LMFDB - Embedded newform 1690.2.b.g.339.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(339,1690)] 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, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.339"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [18,0,0,-18,0,14,0,0,-16,2,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == 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			339.9
Root			$-2.39737i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.g.339.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$			3.41573i			1.97208i	0.166522	+	0.986038i	$0.446746\pi$
$3$			3.41573i			1.97208i	−0.166522	+	0.986038i	$0.553254\pi$
$4$	−1.00000			−0.500000
$5$	1.44308	+	1.70807i	0.645366	+	0.763874i
$5$	1.44308	+	1.70807i	0.645366	+	0.763874i
$6$	3.41573			1.39447
$7$			0.459770i			0.173777i	0.996218	+	0.0868883i	$0.0276923\pi$
$7$			0.459770i			0.173777i	−0.996218	+	0.0868883i	$0.972308\pi$
$8$			1.00000i			0.353553i
$9$	−8.66724			−2.88908
$10$	1.70807	−	1.44308i	0.540140	−	0.456342i
$11$	−2.03092			−0.612346			−0.306173	−	0.951976i	$-0.599049\pi$
$11$	−2.03092			−0.612346			−0.306173	+	0.951976i	$0.599049\pi$
$12$		−	3.41573i		−	0.986038i
$13$		0			0
$13$		0			0
$14$	0.459770			0.122879
$15$	−5.83433	+	4.92918i	−1.50642	+	1.27271i
$16$	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	$-0.226851\pi$
$18$			8.66724i			2.04289i
$19$	−3.30639			−0.758537			−0.379269	−	0.925287i	$-0.623824\pi$
$19$	−3.30639			−0.758537			−0.379269	+	0.925287i	$0.623824\pi$
$20$	−1.44308	−	1.70807i	−0.322683	−	0.381937i
$21$	−1.57045			−0.342701
$22$			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	$-0.142628\pi$
$24$	−3.41573			−0.697234
$25$	−0.835031	+	4.92978i	−0.167006	+	0.985956i
$26$		0			0
$27$		−	19.3578i		−	3.72541i
$28$		−	0.459770i		−	0.0868883i
$29$	−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
$31$	−6.52262			−1.17150			−0.585749	−	0.810493i	$-0.699200\pi$
$31$	−6.52262			−1.17150			−0.585749	+	0.810493i	$0.699200\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	6.93709i		−	1.20759i
$34$	−5.39187			−0.924698
$35$	−0.785321	+	0.663485i	−0.132743	+	0.112149i
$36$	8.66724			1.44454
$37$			8.07307i			1.32720i	0.748086	+	0.663602i	$0.230973\pi$
$37$			8.07307i			1.32720i	−0.748086	+	0.663602i	$0.769027\pi$
$38$			3.30639i			0.536367i
$39$		0			0
$40$	−1.70807	+	1.44308i	−0.270070	+	0.228171i
$41$	4.14511			0.647358			0.323679	−	0.946167i	$-0.395080\pi$
$41$	4.14511			0.647358			0.323679	+	0.946167i	$0.395080\pi$
$42$			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	$0.969195\pi$
$44$	2.03092			0.306173
$45$	−12.5075	−	14.8043i	−1.86451	−	2.20689i
$46$	−4.15544			−0.612686
$47$			1.29310i			0.188618i	0.995543	+	0.0943088i	$0.0300641\pi$
$47$			1.29310i			0.188618i	−0.995543	+	0.0943088i	$0.969936\pi$
$48$			3.41573i			0.493019i
$49$	6.78861			0.969802
$50$	4.92978	+	0.835031i	0.697176	+	0.118091i
$51$	18.4172			2.57892
$52$		0			0
$53$			5.78588i			0.794751i	0.917656	+	0.397376i	$0.130079\pi$
$53$			5.78588i			0.794751i	−0.917656	+	0.397376i	$0.869921\pi$
$54$	−19.3578			−2.63426
$55$	−2.93078	−	3.46896i	−0.395187	−	0.467755i
$56$	−0.459770			−0.0614393
$57$		−	11.2937i		−	1.49589i
$58$			6.05566i			0.795147i
$59$	−6.77070			−0.881470			−0.440735	−	0.897637i	$-0.645282\pi$
$59$	−6.77070			−0.881470			−0.440735	+	0.897637i	$0.645282\pi$
$60$	5.83433	−	4.92918i	0.753208	−	0.636355i
$61$	−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
$63$		−	3.98494i		−	0.502055i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.93709			−0.853896
$67$		−	8.41427i		−	1.02797i	−0.857800	−	0.513983i	$-0.828169\pi$
$67$		−	8.41427i		−	1.02797i	0.857800	−	0.513983i	$-0.171831\pi$
$68$			5.39187i			0.653860i
$69$	14.1939			1.70874
$70$	0.663485	+	0.785321i	0.0793017	+	0.0938638i
$71$	1.47782			0.175385			0.0876927	−	0.996148i	$-0.472051\pi$
$71$	1.47782			0.175385			0.0876927	+	0.996148i	$0.472051\pi$
$72$		−	8.66724i		−	1.02144i
$73$			8.05573i			0.942852i	0.881906	+	0.471426i	$0.156261\pi$
$73$			8.05573i			0.942852i	−0.881906	+	0.471426i	$0.843739\pi$
$74$	8.07307			0.938475
$75$	−16.8388	−	2.85224i	−1.94438	−	0.329349i
$76$	3.30639			0.379269
$77$		−	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	$0.469821\pi$
$80$	1.44308	+	1.70807i	0.161341	+	0.190968i
$81$	40.1194			4.45771
$82$		−	4.14511i		−	0.457751i
$83$			9.99259i			1.09683i	0.836207	+	0.548415i	$0.184768\pi$
$83$			9.99259i			1.09683i	−0.836207	+	0.548415i	$0.815232\pi$
$84$	1.57045			0.171350
$85$	9.20971	−	7.78090i	0.998933	−	0.843957i
$86$	1.26725			0.136651
$87$		−	20.6845i		−	2.21761i
$88$		−	2.03092i		−	0.216497i
$89$	3.93934			0.417569			0.208785	−	0.977962i	$-0.433049\pi$
$89$	3.93934			0.417569			0.208785	+	0.977962i	$0.433049\pi$
$90$	−14.8043	+	12.5075i	−1.56051	+	1.31841i
$91$		0			0
$92$			4.15544i			0.433234i
$93$		−	22.2796i		−	2.31028i
$94$	1.29310			0.133373
$95$	−4.77139	−	5.64755i	−0.489534	−	0.579427i
$96$	3.41573			0.348617
$97$			7.05844i			0.716676i	0.933592	+	0.358338i	$0.116657\pi$
$97$			7.05844i			0.716676i	−0.933592	+	0.358338i	$0.883343\pi$
$98$		−	6.78861i		−	0.685753i
$99$	17.6025			1.76912
$100$	0.835031	−	4.92978i	0.0835031	−	0.492978i
$101$	2.37044			0.235868			0.117934	−	0.993021i	$-0.462373\pi$
$101$	2.37044			0.235868			0.117934	+	0.993021i	$0.462373\pi$
$102$		−	18.4172i		−	1.82357i
$103$		−	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
$106$	5.78588			0.561974
$107$		−	0.0114398i		−	0.00110593i	−1.00000		0.000552966i	$-0.999824\pi$
