LMFDB - Embedded newform 700.2.t.c.299.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [700,2,Mod(199,700)] 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("700.199"); 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, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	700.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,2,0,0,0,0,16,0,0,-14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == 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			299.16
Character	$\chi$	$=$	700.299
Dual form			700.2.t.c.199.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41125 - 0.0915727i) q^{2} +(-2.59647 + 1.49907i) q^{3} +(1.98323 - 0.258463i) q^{4} +(-3.52698 + 2.35332i) q^{6} +(-1.65899 - 2.06101i) q^{7} +(2.77516 - 0.546365i) q^{8} +(2.99443 - 5.18651i) q^{9} +(1.93693 - 1.11828i) q^{11} +(-4.76194 + 3.64409i) q^{12} +3.17109 q^{13} +(-2.52997 - 2.75667i) q^{14} +(3.86639 - 1.02518i) q^{16} +(1.72275 + 2.98390i) q^{17} +(3.75094 - 7.59365i) q^{18} +(1.02618 - 1.77739i) q^{19} +(7.39711 + 2.86441i) q^{21} +(2.63107 - 1.75554i) q^{22} +(-1.33068 + 2.30481i) q^{23} +(-6.38656 + 5.57878i) q^{24} +(4.47519 - 0.290385i) q^{26} +8.96105i q^{27} +(-3.82285 - 3.65867i) q^{28} +7.38092 q^{29} +(2.44599 + 4.23658i) q^{31} +(5.36255 - 1.80084i) q^{32} +(-3.35278 + 5.80718i) q^{33} +(2.70447 + 4.05325i) q^{34} +(4.59812 - 11.0600i) q^{36} +(-9.69410 - 5.59689i) q^{37} +(1.28543 - 2.60230i) q^{38} +(-8.23364 + 4.75369i) q^{39} -1.46011i q^{41} +(10.7014 + 3.36501i) q^{42} +9.95752 q^{43} +(3.55233 - 2.71844i) q^{44} +(-1.66686 + 3.37451i) q^{46} +(5.30601 + 3.06343i) q^{47} +(-8.50215 + 8.45786i) q^{48} +(-1.49553 + 6.83838i) q^{49} +(-8.94615 - 5.16506i) q^{51} +(6.28900 - 0.819610i) q^{52} +(4.03374 - 2.32888i) q^{53} +(0.820587 + 12.6462i) q^{54} +(-5.73001 - 4.81321i) q^{56} +6.15325i q^{57} +(10.4163 - 0.675891i) q^{58} +(-3.55938 - 6.16503i) q^{59} +(-2.19681 - 1.26833i) q^{61} +(3.83985 + 5.75488i) q^{62} +(-15.6572 + 2.43279i) q^{63} +(7.40297 - 3.03249i) q^{64} +(-4.19981 + 8.50238i) q^{66} +(-0.0263848 - 0.0456998i) q^{67} +(4.18784 + 5.47248i) q^{68} -7.97917i q^{69} -0.212347i q^{71} +(5.47629 - 16.0294i) q^{72} +(-7.43720 - 12.8816i) q^{73} +(-14.1933 - 7.01088i) q^{74} +(1.57575 - 3.79020i) q^{76} +(-5.51813 - 2.13680i) q^{77} +(-11.1844 + 7.46261i) q^{78} +(0.399413 + 0.230601i) q^{79} +(-4.44995 - 7.70755i) q^{81} +(-0.133707 - 2.06058i) q^{82} -10.9174i q^{83} +(15.4105 + 3.76890i) q^{84} +(14.0525 - 0.911837i) q^{86} +(-19.1643 + 11.0645i) q^{87} +(4.76428 - 4.16168i) q^{88} +(-6.07992 - 3.51024i) q^{89} +(-5.26080 - 6.53565i) q^{91} +(-2.04334 + 4.91490i) q^{92} +(-12.7019 - 7.33344i) q^{93} +(7.76862 + 3.83736i) q^{94} +(-11.2241 + 12.7147i) q^{96} +0.185459 q^{97} +(-1.48435 + 9.78758i) q^{98} -13.3945i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38}+ \cdots - 124 q^{98}+O(q^{100}) $ 32 * q + 2 * q^4 + 16 * q^9 - 14 * q^12 - 8 * q^13 - 2 * q^14 - 14 * q^16 + 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 + 32 * q^28 + 40 * q^29 + 60 * q^32 - 24 * q^33 + 60 * q^36 - 60 * q^37 - 46 * q^38 + 78 * q^42 + 18 * q^44 + 2 * q^46 - 28 * q^48 + 16 * q^49 - 46 * q^52 - 12 * q^53 - 12 * q^54 - 4 * q^56 + 42 * q^58 + 24 * q^61 + 8 * q^62 - 4 * q^64 + 24 * q^66 - 4 * q^68 + 90 * q^72 - 24 * q^73 - 38 * q^74 + 20 * q^77 - 36 * q^81 + 8 * q^82 + 20 * q^84 + 28 * q^86 - 78 * q^88 + 60 * q^89 + 72 * q^93 - 18 * q^94 - 60 * q^96 - 48 * q^97 - 124 * 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 $

$2$	1.41125	−	0.0915727i	0.997901	−	0.0647517i
$2$	1.41125	−	0.0915727i	0.997901	−	0.0647517i
$3$	−2.59647	+	1.49907i	−1.49907	+	0.865490i	−0.999999	−	0.00107081i	$-0.999659\pi$
$3$	−2.59647	+	1.49907i	−1.49907	+	0.865490i	−0.499072	+	0.866560i	$0.666326\pi$
$4$	1.98323	−	0.258463i	0.991614	−	0.129232i
$5$		0			0
$5$		0			0
$6$	−3.52698	+	2.35332i	−1.43988	+	0.960741i
$7$	−1.65899	−	2.06101i	−0.627038	−	0.778989i
$7$	−1.65899	−	2.06101i	−0.627038	−	0.778989i
$8$	2.77516	−	0.546365i	0.981165	−	0.193169i
$9$	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	$0.223862\pi$
$12$	−4.76194	+	3.64409i	−1.37465	+	1.05196i
$13$	3.17109			0.879502			0.439751	−	0.898120i	$-0.355067\pi$
$13$	3.17109			0.879502			0.439751	+	0.898120i	$0.355067\pi$
$14$	−2.52997	−	2.75667i	−0.676163	−	0.736752i
$15$		0			0
$16$	3.86639	−	1.02518i	0.966598	−	0.256296i
$17$	1.72275	+	2.98390i	0.417829	+	0.723701i	0.995721	−	0.0924124i	$-0.0294578\pi$
$17$	1.72275	+	2.98390i	0.417829	+	0.723701i	−0.577892	+	0.816113i	$0.696124\pi$
$18$	3.75094	−	7.59365i	0.884104	−	1.78984i
$19$	1.02618	−	1.77739i	0.235421	−	0.407761i	−0.723974	−	0.689827i	$-0.757686\pi$
$19$	1.02618	−	1.77739i	0.235421	−	0.407761i	0.959395	+	0.282066i	$0.0910198\pi$
$20$		0			0
$21$	7.39711	+	2.86441i	1.61418	+	0.625065i
$22$	2.63107	−	1.75554i	0.560947	−	0.374283i
$23$	−1.33068	+	2.30481i	−0.277467	+	0.480587i	−0.970755	−	0.240074i	$-0.922828\pi$
$23$	−1.33068	+	2.30481i	−0.277467	+	0.480587i	0.693288	+	0.720661i	$0.256162\pi$
$24$	−6.38656	+	5.57878i	−1.30365	+	1.13876i
$25$		0			0
$26$	4.47519	−	0.290385i	0.877657	−	0.0569493i
$27$			8.96105i			1.72455i
$28$	−3.82285	−	3.65867i	−0.722450	−	0.691423i
$29$	7.38092			1.37060			0.685301	−	0.728260i	$-0.259671\pi$
$29$	7.38092			1.37060			0.685301	+	0.728260i	$0.259671\pi$
$30$		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	$0.688555\pi$
$32$	5.36255	−	1.80084i	0.947974	−	0.318347i
$33$	−3.35278	+	5.80718i	−0.583643	+	1.01090i
$34$	2.70447	+	4.05325i	0.463813	+	0.695127i
$35$		0			0
$36$	4.59812	−	11.0600i	0.766354	−	1.84333i
$37$	−9.69410	−	5.59689i	−1.59370	−	0.920123i	−0.992664	−	0.120902i	$-0.961421\pi$
$37$	−9.69410	−	5.59689i	−1.59370	−	0.920123i	−0.601036	−	0.799222i	$-0.705245\pi$
$38$	1.28543	−	2.60230i	0.208524	−	0.422149i
$39$	−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	$-0.0363714\pi$
$42$	10.7014	+	3.36501i	1.65127	+	0.519233i
$43$	9.95752			1.51851			0.759254	−	0.650794i	$-0.225564\pi$
$43$	9.95752			1.51851			0.759254	+	0.650794i	$0.225564\pi$
$44$	3.55233	−	2.71844i	0.535534	−	0.409820i
$45$		0			0
$46$	−1.66686	+	3.37451i	−0.245766	+	0.497545i
$47$	5.30601	+	3.06343i	0.773962	+	0.446847i	0.834286	−	0.551332i	$-0.185880\pi$
$47$	5.30601	+	3.06343i	0.773962	+	0.446847i	−0.0603243	+	0.998179i	$0.519213\pi$
$48$	−8.50215	+	8.45786i	−1.22718	+	1.22079i
$49$	−1.49553	+	6.83838i	−0.213647	+	0.976911i
$50$		0			0
$51$	−8.94615	−	5.16506i	−1.25271	−	0.723253i
$52$	6.28900	−	0.819610i	0.872127	−	0.113659i
$53$	4.03374	−	2.32888i	0.554077	−	0.319897i	−0.196688	−	0.980466i	$-0.563018\pi$
$53$	4.03374	−	2.32888i	0.554077	−	0.319897i	0.750765	+	0.660570i	$0.229685\pi$
$54$	0.820587	+	12.6462i	0.111668	+	1.72094i
$55$		0			0
$56$	−5.73001	−	4.81321i	−0.765705	−	0.643193i
$57$			6.15325i			0.815018i
$58$	10.4163	−	0.675891i	1.36773	−	0.0887488i
$59$	−3.55938	−	6.16503i	−0.463392	−	0.802619i	0.535735	−	0.844386i	$-0.320035\pi$
$59$	−3.55938	−	6.16503i	−0.463392	−	0.802619i	−0.999127	+	0.0417674i	$0.986701\pi$
$60$		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	$0.718588\pi$
$62$	3.83985	+	5.75488i	0.487662	+	0.730870i
$63$	−15.6572	+	2.43279i	−1.97262	+	0.306503i
$64$	7.40297	−	3.03249i	0.925371	−	0.379062i
$65$		0			0
$66$	−4.19981	+	8.50238i	−0.516961	+	1.04657i
$67$	−0.0263848	−	0.0456998i	−0.00322341	−	0.00558311i	0.864409	−	0.502789i	$-0.167693\pi$
$67$	−0.0263848	−	0.0456998i	−0.00322341	−	0.00558311i	−0.867633	+	0.497206i	$0.834359\pi$
$68$	4.18784	+	5.47248i	0.507850	+	0.663636i
$69$		−	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	$-0.00401095\pi$
$72$	5.47629	−	16.0294i	0.645387	−	1.88909i
