LMFDB - Embedded newform 1386.2.bu.b.827.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			827.8
Character	$\chi$	$=$	1386.827
Dual form			1386.2.bu.b.1205.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(1.69500 - 0.550738i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(1.69500 - 0.550738i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +1.78222i q^{10} +(-2.97067 - 1.47483i) q^{11} +(0.352326 + 0.114478i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.79294 + 5.51810i) q^{17} +(-0.665367 - 0.915799i) q^{19} +(-1.69500 - 0.550738i) q^{20} +(2.32064 - 2.36952i) q^{22} +5.35130i q^{23} +(-1.47538 + 1.07193i) q^{25} +(-0.217749 + 0.299706i) q^{26} +(0.951057 - 0.309017i) q^{28} +(6.33815 + 4.60493i) q^{29} +(0.927578 - 2.85479i) q^{31} -1.00000 q^{32} -5.80207 q^{34} +(-0.550738 + 1.69500i) q^{35} +(7.14769 + 5.19310i) q^{37} +(1.07659 - 0.349804i) q^{38} +(1.04757 - 1.44185i) q^{40} +(-4.50822 + 3.27542i) q^{41} -8.57919i q^{43} +(1.53643 + 2.93928i) q^{44} +(-5.08938 - 1.65364i) q^{46} +(7.43328 + 10.2310i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-0.563546 - 1.73442i) q^{50} +(-0.217749 - 0.299706i) q^{52} +(11.8103 + 3.83741i) q^{53} +(-5.84752 - 0.863780i) q^{55} +1.00000i q^{56} +(-6.33815 + 4.60493i) q^{58} +(8.16442 - 11.2374i) q^{59} +(-7.20026 + 2.33951i) q^{61} +(2.42843 + 1.76436i) q^{62} +(0.309017 - 0.951057i) q^{64} +0.660238 q^{65} +5.02927 q^{67} +(1.79294 - 5.51810i) q^{68} +(-1.44185 - 1.04757i) q^{70} +(-7.04101 + 2.28776i) q^{71} +(-6.87198 + 9.45847i) q^{73} +(-7.14769 + 5.19310i) q^{74} +1.13199i q^{76} +(2.93928 - 1.53643i) q^{77} +(5.62124 + 1.82645i) q^{79} +(1.04757 + 1.44185i) q^{80} +(-1.72199 - 5.29973i) q^{82} +(2.46347 + 7.58177i) q^{83} +(6.07805 + 8.36572i) q^{85} +(8.15929 + 2.65111i) q^{86} +(-3.27021 + 0.552949i) q^{88} -0.106545i q^{89} +(-0.299706 + 0.217749i) q^{91} +(3.14541 - 4.32929i) q^{92} +(-12.0273 + 3.90791i) q^{94} +(-1.63216 - 1.18583i) q^{95} +(5.52369 - 17.0002i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	$ 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) $ 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.69500	−	0.550738i	0.758026	−	0.246297i	0.0955945	−	0.995420i	$-0.469525\pi$
$5$	1.69500	−	0.550738i	0.758026	−	0.246297i	0.662431	+	0.749123i	$0.269525\pi$
$6$		0			0
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$7$	−0.587785	+	0.809017i	−0.222162	+	0.305780i
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$			1.78222i			0.563589i
$11$	−2.97067	−	1.47483i	−0.895690	−	0.444679i
$11$	−2.97067	−	1.47483i	−0.895690	−	0.444679i
$12$		0			0
$13$	0.352326	+	0.114478i	0.0977175	+	0.0317504i	0.357468	−	0.933925i	$-0.383640\pi$
$13$	0.352326	+	0.114478i	0.0977175	+	0.0317504i	−0.259750	+	0.965676i	$0.583640\pi$
$14$	−0.587785	−	0.809017i	−0.157092	−	0.216219i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	1.79294	+	5.51810i	0.434851	+	1.33834i	0.893239	+	0.449583i	$0.148427\pi$
$17$	1.79294	+	5.51810i	0.434851	+	1.33834i	−0.458387	+	0.888753i	$0.651573\pi$
$18$		0			0
$19$	−0.665367	−	0.915799i	−0.152646	−	0.210099i	0.725845	−	0.687858i	$-0.241449\pi$
$19$	−0.665367	−	0.915799i	−0.152646	−	0.210099i	−0.878491	+	0.477760i	$0.841449\pi$
$20$	−1.69500	−	0.550738i	−0.379013	−	0.123149i
$21$		0			0
$22$	2.32064	−	2.36952i	0.494762	−	0.505184i
$23$			5.35130i			1.11582i	0.829901	+	0.557911i	$0.188397\pi$
$23$			5.35130i			1.11582i	−0.829901	+	0.557911i	$0.811603\pi$
$24$		0			0
$25$	−1.47538	+	1.07193i	−0.295077	+	0.214386i
$26$	−0.217749	+	0.299706i	−0.0427041	+	0.0587772i
$27$		0			0
$28$	0.951057	−	0.309017i	0.179733	−	0.0583987i
$29$	6.33815	+	4.60493i	1.17696	+	0.855115i	0.991826	−	0.127598i	$-0.0407267\pi$
$29$	6.33815	+	4.60493i	1.17696	+	0.855115i	0.185138	+	0.982712i	$0.440727\pi$
$30$		0			0
$31$	0.927578	−	2.85479i	0.166598	−	0.512735i	−0.832553	−	0.553946i	$-0.813121\pi$
$31$	0.927578	−	2.85479i	0.166598	−	0.512735i	0.999150	+	0.0412105i	$0.0131214\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	−5.80207			−0.995047
$35$	−0.550738	+	1.69500i	−0.0930917	+	0.286507i
$36$		0			0
$37$	7.14769	+	5.19310i	1.17507	+	0.853740i	0.991607	−	0.129286i	$-0.0412686\pi$
$37$	7.14769	+	5.19310i	1.17507	+	0.853740i	0.183465	+	0.983026i	$0.441269\pi$
$38$	1.07659	−	0.349804i	0.174645	−	0.0567457i
$39$		0			0
$40$	1.04757	−	1.44185i	0.165635	−	0.227977i
$41$	−4.50822	+	3.27542i	−0.704066	+	0.511534i	−0.881254	−	0.472643i	$-0.843300\pi$
$41$	−4.50822	+	3.27542i	−0.704066	+	0.511534i	0.177188	+	0.984177i	$0.443300\pi$
$42$		0			0
$43$		−	8.57919i		−	1.30831i	−0.756359	−	0.654157i	$-0.773024\pi$
$43$		−	8.57919i		−	1.30831i	0.756359	−	0.654157i	$-0.226976\pi$
$44$	1.53643	+	2.93928i	0.231626	+	0.443113i
$45$		0			0
$46$	−5.08938	−	1.65364i	−0.750389	−	0.243816i
$47$	7.43328	+	10.2310i	1.08426	+	1.49235i	0.854748	+	0.519043i	$0.173712\pi$
$47$	7.43328	+	10.2310i	1.08426	+	1.49235i	0.229508	+	0.973307i	$0.426288\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$	−0.563546	−	1.73442i	−0.0796975	−	0.245284i
$51$		0			0
$52$	−0.217749	−	0.299706i	−0.0301964	−	0.0415618i
$53$	11.8103	+	3.83741i	1.62228	+	0.527109i	0.972477	−	0.232997i	$-0.0748533\pi$
$53$	11.8103	+	3.83741i	1.62228	+	0.527109i	0.649798	+	0.760107i	$0.274853\pi$
$54$		0			0
$55$	−5.84752	−	0.863780i	−0.788479	−	0.116472i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−6.33815	+	4.60493i	−0.832239	+	0.604657i
$59$	8.16442	−	11.2374i	1.06292	−	1.46298i	0.185869	−	0.982574i	$-0.440490\pi$
$59$	8.16442	−	11.2374i	1.06292	−	1.46298i	0.877047	−	0.480404i	$-0.159510\pi$
$60$		0			0
$61$	−7.20026	+	2.33951i	−0.921899	+	0.299543i	−0.731245	−	0.682114i	$-0.761061\pi$
$61$	−7.20026	+	2.33951i	−0.921899	+	0.299543i	−0.190653	+	0.981657i	$0.561061\pi$
$62$	2.42843	+	1.76436i	0.308411	+	0.224074i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.660238			0.0818924
$66$		0			0
$67$	5.02927			0.614423			0.307211	−	0.951641i	$-0.400604\pi$
$67$	5.02927			0.614423			0.307211	+	0.951641i	$0.400604\pi$
$68$	1.79294	−	5.51810i	0.217426	−	0.669168i
$69$		0			0
$70$	−1.44185	−	1.04757i	−0.172334	−	0.125208i
$71$	−7.04101	+	2.28776i	−0.835614	+	0.271508i	−0.695408	−	0.718615i	$-0.744776\pi$
$71$	−7.04101	+	2.28776i	−0.835614	+	0.271508i	−0.140206	+	0.990122i	$0.544776\pi$
$72$		0			0
$73$	−6.87198	+	9.45847i	−0.804304	+	1.10703i	0.187873	+	0.982193i	$0.439841\pi$
$73$	−6.87198	+	9.45847i	−0.804304	+	1.10703i	−0.992177	+	0.124837i	$0.960159\pi$
$74$	−7.14769	+	5.19310i	−0.830902	+	0.603685i
$75$		0			0
$76$			1.13199i			0.129848i
$77$	2.93928	−	1.53643i	0.334962	−	0.175093i
$78$		0			0
$79$	5.62124	+	1.82645i	0.632439	+	0.205492i	0.607655	−	0.794201i	$-0.292110\pi$
$79$	5.62124	+	1.82645i	0.632439	+	0.205492i	0.0247838	+	0.999693i	$0.492110\pi$
$80$	1.04757	+	1.44185i	0.117121	+	0.161204i
$81$		0			0
$82$	−1.72199	−	5.29973i	−0.190162	−	0.585258i
$83$	2.46347	+	7.58177i	0.270400	+	0.832207i	0.990400	+	0.138232i	$0.0441421\pi$
$83$	2.46347	+	7.58177i	0.270400	+	0.832207i	−0.719999	+	0.693975i	$0.755858\pi$
$84$		0			0
$85$	6.07805	+	8.36572i	0.659257	+	0.907389i
$86$	8.15929	+	2.65111i	0.879839	+	0.285877i
$87$		0			0
$88$	−3.27021	+	0.552949i	−0.348605	+	0.0589445i
$89$		−	0.106545i		−	0.0112937i	−0.999984	−	0.00564686i	$-0.998203\pi$
$89$		−	0.106545i		−	0.0112937i	0.999984	−	0.00564686i	$-0.00179746\pi$
