LMFDB - Embedded newform 1690.2.b.a.339.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(339,1690)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.3534400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 3x^{4} + 16x^{3} + x^{2} - 12x + 40 $ x^6 - 2x^5 - 3x^4 + 16x^3 + x^2 - 12x + 40
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.3
Root			$2.19082 + 1.44755i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.a.339.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +2.89511i q^{3} -1.00000 q^{4} +(-1.44755 - 1.70429i) q^{5} +2.89511 q^{6} +4.38164i q^{7} +1.00000i q^{8} -5.38164 q^{9} +(-1.70429 + 1.44755i) q^{10} -2.00000 q^{11} -2.89511i q^{12} +4.38164 q^{14} +(4.93409 - 4.19082i) q^{15} +1.00000 q^{16} +5.86818i q^{17} +5.38164i q^{18} -0.973070 q^{19} +(1.44755 + 1.70429i) q^{20} -12.6853 q^{21} +2.00000i q^{22} -7.79021i q^{23} -2.89511 q^{24} +(-0.809179 + 4.93409i) q^{25} -6.89511i q^{27} -4.38164i q^{28} -0.973070 q^{29} +(-4.19082 - 4.93409i) q^{30} +1.79021 q^{31} -1.00000i q^{32} -5.79021i q^{33} +5.86818 q^{34} +(7.46757 - 6.34266i) q^{35} +5.38164 q^{36} +0.591429i q^{37} +0.973070i q^{38} +(1.70429 - 1.44755i) q^{40} -4.81714 q^{41} +12.6853i q^{42} -4.68532i q^{43} +2.00000 q^{44} +(7.79021 + 9.17185i) q^{45} -7.79021 q^{46} -0.381642i q^{47} +2.89511i q^{48} -12.1988 q^{49} +(4.93409 + 0.809179i) q^{50} -16.9890 q^{51} -7.79021i q^{53} -6.89511 q^{54} +(2.89511 + 3.40857i) q^{55} -4.38164 q^{56} -2.81714i q^{57} +0.973070i q^{58} -0.973070 q^{59} +(-4.93409 + 4.19082i) q^{60} -0.817143 q^{61} -1.79021i q^{62} -23.5804i q^{63} -1.00000 q^{64} -5.79021 q^{66} -1.79021i q^{67} -5.86818i q^{68} +22.5535 q^{69} +(-6.34266 - 7.46757i) q^{70} +3.92204 q^{71} -5.38164i q^{72} -6.00000i q^{73} +0.591429 q^{74} +(-14.2847 - 2.34266i) q^{75} +0.973070 q^{76} -8.76328i q^{77} -10.9731 q^{79} +(-1.44755 - 1.70429i) q^{80} +3.81714 q^{81} +4.81714i q^{82} -6.97307i q^{83} +12.6853 q^{84} +(10.0010 - 8.49450i) q^{85} -4.68532 q^{86} -2.81714i q^{87} -2.00000i q^{88} +0.973070 q^{89} +(9.17185 - 7.79021i) q^{90} +7.79021i q^{92} +5.18286i q^{93} -0.381642 q^{94} +(1.40857 + 1.65839i) q^{95} +2.89511 q^{96} +18.6074i q^{97} +12.1988i q^{98} +10.7633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 10 q^{9} - 4 q^{10} - 12 q^{11} + 4 q^{14} + 16 q^{15} + 6 q^{16} + 4 q^{19} - 24 q^{21} - 16 q^{25} + 4 q^{29} - 14 q^{30} - 24 q^{31} + 8 q^{34} - 6 q^{35} + 10 q^{36} + 4 q^{40} - 4 q^{41}+ \cdots + 20 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 10 * q^9 - 4 * q^10 - 12 * q^11 + 4 * q^14 + 16 * q^15 + 6 * q^16 + 4 * q^19 - 24 * q^21 - 16 * q^25 + 4 * q^29 - 14 * q^30 - 24 * q^31 + 8 * q^34 - 6 * q^35 + 10 * q^36 + 4 * q^40 - 4 * q^41 + 12 * q^44 + 12 * q^45 - 12 * q^46 - 26 * q^49 + 16 * q^50 - 20 * q^51 - 24 * q^54 - 4 * q^56 + 4 * q^59 - 16 * q^60 + 20 * q^61 - 6 * q^64 + 56 * q^69 - 12 * q^70 + 16 * q^71 + 16 * q^74 - 10 * q^75 - 4 * q^76 - 56 * q^79 - 2 * q^81 + 24 * q^84 - 28 * q^85 + 24 * q^86 - 4 * q^89 - 2 * q^90 + 20 * q^94 - 4 * q^95 + 20 * 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
$3$			2.89511i			1.67149i	0.549117	+	0.835745i	$0.314964\pi$
$3$			2.89511i			1.67149i	−0.549117	+	0.835745i	$0.685036\pi$
$4$	−1.00000			−0.500000
$5$	−1.44755	−	1.70429i	−0.647365	−	0.762180i
$5$	−1.44755	−	1.70429i	−0.647365	−	0.762180i
$6$	2.89511			1.18192
$7$			4.38164i			1.65610i	0.560651	+	0.828052i	$0.310551\pi$
$7$			4.38164i			1.65610i	−0.560651	+	0.828052i	$0.689449\pi$
$8$			1.00000i			0.353553i
$9$	−5.38164			−1.79388
$10$	−1.70429	+	1.44755i	−0.538942	+	0.457757i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		−	2.89511i		−	0.835745i
$13$		0			0
$13$		0			0
$14$	4.38164			1.17104
$15$	4.93409	−	4.19082i	1.27398	−	1.08207i
$16$	1.00000			0.250000
$17$			5.86818i			1.42324i	0.702564	+	0.711621i	$0.252039\pi$
$17$			5.86818i			1.42324i	−0.702564	+	0.711621i	$0.747961\pi$
$18$			5.38164i			1.26847i
$19$	−0.973070			−0.223238			−0.111619	−	0.993751i	$-0.535604\pi$
$19$	−0.973070			−0.223238			−0.111619	+	0.993751i	$0.535604\pi$
$20$	1.44755	+	1.70429i	0.323683	+	0.381090i
$21$	−12.6853			−2.76816
$22$			2.00000i			0.426401i
$23$		−	7.79021i		−	1.62437i	−0.583399	−	0.812186i	$-0.698278\pi$
$23$		−	7.79021i		−	1.62437i	0.583399	−	0.812186i	$-0.301722\pi$
$24$	−2.89511			−0.590961
$25$	−0.809179	+	4.93409i	−0.161836	+	0.986818i
$26$		0			0
$27$		−	6.89511i		−	1.32696i
$28$		−	4.38164i		−	0.828052i
$29$	−0.973070			−0.180695			−0.0903473	−	0.995910i	$-0.528798\pi$
$29$	−0.973070			−0.180695			−0.0903473	+	0.995910i	$0.528798\pi$
$30$	−4.19082	−	4.93409i	−0.765136	−	0.900837i
$31$	1.79021			0.321532			0.160766	−	0.986993i	$-0.448604\pi$
$31$	1.79021			0.321532			0.160766	+	0.986993i	$0.448604\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	5.79021i		−	1.00795i
$34$	5.86818			1.00638
$35$	7.46757	−	6.34266i	1.26225	−	1.07211i
$36$	5.38164			0.896940
$37$			0.591429i			0.0972303i	0.998818	+	0.0486151i	$0.0154808\pi$
$37$			0.591429i			0.0972303i	−0.998818	+	0.0486151i	$0.984519\pi$
$38$			0.973070i			0.157853i
$39$		0			0
$40$	1.70429	−	1.44755i	0.269471	−	0.228878i
$41$	−4.81714			−0.752311			−0.376156	−	0.926556i	$-0.622754\pi$
$41$	−4.81714			−0.752311			−0.376156	+	0.926556i	$0.622754\pi$
$42$			12.6853i			1.95739i
$43$		−	4.68532i		−	0.714505i	−0.934008	−	0.357252i	$-0.883714\pi$
$43$		−	4.68532i		−	0.714505i	0.934008	−	0.357252i	$-0.116286\pi$
$44$	2.00000			0.301511
$45$	7.79021	+	9.17185i	1.16130	+	1.36726i
$46$	−7.79021			−1.14860
$47$		−	0.381642i		−	0.0556682i	−0.999613	−	0.0278341i	$-0.991139\pi$
$47$		−	0.381642i		−	0.0556682i	0.999613	−	0.0278341i	$-0.00886101\pi$
$48$			2.89511i			0.417873i
$49$	−12.1988			−1.74268
$50$	4.93409	+	0.809179i	0.697785	+	0.114435i
$51$	−16.9890			−2.37894
$52$		0			0
$53$		−	7.79021i		−	1.07007i	−0.844831	−	0.535034i	$-0.820299\pi$
$53$		−	7.79021i		−	1.07007i	0.844831	−	0.535034i	$-0.179701\pi$
$54$	−6.89511			−0.938305
$55$	2.89511	+	3.40857i	0.390376	+	0.459612i
$56$	−4.38164			−0.585522
$57$		−	2.81714i		−	0.373140i
$58$			0.973070i			0.127770i
$59$	−0.973070			−0.126683			−0.0633415	−	0.997992i	$-0.520176\pi$
$59$	−0.973070			−0.126683			−0.0633415	+	0.997992i	$0.520176\pi$
$60$	−4.93409	+	4.19082i	−0.636988	+	0.541033i
$61$	−0.817143			−0.104624			−0.0523122	−	0.998631i	$-0.516659\pi$
$61$	−0.817143			−0.104624			−0.0523122	+	0.998631i	$0.516659\pi$
$62$		−	1.79021i		−	0.227357i
$63$		−	23.5804i		−	2.97085i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.79021			−0.712726
$67$		−	1.79021i		−	0.218709i	−0.994003	−	0.109355i	$-0.965122\pi$
$67$		−	1.79021i		−	0.218709i	0.994003	−	0.109355i	$-0.0348784\pi$
$68$		−	5.86818i		−	0.711621i
$69$	22.5535			2.71512
$70$	−6.34266	−	7.46757i	−0.758093	−	0.892545i
