LMFDB - Embedded newform 2646.2.l.a.521.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(521,2646)] 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("2646.521"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-16,0,0,0,0,0,0,-12,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$21.1284163748$
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:	$\Z[a_1, \ldots, a_{13}]$
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			521.5
Root			$1.71298 + 0.256290i$ of defining polynomial
Character	$\chi$	$=$	2646.521
Dual form			2646.2.l.a.1097.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.80966 + 3.13442i) q^{5} -1.00000i q^{8} +(-3.13442 - 1.80966i) q^{10} +(1.73534 - 1.00190i) q^{11} +(-2.95206 + 1.70437i) q^{13} +1.00000 q^{16} +(-3.08709 + 5.34700i) q^{17} +(-0.877353 + 0.506540i) q^{19} +(1.80966 - 3.13442i) q^{20} +(1.00190 + 1.73534i) q^{22} +(2.62232 + 1.51400i) q^{23} +(-4.04972 - 7.01433i) q^{25} +(-1.70437 - 2.95206i) q^{26} +(-5.04560 - 2.91308i) q^{29} -0.909687i q^{31} +1.00000i q^{32} +(-5.34700 - 3.08709i) q^{34} +(3.66825 + 6.35359i) q^{37} +(-0.506540 - 0.877353i) q^{38} +(3.13442 + 1.80966i) q^{40} +(-2.85045 - 4.93712i) q^{41} +(-2.39949 + 4.15605i) q^{43} +(-1.73534 + 1.00190i) q^{44} +(-1.51400 + 2.62232i) q^{46} -2.23022 q^{47} +(7.01433 - 4.04972i) q^{50} +(2.95206 - 1.70437i) q^{52} +(-7.58088 - 4.37683i) q^{53} +7.25237i q^{55} +(2.91308 - 5.04560i) q^{58} +8.98627 q^{59} -14.7121i q^{61} +0.909687 q^{62} -1.00000 q^{64} -12.3373i q^{65} -8.31641 q^{67} +(3.08709 - 5.34700i) q^{68} +0.466287i q^{71} +(3.65022 + 2.10746i) q^{73} +(-6.35359 + 3.66825i) q^{74} +(0.877353 - 0.506540i) q^{76} +3.82533 q^{79} +(-1.80966 + 3.13442i) q^{80} +(4.93712 - 2.85045i) q^{82} +(-4.00481 + 6.93654i) q^{83} +(-11.1732 - 19.3525i) q^{85} +(-4.15605 - 2.39949i) q^{86} +(-1.00190 - 1.73534i) q^{88} +(-2.39324 - 4.14521i) q^{89} +(-2.62232 - 1.51400i) q^{92} -2.23022i q^{94} -3.66666i q^{95} +(10.1835 + 5.87944i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} - 12 q^{11} - 6 q^{13} + 16 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 6 q^{29} - 2 q^{37} - 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} - 36 q^{47} + 12 q^{50} + 6 q^{52} + 36 q^{53}+ \cdots - 6 q^{97}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^11 - 6 * q^13 + 16 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 6 * q^29 - 2 * q^37 - 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 - 36 * q^47 + 12 * q^50 + 6 * q^52 + 36 * q^53 + 6 * q^58 + 60 * q^59 + 36 * q^62 - 16 * q^64 - 28 * q^67 + 18 * q^68 - 18 * q^74 + 32 * q^79 - 12 * q^85 - 24 * q^86 - 24 * q^89 - 6 * q^92 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	−1.80966	+	3.13442i	−0.809304	+	1.40175i	0.104043	+	0.994573i	$0.466822\pi$
$5$	−1.80966	+	3.13442i	−0.809304	+	1.40175i	−0.913347	+	0.407182i	$0.866511\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	−3.13442	−	1.80966i	−0.991190	−	0.572264i
$11$	1.73534	−	1.00190i	0.523224	−	0.302083i	−0.215029	−	0.976608i	$-0.568985\pi$
$11$	1.73534	−	1.00190i	0.523224	−	0.302083i	0.738253	+	0.674524i	$0.235651\pi$
$12$		0			0
$13$	−2.95206	+	1.70437i	−0.818754	+	0.472708i	−0.849987	−	0.526804i	$-0.823390\pi$
$13$	−2.95206	+	1.70437i	−0.818754	+	0.472708i	0.0312328	+	0.999512i	$0.490057\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	−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	−0.597252	−	0.802054i	$-0.703741\pi$
$19$	−0.877353	+	0.506540i	−0.201279	+	0.116208i	0.395973	+	0.918262i	$0.370407\pi$
$20$	1.80966	−	3.13442i	0.404652	−	0.700877i
$21$		0			0
$22$	1.00190	+	1.73534i	0.213605	+	0.369975i
$23$	2.62232	+	1.51400i	0.546791	+	0.315690i	0.747827	−	0.663894i	$-0.231097\pi$
$23$	2.62232	+	1.51400i	0.546791	+	0.315690i	−0.201035	+	0.979584i	$0.564431\pi$
$24$		0			0
$25$	−4.04972	−	7.01433i	−0.809945	−	1.40287i
$26$	−1.70437	−	2.95206i	−0.334255	−	0.578946i
$27$		0			0
$28$		0			0
$29$	−5.04560	−	2.91308i	−0.936945	−	0.540945i	−0.0479434	−	0.998850i	$-0.515267\pi$
$29$	−5.04560	−	2.91308i	−0.936945	−	0.540945i	−0.889001	+	0.457905i	$0.848600\pi$
$30$		0			0
$31$		−	0.909687i		−	0.163385i	−0.996658	−	0.0816923i	$-0.973968\pi$
$31$		−	0.909687i		−	0.163385i	0.996658	−	0.0816923i	$-0.0260325\pi$
$32$			1.00000i			0.176777i
$33$		0			0
$34$	−5.34700	−	3.08709i	−0.917003	−	0.529432i
$35$		0			0
$36$		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	$0.627283\pi$
$38$	−0.506540	−	0.877353i	−0.0821717	−	0.142325i
$39$		0			0
$40$	3.13442	+	1.80966i	0.495595	+	0.286132i
$41$	−2.85045	−	4.93712i	−0.445165	−	0.771048i	0.552899	−	0.833248i	$-0.313522\pi$
$41$	−2.85045	−	4.93712i	−0.445165	−	0.771048i	−0.998064	+	0.0622002i	$0.980188\pi$
$42$		0			0
$43$	−2.39949	+	4.15605i	−0.365919	+	0.633791i	−0.988923	−	0.148428i	$-0.952579\pi$
$43$	−2.39949	+	4.15605i	−0.365919	+	0.633791i	0.623004	+	0.782219i	$0.285912\pi$
$44$	−1.73534	+	1.00190i	−0.261612	+	0.151042i
$45$		0			0
$46$	−1.51400	+	2.62232i	−0.223227	+	0.386640i
$47$	−2.23022			−0.325311			−0.162655	−	0.986683i	$-0.552006\pi$
$47$	−2.23022			−0.325311			−0.162655	+	0.986683i	$0.552006\pi$
$48$		0			0
$49$		0			0
$50$	7.01433	−	4.04972i	0.991975	−	0.572717i
$51$		0			0
$52$	2.95206	−	1.70437i	0.409377	−	0.236354i
$53$	−7.58088	−	4.37683i	−1.04131	−	0.601203i	−0.121109	−	0.992639i	$-0.538645\pi$
$53$	−7.58088	−	4.37683i	−1.04131	−	0.601203i	−0.920205	+	0.391436i	$0.871978\pi$
$54$		0			0
$55$			7.25237i			0.977909i
$56$		0			0
$57$		0			0
$58$	2.91308	−	5.04560i	0.382506	−	0.662520i
$59$	8.98627			1.16991			0.584956	−	0.811065i	$-0.301112\pi$
$59$	8.98627			1.16991			0.584956	+	0.811065i	$0.301112\pi$
$60$		0			0
$61$		−	14.7121i		−	1.88369i	−0.336053	−	0.941843i	$-0.609092\pi$
$61$		−	14.7121i		−	1.88369i	0.336053	−	0.941843i	$-0.390908\pi$
$62$	0.909687			0.115530
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	12.3373i		−	1.53026i
$66$		0			0
$67$	−8.31641			−1.01601			−0.508006	−	0.861354i	$-0.669617\pi$
$67$	−8.31641			−1.01601			−0.508006	+	0.861354i	$0.669617\pi$
$68$	3.08709	−	5.34700i	0.374365	−	0.648419i
$69$		0			0
$70$		0			0
$71$			0.466287i			0.0553381i	0.999617	+	0.0276691i	$0.00880846\pi$