$107$		−	0.0114398i		−	0.00110593i	1.00000		0.000552966i	$-0.000176014\pi$
$108$			19.3578i			1.86271i
$109$	3.79448			0.363445			0.181723	−	0.983350i	$-0.441833\pi$
$109$	3.79448			0.363445			0.181723	+	0.983350i	$0.441833\pi$
$110$	−3.46896	+	2.93078i	−0.330753	+	0.279439i
$111$	−27.5755			−2.61735
$112$			0.459770i			0.0434442i
$113$		−	5.57377i		−	0.524336i	−0.965022	−	0.262168i	$-0.915562\pi$
$113$		−	5.57377i		−	0.524336i	0.965022	−	0.262168i	$-0.0844375\pi$
$114$	−11.2937			−1.05776
$115$	7.09779	−	5.99663i	0.661872	−	0.559189i
$116$	6.05566			0.562254
$117$		0			0
$118$			6.77070i			0.623294i
$119$	2.47902			0.227251
$120$	−4.92918	−	5.83433i	−0.449971	−	0.532599i
$121$	−6.87536			−0.625033
$122$			5.98450i			0.541812i
$123$			14.1586i			1.27664i
$124$	6.52262			0.585749
$125$	−9.62544	+	5.68778i	−0.860926	+	0.508730i
$126$	−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	$-0.168803\pi$
$128$			1.00000i			0.0883883i
$129$	−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	$0.727276\pi$
$132$			6.93709i			0.603796i
$133$		−	1.52018i		−	0.131816i
$134$	−8.41427			−0.726882
$135$	33.0645	−	27.9349i	2.84574	−	2.40425i
$136$	5.39187			0.462349
$137$			13.6727i			1.16814i	0.811704	+	0.584069i	$0.198540\pi$
$137$			13.6727i			1.16814i	−0.811704	+	0.584069i	$0.801460\pi$
$138$		−	14.1939i		−	1.20826i
$139$	−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
$141$	−4.41688			−0.371968
$142$		−	1.47782i		−	0.124016i
$143$		0			0
$144$	−8.66724			−0.722270
$145$	−8.73881	−	10.3435i	−0.725718	−	0.858982i
$146$	8.05573			0.666697
$147$			23.1881i			1.91252i
$148$		−	8.07307i		−	0.663602i
$149$	−21.3478			−1.74888			−0.874439	−	0.485136i	$-0.838770\pi$
$149$	−21.3478			−1.74888			−0.874439	+	0.485136i	$0.838770\pi$
$150$	−2.85224	+	16.8388i	−0.232885	+	1.37488i
$151$	−22.9456			−1.86729			−0.933644	−	0.358203i	$-0.883390\pi$
$151$	−22.9456			−1.86729			−0.933644	+	0.358203i	$0.883390\pi$
$152$		−	3.30639i		−	0.268183i
$153$			46.7326i			3.77811i
$154$	−0.933756			−0.0752442
$155$	−9.41268	−	11.1411i	−0.756045	−	0.894876i
$156$		0			0
$157$			15.2264i			1.21520i	0.794244	+	0.607599i	$0.207867\pi$
$157$			15.2264i			1.21520i	−0.794244	+	0.607599i	$0.792133\pi$
$158$		−	1.68287i		−	0.133882i
$159$	−19.7630			−1.56731
$160$	1.70807	−	1.44308i	0.135035	−	0.114086i
$161$	1.91054			0.150572
$162$		−	40.1194i		−	3.15208i
$163$		−	5.47677i		−	0.428974i	−0.976727	−	0.214487i	$-0.931192\pi$
$163$		−	5.47677i		−	0.428974i	0.976727	−	0.214487i	$-0.0688079\pi$
$164$	−4.14511			−0.323679
$165$	11.8491	−	10.0108i	0.922448	−	0.779338i
$166$	9.99259			0.775575
$167$		−	2.94085i		−	0.227569i	−0.993505	−	0.113785i	$-0.963703\pi$
$167$		−	2.94085i		−	0.227569i	0.993505	−	0.113785i	$-0.0362974\pi$
$168$		−	1.57045i		−	0.121163i
$169$		0			0
$170$	−7.78090	−	9.20971i	−0.596768	−	0.706352i
$171$	28.6573			2.19148
$172$		−	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	$-0.0472007\pi$
$174$	−20.6845			−1.56809
$175$	−2.26656	−	0.383922i	−0.171336	−	0.0290218i
$176$	−2.03092			−0.153086
$177$		−	23.1269i		−	1.73833i
$178$		−	3.93934i		−	0.295266i
$179$	−10.3238			−0.771636			−0.385818	−	0.922575i	$-0.626081\pi$
$179$	−10.3238			−0.771636			−0.385818	+	0.922575i	$0.626081\pi$
$180$	12.5075	+	14.8043i	0.932257	+	1.10345i
$181$	3.68088			0.273598			0.136799	−	0.990599i	$-0.456319\pi$
$181$	3.68088			0.273598			0.136799	+	0.990599i	$0.456319\pi$
$182$		0			0
$183$		−	20.4415i		−	1.51108i
$184$	4.15544			0.306343
$185$	−13.7894	+	11.6501i	−1.01382	+	0.856532i
$186$	−22.2796			−1.63362
$187$			10.9505i			0.800777i
$188$		−	1.29310i		−	0.0943088i
$189$	8.90013			0.647389
$190$	−5.64755	+	4.77139i	−0.409717	+	0.346153i
$191$	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
$193$			1.97401i			0.142093i	0.997473	+	0.0710463i	$0.0226338\pi$
$193$			1.97401i			0.142093i	−0.997473	+	0.0710463i	$0.977366\pi$
$194$	7.05844			0.506767
$195$		0			0
$196$	−6.78861			−0.484901
$197$			17.6446i			1.25712i	0.777760	+	0.628562i	$0.216356\pi$
$197$			17.6446i			1.25712i	−0.777760	+	0.628562i	$0.783644\pi$
$198$		−	17.6025i		−	1.25095i
$199$	16.1718			1.14639			0.573193	−	0.819421i	$-0.305705\pi$
$199$	16.1718			1.14639			0.573193	+	0.819421i	$0.305705\pi$
$200$	−4.92978	−	0.835031i	−0.348588	−	0.0590456i
$201$	28.7409			2.02723
$202$		−	2.37044i		−	0.166784i
$203$		−	2.78421i		−	0.195413i
$204$	−18.4172			−1.28946
$205$	5.98173	+	7.08015i	0.417782	+	0.494499i
$206$	−6.75491			−0.470637
$207$			36.0162i			2.50330i
$208$		0			0
$209$	6.71501			0.464487
$210$	−2.68245	+	2.26629i	−0.185106	+	0.156389i
$211$	−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
$213$			5.04785i			0.345873i
$214$	−0.0114398			−0.000782011
$215$	−2.16455	+	1.82874i	−0.147621	+	0.124719i
$216$	19.3578			1.31713
$217$		−	2.99890i		−	0.203579i
$218$		−	3.79448i		−	0.256995i
$219$	−27.5162			−1.85937
$220$	2.93078	+	3.46896i	0.197593	+	0.233877i
$221$		0			0
$222$			27.5755i			1.85074i
$223$		−	3.02345i		−	0.202465i	−0.994863	−	0.101233i	$-0.967721\pi$
$223$		−	3.02345i		−	0.202465i	0.994863	−	0.101233i	$-0.0322786\pi$
$224$	0.459770			0.0307197
$225$	7.23742	−	42.7276i	0.482494	−	2.84851i
$226$	−5.57377			−0.370762
$227$			14.6074i			0.969525i	0.874646	+	0.484762i	$0.161094\pi$
$227$			14.6074i			0.969525i	−0.874646	+	0.484762i	$0.838906\pi$
$228$			11.2937i			0.747946i
$229$	−14.0176			−0.926308			−0.463154	−	0.886278i	$-0.653282\pi$
$229$	−14.0176			−0.926308			−0.463154	+	0.886278i	$0.653282\pi$
$230$	−5.99663	−	7.09779i	−0.395406	−	0.468014i
$231$	3.18946			0.209851
$232$		−	6.05566i		−	0.397573i
