LMFDB - Embedded newform 637.2.g.j.263.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(263,637)] 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("637.263"); 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, 2])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [8,1,-2,-5,-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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.1
Root			$-1.11000 + 1.92258i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.j.373.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.11000 + 1.92258i) q^{2} -0.549551 q^{3} +(-1.46422 - 2.53610i) q^{4} +(-2.11000 - 3.65463i) q^{5} +(0.610004 - 1.05656i) q^{6} +2.06113 q^{8} -2.69799 q^{9} +9.36845 q^{10} -0.549551 q^{11} +(0.804662 + 1.39372i) q^{12} +(2.95900 + 2.06017i) q^{13} +(1.15956 + 2.00841i) q^{15} +(0.640570 - 1.10950i) q^{16} +(-1.18944 - 2.06017i) q^{17} +(2.99478 - 5.18712i) q^{18} +3.61068 q^{19} +(-6.17901 + 10.7024i) q^{20} +(0.610004 - 1.05656i) q^{22} +(-2.90945 + 5.03931i) q^{23} -1.13270 q^{24} +(-6.40423 + 11.0925i) q^{25} +(-7.24536 + 3.40212i) q^{26} +3.13134 q^{27} +(1.79945 + 3.11673i) q^{29} -5.14844 q^{30} +(-2.57422 + 4.45868i) q^{31} +(3.48320 + 6.03308i) q^{32} +0.302006 q^{33} +5.28114 q^{34} +(3.95045 + 6.84238i) q^{36} +(0.164772 - 0.285393i) q^{37} +(-4.00787 + 6.94184i) q^{38} +(-1.62612 - 1.13217i) 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} +(5.69278 + 9.86018i) q^{45} +(-6.45900 - 11.1873i) 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} +(0.892184 - 10.5209i) q^{52} +(-1.32933 + 2.30247i) q^{53} +(-3.47580 + 6.02026i) q^{54} +(1.15956 + 2.00841i) q^{55} -1.98426 q^{57} -7.98957 q^{58} +(-0.903765 - 1.56537i) q^{59} +(3.39568 - 5.88149i) q^{60} -0.609325 q^{61} +(-5.71479 - 9.89831i) q^{62} -12.9032 q^{64} +(1.28568 - 15.1610i) q^{65} +(-0.335228 + 0.580633i) q^{66} +10.3698 q^{67} +(-3.48320 + 6.03308i) q^{68} +(1.59889 - 2.76936i) q^{69} +(5.59889 - 9.69756i) q^{71} -5.56092 q^{72} +(2.45310 - 4.24890i) q^{73} +(0.365794 + 0.633574i) q^{74} +(3.51945 - 6.09587i) q^{75} +(-5.28682 - 9.15705i) q^{76} +(3.98169 - 1.86964i) q^{78} +(7.00855 + 12.1392i) q^{79} -5.40642 q^{80} +6.37315 q^{81} +13.9673 q^{82} +5.73159 q^{83} +(-5.01945 + 8.69395i) q^{85} +(-3.57422 - 6.19073i) q^{86} +(-0.988887 - 1.71280i) q^{87} -1.13270 q^{88} +(-3.73378 + 6.46709i) q^{89} -25.2760 q^{90} +17.0403 q^{92} +(1.41467 - 2.45027i) q^{93} -18.2253 q^{94} +(-7.61856 - 13.1957i) 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 + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9} + 22 q^{10} - 2 q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} + 3 q^{18} - 2 q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23}+ \cdots + 46 q^{99}+O(q^{100}) $ 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9 + 22 * q^10 - 2 * q^11 + 12 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 + 3 * q^18 - 2 * q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 + 6 * q^24 - 5 * q^25 - 3 * q^26 + 52 * q^27 - q^29 - 8 * q^30 - 4 * q^31 + 33 * q^32 + 38 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 - 23 * q^38 - 19 * q^39 - 17 * q^40 - 22 * q^41 - 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 + 11 * q^48 - 43 * q^50 - 7 * q^51 + 34 * q^52 - 2 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 - 22 * q^58 - 8 * q^59 + 11 * q^60 - 16 * q^61 - 5 * q^62 + 28 * q^64 + 4 * q^65 + 6 * q^66 - 12 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 + 10 * q^72 - 8 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 + 26 * q^79 - 14 * q^80 + 48 * q^81 + 28 * q^82 - 5 * q^85 - 12 * q^86 + 13 * q^87 + 6 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 - 66 * q^94 - 21 * q^95 - 58 * q^96 + 3 * q^97 + 46 * q^99

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.11000	+	1.92258i	−0.784891	+	1.35947i	0.144173	+	0.989553i	$0.453948\pi$
$2$	−1.11000	+	1.92258i	−0.784891	+	1.35947i	−0.929064	+	0.369919i	$0.879385\pi$
$3$	−0.549551			−0.317283			−0.158642	−	0.987336i	$-0.550711\pi$
$3$	−0.549551			−0.317283			−0.158642	+	0.987336i	$0.550711\pi$
$4$	−1.46422	−	2.53610i	−0.732109	−	1.26805i
$5$	−2.11000	−	3.65463i	−0.943622	−	1.63440i	−0.758486	−	0.651689i	$-0.774061\pi$
$5$	−2.11000	−	3.65463i	−0.943622	−	1.63440i	−0.185136	−	0.982713i	$-0.559273\pi$
$6$	0.610004	−	1.05656i	0.249033	−	0.431338i
$7$		0			0
$7$		0			0
$8$	2.06113			0.728720
$9$	−2.69799			−0.899331
$10$	9.36845			2.96256
$11$	−0.549551			−0.165696			−0.0828480	−	0.996562i	$-0.526402\pi$
$11$	−0.549551			−0.165696			−0.0828480	+	0.996562i	$0.526402\pi$
$12$	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
$16$	0.640570	−	1.10950i	0.160142	−	0.277375i
$17$	−1.18944	−	2.06017i	−0.288482	−	0.499665i	0.684966	−	0.728575i	$-0.259817\pi$
$17$	−1.18944	−	2.06017i	−0.288482	−	0.499665i	−0.973448	+	0.228910i	$0.926484\pi$
$18$	2.99478	−	5.18712i	0.705877	−	1.22262i
$19$	3.61068			0.828348			0.414174	−	0.910198i	$-0.364071\pi$
$19$	3.61068			0.828348			0.414174	+	0.910198i	$0.364071\pi$
$20$	−6.17901	+	10.7024i	−1.38167	+	2.39312i
$21$		0			0
$22$	0.610004	−	1.05656i	0.130053	−	0.225259i
$23$	−2.90945	+	5.03931i	−0.606662	+	1.05077i	0.385124	+	0.922865i	$0.374159\pi$
$23$	−2.90945	+	5.03931i	−0.606662	+	1.05077i	−0.991786	+	0.127905i	$0.959175\pi$
$24$	−1.13270			−0.231211
$25$	−6.40423	+	11.0925i	−1.28085	+	2.21849i
$26$	−7.24536	+	3.40212i	−1.42093	+	0.667211i
$27$	3.13134			0.602626
$28$		0			0
$29$	1.79945	+	3.11673i	0.334149	+	0.578762i	0.983321	−	0.181879i	$-0.0582179\pi$
$29$	1.79945	+	3.11673i	0.334149	+	0.578762i	−0.649172	+	0.760641i	$0.724885\pi$
$30$	−5.14844			−0.939973
$31$	−2.57422	+	4.45868i	−0.462344	+	0.800803i	−0.999077	−	0.0429489i	$-0.986325\pi$
$31$	−2.57422	+	4.45868i	−0.462344	+	0.800803i	0.536733	+	0.843752i	$0.319658\pi$
$32$	3.48320	+	6.03308i	0.615749	+	1.06651i
$33$	0.302006			0.0525726
$34$	5.28114			0.905708
$35$		0			0
$36$	3.95045	+	6.84238i	0.658408	+	1.14040i
$37$	0.164772	−	0.285393i	0.0270883	−	0.0469183i	−0.852163	−	0.523276i	$-0.824710\pi$
$37$	0.164772	−	0.285393i	0.0270883	−	0.0469183i	0.879252	+	0.476357i	$0.158043\pi$
$38$	−4.00787	+	6.94184i	−0.650163	+	1.12611i
$39$	−1.62612	−	1.13217i	−0.260388	−	0.181292i
$40$	−4.34900	−	7.53268i	−0.687637	−	1.19102i
$41$	−3.14579	−	5.44866i	−0.491289	−	0.850938i	0.508660	−	0.860967i	$-0.330141\pi$
$41$	−3.14579	−	5.44866i	−0.491289	−	0.850938i	−0.999950	+	0.0100292i	$0.996808\pi$
$42$		0			0
$43$	−1.61000	+	2.78861i	−0.245523	+	0.425259i	−0.962279	−	0.272066i	$-0.912293\pi$
$43$	−1.61000	+	2.78861i	−0.245523	+	0.425259i	0.716755	+	0.697325i	$0.245626\pi$
$44$	0.804662	+	1.39372i	0.121307	+	0.210111i
$45$	5.69278	+	9.86018i	0.848629	+	1.46987i
$46$	−6.45900	−	11.1873i	−0.952328	−	1.64948i
$47$	4.10479	+	7.10970i	0.598745	+	1.03706i	0.993007	+	0.118058i	$0.0376669\pi$
$47$	4.10479	+	7.10970i	0.598745	+	1.03706i	−0.394262	+	0.918998i	$0.629000\pi$
$48$	−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
$52$	0.892184	−	10.5209i	0.123724	−	1.45898i
$53$	−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	$0.225117\pi$
$54$	−3.47580	+	6.02026i	−0.472996	+	0.819254i
$55$	1.15956	+	2.00841i	0.156354	+	0.270814i
$56$		0			0
$57$	−1.98426			−0.262821