$73$	−7.43720	−	12.8816i	−0.870459	−	1.50768i	−0.861523	−	0.507719i	$-0.830489\pi$
$73$	−7.43720	−	12.8816i	−0.870459	−	1.50768i	−0.00893589	−	0.999960i	$-0.502844\pi$
$74$	−14.1933	−	7.01088i	−1.64994	−	0.814998i
$75$		0			0
$76$	1.57575	−	3.79020i	0.180751	−	0.434766i
$77$	−5.51813	−	2.13680i	−0.628849	−	0.243511i
$78$	−11.1844	+	7.46261i	−1.26638	+	0.844974i
$79$	0.399413	+	0.230601i	0.0449375	+	0.0259447i	0.522300	−	0.852762i	$-0.325074\pi$
$79$	0.399413	+	0.230601i	0.0449375	+	0.0259447i	−0.477363	+	0.878706i	$0.658407\pi$
$80$		0			0
$81$	−4.44995	−	7.70755i	−0.494439	−	0.856394i
$82$	−0.133707	−	2.06058i	−0.0147654	−	0.227553i
$83$		−	10.9174i		−	1.19834i	−0.800624	−	0.599168i	$-0.795498\pi$
$83$		−	10.9174i		−	1.19834i	0.800624	−	0.599168i	$-0.204502\pi$
$84$	15.4105	+	3.76890i	1.68142	+	0.411221i
$85$		0			0
$86$	14.0525	−	0.911837i	1.51532	−	0.0983259i
$87$	−19.1643	+	11.0645i	−2.05463	+	1.18624i
$88$	4.76428	−	4.16168i	0.507874	−	0.443637i
$89$	−6.07992	−	3.51024i	−0.644470	−	0.372085i	0.141864	−	0.989886i	$-0.454690\pi$
$89$	−6.07992	−	3.51024i	−0.644470	−	0.372085i	−0.786334	+	0.617801i	$0.788024\pi$
$90$		0			0
$91$	−5.26080	−	6.53565i	−0.551481	−	0.685122i
$92$	−2.04334	+	4.91490i	−0.213033	+	0.512414i
$93$	−12.7019	−	7.33344i	−1.31712	−	0.760442i
$94$	7.76862	+	3.83736i	0.801272	+	0.395794i
$95$		0			0
$96$	−11.2241	+	12.7147i	−1.14556	+	1.29769i
$97$	0.185459			0.0188305			0.00941523	−	0.999956i	$-0.497003\pi$
$97$	0.185459			0.0188305			0.00941523	+	0.999956i	$0.497003\pi$
$98$	−1.48435	+	9.78758i	−0.149942	+	0.988695i
$99$		−	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	$0.433962\pi$
$102$	−13.0982	−	6.46995i	−1.29691	−	0.640620i
$103$	9.88858	+	5.70918i	0.974351	+	0.562542i	0.900560	−	0.434732i	$-0.143157\pi$
$103$	9.88858	+	5.70918i	0.974351	+	0.562542i	0.0737911	+	0.997274i	$0.476490\pi$
$104$	8.80027	−	1.73257i	0.862937	−	0.169893i
$105$		0			0
$106$	5.47934	−	3.65601i	0.532201	−	0.355103i
$107$	−1.30194	+	2.25502i	−0.125863	+	0.218001i	−0.922070	−	0.387023i	$-0.873503\pi$
$107$	−1.30194	+	2.25502i	−0.125863	+	0.218001i	0.796207	+	0.605024i	$0.206837\pi$
$108$	2.31610	+	17.7718i	0.222867	+	1.71009i
$109$	0.500946	+	0.867663i	0.0479819	+	0.0831071i	0.889019	−	0.457871i	$-0.151388\pi$
$109$	0.500946	+	0.867663i	0.0479819	+	0.0831071i	−0.841037	+	0.540978i	$0.818054\pi$
$110$		0			0
$111$	33.5606			3.18543
$112$	−8.52721	−	6.26791i	−0.805745	−	0.592262i
$113$			14.8588i			1.39780i	0.715220	+	0.698899i	$0.246326\pi$
$113$			14.8588i			1.39780i	−0.715220	+	0.698899i	$0.753674\pi$
$114$	0.563470	+	8.68375i	0.0527738	+	0.813307i
$115$		0			0
$116$	14.6381	−	1.90770i	1.35911	−	0.177125i
$117$	9.49562	−	16.4469i	0.877870	−	1.52052i
$118$	−5.58771	−	8.37443i	−0.514391	−	0.770929i
$119$	3.29182	−	8.50085i	0.301760	−	0.779272i
$120$		0			0
$121$	−2.99888	+	5.19421i	−0.272626	+	0.472201i
$122$	−3.21638	−	1.58875i	−0.291197	−	0.143839i
$123$	2.18882	+	3.79114i	0.197359	+	0.341836i
$124$	5.94597	+	7.76992i	0.533963	+	0.697759i
$125$		0			0
$126$	−21.8733	+	4.86704i	−1.94863	+	0.433590i
$127$	3.02360			0.268301			0.134151	−	0.990961i	$-0.457169\pi$
$127$	3.02360			0.268301			0.134151	+	0.990961i	$0.457169\pi$
$128$	10.1697	−	4.95750i	0.898885	−	0.438186i
$129$	−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	$0.925992\pi$
$132$	−5.14838	+	12.3835i	−0.448109	+	1.07785i
$133$	−5.36563	+	0.833705i	−0.465259	+	0.0722914i
$134$	−0.0414202	−	0.0620775i	−0.00357816	−	0.00536268i
$135$		0			0
$136$	6.41120	+	7.33952i	0.549756	+	0.629359i
$137$	−8.32628	+	4.80718i	−0.711362	+	0.410705i	−0.811565	−	0.584262i	$-0.801384\pi$
$137$	−8.32628	+	4.80718i	−0.711362	+	0.410705i	0.100203	+	0.994967i	$0.468051\pi$
$138$	−0.730674	−	11.2606i	−0.0621991	−	0.958563i
$139$	−7.49745			−0.635925			−0.317963	−	0.948103i	$-0.602999\pi$
$139$	−7.49745			−0.635925			−0.317963	+	0.948103i	$0.602999\pi$
$140$		0			0
$141$	−18.3692			−1.54697
$142$	−0.0194451	−	0.299673i	−0.00163180	−	0.0251480i
$143$	6.14217	−	3.54618i	0.513634	−	0.296547i
$144$	6.26053	−	23.1229i	0.521711	−	1.92691i
$145$		0			0
$146$	−11.6753	−	17.4981i	−0.966257	−	1.44815i
$147$	−6.36813	−	19.9975i	−0.525234	−	1.64937i
$148$	−20.6722	−	8.59435i	−1.69925	−	0.706451i
$149$	3.25066	−	5.63031i	0.266305	−	0.461253i	−0.701600	−	0.712571i	$-0.747531\pi$
$149$	3.25066	−	5.63031i	0.266305	−	0.461253i	0.967905	+	0.251318i	$0.0808640\pi$
$150$		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	$0.919827\pi$
$152$	1.87670	−	5.49320i	0.152220	−	0.445557i
$153$	20.6347			1.66821
$154$	−7.98311	−	2.51025i	−0.643297	−	0.202281i
$155$		0			0
$156$	−15.1005	+	11.5558i	−1.20901	+	0.925201i
$157$	−3.91624	−	6.78313i	−0.312550	−	0.541353i	0.666363	−	0.745627i	$-0.267850\pi$
$157$	−3.91624	−	6.78313i	−0.312550	−	0.541353i	−0.978914	+	0.204274i	$0.934517\pi$
$158$	0.584787	+	0.288860i	0.0465232	+	0.0229805i
$159$	−6.98233	+	12.0937i	−0.553734	+	0.959096i
$160$		0			0
$161$	6.95783	−	1.08110i	0.548354	−	0.0852026i
$162$	−6.98578	−	10.4697i	−0.548855	−	0.822581i
$163$	−5.42579	+	9.39774i	−0.424980	+	0.736088i	−0.996419	−	0.0845574i	$-0.973052\pi$
$163$	−5.42579	+	9.39774i	−0.424980	+	0.736088i	0.571438	+	0.820645i	$0.306386\pi$
$164$	−0.377386	−	2.89574i	−0.0294689	−	0.226119i
$165$		0			0
$166$	−0.999731	−	15.4071i	−0.0775942	−	1.19582i
$167$		−	11.7476i		−	0.909058i	−0.890732	−	0.454529i	$-0.849808\pi$
$167$		−	11.7476i		−	0.909058i	0.890732	−	0.454529i	$-0.150192\pi$
$168$	22.0931	+	3.90766i	1.70452	+	0.301483i
$169$	−2.94418			−0.226476
$170$		0			0
$171$	−6.14563	−	10.6445i	−0.469968	−	0.814009i
$172$	19.7480	−	2.57365i	1.50577	−	0.196239i
$173$	8.24371	−	14.2785i	0.626758	−	1.08558i	−0.361440	−	0.932395i	$-0.617715\pi$
$173$	8.24371	−	14.2785i	0.626758	−	1.08558i	0.988198	−	0.153181i	$-0.0489518\pi$
$174$	−26.0324	+	17.3697i	−1.97351	+	1.31679i
$175$		0			0
$176$	6.34247	−	6.30943i	0.478082	−	0.475591i
$177$	18.4836	+	10.6715i	1.38932	+	0.802122i
$178$	−8.90170	−	4.39706i	−0.667211	−	0.329574i
$179$	−7.88914	+	4.55480i	−0.589662	+	0.340441i	−0.764964	−	0.644073i	$-0.777243\pi$
$179$	−7.88914	+	4.55480i	−0.589662	+	0.340441i	0.175302	+	0.984515i	$0.443910\pi$
$180$		0			0
$181$			16.5755i			1.23205i	0.787728	+	0.616023i	$0.211257\pi$
$181$			16.5755i			1.23205i	−0.787728	+	0.616023i	$0.788743\pi$
$182$	−8.02276	−	8.74166i	−0.594687	−	0.647975i
$183$	7.60525			0.562196
$184$	−2.43359	+	7.12325i	−0.179406	+	0.525133i
$185$		0			0
$186$	−18.5970	−	9.18614i	−1.36360	−	0.673560i
$187$	6.67369	+	3.85305i	0.488028	+	0.281763i
$188$	11.3148	+	4.70407i	0.825218	+	0.343080i
$189$	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	$0.632132\pi$
$192$	−14.6757	+	18.9714i	−1.05912	+	1.36914i
$193$	−12.7382	+	7.35442i	−0.916918	+	0.529383i	−0.882651	−	0.470030i	$-0.844243\pi$
$193$	−12.7382	+	7.35442i	−0.916918	+	0.529383i	−0.0342676	+	0.999413i	$0.510910\pi$
$194$	0.261728	−	0.0169829i	0.0187909	−	0.00121930i
$195$		0			0
$196$	−1.19851	+	13.9486i	−0.0856075	+	0.996329i
$197$		−	4.81748i		−	0.343231i	−0.985164	−	0.171616i	$-0.945101\pi$
$197$		−	4.81748i		−	0.343231i	0.985164	−	0.171616i	$-0.0548987\pi$
$198$	−1.22657	−	18.9029i	−0.0871686	−	1.34337i
$199$	−0.637180	−	1.10363i	−0.0451685	−	0.0782342i	0.842557	−	0.538607i	$-0.181049\pi$
$199$	−0.637180	−	1.10363i	−0.0451685	−	0.0782342i	−0.887726	+	0.460373i	$0.847716\pi$
$200$		0			0
$201$	0.137014	+	0.0791053i	0.00966425	+	0.00557966i
$202$	−7.35115	+	4.90494i	−0.517225	+	0.345110i
$203$	−12.2448	−	15.2122i	−0.859420	−	1.06768i
$204$	−19.0772	−	7.93125i	−1.33567	−	0.555298i
$205$		0			0
$206$	14.4780	+	7.15153i	1.00873	+	0.498270i
