LMFDB - Embedded newform 700.2.p.c.451.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			451.14
Character	$\chi$	$=$	700.451
Dual form			700.2.p.c.551.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26796 + 0.626319i) q^{2} +(1.49907 - 2.59647i) q^{3} +(1.21545 + 1.58830i) q^{4} +(3.52698 - 2.35332i) q^{6} +(2.06101 + 1.65899i) q^{7} +(0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +(-1.93693 - 1.11828i) q^{11} +(5.94600 - 0.774910i) q^{12} -3.17109i q^{13} +(1.57423 + 3.39438i) q^{14} +(-1.04536 + 3.86099i) q^{16} +(2.98390 + 1.72275i) q^{17} +(-0.548417 - 8.45176i) q^{18} +(1.02618 + 1.77739i) q^{19} +(7.39711 - 2.86441i) q^{21} +(-1.75554 - 2.63107i) q^{22} +(2.30481 - 1.33068i) q^{23} +(8.02464 + 2.74154i) q^{24} +(1.98611 - 4.02082i) q^{26} -8.96105 q^{27} +(-0.129905 + 5.28991i) q^{28} -7.38092 q^{29} +(-2.44599 + 4.23658i) q^{31} +(-3.74369 + 4.24085i) q^{32} +(-5.80718 + 3.35278i) q^{33} +(2.70447 + 4.05325i) q^{34} +(4.59812 - 11.0600i) q^{36} +(-5.59689 - 9.69410i) q^{37} +(0.187940 + 2.89637i) q^{38} +(-8.23364 - 4.75369i) q^{39} +1.46011i q^{41} +(11.1733 + 1.00099i) q^{42} +9.95752i q^{43} +(-0.578071 - 4.43563i) q^{44} +(3.75585 - 0.243709i) q^{46} +(-3.06343 - 5.30601i) q^{47} +(8.45786 + 8.50215i) q^{48} +(1.49553 + 6.83838i) q^{49} +(8.94615 - 5.16506i) q^{51} +(5.03663 - 3.85430i) q^{52} +(2.32888 - 4.03374i) q^{53} +(-11.3623 - 5.61247i) q^{54} +(-3.47788 + 6.62604i) q^{56} +6.15325 q^{57} +(-9.35872 - 4.62281i) q^{58} +(-3.55938 + 6.16503i) q^{59} +(-2.19681 + 1.26833i) q^{61} +(-5.75488 + 3.83985i) q^{62} +(2.43279 - 15.6572i) q^{63} +(-7.40297 + 3.03249i) q^{64} +(-9.46318 + 0.614046i) q^{66} +(0.0456998 + 0.0263848i) q^{67} +(0.890536 + 6.83323i) q^{68} -7.97917i q^{69} -0.212347i q^{71} +(12.7573 - 11.1437i) q^{72} +(12.8816 + 7.43720i) q^{73} +(-1.02505 - 15.7972i) q^{74} +(-1.57575 + 3.79020i) q^{76} +(-2.13680 - 5.51813i) q^{77} +(-7.46261 - 11.1844i) q^{78} +(0.399413 - 0.230601i) q^{79} +(-4.44995 + 7.70755i) q^{81} +(-0.914496 + 1.85137i) q^{82} -10.9174 q^{83} +(13.5403 + 8.26724i) q^{84} +(-6.23658 + 12.6257i) q^{86} +(-11.0645 + 19.1643i) q^{87} +(2.04514 - 5.98626i) q^{88} +(6.07992 - 3.51024i) q^{89} +(5.26080 - 6.53565i) q^{91} +(4.91490 + 2.04334i) q^{92} +(7.33344 + 12.7019i) q^{93} +(-0.561053 - 8.64650i) q^{94} +(5.39918 + 16.0777i) q^{96} +0.185459i q^{97} +(-2.38673 + 9.60747i) q^{98} +13.3945i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 16 q^{9} + 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} + 8 q^{22} + 36 q^{24} + 30 q^{26} - 2 q^{28} - 40 q^{29} - 2 q^{32} + 60 q^{36} - 8 q^{37} + 60 q^{38} + 62 q^{42}+ \cdots - 78 q^{98}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 16 * q^9 + 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 + 8 * q^22 + 36 * q^24 + 30 * q^26 - 2 * q^28 - 40 * q^29 - 2 * q^32 + 60 * q^36 - 8 * q^37 + 60 * q^38 + 62 * q^42 - 18 * q^44 + 2 * q^46 - 16 * q^49 + 36 * q^52 + 8 * q^53 + 12 * q^54 - 4 * q^56 - 48 * q^57 - 2 * q^58 + 24 * q^61 + 4 * q^64 + 24 * q^66 - 60 * q^68 - 4 * q^72 + 72 * q^73 + 38 * q^74 + 40 * q^77 - 120 * q^78 - 36 * q^81 - 42 * q^82 - 20 * q^84 + 28 * q^86 - 4 * q^88 - 60 * q^89 + 4 * q^92 + 8 * q^93 + 18 * q^94 - 60 * q^96 - 78 * q^98

Character values

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

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

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 $

$2$	1.26796	+	0.626319i	0.896584	+	0.442874i
$2$	1.26796	+	0.626319i	0.896584	+	0.442874i
$3$	1.49907	−	2.59647i	0.865490	−	1.49907i	−0.00107081	−	0.999999i	$-0.500341\pi$
$3$	1.49907	−	2.59647i	0.865490	−	1.49907i	0.866560	−	0.499072i	$-0.166326\pi$
$4$	1.21545	+	1.58830i	0.607725	+	0.794148i
$5$		0			0
$5$		0			0
$6$	3.52698	−	2.35332i	1.43988	−	0.960741i
$7$	2.06101	+	1.65899i	0.778989	+	0.627038i
$7$	2.06101	+	1.65899i	0.778989	+	0.627038i
$8$	0.546365	+	2.77516i	0.193169	+	0.981165i
$9$	−2.99443	−	5.18651i	−0.998144	−	1.72884i
$10$		0			0
$11$	−1.93693	−	1.11828i	−0.584005	−	0.337175i	0.178718	−	0.983900i	$-0.442805\pi$
$11$	−1.93693	−	1.11828i	−0.584005	−	0.337175i	−0.762723	+	0.646725i	$0.776138\pi$
$12$	5.94600	−	0.774910i	1.71646	−	0.223697i
$13$		−	3.17109i		−	0.879502i	−0.898120	−	0.439751i	$-0.855067\pi$
$13$		−	3.17109i		−	0.879502i	0.898120	−	0.439751i	$-0.144933\pi$
$14$	1.57423	+	3.39438i	0.420730	+	0.907186i
$15$		0			0
$16$	−1.04536	+	3.86099i	−0.261341	+	0.965247i
$17$	2.98390	+	1.72275i	0.723701	+	0.417829i	0.816113	−	0.577892i	$-0.196124\pi$
$17$	2.98390	+	1.72275i	0.723701	+	0.417829i	−0.0924124	+	0.995721i	$0.529458\pi$
$18$	−0.548417	−	8.45176i	−0.129263	−	1.99210i
$19$	1.02618	+	1.77739i	0.235421	+	0.407761i	0.959395	−	0.282066i	$-0.0910198\pi$
$19$	1.02618	+	1.77739i	0.235421	+	0.407761i	−0.723974	+	0.689827i	$0.757686\pi$
$20$		0			0
$21$	7.39711	−	2.86441i	1.61418	−	0.625065i
$22$	−1.75554	−	2.63107i	−0.374283	−	0.560947i
$23$	2.30481	−	1.33068i	0.480587	−	0.277467i	−0.240074	−	0.970755i	$-0.577172\pi$
$23$	2.30481	−	1.33068i	0.480587	−	0.277467i	0.720661	+	0.693288i	$0.243838\pi$
$24$	8.02464	+	2.74154i	1.63802	+	0.559614i
$25$		0			0
$26$	1.98611	−	4.02082i	0.389509	−	0.788548i
$27$	−8.96105			−1.72455
$28$	−0.129905	+	5.28991i	−0.0245497	+	0.999699i
$29$	−7.38092			−1.37060			−0.685301	−	0.728260i	$-0.740329\pi$
$29$	−7.38092			−1.37060			−0.685301	+	0.728260i	$0.740329\pi$
$30$		0			0
$31$	−2.44599	+	4.23658i	−0.439313	+	0.760913i	−0.997637	−	0.0687104i	$-0.978112\pi$
$31$	−2.44599	+	4.23658i	−0.439313	+	0.760913i	0.558323	+	0.829623i	$0.311445\pi$
$32$	−3.74369	+	4.24085i	−0.661796	+	0.749684i
$33$	−5.80718	+	3.35278i	−1.01090	+	0.583643i
$34$	2.70447	+	4.05325i	0.463813	+	0.695127i
$35$		0			0
$36$	4.59812	−	11.0600i	0.766354	−	1.84333i
$37$	−5.59689	−	9.69410i	−0.920123	−	1.59370i	−0.799222	−	0.601036i	$-0.794755\pi$
$37$	−5.59689	−	9.69410i	−0.920123	−	1.59370i	−0.120902	−	0.992664i	$-0.538579\pi$
$38$	0.187940	+	2.89637i	0.0304878	+	0.469854i
$39$	−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	$0.963629\pi$
$42$	11.1733	+	1.00099i	1.72407	+	0.154456i
$43$			9.95752i			1.51851i	0.650794	+	0.759254i	$0.274436\pi$
$43$			9.95752i			1.51851i	−0.650794	+	0.759254i	$0.725564\pi$
$44$	−0.578071	−	4.43563i	−0.0871474	−	0.668696i
$45$		0			0
$46$	3.75585	−	0.243709i	0.553769	−	0.0359329i
$47$	−3.06343	−	5.30601i	−0.446847	−	0.773962i	0.551332	−	0.834286i	$-0.314120\pi$
$47$	−3.06343	−	5.30601i	−0.446847	−	0.773962i	−0.998179	+	0.0603243i	$0.980787\pi$
$48$	8.45786	+	8.50215i	1.22079	+	1.22718i
$49$	1.49553	+	6.83838i	0.213647	+	0.976911i
$50$		0			0
$51$	8.94615	−	5.16506i	1.25271	−	0.723253i
$52$	5.03663	−	3.85430i	0.698455	−	0.534496i
$53$	2.32888	−	4.03374i	0.319897	−	0.554077i	−0.660570	−	0.750765i	$-0.729685\pi$
$53$	2.32888	−	4.03374i	0.319897	−	0.554077i	0.980466	+	0.196688i	$0.0630185\pi$
$54$	−11.3623	−	5.61247i	−1.54621	−	0.763760i
$55$		0			0
$56$	−3.47788	+	6.62604i	−0.464751	+	0.885441i
$57$	6.15325			0.815018
$58$	−9.35872	−	4.62281i	−1.22886	−	0.607004i
$59$	−3.55938	+	6.16503i	−0.463392	+	0.802619i	−0.999127	−	0.0417674i	$-0.986701\pi$
$59$	−3.55938	+	6.16503i	−0.463392	+	0.802619i	0.535735	+	0.844386i	$0.320035\pi$
$60$		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	$0.385254\pi$
$62$	−5.75488	+	3.83985i	−0.730870	+	0.487662i
$63$	2.43279	−	15.6572i	0.306503	−	1.97262i
$64$	−7.40297	+	3.03249i	−0.925371	+	0.379062i
$65$		0			0
$66$	−9.46318	+	0.614046i	−1.16484	+	0.0755838i
$67$	0.0456998	+	0.0263848i	0.00558311	+	0.00322341i	0.502789	−	0.864409i	$-0.332307\pi$
$67$	0.0456998	+	0.0263848i	0.00558311	+	0.00322341i	−0.497206	+	0.867633i	$0.665641\pi$
$68$	0.890536	+	6.83323i	0.107993	+	0.828650i
