LMFDB - Embedded newform 1690.2.c.h.1689.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(1689,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.1689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [18,18,0,18,-2] 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:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 29x^{16} + 336x^{14} + 1977x^{12} + 6147x^{10} + 9369x^{8} + 5559x^{6} + 1342x^{4} + 116x^{2} + 1 $ x^18 + 29x^16 + 336x^14 + 1977x^12 + 6147x^10 + 9369x^8 + 5559x^6 + 1342x^4 + 116x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1689.1
Root			$2.39737i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.h.1689.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -3.41573i q^{3} +1.00000 q^{4} +(-1.70807 - 1.44308i) q^{5} -3.41573i q^{6} +0.459770 q^{7} +1.00000 q^{8} -8.66724 q^{9} +(-1.70807 - 1.44308i) q^{10} -2.03092i q^{11} -3.41573i q^{12} +0.459770 q^{14} +(-4.92918 + 5.83433i) q^{15} +1.00000 q^{16} -5.39187i q^{17} -8.66724 q^{18} +3.30639i q^{19} +(-1.70807 - 1.44308i) q^{20} -1.57045i q^{21} -2.03092i q^{22} -4.15544i q^{23} -3.41573i q^{24} +(0.835031 + 4.92978i) q^{25} +19.3578i q^{27} +0.459770 q^{28} -6.05566 q^{29} +(-4.92918 + 5.83433i) q^{30} +6.52262i q^{31} +1.00000 q^{32} -6.93709 q^{33} -5.39187i q^{34} +(-0.785321 - 0.663485i) q^{35} -8.66724 q^{36} +8.07307 q^{37} +3.30639i q^{38} +(-1.70807 - 1.44308i) q^{40} -4.14511i q^{41} -1.57045i q^{42} +1.26725i q^{43} -2.03092i q^{44} +(14.8043 + 12.5075i) q^{45} -4.15544i q^{46} +1.29310 q^{47} -3.41573i q^{48} -6.78861 q^{49} +(0.835031 + 4.92978i) q^{50} -18.4172 q^{51} -5.78588i q^{53} +19.3578i q^{54} +(-2.93078 + 3.46896i) q^{55} +0.459770 q^{56} +11.2937 q^{57} -6.05566 q^{58} -6.77070i q^{59} +(-4.92918 + 5.83433i) q^{60} -5.98450 q^{61} +6.52262i q^{62} -3.98494 q^{63} +1.00000 q^{64} -6.93709 q^{66} +8.41427 q^{67} -5.39187i q^{68} -14.1939 q^{69} +(-0.785321 - 0.663485i) q^{70} -1.47782i q^{71} -8.66724 q^{72} +8.05573 q^{73} +8.07307 q^{74} +(16.8388 - 2.85224i) q^{75} +3.30639i q^{76} -0.933756i q^{77} +1.68287 q^{79} +(-1.70807 - 1.44308i) q^{80} +40.1194 q^{81} -4.14511i q^{82} -9.99259 q^{83} -1.57045i q^{84} +(-7.78090 + 9.20971i) q^{85} +1.26725i q^{86} +20.6845i q^{87} -2.03092i q^{88} +3.93934i q^{89} +(14.8043 + 12.5075i) q^{90} -4.15544i q^{92} +22.2796 q^{93} +1.29310 q^{94} +(4.77139 - 5.64755i) q^{95} -3.41573i q^{96} -7.05844 q^{97} -6.78861 q^{98} +17.6025i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 18 q^{2} + 18 q^{4} - 2 q^{5} - 2 q^{7} + 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} + 14 q^{15} + 18 q^{16} - 16 q^{18} - 2 q^{20} - 22 q^{25} - 2 q^{28} - 30 q^{29} + 14 q^{30} + 18 q^{32} - 28 q^{33}+ \cdots - 20 q^{98}+O(q^{100}) $ 18 * q + 18 * q^2 + 18 * q^4 - 2 * q^5 - 2 * q^7 + 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 + 14 * q^15 + 18 * q^16 - 16 * q^18 - 2 * q^20 - 22 * q^25 - 2 * q^28 - 30 * q^29 + 14 * q^30 + 18 * q^32 - 28 * q^33 - 4 * q^35 - 16 * q^36 + 20 * q^37 - 2 * q^40 + 20 * q^45 - 10 * q^47 - 20 * q^49 - 22 * q^50 - 24 * q^51 - 2 * q^56 - 24 * q^57 - 30 * q^58 + 14 * q^60 - 38 * q^61 + 78 * q^63 + 18 * q^64 - 28 * q^66 - 2 * q^67 - 28 * q^69 - 4 * q^70 - 16 * q^72 - 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 - 2 * q^80 + 106 * q^81 - 2 * q^83 - 16 * q^85 + 20 * q^90 + 56 * q^93 - 10 * q^94 + 54 * q^95 + 12 * q^97 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	3.41573i		−	1.97208i	−0.166522	−	0.986038i	$-0.553254\pi$
$3$		−	3.41573i		−	1.97208i	0.166522	−	0.986038i	$-0.446746\pi$
$4$	1.00000			0.500000
$5$	−1.70807	−	1.44308i	−0.763874	−	0.645366i
$5$	−1.70807	−	1.44308i	−0.763874	−	0.645366i
$6$		−	3.41573i		−	1.39447i
$7$	0.459770			0.173777			0.0868883	−	0.996218i	$-0.472308\pi$
$7$	0.459770			0.173777			0.0868883	+	0.996218i	$0.472308\pi$
$8$	1.00000			0.353553
$9$	−8.66724			−2.88908
$10$	−1.70807	−	1.44308i	−0.540140	−	0.456342i
$11$		−	2.03092i		−	0.612346i	−0.951976	−	0.306173i	$-0.900951\pi$
$11$		−	2.03092i		−	0.612346i	0.951976	−	0.306173i	$-0.0990485\pi$
$12$		−	3.41573i		−	0.986038i
$13$		0			0
$13$		0			0
$14$	0.459770			0.122879
$15$	−4.92918	+	5.83433i	−1.27271	+	1.50642i
$16$	1.00000			0.250000
$17$		−	5.39187i		−	1.30772i	−0.756616	−	0.653860i	$-0.773149\pi$
$17$		−	5.39187i		−	1.30772i	0.756616	−	0.653860i	$-0.226851\pi$
$18$	−8.66724			−2.04289
$19$			3.30639i			0.758537i	0.925287	+	0.379269i	$0.123824\pi$
$19$			3.30639i			0.758537i	−0.925287	+	0.379269i	$0.876176\pi$
$20$	−1.70807	−	1.44308i	−0.381937	−	0.322683i
$21$		−	1.57045i		−	0.342701i
$22$		−	2.03092i		−	0.432994i
$23$		−	4.15544i		−	0.866468i	−0.901281	−	0.433234i	$-0.857372\pi$
$23$		−	4.15544i		−	0.866468i	0.901281	−	0.433234i	$-0.142628\pi$
$24$		−	3.41573i		−	0.697234i
$25$	0.835031	+	4.92978i	0.167006	+	0.985956i
$26$		0			0
$27$			19.3578i			3.72541i
$28$	0.459770			0.0868883
$29$	−6.05566			−1.12451			−0.562254	−	0.826965i	$-0.690066\pi$
$29$	−6.05566			−1.12451			−0.562254	+	0.826965i	$0.690066\pi$
$30$	−4.92918	+	5.83433i	−0.899942	+	1.06520i
$31$			6.52262i			1.17150i	0.810493	+	0.585749i	$0.199200\pi$
$31$			6.52262i			1.17150i	−0.810493	+	0.585749i	$0.800800\pi$
$32$	1.00000			0.176777
$33$	−6.93709			−1.20759
$34$		−	5.39187i		−	0.924698i
$35$	−0.785321	−	0.663485i	−0.132743	−	0.112149i
$36$	−8.66724			−1.44454
$37$	8.07307			1.32720			0.663602	−	0.748086i	$-0.269027\pi$
$37$	8.07307			1.32720			0.663602	+	0.748086i	$0.269027\pi$
$38$			3.30639i			0.536367i
$39$		0			0
$40$	−1.70807	−	1.44308i	−0.270070	−	0.228171i
$41$		−	4.14511i		−	0.647358i	−0.946167	−	0.323679i	$-0.895080\pi$
$41$		−	4.14511i		−	0.647358i	0.946167	−	0.323679i	$-0.104920\pi$
$42$		−	1.57045i		−	0.242326i
$43$			1.26725i			0.193253i	0.995321	+	0.0966265i	$0.0308052\pi$
$43$			1.26725i			0.193253i	−0.995321	+	0.0966265i	$0.969195\pi$
$44$		−	2.03092i		−	0.306173i
$45$	14.8043	+	12.5075i	2.20689	+	1.86451i
$46$		−	4.15544i		−	0.612686i
$47$	1.29310			0.188618			0.0943088	−	0.995543i	$-0.469936\pi$
$47$	1.29310			0.188618			0.0943088	+	0.995543i	$0.469936\pi$
$48$		−	3.41573i		−	0.493019i
$49$	−6.78861			−0.969802
$50$	0.835031	+	4.92978i	0.118091	+	0.697176i
$51$	−18.4172			−2.57892
$52$		0			0
$53$		−	5.78588i		−	0.794751i	−0.917656	−	0.397376i	$-0.869921\pi$
$53$		−	5.78588i		−	0.794751i	0.917656	−	0.397376i	$-0.130079\pi$
$54$			19.3578i			2.63426i
$55$	−2.93078	+	3.46896i	−0.395187	+	0.467755i
$56$	0.459770			0.0614393
$57$	11.2937			1.49589
$58$	−6.05566			−0.795147
$59$		−	6.77070i		−	0.881470i	−0.897637	−	0.440735i	$-0.854718\pi$
$59$		−	6.77070i		−	0.881470i	0.897637	−	0.440735i	$-0.145282\pi$
$60$	−4.92918	+	5.83433i	−0.636355	+	0.753208i
$61$	−5.98450			−0.766237			−0.383119	−	0.923699i	$-0.625150\pi$
$61$	−5.98450			−0.766237			−0.383119	+	0.923699i	$0.625150\pi$
$62$			6.52262i			0.828374i