$207$	7.96929	+	13.8032i	0.553904	+	0.959390i
$208$	12.2607	−	3.25095i	0.850126	−	0.225413i
$209$		−	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	$0.959241\pi$
$212$	7.39791	−	5.66128i	0.508090	−	0.388818i
$213$	0.318323	+	0.551351i	0.0218111	+	0.0377780i
$214$	−1.63085	+	3.30161i	−0.111483	+	0.225693i
$215$		0			0
$216$	4.89600	+	24.8683i	0.333131	+	1.69207i
$217$	4.67378	−	12.0697i	0.317277	−	0.819342i
$218$	0.786412	+	1.17861i	0.0532625	+	0.0798258i
$219$	38.6209	+	22.2978i	2.60976	+	1.50675i
$220$		0			0
$221$	5.46301	+	9.46220i	0.367482	+	0.636497i
$222$	47.3622	−	3.07323i	3.17874	−	0.206262i
$223$			12.9581i			0.867737i	0.900976	+	0.433869i	$0.142852\pi$
$223$			12.9581i			0.867737i	−0.900976	+	0.433869i	$0.857148\pi$
$224$	−12.6080	−	8.06471i	−0.842404	−	0.538846i
$225$		0			0
$226$	1.36066	+	20.9694i	0.0905098	+	1.39487i
$227$	7.70115	−	4.44626i	0.511143	−	0.295109i	−0.222160	−	0.975010i	$-0.571311\pi$
$227$	7.70115	−	4.44626i	0.511143	−	0.295109i	0.733304	+	0.679901i	$0.237977\pi$
$228$	1.59039	+	12.2033i	0.105326	+	0.808183i
$229$	11.2113	+	6.47287i	0.740866	+	0.427739i	0.822384	−	0.568933i	$-0.192643\pi$
$229$	11.2113	+	6.47287i	0.740866	+	0.427739i	−0.0815180	+	0.996672i	$0.525977\pi$
$230$		0			0
$231$	17.5309	−	2.72392i	1.15345	−	0.179221i
$232$	20.4832	−	4.03267i	1.34479	−	0.264758i
$233$	13.1776	+	7.60809i	0.863294	+	0.498423i	0.865114	−	0.501576i	$-0.167246\pi$
$233$	13.1776	+	7.60809i	0.863294	+	0.498423i	−0.00182020	+	0.999998i	$0.500579\pi$
$234$	11.8946	−	24.0801i	0.777572	−	1.57417i
$235$		0			0
$236$	−8.65250	−	11.3067i	−0.563230	−	0.736003i
$237$	−1.38275			−0.0898194
$238$	3.86712	−	12.2982i	0.250668	−	0.797176i
$239$			0.0438513i			0.00283650i	0.999999	+	0.00141825i	$0.000451444\pi$
$239$			0.0438513i			0.00283650i	−0.999999	+	0.00141825i	$0.999549\pi$
$240$		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	$0.309726\pi$
$242$	−3.75651	+	7.60493i	−0.241478	+	0.488863i
$243$	−0.173149	−	0.0999675i	−0.0111075	−	0.00641292i
$244$	−4.68458	−	1.94759i	−0.299900	−	0.124682i
$245$		0			0
$246$	3.43612	+	5.14979i	0.219079	+	0.328339i
$247$	3.25410	−	5.63627i	0.207053	−	0.358627i
$248$	9.10273	+	10.4208i	0.578024	+	0.661720i
$249$	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	$0.563960\pi$
$252$	−30.4230	+	8.87159i	−1.91647	+	0.558857i
$253$			5.95233i			0.374220i
$254$	4.26704	−	0.276879i	0.267738	−	0.0173729i
$255$		0			0
$256$	13.8980	−	7.92752i	0.868625	−	0.495470i
$257$	−7.12068	+	12.3334i	−0.444176	+	0.769335i	−0.997994	−	0.0633025i	$-0.979837\pi$
$257$	−7.12068	+	12.3334i	−0.444176	+	0.769335i	0.553819	+	0.832637i	$0.313170\pi$
$258$	−35.1200	+	23.4333i	−2.18648	+	1.45889i
$259$	4.54713	+	29.2648i	0.282545	+	1.81843i
$260$		0			0
$261$	22.1017	−	38.2812i	1.36806	−	2.36955i
$262$	−9.83654	+	19.9138i	−0.607704	+	1.23028i
$263$	−5.87421	−	10.1744i	−0.362219	−	0.627382i	0.626107	−	0.779738i	$-0.284647\pi$
$263$	−5.87421	−	10.1744i	−0.362219	−	0.627382i	−0.988326	+	0.152355i	$0.951314\pi$
$264$	−6.13164	+	17.9477i	−0.377376	+	1.10460i
$265$		0			0
$266$	−7.49588	+	1.66791i	−0.459602	+	0.102266i
$267$	21.0484			1.28814
$268$	−0.0641387	−	0.0838136i	−0.00391790	−	0.00511973i
$269$	7.35196	−	4.24466i	0.448257	−	0.258801i	−0.258837	−	0.965921i	$-0.583339\pi$
$269$	7.35196	−	4.24466i	0.448257	−	0.258801i	0.707094	+	0.707120i	$0.250006\pi$
$270$		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	$0.0888028\pi$
$272$	9.71988	+	9.77078i	0.589354	+	0.592440i
$273$	23.4569	+	9.08330i	1.41968	+	0.549746i
$274$	−11.3102	+	7.54657i	−0.683275	+	0.455905i
$275$		0			0
$276$	−2.06232	−	15.8245i	−0.124137	−	0.952524i
$277$	11.7737	−	6.79754i	0.707412	−	0.408425i	−0.102690	−	0.994713i	$-0.532745\pi$
$277$	11.7737	−	6.79754i	0.707412	−	0.408425i	0.810102	+	0.586289i	$0.199412\pi$
$278$	−10.5807	+	0.686562i	−0.634591	+	0.0411772i
$279$	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	$0.408720\pi$
$282$	−25.9235	+	1.68212i	−1.54372	+	0.100169i
$283$	−18.6621	+	10.7746i	−1.10935	+	0.640483i	−0.938661	−	0.344842i	$-0.887933\pi$
$283$	−18.6621	+	10.7746i	−1.10935	+	0.640483i	−0.170689	+	0.985325i	$0.554599\pi$
$284$	−0.0548838	−	0.421132i	−0.00325675	−	0.0249896i
$285$		0			0
$286$	8.34337	−	5.56699i	0.493354	−	0.329183i
$287$	−3.00931	+	2.42231i	−0.177634	+	0.142984i
$288$	6.71772	−	33.2054i	0.395845	−	1.95665i
$289$	2.56424	−	4.44140i	0.150838	−	0.261259i
$290$		0			0
$291$	−0.481537	+	0.278016i	−0.0282282	+	0.0162976i
$292$	−18.0791	−	23.6249i	−1.05800	−	1.38255i
$293$	28.9496			1.69125			0.845626	−	0.533776i	$-0.179227\pi$
$293$	28.9496			1.69125			0.845626	+	0.533776i	$0.179227\pi$
$294$	−10.8182	−	27.6383i	−0.630931	−	1.61190i
$295$		0			0
$296$	−29.9606	−	10.2357i	−1.74142	−	0.594940i
$297$	10.0210	+	17.3569i	0.581477	+	1.00715i
$298$	4.07190	−	8.24342i	0.235879	−	0.477529i
$299$	−4.21972	+	7.30877i	−0.244033	+	0.422677i
$300$		0			0
$301$	−16.5194	−	20.5226i	−0.952162	−	1.18290i
$302$	−27.8506	+	18.5829i	−1.60262	+	1.06933i
$303$	9.36757	−	16.2251i	0.538153	−	0.932108i
$304$	2.14545	−	7.92411i	0.123050	−	0.454479i
$305$		0			0
$306$	29.1206	−	1.88957i	1.66471	−	0.108020i
$307$		−	8.00589i		−	0.456920i	−0.973553	−	0.228460i	$-0.926631\pi$
$307$		−	8.00589i		−	0.456920i	0.973553	−	0.228460i	$-0.0733690\pi$
$308$	−11.4960	−	2.81154i	−0.655045	−	0.160202i
$309$	−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	$0.960831\pi$
$312$	−20.2524	+	17.6908i	−1.14656	+	1.00154i
$313$	−5.31792	+	9.21091i	−0.300587	+	0.520631i	−0.976269	−	0.216562i	$-0.930516\pi$
$313$	−5.31792	+	9.21091i	−0.300587	+	0.520631i	0.675682	+	0.737193i	$0.263849\pi$
$314$	−6.14793	−	9.21404i	−0.346948	−	0.519979i
$315$		0			0
$316$	0.851730	+	0.354102i	0.0479136	+	0.0199198i
$317$	−14.7081	−	8.49175i	−0.826091	−	0.476944i	0.0264211	−	0.999651i	$-0.491589\pi$
$317$	−14.7081	−	8.49175i	−0.826091	−	0.476944i	−0.852513	+	0.522707i	$0.824922\pi$
$318$	−8.74632	+	17.7066i	−0.490469	+	0.992939i
$319$	14.2963	−	8.25397i	0.800439	−	0.462133i
$320$		0			0
$321$		−	7.80679i		−	0.435732i
$322$	9.72021	−	2.16284i	0.541686	−	0.120531i
$323$	7.07140			0.393463
$324$	−10.8174	−	14.1357i	−0.600966	−	0.785316i
$325$		0			0
$326$	−6.79654	+	13.7594i	−0.376426	+	0.762061i
$327$	−2.60138	−	1.50191i	−0.143857	−	0.0830557i
$328$	−0.797755	−	4.05204i	−0.0440486	−	0.223737i
$329$	−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	$0.740191\pi$
$332$	−2.82173	−	21.6516i	−0.154863	−	1.18829i
$333$	−58.0567	+	33.5190i	−3.18149	+	1.83683i
$334$	−1.07576	−	16.5788i	−0.0588630	−	0.907150i
$335$		0			0
$336$	31.5367	+	3.49154i	1.72047	+	0.190479i
$337$			27.0772i			1.47499i	0.675353	+	0.737495i	$0.263991\pi$
$337$			27.0772i			1.47499i	−0.675353	+	0.737495i	$0.736009\pi$
$338$	−4.15496	+	0.269607i	−0.226000	+	0.0146647i
$339$	−22.2744	−	38.5804i	−1.20978	−	2.09540i
$340$		0			0
$341$	9.47541	+	5.47063i	0.513122	+	0.296251i
$342$	−9.64775	−	14.4593i	−0.521690	−	0.781870i
$343$	16.5750	−	8.26248i	0.894967	−	0.446132i
$344$	27.6337	−	5.44044i	1.48991	−	0.293329i
$345$		0			0
$346$	10.3264	−	20.9054i	0.555150	−	1.12388i
$347$	−13.8861	−	24.0514i	−0.745443	−	1.29115i	−0.949987	−	0.312288i	$-0.898905\pi$
$347$	−13.8861	−	24.0514i	−0.745443	−	1.29115i	0.204544	−	0.978857i	$-0.434429\pi$
$348$	−35.1475	+	26.8968i	−1.88410	+	1.44182i
$349$			9.64063i			0.516051i	0.966138	+	0.258026i	$0.0830719\pi$
$349$			9.64063i			0.516051i	−0.966138	+	0.258026i	$0.916928\pi$
$350$		0			0
$351$			28.4163i			1.51675i
$352$	8.37301	−	9.48495i	0.446283	−	0.505550i
$353$	−8.15697	−	14.1283i	−0.434152	−	0.751973i	0.563074	−	0.826406i	$-0.309619\pi$