$71$	3.92204			0.465460			0.232730	−	0.972541i	$-0.425234\pi$
$71$	3.92204			0.465460			0.232730	+	0.972541i	$0.425234\pi$
$72$		−	5.38164i		−	0.634233i
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	0.591429			0.0687522
$75$	−14.2847	−	2.34266i	−1.64946	−	0.270507i
$76$	0.973070			0.111619
$77$		−	8.76328i		−	0.998669i
$78$		0			0
$79$	−10.9731			−1.23457			−0.617283	−	0.786741i	$-0.711767\pi$
$79$	−10.9731			−1.23457			−0.617283	+	0.786741i	$0.711767\pi$
$80$	−1.44755	−	1.70429i	−0.161841	−	0.190545i
$81$	3.81714			0.424127
$82$			4.81714i			0.531964i
$83$		−	6.97307i		−	0.765394i	−0.923874	−	0.382697i	$-0.874995\pi$
$83$		−	6.97307i		−	0.765394i	0.923874	−	0.382697i	$-0.125005\pi$
$84$	12.6853			1.38408
$85$	10.0010	−	8.49450i	1.08477	−	0.921358i
$86$	−4.68532			−0.505231
$87$		−	2.81714i		−	0.302029i
$88$		−	2.00000i		−	0.213201i
$89$	0.973070			0.103145			0.0515726	−	0.998669i	$-0.483577\pi$
$89$	0.973070			0.103145			0.0515726	+	0.998669i	$0.483577\pi$
$90$	9.17185	−	7.79021i	0.966798	−	0.821161i
$91$		0			0
$92$			7.79021i			0.812186i
$93$			5.18286i			0.537437i
$94$	−0.381642			−0.0393633
$95$	1.40857	+	1.65839i	0.144516	+	0.170147i
$96$	2.89511			0.295481
$97$			18.6074i			1.88929i	0.328093	+	0.944645i	$0.393594\pi$
$97$			18.6074i			1.88929i	−0.328093	+	0.944645i	$0.606406\pi$
$98$			12.1988i			1.23226i
$99$	10.7633			1.08175
$100$	0.809179	−	4.93409i	0.0809179	−	0.493409i
$101$	14.3437			1.42725			0.713626	−	0.700527i	$-0.247052\pi$
$101$	14.3437			1.42725			0.713626	+	0.700527i	$0.247052\pi$
$102$			16.9890i			1.68216i
$103$		−	9.73635i		−	0.959351i	−0.877446	−	0.479676i	$-0.840754\pi$
$103$		−	9.73635i		−	0.959351i	0.877446	−	0.479676i	$-0.159246\pi$
$104$		0			0
$105$	18.3627	+	21.6194i	1.79201	+	2.10984i
$106$	−7.79021			−0.756652
$107$		−	5.79021i		−	0.559761i	−0.960035	−	0.279881i	$-0.909705\pi$
$107$		−	5.79021i		−	0.559761i	0.960035	−	0.279881i	$-0.0902949\pi$
$108$			6.89511i			0.663482i
$109$	−0.685320			−0.0656417			−0.0328209	−	0.999461i	$-0.510449\pi$
$109$	−0.685320			−0.0656417			−0.0328209	+	0.999461i	$0.510449\pi$
$110$	3.40857	−	2.89511i	0.324995	−	0.276038i
$111$	−1.71225			−0.162519
$112$			4.38164i			0.414026i
$113$		−	4.00000i		−	0.376288i	−0.982141	−	0.188144i	$-0.939753\pi$
$113$		−	4.00000i		−	0.376288i	0.982141	−	0.188144i	$-0.0602472\pi$
$114$	−2.81714			−0.263850
$115$	−13.2767	+	11.2767i	−1.23806	+	1.05156i
$116$	0.973070			0.0903473
$117$		0			0
$118$			0.973070i			0.0895784i
$119$	−25.7122			−2.35704
$120$	4.19082	+	4.93409i	0.382568	+	0.450419i
$121$	−7.00000			−0.636364
$122$			0.817143i			0.0739806i
$123$		−	13.9461i		−	1.25748i
$124$	−1.79021			−0.160766
$125$	9.58043	−	5.76328i	0.856899	−	0.515484i
$126$	−23.5804			−2.10071
$127$			11.7902i			1.04621i	0.852268	+	0.523106i	$0.175227\pi$
$127$			11.7902i			1.04621i	−0.852268	+	0.523106i	$0.824773\pi$
$128$			1.00000i			0.0883883i
$129$	13.5645			1.19429
$130$		0			0
$131$	−16.9890			−1.48434			−0.742168	−	0.670214i	$-0.766202\pi$
$131$	−16.9890			−1.48434			−0.742168	+	0.670214i	$0.766202\pi$
$132$			5.79021i			0.503973i
$133$		−	4.26365i		−	0.369705i
$134$	−1.79021			−0.154651
$135$	−11.7512	+	9.98103i	−1.01138	+	0.859031i
$136$	−5.86818			−0.503192
$137$		−	4.20979i		−	0.359666i	−0.983697	−	0.179833i	$-0.942444\pi$
$137$		−	4.20979i		−	0.359666i	0.983697	−	0.179833i	$-0.0575558\pi$
$138$		−	22.5535i		−	1.91988i
$139$	6.17185			0.523490			0.261745	−	0.965137i	$-0.415702\pi$
$139$	6.17185			0.523490			0.261745	+	0.965137i	$0.415702\pi$
$140$	−7.46757	+	6.34266i	−0.631125	+	0.536053i
$141$	1.10489			0.0930488
$142$		−	3.92204i		−	0.329130i
$143$		0			0
$144$	−5.38164			−0.448470
$145$	1.40857	+	1.65839i	0.116975	+	0.137722i
$146$	−6.00000			−0.496564
$147$		−	35.3168i		−	2.91288i
$148$		−	0.591429i		−	0.0486151i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	−2.34266	+	14.2847i	−0.191277	+	1.16634i
$151$	−15.5025			−1.26157			−0.630786	−	0.775957i	$-0.717268\pi$
$151$	−15.5025			−1.26157			−0.630786	+	0.775957i	$0.717268\pi$
$152$		−	0.973070i		−	0.0789264i
$153$		−	31.5804i		−	2.55313i
$154$	−8.76328			−0.706166
$155$	−2.59143	−	3.05103i	−0.208149	−	0.245065i
$156$		0			0
$157$			8.97307i			0.716129i	0.933697	+	0.358064i	$0.116563\pi$
$157$			8.97307i			0.716129i	−0.933697	+	0.358064i	$0.883437\pi$
$158$			10.9731i			0.872971i
$159$	22.5535			1.78861
$160$	−1.70429	+	1.44755i	−0.134736	+	0.114439i
$161$	34.1339			2.69013
$162$		−	3.81714i		−	0.299903i
$163$		−	12.6074i		−	0.987484i	−0.869608	−	0.493742i	$-0.835629\pi$
$163$		−	12.6074i		−	0.987484i	0.869608	−	0.493742i	$-0.164371\pi$
$164$	4.81714			0.376156
$165$	−9.86818	+	8.38164i	−0.768237	+	0.652510i
$166$	−6.97307			−0.541215
$167$		−	23.1609i		−	1.79224i	−0.443811	−	0.896120i	$-0.646374\pi$
$167$		−	23.1609i		−	1.79224i	0.443811	−	0.896120i	$-0.353626\pi$
$168$		−	12.6853i		−	0.978694i
$169$		0			0
$170$	−8.49450	−	10.0010i	−0.651498	−	0.767046i
$171$	5.23672			0.400462
$172$			4.68532i			0.357252i
$173$			19.7902i			1.50462i	0.658808	+	0.752311i	$0.271061\pi$
$173$			19.7902i			1.50462i	−0.658808	+	0.752311i	$0.728939\pi$
$174$	−2.81714			−0.213567
$175$	−21.6194	−	3.54553i	−1.63427	−	0.268017i
$176$	−2.00000			−0.150756
$177$		−	2.81714i		−	0.211749i
$178$		−	0.973070i		−	0.0729347i
$179$	−6.17185			−0.461306			−0.230653	−	0.973036i	$-0.574086\pi$
$179$	−6.17185			−0.461306			−0.230653	+	0.973036i	$0.574086\pi$
$180$	−7.79021	−	9.17185i	−0.580648	−	0.683630i
$181$	−19.3706			−1.43981			−0.719904	−	0.694074i	$-0.755814\pi$
$181$	−19.3706			−1.43981			−0.719904	+	0.694074i	$0.755814\pi$
$182$		0			0
$183$		−	2.36571i		−	0.174879i
$184$	7.79021			0.574302
$185$	1.00796	−	0.856125i	0.0741069	−	0.0629435i
$186$	5.18286			0.380026
$187$		−	11.7364i		−	0.858247i
$188$			0.381642i			0.0278341i
$189$	30.2119			2.19759
$190$	1.65839	−	1.40857i	0.120312	−	0.102189i
$191$	−3.73635			−0.270353			−0.135177	−	0.990822i	$-0.543160\pi$
$191$	−3.73635			−0.270353			−0.135177	+	0.990822i	$0.543160\pi$
$192$		−	2.89511i		−	0.208936i
$193$			15.3706i			1.10640i	0.833048	+	0.553201i	$0.186594\pi$
$193$			15.3706i			1.10640i	−0.833048	+	0.553201i	$0.813406\pi$
$194$	18.6074			1.33593
$195$		0			0
$196$	12.1988			0.871342
$197$		−	26.9890i		−	1.92289i	−0.275004	−	0.961443i	$-0.588679\pi$
$197$		−	26.9890i		−	1.92289i	0.275004	−	0.961443i	$-0.411321\pi$
$198$		−	10.7633i		−	0.764913i
$199$	−23.3168			−1.65288			−0.826441	−	0.563023i	$-0.809638\pi$
$199$	−23.3168			−1.65288			−0.826441	+	0.563023i	$0.809638\pi$
$200$	−4.93409	−	0.809179i	−0.348893	−	0.0572176i
$201$	5.18286			0.365571
$202$		−	14.3437i		−	1.00922i
$203$		−	4.26365i		−	0.299249i
$204$	16.9890			1.18947
$205$	6.97307	+	8.20979i	0.487020	+	0.573396i
$206$	−9.73635			−0.678364
$207$			41.9241i			2.91393i