$58$	−7.98957			−1.04908
$59$	−0.903765	−	1.56537i	−0.117660	−	0.203793i	0.801180	−	0.598424i	$-0.204206\pi$
$59$	−0.903765	−	1.56537i	−0.117660	−	0.203793i	−0.918840	+	0.394630i	$0.870873\pi$
$60$	3.39568	−	5.88149i	0.438381	−	0.759297i
$61$	−0.609325			−0.0780160			−0.0390080	−	0.999239i	$-0.512420\pi$
$61$	−0.609325			−0.0780160			−0.0390080	+	0.999239i	$0.512420\pi$
$62$	−5.71479	−	9.89831i	−0.725779	−	1.25709i
$63$		0			0
$64$	−12.9032			−1.61290
$65$	1.28568	−	15.1610i	0.159469	−	1.88050i
$66$	−0.335228	+	0.580633i	−0.0412638	+	0.0714709i
$67$	10.3698			1.26687			0.633437	−	0.773794i	$-0.281644\pi$
$67$	10.3698			1.26687			0.633437	+	0.773794i	$0.281644\pi$
$68$	−3.48320	+	6.03308i	−0.422400	+	0.731619i
$69$	1.59889	−	2.76936i	0.192484	−	0.333392i
$70$		0			0
$71$	5.59889	−	9.69756i	0.664466	−	1.15089i	−0.314964	−	0.949104i	$-0.601992\pi$
$71$	5.59889	−	9.69756i	0.664466	−	1.15089i	0.979430	−	0.201785i	$-0.0646743\pi$
$72$	−5.56092			−0.655361
$73$	2.45310	−	4.24890i	0.287114	−	0.497296i	−0.686005	−	0.727596i	$-0.740637\pi$
$73$	2.45310	−	4.24890i	0.287114	−	0.497296i	0.973120	+	0.230300i	$0.0739707\pi$
$74$	0.365794	+	0.633574i	0.0425227	+	0.0736515i
$75$	3.51945	−	6.09587i	0.406391	−	0.703891i
$76$	−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	$0.544179\pi$
$80$	−5.40642			−0.604456
$81$	6.37315			0.708128
$82$	13.9673			1.54243
$83$	5.73159			0.629124			0.314562	−	0.949237i	$-0.398142\pi$
$83$	5.73159			0.629124			0.314562	+	0.949237i	$0.398142\pi$
$84$		0			0
$85$	−5.01945	+	8.69395i	−0.544436	+	0.942991i
$86$	−3.57422	−	6.19073i	−0.385418	−	0.667564i
$87$	−0.988887	−	1.71280i	−0.106020	−	0.183632i
$88$	−1.13270			−0.120746
$89$	−3.73378	+	6.46709i	−0.395779	+	0.685510i	−0.993200	−	0.116418i	$-0.962859\pi$
$89$	−3.73378	+	6.46709i	−0.395779	+	0.685510i	0.597421	+	0.801928i	$0.296192\pi$
$90$	−25.2760			−2.66433
$91$		0			0
$92$	17.0403			1.77657
$93$	1.41467	−	2.45027i	0.146694	−	0.254082i
$94$	−18.2253			−1.87980
$95$	−7.61856	−	13.1957i	−0.781647	−	1.35385i
$96$	−1.91420	−	3.31549i	−0.195367	−	0.338386i
$97$	−3.42035	+	5.92422i	−0.347284	+	0.601514i	−0.985766	−	0.168123i	$-0.946229\pi$
$97$	−3.42035	+	5.92422i	−0.347284	+	0.601514i	0.638482	+	0.769637i	$0.279563\pi$
$98$		0			0
$99$	1.48269			0.149015
$100$	37.5088			3.75088
$101$	−5.75913			−0.573054			−0.286527	−	0.958072i	$-0.592501\pi$
$101$	−5.75913			−0.573054			−0.286527	+	0.958072i	$0.592501\pi$
$102$	−2.90226			−0.287366
$103$	0.285888	+	0.495173i	0.0281694	+	0.0487908i	0.879766	−	0.475406i	$-0.157699\pi$
$103$	0.285888	+	0.495173i	0.0281694	+	0.0487908i	−0.851597	+	0.524197i	$0.824366\pi$
$104$	6.09889	+	4.24629i	0.598045	+	0.416383i
$105$		0			0
$106$	−2.95113	−	5.11150i	−0.286639	−	0.496473i
$107$	−2.03578	+	3.52608i	−0.196807	+	0.340879i	−0.947491	−	0.319782i	$-0.896390\pi$
$107$	−2.03578	+	3.52608i	−0.196807	+	0.340879i	0.750685	+	0.660661i	$0.229724\pi$
$108$	−4.58496	−	7.94138i	−0.441188	−	0.764160i
$109$	−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	$0.904715\pi$
$110$	−5.14844			−0.490885
$111$	−0.0905505	+	0.156838i	−0.00859467	+	0.0148864i
$112$		0			0
$113$	−6.08846	+	10.5455i	−0.572754	+	0.992039i	0.423528	+	0.905883i	$0.360792\pi$
$113$	−6.08846	+	10.5455i	−0.572754	+	0.992039i	−0.996282	+	0.0861558i	$0.972542\pi$
$114$	2.20253	−	3.81490i	0.206286	−	0.357298i
$115$	24.5558			2.28984
$116$	5.26956	−	9.12714i	0.489266	−	0.847434i
$117$	−7.98336	−	5.55833i	−0.738062	−	0.513868i
$118$	4.01273			0.369402
$119$		0			0
$120$	2.39000	+	4.13959i	0.218176	+	0.377892i
$121$	−10.6980			−0.972545
$122$	0.676353	−	1.17148i	0.0612341	−	0.106061i
$123$	1.72877	+	2.99432i	0.155878	+	0.269989i
$124$	15.0769			1.35394
$125$	32.9518			2.94730
$126$		0			0
$127$	−0.980336	−	1.69799i	−0.0869907	−	0.150672i	0.819247	−	0.573441i	$-0.194392\pi$
$127$	−0.980336	−	1.69799i	−0.0869907	−	0.150672i	−0.906238	+	0.422768i	$0.861058\pi$
$128$	7.35619	−	12.7413i	0.650201	−	1.12618i
$129$	0.884779	−	1.53248i	0.0779005	−	0.134928i
$130$	27.7213	+	19.3006i	2.43131	+	1.69278i
$131$	−3.25011	−	5.62935i	−0.283963	−	0.491838i	0.688394	−	0.725337i	$-0.258316\pi$
$131$	−3.25011	−	5.62935i	−0.283963	−	0.491838i	−0.972357	+	0.233498i	$0.924983\pi$
$132$	−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
$136$	−2.45160	−	4.24629i	−0.210223	−	0.364116i
$137$	7.62878	+	13.2134i	0.651770	+	1.12890i	0.982693	+	0.185242i	$0.0593068\pi$
$137$	7.62878	+	13.2134i	0.651770	+	1.12890i	−0.330923	+	0.943658i	$0.607360\pi$
$138$	3.54955	+	6.14800i	0.302158	+	0.523353i
$139$	−8.74801	+	15.1520i	−0.741997	+	1.28518i	0.209588	+	0.977790i	$0.432788\pi$
$139$	−8.74801	+	15.1520i	−0.741997	+	1.28518i	−0.951585	+	0.307386i	$0.900546\pi$
$140$		0			0
$141$	−2.25579	−	3.90714i	−0.189972	−	0.329041i
$142$	12.4296	+	21.5287i	1.04307	+	1.80665i
$143$	−1.62612	−	1.13217i	−0.135983	−	0.0946769i
$144$	−1.72825	+	2.99342i	−0.144021	+	0.249452i
$145$	7.59367	−	13.1526i	0.630620	−	1.09227i
$146$	5.44591	+	9.43260i	0.450707	+	0.780647i
$147$		0			0
$148$	−0.965046			−0.0793263
$149$	4.55486			0.373149			0.186574	−	0.982441i	$-0.440261\pi$
$149$	4.55486			0.373149			0.186574	+	0.982441i	$0.440261\pi$
$150$	7.81321	+	13.5329i	0.637946	+	1.10496i
$151$	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	$0.0837586\pi$
$152$	7.44210			0.603634
$153$	3.20911	+	5.55833i	0.259441	+	0.449365i
$154$		0			0
$155$	21.7265			1.74511
$156$	−0.490300	+	5.78175i	−0.0392555	+	0.462911i
$157$	8.15502	−	14.1249i	0.650841	−	1.12729i	−0.332078	−	0.943252i	$-0.607750\pi$
$157$	8.15502	−	14.1249i	0.650841	−	1.12729i	0.982919	−	0.184038i	$-0.0589170\pi$
$158$	−31.1181			−2.47562
$159$	0.730536	−	1.26533i	0.0579353	−	0.100347i
$160$	14.6991	−	25.4597i	1.16207	−	2.01276i
$161$		0			0
$162$	−7.07422	+	12.2529i	−0.555803	+	0.962680i
$163$	23.5998			1.84848			0.924241	−	0.381811i	$-0.124699\pi$
$163$	23.5998			1.84848			0.924241	+	0.381811i	$0.124699\pi$
$164$	−9.21223	+	15.9561i	−0.719354	+	1.24596i
$165$	−0.637235	−	1.10372i	−0.0496087	−	0.0859247i
$166$	−6.36209	+	11.0195i	−0.493794	+	0.855276i
$167$	−8.91513	−	15.4415i	−0.689874	−	1.19490i	−0.971878	−	0.235483i	$-0.924333\pi$
$167$	−8.91513	−	15.4415i	−0.689874	−	1.19490i	0.282005	−	0.959413i	$-0.409001\pi$
$168$		0			0
$169$	4.51137	+	12.1921i	0.347028	+	0.937855i
$170$	−11.1432	−	19.3006i	−0.854646	−	1.48029i
$171$	−9.74160			−0.744959
$172$	9.42958			0.718999
$173$	7.57135			0.575639			0.287820	−	0.957685i	$-0.407070\pi$
$173$	7.57135			0.575639			0.287820	+	0.957685i	$0.407070\pi$
$174$	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
$178$	−8.28901	−	14.3570i	−0.621288	−	1.07610i
$179$	−22.8033			−1.70440			−0.852201	−	0.523215i	$-0.824733\pi$
$179$	−22.8033			−1.70440			−0.852201	+	0.523215i	$0.824733\pi$
$180$	16.6709	−	28.8749i	1.24258	−	2.15221i
$181$	−13.9294			−1.03536			−0.517681	−	0.855574i	$-0.673205\pi$
$181$	−13.9294			−1.03536			−0.517681	+	0.855574i	$0.673205\pi$
$182$		0			0
$183$	0.334855			0.0247532
$184$	−5.99676	+	10.3867i	−0.442087	+	0.765717i
$185$	−1.39068			−0.102244
$186$	3.14057	+	5.43963i	0.230278	+	0.398853i
$187$	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
$191$	−12.6718			−0.916900			−0.458450	−	0.888720i	$-0.651595\pi$
