LMFDB - Embedded newform 783.2.k.f.136.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [783,2,Mod(82,783)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(783, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("783.82"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.k (of order $7$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,-10,0,0,4,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{7})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			136.7
Character	$\chi$	$=$	783.136
Dual form			783.2.k.f.190.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.959163 - 0.461908i) q^{2} +(-0.540346 + 0.677573i) q^{4} +(0.748493 - 0.360455i) q^{5} +(-2.74812 - 3.44603i) q^{7} +(-0.679091 + 2.97529i) q^{8} +(0.551429 - 0.691470i) q^{10} +(-0.939896 - 4.11795i) q^{11} +(-0.238566 - 1.04523i) q^{13} +(-4.22764 - 2.03592i) q^{14} +(0.337258 + 1.47763i) q^{16} +1.13164 q^{17} +(2.60592 - 3.26772i) q^{19} +(-0.160211 + 0.701929i) q^{20} +(-2.80363 - 3.51564i) q^{22} +(-6.55514 - 3.15679i) q^{23} +(-2.68714 + 3.36956i) q^{25} +(-0.711623 - 0.892346i) q^{26} +3.81987 q^{28} +(-2.29459 - 4.87184i) q^{29} +(4.15464 - 2.00077i) q^{31} +(-2.79953 - 3.51049i) q^{32} +(1.08542 - 0.522712i) q^{34} +(-3.29908 - 1.58875i) q^{35} +(0.500358 - 2.19221i) q^{37} +(0.990113 - 4.33797i) q^{38} +(0.564164 + 2.47176i) q^{40} +5.82942 q^{41} +(4.83166 + 2.32680i) q^{43} +(3.29808 + 1.58827i) q^{44} -7.74560 q^{46} +(-1.62790 - 7.13229i) q^{47} +(-2.76532 + 12.1157i) q^{49} +(-1.02097 + 4.47317i) q^{50} +(0.837125 + 0.403138i) q^{52} +(-11.0118 + 5.30301i) q^{53} +(-2.18784 - 2.74347i) q^{55} +(12.1192 - 5.83628i) q^{56} +(-4.45123 - 3.61300i) q^{58} +10.6337 q^{59} +(-0.552358 - 0.692635i) q^{61} +(3.06080 - 3.83812i) q^{62} +(-7.03779 - 3.38922i) q^{64} +(-0.555322 - 0.696352i) q^{65} +(-1.66078 + 7.27633i) q^{67} +(-0.611475 + 0.766765i) q^{68} -3.89822 q^{70} +(-2.44240 - 10.7008i) q^{71} +(10.7277 + 5.16618i) q^{73} +(-0.532676 - 2.33381i) q^{74} +(0.806018 + 3.53140i) q^{76} +(-11.6076 + 14.5555i) q^{77} +(-0.463072 + 2.02885i) q^{79} +(0.785053 + 0.984426i) q^{80} +(5.59136 - 2.69266i) q^{82} +(-3.78257 + 4.74320i) q^{83} +(0.847021 - 0.407904i) q^{85} +5.70912 q^{86} +12.8904 q^{88} +(-14.0249 + 6.75406i) q^{89} +(-2.94627 + 3.69451i) q^{91} +(5.68100 - 2.73583i) q^{92} +(-4.85588 - 6.08909i) q^{94} +(0.772645 - 3.38518i) q^{95} +(9.72341 - 12.1928i) q^{97} +(2.94394 + 12.8982i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 10 q^{4} + 4 q^{7} + 4 q^{10} - 24 q^{13} - 26 q^{16} + 4 q^{19} - 8 q^{22} - 16 q^{25} + 112 q^{28} - 4 q^{31} + 26 q^{34} - 18 q^{37} - 78 q^{40} - 8 q^{43} + 72 q^{46} + 14 q^{49} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) $ 60 * q - 10 * q^4 + 4 * q^7 + 4 * q^10 - 24 * q^13 - 26 * q^16 + 4 * q^19 - 8 * q^22 - 16 * q^25 + 112 * q^28 - 4 * q^31 + 26 * q^34 - 18 * q^37 - 78 * q^40 - 8 * q^43 + 72 * q^46 + 14 * q^49 - 12 * q^52 + 24 * q^55 - 162 * q^58 - 10 * q^61 + 116 * q^64 + 60 * q^67 - 12 * q^70 + 66 * q^73 - 120 * q^76 + 46 * q^79 - 84 * q^82 - 122 * q^85 - 152 * q^88 - 30 * q^91 - 68 * q^94 + 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{6}{7}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.959163	−	0.461908i	0.678230	−	0.326619i	−0.0628614	−	0.998022i	$-0.520023\pi$
$2$	0.959163	−	0.461908i	0.678230	−	0.326619i	0.741092	+	0.671404i	$0.234308\pi$
$3$		0			0
$3$		0			0
$4$	−0.540346	+	0.677573i	−0.270173	+	0.338786i
$5$	0.748493	−	0.360455i	0.334736	−	0.161200i	−0.258964	−	0.965887i	$-0.583381\pi$
$5$	0.748493	−	0.360455i	0.334736	−	0.161200i	0.593700	+	0.804687i	$0.297667\pi$
$6$		0			0
$7$	−2.74812	−	3.44603i	−1.03869	−	1.30248i	−0.951953	−	0.306245i	$-0.900927\pi$
$7$	−2.74812	−	3.44603i	−1.03869	−	1.30248i	−0.0867373	−	0.996231i	$-0.527644\pi$
$8$	−0.679091	+	2.97529i	−0.240095	+	1.05192i
$9$		0			0
$10$	0.551429	−	0.691470i	0.174377	−	0.218662i
$11$	−0.939896	−	4.11795i	−0.283389	−	1.24161i	−0.893416	−	0.449229i	$-0.851699\pi$
$11$	−0.939896	−	4.11795i	−0.283389	−	1.24161i	0.610027	−	0.792381i	$-0.291159\pi$
$12$		0			0
$13$	−0.238566	−	1.04523i	−0.0661663	−	0.289894i	0.931010	−	0.364995i	$-0.118929\pi$
$13$	−0.238566	−	1.04523i	−0.0661663	−	0.289894i	−0.997176	+	0.0751010i	$0.976072\pi$
$14$	−4.22764	−	2.03592i	−1.12988	−	0.544123i
$15$		0			0
$16$	0.337258	+	1.47763i	0.0843146	+	0.369406i
$17$	1.13164			0.274462			0.137231	−	0.990539i	$-0.456180\pi$
$17$	1.13164			0.274462			0.137231	+	0.990539i	$0.456180\pi$
$18$		0			0
$19$	2.60592	−	3.26772i	0.597838	−	0.749666i	−0.387201	−	0.921995i	$-0.626558\pi$
$19$	2.60592	−	3.26772i	0.597838	−	0.749666i	0.985039	+	0.172330i	$0.0551295\pi$
$20$	−0.160211	+	0.701929i	−0.0358242	+	0.156956i
$21$		0			0
$22$	−2.80363	−	3.51564i	−0.597736	−	0.749537i
$23$	−6.55514	−	3.15679i	−1.36684	−	0.658236i	−0.400691	−	0.916213i	$-0.631230\pi$
$23$	−6.55514	−	3.15679i	−1.36684	−	0.658236i	−0.966151	+	0.257977i	$0.916944\pi$
$24$		0			0
$25$	−2.68714	+	3.36956i	−0.537427	+	0.673912i
$26$	−0.711623	−	0.892346i	−0.139561	−	0.175004i
$27$		0			0
$28$	3.81987			0.721887
$29$	−2.29459	−	4.87184i	−0.426094	−	0.904679i
$29$	−2.29459	−	4.87184i	−0.426094	−	0.904679i
$30$		0			0
$31$	4.15464	−	2.00077i	0.746195	−	0.359349i	−0.0218357	−	0.999762i	$-0.506951\pi$
$31$	4.15464	−	2.00077i	0.746195	−	0.359349i	0.768031	+	0.640413i	$0.221237\pi$
$32$	−2.79953	−	3.51049i	−0.494891	−	0.620573i
$33$		0			0
$34$	1.08542	−	0.522712i	0.186148	−	0.0896444i
$35$	−3.29908	−	1.58875i	−0.557647	−	0.268549i
$36$		0			0
$37$	0.500358	−	2.19221i	0.0822584	−	0.360398i	−0.917001	−	0.398886i	$-0.869397\pi$
$37$	0.500358	−	2.19221i	0.0822584	−	0.360398i	0.999259	+	0.0384881i	$0.0122542\pi$
$38$	0.990113	−	4.33797i	0.160617	−	0.703711i
$39$		0			0
$40$	0.564164	+	2.47176i	0.0892022	+	0.390820i
$41$	5.82942			0.910402			0.455201	−	0.890389i	$-0.349567\pi$
$41$	5.82942			0.910402			0.455201	+	0.890389i	$0.349567\pi$
$42$		0			0
$43$	4.83166	+	2.32680i	0.736821	+	0.354834i	0.764363	−	0.644786i	$-0.223054\pi$
$43$	4.83166	+	2.32680i	0.736821	+	0.354834i	−0.0275418	+	0.999621i	$0.508768\pi$
$44$	3.29808	+	1.58827i	0.497205	+	0.239441i
$45$		0			0
$46$	−7.74560			−1.14203
$47$	−1.62790	−	7.13229i	−0.237453	−	1.04035i	−0.943288	−	0.331975i	$-0.892285\pi$
$47$	−1.62790	−	7.13229i	−0.237453	−	1.04035i	0.705835	−	0.708376i	$-0.250572\pi$
$48$		0			0
$49$	−2.76532	+	12.1157i	−0.395046	+	1.73081i
$50$	−1.02097	+	4.47317i	−0.144387	+	0.632601i
$51$		0			0
$52$	0.837125	+	0.403138i	0.116088	+	0.0559052i
$53$	−11.0118	+	5.30301i	−1.51259	+	0.728424i	−0.992100	−	0.125446i	$-0.959964\pi$
$53$	−11.0118	+	5.30301i	−1.51259	+	0.728424i	−0.520487	+	0.853870i	$0.674250\pi$
$54$		0			0
$55$	−2.18784	−	2.74347i	−0.295009	−	0.369929i
$56$	12.1192	−	5.83628i	1.61949	−	0.779905i
$57$		0			0
$58$	−4.45123	−	3.61300i	−0.584475	−	0.474410i
$59$	10.6337			1.38439			0.692194	−	0.721712i	$-0.256644\pi$
$59$	10.6337			1.38439			0.692194	+	0.721712i	$0.256644\pi$
$60$		0			0
$61$	−0.552358	−	0.692635i	−0.0707222	−	0.0886829i	0.745212	−	0.666828i	$-0.232348\pi$
$61$	−0.552358	−	0.692635i	−0.0707222	−	0.0886829i	−0.815934	+	0.578145i	$0.803777\pi$
$62$	3.06080	−	3.83812i	0.388722	−	0.487442i
$63$		0			0
$64$	−7.03779	−	3.38922i	−0.879724	−	0.423653i
$65$	−0.555322	−	0.696352i	−0.0688792	−	0.0863718i
$66$		0			0
$67$	−1.66078	+	7.27633i	−0.202896	+	0.888946i	0.766266	+	0.642523i	$0.222112\pi$
$67$	−1.66078	+	7.27633i	−0.202896	+	0.888946i	−0.969162	+	0.246423i	$0.920745\pi$
