LMFDB - Embedded newform 378.2.t.a.17.8

Error: no document with id 257420612 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(17,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.8
Root			$1.71298 - 0.256290i$ of defining polynomial
Character	$\chi$	$=$	378.17
Dual form			378.2.t.a.89.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.61932 q^{5} +(0.266972 - 2.63225i) q^{7} +1.00000i q^{8} +(3.13442 + 1.80966i) q^{10} -2.00379i q^{11} +(-2.95206 - 1.70437i) q^{13} +(1.54733 - 2.14611i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.08709 + 5.34700i) q^{17} +(0.877353 - 0.506540i) q^{19} +(1.80966 + 3.13442i) q^{20} +(1.00190 - 1.73534i) q^{22} +3.02799i q^{23} +8.09945 q^{25} +(-1.70437 - 2.95206i) q^{26} +(2.41308 - 1.08492i) q^{28} +(-5.04560 + 2.91308i) q^{29} +(0.787812 - 0.454844i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.34700 + 3.08709i) q^{34} +(0.966257 - 9.52693i) q^{35} +(3.66825 + 6.35359i) q^{37} +1.01308 q^{38} +3.61932i q^{40} +(-2.85045 + 4.93712i) q^{41} +(-2.39949 - 4.15605i) q^{43} +(1.73534 - 1.00190i) q^{44} +(-1.51400 + 2.62232i) q^{46} +(1.11511 - 1.93143i) q^{47} +(-6.85745 - 1.40547i) q^{49} +(7.01433 + 4.04972i) q^{50} -3.40874i q^{52} +(7.58088 + 4.37683i) q^{53} -7.25237i q^{55} +(2.63225 + 0.266972i) q^{56} -5.82616 q^{58} +(-4.49313 - 7.78233i) q^{59} +(-12.7410 - 7.35603i) q^{61} +0.909687 q^{62} -1.00000 q^{64} +(-10.6844 - 6.16866i) q^{65} +(4.15821 + 7.20222i) q^{67} -6.17418 q^{68} +(5.60027 - 7.76744i) q^{70} -0.466287i q^{71} +(-3.65022 - 2.10746i) q^{73} +7.33650i q^{74} +(0.877353 + 0.506540i) q^{76} +(-5.27448 - 0.534957i) q^{77} +(-1.91267 + 3.31284i) q^{79} +(-1.80966 + 3.13442i) q^{80} +(-4.93712 + 2.85045i) q^{82} +(-4.00481 - 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} -4.79899i q^{86} +2.00379 q^{88} +(-2.39324 - 4.14521i) q^{89} +(-5.27445 + 7.31553i) q^{91} +(-2.62232 + 1.51400i) q^{92} +(1.93143 - 1.11511i) q^{94} +(3.17542 - 1.83333i) q^{95} +(10.1835 - 5.87944i) q^{97} +(-5.23599 - 4.64590i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47}+ \cdots - 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	3.61932			1.61861			0.809304	−	0.587391i	$-0.199845\pi$
$5$	3.61932			1.61861			0.809304	+	0.587391i	$0.199845\pi$
$6$		0			0
$7$	0.266972	−	2.63225i	0.100906	−	0.994896i
$7$	0.266972	−	2.63225i	0.100906	−	0.994896i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	3.13442	+	1.80966i	0.991190	+	0.572264i
$11$		−	2.00379i		−	0.604167i	−0.953281	−	0.302083i	$-0.902318\pi$
$11$		−	2.00379i		−	0.604167i	0.953281	−	0.302083i	$-0.0976821\pi$
$12$		0			0
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	0.0312328	−	0.999512i	$-0.490057\pi$
$13$	−2.95206	−	1.70437i	−0.818754	−	0.472708i	−0.849987	+	0.526804i	$0.823390\pi$
$14$	1.54733	−	2.14611i	0.413541	−	0.573571i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.08709	+	5.34700i	−0.748730	+	1.29684i	0.199702	+	0.979857i	$0.436002\pi$
$17$	−3.08709	+	5.34700i	−0.748730	+	1.29684i	−0.948432	+	0.316981i	$0.897331\pi$
$18$		0			0
$19$	0.877353	−	0.506540i	0.201279	−	0.116208i	−0.395973	−	0.918262i	$-0.629593\pi$
$19$	0.877353	−	0.506540i	0.201279	−	0.116208i	0.597252	+	0.802054i	$0.296259\pi$
$20$	1.80966	+	3.13442i	0.404652	+	0.700877i
$21$		0			0
$22$	1.00190	−	1.73534i	0.213605	−	0.369975i
$23$			3.02799i			0.631380i	0.948862	+	0.315690i	$0.102236\pi$
$23$			3.02799i			0.631380i	−0.948862	+	0.315690i	$0.897764\pi$
$24$		0			0
$25$	8.09945			1.61989
$26$	−1.70437	−	2.95206i	−0.334255	−	0.578946i
$27$		0			0
$28$	2.41308	−	1.08492i	0.456029	−	0.205030i
$29$	−5.04560	+	2.91308i	−0.936945	+	0.540945i	−0.889001	−	0.457905i	$-0.848600\pi$
$29$	−5.04560	+	2.91308i	−0.936945	+	0.540945i	−0.0479434	+	0.998850i	$0.515267\pi$
$30$		0			0
$31$	0.787812	−	0.454844i	0.141495	−	0.0816923i	−0.427581	−	0.903977i	$-0.640634\pi$
$31$	0.787812	−	0.454844i	0.141495	−	0.0816923i	0.569076	+	0.822285i	$0.307301\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−5.34700	+	3.08709i	−0.917003	+	0.529432i
$35$	0.966257	−	9.52693i	0.163327	−	1.61035i
$36$		0			0
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	0.992355	+	0.123413i	$0.0393839\pi$
$37$	3.66825	+	6.35359i	0.603056	+	1.04452i	−0.389299	+	0.921111i	$0.627283\pi$
$38$	1.01308			0.164343
$39$		0			0
$40$			3.61932i			0.572264i
$41$	−2.85045	+	4.93712i	−0.445165	+	0.771048i	−0.998064	−	0.0622002i	$-0.980188\pi$
$41$	−2.85045	+	4.93712i	−0.445165	+	0.771048i	0.552899	+	0.833248i	$0.313522\pi$
$42$		0			0
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	0.623004	−	0.782219i	$-0.285912\pi$
$43$	−2.39949	−	4.15605i	−0.365919	−	0.633791i	−0.988923	+	0.148428i	$0.952579\pi$
$44$	1.73534	−	1.00190i	0.261612	−	0.151042i
$45$		0			0
$46$	−1.51400	+	2.62232i	−0.223227	+	0.386640i
$47$	1.11511	−	1.93143i	0.162655	−	0.281727i	−0.773165	−	0.634205i	$-0.781327\pi$
$47$	1.11511	−	1.93143i	0.162655	−	0.281727i	0.935820	+	0.352478i	$0.114661\pi$
$48$		0			0
$49$	−6.85745	−	1.40547i	−0.979636	−	0.200782i
$50$	7.01433	+	4.04972i	0.991975	+	0.572717i
$51$		0			0
$52$		−	3.40874i		−	0.472708i
$53$	7.58088	+	4.37683i	1.04131	+	0.601203i	0.920205	−	0.391436i	$-0.128022\pi$
$53$	7.58088	+	4.37683i	1.04131	+	0.601203i	0.121109	+	0.992639i	$0.461355\pi$
$54$		0			0
$55$		−	7.25237i		−	0.977909i
$56$	2.63225	+	0.266972i	0.351749	+	0.0356757i
$57$		0			0
$58$	−5.82616			−0.765012
$59$	−4.49313	−	7.78233i	−0.584956	−	1.01317i	−0.994881	−	0.101054i	$-0.967778\pi$
$59$	−4.49313	−	7.78233i	−0.584956	−	1.01317i	0.409925	−	0.912119i	$-0.365555\pi$
$60$		0			0
$61$	−12.7410	−	7.35603i	−1.63132	−	0.941843i	−0.983686	−	0.179892i	$-0.942425\pi$
$61$	−12.7410	−	7.35603i	−1.63132	−	0.941843i	−0.647634	−	0.761952i	$-0.724241\pi$
$62$	0.909687			0.115530
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−10.6844	−	6.16866i	−1.32524	−	0.765128i
$66$		0			0
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	0.999957	+	0.00926908i	$0.00295048\pi$
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	−0.491951	+	0.870623i	$0.663716\pi$
$68$	−6.17418			−0.748730
$69$		0			0
$70$	5.60027	−	7.76744i	0.669360	−	0.928386i
$71$		−	0.466287i		−	0.0553381i	−0.999617	−	0.0276691i	$-0.991192\pi$
$71$		−	0.466287i		−	0.0553381i	0.999617	−	0.0276691i	$-0.00880846\pi$
$72$		0			0
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	0.270938	−	0.962597i	$-0.412666\pi$
$73$	−3.65022	−	2.10746i	−0.427226	−	0.246659i	−0.698164	+	0.715938i	$0.746000\pi$
$74$			7.33650i			0.852850i
$75$		0			0
$76$	0.877353	+	0.506540i	0.100639	+	0.0581041i
$77$	−5.27448	−	0.534957i	−0.601083	−	0.0609641i
$78$		0			0
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	−0.953332	−	0.301924i	$-0.902371\pi$
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	0.738140	+	0.674648i	$0.235704\pi$
$80$	−1.80966	+	3.13442i	−0.202326	+	0.350439i
$81$		0			0
$82$	−4.93712	+	2.85045i	−0.545213	+	0.314779i
$83$	−4.00481	−	6.93654i	−0.439585	−	0.761384i	0.558072	−	0.829792i	$-0.311541\pi$
$83$	−4.00481	−	6.93654i	−0.439585	−	0.761384i	−0.997657	+	0.0684084i	$0.978208\pi$
$84$		0			0
$85$	−11.1732	+	19.3525i	−1.21190	+	2.09907i
$86$		−	4.79899i		−	0.517488i
$87$		0			0
$88$	2.00379			0.213605
$89$	−2.39324	−	4.14521i	−0.253683	−	0.439391i	0.710854	−	0.703339i	$-0.248309\pi$
