LMFDB - Embedded newform 700.2.p.c.551.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(451,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.451"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.58952814149$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			551.9
Character	$\chi$	$=$	700.551
Dual form			700.2.p.c.451.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0915727 - 1.41125i) q^{2} +(-1.49907 - 2.59647i) q^{3} +(-1.98323 + 0.258463i) q^{4} +(-3.52698 + 2.35332i) q^{6} +(-2.06101 + 1.65899i) q^{7} +(0.546365 + 2.77516i) q^{8} +(-2.99443 + 5.18651i) q^{9} +(1.93693 - 1.11828i) q^{11} +(3.64409 + 4.76194i) q^{12} +3.17109i q^{13} +(2.52997 + 2.75667i) q^{14} +(3.86639 - 1.02518i) q^{16} +(2.98390 - 1.72275i) q^{17} +(7.59365 + 3.75094i) q^{18} +(-1.02618 + 1.77739i) q^{19} +(7.39711 + 2.86441i) q^{21} +(-1.75554 - 2.63107i) q^{22} +(-2.30481 - 1.33068i) q^{23} +(6.38656 - 5.57878i) q^{24} +(4.47519 - 0.290385i) q^{26} +8.96105 q^{27} +(3.65867 - 3.82285i) q^{28} -7.38092 q^{29} +(2.44599 + 4.23658i) q^{31} +(-1.80084 - 5.36255i) q^{32} +(-5.80718 - 3.35278i) q^{33} +(-2.70447 - 4.05325i) q^{34} +(4.59812 - 11.0600i) q^{36} +(-5.59689 + 9.69410i) q^{37} +(2.60230 + 1.28543i) q^{38} +(8.23364 - 4.75369i) q^{39} -1.46011i q^{41} +(3.36501 - 10.7014i) q^{42} +9.95752i q^{43} +(-3.55233 + 2.71844i) q^{44} +(-1.66686 + 3.37451i) q^{46} +(3.06343 - 5.30601i) q^{47} +(-8.45786 - 8.50215i) q^{48} +(1.49553 - 6.83838i) q^{49} +(-8.94615 - 5.16506i) q^{51} +(-0.819610 - 6.28900i) q^{52} +(2.32888 + 4.03374i) q^{53} +(-0.820587 - 12.6462i) q^{54} +(-5.73001 - 4.81321i) q^{56} +6.15325 q^{57} +(0.675891 + 10.4163i) q^{58} +(3.55938 + 6.16503i) q^{59} +(-2.19681 - 1.26833i) q^{61} +(5.75488 - 3.83985i) q^{62} +(-2.43279 - 15.6572i) q^{63} +(-7.40297 + 3.03249i) q^{64} +(-4.19981 + 8.50238i) q^{66} +(-0.0456998 + 0.0263848i) q^{67} +(-5.47248 + 4.18784i) q^{68} +7.97917i q^{69} -0.212347i q^{71} +(-16.0294 - 5.47629i) q^{72} +(12.8816 - 7.43720i) q^{73} +(14.1933 + 7.01088i) q^{74} +(1.57575 - 3.79020i) q^{76} +(-2.13680 + 5.51813i) q^{77} +(-7.46261 - 11.1844i) q^{78} +(-0.399413 - 0.230601i) q^{79} +(-4.44995 - 7.70755i) q^{81} +(-2.06058 + 0.133707i) q^{82} +10.9174 q^{83} +(-15.4105 - 3.76890i) q^{84} +(14.0525 - 0.911837i) q^{86} +(11.0645 + 19.1643i) q^{87} +(4.16168 + 4.76428i) q^{88} +(6.07992 + 3.51024i) q^{89} +(-5.26080 - 6.53565i) q^{91} +(4.91490 + 2.04334i) q^{92} +(7.33344 - 12.7019i) q^{93} +(-7.76862 - 3.83736i) q^{94} +(-11.2241 + 12.7147i) q^{96} -0.185459i q^{97} +(-9.78758 - 1.48435i) q^{98} +13.3945i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 16 q^{9} + 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} + 8 q^{22} + 36 q^{24} + 30 q^{26} - 2 q^{28} - 40 q^{29} - 2 q^{32} + 60 q^{36} - 8 q^{37} + 60 q^{38} + 62 q^{42}+ \cdots - 78 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 16 * q^9 + 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 + 8 * q^22 + 36 * q^24 + 30 * q^26 - 2 * q^28 - 40 * q^29 - 2 * q^32 + 60 * q^36 - 8 * q^37 + 60 * q^38 + 62 * q^42 - 18 * q^44 + 2 * q^46 - 16 * q^49 + 36 * q^52 + 8 * q^53 + 12 * q^54 - 4 * q^56 - 48 * q^57 - 2 * q^58 + 24 * q^61 + 4 * q^64 + 24 * q^66 - 60 * q^68 - 4 * q^72 + 72 * q^73 + 38 * q^74 + 40 * q^77 - 120 * q^78 - 36 * q^81 - 42 * q^82 - 20 * q^84 + 28 * q^86 - 4 * q^88 - 60 * q^89 + 4 * q^92 + 8 * q^93 + 18 * q^94 - 60 * q^96 - 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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 $

$2$	−0.0915727	−	1.41125i	−0.0647517	−	0.997901i
$2$	−0.0915727	−	1.41125i	−0.0647517	−	0.997901i
$3$	−1.49907	−	2.59647i	−0.865490	−	1.49907i	−0.866560	−	0.499072i	$-0.833674\pi$
$3$	−1.49907	−	2.59647i	−0.865490	−	1.49907i	0.00107081	−	0.999999i	$-0.499659\pi$
$4$	−1.98323	+	0.258463i	−0.991614	+	0.129232i
$5$		0			0
$5$		0			0
$6$	−3.52698	+	2.35332i	−1.43988	+	0.960741i
$7$	−2.06101	+	1.65899i	−0.778989	+	0.627038i
$7$	−2.06101	+	1.65899i	−0.778989	+	0.627038i
$8$	0.546365	+	2.77516i	0.193169	+	0.981165i
$9$	−2.99443	+	5.18651i	−0.998144	+	1.72884i
$10$		0			0
$11$	1.93693	−	1.11828i	0.584005	−	0.337175i	−0.178718	−	0.983900i	$-0.557195\pi$
$11$	1.93693	−	1.11828i	0.584005	−	0.337175i	0.762723	+	0.646725i	$0.223862\pi$
$12$	3.64409	+	4.76194i	1.05196	+	1.37465i
$13$			3.17109i			0.879502i	0.898120	+	0.439751i	$0.144933\pi$
$13$			3.17109i			0.879502i	−0.898120	+	0.439751i	$0.855067\pi$
$14$	2.52997	+	2.75667i	0.676163	+	0.736752i
$15$		0			0
$16$	3.86639	−	1.02518i	0.966598	−	0.256296i
$17$	2.98390	−	1.72275i	0.723701	−	0.417829i	−0.0924124	−	0.995721i	$-0.529458\pi$
$17$	2.98390	−	1.72275i	0.723701	−	0.417829i	0.816113	+	0.577892i	$0.196124\pi$
$18$	7.59365	+	3.75094i	1.78984	+	0.884104i
$19$	−1.02618	+	1.77739i	−0.235421	+	0.407761i	−0.959395	−	0.282066i	$-0.908980\pi$
$19$	−1.02618	+	1.77739i	−0.235421	+	0.407761i	0.723974	+	0.689827i	$0.242314\pi$
$20$		0			0
$21$	7.39711	+	2.86441i	1.61418	+	0.625065i
$22$	−1.75554	−	2.63107i	−0.374283	−	0.560947i
$23$	−2.30481	−	1.33068i	−0.480587	−	0.277467i	0.240074	−	0.970755i	$-0.422828\pi$
$23$	−2.30481	−	1.33068i	−0.480587	−	0.277467i	−0.720661	+	0.693288i	$0.756162\pi$
$24$	6.38656	−	5.57878i	1.30365	−	1.13876i
$25$		0			0
$26$	4.47519	−	0.290385i	0.877657	−	0.0569493i
$27$	8.96105			1.72455
$28$	3.65867	−	3.82285i	0.691423	−	0.722450i
$29$	−7.38092			−1.37060			−0.685301	−	0.728260i	$-0.740329\pi$
$29$	−7.38092			−1.37060			−0.685301	+	0.728260i	$0.740329\pi$
$30$		0			0
$31$	2.44599	+	4.23658i	0.439313	+	0.760913i	0.997637	−	0.0687104i	$-0.0218884\pi$
$31$	2.44599	+	4.23658i	0.439313	+	0.760913i	−0.558323	+	0.829623i	$0.688555\pi$
$32$	−1.80084	−	5.36255i	−0.318347	−	0.947974i
$33$	−5.80718	−	3.35278i	−1.01090	−	0.583643i
$34$	−2.70447	−	4.05325i	−0.463813	−	0.695127i
$35$		0			0
$36$	4.59812	−	11.0600i	0.766354	−	1.84333i
$37$	−5.59689	+	9.69410i	−0.920123	+	1.59370i	−0.120902	+	0.992664i	$0.538579\pi$
$37$	−5.59689	+	9.69410i	−0.920123	+	1.59370i	−0.799222	+	0.601036i	$0.794755\pi$
$38$	2.60230	+	1.28543i	0.422149	+	0.208524i
$39$	8.23364	−	4.75369i	1.31844	−	0.761200i
$40$		0			0
$41$		−	1.46011i		−	0.228031i	−0.993479	−	0.114016i	$-0.963629\pi$
$41$		−	1.46011i		−	0.228031i	0.993479	−	0.114016i	$-0.0363714\pi$
$42$	3.36501	−	10.7014i	0.519233	−	1.65127i
$43$			9.95752i			1.51851i	0.650794	+	0.759254i	$0.274436\pi$
$43$			9.95752i			1.51851i	−0.650794	+	0.759254i	$0.725564\pi$
$44$	−3.55233	+	2.71844i	−0.535534	+	0.409820i
$45$		0			0
$46$	−1.66686	+	3.37451i	−0.245766	+	0.497545i
$47$	3.06343	−	5.30601i	0.446847	−	0.773962i	−0.551332	−	0.834286i	$-0.685880\pi$
$47$	3.06343	−	5.30601i	0.446847	−	0.773962i	0.998179	+	0.0603243i	$0.0192135\pi$
$48$	−8.45786	−	8.50215i	−1.22079	−	1.22718i
$49$	1.49553	−	6.83838i	0.213647	−	0.976911i
$50$		0			0
$51$	−8.94615	−	5.16506i	−1.25271	−	0.723253i
$52$	−0.819610	−	6.28900i	−0.113659	−	0.872127i
$53$	2.32888	+	4.03374i	0.319897	+	0.554077i	0.980466	−	0.196688i	$-0.0630185\pi$
$53$	2.32888	+	4.03374i	0.319897	+	0.554077i	−0.660570	+	0.750765i	$0.729685\pi$
$54$	−0.820587	−	12.6462i	−0.111668	−	1.72094i
$55$		0			0
$56$	−5.73001	−	4.81321i	−0.765705	−	0.643193i
$57$	6.15325			0.815018
$58$	0.675891	+	10.4163i	0.0887488	+	1.36773i
$59$	3.55938	+	6.16503i	0.463392	+	0.802619i	0.999127	−	0.0417674i	$-0.0132988\pi$
$59$	3.55938	+	6.16503i	0.463392	+	0.802619i	−0.535735	+	0.844386i	$0.679965\pi$
$60$		0			0
$61$	−2.19681	−	1.26833i	−0.281272	−	0.162393i	0.352727	−	0.935726i	$-0.385254\pi$
$61$	−2.19681	−	1.26833i	−0.281272	−	0.162393i	−0.633999	+	0.773334i	$0.718588\pi$
$62$	5.75488	−	3.83985i	0.730870	−	0.487662i
$63$	−2.43279	−	15.6572i	−0.306503	−	1.97262i
$64$	−7.40297	+	3.03249i	−0.925371	+	0.379062i
$65$		0			0
$66$	−4.19981	+	8.50238i	−0.516961	+	1.04657i
$67$	−0.0456998	+	0.0263848i	−0.00558311	+	0.00322341i	−0.502789	−	0.864409i	$-0.667693\pi$
$67$	−0.0456998	+	0.0263848i	−0.00558311	+	0.00322341i	0.497206	+	0.867633i	$0.334359\pi$
$68$	−5.47248	+	4.18784i	−0.663636	+	0.507850i
$69$			7.97917i			0.960579i
$70$		0			0
$71$		−	0.212347i		−	0.0252009i	−0.999921	−	0.0126005i	$-0.995989\pi$
$71$		−	0.212347i		−	0.0252009i	0.999921	−	0.0126005i	$-0.00401095\pi$
$72$	−16.0294	−	5.47629i	−1.88909	−	0.645387i
