LMFDB - Embedded newform 429.2.b.a.298.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(298,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("429.298");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 13x^{8} + 54x^{6} + 74x^{4} + 21x^{2} + 1 $ x^10 + 13x^8 + 54x^6 + 74x^4 + 21x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			298.5
Root			$-0.244130i$ of defining polynomial
Character	$\chi$	$=$	429.298
Dual form			429.2.b.a.298.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.244130i q^{2} -1.00000 q^{3} +1.94040 q^{4} +0.949685i q^{5} +0.244130i q^{6} -2.34031i q^{7} -0.961969i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.244130i q^{2} -1.00000 q^{3} +1.94040 q^{4} +0.949685i q^{5} +0.244130i q^{6} -2.34031i q^{7} -0.961969i q^{8} +1.00000 q^{9} +0.231846 q^{10} -1.00000i q^{11} -1.94040 q^{12} +(2.15578 - 2.89009i) q^{13} -0.571340 q^{14} -0.949685i q^{15} +3.64596 q^{16} -1.81402 q^{17} -0.244130i q^{18} +4.67470i q^{19} +1.84277i q^{20} +2.34031i q^{21} -0.244130 q^{22} +8.38618 q^{23} +0.961969i q^{24} +4.09810 q^{25} +(-0.705556 - 0.526291i) q^{26} -1.00000 q^{27} -4.54115i q^{28} -5.96052 q^{29} -0.231846 q^{30} -10.7544i q^{31} -2.81402i q^{32} +1.00000i q^{33} +0.442857i q^{34} +2.22256 q^{35} +1.94040 q^{36} -0.792455i q^{37} +1.14123 q^{38} +(-2.15578 + 2.89009i) q^{39} +0.913567 q^{40} +10.9102i q^{41} +0.571340 q^{42} +1.32576 q^{43} -1.94040i q^{44} +0.949685i q^{45} -2.04732i q^{46} -3.28071i q^{47} -3.64596 q^{48} +1.52293 q^{49} -1.00047i q^{50} +1.81402 q^{51} +(4.18308 - 5.60792i) q^{52} -4.54533 q^{53} +0.244130i q^{54} +0.949685 q^{55} -2.25131 q^{56} -4.67470i q^{57} +1.45514i q^{58} -1.68843i q^{59} -1.84277i q^{60} -11.7068 q^{61} -2.62547 q^{62} -2.34031i q^{63} +6.60493 q^{64} +(2.74467 + 2.04732i) q^{65} +0.244130 q^{66} +5.67728i q^{67} -3.51993 q^{68} -8.38618 q^{69} -0.542593i q^{70} +13.0609i q^{71} -0.961969i q^{72} +4.26425i q^{73} -0.193462 q^{74} -4.09810 q^{75} +9.07080i q^{76} -2.34031 q^{77} +(0.705556 + 0.526291i) q^{78} -8.39402 q^{79} +3.46251i q^{80} +1.00000 q^{81} +2.66351 q^{82} -15.9379i q^{83} +4.54115i q^{84} -1.72275i q^{85} -0.323658i q^{86} +5.96052 q^{87} -0.961969 q^{88} +17.2696i q^{89} +0.231846 q^{90} +(-6.76371 - 5.04521i) q^{91} +16.2726 q^{92} +10.7544i q^{93} -0.800920 q^{94} -4.43950 q^{95} +2.81402i q^{96} +13.4976i q^{97} -0.371793i q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9	$ 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9} + 6 q^{12} + 12 q^{13} - 32 q^{14} + 6 q^{16} + 20 q^{17} - 2 q^{22} + 8 q^{23} - 14 q^{25} - 2 q^{26} - 10 q^{27} + 8 q^{29} - 6 q^{36} - 12 q^{39} - 20 q^{40} + 32 q^{42} - 24 q^{43} - 6 q^{48} - 26 q^{49} - 20 q^{51} - 48 q^{52} - 4 q^{53} + 4 q^{55} + 16 q^{56} + 36 q^{61} + 24 q^{62} + 50 q^{64} + 28 q^{65} + 2 q^{66} - 12 q^{68} - 8 q^{69} + 24 q^{74} + 14 q^{75} + 12 q^{77} + 2 q^{78} + 36 q^{79} + 10 q^{81} - 20 q^{82} - 8 q^{87} - 6 q^{88} - 24 q^{91} - 8 q^{92} - 32 q^{94} + 44 q^{95}+O(q^{100}) $ 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9 + 6 * q^12 + 12 * q^13 - 32 * q^14 + 6 * q^16 + 20 * q^17 - 2 * q^22 + 8 * q^23 - 14 * q^25 - 2 * q^26 - 10 * q^27 + 8 * q^29 - 6 * q^36 - 12 * q^39 - 20 * q^40 + 32 * q^42 - 24 * q^43 - 6 * q^48 - 26 * q^49 - 20 * q^51 - 48 * q^52 - 4 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^61 + 24 * q^62 + 50 * q^64 + 28 * q^65 + 2 * q^66 - 12 * q^68 - 8 * q^69 + 24 * q^74 + 14 * q^75 + 12 * q^77 + 2 * q^78 + 36 * q^79 + 10 * q^81 - 20 * q^82 - 8 * q^87 - 6 * q^88 - 24 * q^91 - 8 * q^92 - 32 * q^94 + 44 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$		−	0.244130i		−	0.172626i	−0.996268	−	0.0863129i	$-0.972492\pi$
$2$		−	0.244130i		−	0.172626i	0.996268	−	0.0863129i	$-0.0275085\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.94040			0.970200
$5$			0.949685i			0.424712i	0.977192	+	0.212356i	$0.0681137\pi$
$5$			0.949685i			0.424712i	−0.977192	+	0.212356i	$0.931886\pi$
$6$			0.244130i			0.0996655i
$7$		−	2.34031i		−	0.884556i	−0.896878	−	0.442278i	$-0.854171\pi$
$7$		−	2.34031i		−	0.884556i	0.896878	−	0.442278i	$-0.145829\pi$
$8$		−	0.961969i		−	0.340107i
$9$	1.00000			0.333333
$10$	0.231846			0.0733162
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−1.94040			−0.560145
$13$	2.15578	−	2.89009i	0.597907	−	0.801566i
$13$	2.15578	−	2.89009i	0.597907	−	0.801566i
$14$	−0.571340			−0.152697
$15$		−	0.949685i		−	0.245208i
$16$	3.64596			0.911489
$17$	−1.81402			−0.439965			−0.219983	−	0.975504i	$-0.570600\pi$
$17$	−1.81402			−0.439965			−0.219983	+	0.975504i	$0.570600\pi$
$18$		−	0.244130i		−	0.0575419i
$19$			4.67470i			1.07245i	0.844075	+	0.536225i	$0.180150\pi$
$19$			4.67470i			1.07245i	−0.844075	+	0.536225i	$0.819850\pi$
$20$			1.84277i			0.412056i
$21$			2.34031i			0.510698i
$22$	−0.244130			−0.0520486
$23$	8.38618			1.74864			0.874320	−	0.485350i	$-0.161308\pi$
$23$	8.38618			1.74864			0.874320	+	0.485350i	$0.161308\pi$
$24$			0.961969i			0.196361i
$25$	4.09810			0.819620
$26$	−0.705556	−	0.526291i	−0.138371	−	0.103214i
$27$	−1.00000			−0.192450
$28$		−	4.54115i		−	0.858196i
$29$	−5.96052			−1.10684			−0.553421	−	0.832902i	$-0.686678\pi$
$29$	−5.96052			−1.10684			−0.553421	+	0.832902i	$0.686678\pi$
$30$	−0.231846			−0.0423292
$31$		−	10.7544i		−	1.93155i	−0.259378	−	0.965776i	$-0.583518\pi$
$31$		−	10.7544i		−	1.93155i	0.259378	−	0.965776i	$-0.416482\pi$
$32$		−	2.81402i		−	0.497454i
$33$			1.00000i			0.174078i
$34$			0.442857i			0.0759493i
$35$	2.22256			0.375682
$36$	1.94040			0.323400
$37$		−	0.792455i		−	0.130279i	−0.997876	−	0.0651394i	$-0.979251\pi$
$37$		−	0.792455i		−	0.130279i	0.997876	−	0.0651394i	$-0.0207492\pi$
$38$	1.14123			0.185133
$39$	−2.15578	+	2.89009i	−0.345202	+	0.462784i
$40$	0.913567			0.144448
$41$			10.9102i			1.70389i	0.523633	+	0.851944i	$0.324576\pi$
$41$			10.9102i			1.70389i	−0.523633	+	0.851944i	$0.675424\pi$
$42$	0.571340			0.0881597
$43$	1.32576			0.202177			0.101089	−	0.994877i	$-0.467767\pi$
$43$	1.32576			0.202177			0.101089	+	0.994877i	$0.467767\pi$
$44$		−	1.94040i		−	0.292526i
$45$			0.949685i			0.141571i
$46$		−	2.04732i		−	0.301860i
$47$		−	3.28071i		−	0.478541i	−0.970953	−	0.239271i	$-0.923092\pi$
$47$		−	3.28071i		−	0.478541i	0.970953	−	0.239271i	$-0.0769083\pi$
$48$	−3.64596			−0.526248
$49$	1.52293			0.217562
$50$		−	1.00047i		−	0.141487i
$51$	1.81402			0.254014
$52$	4.18308	−	5.60792i	0.580089	−	0.777679i
$53$	−4.54533			−0.624349			−0.312174	−	0.950025i	$-0.601057\pi$
$53$	−4.54533			−0.624349			−0.312174	+	0.950025i	$0.601057\pi$
$54$			0.244130i			0.0332218i
$55$	0.949685			0.128056
$56$	−2.25131			−0.300844
$57$		−	4.67470i		−	0.619180i
$58$			1.45514i			0.191069i
$59$		−	1.68843i		−	0.219815i	−0.993942	−	0.109908i	$-0.964944\pi$