$89$	−2.39324	−	4.14521i	−0.253683	−	0.439391i	−0.964537	+	0.263948i	$0.914975\pi$
$90$		0			0
$91$	−5.27445	+	7.31553i	−0.552912	+	0.766876i
$92$	−2.62232	+	1.51400i	−0.273396	+	0.157845i
$93$		0			0
$94$	1.93143	−	1.11511i	0.199211	−	0.115015i
$95$	3.17542	−	1.83333i	0.325791	−	0.188096i
$96$		0			0
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.115856	−	0.993266i	$-0.463039\pi$
$97$	10.1835	−	5.87944i	1.03398	−	0.596967i	0.918121	+	0.396299i	$0.129706\pi$
$98$	−5.23599	−	4.64590i	−0.528915	−	0.469307i
$99$		0			0
$100$	4.04972	+	7.01433i	0.404972	+	0.701433i
$101$	12.8922			1.28282			0.641411	−	0.767197i	$-0.278349\pi$
$101$	12.8922			1.28282			0.641411	+	0.767197i	$0.278349\pi$
$102$		0			0
$103$		−	10.7588i		−	1.06010i	−0.847968	−	0.530048i	$-0.822174\pi$
$103$		−	10.7588i		−	1.06010i	0.847968	−	0.530048i	$-0.177826\pi$
$104$	1.70437	−	2.95206i	0.167127	−	0.289473i
$105$		0			0
$106$	4.37683	+	7.58088i	0.425115	+	0.736321i
$107$	−2.28602	+	1.31983i	−0.220998	+	0.127593i	−0.606412	−	0.795151i	$-0.707392\pi$
$107$	−2.28602	+	1.31983i	−0.220998	+	0.127593i	0.385414	+	0.922744i	$0.374058\pi$
$108$		0			0
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	−0.564391	−	0.825507i	$-0.690889\pi$
$109$	4.51768	−	7.82484i	0.432715	−	0.749484i	0.997106	+	0.0760233i	$0.0242224\pi$
$110$	3.62618	−	6.28073i	0.345743	−	0.598844i
$111$		0			0
$112$	2.14611	+	1.54733i	0.202788	+	0.146209i
$113$	1.46411	+	0.845306i	0.137732	+	0.0795197i	0.567283	−	0.823523i	$-0.307995\pi$
$113$	1.46411	+	0.845306i	0.137732	+	0.0795197i	−0.429551	+	0.903043i	$0.641328\pi$
$114$		0			0
$115$			10.9593i			1.02196i
$116$	−5.04560	−	2.91308i	−0.468472	−	0.270473i
$117$		0			0
$118$		−	8.98627i		−	0.827253i
$119$	13.2505	+	9.55349i	1.21467	+	0.875767i
$120$		0			0
$121$	6.98481			0.634982
$122$	−7.35603	−	12.7410i	−0.665984	−	1.15352i
$123$		0			0
$124$	0.787812	+	0.454844i	0.0707476	+	0.0408462i
$125$	11.2179			1.00336
$126$		0			0
$127$	17.9292			1.59096			0.795478	−	0.605983i	$-0.207220\pi$
$127$	17.9292			1.59096			0.795478	+	0.605983i	$0.207220\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−6.16866	−	10.6844i	−0.541027	−	0.937087i
$131$	−17.3313			−1.51425			−0.757123	−	0.653272i	$-0.773396\pi$
$131$	−17.3313			−1.51425			−0.757123	+	0.653272i	$0.773396\pi$
$132$		0			0
$133$	−1.09911	−	2.44464i	−0.0953049	−	0.211977i
$134$			8.31641i			0.718429i
$135$		0			0
$136$	−5.34700	−	3.08709i	−0.458501	−	0.264716i
$137$		0	0.000645123i		0	5.51166e-5i	1.00000		2.75583e-5i	$8.77208e-6\pi$
$137$		0	0.000645123i		0	5.51166e-5i	−1.00000		2.75583e-5i	$0.999991\pi$
$138$		0			0
$139$	8.73273	+	5.04185i	0.740701	+	0.427644i	0.822324	−	0.569019i	$-0.192677\pi$
$139$	8.73273	+	5.04185i	0.740701	+	0.427644i	−0.0816233	+	0.996663i	$0.526010\pi$
$140$	8.73370	−	3.92666i	0.738132	−	0.331864i
$141$		0			0
$142$	0.233144	−	0.403817i	0.0195650	−	0.0338875i
$143$	−3.41521	+	5.91532i	−0.285594	+	0.494664i
$144$		0			0
$145$	−18.2616	+	10.5434i	−1.51655	+	0.875578i
$146$	−2.10746	−	3.65022i	−0.174414	−	0.302095i
$147$		0			0
$148$	−3.66825	+	6.35359i	−0.301528	+	0.522262i
$149$			11.2475i			0.921433i	0.887547	+	0.460716i	$0.152407\pi$
$149$			11.2475i			0.921433i	−0.887547	+	0.460716i	$0.847593\pi$
$150$		0			0
$151$	−4.72379			−0.384417			−0.192208	−	0.981354i	$-0.561565\pi$
$151$	−4.72379			−0.384417			−0.192208	+	0.981354i	$0.561565\pi$
$152$	0.506540	+	0.877353i	0.0410858	+	0.0711627i
$153$		0			0
$154$	−4.30036	−	3.10053i	−0.346533	−	0.249848i
$155$	2.85134	−	1.64622i	0.229025	−	0.132228i
$156$		0			0
$157$	2.65845	−	1.53486i	0.212168	−	0.122495i	−0.390151	−	0.920751i	$-0.627577\pi$
$157$	2.65845	−	1.53486i	0.212168	−	0.122495i	0.602318	+	0.798256i	$0.294244\pi$
$158$	−3.31284	+	1.91267i	−0.263555	+	0.152164i
$159$		0			0
$160$	−3.13442	+	1.80966i	−0.247798	+	0.143066i
$161$	7.97043	+	0.808390i	0.628158	+	0.0637101i
$162$		0			0
$163$	−1.43687	−	2.48873i	−0.112544	−	0.194932i	0.804251	−	0.594289i	$-0.202567\pi$
$163$	−1.43687	−	2.48873i	−0.112544	−	0.194932i	−0.916795	+	0.399357i	$0.869233\pi$
$164$	−5.70089			−0.445165
$165$		0			0
$166$		−	8.00963i		−	0.621668i
$167$	0.730517	−	1.26529i	0.0565291	−	0.0979113i	−0.836376	−	0.548156i	$-0.815330\pi$
$167$	0.730517	−	1.26529i	0.0565291	−	0.0979113i	0.892905	+	0.450245i	$0.148663\pi$
$168$		0			0
$169$	−0.690233	−	1.19552i	−0.0530948	−	0.0919630i
$170$	−19.3525	+	11.1732i	−1.48427	+	0.856942i
$171$		0			0
$172$	2.39949	−	4.15605i	0.182960	−	0.316896i
$173$	1.53541	−	2.65940i	0.116735	−	0.202191i	−0.801737	−	0.597677i	$-0.796091\pi$
$173$	1.53541	−	2.65940i	0.116735	−	0.202191i	0.918472	+	0.395486i	$0.129424\pi$
$174$		0			0
$175$	2.16233	−	21.3197i	0.163457	−	1.61162i
$176$	1.73534	+	1.00190i	0.130806	+	0.0755209i
$177$		0			0
$178$		−	4.78647i		−	0.358761i
$179$	16.7310	+	9.65966i	1.25054	+	0.721997i	0.971216	−	0.238201i	$-0.0765578\pi$
$179$	16.7310	+	9.65966i	1.25054	+	0.721997i	0.279320	+	0.960198i	$0.409891\pi$
$180$		0			0
$181$			7.89318i			0.586695i	0.956006	+	0.293348i	$0.0947693\pi$
$181$			7.89318i			0.586695i	−0.956006	+	0.293348i	$0.905231\pi$
$182$	−8.22557	+	3.69821i	−0.609720	+	0.274130i
$183$		0			0
$184$	−3.02799			−0.223227
$185$	13.2765	+	22.9957i	0.976111	+	1.69067i
$186$		0			0
$187$	10.7143	+	6.18590i	0.783506	+	0.452358i
$188$	2.23022			0.162655
$189$		0			0
$190$	3.66666			0.266007
$191$	−11.5218	−	6.65211i	−0.833688	−	0.481330i	0.0214259	−	0.999770i	$-0.493179\pi$
$191$	−11.5218	−	6.65211i	−0.833688	−	0.481330i	−0.855114	+	0.518441i	$0.826513\pi$
$192$		0			0
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	0.724112	−	0.689682i	$-0.242250\pi$
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	−0.959338	+	0.282259i	$0.908916\pi$
$194$	11.7589			0.844239
$195$		0			0
$196$	−2.21155	−	6.64146i	−0.157968	−	0.474390i
$197$			4.44250i			0.316515i	0.987398	+	0.158258i	$0.0505876\pi$
$197$			4.44250i			0.316515i	−0.987398	+	0.158258i	$0.949412\pi$
$198$		0			0
$199$	9.96868	+	5.75542i	0.706661	+	0.407991i	0.809823	−	0.586674i	$-0.199563\pi$
$199$	9.96868	+	5.75542i	0.706661	+	0.407991i	−0.103163	+	0.994665i	$0.532896\pi$
$200$			8.09945i			0.572717i
$201$		0			0
$202$	11.1650	+	6.44610i	0.785565	+	0.453546i
$203$	6.32091	+	14.0590i	0.443641	+	0.986747i
$204$		0			0
$205$	−10.3167	+	17.8690i	−0.720547	+	1.24802i
$206$	5.37940	−	9.31740i	0.374801	−	0.649174i
$207$		0			0
$208$	2.95206	−	1.70437i	0.204688	−	0.118177i
$209$	−1.01500	−	1.75804i	−0.0702092	−	0.121606i
$210$		0			0
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	−0.155155	−	0.987890i	$-0.549588\pi$
$211$	11.3005	−	19.5731i	0.777961	−	1.34747i	0.933115	−	0.359577i	$-0.117079\pi$
$212$			8.75365i			0.601203i
$213$		0			0
$214$	−2.63967			−0.180444
$215$	−8.68453	−	15.0420i	−0.592280	−	1.02586i
$216$		0			0
$217$	−0.986937	−	2.19515i	−0.0669976	−	0.149016i
$218$	7.82484	−	4.51768i	0.529965	−	0.305976i
$219$		0			0
$220$	6.28073	−	3.62618i	0.423447	−	0.244477i
$221$	18.2265	−	10.5231i	1.22605	−	0.707860i
$222$		0			0
$223$	−16.2994	+	9.41045i	−1.09149	+	0.630170i	−0.933972	−	0.357346i	$-0.883682\pi$
$223$	−16.2994	+	9.41045i	−1.09149	+	0.630170i	−0.157515	+	0.987517i	$0.550348\pi$
$224$	1.08492	+	2.41308i	0.0724892	+	0.161231i
$225$		0			0
$226$	0.845306	+	1.46411i	0.0562289	+	0.0973914i
$227$	14.6133			0.969919			0.484960	−	0.874537i	$-0.338834\pi$