$69$		−	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	$-0.00401095\pi$
$72$	12.7573	−	11.1437i	1.50346	−	1.31330i
$73$	12.8816	+	7.43720i	1.50768	+	0.870459i	0.999960	+	0.00893589i	$0.00284442\pi$
$73$	12.8816	+	7.43720i	1.50768	+	0.870459i	0.507719	+	0.861523i	$0.330489\pi$
$74$	−1.02505	−	15.7972i	−0.119159	−	1.83639i
$75$		0			0
$76$	−1.57575	+	3.79020i	−0.180751	+	0.434766i
$77$	−2.13680	−	5.51813i	−0.243511	−	0.628849i
$78$	−7.46261	−	11.1844i	−0.844974	−	1.26638i
$79$	0.399413	−	0.230601i	0.0449375	−	0.0259447i	−0.477363	−	0.878706i	$-0.658407\pi$
$79$	0.399413	−	0.230601i	0.0449375	−	0.0259447i	0.522300	+	0.852762i	$0.325074\pi$
$80$		0			0
$81$	−4.44995	+	7.70755i	−0.494439	+	0.856394i
$82$	−0.914496	+	1.85137i	−0.100989	+	0.204449i
$83$	−10.9174			−1.19834			−0.599168	−	0.800624i	$-0.704502\pi$
$83$	−10.9174			−1.19834			−0.599168	+	0.800624i	$0.704502\pi$
$84$	13.5403	+	8.26724i	1.47737	+	0.902030i
$85$		0			0
$86$	−6.23658	+	12.6257i	−0.672508	+	1.36147i
$87$	−11.0645	+	19.1643i	−1.18624	+	2.05463i
$88$	2.04514	−	5.98626i	0.218013	−	0.638137i
$89$	6.07992	−	3.51024i	0.644470	−	0.372085i	−0.141864	−	0.989886i	$-0.545310\pi$
$89$	6.07992	−	3.51024i	0.644470	−	0.372085i	0.786334	+	0.617801i	$0.211976\pi$
$90$		0			0
$91$	5.26080	−	6.53565i	0.551481	−	0.685122i
$92$	4.91490	+	2.04334i	0.512414	+	0.213033i
$93$	7.33344	+	12.7019i	0.760442	+	1.31712i
$94$	−0.561053	−	8.64650i	−0.0578682	−	0.891819i
$95$		0			0
$96$	5.39918	+	16.0777i	0.551052	+	1.64092i
$97$			0.185459i			0.0188305i	0.999956	+	0.00941523i	$0.00299701\pi$
$97$			0.185459i			0.0188305i	−0.999956	+	0.00941523i	$0.997003\pi$
$98$	−2.38673	+	9.60747i	−0.241096	+	0.970501i
$99$			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	$0.767295\pi$
$102$	14.5783	−	0.945957i	1.44347	−	0.0936637i
$103$	5.70918	+	9.88858i	0.562542	+	0.974351i	0.997274	+	0.0737911i	$0.0235098\pi$
$103$	5.70918	+	9.88858i	0.562542	+	0.974351i	−0.434732	+	0.900560i	$0.643157\pi$
$104$	8.80027	−	1.73257i	0.862937	−	0.169893i
$105$		0			0
$106$	5.47934	−	3.65601i	0.532201	−	0.355103i
$107$	−2.25502	+	1.30194i	−0.218001	+	0.125863i	−0.605024	−	0.796207i	$-0.706837\pi$
$107$	−2.25502	+	1.30194i	−0.218001	+	0.125863i	0.387023	+	0.922070i	$0.373503\pi$
$108$	−10.8917	−	14.2328i	−1.04805	−	1.36955i
$109$	−0.500946	+	0.867663i	−0.0479819	+	0.0831071i	−0.889019	−	0.457871i	$-0.848612\pi$
$109$	−0.500946	+	0.867663i	−0.0479819	+	0.0831071i	0.841037	+	0.540978i	$0.181946\pi$
$110$		0			0
$111$	−33.5606			−3.18543
$112$	−8.55983	+	6.22329i	−0.808828	+	0.588046i
$113$	−14.8588			−1.39780			−0.698899	−	0.715220i	$-0.746326\pi$
$113$	−14.8588			−1.39780			−0.698899	+	0.715220i	$0.746326\pi$
$114$	7.80208	+	3.85389i	0.730732	+	0.360950i
$115$		0			0
$116$	−8.97114	−	11.7231i	−0.832949	−	1.08846i
$117$	−16.4469	+	9.49562i	−1.52052	+	0.877870i
$118$	−8.37443	+	5.58771i	−0.770929	+	0.514391i
$119$	3.29182	+	8.50085i	0.301760	+	0.779272i
$120$		0			0
$121$	−2.99888	−	5.19421i	−0.272626	−	0.472201i
$122$	−3.57984	+	0.232288i	−0.324104	+	0.0210304i
$123$	3.79114	+	2.18882i	0.341836	+	0.197359i
$124$	−9.70193	+	1.26440i	−0.871259	+	0.113546i
$125$		0			0
$126$	12.8911	−	18.3290i	1.14843	−	1.63288i
$127$		−	3.02360i		−	0.268301i	−0.990961	−	0.134151i	$-0.957169\pi$
$127$		−	3.02360i		−	0.268301i	0.990961	−	0.134151i	$-0.0428306\pi$
$128$	−11.2860	−	0.791535i	−0.997550	−	0.0699625i
$129$	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	$0.592659\pi$
$132$	−12.3835	−	5.14838i	−1.07785	−	0.448109i
$133$	−0.833705	+	5.36563i	−0.0722914	+	0.465259i
$134$	0.0414202	+	0.0620775i	0.00357816	+	0.00536268i
$135$		0			0
$136$	−3.15061	+	9.22202i	−0.270163	+	0.790782i
$137$	4.80718	−	8.32628i	0.410705	−	0.711362i	−0.584262	−	0.811565i	$-0.698616\pi$
$137$	4.80718	−	8.32628i	0.410705	−	0.711362i	0.994967	+	0.100203i	$0.0319493\pi$
$138$	4.99750	−	10.1173i	0.425415	−	0.861239i
$139$	−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
$142$	0.132997	−	0.269247i	0.0111608	−	0.0225947i
$143$	−3.54618	+	6.14217i	−0.296547	+	0.513634i
$144$	23.1553	−	6.13968i	1.92961	−	0.511640i
$145$		0			0
$146$	11.6753	+	17.4981i	0.966257	+	1.44815i
$147$	19.9975	+	6.36813i	1.64937	+	0.525234i
$148$	8.59435	−	20.6722i	0.706451	−	1.69925i
$149$	−3.25066	−	5.63031i	−0.266305	−	0.461253i	0.701600	−	0.712571i	$-0.252469\pi$
$149$	−3.25066	−	5.63031i	−0.266305	−	0.461253i	−0.967905	+	0.251318i	$0.919136\pi$
$150$		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	$0.253160\pi$
$152$	−4.37187	+	3.81890i	−0.354605	+	0.309754i
$153$		−	20.6347i		−	1.66821i
$154$	0.746721	−	8.33509i	0.0601725	−	0.671661i
$155$		0			0
$156$	−2.45731	−	18.8553i	−0.196742	−	1.50963i
$157$	−6.78313	−	3.91624i	−0.541353	−	0.312550i	0.204274	−	0.978914i	$-0.434517\pi$
$157$	−6.78313	−	3.91624i	−0.541353	−	0.312550i	−0.745627	+	0.666363i	$0.767850\pi$
$158$	0.650870	−	0.0422336i	0.0517805	−	0.00335992i
$159$	−6.98233	−	12.0937i	−0.553734	−	0.959096i
$160$		0			0
$161$	6.95783	+	1.08110i	0.548354	+	0.0852026i
$162$	−10.4697	+	6.98578i	−0.822581	+	0.548855i
$163$	9.39774	−	5.42579i	0.736088	−	0.424980i	−0.0845574	−	0.996419i	$-0.526948\pi$
$163$	9.39774	−	5.42579i	0.736088	−	0.424980i	0.820645	+	0.571438i	$0.193614\pi$
$164$	−2.31909	+	1.77470i	−0.181091	+	0.138580i
$165$		0			0
$166$	−13.8428	−	6.83774i	−1.07441	−	0.530712i
$167$	11.7476			0.909058			0.454529	−	0.890732i	$-0.349808\pi$
$167$	11.7476			0.909058			0.454529	+	0.890732i	$0.349808\pi$
$168$	11.9907	+	18.9631i	0.925102	+	1.46304i
$169$	2.94418			0.226476
$170$		0			0
$171$	6.14563	−	10.6445i	0.469968	−	0.814009i
$172$	−15.8155	+	12.1029i	−1.20592	+	0.922835i
$173$	14.2785	−	8.24371i	1.08558	−	0.626758i	0.153181	−	0.988198i	$-0.451048\pi$
$173$	14.2785	−	8.24371i	1.08558	−	0.626758i	0.932395	+	0.361440i	$0.117715\pi$
$174$	−26.0324	+	17.3697i	−1.97351	+	1.31679i
$175$		0			0
$176$	6.34247	−	6.30943i	0.478082	−	0.475591i
$177$	10.6715	+	18.4836i	0.802122	+	1.38932i
$178$	9.90763	−	0.642885i	0.742608	−	0.0481863i
$179$	−7.88914	−	4.55480i	−0.589662	−	0.340441i	0.175302	−	0.984515i	$-0.443910\pi$
$179$	−7.88914	−	4.55480i	−0.589662	−	0.340441i	−0.764964	+	0.644073i	$0.777243\pi$
$180$		0			0
$181$		−	16.5755i		−	1.23205i	−0.787728	−	0.616023i	$-0.788743\pi$
$181$		−	16.5755i		−	1.23205i	0.787728	−	0.616023i	$-0.211257\pi$
$182$	10.7639	−	4.99202i	0.797872	−	0.370033i
$183$			7.60525i			0.562196i
$184$	4.95212	+	5.66917i	0.365075	+	0.417937i
$185$		0			0
$186$	1.34309	+	20.6986i	0.0984798	+	1.51769i
$187$	−3.85305	−	6.67369i	−0.281763	−	0.488028i
$188$	4.70407	−	11.3148i	0.343080	−	0.825218i
$189$	−18.4688	−	14.8663i	−1.34341	−	1.08136i
$190$		0			0
$191$	−2.59197	+	1.49648i	−0.187549	+	0.108281i	−0.590834	−	0.806793i	$-0.701201\pi$
$191$	−2.59197	+	1.49648i	−0.187549	+	0.108281i	0.403286	+	0.915074i	$0.367868\pi$
$192$	−3.22381	+	23.7675i	−0.232659	+	1.71527i
$193$	−7.35442	+	12.7382i	−0.529383	+	0.916918i	0.470030	+	0.882651i	$0.344243\pi$
$193$	−7.35442	+	12.7382i	−0.529383	+	0.916918i	−0.999413	+	0.0342676i	$0.989090\pi$
$194$	−0.116156	+	0.235154i	−0.00833953	+	0.0168831i
$195$		0			0
$196$	−9.04362	+	10.6870i	−0.645973	+	0.763360i
$197$	−4.81748			−0.343231			−0.171616	−	0.985164i	$-0.554899\pi$
$197$	−4.81748			−0.343231			−0.171616	+	0.985164i	$0.554899\pi$
$198$	−8.38923	+	16.9837i	−0.596196	+	1.20698i
$199$	−0.637180	+	1.10363i	−0.0451685	+	0.0782342i	−0.887726	−	0.460373i	$-0.847716\pi$
$199$	−0.637180	+	1.10363i	−0.0451685	+	0.0782342i	0.842557	+	0.538607i	$0.181049\pi$
$200$		0			0
$201$	0.137014	−	0.0791053i	0.00966425	−	0.00557966i
$202$	−4.90494	−	7.35115i	−0.345110	−	0.517225i
$203$	−15.2122	−	12.2448i	−1.06768	−	0.859420i