$59$		−	1.68843i		−	0.219815i	0.993942	−	0.109908i	$-0.0350555\pi$
$60$		−	1.84277i		−	0.237901i
$61$	−11.7068			−1.49891			−0.749454	−	0.662057i	$-0.769684\pi$
$61$	−11.7068			−1.49891			−0.749454	+	0.662057i	$0.769684\pi$
$62$	−2.62547			−0.333435
$63$		−	2.34031i		−	0.294852i
$64$	6.60493			0.825616
$65$	2.74467	+	2.04732i	0.340435	+	0.253938i
$66$	0.244130			0.0300503
$67$			5.67728i			0.693590i	0.937941	+	0.346795i	$0.112730\pi$
$67$			5.67728i			0.693590i	−0.937941	+	0.346795i	$0.887270\pi$
$68$	−3.51993			−0.426854
$69$	−8.38618			−1.00958
$70$		−	0.542593i		−	0.0648523i
$71$			13.0609i			1.55004i	0.631935	+	0.775021i	$0.282261\pi$
$71$			13.0609i			1.55004i	−0.631935	+	0.775021i	$0.717739\pi$
$72$		−	0.961969i		−	0.113369i
$73$			4.26425i			0.499093i	0.968363	+	0.249546i	$0.0802815\pi$
$73$			4.26425i			0.499093i	−0.968363	+	0.249546i	$0.919718\pi$
$74$	−0.193462			−0.0224895
$75$	−4.09810			−0.473208
$76$			9.07080i			1.04049i
$77$	−2.34031			−0.266704
$78$	0.705556	+	0.526291i	0.0798884	+	0.0595907i
$79$	−8.39402			−0.944401			−0.472201	−	0.881491i	$-0.656540\pi$
$79$	−8.39402			−0.944401			−0.472201	+	0.881491i	$0.656540\pi$
$80$			3.46251i			0.387121i
$81$	1.00000			0.111111
$82$	2.66351			0.294135
$83$		−	15.9379i		−	1.74941i	−0.484657	−	0.874704i	$-0.661056\pi$
$83$		−	15.9379i		−	1.74941i	0.484657	−	0.874704i	$-0.338944\pi$
$84$			4.54115i			0.495480i
$85$		−	1.72275i		−	0.186859i
$86$		−	0.323658i		−	0.0349010i
$87$	5.96052			0.639035
$88$	−0.961969			−0.102546
$89$			17.2696i			1.83057i	0.402807	+	0.915285i	$0.368034\pi$
$89$			17.2696i			1.83057i	−0.402807	+	0.915285i	$0.631966\pi$
$90$	0.231846			0.0244387
$91$	−6.76371	−	5.04521i	−0.709029	−	0.528882i
$92$	16.2726			1.69653
$93$			10.7544i			1.11518i
$94$	−0.800920			−0.0826086
$95$	−4.43950			−0.455483
$96$			2.81402i			0.287205i
$97$			13.4976i			1.37048i	0.728318	+	0.685239i	$0.240302\pi$
$97$			13.4976i			1.37048i	−0.728318	+	0.685239i	$0.759698\pi$
$98$		−	0.371793i		−	0.0375567i
$99$		−	1.00000i		−	0.100504i
$100$	7.95195			0.795195
$101$	−15.1820			−1.51067			−0.755333	−	0.655342i	$-0.772525\pi$
$101$	−15.1820			−1.51067			−0.755333	+	0.655342i	$0.772525\pi$
$102$		−	0.442857i		−	0.0438494i
$103$	−17.2505			−1.69974			−0.849872	−	0.526989i	$-0.823321\pi$
$103$	−17.2505			−1.69974			−0.849872	+	0.526989i	$0.823321\pi$
$104$	−2.78017	−	2.07380i	−0.272618	−	0.203352i
$105$	−2.22256			−0.216900
$106$			1.10965i			0.107779i
$107$	−2.61128			−0.252442			−0.126221	−	0.992002i	$-0.540285\pi$
$107$	−2.61128			−0.252442			−0.126221	+	0.992002i	$0.540285\pi$
$108$	−1.94040			−0.186715
$109$			9.33634i			0.894259i	0.894469	+	0.447129i	$0.147554\pi$
$109$			9.33634i			0.894259i	−0.894469	+	0.447129i	$0.852446\pi$
$110$		−	0.231846i		−	0.0221057i
$111$			0.792455i			0.0752165i
$112$		−	8.53268i		−	0.806263i
$113$	−5.13422			−0.482986			−0.241493	−	0.970403i	$-0.577637\pi$
$113$	−5.13422			−0.482986			−0.241493	+	0.970403i	$0.577637\pi$
$114$	−1.14123			−0.106886
$115$			7.96424i			0.742669i
$116$	−11.5658			−1.07386
$117$	2.15578	−	2.89009i	0.199302	−	0.267189i
$118$	−0.412197			−0.0379458
$119$			4.24538i			0.389174i
$120$	−0.913567			−0.0833969
$121$	−1.00000			−0.0909091
$122$			2.85799i			0.258750i
$123$		−	10.9102i		−	0.983740i
$124$		−	20.8679i		−	1.87399i
$125$			8.64033i			0.772815i
$126$	−0.571340			−0.0508990
$127$	17.9174			1.58991			0.794955	−	0.606668i	$-0.207494\pi$
$127$	17.9174			1.58991			0.794955	+	0.606668i	$0.207494\pi$
$128$		−	7.24050i		−	0.639976i
$129$	−1.32576			−0.116727
$130$	0.499811	−	0.670056i	0.0438363	−	0.0587678i
$131$	−8.76052			−0.765410			−0.382705	−	0.923871i	$-0.625007\pi$
$131$	−8.76052			−0.765410			−0.382705	+	0.923871i	$0.625007\pi$
$132$			1.94040i			0.168890i
$133$	10.9403			0.948642
$134$	1.38599			0.119731
$135$		−	0.949685i		−	0.0817359i
$136$			1.74503i			0.149635i
$137$		−	16.3713i		−	1.39869i	−0.714783	−	0.699346i	$-0.753475\pi$
$137$		−	16.3713i		−	1.39869i	0.714783	−	0.699346i	$-0.246525\pi$
$138$			2.04732i			0.174279i
$139$	14.6226			1.24027			0.620136	−	0.784495i	$-0.287078\pi$
$139$	14.6226			1.24027			0.620136	+	0.784495i	$0.287078\pi$
$140$	4.31266			0.364486
$141$			3.28071i			0.276286i
$142$	3.18855			0.267577
$143$	−2.89009	−	2.15578i	−0.241681	−	0.180276i
$144$	3.64596			0.303830
$145$		−	5.66062i		−	0.470089i
$146$	1.04103			0.0861563
$147$	−1.52293			−0.125609
$148$		−	1.53768i		−	0.126397i
$149$		−	9.37815i		−	0.768288i	−0.923273	−	0.384144i	$-0.874497\pi$
$149$		−	9.37815i		−	0.768288i	0.923273	−	0.384144i	$-0.125503\pi$
$150$			1.00047i			0.0816878i
$151$			3.77042i			0.306832i	0.988162	+	0.153416i	$0.0490275\pi$
$151$			3.77042i			0.306832i	−0.988162	+	0.153416i	$0.950972\pi$
$152$	4.49692			0.364748
$153$	−1.81402			−0.146655
$154$			0.571340i			0.0460399i
$155$	10.2133			0.820353
$156$	−4.18308	+	5.60792i	−0.334915	+	0.448993i
$157$	−11.2866			−0.900772			−0.450386	−	0.892834i	$-0.648714\pi$
$157$	−11.2866			−0.900772			−0.450386	+	0.892834i	$0.648714\pi$
$158$			2.04923i			0.163028i
$159$	4.54533			0.360468
$160$	2.67244			0.211275
$161$		−	19.6263i		−	1.54677i
$162$		−	0.244130i		−	0.0191806i
$163$			11.7607i			0.921170i	0.887616	+	0.460585i	$0.152360\pi$
$163$			11.7607i			0.921170i	−0.887616	+	0.460585i	$0.847640\pi$
$164$			21.1702i			1.65311i
$165$	−0.949685			−0.0739329
$166$	−3.89091			−0.301993
$167$			1.25384i			0.0970251i	0.998823	+	0.0485125i	$0.0154481\pi$
$167$			1.25384i			0.0970251i	−0.998823	+	0.0485125i	$0.984552\pi$
$168$	2.25131			0.173692
$169$	−3.70519	−	12.4608i	−0.285015	−	0.958523i
$170$	−0.420575			−0.0322566
$171$			4.67470i			0.357483i
$172$	2.57251			0.196152
$173$	20.1451			1.53160			0.765802	−	0.643077i	$-0.222342\pi$
$173$	20.1451			1.53160			0.765802	+	0.643077i	$0.222342\pi$
$174$		−	1.45514i		−	0.110314i
$175$		−	9.59084i		−	0.724999i
$176$		−	3.64596i		−	0.274824i
$177$			1.68843i			0.126910i
$178$	4.21601			0.316003
$179$	7.45106			0.556918			0.278459	−	0.960448i	$-0.410176\pi$
$179$	7.45106			0.556918			0.278459	+	0.960448i	$0.410176\pi$
$180$			1.84277i			0.137352i
$181$	−7.83022			−0.582016			−0.291008	−	0.956721i	$-0.593991\pi$
$181$	−7.83022			−0.582016			−0.291008	+	0.956721i	$0.593991\pi$
$182$	−1.23169	+	1.65122i	−0.0912986	+	0.122397i
$183$	11.7068			0.865395
$184$		−	8.06725i		−	0.594725i
$185$	0.752583			0.0553310
$186$	2.62547			0.192509
$187$			1.81402i			0.132655i
$188$		−	6.36590i		−	0.464281i
$189$			2.34031i			0.170233i
$190$			1.08381i			0.0786280i
$191$	6.40156			0.463201			0.231600	−	0.972811i	$-0.425604\pi$
$191$	6.40156			0.463201			0.231600	+	0.972811i	$0.425604\pi$
$192$	−6.60493			−0.476669
$193$			17.4615i			1.25691i	0.777847	+	0.628454i	$0.216312\pi$
$193$			17.4615i			1.25691i	−0.777847	+	0.628454i	$0.783688\pi$