$90$		0			0
$91$	−0.299706	+	0.217749i	−0.0314177	+	0.0228263i
$92$	3.14541	−	4.32929i	0.327932	−	0.451360i
$93$		0			0
$94$	−12.0273	+	3.90791i	−1.24052	+	0.403070i
$95$	−1.63216	−	1.18583i	−0.167456	−	0.121664i
$96$		0			0
$97$	5.52369	−	17.0002i	0.560846	−	1.72611i	−0.119136	−	0.992878i	$-0.538012\pi$
$97$	5.52369	−	17.0002i	0.560846	−	1.72611i	0.679982	−	0.733229i	$-0.261988\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	1.82367			0.182367
$101$	−5.25103	+	16.1610i	−0.522497	+	1.60808i	0.246717	+	0.969088i	$0.420648\pi$
$101$	−5.25103	+	16.1610i	−0.522497	+	1.60808i	−0.769213	+	0.638992i	$0.779352\pi$
$102$		0			0
$103$	−5.83607	−	4.24016i	−0.575045	−	0.417795i	0.261889	−	0.965098i	$-0.415655\pi$
$103$	−5.83607	−	4.24016i	−0.575045	−	0.417795i	−0.836935	+	0.547303i	$0.815655\pi$
$104$	0.352326	−	0.114478i	0.0345484	−	0.0112254i
$105$		0			0
$106$	−7.29920	+	10.0465i	−0.708961	+	0.975800i
$107$	−1.57834	+	1.14673i	−0.152584	+	0.110859i	−0.661458	−	0.749982i	$-0.730062\pi$
$107$	−1.57834	+	1.14673i	−0.152584	+	0.110859i	0.508874	+	0.860841i	$0.330062\pi$
$108$		0			0
$109$			1.88659i			0.180703i	0.995910	+	0.0903515i	$0.0287990\pi$
$109$			1.88659i			0.180703i	−0.995910	+	0.0903515i	$0.971201\pi$
$110$	2.62849	−	5.29440i	0.250616	−	0.504801i
$111$		0			0
$112$	−0.951057	−	0.309017i	−0.0898664	−	0.0291994i
$113$	−1.80181	−	2.47998i	−0.169500	−	0.233297i	0.715813	−	0.698292i	$-0.246056\pi$
$113$	−1.80181	−	2.47998i	−0.169500	−	0.233297i	−0.885313	+	0.464995i	$0.846056\pi$
$114$		0			0
$115$	2.94716	+	9.07043i	0.274824	+	0.845822i
$116$	−2.42096	−	7.45094i	−0.224780	−	0.691802i
$117$		0			0
$118$	8.16442	+	11.2374i	0.751595	+	1.03448i
$119$	−5.51810	−	1.79294i	−0.505843	−	0.164358i
$120$		0			0
$121$	6.64973	+	8.76248i	0.604521	+	0.796589i
$122$		−	7.57080i		−	0.685428i
$123$		0			0
$124$	−2.42843	+	1.76436i	−0.218079	+	0.158444i
$125$	−7.14825	+	9.83872i	−0.639359	+	0.880002i
$126$		0			0
$127$	−5.75804	+	1.87090i	−0.510944	+	0.166016i	−0.553131	−	0.833094i	$-0.686567\pi$
$127$	−5.75804	+	1.87090i	−0.510944	+	0.166016i	0.0421877	+	0.999110i	$0.486567\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−0.204025	+	0.627923i	−0.0178941	+	0.0550725i
$131$	8.73573			0.763245			0.381622	−	0.924318i	$-0.375366\pi$
$131$	8.73573			0.763245			0.381622	+	0.924318i	$0.375366\pi$
$132$		0			0
$133$	1.13199			0.0981560
$134$	−1.55413	+	4.78312i	−0.134256	+	0.413198i
$135$		0			0
$136$	4.69397	+	3.41037i	0.402505	+	0.292437i
$137$	−20.7708	+	6.74884i	−1.77457	+	0.576592i	−0.998535	−	0.0541009i	$-0.982771\pi$
$137$	−20.7708	+	6.74884i	−1.77457	+	0.576592i	−0.776032	+	0.630693i	$0.782771\pi$
$138$		0			0
$139$	1.12840	−	1.55311i	0.0957098	−	0.131733i	−0.758476	−	0.651701i	$-0.774056\pi$
$139$	1.12840	−	1.55311i	0.0957098	−	0.131733i	0.854186	+	0.519967i	$0.174056\pi$
$140$	1.44185	−	1.04757i	0.121859	−	0.0885354i
$141$		0			0
$142$		−	7.40336i		−	0.621276i
$143$	−0.877807	−	0.859696i	−0.0734059	−	0.0718914i
$144$		0			0
$145$	13.2792	+	4.31469i	1.10278	+	0.358315i
$146$	−6.87198	−	9.45847i	−0.568729	−	0.782789i
$147$		0			0
$148$	−2.73017	−	8.40261i	−0.224419	−	0.690690i
$149$	0.827308	+	2.54619i	0.0677757	+	0.208592i	0.979208	−	0.202857i	$-0.0650227\pi$
$149$	0.827308	+	2.54619i	0.0677757	+	0.208592i	−0.911433	+	0.411449i	$0.865023\pi$
$150$		0			0
$151$	−7.15559	−	9.84882i	−0.582313	−	0.801486i	0.411633	−	0.911350i	$-0.364958\pi$
$151$	−7.15559	−	9.84882i	−0.582313	−	0.801486i	−0.993947	+	0.109864i	$0.964958\pi$
$152$	−1.07659	−	0.349804i	−0.0873227	−	0.0283729i
$153$		0			0
$154$	0.552949	+	3.27021i	0.0445579	+	0.263521i
$155$		−	5.34971i		−	0.429699i
$156$		0			0
$157$	−0.982485	+	0.713817i	−0.0784108	+	0.0569688i	−0.626300	−	0.779582i	$-0.715432\pi$
$157$	−0.982485	+	0.713817i	−0.0784108	+	0.0569688i	0.547889	+	0.836551i	$0.315432\pi$
$158$	−3.47412	+	4.78171i	−0.276386	+	0.380413i
$159$		0			0
$160$	−1.69500	+	0.550738i	−0.134001	+	0.0435396i
$161$	−4.32929	−	3.14541i	−0.341196	−	0.247893i
$162$		0			0
$163$	−6.26261	+	19.2743i	−0.490525	+	1.50968i	0.333291	+	0.942824i	$0.391841\pi$
$163$	−6.26261	+	19.2743i	−0.490525	+	1.50968i	−0.823816	+	0.566857i	$0.808159\pi$
$164$	5.57247			0.435137
$165$		0			0
$166$	−7.97194			−0.618743
$167$	0.365407	−	1.12461i	0.0282760	−	0.0870246i	−0.935923	−	0.352206i	$-0.885432\pi$
$167$	0.365407	−	1.12461i	0.0282760	−	0.0870246i	0.964199	+	0.265181i	$0.0854317\pi$
$168$		0			0
$169$	−10.4062	−	7.56054i	−0.800476	−	0.581580i
$170$	−9.83449	+	3.19542i	−0.754271	+	0.245077i
$171$		0			0
$172$	−5.04272	+	6.94071i	−0.384504	+	0.529224i
$173$	8.68422	−	6.30946i	0.660249	−	0.479699i	−0.206498	−	0.978447i	$-0.566207\pi$
$173$	8.68422	−	6.30946i	0.660249	−	0.479699i	0.866747	+	0.498748i	$0.166207\pi$
$174$		0			0
$175$		−	1.82367i		−	0.137857i
$176$	0.484664	−	3.28102i	0.0365329	−	0.247316i
$177$		0			0
$178$	0.101330	+	0.0329242i	0.00759501	+	0.00246777i
$179$	−13.4072	−	18.4535i	−1.00210	−	1.37928i	−0.924025	−	0.382332i	$-0.875121\pi$
$179$	−13.4072	−	18.4535i	−1.00210	−	1.37928i	−0.0780795	−	0.996947i	$-0.524879\pi$
$180$		0			0
$181$	−1.43602	−	4.41962i	−0.106739	−	0.328508i	0.883396	−	0.468627i	$-0.155251\pi$
$181$	−1.43602	−	4.41962i	−0.106739	−	0.328508i	−0.990135	+	0.140120i	$0.955251\pi$
$182$	−0.114478	−	0.352326i	−0.00848564	−	0.0261161i
$183$		0			0
$184$	3.14541	+	4.32929i	0.231883	+	0.319159i
$185$	14.9753	+	4.86578i	1.10101	+	0.357739i
$186$		0			0
$187$	2.81205	−	19.0367i	0.205638	−	1.39210i
$188$		−	12.6463i		−	0.922323i
$189$		0			0
$190$	1.63216	−	1.18583i	0.118409	−	0.0860294i
$191$	10.1786	−	14.0097i	0.736498	−	1.01370i	−0.262314	−	0.964983i	$-0.584486\pi$
$191$	10.1786	−	14.0097i	0.736498	−	1.01370i	0.998812	−	0.0487206i	$-0.0155144\pi$
$192$		0			0
$193$	11.1615	−	3.62659i	0.803422	−	0.261048i	0.121613	−	0.992578i	$-0.461193\pi$
$193$	11.1615	−	3.62659i	0.803422	−	0.261048i	0.681809	+	0.731530i	$0.261193\pi$
$194$	14.4612	+	10.5067i	1.03826	+	0.754336i
$195$		0			0
$196$	−0.309017	+	0.951057i	−0.0220726	+	0.0679326i
$197$	−25.8087			−1.83879			−0.919395	−	0.393335i	$-0.871321\pi$
$197$	−25.8087			−1.83879			−0.919395	+	0.393335i	$0.871321\pi$
$198$		0			0
$199$	0.122125			0.00865722			0.00432861	−	0.999991i	$-0.498622\pi$
$199$	0.122125			0.00865722			0.00432861	+	0.999991i	$0.498622\pi$
$200$	−0.563546	+	1.73442i	−0.0398487	+	0.122642i
$201$		0			0
$202$	−13.7474	−	9.98805i	−0.967262	−	0.702757i
$203$	−7.45094	+	2.42096i	−0.522953	+	0.169918i
$204$		0			0
$205$	−5.83753	+	8.03467i	−0.407711	+	0.561165i
$206$	5.83607	−	4.24016i	0.406618	−	0.295426i
$207$		0			0
$208$			0.370457i			0.0256866i
$209$	0.625932	+	3.70184i	0.0432966	+	0.256062i
$210$		0			0
$211$	−1.93171	−	0.627650i	−0.132984	−	0.0432092i	0.241769	−	0.970334i	$-0.422272\pi$
$211$	−1.93171	−	0.627650i	−0.132984	−	0.0432092i	−0.374753	+	0.927125i	$0.622272\pi$
$212$	−7.29920	−	10.0465i	−0.501311	−	0.689995i
$213$		0			0
$214$	−0.602872	−	1.85545i	−0.0412115	−	0.126836i
$215$	−4.72488	−	14.5417i	−0.322234	−	0.991735i
$216$		0			0
$217$	1.76436	+	2.42843i	0.119772	+	0.164853i
$218$	−1.79426	−	0.582990i	−0.121522	−	0.0394851i
$219$		0			0
$220$	4.22302	+	4.13590i	0.284716	+	0.278842i
$221$			2.14942i			0.144586i
$222$		0			0
$223$	15.8622	−	11.5246i	1.06221	−	0.771744i	0.0877172	−	0.996145i	$-0.472043\pi$
