7643	+	73.1389i	0.770609	+	2.37169i
$952$		0			0
$953$	−2.76187	−	8.50016i	−0.0894657	−	0.275347i	0.896306	−	0.443436i	$-0.146241\pi$
$953$	−2.76187	−	8.50016i	−0.0894657	−	0.275347i	−0.985772	+	0.168089i	$0.946241\pi$
$954$		0			0
$955$	−7.39575	−	2.40303i	−0.239321	−	0.0777601i
$956$		0			0
$957$		−	0.849402i		−	0.0274573i
$958$		0			0
$959$	48.9331	+	35.5519i	1.58013	+	1.14803i
$960$		0			0
$961$	−42.9516	+	31.2062i	−1.38554	+	1.00665i
$962$		0			0
$963$	−6.22911	−	4.52571i	−0.200730	−	0.145839i
$964$		0			0
$965$	12.4923	−	17.1942i	0.402141	−	0.553500i
$966$		0			0
$967$	47.4002	−	15.4013i	1.52429	−	0.495271i	0.577297	−	0.816534i	$-0.304107\pi$
$967$	47.4002	−	15.4013i	1.52429	−	0.495271i	0.946990	+	0.321263i	$0.104107\pi$
$968$		0			0
$969$	−72.3311	−	23.5018i	−2.32361	−	0.754986i
$970$		0			0
$971$	28.8587	+	39.7205i	0.926118	+	1.27469i	0.961355	+	0.275313i	$0.0887816\pi$
$971$	28.8587	+	39.7205i	0.926118	+	1.27469i	−0.0352363	+	0.999379i	$0.511218\pi$
$972$		0			0
$973$	61.7216	−	20.0545i	1.97870	−	0.642919i
$974$		0			0
$975$	11.7662			0.376820
$976$		0			0
$977$	−4.05110	+	5.57586i	−0.129606	+	0.178387i	−0.868888	−	0.495008i	$-0.835165\pi$
$977$	−4.05110	+	5.57586i	−0.129606	+	0.178387i	0.739282	+	0.673396i	$0.235165\pi$
$978$		0			0
$979$	0.999707	−	3.07678i	0.0319508	−	0.0983343i
$980$		0			0
$981$		−	14.5701i		−	0.465188i
$982$		0			0
$983$	−41.4969			−1.32354			−0.661772	−	0.749705i	$-0.730196\pi$
$983$	−41.4969			−1.32354			−0.661772	+	0.749705i	$0.730196\pi$
$984$		0			0
$985$	1.59143			0.0507071
$986$		0			0
$987$			10.6729i			0.339721i
$988$		0			0
$989$	3.43891	−	10.5839i	0.109351	−	0.336548i
$990$		0			0
$991$	−20.7075	+	28.5015i	−0.657796	+	0.905378i	−0.999406	−	0.0344633i	$-0.989028\pi$
$991$	−20.7075	+	28.5015i	−0.657796	+	0.905378i	0.341610	+	0.939842i	$0.389028\pi$
$992$		0			0
$993$	37.7665			1.19848
$994$		0			0
$995$	−10.6696	+	3.46675i	−0.338248	+	0.109903i
$996$		0			0
$997$	13.1909	+	18.1557i	0.417760	+	0.574998i	0.965090	−	0.261919i	$-0.0843555\pi$
$997$	13.1909	+	18.1557i	0.417760	+	0.574998i	−0.547329	+	0.836917i	$0.684355\pi$
$998$		0			0
$999$	13.6125	+	4.42296i	0.430680	+	0.139936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bg.a.701.1	yes	24
41.31	even	10	inner	820.2.bg.a.441.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bg.a.441.6	✓	24	41.31	even	10	inner
820.2.bg.a.701.1	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q-2.32495i q^{3} +(-0.309017 + 0.951057i) q^{5} +(-1.65518 + 2.27816i) q^{7} -2.40537 q^{9} +(0.385336 - 0.125203i) q^{11} +(-2.97470 - 4.09432i) q^{13} +(2.21115 + 0.718448i) q^{15} +(-5.17450 + 1.68130i) q^{17} +(-3.53396 + 4.86408i) q^{19} +(5.29661 + 3.84821i) q^{21} +(-5.65628 + 4.10953i) q^{23} +(-0.809017 - 0.587785i) q^{25} -1.38247i q^{27} +(0.857577 + 0.278644i) q^{29} +(-2.83372 - 8.72130i) q^{31} +(-0.291091 - 0.895886i) q^{33} +(-1.65518 - 2.27816i) q^{35} +(-3.19931 + 9.84646i) q^{37} +(-9.51907 + 6.91601i) q^{39} +(3.14992 - 5.57476i) q^{41} +(-1.28772 + 0.935586i) q^{43} +(0.743301 - 2.28765i) q^{45} +(0.958207 + 1.31886i) q^{47} +(-0.287280 - 0.884158i) q^{49} +(3.90893 + 12.0304i) q^{51} +(6.06629 + 1.97106i) q^{53} +0.405167i q^{55} +(11.3087 + 8.21627i) q^{57} +(1.37590 - 0.999652i) q^{59} +(10.4083 + 7.56207i) q^{61} +(3.98133 - 5.47983i) q^{63} +(4.81316 - 1.56389i) q^{65} +(-9.68499 - 3.14684i) q^{67} +(9.55444 + 13.1506i) q^{69} +(-7.93370 + 2.57782i) q^{71} +12.5020 q^{73} +(-1.36657 + 1.88092i) q^{75} +(-0.352568 + 1.08509i) q^{77} -5.50739i q^{79} -10.4303 q^{81} -14.1071 q^{83} -5.44080i q^{85} +(0.647831 - 1.99382i) q^{87} +(4.69327 - 6.45973i) q^{89} +14.2512 q^{91} +(-20.2766 + 6.58825i) q^{93} +(-3.53396 - 4.86408i) q^{95} +(-10.1695 - 3.30427i) q^{97} +(-0.926878 + 0.301161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{5} + 5 q^{7} - 6 q^{9} + 5 q^{11} - 5 q^{13} - 5 q^{17} - 5 q^{19} - 6 q^{21} + 10 q^{23} - 6 q^{25} - 25 q^{29} + 7 q^{31} - 12 q^{33} + 5 q^{35} - 13 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{43}+ \cdots - 60 q^{99}+O(q^{100}) \) 24 * q + 6 * q^5 + 5 * q^7 - 6 * q^9 + 5 * q^11 - 5 * q^13 - 5 * q^17 - 5 * q^19 - 6 * q^21 + 10 * q^23 - 6 * q^25 - 25 * q^29 + 7 * q^31 - 12 * q^33 + 5 * q^35 - 13 * q^37 + 4 * q^39 + 6 * q^41 + 14 * q^43 + q^45 - 35 * q^47 + 23 * q^49 - 27 * q^51 + 35 * q^53 + 9 * q^57 - 14 * q^59 + 22 * q^61 - 10 * q^63 + 5 * q^65 - 20 * q^67 - 55 * q^71 + 8 * q^73 - 5 * q^75 + 6 * q^77 - 28 * q^81 - 82 * q^83 - 27 * q^87 + 50 * q^89 + 70 * q^91 - 80 * q^93 - 5 * q^95 - 20 * q^97 - 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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