$233$		−	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
$236$	6.77070			0.440735
$237$			5.74825i			0.373389i
$238$		−	2.47902i		−	0.160691i
$239$	12.3423			0.798356			0.399178	−	0.916874i	$-0.369296\pi$
$239$	12.3423			0.798356			0.399178	+	0.916874i	$0.369296\pi$
$240$	−5.83433	+	4.92918i	−0.376604	+	0.318177i
$241$	3.79308			0.244334			0.122167	−	0.992510i	$-0.461016\pi$
$241$	3.79308			0.244334			0.122167	+	0.992510i	$0.461016\pi$
$242$			6.87536i			0.441965i
$243$			78.9638i			5.06553i
$244$	5.98450			0.383119
$245$	9.79652	+	11.5954i	0.625877	+	0.740806i
$246$	14.1586			0.902719
$247$		0			0
$248$		−	6.52262i		−	0.414187i
$249$	−34.1320			−2.16303
$250$	5.68778	+	9.62544i	0.359727	+	0.608767i
$251$	−0.547631			−0.0345662			−0.0172831	−	0.999851i	$-0.505502\pi$
$251$	−0.547631			−0.0345662			−0.0172831	+	0.999851i	$0.505502\pi$
$252$			3.98494i			0.251027i
$253$			8.43936i			0.530578i
$254$	−11.4002			−0.715311
$255$	26.5775	+	31.4579i	1.66435	+	1.96997i
$256$	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	$-0.182633\pi$
$258$			4.32857i			0.269485i
$259$	−3.71175			−0.230637
$260$		0			0
$261$	52.4859			3.24879
$262$			14.9906i			0.926124i
$263$			11.6459i			0.718114i	0.933316	+	0.359057i	$0.116902\pi$
$263$			11.6459i			0.718114i	−0.933316	+	0.359057i	$0.883098\pi$
$264$	6.93709			0.426948
$265$	−9.88271	+	8.34949i	−0.607090	+	0.512905i
$266$	−1.52018			−0.0932080
$267$			13.4557i			0.823478i
$268$			8.41427i			0.513983i
$269$	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
$271$	−9.94128			−0.603889			−0.301945	−	0.953325i	$-0.597636\pi$
$271$	−9.94128			−0.603889			−0.301945	+	0.953325i	$0.597636\pi$
$272$		−	5.39187i		−	0.326930i
$273$		0			0
$274$	13.6727			0.825999
$275$	1.69588	−	10.0120i	0.102266	−	0.603746i
$276$	−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	$0.959298\pi$
$278$			11.8128i			0.708487i
$279$	56.5332			3.38455
$280$	−0.663485	−	0.785321i	−0.0396508	−	0.0469319i
$281$	24.6567			1.47090			0.735449	−	0.677580i	$-0.236971\pi$
$281$	24.6567			1.47090			0.735449	+	0.677580i	$0.236971\pi$
$282$			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	$0.907498\pi$
$284$	−1.47782			−0.0876927
$285$	19.2905	−	16.2978i	1.14267	−	0.965398i
$286$		0			0
$287$			1.90580i			0.112496i
$288$			8.66724i			0.510722i
$289$	−12.0722			−0.710131
$290$	−10.3435	+	8.73881i	−0.607392	+	0.513160i
$291$	−24.1098			−1.41334
$292$		−	8.05573i		−	0.471426i
$293$		−	6.02494i		−	0.351981i	−0.984392	−	0.175990i	$-0.943687\pi$
$293$		−	6.02494i		−	0.351981i	0.984392	−	0.175990i	$-0.0563128\pi$
$294$	23.1881			1.35236
$295$	−9.77067	−	11.5649i	−0.568871	−	0.673332i
$296$	−8.07307			−0.469238
$297$			39.3142i			2.28124i
$298$			21.3478i			1.23664i
$299$		0			0
$300$	16.8388	+	2.85224i	0.972190	+	0.164674i
$301$	−0.582641			−0.0335829
$302$			22.9456i			1.32037i
$303$			8.09679i			0.465149i
$304$	−3.30639			−0.189634
$305$	−8.63613	−	10.2220i	−0.494503	−	0.585308i
$306$	46.7326			2.67153
$307$			24.5247i			1.39970i	0.714290	+	0.699850i	$0.246750\pi$
$307$			24.5247i			1.39970i	−0.714290	+	0.699850i	$0.753250\pi$
$308$			0.933756i			0.0532057i
$309$	23.0730			1.31258
$310$	−11.1411	+	9.41268i	−0.632773	+	0.534604i
$311$	−20.6188			−1.16918			−0.584591	−	0.811328i	$-0.698745\pi$
$311$	−20.6188			−1.16918			−0.584591	+	0.811328i	$0.698745\pi$
$312$		0			0
$313$			7.35529i			0.415746i	0.978156	+	0.207873i	$0.0666540\pi$
$313$			7.35529i			0.415746i	−0.978156	+	0.207873i	$0.933346\pi$
$314$	15.2264			0.859275
$315$	6.80656	−	5.75059i	0.383506	−	0.324009i
$316$	−1.68287			−0.0946690
$317$			17.4476i			0.979954i	0.871735	+	0.489977i	$0.162995\pi$
$317$			17.4476i			0.979954i	−0.871735	+	0.489977i	$0.837005\pi$
$318$			19.7630i			1.10826i
$319$	12.2986			0.688587
$320$	−1.44308	−	1.70807i	−0.0806707	−	0.0954842i
$321$	0.0390755			0.00218098
$322$		−	1.91054i		−	0.106470i
$323$			17.8276i			0.991954i
$324$	−40.1194			−2.22885
$325$		0			0
$326$	−5.47677			−0.303330
$327$			12.9609i			0.716742i
$328$			4.14511i			0.228875i
$329$	−0.594527			−0.0327773
$330$	−10.0108	−	11.8491i	−0.551075	−	0.652269i
$331$	−18.5906			−1.02183			−0.510917	−	0.859630i	$-0.670694\pi$
$331$	−18.5906			−1.02183			−0.510917	+	0.859630i	$0.670694\pi$
$332$		−	9.99259i		−	0.548415i
$333$		−	69.9713i		−	3.83440i
$334$	−2.94085			−0.160916
$335$	14.3722	−	12.1425i	0.785237	−	0.663414i
$336$	−1.57045			−0.0856752
$337$		−	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
$340$	−9.20971	+	7.78090i	−0.499466	+	0.421979i
$341$	13.2469			0.717362
$342$		−	28.6573i		−	1.54961i
$343$			6.33959i			0.342305i
$344$	−1.26725			−0.0683253
$345$	20.4829	+	24.2442i	1.10276	+	1.30526i
$346$	−3.88650			−0.208939
$347$			22.2403i			1.19392i	0.802270	+	0.596961i	$0.203625\pi$
$347$			22.2403i			1.19392i	−0.802270	+	0.596961i	$0.796375\pi$
$348$			20.6845i			1.10881i
$349$	−22.6265			−1.21117			−0.605585	−	0.795781i	$-0.707061\pi$
$349$	−22.6265			−1.21117			−0.605585	+	0.795781i	$0.707061\pi$
$350$	−0.383922	+	2.26656i	−0.0205215	+	0.121153i
$351$		0			0
$352$			2.03092i			0.108248i
$353$			7.66644i			0.408044i	0.978966	+	0.204022i	$0.0654013\pi$
$353$			7.66644i			0.408044i	−0.978966	+	0.204022i	$0.934599\pi$
$354$	−23.1269			−1.22918
$355$	2.13262	+	2.52423i	0.113188	+	0.133972i
$356$	−3.93934			−0.208785
$357$			8.46766i			0.448156i
$358$			10.3238i			0.545629i
$359$	−31.5137			−1.66323			−0.831615	−	0.555353i	$-0.812583\pi$
$359$	−31.5137			−1.66323			−0.831615	+	0.555353i	$0.812583\pi$
$360$	14.8043	−	12.5075i	0.780255	−	0.659205i