$194$	3.29518			0.236580
$195$	−2.74467	−	2.04732i	−0.196550	−	0.146611i
$196$	2.95510			0.211078
$197$		−	2.32132i		−	0.165387i	−0.996575	−	0.0826936i	$-0.973648\pi$
$197$		−	2.32132i		−	0.165387i	0.996575	−	0.0826936i	$-0.0263523\pi$
$198$	−0.244130			−0.0173495
$199$	−0.904709			−0.0641331			−0.0320666	−	0.999486i	$-0.510209\pi$
$199$	−0.904709			−0.0641331			−0.0320666	+	0.999486i	$0.510209\pi$
$200$		−	3.94224i		−	0.278759i
$201$		−	5.67728i		−	0.400444i
$202$			3.70638i			0.260780i
$203$			13.9495i			0.979062i
$204$	3.51993			0.246445
$205$	−10.3613			−0.723662
$206$			4.21136i			0.293420i
$207$	8.38618			0.582880
$208$	7.85989	−	10.5371i	0.544986	−	0.730618i
$209$	4.67470			0.323356
$210$			0.542593i			0.0374425i
$211$	−0.589283			−0.0405679			−0.0202840	−	0.999794i	$-0.506457\pi$
$211$	−0.589283			−0.0405679			−0.0202840	+	0.999794i	$0.506457\pi$
$212$	−8.81976			−0.605743
$213$		−	13.0609i		−	0.894917i
$214$			0.637492i			0.0435781i
$215$			1.25906i			0.0858671i
$216$			0.961969i			0.0654537i
$217$	−25.1687			−1.70856
$218$	2.27928			0.154372
$219$		−	4.26425i		−	0.288151i
$220$	1.84277			0.124240
$221$	−3.91064	+	5.24268i	−0.263058	+	0.352661i
$222$	0.193462			0.0129843
$223$		−	22.3663i		−	1.49776i	−0.662708	−	0.748878i	$-0.730593\pi$
$223$		−	22.3663i		−	1.49776i	0.662708	−	0.748878i	$-0.269407\pi$
$224$	−6.58570			−0.440025
$225$	4.09810			0.273207
$226$			1.25341i			0.0833759i
$227$		−	6.34031i		−	0.420821i	−0.977613	−	0.210411i	$-0.932520\pi$
$227$		−	6.34031i		−	0.420821i	0.977613	−	0.210411i	$-0.0674801\pi$
$228$		−	9.07080i		−	0.600728i
$229$			3.02064i			0.199610i	0.995007	+	0.0998049i	$0.0318219\pi$
$229$			3.02064i			0.199610i	−0.995007	+	0.0998049i	$0.968178\pi$
$230$	1.94431			0.128204
$231$	2.34031			0.153981
$232$			5.73384i			0.376445i
$233$	−6.98018			−0.457287			−0.228643	−	0.973510i	$-0.573429\pi$
$233$	−6.98018			−0.457287			−0.228643	+	0.973510i	$0.573429\pi$
$234$	−0.705556	−	0.526291i	−0.0461236	−	0.0344047i
$235$	3.11565			0.203242
$236$		−	3.27624i		−	0.213265i
$237$	8.39402			0.545250
$238$	1.03642			0.0671814
$239$		−	18.0406i		−	1.16695i	−0.812131	−	0.583475i	$-0.801693\pi$
$239$		−	18.0406i		−	1.16695i	0.812131	−	0.583475i	$-0.198307\pi$
$240$		−	3.46251i		−	0.223504i
$241$			6.07781i			0.391506i	0.980653	+	0.195753i	$0.0627151\pi$
$241$			6.07781i			0.391506i	−0.980653	+	0.195753i	$0.937285\pi$
$242$			0.244130i			0.0156932i
$243$	−1.00000			−0.0641500
$244$	−22.7160			−1.45424
$245$			1.44630i			0.0924010i
$246$	−2.66351			−0.169819
$247$	13.5103	+	10.0776i	0.859639	+	0.641225i
$248$	−10.3454			−0.656935
$249$			15.9379i			1.01002i
$250$	2.10936			0.133408
$251$	8.87125			0.559948			0.279974	−	0.960008i	$-0.409674\pi$
$251$	8.87125			0.559948			0.279974	+	0.960008i	$0.409674\pi$
$252$		−	4.54115i		−	0.286065i
$253$		−	8.38618i		−	0.527235i
$254$		−	4.37417i		−	0.274460i
$255$			1.72275i			0.107883i
$256$	11.4422			0.715139
$257$	4.96352			0.309616			0.154808	−	0.987945i	$-0.450524\pi$
$257$	4.96352			0.309616			0.154808	+	0.987945i	$0.450524\pi$
$258$			0.323658i			0.0201501i
$259$	−1.85459			−0.115239
$260$	5.32576	+	3.97261i	0.330290	+	0.246371i
$261$	−5.96052			−0.368947
$262$			2.13870i			0.132129i
$263$	27.9087			1.72092			0.860461	−	0.509516i	$-0.170176\pi$
$263$	27.9087			1.72092			0.860461	+	0.509516i	$0.170176\pi$
$264$	0.961969			0.0592051
$265$		−	4.31663i		−	0.265168i
$266$		−	2.67084i		−	0.163760i
$267$		−	17.2696i		−	1.05688i
$268$			11.0162i			0.672921i
$269$	10.0834			0.614794			0.307397	−	0.951581i	$-0.400542\pi$
$269$	10.0834			0.614794			0.307397	+	0.951581i	$0.400542\pi$
$270$	−0.231846			−0.0141097
$271$			26.3949i			1.60338i	0.597742	+	0.801688i	$0.296065\pi$
$271$			26.3949i			1.60338i	−0.597742	+	0.801688i	$0.703935\pi$
$272$	−6.61385			−0.401024
$273$	6.76371	+	5.04521i	0.409358	+	0.305350i
$274$	−3.99671			−0.241450
$275$		−	4.09810i		−	0.247125i
$276$	−16.2726			−0.979493
$277$	−14.5800			−0.876027			−0.438014	−	0.898968i	$-0.644318\pi$
$277$	−14.5800			−0.876027			−0.438014	+	0.898968i	$0.644318\pi$
$278$		−	3.56981i		−	0.214103i
$279$		−	10.7544i		−	0.643851i
$280$		−	2.13803i		−	0.127772i
$281$		−	21.7172i		−	1.29554i	−0.761835	−	0.647771i	$-0.775701\pi$
$281$		−	21.7172i		−	1.29554i	0.761835	−	0.647771i	$-0.224299\pi$
$282$	0.800920			0.0476941
$283$	−3.90686			−0.232238			−0.116119	−	0.993235i	$-0.537045\pi$
$283$	−3.90686			−0.232238			−0.116119	+	0.993235i	$0.537045\pi$
$284$			25.3434i			1.50385i
$285$	4.43950			0.262973
$286$	−0.526291	+	0.705556i	−0.0311202	+	0.0417204i
$287$	25.5333			1.50718
$288$		−	2.81402i		−	0.165818i
$289$	−13.7093			−0.806431
$290$	−1.38193			−0.0811494
$291$		−	13.4976i		−	0.791246i
$292$			8.27436i			0.484220i
$293$			2.54115i			0.148455i	0.997241	+	0.0742277i	$0.0236492\pi$
$293$			2.54115i			0.148455i	−0.997241	+	0.0742277i	$0.976351\pi$
$294$			0.371793i			0.0216834i
$295$	1.60348			0.0933582
$296$	−0.762317			−0.0443088
$297$			1.00000i			0.0580259i
$298$	−2.28949			−0.132626
$299$	18.0788	−	24.2368i	1.04552	−	1.40165i
$300$	−7.95195			−0.459106
$301$		−	3.10270i		−	0.178837i
$302$	0.920471			0.0529672
$303$	15.1820			0.872183
$304$			17.0438i			0.977527i
$305$		−	11.1178i		−	0.636604i
$306$			0.442857i			0.0253164i
$307$			18.6591i			1.06493i	0.846452	+	0.532465i	$0.178734\pi$
$307$			18.6591i			1.06493i	−0.846452	+	0.532465i	$0.821266\pi$
$308$	−4.54115			−0.258756
$309$	17.2505			0.981348
$310$		−	2.49337i		−	0.141614i
$311$	2.33758			0.132552			0.0662760	−	0.997801i	$-0.478888\pi$
$311$	2.33758			0.132552			0.0662760	+	0.997801i	$0.478888\pi$
$312$	2.78017	+	2.07380i	0.157396	+	0.117406i
$313$	13.0753			0.739058			0.369529	−	0.929219i	$-0.379519\pi$
$313$	13.0753			0.739058			0.369529	+	0.929219i	$0.379519\pi$
$314$			2.75540i			0.155496i
$315$	2.22256			0.125227
$316$	−16.2878			−0.916258
$317$			13.7578i			0.772716i	0.922349	+	0.386358i	$0.126267\pi$
$317$			13.7578i			0.772716i	−0.922349	+	0.386358i	$0.873733\pi$
$318$		−	1.10965i		−	0.0622260i
$319$			5.96052i			0.333725i
$320$			6.27260i			0.350649i
$321$	2.61128			0.145748
$322$	−4.79136			−0.267012
$323$		−	8.48002i		−	0.471841i
$324$	1.94040			0.107800
$325$	8.83461	−	11.8439i	0.490056	−	0.656979i
$326$	2.87114			0.159018
$327$		−	9.33634i		−	0.516301i
$328$	10.4953			0.579505
$329$	−7.67790			−0.423296
$330$			0.231846i			0.0127627i
$331$			32.1857i			1.76909i	0.466459	+	0.884543i	$0.345529\pi$
$331$			32.1857i			1.76909i	−0.466459	+	0.884543i	$0.654471\pi$
$332$		−	30.9259i		−	1.69728i
$333$		−	0.792455i		−	0.0434263i
$334$	0.306100			0.0167490
$335$	−5.39163			−0.294576
$336$			8.53268i			0.465496i
$337$	5.63694			0.307064			0.153532	−	0.988144i	$-0.450935\pi$
$337$	5.63694			0.307064			0.153532	+	0.988144i	$0.450935\pi$
