LMFDB - Embedded newform 740.2.i.a.121.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(121,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 204x^{10} + 727x^{8} + 1008x^{6} + 426x^{4} + 64x^{2} + 3 $ x^14 + 24x^12 + 204x^10 + 727x^8 + 1008x^6 + 426x^4 + 64x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.6
Root			$-1.39878i$ of defining polynomial
Character	$\chi$	$=$	740.121
Dual form			740.2.i.a.581.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.13042 + 1.95795i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.38845 - 2.40487i) q^{7} +(-1.05570 + 1.82853i) q^{9} +3.65006 q^{11} +(2.34673 + 4.06465i) q^{13} +(1.13042 - 1.95795i) q^{15} +(-2.27125 + 3.93392i) q^{17} +(3.55811 + 6.16283i) q^{19} +(3.13907 - 5.43704i) q^{21} +3.14495 q^{23} +(-0.500000 + 0.866025i) q^{25} +2.00898 q^{27} +5.45368 q^{29} -1.74599 q^{31} +(4.12610 + 7.14661i) q^{33} +(-1.38845 + 2.40487i) q^{35} +(3.90987 - 4.65971i) q^{37} +(-5.30558 + 9.18954i) q^{39} +(-0.109792 - 0.190166i) q^{41} -6.03476 q^{43} +2.11140 q^{45} -8.40286 q^{47} +(-0.355611 + 0.615937i) q^{49} -10.2699 q^{51} +(3.45545 - 5.98501i) q^{53} +(-1.82503 - 3.16104i) q^{55} +(-8.04433 + 13.9332i) q^{57} +(0.792524 - 1.37269i) q^{59} +(-0.338386 - 0.586103i) q^{61} +5.86317 q^{63} +(2.34673 - 4.06465i) q^{65} +(-6.11900 - 10.5984i) q^{67} +(3.55512 + 6.15765i) q^{69} +(-0.433892 - 0.751522i) q^{71} -7.79501 q^{73} -2.26084 q^{75} +(-5.06794 - 8.77792i) q^{77} +(-1.52587 - 2.64288i) q^{79} +(5.43809 + 9.41905i) q^{81} +(-8.03468 + 13.9165i) q^{83} +4.54250 q^{85} +(6.16495 + 10.6780i) q^{87} +(1.38304 - 2.39549i) q^{89} +(6.51665 - 11.2872i) q^{91} +(-1.97371 - 3.41856i) q^{93} +(3.55811 - 6.16283i) q^{95} +12.3102 q^{97} +(-3.85337 + 6.67423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) $ 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.13042	+	1.95795i	0.652649	+	1.13042i	0.982478	+	0.186380i	$0.0596755\pi$
$3$	1.13042	+	1.95795i	0.652649	+	1.13042i	−0.329829	+	0.944041i	$0.606991\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.38845	−	2.40487i	−0.524786	−	0.908957i	−0.999583	−	0.0288614i	$-0.990812\pi$
$7$	−1.38845	−	2.40487i	−0.524786	−	0.908957i	0.474797	−	0.880095i	$-0.342521\pi$
$8$		0			0
$9$	−1.05570	+	1.82853i	−0.351900	+	0.609509i
$10$		0			0
$11$	3.65006			1.10053			0.550267	−	0.834989i	$-0.314526\pi$
$11$	3.65006			1.10053			0.550267	+	0.834989i	$0.314526\pi$
$12$		0			0
$13$	2.34673	+	4.06465i	0.650866	+	1.12733i	0.982913	+	0.184070i	$0.0589272\pi$
$13$	2.34673	+	4.06465i	0.650866	+	1.12733i	−0.332048	+	0.943263i	$0.607739\pi$
$14$		0			0
$15$	1.13042	−	1.95795i	0.291873	−	0.505539i
$16$		0			0
$17$	−2.27125	+	3.93392i	−0.550859	+	0.954115i	0.447354	+	0.894357i	$0.352366\pi$
$17$	−2.27125	+	3.93392i	−0.550859	+	0.954115i	−0.998213	+	0.0597583i	$0.980967\pi$
$18$		0			0
$19$	3.55811	+	6.16283i	0.816287	+	1.41385i	0.908400	+	0.418102i	$0.137304\pi$
$19$	3.55811	+	6.16283i	0.816287	+	1.41385i	−0.0921133	+	0.995749i	$0.529362\pi$
$20$		0			0
$21$	3.13907	−	5.43704i	0.685002	−	1.18646i
$22$		0			0
$23$	3.14495			0.655768			0.327884	−	0.944718i	$-0.393665\pi$
$23$	3.14495			0.655768			0.327884	+	0.944718i	$0.393665\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	2.00898			0.386628
$28$		0			0
$29$	5.45368			1.01272			0.506362	−	0.862321i	$-0.330990\pi$
$29$	5.45368			1.01272			0.506362	+	0.862321i	$0.330990\pi$
$30$		0			0
$31$	−1.74599			−0.313590			−0.156795	−	0.987631i	$-0.550116\pi$
$31$	−1.74599			−0.313590			−0.156795	+	0.987631i	$0.550116\pi$
$32$		0			0
$33$	4.12610	+	7.14661i	0.718262	+	1.24407i
$34$		0			0
$35$	−1.38845	+	2.40487i	−0.234692	+	0.406498i
$36$		0			0
$37$	3.90987	−	4.65971i	0.642779	−	0.766052i
$37$	3.90987	−	4.65971i	0.642779	−	0.766052i
$38$		0			0
$39$	−5.30558	+	9.18954i	−0.849573	+	1.47150i
$40$		0			0
$41$	−0.109792	−	0.190166i	−0.0171467	−	0.0296989i	0.857325	−	0.514776i	$-0.172125\pi$
$41$	−0.109792	−	0.190166i	−0.0171467	−	0.0296989i	−0.874471	+	0.485077i	$0.838792\pi$
$42$		0			0
$43$	−6.03476			−0.920292			−0.460146	−	0.887843i	$-0.652203\pi$
$43$	−6.03476			−0.920292			−0.460146	+	0.887843i	$0.652203\pi$
$44$		0			0
$45$	2.11140			0.314749
$46$		0			0
$47$	−8.40286			−1.22568			−0.612841	−	0.790206i	$-0.709974\pi$
$47$	−8.40286			−1.22568			−0.612841	+	0.790206i	$0.709974\pi$
$48$		0			0
$49$	−0.355611	+	0.615937i	−0.0508016	+	0.0879910i
$50$		0			0
$51$	−10.2699			−1.43807
$52$		0			0
$53$	3.45545	−	5.98501i	0.474642	−	0.822105i	−0.524936	−	0.851142i	$-0.675911\pi$
$53$	3.45545	−	5.98501i	0.474642	−	0.822105i	0.999578	+	0.0290370i	$0.00924407\pi$
$54$		0			0
$55$	−1.82503	−	3.16104i	−0.246087	−	0.426235i
$56$		0			0
$57$	−8.04433	+	13.9332i	−1.06550	+	1.84549i
$58$		0			0
$59$	0.792524	−	1.37269i	0.103178	−	0.178709i	−0.809814	−	0.586686i	$-0.800432\pi$
$59$	0.792524	−	1.37269i	0.103178	−	0.178709i	0.912992	+	0.407977i	$0.133766\pi$
$60$		0			0
$61$	−0.338386	−	0.586103i	−0.0433259	−	0.0750427i	0.843549	−	0.537052i	$-0.180462\pi$
$61$	−0.338386	−	0.586103i	−0.0433259	−	0.0750427i	−0.886875	+	0.462009i	$0.847129\pi$
$62$		0			0
$63$	5.86317			0.738690
$64$		0			0
$65$	2.34673	−	4.06465i	0.291076	−	0.504158i
$66$		0			0
$67$	−6.11900	−	10.5984i	−0.747555	−	1.29480i	−0.948991	−	0.315302i	$-0.897894\pi$
$67$	−6.11900	−	10.5984i	−0.747555	−	1.29480i	0.201436	−	0.979502i	$-0.435439\pi$
$68$		0			0
$69$	3.55512	+	6.15765i	0.427986	+	0.741293i
$70$		0			0
$71$	−0.433892	−	0.751522i	−0.0514935	−	0.0891893i	0.839130	−	0.543931i	$-0.183065\pi$
$71$	−0.433892	−	0.751522i	−0.0514935	−	0.0891893i	−0.890623	+	0.454742i	$0.849731\pi$
$72$		0			0
$73$	−7.79501			−0.912337			−0.456168	−	0.889893i	$-0.650779\pi$
$73$	−7.79501			−0.912337			−0.456168	+	0.889893i	$0.650779\pi$
$74$		0			0
$75$	−2.26084			−0.261059
$76$		0			0
$77$	−5.06794	−	8.77792i	−0.577545	−	1.00034i
$78$		0			0
$79$	−1.52587	−	2.64288i	−0.171673	−	0.297347i	0.767332	−	0.641250i	$-0.221584\pi$
$79$	−1.52587	−	2.64288i	−0.171673	−	0.297347i	−0.939005	+	0.343904i	$0.888251\pi$
$80$		0			0
$81$	5.43809	+	9.41905i	0.604233	+	1.04656i
$82$		0			0
$83$	−8.03468	+	13.9165i	−0.881921	+	1.52753i	−0.0327177	+	0.999465i	$0.510416\pi$