$68$	−0.611475	+	0.766765i	−0.0741522	+	0.0929840i
$69$		0			0
$70$	−3.89822			−0.465926
$71$	−2.44240	−	10.7008i	−0.289859	−	1.26996i	−0.884718	−	0.466126i	$-0.845649\pi$
$71$	−2.44240	−	10.7008i	−0.289859	−	1.26996i	0.594859	−	0.803830i	$-0.297208\pi$
$72$		0			0
$73$	10.7277	+	5.16618i	1.25558	+	0.604656i	0.939003	−	0.343910i	$-0.111752\pi$
$73$	10.7277	+	5.16618i	1.25558	+	0.604656i	0.316579	+	0.948566i	$0.397466\pi$
$74$	−0.532676	−	2.33381i	−0.0619224	−	0.271300i
$75$		0			0
$76$	0.806018	+	3.53140i	0.0924566	+	0.405079i
$77$	−11.6076	+	14.5555i	−1.32281	+	1.65876i
$78$		0			0
$79$	−0.463072	+	2.02885i	−0.0520996	+	0.228263i	−0.994274	−	0.106859i	$-0.965921\pi$
$79$	−0.463072	+	2.02885i	−0.0520996	+	0.228263i	0.942175	+	0.335123i	$0.108778\pi$
$80$	0.785053	+	0.984426i	0.0877716	+	0.110062i
$81$		0			0
$82$	5.59136	−	2.69266i	0.617462	−	0.297354i
$83$	−3.78257	+	4.74320i	−0.415191	+	0.520634i	−0.944817	−	0.327598i	$-0.893761\pi$
$83$	−3.78257	+	4.74320i	−0.415191	+	0.520634i	0.529626	+	0.848231i	$0.322332\pi$
$84$		0			0
$85$	0.847021	−	0.407904i	0.0918724	−	0.0442434i
$86$	5.70912			0.615630
$87$		0			0
$88$	12.8904			1.37412
$89$	−14.0249	+	6.75406i	−1.48664	+	0.715929i	−0.988508	−	0.151172i	$-0.951695\pi$
$89$	−14.0249	+	6.75406i	−1.48664	+	0.715929i	−0.498134	+	0.867100i	$0.665981\pi$
$90$		0			0
$91$	−2.94627	+	3.69451i	−0.308853	+	0.387290i
$92$	5.68100	−	2.73583i	0.592285	−	0.285230i
$93$		0			0
$94$	−4.85588	−	6.08909i	−0.500846	−	0.628041i
$95$	0.772645	−	3.38518i	0.0792717	−	0.347312i
$96$		0			0
$97$	9.72341	−	12.1928i	0.987263	−	1.23799i	0.0160260	−	0.999872i	$-0.494899\pi$
$97$	9.72341	−	12.1928i	0.987263	−	1.23799i	0.971237	−	0.238117i	$-0.0765300\pi$
$98$	2.94394	+	12.8982i	0.297382	+	1.30292i
$99$		0			0
$100$	−0.831139	−	3.64146i	−0.0831139	−	0.364146i
$101$	−3.09134	−	1.48871i	−0.307600	−	0.148132i	0.273715	−	0.961811i	$-0.411747\pi$
$101$	−3.09134	−	1.48871i	−0.307600	−	0.148132i	−0.581315	+	0.813679i	$0.697462\pi$
$102$		0			0
$103$	1.65433	+	7.24809i	0.163006	+	0.714175i	0.988681	+	0.150030i	$0.0479371\pi$
$103$	1.65433	+	7.24809i	0.163006	+	0.714175i	−0.825676	+	0.564145i	$0.809206\pi$
$104$	3.27186			0.320832
$105$		0			0
$106$	−8.11261	+	10.1729i	−0.787966	+	0.988078i
$107$	−0.328057	+	1.43731i	−0.0317145	+	0.138950i	−0.988307	−	0.152480i	$-0.951274\pi$
$107$	−0.328057	+	1.43731i	−0.0317145	+	0.138950i	0.956592	+	0.291430i	$0.0941311\pi$
$108$		0			0
$109$	9.93069	+	12.4527i	0.951188	+	1.19275i	0.981159	+	0.193201i	$0.0618868\pi$
$109$	9.93069	+	12.4527i	0.951188	+	1.19275i	−0.0299718	+	0.999551i	$0.509542\pi$
$110$	−3.36573	−	1.62085i	−0.320910	−	0.154542i
$111$		0			0
$112$	4.16512	−	5.22289i	0.393566	−	0.493517i
$113$	1.42886	+	1.79174i	0.134416	+	0.168553i	0.844484	−	0.535581i	$-0.179907\pi$
$113$	1.42886	+	1.79174i	0.134416	+	0.168553i	−0.710068	+	0.704133i	$0.751336\pi$
$114$		0			0
$115$	−6.04436			−0.563639
$116$	4.54090	+	1.07773i	0.421612	+	0.100065i
$117$		0			0
$118$	10.1994	−	4.91179i	0.938934	−	0.452167i
$119$	−3.10987	−	3.89965i	−0.285081	−	0.357480i
$120$		0			0
$121$	−6.16348	+	2.96818i	−0.560317	+	0.269834i
$122$	−0.849735	−	0.409211i	−0.0769314	−	0.0370482i
$123$		0			0
$124$	−0.889277	+	3.89618i	−0.0798594	+	0.349887i
$125$	−1.72104	+	7.54036i	−0.153934	+	0.674430i
$126$		0			0
$127$	−1.73199	−	7.58835i	−0.153689	−	0.673357i	−0.991794	−	0.127847i	$-0.959193\pi$
$127$	−1.73199	−	7.58835i	−0.153689	−	0.673357i	0.838105	−	0.545510i	$-0.183664\pi$
$128$	0.664286			0.0587151
$129$		0			0
$130$	−0.854295	−	0.411407i	−0.0749266	−	0.0360828i
$131$	0.724749	+	0.349021i	0.0633216	+	0.0304941i	0.465277	−	0.885165i	$-0.345955\pi$
$131$	0.724749	+	0.349021i	0.0633216	+	0.0304941i	−0.401955	+	0.915659i	$0.631669\pi$
$132$		0			0
$133$	−18.4220			−1.59739
$134$	1.76805	+	7.74631i	0.152736	+	0.669179i
$135$		0			0
$136$	−0.768483	+	3.36695i	−0.0658969	+	0.288713i
$137$	0.782329	−	3.42761i	0.0668388	−	0.292840i	−0.930451	−	0.366417i	$-0.880584\pi$
$137$	0.782329	−	3.42761i	0.0668388	−	0.292840i	0.997290	+	0.0735770i	$0.0234415\pi$
$138$		0			0
$139$	−11.3232	−	5.45296i	−0.960421	−	0.462514i	−0.113093	−	0.993584i	$-0.536076\pi$
$139$	−11.3232	−	5.45296i	−0.960421	−	0.462514i	−0.847328	+	0.531070i	$0.821790\pi$
$140$	2.85914	−	1.37689i	0.241642	−	0.116369i
$141$		0			0
$142$	−7.28546	−	9.13568i	−0.611382	−	0.766649i
$143$	−4.07997	+	1.96481i	−0.341184	+	0.164306i
$144$		0			0
$145$	−3.47356	−	2.81944i	−0.288464	−	0.234142i
$146$	12.6759			1.04907
$147$		0			0
$148$	1.21502	+	1.52358i	0.0998738	+	0.125238i
$149$	−1.99853	+	2.50607i	−0.163726	+	0.205306i	−0.856926	−	0.515439i	$-0.827629\pi$
$149$	−1.99853	+	2.50607i	−0.163726	+	0.205306i	0.693200	+	0.720745i	$0.256200\pi$
$150$		0			0
$151$	16.8087	+	8.09462i	1.36787	+	0.658731i	0.966377	−	0.257131i	$-0.0827772\pi$
$151$	16.8087	+	8.09462i	1.36787	+	0.658731i	0.401493	+	0.915862i	$0.368492\pi$
$152$	7.95275	+	9.97243i	0.645053	+	0.808871i
$153$		0			0
$154$	−4.41030	+	19.3228i	−0.355392	+	1.55707i
$155$	2.38853	−	2.99512i	0.191851	−	0.240574i
$156$		0			0
$157$	1.52265			0.121521			0.0607604	−	0.998152i	$-0.480647\pi$
$157$	1.52265			0.121521			0.0607604	+	0.998152i	$0.480647\pi$
$158$	0.492982	+	2.15989i	0.0392195	+	0.171832i
$159$		0			0
$160$	−3.36080	−	1.61848i	−0.265695	−	0.127952i
$161$	7.13590	+	31.2644i	0.562388	+	2.46398i
$162$		0			0
$163$	1.63293	+	7.15431i	0.127901	+	0.560369i	0.997750	+	0.0670510i	$0.0213590\pi$
$163$	1.63293	+	7.15431i	0.127901	+	0.560369i	−0.869849	+	0.493318i	$0.835784\pi$
$164$	−3.14990	+	3.94985i	−0.245966	+	0.308432i
$165$		0			0
$166$	−1.43718	+	6.29670i	−0.111547	+	0.488719i
$167$	5.76095	+	7.22400i	0.445796	+	0.559010i	0.953060	−	0.302780i	$-0.0979148\pi$
$167$	5.76095	+	7.22400i	0.445796	+	0.559010i	−0.507265	+	0.861790i	$0.669343\pi$
$168$		0			0
$169$	10.6770	−	5.14178i	0.821309	−	0.395521i
$170$	0.624017	−	0.782492i	0.0478599	−	0.0600144i
$171$		0			0
$172$	−4.18735	+	2.01652i	−0.319282	+	0.153758i
$173$	19.2315			1.46215			0.731073	−	0.682299i	$-0.239020\pi$
$173$	19.2315			1.46215			0.731073	+	0.682299i	$0.239020\pi$
$174$		0			0
$175$	18.9962			1.43597
$176$	5.76781	−	2.77763i	0.434765	−	0.209372i
$177$		0			0
$178$	−10.3324	+	12.9565i	−0.774450	+	0.971129i
$179$	19.9160	−	9.59105i	1.48859	−	0.716869i	0.499798	−	0.866142i	$-0.333408\pi$
$179$	19.9160	−	9.59105i	1.48859	−	0.716869i	0.988796	+	0.149273i	$0.0476934\pi$
$180$		0			0
$181$	−13.5132	−	16.9450i	−1.00443	−	1.25951i	−0.965537	−	0.260266i	$-0.916190\pi$
$181$	−13.5132	−	16.9450i	−1.00443	−	1.25951i	−0.0388884	−	0.999244i	$-0.512382\pi$
$182$	−1.11943	+	4.90454i	−0.0829777	+	0.363549i
$183$		0			0
$184$	13.8439	−	17.3597i	1.02059	−	1.27977i
$185$	−0.415680	−	1.82121i	−0.0305614	−	0.133898i
$186$		0			0
$187$	−1.06362	−	4.66002i	−0.0777796	−	0.340775i
$188$	5.71227	+	2.75089i	0.416610	+	0.200629i
$189$		0			0
$190$	−0.822550	−	3.60383i	−0.0596741	−	0.261449i
$191$	13.0680			0.945570			0.472785	−	0.881178i	$-0.343249\pi$
$191$	13.0680			0.945570			0.472785	+	0.881178i	$0.343249\pi$
$192$		0			0
$193$	5.88625	−	7.38113i	0.423702	−	0.531305i	−0.523465	−	0.852047i	$-0.675361\pi$
$193$	5.88625	−	7.38113i	0.423702	−	0.531305i	0.947167	+	0.320742i	$0.103932\pi$
$194$	3.69439	−	16.1862i	0.265242	−	1.16210i
$195$		0			0
$196$	−6.71502	−	8.42036i	−0.479644	−	0.601454i
$197$	−15.0975	−	7.27058i	−1.07565	−	0.518007i	−0.189729	−	0.981837i	$-0.560761\pi$
$197$	−15.0975	−	7.27058i	−1.07565	−	0.518007i	−0.885925	+	0.463829i	$0.846475\pi$