$63$	−3.98494			−0.502055
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.93709			−0.853896
$67$	8.41427			1.02797			0.513983	−	0.857800i	$-0.328169\pi$
$67$	8.41427			1.02797			0.513983	+	0.857800i	$0.328169\pi$
$68$		−	5.39187i		−	0.653860i
$69$	−14.1939			−1.70874
$70$	−0.785321	−	0.663485i	−0.0938638	−	0.0793017i
$71$		−	1.47782i		−	0.175385i	−0.996148	−	0.0876927i	$-0.972051\pi$
$71$		−	1.47782i		−	0.175385i	0.996148	−	0.0876927i	$-0.0279494\pi$
$72$	−8.66724			−1.02144
$73$	8.05573			0.942852			0.471426	−	0.881906i	$-0.343739\pi$
$73$	8.05573			0.942852			0.471426	+	0.881906i	$0.343739\pi$
$74$	8.07307			0.938475
$75$	16.8388	−	2.85224i	1.94438	−	0.329349i
$76$			3.30639i			0.379269i
$77$		−	0.933756i		−	0.106411i
$78$		0			0
$79$	1.68287			0.189338			0.0946690	−	0.995509i	$-0.469821\pi$
$79$	1.68287			0.189338			0.0946690	+	0.995509i	$0.469821\pi$
$80$	−1.70807	−	1.44308i	−0.190968	−	0.161341i
$81$	40.1194			4.45771
$82$		−	4.14511i		−	0.457751i
$83$	−9.99259			−1.09683			−0.548415	−	0.836207i	$-0.684768\pi$
$83$	−9.99259			−1.09683			−0.548415	+	0.836207i	$0.684768\pi$
$84$		−	1.57045i		−	0.171350i
$85$	−7.78090	+	9.20971i	−0.843957	+	0.998933i
$86$			1.26725i			0.136651i
$87$			20.6845i			2.21761i
$88$		−	2.03092i		−	0.216497i
$89$			3.93934i			0.417569i	0.977962	+	0.208785i	$0.0669508\pi$
$89$			3.93934i			0.417569i	−0.977962	+	0.208785i	$0.933049\pi$
$90$	14.8043	+	12.5075i	1.56051	+	1.31841i
$91$		0			0
$92$		−	4.15544i		−	0.433234i
$93$	22.2796			2.31028
$94$	1.29310			0.133373
$95$	4.77139	−	5.64755i	0.489534	−	0.579427i
$96$		−	3.41573i		−	0.348617i
$97$	−7.05844			−0.716676			−0.358338	−	0.933592i	$-0.616657\pi$
$97$	−7.05844			−0.716676			−0.358338	+	0.933592i	$0.616657\pi$
$98$	−6.78861			−0.685753
$99$			17.6025i			1.76912i
$100$	0.835031	+	4.92978i	0.0835031	+	0.492978i
$101$	−2.37044			−0.235868			−0.117934	−	0.993021i	$-0.537627\pi$
$101$	−2.37044			−0.235868			−0.117934	+	0.993021i	$0.537627\pi$
$102$	−18.4172			−1.82357
$103$		−	6.75491i		−	0.665581i	−0.943001	−	0.332790i	$-0.892010\pi$
$103$		−	6.75491i		−	0.665581i	0.943001	−	0.332790i	$-0.107990\pi$
$104$		0			0
$105$	−2.26629	+	2.68245i	−0.221167	+	0.261780i
$106$		−	5.78588i		−	0.561974i
$107$			0.0114398i			0.00110593i	1.00000		0.000552966i	$0.000176014\pi$
$107$			0.0114398i			0.00110593i	−1.00000		0.000552966i	$0.999824\pi$
$108$			19.3578i			1.86271i
$109$		−	3.79448i		−	0.363445i	−0.983350	−	0.181723i	$-0.941833\pi$
$109$		−	3.79448i		−	0.363445i	0.983350	−	0.181723i	$-0.0581673\pi$
$110$	−2.93078	+	3.46896i	−0.279439	+	0.330753i
$111$		−	27.5755i		−	2.61735i
$112$	0.459770			0.0434442
$113$			5.57377i			0.524336i	0.965022	+	0.262168i	$0.0844375\pi$
$113$			5.57377i			0.524336i	−0.965022	+	0.262168i	$0.915562\pi$
$114$	11.2937			1.05776
$115$	−5.99663	+	7.09779i	−0.559189	+	0.661872i
$116$	−6.05566			−0.562254
$117$		0			0
$118$		−	6.77070i		−	0.623294i
$119$		−	2.47902i		−	0.227251i
$120$	−4.92918	+	5.83433i	−0.449971	+	0.532599i
$121$	6.87536			0.625033
$122$	−5.98450			−0.541812
$123$	−14.1586			−1.27664
$124$			6.52262i			0.585749i
$125$	5.68778	−	9.62544i	0.508730	−	0.860926i
$126$	−3.98494			−0.355006
$127$		−	11.4002i		−	1.01160i	−0.862650	−	0.505801i	$-0.831197\pi$
$127$		−	11.4002i		−	1.01160i	0.862650	−	0.505801i	$-0.168803\pi$
$128$	1.00000			0.0883883
$129$	4.32857			0.381110
$130$		0			0
$131$	−14.9906			−1.30974			−0.654869	−	0.755743i	$-0.727276\pi$
$131$	−14.9906			−1.30974			−0.654869	+	0.755743i	$0.727276\pi$
$132$	−6.93709			−0.603796
$133$			1.52018i			0.131816i
$134$	8.41427			0.726882
$135$	27.9349	−	33.0645i	2.40425	−	2.84574i
$136$		−	5.39187i		−	0.462349i
$137$	13.6727			1.16814			0.584069	−	0.811704i	$-0.301460\pi$
$137$	13.6727			1.16814			0.584069	+	0.811704i	$0.301460\pi$
$138$	−14.1939			−1.20826
$139$	−11.8128			−1.00195			−0.500976	−	0.865461i	$-0.667026\pi$
$139$	−11.8128			−1.00195			−0.500976	+	0.865461i	$0.667026\pi$
$140$	−0.785321	−	0.663485i	−0.0663717	−	0.0560747i
$141$		−	4.41688i		−	0.371968i
$142$		−	1.47782i		−	0.124016i
$143$		0			0
$144$	−8.66724			−0.722270
$145$	10.3435	+	8.73881i	0.858982	+	0.725718i
$146$	8.05573			0.666697
$147$			23.1881i			1.91252i
$148$	8.07307			0.663602
$149$			21.3478i			1.74888i	0.485136	+	0.874439i	$0.338770\pi$
$149$			21.3478i			1.74888i	−0.485136	+	0.874439i	$0.661230\pi$
$150$	16.8388	−	2.85224i	1.37488	−	0.232885i
$151$		−	22.9456i		−	1.86729i	−0.358203	−	0.933644i	$-0.616610\pi$
$151$		−	22.9456i		−	1.86729i	0.358203	−	0.933644i	$-0.383390\pi$
$152$			3.30639i			0.268183i
$153$			46.7326i			3.77811i
$154$		−	0.933756i		−	0.0752442i
$155$	9.41268	−	11.1411i	0.756045	−	0.894876i
$156$		0			0
$157$		−	15.2264i		−	1.21520i	−0.794244	−	0.607599i	$-0.792133\pi$
$157$		−	15.2264i		−	1.21520i	0.794244	−	0.607599i	$-0.207867\pi$
$158$	1.68287			0.133882
$159$	−19.7630			−1.56731
$160$	−1.70807	−	1.44308i	−0.135035	−	0.114086i
$161$		−	1.91054i		−	0.150572i
$162$	40.1194			3.15208
$163$	−5.47677			−0.428974			−0.214487	−	0.976727i	$-0.568808\pi$
$163$	−5.47677			−0.428974			−0.214487	+	0.976727i	$0.568808\pi$
$164$		−	4.14511i		−	0.323679i
$165$	11.8491	+	10.0108i	0.922448	+	0.779338i
$166$	−9.99259			−0.775575
$167$	−2.94085			−0.227569			−0.113785	−	0.993505i	$-0.536297\pi$
$167$	−2.94085			−0.227569			−0.113785	+	0.993505i	$0.536297\pi$
$168$		−	1.57045i		−	0.121163i
$169$		0			0
$170$	−7.78090	+	9.20971i	−0.596768	+	0.706352i
$171$		−	28.6573i		−	2.19148i
$172$			1.26725i			0.0966265i
$173$		−	3.88650i		−	0.295485i	−0.989026	−	0.147742i	$-0.952799\pi$
$173$		−	3.88650i		−	0.295485i	0.989026	−	0.147742i	$-0.0472007\pi$
$174$			20.6845i			1.56809i
$175$	0.383922	+	2.26656i	0.0290218	+	0.171336i
$176$		−	2.03092i		−	0.153086i
$177$	−23.1269			−1.73833
$178$			3.93934i			0.295266i
$179$	10.3238			0.771636			0.385818	−	0.922575i	$-0.373919\pi$
$179$	10.3238			0.771636			0.385818	+	0.922575i	$0.373919\pi$
$180$	14.8043	+	12.5075i	1.10345	+	0.932257i
$181$	−3.68088			−0.273598			−0.136799	−	0.990599i	$-0.543681\pi$
$181$	−3.68088			−0.273598			−0.136799	+	0.990599i	$0.543681\pi$
$182$		0			0
$183$			20.4415i			1.51108i
$184$		−	4.15544i		−	0.306343i
$185$	−13.7894	−	11.6501i	−1.01382	−	0.856532i
$186$	22.2796			1.63362
$187$	−10.9505			−0.800777
$188$	1.29310			0.0943088
$189$			8.90013i			0.647389i
$190$	4.77139	−	5.64755i	0.346153	−	0.409717i
$191$	25.0076			1.80948			0.904742	−	0.425959i	$-0.140063\pi$
$191$	25.0076			1.80948			0.904742	+	0.425959i	$0.140063\pi$
$192$		−	3.41573i		−	0.246509i
$193$	1.97401			0.142093			0.0710463	−	0.997473i	$-0.477366\pi$
$193$	1.97401			0.142093			0.0710463	+	0.997473i	$0.477366\pi$
$194$	−7.05844			−0.506767
$195$		0			0
$196$	−6.78861			−0.484901
$197$	−17.6446			−1.25712			−0.628562	−	0.777760i	$-0.716356\pi$
