LMFDB - Embedded newform 1690.2.b.d.339.7

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 = [8,0,0,-8,0,0,0,0,-4,6,0] 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:	$8$
Coefficient field:	8.0.303595776.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 $ x^8 + 5x^6 + 16x^4 + 45*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.7
Root			$-0.396143 - 1.68614i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.d.339.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +0.792287i q^{3} -1.00000 q^{4} +(-2.12819 + 0.686141i) q^{5} -0.792287 q^{6} +3.37228i q^{7} -1.00000i q^{8} +2.37228 q^{9} +(-0.686141 - 2.12819i) q^{10} -5.04868 q^{11} -0.792287i q^{12} -3.37228 q^{14} +(-0.543620 - 1.68614i) q^{15} +1.00000 q^{16} -2.67181i q^{17} +2.37228i q^{18} -3.46410 q^{19} +(2.12819 - 0.686141i) q^{20} -2.67181 q^{21} -5.04868i q^{22} +6.63325i q^{23} +0.792287 q^{24} +(4.05842 - 2.92048i) q^{25} +4.25639i q^{27} -3.37228i q^{28} -8.74456 q^{29} +(1.68614 - 0.543620i) q^{30} +3.46410 q^{31} +1.00000i q^{32} -4.00000i q^{33} +2.67181 q^{34} +(-2.31386 - 7.17687i) q^{35} -2.37228 q^{36} -8.11684i q^{37} -3.46410i q^{38} +(0.686141 + 2.12819i) q^{40} -3.16915 q^{41} -2.67181i q^{42} -9.30506i q^{43} +5.04868 q^{44} +(-5.04868 + 1.62772i) q^{45} -6.63325 q^{46} +4.62772i q^{47} +0.792287i q^{48} -4.37228 q^{49} +(2.92048 + 4.05842i) q^{50} +2.11684 q^{51} +1.58457i q^{53} -4.25639 q^{54} +(10.7446 - 3.46410i) q^{55} +3.37228 q^{56} -2.74456i q^{57} -8.74456i q^{58} +6.63325 q^{59} +(0.543620 + 1.68614i) q^{60} +4.74456 q^{61} +3.46410i q^{62} +8.00000i q^{63} -1.00000 q^{64} +4.00000 q^{66} +4.00000i q^{67} +2.67181i q^{68} -5.25544 q^{69} +(7.17687 - 2.31386i) q^{70} +3.96143 q^{71} -2.37228i q^{72} -10.0000i q^{73} +8.11684 q^{74} +(2.31386 + 3.21543i) q^{75} +3.46410 q^{76} -17.0256i q^{77} -6.74456 q^{79} +(-2.12819 + 0.686141i) q^{80} +3.74456 q^{81} -3.16915i q^{82} -2.74456i q^{83} +2.67181 q^{84} +(1.83324 + 5.68614i) q^{85} +9.30506 q^{86} -6.92820i q^{87} +5.04868i q^{88} -8.51278 q^{89} +(-1.62772 - 5.04868i) q^{90} -6.63325i q^{92} +2.74456i q^{93} -4.62772 q^{94} +(7.37228 - 2.37686i) q^{95} -0.792287 q^{96} -4.74456i q^{97} -4.37228i q^{98} -11.9769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 4 q^{9} + 6 q^{10} - 4 q^{14} + 8 q^{16} - 2 q^{25} - 24 q^{29} + 2 q^{30} - 30 q^{35} + 4 q^{36} - 6 q^{40} - 12 q^{49} - 52 q^{51} + 40 q^{55} + 4 q^{56} - 8 q^{61} - 8 q^{64} + 32 q^{66}+ \cdots + 36 q^{95}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^9 + 6 * q^10 - 4 * q^14 + 8 * q^16 - 2 * q^25 - 24 * q^29 + 2 * q^30 - 30 * q^35 + 4 * q^36 - 6 * q^40 - 12 * q^49 - 52 * q^51 + 40 * q^55 + 4 * q^56 - 8 * q^61 - 8 * q^64 + 32 * q^66 - 88 * q^69 - 4 * q^74 + 30 * q^75 - 8 * q^79 - 16 * q^81 - 36 * q^90 - 60 * q^94 + 36 * q^95

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
$3$			0.792287i			0.457427i	0.973494	+	0.228714i	$0.0734519\pi$
$3$			0.792287i			0.457427i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	−1.00000			−0.500000
$5$	−2.12819	+	0.686141i	−0.951757	+	0.306851i
$5$	−2.12819	+	0.686141i	−0.951757	+	0.306851i
$6$	−0.792287			−0.323450
$7$			3.37228i			1.27460i	0.770615	+	0.637301i	$0.219949\pi$
$7$			3.37228i			1.27460i	−0.770615	+	0.637301i	$0.780051\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.37228			0.790760
$10$	−0.686141	−	2.12819i	−0.216977	−	0.672994i
$11$	−5.04868			−1.52223			−0.761116	−	0.648615i	$-0.775348\pi$
$11$	−5.04868			−1.52223			−0.761116	+	0.648615i	$0.775348\pi$
$12$		−	0.792287i		−	0.228714i
$13$		0			0
$13$		0			0
$14$	−3.37228			−0.901280
$15$	−0.543620	−	1.68614i	−0.140362	−	0.435360i
$16$	1.00000			0.250000
$17$		−	2.67181i		−	0.648010i	−0.946055	−	0.324005i	$-0.894970\pi$
$17$		−	2.67181i		−	0.648010i	0.946055	−	0.324005i	$-0.105030\pi$
$18$			2.37228i			0.559152i
$19$	−3.46410			−0.794719			−0.397360	−	0.917663i	$-0.630073\pi$
$19$	−3.46410			−0.794719			−0.397360	+	0.917663i	$0.630073\pi$
$20$	2.12819	−	0.686141i	0.475879	−	0.153426i
$21$	−2.67181			−0.583038
$22$		−	5.04868i		−	1.07638i
$23$			6.63325i			1.38313i	0.722315	+	0.691564i	$0.243078\pi$
$23$			6.63325i			1.38313i	−0.722315	+	0.691564i	$0.756922\pi$
$24$	0.792287			0.161725
$25$	4.05842	−	2.92048i	0.811684	−	0.584096i
$26$		0			0
$27$			4.25639i			0.819142i
$28$		−	3.37228i		−	0.637301i
$29$	−8.74456			−1.62382			−0.811912	−	0.583779i	$-0.801573\pi$
$29$	−8.74456			−1.62382			−0.811912	+	0.583779i	$0.801573\pi$
$30$	1.68614	−	0.543620i	0.307846	−	0.0992510i
$31$	3.46410			0.622171			0.311086	−	0.950382i	$-0.399307\pi$
$31$	3.46410			0.622171			0.311086	+	0.950382i	$0.399307\pi$
$32$			1.00000i			0.176777i
$33$		−	4.00000i		−	0.696311i
$34$	2.67181			0.458212
$35$	−2.31386	−	7.17687i	−0.391114	−	1.21311i
$36$	−2.37228			−0.395380
$37$		−	8.11684i		−	1.33440i	−0.744878	−	0.667200i	$-0.767492\pi$
$37$		−	8.11684i		−	1.33440i	0.744878	−	0.667200i	$-0.232508\pi$
$38$		−	3.46410i		−	0.561951i
$39$		0			0
$40$	0.686141	+	2.12819i	0.108488	+	0.336497i
$41$	−3.16915			−0.494938			−0.247469	−	0.968896i	$-0.579599\pi$
$41$	−3.16915			−0.494938			−0.247469	+	0.968896i	$0.579599\pi$
$42$		−	2.67181i		−	0.412270i
$43$		−	9.30506i		−	1.41901i	−0.704701	−	0.709504i	$-0.748919\pi$
$43$		−	9.30506i		−	1.41901i	0.704701	−	0.709504i	$-0.251081\pi$
$44$	5.04868			0.761116
$45$	−5.04868	+	1.62772i	−0.752612	+	0.242646i
$46$	−6.63325			−0.978019
$47$			4.62772i			0.675022i	0.941322	+	0.337511i	$0.109585\pi$
$47$			4.62772i			0.675022i	−0.941322	+	0.337511i	$0.890415\pi$
$48$			0.792287i			0.114357i
$49$	−4.37228			−0.624612
$50$	2.92048	+	4.05842i	0.413018	+	0.573948i
$51$	2.11684			0.296417
$52$		0			0
$53$			1.58457i			0.217658i	0.994060	+	0.108829i	$0.0347101\pi$
$53$			1.58457i			0.217658i	−0.994060	+	0.108829i	$0.965290\pi$
$54$	−4.25639			−0.579221
$55$	10.7446	−	3.46410i	1.44880	−	0.467099i
$56$	3.37228			0.450640
$57$		−	2.74456i		−	0.363526i
$58$		−	8.74456i		−	1.14822i
$59$	6.63325			0.863576			0.431788	−	0.901975i	$-0.357883\pi$
$59$	6.63325			0.863576			0.431788	+	0.901975i	$0.357883\pi$
$60$	0.543620	+	1.68614i	0.0701811	+	0.217680i
$61$	4.74456			0.607479			0.303739	−	0.952755i	$-0.401765\pi$
$61$	4.74456			0.607479			0.303739	+	0.952755i	$0.401765\pi$
$62$			3.46410i			0.439941i
$63$			8.00000i			1.00791i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.00000			0.492366
$67$			4.00000i			0.488678i	0.969690	+	0.244339i	$0.0785709\pi$
$67$			4.00000i			0.488678i	−0.969690	+	0.244339i	$0.921429\pi$
$68$			2.67181i			0.324005i
$69$	−5.25544			−0.632680
$70$	7.17687	−	2.31386i	0.857800	−	0.276559i
$71$	3.96143			0.470136			0.235068	−	0.971979i	$-0.424469\pi$
$71$	3.96143			0.470136			0.235068	+	0.971979i	$0.424469\pi$
$72$		−	2.37228i		−	0.279576i
