LMFDB - Embedded newform 637.2.h.h.165.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(165,637)] 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("637.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-2,-1,10,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.59066497296.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 7x^{6} + 38x^{4} - 16x^{3} + 15x^{2} + 3x + 1 $ x^8 - x^7 + 7x^6 + 38x^4 - 16x^3 + 15x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.4
Root			$-1.11000 - 1.92258i$ of defining polynomial
Character	$\chi$	$=$	637.165
Dual form			637.2.h.h.471.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.22001 q^{2} +(-0.274776 - 0.475925i) q^{3} +2.92843 q^{4} +(2.11000 + 3.65463i) q^{5} +(-0.610004 - 1.05656i) q^{6} +2.06113 q^{8} +(1.34900 - 2.33653i) q^{9} +(4.68423 + 8.11332i) q^{10} +(0.274776 + 0.475925i) q^{11} +(-0.804662 - 1.39372i) q^{12} +(-2.95900 + 2.06017i) q^{13} +(1.15956 - 2.00841i) q^{15} -1.28114 q^{16} -2.37888 q^{17} +(2.99478 - 5.18712i) q^{18} +(1.80534 - 3.12694i) q^{19} +(6.17901 + 10.7024i) q^{20} +(0.610004 + 1.05656i) q^{22} +5.81890 q^{23} +(-0.566349 - 0.980945i) q^{24} +(-6.40423 + 11.0925i) q^{25} +(-6.56900 + 4.57360i) q^{26} -3.13134 q^{27} +(1.79945 - 3.11673i) q^{29} +(2.57422 - 4.45868i) q^{30} +(2.57422 - 4.45868i) q^{31} -6.96640 q^{32} +(0.151003 - 0.261545i) q^{33} -5.28114 q^{34} +(3.95045 - 6.84238i) q^{36} -0.329543 q^{37} +(4.00787 - 6.94184i) q^{38} +(1.79355 + 0.842178i) q^{39} +(4.34900 + 7.53268i) q^{40} +(3.14579 - 5.44866i) q^{41} +(-1.61000 - 2.78861i) q^{43} +(0.804662 + 1.39372i) q^{44} +11.3856 q^{45} +12.9180 q^{46} +(-4.10479 - 7.10970i) q^{47} +(0.352026 + 0.609727i) q^{48} +(-14.2174 + 24.6253i) q^{50} +(0.653659 + 1.13217i) q^{51} +(-8.66524 + 6.03308i) q^{52} +(-1.32933 + 2.30247i) q^{53} -6.95160 q^{54} +(-1.15956 + 2.00841i) q^{55} -1.98426 q^{57} +(3.99478 - 6.91917i) q^{58} -1.80753 q^{59} +(3.39568 - 5.88149i) q^{60} +(-0.304662 + 0.527691i) q^{61} +(5.71479 - 9.89831i) q^{62} -12.9032 q^{64} +(-13.7727 - 6.46709i) q^{65} +(0.335228 - 0.580633i) q^{66} +(-5.18490 - 8.98052i) q^{67} -6.96640 q^{68} +(-1.59889 - 2.76936i) q^{69} +(5.59889 + 9.69756i) q^{71} +(2.78046 - 4.81590i) q^{72} +(-2.45310 + 4.24890i) q^{73} -0.731589 q^{74} +7.03891 q^{75} +(5.28682 - 9.15705i) q^{76} +(3.98169 + 1.86964i) q^{78} +(7.00855 + 12.1392i) q^{79} +(-2.70321 - 4.68210i) q^{80} +(-3.18657 - 5.51931i) q^{81} +(6.98367 - 12.0961i) q^{82} -5.73159 q^{83} +(-5.01945 - 8.69395i) q^{85} +(-3.57422 - 6.19073i) q^{86} -1.97777 q^{87} +(0.566349 + 0.980945i) q^{88} -7.46755 q^{89} +25.2760 q^{90} +17.0403 q^{92} -2.82933 q^{93} +(-9.11266 - 15.7836i) q^{94} +15.2371 q^{95} +(1.91420 + 3.31549i) q^{96} +(3.42035 + 5.92422i) q^{97} +1.48269 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - q^{3} + 10 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} - 12 q^{12} + 4 q^{13} - 3 q^{15} + 38 q^{16} - 8 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} - 5 q^{22} - 4 q^{23}+ \cdots + 46 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - q^3 + 10 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 - 12 * q^12 + 4 * q^13 - 3 * q^15 + 38 * q^16 - 8 * q^17 + 3 * q^18 - q^19 + 2 * q^20 - 5 * q^22 - 4 * q^23 + 3 * q^24 - 5 * q^25 - 15 * q^26 - 52 * q^27 - q^29 + 4 * q^30 + 4 * q^31 - 66 * q^32 + 19 * q^33 + 6 * q^34 + 34 * q^36 - 20 * q^37 + 23 * q^38 - q^39 + 17 * q^40 + 22 * q^41 - 3 * q^43 + 12 * q^44 - 22 * q^45 + 48 * q^46 - 2 * q^47 - 11 * q^48 - 43 * q^50 - 7 * q^51 - 31 * q^52 - 2 * q^53 + 10 * q^54 + 3 * q^55 - 34 * q^57 + 11 * q^58 - 16 * q^59 + 11 * q^60 - 8 * q^61 + 5 * q^62 + 28 * q^64 - 11 * q^65 - 6 * q^66 + 6 * q^67 - 66 * q^68 + 18 * q^69 + 14 * q^71 - 5 * q^72 + 8 * q^73 + 40 * q^74 - 14 * q^75 - 32 * q^76 - q^78 + 26 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 - 5 * q^85 - 12 * q^86 + 26 * q^87 - 3 * q^88 - 2 * q^89 + 52 * q^90 + 24 * q^92 - 14 * q^93 - 33 * q^94 + 42 * q^95 + 58 * q^96 - 3 * q^97 + 46 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.22001			1.56978			0.784891	−	0.619633i	$-0.212719\pi$
$2$	2.22001			1.56978			0.784891	+	0.619633i	$0.212719\pi$
$3$	−0.274776	−	0.475925i	−0.158642	−	0.274776i	0.775737	−	0.631056i	$-0.217378\pi$
$3$	−0.274776	−	0.475925i	−0.158642	−	0.274776i	−0.934379	+	0.356280i	$0.884045\pi$
$4$	2.92843			1.46422
$5$	2.11000	+	3.65463i	0.943622	+	1.63440i	0.758486	+	0.651689i	$0.225939\pi$
$5$	2.11000	+	3.65463i	0.943622	+	1.63440i	0.185136	+	0.982713i	$0.440727\pi$
$6$	−0.610004	−	1.05656i	−0.249033	−	0.431338i
$7$		0			0
$7$		0			0
$8$	2.06113			0.728720
$9$	1.34900	−	2.33653i	0.449666	−	0.778844i
$10$	4.68423	+	8.11332i	1.48128	+	2.56566i
$11$	0.274776	+	0.475925i	0.0828480	+	0.143497i	0.904472	−	0.426533i	$-0.140265\pi$
$11$	0.274776	+	0.475925i	0.0828480	+	0.143497i	−0.821624	+	0.570030i	$0.806932\pi$
$12$	−0.804662	−	1.39372i	−0.232286	−	0.402331i
$13$	−2.95900	+	2.06017i	−0.820679	+	0.571389i
$13$	−2.95900	+	2.06017i	−0.820679	+	0.571389i
$14$		0			0
$15$	1.15956	−	2.00841i	0.299396	−	0.518569i
$16$	−1.28114			−0.320285
$17$	−2.37888			−0.576964			−0.288482	−	0.957485i	$-0.593151\pi$
$17$	−2.37888			−0.576964			−0.288482	+	0.957485i	$0.593151\pi$
$18$	2.99478	−	5.18712i	0.705877	−	1.22262i
$19$	1.80534	−	3.12694i	0.414174	−	0.717370i	−0.581168	−	0.813784i	$-0.697404\pi$
$19$	1.80534	−	3.12694i	0.414174	−	0.717370i	0.995341	+	0.0964139i	$0.0307372\pi$
$20$	6.17901	+	10.7024i	1.38167	+	2.39312i
$21$		0			0
$22$	0.610004	+	1.05656i	0.130053	+	0.225259i
$23$	5.81890			1.21332			0.606662	−	0.794960i	$-0.292508\pi$
$23$	5.81890			1.21332			0.606662	+	0.794960i	$0.292508\pi$
$24$	−0.566349	−	0.980945i	−0.115605	−	0.200235i
$25$	−6.40423	+	11.0925i	−1.28085	+	2.21849i
$26$	−6.56900	+	4.57360i	−1.28829	+	0.896957i
$27$	−3.13134			−0.602626
$28$		0			0
$29$	1.79945	−	3.11673i	0.334149	−	0.578762i	−0.649172	−	0.760641i	$-0.724885\pi$
$29$	1.79945	−	3.11673i	0.334149	−	0.578762i	0.983321	+	0.181879i	$0.0582179\pi$
$30$	2.57422	−	4.45868i	0.469986	−	0.814040i
$31$	2.57422	−	4.45868i	0.462344	−	0.800803i	−0.536733	−	0.843752i	$-0.680342\pi$
$31$	2.57422	−	4.45868i	0.462344	−	0.800803i	0.999077	+	0.0429489i	$0.0136753\pi$
$32$	−6.96640			−1.23150
$33$	0.151003	−	0.261545i	0.0262863	−	0.0455292i
$34$	−5.28114			−0.905708
$35$		0			0
$36$	3.95045	−	6.84238i	0.658408	−	1.14040i
$37$	−0.329543			−0.0541766			−0.0270883	−	0.999633i	$-0.508624\pi$
$37$	−0.329543			−0.0541766			−0.0270883	+	0.999633i	$0.508624\pi$
$38$	4.00787	−	6.94184i	0.650163	−	1.12611i
$39$	1.79355	+	0.842178i	0.287198	+	0.134856i
$40$	4.34900	+	7.53268i	0.687637	+	1.19102i
$41$	3.14579	−	5.44866i	0.491289	−	0.850938i	−0.508660	−	0.860967i	$-0.669859\pi$
$41$	3.14579	−	5.44866i	0.491289	−	0.850938i	0.999950	+	0.0100292i	$0.00319244\pi$
$42$		0			0
$43$	−1.61000	−	2.78861i	−0.245523	−	0.425259i	0.716755	−	0.697325i	$-0.245626\pi$
$43$	−1.61000	−	2.78861i	−0.245523	−	0.425259i	−0.962279	+	0.272066i	$0.912293\pi$
$44$	0.804662	+	1.39372i	0.121307	+	0.210111i
$45$	11.3856			1.69726
$46$	12.9180			1.90466
$47$	−4.10479	−	7.10970i	−0.598745	−	1.03706i	−0.993007	−	0.118058i	$-0.962333\pi$
$47$	−4.10479	−	7.10970i	−0.598745	−	1.03706i	0.394262	−	0.918998i	$-0.371000\pi$
$48$	0.352026	+	0.609727i	0.0508106	+	0.0880065i
$49$		0			0
$50$	−14.2174	+	24.6253i	−2.01065	+	3.48255i
$51$	0.653659	+	1.13217i	0.0915306	+	0.158536i
$52$	−8.66524	+	6.03308i	−1.20165	+	0.836638i
$53$	−1.32933	+	2.30247i	−0.182598	+	0.316269i	−0.942764	−	0.333459i	$-0.891784\pi$
$53$	−1.32933	+	2.30247i	−0.182598	+	0.316269i	0.760167	+	0.649728i	$0.225117\pi$
$54$	−6.95160			−0.945992
$55$	−1.15956	+	2.00841i	−0.156354	+	0.270814i
$56$		0			0
$57$	−1.98426			−0.262821
$58$	3.99478	−	6.91917i	0.524541	−	0.908531i
$59$	−1.80753			−0.235320			−0.117660	−	0.993054i	$-0.537539\pi$
$59$	−1.80753			−0.235320			−0.117660	+	0.993054i	$0.537539\pi$
$60$	3.39568	−	5.88149i	0.438381	−	0.759297i
$61$	−0.304662	+	0.527691i	−0.0390080	+	0.0675639i	−0.884870	−	0.465838i	$-0.845753\pi$
$61$	−0.304662	+	0.527691i	−0.0390080	+	0.0675639i	0.845862	+	0.533401i	$0.179086\pi$