$353$	−8.15697	−	14.1283i	−0.434152	−	0.751973i	−0.997226	+	0.0744333i	$0.976285\pi$
$354$	27.0622	+	13.3676i	1.43834	+	0.710478i
$355$		0			0
$356$	−12.9651	−	5.39018i	−0.687151	−	0.285679i
$357$	4.19629	+	27.0069i	0.222091	+	1.42936i
$358$	−10.7164	+	7.15037i	−0.566380	+	0.377909i
$359$	1.38744	+	0.801040i	0.0732264	+	0.0422773i	0.536166	−	0.844112i	$-0.319872\pi$
$359$	1.38744	+	0.801040i	0.0732264	+	0.0422773i	−0.462940	+	0.886390i	$0.653205\pi$
$360$		0			0
$361$	7.39392	+	12.8067i	0.389154	+	0.674034i
$362$	1.51786	+	23.3921i	0.0797771	+	1.22946i
$363$		−	17.9822i		−	0.943818i
$364$	−12.1226	−	11.6020i	−0.635396	−	0.608108i
$365$		0			0
$366$	10.7329	−	0.696433i	0.561016	−	0.0364031i
$367$	1.09164	−	0.630259i	0.0569832	−	0.0328993i	−0.471238	−	0.882006i	$-0.656193\pi$
$367$	1.09164	−	0.630259i	0.0569832	−	0.0328993i	0.528221	+	0.849107i	$0.322859\pi$
$368$	−2.78209	+	10.2755i	−0.145027	+	0.535648i
$369$	−7.57289	−	4.37221i	−0.394229	−	0.227608i
$370$		0			0
$371$	−11.4918	−	4.45000i	−0.596623	−	0.231033i
$372$	−27.0862	−	11.2609i	−1.40435	−	0.583851i
$373$	−7.99120	−	4.61372i	−0.413768	−	0.238889i	0.278639	−	0.960396i	$-0.410117\pi$
$373$	−7.99120	−	4.61372i	−0.413768	−	0.238889i	−0.692408	+	0.721507i	$0.743450\pi$
$374$	9.77105	+	4.82648i	0.505249	+	0.249571i
$375$		0			0
$376$	16.3988	+	5.60247i	0.845702	+	0.288925i
$377$	23.4056			1.20545
$378$	24.7027	−	22.6712i	1.27057	−	1.16608i
$379$		−	2.53516i		−	0.130223i	−0.997878	−	0.0651113i	$-0.979260\pi$
$379$		−	2.53516i		−	0.130223i	0.997878	−	0.0651113i	$-0.0207403\pi$
$380$		0			0
$381$	−7.85068	+	4.53259i	−0.402203	+	0.232212i
$382$	3.79495	+	1.87454i	0.194166	+	0.0959099i
$383$	1.14737	+	0.662435i	0.0586279	+	0.0338489i	0.529027	−	0.848605i	$-0.322557\pi$
$383$	1.14737	+	0.662435i	0.0586279	+	0.0338489i	−0.470400	+	0.882454i	$0.655890\pi$
$384$	−18.9737	+	28.1171i	−0.968248	+	1.43485i
$385$		0			0
$386$	−17.3033	+	11.5454i	−0.880715	+	0.587644i
$387$	29.8171	−	51.6448i	1.51569	−	2.62525i
$388$	0.367807	−	0.0479342i	0.0186726	−	0.00243349i
$389$	16.1134	+	27.9093i	0.816983	+	1.41506i	0.907895	+	0.419197i	$0.137688\pi$
$389$	16.1134	+	27.9093i	0.816983	+	1.41506i	−0.0909120	+	0.995859i	$0.528978\pi$
$390$		0			0
$391$	−9.16976			−0.463735
$392$	−0.414074	+	19.7947i	−0.0209139	+	0.999781i
$393$		−	47.0869i		−	2.37522i
$394$	−0.441150	−	6.79865i	−0.0222248	−	0.342511i
$395$		0			0
$396$	−3.46199	−	26.5644i	−0.173971	−	1.33491i
$397$	−17.5871	+	30.4617i	−0.882670	+	1.52883i	−0.0343095	+	0.999411i	$0.510923\pi$
$397$	−17.5871	+	30.4617i	−0.882670	+	1.52883i	−0.848361	+	0.529419i	$0.822410\pi$
$398$	−1.00028	−	1.49914i	−0.0501395	−	0.0751452i
$399$	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	$0.873022\pi$
$402$	0.200605	+	0.0990903i	0.0100053	+	0.00494217i
$403$	7.75647	+	13.4346i	0.386377	+	0.669225i
$404$	−9.92512	+	7.59524i	−0.493793	+	0.377877i
$405$		0			0
$406$	−18.6735	−	20.3468i	−0.926751	−	1.00979i
$407$	−25.0357			−1.24097
$408$	−27.6490	−	9.44599i	−1.36883	−	0.467646i
$409$	−14.2151	+	8.20712i	−0.702894	+	0.405816i	−0.808424	−	0.588600i	$-0.799679\pi$
$409$	−14.2151	+	8.20712i	−0.702894	+	0.405816i	0.105530	+	0.994416i	$0.466346\pi$
$410$		0			0
$411$	14.4126	−	24.9634i	0.710922	−	1.23135i
$412$	21.0869	+	8.76677i	1.03888	+	0.431908i
$413$	−6.80123	+	17.5636i	−0.334666	+	0.864250i
$414$	12.5106	+	18.7500i	0.614864	+	0.921510i
$415$		0			0
$416$	17.0051	−	5.71063i	0.833746	−	0.279987i
$417$	19.4669	−	11.2392i	0.953298	−	0.550387i
$418$	−0.420340	−	6.47794i	−0.0205595	−	0.316846i
$419$	−11.8654			−0.579665			−0.289832	−	0.957077i	$-0.593600\pi$
$419$	−11.8654			−0.579665			−0.289832	+	0.957077i	$0.593600\pi$
$420$		0			0
$421$	10.3433			0.504101			0.252051	−	0.967714i	$-0.418895\pi$
$421$	10.3433			0.504101			0.252051	+	0.967714i	$0.418895\pi$
$422$	0.339721	+	5.23552i	0.0165374	+	0.254861i
$423$	31.7770	−	18.3465i	1.54505	−	0.892035i
$424$	9.92185	−	8.66691i	0.481847	−	0.420902i
$425$		0			0
$426$	0.499720	+	0.748942i	0.0242115	+	0.0362864i
$427$	1.03044	+	6.63178i	0.0498663	+	0.320934i
$428$	−1.99920	+	4.80873i	−0.0966349	+	0.232439i
$429$	−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	$0.0800937\pi$
$432$	9.18671	+	34.6469i	0.441996	+	1.66695i
$433$	−29.4107			−1.41339			−0.706693	−	0.707520i	$-0.749814\pi$
$433$	−29.4107			−1.41339			−0.706693	+	0.707520i	$0.749814\pi$
$434$	5.49059	−	17.4612i	0.263557	−	0.838166i
$435$		0			0
$436$	1.21775	+	1.59130i	0.0583196	+	0.0762094i
$437$	2.73103	+	4.73029i	0.130643	+	0.226280i
$438$	56.5455	+	27.9311i	2.70185	+	1.33460i
$439$	4.41191	−	7.64165i	0.210569	−	0.364716i	−0.741324	−	0.671147i	$-0.765802\pi$
$439$	4.41191	−	7.64165i	0.210569	−	0.364716i	0.951893	+	0.306432i	$0.0991351\pi$
$440$		0			0
$441$	30.9890	+	28.2336i	1.47567	+	1.34446i
$442$	8.57612	+	12.8532i	0.407925	+	0.611366i
$443$	−9.78342	+	16.9454i	−0.464824	+	0.805099i	−0.999194	−	0.0401518i	$-0.987216\pi$
$443$	−9.78342	+	16.9454i	−0.464824	+	0.805099i	0.534369	+	0.845251i	$0.320549\pi$
$444$	66.5583	−	8.67417i	3.15872	−	0.411658i
$445$		0			0
$446$	1.18661	+	18.2870i	0.0561874	+	0.865916i
$447$			19.4919i			0.921935i
$448$	−18.5314	−	10.2267i	−0.875528	−	0.483168i
$449$	−5.02309			−0.237054			−0.118527	−	0.992951i	$-0.537817\pi$
$449$	−5.02309			−0.237054			−0.118527	+	0.992951i	$0.537817\pi$
$450$		0			0
$451$	−1.63282	−	2.82813i	−0.0768866	−	0.133171i
$452$	3.84045	+	29.4684i	0.180640	+	1.38608i
$453$	35.4900	−	61.4705i	1.66747	−	2.88814i
$454$	10.4611	−	6.97998i	0.490962	−	0.327587i
$455$		0			0
$456$	3.36192	+	17.0762i	0.157436	+	0.799667i
$457$	−24.1144	−	13.9225i	−1.12802	−	0.651265i	−0.184587	−	0.982816i	$-0.559095\pi$
$457$	−24.1144	−	13.9225i	−1.12802	−	0.651265i	−0.943437	+	0.331551i	$0.892428\pi$
$458$	16.4147	+	8.10816i	0.767008	+	0.378869i
$459$	−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	$-0.152954\pi$
$462$	24.4909	−	5.44948i	1.13942	−	0.253533i
$463$	−35.7118			−1.65967			−0.829833	−	0.558012i	$-0.811564\pi$
$463$	−35.7118			−1.65967			−0.829833	+	0.558012i	$0.811564\pi$
$464$	28.5375	−	7.56680i	1.32482	−	0.351280i
$465$		0			0
$466$	19.2935	+	9.53018i	0.893756	+	0.441477i
$467$	19.5818	+	11.3055i	0.906136	+	0.523158i	0.879186	−	0.476479i	$-0.158087\pi$
$467$	19.5818	+	11.3055i	0.906136	+	0.523158i	0.0269503	+	0.999637i	$0.491420\pi$
$468$	14.5811	−	35.0722i	0.674010	−	1.62121i
$469$	−0.0504157	+	0.130195i	−0.00232798	+	0.00601183i
$470$		0			0
$471$	20.3368	+	11.7415i	0.937070	+	0.541018i
$472$	−13.2462	−	15.1642i	−0.609705	−	0.697989i
$473$	19.2870	−	11.1353i	0.886816	−	0.512003i
$474$	−1.95140	+	0.126622i	−0.0896309	+	0.00581596i
$475$		0			0
$476$	4.33127	−	17.7100i	0.198523	−	0.811734i
$477$		−	27.8947i		−	1.27721i
$478$	0.00401558	+	0.0618849i	0.000183668	+	0.00283055i
$479$	−4.28200	−	7.41664i	−0.195649	−	0.338875i	0.751464	−	0.659774i	$-0.229348\pi$
$479$	−4.28200	−	7.41664i	−0.195649	−	0.338875i	−0.947113	+	0.320900i	$0.896015\pi$
$480$		0			0
$481$	−30.7409	−	17.7483i	−1.40166	−	0.809251i
$482$	2.70638	−	1.80579i	0.123272	−	0.0822515i
$483$	−16.4451	+	13.2373i	−0.748280	+	0.602319i
$484$	−4.60495	+	11.0764i	−0.209316	+	0.503473i
$485$		0			0
$486$	−0.253510	−	0.125223i	−0.0114994	−	0.00568023i
$487$	15.8225	+	27.4054i	0.716987	+	1.24186i	0.962188	+	0.272386i	$0.0878128\pi$
$487$	15.8225	+	27.4054i	0.716987	+	1.24186i	−0.245201	+	0.969472i	$0.578854\pi$
$488$	−6.78945	−	2.31955i	−0.307344	−	0.105001i
$489$		−	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	$-0.299083\pi$
$492$	5.32079	+	6.95297i	0.239880	+	0.313464i
$493$	12.7155	+	22.0239i	0.572677	+	0.991906i
$494$	4.07621	−	8.25214i	0.183397	−	0.371281i
$495$		0			0