$204$	19.0772	+	7.93125i	1.33567	+	0.555298i
$205$		0			0
$206$	1.04561	+	16.1141i	0.0728511	+	1.12272i
$207$	−13.8032	−	7.96929i	−0.959390	−	0.553904i
$208$	12.2435	+	3.31494i	0.848937	+	0.229850i
$209$		−	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	$0.959241\pi$
$212$	9.23742	−	1.20386i	0.634428	−	0.0826815i
$213$	−0.551351	−	0.318323i	−0.0377780	−	0.0218111i
$214$	−3.67471	+	0.238444i	−0.251198	+	0.0162997i
$215$		0			0
$216$	−4.89600	−	24.8683i	−0.333131	−	1.69207i
$217$	−12.0697	+	4.67378i	−0.819342	+	0.317277i
$218$	−1.17861	+	0.786412i	−0.0798258	+	0.0532625i
$219$	38.6209	−	22.2978i	2.60976	−	1.50675i
$220$		0			0
$221$	5.46301	−	9.46220i	0.367482	−	0.636497i
$222$	−42.5535	−	21.0196i	−2.85600	−	1.41074i
$223$	12.9581			0.867737			0.433869	−	0.900976i	$-0.357148\pi$
$223$	12.9581			0.867737			0.433869	+	0.900976i	$0.357148\pi$
$224$	−14.7513	+	2.52971i	−0.985612	+	0.169024i
$225$		0			0
$226$	−18.8404	−	9.30634i	−1.25324	−	0.619049i
$227$	4.44626	−	7.70115i	0.295109	−	0.511143i	−0.679901	−	0.733304i	$-0.737977\pi$
$227$	4.44626	−	7.70115i	0.295109	−	0.511143i	0.975010	+	0.222160i	$0.0713108\pi$
$228$	7.47897	+	9.77318i	0.495307	+	0.647244i
$229$	−11.2113	+	6.47287i	−0.740866	+	0.427739i	−0.822384	−	0.568933i	$-0.807357\pi$
$229$	−11.2113	+	6.47287i	−0.740866	+	0.427739i	0.0815180	+	0.996672i	$0.474023\pi$
$230$		0			0
$231$	−17.5309	−	2.72392i	−1.15345	−	0.179221i
$232$	−4.03267	−	20.4832i	−0.264758	−	1.34479i
$233$	−7.60809	−	13.1776i	−0.498423	−	0.863294i	0.501576	−	0.865114i	$-0.332754\pi$
$233$	−7.60809	−	13.1776i	−0.498423	−	0.863294i	−0.999998	+	0.00182020i	$0.999421\pi$
$234$	−26.8013	+	1.73908i	−1.75206	+	0.113687i
$235$		0			0
$236$	−14.1181	+	1.83994i	−0.919013	+	0.119770i
$237$		−	1.38275i		−	0.0898194i
$238$	−1.15035	+	12.8405i	−0.0745660	+	0.832324i
$239$		−	0.0438513i		−	0.00283650i	−0.999999	−	0.00141825i	$-0.999549\pi$
$239$		−	0.0438513i		−	0.00283650i	0.999999	−	0.00141825i	$-0.000451444\pi$
$240$		0			0
$241$	1.99236	+	1.15029i	0.128339	+	0.0740968i	0.562795	−	0.826596i	$-0.309726\pi$
$241$	1.99236	+	1.15029i	0.128339	+	0.0740968i	−0.434456	+	0.900693i	$0.643059\pi$
$242$	−0.549231	−	8.46432i	−0.0353059	−	0.544107i
$243$	−0.0999675	−	0.173149i	−0.00641292	−	0.0111075i
$244$	−4.68458	−	1.94759i	−0.299900	−	0.124682i
$245$		0			0
$246$	3.43612	+	5.14979i	0.219079	+	0.328339i
$247$	5.63627	−	3.25410i	0.358627	−	0.207053i
$248$	−13.0936	−	4.47329i	−0.831443	−	0.284054i
$249$	−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	$0.436040\pi$
$252$	27.8251	−	15.1665i	1.75282	−	0.955401i
$253$	−5.95233			−0.374220
$254$	1.89374	−	3.83381i	0.118824	−	0.240554i
$255$		0			0
$256$	−13.8144	−	8.07226i	−0.863402	−	0.504516i
$257$	12.3334	−	7.12068i	0.769335	−	0.444176i	−0.0633025	−	0.997994i	$-0.520163\pi$
$257$	12.3334	−	7.12068i	0.769335	−	0.444176i	0.832637	+	0.553819i	$0.186830\pi$
$258$	23.4333	+	35.1200i	1.45889	+	2.18648i
$259$	4.54713	−	29.2648i	0.282545	−	1.81843i
$260$		0			0
$261$	22.1017	+	38.2812i	1.36806	+	2.36955i
$262$	1.43818	+	22.1641i	0.0888511	+	1.36930i
$263$	−10.1744	−	5.87421i	−0.627382	−	0.362219i	0.152355	−	0.988326i	$-0.451314\pi$
$263$	−10.1744	−	5.87421i	−0.627382	−	0.362219i	−0.779738	+	0.626107i	$0.784647\pi$
$264$	−12.4773	−	14.2840i	−0.767925	−	0.879118i
$265$		0			0
$266$	−4.41770	+	6.28125i	−0.270867	+	0.385128i
$267$		−	21.0484i		−	1.28814i
$268$	0.0136390	+	0.104654i	0.000833133	+	0.00639276i
$269$	−7.35196	−	4.24466i	−0.448257	−	0.258801i	0.258837	−	0.965921i	$-0.416661\pi$
$269$	−7.35196	−	4.24466i	−0.448257	−	0.258801i	−0.707094	+	0.707120i	$0.749994\pi$
$270$		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	$0.911197\pi$
$272$	−9.77078	+	9.71988i	−0.592440	+	0.589354i
$273$	−9.08330	−	23.4569i	−0.549746	−	1.41968i
$274$	11.3102	−	7.54657i	0.683275	−	0.455905i
$275$		0			0
$276$	12.6733	−	9.69828i	0.762841	−	0.583768i
$277$	−6.79754	+	11.7737i	−0.408425	+	0.707412i	−0.994713	−	0.102690i	$-0.967255\pi$
$277$	−6.79754	+	11.7737i	−0.408425	+	0.707412i	0.586289	+	0.810102i	$0.300588\pi$
$278$	−9.50647	−	4.69579i	−0.570160	−	0.281635i
$279$	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	$0.408720\pi$
$282$	−23.2914	−	11.5050i	−1.38698	−	0.685111i
$283$	10.7746	−	18.6621i	0.640483	−	1.10935i	−0.344842	−	0.938661i	$-0.612067\pi$
$283$	10.7746	−	18.6621i	0.640483	−	1.10935i	0.985325	−	0.170689i	$-0.0545993\pi$
$284$	0.337269	−	0.258097i	0.0200132	−	0.0153152i
$285$		0			0
$286$	−8.34337	+	5.56699i	−0.493354	+	0.329183i
$287$	−2.42231	+	3.00931i	−0.142984	+	0.177634i
$288$	33.2054	+	6.71772i	1.95665	+	0.395845i
$289$	−2.56424	−	4.44140i	−0.150838	−	0.261259i
$290$		0			0
$291$	0.481537	+	0.278016i	0.0282282	+	0.0162976i
$292$	3.84449	+	29.4994i	0.224982	+	1.72632i
$293$		−	28.9496i		−	1.69125i	−0.533776	−	0.845626i	$-0.679227\pi$
$293$		−	28.9496i		−	1.69125i	0.533776	−	0.845626i	$-0.320773\pi$
$294$	21.3676	+	20.5994i	1.24618	+	1.20138i
$295$		0			0
$296$	23.8447	−	20.8288i	1.38594	−	1.21065i
$297$	17.3569	+	10.0210i	1.00715	+	0.581477i
$298$	−0.595344	−	9.17496i	−0.0344873	−	0.531491i
$299$	−4.21972	−	7.30877i	−0.244033	−	0.422677i
$300$		0			0
$301$	−16.5194	+	20.5226i	−0.952162	+	1.18290i
$302$	18.5829	+	27.8506i	1.06933	+	1.60262i
$303$	−16.2251	+	9.36757i	−0.932108	+	0.538153i
$304$	−7.93521	+	2.10404i	−0.455115	+	0.120675i
$305$		0			0
$306$	12.9239	−	26.1640i	0.738809	−	1.49569i
$307$	8.00589			0.456920			0.228460	−	0.973553i	$-0.426631\pi$
$307$	8.00589			0.456920			0.228460	+	0.973553i	$0.426631\pi$
$308$	6.16724	−	10.1009i	0.351411	−	0.575551i
$309$	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	$0.0391691\pi$
$312$	8.69367	−	25.4469i	0.492182	−	1.44065i
$313$	−9.21091	+	5.31792i	−0.520631	+	0.300587i	−0.737193	−	0.675682i	$-0.763849\pi$
$313$	−9.21091	+	5.31792i	−0.520631	+	0.300587i	0.216562	+	0.976269i	$0.430516\pi$
$314$	−6.14793	−	9.21404i	−0.346948	−	0.519979i
$315$		0			0
$316$	0.851730	+	0.354102i	0.0479136	+	0.0199198i
$317$	−8.49175	−	14.7081i	−0.476944	−	0.826091i	0.522707	−	0.852513i	$-0.324922\pi$
$317$	−8.49175	−	14.7081i	−0.476944	−	0.826091i	−0.999651	+	0.0264211i	$0.991589\pi$
$318$	−1.27878	−	19.7076i	−0.0717105	−	1.10514i
$319$	14.2963	+	8.25397i	0.800439	+	0.462133i
$320$		0			0
$321$			7.80679i			0.435732i
$322$	8.14515	+	5.72861i	0.453911	+	0.319243i
$323$			7.07140i			0.393463i
$324$	−17.6506	+	2.30030i	−0.980586	+	0.127794i
$325$		0			0
$326$	15.3142	−	0.993708i	0.848177	−	0.0550364i
$327$	1.50191	+	2.60138i	0.0830557	+	0.143857i
$328$	−4.05204	+	0.797755i	−0.223737	+	0.0440486i
$329$	2.48885	−	16.0179i	0.137215	−	0.883097i
$330$		0			0
$331$	7.21415	−	4.16509i	0.396525	−	0.228934i	−0.288458	−	0.957492i	$-0.593143\pi$
$331$	7.21415	−	4.16509i	0.396525	−	0.228934i	0.684984	+	0.728558i	$0.259809\pi$
$332$	−13.2695	−	17.3400i	−0.728258	−	0.951655i
$333$	−33.5190	+	58.0567i	−1.83683	+	3.18149i
$334$	14.8955	+	7.35775i	0.815046	+	0.402598i
$335$		0			0
$336$	3.32679	+	31.5545i	0.181491	+	1.72144i
$337$	27.0772			1.47499			0.737495	−	0.675353i	$-0.236009\pi$
$337$	27.0772			1.47499			0.737495	+	0.675353i	$0.236009\pi$
$338$	3.73311	+	1.84400i	0.203054	+	0.100300i
$339$	−22.2744	+	38.5804i	−1.20978	+	2.09540i
$340$		0			0
$341$	9.47541	−	5.47063i	0.513122	−	0.296251i
$342$	14.4593	−	9.64775i	0.781870	−	0.521690i
$343$	−8.26248	+	16.5750i	−0.446132	+	0.894967i
$344$	−27.6337	+	5.44044i	−1.48991	+	0.293329i
$345$		0			0
$346$	23.2678	−	1.50980i	1.25089	−	0.0811672i
$347$	24.0514	+	13.8861i	1.29115	+	0.745443i	0.978857	−	0.204544i	$-0.0655713\pi$
$347$	24.0514	+	13.8861i	1.29115	+	0.745443i	0.312288	+	0.949987i	$0.398905\pi$
$348$	−43.8870	+	5.71955i	−2.35259	+	0.306600i