$83$	−8.03468	+	13.9165i	−0.881921	+	1.52753i	−0.849203	+	0.528067i	$0.822917\pi$
$84$		0			0
$85$	4.54250			0.492703
$86$		0			0
$87$	6.16495	+	10.6780i	0.660952	+	1.14480i
$88$		0			0
$89$	1.38304	−	2.39549i	0.146602	−	0.253922i	−0.783368	−	0.621559i	$-0.786500\pi$
$89$	1.38304	−	2.39549i	0.146602	−	0.253922i	0.929969	+	0.367637i	$0.119833\pi$
$90$		0			0
$91$	6.51665	−	11.2872i	0.683131	−	1.18322i
$92$		0			0
$93$	−1.97371	−	3.41856i	−0.204664	−	0.354488i
$94$		0			0
$95$	3.55811	−	6.16283i	0.365055	−	0.632293i
$96$		0			0
$97$	12.3102			1.24992			0.624958	−	0.780658i	$-0.285116\pi$
$97$	12.3102			1.24992			0.624958	+	0.780658i	$0.285116\pi$
$98$		0			0
$99$	−3.85337	+	6.67423i	−0.387278	+	0.670785i
$100$		0			0
$101$	13.2686			1.32027			0.660136	−	0.751146i	$-0.270499\pi$
$101$	13.2686			1.32027			0.660136	+	0.751146i	$0.270499\pi$
$102$		0			0
$103$	−15.6115			−1.53825			−0.769123	−	0.639100i	$-0.779307\pi$
$103$	−15.6115			−1.53825			−0.769123	+	0.639100i	$0.779307\pi$
$104$		0			0
$105$	−6.27815			−0.612685
$106$		0			0
$107$	3.72624	+	6.45404i	0.360230	+	0.623936i	0.987998	−	0.154464i	$-0.0493650\pi$
$107$	3.72624	+	6.45404i	0.360230	+	0.623936i	−0.627769	+	0.778400i	$0.716032\pi$
$108$		0			0
$109$	2.58823	−	4.48295i	0.247908	−	0.429389i	−0.715037	−	0.699086i	$-0.753590\pi$
$109$	2.58823	−	4.48295i	0.247908	−	0.429389i	0.962945	+	0.269697i	$0.0869237\pi$
$110$		0			0
$111$	13.5433	+	2.38788i	1.28547	+	0.226648i
$112$		0			0
$113$	7.84140	−	13.5817i	0.737657	−	1.27766i	−0.215891	−	0.976418i	$-0.569266\pi$
$113$	7.84140	−	13.5817i	0.737657	−	1.27766i	0.953548	−	0.301242i	$-0.0974012\pi$
$114$		0			0
$115$	−1.57248	−	2.72361i	−0.146634	−	0.253978i
$116$		0			0
$117$	−9.90978			−0.916159
$118$		0			0
$119$	12.6141			1.15633
$120$		0			0
$121$	2.32291			0.211174
$122$		0			0
$123$	0.248223	−	0.429935i	0.0223815	−	0.0387659i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	1.50667	−	2.60962i	0.133695	−	0.231567i	−0.791403	−	0.611295i	$-0.790649\pi$
$127$	1.50667	−	2.60962i	0.133695	−	0.231567i	0.925098	+	0.379728i	$0.123982\pi$
$128$		0			0
$129$	−6.82181	−	11.8157i	−0.600627	−	1.04032i
$130$		0			0
$131$	9.98041	−	17.2866i	0.871992	−	1.51034i	0.0120599	−	0.999927i	$-0.496161\pi$
$131$	9.98041	−	17.2866i	0.871992	−	1.51034i	0.859932	−	0.510408i	$-0.170506\pi$
$132$		0			0
$133$	9.88055	−	17.1136i	0.856753	−	1.48394i
$134$		0			0
$135$	−1.00449	−	1.73983i	−0.0864527	−	0.149740i
$136$		0			0
$137$	−14.7473			−1.25995			−0.629973	−	0.776617i	$-0.716934\pi$
$137$	−14.7473			−1.25995			−0.629973	+	0.776617i	$0.716934\pi$
$138$		0			0
$139$	−9.11621	+	15.7897i	−0.773226	+	1.33927i	0.162559	+	0.986699i	$0.448025\pi$
$139$	−9.11621	+	15.7897i	−0.773226	+	1.33927i	−0.935786	+	0.352569i	$0.885308\pi$
$140$		0			0
$141$	−9.49876	−	16.4523i	−0.799940	−	1.38554i
$142$		0			0
$143$	8.56569	+	14.8362i	0.716299	+	1.24067i
$144$		0			0
$145$	−2.72684	−	4.72303i	−0.226452	−	0.392226i
$146$		0			0
$147$	−1.60796			−0.132622
$148$		0			0
$149$	−5.36500			−0.439518			−0.219759	−	0.975554i	$-0.570527\pi$
$149$	−5.36500			−0.439518			−0.219759	+	0.975554i	$0.570527\pi$
$150$		0			0
$151$	−5.66740	−	9.81623i	−0.461207	−	0.798833i	0.537815	−	0.843063i	$-0.319250\pi$
$151$	−5.66740	−	9.81623i	−0.461207	−	0.798833i	−0.999021	+	0.0442299i	$0.985917\pi$
$152$		0			0
$153$	−4.79552	−	8.30608i	−0.387695	−	0.671507i
$154$		0			0
$155$	0.872997	+	1.51207i	0.0701208	+	0.121453i
$156$		0			0
$157$	−7.38331	+	12.7883i	−0.589252	+	1.02061i	0.405078	+	0.914282i	$0.367244\pi$
$157$	−7.38331	+	12.7883i	−0.589252	+	1.02061i	−0.994331	+	0.106333i	$0.966089\pi$
$158$		0			0
$159$	15.6244			1.23910
$160$		0			0
$161$	−4.36662	−	7.56321i	−0.344138	−	0.596065i
$162$		0			0
$163$	−5.99463	+	10.3830i	−0.469536	+	0.813260i	−0.999393	−	0.0348268i	$-0.988912\pi$
$163$	−5.99463	+	10.3830i	−0.469536	+	0.813260i	0.529858	+	0.848087i	$0.322245\pi$
$164$		0			0
$165$	4.12610	−	7.14661i	0.321216	−	0.556363i
$166$		0			0
$167$	0.943988	+	1.63503i	0.0730480	+	0.126523i	0.900236	−	0.435403i	$-0.143394\pi$
$167$	0.943988	+	1.63503i	0.0730480	+	0.126523i	−0.827188	+	0.561926i	$0.810061\pi$
$168$		0			0
$169$	−4.51427	+	7.81895i	−0.347252	+	0.601458i
$170$		0			0
$171$	−15.0252			−1.14901
$172$		0			0
$173$	5.40886	−	9.36842i	0.411228	−	0.712268i	−0.583796	−	0.811900i	$-0.698433\pi$
$173$	5.40886	−	9.36842i	0.411228	−	0.712268i	0.995024	+	0.0996322i	$0.0317666\pi$
$174$		0			0
$175$	2.77691			0.209915
$176$		0			0
$177$	3.58354			0.269356
$178$		0			0
$179$	−8.66609			−0.647734			−0.323867	−	0.946103i	$-0.604983\pi$
$179$	−8.66609			−0.647734			−0.323867	+	0.946103i	$0.604983\pi$
$180$		0			0
$181$	4.96194	+	8.59433i	0.368818	+	0.638811i	0.989381	−	0.145345i	$-0.0464293\pi$
$181$	4.96194	+	8.59433i	0.368818	+	0.638811i	−0.620563	+	0.784156i	$0.713096\pi$
$182$		0			0
$183$	0.765038	−	1.32508i	0.0565532	−	0.0979531i
$184$		0			0
$185$	−5.99036	−	1.05619i	−0.440420	−	0.0776527i
$186$		0			0
$187$	−8.29018	+	14.3590i	−0.606238	+	1.05004i
$188$		0			0
$189$	−2.78938	−	4.83134i	−0.202897	−	0.351428i
$190$		0			0
$191$	15.6920			1.13543			0.567716	−	0.823224i	$-0.307827\pi$
$191$	15.6920			1.13543			0.567716	+	0.823224i	$0.307827\pi$
$192$		0			0
$193$	−13.9344			−1.00302			−0.501510	−	0.865152i	$-0.667222\pi$
$193$	−13.9344			−1.00302			−0.501510	+	0.865152i	$0.667222\pi$
$194$		0			0
$195$	10.6112			0.759881
$196$		0			0
$197$	4.92470	−	8.52983i	0.350870	−	0.607725i	−0.635532	−	0.772075i	$-0.719219\pi$
$197$	4.92470	−	8.52983i	0.350870	−	0.607725i	0.986402	+	0.164350i	$0.0525525\pi$
$198$		0			0
$199$	−15.2654			−1.08213			−0.541067	−	0.840980i	$-0.681979\pi$
$199$	−15.2654			−1.08213			−0.541067	+	0.840980i	$0.681979\pi$
$200$		0			0
$201$	13.8341	−	23.9614i	0.975782	−	1.69010i
$202$		0			0
$203$	−7.57219	−	13.1154i	−0.531463	−	0.920522i
$204$		0			0
$205$	−0.109792	+	0.190166i	−0.00766823	+	0.0132818i
$206$		0			0
$207$	−3.32013	+	5.75063i	−0.230765	+	0.399697i
$208$		0			0
$209$	12.9873	+	22.4947i	0.898351	+	1.55599i
$210$		0			0
$211$	−19.5301			−1.34451			−0.672254	−	0.740321i	$-0.734674\pi$