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$	8.11684			0.943564
$75$	2.31386	+	3.21543i	0.267181	+	0.371286i
$76$	3.46410			0.397360
$77$		−	17.0256i		−	1.94024i
$78$		0			0
$79$	−6.74456			−0.758823			−0.379411	−	0.925228i	$-0.623873\pi$
$79$	−6.74456			−0.758823			−0.379411	+	0.925228i	$0.623873\pi$
$80$	−2.12819	+	0.686141i	−0.237939	+	0.0767129i
$81$	3.74456			0.416063
$82$		−	3.16915i		−	0.349974i
$83$		−	2.74456i		−	0.301255i	−0.988591	−	0.150627i	$-0.951871\pi$
$83$		−	2.74456i		−	0.301255i	0.988591	−	0.150627i	$-0.0481294\pi$
$84$	2.67181			0.291519
$85$	1.83324	+	5.68614i	0.198843	+	0.616749i
$86$	9.30506			1.00339
$87$		−	6.92820i		−	0.742781i
$88$			5.04868i			0.538191i
$89$	−8.51278			−0.902353			−0.451176	−	0.892435i	$-0.648995\pi$
$89$	−8.51278			−0.902353			−0.451176	+	0.892435i	$0.648995\pi$
$90$	−1.62772	−	5.04868i	−0.171577	−	0.532177i
$91$		0			0
$92$		−	6.63325i		−	0.691564i
$93$			2.74456i			0.284598i
$94$	−4.62772			−0.477313
$95$	7.37228	−	2.37686i	0.756380	−	0.243861i
$96$	−0.792287			−0.0808625
$97$		−	4.74456i		−	0.481737i	−0.970558	−	0.240869i	$-0.922568\pi$
$97$		−	4.74456i		−	0.481737i	0.970558	−	0.240869i	$-0.0774323\pi$
$98$		−	4.37228i		−	0.441667i
$99$	−11.9769			−1.20372
$100$	−4.05842	+	2.92048i	−0.405842	+	0.292048i
$101$	3.25544			0.323928			0.161964	−	0.986797i	$-0.448217\pi$
$101$	3.25544			0.323928			0.161964	+	0.986797i	$0.448217\pi$
$102$			2.11684i			0.209599i
$103$		−	10.3923i		−	1.02398i	−0.858990	−	0.511992i	$-0.828908\pi$
$103$		−	10.3923i		−	1.02398i	0.858990	−	0.511992i	$-0.171092\pi$
$104$		0			0
$105$	5.68614	−	1.83324i	0.554911	−	0.178906i
$106$	−1.58457			−0.153907
$107$			0.294954i			0.0285142i	0.999898	+	0.0142571i	$0.00453834\pi$
$107$			0.294954i			0.0285142i	−0.999898	+	0.0142571i	$0.995462\pi$
$108$		−	4.25639i		−	0.409571i
$109$	−12.7692			−1.22306			−0.611532	−	0.791220i	$-0.709446\pi$
$109$	−12.7692			−1.22306			−0.611532	+	0.791220i	$0.709446\pi$
$110$	3.46410	+	10.7446i	0.330289	+	1.02445i
$111$	6.43087			0.610391
$112$			3.37228i			0.318651i
$113$		−	17.0256i		−	1.60163i	−0.598912	−	0.800815i	$-0.704400\pi$
$113$		−	17.0256i		−	1.60163i	0.598912	−	0.800815i	$-0.295600\pi$
$114$	2.74456			0.257052
$115$	−4.55134	−	14.1168i	−0.424415	−	1.31640i
$116$	8.74456			0.811912
$117$		0			0
$118$			6.63325i			0.610640i
$119$	9.01011			0.825955
$120$	−1.68614	+	0.543620i	−0.153923	+	0.0496255i
$121$	14.4891			1.31719
$122$			4.74456i			0.429553i
$123$		−	2.51087i		−	0.226398i
$124$	−3.46410			−0.311086
$125$	−6.63325	+	9.00000i	−0.593296	+	0.804984i
$126$	−8.00000			−0.712697
$127$			3.46410i			0.307389i	0.988118	+	0.153695i	$0.0491172\pi$
$127$			3.46410i			0.307389i	−0.988118	+	0.153695i	$0.950883\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	7.37228			0.649093
$130$		0			0
$131$	−7.37228			−0.644119			−0.322060	−	0.946719i	$-0.604375\pi$
$131$	−7.37228			−0.644119			−0.322060	+	0.946719i	$0.604375\pi$
$132$			4.00000i			0.348155i
$133$		−	11.6819i		−	1.01295i
$134$	−4.00000			−0.345547
$135$	−2.92048	−	9.05842i	−0.251355	−	0.779625i
$136$	−2.67181			−0.229106
$137$			6.00000i			0.512615i	0.966595	+	0.256307i	$0.0825059\pi$
$137$			6.00000i			0.512615i	−0.966595	+	0.256307i	$0.917494\pi$
$138$		−	5.25544i		−	0.447373i
$139$	0.627719			0.0532424			0.0266212	−	0.999646i	$-0.491525\pi$
$139$	0.627719			0.0532424			0.0266212	+	0.999646i	$0.491525\pi$
$140$	2.31386	+	7.17687i	0.195557	+	0.606556i
$141$	−3.66648			−0.308773
$142$			3.96143i			0.332436i
$143$		0			0
$144$	2.37228			0.197690
$145$	18.6101	−	6.00000i	1.54549	−	0.498273i
$146$	10.0000			0.827606
$147$		−	3.46410i		−	0.285714i
$148$			8.11684i			0.667200i
$149$	3.75906			0.307954			0.153977	−	0.988074i	$-0.450792\pi$
$149$	3.75906			0.307954			0.153977	+	0.988074i	$0.450792\pi$
$150$	−3.21543	+	2.31386i	−0.262539	+	0.188926i
$151$	2.37686			0.193426			0.0967131	−	0.995312i	$-0.469167\pi$
$151$	2.37686			0.193426			0.0967131	+	0.995312i	$0.469167\pi$
$152$			3.46410i			0.280976i
$153$		−	6.33830i		−	0.512421i
$154$	17.0256			1.37196
$155$	−7.37228	+	2.37686i	−0.592156	+	0.190914i
$156$		0			0
$157$			4.75372i			0.379388i	0.981843	+	0.189694i	$0.0607496\pi$
$157$			4.75372i			0.379388i	−0.981843	+	0.189694i	$0.939250\pi$
$158$		−	6.74456i		−	0.536569i
$159$	−1.25544			−0.0995627
$160$	−0.686141	−	2.12819i	−0.0542442	−	0.168249i
$161$	−22.3692			−1.76294
$162$			3.74456i			0.294201i
$163$		−	13.2554i		−	1.03825i	−0.854700	−	0.519123i	$-0.826259\pi$
$163$		−	13.2554i		−	1.03825i	0.854700	−	0.519123i	$-0.173741\pi$
$164$	3.16915			0.247469
$165$	2.74456	+	8.51278i	0.213664	+	0.662719i
$166$	2.74456			0.213019
$167$			5.48913i			0.424761i	0.977187	+	0.212381i	$0.0681217\pi$
$167$			5.48913i			0.424761i	−0.977187	+	0.212381i	$0.931878\pi$
$168$			2.67181i			0.206135i
$169$		0			0
$170$	−5.68614	+	1.83324i	−0.436107	+	0.140603i
$171$	−8.21782			−0.628433
$172$			9.30506i			0.709504i
$173$			12.2718i			0.933010i	0.884519	+	0.466505i	$0.154487\pi$
$173$			12.2718i			0.933010i	−0.884519	+	0.466505i	$0.845513\pi$
$174$	6.92820			0.525226
$175$	9.84868	+	13.6861i	0.744491	+	1.03457i
$176$	−5.04868			−0.380558
$177$			5.25544i			0.395023i
$178$		−	8.51278i		−	0.638060i
$179$	−22.1168			−1.65309			−0.826545	−	0.562870i	$-0.809697\pi$
$179$	−22.1168			−1.65309			−0.826545	+	0.562870i	$0.809697\pi$
$180$	5.04868	−	1.62772i	0.376306	−	0.121323i
$181$	−19.4891			−1.44862			−0.724308	−	0.689477i	$-0.757840\pi$
$181$	−19.4891			−1.44862			−0.724308	+	0.689477i	$0.757840\pi$
$182$		0			0
$183$			3.75906i			0.277877i
$184$	6.63325			0.489010
$185$	5.56930	+	17.2742i	0.409463	+	1.27003i
$186$	−2.74456			−0.201241
$187$			13.4891i			0.986423i
$188$		−	4.62772i		−	0.337511i
$189$	−14.3537			−1.04408
$190$	2.37686	+	7.37228i	0.172436	+	0.534842i
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		−	0.792287i		−	0.0571784i
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	4.74456			0.340640
$195$		0			0
$196$	4.37228			0.312306
$197$			1.37228i			0.0977710i	0.998804	+	0.0488855i	$0.0155669\pi$
$197$			1.37228i			0.0977710i	−0.998804	+	0.0488855i	$0.984433\pi$
$198$		−	11.9769i		−	0.851160i
$199$	−8.00000			−0.567105			−0.283552	−	0.958957i	$-0.591513\pi$
$199$	−8.00000			−0.567105			−0.283552	+	0.958957i	$0.591513\pi$
$200$	−2.92048	−	4.05842i	−0.206509	−	0.286974i
$201$	−3.16915			−0.223534
$202$			3.25544i			0.229052i
$203$		−	29.4891i		−	2.06973i
$204$	−2.11684			−0.148209
$205$	6.74456	−	2.17448i	0.471061	−	0.151872i
$206$	10.3923			0.724066
$207$			15.7359i			1.09372i
$208$		0			0
$209$	17.4891			1.20975
$210$	1.83324	+	5.68614i	0.126506	+	0.392381i
$211$	−14.1168			−0.971844			−0.485922	−	0.874002i	$-0.661516\pi$
$211$	−14.1168			−0.971844			−0.485922	+	0.874002i	$0.661516\pi$
$212$		−	1.58457i		−	0.108829i