$361$	−8.06780			−0.424621
$362$		−	3.68088i		−	0.193463i
$363$		−	23.4844i		−	1.23261i
$364$		0			0
$365$	−13.7598	+	11.6251i	−0.720220	+	0.608484i
$366$	−20.4415			−1.06849
$367$		−	25.5000i		−	1.33109i	−0.746359	−	0.665544i	$-0.768200\pi$
$367$		−	25.5000i		−	1.33109i	0.746359	−	0.665544i	$-0.231800\pi$
$368$		−	4.15544i		−	0.216617i
$369$	−35.9267			−1.87027
$370$	11.6501	+	13.7894i	0.605660	+	0.716877i
$371$	−2.66017			−0.138109
$372$			22.2796i			1.15514i
$373$			15.2112i			0.787604i	0.919195	+	0.393802i	$0.128841\pi$
$373$			15.2112i			0.787604i	−0.919195	+	0.393802i	$0.871159\pi$
$374$	10.9505			0.566235
$375$	−19.4279	−	32.8780i	−1.00325	−	1.69781i
$376$	−1.29310			−0.0666864
$377$		0			0
$378$		−	8.90013i		−	0.457773i
$379$	17.2766			0.887439			0.443719	−	0.896166i	$-0.353659\pi$
$379$	17.2766			0.887439			0.443719	+	0.896166i	$0.353659\pi$
$380$	4.77139	+	5.64755i	0.244767	+	0.289713i
$381$	38.9400			1.99496
$382$		−	25.0076i		−	1.27950i
$383$		−	15.1262i		−	0.772915i	−0.922307	−	0.386458i	$-0.873699\pi$
$383$		−	15.1262i		−	0.772915i	0.922307	−	0.386458i	$-0.126301\pi$
$384$	−3.41573			−0.174308
$385$	1.59492	−	1.34749i	0.0812848	−	0.0686742i
$386$	1.97401			0.100475
$387$		−	10.9835i		−	0.558324i
$388$		−	7.05844i		−	0.358338i
$389$	32.0553			1.62527			0.812635	−	0.582774i	$-0.198033\pi$
$389$	32.0553			1.62527			0.812635	+	0.582774i	$0.198033\pi$
$390$		0			0
$391$	−22.4056			−1.13310
$392$			6.78861i			0.342877i
$393$		−	51.2040i		−	2.58290i
$394$	17.6446			0.888920
$395$	2.42852	+	2.87447i	0.122192	+	0.144630i
$396$	−17.6025			−0.884558
$397$			7.52503i			0.377670i	0.982009	+	0.188835i	$0.0604712\pi$
$397$			7.52503i			0.377670i	−0.982009	+	0.188835i	$0.939529\pi$
$398$		−	16.1718i		−	0.810617i
$399$	5.19252			0.259951
$400$	−0.835031	+	4.92978i	−0.0417515	+	0.246489i
$401$	37.3359			1.86447			0.932233	−	0.361860i	$-0.117858\pi$
$401$	37.3359			1.86447			0.932233	+	0.361860i	$0.117858\pi$
$402$		−	28.7409i		−	1.43347i
$403$		0			0
$404$	−2.37044			−0.117934
$405$	57.8955	+	68.5269i	2.87685	+	3.40513i
$406$	−2.78421			−0.138178
$407$		−	16.3958i		−	0.812708i
$408$			18.4172i			0.911787i
$409$	−19.7733			−0.977729			−0.488864	−	0.872360i	$-0.662589\pi$
$409$	−19.7733			−0.977729			−0.488864	+	0.872360i	$0.662589\pi$
$410$	7.08015	−	5.98173i	0.349664	−	0.295417i
$411$	−46.7024			−2.30366
$412$			6.75491i			0.332790i
$413$		−	3.11296i		−	0.153179i
$414$	36.0162			1.77010
$415$	−17.0681	+	14.4201i	−0.837839	+	0.707856i
$416$		0			0
$417$		−	40.3495i		−	1.97592i
$418$		−	6.71501i		−	0.328442i
$419$	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
$421$	1.36944			0.0667423			0.0333712	−	0.999443i	$-0.489376\pi$
$421$	1.36944			0.0667423			0.0333712	+	0.999443i	$0.489376\pi$
$422$			13.3757i			0.651118i
$423$		−	11.2076i		−	0.544932i
$424$	−5.78588			−0.280987
$425$	26.5807	+	4.50238i	1.28935	+	0.218397i
$426$	5.04785			0.244569
$427$		−	2.75149i		−	0.133154i
$428$			0.0114398i			0.000552966i
$429$		0			0
$430$	1.82874	+	2.16455i	0.0881896	+	0.104384i
$431$	−11.1142			−0.535354			−0.267677	−	0.963509i	$-0.586256\pi$
$431$	−11.1142			−0.535354			−0.267677	+	0.963509i	$0.586256\pi$
$432$		−	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	$0.741492\pi$
$434$	−2.99890			−0.143952
$435$	35.3307	−	29.8494i	1.69398	−	1.43117i
$436$	−3.79448			−0.181723
$437$			13.7395i			0.657249i
$438$			27.5162i			1.31478i
$439$	−30.0084			−1.43223			−0.716113	−	0.697985i	$-0.754080\pi$
$439$	−30.0084			−1.43223			−0.716113	+	0.697985i	$0.754080\pi$
$440$	3.46896	−	2.93078i	0.165376	−	0.139720i
$441$	−58.8386			−2.80184
$442$		0			0
$443$		−	10.0957i		−	0.479661i	−0.970815	−	0.239830i	$-0.922908\pi$
$443$		−	10.0957i		−	0.479661i	0.970815	−	0.239830i	$-0.0770918\pi$
$444$	27.5755			1.30867
$445$	5.68479	+	6.72868i	0.269485	+	0.318970i
$446$	−3.02345			−0.143165
$447$		−	72.9183i		−	3.44892i
$448$		−	0.459770i		−	0.0217221i
$449$	28.9563			1.36653			0.683266	−	0.730169i	$-0.260559\pi$
$449$	28.9563			1.36653			0.683266	+	0.730169i	$0.260559\pi$
$450$	−42.7276	−	7.23742i	−2.01420	−	0.341175i
$451$	−8.41839			−0.396407
$452$			5.57377i			0.262168i
$453$		−	78.3761i		−	3.68243i
$454$	14.6074			0.685558
$455$		0			0
$456$	11.2937			0.528878
$457$		−	40.4620i		−	1.89273i	−0.323094	−	0.946367i	$-0.604723\pi$
$457$		−	40.4620i		−	1.89273i	0.323094	−	0.946367i	$-0.395277\pi$
$458$			14.0176i			0.654998i
$459$	−104.375			−4.87179
$460$	−7.09779	+	5.99663i	−0.330936	+	0.279594i
$461$	−6.39717			−0.297946			−0.148973	−	0.988841i	$-0.547597\pi$
$461$	−6.39717			−0.297946			−0.148973	+	0.988841i	$0.547597\pi$
$462$		−	3.18946i		−	0.148387i
$463$			15.3751i			0.714541i	0.934001	+	0.357270i	$0.116293\pi$
$463$			15.3751i			0.714541i	−0.934001	+	0.357270i	$0.883707\pi$
$464$	−6.05566			−0.281127
$465$	38.0551	−	32.1512i	1.76476	−	1.49098i
$466$	−26.5904			−1.23178
$467$		−	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
$470$	1.86604	+	2.20870i	0.0860742	+	0.101880i
$471$	−52.0093			−2.39646
$472$		−	6.77070i		−	0.311647i
$473$		−	2.57367i		−	0.118338i
$474$	5.74825			0.264026
$475$	2.76094	−	16.2998i	0.126680	−	0.747884i
$476$	−2.47902			−0.113626
$477$		−	50.1476i		−	2.29610i
$478$		−	12.3423i		−	0.564523i
$479$	24.7651			1.13155			0.565774	−	0.824560i	$-0.308577\pi$
$479$	24.7651			1.13155			0.565774	+	0.824560i	$0.308577\pi$
$480$	4.92918	+	5.83433i	0.224985	+	0.266299i
$481$		0			0
$482$		−	3.79308i		−	0.172770i
$483$			6.52591i			0.296939i
$484$	6.87536			0.312516
$485$	−12.0563	+	10.1859i	−0.547450	+	0.462518i