$223$	15.8622	−	11.5246i	1.06221	−	0.771744i	0.974497	+	0.224402i	$0.0720428\pi$
$224$	0.587785	−	0.809017i	0.0392731	−	0.0540547i
$225$		0			0
$226$	2.91539	−	0.947268i	0.193929	−	0.0630113i
$227$	12.0385	+	8.74651i	0.799026	+	0.580526i	0.910628	−	0.413227i	$-0.135598\pi$
$227$	12.0385	+	8.74651i	0.799026	+	0.580526i	−0.111603	+	0.993753i	$0.535598\pi$
$228$		0			0
$229$	4.54673	−	13.9934i	0.300456	−	0.924709i	−0.680878	−	0.732397i	$-0.738401\pi$
$229$	4.54673	−	13.9934i	0.300456	−	0.924709i	0.981334	−	0.192312i	$-0.0615986\pi$
$230$	−9.53721			−0.628865
$231$		0			0
$232$	7.83438			0.514352
$233$	−0.173535	+	0.534085i	−0.0113686	+	0.0349890i	−0.956580	−	0.291470i	$-0.905856\pi$
$233$	−0.173535	+	0.534085i	−0.0113686	+	0.0349890i	0.945211	+	0.326459i	$0.105856\pi$
$234$		0			0
$235$	18.2340	+	13.2478i	1.18946	+	0.864190i
$236$	−13.2103	+	4.29229i	−0.859917	+	0.279404i
$237$		0			0
$238$	3.41037	−	4.69397i	0.221062	−	0.304265i
$239$	−0.963848	+	0.700276i	−0.0623461	+	0.0452971i	−0.618522	−	0.785768i	$-0.712268\pi$
$239$	−0.963848	+	0.700276i	−0.0623461	+	0.0452971i	0.556176	+	0.831065i	$0.312268\pi$
$240$		0			0
$241$			7.31634i			0.471287i	0.971840	+	0.235644i	$0.0757198\pi$
$241$			7.31634i			0.471287i	−0.971840	+	0.235644i	$0.924280\pi$
$242$	−10.3885	+	3.61651i	−0.667798	+	0.232478i
$243$		0			0
$244$	7.20026	+	2.33951i	0.460949	+	0.149772i
$245$	−1.04757	−	1.44185i	−0.0669265	−	0.0921164i
$246$		0			0
$247$	−0.129587	−	0.398829i	−0.00824545	−	0.0253769i
$248$	−0.927578	−	2.85479i	−0.0589012	−	0.181279i
$249$		0			0
$250$	−7.14825	−	9.83872i	−0.452095	−	0.622255i
$251$	1.52861	+	0.496676i	0.0964850	+	0.0313499i	0.356862	−	0.934157i	$-0.383847\pi$
$251$	1.52861	+	0.496676i	0.0964850	+	0.0313499i	−0.260377	+	0.965507i	$0.583847\pi$
$252$		0			0
$253$	7.89227	−	15.8969i	0.496183	−	0.999431i
$254$		−	6.05436i		−	0.379885i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	15.0119	−	20.6621i	0.936417	−	1.28887i	−0.0208869	−	0.999782i	$-0.506649\pi$
$257$	15.0119	−	20.6621i	0.936417	−	1.28887i	0.957303	−	0.289085i	$-0.0933510\pi$
$258$		0			0
$259$	−8.40261	+	2.73017i	−0.522113	+	0.169645i
$260$	−0.534144	−	0.388078i	−0.0331262	−	0.0240676i
$261$		0			0
$262$	−2.69949	+	8.30818i	−0.166775	+	0.513281i
$263$	4.42392			0.272791			0.136395	−	0.990654i	$-0.456448\pi$
$263$	4.42392			0.272791			0.136395	+	0.990654i	$0.456448\pi$
$264$		0			0
$265$	22.1319			1.35955
$266$	−0.349804	+	1.07659i	−0.0214479	+	0.0660098i
$267$		0			0
$268$	−4.06876	−	2.95613i	−0.248539	−	0.180574i
$269$	19.7011	−	6.40129i	1.20120	−	0.390293i	0.360997	−	0.932567i	$-0.382436\pi$
$269$	19.7011	−	6.40129i	1.20120	−	0.390293i	0.840202	+	0.542274i	$0.182436\pi$
$270$		0			0
$271$	−11.8239	+	16.2742i	−0.718252	+	0.988589i	0.281328	+	0.959612i	$0.409225\pi$
$271$	−11.8239	+	16.2742i	−0.718252	+	0.988589i	−0.999580	+	0.0289777i	$0.990775\pi$
$272$	−4.69397	+	3.41037i	−0.284614	+	0.206784i
$273$		0			0
$274$		−	21.8397i		−	1.31938i
$275$	5.96379	−	1.00840i	0.359630	−	0.0608087i
$276$		0			0
$277$	18.6799	+	6.06945i	1.12236	+	0.364678i	0.810669	−	0.585504i	$-0.199104\pi$
$277$	18.6799	+	6.06945i	1.12236	+	0.364678i	0.311694	+	0.950182i	$0.399104\pi$
$278$	1.12840	+	1.55311i	0.0676770	+	0.0931495i
$279$		0			0
$280$	0.550738	+	1.69500i	0.0329129	+	0.101295i
$281$	−1.03878	−	3.19705i	−0.0619687	−	0.190720i	0.915279	−	0.402820i	$-0.131970\pi$
$281$	−1.03878	−	3.19705i	−0.0619687	−	0.190720i	−0.977248	+	0.212100i	$0.931970\pi$
$282$		0			0
$283$	9.20235	+	12.6660i	0.547023	+	0.752913i	0.989605	−	0.143816i	$-0.0459372\pi$
$283$	9.20235	+	12.6660i	0.547023	+	0.752913i	−0.442581	+	0.896728i	$0.645937\pi$
$284$	7.04101	+	2.28776i	0.417807	+	0.135754i
$285$		0			0
$286$	1.08888	−	0.569183i	0.0643867	−	0.0336565i
$287$		−	5.57247i		−	0.328932i
$288$		0			0
$289$	−13.4815	+	9.79487i	−0.793028	+	0.576169i
$290$	−8.20703	+	11.2960i	−0.481933	+	0.663324i
$291$		0			0
$292$	11.1191	−	3.61281i	0.650696	−	0.211424i
$293$	−13.0898	−	9.51033i	−0.764717	−	0.555599i	0.135637	−	0.990759i	$-0.456692\pi$
$293$	−13.0898	−	9.51033i	−0.764717	−	0.555599i	−0.900353	+	0.435159i	$0.856692\pi$
$294$		0			0
$295$	7.64982	−	23.5437i	0.445390	−	1.37077i
$296$	8.83503			0.513525
$297$		0			0
$298$	−2.67722			−0.155087
$299$	−0.612603	+	1.88540i	−0.0354277	+	0.109035i
$300$		0			0
$301$	6.94071	+	5.04272i	0.400056	+	0.290658i
$302$	11.5780	−	3.76191i	0.666238	−	0.216474i
$303$		0			0
$304$	0.665367	−	0.915799i	0.0381614	−	0.0525247i
$305$	−10.9160	+	7.93091i	−0.625046	+	0.454123i
$306$		0			0
$307$		−	27.0080i		−	1.54143i	−0.637180	−	0.770715i	$-0.719899\pi$
$307$		−	27.0080i		−	1.54143i	0.637180	−	0.770715i	$-0.280101\pi$
$308$	−3.28102	−	0.484664i	−0.186954	−	0.0276163i
$309$		0			0
$310$	5.08788	+	1.65315i	0.288972	+	0.0938927i
$311$	−1.70243	−	2.34320i	−0.0965362	−	0.132871i	0.758017	−	0.652235i	$-0.226169\pi$
$311$	−1.70243	−	2.34320i	−0.0965362	−	0.132871i	−0.854553	+	0.519365i	$0.826169\pi$
$312$		0			0
$313$	3.46052	+	10.6504i	0.195600	+	0.601995i	0.999969	+	0.00786500i	$0.00250353\pi$
$313$	3.46052	+	10.6504i	0.195600	+	0.601995i	−0.804369	+	0.594130i	$0.797496\pi$
$314$	−0.375276	−	1.15498i	−0.0211780	−	0.0651793i
$315$		0			0
$316$	−3.47412	−	4.78171i	−0.195434	−	0.268992i
$317$	−0.0890730	−	0.0289416i	−0.00500284	−	0.00162552i	0.306515	−	0.951866i	$-0.400837\pi$
$317$	−0.0890730	−	0.0289416i	−0.00500284	−	0.00162552i	−0.311517	+	0.950240i	$0.600837\pi$
$318$		0			0
$319$	−12.0370	−	23.0274i	−0.673943	−	1.28929i
$320$		−	1.78222i		−	0.0996294i
$321$		0			0
$322$	4.32929	−	3.14541i	0.241262	−	0.175287i
$323$	3.86051	−	5.31353i	0.214804	−	0.295653i
$324$		0			0
$325$	−0.642527	+	0.208770i	−0.0356410	+	0.0115805i
$326$	−16.3957	−	11.9122i	−0.908075	−	0.659755i
$327$		0			0
$328$	−1.72199	+	5.29973i	−0.0950809	+	0.292629i
$329$	−12.6463			−0.697211
$330$		0			0
$331$	−10.9150			−0.599945			−0.299972	−	0.953948i	$-0.596977\pi$
$331$	−10.9150			−0.599945			−0.299972	+	0.953948i	$0.596977\pi$
$332$	2.46347	−	7.58177i	0.135200	−	0.416103i
$333$		0			0
$334$	0.956647	+	0.695045i	0.0523454	+	0.0380312i
$335$	8.52459	−	2.76981i	0.465748	−	0.151331i
$336$		0			0
$337$	7.32956	−	10.0883i	0.399267	−	0.549543i	−0.561293	−	0.827617i	$-0.689696\pi$
$337$	7.32956	−	10.0883i	0.399267	−	0.549543i	0.960560	+	0.278074i	$0.0896960\pi$
$338$	10.4062	−	7.56054i	0.566022	−	0.411239i
$339$		0			0
$340$		−	10.3406i		−	0.560797i
$341$	−6.96587	+	7.11261i	−0.377223	+	0.385169i
$342$		0			0
$343$	0.951057	+	0.309017i	0.0513522	+	0.0166853i
$344$	−5.04272	−	6.94071i	−0.271885	−	0.374218i
$345$		0			0
$346$	3.31708	+	10.2089i	0.178327	+	0.548835i
$347$	−2.46060	−	7.57293i	−0.132092	−	0.406536i	0.863035	−	0.505145i	$-0.168561\pi$
$347$	−2.46060	−	7.57293i	−0.132092	−	0.406536i	−0.995126	+	0.0986083i	$0.968561\pi$
$348$		0			0
$349$	1.25077	+	1.72154i	0.0669524	+	0.0921521i	0.841180	−	0.540755i	$-0.181861\pi$
$349$	1.25077	+	1.72154i	0.0669524	+	0.0921521i	−0.774228	+	0.632907i	$0.781861\pi$
$350$	1.73442	+	0.563546i	0.0927085	+	0.0301228i
$351$		0			0
$352$	2.97067	+	1.47483i	0.158337	+	0.0786089i
$353$		−	8.80028i		−	0.468391i	−0.972189	−	0.234196i	$-0.924754\pi$
$353$		−	8.80028i		−	0.468391i	0.972189	−	0.234196i	$-0.0752457\pi$
$354$		0			0
$355$	−10.6745	+	7.75550i	−0.566545	+	0.411619i
$356$	−0.0626255	+	0.0861966i	−0.00331914	+	0.00456841i