$71$			0.466287i			0.0553381i	−0.999617	+	0.0276691i	$0.991192\pi$
$72$		0			0
$73$	3.65022	+	2.10746i	0.427226	+	0.246659i	0.698164	−	0.715938i	$-0.254000\pi$
$73$	3.65022	+	2.10746i	0.427226	+	0.246659i	−0.270938	+	0.962597i	$0.587334\pi$
$74$	−6.35359	+	3.66825i	−0.738590	+	0.426425i
$75$		0			0
$76$	0.877353	−	0.506540i	0.100639	−	0.0581041i
$77$		0			0
$78$		0			0
$79$	3.82533			0.430384			0.215192	−	0.976572i	$-0.430962\pi$
$79$	3.82533			0.430384			0.215192	+	0.976572i	$0.430962\pi$
$80$	−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	−0.997657	−	0.0684084i	$-0.978208\pi$
$83$	−4.00481	+	6.93654i	−0.439585	+	0.761384i	0.558072	+	0.829792i	$0.311541\pi$
$84$		0			0
$85$	−11.1732	−	19.3525i	−1.21190	−	2.09907i
$86$	−4.15605	−	2.39949i	−0.448158	−	0.258744i
$87$		0			0
$88$	−1.00190	−	1.73534i	−0.106803	−	0.184988i
$89$	−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
$91$		0			0
$92$	−2.62232	−	1.51400i	−0.273396	−	0.157845i
$93$		0			0
$94$		−	2.23022i		−	0.230029i
$95$		−	3.66666i		−	0.376191i
$96$		0			0
$97$	10.1835	+	5.87944i	1.03398	+	0.596967i	0.918121	−	0.396299i	$-0.129706\pi$
$97$	10.1835	+	5.87944i	1.03398	+	0.596967i	0.115856	+	0.993266i	$0.463039\pi$
$98$		0			0
$99$		0			0
$100$	4.04972	+	7.01433i	0.404972	+	0.701433i
$101$	−6.44610	−	11.1650i	−0.641411	−	1.11096i	−0.985118	−	0.171879i	$-0.945016\pi$
$101$	−6.44610	−	11.1650i	−0.641411	−	1.11096i	0.343707	−	0.939077i	$-0.388317\pi$
$102$		0			0
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.0350515	−	0.999386i	$-0.511160\pi$
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.883019	+	0.469337i	$0.844493\pi$
$104$	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	−0.385414	−	0.922744i	$-0.625942\pi$
$107$	2.28602	−	1.31983i	0.220998	−	0.127593i	0.606412	+	0.795151i	$0.292608\pi$
$108$		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	$0.0242224\pi$
$110$	−7.25237			−0.691486
$111$		0			0
$112$		0			0
$113$	1.46411	−	0.845306i	0.137732	−	0.0795197i	−0.429551	−	0.903043i	$-0.641328\pi$
$113$	1.46411	−	0.845306i	0.137732	−	0.0795197i	0.567283	+	0.823523i	$0.307995\pi$
$114$		0			0
$115$	−9.49100	+	5.47963i	−0.885041	+	0.510978i
$116$	5.04560	+	2.91308i	0.468472	+	0.270473i
$117$		0			0
$118$			8.98627i			0.827253i
$119$		0			0
$120$		0			0
$121$	−3.49240	+	6.04902i	−0.317491	+	0.549911i
$122$	14.7121			1.33197
$123$		0			0
$124$			0.909687i			0.0816923i
$125$	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	$0.207220\pi$
$128$		−	1.00000i		−	0.0883883i
$129$		0			0
$130$	12.3373			1.08205
$131$	8.66567	−	15.0094i	0.757123	−	1.31138i	−0.187188	−	0.982324i	$-0.559938\pi$
$131$	8.66567	−	15.0094i	0.757123	−	1.31138i	0.944312	−	0.329052i	$-0.106729\pi$
$132$		0			0
$133$		0			0
$134$		−	8.31641i		−	0.718429i
$135$		0			0
$136$	5.34700	+	3.08709i	0.458501	+	0.264716i
$137$	−0.000558693	0	0.000322562i	−4.77324e−5	0	2.75583e-5i	−0.500024	−	0.866012i	$-0.666675\pi$
$137$	−0.000558693	0	0.000322562i	−4.77324e−5	0	2.75583e-5i	0.499976	+	0.866039i	$0.333342\pi$
$138$		0			0
$139$	8.73273	−	5.04185i	0.740701	−	0.427644i	−0.0816233	−	0.996663i	$-0.526010\pi$
$139$	8.73273	−	5.04185i	0.740701	−	0.427644i	0.822324	+	0.569019i	$0.192677\pi$
$140$		0			0
$141$		0			0
$142$	−0.466287			−0.0391300
$143$	−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
$149$	9.74064	+	5.62376i	0.797984	+	0.460716i	0.842766	−	0.538280i	$-0.180926\pi$
$149$	9.74064	+	5.62376i	0.797984	+	0.460716i	−0.0447816	+	0.998997i	$0.514259\pi$
$150$		0			0
$151$	2.36189	+	4.09092i	0.192208	+	0.332914i	0.945982	−	0.324220i	$-0.105102\pi$
$151$	2.36189	+	4.09092i	0.192208	+	0.332914i	−0.753774	+	0.657134i	$0.771768\pi$
$152$	0.506540	+	0.877353i	0.0410858	+	0.0711627i
$153$		0			0
$154$		0			0
$155$	2.85134	+	1.64622i	0.229025	+	0.132228i
$156$		0			0
$157$		−	3.06972i		−	0.244990i	−0.992469	−	0.122495i	$-0.960910\pi$
$157$		−	3.06972i		−	0.244990i	0.992469	−	0.122495i	$-0.0390895\pi$
$158$			3.82533i			0.304327i
$159$		0			0
$160$	−3.13442	−	1.80966i	−0.247798	−	0.143066i
$161$		0			0
$162$		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	$0.869233\pi$
$164$	2.85045	+	4.93712i	0.222582	+	0.385524i
$165$		0			0
$166$	−6.93654	−	4.00481i	−0.538380	−	0.310834i
$167$	0.730517	+	1.26529i	0.0565291	+	0.0979113i	0.892905	−	0.450245i	$-0.148663\pi$
$167$	0.730517	+	1.26529i	0.0565291	+	0.0979113i	−0.836376	+	0.548156i	$0.815330\pi$
$168$		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
$173$	−3.07081			−0.233470			−0.116735	−	0.993163i	$-0.537243\pi$
$173$	−3.07081			−0.233470			−0.116735	+	0.993163i	$0.537243\pi$
$174$		0			0
$175$		0			0
$176$	1.73534	−	1.00190i	0.130806	−	0.0755209i
$177$		0			0
$178$	4.14521	−	2.39324i	0.310696	−	0.179381i
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.279320	−	0.960198i	$-0.590109\pi$
$179$	−16.7310	−	9.65966i	−1.25054	−	0.721997i	−0.971216	+	0.238201i	$0.923442\pi$
$180$		0			0
$181$		−	7.89318i		−	0.586695i	−0.956006	−	0.293348i	$-0.905231\pi$
$181$		−	7.89318i		−	0.586695i	0.956006	−	0.293348i	$-0.0947693\pi$
$182$		0			0
$183$		0			0
$184$	1.51400	−	2.62232i	0.111613	−	0.193320i
$185$	−26.5531			−1.95222
$186$		0			0
$187$			12.3718i			0.904715i
$188$	2.23022			0.162655
$189$		0			0
$190$	3.66666			0.266007
$191$		−	13.3042i		−	0.962660i	−0.876540	−	0.481330i	$-0.840154\pi$
$191$		−	13.3042i		−	0.962660i	0.876540	−	0.481330i	$-0.159846\pi$
$192$		0			0
$193$	6.53573			0.470452			0.235226	−	0.971941i	$-0.424417\pi$
$193$	6.53573			0.470452			0.235226	+	0.971941i	$0.424417\pi$
$194$	−5.87944	+	10.1835i	−0.422119	+	0.731132i
$195$		0			0
$196$		0			0
$197$		−	4.44250i		−	0.316515i	−0.987398	−	0.158258i	$-0.949412\pi$
$197$		−	4.44250i		−	0.316515i	0.987398	−	0.158258i	$-0.0505876\pi$
$198$		0			0
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	0.103163	−	0.994665i	$-0.467104\pi$
$199$	−9.96868	−	5.75542i	−0.706661	−	0.407991i	−0.809823	+	0.586674i	$0.800437\pi$
$200$	−7.01433	+	4.04972i	−0.495988	+	0.286359i
$201$		0			0
$202$	11.1650	−	6.44610i	0.785565	−	0.453546i
$203$		0			0
$204$		0			0
$205$	20.6333			1.44109