$208$		0			0
$209$	1.94614			0.134617
$210$	21.6194	−	18.3627i	1.49188	−	1.26715i
$211$	15.3547			1.05706			0.528531	−	0.848914i	$-0.322743\pi$
$211$	15.3547			1.05706			0.528531	+	0.848914i	$0.322743\pi$
$212$			7.79021i			0.535034i
$213$			11.3547i			0.778012i
$214$	−5.79021			−0.395811
$215$	−7.98512	+	6.78225i	−0.544581	+	0.462546i
$216$	6.89511			0.469153
$217$			7.84407i			0.532490i
$218$			0.685320i			0.0464157i
$219$	17.3706			1.17380
$220$	−2.89511	−	3.40857i	−0.195188	−	0.229806i
$221$		0			0
$222$			1.71225i			0.114919i
$223$			24.8331i			1.66295i	0.555566	+	0.831473i	$0.312502\pi$
$223$			24.8331i			1.66295i	−0.555566	+	0.831473i	$0.687498\pi$
$224$	4.38164			0.292761
$225$	4.35471	−	26.5535i	0.290314	−	1.77023i
$226$	−4.00000			−0.266076
$227$			21.5266i			1.42877i	0.699754	+	0.714384i	$0.253293\pi$
$227$			21.5266i			1.42877i	−0.699754	+	0.714384i	$0.746707\pi$
$228$			2.81714i			0.186570i
$229$	−2.63146			−0.173892			−0.0869459	−	0.996213i	$-0.527711\pi$
$229$	−2.63146			−0.173892			−0.0869459	+	0.996213i	$0.527711\pi$
$230$	11.2767	+	13.2767i	0.743567	+	0.875443i
$231$	25.3706			1.66927
$232$		−	0.973070i		−	0.0638852i
$233$			29.0290i			1.90175i	0.309568	+	0.950877i	$0.399816\pi$
$233$			29.0290i			1.90175i	−0.309568	+	0.950877i	$0.600184\pi$
$234$		0			0
$235$	−0.650427	+	0.552447i	−0.0424291	+	0.0360377i
$236$	0.973070			0.0633415
$237$		−	31.7682i		−	2.06357i
$238$			25.7122i			1.66668i
$239$	2.13182			0.137896			0.0689481	−	0.997620i	$-0.478036\pi$
$239$	2.13182			0.137896			0.0689481	+	0.997620i	$0.478036\pi$
$240$	4.93409	−	4.19082i	0.318494	−	0.270516i
$241$	−22.4996			−1.44933			−0.724665	−	0.689102i	$-0.758005\pi$
$241$	−22.4996			−1.44933			−0.724665	+	0.689102i	$0.758005\pi$
$242$			7.00000i			0.449977i
$243$		−	9.63429i		−	0.618040i
$244$	0.817143			0.0523122
$245$	17.6584	+	20.7902i	1.12815	+	1.32824i
$246$	−13.9461			−0.889173
$247$		0			0
$248$			1.79021i			0.113679i
$249$	20.1878			1.27935
$250$	−5.76328	−	9.58043i	−0.364502	−	0.605919i
$251$	−0.419574			−0.0264833			−0.0132416	−	0.999912i	$-0.504215\pi$
$251$	−0.419574			−0.0264833			−0.0132416	+	0.999912i	$0.504215\pi$
$252$			23.5804i			1.48543i
$253$			15.5804i			0.979533i
$254$	11.7902			0.739784
$255$	24.5925	+	28.9541i	1.54004	+	1.81318i
$256$	1.00000			0.0625000
$257$			19.6584i			1.22626i	0.789983	+	0.613128i	$0.210089\pi$
$257$			19.6584i			1.22626i	−0.789983	+	0.613128i	$0.789911\pi$
$258$		−	13.5645i		−	0.844489i
$259$	−2.59143			−0.161024
$260$		0			0
$261$	5.23672			0.324145
$262$			16.9890i			1.04958i
$263$			10.7633i			0.663692i	0.943333	+	0.331846i	$0.107672\pi$
$263$			10.7633i			0.663692i	−0.943333	+	0.331846i	$0.892328\pi$
$264$	5.79021			0.356363
$265$	−13.2767	+	11.2767i	−0.815584	+	0.692725i
$266$	−4.26365			−0.261421
$267$			2.81714i			0.172406i
$268$			1.79021i			0.109355i
$269$	14.7633			0.900133			0.450067	−	0.892995i	$-0.351400\pi$
$269$	14.7633			0.900133			0.450067	+	0.892995i	$0.351400\pi$
$270$	9.98103	+	11.7512i	0.607426	+	0.715157i
$271$	27.2388			1.65464			0.827320	−	0.561731i	$-0.189864\pi$
$271$	27.2388			1.65464			0.827320	+	0.561731i	$0.189864\pi$
$272$			5.86818i			0.355810i
$273$		0			0
$274$	−4.20979			−0.254323
$275$	1.61836	−	9.86818i	0.0975907	−	0.595073i
$276$	−22.5535			−1.35756
$277$		−	2.87100i		−	0.172502i	−0.996273	−	0.0862509i	$-0.972511\pi$
$277$		−	2.87100i		−	0.172502i	0.996273	−	0.0862509i	$-0.0274887\pi$
$278$		−	6.17185i		−	0.370163i
$279$	−9.63429			−0.576790
$280$	6.34266	+	7.46757i	0.379046	+	0.446273i
$281$	−5.39264			−0.321698			−0.160849	−	0.986979i	$-0.551423\pi$
$281$	−5.39264			−0.321698			−0.160849	+	0.986979i	$0.551423\pi$
$282$		−	1.10489i		−	0.0657954i
$283$			24.9511i			1.48319i	0.670850	+	0.741593i	$0.265930\pi$
$283$			24.9511i			1.48319i	−0.670850	+	0.741593i	$0.734070\pi$
$284$	−3.92204			−0.232730
$285$	−4.80122	+	4.07796i	−0.284399	+	0.241558i
$286$		0			0
$287$		−	21.1070i		−	1.24591i
$288$			5.38164i			0.317116i
$289$	−17.4355			−1.02562
$290$	1.65839	−	1.40857i	0.0973840	−	0.0827142i
$291$	−53.8703			−3.15793
$292$			6.00000i			0.351123i
$293$			24.9351i			1.45673i	0.685191	+	0.728363i	$0.259719\pi$
$293$			24.9351i			1.45673i	−0.685191	+	0.728363i	$0.740281\pi$
$294$	−35.3168			−2.05972
$295$	1.40857	+	1.65839i	0.0820102	+	0.0965552i
$296$	−0.591429			−0.0343761
$297$			13.7902i			0.800189i
$298$		0			0
$299$		0			0
$300$	14.2847	+	2.34266i	0.824728	+	0.135254i
$301$	20.5294			1.18329
$302$			15.5025i			0.892066i
$303$			41.5266i			2.38564i
$304$	−0.973070			−0.0558094
$305$	1.18286	+	1.39264i	0.0677302	+	0.0797426i
$306$	−31.5804			−1.80533
$307$			14.8171i			0.845659i	0.906209	+	0.422829i	$0.138963\pi$
$307$			14.8171i			0.845659i	−0.906209	+	0.422829i	$0.861037\pi$
$308$			8.76328i			0.499334i
$309$	28.1878			1.60355
$310$	−3.05103	+	2.59143i	−0.173287	+	0.147183i
$311$	12.8710			0.729848			0.364924	−	0.931037i	$-0.381095\pi$
$311$	12.8710			0.729848			0.364924	+	0.931037i	$0.381095\pi$
$312$		0			0
$313$		−	19.9220i		−	1.12606i	−0.826436	−	0.563030i	$-0.809636\pi$
$313$		−	19.9220i		−	1.12606i	0.826436	−	0.563030i	$-0.190364\pi$
$314$	8.97307			0.506380
$315$	−40.1878	+	34.1339i	−2.26432	+	1.92323i
$316$	10.9731			0.617283
$317$			3.94614i			0.221637i	0.993841	+	0.110819i	$0.0353473\pi$
$317$			3.94614i			0.221637i	−0.993841	+	0.110819i	$0.964653\pi$
$318$		−	22.5535i		−	1.26474i
$319$	1.94614			0.108963
$320$	1.44755	+	1.70429i	0.0809207	+	0.0952725i
$321$	16.7633			0.935635
$322$		−	34.1339i		−	1.90221i
$323$		−	5.71015i		−	0.317721i
$324$	−3.81714			−0.212063
$325$		0			0
$326$	−12.6074			−0.698257
$327$		−	1.98407i		−	0.109719i
$328$		−	4.81714i		−	0.265982i
$329$	1.67222			0.0921923
$330$	8.38164	+	9.86818i	0.461394	+	0.543225i
$331$	−21.4245			−1.17760			−0.588798	−	0.808280i	$-0.700399\pi$
$331$	−21.4245			−1.17760			−0.588798	+	0.808280i	$0.700399\pi$
$332$			6.97307i			0.382697i
$333$		−	3.18286i		−	0.174420i
$334$	−23.1609			−1.26731
$335$	−3.05103	+	2.59143i	−0.166696	+	0.141585i
$336$	−12.6853			−0.692041
$337$		−	11.2388i		−	0.612217i	−0.951997	−	0.306109i	$-0.900973\pi$
$337$		−	11.2388i		−	0.612217i	0.951997	−	0.306109i	$-0.0990271\pi$
$338$		0			0
$339$	11.5804			0.628962
$340$	−10.0010	+	8.49450i	−0.542383	+	0.460679i
$341$	−3.58043			−0.193891
$342$		−	5.23672i		−	0.283169i
$343$		−	22.7792i		−	1.22996i
$344$	4.68532			0.252616
$345$	−32.6474	−	38.4376i	−1.75768	−	2.06941i
$346$	19.7902			1.06393
$347$		−	16.9490i		−	0.909868i	−0.890525	−	0.454934i	$-0.849663\pi$
$347$		−	16.9490i		−	0.909868i	0.890525	−	0.454934i	$-0.150337\pi$
$348$			2.81714i			0.151015i
$349$	−10.2119			−0.546630			−0.273315	−	0.961925i	$-0.588120\pi$
$349$	−10.2119			−0.546630			−0.273315	+	0.961925i	$0.588120\pi$
$350$	−3.54553	+	21.6194i	−0.189517	+	1.15561i