$73$	12.8816	−	7.43720i	1.50768	−	0.870459i	0.507719	−	0.861523i	$-0.330489\pi$
$73$	12.8816	−	7.43720i	1.50768	−	0.870459i	0.999960	−	0.00893589i	$-0.00284442\pi$
$74$	14.1933	+	7.01088i	1.64994	+	0.814998i
$75$		0			0
$76$	1.57575	−	3.79020i	0.180751	−	0.434766i
$77$	−2.13680	+	5.51813i	−0.243511	+	0.628849i
$78$	−7.46261	−	11.1844i	−0.844974	−	1.26638i
$79$	−0.399413	−	0.230601i	−0.0449375	−	0.0259447i	0.477363	−	0.878706i	$-0.341593\pi$
$79$	−0.399413	−	0.230601i	−0.0449375	−	0.0259447i	−0.522300	+	0.852762i	$0.674926\pi$
$80$		0			0
$81$	−4.44995	−	7.70755i	−0.494439	−	0.856394i
$82$	−2.06058	+	0.133707i	−0.227553	+	0.0147654i
$83$	10.9174			1.19834			0.599168	−	0.800624i	$-0.295498\pi$
$83$	10.9174			1.19834			0.599168	+	0.800624i	$0.295498\pi$
$84$	−15.4105	−	3.76890i	−1.68142	−	0.411221i
$85$		0			0
$86$	14.0525	−	0.911837i	1.51532	−	0.0983259i
$87$	11.0645	+	19.1643i	1.18624	+	2.05463i
$88$	4.16168	+	4.76428i	0.443637	+	0.507874i
$89$	6.07992	+	3.51024i	0.644470	+	0.372085i	0.786334	−	0.617801i	$-0.211976\pi$
$89$	6.07992	+	3.51024i	0.644470	+	0.372085i	−0.141864	+	0.989886i	$0.545310\pi$
$90$		0			0
$91$	−5.26080	−	6.53565i	−0.551481	−	0.685122i
$92$	4.91490	+	2.04334i	0.512414	+	0.213033i
$93$	7.33344	−	12.7019i	0.760442	−	1.31712i
$94$	−7.76862	−	3.83736i	−0.801272	−	0.395794i
$95$		0			0
$96$	−11.2241	+	12.7147i	−1.14556	+	1.29769i
$97$		−	0.185459i		−	0.0188305i	−0.999956	−	0.00941523i	$-0.997003\pi$
$97$		−	0.185459i		−	0.0188305i	0.999956	−	0.00941523i	$-0.00299701\pi$
$98$	−9.78758	−	1.48435i	−0.988695	−	0.149942i
$99$			13.3945i			1.34620i
$100$		0			0
$101$	−5.41172	+	3.12446i	−0.538486	+	0.310895i	−0.744465	−	0.667661i	$-0.767295\pi$
$101$	−5.41172	+	3.12446i	−0.538486	+	0.310895i	0.205979	+	0.978556i	$0.433962\pi$
$102$	−6.46995	+	13.0982i	−0.640620	+	1.29691i
$103$	−5.70918	+	9.88858i	−0.562542	+	0.974351i	0.434732	+	0.900560i	$0.356843\pi$
$103$	−5.70918	+	9.88858i	−0.562542	+	0.974351i	−0.997274	+	0.0737911i	$0.976490\pi$
$104$	−8.80027	+	1.73257i	−0.862937	+	0.169893i
$105$		0			0
$106$	5.47934	−	3.65601i	0.532201	−	0.355103i
$107$	2.25502	+	1.30194i	0.218001	+	0.125863i	0.605024	−	0.796207i	$-0.293163\pi$
$107$	2.25502	+	1.30194i	0.218001	+	0.125863i	−0.387023	+	0.922070i	$0.626497\pi$
$108$	−17.7718	+	2.31610i	−1.71009	+	0.222867i
$109$	−0.500946	−	0.867663i	−0.0479819	−	0.0831071i	0.841037	−	0.540978i	$-0.181946\pi$
$109$	−0.500946	−	0.867663i	−0.0479819	−	0.0831071i	−0.889019	+	0.457871i	$0.848612\pi$
$110$		0			0
$111$	33.5606			3.18543
$112$	−6.26791	+	8.52721i	−0.592262	+	0.805745i
$113$	−14.8588			−1.39780			−0.698899	−	0.715220i	$-0.746326\pi$
$113$	−14.8588			−1.39780			−0.698899	+	0.715220i	$0.746326\pi$
$114$	−0.563470	−	8.68375i	−0.0527738	−	0.813307i
$115$		0			0
$116$	14.6381	−	1.90770i	1.35911	−	0.177125i
$117$	−16.4469	−	9.49562i	−1.52052	−	0.877870i
$118$	8.37443	−	5.58771i	0.770929	−	0.514391i
$119$	−3.29182	+	8.50085i	−0.301760	+	0.779272i
$120$		0			0
$121$	−2.99888	+	5.19421i	−0.272626	+	0.472201i
$122$	−1.58875	+	3.21638i	−0.143839	+	0.291197i
$123$	−3.79114	+	2.18882i	−0.341836	+	0.197359i
$124$	−5.94597	−	7.76992i	−0.533963	−	0.697759i
$125$		0			0
$126$	−21.8733	+	4.86704i	−1.94863	+	0.433590i
$127$		−	3.02360i		−	0.268301i	−0.990961	−	0.134151i	$-0.957169\pi$
$127$		−	3.02360i		−	0.268301i	0.990961	−	0.134151i	$-0.0428306\pi$
$128$	4.95750	+	10.1697i	0.438186	+	0.898885i
$129$	25.8544	−	14.9270i	2.27635	−	1.31425i
$130$		0			0
$131$	−7.85267	+	13.6012i	−0.686091	+	1.18834i	0.287002	+	0.957930i	$0.407341\pi$
$131$	−7.85267	+	13.6012i	−0.686091	+	1.18834i	−0.973093	+	0.230414i	$0.925992\pi$
$132$	12.3835	+	5.14838i	1.07785	+	0.448109i
$133$	−0.833705	−	5.36563i	−0.0722914	−	0.465259i
$134$	0.0414202	+	0.0620775i	0.00357816	+	0.00536268i
$135$		0			0
$136$	6.41120	+	7.33952i	0.549756	+	0.629359i
$137$	4.80718	+	8.32628i	0.410705	+	0.711362i	0.994967	−	0.100203i	$-0.0319493\pi$
$137$	4.80718	+	8.32628i	0.410705	+	0.711362i	−0.584262	+	0.811565i	$0.698616\pi$
$138$	11.2606	−	0.730674i	0.958563	−	0.0621991i
$139$	7.49745			0.635925			0.317963	−	0.948103i	$-0.397001\pi$
$139$	7.49745			0.635925			0.317963	+	0.948103i	$0.397001\pi$
$140$		0			0
$141$	−18.3692			−1.54697
$142$	−0.299673	+	0.0194451i	−0.0251480	+	0.00163180i
$143$	3.54618	+	6.14217i	0.296547	+	0.513634i
$144$	−6.26053	+	23.1229i	−0.521711	+	1.92691i
$145$		0			0
$146$	−11.6753	−	17.4981i	−0.966257	−	1.44815i
$147$	−19.9975	+	6.36813i	−1.64937	+	0.525234i
$148$	8.59435	−	20.6722i	0.706451	−	1.69925i
$149$	−3.25066	+	5.63031i	−0.266305	+	0.461253i	−0.967905	−	0.251318i	$-0.919136\pi$
$149$	−3.25066	+	5.63031i	−0.266305	+	0.461253i	0.701600	+	0.712571i	$0.252469\pi$
$150$		0			0
$151$	−20.5029	+	11.8373i	−1.66850	+	0.963309i	−0.700052	+	0.714092i	$0.746840\pi$
$151$	−20.5029	+	11.8373i	−1.66850	+	0.963309i	−0.968448	+	0.249217i	$0.919827\pi$
$152$	−5.49320	−	1.87670i	−0.445557	−	0.152220i
$153$			20.6347i			1.66821i
$154$	7.98311	+	2.51025i	0.643297	+	0.202281i
$155$		0			0
$156$	−15.1005	+	11.5558i	−1.20901	+	0.925201i
$157$	−6.78313	+	3.91624i	−0.541353	+	0.312550i	−0.745627	−	0.666363i	$-0.767850\pi$
$157$	−6.78313	+	3.91624i	−0.541353	+	0.312550i	0.204274	+	0.978914i	$0.434517\pi$
$158$	−0.288860	+	0.584787i	−0.0229805	+	0.0465232i
$159$	6.98233	−	12.0937i	0.553734	−	0.959096i
$160$		0			0
$161$	6.95783	−	1.08110i	0.548354	−	0.0852026i
$162$	−10.4697	+	6.98578i	−0.822581	+	0.548855i
$163$	−9.39774	−	5.42579i	−0.736088	−	0.424980i	0.0845574	−	0.996419i	$-0.473052\pi$
$163$	−9.39774	−	5.42579i	−0.736088	−	0.424980i	−0.820645	+	0.571438i	$0.806386\pi$
$164$	0.377386	+	2.89574i	0.0294689	+	0.226119i
$165$		0			0
$166$	−0.999731	−	15.4071i	−0.0775942	−	1.19582i
$167$	−11.7476			−0.909058			−0.454529	−	0.890732i	$-0.650192\pi$
$167$	−11.7476			−0.909058			−0.454529	+	0.890732i	$0.650192\pi$
$168$	−3.90766	+	22.0931i	−0.301483	+	1.70452i
$169$	2.94418			0.226476
$170$		0			0
$171$	−6.14563	−	10.6445i	−0.469968	−	0.814009i
$172$	−2.57365	−	19.7480i	−0.196239	−	1.50577i
$173$	14.2785	+	8.24371i	1.08558	+	0.626758i	0.932395	−	0.361440i	$-0.117715\pi$
$173$	14.2785	+	8.24371i	1.08558	+	0.626758i	0.153181	+	0.988198i	$0.451048\pi$
$174$	26.0324	−	17.3697i	1.97351	−	1.31679i
$175$		0			0
$176$	6.34247	−	6.30943i	0.478082	−	0.475591i
$177$	10.6715	−	18.4836i	0.802122	−	1.38932i
$178$	4.39706	−	8.90170i	0.329574	−	0.667211i
$179$	7.88914	−	4.55480i	0.589662	−	0.340441i	−0.175302	−	0.984515i	$-0.556090\pi$
$179$	7.88914	−	4.55480i	0.589662	−	0.340441i	0.764964	+	0.644073i	$0.222757\pi$
$180$		0			0
$181$			16.5755i			1.23205i	0.787728	+	0.616023i	$0.211257\pi$
$181$			16.5755i			1.23205i	−0.787728	+	0.616023i	$0.788743\pi$
$182$	−8.74166	+	8.02276i	−0.647975	+	0.594687i
$183$			7.60525i			0.562196i
$184$	2.43359	−	7.12325i	0.179406	−	0.525133i
$185$		0			0
$186$	−18.5970	−	9.18614i	−1.36360	−	0.673560i
$187$	3.85305	−	6.67369i	0.281763	−	0.488028i
$188$	−4.70407	+	11.3148i	−0.343080	+	0.825218i
$189$	−18.4688	+	14.8663i	−1.34341	+	1.08136i
$190$		0			0
$191$	2.59197	+	1.49648i	0.187549	+	0.108281i	0.590834	−	0.806793i	$-0.298799\pi$
$191$	2.59197	+	1.49648i	0.187549	+	0.108281i	−0.403286	+	0.915074i	$0.632132\pi$
$192$	18.9714	+	14.6757i	1.36914	+	1.05912i
$193$	−7.35442	−	12.7382i	−0.529383	−	0.916918i	−0.999413	−	0.0342676i	$-0.989090\pi$
$193$	−7.35442	−	12.7382i	−0.529383	−	0.916918i	0.470030	−	0.882651i	$-0.344243\pi$
$194$	−0.261728	+	0.0169829i	−0.0187909	+	0.00121930i
$195$		0			0
$196$	−1.19851	+	13.9486i	−0.0856075	+	0.996329i
$197$	−4.81748			−0.343231			−0.171616	−	0.985164i	$-0.554899\pi$
$197$	−4.81748			−0.343231			−0.171616	+	0.985164i	$0.554899\pi$
$198$	18.9029	−	1.22657i	1.34337	−	0.0871686i
$199$	0.637180	+	1.10363i	0.0451685	+	0.0782342i	0.887726	−	0.460373i	$-0.152284\pi$
$199$	0.637180	+	1.10363i	0.0451685	+	0.0782342i	−0.842557	+	0.538607i	$0.818951\pi$
$200$		0			0
$201$	0.137014	+	0.0791053i	0.00966425	+	0.00557966i
$202$	4.90494	+	7.35115i	0.345110	+	0.517225i
$203$	15.2122	−	12.2448i	1.06768	−	0.859420i
$204$	19.0772	+	7.93125i	1.33567	+	0.555298i
$205$		0			0
$206$	14.4780	+	7.15153i	1.00873	+	0.498270i
$207$	13.8032	−	7.96929i	0.959390	−	0.553904i
$208$	3.25095	+	12.2607i	0.225413	+	0.850126i