$211$	−19.5301			−1.34451			−0.672254	+	0.740321i	$0.734674\pi$
$212$		0			0
$213$	0.980960	−	1.69907i	0.0672143	−	0.116419i
$214$		0			0
$215$	3.01738	+	5.22625i	0.205784	+	0.356428i
$216$		0			0
$217$	2.42423	+	4.19889i	0.164568	+	0.285039i
$218$		0			0
$219$	−8.81164	−	15.2622i	−0.595435	−	1.03132i
$220$		0			0
$221$	−21.3200			−1.43414
$222$		0			0
$223$	−22.7756			−1.52517			−0.762584	−	0.646890i	$-0.776069\pi$
$223$	−22.7756			−1.52517			−0.762584	+	0.646890i	$0.776069\pi$
$224$		0			0
$225$	−1.05570	−	1.82853i	−0.0703801	−	0.121902i
$226$		0			0
$227$	7.35119	+	12.7326i	0.487915	+	0.845094i	0.999903	−	0.0138984i	$-0.00442413\pi$
$227$	7.35119	+	12.7326i	0.487915	+	0.845094i	−0.511988	+	0.858993i	$0.671091\pi$
$228$		0			0
$229$	−12.6769	−	21.9570i	−0.837711	−	1.45096i	−0.891804	−	0.452423i	$-0.850560\pi$
$229$	−12.6769	−	21.9570i	−0.837711	−	1.45096i	0.0540924	−	0.998536i	$-0.482773\pi$
$230$		0			0
$231$	11.4578	−	19.8455i	0.753868	−	1.30574i
$232$		0			0
$233$	19.2556			1.26148			0.630738	−	0.775996i	$-0.282752\pi$
$233$	19.2556			1.26148			0.630738	+	0.775996i	$0.282752\pi$
$234$		0			0
$235$	4.20143	+	7.27709i	0.274071	+	0.474705i
$236$		0			0
$237$	3.44974	−	5.97512i	0.224085	−	0.388126i
$238$		0			0
$239$	13.4323	−	23.2654i	0.868864	−	1.50492i	0.00570533	−	0.999984i	$-0.498184\pi$
$239$	13.4323	−	23.2654i	0.868864	−	1.50492i	0.863159	−	0.504933i	$-0.168483\pi$
$240$		0			0
$241$	−5.47133	−	9.47663i	−0.352440	−	0.610443i	0.634237	−	0.773139i	$-0.281314\pi$
$241$	−5.47133	−	9.47663i	−0.352440	−	0.610443i	−0.986676	+	0.162696i	$0.947981\pi$
$242$		0			0
$243$	−9.28120	+	16.0755i	−0.595389	+	1.03124i
$244$		0			0
$245$	0.711223			0.0454383
$246$		0			0
$247$	−16.6998	+	28.9250i	−1.06259	+	1.84045i
$248$		0			0
$249$	−36.3303			−2.30234
$250$		0			0
$251$	1.98639			0.125380			0.0626898	−	0.998033i	$-0.480032\pi$
$251$	1.98639			0.125380			0.0626898	+	0.998033i	$0.480032\pi$
$252$		0			0
$253$	11.4793			0.721694
$254$		0			0
$255$	5.13493	+	8.89396i	0.321562	+	0.556961i
$256$		0			0
$257$	−9.12955	+	15.8128i	−0.569486	+	0.986378i	0.427131	+	0.904190i	$0.359524\pi$
$257$	−9.12955	+	15.8128i	−0.569486	+	0.986378i	−0.996617	+	0.0821885i	$0.973809\pi$
$258$		0			0
$259$	−16.6347	−	2.93295i	−1.03363	−	0.182244i
$260$		0			0
$261$	−5.75746	+	9.97221i	−0.356378	+	0.617264i
$262$		0			0
$263$	6.14097	+	10.6365i	0.378668	+	0.655873i	0.990869	−	0.134830i	$-0.0430488\pi$
$263$	6.14097	+	10.6365i	0.378668	+	0.655873i	−0.612200	+	0.790703i	$0.709715\pi$
$264$		0			0
$265$	−6.91090			−0.424533
$266$		0			0
$267$	6.25366			0.382718
$268$		0			0
$269$	−19.6819			−1.20003			−0.600014	−	0.799990i	$-0.704838\pi$
$269$	−19.6819			−1.20003			−0.600014	+	0.799990i	$0.704838\pi$
$270$		0			0
$271$	11.0364	−	19.1157i	0.670416	−	1.16119i	−0.307371	−	0.951590i	$-0.599449\pi$
$271$	11.0364	−	19.1157i	0.670416	−	1.16119i	0.977786	−	0.209604i	$-0.0672175\pi$
$272$		0			0
$273$	29.4662			1.78338
$274$		0			0
$275$	−1.82503	+	3.16104i	−0.110053	+	0.190618i
$276$		0			0
$277$	6.33743	+	10.9767i	0.380779	+	0.659529i	0.991174	−	0.132569i	$-0.0423225\pi$
$277$	6.33743	+	10.9767i	0.380779	+	0.659529i	−0.610395	+	0.792097i	$0.708989\pi$
$278$		0			0
$279$	1.84325	−	3.19260i	0.110352	−	0.191136i
$280$		0			0
$281$	11.7500	−	20.3516i	0.700948	−	1.21408i	−0.267186	−	0.963645i	$-0.586094\pi$
$281$	11.7500	−	20.3516i	0.700948	−	1.21408i	0.968134	−	0.250433i	$-0.0805728\pi$
$282$		0			0
$283$	−2.99288	−	5.18382i	−0.177908	−	0.308146i	0.763256	−	0.646097i	$-0.223600\pi$
$283$	−2.99288	−	5.18382i	−0.177908	−	0.308146i	−0.941164	+	0.337951i	$0.890266\pi$
$284$		0			0
$285$	16.0887			0.953009
$286$		0			0
$287$	−0.304883	+	0.528073i	−0.0179967	+	0.0311712i
$288$		0			0
$289$	−1.81714	−	3.14738i	−0.106890	−	0.185140i
$290$		0			0
$291$	13.9158	+	24.1028i	0.815756	+	1.41293i
$292$		0			0
$293$	−10.7917	−	18.6917i	−0.630456	−	1.09198i	−0.987459	−	0.157878i	$-0.949535\pi$
$293$	−10.7917	−	18.6917i	−0.630456	−	1.09198i	0.357003	−	0.934103i	$-0.383799\pi$
$294$		0			0
$295$	−1.58505			−0.0922851
$296$		0			0
$297$	7.33289			0.425497
$298$		0			0
$299$	7.38035	+	12.7831i	0.426817	+	0.739268i
$300$		0			0
$301$	8.37899	+	14.5128i	0.482957	+	0.836506i
$302$		0			0
$303$	14.9991	+	25.9791i	0.861673	+	1.49246i
$304$		0			0
$305$	−0.338386	+	0.586103i	−0.0193760	+	0.0335601i
$306$		0			0
$307$	13.8693			0.791561			0.395781	−	0.918345i	$-0.370474\pi$
$307$	13.8693			0.791561			0.395781	+	0.918345i	$0.370474\pi$
$308$		0			0
$309$	−17.6476	−	30.5665i	−1.00393	−	1.73887i
$310$		0			0
$311$	−6.87157	+	11.9019i	−0.389651	+	0.674895i	−0.992402	−	0.123034i	$-0.960738\pi$
$311$	−6.87157	+	11.9019i	−0.389651	+	0.674895i	0.602752	+	0.797929i	$0.294071\pi$
$312$		0			0
$313$	3.19093	−	5.52686i	0.180362	−	0.312397i	−0.761642	−	0.647998i	$-0.775606\pi$
$313$	3.19093	−	5.52686i	0.180362	−	0.312397i	0.942004	+	0.335602i	$0.108940\pi$
$314$		0			0
$315$	−2.93159	−	5.07765i	−0.165176	−	0.286093i
$316$		0			0
$317$	5.41315	−	9.37585i	0.304033	−	0.526600i	−0.673013	−	0.739631i	$-0.735000\pi$
$317$	5.41315	−	9.37585i	0.304033	−	0.526600i	0.977045	+	0.213031i	$0.0683335\pi$
$318$		0			0
$319$	19.9062			1.11454
$320$		0			0
$321$	−8.42445	+	14.5916i	−0.470207	+	0.814422i
$322$		0			0
$323$	−32.3254			−1.79863
$324$		0			0
$325$	−4.69346			−0.260346
$326$		0			0
$327$	11.7032			0.647186
$328$		0			0
$329$	11.6670	+	20.2078i	0.643222	+	1.11409i
$330$		0			0
$331$	13.4748	−	23.3391i	0.740644	−	1.28283i	−0.211558	−	0.977365i	$-0.567854\pi$
$331$	13.4748	−	23.3391i	0.740644	−	1.28283i	0.952202	−	0.305468i	$-0.0988129\pi$
$332$		0			0
$333$	4.39276	+	12.0686i	0.240722	+	0.661353i
$334$		0			0
$335$	−6.11900	+	10.5984i	−0.334317	+	0.579054i
$336$		0			0
$337$	6.14610	+	10.6454i	0.334799	+	0.579890i	0.983446	−	0.181200i	$-0.0579981\pi$
$337$	6.14610	+	10.6454i	0.334799	+	0.579890i	−0.648647	+	0.761089i	$0.724665\pi$
$338$		0			0
$339$	35.4563			1.92572
$340$		0			0
$341$	−6.37297			−0.345116
$342$		0			0
$343$	−17.4634			−0.942933
$344$		0			0
$345$	3.55512	−	6.15765i	0.191401	−	0.331517i
$346$		0			0
$347$	−1.34170			−0.0720265			−0.0360132	−	0.999351i	$-0.511466\pi$