$197$	−17.6446			−1.25712			−0.628562	+	0.777760i	$0.716356\pi$
$198$			17.6025i			1.25095i
$199$	−16.1718			−1.14639			−0.573193	−	0.819421i	$-0.694295\pi$
$199$	−16.1718			−1.14639			−0.573193	+	0.819421i	$0.694295\pi$
$200$	0.835031	+	4.92978i	0.0590456	+	0.348588i
$201$		−	28.7409i		−	2.02723i
$202$	−2.37044			−0.166784
$203$	−2.78421			−0.195413
$204$	−18.4172			−1.28946
$205$	−5.98173	+	7.08015i	−0.417782	+	0.494499i
$206$		−	6.75491i		−	0.470637i
$207$			36.0162i			2.50330i
$208$		0			0
$209$	6.71501			0.464487
$210$	−2.26629	+	2.68245i	−0.156389	+	0.185106i
$211$	−13.3757			−0.920819			−0.460410	−	0.887707i	$-0.652297\pi$
$211$	−13.3757			−0.920819			−0.460410	+	0.887707i	$0.652297\pi$
$212$		−	5.78588i		−	0.397376i
$213$	−5.04785			−0.345873
$214$			0.0114398i			0.000782011i
$215$	1.82874	−	2.16455i	0.124719	−	0.147621i
$216$			19.3578i			1.31713i
$217$			2.99890i			0.203579i
$218$		−	3.79448i		−	0.256995i
$219$		−	27.5162i		−	1.85937i
$220$	−2.93078	+	3.46896i	−0.197593	+	0.233877i
$221$		0			0
$222$		−	27.5755i		−	1.85074i
$223$	3.02345			0.202465			0.101233	−	0.994863i	$-0.467721\pi$
$223$	3.02345			0.202465			0.101233	+	0.994863i	$0.467721\pi$
$224$	0.459770			0.0307197
$225$	−7.23742	−	42.7276i	−0.482494	−	2.84851i
$226$			5.57377i			0.370762i
$227$	−14.6074			−0.969525			−0.484762	−	0.874646i	$-0.661094\pi$
$227$	−14.6074			−0.969525			−0.484762	+	0.874646i	$0.661094\pi$
$228$	11.2937			0.747946
$229$		−	14.0176i		−	0.926308i	−0.886278	−	0.463154i	$-0.846718\pi$
$229$		−	14.0176i		−	0.926308i	0.886278	−	0.463154i	$-0.153282\pi$
$230$	−5.99663	+	7.09779i	−0.395406	+	0.468014i
$231$	−3.18946			−0.209851
$232$	−6.05566			−0.397573
$233$		−	26.5904i		−	1.74200i	−0.491286	−	0.870998i	$-0.663473\pi$
$233$		−	26.5904i		−	1.74200i	0.491286	−	0.870998i	$-0.336527\pi$
$234$		0			0
$235$	−2.20870	−	1.86604i	−0.144080	−	0.121727i
$236$		−	6.77070i		−	0.440735i
$237$		−	5.74825i		−	0.373389i
$238$		−	2.47902i		−	0.160691i
$239$		−	12.3423i		−	0.798356i	−0.916874	−	0.399178i	$-0.869296\pi$
$239$		−	12.3423i		−	0.798356i	0.916874	−	0.399178i	$-0.130704\pi$
$240$	−4.92918	+	5.83433i	−0.318177	+	0.376604i
$241$			3.79308i			0.244334i	0.992510	+	0.122167i	$0.0389843\pi$
$241$			3.79308i			0.244334i	−0.992510	+	0.122167i	$0.961016\pi$
$242$	6.87536			0.441965
$243$		−	78.9638i		−	5.06553i
$244$	−5.98450			−0.383119
$245$	11.5954	+	9.79652i	0.740806	+	0.625877i
$246$	−14.1586			−0.902719
$247$		0			0
$248$			6.52262i			0.414187i
$249$			34.1320i			2.16303i
$250$	5.68778	−	9.62544i	0.359727	−	0.608767i
$251$	0.547631			0.0345662			0.0172831	−	0.999851i	$-0.494498\pi$
$251$	0.547631			0.0345662			0.0172831	+	0.999851i	$0.494498\pi$
$252$	−3.98494			−0.251027
$253$	−8.43936			−0.530578
$254$		−	11.4002i		−	0.715311i
$255$	31.4579	+	26.5775i	1.96997	+	1.66435i
$256$	1.00000			0.0625000
$257$		−	17.4033i		−	1.08559i	−0.839866	−	0.542793i	$-0.817367\pi$
$257$		−	17.4033i		−	1.08559i	0.839866	−	0.542793i	$-0.182633\pi$
$258$	4.32857			0.269485
$259$	3.71175			0.230637
$260$		0			0
$261$	52.4859			3.24879
$262$	−14.9906			−0.926124
$263$		−	11.6459i		−	0.718114i	−0.933316	−	0.359057i	$-0.883098\pi$
$263$		−	11.6459i		−	0.718114i	0.933316	−	0.359057i	$-0.116902\pi$
$264$	−6.93709			−0.426948
$265$	−8.34949	+	9.88271i	−0.512905	+	0.607090i
$266$			1.52018i			0.0932080i
$267$	13.4557			0.823478
$268$	8.41427			0.513983
$269$	16.9075			1.03087			0.515434	−	0.856929i	$-0.327631\pi$
$269$	16.9075			1.03087			0.515434	+	0.856929i	$0.327631\pi$
$270$	27.9349	−	33.0645i	1.70006	−	2.01224i
$271$		−	9.94128i		−	0.603889i	−0.953325	−	0.301945i	$-0.902364\pi$
$271$		−	9.94128i		−	0.603889i	0.953325	−	0.301945i	$-0.0976358\pi$
$272$		−	5.39187i		−	0.326930i
$273$		0			0
$274$	13.6727			0.825999
$275$	10.0120	−	1.69588i	0.603746	−	0.102266i
$276$	−14.1939			−0.854370
$277$			4.24476i			0.255043i	0.991836	+	0.127521i	$0.0407022\pi$
$277$			4.24476i			0.255043i	−0.991836	+	0.127521i	$0.959298\pi$
$278$	−11.8128			−0.708487
$279$		−	56.5332i		−	3.38455i
$280$	−0.785321	−	0.663485i	−0.0469319	−	0.0396508i
$281$			24.6567i			1.47090i	0.677580	+	0.735449i	$0.263029\pi$
$281$			24.6567i			1.47090i	−0.677580	+	0.735449i	$0.736971\pi$
$282$		−	4.41688i		−	0.263021i
$283$			9.64034i			0.573059i	0.958071	+	0.286529i	$0.0925016\pi$
$283$			9.64034i			0.573059i	−0.958071	+	0.286529i	$0.907498\pi$
$284$		−	1.47782i		−	0.0876927i
$285$	−19.2905	−	16.2978i	−1.14267	−	0.965398i
$286$		0			0
$287$		−	1.90580i		−	0.112496i
$288$	−8.66724			−0.510722
$289$	−12.0722			−0.710131
$290$	10.3435	+	8.73881i	0.607392	+	0.513160i
$291$			24.1098i			1.41334i
$292$	8.05573			0.471426
$293$	−6.02494			−0.351981			−0.175990	−	0.984392i	$-0.556313\pi$
$293$	−6.02494			−0.351981			−0.175990	+	0.984392i	$0.556313\pi$
$294$			23.1881i			1.35236i
$295$	−9.77067	+	11.5649i	−0.568871	+	0.673332i
$296$	8.07307			0.469238
$297$	39.3142			2.28124
$298$			21.3478i			1.23664i
$299$		0			0
$300$	16.8388	−	2.85224i	0.972190	−	0.164674i
$301$			0.582641i			0.0335829i
$302$		−	22.9456i		−	1.32037i
$303$			8.09679i			0.465149i
$304$			3.30639i			0.189634i
$305$	10.2220	+	8.63613i	0.585308	+	0.494503i
$306$			46.7326i			2.67153i
$307$	24.5247			1.39970			0.699850	−	0.714290i	$-0.253250\pi$
$307$	24.5247			1.39970			0.699850	+	0.714290i	$0.253250\pi$
$308$		−	0.933756i		−	0.0532057i
$309$	−23.0730			−1.31258
$310$	9.41268	−	11.1411i	0.534604	−	0.632773i
$311$	20.6188			1.16918			0.584591	−	0.811328i	$-0.301255\pi$
$311$	20.6188			1.16918			0.584591	+	0.811328i	$0.301255\pi$
$312$		0			0
$313$		−	7.35529i		−	0.415746i	−0.978156	−	0.207873i	$-0.933346\pi$
$313$		−	7.35529i		−	0.415746i	0.978156	−	0.207873i	$-0.0666540\pi$
$314$		−	15.2264i		−	0.859275i
$315$	6.80656	+	5.75059i	0.383506	+	0.324009i
$316$	1.68287			0.0946690
$317$	−17.4476			−0.979954			−0.489977	−	0.871735i	$-0.662995\pi$
$317$	−17.4476			−0.979954			−0.489977	+	0.871735i	$0.662995\pi$
$318$	−19.7630			−1.10826
$319$			12.2986i			0.688587i
$320$	−1.70807	−	1.44308i	−0.0954842	−	0.0806707i
$321$	0.0390755			0.00218098
$322$		−	1.91054i		−	0.106470i
$323$	17.8276			0.991954
$324$	40.1194			2.22885
$325$		0			0
$326$	−5.47677			−0.303330
$327$	−12.9609			−0.716742
$328$		−	4.14511i		−	0.228875i
$329$	0.594527			0.0327773
$330$	11.8491	+	10.0108i	0.652269	+	0.551075i
$331$			18.5906i			1.02183i	0.859630	+	0.510917i	$0.170694\pi$
$331$			18.5906i			1.02183i	−0.859630	+	0.510917i	$0.829306\pi$
$332$	−9.99259			−0.548415
$333$	−69.9713			−3.83440
$334$	−2.94085			−0.160916
$335$	−14.3722	−	12.1425i	−0.785237	−	0.663414i
$336$		−	1.57045i		−	0.0856752i
$337$		−	11.2984i		−	0.615463i	−0.951473	−	0.307732i	$-0.900430\pi$
$337$		−	11.2984i		−	0.615463i	0.951473	−	0.307732i	$-0.0995699\pi$
$338$		0			0
$339$	19.0385			1.03403
$340$	−7.78090	+	9.20971i	−0.421979	+	0.499466i
$341$	13.2469			0.717362