$351$		0			0
$352$			2.00000i			0.106600i
$353$		−	14.9511i		−	0.795765i	−0.917436	−	0.397882i	$-0.869745\pi$
$353$		−	14.9511i		−	0.795765i	0.917436	−	0.397882i	$-0.130255\pi$
$354$	−2.81714			−0.149729
$355$	−5.67736	−	6.68427i	−0.301323	−	0.354764i
$356$	−0.973070			−0.0515726
$357$		−	74.4397i		−	3.93977i
$358$			6.17185i			0.326193i
$359$	11.8441			0.625106			0.312553	−	0.949900i	$-0.398816\pi$
$359$	11.8441			0.625106			0.312553	+	0.949900i	$0.398816\pi$
$360$	−9.17185	+	7.79021i	−0.483399	+	0.410580i
$361$	−18.0531			−0.950165
$362$			19.3706i			1.01810i
$363$		−	20.2657i		−	1.06368i
$364$		0			0
$365$	−10.2257	+	8.68532i	−0.535238	+	0.454610i
$366$	−2.36571			−0.123658
$367$			16.0539i			0.838005i	0.907985	+	0.419002i	$0.137620\pi$
$367$			16.0539i			0.838005i	−0.907985	+	0.419002i	$0.862380\pi$
$368$		−	7.79021i		−	0.406093i
$369$	25.9241			1.34956
$370$	−0.856125	−	1.00796i	−0.0445078	−	0.0524015i
$371$	34.1339			1.77214
$372$		−	5.18286i		−	0.268719i
$373$			6.87100i			0.355767i	0.984052	+	0.177883i	$0.0569250\pi$
$373$			6.87100i			0.355767i	−0.984052	+	0.177883i	$0.943075\pi$
$374$	−11.7364			−0.606872
$375$	16.6853	+	27.7364i	0.861626	+	1.43230i
$376$	0.381642			0.0196817
$377$		0			0
$378$		−	30.2119i		−	1.55393i
$379$	1.84407			0.0947236			0.0473618	−	0.998878i	$-0.484919\pi$
$379$	1.84407			0.0947236			0.0473618	+	0.998878i	$0.484919\pi$
$380$	−1.40857	−	1.65839i	−0.0722582	−	0.0850736i
$381$	−34.1339			−1.74873
$382$			3.73635i			0.191168i
$383$		−	9.25264i		−	0.472788i	−0.971657	−	0.236394i	$-0.924034\pi$
$383$		−	9.25264i		−	0.472788i	0.971657	−	0.236394i	$-0.0759656\pi$
$384$	−2.89511			−0.147740
$385$	−14.9351	+	12.6853i	−0.761165	+	0.646504i
$386$	15.3706			0.782345
$387$			25.2147i			1.28174i
$388$		−	18.6074i		−	0.944645i
$389$	21.2686			1.07836			0.539180	−	0.842191i	$-0.318734\pi$
$389$	21.2686			1.07836			0.539180	+	0.842191i	$0.318734\pi$
$390$		0			0
$391$	45.7143			2.31187
$392$		−	12.1988i		−	0.616132i
$393$		−	49.1850i		−	2.48105i
$394$	−26.9890			−1.35969
$395$	15.8841	+	18.7012i	0.799216	+	0.940962i
$396$	−10.7633			−0.540875
$397$			33.4727i			1.67995i	0.542627	+	0.839974i	$0.317430\pi$
$397$			33.4727i			1.67995i	−0.542627	+	0.839974i	$0.682570\pi$
$398$			23.3168i			1.16876i
$399$	12.3437			0.617958
$400$	−0.809179	+	4.93409i	−0.0404590	+	0.246704i
$401$	−17.7364			−0.885711			−0.442856	−	0.896593i	$-0.646035\pi$
$401$	−17.7364			−0.885711			−0.442856	+	0.896593i	$0.646035\pi$
$402$		−	5.18286i		−	0.258497i
$403$		0			0
$404$	−14.3437			−0.713626
$405$	−5.52552	−	6.50550i	−0.274565	−	0.323261i
$406$	−4.26365			−0.211601
$407$		−	1.18286i		−	0.0586321i
$408$		−	16.9890i		−	0.841081i
$409$	7.68249			0.379875			0.189937	−	0.981796i	$-0.439171\pi$
$409$	7.68249			0.379875			0.189937	+	0.981796i	$0.439171\pi$
$410$	8.20979	−	6.97307i	0.405452	−	0.344375i
$411$	12.1878			0.601179
$412$			9.73635i			0.479676i
$413$		−	4.26365i		−	0.209800i
$414$	41.9241			2.06046
$415$	−11.8841	+	10.0939i	−0.583368	+	0.495490i
$416$		0			0
$417$			17.8682i			0.875008i
$418$		−	1.94614i		−	0.0951889i
$419$	−11.8061			−0.576768			−0.288384	−	0.957515i	$-0.593118\pi$
$419$	−11.8061			−0.576768			−0.288384	+	0.957515i	$0.593118\pi$
$420$	−18.3627	−	21.6194i	−0.896007	−	1.05492i
$421$	26.3678			1.28509			0.642544	−	0.766249i	$-0.277879\pi$
$421$	26.3678			1.28509			0.642544	+	0.766249i	$0.277879\pi$
$422$		−	15.3547i		−	0.747456i
$423$			2.05386i			0.0998620i
$424$	7.79021			0.378326
$425$	−28.9541	−	4.74841i	−1.40448	−	0.230332i
$426$	11.3547			0.550138
$427$		−	3.58043i		−	0.173269i
$428$			5.79021i			0.279881i
$429$		0			0
$430$	6.78225	+	7.98512i	0.327069	+	0.385077i
$431$	−1.71225			−0.0824761			−0.0412381	−	0.999149i	$-0.513130\pi$
$431$	−1.71225			−0.0824761			−0.0412381	+	0.999149i	$0.513130\pi$
$432$		−	6.89511i		−	0.331741i
$433$			11.9220i			0.572936i	0.958090	+	0.286468i	$0.0924813\pi$
$433$			11.9220i			0.572936i	−0.958090	+	0.286468i	$0.907519\pi$
$434$	7.84407			0.376528
$435$	−4.80122	+	4.07796i	−0.230201	+	0.195523i
$436$	0.685320			0.0328209
$437$			7.58043i			0.362621i
$438$		−	17.3706i		−	0.830001i
$439$	12.3437			0.589133			0.294567	−	0.955631i	$-0.404825\pi$
$439$	12.3437			0.589133			0.294567	+	0.955631i	$0.404825\pi$
$440$	−3.40857	+	2.89511i	−0.162497	+	0.138019i
$441$	65.6495			3.12617
$442$		0			0
$443$			28.1580i			1.33783i	0.743340	+	0.668914i	$0.233241\pi$
$443$			28.1580i			1.33783i	−0.743340	+	0.668914i	$0.766759\pi$
$444$	1.71225			0.0812597
$445$	−1.40857	−	1.65839i	−0.0667727	−	0.0786152i
$446$	24.8331			1.17588
$447$		0			0
$448$		−	4.38164i		−	0.207013i
$449$	−29.0531			−1.37110			−0.685551	−	0.728025i	$-0.740439\pi$
$449$	−29.0531			−1.37110			−0.685551	+	0.728025i	$0.740439\pi$
$450$	−26.5535	−	4.35471i	−1.25174	−	0.205283i
$451$	9.63429			0.453661
$452$			4.00000i			0.188144i
$453$		−	44.8813i		−	2.10871i
$454$	21.5266			1.01029
$455$		0			0
$456$	2.81714			0.131925
$457$			11.5266i			0.539190i	0.962974	+	0.269595i	$0.0868898\pi$
$457$			11.5266i			0.539190i	−0.962974	+	0.269595i	$0.913110\pi$
$458$			2.63146i			0.122960i
$459$	40.4617			1.88859
$460$	13.2767	−	11.2767i	0.619032	−	0.525781i
$461$	−28.4217			−1.32373			−0.661865	−	0.749623i	$-0.730235\pi$
$461$	−28.4217			−1.32373			−0.661865	+	0.749623i	$0.730235\pi$
$462$		−	25.3706i		−	1.18035i
$463$		−	27.4727i		−	1.27677i	−0.769719	−	0.638383i	$-0.779604\pi$
$463$		−	27.4727i		−	1.27677i	0.769719	−	0.638383i	$-0.220396\pi$
$464$	−0.973070			−0.0451737
$465$	8.83307	−	7.50246i	0.409624	−	0.347918i
$466$	29.0290			1.34474
$467$		−	18.2098i		−	0.842648i	−0.906910	−	0.421324i	$-0.861565\pi$
$467$		−	18.2098i		−	0.842648i	0.906910	−	0.421324i	$-0.138435\pi$
$468$		0			0
$469$	7.84407			0.362206
$470$	0.552447	+	0.650427i	0.0254825	+	0.0300019i
$471$	−25.9780			−1.19700
$472$		−	0.973070i		−	0.0447892i
$473$			9.37064i			0.430862i
$474$	−31.7682			−1.45916
$475$	0.787388	−	4.80122i	0.0361279	−	0.220295i
$476$	25.7122			1.17852
$477$			41.9241i			1.91957i
$478$		−	2.13182i		−	0.0975073i
$479$	−33.6045			−1.53543			−0.767715	−	0.640791i	$-0.778606\pi$
$479$	−33.6045			−1.53543			−0.767715	+	0.640791i	$0.778606\pi$
$480$	−4.19082	−	4.93409i	−0.191284	−	0.225209i
$481$		0			0
$482$			22.4996i			1.02483i
$483$			98.8213i			4.49653i
$484$	7.00000			0.318182
$485$	31.7122	−	26.9351i	1.43998	−	1.22306i
$486$	−9.63429			−0.437020
$487$		−	8.00000i		−	0.362515i	−0.983436	−	0.181257i	$-0.941983\pi$
$487$		−	8.00000i		−	0.362515i	0.983436	−	0.181257i	$-0.0580167\pi$
$488$		−	0.817143i		−	0.0369903i
$489$	36.4996			1.65057
$490$	20.7902	−	17.6584i	0.939206	−	0.797725i
$491$	−19.8061			−0.893839			−0.446919	−	0.894574i	$-0.647479\pi$
$491$	−19.8061			−0.893839			−0.446919	+	0.894574i	$0.647479\pi$