$496$	13.8004	+	13.8727i	0.619658	+	0.622903i
$497$	−0.437649	+	0.352280i	−0.0196312	+	0.0158019i
$498$	25.6921	+	38.5053i	1.15129	+	1.72546i
$499$	−35.7797	−	20.6574i	−1.60172	−	0.924752i	−0.991144	−	0.132793i	$-0.957605\pi$
$499$	−35.7797	−	20.6574i	−1.60172	−	0.924752i	−0.610574	−	0.791959i	$-0.709061\pi$
$500$		0			0
$501$	17.6105	+	30.5023i	0.786780	+	1.36274i
$502$	−8.92485	+	0.579114i	−0.398336	+	0.0258471i
$503$			29.0170i			1.29381i	0.762572	+	0.646903i	$0.223936\pi$
$503$			29.0170i			1.29381i	−0.762572	+	0.646903i	$0.776064\pi$
$504$	−42.1219	+	15.3059i	−1.87626	+	0.681779i
$505$		0			0
$506$	0.545071	+	8.40021i	0.0242314	+	0.373435i
$507$	7.64448	−	4.41354i	0.339503	−	0.196012i
$508$	5.99649	−	0.781489i	0.266051	−	0.0346730i
$509$	−17.3474	−	10.0155i	−0.768910	−	0.443931i	0.0635754	−	0.997977i	$-0.479750\pi$
$509$	−17.3474	−	10.0155i	−0.768910	−	0.443931i	−0.832486	+	0.554046i	$0.813083\pi$
$510$		0			0
$511$	−14.2109	+	36.6986i	−0.628654	+	1.62345i
$512$	18.8875	−	12.4604i	0.834720	−	0.550675i
$513$	15.9273	+	9.19562i	0.703206	+	0.405996i
$514$	−8.91962	+	18.0575i	−0.393428	+	0.796481i
$515$		0			0
$516$	−47.4171	+	36.2861i	−2.08742	+	1.59741i
$517$	13.7031			0.602663
$518$	9.09698	+	40.8835i	0.399698	+	1.79632i
$519$			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	$0.177680\pi$
$522$	27.6854	−	56.0481i	1.21176	−	2.45316i
$523$	35.5105	+	20.5020i	1.55277	+	0.896491i	0.997915	+	0.0645418i	$0.0205586\pi$
$523$	35.5105	+	20.5020i	1.55277	+	0.896491i	0.554852	+	0.831949i	$0.312775\pi$
$524$	−12.0582	+	29.0040i	−0.526766	+	1.26704i
$525$		0			0
$526$	−9.22165	−	13.8207i	−0.402083	−	0.602611i
$527$	−8.42768	+	14.5972i	−0.367116	+	0.635863i
$528$	−7.00973	+	25.8901i	−0.305059	+	1.12672i
$529$	7.95856	+	13.7846i	0.346024	+	0.599332i
$530$		0			0
$531$	−42.6333			−1.85013
$532$	−10.4258	+	3.04025i	−0.452016	+	0.131811i
$533$		−	4.63015i		−	0.200554i
$534$	29.7045	−	1.92746i	1.28544	−	0.0834094i
$535$		0			0
$536$	−0.0981906	−	0.112408i	−0.00424119	−	0.00485530i
$537$	13.6559	−	23.6528i	0.589297	−	1.02069i
$538$	9.98673	−	6.66349i	0.430559	−	0.287284i
$539$	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	$0.190315\pi$
$542$	4.99409	−	10.1104i	0.214514	−	0.434277i
$543$	−24.8479	−	43.0377i	−1.06632	−	1.84693i
$544$	14.6119	+	12.8989i	0.626479	+	0.553035i
$545$		0			0
$546$	33.9352	+	10.6708i	1.45229	+	0.456666i
$547$	−28.2607			−1.20834			−0.604170	−	0.796855i	$-0.706495\pi$
$547$	−28.2607			−1.20834			−0.604170	+	0.796855i	$0.706495\pi$
$548$	−15.2704	+	11.6858i	−0.652321	+	0.499191i
$549$	−13.1564	+	7.59584i	−0.561500	+	0.324182i
$550$		0			0
$551$	7.57413	−	13.1188i	0.322669	−	0.558879i
$552$	−4.35953	−	22.1434i	−0.185554	−	0.942487i
$553$	−0.187349	−	1.20576i	−0.00796691	−	0.0512741i
$554$	15.9931	−	10.6711i	0.679481	−	0.453374i
$555$		0			0
$556$	−14.8692	+	1.93781i	−0.630593	+	0.0821816i
$557$	−1.79833	+	1.03826i	−0.0761976	+	0.0439927i	−0.537615	−	0.843191i	$-0.680674\pi$
$557$	−1.79833	+	1.03826i	−0.0761976	+	0.0439927i	0.461417	+	0.887183i	$0.347341\pi$
$558$	41.3459	−	2.68285i	1.75031	−	0.113574i
$559$	31.5762			1.33553
$560$		0			0
$561$	−23.1040			−0.975453
$562$	13.3826	−	0.868371i	0.564513	−	0.0366300i
$563$	39.7588	−	22.9547i	1.67563	−	0.967426i	0.711240	−	0.702949i	$-0.248134\pi$
$563$	39.7588	−	22.9547i	1.67563	−	0.967426i	0.964392	−	0.264477i	$-0.0851993\pi$
$564$	−36.4303	+	4.74776i	−1.53399	+	0.199917i
$565$		0			0
$566$	−25.3502	+	16.9145i	−1.06555	+	0.710971i
$567$	−8.50292	+	21.9581i	−0.357089	+	0.922154i
$568$	−0.116019	−	0.589295i	−0.00486803	−	0.0247263i
$569$	3.96413	−	6.86607i	0.166185	−	0.287840i	−0.770891	−	0.636968i	$-0.780189\pi$
$569$	3.96413	−	6.86607i	0.166185	−	0.287840i	0.937075	+	0.349127i	$0.113522\pi$
$570$		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	$0.479388\pi$
$572$	11.2648	−	8.62041i	0.471003	−	0.360438i
$573$	−8.97330			−0.374865
$574$	−4.02506	+	3.69404i	−0.168003	+	0.154186i
$575$		0			0
$576$	6.43964	−	47.4762i	0.268318	−	1.97817i
$577$	−5.16573	−	8.94731i	−0.215052	−	0.372481i	0.738237	−	0.674542i	$-0.235659\pi$
$577$	−5.16573	−	8.94731i	−0.215052	−	0.372481i	−0.953289	+	0.302061i	$0.902325\pi$
$578$	3.21207	−	6.50272i	0.133604	−	0.270478i
$579$	22.0496	−	38.1911i	0.916351	−	1.58717i
$580$		0			0
$581$	−22.5008	+	18.1117i	−0.933490	+	0.751402i
$582$	−0.654109	+	0.436444i	−0.0271137	+	0.0180912i
$583$	5.20871	−	9.02174i	0.215723	−	0.373642i
$584$	−27.6774	−	31.6851i	−1.14530	−	1.31114i
$585$		0			0
$586$	40.8550	−	2.65099i	1.68770	−	0.109511i
$587$		−	20.4660i		−	0.844722i	−0.906428	−	0.422361i	$-0.861201\pi$
$587$		−	20.4660i		−	0.844722i	0.906428	−	0.422361i	$-0.138799\pi$
$588$	−17.7981	−	38.0138i	−0.733980	−	1.56766i
$589$	10.0401			0.413694
$590$		0			0
$591$	7.22175	+	12.5084i	0.297063	+	0.514529i
$592$	−43.2191	−	11.7016i	−1.77629	−	0.480931i
$593$	−22.4236	+	38.8389i	−0.920828	+	1.59492i	−0.122692	+	0.992445i	$0.539153\pi$
$593$	−22.4236	+	38.8389i	−0.920828	+	1.59492i	−0.798136	+	0.602477i	$0.794181\pi$
$594$	15.7315	+	23.5772i	0.645471	+	0.967383i
$595$		0			0
$596$	4.99158	−	12.0064i	0.204463	−	0.491800i
$597$	3.30884	+	1.91036i	0.135422	+	0.0781857i
$598$	−5.28578	+	10.7009i	−0.216152	+	0.437592i
$599$	−14.1499	+	8.16942i	−0.578147	+	0.333793i	−0.760397	−	0.649459i	$-0.774995\pi$
$599$	−14.1499	+	8.16942i	−0.578147	+	0.333793i	0.182250	+	0.983252i	$0.441662\pi$
$600$		0			0
$601$		−	39.8029i		−	1.62359i	−0.583941	−	0.811796i	$-0.698490\pi$
$601$		−	39.8029i		−	1.62359i	0.583941	−	0.811796i	$-0.301510\pi$
$602$	−25.1922	−	27.4496i	−1.02676	−	1.11876i
$603$	−0.316030			−0.0128697
$604$	−37.6024	+	28.7754i	−1.53002	+	1.17085i
$605$		0			0
$606$	11.7342	−	23.7554i	0.476668	−	0.964998i
$607$	8.14710	+	4.70373i	0.330681	+	0.190919i	0.656143	−	0.754636i	$-0.272187\pi$
$607$	8.14710	+	4.70373i	0.330681	+	0.190919i	−0.325463	+	0.945555i	$0.605520\pi$
$608$	2.30213	−	11.3793i	0.0933636	−	0.461493i
$609$	54.5975	+	21.1420i	2.21240	+	0.856716i
$610$		0			0
$611$	16.8259	+	9.71441i	0.680701	+	0.393003i
$612$	40.9233	−	5.33330i	1.65423	−	0.215586i
$613$	11.8091	−	6.81796i	0.476963	−	0.275375i	−0.242187	−	0.970230i	$-0.577865\pi$
$613$	11.8091	−	6.81796i	0.476963	−	0.275375i	0.719150	+	0.694855i	$0.244531\pi$
$614$	−0.733121	−	11.2983i	−0.0295863	−	0.455961i
$615$		0			0
$616$	−16.4811	−	2.91505i	−0.664044	−	0.117451i
$617$		−	39.1144i		−	1.57469i	−0.616515	−	0.787343i	$-0.711456\pi$
$617$		−	39.1144i		−	1.57469i	0.616515	−	0.787343i	$-0.288544\pi$
$618$	−48.3124	+	3.13489i	−1.94341	+	0.126104i
$619$	9.50950	+	16.4709i	0.382219	+	0.662023i	0.991379	−	0.131024i	$-0.0418266\pi$
$619$	9.50950	+	16.4709i	0.382219	+	0.662023i	−0.609160	+	0.793047i	$0.708493\pi$
$620$		0			0
$621$	−20.6535	−	11.9243i	−0.828798	−	0.478507i
$622$	−10.7948	−	16.1785i	−0.432833	−	0.648697i
$623$	2.85186	+	18.3542i	0.114257	+	0.735347i
$624$	−26.9611	+	26.8206i	−1.07931	+	1.07368i
$625$		0			0
$626$	−6.66143	+	13.4858i	−0.266244	+	0.539002i
$627$	6.88108	+	11.9184i	0.274804	+	0.475974i
$628$	−9.52000	−	12.4403i	−0.379889	−	0.496422i
$629$		−	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	$0.893490\pi$
$632$	1.23443	+	0.421729i	0.0491028	+	0.0167755i
$633$	−5.56134	−	9.63252i	−0.221043	−	0.382858i
$634$	−21.5344	−	10.6371i	−0.855241	−	0.422452i
$635$		0			0
$636$	−10.7218	+	25.7893i	−0.425146	+	1.02261i
$637$	−4.74245	+	21.6851i	−0.187903	+	0.859196i
$638$	19.4197	−	12.9575i	0.768835	−	0.512993i
$639$	−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	$-0.345272\pi$
$642$	−0.714889	−	11.0173i	−0.0282144	−	0.434818i
$643$			43.6730i			1.72229i	0.508355	+	0.861147i	$0.330254\pi$