$206$	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	0.933115	+	0.359577i	$0.117079\pi$
$211$	11.3005	+	19.5731i	0.777961	+	1.34747i	−0.155155	+	0.987890i	$0.549588\pi$
$212$	7.58088	+	4.37683i	0.520657	+	0.300602i
$213$		0			0
$214$	1.31983	+	2.28602i	0.0902219	+	0.156269i
$215$	−8.68453	−	15.0420i	−0.592280	−	1.02586i
$216$		0			0
$217$		0			0
$218$	7.82484	+	4.51768i	0.529965	+	0.305976i
$219$		0			0
$220$		−	7.25237i		−	0.488954i
$221$		−	21.0462i		−	1.41572i
$222$		0			0
$223$	−16.2994	−	9.41045i	−1.09149	−	0.630170i	−0.157515	−	0.987517i	$-0.550348\pi$
$223$	−16.2994	−	9.41045i	−1.09149	−	0.630170i	−0.933972	+	0.357346i	$0.883682\pi$
$224$		0			0
$225$		0			0
$226$	0.845306	+	1.46411i	0.0562289	+	0.0973914i
$227$	−7.30665	−	12.6555i	−0.484960	−	0.839975i	0.514891	−	0.857256i	$-0.327832\pi$
$227$	−7.30665	−	12.6555i	−0.484960	−	0.839975i	−0.999851	+	0.0172809i	$0.994499\pi$
$228$		0			0
$229$	−2.06044	−	1.18959i	−0.136158	−	0.0786106i	0.430374	−	0.902651i	$-0.358382\pi$
$229$	−2.06044	−	1.18959i	−0.136158	−	0.0786106i	−0.566531	+	0.824040i	$0.691715\pi$
$230$	−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	−0.765842	−	0.643029i	$-0.777677\pi$
$233$	−9.03470	+	5.21619i	−0.591883	+	0.341724i	0.173959	+	0.984753i	$0.444344\pi$
$234$		0			0
$235$	4.03593	−	6.99044i	0.263275	−	0.456006i
$236$	−8.98627			−0.584956
$237$		0			0
$238$		0			0
$239$	−20.5971	+	11.8917i	−1.33232	+	0.769213i	−0.985654	−	0.168777i	$-0.946018\pi$
$239$	−20.5971	+	11.8917i	−1.33232	+	0.769213i	−0.346662	+	0.937990i	$0.612685\pi$
$240$		0			0
$241$	−24.8105	+	14.3243i	−1.59818	+	0.922712i	−0.606348	+	0.795200i	$0.707366\pi$
$241$	−24.8105	+	14.3243i	−1.59818	+	0.922712i	−0.991837	+	0.127513i	$0.959301\pi$
$242$	−6.04902	−	3.49240i	−0.388846	−	0.224500i
$243$		0			0
$244$			14.7121i			0.941843i
$245$		0			0
$246$		0			0
$247$	1.72667	−	2.99067i	0.109865	−	0.190292i
$248$	−0.909687			−0.0577652
$249$		0			0
$250$			11.2179i			0.709481i
$251$	−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
$254$			17.9292i			1.12498i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−7.54890	+	13.0751i	−0.470888	+	0.815601i	−0.999446	−	0.0332960i	$-0.989400\pi$
$257$	−7.54890	+	13.0751i	−0.470888	+	0.815601i	0.528558	+	0.848897i	$0.322733\pi$
$258$		0			0
$259$		0			0
$260$			12.3373i			0.765128i
$261$		0			0
$262$	15.0094	+	8.66567i	0.927283	+	0.535367i
$263$	−17.0075	+	9.81926i	−1.04873	+	0.605482i	−0.922292	−	0.386493i	$-0.873686\pi$
$263$	−17.0075	+	9.81926i	−1.04873	+	0.605482i	−0.126433	+	0.991975i	$0.540353\pi$
$264$		0			0
$265$	27.4376	−	15.8411i	1.68548	−	0.973112i
$266$		0			0
$267$		0			0
$268$	8.31641			0.508006
$269$	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	−0.0816537	−	0.996661i	$-0.526020\pi$
$271$	12.1927	−	7.03945i	0.740653	−	0.427616i	0.822307	+	0.569045i	$0.192687\pi$
$272$	−3.08709	+	5.34700i	−0.187182	+	0.324209i
$273$		0			0
$274$	−0.000322562	0	0.000558693i	−1.94867e−5	0	3.37519e-5i
$275$	−14.0553	−	8.11481i	−0.847565	−	0.489342i
$276$		0			0
$277$	−15.3600	−	26.6043i	−0.922894	−	1.59850i	−0.794913	−	0.606723i	$-0.792484\pi$
$277$	−15.3600	−	26.6043i	−0.922894	−	1.59850i	−0.127981	−	0.991777i	$-0.540850\pi$
$278$	5.04185	+	8.73273i	0.302390	+	0.523755i
$279$		0			0
$280$		0			0
$281$	−6.86286	−	3.96227i	−0.409404	−	0.236369i	0.281130	−	0.959670i	$-0.409291\pi$
$281$	−6.86286	−	3.96227i	−0.409404	−	0.236369i	−0.690534	+	0.723300i	$0.742624\pi$
$282$		0			0
$283$			11.5159i			0.684547i	0.939600	+	0.342273i	$0.111197\pi$
$283$			11.5159i			0.684547i	−0.939600	+	0.342273i	$0.888803\pi$
$284$		−	0.466287i		−	0.0276691i
$285$		0			0
$286$	−5.91532	−	3.41521i	−0.349780	−	0.201946i
$287$		0			0
$288$		0			0
$289$	−10.5603	−	18.2909i	−0.621192	−	1.07594i
$290$	10.5434	+	18.2616i	0.619127	+	1.07236i
$291$		0			0
$292$	−3.65022	−	2.10746i	−0.213613	−	0.123330i
$293$	−2.50937	−	4.34636i	−0.146599	−	0.253917i	0.783369	−	0.621557i	$-0.213499\pi$
$293$	−2.50937	−	4.34636i	−0.146599	−	0.253917i	−0.929968	+	0.367639i	$0.880166\pi$
$294$		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
$299$	−10.3217			−0.596917
$300$		0			0
$301$		0			0
$302$	−4.09092	+	2.36189i	−0.235406	+	0.135912i
$303$		0			0
$304$	−0.877353	+	0.506540i	−0.0503197	+	0.0290521i
$305$	46.1138	+	26.6238i	2.64047	+	1.52447i
$306$		0			0
$307$			17.5309i			1.00054i	0.865869	+	0.500271i	$0.166766\pi$
$307$			17.5309i			1.00054i	−0.865869	+	0.500271i	$0.833234\pi$
$308$		0			0
$309$		0			0
$310$	−1.64622	+	2.85134i	−0.0934992	+	0.161945i
$311$	17.2952			0.980720			0.490360	−	0.871520i	$-0.336865\pi$
$311$	17.2952			0.980720			0.490360	+	0.871520i	$0.336865\pi$
$312$		0			0
$313$			8.99498i			0.508426i	0.967148	+	0.254213i	$0.0818165\pi$
$313$			8.99498i			0.508426i	−0.967148	+	0.254213i	$0.918184\pi$
$314$	3.06972			0.173234
$315$		0			0
$316$	−3.82533			−0.215192
$317$			6.72038i			0.377454i	0.982030	+	0.188727i	$0.0604362\pi$
$317$			6.72038i			0.377454i	−0.982030	+	0.188727i	$0.939564\pi$
$318$		0			0
$319$	−11.6744			−0.653642
$320$	1.80966	−	3.13442i	0.101163	−	0.175219i
$321$		0			0
$322$		0			0
$323$		−	6.25494i		−	0.348034i
$324$		0			0
$325$	23.9100	+	13.8045i	1.32629	+	0.765734i
$326$	2.48873	−	1.43687i	0.137838	−	0.0795807i
$327$		0			0
$328$	−4.93712	+	2.85045i	−0.272607	+	0.157390i
$329$		0			0
$330$		0			0
$331$	−18.7745			−1.03194			−0.515970	−	0.856607i	$-0.672568\pi$
$331$	−18.7745			−1.03194			−0.515970	+	0.856607i	$0.672568\pi$
$332$	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	0.924441	−	0.381326i	$-0.124532\pi$
$337$	2.42287	+	4.19654i	0.131982	+	0.228600i	−0.792458	+	0.609926i	$0.791199\pi$
$338$	−1.19552	−	0.690233i	−0.0650276	−	0.0375437i
$339$		0			0
$340$	11.1732	+	19.3525i	0.605949	+	1.04954i
$341$	−0.911413	−	1.57861i	−0.0493558	−	0.0854868i
$342$		0			0
$343$		0			0
$344$	4.15605	+	2.39949i	0.224079	+	0.129372i
$345$		0			0
$346$		−	3.07081i		−	0.165088i
$347$		−	17.4712i		−	0.937902i	−0.883224	−	0.468951i	$-0.844632\pi$
$347$		−	17.4712i		−	0.937902i	0.883224	−	0.468951i	$-0.155368\pi$
$348$		0			0
$349$	−20.6338	−	11.9129i	−1.10450	−	0.637683i	−0.167101	−	0.985940i	$-0.553440\pi$