$227$	14.6133			0.969919			0.484960	+	0.874537i	$0.338834\pi$
$228$		0			0
$229$		−	2.37919i		−	0.157221i	−0.996905	−	0.0786106i	$-0.974952\pi$
$229$		−	2.37919i		−	0.157221i	0.996905	−	0.0786106i	$-0.0250484\pi$
$230$	−5.47963	+	9.49100i	−0.361316	+	0.625818i
$231$		0			0
$232$	−2.91308	−	5.04560i	−0.191253	−	0.331260i
$233$	9.03470	−	5.21619i	0.591883	−	0.341724i	−0.173959	−	0.984753i	$-0.555656\pi$
$233$	9.03470	−	5.21619i	0.591883	−	0.341724i	0.765842	+	0.643029i	$0.222323\pi$
$234$		0			0
$235$	4.03593	−	6.99044i	0.263275	−	0.456006i
$236$	4.49313	−	7.78233i	0.292478	−	0.506587i
$237$		0			0
$238$	6.69849	+	14.8988i	0.434198	+	0.965745i
$239$	−20.5971	−	11.8917i	−1.33232	−	0.769213i	−0.346662	−	0.937990i	$-0.612685\pi$
$239$	−20.5971	−	11.8917i	−1.33232	−	0.769213i	−0.985654	+	0.168777i	$0.946018\pi$
$240$		0			0
$241$			28.6487i			1.84542i	0.385489	+	0.922712i	$0.374033\pi$
$241$			28.6487i			1.84542i	−0.385489	+	0.922712i	$0.625967\pi$
$242$	6.04902	+	3.49240i	0.388846	+	0.224500i
$243$		0			0
$244$		−	14.7121i		−	0.941843i
$245$	−24.8193	−	5.08685i	−1.58565	−	0.324987i
$246$		0			0
$247$	−3.45333			−0.219730
$248$	0.454844	+	0.787812i	0.0288826	+	0.0500261i
$249$		0			0
$250$	9.71496	+	5.60894i	0.614428	+	0.354740i
$251$	−11.0301			−0.696216			−0.348108	−	0.937454i	$-0.613176\pi$
$251$	−11.0301			−0.696216			−0.348108	+	0.937454i	$0.613176\pi$
$252$		0			0
$253$	6.06748			0.381459
$254$	15.5271	+	8.96458i	0.974257	+	0.562488i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.0978			0.941775			0.470888	−	0.882193i	$-0.343934\pi$
$257$	15.0978			0.941775			0.470888	+	0.882193i	$0.343934\pi$
$258$		0			0
$259$	17.7035	−	7.95950i	1.10004	−	0.494579i
$260$		−	12.3373i		−	0.765128i
$261$		0			0
$262$	−15.0094	−	8.66567i	−0.927283	−	0.535367i
$263$			19.6385i			1.21096i	0.795859	+	0.605482i	$0.207020\pi$
$263$			19.6385i			1.21096i	−0.795859	+	0.605482i	$0.792980\pi$
$264$		0			0
$265$	27.4376	+	15.8411i	1.68548	+	0.973112i
$266$	0.270464	−	2.66668i	0.0165832	−	0.163504i
$267$		0			0
$268$	−4.15821	+	7.20222i	−0.254003	+	0.439946i
$269$	0.245503	−	0.425223i	0.0149686	−	0.0259263i	−0.858444	−	0.512907i	$-0.828569\pi$
$269$	0.245503	−	0.425223i	0.0149686	−	0.0259263i	0.873413	+	0.486981i	$0.161902\pi$
$270$		0			0
$271$	−12.1927	+	7.03945i	−0.740653	+	0.427616i	−0.822307	−	0.569045i	$-0.807313\pi$
$271$	−12.1927	+	7.03945i	−0.740653	+	0.427616i	0.0816537	+	0.996661i	$0.473980\pi$
$272$	−3.08709	−	5.34700i	−0.187182	−	0.324209i
$273$		0			0
$274$	−0.000322562	0	0.000558693i	−1.94867e−5	0	3.37519e-5i
$275$		−	16.2296i		−	0.978683i
$276$		0			0
$277$	30.7200			1.84579			0.922894	−	0.385054i	$-0.125817\pi$
$277$	30.7200			1.84579			0.922894	+	0.385054i	$0.125817\pi$
$278$	5.04185	+	8.73273i	0.302390	+	0.523755i
$279$		0			0
$280$	9.52693	+	0.966257i	0.569343	+	0.0577449i
$281$	−6.86286	+	3.96227i	−0.409404	+	0.236369i	−0.690534	−	0.723300i	$-0.742624\pi$
$281$	−6.86286	+	3.96227i	−0.409404	+	0.236369i	0.281130	+	0.959670i	$0.409291\pi$
$282$		0			0
$283$	−9.97303	+	5.75793i	−0.592835	+	0.342273i	−0.766218	−	0.642581i	$-0.777864\pi$
$283$	−9.97303	+	5.75793i	−0.592835	+	0.342273i	0.173383	+	0.984855i	$0.444530\pi$
$284$	0.403817	−	0.233144i	0.0239621	−	0.0138345i
$285$		0			0
$286$	−5.91532	+	3.41521i	−0.349780	+	0.201946i
$287$	12.2347	+	8.82115i	0.722193	+	0.520696i
$288$		0			0
$289$	−10.5603	−	18.2909i	−0.621192	−	1.07594i
$290$	−21.0867			−1.23825
$291$		0			0
$292$		−	4.21492i		−	0.246659i
$293$	−2.50937	+	4.34636i	−0.146599	+	0.253917i	−0.929968	−	0.367639i	$-0.880166\pi$
$293$	−2.50937	+	4.34636i	−0.146599	+	0.253917i	0.783369	+	0.621557i	$0.213499\pi$
$294$		0			0
$295$	−16.2621	−	28.1667i	−0.946814	−	1.63993i
$296$	−6.35359	+	3.66825i	−0.369295	+	0.213213i
$297$		0			0
$298$	−5.62376	+	9.74064i	−0.325776	+	0.564260i
$299$	5.16083	−	8.93882i	0.298458	−	0.516945i
$300$		0			0
$301$	−11.5803	+	5.20651i	−0.667480	+	0.300098i
$302$	−4.09092	−	2.36189i	−0.235406	−	0.135912i
$303$		0			0
$304$			1.01308i			0.0581041i
$305$	−46.1138	−	26.6238i	−2.64047	−	1.52447i
$306$		0			0
$307$		−	17.5309i		−	1.00054i	−0.865869	−	0.500271i	$-0.833234\pi$
$307$		−	17.5309i		−	1.00054i	0.865869	−	0.500271i	$-0.166766\pi$
$308$	−2.17395	−	4.83532i	−0.123873	−	0.275518i
$309$		0			0
$310$	3.29245			0.186998
$311$	−8.64759	−	14.9781i	−0.490360	−	0.849328i	0.509579	−	0.860424i	$-0.329801\pi$
$311$	−8.64759	−	14.9781i	−0.490360	−	0.849328i	−0.999938	+	0.0110959i	$0.996468\pi$
$312$		0			0
$313$	7.78988	+	4.49749i	0.440310	+	0.254213i	0.703729	−	0.710468i	$-0.251517\pi$
$313$	7.78988	+	4.49749i	0.440310	+	0.254213i	−0.263419	+	0.964681i	$0.584850\pi$
$314$	3.06972			0.173234
$315$		0			0
$316$	−3.82533			−0.215192
$317$	5.82002	+	3.36019i	0.326885	+	0.188727i	0.654457	−	0.756099i	$-0.272897\pi$
$317$	5.82002	+	3.36019i	0.326885	+	0.188727i	−0.327572	+	0.944826i	$0.606230\pi$
$318$		0			0
$319$	5.83721	+	10.1103i	0.326821	+	0.566071i
$320$	−3.61932			−0.202326
$321$		0			0
$322$	6.49840	+	4.68530i	0.362142	+	0.261102i
$323$			6.25494i			0.348034i
$324$		0			0
$325$	−23.9100	−	13.8045i	−1.32629	−	0.765734i
$326$		−	2.87373i		−	0.159161i
$327$		0			0
$328$	−4.93712	−	2.85045i	−0.272607	−	0.157390i
$329$	−4.78629	−	3.45088i	−0.263876	−	0.190253i
$330$		0			0
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	−0.483858	−	0.875146i	$-0.660765\pi$
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	0.999828	−	0.0185396i	$-0.00590167\pi$
$332$	4.00481	−	6.93654i	0.219793	−	0.380692i
$333$		0			0
$334$	1.26529	−	0.730517i	0.0692338	−	0.0399721i
$335$	15.0499	+	26.0671i	0.822262	+	1.42420i
$336$		0			0
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	−0.792458	−	0.609926i	$-0.791199\pi$
$337$	2.42287	−	4.19654i	0.131982	−	0.228600i	0.924441	+	0.381326i	$0.124532\pi$
$338$		−	1.38047i		−	0.0750874i
$339$		0			0
$340$	−22.3463			−1.21190
$341$	−0.911413	−	1.57861i	−0.0493558	−	0.0854868i
$342$		0			0
$343$	−5.53030	+	17.6753i	−0.298608	+	0.954376i
$344$	4.15605	−	2.39949i	0.224079	−	0.129372i
$345$		0			0
$346$	2.65940	−	1.53541i	0.142970	−	0.0825440i
$347$	15.1305	−	8.73559i	0.812247	−	0.468951i	−0.0354887	−	0.999370i	$-0.511299\pi$
$347$	15.1305	−	8.73559i	0.812247	−	0.468951i	0.847736	+	0.530419i	$0.177965\pi$
$348$		0			0
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.937399	−	0.348257i	$-0.886774\pi$
$349$	−20.6338	+	11.9129i	−1.10450	+	0.637683i	−0.167101	+	0.985940i	$0.553440\pi$
$350$	12.5325	−	17.3823i	0.669890	−	0.929122i
$351$		0			0
$352$	1.00190	+	1.73534i	0.0534013	+	0.0924938i
$353$	−10.0412			−0.534441			−0.267220	−	0.963635i	$-0.586105\pi$
$353$	−10.0412			−0.534441			−0.267220	+	0.963635i	$0.586105\pi$
$354$		0			0
$355$		−	1.68764i		−	0.0895707i
$356$	2.39324	−	4.14521i	0.126841	−	0.219696i
$357$		0			0
$358$	9.65966	+	16.7310i	0.510529	+	0.884262i
$359$	−10.5353	+	6.08254i	−0.556030	+	0.321024i	−0.751550	−	0.659676i	$-0.770694\pi$
$359$	−10.5353	+	6.08254i	−0.556030	+	0.321024i	0.195521	+	0.980700i	$0.437360\pi$
$360$		0			0
$361$	−8.98683	+	15.5657i	−0.472991	+	0.819245i
$362$	−3.94659	+	6.83569i	−0.207428	+	0.359276i
$363$		0			0
$364$	−8.97266	−	0.910040i	−0.470295	−	0.0476990i
$365$	−13.2113	−	7.62756i	−0.691512	−	0.399245i
$366$		0			0
$367$			3.63061i			0.189516i	0.995500	+	0.0947582i	$0.0302078\pi$