$347$	−1.34170			−0.0720265			−0.0360132	+	0.999351i	$0.511466\pi$
$348$		0			0
$349$	−2.42263	+	4.19613i	−0.129681	+	0.224614i	−0.923553	−	0.383471i	$-0.874729\pi$
$349$	−2.42263	+	4.19613i	−0.129681	+	0.224614i	0.793872	+	0.608085i	$0.208062\pi$
$350$		0			0
$351$	4.71453	+	8.16581i	0.251643	+	0.435858i
$352$		0			0
$353$	−6.60495	+	11.4401i	−0.351546	+	0.608896i	−0.986521	−	0.163637i	$-0.947677\pi$
$353$	−6.60495	+	11.4401i	−0.351546	+	0.608896i	0.634974	+	0.772533i	$0.281011\pi$
$354$		0			0
$355$	−0.433892	+	0.751522i	−0.0230286	+	0.0398867i
$356$		0			0
$357$	14.2592	+	24.6977i	0.754679	+	1.30714i
$358$		0			0
$359$	19.8008			1.04505			0.522523	−	0.852625i	$-0.324991\pi$
$359$	19.8008			1.04505			0.522523	+	0.852625i	$0.324991\pi$
$360$		0			0
$361$	−15.8203	+	27.4016i	−0.832649	+	1.44219i
$362$		0			0
$363$	2.62587	+	4.54814i	0.137822	+	0.238715i
$364$		0			0
$365$	3.89750	+	6.75068i	0.204005	+	0.353347i
$366$		0			0
$367$	−16.4486	−	28.4898i	−0.858610	−	1.48716i	−0.873255	−	0.487263i	$-0.837995\pi$
$367$	−16.4486	−	28.4898i	−0.858610	−	1.48716i	0.0146450	−	0.999893i	$-0.495338\pi$
$368$		0			0
$369$	0.463631			0.0241357
$370$		0			0
$371$	−19.1909			−0.996344
$372$		0			0
$373$	11.4751	+	19.8755i	0.594160	+	1.02912i	0.993665	+	0.112385i	$0.0358489\pi$
$373$	11.4751	+	19.8755i	0.594160	+	1.02912i	−0.399504	+	0.916731i	$0.630818\pi$
$374$		0			0
$375$	1.13042	+	1.95795i	0.0583747	+	0.101108i
$376$		0			0
$377$	12.7983	+	22.1673i	0.659147	+	1.14168i
$378$		0			0
$379$	−10.4292	+	18.0639i	−0.535711	+	0.927878i	0.463418	+	0.886140i	$0.346623\pi$
$379$	−10.4292	+	18.0639i	−0.535711	+	0.927878i	−0.999129	+	0.0417381i	$0.986710\pi$
$380$		0			0
$381$	6.81267			0.349023
$382$		0			0
$383$	−10.6319	−	18.4150i	−0.543264	−	0.940961i	−0.998714	−	0.0506995i	$-0.983855\pi$
$383$	−10.6319	−	18.4150i	−0.543264	−	0.940961i	0.455450	−	0.890261i	$-0.349478\pi$
$384$		0			0
$385$	−5.06794	+	8.77792i	−0.258286	+	0.447364i
$386$		0			0
$387$	6.37090	−	11.0347i	0.323851	−	0.560926i
$388$		0			0
$389$	1.43253	+	2.48122i	0.0726324	+	0.125803i	0.900054	−	0.435778i	$-0.143527\pi$
$389$	1.43253	+	2.48122i	0.0726324	+	0.125803i	−0.827422	+	0.561581i	$0.810193\pi$
$390$		0			0
$391$	−7.14297	+	12.3720i	−0.361235	+	0.625678i
$392$		0			0
$393$	45.1282			2.27642
$394$		0			0
$395$	−1.52587	+	2.64288i	−0.0767746	+	0.132978i
$396$		0			0
$397$	25.5205			1.28084			0.640418	−	0.768026i	$-0.278761\pi$
$397$	25.5205			1.28084			0.640418	+	0.768026i	$0.278761\pi$
$398$		0			0
$399$	44.6767			2.23663
$400$		0			0
$401$	28.0354			1.40002			0.700010	−	0.714133i	$-0.253179\pi$
$401$	28.0354			1.40002			0.700010	+	0.714133i	$0.253179\pi$
$402$		0			0
$403$	−4.09737	−	7.09686i	−0.204105	−	0.353520i
$404$		0			0
$405$	5.43809	−	9.41905i	0.270221	−	0.468037i
$406$		0			0
$407$	14.2712	−	17.0082i	0.707399	−	0.843066i
$408$		0			0
$409$	17.3809	−	30.1047i	0.859433	−	1.48858i	−0.0130384	−	0.999915i	$-0.504150\pi$
$409$	17.3809	−	30.1047i	0.859433	−	1.48858i	0.872471	−	0.488666i	$-0.162516\pi$
$410$		0			0
$411$	−16.6706	−	28.8744i	−0.822302	−	1.42427i
$412$		0			0
$413$	−4.40153			−0.216585
$414$		0			0
$415$	16.0694			0.788814
$416$		0			0
$417$	−41.2206			−2.01858
$418$		0			0
$419$	11.9408	−	20.6821i	0.583346	−	1.01038i	−0.411734	−	0.911304i	$-0.635077\pi$
$419$	11.9408	−	20.6821i	0.583346	−	1.01038i	0.995079	−	0.0990802i	$-0.0315900\pi$
$420$		0			0
$421$	27.5876			1.34454			0.672269	−	0.740307i	$-0.265320\pi$
$421$	27.5876			1.34454			0.672269	+	0.740307i	$0.265320\pi$
$422$		0			0
$423$	8.87090	−	15.3649i	0.431318	−	0.747065i
$424$		0			0
$425$	−2.27125	−	3.93392i	−0.110172	−	0.190823i
$426$		0			0
$427$	−0.939668	+	1.62755i	−0.0454737	+	0.0787628i
$428$		0			0
$429$	−19.3657	+	33.5423i	−0.934983	+	1.61944i
$430$		0			0
$431$	6.56065	+	11.3634i	0.316016	+	0.547355i	0.979653	−	0.200700i	$-0.0643215\pi$
$431$	6.56065	+	11.3634i	0.316016	+	0.547355i	−0.663637	+	0.748054i	$0.730988\pi$
$432$		0			0
$433$	−11.2730			−0.541748			−0.270874	−	0.962615i	$-0.587313\pi$
$433$	−11.2730			−0.541748			−0.270874	+	0.962615i	$0.587313\pi$
$434$		0			0
$435$	6.16495	−	10.6780i	0.295587	−	0.511972i
$436$		0			0
$437$	11.1901	+	19.3818i	0.535295	+	0.927158i
$438$		0			0
$439$	3.57967	+	6.20017i	0.170848	+	0.295918i	0.938717	−	0.344690i	$-0.112016\pi$
$439$	3.57967	+	6.20017i	0.170848	+	0.295918i	−0.767868	+	0.640608i	$0.778683\pi$
$440$		0			0
$441$	−0.750838	−	1.30049i	−0.0357542	−	0.0619281i
$442$		0			0
$443$	−15.5675			−0.739636			−0.369818	−	0.929104i	$-0.620580\pi$
$443$	−15.5675			−0.739636			−0.369818	+	0.929104i	$0.620580\pi$
$444$		0			0
$445$	−2.76608			−0.131125
$446$		0			0
$447$	−6.06470	−	10.5044i	−0.286851	−	0.496840i
$448$		0			0
$449$	20.2874	+	35.1388i	0.957421	+	1.65830i	0.728727	+	0.684804i	$0.240112\pi$
$449$	20.2874	+	35.1388i	0.957421	+	1.65830i	0.228695	+	0.973498i	$0.426554\pi$
$450$		0			0
$451$	−0.400748	−	0.694116i	−0.0188705	−	0.0326846i
$452$		0			0
$453$	12.8131	−	22.1929i	0.602012	−	1.04271i
$454$		0			0
$455$	−13.0333			−0.611011
$456$		0			0
$457$	−10.0301	−	17.3726i	−0.469187	−	0.812656i	0.530192	−	0.847878i	$-0.322120\pi$
$457$	−10.0301	−	17.3726i	−0.469187	−	0.812656i	−0.999380	+	0.0352211i	$0.988786\pi$
$458$		0			0
$459$	−4.56289	+	7.90316i	−0.212978	+	0.368888i
$460$		0			0
$461$	−10.7214	+	18.5701i	−0.499347	+	0.864895i	−1.00000		0.000753292i	$-0.999760\pi$
$461$	−10.7214	+	18.5701i	−0.499347	+	0.864895i	0.500652	+	0.865649i	$0.333094\pi$
$462$		0			0
$463$	8.85955	+	15.3452i	0.411738	+	0.713152i	0.995080	−	0.0990751i	$-0.0315884\pi$
$463$	8.85955	+	15.3452i	0.411738	+	0.713152i	−0.583342	+	0.812227i	$0.698255\pi$
$464$		0			0
$465$	−1.97371	+	3.41856i	−0.0915284	+	0.158532i
$466$		0			0
$467$	4.34021			0.200841			0.100420	−	0.994945i	$-0.467981\pi$
$467$	4.34021			0.200841			0.100420	+	0.994945i	$0.467981\pi$
$468$		0			0
$469$	−16.9919	+	29.4309i	−0.784614	+	1.35899i
$470$		0			0
$471$	−33.3850			−1.53830
$472$		0			0
$473$	−22.0272			−1.01281
$474$		0			0
$475$	−7.11622			−0.326515
$476$		0			0
$477$	7.29584	+	12.6368i	0.334054	+	0.578598i
$478$		0			0