$198$		0			0
$199$	8.17741	−	10.2541i	0.579681	−	0.726897i	−0.402377	−	0.915474i	$-0.631816\pi$
$199$	8.17741	−	10.2541i	0.579681	−	0.726897i	0.982058	+	0.188577i	$0.0603875\pi$
$200$	−8.20061	−	10.2832i	−0.579871	−	0.727135i
$201$		0			0
$202$	−3.65274			−0.257006
$203$	−10.4827	+	21.2956i	−0.735743	+	1.49466i
$204$		0			0
$205$	4.36327	−	2.10124i	0.304744	−	0.146757i
$206$	4.93472	+	6.18795i	0.343818	+	0.431135i
$207$		0			0
$208$	1.46400	−	0.705023i	0.101510	−	0.0488846i
$209$	−15.9056	−	7.65973i	−1.10021	−	0.529835i
$210$		0			0
$211$	2.82919	−	12.3955i	0.194769	−	0.853340i	−0.779221	−	0.626750i	$-0.784385\pi$
$211$	2.82919	−	12.3955i	0.194769	−	0.853340i	0.973990	−	0.226591i	$-0.0727580\pi$
$212$	2.35701	−	10.3268i	0.161880	−	0.709244i
$213$		0			0
$214$	0.349246	+	1.53015i	0.0238740	+	0.104599i
$215$	4.45517			0.303840
$216$		0			0
$217$	−18.3121	−	8.81866i	−1.24311	−	0.598649i
$218$	15.2771	+	7.35709i	1.03470	+	0.498285i
$219$		0			0
$220$	3.04109			0.205030
$221$	−0.269970	−	1.18282i	−0.0181601	−	0.0795648i
$222$		0			0
$223$	0.763635	−	3.34571i	0.0511368	−	0.224045i	−0.942902	−	0.333070i	$-0.891916\pi$
$223$	0.763635	−	3.34571i	0.0511368	−	0.224045i	0.994039	+	0.109025i	$0.0347727\pi$
$224$	−4.40384	+	19.2945i	−0.294244	+	1.28917i
$225$		0			0
$226$	2.19813	+	1.05857i	0.146218	+	0.0704147i
$227$	−9.46378	+	4.55752i	−0.628133	+	0.302493i	−0.720736	−	0.693210i	$-0.756196\pi$
$227$	−9.46378	+	4.55752i	−0.628133	+	0.302493i	0.0926022	+	0.995703i	$0.470482\pi$
$228$		0			0
$229$	0.307829	+	0.386005i	0.0203419	+	0.0255080i	0.791898	−	0.610653i	$-0.209093\pi$
$229$	0.307829	+	0.386005i	0.0203419	+	0.0255080i	−0.771556	+	0.636161i	$0.780521\pi$
$230$	−5.79752	+	2.79194i	−0.382277	+	0.184095i
$231$		0			0
$232$	16.0534	−	3.51864i	1.05396	−	0.231010i
$233$	−15.5122			−1.01624			−0.508119	−	0.861287i	$-0.669659\pi$
$233$	−15.5122			−1.01624			−0.508119	+	0.861287i	$0.669659\pi$
$234$		0			0
$235$	−3.78934	−	4.75168i	−0.247189	−	0.309966i
$236$	−5.74587	+	7.20509i	−0.374024	+	0.469012i
$237$		0			0
$238$	−4.78415	−	2.30392i	−0.310110	−	0.149341i
$239$	−12.0563	−	15.1182i	−0.779859	−	0.977913i	−0.999997	−	0.00244380i	$-0.999222\pi$
$239$	−12.0563	−	15.1182i	−0.779859	−	0.977913i	0.220138	−	0.975469i	$-0.429349\pi$
$240$		0			0
$241$	5.99191	−	26.2523i	0.385973	−	1.69106i	−0.292365	−	0.956307i	$-0.594442\pi$
$241$	5.99191	−	26.2523i	0.385973	−	1.69106i	0.678338	−	0.734750i	$-0.262701\pi$
$242$	−4.54076	+	5.69393i	−0.291891	+	0.366020i
$243$		0			0
$244$	0.767775			0.0491518
$245$	2.29733	+	10.0653i	0.146771	+	0.643046i
$246$		0			0
$247$	−4.03719	−	1.94421i	−0.256880	−	0.123707i
$248$	3.13149	+	13.7200i	0.198850	+	0.871218i
$249$		0			0
$250$	1.83220	+	8.02739i	0.115879	+	0.507697i
$251$	13.9375	−	17.4770i	0.879725	−	1.10314i	−0.114241	−	0.993453i	$-0.536444\pi$
$251$	13.9375	−	17.4770i	0.879725	−	1.10314i	0.993966	−	0.109687i	$-0.0349849\pi$
$252$		0			0
$253$	−6.83836	+	29.9608i	−0.429924	+	1.88362i
$254$	−5.16638	−	6.47844i	−0.324168	−	0.406493i
$255$		0			0
$256$	14.7127	−	7.08528i	0.919546	−	0.442830i
$257$	−0.0446906	+	0.0560403i	−0.00278773	+	0.00349570i	−0.783223	−	0.621740i	$-0.786426\pi$
$257$	−0.0446906	+	0.0560403i	−0.00278773	+	0.00349570i	0.780436	+	0.625236i	$0.214997\pi$
$258$		0			0
$259$	−8.92947	+	4.30021i	−0.554850	+	0.267202i
$260$	0.771895			0.0478709
$261$		0			0
$262$	0.856367			0.0529065
$263$	−3.80271	+	1.83129i	−0.234485	+	0.112922i	−0.547437	−	0.836847i	$-0.684396\pi$
$263$	−3.80271	+	1.83129i	−0.234485	+	0.112922i	0.312952	+	0.949769i	$0.398682\pi$
$264$		0			0
$265$	−6.33076	+	7.93852i	−0.388895	+	0.487659i
$266$	−17.6697	+	8.50928i	−1.08340	+	0.521737i
$267$		0			0
$268$	−4.03285	−	5.05703i	−0.246346	−	0.308908i
$269$	5.50670	−	24.1264i	0.335750	−	1.47102i	−0.472057	−	0.881568i	$-0.656488\pi$
$269$	5.50670	−	24.1264i	0.335750	−	1.47102i	0.807807	−	0.589447i	$-0.200654\pi$
$270$		0			0
$271$	−16.6206	+	20.8416i	−1.00963	+	1.26604i	−0.0459625	+	0.998943i	$0.514635\pi$
$271$	−16.6206	+	20.8416i	−1.00963	+	1.26604i	−0.963670	+	0.267096i	$0.913936\pi$
$272$	0.381654	+	1.67213i	0.0231412	+	0.101388i
$273$		0			0
$274$	−0.832859	−	3.64899i	−0.0503149	−	0.220444i
$275$	16.4013	+	7.89846i	0.989037	+	0.476295i
$276$		0			0
$277$	4.13271	+	18.1066i	0.248311	+	1.08792i	0.933224	+	0.359296i	$0.116983\pi$
$277$	4.13271	+	18.1066i	0.248311	+	1.08792i	−0.684913	+	0.728625i	$0.740160\pi$
$278$	−13.3796			−0.802452
$279$		0			0
$280$	6.96738	−	8.73682i	0.416381	−	0.522125i
$281$	−1.11169	+	4.87061i	−0.0663176	+	0.290557i	−0.997202	−	0.0747582i	$-0.976181\pi$
$281$	−1.11169	+	4.87061i	−0.0663176	+	0.290557i	0.930884	+	0.365315i	$0.119039\pi$
$282$		0			0
$283$	13.4277	+	16.8378i	0.798194	+	1.00090i	0.999770	+	0.0214309i	$0.00682218\pi$
$283$	13.4277	+	16.8378i	0.798194	+	1.00090i	−0.201576	+	0.979473i	$0.564606\pi$
$284$	8.57033	+	4.12725i	0.508556	+	0.244908i
$285$		0			0
$286$	−3.00579	+	3.76914i	−0.177736	+	0.222874i
$287$	−16.0199	−	20.0883i	−0.945625	−	1.18578i
$288$		0			0
$289$	−15.7194			−0.924671
$290$	−4.63404	−	1.09984i	−0.272120	−	0.0645847i
$291$		0			0
$292$	−9.29713	+	4.47726i	−0.544073	+	0.262012i
$293$	4.96021	+	6.21990i	0.289778	+	0.363371i	0.905317	−	0.424736i	$-0.139633\pi$
$293$	4.96021	+	6.21990i	0.289778	+	0.363371i	−0.615539	+	0.788107i	$0.711062\pi$
$294$		0			0
$295$	7.95924	−	3.83297i	0.463405	−	0.223164i
$296$	6.18268	+	2.97742i	0.359361	+	0.173059i
$297$		0			0
$298$	−0.759336	+	3.32687i	−0.0439872	+	0.192720i
$299$	−1.73573	+	7.60471i	−0.100380	+	0.439792i
$300$		0			0
$301$	−5.25972	−	23.0444i	−0.303165	−	1.32825i
$302$	19.8612			1.14288
$303$		0			0
$304$	5.70733	+	2.74851i	0.327338	+	0.157638i
$305$	−0.663100	−	0.319332i	−0.0379690	−	0.0182849i
$306$		0			0
$307$	1.02414			0.0584508			0.0292254	−	0.999573i	$-0.490696\pi$
$307$	1.02414			0.0584508			0.0292254	+	0.999573i	$0.490696\pi$
$308$	−3.59028	−	15.7300i	−0.204575	−	0.896302i
$309$		0			0
$310$	0.907516	−	3.97609i	0.0515435	−	0.225827i
$311$	1.93523	−	8.47879i	0.109737	−	0.480788i	−0.889957	−	0.456044i	$-0.849266\pi$
$311$	1.93523	−	8.47879i	0.109737	−	0.480788i	0.999694	−	0.0247439i	$-0.00787703\pi$
$312$		0			0
$313$	−17.3701	−	8.36498i	−0.981814	−	0.472817i	−0.127085	−	0.991892i	$-0.540562\pi$
$313$	−17.3701	−	8.36498i	−0.981814	−	0.472817i	−0.854729	+	0.519075i	$0.826277\pi$
$314$	1.46047	−	0.703326i	0.0824191	−	0.0396910i
$315$		0			0
$316$	−1.12447	−	1.41005i	−0.0632566	−	0.0793213i
$317$	25.3561	−	12.2108i	1.42414	−	0.685830i	0.446242	−	0.894912i	$-0.352762\pi$
$317$	25.3561	−	12.2108i	1.42414	−	0.685830i	0.977898	+	0.209083i	$0.0670478\pi$
$318$		0			0
$319$	−17.9054	+	14.0280i	−1.00251	+	0.785419i
$320$	−6.48940			−0.362768
$321$		0			0
$322$	21.2858	+	26.6915i	1.18621	+	1.48746i
$323$	2.94895	−	3.69787i	0.164084	−	0.205755i
$324$		0			0
$325$	4.16301	+	2.00480i	0.230922	+	0.111206i
$326$	4.87088	+	6.10789i	0.269773	+	0.338285i
$327$		0			0
$328$	−3.95870	+	17.3442i	−0.218583	+	0.957673i
$329$	−20.1044	+	25.2101i	−1.10839	+	1.38988i
$330$		0			0
$331$	−27.7225			−1.52377			−0.761883	−	0.647714i	$-0.775725\pi$
$331$	−27.7225			−1.52377			−0.761883	+	0.647714i	$0.775725\pi$
$332$	−1.16996	−	5.12594i	−0.0642100	−	0.281322i
$333$		0			0
$334$	8.86252	+	4.26796i	0.484935	+	0.233533i
$335$	1.37971	+	6.04492i	0.0753818	+	0.330269i
$336$		0			0
$337$	1.41275	+	6.18965i	0.0769572	+	0.337172i	0.998720	−	0.0505830i	$-0.0161080\pi$
$337$	1.41275	+	6.18965i	0.0769572	+	0.337172i	−0.921763	+	0.387755i	$0.873251\pi$