$62$	5.71479	−	9.89831i	0.725779	−	1.25709i
$63$		0			0
$64$	−12.9032			−1.61290
$65$	−13.7727	−	6.46709i	−1.70829	−	0.802144i
$66$	0.335228	−	0.580633i	0.0412638	−	0.0714709i
$67$	−5.18490	−	8.98052i	−0.633437	−	1.09714i	−0.986844	−	0.161675i	$-0.948310\pi$
$67$	−5.18490	−	8.98052i	−0.633437	−	1.09714i	0.353407	−	0.935470i	$-0.385023\pi$
$68$	−6.96640			−0.844801
$69$	−1.59889	−	2.76936i	−0.192484	−	0.333392i
$70$		0			0
$71$	5.59889	+	9.69756i	0.664466	+	1.15089i	0.979430	+	0.201785i	$0.0646743\pi$
$71$	5.59889	+	9.69756i	0.664466	+	1.15089i	−0.314964	+	0.949104i	$0.601992\pi$
$72$	2.78046	−	4.81590i	0.327680	−	0.567559i
$73$	−2.45310	+	4.24890i	−0.287114	+	0.497296i	−0.973120	−	0.230300i	$-0.926029\pi$
$73$	−2.45310	+	4.24890i	−0.287114	+	0.497296i	0.686005	+	0.727596i	$0.259363\pi$
$74$	−0.731589			−0.0850455
$75$	7.03891			0.812783
$76$	5.28682	−	9.15705i	0.606440	−	1.05039i
$77$		0			0
$78$	3.98169	+	1.86964i	0.450838	+	0.211695i
$79$	7.00855	+	12.1392i	0.788524	+	1.36576i	0.926871	+	0.375379i	$0.122488\pi$
$79$	7.00855	+	12.1392i	0.788524	+	1.36576i	−0.138348	+	0.990384i	$0.544179\pi$
$80$	−2.70321	−	4.68210i	−0.302228	−	0.523474i
$81$	−3.18657	−	5.51931i	−0.354064	−	0.613257i
$82$	6.98367	−	12.0961i	0.771217	−	1.33579i
$83$	−5.73159			−0.629124			−0.314562	−	0.949237i	$-0.601858\pi$
$83$	−5.73159			−0.629124			−0.314562	+	0.949237i	$0.601858\pi$
$84$		0			0
$85$	−5.01945	−	8.69395i	−0.544436	−	0.942991i
$86$	−3.57422	−	6.19073i	−0.385418	−	0.667564i
$87$	−1.97777			−0.212040
$88$	0.566349	+	0.980945i	0.0603730	+	0.104569i
$89$	−7.46755			−0.791559			−0.395779	−	0.918346i	$-0.629526\pi$
$89$	−7.46755			−0.791559			−0.395779	+	0.918346i	$0.629526\pi$
$90$	25.2760			2.66433
$91$		0			0
$92$	17.0403			1.77657
$93$	−2.82933			−0.293388
$94$	−9.11266	−	15.7836i	−0.939899	−	1.62795i
$95$	15.2371			1.56329
$96$	1.91420	+	3.31549i	0.195367	+	0.338386i
$97$	3.42035	+	5.92422i	0.347284	+	0.601514i	0.985766	−	0.168123i	$-0.0537706\pi$
$97$	3.42035	+	5.92422i	0.347284	+	0.601514i	−0.638482	+	0.769637i	$0.720437\pi$
$98$		0			0
$99$	1.48269			0.149015
$100$	−18.7544	+	32.4835i	−1.87544	+	3.24835i
$101$	−2.87956	−	4.98755i	−0.286527	−	0.496280i	0.686451	−	0.727176i	$-0.259168\pi$
$101$	−2.87956	−	4.98755i	−0.286527	−	0.496280i	−0.972978	+	0.230896i	$0.925834\pi$
$102$	1.45113	+	2.51343i	0.143683	+	0.248866i
$103$	−0.285888	−	0.495173i	−0.0281694	−	0.0487908i	0.851597	−	0.524197i	$-0.175634\pi$
$103$	−0.285888	−	0.495173i	−0.0281694	−	0.0487908i	−0.879766	+	0.475406i	$0.842301\pi$
$104$	−6.09889	+	4.24629i	−0.598045	+	0.416383i
$105$		0			0
$106$	−2.95113	+	5.11150i	−0.286639	+	0.496473i
$107$	4.07157			0.393613			0.196807	−	0.980442i	$-0.436943\pi$
$107$	4.07157			0.393613			0.196807	+	0.980442i	$0.436943\pi$
$108$	−9.16992			−0.882376
$109$	−7.65434	+	13.2577i	−0.733153	+	1.26986i	0.222376	+	0.974961i	$0.428619\pi$
$109$	−7.65434	+	13.2577i	−0.733153	+	1.26986i	−0.955529	+	0.294897i	$0.904715\pi$
$110$	−2.57422	+	4.45868i	−0.245442	+	0.425119i
$111$	0.0905505	+	0.156838i	0.00859467	+	0.0148864i
$112$		0			0
$113$	−6.08846	−	10.5455i	−0.572754	−	0.992039i	−0.996282	−	0.0861558i	$-0.972542\pi$
$113$	−6.08846	−	10.5455i	−0.572754	−	0.992039i	0.423528	−	0.905883i	$-0.360792\pi$
$114$	−4.40506			−0.412572
$115$	12.2779	+	21.2659i	1.14492	+	1.98306i
$116$	5.26956	−	9.12714i	0.489266	−	0.847434i
$117$	0.821977	+	9.69296i	0.0759918	+	0.896115i
$118$	−4.01273			−0.369402
$119$		0			0
$120$	2.39000	−	4.13959i	0.218176	−	0.377892i
$121$	5.34900	−	9.26473i	0.486272	−	0.842249i
$122$	−0.676353	+	1.17148i	−0.0612341	+	0.106061i
$123$	−3.45754			−0.311756
$124$	7.53844	−	13.0570i	0.676972	−	1.17255i
$125$	−32.9518			−2.94730
$126$		0			0
$127$	−0.980336	+	1.69799i	−0.0869907	+	0.150672i	−0.906238	−	0.422768i	$-0.861058\pi$
$127$	−0.980336	+	1.69799i	−0.0869907	+	0.150672i	0.819247	+	0.573441i	$0.194392\pi$
$128$	−14.7124			−1.30040
$129$	−0.884779	+	1.53248i	−0.0779005	+	0.134928i
$130$	−30.5755	−	14.3570i	−2.68165	−	1.25919i
$131$	3.25011	+	5.62935i	0.283963	+	0.491838i	0.972357	−	0.233498i	$-0.0750174\pi$
$131$	3.25011	+	5.62935i	0.283963	+	0.491838i	−0.688394	+	0.725337i	$0.741684\pi$
$132$	0.442203	−	0.765918i	0.0384888	−	0.0666646i
$133$		0			0
$134$	−11.5105	−	19.9368i	−0.994358	−	1.72228i
$135$	−6.60714	−	11.4439i	−0.568652	−	0.984934i
$136$	−4.90319			−0.420445
$137$	−15.2576			−1.30354			−0.651770	−	0.758416i	$-0.725973\pi$
$137$	−15.2576			−1.30354			−0.651770	+	0.758416i	$0.725973\pi$
$138$	−3.54955	−	6.14800i	−0.302158	−	0.523353i
$139$	8.74801	+	15.1520i	0.741997	+	1.28518i	0.951585	+	0.307386i	$0.0994544\pi$
$139$	8.74801	+	15.1520i	0.741997	+	1.28518i	−0.209588	+	0.977790i	$0.567212\pi$
$140$		0			0
$141$	−2.25579	+	3.90714i	−0.189972	+	0.329041i
$142$	12.4296	+	21.5287i	1.04307	+	1.80665i
$143$	−1.79355	−	0.842178i	−0.149984	−	0.0704264i
$144$	−1.72825	+	2.99342i	−0.144021	+	0.249452i
$145$	15.1873			1.26124
$146$	−5.44591	+	9.43260i	−0.450707	+	0.780647i
$147$		0			0
$148$	−0.965046			−0.0793263
$149$	−2.27743	+	3.94463i	−0.186574	+	0.323156i	−0.944106	−	0.329642i	$-0.893072\pi$
$149$	−2.27743	+	3.94463i	−0.186574	+	0.323156i	0.757531	+	0.652799i	$0.226405\pi$
$150$	15.6264			1.27589
$151$	3.16456	−	5.48118i	0.257528	−	0.446052i	−0.708051	−	0.706161i	$-0.750425\pi$
$151$	3.16456	−	5.48118i	0.257528	−	0.446052i	0.965579	+	0.260109i	$0.0837586\pi$
$152$	3.72105	−	6.44504i	0.301817	−	0.522762i
$153$	−3.20911	+	5.55833i	−0.259441	+	0.449365i
$154$		0			0
$155$	21.7265			1.74511
$156$	5.25229	+	2.46626i	0.420520	+	0.197459i
$157$	−8.15502	+	14.1249i	−0.650841	+	1.12729i	0.332078	+	0.943252i	$0.392250\pi$
$157$	−8.15502	+	14.1249i	−0.650841	+	1.12729i	−0.982919	+	0.184038i	$0.941083\pi$
$158$	15.5590	+	26.9490i	1.23781	+	2.14395i
$159$	1.46107			0.115871
$160$	−14.6991	−	25.4597i	−1.16207	−	2.01276i
$161$		0			0
$162$	−7.07422	−	12.2529i	−0.555803	−	0.962680i
$163$	−11.7999	+	20.4381i	−0.924241	+	1.60083i	−0.131463	+	0.991321i	$0.541967\pi$
$163$	−11.7999	+	20.4381i	−0.924241	+	1.60083i	−0.792778	+	0.609511i	$0.791366\pi$
$164$	9.21223	−	15.9561i	0.719354	−	1.24596i
$165$	1.27447			0.0992173
$166$	−12.7242			−0.987587
$167$	8.91513	−	15.4415i	0.689874	−	1.19490i	−0.282005	−	0.959413i	$-0.590999\pi$
$167$	8.91513	−	15.4415i	0.689874	−	1.19490i	0.971878	−	0.235483i	$-0.0756673\pi$
$168$		0			0
$169$	4.51137	−	12.1921i	0.347028	−	0.937855i
$170$	−11.1432	−	19.3006i	−0.854646	−	1.48029i
$171$	−4.87080	−	8.43647i	−0.372479	−	0.645153i
$172$	−4.71479	−	8.16626i	−0.359499	−	0.622671i
$173$	3.78568	−	6.55699i	0.287820	−	0.498518i	−0.685469	−	0.728101i	$-0.740403\pi$
$173$	3.78568	−	6.55699i	0.287820	−	0.498518i	0.973289	+	0.229583i	$0.0737363\pi$
$174$	−4.39068			−0.332856
$175$		0			0
$176$	−0.352026	−	0.609727i	−0.0265350	−	0.0459599i
$177$	0.496665	+	0.860249i	0.0373316	+	0.0646603i
$178$	−16.5780			−1.24258
$179$	11.4017	+	19.7483i	0.852201	+	1.47606i	0.879218	+	0.476420i	$0.158066\pi$
$179$	11.4017	+	19.7483i	0.852201	+	1.47606i	−0.0270166	+	0.999635i	$0.508601\pi$
$180$	33.3419			2.48515
$181$	13.9294			1.03536			0.517681	−	0.855574i	$-0.326795\pi$
$181$	13.9294			1.03536			0.517681	+	0.855574i	$0.326795\pi$
$182$		0			0
$183$	0.334855			0.0247532
$184$	11.9935			0.884174
$185$	−0.695338	−	1.20436i	−0.0511222	−	0.0885463i
$186$	−6.28114			−0.460556
$187$	−0.653659	−	1.13217i	−0.0478003	−	0.0827925i
$188$	−12.0206	−	20.8203i	−0.876692	−	1.51848i
$189$		0			0
$190$	33.8265			2.45403
$191$	6.33591	−	10.9741i	0.458450	−	0.794059i	−0.540429	−	0.841390i	$-0.681738\pi$
$191$	6.33591	−	10.9741i	0.458450	−	0.794059i	0.998879	+	0.0473305i	$0.0150714\pi$
$192$	3.54548	+	6.14096i	0.255873	+	0.443185i
$193$	2.07746	+	3.59827i	0.149539	+	0.259009i	0.931057	−	0.364873i	$-0.118888\pi$
$193$	2.07746	+	3.59827i	0.149539	+	0.259009i	−0.781518	+	0.623882i	$0.785554\pi$
$194$	7.59321	+	13.1518i	0.545160	+	0.944246i
$195$	0.706545	+	8.33177i	0.0505968	+	0.596650i
$196$		0			0
$197$	3.42510	−	5.93245i	0.244028	−	0.422669i	−0.717830	−	0.696219i	$-0.754864\pi$
$197$	3.42510	−	5.93245i	0.244028	−	0.422669i	0.961858	+	0.273549i	$0.0881977\pi$