$479$	−10.3402	+	17.9097i	−0.472455	+	0.818315i	−0.999503	−	0.0315198i	$-0.989965\pi$
$479$	−10.3402	+	17.9097i	−0.472455	+	0.818315i	0.527048	+	0.849835i	$0.323299\pi$
$480$		0			0
$481$	28.1155	+	4.95719i	1.28196	+	0.226028i
$482$		0			0
$483$	9.87224	−	17.0992i	0.449202	−	0.778041i
$484$		0			0
$485$	−6.15512	−	10.6610i	−0.279490	−	0.484090i
$486$		0			0
$487$	−28.8185			−1.30589			−0.652945	−	0.757406i	$-0.726467\pi$
$487$	−28.8185			−1.30589			−0.652945	+	0.757406i	$0.726467\pi$
$488$		0			0
$489$	−27.1058			−1.22577
$490$		0			0
$491$	−6.07413			−0.274122			−0.137061	−	0.990563i	$-0.543766\pi$
$491$	−6.07413			−0.274122			−0.137061	+	0.990563i	$0.543766\pi$
$492$		0			0
$493$	−12.3867	+	21.4543i	−0.557867	+	0.966255i
$494$		0			0
$495$	7.70674			0.346392
$496$		0			0
$497$	−1.20488	+	2.08691i	−0.0540462	+	0.0936107i
$498$		0			0
$499$	−19.9278	−	34.5159i	−0.892089	−	1.54514i	−0.837366	−	0.546642i	$-0.815906\pi$
$499$	−19.9278	−	34.5159i	−0.892089	−	1.54514i	−0.0547225	−	0.998502i	$-0.517427\pi$
$500$		0			0
$501$	−2.13421	+	3.69655i	−0.0953493	+	0.165150i
$502$		0			0
$503$	9.88028	−	17.1131i	0.440540	−	0.763038i	−0.557190	−	0.830385i	$-0.688120\pi$
$503$	9.88028	−	17.1131i	0.440540	−	0.763038i	0.997730	+	0.0673477i	$0.0214537\pi$
$504$		0			0
$505$	−6.63428	−	11.4909i	−0.295222	−	0.511339i
$506$		0			0
$507$	−20.4121			−0.906534
$508$		0			0
$509$	−16.5275	+	28.6265i	−0.732568	+	1.26885i	0.223214	+	0.974770i	$0.428345\pi$
$509$	−16.5275	+	28.6265i	−0.732568	+	1.26885i	−0.955782	+	0.294076i	$0.904988\pi$
$510$		0			0
$511$	10.8230	+	18.7460i	0.478782	+	0.829275i
$512$		0			0
$513$	7.14817	+	12.3810i	0.315600	+	0.546634i
$514$		0			0
$515$	7.80575	+	13.5200i	0.343962	+	0.595760i
$516$		0			0
$517$	−30.6709			−1.34890
$518$		0			0
$519$	24.4572			1.07355
$520$		0			0
$521$	−1.27784	−	2.21328i	−0.0559832	−	0.0969657i	0.836676	−	0.547699i	$-0.184496\pi$
$521$	−1.27784	−	2.21328i	−0.0559832	−	0.0969657i	−0.892659	+	0.450733i	$0.851163\pi$
$522$		0			0
$523$	−9.22576	−	15.9795i	−0.403415	−	0.698734i	0.590721	−	0.806876i	$-0.298843\pi$
$523$	−9.22576	−	15.9795i	−0.403415	−	0.698734i	−0.994136	+	0.108141i	$0.965510\pi$
$524$		0			0
$525$	3.13907	+	5.43704i	0.137000	+	0.237292i
$526$		0			0
$527$	3.96558	−	6.86859i	0.172744	−	0.299201i
$528$		0			0
$529$	−13.1093			−0.569968
$530$		0			0
$531$	1.67334	+	2.89830i	0.0726166	+	0.125776i
$532$		0			0
$533$	0.515305	−	0.892535i	0.0223204	−	0.0386600i
$534$		0			0
$535$	3.72624	−	6.45404i	0.161100	−	0.279033i
$536$		0			0
$537$	−9.79633	−	16.9677i	−0.422743	−	0.732212i
$538$		0			0
$539$	−1.29800	+	2.24820i	−0.0559089	+	0.0968370i
$540$		0			0
$541$	−33.7309			−1.45020			−0.725102	−	0.688641i	$-0.758207\pi$
$541$	−33.7309			−1.45020			−0.725102	+	0.688641i	$0.758207\pi$
$542$		0			0
$543$	−11.2181	+	19.4304i	−0.481417	+	0.833838i
$544$		0			0
$545$	−5.17646			−0.221735
$546$		0			0
$547$	−0.515707			−0.0220501			−0.0110250	−	0.999939i	$-0.503509\pi$
$547$	−0.515707			−0.0220501			−0.0110250	+	0.999939i	$0.503509\pi$
$548$		0			0
$549$	1.42894			0.0609857
$550$		0			0
$551$	19.4048	+	33.6101i	0.826673	+	1.43184i
$552$		0			0
$553$	−4.23719	+	7.33903i	−0.180184	+	0.312087i
$554$		0			0
$555$	−4.70366	−	12.9227i	−0.199659	−	0.548540i
$556$		0			0
$557$	18.5543	−	32.1370i	0.786171	−	1.36169i	−0.142127	−	0.989848i	$-0.545394\pi$
$557$	18.5543	−	32.1370i	0.786171	−	1.36169i	0.928297	−	0.371839i	$-0.121273\pi$
$558$		0			0
$559$	−14.1619	−	24.5292i	−0.598986	−	1.03747i
$560$		0			0
$561$	−37.4856			−1.58264
$562$		0			0
$563$	4.86469			0.205022			0.102511	−	0.994732i	$-0.467312\pi$
$563$	4.86469			0.205022			0.102511	+	0.994732i	$0.467312\pi$
$564$		0			0
$565$	−15.6828			−0.659780
$566$		0			0
$567$	15.1011	−	26.1559i	0.634186	−	1.09844i
$568$		0			0
$569$	21.1284			0.885747			0.442873	−	0.896584i	$-0.353959\pi$
$569$	21.1284			0.885747			0.442873	+	0.896584i	$0.353959\pi$
$570$		0			0
$571$	−1.12931	+	1.95602i	−0.0472601	+	0.0818569i	−0.888688	−	0.458513i	$-0.848382\pi$
$571$	−1.12931	+	1.95602i	−0.0472601	+	0.0818569i	0.841428	+	0.540370i	$0.181716\pi$
$572$		0			0
$573$	17.7385	+	30.7241i	0.741038	+	1.28352i
$574$		0			0
$575$	−1.57248	+	2.72361i	−0.0655768	+	0.113582i
$576$		0			0
$577$	1.87251	−	3.24329i	0.0779538	−	0.135020i	−0.824413	−	0.565988i	$-0.808495\pi$
$577$	1.87251	−	3.24329i	0.0779538	−	0.135020i	0.902367	+	0.430969i	$0.141828\pi$
$578$		0			0
$579$	−15.7517	−	27.2828i	−0.654619	−	1.13383i
$580$		0			0
$581$	44.6231			1.85128
$582$		0			0
$583$	12.6126	−	21.8456i	0.522360	−	0.904754i
$584$		0			0
$585$	4.95489	+	8.58212i	0.204859	+	0.354827i
$586$		0			0
$587$	−4.08936	−	7.08298i	−0.168786	−	0.292346i	0.769207	−	0.638999i	$-0.220651\pi$
$587$	−4.08936	−	7.08298i	−0.168786	−	0.292346i	−0.937993	+	0.346653i	$0.887318\pi$
$588$		0			0
$589$	−6.21244	−	10.7603i	−0.255979	−	0.443369i
$590$		0			0
$591$	22.2679			0.915980
$592$		0			0
$593$	−41.7565			−1.71473			−0.857367	−	0.514706i	$-0.827901\pi$
$593$	−41.7565			−1.71473			−0.857367	+	0.514706i	$0.827901\pi$
$594$		0			0
$595$	−6.30705	−	10.9241i	−0.258564	−	0.447846i
$596$		0			0
$597$	−17.2563	−	29.8888i	−0.706253	−	1.22327i
$598$		0			0
$599$	−5.73506	−	9.93342i	−0.234328	−	0.405869i	0.724749	−	0.689013i	$-0.241956\pi$
$599$	−5.73506	−	9.93342i	−0.234328	−	0.405869i	−0.959077	+	0.283144i	$0.908622\pi$
$600$		0			0
$601$	−0.891974	+	1.54494i	−0.0363844	+	0.0630196i	−0.883644	−	0.468159i	$-0.844917\pi$
$601$	−0.891974	+	1.54494i	−0.0363844	+	0.0630196i	0.847260	+	0.531179i	$0.178251\pi$
$602$		0			0
$603$	25.8394			1.05226
$604$		0			0
$605$	−1.16146	−	2.01170i	−0.0472199	−	0.0817873i
$606$		0			0
$607$	7.87875	−	13.6464i	0.319789	−	0.553890i	−0.660655	−	0.750690i	$-0.729721\pi$
$607$	7.87875	−	13.6464i	0.319789	−	0.553890i	0.980444	+	0.196799i	$0.0630547\pi$
$608$		0			0
$609$	17.1195	−	29.6519i	0.693718	−	1.20155i
$610$		0			0
$611$	−19.7192	−	34.1547i	−0.797755	−	1.38175i
$612$		0			0
$613$	−5.13544	+	8.89485i	−0.207419	+	0.359260i	−0.950901	−	0.309496i	$-0.899840\pi$
$613$	−5.13544	+	8.89485i	−0.207419	+	0.359260i	0.743482	+	0.668756i	$0.233173\pi$
$614$		0			0
$615$	−0.496446			−0.0200186
$616$		0			0