$338$	7.86596	−	9.86360i	0.427852	−	0.536509i
$339$		0			0
$340$	−0.181300	+	0.794328i	−0.00983238	+	0.0430785i
$341$	−12.1440	−	15.2281i	−0.657634	−	0.824648i
$342$		0			0
$343$	21.5524	−	10.3791i	1.16372	−	0.560418i
$344$	−10.2041	+	12.7955i	−0.550166	+	0.689886i
$345$		0			0
$346$	18.4462	−	8.88321i	0.991672	−	0.477564i
$347$	−17.7801			−0.954488			−0.477244	−	0.878771i	$-0.658364\pi$
$347$	−17.7801			−0.954488			−0.477244	+	0.878771i	$0.658364\pi$
$348$		0			0
$349$	16.5173			0.884152			0.442076	−	0.896978i	$-0.354242\pi$
$349$	16.5173			0.884152			0.442076	+	0.896978i	$0.354242\pi$
$350$	18.2204	−	8.77449i	0.973922	−	0.469016i
$351$		0			0
$352$	−11.8248	+	14.8278i	−0.630263	+	0.790325i
$353$	−4.74503	+	2.28509i	−0.252552	+	0.121623i	−0.555877	−	0.831264i	$-0.687618\pi$
$353$	−4.74503	+	2.28509i	−0.252552	+	0.121623i	0.303325	+	0.952887i	$0.401903\pi$
$354$		0			0
$355$	−5.68529	−	7.12912i	−0.301744	−	0.378375i
$356$	3.00196	−	13.1524i	0.159104	−	0.697078i
$357$		0			0
$358$	14.6725	−	18.3988i	0.775467	−	0.972405i
$359$	−4.03139	−	17.6627i	−0.212768	−	0.932199i	−0.962676	−	0.270657i	$-0.912759\pi$
$359$	−4.03139	−	17.6627i	−0.212768	−	0.932199i	0.749908	−	0.661543i	$-0.230098\pi$
$360$		0			0
$361$	0.340730	+	1.49283i	0.0179331	+	0.0785702i
$362$	−20.7883	−	10.0111i	−1.09261	−	0.526174i
$363$		0			0
$364$	−0.911291	−	3.99263i	−0.0477646	−	0.209271i
$365$	9.89178			0.517759
$366$		0			0
$367$	−8.77254	+	11.0004i	−0.457923	+	0.574217i	−0.956168	−	0.292819i	$-0.905407\pi$
$367$	−8.77254	+	11.0004i	−0.457923	+	0.574217i	0.498245	+	0.867036i	$0.333978\pi$
$368$	2.45378	−	10.7507i	0.127912	−	0.560419i
$369$		0			0
$370$	−1.23994	−	1.55483i	−0.0644613	−	0.0808319i
$371$	48.5360	+	23.3737i	2.51986	+	1.21350i
$372$		0			0
$373$	15.3591	−	19.2598i	0.795266	−	0.997232i	−0.204565	−	0.978853i	$-0.565578\pi$
$373$	15.3591	−	19.2598i	0.795266	−	0.997232i	0.999831	−	0.0183792i	$-0.00585060\pi$
$374$	−3.17269	−	3.97843i	−0.164056	−	0.205720i
$375$		0			0
$376$	22.3261			1.15138
$377$	−4.54477	+	3.56062i	−0.234068	+	0.183381i
$378$		0			0
$379$	16.0947	−	7.75078i	0.826727	−	0.398131i	0.0278406	−	0.999612i	$-0.491137\pi$
$379$	16.0947	−	7.75078i	0.826727	−	0.398131i	0.798887	+	0.601481i	$0.205423\pi$
$380$	1.87621	+	2.35269i	0.0962474	+	0.120690i
$381$		0			0
$382$	12.5344	−	6.03623i	0.641314	−	0.308841i
$383$	−2.88501	−	1.38935i	−0.147417	−	0.0709924i	0.358721	−	0.933445i	$-0.383213\pi$
$383$	−2.88501	−	1.38935i	−0.147417	−	0.0709924i	−0.506138	+	0.862453i	$0.668927\pi$
$384$		0			0
$385$	−3.44162	+	15.0787i	−0.175401	+	0.768484i
$386$	2.23647	−	9.79861i	0.113833	−	0.498736i
$387$		0			0
$388$	3.00748	+	13.1766i	0.152682	+	0.668942i
$389$	−38.3076			−1.94227			−0.971137	−	0.238521i	$-0.923337\pi$
$389$	−38.3076			−1.94227			−0.971137	+	0.238521i	$0.923337\pi$
$390$		0			0
$391$	−7.41804	−	3.57234i	−0.375146	−	0.180661i
$392$	−34.1697	−	16.4553i	−1.72583	−	0.831117i
$393$		0			0
$394$	−17.8393			−0.898731
$395$	0.384703	+	1.68550i	0.0193565	+	0.0848065i
$396$		0			0
$397$	−6.84366	+	29.9840i	−0.343473	+	1.50486i	0.448213	+	0.893927i	$0.352061\pi$
$397$	−6.84366	+	29.9840i	−0.343473	+	1.50486i	−0.791686	+	0.610928i	$0.790796\pi$
$398$	3.10699	−	13.6126i	0.155739	−	0.682338i
$399$		0			0
$400$	−5.88521	−	2.83417i	−0.294261	−	0.141708i
$401$	27.6448	−	13.3130i	1.38051	−	0.664821i	0.411405	−	0.911453i	$-0.365038\pi$
$401$	27.6448	−	13.3130i	1.38051	−	0.664821i	0.969109	+	0.246632i	$0.0793238\pi$
$402$		0			0
$403$	−3.08241	−	3.86522i	−0.153546	−	0.192540i
$404$	2.67910	−	1.29019i	0.133290	−	0.0641892i
$405$		0			0
$406$	−0.218018	+	25.2680i	−0.0108201	+	1.25403i
$407$	−9.49772			−0.470784
$408$		0			0
$409$	14.6601	+	18.3832i	0.724898	+	0.908993i	0.998604	−	0.0528203i	$-0.0168211\pi$
$409$	14.6601	+	18.3832i	0.724898	+	0.908993i	−0.273706	+	0.961813i	$0.588250\pi$
$410$	3.21451	−	4.03087i	0.158753	−	0.199070i
$411$		0			0
$412$	−5.80502	−	2.79555i	−0.285993	−	0.137727i
$413$	−29.2226	−	36.6440i	−1.43795	−	1.80313i
$414$		0			0
$415$	−1.12152	+	4.91370i	−0.0550532	+	0.241204i
$416$	−3.00139	+	3.76362i	−0.147155	+	0.184527i
$417$		0			0
$418$	−18.7941			−0.919252
$419$	−6.60936	−	28.9575i	−0.322889	−	1.41467i	−0.832387	−	0.554195i	$-0.813026\pi$
$419$	−6.60936	−	28.9575i	−0.322889	−	1.41467i	0.509498	−	0.860472i	$-0.329831\pi$
$420$		0			0
$421$	−7.55193	−	3.63682i	−0.368058	−	0.177248i	0.240707	−	0.970598i	$-0.422621\pi$
$421$	−7.55193	−	3.63682i	−0.368058	−	0.177248i	−0.608766	+	0.793350i	$0.708335\pi$
$422$	−3.01193	−	13.1961i	−0.146618	−	0.642377i
$423$		0			0
$424$	−8.29997	−	36.3645i	−0.403082	−	1.76602i
$425$	−3.04086	+	3.81312i	−0.147503	+	0.184963i
$426$		0			0
$427$	−0.868896	+	3.80688i	−0.0420488	+	0.184228i
$428$	−0.796619	−	0.998928i	−0.0385060	−	0.0482850i
$429$		0			0
$430$	4.27323	−	2.05788i	0.206074	−	0.0992398i
$431$	−14.8848	+	18.6650i	−0.716977	+	0.899061i	−0.998163	−	0.0605928i	$-0.980701\pi$
$431$	−14.8848	+	18.6650i	−0.716977	+	0.899061i	0.281186	+	0.959653i	$0.409272\pi$
$432$		0			0
$433$	18.8653	−	9.08504i	0.906608	−	0.436599i	0.0783369	−	0.996927i	$-0.475039\pi$
$433$	18.8653	−	9.08504i	0.906608	−	0.436599i	0.828271	+	0.560328i	$0.189325\pi$
$434$	−21.6377			−1.03864
$435$		0			0
$436$	−13.8036			−0.661073
$437$	−27.3977	+	13.1940i	−1.31061	+	0.631155i
$438$		0			0
$439$	0.214654	−	0.269168i	0.0102449	−	0.0128467i	−0.776683	−	0.629892i	$-0.783099\pi$
$439$	0.214654	−	0.269168i	0.0102449	−	0.0128467i	0.786928	+	0.617045i	$0.211671\pi$
$440$	9.64836	−	4.64640i	0.459967	−	0.221509i
$441$		0			0
$442$	−0.805298	−	1.00981i	−0.0383041	−	0.0480318i
$443$	0.448040	−	1.96299i	0.0212870	−	0.0932646i	−0.963169	−	0.268899i	$-0.913340\pi$
$443$	0.448040	−	1.96299i	0.0212870	−	0.0932646i	0.984456	+	0.175634i	$0.0561975\pi$
$444$		0			0
$445$	−8.06303	+	10.1107i	−0.382224	+	0.479294i
$446$	−0.812959	−	3.56181i	−0.0384947	−	0.168656i
$447$		0			0
$448$	7.66131	+	33.5664i	0.361963	+	1.58586i
$449$	17.8977	+	8.61907i	0.844644	+	0.406759i	0.805587	−	0.592478i	$-0.201850\pi$
$449$	17.8977	+	8.61907i	0.844644	+	0.406759i	0.0390570	+	0.999237i	$0.487565\pi$
$450$		0			0
$451$	−5.47904	−	24.0053i	−0.257998	−	1.13036i
$452$	−1.98612			−0.0934190
$453$		0			0
$454$	−6.97215	+	8.74280i	−0.327219	+	0.410320i
$455$	−0.873559	+	3.82731i	−0.0409531	+	0.179427i
$456$		0			0
$457$	−20.9585	−	26.2812i	−0.980398	−	1.22938i	−0.973331	−	0.229405i	$-0.926322\pi$
$457$	−20.9585	−	26.2812i	−0.980398	−	1.22938i	−0.00706724	−	0.999975i	$-0.502250\pi$
$458$	0.473557	+	0.228053i	0.0221279	+	0.0106562i
$459$		0			0
$460$	3.26605	−	4.09549i	0.152280	−	0.190953i
$461$	−8.43993	−	10.5833i	−0.393087	−	0.492915i	0.545426	−	0.838159i	$-0.316368\pi$
$461$	−8.43993	−	10.5833i	−0.393087	−	0.492915i	−0.938513	+	0.345243i	$0.887796\pi$
$462$		0			0
$463$	26.2798			1.22133			0.610664	−	0.791890i	$-0.290903\pi$
$463$	26.2798			1.22133			0.610664	+	0.791890i	$0.290903\pi$
$464$	6.42490	−	5.03361i	0.298268	−	0.233680i
$465$		0			0
$466$	−14.8787	+	7.16521i	−0.689243	+	0.331922i
$467$	10.7020	+	13.4198i	0.495228	+	0.620996i	0.965145	−	0.261714i	$-0.0842878\pi$
$467$	10.7020	+	13.4198i	0.495228	+	0.620996i	−0.469917	+	0.882710i	$0.655716\pi$
$468$		0			0
$469$	29.6385	−	14.2731i	1.36858	−	0.659072i
$470$	−5.82943	−	2.80731i	−0.268892	−	0.129491i
$471$		0			0
$472$	−7.22123	+	31.6383i	−0.332384	+	1.45627i
$473$	5.04042	−	22.0835i	0.231759	−	1.01540i
$474$		0			0
$475$	4.00832	+	17.5616i	0.183914	+	0.805781i
$476$	4.32270			0.198131
$477$		0			0