$492$			13.9461i			0.628741i
$493$		−	5.71015i		−	0.257172i
$494$		0			0
$495$	−15.5804	−	18.3437i	−0.700288	−	0.824488i
$496$	1.79021			0.0803829
$497$			17.1850i			0.770851i
$498$		−	20.1878i		−	0.904636i
$499$	9.12900			0.408670			0.204335	−	0.978901i	$-0.434497\pi$
$499$	9.12900			0.408670			0.204335	+	0.978901i	$0.434497\pi$
$500$	−9.58043	+	5.76328i	−0.428450	+	0.257742i
$501$	67.0531			2.99571
$502$			0.419574i			0.0187265i
$503$		−	10.6074i		−	0.472959i	−0.971637	−	0.236479i	$-0.924006\pi$
$503$		−	10.6074i		−	0.472959i	0.971637	−	0.236479i	$-0.0759935\pi$
$504$	23.5804			1.05036
$505$	−20.7633	−	24.4458i	−0.923954	−	1.08782i
$506$	15.5804			0.692634
$507$		0			0
$508$		−	11.7902i		−	0.523106i
$509$	−5.63429			−0.249735			−0.124868	−	0.992173i	$-0.539851\pi$
$509$	−5.63429			−0.249735			−0.124868	+	0.992173i	$0.539851\pi$
$510$	28.9541	−	24.5925i	1.28211	−	1.08897i
$511$	26.2899			1.16299
$512$		−	1.00000i		−	0.0441942i
$513$			6.70942i			0.296228i
$514$	19.6584			0.867094
$515$	−16.5935	+	14.0939i	−0.731198	+	0.621051i
$516$	−13.5645			−0.597144
$517$			0.763283i			0.0335692i
$518$			2.59143i			0.113861i
$519$	−57.2948			−2.51496
$520$		0			0
$521$	−22.8012			−0.998939			−0.499470	−	0.866331i	$-0.666472\pi$
$521$	−22.8012			−0.998939			−0.499470	+	0.866331i	$0.666472\pi$
$522$		−	5.23672i		−	0.229205i
$523$		−	23.6286i		−	1.03321i	−0.856224	−	0.516604i	$-0.827196\pi$
$523$		−	23.6286i		−	1.03321i	0.856224	−	0.516604i	$-0.172804\pi$
$524$	16.9890			0.742168
$525$	10.2647	−	62.5905i	0.447988	−	2.73167i
$526$	10.7633			0.469301
$527$			10.5053i			0.457617i
$528$		−	5.79021i		−	0.251987i
$529$	−37.6874			−1.63858
$530$	11.2767	+	13.2767i	0.489831	+	0.576705i
$531$	5.23672			0.227254
$532$			4.26365i			0.184853i
$533$		0			0
$534$	2.81714			0.121910
$535$	−9.86818	+	8.38164i	−0.426638	+	0.362370i
$536$	1.79021			0.0773254
$537$		−	17.8682i		−	0.771069i
$538$		−	14.7633i		−	0.636490i
$539$	24.3976			1.05088
$540$	11.7512	−	9.98103i	0.505692	−	0.429515i
$541$	−11.3147			−0.486456			−0.243228	−	0.969969i	$-0.578206\pi$
$541$	−11.3147			−0.486456			−0.243228	+	0.969969i	$0.578206\pi$
$542$		−	27.2388i		−	1.17001i
$543$		−	56.0801i		−	2.40663i
$544$	5.86818			0.251596
$545$	0.992037	+	1.16798i	0.0424942	+	0.0500308i
$546$		0			0
$547$			16.8412i			0.720080i	0.932937	+	0.360040i	$0.117237\pi$
$547$			16.8412i			0.720080i	−0.932937	+	0.360040i	$0.882763\pi$
$548$			4.20979i			0.179833i
$549$	4.39757			0.187684
$550$	−9.86818	−	1.61836i	−0.420780	−	0.0690070i
$551$	0.946866			0.0403379
$552$			22.5535i			0.959941i
$553$		−	48.0801i		−	2.04457i
$554$	−2.87100			−0.121977
$555$	2.47857	+	2.91816i	0.105210	+	0.123869i
$556$	−6.17185			−0.261745
$557$			35.7523i			1.51487i	0.652909	+	0.757436i	$0.273548\pi$
$557$			35.7523i			1.51487i	−0.652909	+	0.757436i	$0.726452\pi$
$558$			9.63429i			0.407852i
$559$		0			0
$560$	7.46757	−	6.34266i	0.315562	−	0.268026i
$561$	33.9780			1.43455
$562$			5.39264i			0.227475i
$563$			13.3685i			0.563417i	0.959500	+	0.281708i	$0.0909011\pi$
$563$			13.3685i			0.563417i	−0.959500	+	0.281708i	$0.909099\pi$
$564$	−1.10489			−0.0465244
$565$	−6.81714	+	5.79021i	−0.286799	+	0.243596i
$566$	24.9511			1.04877
$567$			16.7254i			0.702399i
$568$			3.92204i			0.164565i
$569$	29.9621			1.25608			0.628038	−	0.778183i	$-0.283858\pi$
$569$	29.9621			1.25608			0.628038	+	0.778183i	$0.283858\pi$
$570$	4.07796	+	4.80122i	0.170807	+	0.201101i
$571$	30.5156			1.27704			0.638518	−	0.769607i	$-0.279548\pi$
$571$	30.5156			1.27704			0.638518	+	0.769607i	$0.279548\pi$
$572$		0			0
$573$		−	10.8171i		−	0.451893i
$574$	−21.1070			−0.880989
$575$	38.4376	+	6.30368i	1.60296	+	0.262882i
$576$	5.38164			0.224235
$577$		−	33.1609i		−	1.38050i	−0.723569	−	0.690252i	$-0.757500\pi$
$577$		−	33.1609i		−	1.38050i	0.723569	−	0.690252i	$-0.242500\pi$
$578$			17.4355i			0.725221i
$579$	−44.4996			−1.84934
$580$	−1.40857	−	1.65839i	−0.0584877	−	0.0688609i
$581$	30.5535			1.26757
$582$			53.8703i			2.23299i
$583$			15.5804i			0.645275i
$584$	6.00000			0.248282
$585$		0			0
$586$	24.9351			1.03006
$587$		−	14.1339i		−	0.583369i	−0.956515	−	0.291685i	$-0.905784\pi$
$587$		−	14.1339i		−	0.583369i	0.956515	−	0.291685i	$-0.0942158\pi$
$588$			35.3168i			1.45644i
$589$	−1.74200			−0.0717780
$590$	1.65839	−	1.40857i	0.0682748	−	0.0579900i
$591$	78.1360			3.21409
$592$			0.591429i			0.0243076i
$593$		−	9.39264i		−	0.385710i	−0.981227	−	0.192855i	$-0.938225\pi$
$593$		−	9.39264i		−	0.385710i	0.981227	−	0.192855i	$-0.0617746\pi$
$594$	13.7902			0.565819
$595$	37.2198	+	43.8210i	1.52587	+	1.79649i
$596$		0			0
$597$		−	67.5046i		−	2.76278i
$598$		0			0
$599$	−45.5584			−1.86147			−0.930733	−	0.365699i	$-0.880830\pi$
$599$	−45.5584			−1.86147			−0.930733	+	0.365699i	$0.880830\pi$
$600$	2.34266	−	14.2847i	0.0956387	−	0.583171i
$601$	26.7254			1.09015			0.545075	−	0.838387i	$-0.316501\pi$
$601$	26.7254			1.09015			0.545075	+	0.838387i	$0.316501\pi$
$602$		−	20.5294i		−	0.836716i
$603$			9.63429i			0.392338i
$604$	15.5025			0.630786
$605$	10.1329	+	11.9300i	0.411960	+	0.485023i
$606$	41.5266			1.68690
$607$		−	30.0801i		−	1.22091i	−0.792050	−	0.610456i	$-0.790986\pi$
$607$		−	30.0801i		−	1.22091i	0.792050	−	0.610456i	$-0.209014\pi$
$608$			0.973070i			0.0394632i
$609$	12.3437			0.500192
$610$	1.39264	−	1.18286i	0.0563865	−	0.0478925i
$611$		0			0
$612$			31.5804i			1.27656i
$613$		−	17.2686i		−	0.697471i	−0.937221	−	0.348735i	$-0.886611\pi$
$613$		−	17.2686i		−	0.697471i	0.937221	−	0.348735i	$-0.113389\pi$
$614$	14.8171			0.597971
$615$	−23.7682	+	20.1878i	−0.958427	+	0.814050i
$616$	8.76328			0.353083
$617$			14.3437i			0.577456i	0.957411	+	0.288728i	$0.0932323\pi$
$617$			14.3437i			0.577456i	−0.957411	+	0.288728i	$0.906768\pi$
$618$		−	28.1878i		−	1.13388i
$619$	−38.4514			−1.54549			−0.772747	−	0.634715i	$-0.781118\pi$
$619$	−38.4514			−1.54549			−0.772747	+	0.634715i	$0.781118\pi$
$620$	2.59143	+	3.05103i	0.104074	+	0.122532i
$621$	−53.7143			−2.15548
$622$		−	12.8710i		−	0.516080i
$623$			4.26365i			0.170819i
$624$		0			0
$625$	−23.6905	−	7.98512i	−0.947618	−	0.319405i
$626$	−19.9220			−0.796245
$627$			5.63429i			0.225012i
$628$		−	8.97307i		−	0.358064i
$629$	−3.47061			−0.138382
$630$	34.1339	+	40.1878i	1.35993	+	1.60112i
$631$	8.18568			0.325867			0.162933	−	0.986637i	$-0.447904\pi$
$631$	8.18568			0.325867			0.162933	+	0.986637i	$0.447904\pi$
$632$		−	10.9731i		−	0.436485i
$633$			44.4535i			1.76687i
$634$	3.94614			0.156721
$635$	20.0939	−	17.0670i	0.797402	−	0.677282i
$636$	−22.5535			−0.894304
$637$		0			0
$638$		−	1.94614i		−	0.0770485i
$639$	−21.1070			−0.834980
$640$	1.70429	−	1.44755i	0.0673678	−	0.0572196i
$641$	−12.3657			−0.488416			−0.244208	−	0.969723i	$-0.578528\pi$
$641$	−12.3657			−0.488416			−0.244208	+	0.969723i	$0.578528\pi$
