LMFDB - Embedded newform 429.2.b.a.298.4

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			298.4
Root			$-0.547285i$ of defining polynomial
Character	$\chi$	$=$	429.298
Dual form			429.2.b.a.298.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.547285i q^{2} -1.00000 q^{3} +1.70048 q^{4} +0.955178i q^{5} +0.547285i q^{6} -4.37449i q^{7} -2.02522i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.547285i q^{2} -1.00000 q^{3} +1.70048 q^{4} +0.955178i q^{5} +0.547285i q^{6} -4.37449i q^{7} -2.02522i q^{8} +1.00000 q^{9} +0.522755 q^{10} +1.00000i q^{11} -1.70048 q^{12} +(-3.52768 + 0.745301i) q^{13} -2.39409 q^{14} -0.955178i q^{15} +2.29259 q^{16} +6.30513 q^{17} -0.547285i q^{18} -7.97346i q^{19} +1.62426i q^{20} +4.37449i q^{21} +0.547285 q^{22} -6.15686 q^{23} +2.02522i q^{24} +4.08764 q^{25} +(0.407892 + 1.93065i) q^{26} -1.00000 q^{27} -7.43872i q^{28} +6.17716 q^{29} -0.522755 q^{30} +2.39535i q^{31} -5.30513i q^{32} -1.00000i q^{33} -3.45071i q^{34} +4.17841 q^{35} +1.70048 q^{36} -4.57944i q^{37} -4.36376 q^{38} +(3.52768 - 0.745301i) q^{39} +1.93444 q^{40} +3.13233i q^{41} +2.39409 q^{42} -5.21056 q^{43} +1.70048i q^{44} +0.955178i q^{45} +3.36956i q^{46} -3.67401i q^{47} -2.29259 q^{48} -12.1361 q^{49} -2.23710i q^{50} -6.30513 q^{51} +(-5.99875 + 1.26737i) q^{52} +0.617769 q^{53} +0.547285i q^{54} -0.955178 q^{55} -8.85928 q^{56} +7.97346i q^{57} -3.38067i q^{58} +13.0554i q^{59} -1.62426i q^{60} +0.890818 q^{61} +1.31094 q^{62} -4.37449i q^{63} +1.68175 q^{64} +(-0.711895 - 3.36956i) q^{65} -0.547285 q^{66} +3.32587i q^{67} +10.7217 q^{68} +6.15686 q^{69} -2.28678i q^{70} -1.81660i q^{71} -2.02522i q^{72} +8.42492i q^{73} -2.50626 q^{74} -4.08764 q^{75} -13.5587i q^{76} +4.37449 q^{77} +(-0.407892 - 1.93065i) q^{78} +16.9645 q^{79} +2.18983i q^{80} +1.00000 q^{81} +1.71428 q^{82} +11.8778i q^{83} +7.43872i q^{84} +6.02252i q^{85} +2.85166i q^{86} -6.17716 q^{87} +2.02522 q^{88} +10.0552i q^{89} +0.522755 q^{90} +(3.26031 + 15.4318i) q^{91} -10.4696 q^{92} -2.39535i q^{93} -2.01073 q^{94} +7.61607 q^{95} +5.30513i q^{96} +7.46849i q^{97} +6.64192i q^{98} +1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.547285i		−	0.386989i	−0.981101	−	0.193495i	$-0.938018\pi$
$2$		−	0.547285i		−	0.386989i	0.981101	−	0.193495i	$-0.0619822\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.70048			0.850239
$5$			0.955178i			0.427168i	0.976925	+	0.213584i	$0.0685138\pi$
$5$			0.955178i			0.427168i	−0.976925	+	0.213584i	$0.931486\pi$
$6$			0.547285i			0.223428i