$198$	3.29157			0.233922
$199$	−0.813587			−0.0576737			−0.0288368	−	0.999584i	$-0.509180\pi$
$199$	−0.813587			−0.0576737			−0.0288368	+	0.999584i	$0.509180\pi$
$200$	−13.2000	+	22.8630i	−0.933379	+	1.61666i
$201$	−2.84937	+	4.93525i	−0.200979	+	0.348106i
$202$	−6.39265	−	11.0724i	−0.449785	−	0.779051i
$203$		0			0
$204$	1.91420	+	3.31549i	0.134021	+	0.232131i
$205$	26.5505			1.85437
$206$	−0.634674	−	1.09929i	−0.0442198	−	0.0765910i
$207$	7.84968	−	13.5960i	0.545590	−	0.944990i
$208$	3.79089	−	2.63937i	0.262851	−	0.183007i
$209$	1.98426			0.137254
$210$		0			0
$211$	6.98670	−	12.1013i	0.480984	−	0.833089i	−0.518778	−	0.854909i	$-0.673613\pi$
$211$	6.98670	−	12.1013i	0.480984	−	0.833089i	0.999762	+	0.0218200i	$0.00694608\pi$
$212$	−3.89286	+	6.74264i	−0.267363	+	0.463086i
$213$	3.07688	−	5.32931i	0.210824	−	0.365158i
$214$	9.03891			0.617887
$215$	6.79423	−	11.7679i	0.463363	−	0.802568i
$216$	−6.45410			−0.439146
$217$		0			0
$218$	−16.9927	+	29.4322i	−1.15089	+	1.99340i
$219$	2.69621			0.182193
$220$	−3.39568	+	5.88149i	−0.228937	+	0.396530i
$221$	7.03912	−	4.90091i	0.473502	−	0.329671i
$222$	0.201023	+	0.348182i	0.0134918	+	0.0233684i
$223$	6.76700	−	11.7208i	0.453152	−	0.784882i	−0.545428	−	0.838158i	$-0.683633\pi$
$223$	6.76700	−	11.7208i	0.453152	−	0.784882i	0.998580	+	0.0532758i	$0.0169662\pi$
$224$		0			0
$225$	17.2786	+	29.9274i	1.15191	+	1.99516i
$226$	−13.5164	−	23.4111i	−0.899099	−	1.55729i
$227$	−5.36751			−0.356254			−0.178127	−	0.984007i	$-0.557004\pi$
$227$	−5.36751			−0.356254			−0.178127	+	0.984007i	$0.557004\pi$
$228$	−5.81076			−0.384827
$229$	−1.54955	−	2.68390i	−0.102397	−	0.177357i	0.810275	−	0.586050i	$-0.199318\pi$
$229$	−1.54955	−	2.68390i	−0.102397	−	0.177357i	−0.912672	+	0.408693i	$0.865985\pi$
$230$	27.2570	+	47.2106i	1.79728	+	3.11297i
$231$		0			0
$232$	3.70890	−	6.42399i	0.243501	−	0.421756i
$233$	10.1856	+	17.6419i	0.667280	+	1.15576i	0.978662	+	0.205478i	$0.0658748\pi$
$233$	10.1856	+	17.6419i	0.667280	+	1.15576i	−0.311382	+	0.950285i	$0.600792\pi$
$234$	1.82480	+	21.5185i	0.119291	+	1.40671i
$235$	17.3222	−	30.0030i	1.12998	−	1.95718i
$236$	−5.29323			−0.344560
$237$	3.85156	−	6.67109i	0.250186	−	0.433334i
$238$		0			0
$239$	−1.29157			−0.0835449			−0.0417725	−	0.999127i	$-0.513300\pi$
$239$	−1.29157			−0.0835449			−0.0417725	+	0.999127i	$0.513300\pi$
$240$	−1.48555	+	2.57305i	−0.0958920	+	0.166090i
$241$	2.13270			0.137379			0.0686896	−	0.997638i	$-0.478118\pi$
$241$	2.13270			0.137379			0.0686896	+	0.997638i	$0.478118\pi$
$242$	11.8748	−	20.5678i	0.763342	−	1.32215i
$243$	−6.44819	+	11.1686i	−0.413652	+	0.716466i
$244$	−0.892184	+	1.54531i	−0.0571162	+	0.0989282i
$245$		0			0
$246$	−7.67577			−0.489389
$247$	1.10004	+	12.9719i	0.0699938	+	0.825385i
$248$	5.30581	−	9.18993i	0.336919	−	0.583561i
$249$	1.57490	+	2.72781i	0.0998053	+	0.172868i
$250$	−73.1532			−4.62662
$251$	15.3856	+	26.6486i	0.971128	+	1.68204i	0.692164	+	0.721741i	$0.256658\pi$
$251$	15.3856	+	26.6486i	0.971128	+	1.68204i	0.278964	+	0.960302i	$0.410009\pi$
$252$		0			0
$253$	1.59889	+	2.76936i	0.100521	+	0.174108i
$254$	−2.17635	+	3.76955i	−0.136557	+	0.236523i
$255$	−2.75845	+	4.77777i	−0.172741	+	0.299196i
$256$	−6.85521			−0.428451
$257$	−1.47361			−0.0919213			−0.0459607	−	0.998943i	$-0.514635\pi$
$257$	−1.47361			−0.0919213			−0.0459607	+	0.998943i	$0.514635\pi$
$258$	−1.96422	+	3.40212i	−0.122287	+	0.211807i
$259$		0			0
$260$	−40.3324	−	18.9385i	−2.50131	−	1.17451i
$261$	−4.85489	−	8.40892i	−0.300510	−	0.520499i
$262$	7.21526	+	12.4972i	0.445760	+	0.772079i
$263$	−3.33847	−	5.78240i	−0.205859	−	0.356558i	0.744547	−	0.667570i	$-0.232665\pi$
$263$	−3.33847	−	5.78240i	−0.205859	−	0.356558i	−0.950406	+	0.311012i	$0.899332\pi$
$264$	0.311238	−	0.539079i	0.0191553	−	0.0331780i
$265$	−11.2196			−0.689214
$266$		0			0
$267$	2.05190	+	3.55400i	0.125574	+	0.217501i
$268$	−15.1837	−	26.2989i	−0.927489	−	1.60646i
$269$	7.57573			0.461900			0.230950	−	0.972966i	$-0.425817\pi$
$269$	7.57573			0.461900			0.230950	+	0.972966i	$0.425817\pi$
$270$	−14.6679	−	25.4055i	−0.892660	−	1.54613i
$271$	20.5680			1.24942			0.624709	−	0.780858i	$-0.285218\pi$
$271$	20.5680			1.24942			0.624709	+	0.780858i	$0.285218\pi$
$272$	3.04768			0.184793
$273$		0			0
$274$	−33.8719			−2.04628
$275$	−7.03891			−0.424462
$276$	−4.68225	−	8.10989i	−0.281838	−	0.488158i
$277$	5.70541			0.342805			0.171402	−	0.985201i	$-0.445170\pi$
$277$	5.70541			0.342805			0.171402	+	0.985201i	$0.445170\pi$
$278$	19.4207	+	33.6376i	1.16477	+	2.01745i
$279$	−6.94523	−	12.0295i	−0.415800	−	0.720187i
$280$		0			0
$281$	−6.37315			−0.380190			−0.190095	−	0.981766i	$-0.560880\pi$
$281$	−6.37315			−0.380190			−0.190095	+	0.981766i	$0.560880\pi$
$282$	−5.00787	+	8.67389i	−0.298214	+	0.516523i
$283$	−13.5097	−	23.3995i	−0.803068	−	1.39096i	−0.917587	−	0.397534i	$-0.869866\pi$
$283$	−13.5097	−	23.3995i	−0.803068	−	1.39096i	0.114519	−	0.993421i	$-0.463467\pi$
$284$	16.3960	+	28.3987i	0.972923	+	1.68515i
$285$	−4.18679	−	7.25173i	−0.248004	−	0.429555i
$286$	−3.98169	−	1.86964i	−0.235443	−	0.110554i
$287$		0			0
$288$	−9.39766	+	16.2772i	−0.553762	+	0.959144i
$289$	−11.3409			−0.667113
$290$	33.7160			1.97987
$291$	1.87966	−	3.25566i	0.110187	−	0.190850i
$292$	−7.18376	+	12.4426i	−0.420398	+	0.728150i
$293$	2.43736	+	4.22163i	0.142392	+	0.246630i	0.928397	−	0.371590i	$-0.121187\pi$
$293$	2.43736	+	4.22163i	0.142392	+	0.246630i	−0.786005	+	0.618220i	$0.787854\pi$
$294$		0			0
$295$	−3.81389	−	6.60586i	−0.222053	−	0.384608i
$296$	−0.679232			−0.0394796
$297$	−0.860415	−	1.49028i	−0.0499264	−	0.0864750i
$298$	−5.05592	+	8.75710i	−0.292881	+	0.507285i
$299$	−17.2181	+	11.9879i	−0.995750	+	0.693281i
$300$	20.6130			1.19009
$301$		0			0
$302$	7.02535	−	12.1683i	0.404263	−	0.700205i
$303$	−1.58247	+	2.74091i	−0.0909104	+	0.157461i
$304$	−2.31290	+	4.00605i	−0.132654	+	0.229763i
$305$	−2.57135			−0.147235
$306$	−7.12424	+	12.3395i	−0.407266	+	0.705405i
$307$	16.1760			0.923212			0.461606	−	0.887085i	$-0.347273\pi$
$307$	16.1760			0.923212			0.461606	+	0.887085i	$0.347273\pi$
$308$		0			0
$309$	−0.157110	+	0.272123i	−0.00893769	+	0.0154805i
$310$	48.2329			2.73945
$311$	0.654032	−	1.13282i	0.0370868	−	0.0642362i	−0.846886	−	0.531774i	$-0.821526\pi$
$311$	0.654032	−	1.13282i	0.0370868	−	0.0642362i	0.883973	+	0.467538i	$0.154859\pi$
$312$	3.69674	+	1.73584i	0.209287	+	0.0982726i
$313$	−6.59889	−	11.4296i	−0.372991	−	0.646040i	0.617033	−	0.786937i	$-0.288335\pi$
$313$	−6.59889	−	11.4296i	−0.372991	−	0.646040i	−0.990024	+	0.140897i	$0.955001\pi$
$314$	−18.1042	+	31.3574i	−1.02168	+	1.76960i
$315$		0			0
$316$	20.5241	+	35.5488i	1.15457	+	1.99977i
$317$	4.03776	+	6.99360i	0.226783	+	0.392800i	0.956853	−	0.290573i	$-0.0938458\pi$
$317$	4.03776	+	6.99360i	0.226783	+	0.392800i	−0.730070	+	0.683373i	$0.760512\pi$
$318$	3.24359			0.181892
$319$	1.97777			0.110734
$320$	−27.2258	−	47.1564i	−1.52197	−	2.63613i
$321$	−1.11877	−	1.93776i	−0.0624435	−	0.108155i
$322$		0			0
$323$	−4.29470	+	7.43863i	−0.238963	+	0.413897i
$324$	−9.33168	−	16.1629i	−0.518426	−	0.897941i
$325$	−3.90226	−	46.0164i	−0.216458	−	2.55253i
$326$	−26.1959	+	45.3726i	−1.45086	+	2.51296i
$327$	8.41290			0.465234
$328$	6.48388	−	11.2304i	0.358012	−	0.620096i
$329$		0			0
$330$	2.82933			0.155750
$331$	7.47256	−	12.9429i	0.410729	−	0.711403i	−0.584241	−	0.811580i	$-0.698608\pi$
$331$	7.47256	−	12.9429i	0.410729	−	0.711403i	0.994970	+	0.100177i	$0.0319409\pi$
$332$	−16.7846			−0.921174
$333$	−0.444553	+	0.769988i	−0.0243613	+	0.0421951i
$334$	19.7917	−	34.2802i	1.08295	−	1.87573i
$335$	21.8803	−	37.8979i	1.19545	−	2.07058i
$336$		0			0
$337$	−17.1695			−0.935282			−0.467641	−	0.883918i	$-0.654896\pi$
$337$	−17.1695			−0.935282			−0.467641	+	0.883918i	$0.654896\pi$
$338$	10.0153	−	27.0666i	0.544759	−	1.47223i
$339$	−3.34592	+	5.79530i	−0.181725	+	0.314758i
$340$	−14.6991	−	25.4597i	−0.797173	−	1.38074i
$341$	2.82933			0.153217
$342$	−10.8132	−	18.7290i	−0.584712	−	1.01275i
$343$		0			0
$344$	−3.31843	−	5.74769i	−0.178918	−	0.309895i
$345$	6.74733	−	11.6867i	0.363264	−	0.629192i