$617$	21.4101	−	37.0833i	0.861936	−	1.49292i	−0.00812097	−	0.999967i	$-0.502585\pi$
$617$	21.4101	−	37.0833i	0.861936	−	1.49292i	0.870057	−	0.492951i	$-0.164082\pi$
$618$		0			0
$619$	44.3120			1.78105			0.890525	−	0.454935i	$-0.150338\pi$
$619$	44.3120			1.78105			0.890525	+	0.454935i	$0.150338\pi$
$620$		0			0
$621$	6.31814			0.253538
$622$		0			0
$623$	−7.68114			−0.307739
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−29.3622	+	50.8569i	−1.17261	+	2.03103i
$628$		0			0
$629$	9.45064	+	25.9645i	0.376821	+	1.03527i
$630$		0			0
$631$	−21.1310	+	36.6000i	−0.841212	+	1.45702i	0.0476592	+	0.998864i	$0.484824\pi$
$631$	−21.1310	+	36.6000i	−0.841212	+	1.45702i	−0.888871	+	0.458158i	$0.848509\pi$
$632$		0			0
$633$	−22.0772	−	38.2389i	−0.877491	−	1.51986i
$634$		0			0
$635$	−3.01333			−0.119580
$636$		0			0
$637$	−3.33809			−0.132260
$638$		0			0
$639$	1.83224			0.0724823
$640$		0			0
$641$	12.0462	−	20.8647i	0.475797	−	0.824105i	−0.523818	−	0.851830i	$-0.675493\pi$
$641$	12.0462	−	20.8647i	0.475797	−	0.824105i	0.999616	+	0.0277248i	$0.00882620\pi$
$642$		0			0
$643$	15.1998			0.599423			0.299712	−	0.954030i	$-0.403110\pi$
$643$	15.1998			0.599423			0.299712	+	0.954030i	$0.403110\pi$
$644$		0			0
$645$	−6.82181	+	11.8157i	−0.268609	+	0.465244i
$646$		0			0
$647$	17.8360	+	30.8928i	0.701205	+	1.21452i	0.968044	+	0.250781i	$0.0806875\pi$
$647$	17.8360	+	30.8928i	0.701205	+	1.21452i	−0.266839	+	0.963741i	$0.585979\pi$
$648$		0			0
$649$	2.89276	−	5.01040i	0.113551	−	0.196676i
$650$		0			0
$651$	−5.48080	+	9.49303i	−0.214810	+	0.372061i
$652$		0			0
$653$	1.19633	+	2.07211i	0.0468162	+	0.0810880i	0.888484	−	0.458908i	$-0.151759\pi$
$653$	1.19633	+	2.07211i	0.0468162	+	0.0810880i	−0.841668	+	0.539996i	$0.818426\pi$
$654$		0			0
$655$	−19.9608			−0.779934
$656$		0			0
$657$	8.22920	−	14.2534i	0.321052	−	0.556078i
$658$		0			0
$659$	3.97523	+	6.88531i	0.154853	+	0.268213i	0.933006	−	0.359862i	$-0.117176\pi$
$659$	3.97523	+	6.88531i	0.154853	+	0.268213i	−0.778152	+	0.628075i	$0.783843\pi$
$660$		0			0
$661$	−11.4734	−	19.8726i	−0.446265	−	0.772954i	0.551874	−	0.833927i	$-0.313913\pi$
$661$	−11.4734	−	19.8726i	−0.446265	−	0.772954i	−0.998139	+	0.0609732i	$0.980580\pi$
$662$		0			0
$663$	−24.1006	−	41.7434i	−0.935989	−	1.62118i
$664$		0			0
$665$	−19.7611			−0.766303
$666$		0			0
$667$	17.1516			0.664111
$668$		0			0
$669$	−25.7460	−	44.5934i	−0.995398	−	1.72408i
$670$		0			0
$671$	−1.23513	−	2.13931i	−0.0476817	−	0.0825870i
$672$		0			0
$673$	15.2397	+	26.3960i	0.587448	+	1.01749i	0.994565	+	0.104114i	$0.0332006\pi$
$673$	15.2397	+	26.3960i	0.587448	+	1.01749i	−0.407118	+	0.913376i	$0.633466\pi$
$674$		0			0
$675$	−1.00449	+	1.73983i	−0.0386628	+	0.0669660i
$676$		0			0
$677$	−4.51190			−0.173406			−0.0867031	−	0.996234i	$-0.527633\pi$
$677$	−4.51190			−0.173406			−0.0867031	+	0.996234i	$0.527633\pi$
$678$		0			0
$679$	−17.0922	−	29.6046i	−0.655939	−	1.13612i
$680$		0			0
$681$	−16.6199	+	28.7864i	−0.636875	+	1.10310i
$682$		0			0
$683$	−6.36019	+	11.0162i	−0.243366	+	0.421522i	−0.961671	−	0.274206i	$-0.911585\pi$
$683$	−6.36019	+	11.0162i	−0.243366	+	0.421522i	0.718305	+	0.695728i	$0.244918\pi$
$684$		0			0
$685$	7.37365	+	12.7715i	0.281733	+	0.487975i
$686$		0			0
$687$	28.6604	−	49.6413i	1.09346	−	1.89393i
$688$		0			0
$689$	32.4360			1.23571
$690$		0			0
$691$	−19.9602	+	34.5721i	−0.759322	+	1.31518i	0.183875	+	0.982950i	$0.441136\pi$
$691$	−19.9602	+	34.5721i	−0.759322	+	1.31518i	−0.943197	+	0.332234i	$0.892198\pi$
$692$		0			0
$693$	21.4009			0.812953
$694$		0			0
$695$	18.2324			0.691595
$696$		0			0
$697$	0.997462			0.0377816
$698$		0			0
$699$	21.7669	+	37.7014i	0.823300	+	1.42600i
$700$		0			0
$701$	−9.80816	+	16.9882i	−0.370449	+	0.641637i	−0.989635	−	0.143608i	$-0.954130\pi$
$701$	−9.80816	+	16.9882i	−0.370449	+	0.641637i	0.619186	+	0.785245i	$0.287463\pi$
$702$		0			0
$703$	42.6288	+	7.51609i	1.60777	+	0.283475i
$704$		0			0
$705$	−9.49876	+	16.4523i	−0.357744	+	0.619631i
$706$		0			0
$707$	−18.4228	−	31.9092i	−0.692861	−	1.20007i
$708$		0			0
$709$	−29.4664			−1.10663			−0.553316	−	0.832971i	$-0.686638\pi$
$709$	−29.4664			−1.10663			−0.553316	+	0.832971i	$0.686638\pi$
$710$		0			0
$711$	6.44343			0.241647
$712$		0			0
$713$	−5.49106			−0.205642
$714$		0			0
$715$	8.56569	−	14.8362i	0.320339	−	0.554843i
$716$		0			0
$717$	60.7366			2.26825
$718$		0			0
$719$	−11.7425	+	20.3386i	−0.437921	+	0.758502i	−0.997529	−	0.0702556i	$-0.977619\pi$
$719$	−11.7425	+	20.3386i	−0.437921	+	0.758502i	0.559608	+	0.828758i	$0.310952\pi$
$720$		0			0
$721$	21.6759	+	37.5437i	0.807251	+	1.39820i
$722$		0			0
$723$	12.3698	−	21.4251i	0.460038	−	0.796810i
$724$		0			0
$725$	−2.72684	+	4.72303i	−0.101272	+	0.175409i
$726$		0			0
$727$	0.686889	+	1.18973i	0.0254753	+	0.0441245i	0.878482	−	0.477775i	$-0.158557\pi$
$727$	0.686889	+	1.18973i	0.0254753	+	0.0441245i	−0.853007	+	0.521900i	$0.825223\pi$
$728$		0			0
$729$	−9.33805			−0.345854
$730$		0			0
$731$	13.7064	−	23.7402i	0.506951	−	0.878064i
$732$		0			0
$733$	8.97826	+	15.5508i	0.331619	+	0.574382i	0.982830	−	0.184516i	$-0.0590717\pi$
$733$	8.97826	+	15.5508i	0.331619	+	0.574382i	−0.651210	+	0.758897i	$0.725738\pi$
$734$		0			0
$735$	0.803981	+	1.39254i	0.0296553	+	0.0513644i
$736$		0			0
$737$	−22.3347	−	38.6849i	−0.822710	−	1.42497i
$738$		0			0
$739$	−16.6087			−0.610960			−0.305480	−	0.952198i	$-0.598817\pi$
$739$	−16.6087			−0.610960			−0.305480	+	0.952198i	$0.598817\pi$
$740$		0			0
$741$	−75.5114			−2.77398
$742$		0			0
$743$	−10.6914	−	18.5180i	−0.392228	−	0.679359i	0.600515	−	0.799614i	$-0.294962\pi$
$743$	−10.6914	−	18.5180i	−0.392228	−	0.679359i	−0.992743	+	0.120254i	$0.961629\pi$
$744$		0			0
$745$	2.68250	+	4.64623i	0.0982792	+	0.170225i
$746$		0			0
$747$	−16.9644	−	29.3833i	−0.620696	−	1.07508i
$748$		0			0
$749$	10.3474	−	17.9223i	0.378087	−	0.654866i
$750$		0			0
$751$	18.8974			0.689575			0.344788	−	0.938681i	$-0.387951\pi$
$751$	18.8974			0.689575			0.344788	+	0.938681i	$0.387951\pi$
$752$		0			0
$753$	2.24545	+	3.88924i	0.0818288	+	0.141732i
$754$		0			0
$755$	−5.66740	+	9.81623i	−0.206258	+	0.357249i
$756$		0			0