$191$	−12.6718			−0.916900			−0.458450	+	0.888720i	$0.651595\pi$
$192$	7.09096			0.511746
$193$	−4.15492			−0.299078			−0.149539	−	0.988756i	$-0.547779\pi$
$193$	−4.15492			−0.299078			−0.149539	+	0.988756i	$0.547779\pi$
$194$	−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	0.961858	−	0.273549i	$-0.0881977\pi$
$197$	3.42510	+	5.93245i	0.244028	+	0.422669i	−0.717830	+	0.696219i	$0.754864\pi$
$198$	−1.64579	+	2.85059i	−0.116961	+	0.202582i
$199$	−0.406794	−	0.704587i	−0.0288368	−	0.0499469i	0.851247	−	0.524766i	$-0.175847\pi$
$199$	−0.406794	−	0.704587i	−0.0288368	−	0.0499469i	−0.880084	+	0.474819i	$0.842514\pi$
$200$	−13.2000	+	22.8630i	−0.933379	+	1.61666i
$201$	−5.69874			−0.401958
$202$	6.39265	−	11.0724i	0.449785	−	0.779051i
$203$		0			0
$204$	1.91420	−	3.31549i	0.134021	−	0.232131i
$205$	−13.2752	+	22.9934i	−0.927183	+	1.60593i
$206$	−1.26935			−0.0884397
$207$	7.84968	−	13.5960i	0.545590	−	0.944990i
$208$	4.18121	−	1.96333i	0.289915	−	0.136132i
$209$	−1.98426			−0.137254
$210$		0			0
$211$	6.98670	+	12.1013i	0.480984	+	0.833089i	0.999762	−	0.0218200i	$-0.00694608\pi$
$211$	6.98670	+	12.1013i	0.480984	+	0.833089i	−0.518778	+	0.854909i	$0.673613\pi$
$212$	7.78573			0.534726
$213$	−3.07688	+	5.32931i	−0.210824	+	0.365158i
$214$	−4.51945	−	7.82792i	−0.308943	−	0.535106i
$215$	13.5885			0.926725
$216$	6.45410			0.439146
$217$		0			0
$218$	−16.9927	−	29.4322i	−1.15089	−	1.99340i
$219$	−1.34811	+	2.33499i	−0.0910966	+	0.157784i
$220$	3.39568	−	5.88149i	0.228937	−	0.396530i
$221$	0.724756	−	8.54651i	0.0487524	−	0.574901i
$222$	−0.201023	−	0.348182i	−0.0134918	−	0.0233684i
$223$	−6.76700	−	11.7208i	−0.453152	−	0.784882i	0.545428	−	0.838158i	$-0.316367\pi$
$223$	−6.76700	−	11.7208i	−0.453152	−	0.784882i	−0.998580	+	0.0532758i	$0.983034\pi$
$224$		0			0
$225$	17.2786	−	29.9274i	1.15191	−	1.99516i
$226$	−13.5164	−	23.4111i	−0.899099	−	1.55729i
$227$	−2.68376	−	4.64840i	−0.178127	−	0.308525i	0.763112	−	0.646266i	$-0.223671\pi$
$227$	−2.68376	−	4.64840i	−0.178127	−	0.308525i	−0.941239	+	0.337741i	$0.890337\pi$
$228$	2.90538	+	5.03227i	0.192414	+	0.333270i
$229$	1.54955	+	2.68390i	0.102397	+	0.177357i	0.912672	−	0.408693i	$-0.134015\pi$
$229$	1.54955	+	2.68390i	0.102397	+	0.177357i	−0.810275	+	0.586050i	$0.800682\pi$
$230$	−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	$0.600792\pi$
$234$	19.5479	−	9.17891i	1.27789	−	0.600044i
$235$	17.3222	−	30.0030i	1.12998	−	1.95718i
$236$	−2.64662	+	4.58407i	−0.172280	+	0.298398i
$237$	−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	$0.513300\pi$
$240$	2.97110			0.191784
$241$	1.06635	+	1.84697i	0.0686896	+	0.118974i	0.898325	−	0.439332i	$-0.144785\pi$
$241$	1.06635	+	1.84697i	0.0686896	+	0.118974i	−0.829635	+	0.558306i	$0.811452\pi$
$242$	11.8748	−	20.5678i	0.763342	−	1.32215i
$243$	−12.8964			−0.827304
$244$	0.892184	+	1.54531i	0.0571162	+	0.0989282i
$245$		0			0
$246$	−7.67577			−0.489389
$247$	10.6840	+	7.43863i	0.679808	+	0.473309i
$248$	−5.30581	+	9.18993i	−0.336919	+	0.583561i
$249$	−3.14980			−0.199611
$250$	−36.5766	+	63.3525i	−2.31331	+	4.00677i
$251$	−15.3856	+	26.6486i	−0.971128	+	1.68204i	−0.278964	+	0.960302i	$0.589991\pi$
$251$	−15.3856	+	26.6486i	−0.971128	+	1.68204i	−0.692164	+	0.721741i	$0.743342\pi$
$252$		0			0
$253$	1.59889	−	2.76936i	0.100521	−	0.174108i
$254$	4.35271			0.273113
$255$	2.75845	−	4.77777i	0.172741	−	0.299196i
$256$	3.42761	+	5.93679i	0.214225	+	0.371049i
$257$	−0.736805	+	1.27618i	−0.0459607	+	0.0796062i	−0.888091	−	0.459669i	$-0.847968\pi$
$257$	−0.736805	+	1.27618i	−0.0459607	+	0.0796062i	0.842130	+	0.539275i	$0.181302\pi$
$258$	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
$262$	14.4305			0.891520
$263$	6.67694			0.411718			0.205859	−	0.978582i	$-0.434001\pi$
$263$	6.67694			0.411718			0.205859	+	0.978582i	$0.434001\pi$
$264$	0.622475			0.0383107
$265$	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
$269$	3.78786	+	6.56077i	0.230950	+	0.400017i	0.958088	−	0.286474i	$-0.0924832\pi$
$269$	3.78786	+	6.56077i	0.230950	+	0.400017i	−0.727138	+	0.686492i	$0.759150\pi$
$270$	29.3358			1.78532
$271$	10.2840	−	17.8124i	0.624709	−	1.08203i	−0.363888	−	0.931443i	$-0.618551\pi$
$271$	10.2840	−	17.8124i	0.624709	−	1.08203i	0.988597	−	0.150585i	$-0.0481157\pi$
$272$	−3.04768			−0.184793
$273$		0			0
$274$	−33.8719			−2.04628
$275$	3.51945	−	6.09587i	0.212231	−	0.367595i
$276$	−9.36450			−0.563676
$277$	−2.85271	−	4.94103i	−0.171402	−	0.296878i	0.767508	−	0.641039i	$-0.221497\pi$
$277$	−2.85271	−	4.94103i	−0.171402	−	0.296878i	−0.938910	+	0.344162i	$0.888163\pi$
$278$	−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	$0.560880\pi$
$282$	10.0157			0.596429
$283$	−27.0194			−1.60614			−0.803068	−	0.595887i	$-0.796801\pi$
$283$	−27.0194			−1.60614			−0.803068	+	0.595887i	$0.796801\pi$
$284$	−32.7920			−1.94585
$285$	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
$289$	5.67046	−	9.82152i	0.333556	−	0.577736i
$290$	16.8580	+	29.1989i	0.989937	+	1.71462i
$291$	1.87966	−	3.25566i	0.110187	−	0.190850i
$292$	−14.3675			−0.840795
$293$	−2.43736	+	4.22163i	−0.142392	+	0.246630i	−0.928397	−	0.371590i	$-0.878813\pi$
$293$	−2.43736	+	4.22163i	−0.142392	+	0.246630i	0.786005	+	0.618220i	$0.212146\pi$
$294$		0			0
$295$	−3.81389	+	6.60586i	−0.222053	+	0.384608i
$296$	0.339616	−	0.588232i	0.0197398	−	0.0341903i
$297$	−1.72083			−0.0998527
$298$	−5.05592	+	8.75710i	−0.292881	+	0.507285i
$299$	−18.9909	+	8.91736i	−1.09827	+	0.515704i
$300$	−20.6130			−1.19009
$301$		0			0
$302$	7.02535	+	12.1683i	0.404263	+	0.700205i
$303$	3.16493			0.181821
$304$	2.31290	−	4.00605i	0.132654	−	0.229763i
$305$	1.28568	+	2.22686i	0.0736177	+	0.127510i
$306$	−14.2485			−0.814531
$307$	−16.1760			−0.923212			−0.461606	−	0.887085i	$-0.652727\pi$
$307$	−16.1760			−0.923212			−0.461606	+	0.887085i	$0.652727\pi$
$308$		0			0
$309$	−0.157110	−	0.272123i	−0.00893769	−	0.0154805i
$310$	−24.1165	+	41.7709i	−1.36972	+	2.37243i
$311$	−0.654032	+	1.13282i	−0.0370868	+	0.0642362i	−0.883973	−	0.467538i	$-0.845141\pi$
$311$	−0.654032	+	1.13282i	−0.0370868	+	0.0642362i	0.846886	+	0.531774i	$0.178474\pi$
$312$	−3.35165	−	2.33355i	−0.189750	−	0.132111i
$313$	6.59889	+	11.4296i	0.372991	+	0.646040i	0.990024	−	0.140897i	$-0.0449988\pi$
$313$	6.59889	+	11.4296i	0.372991	+	0.646040i	−0.617033	+	0.786937i	$0.711665\pi$
$314$	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	$0.760512\pi$
$318$	1.62180	+	2.80903i	0.0909458	+	0.157523i
$319$	−0.988887	−	1.71280i	−0.0553671	−	0.0958986i
$320$	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
$325$	−41.8025	+	19.6288i	−2.31879	+	1.08881i
$326$	−26.1959	+	45.3726i	−1.45086	+	2.51296i
$327$	4.20645	−	7.28579i	0.232617	−	0.402905i
$328$	−6.48388	−	11.2304i	−0.358012	−	0.620096i
$329$		0			0
$330$	2.82933			0.155750
$331$	−14.9451			−0.821458			−0.410729	−	0.911757i	$-0.634726\pi$
$331$	−14.9451			−0.821458			−0.410729	+	0.911757i	$0.634726\pi$
$332$	−8.39229	−	14.5359i	−0.460587	−	0.797760i
$333$	−0.444553	+	0.769988i	−0.0243613	+	0.0421951i
$334$	39.5833			2.16590
$335$	−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	$0.654896\pi$
$338$	−28.4480	−	4.85981i	−1.54737	−	0.264339i
$339$	3.34592	−	5.79530i	0.181725	−	0.314758i