$346$	8.40423	−	14.5566i	0.451814	−	0.782565i
$347$	−3.93845			−0.211427			−0.105713	−	0.994397i	$-0.533713\pi$
$347$	−3.93845			−0.211427			−0.105713	+	0.994397i	$0.533713\pi$
$348$	−5.79178			−0.310472
$349$	−8.58883	+	14.8763i	−0.459750	+	0.796310i	−0.998947	−	0.0458695i	$-0.985394\pi$
$349$	−8.58883	+	14.8763i	−0.459750	+	0.796310i	0.539198	+	0.842179i	$0.318728\pi$
$350$		0			0
$351$	9.26563	−	6.45110i	0.494563	−	0.344334i
$352$	−1.91420	−	3.31549i	−0.102027	−	0.176716i
$353$	9.09821	+	15.7586i	0.484249	+	0.838744i	0.999836	−	0.0180932i	$-0.00575957\pi$
$353$	9.09821	+	15.7586i	0.484249	+	0.838744i	−0.515587	+	0.856837i	$0.672426\pi$
$354$	1.10260	+	1.90976i	0.0586025	+	0.101503i
$355$	−23.6274	+	40.9238i	−1.25401	+	2.17201i
$356$	−21.8682			−1.15901
$357$		0			0
$358$	25.3118	+	43.8413i	1.33777	+	2.31709i
$359$	−8.15631	−	14.1272i	−0.430474	−	0.745603i	0.566440	−	0.824103i	$-0.308320\pi$
$359$	−8.15631	−	14.1272i	−0.430474	−	0.745603i	−0.996914	+	0.0785003i	$0.974987\pi$
$360$	23.4671			1.23683
$361$	2.98148	+	5.16408i	0.156920	+	0.271794i
$362$	30.9233			1.62529
$363$	−5.87909			−0.308572
$364$		0			0
$365$	−20.7042			−1.08371
$366$	0.743381			0.0388571
$367$	18.0982	+	31.3469i	0.944716	+	1.63630i	0.756319	+	0.654203i	$0.226996\pi$
$367$	18.0982	+	31.3469i	0.944716	+	1.63630i	0.188398	+	0.982093i	$0.439671\pi$
$368$	−7.45482			−0.388610
$369$	−8.48731	−	14.7005i	−0.441832	−	0.765275i
$370$	−1.54366	−	2.67369i	−0.0802508	−	0.138998i
$371$		0			0
$372$	−8.28551			−0.429584
$373$	−4.89892	+	8.48518i	−0.253657	+	0.439346i	−0.964530	−	0.263974i	$-0.914967\pi$
$373$	−4.89892	+	8.48518i	−0.253657	+	0.439346i	0.710873	+	0.703320i	$0.248300\pi$
$374$	−1.45113	−	2.51343i	−0.0750361	−	0.129966i
$375$	9.05435	+	15.6826i	0.467564	+	0.809845i
$376$	−8.46051	−	14.6540i	−0.436317	−	0.755724i
$377$	1.09645	+	12.9296i	0.0564699	+	0.665907i
$378$		0			0
$379$	−6.53275	+	11.3151i	−0.335565	+	0.581216i	−0.983593	−	0.180401i	$-0.942261\pi$
$379$	−6.53275	+	11.3151i	−0.335565	+	0.581216i	0.648028	+	0.761616i	$0.275594\pi$
$380$	44.6209			2.28900
$381$	1.07749			0.0552014
$382$	14.0658	−	24.3626i	0.719667	−	1.24650i
$383$	−13.8965	+	24.0694i	−0.710076	+	1.22989i	0.254753	+	0.967006i	$0.418006\pi$
$383$	−13.8965	+	24.0694i	−0.710076	+	1.22989i	−0.964828	+	0.262881i	$0.915327\pi$
$384$	4.04260	+	7.00199i	0.206298	+	0.357319i
$385$		0			0
$386$	4.61198	+	7.98818i	0.234744	+	0.406588i
$387$	−8.68756			−0.441614
$388$	10.0163	+	17.3487i	0.508499	+	0.880747i
$389$	−6.85233	+	11.8686i	−0.347427	+	0.601761i	−0.985792	−	0.167973i	$-0.946278\pi$
$389$	−6.85233	+	11.8686i	−0.347427	+	0.601761i	0.638365	+	0.769734i	$0.279611\pi$
$390$	1.56854	+	18.4966i	0.0794259	+	0.936611i
$391$	−13.8425			−0.700044
$392$		0			0
$393$	1.78610	−	3.09361i	0.0900968	−	0.156052i
$394$	7.60375	−	13.1701i	0.383071	−	0.663499i
$395$	−29.5761	+	51.2274i	−1.48814	+	2.57753i
$396$	4.34195			0.218191
$397$	−3.95597	+	6.85194i	−0.198545	+	0.343889i	−0.948057	−	0.318101i	$-0.896955\pi$
$397$	−3.95597	+	6.85194i	−0.198545	+	0.343889i	0.749512	+	0.661991i	$0.230288\pi$
$398$	−1.80617			−0.0905351
$399$		0			0
$400$	8.20472	−	14.2110i	0.410236	−	0.710549i
$401$	−16.5442			−0.826180			−0.413090	−	0.910690i	$-0.635550\pi$
$401$	−16.5442			−0.826180			−0.413090	+	0.910690i	$0.635550\pi$
$402$	−6.32562	+	10.9563i	−0.315493	+	0.546451i
$403$	1.56854	+	18.4966i	0.0781344	+	0.921381i
$404$	−8.43261	−	14.6057i	−0.419538	−	0.726661i
$405$	13.4474	−	23.2915i	0.668205	−	1.15737i
$406$		0			0
$407$	−0.0905505	−	0.156838i	−0.00448842	−	0.00777417i
$408$	1.34728	+	2.33355i	0.0667002	+	0.115528i
$409$	25.7819			1.27483			0.637416	−	0.770520i	$-0.280003\pi$
$409$	25.7819			1.27483			0.637416	+	0.770520i	$0.280003\pi$
$410$	58.9423			2.91095
$411$	4.19240	+	7.26146i	0.206796	+	0.358181i
$412$	−0.837205	−	1.45008i	−0.0412461	−	0.0714404i
$413$		0			0
$414$	17.4263	−	30.1833i	0.856458	−	1.48343i
$415$	−12.0937	−	20.9469i	−0.593655	−	1.02824i
$416$	20.6136	−	14.3520i	1.01066	−	0.703665i
$417$	4.80748	−	8.32680i	0.235423	−	0.407765i
$418$	4.40506			0.215459
$419$	−11.8436	+	20.5137i	−0.578596	+	1.00216i	0.417044	+	0.908886i	$0.363066\pi$
$419$	−11.8436	+	20.5137i	−0.578596	+	1.00216i	−0.995641	+	0.0932720i	$0.970267\pi$
$420$		0			0
$421$	−20.8246			−1.01493			−0.507465	−	0.861672i	$-0.669417\pi$
$421$	−20.8246			−1.01493			−0.507465	+	0.861672i	$0.669417\pi$
$422$	15.5105	−	26.8650i	0.755041	−	1.30777i
$423$	−22.1494			−1.07694
$424$	−2.73993	+	4.74570i	−0.133063	+	0.230471i
$425$	15.2349	−	26.3877i	0.739002	−	1.27999i
$426$	6.83069	−	11.8311i	0.330948	−	0.573219i
$427$		0			0
$428$	11.9233			0.576335
$429$	0.0920100	+	1.08501i	0.00444228	+	0.0523846i
$430$	15.0832	−	26.1249i	0.727378	−	1.25986i
$431$	−9.97521	−	17.2776i	−0.480489	−	0.832232i	0.519260	−	0.854616i	$-0.326208\pi$
$431$	−9.97521	−	17.2776i	−0.480489	−	0.832232i	−0.999749	+	0.0223845i	$0.992874\pi$
$432$	4.01168			0.193012
$433$	−0.00834083	−	0.0144467i	−0.000400835	−	0.000694266i	0.865825	−	0.500347i	$-0.166794\pi$
$433$	−0.00834083	−	0.0144467i	−0.000400835	−	0.000694266i	−0.866226	+	0.499653i	$0.833461\pi$
$434$		0			0
$435$	−4.17311	−	7.22804i	−0.200085	−	0.346558i
$436$	−22.4152	+	38.8243i	−1.07349	+	1.85935i
$437$	10.5051	−	18.1954i	0.502527	−	0.870402i
$438$	5.98561			0.286004
$439$	13.4960			0.644130			0.322065	−	0.946718i	$-0.395623\pi$
$439$	13.4960			0.644130			0.322065	+	0.946718i	$0.395623\pi$
$440$	−2.39000	+	4.13959i	−0.113939	+	0.197347i
$441$		0			0
$442$	15.6269	−	10.8801i	0.743296	−	0.517512i
$443$	7.50552	+	12.9999i	0.356598	+	0.617646i	0.987390	−	0.158306i	$-0.0506032\pi$
$443$	7.50552	+	12.9999i	0.356598	+	0.617646i	−0.630792	+	0.775952i	$0.717270\pi$
$444$	0.265171	+	0.459290i	0.0125845	+	0.0217969i
$445$	−15.7566	−	27.2912i	−0.746933	−	1.29373i
$446$	15.0228	−	26.0202i	0.711350	−	1.23209i
$447$	2.50313			0.118394
$448$		0			0
$449$	11.8918	+	20.5972i	0.561210	+	0.972044i	0.997391	+	0.0721852i	$0.0229973\pi$
$449$	11.8918	+	20.5972i	0.561210	+	0.972044i	−0.436181	+	0.899859i	$0.643669\pi$
$450$	38.3586	+	66.4390i	1.80824	+	3.13196i
$451$	3.45754			0.162809
$452$	−17.8297	−	30.8819i	−0.838636	−	1.45256i
$453$	−3.47818			−0.163419
$454$	−11.9159			−0.559242
$455$		0			0
$456$	−4.08981			−0.191523
$457$	18.1313			0.848148			0.424074	−	0.905627i	$-0.360600\pi$
$457$	18.1313			0.848148			0.424074	+	0.905627i	$0.360600\pi$
$458$	−3.44002	−	5.95828i	−0.160741	−	0.278412i
$459$	7.44909			0.347694
$460$	35.9550	+	62.2759i	1.67641	+	2.90363i
$461$	3.03980	+	5.26508i	0.141577	+	0.245219i	0.928091	−	0.372354i	$-0.121449\pi$
$461$	3.03980	+	5.26508i	0.141577	+	0.245219i	−0.786513	+	0.617573i	$0.788116\pi$
$462$		0			0
$463$	5.19289			0.241334			0.120667	−	0.992693i	$-0.461497\pi$
$463$	5.19289			0.241334			0.120667	+	0.992693i	$0.461497\pi$
$464$	−2.30534	+	3.99297i	−0.107023	+	0.185369i
$465$	−5.96990	−	10.3402i	−0.276848	−	0.479514i
$466$	22.6121	+	39.1653i	1.04748	+	1.81430i
$467$	4.34984	+	7.53414i	0.201287	+	0.348638i	0.948943	−	0.315447i	$-0.102154\pi$
$467$	4.34984	+	7.53414i	0.201287	+	0.348638i	−0.747657	+	0.664085i	$0.768821\pi$
$468$	2.40711	+	28.3852i	0.111268	+	1.31211i
$469$		0			0
$470$	38.4555	−	66.6069i	1.77382	−	3.07235i
$471$	8.96320			0.413002
$472$	−3.72556			−0.171483
$473$	0.884779	−	1.53248i	0.0406822	−	0.0704636i
$474$	8.55049	−	14.8099i	0.392737	−	0.680240i
$475$	23.1237	+	40.0513i	1.06099	+	1.83768i
$476$		0			0
$477$	3.58653	+	6.21205i	0.164216	+	0.284430i
$478$	−2.86730			−0.131147
$479$	−12.1094	−	20.9741i	−0.553294	−	0.958332i	−0.998034	−	0.0626730i	$-0.980037\pi$
$479$	−12.1094	−	20.9741i	−0.553294	−	0.958332i	0.444741	−	0.895659i	$-0.353296\pi$
$480$	−8.07793	+	13.9914i	−0.368705	+	0.638616i
$481$	0.975119	−	0.678916i	0.0444616	−	0.0309559i
$482$	4.73461			0.215655
$483$		0			0
$484$	15.6642	−	27.1312i	0.712009	−	1.23323i
$485$	−14.4339	+	25.0003i	−0.655410	+	1.13520i
$486$	−14.3150	+	24.7944i	−0.649343	+	1.12470i
$487$	1.77393			0.0803846			0.0401923	−	0.999192i	$-0.487203\pi$
$487$	1.77393			0.0803846			0.0401923	+	0.999192i	$0.487203\pi$
$488$	−0.627949	+	1.08764i	−0.0284259	+	0.0492351i