$643$			43.6730i			1.72229i	−0.508355	+	0.861147i	$0.669746\pi$
$644$	13.5195	−	3.94241i	0.532745	−	0.155353i
$645$		0			0
$646$	9.97948	−	0.647547i	0.392637	−	0.0254774i
$647$	−24.3422	+	14.0540i	−0.956989	+	0.552518i	−0.895245	−	0.445574i	$-0.853000\pi$
$647$	−24.3422	+	14.0540i	−0.956989	+	0.552518i	−0.0617443	+	0.998092i	$0.519666\pi$
$648$	−16.5604	−	18.9583i	−0.650556	−	0.744754i
$649$	−13.7885	−	7.96080i	−0.541246	−	0.312489i
$650$		0			0
$651$	5.95797	+	38.3448i	0.233511	+	1.50285i
$652$	−8.33161	+	20.0402i	−0.326291	+	0.784836i
$653$	36.0902	+	20.8367i	1.41232	+	0.815403i	0.995607	−	0.0936346i	$-0.0298485\pi$
$653$	36.0902	+	20.8367i	1.41232	+	0.815403i	0.416713	+	0.909038i	$0.363182\pi$
$654$	−3.80872	−	1.88134i	−0.148933	−	0.0735664i
$655$		0			0
$656$	−1.49688	−	5.64538i	−0.0584435	−	0.220415i
$657$	−89.0808			−3.47537
$658$	−4.97918	−	22.3773i	−0.194109	−	0.872359i
$659$		−	47.0951i		−	1.83457i	−0.398236	−	0.917283i	$-0.630378\pi$
$659$		−	47.0951i		−	1.83457i	0.398236	−	0.917283i	$-0.369622\pi$
$660$		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	$0.406010\pi$
$662$	−10.5623	−	5.21735i	−0.410517	−	0.202778i
$663$	−28.3690	−	16.3789i	−1.10176	−	0.636103i
$664$	−5.96486	−	30.2973i	−0.231481	−	1.17577i
$665$		0			0
$666$	−78.8628	+	52.6200i	−3.05587	+	2.03898i
$667$	−9.82168	+	17.0116i	−0.380297	+	0.658693i
$668$	−3.03633	−	23.2982i	−0.117479	−	0.901435i
$669$	−19.4251	−	33.6452i	−0.751017	−	1.30080i
$670$		0			0
$671$	−5.67340			−0.219019
$672$	44.8257	+	2.03952i	1.72919	+	0.0786763i
$673$			14.9849i			0.577626i	0.957385	+	0.288813i	$0.0932606\pi$
$673$			14.9849i			0.577626i	−0.957385	+	0.288813i	$0.906739\pi$
$674$	2.47953	+	38.2126i	0.0955080	+	1.47189i
$675$		0			0
$676$	−5.83899	+	0.760963i	−0.224576	+	0.0292678i
$677$	11.5093	−	19.9347i	0.442339	−	0.766154i	−0.555524	−	0.831501i	$-0.687482\pi$
$677$	11.5093	−	19.9347i	0.442339	−	0.766154i	0.997863	+	0.0653470i	$0.0208154\pi$
$678$	−34.9676	−	52.4067i	−1.34292	−	2.01267i
$679$	−0.307673	−	0.382232i	−0.0118074	−	0.0146687i
$680$		0			0
$681$	−13.3305	+	23.0892i	−0.510827	+	0.884779i
$682$	13.8731	+	6.85272i	0.531228	+	0.262404i
$683$	−18.6347	−	32.2762i	−0.713037	−	1.23502i	−0.963712	−	0.266945i	$-0.913986\pi$
$683$	−18.6347	−	32.2762i	−0.713037	−	1.23502i	0.250675	−	0.968071i	$-0.419348\pi$
$684$	−14.9394	−	19.5222i	−0.571223	−	0.746448i
$685$		0			0
$686$	22.6348	−	13.1782i	0.864201	−	0.503146i
$687$	−38.8132			−1.48082
$688$	38.4997	−	10.2083i	1.46779	−	0.389187i
$689$	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	$-0.0120682\pi$
$692$	12.6587	−	30.4483i	0.481211	−	1.15747i
$693$	−27.6062	+	22.2213i	−1.04867	+	0.844118i
$694$	−21.7991	−	32.6708i	−0.827483	−	1.24017i
$695$		0			0
$696$	−47.1387	+	41.1765i	−1.78679	+	1.56079i
$697$	4.35683	−	2.51542i	0.165027	−	0.0952782i
$698$	0.882819	+	13.6053i	0.0334152	+	0.514968i
$699$	−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	$0.313840\pi$
$702$	2.60216	+	40.1024i	0.0982121	+	1.51357i
$703$	−19.8957	+	11.4868i	−0.750381	+	0.433233i
$704$	10.9478	−	14.1523i	0.412611	−	0.533386i
$705$		0			0
$706$	−12.8053	−	19.1915i	−0.481932	−	0.722283i
$707$	15.4175	+	5.97017i	0.579835	+	0.224532i
$708$	39.4155	+	16.3868i	1.48133	+	0.615852i
$709$	−2.08074	+	3.60395i	−0.0781440	+	0.135349i	−0.902449	−	0.430796i	$-0.858233\pi$
$709$	−2.08074	+	3.60395i	−0.0781440	+	0.135349i	0.824305	+	0.566146i	$0.191566\pi$
$710$		0			0
$711$	2.39203	−	1.38104i	0.0897082	−	0.0517931i
$712$	−18.7906	−	6.41962i	−0.704207	−	0.240585i
$713$	−13.0194			−0.487580
$714$	8.39509	+	37.7291i	0.314178	+	1.41197i
$715$		0			0
$716$	−14.4687	+	11.0723i	−0.540722	+	0.413790i
$717$	−0.0657362	−	0.113858i	−0.00245496	−	0.00425212i
$718$	2.03137	+	1.00341i	0.0758102	+	0.0374470i
$719$	−21.1113	+	36.5658i	−0.787318	+	1.36368i	0.140286	+	0.990111i	$0.455198\pi$
$719$	−21.1113	+	36.5658i	−0.787318	+	1.36368i	−0.927604	+	0.373564i	$0.878135\pi$
$720$		0			0
$721$	−4.63835	−	29.8519i	−0.172741	−	1.11174i
$722$	11.6074	+	17.3962i	0.431982	+	0.647421i
$723$	−3.44874	+	5.97339i	−0.128260	+	0.222153i
$724$	4.28415	+	32.8730i	0.159219	+	1.22172i
$725$		0			0
$726$	−1.64667	−	25.3772i	−0.0611138	−	0.941837i
$727$			27.2605i			1.01104i	0.862816	+	0.505519i	$0.168699\pi$
$727$			27.2605i			1.01104i	−0.862816	+	0.505519i	$0.831301\pi$
$728$	−18.1704	−	15.2631i	−0.673439	−	0.565689i
$729$	27.2992			1.01108
$730$		0			0
$731$	17.1544	+	29.7122i	0.634477	+	1.09895i
$732$	15.0830	−	1.96568i	0.557482	−	0.0726535i
$733$	−7.65300	+	13.2554i	−0.282670	+	0.489599i	−0.972041	−	0.234809i	$-0.924553\pi$
$733$	−7.65300	+	13.2554i	−0.282670	+	0.489599i	0.689372	+	0.724408i	$0.257887\pi$
$734$	1.48286	−	0.989415i	0.0547333	−	0.0365200i
$735$		0			0
$736$	−2.98526	+	14.7560i	−0.110038	+	0.543915i
$737$	−0.102211	−	0.0590113i	−0.00376498	−	0.00217371i
$738$	−11.0876	−	5.47680i	−0.408140	−	0.201604i
$739$	42.5694	−	24.5774i	1.56594	−	0.904096i	0.569305	−	0.822126i	$-0.307212\pi$
$739$	42.5694	−	24.5774i	1.56594	−	0.904096i	0.996635	−	0.0819692i	$-0.0261209\pi$
$740$		0			0
$741$			19.5125i			0.716810i
$742$	−16.6252	−	5.22771i	−0.610331	−	0.191915i
$743$	−35.2067			−1.29161			−0.645805	−	0.763503i	$-0.723478\pi$
$743$	−35.2067			−1.29161			−0.645805	+	0.763503i	$0.723478\pi$
$744$	−39.2564	−	13.4116i	−1.43921	−	0.491692i
$745$		0			0
$746$	−11.7000	−	5.77932i	−0.428369	−	0.211596i
$747$	−56.6229	−	32.6913i	−2.07173	−	1.19611i
$748$	14.2313	+	5.91659i	0.520349	+	0.216332i
$749$	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	$0.670585\pi$
$752$	23.6557	+	6.40478i	0.862635	+	0.233558i
$753$	16.4203	−	9.48027i	0.598389	−	0.345480i
$754$	33.0310	−	2.14331i	1.20292	−	0.0780548i
$755$		0			0
$756$	32.7855	−	34.2567i	1.19240	−	1.24590i
$757$			45.8640i			1.66695i	0.552553	+	0.833477i	$0.313654\pi$
$757$			45.8640i			1.66695i	−0.552553	+	0.833477i	$0.686346\pi$
$758$	−0.232152	−	3.57774i	−0.00843214	−	0.129949i
$759$	−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	$0.537052\pi$
$762$	−10.6642	+	7.11551i	−0.386322	+	0.257768i
$763$	0.957201	−	2.47190i	0.0346530	−	0.0894886i
$764$	5.52726	+	2.29793i	0.199969	+	0.0831360i
$765$		0			0
$766$	1.67988	+	0.829791i	0.0606967	+	0.0299816i
$767$	−11.2871	−	19.5499i	−0.407554	−	0.705905i
$768$	−24.2018	+	41.4177i	−0.873307	+	1.49453i
$769$		−	16.0214i		−	0.577745i	−0.957368	−	0.288872i	$-0.906720\pi$
$769$		−	16.0214i		−	0.577745i	0.957368	−	0.288872i	$-0.0932803\pi$
$770$		0			0
$771$		−	42.6976i		−	1.53772i
$772$	−23.3620	+	17.8779i	−0.840816	+	0.643439i
$773$	−21.1707	−	36.6688i	−0.761458	−	1.31888i	−0.942099	−	0.335335i	$-0.891150\pi$
$773$	−21.1707	−	36.6688i	−0.761458	−	1.31888i	0.180641	−	0.983549i	$-0.442183\pi$
$774$	37.3500	−	75.6139i	1.34252	−	2.71789i
$775$		0			0
$776$	0.514676	−	0.101328i	0.0184758	−	0.00363746i
$777$	−55.6765	−	69.1687i	−1.99738	−	2.48141i
$778$	25.2957	+	37.9113i	0.906896	+	1.35919i
$779$	−2.59519	−	1.49833i	−0.0929824	−	0.0536834i
$780$		0			0
$781$	−0.237464	−	0.411299i	−0.00849712	−	0.0147174i
$782$	−12.9408	+	0.839700i	−0.462762	+	0.0300276i
$783$			66.1408i			2.36368i
$784$	1.22829	+	27.9730i	0.0438675	+	0.999037i
$785$		0			0
$786$	−4.31187	−	66.4511i	−0.153799	−	2.37023i
$787$	3.79528	−	2.19121i	0.135287	−	0.0781081i	−0.430829	−	0.902434i	$-0.641779\pi$
$787$	3.79528	−	2.19121i	0.135287	−	0.0781081i	0.566116	+	0.824326i	$0.308445\pi$
$788$	−1.24514	−	9.55417i	−0.0443563	−	0.340353i
$789$	30.5044	+	17.6117i	1.08599	+	0.626994i
$790$		0			0
$791$	30.6241	−	24.6506i	1.08887	−	0.876473i
$792$	−7.31828	−	37.1718i	−0.260044	−	1.32084i
$793$	−6.96627	−	4.02198i	−0.247380	−	0.142825i