$642$		−	16.7633i		−	0.661594i
$643$		−	46.8972i		−	1.84945i	−0.380642	−	0.924723i	$-0.624297\pi$
$643$		−	46.8972i		−	1.84945i	0.380642	−	0.924723i	$-0.375703\pi$
$644$	−34.1339			−1.34506
$645$	−19.6353	−	23.1178i	−0.773141	−	0.910262i
$646$	−5.71015			−0.224663
$647$		−	26.1878i		−	1.02955i	−0.857326	−	0.514774i	$-0.827876\pi$
$647$		−	26.1878i		−	1.02955i	0.857326	−	0.514774i	$-0.172124\pi$
$648$			3.81714i			0.149952i
$649$	1.94614			0.0763927
$650$		0			0
$651$	−22.7094			−0.890053
$652$			12.6074i			0.493742i
$653$			10.7633i			0.421200i	0.977572	+	0.210600i	$0.0675417\pi$
$653$			10.7633i			0.421200i	−0.977572	+	0.210600i	$0.932458\pi$
$654$	−1.98407			−0.0775834
$655$	24.5925	+	28.9541i	0.960908	+	1.13133i
$656$	−4.81714			−0.188078
$657$			32.2899i			1.25975i
$658$		−	1.67222i		−	0.0651898i
$659$	−31.4727			−1.22600			−0.613001	−	0.790082i	$-0.710038\pi$
$659$	−31.4727			−1.22600			−0.613001	+	0.790082i	$0.710038\pi$
$660$	9.86818	−	8.38164i	0.384118	−	0.326255i
$661$	−25.2147			−0.980739			−0.490369	−	0.871515i	$-0.663138\pi$
$661$	−25.2147			−0.980739			−0.490369	+	0.871515i	$0.663138\pi$
$662$			21.4245i			0.832687i
$663$		0			0
$664$	6.97307			0.270608
$665$	−7.26647	+	6.17185i	−0.281782	+	0.239334i
$666$	−3.18286			−0.123333
$667$			7.58043i			0.293515i
$668$			23.1609i			0.896120i
$669$	−71.8944			−2.77960
$670$	2.59143	+	3.05103i	0.100116	+	0.117872i
$671$	1.63429			0.0630909
$672$			12.6853i			0.489347i
$673$		−	23.2388i		−	0.895791i	−0.894086	−	0.447895i	$-0.852174\pi$
$673$		−	23.2388i		−	0.895791i	0.894086	−	0.447895i	$-0.147826\pi$
$674$	−11.2388			−0.432903
$675$	34.0211	+	5.57938i	1.30947	+	0.214750i
$676$		0			0
$677$		−	47.2629i		−	1.81646i	−0.418470	−	0.908231i	$-0.637433\pi$
$677$		−	47.2629i		−	1.81646i	0.418470	−	0.908231i	$-0.362567\pi$
$678$		−	11.5804i		−	0.444744i
$679$	−81.5308			−3.12886
$680$	8.49450	+	10.0010i	0.325749	+	0.383523i
$681$	−62.3217			−2.38817
$682$			3.58043i			0.137102i
$683$		−	6.97307i		−	0.266817i	−0.991061	−	0.133409i	$-0.957408\pi$
$683$		−	6.97307i		−	0.266817i	0.991061	−	0.133409i	$-0.0425922\pi$
$684$	−5.23672			−0.200231
$685$	−7.17468	+	6.09389i	−0.274130	+	0.232836i
$686$	−22.7792			−0.869714
$687$		−	7.61836i		−	0.290658i
$688$		−	4.68532i		−	0.178626i
$689$		0			0
$690$	−38.4376	+	32.6474i	−1.46329	+	1.24286i
$691$	32.2899			1.22836			0.614182	−	0.789164i	$-0.289486\pi$
$691$	32.2899			1.22836			0.614182	+	0.789164i	$0.289486\pi$
$692$		−	19.7902i		−	0.752311i
$693$			47.1609i			1.79149i
$694$	−16.9490			−0.643374
$695$	−8.93409	−	10.5186i	−0.338889	−	0.398993i
$696$	2.81714			0.106784
$697$		−	28.2678i		−	1.07072i
$698$			10.2119i			0.386526i
$699$	−84.0421			−3.17877
$700$	21.6194	+	3.54553i	0.817137	+	0.134009i
$701$	−0.521643			−0.0197022			−0.00985109	−	0.999951i	$-0.503136\pi$
$701$	−0.521643			−0.0197022			−0.00985109	+	0.999951i	$0.503136\pi$
$702$		0			0
$703$		−	0.575502i		−	0.0217055i
$704$	2.00000			0.0753778
$705$	−1.59939	−	1.88305i	−0.0602366	−	0.0709199i
$706$	−14.9511			−0.562691
$707$			62.8490i			2.36368i
$708$			2.81714i			0.105875i
$709$	−33.2147			−1.24740			−0.623702	−	0.781662i	$-0.714372\pi$
$709$	−33.2147			−1.24740			−0.623702	+	0.781662i	$0.714372\pi$
$710$	−6.68427	+	5.67736i	−0.250856	+	0.213067i
$711$	59.0531			2.21467
$712$			0.973070i			0.0364674i
$713$		−	13.9461i		−	0.522287i
$714$	−74.4397			−2.78584
$715$		0			0
$716$	6.17185			0.230653
$717$			6.17185i			0.230492i
$718$		−	11.8441i		−	0.442017i
$719$	4.26365			0.159007			0.0795036	−	0.996835i	$-0.474666\pi$
$719$	4.26365			0.159007			0.0795036	+	0.996835i	$0.474666\pi$
$720$	7.79021	+	9.17185i	0.290324	+	0.341815i
$721$	42.6612			1.58879
$722$			18.0531i			0.671868i
$723$		−	65.1388i		−	2.42254i
$724$	19.3706			0.719904
$725$	0.787388	−	4.80122i	0.0292429	−	0.178313i
$726$	−20.2657			−0.752132
$727$			47.5266i			1.76266i	0.472499	+	0.881331i	$0.343352\pi$
$727$			47.5266i			1.76266i	−0.472499	+	0.881331i	$0.656648\pi$
$728$		0			0
$729$	39.3437			1.45717
$730$	8.68532	+	10.2257i	0.321458	+	0.378471i
$731$	27.4943			1.01691
$732$			2.36571i			0.0874393i
$733$			44.8593i			1.65692i	0.560052	+	0.828458i	$0.310781\pi$
$733$			44.8593i			1.65692i	−0.560052	+	0.828458i	$0.689219\pi$
$734$	16.0539			0.592559
$735$	−60.1899	+	51.1229i	−2.22014	+	1.88570i
$736$	−7.79021			−0.287151
$737$			3.58043i			0.131887i
$738$		−	25.9241i		−	0.954281i
$739$	−18.4514			−0.678747			−0.339373	−	0.940652i	$-0.610215\pi$
$739$	−18.4514			−0.678747			−0.339373	+	0.940652i	$0.610215\pi$
$740$	−1.00796	+	0.856125i	−0.0370535	+	0.0314718i
$741$		0			0
$742$		−	34.1339i		−	1.25310i
$743$		−	14.2201i		−	0.521684i	−0.965382	−	0.260842i	$-0.916000\pi$
$743$		−	14.2201i		−	0.521684i	0.965382	−	0.260842i	$-0.0840001\pi$
$744$	−5.18286			−0.190013
$745$		0			0
$746$	6.87100			0.251565
$747$			37.5266i			1.37303i
$748$			11.7364i			0.429124i
$749$	25.3706			0.927023
$750$	27.7364	−	16.6853i	1.01279	−	0.609262i
$751$	−28.7951			−1.05075			−0.525375	−	0.850871i	$-0.676075\pi$
$751$	−28.7951			−1.05075			−0.525375	+	0.850871i	$0.676075\pi$
$752$		−	0.381642i		−	0.0139170i
$753$		−	1.21471i		−	0.0442665i
$754$		0			0
$755$	22.4406	+	26.4206i	0.816698	+	0.961545i
$756$	−30.2119			−1.09880
$757$			13.7364i			0.499256i	0.968342	+	0.249628i	$0.0803084\pi$
$757$			13.7364i			0.499256i	−0.968342	+	0.249628i	$0.919692\pi$
$758$		−	1.84407i		−	0.0669797i
$759$	−45.1070			−1.63728
$760$	−1.65839	+	1.40857i	−0.0601561	+	0.0510943i
$761$	−5.39264			−0.195483			−0.0977416	−	0.995212i	$-0.531162\pi$
$761$	−5.39264			−0.195483			−0.0977416	+	0.995212i	$0.531162\pi$
$762$			34.1339i			1.23654i
$763$		−	3.00282i		−	0.108710i
$764$	3.73635			0.135177
$765$	−53.8221	+	45.7143i	−1.94594	+	1.65281i
$766$	−9.25264			−0.334312
$767$		0			0
$768$			2.89511i			0.104468i
$769$	−2.34371			−0.0845163			−0.0422582	−	0.999107i	$-0.513455\pi$
$769$	−2.34371			−0.0845163			−0.0422582	+	0.999107i	$0.513455\pi$
$770$	12.6853	+	14.9351i	0.457147	+	0.538225i
$771$	−56.9131			−2.04968
$772$		−	15.3706i		−	0.553201i
$773$		−	29.3547i		−	1.05582i	−0.849302	−	0.527908i	$-0.822977\pi$
$773$		−	29.3547i		−	1.05582i	0.849302	−	0.527908i	$-0.177023\pi$
$774$	25.2147			0.906324
$775$	−1.44860	+	8.83307i	−0.0520354	+	0.317293i
$776$	−18.6074			−0.667965
$777$		−	7.50246i		−	0.269149i
$778$		−	21.2686i		−	0.762515i
$779$	4.68742			0.167944
$780$		0			0
$781$	−7.84407			−0.280683
$782$		−	45.7143i		−	1.63474i
$783$			6.70942i			0.239775i
$784$	−12.1988			−0.435671
$785$	15.2927	−	12.9890i	0.545819	−	0.463597i
$786$	−49.1850			−1.75437
$787$		−	34.6336i		−	1.23455i	−0.786746	−	0.617277i	$-0.788236\pi$
$787$		−	34.6336i		−	1.23455i	0.786746	−	0.617277i	$-0.211764\pi$
$788$			26.9890i			0.961443i
$789$	−31.1609			−1.10936