$209$			4.59023i			0.317513i
$210$		0			0
$211$			3.70986i			0.255397i	0.991813	+	0.127698i	$0.0407590\pi$
$211$			3.70986i			0.255397i	−0.991813	+	0.127698i	$0.959241\pi$
$212$	−5.66128	−	7.39791i	−0.388818	−	0.508090i
$213$	−0.551351	+	0.318323i	−0.0377780	+	0.0218111i
$214$	1.63085	−	3.30161i	0.111483	−	0.225693i
$215$		0			0
$216$	4.89600	+	24.8683i	0.333131	+	1.69207i
$217$	−12.0697	−	4.67378i	−0.819342	−	0.317277i
$218$	−1.17861	+	0.786412i	−0.0798258	+	0.0532625i
$219$	−38.6209	−	22.2978i	−2.60976	−	1.50675i
$220$		0			0
$221$	5.46301	+	9.46220i	0.367482	+	0.636497i
$222$	−3.07323	−	47.3622i	−0.206262	−	3.17874i
$223$	−12.9581			−0.867737			−0.433869	−	0.900976i	$-0.642852\pi$
$223$	−12.9581			−0.867737			−0.433869	+	0.900976i	$0.642852\pi$
$224$	12.6080	+	8.06471i	0.842404	+	0.538846i
$225$		0			0
$226$	1.36066	+	20.9694i	0.0905098	+	1.39487i
$227$	−4.44626	−	7.70115i	−0.295109	−	0.511143i	0.679901	−	0.733304i	$-0.262023\pi$
$227$	−4.44626	−	7.70115i	−0.295109	−	0.511143i	−0.975010	+	0.222160i	$0.928689\pi$
$228$	−12.2033	+	1.59039i	−0.808183	+	0.105326i
$229$	−11.2113	−	6.47287i	−0.740866	−	0.427739i	0.0815180	−	0.996672i	$-0.474023\pi$
$229$	−11.2113	−	6.47287i	−0.740866	−	0.427739i	−0.822384	+	0.568933i	$0.807357\pi$
$230$		0			0
$231$	17.5309	−	2.72392i	1.15345	−	0.179221i
$232$	−4.03267	−	20.4832i	−0.264758	−	1.34479i
$233$	−7.60809	+	13.1776i	−0.498423	+	0.863294i	−0.999998	−	0.00182020i	$-0.999421\pi$
$233$	−7.60809	+	13.1776i	−0.498423	+	0.863294i	0.501576	+	0.865114i	$0.332754\pi$
$234$	−11.8946	+	24.0801i	−0.777572	+	1.57417i
$235$		0			0
$236$	−8.65250	−	11.3067i	−0.563230	−	0.736003i
$237$			1.38275i			0.0898194i
$238$	12.2982	+	3.86712i	0.797176	+	0.250668i
$239$		−	0.0438513i		−	0.00283650i	−0.999999	−	0.00141825i	$-0.999549\pi$
$239$		−	0.0438513i		−	0.00283650i	0.999999	−	0.00141825i	$-0.000451444\pi$
$240$		0			0
$241$	1.99236	−	1.15029i	0.128339	−	0.0740968i	−0.434456	−	0.900693i	$-0.643059\pi$
$241$	1.99236	−	1.15029i	0.128339	−	0.0740968i	0.562795	+	0.826596i	$0.309726\pi$
$242$	7.60493	+	3.75651i	0.488863	+	0.241478i
$243$	0.0999675	−	0.173149i	0.00641292	−	0.0111075i
$244$	4.68458	+	1.94759i	0.299900	+	0.124682i
$245$		0			0
$246$	3.43612	+	5.14979i	0.219079	+	0.328339i
$247$	−5.63627	−	3.25410i	−0.358627	−	0.207053i
$248$	−10.4208	+	9.10273i	−0.661720	+	0.578024i
$249$	−16.3659	−	28.3466i	−1.03715	−	1.79639i
$250$		0			0
$251$	−6.32409			−0.399173			−0.199587	−	0.979880i	$-0.563960\pi$
$251$	−6.32409			−0.399173			−0.199587	+	0.979880i	$0.563960\pi$
$252$	8.87159	+	30.4230i	0.558857	+	1.91647i
$253$	−5.95233			−0.374220
$254$	−4.26704	+	0.276879i	−0.267738	+	0.0173729i
$255$		0			0
$256$	13.8980	−	7.92752i	0.868625	−	0.495470i
$257$	12.3334	+	7.12068i	0.769335	+	0.444176i	0.832637	−	0.553819i	$-0.186830\pi$
$257$	12.3334	+	7.12068i	0.769335	+	0.444176i	−0.0633025	+	0.997994i	$0.520163\pi$
$258$	−23.4333	−	35.1200i	−1.45889	−	2.18648i
$259$	−4.54713	−	29.2648i	−0.282545	−	1.81843i
$260$		0			0
$261$	22.1017	−	38.2812i	1.36806	−	2.36955i
$262$	19.9138	+	9.83654i	1.23028	+	0.607704i
$263$	10.1744	−	5.87421i	0.627382	−	0.362219i	−0.152355	−	0.988326i	$-0.548686\pi$
$263$	10.1744	−	5.87421i	0.627382	−	0.362219i	0.779738	+	0.626107i	$0.215353\pi$
$264$	6.13164	−	17.9477i	0.377376	−	1.10460i
$265$		0			0
$266$	−7.49588	+	1.66791i	−0.459602	+	0.102266i
$267$		−	21.0484i		−	1.28814i
$268$	0.0838136	−	0.0641387i	0.00511973	−	0.00391790i
$269$	−7.35196	+	4.24466i	−0.448257	+	0.258801i	−0.707094	−	0.707120i	$-0.749994\pi$
$269$	−7.35196	+	4.24466i	−0.448257	+	0.258801i	0.258837	+	0.965921i	$0.416661\pi$
$270$		0			0
$271$	3.98686	−	6.90544i	0.242184	−	0.419476i	−0.719152	−	0.694853i	$-0.755469\pi$
$271$	3.98686	−	6.90544i	0.242184	−	0.419476i	0.961336	+	0.275377i	$0.0888028\pi$
$272$	9.77078	−	9.71988i	0.592440	−	0.589354i
$273$	−9.08330	+	23.4569i	−0.549746	+	1.41968i
$274$	11.3102	−	7.54657i	0.683275	−	0.455905i
$275$		0			0
$276$	−2.06232	−	15.8245i	−0.124137	−	0.952524i
$277$	−6.79754	−	11.7737i	−0.408425	−	0.707412i	0.586289	−	0.810102i	$-0.300588\pi$
$277$	−6.79754	−	11.7737i	−0.408425	−	0.707412i	−0.994713	+	0.102690i	$0.967255\pi$
$278$	−0.686562	−	10.5807i	−0.0411772	−	0.634591i
$279$	−29.2974			−1.75399
$280$		0			0
$281$	9.48286			0.565700			0.282850	−	0.959164i	$-0.408720\pi$
$281$	9.48286			0.565700			0.282850	+	0.959164i	$0.408720\pi$
$282$	1.68212	+	25.9235i	0.100169	+	1.54372i
$283$	−10.7746	−	18.6621i	−0.640483	−	1.10935i	−0.985325	−	0.170689i	$-0.945401\pi$
$283$	−10.7746	−	18.6621i	−0.640483	−	1.10935i	0.344842	−	0.938661i	$-0.387933\pi$
$284$	0.0548838	+	0.421132i	0.00325675	+	0.0249896i
$285$		0			0
$286$	8.34337	−	5.56699i	0.493354	−	0.329183i
$287$	2.42231	+	3.00931i	0.142984	+	0.177634i
$288$	33.2054	+	6.71772i	1.95665	+	0.395845i
$289$	−2.56424	+	4.44140i	−0.150838	+	0.261259i
$290$		0			0
$291$	−0.481537	+	0.278016i	−0.0282282	+	0.0162976i
$292$	−23.6249	+	18.0791i	−1.38255	+	1.05800i
$293$			28.9496i			1.69125i	0.533776	+	0.845626i	$0.320773\pi$
$293$			28.9496i			1.69125i	−0.533776	+	0.845626i	$0.679227\pi$
$294$	10.8182	+	27.6383i	0.630931	+	1.61190i
$295$		0			0
$296$	−29.9606	−	10.2357i	−1.74142	−	0.594940i
$297$	17.3569	−	10.0210i	1.00715	−	0.581477i
$298$	8.24342	+	4.07190i	0.477529	+	0.235879i
$299$	4.21972	−	7.30877i	0.244033	−	0.422677i
$300$		0			0
$301$	−16.5194	−	20.5226i	−0.952162	−	1.18290i
$302$	18.5829	+	27.8506i	1.06933	+	1.60262i
$303$	16.2251	+	9.36757i	0.932108	+	0.538153i
$304$	−2.14545	+	7.92411i	−0.123050	+	0.454479i
$305$		0			0
$306$	29.1206	−	1.88957i	1.66471	−	0.108020i
$307$	−8.00589			−0.456920			−0.228460	−	0.973553i	$-0.573369\pi$
$307$	−8.00589			−0.456920			−0.228460	+	0.973553i	$0.573369\pi$
$308$	2.81154	−	11.4960i	0.160202	−	0.655045i
$309$	34.2339			1.94750
$310$		0			0
$311$	−6.87633	−	11.9101i	−0.389921	−	0.675363i	0.602518	−	0.798105i	$-0.294164\pi$
$311$	−6.87633	−	11.9101i	−0.389921	−	0.675363i	−0.992438	+	0.122743i	$0.960831\pi$
$312$	17.6908	+	20.2524i	1.00154	+	1.14656i
$313$	−9.21091	−	5.31792i	−0.520631	−	0.300587i	0.216562	−	0.976269i	$-0.430516\pi$
$313$	−9.21091	−	5.31792i	−0.520631	−	0.300587i	−0.737193	+	0.675682i	$0.763849\pi$
$314$	6.14793	+	9.21404i	0.346948	+	0.519979i
$315$		0			0
$316$	0.851730	+	0.354102i	0.0479136	+	0.0199198i
$317$	−8.49175	+	14.7081i	−0.476944	+	0.826091i	−0.999651	−	0.0264211i	$-0.991589\pi$
$317$	−8.49175	+	14.7081i	−0.476944	+	0.826091i	0.522707	+	0.852513i	$0.324922\pi$
$318$	−17.7066	−	8.74632i	−0.992939	−	0.490469i
$319$	−14.2963	+	8.25397i	−0.800439	+	0.462133i
$320$		0			0
$321$		−	7.80679i		−	0.435732i
$322$	−2.16284	−	9.72021i	−0.120531	−	0.541686i
$323$			7.07140i			0.393463i
$324$	10.8174	+	14.1357i	0.600966	+	0.785316i
$325$		0			0
$326$	−6.79654	+	13.7594i	−0.376426	+	0.762061i
$327$	−1.50191	+	2.60138i	−0.0830557	+	0.143857i
$328$	4.05204	−	0.797755i	0.223737	−	0.0440486i
$329$	2.48885	+	16.0179i	0.137215	+	0.883097i
$330$		0			0
$331$	−7.21415	−	4.16509i	−0.396525	−	0.228934i	0.288458	−	0.957492i	$-0.406857\pi$
$331$	−7.21415	−	4.16509i	−0.396525	−	0.228934i	−0.684984	+	0.728558i	$0.740191\pi$
$332$	−21.6516	+	2.82173i	−1.18829	+	0.154863i
$333$	−33.5190	−	58.0567i	−1.83683	−	3.18149i
$334$	1.07576	+	16.5788i	0.0588630	+	0.907150i
$335$		0			0
$336$	31.5367	+	3.49154i	1.72047	+	0.190479i
$337$	27.0772			1.47499			0.737495	−	0.675353i	$-0.236009\pi$
$337$	27.0772			1.47499			0.737495	+	0.675353i	$0.236009\pi$
$338$	−0.269607	−	4.15496i	−0.0146647	−	0.226000i
$339$	22.2744	+	38.5804i	1.20978	+	2.09540i
$340$		0			0
$341$	9.47541	+	5.47063i	0.513122	+	0.296251i
$342$	−14.4593	+	9.64775i	−0.781870	+	0.521690i
$343$	8.26248	+	16.5750i	0.446132	+	0.894967i
$344$	−27.6337	+	5.44044i	−1.48991	+	0.293329i
$345$		0			0
$346$	10.3264	−	20.9054i	0.555150	−	1.12388i
$347$	−24.0514	+	13.8861i	−1.29115	+	0.745443i	−0.978857	−	0.204544i	$-0.934429\pi$
$347$	−24.0514	+	13.8861i	−1.29115	+	0.745443i	−0.312288	+	0.949987i	$0.601095\pi$
$348$	−26.8968	−	35.1475i	−1.44182	−	1.88410i
$349$		−	9.64063i		−	0.516051i	−0.966138	−	0.258026i	$-0.916928\pi$
$349$		−	9.64063i		−	0.516051i	0.966138	−	0.258026i	$-0.0830719\pi$
$350$		0			0
$351$			28.4163i			1.51675i