$794$	−22.0302	+	44.5995i	−0.781824	+	1.58278i
$795$		0			0
$796$	−1.54892	−	2.02406i	−0.0549001	−	0.0717409i
$797$	53.6019			1.89868			0.949339	−	0.314255i	$-0.101755\pi$
$797$	53.6019			1.89868			0.949339	+	0.314255i	$0.101755\pi$
$798$	16.9625	−	15.5675i	0.600466	−	0.551085i
$799$			21.1101i			0.746822i
$800$		0			0
$801$	−36.4118	+	21.0224i	−1.28655	+	0.742789i
$802$	−19.9950	+	40.4792i	−0.706048	+	1.42937i
$803$	−28.8106	−	16.6338i	−1.01670	−	0.586995i
$804$	0.292177	+	0.121471i	0.0103043	+	0.00428394i
$805$		0			0
$806$	12.1765	+	18.2492i	0.428900	+	0.642802i
$807$	−12.7261	+	22.0422i	−0.447980	+	0.775924i
$808$	−13.3113	+	11.6276i	−0.468289	+	0.409058i
$809$	−0.754693	−	1.30717i	−0.0265336	−	0.0459575i	0.852454	−	0.522803i	$-0.175114\pi$
$809$	−0.754693	−	1.30717i	−0.0265336	−	0.0459575i	−0.878987	+	0.476845i	$0.841780\pi$
$810$		0			0
$811$	−43.1894			−1.51658			−0.758292	−	0.651915i	$-0.773966\pi$
$811$	−43.1894			−1.51658			−0.758292	+	0.651915i	$0.773966\pi$
$812$	−28.2161	−	27.0043i	−0.990192	−	0.947667i
$813$			23.9063i			0.838432i
$814$	−35.3315	+	2.29258i	−1.23837	+	0.0803550i
$815$		0			0
$816$	−39.8845	−	10.7987i	−1.39624	−	0.378031i
$817$	10.2182	−	17.6984i	0.357489	−	0.619189i
$818$	−19.3095	+	12.8840i	−0.675142	+	0.450478i
$819$	−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	$0.115739\pi$
$822$	18.0538	−	36.5493i	0.629698	−	1.27480i
$823$	0.190193	+	0.329424i	0.00662972	+	0.0114830i	0.869321	−	0.494248i	$-0.164556\pi$
$823$	0.190193	+	0.329424i	0.00662972	+	0.0114830i	−0.862692	+	0.505731i	$0.831223\pi$
$824$	30.5616	+	10.4411i	1.06467	+	0.363732i
$825$		0			0
$826$	−7.98985	+	25.4094i	−0.278003	+	0.884106i
$827$	23.9044			0.831236			0.415618	−	0.909539i	$-0.363565\pi$
$827$	23.9044			0.831236			0.415618	+	0.909539i	$0.363565\pi$
$828$	19.3725	+	25.3152i	0.673243	+	0.879763i
$829$	−35.8241	+	20.6830i	−1.24422	+	0.718352i	−0.969951	−	0.243301i	$-0.921770\pi$
$829$	−35.8241	+	20.6830i	−1.24422	+	0.718352i	−0.274271	+	0.961653i	$0.588436\pi$
$830$		0			0
$831$	−20.3800	+	35.2992i	−0.706974	+	1.22452i
$832$	23.4755	−	9.61631i	0.813866	−	0.333386i
$833$	−22.9814	+	7.31833i	−0.796259	+	0.253565i
$834$	26.4434	−	17.6439i	0.915659	−	0.610959i
$835$		0			0
$836$	−1.18640	−	9.10347i	−0.0410327	−	0.314850i
$837$	−37.9642	+	21.9187i	−1.31224	+	0.757620i
$838$	−16.7451	+	1.08655i	−0.578448	+	0.0375343i
$839$	46.4174			1.60251			0.801253	−	0.598326i	$-0.204167\pi$
$839$	46.4174			1.60251			0.801253	+	0.598326i	$0.204167\pi$
$840$		0			0
$841$	25.4780			0.878551
$842$	14.5969	−	0.947163i	0.503043	−	0.0326414i
$843$	−24.6219	+	14.2155i	−0.848025	+	0.489607i
$844$	0.958861	+	7.35749i	0.0330054	+	0.253255i
$845$		0			0
$846$	43.1651	−	28.8013i	1.48405	−	0.990208i
$847$	15.6804	−	2.43641i	0.538786	−	0.0837159i
$848$	13.2085	−	13.1397i	0.453582	−	0.451219i
$849$	32.3038	−	55.9518i	1.10866	−	1.92026i
$850$		0			0
$851$	25.7996	−	14.8954i	0.884398	−	0.510608i
$852$	0.773811	+	1.01118i	0.0265103	+	0.0346425i
$853$	−10.5928			−0.362692			−0.181346	−	0.983419i	$-0.558045\pi$
$853$	−10.5928			−0.362692			−0.181346	+	0.983419i	$0.558045\pi$
$854$	2.06149	+	9.26471i	0.0705427	+	0.317032i
$855$		0			0
$856$	−2.38101	+	6.96937i	−0.0813814	+	0.238208i
$857$	0.141688	+	0.245410i	0.00483996	+	0.00838305i	0.868435	−	0.495803i	$-0.165126\pi$
$857$	0.141688	+	0.245410i	0.00483996	+	0.00838305i	−0.863595	+	0.504186i	$0.831793\pi$
$858$	−13.3180	+	26.9618i	−0.454669	+	0.920461i
$859$	4.93861	−	8.55393i	0.168503	−	0.291856i	−0.769391	−	0.638779i	$-0.779440\pi$
$859$	4.93861	−	8.55393i	0.168503	−	0.291856i	0.937894	+	0.346922i	$0.112773\pi$
$860$		0			0
$861$	4.18236	−	10.8006i	0.142535	−	0.368084i
$862$	34.8883	−	23.2787i	1.18830	−	0.792875i
$863$	16.2817	−	28.2007i	0.554235	−	0.959963i	−0.443728	−	0.896162i	$-0.646344\pi$
$863$	16.2817	−	28.2007i	0.554235	−	0.959963i	0.997963	−	0.0638012i	$-0.0203224\pi$
$864$	16.1374	+	48.0541i	0.549006	+	1.63483i
$865$		0			0
$866$	−41.5057	+	2.69321i	−1.41042	+	0.0915192i
$867$			15.3759i			0.522195i
$868$	6.14961	−	25.1449i	0.208731	−	0.853473i
$869$	1.03151			0.0349916
$870$		0			0
$871$	−0.0836685	−	0.144918i	−0.00283500	−	0.00491036i
$872$	1.86426	+	2.13420i	0.0631319	+	0.0722732i
$873$	0.555343	−	0.961883i	0.0187955	−	0.0325548i
$874$	4.28733	+	6.42551i	0.145021	+	0.217346i
$875$		0			0
$876$	82.3573	+	34.2396i	2.78260	+	1.15685i
$877$	32.9700	+	19.0353i	1.11332	+	0.642775i	0.939687	−	0.342036i	$-0.111116\pi$
$877$	32.9700	+	19.0353i	1.11332	+	0.642775i	0.173632	+	0.984811i	$0.444450\pi$
$878$	5.52652	−	11.1883i	0.186511	−	0.377585i
$879$	−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	$-0.154849\pi$
$882$	46.3186	+	37.0068i	1.55963	+	1.24608i
$883$	44.1707			1.48646			0.743232	−	0.669034i	$-0.233292\pi$
$883$	44.1707			1.48646			0.743232	+	0.669034i	$0.233292\pi$
$884$	13.2800	+	17.3537i	0.446656	+	0.583669i
$885$		0			0
$886$	−12.2551	+	24.8100i	−0.411717	+	0.833508i
$887$	17.4310	+	10.0638i	0.585275	+	0.337909i	0.763227	−	0.646130i	$-0.223614\pi$
$887$	17.4310	+	10.0638i	0.585275	+	0.337909i	−0.177952	+	0.984039i	$0.556947\pi$
$888$	93.1358	−	18.3363i	3.12543	−	0.615326i
$889$	−5.01611	−	6.23167i	−0.168235	−	0.209003i
$890$		0			0
$891$	−17.2385	−	9.95263i	−0.577510	−	0.333426i
$892$	3.34919	+	25.6988i	0.112139	+	0.860461i
$893$	10.8898	−	6.28724i	0.364414	−	0.210394i
$894$	1.78493	+	27.5079i	0.0596968	+	0.920000i
$895$		0			0
$896$	−27.0889	−	12.7355i	−0.904976	−	0.425462i
$897$		−	25.3027i		−	0.844831i
$898$	−7.08882	+	0.459978i	−0.236557	+	0.0153497i
$899$	18.0537	+	31.2699i	0.602124	+	1.04291i
$900$		0			0
$901$	13.8983	+	8.02418i	0.463019	+	0.267324i
$902$	−2.56329	−	3.84167i	−0.0853483	−	0.127913i
$903$	73.6569	+	28.5224i	2.45115	+	0.949167i
$904$	8.11832	+	41.2355i	0.270011	+	1.37147i
$905$		0			0
$906$	44.4561	−	90.0000i	1.47696	−	2.99005i
$907$	−7.50854	−	13.0052i	−0.249317	−	0.431830i	0.714020	−	0.700126i	$-0.246873\pi$
$907$	−7.50854	−	13.0052i	−0.249317	−	0.431830i	−0.963336	+	0.268296i	$0.913539\pi$
$908$	14.1240	−	10.8084i	0.468720	−	0.358690i
$909$			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	$0.869737\pi$
$912$	6.30821	+	23.7909i	0.208886	+	0.787795i
$913$	−12.2087	−	21.1461i	−0.404049	−	0.699834i
$914$	−35.3063	−	17.4398i	−1.16783	−	0.576857i
$915$		0			0
$916$	23.9076	+	9.93946i	0.789931	+	0.328409i
$917$	41.0597	−	6.37981i	1.35591	−	0.210680i
$918$	−36.3214	+	24.2349i	−1.19878	+	0.799871i
$919$	−49.7575	−	28.7275i	−1.64135	−	0.947632i	−0.980355	−	0.197239i	$-0.936802\pi$
$919$	−49.7575	−	28.7275i	−1.64135	−	0.947632i	−0.660992	−	0.750393i	$-0.729864\pi$
$920$		0			0
$921$	12.0014	+	20.7870i	0.395459	+	0.684956i
$922$	−1.81767	−	28.0124i	−0.0598617	−	0.922541i
$923$		−	0.673370i		−	0.0221643i
$924$	34.0637	−	9.93325i	1.12061	−	0.326780i
$925$		0			0
$926$	−50.3981	+	3.27022i	−1.65618	+	0.107466i
$927$	59.2214	−	34.1915i	1.94509	−	1.12300i
$928$	39.5806	−	13.2919i	1.29930	−	0.436327i
$929$	−3.45964	−	1.99743i	−0.113507	−	0.0655334i	0.442172	−	0.896930i	$-0.354208\pi$
$929$	−3.45964	−	1.99743i	−0.113507	−	0.0655334i	−0.555679	+	0.831397i	$0.687542\pi$
$930$		0			0
$931$	10.6198	+	9.67552i	0.348049	+	0.317102i
$932$	28.1006	+	11.6827i	0.920466	+	0.382678i
$933$	35.7083	+	20.6162i	1.16904	+	0.674945i
$934$	28.6700	+	14.1617i	0.938110	+	0.463386i
$935$		0			0
$936$	17.3658	−	50.8307i	0.567619	−	1.66145i
$937$	−43.2204			−1.41195			−0.705975	−	0.708237i	$-0.749491\pi$
$937$	−43.2204			−1.41195			−0.705975	+	0.708237i	$0.749491\pi$
$938$	−0.0592267	+	0.188353i	−0.00193382	+	0.00614995i
$939$		−	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	$0.529227\pi$