$357$		0			0
$358$	21.6934	−	7.04861i	1.14653	−	0.372530i
$359$	11.9212	+	8.66124i	0.629175	+	0.457123i	0.856114	−	0.516786i	$-0.172872\pi$
$359$	11.9212	+	8.66124i	0.629175	+	0.457123i	−0.226939	+	0.973909i	$0.572872\pi$
$360$		0			0
$361$	5.47535	−	16.8514i	0.288176	−	0.886915i
$362$	4.64706			0.244244
$363$		0			0
$364$	0.370457			0.0194172
$365$	−6.43885	+	19.8167i	−0.337025	+	1.03726i
$366$		0			0
$367$	−16.4551	−	11.9553i	−0.858949	−	0.624063i	0.0686497	−	0.997641i	$-0.478131\pi$
$367$	−16.4551	−	11.9553i	−0.858949	−	0.624063i	−0.927599	+	0.373578i	$0.878131\pi$
$368$	−5.08938	+	1.65364i	−0.265302	+	0.0862020i
$369$		0			0
$370$	−9.25527	+	12.7388i	−0.481158	+	0.662258i
$371$	−10.0465	+	7.29920i	−0.521587	+	0.378955i
$372$		0			0
$373$		−	10.3969i		−	0.538329i	−0.963094	−	0.269165i	$-0.913252\pi$
$373$		−	10.3969i		−	0.538329i	0.963094	−	0.269165i	$-0.0867475\pi$
$374$	17.2360	+	8.55709i	0.891253	+	0.442477i
$375$		0			0
$376$	12.0273	+	3.90791i	0.620261	+	0.201535i
$377$	1.70593	+	2.34801i	0.0878599	+	0.120929i
$378$		0			0
$379$	8.27201	+	25.4586i	0.424905	+	1.30772i	0.903085	+	0.429461i	$0.141296\pi$
$379$	8.27201	+	25.4586i	0.424905	+	1.30772i	−0.478181	+	0.878261i	$0.658704\pi$
$380$	0.623430	+	1.91872i	0.0319813	+	0.0984282i
$381$		0			0
$382$	10.1786	+	14.0097i	0.520783	+	0.716796i
$383$	17.0455	+	5.53842i	0.870985	+	0.283000i	0.710209	−	0.703991i	$-0.248600\pi$
$383$	17.0455	+	5.53842i	0.870985	+	0.283000i	0.160776	+	0.986991i	$0.448600\pi$
$384$		0			0
$385$	4.13590	−	4.22302i	0.210785	−	0.215225i
$386$			11.7359i			0.597341i
$387$		0			0
$388$	−14.4612	+	10.5067i	−0.734157	+	0.533396i
$389$	13.8494	−	19.0620i	0.702190	−	0.966482i	−0.297740	−	0.954647i	$-0.596233\pi$
$389$	13.8494	−	19.0620i	0.702190	−	0.966482i	0.999930	−	0.0118350i	$-0.00376729\pi$
$390$		0			0
$391$	−29.5290	+	9.59454i	−1.49334	+	0.485217i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$		0			0
$394$	7.97531	−	24.5455i	0.401790	−	1.23658i
$395$	10.5339			0.530017
$396$		0			0
$397$	31.6344			1.58768			0.793842	−	0.608124i	$-0.208078\pi$
$397$	31.6344			1.58768			0.793842	+	0.608124i	$0.208078\pi$
$398$	−0.0377387	+	0.116148i	−0.00189167	+	0.00582197i
$399$		0			0
$400$	−1.47538	−	1.07193i	−0.0737692	−	0.0535964i
$401$	−23.1807	+	7.53186i	−1.15759	+	0.376123i	−0.823997	−	0.566595i	$-0.808261\pi$
$401$	−23.1807	+	7.53186i	−1.15759	+	0.376123i	−0.333591	+	0.942718i	$0.608261\pi$
$402$		0			0
$403$	0.653619	−	0.899629i	0.0325591	−	0.0448137i
$404$	13.7474	−	9.98805i	0.683957	−	0.496924i
$405$		0			0
$406$		−	7.83438i		−	0.388814i
$407$	−13.5744	−	25.9686i	−0.672860	−	1.28722i
$408$		0			0
$409$	26.0153	+	8.45289i	1.28637	+	0.417968i	0.870821	−	0.491600i	$-0.163588\pi$
$409$	26.0153	+	8.45289i	1.28637	+	0.417968i	0.415554	+	0.909569i	$0.363588\pi$
$410$	−5.83753	−	8.03467i	−0.288295	−	0.396804i
$411$		0			0
$412$	2.22918	+	6.86072i	0.109824	+	0.338003i
$413$	4.29229	+	13.2103i	0.211210	+	0.650036i
$414$		0			0
$415$	8.35113	+	11.4943i	0.409941	+	0.564235i
$416$	−0.352326	−	0.114478i	−0.0172742	−	0.00561272i
$417$		0			0
$418$	−3.71408	−	0.548635i	−0.181662	−	0.0268346i
$419$		−	36.8160i		−	1.79858i	−0.437354	−	0.899290i	$-0.644084\pi$
$419$		−	36.8160i		−	1.79858i	0.437354	−	0.899290i	$-0.355916\pi$
$420$		0			0
$421$	9.26628	−	6.73234i	0.451611	−	0.328114i	−0.338621	−	0.940923i	$-0.609960\pi$
$421$	9.26628	−	6.73234i	0.451611	−	0.328114i	0.790231	+	0.612809i	$0.209960\pi$
$422$	1.19386	−	1.64321i	0.0581163	−	0.0799902i
$423$		0			0
$424$	11.8103	−	3.83741i	0.573561	−	0.186361i
$425$	−8.56028	−	6.21941i	−0.415235	−	0.301686i
$426$		0			0
$427$	2.33951	−	7.20026i	0.113217	−	0.348445i
$428$	1.95094			0.0943020
$429$		0			0
$430$	15.2900			0.737351
$431$	−6.94038	+	21.3603i	−0.334307	+	1.02889i	0.632756	+	0.774351i	$0.281924\pi$
$431$	−6.94038	+	21.3603i	−0.334307	+	1.02889i	−0.967063	+	0.254539i	$0.918076\pi$
$432$		0			0
$433$	−6.09001	−	4.42465i	−0.292667	−	0.212635i	0.431756	−	0.901990i	$-0.357894\pi$
$433$	−6.09001	−	4.42465i	−0.292667	−	0.212635i	−0.724424	+	0.689355i	$0.757894\pi$
$434$	−2.85479	+	0.927578i	−0.137034	+	0.0445252i
$435$		0			0
$436$	1.10891	−	1.52629i	0.0531073	−	0.0730959i
$437$	4.90071	−	3.56058i	0.234433	−	0.170325i
$438$		0			0
$439$		−	10.1244i		−	0.483211i	−0.970375	−	0.241605i	$-0.922326\pi$
$439$		−	10.1244i		−	0.483211i	0.970375	−	0.241605i	$-0.0776740\pi$
$440$	−5.23846	+	2.73827i	−0.249734	+	0.130542i
$441$		0			0
$442$	−2.04422	−	0.664207i	−0.0972335	−	0.0315931i
$443$	−1.29972	−	1.78892i	−0.0617517	−	0.0849939i	0.777024	−	0.629471i	$-0.216728\pi$
$443$	−1.29972	−	1.78892i	−0.0617517	−	0.0849939i	−0.838776	+	0.544477i	$0.816728\pi$
$444$		0			0
$445$	−0.0586783	−	0.180593i	−0.00278162	−	0.00856093i
$446$	6.05884	+	18.6472i	0.286894	+	0.882969i
$447$		0			0
$448$	0.587785	+	0.809017i	0.0277702	+	0.0382225i
$449$	−4.40210	−	1.43033i	−0.207748	−	0.0675015i	0.203294	−	0.979118i	$-0.434835\pi$
$449$	−4.40210	−	1.43033i	−0.207748	−	0.0675015i	−0.411042	+	0.911616i	$0.634835\pi$
$450$		0			0
$451$	18.2231	−	3.08129i	0.858093	−	0.145092i
$452$			3.06542i			0.144185i
$453$		0			0
$454$	−12.0385	+	8.74651i	−0.564996	+	0.410494i
$455$	−0.388078	+	0.534144i	−0.0181934	+	0.0250410i
$456$		0			0
$457$	−11.8431	+	3.84806i	−0.553997	+	0.180005i	−0.572618	−	0.819822i	$-0.694072\pi$
$457$	−11.8431	+	3.84806i	−0.553997	+	0.180005i	0.0186213	+	0.999827i	$0.494072\pi$
$458$	11.9035	+	8.64839i	0.556213	+	0.404113i
$459$		0			0
$460$	2.94716	−	9.07043i	0.137412	−	0.422911i
$461$	12.5544			0.584717			0.292358	−	0.956309i	$-0.405560\pi$
$461$	12.5544			0.584717			0.292358	+	0.956309i	$0.405560\pi$
$462$		0			0
$463$	−37.8718			−1.76005			−0.880025	−	0.474928i	$-0.842474\pi$
$463$	−37.8718			−1.76005			−0.880025	+	0.474928i	$0.842474\pi$
$464$	−2.42096	+	7.45094i	−0.112390	+	0.345901i
$465$		0			0
$466$	−0.454319	−	0.330082i	−0.0210459	−	0.0152908i
$467$	−34.0020	+	11.0479i	−1.57343	+	0.511237i	−0.960353	−	0.278788i	$-0.910067\pi$
$467$	−34.0020	+	11.0479i	−1.57343	+	0.511237i	−0.613074	+	0.790025i	$0.710067\pi$
$468$		0			0
$469$	−2.95613	+	4.06876i	−0.136501	+	0.187878i
$470$	−18.2340	+	13.2478i	−0.841072	+	0.611075i
$471$		0			0
$472$		−	13.8901i		−	0.639345i
$473$	−12.6529	+	25.4859i	−0.581780	+	1.17184i
$474$		0			0
$475$	1.96334	+	0.637929i	0.0900844	+	0.0292702i
$476$	3.41037	+	4.69397i	0.156314	+	0.215148i
$477$		0			0
$478$	−0.368157	−	1.13307i	−0.0168391	−	0.0518255i
$479$	8.75193	+	26.9357i	0.399886	+	1.23072i	0.925091	+	0.379747i	$0.123989\pi$
$479$	8.75193	+	26.9357i	0.399886	+	1.23072i	−0.525204	+	0.850976i	$0.676011\pi$
$480$		0			0
$481$	1.92382	+	2.64791i	0.0877186	+	0.120734i
$482$	−6.95826	−	2.26087i	−0.316940	−	0.102980i
$483$		0			0
$484$	−0.229285	−	10.9976i	−0.0104221	−	0.499891i
$485$		−	31.8574i		−	1.44657i
$486$		0			0
$487$	−22.9426	+	16.6687i	−1.03963	+	0.755333i	−0.970213	−	0.242255i	$-0.922113\pi$
$487$	−22.9426	+	16.6687i	−1.03963	+	0.755333i	−0.0694139	+	0.997588i	$0.522113\pi$
$488$	−4.45000	+	6.12491i	−0.201442	+	0.277261i
$489$		0			0
$490$	1.69500	−	0.550738i	0.0765721	−	0.0248798i
$491$	−30.8565	−	22.4186i	−1.39254	−	1.01174i	−0.995582	−	0.0938984i	$-0.970067\pi$
$491$	−30.8565	−	22.4186i	−1.39254	−	1.01174i	−0.396954	−	0.917838i	$-0.629933\pi$
$492$		0			0
$493$	−14.0466	+	43.2309i	−0.632625	+	1.94702i