$352$	−9.48495	−	8.37301i	−0.505550	−	0.446283i
$353$	14.1283	−	8.15697i	0.751973	−	0.434152i	−0.0744333	−	0.997226i	$-0.523715\pi$
$353$	14.1283	−	8.15697i	0.751973	−	0.434152i	0.826406	+	0.563074i	$0.190381\pi$
$354$	−27.0622	−	13.3676i	−1.43834	−	0.710478i
$355$		0			0
$356$	−12.9651	−	5.39018i	−0.687151	−	0.285679i
$357$	27.0069	−	4.19629i	1.42936	−	0.222091i
$358$	−7.15037	−	10.7164i	−0.377909	−	0.566380i
$359$	−1.38744	−	0.801040i	−0.0732264	−	0.0422773i	0.462940	−	0.886390i	$-0.346795\pi$
$359$	−1.38744	−	0.801040i	−0.0732264	−	0.0422773i	−0.536166	+	0.844112i	$0.680128\pi$
$360$		0			0
$361$	7.39392	+	12.8067i	0.389154	+	0.674034i
$362$	23.3921	−	1.51786i	1.22946	−	0.0797771i
$363$	17.9822			0.943818
$364$	12.1226	+	11.6020i	0.635396	+	0.608108i
$365$		0			0
$366$	10.7329	−	0.696433i	0.561016	−	0.0364031i
$367$	−0.630259	−	1.09164i	−0.0328993	−	0.0569832i	0.849107	−	0.528221i	$-0.177141\pi$
$367$	−0.630259	−	1.09164i	−0.0328993	−	0.0569832i	−0.882006	+	0.471238i	$0.843807\pi$
$368$	−10.2755	−	2.78209i	−0.535648	−	0.145027i
$369$	7.57289	+	4.37221i	0.394229	+	0.227608i
$370$		0			0
$371$	−11.4918	−	4.45000i	−0.596623	−	0.231033i
$372$	−11.2609	+	27.0862i	−0.583851	+	1.40435i
$373$	4.61372	−	7.99120i	0.238889	−	0.413768i	−0.721507	−	0.692408i	$-0.756550\pi$
$373$	4.61372	−	7.99120i	0.238889	−	0.413768i	0.960396	+	0.278639i	$0.0898833\pi$
$374$	−9.77105	−	4.82648i	−0.505249	−	0.249571i
$375$		0			0
$376$	16.3988	+	5.60247i	0.845702	+	0.288925i
$377$		−	23.4056i		−	1.20545i
$378$	22.6712	+	24.7027i	1.16608	+	1.27057i
$379$			2.53516i			0.130223i	0.997878	+	0.0651113i	$0.0207403\pi$
$379$			2.53516i			0.130223i	−0.997878	+	0.0651113i	$0.979260\pi$
$380$		0			0
$381$	−7.85068	+	4.53259i	−0.402203	+	0.232212i
$382$	1.87454	−	3.79495i	0.0959099	−	0.194166i
$383$	−0.662435	+	1.14737i	−0.0338489	+	0.0586279i	−0.882454	−	0.470400i	$-0.844110\pi$
$383$	−0.662435	+	1.14737i	−0.0338489	+	0.0586279i	0.848605	+	0.529027i	$0.177443\pi$
$384$	18.9737	−	28.1171i	0.968248	−	1.43485i
$385$		0			0
$386$	−17.3033	+	11.5454i	−0.880715	+	0.587644i
$387$	−51.6448	−	29.8171i	−2.62525	−	1.51569i
$388$	0.0479342	+	0.367807i	0.00243349	+	0.0186726i
$389$	−16.1134	−	27.9093i	−0.816983	−	1.41506i	−0.907895	−	0.419197i	$-0.862312\pi$
$389$	−16.1134	−	27.9093i	−0.816983	−	1.41506i	0.0909120	−	0.995859i	$-0.471022\pi$
$390$		0			0
$391$	−9.16976			−0.463735
$392$	19.7947	+	0.414074i	0.999781	+	0.0209139i
$393$	47.0869			2.37522
$394$	0.441150	+	6.79865i	0.0222248	+	0.342511i
$395$		0			0
$396$	−3.46199	−	26.5644i	−0.173971	−	1.33491i
$397$	30.4617	+	17.5871i	1.52883	+	0.882670i	0.999411	+	0.0343095i	$0.0109232\pi$
$397$	30.4617	+	17.5871i	1.52883	+	0.882670i	0.529419	+	0.848361i	$0.322410\pi$
$398$	1.49914	−	1.00028i	0.0751452	−	0.0501395i
$399$	−12.6819	+	10.2082i	−0.634890	+	0.511047i
$400$		0			0
$401$	−15.9623	+	27.6476i	−0.797120	+	1.38065i	0.124364	+	0.992237i	$0.460311\pi$
$401$	−15.9623	+	27.6476i	−0.797120	+	1.38065i	−0.921484	+	0.388416i	$0.873022\pi$
$402$	0.0990903	−	0.200605i	0.00494217	−	0.0100053i
$403$	−13.4346	+	7.75647i	−0.669225	+	0.386377i
$404$	9.92512	−	7.59524i	0.493793	−	0.377877i
$405$		0			0
$406$	−18.6735	−	20.3468i	−0.926751	−	1.00979i
$407$			25.0357i			1.24097i
$408$	9.44599	−	27.6490i	0.467646	−	1.36883i
$409$	14.2151	−	8.20712i	0.702894	−	0.405816i	−0.105530	−	0.994416i	$-0.533654\pi$
$409$	14.2151	−	8.20712i	0.702894	−	0.405816i	0.808424	+	0.588600i	$0.200321\pi$
$410$		0			0
$411$	14.4126	−	24.9634i	0.710922	−	1.23135i
$412$	8.76677	−	21.0869i	0.431908	−	1.03888i
$413$	−17.5636	−	6.80123i	−0.864250	−	0.334666i
$414$	−12.5106	−	18.7500i	−0.614864	−	0.921510i
$415$		0			0
$416$	17.0051	−	5.71063i	0.833746	−	0.279987i
$417$	−11.2392	−	19.4669i	−0.550387	−	0.953298i
$418$	6.47794	−	0.420340i	0.316846	−	0.0205595i
$419$	11.8654			0.579665			0.289832	−	0.957077i	$-0.406400\pi$
$419$	11.8654			0.579665			0.289832	+	0.957077i	$0.406400\pi$
$420$		0			0
$421$	10.3433			0.504101			0.252051	−	0.967714i	$-0.418895\pi$
$421$	10.3433			0.504101			0.252051	+	0.967714i	$0.418895\pi$
$422$	5.23552	−	0.339721i	0.254861	−	0.0165374i
$423$	18.3465	+	31.7770i	0.892035	+	1.54505i
$424$	−9.92185	+	8.66691i	−0.481847	+	0.420902i
$425$		0			0
$426$	0.499720	+	0.748942i	0.0242115	+	0.0362864i
$427$	6.63178	−	1.03044i	0.320934	−	0.0498663i
$428$	−4.80873	−	1.99920i	−0.232439	−	0.0966349i
$429$	10.6320	−	18.4151i	0.513316	−	0.889089i
$430$		0			0
$431$	25.6838	−	14.8286i	1.23715	−	0.714267i	0.268636	−	0.963242i	$-0.413427\pi$
$431$	25.6838	−	14.8286i	1.23715	−	0.714267i	0.968510	+	0.248975i	$0.0800937\pi$
$432$	34.6469	−	9.18671i	1.66695	−	0.441996i
$433$		−	29.4107i		−	1.41339i	−0.707520	−	0.706693i	$-0.750186\pi$
$433$		−	29.4107i		−	1.41339i	0.707520	−	0.706693i	$-0.249814\pi$
$434$	−5.49059	+	17.4612i	−0.263557	+	0.838166i
$435$		0			0
$436$	1.21775	+	1.59130i	0.0583196	+	0.0762094i
$437$	4.73029	−	2.73103i	0.226280	−	0.130643i
$438$	−27.9311	+	56.5455i	−1.33460	+	2.70185i
$439$	−4.41191	+	7.64165i	−0.210569	+	0.364716i	−0.951893	−	0.306432i	$-0.900865\pi$
$439$	−4.41191	+	7.64165i	−0.210569	+	0.364716i	0.741324	+	0.671147i	$0.234198\pi$
$440$		0			0
$441$	30.9890	+	28.2336i	1.47567	+	1.34446i
$442$	12.8532	−	8.57612i	0.611366	−	0.407925i
$443$	−16.9454	−	9.78342i	−0.805099	−	0.464824i	0.0401518	−	0.999194i	$-0.487216\pi$
$443$	−16.9454	−	9.78342i	−0.805099	−	0.464824i	−0.845251	+	0.534369i	$0.820549\pi$
$444$	−66.5583	+	8.67417i	−3.15872	+	0.411658i
$445$		0			0
$446$	1.18661	+	18.2870i	0.0561874	+	0.865916i
$447$	19.4919			0.921935
$448$	10.2267	−	18.5314i	0.483168	−	0.875528i
$449$	5.02309			0.237054			0.118527	−	0.992951i	$-0.462183\pi$
$449$	5.02309			0.237054			0.118527	+	0.992951i	$0.462183\pi$
$450$		0			0
$451$	−1.63282	−	2.82813i	−0.0768866	−	0.133171i
$452$	29.4684	−	3.84045i	1.38608	−	0.180640i
$453$	61.4705	+	35.4900i	2.88814	+	1.66747i
$454$	−10.4611	+	6.97998i	−0.490962	+	0.327587i
$455$		0			0
$456$	3.36192	+	17.0762i	0.157436	+	0.799667i
$457$	−13.9225	+	24.1144i	−0.651265	+	1.12802i	0.331551	+	0.943437i	$0.392428\pi$
$457$	−13.9225	+	24.1144i	−0.651265	+	1.12802i	−0.982816	+	0.184587i	$0.940905\pi$
$458$	−8.10816	+	16.4147i	−0.378869	+	0.767008i
$459$	26.7388	−	15.4377i	1.24806	−	0.720569i
$460$		0			0
$461$		−	19.8494i		−	0.924481i	−0.886755	−	0.462240i	$-0.847046\pi$
$461$		−	19.8494i		−	0.924481i	0.886755	−	0.462240i	$-0.152954\pi$
$462$	−5.44948	−	24.4909i	−0.253533	−	1.13942i
$463$		−	35.7118i		−	1.65967i	−0.558012	−	0.829833i	$-0.688436\pi$
$463$		−	35.7118i		−	1.65967i	0.558012	−	0.829833i	$-0.311564\pi$
$464$	−28.5375	+	7.56680i	−1.32482	+	0.351280i
$465$		0			0
$466$	19.2935	+	9.53018i	0.893756	+	0.441477i
$467$	11.3055	−	19.5818i	0.523158	−	0.906136i	−0.476479	−	0.879186i	$-0.658087\pi$
$467$	11.3055	−	19.5818i	0.523158	−	0.906136i	0.999637	−	0.0269503i	$-0.00857959\pi$
$468$	35.0722	+	14.5811i	1.62121	+	0.674010i
$469$	0.0504157	−	0.130195i	0.00232798	−	0.00601183i
$470$		0			0
$471$	20.3368	+	11.7415i	0.937070	+	0.541018i
$472$	−15.1642	+	13.2462i	−0.697989	+	0.609705i
$473$	11.1353	+	19.2870i	0.512003	+	0.886816i
$474$	1.95140	−	0.126622i	0.0896309	−	0.00581596i
$475$		0			0
$476$	4.33127	−	17.7100i	0.198523	−	0.811734i
$477$	−27.8947			−1.27721
$478$	−0.0618849	+	0.00401558i	−0.00283055	+	0.000183668i
$479$	4.28200	+	7.41664i	0.195649	+	0.338875i	0.947113	−	0.320900i	$-0.103985\pi$
$479$	4.28200	+	7.41664i	0.195649	+	0.338875i	−0.751464	+	0.659774i	$0.770652\pi$
$480$		0			0
$481$	−30.7409	−	17.7483i	−1.40166	−	0.809251i
$482$	−1.80579	−	2.70638i	−0.0822515	−	0.123272i
$483$	−13.2373	−	16.4451i	−0.602319	−	0.748280i
$484$	4.60495	−	11.0764i	0.209316	−	0.503473i
$485$		0			0
$486$	−0.253510	−	0.125223i	−0.0114994	−	0.00568023i
$487$	27.4054	−	15.8225i	1.24186	−	0.716987i	0.272386	−	0.962188i	$-0.412187\pi$
$487$	27.4054	−	15.8225i	1.24186	−	0.716987i	0.969472	+	0.245201i	$0.0788539\pi$
$488$	2.31955	−	6.78945i	0.105001	−	0.307344i
$489$			32.5346i			1.47126i
$490$		0			0
$491$		−	35.7781i		−	1.61464i	−0.590113	−	0.807321i	$-0.700917\pi$
$491$		−	35.7781i		−	1.61464i	0.590113	−	0.807321i	$-0.299083\pi$
$492$	6.95297	−	5.32079i	0.313464	−	0.239880i
$493$	−22.0239	+	12.7155i	−0.991906	+	0.572677i
$494$	−4.07621	+	8.25214i	−0.183397	+	0.371281i
