LMFDB - Embedded newform 700.2.t.d.199.6

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			199.6
Character	$\chi$	$=$	700.199
Dual form			700.2.t.d.299.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.626319 + 1.26796i) q^{2} +(-2.59647 - 1.49907i) q^{3} +(-1.21545 - 1.58830i) 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} +(0.774910 + 5.94600i) q^{12} -3.17109 q^{13} +(-1.57423 - 3.39438i) q^{14} +(-1.04536 + 3.86099i) q^{16} +(-1.72275 + 2.98390i) q^{17} +(-8.45176 + 0.548417i) 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} +(-8.02464 - 2.74154i) q^{24} +(1.98611 - 4.02082i) q^{26} -8.96105i q^{27} +(5.28991 + 0.129905i) q^{28} +7.38092 q^{29} +(-2.44599 + 4.23658i) q^{31} +(-4.24085 - 3.74369i) 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} +(2.89637 - 0.187940i) q^{38} +(8.23364 + 4.75369i) q^{39} +1.46011i q^{41} +(-1.00099 + 11.1733i) q^{42} +9.95752 q^{43} +(0.578071 + 4.43563i) q^{44} +(3.75585 - 0.243709i) 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} +(3.85430 + 5.03663i) q^{52} +(-4.03374 - 2.32888i) q^{53} +(11.3623 + 5.61247i) q^{54} +(-3.47788 + 6.62604i) q^{56} +6.15325i q^{57} +(-4.62281 + 9.35872i) 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} +(-9.46318 + 0.614046i) q^{66} +(-0.0263848 + 0.0456998i) q^{67} +(6.83323 - 0.890536i) q^{68} +7.97917i q^{69} -0.212347i q^{71} +(11.1437 + 12.7573i) q^{72} +(7.43720 - 12.8816i) q^{73} +(1.02505 + 15.7972i) 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} +(-1.85137 - 0.914496i) q^{82} +10.9174i q^{83} +(-13.5403 - 8.26724i) q^{84} +(-6.23658 + 12.6257i) q^{86} +(-19.1643 - 11.0645i) q^{87} +(-5.98626 - 2.04514i) 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} +(0.561053 + 8.64650i) q^{94} +(5.39918 + 16.0777i) q^{96} -0.185459 q^{97} +(9.60747 + 2.38673i) 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 $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.626319	+	1.26796i	−0.442874	+	0.896584i
$2$	−0.626319	+	1.26796i	−0.442874	+	0.896584i
$3$	−2.59647	−	1.49907i	−1.49907	−	0.865490i	−0.499072	−	0.866560i	$-0.666326\pi$
$3$	−2.59647	−	1.49907i	−1.49907	−	0.865490i	−0.999999	+	0.00107081i	$0.999659\pi$
$4$	−1.21545	−	1.58830i	−0.607725	−	0.794148i
$5$		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	$-0.442805\pi$
$11$	−1.93693	−	1.11828i	−0.584005	−	0.337175i	−0.762723	+	0.646725i	$0.776138\pi$
$12$	0.774910	+	5.94600i	0.223697	+	1.71646i
$13$	−3.17109			−0.879502			−0.439751	−	0.898120i	$-0.644933\pi$
$13$	−3.17109			−0.879502			−0.439751	+	0.898120i	$0.644933\pi$
$14$	−1.57423	−	3.39438i	−0.420730	−	0.907186i
$15$		0			0
$16$	−1.04536	+	3.86099i	−0.261341	+	0.965247i
$17$	−1.72275	+	2.98390i	−0.417829	+	0.723701i	−0.995721	−	0.0924124i	$-0.970542\pi$
$17$	−1.72275	+	2.98390i	−0.417829	+	0.723701i	0.577892	+	0.816113i	$0.303876\pi$
$18$	−8.45176	+	0.548417i	−1.99210	+	0.129263i
$19$	−1.02618	−	1.77739i	−0.235421	−	0.407761i	0.723974	−	0.689827i	$-0.242314\pi$
$19$	−1.02618	−	1.77739i	−0.235421	−	0.407761i	−0.959395	+	0.282066i	$0.908980\pi$
$20$		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	0.693288	−	0.720661i	$-0.256162\pi$
$23$	−1.33068	−	2.30481i	−0.277467	−	0.480587i	−0.970755	+	0.240074i	$0.922828\pi$
$24$	−8.02464	−	2.74154i	−1.63802	−	0.559614i
$25$		0			0
$26$	1.98611	−	4.02082i	0.389509	−	0.788548i
$27$		−	8.96105i		−	1.72455i
$28$	5.28991	+	0.129905i	0.999699	+	0.0245497i
$29$	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	$-0.978112\pi$
$31$	−2.44599	+	4.23658i	−0.439313	+	0.760913i	0.558323	+	0.829623i	$0.311445\pi$
$32$	−4.24085	−	3.74369i	−0.749684	−	0.661796i
$33$	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	0.601036	−	0.799222i	$-0.294755\pi$
$37$	9.69410	−	5.59689i	1.59370	−	0.920123i	0.992664	−	0.120902i	$-0.0385785\pi$
$38$	2.89637	−	0.187940i	0.469854	−	0.0304878i
$39$	8.23364	+	4.75369i	1.31844	+	0.761200i
$40$		0			0
$41$			1.46011i			0.228031i	0.993479	+	0.114016i	$0.0363714\pi$
$41$			1.46011i			0.228031i	−0.993479	+	0.114016i	$0.963629\pi$
$42$	−1.00099	+	11.1733i	−0.154456	+	1.72407i
$43$	9.95752			1.51851			0.759254	−	0.650794i	$-0.225564\pi$
$43$	9.95752			1.51851			0.759254	+	0.650794i	$0.225564\pi$
$44$	0.578071	+	4.43563i	0.0871474	+	0.668696i
$45$		0			0
$46$	3.75585	−	0.243709i	0.553769	−	0.0359329i
$47$	5.30601	−	3.06343i	0.773962	−	0.446847i	−0.0603243	−	0.998179i	$-0.519213\pi$
$47$	5.30601	−	3.06343i	0.773962	−	0.446847i	0.834286	+	0.551332i	$0.185880\pi$
$48$	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
$52$	3.85430	+	5.03663i	0.534496	+	0.698455i
$53$	−4.03374	−	2.32888i	−0.554077	−	0.319897i	0.196688	−	0.980466i	$-0.436982\pi$
$53$	−4.03374	−	2.32888i	−0.554077	−	0.319897i	−0.750765	+	0.660570i	$0.770315\pi$
$54$	11.3623	+	5.61247i	1.54621	+	0.763760i
$55$		0			0
$56$	−3.47788	+	6.62604i	−0.464751	+	0.885441i
$57$			6.15325i			0.815018i
$58$	−4.62281	+	9.35872i	−0.607004	+	1.22886i
$59$	3.55938	−	6.16503i	0.463392	−	0.802619i	−0.535735	−	0.844386i	$-0.679965\pi$
$59$	3.55938	−	6.16503i	0.463392	−	0.802619i	0.999127	+	0.0417674i	$0.0132988\pi$
$60$		0			0
$61$	−2.19681	+	1.26833i	−0.281272	+	0.162393i	−0.633999	−	0.773334i	$-0.718588\pi$
$61$	−2.19681	+	1.26833i	−0.281272	+	0.162393i	0.352727	+	0.935726i	$0.385254\pi$
$62$	−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
$66$	−9.46318	+	0.614046i	−1.16484	+	0.0755838i
$67$	−0.0263848	+	0.0456998i	−0.00322341	+	0.00558311i	−0.867633	−	0.497206i	$-0.834359\pi$
$67$	−0.0263848	+	0.0456998i	−0.00322341	+	0.00558311i	0.864409	+	0.502789i	$0.167693\pi$
$68$	6.83323	−	0.890536i	0.828650	−	0.107993i
$69$			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	$-0.00401095\pi$
$72$	11.1437	+	12.7573i	1.31330	+	1.50346i
$73$	7.43720	−	12.8816i	0.870459	−	1.50768i	0.00893589	−	0.999960i	$-0.497156\pi$
$73$	7.43720	−	12.8816i	0.870459	−	1.50768i	0.861523	−	0.507719i	$-0.169511\pi$
$74$	1.02505	+	15.7972i	0.119159	+	1.83639i
$75$		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	$-0.674926\pi$
$79$	−0.399413	+	0.230601i	−0.0449375	+	0.0259447i	0.477363	+	0.878706i	$0.341593\pi$
$80$		0			0
$81$	−4.44995	+	7.70755i	−0.494439	+	0.856394i
$82$	−1.85137	−	0.914496i	−0.204449	−	0.100989i
$83$			10.9174i			1.19834i	0.800624	+	0.599168i	$0.204502\pi$
$83$			10.9174i			1.19834i	−0.800624	+	0.599168i	$0.795498\pi$
$84$	−13.5403	−	8.26724i	−1.47737	−	0.902030i