$757$	13.3448	−	23.1138i	0.485024	−	0.840086i	−0.514828	−	0.857294i	$-0.672144\pi$
$757$	13.3448	−	23.1138i	0.485024	−	0.840086i	0.999852	+	0.0172073i	$0.00547752\pi$
$758$		0			0
$759$	12.9764	+	22.4758i	0.471013	+	0.815818i
$760$		0			0
$761$	4.73204	−	8.19614i	0.171536	−	0.297110i	−0.767421	−	0.641144i	$-0.778460\pi$
$761$	4.73204	−	8.19614i	0.171536	−	0.297110i	0.938957	+	0.344034i	$0.111794\pi$
$762$		0			0
$763$	−14.3746			−0.520394
$764$		0			0
$765$	−4.79552	+	8.30608i	−0.173382	+	0.300307i
$766$		0			0
$767$	7.43936			0.268620
$768$		0			0
$769$	42.4913			1.53227			0.766137	−	0.642677i	$-0.222176\pi$
$769$	42.4913			1.53227			0.766137	+	0.642677i	$0.222176\pi$
$770$		0			0
$771$	−41.2809			−1.48670
$772$		0			0
$773$	−1.92974	−	3.34240i	−0.0694079	−	0.120218i	0.829233	−	0.558903i	$-0.188778\pi$
$773$	−1.92974	−	3.34240i	−0.0694079	−	0.120218i	−0.898641	+	0.438685i	$0.855444\pi$
$774$		0			0
$775$	0.872997	−	1.51207i	0.0313590	−	0.0543153i
$776$		0			0
$777$	−13.0616	−	35.8853i	−0.468584	−	1.28738i
$778$		0			0
$779$	0.781306	−	1.35326i	0.0279932	−	0.0484857i
$780$		0			0
$781$	−1.58373	−	2.74310i	−0.0566703	−	0.0981558i
$782$		0			0
$783$	10.9563			0.391547
$784$		0			0
$785$	14.7666			0.527043
$786$		0			0
$787$	−15.7883			−0.562791			−0.281396	−	0.959592i	$-0.590797\pi$
$787$	−15.7883			−0.562791			−0.281396	+	0.959592i	$0.590797\pi$
$788$		0			0
$789$	−13.8838	+	24.0474i	−0.494275	+	0.856109i
$790$		0			0
$791$	−43.5497			−1.54845
$792$		0			0
$793$	1.58820	−	2.75085i	0.0563987	−	0.0976855i
$794$		0			0
$795$	−7.81222	−	13.5312i	−0.277071	−	0.479901i
$796$		0			0
$797$	0.829269	−	1.43634i	0.0293742	−	0.0508776i	−0.850965	−	0.525223i	$-0.823982\pi$
$797$	0.829269	−	1.43634i	0.0293742	−	0.0508776i	0.880339	+	0.474345i	$0.157315\pi$
$798$		0			0
$799$	19.0850	−	33.0561i	0.675178	−	1.16944i
$800$		0			0
$801$	2.92015	+	5.05785i	0.103178	+	0.178710i
$802$		0			0
$803$	−28.4522			−1.00406
$804$		0			0
$805$	−4.36662	+	7.56321i	−0.153903	+	0.266568i
$806$		0			0
$807$	−22.2488	−	38.5361i	−0.783196	−	1.35654i
$808$		0			0
$809$	18.2006	+	31.5243i	0.639898	+	1.10834i	0.985455	+	0.169938i	$0.0543568\pi$
$809$	18.2006	+	31.5243i	0.639898	+	1.10834i	−0.345557	+	0.938398i	$0.612310\pi$
$810$		0			0
$811$	−13.6686	−	23.6747i	−0.479970	−	0.831333i	0.519766	−	0.854309i	$-0.326019\pi$
$811$	−13.6686	−	23.6747i	−0.479970	−	0.831333i	−0.999736	+	0.0229759i	$0.992686\pi$
$812$		0			0
$813$	49.9032			1.75018
$814$		0			0
$815$	11.9893			0.419966
$816$		0			0
$817$	−21.4723	−	37.1912i	−0.751222	−	1.30116i
$818$		0			0
$819$	13.7593	+	23.8318i	0.480788	+	0.832749i
$820$		0			0
$821$	−2.36628	−	4.09851i	−0.0825836	−	0.143039i	0.821775	−	0.569812i	$-0.192984\pi$
$821$	−2.36628	−	4.09851i	−0.0825836	−	0.143039i	−0.904359	+	0.426773i	$0.859650\pi$
$822$		0			0
$823$	−12.1070	+	20.9700i	−0.422024	+	0.730968i	−0.996137	−	0.0878083i	$-0.972014\pi$
$823$	−12.1070	+	20.9700i	−0.422024	+	0.730968i	0.574113	+	0.818776i	$0.305347\pi$
$824$		0			0
$825$	−8.25220			−0.287305
$826$		0			0
$827$	−12.8973	−	22.3388i	−0.448484	−	0.776797i	0.549803	−	0.835294i	$-0.314703\pi$
$827$	−12.8973	−	22.3388i	−0.448484	−	0.776797i	−0.998288	+	0.0584967i	$0.981369\pi$
$828$		0			0
$829$	−20.8250	+	36.0700i	−0.723282	+	1.25276i	0.236395	+	0.971657i	$0.424034\pi$
$829$	−20.8250	+	36.0700i	−0.723282	+	1.25276i	−0.959677	+	0.281105i	$0.909299\pi$
$830$		0			0
$831$	−14.3279	+	24.8167i	−0.497030	+	0.860881i
$832$		0			0
$833$	−1.61536	−	2.79789i	−0.0559690	−	0.0969412i
$834$		0			0
$835$	0.943988	−	1.63503i	0.0326680	−	0.0565827i
$836$		0			0
$837$	−3.50766			−0.121243
$838$		0			0
$839$	11.8045	−	20.4460i	0.407537	−	0.705876i	−0.587076	−	0.809532i	$-0.699721\pi$
$839$	11.8045	−	20.4460i	0.407537	−	0.705876i	0.994613	+	0.103656i	$0.0330542\pi$
$840$		0			0
$841$	0.742645			0.0256084
$842$		0			0
$843$	53.1299			1.82989
$844$		0			0
$845$	9.02855			0.310592
$846$		0			0
$847$	−3.22526	−	5.58631i	−0.110821	−	0.191948i
$848$		0			0
$849$	6.76642	−	11.7198i	0.232223	−	0.402222i
$850$		0			0
$851$	12.2964	−	14.6546i	0.421514	−	0.502352i
$852$		0			0
$853$	−14.2378	+	24.6606i	−0.487493	+	0.844363i	−0.999897	−	0.0143819i	$-0.995422\pi$
$853$	−14.2378	+	24.6606i	−0.487493	+	0.844363i	0.512403	+	0.858745i	$0.328755\pi$
$854$		0			0
$855$	7.51260	+	13.0122i	0.256926	+	0.445008i
$856$		0			0
$857$	−23.8806			−0.815746			−0.407873	−	0.913039i	$-0.633729\pi$
$857$	−23.8806			−0.815746			−0.407873	+	0.913039i	$0.633729\pi$
$858$		0			0
$859$	41.8254			1.42707			0.713533	−	0.700622i	$-0.247094\pi$
$859$	41.8254			1.42707			0.713533	+	0.700622i	$0.247094\pi$
$860$		0			0
$861$	−1.37858			−0.0469820
$862$		0			0
$863$	−6.20954	+	10.7552i	−0.211375	+	0.366113i	−0.952145	−	0.305646i	$-0.901128\pi$
$863$	−6.20954	+	10.7552i	−0.211375	+	0.366113i	0.740770	+	0.671759i	$0.234461\pi$
$864$		0			0
$865$	−10.8177			−0.367814
$866$		0			0
$867$	4.10826	−	7.11572i	0.139524	−	0.241662i
$868$		0			0
$869$	−5.56949	−	9.64665i	−0.188932	−	0.327240i
$870$		0			0
$871$	28.7193	−	49.7433i	0.973116	−	1.68549i
$872$		0			0
$873$	−12.9959	+	22.5096i	−0.439846	+	0.761835i
$874$		0			0
$875$	−1.38845	−	2.40487i	−0.0469383	−	0.0812996i
$876$		0			0
$877$	28.4409			0.960381			0.480190	−	0.877164i	$-0.340568\pi$
$877$	28.4409			0.960381			0.480190	+	0.877164i	$0.340568\pi$
$878$		0			0
$879$	24.3982	−	42.2590i	0.822932	−	1.42536i
$880$		0			0
$881$	15.5464	+	26.9271i	0.523770	+	0.907197i	0.999617	+	0.0276684i	$0.00880826\pi$
$881$	15.5464	+	26.9271i	0.523770	+	0.907197i	−0.475847	+	0.879528i	$0.657858\pi$
$882$		0			0
$883$	−4.05168	−	7.01772i	−0.136350	−	0.236165i	0.789762	−	0.613413i	$-0.210204\pi$
$883$	−4.05168	−	7.01772i	−0.136350	−	0.236165i	−0.926112	+	0.377248i	$0.876870\pi$
$884$		0			0
$885$	−1.79177	−	3.10344i	−0.0602297	−	0.104321i
$886$		0			0
$887$	31.6730			1.06348			0.531738	−	0.846909i	$-0.321539\pi$
$887$	31.6730			1.06348			0.531738	+	0.846909i	$0.321539\pi$
$888$		0			0
$889$	−8.36775			−0.280645
$890$		0			0
$891$	19.8493	+	34.3801i	0.664978	+	1.15178i
$892$		0			0
$893$	−29.8983	−	51.7854i	−1.00051	−	1.73293i
$894$		0			0
$895$	4.33305	+	7.50506i	0.144838	+	0.250866i