$478$	−18.5472	−	8.93185i	−0.848329	−	0.408534i
$479$	−0.578231	−	0.278461i	−0.0264200	−	0.0127232i	0.420627	−	0.907234i	$-0.361810\pi$
$479$	−0.578231	−	0.278461i	−0.0264200	−	0.0127232i	−0.447047	+	0.894510i	$0.647524\pi$
$480$		0			0
$481$	−2.41073			−0.109920
$482$	−6.37893	−	27.9479i	−0.290552	−	1.27299i
$483$		0			0
$484$	1.31926	−	5.78005i	0.0599663	−	0.262730i
$485$	2.88295	−	12.6311i	0.130908	−	0.573546i
$486$		0			0
$487$	−19.1297	−	9.21236i	−0.866847	−	0.417452i	−0.0530441	−	0.998592i	$-0.516892\pi$
$487$	−19.1297	−	9.21236i	−0.866847	−	0.417452i	−0.813803	+	0.581140i	$0.802607\pi$
$488$	2.43589	−	1.17306i	0.110268	−	0.0531021i
$489$		0			0
$490$	6.85275	+	8.59307i	0.309575	+	0.388195i
$491$	10.1881	−	4.90635i	0.459785	−	0.221421i	−0.189629	−	0.981856i	$-0.560729\pi$
$491$	10.1881	−	4.90635i	0.459785	−	0.221421i	0.649414	+	0.760435i	$0.275014\pi$
$492$		0			0
$493$	−2.59664	−	5.51315i	−0.116947	−	0.248300i
$494$	−4.77036			−0.214629
$495$		0			0
$496$	4.35757	+	5.46423i	0.195661	+	0.245351i
$497$	−30.1634	+	37.8237i	−1.35301	+	1.69662i
$498$		0			0
$499$	7.45316	+	3.58925i	0.333649	+	0.160677i	0.593206	−	0.805051i	$-0.297862\pi$
$499$	7.45316	+	3.58925i	0.333649	+	0.160677i	−0.259557	+	0.965728i	$0.583576\pi$
$500$	−4.17918	−	5.24053i	−0.186899	−	0.234364i
$501$		0			0
$502$	5.29551	−	23.2011i	0.236350	−	1.03552i
$503$	10.9077	−	13.6778i	0.486348	−	0.609861i	−0.476741	−	0.879044i	$-0.658182\pi$
$503$	10.9077	−	13.6778i	0.486348	−	0.609861i	0.963089	+	0.269183i	$0.0867535\pi$
$504$		0			0
$505$	−2.85046			−0.126844
$506$	7.28006	+	31.8960i	0.323638	+	1.41795i
$507$		0			0
$508$	6.07753	+	2.92678i	0.269647	+	0.129855i
$509$	3.59717	+	15.7602i	0.159442	+	0.698560i	0.989934	+	0.141530i	$0.0452022\pi$
$509$	3.59717	+	15.7602i	0.159442	+	0.698560i	−0.830492	+	0.557030i	$0.811941\pi$
$510$		0			0
$511$	−11.6781	−	51.1652i	−0.516610	−	2.26342i
$512$	10.0108	−	12.5532i	0.442419	−	0.554776i
$513$		0			0
$514$	−0.0169801	+	0.0743947i	−0.000748961	+	0.00328141i
$515$	3.85086	+	4.82883i	0.169689	+	0.212784i
$516$		0			0
$517$	−27.8404	+	13.4072i	−1.22442	+	0.589649i
$518$	−6.57851	+	8.24919i	−0.289043	+	0.362449i
$519$		0			0
$520$	2.44896	−	1.17936i	0.107394	−	0.0517183i
$521$	−11.2836			−0.494344			−0.247172	−	0.968972i	$-0.579501\pi$
$521$	−11.2836			−0.494344			−0.247172	+	0.968972i	$0.579501\pi$
$522$		0			0
$523$	−30.1685			−1.31918			−0.659588	−	0.751627i	$-0.729269\pi$
$523$	−30.1685			−1.31918			−0.659588	+	0.751627i	$0.729269\pi$
$524$	−0.628102	+	0.302478i	−0.0274388	+	0.0132138i
$525$		0			0
$526$	−2.80153	+	3.51301i	−0.122153	+	0.153174i
$527$	4.70154	−	2.26414i	0.204802	−	0.0986275i
$528$		0			0
$529$	18.6643	+	23.4043i	0.811492	+	1.01758i
$530$	−2.40536	+	10.5386i	−0.104482	+	0.457766i
$531$		0			0
$532$	9.95426	−	12.4822i	0.431572	−	0.541174i
$533$	−1.39070	−	6.09306i	−0.0602379	−	0.263920i
$534$		0			0
$535$	0.272538	+	1.19407i	0.0117828	+	0.0516240i
$536$	−20.5214	−	9.88258i	−0.886389	−	0.426862i
$537$		0			0
$538$	−5.86238	−	25.6848i	−0.252745	−	1.10735i
$539$	52.4909			2.26094
$540$		0			0
$541$	8.77276	−	11.0007i	0.377170	−	0.472957i	−0.556625	−	0.830764i	$-0.687904\pi$
$541$	8.77276	−	11.0007i	0.377170	−	0.472957i	0.933796	+	0.357807i	$0.116475\pi$
$542$	−6.31498	+	27.6677i	−0.271252	+	1.18843i
$543$		0			0
$544$	−3.16804	−	3.97260i	−0.135829	−	0.170324i
$545$	11.9217	+	5.74118i	0.510669	+	0.245925i
$546$		0			0
$547$	5.25928	−	6.59493i	0.224870	−	0.281979i	−0.656579	−	0.754258i	$-0.727997\pi$
$547$	5.25928	−	6.59493i	0.224870	−	0.281979i	0.881449	+	0.472279i	$0.156568\pi$
$548$	1.89972	+	2.38218i	0.0811521	+	0.101762i
$549$		0			0
$550$	19.3799			0.826362
$551$	−21.8993	−	5.19756i	−0.932942	−	0.221424i
$552$		0			0
$553$	8.26405	−	3.97976i	0.351423	−	0.169236i
$554$	12.3275	+	15.4582i	0.523747	+	0.656758i
$555$		0			0
$556$	9.81322	−	4.72580i	0.416173	−	0.200418i
$557$	−6.94571	−	3.34488i	−0.294299	−	0.141727i	0.280908	−	0.959735i	$-0.409364\pi$
$557$	−6.94571	−	3.34488i	−0.294299	−	0.141727i	−0.575207	+	0.818008i	$0.695079\pi$
$558$		0			0
$559$	1.27937	−	5.60527i	0.0541115	−	0.237078i
$560$	1.23494	−	5.41063i	0.0521858	−	0.228641i
$561$		0			0
$562$	1.18349	+	5.18521i	0.0499225	+	0.218725i
$563$	35.6657			1.50313			0.751564	−	0.659660i	$-0.229300\pi$
$563$	35.6657			1.50313			0.751564	+	0.659660i	$0.229300\pi$
$564$		0			0
$565$	1.71534	+	0.826063i	0.0721648	+	0.0347527i
$566$	20.6569	+	9.94783i	0.868273	+	0.418138i
$567$		0			0
$568$	33.4967			1.40549
$569$	−4.60723	−	20.1856i	−0.193145	−	0.846224i	−0.974901	−	0.222640i	$-0.928533\pi$
$569$	−4.60723	−	20.1856i	−0.193145	−	0.846224i	0.781756	−	0.623585i	$-0.214324\pi$
$570$		0			0
$571$	3.27652	−	14.3554i	0.137118	−	0.600753i	−0.858942	−	0.512072i	$-0.828878\pi$
$571$	3.27652	−	14.3554i	0.137118	−	0.600753i	0.996060	−	0.0886803i	$-0.0282649\pi$
$572$	0.873294	−	3.82615i	0.0365143	−	0.159979i
$573$		0			0
$574$	−24.6447	−	11.8682i	−1.02865	−	0.495371i
$575$	28.2516	−	13.6052i	1.17817	−	0.567377i
$576$		0			0
$577$	0.583537	+	0.731733i	0.0242930	+	0.0304624i	0.793830	−	0.608140i	$-0.208084\pi$
$577$	0.583537	+	0.731733i	0.0242930	+	0.0304624i	−0.769537	+	0.638603i	$0.779513\pi$
$578$	−15.0775	+	7.26092i	−0.627140	+	0.302015i
$579$		0			0
$580$	3.78730	−	0.830115i	0.157259	−	0.0344686i
$581$	26.7401			1.10937
$582$		0			0
$583$	32.1875	+	40.3618i	1.33307	+	1.67162i
$584$	−22.6560	+	28.4097i	−0.937511	+	1.17560i
$585$		0			0
$586$	7.63067	+	3.67474i	0.315220	+	0.151802i
$587$	12.2405	+	15.3491i	0.505219	+	0.633524i	0.967398	−	0.253263i	$-0.0815037\pi$
$587$	12.2405	+	15.3491i	0.505219	+	0.633524i	−0.462179	+	0.886787i	$0.652932\pi$
$588$		0			0
$589$	4.28870	−	18.7900i	0.176713	−	0.774229i
$590$	5.86372	−	7.35287i	0.241406	−	0.302713i
$591$		0			0
$592$	3.40802			0.140069
$593$	−2.01719	−	8.83790i	−0.0828362	−	0.362929i	0.916473	−	0.400097i	$-0.131024\pi$
$593$	−2.01719	−	8.83790i	−0.0828362	−	0.362929i	−0.999309	+	0.0371678i	$0.988166\pi$
$594$		0			0
$595$	−3.73336	−	1.79789i	−0.153053	−	0.0737064i
$596$	−0.618151	−	2.70830i	−0.0253204	−	0.110936i
$597$		0			0
$598$	1.84784	+	8.09590i	0.0755637	+	0.331066i
$599$	3.16289	−	3.96614i	0.129232	−	0.162052i	−0.713005	−	0.701158i	$-0.752667\pi$
$599$	3.16289	−	3.96614i	0.129232	−	0.162052i	0.842238	+	0.539107i	$0.181238\pi$
$600$		0			0
$601$	−9.25367	+	40.5430i	−0.377465	+	1.65378i	0.327732	+	0.944771i	$0.393716\pi$
$601$	−9.25367	+	40.5430i	−0.377465	+	1.65378i	−0.705197	+	0.709011i	$0.749142\pi$
$602$	−15.6893	−	19.6738i	−0.639449	−	0.801843i
$603$		0			0
$604$	−14.5672	+	7.01519i	−0.592730	+	0.285444i
$605$	−3.54343	+	4.44332i	−0.144061	+	0.180647i
$606$		0			0
$607$	−21.3641	+	10.2884i	−0.867140	+	0.417593i	−0.813911	−	0.580990i	$-0.802666\pi$
$607$	−21.3641	+	10.2884i	−0.867140	+	0.417593i	−0.0532293	+	0.998582i	$0.516951\pi$
$608$	−18.7666			−0.761087
$609$		0			0
$610$	−0.783523			−0.0317239
$611$	−7.06650	+	3.40305i	−0.285880	+	0.137672i
$612$		0			0
$613$	19.1663	−	24.0337i	0.774118	−	0.970714i	−0.225876	−	0.974156i	$-0.572524\pi$
$613$	19.1663	−	24.0337i	0.774118	−	0.970714i	0.999994	+	0.00344237i	$0.00109574\pi$
$614$	0.982318	−	0.473059i	0.0396431	−	0.0190911i
$615$		0			0
$616$	−35.4243	−	44.4206i	−1.42728	−	1.78976i
$617$	−4.95323	+	21.7015i	−0.199409	+	0.873670i	0.771880	+	0.635768i	$0.219317\pi$
$617$	−4.95323	+	21.7015i	−0.199409	+	0.873670i	−0.971289	+	0.237901i	$0.923540\pi$
$618$		0			0
$619$	−7.69045	+	9.64352i	−0.309105	+	0.387606i	−0.911983	−	0.410228i	$-0.865449\pi$