$85$		0			0
$86$	−6.23658	+	12.6257i	−0.672508	+	1.36147i
$87$	−19.1643	−	11.0645i	−2.05463	−	1.18624i
$88$	−5.98626	−	2.04514i	−0.638137	−	0.218013i
$89$	−6.07992	+	3.51024i	−0.644470	+	0.372085i	−0.786334	−	0.617801i	$-0.788024\pi$
$89$	−6.07992	+	3.51024i	−0.644470	+	0.372085i	0.141864	+	0.989886i	$0.454690\pi$
$90$		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
$94$	0.561053	+	8.64650i	0.0578682	+	0.891819i
$95$		0			0
$96$	5.39918	+	16.0777i	0.551052	+	1.64092i
$97$	−0.185459			−0.0188305			−0.00941523	−	0.999956i	$-0.502997\pi$
$97$	−0.185459			−0.0188305			−0.00941523	+	0.999956i	$0.502997\pi$
$98$	9.60747	+	2.38673i	0.970501	+	0.241096i
$99$		−	13.3945i		−	1.34620i
$100$		0			0
$101$	−5.41172	−	3.12446i	−0.538486	−	0.310895i	0.205979	−	0.978556i	$-0.433962\pi$
$101$	−5.41172	−	3.12446i	−0.538486	−	0.310895i	−0.744465	+	0.667661i	$0.767295\pi$
$102$	0.945957	+	14.5783i	0.0936637	+	1.44347i
$103$	9.88858	−	5.70918i	0.974351	−	0.562542i	0.0737911	−	0.997274i	$-0.476490\pi$
$103$	9.88858	−	5.70918i	0.974351	−	0.562542i	0.900560	+	0.434732i	$0.143157\pi$
$104$	−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	0.796207	−	0.605024i	$-0.206837\pi$
$107$	−1.30194	−	2.25502i	−0.125863	−	0.218001i	−0.922070	+	0.387023i	$0.873503\pi$
$108$	−14.2328	+	10.8917i	−1.36955	+	1.04805i
$109$	0.500946	−	0.867663i	0.0479819	−	0.0831071i	−0.841037	−	0.540978i	$-0.818054\pi$
$109$	0.500946	−	0.867663i	0.0479819	−	0.0831071i	0.889019	+	0.457871i	$0.151388\pi$
$110$		0			0
$111$	−33.5606			−3.18543
$112$	−6.22329	−	8.55983i	−0.588046	−	0.808828i
$113$			14.8588i			1.39780i	0.715220	+	0.698899i	$0.246326\pi$
$113$			14.8588i			1.39780i	−0.715220	+	0.698899i	$0.753674\pi$
$114$	−7.80208	−	3.85389i	−0.730732	−	0.360950i
$115$		0			0
$116$	−8.97114	−	11.7231i	−0.832949	−	1.08846i
$117$	−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
$122$	−0.232288	−	3.57984i	−0.0210304	−	0.324104i
$123$	2.18882	−	3.79114i	0.197359	−	0.341836i
$124$	9.70193	−	1.26440i	0.871259	−	0.113546i
$125$		0			0
$126$	12.8911	−	18.3290i	1.14843	−	1.63288i
$127$	3.02360			0.268301			0.134151	−	0.990961i	$-0.457169\pi$
$127$	3.02360			0.268301			0.134151	+	0.990961i	$0.457169\pi$
$128$	−0.791535	+	11.2860i	−0.0699625	+	0.997550i
$129$	−25.8544	−	14.9270i	−2.27635	−	1.31425i
$130$		0			0
$131$	7.85267	+	13.6012i	0.686091	+	1.18834i	0.973093	+	0.230414i	$0.0740081\pi$
$131$	7.85267	+	13.6012i	0.686091	+	1.18834i	−0.287002	+	0.957930i	$0.592659\pi$
$132$	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
$136$	−3.15061	+	9.22202i	−0.270163	+	0.790782i
$137$	8.32628	+	4.80718i	0.711362	+	0.410705i	0.811565	−	0.584262i	$-0.198616\pi$
$137$	8.32628	+	4.80718i	0.711362	+	0.410705i	−0.100203	+	0.994967i	$0.531949\pi$
$138$	−10.1173	−	4.99750i	−0.861239	−	0.425415i
$139$	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
$142$	0.269247	+	0.132997i	0.0225947	+	0.0111608i
$143$	6.14217	+	3.54618i	0.513634	+	0.296547i
$144$	−23.1553	+	6.13968i	−1.92961	+	0.511640i
$145$		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	0.967905	−	0.251318i	$-0.0808640\pi$
$149$	3.25066	+	5.63031i	0.266305	+	0.461253i	−0.701600	+	0.712571i	$0.747531\pi$
$150$		0			0
$151$	20.5029	+	11.8373i	1.66850	+	0.963309i	0.968448	+	0.249217i	$0.0801731\pi$
$151$	20.5029	+	11.8373i	1.66850	+	0.963309i	0.700052	+	0.714092i	$0.253160\pi$
$152$	−3.81890	−	4.37187i	−0.309754	−	0.354605i
$153$	−20.6347			−1.66821
$154$	−0.746721	+	8.33509i	−0.0601725	+	0.671661i
$155$		0			0
$156$	−2.45731	−	18.8553i	−0.196742	−	1.50963i
$157$	3.91624	−	6.78313i	0.312550	−	0.541353i	−0.666363	−	0.745627i	$-0.732150\pi$
$157$	3.91624	−	6.78313i	0.312550	−	0.541353i	0.978914	+	0.204274i	$0.0654834\pi$
$158$	−0.0422336	−	0.650870i	−0.00335992	−	0.0517805i
$159$	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	0.571438	−	0.820645i	$-0.306386\pi$
$163$	−5.42579	−	9.39774i	−0.424980	−	0.736088i	−0.996419	+	0.0845574i	$0.973052\pi$
$164$	2.31909	−	1.77470i	0.181091	−	0.138580i
$165$		0			0
$166$	−13.8428	−	6.83774i	−1.07441	−	0.530712i
$167$			11.7476i			0.909058i	0.890732	+	0.454529i	$0.150192\pi$
$167$			11.7476i			0.909058i	−0.890732	+	0.454529i	$0.849808\pi$
$168$	18.9631	−	11.9907i	1.46304	−	0.925102i
$169$	−2.94418			−0.226476
$170$		0			0
$171$	6.14563	−	10.6445i	0.469968	−	0.814009i
$172$	−12.1029	−	15.8155i	−0.922835	−	1.20592i
$173$	−8.24371	−	14.2785i	−0.626758	−	1.08558i	−0.988198	−	0.153181i	$-0.951048\pi$
$173$	−8.24371	−	14.2785i	−0.626758	−	1.08558i	0.361440	−	0.932395i	$-0.382285\pi$
$174$	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
$178$	−0.642885	−	9.90763i	−0.0481863	−	0.742608i
$179$	7.88914	+	4.55480i	0.589662	+	0.340441i	0.764964	−	0.644073i	$-0.222757\pi$
$179$	7.88914	+	4.55480i	0.589662	+	0.340441i	−0.175302	+	0.984515i	$0.556090\pi$
$180$		0			0
$181$		−	16.5755i		−	1.23205i	−0.787728	−	0.616023i	$-0.788743\pi$
$181$		−	16.5755i		−	1.23205i	0.787728	−	0.616023i	$-0.211257\pi$
$182$	4.99202	+	10.7639i	0.370033	+	0.797872i
$183$	7.60525			0.562196
$184$	−4.95212	−	5.66917i	−0.365075	−	0.417937i
$185$		0			0
$186$	1.34309	+	20.6986i	0.0984798	+	1.51769i
$187$	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	$-0.701201\pi$
$191$	−2.59197	+	1.49648i	−0.187549	+	0.108281i	0.403286	+	0.915074i	$0.367868\pi$
$192$	−23.7675	−	3.22381i	−1.71527	−	0.232659i
$193$	12.7382	+	7.35442i	0.916918	+	0.529383i	0.882651	−	0.470030i	$-0.155757\pi$
$193$	12.7382	+	7.35442i	0.916918	+	0.529383i	0.0342676	+	0.999413i	$0.489090\pi$
$194$	0.116156	−	0.235154i	0.00833953	−	0.0168831i
$195$		0			0
$196$	−9.04362	+	10.6870i	−0.645973	+	0.763360i
$197$		−	4.81748i		−	0.343231i	−0.985164	−	0.171616i	$-0.945101\pi$
$197$		−	4.81748i		−	0.343231i	0.985164	−	0.171616i	$-0.0548987\pi$
$198$	16.9837	+	8.38923i	1.20698	+	0.596196i
$199$	0.637180	−	1.10363i	0.0451685	−	0.0782342i	−0.842557	−	0.538607i	$-0.818951\pi$
$199$	0.637180	−	1.10363i	0.0451685	−	0.0782342i	0.887726	+	0.460373i	$0.152284\pi$
$200$		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
$206$	1.04561	+	16.1141i	0.0728511	+	1.12272i
$207$	7.96929	−	13.8032i	0.553904	−	0.959390i
$208$	3.31494	−	12.2435i	0.229850	−	0.848937i
$209$			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	$0.959241\pi$
$212$	1.20386	+	9.23742i	0.0826815	+	0.634428i
$213$	−0.318323	+	0.551351i	−0.0218111	+	0.0377780i