$486$	78.9638			3.58187
$487$			27.2037i			1.23272i	0.787466	+	0.616358i	$0.211393\pi$
$487$			27.2037i			1.23272i	−0.787466	+	0.616358i	$0.788607\pi$
$488$		−	5.98450i		−	0.270906i
$489$	18.7072			0.845969
$490$	11.5954	−	9.79652i	0.523829	−	0.442562i
$491$	−27.4578			−1.23915			−0.619576	−	0.784937i	$-0.712695\pi$
$491$	−27.4578			−1.23915			−0.619576	+	0.784937i	$0.712695\pi$
$492$		−	14.1586i		−	0.638319i
$493$			32.6513i			1.47054i
$494$		0			0
$495$	25.4018	+	30.0663i	1.14173	+	1.35138i
$496$	−6.52262			−0.292874
$497$			0.679459i			0.0304779i
$498$			34.1320i			1.52949i
$499$	2.92681			0.131022			0.0655109	−	0.997852i	$-0.479132\pi$
$499$	2.92681			0.131022			0.0655109	+	0.997852i	$0.479132\pi$
$500$	9.62544	−	5.68778i	0.430463	−	0.254365i
$501$	10.0451			0.448784
$502$			0.547631i			0.0244420i
$503$		−	0.113123i		−	0.00504392i	−0.999997	−	0.00252196i	$-0.999197\pi$
$503$		−	0.113123i		−	0.00504392i	0.999997	−	0.00252196i	$-0.000802766\pi$
$504$	3.98494			0.177503
$505$	3.42074	+	4.04888i	0.152221	+	0.180173i
$506$	8.43936			0.375175
$507$		0			0
$508$			11.4002i			0.505801i
$509$	19.0806			0.845731			0.422865	−	0.906193i	$-0.361024\pi$
$509$	19.0806			0.845731			0.422865	+	0.906193i	$0.361024\pi$
$510$	31.4579	−	26.5775i	1.39298	−	1.17687i
$511$	−3.70378			−0.163846
$512$		−	1.00000i		−	0.0441942i
$513$			64.0044i			2.82586i
$514$	−17.4033			−0.767626
$515$	11.5379	−	9.74788i	0.508420	−	0.429543i
$516$	4.32857			0.190555
$517$		−	2.62618i		−	0.115499i
$518$			3.71175i			0.163085i
$519$	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	$0.548164\pi$
$522$		−	52.4859i		−	2.29724i
$523$			19.7227i			0.862414i	0.902253	+	0.431207i	$0.141912\pi$
$523$			19.7227i			0.862414i	−0.902253	+	0.431207i	$0.858088\pi$
$524$	14.9906			0.654869
$525$	1.31138	−	7.74198i	0.0572331	−	0.337888i
$526$	11.6459			0.507783
$527$			35.1691i			1.53199i
$528$		−	6.93709i		−	0.301898i
$529$	5.73235			0.249233
$530$	8.34949	+	9.88271i	0.362679	+	0.429277i
$531$	58.6833			2.54664
$532$			1.52018i			0.0659080i
$533$		0			0
$534$	13.4557			0.582287
$535$	0.0195401	−	0.0165086i	0.000844792	−	0.000713730i
$536$	8.41427			0.363441
$537$		−	35.2633i		−	1.52173i
$538$		−	16.9075i		−	0.728934i
$539$	−13.7871			−0.593854
$540$	−33.0645	+	27.9349i	−1.42287	+	1.20213i
$541$	41.8747			1.80034			0.900168	−	0.435543i	$-0.143444\pi$
$541$	41.8747			1.80034			0.900168	+	0.435543i	$0.143444\pi$
$542$			9.94128i			0.427014i
$543$			12.5729i			0.539555i
$544$	−5.39187			−0.231174
$545$	5.47575	+	6.48125i	0.234555	+	0.277626i
$546$		0			0
$547$			28.0881i			1.20096i	0.799639	+	0.600481i	$0.205024\pi$
$547$			28.0881i			1.20096i	−0.799639	+	0.600481i	$0.794976\pi$
$548$		−	13.6727i		−	0.584069i
$549$	51.8692			2.21372
$550$	−10.0120	−	1.69588i	−0.426913	−	0.0723126i
$551$	20.0224			0.852981
$552$			14.1939i			0.604131i
$553$			0.773734i			0.0329025i
$554$	4.24476			0.180343
$555$	−39.7936	−	47.1009i	−1.68915	−	1.99932i
$556$	11.8128			0.500976
$557$			29.3170i			1.24220i	0.783730	+	0.621101i	$0.213315\pi$
$557$			29.3170i			1.24220i	−0.783730	+	0.621101i	$0.786685\pi$
$558$		−	56.5332i		−	2.39324i
$559$		0			0
$560$	−0.785321	+	0.663485i	−0.0331859	+	0.0280374i
$561$	−37.4038			−1.57919
$562$		−	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	$0.985847\pi$
$564$	4.41688			0.185984
$565$	9.52041	−	8.04341i	0.400527	−	0.338389i
$566$	9.64034			0.405214
$567$			18.4457i			0.774646i
$568$			1.47782i			0.0620081i
$569$	−14.0188			−0.587697			−0.293849	−	0.955852i	$-0.594936\pi$
$569$	−14.0188			−0.587697			−0.293849	+	0.955852i	$0.594936\pi$
$570$	−16.2978	−	19.2905i	−0.682640	−	0.807992i
$571$	−27.5675			−1.15366			−0.576831	−	0.816864i	$-0.695711\pi$
$571$	−27.5675			−1.15366			−0.576831	+	0.816864i	$0.695711\pi$
$572$		0			0
$573$			85.4192i			3.56844i
$574$	1.90580			0.0795464
$575$	20.4854	+	3.46992i	0.854300	+	0.144706i
$576$	8.66724			0.361135
$577$		−	19.0434i		−	0.792788i	−0.918080	−	0.396394i	$-0.870261\pi$
$577$		−	19.0434i		−	0.792788i	0.918080	−	0.396394i	$-0.129739\pi$
$578$			12.0722i			0.502138i
$579$	−6.74271			−0.280217
$580$	8.73881	+	10.3435i	0.362859	+	0.429491i
$581$	−4.59429			−0.190603
$582$			24.1098i			0.999382i
$583$		−	11.7507i		−	0.486663i
$584$	−8.05573			−0.333348
$585$		0			0
$586$	−6.02494			−0.248888
$587$			16.0453i			0.662260i	0.943585	+	0.331130i	$0.107430\pi$
$587$			16.0453i			0.662260i	−0.943585	+	0.331130i	$0.892570\pi$
$588$		−	23.1881i		−	0.956261i
$589$	21.5663			0.888625
$590$	−11.5649	+	9.77067i	−0.476118	+	0.402252i
$591$	−60.2691			−2.47914
$592$			8.07307i			0.331801i
$593$			43.3422i			1.77985i	0.456107	+	0.889925i	$0.349244\pi$
$593$			43.3422i			1.77985i	−0.456107	+	0.889925i	$0.650756\pi$
$594$	39.3142			1.61308
$595$	3.57742	+	4.23434i	0.146660	+	0.173591i
$596$	21.3478			0.874439
$597$			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	$0.444194\pi$
$600$	2.85224	−	16.8388i	0.116442	−	0.687442i
$601$	−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
$603$			72.9285i			2.96988i
$604$	22.9456			0.933644
$605$	−9.92171	−	11.7436i	−0.403375	−	0.477446i
$606$	8.09679			0.328910
$607$			14.8586i			0.603093i	0.953451	+	0.301546i	$0.0975028\pi$
$607$			14.8586i			0.603093i	−0.953451	+	0.301546i	$0.902497\pi$
$608$			3.30639i			0.134092i
$609$	9.51012			0.385369
$610$	−10.2220	+	8.63613i	−0.413876	+	0.349667i
$611$		0			0
$612$		−	46.7326i		−	1.88905i
$613$		−	24.9342i		−	1.00708i	−0.863971	−	0.503541i	$-0.832030\pi$
$613$		−	24.9342i		−	1.00708i	0.863971	−	0.503541i	$-0.167970\pi$