$213$			3.13859i			0.215053i
$214$	−0.294954			−0.0201626
$215$	6.38458	+	19.8030i	0.435425	+	1.35055i
$216$	4.25639			0.289611
$217$			11.6819i			0.793021i
$218$		−	12.7692i		−	0.864837i
$219$	7.92287			0.535378
$220$	−10.7446	+	3.46410i	−0.724398	+	0.233550i
$221$		0			0
$222$			6.43087i			0.431612i
$223$			2.11684i			0.141754i	0.997485	+	0.0708772i	$0.0225798\pi$
$223$			2.11684i			0.141754i	−0.997485	+	0.0708772i	$0.977420\pi$
$224$	−3.37228			−0.225320
$225$	9.62772	−	6.92820i	0.641848	−	0.461880i
$226$	17.0256			1.13252
$227$			17.4891i			1.16079i	0.814334	+	0.580397i	$0.197103\pi$
$227$			17.4891i			1.16079i	−0.814334	+	0.580397i	$0.802897\pi$
$228$			2.74456i			0.181763i
$229$	14.9436			0.987504			0.493752	−	0.869603i	$-0.335625\pi$
$229$	14.9436			0.987504			0.493752	+	0.869603i	$0.335625\pi$
$230$	14.1168	−	4.55134i	0.930837	−	0.300107i
$231$	13.4891			0.887519
$232$			8.74456i			0.574109i
$233$			11.1846i			0.732727i	0.930472	+	0.366363i	$0.119397\pi$
$233$			11.1846i			0.732727i	−0.930472	+	0.366363i	$0.880603\pi$
$234$		0			0
$235$	−3.17527	−	9.84868i	−0.207132	−	0.642457i
$236$	−6.63325			−0.431788
$237$		−	5.34363i		−	0.347106i
$238$			9.01011i			0.584039i
$239$	6.13592			0.396899			0.198450	−	0.980111i	$-0.436409\pi$
$239$	6.13592			0.396899			0.198450	+	0.980111i	$0.436409\pi$
$240$	−0.543620	−	1.68614i	−0.0350905	−	0.108840i
$241$	−11.6819			−0.752499			−0.376249	−	0.926518i	$-0.622786\pi$
$241$	−11.6819			−0.752499			−0.376249	+	0.926518i	$0.622786\pi$
$242$			14.4891i			0.931396i
$243$			15.7359i			1.00946i
$244$	−4.74456			−0.303739
$245$	9.30506	−	3.00000i	0.594479	−	0.191663i
$246$	2.51087			0.160088
$247$		0			0
$248$		−	3.46410i		−	0.219971i
$249$	2.17448			0.137802
$250$	−9.00000	−	6.63325i	−0.569210	−	0.419524i
$251$	−22.9783			−1.45037			−0.725187	−	0.688552i	$-0.758247\pi$
$251$	−22.9783			−1.45037			−0.725187	+	0.688552i	$0.758247\pi$
$252$		−	8.00000i		−	0.503953i
$253$		−	33.4891i		−	2.10544i
$254$	−3.46410			−0.217357
$255$	−4.50506	+	1.45245i	−0.282118	+	0.0909561i
$256$	1.00000			0.0625000
$257$			9.01011i			0.562035i	0.959703	+	0.281018i	$0.0906719\pi$
$257$			9.01011i			0.562035i	−0.959703	+	0.281018i	$0.909328\pi$
$258$			7.37228i			0.458978i
$259$	27.3723			1.70083
$260$		0			0
$261$	−20.7446			−1.28406
$262$		−	7.37228i		−	0.455461i
$263$			28.4125i			1.75199i	0.482319	+	0.875996i	$0.339795\pi$
$263$			28.4125i			1.75199i	−0.482319	+	0.875996i	$0.660205\pi$
$264$	−4.00000			−0.246183
$265$	−1.08724	−	3.37228i	−0.0667887	−	0.207158i
$266$	11.6819			0.716265
$267$		−	6.74456i		−	0.412761i
$268$		−	4.00000i		−	0.244339i
$269$	−8.74456			−0.533165			−0.266583	−	0.963812i	$-0.585895\pi$
$269$	−8.74456			−0.533165			−0.266583	+	0.963812i	$0.585895\pi$
$270$	9.05842	−	2.92048i	0.551278	−	0.177735i
$271$	−11.4795			−0.697333			−0.348666	−	0.937247i	$-0.613365\pi$
$271$	−11.4795			−0.697333			−0.348666	+	0.937247i	$0.613365\pi$
$272$		−	2.67181i		−	0.162003i
$273$		0			0
$274$	−6.00000			−0.362473
$275$	−20.4897	+	14.7446i	−1.23557	+	0.889131i
$276$	5.25544			0.316340
$277$			16.4356i			0.987522i	0.869598	+	0.493761i	$0.164378\pi$
$277$			16.4356i			0.987522i	−0.869598	+	0.493761i	$0.835622\pi$
$278$			0.627719i			0.0376481i
$279$	8.21782			0.491988
$280$	−7.17687	+	2.31386i	−0.428900	+	0.138280i
$281$	−8.51278			−0.507830			−0.253915	−	0.967227i	$-0.581718\pi$
$281$	−8.51278			−0.507830			−0.253915	+	0.967227i	$0.581718\pi$
$282$		−	3.66648i		−	0.218336i
$283$		−	17.3205i		−	1.02960i	−0.857311	−	0.514799i	$-0.827867\pi$
$283$		−	17.3205i		−	1.02960i	0.857311	−	0.514799i	$-0.172133\pi$
$284$	−3.96143			−0.235068
$285$	1.88316	+	5.84096i	0.111549	+	0.345989i
$286$		0			0
$287$		−	10.6873i		−	0.630849i
$288$			2.37228i			0.139788i
$289$	9.86141			0.580083
$290$	6.00000	+	18.6101i	0.352332	+	1.09282i
$291$	3.75906			0.220360
$292$			10.0000i			0.585206i
$293$		−	30.8614i		−	1.80294i	−0.432839	−	0.901471i	$-0.642488\pi$
$293$		−	30.8614i		−	1.80294i	0.432839	−	0.901471i	$-0.357512\pi$
$294$	3.46410			0.202031
$295$	−14.1168	+	4.55134i	−0.821914	+	0.264989i
$296$	−8.11684			−0.471782
$297$		−	21.4891i		−	1.24693i
$298$			3.75906i			0.217756i
$299$		0			0
$300$	−2.31386	−	3.21543i	−0.133591	−	0.185643i
$301$	31.3793			1.80867
$302$			2.37686i			0.136773i
$303$			2.57924i			0.148174i
$304$	−3.46410			−0.198680
$305$	−10.0974	+	3.25544i	−0.578173	+	0.186406i
$306$	6.33830			0.362336
$307$			16.2337i			0.926506i	0.886226	+	0.463253i	$0.153318\pi$
$307$			16.2337i			0.926506i	−0.886226	+	0.463253i	$0.846682\pi$
$308$			17.0256i			0.970121i
$309$	8.23369			0.468398
$310$	−2.37686	−	7.37228i	−0.134997	−	0.418717i
$311$	−14.7446			−0.836087			−0.418044	−	0.908427i	$-0.637284\pi$
$311$	−14.7446			−0.836087			−0.418044	+	0.908427i	$0.637284\pi$
$312$		0			0
$313$		−	17.5229i		−	0.990452i	−0.868764	−	0.495226i	$-0.835085\pi$
$313$		−	17.5229i		−	0.990452i	0.868764	−	0.495226i	$-0.164915\pi$
$314$	−4.75372			−0.268268
$315$	−5.48913	−	17.0256i	−0.309277	−	0.959281i
$316$	6.74456			0.379411
$317$		−	28.9783i		−	1.62758i	−0.581159	−	0.813790i	$-0.697400\pi$
$317$		−	28.9783i		−	1.62758i	0.581159	−	0.813790i	$-0.302600\pi$
$318$		−	1.25544i		−	0.0704014i
$319$	44.1485			2.47184
$320$	2.12819	−	0.686141i	0.118970	−	0.0383564i
$321$	−0.233688			−0.0130432
$322$		−	22.3692i		−	1.24659i
$323$			9.25544i			0.514986i
$324$	−3.74456			−0.208031
$325$		0			0
$326$	13.2554			0.734151
$327$		−	10.1168i		−	0.559463i
$328$			3.16915i			0.174987i
$329$	−15.6060			−0.860385
$330$	−8.51278	+	2.74456i	−0.468613	+	0.151083i
$331$	10.3923			0.571213			0.285606	−	0.958347i	$-0.407805\pi$
$331$	10.3923			0.571213			0.285606	+	0.958347i	$0.407805\pi$
$332$			2.74456i			0.150627i
$333$		−	19.2554i		−	1.05519i
$334$	−5.48913			−0.300352
$335$	−2.74456	−	8.51278i	−0.149951	−	0.465103i
$336$	−2.67181			−0.145759
$337$			31.3793i			1.70934i	0.519172	+	0.854670i	$0.326240\pi$
$337$			31.3793i			1.70934i	−0.519172	+	0.854670i	$0.673760\pi$
$338$		0			0
$339$	13.4891			0.732629
$340$	−1.83324	−	5.68614i	−0.0994214	−	0.308374i
$341$	−17.4891			−0.947089
$342$		−	8.21782i		−	0.444369i
$343$			8.86141i			0.478471i
$344$	−9.30506			−0.501695
$345$	11.1846	−	3.60597i	0.602158	−	0.194139i
$346$	−12.2718			−0.659738
$347$			15.6434i			0.839780i	0.907575	+	0.419890i	$0.137931\pi$
$347$			15.6434i			0.839780i	−0.907575	+	0.419890i	$0.862069\pi$
$348$			6.92820i			0.371391i
$349$	−22.2766			−1.19244			−0.596220	−	0.802821i	$-0.703331\pi$
$349$	−22.2766			−1.19244			−0.596220	+	0.802821i	$0.703331\pi$
$350$	−13.6861	+	9.84868i	−0.731555	+	0.526434i
$351$		0			0
$352$		−	5.04868i		−	0.269095i
$353$		−	11.4891i		−	0.611504i	−0.952111	−	0.305752i	$-0.901092\pi$
$353$		−	11.4891i		−	0.611504i	0.952111	−	0.305752i	$-0.0989079\pi$