$489$	12.9693			0.586493
$490$		0			0
$491$	3.34483	−	5.79342i	0.150950	−	0.261453i	−0.780627	−	0.624997i	$-0.785100\pi$
$491$	3.34483	−	5.79342i	0.150950	−	0.261453i	0.931577	+	0.363544i	$0.118433\pi$
$492$	−10.1252			−0.456479
$493$	−4.28067	+	7.41434i	−0.192792	+	0.333925i
$494$	2.44210	+	28.7978i	0.109875	+	1.29568i
$495$	3.12847	+	5.41867i	0.140614	+	0.243551i
$496$	−3.29794	+	5.71220i	−0.148082	+	0.256485i
$497$		0			0
$498$	3.49629	+	6.05575i	0.156673	+	0.271365i
$499$	−12.3194	−	21.3378i	−0.551491	−	0.955210i	−0.998167	−	0.0605143i	$-0.980726\pi$
$499$	−12.3194	−	21.3378i	−0.551491	−	0.955210i	0.446677	−	0.894695i	$-0.352607\pi$
$500$	−96.4972			−4.31548
$501$	−9.79864			−0.437771
$502$	34.1560	+	59.1600i	1.52446	+	2.64044i
$503$	−16.5726	−	28.7046i	−0.738936	−	1.27987i	−0.952975	−	0.303049i	$-0.901995\pi$
$503$	−16.5726	−	28.7046i	−0.738936	−	1.27987i	0.214039	−	0.976825i	$-0.431338\pi$
$504$		0			0
$505$	12.1518	−	21.0475i	0.540747	−	0.936601i
$506$	3.54955	+	6.14800i	0.157797	+	0.273312i
$507$	−7.04215	+	1.20302i	−0.312753	+	0.0534279i
$508$	−2.87085	+	4.97246i	−0.127373	+	0.220617i
$509$	−27.6580			−1.22592			−0.612961	−	0.790114i	$-0.710022\pi$
$509$	−27.6580			−1.22592			−0.612961	+	0.790114i	$0.710022\pi$
$510$	−6.12377	+	10.6067i	−0.271165	+	0.469672i
$511$		0			0
$512$	14.2061			0.627828
$513$	−5.65314	+	9.79152i	−0.249592	+	0.432306i
$514$	−3.27143			−0.144296
$515$	1.20645	−	2.08963i	0.0531626	−	0.0920802i
$516$	−2.59102	+	4.48778i	−0.114063	+	0.197563i
$517$	2.25579	−	3.90714i	0.0992096	−	0.171836i
$518$		0			0
$519$	−4.16085			−0.182641
$520$	−28.3873	−	13.3295i	−1.24487	−	0.584538i
$521$	−0.711083	+	1.23163i	−0.0311531	+	0.0539587i	−0.881182	−	0.472778i	$-0.843251\pi$
$521$	−0.711083	+	1.23163i	−0.0311531	+	0.0539587i	0.850029	+	0.526737i	$0.176585\pi$
$522$	−10.7779	−	18.6679i	−0.471736	−	0.817070i
$523$	−3.36178			−0.147000			−0.0735002	−	0.997295i	$-0.523417\pi$
$523$	−3.36178			−0.147000			−0.0735002	+	0.997295i	$0.523417\pi$
$524$	9.51772	+	16.4852i	0.415784	+	0.720158i
$525$		0			0
$526$	−7.41143	−	12.8370i	−0.323154	−	0.559718i
$527$	−6.12377	+	10.6067i	−0.266756	+	0.462034i
$528$	−0.193456	+	0.335076i	−0.00841910	+	0.0145823i
$529$	10.8596			0.472156
$530$	−24.9076			−1.08192
$531$	−2.43835	+	4.22335i	−0.105815	+	0.183278i
$532$		0			0
$533$	1.91681	+	22.6035i	0.0830260	+	0.979065i
$534$	4.55524	+	7.88990i	0.197124	+	0.341429i
$535$	8.59102	+	14.8801i	0.371422	+	0.643322i
$536$	−10.6868	−	18.5100i	−0.461598	−	0.799512i
$537$	6.26580	−	10.8527i	0.270389	−	0.468328i
$538$	16.8182			0.725083
$539$		0			0
$540$	−19.3486	−	33.5127i	−0.832630	−	1.44216i
$541$	−3.88144	−	6.72286i	−0.166876	−	0.289038i	0.770444	−	0.637508i	$-0.220035\pi$
$541$	−3.88144	−	6.72286i	−0.166876	−	0.289038i	−0.937320	+	0.348470i	$0.886701\pi$
$542$	45.6612			1.96131
$543$	−3.82745	−	6.62934i	−0.164252	−	0.284492i
$544$	16.5723			0.710530
$545$	−64.6027			−2.76728
$546$		0			0
$547$	−6.19247			−0.264771			−0.132385	−	0.991198i	$-0.542264\pi$
$547$	−6.19247			−0.264771			−0.132385	+	0.991198i	$0.542264\pi$
$548$	−44.6808			−1.90867
$549$	0.821977	+	1.42371i	0.0350811	+	0.0607623i
$550$	−15.6264			−0.666313
$551$	−6.49723	−	11.2535i	−0.276791	−	0.479416i
$552$	−3.29553	−	5.70802i	−0.140267	−	0.242949i
$553$		0			0
$554$	12.6661			0.538129
$555$	−0.382124	+	0.661858i	−0.0162202	+	0.0280943i
$556$	25.6180	+	44.3717i	1.08644	+	1.88178i
$557$	−14.7729	−	25.5874i	−0.625948	−	1.08417i	−0.988357	−	0.152154i	$-0.951379\pi$
$557$	−14.7729	−	25.5874i	−0.625948	−	1.08417i	0.362409	−	0.932019i	$-0.381954\pi$
$558$	−15.4185	−	26.7056i	−0.652716	−	1.13054i
$559$	10.5090	+	4.93461i	0.444484	+	0.208712i
$560$		0			0
$561$	−0.359219	+	0.622186i	−0.0151662	+	0.0262687i
$562$	−14.1484			−0.596816
$563$	6.46736			0.272567			0.136283	−	0.990670i	$-0.456484\pi$
$563$	6.46736			0.272567			0.136283	+	0.990670i	$0.456484\pi$
$564$	−6.60593	+	11.4418i	−0.278160	+	0.481787i
$565$	25.6933	−	44.5022i	1.08093	−	1.87222i
$566$	−29.9916	−	51.9470i	−1.26064	−	2.18350i
$567$		0			0
$568$	11.5401	+	19.9880i	0.484210	+	0.838676i
$569$	21.6956			0.909526			0.454763	−	0.890612i	$-0.349724\pi$
$569$	21.6956			0.909526			0.454763	+	0.890612i	$0.349724\pi$
$570$	−9.29470	−	16.0989i	−0.389312	−	0.674308i
$571$	8.32088	−	14.4122i	0.348218	−	0.603131i	−0.637715	−	0.770272i	$-0.720120\pi$
$571$	8.32088	−	14.4122i	0.348218	−	0.603131i	0.985933	+	0.167141i	$0.0534536\pi$
$572$	−5.25229	−	2.46626i	−0.219609	−	0.103120i
$573$	−6.96381			−0.290917
$574$		0			0
$575$	−37.2656	+	64.5459i	−1.55408	+	2.69175i
$576$	−17.4064	+	30.1487i	−0.725265	+	1.25620i
$577$	1.32120	−	2.28839i	0.0550024	−	0.0952669i	−0.837213	−	0.546877i	$-0.815817\pi$
$577$	1.32120	−	2.28839i	0.0550024	−	0.0952669i	0.892216	+	0.451610i	$0.149150\pi$
$578$	−25.1769			−1.04722
$579$	1.14167	−	1.97743i	0.0474462	−	0.0821793i
$580$	44.4752			1.84673
$581$		0			0
$582$	4.17286	−	7.22760i	0.172970	−	0.299594i
$583$	−1.46107			−0.0605114
$584$	−5.05617	+	8.75755i	−0.209226	+	0.362390i
$585$	−33.6899	+	23.4562i	−1.39290	+	0.969795i
$586$	5.41096	+	9.37205i	0.223525	+	0.387156i
$587$	−3.69407	+	6.39832i	−0.152471	+	0.264087i	−0.932135	−	0.362110i	$-0.882056\pi$
$587$	−3.69407	+	6.39832i	−0.152471	+	0.264087i	0.779664	+	0.626198i	$0.215390\pi$
$588$		0			0
$589$	−9.29470	−	16.0989i	−0.382981	−	0.663343i
$590$	−8.46687	−	14.6651i	−0.348576	−	0.603751i
$591$	−3.76453			−0.154852
$592$	0.422191			0.0173519
$593$	−23.4515	−	40.6192i	−0.963037	−	1.66803i	−0.714799	−	0.699330i	$-0.753482\pi$
$593$	−23.4515	−	40.6192i	−0.963037	−	1.66803i	−0.248238	−	0.968699i	$-0.579851\pi$
$594$	−1.91013	−	3.30844i	−0.0783735	−	0.135747i
$595$		0			0
$596$	−6.66931	+	11.5516i	−0.273186	+	0.473171i
$597$	0.223554	+	0.387207i	0.00914945	+	0.0158473i
$598$	−38.2244	+	26.6133i	−1.56311	+	1.08830i
$599$	−0.811449	+	1.40547i	−0.0331549	+	0.0574260i	−0.882127	−	0.471012i	$-0.843889\pi$
$599$	−0.811449	+	1.40547i	−0.0331549	+	0.0574260i	0.848972	+	0.528438i	$0.177222\pi$
$600$	14.5081			0.592291
$601$	23.5174	−	40.7333i	0.959293	−	1.66154i	0.235070	−	0.971978i	$-0.424468\pi$
$601$	23.5174	−	40.7333i	0.959293	−	1.66154i	0.724223	−	0.689566i	$-0.242199\pi$
$602$		0			0
$603$	−27.9777			−1.13934
$604$	9.26721	−	16.0513i	0.377077	−	0.653117i
$605$	45.1456			1.83543
$606$	−3.51309	+	6.08485i	−0.142709	+	0.247180i
$607$	14.1935	−	24.5838i	0.576095	−	0.997825i	−0.419827	−	0.907604i	$-0.637909\pi$
$607$	14.1935	−	24.5838i	0.576095	−	0.997825i	0.995922	−	0.0902211i	$-0.0287574\pi$
$608$	−12.5767	+	21.7836i	−0.510054	+	0.883440i
$609$		0			0
$610$	−5.70843			−0.231127
$611$	26.7933	+	12.5810i	1.08394	+	0.508974i
$612$	−9.39766	+	16.2772i	−0.379878	+	0.657968i
$613$	23.7782	+	41.1851i	0.960393	+	1.66345i	0.721514	+	0.692399i	$0.243446\pi$
$613$	23.7782	+	41.1851i	0.960393	+	1.66345i	0.238878	+	0.971050i	$0.423220\pi$
$614$	35.9108			1.44924
$615$	−7.29543	−	12.6360i	−0.294180	−	0.509535i
$616$		0			0
$617$	8.24338	+	14.2780i	0.331866	+	0.574809i	0.982878	−	0.184259i	$-0.0589885\pi$
$617$	8.24338	+	14.2780i	0.331866	+	0.574809i	−0.651012	+	0.759068i	$0.725655\pi$
$618$	−0.348786	+	0.604115i	−0.0140302	+	0.0243011i
$619$	15.9706	−	27.6619i	0.641912	−	1.11182i	−0.343094	−	0.939301i	$-0.611475\pi$
$619$	15.9706	−	27.6619i	0.641912	−	1.11182i	0.985006	−	0.172523i	$-0.0551918\pi$
$620$	63.6245			2.55522
$621$	−18.2209			−0.731181
$622$	1.45196	−	2.51486i	0.0582182	−	0.100837i
$623$		0			0
$624$	−2.29779	−	1.07895i	−0.0919851	−	0.0431925i
$625$	−37.5072	−	64.9644i	−1.50029	−	2.59858i
$626$	−14.6496	−	25.3738i	−0.585515	−	1.01414i
$627$	−0.545225	−	0.944357i	−0.0217742	−	0.0377140i
$628$	−23.8814	+	41.3639i	−0.952973	+	1.65060i
$629$	0.783945			0.0312579
$630$		0			0
$631$	−6.59577	−	11.4242i	−0.262573	−	0.454790i	0.704352	−	0.709851i	$-0.251238\pi$
$631$	−6.59577	−	11.4242i	−0.262573	−	0.454790i	−0.966925	+	0.255061i	$0.917905\pi$
$632$	14.4456	+	25.0204i	0.574613	+	0.995259i
$633$	−7.67910			−0.305217
$634$	8.96386	+	15.5259i	0.356000	+	0.616610i
$635$	−8.27405			−0.328346
$636$	4.27865			0.169660
$637$		0			0
$638$	4.39068			0.173829