$214$	3.67471	−	0.238444i	0.251198	−	0.0162997i
$215$		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
$222$	21.0196	−	42.5535i	1.41074	−	2.85600i
$223$		−	12.9581i		−	0.867737i	−0.900976	−	0.433869i	$-0.857148\pi$
$223$		−	12.9581i		−	0.867737i	0.900976	−	0.433869i	$-0.142852\pi$
$224$	14.7513	−	2.52971i	0.985612	−	0.169024i
$225$		0			0
$226$	−18.8404	−	9.30634i	−1.25324	−	0.619049i
$227$	7.70115	+	4.44626i	0.511143	+	0.295109i	0.733304	−	0.679901i	$-0.237977\pi$
$227$	7.70115	+	4.44626i	0.511143	+	0.295109i	−0.222160	+	0.975010i	$0.571311\pi$
$228$	9.77318	−	7.47897i	0.647244	−	0.495307i
$229$	11.2113	−	6.47287i	0.740866	−	0.427739i	−0.0815180	−	0.996672i	$-0.525977\pi$
$229$	11.2113	−	6.47287i	0.740866	−	0.427739i	0.822384	+	0.568933i	$0.192643\pi$
$230$		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	$-0.832754\pi$
$233$	−13.1776	+	7.60809i	−0.863294	+	0.498423i	0.00182020	+	0.999998i	$0.499421\pi$
$234$	26.8013	−	1.73908i	1.75206	−	0.113687i
$235$		0			0
$236$	−14.1181	+	1.83994i	−0.919013	+	0.119770i
$237$	1.38275			0.0898194
$238$	12.8405	+	1.15035i	0.832324	+	0.0745660i
$239$			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	0.562795	−	0.826596i	$-0.309726\pi$
$241$	1.99236	+	1.15029i	0.128339	+	0.0740968i	−0.434456	+	0.900693i	$0.643059\pi$
$242$	8.46432	−	0.549231i	0.544107	−	0.0353059i
$243$	−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
$248$	−4.47329	+	13.0936i	−0.284054	+	0.831443i
$249$	16.3659	−	28.3466i	1.03715	−	1.79639i
$250$		0			0
$251$	6.32409			0.399173			0.199587	−	0.979880i	$-0.436040\pi$
$251$	6.32409			0.399173			0.199587	+	0.979880i	$0.436040\pi$
$252$	15.1665	+	27.8251i	0.955401	+	1.75282i
$253$			5.95233i			0.374220i
$254$	−1.89374	+	3.83381i	−0.118824	+	0.240554i
$255$		0			0
$256$	−13.8144	−	8.07226i	−0.863402	−	0.504516i
$257$	7.12068	+	12.3334i	0.444176	+	0.769335i	0.997994	−	0.0633025i	$-0.0201633\pi$
$257$	7.12068	+	12.3334i	0.444176	+	0.769335i	−0.553819	+	0.832637i	$0.686830\pi$
$258$	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
$262$	−22.1641	+	1.43818i	−1.36930	+	0.0888511i
$263$	−5.87421	+	10.1744i	−0.362219	+	0.627382i	−0.988326	−	0.152355i	$-0.951314\pi$
$263$	−5.87421	+	10.1744i	−0.362219	+	0.627382i	0.626107	+	0.779738i	$0.284647\pi$
$264$	12.4773	+	14.2840i	0.767925	+	0.879118i
$265$		0			0
$266$	−4.41770	+	6.28125i	−0.270867	+	0.385128i
$267$	21.0484			1.28814
$268$	0.104654	−	0.0136390i	0.00639276	−	0.000833133i
$269$	7.35196	+	4.24466i	0.448257	+	0.258801i	0.707094	−	0.707120i	$-0.250006\pi$
$269$	7.35196	+	4.24466i	0.448257	+	0.258801i	−0.258837	+	0.965921i	$0.583339\pi$
$270$		0			0
$271$	−3.98686	−	6.90544i	−0.242184	−	0.419476i	0.719152	−	0.694853i	$-0.244531\pi$
$271$	−3.98686	−	6.90544i	−0.242184	−	0.419476i	−0.961336	+	0.275377i	$0.911197\pi$
$272$	−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
$276$	12.6733	−	9.69828i	0.762841	−	0.583768i
$277$	−11.7737	−	6.79754i	−0.707412	−	0.408425i	0.102690	−	0.994713i	$-0.467255\pi$
$277$	−11.7737	−	6.79754i	−0.707412	−	0.408425i	−0.810102	+	0.586289i	$0.800588\pi$
$278$	−4.69579	+	9.50647i	−0.281635	+	0.570160i
$279$	−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	$0.408720\pi$
$282$	11.5050	−	23.2914i	0.685111	−	1.38698i
$283$	−18.6621	−	10.7746i	−1.10935	−	0.640483i	−0.170689	−	0.985325i	$-0.554599\pi$
$283$	−18.6621	−	10.7746i	−1.10935	−	0.640483i	−0.938661	+	0.344842i	$0.887933\pi$
$284$	−0.337269	+	0.258097i	−0.0200132	+	0.0153152i
$285$		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
$292$	−29.4994	+	3.84449i	−1.72632	+	0.224982i
$293$	−28.9496			−1.69125			−0.845626	−	0.533776i	$-0.820773\pi$
$293$	−28.9496			−1.69125			−0.845626	+	0.533776i	$0.820773\pi$
$294$	−21.3676	−	20.5994i	−1.24618	−	1.20138i
$295$		0			0
$296$	23.8447	−	20.8288i	1.38594	−	1.21065i
$297$	−10.0210	+	17.3569i	−0.581477	+	1.00715i
$298$	−9.17496	+	0.595344i	−0.531491	+	0.0344873i
$299$	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
$304$	7.93521	−	2.10404i	0.455115	−	0.120675i
$305$		0			0
$306$	12.9239	−	26.1640i	0.738809	−	1.49569i
$307$			8.00589i			0.456920i	0.973553	+	0.228460i	$0.0733690\pi$
$307$			8.00589i			0.456920i	−0.973553	+	0.228460i	$0.926631\pi$
$308$	−10.1009	−	6.16724i	−0.575551	−	0.351411i
$309$	−34.2339			−1.94750
$310$		0			0
$311$	6.87633	−	11.9101i	0.389921	−	0.675363i	−0.602518	−	0.798105i	$-0.705836\pi$
$311$	6.87633	−	11.9101i	0.389921	−	0.675363i	0.992438	+	0.122743i	$0.0391691\pi$
$312$	25.4469	+	8.69367i	1.44065	+	0.492182i
$313$	5.31792	+	9.21091i	0.300587	+	0.520631i	0.976269	−	0.216562i	$-0.0694842\pi$
$313$	5.31792	+	9.21091i	0.300587	+	0.520631i	−0.675682	+	0.737193i	$0.736151\pi$
$314$	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	$-0.508411\pi$
$317$	14.7081	−	8.49175i	0.826091	−	0.476944i	0.852513	+	0.522707i	$0.175078\pi$
$318$	−19.7076	+	1.27878i	−1.10514	+	0.0717105i
$319$	−14.2963	−	8.25397i	−0.800439	−	0.462133i
$320$		0			0
$321$			7.80679i			0.435732i
$322$	−5.72861	+	8.14515i	−0.319243	+	0.453911i
$323$	7.07140			0.393463
$324$	17.6506	−	2.30030i	0.980586	−	0.127794i
$325$		0			0
$326$	15.3142	−	0.993708i	0.848177	−	0.0550364i
$327$	−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	$-0.593143\pi$
$331$	7.21415	−	4.16509i	0.396525	−	0.228934i	0.684984	+	0.728558i	$0.259809\pi$
$332$	17.3400	−	13.2695i	0.951655	−	0.728258i
$333$	58.0567	+	33.5190i	3.18149	+	1.83683i
$334$	−14.8955	−	7.35775i	−0.815046	−	0.402598i
$335$		0			0
$336$	3.32679	+	31.5545i	0.181491	+	1.72144i
$337$			27.0772i			1.47499i	0.675353	+	0.737495i	$0.263991\pi$
$337$			27.0772i			1.47499i	−0.675353	+	0.737495i	$0.736009\pi$
$338$	1.84400	−	3.73311i	0.100300	−	0.203054i
$339$	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
$346$	23.2678	−	1.50980i	1.25089	−	0.0811672i
$347$	−13.8861	+	24.0514i	−0.745443	+	1.29115i	0.204544	+	0.978857i	$0.434429\pi$
$347$	−13.8861	+	24.0514i	−0.745443	+	1.29115i	−0.949987	+	0.312288i	$0.898905\pi$
$348$	5.71955	+	43.8870i	0.306600	+	2.35259i
$349$		−	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
$352$	4.02771	+	11.9937i	0.214677	+	0.639267i
$353$	8.15697	−	14.1283i	0.434152	−	0.751973i	−0.563074	−	0.826406i	$-0.690381\pi$
$353$	8.15697	−	14.1283i	0.434152	−	0.751973i	0.997226	+	0.0744333i	$0.0237148\pi$
$354$	−1.95444	−	30.1203i	−0.103877	−	1.60088i
$355$		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	$-0.680128\pi$