$494$	0.419354			0.0188676
$495$		0			0
$496$	3.00170			0.134781
$497$	2.28776	−	7.04101i	0.102620	−	0.315833i
$498$		0			0
$499$	0.203521	+	0.147866i	0.00911084	+	0.00661941i	0.592331	−	0.805694i	$-0.298208\pi$
$499$	0.203521	+	0.147866i	0.00911084	+	0.00661941i	−0.583221	+	0.812314i	$0.698208\pi$
$500$	11.5661	−	3.75806i	0.517252	−	0.168065i
$501$		0			0
$502$	−0.944733	+	1.30031i	−0.0421655	+	0.0580358i
$503$	12.8649	−	9.34688i	0.573617	−	0.416757i	−0.262801	−	0.964850i	$-0.584646\pi$
$503$	12.8649	−	9.34688i	0.573617	−	0.416757i	0.836417	+	0.548093i	$0.184646\pi$
$504$		0			0
$505$			30.2848i			1.34766i
$506$	12.6800	+	12.4184i	0.563696	+	0.552066i
$507$		0			0
$508$	5.75804	+	1.87090i	0.255472	+	0.0830078i
$509$	5.96949	+	8.21630i	0.264593	+	0.364181i	0.920555	−	0.390613i	$-0.127737\pi$
$509$	5.96949	+	8.21630i	0.264593	+	0.364181i	−0.655962	+	0.754794i	$0.727737\pi$
$510$		0			0
$511$	−3.61281	−	11.1191i	−0.159821	−	0.491880i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	15.0119	+	20.6621i	0.662146	+	0.911366i
$515$	−12.2273	−	3.97290i	−0.538801	−	0.175067i
$516$		0			0
$517$	−6.99273	−	41.3559i	−0.307540	−	1.81883i
$518$		−	8.83503i		−	0.388189i
$519$		0			0
$520$	0.534144	−	0.388078i	0.0234237	−	0.0170183i
$521$	16.5130	−	22.7282i	0.723449	−	0.995742i	−0.275953	−	0.961171i	$-0.588993\pi$
$521$	16.5130	−	22.7282i	0.723449	−	0.995742i	0.999402	−	0.0345713i	$-0.0110066\pi$
$522$		0			0
$523$	−3.87556	+	1.25924i	−0.169466	+	0.0550629i	−0.392521	−	0.919743i	$-0.628397\pi$
$523$	−3.87556	+	1.25924i	−0.169466	+	0.0550629i	0.223055	+	0.974806i	$0.428397\pi$
$524$	−7.06736	−	5.13474i	−0.308739	−	0.224312i
$525$		0			0
$526$	−1.36707	+	4.20740i	−0.0596070	+	0.183451i
$527$	17.4161			0.758657
$528$		0			0
$529$	−5.63636			−0.245059
$530$	−6.83914	+	21.0487i	−0.297073	+	0.914297i
$531$		0			0
$532$	−0.915799	−	0.665367i	−0.0397049	−	0.0288473i
$533$	−1.96332	+	0.637923i	−0.0850410	+	0.0276315i
$534$		0			0
$535$	−2.04373	+	2.81296i	−0.0883583	+	0.121615i
$536$	4.06876	−	2.95613i	0.175744	−	0.127685i
$537$		0			0
$538$			20.7150i			0.893087i
$539$	−0.484664	+	3.28102i	−0.0208760	+	0.141324i
$540$		0			0
$541$	12.8177	+	4.16471i	0.551074	+	0.179055i	0.571301	−	0.820740i	$-0.306439\pi$
$541$	12.8177	+	4.16471i	0.551074	+	0.179055i	−0.0202268	+	0.999795i	$0.506439\pi$
$542$	−11.8239	−	16.2742i	−0.507881	−	0.699038i
$543$		0			0
$544$	−1.79294	−	5.51810i	−0.0768716	−	0.236586i
$545$	1.03902	+	3.19777i	0.0445067	+	0.136977i
$546$		0			0
$547$	−23.1846	−	31.9109i	−0.991303	−	1.36441i	−0.930512	−	0.366261i	$-0.880638\pi$
$547$	−23.1846	−	31.9109i	−0.991303	−	1.36441i	−0.0607905	−	0.998151i	$-0.519362\pi$
$548$	20.7708	+	6.74884i	0.887284	+	0.288296i
$549$		0			0
$550$	−0.883869	+	5.98351i	−0.0376883	+	0.255138i
$551$		−	8.86844i		−	0.377808i
$552$		0			0
$553$	−4.78171	+	3.47412i	−0.203339	+	0.147735i
$554$	−11.5448	+	15.8900i	−0.490491	+	0.675103i
$555$		0			0
$556$	−1.82579	+	0.593236i	−0.0774309	+	0.0251588i
$557$	−26.9830	−	19.6043i	−1.14331	−	0.830660i	−0.155729	−	0.987800i	$-0.549773\pi$
$557$	−26.9830	−	19.6043i	−1.14331	−	0.830660i	−0.987576	+	0.157140i	$0.949773\pi$
$558$		0			0
$559$	0.982124	−	3.02267i	0.0415394	−	0.127845i
$560$	−1.78222			−0.0753127
$561$		0			0
$562$	3.36158			0.141800
$563$	−4.32718	+	13.3177i	−0.182369	+	0.561274i	−0.999893	−	0.0146204i	$-0.995346\pi$
$563$	−4.32718	+	13.3177i	−0.182369	+	0.561274i	0.817524	+	0.575894i	$0.195346\pi$
$564$		0			0
$565$	−4.41988	−	3.21123i	−0.185946	−	0.135097i
$566$	−14.8897	+	4.83796i	−0.625862	+	0.203355i
$567$		0			0
$568$	−4.35158	+	5.98944i	−0.182588	+	0.251311i
$569$	−6.23712	+	4.53153i	−0.261474	+	0.189972i	−0.710796	−	0.703398i	$-0.751665\pi$
$569$	−6.23712	+	4.53153i	−0.261474	+	0.189972i	0.449323	+	0.893369i	$0.351665\pi$
$570$		0			0
$571$		−	21.1898i		−	0.886765i	−0.896333	−	0.443382i	$-0.853778\pi$
$571$		−	21.1898i		−	0.886765i	0.896333	−	0.443382i	$-0.146222\pi$
$572$	0.204844	+	1.21147i	0.00856495	+	0.0506541i
$573$		0			0
$574$	5.29973	+	1.72199i	0.221207	+	0.0718744i
$575$	−5.73621	−	7.89521i	−0.239216	−	0.329253i
$576$		0			0
$577$	8.48830	+	26.1243i	0.353372	+	1.08757i	0.956947	+	0.290262i	$0.0937425\pi$
$577$	8.48830	+	26.1243i	0.353372	+	1.08757i	−0.603575	+	0.797306i	$0.706257\pi$
$578$	−5.14947	−	15.8484i	−0.214190	−	0.659208i
$579$		0			0
$580$	−8.20703	−	11.2960i	−0.340778	−	0.469041i
$581$	−7.58177	−	2.46347i	−0.314545	−	0.102202i
$582$		0			0
$583$	−29.4251	−	28.8180i	−1.21866	−	1.19352i
$584$			11.6913i			0.483790i
$585$		0			0
$586$	13.0898	−	9.51033i	0.540736	−	0.392868i
$587$	8.56296	−	11.7859i	0.353431	−	0.486456i	−0.594873	−	0.803820i	$-0.702798\pi$
$587$	8.56296	−	11.7859i	0.353431	−	0.486456i	0.948304	+	0.317364i	$0.102798\pi$
$588$		0			0
$589$	−3.23159	+	1.05001i	−0.133156	+	0.0432649i
$590$	20.0275	+	14.5508i	0.824519	+	0.599048i
$591$		0			0
$592$	−2.73017	+	8.40261i	−0.112209	+	0.345345i
$593$	20.9170			0.858957			0.429479	−	0.903077i	$-0.358697\pi$
$593$	20.9170			0.858957			0.429479	+	0.903077i	$0.358697\pi$
$594$		0			0
$595$	−10.3406			−0.423923
$596$	0.827308	−	2.54619i	0.0338878	−	0.104296i
$597$		0			0
$598$	−1.60382	−	1.16524i	−0.0655849	−	0.0476502i
$599$	39.0725	−	12.6954i	1.59646	−	0.518721i	0.630231	−	0.776408i	$-0.282960\pi$
$599$	39.0725	−	12.6954i	1.59646	−	0.518721i	0.966228	+	0.257687i	$0.0829604\pi$
$600$		0			0
$601$	19.8554	−	27.3286i	0.809919	−	1.11476i	−0.181417	−	0.983406i	$-0.558068\pi$
$601$	19.8554	−	27.3286i	0.809919	−	1.11476i	0.991336	−	0.131351i	$-0.0419315\pi$
$602$	−6.94071	+	5.04272i	−0.282882	+	0.205526i
$603$		0			0
$604$			12.1738i			0.495345i
$605$	16.0971	+	11.1901i	0.654440	+	0.454943i
$606$		0			0
$607$	−7.41940	−	2.41071i	−0.301144	−	0.0978476i	0.154548	−	0.987985i	$-0.450608\pi$
$607$	−7.41940	−	2.41071i	−0.301144	−	0.0978476i	−0.455692	+	0.890138i	$0.650608\pi$
$608$	0.665367	+	0.915799i	0.0269842	+	0.0371406i
$609$		0			0
$610$	−4.16953	−	12.8325i	−0.168819	−	0.519572i
$611$	1.44771	+	4.45560i	0.0585682	+	0.180254i
$612$		0			0
$613$	3.31700	+	4.56546i	0.133972	+	0.184397i	0.870732	−	0.491757i	$-0.163645\pi$
$613$	3.31700	+	4.56546i	0.133972	+	0.184397i	−0.736760	+	0.676154i	$0.763645\pi$
$614$	25.6862	+	8.34594i	1.03661	+	0.336815i
$615$		0			0
$616$	1.47483	−	2.97067i	0.0594228	−	0.119692i
$617$		−	15.1677i		−	0.610628i	−0.952252	−	0.305314i	$-0.901239\pi$
$617$		−	15.1677i		−	0.610628i	0.952252	−	0.305314i	$-0.0987614\pi$
$618$		0			0
$619$	−25.1527	+	18.2745i	−1.01097	+	0.734515i	−0.964413	−	0.264400i	$-0.914826\pi$
$619$	−25.1527	+	18.2745i	−1.01097	+	0.734515i	−0.0465604	+	0.998915i	$0.514826\pi$
$620$	−3.14448	+	4.32801i	−0.126285	+	0.173817i
$621$		0			0
$622$	2.75460	−	0.895023i	0.110449	−	0.0358871i
$623$	0.0861966	+	0.0626255i	0.00345339	+	0.00250904i
$624$		0			0
$625$	−3.87997	+	11.9413i	−0.155199	+	0.477653i
$626$	−11.1985			−0.447581
$627$		0			0
$628$	1.21442			0.0484606
$629$	−15.8407	+	48.7525i	−0.631608	+	1.94389i
$630$		0			0
$631$	12.1727	+	8.84397i	0.484587	+	0.352073i	0.803099	−	0.595846i	$-0.203183\pi$
$631$	12.1727	+	8.84397i	0.484587	+	0.352073i	−0.318512	+	0.947919i	$0.603183\pi$
$632$	5.62124	−	1.82645i	0.223601	−	0.0726524i
$633$		0			0
$634$	0.0550501	−	0.0757700i	0.00218632	−	0.00300921i
$635$	−8.72949	+	6.34234i	−0.346419	+	0.251688i
$636$		0			0
$637$		−	0.370457i		−	0.0146780i