$338$	−3.04205	+	0.904548i	−0.165466	+	0.0492009i
$339$	5.13422			0.278852
$340$		−	3.34283i		−	0.181290i
$341$	−10.7544			−0.582385
$342$	1.14123			0.0617108
$343$		−	19.9463i		−	1.07700i
$344$		−	1.27534i		−	0.0687619i
$345$		−	7.96424i		−	0.428780i
$346$		−	4.91801i		−	0.264394i
$347$	−8.26734			−0.443814			−0.221907	−	0.975068i	$-0.571228\pi$
$347$	−8.26734			−0.443814			−0.221907	+	0.975068i	$0.571228\pi$
$348$	11.5658			0.619992
$349$			0.812970i			0.0435173i	0.999763	+	0.0217586i	$0.00692653\pi$
$349$			0.812970i			0.0435173i	−0.999763	+	0.0217586i	$0.993073\pi$
$350$	−2.34141			−0.125153
$351$	−2.15578	+	2.89009i	−0.115067	+	0.154261i
$352$	−2.81402			−0.149988
$353$			20.2314i			1.07681i	0.842687	+	0.538404i	$0.180973\pi$
$353$			20.2314i			1.07681i	−0.842687	+	0.538404i	$0.819027\pi$
$354$	0.412197			0.0219080
$355$	−12.4037			−0.658322
$356$			33.5099i			1.77602i
$357$		−	4.24538i		−	0.224690i
$358$		−	1.81902i		−	0.0961384i
$359$			2.55283i			0.134733i	0.997728	+	0.0673665i	$0.0214597\pi$
$359$			2.55283i			0.134733i	−0.997728	+	0.0673665i	$0.978540\pi$
$360$	0.913567			0.0481492
$361$	−2.85285			−0.150150
$362$			1.91159i			0.100471i
$363$	1.00000			0.0524864
$364$	−13.1243	−	9.78973i	−0.687900	−	0.513121i
$365$	−4.04970			−0.211971
$366$		−	2.85799i		−	0.149389i
$367$	−28.2756			−1.47598			−0.737988	−	0.674814i	$-0.764224\pi$
$367$	−28.2756			−1.47598			−0.737988	+	0.674814i	$0.764224\pi$
$368$	30.5757			1.59387
$369$			10.9102i			0.567963i
$370$		−	0.183728i		−	0.00955156i
$371$			10.6375i			0.552271i
$372$			20.8679i			1.08195i
$373$	−15.9911			−0.827988			−0.413994	−	0.910280i	$-0.635867\pi$
$373$	−15.9911			−0.827988			−0.413994	+	0.910280i	$0.635867\pi$
$374$	0.442857			0.0228996
$375$		−	8.64033i		−	0.446185i
$376$	−3.15594			−0.162755
$377$	−12.8496	+	17.2264i	−0.661788	+	0.887206i
$378$	0.571340			0.0293866
$379$		−	8.69626i		−	0.446697i	−0.974739	−	0.223349i	$-0.928301\pi$
$379$		−	8.69626i		−	0.446697i	0.974739	−	0.223349i	$-0.0716988\pi$
$380$	−8.61440			−0.441910
$381$	−17.9174			−0.917936
$382$		−	1.56281i		−	0.0799604i
$383$		−	34.7040i		−	1.77329i	−0.462451	−	0.886645i	$-0.653030\pi$
$383$		−	34.7040i		−	1.77329i	0.462451	−	0.886645i	$-0.346970\pi$
$384$			7.24050i			0.369490i
$385$		−	2.22256i		−	0.113272i
$386$	4.26288			0.216975
$387$	1.32576			0.0673924
$388$			26.1908i			1.32964i
$389$	8.50776			0.431361			0.215680	−	0.976464i	$-0.430803\pi$
$389$	8.50776			0.431361			0.215680	+	0.976464i	$0.430803\pi$
$390$	−0.499811	+	0.670056i	−0.0253089	+	0.0339296i
$391$	−15.2127			−0.769341
$392$		−	1.46501i		−	0.0739943i
$393$	8.76052			0.441910
$394$	−0.566703			−0.0285501
$395$		−	7.97168i		−	0.401099i
$396$		−	1.94040i		−	0.0975088i
$397$			6.65375i			0.333942i	0.985962	+	0.166971i	$0.0533987\pi$
$397$			6.65375i			0.333942i	−0.985962	+	0.166971i	$0.946601\pi$
$398$			0.220866i			0.0110710i
$399$	−10.9403			−0.547699
$400$	14.9415			0.747074
$401$			15.3315i			0.765620i	0.923827	+	0.382810i	$0.125044\pi$
$401$			15.3315i			0.765620i	−0.923827	+	0.382810i	$0.874956\pi$
$402$	−1.38599			−0.0691270
$403$	−31.0812	−	23.1842i	−1.54827	−	1.15489i
$404$	−29.4592			−1.46565
$405$			0.949685i			0.0471902i
$406$	3.40548			0.169011
$407$	−0.792455			−0.0392806
$408$		−	1.74503i		−	0.0863920i
$409$			10.9241i			0.540164i	0.962837	+	0.270082i	$0.0870508\pi$
$409$			10.9241i			0.540164i	−0.962837	+	0.270082i	$0.912949\pi$
$410$			2.52949i			0.124923i
$411$			16.3713i			0.807535i
$412$	−33.4729			−1.64909
$413$	−3.95146			−0.194439
$414$		−	2.04732i		−	0.100620i
$415$	15.1360			0.742995
$416$	−8.13277	−	6.06643i	−0.398742	−	0.297431i
$417$	−14.6226			−0.716071
$418$		−	1.14123i		−	0.0558196i
$419$	−29.7182			−1.45183			−0.725915	−	0.687784i	$-0.758584\pi$
$419$	−29.7182			−1.45183			−0.725915	+	0.687784i	$0.758584\pi$
$420$	−4.31266			−0.210436
$421$		−	12.6413i		−	0.616100i	−0.951370	−	0.308050i	$-0.900324\pi$
$421$		−	12.6413i		−	0.616100i	0.951370	−	0.308050i	$-0.0996764\pi$
$422$			0.143861i			0.00700307i
$423$		−	3.28071i		−	0.159514i
$424$			4.37246i			0.212346i
$425$	−7.43404			−0.360604
$426$	−3.18855			−0.154486
$427$			27.3977i			1.32587i
$428$	−5.06694			−0.244920
$429$	2.89009	+	2.15578i	0.139535	+	0.104082i
$430$	0.307374			0.0148229
$431$			24.5301i			1.18158i	0.806827	+	0.590788i	$0.201183\pi$
$431$			24.5301i			1.18158i	−0.806827	+	0.590788i	$0.798817\pi$
$432$	−3.64596			−0.175416
$433$	22.3476			1.07396			0.536979	−	0.843596i	$-0.319566\pi$
$433$	22.3476			1.07396			0.536979	+	0.843596i	$0.319566\pi$
$434$			6.14443i			0.294942i
$435$			5.66062i			0.271406i
$436$			18.1162i			0.867610i
$437$			39.2029i			1.87533i
$438$	−1.04103			−0.0497423
$439$	25.9886			1.24037			0.620184	−	0.784456i	$-0.287058\pi$
$439$	25.9886			1.24037			0.620184	+	0.784456i	$0.287058\pi$
$440$		−	0.913567i		−	0.0435526i
$441$	1.52293			0.0725205
$442$	1.27989	+	0.954704i	0.0608784	+	0.0454106i
$443$	30.3163			1.44037			0.720186	−	0.693781i	$-0.244057\pi$
$443$	30.3163			1.44037			0.720186	+	0.693781i	$0.244057\pi$
$444$			1.53768i			0.0729751i
$445$	−16.4006			−0.777465
$446$	−5.46027			−0.258551
$447$			9.37815i			0.443571i
$448$		−	15.4576i		−	0.730303i
$449$		−	25.9541i		−	1.22485i	−0.790529	−	0.612424i	$-0.790195\pi$
$449$		−	25.9541i		−	1.22485i	0.790529	−	0.612424i	$-0.209805\pi$
$450$		−	1.00047i		−	0.0471625i
$451$	10.9102			0.513742
$452$	−9.96244			−0.468594
$453$		−	3.77042i		−	0.177150i
$454$	−1.54786			−0.0726446
$455$	4.79136	−	6.42339i	0.224623	−	0.301133i
$456$	−4.49692			−0.210587
$457$			0.633665i			0.0296416i	0.999890	+	0.0148208i	$0.00471778\pi$
$457$			0.633665i			0.0296416i	−0.999890	+	0.0148208i	$0.995282\pi$
$458$	0.737429			0.0344578
$459$	1.81402			0.0846714
$460$			15.4538i			0.720538i
$461$		−	13.6951i		−	0.637847i	−0.947781	−	0.318923i	$-0.896679\pi$
$461$		−	13.6951i		−	0.637847i	0.947781	−	0.318923i	$-0.103321\pi$
$462$		−	0.571340i		−	0.0265811i
$463$			1.97322i			0.0917034i	0.998948	+	0.0458517i	$0.0146002\pi$
$463$			1.97322i			0.0917034i	−0.998948	+	0.0458517i	$0.985400\pi$
$464$	−21.7318			−1.00887
$465$	−10.2133			−0.473631
$466$			1.70407i			0.0789394i
$467$	−16.5197			−0.764442			−0.382221	−	0.924071i	$-0.624841\pi$
$467$	−16.5197			−0.764442			−0.382221	+	0.924071i	$0.624841\pi$
$468$	4.18308	−	5.60792i	0.193363	−	0.259226i
$469$	13.2866			0.613519
$470$		−	0.760622i		−	0.0350849i
$471$	11.2866			0.520061
$472$	−1.62422			−0.0747608
$473$		−	1.32576i		−	0.0609587i
$474$		−	2.04923i		−	0.0941242i
$475$			19.1574i			0.879001i
$476$			8.23775i			0.377576i
$477$	−4.54533			−0.208116
$478$	−4.40424			−0.201445
$479$		−	10.5909i		−	0.483911i	−0.970287	−	0.241955i	$-0.922211\pi$
$479$		−	10.5909i		−	0.483911i	0.970287	−	0.241955i	$-0.0777887\pi$