$340$	29.3983			1.59435
$341$	1.41467	−	2.45027i	0.0766085	−	0.132690i
$342$	10.8132	−	18.7290i	0.584712	−	1.01275i
$343$		0			0
$344$	−3.31843	+	5.74769i	−0.178918	+	0.309895i
$345$	−13.4947			−0.726528
$346$	−8.40423	+	14.5566i	−0.451814	+	0.782565i
$347$	1.96922	+	3.41079i	0.105713	+	0.183101i	0.914029	−	0.405648i	$-0.132954\pi$
$347$	1.96922	+	3.41079i	0.105713	+	0.183101i	−0.808316	+	0.588749i	$0.799621\pi$
$348$	−2.89589	+	5.01583i	−0.155236	+	0.268877i
$349$	8.58883	+	14.8763i	0.459750	+	0.796310i	0.998947	−	0.0458695i	$-0.0146058\pi$
$349$	8.58883	+	14.8763i	0.459750	+	0.796310i	−0.539198	+	0.842179i	$0.681272\pi$
$350$		0			0
$351$	9.26563	+	6.45110i	0.494563	+	0.344334i
$352$	−1.91420	−	3.31549i	−0.102027	−	0.176716i
$353$	18.1964			0.968498			0.484249	−	0.874930i	$-0.339093\pi$
$353$	18.1964			0.968498			0.484249	+	0.874930i	$0.339093\pi$
$354$	−2.20520			−0.117205
$355$	−47.2547			−2.50802
$356$	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	$0.974987\pi$
$360$	11.7336	+	20.3231i	0.618413	+	1.07112i
$361$	−5.96297			−0.313840
$362$	15.4617	−	26.7804i	0.812647	−	1.40755i
$363$	5.87909			0.308572
$364$		0			0
$365$	−20.7042			−1.08371
$366$	−0.371690	+	0.643787i	−0.0194286	+	0.0336513i
$367$	36.1963			1.88943			0.944716	−	0.327889i	$-0.106337\pi$
$367$	36.1963			1.88943			0.944716	+	0.327889i	$0.106337\pi$
$368$	3.72741	+	6.45607i	0.194305	+	0.336546i
$369$	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
$373$	9.79784			0.507313			0.253657	−	0.967294i	$-0.418367\pi$
$373$	9.79784			0.507313			0.253657	+	0.967294i	$0.418367\pi$
$374$	−2.90226			−0.150072
$375$	−18.1087			−0.935129
$376$	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	0.648028	−	0.761616i	$-0.275594\pi$
$379$	−6.53275	−	11.3151i	−0.335565	−	0.581216i	−0.983593	+	0.180401i	$0.942261\pi$
$380$	−22.3104	+	38.6428i	−1.14450	+	1.98233i
$381$	0.538745	+	0.933133i	0.0276007	+	0.0478058i
$382$	14.0658	−	24.3626i	0.719667	−	1.24650i
$383$	−27.7929			−1.42015			−0.710076	−	0.704125i	$-0.751339\pi$
$383$	−27.7929			−1.42015			−0.710076	+	0.704125i	$0.751339\pi$
$384$	−4.04260	+	7.00199i	−0.206298	+	0.357319i
$385$		0			0
$386$	4.61198	−	7.98818i	0.234744	−	0.406588i
$387$	4.34378	−	7.52365i	0.220807	−	0.382449i
$388$	20.0325			1.01700
$389$	−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	$0.279611\pi$
$390$	−15.2342	−	10.6067i	−0.771416	−	0.537090i
$391$	13.8425			0.700044
$392$		0			0
$393$	1.78610	+	3.09361i	0.0900968	+	0.156052i
$394$	−15.2075			−0.766143
$395$	29.5761	−	51.2274i	1.48814	−	2.57753i
$396$	−2.17097	−	3.76024i	−0.109096	−	0.188959i
$397$	−7.91194			−0.397089			−0.198545	−	0.980092i	$-0.563621\pi$
$397$	−7.91194			−0.397089			−0.198545	+	0.980092i	$0.563621\pi$
$398$	1.80617			0.0905351
$399$		0			0
$400$	8.20472	+	14.2110i	0.410236	+	0.710549i
$401$	8.27212	−	14.3277i	0.413090	−	0.715493i	−0.582136	−	0.813092i	$-0.697783\pi$
$401$	8.27212	−	14.3277i	0.413090	−	0.715493i	0.995226	+	0.0975987i	$0.0311162\pi$
$402$	6.32562	−	10.9563i	0.315493	−	0.546451i
$403$	−16.8028	+	7.88990i	−0.837006	+	0.393024i
$404$	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
$409$	12.8909	+	22.3278i	0.637416	+	1.10404i	0.985998	+	0.166758i	$0.0533299\pi$
$409$	12.8909	+	22.3278i	0.637416	+	1.10404i	−0.348582	+	0.937278i	$0.613337\pi$
$410$	−29.4711	−	51.0455i	−1.45548	−	2.52096i
$411$	−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
$416$	−2.12240	+	25.0279i	−0.104059	+	1.22709i
$417$	4.80748	−	8.32680i	0.235423	−	0.407765i
$418$	2.20253	−	3.81490i	0.107729	−	0.186593i
$419$	11.8436	+	20.5137i	0.578596	+	1.00216i	0.995641	+	0.0932720i	$0.0297326\pi$
$419$	11.8436	+	20.5137i	0.578596	+	1.00216i	−0.417044	+	0.908886i	$0.636934\pi$
$420$		0			0
$421$	−20.8246			−1.01493			−0.507465	−	0.861672i	$-0.669417\pi$
$421$	−20.8246			−1.01493			−0.507465	+	0.861672i	$0.669417\pi$
$422$	−31.0211			−1.51008
$423$	−11.0747	−	19.1819i	−0.538470	−	0.932657i
$424$	−2.73993	+	4.74570i	−0.133063	+	0.230471i
$425$	30.4698			1.47800
$426$	−6.83069	−	11.8311i	−0.330948	−	0.573219i
$427$		0			0
$428$	11.9233			0.576335
$429$	0.893637	+	0.622186i	0.0431452	+	0.0300394i
$430$	−15.0832	+	26.1249i	−0.727378	+	1.25986i
$431$	19.9504			0.960978			0.480489	−	0.877001i	$-0.340459\pi$
$431$	19.9504			0.960978			0.480489	+	0.877001i	$0.340459\pi$
$432$	2.00584	−	3.47422i	0.0965061	−	0.167153i
$433$	0.00834083	−	0.0144467i	0.000400835	−	0.000694266i	−0.865825	−	0.500347i	$-0.833206\pi$
$433$	0.00834083	−	0.0144467i	0.000400835	−	0.000694266i	0.866226	+	0.499653i	$0.166539\pi$
$434$		0			0
$435$	−4.17311	+	7.22804i	−0.200085	+	0.346558i
$436$	44.8305			2.14699
$437$	−10.5051	+	18.1954i	−0.502527	+	0.870402i
$438$	−2.99281	−	5.18369i	−0.143002	−	0.247686i
$439$	6.74801	−	11.6879i	0.322065	−	0.557833i	−0.658849	−	0.752275i	$-0.728956\pi$
$439$	6.74801	−	11.6879i	0.322065	−	0.557833i	0.980914	+	0.194442i	$0.0622897\pi$
$440$	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	$0.717270\pi$
$444$	0.530342			0.0251689
$445$	31.5131			1.49387
$446$	30.0456			1.42270
$447$	−2.50313			−0.118394
$448$		0			0
$449$	11.8918	−	20.5972i	0.561210	−	0.972044i	−0.436181	−	0.899859i	$-0.643669\pi$
$449$	11.8918	−	20.5972i	0.561210	−	0.972044i	0.997391	−	0.0721852i	$-0.0229973\pi$
$450$	38.3586	+	66.4390i	1.80824	+	3.13196i
$451$	1.72877	+	2.99432i	0.0814046	+	0.140997i
$452$	35.6593			1.67727
$453$	−1.73909	+	3.01219i	−0.0817095	+	0.141525i
$454$	11.9159			0.559242
$455$		0			0
$456$	−4.08981			−0.191523
$457$	−9.06567	+	15.7022i	−0.424074	+	0.734518i	−0.996333	−	0.0855548i	$-0.972734\pi$
$457$	−9.06567	+	15.7022i	−0.424074	+	0.734518i	0.572259	+	0.820073i	$0.306067\pi$
$458$	−6.88003			−0.321483
$459$	−3.72455	−	6.45110i	−0.173847	−	0.301112i
$460$	−35.9550	−	62.2759i	−1.67641	−	2.90363i
$461$	−3.03980	+	5.26508i	−0.141577	+	0.245219i	−0.928091	−	0.372354i	$-0.878551\pi$
$461$	−3.03980	+	5.26508i	−0.141577	+	0.245219i	0.786513	+	0.617573i	$0.211884\pi$
$462$		0			0
$463$	5.19289			0.241334			0.120667	−	0.992693i	$-0.461497\pi$
$463$	5.19289			0.241334			0.120667	+	0.992693i	$0.461497\pi$
$464$	4.61068			0.214046
$465$	−11.9398			−0.553695
$466$	−45.2242			−2.09497
$467$	−4.34984	−	7.53414i	−0.201287	−	0.348638i	0.747657	−	0.664085i	$-0.231179\pi$
$467$	−4.34984	−	7.53414i	−0.201287	−	0.348638i	−0.948943	+	0.315447i	$0.897846\pi$
$468$	−2.40711	+	28.3852i	−0.111268	+	1.31211i
$469$		0			0
$470$	38.4555	+	66.6069i	1.77382	+	3.07235i
$471$	−4.48160	+	7.76236i	−0.206501	+	0.357671i
$472$	−1.86278	−	3.22643i	−0.0857413	−	0.148508i
$473$	0.884779	−	1.53248i	0.0406822	−	0.0704636i
$474$	17.1010			0.785474
$475$	−23.1237	+	40.0513i	−1.06099	+	1.83768i
$476$		0			0
$477$	3.58653	−	6.21205i	0.164216	−	0.284430i
$478$	1.43365	−	2.48316i	0.0655737	−	0.113577i
$479$	−24.2188			−1.10659			−0.553294	−	0.832986i	$-0.686629\pi$
$479$	−24.2188			−1.10659			−0.553294	+	0.832986i	$0.686629\pi$
$480$	−8.07793	+	13.9914i	−0.368705	+	0.638616i
$481$	1.07552	−	0.505020i	0.0490394	−	0.0230269i
$482$	−4.73461			−0.215655
$483$		0			0
$484$	15.6642	+	27.1312i	0.712009	+	1.23323i
$485$	28.8678			1.31082
$486$	14.3150	−	24.7944i	0.649343	−	1.12470i