$354$	−5.25544			−0.279323
$355$	−8.43070	+	2.71810i	−0.447455	+	0.144262i
$356$	8.51278			0.451176
$357$			7.13859i			0.377814i
$358$		−	22.1168i		−	1.16891i
$359$	−23.6588			−1.24866			−0.624332	−	0.781159i	$-0.714629\pi$
$359$	−23.6588			−1.24866			−0.624332	+	0.781159i	$0.714629\pi$
$360$	1.62772	+	5.04868i	0.0857883	+	0.266089i
$361$	−7.00000			−0.368421
$362$		−	19.4891i		−	1.02433i
$363$			11.4795i			0.602520i
$364$		0			0
$365$	6.86141	+	21.2819i	0.359142	+	1.11395i
$366$	−3.75906			−0.196489
$367$		−	15.1460i		−	0.790616i	−0.918549	−	0.395308i	$-0.870638\pi$
$367$		−	15.1460i		−	0.790616i	0.918549	−	0.395308i	$-0.129362\pi$
$368$			6.63325i			0.345782i
$369$	−7.51811			−0.391377
$370$	−17.2742	+	5.56930i	−0.898044	+	0.289534i
$371$	−5.34363			−0.277427
$372$		−	2.74456i		−	0.142299i
$373$			30.2921i			1.56846i	0.620468	+	0.784232i	$0.286943\pi$
$373$			30.2921i			1.56846i	−0.620468	+	0.784232i	$0.713057\pi$
$374$	−13.4891			−0.697506
$375$	−7.13058	−	5.25544i	−0.368222	−	0.271390i
$376$	4.62772			0.238656
$377$		0			0
$378$		−	14.3537i		−	0.738277i
$379$	−17.3205			−0.889695			−0.444847	−	0.895606i	$-0.646742\pi$
$379$	−17.3205			−0.889695			−0.444847	+	0.895606i	$0.646742\pi$
$380$	−7.37228	+	2.37686i	−0.378190	+	0.121930i
$381$	−2.74456			−0.140608
$382$		0			0
$383$		−	34.1168i		−	1.74329i	−0.490138	−	0.871645i	$-0.663054\pi$
$383$		−	34.1168i		−	1.74329i	0.490138	−	0.871645i	$-0.336946\pi$
$384$	0.792287			0.0404312
$385$	11.6819	+	36.2337i	0.595366	+	1.84664i
$386$	−14.0000			−0.712581
$387$		−	22.0742i		−	1.12210i
$388$			4.74456i			0.240869i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	17.7228			0.896281
$392$			4.37228i			0.220834i
$393$		−	5.84096i		−	0.294638i
$394$	−1.37228			−0.0691345
$395$	14.3537	−	4.62772i	0.722215	−	0.232846i
$396$	11.9769			0.601861
$397$			31.4891i			1.58039i	0.612853	+	0.790197i	$0.290022\pi$
$397$			31.4891i			1.58039i	−0.612853	+	0.790197i	$0.709978\pi$
$398$		−	8.00000i		−	0.401004i
$399$	9.25544			0.463351
$400$	4.05842	−	2.92048i	0.202921	−	0.146024i
$401$	0.994667			0.0496713			0.0248356	−	0.999692i	$-0.492094\pi$
$401$	0.994667			0.0496713			0.0248356	+	0.999692i	$0.492094\pi$
$402$		−	3.16915i		−	0.158063i
$403$		0			0
$404$	−3.25544			−0.161964
$405$	−7.96916	+	2.56930i	−0.395991	+	0.127669i
$406$	29.4891			1.46352
$407$			40.9793i			2.03127i
$408$		−	2.11684i		−	0.104799i
$409$	−25.5383			−1.26279			−0.631395	−	0.775462i	$-0.717517\pi$
$409$	−25.5383			−1.26279			−0.631395	+	0.775462i	$0.717517\pi$
$410$	2.17448	+	6.74456i	0.107390	+	0.333090i
$411$	−4.75372			−0.234484
$412$			10.3923i			0.511992i
$413$			22.3692i			1.10072i
$414$	−15.7359			−0.773379
$415$	1.88316	+	5.84096i	0.0924405	+	0.286722i
$416$		0			0
$417$			0.497333i			0.0243545i
$418$			17.4891i			0.855421i
$419$	1.88316			0.0919982			0.0459991	−	0.998941i	$-0.485353\pi$
$419$	1.88316			0.0919982			0.0459991	+	0.998941i	$0.485353\pi$
$420$	−5.68614	+	1.83324i	−0.277455	+	0.0894530i
$421$	1.08724			0.0529889			0.0264944	−	0.999649i	$-0.491566\pi$
$421$	1.08724			0.0529889			0.0264944	+	0.999649i	$0.491566\pi$
$422$		−	14.1168i		−	0.687197i
$423$			10.9783i			0.533781i
$424$	1.58457			0.0769537
$425$	−7.80298	−	10.8434i	−0.378500	−	0.525980i
$426$	−3.13859			−0.152065
$427$			16.0000i			0.774294i
$428$		−	0.294954i		−	0.0142571i
$429$		0			0
$430$	−19.8030	+	6.38458i	−0.954985	+	0.307892i
$431$	−9.89497			−0.476624			−0.238312	−	0.971189i	$-0.576594\pi$
$431$	−9.89497			−0.476624			−0.238312	+	0.971189i	$0.576594\pi$
$432$			4.25639i			0.204786i
$433$		−	15.3484i		−	0.737597i	−0.929509	−	0.368799i	$-0.879769\pi$
$433$		−	15.3484i		−	0.737597i	0.929509	−	0.368799i	$-0.120231\pi$
$434$	−11.6819			−0.560750
$435$	4.75372	+	14.7446i	0.227924	+	0.706948i
$436$	12.7692			0.611532
$437$		−	22.9783i		−	1.09920i
$438$			7.92287i			0.378569i
$439$	12.2337			0.583882			0.291941	−	0.956436i	$-0.405699\pi$
$439$	12.2337			0.583882			0.291941	+	0.956436i	$0.405699\pi$
$440$	−3.46410	−	10.7446i	−0.165145	−	0.512227i
$441$	−10.3723			−0.493918
$442$		0			0
$443$		−	7.72049i		−	0.366812i	−0.983037	−	0.183406i	$-0.941288\pi$
$443$		−	7.72049i		−	0.366812i	0.983037	−	0.183406i	$-0.0587122\pi$
$444$	−6.43087			−0.305196
$445$	18.1168	−	5.84096i	0.858821	−	0.276888i
$446$	−2.11684			−0.100235
$447$			2.97825i			0.140866i
$448$		−	3.37228i		−	0.159325i
$449$	−34.0511			−1.60697			−0.803486	−	0.595324i	$-0.797024\pi$
$449$	−34.0511			−1.60697			−0.803486	+	0.595324i	$0.797024\pi$
$450$	6.92820	+	9.62772i	0.326599	+	0.453855i
$451$	16.0000			0.753411
$452$			17.0256i			0.800815i
$453$			1.88316i			0.0884784i
$454$	−17.4891			−0.820805
$455$		0			0
$456$	−2.74456			−0.128526
$457$			20.9783i			0.981321i	0.871351	+	0.490661i	$0.163244\pi$
$457$			20.9783i			0.981321i	−0.871351	+	0.490661i	$0.836756\pi$
$458$			14.9436i			0.698271i
$459$	11.3723			0.530813
$460$	4.55134	+	14.1168i	0.212207	+	0.658201i
$461$	−41.4766			−1.93176			−0.965880	−	0.258990i	$-0.916610\pi$
$461$	−41.4766			−1.93176			−0.965880	+	0.258990i	$0.916610\pi$
$462$			13.4891i			0.627571i
$463$		−	16.0000i		−	0.743583i	−0.928316	−	0.371792i	$-0.878744\pi$
$463$		−	16.0000i		−	0.743583i	0.928316	−	0.371792i	$-0.121256\pi$
$464$	−8.74456			−0.405956
$465$	−1.88316	−	5.84096i	−0.0873293	−	0.270868i
$466$	−11.1846			−0.518116
$467$		−	14.1514i		−	0.654847i	−0.944878	−	0.327423i	$-0.893820\pi$
$467$		−	14.1514i		−	0.654847i	0.944878	−	0.327423i	$-0.106180\pi$
$468$		0			0
$469$	−13.4891			−0.622870
$470$	9.84868	−	3.17527i	0.454286	−	0.146464i
$471$	−3.76631			−0.173542
$472$		−	6.63325i		−	0.305320i
$473$			46.9783i			2.16006i
$474$	5.34363			0.245441
$475$	−14.0588	+	10.1168i	−0.645061	+	0.464193i
$476$	−9.01011			−0.412978
$477$			3.75906i			0.172115i
$478$			6.13592i			0.280650i
$479$	21.5769			0.985874			0.492937	−	0.870065i	$-0.335923\pi$
$479$	21.5769			0.985874			0.492937	+	0.870065i	$0.335923\pi$
$480$	1.68614	−	0.543620i	0.0769614	−	0.0248128i
$481$		0			0
$482$		−	11.6819i		−	0.532097i
$483$		−	17.7228i		−	0.806416i
$484$	−14.4891			−0.658597
$485$	3.25544	+	10.0974i	0.147822	+	0.458497i
$486$	−15.7359			−0.713796
$487$			21.4891i			0.973765i	0.873467	+	0.486883i	$0.161866\pi$
$487$			21.4891i			0.973765i	−0.873467	+	0.486883i	$0.838134\pi$
$488$		−	4.74456i		−	0.214776i
$489$	10.5021			0.474922
$490$	3.00000	+	9.30506i	0.135526	+	0.420360i
$491$	31.3723			1.41581			0.707906	−	0.706307i	$-0.249640\pi$
$491$	31.3723			1.41581			0.707906	+	0.706307i	$0.249640\pi$
$492$			2.51087i			0.113199i
$493$			23.3639i			1.05225i
$494$		0			0
$495$	25.4891	−	8.21782i	1.14565	−	0.369364i
$496$	3.46410			0.155543
$497$			13.3591i			0.599236i
$498$			2.17448i			0.0974408i
$499$	35.9306			1.60848			0.804238	−	0.594307i	$-0.202574\pi$