$359$	−1.38744	+	0.801040i	−0.0732264	+	0.0422773i	0.462940	+	0.886390i	$0.346795\pi$
$360$		0			0
$361$	7.39392	−	12.8067i	0.389154	−	0.674034i
$362$	21.0171	+	10.3815i	1.10463	+	0.545642i
$363$			17.9822i			0.943818i
$364$	−16.7748	−	0.411939i	−0.879237	−	0.0215915i
$365$		0			0
$366$	−4.76331	+	9.64316i	−0.248982	+	0.504056i
$367$	1.09164	+	0.630259i	0.0569832	+	0.0328993i	0.528221	−	0.849107i	$-0.322859\pi$
$367$	1.09164	+	0.630259i	0.0569832	+	0.0328993i	−0.471238	+	0.882006i	$0.656193\pi$
$368$	10.2899	−	2.72839i	0.536398	−	0.142227i
$369$	−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	$-0.589883\pi$
$373$	7.99120	−	4.61372i	0.413768	−	0.238889i	0.692408	+	0.721507i	$0.256550\pi$
$374$	0.705669	+	10.8752i	0.0364893	+	0.562344i
$375$		0			0
$376$	13.0513	−	11.4005i	0.673068	−	0.587936i
$377$	−23.4056			−1.20545
$378$	−30.4172	+	14.1067i	−1.56449	+	0.725571i
$379$		−	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
$382$	−0.274073	−	4.22379i	−0.0140228	−	0.216108i
$383$	1.14737	−	0.662435i	0.0586279	−	0.0338489i	−0.470400	−	0.882454i	$-0.655890\pi$
$383$	1.14737	−	0.662435i	0.0586279	−	0.0338489i	0.529027	+	0.848605i	$0.322557\pi$
$384$	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
$388$	0.225416	+	0.294563i	0.0114437	+	0.0149542i
$389$	16.1134	−	27.9093i	0.816983	−	1.41506i	−0.0909120	−	0.995859i	$-0.528978\pi$
$389$	16.1134	−	27.9093i	0.816983	−	1.41506i	0.907895	−	0.419197i	$-0.137688\pi$
$390$		0			0
$391$	9.16976			0.463735
$392$	−7.88657	−	18.1605i	−0.398332	−	0.917241i
$393$		−	47.0869i		−	2.37522i
$394$	6.10838	+	3.01728i	0.307736	+	0.152008i
$395$		0			0
$396$	−21.2744	+	16.2804i	−1.06908	+	0.818119i
$397$	17.5871	+	30.4617i	0.882670	+	1.52883i	0.848361	+	0.529419i	$0.177590\pi$
$397$	17.5871	+	30.4617i	0.882670	+	1.52883i	0.0343095	+	0.999411i	$0.489077\pi$
$398$	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	−0.921484	−	0.388416i	$-0.873022\pi$
$401$	−15.9623	−	27.6476i	−0.797120	−	1.38065i	0.124364	−	0.992237i	$-0.460311\pi$
$402$	0.0144878	+	0.223274i	0.000722585	+	0.0111359i
$403$	7.75647	−	13.4346i	0.386377	−	0.669225i
$404$	1.61511	+	12.3930i	0.0803549	+	0.616576i
$405$		0			0
$406$	−11.6192	−	25.0536i	−0.576653	−	1.24339i
$407$	−25.0357			−1.24097
$408$	22.0049	−	19.2217i	1.08941	−	0.951616i
$409$	−14.2151	−	8.20712i	−0.702894	−	0.405816i	0.105530	−	0.994416i	$-0.466346\pi$
$409$	−14.2151	−	8.20712i	−0.702894	−	0.405816i	−0.808424	+	0.588600i	$0.799679\pi$
$410$		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
$416$	13.4481	+	11.8716i	0.659349	+	0.582052i
$417$	−19.4669	−	11.2392i	−0.953298	−	0.550387i
$418$	−5.82023	−	2.87495i	−0.284677	−	0.140618i
$419$	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	$0.418895\pi$
$422$	−4.70395	−	2.32355i	−0.228985	−	0.113109i
$423$	31.7770	+	18.3465i	1.54505	+	0.892035i
$424$	−12.4667	−	4.25912i	−0.605436	−	0.206841i
$425$		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	$-0.586573\pi$
$431$	−25.6838	−	14.8286i	−1.23715	−	0.714267i	−0.968510	+	0.248975i	$0.919906\pi$
$432$	34.5985	+	9.36754i	1.66462	+	0.450696i
$433$	29.4107			1.41339			0.706693	−	0.707520i	$-0.250186\pi$
$433$	29.4107			1.41339			0.706693	+	0.707520i	$0.250186\pi$
$434$	18.2311	+	1.63328i	0.875122	+	0.0784001i
$435$		0			0
$436$	−1.98698	+	0.258952i	−0.0951591	+	0.0124016i
$437$	−2.73103	+	4.73029i	−0.130643	+	0.226280i
$438$	−4.08374	−	62.9354i	−0.195129	−	3.00717i
$439$	−4.41191	−	7.64165i	−0.210569	−	0.364716i	0.741324	−	0.671147i	$-0.234198\pi$
$439$	−4.41191	−	7.64165i	−0.210569	−	0.364716i	−0.951893	+	0.306432i	$0.900865\pi$
$440$		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	0.534369	−	0.845251i	$-0.320549\pi$
$443$	−9.78342	−	16.9454i	−0.464824	−	0.805099i	−0.999194	+	0.0401518i	$0.987216\pi$
$444$	40.7912	+	53.3041i	1.93586	+	2.52970i
$445$		0			0
$446$	16.4303	+	8.11589i	0.777999	+	0.384298i
$447$		−	19.4919i		−	0.921935i
$448$	−6.03143	+	20.2885i	−0.284958	+	0.958540i
$449$	−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
$452$	23.6002	−	18.0601i	1.11006	−	0.849477i
$453$	−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	$-0.440905\pi$
$457$	24.1144	−	13.9225i	1.12802	−	0.651265i	0.943437	+	0.331551i	$0.107572\pi$
$458$	1.18548	+	18.2696i	0.0553937	+	0.853683i
$459$	26.7388	+	15.4377i	1.24806	+	0.720569i
$460$		0			0
$461$			19.8494i			0.924481i	0.886755	+	0.462240i	$0.152954\pi$
$461$			19.8494i			0.924481i	−0.886755	+	0.462240i	$0.847046\pi$
$462$	14.4337	−	20.5224i	0.671518	−	0.954789i
$463$	−35.7118			−1.65967			−0.829833	−	0.558012i	$-0.811564\pi$
$463$	−35.7118			−1.65967			−0.829833	+	0.558012i	$0.811564\pi$
$464$	−7.71573	+	28.4976i	−0.358194	+	1.32297i
$465$		0			0
$466$	−1.39339	−	21.4738i	−0.0645474	−	0.994754i
$467$	19.5818	−	11.3055i	0.906136	−	0.523158i	0.0269503	−	0.999637i	$-0.491420\pi$
$467$	19.5818	−	11.3055i	0.906136	−	0.523158i	0.879186	+	0.476479i	$0.158087\pi$
$468$	−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
$472$	6.50948	−	19.0536i	0.299623	−	0.877015i
$473$	−19.2870	−	11.1353i	−0.886816	−	0.512003i
$474$	−0.866043	+	1.75328i	−0.0397787	+	0.0805306i
$475$		0			0
$476$	−9.50083	+	15.5607i	−0.435470	+	0.713225i
$477$		−	27.8947i		−	1.27721i
$478$	−0.0556017	−	0.0274649i	−0.00254316	−	0.00125621i
$479$	4.28200	−	7.41664i	0.195649	−	0.338875i	−0.751464	−	0.659774i	$-0.770652\pi$
$479$	4.28200	−	7.41664i	0.195649	−	0.338875i	0.947113	+	0.320900i	$0.103985\pi$
$480$		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
$486$	−0.0183086	−	0.282157i	−0.000830494	−	0.0127989i
$487$	15.8225	−	27.4054i	0.716987	−	1.24186i	−0.245201	−	0.969472i	$-0.578854\pi$
$487$	15.8225	−	27.4054i	0.716987	−	1.24186i	0.962188	−	0.272386i	$-0.0878128\pi$
$488$	−5.40351	+	4.72006i	−0.244605	+	0.213667i
$489$			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	$-0.299083\pi$
$492$	−8.68184	+	1.13146i	−0.391408	+	0.0510100i
$493$	−12.7155	+	22.0239i	−0.572677	+	0.991906i
$494$	−9.18467	+	0.595973i	−0.413238	+	0.0268141i
$495$		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	0.610574	−	0.791959i	$-0.290939\pi$
$499$	35.7797	−	20.6574i	1.60172	−	0.924752i	0.991144	−	0.132793i	$-0.0423947\pi$
$500$		0			0
$501$	17.6105	−	30.5023i	0.786780	−	1.36274i
$502$	−3.96090	+	8.01870i	−0.176783	+	0.357892i
$503$		−	29.0170i		−	1.29381i	−0.762572	−	0.646903i	$-0.776064\pi$