$487$	−0.886967	−	1.53627i	−0.0401923	−	0.0696151i	0.845229	−	0.534404i	$-0.179464\pi$
$487$	−0.886967	−	1.53627i	−0.0401923	−	0.0696151i	−0.885422	+	0.464788i	$0.846130\pi$
$488$	−1.25590			−0.0568519
$489$	−12.9693			−0.586493
$490$		0			0
$491$	3.34483	+	5.79342i	0.150950	+	0.261453i	0.931577	−	0.363544i	$-0.118433\pi$
$491$	3.34483	+	5.79342i	0.150950	+	0.261453i	−0.780627	+	0.624997i	$0.785100\pi$
$492$	5.06259	−	8.76867i	0.228239	−	0.395322i
$493$	4.28067	−	7.41434i	0.192792	−	0.333925i
$494$	−26.1607	+	12.2840i	−1.17703	+	0.552683i
$495$	−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	$-0.352607\pi$
$500$	−48.2486	−	83.5690i	−2.15774	−	3.73732i
$501$	4.89932	+	8.48588i	0.218886	+	0.379121i
$502$	−34.1560	−	59.1600i	−1.52446	−	2.64044i
$503$	16.5726	−	28.7046i	0.738936	−	1.27987i	−0.214039	−	0.976825i	$-0.568662\pi$
$503$	16.5726	−	28.7046i	0.738936	−	1.27987i	0.952975	−	0.303049i	$-0.0980046\pi$
$504$		0			0
$505$	12.1518	+	21.0475i	0.540747	+	0.936601i
$506$	3.54955	+	6.14800i	0.157797	+	0.273312i
$507$	−2.47923	−	6.70019i	−0.110106	−	0.297566i
$508$	−2.87085	+	4.97246i	−0.127373	+	0.220617i
$509$	−13.8290	+	23.9526i	−0.612961	+	1.06168i	0.377778	+	0.925896i	$0.376688\pi$
$509$	−13.8290	+	23.9526i	−0.612961	+	1.06168i	−0.990739	+	0.135783i	$0.956645\pi$
$510$	6.12377	+	10.6067i	0.271165	+	0.469672i
$511$		0			0
$512$	14.2061			0.627828
$513$	11.3063			0.499184
$514$	−1.63571	−	2.83314i	−0.0721482	−	0.124964i
$515$	1.20645	−	2.08963i	0.0531626	−	0.0920802i
$516$	−5.18204			−0.228126
$517$	−2.25579	−	3.90714i	−0.0992096	−	0.171836i
$518$		0			0
$519$	−4.16085			−0.182641
$520$	2.64995	−	31.2489i	0.116208	−	1.37036i
$521$	0.711083	−	1.23163i	0.0311531	−	0.0539587i	−0.850029	−	0.526737i	$-0.823415\pi$
$521$	0.711083	−	1.23163i	0.0311531	−	0.0539587i	0.881182	+	0.472778i	$0.156749\pi$
$522$	21.5558			0.943472
$523$	−1.68089	+	2.91139i	−0.0735002	+	0.127306i	−0.900433	−	0.434995i	$-0.856750\pi$
$523$	−1.68089	+	2.91139i	−0.0735002	+	0.127306i	0.826933	+	0.562301i	$0.190084\pi$
$524$	−9.51772	+	16.4852i	−0.415784	+	0.720158i
$525$		0			0
$526$	−7.41143	+	12.8370i	−0.323154	+	0.559718i
$527$	12.2475			0.533511
$528$	0.193456	−	0.335076i	0.00841910	−	0.0145823i
$529$	−5.42979	−	9.40468i	−0.236078	−	0.408899i
$530$	−12.4538	+	21.5706i	−0.540958	+	0.936966i
$531$	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
$535$	17.1820			0.742844
$536$	21.3735			0.923197
$537$	12.5316			0.540779
$538$	−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	$0.886701\pi$
$542$	22.8306	+	39.5437i	0.980657	+	1.69855i
$543$	7.65490			0.328503
$544$	8.28613	−	14.3520i	0.355265	−	0.615337i
$545$	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	$0.542264\pi$
$548$	22.3404	−	38.6947i	0.954334	−	1.65295i
$549$	1.64395			0.0701622
$550$	7.81321	+	13.5329i	0.333157	+	0.577044i
$551$	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
$555$	0.764247			0.0324405
$556$	51.2360			2.17289
$557$	29.5458			1.25190			0.625948	−	0.779865i	$-0.284712\pi$
$557$	29.5458			1.25190			0.625948	+	0.779865i	$0.284712\pi$
$558$	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
$562$	7.07422	−	12.2529i	0.298408	−	0.516858i
$563$	3.23368	+	5.60090i	0.136283	+	0.236050i	0.926087	−	0.377310i	$-0.123151\pi$
$563$	3.23368	+	5.60090i	0.136283	+	0.236050i	−0.789804	+	0.613360i	$0.789818\pi$
$564$	−6.60593	+	11.4418i	−0.278160	+	0.481787i
$565$	51.3867			2.16185
$566$	29.9916	−	51.9470i	1.26064	−	2.18350i
$567$		0			0
$568$	11.5401	−	19.9880i	0.484210	−	0.838676i
$569$	−10.8478	+	18.7889i	−0.454763	+	0.787673i	−0.998675	−	0.0514697i	$-0.983609\pi$
$569$	−10.8478	+	18.7889i	−0.454763	+	0.787673i	0.543911	+	0.839143i	$0.316943\pi$
$570$	−18.5894			−0.778624
$571$	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	$0.0534536\pi$
$572$	−0.490300	+	5.78175i	−0.0205005	+	0.241747i
$573$	6.96381			0.290917
$574$		0			0
$575$	−37.2656	−	64.5459i	−1.55408	−	2.69175i
$576$	34.8127			1.45053
$577$	−1.32120	+	2.28839i	−0.0550024	+	0.0952669i	−0.892216	−	0.451610i	$-0.850850\pi$
$577$	−1.32120	+	2.28839i	−0.0550024	+	0.0952669i	0.837213	+	0.546877i	$0.184183\pi$
$578$	12.5885	+	21.8038i	0.523611	+	0.906921i
$579$	2.28334			0.0948925
$580$	−44.4752			−1.84673
$581$		0			0
$582$	4.17286	+	7.22760i	0.172970	+	0.299594i
$583$	0.730536	−	1.26533i	0.0302557	−	0.0524044i
$584$	5.05617	−	8.75755i	0.209226	−	0.362390i
$585$	−3.46875	+	40.9044i	−0.143415	+	1.69119i
$586$	−5.41096	−	9.37205i	−0.223525	−	0.387156i
$587$	3.69407	+	6.39832i	0.152471	+	0.264087i	0.932135	−	0.362110i	$-0.117944\pi$
$587$	3.69407	+	6.39832i	0.152471	+	0.264087i	−0.779664	+	0.626198i	$0.784610\pi$
$588$		0			0
$589$	−9.29470	+	16.0989i	−0.382981	+	0.663343i
$590$	−8.46687	−	14.6651i	−0.348576	−	0.603751i
$591$	−1.88227	−	3.26018i	−0.0774261	−	0.134106i
$592$	−0.211096	−	0.365628i	−0.00867597	−	0.0150272i
$593$	23.4515	+	40.6192i	0.963037	+	1.66803i	0.714799	+	0.699330i	$0.246518\pi$
$593$	23.4515	+	40.6192i	0.963037	+	1.66803i	0.248238	+	0.968699i	$0.420149\pi$
$594$	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
$598$	3.93563	−	46.4099i	0.160940	−	1.89784i
$599$	−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	$0.177222\pi$
$600$	7.25406	−	12.5644i	0.296146	−	0.512939i
$601$	−23.5174	−	40.7333i	−0.959293	−	1.66154i	−0.724223	−	0.689566i	$-0.757801\pi$
$601$	−23.5174	−	40.7333i	−0.959293	−	1.66154i	−0.235070	−	0.971978i	$-0.575532\pi$
$602$		0			0
$603$	−27.9777			−1.13934
$604$	−18.5344			−0.754155
$605$	22.5728	+	39.0973i	0.917715	+	1.58953i
$606$	−3.51309	+	6.08485i	−0.142709	+	0.247180i
$607$	28.3869			1.15219			0.576095	−	0.817383i	$-0.304576\pi$
$607$	28.3869			1.15219			0.576095	+	0.817383i	$0.304576\pi$
$608$	12.5767	+	21.7836i	0.510054	+	0.883440i
$609$		0			0
$610$	−5.70843			−0.231127
$611$	−2.50115	+	29.4942i	−0.101186	+	1.19321i
$612$	9.39766	−	16.2772i	0.379878	−	0.657968i
$613$	−47.5564			−1.92079			−0.960393	−	0.278650i	$-0.910113\pi$
$613$	−47.5564			−1.92079			−0.960393	+	0.278650i	$0.910113\pi$
$614$	17.9554	−	31.0997i	0.724621	−	1.25508i
$615$	7.29543	−	12.6360i	0.294180	−	0.509535i
$616$		0			0
$617$	8.24338	−	14.2780i	0.331866	−	0.574809i	−0.651012	−	0.759068i	$-0.725655\pi$
$617$	8.24338	−	14.2780i	0.331866	−	0.574809i	0.982878	+	0.184259i	$0.0589885\pi$
$618$	0.697572			0.0280604
$619$	−15.9706	+	27.6619i	−0.641912	+	1.11182i	0.343094	+	0.939301i	$0.388525\pi$
$619$	−15.9706	+	27.6619i	−0.641912	+	1.11182i	−0.985006	+	0.172523i	$0.944808\pi$
$620$	−31.8123	−	55.1005i	−1.27761	−	2.21289i
$621$	−9.11047	+	15.7798i	−0.365591	+	0.633222i
$622$	−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
$626$	−29.2992			−1.17103
$627$	1.09045			0.0435484
$628$	−47.7629			−1.90595
$629$	−0.783945			−0.0312579
$630$		0			0
$631$	−6.59577	+	11.4242i	−0.262573	+	0.454790i	−0.966925	−	0.255061i	$-0.917905\pi$
$631$	−6.59577	+	11.4242i	−0.262573	+	0.454790i	0.704352	+	0.709851i	$0.251238\pi$
$632$	14.4456	+	25.0204i	0.574613	+	0.995259i
$633$	−3.83955	−	6.65029i	−0.152608	−	0.264325i
$634$	−17.9277			−0.712000
$635$	−4.13702	+	7.16554i	−0.164173	+	0.284356i
$636$	−4.27865			−0.169660
$637$		0			0
$638$	4.39068			0.173829
$639$	−15.1058	+	26.1640i	−0.597575	+	1.03503i
$640$	−62.0864			−2.45418