$480$	−2.67244			−0.121979
$481$	−2.29026	−	1.70836i	−0.104427	−	0.0778946i
$482$	1.48377			0.0675840
$483$			19.6263i			0.893028i
$484$	−1.94040			−0.0882000
$485$	−12.8185			−0.582059
$486$			0.244130i			0.0110739i
$487$		−	26.0777i		−	1.18170i	−0.806783	−	0.590848i	$-0.798793\pi$
$487$		−	26.0777i		−	1.18170i	0.806783	−	0.590848i	$-0.201207\pi$
$488$			11.2616i			0.509789i
$489$		−	11.7607i		−	0.531838i
$490$	0.353086			0.0159508
$491$	−15.0038			−0.677113			−0.338556	−	0.940946i	$-0.609939\pi$
$491$	−15.0038			−0.677113			−0.338556	+	0.940946i	$0.609939\pi$
$492$		−	21.1702i		−	0.954425i
$493$	10.8125			0.486972
$494$	2.46025	−	3.29826i	0.110692	−	0.148396i
$495$	0.949685			0.0426852
$496$		−	39.2102i		−	1.76059i
$497$	30.5666			1.37110
$498$	3.89091			0.174356
$499$		−	22.6905i		−	1.01577i	−0.861425	−	0.507884i	$-0.830428\pi$
$499$		−	22.6905i		−	1.01577i	0.861425	−	0.507884i	$-0.169572\pi$
$500$			16.7657i			0.749785i
$501$		−	1.25384i		−	0.0560174i
$502$		−	2.16574i		−	0.0966615i
$503$	27.7333			1.23657			0.618283	−	0.785955i	$-0.287828\pi$
$503$	27.7333			1.23657			0.618283	+	0.785955i	$0.287828\pi$
$504$	−2.25131			−0.100281
$505$		−	14.4181i		−	0.641598i
$506$	−2.04732			−0.0910143
$507$	3.70519	+	12.4608i	0.164553	+	0.553404i
$508$	34.7669			1.54253
$509$			27.2746i			1.20893i	0.796633	+	0.604463i	$0.206612\pi$
$509$			27.2746i			1.20893i	−0.796633	+	0.604463i	$0.793388\pi$
$510$	0.420575			0.0186234
$511$	9.97969			0.441475
$512$		−	17.2744i		−	0.763428i
$513$		−	4.67470i		−	0.206393i
$514$		−	1.21174i		−	0.0534477i
$515$		−	16.3826i		−	0.721902i
$516$	−2.57251			−0.113249
$517$	−3.28071			−0.144286
$518$			0.452761i			0.0198932i
$519$	−20.1451			−0.884271
$520$	1.96945	−	2.64029i	0.0863663	−	0.115784i
$521$	−21.7214			−0.951633			−0.475816	−	0.879545i	$-0.657847\pi$
$521$	−21.7214			−0.951633			−0.475816	+	0.879545i	$0.657847\pi$
$522$			1.45514i			0.0636898i
$523$	−24.8286			−1.08568			−0.542839	−	0.839837i	$-0.682651\pi$
$523$	−24.8286			−1.08568			−0.542839	+	0.839837i	$0.682651\pi$
$524$	−16.9989			−0.742601
$525$			9.59084i			0.418578i
$526$		−	6.81333i		−	0.297075i
$527$			19.5088i			0.849816i
$528$			3.64596i			0.158670i
$529$	47.3281			2.05774
$530$	−1.05382			−0.0457749
$531$		−	1.68843i		−	0.0732717i
$532$	21.2285			0.920373
$533$	31.5314	+	23.5200i	1.36578	+	1.01877i
$534$	−4.21601			−0.182445
$535$		−	2.47990i		−	0.107215i
$536$	5.46136			0.235895
$537$	−7.45106			−0.321537
$538$		−	2.46165i		−	0.106129i
$539$		−	1.52293i		−	0.0655973i
$540$		−	1.84277i		−	0.0793002i
$541$		−	4.58817i		−	0.197261i	−0.995124	−	0.0986303i	$-0.968554\pi$
$541$		−	4.58817i		−	0.197261i	0.995124	−	0.0986303i	$-0.0314461\pi$
$542$	6.44378			0.276784
$543$	7.83022			0.336027
$544$			5.10470i			0.218862i
$545$	−8.86658			−0.379803
$546$	1.23169	−	1.65122i	0.0527113	−	0.0706658i
$547$	−6.11937			−0.261645			−0.130823	−	0.991406i	$-0.541762\pi$
$547$	−6.11937			−0.261645			−0.130823	+	0.991406i	$0.541762\pi$
$548$		−	31.7668i		−	1.35701i
$549$	−11.7068			−0.499636
$550$	−1.00047			−0.0426601
$551$		−	27.8637i		−	1.18703i
$552$			8.06725i			0.343365i
$553$			19.6446i			0.835375i
$554$			3.55941i			0.151225i
$555$	−0.752583			−0.0319454
$556$	28.3737			1.20331
$557$		−	26.4697i		−	1.12156i	−0.827965	−	0.560779i	$-0.810502\pi$
$557$		−	26.4697i		−	1.12156i	0.827965	−	0.560779i	$-0.189498\pi$
$558$	−2.62547			−0.111145
$559$	2.85806	−	3.83157i	0.120883	−	0.162058i
$560$	8.10336			0.342430
$561$		−	1.81402i		−	0.0765881i
$562$	−5.30182			−0.223644
$563$	−19.4450			−0.819508			−0.409754	−	0.912196i	$-0.634385\pi$
$563$	−19.4450			−0.819508			−0.409754	+	0.912196i	$0.634385\pi$
$564$			6.36590i			0.268053i
$565$		−	4.87589i		−	0.205130i
$566$			0.953779i			0.0400903i
$567$		−	2.34031i		−	0.0982839i
$568$	12.5642			0.527181
$569$	28.1227			1.17896			0.589482	−	0.807781i	$-0.299332\pi$
$569$	28.1227			1.17896			0.589482	+	0.807781i	$0.299332\pi$
$570$		−	1.08381i		−	0.0453959i
$571$	−0.383491			−0.0160486			−0.00802430	−	0.999968i	$-0.502554\pi$
$571$	−0.383491			−0.0160486			−0.00802430	+	0.999968i	$0.502554\pi$
$572$	−5.60792	−	4.18308i	−0.234479	−	0.174904i
$573$	−6.40156			−0.267429
$574$		−	6.23344i		−	0.260179i
$575$	34.3674			1.43322
$576$	6.60493			0.275205
$577$		−	12.6561i		−	0.526879i	−0.964676	−	0.263439i	$-0.915143\pi$
$577$		−	12.6561i		−	0.526879i	0.964676	−	0.263439i	$-0.0848569\pi$
$578$			3.34685i			0.139211i
$579$		−	17.4615i		−	0.725677i
$580$		−	10.9839i		−	0.456080i
$581$	−37.2996			−1.54745
$582$	−3.29518			−0.136589
$583$			4.54533i			0.188248i
$584$	4.10208			0.169745
$585$	2.74467	+	2.04732i	0.113478	+	0.0846461i
$586$	0.620369			0.0256272
$587$			30.2694i			1.24935i	0.780885	+	0.624675i	$0.214769\pi$
$587$			30.2694i			1.24935i	−0.780885	+	0.624675i	$0.785231\pi$
$588$	−2.95510			−0.121866
$589$	50.2737			2.07149
$590$		−	0.391457i		−	0.0161160i
$591$			2.32132i			0.0954863i
$592$		−	2.88926i		−	0.118748i
$593$			2.13565i			0.0877008i	0.999038	+	0.0438504i	$0.0139625\pi$
$593$			2.13565i			0.0877008i	−0.999038	+	0.0438504i	$0.986038\pi$
$594$	0.244130			0.0100168
$595$	−4.03178			−0.165287
$596$		−	18.1974i		−	0.745394i
$597$	0.904709			0.0370273
$598$	−5.91692	−	4.41357i	−0.241961	−	0.180484i
$599$	3.35115			0.136924			0.0684622	−	0.997654i	$-0.478191\pi$
$599$	3.35115			0.136924			0.0684622	+	0.997654i	$0.478191\pi$
$600$			3.94224i			0.160941i
$601$	33.5312			1.36777			0.683884	−	0.729591i	$-0.260289\pi$
$601$	33.5312			1.36777			0.683884	+	0.729591i	$0.260289\pi$
$602$	−0.757462			−0.0308718
$603$			5.67728i			0.231197i
$604$			7.31613i			0.297689i
$605$		−	0.949685i		−	0.0386102i
$606$		−	3.70638i		−	0.150561i
$607$	−11.6742			−0.473843			−0.236921	−	0.971529i	$-0.576138\pi$
$607$	−11.6742			−0.473843			−0.236921	+	0.971529i	$0.576138\pi$
$608$	13.1547			0.533494
$609$		−	13.9495i		−	0.565262i
$610$	−2.71419			−0.109894
$611$	−9.48155	−	7.07251i	−0.383582	−	0.286123i
$612$	−3.51993			−0.142285
$613$			6.17292i			0.249322i	0.992199	+	0.124661i	$0.0397843\pi$
$613$			6.17292i			0.249322i	−0.992199	+	0.124661i	$0.960216\pi$
$614$	4.55524			0.183834
$615$	10.3613			0.417806
$616$			2.25131i			0.0907078i
$617$		−	6.80428i		−	0.273930i	−0.990576	−	0.136965i	$-0.956265\pi$
$617$		−	6.80428i		−	0.273930i	0.990576	−	0.136965i	$-0.0437348\pi$
$618$		−	4.21136i		−	0.169406i
$619$		−	25.9479i		−	1.04294i	−0.853271	−	0.521468i	$-0.825385\pi$
$619$		−	25.9479i		−	1.04294i	0.853271	−	0.521468i	$-0.174615\pi$
$620$	19.8179			0.795907
$621$	−8.38618			−0.336526
$622$		−	0.570673i		−	0.0228819i
$623$	40.4162			1.61924
$624$	−7.85989	+	10.5371i	−0.314648	+	0.421823i
$625$	12.2849			0.491396
$626$		−	3.19206i		−	0.127580i
$627$	−4.67470			−0.186690
$628$	−21.9006			−0.873929
$629$			1.43753i			0.0573182i