$367$			3.63061i			0.189516i	−0.995500	+	0.0947582i	$0.969792\pi$
$368$	−2.62232	−	1.51400i	−0.136698	−	0.0789225i
$369$		0			0
$370$			26.5531i			1.38043i
$371$	13.5448	−	18.7863i	0.703210	−	0.975335i
$372$		0			0
$373$	5.49231			0.284381			0.142191	−	0.989839i	$-0.454585\pi$
$373$	5.49231			0.284381			0.142191	+	0.989839i	$0.454585\pi$
$374$	6.18590	+	10.7143i	0.319865	+	0.554023i
$375$		0			0
$376$	1.93143	+	1.11511i	0.0996057	+	0.0575074i
$377$	19.8599			1.02284
$378$		0			0
$379$	−15.5960			−0.801112			−0.400556	−	0.916272i	$-0.631183\pi$
$379$	−15.5960			−0.801112			−0.400556	+	0.916272i	$0.631183\pi$
$380$	3.17542	+	1.83333i	0.162896	+	0.0940478i
$381$		0			0
$382$	−6.65211	−	11.5218i	−0.340352	−	0.589506i
$383$	−9.43067			−0.481885			−0.240942	−	0.970539i	$-0.577456\pi$
$383$	−9.43067			−0.481885			−0.240942	+	0.970539i	$0.577456\pi$
$384$		0			0
$385$	−19.0900	−	1.93618i	−0.972918	−	0.0986769i
$386$		−	6.53573i		−	0.332660i
$387$		0			0
$388$	10.1835	+	5.87944i	0.516989	+	0.298483i
$389$			6.42177i			0.325597i	0.986659	+	0.162798i	$0.0520520\pi$
$389$			6.42177i			0.325597i	−0.986659	+	0.162798i	$0.947948\pi$
$390$		0			0
$391$	−16.1907	−	9.34769i	−0.818798	−	0.472733i
$392$	1.40547	−	6.85745i	0.0709871	−	0.346354i
$393$		0			0
$394$	−2.22125	+	3.84732i	−0.111905	+	0.193825i
$395$	−6.92255	+	11.9902i	−0.348311	+	0.603293i
$396$		0			0
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	−0.341889	−	0.939740i	$-0.611067\pi$
$397$	5.99750	−	3.46266i	0.301006	−	0.173786i	0.642895	+	0.765955i	$0.277733\pi$
$398$	5.75542	+	9.96868i	0.288493	+	0.499685i
$399$		0			0
$400$	−4.04972	+	7.01433i	−0.202486	+	0.350716i
$401$			10.5869i			0.528682i	0.964429	+	0.264341i	$0.0851545\pi$
$401$			10.5869i			0.528682i	−0.964429	+	0.264341i	$0.914846\pi$
$402$		0			0
$403$	−3.10089			−0.154466
$404$	6.44610	+	11.1650i	0.320705	+	0.555478i
$405$		0			0
$406$	−1.55542	+	15.3359i	−0.0771943	+	0.761107i
$407$	12.7313	−	7.35042i	0.631067	−	0.364347i
$408$		0			0
$409$	7.72792	−	4.46172i	0.382121	−	0.220618i	−0.296620	−	0.954996i	$-0.595859\pi$
$409$	7.72792	−	4.46172i	0.382121	−	0.220618i	0.678741	+	0.734378i	$0.262526\pi$
$410$	−17.8690	+	10.3167i	−0.882486	+	0.509504i
$411$		0			0
$412$	9.31740	−	5.37940i	0.459035	−	0.265024i
$413$	−21.6846	+	9.74937i	−1.06703	+	0.479735i
$414$		0			0
$415$	−14.4947	−	25.1055i	−0.711516	−	1.23238i
$416$	3.40874			0.167127
$417$		0			0
$418$		−	2.03000i		−	0.0992908i
$419$	17.1924	−	29.7781i	0.839903	−	1.45475i	−0.0500724	−	0.998746i	$-0.515945\pi$
$419$	17.1924	−	29.7781i	0.839903	−	1.45475i	0.889975	−	0.456009i	$-0.150721\pi$
$420$		0			0
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.865310	−	0.501237i	$-0.832879\pi$
$421$	−17.7840	−	30.8028i	−0.866739	−	1.50124i	−0.00142877	−	0.999999i	$-0.500455\pi$
$422$	19.5731	−	11.3005i	0.952803	−	0.550101i
$423$		0			0
$424$	−4.37683	+	7.58088i	−0.212557	+	0.368160i
$425$	−25.0037	+	43.3077i	−1.21286	+	2.10073i
$426$		0			0
$427$	−22.7644	+	31.5737i	−1.10165	+	1.52796i
$428$	−2.28602	−	1.31983i	−0.110499	−	0.0637965i
$429$		0			0
$430$		−	17.3691i		−	0.837610i
$431$	−26.7338	−	15.4348i	−1.28772	−	0.743466i	−0.309474	−	0.950908i	$-0.600153\pi$
$431$	−26.7338	−	15.4348i	−1.28772	−	0.743466i	−0.978247	+	0.207442i	$0.933486\pi$
$432$		0			0
$433$		−	23.2463i		−	1.11715i	−0.829455	−	0.558574i	$-0.811349\pi$
$433$		−	23.2463i		−	1.11715i	0.829455	−	0.558574i	$-0.188651\pi$
$434$	0.242861	−	2.39452i	0.0116577	−	0.114941i
$435$		0			0
$436$	9.03535			0.432715
$437$	1.53380	+	2.65662i	0.0733716	+	0.127083i
$438$		0			0
$439$	19.2887	+	11.1364i	0.920601	+	0.531509i	0.883827	−	0.467814i	$-0.154958\pi$
$439$	19.2887	+	11.1364i	0.920601	+	0.531509i	0.0367744	+	0.999324i	$0.488292\pi$
$440$	7.25237			0.345743
$441$		0			0
$442$	21.0462			1.00107
$443$	−15.5756	−	8.99259i	−0.740020	−	0.427251i	0.0820566	−	0.996628i	$-0.473851\pi$
$443$	−15.5756	−	8.99259i	−0.740020	−	0.427251i	−0.822077	+	0.569377i	$0.807185\pi$
$444$		0			0
$445$	−8.66188	−	15.0028i	−0.410612	−	0.711202i
$446$	−18.8209			−0.891195
$447$		0			0
$448$	−0.266972	+	2.63225i	−0.0126133	+	0.124362i
$449$		−	9.44363i		−	0.445673i	−0.974856	−	0.222836i	$-0.928468\pi$
$449$		−	9.44363i		−	0.445673i	0.974856	−	0.222836i	$-0.0715315\pi$
$450$		0			0
$451$	9.89297	+	5.71171i	0.465842	+	0.268954i
$452$			1.69061i			0.0795197i
$453$		0			0
$454$	12.6555	+	7.30665i	0.593952	+	0.342918i
$455$	−19.0899	+	26.4772i	−0.894948	+	1.24127i
$456$		0			0
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	−0.843649	−	0.536896i	$-0.819597\pi$
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	0.886790	+	0.462173i	$0.152930\pi$
$458$	1.18959	−	2.06044i	0.0555861	−	0.0962779i
$459$		0			0
$460$	−9.49100	+	5.47963i	−0.442520	+	0.255489i
$461$	−18.1869	−	31.5007i	−0.847050	−	1.46713i	−0.883829	−	0.467810i	$-0.845043\pi$
$461$	−18.1869	−	31.5007i	−0.847050	−	1.46713i	0.0367790	−	0.999323i	$-0.488290\pi$
$462$		0			0
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	0.208425	+	0.978038i	$0.433166\pi$
$463$	−15.9830	+	27.6834i	−0.742794	+	1.28656i	−0.951219	+	0.308518i	$0.900167\pi$
$464$		−	5.82616i		−	0.270473i
$465$		0			0
$466$	10.4324			0.483271
$467$	12.2206	+	21.1666i	0.565500	+	0.979475i	0.997003	+	0.0773632i	$0.0246501\pi$
$467$	12.2206	+	21.1666i	0.565500	+	0.979475i	−0.431503	+	0.902112i	$0.642017\pi$
$468$		0			0
$469$	20.0682	−	9.02263i	0.926662	−	0.416627i
$470$	6.99044	−	4.03593i	0.322445	−	0.186164i
$471$		0			0
$472$	7.78233	−	4.49313i	0.358211	−	0.206813i
$473$	−8.32786	+	4.80809i	−0.382916	+	0.221076i
$474$		0			0
$475$	7.10607	−	4.10269i	0.326049	−	0.188245i
$476$	−1.64833	+	16.2520i	−0.0755513	+	0.744908i
$477$		0			0
$478$	−11.8917	−	20.5971i	−0.543916	−	0.942090i
$479$	−10.9606			−0.500805			−0.250402	−	0.968142i	$-0.580563\pi$
$479$	−10.9606			−0.500805			−0.250402	+	0.968142i	$0.580563\pi$
$480$		0			0
$481$		−	25.0082i		−	1.14028i
$482$	−14.3243	+	24.8105i	−0.652456	+	1.13009i
$483$		0			0
$484$	3.49240	+	6.04902i	0.158746	+	0.274955i
$485$	36.8573	−	21.2796i	1.67360	−	0.966255i
$486$		0			0
$487$	−16.8087	+	29.1136i	−0.761677	+	1.31926i	0.180309	+	0.983610i	$0.442290\pi$
$487$	−16.8087	+	29.1136i	−0.761677	+	1.31926i	−0.941986	+	0.335653i	$0.891043\pi$
$488$	7.35603	−	12.7410i	0.332992	−	0.576759i
$489$		0			0
$490$	−18.9507	−	16.8150i	−0.856105	−	0.759624i
$491$	19.6893	+	11.3676i	0.888568	+	0.513015i	0.873474	−	0.486871i	$-0.161862\pi$
$491$	19.6893	+	11.3676i	0.888568	+	0.513015i	0.0150939	+	0.999886i	$0.495195\pi$
$492$		0			0
$493$		−	35.9718i		−	1.62009i
$494$	−2.99067	−	1.72667i	−0.134557	−	0.0776863i
$495$		0			0
$496$			0.909687i			0.0408462i
$497$	−1.22738	−	0.124486i	−0.0550557	−	0.00558395i
$498$		0			0
$499$	19.5235			0.873992			0.436996	−	0.899463i	$-0.356042\pi$
$499$	19.5235			0.873992			0.436996	+	0.899463i	$0.356042\pi$
$500$	5.60894	+	9.71496i	0.250839	+	0.434466i
$501$		0			0
$502$	−9.55238	−	5.51507i	−0.426343	−	0.246149i
$503$	−13.6867			−0.610262			−0.305131	−	0.952310i	$-0.598700\pi$
$503$	−13.6867			−0.610262			−0.305131	+	0.952310i	$0.598700\pi$
$504$		0			0
$505$	46.6609			2.07638
$506$	5.25459	+	3.03374i	0.233595	+	0.134866i
$507$		0			0
$508$	8.96458	+	15.5271i	0.397739	+	0.688904i
$509$	2.29166			0.101576			0.0507881	−	0.998709i	$-0.483827\pi$