$503$		−	29.0170i		−	1.29381i	0.762572	−	0.646903i	$-0.223936\pi$
$504$	−44.7803	+	1.80315i	−1.99467	+	0.0803187i
$505$		0			0
$506$	−7.54733	−	3.72806i	−0.335520	−	0.165732i
$507$	7.64448	+	4.41354i	0.339503	+	0.196012i
$508$	−3.67503	−	4.80237i	−0.163053	−	0.213071i
$509$	−17.3474	+	10.0155i	−0.768910	+	0.443931i	−0.832486	−	0.554046i	$-0.813083\pi$
$509$	−17.3474	+	10.0155i	−0.768910	+	0.443931i	0.0635754	+	0.997977i	$0.479750\pi$
$510$		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
$514$	−20.0981	+	1.30412i	−0.886487	+	0.0575222i
$515$		0			0
$516$	7.71618	+	59.2075i	0.339686	+	2.60646i
$517$	−13.7031			−0.602663
$518$	−34.2587	−	24.0947i	−1.50524	−	1.05866i
$519$			49.4317i			2.16981i
$520$		0			0
$521$	18.5712	+	10.7221i	0.813620	+	0.469743i	0.848211	−	0.529658i	$-0.177680\pi$
$521$	18.5712	+	10.7221i	0.813620	+	0.469743i	−0.0345917	+	0.999402i	$0.511013\pi$
$522$	−62.3818	+	4.04782i	−2.73038	+	0.177168i
$523$	35.5105	−	20.5020i	1.55277	−	0.896491i	0.554852	−	0.831949i	$-0.312775\pi$
$523$	35.5105	−	20.5020i	1.55277	−	0.896491i	0.997915	−	0.0645418i	$-0.0205586\pi$
$524$	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
$528$	−25.9263	+	6.87442i	−1.12830	+	0.299171i
$529$	7.95856	−	13.7846i	0.346024	−	0.599332i
$530$		0			0
$531$	42.6333			1.85013
$532$	−5.19749	−	9.53553i	−0.225340	−	0.413418i
$533$		−	4.63015i		−	0.200554i
$534$	−13.1830	+	26.6886i	−0.570485	+	1.15493i
$535$		0			0
$536$	−0.0482531	+	0.141240i	−0.00208422	+	0.00610062i
$537$	−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	0.826524	−	0.562901i	$-0.190315\pi$
$541$	−1.72641	−	2.99023i	−0.0742242	−	0.128560i	−0.900749	+	0.434341i	$0.856981\pi$
$542$	11.2529	−	0.730175i	0.483352	−	0.0313637i
$543$	−24.8479	+	43.0377i	−1.06632	+	1.84693i
$544$	18.4767	−	6.20481i	0.792182	−	0.266029i
$545$		0			0
$546$	3.17422	−	35.4315i	0.135844	−	1.51633i
$547$	−28.2607			−1.20834			−0.604170	−	0.796855i	$-0.706495\pi$
$547$	−28.2607			−1.20834			−0.604170	+	0.796855i	$0.706495\pi$
$548$	−2.48496	−	19.0675i	−0.106152	−	0.814522i
$549$	−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
$556$	−9.11277	−	11.9082i	−0.386468	−	0.505018i
$557$	1.79833	+	1.03826i	0.0761976	+	0.0439927i	0.537615	−	0.843191i	$-0.319326\pi$
$557$	1.79833	+	1.03826i	0.0761976	+	0.0439927i	−0.461417	+	0.887183i	$0.652659\pi$
$558$	18.3495	−	37.1480i	0.776798	−	1.57260i
$559$	−31.5762			−1.33553
$560$		0			0
$561$	−23.1040			−0.975453
$562$	−5.93929	+	12.0239i	−0.250534	+	0.507197i
$563$	39.7588	+	22.9547i	1.67563	+	0.967426i	0.964392	+	0.264477i	$0.0851993\pi$
$563$	39.7588	+	22.9547i	1.67563	+	0.967426i	0.711240	+	0.702949i	$0.248134\pi$
$564$	22.3268	+	29.1757i	0.940130	+	1.22852i
$565$		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	0.937075	−	0.349127i	$-0.113522\pi$
$569$	3.96413	+	6.86607i	0.166185	+	0.287840i	−0.770891	+	0.636968i	$0.780189\pi$
$570$		0			0
$571$	18.3314	+	10.5837i	0.767147	+	0.442912i	0.831856	−	0.554992i	$-0.187279\pi$
$571$	18.3314	+	10.5837i	0.767147	+	0.442912i	−0.0647092	+	0.997904i	$0.520612\pi$
$572$	−1.83311	−	14.0658i	−0.0766464	−	0.588120i
$573$	8.97330			0.374865
$574$	4.95618	−	2.29855i	0.206867	−	0.0959396i
$575$		0			0
$576$	37.8958	+	29.3150i	1.57899	+	1.22146i
$577$	5.16573	−	8.94731i	0.215052	−	0.372481i	−0.738237	−	0.674542i	$-0.764341\pi$
$577$	5.16573	−	8.94731i	0.215052	−	0.372481i	0.953289	+	0.302061i	$0.0976745\pi$
$578$	−7.23756	+	0.469630i	−0.301043	+	0.0195340i
$579$	−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
$584$	13.6013	−	39.8119i	0.562827	−	1.64743i
$585$		0			0
$586$	18.1317	−	36.7069i	0.749012	−	1.51635i
$587$			20.4660i			0.844722i	0.906428	+	0.422361i	$0.138799\pi$
$587$			20.4660i			0.844722i	−0.906428	+	0.422361i	$0.861201\pi$
$588$	39.5021	−	14.1915i	1.62904	−	0.585249i
$589$	10.0401			0.413694
$590$		0			0
$591$	−7.22175	+	12.5084i	−0.297063	+	0.514529i
$592$	11.4757	+	43.2796i	0.471648	+	1.77878i
$593$	22.4236	+	38.8389i	0.920828	+	1.59492i	0.798136	+	0.602477i	$0.205819\pi$
$593$	22.4236	+	38.8389i	0.920828	+	1.59492i	0.122692	+	0.992445i	$0.460847\pi$
$594$	−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
$598$	−11.9101	+	0.772823i	−0.487041	+	0.0316031i
$599$	14.1499	+	8.16942i	0.578147	+	0.333793i	0.760397	−	0.649459i	$-0.225005\pi$
$599$	14.1499	+	8.16942i	0.578147	+	0.333793i	−0.182250	+	0.983252i	$0.558338\pi$
$600$		0			0
$601$			39.8029i			1.62359i	0.583941	+	0.811796i	$0.301510\pi$
$601$			39.8029i			1.62359i	−0.583941	+	0.811796i	$0.698490\pi$
$602$	−15.6754	−	33.7996i	−0.638882	−	1.37757i
$603$	−0.316030			−0.0128697
$604$	−6.11903	−	46.9523i	−0.248980	−	1.91046i
$605$		0			0
$606$	−26.4399	+	1.71563i	−1.07405	+	0.0696926i
$607$	8.14710	−	4.70373i	0.330681	−	0.190919i	−0.325463	−	0.945555i	$-0.605520\pi$
$607$	8.14710	−	4.70373i	0.330681	−	0.190919i	0.656143	+	0.754636i	$0.272187\pi$
$608$	−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
$612$	25.0804	+	32.7739i	1.01382	+	1.32481i
$613$	−11.8091	−	6.81796i	−0.476963	−	0.275375i	0.242187	−	0.970230i	$-0.422135\pi$
$613$	−11.8091	−	6.81796i	−0.476963	−	0.275375i	−0.719150	+	0.694855i	$0.755469\pi$
$614$	−10.1512	−	5.01423i	−0.409667	−	0.202358i
$615$		0			0
$616$	14.1462	−	8.94487i	0.569966	−	0.360399i
$617$		−	39.1144i		−	1.57469i	−0.616515	−	0.787343i	$-0.711456\pi$
$617$		−	39.1144i		−	1.57469i	0.616515	−	0.787343i	$-0.288544\pi$
$618$	21.4413	−	43.4072i	0.862496	−	1.74609i
$619$	−9.50950	+	16.4709i	−0.382219	+	0.662023i	−0.991379	−	0.131024i	$-0.958173\pi$
$619$	−9.50950	+	16.4709i	−0.382219	+	0.662023i	0.609160	+	0.793047i	$0.291507\pi$
$620$		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
$626$	−15.0098	+	0.973953i	−0.599912	+	0.0389270i
$627$	6.88108	−	11.9184i	0.274804	−	0.475974i
$628$	−15.5336	+	2.02441i	−0.619859	+	0.0807827i
$629$			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	$0.893490\pi$
$632$	−0.982441	+	0.858180i	−0.0390794	+	0.0341366i
$633$	5.56134	−	9.63252i	0.221043	−	0.382858i
$634$	1.55522	+	23.9679i	0.0617659	+	0.951886i
$635$		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	0.467173	+	0.884166i	$0.345272\pi$
$641$	−13.4723	+	23.3347i	−0.532124	+	0.921665i	−0.999297	+	0.0374991i	$0.988061\pi$
$642$	−9.89870	−	4.88954i	−0.390671	−	0.192975i
$643$		−	43.6730i		−	1.72229i	−0.508355	−	0.861147i	$-0.669746\pi$
$643$		−	43.6730i		−	1.72229i	0.508355	−	0.861147i	$-0.330254\pi$