$614$	24.5247			0.989737
$615$	−24.1839	+	20.4320i	−0.975190	+	0.823898i
$616$	0.933756			0.0376221
$617$		−	20.7921i		−	0.837057i	−0.908204	−	0.418528i	$-0.862546\pi$
$617$		−	20.7921i		−	0.837057i	0.908204	−	0.418528i	$-0.137454\pi$
$618$		−	23.0730i		−	0.928131i
$619$	22.8769			0.919501			0.459751	−	0.888048i	$-0.347939\pi$
$619$	22.8769			0.919501			0.459751	+	0.888048i	$0.347939\pi$
$620$	9.41268	+	11.1411i	0.378022	+	0.447438i
$621$	−80.4401			−3.22795
$622$			20.6188i			0.826737i
$623$			1.81119i			0.0725638i
$624$		0			0
$625$	−23.6054	−	8.23304i	−0.944218	−	0.329321i
$626$	7.35529			0.293977
$627$			22.9367i			0.916004i
$628$		−	15.2264i		−	0.607599i
$629$	43.5289			1.73561
$630$	−5.75059	−	6.80656i	−0.229109	−	0.271180i
$631$	22.6688			0.902429			0.451214	−	0.892416i	$-0.350991\pi$
$631$	22.6688			0.902429			0.451214	+	0.892416i	$0.350991\pi$
$632$			1.68287i			0.0669411i
$633$		−	45.6877i		−	1.81592i
$634$	17.4476			0.692932
$635$	19.4724	−	16.4514i	0.772737	−	0.652854i
$636$	19.7630			0.783655
$637$		0			0
$638$		−	12.2986i		−	0.486905i
$639$	−12.8087			−0.506703
$640$	−1.70807	+	1.44308i	−0.0675175	+	0.0570428i
$641$	−11.5650			−0.456789			−0.228394	−	0.973569i	$-0.573348\pi$
$641$	−11.5650			−0.456789			−0.228394	+	0.973569i	$0.573348\pi$
$642$		−	0.0390755i		−	0.00154219i
$643$		−	25.4887i		−	1.00518i	−0.864526	−	0.502588i	$-0.832381\pi$
$643$		−	25.4887i		−	1.00518i	0.864526	−	0.502588i	$-0.167619\pi$
$644$	−1.91054			−0.0752860
$645$	−6.24648	−	7.39352i	−0.245955	−	0.291120i
$646$	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	$0.995706\pi$
$648$			40.1194i			1.57604i
$649$	13.7508			0.539764
$650$		0			0
$651$	10.2435			0.401473
$652$			5.47677i			0.214487i
$653$		−	20.7584i		−	0.812338i	−0.913798	−	0.406169i	$-0.866864\pi$
$653$		−	20.7584i		−	0.812338i	0.913798	−	0.406169i	$-0.133136\pi$
$654$	12.9609			0.506813
$655$	−21.6327	−	25.6051i	−0.845259	−	1.00047i
$656$	4.14511			0.161839
$657$		−	69.8210i		−	2.72398i
$658$			0.594527i			0.0231771i
$659$	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
$661$	−14.9740			−0.582422			−0.291211	−	0.956659i	$-0.594058\pi$
$661$	−14.9740			−0.582422			−0.291211	+	0.956659i	$0.594058\pi$
$662$			18.5906i			0.722546i
$663$		0			0
$664$	−9.99259			−0.387788
$665$	2.59657	−	2.19374i	0.100691	−	0.0850696i
$666$	−69.9713			−2.71133
$667$			25.1639i			0.974350i
$668$			2.94085i			0.113785i
$669$	10.3273			0.399277
$670$	−12.1425	−	14.3722i	−0.469105	−	0.555246i
$671$	12.1541			0.469202
$672$			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	$0.892218\pi$
$674$	−11.2984			−0.435198
$675$	95.4297	+	16.1644i	3.67309	+	0.622167i
$676$		0			0
$677$		−	12.1285i		−	0.466136i	−0.972460	−	0.233068i	$-0.925124\pi$
$677$		−	12.1285i		−	0.466136i	0.972460	−	0.233068i	$-0.0748765\pi$
$678$		−	19.0385i		−	0.731170i
$679$	−3.24526			−0.124542
$680$	7.78090	+	9.20971i	0.298384	+	0.353176i
$681$	−49.8949			−1.91198
$682$		−	13.2469i		−	0.507251i
$683$			20.0828i			0.768449i	0.923240	+	0.384224i	$0.125531\pi$
$683$			20.0828i			0.768449i	−0.923240	+	0.384224i	$0.874469\pi$
$684$	−28.6573			−1.09574
$685$	−23.3540	+	19.7308i	−0.892311	+	0.753877i
$686$	6.33959			0.242047
$687$		−	47.8803i		−	1.82675i
$688$			1.26725i			0.0483133i
$689$		0			0
$690$	24.2442	−	20.4829i	0.922960	−	0.779771i
$691$	−24.8495			−0.945320			−0.472660	−	0.881245i	$-0.656706\pi$
$691$	−24.8495			−0.945320			−0.472660	+	0.881245i	$0.656706\pi$
$692$			3.88650i			0.147742i
$693$			8.09309i			0.307431i
$694$	22.2403			0.844231
$695$	−17.0469	−	20.1772i	−0.646625	−	0.765365i
$696$	20.6845			0.784045
$697$		−	22.3499i		−	0.846562i
$698$			22.6265i			0.856427i
$699$	90.8258			3.43535
$700$	2.26656	+	0.383922i	0.0856680	+	0.0145109i
$701$	−26.3896			−0.996720			−0.498360	−	0.866970i	$-0.666064\pi$
$701$	−26.3896			−0.996720			−0.498360	+	0.866970i	$0.666064\pi$
$702$		0			0
$703$		−	26.6927i		−	1.00673i
$704$	2.03092			0.0765432
$705$	−6.37391	−	7.54435i	−0.240055	−	0.284137i
$706$	7.66644			0.288530
$707$			1.08986i			0.0409883i
$708$			23.1269i			0.869163i
$709$	−28.0118			−1.05201			−0.526003	−	0.850483i	$-0.676310\pi$
$709$	−28.0118			−1.05201			−0.526003	+	0.850483i	$0.676310\pi$
$710$	2.52423	−	2.13262i	0.0947327	−	0.0800358i
$711$	−14.5859			−0.547013
$712$			3.93934i			0.147633i
$713$			27.1043i			1.01507i
$714$	8.46766			0.316894
$715$		0			0
$716$	10.3238			0.385818
$717$			42.1580i			1.57442i
$718$			31.5137i			1.17608i
$719$	40.0185			1.49244			0.746219	−	0.665700i	$-0.231867\pi$
$719$	40.0185			1.49244			0.746219	+	0.665700i	$0.231867\pi$
$720$	−12.5075	−	14.8043i	−0.466128	−	0.551723i
$721$	3.10570			0.115662
$722$			8.06780i			0.300252i
$723$			12.9562i			0.481845i
$724$	−3.68088			−0.136799
$725$	5.05666	−	29.8531i	0.187800	−	1.10871i
$726$	−23.4844			−0.871588
$727$		−	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
$730$	11.6251	+	13.7598i	0.430263	+	0.509272i
$731$	6.83282			0.252721
$732$			20.4415i			0.755539i
$733$		−	6.65212i		−	0.245701i	−0.992425	−	0.122851i	$-0.960796\pi$
$733$		−	6.65212i		−	0.245701i	0.992425	−	0.122851i	$-0.0392036\pi$
$734$	−25.5000			−0.941221
$735$	−39.6070	+	33.4623i	−1.46093	+	1.23428i
$736$	−4.15544			−0.153171
$737$			17.0887i			0.629471i
$738$			35.9267i			1.32248i
$739$	−28.4479			−1.04647			−0.523236	−	0.852188i	$-0.675275\pi$
$739$	−28.4479			−1.04647			−0.523236	+	0.852188i	$0.675275\pi$
$740$	13.7894	−	11.6501i	0.506908	−	0.428266i
$741$		0			0
$742$			2.66017i			0.0976580i
$743$			16.3224i			0.598809i	0.954126	+	0.299405i	$0.0967881\pi$