$790$	18.7012	−	15.8841i	0.665360	−	0.565131i
$791$	17.5266			0.623173
$792$			10.7633i			0.382457i
$793$		0			0
$794$	33.4727			1.18790
$795$	−32.6474	−	38.4376i	−1.15788	−	1.36324i
$796$	23.3168			0.826441
$797$			27.8221i			0.985508i	0.870169	+	0.492754i	$0.164010\pi$
$797$			27.8221i			0.985508i	−0.870169	+	0.492754i	$0.835990\pi$
$798$		−	12.3437i		−	0.436963i
$799$	2.23954			0.0792293
$800$	4.93409	+	0.809179i	0.174446	+	0.0286088i
$801$	−5.23672			−0.185030
$802$			17.7364i			0.626292i
$803$			12.0000i			0.423471i
$804$	−5.18286			−0.182785
$805$	−49.4107	−	58.1740i	−1.74150	−	2.05036i
$806$		0			0
$807$			42.7413i			1.50456i
$808$			14.3437i			0.504610i
$809$	23.1768			0.814852			0.407426	−	0.913238i	$-0.366426\pi$
$809$	23.1768			0.814852			0.407426	+	0.913238i	$0.366426\pi$
$810$	−6.50550	+	5.52552i	−0.228580	+	0.194147i
$811$	−36.0857			−1.26714			−0.633570	−	0.773685i	$-0.718411\pi$
$811$	−36.0857			−1.26714			−0.633570	+	0.773685i	$0.718411\pi$
$812$			4.26365i			0.149625i
$813$			78.8593i			2.76572i
$814$	−1.18286			−0.0414591
$815$	−21.4865	+	18.2498i	−0.752641	+	0.639263i
$816$	−16.9890			−0.594734
$817$			4.55915i			0.159504i
$818$		−	7.68249i		−	0.268612i
$819$		0			0
$820$	−6.97307	−	8.20979i	−0.243510	−	0.286698i
$821$	−38.3196			−1.33736			−0.668682	−	0.743549i	$-0.733141\pi$
$821$	−38.3196			−1.33736			−0.668682	+	0.743549i	$0.733141\pi$
$822$		−	12.1878i		−	0.425098i
$823$		−	53.3486i		−	1.85962i	−0.368044	−	0.929808i	$-0.619973\pi$
$823$		−	53.3486i		−	1.85962i	0.368044	−	0.929808i	$-0.380027\pi$
$824$	9.73635			0.339182
$825$	28.5694	+	4.68532i	0.994660	+	0.163122i
$826$	−4.26365			−0.148351
$827$		−	14.5053i		−	0.504398i	−0.967675	−	0.252199i	$-0.918846\pi$
$827$		−	14.5053i		−	0.504398i	0.967675	−	0.252199i	$-0.0811538\pi$
$828$		−	41.9241i		−	1.45696i
$829$	13.3926			0.465146			0.232573	−	0.972579i	$-0.425286\pi$
$829$	13.3926			0.465146			0.232573	+	0.972579i	$0.425286\pi$
$830$	10.0939	+	11.8841i	0.350364	+	0.412503i
$831$	8.31186			0.288335
$832$		0			0
$833$		−	71.5846i		−	2.48026i
$834$	17.8682			0.618724
$835$	−39.4727	+	33.5266i	−1.36601	+	1.16023i
$836$	−1.94614			−0.0673087
$837$		−	12.3437i		−	0.426661i
$838$			11.8061i			0.407836i
$839$	2.52164			0.0870568			0.0435284	−	0.999052i	$-0.486140\pi$
$839$	2.52164			0.0870568			0.0435284	+	0.999052i	$0.486140\pi$
$840$	−21.6194	+	18.3627i	−0.745940	+	0.633573i
$841$	−28.0531			−0.967349
$842$		−	26.3678i		−	0.908695i
$843$		−	15.6123i		−	0.537715i
$844$	−15.3547			−0.528531
$845$		0			0
$846$	2.05386			0.0706131
$847$		−	30.6715i		−	1.05388i
$848$		−	7.79021i		−	0.267517i
$849$	−72.2360			−2.47913
$850$	−4.74841	+	28.9541i	−0.162869	+	0.993118i
$851$	4.60736			0.157938
$852$		−	11.3547i		−	0.389006i
$853$			36.4078i			1.24658i	0.781990	+	0.623290i	$0.214205\pi$
$853$			36.4078i			1.24658i	−0.781990	+	0.623290i	$0.785795\pi$
$854$	−3.58043			−0.122520
$855$	−7.58043	−	8.92486i	−0.259245	−	0.305224i
$856$	5.79021			0.197905
$857$			21.4188i			0.731654i	0.930683	+	0.365827i	$0.119214\pi$
$857$			21.4188i			0.731654i	−0.930683	+	0.365827i	$0.880786\pi$
$858$		0			0
$859$	41.9461			1.43118			0.715592	−	0.698519i	$-0.246157\pi$
$859$	41.9461			1.43118			0.715592	+	0.698519i	$0.246157\pi$
$860$	7.98512	−	6.78225i	0.272290	−	0.231273i
$861$	61.1070			2.08252
$862$			1.71225i			0.0583194i
$863$			38.3278i			1.30469i	0.757921	+	0.652346i	$0.226215\pi$
$863$			38.3278i			1.30469i	−0.757921	+	0.652346i	$0.773785\pi$
$864$	−6.89511			−0.234576
$865$	33.7282	−	28.6474i	1.14679	−	0.974040i
$866$	11.9220			0.405127
$867$		−	50.4776i		−	1.71431i
$868$		−	7.84407i		−	0.266245i
$869$	21.9461			0.744472
$870$	4.07796	+	4.80122i	0.138256	+	0.162776i
$871$		0			0
$872$		−	0.685320i		−	0.0232078i
$873$		−	100.138i		−	3.38916i
$874$	7.58043			0.256412
$875$	25.2526	+	41.9780i	0.853695	+	1.41912i
$876$	−17.3706			−0.586900
$877$			43.3327i			1.46324i	0.681712	+	0.731621i	$0.261236\pi$
$877$			43.3327i			1.46324i	−0.681712	+	0.731621i	$0.738764\pi$
$878$		−	12.3437i		−	0.416580i
$879$	−72.1899			−2.43490
$880$	2.89511	+	3.40857i	0.0975940	+	0.114903i
$881$	1.09107			0.0367590			0.0183795	−	0.999831i	$-0.494149\pi$
$881$	1.09107			0.0367590			0.0183795	+	0.999831i	$0.494149\pi$
$882$		−	65.6495i		−	2.21053i
$883$		−	28.3735i		−	0.954843i	−0.878674	−	0.477422i	$-0.841571\pi$
$883$		−	28.3735i		−	0.954843i	0.878674	−	0.477422i	$-0.158429\pi$
$884$		0			0
$885$	−4.80122	+	4.07796i	−0.161391	+	0.137079i
$886$	28.1580			0.945987
$887$			4.50529i			0.151273i	0.997135	+	0.0756364i	$0.0240988\pi$
$887$			4.50529i			0.151273i	−0.997135	+	0.0756364i	$0.975901\pi$
$888$		−	1.71225i		−	0.0574593i
$889$	−51.6605			−1.73264
$890$	−1.65839	+	1.40857i	−0.0555894	+	0.0472154i
$891$	−7.63429			−0.255758
$892$		−	24.8331i		−	0.831473i
$893$			0.371364i			0.0124272i
$894$		0			0
$895$	8.93409	+	10.5186i	0.298634	+	0.351598i
$896$	−4.38164			−0.146380
$897$		0			0
$898$			29.0531i			0.969516i
$899$	−1.74200			−0.0580991
$900$	−4.35471	+	26.5535i	−0.145157	+	0.885117i
$901$	45.7143			1.52297
$902$		−	9.63429i		−	0.320787i
$903$			59.4348i			1.97787i
$904$	4.00000			0.133038
$905$	28.0400	+	33.0131i	0.932082	+	1.09739i
$906$	−44.8813			−1.49108
$907$		−	48.0503i		−	1.59548i	−0.602999	−	0.797742i	$-0.706028\pi$
$907$		−	48.0503i		−	1.59548i	0.602999	−	0.797742i	$-0.293972\pi$
$908$		−	21.5266i		−	0.714384i
$909$	−77.1927			−2.56032
$910$		0			0
$911$	12.5755			0.416645			0.208322	−	0.978060i	$-0.433200\pi$
$911$	12.5755			0.416645			0.208322	+	0.978060i	$0.433200\pi$
$912$		−	2.81714i		−	0.0932849i
$913$			13.9461i			0.461550i
$914$	11.5266			0.381265
$915$	−4.03185	+	3.42450i	−0.133289	+	0.113210i
$916$	2.63146			0.0869459
$917$		−	74.4397i		−	2.45822i
$918$		−	40.4617i		−	1.33544i
$919$	−23.6881			−0.781400			−0.390700	−	0.920518i	$-0.627767\pi$
$919$	−23.6881			−0.781400			−0.390700	+	0.920518i	$0.627767\pi$
$920$	−11.2767	−	13.2767i	−0.371783	−	0.437721i
$921$	−42.8972			−1.41351
$922$			28.4217i			0.936018i
$923$		0			0
$924$	−25.3706			−0.834633
$925$	−2.91816	−	0.478572i	−0.0959486	−	0.0157353i
$926$	−27.4727			−0.902809
$927$			52.3976i			1.72096i
$928$			0.973070i			0.0319426i
$929$	45.0850			1.47919			0.739595	−	0.673052i	$-0.235017\pi$
$929$	45.0850			1.47919			0.739595	+	0.673052i	$0.235017\pi$
$930$	−7.50246	−	8.83307i	−0.246015	−	0.289648i
$931$	11.8703			0.389033
$932$		−	29.0290i		−	0.950877i
$933$			37.2629i			1.21993i
$934$	−18.2098			−0.595842
$935$	−20.0021	+	16.9890i	−0.654139	+	0.555600i
$936$		0			0
$937$			28.7951i			0.940696i	0.882481	+	0.470348i	$0.155872\pi$
$937$			28.7951i			0.940696i	−0.882481	+	0.470348i	$0.844128\pi$
$938$		−	7.84407i		−	0.256118i
$939$	57.6764			1.88220
$940$	0.650427	−	0.552447i	0.0212146	−	0.0180188i