$342$		−	28.6573i		−	1.54961i
$343$	−6.33959			−0.342305
$344$			1.26725i			0.0683253i
$345$	24.2442	+	20.4829i	1.30526	+	1.10276i
$346$		−	3.88650i		−	0.208939i
$347$		−	22.2403i		−	1.19392i	−0.802270	−	0.596961i	$-0.796375\pi$
$347$		−	22.2403i		−	1.19392i	0.802270	−	0.596961i	$-0.203625\pi$
$348$			20.6845i			1.10881i
$349$		−	22.6265i		−	1.21117i	−0.795781	−	0.605585i	$-0.792939\pi$
$349$		−	22.6265i		−	1.21117i	0.795781	−	0.605585i	$-0.207061\pi$
$350$	0.383922	+	2.26656i	0.0205215	+	0.121153i
$351$		0			0
$352$		−	2.03092i		−	0.108248i
$353$	−7.66644			−0.408044			−0.204022	−	0.978966i	$-0.565401\pi$
$353$	−7.66644			−0.408044			−0.204022	+	0.978966i	$0.565401\pi$
$354$	−23.1269			−1.22918
$355$	−2.13262	+	2.52423i	−0.113188	+	0.133972i
$356$			3.93934i			0.208785i
$357$	−8.46766			−0.448156
$358$	10.3238			0.545629
$359$		−	31.5137i		−	1.66323i	−0.555353	−	0.831615i	$-0.687417\pi$
$359$		−	31.5137i		−	1.66323i	0.555353	−	0.831615i	$-0.312583\pi$
$360$	14.8043	+	12.5075i	0.780255	+	0.659205i
$361$	8.06780			0.424621
$362$	−3.68088			−0.193463
$363$		−	23.4844i		−	1.23261i
$364$		0			0
$365$	−13.7598	−	11.6251i	−0.720220	−	0.608484i
$366$			20.4415i			1.06849i
$367$			25.5000i			1.33109i	0.746359	+	0.665544i	$0.231800\pi$
$367$			25.5000i			1.33109i	−0.746359	+	0.665544i	$0.768200\pi$
$368$		−	4.15544i		−	0.216617i
$369$			35.9267i			1.87027i
$370$	−13.7894	−	11.6501i	−0.716877	−	0.605660i
$371$		−	2.66017i		−	0.138109i
$372$	22.2796			1.15514
$373$		−	15.2112i		−	0.787604i	−0.919195	−	0.393802i	$-0.871159\pi$
$373$		−	15.2112i		−	0.787604i	0.919195	−	0.393802i	$-0.128841\pi$
$374$	−10.9505			−0.566235
$375$	−32.8780	−	19.4279i	−1.69781	−	1.00325i
$376$	1.29310			0.0666864
$377$		0			0
$378$			8.90013i			0.457773i
$379$		−	17.2766i		−	0.887439i	−0.896166	−	0.443719i	$-0.853659\pi$
$379$		−	17.2766i		−	0.887439i	0.896166	−	0.443719i	$-0.146341\pi$
$380$	4.77139	−	5.64755i	0.244767	−	0.289713i
$381$	−38.9400			−1.99496
$382$	25.0076			1.27950
$383$	15.1262			0.772915			0.386458	−	0.922307i	$-0.373699\pi$
$383$	15.1262			0.772915			0.386458	+	0.922307i	$0.373699\pi$
$384$		−	3.41573i		−	0.174308i
$385$	−1.34749	+	1.59492i	−0.0686742	+	0.0812848i
$386$	1.97401			0.100475
$387$		−	10.9835i		−	0.558324i
$388$	−7.05844			−0.358338
$389$	−32.0553			−1.62527			−0.812635	−	0.582774i	$-0.801967\pi$
$389$	−32.0553			−1.62527			−0.812635	+	0.582774i	$0.801967\pi$
$390$		0			0
$391$	−22.4056			−1.13310
$392$	−6.78861			−0.342877
$393$			51.2040i			2.58290i
$394$	−17.6446			−0.888920
$395$	−2.87447	−	2.42852i	−0.144630	−	0.122192i
$396$			17.6025i			0.884558i
$397$	7.52503			0.377670			0.188835	−	0.982009i	$-0.439529\pi$
$397$	7.52503			0.377670			0.188835	+	0.982009i	$0.439529\pi$
$398$	−16.1718			−0.810617
$399$	5.19252			0.259951
$400$	0.835031	+	4.92978i	0.0417515	+	0.246489i
$401$			37.3359i			1.86447i	0.361860	+	0.932233i	$0.382142\pi$
$401$			37.3359i			1.86447i	−0.361860	+	0.932233i	$0.617858\pi$
$402$		−	28.7409i		−	1.43347i
$403$		0			0
$404$	−2.37044			−0.117934
$405$	−68.5269	−	57.8955i	−3.40513	−	2.87685i
$406$	−2.78421			−0.138178
$407$		−	16.3958i		−	0.812708i
$408$	−18.4172			−0.911787
$409$			19.7733i			0.977729i	0.872360	+	0.488864i	$0.162589\pi$
$409$			19.7733i			0.977729i	−0.872360	+	0.488864i	$0.837411\pi$
$410$	−5.98173	+	7.08015i	−0.295417	+	0.349664i
$411$		−	46.7024i		−	2.30366i
$412$		−	6.75491i		−	0.332790i
$413$		−	3.11296i		−	0.153179i
$414$			36.0162i			1.77010i
$415$	17.0681	+	14.4201i	0.837839	+	0.707856i
$416$		0			0
$417$			40.3495i			1.97592i
$418$	6.71501			0.328442
$419$	12.4677			0.609086			0.304543	−	0.952499i	$-0.401496\pi$
$419$	12.4677			0.609086			0.304543	+	0.952499i	$0.401496\pi$
$420$	−2.26629	+	2.68245i	−0.110584	+	0.130890i
$421$		−	1.36944i		−	0.0667423i	−0.999443	−	0.0333712i	$-0.989376\pi$
$421$		−	1.36944i		−	0.0667423i	0.999443	−	0.0333712i	$-0.0106243\pi$
$422$	−13.3757			−0.651118
$423$	−11.2076			−0.544932
$424$		−	5.78588i		−	0.280987i
$425$	26.5807	−	4.50238i	1.28935	−	0.218397i
$426$	−5.04785			−0.244569
$427$	−2.75149			−0.133154
$428$			0.0114398i			0.000552966i
$429$		0			0
$430$	1.82874	−	2.16455i	0.0881896	−	0.104384i
$431$			11.1142i			0.535354i	0.963509	+	0.267677i	$0.0862560\pi$
$431$			11.1142i			0.535354i	−0.963509	+	0.267677i	$0.913744\pi$
$432$			19.3578i			0.931353i
$433$			30.2038i			1.45150i	0.687957	+	0.725752i	$0.258508\pi$
$433$			30.2038i			1.45150i	−0.687957	+	0.725752i	$0.741492\pi$
$434$			2.99890i			0.143952i
$435$	29.8494	−	35.3307i	1.43117	−	1.69398i
$436$		−	3.79448i		−	0.181723i
$437$	13.7395			0.657249
$438$		−	27.5162i		−	1.31478i
$439$	30.0084			1.43223			0.716113	−	0.697985i	$-0.245920\pi$
$439$	30.0084			1.43223			0.716113	+	0.697985i	$0.245920\pi$
$440$	−2.93078	+	3.46896i	−0.139720	+	0.165376i
$441$	58.8386			2.80184
$442$		0			0
$443$			10.0957i			0.479661i	0.970815	+	0.239830i	$0.0770918\pi$
$443$			10.0957i			0.479661i	−0.970815	+	0.239830i	$0.922908\pi$
$444$		−	27.5755i		−	1.30867i
$445$	5.68479	−	6.72868i	0.269485	−	0.318970i
$446$	3.02345			0.143165
$447$	72.9183			3.44892
$448$	0.459770			0.0217221
$449$			28.9563i			1.36653i	0.730169	+	0.683266i	$0.239441\pi$
$449$			28.9563i			1.36653i	−0.730169	+	0.683266i	$0.760559\pi$
$450$	−7.23742	−	42.7276i	−0.341175	−	2.01420i
$451$	−8.41839			−0.396407
$452$			5.57377i			0.262168i
$453$	−78.3761			−3.68243
$454$	−14.6074			−0.685558
$455$		0			0
$456$	11.2937			0.528878
$457$	40.4620			1.89273			0.946367	−	0.323094i	$-0.104723\pi$
$457$	40.4620			1.89273			0.946367	+	0.323094i	$0.104723\pi$
$458$		−	14.0176i		−	0.654998i
$459$	104.375			4.87179
$460$	−5.99663	+	7.09779i	−0.279594	+	0.330936i
$461$			6.39717i			0.297946i	0.988841	+	0.148973i	$0.0475967\pi$
$461$			6.39717i			0.297946i	−0.988841	+	0.148973i	$0.952403\pi$
$462$	−3.18946			−0.148387
$463$	15.3751			0.714541			0.357270	−	0.934001i	$-0.383707\pi$
$463$	15.3751			0.714541			0.357270	+	0.934001i	$0.383707\pi$
$464$	−6.05566			−0.281127
$465$	−38.0551	−	32.1512i	−1.76476	−	1.49098i
$466$		−	26.5904i		−	1.23178i
$467$		−	9.41379i		−	0.435618i	−0.975991	−	0.217809i	$-0.930109\pi$
$467$		−	9.41379i		−	0.435618i	0.975991	−	0.217809i	$-0.0698911\pi$
$468$		0			0
$469$	3.86863			0.178637
$470$	−2.20870	−	1.86604i	−0.101880	−	0.0860742i
$471$	−52.0093			−2.39646
$472$		−	6.77070i		−	0.311647i
$473$	2.57367			0.118338
$474$		−	5.74825i		−	0.264026i
$475$	−16.2998	+	2.76094i	−0.747884	+	0.126680i
$476$		−	2.47902i		−	0.113626i
$477$			50.1476i			2.29610i
$478$		−	12.3423i		−	0.564523i
$479$			24.7651i			1.13155i	0.824560	+	0.565774i	$0.191423\pi$
$479$			24.7651i			1.13155i	−0.824560	+	0.565774i	$0.808577\pi$
$480$	−4.92918	+	5.83433i	−0.224985	+	0.266299i
$481$		0			0
$482$			3.79308i			0.172770i
$483$	−6.52591			−0.296939
$484$	6.87536			0.312516