$743$			16.3224i			0.598809i	−0.954126	+	0.299405i	$0.903212\pi$
$744$	22.2796			0.816808
$745$	−30.8066	−	36.4636i	−1.12867	−	1.33592i
$746$	15.2112			0.556920
$747$		−	86.6082i		−	3.16883i
$748$		−	10.9505i		−	0.400388i
$749$	0.00525969			0.000192185
$750$	−32.8780	+	19.4279i	−1.20053	+	0.709408i
$751$	−0.398628			−0.0145461			−0.00727307	−	0.999974i	$-0.502315\pi$
$751$	−0.398628			−0.0145461			−0.00727307	+	0.999974i	$0.502315\pi$
$752$			1.29310i			0.0471544i
$753$		−	1.87056i		−	0.0681671i
$754$		0			0
$755$	−33.1124	−	39.1928i	−1.20508	−	1.42637i
$756$	−8.90013			−0.323695
$757$		−	40.1310i		−	1.45859i	−0.684201	−	0.729293i	$-0.739849\pi$
$757$		−	40.1310i		−	1.45859i	0.684201	−	0.729293i	$-0.260151\pi$
$758$		−	17.2766i		−	0.627514i
$759$	−28.8266			−1.04634
$760$	5.64755	−	4.77139i	0.204858	−	0.173076i
$761$	3.64226			0.132032			0.0660158	−	0.997819i	$-0.478971\pi$
$761$	3.64226			0.132032			0.0660158	+	0.997819i	$0.478971\pi$
$762$		−	38.9400i		−	1.41065i
$763$			1.74459i			0.0631583i
$764$	−25.0076			−0.904742
$765$	−79.8228	+	67.4390i	−2.88600	+	2.43826i
$766$	−15.1262			−0.546533
$767$		0			0
$768$			3.41573i			0.123255i
$769$	16.4037			0.591533			0.295767	−	0.955260i	$-0.404425\pi$
$769$	16.4037			0.591533			0.295767	+	0.955260i	$0.404425\pi$
$770$	−1.34749	−	1.59492i	−0.0485600	−	0.0574771i
$771$	59.4450			2.14086
$772$		−	1.97401i		−	0.0710463i
$773$			11.3166i			0.407028i	0.979072	+	0.203514i	$0.0652363\pi$
$773$			11.3166i			0.407028i	−0.979072	+	0.203514i	$0.934764\pi$
$774$	−10.9835			−0.394795
$775$	5.44659	−	32.1551i	0.195647	−	1.15505i
$776$	−7.05844			−0.253383
$777$		−	12.6784i		−	0.454834i
$778$		−	32.0553i		−	1.14924i
$779$	−13.7053			−0.491045
$780$		0			0
$781$	−3.00134			−0.107396
$782$			22.4056i			0.801221i
$783$			117.224i			4.18925i
$784$	6.78861			0.242450
$785$	−26.0078	+	21.9729i	−0.928258	+	0.784247i
$786$	−51.2040			−1.82639
$787$			23.6730i			0.843850i	0.906631	+	0.421925i	$0.138646\pi$
$787$			23.6730i			0.843850i	−0.906631	+	0.421925i	$0.861354\pi$
$788$		−	17.6446i		−	0.628562i
$789$	−39.7791			−1.41618
$790$	2.87447	−	2.42852i	0.102269	−	0.0864030i
$791$	2.56265			0.0911174
$792$			17.6025i			0.625477i
$793$		0			0
$794$	7.52503			0.267053
$795$	−28.5197	−	33.7567i	−1.01149	−	1.19723i
$796$	−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	$0.975449\pi$
$798$		−	5.19252i		−	0.183813i
$799$	6.97221			0.246659
$800$	4.92978	+	0.835031i	0.174294	+	0.0295228i
$801$	−34.1432			−1.20639
$802$		−	37.3359i		−	1.31838i
$803$		−	16.3605i		−	0.577351i
$804$	−28.7409			−1.01361
$805$	2.75707	+	3.26335i	0.0971740	+	0.115018i
$806$		0			0
$807$			57.7516i			2.03295i
$808$			2.37044i			0.0833918i
$809$	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
$811$	−30.1105			−1.05732			−0.528661	−	0.848833i	$-0.677306\pi$
$811$	−30.1105			−1.05732			−0.528661	+	0.848833i	$0.677306\pi$
$812$			2.78421i			0.0977065i
$813$		−	33.9568i		−	1.19092i
$814$	−16.3958			−0.574671
$815$	9.35473	−	7.90343i	0.327682	−	0.276845i
$816$	18.4172			0.644730
$817$		−	4.19000i		−	0.146590i
$818$			19.7733i			0.691359i
$819$		0			0
$820$	−5.98173	−	7.08015i	−0.208891	−	0.247250i
$821$	−33.9761			−1.18577			−0.592887	−	0.805286i	$-0.702012\pi$
$821$	−33.9761			−1.18577			−0.592887	+	0.805286i	$0.702012\pi$
$822$			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	$0.893854\pi$
$824$	6.75491			0.235318
$825$	34.1983	+	5.79268i	1.19063	+	0.201675i
$826$	−3.11296			−0.108314
$827$		−	56.4739i		−	1.96379i	−0.189426	−	0.981895i	$-0.560663\pi$
$827$		−	56.4739i		−	1.96379i	0.189426	−	0.981895i	$-0.439337\pi$
$828$		−	36.0162i		−	1.25165i
$829$	−37.9617			−1.31846			−0.659231	−	0.751940i	$-0.729118\pi$
$829$	−37.9617			−1.31846			−0.659231	+	0.751940i	$0.729118\pi$
$830$	14.4201	+	17.0681i	0.500530	+	0.592442i
$831$	−14.4990			−0.502964
$832$		0			0
$833$		−	36.6033i		−	1.26823i
$834$	−40.3495			−1.39719
$835$	5.02318	−	4.24388i	0.173834	−	0.146866i
$836$	−6.71501			−0.232244
$837$			126.264i			4.36431i
$838$		−	12.4677i		−	0.430689i
$839$	17.7895			0.614162			0.307081	−	0.951683i	$-0.400648\pi$
$839$	17.7895			0.614162			0.307081	+	0.951683i	$0.400648\pi$
$840$	2.68245	−	2.26629i	0.0925532	−	0.0781944i
$841$	7.67098			0.264517
$842$		−	1.36944i		−	0.0471940i
$843$			84.2209i			2.90072i
$844$	13.3757			0.460410
$845$		0			0
$846$	−11.2076			−0.385325
$847$		−	3.16108i		−	0.108616i
$848$			5.78588i			0.198688i
$849$	−32.9289			−1.13012
$850$	4.50238	−	26.5807i	0.154430	−	0.911711i
$851$	33.5471			1.14998
$852$		−	5.04785i		−	0.172937i
$853$		−	12.0381i		−	0.412178i	−0.978533	−	0.206089i	$-0.933926\pi$
$853$		−	12.0381i		−	0.412178i	0.978533	−	0.206089i	$-0.0660737\pi$
$854$	−2.75149			−0.0941542
$855$	41.3548	+	48.9487i	1.41430	+	1.67401i
$856$	0.0114398			0.000391006
$857$			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	$0.125056\pi$
$860$	2.16455	−	1.82874i	0.0738105	−	0.0623595i
$861$	−6.50969			−0.221850
$862$			11.1142i			0.378553i
$863$			41.6531i			1.41789i	0.705265	+	0.708943i	$0.250828\pi$
$863$			41.6531i			1.41789i	−0.705265	+	0.708943i	$0.749172\pi$
$864$	−19.3578			−0.658566
$865$	6.63842	−	5.60853i	0.225713	−	0.190696i
$866$	30.2038			1.02637
$867$		−	41.2355i		−	1.40043i
$868$			2.99890i			0.101789i
$869$	−3.41778			−0.115940
$870$	−29.8494	−	35.3307i	−1.01199	−	1.19782i
$871$		0			0
$872$			3.79448i			0.128497i
$873$		−	61.1773i		−	2.07054i
$874$	13.7395			0.464745
$875$	−2.61507	−	4.42549i	−0.0884055	−	0.149609i
$876$	27.5162			0.929687
$877$		−	51.8500i		−	1.75085i	−0.483355	−	0.875425i	$-0.660582\pi$