$630$		−	0.542593i		−	0.0216174i
$631$			8.46677i			0.337057i	0.985697	+	0.168528i	$0.0539015\pi$
$631$			8.46677i			0.337057i	−0.985697	+	0.168528i	$0.946098\pi$
$632$			8.07479i			0.321198i
$633$	0.589283			0.0234219
$634$	3.35869			0.133391
$635$			17.0159i			0.675255i
$636$	8.81976			0.349726
$637$	3.28311	−	4.40140i	0.130082	−	0.174390i
$638$	1.45514			0.0576096
$639$			13.0609i			0.516681i
$640$	6.87620			0.271806
$641$	9.22987			0.364558			0.182279	−	0.983247i	$-0.441653\pi$
$641$	9.22987			0.364558			0.182279	+	0.983247i	$0.441653\pi$
$642$		−	0.637492i		−	0.0251598i
$643$		−	12.0278i		−	0.474329i	−0.971470	−	0.237164i	$-0.923782\pi$
$643$		−	12.0278i		−	0.474329i	0.971470	−	0.237164i	$-0.0762180\pi$
$644$		−	38.0829i		−	1.50068i
$645$		−	1.25906i		−	0.0495754i
$646$	−2.07022			−0.0814519
$647$	−33.2103			−1.30563			−0.652817	−	0.757516i	$-0.726413\pi$
$647$	−33.2103			−1.30563			−0.652817	+	0.757516i	$0.726413\pi$
$648$		−	0.961969i		−	0.0377897i
$649$	−1.68843			−0.0662768
$650$	−2.89144	−	2.15679i	−0.113411	−	0.0845963i
$651$	25.1687			0.986440
$652$			22.8205i			0.893719i
$653$	−44.0416			−1.72348			−0.861741	−	0.507349i	$-0.830625\pi$
$653$	−44.0416			−1.72348			−0.861741	+	0.507349i	$0.830625\pi$
$654$	−2.27928			−0.0891268
$655$		−	8.31973i		−	0.325079i
$656$			39.7781i			1.55308i
$657$			4.26425i			0.166364i
$658$			1.87440i			0.0730719i
$659$	−22.2675			−0.867418			−0.433709	−	0.901053i	$-0.642795\pi$
$659$	−22.2675			−0.867418			−0.433709	+	0.901053i	$0.642795\pi$
$660$	−1.84277			−0.0717297
$661$			1.28521i			0.0499888i	0.999688	+	0.0249944i	$0.00795680\pi$
$661$			1.28521i			0.0499888i	−0.999688	+	0.0249944i	$0.992043\pi$
$662$	7.85748			0.305390
$663$	3.91064	−	5.24268i	0.151877	−	0.203609i
$664$	−15.3317			−0.594987
$665$			10.3898i			0.402900i
$666$	−0.193462			−0.00749649
$667$	−49.9860			−1.93547
$668$			2.43295i			0.0941337i
$669$			22.3663i			0.864730i
$670$			1.31626i			0.0508514i
$671$			11.7068i			0.451938i
$672$	6.58570			0.254049
$673$	2.42461			0.0934618			0.0467309	−	0.998908i	$-0.485120\pi$
$673$	2.42461			0.0934618			0.0467309	+	0.998908i	$0.485120\pi$
$674$		−	1.37614i		−	0.0530071i
$675$	−4.09810			−0.157736
$676$	−7.18956	−	24.1789i	−0.276522	−	0.929959i
$677$	−51.0188			−1.96081			−0.980406	−	0.196990i	$-0.936883\pi$
$677$	−51.0188			−1.96081			−0.980406	+	0.196990i	$0.936883\pi$
$678$		−	1.25341i		−	0.0481371i
$679$	31.5887			1.21226
$680$	−1.65723			−0.0635520
$681$			6.34031i			0.242961i
$682$			2.62547i			0.100535i
$683$		−	24.5461i		−	0.939231i	−0.882871	−	0.469615i	$-0.844393\pi$
$683$		−	24.5461i		−	0.939231i	0.882871	−	0.469615i	$-0.155607\pi$
$684$			9.07080i			0.346831i
$685$	15.5476			0.594042
$686$	−4.86949			−0.185918
$687$		−	3.02064i		−	0.115245i
$688$	4.83368			0.184282
$689$	−9.79874	+	13.1364i	−0.373302	+	0.500456i
$690$	−1.94431			−0.0740185
$691$		−	15.2912i		−	0.581703i	−0.956768	−	0.290852i	$-0.906061\pi$
$691$		−	15.2912i		−	0.581703i	0.956768	−	0.290852i	$-0.0939386\pi$
$692$	39.0896			1.48596
$693$	−2.34031			−0.0889012
$694$			2.01830i			0.0766137i
$695$			13.8869i			0.526758i
$696$		−	5.73384i		−	0.217340i
$697$		−	19.7914i		−	0.749652i
$698$	0.198470			0.00751220
$699$	6.98018			0.264015
$700$		−	18.6101i		−	0.703394i
$701$	35.2527			1.33147			0.665737	−	0.746186i	$-0.268117\pi$
$701$	35.2527			1.33147			0.665737	+	0.746186i	$0.268117\pi$
$702$	0.705556	+	0.526291i	0.0266295	+	0.0198636i
$703$	3.70449			0.139718
$704$		−	6.60493i		−	0.248933i
$705$	−3.11565			−0.117342
$706$	4.93908			0.185885
$707$			35.5306i			1.33627i
$708$			3.27624i			0.123129i
$709$			36.4751i			1.36985i	0.728613	+	0.684926i	$0.240165\pi$
$709$			36.4751i			1.36985i	−0.728613	+	0.684926i	$0.759835\pi$
$710$			3.02812i			0.113643i
$711$	−8.39402			−0.314800
$712$	16.6128			0.622590
$713$		−	90.1886i		−	3.37759i
$714$	−1.03642			−0.0387872
$715$	2.04732	−	2.74467i	0.0765653	−	0.102645i
$716$	14.4580			0.540322
$717$			18.0406i			0.673738i
$718$	0.623220			0.0232584
$719$	32.4563			1.21041			0.605207	−	0.796068i	$-0.293090\pi$
$719$	32.4563			1.21041			0.605207	+	0.796068i	$0.293090\pi$
$720$			3.46251i			0.129040i
$721$			40.3716i			1.50352i
$722$			0.696465i			0.0259198i
$723$		−	6.07781i		−	0.226036i
$724$	−15.1938			−0.564672
$725$	−24.4268			−0.907189
$726$		−	0.244130i		−	0.00906050i
$727$	−5.81052			−0.215500			−0.107750	−	0.994178i	$-0.534365\pi$
$727$	−5.81052			−0.215500			−0.107750	+	0.994178i	$0.534365\pi$
$728$	−4.85333	+	6.50648i	−0.179877	+	0.241146i
$729$	1.00000			0.0370370
$730$			0.988651i			0.0365916i
$731$	−2.40497			−0.0889509
$732$	22.7160			0.839606
$733$		−	43.4035i		−	1.60315i	−0.597897	−	0.801573i	$-0.703997\pi$
$733$		−	43.4035i		−	1.60315i	0.597897	−	0.801573i	$-0.296003\pi$
$734$			6.90292i			0.254792i
$735$		−	1.44630i		−	0.0533478i
$736$		−	23.5989i		−	0.869868i
$737$	5.67728			0.209125
$738$	2.66351			0.0980450
$739$			17.9184i			0.659140i	0.944131	+	0.329570i	$0.106904\pi$
$739$			17.9184i			0.659140i	−0.944131	+	0.329570i	$0.893096\pi$
$740$	1.46031			0.0536822
$741$	−13.5103	−	10.0776i	−0.496313	−	0.370212i
$742$	2.59693			0.0953362
$743$		−	28.8438i		−	1.05818i	−0.848567	−	0.529088i	$-0.822534\pi$
$743$		−	28.8438i		−	1.05818i	0.848567	−	0.529088i	$-0.177466\pi$
$744$	10.3454			0.379281
$745$	8.90629			0.326301
$746$			3.90390i			0.142932i
$747$		−	15.9379i		−	0.583136i
$748$			3.51993i			0.128701i
$749$			6.11123i			0.223299i
$750$	−2.10936			−0.0770230
$751$	−17.8999			−0.653176			−0.326588	−	0.945167i	$-0.605899\pi$
$751$	−17.8999			−0.653176			−0.326588	+	0.945167i	$0.605899\pi$
$752$		−	11.9613i		−	0.436185i
$753$	−8.87125			−0.323286
$754$	4.20548	+	3.13697i	0.153155	+	0.114242i
$755$	−3.58071			−0.130315
$756$			4.54115i			0.165160i
$757$	17.7915			0.646643			0.323322	−	0.946289i	$-0.395200\pi$
$757$	17.7915			0.646643			0.323322	+	0.946289i	$0.395200\pi$
$758$	−2.12302			−0.0771114
$759$			8.38618i			0.304399i
$760$			4.27066i			0.154913i
$761$			27.3832i			0.992640i	0.868140	+	0.496320i	$0.165316\pi$
$761$			27.3832i			0.992640i	−0.868140	+	0.496320i	$0.834684\pi$
$762$			4.37417i			0.158459i
$763$	21.8500			0.791022
$764$	12.4216			0.449398
$765$		−	1.72275i		−	0.0622862i
$766$	−8.47226			−0.306115
$767$	−4.87972	−	3.63990i	−0.176196	−	0.131429i
$768$	−11.4422			−0.412886
$769$		−	42.9715i		−	1.54959i	−0.632211	−	0.774796i	$-0.717852\pi$
$769$		−	42.9715i		−	1.54959i	0.632211	−	0.774796i	$-0.282148\pi$
$770$	−0.542593			−0.0195537
$771$	−4.96352			−0.178757
$772$			33.8824i			1.21945i
$773$			23.5054i			0.845430i	0.906263	+	0.422715i	$0.138923\pi$
$773$			23.5054i			0.845430i	−0.906263	+	0.422715i	$0.861077\pi$
$774$		−	0.323658i		−	0.0116337i
$775$		−	44.0727i		−	1.58314i
$776$	12.9843			0.466110