$495$		0			0
$496$	13.8004	+	13.8727i	0.619658	+	0.622903i
$497$	0.352280	+	0.437649i	0.0158019	+	0.0196312i
$498$	−38.5053	+	25.6921i	−1.72546	+	1.15129i
$499$	35.7797	+	20.6574i	1.60172	+	0.924752i	0.991144	+	0.132793i	$0.0423947\pi$
$499$	35.7797	+	20.6574i	1.60172	+	0.924752i	0.610574	+	0.791959i	$0.290939\pi$
$500$		0			0
$501$	17.6105	+	30.5023i	0.786780	+	1.36274i
$502$	0.579114	+	8.92485i	0.0258471	+	0.398336i
$503$	−29.0170			−1.29381			−0.646903	−	0.762572i	$-0.723936\pi$
$503$	−29.0170			−1.29381			−0.646903	+	0.762572i	$0.723936\pi$
$504$	42.1219	−	15.3059i	1.87626	−	0.681779i
$505$		0			0
$506$	0.545071	+	8.40021i	0.0242314	+	0.373435i
$507$	−4.41354	−	7.64448i	−0.196012	−	0.339503i
$508$	0.781489	+	5.99649i	0.0346730	+	0.266051i
$509$	17.3474	+	10.0155i	0.768910	+	0.443931i	0.832486	−	0.554046i	$-0.186917\pi$
$509$	17.3474	+	10.0155i	0.768910	+	0.443931i	−0.0635754	+	0.997977i	$0.520250\pi$
$510$		0			0
$511$	−14.2109	+	36.6986i	−0.628654	+	1.62345i
$512$	−12.4604	−	18.8875i	−0.550675	−	0.834720i
$513$	−9.19562	+	15.9273i	−0.405996	+	0.703206i
$514$	8.91962	−	18.0575i	0.393428	−	0.796481i
$515$		0			0
$516$	−47.4171	+	36.2861i	−2.08742	+	1.59741i
$517$		−	13.7031i		−	0.602663i
$518$	−40.8835	+	9.09698i	−1.79632	+	0.399698i
$519$		−	49.4317i		−	2.16981i
$520$		0			0
$521$	18.5712	−	10.7221i	0.813620	−	0.469743i	−0.0345917	−	0.999402i	$-0.511013\pi$
$521$	18.5712	−	10.7221i	0.813620	−	0.469743i	0.848211	+	0.529658i	$0.177680\pi$
$522$	−56.0481	−	27.6854i	−2.45316	−	1.21176i
$523$	−20.5020	+	35.5105i	−0.896491	+	1.55277i	−0.0645418	+	0.997915i	$0.520559\pi$
$523$	−20.5020	+	35.5105i	−0.896491	+	1.55277i	−0.831949	+	0.554852i	$0.812775\pi$
$524$	12.0582	−	29.0040i	0.526766	−	1.26704i
$525$		0			0
$526$	−9.22165	−	13.8207i	−0.402083	−	0.602611i
$527$	14.5972	+	8.42768i	0.635863	+	0.367116i
$528$	−25.8901	−	7.00973i	−1.12672	−	0.305059i
$529$	−7.95856	−	13.7846i	−0.346024	−	0.599332i
$530$		0			0
$531$	−42.6333			−1.85013
$532$	3.04025	+	10.4258i	0.131811	+	0.452016i
$533$	4.63015			0.200554
$534$	−29.7045	+	1.92746i	−1.28544	+	0.0834094i
$535$		0			0
$536$	−0.0981906	−	0.112408i	−0.00424119	−	0.00485530i
$537$	−23.6528	−	13.6559i	−1.02069	−	0.589297i
$538$	6.66349	+	9.98673i	0.287284	+	0.430559i
$539$	−4.75052	−	14.9178i	−0.204620	−	0.642557i
$540$		0			0
$541$	−1.72641	+	2.99023i	−0.0742242	+	0.128560i	−0.900749	−	0.434341i	$-0.856981\pi$
$541$	−1.72641	+	2.99023i	−0.0742242	+	0.128560i	0.826524	+	0.562901i	$0.190315\pi$
$542$	−10.1104	−	4.99409i	−0.434277	−	0.214514i
$543$	43.0377	−	24.8479i	1.84693	−	1.06632i
$544$	−14.6119	−	12.8989i	−0.626479	−	0.553035i
$545$		0			0
$546$	33.9352	+	10.6708i	1.45229	+	0.456666i
$547$			28.2607i			1.20834i	0.796855	+	0.604170i	$0.206495\pi$
$547$			28.2607i			1.20834i	−0.796855	+	0.604170i	$0.793505\pi$
$548$	−11.6858	−	15.2704i	−0.499191	−	0.652321i
$549$	13.1564	−	7.59584i	0.561500	−	0.324182i
$550$		0			0
$551$	7.57413	−	13.1188i	0.322669	−	0.558879i
$552$	−22.1434	+	4.35953i	−0.942487	+	0.185554i
$553$	1.20576	−	0.187349i	0.0512741	−	0.00796691i
$554$	−15.9931	+	10.6711i	−0.679481	+	0.453374i
$555$		0			0
$556$	−14.8692	+	1.93781i	−0.630593	+	0.0821816i
$557$	1.03826	+	1.79833i	0.0439927	+	0.0761976i	0.887183	−	0.461417i	$-0.152659\pi$
$557$	1.03826	+	1.79833i	0.0439927	+	0.0761976i	−0.843191	+	0.537615i	$0.819326\pi$
$558$	2.68285	+	41.3459i	0.113574	+	1.75031i
$559$	−31.5762			−1.33553
$560$		0			0
$561$	−23.1040			−0.975453
$562$	−0.868371	−	13.3826i	−0.0366300	−	0.564513i
$563$	22.9547	+	39.7588i	0.967426	+	1.67563i	0.702949	+	0.711240i	$0.251866\pi$
$563$	22.9547	+	39.7588i	0.967426	+	1.67563i	0.264477	+	0.964392i	$0.414801\pi$
$564$	36.4303	−	4.74776i	1.53399	−	0.199917i
$565$		0			0
$566$	−25.3502	+	16.9145i	−1.06555	+	0.710971i
$567$	21.9581	+	8.50292i	0.922154	+	0.357089i
$568$	0.589295	−	0.116019i	0.0247263	−	0.00486803i
$569$	−3.96413	+	6.86607i	−0.166185	+	0.287840i	−0.937075	−	0.349127i	$-0.886478\pi$
$569$	−3.96413	+	6.86607i	−0.166185	+	0.287840i	0.770891	+	0.636968i	$0.219811\pi$
$570$		0			0
$571$	−18.3314	+	10.5837i	−0.767147	+	0.442912i	−0.831856	−	0.554992i	$-0.812721\pi$
$571$	−18.3314	+	10.5837i	−0.767147	+	0.442912i	0.0647092	+	0.997904i	$0.479388\pi$
$572$	−8.62041	−	11.2648i	−0.360438	−	0.471003i
$573$		−	8.97330i		−	0.374865i
$574$	4.02506	−	3.69404i	0.168003	−	0.154186i
$575$		0			0
$576$	6.43964	−	47.4762i	0.268318	−	1.97817i
$577$	−8.94731	+	5.16573i	−0.372481	+	0.215052i	−0.674542	−	0.738237i	$-0.735659\pi$
$577$	−8.94731	+	5.16573i	−0.372481	+	0.215052i	0.302061	+	0.953289i	$0.402325\pi$
$578$	6.50272	+	3.21207i	0.270478	+	0.133604i
$579$	−22.0496	+	38.1911i	−0.916351	+	1.58717i
$580$		0			0
$581$	−22.5008	+	18.1117i	−0.933490	+	0.751402i
$582$	0.436444	+	0.654109i	0.0180912	+	0.0271137i
$583$	9.02174	+	5.20871i	0.373642	+	0.215723i
$584$	27.6774	+	31.6851i	1.14530	+	1.31114i
$585$		0			0
$586$	40.8550	−	2.65099i	1.68770	−	0.109511i
$587$	−20.4660			−0.844722			−0.422361	−	0.906428i	$-0.638799\pi$
$587$	−20.4660			−0.844722			−0.422361	+	0.906428i	$0.638799\pi$
$588$	38.0138	−	17.7981i	1.56766	−	0.733980i
$589$	−10.0401			−0.413694
$590$		0			0
$591$	7.22175	+	12.5084i	0.297063	+	0.514529i
$592$	−11.7016	+	43.2191i	−0.480931	+	1.77629i
$593$	−38.8389	−	22.4236i	−1.59492	−	0.920828i	−0.992445	−	0.122692i	$-0.960847\pi$
$593$	−38.8389	−	22.4236i	−1.59492	−	0.920828i	−0.602477	−	0.798136i	$-0.705819\pi$
$594$	−15.7315	−	23.5772i	−0.645471	−	0.967383i
$595$		0			0
$596$	4.99158	−	12.0064i	0.204463	−	0.491800i
$597$	1.91036	−	3.30884i	0.0781857	−	0.135422i
$598$	−10.7009	−	5.28578i	−0.437592	−	0.216152i
$599$	14.1499	−	8.16942i	0.578147	−	0.333793i	−0.182250	−	0.983252i	$-0.558338\pi$
$599$	14.1499	−	8.16942i	0.578147	−	0.333793i	0.760397	+	0.649459i	$0.225005\pi$
$600$		0			0
$601$		−	39.8029i		−	1.62359i	−0.583941	−	0.811796i	$-0.698490\pi$
$601$		−	39.8029i		−	1.62359i	0.583941	−	0.811796i	$-0.301510\pi$
$602$	−27.4496	+	25.1922i	−1.11876	+	1.02676i
$603$		−	0.316030i		−	0.0128697i
$604$	37.6024	−	28.7754i	1.53002	−	1.17085i
$605$		0			0
$606$	11.7342	−	23.7554i	0.476668	−	0.964998i
$607$	4.70373	−	8.14710i	0.190919	−	0.330681i	−0.754636	−	0.656143i	$-0.772187\pi$
$607$	4.70373	−	8.14710i	0.190919	−	0.330681i	0.945555	+	0.325463i	$0.105520\pi$
$608$	11.3793	+	2.30213i	0.461493	+	0.0933636i
$609$	−54.5975	−	21.1420i	−2.21240	−	0.856716i
$610$		0			0
$611$	16.8259	+	9.71441i	0.680701	+	0.393003i
$612$	−5.33330	−	40.9233i	−0.215586	−	1.65423i
$613$	6.81796	+	11.8091i	0.275375	+	0.476963i	0.970230	−	0.242187i	$-0.0778646\pi$
$613$	6.81796	+	11.8091i	0.275375	+	0.476963i	−0.694855	+	0.719150i	$0.744531\pi$
$614$	0.733121	+	11.2983i	0.0295863	+	0.455961i
$615$		0			0
$616$	−16.4811	−	2.91505i	−0.664044	−	0.117451i
$617$	−39.1144			−1.57469			−0.787343	−	0.616515i	$-0.788544\pi$
$617$	−39.1144			−1.57469			−0.787343	+	0.616515i	$0.788544\pi$
$618$	−3.13489	−	48.3124i	−0.126104	−	1.94341i
$619$	−9.50950	−	16.4709i	−0.382219	−	0.662023i	0.609160	−	0.793047i	$-0.291507\pi$
$619$	−9.50950	−	16.4709i	−0.382219	−	0.662023i	−0.991379	+	0.131024i	$0.958173\pi$
$620$		0			0
$621$	−20.6535	−	11.9243i	−0.828798	−	0.478507i
$622$	−16.1785	+	10.7948i	−0.648697	+	0.432833i
$623$	−18.3542	+	2.85186i	−0.735347	+	0.114257i
$624$	26.9611	−	26.8206i	1.07931	−	1.07368i
$625$		0			0
$626$	−6.66143	+	13.4858i	−0.266244	+	0.539002i
$627$	11.9184	−	6.88108i	0.475974	−	0.274804i
$628$	12.4403	−	9.52000i	0.496422	−	0.379889i
$629$			38.5683i			1.53782i
$630$		0			0
$631$			16.4987i			0.656802i	0.944538	+	0.328401i	$0.106510\pi$
$631$			16.4987i			0.656802i	−0.944538	+	0.328401i	$0.893490\pi$
$632$	0.421729	−	1.23443i	0.0167755	−	0.0491028i
$633$	9.63252	−	5.56134i	0.382858	−	0.221043i
$634$	21.5344	+	10.6371i	0.855241	+	0.422452i
$635$		0			0
$636$	−10.7218	+	25.7893i	−0.425146	+	1.02261i
$637$	21.6851	+	4.74245i	0.859196	+	0.187903i
$638$	12.9575	+	19.4197i	0.512993	+	0.768835i
$639$	1.10134	+	0.635857i	0.0435682	+	0.0251541i
$640$		0			0
$641$	−13.4723	−	23.3347i	−0.532124	−	0.921665i	−0.999297	−	0.0374991i	$-0.988061\pi$
$641$	−13.4723	−	23.3347i	−0.532124	−	0.921665i	0.467173	−	0.884166i	$-0.345272\pi$
$642$	−11.0173	+	0.714889i	−0.434818	+	0.0282144i