$509$	2.29166			0.101576			0.0507881	+	0.998709i	$0.483827\pi$
$510$		0			0
$511$	−6.52186	+	9.04566i	−0.288510	+	0.400156i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	13.0751	+	7.54890i	0.576717	+	0.332968i
$515$		−	38.9395i		−	1.71588i
$516$		0			0
$517$	−3.87018	−	2.23445i	−0.170210	−	0.0982710i
$518$	19.3115	+	1.95864i	0.848497	+	0.0860577i
$519$		0			0
$520$	6.16866	−	10.6844i	0.270514	−	0.468543i
$521$	8.54102	−	14.7935i	0.374189	−	0.648114i	−0.616017	−	0.787733i	$-0.711255\pi$
$521$	8.54102	−	14.7935i	0.374189	−	0.648114i	0.990205	+	0.139619i	$0.0445879\pi$
$522$		0			0
$523$	35.7462	−	20.6381i	1.56307	−	0.902440i	0.566128	−	0.824317i	$-0.308441\pi$
$523$	35.7462	−	20.6381i	1.56307	−	0.902440i	0.996944	−	0.0781229i	$-0.0248927\pi$
$524$	−8.66567	−	15.0094i	−0.378562	−	0.655688i
$525$		0			0
$526$	−9.81926	+	17.0075i	−0.428140	+	0.741561i
$527$			5.61657i			0.244662i
$528$		0			0
$529$	13.8313			0.601359
$530$	15.8411	+	27.4376i	0.688094	+	1.19181i
$531$		0			0
$532$	1.56757	−	2.17418i	0.0679627	−	0.0942626i
$533$	16.8294	−	9.71644i	0.728961	−	0.420866i
$534$		0			0
$535$	−8.27382	+	4.77689i	−0.357708	+	0.206523i
$536$	−7.20222	+	4.15821i	−0.311089	+	0.179607i
$537$		0			0
$538$	0.425223	−	0.245503i	0.0183327	−	0.0105844i
$539$	−2.81628	+	13.7409i	−0.121306	+	0.591864i
$540$		0			0
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.673880	+	0.738841i	$0.264627\pi$
$541$	22.7197	+	39.3516i	0.976795	+	1.69186i	0.302915	+	0.953018i	$0.402040\pi$
$542$	−14.0789			−0.604741
$543$		0			0
$544$		−	6.17418i		−	0.264716i
$545$	16.3509	−	28.3206i	0.700395	−	1.21312i
$546$		0			0
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	0.984061	+	0.177832i	$0.0569082\pi$
$547$	15.1095	+	26.1705i	0.646037	+	1.11897i	−0.338024	+	0.941138i	$0.609758\pi$
$548$	−0.000558693	0	0.000322562i	−2.38662e−5	0	1.37791e-5i
$549$		0			0
$550$	8.11481	−	14.0553i	0.346017	−	0.599319i
$551$	−2.95118	+	5.11160i	−0.125725	+	0.217761i
$552$		0			0
$553$	8.20958	+	5.91905i	0.349107	+	0.251704i
$554$	26.6043	+	15.3600i	1.13031	+	0.652585i
$555$		0			0
$556$			10.0837i			0.427644i
$557$	22.0154	+	12.7106i	0.932822	+	0.538565i	0.887703	−	0.460417i	$-0.152300\pi$
$557$	22.0154	+	12.7106i	0.932822	+	0.538565i	0.0451189	+	0.998982i	$0.485633\pi$
$558$		0			0
$559$			16.3585i			0.691892i
$560$	7.76744	+	5.60027i	0.328234	+	0.236655i
$561$		0			0
$562$	−7.92455			−0.334277
$563$	−1.44346	−	2.50015i	−0.0608346	−	0.105369i	0.834004	−	0.551758i	$-0.186043\pi$
$563$	−1.44346	−	2.50015i	−0.0608346	−	0.105369i	−0.894839	+	0.446390i	$0.852710\pi$
$564$		0			0
$565$	5.29909	+	3.05943i	0.222934	+	0.128711i
$566$	−11.5159			−0.484048
$567$		0			0
$568$	0.466287			0.0195650
$569$	38.5945	+	22.2826i	1.61797	+	0.934134i	0.987445	+	0.157963i	$0.0504927\pi$
$569$	38.5945	+	22.2826i	1.61797	+	0.934134i	0.630523	+	0.776171i	$0.282841\pi$
$570$		0			0
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	0.926216	−	0.376992i	$-0.123042\pi$
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	−0.789593	+	0.613631i	$0.789708\pi$
$572$	−6.83042			−0.285594
$573$		0			0
$574$	6.18501	+	13.7567i	0.258157	+	0.574194i
$575$			24.5251i			1.02277i
$576$		0			0
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	0.524304	−	0.851531i	$-0.324326\pi$
$577$	1.17720	+	0.679658i	0.0490076	+	0.0282945i	−0.475296	+	0.879826i	$0.657659\pi$
$578$		−	21.1205i		−	0.878498i
$579$		0			0
$580$	−18.2616	−	10.5434i	−0.758273	−	0.437789i
$581$	−19.3279	+	8.68979i	−0.801855	+	0.360513i
$582$		0			0
$583$	8.77026	−	15.1905i	0.363227	−	0.629128i
$584$	2.10746	−	3.65022i	0.0872072	−	0.151047i
$585$		0			0
$586$	−4.34636	+	2.50937i	−0.179547	+	0.103661i
$587$	22.2025	+	38.4559i	0.916397	+	1.58725i	0.804843	+	0.593488i	$0.202250\pi$
$587$	22.2025	+	38.4559i	0.916397	+	1.58725i	0.111555	+	0.993758i	$0.464417\pi$
$588$		0			0
$589$	0.460793	−	0.798117i	0.0189866	−	0.0328858i
$590$		−	32.5241i		−	1.33900i
$591$		0			0
$592$	−7.33650			−0.301528
$593$	7.17564	+	12.4286i	0.294668	+	0.510380i	0.974908	−	0.222610i	$-0.0714576\pi$
$593$	7.17564	+	12.4286i	0.294668	+	0.510380i	−0.680240	+	0.732990i	$0.738124\pi$
$594$		0			0
$595$	47.9576	+	34.5771i	1.96607	+	1.41752i
$596$	−9.74064	+	5.62376i	−0.398992	+	0.230358i
$597$		0			0
$598$	8.93882	−	5.16083i	0.365535	−	0.211042i
$599$	3.03349	−	1.75139i	0.123945	−	0.0715597i	−0.436746	−	0.899585i	$-0.643869\pi$
$599$	3.03349	−	1.75139i	0.123945	−	0.0715597i	0.560691	+	0.828025i	$0.310536\pi$
$600$		0			0
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	−0.776633	−	0.629953i	$-0.783074\pi$
$601$	−15.1846	+	8.76685i	−0.619394	+	0.357607i	0.157239	+	0.987561i	$0.449741\pi$
$602$	−12.6321	−	1.28120i	−0.514847	−	0.0522177i
$603$		0			0
$604$	−2.36189	−	4.09092i	−0.0961041	−	0.166457i
$605$	25.2802			1.02779
$606$		0			0
$607$		−	0.0872864i		−	0.00354285i	−0.999998	−	0.00177142i	$-0.999436\pi$
$607$		−	0.0872864i		−	0.00354285i	0.999998	−	0.00177142i	$-0.000563862\pi$
$608$	−0.506540	+	0.877353i	−0.0205429	+	0.0355814i
$609$		0			0
$610$	−26.6238	−	46.1138i	−1.07797	−	1.86709i
$611$	−6.58373	+	3.80112i	−0.266349	+	0.153777i
$612$		0			0
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	−0.493681	−	0.869643i	$-0.664349\pi$
$613$	12.5352	−	21.7116i	0.506292	−	0.876924i	0.999973	−	0.00728071i	$-0.00231754\pi$
$614$	8.76545	−	15.1822i	0.353745	−	0.612704i
$615$		0			0
$616$	0.534957	−	5.27448i	0.0215541	−	0.212515i
$617$	10.6365	+	6.14101i	0.428211	+	0.247228i	0.698584	−	0.715528i	$-0.253814\pi$
$617$	10.6365	+	6.14101i	0.428211	+	0.247228i	−0.270373	+	0.962756i	$0.587147\pi$
$618$		0			0
$619$		−	20.3076i		−	0.816229i	−0.912931	−	0.408115i	$-0.866186\pi$
$619$		−	20.3076i		−	0.816229i	0.912931	−	0.408115i	$-0.133814\pi$
$620$	2.85134	+	1.64622i	0.114513	+	0.0661139i
$621$		0			0
$622$		−	17.2952i		−	0.693474i
$623$	−11.5501	+	5.19294i	−0.462747	+	0.208051i
$624$		0			0
$625$	0.103794			0.00415176
$626$	4.49749	+	7.78988i	0.179756	+	0.311346i
$627$		0			0
$628$	2.65845	+	1.53486i	0.106084	+	0.0612475i
$629$	−45.2969			−1.80610
$630$		0			0
$631$	−45.9665			−1.82990			−0.914950	−	0.403568i	$-0.867770\pi$
$631$	−45.9665			−1.82990			−0.914950	+	0.403568i	$0.867770\pi$
$632$	−3.31284	−	1.91267i	−0.131778	−	0.0760818i
$633$		0			0
$634$	3.36019	+	5.82002i	0.133450	+	0.231143i
$635$	64.8913			2.57513
$636$		0			0
$637$	17.8482	+	15.8367i	0.707169	+	0.627472i
$638$			11.6744i			0.462195i
$639$		0			0
$640$	−3.13442	−	1.80966i	−0.123899	−	0.0715330i
$641$		−	31.6509i		−	1.25013i	−0.780571	−	0.625067i	$-0.785072\pi$
$641$		−	31.6509i		−	1.25013i	0.780571	−	0.625067i	$-0.214928\pi$
$642$		0			0
$643$	10.0106	+	5.77960i	0.394778	+	0.227925i	0.684228	−	0.729268i	$-0.260139\pi$
$643$	10.0106	+	5.77960i	0.394778	+	0.227925i	−0.289450	+	0.957193i	$0.593472\pi$
$644$	3.28513	+	7.30679i	0.129452	+	0.287928i
$645$		0			0
$646$	−3.12747	+	5.41694i	−0.123049	+	0.213127i
$647$	−13.0365	+	22.5799i	−0.512519	+	0.887708i	0.487376	+	0.873192i	$0.337954\pi$
$647$	−13.0365	+	22.5799i	−0.512519	+	0.887708i	−0.999895	+	0.0145160i	$0.995379\pi$
$648$		0			0
$649$	−15.5942	+	9.00332i	−0.612126	+	0.353411i
$650$	−13.8045	−	23.9100i	−0.541456	−	0.937829i
$651$		0			0
$652$	1.43687	−	2.48873i	0.0562720	−	0.0974660i
$653$		−	18.9315i		−	0.740847i	−0.928863	−	0.370424i	$-0.879212\pi$