$349$	−20.6338	−	11.9129i	−1.10450	−	0.637683i	−0.937399	+	0.348257i	$0.886774\pi$
$350$		0			0
$351$		0			0
$352$	1.00190	+	1.73534i	0.0534013	+	0.0924938i
$353$	5.02061	+	8.69596i	0.267220	+	0.462839i	0.968143	−	0.250398i	$-0.0805615\pi$
$353$	5.02061	+	8.69596i	0.267220	+	0.462839i	−0.700923	+	0.713237i	$0.747228\pi$
$354$		0			0
$355$	−1.46154	−	0.843820i	−0.0775705	−	0.0447853i
$356$	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	−0.195521	−	0.980700i	$-0.562640\pi$
$359$	10.5353	−	6.08254i	0.556030	−	0.321024i	0.751550	+	0.659676i	$0.229306\pi$
$360$		0			0
$361$	−8.98683	+	15.5657i	−0.472991	+	0.819245i
$362$	7.89318			0.414856
$363$		0			0
$364$		0			0
$365$	−13.2113	+	7.62756i	−0.691512	+	0.399245i
$366$		0			0
$367$	−3.14420	+	1.81531i	−0.164126	+	0.0947582i	−0.579813	−	0.814749i	$-0.696874\pi$
$367$	−3.14420	+	1.81531i	−0.164126	+	0.0947582i	0.415687	+	0.909508i	$0.363541\pi$
$368$	2.62232	+	1.51400i	0.136698	+	0.0789225i
$369$		0			0
$370$		−	26.5531i		−	1.38043i
$371$		0			0
$372$		0			0
$373$	−2.74616	+	4.75648i	−0.142191	+	0.246281i	−0.928321	−	0.371779i	$-0.878748\pi$
$373$	−2.74616	+	4.75648i	−0.142191	+	0.246281i	0.786131	+	0.618060i	$0.212081\pi$
$374$	−12.3718			−0.639730
$375$		0			0
$376$			2.23022i			0.115015i
$377$	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	$0.631183\pi$
$380$			3.66666i			0.188096i
$381$		0			0
$382$	13.3042			0.680703
$383$	4.71534	−	8.16720i	0.240942	−	0.417324i	−0.720041	−	0.693932i	$-0.755877\pi$
$383$	4.71534	−	8.16720i	0.240942	−	0.417324i	0.960983	+	0.276607i	$0.0892102\pi$
$384$		0			0
$385$		0			0
$386$			6.53573i			0.332660i
$387$		0			0
$388$	−10.1835	−	5.87944i	−0.516989	−	0.298483i
$389$	−5.56142	+	3.21089i	−0.281975	+	0.162798i	−0.634317	−	0.773073i	$-0.718719\pi$
$389$	−5.56142	+	3.21089i	−0.281975	+	0.162798i	0.352342	+	0.935871i	$0.385385\pi$
$390$		0			0
$391$	−16.1907	+	9.34769i	−0.818798	+	0.472733i
$392$		0			0
$393$		0			0
$394$	4.44250			0.223810
$395$	−6.92255	+	11.9902i	−0.348311	+	0.603293i
$396$		0			0
$397$	−5.99750	+	3.46266i	−0.301006	+	0.173786i	−0.642895	−	0.765955i	$-0.722267\pi$
$397$	−5.99750	+	3.46266i	−0.301006	+	0.173786i	0.341889	+	0.939740i	$0.388933\pi$
$398$	5.75542	−	9.96868i	0.288493	−	0.499685i
$399$		0			0
$400$	−4.04972	−	7.01433i	−0.202486	−	0.350716i
$401$	9.16848	+	5.29343i	0.457852	+	0.264341i	0.711141	−	0.703050i	$-0.248179\pi$
$401$	9.16848	+	5.29343i	0.457852	+	0.264341i	−0.253289	+	0.967391i	$0.581512\pi$
$402$		0			0
$403$	1.55045	+	2.68545i	0.0772332	+	0.133772i
$404$	6.44610	+	11.1650i	0.320705	+	0.555478i
$405$		0			0
$406$		0			0
$407$	12.7313	+	7.35042i	0.631067	+	0.364347i
$408$		0			0
$409$		−	8.92343i		−	0.441235i	−0.975360	−	0.220618i	$-0.929193\pi$
$409$		−	8.92343i		−	0.441235i	0.975360	−	0.220618i	$-0.0708073\pi$
$410$			20.6333i			1.01901i
$411$		0			0
$412$	9.31740	+	5.37940i	0.459035	+	0.265024i
$413$		0			0
$414$		0			0
$415$	−14.4947	−	25.1055i	−0.711516	−	1.23238i
$416$	−1.70437	−	2.95206i	−0.0835637	−	0.144737i
$417$		0			0
$418$	−1.75804	−	1.01500i	−0.0859883	−	0.0496454i
$419$	17.1924	+	29.7781i	0.839903	+	1.45475i	0.889975	+	0.456009i	$0.150721\pi$
$419$	17.1924	+	29.7781i	0.839903	+	1.45475i	−0.0500724	+	0.998746i	$0.515945\pi$
$420$		0			0
$421$	−17.7840	+	30.8028i	−0.866739	+	1.50124i	−0.00142877	+	0.999999i	$0.500455\pi$
$421$	−17.7840	+	30.8028i	−0.866739	+	1.50124i	−0.865310	+	0.501237i	$0.832879\pi$
$422$	−19.5731	+	11.3005i	−0.952803	+	0.550101i
$423$		0			0
$424$	−4.37683	+	7.58088i	−0.212557	+	0.368160i
$425$	50.0075			2.42572
$426$		0			0
$427$		0			0
$428$	−2.28602	+	1.31983i	−0.110499	+	0.0637965i
$429$		0			0
$430$	15.0420	−	8.68453i	0.725392	−	0.418805i
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.978247	−	0.207442i	$-0.0665138\pi$
$431$	26.7338	+	15.4348i	1.28772	+	0.743466i	0.309474	+	0.950908i	$0.399847\pi$
$432$		0			0
$433$			23.2463i			1.11715i	0.829455	+	0.558574i	$0.188651\pi$
$433$			23.2463i			1.11715i	−0.829455	+	0.558574i	$0.811349\pi$
$434$		0			0
$435$		0			0
$436$	−4.51768	+	7.82484i	−0.216357	+	0.374742i
$437$	−3.06760			−0.146743
$438$		0			0
$439$			22.2727i			1.06302i	0.847052	+	0.531509i	$0.178375\pi$
$439$			22.2727i			1.06302i	−0.847052	+	0.531509i	$0.821625\pi$
$440$	7.25237			0.345743
$441$		0			0
$442$	21.0462			1.00107
$443$		−	17.9852i		−	0.854501i	−0.904133	−	0.427251i	$-0.859482\pi$
$443$		−	17.9852i		−	0.854501i	0.904133	−	0.427251i	$-0.140518\pi$
$444$		0			0
$445$	17.3238			0.821225
$446$	9.41045	−	16.2994i	0.445598	−	0.771798i
$447$		0			0
$448$		0			0
$449$			9.44363i			0.445673i	0.974856	+	0.222836i	$0.0715315\pi$
$449$			9.44363i			0.445673i	−0.974856	+	0.222836i	$0.928468\pi$
$450$		0			0
$451$	−9.89297	−	5.71171i	−0.465842	−	0.268954i
$452$	−1.46411	+	0.845306i	−0.0688661	+	0.0397599i
$453$		0			0
$454$	12.6555	−	7.30665i	0.593952	−	0.342918i
$455$		0			0
$456$		0			0
$457$	−1.84450			−0.0862821			−0.0431411	−	0.999069i	$-0.513736\pi$
$457$	−1.84450			−0.0862821			−0.0431411	+	0.999069i	$0.513736\pi$
$458$	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	0.0367790	+	0.999323i	$0.488290\pi$
$461$	−18.1869	+	31.5007i	−0.847050	+	1.46713i	−0.883829	+	0.467810i	$0.845043\pi$
$462$		0			0
$463$	−15.9830	−	27.6834i	−0.742794	−	1.28656i	−0.951219	−	0.308518i	$-0.900167\pi$
$463$	−15.9830	−	27.6834i	−0.742794	−	1.28656i	0.208425	−	0.978038i	$-0.433166\pi$
$464$	−5.04560	−	2.91308i	−0.234236	−	0.135236i
$465$		0			0
$466$	−5.21619	−	9.03470i	−0.241635	−	0.418525i
$467$	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
$469$		0			0
$470$	6.99044	+	4.03593i	0.322445	+	0.186164i
$471$		0			0
$472$		−	8.98627i		−	0.413626i
$473$			9.61619i			0.442153i
$474$		0			0
$475$	7.10607	+	4.10269i	0.326049	+	0.188245i
$476$		0			0
$477$		0			0
$478$	−11.8917	−	20.5971i	−0.543916	−	0.942090i
$479$	5.48032	+	9.49220i	0.250402	+	0.433710i	0.963637	−	0.267216i	$-0.0861037\pi$
$479$	5.48032	+	9.49220i	0.250402	+	0.433710i	−0.713234	+	0.700926i	$0.752770\pi$
$480$		0			0
$481$	−21.6578	−	12.5041i	−0.987509	−	0.570139i
$482$	−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	$0.891043\pi$
$488$	−14.7121			−0.665984