$638$	25.6200	−	4.33201i	1.01431	−	0.171506i
$639$		0			0
$640$	1.69500	+	0.550738i	0.0670006	+	0.0217698i
$641$	6.80811	+	9.37056i	0.268904	+	0.370115i	0.922019	−	0.387144i	$-0.126538\pi$
$641$	6.80811	+	9.37056i	0.268904	+	0.370115i	−0.653115	+	0.757258i	$0.726538\pi$
$642$		0			0
$643$	1.20487	+	3.70821i	0.0475155	+	0.146238i	0.971999	−	0.234984i	$-0.0755036\pi$
$643$	1.20487	+	3.70821i	0.0475155	+	0.146238i	−0.924484	+	0.381221i	$0.875504\pi$
$644$	1.65364	+	5.08938i	0.0651626	+	0.200550i
$645$		0			0
$646$	3.86051	+	5.31353i	0.151890	+	0.209058i
$647$	18.4121	+	5.98244i	0.723853	+	0.235194i	0.647693	−	0.761902i	$-0.275734\pi$
$647$	18.4121	+	5.98244i	0.723853	+	0.235194i	0.0761601	+	0.997096i	$0.475734\pi$
$648$		0			0
$649$	−40.8270	+	21.3413i	−1.60260	+	0.837719i
$650$		−	0.675593i		−	0.0264989i
$651$		0			0
$652$	16.3957	−	11.9122i	0.642106	−	0.466517i
$653$	−3.97176	+	5.46667i	−0.155427	+	0.213927i	−0.879628	−	0.475662i	$-0.842209\pi$
$653$	−3.97176	+	5.46667i	−0.155427	+	0.213927i	0.724201	+	0.689589i	$0.242209\pi$
$654$		0			0
$655$	14.8070	−	4.81110i	0.578559	−	0.187985i
$656$	−4.50822	−	3.27542i	−0.176017	−	0.127883i
$657$		0			0
$658$	3.90791	−	12.0273i	0.152346	−	0.468873i
$659$	−5.55571			−0.216420			−0.108210	−	0.994128i	$-0.534512\pi$
$659$	−5.55571			−0.216420			−0.108210	+	0.994128i	$0.534512\pi$
$660$		0			0
$661$	−45.0207			−1.75110			−0.875551	−	0.483125i	$-0.839502\pi$
$661$	−45.0207			−1.75110			−0.875551	+	0.483125i	$0.839502\pi$
$662$	3.37293	−	10.3808i	0.131093	−	0.403462i
$663$		0			0
$664$	6.44944	+	4.68579i	0.250287	+	0.181844i
$665$	1.91872	−	0.623430i	0.0744048	−	0.0241756i
$666$		0			0
$667$	−24.6424	+	33.9173i	−0.954156	+	1.31328i
$668$	−0.956647	+	0.695045i	−0.0370138	+	0.0268921i
$669$		0			0
$670$			8.96329i			0.346282i
$671$	24.8400	+	3.66929i	0.958936	+	0.141652i
$672$		0			0
$673$	−4.90288	−	1.59304i	−0.188992	−	0.0614072i	0.212992	−	0.977054i	$-0.431679\pi$
$673$	−4.90288	−	1.59304i	−0.188992	−	0.0614072i	−0.401984	+	0.915647i	$0.631679\pi$
$674$	7.32956	+	10.0883i	0.282324	+	0.388586i
$675$		0			0
$676$	3.97481	+	12.2332i	0.152877	+	0.470508i
$677$	7.09085	+	21.8234i	0.272524	+	0.838741i	0.989864	+	0.142018i	$0.0453592\pi$
$677$	7.09085	+	21.8234i	0.272524	+	0.838741i	−0.717340	+	0.696723i	$0.754641\pi$
$678$		0			0
$679$	10.5067	+	14.4612i	0.403210	+	0.554971i
$680$	9.83449	+	3.19542i	0.377135	+	0.122539i
$681$		0			0
$682$	−4.61192	−	8.82285i	−0.176600	−	0.337844i
$683$		−	9.41944i		−	0.360425i	−0.983628	−	0.180212i	$-0.942322\pi$
$683$		−	9.41944i		−	0.360425i	0.983628	−	0.180212i	$-0.0576785\pi$
$684$		0			0
$685$	−31.4896	+	22.8785i	−1.20315	+	0.874143i
$686$	−0.587785	+	0.809017i	−0.0224417	+	0.0308884i
$687$		0			0
$688$	8.15929	−	2.65111i	0.311070	−	0.101073i
$689$	3.72179	+	2.70404i	0.141789	+	0.103016i
$690$		0			0
$691$	−6.93446	+	21.3421i	−0.263799	+	0.811891i	0.728168	+	0.685398i	$0.240372\pi$
$691$	−6.93446	+	21.3421i	−0.263799	+	0.811891i	−0.991968	+	0.126492i	$0.959628\pi$
$692$	−10.7343			−0.408056
$693$		0			0
$694$	7.96265			0.302258
$695$	1.05728	−	3.25397i	0.0401049	−	0.123430i
$696$		0			0
$697$	−26.1570	−	19.0042i	−0.990768	−	0.719835i
$698$	−2.02380	+	0.657571i	−0.0766018	+	0.0248894i
$699$		0			0
$700$	−1.07193	+	1.47538i	−0.0405151	+	0.0557643i
$701$	−22.1739	+	16.1103i	−0.837496	+	0.608477i	−0.921670	−	0.387974i	$-0.873175\pi$
$701$	−22.1739	+	16.1103i	−0.837496	+	0.608477i	0.0841739	+	0.996451i	$0.473175\pi$
$702$		0			0
$703$		−	10.0012i		−	0.377201i
$704$	−2.32064	+	2.36952i	−0.0874623	+	0.0893048i
$705$		0			0
$706$	8.36956	+	2.71943i	0.314993	+	0.102347i
$707$	−9.98805	−	13.7474i	−0.375639	−	0.517023i
$708$		0			0
$709$	2.49594	+	7.68170i	0.0937368	+	0.288492i	0.986922	−	0.161196i	$-0.0515351\pi$
$709$	2.49594	+	7.68170i	0.0937368	+	0.288492i	−0.893186	+	0.449688i	$0.851535\pi$
$710$	−4.07731	−	12.5487i	−0.153019	−	0.470943i
$711$		0			0
$712$	−0.0626255	−	0.0861966i	−0.00234699	−	0.00323035i
$713$	15.2768	+	4.96374i	0.572122	+	0.185894i
$714$		0			0
$715$	−1.96135	−	0.973741i	−0.0733502	−	0.0364159i
$716$			22.8098i			0.852441i
$717$		0			0
$718$	−11.9212	+	8.66124i	−0.444894	+	0.323235i
$719$	−1.55136	+	2.13526i	−0.0578560	+	0.0796319i	−0.836965	−	0.547257i	$-0.815672\pi$
$719$	−1.55136	+	2.13526i	−0.0578560	+	0.0796319i	0.779109	+	0.626889i	$0.215672\pi$
$720$		0			0
$721$	6.86072	−	2.22918i	0.255506	−	0.0830191i
$722$	14.3346	+	10.4147i	0.533480	+	0.387596i
$723$		0			0
$724$	−1.43602	+	4.41962i	−0.0533693	+	0.164254i
$725$	−14.2874			−0.530619
$726$		0			0
$727$	19.2450			0.713756			0.356878	−	0.934151i	$-0.383841\pi$
$727$	19.2450			0.713756			0.356878	+	0.934151i	$0.383841\pi$
$728$	−0.114478	+	0.352326i	−0.00424282	+	0.0130581i
$729$		0			0
$730$	−16.8571	−	12.2474i	−0.623910	−	0.453297i
$731$	47.3408	−	15.3820i	1.75096	−	0.568922i
$732$		0			0
$733$	−19.8895	+	27.3755i	−0.734635	+	1.01114i	0.264274	+	0.964448i	$0.414868\pi$
$733$	−19.8895	+	27.3755i	−0.734635	+	1.01114i	−0.998909	+	0.0466912i	$0.985132\pi$
$734$	16.4551	−	11.9553i	0.607369	−	0.441279i
$735$		0			0
$736$		−	5.35130i		−	0.197251i
$737$	−14.9403	−	7.41734i	−0.550332	−	0.273221i
$738$		0			0
$739$	−34.0170	−	11.0528i	−1.25133	−	0.406583i	−0.392935	−	0.919566i	$-0.628540\pi$
$739$	−34.0170	−	11.0528i	−1.25133	−	0.406583i	−0.858399	+	0.512983i	$0.828540\pi$
$740$	−9.25527	−	12.7388i	−0.340230	−	0.468287i
$741$		0			0
$742$	−3.83741	−	11.8103i	−0.140876	−	0.433571i
$743$	−4.52623	−	13.9303i	−0.166051	−	0.511054i	0.833061	−	0.553181i	$-0.186586\pi$
$743$	−4.52623	−	13.9303i	−0.166051	−	0.511054i	−0.999112	+	0.0421277i	$0.986586\pi$
$744$		0			0
$745$	2.80457	+	3.86016i	0.102751	+	0.141425i
$746$	9.88800	+	3.21281i	0.362025	+	0.117629i
$747$		0			0
$748$	−13.4645	+	13.7481i	−0.492311	+	0.502682i
$749$		−	1.95094i		−	0.0712856i
$750$		0			0
$751$	−28.3501	+	20.5976i	−1.03451	+	0.751615i	−0.969206	−	0.246250i	$-0.920802\pi$
$751$	−28.3501	+	20.5976i	−1.03451	+	0.751615i	−0.0653035	+	0.997865i	$0.520802\pi$
$752$	−7.43328	+	10.2310i	−0.271064	+	0.373088i
$753$		0			0
$754$	−2.76025	+	0.896861i	−0.100522	+	0.0326617i
$755$	−17.5528	−	12.7529i	−0.638812	−	0.464124i
$756$		0			0
$757$	13.6015	−	41.8610i	0.494353	−	1.52146i	−0.323609	−	0.946191i	$-0.604896\pi$
$757$	13.6015	−	41.8610i	0.494353	−	1.52146i	0.817962	−	0.575272i	$-0.195104\pi$
$758$	−26.7688			−0.972286
$759$		0			0
$760$	−2.01746			−0.0731810
$761$	−7.50389	+	23.0946i	−0.272016	+	0.837178i	0.717978	+	0.696066i	$0.245068\pi$
$761$	−7.50389	+	23.0946i	−0.272016	+	0.837178i	−0.989994	+	0.141112i	$0.954932\pi$
$762$		0			0
$763$	−1.52629	−	1.10891i	−0.0552553	−	0.0401453i
$764$	−16.4693	+	5.35121i	−0.595840	+	0.193600i
$765$		0			0
$766$	−10.5347	+	14.4998i	−0.380634	+	0.523898i
$767$	4.16296	−	3.02457i	0.150316	−	0.109211i
$768$		0			0
$769$			7.09760i			0.255946i	0.991778	+	0.127973i	$0.0408471\pi$
$769$			7.09760i			0.255946i	−0.991778	+	0.127973i	$0.959153\pi$
$770$	2.73827	+	5.23846i	0.0986805	+	0.188781i
$771$		0			0
$772$	−11.1615	−	3.62659i	−0.401711	−	0.130524i
$773$	7.01174	+	9.65084i	0.252195	+	0.347116i	0.916278	−	0.400542i	$-0.131178\pi$
$773$	7.01174	+	9.65084i	0.252195	+	0.347116i	−0.664084	+	0.747658i	$0.731178\pi$
$774$		0			0
$775$	1.69160	+	5.20621i	0.0607641	+	0.187013i
$776$	−5.52369	−	17.0002i	−0.198289	−	0.610271i
$777$		0			0