$485$	12.0563	+	10.1859i	0.547450	+	0.462518i
$486$		−	78.9638i		−	3.58187i
$487$	−27.2037			−1.23272			−0.616358	−	0.787466i	$-0.711393\pi$
$487$	−27.2037			−1.23272			−0.616358	+	0.787466i	$0.711393\pi$
$488$	−5.98450			−0.270906
$489$			18.7072i			0.845969i
$490$	11.5954	+	9.79652i	0.523829	+	0.442562i
$491$	27.4578			1.23915			0.619576	−	0.784937i	$-0.287305\pi$
$491$	27.4578			1.23915			0.619576	+	0.784937i	$0.287305\pi$
$492$	−14.1586			−0.638319
$493$			32.6513i			1.47054i
$494$		0			0
$495$	25.4018	−	30.0663i	1.14173	−	1.35138i
$496$			6.52262i			0.292874i
$497$		−	0.679459i		−	0.0304779i
$498$			34.1320i			1.52949i
$499$		−	2.92681i		−	0.131022i	−0.997852	−	0.0655109i	$-0.979132\pi$
$499$		−	2.92681i		−	0.131022i	0.997852	−	0.0655109i	$-0.0208677\pi$
$500$	5.68778	−	9.62544i	0.254365	−	0.430463i
$501$			10.0451i			0.448784i
$502$	0.547631			0.0244420
$503$			0.113123i			0.00504392i	0.999997	+	0.00252196i	$0.000802766\pi$
$503$			0.113123i			0.00504392i	−0.999997	+	0.00252196i	$0.999197\pi$
$504$	−3.98494			−0.177503
$505$	4.04888	+	3.42074i	0.180173	+	0.152221i
$506$	−8.43936			−0.375175
$507$		0			0
$508$		−	11.4002i		−	0.505801i
$509$		−	19.0806i		−	0.845731i	−0.906193	−	0.422865i	$-0.861024\pi$
$509$		−	19.0806i		−	0.845731i	0.906193	−	0.422865i	$-0.138976\pi$
$510$	31.4579	+	26.5775i	1.39298	+	1.17687i
$511$	3.70378			0.163846
$512$	1.00000			0.0441942
$513$	−64.0044			−2.82586
$514$		−	17.4033i		−	0.767626i
$515$	−9.74788	+	11.5379i	−0.429543	+	0.508420i
$516$	4.32857			0.190555
$517$		−	2.62618i		−	0.115499i
$518$	3.71175			0.163085
$519$	−13.2752			−0.582718
$520$		0			0
$521$	−6.88125			−0.301473			−0.150736	−	0.988574i	$-0.548164\pi$
$521$	−6.88125			−0.301473			−0.150736	+	0.988574i	$0.548164\pi$
$522$	52.4859			2.29724
$523$		−	19.7227i		−	0.862414i	−0.902253	−	0.431207i	$-0.858088\pi$
$523$		−	19.7227i		−	0.862414i	0.902253	−	0.431207i	$-0.141912\pi$
$524$	−14.9906			−0.654869
$525$	7.74198	−	1.31138i	0.337888	−	0.0572331i
$526$		−	11.6459i		−	0.507783i
$527$	35.1691			1.53199
$528$	−6.93709			−0.301898
$529$	5.73235			0.249233
$530$	−8.34949	+	9.88271i	−0.362679	+	0.429277i
$531$			58.6833i			2.54664i
$532$			1.52018i			0.0659080i
$533$		0			0
$534$	13.4557			0.582287
$535$	0.0165086	−	0.0195401i	0.000713730	−	0.000844792i
$536$	8.41427			0.363441
$537$		−	35.2633i		−	1.52173i
$538$	16.9075			0.728934
$539$			13.7871i			0.593854i
$540$	27.9349	−	33.0645i	1.20213	−	1.42287i
$541$			41.8747i			1.80034i	0.435543	+	0.900168i	$0.356556\pi$
$541$			41.8747i			1.80034i	−0.435543	+	0.900168i	$0.643444\pi$
$542$		−	9.94128i		−	0.427014i
$543$			12.5729i			0.539555i
$544$		−	5.39187i		−	0.231174i
$545$	−5.47575	+	6.48125i	−0.234555	+	0.277626i
$546$		0			0
$547$		−	28.0881i		−	1.20096i	−0.799639	−	0.600481i	$-0.794976\pi$
$547$		−	28.0881i		−	1.20096i	0.799639	−	0.600481i	$-0.205024\pi$
$548$	13.6727			0.584069
$549$	51.8692			2.21372
$550$	10.0120	−	1.69588i	0.426913	−	0.0723126i
$551$		−	20.0224i		−	0.852981i
$552$	−14.1939			−0.604131
$553$	0.773734			0.0329025
$554$			4.24476i			0.180343i
$555$	−39.7936	+	47.1009i	−1.68915	+	1.99932i
$556$	−11.8128			−0.500976
$557$	29.3170			1.24220			0.621101	−	0.783730i	$-0.286685\pi$
$557$	29.3170			1.24220			0.621101	+	0.783730i	$0.286685\pi$
$558$		−	56.5332i		−	2.39324i
$559$		0			0
$560$	−0.785321	−	0.663485i	−0.0331859	−	0.0280374i
$561$			37.4038i			1.57919i
$562$			24.6567i			1.04008i
$563$			2.10937i			0.0888995i	0.999012	+	0.0444497i	$0.0141535\pi$
$563$			2.10937i			0.0888995i	−0.999012	+	0.0444497i	$0.985847\pi$
$564$		−	4.41688i		−	0.185984i
$565$	8.04341	−	9.52041i	0.338389	−	0.400527i
$566$			9.64034i			0.405214i
$567$	18.4457			0.774646
$568$		−	1.47782i		−	0.0620081i
$569$	14.0188			0.587697			0.293849	−	0.955852i	$-0.405064\pi$
$569$	14.0188			0.587697			0.293849	+	0.955852i	$0.405064\pi$
$570$	−19.2905	−	16.2978i	−0.807992	−	0.682640i
$571$	27.5675			1.15366			0.576831	−	0.816864i	$-0.304289\pi$
$571$	27.5675			1.15366			0.576831	+	0.816864i	$0.304289\pi$
$572$		0			0
$573$		−	85.4192i		−	3.56844i
$574$		−	1.90580i		−	0.0795464i
$575$	20.4854	−	3.46992i	0.854300	−	0.144706i
$576$	−8.66724			−0.361135
$577$	19.0434			0.792788			0.396394	−	0.918080i	$-0.370261\pi$
$577$	19.0434			0.792788			0.396394	+	0.918080i	$0.370261\pi$
$578$	−12.0722			−0.502138
$579$		−	6.74271i		−	0.280217i
$580$	10.3435	+	8.73881i	0.429491	+	0.362859i
$581$	−4.59429			−0.190603
$582$			24.1098i			0.999382i
$583$	−11.7507			−0.486663
$584$	8.05573			0.333348
$585$		0			0
$586$	−6.02494			−0.248888
$587$	−16.0453			−0.662260			−0.331130	−	0.943585i	$-0.607430\pi$
$587$	−16.0453			−0.662260			−0.331130	+	0.943585i	$0.607430\pi$
$588$			23.1881i			0.956261i
$589$	−21.5663			−0.888625
$590$	−9.77067	+	11.5649i	−0.402252	+	0.476118i
$591$			60.2691i			2.47914i
$592$	8.07307			0.331801
$593$	43.3422			1.77985			0.889925	−	0.456107i	$-0.150756\pi$
$593$	43.3422			1.77985			0.889925	+	0.456107i	$0.150756\pi$
$594$	39.3142			1.61308
$595$	−3.57742	+	4.23434i	−0.146660	+	0.173591i
$596$			21.3478i			0.874439i
$597$			55.2384i			2.26076i
$598$		0			0
$599$	8.53779			0.348845			0.174422	−	0.984671i	$-0.444194\pi$
$599$	8.53779			0.348845			0.174422	+	0.984671i	$0.444194\pi$
$600$	16.8388	−	2.85224i	0.687442	−	0.116442i
$601$	−31.5044			−1.28509			−0.642545	−	0.766248i	$-0.722121\pi$
$601$	−31.5044			−1.28509			−0.642545	+	0.766248i	$0.722121\pi$
$602$			0.582641i			0.0237467i
$603$	−72.9285			−2.96988
$604$		−	22.9456i		−	0.933644i
$605$	−11.7436	−	9.92171i	−0.477446	−	0.403375i
$606$			8.09679i			0.328910i
$607$		−	14.8586i		−	0.603093i	−0.953451	−	0.301546i	$-0.902497\pi$
$607$		−	14.8586i		−	0.603093i	0.953451	−	0.301546i	$-0.0975028\pi$
$608$			3.30639i			0.134092i
$609$			9.51012i			0.385369i
$610$	10.2220	+	8.63613i	0.413876	+	0.349667i
$611$		0			0
$612$			46.7326i			1.88905i
$613$	24.9342			1.00708			0.503541	−	0.863971i	$-0.332030\pi$
$613$	24.9342			1.00708			0.503541	+	0.863971i	$0.332030\pi$
$614$	24.5247			0.989737
$615$	24.1839	+	20.4320i	0.975190	+	0.823898i
$616$		−	0.933756i		−	0.0376221i
$617$	20.7921			0.837057			0.418528	−	0.908204i	$-0.362546\pi$
$617$	20.7921			0.837057			0.418528	+	0.908204i	$0.362546\pi$
$618$	−23.0730			−0.928131
$619$			22.8769i			0.919501i	0.888048	+	0.459751i	$0.152061\pi$
$619$			22.8769i			0.919501i	−0.888048	+	0.459751i	$0.847939\pi$
$620$	9.41268	−	11.1411i	0.378022	−	0.447438i
$621$	80.4401			3.22795
$622$	20.6188			0.826737
$623$			1.81119i			0.0725638i
$624$		0			0
$625$	−23.6054	+	8.23304i	−0.944218	+	0.329321i
$626$		−	7.35529i		−	0.293977i
$627$		−	22.9367i		−	0.916004i
$628$		−	15.2264i		−	0.607599i
$629$		−	43.5289i		−	1.73561i
$630$	6.80656	+	5.75059i	0.271180	+	0.229109i
$631$			22.6688i			0.902429i	0.892416	+	0.451214i	$0.149009\pi$