$499$	35.9306			1.60848			0.804238	+	0.594307i	$0.202574\pi$
$500$	6.63325	−	9.00000i	0.296648	−	0.402492i
$501$	−4.34896			−0.194297
$502$		−	22.9783i		−	1.02557i
$503$		−	6.63325i		−	0.295762i	−0.989005	−	0.147881i	$-0.952755\pi$
$503$		−	6.63325i		−	0.295762i	0.989005	−	0.147881i	$-0.0472453\pi$
$504$	8.00000			0.356348
$505$	−6.92820	+	2.23369i	−0.308301	+	0.0993978i
$506$	33.4891			1.48877
$507$		0			0
$508$		−	3.46410i		−	0.153695i
$509$	−10.0974			−0.447557			−0.223779	−	0.974640i	$-0.571839\pi$
$509$	−10.0974			−0.447557			−0.223779	+	0.974640i	$0.571839\pi$
$510$	−1.45245	−	4.50506i	−0.0643157	−	0.199487i
$511$	33.7228			1.49181
$512$			1.00000i			0.0441942i
$513$		−	14.7446i		−	0.650988i
$514$	−9.01011			−0.397419
$515$	7.13058	+	22.1168i	0.314211	+	0.974585i
$516$	−7.37228			−0.324547
$517$		−	23.3639i		−	1.02754i
$518$			27.3723i			1.20267i
$519$	−9.72281			−0.426784
$520$		0			0
$521$	−21.6060			−0.946575			−0.473287	−	0.880908i	$-0.656933\pi$
$521$	−21.6060			−0.946575			−0.473287	+	0.880908i	$0.656933\pi$
$522$		−	20.7446i		−	0.907965i
$523$		−	10.3923i		−	0.454424i	−0.973845	−	0.227212i	$-0.927039\pi$
$523$		−	10.3923i		−	0.454424i	0.973845	−	0.227212i	$-0.0729610\pi$
$524$	7.37228			0.322060
$525$	−10.8434	+	7.80298i	−0.473243	+	0.340550i
$526$	−28.4125			−1.23885
$527$		−	9.25544i		−	0.403173i
$528$		−	4.00000i		−	0.174078i
$529$	−21.0000			−0.913043
$530$	3.37228	−	1.08724i	0.146483	−	0.0472267i
$531$	15.7359			0.682881
$532$			11.6819i			0.506476i
$533$		0			0
$534$	6.74456			0.291866
$535$	−0.202380	−	0.627719i	−0.00874964	−	0.0271386i
$536$	4.00000			0.172774
$537$		−	17.5229i		−	0.756168i
$538$		−	8.74456i		−	0.377005i
$539$	22.0742			0.950804
$540$	2.92048	+	9.05842i	0.125678	+	0.389812i
$541$	40.4820			1.74046			0.870228	−	0.492649i	$-0.163971\pi$
$541$	40.4820			1.74046			0.870228	+	0.492649i	$0.163971\pi$
$542$		−	11.4795i		−	0.493089i
$543$		−	15.4410i		−	0.662636i
$544$	2.67181			0.114553
$545$	27.1753	−	8.76144i	1.16406	−	0.375299i
$546$		0			0
$547$			11.4795i			0.490830i	0.969418	+	0.245415i	$0.0789242\pi$
$547$			11.4795i			0.490830i	−0.969418	+	0.245415i	$0.921076\pi$
$548$		−	6.00000i		−	0.256307i
$549$	11.2554			0.480370
$550$	−14.7446	−	20.4897i	−0.628710	−	0.873682i
$551$	30.2921			1.29048
$552$			5.25544i			0.223686i
$553$		−	22.7446i		−	0.967197i
$554$	−16.4356			−0.698284
$555$	−13.6861	+	4.41248i	−0.580944	+	0.187299i
$556$	−0.627719			−0.0266212
$557$		−	16.1168i		−	0.682893i	−0.939901	−	0.341446i	$-0.889083\pi$
$557$		−	16.1168i		−	0.682893i	0.939901	−	0.341446i	$-0.110917\pi$
$558$			8.21782i			0.347888i
$559$		0			0
$560$	−2.31386	−	7.17687i	−0.0977784	−	0.303278i
$561$	−10.6873			−0.451216
$562$		−	8.51278i		−	0.359090i
$563$			44.9407i			1.89403i	0.321194	+	0.947013i	$0.395916\pi$
$563$			44.9407i			1.89403i	−0.321194	+	0.947013i	$0.604084\pi$
$564$	3.66648			0.154387
$565$	11.6819	+	36.2337i	0.491462	+	1.52436i
$566$	17.3205			0.728035
$567$			12.6277i			0.530314i
$568$		−	3.96143i		−	0.166218i
$569$	10.6277			0.445537			0.222769	−	0.974871i	$-0.428491\pi$
$569$	10.6277			0.445537			0.222769	+	0.974871i	$0.428491\pi$
$570$	−5.84096	+	1.88316i	−0.244651	+	0.0788767i
$571$	−30.1168			−1.26035			−0.630175	−	0.776453i	$-0.717017\pi$
$571$	−30.1168			−1.26035			−0.630175	+	0.776453i	$0.717017\pi$
$572$		0			0
$573$		0			0
$574$	10.6873			0.446078
$575$	19.3723	+	26.9205i	0.807880	+	1.12266i
$576$	−2.37228			−0.0988451
$577$		−	24.9783i		−	1.03986i	−0.854209	−	0.519929i	$-0.825958\pi$
$577$		−	24.9783i		−	1.03986i	0.854209	−	0.519929i	$-0.174042\pi$
$578$			9.86141i			0.410180i
$579$	−11.0920			−0.460969
$580$	−18.6101	+	6.00000i	−0.772744	+	0.249136i
$581$	9.25544			0.383980
$582$			3.75906i			0.155818i
$583$		−	8.00000i		−	0.331326i
$584$	−10.0000			−0.413803
$585$		0			0
$586$	30.8614			1.27487
$587$		−	37.7228i		−	1.55699i	−0.627653	−	0.778494i	$-0.715984\pi$
$587$		−	37.7228i		−	1.55699i	0.627653	−	0.778494i	$-0.284016\pi$
$588$			3.46410i			0.142857i
$589$	−12.0000			−0.494451
$590$	−4.55134	−	14.1168i	−0.187376	−	0.581181i
$591$	−1.08724			−0.0447231
$592$		−	8.11684i		−	0.333600i
$593$			2.23369i			0.0917266i	0.998948	+	0.0458633i	$0.0146039\pi$
$593$			2.23369i			0.0917266i	−0.998948	+	0.0458633i	$0.985396\pi$
$594$	21.4891			0.881709
$595$	−19.1753	+	6.18220i	−0.786109	+	0.253446i
$596$	−3.75906			−0.153977
$597$		−	6.33830i		−	0.259409i
$598$		0			0
$599$	−25.7228			−1.05101			−0.525503	−	0.850792i	$-0.676123\pi$
$599$	−25.7228			−1.05101			−0.525503	+	0.850792i	$0.676123\pi$
$600$	3.21543	−	2.31386i	0.131270	−	0.0944629i
$601$	−26.6277			−1.08617			−0.543084	−	0.839679i	$-0.682743\pi$
$601$	−26.6277			−1.08617			−0.543084	+	0.839679i	$0.682743\pi$
$602$			31.3793i			1.27892i
$603$			9.48913i			0.386427i
$604$	−2.37686			−0.0967131
$605$	−30.8357	+	9.94158i	−1.25365	+	0.404183i
$606$	−2.57924			−0.104774
$607$		−	3.46410i		−	0.140604i	−0.997526	−	0.0703018i	$-0.977604\pi$
$607$		−	3.46410i		−	0.140604i	0.997526	−	0.0703018i	$-0.0223962\pi$
$608$		−	3.46410i		−	0.140488i
$609$	23.3639			0.946751
$610$	−3.25544	−	10.0974i	−0.131809	−	0.408830i
$611$		0			0
$612$			6.33830i			0.256210i
$613$			3.48913i			0.140924i	0.997514	+	0.0704622i	$0.0224474\pi$
$613$			3.48913i			0.140924i	−0.997514	+	0.0704622i	$0.977553\pi$
$614$	−16.2337			−0.655138
$615$	1.72281	+	5.34363i	0.0694705	+	0.215476i
$616$	−17.0256			−0.685979
$617$			3.25544i			0.131059i	0.997851	+	0.0655295i	$0.0208736\pi$
$617$			3.25544i			0.131059i	−0.997851	+	0.0655295i	$0.979126\pi$
$618$			8.23369i			0.331208i
$619$	29.0024			1.16571			0.582853	−	0.812578i	$-0.301936\pi$
$619$	29.0024			1.16571			0.582853	+	0.812578i	$0.301936\pi$
$620$	7.37228	−	2.37686i	0.296078	−	0.0954570i
$621$	−28.2337			−1.13298
$622$		−	14.7446i		−	0.591203i
$623$		−	28.7075i		−	1.15014i
$624$		0			0
$625$	7.94158	−	23.7051i	0.317663	−	0.948204i
$626$	17.5229			0.700355
$627$			13.8564i			0.553372i
$628$		−	4.75372i		−	0.189694i
$629$	−21.6867			−0.864705
$630$	17.0256	−	5.48913i	0.678314	−	0.218692i
$631$	49.1046			1.95482			0.977411	−	0.211348i	$-0.0677853\pi$
$631$	49.1046			1.95482			0.977411	+	0.211348i	$0.0677853\pi$
$632$			6.74456i			0.268284i
$633$		−	11.1846i		−	0.444548i
$634$	28.9783			1.15087
$635$	−2.37686	−	7.37228i	−0.0943229	−	0.292560i
$636$	1.25544			0.0497813
$637$		0			0
$638$			44.1485i			1.74785i
$639$	9.39764			0.371765
$640$	0.686141	+	2.12819i	0.0271221	+	0.0841243i
$641$	−28.9783			−1.14457			−0.572286	−	0.820054i	$-0.693943\pi$
$641$	−28.9783			−1.14457			−0.572286	+	0.820054i	$0.693943\pi$
$642$		−	0.233688i		−	0.00922293i
$643$		−	14.5109i		−	0.572253i	−0.958192	−	0.286127i	$-0.907632\pi$
$643$		−	14.5109i		−	0.572253i	0.958192	−	0.286127i	$-0.0923678\pi$
$644$	22.3692			0.881469