$778$	13.8494	+	19.0620i	0.496524	+	0.683406i
$779$	5.99925	+	1.94927i	0.214945	+	0.0698400i
$780$		0			0
$781$	24.2906	+	3.58814i	0.869185	+	0.128394i
$782$		−	31.0486i		−	1.11030i
$783$		0			0
$784$	0.809017	−	0.587785i	0.0288935	−	0.0209923i
$785$	−1.27218	+	1.75101i	−0.0454061	+	0.0624962i
$786$		0			0
$787$	7.01392	−	2.27896i	0.250019	−	0.0812362i	−0.181326	−	0.983423i	$-0.558039\pi$
$787$	7.01392	−	2.27896i	0.250019	−	0.0812362i	0.431345	+	0.902187i	$0.358039\pi$
$788$	20.8796	+	15.1699i	0.743806	+	0.540407i
$789$		0			0
$790$	−3.25515	+	10.0183i	−0.115813	+	0.356436i
$791$	3.06542			0.108994
$792$		0			0
$793$	−2.80466			−0.0995963
$794$	−9.77556	+	30.0861i	−0.346922	+	1.06772i
$795$		0			0
$796$	−0.0988013	−	0.0717834i	−0.00350192	−	0.00254429i
$797$	−14.5959	+	4.74249i	−0.517012	+	0.167988i	−0.555889	−	0.831256i	$-0.687622\pi$
$797$	−14.5959	+	4.74249i	−0.517012	+	0.167988i	0.0388766	+	0.999244i	$0.487622\pi$
$798$		0			0
$799$	−43.1284	+	59.3612i	−1.52577	+	2.10005i
$800$	1.47538	−	1.07193i	0.0521627	−	0.0378984i
$801$		0			0
$802$		−	24.3736i		−	0.860662i
$803$	34.3640	−	17.9629i	1.21268	−	0.633898i
$804$		0			0
$805$	−9.07043	−	2.94716i	−0.319691	−	0.103874i
$806$	0.653619	+	0.899629i	0.0230227	+	0.0316881i
$807$		0			0
$808$	5.25103	+	16.1610i	0.184731	+	0.568542i
$809$	16.0254	+	49.3211i	0.563423	+	1.73404i	0.672592	+	0.740014i	$0.265181\pi$
$809$	16.0254	+	49.3211i	0.563423	+	1.73404i	−0.109169	+	0.994023i	$0.534819\pi$
$810$		0			0
$811$	23.2925	+	32.0593i	0.817909	+	1.12576i	0.990055	+	0.140684i	$0.0449302\pi$
$811$	23.2925	+	32.0593i	0.817909	+	1.12576i	−0.172145	+	0.985072i	$0.555070\pi$
$812$	7.45094	+	2.42096i	0.261477	+	0.0849589i
$813$		0			0
$814$	28.8924	−	4.88532i	1.01268	−	0.171230i
$815$			36.1190i			1.26519i
$816$		0			0
$817$	−7.85681	+	5.70831i	−0.274875	+	0.199708i
$818$	−16.0784	+	22.1300i	−0.562166	+	0.773756i
$819$		0			0
$820$	9.44532	−	3.06897i	0.329845	−	0.107173i
$821$	−17.8616	−	12.9772i	−0.623374	−	0.452908i	0.230724	−	0.973019i	$-0.425890\pi$
$821$	−17.8616	−	12.9772i	−0.623374	−	0.452908i	−0.854098	+	0.520111i	$0.825890\pi$
$822$		0			0
$823$	9.28496	−	28.5762i	0.323653	−	0.996102i	−0.648392	−	0.761307i	$-0.724558\pi$
$823$	9.28496	−	28.5762i	0.323653	−	0.996102i	0.972045	−	0.234795i	$-0.0754420\pi$
$824$	−7.21378			−0.251304
$825$		0			0
$826$	−13.8901			−0.483300
$827$	−17.0736	+	52.5473i	−0.593709	+	1.82725i	−0.0326566	+	0.999467i	$0.510397\pi$
$827$	−17.0736	+	52.5473i	−0.593709	+	1.82725i	−0.561052	+	0.827781i	$0.689603\pi$
$828$		0			0
$829$	13.4324	+	9.75922i	0.466527	+	0.338952i	0.796086	−	0.605183i	$-0.206900\pi$
$829$	13.4324	+	9.75922i	0.466527	+	0.338952i	−0.329559	+	0.944135i	$0.606900\pi$
$830$	−13.5124	+	4.39045i	−0.469023	+	0.152395i
$831$		0			0
$832$	0.217749	−	0.299706i	0.00754910	−	0.0103904i
$833$	4.69397	−	3.41037i	0.162637	−	0.118162i
$834$		0			0
$835$		−	2.10745i		−	0.0729312i
$836$	1.66950	−	3.36277i	0.0577408	−	0.116304i
$837$		0			0
$838$	35.0141	+	11.3768i	1.20954	+	0.393004i
$839$	26.4395	+	36.3908i	0.912793	+	1.25635i	0.966204	+	0.257779i	$0.0829905\pi$
$839$	26.4395	+	36.3908i	0.912793	+	1.25635i	−0.0534115	+	0.998573i	$0.517010\pi$
$840$		0			0
$841$	10.0052	+	30.7929i	0.345007	+	1.06182i
$842$	3.53940	+	10.8932i	0.121976	+	0.375403i
$843$		0			0
$844$	1.19386	+	1.64321i	0.0410944	+	0.0565616i
$845$	−21.8023	−	7.08401i	−0.750023	−	0.243697i
$846$		0			0
$847$	−10.9976	+	0.229285i	−0.377882	+	0.00787834i
$848$			12.4181i			0.426440i
$849$		0			0
$850$	8.56028	−	6.21941i	0.293615	−	0.213324i
$851$	−27.7898	+	38.2494i	−0.952622	+	1.31117i
$852$		0			0
$853$	42.7100	−	13.8773i	1.46236	−	0.475150i	0.533572	−	0.845755i	$-0.320849\pi$
$853$	42.7100	−	13.8773i	1.46236	−	0.475150i	0.928791	+	0.370604i	$0.120849\pi$
$854$	6.12491	+	4.45000i	0.209590	+	0.152276i
$855$		0			0
$856$	−0.602872	+	1.85545i	−0.0206058	+	0.0634180i
$857$	31.6377			1.08072			0.540362	−	0.841433i	$-0.318287\pi$
$857$	31.6377			1.08072			0.540362	+	0.841433i	$0.318287\pi$
$858$		0			0
$859$	15.1500			0.516911			0.258456	−	0.966023i	$-0.416786\pi$
$859$	15.1500			0.516911			0.258456	+	0.966023i	$0.416786\pi$
$860$	−4.72488	+	14.5417i	−0.161117	+	0.495868i
$861$		0			0
$862$	−18.1702	−	13.2014i	−0.618878	−	0.449641i
$863$	15.7020	−	5.10190i	0.534504	−	0.173671i	−0.0293137	−	0.999570i	$-0.509332\pi$
$863$	15.7020	−	5.10190i	0.534504	−	0.173671i	0.563817	+	0.825899i	$0.309332\pi$
$864$		0			0
$865$	11.2449	−	15.4772i	0.382337	−	0.526242i
$866$	6.09001	−	4.42465i	0.206947	−	0.150356i
$867$		0			0
$868$		−	3.00170i		−	0.101884i
$869$	−14.0051	−	13.7162i	−0.475091	−	0.465290i
$870$		0			0
$871$	1.77194	+	0.575738i	0.0600399	+	0.0195081i
$872$	1.10891	+	1.52629i	0.0375525	+	0.0516866i
$873$		0			0
$874$	1.87191	+	5.76113i	0.0633182	+	0.194873i
$875$	−3.75806	−	11.5661i	−0.127045	−	0.391006i
$876$		0			0
$877$	−4.27889	−	5.88939i	−0.144488	−	0.198871i	0.730639	−	0.682764i	$-0.239222\pi$
$877$	−4.27889	−	5.88939i	−0.144488	−	0.198871i	−0.875127	+	0.483893i	$0.839222\pi$
$878$	9.62887	+	3.12861i	0.324959	+	0.105585i
$879$		0			0
$880$	−0.985479	−	5.82824i	−0.0332205	−	0.196470i
$881$		−	0.947132i		−	0.0319097i	−0.999873	−	0.0159548i	$-0.994921\pi$
$881$		−	0.947132i		−	0.0319097i	0.999873	−	0.0159548i	$-0.00507880\pi$
$882$		0			0
$883$	−4.97065	+	3.61139i	−0.167276	+	0.121533i	−0.668274	−	0.743916i	$-0.732966\pi$
$883$	−4.97065	+	3.61139i	−0.167276	+	0.121533i	0.500998	+	0.865449i	$0.332966\pi$
$884$	1.26340	−	1.73892i	0.0424926	−	0.0584861i
$885$		0			0
$886$	2.10300	−	0.683305i	0.0706515	−	0.0229561i
$887$	−37.8500	−	27.4997i	−1.27088	−	0.923348i	−0.271642	−	0.962398i	$-0.587567\pi$
$887$	−37.8500	−	27.4997i	−1.27088	−	0.923348i	−0.999237	+	0.0390500i	$0.987567\pi$
$888$		0			0
$889$	1.87090	−	5.75804i	0.0627480	−	0.193119i
$890$	0.189887			0.00636502
$891$		0			0
$892$	−19.6068			−0.656484
$893$	4.42371	−	13.6148i	0.148034	−	0.455602i
$894$		0			0
$895$	−32.8883	−	23.8947i	−1.09933	−	0.798713i
$896$	−0.951057	+	0.309017i	−0.0317726	+	0.0103235i
$897$		0			0
$898$	2.72065	−	3.74465i	0.0907893	−	0.124961i
$899$	19.0252	−	13.8226i	0.634527	−	0.461011i
$900$		0			0
$901$			72.0509i			2.40036i
$902$	−2.70077	+	18.2834i	−0.0899260	+	0.608770i
$903$		0			0
$904$	−2.91539	−	0.947268i	−0.0969644	−	0.0315056i
$905$	−4.86810	−	6.70037i	−0.161821	−	0.222728i
$906$		0			0
$907$	−5.89286	−	18.1364i	−0.195669	−	0.602208i	−0.999968	−	0.00798326i	$-0.997459\pi$
$907$	−5.89286	−	18.1364i	−0.195669	−	0.602208i	0.804299	−	0.594225i	$-0.202541\pi$
$908$	−4.59831	−	14.1521i	−0.152600	−	0.469655i
$909$		0			0
$910$	−0.388078	−	0.534144i	−0.0128647	−	0.0177067i
$911$	32.8872	+	10.6857i	1.08960	+	0.354033i	0.798093	−	0.602535i	$-0.205842\pi$
$911$	32.8872	+	10.6857i	1.08960	+	0.354033i	0.291510	+	0.956568i	$0.405842\pi$
$912$		0			0
$913$	3.86371	−	26.1561i	0.127870	−	0.865641i
$914$		−	12.4526i		−	0.411895i
$915$		0			0
$916$	−11.9035	+	8.64839i	−0.393302	+	0.285751i
$917$	−5.13474	+	7.06736i	−0.169564	+	0.233385i
$918$		0			0
$919$	−6.80092	+	2.20975i	−0.224342	+	0.0728931i	−0.419031	−	0.907972i	$-0.637630\pi$
$919$	−6.80092	+	2.20975i	−0.224342	+	0.0728931i	0.194689	+	0.980865i	$0.437630\pi$
$920$	7.71577	+	5.60583i	0.254381	+	0.184819i
$921$		0			0
$922$	−3.87952	+	11.9399i	−0.127765	+	0.393221i
$923$	−2.74263			−0.0902746