$631$			22.6688i			0.902429i	−0.892416	+	0.451214i	$0.850991\pi$
$632$	1.68287			0.0669411
$633$			45.6877i			1.81592i
$634$	−17.4476			−0.692932
$635$	−16.4514	+	19.4724i	−0.652854	+	0.772737i
$636$	−19.7630			−0.783655
$637$		0			0
$638$			12.2986i			0.486905i
$639$			12.8087i			0.506703i
$640$	−1.70807	−	1.44308i	−0.0675175	−	0.0570428i
$641$	11.5650			0.456789			0.228394	−	0.973569i	$-0.426652\pi$
$641$	11.5650			0.456789			0.228394	+	0.973569i	$0.426652\pi$
$642$	0.0390755			0.00154219
$643$	25.4887			1.00518			0.502588	−	0.864526i	$-0.332381\pi$
$643$	25.4887			1.00518			0.502588	+	0.864526i	$0.332381\pi$
$644$		−	1.91054i		−	0.0752860i
$645$	−7.39352	−	6.24648i	−0.291120	−	0.245955i
$646$	17.8276			0.701418
$647$			0.686256i			0.0269795i	0.999909	+	0.0134897i	$0.00429405\pi$
$647$			0.686256i			0.0269795i	−0.999909	+	0.0134897i	$0.995706\pi$
$648$	40.1194			1.57604
$649$	−13.7508			−0.539764
$650$		0			0
$651$	10.2435			0.401473
$652$	−5.47677			−0.214487
$653$			20.7584i			0.812338i	0.913798	+	0.406169i	$0.133136\pi$
$653$			20.7584i			0.812338i	−0.913798	+	0.406169i	$0.866864\pi$
$654$	−12.9609			−0.506813
$655$	25.6051	+	21.6327i	1.00047	+	0.845259i
$656$		−	4.14511i		−	0.161839i
$657$	−69.8210			−2.72398
$658$	0.594527			0.0231771
$659$	23.2146			0.904312			0.452156	−	0.891939i	$-0.350655\pi$
$659$	23.2146			0.904312			0.452156	+	0.891939i	$0.350655\pi$
$660$	11.8491	+	10.0108i	0.461224	+	0.389669i
$661$		−	14.9740i		−	0.582422i	−0.956659	−	0.291211i	$-0.905942\pi$
$661$		−	14.9740i		−	0.582422i	0.956659	−	0.291211i	$-0.0940581\pi$
$662$			18.5906i			0.722546i
$663$		0			0
$664$	−9.99259			−0.387788
$665$	2.19374	−	2.59657i	0.0850696	−	0.100691i
$666$	−69.9713			−2.71133
$667$			25.1639i			0.974350i
$668$	−2.94085			−0.113785
$669$		−	10.3273i		−	0.399277i
$670$	−14.3722	−	12.1425i	−0.555246	−	0.469105i
$671$			12.1541i			0.469202i
$672$		−	1.57045i		−	0.0605815i
$673$			17.2347i			0.664348i	0.943218	+	0.332174i	$0.107782\pi$
$673$			17.2347i			0.664348i	−0.943218	+	0.332174i	$0.892218\pi$
$674$		−	11.2984i		−	0.435198i
$675$	−95.4297	+	16.1644i	−3.67309	+	0.622167i
$676$		0			0
$677$			12.1285i			0.466136i	0.972460	+	0.233068i	$0.0748765\pi$
$677$			12.1285i			0.466136i	−0.972460	+	0.233068i	$0.925124\pi$
$678$	19.0385			0.731170
$679$	−3.24526			−0.124542
$680$	−7.78090	+	9.20971i	−0.298384	+	0.353176i
$681$			49.8949i			1.91198i
$682$	13.2469			0.507251
$683$	20.0828			0.768449			0.384224	−	0.923240i	$-0.374469\pi$
$683$	20.0828			0.768449			0.384224	+	0.923240i	$0.374469\pi$
$684$		−	28.6573i		−	1.09574i
$685$	−23.3540	−	19.7308i	−0.892311	−	0.753877i
$686$	−6.33959			−0.242047
$687$	−47.8803			−1.82675
$688$			1.26725i			0.0483133i
$689$		0			0
$690$	24.2442	+	20.4829i	0.922960	+	0.779771i
$691$			24.8495i			0.945320i	0.881245	+	0.472660i	$0.156706\pi$
$691$			24.8495i			0.945320i	−0.881245	+	0.472660i	$0.843294\pi$
$692$		−	3.88650i		−	0.147742i
$693$			8.09309i			0.307431i
$694$		−	22.2403i		−	0.844231i
$695$	20.1772	+	17.0469i	0.765365	+	0.646625i
$696$			20.6845i			0.784045i
$697$	−22.3499			−0.846562
$698$		−	22.6265i		−	0.856427i
$699$	−90.8258			−3.43535
$700$	0.383922	+	2.26656i	0.0145109	+	0.0856680i
$701$	26.3896			0.996720			0.498360	−	0.866970i	$-0.333936\pi$
$701$	26.3896			0.996720			0.498360	+	0.866970i	$0.333936\pi$
$702$		0			0
$703$			26.6927i			1.00673i
$704$		−	2.03092i		−	0.0765432i
$705$	−6.37391	+	7.54435i	−0.240055	+	0.284137i
$706$	−7.66644			−0.288530
$707$	−1.08986			−0.0409883
$708$	−23.1269			−0.869163
$709$		−	28.0118i		−	1.05201i	−0.850483	−	0.526003i	$-0.823690\pi$
$709$		−	28.0118i		−	1.05201i	0.850483	−	0.526003i	$-0.176310\pi$
$710$	−2.13262	+	2.52423i	−0.0800358	+	0.0947327i
$711$	−14.5859			−0.547013
$712$			3.93934i			0.147633i
$713$	27.1043			1.01507
$714$	−8.46766			−0.316894
$715$		0			0
$716$	10.3238			0.385818
$717$	−42.1580			−1.57442
$718$		−	31.5137i		−	1.17608i
$719$	−40.0185			−1.49244			−0.746219	−	0.665700i	$-0.768133\pi$
$719$	−40.0185			−1.49244			−0.746219	+	0.665700i	$0.768133\pi$
$720$	14.8043	+	12.5075i	0.551723	+	0.466128i
$721$		−	3.10570i		−	0.115662i
$722$	8.06780			0.300252
$723$	12.9562			0.481845
$724$	−3.68088			−0.136799
$725$	−5.05666	−	29.8531i	−0.187800	−	1.10871i
$726$		−	23.4844i		−	0.871588i
$727$		−	37.8003i		−	1.40193i	−0.713194	−	0.700967i	$-0.752752\pi$
$727$		−	37.8003i		−	1.40193i	0.713194	−	0.700967i	$-0.247248\pi$
$728$		0			0
$729$	−149.361			−5.53189
$730$	−13.7598	−	11.6251i	−0.509272	−	0.430263i
$731$	6.83282			0.252721
$732$			20.4415i			0.755539i
$733$	6.65212			0.245701			0.122851	−	0.992425i	$-0.460796\pi$
$733$	6.65212			0.245701			0.122851	+	0.992425i	$0.460796\pi$
$734$			25.5000i			0.941221i
$735$	33.4623	−	39.6070i	1.23428	−	1.46093i
$736$		−	4.15544i		−	0.153171i
$737$		−	17.0887i		−	0.629471i
$738$			35.9267i			1.32248i
$739$		−	28.4479i		−	1.04647i	−0.852188	−	0.523236i	$-0.824725\pi$
$739$		−	28.4479i		−	1.04647i	0.852188	−	0.523236i	$-0.175275\pi$
$740$	−13.7894	−	11.6501i	−0.506908	−	0.428266i
$741$		0			0
$742$		−	2.66017i		−	0.0976580i
$743$	−16.3224			−0.598809			−0.299405	−	0.954126i	$-0.596788\pi$
$743$	−16.3224			−0.598809			−0.299405	+	0.954126i	$0.596788\pi$
$744$	22.2796			0.816808
$745$	30.8066	−	36.4636i	1.12867	−	1.33592i
$746$		−	15.2112i		−	0.556920i
$747$	86.6082			3.16883
$748$	−10.9505			−0.400388
$749$			0.00525969i			0.000192185i
$750$	−32.8780	−	19.4279i	−1.20053	−	0.709408i
$751$	0.398628			0.0145461			0.00727307	−	0.999974i	$-0.497685\pi$
$751$	0.398628			0.0145461			0.00727307	+	0.999974i	$0.497685\pi$
$752$	1.29310			0.0471544
$753$		−	1.87056i		−	0.0681671i
$754$		0			0
$755$	−33.1124	+	39.1928i	−1.20508	+	1.42637i
$756$			8.90013i			0.323695i
$757$			40.1310i			1.45859i	0.684201	+	0.729293i	$0.260151\pi$
$757$			40.1310i			1.45859i	−0.684201	+	0.729293i	$0.739849\pi$
$758$		−	17.2766i		−	0.627514i
$759$			28.8266i			1.04634i
$760$	4.77139	−	5.64755i	0.173076	−	0.204858i
$761$			3.64226i			0.132032i	0.997819	+	0.0660158i	$0.0210288\pi$
$761$			3.64226i			0.132032i	−0.997819	+	0.0660158i	$0.978971\pi$
$762$	−38.9400			−1.41065
$763$		−	1.74459i		−	0.0631583i
$764$	25.0076			0.904742
$765$	67.4390	−	79.8228i	2.43826	−	2.88600i
$766$	15.1262			0.546533
$767$		0			0
$768$		−	3.41573i		−	0.123255i
$769$		−	16.4037i		−	0.591533i	−0.955260	−	0.295767i	$-0.904425\pi$
$769$		−	16.4037i		−	0.591533i	0.955260	−	0.295767i	$-0.0955750\pi$
$770$	−1.34749	+	1.59492i	−0.0485600	+	0.0574771i
$771$	−59.4450			−2.14086
$772$	1.97401			0.0710463
$773$	−11.3166			−0.407028			−0.203514	−	0.979072i	$-0.565236\pi$
$773$	−11.3166			−0.407028			−0.203514	+	0.979072i	$0.565236\pi$
$774$		−	10.9835i		−	0.394795i
$775$	−32.1551	+	5.44659i	−1.15505	+	0.195647i
$776$	−7.05844			−0.253383
$777$		−	12.6784i		−	0.454834i
$778$	−32.0553			−1.14924
$779$	13.7053			0.491045