$489$		0			0
$490$		0			0
$491$	19.6893	−	11.3676i	0.888568	−	0.513015i	0.0150939	−	0.999886i	$-0.495195\pi$
$491$	19.6893	−	11.3676i	0.888568	−	0.513015i	0.873474	+	0.486871i	$0.161862\pi$
$492$		0			0
$493$	31.1525	−	17.9859i	1.40304	−	0.810043i
$494$	2.99067	+	1.72667i	0.134557	+	0.0776863i
$495$		0			0
$496$		−	0.909687i		−	0.0408462i
$497$		0			0
$498$		0			0
$499$	−9.76175	+	16.9079i	−0.436996	+	0.756899i	−0.997456	−	0.0712820i	$-0.977291\pi$
$499$	−9.76175	+	16.9079i	−0.436996	+	0.756899i	0.560460	+	0.828181i	$0.310624\pi$
$500$	−11.2179			−0.501679
$501$		0			0
$502$		−	11.0301i		−	0.492299i
$503$	−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
$506$			6.06748i			0.269732i
$507$		0			0
$508$	−17.9292			−0.795478
$509$	−1.14583	+	1.98464i	−0.0507881	+	0.0879675i	−0.890302	−	0.455371i	$-0.849507\pi$
$509$	−1.14583	+	1.98464i	−0.0507881	+	0.0879675i	0.839514	+	0.543338i	$0.182840\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−13.0751	−	7.54890i	−0.576717	−	0.332968i
$515$	33.7226	−	19.4698i	1.48600	−	0.857940i
$516$		0			0
$517$	−3.87018	+	2.23445i	−0.170210	+	0.0982710i
$518$		0			0
$519$		0			0
$520$	−12.3373			−0.541027
$521$	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	$0.691559\pi$
$523$	−35.7462	+	20.6381i	−1.56307	+	0.902440i	−0.996944	+	0.0781229i	$0.975107\pi$
$524$	−8.66567	+	15.0094i	−0.378562	+	0.655688i
$525$		0			0
$526$	−9.81926	−	17.0075i	−0.428140	−	0.741561i
$527$	4.86410	+	2.80829i	0.211883	+	0.122331i
$528$		0			0
$529$	−6.91563	−	11.9782i	−0.300679	−	0.520792i
$530$	15.8411	+	27.4376i	0.688094	+	1.19181i
$531$		0			0
$532$		0			0
$533$	16.8294	+	9.71644i	0.728961	+	0.420866i
$534$		0			0
$535$			9.55378i			0.413046i
$536$			8.31641i			0.359214i
$537$		0			0
$538$	0.425223	+	0.245503i	0.0183327	+	0.0105844i
$539$		0			0
$540$		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	$0.402040\pi$
$542$	7.03945	+	12.1927i	0.302370	+	0.523721i
$543$		0			0
$544$	−5.34700	−	3.08709i	−0.229251	−	0.132358i
$545$	16.3509	+	28.3206i	0.700395	+	1.21312i
$546$		0			0
$547$	15.1095	−	26.1705i	0.646037	−	1.11897i	−0.338024	−	0.941138i	$-0.609758\pi$
$547$	15.1095	−	26.1705i	0.646037	−	1.11897i	0.984061	−	0.177832i	$-0.0569082\pi$
$548$	0.000558693	0	0.000322562i	2.38662e−5	0	1.37791e-5i
$549$		0			0
$550$	8.11481	−	14.0553i	0.346017	−	0.599319i
$551$	5.90237			0.251449
$552$		0			0
$553$		0			0
$554$	26.6043	−	15.3600i	1.13031	−	0.652585i
$555$		0			0
$556$	−8.73273	+	5.04185i	−0.370350	+	0.213822i
$557$	−22.0154	−	12.7106i	−0.932822	−	0.538565i	−0.0451189	−	0.998982i	$-0.514367\pi$
$557$	−22.0154	−	12.7106i	−0.932822	−	0.538565i	−0.887703	+	0.460417i	$0.847700\pi$
$558$		0			0
$559$		−	16.3585i		−	0.691892i
$560$		0			0
$561$		0			0
$562$	3.96227	−	6.86286i	0.167138	−	0.289492i
$563$	2.88692			0.121669			0.0608346	−	0.998148i	$-0.480624\pi$
$563$	2.88692			0.121669			0.0608346	+	0.998148i	$0.480624\pi$
$564$		0			0
$565$			6.11886i			0.257422i
$566$	−11.5159			−0.484048
$567$		0			0
$568$	0.466287			0.0195650
$569$			44.5651i			1.86827i	0.356922	+	0.934134i	$0.383826\pi$
$569$			44.5651i			1.86827i	−0.356922	+	0.934134i	$0.616174\pi$
$570$		0			0
$571$	−6.52939			−0.273247			−0.136623	−	0.990623i	$-0.543625\pi$
$571$	−6.52939			−0.273247			−0.136623	+	0.990623i	$0.543625\pi$
$572$	3.41521	−	5.91532i	0.142797	−	0.247332i
$573$		0			0
$574$		0			0
$575$		−	24.5251i		−	1.02277i
$576$		0			0
$577$	−1.17720	−	0.679658i	−0.0490076	−	0.0282945i	0.475296	−	0.879826i	$-0.342341\pi$
$577$	−1.17720	−	0.679658i	−0.0490076	−	0.0282945i	−0.524304	+	0.851531i	$0.675674\pi$
$578$	18.2909	−	10.5603i	0.760802	−	0.439249i
$579$		0			0
$580$	−18.2616	+	10.5434i	−0.758273	+	0.437789i
$581$		0			0
$582$		0			0
$583$	−17.5405			−0.726454
$584$	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	0.111555	−	0.993758i	$-0.464417\pi$
$587$	22.2025	−	38.4559i	0.916397	−	1.58725i	0.804843	−	0.593488i	$-0.202250\pi$
$588$		0			0
$589$	0.460793	+	0.798117i	0.0189866	+	0.0328858i
$590$	−28.1667	−	16.2621i	−1.15961	−	0.669499i
$591$		0			0
$592$	3.66825	+	6.35359i	0.150764	+	0.261131i
$593$	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
$595$		0			0
$596$	−9.74064	−	5.62376i	−0.398992	−	0.230358i
$597$		0			0
$598$		−	10.3217i		−	0.422084i
$599$		−	3.50277i		−	0.143119i	−0.997436	−	0.0715597i	$-0.977202\pi$
$599$		−	3.50277i		−	0.143119i	0.997436	−	0.0715597i	$-0.0227977\pi$
$600$		0			0
$601$	−15.1846	−	8.76685i	−0.619394	−	0.357607i	0.157239	−	0.987561i	$-0.449741\pi$
$601$	−15.1846	−	8.76685i	−0.619394	−	0.357607i	−0.776633	+	0.629953i	$0.783074\pi$
$602$		0			0
$603$		0			0
$604$	−2.36189	−	4.09092i	−0.0961041	−	0.166457i
$605$	−12.6401	−	21.8933i	−0.513894	−	0.890090i
$606$		0			0
$607$	−0.0755923	−	0.0436432i	−0.00306820	−	0.00177142i	0.498465	−	0.866910i	$-0.333897\pi$
$607$	−0.0755923	−	0.0436432i	−0.00306820	−	0.00177142i	−0.501533	+	0.865138i	$0.667231\pi$
$608$	−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	$-0.00231754\pi$
$614$	−17.5309			−0.707490
$615$		0			0
$616$		0			0
$617$	10.6365	−	6.14101i	0.428211	−	0.247228i	−0.270373	−	0.962756i	$-0.587147\pi$
$617$	10.6365	−	6.14101i	0.428211	−	0.247228i	0.698584	+	0.715528i	$0.253814\pi$
$618$		0			0
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	−0.103028	−	0.994678i	$-0.532853\pi$
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	0.809903	+	0.586564i	$0.199520\pi$
$620$	−2.85134	−	1.64622i	−0.114513	−	0.0661139i
$621$		0			0
$622$			17.2952i			0.693474i
$623$		0			0
$624$		0			0
$625$	−0.0518970	+	0.0898882i	−0.00207588	+	0.00359553i
$626$	−8.99498			−0.359512
$627$		0			0
$628$			3.06972i			0.122495i
$629$	−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	$0.867770\pi$
$632$		−	3.82533i		−	0.152164i
$633$		0			0
$634$	−6.72038			−0.266901
$635$	−32.4456	+	56.1975i	−1.28757	+	2.23013i
$636$		0			0
$637$		0			0
$638$		−	11.6744i		−	0.462195i
$639$		0			0
$640$	3.13442	+	1.80966i	0.123899	+	0.0715330i
$641$	27.4104	−	15.8254i	1.08265	−	0.625067i	0.151038	−	0.988528i	$-0.451738\pi$
$641$	27.4104	−	15.8254i	1.08265	−	0.625067i	0.931609	+	0.363461i	$0.118405\pi$
$642$		0			0