$639$	30.2115			1.19515
$640$	−31.0432	−	53.7684i	−1.22709	−	2.12538i
$641$	−47.1627			−1.86282			−0.931408	−	0.363978i	$-0.881418\pi$
$641$	−47.1627			−1.86282			−0.931408	+	0.363978i	$0.881418\pi$
$642$	−2.48367	−	4.30184i	−0.0980227	−	0.169780i
$643$	1.40679	+	2.43664i	0.0554785	+	0.0960916i	0.892431	−	0.451184i	$-0.148998\pi$
$643$	1.40679	+	2.43664i	0.0554785	+	0.0960916i	−0.836952	+	0.547276i	$0.815665\pi$
$644$		0			0
$645$	−7.46755			−0.294035
$646$	−9.53426	+	16.5138i	−0.375121	+	0.649728i
$647$	−12.9891	−	22.4979i	−0.510656	−	0.884482i	−0.999924	−	0.0123485i	$-0.996069\pi$
$647$	−12.9891	−	22.4979i	−0.510656	−	0.884482i	0.489268	−	0.872134i	$-0.337264\pi$
$648$	−6.56795	−	11.3760i	−0.258014	−	0.446893i
$649$	−0.496665	−	0.860249i	−0.0194958	−	0.0337677i
$650$	−8.66304	−	102.157i	−0.339792	−	4.00692i
$651$		0			0
$652$	−34.5553	+	59.8515i	−1.35329	+	2.34397i
$653$	−26.8426			−1.05043			−0.525216	−	0.850969i	$-0.676015\pi$
$653$	−26.8426			−1.05043			−0.525216	+	0.850969i	$0.676015\pi$
$654$	18.6767			0.730317
$655$	−13.7155	+	23.7559i	−0.535908	+	0.928219i
$656$	−4.03019	+	6.98050i	−0.157353	+	0.272543i
$657$	6.61846	+	11.4635i	0.258211	+	0.447234i
$658$		0			0
$659$	−7.78666	−	13.4869i	−0.303325	−	0.525375i	0.673562	−	0.739131i	$-0.264764\pi$
$659$	−7.78666	−	13.4869i	−0.303325	−	0.525375i	−0.976887	+	0.213756i	$0.931430\pi$
$660$	3.73220			0.145276
$661$	−16.6902	−	28.9083i	−0.649174	−	1.12440i	−0.983320	−	0.181881i	$-0.941781\pi$
$661$	−16.6902	−	28.9083i	−0.649174	−	1.12440i	0.334146	−	0.942521i	$-0.391552\pi$
$662$	16.5891	−	28.7332i	0.644755	−	1.11675i
$663$	−4.26665	−	2.00344i	−0.165703	−	0.0778073i
$664$	−11.8136			−0.458455
$665$		0			0
$666$	−0.986911	+	1.70938i	−0.0382420	+	0.0662371i
$667$	10.4708	−	18.1359i	0.405431	−	0.702227i
$668$	26.1074	−	45.2193i	1.01013	−	1.74959i
$669$	−7.43762			−0.287555
$670$	48.5745	−	84.1335i	1.87660	−	3.25036i
$671$	−0.334855			−0.0129269
$672$		0			0
$673$	−0.427076	+	0.739717i	−0.0164626	+	0.0285140i	−0.874139	−	0.485675i	$-0.838574\pi$
$673$	−0.427076	+	0.739717i	−0.0164626	+	0.0285140i	0.857677	+	0.514189i	$0.171907\pi$
$674$	−38.1164			−1.46819
$675$	20.0538	−	34.7342i	0.771872	−	1.33692i
$676$	13.2113	−	35.7038i	0.508125	−	1.37322i
$677$	12.2725	+	21.2565i	0.471669	+	0.816955i	0.999475	−	0.0324100i	$-0.0103182\pi$
$677$	12.2725	+	21.2565i	0.471669	+	0.816955i	−0.527805	+	0.849365i	$0.676985\pi$
$678$	−7.42797	+	12.8656i	−0.285269	+	0.494101i
$679$		0			0
$680$	−10.3458	−	17.9194i	−0.396742	−	0.687177i
$681$	1.47486	+	2.55454i	0.0565168	+	0.0978900i
$682$	6.28114			0.240517
$683$	−43.0372			−1.64677			−0.823387	−	0.567480i	$-0.807918\pi$
$683$	−43.0372			−1.64677			−0.823387	+	0.567480i	$0.807918\pi$
$684$	−14.2638	−	24.7057i	−0.545391	−	0.944645i
$685$	−32.1935	−	55.7608i	−1.23005	−	2.13051i
$686$		0			0
$687$	−0.851558	+	1.47494i	−0.0324889	+	0.0562725i
$688$	2.06264	+	3.57260i	0.0786374	+	0.136204i
$689$	−0.809995	−	9.55167i	−0.0308583	−	0.363890i
$690$	14.9791	−	25.9446i	0.570246	−	0.987695i
$691$	−25.8195			−0.982220			−0.491110	−	0.871097i	$-0.663409\pi$
$691$	−25.8195			−0.982220			−0.491110	+	0.871097i	$0.663409\pi$
$692$	11.0861	−	19.2017i	0.421431	−	0.729939i
$693$		0			0
$694$	−8.74338			−0.331894
$695$	−36.9167	+	63.9416i	−1.40033	+	2.42544i
$696$	−4.07646			−0.154518
$697$	−7.48346	+	12.9617i	−0.283456	+	0.490961i
$698$	−19.0673	+	33.0255i	−0.721707	+	1.25003i
$699$	5.59750	−	9.69515i	0.211717	−	0.366704i
$700$		0			0
$701$	16.3178			0.616313			0.308156	−	0.951336i	$-0.400288\pi$
$701$	16.3178			0.616313			0.308156	+	0.951336i	$0.400288\pi$
$702$	20.5698	−	14.3215i	0.776356	−	0.540530i
$703$	−0.594938	+	1.03046i	−0.0224385	+	0.0388647i
$704$	−3.54548	−	6.14096i	−0.133625	−	0.231446i
$705$	−19.0389			−0.717047
$706$	20.1981	+	34.9841i	0.760166	+	1.31665i
$707$		0			0
$708$	1.45445	+	2.51918i	0.0546616	+	0.0946767i
$709$	11.1897	−	19.3811i	0.420238	−	0.727874i	−0.575725	−	0.817644i	$-0.695280\pi$
$709$	11.1897	−	19.3811i	0.420238	−	0.727874i	0.995963	+	0.0897702i	$0.0286133\pi$
$710$	−52.4529	+	90.8511i	−1.96852	+	3.40958i
$711$	37.8181			1.41829
$712$	−15.3916			−0.576825
$713$	14.9791	−	25.9446i	0.560973	−	0.971634i
$714$		0			0
$715$	−0.706545	−	8.33177i	−0.0264233	−	0.311590i
$716$	33.3891	+	57.8315i	1.24781	+	2.16127i
$717$	0.354893	+	0.614692i	0.0132537	+	0.0229561i
$718$	−18.1071	−	31.3624i	−0.675750	−	1.17043i
$719$	11.3723	−	19.6973i	0.424113	−	0.734586i	−0.572224	−	0.820098i	$-0.693919\pi$
$719$	11.3723	−	19.6973i	0.424113	−	0.734586i	0.996337	+	0.0855115i	$0.0272524\pi$
$720$	−14.5865			−0.543606
$721$		0			0
$722$	6.61892	+	11.4643i	0.246331	+	0.426657i
$723$	−0.586013	−	1.01500i	−0.0217941	−	0.0377484i
$724$	40.7913			1.51599
$725$	23.0481	+	39.9205i	0.855986	+	1.48261i
$726$	−13.0516			−0.484392
$727$	18.7274			0.694561			0.347280	−	0.937761i	$-0.387105\pi$
$727$	18.7274			0.694561			0.347280	+	0.937761i	$0.387105\pi$
$728$		0			0
$729$	−12.0322			−0.445638
$730$	−45.9636			−1.70119
$731$	3.83001	+	6.63377i	0.141658	+	0.245359i
$732$	0.980601			0.0362441
$733$	0.846341	+	1.46591i	0.0312603	+	0.0541445i	0.881232	−	0.472683i	$-0.156715\pi$
$733$	0.846341	+	1.46591i	0.0312603	+	0.0541445i	−0.849972	+	0.526828i	$0.823381\pi$
$734$	40.1781	+	69.5904i	1.48300	+	2.56863i
$735$		0			0
$736$	−40.5368			−1.49421
$737$	2.84937	−	4.93525i	0.104958	−	0.181792i
$738$	−18.8419	−	32.6351i	−0.693580	−	1.20132i
$739$	−23.4581	−	40.6305i	−0.862919	−	1.49462i	−0.869099	−	0.494638i	$-0.835301\pi$
$739$	−23.4581	−	40.6305i	−0.862919	−	1.49462i	0.00618065	−	0.999981i	$-0.498033\pi$
$740$	−2.03625	−	3.52689i	−0.0748541	−	0.129651i
$741$	5.87141	−	4.08791i	0.215692	−	0.150173i
$742$		0			0
$743$	−6.44831	+	11.1688i	−0.236566	+	0.409744i	−0.959727	−	0.280936i	$-0.909355\pi$
$743$	−6.44831	+	11.1688i	−0.236566	+	0.409744i	0.723161	+	0.690680i	$0.242688\pi$
$744$	−5.83163			−0.213798
$745$	−19.2216			−0.704223
$746$	−10.8756	+	18.8372i	−0.398186	+	0.689678i
$747$	−7.73189	+	13.3920i	−0.282895	+	0.489989i
$748$	−1.91420	−	3.31549i	−0.0699900	−	0.121226i
$749$		0			0
$750$	20.1007	+	34.8155i	0.733974	+	1.27128i
$751$	−45.6333			−1.66518			−0.832591	−	0.553888i	$-0.813144\pi$
$751$	−45.6333			−1.66518			−0.832591	+	0.553888i	$0.813144\pi$
$752$	5.25881	+	9.10852i	0.191769	+	0.332154i
$753$	8.45515	−	14.6447i	0.308123	−	0.533684i
$754$	2.43412	+	28.7038i	0.0886454	+	1.04533i
$755$	26.7089			0.972038
$756$		0			0
$757$	19.0782	−	33.0445i	0.693410	−	1.20102i	−0.277303	−	0.960782i	$-0.589441\pi$
$757$	19.0782	−	33.0445i	0.693410	−	1.20102i	0.970714	−	0.240239i	$-0.0772260\pi$
$758$	−14.5028	+	25.1195i	−0.526764	+	0.912382i
$759$	0.878673	−	1.52191i	0.0318938	−	0.0552417i
$760$	31.4057			1.13920
$761$	−21.3672	+	37.0092i	−0.774562	+	1.34158i	0.160478	+	0.987039i	$0.448696\pi$
$761$	−21.3672	+	37.0092i	−0.774562	+	1.34158i	−0.935040	+	0.354542i	$0.884637\pi$
$762$	2.39203			0.0866543
$763$		0			0
$764$	18.5543	−	32.1370i	0.671271	−	1.16267i
$765$	−27.0849			−0.979257
$766$	−30.8502	+	53.4342i	−1.11466	+	1.93066i
$767$	5.34848	−	3.72382i	0.193122	−	0.134459i
$768$	1.88364	+	3.26257i	0.0679702	+	0.117728i
$769$	−10.8088	+	18.7215i	−0.389777	+	0.675113i	−0.992419	−	0.122898i	$-0.960781\pi$
$769$	−10.8088	+	18.7215i	−0.389777	+	0.675113i	0.602643	+	0.798011i	$0.294114\pi$
$770$		0			0
$771$	0.404912	+	0.701329i	0.0145826	+	0.0252577i
$772$	6.08371	+	10.5373i	0.218958	+	0.379246i
$773$	10.0011			0.359716			0.179858	−	0.983693i	$-0.442436\pi$
$773$	10.0011			0.359716			0.179858	+	0.983693i	$0.442436\pi$
$774$	−19.2865			−0.693237
$775$	32.9718	+	57.1089i	1.18438	+	2.05141i
$776$	7.04980	+	12.2106i	0.253073	+	0.438335i
$777$		0			0
$778$	−15.2122	+	26.3484i	−0.545385	+	0.944634i
$779$	−11.3584	−	19.6734i	−0.406958	−	0.704872i
$780$	2.06907	+	24.3990i	0.0740847	+	0.873625i
$781$	−3.07688	+	5.32931i	−0.110099	+	0.190698i
$782$	−30.7304			−1.09892
$783$	−5.63467	+	9.75954i	−0.201367	+	0.348778i
$784$		0			0
$785$	−68.8285			−2.45659
$786$	3.96515	−	6.86785i	0.141432	−	0.244968i
$787$	41.7878			1.48957			0.744787	−	0.667302i	$-0.232551\pi$