$653$		−	18.9315i		−	0.740847i	0.928863	−	0.370424i	$-0.120788\pi$
$654$		0			0
$655$	−62.7276			−2.45097
$656$	−2.85045	−	4.93712i	−0.111291	−	0.192762i
$657$		0			0
$658$	−2.41961	−	5.38169i	−0.0943260	−	0.209800i
$659$	−23.3508	+	13.4816i	−0.909618	+	0.525168i	−0.880308	−	0.474402i	$-0.842664\pi$
$659$	−23.3508	+	13.4816i	−0.909618	+	0.525168i	−0.0293098	+	0.999570i	$0.509331\pi$
$660$		0			0
$661$	22.3201	−	12.8865i	0.868151	−	0.501227i	0.00141768	−	0.999999i	$-0.499549\pi$
$661$	22.3201	−	12.8865i	0.868151	−	0.501227i	0.866733	+	0.498772i	$0.166215\pi$
$662$	16.2592	−	9.38725i	0.631931	−	0.364846i
$663$		0			0
$664$	6.93654	−	4.00481i	0.269190	−	0.155417i
$665$	−3.97803	−	8.84793i	−0.154261	−	0.343108i
$666$		0			0
$667$	−8.82079	−	15.2780i	−0.341542	−	0.591568i
$668$	1.46103			0.0565291
$669$		0			0
$670$			30.0997i			1.16285i
$671$	−14.7400	+	25.5304i	−0.569030	+	0.985590i
$672$		0			0
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	0.500398	−	0.865795i	$-0.333187\pi$
$673$	−12.9608	−	22.4487i	−0.499601	−	0.865335i	−1.00000		0.000460130i	$0.999854\pi$
$674$	4.19654	−	2.42287i	0.161645	−	0.0933256i
$675$		0			0
$676$	0.690233	−	1.19552i	0.0265474	−	0.0459815i
$677$	−6.55382	+	11.3515i	−0.251884	+	0.436275i	−0.964044	−	0.265741i	$-0.914383\pi$
$677$	−6.55382	+	11.3515i	−0.251884	+	0.436275i	0.712161	+	0.702016i	$0.247717\pi$
$678$		0			0
$679$	−12.7574	−	28.3751i	−0.489585	−	1.08894i
$680$	−19.3525	−	11.1732i	−0.742134	−	0.428471i
$681$		0			0
$682$		−	1.82283i		−	0.0697996i
$683$	25.6910	+	14.8327i	0.983038	+	0.567557i	0.903186	−	0.429249i	$-0.141222\pi$
$683$	25.6910	+	14.8327i	0.983038	+	0.567557i	0.0798523	+	0.996807i	$0.474555\pi$
$684$		0			0
$685$			0.00233490i			8.92121e-5i
$686$	−13.6270	+	12.5421i	−0.520282	+	0.478859i
$687$		0			0
$688$	4.79899			0.182960
$689$	−14.9195	−	25.8413i	−0.568387	−	0.984475i
$690$		0			0
$691$	40.9767	+	23.6579i	1.55883	+	0.899990i	0.997369	+	0.0724857i	$0.0230932\pi$
$691$	40.9767	+	23.6579i	1.55883	+	0.899990i	0.561459	+	0.827504i	$0.310240\pi$
$692$	3.07081			0.116735
$693$		0			0
$694$	17.4712			0.663197
$695$	31.6065	+	18.2480i	1.19890	+	0.692187i
$696$		0			0
$697$	−17.5992	−	30.4827i	−0.666616	−	1.15461i
$698$	−23.8258			−0.901820
$699$		0			0
$700$	19.5446	−	8.78724i	0.738717	−	0.332127i
$701$		−	13.7742i		−	0.520244i	−0.965576	−	0.260122i	$-0.916237\pi$
$701$		−	13.7742i		−	0.520244i	0.965576	−	0.260122i	$-0.0837627\pi$
$702$		0			0
$703$	6.43670	+	3.71623i	0.242765	+	0.140160i
$704$			2.00379i			0.0755209i
$705$		0			0
$706$	−8.69596	−	5.02061i	−0.327277	−	0.188953i
$707$	3.44186	−	33.9355i	0.129444	−	1.27627i
$708$		0			0
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	−0.0767981	−	0.997047i	$-0.524470\pi$
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	0.901867	−	0.432014i	$-0.142197\pi$
$710$	0.843820	−	1.46154i	0.0316680	−	0.0548506i
$711$		0			0
$712$	4.14521	−	2.39324i	0.155348	−	0.0896903i
$713$	1.37726	+	2.38549i	0.0515789	+	0.0893373i
$714$		0			0
$715$	−12.3607	+	21.4094i	−0.462265	+	0.800667i
$716$			19.3193i			0.721997i
$717$		0			0
$718$	−12.1651			−0.453997
$719$	−14.7930	−	25.6223i	−0.551687	−	0.955549i	−0.998153	−	0.0607489i	$-0.980651\pi$
$719$	−14.7930	−	25.6223i	−0.551687	−	0.955549i	0.446466	−	0.894800i	$-0.352682\pi$
$720$		0			0
$721$	−28.3198	−	2.87230i	−1.05469	−	0.106970i
$722$	−15.5657	+	8.98683i	−0.579294	+	0.334455i
$723$		0			0
$724$	−6.83569	+	3.94659i	−0.254046	+	0.146674i
$725$	−40.8666	+	23.5943i	−1.51775	+	0.876271i
$726$		0			0
$727$	−10.1244	+	5.84534i	−0.375494	+	0.216792i	−0.675856	−	0.737034i	$-0.736226\pi$
$727$	−10.1244	+	5.84534i	−0.375494	+	0.216792i	0.300362	+	0.953825i	$0.402893\pi$
$728$	−7.31553	−	5.27445i	−0.271132	−	0.195484i
$729$		0			0
$730$	−7.62756	−	13.2113i	−0.282308	−	0.488973i
$731$	29.6298			1.09590
$732$		0			0
$733$			33.0733i			1.22159i	0.791789	+	0.610795i	$0.209150\pi$
$733$			33.0733i			1.22159i	−0.791789	+	0.610795i	$0.790850\pi$
$734$	−1.81531	+	3.14420i	−0.0670042	+	0.116055i
$735$		0			0
$736$	−1.51400	−	2.62232i	−0.0558067	−	0.0966600i
$737$	14.4318	−	8.33219i	0.531601	−	0.306920i
$738$		0			0
$739$	−21.7528	+	37.6770i	−0.800190	+	1.38597i	0.119301	+	0.992858i	$0.461935\pi$
$739$	−21.7528	+	37.6770i	−0.800190	+	1.38597i	−0.919491	+	0.393111i	$0.871399\pi$
$740$	−13.2765	+	22.9957i	−0.488056	+	0.845337i
$741$		0			0
$742$	21.1233	−	9.49700i	0.775459	−	0.348646i
$743$	−18.0206	−	10.4042i	−0.661112	−	0.381693i	0.131589	−	0.991304i	$-0.457992\pi$
$743$	−18.0206	−	10.4042i	−0.661112	−	0.381693i	−0.792701	+	0.609611i	$0.791326\pi$
$744$		0			0
$745$			40.7083i			1.49144i
$746$	4.75648	+	2.74616i	0.174147	+	0.100544i
$747$		0			0
$748$			12.3718i			0.452358i
$749$	2.86382	+	6.36972i	0.104642	+	0.232745i
$750$		0			0
$751$	−39.8984			−1.45591			−0.727957	−	0.685623i	$-0.759530\pi$
$751$	−39.8984			−1.45591			−0.727957	+	0.685623i	$0.759530\pi$
$752$	1.11511	+	1.93143i	0.0406638	+	0.0704318i
$753$		0			0
$754$	17.1992	+	9.92994i	0.626357	+	0.361627i
$755$	−17.0969			−0.622219
$756$		0			0
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$	−13.5065	−	7.79800i	−0.490579	−	0.283236i
$759$		0			0
$760$	1.83333	+	3.17542i	0.0665018	+	0.115185i
$761$	8.64924			0.313535			0.156767	−	0.987636i	$-0.449893\pi$
$761$	8.64924			0.313535			0.156767	+	0.987636i	$0.449893\pi$
$762$		0			0
$763$	−19.3908	−	13.9807i	−0.701995	−	0.506134i
$764$		−	13.3042i		−	0.481330i
$765$		0			0
$766$	−8.16720	−	4.71534i	−0.295093	−	0.170372i
$767$			30.6319i			1.10605i
$768$		0			0
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	0.0829652	−	0.996552i	$-0.473561\pi$
$769$	−20.4818	−	11.8252i	−0.738592	−	0.426426i	−0.821557	+	0.570126i	$0.806894\pi$
$770$	−15.5644	−	11.2218i	−0.560900	−	0.404405i
$771$		0			0
$772$	3.26786	−	5.66011i	0.117613	−	0.203712i
$773$	23.2849	−	40.3307i	0.837501	−	1.45059i	−0.0544774	−	0.998515i	$-0.517349\pi$
$773$	23.2849	−	40.3307i	0.837501	−	1.45059i	0.891978	−	0.452079i	$-0.149317\pi$
$774$		0			0
$775$	6.38084	−	3.68398i	0.229207	−	0.132333i
$776$	5.87944	+	10.1835i	0.211060	+	0.365566i
$777$		0			0
$778$	−3.21089	+	5.56142i	−0.115116	+	0.199387i
$779$			5.77546i			0.206927i
$780$		0			0
$781$	−0.934344			−0.0334335
$782$	−9.34769	−	16.1907i	−0.334273	−	0.578977i
$783$		0			0
$784$	4.64590	−	5.23599i	0.165925	−	0.187000i
$785$	9.62178	−	5.55513i	0.343416	−	0.198271i
$786$		0			0
$787$	−21.1657	+	12.2200i	−0.754474	+	0.435596i	−0.827308	−	0.561748i	$-0.810129\pi$
$787$	−21.1657	+	12.2200i	−0.754474	+	0.435596i	0.0728341	+	0.997344i	$0.476796\pi$
$788$	−3.84732	+	2.22125i	−0.137055	+	0.0791288i
$789$		0			0
$790$	−11.9902	+	6.92255i	−0.426592	+	0.246293i
$791$	2.61593	−	3.62823i	0.0930118	−	0.129005i
$792$		0			0
$793$	25.0748	+	43.4309i	0.890433	+	1.54228i
$794$	6.92531			0.245770
$795$		0			0
$796$			11.5108i			0.407991i
$797$	−24.9202	+	43.1631i	−0.882719	+	1.52891i	−0.0344128	+	0.999408i	$0.510956\pi$
$797$	−24.9202	+	43.1631i	−0.882719	+	1.52891i	−0.848306	+	0.529506i	$0.822377\pi$
$798$		0			0
$799$	6.88489	+	11.9250i	0.243570	+	0.421875i
$800$	−7.01433	+	4.04972i	−0.247994	+	0.143179i
$801$		0			0
$802$	−5.29343	+	9.16848i	−0.186917	+	0.323750i
$803$	−4.22291	+	7.31430i	−0.149023	+	0.258116i
$804$		0			0
$805$	28.8475	+	2.92582i	1.01674	+	0.103122i
$806$	−2.68545	−	1.55045i	−0.0945910	−	0.0546121i