$619$	−7.69045	+	9.64352i	−0.309105	+	0.387606i	0.602878	+	0.797833i	$0.294021\pi$
$620$	0.738779	+	3.23680i	0.0296701	+	0.129993i
$621$		0			0
$622$	−2.06023	−	9.02644i	−0.0826075	−	0.361927i
$623$	61.8168	+	29.7694i	2.47664	+	1.19269i
$624$		0			0
$625$	−3.36536	−	14.7446i	−0.134614	−	0.589784i
$626$	−20.5246			−0.820327
$627$		0			0
$628$	−0.822759	+	1.03171i	−0.0328317	+	0.0411696i
$629$	0.566223	−	2.48079i	0.0225768	−	0.0989155i
$630$		0			0
$631$	14.7894	+	18.5453i	0.588756	+	0.738277i	0.983579	−	0.180480i	$-0.0577652\pi$
$631$	14.7894	+	18.5453i	0.588756	+	0.738277i	−0.394822	+	0.918758i	$0.629194\pi$
$632$	−5.72195	−	2.75555i	−0.227607	−	0.109610i
$633$		0			0
$634$	18.6803	−	23.4244i	0.741890	−	0.930301i
$635$	−4.03164	−	5.05552i	−0.159991	−	0.200622i
$636$		0			0
$637$	13.3233			0.527890
$638$	−10.6945	+	21.7258i	−0.423399	+	0.860133i
$639$		0			0
$640$	0.497213	−	0.239445i	0.0196541	−	0.00946490i
$641$	24.8752	+	31.1925i	0.982511	+	1.23203i	0.972697	+	0.232078i	$0.0745523\pi$
$641$	24.8752	+	31.1925i	0.982511	+	1.23203i	0.00981337	+	0.999952i	$0.496876\pi$
$642$		0			0
$643$	5.57462	−	2.68460i	0.219842	−	0.105870i	−0.320722	−	0.947173i	$-0.603925\pi$
$643$	5.57462	−	2.68460i	0.219842	−	0.105870i	0.540563	+	0.841303i	$0.318211\pi$
$644$	−25.0398	−	12.0585i	−0.986705	−	0.475172i
$645$		0			0
$646$	1.12045	−	4.90900i	0.0440834	−	0.193142i
$647$	3.33991	−	14.6331i	0.131305	−	0.575286i	−0.865876	−	0.500258i	$-0.833238\pi$
$647$	3.33991	−	14.6331i	0.131305	−	0.575286i	0.997181	−	0.0750276i	$-0.0239045\pi$
$648$		0			0
$649$	−9.99456	−	43.7890i	−0.392321	−	1.71887i
$650$	4.91904			0.192941
$651$		0			0
$652$	−5.72991	−	2.75938i	−0.224401	−	0.108066i
$653$	38.8178	+	18.6937i	1.51906	+	0.731540i	0.992912	−	0.118854i	$-0.0379220\pi$
$653$	38.8178	+	18.6937i	1.51906	+	0.731540i	0.526147	+	0.850394i	$0.323636\pi$
$654$		0			0
$655$	0.668275			0.0261117
$656$	1.96602	+	8.61370i	0.0767602	+	0.336308i
$657$		0			0
$658$	−7.63863	+	33.4670i	−0.297785	+	1.30468i
$659$	0.130239	−	0.570613i	0.00507338	−	0.0222279i	−0.972328	−	0.233620i	$-0.924943\pi$
$659$	0.130239	−	0.570613i	0.00507338	−	0.0222279i	0.977401	+	0.211393i	$0.0677998\pi$
$660$		0			0
$661$	−18.5562	−	8.93619i	−0.721752	−	0.347577i	0.0366823	−	0.999327i	$-0.488321\pi$
$661$	−18.5562	−	8.93619i	−0.721752	−	0.347577i	−0.758434	+	0.651750i	$0.774035\pi$
$662$	−26.5904	+	12.8053i	−1.03346	+	0.497690i
$663$		0			0
$664$	−11.5437	−	14.4753i	−0.447982	−	0.561751i
$665$	−13.7887	+	6.64031i	−0.534704	+	0.257500i
$666$		0			0
$667$	−0.338047	+	39.1792i	−0.0130892	+	1.51702i
$668$	−8.00769			−0.309827
$669$		0			0
$670$	4.11557	+	5.16076i	0.158998	+	0.199377i
$671$	−2.33308	+	2.92559i	−0.0900676	+	0.112941i
$672$		0			0
$673$	20.2005	+	9.72806i	0.778673	+	0.374989i	0.780618	−	0.625009i	$-0.214905\pi$
$673$	20.2005	+	9.72806i	0.778673	+	0.374989i	−0.00194440	+	0.999998i	$0.500619\pi$
$674$	4.21410	+	5.28432i	0.162321	+	0.203544i
$675$		0			0
$676$	−2.28535	+	10.0128i	−0.0878982	+	0.385107i
$677$	−23.0162	+	28.8614i	−0.884584	+	1.10923i	0.108763	+	0.994068i	$0.465311\pi$
$677$	−23.0162	+	28.8614i	−0.884584	+	1.10923i	−0.993346	+	0.115165i	$0.963260\pi$
$678$		0			0
$679$	−68.7377			−2.63791
$680$	0.638428	+	2.79714i	0.0244826	+	0.107265i
$681$		0			0
$682$	−18.6821	−	8.99680i	−0.715373	−	0.344505i
$683$	−9.06524	−	39.7174i	−0.346872	−	1.51974i	−0.784238	−	0.620460i	$-0.786946\pi$
$683$	−9.06524	−	39.7174i	−0.346872	−	1.51974i	0.437366	−	0.899284i	$-0.355911\pi$
$684$		0			0
$685$	−0.649931	−	2.84753i	−0.0248326	−	0.108799i
$686$	15.8781	−	19.9104i	0.606227	−	0.760184i
$687$		0			0
$688$	−1.80863	+	7.92412i	−0.0689533	+	0.302104i
$689$	8.16989	+	10.2447i	0.311248	+	0.390292i
$690$		0			0
$691$	26.6698	−	12.8435i	1.01457	−	0.488590i	0.148710	−	0.988881i	$-0.452488\pi$
$691$	26.6698	−	12.8435i	1.01457	−	0.488590i	0.865858	+	0.500291i	$0.166773\pi$
$692$	−10.3917	+	13.0308i	−0.395033	+	0.495355i
$693$		0			0
$694$	−17.0540	+	8.21280i	−0.647363	+	0.311754i
$695$	−10.4409			−0.396045
$696$		0			0
$697$	6.59678			0.249871
$698$	15.8428	−	7.62949i	0.599659	−	0.288781i
$699$		0			0
$700$	−10.2645	+	12.8713i	−0.387962	+	0.486489i
$701$	1.37195	−	0.660697i	0.0518179	−	0.0249542i	−0.407795	−	0.913073i	$-0.633702\pi$
$701$	1.37195	−	0.660697i	0.0518179	−	0.0249542i	0.459613	+	0.888119i	$0.347988\pi$
$702$		0			0
$703$	−5.85964	−	7.34775i	−0.221000	−	0.277126i
$704$	−7.34186	+	32.1668i	−0.276707	+	1.21233i
$705$		0			0
$706$	−3.49576	+	4.38354i	−0.131564	+	0.164977i
$707$	3.36522	+	14.7440i	0.126562	+	0.554505i
$708$		0			0
$709$	5.70947	+	25.0148i	0.214424	+	0.939451i	0.961520	+	0.274735i	$0.0885903\pi$
$709$	5.70947	+	25.0148i	0.214424	+	0.939451i	−0.747096	+	0.664716i	$0.768553\pi$
$710$	−8.74612	−	4.21191i	−0.328236	−	0.158070i
$711$		0			0
$712$	−10.5711	−	46.3149i	−0.396168	−	1.73572i
$713$	−33.5503			−1.25647
$714$		0			0
$715$	−2.34560	+	2.94129i	−0.0877205	+	0.109998i
$716$	−4.26291	+	18.6770i	−0.159313	+	0.697994i
$717$		0			0
$718$	−12.0253	−	15.0792i	−0.448780	−	0.562752i
$719$	−29.6289	−	14.2685i	−1.10497	−	0.532127i	−0.209754	−	0.977754i	$-0.567266\pi$
$719$	−29.6289	−	14.2685i	−1.10497	−	0.532127i	−0.895219	+	0.445627i	$0.852981\pi$
$720$		0			0
$721$	20.4308	−	25.6195i	0.760884	−	0.954118i
$722$	1.01637	+	1.27448i	0.0378253	+	0.0474314i
$723$		0			0
$724$	18.7832			0.698073
$725$	22.5818	+	5.35956i	0.838669	+	0.199049i
$726$		0			0
$727$	−8.56057	+	4.12256i	−0.317494	+	0.152897i	−0.585843	−	0.810425i	$-0.699236\pi$
$727$	−8.56057	+	4.12256i	−0.317494	+	0.152897i	0.268349	+	0.963322i	$0.413522\pi$
$728$	−8.99145	−	11.2749i	−0.333245	−	0.417876i
$729$		0			0
$730$	9.48782	−	4.56909i	0.351160	−	0.169110i
$731$	5.46768	+	2.63310i	0.202229	+	0.0973886i
$732$		0			0
$733$	−4.34961	+	19.0569i	−0.160656	+	0.703881i	0.828859	+	0.559457i	$0.188990\pi$
$733$	−4.34961	+	19.0569i	−0.160656	+	0.703881i	−0.989516	+	0.144425i	$0.953867\pi$
$734$	−3.33311	+	14.6033i	−0.123027	+	0.539018i
$735$		0			0
$736$	7.26940	+	31.8493i	0.267953	+	1.17398i
$737$	31.5246			1.16122
$738$		0			0
$739$	−13.9431	−	6.71465i	−0.512906	−	0.247003i	0.159483	−	0.987201i	$-0.449017\pi$
$739$	−13.9431	−	6.71465i	−0.512906	−	0.247003i	−0.672389	+	0.740198i	$0.734732\pi$
$740$	1.45861	+	0.702432i	0.0536197	+	0.0258219i
$741$		0			0
$742$	57.3504			2.10540
$743$	1.93584	+	8.48146i	0.0710190	+	0.311155i	0.997944	−	0.0640920i	$-0.0204151\pi$
$743$	1.93584	+	8.48146i	0.0710190	+	0.311155i	−0.926925	+	0.375247i	$0.877558\pi$
$744$		0			0
$745$	−0.592556	+	2.59616i	−0.0217096	+	0.0951159i
$746$	5.83567	−	25.5677i	0.213659	−	0.936102i
$747$		0			0
$748$	3.73223	+	1.79735i	0.136464	+	0.0657175i
$749$	5.85456	−	2.81941i	0.213921	−	0.103019i
$750$		0			0
$751$	29.5091	+	37.0033i	1.07680	+	1.35027i	0.932678	+	0.360710i	$0.117466\pi$
$751$	29.5091	+	37.0033i	1.07680	+	1.35027i	0.144126	+	0.989559i	$0.453963\pi$
$752$	9.98983	−	4.81085i	0.364292	−	0.175434i
$753$		0			0
$754$	−2.71449	+	5.51448i	−0.0988560	+	0.200826i
$755$	15.4989			0.564063
$756$		0			0
$757$	32.8236	+	41.1595i	1.19299	+	1.49597i	0.824053	+	0.566513i	$0.191708\pi$
$757$	32.8236	+	41.1595i	1.19299	+	1.49597i	0.368940	+	0.929453i	$0.379721\pi$
$758$	11.8572	−	14.8685i	0.430675	−	0.540049i
$759$		0			0
$760$	9.54719	+	4.59768i	0.346313	+	0.166776i
$761$	14.1317	+	17.7206i	0.512275	+	0.642373i	0.968949	−	0.247261i	$-0.0795306\pi$
$761$	14.1317	+	17.7206i	0.512275	+	0.642373i	−0.456673	+	0.889634i	$0.650959\pi$
$762$		0			0