$349$			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
$352$	11.9937	−	4.02771i	0.639267	−	0.214677i
$353$	14.1283	+	8.15697i	0.751973	+	0.434152i	0.826406	−	0.563074i	$-0.190381\pi$
$353$	14.1283	+	8.15697i	0.751973	+	0.434152i	−0.0744333	+	0.997226i	$0.523715\pi$
$354$	1.95444	+	30.1203i	0.103877	+	1.60088i
$355$		0			0
$356$	12.9651	+	5.39018i	0.687151	+	0.285679i
$357$	27.0069	+	4.19629i	1.42936	+	0.222091i
$358$	−7.15037	−	10.7164i	−0.377909	−	0.566380i
$359$	1.38744	−	0.801040i	0.0732264	−	0.0422773i	−0.462940	−	0.886390i	$-0.653205\pi$
$359$	1.38744	−	0.801040i	0.0732264	−	0.0422773i	0.536166	+	0.844112i	$0.319872\pi$
$360$		0			0
$361$	7.39392	−	12.8067i	0.389154	−	0.674034i
$362$	10.3815	−	21.0171i	0.545642	−	1.10463i
$363$	−17.9822			−0.943818
$364$	16.7748	+	0.411939i	0.879237	+	0.0215915i
$365$		0			0
$366$	−4.76331	+	9.64316i	−0.248982	+	0.504056i
$367$	0.630259	−	1.09164i	0.0328993	−	0.0569832i	−0.849107	−	0.528221i	$-0.822859\pi$
$367$	0.630259	−	1.09164i	0.0328993	−	0.0569832i	0.882006	+	0.471238i	$0.156193\pi$
$368$	2.72839	+	10.2899i	0.142227	+	0.536398i
$369$	7.57289	−	4.37221i	0.394229	−	0.227608i
$370$		0			0
$371$	11.4918	−	4.45000i	0.596623	−	0.231033i
$372$	−11.2609	+	27.0862i	−0.583851	+	1.40435i
$373$	4.61372	+	7.99120i	0.238889	+	0.413768i	0.960396	−	0.278639i	$-0.0898833\pi$
$373$	4.61372	+	7.99120i	0.238889	+	0.413768i	−0.721507	+	0.692408i	$0.756550\pi$
$374$	−0.705669	−	10.8752i	−0.0364893	−	0.562344i
$375$		0			0
$376$	13.0513	−	11.4005i	0.673068	−	0.587936i
$377$			23.4056i			1.20545i
$378$	−14.1067	−	30.4172i	−0.725571	−	1.56449i
$379$			2.53516i			0.130223i	0.997878	+	0.0651113i	$0.0207403\pi$
$379$			2.53516i			0.130223i	−0.997878	+	0.0651113i	$0.979260\pi$
$380$		0			0
$381$	−7.85068	−	4.53259i	−0.402203	−	0.232212i
$382$	−4.22379	+	0.274073i	−0.216108	+	0.0140228i
$383$	0.662435	+	1.14737i	0.0338489	+	0.0586279i	0.882454	−	0.470400i	$-0.155890\pi$
$383$	0.662435	+	1.14737i	0.0338489	+	0.0586279i	−0.848605	+	0.529027i	$0.822557\pi$
$384$	−18.9737	+	28.1171i	−0.968248	+	1.43485i
$385$		0			0
$386$	−17.3033	+	11.5454i	−0.880715	+	0.587644i
$387$	51.6448	−	29.8171i	2.62525	−	1.51569i
$388$	−0.294563	+	0.225416i	−0.0149542	+	0.0114437i
$389$	−16.1134	+	27.9093i	−0.816983	+	1.41506i	0.0909120	+	0.995859i	$0.471022\pi$
$389$	−16.1134	+	27.9093i	−0.816983	+	1.41506i	−0.907895	+	0.419197i	$0.862312\pi$
$390$		0			0
$391$	9.16976			0.463735
$392$	−18.1605	+	7.88657i	−0.917241	+	0.398332i
$393$	47.0869			2.37522
$394$	−6.10838	−	3.01728i	−0.307736	−	0.152008i
$395$		0			0
$396$	−21.2744	+	16.2804i	−1.06908	+	0.818119i
$397$	30.4617	−	17.5871i	1.52883	−	0.882670i	0.529419	−	0.848361i	$-0.322410\pi$
$397$	30.4617	−	17.5871i	1.52883	−	0.882670i	0.999411	−	0.0343095i	$-0.0109232\pi$
$398$	−1.49914	+	1.00028i	−0.0751452	+	0.0501395i
$399$	12.6819	+	10.2082i	0.634890	+	0.511047i
$400$		0			0
$401$	−15.9623	−	27.6476i	−0.797120	−	1.38065i	−0.921484	−	0.388416i	$-0.873022\pi$
$401$	−15.9623	−	27.6476i	−0.797120	−	1.38065i	0.124364	−	0.992237i	$-0.460311\pi$
$402$	0.223274	−	0.0144878i	0.0111359	−	0.000722585i
$403$	13.4346	+	7.75647i	0.669225	+	0.386377i
$404$	−1.61511	−	12.3930i	−0.0803549	−	0.616576i
$405$		0			0
$406$	−11.6192	−	25.0536i	−0.576653	−	1.24339i
$407$			25.0357i			1.24097i
$408$	19.2217	+	22.0049i	0.951616	+	1.08941i
$409$	14.2151	+	8.20712i	0.702894	+	0.405816i	0.808424	−	0.588600i	$-0.200321\pi$
$409$	14.2151	+	8.20712i	0.702894	+	0.405816i	−0.105530	+	0.994416i	$0.533654\pi$
$410$		0			0
$411$	−14.4126	−	24.9634i	−0.710922	−	1.23135i
$412$	−8.76677	+	21.0869i	−0.431908	+	1.03888i
$413$	−17.5636	+	6.80123i	−0.864250	+	0.334666i
$414$	−12.5106	−	18.7500i	−0.614864	−	0.921510i
$415$		0			0
$416$	13.4481	+	11.8716i	0.659349	+	0.582052i
$417$	−11.2392	+	19.4669i	−0.550387	+	0.953298i
$418$	2.87495	−	5.82023i	0.140618	−	0.284677i
$419$	−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	$0.418895\pi$
$422$	−2.32355	+	4.70395i	−0.113109	+	0.228985i
$423$	−18.3465	+	31.7770i	−0.892035	+	1.54505i
$424$	12.4667	+	4.25912i	0.605436	+	0.206841i
$425$		0			0
$426$	−0.499720	−	0.748942i	−0.0242115	−	0.0362864i
$427$	−6.63178	−	1.03044i	−0.320934	−	0.0498663i
$428$	−4.80873	−	1.99920i	−0.232439	−	0.0966349i
$429$	10.6320	+	18.4151i	0.513316	+	0.889089i
$430$		0			0
$431$	−25.6838	−	14.8286i	−1.23715	−	0.714267i	−0.268636	−	0.963242i	$-0.586573\pi$
$431$	−25.6838	−	14.8286i	−1.23715	−	0.714267i	−0.968510	+	0.248975i	$0.919906\pi$
$432$	9.36754	−	34.5985i	0.450696	−	1.66462i
$433$			29.4107i			1.41339i	0.707520	+	0.706693i	$0.249814\pi$
$433$			29.4107i			1.41339i	−0.707520	+	0.706693i	$0.750186\pi$
$434$	−18.2311	−	1.63328i	−0.875122	−	0.0784001i
$435$		0			0
$436$	−1.98698	+	0.258952i	−0.0951591	+	0.0124016i
$437$	4.73029	+	2.73103i	0.226280	+	0.130643i
$438$	62.9354	−	4.08374i	3.00717	−	0.195129i
$439$	4.41191	+	7.64165i	0.210569	+	0.364716i	0.951893	−	0.306432i	$-0.0991351\pi$
$439$	4.41191	+	7.64165i	0.210569	+	0.364716i	−0.741324	+	0.671147i	$0.765802\pi$
$440$		0			0
$441$	30.9890	−	28.2336i	1.47567	−	1.34446i
$442$	12.8532	−	8.57612i	0.611366	−	0.407925i
$443$	16.9454	−	9.78342i	0.805099	−	0.464824i	−0.0401518	−	0.999194i	$-0.512784\pi$
$443$	16.9454	−	9.78342i	0.805099	−	0.464824i	0.845251	+	0.534369i	$0.179451\pi$
$444$	−40.7912	−	53.3041i	−1.93586	−	2.52970i
$445$		0			0
$446$	16.4303	+	8.11589i	0.777999	+	0.384298i
$447$	−19.4919			−0.921935
$448$	−20.2885	−	6.03143i	−0.958540	−	0.284958i
$449$	5.02309			0.237054			0.118527	−	0.992951i	$-0.462183\pi$
$449$	5.02309			0.237054			0.118527	+	0.992951i	$0.462183\pi$
$450$		0			0
$451$	1.63282	−	2.82813i	0.0768866	−	0.133171i
$452$	−18.0601	−	23.6002i	−0.849477	−	1.11006i
$453$	61.4705	−	35.4900i	2.88814	−	1.66747i
$454$	10.4611	−	6.97998i	0.490962	−	0.327587i
$455$		0			0
$456$	3.36192	+	17.0762i	0.157436	+	0.799667i
$457$	−13.9225	−	24.1144i	−0.651265	−	1.12802i	−0.982816	−	0.184587i	$-0.940905\pi$
$457$	−13.9225	−	24.1144i	−0.651265	−	1.12802i	0.331551	−	0.943437i	$-0.392428\pi$
$458$	−18.2696	+	1.18548i	−0.853683	+	0.0553937i
$459$	−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	$0.847046\pi$
$462$	−20.5224	−	14.4337i	−0.954789	−	0.671518i
$463$		−	35.7118i		−	1.65967i	−0.558012	−	0.829833i	$-0.688436\pi$
$463$		−	35.7118i		−	1.65967i	0.558012	−	0.829833i	$-0.311564\pi$
$464$	7.71573	−	28.4976i	0.358194	−	1.32297i
$465$		0			0
$466$	−1.39339	−	21.4738i	−0.0645474	−	0.994754i
$467$	−11.3055	−	19.5818i	−0.523158	−	0.906136i	−0.999637	−	0.0269503i	$-0.991420\pi$
$467$	−11.3055	−	19.5818i	−0.523158	−	0.906136i	0.476479	−	0.879186i	$-0.341913\pi$
$468$	−35.0722	−	14.5811i	−1.62121	−	0.674010i
$469$	0.0504157	+	0.130195i	0.00232798	+	0.00601183i
$470$		0			0
$471$	−20.3368	+	11.7415i	−0.937070	+	0.541018i
$472$	−19.0536	−	6.50948i	−0.877015	−	0.299623i
$473$	11.1353	−	19.2870i	0.512003	−	0.886816i
$474$	0.866043	−	1.75328i	0.0397787	−	0.0805306i
$475$		0			0
$476$	−9.50083	+	15.5607i	−0.435470	+	0.713225i
$477$	−27.8947			−1.27721
$478$	0.0274649	−	0.0556017i	0.00125621	−	0.00254316i
$479$	−4.28200	+	7.41664i	−0.195649	+	0.338875i	−0.947113	−	0.320900i	$-0.896015\pi$
$479$	−4.28200	+	7.41664i	−0.195649	+	0.338875i	0.751464	+	0.659774i	$0.229348\pi$
$480$		0			0
$481$	−30.7409	+	17.7483i	−1.40166	+	0.809251i
$482$	1.80579	+	2.70638i	0.0822515	+	0.123272i
$483$	13.2373	−	16.4451i	0.602319	−	0.748280i
$484$	4.60495	−	11.0764i	0.209316	−	0.503473i
$485$		0			0
$486$	−0.0183086	−	0.282157i	−0.000830494	−	0.0127989i
$487$	−27.4054	−	15.8225i	−1.24186	−	0.716987i	−0.272386	−	0.962188i	$-0.587813\pi$
$487$	−27.4054	−	15.8225i	−1.24186	−	0.716987i	−0.969472	+	0.245201i	$0.921146\pi$