$896$		0			0
$897$	−16.6858	+	28.9007i	−0.557123	+	0.964965i
$898$		0			0
$899$	−9.52209			−0.317579
$900$		0			0
$901$	15.6964	+	27.1869i	0.522922	+	0.905727i
$902$		0			0
$903$	−18.9436	+	32.8112i	−0.630402	+	1.09189i
$904$		0			0
$905$	4.96194	−	8.59433i	0.164940	−	0.285685i
$906$		0			0
$907$	29.9710	+	51.9113i	0.995171	+	1.72369i	0.582591	+	0.812766i	$0.302039\pi$
$907$	29.9710	+	51.9113i	0.995171	+	1.72369i	0.412580	+	0.910921i	$0.364628\pi$
$908$		0			0
$909$	−14.0076	+	24.2619i	−0.464604	+	0.804718i
$910$		0			0
$911$	−27.4317			−0.908852			−0.454426	−	0.890784i	$-0.650156\pi$
$911$	−27.4317			−0.908852			−0.454426	+	0.890784i	$0.650156\pi$
$912$		0			0
$913$	−29.3270	+	50.7959i	−0.970583	+	1.68110i
$914$		0			0
$915$	−1.53008			−0.0505828
$916$		0			0
$917$	−55.4294			−1.83044
$918$		0			0
$919$	−26.0316			−0.858704			−0.429352	−	0.903137i	$-0.641258\pi$
$919$	−26.0316			−0.858704			−0.429352	+	0.903137i	$0.641258\pi$
$920$		0			0
$921$	15.6781	+	27.1553i	0.516611	+	0.894797i
$922$		0			0
$923$	2.03645	−	3.52724i	0.0670307	−	0.116100i
$924$		0			0
$925$	2.08049	+	5.71590i	0.0684062	+	0.187938i
$926$		0			0
$927$	16.4811	−	28.5461i	0.541309	−	0.937575i
$928$		0			0
$929$	−26.1923	−	45.3664i	−0.859342	−	1.48842i	−0.872557	−	0.488512i	$-0.837540\pi$
$929$	−26.1923	−	45.3664i	−0.859342	−	1.48842i	0.0132152	−	0.999913i	$-0.495793\pi$
$930$		0			0
$931$	−5.06122			−0.165875
$932$		0			0
$933$	−31.0710			−1.01722
$934$		0			0
$935$	16.5804			0.542236
$936$		0			0
$937$	1.12548	−	1.94938i	0.0367678	−	0.0636836i	−0.847056	−	0.531504i	$-0.821627\pi$
$937$	1.12548	−	1.94938i	0.0367678	−	0.0636836i	0.883824	+	0.467820i	$0.154960\pi$
$938$		0			0
$939$	14.4284			0.470853
$940$		0			0
$941$	−3.87789	+	6.71670i	−0.126416	+	0.218958i	−0.922285	−	0.386510i	$-0.873681\pi$
$941$	−3.87789	+	6.71670i	−0.126416	+	0.218958i	0.795870	+	0.605468i	$0.207014\pi$
$942$		0			0
$943$	−0.345291	−	0.598062i	−0.0112442	−	0.0194756i
$944$		0			0
$945$	−2.78938	+	4.83134i	−0.0907384	+	0.157164i
$946$		0			0
$947$	−23.1800	+	40.1489i	−0.753248	+	1.30466i	0.192993	+	0.981200i	$0.438181\pi$
$947$	−23.1800	+	40.1489i	−0.753248	+	1.30466i	−0.946241	+	0.323463i	$0.895153\pi$
$948$		0			0
$949$	−18.2928	−	31.6840i	−0.593809	−	1.02851i
$950$		0			0
$951$	24.4765			0.793706
$952$		0			0
$953$	24.7015	−	42.7842i	0.800160	−	1.38592i	−0.119351	−	0.992852i	$-0.538081\pi$
$953$	24.7015	−	42.7842i	0.800160	−	1.38592i	0.919511	−	0.393065i	$-0.128585\pi$
$954$		0			0
$955$	−7.84599	−	13.5897i	−0.253890	−	0.439751i
$956$		0			0
$957$	22.5024	+	38.9753i	0.727400	+	1.25989i
$958$		0			0
$959$	20.4759	+	35.4654i	0.661203	+	1.14524i
$960$		0			0
$961$	−27.9515			−0.901662
$962$		0			0
$963$	−15.7352			−0.507060
$964$		0			0
$965$	6.96719	+	12.0675i	0.224282	+	0.388468i
$966$		0			0
$967$	17.5533	+	30.4032i	0.564476	+	0.977701i	0.997098	+	0.0761257i	$0.0242550\pi$
$967$	17.5533	+	30.4032i	0.564476	+	0.977701i	−0.432622	+	0.901575i	$0.642412\pi$
$968$		0			0
$969$	−36.5413	−	63.2914i	−1.17388	−	2.03321i
$970$		0			0
$971$	−24.8907	+	43.1119i	−0.798780	+	1.38353i	0.121631	+	0.992575i	$0.461188\pi$
$971$	−24.8907	+	43.1119i	−0.798780	+	1.38353i	−0.920411	+	0.390952i	$0.872146\pi$
$972$		0			0
$973$	50.6297			1.62311
$974$		0			0
$975$	−5.30558	−	9.18954i	−0.169915	−	0.294301i
$976$		0			0
$977$	−1.87383	+	3.24557i	−0.0599491	+	0.103835i	−0.894442	−	0.447183i	$-0.852427\pi$
$977$	−1.87383	+	3.24557i	−0.0599491	+	0.103835i	0.834493	+	0.551018i	$0.185761\pi$
$978$		0			0
$979$	5.04817	−	8.74369i	0.161340	−	0.279449i
$980$		0			0
$981$	5.46480	+	9.46531i	0.174478	+	0.302204i
$982$		0			0
$983$	12.2054	−	21.1403i	0.389291	−	0.674272i	−0.603063	−	0.797693i	$-0.706053\pi$
$983$	12.2054	−	21.1403i	0.389291	−	0.674272i	0.992354	+	0.123421i	$0.0393867\pi$
$984$		0			0
$985$	−9.84940			−0.313828
$986$		0			0
$987$	−26.3772	+	45.6866i	−0.839595	+	1.45422i
$988$		0			0
$989$	−18.9790			−0.603498
$990$		0			0
$991$	−21.9021			−0.695742			−0.347871	−	0.937542i	$-0.613095\pi$
$991$	−21.9021			−0.695742			−0.347871	+	0.937542i	$0.613095\pi$
$992$		0			0
$993$	60.9289			1.93352
$994$		0			0
$995$	7.63269	+	13.2202i	0.241972	+	0.419109i
$996$		0			0
$997$	23.3426	−	40.4306i	0.739267	−	1.28045i	−0.213558	−	0.976930i	$-0.568505\pi$
$997$	23.3426	−	40.4306i	0.739267	−	1.28045i	0.952826	−	0.303518i	$-0.0981614\pi$
$998$		0			0
$999$	7.85485	−	9.36126i	0.248516	−	0.296177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.i.a.121.6	✓	14
37.26	even	3	inner	740.2.i.a.581.6	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.i.a.121.6	✓	14	1.1	even	1	trivial
740.2.i.a.581.6	yes	14	37.26	even	3	inner

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13042 + 1.95795i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.38845 - 2.40487i) q^{7} +(-1.05570 + 1.82853i) q^{9} +3.65006 q^{11} +(2.34673 + 4.06465i) q^{13} +(1.13042 - 1.95795i) q^{15} +(-2.27125 + 3.93392i) q^{17} +(3.55811 + 6.16283i) q^{19} +(3.13907 - 5.43704i) q^{21} +3.14495 q^{23} +(-0.500000 + 0.866025i) q^{25} +2.00898 q^{27} +5.45368 q^{29} -1.74599 q^{31} +(4.12610 + 7.14661i) q^{33} +(-1.38845 + 2.40487i) q^{35} +(3.90987 - 4.65971i) q^{37} +(-5.30558 + 9.18954i) q^{39} +(-0.109792 - 0.190166i) q^{41} -6.03476 q^{43} +2.11140 q^{45} -8.40286 q^{47} +(-0.355611 + 0.615937i) q^{49} -10.2699 q^{51} +(3.45545 - 5.98501i) q^{53} +(-1.82503 - 3.16104i) q^{55} +(-8.04433 + 13.9332i) q^{57} +(0.792524 - 1.37269i) q^{59} +(-0.338386 - 0.586103i) q^{61} +5.86317 q^{63} +(2.34673 - 4.06465i) q^{65} +(-6.11900 - 10.5984i) q^{67} +(3.55512 + 6.15765i) q^{69} +(-0.433892 - 0.751522i) q^{71} -7.79501 q^{73} -2.26084 q^{75} +(-5.06794 - 8.77792i) q^{77} +(-1.52587 - 2.64288i) q^{79} +(5.43809 + 9.41905i) q^{81} +(-8.03468 + 13.9165i) q^{83} +4.54250 q^{85} +(6.16495 + 10.6780i) q^{87} +(1.38304 - 2.39549i) q^{89} +(6.51665 - 11.2872i) q^{91} +(-1.97371 - 3.41856i) q^{93} +(3.55811 - 6.16283i) q^{95} +12.3102 q^{97} +(-3.85337 + 6.67423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) \) 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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