$924$		0			0
$925$	−16.1122			−0.529766
$926$	11.7030	−	36.0182i	0.384585	−	1.18363i
$927$		0			0
$928$	−6.33815	−	4.60493i	−0.208060	−	0.151164i
$929$	−40.5578	+	13.1780i	−1.33066	+	0.432357i	−0.886142	−	0.463413i	$-0.846625\pi$
$929$	−40.5578	+	13.1780i	−1.33066	+	0.432357i	−0.444517	+	0.895770i	$0.646625\pi$
$930$		0			0
$931$	−0.665367	+	0.915799i	−0.0218065	+	0.0300141i
$932$	0.454319	−	0.330082i	0.0148817	−	0.0108122i
$933$		0			0
$934$		−	35.7519i		−	1.16984i
$935$	−5.71782	−	33.8159i	−0.186993	−	1.10590i
$936$		0			0
$937$	37.5673	+	12.2064i	1.22727	+	0.398765i	0.849725	−	0.527226i	$-0.176768\pi$
$937$	37.5673	+	12.2064i	1.22727	+	0.398765i	0.377546	+	0.925991i	$0.376768\pi$
$938$	−2.95613	−	4.06876i	−0.0965210	−	0.132850i
$939$		0			0
$940$	−6.96477	−	21.4354i	−0.227166	−	0.699145i
$941$	−16.2033	−	49.8687i	−0.528213	−	1.62567i	−0.757874	−	0.652401i	$-0.773762\pi$
$941$	−16.2033	−	49.8687i	−0.528213	−	1.62567i	0.229661	−	0.973271i	$-0.426238\pi$
$942$		0			0
$943$	−17.5277	−	24.1248i	−0.570781	−	0.785613i
$944$	13.2103	+	4.29229i	0.429959	+	0.139702i
$945$		0			0
$946$	−20.3286	−	19.9092i	−0.660939	−	0.647303i
$947$			26.8053i			0.871056i	0.900175	+	0.435528i	$0.143438\pi$
$947$			26.8053i			0.871056i	−0.900175	+	0.435528i	$0.856562\pi$
$948$		0			0
$949$	−3.50396	+	2.54577i	−0.113743	+	0.0826393i
$950$	−1.21341	+	1.67012i	−0.0393683	+	0.0541858i
$951$		0			0
$952$	−5.51810	+	1.79294i	−0.178843	+	0.0581095i
$953$	35.1109	+	25.5095i	1.13735	+	0.826335i	0.986748	−	0.162259i	$-0.0518780\pi$
$953$	35.1109	+	25.5095i	1.13735	+	0.826335i	0.150605	+	0.988594i	$0.451878\pi$
$954$		0			0
$955$	9.53706	−	29.3521i	0.308612	−	0.949811i
$956$	1.19138			0.0385320
$957$		0			0
$958$	−28.3219			−0.915037
$959$	6.74884	−	20.7708i	0.217931	−	0.670724i
$960$		0			0
$961$	17.7901	+	12.9253i	0.573874	+	0.416944i
$962$	−3.11281	+	1.01141i	−0.100361	+	0.0326092i
$963$		0			0
$964$	4.30044	−	5.91905i	0.138508	−	0.190640i
$965$	16.9214	−	12.2941i	0.544719	−	0.395761i
$966$		0			0
$967$		−	18.3681i		−	0.590680i	−0.955392	−	0.295340i	$-0.904567\pi$
$967$		−	18.3681i		−	0.590680i	0.955392	−	0.295340i	$-0.0954329\pi$
$968$	10.5302	+	3.18039i	0.338454	+	0.102221i
$969$		0			0
$970$	30.2981	+	9.84447i	0.972815	+	0.316087i
$971$	−13.2802	−	18.2786i	−0.426182	−	0.586589i	0.540890	−	0.841094i	$-0.318088\pi$
$971$	−13.2802	−	18.2786i	−0.426182	−	0.586589i	−0.967072	+	0.254504i	$0.918088\pi$
$972$		0			0
$973$	0.593236	+	1.82579i	0.0190183	+	0.0585322i
$974$	−8.76328	−	26.9706i	−0.280794	−	0.864194i
$975$		0			0
$976$	−4.45000	−	6.12491i	−0.142441	−	0.196053i
$977$	38.0046	+	12.3484i	1.21587	+	0.395061i	0.845578	−	0.533852i	$-0.179256\pi$
$977$	38.0046	+	12.3484i	1.21587	+	0.395061i	0.370296	+	0.928914i	$0.379256\pi$
$978$		0			0
$979$	−0.157136	+	0.316509i	−0.00502209	+	0.0101157i
$980$			1.78222i			0.0569311i
$981$		0			0
$982$	30.8565	−	22.4186i	0.984672	−	0.715406i
$983$	17.7747	−	24.4648i	0.566925	−	0.780305i	−0.425261	−	0.905071i	$-0.639818\pi$
$983$	17.7747	−	24.4648i	0.566925	−	0.780305i	0.992186	+	0.124765i	$0.0398178\pi$
$984$		0			0
$985$	−43.7456	+	14.2138i	−1.39385	+	0.452889i
$986$	−36.7744	−	26.7181i	−1.17113	−	0.850879i
$987$		0			0
$988$	−0.129587	+	0.398829i	−0.00412273	+	0.0126884i
$989$	45.9098			1.45985
$990$		0			0
$991$	−33.1620			−1.05342			−0.526712	−	0.850044i	$-0.676575\pi$
$991$	−33.1620			−1.05342			−0.526712	+	0.850044i	$0.676575\pi$
$992$	−0.927578	+	2.85479i	−0.0294506	+	0.0906397i
$993$		0			0
$994$	5.98944	+	4.35158i	0.189974	+	0.138024i
$995$	0.207002	−	0.0672589i	0.00656240	−	0.00213225i
$996$		0			0
$997$	29.5418	−	40.6608i	0.935599	−	1.28774i	−0.0220365	−	0.999757i	$-0.507015\pi$
$997$	29.5418	−	40.6608i	0.935599	−	1.28774i	0.957635	−	0.287984i	$-0.0929850\pi$
$998$	−0.203521	+	0.147866i	−0.00644234	+	0.00468063i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.b.827.8	yes	48
3.2	odd	2		1386.2.bu.a.827.5	✓	48
11.6	odd	10		1386.2.bu.a.1205.5	yes	48
33.17	even	10	inner	1386.2.bu.b.1205.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.827.5	✓	48	3.2	odd	2
1386.2.bu.a.1205.5	yes	48	11.6	odd	10
1386.2.bu.b.827.8	yes	48	1.1	even	1	trivial
1386.2.bu.b.1205.8	yes	48	33.17	even	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(1.69500 - 0.550738i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(1.69500 - 0.550738i) q^{5} +(-0.587785 + 0.809017i) q^{7} +(0.809017 - 0.587785i) q^{8} +1.78222i q^{10} +(-2.97067 - 1.47483i) q^{11} +(0.352326 + 0.114478i) q^{13} +(-0.587785 - 0.809017i) q^{14} +(0.309017 + 0.951057i) q^{16} +(1.79294 + 5.51810i) q^{17} +(-0.665367 - 0.915799i) q^{19} +(-1.69500 - 0.550738i) q^{20} +(2.32064 - 2.36952i) q^{22} +5.35130i q^{23} +(-1.47538 + 1.07193i) q^{25} +(-0.217749 + 0.299706i) q^{26} +(0.951057 - 0.309017i) q^{28} +(6.33815 + 4.60493i) q^{29} +(0.927578 - 2.85479i) q^{31} -1.00000 q^{32} -5.80207 q^{34} +(-0.550738 + 1.69500i) q^{35} +(7.14769 + 5.19310i) q^{37} +(1.07659 - 0.349804i) q^{38} +(1.04757 - 1.44185i) q^{40} +(-4.50822 + 3.27542i) q^{41} -8.57919i q^{43} +(1.53643 + 2.93928i) q^{44} +(-5.08938 - 1.65364i) q^{46} +(7.43328 + 10.2310i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-0.563546 - 1.73442i) q^{50} +(-0.217749 - 0.299706i) q^{52} +(11.8103 + 3.83741i) q^{53} +(-5.84752 - 0.863780i) q^{55} +1.00000i q^{56} +(-6.33815 + 4.60493i) q^{58} +(8.16442 - 11.2374i) q^{59} +(-7.20026 + 2.33951i) q^{61} +(2.42843 + 1.76436i) q^{62} +(0.309017 - 0.951057i) q^{64} +0.660238 q^{65} +5.02927 q^{67} +(1.79294 - 5.51810i) q^{68} +(-1.44185 - 1.04757i) q^{70} +(-7.04101 + 2.28776i) q^{71} +(-6.87198 + 9.45847i) q^{73} +(-7.14769 + 5.19310i) q^{74} +1.13199i q^{76} +(2.93928 - 1.53643i) q^{77} +(5.62124 + 1.82645i) q^{79} +(1.04757 + 1.44185i) q^{80} +(-1.72199 - 5.29973i) q^{82} +(2.46347 + 7.58177i) q^{83} +(6.07805 + 8.36572i) q^{85} +(8.15929 + 2.65111i) q^{86} +(-3.27021 + 0.552949i) q^{88} -0.106545i q^{89} +(-0.299706 + 0.217749i) q^{91} +(3.14541 - 4.32929i) q^{92} +(-12.0273 + 3.90791i) q^{94} +(-1.63216 - 1.18583i) q^{95} +(5.52369 - 17.0002i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8}+O(q^{10}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8	\( 48 q + 12 q^{2} - 12 q^{4} + 12 q^{8} - 4 q^{11} - 12 q^{16} - 24 q^{17} + 4 q^{22} + 24 q^{25} - 40 q^{26} + 16 q^{29} + 40 q^{31} - 48 q^{32} - 16 q^{34} + 12 q^{35} + 16 q^{37} + 40 q^{38} - 24 q^{41} - 4 q^{44} - 40 q^{46} + 40 q^{47} + 12 q^{49} - 4 q^{50} - 40 q^{52} + 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} + 40 q^{62} - 12 q^{64} + 48 q^{67} - 24 q^{68} + 8 q^{70} + 40 q^{73} - 16 q^{74} - 32 q^{77} + 40 q^{79} - 16 q^{82} + 16 q^{83} - 20 q^{85} + 4 q^{88} + 20 q^{92} + 52 q^{95} - 8 q^{97} + 48 q^{98}+O(q^{100}) \) 48 * q + 12 * q^2 - 12 * q^4 + 12 * q^8 - 4 * q^11 - 12 * q^16 - 24 * q^17 + 4 * q^22 + 24 * q^25 - 40 * q^26 + 16 * q^29 + 40 * q^31 - 48 * q^32 - 16 * q^34 + 12 * q^35 + 16 * q^37 + 40 * q^38 - 24 * q^41 - 4 * q^44 - 40 * q^46 + 40 * q^47 + 12 * q^49 - 4 * q^50 - 40 * q^52 + 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 + 40 * q^62 - 12 * q^64 + 48 * q^67 - 24 * q^68 + 8 * q^70 + 40 * q^73 - 16 * q^74 - 32 * q^77 + 40 * q^79 - 16 * q^82 + 16 * q^83 - 20 * q^85 + 4 * q^88 + 20 * q^92 + 52 * q^95 - 8 * q^97 + 48 * q^98

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