$643$	−43.6730			−1.72229			−0.861147	−	0.508355i	$-0.830254\pi$
$643$	−43.6730			−1.72229			−0.861147	+	0.508355i	$0.830254\pi$
$644$	−13.5195	+	3.94241i	−0.532745	+	0.155353i
$645$		0			0
$646$	9.97948	−	0.647547i	0.392637	−	0.0254774i
$647$	14.0540	+	24.3422i	0.552518	+	0.956989i	0.998092	+	0.0617443i	$0.0196663\pi$
$647$	14.0540	+	24.3422i	0.552518	+	0.956989i	−0.445574	+	0.895245i	$0.647000\pi$
$648$	18.9583	−	16.5604i	0.744754	−	0.650556i
$649$	13.7885	+	7.96080i	0.541246	+	0.312489i
$650$		0			0
$651$	5.95797	+	38.3448i	0.233511	+	1.50285i
$652$	20.0402	+	8.33161i	0.784836	+	0.326291i
$653$	−20.8367	+	36.0902i	−0.815403	+	1.41232i	0.0936346	+	0.995607i	$0.470151\pi$
$653$	−20.8367	+	36.0902i	−0.815403	+	1.41232i	−0.909038	+	0.416713i	$0.863182\pi$
$654$	3.80872	+	1.88134i	0.148933	+	0.0735664i
$655$		0			0
$656$	−1.49688	−	5.64538i	−0.0584435	−	0.220415i
$657$			89.0808i			3.47537i
$658$	22.3773	−	4.97918i	0.872359	−	0.194109i
$659$			47.0951i			1.83457i	0.398236	+	0.917283i	$0.369622\pi$
$659$			47.0951i			1.83457i	−0.398236	+	0.917283i	$0.630378\pi$
$660$		0			0
$661$	−10.0792	+	5.81924i	−0.392036	+	0.226342i	−0.683042	−	0.730379i	$-0.739343\pi$
$661$	−10.0792	+	5.81924i	−0.392036	+	0.226342i	0.291006	+	0.956721i	$0.406010\pi$
$662$	−5.21735	+	10.5623i	−0.202778	+	0.410517i
$663$	16.3789	−	28.3690i	0.636103	−	1.10176i
$664$	5.96486	+	30.2973i	0.231481	+	1.17577i
$665$		0			0
$666$	−78.8628	+	52.6200i	−3.05587	+	2.03898i
$667$	17.0116	+	9.82168i	0.658693	+	0.380297i
$668$	23.2982	−	3.03633i	0.901435	−	0.117479i
$669$	19.4251	+	33.6452i	0.751017	+	1.30080i
$670$		0			0
$671$	−5.67340			−0.219019
$672$	2.03952	−	44.8257i	0.0786763	−	1.72919i
$673$	−14.9849			−0.577626			−0.288813	−	0.957385i	$-0.593261\pi$
$673$	−14.9849			−0.577626			−0.288813	+	0.957385i	$0.593261\pi$
$674$	−2.47953	−	38.2126i	−0.0955080	−	1.47189i
$675$		0			0
$676$	−5.83899	+	0.760963i	−0.224576	+	0.0292678i
$677$	−19.9347	−	11.5093i	−0.766154	−	0.442339i	0.0653470	−	0.997863i	$-0.479185\pi$
$677$	−19.9347	−	11.5093i	−0.766154	−	0.442339i	−0.831501	+	0.555524i	$0.812518\pi$
$678$	52.4067	−	34.9676i	2.01267	−	1.34292i
$679$	0.307673	+	0.382232i	0.0118074	+	0.0146687i
$680$		0			0
$681$	−13.3305	+	23.0892i	−0.510827	+	0.884779i
$682$	6.85272	−	13.8731i	0.262404	−	0.531228i
$683$	32.2762	−	18.6347i	1.23502	−	0.713037i	0.266945	−	0.963712i	$-0.413986\pi$
$683$	32.2762	−	18.6347i	1.23502	−	0.713037i	0.968071	+	0.250675i	$0.0806525\pi$
$684$	14.9394	+	19.5222i	0.571223	+	0.746448i
$685$		0			0
$686$	22.6348	−	13.1782i	0.864201	−	0.503146i
$687$			38.8132i			1.48082i
$688$	10.2083	+	38.4997i	0.389187	+	1.46779i
$689$	−12.7914	+	7.38510i	−0.487312	+	0.281350i
$690$		0			0
$691$	13.9969	−	24.2433i	0.532467	−	0.922260i	−0.466815	−	0.884355i	$-0.654598\pi$
$691$	13.9969	−	24.2433i	0.532467	−	0.922260i	0.999281	−	0.0379044i	$-0.0120682\pi$
$692$	−30.4483	−	12.6587i	−1.15747	−	0.481211i
$693$	−22.2213	−	27.6062i	−0.844118	−	1.04867i
$694$	21.7991	+	32.6708i	0.827483	+	1.24017i
$695$		0			0
$696$	−47.1387	+	41.1765i	−1.78679	+	1.56079i
$697$	−2.51542	−	4.35683i	−0.0952782	−	0.165027i
$698$	−13.6053	+	0.882819i	−0.514968	+	0.0334152i
$699$	45.6203			1.72552
$700$		0			0
$701$	29.2334			1.10413			0.552065	−	0.833801i	$-0.313840\pi$
$701$	29.2334			1.10413			0.552065	+	0.833801i	$0.313840\pi$
$702$	40.1024	−	2.60216i	1.51357	−	0.0982121i
$703$	−11.4868	−	19.8957i	−0.433233	−	0.750381i
$704$	−10.9478	+	14.1523i	−0.412611	+	0.533386i
$705$		0			0
$706$	−12.8053	−	19.1915i	−0.481932	−	0.722283i
$707$	5.97017	−	15.4175i	0.224532	−	0.579835i
$708$	−16.3868	+	39.4155i	−0.615852	+	1.48133i
$709$	2.08074	−	3.60395i	0.0781440	−	0.135349i	−0.824305	−	0.566146i	$-0.808434\pi$
$709$	2.08074	−	3.60395i	0.0781440	−	0.135349i	0.902449	+	0.430796i	$0.141767\pi$
$710$		0			0
$711$	2.39203	−	1.38104i	0.0897082	−	0.0517931i
$712$	−6.41962	+	18.7906i	−0.240585	+	0.704207i
$713$		−	13.0194i		−	0.487580i
$714$	−8.39509	−	37.7291i	−0.314178	−	1.41197i
$715$		0			0
$716$	−14.4687	+	11.0723i	−0.540722	+	0.413790i
$717$	−0.113858	+	0.0657362i	−0.00425212	+	0.00245496i
$718$	−1.00341	+	2.03137i	−0.0374470	+	0.0758102i
$719$	21.1113	−	36.5658i	0.787318	−	1.36368i	−0.140286	−	0.990111i	$-0.544802\pi$
$719$	21.1113	−	36.5658i	0.787318	−	1.36368i	0.927604	−	0.373564i	$-0.121865\pi$
$720$		0			0
$721$	−4.63835	−	29.8519i	−0.172741	−	1.11174i
$722$	17.3962	−	11.6074i	0.647421	−	0.431982i
$723$	−5.97339	−	3.44874i	−0.222153	−	0.128260i
$724$	−4.28415	−	32.8730i	−0.159219	−	1.22172i
$725$		0			0
$726$	−1.64667	−	25.3772i	−0.0611138	−	0.941837i
$727$	27.2605			1.01104			0.505519	−	0.862816i	$-0.331301\pi$
$727$	27.2605			1.01104			0.505519	+	0.862816i	$0.331301\pi$
$728$	15.2631	−	18.1704i	0.565689	−	0.673439i
$729$	−27.2992			−1.01108
$730$		0			0
$731$	17.1544	+	29.7122i	0.634477	+	1.09895i
$732$	−1.96568	−	15.0830i	−0.0726535	−	0.557482i
$733$	−13.2554	−	7.65300i	−0.489599	−	0.282670i	0.234809	−	0.972041i	$-0.424553\pi$
$733$	−13.2554	−	7.65300i	−0.489599	−	0.282670i	−0.724408	+	0.689372i	$0.757887\pi$
$734$	−1.48286	+	0.989415i	−0.0547333	+	0.0365200i
$735$		0			0
$736$	−2.98526	+	14.7560i	−0.110038	+	0.543915i
$737$	−0.0590113	+	0.102211i	−0.00217371	+	0.00376498i
$738$	5.47680	−	11.0876i	0.201604	−	0.408140i
$739$	−42.5694	+	24.5774i	−1.56594	+	0.904096i	−0.569305	+	0.822126i	$0.692788\pi$
$739$	−42.5694	+	24.5774i	−1.56594	+	0.904096i	−0.996635	+	0.0819692i	$0.973879\pi$
$740$		0			0
$741$			19.5125i			0.716810i
$742$	−5.22771	+	16.6252i	−0.191915	+	0.610331i
$743$		−	35.2067i		−	1.29161i	−0.763503	−	0.645805i	$-0.776522\pi$
$743$		−	35.2067i		−	1.29161i	0.763503	−	0.645805i	$-0.223478\pi$
$744$	39.2564	+	13.4116i	1.43921	+	0.491692i
$745$		0			0
$746$	−11.7000	−	5.77932i	−0.428369	−	0.211596i
$747$	−32.6913	+	56.6229i	−1.19611	+	2.07173i
$748$	−5.91659	+	14.2313i	−0.216332	+	0.520349i
$749$	−6.80752	+	1.05774i	−0.248741	+	0.0386491i
$750$		0			0
$751$	−0.584292	−	0.337341i	−0.0213211	−	0.0123098i	0.489302	−	0.872115i	$-0.337252\pi$
$751$	−0.584292	−	0.337341i	−0.0213211	−	0.0123098i	−0.510623	+	0.859805i	$0.670585\pi$
$752$	6.40478	−	23.6557i	0.233558	−	0.862635i
$753$	9.48027	+	16.4203i	0.345480	+	0.598389i
$754$	−33.0310	+	2.14331i	−1.20292	+	0.0780548i
$755$		0			0
$756$	32.7855	−	34.2567i	1.19240	−	1.24590i
$757$	45.8640			1.66695			0.833477	−	0.552553i	$-0.186346\pi$
$757$	45.8640			1.66695			0.833477	+	0.552553i	$0.186346\pi$
$758$	3.57774	−	0.232152i	0.129949	−	0.00843214i
$759$	8.92298	+	15.4550i	0.323883	+	0.560983i
$760$		0			0
$761$	18.9229	+	10.9252i	0.685956	+	0.396037i	0.802095	−	0.597196i	$-0.203719\pi$
$761$	18.9229	+	10.9252i	0.685956	+	0.396037i	−0.116139	+	0.993233i	$0.537052\pi$
$762$	7.11551	+	10.6642i	0.257768	+	0.386322i
$763$	2.47190	+	0.957201i	0.0894886	+	0.0346530i
$764$	−5.52726	−	2.29793i	−0.199969	−	0.0831360i
$765$		0			0
$766$	1.67988	+	0.829791i	0.0606967	+	0.0299816i
$767$	−19.5499	+	11.2871i	−0.705905	+	0.407554i
$768$	−41.4177	−	24.2018i	−1.49453	−	0.873307i
$769$			16.0214i			0.577745i	0.957368	+	0.288872i	$0.0932803\pi$
$769$			16.0214i			0.577745i	−0.957368	+	0.288872i	$0.906720\pi$
$770$		0			0
$771$		−	42.6976i		−	1.53772i
$772$	17.8779	+	23.3620i	0.643439	+	0.840816i
$773$	36.6688	−	21.1707i	1.31888	−	0.761458i	0.335335	−	0.942099i	$-0.391150\pi$
$773$	36.6688	−	21.1707i	1.31888	−	0.761458i	0.983549	+	0.180641i	$0.0578171\pi$
$774$	−37.3500	+	75.6139i	−1.34252	+	2.71789i
$775$		0			0
$776$	0.514676	−	0.101328i	0.0184758	−	0.00363746i
$777$	−69.1687	+	55.6765i	−2.48141	+	1.99738i
$778$	−37.9113	+	25.2957i	−1.35919	+	0.906896i
$779$	2.59519	+	1.49833i	0.0929824	+	0.0536834i
$780$		0			0
$781$	−0.237464	−	0.411299i	−0.00849712	−	0.0147174i
$782$	0.839700	+	12.9408i	0.0300276	+	0.462762i
$783$	−66.1408			−2.36368
$784$	−1.22829	−	27.9730i	−0.0438675	−	0.999037i
$785$		0			0
$786$	−4.31187	−	66.4511i	−0.153799	−	2.37023i
$787$	−2.19121	−	3.79528i	−0.0781081	−	0.135287i	0.824326	−	0.566116i	$-0.191555\pi$
$787$	−2.19121	−	3.79528i	−0.0781081	−	0.135287i	−0.902434	+	0.430829i	$0.858221\pi$
$788$	9.55417	−	1.24514i	0.340353	−	0.0443563i
$789$	−30.5044	−	17.6117i	−1.08599	−	0.626994i
$790$		0			0
$791$	30.6241	−	24.6506i	1.08887	−	0.876473i