$807$		0			0
$808$			12.8922i			0.453546i
$809$	−10.6735	−	6.16237i	−0.375262	−	0.216657i	0.300493	−	0.953784i	$-0.402849\pi$
$809$	−10.6735	−	6.16237i	−0.375262	−	0.216657i	−0.675755	+	0.737127i	$0.736182\pi$
$810$		0			0
$811$		−	24.8017i		−	0.870906i	−0.900212	−	0.435453i	$-0.856588\pi$
$811$		−	24.8017i		−	0.870906i	0.900212	−	0.435453i	$-0.143412\pi$
$812$	−9.01498	+	12.5036i	−0.316364	+	0.438789i
$813$		0			0
$814$	14.7008			0.515264
$815$	−5.20047	−	9.00748i	−0.182165	−	0.315518i
$816$		0			0
$817$	−4.21041	−	2.43088i	−0.147304	−	0.0850457i
$818$	8.92343			0.312000
$819$		0			0
$820$	−20.6333			−0.720547
$821$	−31.3573	−	18.1041i	−1.09438	−	0.631839i	−0.159639	−	0.987175i	$-0.551033\pi$
$821$	−31.3573	−	18.1041i	−1.09438	−	0.631839i	−0.934738	+	0.355336i	$0.884366\pi$
$822$		0			0
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	0.983016	−	0.183519i	$-0.0587489\pi$
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	−0.650440	+	0.759557i	$0.725416\pi$
$824$	10.7588			0.374801
$825$		0			0
$826$	−23.6541	−	2.39908i	−0.823030	−	0.0834748i
$827$		−	31.9013i		−	1.10932i	−0.832079	−	0.554658i	$-0.812849\pi$
$827$		−	31.9013i		−	1.10932i	0.832079	−	0.554658i	$-0.187151\pi$
$828$		0			0
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	0.709412	−	0.704794i	$-0.248961\pi$
$829$	13.0645	+	7.54278i	0.453748	+	0.261971i	−0.255664	+	0.966766i	$0.582294\pi$
$830$		−	28.9894i		−	1.00624i
$831$		0			0
$832$	2.95206	+	1.70437i	0.102344	+	0.0590885i
$833$	28.6846	−	32.3280i	0.993864	−	1.12010i
$834$		0			0
$835$	2.64397	−	4.57950i	0.0914985	−	0.158480i
$836$	1.01500	−	1.75804i	0.0351046	−	0.0608029i
$837$		0			0
$838$	29.7781	−	17.1924i	1.02867	−	0.593901i
$839$	−8.19860	−	14.2004i	−0.283047	−	0.490252i	0.689087	−	0.724679i	$-0.258012\pi$
$839$	−8.19860	−	14.2004i	−0.283047	−	0.490252i	−0.972134	+	0.234427i	$0.924679\pi$
$840$		0			0
$841$	2.47206	−	4.28173i	0.0852434	−	0.147646i
$842$		−	35.5680i		−	1.22575i
$843$		0			0
$844$	22.6011			0.777961
$845$	−2.49817	−	4.32696i	−0.0859397	−	0.148852i
$846$		0			0
$847$	1.86475	−	18.3857i	0.0640735	−	0.631741i
$848$	−7.58088	+	4.37683i	−0.260329	+	0.150301i
$849$		0			0
$850$	−43.3077	+	25.0037i	−1.48544	+	0.857621i
$851$	−19.2386	+	11.1074i	−0.659492	+	0.380758i
$852$		0			0
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	−0.756411	−	0.654096i	$-0.773049\pi$
$853$	−16.5936	+	9.58030i	−0.568153	+	0.328023i	0.188258	+	0.982120i	$0.439716\pi$
$854$	−35.5014	+	15.9614i	−1.21483	+	0.546188i
$855$		0			0
$856$	−1.31983	−	2.28602i	−0.0451110	−	0.0781345i
$857$	−16.1145			−0.550460			−0.275230	−	0.961378i	$-0.588754\pi$
$857$	−16.1145			−0.550460			−0.275230	+	0.961378i	$0.588754\pi$
$858$		0			0
$859$		−	12.1048i		−	0.413009i	−0.978446	−	0.206505i	$-0.933791\pi$
$859$		−	12.1048i		−	0.413009i	0.978446	−	0.206505i	$-0.0662089\pi$
$860$	8.68453	−	15.0420i	0.296140	−	0.512929i
$861$		0			0
$862$	−15.4348	−	26.7338i	−0.525710	−	0.910556i
$863$	32.2728	−	18.6327i	1.09858	−	0.634265i	0.162732	−	0.986670i	$-0.447969\pi$
$863$	32.2728	−	18.6327i	1.09858	−	0.634265i	0.935848	+	0.352405i	$0.114636\pi$
$864$		0			0
$865$	5.55712	−	9.62522i	0.188948	−	0.327267i
$866$	11.6232	−	20.1319i	0.394971	−	0.684110i
$867$		0			0
$868$	1.40758	−	1.95229i	0.0477765	−	0.0662649i
$869$	6.63824	+	3.83259i	0.225187	+	0.130012i
$870$		0			0
$871$		−	28.3485i		−	0.960553i
$872$	7.82484	+	4.51768i	0.264983	+	0.152988i
$873$		0			0
$874$			3.06760i			0.103763i
$875$	2.99486	−	29.5282i	0.101245	−	0.998236i
$876$		0			0
$877$	−9.70948			−0.327866			−0.163933	−	0.986471i	$-0.552418\pi$
$877$	−9.70948			−0.327866			−0.163933	+	0.986471i	$0.552418\pi$
$878$	11.1364	+	19.2887i	0.375834	+	0.650963i
$879$		0			0
$880$	6.28073	+	3.62618i	0.211723	+	0.122239i
$881$	−2.63241			−0.0886881			−0.0443440	−	0.999016i	$-0.514120\pi$
$881$	−2.63241			−0.0886881			−0.0443440	+	0.999016i	$0.514120\pi$
$882$		0			0
$883$	−36.3181			−1.22220			−0.611101	−	0.791553i	$-0.709273\pi$
$883$	−36.3181			−1.22220			−0.611101	+	0.791553i	$0.709273\pi$
$884$	18.2265	+	10.5231i	0.613025	+	0.353930i
$885$		0			0
$886$	−8.99259	−	15.5756i	−0.302112	−	0.523273i
$887$	16.3642			0.549455			0.274728	−	0.961522i	$-0.411412\pi$
$887$	16.3642			0.549455			0.274728	+	0.961522i	$0.411412\pi$
$888$		0			0
$889$	4.78659	−	47.1940i	0.160537	−	1.58284i
$890$		−	17.3238i		−	0.580694i
$891$		0			0
$892$	−16.2994	−	9.41045i	−0.545744	−	0.315085i
$893$		−	2.25939i		−	0.0756076i
$894$		0			0
$895$	60.5549	+	34.9614i	2.02413	+	1.16863i
$896$	−1.54733	+	2.14611i	−0.0516926	+	0.0716964i
$897$		0			0
$898$	4.72182	−	8.17843i	0.157569	−	0.272918i
$899$	−2.64999	+	4.58992i	−0.0883822	+	0.153082i
$900$		0			0
$901$	−46.8058	+	27.0233i	−1.55933	+	0.900277i
$902$	5.71171	+	9.89297i	0.190179	+	0.329400i
$903$		0			0
$904$	−0.845306	+	1.46411i	−0.0281145	+	0.0486957i
$905$			28.5679i			0.949629i
$906$		0			0
$907$	10.8333			0.359714			0.179857	−	0.983693i	$-0.442436\pi$
$907$	10.8333			0.359714			0.179857	+	0.983693i	$0.442436\pi$
$908$	7.30665	+	12.6555i	0.242480	+	0.419987i
$909$		0			0
$910$	−29.7709	+	13.3850i	−0.986897	+	0.443708i
$911$	−36.8512	+	21.2760i	−1.22093	+	0.704907i	−0.965117	−	0.261818i	$-0.915678\pi$
$911$	−36.8512	+	21.2760i	−1.22093	+	0.704907i	−0.255817	+	0.966725i	$0.582345\pi$
$912$		0			0
$913$	−13.8994	+	8.02482i	−0.460003	+	0.265583i
$914$	1.59739	−	0.922251i	0.0528368	−	0.0305053i
$915$		0			0
$916$	2.06044	−	1.18959i	0.0680788	−	0.0393053i
$917$	−4.62699	+	45.6204i	−0.152797	+	1.50652i
$918$		0			0
$919$	−12.9697	−	22.4641i	−0.427829	−	0.741022i	0.568851	−	0.822441i	$-0.307388\pi$
$919$	−12.9697	−	22.4641i	−0.427829	−	0.741022i	−0.996680	+	0.0814187i	$0.974055\pi$
$920$	−10.9593			−0.361316
$921$		0			0
$922$		−	36.3739i		−	1.19791i
$923$	−0.794727	+	1.37651i	−0.0261588	+	0.0453083i
$924$		0			0
$925$	29.7108	+	51.4606i	0.976884	+	1.69201i
$926$	−27.6834	+	15.9830i	−0.909733	+	0.525234i
$927$		0			0
$928$	2.91308	−	5.04560i	0.0956265	−	0.165630i
$929$	−23.4456	+	40.6089i	−0.769224	+	1.33234i	0.168760	+	0.985657i	$0.446024\pi$
$929$	−23.4456	+	40.6089i	−0.769224	+	1.33234i	−0.937984	+	0.346678i	$0.887310\pi$
$930$		0			0
$931$	−6.72834	+	2.24048i	−0.220512	+	0.0734287i
$932$	9.03470	+	5.21619i	0.295942	+	0.170862i
$933$		0			0
$934$			24.4411i			0.799738i
$935$	38.7784	+	22.3887i	1.26819	+	0.732189i
$936$		0			0
$937$		−	0.209357i		−	0.00683939i	−0.999994	−	0.00341969i	$-0.998911\pi$
$937$		−	0.209357i		−	0.00683939i	0.999994	−	0.00341969i	$-0.00108852\pi$
$938$	21.8909	+	2.22025i	0.714762	+	0.0724938i
$939$		0			0
$940$	8.07186			0.263275
$941$	0.388565	+	0.673014i	0.0126669	+	0.0219396i	0.872289	−	0.488990i	$-0.162635\pi$
$941$	0.388565	+	0.673014i	0.0126669	+	0.0219396i	−0.859622	+	0.510930i	$0.829301\pi$
$942$		0			0
$943$	−14.9496	−	8.63113i	−0.486825	−	0.281068i
$944$	8.98627			0.292478
$945$		0			0
$946$	−9.61619			−0.312649
$947$	−43.1233	−	24.8972i	−1.40132	−	0.809052i	−0.406791	−	0.913521i	$-0.633352\pi$
$947$	−43.1233	−	24.8972i	−1.40132	−	0.809052i	−0.994528	+	0.104470i	$0.966686\pi$
$948$		0			0
$949$	7.18378	+	12.4427i	0.233196	+	0.403906i
$950$	8.20539			0.266218
$951$		0			0
$952$	−9.55349	+	13.2505i	−0.309630	+	0.429450i
$953$		−	41.4104i		−	1.34141i	−0.741722	−	0.670707i	$-0.765991\pi$