$780$		0			0
$781$	−3.00134			−0.107396
$782$	−22.4056			−0.801221
$783$		−	117.224i		−	4.18925i
$784$	−6.78861			−0.242450
$785$	−21.9729	+	26.0078i	−0.784247	+	0.928258i
$786$			51.2040i			1.82639i
$787$	23.6730			0.843850			0.421925	−	0.906631i	$-0.361354\pi$
$787$	23.6730			0.843850			0.421925	+	0.906631i	$0.361354\pi$
$788$	−17.6446			−0.628562
$789$	−39.7791			−1.41618
$790$	−2.87447	−	2.42852i	−0.102269	−	0.0864030i
$791$			2.56265i			0.0911174i
$792$			17.6025i			0.625477i
$793$		0			0
$794$	7.52503			0.267053
$795$	33.7567	+	28.5197i	1.19723	+	1.01149i
$796$	−16.1718			−0.573193
$797$			4.35054i			0.154104i	0.997027	+	0.0770520i	$0.0245507\pi$
$797$			4.35054i			0.154104i	−0.997027	+	0.0770520i	$0.975449\pi$
$798$	5.19252			0.183813
$799$		−	6.97221i		−	0.246659i
$800$	0.835031	+	4.92978i	0.0295228	+	0.174294i
$801$		−	34.1432i		−	1.20639i
$802$			37.3359i			1.31838i
$803$		−	16.3605i		−	0.577351i
$804$		−	28.7409i		−	1.01361i
$805$	−2.75707	+	3.26335i	−0.0971740	+	0.115018i
$806$		0			0
$807$		−	57.7516i		−	2.03295i
$808$	−2.37044			−0.0833918
$809$	24.9033			0.875552			0.437776	−	0.899084i	$-0.355766\pi$
$809$	24.9033			0.875552			0.437776	+	0.899084i	$0.355766\pi$
$810$	−68.5269	−	57.8955i	−2.40779	−	2.03424i
$811$			30.1105i			1.05732i	0.848833	+	0.528661i	$0.177306\pi$
$811$			30.1105i			1.05732i	−0.848833	+	0.528661i	$0.822694\pi$
$812$	−2.78421			−0.0977065
$813$	−33.9568			−1.19092
$814$		−	16.3958i		−	0.574671i
$815$	9.35473	+	7.90343i	0.327682	+	0.276845i
$816$	−18.4172			−0.644730
$817$	−4.19000			−0.146590
$818$			19.7733i			0.691359i
$819$		0			0
$820$	−5.98173	+	7.08015i	−0.208891	+	0.247250i
$821$			33.9761i			1.18577i	0.805286	+	0.592887i	$0.202012\pi$
$821$			33.9761i			1.18577i	−0.805286	+	0.592887i	$0.797988\pi$
$822$		−	46.7024i		−	1.62893i
$823$			18.7804i			0.654644i	0.944913	+	0.327322i	$0.106146\pi$
$823$			18.7804i			0.654644i	−0.944913	+	0.327322i	$0.893854\pi$
$824$		−	6.75491i		−	0.235318i
$825$	−5.79268	−	34.1983i	−0.201675	−	1.19063i
$826$		−	3.11296i		−	0.108314i
$827$	−56.4739			−1.96379			−0.981895	−	0.189426i	$-0.939337\pi$
$827$	−56.4739			−1.96379			−0.981895	+	0.189426i	$0.939337\pi$
$828$			36.0162i			1.25165i
$829$	37.9617			1.31846			0.659231	−	0.751940i	$-0.270882\pi$
$829$	37.9617			1.31846			0.659231	+	0.751940i	$0.270882\pi$
$830$	17.0681	+	14.4201i	0.592442	+	0.500530i
$831$	14.4990			0.502964
$832$		0			0
$833$			36.6033i			1.26823i
$834$			40.3495i			1.39719i
$835$	5.02318	+	4.24388i	0.173834	+	0.146866i
$836$	6.71501			0.232244
$837$	−126.264			−4.36431
$838$	12.4677			0.430689
$839$			17.7895i			0.614162i	0.951683	+	0.307081i	$0.0993522\pi$
$839$			17.7895i			0.614162i	−0.951683	+	0.307081i	$0.900648\pi$
$840$	−2.26629	+	2.68245i	−0.0781944	+	0.0925532i
$841$	7.67098			0.264517
$842$		−	1.36944i		−	0.0471940i
$843$	84.2209			2.90072
$844$	−13.3757			−0.460410
$845$		0			0
$846$	−11.2076			−0.385325
$847$	3.16108			0.108616
$848$		−	5.78588i		−	0.198688i
$849$	32.9289			1.13012
$850$	26.5807	−	4.50238i	0.911711	−	0.154430i
$851$		−	33.5471i		−	1.14998i
$852$	−5.04785			−0.172937
$853$	−12.0381			−0.412178			−0.206089	−	0.978533i	$-0.566074\pi$
$853$	−12.0381			−0.412178			−0.206089	+	0.978533i	$0.566074\pi$
$854$	−2.75149			−0.0941542
$855$	−41.3548	+	48.9487i	−1.41430	+	1.67401i
$856$			0.0114398i			0.000391006i
$857$			21.6745i			0.740388i	0.928954	+	0.370194i	$0.120709\pi$
$857$			21.6745i			0.740388i	−0.928954	+	0.370194i	$0.879291\pi$
$858$		0			0
$859$	54.1515			1.84762			0.923812	−	0.382846i	$-0.125056\pi$
$859$	54.1515			1.84762			0.923812	+	0.382846i	$0.125056\pi$
$860$	1.82874	−	2.16455i	0.0623595	−	0.0738105i
$861$	−6.50969			−0.221850
$862$			11.1142i			0.378553i
$863$	−41.6531			−1.41789			−0.708943	−	0.705265i	$-0.750828\pi$
$863$	−41.6531			−1.41789			−0.708943	+	0.705265i	$0.750828\pi$
$864$			19.3578i			0.658566i
$865$	−5.60853	+	6.63842i	−0.190696	+	0.225713i
$866$			30.2038i			1.02637i
$867$			41.2355i			1.40043i
$868$			2.99890i			0.101789i
$869$		−	3.41778i		−	0.115940i
$870$	29.8494	−	35.3307i	1.01199	−	1.19782i
$871$		0			0
$872$		−	3.79448i		−	0.128497i
$873$	61.1773			2.07054
$874$	13.7395			0.464745
$875$	2.61507	−	4.42549i	0.0884055	−	0.149609i
$876$		−	27.5162i		−	0.929687i
$877$	51.8500			1.75085			0.875425	−	0.483355i	$-0.160582\pi$
$877$	51.8500			1.75085			0.875425	+	0.483355i	$0.160582\pi$
$878$	30.0084			1.01274
$879$			20.5796i			0.694133i
$880$	−2.93078	+	3.46896i	−0.0987967	+	0.116939i
$881$	−11.0112			−0.370977			−0.185488	−	0.982646i	$-0.559387\pi$
$881$	−11.0112			−0.370977			−0.185488	+	0.982646i	$0.559387\pi$
$882$	58.8386			1.98120
$883$		−	42.0418i		−	1.41482i	−0.706803	−	0.707410i	$-0.749863\pi$
$883$		−	42.0418i		−	1.41482i	0.706803	−	0.707410i	$-0.250137\pi$
$884$		0			0
$885$	39.5025	+	33.3740i	1.32786	+	1.12186i
$886$			10.0957i			0.339171i
$887$		−	50.3024i		−	1.68899i	−0.535563	−	0.844495i	$-0.679900\pi$
$887$		−	50.3024i		−	1.68899i	0.535563	−	0.844495i	$-0.320100\pi$
$888$		−	27.5755i		−	0.925372i
$889$		−	5.24146i		−	0.175793i
$890$	5.68479	−	6.72868i	0.190555	−	0.225546i
$891$		−	81.4793i		−	2.72966i
$892$	3.02345			0.101233
$893$			4.27548i			0.143073i
$894$	72.9183			2.43875
$895$	−17.6338	−	14.8981i	−0.589433	−	0.497988i
$896$	0.459770			0.0153598
$897$		0			0
$898$			28.9563i			0.966284i
$899$		−	39.4988i		−	1.31736i
$900$	−7.23742	−	42.7276i	−0.241247	−	1.42425i
$901$	−31.1967			−1.03931
$902$	−8.41839			−0.280302
$903$	1.99015			0.0662279
$904$			5.57377i			0.185381i
$905$	6.28721	+	5.31181i	0.208994	+	0.176571i
$906$	−78.3761			−2.60387
$907$			1.54390i			0.0512642i	0.999671	+	0.0256321i	$0.00815985\pi$
$907$			1.54390i			0.0512642i	−0.999671	+	0.0256321i	$0.991840\pi$
$908$	−14.6074			−0.484762
$909$	20.5452			0.681440
$910$		0			0
$911$	25.5772			0.847411			0.423705	−	0.905800i	$-0.360729\pi$
$911$	25.5772			0.847411			0.423705	+	0.905800i	$0.360729\pi$
$912$	11.2937			0.373973
$913$			20.2942i			0.671639i
$914$	40.4620			1.33836
$915$	29.4987	−	34.9155i	0.975198	−	1.15427i
$916$		−	14.0176i		−	0.463154i
$917$	−6.89224			−0.227602
$918$	104.375			3.44488
$919$	−49.1848			−1.62246			−0.811228	−	0.584730i	$-0.801201\pi$
$919$	−49.1848			−1.62246			−0.811228	+	0.584730i	$0.801201\pi$
$920$	−5.99663	+	7.09779i	−0.197703	+	0.234007i
$921$		−	83.7700i		−	2.76031i
$922$			6.39717i			0.210680i
$923$		0			0
$924$	−3.18946			−0.104926
$925$	6.74126	+	39.7985i	0.221651	+	1.30856i
$926$	15.3751			0.505257
$927$			58.5464i			1.92292i
$928$	−6.05566			−0.198787
$929$		−	9.91513i		−	0.325305i	−0.986683	−	0.162652i	$-0.947995\pi$
$929$		−	9.91513i		−	0.325305i	0.986683	−	0.162652i	$-0.0520049\pi$
$930$	−38.0551	−	32.1512i	−1.24788	−	1.05428i
$931$		−	22.4458i		−	0.735631i
$932$		−	26.5904i		−	0.870998i
$933$		−	70.4282i		−	2.30572i