$7$		−	4.37449i		−	1.65340i	−0.562643	−	0.826700i	$-0.690215\pi$
$7$		−	4.37449i		−	1.65340i	0.562643	−	0.826700i	$-0.309785\pi$
$8$		−	2.02522i		−	0.716022i
$9$	1.00000			0.333333
$10$	0.522755			0.165309
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	−1.70048			−0.490886
$13$	−3.52768	+	0.745301i	−0.978402	+	0.206709i
$13$	−3.52768	+	0.745301i	−0.978402	+	0.206709i
$14$	−2.39409			−0.639848
$15$		−	0.955178i		−	0.246626i
$16$	2.29259			0.573147
$17$	6.30513			1.52922			0.764610	−	0.644494i	$-0.222932\pi$
$17$	6.30513			1.52922			0.764610	+	0.644494i	$0.222932\pi$
$18$		−	0.547285i		−	0.128996i
$19$		−	7.97346i		−	1.82924i	−0.404318	−	0.914619i	$-0.632491\pi$
$19$		−	7.97346i		−	1.82924i	0.404318	−	0.914619i	$-0.367509\pi$
$20$			1.62426i			0.363195i
$21$			4.37449i			0.954591i
$22$	0.547285			0.116682
$23$	−6.15686			−1.28380			−0.641898	−	0.766790i	$-0.721853\pi$
$23$	−6.15686			−1.28380			−0.641898	+	0.766790i	$0.721853\pi$
$24$			2.02522i			0.413396i
$25$	4.08764			0.817527
$26$	0.407892	+	1.93065i	0.0799943	+	0.378631i
$27$	−1.00000			−0.192450
$28$		−	7.43872i		−	1.40579i
$29$	6.17716			1.14707			0.573535	−	0.819181i	$-0.305572\pi$
$29$	6.17716			1.14707			0.573535	+	0.819181i	$0.305572\pi$
$30$	−0.522755			−0.0954415
$31$			2.39535i			0.430217i	0.976590	+	0.215108i	$0.0690105\pi$
$31$			2.39535i			0.430217i	−0.976590	+	0.215108i	$0.930990\pi$
$32$		−	5.30513i		−	0.937824i
$33$		−	1.00000i		−	0.174078i
$34$		−	3.45071i		−	0.591791i
$35$	4.17841			0.706280
$36$	1.70048			0.283413
$37$		−	4.57944i		−	0.752855i	−0.926446	−	0.376427i	$-0.877152\pi$
$37$		−	4.57944i		−	0.752855i	0.926446	−	0.376427i	$-0.122848\pi$
$38$	−4.36376			−0.707895
$39$	3.52768	−	0.745301i	0.564881	−	0.119344i
$40$	1.93444			0.305862
$41$			3.13233i			0.489188i	0.969626	+	0.244594i	$0.0786547\pi$
$41$			3.13233i			0.489188i	−0.969626	+	0.244594i	$0.921345\pi$
$42$	2.39409			0.369416
$43$	−5.21056			−0.794603			−0.397302	−	0.917688i	$-0.630053\pi$
$43$	−5.21056			−0.794603			−0.397302	+	0.917688i	$0.630053\pi$
$44$			1.70048i			0.256357i
$45$			0.955178i			0.142389i
$46$			3.36956i			0.496815i
$47$		−	3.67401i		−	0.535909i	−0.963432	−	0.267955i	$-0.913652\pi$
$47$		−	3.67401i		−	0.535909i	0.963432	−	0.267955i	$-0.0863477\pi$
$48$	−2.29259			−0.330906
$49$	−12.1361			−1.73373
$50$		−	2.23710i		−	0.316374i
$51$	−6.30513			−0.882895
$52$	−5.99875	+	1.26737i	−0.831876	+	0.175753i
$53$	0.617769			0.0848570			0.0424285	−	0.999100i	$-0.486491\pi$
$53$	0.617769			0.0848570			0.0424285	+	0.999100i	$0.486491\pi$
$54$			0.547285i			0.0744761i