$777$	1.85459			0.0665332
$778$		−	2.07700i		−	0.0744640i
$779$	−51.0020			−1.82734
$780$	−5.32576	−	3.97261i	−0.190693	−	0.142242i
$781$	13.0609			0.467355
$782$			3.71388i			0.132808i
$783$	5.96052			0.213012
$784$	5.55254			0.198305
$785$		−	10.7188i		−	0.382569i
$786$		−	2.13870i		−	0.0762850i
$787$			17.7319i			0.632075i	0.948747	+	0.316037i	$0.102353\pi$
$787$			17.7319i			0.632075i	−0.948747	+	0.316037i	$0.897647\pi$
$788$		−	4.50429i		−	0.160459i
$789$	−27.9087			−0.993575
$790$	−1.94612			−0.0692400
$791$			12.0157i			0.427228i
$792$	−0.961969			−0.0341821
$793$	−25.2374	+	33.8338i	−0.896207	+	1.20147i
$794$	1.62438			0.0576470
$795$			4.31663i			0.153095i
$796$	−1.75550			−0.0622220
$797$	9.52106			0.337253			0.168627	−	0.985680i	$-0.446067\pi$
$797$	9.52106			0.337253			0.168627	+	0.985680i	$0.446067\pi$
$798$			2.67084i			0.0945469i
$799$			5.95129i			0.210542i
$800$		−	11.5321i		−	0.407723i
$801$			17.2696i			0.610190i
$802$	3.74288			0.132166
$803$	4.26425			0.150482
$804$		−	11.0162i		−	0.388511i
$805$	18.6388			0.656932
$806$	−5.65995	+	7.58784i	−0.199363	+	0.267270i
$807$	−10.0834			−0.354952
$808$			14.6046i			0.513788i
$809$	13.5622			0.476822			0.238411	−	0.971164i	$-0.423374\pi$
$809$	13.5622			0.476822			0.238411	+	0.971164i	$0.423374\pi$
$810$	0.231846			0.00814625
$811$		−	15.9033i		−	0.558439i	−0.960227	−	0.279220i	$-0.909924\pi$
$811$		−	15.9033i		−	0.558439i	0.960227	−	0.279220i	$-0.0900758\pi$
$812$			27.0676i			0.949887i
$813$		−	26.3949i		−	0.925710i
$814$			0.193462i			0.00678083i
$815$	−11.1690			−0.391232
$816$	6.61385			0.231531
$817$			6.19755i			0.216825i
$818$	2.66691			0.0932462
$819$	−6.76371	−	5.04521i	−0.236343	−	0.176294i
$820$	−20.1050			−0.702097
$821$		−	32.6516i		−	1.13955i	−0.821802	−	0.569774i	$-0.807031\pi$
$821$		−	32.6516i		−	1.13955i	0.821802	−	0.569774i	$-0.192969\pi$
$822$	3.99671			0.139401
$823$	−21.6951			−0.756245			−0.378122	−	0.925756i	$-0.623430\pi$
$823$	−21.6951			−0.756245			−0.378122	+	0.925756i	$0.623430\pi$
$824$			16.5945i			0.578095i
$825$			4.09810i			0.142677i
$826$			0.964669i			0.0335651i
$827$		−	5.83855i		−	0.203026i	−0.994834	−	0.101513i	$-0.967632\pi$
$827$		−	5.83855i		−	0.203026i	0.994834	−	0.101513i	$-0.0323684\pi$
$828$	16.2726			0.565510
$829$	10.7136			0.372098			0.186049	−	0.982540i	$-0.440432\pi$
$829$	10.7136			0.372098			0.186049	+	0.982540i	$0.440432\pi$
$830$		−	3.69514i		−	0.128260i
$831$	14.5800			0.505775
$832$	14.2388	−	19.0888i	0.493641	−	0.661785i
$833$	−2.76263			−0.0957195
$834$			3.56981i			0.123612i
$835$	−1.19075			−0.0412077
$836$	9.07080			0.313720
$837$			10.7544i			0.371727i
$838$			7.25510i			0.250623i
$839$			4.96178i			0.171300i	0.996325	+	0.0856498i	$0.0272966\pi$
$839$			4.96178i			0.171300i	−0.996325	+	0.0856498i	$0.972703\pi$
$840$			2.13803i			0.0737692i
$841$	6.52783			0.225097
$842$	−3.08612			−0.106355
$843$			21.7172i			0.747982i
$844$	−1.14345			−0.0393590
$845$	11.8338	−	3.51877i	0.407096	−	0.121049i
$846$	−0.800920			−0.0275362
$847$			2.34031i			0.0804141i
$848$	−16.5721			−0.569087
$849$	3.90686			0.134083
$850$			1.81487i			0.0622496i
$851$		−	6.64568i		−	0.227811i
$852$		−	25.3434i		−	0.868249i
$853$		−	15.2322i		−	0.521542i	−0.965401	−	0.260771i	$-0.916023\pi$
$853$		−	15.2322i		−	0.521542i	0.965401	−	0.260771i	$-0.0839767\pi$
$854$	6.68859			0.228879
$855$	−4.43950			−0.151828
$856$			2.51197i			0.0858575i
$857$	−39.3831			−1.34530			−0.672651	−	0.739960i	$-0.734844\pi$
$857$	−39.3831			−1.34530			−0.672651	+	0.739960i	$0.734844\pi$
$858$	0.526291	−	0.705556i	0.0179673	−	0.0240873i
$859$	21.3316			0.727826			0.363913	−	0.931433i	$-0.381441\pi$
$859$	21.3316			0.727826			0.363913	+	0.931433i	$0.381441\pi$
$860$			2.44308i			0.0833083i
$861$	−25.5333			−0.870173
$862$	5.98853			0.203970
$863$		−	14.2578i		−	0.485342i	−0.970109	−	0.242671i	$-0.921976\pi$
$863$		−	14.2578i		−	0.485342i	0.970109	−	0.242671i	$-0.0780235\pi$
$864$			2.81402i			0.0957350i
$865$			19.1315i			0.650491i
$866$		−	5.45571i		−	0.185393i
$867$	13.7093			0.465593
$868$	−48.8374			−1.65765
$869$			8.39402i			0.284748i
$870$	1.38193			0.0468517
$871$	16.4078	+	12.2390i	0.555958	+	0.414702i
$872$	8.98126			0.304144
$873$			13.4976i			0.456826i
$874$	9.57059			0.323730
$875$	20.2211			0.683597
$876$		−	8.27436i		−	0.279565i
$877$		−	5.01119i		−	0.169216i	−0.996414	−	0.0846079i	$-0.973036\pi$
$877$		−	5.01119i		−	0.169216i	0.996414	−	0.0846079i	$-0.0269638\pi$
$878$		−	6.34459i		−	0.214120i
$879$		−	2.54115i		−	0.0857108i
$880$	3.46251			0.116721
$881$	−15.3769			−0.518062			−0.259031	−	0.965869i	$-0.583403\pi$
$881$	−15.3769			−0.518062			−0.259031	+	0.965869i	$0.583403\pi$
$882$		−	0.371793i		−	0.0125189i
$883$	22.6842			0.763383			0.381691	−	0.924290i	$-0.375342\pi$
$883$	22.6842			0.763383			0.381691	+	0.924290i	$0.375342\pi$
$884$	−7.58821	+	10.1729i	−0.255219	+	0.342152i
$885$	−1.60348			−0.0539004
$886$		−	7.40111i		−	0.248645i
$887$	−28.2155			−0.947385			−0.473693	−	0.880690i	$-0.657079\pi$
$887$	−28.2155			−0.947385			−0.473693	+	0.880690i	$0.657079\pi$
$888$	0.762317			0.0255817
$889$		−	41.9323i		−	1.40636i
$890$			4.00388i			0.134210i
$891$		−	1.00000i		−	0.0335013i
$892$		−	43.3995i		−	1.45312i
$893$	15.3364			0.513212
$894$	2.28949			0.0765718
$895$			7.07616i			0.236530i
$896$	−16.9451			−0.566095
$897$	−18.0788	+	24.2368i	−0.603633	+	0.809243i
$898$	−6.33616			−0.211440
$899$			64.1020i			2.13792i
$900$	7.95195			0.265065
$901$	8.24533			0.274692
$902$		−	2.66351i		−	0.0886850i
$903$			3.10270i			0.103252i
$904$			4.93895i			0.164267i
$905$		−	7.43625i		−	0.247189i
$906$	−0.920471			−0.0305806
$907$	−27.8360			−0.924279			−0.462139	−	0.886807i	$-0.652918\pi$
$907$	−27.8360			−0.924279			−0.462139	+	0.886807i	$0.652918\pi$
$908$		−	12.3027i		−	0.408281i
$909$	−15.1820			−0.503555
$910$	−1.56814	−	1.16971i	−0.0519834	−	0.0387756i
$911$	−4.42415			−0.146579			−0.0732893	−	0.997311i	$-0.523350\pi$
$911$	−4.42415			−0.146579			−0.0732893	+	0.997311i	$0.523350\pi$
$912$		−	17.0438i		−	0.564375i
$913$	−15.9379			−0.527466
$914$	0.154696			0.00511690
$915$			11.1178i			0.367544i
$916$			5.86126i			0.193661i
$917$			20.5024i			0.677048i
$918$		−	0.442857i		−	0.0146165i
$919$	−2.94829			−0.0972552			−0.0486276	−	0.998817i	$-0.515485\pi$
$919$	−2.94829			−0.0972552			−0.0486276	+	0.998817i	$0.515485\pi$
$920$	7.66134			0.252587
$921$		−	18.6591i		−	0.614838i
$922$	−3.34339			−0.110109
$923$	37.7471	+	28.1564i	1.24246	+	0.926781i
$924$	4.54115			0.149393
$925$		−	3.24756i		−	0.106779i
$926$	0.481722			0.0158304
$927$	−17.2505			−0.566581
$928$			16.7730i			0.550602i
$929$		−	2.40399i		−	0.0788723i	−0.999222	−	0.0394361i	$-0.987444\pi$
$929$		−	2.40399i		−	0.0788723i	0.999222	−	0.0394361i	$-0.0125562\pi$