$645$	−15.6896	+	5.05842i	−0.617779	+	0.199175i
$646$	−9.25544			−0.364150
$647$			34.3461i			1.35028i	0.737688	+	0.675142i	$0.235917\pi$
$647$			34.3461i			1.35028i	−0.737688	+	0.675142i	$0.764083\pi$
$648$		−	3.74456i		−	0.147100i
$649$	−33.4891			−1.31456
$650$		0			0
$651$	−9.25544			−0.362749
$652$			13.2554i			0.519123i
$653$			3.75906i			0.147103i	0.997291	+	0.0735516i	$0.0234334\pi$
$653$			3.75906i			0.147103i	−0.997291	+	0.0735516i	$0.976567\pi$
$654$	10.1168			0.395600
$655$	15.6896	−	5.05842i	0.613045	−	0.197649i
$656$	−3.16915			−0.123734
$657$		−	23.7228i		−	0.925515i
$658$		−	15.6060i		−	0.608384i
$659$	28.4674			1.10893			0.554466	−	0.832207i	$-0.312923\pi$
$659$	28.4674			1.10893			0.554466	+	0.832207i	$0.312923\pi$
$660$	−2.74456	−	8.51278i	−0.106832	−	0.331359i
$661$	30.2921			1.17822			0.589112	−	0.808051i	$-0.299478\pi$
$661$	30.2921			1.17822			0.589112	+	0.808051i	$0.299478\pi$
$662$			10.3923i			0.403908i
$663$		0			0
$664$	−2.74456			−0.106510
$665$	8.01544	+	24.8614i	0.310826	+	0.964084i
$666$	19.2554			0.746133
$667$		−	58.0049i		−	2.24596i
$668$		−	5.48913i		−	0.212381i
$669$	−1.67715			−0.0648423
$670$	8.51278	−	2.74456i	0.328877	−	0.106032i
$671$	−23.9538			−0.924725
$672$		−	2.67181i		−	0.103067i
$673$		−	19.6974i		−	0.759278i	−0.925135	−	0.379639i	$-0.876048\pi$
$673$		−	19.6974i		−	0.759278i	0.925135	−	0.379639i	$-0.123952\pi$
$674$	−31.3793			−1.20869
$675$	12.4307	+	17.2742i	0.478458	+	0.664885i
$676$		0			0
$677$			5.93354i			0.228044i	0.993478	+	0.114022i	$0.0363735\pi$
$677$			5.93354i			0.228044i	−0.993478	+	0.114022i	$0.963627\pi$
$678$			13.4891i			0.518047i
$679$	16.0000			0.614024
$680$	5.68614	−	1.83324i	0.218054	−	0.0703016i
$681$	−13.8564			−0.530979
$682$		−	17.4891i		−	0.669693i
$683$		−	2.74456i		−	0.105018i	−0.998620	−	0.0525089i	$-0.983278\pi$
$683$		−	2.74456i		−	0.105018i	0.998620	−	0.0525089i	$-0.0167218\pi$
$684$	8.21782			0.314216
$685$	−4.11684	−	12.7692i	−0.157297	−	0.487885i
$686$	−8.86141			−0.338330
$687$			11.8397i			0.451711i
$688$		−	9.30506i		−	0.354752i
$689$		0			0
$690$	3.60597	+	11.1846i	0.137277	+	0.425790i
$691$	−19.4950			−0.741624			−0.370812	−	0.928708i	$-0.620921\pi$
$691$	−19.4950			−0.741624			−0.370812	+	0.928708i	$0.620921\pi$
$692$		−	12.2718i		−	0.466505i
$693$		−	40.3894i		−	1.53427i
$694$	−15.6434			−0.593814
$695$	−1.33591	+	0.430703i	−0.0506739	+	0.0163375i
$696$	−6.92820			−0.262613
$697$			8.46738i			0.320725i
$698$		−	22.2766i		−	0.843182i
$699$	−8.86141			−0.335169
$700$	−9.84868	−	13.6861i	−0.372245	−	0.517287i
$701$	28.9783			1.09449			0.547247	−	0.836971i	$-0.315676\pi$
$701$	28.9783			1.09449			0.547247	+	0.836971i	$0.315676\pi$
$702$		0			0
$703$			28.1176i			1.06047i
$704$	5.04868			0.190279
$705$	7.80298	−	2.51572i	0.293877	−	0.0947476i
$706$	11.4891			0.432399
$707$			10.9783i			0.412880i
$708$		−	5.25544i		−	0.197511i
$709$	−20.7846			−0.780582			−0.390291	−	0.920691i	$-0.627626\pi$
$709$	−20.7846			−0.780582			−0.390291	+	0.920691i	$0.627626\pi$
$710$	−2.71810	−	8.43070i	−0.102009	−	0.316399i
$711$	−16.0000			−0.600047
$712$			8.51278i			0.319030i
$713$			22.9783i			0.860542i
$714$	−7.13859			−0.267155
$715$		0			0
$716$	22.1168			0.826545
$717$			4.86141i			0.181553i
$718$		−	23.6588i		−	0.882939i
$719$	48.0000			1.79010			0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000			1.79010			0.895049	+	0.445968i	$0.147140\pi$
$720$	−5.04868	+	1.62772i	−0.188153	+	0.0606615i
$721$	35.0458			1.30517
$722$		−	7.00000i		−	0.260513i
$723$		−	9.25544i		−	0.344213i
$724$	19.4891			0.724308
$725$	−35.4891	+	25.5383i	−1.31803	+	0.948470i
$726$	−11.4795			−0.426046
$727$		−	22.0742i		−	0.818688i	−0.912380	−	0.409344i	$-0.865758\pi$
$727$		−	22.0742i		−	0.818688i	0.912380	−	0.409344i	$-0.134242\pi$
$728$		0			0
$729$	−1.23369			−0.0456921
$730$	−21.2819	+	6.86141i	−0.787680	+	0.253952i
$731$	−24.8614			−0.919532
$732$		−	3.75906i		−	0.138939i
$733$		−	47.0951i		−	1.73950i	−0.493495	−	0.869749i	$-0.664281\pi$
$733$		−	47.0951i		−	1.73950i	0.493495	−	0.869749i	$-0.335719\pi$
$734$	15.1460			0.559050
$735$	2.37686	+	7.37228i	0.0876718	+	0.271931i
$736$	−6.63325			−0.244505
$737$		−	20.1947i		−	0.743881i
$738$		−	7.51811i		−	0.276745i
$739$	−31.5817			−1.16175			−0.580875	−	0.813993i	$-0.697290\pi$
$739$	−31.5817			−1.16175			−0.580875	+	0.813993i	$0.697290\pi$
$740$	−5.56930	−	17.2742i	−0.204731	−	0.635013i
$741$		0			0
$742$		−	5.34363i		−	0.196171i
$743$			10.1168i			0.371151i	0.982630	+	0.185576i	$0.0594149\pi$
$743$			10.1168i			0.371151i	−0.982630	+	0.185576i	$0.940585\pi$
$744$	2.74456			0.100621
$745$	−8.00000	+	2.57924i	−0.293097	+	0.0944961i
$746$	−30.2921			−1.10907
$747$		−	6.51087i		−	0.238220i
$748$		−	13.4891i		−	0.493211i
$749$	−0.994667			−0.0363443
$750$	5.25544	−	7.13058i	0.191901	−	0.260372i
$751$	−2.51087			−0.0916231			−0.0458116	−	0.998950i	$-0.514587\pi$
$751$	−2.51087			−0.0916231			−0.0458116	+	0.998950i	$0.514587\pi$
$752$			4.62772i			0.168756i
$753$		−	18.2054i		−	0.663441i
$754$		0			0
$755$	−5.05842	+	1.63086i	−0.184095	+	0.0593531i
$756$	14.3537			0.522040
$757$			14.2612i			0.518331i	0.965833	+	0.259165i	$0.0834475\pi$
$757$			14.2612i			0.518331i	−0.965833	+	0.259165i	$0.916553\pi$
$758$		−	17.3205i		−	0.629109i
$759$	26.5330			0.963087
$760$	−2.37686	−	7.37228i	−0.0862178	−	0.267421i
$761$	−8.51278			−0.308588			−0.154294	−	0.988025i	$-0.549310\pi$
$761$	−8.51278			−0.308588			−0.154294	+	0.988025i	$0.549310\pi$
$762$		−	2.74456i		−	0.0994250i
$763$		−	43.0612i		−	1.55892i
$764$		0			0
$765$	4.34896	+	13.4891i	0.157237	+	0.487700i
$766$	34.1168			1.23269
$767$		0			0
$768$			0.792287i			0.0285892i
$769$	23.3639			0.842522			0.421261	−	0.906939i	$-0.361588\pi$
$769$	23.3639			0.842522			0.421261	+	0.906939i	$0.361588\pi$
$770$	−36.2337	+	11.6819i	−1.30577	+	0.420987i
$771$	−7.13859			−0.257090
$772$		−	14.0000i		−	0.503871i
$773$		−	9.60597i		−	0.345503i	−0.984965	−	0.172751i	$-0.944734\pi$
$773$		−	9.60597i		−	0.345503i	0.984965	−	0.172751i	$-0.0552657\pi$
$774$	22.0742			0.793442
$775$	14.0588	−	10.1168i	0.505007	−	0.363408i
$776$	−4.74456			−0.170320
$777$			21.6867i			0.778006i
$778$		−	6.00000i		−	0.215110i
$779$	10.9783			0.393337
$780$		0			0
$781$	−20.0000			−0.715656
$782$			17.7228i			0.633767i
$783$		−	37.2203i		−	1.33014i
$784$	−4.37228			−0.156153
$785$	−3.26172	−	10.1168i	−0.116416	−	0.361086i
$786$	5.84096			0.208340
$787$			44.0000i			1.56843i	0.620489	+	0.784215i	$0.286934\pi$
$787$			44.0000i			1.56843i	−0.620489	+	0.784215i	$0.713066\pi$
$788$		−	1.37228i		−	0.0488855i
$789$	−22.5109			−0.801408
$790$	4.62772	+	14.3537i	0.164647	+	0.510683i
$791$	57.4150			2.04144
$792$			11.9769i			0.425580i
$793$		0			0
$794$	−31.4891			−1.11751
$795$	2.67181	−	0.861407i	0.0947595	−	0.0305509i