$643$	10.0106	−	5.77960i	0.394778	−	0.227925i	−0.289450	−	0.957193i	$-0.593472\pi$
$643$	10.0106	−	5.77960i	0.394778	−	0.227925i	0.684228	+	0.729268i	$0.260139\pi$
$644$		0			0
$645$		0			0
$646$	6.25494			0.246097
$647$	−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
$653$	−16.3952	−	9.46576i	−0.641593	−	0.370424i	0.143635	−	0.989631i	$-0.454121\pi$
$653$	−16.3952	−	9.46576i	−0.641593	−	0.370424i	−0.785228	+	0.619207i	$0.787454\pi$
$654$		0			0
$655$	31.3638	+	54.3237i	1.22549	+	2.12260i
$656$	−2.85045	−	4.93712i	−0.111291	−	0.192762i
$657$		0			0
$658$		0			0
$659$	−23.3508	−	13.4816i	−0.909618	−	0.525168i	−0.0293098	−	0.999570i	$-0.509331\pi$
$659$	−23.3508	−	13.4816i	−0.909618	−	0.525168i	−0.880308	+	0.474402i	$0.842664\pi$
$660$		0			0
$661$		−	25.7730i		−	1.00245i	−0.865316	−	0.501227i	$-0.832882\pi$
$661$		−	25.7730i		−	1.00245i	0.865316	−	0.501227i	$-0.167118\pi$
$662$		−	18.7745i		−	0.729691i
$663$		0			0
$664$	6.93654	+	4.00481i	0.269190	+	0.155417i
$665$		0			0
$666$		0			0
$667$	−8.82079	−	15.2780i	−0.341542	−	0.591568i
$668$	−0.730517	−	1.26529i	−0.0282646	−	0.0489557i
$669$		0			0
$670$	26.0671	+	15.0499i	1.00706	+	0.581427i
$671$	−14.7400	−	25.5304i	−0.569030	−	0.985590i
$672$		0			0
$673$	−12.9608	+	22.4487i	−0.499601	+	0.865335i	−1.00000		0.000460130i	$-0.999854\pi$
$673$	−12.9608	+	22.4487i	−0.499601	+	0.865335i	0.500398	+	0.865795i	$0.333187\pi$
$674$	−4.19654	+	2.42287i	−0.161645	+	0.0933256i
$675$		0			0
$676$	0.690233	−	1.19552i	0.0265474	−	0.0459815i
$677$	13.1076			0.503767			0.251884	−	0.967758i	$-0.418950\pi$
$677$	13.1076			0.503767			0.251884	+	0.967758i	$0.418950\pi$
$678$		0			0
$679$		0			0
$680$	−19.3525	+	11.1732i	−0.742134	+	0.428471i
$681$		0			0
$682$	1.57861	−	0.911413i	0.0604483	−	0.0348998i
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.0798523	−	0.996807i	$-0.525445\pi$
$683$	−25.6910	−	14.8327i	−0.983038	−	0.567557i	−0.903186	+	0.429249i	$0.858778\pi$
$684$		0			0
$685$		−	0.00233490i		−	8.92121e-5i
$686$		0			0
$687$		0			0
$688$	−2.39949	+	4.15605i	−0.0914799	+	0.158448i
$689$	29.8390			1.13677
$690$		0			0
$691$			47.3159i			1.79998i	0.435910	+	0.899990i	$0.356427\pi$
$691$			47.3159i			1.79998i	−0.435910	+	0.899990i	$0.643573\pi$
$692$	3.07081			0.116735
$693$		0			0
$694$	17.4712			0.663197
$695$			36.4961i			1.38437i
$696$		0			0
$697$	35.1983			1.33323
$698$	11.9129	−	20.6338i	0.450910	−	0.780999i
$699$		0			0
$700$		0			0
$701$			13.7742i			0.520244i	0.965576	+	0.260122i	$0.0837627\pi$
$701$			13.7742i			0.520244i	−0.965576	+	0.260122i	$0.916237\pi$
$702$		0			0
$703$	−6.43670	−	3.71623i	−0.242765	−	0.140160i
$704$	−1.73534	+	1.00190i	−0.0654030	+	0.0377604i
$705$		0			0
$706$	−8.69596	+	5.02061i	−0.327277	+	0.188953i
$707$		0			0
$708$		0			0
$709$	−43.9383			−1.65014			−0.825069	−	0.565032i	$-0.808864\pi$
$709$	−43.9383			−1.65014			−0.825069	+	0.565032i	$0.808864\pi$
$710$	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
$716$	16.7310	+	9.65966i	0.625268	+	0.360998i
$717$		0			0
$718$	6.08254	+	10.5353i	0.226998	+	0.393173i
$719$	−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
$721$		0			0
$722$	−15.5657	−	8.98683i	−0.579294	−	0.334455i
$723$		0			0
$724$			7.89318i			0.293348i
$725$			47.1887i			1.75254i
$726$		0			0
$727$	−10.1244	−	5.84534i	−0.375494	−	0.216792i	0.300362	−	0.953825i	$-0.402893\pi$
$727$	−10.1244	−	5.84534i	−0.375494	−	0.216792i	−0.675856	+	0.737034i	$0.736226\pi$
$728$		0			0
$729$		0			0
$730$	−7.62756	−	13.2113i	−0.282308	−	0.488973i
$731$	−14.8149	−	25.6602i	−0.547949	−	0.949076i
$732$		0			0
$733$	28.6423	+	16.5366i	1.05793	+	0.610795i	0.924858	−	0.380312i	$-0.124183\pi$
$733$	28.6423	+	16.5366i	1.05793	+	0.610795i	0.133070	+	0.991107i	$0.457517\pi$
$734$	−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	$0.871399\pi$
$740$	26.5531			0.976111
$741$		0			0
$742$		0			0
$743$	−18.0206	+	10.4042i	−0.661112	+	0.381693i	−0.792701	−	0.609611i	$-0.791326\pi$
$743$	−18.0206	+	10.4042i	−0.661112	+	0.381693i	0.131589	+	0.991304i	$0.457992\pi$
$744$		0			0
$745$	−35.2544	+	20.3542i	−1.29162	+	0.745719i
$746$	−4.75648	−	2.74616i	−0.174147	−	0.100544i
$747$		0			0
$748$		−	12.3718i		−	0.452358i
$749$		0			0
$750$		0			0
$751$	19.9492	−	34.5531i	0.727957	−	1.26086i	−0.229788	−	0.973241i	$-0.573803\pi$
$751$	19.9492	−	34.5531i	0.727957	−	1.26086i	0.957745	−	0.287618i	$-0.0928634\pi$
$752$	−2.23022			−0.0813277
$753$		0			0
$754$			19.8599i			0.723254i
$755$	−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	$0.456740\pi$
$758$		−	15.5960i		−	0.566472i
$759$		0			0
$760$	−3.66666			−0.133004
$761$	−4.32462	+	7.49046i	−0.156767	+	0.271529i	−0.933701	−	0.358053i	$-0.883441\pi$
$761$	−4.32462	+	7.49046i	−0.156767	+	0.271529i	0.776934	+	0.629582i	$0.216774\pi$
$762$		0			0
$763$		0			0
$764$			13.3042i			0.481330i
$765$		0			0
$766$	8.16720	+	4.71534i	0.295093	+	0.170372i
$767$	−26.5280	+	15.3159i	−0.957870	+	0.553026i
$768$		0			0
$769$	−20.4818	+	11.8252i	−0.738592	+	0.426426i	−0.821557	−	0.570126i	$-0.806894\pi$
$769$	−20.4818	+	11.8252i	−0.738592	+	0.426426i	0.0829652	+	0.996552i	$0.473561\pi$
$770$		0			0
$771$		0			0
$772$	−6.53573			−0.235226
$773$	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
$779$	5.00170	+	2.88773i	0.179204	+	0.103464i
$780$		0			0
$781$	0.467172	+	0.809166i	0.0167167	+	0.0289542i
$782$	−9.34769	−	16.1907i	−0.334273	−	0.578977i
$783$		0			0
$784$		0			0
$785$	9.62178	+	5.55513i	0.343416	+	0.198271i
$786$		0			0
$787$			24.4400i			0.871192i	0.900142	+	0.435596i	$0.143462\pi$
$787$			24.4400i			0.871192i	−0.900142	+	0.435596i	$0.856538\pi$
$788$			4.44250i			0.158258i
$789$		0			0
$790$	−11.9902	−	6.92255i	−0.426592	−	0.246293i
$791$		0			0
$792$		0			0
$793$	25.0748	+	43.4309i	0.890433	+	1.54228i
$794$	−3.46266	−	5.99750i	−0.122885	−	0.212843i
$795$		0			0
$796$	9.96868	+	5.75542i	0.353330	+	0.203995i
$797$	−24.9202	−	43.1631i	−0.882719	−	1.52891i	−0.848306	−	0.529506i	$-0.822377\pi$
$797$	−24.9202	−	43.1631i	−0.882719	−	1.52891i	−0.0344128	−	0.999408i	$-0.510956\pi$
$798$		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
$803$	8.44583			0.298047