$488$	−4.72006	−	5.40351i	−0.213667	−	0.244605i
$489$		−	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	$-0.299083\pi$
$492$	1.13146	+	8.68184i	0.0510100	+	0.391408i
$493$	−22.0239	−	12.7155i	−0.991906	−	0.572677i
$494$	9.18467	−	0.595973i	0.413238	−	0.0268141i
$495$		0			0
$496$	−13.8004	−	13.8727i	−0.619658	−	0.622903i
$497$	0.352280	−	0.437649i	0.0158019	−	0.0196312i
$498$	−38.5053	+	25.6921i	−1.72546	+	1.15129i
$499$	−35.7797	+	20.6574i	−1.60172	+	0.924752i	−0.610574	+	0.791959i	$0.709061\pi$
$499$	−35.7797	+	20.6574i	−1.60172	+	0.924752i	−0.991144	+	0.132793i	$0.957605\pi$
$500$		0			0
$501$	17.6105	−	30.5023i	0.786780	−	1.36274i
$502$	8.01870	+	3.96090i	0.357892	+	0.176783i
$503$	29.0170			1.29381			0.646903	−	0.762572i	$-0.276064\pi$
$503$	29.0170			1.29381			0.646903	+	0.762572i	$0.276064\pi$
$504$	44.7803	−	1.80315i	1.99467	−	0.0803187i
$505$		0			0
$506$	−7.54733	−	3.72806i	−0.335520	−	0.165732i
$507$	4.41354	−	7.64448i	0.196012	−	0.339503i
$508$	4.80237	−	3.67503i	0.213071	−	0.163053i
$509$	17.3474	−	10.0155i	0.768910	−	0.443931i	−0.0635754	−	0.997977i	$-0.520250\pi$
$509$	17.3474	−	10.0155i	0.768910	−	0.443931i	0.832486	+	0.554046i	$0.186917\pi$
$510$		0			0
$511$	14.2109	+	36.6986i	0.628654	+	1.62345i
$512$	−12.4604	−	18.8875i	−0.550675	−	0.834720i
$513$	−9.19562	−	15.9273i	−0.405996	−	0.703206i
$514$	20.0981	−	1.30412i	0.886487	−	0.0575222i
$515$		0			0
$516$	7.71618	+	59.2075i	0.339686	+	2.60646i
$517$			13.7031i			0.602663i
$518$	24.0947	−	34.2587i	1.05866	−	1.50524i
$519$		−	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	$0.511013\pi$
$522$	4.04782	+	62.3818i	0.177168	+	2.73038i
$523$	20.5020	+	35.5105i	0.896491	+	1.55277i	0.831949	+	0.554852i	$0.187225\pi$
$523$	20.5020	+	35.5105i	0.896491	+	1.55277i	0.0645418	+	0.997915i	$0.479441\pi$
$524$	−12.0582	+	29.0040i	−0.526766	+	1.26704i
$525$		0			0
$526$	−9.22165	−	13.8207i	−0.402083	−	0.602611i
$527$	−14.5972	+	8.42768i	−0.635863	+	0.367116i
$528$	−6.87442	−	25.9263i	−0.299171	−	1.12830i
$529$	−7.95856	+	13.7846i	−0.346024	+	0.599332i
$530$		0			0
$531$	42.6333			1.85013
$532$	−9.53553	+	5.19749i	−0.413418	+	0.225340i
$533$	4.63015			0.200554
$534$	13.1830	−	26.6886i	0.570485	−	1.15493i
$535$		0			0
$536$	−0.0482531	+	0.141240i	−0.00208422	+	0.00610062i
$537$	−23.6528	+	13.6559i	−1.02069	+	0.589297i
$538$	−6.66349	−	9.98673i	−0.287284	−	0.430559i
$539$	4.75052	−	14.9178i	0.204620	−	0.642557i
$540$		0			0
$541$	−1.72641	−	2.99023i	−0.0742242	−	0.128560i	0.826524	−	0.562901i	$-0.190315\pi$
$541$	−1.72641	−	2.99023i	−0.0742242	−	0.128560i	−0.900749	+	0.434341i	$0.856981\pi$
$542$	−0.730175	−	11.2529i	−0.0313637	−	0.483352i
$543$	−43.0377	−	24.8479i	−1.84693	−	1.06632i
$544$	−18.4767	+	6.20481i	−0.792182	+	0.266029i
$545$		0			0
$546$	3.17422	−	35.4315i	0.135844	−	1.51633i
$547$			28.2607i			1.20834i	0.796855	+	0.604170i	$0.206495\pi$
$547$			28.2607i			1.20834i	−0.796855	+	0.604170i	$0.793505\pi$
$548$	19.0675	−	2.48496i	0.814522	−	0.106152i
$549$	13.1564	+	7.59584i	0.561500	+	0.324182i
$550$		0			0
$551$	−7.57413	−	13.1188i	−0.322669	−	0.558879i
$552$	22.1434	−	4.35953i	0.942487	−	0.185554i
$553$	1.20576	+	0.187349i	0.0512741	+	0.00796691i
$554$	−15.9931	+	10.6711i	−0.679481	+	0.453374i
$555$		0			0
$556$	−9.11277	−	11.9082i	−0.386468	−	0.505018i
$557$	1.03826	−	1.79833i	0.0439927	−	0.0761976i	−0.843191	−	0.537615i	$-0.819326\pi$
$557$	1.03826	−	1.79833i	0.0439927	−	0.0761976i	0.887183	+	0.461417i	$0.152659\pi$
$558$	37.1480	+	18.3495i	1.57260	+	0.776798i
$559$	31.5762			1.33553
$560$		0			0
$561$	−23.1040			−0.975453
$562$	12.0239	+	5.93929i	0.507197	+	0.250534i
$563$	−22.9547	+	39.7588i	−0.967426	+	1.67563i	−0.264477	+	0.964392i	$0.585199\pi$
$563$	−22.9547	+	39.7588i	−0.967426	+	1.67563i	−0.702949	+	0.711240i	$0.748134\pi$
$564$	−22.3268	−	29.1757i	−0.940130	−	1.22852i
$565$		0			0
$566$	25.3502	−	16.9145i	1.06555	−	0.710971i
$567$	−21.9581	+	8.50292i	−0.922154	+	0.357089i
$568$	0.589295	−	0.116019i	0.0247263	−	0.00486803i
$569$	−3.96413	−	6.86607i	−0.166185	−	0.287840i	0.770891	−	0.636968i	$-0.219811\pi$
$569$	−3.96413	−	6.86607i	−0.166185	−	0.287840i	−0.937075	+	0.349127i	$0.886478\pi$
$570$		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	$0.520612\pi$
$572$	−14.0658	+	1.83311i	−0.588120	+	0.0766464i
$573$			8.97330i			0.374865i
$574$	−4.95618	+	2.29855i	−0.206867	+	0.0959396i
$575$		0			0
$576$	37.8958	+	29.3150i	1.57899	+	1.22146i
$577$	−8.94731	−	5.16573i	−0.372481	−	0.215052i	0.302061	−	0.953289i	$-0.402325\pi$
$577$	−8.94731	−	5.16573i	−0.372481	−	0.215052i	−0.674542	+	0.738237i	$0.735659\pi$
$578$	−0.469630	−	7.23756i	−0.0195340	−	0.301043i
$579$	22.0496	+	38.1911i	0.916351	+	1.58717i
$580$		0			0
$581$	−22.5008	−	18.1117i	−0.933490	−	0.751402i
$582$	0.436444	+	0.654109i	0.0180912	+	0.0271137i
$583$	−9.02174	+	5.20871i	−0.373642	+	0.215723i
$584$	−13.6013	+	39.8119i	−0.562827	+	1.64743i
$585$		0			0
$586$	18.1317	−	36.7069i	0.749012	−	1.51635i
$587$	20.4660			0.844722			0.422361	−	0.906428i	$-0.361201\pi$
$587$	20.4660			0.844722			0.422361	+	0.906428i	$0.361201\pi$
$588$	14.1915	+	39.5021i	0.585249	+	1.62904i
$589$	−10.0401			−0.413694
$590$		0			0
$591$	−7.22175	+	12.5084i	−0.297063	+	0.514529i
$592$	43.2796	−	11.4757i	1.77878	−	0.471648i
$593$	−38.8389	+	22.4236i	−1.59492	+	0.920828i	−0.602477	+	0.798136i	$0.705819\pi$
$593$	−38.8389	+	22.4236i	−1.59492	+	0.920828i	−0.992445	+	0.122692i	$0.960847\pi$
$594$	15.7315	+	23.5772i	0.645471	+	0.967383i
$595$		0			0
$596$	4.99158	−	12.0064i	0.204463	−	0.491800i
$597$	1.91036	+	3.30884i	0.0781857	+	0.135422i
$598$	−0.772823	−	11.9101i	−0.0316031	−	0.487041i
$599$	−14.1499	−	8.16942i	−0.578147	−	0.333793i	0.182250	−	0.983252i	$-0.441662\pi$
$599$	−14.1499	−	8.16942i	−0.578147	−	0.333793i	−0.760397	+	0.649459i	$0.774995\pi$
$600$		0			0
$601$			39.8029i			1.62359i	0.583941	+	0.811796i	$0.301510\pi$
$601$			39.8029i			1.62359i	−0.583941	+	0.811796i	$0.698490\pi$
$602$	−33.7996	+	15.6754i	−1.37757	+	0.638882i
$603$		−	0.316030i		−	0.0128697i
$604$	6.11903	+	46.9523i	0.248980	+	1.91046i
$605$		0			0
$606$	−26.4399	+	1.71563i	−1.07405	+	0.0696926i
$607$	−4.70373	−	8.14710i	−0.190919	−	0.330681i	0.754636	−	0.656143i	$-0.227813\pi$
$607$	−4.70373	−	8.14710i	−0.190919	−	0.330681i	−0.945555	+	0.325463i	$0.894480\pi$
$608$	−11.3793	−	2.30213i	−0.461493	−	0.0933636i
$609$	−54.5975	+	21.1420i	−2.21240	+	0.856716i
$610$		0			0
$611$	−16.8259	+	9.71441i	−0.680701	+	0.393003i
$612$	32.7739	−	25.0804i	1.32481	−	1.01382i
$613$	6.81796	−	11.8091i	0.275375	−	0.476963i	−0.694855	−	0.719150i	$-0.744531\pi$
$613$	6.81796	−	11.8091i	0.275375	−	0.476963i	0.970230	+	0.242187i	$0.0778646\pi$
$614$	10.1512	+	5.01423i	0.409667	+	0.202358i
$615$		0			0
$616$	14.1462	−	8.94487i	0.569966	−	0.360399i
$617$	−39.1144			−1.57469			−0.787343	−	0.616515i	$-0.788544\pi$
$617$	−39.1144			−1.57469			−0.787343	+	0.616515i	$0.788544\pi$
$618$	43.4072	+	21.4413i	1.74609	+	0.862496i
$619$	9.50950	−	16.4709i	0.382219	−	0.662023i	−0.609160	−	0.793047i	$-0.708493\pi$
$619$	9.50950	−	16.4709i	0.382219	−	0.662023i	0.991379	+	0.131024i	$0.0418266\pi$
$620$		0			0
$621$	−20.6535	+	11.9243i	−0.828798	+	0.478507i
$622$	16.1785	−	10.7948i	0.648697	−	0.432833i
$623$	18.3542	+	2.85186i	0.735347	+	0.114257i
$624$	26.9611	−	26.8206i	1.07931	−	1.07368i
$625$		0			0
$626$	−15.0098	+	0.973953i	−0.599912	+	0.0389270i
$627$	−11.9184	−	6.88108i	−0.475974	−	0.274804i
$628$	−2.02441	−	15.5336i	−0.0807827	−	0.619859i
$629$		−	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	$0.893490\pi$
$632$	0.858180	+	0.982441i	0.0341366	+	0.0390794i
$633$	9.63252	+	5.56134i	0.382858	+	0.221043i
$634$	−1.55522	−	23.9679i	−0.0617659	−	0.951886i