$796$	8.00000			0.283552
$797$			7.92287i			0.280642i	0.990106	+	0.140321i	$0.0448135\pi$
$797$			7.92287i			0.280642i	−0.990106	+	0.140321i	$0.955186\pi$
$798$			9.25544i			0.327639i
$799$	12.3644			0.437421
$800$	2.92048	+	4.05842i	0.103255	+	0.143487i
$801$	−20.1947			−0.713545
$802$			0.994667i			0.0351229i
$803$			50.4868i			1.78164i
$804$	3.16915			0.111767
$805$	47.6060	−	15.3484i	1.67789	−	0.540960i
$806$		0			0
$807$		−	6.92820i		−	0.243884i
$808$		−	3.25544i		−	0.114526i
$809$	−12.3505			−0.434222			−0.217111	−	0.976147i	$-0.569663\pi$
$809$	−12.3505			−0.434222			−0.217111	+	0.976147i	$0.569663\pi$
$810$	−2.56930	−	7.96916i	−0.0902759	−	0.280008i
$811$	17.7253			0.622418			0.311209	−	0.950341i	$-0.399266\pi$
$811$	17.7253			0.622418			0.311209	+	0.950341i	$0.399266\pi$
$812$			29.4891i			1.03487i
$813$		−	9.09509i		−	0.318979i
$814$	−40.9793			−1.43632
$815$	9.09509	+	28.2101i	0.318587	+	0.988158i
$816$	2.11684			0.0741044
$817$			32.2337i			1.12771i
$818$		−	25.5383i		−	0.892927i
$819$		0			0
$820$	−6.74456	+	2.17448i	−0.235530	+	0.0759362i
$821$	30.7894			1.07456			0.537279	−	0.843405i	$-0.319452\pi$
$821$	30.7894			1.07456			0.537279	+	0.843405i	$0.319452\pi$
$822$		−	4.75372i		−	0.165805i
$823$		−	14.7413i		−	0.513848i	−0.966432	−	0.256924i	$-0.917291\pi$
$823$		−	14.7413i		−	0.513848i	0.966432	−	0.256924i	$-0.0827091\pi$
$824$	−10.3923			−0.362033
$825$	−11.6819	−	16.2337i	−0.406712	−	0.565184i
$826$	−22.3692			−0.778323
$827$			26.7446i			0.930000i	0.885311	+	0.465000i	$0.153946\pi$
$827$			26.7446i			0.930000i	−0.885311	+	0.465000i	$0.846054\pi$
$828$		−	15.7359i		−	0.546862i
$829$	13.7663			0.478124			0.239062	−	0.971004i	$-0.423160\pi$
$829$	13.7663			0.478124			0.239062	+	0.971004i	$0.423160\pi$
$830$	−5.84096	+	1.88316i	−0.202743	+	0.0653653i
$831$	−13.0217			−0.451719
$832$		0			0
$833$			11.6819i			0.404755i
$834$	−0.497333			−0.0172212
$835$	−3.76631	−	11.6819i	−0.130339	−	0.404270i
$836$	−17.4891			−0.604874
$837$			14.7446i			0.509647i
$838$			1.88316i			0.0650525i
$839$	−0.294954			−0.0101829			−0.00509147	−	0.999987i	$-0.501621\pi$
$839$	−0.294954			−0.0101829			−0.00509147	+	0.999987i	$0.501621\pi$
$840$	−1.83324	−	5.68614i	−0.0632528	−	0.196190i
$841$	47.4674			1.63681
$842$			1.08724i			0.0374688i
$843$		−	6.74456i		−	0.232295i
$844$	14.1168			0.485922
$845$		0			0
$846$	−10.9783			−0.377440
$847$			48.8614i			1.67890i
$848$			1.58457i			0.0544145i
$849$	13.7228			0.470966
$850$	10.8434	−	7.80298i	0.371924	−	0.267640i
$851$	53.8411			1.84565
$852$		−	3.13859i		−	0.107526i
$853$			12.1168i			0.414873i	0.978249	+	0.207436i	$0.0665120\pi$
$853$			12.1168i			0.414873i	−0.978249	+	0.207436i	$0.933488\pi$
$854$	−16.0000			−0.547509
$855$	17.4891	−	5.63858i	0.598115	−	0.192835i
$856$	0.294954			0.0100813
$857$		−	43.5586i		−	1.48793i	−0.668218	−	0.743966i	$-0.732942\pi$
$857$		−	43.5586i		−	1.48793i	0.668218	−	0.743966i	$-0.267058\pi$
$858$		0			0
$859$	36.4674			1.24425			0.622125	−	0.782918i	$-0.286269\pi$
$859$	36.4674			1.24425			0.622125	+	0.782918i	$0.286269\pi$
$860$	−6.38458	−	19.8030i	−0.217712	−	0.675276i
$861$	8.46738			0.288567
$862$		−	9.89497i		−	0.337024i
$863$			24.8614i			0.846292i	0.906061	+	0.423146i	$0.139074\pi$
$863$			24.8614i			0.846292i	−0.906061	+	0.423146i	$0.860926\pi$
$864$	−4.25639			−0.144805
$865$	−8.42020	−	26.1168i	−0.286295	−	0.887999i
$866$	15.3484			0.521560
$867$			7.81306i			0.265346i
$868$		−	11.6819i		−	0.396510i
$869$	34.0511			1.15510
$870$	−14.7446	+	4.75372i	−0.499887	+	0.161166i
$871$		0			0
$872$			12.7692i			0.432419i
$873$		−	11.2554i		−	0.380939i
$874$	22.9783			0.777251
$875$	−30.3505	−	22.3692i	−1.02604	−	0.756216i
$876$	−7.92287			−0.267689
$877$			4.35053i			0.146907i	0.997299	+	0.0734535i	$0.0234021\pi$
$877$			4.35053i			0.146907i	−0.997299	+	0.0734535i	$0.976598\pi$
$878$			12.2337i			0.412867i
$879$	24.4511			0.824715
$880$	10.7446	−	3.46410i	0.362199	−	0.116775i
$881$	14.3940			0.484947			0.242474	−	0.970158i	$-0.422041\pi$
$881$	14.3940			0.484947			0.242474	+	0.970158i	$0.422041\pi$
$882$		−	10.3723i		−	0.349253i
$883$			8.90030i			0.299519i	0.988722	+	0.149760i	$0.0478500\pi$
$883$			8.90030i			0.299519i	−0.988722	+	0.149760i	$0.952150\pi$
$884$		0			0
$885$	−3.60597	−	11.1846i	−0.121213	−	0.375966i
$886$	7.72049			0.259375
$887$			0.699713i			0.0234941i	0.999931	+	0.0117470i	$0.00373928\pi$
$887$			0.699713i			0.0234941i	−0.999931	+	0.0117470i	$0.996261\pi$
$888$		−	6.43087i		−	0.215806i
$889$	−11.6819			−0.391799
$890$	5.84096	+	18.1168i	0.195790	+	0.607278i
$891$	−18.9051			−0.633344
$892$		−	2.11684i		−	0.0708772i
$893$		−	16.0309i		−	0.536453i
$894$	−2.97825			−0.0996076
$895$	47.0689	−	15.1753i	1.57334	−	0.507253i
$896$	3.37228			0.112660
$897$		0			0
$898$		−	34.0511i		−	1.13630i
$899$	−30.2921			−1.01030
$900$	−9.62772	+	6.92820i	−0.320924	+	0.230940i
$901$	4.23369			0.141045
$902$			16.0000i			0.532742i
$903$			24.8614i			0.827336i
$904$	−17.0256			−0.566262
$905$	41.4766	−	13.3723i	1.37873	−	0.444510i
$906$	−1.88316			−0.0625637
$907$		−	9.30506i		−	0.308970i	−0.987995	−	0.154485i	$-0.950628\pi$
$907$		−	9.30506i		−	0.308970i	0.987995	−	0.154485i	$-0.0493718\pi$
$908$		−	17.4891i		−	0.580397i
$909$	7.72281			0.256150
$910$		0			0
$911$	−10.9783			−0.363726			−0.181863	−	0.983324i	$-0.558213\pi$
$911$	−10.9783			−0.363726			−0.181863	+	0.983324i	$0.558213\pi$
$912$		−	2.74456i		−	0.0908816i
$913$			13.8564i			0.458580i
$914$	−20.9783			−0.693899
$915$	−2.57924	−	8.00000i	−0.0852671	−	0.264472i
$916$	−14.9436			−0.493752
$917$		−	24.8614i		−	0.820996i
$918$			11.3723i			0.375341i
$919$	−2.97825			−0.0982434			−0.0491217	−	0.998793i	$-0.515642\pi$
$919$	−2.97825			−0.0982434			−0.0491217	+	0.998793i	$0.515642\pi$
$920$	−14.1168	+	4.55134i	−0.465419	+	0.150053i
$921$	−12.8617			−0.423809
$922$		−	41.4766i		−	1.36596i
$923$		0			0
$924$	−13.4891			−0.443760
$925$	−23.7051	−	32.9416i	−0.779419	−	1.08311i
$926$	16.0000			0.525793
$927$		−	24.6535i		−	0.809726i
$928$		−	8.74456i		−	0.287054i
$929$	−21.3745			−0.701275			−0.350638	−	0.936511i	$-0.614035\pi$
$929$	−21.3745			−0.701275			−0.350638	+	0.936511i	$0.614035\pi$
$930$	5.84096	−	1.88316i	0.191533	−	0.0617511i
$931$	15.1460			0.496391
$932$		−	11.1846i		−	0.366363i
$933$		−	11.6819i		−	0.382449i
$934$	14.1514			0.463047
$935$	−9.25544	−	28.7075i	−0.302685	−	0.938835i
$936$		0			0
$937$		−	9.50744i		−	0.310595i	−0.987868	−	0.155297i	$-0.950366\pi$
$937$		−	9.50744i		−	0.310595i	0.987868	−	0.155297i	$-0.0496336\pi$
$938$		−	13.4891i		−	0.440436i
$939$	13.8832			0.453060
$940$	3.17527	+	9.84868i	0.103566	+	0.321229i
$941$	37.3128			1.21636			0.608182	−	0.793798i	$-0.291899\pi$
$941$	37.3128			1.21636			0.608182	+	0.793798i	$0.291899\pi$
$942$		−	3.76631i		−	0.122713i