$804$		0			0
$805$		0			0
$806$	−2.68545	+	1.55045i	−0.0945910	+	0.0546121i
$807$		0			0
$808$	−11.1650	+	6.44610i	−0.392782	+	0.226773i
$809$	10.6735	+	6.16237i	0.375262	+	0.216657i	0.675755	−	0.737127i	$-0.263818\pi$
$809$	10.6735	+	6.16237i	0.375262	+	0.216657i	−0.300493	+	0.953784i	$0.597151\pi$
$810$		0			0
$811$			24.8017i			0.870906i	0.900212	+	0.435453i	$0.143412\pi$
$811$			24.8017i			0.870906i	−0.900212	+	0.435453i	$0.856588\pi$
$812$		0			0
$813$		0			0
$814$	−7.35042	+	12.7313i	−0.257632	+	0.446232i
$815$	10.4009			0.364329
$816$		0			0
$817$		−	4.86176i		−	0.170091i
$818$	8.92343			0.312000
$819$		0			0
$820$	−20.6333			−0.720547
$821$		−	36.2083i		−	1.26368i	−0.775100	−	0.631839i	$-0.782300\pi$
$821$		−	36.2083i		−	1.26368i	0.775100	−	0.631839i	$-0.217700\pi$
$822$		0			0
$823$	−19.0819			−0.665152			−0.332576	−	0.943076i	$-0.607918\pi$
$823$	−19.0819			−0.665152			−0.332576	+	0.943076i	$0.607918\pi$
$824$	−5.37940	+	9.31740i	−0.187400	+	0.324587i
$825$		0			0
$826$		0			0
$827$			31.9013i			1.10932i	0.832079	+	0.554658i	$0.187151\pi$
$827$			31.9013i			1.10932i	−0.832079	+	0.554658i	$0.812849\pi$
$828$		0			0
$829$	−13.0645	−	7.54278i	−0.453748	−	0.261971i	0.255664	−	0.966766i	$-0.417706\pi$
$829$	−13.0645	−	7.54278i	−0.453748	−	0.261971i	−0.709412	+	0.704794i	$0.751039\pi$
$830$	25.1055	−	14.4947i	0.871425	−	0.503118i
$831$		0			0
$832$	2.95206	−	1.70437i	0.102344	−	0.0590885i
$833$		0			0
$834$		0			0
$835$	−5.28795			−0.182997
$836$	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	−0.972134	−	0.234427i	$-0.924679\pi$
$839$	−8.19860	+	14.2004i	−0.283047	+	0.490252i	0.689087	+	0.724679i	$0.258012\pi$
$840$		0			0
$841$	2.47206	+	4.28173i	0.0852434	+	0.147646i
$842$	−30.8028	−	17.7840i	−1.06153	−	0.612877i
$843$		0			0
$844$	−11.3005	−	19.5731i	−0.388980	−	0.673734i
$845$	−2.49817	−	4.32696i	−0.0859397	−	0.148852i
$846$		0			0
$847$		0			0
$848$	−7.58088	−	4.37683i	−0.260329	−	0.150301i
$849$		0			0
$850$			50.0075i			1.71524i
$851$			22.2149i			0.761516i
$852$		0			0
$853$	−16.5936	−	9.58030i	−0.568153	−	0.328023i	0.188258	−	0.982120i	$-0.439716\pi$
$853$	−16.5936	−	9.58030i	−0.568153	−	0.328023i	−0.756411	+	0.654096i	$0.773049\pi$
$854$		0			0
$855$		0			0
$856$	−1.31983	−	2.28602i	−0.0451110	−	0.0781345i
$857$	8.05723	+	13.9555i	0.275230	+	0.476712i	0.970193	−	0.242333i	$-0.0779127\pi$
$857$	8.05723	+	13.9555i	0.275230	+	0.476712i	−0.694963	+	0.719045i	$0.744579\pi$
$858$		0			0
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	0.310384	−	0.950611i	$-0.399542\pi$
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	−0.668061	+	0.744106i	$0.732876\pi$
$860$	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	−0.935848	−	0.352405i	$-0.885364\pi$
$863$	−32.2728	+	18.6327i	−1.09858	+	0.634265i	−0.162732	+	0.986670i	$0.552031\pi$
$864$		0			0
$865$	5.55712	−	9.62522i	0.188948	−	0.327267i
$866$	−23.2463			−0.789942
$867$		0			0
$868$		0			0
$869$	6.63824	−	3.83259i	0.225187	−	0.130012i
$870$		0			0
$871$	24.5505	−	14.1743i	0.831863	−	0.480276i
$872$	−7.82484	−	4.51768i	−0.264983	−	0.152988i
$873$		0			0
$874$		−	3.06760i		−	0.103763i
$875$		0			0
$876$		0			0
$877$	4.85474	−	8.40866i	0.163933	−	0.283940i	−0.772343	−	0.635206i	$-0.780915\pi$
$877$	4.85474	−	8.40866i	0.163933	−	0.283940i	0.936276	+	0.351266i	$0.114249\pi$
$878$	−22.2727			−0.751668
$879$		0			0
$880$			7.25237i			0.244477i
$881$	−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	$0.709273\pi$
$884$			21.0462i			0.707860i
$885$		0			0
$886$	17.9852			0.604224
$887$	−8.18209	+	14.1718i	−0.274728	+	0.475842i	−0.970066	−	0.242840i	$-0.921921\pi$
$887$	−8.18209	+	14.1718i	−0.274728	+	0.475842i	0.695339	+	0.718682i	$0.255254\pi$
$888$		0			0
$889$		0			0
$890$			17.3238i			0.580694i
$891$		0			0
$892$	16.2994	+	9.41045i	0.545744	+	0.315085i
$893$	1.95669	−	1.12969i	0.0654781	−	0.0378038i
$894$		0			0
$895$	60.5549	−	34.9614i	2.02413	−	1.16863i
$896$		0			0
$897$		0			0
$898$	−9.44363			−0.315138
$899$	−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
$905$	24.7405	+	14.2839i	0.822403	+	0.474814i
$906$		0			0
$907$	−5.41666	−	9.38192i	−0.179857	−	0.311522i	0.761974	−	0.647607i	$-0.224230\pi$
$907$	−5.41666	−	9.38192i	−0.179857	−	0.311522i	−0.941831	+	0.336086i	$0.890897\pi$
$908$	7.30665	+	12.6555i	0.242480	+	0.419987i
$909$		0			0
$910$		0			0
$911$	−36.8512	−	21.2760i	−1.22093	−	0.704907i	−0.255817	−	0.966725i	$-0.582345\pi$
$911$	−36.8512	−	21.2760i	−1.22093	−	0.704907i	−0.965117	+	0.261818i	$0.915678\pi$
$912$		0			0
$913$			16.0496i			0.531166i
$914$		−	1.84450i		−	0.0610107i
$915$		0			0
$916$	2.06044	+	1.18959i	0.0680788	+	0.0393053i
$917$		0			0
$918$		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	$0.974055\pi$
$920$	5.47963	+	9.49100i	0.180658	+	0.312909i
$921$		0			0
$922$	−31.5007	−	18.1869i	−1.03742	−	0.598955i
$923$	−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
$929$	46.8911			1.53845			0.769224	−	0.638979i	$-0.220643\pi$
$929$	46.8911			1.53845			0.769224	+	0.638979i	$0.220643\pi$
$930$		0			0
$931$		0			0
$932$	9.03470	−	5.21619i	0.295942	−	0.170862i
$933$		0			0
$934$	−21.1666	+	12.2206i	−0.692593	+	0.399869i
$935$	−38.7784	−	22.3887i	−1.26819	−	0.732189i
$936$		0			0
$937$			0.209357i			0.00683939i	0.999994	+	0.00341969i	$0.00108852\pi$
$937$			0.209357i			0.00683939i	−0.999994	+	0.00341969i	$0.998911\pi$
$938$		0			0
$939$		0			0
$940$	−4.03593	+	6.99044i	−0.131638	+	0.228003i
$941$	−0.777130			−0.0253337			−0.0126669	−	0.999920i	$-0.504032\pi$
$941$	−0.777130			−0.0253337			−0.0126669	+	0.999920i	$0.504032\pi$
$942$		0			0
$943$		−	17.2623i		−	0.562137i
$944$	8.98627			0.292478
$945$		0			0
$946$	−9.61619			−0.312649
$947$		−	49.7945i		−	1.61810i	−0.587737	−	0.809052i	$-0.699981\pi$
$947$		−	49.7945i		−	1.61810i	0.587737	−	0.809052i	$-0.300019\pi$
$948$		0			0
$949$	−14.3676			−0.466391
$950$	−4.10269	+	7.10607i	−0.133109	+	0.230552i
$951$		0			0
$952$		0			0
$953$			41.4104i			1.34141i	0.741722	+	0.670707i	$0.234009\pi$
$953$			41.4104i			1.34141i	−0.741722	+	0.670707i	$0.765991\pi$
$954$		0			0
$955$	41.7010	+	24.0761i	1.34941	+	0.779084i