$930$			2.49337i			0.0817609i
$931$			7.11925i			0.233324i
$932$	−13.5443			−0.443660
$933$	−2.33758			−0.0765289
$934$			4.03296i			0.131962i
$935$	−1.72275			−0.0563400
$936$	−2.78017	−	2.07380i	−0.0908728	−	0.0677841i
$937$	9.01186			0.294405			0.147202	−	0.989106i	$-0.452973\pi$
$937$	9.01186			0.294405			0.147202	+	0.989106i	$0.452973\pi$
$938$		−	3.24365i		−	0.105909i
$939$	−13.0753			−0.426695
$940$	6.04560			0.197186
$941$			58.9978i			1.92327i	0.274326	+	0.961637i	$0.411545\pi$
$941$			58.9978i			1.92327i	−0.274326	+	0.961637i	$0.588455\pi$
$942$		−	2.75540i		−	0.0897759i
$943$			91.4950i			2.97949i
$944$		−	6.15595i		−	0.200359i
$945$	−2.22256			−0.0722999
$946$	−0.323658			−0.0105230
$947$		−	15.4055i		−	0.500612i	−0.968167	−	0.250306i	$-0.919469\pi$
$947$		−	15.4055i		−	0.500612i	0.968167	−	0.250306i	$-0.0805313\pi$
$948$	16.2878			0.529002
$949$	12.3241	+	9.19280i	0.400056	+	0.298411i
$950$	4.67689			0.151738
$951$		−	13.7578i		−	0.446128i
$952$	4.08393			0.132361
$953$	−26.7856			−0.867672			−0.433836	−	0.900992i	$-0.642840\pi$
$953$	−26.7856			−0.867672			−0.433836	+	0.900992i	$0.642840\pi$
$954$			1.10965i			0.0359262i
$955$			6.07947i			0.196727i
$956$		−	35.0060i		−	1.13217i
$957$		−	5.96052i		−	0.192676i
$958$	−2.58555			−0.0835354
$959$	−38.3139			−1.23722
$960$		−	6.27260i		−	0.202447i
$961$	−84.6576			−2.73089
$962$	−0.417062	+	0.559121i	−0.0134466	+	0.0180268i
$963$	−2.61128			−0.0841475
$964$			11.7934i			0.379839i
$965$	−16.5830			−0.533824
$966$	4.79136			0.154160
$967$			7.90477i			0.254200i	0.991890	+	0.127100i	$0.0405669\pi$
$967$			7.90477i			0.254200i	−0.991890	+	0.127100i	$0.959433\pi$
$968$			0.961969i			0.0309188i
$969$			8.48002i			0.272417i
$970$			3.12938i			0.100478i
$971$	−24.8695			−0.798101			−0.399051	−	0.916929i	$-0.630660\pi$
$971$	−24.8695			−0.798101			−0.399051	+	0.916929i	$0.630660\pi$
$972$	−1.94040			−0.0622384
$973$		−	34.2214i		−	1.09709i
$974$	−6.36635			−0.203991
$975$	−8.83461	+	11.8439i	−0.282934	+	0.379307i
$976$	−42.6826			−1.36624
$977$			12.3696i			0.395740i	0.980228	+	0.197870i	$0.0634023\pi$
$977$			12.3696i			0.395740i	−0.980228	+	0.197870i	$0.936598\pi$
$978$	−2.87114			−0.0918089
$979$	17.2696			0.551937
$980$			2.80641i			0.0896475i
$981$			9.33634i			0.298086i
$982$			3.66288i			0.116887i
$983$		−	44.0719i		−	1.40568i	−0.711350	−	0.702838i	$-0.751916\pi$
$983$		−	44.0719i		−	1.40568i	0.711350	−	0.702838i	$-0.248084\pi$
$984$	−10.4953			−0.334577
$985$	2.20452			0.0702419
$986$		−	2.63966i		−	0.0840638i
$987$	7.67790			0.244390
$988$	26.2154	+	19.5547i	0.834022	+	0.622117i
$989$	11.1181			0.353535
$990$		−	0.231846i		−	0.00736856i
$991$	−47.9660			−1.52369			−0.761846	−	0.647759i	$-0.775707\pi$
$991$	−47.9660			−1.52369			−0.761846	+	0.647759i	$0.775707\pi$
$992$	−30.2632			−0.960858
$993$		−	32.1857i		−	1.02138i
$994$		−	7.46221i		−	0.236687i
$995$		−	0.859189i		−	0.0272381i
$996$			30.9259i			0.979923i
$997$	−23.4404			−0.742366			−0.371183	−	0.928560i	$-0.621048\pi$
$997$	−23.4404			−0.742366			−0.371183	+	0.928560i	$0.621048\pi$
$998$	−5.53944			−0.175348
$999$			0.792455i			0.0250722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.b.a.298.5	✓	10
3.2	odd	2		1287.2.b.a.298.6		10
13.5	odd	4		5577.2.a.q.1.3		5
13.8	odd	4		5577.2.a.t.1.3		5
13.12	even	2	inner	429.2.b.a.298.6	yes	10
39.38	odd	2		1287.2.b.a.298.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.a.298.5	✓	10	1.1	even	1	trivial
429.2.b.a.298.6	yes	10	13.12	even	2	inner
1287.2.b.a.298.5		10	39.38	odd	2
1287.2.b.a.298.6		10	3.2	odd	2
5577.2.a.q.1.3		5	13.5	odd	4
5577.2.a.t.1.3		5	13.8	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.244130i q^{2} -1.00000 q^{3} +1.94040 q^{4} +0.949685i q^{5} +0.244130i q^{6} -2.34031i q^{7} -0.961969i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.244130i q^{2} -1.00000 q^{3} +1.94040 q^{4} +0.949685i q^{5} +0.244130i q^{6} -2.34031i q^{7} -0.961969i q^{8} +1.00000 q^{9} +0.231846 q^{10} -1.00000i q^{11} -1.94040 q^{12} +(2.15578 - 2.89009i) q^{13} -0.571340 q^{14} -0.949685i q^{15} +3.64596 q^{16} -1.81402 q^{17} -0.244130i q^{18} +4.67470i q^{19} +1.84277i q^{20} +2.34031i q^{21} -0.244130 q^{22} +8.38618 q^{23} +0.961969i q^{24} +4.09810 q^{25} +(-0.705556 - 0.526291i) q^{26} -1.00000 q^{27} -4.54115i q^{28} -5.96052 q^{29} -0.231846 q^{30} -10.7544i q^{31} -2.81402i q^{32} +1.00000i q^{33} +0.442857i q^{34} +2.22256 q^{35} +1.94040 q^{36} -0.792455i q^{37} +1.14123 q^{38} +(-2.15578 + 2.89009i) q^{39} +0.913567 q^{40} +10.9102i q^{41} +0.571340 q^{42} +1.32576 q^{43} -1.94040i q^{44} +0.949685i q^{45} -2.04732i q^{46} -3.28071i q^{47} -3.64596 q^{48} +1.52293 q^{49} -1.00047i q^{50} +1.81402 q^{51} +(4.18308 - 5.60792i) q^{52} -4.54533 q^{53} +0.244130i q^{54} +0.949685 q^{55} -2.25131 q^{56} -4.67470i q^{57} +1.45514i q^{58} -1.68843i q^{59} -1.84277i q^{60} -11.7068 q^{61} -2.62547 q^{62} -2.34031i q^{63} +6.60493 q^{64} +(2.74467 + 2.04732i) q^{65} +0.244130 q^{66} +5.67728i q^{67} -3.51993 q^{68} -8.38618 q^{69} -0.542593i q^{70} +13.0609i q^{71} -0.961969i q^{72} +4.26425i q^{73} -0.193462 q^{74} -4.09810 q^{75} +9.07080i q^{76} -2.34031 q^{77} +(0.705556 + 0.526291i) q^{78} -8.39402 q^{79} +3.46251i q^{80} +1.00000 q^{81} +2.66351 q^{82} -15.9379i q^{83} +4.54115i q^{84} -1.72275i q^{85} -0.323658i q^{86} +5.96052 q^{87} -0.961969 q^{88} +17.2696i q^{89} +0.231846 q^{90} +(-6.76371 - 5.04521i) q^{91} +16.2726 q^{92} +10.7544i q^{93} -0.800920 q^{94} -4.43950 q^{95} +2.81402i q^{96} +13.4976i q^{97} -0.371793i q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9	\( 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9} + 6 q^{12} + 12 q^{13} - 32 q^{14} + 6 q^{16} + 20 q^{17} - 2 q^{22} + 8 q^{23} - 14 q^{25} - 2 q^{26} - 10 q^{27} + 8 q^{29} - 6 q^{36} - 12 q^{39} - 20 q^{40} + 32 q^{42} - 24 q^{43} - 6 q^{48} - 26 q^{49} - 20 q^{51} - 48 q^{52} - 4 q^{53} + 4 q^{55} + 16 q^{56} + 36 q^{61} + 24 q^{62} + 50 q^{64} + 28 q^{65} + 2 q^{66} - 12 q^{68} - 8 q^{69} + 24 q^{74} + 14 q^{75} + 12 q^{77} + 2 q^{78} + 36 q^{79} + 10 q^{81} - 20 q^{82} - 8 q^{87} - 6 q^{88} - 24 q^{91} - 8 q^{92} - 32 q^{94} + 44 q^{95}+O(q^{100}) \) 10 * q - 10 * q^3 - 6 * q^4 + 10 * q^9 + 6 * q^12 + 12 * q^13 - 32 * q^14 + 6 * q^16 + 20 * q^17 - 2 * q^22 + 8 * q^23 - 14 * q^25 - 2 * q^26 - 10 * q^27 + 8 * q^29 - 6 * q^36 - 12 * q^39 - 20 * q^40 + 32 * q^42 - 24 * q^43 - 6 * q^48 - 26 * q^49 - 20 * q^51 - 48 * q^52 - 4 * q^53 + 4 * q^55 + 16 * q^56 + 36 * q^61 + 24 * q^62 + 50 * q^64 + 28 * q^65 + 2 * q^66 - 12 * q^68 - 8 * q^69 + 24 * q^74 + 14 * q^75 + 12 * q^77 + 2 * q^78 + 36 * q^79 + 10 * q^81 - 20 * q^82 - 8 * q^87 - 6 * q^88 - 24 * q^91 - 8 * q^92 - 32 * q^94 + 44 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more