$942$	29.7754	+	14.7078i	0.970136	+	0.479206i
$943$	3.36529	+	1.94295i	0.109589	+	0.0632712i
$944$	−20.0823	−	20.1874i	−0.653622	−	0.657044i
$945$		0			0
$946$	26.1990	−	17.4809i	0.851802	−	0.568352i
$947$	−24.3466	+	42.1696i	−0.791159	+	1.37033i	0.134091	+	0.990969i	$0.457188\pi$
$947$	−24.3466	+	42.1696i	−0.791159	+	1.37033i	−0.925250	+	0.379358i	$0.876145\pi$
$948$	−2.74231	+	0.357390i	−0.0890662	+	0.0116075i
$949$	−23.5840	−	40.8488i	−0.765571	−	1.32601i
$950$		0			0
$951$	50.9190			1.65116
$952$	4.49073	−	25.3897i	0.145546	−	0.822886i
$953$		−	47.5308i		−	1.53967i	−0.638241	−	0.769837i	$-0.720338\pi$
$953$		−	47.5308i		−	1.53967i	0.638241	−	0.769837i	$-0.279662\pi$
$954$	−2.55440	−	39.3663i	−0.0827016	−	1.27453i
$955$		0			0
$956$	0.0113339	+	0.0869671i	0.000366566	+	0.00281272i
$957$	−24.7466	+	42.8623i	−0.799943	+	1.38554i
$958$	−6.72211	−	10.0746i	−0.217182	−	0.325495i
$959$	23.7208	+	9.18550i	0.765986	+	0.296615i
$960$		0			0
$961$	3.53423	−	6.12147i	0.114008	−	0.197467i
$962$	−45.0082	−	22.2321i	−1.45112	−	0.716792i
$963$	7.79713	+	13.5050i	0.251259	+	0.435193i
$964$	3.65400	−	2.79624i	0.117688	−	0.0900609i
$965$		0			0
$966$	−21.9960	+	20.1870i	−0.707708	+	0.649508i
$967$	29.3643			0.944292			0.472146	−	0.881520i	$-0.343479\pi$
$967$	29.3643			0.944292			0.472146	+	0.881520i	$0.343479\pi$
$968$	−5.48442	+	16.0532i	−0.176276	+	0.515970i
$969$	−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	$0.307244\pi$
$972$	−0.369231	−	0.153506i	−0.0118431	−	0.00492370i
$973$	12.4382	+	15.4523i	0.398749	+	0.495379i
$974$	24.8391	+	37.2269i	0.795895	+	1.19283i
$975$		0			0
$976$	−9.79398	−	2.65172i	−0.313498	−	0.0848795i
$977$	−13.3970	+	7.73476i	−0.428608	+	0.247457i	−0.698753	−	0.715363i	$-0.746261\pi$
$977$	−13.3970	+	7.73476i	−0.428608	+	0.247457i	0.270146	+	0.962819i	$0.412928\pi$
$978$	−2.97928	−	45.9143i	−0.0952668	−	1.46818i
$979$	−15.7018			−0.501832
$980$		0			0
$981$	6.00019			0.191571
$982$	−3.27629	−	50.4916i	−0.104551	−	1.61125i
$983$	38.1277	−	22.0131i	1.21609	−	0.702107i	0.252007	−	0.967725i	$-0.418909\pi$
$983$	38.1277	−	22.0131i	1.21609	−	0.702107i	0.964078	+	0.265618i	$0.0855760\pi$
$984$	8.14565	+	9.32511i	0.259674	+	0.297274i
$985$		0			0
$986$	19.9615	+	29.9167i	0.635703	+	0.952743i
$987$	30.4743	+	37.8591i	0.970006	+	1.20507i
$988$	4.99686	−	12.0191i	0.158971	−	0.382378i
$989$	−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	$0.247789\pi$
$992$	20.7462	+	18.3141i	0.658692	+	0.581472i
$993$	24.9751			0.792560
$994$	−0.585370	+	0.537230i	−0.0185668	+	0.0170399i
$995$		0			0
$996$	39.7839	+	51.9877i	1.26060	+	1.64729i
$997$	−13.7897	−	23.8844i	−0.436723	−	0.756427i	0.560711	−	0.828011i	$-0.310528\pi$
$997$	−13.7897	−	23.8844i	−0.436723	−	0.756427i	−0.997435	+	0.0715845i	$0.977194\pi$
$998$	−52.3856	−	25.8762i	−1.65824	−	0.819098i
$999$	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.t.c.299.16		32
4.3	odd	2	inner	700.2.t.c.299.11		32
5.2	odd	4		140.2.o.a.131.8	yes	32
5.3	odd	4		700.2.p.c.551.9		32
5.4	even	2		700.2.t.d.299.1		32
7.3	odd	6		700.2.t.d.199.6		32
20.3	even	4		700.2.p.c.551.14		32
20.7	even	4		140.2.o.a.131.3	yes	32
20.19	odd	2		700.2.t.d.299.6		32
28.3	even	6		700.2.t.d.199.1		32
35.2	odd	12		980.2.g.a.391.25		32
35.3	even	12		700.2.p.c.451.14		32
35.12	even	12		980.2.g.a.391.26		32
35.17	even	12		140.2.o.a.31.3	✓	32
35.24	odd	6	inner	700.2.t.c.199.11		32
35.27	even	4		980.2.o.f.411.8		32
35.32	odd	12		980.2.o.f.31.3		32
140.3	odd	12		700.2.p.c.451.9		32
140.27	odd	4		980.2.o.f.411.3		32
140.47	odd	12		980.2.g.a.391.27		32
140.59	even	6	inner	700.2.t.c.199.16		32
140.67	even	12		980.2.o.f.31.8		32
140.87	odd	12		140.2.o.a.31.8	yes	32
140.107	even	12		980.2.g.a.391.28		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.3	✓	32	35.17	even	12
140.2.o.a.31.8	yes	32	140.87	odd	12
140.2.o.a.131.3	yes	32	20.7	even	4
140.2.o.a.131.8	yes	32	5.2	odd	4
700.2.p.c.451.9		32	140.3	odd	12
700.2.p.c.451.14		32	35.3	even	12
700.2.p.c.551.9		32	5.3	odd	4
700.2.p.c.551.14		32	20.3	even	4
700.2.t.c.199.11		32	35.24	odd	6	inner
700.2.t.c.199.16		32	140.59	even	6	inner
700.2.t.c.299.11		32	4.3	odd	2	inner
700.2.t.c.299.16		32	1.1	even	1	trivial
700.2.t.d.199.1		32	28.3	even	6
700.2.t.d.199.6		32	7.3	odd	6
700.2.t.d.299.1		32	5.4	even	2
700.2.t.d.299.6		32	20.19	odd	2
980.2.g.a.391.25		32	35.2	odd	12
980.2.g.a.391.26		32	35.12	even	12
980.2.g.a.391.27		32	140.47	odd	12
980.2.g.a.391.28		32	140.107	even	12
980.2.o.f.31.3		32	35.32	odd	12
980.2.o.f.31.8		32	140.67	even	12
980.2.o.f.411.3		32	140.27	odd	4
980.2.o.f.411.8		32	35.27	even	4

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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.41125 - 0.0915727i) q^{2} +(-2.59647 + 1.49907i) q^{3} +(1.98323 - 0.258463i) q^{4} +(-3.52698 + 2.35332i) q^{6} +(-1.65899 - 2.06101i) q^{7} +(2.77516 - 0.546365i) q^{8} +(2.99443 - 5.18651i) q^{9} +(1.93693 - 1.11828i) q^{11} +(-4.76194 + 3.64409i) q^{12} +3.17109 q^{13} +(-2.52997 - 2.75667i) q^{14} +(3.86639 - 1.02518i) q^{16} +(1.72275 + 2.98390i) q^{17} +(3.75094 - 7.59365i) q^{18} +(1.02618 - 1.77739i) q^{19} +(7.39711 + 2.86441i) q^{21} +(2.63107 - 1.75554i) q^{22} +(-1.33068 + 2.30481i) q^{23} +(-6.38656 + 5.57878i) q^{24} +(4.47519 - 0.290385i) q^{26} +8.96105i q^{27} +(-3.82285 - 3.65867i) q^{28} +7.38092 q^{29} +(2.44599 + 4.23658i) q^{31} +(5.36255 - 1.80084i) q^{32} +(-3.35278 + 5.80718i) q^{33} +(2.70447 + 4.05325i) q^{34} +(4.59812 - 11.0600i) q^{36} +(-9.69410 - 5.59689i) q^{37} +(1.28543 - 2.60230i) q^{38} +(-8.23364 + 4.75369i) q^{39} -1.46011i q^{41} +(10.7014 + 3.36501i) q^{42} +9.95752 q^{43} +(3.55233 - 2.71844i) q^{44} +(-1.66686 + 3.37451i) q^{46} +(5.30601 + 3.06343i) q^{47} +(-8.50215 + 8.45786i) q^{48} +(-1.49553 + 6.83838i) q^{49} +(-8.94615 - 5.16506i) q^{51} +(6.28900 - 0.819610i) q^{52} +(4.03374 - 2.32888i) q^{53} +(0.820587 + 12.6462i) q^{54} +(-5.73001 - 4.81321i) q^{56} +6.15325i q^{57} +(10.4163 - 0.675891i) q^{58} +(-3.55938 - 6.16503i) q^{59} +(-2.19681 - 1.26833i) q^{61} +(3.83985 + 5.75488i) q^{62} +(-15.6572 + 2.43279i) q^{63} +(7.40297 - 3.03249i) q^{64} +(-4.19981 + 8.50238i) q^{66} +(-0.0263848 - 0.0456998i) q^{67} +(4.18784 + 5.47248i) q^{68} -7.97917i q^{69} -0.212347i q^{71} +(5.47629 - 16.0294i) q^{72} +(-7.43720 - 12.8816i) q^{73} +(-14.1933 - 7.01088i) q^{74} +(1.57575 - 3.79020i) q^{76} +(-5.51813 - 2.13680i) q^{77} +(-11.1844 + 7.46261i) q^{78} +(0.399413 + 0.230601i) q^{79} +(-4.44995 - 7.70755i) q^{81} +(-0.133707 - 2.06058i) q^{82} -10.9174i q^{83} +(15.4105 + 3.76890i) q^{84} +(14.0525 - 0.911837i) q^{86} +(-19.1643 + 11.0645i) q^{87} +(4.76428 - 4.16168i) q^{88} +(-6.07992 - 3.51024i) q^{89} +(-5.26080 - 6.53565i) q^{91} +(-2.04334 + 4.91490i) q^{92} +(-12.7019 - 7.33344i) q^{93} +(7.76862 + 3.83736i) q^{94} +(-11.2241 + 12.7147i) q^{96} +0.185459 q^{97} +(-1.48435 + 9.78758i) q^{98} -13.3945i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38}+ \cdots - 124 q^{98}+O(q^{100}) \) 32 * q + 2 * q^4 + 16 * q^9 - 14 * q^12 - 8 * q^13 - 2 * q^14 - 14 * q^16 + 54 * q^18 - 12 * q^21 - 36 * q^24 + 30 * q^26 + 32 * q^28 + 40 * q^29 + 60 * q^32 - 24 * q^33 + 60 * q^36 - 60 * q^37 - 46 * q^38 + 78 * q^42 + 18 * q^44 + 2 * q^46 - 28 * q^48 + 16 * q^49 - 46 * q^52 - 12 * q^53 - 12 * q^54 - 4 * q^56 + 42 * q^58 + 24 * q^61 + 8 * q^62 - 4 * q^64 + 24 * q^66 - 4 * q^68 + 90 * q^72 - 24 * q^73 - 38 * q^74 + 20 * q^77 - 36 * q^81 + 8 * q^82 + 20 * q^84 + 28 * q^86 - 78 * q^88 + 60 * q^89 + 72 * q^93 - 18 * q^94 - 60 * q^96 - 48 * q^97 - 124 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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