$956$	20.5971	−	11.8917i	0.666158	−	0.384607i
$957$		0			0
$958$	−9.49220	+	5.48032i	−0.306679	+	0.177061i
$959$		0			0
$960$		0			0
$961$	30.1725			0.973305
$962$	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	0.955470	+	0.295088i	$0.0953491\pi$
$967$	22.8028	+	39.4956i	0.733289	+	1.27009i	−0.222181	+	0.975005i	$0.571318\pi$
$968$	6.04902	+	3.49240i	0.194423	+	0.112250i
$969$		0			0
$970$	−21.2796	−	36.8573i	−0.683245	−	1.18342i
$971$	−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
$973$		0			0
$974$	−29.1136	−	16.8087i	−0.932860	−	0.538587i
$975$		0			0
$976$		−	14.7121i		−	0.470922i
$977$		−	14.9023i		−	0.476766i	−0.971171	−	0.238383i	$-0.923383\pi$
$977$		−	14.9023i		−	0.476766i	0.971171	−	0.238383i	$-0.0766174\pi$
$978$		0			0
$979$	−8.30615	−	4.79556i	−0.265466	−	0.153267i
$980$		0			0
$981$		0			0
$982$	11.3676	+	19.6893i	0.362756	+	0.628312i
$983$	−1.53458	−	2.65798i	−0.0489456	−	0.0847763i	0.840515	−	0.541789i	$-0.182253\pi$
$983$	−1.53458	−	2.65798i	−0.0489456	−	0.0847763i	−0.889460	+	0.457013i	$0.848919\pi$
$984$		0			0
$985$	13.9247	+	8.03941i	0.443677	+	0.256157i
$986$	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	$-0.180211\pi$
$992$	0.909687			0.0288826
$993$		0			0
$994$		0			0
$995$	36.0798	−	20.8307i	1.14381	−	0.660377i
$996$		0			0
$997$	−5.30607	+	3.06346i	−0.168045	+	0.0970208i	−0.581664	−	0.813429i	$-0.697598\pi$
$997$	−5.30607	+	3.06346i	−0.168045	+	0.0970208i	0.413619	+	0.910450i	$0.364265\pi$
$998$	−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	2646.2.l.a.521.5		16
3.2	odd	2		882.2.l.b.227.4		16
7.2	even	3		378.2.t.a.89.8		16
7.3	odd	6		2646.2.m.b.1763.4		16
7.4	even	3		2646.2.m.a.1763.1		16
7.5	odd	6		2646.2.t.b.1979.5		16
7.6	odd	2		378.2.l.a.143.8		16
9.4	even	3		882.2.t.a.815.3		16
9.5	odd	6		2646.2.t.b.2285.5		16
21.2	odd	6		126.2.t.a.47.2	yes	16
21.5	even	6		882.2.t.a.803.3		16
21.11	odd	6		882.2.m.a.587.6		16
21.17	even	6		882.2.m.b.587.7		16
21.20	even	2		126.2.l.a.101.1	yes	16
28.23	odd	6		3024.2.df.c.1601.7		16
28.27	even	2		3024.2.ca.c.2033.7		16
63.2	odd	6		1134.2.k.b.971.8		16
63.4	even	3		882.2.m.b.293.7		16
63.5	even	6	inner	2646.2.l.a.1097.1		16
63.13	odd	6		126.2.t.a.59.2	yes	16
63.16	even	3		1134.2.k.a.971.1		16
63.20	even	6		1134.2.k.a.647.1		16
63.23	odd	6		378.2.l.a.341.4		16
63.31	odd	6		882.2.m.a.293.6		16
63.32	odd	6		2646.2.m.b.881.4		16
63.34	odd	6		1134.2.k.b.647.8		16
63.40	odd	6		882.2.l.b.509.8		16
63.41	even	6		378.2.t.a.17.8		16
63.58	even	3		126.2.l.a.5.5	✓	16
63.59	even	6		2646.2.m.a.881.1		16
84.23	even	6		1008.2.df.c.929.5		16
84.83	odd	2		1008.2.ca.c.353.8		16
252.23	even	6		3024.2.ca.c.2609.7		16
252.139	even	6		1008.2.df.c.689.5		16
252.167	odd	6		3024.2.df.c.17.7		16
252.247	odd	6		1008.2.ca.c.257.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	63.58	even	3
126.2.l.a.101.1	yes	16	21.20	even	2
126.2.t.a.47.2	yes	16	21.2	odd	6
126.2.t.a.59.2	yes	16	63.13	odd	6
378.2.l.a.143.8		16	7.6	odd	2
378.2.l.a.341.4		16	63.23	odd	6
378.2.t.a.17.8		16	63.41	even	6
378.2.t.a.89.8		16	7.2	even	3
882.2.l.b.227.4		16	3.2	odd	2
882.2.l.b.509.8		16	63.40	odd	6
882.2.m.a.293.6		16	63.31	odd	6
882.2.m.a.587.6		16	21.11	odd	6
882.2.m.b.293.7		16	63.4	even	3
882.2.m.b.587.7		16	21.17	even	6
882.2.t.a.803.3		16	21.5	even	6
882.2.t.a.815.3		16	9.4	even	3
1008.2.ca.c.257.8		16	252.247	odd	6
1008.2.ca.c.353.8		16	84.83	odd	2
1008.2.df.c.689.5		16	252.139	even	6
1008.2.df.c.929.5		16	84.23	even	6
1134.2.k.a.647.1		16	63.20	even	6
1134.2.k.a.971.1		16	63.16	even	3
1134.2.k.b.647.8		16	63.34	odd	6
1134.2.k.b.971.8		16	63.2	odd	6
2646.2.l.a.521.5		16	1.1	even	1	trivial
2646.2.l.a.1097.1		16	63.5	even	6	inner
2646.2.m.a.881.1		16	63.59	even	6
2646.2.m.a.1763.1		16	7.4	even	3
2646.2.m.b.881.4		16	63.32	odd	6
2646.2.m.b.1763.4		16	7.3	odd	6
2646.2.t.b.1979.5		16	7.5	odd	6
2646.2.t.b.2285.5		16	9.5	odd	6
3024.2.ca.c.2033.7		16	28.27	even	2
3024.2.ca.c.2609.7		16	252.23	even	6
3024.2.df.c.17.7		16	252.167	odd	6
3024.2.df.c.1601.7		16	28.23	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{4} +(-1.80966 + 3.13442i) q^{5} -1.00000i q^{8} +(-3.13442 - 1.80966i) q^{10} +(1.73534 - 1.00190i) q^{11} +(-2.95206 + 1.70437i) q^{13} +1.00000 q^{16} +(-3.08709 + 5.34700i) q^{17} +(-0.877353 + 0.506540i) q^{19} +(1.80966 - 3.13442i) q^{20} +(1.00190 + 1.73534i) q^{22} +(2.62232 + 1.51400i) q^{23} +(-4.04972 - 7.01433i) q^{25} +(-1.70437 - 2.95206i) q^{26} +(-5.04560 - 2.91308i) q^{29} -0.909687i q^{31} +1.00000i q^{32} +(-5.34700 - 3.08709i) q^{34} +(3.66825 + 6.35359i) q^{37} +(-0.506540 - 0.877353i) q^{38} +(3.13442 + 1.80966i) q^{40} +(-2.85045 - 4.93712i) q^{41} +(-2.39949 + 4.15605i) q^{43} +(-1.73534 + 1.00190i) q^{44} +(-1.51400 + 2.62232i) q^{46} -2.23022 q^{47} +(7.01433 - 4.04972i) q^{50} +(2.95206 - 1.70437i) q^{52} +(-7.58088 - 4.37683i) q^{53} +7.25237i q^{55} +(2.91308 - 5.04560i) q^{58} +8.98627 q^{59} -14.7121i q^{61} +0.909687 q^{62} -1.00000 q^{64} -12.3373i q^{65} -8.31641 q^{67} +(3.08709 - 5.34700i) q^{68} +0.466287i q^{71} +(3.65022 + 2.10746i) q^{73} +(-6.35359 + 3.66825i) q^{74} +(0.877353 - 0.506540i) q^{76} +3.82533 q^{79} +(-1.80966 + 3.13442i) q^{80} +(4.93712 - 2.85045i) q^{82} +(-4.00481 + 6.93654i) q^{83} +(-11.1732 - 19.3525i) q^{85} +(-4.15605 - 2.39949i) q^{86} +(-1.00190 - 1.73534i) q^{88} +(-2.39324 - 4.14521i) q^{89} +(-2.62232 - 1.51400i) q^{92} -2.23022i q^{94} -3.66666i q^{95} +(10.1835 + 5.87944i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} - 12 q^{11} - 6 q^{13} + 16 q^{16} - 18 q^{17} + 6 q^{23} - 8 q^{25} + 12 q^{26} - 6 q^{29} - 2 q^{37} - 6 q^{41} - 2 q^{43} + 12 q^{44} + 6 q^{46} - 36 q^{47} + 12 q^{50} + 6 q^{52} + 36 q^{53}+ \cdots - 6 q^{97}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^11 - 6 * q^13 + 16 * q^16 - 18 * q^17 + 6 * q^23 - 8 * q^25 + 12 * q^26 - 6 * q^29 - 2 * q^37 - 6 * q^41 - 2 * q^43 + 12 * q^44 + 6 * q^46 - 36 * q^47 + 12 * q^50 + 6 * q^52 + 36 * q^53 + 6 * q^58 + 60 * q^59 + 36 * q^62 - 16 * q^64 - 28 * q^67 + 18 * q^68 - 18 * q^74 + 32 * q^79 - 12 * q^85 - 24 * q^86 - 24 * q^89 - 6 * q^92 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more