$953$		−	41.4104i		−	1.34141i	0.741722	−	0.670707i	$-0.234009\pi$
$954$		0			0
$955$	−41.7010	−	24.0761i	−1.34941	−	0.779084i
$956$		−	23.7835i		−	0.769213i
$957$		0			0
$958$	−9.49220	−	5.48032i	−0.306679	−	0.177061i
$959$	0.00169812		0.000172230i	5.48353e−5		5.56160e-6i
$960$		0			0
$961$	−15.0862	+	26.1301i	−0.486653	+	0.842907i
$962$	12.5041	−	21.6578i	0.403149	−	0.698274i
$963$		0			0
$964$	−24.8105	+	14.3243i	−0.799092	+	0.461356i
$965$	−11.8274	−	20.4857i	−0.380739	−	0.659459i
$966$		0			0
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	−0.222181	−	0.975005i	$-0.571318\pi$
$967$	22.8028	−	39.4956i	0.733289	−	1.27009i	0.955470	−	0.295088i	$-0.0953491\pi$
$968$			6.98481i			0.224500i
$969$		0			0
$970$	42.5591			1.36649
$971$	−4.36733	−	7.56444i	−0.140154	−	0.242754i	0.787400	−	0.616442i	$-0.211427\pi$
$971$	−4.36733	−	7.56444i	−0.140154	−	0.242754i	−0.927555	+	0.373688i	$0.878093\pi$
$972$		0			0
$973$	15.6028	−	21.6407i	0.500202	−	0.693768i
$974$	−29.1136	+	16.8087i	−0.932860	+	0.538587i
$975$		0			0
$976$	12.7410	−	7.35603i	0.407830	−	0.235461i
$977$	12.9058	−	7.45114i	0.412892	−	0.238383i	−0.279140	−	0.960250i	$-0.590049\pi$
$977$	12.9058	−	7.45114i	0.412892	−	0.238383i	0.692031	+	0.721867i	$0.256716\pi$
$978$		0			0
$979$	−8.30615	+	4.79556i	−0.265466	+	0.153267i
$980$	−8.00430	−	24.0376i	−0.255688	−	0.767852i
$981$		0			0
$982$	11.3676	+	19.6893i	0.362756	+	0.628312i
$983$	3.06917			0.0978912			0.0489456	−	0.998801i	$-0.484414\pi$
$983$	3.06917			0.0978912			0.0489456	+	0.998801i	$0.484414\pi$
$984$		0			0
$985$			16.0788i			0.512314i
$986$	17.9859	−	31.1525i	0.572787	−	0.992096i
$987$		0			0
$988$	−1.72667	−	2.99067i	−0.0549325	−	0.0951460i
$989$	12.5845	−	7.26565i	0.400163	−	0.231034i
$990$		0			0
$991$	27.9075	−	48.3372i	0.886510	−	1.53548i	0.0425375	−	0.999095i	$-0.486456\pi$
$991$	27.9075	−	48.3372i	0.886510	−	1.53548i	0.843973	−	0.536386i	$-0.180211\pi$
$992$	−0.454844	+	0.787812i	−0.0144413	+	0.0250131i
$993$		0			0
$994$	−1.00070	−	0.721500i	−0.0317404	−	0.0228846i
$995$	36.0798	+	20.8307i	1.14381	+	0.660377i
$996$		0			0
$997$			6.12692i			0.194042i	0.995282	+	0.0970208i	$0.0309313\pi$
$997$			6.12692i			0.194042i	−0.995282	+	0.0970208i	$0.969069\pi$
$998$	16.9079	+	9.76175i	0.535209	+	0.309003i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.t.a.17.8		16
3.2	odd	2		126.2.t.a.59.2	yes	16
4.3	odd	2		3024.2.df.c.17.7		16
7.2	even	3		2646.2.l.a.1097.1		16
7.3	odd	6		2646.2.m.b.881.4		16
7.4	even	3		2646.2.m.a.881.1		16
7.5	odd	6		378.2.l.a.341.4		16
7.6	odd	2		2646.2.t.b.2285.5		16
9.2	odd	6		378.2.l.a.143.8		16
9.4	even	3		1134.2.k.a.647.1		16
9.5	odd	6		1134.2.k.b.647.8		16
9.7	even	3		126.2.l.a.101.1	yes	16
12.11	even	2		1008.2.df.c.689.5		16
21.2	odd	6		882.2.l.b.509.8		16
21.5	even	6		126.2.l.a.5.5	✓	16
21.11	odd	6		882.2.m.a.293.6		16
21.17	even	6		882.2.m.b.293.7		16
21.20	even	2		882.2.t.a.815.3		16
28.19	even	6		3024.2.ca.c.2609.7		16
36.7	odd	6		1008.2.ca.c.353.8		16
36.11	even	6		3024.2.ca.c.2033.7		16
63.2	odd	6		2646.2.t.b.1979.5		16
63.5	even	6		1134.2.k.a.971.1		16
63.11	odd	6		2646.2.m.b.1763.4		16
63.16	even	3		882.2.t.a.803.3		16
63.20	even	6		2646.2.l.a.521.5		16
63.25	even	3		882.2.m.b.587.7		16
63.34	odd	6		882.2.l.b.227.4		16
63.38	even	6		2646.2.m.a.1763.1		16
63.40	odd	6		1134.2.k.b.971.8		16
63.47	even	6	inner	378.2.t.a.89.8		16
63.52	odd	6		882.2.m.a.587.6		16
63.61	odd	6		126.2.t.a.47.2	yes	16
84.47	odd	6		1008.2.ca.c.257.8		16
252.47	odd	6		3024.2.df.c.1601.7		16
252.187	even	6		1008.2.df.c.929.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	21.5	even	6
126.2.l.a.101.1	yes	16	9.7	even	3
126.2.t.a.47.2	yes	16	63.61	odd	6
126.2.t.a.59.2	yes	16	3.2	odd	2
378.2.l.a.143.8		16	9.2	odd	6
378.2.l.a.341.4		16	7.5	odd	6
378.2.t.a.17.8		16	1.1	even	1	trivial
378.2.t.a.89.8		16	63.47	even	6	inner
882.2.l.b.227.4		16	63.34	odd	6
882.2.l.b.509.8		16	21.2	odd	6
882.2.m.a.293.6		16	21.11	odd	6
882.2.m.a.587.6		16	63.52	odd	6
882.2.m.b.293.7		16	21.17	even	6
882.2.m.b.587.7		16	63.25	even	3
882.2.t.a.803.3		16	63.16	even	3
882.2.t.a.815.3		16	21.20	even	2
1008.2.ca.c.257.8		16	84.47	odd	6
1008.2.ca.c.353.8		16	36.7	odd	6
1008.2.df.c.689.5		16	12.11	even	2
1008.2.df.c.929.5		16	252.187	even	6
1134.2.k.a.647.1		16	9.4	even	3
1134.2.k.a.971.1		16	63.5	even	6
1134.2.k.b.647.8		16	9.5	odd	6
1134.2.k.b.971.8		16	63.40	odd	6
2646.2.l.a.521.5		16	63.20	even	6
2646.2.l.a.1097.1		16	7.2	even	3
2646.2.m.a.881.1		16	7.4	even	3
2646.2.m.a.1763.1		16	63.38	even	6
2646.2.m.b.881.4		16	7.3	odd	6
2646.2.m.b.1763.4		16	63.11	odd	6
2646.2.t.b.1979.5		16	63.2	odd	6
2646.2.t.b.2285.5		16	7.6	odd	2
3024.2.ca.c.2033.7		16	36.11	even	6
3024.2.ca.c.2609.7		16	28.19	even	6
3024.2.df.c.17.7		16	4.3	odd	2
3024.2.df.c.1601.7		16	252.47	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +3.61932 q^{5} +(0.266972 - 2.63225i) q^{7} +1.00000i q^{8} +(3.13442 + 1.80966i) q^{10} -2.00379i q^{11} +(-2.95206 - 1.70437i) q^{13} +(1.54733 - 2.14611i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.08709 + 5.34700i) q^{17} +(0.877353 - 0.506540i) q^{19} +(1.80966 + 3.13442i) q^{20} +(1.00190 - 1.73534i) q^{22} +3.02799i q^{23} +8.09945 q^{25} +(-1.70437 - 2.95206i) q^{26} +(2.41308 - 1.08492i) q^{28} +(-5.04560 + 2.91308i) q^{29} +(0.787812 - 0.454844i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.34700 + 3.08709i) q^{34} +(0.966257 - 9.52693i) q^{35} +(3.66825 + 6.35359i) q^{37} +1.01308 q^{38} +3.61932i q^{40} +(-2.85045 + 4.93712i) q^{41} +(-2.39949 - 4.15605i) q^{43} +(1.73534 - 1.00190i) q^{44} +(-1.51400 + 2.62232i) q^{46} +(1.11511 - 1.93143i) q^{47} +(-6.85745 - 1.40547i) q^{49} +(7.01433 + 4.04972i) q^{50} -3.40874i q^{52} +(7.58088 + 4.37683i) q^{53} -7.25237i q^{55} +(2.63225 + 0.266972i) q^{56} -5.82616 q^{58} +(-4.49313 - 7.78233i) q^{59} +(-12.7410 - 7.35603i) q^{61} +0.909687 q^{62} -1.00000 q^{64} +(-10.6844 - 6.16866i) q^{65} +(4.15821 + 7.20222i) q^{67} -6.17418 q^{68} +(5.60027 - 7.76744i) q^{70} -0.466287i q^{71} +(-3.65022 - 2.10746i) q^{73} +7.33650i q^{74} +(0.877353 + 0.506540i) q^{76} +(-5.27448 - 0.534957i) q^{77} +(-1.91267 + 3.31284i) q^{79} +(-1.80966 + 3.13442i) q^{80} +(-4.93712 + 2.85045i) q^{82} +(-4.00481 - 6.93654i) q^{83} +(-11.1732 + 19.3525i) q^{85} -4.79899i q^{86} +2.00379 q^{88} +(-2.39324 - 4.14521i) q^{89} +(-5.27445 + 7.31553i) q^{91} +(-2.62232 + 1.51400i) q^{92} +(1.93143 - 1.11511i) q^{94} +(3.17542 - 1.83333i) q^{95} +(10.1835 - 5.87944i) q^{97} +(-5.23599 - 4.64590i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} - 6 q^{13} + 6 q^{14} - 8 q^{16} - 18 q^{17} + 16 q^{25} + 12 q^{26} - 2 q^{28} - 6 q^{29} + 6 q^{31} + 30 q^{35} - 2 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{44} + 6 q^{46} + 18 q^{47}+ \cdots - 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 - 6 * q^13 + 6 * q^14 - 8 * q^16 - 18 * q^17 + 16 * q^25 + 12 * q^26 - 2 * q^28 - 6 * q^29 + 6 * q^31 + 30 * q^35 - 2 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^44 + 6 * q^46 + 18 * q^47 + 10 * q^49 + 12 * q^50 - 36 * q^53 - 12 * q^58 - 30 * q^59 - 60 * q^61 + 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 36 * q^68 + 18 * q^77 - 16 * q^79 - 12 * q^85 - 24 * q^89 - 12 * q^91 - 6 * q^92 + 66 * q^95 - 6 * q^97 - 24 * q^98

Introduction

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