$641$	23.5814	+	40.8441i	0.931408	+	1.61325i	0.780918	+	0.624634i	$0.214752\pi$
$641$	23.5814	+	40.8441i	0.931408	+	1.61325i	0.150490	+	0.988612i	$0.451915\pi$
$642$	2.48367	+	4.30184i	0.0980227	+	0.169780i
$643$	−1.40679	+	2.43664i	−0.0554785	+	0.0960916i	−0.892431	−	0.451184i	$-0.851002\pi$
$643$	−1.40679	+	2.43664i	−0.0554785	+	0.0960916i	0.836952	+	0.547276i	$0.184335\pi$
$644$		0			0
$645$	−7.46755			−0.294035
$646$	19.0685			0.750241
$647$	−25.9783			−1.02131			−0.510656	−	0.859785i	$-0.670597\pi$
$647$	−25.9783			−1.02131			−0.510656	+	0.859785i	$0.670597\pi$
$648$	13.1359			0.516027
$649$	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
$653$	13.4213	−	23.2464i	0.525216	−	0.909700i	−0.474353	−	0.880335i	$-0.657318\pi$
$653$	13.4213	−	23.2464i	0.525216	−	0.909700i	0.999569	−	0.0293654i	$-0.00934865\pi$
$654$	9.33835	+	16.1745i	0.365158	+	0.632473i
$655$	−13.7155	+	23.7559i	−0.535908	+	0.928219i
$656$	−8.06039			−0.314705
$657$	−6.61846	+	11.4635i	−0.258211	+	0.447234i
$658$		0			0
$659$	−7.78666	+	13.4869i	−0.303325	+	0.525375i	−0.976887	−	0.213756i	$-0.931430\pi$
$659$	−7.78666	+	13.4869i	−0.303325	+	0.525375i	0.673562	+	0.739131i	$0.264764\pi$
$660$	−1.86610	+	3.23218i	−0.0726379	+	0.125812i
$661$	−33.3804			−1.29835			−0.649174	−	0.760640i	$-0.724885\pi$
$661$	−33.3804			−1.29835			−0.649174	+	0.760640i	$0.724885\pi$
$662$	16.5891	−	28.7332i	0.644755	−	1.11675i
$663$	−0.398291	+	4.69674i	−0.0154683	+	0.182406i
$664$	11.8136			0.458455
$665$		0			0
$666$	−0.986911	−	1.70938i	−0.0382420	−	0.0662371i
$667$	−20.9416			−0.810861
$668$	−26.1074	+	45.2193i	−1.01013	+	1.74959i
$669$	3.71881	+	6.44117i	0.143778	+	0.249030i
$670$	97.1490			3.75319
$671$	0.334855			0.0129269
$672$		0			0
$673$	−0.427076	−	0.739717i	−0.0164626	−	0.0285140i	0.857677	−	0.514189i	$-0.171907\pi$
$673$	−0.427076	−	0.739717i	−0.0164626	−	0.0285140i	−0.874139	+	0.485675i	$0.838574\pi$
$674$	19.0582	−	33.0098i	0.734095	−	1.27149i
$675$	−20.0538	+	34.7342i	−0.771872	+	1.33692i
$676$	24.3148	−	29.2932i	0.935183	−	1.12666i
$677$	−12.2725	−	21.2565i	−0.471669	−	0.816955i	0.527805	−	0.849365i	$-0.323015\pi$
$677$	−12.2725	−	21.2565i	−0.471669	−	0.816955i	−0.999475	+	0.0324100i	$0.989682\pi$
$678$	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
$682$	3.14057	+	5.43963i	0.120259	+	0.208294i
$683$	21.5186	+	37.2714i	0.823387	+	1.42615i	0.903146	+	0.429334i	$0.141252\pi$
$683$	21.5186	+	37.2714i	0.823387	+	1.42615i	−0.0797583	+	0.996814i	$0.525415\pi$
$684$	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
$689$	−8.67699	+	4.07436i	−0.330567	+	0.155221i
$690$	14.9791	−	25.9446i	0.570246	−	0.987695i
$691$	−12.9098	+	22.3604i	−0.491110	+	0.850628i	−0.999948	−	0.0102348i	$-0.996742\pi$
$691$	−12.9098	+	22.3604i	−0.491110	+	0.850628i	0.508837	+	0.860863i	$0.330075\pi$
$692$	−11.0861	−	19.2017i	−0.421431	−	0.729939i
$693$		0			0
$694$	−8.74338			−0.331894
$695$	73.8334			2.80066
$696$	−2.03823	−	3.53031i	−0.0772588	−	0.133816i
$697$	−7.48346	+	12.9617i	−0.283456	+	0.490961i
$698$	−38.1345			−1.44341
$699$	−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	$0.400288\pi$
$702$	−22.6877	+	10.6532i	−0.856291	+	0.402079i
$703$	0.594938	−	1.03046i	0.0224385	−	0.0388647i
$704$	7.09096			0.267251
$705$	−9.51945	+	16.4882i	−0.358523	+	0.620981i
$706$	−20.1981	+	34.9841i	−0.760166	+	1.31665i
$707$		0			0
$708$	1.45445	−	2.51918i	0.0546616	−	0.0946767i
$709$	−22.3794			−0.840476			−0.420238	−	0.907414i	$-0.638053\pi$
$709$	−22.3794			−0.840476			−0.420238	+	0.907414i	$0.638053\pi$
$710$	52.4529	−	90.8511i	1.96852	−	3.40958i
$711$	−18.9090	−	32.7514i	−0.709144	−	1.22827i
$712$	−7.69581	+	13.3295i	−0.288413	+	0.499545i
$713$	−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
$717$	0.709785			0.0265074
$718$	36.2142			1.35150
$719$	22.7445			0.848227			0.424113	−	0.905609i	$-0.360586\pi$
$719$	22.7445			0.848227			0.424113	+	0.905609i	$0.360586\pi$
$720$	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
$724$	20.3956	+	35.3263i	0.757997	+	1.31289i
$725$	−46.0963			−1.71197
$726$	−6.52582	+	11.3030i	−0.242196	+	0.419495i
$727$	−18.7274			−0.694561			−0.347280	−	0.937761i	$-0.612895\pi$
$727$	−18.7274			−0.694561			−0.347280	+	0.937761i	$0.612895\pi$
$728$		0			0
$729$	−12.0322			−0.445638
$730$	22.9818	−	39.8056i	0.850594	−	1.47327i
$731$	7.66002			0.283316
$732$	−0.490300	−	0.849225i	−0.0181220	−	0.0313883i
$733$	−0.846341	−	1.46591i	−0.0312603	−	0.0541445i	0.849972	−	0.526828i	$-0.176619\pi$
$733$	−0.846341	−	1.46591i	−0.0312603	−	0.0541445i	−0.881232	+	0.472683i	$0.843285\pi$
$734$	−40.1781	+	69.5904i	−1.48300	+	2.56863i
$735$		0			0
$736$	−40.5368			−1.49421
$737$	−5.69874			−0.209916
$738$	−37.6838			−1.38716
$739$	46.9161			1.72584			0.862919	−	0.505343i	$-0.168634\pi$
$739$	46.9161			1.72584			0.862919	+	0.505343i	$0.168634\pi$
$740$	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	0.723161	−	0.690680i	$-0.242688\pi$
$743$	−6.44831	−	11.1688i	−0.236566	−	0.409744i	−0.959727	+	0.280936i	$0.909355\pi$
$744$	2.91581	−	5.05034i	0.106899	−	0.185154i
$745$	−9.61078	−	16.6464i	−0.352112	−	0.609875i
$746$	−10.8756	+	18.8372i	−0.398186	+	0.689678i
$747$	−15.4638			−0.565790
$748$	1.91420	−	3.31549i	0.0699900	−	0.121226i
$749$		0			0
$750$	20.1007	−	34.8155i	0.733974	−	1.27128i
$751$	22.8166	−	39.5196i	0.832591	−	1.44209i	−0.0633855	−	0.997989i	$-0.520190\pi$
$751$	22.8166	−	39.5196i	0.832591	−	1.44209i	0.895977	−	0.444101i	$-0.146477\pi$
$752$	10.5176			0.383538
$753$	8.45515	−	14.6447i	0.308123	−	0.533684i
$754$	−23.6411	−	16.4599i	−0.860959	−	0.599434i
$755$	−26.7089			−0.972038
$756$		0			0
$757$	19.0782	+	33.0445i	0.693410	+	1.20102i	0.970714	+	0.240239i	$0.0772260\pi$
$757$	19.0782	+	33.0445i	0.693410	+	1.20102i	−0.277303	+	0.960782i	$0.589441\pi$
$758$	29.0055			1.05353
$759$	−0.878673	+	1.52191i	−0.0318938	+	0.0552417i
$760$	−15.7028	−	27.1981i	−0.569602	−	0.986580i
$761$	−42.7345			−1.54912			−0.774562	−	0.632498i	$-0.782030\pi$
$761$	−42.7345			−1.54912			−0.774562	+	0.632498i	$0.782030\pi$
$762$	−2.39203			−0.0866543
$763$		0			0
$764$	18.5543	+	32.1370i	0.671271	+	1.16267i
$765$	13.5425	−	23.4562i	0.489628	−	0.848061i
$766$	30.8502	−	53.4342i	1.11466	−	1.93066i
$767$	0.550686	−	6.49383i	0.0198841	−	0.234479i
$768$	−1.88364	−	3.26257i	−0.0679702	−	0.117728i
$769$	10.8088	+	18.7215i	0.389777	+	0.675113i	0.992419	−	0.122898i	$-0.0392189\pi$
$769$	10.8088	+	18.7215i	0.389777	+	0.675113i	−0.602643	+	0.798011i	$0.705886\pi$
$770$		0			0
$771$	0.404912	−	0.701329i	0.0145826	−	0.0252577i
$772$	6.08371	+	10.5373i	0.218958	+	0.379246i
$773$	5.00056	+	8.66123i	0.179858	+	0.311523i	0.941832	−	0.336085i	$-0.109103\pi$
$773$	5.00056	+	8.66123i	0.179858	+	0.311523i	−0.761974	+	0.647608i	$0.775770\pi$
$774$	9.64323	+	16.7026i	0.346619	+	0.600361i
$775$	−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
$780$	22.1647	−	10.4076i	0.793624	−	0.372654i
$781$	−3.07688	+	5.32931i	−0.110099	+	0.190698i
$782$	−15.3652	+	26.6133i	−0.549459	+	0.951691i
$783$	5.63467	+	9.75954i	0.201367	+	0.348778i
$784$		0			0
$785$	−68.8285			−2.45659
$786$	−7.93031			−0.282865
$787$	20.8939	+	36.1893i	0.744787	+	1.29001i	0.950294	+	0.311353i	$0.100782\pi$