$941$	2.84690			0.0928062			0.0464031	−	0.998923i	$-0.485224\pi$
$941$	2.84690			0.0928062			0.0464031	+	0.998923i	$0.485224\pi$
$942$			25.9780i			0.846409i
$943$			37.5266i			1.22203i
$944$	−0.973070			−0.0316707
$945$	−43.7333	−	51.4897i	−1.42264	−	1.67496i
$946$	9.37064			0.304666
$947$		−	11.3168i		−	0.367746i	−0.982950	−	0.183873i	$-0.941136\pi$
$947$		−	11.3168i		−	0.367746i	0.982950	−	0.183873i	$-0.0588635\pi$
$948$			31.7682i			1.03178i
$949$		0			0
$950$	−4.80122	−	0.787388i	−0.155772	−	0.0255462i
$951$	−11.4245			−0.370465
$952$		−	25.7122i		−	0.833339i
$953$			28.4535i			0.921700i	0.887478	+	0.460850i	$0.152455\pi$
$953$			28.4535i			0.921700i	−0.887478	+	0.460850i	$0.847545\pi$
$954$	41.9241			1.35734
$955$	5.40857	+	6.36781i	0.175017	+	0.206058i
$956$	−2.13182			−0.0689481
$957$			5.63429i			0.182131i
$958$			33.6045i			1.08571i
$959$	18.4458			0.595645
$960$	−4.93409	+	4.19082i	−0.159247	+	0.135258i
$961$	−27.7951			−0.896617
$962$		0			0
$963$			31.1609i			1.00414i
$964$	22.4996			0.724665
$965$	26.1960	−	22.2498i	0.843278	−	0.716247i
$966$	98.8213			3.17952
$967$			1.48863i			0.0478713i	0.999714	+	0.0239356i	$0.00761968\pi$
$967$			1.48863i			0.0478713i	−0.999714	+	0.0239356i	$0.992380\pi$
$968$		−	7.00000i		−	0.224989i
$969$	16.5315			0.531068
$970$	−26.9351	−	31.7122i	−0.864835	−	1.01822i
$971$	49.6446			1.59317			0.796585	−	0.604527i	$-0.206638\pi$
$971$	49.6446			1.59317			0.796585	+	0.604527i	$0.206638\pi$
$972$			9.63429i			0.309020i
$973$			27.0429i			0.866954i
$974$	−8.00000			−0.256337
$975$		0			0
$976$	−0.817143			−0.0261561
$977$			39.6066i			1.26713i	0.773690	+	0.633564i	$0.218409\pi$
$977$			39.6066i			1.26713i	−0.773690	+	0.633564i	$0.781591\pi$
$978$		−	36.4996i		−	1.16713i
$979$	−1.94614			−0.0621989
$980$	−17.6584	−	20.7902i	−0.564077	−	0.664119i
$981$	3.68814			0.117753
$982$			19.8061i			0.632039i
$983$		−	0.725351i		−	0.0231351i	−0.999933	−	0.0115676i	$-0.996318\pi$
$983$		−	0.725351i		−	0.0231351i	0.999933	−	0.0115676i	$-0.00368215\pi$
$984$	13.9461			0.444587
$985$	−45.9970	+	39.0680i	−1.46559	+	1.24481i
$986$	−5.71015			−0.181848
$987$			4.84125i			0.154099i
$988$		0			0
$989$	−36.4996			−1.16062
$990$	−18.3437	+	15.5804i	−0.583001	+	0.495178i
$991$	−35.5046			−1.12784			−0.563920	−	0.825830i	$-0.690707\pi$
$991$	−35.5046			−1.12784			−0.563920	+	0.825830i	$0.690707\pi$
$992$		−	1.79021i		−	0.0568393i
$993$		−	62.0262i		−	1.96834i
$994$	17.1850			0.545074
$995$	33.7523	+	39.7385i	1.07002	+	1.25979i
$996$	−20.1878			−0.639674
$997$			10.4196i			0.329991i	0.986294	+	0.164996i	$0.0527610\pi$
$997$			10.4196i			0.329991i	−0.986294	+	0.164996i	$0.947239\pi$
$998$		−	9.12900i		−	0.288973i
$999$	4.07796			0.129021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.a.339.3		6
5.2	odd	4		8450.2.a.cc.1.3		3
5.3	odd	4		8450.2.a.bs.1.1		3
5.4	even	2	inner	1690.2.b.a.339.4		6
13.5	odd	4		1690.2.c.a.1689.6		6
13.8	odd	4		1690.2.c.d.1689.6		6
13.12	even	2		130.2.b.a.79.6	yes	6
39.38	odd	2		1170.2.e.f.469.1		6
52.51	odd	2		1040.2.d.b.209.1		6
65.12	odd	4		650.2.a.n.1.3		3
65.34	odd	4		1690.2.c.a.1689.1		6
65.38	odd	4		650.2.a.o.1.1		3
65.44	odd	4		1690.2.c.d.1689.1		6
65.64	even	2		130.2.b.a.79.1	✓	6
195.38	even	4		5850.2.a.cp.1.1		3
195.77	even	4		5850.2.a.cs.1.3		3
195.194	odd	2		1170.2.e.f.469.4		6
260.103	even	4		5200.2.a.cf.1.3		3
260.207	even	4		5200.2.a.ce.1.1		3
260.259	odd	2		1040.2.d.b.209.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.b.a.79.1	✓	6	65.64	even	2
130.2.b.a.79.6	yes	6	13.12	even	2
650.2.a.n.1.3		3	65.12	odd	4
650.2.a.o.1.1		3	65.38	odd	4
1040.2.d.b.209.1		6	52.51	odd	2
1040.2.d.b.209.6		6	260.259	odd	2
1170.2.e.f.469.1		6	39.38	odd	2
1170.2.e.f.469.4		6	195.194	odd	2
1690.2.b.a.339.3		6	1.1	even	1	trivial
1690.2.b.a.339.4		6	5.4	even	2	inner
1690.2.c.a.1689.1		6	65.34	odd	4
1690.2.c.a.1689.6		6	13.5	odd	4
1690.2.c.d.1689.1		6	65.44	odd	4
1690.2.c.d.1689.6		6	13.8	odd	4
5200.2.a.ce.1.1		3	260.207	even	4
5200.2.a.cf.1.3		3	260.103	even	4
5850.2.a.cp.1.1		3	195.38	even	4
5850.2.a.cs.1.3		3	195.77	even	4
8450.2.a.bs.1.1		3	5.3	odd	4
8450.2.a.cc.1.3		3	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +2.89511i q^{3} -1.00000 q^{4} +(-1.44755 - 1.70429i) q^{5} +2.89511 q^{6} +4.38164i q^{7} +1.00000i q^{8} -5.38164 q^{9} +(-1.70429 + 1.44755i) q^{10} -2.00000 q^{11} -2.89511i q^{12} +4.38164 q^{14} +(4.93409 - 4.19082i) q^{15} +1.00000 q^{16} +5.86818i q^{17} +5.38164i q^{18} -0.973070 q^{19} +(1.44755 + 1.70429i) q^{20} -12.6853 q^{21} +2.00000i q^{22} -7.79021i q^{23} -2.89511 q^{24} +(-0.809179 + 4.93409i) q^{25} -6.89511i q^{27} -4.38164i q^{28} -0.973070 q^{29} +(-4.19082 - 4.93409i) q^{30} +1.79021 q^{31} -1.00000i q^{32} -5.79021i q^{33} +5.86818 q^{34} +(7.46757 - 6.34266i) q^{35} +5.38164 q^{36} +0.591429i q^{37} +0.973070i q^{38} +(1.70429 - 1.44755i) q^{40} -4.81714 q^{41} +12.6853i q^{42} -4.68532i q^{43} +2.00000 q^{44} +(7.79021 + 9.17185i) q^{45} -7.79021 q^{46} -0.381642i q^{47} +2.89511i q^{48} -12.1988 q^{49} +(4.93409 + 0.809179i) q^{50} -16.9890 q^{51} -7.79021i q^{53} -6.89511 q^{54} +(2.89511 + 3.40857i) q^{55} -4.38164 q^{56} -2.81714i q^{57} +0.973070i q^{58} -0.973070 q^{59} +(-4.93409 + 4.19082i) q^{60} -0.817143 q^{61} -1.79021i q^{62} -23.5804i q^{63} -1.00000 q^{64} -5.79021 q^{66} -1.79021i q^{67} -5.86818i q^{68} +22.5535 q^{69} +(-6.34266 - 7.46757i) q^{70} +3.92204 q^{71} -5.38164i q^{72} -6.00000i q^{73} +0.591429 q^{74} +(-14.2847 - 2.34266i) q^{75} +0.973070 q^{76} -8.76328i q^{77} -10.9731 q^{79} +(-1.44755 - 1.70429i) q^{80} +3.81714 q^{81} +4.81714i q^{82} -6.97307i q^{83} +12.6853 q^{84} +(10.0010 - 8.49450i) q^{85} -4.68532 q^{86} -2.81714i q^{87} -2.00000i q^{88} +0.973070 q^{89} +(9.17185 - 7.79021i) q^{90} +7.79021i q^{92} +5.18286i q^{93} -0.381642 q^{94} +(1.40857 + 1.65839i) q^{95} +2.89511 q^{96} +18.6074i q^{97} +12.1988i q^{98} +10.7633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 10 q^{9} - 4 q^{10} - 12 q^{11} + 4 q^{14} + 16 q^{15} + 6 q^{16} + 4 q^{19} - 24 q^{21} - 16 q^{25} + 4 q^{29} - 14 q^{30} - 24 q^{31} + 8 q^{34} - 6 q^{35} + 10 q^{36} + 4 q^{40} - 4 q^{41}+ \cdots + 20 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 10 * q^9 - 4 * q^10 - 12 * q^11 + 4 * q^14 + 16 * q^15 + 6 * q^16 + 4 * q^19 - 24 * q^21 - 16 * q^25 + 4 * q^29 - 14 * q^30 - 24 * q^31 + 8 * q^34 - 6 * q^35 + 10 * q^36 + 4 * q^40 - 4 * q^41 + 12 * q^44 + 12 * q^45 - 12 * q^46 - 26 * q^49 + 16 * q^50 - 20 * q^51 - 24 * q^54 - 4 * q^56 + 4 * q^59 - 16 * q^60 + 20 * q^61 - 6 * q^64 + 56 * q^69 - 12 * q^70 + 16 * q^71 + 16 * q^74 - 10 * q^75 - 4 * q^76 - 56 * q^79 - 2 * q^81 + 24 * q^84 - 28 * q^85 + 24 * q^86 - 4 * q^89 - 2 * q^90 + 20 * q^94 - 4 * q^95 + 20 * q^99

Introduction

L-functions

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