$792$	−37.1718	+	7.31828i	−1.32084	+	0.260044i
$793$	4.02198	−	6.96627i	0.142825	−	0.247380i
$794$	22.0302	−	44.5995i	0.781824	−	1.58278i
$795$		0			0
$796$	−1.54892	−	2.02406i	−0.0549001	−	0.0717409i
$797$		−	53.6019i		−	1.89868i	−0.314255	−	0.949339i	$-0.601755\pi$
$797$		−	53.6019i		−	1.89868i	0.314255	−	0.949339i	$-0.398245\pi$
$798$	15.5675	+	16.9625i	0.551085	+	0.600466i
$799$		−	21.1101i		−	0.746822i
$800$		0			0
$801$	−36.4118	+	21.0224i	−1.28655	+	0.742789i
$802$	40.4792	+	19.9950i	1.42937	+	0.706048i
$803$	16.6338	−	28.8106i	0.586995	−	1.01670i
$804$	−0.292177	−	0.121471i	−0.0103043	−	0.00428394i
$805$		0			0
$806$	12.1765	+	18.2492i	0.428900	+	0.642802i
$807$	22.0422	+	12.7261i	0.775924	+	0.447980i
$808$	−11.6276	−	13.3113i	−0.409058	−	0.468289i
$809$	0.754693	+	1.30717i	0.0265336	+	0.0459575i	0.878987	−	0.476845i	$-0.158220\pi$
$809$	0.754693	+	1.30717i	0.0265336	+	0.0459575i	−0.852454	+	0.522803i	$0.824886\pi$
$810$		0			0
$811$	−43.1894			−1.51658			−0.758292	−	0.651915i	$-0.773966\pi$
$811$	−43.1894			−1.51658			−0.758292	+	0.651915i	$0.773966\pi$
$812$	−27.0043	+	28.2161i	−0.947667	+	0.990192i
$813$	−23.9063			−0.838432
$814$	35.3315	−	2.29258i	1.23837	−	0.0803550i
$815$		0			0
$816$	−39.8845	−	10.7987i	−1.39624	−	0.378031i
$817$	−17.6984	−	10.2182i	−0.619189	−	0.357489i
$818$	−12.8840	−	19.3095i	−0.450478	−	0.675142i
$819$	49.6503	−	7.71460i	1.73492	−	0.269570i
$820$		0			0
$821$	4.56478	−	7.90644i	0.159312	−	0.275937i	−0.775309	−	0.631582i	$-0.782406\pi$
$821$	4.56478	−	7.90644i	0.159312	−	0.275937i	0.934621	+	0.355646i	$0.115739\pi$
$822$	−36.5493	−	18.0538i	−1.27480	−	0.629698i
$823$	−0.329424	+	0.190193i	−0.0114830	+	0.00662972i	−0.505731	−	0.862692i	$-0.668777\pi$
$823$	−0.329424	+	0.190193i	−0.0114830	+	0.00662972i	0.494248	+	0.869321i	$0.335444\pi$
$824$	−30.5616	−	10.4411i	−1.06467	−	0.363732i
$825$		0			0
$826$	−7.98985	+	25.4094i	−0.278003	+	0.884106i
$827$		−	23.9044i		−	0.831236i	−0.909539	−	0.415618i	$-0.863565\pi$
$827$		−	23.9044i		−	0.831236i	0.909539	−	0.415618i	$-0.136435\pi$
$828$	−25.3152	+	19.3725i	−0.879763	+	0.673243i
$829$	35.8241	−	20.6830i	1.24422	−	0.718352i	0.274271	−	0.961653i	$-0.411564\pi$
$829$	35.8241	−	20.6830i	1.24422	−	0.718352i	0.969951	+	0.243301i	$0.0782303\pi$
$830$		0			0
$831$	−20.3800	+	35.2992i	−0.706974	+	1.22452i
$832$	−9.61631	−	23.4755i	−0.333386	−	0.813866i
$833$	−7.31833	−	22.9814i	−0.253565	−	0.796259i
$834$	−26.4434	+	17.6439i	−0.915659	+	0.610959i
$835$		0			0
$836$	−1.18640	−	9.10347i	−0.0410327	−	0.314850i
$837$	21.9187	+	37.9642i	0.757620	+	1.31224i
$838$	−1.08655	−	16.7451i	−0.0375343	−	0.578448i
$839$	−46.4174			−1.60251			−0.801253	−	0.598326i	$-0.795833\pi$
$839$	−46.4174			−1.60251			−0.801253	+	0.598326i	$0.795833\pi$
$840$		0			0
$841$	25.4780			0.878551
$842$	−0.947163	−	14.5969i	−0.0326414	−	0.503043i
$843$	−14.2155	−	24.6219i	−0.489607	−	0.848025i
$844$	−0.958861	−	7.35749i	−0.0330054	−	0.253255i
$845$		0			0
$846$	43.1651	−	28.8013i	1.48405	−	0.990208i
$847$	−2.43641	−	15.6804i	−0.0837159	−	0.538786i
$848$	13.1397	+	13.2085i	0.451219	+	0.453582i
$849$	−32.3038	+	55.9518i	−1.10866	+	1.92026i
$850$		0			0
$851$	25.7996	−	14.8954i	0.884398	−	0.510608i
$852$	1.01118	−	0.773811i	0.0346425	−	0.0265103i
$853$		−	10.5928i		−	0.362692i	−0.983419	−	0.181346i	$-0.941955\pi$
$853$		−	10.5928i		−	0.362692i	0.983419	−	0.181346i	$-0.0580454\pi$
$854$	−2.06149	−	9.26471i	−0.0705427	−	0.317032i
$855$		0			0
$856$	−2.38101	+	6.96937i	−0.0813814	+	0.238208i
$857$	0.245410	−	0.141688i	0.00838305	−	0.00483996i	−0.495803	−	0.868435i	$-0.665126\pi$
$857$	0.245410	−	0.141688i	0.00838305	−	0.00483996i	0.504186	+	0.863595i	$0.331793\pi$
$858$	−26.9618	−	13.3180i	−0.920461	−	0.454669i
$859$	−4.93861	+	8.55393i	−0.168503	+	0.291856i	−0.937894	−	0.346922i	$-0.887227\pi$
$859$	−4.93861	+	8.55393i	−0.168503	+	0.291856i	0.769391	+	0.638779i	$0.220560\pi$
$860$		0			0
$861$	4.18236	−	10.8006i	0.142535	−	0.368084i
$862$	−23.2787	−	34.8883i	−0.792875	−	1.18830i
$863$	28.2007	+	16.2817i	0.959963	+	0.554235i	0.896162	−	0.443728i	$-0.146344\pi$
$863$	28.2007	+	16.2817i	0.959963	+	0.554235i	0.0638012	+	0.997963i	$0.479678\pi$
$864$	−16.1374	−	48.0541i	−0.549006	−	1.63483i
$865$		0			0
$866$	−41.5057	+	2.69321i	−1.41042	+	0.0915192i
$867$	15.3759			0.522195
$868$	25.1449	+	6.14961i	0.853473	+	0.208731i
$869$	−1.03151			−0.0349916
$870$		0			0
$871$	−0.0836685	−	0.144918i	−0.00283500	−	0.00491036i
$872$	2.13420	−	1.86426i	0.0722732	−	0.0631319i
$873$	0.961883	+	0.555343i	0.0325548	+	0.0187955i
$874$	−4.28733	−	6.42551i	−0.145021	−	0.217346i
$875$		0			0
$876$	82.3573	+	34.2396i	2.78260	+	1.15685i
$877$	19.0353	−	32.9700i	0.642775	−	1.11332i	−0.342036	−	0.939687i	$-0.611116\pi$
$877$	19.0353	−	32.9700i	0.642775	−	1.11332i	0.984811	−	0.173632i	$-0.0555503\pi$
$878$	11.1883	+	5.52652i	0.377585	+	0.186511i
$879$	75.1666	−	43.3975i	2.53531	−	1.46376i
$880$		0			0
$881$		−	27.7529i		−	0.935019i	−0.883988	−	0.467509i	$-0.845151\pi$
$881$		−	27.7529i		−	0.935019i	0.883988	−	0.467509i	$-0.154849\pi$
$882$	37.0068	−	46.3186i	1.24608	−	1.55963i
$883$			44.1707i			1.48646i	0.669034	+	0.743232i	$0.266708\pi$
$883$			44.1707i			1.48646i	−0.669034	+	0.743232i	$0.733292\pi$
$884$	−13.2800	−	17.3537i	−0.446656	−	0.583669i
$885$		0			0
$886$	−12.2551	+	24.8100i	−0.411717	+	0.833508i
$887$	10.0638	−	17.4310i	0.337909	−	0.585275i	−0.646130	−	0.763227i	$-0.723614\pi$
$887$	10.0638	−	17.4310i	0.337909	−	0.585275i	0.984039	+	0.177952i	$0.0569471\pi$
$888$	18.3363	+	93.1358i	0.615326	+	3.12543i
$889$	5.01611	+	6.23167i	0.168235	+	0.209003i
$890$		0			0
$891$	−17.2385	−	9.95263i	−0.577510	−	0.333426i
$892$	25.6988	−	3.34919i	0.860461	−	0.112139i
$893$	6.28724	+	10.8898i	0.210394	+	0.364414i
$894$	−1.78493	−	27.5079i	−0.0596968	−	0.920000i
$895$		0			0
$896$	−27.0889	−	12.7355i	−0.904976	−	0.425462i
$897$	−25.3027			−0.844831
$898$	−0.459978	−	7.08882i	−0.0153497	−	0.236557i
$899$	−18.0537	−	31.2699i	−0.602124	−	1.04291i
$900$		0			0
$901$	13.8983	+	8.02418i	0.463019	+	0.267324i
$902$	−3.84167	+	2.56329i	−0.127913	+	0.0853483i
$903$	−28.5224	+	73.6569i	−0.949167	+	2.45115i
$904$	−8.11832	−	41.2355i	−0.270011	−	1.37147i
$905$		0			0
$906$	44.4561	−	90.0000i	1.47696	−	2.99005i
$907$	−13.0052	+	7.50854i	−0.431830	+	0.249317i	−0.700126	−	0.714020i	$-0.746873\pi$
$907$	−13.0052	+	7.50854i	−0.431830	+	0.249317i	0.268296	+	0.963336i	$0.413539\pi$
$908$	10.8084	+	14.1240i	0.358690	+	0.468720i
$909$		−	37.4239i		−	1.24127i
$910$		0			0
$911$			24.0198i			0.795811i	0.917426	+	0.397906i	$0.130263\pi$
$911$			24.0198i			0.795811i	−0.917426	+	0.397906i	$0.869737\pi$
$912$	23.7909	−	6.30821i	0.787795	−	0.208886i
$913$	21.1461	−	12.2087i	0.699834	−	0.404049i
$914$	35.3063	+	17.4398i	1.16783	+	0.576857i
$915$		0			0
$916$	23.9076	+	9.93946i	0.789931	+	0.328409i
$917$	−6.37981	−	41.0597i	−0.210680	−	1.35591i
$918$	−24.2349	−	36.3214i	−0.799871	−	1.19878i
$919$	49.7575	+	28.7275i	1.64135	+	0.947632i	0.980355	+	0.197239i	$0.0631976\pi$
$919$	49.7575	+	28.7275i	1.64135	+	0.947632i	0.660992	+	0.750393i	$0.270136\pi$
$920$		0			0
$921$	12.0014	+	20.7870i	0.395459	+	0.684956i
$922$	−28.0124	+	1.81767i	−0.922541	+	0.0598617i
$923$	0.673370			0.0221643
$924$	−34.0637	+	9.93325i	−1.12061	+	0.326780i
$925$		0			0
$926$	−50.3981	+	3.27022i	−1.65618	+	0.107466i
$927$	−34.1915	−	59.2214i	−1.12300	−	1.94509i
$928$	13.2919	+	39.5806i	0.436327	+	1.29930i
$929$	3.45964	+	1.99743i	0.113507	+	0.0655334i	0.555679	−	0.831397i	$-0.312458\pi$
$929$	3.45964	+	1.99743i	0.113507	+	0.0655334i	−0.442172	+	0.896930i	$0.645792\pi$
$930$		0			0
$931$	10.6198	+	9.67552i	0.348049	+	0.317102i
$932$	11.6827	−	28.1006i	0.382678	−	0.920466i
$933$	−20.6162	+	35.7083i	−0.674945	+	1.16904i
$934$	−28.6700	−	14.1617i	−0.938110	−	0.463386i
$935$		0			0
$936$	17.3658	−	50.8307i	0.567619	−	1.66145i
$937$			43.2204i			1.41195i	0.708237	+	0.705975i	$0.249491\pi$
$937$			43.2204i			1.41195i	−0.708237	+	0.705975i	$0.750509\pi$
$938$	−0.188353	−	0.0592267i	−0.00614995	−	0.00193382i
$939$			31.8878i			1.04062i
$940$		0			0
$941$	−30.6731	+	17.7091i	−0.999915	+	0.577301i	−0.908223	−	0.418486i	$-0.862561\pi$
$941$	−30.6731	+	17.7091i	−0.999915	+	0.577301i	−0.0916918	+	0.995787i	$0.529227\pi$