$644$	−6.73979	−	12.3651i	−0.265585	−	0.487254i
$645$		0			0
$646$	−4.42895	+	8.96625i	−0.174255	+	0.352773i
$647$	−24.3422	−	14.0540i	−0.956989	−	0.552518i	−0.0617443	−	0.998092i	$-0.519666\pi$
$647$	−24.3422	−	14.0540i	−0.956989	−	0.552518i	−0.895245	+	0.445574i	$0.853000\pi$
$648$	−8.13818	+	23.8209i	−0.319698	+	0.935775i
$649$	−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	$-0.970151\pi$
$653$	−36.0902	+	20.8367i	−1.41232	+	0.815403i	−0.416713	+	0.909038i	$0.636818\pi$
$654$	−0.275067	−	4.23912i	−0.0107560	−	0.165763i
$655$		0			0
$656$	−5.63748	−	1.52635i	−0.220107	−	0.0595939i
$657$	89.0808			3.47537
$658$	−18.7513	−	13.1881i	−0.731002	−	0.514125i
$659$		−	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	0.291006	−	0.956721i	$-0.406010\pi$
$661$	−10.0792	−	5.81924i	−0.392036	−	0.226342i	−0.683042	+	0.730379i	$0.739343\pi$
$662$	0.762817	+	11.7559i	0.0296477	+	0.456907i
$663$	−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
$668$	18.6587	−	14.2786i	0.721926	−	0.552457i
$669$	−19.4251	+	33.6452i	−0.751017	+	1.30080i
$670$		0			0
$671$	5.67340			0.219019
$672$	−42.0935	−	15.5449i	−1.62379	−	0.599658i
$673$			14.9849i			0.577626i	0.957385	+	0.288813i	$0.0932606\pi$
$673$			14.9849i			0.577626i	−0.957385	+	0.288813i	$0.906739\pi$
$674$	−34.3328	−	16.9590i	−1.32245	−	0.653234i
$675$		0			0
$676$	3.57851	+	4.67623i	0.137635	+	0.179855i
$677$	−11.5093	−	19.9347i	−0.442339	−	0.766154i	0.555524	−	0.831501i	$-0.312518\pi$
$677$	−11.5093	−	19.9347i	−0.442339	−	0.766154i	−0.997863	+	0.0653470i	$0.979185\pi$
$678$	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
$682$	1.00192	+	15.4408i	0.0383655	+	0.591259i
$683$	−18.6347	+	32.2762i	−0.713037	+	1.23502i	0.250675	+	0.968071i	$0.419348\pi$
$683$	−18.6347	+	32.2762i	−0.713037	+	1.23502i	−0.963712	+	0.266945i	$0.913986\pi$
$684$	−24.3764	+	3.17684i	−0.932055	+	0.121469i
$685$		0			0
$686$	−20.8577	+	15.8415i	−0.796352	+	0.604833i
$687$	−38.8132			−1.48082
$688$	−10.4092	+	38.4459i	−0.396848	+	1.46573i
$689$	12.7914	+	7.38510i	0.487312	+	0.281350i
$690$		0			0
$691$	−13.9969	−	24.2433i	−0.532467	−	0.922260i	−0.999281	−	0.0379044i	$-0.987932\pi$
$691$	−13.9969	−	24.2433i	−0.532467	−	0.922260i	0.466815	−	0.884355i	$-0.345402\pi$
$692$	−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
$696$	−59.2292	−	20.2351i	−2.24508	−	0.767009i
$697$	−4.35683	−	2.51542i	−0.165027	−	0.0952782i
$698$	12.2239	+	6.03811i	0.462683	+	0.228546i
$699$	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	$0.313840\pi$
$702$	−36.0308	−	17.7977i	−1.35989	−	0.671729i
$703$	−19.8957	−	11.4868i	−0.750381	−	0.433233i
$704$	−17.7302	−	2.40491i	−0.668232	−	0.0906386i
$705$		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	0.824305	−	0.566146i	$-0.191566\pi$
$709$	−2.08074	−	3.60395i	−0.0781440	−	0.135349i	−0.902449	+	0.430796i	$0.858233\pi$
$710$		0			0
$711$	−2.39203	−	1.38104i	−0.0897082	−	0.0517931i
$712$	−14.9548	+	13.0633i	−0.560457	+	0.489569i
$713$	13.0194			0.487580
$714$	−31.6154	−	22.2356i	−1.18318	−	0.832148i
$715$		0			0
$716$	−2.35449	−	18.0664i	−0.0879916	−	0.675173i
$717$	0.0657362	−	0.113858i	0.00245496	−	0.00425212i
$718$	−0.146707	−	2.26093i	−0.00547505	−	0.0843771i
$719$	21.1113	+	36.5658i	0.787318	+	1.36368i	0.927604	+	0.373564i	$0.121865\pi$
$719$	21.1113	+	36.5658i	0.787318	+	1.36368i	−0.140286	+	0.990111i	$0.544802\pi$
$720$		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
$724$	−26.3268	+	20.1467i	−0.978427	+	0.748746i
$725$		0			0
$726$	−22.8007	−	11.2626i	−0.846212	−	0.417993i
$727$		−	27.2605i		−	1.01104i	−0.862816	−	0.505519i	$-0.831301\pi$
$727$		−	27.2605i		−	1.01104i	0.862816	−	0.505519i	$-0.168699\pi$
$728$	11.0287	−	21.0118i	0.408750	−	0.778748i
$729$	27.2992			1.01108
$730$		0			0
$731$	−17.1544	+	29.7122i	−0.634477	+	1.09895i
$732$	−9.24380	−	12.0794i	−0.341661	−	0.446467i
$733$	7.65300	+	13.2554i	0.282670	+	0.489599i	0.972041	−	0.234809i	$-0.0754466\pi$
$733$	7.65300	+	13.2554i	0.282670	+	0.489599i	−0.689372	+	0.724408i	$0.742113\pi$
$734$	−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
$738$	−0.800751	−	12.3405i	−0.0294760	−	0.454261i
$739$	−42.5694	−	24.5774i	−1.56594	−	0.904096i	−0.996635	−	0.0819692i	$-0.973879\pi$
$739$	−42.5694	−	24.5774i	−1.56594	−	0.904096i	−0.569305	−	0.822126i	$-0.692788\pi$
$740$		0			0
$741$		−	19.5125i		−	0.716810i
$742$	−1.55508	+	17.3582i	−0.0570890	+	0.637241i
$743$	−35.2067			−1.29161			−0.645805	−	0.763503i	$-0.723478\pi$
$743$	−35.2067			−1.29161			−0.645805	+	0.763503i	$0.723478\pi$
$744$	31.2430	−	27.2913i	1.14542	−	1.00055i
$745$		0			0
$746$	0.844982	+	13.0222i	0.0309370	+	0.476776i
$747$	−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	$-0.662748\pi$
$751$	0.584292	−	0.337341i	0.0213211	−	0.0123098i	0.510623	+	0.859805i	$0.329415\pi$
$752$	6.28115	+	23.6888i	0.229050	+	0.863843i
$753$	−16.4203	−	9.48027i	−0.598389	−	0.345480i
$754$	14.6593	−	29.6773i	0.533862	−	1.08079i
$755$		0			0
$756$	1.16408	−	47.4031i	0.0423372	−	1.72403i
$757$			45.8640i			1.66695i	0.552553	+	0.833477i	$0.313654\pi$
$757$			45.8640i			1.66695i	−0.552553	+	0.833477i	$0.686346\pi$
$758$	3.21449	+	1.58782i	0.116756	+	0.0576723i
$759$	8.92298	−	15.4550i	0.323883	−	0.560983i
$760$		0			0
$761$	18.9229	−	10.9252i	0.685956	−	0.396037i	−0.116139	−	0.993233i	$-0.537052\pi$
$761$	18.9229	−	10.9252i	0.685956	−	0.396037i	0.802095	+	0.597196i	$0.203719\pi$
$762$	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
$766$	0.121322	+	1.86972i	0.00438354	+	0.0675556i
$767$	−11.2871	+	19.5499i	−0.407554	+	0.705905i
$768$	23.7679	+	41.6682i	0.857649	+	1.50357i
$769$			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
$772$	−3.80169	−	29.1710i	−0.136826	−	1.04989i
$773$	21.1707	−	36.6688i	0.761458	−	1.31888i	−0.180641	−	0.983549i	$-0.557817\pi$
$773$	21.1707	−	36.6688i	0.761458	−	1.31888i	0.942099	−	0.335335i	$-0.108850\pi$
$774$	−84.1586	+	5.46087i	−3.02502	+	0.196287i
$775$		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
$782$	−5.74319	+	11.6269i	−0.205376	+	0.415777i
$783$		−	66.1408i		−	2.36368i
$784$	27.9662	+	1.37437i	0.998795	+	0.0490845i
$785$		0			0
$786$	59.7043	+	29.4914i	2.12958	+	1.05192i
$787$	3.79528	+	2.19121i	0.135287	+	0.0781081i	0.566116	−	0.824326i	$-0.308445\pi$
$787$	3.79528	+	2.19121i	0.135287	+	0.0781081i	−0.430829	+	0.902434i	$0.641779\pi$