$763$	15.6216	−	68.4429i	0.565541	−	2.47780i
$764$	−7.06126	+	8.85454i	−0.255467	+	0.320346i
$765$		0			0
$766$	−3.40895			−0.123170
$767$	−2.53684	−	11.1146i	−0.0915999	−	0.401325i
$768$		0			0
$769$	32.0417	+	15.4305i	1.15545	+	0.556437i	0.910667	−	0.413140i	$-0.135568\pi$
$769$	32.0417	+	15.4305i	1.15545	+	0.556437i	0.244786	+	0.969577i	$0.421282\pi$
$770$	3.66392	+	16.0527i	0.132038	+	0.578498i
$771$		0			0
$772$	1.82064	+	7.97672i	0.0655261	+	0.287089i
$773$	7.25335	−	9.09542i	0.260885	−	0.327139i	−0.634087	−	0.773262i	$-0.718624\pi$
$773$	7.25335	−	9.09542i	0.260885	−	0.327139i	0.894972	+	0.446122i	$0.147195\pi$
$774$		0			0
$775$	−4.42236	+	19.3756i	−0.158856	+	0.695994i
$776$	29.6739	+	37.2100i	1.06523	+	1.33576i
$777$		0			0
$778$	−36.7433	+	17.6946i	−1.31731	+	0.634383i
$779$	15.1910	−	19.0489i	0.544273	−	0.682497i
$780$		0			0
$781$	−41.7700	+	20.1154i	−1.49465	+	0.719784i
$782$	−8.76520			−0.313443
$783$		0			0
$784$	−18.8351			−0.672681
$785$	1.13969	−	0.548848i	0.0406774	−	0.0195892i
$786$		0			0
$787$	5.09963	−	6.39473i	0.181782	−	0.227948i	−0.682588	−	0.730803i	$-0.739146\pi$
$787$	5.09963	−	6.39473i	0.181782	−	0.227948i	0.864370	+	0.502855i	$0.167717\pi$
$788$	13.0842	−	6.30103i	0.466106	−	0.224465i
$789$		0			0
$790$	1.14754	+	1.43897i	0.0408276	+	0.0511961i
$791$	2.24770	−	9.84782i	0.0799190	−	0.350148i
$792$		0			0
$793$	−0.592187	+	0.742579i	−0.0210292	+	0.0263697i
$794$	7.28569	+	31.9207i	0.258559	+	1.13282i
$795$		0			0
$796$	2.52930	+	11.0816i	0.0896485	+	0.392776i
$797$	25.3234	+	12.1951i	0.896999	+	0.431972i	0.824804	−	0.565418i	$-0.191285\pi$
$797$	25.3234	+	12.1951i	0.896999	+	0.431972i	0.0721952	+	0.997391i	$0.477000\pi$
$798$		0			0
$799$	−1.84219	−	8.07116i	−0.0651719	−	0.285537i
$800$	19.3515			0.684180
$801$		0			0
$802$	20.3664	−	25.5387i	0.719164	−	0.901803i
$803$	11.1912	−	49.0318i	0.394929	−	1.73030i
$804$		0			0
$805$	16.6106	+	20.8290i	0.585447	+	0.734127i
$806$	−4.74191	−	2.28358i	−0.167027	−	0.0804358i
$807$		0			0
$808$	6.52864	−	8.18666i	0.229677	−	0.288006i
$809$	29.9751	+	37.5876i	1.05387	+	1.32151i	0.944862	+	0.327470i	$0.106196\pi$
$809$	29.9751	+	37.5876i	1.05387	+	1.32151i	0.109008	+	0.994041i	$0.465232\pi$
$810$		0			0
$811$	5.71044			0.200521			0.100260	−	0.994961i	$-0.468032\pi$
$811$	5.71044			0.200521			0.100260	+	0.994961i	$0.468032\pi$
$812$	−8.76502	−	18.6098i	−0.307592	−	0.653076i
$813$		0			0
$814$	−9.10985	+	4.38707i	−0.319300	+	0.153767i
$815$	3.80104	+	4.76636i	0.133145	+	0.166958i
$816$		0			0
$817$	20.1942	−	9.72503i	0.706507	−	0.340236i
$818$	22.5528	+	10.8609i	0.788542	+	0.379742i
$819$		0			0
$820$	−0.933934	+	4.09183i	−0.0326144	+	0.142893i
$821$	−8.59478	+	37.6562i	−0.299960	+	1.31421i	0.570227	+	0.821487i	$0.306855\pi$
$821$	−8.59478	+	37.6562i	−0.299960	+	1.31421i	−0.870187	+	0.492722i	$0.836002\pi$
$822$		0			0
$823$	−5.29693	−	23.2074i	−0.184639	−	0.808957i	−0.979383	−	0.202012i	$-0.935252\pi$
$823$	−5.29693	−	23.2074i	−0.184639	−	0.808957i	0.794744	−	0.606945i	$-0.207605\pi$
$824$	−22.6886			−0.790395
$825$		0			0
$826$	−44.9554	−	21.6494i	−1.56420	−	0.753278i
$827$	−26.9217	−	12.9648i	−0.936160	−	0.450831i	−0.0973469	−	0.995251i	$-0.531036\pi$
$827$	−26.9217	−	12.9648i	−0.936160	−	0.450831i	−0.838813	+	0.544420i	$0.816750\pi$
$828$		0			0
$829$	−26.7824			−0.930189			−0.465095	−	0.885261i	$-0.653980\pi$
$829$	−26.7824			−0.930189			−0.465095	+	0.885261i	$0.653980\pi$
$830$	1.19396	+	5.23107i	0.0414429	+	0.181573i
$831$		0			0
$832$	−1.86353	+	8.16464i	−0.0646061	+	0.283058i
$833$	−3.12934	+	13.7105i	−0.108425	+	0.475042i
$834$		0			0
$835$	6.91596	+	3.33055i	0.239337	+	0.115258i
$836$	13.7846	−	6.63829i	0.476749	−	0.229590i
$837$		0			0
$838$	−19.7152	−	24.7220i	−0.681049	−	0.854009i
$839$	41.2289	−	19.8548i	1.42338	−	0.685464i	0.445627	−	0.895219i	$-0.352981\pi$
$839$	41.2289	−	19.8548i	1.42338	−	0.685464i	0.977754	+	0.209755i	$0.0672665\pi$
$840$		0			0
$841$	−18.4697	+	22.3577i	−0.636888	+	0.770957i
$842$	−8.92340			−0.307521
$843$		0			0
$844$	6.87010	+	8.61483i	0.236479	+	0.296535i
$845$	6.13828	−	7.69717i	0.211163	−	0.264791i
$846$		0			0
$847$	27.1664	+	13.0826i	0.933448	+	0.449525i
$848$	−11.5497	−	14.4828i	−0.396618	−	0.497343i
$849$		0			0
$850$	−1.15537	+	5.06200i	−0.0396288	+	0.173625i
$851$	−10.2003	+	12.7907i	−0.349661	+	0.438461i
$852$		0			0
$853$	−12.8830			−0.441105			−0.220552	−	0.975375i	$-0.570786\pi$
$853$	−12.8830			−0.441105			−0.220552	+	0.975375i	$0.570786\pi$
$854$	0.925018	+	4.05277i	0.0316535	+	0.138683i
$855$		0			0
$856$	−4.05364	−	1.95213i	−0.138551	−	0.0667224i
$857$	5.07366	+	22.2292i	0.173313	+	0.759334i	0.984619	+	0.174713i	$0.0558996\pi$
$857$	5.07366	+	22.2292i	0.173313	+	0.759334i	−0.811307	+	0.584621i	$0.801243\pi$
$858$		0			0
$859$	−8.50635	−	37.2688i	−0.290233	−	1.27159i	−0.884201	−	0.467106i	$-0.845297\pi$
$859$	−8.50635	−	37.2688i	−0.290233	−	1.27159i	0.593968	−	0.804488i	$-0.297560\pi$
$860$	−2.40733	+	3.01870i	−0.0820894	+	0.102937i
$861$		0			0
$862$	−5.65546	+	24.7782i	−0.192626	+	0.843948i
$863$	29.1909	+	36.6043i	0.993671	+	1.24602i	0.969188	+	0.246324i	$0.0792228\pi$
$863$	29.1909	+	36.6043i	0.993671	+	1.24602i	0.0244837	+	0.999700i	$0.492206\pi$
$864$		0			0
$865$	14.3947	−	6.93211i	0.489433	−	0.235699i
$866$	13.8984	−	17.4281i	0.472288	−	0.592230i
$867$		0			0
$868$	15.8702	−	7.64267i	0.538669	−	0.259409i
$869$	8.78995			0.298179
$870$		0			0
$871$	8.00162			0.271125
$872$	−43.7942	+	21.0902i	−1.48306	+	0.714203i
$873$		0			0
$874$	−20.1844	+	25.3104i	−0.682747	+	0.856137i
$875$	30.7139	−	14.7910i	1.03832	−	0.500028i
$876$		0			0
$877$	−20.3595	−	25.5300i	−0.687490	−	0.862086i	0.308530	−	0.951215i	$-0.400163\pi$
$877$	−20.3595	−	25.5300i	−0.687490	−	0.862086i	−0.996020	+	0.0891290i	$0.971592\pi$
$878$	0.0815574	−	0.357326i	0.00275243	−	0.0120592i
$879$		0			0
$880$	3.31595	−	4.15807i	0.111781	−	0.140169i
$881$	12.9540	+	56.7554i	0.436433	+	1.91214i	0.409051	+	0.912511i	$0.365860\pi$
$881$	12.9540	+	56.7554i	0.436433	+	1.91214i	0.0273816	+	0.999625i	$0.491283\pi$
$882$		0			0
$883$	9.60627	+	42.0878i	0.323277	+	1.41637i	0.831683	+	0.555251i	$0.187378\pi$
$883$	9.60627	+	42.0878i	0.323277	+	1.41637i	−0.508406	+	0.861117i	$0.669765\pi$
$884$	0.947321	+	0.456206i	0.0318618	+	0.0153439i
$885$		0			0
$886$	−0.476979	−	2.08978i	−0.0160244	−	0.0702076i
$887$	−14.5588			−0.488836			−0.244418	−	0.969670i	$-0.578597\pi$
$887$	−14.5588			−0.488836			−0.244418	+	0.969670i	$0.578597\pi$
$888$		0			0
$889$	−21.3899	+	26.8221i	−0.717396	+	0.899586i
$890$	−3.06353	+	13.4222i	−0.102690	+	0.449914i
$891$		0			0
$892$	1.85433	+	2.32526i	0.0620876	+	0.0778554i
$893$	−27.5485	−	13.2666i	−0.921874	−	0.443951i
$894$		0			0
$895$	11.4499	−	14.3577i	0.382726	−	0.479924i
$896$	−1.82553	−	2.28915i	−0.0609868	−	0.0764750i
$897$		0			0
$898$	21.1480			0.705718
$899$	−19.2806	−	15.6498i	−0.643044	−	0.521951i
$900$		0			0
$901$	−12.4614	+	6.00107i	−0.415148	+	0.199925i
$902$	−16.3435	−	20.4941i	−0.544180	−	0.682380i
$903$		0			0
$904$	−6.30127	+	3.03453i	−0.209577	+	0.100927i
$905$	−16.2224	−	7.81230i	−0.539251	−	0.259690i
$906$		0			0
$907$	−1.62680	+	7.12746i	−0.0540169	+	0.236663i	−0.994728	−	0.102544i	$-0.967302\pi$
$907$	−1.62680	+	7.12746i	−0.0540169	+	0.236663i	0.940712	+	0.339207i	$0.110159\pi$
$908$	2.02567	−	8.87504i	0.0672242	−	0.294528i
$909$		0			0
$910$	0.929982	+	4.07452i	0.0308286	+	0.135069i
$911$	42.6967			1.41461			0.707303	−	0.706911i	$-0.249912\pi$
$911$	42.6967			1.41461			0.707303	+	0.706911i	$0.249912\pi$