$943$		−	21.0217i		−	0.684562i
$944$	6.63325			0.215894
$945$	30.5475	−	9.84868i	0.993712	−	0.320378i
$946$	−46.9783			−1.52739
$947$		−	6.51087i		−	0.211575i	−0.994389	−	0.105787i	$-0.966264\pi$
$947$		−	6.51087i		−	0.211575i	0.994389	−	0.105787i	$-0.0337363\pi$
$948$			5.34363i			0.173553i
$949$		0			0
$950$	−10.1168	−	14.0588i	−0.328234	−	0.456127i
$951$	22.9591			0.744500
$952$		−	9.01011i		−	0.292019i
$953$		−	0.497333i		−	0.0161102i	−0.999968	−	0.00805510i	$-0.997436\pi$
$953$		−	0.497333i		−	0.0161102i	0.999968	−	0.00805510i	$-0.00256405\pi$
$954$	−3.75906			−0.121704
$955$		0			0
$956$	−6.13592			−0.198450
$957$			34.9783i			1.13069i
$958$			21.5769i			0.697118i
$959$	−20.2337			−0.653380
$960$	0.543620	+	1.68614i	0.0175453	+	0.0544200i
$961$	−19.0000			−0.612903
$962$		0			0
$963$			0.699713i			0.0225479i
$964$	11.6819			0.376249
$965$	−9.60597	−	29.7947i	−0.309227	−	0.959126i
$966$	17.7228			0.570222
$967$			46.3505i			1.49053i	0.666767	+	0.745266i	$0.267678\pi$
$967$			46.3505i			1.49053i	−0.666767	+	0.745266i	$0.732322\pi$
$968$		−	14.4891i		−	0.465698i
$969$	−7.33296			−0.235569
$970$	−10.0974	+	3.25544i	−0.324206	+	0.104526i
$971$	27.6060			0.885918			0.442959	−	0.896542i	$-0.353929\pi$
$971$	27.6060			0.885918			0.442959	+	0.896542i	$0.353929\pi$
$972$		−	15.7359i		−	0.504730i
$973$			2.11684i			0.0678629i
$974$	−21.4891			−0.688556
$975$		0			0
$976$	4.74456			0.151870
$977$		−	31.7228i		−	1.01490i	−0.861680	−	0.507451i	$-0.830588\pi$
$977$		−	31.7228i		−	1.01490i	0.861680	−	0.507451i	$-0.169412\pi$
$978$			10.5021i			0.335820i
$979$	42.9783			1.37359
$980$	−9.30506	+	3.00000i	−0.297239	+	0.0958315i
$981$	−30.2921			−0.967151
$982$			31.3723i			1.00113i
$983$		−	21.0951i		−	0.672829i	−0.941714	−	0.336415i	$-0.890786\pi$
$983$		−	21.0951i		−	0.672829i	0.941714	−	0.336415i	$-0.109214\pi$
$984$	−2.51087			−0.0800438
$985$	−0.941578	−	2.92048i	−0.0300012	−	0.0930543i
$986$	−23.3639			−0.744057
$987$		−	12.3644i		−	0.393563i
$988$		0			0
$989$	61.7228			1.96267
$990$	8.21782	+	25.4891i	0.261180	+	0.810098i
$991$	−36.2337			−1.15100			−0.575501	−	0.817801i	$-0.695193\pi$
$991$	−36.2337			−1.15100			−0.575501	+	0.817801i	$0.695193\pi$
$992$			3.46410i			0.109985i
$993$			8.23369i			0.261288i
$994$	−13.3591			−0.423724
$995$	17.0256	−	5.48913i	0.539746	−	0.174017i
$996$	−2.17448			−0.0689011
$997$		−	44.1485i		−	1.39820i	−0.715026	−	0.699098i	$-0.753585\pi$
$997$		−	44.1485i		−	1.39820i	0.715026	−	0.699098i	$-0.246415\pi$
$998$			35.9306i			1.13736i
$999$	34.5484			1.09306

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.d.339.7		8
5.2	odd	4		8450.2.a.cj.1.3		4
5.3	odd	4		8450.2.a.cn.1.2		4
5.4	even	2	inner	1690.2.b.d.339.2		8
13.5	odd	4		130.2.c.b.129.3	yes	4
13.8	odd	4		130.2.c.a.129.3	yes	4
13.12	even	2	inner	1690.2.b.d.339.3		8
39.5	even	4		1170.2.f.a.649.1		4
39.8	even	4		1170.2.f.b.649.4		4
52.31	even	4		1040.2.f.c.129.2		4
52.47	even	4		1040.2.f.d.129.2		4
65.8	even	4		650.2.d.e.51.6		8
65.12	odd	4		8450.2.a.cn.1.3		4
65.18	even	4		650.2.d.e.51.2		8
65.34	odd	4		130.2.c.b.129.2	yes	4
65.38	odd	4		8450.2.a.cj.1.2		4
65.44	odd	4		130.2.c.a.129.2	✓	4
65.47	even	4		650.2.d.e.51.3		8
65.57	even	4		650.2.d.e.51.7		8
65.64	even	2	inner	1690.2.b.d.339.6		8
195.44	even	4		1170.2.f.b.649.3		4
195.164	even	4		1170.2.f.a.649.2		4
260.99	even	4		1040.2.f.c.129.3		4
260.239	even	4		1040.2.f.d.129.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.c.a.129.2	✓	4	65.44	odd	4
130.2.c.a.129.3	yes	4	13.8	odd	4
130.2.c.b.129.2	yes	4	65.34	odd	4
130.2.c.b.129.3	yes	4	13.5	odd	4
650.2.d.e.51.2		8	65.18	even	4
650.2.d.e.51.3		8	65.47	even	4
650.2.d.e.51.6		8	65.8	even	4
650.2.d.e.51.7		8	65.57	even	4
1040.2.f.c.129.2		4	52.31	even	4
1040.2.f.c.129.3		4	260.99	even	4
1040.2.f.d.129.2		4	52.47	even	4
1040.2.f.d.129.3		4	260.239	even	4
1170.2.f.a.649.1		4	39.5	even	4
1170.2.f.a.649.2		4	195.164	even	4
1170.2.f.b.649.3		4	195.44	even	4
1170.2.f.b.649.4		4	39.8	even	4
1690.2.b.d.339.2		8	5.4	even	2	inner
1690.2.b.d.339.3		8	13.12	even	2	inner
1690.2.b.d.339.6		8	65.64	even	2	inner
1690.2.b.d.339.7		8	1.1	even	1	trivial
8450.2.a.cj.1.2		4	65.38	odd	4
8450.2.a.cj.1.3		4	5.2	odd	4
8450.2.a.cn.1.2		4	5.3	odd	4
8450.2.a.cn.1.3		4	65.12	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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +0.792287i q^{3} -1.00000 q^{4} +(-2.12819 + 0.686141i) q^{5} -0.792287 q^{6} +3.37228i q^{7} -1.00000i q^{8} +2.37228 q^{9} +(-0.686141 - 2.12819i) q^{10} -5.04868 q^{11} -0.792287i q^{12} -3.37228 q^{14} +(-0.543620 - 1.68614i) q^{15} +1.00000 q^{16} -2.67181i q^{17} +2.37228i q^{18} -3.46410 q^{19} +(2.12819 - 0.686141i) q^{20} -2.67181 q^{21} -5.04868i q^{22} +6.63325i q^{23} +0.792287 q^{24} +(4.05842 - 2.92048i) q^{25} +4.25639i q^{27} -3.37228i q^{28} -8.74456 q^{29} +(1.68614 - 0.543620i) q^{30} +3.46410 q^{31} +1.00000i q^{32} -4.00000i q^{33} +2.67181 q^{34} +(-2.31386 - 7.17687i) q^{35} -2.37228 q^{36} -8.11684i q^{37} -3.46410i q^{38} +(0.686141 + 2.12819i) q^{40} -3.16915 q^{41} -2.67181i q^{42} -9.30506i q^{43} +5.04868 q^{44} +(-5.04868 + 1.62772i) q^{45} -6.63325 q^{46} +4.62772i q^{47} +0.792287i q^{48} -4.37228 q^{49} +(2.92048 + 4.05842i) q^{50} +2.11684 q^{51} +1.58457i q^{53} -4.25639 q^{54} +(10.7446 - 3.46410i) q^{55} +3.37228 q^{56} -2.74456i q^{57} -8.74456i q^{58} +6.63325 q^{59} +(0.543620 + 1.68614i) q^{60} +4.74456 q^{61} +3.46410i q^{62} +8.00000i q^{63} -1.00000 q^{64} +4.00000 q^{66} +4.00000i q^{67} +2.67181i q^{68} -5.25544 q^{69} +(7.17687 - 2.31386i) q^{70} +3.96143 q^{71} -2.37228i q^{72} -10.0000i q^{73} +8.11684 q^{74} +(2.31386 + 3.21543i) q^{75} +3.46410 q^{76} -17.0256i q^{77} -6.74456 q^{79} +(-2.12819 + 0.686141i) q^{80} +3.74456 q^{81} -3.16915i q^{82} -2.74456i q^{83} +2.67181 q^{84} +(1.83324 + 5.68614i) q^{85} +9.30506 q^{86} -6.92820i q^{87} +5.04868i q^{88} -8.51278 q^{89} +(-1.62772 - 5.04868i) q^{90} -6.63325i q^{92} +2.74456i q^{93} -4.62772 q^{94} +(7.37228 - 2.37686i) q^{95} -0.792287 q^{96} -4.74456i q^{97} -4.37228i q^{98} -11.9769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 4 q^{9} + 6 q^{10} - 4 q^{14} + 8 q^{16} - 2 q^{25} - 24 q^{29} + 2 q^{30} - 30 q^{35} + 4 q^{36} - 6 q^{40} - 12 q^{49} - 52 q^{51} + 40 q^{55} + 4 q^{56} - 8 q^{61} - 8 q^{64} + 32 q^{66}+ \cdots + 36 q^{95}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^9 + 6 * q^10 - 4 * q^14 + 8 * q^16 - 2 * q^25 - 24 * q^29 + 2 * q^30 - 30 * q^35 + 4 * q^36 - 6 * q^40 - 12 * q^49 - 52 * q^51 + 40 * q^55 + 4 * q^56 - 8 * q^61 - 8 * q^64 + 32 * q^66 - 88 * q^69 - 4 * q^74 + 30 * q^75 - 8 * q^79 - 16 * q^81 - 36 * q^90 - 60 * q^94 + 36 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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