$787$	20.8939	+	36.1893i	0.744787	+	1.29001i	−0.205507	+	0.978656i	$0.565884\pi$
$788$	10.0302	−	17.3728i	0.357310	−	0.618880i
$789$	−3.66932			−0.130631
$790$	65.6593	+	113.725i	2.33605	+	4.04616i
$791$		0			0
$792$	3.05601			0.108591
$793$	−1.80299	−	1.25531i	−0.0640261	−	0.0445775i
$794$	8.78229	−	15.2114i	0.311672	−	0.539831i
$795$	−6.16574			−0.218676
$796$	−1.19127	+	2.06334i	−0.0422234	+	0.0731331i
$797$	−11.3856	+	19.7204i	−0.403297	+	0.698531i	−0.994122	−	0.108269i	$-0.965469\pi$
$797$	−11.3856	+	19.7204i	−0.403297	+	0.698531i	0.590825	+	0.806800i	$0.298803\pi$
$798$		0			0
$799$	9.76481	−	16.9131i	0.345454	−	0.598344i
$800$	−89.2290			−3.15472
$801$	10.0737	−	17.4482i	0.355937	−	0.616501i
$802$	18.3642	+	31.8077i	0.648461	+	1.12317i
$803$	−1.34811	+	2.33499i	−0.0475736	+	0.0824000i
$804$	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
$808$	−11.8703			−0.417596
$809$	−37.5702			−1.32090			−0.660449	−	0.750871i	$-0.729634\pi$
$809$	−37.5702			−1.32090			−0.660449	+	0.750871i	$0.729634\pi$
$810$	59.7065			2.09787
$811$	−11.5936			−0.407106			−0.203553	−	0.979064i	$-0.565249\pi$
$811$	−11.5936			−0.407106			−0.203553	+	0.979064i	$0.565249\pi$
$812$		0			0
$813$	−5.65159	+	9.78884i	−0.198210	+	0.343309i
$814$	−0.201023	−	0.348182i	−0.00704584	−	0.0122038i
$815$	−49.7957	−	86.2487i	−1.74427	−	3.02116i
$816$	1.67486			0.0586317
$817$	−5.81321	+	10.0688i	−0.203379	+	0.352262i
$818$	−57.2359			−2.00121
$819$		0			0
$820$	77.7514			2.71520
$821$	−15.5121	+	26.8678i	−0.541378	+	0.937693i	0.457448	+	0.889237i	$0.348764\pi$
$821$	−15.5121	+	26.8678i	−0.541378	+	0.937693i	−0.998825	+	0.0484569i	$0.984570\pi$
$822$	18.6143			0.649250
$823$	−14.5387	−	25.1818i	−0.506789	−	0.877784i	−0.999969	−	0.00785682i	$-0.997499\pi$
$823$	−14.5387	−	25.1818i	−0.506789	−	0.877784i	0.493180	−	0.869927i	$-0.335834\pi$
$824$	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	$0.416632\pi$
$828$	−45.9745			−1.59773
$829$	4.37189			0.151842			0.0759210	−	0.997114i	$-0.475810\pi$
$829$	4.37189			0.151842			0.0759210	+	0.997114i	$0.475810\pi$
$830$	53.6961			1.86382
$831$	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
$835$	−37.6219	+	65.1631i	−1.30196	+	2.25506i
$836$	2.90538	+	5.03227i	0.100485	+	0.174045i
$837$	−8.06076	+	13.9616i	−0.278621	+	0.482585i
$838$	−52.5856			−1.81654
$839$	11.4109	−	19.7643i	0.393948	−	0.682338i	−0.599018	−	0.800735i	$-0.704442\pi$
$839$	11.4109	−	19.7643i	0.393948	−	0.682338i	0.992966	+	0.118397i	$0.0377756\pi$
$840$		0			0
$841$	8.02399	−	13.8980i	0.276689	−	0.479240i
$842$	23.1154	−	40.0371i	0.796610	−	1.37977i
$843$	3.50237			0.120628
$844$	20.4601	−	35.4379i	0.704265	−	1.21982i
$845$	35.0387	−	42.2128i	1.20537	−	1.45216i
$846$	49.1718			1.69056
$847$		0			0
$848$	1.70306	+	2.94979i	0.0584833	+	0.101296i
$849$	14.8485			0.509601
$850$	−33.8216	+	58.5808i	−1.16007	+	2.00931i
$851$	0.958790	+	1.66067i	0.0328669	+	0.0569271i
$852$	18.0209			0.617385
$853$	−23.3549			−0.799656			−0.399828	−	0.916590i	$-0.630930\pi$
$853$	−23.3549			−0.799656			−0.399828	+	0.916590i	$0.630930\pi$
$854$		0			0
$855$	20.5548	+	35.6020i	0.702960	+	1.21756i
$856$	−4.19602	+	7.26771i	−0.143417	+	0.248405i
$857$	−21.7653	+	37.6986i	−0.743488	+	1.28776i	0.207410	+	0.978254i	$0.433497\pi$
$857$	−21.7653	+	37.6986i	−0.743488	+	1.28776i	−0.950898	+	0.309505i	$0.899837\pi$
$858$	−2.18814	+	1.02746i	−0.0747020	+	0.0350770i
$859$	10.2557	+	17.7633i	0.349919	+	0.606078i	0.986235	−	0.165351i	$-0.0528757\pi$
$859$	10.2557	+	17.7633i	0.349919	+	0.606078i	−0.636316	+	0.771429i	$0.719542\pi$
$860$	−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	$0.502309\pi$
$864$	10.9071	+	18.8916i	0.371067	+	0.642706i
$865$	−15.9756	−	27.6705i	−0.543186	−	0.940826i
$866$	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
$871$	30.6843	+	21.3636i	1.03970	+	0.723878i
$872$	−15.7766	+	27.3259i	−0.534263	+	0.925371i
$873$	9.22809	−	15.9835i	0.312323	−	0.540960i
$874$	−23.3214	−	40.3939i	−0.788858	−	1.36634i
$875$		0			0
$876$	7.89568			0.266770
$877$	−47.0361			−1.58830			−0.794148	−	0.607725i	$-0.792082\pi$
$877$	−47.0361			−1.58830			−0.794148	+	0.607725i	$0.792082\pi$
$878$	14.9806	+	25.9472i	0.505572	+	0.875677i
$879$	1.33945	−	2.32000i	0.0451787	−	0.0782517i
$880$	2.97110			0.100156
$881$	−8.05674	−	13.9547i	−0.271439	−	0.470145i	0.697792	−	0.716301i	$-0.254166\pi$
$881$	−8.05674	−	13.9547i	−0.271439	−	0.470145i	−0.969230	+	0.246155i	$0.920833\pi$
$882$		0			0
$883$	42.0733			1.41588			0.707940	−	0.706273i	$-0.249625\pi$
$883$	42.0733			1.41588			0.707940	+	0.706273i	$0.249625\pi$
$884$	−22.7360	+	10.6759i	−0.764694	+	0.359069i
$885$	2.09593	−	3.63026i	0.0704539	−	0.122030i
$886$	−33.3246			−1.11956
$887$	−20.8814	+	36.1676i	−0.701128	+	1.21439i	0.266942	+	0.963713i	$0.413987\pi$
$887$	−20.8814	+	36.1676i	−0.701128	+	1.21439i	−0.968071	+	0.250678i	$0.919347\pi$
$888$	−0.186636	+	0.323264i	−0.00626311	+	0.0108480i
$889$		0			0
$890$	−34.9797	+	60.5866i	−1.17252	+	2.03087i
$891$	−3.50237			−0.117334
$892$	−19.8167	+	34.3236i	−0.663513	+	1.14924i
$893$	14.8211	+	25.6709i	0.495969	+	0.859043i
$894$	2.77848	−	4.81248i	0.0929264	−	0.160953i
$895$	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
$899$	−18.5287			−0.617966
$900$	−101.198			−3.37328
$901$	6.32465			0.210705
$902$	−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
$906$	−3.86079	−	6.68708i	−0.128266	−	0.222163i
$907$	−15.4225			−0.512095			−0.256048	−	0.966664i	$-0.582420\pi$
$907$	−15.4225			−0.512095			−0.256048	+	0.966664i	$0.582420\pi$
$908$	−7.85921	+	13.6125i	−0.260817	+	0.451748i
$909$	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	$0.286328\pi$
$912$	−1.27105	+	2.20153i	−0.0420888	+	0.0729000i
$913$	−3.14980			−0.104243
$914$	−20.1259	−	34.8590i	−0.665704	−	1.15303i
$915$	−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
$919$	−9.47464			−0.312540			−0.156270	−	0.987714i	$-0.549947\pi$
$919$	−9.47464			−0.312540			−0.156270	+	0.987714i	$0.549947\pi$
$920$	50.6127			1.66865
$921$	8.88953			0.292920
$922$	−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
$926$	−5.76413	+	9.98377i	−0.189421	+	0.328087i
$927$	−0.771324	−	1.33597i	−0.0253336	−	0.0438791i
$928$	−12.5357	+	21.7124i	−0.411503	+	0.712745i
$929$	−35.8439			−1.17600			−0.588001	−	0.808860i	$-0.700085\pi$
$929$	−35.8439			−1.17600			−0.588001	+	0.808860i	$0.700085\pi$
$930$	13.2532	−	22.9553i	0.434591	−	0.752733i
$931$		0			0
$932$	29.8278	−	51.6633i	0.977043	−	1.69229i
$933$	0.359424	−	0.622541i	0.0117670	−	0.0203811i
$934$	19.3134			0.631952
$935$	2.75845	−	4.77777i	0.0902108	−	0.156250i
$936$	−16.4548	−	11.4565i	−0.537841	−	0.374466i
$937$	31.3709			1.02484			0.512422	−	0.858734i	$-0.328748\pi$
$937$	31.3709			1.02484			0.512422	+	0.858734i	$0.328748\pi$
$938$		0			0
$939$	−3.62643	−	6.28116i	−0.118344	−	0.204978i
$940$	−101.454			−3.30907
$941$	22.3922	−	38.7844i	0.729964	−	1.26433i	−0.226934	−	0.973910i	$-0.572870\pi$
$941$	22.3922	−	38.7844i	0.729964	−	1.26433i	0.956898	−	0.290425i	$-0.0937966\pi$
$942$	−9.94919	−	17.2325i	−0.324162	−	0.561465i
$943$	36.6100			1.19219
$944$	−2.31570			−0.0753695
$945$		0			0
$946$	1.96422	+	3.40212i	0.0638622	+	0.110613i
$947$	17.5337	−	30.3692i	0.569768	−	0.986868i	−0.426820	−	0.904337i	$-0.640366\pi$