$787$	41.7878			1.48957			0.744787	+	0.667302i	$0.232551\pi$
$788$	10.0302	−	17.3728i	0.357310	−	0.618880i
$789$	−1.83466	+	3.17772i	−0.0653156	+	0.113130i
$790$	−65.6593	+	113.725i	−2.33605	+	4.04616i
$791$		0			0
$792$	3.05601			0.108591
$793$	−0.185638	−	2.18909i	−0.00659221	−	0.0777370i
$794$	−8.78229	+	15.2114i	−0.311672	+	0.539831i
$795$	3.08287	+	5.33968i	0.109338	+	0.189379i
$796$	−2.38254			−0.0844468
$797$	11.3856	+	19.7204i	0.403297	+	0.698531i	0.994122	−	0.108269i	$-0.0345308\pi$
$797$	11.3856	+	19.7204i	0.403297	+	0.698531i	−0.590825	+	0.806800i	$0.701197\pi$
$798$		0			0
$799$	9.76481	+	16.9131i	0.345454	+	0.598344i
$800$	44.6145	−	77.2745i	1.57736	−	2.73207i
$801$	−10.0737	+	17.4482i	−0.355937	+	0.616501i
$802$	−36.7283			−1.29692
$803$	−2.69621			−0.0951473
$804$	−8.34419	+	14.4526i	−0.294277	+	0.509703i
$805$		0			0
$806$	3.48216	+	41.0626i	0.122654	+	1.44637i
$807$	−2.08163	−	3.60548i	−0.0732767	−	0.126919i
$808$	−5.93516	−	10.2800i	−0.208798	−	0.361649i
$809$	18.7851	+	32.5367i	0.660449	+	1.14393i	0.980498	+	0.196530i	$0.0629672\pi$
$809$	18.7851	+	32.5367i	0.660449	+	1.14393i	−0.320049	+	0.947401i	$0.603699\pi$
$810$	29.8533	−	51.7074i	1.04894	−	1.81681i
$811$	11.5936			0.407106			0.203553	−	0.979064i	$-0.434751\pi$
$811$	11.5936			0.407106			0.203553	+	0.979064i	$0.434751\pi$
$812$		0			0
$813$	−5.65159	−	9.78884i	−0.198210	−	0.343309i
$814$	−0.201023	−	0.348182i	−0.00704584	−	0.0122038i
$815$	−99.5915			−3.48854
$816$	−0.837429	−	1.45047i	−0.0293159	−	0.0507766i
$817$	−11.6264			−0.406757
$818$	57.2359			2.00121
$819$		0			0
$820$	77.7514			2.71520
$821$	31.0243			1.08276			0.541378	−	0.840780i	$-0.317903\pi$
$821$	31.0243			1.08276			0.541378	+	0.840780i	$0.317903\pi$
$822$	9.30717	+	16.1205i	0.324625	+	0.562267i
$823$	29.0775			1.01358			0.506789	−	0.862070i	$-0.330832\pi$
$823$	29.0775			1.01358			0.506789	+	0.862070i	$0.330832\pi$
$824$	−0.589253	−	1.02062i	−0.0205276	−	0.0355549i
$825$	1.93412	+	3.34999i	0.0673374	+	0.116632i
$826$		0			0
$827$	14.8920			0.517846			0.258923	−	0.965898i	$-0.416632\pi$
$827$	14.8920			0.517846			0.258923	+	0.965898i	$0.416632\pi$
$828$	22.9873	−	39.8151i	0.798863	−	1.38367i
$829$	2.18594	+	3.78617i	0.0759210	+	0.131499i	0.901486	−	0.432807i	$-0.142477\pi$
$829$	2.18594	+	3.78617i	0.0759210	+	0.131499i	−0.825565	+	0.564306i	$0.809144\pi$
$830$	−26.8481	−	46.5022i	−0.931909	−	1.61411i
$831$	−1.56771	−	2.71535i	−0.0543832	−	0.0941944i
$832$	38.1806	−	26.5828i	1.32367	−	0.921593i
$833$		0			0
$834$	10.6726	−	18.4856i	0.369563	−	0.640103i
$835$	75.2439			2.60392
$836$	5.81076			0.200969
$837$	−8.06076	+	13.9616i	−0.278621	+	0.482585i
$838$	−26.2928	+	45.5405i	−0.908270	+	1.57317i
$839$	−11.4109	−	19.7643i	−0.393948	−	0.682338i	0.599018	−	0.800735i	$-0.295558\pi$
$839$	−11.4109	−	19.7643i	−0.393948	−	0.682338i	−0.992966	+	0.118397i	$0.962224\pi$
$840$		0			0
$841$	8.02399	+	13.8980i	0.276689	+	0.479240i
$842$	−46.2308			−1.59322
$843$	1.75119	+	3.03314i	0.0603140	+	0.104467i
$844$	20.4601	−	35.4379i	0.704265	−	1.21982i
$845$	54.0767	−	9.23799i	1.86030	−	0.317797i
$846$	−49.1718			−1.69056
$847$		0			0
$848$	1.70306	−	2.94979i	0.0584833	−	0.101296i
$849$	−7.42427	+	12.8592i	−0.254800	+	0.441327i
$850$	33.8216	−	58.5808i	1.16007	−	2.00931i
$851$	−1.91758			−0.0657338
$852$	9.01043	−	15.6065i	0.308692	−	0.534671i
$853$	23.3549			0.799656			0.399828	−	0.916590i	$-0.369070\pi$
$853$	23.3549			0.799656			0.399828	+	0.916590i	$0.369070\pi$
$854$		0			0
$855$	20.5548	−	35.6020i	0.702960	−	1.21756i
$856$	8.39203			0.286834
$857$	21.7653	−	37.6986i	0.743488	−	1.28776i	−0.207410	−	0.978254i	$-0.566503\pi$
$857$	21.7653	−	37.6986i	0.743488	−	1.28776i	0.950898	−	0.309505i	$-0.100163\pi$
$858$	0.204263	+	2.40872i	0.00697342	+	0.0822324i
$859$	−10.2557	−	17.7633i	−0.349919	−	0.606078i	0.636316	−	0.771429i	$-0.280458\pi$
$859$	−10.2557	−	17.7633i	−0.349919	−	0.606078i	−0.986235	+	0.165351i	$0.947124\pi$
$860$	19.8965	−	34.4617i	0.678464	−	1.17513i
$861$		0			0
$862$	−22.1451	−	38.3564i	−0.754263	−	1.30642i
$863$	25.3339	+	43.8796i	0.862376	+	1.49368i	0.869629	+	0.493706i	$0.164358\pi$
$863$	25.3339	+	43.8796i	0.862376	+	1.49368i	−0.00725258	+	0.999974i	$0.502309\pi$
$864$	21.8142			0.742133
$865$	31.9512			1.08637
$866$	−0.0185167	−	0.0320719i	−0.000629224	−	0.00108985i
$867$	3.11621	+	5.39743i	0.105832	+	0.183306i
$868$		0			0
$869$	−3.85156	+	6.67109i	−0.130655	+	0.226301i
$870$	−9.26434	−	16.0463i	−0.314091	−	0.544021i
$871$	33.8436	+	15.8916i	1.14675	+	0.538465i
$872$	−15.7766	+	27.3259i	−0.534263	+	0.925371i
$873$	18.4562			0.624647
$874$	23.3214	−	40.3939i	0.788858	−	1.36634i
$875$		0			0
$876$	7.89568			0.266770
$877$	23.5180	−	40.7344i	0.794148	−	1.37550i	−0.129231	−	0.991615i	$-0.541251\pi$
$877$	23.5180	−	40.7344i	0.794148	−	1.37550i	0.923379	−	0.383890i	$-0.125416\pi$
$878$	29.9613			1.01114
$879$	1.33945	−	2.32000i	0.0451787	−	0.0782517i
$880$	1.48555	−	2.57305i	0.0500780	−	0.0867376i
$881$	8.05674	−	13.9547i	0.271439	−	0.470145i	−0.697792	−	0.716301i	$-0.745834\pi$
$881$	8.05674	−	13.9547i	0.271439	−	0.470145i	0.969230	+	0.246155i	$0.0791673\pi$
$882$		0			0
$883$	42.0733			1.41588			0.707940	−	0.706273i	$-0.249625\pi$
$883$	42.0733			1.41588			0.707940	+	0.706273i	$0.249625\pi$
$884$	20.6136	−	14.3520i	0.693310	−	0.482710i
$885$	−2.09593	+	3.63026i	−0.0704539	+	0.122030i
$886$	16.6623	+	28.8600i	0.559782	+	0.969570i
$887$	−41.7628			−1.40226			−0.701128	−	0.713035i	$-0.747320\pi$
$887$	−41.7628			−1.40226			−0.701128	+	0.713035i	$0.747320\pi$
$888$	0.186636	+	0.323264i	0.00626311	+	0.0108480i
$889$		0			0
$890$	−34.9797	−	60.5866i	−1.17252	−	2.03087i
$891$	1.75119	−	3.03314i	0.0586669	−	0.101614i
$892$	19.8167	−	34.3236i	0.663513	−	1.14924i
$893$	−29.6422			−0.991938
$894$	5.55697			0.185853
$895$	−48.1151	+	83.3379i	−1.60831	+	2.78568i
$896$		0			0
$897$	10.4365	+	4.90055i	0.348464	+	0.163625i
$898$	26.3999	+	45.7260i	0.880977	+	1.52590i
$899$	−9.26434	−	16.0463i	−0.308983	−	0.535174i
$900$	50.5992	+	87.6404i	1.68664	+	2.92135i
$901$	3.16233	−	5.47731i	0.105352	−	0.182476i
$902$	7.67577			0.255575
$903$		0			0
$904$	−12.5491	−	21.7357i	−0.417377	−	0.722919i
$905$	29.3910	+	50.9068i	0.976991	+	1.69220i
$906$	−7.72158			−0.256532
$907$	7.71125	+	13.3563i	0.256048	+	0.443488i	0.965180	−	0.261588i	$-0.0842463\pi$
$907$	7.71125	+	13.3563i	0.256048	+	0.443488i	−0.709132	+	0.705076i	$0.750913\pi$
$908$	−15.7184			−0.521634
$909$	−15.5381			−0.515366
$910$		0			0
$911$	37.5462			1.24396			0.621981	−	0.783033i	$-0.286328\pi$
$911$	37.5462			1.24396			0.621981	+	0.783033i	$0.286328\pi$
$912$	2.54211			0.0841776
$913$	−1.57490	−	2.72781i	−0.0521216	−	0.0902773i
$914$	40.2517			1.33141
$915$	0.706545	+	1.22377i	0.0233577	+	0.0404567i
$916$	−4.53776	−	7.85963i	−0.149932	−	0.259689i
$917$		0			0
$918$	16.5370			0.545804
$919$	4.73732	−	8.20528i	0.156270	−	0.270667i	−0.777251	−	0.629191i	$-0.783386\pi$
$919$	4.73732	−	8.20528i	0.156270	−	0.270667i	0.933521	+	0.358524i	$0.116720\pi$
$920$	25.3064	+	43.8319i	0.834326	+	1.44510i
$921$	−4.44476	−	7.69856i	−0.146460	−	0.253676i
$922$	6.74837	+	11.6885i	0.222246	+	0.384941i
$923$	−36.5458	−	17.1604i	−1.20292	−	0.564842i
$924$		0			0
$925$	2.11047	−	3.65545i	0.0693919	−	0.120190i
$926$	11.5283			0.378842
$927$	−1.54265			−0.0506672
$928$	−12.5357	+	21.7124i	−0.411503	+	0.712745i
$929$	−17.9220	+	31.0418i	−0.588001	+	1.01845i	0.406493	+	0.913654i	$0.366751\pi$
$929$	−17.9220	+	31.0418i	−0.588001	+	1.01845i	−0.994494	+	0.104793i	$0.966582\pi$
$930$	−13.2532	−	22.9553i	−0.434591	−	0.752733i
$931$		0			0
$932$	29.8278	+	51.6633i	0.977043	+	1.69229i
$933$	−0.718848			−0.0235340
$934$	9.65668	+	16.7259i	0.315976	+	0.547287i
$935$	2.75845	−	4.77777i	0.0902108	−	0.156250i
$936$	1.69420	+	19.9785i	0.0553768	+	0.653017i
$937$	−31.3709			−1.02484			−0.512422	−	0.858734i	$-0.671252\pi$
$937$	−31.3709			−1.02484			−0.512422	+	0.858734i	$0.671252\pi$
$938$		0			0
$939$	−3.62643	+	6.28116i	−0.118344	+	0.204978i
$940$	50.7270	−	87.8618i	1.65453	−	2.86574i
$941$	−22.3922	+	38.7844i	−0.729964	+	1.26433i	0.226934	+	0.973910i	$0.427130\pi$