$877$		−	51.8500i		−	1.75085i	0.483355	−	0.875425i	$-0.339418\pi$
$878$			30.0084i			1.01274i
$879$	20.5796			0.694133
$880$	−2.93078	−	3.46896i	−0.0987967	−	0.116939i
$881$	11.0112			0.370977			0.185488	−	0.982646i	$-0.440613\pi$
$881$	11.0112			0.370977			0.185488	+	0.982646i	$0.440613\pi$
$882$			58.8386i			1.98120i
$883$		−	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
$886$	−10.0957			−0.339171
$887$			50.3024i			1.68899i	0.535563	+	0.844495i	$0.320100\pi$
$887$			50.3024i			1.68899i	−0.535563	+	0.844495i	$0.679900\pi$
$888$		−	27.5755i		−	0.925372i
$889$	5.24146			0.175793
$890$	6.72868	−	5.68479i	0.225546	−	0.190555i
$891$	−81.4793			−2.72966
$892$			3.02345i			0.101233i
$893$		−	4.27548i		−	0.143073i
$894$	−72.9183			−2.43875
$895$	−14.8981	−	17.6338i	−0.497988	−	0.589433i
$896$	−0.459770			−0.0153598
$897$		0			0
$898$		−	28.9563i		−	0.966284i
$899$	39.4988			1.31736
$900$	−7.23742	+	42.7276i	−0.241247	+	1.42425i
$901$	31.1967			1.03931
$902$			8.41839i			0.280302i
$903$		−	1.99015i		−	0.0662279i
$904$	5.57377			0.185381
$905$	5.31181	+	6.28721i	0.176571	+	0.208994i
$906$	−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	$0.991840\pi$
$908$		−	14.6074i		−	0.484762i
$909$	−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	$0.360729\pi$
$912$		−	11.2937i		−	0.373973i
$913$		−	20.2942i		−	0.671639i
$914$	−40.4620			−1.33836
$915$	34.9155	−	29.4987i	1.15427	−	0.975198i
$916$	14.0176			0.463154
$917$		−	6.89224i		−	0.227602i
$918$			104.375i			3.44488i
$919$	−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
$921$	−83.7700			−2.76031
$922$			6.39717i			0.210680i
$923$		0			0
$924$	−3.18946			−0.104926
$925$	−39.7985	−	6.74126i	−1.30856	−	0.221651i
$926$	15.3751			0.505257
$927$			58.5464i			1.92292i
$928$			6.05566i			0.198787i
$929$	9.91513			0.325305			0.162652	−	0.986683i	$-0.447995\pi$
$929$	9.91513			0.325305			0.162652	+	0.986683i	$0.447995\pi$
$930$	−32.1512	−	38.0551i	−1.05428	−	1.24788i
$931$	−22.4458			−0.735631
$932$			26.5904i			0.870998i
$933$		−	70.4282i		−	2.30572i
$934$	−9.41379			−0.308029
$935$	−18.7042	+	15.8024i	−0.611692	+	0.516794i
$936$		0			0
$937$			24.7485i			0.808497i	0.914649	+	0.404248i	$0.132467\pi$
$937$			24.7485i			0.808497i	−0.914649	+	0.404248i	$0.867533\pi$
$938$		−	3.86863i		−	0.126315i
$939$	−25.1237			−0.819882
$940$	2.20870	−	1.86604i	0.0720400	−	0.0608637i
$941$	40.4541			1.31877			0.659383	−	0.751807i	$-0.270817\pi$
$941$	40.4541			1.31877			0.659383	+	0.751807i	$0.270817\pi$
$942$			52.0093i			1.69455i
$943$		−	17.2247i		−	0.560915i
$944$	−6.77070			−0.220368
$945$	12.8436	+	15.2021i	0.417803	+	0.494524i
$946$	−2.57367			−0.0836774
$947$		−	18.3367i		−	0.595864i	−0.954587	−	0.297932i	$-0.903703\pi$
$947$		−	18.3367i		−	0.595864i	0.954587	−	0.297932i	$-0.0962968\pi$
$948$		−	5.74825i		−	0.186694i
$949$		0			0
$950$	−16.2998	−	2.76094i	−0.528834	−	0.0895766i
$951$	−59.5963			−1.93254
$952$			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	$-0.0217594\pi$
$954$	−50.1476			−1.62359
$955$	36.0880	+	42.7148i	1.16778	+	1.38222i
$956$	−12.3423			−0.399178
$957$			42.0086i			1.35795i
$958$		−	24.7651i		−	0.800125i
$959$	−6.28630			−0.202995
$960$	5.83433	−	4.92918i	0.188302	−	0.159089i
$961$	11.5446			0.372407
$962$		0			0
$963$			0.0991519i			0.00319512i
$964$	−3.79308			−0.122167
$965$	−3.37176	+	2.84866i	−0.108541	+	0.0917018i
$966$	6.52591			0.209968
$967$			46.9135i			1.50864i	0.656509	+	0.754318i	$0.272033\pi$
$967$			46.9135i			1.50864i	−0.656509	+	0.754318i	$0.727967\pi$
$968$		−	6.87536i		−	0.220982i
$969$	−60.8944			−1.95621
$970$	10.1859	+	12.0563i	0.327050	+	0.387106i
$971$	−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
$973$		−	5.43119i		−	0.174116i
$974$	27.2037			0.871662
$975$		0			0
$976$	−5.98450			−0.191559
$977$			51.0911i			1.63455i	0.576248	+	0.817275i	$0.304516\pi$
$977$			51.0911i			1.63455i	−0.576248	+	0.817275i	$0.695484\pi$
$978$		−	18.7072i		−	0.598190i
$979$	−8.00049			−0.255697
$980$	−9.79652	−	11.5954i	−0.312938	−	0.370403i
$981$	−32.8877			−1.05002
$982$			27.4578i			0.876213i
$983$		−	47.7672i		−	1.52354i	−0.647850	−	0.761768i	$-0.724332\pi$
$983$		−	47.7672i		−	1.52354i	0.647850	−	0.761768i	$-0.275668\pi$
$984$	−14.1586			−0.451360
$985$	−30.1382	+	25.4625i	−0.960283	+	0.811304i
$986$	32.6513			1.03983
$987$		−	2.03075i		−	0.0646394i
$988$		0			0
$989$	5.26596			0.167448
$990$	30.0663	−	25.4018i	0.955571	−	0.807323i
$991$	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
$993$		−	63.5007i		−	2.01513i
$994$	0.679459			0.0215511
$995$	23.3372	+	27.6225i	0.739838	+	0.875693i
$996$	34.1320			1.08151
$997$			52.9031i			1.67546i	0.546087	+	0.837729i	$0.316117\pi$
$997$			52.9031i			1.67546i	−0.546087	+	0.837729i	$0.683883\pi$
$998$		−	2.92681i		−	0.0926464i
$999$	156.277			4.94438

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1690.2.b.f.339.1	✓	18	65.64	even	2
1690.2.b.f.339.18	yes	18	13.12	even	2
1690.2.b.g.339.9	yes	18	1.1	even	1	trivial
1690.2.b.g.339.10	yes	18	5.4	even	2	inner
1690.2.c.g.1689.1		18	65.34	odd	4
1690.2.c.g.1689.18		18	13.5	odd	4
1690.2.c.h.1689.1		18	65.44	odd	4
1690.2.c.h.1689.18		18	13.8	odd	4
8450.2.a.ct.1.1		9	5.3	odd	4
8450.2.a.cw.1.9		9	65.12	odd	4
8450.2.a.cx.1.1		9	65.38	odd	4
8450.2.a.da.1.9		9	5.2	odd	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.b (of order \(2\), degree \(1\), minimal)

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

Introduction

L-functions

Modular forms

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