$788$	−7.65158	+	5.85541i	−0.272576	+	0.208590i
$789$	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
$794$	−49.6394	+	3.22099i	−1.76164	+	0.114309i
$795$		0			0
$796$	−2.52735	+	0.329375i	−0.0895795	+	0.0116744i
$797$	−53.6019			−1.89868			−0.949339	−	0.314255i	$-0.898245\pi$
$797$	−53.6019			−1.89868			−0.949339	+	0.314255i	$0.898245\pi$
$798$	20.8865	−	9.68661i	0.739373	−	0.342902i
$799$			21.1101i			0.746822i
$800$		0			0
$801$	−36.4118	−	21.0224i	−1.28655	−	0.742789i
$802$	45.0535	−	2.92343i	1.59090	−	0.103230i
$803$	−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
$808$	−16.7254	−	5.71408i	−0.588399	−	0.201021i
$809$	−0.754693	+	1.30717i	−0.0265336	+	0.0459575i	−0.878987	−	0.476845i	$-0.841780\pi$
$809$	−0.754693	+	1.30717i	−0.0265336	+	0.0459575i	0.852454	+	0.522803i	$0.175114\pi$
$810$		0			0
$811$	43.1894			1.51658			0.758292	−	0.651915i	$-0.226034\pi$
$811$	43.1894			1.51658			0.758292	+	0.651915i	$0.226034\pi$
$812$	39.0444	+	0.958815i	1.37019	+	0.0336478i
$813$			23.9063i			0.838432i
$814$	15.6803	−	31.7442i	0.549594	−	1.11264i
$815$		0			0
$816$	10.5903	+	39.9403i	0.370733	+	1.39819i
$817$	−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	0.934621	−	0.355646i	$-0.115739\pi$
$821$	4.56478	+	7.90644i	0.159312	+	0.275937i	−0.775309	+	0.631582i	$0.782406\pi$
$822$	40.6795	−	2.63960i	1.41886	−	0.0920668i
$823$	0.190193	−	0.329424i	0.00662972	−	0.0114830i	−0.862692	−	0.505731i	$-0.831223\pi$
$823$	0.190193	−	0.329424i	0.00662972	−	0.0114830i	0.869321	+	0.494248i	$0.164556\pi$
$824$	24.3231	−	21.2466i	0.847334	−	0.740161i
$825$		0			0
$826$	−26.5297	−	2.37674i	−0.923087	−	0.0826972i
$827$	23.9044			0.831236			0.415618	−	0.909539i	$-0.363565\pi$
$827$	23.9044			0.831236			0.415618	+	0.909539i	$0.363565\pi$
$828$	−31.6099	+	4.11954i	−1.09852	+	0.143164i
$829$	−35.8241	−	20.6830i	−1.24422	−	0.718352i	−0.274271	−	0.961653i	$-0.588436\pi$
$829$	−35.8241	−	20.6830i	−1.24422	−	0.718352i	−0.969951	+	0.243301i	$0.921770\pi$
$830$		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
$836$	7.29064	−	5.57919i	0.252152	−	0.192960i
$837$	37.9642	+	21.9187i	1.31224	+	0.757620i
$838$	−7.43155	+	15.0449i	−0.256718	+	0.519718i
$839$	−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
$842$	−6.47819	+	13.1149i	−0.223253	+	0.451969i
$843$	−24.6219	−	14.2155i	−0.848025	−	0.489607i
$844$	5.89234	−	4.50914i	0.202823	−	0.155211i
$845$		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
$852$	1.26261	−	0.164549i	0.0432564	−	0.00563737i
$853$	10.5928			0.362692			0.181346	−	0.983419i	$-0.441955\pi$
$853$	10.5928			0.362692			0.181346	+	0.983419i	$0.441955\pi$
$854$	7.76345	+	5.46016i	0.265660	+	0.186843i
$855$		0			0
$856$	−4.84514	−	5.54670i	−0.165604	−	0.189582i
$857$	−0.141688	+	0.245410i	−0.00483996	+	0.00838305i	−0.868435	−	0.495803i	$-0.834874\pi$
$857$	−0.141688	+	0.245410i	−0.00483996	+	0.00838305i	0.863595	+	0.504186i	$0.168207\pi$
$858$	30.0086	−	1.94719i	1.02448	−	0.0664761i
$859$	−4.93861	−	8.55393i	−0.168503	−	0.291856i	0.769391	−	0.638779i	$-0.220560\pi$
$859$	−4.93861	−	8.55393i	−0.168503	−	0.291856i	−0.937894	+	0.346922i	$0.887227\pi$
$860$		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	0.997963	+	0.0638012i	$0.0203224\pi$
$863$	16.2817	+	28.2007i	0.554235	+	0.959963i	−0.443728	+	0.896162i	$0.646344\pi$
$864$	−33.5473	+	38.0025i	−1.14130	+	1.29287i
$865$		0			0
$866$	−18.4205	+	37.2916i	−0.625952	+	1.26722i
$867$		−	15.3759i		−	0.522195i
$868$	−13.4894	+	22.0934i	−0.457861	+	0.749899i
$869$	1.03151			0.0349916
$870$		0			0
$871$	0.0836685	−	0.144918i	0.00283500	−	0.00491036i
$872$	0.916141	−	2.68160i	0.0310245	−	0.0908104i
$873$	−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	$-0.888884\pi$
$877$	−32.9700	+	19.0353i	−1.11332	+	0.642775i	−0.173632	+	0.984811i	$0.555550\pi$
$878$	12.4526	−	0.808020i	0.420254	−	0.0272694i
$879$	75.1666	+	43.3975i	2.53531	+	1.46376i
$880$		0			0
$881$			27.7529i			0.935019i	0.883988	+	0.467509i	$0.154849\pi$
$881$			27.7529i			0.935019i	−0.883988	+	0.467509i	$0.845151\pi$
$882$	16.3901	+	56.9761i	0.551884	+	1.91849i
$883$	44.1707			1.48646			0.743232	−	0.669034i	$-0.233292\pi$
$883$	44.1707			1.48646			0.743232	+	0.669034i	$0.233292\pi$
$884$	−21.6688	+	2.82397i	−0.728800	+	0.0949804i
$885$		0			0
$886$	27.6136	−	1.79179i	0.927698	−	0.0601963i
$887$	17.4310	−	10.0638i	0.585275	−	0.337909i	−0.177952	−	0.984039i	$-0.556947\pi$
$887$	17.4310	−	10.0638i	0.585275	−	0.337909i	0.763227	+	0.646130i	$0.223614\pi$
$888$	−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
$892$	−20.5813	+	15.7499i	−0.689111	+	0.527346i
$893$	−10.8898	−	6.28724i	−0.364414	−	0.210394i
$894$	24.7150	+	12.2081i	0.826592	+	0.408301i
$895$		0			0
$896$	−21.9474	−	20.3547i	−0.733211	−	0.680001i
$897$		−	25.3027i		−	0.844831i
$898$	3.14606	−	6.36909i	0.104985	−	0.212539i
$899$	−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
$906$	100.170	−	6.49984i	3.32794	−	0.215943i
$907$	−7.50854	+	13.0052i	−0.249317	+	0.431830i	−0.963336	−	0.268296i	$-0.913539\pi$
$907$	−7.50854	+	13.0052i	−0.249317	+	0.431830i	0.714020	+	0.700126i	$0.246873\pi$
$908$	−2.29839	−	17.6359i	−0.0762748	−	0.585268i
$909$		−	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	$0.869737\pi$
$912$	−23.7576	−	6.43237i	−0.786693	−	0.212997i
$913$	12.2087	−	21.1461i	0.404049	−	0.699834i
$914$	2.54983	+	39.2960i	0.0843410	+	1.29980i
$915$		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	0.660992	−	0.750393i	$-0.270136\pi$
$919$	49.7575	−	28.7275i	1.64135	−	0.947632i	0.980355	−	0.197239i	$-0.0631976\pi$
$920$		0			0
$921$	12.0014	−	20.7870i	0.395459	−	0.684956i
$922$	−25.1683	−	12.4321i	−0.828875	−	0.409429i
$923$			0.673370i			0.0221643i
$924$	16.9815	+	31.1550i	0.558650	+	1.02492i
$925$		0			0
$926$	22.3669	−	45.2811i	0.735023	−	1.48803i
$927$	59.2214	+	34.1915i	1.94509	+	1.12300i
$928$	−31.3014	−	27.6318i	−1.02752	−	0.907060i
$929$	−3.45964	+	1.99743i	−0.113507	+	0.0655334i	−0.555679	−	0.831397i	$-0.687542\pi$
$929$	−3.45964	+	1.99743i	−0.113507	+	0.0655334i	0.442172	+	0.896930i	$0.354208\pi$
$930$		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
$934$	2.07056	+	31.9098i	0.0677507	+	1.04412i
$935$		0			0
$936$	−35.3378	−	40.4546i	−1.15505	−	1.32230i
$937$	43.2204			1.41195			0.705975	−	0.708237i	$-0.250509\pi$
$937$	43.2204			1.41195			0.705975	+	0.708237i	$0.250509\pi$
$938$	0.196658	+	0.0176181i	0.00642111	+	0.000575252i