$947$	17.5337	−	30.3692i	0.569768	−	0.986868i	0.996588	−	0.0825312i	$-0.0263004\pi$
$948$	−11.2790	+	19.5359i	−0.366326	+	0.634495i
$949$	16.0122	−	7.51868i	0.519778	−	0.244067i
$950$	−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	−0.221027	+	0.975268i	$0.570941\pi$
$953$	−29.4852	+	51.0699i	−0.955120	+	1.65432i	−0.734093	+	0.679048i	$0.762393\pi$
$954$	7.96212	+	13.7908i	0.257783	+	0.446494i
$955$	26.7376	+	46.3108i	0.865208	+	1.49858i
$956$	1.89114	+	3.27556i	0.0611640	+	0.105939i
$957$	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
$962$	−0.222888	+	2.62835i	−0.00718618	+	0.0847413i
$963$	5.49253	−	9.51334i	0.176994	−	0.306563i
$964$	3.12273	−	5.40873i	0.100576	−	0.174204i
$965$	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	$0.337628\pi$
$968$	−22.0500			−0.708713
$969$	2.36016	+	4.08791i	0.0758191	+	0.131323i
$970$	−32.0434	+	55.5008i	−1.02885	+	1.78202i
$971$	49.5175			1.58909			0.794546	−	0.607204i	$-0.207709\pi$
$971$	49.5175			1.58909			0.794546	+	0.607204i	$0.207709\pi$
$972$	18.8831	+	32.7065i	0.605676	+	1.04906i
$973$		0			0
$974$	3.93815			0.126186
$975$	22.9726	−	10.7870i	0.735713	−	0.345461i
$976$	−0.390315	+	0.676045i	−0.0124937	+	0.0216397i
$977$	−10.8671			−0.347670			−0.173835	−	0.984775i	$-0.555616\pi$
$977$	−10.8671			−0.347670			−0.173835	+	0.984775i	$0.555616\pi$
$978$	14.3960	−	24.9346i	0.460333	−	0.797320i
$979$	2.05190	−	3.55400i	0.0655790	−	0.113586i
$980$		0			0
$981$	20.6514	−	35.7692i	0.659347	−	1.14202i
$982$	−14.8511			−0.473918
$983$	1.17417	−	2.03371i	0.0374501	−	0.0648654i	−0.846693	−	0.532082i	$-0.821410\pi$
$983$	1.17417	−	2.03371i	0.0374501	−	0.0648654i	0.884143	+	0.467217i	$0.154743\pi$
$984$	3.56322	+	6.17169i	0.113591	+	0.196746i
$985$	14.4539	−	25.0350i	0.460541	−	0.797680i
$986$	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
$990$	13.8905			0.441468
$991$	24.4815			0.777681			0.388841	−	0.921305i	$-0.372876\pi$
$991$	24.4815			0.777681			0.388841	+	0.921305i	$0.372876\pi$
$992$	−35.8661			−1.13875
$993$	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
$997$	−3.31171	−	5.73604i	−0.104883	−	0.181662i	0.808808	−	0.588073i	$-0.200113\pi$
$997$	−3.31171	−	5.73604i	−0.104883	−	0.181662i	−0.913690	+	0.406411i	$0.866780\pi$
$998$	54.6982			1.73144
$999$	0.515956	−	0.893662i	0.0163241	−	0.0282742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.g.j.263.1		8
7.2	even	3		637.2.h.i.471.4		8
7.3	odd	6		91.2.f.c.29.1	yes	8
7.4	even	3		637.2.f.i.393.1		8
7.5	odd	6		637.2.h.h.471.4		8
7.6	odd	2		637.2.g.k.263.1		8
13.9	even	3		637.2.h.i.165.4		8
21.17	even	6		819.2.o.h.757.4		8
28.3	even	6		1456.2.s.q.1121.2		8
91.3	odd	6		1183.2.a.k.1.4		4
91.9	even	3	inner	637.2.g.j.373.1		8
91.10	odd	6		1183.2.a.l.1.1		4
91.24	even	12		1183.2.c.g.337.7		8
91.48	odd	6		637.2.h.h.165.4		8
91.61	odd	6		637.2.g.k.373.1		8
91.74	even	3		637.2.f.i.295.1		8
91.80	even	12		1183.2.c.g.337.2		8
91.81	even	3		8281.2.a.bp.1.4		4
91.87	odd	6		91.2.f.c.22.1	✓	8
91.88	even	6		8281.2.a.bt.1.1		4
273.269	even	6		819.2.o.h.568.4		8
364.87	even	6		1456.2.s.q.113.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.1	✓	8	91.87	odd	6
91.2.f.c.29.1	yes	8	7.3	odd	6
637.2.f.i.295.1		8	91.74	even	3
637.2.f.i.393.1		8	7.4	even	3
637.2.g.j.263.1		8	1.1	even	1	trivial
637.2.g.j.373.1		8	91.9	even	3	inner
637.2.g.k.263.1		8	7.6	odd	2
637.2.g.k.373.1		8	91.61	odd	6
637.2.h.h.165.4		8	91.48	odd	6
637.2.h.h.471.4		8	7.5	odd	6
637.2.h.i.165.4		8	13.9	even	3
637.2.h.i.471.4		8	7.2	even	3
819.2.o.h.568.4		8	273.269	even	6
819.2.o.h.757.4		8	21.17	even	6
1183.2.a.k.1.4		4	91.3	odd	6
1183.2.a.l.1.1		4	91.10	odd	6
1183.2.c.g.337.2		8	91.80	even	12
1183.2.c.g.337.7		8	91.24	even	12
1456.2.s.q.113.2		8	364.87	even	6
1456.2.s.q.1121.2		8	28.3	even	6
8281.2.a.bp.1.4		4	91.81	even	3
8281.2.a.bt.1.1		4	91.88	even	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.11000 + 1.92258i) q^{2} -0.549551 q^{3} +(-1.46422 - 2.53610i) q^{4} +(-2.11000 - 3.65463i) q^{5} +(0.610004 - 1.05656i) q^{6} +2.06113 q^{8} -2.69799 q^{9} +9.36845 q^{10} -0.549551 q^{11} +(0.804662 + 1.39372i) q^{12} +(2.95900 + 2.06017i) q^{13} +(1.15956 + 2.00841i) q^{15} +(0.640570 - 1.10950i) q^{16} +(-1.18944 - 2.06017i) q^{17} +(2.99478 - 5.18712i) q^{18} +3.61068 q^{19} +(-6.17901 + 10.7024i) q^{20} +(0.610004 - 1.05656i) q^{22} +(-2.90945 + 5.03931i) q^{23} -1.13270 q^{24} +(-6.40423 + 11.0925i) q^{25} +(-7.24536 + 3.40212i) q^{26} +3.13134 q^{27} +(1.79945 + 3.11673i) q^{29} -5.14844 q^{30} +(-2.57422 + 4.45868i) q^{31} +(3.48320 + 6.03308i) q^{32} +0.302006 q^{33} +5.28114 q^{34} +(3.95045 + 6.84238i) q^{36} +(0.164772 - 0.285393i) q^{37} +(-4.00787 + 6.94184i) q^{38} +(-1.62612 - 1.13217i) 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} +(5.69278 + 9.86018i) q^{45} +(-6.45900 - 11.1873i) 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} +(0.892184 - 10.5209i) q^{52} +(-1.32933 + 2.30247i) q^{53} +(-3.47580 + 6.02026i) q^{54} +(1.15956 + 2.00841i) q^{55} -1.98426 q^{57} -7.98957 q^{58} +(-0.903765 - 1.56537i) q^{59} +(3.39568 - 5.88149i) q^{60} -0.609325 q^{61} +(-5.71479 - 9.89831i) q^{62} -12.9032 q^{64} +(1.28568 - 15.1610i) q^{65} +(-0.335228 + 0.580633i) q^{66} +10.3698 q^{67} +(-3.48320 + 6.03308i) q^{68} +(1.59889 - 2.76936i) q^{69} +(5.59889 - 9.69756i) q^{71} -5.56092 q^{72} +(2.45310 - 4.24890i) q^{73} +(0.365794 + 0.633574i) q^{74} +(3.51945 - 6.09587i) q^{75} +(-5.28682 - 9.15705i) q^{76} +(3.98169 - 1.86964i) q^{78} +(7.00855 + 12.1392i) q^{79} -5.40642 q^{80} +6.37315 q^{81} +13.9673 q^{82} +5.73159 q^{83} +(-5.01945 + 8.69395i) q^{85} +(-3.57422 - 6.19073i) q^{86} +(-0.988887 - 1.71280i) q^{87} -1.13270 q^{88} +(-3.73378 + 6.46709i) q^{89} -25.2760 q^{90} +17.0403 q^{92} +(1.41467 - 2.45027i) q^{93} -18.2253 q^{94} +(-7.61856 - 13.1957i) q^{95} +(-1.91420 - 3.31549i) q^{96} +(-3.42035 + 5.92422i) q^{97} +1.48269 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 2 q^{3} - 5 q^{4} - 7 q^{5} - 5 q^{6} - 12 q^{8} + 14 q^{9} + 22 q^{10} - 2 q^{11} + 12 q^{12} - 4 q^{13} - 3 q^{15} - 19 q^{16} - 4 q^{17} + 3 q^{18} - 2 q^{19} - 2 q^{20} - 5 q^{22} + 2 q^{23}+ \cdots + 46 q^{99}+O(q^{100}) \) 8 * q + q^2 - 2 * q^3 - 5 * q^4 - 7 * q^5 - 5 * q^6 - 12 * q^8 + 14 * q^9 + 22 * q^10 - 2 * q^11 + 12 * q^12 - 4 * q^13 - 3 * q^15 - 19 * q^16 - 4 * q^17 + 3 * q^18 - 2 * q^19 - 2 * q^20 - 5 * q^22 + 2 * q^23 + 6 * q^24 - 5 * q^25 - 3 * q^26 + 52 * q^27 - q^29 - 8 * q^30 - 4 * q^31 + 33 * q^32 + 38 * q^33 - 6 * q^34 + 34 * q^36 + 10 * q^37 - 23 * q^38 - 19 * q^39 - 17 * q^40 - 22 * q^41 - 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 + 11 * q^48 - 43 * q^50 - 7 * q^51 + 34 * q^52 - 2 * q^53 + 5 * q^54 - 3 * q^55 - 34 * q^57 - 22 * q^58 - 8 * q^59 + 11 * q^60 - 16 * q^61 - 5 * q^62 + 28 * q^64 + 4 * q^65 + 6 * q^66 - 12 * q^67 - 33 * q^68 - 18 * q^69 + 14 * q^71 + 10 * q^72 - 8 * q^73 - 20 * q^74 - 7 * q^75 + 32 * q^76 - q^78 + 26 * q^79 - 14 * q^80 + 48 * q^81 + 28 * q^82 - 5 * q^85 - 12 * q^86 + 13 * q^87 + 6 * q^88 - q^89 - 52 * q^90 + 24 * q^92 + 7 * q^93 - 66 * q^94 - 21 * q^95 - 58 * q^96 + 3 * q^97 + 46 * q^99

Introduction

L-functions

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