$635$		0			0
$636$	10.7218	−	25.7893i	0.425146	−	1.02261i
$637$	21.6851	−	4.74245i	0.859196	−	0.187903i
$638$	12.9575	+	19.4197i	0.512993	+	0.768835i
$639$	−1.10134	+	0.635857i	−0.0435682	+	0.0251541i
$640$		0			0
$641$	−13.4723	+	23.3347i	−0.532124	+	0.921665i	0.467173	+	0.884166i	$0.345272\pi$
$641$	−13.4723	+	23.3347i	−0.532124	+	0.921665i	−0.999297	+	0.0374991i	$0.988061\pi$
$642$	−4.88954	+	9.89870i	−0.192975	+	0.390671i
$643$	43.6730			1.72229			0.861147	−	0.508355i	$-0.169746\pi$
$643$	43.6730			1.72229			0.861147	+	0.508355i	$0.169746\pi$
$644$	6.73979	+	12.3651i	0.265585	+	0.487254i
$645$		0			0
$646$	−4.42895	+	8.96625i	−0.174255	+	0.352773i
$647$	−14.0540	+	24.3422i	−0.552518	+	0.956989i	0.445574	+	0.895245i	$0.353000\pi$
$647$	−14.0540	+	24.3422i	−0.552518	+	0.956989i	−0.998092	+	0.0617443i	$0.980334\pi$
$648$	−23.8209	−	8.13818i	−0.935775	−	0.319698i
$649$	13.7885	−	7.96080i	0.541246	−	0.312489i
$650$		0			0
$651$	−5.95797	+	38.3448i	−0.233511	+	1.50285i
$652$	20.0402	+	8.33161i	0.784836	+	0.326291i
$653$	−20.8367	−	36.0902i	−0.815403	−	1.41232i	−0.909038	−	0.416713i	$-0.863182\pi$
$653$	−20.8367	−	36.0902i	−0.815403	−	1.41232i	0.0936346	−	0.995607i	$-0.470151\pi$
$654$	0.275067	+	4.23912i	0.0107560	+	0.165763i
$655$		0			0
$656$	−5.63748	−	1.52635i	−0.220107	−	0.0595939i
$657$		−	89.0808i		−	3.47537i
$658$	13.1881	−	18.7513i	0.514125	−	0.731002i
$659$			47.0951i			1.83457i	0.398236	+	0.917283i	$0.369622\pi$
$659$			47.0951i			1.83457i	−0.398236	+	0.917283i	$0.630378\pi$
$660$		0			0
$661$	−10.0792	−	5.81924i	−0.392036	−	0.226342i	0.291006	−	0.956721i	$-0.406010\pi$
$661$	−10.0792	−	5.81924i	−0.392036	−	0.226342i	−0.683042	+	0.730379i	$0.739343\pi$
$662$	11.7559	−	0.762817i	0.456907	−	0.0296477i
$663$	−16.3789	−	28.3690i	−0.636103	−	1.10176i
$664$	−5.96486	−	30.2973i	−0.231481	−	1.17577i
$665$		0			0
$666$	−78.8628	+	52.6200i	−3.05587	+	2.03898i
$667$	−17.0116	+	9.82168i	−0.658693	+	0.380297i
$668$	14.2786	+	18.6587i	0.552457	+	0.721926i
$669$	19.4251	−	33.6452i	0.751017	−	1.30080i
$670$		0			0
$671$	5.67340			0.219019
$672$	−15.5449	+	42.0935i	−0.599658	+	1.62379i
$673$	−14.9849			−0.577626			−0.288813	−	0.957385i	$-0.593261\pi$
$673$	−14.9849			−0.577626			−0.288813	+	0.957385i	$0.593261\pi$
$674$	34.3328	+	16.9590i	1.32245	+	0.653234i
$675$		0			0
$676$	3.57851	+	4.67623i	0.137635	+	0.179855i
$677$	−19.9347	+	11.5093i	−0.766154	+	0.442339i	−0.831501	−	0.555524i	$-0.812518\pi$
$677$	−19.9347	+	11.5093i	−0.766154	+	0.442339i	0.0653470	+	0.997863i	$0.479185\pi$
$678$	−52.4067	+	34.9676i	−2.01267	+	1.34292i
$679$	−0.307673	+	0.382232i	−0.0118074	+	0.0146687i
$680$		0			0
$681$	−13.3305	−	23.0892i	−0.510827	−	0.884779i
$682$	15.4408	−	1.00192i	0.591259	−	0.0383655i
$683$	−32.2762	−	18.6347i	−1.23502	−	0.713037i	−0.266945	−	0.963712i	$-0.586014\pi$
$683$	−32.2762	−	18.6347i	−1.23502	−	0.713037i	−0.968071	+	0.250675i	$0.919348\pi$
$684$	24.3764	−	3.17684i	0.932055	−	0.121469i
$685$		0			0
$686$	−20.8577	+	15.8415i	−0.796352	+	0.604833i
$687$			38.8132i			1.48082i
$688$	−38.4459	−	10.4092i	−1.46573	−	0.396848i
$689$	−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	$-0.345402\pi$
$692$	30.4483	+	12.6587i	1.15747	+	0.481211i
$693$	−22.2213	+	27.6062i	−0.844118	+	1.04867i
$694$	21.7991	+	32.6708i	0.827483	+	1.24017i
$695$		0			0
$696$	−59.2292	−	20.2351i	−2.24508	−	0.767009i
$697$	−2.51542	+	4.35683i	−0.0952782	+	0.165027i
$698$	−6.03811	+	12.2239i	−0.228546	+	0.462683i
$699$	−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	$0.313840\pi$
$702$	−17.7977	+	36.0308i	−0.671729	+	1.35989i
$703$	11.4868	−	19.8957i	0.433233	−	0.750381i
$704$	17.7302	+	2.40491i	0.668232	+	0.0906386i
$705$		0			0
$706$	12.8053	+	19.1915i	0.481932	+	0.722283i
$707$	−5.97017	−	15.4175i	−0.224532	−	0.579835i
$708$	−16.3868	+	39.4155i	−0.615852	+	1.48133i
$709$	2.08074	+	3.60395i	0.0781440	+	0.135349i	0.902449	−	0.430796i	$-0.141767\pi$
$709$	2.08074	+	3.60395i	0.0781440	+	0.135349i	−0.824305	+	0.566146i	$0.808434\pi$
$710$		0			0
$711$	−2.39203	−	1.38104i	−0.0897082	−	0.0517931i
$712$	13.0633	+	14.9548i	0.489569	+	0.560457i
$713$			13.0194i			0.487580i
$714$	31.6154	+	22.2356i	1.18318	+	0.832148i
$715$		0			0
$716$	−2.35449	−	18.0664i	−0.0879916	−	0.675173i
$717$	−0.113858	−	0.0657362i	−0.00425212	−	0.00245496i
$718$	2.26093	−	0.146707i	0.0843771	−	0.00547505i
$719$	−21.1113	−	36.5658i	−0.787318	−	1.36368i	−0.927604	−	0.373564i	$-0.878135\pi$
$719$	−21.1113	−	36.5658i	−0.787318	−	1.36368i	0.140286	−	0.990111i	$-0.455198\pi$
$720$		0			0
$721$	−4.63835	+	29.8519i	−0.172741	+	1.11174i
$722$	17.3962	−	11.6074i	0.647421	−	0.431982i
$723$	5.97339	−	3.44874i	0.222153	−	0.128260i
$724$	26.3268	−	20.1467i	0.978427	−	0.748746i
$725$		0			0
$726$	−22.8007	−	11.2626i	−0.846212	−	0.417993i
$727$	−27.2605			−1.01104			−0.505519	−	0.862816i	$-0.668699\pi$
$727$	−27.2605			−1.01104			−0.505519	+	0.862816i	$0.668699\pi$
$728$	21.0118	+	11.0287i	0.778748	+	0.408750i
$729$	−27.2992			−1.01108
$730$		0			0
$731$	−17.1544	+	29.7122i	−0.634477	+	1.09895i
$732$	−12.0794	+	9.24380i	−0.446467	+	0.341661i
$733$	−13.2554	+	7.65300i	−0.489599	+	0.282670i	−0.724408	−	0.689372i	$-0.757887\pi$
$733$	−13.2554	+	7.65300i	−0.489599	+	0.282670i	0.234809	+	0.972041i	$0.424553\pi$
$734$	1.48286	−	0.989415i	0.0547333	−	0.0365200i
$735$		0			0
$736$	−2.98526	+	14.7560i	−0.110038	+	0.543915i
$737$	−0.0590113	−	0.102211i	−0.00217371	−	0.00376498i
$738$	12.3405	−	0.800751i	0.454261	−	0.0294760i
$739$	42.5694	+	24.5774i	1.56594	+	0.904096i	0.996635	+	0.0819692i	$0.0261209\pi$
$739$	42.5694	+	24.5774i	1.56594	+	0.904096i	0.569305	+	0.822126i	$0.307212\pi$
$740$		0			0
$741$		−	19.5125i		−	0.716810i
$742$	17.3582	+	1.55508i	0.637241	+	0.0570890i
$743$		−	35.2067i		−	1.29161i	−0.763503	−	0.645805i	$-0.776522\pi$
$743$		−	35.2067i		−	1.29161i	0.763503	−	0.645805i	$-0.223478\pi$
$744$	−31.2430	+	27.2913i	−1.14542	+	1.00055i
$745$		0			0
$746$	0.844982	+	13.0222i	0.0309370	+	0.476776i
$747$	32.6913	+	56.6229i	1.19611	+	2.07173i
$748$	5.91659	−	14.2313i	0.216332	−	0.520349i
$749$	−6.80752	−	1.05774i	−0.248741	−	0.0386491i
$750$		0			0
$751$	0.584292	−	0.337341i	0.0213211	−	0.0123098i	−0.489302	−	0.872115i	$-0.662748\pi$
$751$	0.584292	−	0.337341i	0.0213211	−	0.0123098i	0.510623	+	0.859805i	$0.329415\pi$
$752$	23.6888	−	6.28115i	0.863843	−	0.229050i
$753$	9.48027	−	16.4203i	0.345480	−	0.598389i
$754$	−14.6593	+	29.6773i	−0.533862	+	1.08079i
$755$		0			0
$756$	1.16408	−	47.4031i	0.0423372	−	1.72403i
$757$	45.8640			1.66695			0.833477	−	0.552553i	$-0.186346\pi$
$757$	45.8640			1.66695			0.833477	+	0.552553i	$0.186346\pi$
$758$	−1.58782	+	3.21449i	−0.0576723	+	0.116756i
$759$	−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	$0.203719\pi$
$762$	−7.11551	−	10.6642i	−0.257768	−	0.386322i
$763$	−2.47190	+	0.957201i	−0.0894886	+	0.0346530i
$764$	−5.52726	−	2.29793i	−0.199969	−	0.0831360i
$765$		0			0
$766$	0.121322	+	1.86972i	0.00438354	+	0.0675556i
$767$	19.5499	+	11.2871i	0.705905	+	0.407554i
$768$	−41.6682	+	23.7679i	−1.50357	+	0.857649i
$769$		−	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
$772$	−29.1710	+	3.80169i	−1.04989	+	0.136826i
$773$	36.6688	+	21.1707i	1.31888	+	0.761458i	0.983549	−	0.180641i	$-0.0578171\pi$
$773$	36.6688	+	21.1707i	1.31888	+	0.761458i	0.335335	+	0.942099i	$0.391150\pi$
$774$	84.1586	−	5.46087i	3.02502	−	0.196287i
$775$		0			0
$776$	−0.514676	+	0.101328i	−0.0184758	+	0.00363746i
$777$	−69.1687	−	55.6765i	−2.48141	−	1.99738i
$778$	−37.9113	+	25.2957i	−1.35919	+	0.906896i
$779$	−2.59519	+	1.49833i	−0.0929824	+	0.0536834i
$780$		0			0
$781$	−0.237464	+	0.411299i	−0.00849712	+	0.0147174i