$934$		−	9.41379i		−	0.308029i
$935$	18.7042	+	15.8024i	0.611692	+	0.516794i
$936$		0			0
$937$		−	24.7485i		−	0.808497i	−0.914649	−	0.404248i	$-0.867533\pi$
$937$		−	24.7485i		−	0.808497i	0.914649	−	0.404248i	$-0.132467\pi$
$938$	3.86863			0.126315
$939$	−25.1237			−0.819882
$940$	−2.20870	−	1.86604i	−0.0720400	−	0.0608637i
$941$		−	40.4541i		−	1.31877i	−0.751807	−	0.659383i	$-0.770817\pi$
$941$		−	40.4541i		−	1.31877i	0.751807	−	0.659383i	$-0.229183\pi$
$942$	−52.0093			−1.69455
$943$	−17.2247			−0.560915
$944$		−	6.77070i		−	0.220368i
$945$	12.8436	−	15.2021i	0.417803	−	0.494524i
$946$	2.57367			0.0836774
$947$	−18.3367			−0.595864			−0.297932	−	0.954587i	$-0.596297\pi$
$947$	−18.3367			−0.595864			−0.297932	+	0.954587i	$0.596297\pi$
$948$		−	5.74825i		−	0.186694i
$949$		0			0
$950$	−16.2998	+	2.76094i	−0.528834	+	0.0895766i
$951$			59.5963i			1.93254i
$952$		−	2.47902i		−	0.0803454i
$953$		−	4.21731i		−	0.136612i	−0.997664	−	0.0683060i	$-0.978241\pi$
$953$		−	4.21731i		−	0.136612i	0.997664	−	0.0683060i	$-0.0217594\pi$
$954$			50.1476i			1.62359i
$955$	−42.7148	−	36.0880i	−1.38222	−	1.16778i
$956$		−	12.3423i		−	0.399178i
$957$	42.0086			1.35795
$958$			24.7651i			0.800125i
$959$	6.28630			0.202995
$960$	−4.92918	+	5.83433i	−0.159089	+	0.188302i
$961$	−11.5446			−0.372407
$962$		0			0
$963$		−	0.0991519i		−	0.00319512i
$964$			3.79308i			0.122167i
$965$	−3.37176	−	2.84866i	−0.108541	−	0.0917018i
$966$	−6.52591			−0.209968
$967$	−46.9135			−1.50864			−0.754318	−	0.656509i	$-0.772033\pi$
$967$	−46.9135			−1.50864			−0.754318	+	0.656509i	$0.772033\pi$
$968$	6.87536			0.220982
$969$		−	60.8944i		−	1.95621i
$970$	12.0563	+	10.1859i	0.387106	+	0.327050i
$971$	−40.5157			−1.30021			−0.650105	−	0.759844i	$-0.725275\pi$
$971$	−40.5157			−1.30021			−0.650105	+	0.759844i	$0.725275\pi$
$972$		−	78.9638i		−	2.53276i
$973$	−5.43119			−0.174116
$974$	−27.2037			−0.871662
$975$		0			0
$976$	−5.98450			−0.191559
$977$	−51.0911			−1.63455			−0.817275	−	0.576248i	$-0.804516\pi$
$977$	−51.0911			−1.63455			−0.817275	+	0.576248i	$0.804516\pi$
$978$			18.7072i			0.598190i
$979$	8.00049			0.255697
$980$	11.5954	+	9.79652i	0.370403	+	0.312938i
$981$			32.8877i			1.05002i
$982$	27.4578			0.876213
$983$	−47.7672			−1.52354			−0.761768	−	0.647850i	$-0.775668\pi$
$983$	−47.7672			−1.52354			−0.761768	+	0.647850i	$0.775668\pi$
$984$	−14.1586			−0.451360
$985$	30.1382	+	25.4625i	0.960283	+	0.811304i
$986$			32.6513i			1.03983i
$987$		−	2.03075i		−	0.0646394i
$988$		0			0
$989$	5.26596			0.167448
$990$	25.4018	−	30.0663i	0.807323	−	0.955571i
$991$	36.5994			1.16262			0.581309	−	0.813683i	$-0.302541\pi$
$991$	36.5994			1.16262			0.581309	+	0.813683i	$0.302541\pi$
$992$			6.52262i			0.207094i
$993$	63.5007			2.01513
$994$		−	0.679459i		−	0.0215511i
$995$	27.6225	+	23.3372i	0.875693	+	0.739838i
$996$			34.1320i			1.08151i
$997$		−	52.9031i		−	1.67546i	−0.546087	−	0.837729i	$-0.683883\pi$
$997$		−	52.9031i		−	1.67546i	0.546087	−	0.837729i	$-0.316117\pi$
$998$		−	2.92681i		−	0.0926464i
$999$			156.277i			4.94438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.c.h.1689.1		18
5.4	even	2		1690.2.c.g.1689.18		18
13.5	odd	4		1690.2.b.f.339.1	✓	18
13.8	odd	4		1690.2.b.g.339.10	yes	18
13.12	even	2		1690.2.c.g.1689.1		18
65.8	even	4		8450.2.a.da.1.9		9
65.18	even	4		8450.2.a.cw.1.9		9
65.34	odd	4		1690.2.b.g.339.9	yes	18
65.44	odd	4		1690.2.b.f.339.18	yes	18
65.47	even	4		8450.2.a.ct.1.1		9
65.57	even	4		8450.2.a.cx.1.1		9
65.64	even	2	inner	1690.2.c.h.1689.18		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.1	✓	18	13.5	odd	4
1690.2.b.f.339.18	yes	18	65.44	odd	4
1690.2.b.g.339.9	yes	18	65.34	odd	4
1690.2.b.g.339.10	yes	18	13.8	odd	4
1690.2.c.g.1689.1		18	13.12	even	2
1690.2.c.g.1689.18		18	5.4	even	2
1690.2.c.h.1689.1		18	1.1	even	1	trivial
1690.2.c.h.1689.18		18	65.64	even	2	inner
8450.2.a.ct.1.1		9	65.47	even	4
8450.2.a.cw.1.9		9	65.18	even	4
8450.2.a.cx.1.1		9	65.57	even	4
8450.2.a.da.1.9		9	65.8	even	4

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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.41573i q^{3} +1.00000 q^{4} +(-1.70807 - 1.44308i) q^{5} -3.41573i q^{6} +0.459770 q^{7} +1.00000 q^{8} -8.66724 q^{9} +(-1.70807 - 1.44308i) q^{10} -2.03092i q^{11} -3.41573i q^{12} +0.459770 q^{14} +(-4.92918 + 5.83433i) q^{15} +1.00000 q^{16} -5.39187i q^{17} -8.66724 q^{18} +3.30639i q^{19} +(-1.70807 - 1.44308i) q^{20} -1.57045i q^{21} -2.03092i q^{22} -4.15544i q^{23} -3.41573i q^{24} +(0.835031 + 4.92978i) q^{25} +19.3578i q^{27} +0.459770 q^{28} -6.05566 q^{29} +(-4.92918 + 5.83433i) q^{30} +6.52262i q^{31} +1.00000 q^{32} -6.93709 q^{33} -5.39187i q^{34} +(-0.785321 - 0.663485i) q^{35} -8.66724 q^{36} +8.07307 q^{37} +3.30639i q^{38} +(-1.70807 - 1.44308i) q^{40} -4.14511i q^{41} -1.57045i q^{42} +1.26725i q^{43} -2.03092i q^{44} +(14.8043 + 12.5075i) q^{45} -4.15544i q^{46} +1.29310 q^{47} -3.41573i q^{48} -6.78861 q^{49} +(0.835031 + 4.92978i) q^{50} -18.4172 q^{51} -5.78588i q^{53} +19.3578i q^{54} +(-2.93078 + 3.46896i) q^{55} +0.459770 q^{56} +11.2937 q^{57} -6.05566 q^{58} -6.77070i q^{59} +(-4.92918 + 5.83433i) q^{60} -5.98450 q^{61} +6.52262i q^{62} -3.98494 q^{63} +1.00000 q^{64} -6.93709 q^{66} +8.41427 q^{67} -5.39187i q^{68} -14.1939 q^{69} +(-0.785321 - 0.663485i) q^{70} -1.47782i q^{71} -8.66724 q^{72} +8.05573 q^{73} +8.07307 q^{74} +(16.8388 - 2.85224i) q^{75} +3.30639i q^{76} -0.933756i q^{77} +1.68287 q^{79} +(-1.70807 - 1.44308i) q^{80} +40.1194 q^{81} -4.14511i q^{82} -9.99259 q^{83} -1.57045i q^{84} +(-7.78090 + 9.20971i) q^{85} +1.26725i q^{86} +20.6845i q^{87} -2.03092i q^{88} +3.93934i q^{89} +(14.8043 + 12.5075i) q^{90} -4.15544i q^{92} +22.2796 q^{93} +1.29310 q^{94} +(4.77139 - 5.64755i) q^{95} -3.41573i q^{96} -7.05844 q^{97} -6.78861 q^{98} +17.6025i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 18 q^{2} + 18 q^{4} - 2 q^{5} - 2 q^{7} + 18 q^{8} - 16 q^{9} - 2 q^{10} - 2 q^{14} + 14 q^{15} + 18 q^{16} - 16 q^{18} - 2 q^{20} - 22 q^{25} - 2 q^{28} - 30 q^{29} + 14 q^{30} + 18 q^{32} - 28 q^{33}+ \cdots - 20 q^{98}+O(q^{100}) \) 18 * q + 18 * q^2 + 18 * q^4 - 2 * q^5 - 2 * q^7 + 18 * q^8 - 16 * q^9 - 2 * q^10 - 2 * q^14 + 14 * q^15 + 18 * q^16 - 16 * q^18 - 2 * q^20 - 22 * q^25 - 2 * q^28 - 30 * q^29 + 14 * q^30 + 18 * q^32 - 28 * q^33 - 4 * q^35 - 16 * q^36 + 20 * q^37 - 2 * q^40 + 20 * q^45 - 10 * q^47 - 20 * q^49 - 22 * q^50 - 24 * q^51 - 2 * q^56 - 24 * q^57 - 30 * q^58 + 14 * q^60 - 38 * q^61 + 78 * q^63 + 18 * q^64 - 28 * q^66 - 2 * q^67 - 28 * q^69 - 4 * q^70 - 16 * q^72 - 24 * q^73 + 20 * q^74 + 72 * q^75 + 28 * q^79 - 2 * q^80 + 106 * q^81 - 2 * q^83 - 16 * q^85 + 20 * q^90 + 56 * q^93 - 10 * q^94 + 54 * q^95 + 12 * q^97 - 20 * q^98

Introduction

L-functions

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