$912$		0			0
$913$	23.0875	+	11.1184i	0.764085	+	0.367964i
$914$	−32.2421	−	15.5270i	−1.06647	−	0.513587i
$915$		0			0
$916$	−0.427881			−0.0141376
$917$	−0.788958	−	3.45665i	−0.0260537	−	0.114149i
$918$		0			0
$919$	7.45917	−	32.6807i	0.246055	−	1.07804i	−0.689341	−	0.724437i	$-0.742100\pi$
$919$	7.45917	−	32.6807i	0.246055	−	1.07804i	0.935396	−	0.353601i	$-0.115043\pi$
$920$	4.10467	−	17.9837i	0.135327	−	0.592906i
$921$		0			0
$922$	−12.9838	−	6.25267i	−0.427599	−	0.205921i
$923$	−10.6021	+	5.10571i	−0.348973	+	0.168057i
$924$		0			0
$925$	6.04227	+	7.57676i	0.198668	+	0.249122i
$926$	25.2066	−	12.1389i	0.828341	−	0.398908i
$927$		0			0
$928$	−10.6788	+	21.6940i	−0.350550	+	0.712140i
$929$	−36.1689			−1.18666			−0.593331	−	0.804959i	$-0.702187\pi$
$929$	−36.1689			−1.18666			−0.593331	+	0.804959i	$0.702187\pi$
$930$		0			0
$931$	32.3844	+	40.6087i	1.06136	+	1.33090i
$932$	8.38195	−	10.5106i	0.274560	−	0.344287i
$933$		0			0
$934$	16.4637	+	7.92848i	0.538708	+	0.259428i
$935$	−2.47584	−	3.10461i	−0.0809687	−	0.101532i
$936$		0			0
$937$	2.77023	−	12.1372i	0.0904995	−	0.396504i	−0.909308	−	0.416124i	$-0.863388\pi$
$937$	2.77023	−	12.1372i	0.0904995	−	0.396504i	0.999808	+	0.0196194i	$0.00624544\pi$
$938$	21.8352	−	27.3805i	0.712945	−	0.894005i
$939$		0			0
$940$	5.26716			0.171796
$941$	−6.98890	−	30.6204i	−0.227832	−	0.998196i	−0.951404	−	0.307947i	$-0.900358\pi$
$941$	−6.98890	−	30.6204i	−0.227832	−	0.998196i	0.723572	−	0.690249i	$-0.242499\pi$
$942$		0			0
$943$	−38.2126	−	18.4022i	−1.24438	−	0.599259i
$944$	3.58630	+	15.7126i	0.116724	+	0.511402i
$945$		0			0
$946$	−5.36598	−	23.5099i	−0.174463	−	0.764372i
$947$	−25.4786	+	31.9492i	−0.827944	+	1.03821i	0.170656	+	0.985331i	$0.445411\pi$
$947$	−25.4786	+	31.9492i	−0.827944	+	1.03821i	−0.998601	+	0.0528789i	$0.983160\pi$
$948$		0			0
$949$	2.84057	−	12.4453i	0.0922088	−	0.403993i
$950$	11.9565	+	14.9929i	0.387919	+	0.486435i
$951$		0			0
$952$	13.7145	−	6.60454i	0.444488	−	0.214054i
$953$	−36.9751	+	46.3654i	−1.19774	+	1.50192i	−0.381342	+	0.924434i	$0.624538\pi$
$953$	−36.9751	+	46.3654i	−1.19774	+	1.50192i	−0.816400	+	0.577487i	$0.804033\pi$
$954$		0			0
$955$	9.78133	−	4.71044i	0.316516	−	0.152426i
$956$	16.7582			0.542000
$957$		0			0
$958$	−0.683241			−0.0220745
$959$	−13.9616	+	6.72353i	−0.450842	+	0.217114i
$960$		0			0
$961$	−6.07024	+	7.61184i	−0.195814	+	0.245543i
$962$	−2.31228	+	1.11354i	−0.0745509	+	0.0359018i
$963$		0			0
$964$	14.5501	+	18.2453i	0.468627	+	0.587640i
$965$	1.74525	−	7.64645i	0.0561816	−	0.246148i
$966$		0			0
$967$	16.0446	−	20.1192i	0.515958	−	0.646991i	−0.453787	−	0.891110i	$-0.649927\pi$
$967$	16.0446	−	20.1192i	0.515958	−	0.646991i	0.969745	+	0.244119i	$0.0784987\pi$
$968$	−4.64562	−	20.3538i	−0.149316	−	0.654196i
$969$		0			0
$970$	−3.06917	−	13.4469i	−0.0985450	−	0.431754i
$971$	2.26135	+	1.08901i	0.0725703	+	0.0349480i	0.469817	−	0.882764i	$-0.344320\pi$
$971$	2.26135	+	1.08901i	0.0725703	+	0.0349480i	−0.397247	+	0.917712i	$0.630034\pi$
$972$		0			0
$973$	12.3264	+	54.0054i	0.395166	+	1.73133i
$974$	−22.6037			−0.724270
$975$		0			0
$976$	0.837168	−	1.04978i	0.0267971	−	0.0336025i
$977$	0.287421	−	1.25928i	0.00919542	−	0.0402878i	−0.970122	−	0.242617i	$-0.921994\pi$
$977$	0.287421	−	1.25928i	0.00919542	−	0.0402878i	0.979317	+	0.202330i	$0.0648512\pi$
$978$		0			0
$979$	40.9949	+	51.4060i	1.31020	+	1.64294i
$980$	−8.06130	−	3.88212i	−0.257509	−	0.124010i
$981$		0			0
$982$	7.50580	−	9.41198i	0.239520	−	0.300348i
$983$	−16.0344	−	20.1065i	−0.511418	−	0.641298i	0.457344	−	0.889290i	$-0.348801\pi$
$983$	−16.0344	−	20.1065i	−0.511418	−	0.641298i	−0.968762	+	0.247992i	$0.920229\pi$
$984$		0			0
$985$	−13.9211			−0.443563
$986$	−5.03717	−	4.08860i	−0.160416	−	0.130208i
$987$		0			0
$988$	3.49882	−	1.68494i	0.111312	−	0.0536052i
$989$	−24.3270	−	30.5051i	−0.773553	−	0.970005i
$990$		0			0
$991$	−9.91307	+	4.77388i	−0.314899	+	0.151647i	−0.584657	−	0.811281i	$-0.698771\pi$
$991$	−9.91307	+	4.77388i	−0.314899	+	0.151647i	0.269758	+	0.962928i	$0.413056\pi$
$992$	−18.6547	−	8.98363i	−0.592287	−	0.285231i
$993$		0			0
$994$	−11.4605	+	50.2118i	−0.363506	+	1.59262i
$995$	2.42457	−	10.6227i	0.0768641	−	0.336763i
$996$		0			0
$997$	−7.17568	−	31.4387i	−0.227256	−	0.995674i	−0.951866	−	0.306514i	$-0.900837\pi$
$997$	−7.17568	−	31.4387i	−0.227256	−	0.995674i	0.724610	−	0.689159i	$-0.242020\pi$
$998$	8.80669			0.278771
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.k.f.136.7	yes	60
3.2	odd	2	inner	783.2.k.f.136.4	✓	60
29.16	even	7	inner	783.2.k.f.190.7	yes	60
87.74	odd	14	inner	783.2.k.f.190.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
783.2.k.f.136.4	✓	60	3.2	odd	2	inner
783.2.k.f.136.7	yes	60	1.1	even	1	trivial
783.2.k.f.190.4	yes	60	87.74	odd	14	inner
783.2.k.f.190.7	yes	60	29.16	even	7	inner

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:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.959163 - 0.461908i) q^{2} +(-0.540346 + 0.677573i) q^{4} +(0.748493 - 0.360455i) q^{5} +(-2.74812 - 3.44603i) q^{7} +(-0.679091 + 2.97529i) q^{8} +(0.551429 - 0.691470i) q^{10} +(-0.939896 - 4.11795i) q^{11} +(-0.238566 - 1.04523i) q^{13} +(-4.22764 - 2.03592i) q^{14} +(0.337258 + 1.47763i) q^{16} +1.13164 q^{17} +(2.60592 - 3.26772i) q^{19} +(-0.160211 + 0.701929i) q^{20} +(-2.80363 - 3.51564i) q^{22} +(-6.55514 - 3.15679i) q^{23} +(-2.68714 + 3.36956i) q^{25} +(-0.711623 - 0.892346i) q^{26} +3.81987 q^{28} +(-2.29459 - 4.87184i) q^{29} +(4.15464 - 2.00077i) q^{31} +(-2.79953 - 3.51049i) q^{32} +(1.08542 - 0.522712i) q^{34} +(-3.29908 - 1.58875i) q^{35} +(0.500358 - 2.19221i) q^{37} +(0.990113 - 4.33797i) q^{38} +(0.564164 + 2.47176i) q^{40} +5.82942 q^{41} +(4.83166 + 2.32680i) q^{43} +(3.29808 + 1.58827i) q^{44} -7.74560 q^{46} +(-1.62790 - 7.13229i) q^{47} +(-2.76532 + 12.1157i) q^{49} +(-1.02097 + 4.47317i) q^{50} +(0.837125 + 0.403138i) q^{52} +(-11.0118 + 5.30301i) q^{53} +(-2.18784 - 2.74347i) q^{55} +(12.1192 - 5.83628i) q^{56} +(-4.45123 - 3.61300i) q^{58} +10.6337 q^{59} +(-0.552358 - 0.692635i) q^{61} +(3.06080 - 3.83812i) q^{62} +(-7.03779 - 3.38922i) q^{64} +(-0.555322 - 0.696352i) q^{65} +(-1.66078 + 7.27633i) q^{67} +(-0.611475 + 0.766765i) q^{68} -3.89822 q^{70} +(-2.44240 - 10.7008i) q^{71} +(10.7277 + 5.16618i) q^{73} +(-0.532676 - 2.33381i) q^{74} +(0.806018 + 3.53140i) q^{76} +(-11.6076 + 14.5555i) q^{77} +(-0.463072 + 2.02885i) q^{79} +(0.785053 + 0.984426i) q^{80} +(5.59136 - 2.69266i) q^{82} +(-3.78257 + 4.74320i) q^{83} +(0.847021 - 0.407904i) q^{85} +5.70912 q^{86} +12.8904 q^{88} +(-14.0249 + 6.75406i) q^{89} +(-2.94627 + 3.69451i) q^{91} +(5.68100 - 2.73583i) q^{92} +(-4.85588 - 6.08909i) q^{94} +(0.772645 - 3.38518i) q^{95} +(9.72341 - 12.1928i) q^{97} +(2.94394 + 12.8982i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 10 q^{4} + 4 q^{7} + 4 q^{10} - 24 q^{13} - 26 q^{16} + 4 q^{19} - 8 q^{22} - 16 q^{25} + 112 q^{28} - 4 q^{31} + 26 q^{34} - 18 q^{37} - 78 q^{40} - 8 q^{43} + 72 q^{46} + 14 q^{49} - 12 q^{52}+ \cdots + 8 q^{97}+O(q^{100}) \) 60 * q - 10 * q^4 + 4 * q^7 + 4 * q^10 - 24 * q^13 - 26 * q^16 + 4 * q^19 - 8 * q^22 - 16 * q^25 + 112 * q^28 - 4 * q^31 + 26 * q^34 - 18 * q^37 - 78 * q^40 - 8 * q^43 + 72 * q^46 + 14 * q^49 - 12 * q^52 + 24 * q^55 - 162 * q^58 - 10 * q^61 + 116 * q^64 + 60 * q^67 - 12 * q^70 + 66 * q^73 - 120 * q^76 + 46 * q^79 - 84 * q^82 - 122 * q^85 - 152 * q^88 - 30 * q^91 - 68 * q^94 + 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more