$782$	11.6269	+	5.74319i	0.415777	+	0.205376i
$783$	66.1408			2.36368
$784$	−27.9662	−	1.37437i	−0.998795	−	0.0490845i
$785$		0			0
$786$	59.7043	+	29.4914i	2.12958	+	1.05192i
$787$	2.19121	−	3.79528i	0.0781081	−	0.135287i	−0.824326	−	0.566116i	$-0.808445\pi$
$787$	2.19121	−	3.79528i	0.0781081	−	0.135287i	0.902434	+	0.430829i	$0.141779\pi$
$788$	−5.85541	−	7.65158i	−0.208590	−	0.272576i
$789$	−30.5044	+	17.6117i	−1.08599	+	0.626994i
$790$		0			0
$791$	−30.6241	−	24.6506i	−1.08887	−	0.876473i
$792$	−37.1718	+	7.31828i	−1.32084	+	0.260044i
$793$	4.02198	+	6.96627i	0.142825	+	0.247380i
$794$	49.6394	−	3.22099i	1.76164	−	0.114309i
$795$		0			0
$796$	−2.52735	+	0.329375i	−0.0895795	+	0.0116744i
$797$			53.6019i			1.89868i	0.314255	+	0.949339i	$0.398245\pi$
$797$			53.6019i			1.89868i	−0.314255	+	0.949339i	$0.601755\pi$
$798$	9.68661	+	20.8865i	0.342902	+	0.739373i
$799$		−	21.1101i		−	0.746822i
$800$		0			0
$801$	−36.4118	−	21.0224i	−1.28655	−	0.742789i
$802$	−2.92343	−	45.0535i	−0.103230	−	1.59090i
$803$	−16.6338	−	28.8106i	−0.586995	−	1.01670i
$804$	0.292177	+	0.121471i	0.0103043	+	0.00428394i
$805$		0			0
$806$	12.1765	+	18.2492i	0.428900	+	0.642802i
$807$	−22.0422	+	12.7261i	−0.775924	+	0.447980i
$808$	5.71408	−	16.7254i	0.201021	−	0.588399i
$809$	0.754693	−	1.30717i	0.0265336	−	0.0459575i	−0.852454	−	0.522803i	$-0.824886\pi$
$809$	0.754693	−	1.30717i	0.0265336	−	0.0459575i	0.878987	+	0.476845i	$0.158220\pi$
$810$		0			0
$811$	43.1894			1.51658			0.758292	−	0.651915i	$-0.226034\pi$
$811$	43.1894			1.51658			0.758292	+	0.651915i	$0.226034\pi$
$812$	0.958815	−	39.0444i	0.0336478	−	1.37019i
$813$	−23.9063			−0.838432
$814$	−15.6803	+	31.7442i	−0.549594	+	1.11264i
$815$		0			0
$816$	10.5903	+	39.9403i	0.370733	+	1.39819i
$817$	−17.6984	+	10.2182i	−0.619189	+	0.357489i
$818$	12.8840	+	19.3095i	0.450478	+	0.675142i
$819$	−49.6503	−	7.71460i	−1.73492	−	0.269570i
$820$		0			0
$821$	4.56478	+	7.90644i	0.159312	+	0.275937i	0.934621	−	0.355646i	$-0.115739\pi$
$821$	4.56478	+	7.90644i	0.159312	+	0.275937i	−0.775309	+	0.631582i	$0.782406\pi$
$822$	−2.63960	−	40.6795i	−0.0920668	−	1.41886i
$823$	0.329424	+	0.190193i	0.0114830	+	0.00662972i	0.505731	−	0.862692i	$-0.331223\pi$
$823$	0.329424	+	0.190193i	0.0114830	+	0.00662972i	−0.494248	+	0.869321i	$0.664556\pi$
$824$	−24.3231	+	21.2466i	−0.847334	+	0.740161i
$825$		0			0
$826$	−26.5297	−	2.37674i	−0.923087	−	0.0826972i
$827$		−	23.9044i		−	0.831236i	−0.909539	−	0.415618i	$-0.863565\pi$
$827$		−	23.9044i		−	0.831236i	0.909539	−	0.415618i	$-0.136435\pi$
$828$	−4.11954	−	31.6099i	−0.143164	−	1.09852i
$829$	35.8241	+	20.6830i	1.24422	+	0.718352i	0.969951	−	0.243301i	$-0.0782303\pi$
$829$	35.8241	+	20.6830i	1.24422	+	0.718352i	0.274271	+	0.961653i	$0.411564\pi$
$830$		0			0
$831$	20.3800	+	35.2992i	0.706974	+	1.22452i
$832$	9.61631	+	23.4755i	0.333386	+	0.813866i
$833$	−7.31833	+	22.9814i	−0.253565	+	0.796259i
$834$	−26.4434	+	17.6439i	−0.915659	+	0.610959i
$835$		0			0
$836$	7.29064	−	5.57919i	0.252152	−	0.192960i
$837$	21.9187	−	37.9642i	0.757620	−	1.31224i
$838$	−15.0449	−	7.43155i	−0.519718	−	0.256718i
$839$	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
$842$	13.1149	+	6.47819i	0.451969	+	0.223253i
$843$	14.2155	−	24.6219i	0.489607	−	0.848025i
$844$	−5.89234	+	4.50914i	−0.202823	+	0.155211i
$845$		0			0
$846$	−43.1651	+	28.8013i	−1.48405	+	0.990208i
$847$	2.43641	−	15.6804i	0.0837159	−	0.538786i
$848$	13.1397	+	13.2085i	0.451219	+	0.453582i
$849$	−32.3038	−	55.9518i	−1.10866	−	1.92026i
$850$		0			0
$851$	−25.7996	−	14.8954i	−0.884398	−	0.510608i
$852$	−0.164549	−	1.26261i	−0.00563737	−	0.0432564i
$853$			10.5928i			0.362692i	0.983419	+	0.181346i	$0.0580454\pi$
$853$			10.5928i			0.362692i	−0.983419	+	0.181346i	$0.941955\pi$
$854$	−7.76345	−	5.46016i	−0.265660	−	0.186843i
$855$		0			0
$856$	−4.84514	−	5.54670i	−0.165604	−	0.189582i
$857$	0.245410	+	0.141688i	0.00838305	+	0.00483996i	0.504186	−	0.863595i	$-0.331793\pi$
$857$	0.245410	+	0.141688i	0.00838305	+	0.00483996i	−0.495803	+	0.868435i	$0.665126\pi$
$858$	1.94719	+	30.0086i	0.0664761	+	1.02448i
$859$	4.93861	+	8.55393i	0.168503	+	0.291856i	0.937894	−	0.346922i	$-0.112773\pi$
$859$	4.93861	+	8.55393i	0.168503	+	0.291856i	−0.769391	+	0.638779i	$0.779440\pi$
$860$		0			0
$861$	4.18236	+	10.8006i	0.142535	+	0.368084i
$862$	−23.2787	−	34.8883i	−0.792875	−	1.18830i
$863$	−28.2007	+	16.2817i	−0.959963	+	0.554235i	−0.896162	−	0.443728i	$-0.853656\pi$
$863$	−28.2007	+	16.2817i	−0.959963	+	0.554235i	−0.0638012	+	0.997963i	$0.520322\pi$
$864$	33.5473	−	38.0025i	1.14130	−	1.29287i
$865$		0			0
$866$	−18.4205	+	37.2916i	−0.625952	+	1.26722i
$867$	−15.3759			−0.522195
$868$	−22.0934	−	13.4894i	−0.749899	−	0.457861i
$869$	−1.03151			−0.0349916
$870$		0			0
$871$	0.0836685	−	0.144918i	0.00283500	−	0.00491036i
$872$	−2.68160	−	0.916141i	−0.0908104	−	0.0310245i
$873$	0.961883	−	0.555343i	0.0325548	−	0.0187955i
$874$	4.28733	+	6.42551i	0.145021	+	0.217346i
$875$		0			0
$876$	82.3573	+	34.2396i	2.78260	+	1.15685i
$877$	19.0353	+	32.9700i	0.642775	+	1.11332i	0.984811	+	0.173632i	$0.0555503\pi$
$877$	19.0353	+	32.9700i	0.642775	+	1.11332i	−0.342036	+	0.939687i	$0.611116\pi$
$878$	0.808020	+	12.4526i	0.0272694	+	0.420254i
$879$	−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	$0.845151\pi$
$882$	56.9761	−	16.3901i	1.91849	−	0.551884i
$883$			44.1707i			1.48646i	0.669034	+	0.743232i	$0.266708\pi$
$883$			44.1707i			1.48646i	−0.669034	+	0.743232i	$0.733292\pi$
$884$	21.6688	−	2.82397i	0.728800	−	0.0949804i
$885$		0			0
$886$	27.6136	−	1.79179i	0.927698	−	0.0601963i
$887$	−10.0638	−	17.4310i	−0.337909	−	0.585275i	0.646130	−	0.763227i	$-0.276386\pi$
$887$	−10.0638	−	17.4310i	−0.337909	−	0.585275i	−0.984039	+	0.177952i	$0.943053\pi$
$888$	−18.3363	−	93.1358i	−0.615326	−	3.12543i
$889$	5.01611	−	6.23167i	0.168235	−	0.209003i
$890$		0			0
$891$	17.2385	−	9.95263i	0.577510	−	0.333426i
$892$	15.7499	+	20.5813i	0.527346	+	0.689111i
$893$	6.28724	−	10.8898i	0.210394	−	0.364414i
$894$	−24.7150	−	12.2081i	−0.826592	−	0.408301i
$895$		0			0
$896$	−21.9474	−	20.3547i	−0.733211	−	0.680001i
$897$	−25.3027			−0.844831
$898$	6.36909	+	3.14606i	0.212539	+	0.104985i
$899$	18.0537	−	31.2699i	0.602124	−	1.04291i
$900$		0			0
$901$	13.8983	−	8.02418i	0.463019	−	0.267324i
$902$	3.84167	−	2.56329i	0.127913	−	0.0853483i
$903$	28.5224	+	73.6569i	0.949167	+	2.45115i
$904$	−8.11832	−	41.2355i	−0.270011	−	1.37147i
$905$		0			0
$906$	100.170	−	6.49984i	3.32794	−	0.215943i
$907$	13.0052	+	7.50854i	0.431830	+	0.249317i	0.700126	−	0.714020i	$-0.253127\pi$
$907$	13.0052	+	7.50854i	0.431830	+	0.249317i	−0.268296	+	0.963336i	$0.586461\pi$
$908$	17.6359	−	2.29839i	0.585268	−	0.0762748i
$909$			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	$0.869737\pi$
$912$	−6.43237	+	23.7576i	−0.212997	+	0.786693i
$913$	21.1461	+	12.2087i	0.699834	+	0.404049i
$914$	−2.54983	−	39.2960i	−0.0843410	−	1.29980i
$915$		0			0
$916$	−23.9076	−	9.93946i	−0.789931	−	0.328409i
$917$	−6.37981	+	41.0597i	−0.210680	+	1.35591i
$918$	−24.2349	−	36.3214i	−0.799871	−	1.19878i
$919$	−49.7575	+	28.7275i	−1.64135	+	0.947632i	−0.660992	+	0.750393i	$0.729864\pi$
$919$	−49.7575	+	28.7275i	−1.64135	+	0.947632i	−0.980355	+	0.197239i	$0.936802\pi$
$920$		0			0
$921$	12.0014	−	20.7870i	0.395459	−	0.684956i
$922$	−12.4321	+	25.1683i	−0.409429	+	0.828875i
$923$	−0.673370			−0.0221643
$924$	−16.9815	−	31.1550i	−0.558650	−	1.02492i
$925$		0			0
$926$	22.3669	−	45.2811i	0.735023	−	1.48803i
$927$	34.1915	−	59.2214i	1.12300	−	1.94509i
$928$	27.6318	−	31.3014i	0.907060	−	1.02752i
$929$	3.45964	−	1.99743i	0.113507	−	0.0655334i	−0.442172	−	0.896930i	$-0.645792\pi$