$939$		−	31.8878i		−	1.04062i
$940$		0			0
$941$	−30.6731	−	17.7091i	−0.999915	−	0.577301i	−0.0916918	−	0.995787i	$-0.529227\pi$
$941$	−30.6731	−	17.7091i	−0.999915	−	0.577301i	−0.908223	+	0.418486i	$0.862561\pi$
$942$	−2.15039	−	33.1402i	−0.0700636	−	1.07976i
$943$	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	−0.925250	−	0.379358i	$-0.876145\pi$
$947$	−24.3466	−	42.1696i	−0.791159	−	1.37033i	0.134091	−	0.990969i	$-0.457188\pi$
$948$	−1.68067	−	2.19622i	−0.0545855	−	0.0713299i
$949$	−23.5840	+	40.8488i	−0.765571	+	1.32601i
$950$		0			0
$951$	−50.9190			−1.65116
$952$	−13.7799	−	21.7927i	−0.446608	−	0.706304i
$953$		−	47.5308i		−	1.53967i	−0.638241	−	0.769837i	$-0.720338\pi$
$953$		−	47.5308i		−	1.53967i	0.638241	−	0.769837i	$-0.279662\pi$
$954$	35.3694	+	17.4710i	1.14513	+	0.565644i
$955$		0			0
$956$	0.0696488	−	0.0532990i	0.00225260	−	0.00172381i
$957$	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
$962$	−3.25051	−	50.0943i	−0.104801	−	1.61510i
$963$	7.79713	−	13.5050i	0.251259	−	0.435193i
$964$	−0.594616	−	4.56258i	−0.0191513	−	0.146951i
$965$		0			0
$966$	27.0843	−	12.5610i	0.871424	−	0.404144i
$967$	29.3643			0.944292			0.472146	−	0.881520i	$-0.343479\pi$
$967$	29.3643			0.944292			0.472146	+	0.881520i	$0.343479\pi$
$968$	−11.1603	−	12.7763i	−0.358705	−	0.410645i
$969$	−18.3607	−	10.6005i	−0.589829	−	0.340538i
$970$		0			0
$971$	13.3188	+	23.0688i	0.427419	+	0.740312i	0.996643	−	0.0818708i	$-0.0260895\pi$
$971$	13.3188	+	23.0688i	0.427419	+	0.740312i	−0.569224	+	0.822183i	$0.692756\pi$
$972$	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
$976$	−2.60053	−	9.80770i	−0.0832411	−	0.313937i
$977$	13.3970	+	7.73476i	0.428608	+	0.247457i	0.698753	−	0.715363i	$-0.253739\pi$
$977$	13.3970	+	7.73476i	0.428608	+	0.247457i	−0.270146	+	0.962819i	$0.587072\pi$
$978$	−41.2526	−	20.3770i	−1.31911	−	0.651585i
$979$	15.7018			0.501832
$980$		0			0
$981$	6.00019			0.191571
$982$	45.3652	+	22.4085i	1.44766	+	0.715083i
$983$	38.1277	+	22.0131i	1.21609	+	0.702107i	0.964078	−	0.265618i	$-0.0855760\pi$
$983$	38.1277	+	22.0131i	1.21609	+	0.702107i	0.252007	+	0.967725i	$0.418909\pi$
$984$	4.00296	−	11.7169i	0.127610	−	0.373521i
$985$		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	$-0.418877\pi$
$991$	−14.4776	−	8.35865i	−0.459896	−	0.265521i	−0.712001	+	0.702179i	$0.752211\pi$
$992$	26.2335	−	8.80969i	0.832916	−	0.279708i
$993$	−24.9751			−0.792560
$994$	−0.720785	+	0.334282i	−0.0228619	+	0.0106028i
$995$		0			0
$996$	−64.9146	+	8.45996i	−2.05690	+	0.268064i
$997$	13.7897	−	23.8844i	0.436723	−	0.756427i	−0.560711	−	0.828011i	$-0.689472\pi$
$997$	13.7897	−	23.8844i	0.436723	−	0.756427i	0.997435	+	0.0715845i	$0.0228056\pi$
$998$	3.78331	+	58.3053i	0.119759	+	1.84562i
$999$	−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.d.199.6		32
4.3	odd	2	inner	700.2.t.d.199.1		32
5.2	odd	4		140.2.o.a.31.3	✓	32
5.3	odd	4		700.2.p.c.451.14		32
5.4	even	2		700.2.t.c.199.11		32
7.5	odd	6		700.2.t.c.299.16		32
20.3	even	4		700.2.p.c.451.9		32
20.7	even	4		140.2.o.a.31.8	yes	32
20.19	odd	2		700.2.t.c.199.16		32
28.19	even	6		700.2.t.c.299.11		32
35.2	odd	12		980.2.o.f.411.8		32
35.12	even	12		140.2.o.a.131.8	yes	32
35.17	even	12		980.2.g.a.391.25		32
35.19	odd	6	inner	700.2.t.d.299.1		32
35.27	even	4		980.2.o.f.31.3		32
35.32	odd	12		980.2.g.a.391.26		32
35.33	even	12		700.2.p.c.551.9		32
140.19	even	6	inner	700.2.t.d.299.6		32
140.27	odd	4		980.2.o.f.31.8		32
140.47	odd	12		140.2.o.a.131.3	yes	32
140.67	even	12		980.2.g.a.391.27		32
140.87	odd	12		980.2.g.a.391.28		32
140.103	odd	12		700.2.p.c.551.14		32
140.107	even	12		980.2.o.f.411.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.3	✓	32	5.2	odd	4
140.2.o.a.31.8	yes	32	20.7	even	4
140.2.o.a.131.3	yes	32	140.47	odd	12
140.2.o.a.131.8	yes	32	35.12	even	12
700.2.p.c.451.9		32	20.3	even	4
700.2.p.c.451.14		32	5.3	odd	4
700.2.p.c.551.9		32	35.33	even	12
700.2.p.c.551.14		32	140.103	odd	12
700.2.t.c.199.11		32	5.4	even	2
700.2.t.c.199.16		32	20.19	odd	2
700.2.t.c.299.11		32	28.19	even	6
700.2.t.c.299.16		32	7.5	odd	6
700.2.t.d.199.1		32	4.3	odd	2	inner
700.2.t.d.199.6		32	1.1	even	1	trivial
700.2.t.d.299.1		32	35.19	odd	6	inner
700.2.t.d.299.6		32	140.19	even	6	inner
980.2.g.a.391.25		32	35.17	even	12
980.2.g.a.391.26		32	35.32	odd	12
980.2.g.a.391.27		32	140.67	even	12
980.2.g.a.391.28		32	140.87	odd	12
980.2.o.f.31.3		32	35.27	even	4
980.2.o.f.31.8		32	140.27	odd	4
980.2.o.f.411.3		32	140.107	even	12
980.2.o.f.411.8		32	35.2	odd	12

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+(-0.626319 + 1.26796i) q^{2} +(-2.59647 - 1.49907i) q^{3} +(-1.21545 - 1.58830i) 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} +(0.774910 + 5.94600i) q^{12} -3.17109 q^{13} +(-1.57423 - 3.39438i) q^{14} +(-1.04536 + 3.86099i) q^{16} +(-1.72275 + 2.98390i) q^{17} +(-8.45176 + 0.548417i) 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} +(-8.02464 - 2.74154i) q^{24} +(1.98611 - 4.02082i) q^{26} -8.96105i q^{27} +(5.28991 + 0.129905i) q^{28} +7.38092 q^{29} +(-2.44599 + 4.23658i) q^{31} +(-4.24085 - 3.74369i) 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} +(2.89637 - 0.187940i) q^{38} +(8.23364 + 4.75369i) q^{39} +1.46011i q^{41} +(-1.00099 + 11.1733i) q^{42} +9.95752 q^{43} +(0.578071 + 4.43563i) q^{44} +(3.75585 - 0.243709i) 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} +(3.85430 + 5.03663i) q^{52} +(-4.03374 - 2.32888i) q^{53} +(11.3623 + 5.61247i) q^{54} +(-3.47788 + 6.62604i) q^{56} +6.15325i q^{57} +(-4.62281 + 9.35872i) 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} +(-9.46318 + 0.614046i) q^{66} +(-0.0263848 + 0.0456998i) q^{67} +(6.83323 - 0.890536i) q^{68} +7.97917i q^{69} -0.212347i q^{71} +(11.1437 + 12.7573i) q^{72} +(7.43720 - 12.8816i) q^{73} +(1.02505 + 15.7972i) 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} +(-1.85137 - 0.914496i) q^{82} +10.9174i q^{83} +(-13.5403 - 8.26724i) q^{84} +(-6.23658 + 12.6257i) q^{86} +(-19.1643 - 11.0645i) q^{87} +(-5.98626 - 2.04514i) 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} +(0.561053 + 8.64650i) q^{94} +(5.39918 + 16.0777i) q^{96} -0.185459 q^{97} +(9.60747 + 2.38673i) 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

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Database

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