$942$	14.7078	−	29.7754i	0.479206	−	0.970136i
$943$	−1.94295	+	3.36529i	−0.0632712	+	0.109589i
$944$	20.0823	+	20.1874i	0.653622	+	0.657044i
$945$		0			0
$946$	26.1990	−	17.4809i	0.851802	−	0.568352i
$947$	42.1696	+	24.3466i	1.37033	+	0.791159i	0.990969	−	0.134091i	$-0.0428116\pi$
$947$	42.1696	+	24.3466i	1.37033	+	0.791159i	0.379358	+	0.925250i	$0.376145\pi$
$948$	−0.357390	−	2.74231i	−0.0116075	−	0.0890662i
$949$	23.5840	+	40.8488i	0.765571	+	1.32601i
$950$		0			0
$951$	50.9190			1.65116
$952$	−25.3897	−	4.49073i	−0.822886	−	0.145546i
$953$	47.5308			1.53967			0.769837	−	0.638241i	$-0.220338\pi$
$953$	47.5308			1.53967			0.769837	+	0.638241i	$0.220338\pi$
$954$	2.55440	+	39.3663i	0.0827016	+	1.27453i
$955$		0			0
$956$	0.0113339	+	0.0869671i	0.000366566	+	0.00281272i
$957$	42.8623	+	24.7466i	1.38554	+	0.799943i
$958$	10.0746	−	6.72211i	0.325495	−	0.217182i
$959$	−23.7208	−	9.18550i	−0.765986	−	0.296615i
$960$		0			0
$961$	3.53423	−	6.12147i	0.114008	−	0.197467i
$962$	−22.2321	+	45.0082i	−0.716792	+	1.45112i
$963$	−13.5050	+	7.79713i	−0.435193	+	0.251259i
$964$	−3.65400	+	2.79624i	−0.117688	+	0.0900609i
$965$		0			0
$966$	−21.9960	+	20.1870i	−0.707708	+	0.649508i
$967$		−	29.3643i		−	0.944292i	−0.881520	−	0.472146i	$-0.843479\pi$
$967$		−	29.3643i		−	0.944292i	0.881520	−	0.472146i	$-0.156521\pi$
$968$	−16.0532	−	5.48442i	−0.515970	−	0.176276i
$969$	18.3607	−	10.6005i	0.589829	−	0.340538i
$970$		0			0
$971$	−13.3188	+	23.0688i	−0.427419	+	0.740312i	−0.996643	−	0.0818708i	$-0.973911\pi$
$971$	−13.3188	+	23.0688i	−0.427419	+	0.740312i	0.569224	+	0.822183i	$0.307244\pi$
$972$	−0.153506	+	0.369231i	−0.00492370	+	0.0118431i
$973$	−15.4523	+	12.4382i	−0.495379	+	0.398749i
$974$	−24.8391	−	37.2269i	−0.795895	−	1.19283i
$975$		0			0
$976$	−9.79398	−	2.65172i	−0.313498	−	0.0848795i
$977$	7.73476	+	13.3970i	0.247457	+	0.428608i	0.962819	−	0.270146i	$-0.0870718\pi$
$977$	7.73476	+	13.3970i	0.247457	+	0.428608i	−0.715363	+	0.698753i	$0.753739\pi$
$978$	45.9143	−	2.97928i	1.46818	−	0.0952668i
$979$	15.7018			0.501832
$980$		0			0
$981$	6.00019			0.191571
$982$	−50.4916	+	3.27629i	−1.61125	+	0.104551i
$983$	22.0131	+	38.1277i	0.702107	+	1.21609i	0.967725	+	0.252007i	$0.0810907\pi$
$983$	22.0131	+	38.1277i	0.702107	+	1.21609i	−0.265618	+	0.964078i	$0.585576\pi$
$984$	−8.14565	−	9.32511i	−0.259674	−	0.297274i
$985$		0			0
$986$	19.9615	+	29.9167i	0.635703	+	0.952743i
$987$	37.8591	−	30.4743i	1.20507	−	0.970006i
$988$	12.0191	+	4.99686i	0.382378	+	0.158971i
$989$	13.2503	−	22.9502i	0.421336	−	0.729775i
$990$		0			0
$991$	14.4776	−	8.35865i	0.459896	−	0.265521i	−0.252104	−	0.967700i	$-0.581123\pi$
$991$	14.4776	−	8.35865i	0.459896	−	0.265521i	0.712001	+	0.702179i	$0.247789\pi$
$992$	18.3141	−	20.7462i	0.581472	−	0.658692i
$993$			24.9751i			0.792560i
$994$	0.585370	−	0.537230i	0.0185668	−	0.0170399i
$995$		0			0
$996$	39.7839	+	51.9877i	1.26060	+	1.64729i
$997$	−23.8844	+	13.7897i	−0.756427	+	0.436723i	−0.828011	−	0.560711i	$-0.810528\pi$
$997$	−23.8844	+	13.7897i	−0.756427	+	0.436723i	0.0715845	+	0.997435i	$0.477194\pi$
$998$	25.8762	−	52.3856i	0.819098	−	1.65824i
$999$	−50.1540	+	86.8693i	−1.58680	+	2.74842i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.2.p.c.551.9		32
4.3	odd	2	inner	700.2.p.c.551.14		32
5.2	odd	4		700.2.t.c.299.16		32
5.3	odd	4		700.2.t.d.299.1		32
5.4	even	2		140.2.o.a.131.8	yes	32
7.3	odd	6	inner	700.2.p.c.451.14		32
20.3	even	4		700.2.t.d.299.6		32
20.7	even	4		700.2.t.c.299.11		32
20.19	odd	2		140.2.o.a.131.3	yes	32
28.3	even	6	inner	700.2.p.c.451.9		32
35.3	even	12		700.2.t.c.199.11		32
35.4	even	6		980.2.o.f.31.3		32
35.9	even	6		980.2.g.a.391.25		32
35.17	even	12		700.2.t.d.199.6		32
35.19	odd	6		980.2.g.a.391.26		32
35.24	odd	6		140.2.o.a.31.3	✓	32
35.34	odd	2		980.2.o.f.411.8		32
140.3	odd	12		700.2.t.c.199.16		32
140.19	even	6		980.2.g.a.391.27		32
140.39	odd	6		980.2.o.f.31.8		32
140.59	even	6		140.2.o.a.31.8	yes	32
140.79	odd	6		980.2.g.a.391.28		32
140.87	odd	12		700.2.t.d.199.1		32
140.139	even	2		980.2.o.f.411.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.3	✓	32	35.24	odd	6
140.2.o.a.31.8	yes	32	140.59	even	6
140.2.o.a.131.3	yes	32	20.19	odd	2
140.2.o.a.131.8	yes	32	5.4	even	2
700.2.p.c.451.9		32	28.3	even	6	inner
700.2.p.c.451.14		32	7.3	odd	6	inner
700.2.p.c.551.9		32	1.1	even	1	trivial
700.2.p.c.551.14		32	4.3	odd	2	inner
700.2.t.c.199.11		32	35.3	even	12
700.2.t.c.199.16		32	140.3	odd	12
700.2.t.c.299.11		32	20.7	even	4
700.2.t.c.299.16		32	5.2	odd	4
700.2.t.d.199.1		32	140.87	odd	12
700.2.t.d.199.6		32	35.17	even	12
700.2.t.d.299.1		32	5.3	odd	4
700.2.t.d.299.6		32	20.3	even	4
980.2.g.a.391.25		32	35.9	even	6
980.2.g.a.391.26		32	35.19	odd	6
980.2.g.a.391.27		32	140.19	even	6
980.2.g.a.391.28		32	140.79	odd	6
980.2.o.f.31.3		32	35.4	even	6
980.2.o.f.31.8		32	140.39	odd	6
980.2.o.f.411.3		32	140.139	even	2
980.2.o.f.411.8		32	35.34	odd	2

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:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	700.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0915727 - 1.41125i) q^{2} +(-1.49907 - 2.59647i) q^{3} +(-1.98323 + 0.258463i) q^{4} +(-3.52698 + 2.35332i) q^{6} +(-2.06101 + 1.65899i) q^{7} +(0.546365 + 2.77516i) q^{8} +(-2.99443 + 5.18651i) q^{9} +(1.93693 - 1.11828i) q^{11} +(3.64409 + 4.76194i) q^{12} +3.17109i q^{13} +(2.52997 + 2.75667i) q^{14} +(3.86639 - 1.02518i) q^{16} +(2.98390 - 1.72275i) q^{17} +(7.59365 + 3.75094i) q^{18} +(-1.02618 + 1.77739i) q^{19} +(7.39711 + 2.86441i) q^{21} +(-1.75554 - 2.63107i) q^{22} +(-2.30481 - 1.33068i) q^{23} +(6.38656 - 5.57878i) q^{24} +(4.47519 - 0.290385i) q^{26} +8.96105 q^{27} +(3.65867 - 3.82285i) q^{28} -7.38092 q^{29} +(2.44599 + 4.23658i) q^{31} +(-1.80084 - 5.36255i) q^{32} +(-5.80718 - 3.35278i) q^{33} +(-2.70447 - 4.05325i) q^{34} +(4.59812 - 11.0600i) q^{36} +(-5.59689 + 9.69410i) q^{37} +(2.60230 + 1.28543i) q^{38} +(8.23364 - 4.75369i) q^{39} -1.46011i q^{41} +(3.36501 - 10.7014i) q^{42} +9.95752i q^{43} +(-3.55233 + 2.71844i) q^{44} +(-1.66686 + 3.37451i) q^{46} +(3.06343 - 5.30601i) q^{47} +(-8.45786 - 8.50215i) q^{48} +(1.49553 - 6.83838i) q^{49} +(-8.94615 - 5.16506i) q^{51} +(-0.819610 - 6.28900i) q^{52} +(2.32888 + 4.03374i) q^{53} +(-0.820587 - 12.6462i) q^{54} +(-5.73001 - 4.81321i) q^{56} +6.15325 q^{57} +(0.675891 + 10.4163i) q^{58} +(3.55938 + 6.16503i) q^{59} +(-2.19681 - 1.26833i) q^{61} +(5.75488 - 3.83985i) q^{62} +(-2.43279 - 15.6572i) q^{63} +(-7.40297 + 3.03249i) q^{64} +(-4.19981 + 8.50238i) q^{66} +(-0.0456998 + 0.0263848i) q^{67} +(-5.47248 + 4.18784i) q^{68} +7.97917i q^{69} -0.212347i q^{71} +(-16.0294 - 5.47629i) q^{72} +(12.8816 - 7.43720i) q^{73} +(14.1933 + 7.01088i) q^{74} +(1.57575 - 3.79020i) q^{76} +(-2.13680 + 5.51813i) q^{77} +(-7.46261 - 11.1844i) q^{78} +(-0.399413 - 0.230601i) q^{79} +(-4.44995 - 7.70755i) q^{81} +(-2.06058 + 0.133707i) q^{82} +10.9174 q^{83} +(-15.4105 - 3.76890i) q^{84} +(14.0525 - 0.911837i) q^{86} +(11.0645 + 19.1643i) q^{87} +(4.16168 + 4.76428i) q^{88} +(6.07992 + 3.51024i) q^{89} +(-5.26080 - 6.53565i) q^{91} +(4.91490 + 2.04334i) q^{92} +(7.33344 - 12.7019i) q^{93} +(-7.76862 - 3.83736i) q^{94} +(-11.2241 + 12.7147i) q^{96} -0.185459i q^{97} +(-9.78758 - 1.48435i) q^{98} +13.3945i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 16 q^{9} + 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} + 8 q^{22} + 36 q^{24} + 30 q^{26} - 2 q^{28} - 40 q^{29} - 2 q^{32} + 60 q^{36} - 8 q^{37} + 60 q^{38} + 62 q^{42}+ \cdots - 78 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 16 * q^9 + 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 + 8 * q^22 + 36 * q^24 + 30 * q^26 - 2 * q^28 - 40 * q^29 - 2 * q^32 + 60 * q^36 - 8 * q^37 + 60 * q^38 + 62 * q^42 - 18 * q^44 + 2 * q^46 - 16 * q^49 + 36 * q^52 + 8 * q^53 + 12 * q^54 - 4 * q^56 - 48 * q^57 - 2 * q^58 + 24 * q^61 + 4 * q^64 + 24 * q^66 - 60 * q^68 - 4 * q^72 + 72 * q^73 + 38 * q^74 + 40 * q^77 - 120 * q^78 - 36 * q^81 - 42 * q^82 - 20 * q^84 + 28 * q^86 - 4 * q^88 - 60 * q^89 + 4 * q^92 + 8 * q^93 + 18 * q^94 - 60 * q^96 - 78 * q^98

Introduction

L-functions

Modular forms

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