$929$	3.45964	−	1.99743i	0.113507	−	0.0655334i	0.555679	+	0.831397i	$0.312458\pi$
$930$		0			0
$931$	−10.6198	+	9.67552i	−0.348049	+	0.317102i
$932$	11.6827	−	28.1006i	0.382678	−	0.920466i
$933$	−20.6162	−	35.7083i	−0.674945	−	1.16904i
$934$	−2.07056	−	31.9098i	−0.0677507	−	1.04412i
$935$		0			0
$936$	−35.3378	−	40.4546i	−1.15505	−	1.32230i
$937$		−	43.2204i		−	1.41195i	−0.708237	−	0.705975i	$-0.750509\pi$
$937$		−	43.2204i		−	1.41195i	0.708237	−	0.705975i	$-0.249491\pi$
$938$	−0.0176181	+	0.196658i	−0.000575252	+	0.00642111i
$939$			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	$0.862561\pi$
$942$	−33.1402	+	2.15039i	−1.07976	+	0.0700636i
$943$	1.94295	+	3.36529i	0.0632712	+	0.109589i
$944$	−20.0823	−	20.1874i	−0.653622	−	0.657044i
$945$		0			0
$946$	26.1990	−	17.4809i	0.851802	−	0.568352i
$947$	−42.1696	+	24.3466i	−1.37033	+	0.791159i	−0.990969	−	0.134091i	$-0.957188\pi$
$947$	−42.1696	+	24.3466i	−1.37033	+	0.791159i	−0.379358	+	0.925250i	$0.623855\pi$
$948$	2.19622	−	1.68067i	0.0713299	−	0.0545855i
$949$	23.5840	−	40.8488i	0.765571	−	1.32601i
$950$		0			0
$951$	−50.9190			−1.65116
$952$	−21.7927	+	13.7799i	−0.706304	+	0.446608i
$953$	47.5308			1.53967			0.769837	−	0.638241i	$-0.220338\pi$
$953$	47.5308			1.53967			0.769837	+	0.638241i	$0.220338\pi$
$954$	−35.3694	−	17.4710i	−1.14513	−	0.565644i
$955$		0			0
$956$	0.0696488	−	0.0532990i	0.00225260	−	0.00172381i
$957$	42.8623	−	24.7466i	1.38554	−	0.799943i
$958$	−10.0746	+	6.72211i	−0.325495	+	0.217182i
$959$	23.7208	−	9.18550i	0.765986	−	0.296615i
$960$		0			0
$961$	3.53423	+	6.12147i	0.114008	+	0.197467i
$962$	−50.0943	+	3.25051i	−1.61510	+	0.104801i
$963$	13.5050	+	7.79713i	0.435193	+	0.251259i
$964$	0.594616	+	4.56258i	0.0191513	+	0.146951i
$965$		0			0
$966$	27.0843	−	12.5610i	0.871424	−	0.404144i
$967$		−	29.3643i		−	0.944292i	−0.881520	−	0.472146i	$-0.843479\pi$
$967$		−	29.3643i		−	0.944292i	0.881520	−	0.472146i	$-0.156521\pi$
$968$	12.7763	−	11.1603i	0.410645	−	0.358705i
$969$	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	$0.692756\pi$
$972$	0.153506	−	0.369231i	0.00492370	−	0.0118431i
$973$	−15.4523	−	12.4382i	−0.495379	−	0.398749i
$974$	−24.8391	−	37.2269i	−0.795895	−	1.19283i
$975$		0			0
$976$	−2.60053	−	9.80770i	−0.0832411	−	0.313937i
$977$	7.73476	−	13.3970i	0.247457	−	0.428608i	−0.715363	−	0.698753i	$-0.753739\pi$
$977$	7.73476	−	13.3970i	0.247457	−	0.428608i	0.962819	+	0.270146i	$0.0870718\pi$
$978$	20.3770	−	41.2526i	0.651585	−	1.31911i
$979$	−15.7018			−0.501832
$980$		0			0
$981$	6.00019			0.191571
$982$	22.4085	−	45.3652i	0.715083	−	1.44766i
$983$	−22.0131	+	38.1277i	−0.702107	+	1.21609i	0.265618	+	0.964078i	$0.414424\pi$
$983$	−22.0131	+	38.1277i	−0.702107	+	1.21609i	−0.967725	+	0.252007i	$0.918909\pi$
$984$	−4.00296	+	11.7169i	−0.127610	+	0.373521i
$985$		0			0
$986$	−19.9615	−	29.9167i	−0.635703	−	0.952743i
$987$	−37.8591	−	30.4743i	−1.20507	−	0.970006i
$988$	12.0191	+	4.99686i	0.382378	+	0.158971i
$989$	13.2503	+	22.9502i	0.421336	+	0.729775i
$990$		0			0
$991$	−14.4776	−	8.35865i	−0.459896	−	0.265521i	0.252104	−	0.967700i	$-0.418877\pi$
$991$	−14.4776	−	8.35865i	−0.459896	−	0.265521i	−0.712001	+	0.702179i	$0.752211\pi$
$992$	−8.80969	−	26.2335i	−0.279708	−	0.832916i
$993$		−	24.9751i		−	0.792560i
$994$	0.720785	−	0.334282i	0.0228619	−	0.0106028i
$995$		0			0
$996$	−64.9146	+	8.45996i	−2.05690	+	0.268064i
$997$	−23.8844	−	13.7897i	−0.756427	−	0.436723i	0.0715845	−	0.997435i	$-0.477194\pi$
$997$	−23.8844	−	13.7897i	−0.756427	−	0.436723i	−0.828011	+	0.560711i	$0.810528\pi$
$998$	−58.3053	+	3.78331i	−1.84562	+	0.119759i
$999$	50.1540	+	86.8693i	1.58680	+	2.74842i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.o.a.31.3	✓	32	5.4	even	2
140.2.o.a.31.8	yes	32	20.19	odd	2
140.2.o.a.131.3	yes	32	140.19	even	6
140.2.o.a.131.8	yes	32	35.19	odd	6
700.2.p.c.451.9		32	4.3	odd	2	inner
700.2.p.c.451.14		32	1.1	even	1	trivial
700.2.p.c.551.9		32	7.5	odd	6	inner
700.2.p.c.551.14		32	28.19	even	6	inner
700.2.t.c.199.11		32	5.3	odd	4
700.2.t.c.199.16		32	20.3	even	4
700.2.t.c.299.11		32	140.47	odd	12
700.2.t.c.299.16		32	35.12	even	12
700.2.t.d.199.1		32	20.7	even	4
700.2.t.d.199.6		32	5.2	odd	4
700.2.t.d.299.1		32	35.33	even	12
700.2.t.d.299.6		32	140.103	odd	12
980.2.g.a.391.25		32	35.24	odd	6
980.2.g.a.391.26		32	35.4	even	6
980.2.g.a.391.27		32	140.39	odd	6
980.2.g.a.391.28		32	140.59	even	6
980.2.o.f.31.3		32	35.34	odd	2
980.2.o.f.31.8		32	140.139	even	2
980.2.o.f.411.3		32	140.79	odd	6
980.2.o.f.411.8		32	35.9	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.26796 + 0.626319i) q^{2} +(1.49907 - 2.59647i) q^{3} +(1.21545 + 1.58830i) q^{4} +(3.52698 - 2.35332i) q^{6} +(2.06101 + 1.65899i) q^{7} +(0.546365 + 2.77516i) q^{8} +(-2.99443 - 5.18651i) q^{9} +(-1.93693 - 1.11828i) q^{11} +(5.94600 - 0.774910i) q^{12} -3.17109i q^{13} +(1.57423 + 3.39438i) q^{14} +(-1.04536 + 3.86099i) q^{16} +(2.98390 + 1.72275i) q^{17} +(-0.548417 - 8.45176i) q^{18} +(1.02618 + 1.77739i) q^{19} +(7.39711 - 2.86441i) q^{21} +(-1.75554 - 2.63107i) q^{22} +(2.30481 - 1.33068i) q^{23} +(8.02464 + 2.74154i) q^{24} +(1.98611 - 4.02082i) q^{26} -8.96105 q^{27} +(-0.129905 + 5.28991i) q^{28} -7.38092 q^{29} +(-2.44599 + 4.23658i) q^{31} +(-3.74369 + 4.24085i) q^{32} +(-5.80718 + 3.35278i) q^{33} +(2.70447 + 4.05325i) q^{34} +(4.59812 - 11.0600i) q^{36} +(-5.59689 - 9.69410i) q^{37} +(0.187940 + 2.89637i) q^{38} +(-8.23364 - 4.75369i) q^{39} +1.46011i q^{41} +(11.1733 + 1.00099i) q^{42} +9.95752i q^{43} +(-0.578071 - 4.43563i) q^{44} +(3.75585 - 0.243709i) q^{46} +(-3.06343 - 5.30601i) q^{47} +(8.45786 + 8.50215i) q^{48} +(1.49553 + 6.83838i) q^{49} +(8.94615 - 5.16506i) q^{51} +(5.03663 - 3.85430i) q^{52} +(2.32888 - 4.03374i) q^{53} +(-11.3623 - 5.61247i) q^{54} +(-3.47788 + 6.62604i) q^{56} +6.15325 q^{57} +(-9.35872 - 4.62281i) q^{58} +(-3.55938 + 6.16503i) q^{59} +(-2.19681 + 1.26833i) q^{61} +(-5.75488 + 3.83985i) q^{62} +(2.43279 - 15.6572i) q^{63} +(-7.40297 + 3.03249i) q^{64} +(-9.46318 + 0.614046i) q^{66} +(0.0456998 + 0.0263848i) q^{67} +(0.890536 + 6.83323i) q^{68} -7.97917i q^{69} -0.212347i q^{71} +(12.7573 - 11.1437i) q^{72} +(12.8816 + 7.43720i) q^{73} +(-1.02505 - 15.7972i) q^{74} +(-1.57575 + 3.79020i) q^{76} +(-2.13680 - 5.51813i) q^{77} +(-7.46261 - 11.1844i) q^{78} +(0.399413 - 0.230601i) q^{79} +(-4.44995 + 7.70755i) q^{81} +(-0.914496 + 1.85137i) q^{82} -10.9174 q^{83} +(13.5403 + 8.26724i) q^{84} +(-6.23658 + 12.6257i) q^{86} +(-11.0645 + 19.1643i) q^{87} +(2.04514 - 5.98626i) q^{88} +(6.07992 - 3.51024i) q^{89} +(5.26080 - 6.53565i) q^{91} +(4.91490 + 2.04334i) q^{92} +(7.33344 + 12.7019i) q^{93} +(-0.561053 - 8.64650i) q^{94} +(5.39918 + 16.0777i) q^{96} +0.185459i q^{97} +(-2.38673 + 9.60747i) q^{98} +13.3945i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 4 q^{8} - 16 q^{9} + 30 q^{12} + 2 q^{14} - 14 q^{16} - 12 q^{21} + 8 q^{22} + 36 q^{24} + 30 q^{26} - 2 q^{28} - 40 q^{29} - 2 q^{32} + 60 q^{36} - 8 q^{37} + 60 q^{38} + 62 q^{42}+ \cdots - 78 q^{98}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 - 16 * q^9 + 30 * q^12 + 2 * q^14 - 14 * q^16 - 12 * q^21 + 8 * q^22 + 36 * q^24 + 30 * q^26 - 2 * q^28 - 40 * q^29 - 2 * q^32 + 60 * q^36 - 8 * q^37 + 60 * q^38 + 62 * q^42 - 18 * q^44 + 2 * q^46 - 16 * q^49 + 36 * q^52 + 8 * q^53 + 12 * q^54 - 4 * q^56 - 48 * q^57 - 2 * q^58 + 24 * q^61 + 4 * q^64 + 24 * q^66 - 60 * q^68 - 4 * q^72 + 72 * q^73 + 38 * q^74 + 40 * q^77 - 120 * q^78 - 36 * q^81 - 42 * q^82 - 20 * q^84 + 28 * q^86 - 4 * q^88 - 60 * q^89 + 4 * q^92 + 8 * q^93 + 18 * q^94 - 60 * q^96 - 78 * q^98

Introduction

L-functions

Modular forms

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