$941$	−22.3922	+	38.7844i	−0.729964	+	1.26433i	−0.956898	+	0.290425i	$0.906203\pi$
$942$	19.8984			0.648324
$943$	18.3050	−	31.7052i	0.596093	−	1.03246i
$944$	2.31570			0.0753695
$945$		0			0
$946$	1.96422	−	3.40212i	0.0638622	−	0.110613i
$947$	−35.0674			−1.13954			−0.569768	−	0.821805i	$-0.692967\pi$
$947$	−35.0674			−1.13954			−0.569768	+	0.821805i	$0.692967\pi$
$948$	11.2790	−	19.5359i	0.366326	−	0.634495i
$949$	−1.49474	−	17.6263i	−0.0485212	−	0.572175i
$950$	51.3347	+	88.9143i	1.66552	+	2.88476i
$951$	2.21896	−	3.84334i	0.0719546	−	0.124629i
$952$		0			0
$953$	−29.4852	−	51.0699i	−0.955120	−	1.65432i	−0.734093	−	0.679048i	$-0.762393\pi$
$953$	−29.4852	−	51.0699i	−0.955120	−	1.65432i	−0.221027	−	0.975268i	$-0.570941\pi$
$954$	7.96212	+	13.7908i	0.257783	+	0.446494i
$955$	53.4752			1.73042
$956$	−3.78229			−0.122328
$957$	−0.543444	−	0.941273i	−0.0175671	−	0.0304270i
$958$	−26.8830	−	46.5627i	−0.868550	−	1.50437i
$959$		0			0
$960$	−14.9620	+	25.9149i	−0.482895	+	0.836399i
$961$	2.24677	+	3.89152i	0.0724765	+	0.125533i
$962$	2.16477	−	1.50720i	0.0697950	−	0.0485941i
$963$	5.49253	−	9.51334i	0.176994	−	0.306563i
$964$	6.24547			0.201153
$965$	−8.76690	+	15.1847i	−0.282217	+	0.488813i
$966$		0			0
$967$	30.3671			0.976540			0.488270	−	0.872693i	$-0.337628\pi$
$967$	30.3671			0.976540			0.488270	+	0.872693i	$0.337628\pi$
$968$	11.0250	−	19.0958i	0.354357	−	0.613764i
$969$	4.72031			0.151638
$970$	−32.0434	+	55.5008i	−1.02885	+	1.78202i
$971$	24.7588	−	42.8834i	0.794546	−	1.37619i	−0.128581	−	0.991699i	$-0.541042\pi$
$971$	24.7588	−	42.8834i	0.794546	−	1.37619i	0.923127	−	0.384495i	$-0.125625\pi$
$972$	−18.8831	+	32.7065i	−0.605676	+	1.04906i
$973$		0			0
$974$	3.93815			0.126186
$975$	−20.8281	+	14.5014i	−0.667034	+	0.464416i
$976$	0.390315	−	0.676045i	0.0124937	−	0.0216397i
$977$	5.43356	+	9.41120i	0.173835	+	0.301091i	0.939757	−	0.341842i	$-0.111051\pi$
$977$	5.43356	+	9.41120i	0.173835	+	0.301091i	−0.765923	+	0.642933i	$0.777717\pi$
$978$	28.7920			0.920666
$979$	−2.05190	−	3.55400i	−0.0655790	−	0.113586i
$980$		0			0
$981$	20.6514	+	35.7692i	0.659347	+	1.14202i
$982$	7.42555	−	12.8614i	0.236959	−	0.410425i
$983$	−1.17417	+	2.03371i	−0.0374501	+	0.0648654i	−0.884143	−	0.467217i	$-0.845257\pi$
$983$	−1.17417	+	2.03371i	−0.0374501	+	0.0648654i	0.846693	+	0.532082i	$0.178590\pi$
$984$	−7.12645			−0.227183
$985$	28.9079			0.921082
$986$	−9.50312	+	16.4599i	−0.302641	+	0.524190i
$987$		0			0
$988$	3.22139	+	37.9875i	0.102486	+	1.20854i
$989$	−9.36845	−	16.2266i	−0.297899	−	0.515977i
$990$	6.94523	+	12.0295i	0.220734	+	0.382322i
$991$	−12.2408	−	21.2016i	−0.388841	−	0.673492i	0.603453	−	0.797398i	$-0.293791\pi$
$991$	−12.2408	−	21.2016i	−0.388841	−	0.673492i	−0.992294	+	0.123907i	$0.960458\pi$
$992$	−17.9331	+	31.0610i	−0.569375	+	0.986187i
$993$	−8.21311			−0.260635
$994$		0			0
$995$	−1.71667	−	2.97336i	−0.0544222	−	0.0942620i
$996$	4.61199	+	7.98821i	0.146137	+	0.253116i
$997$	−6.62341			−0.209766			−0.104883	−	0.994485i	$-0.533447\pi$
$997$	−6.62341			−0.209766			−0.104883	+	0.994485i	$0.533447\pi$
$998$	−27.3491	−	47.3700i	−0.865720	−	1.49947i
$999$	1.03191			0.0326482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.h.h.165.4		8
7.2	even	3		637.2.g.k.373.1		8
7.3	odd	6		637.2.f.i.295.1		8
7.4	even	3		91.2.f.c.22.1	✓	8
7.5	odd	6		637.2.g.j.373.1		8
7.6	odd	2		637.2.h.i.165.4		8
13.3	even	3		637.2.g.k.263.1		8
21.11	odd	6		819.2.o.h.568.4		8
28.11	odd	6		1456.2.s.q.113.2		8
91.3	odd	6		637.2.f.i.393.1		8
91.4	even	6		1183.2.a.l.1.1		4
91.16	even	3	inner	637.2.h.h.471.4		8
91.17	odd	6		8281.2.a.bt.1.1		4
91.32	odd	12		1183.2.c.g.337.2		8
91.46	odd	12		1183.2.c.g.337.7		8
91.55	odd	6		637.2.g.j.263.1		8
91.68	odd	6		637.2.h.i.471.4		8
91.74	even	3		1183.2.a.k.1.4		4
91.81	even	3		91.2.f.c.29.1	yes	8
91.87	odd	6		8281.2.a.bp.1.4		4
273.263	odd	6		819.2.o.h.757.4		8
364.263	odd	6		1456.2.s.q.1121.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.1	✓	8	7.4	even	3
91.2.f.c.29.1	yes	8	91.81	even	3
637.2.f.i.295.1		8	7.3	odd	6
637.2.f.i.393.1		8	91.3	odd	6
637.2.g.j.263.1		8	91.55	odd	6
637.2.g.j.373.1		8	7.5	odd	6
637.2.g.k.263.1		8	13.3	even	3
637.2.g.k.373.1		8	7.2	even	3
637.2.h.h.165.4		8	1.1	even	1	trivial
637.2.h.h.471.4		8	91.16	even	3	inner
637.2.h.i.165.4		8	7.6	odd	2
637.2.h.i.471.4		8	91.68	odd	6
819.2.o.h.568.4		8	21.11	odd	6
819.2.o.h.757.4		8	273.263	odd	6
1183.2.a.k.1.4		4	91.74	even	3
1183.2.a.l.1.1		4	91.4	even	6
1183.2.c.g.337.2		8	91.32	odd	12
1183.2.c.g.337.7		8	91.46	odd	12
1456.2.s.q.113.2		8	28.11	odd	6
1456.2.s.q.1121.2		8	364.263	odd	6
8281.2.a.bp.1.4		4	91.87	odd	6
8281.2.a.bt.1.1		4	91.17	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.22001 q^{2} +(-0.274776 - 0.475925i) q^{3} +2.92843 q^{4} +(2.11000 + 3.65463i) q^{5} +(-0.610004 - 1.05656i) q^{6} +2.06113 q^{8} +(1.34900 - 2.33653i) q^{9} +(4.68423 + 8.11332i) q^{10} +(0.274776 + 0.475925i) q^{11} +(-0.804662 - 1.39372i) q^{12} +(-2.95900 + 2.06017i) q^{13} +(1.15956 - 2.00841i) q^{15} -1.28114 q^{16} -2.37888 q^{17} +(2.99478 - 5.18712i) q^{18} +(1.80534 - 3.12694i) q^{19} +(6.17901 + 10.7024i) q^{20} +(0.610004 + 1.05656i) q^{22} +5.81890 q^{23} +(-0.566349 - 0.980945i) q^{24} +(-6.40423 + 11.0925i) q^{25} +(-6.56900 + 4.57360i) q^{26} -3.13134 q^{27} +(1.79945 - 3.11673i) q^{29} +(2.57422 - 4.45868i) q^{30} +(2.57422 - 4.45868i) q^{31} -6.96640 q^{32} +(0.151003 - 0.261545i) q^{33} -5.28114 q^{34} +(3.95045 - 6.84238i) q^{36} -0.329543 q^{37} +(4.00787 - 6.94184i) q^{38} +(1.79355 + 0.842178i) q^{39} +(4.34900 + 7.53268i) q^{40} +(3.14579 - 5.44866i) q^{41} +(-1.61000 - 2.78861i) q^{43} +(0.804662 + 1.39372i) q^{44} +11.3856 q^{45} +12.9180 q^{46} +(-4.10479 - 7.10970i) q^{47} +(0.352026 + 0.609727i) q^{48} +(-14.2174 + 24.6253i) q^{50} +(0.653659 + 1.13217i) q^{51} +(-8.66524 + 6.03308i) q^{52} +(-1.32933 + 2.30247i) q^{53} -6.95160 q^{54} +(-1.15956 + 2.00841i) q^{55} -1.98426 q^{57} +(3.99478 - 6.91917i) q^{58} -1.80753 q^{59} +(3.39568 - 5.88149i) q^{60} +(-0.304662 + 0.527691i) q^{61} +(5.71479 - 9.89831i) q^{62} -12.9032 q^{64} +(-13.7727 - 6.46709i) q^{65} +(0.335228 - 0.580633i) q^{66} +(-5.18490 - 8.98052i) q^{67} -6.96640 q^{68} +(-1.59889 - 2.76936i) q^{69} +(5.59889 + 9.69756i) q^{71} +(2.78046 - 4.81590i) q^{72} +(-2.45310 + 4.24890i) q^{73} -0.731589 q^{74} +7.03891 q^{75} +(5.28682 - 9.15705i) q^{76} +(3.98169 + 1.86964i) q^{78} +(7.00855 + 12.1392i) q^{79} +(-2.70321 - 4.68210i) q^{80} +(-3.18657 - 5.51931i) q^{81} +(6.98367 - 12.0961i) q^{82} -5.73159 q^{83} +(-5.01945 - 8.69395i) q^{85} +(-3.57422 - 6.19073i) q^{86} -1.97777 q^{87} +(0.566349 + 0.980945i) q^{88} -7.46755 q^{89} +25.2760 q^{90} +17.0403 q^{92} -2.82933 q^{93} +(-9.11266 - 15.7836i) q^{94} +15.2371 q^{95} +(1.91420 + 3.31549i) q^{96} +(3.42035 + 5.92422i) q^{97} +1.48269 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - q^{3} + 10 q^{4} + 7 q^{5} + 5 q^{6} - 12 q^{8} - 7 q^{9} + 11 q^{10} + q^{11} - 12 q^{12} + 4 q^{13} - 3 q^{15} + 38 q^{16} - 8 q^{17} + 3 q^{18} - q^{19} + 2 q^{20} - 5 q^{22} - 4 q^{23}+ \cdots + 46 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 + 10 * q^4 + 7 * q^5 + 5 * q^6 - 12 * q^8 - 7 * q^9 + 11 * q^10 + q^11 - 12 * q^12 + 4 * q^13 - 3 * q^15 + 38 * q^16 - 8 * q^17 + 3 * q^18 - q^19 + 2 * q^20 - 5 * q^22 - 4 * q^23 + 3 * q^24 - 5 * q^25 - 15 * q^26 - 52 * q^27 - q^29 + 4 * q^30 + 4 * q^31 - 66 * q^32 + 19 * q^33 + 6 * q^34 + 34 * q^36 - 20 * q^37 + 23 * q^38 - q^39 + 17 * q^40 + 22 * q^41 - 3 * q^43 + 12 * q^44 - 22 * q^45 + 48 * q^46 - 2 * q^47 - 11 * q^48 - 43 * q^50 - 7 * q^51 - 31 * q^52 - 2 * q^53 + 10 * q^54 + 3 * q^55 - 34 * q^57 + 11 * q^58 - 16 * q^59 + 11 * q^60 - 8 * q^61 + 5 * q^62 + 28 * q^64 - 11 * q^65 - 6 * q^66 + 6 * q^67 - 66 * q^68 + 18 * q^69 + 14 * q^71 - 5 * q^72 + 8 * q^73 + 40 * q^74 - 14 * q^75 - 32 * q^76 - q^78 + 26 * q^79 - 7 * q^80 - 24 * q^81 + 14 * q^82 - 5 * q^85 - 12 * q^86 + 26 * q^87 - 3 * q^88 - 2 * q^89 + 52 * q^90 + 24 * q^92 - 14 * q^93 - 33 * q^94 + 42 * q^95 + 58 * q^96 - 3 * q^97 + 46 * q^99

Introduction

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