$55$	−0.955178			−0.128796
$56$	−8.85928			−1.18387
$57$			7.97346i			1.05611i
$58$		−	3.38067i		−	0.443903i
$59$			13.0554i			1.69966i	0.527054	+	0.849832i	$0.323296\pi$
$59$			13.0554i			1.69966i	−0.527054	+	0.849832i	$0.676704\pi$
$60$		−	1.62426i		−	0.209691i
$61$	0.890818			0.114058			0.0570288	−	0.998373i	$-0.481837\pi$
$61$	0.890818			0.114058			0.0570288	+	0.998373i	$0.481837\pi$
$62$	1.31094			0.166489
$63$		−	4.37449i		−	0.551133i
$64$	1.68175			0.210219
$65$	−0.711895	−	3.36956i	−0.0882997	−	0.417943i
$66$	−0.547285			−0.0673661
$67$			3.32587i			0.406320i	0.979146	+	0.203160i	$0.0651211\pi$
$67$			3.32587i			0.406320i	−0.979146	+	0.203160i	$0.934879\pi$
$68$	10.7217			1.30020
$69$	6.15686			0.741199
$70$		−	2.28678i		−	0.273323i
$71$		−	1.81660i		−	0.215590i	−0.994173	−	0.107795i	$-0.965621\pi$
$71$		−	1.81660i		−	0.215590i	0.994173	−	0.107795i	$-0.0343791\pi$
$72$		−	2.02522i		−	0.238674i
$73$			8.42492i			0.986062i	0.870012	+	0.493031i	$0.164111\pi$
$73$			8.42492i			0.986062i	−0.870012	+	0.493031i	$0.835889\pi$
$74$	−2.50626			−0.291347
$75$	−4.08764			−0.472000
$76$		−	13.5587i		−	1.55529i
$77$	4.37449			0.498519
$78$	−0.407892	−	1.93065i	−0.0461847	−	0.218603i
$79$	16.9645			1.90865			0.954325	−	0.298769i	$-0.0965760\pi$
$79$	16.9645			1.90865			0.954325	+	0.298769i	$0.0965760\pi$
$80$			2.18983i			0.244830i
$81$	1.00000			0.111111
$82$	1.71428			0.189311
$83$			11.8778i			1.30375i	0.758325	+	0.651877i	$0.226018\pi$
$83$			11.8778i			1.30375i	−0.758325	+	0.651877i	$0.773982\pi$
$84$			7.43872i			0.811631i
$85$			6.02252i			0.653234i
$86$			2.85166i			0.307503i
$87$	−6.17716			−0.662261
$88$	2.02522			0.215889
$89$			10.0552i			1.06585i	0.846162	+	0.532926i	$0.178908\pi$
$89$			10.0552i			1.06585i	−0.846162	+	0.532926i	$0.821092\pi$
$90$	0.522755			0.0551032
$91$	3.26031	+	15.4318i	0.341773	+	1.61769i
$92$	−10.4696			−1.09153
$93$		−	2.39535i		−	0.248386i
$94$	−2.01073			−0.207391
$95$	7.61607			0.781392
$96$			5.30513i			0.541453i
$97$			7.46849i			0.758310i	0.925333	+	0.379155i	$0.123785\pi$
$97$			7.46849i			0.758310i	−0.925333	+	0.379155i	$0.876215\pi$
$98$			6.64192i			0.670936i
$99$			1.00000i			0.100504i
$100$	6.95094			0.695094
$101$	−10.3305			−1.02792			−0.513960	−	0.857814i	$-0.671822\pi$
$101$	−10.3305			−1.02792			−0.513960	+	0.857814i	$0.671822\pi$
$102$			3.45071i			0.341671i
$103$	3.50682			0.345537			0.172769	−	0.984962i	$-0.444729\pi$
$103$	3.50682			0.345537			0.172769	+	0.984962i	$0.444729\pi$
$104$	1.50940	+	7.14432i	0.148009	+	0.700558i
$105$	−4.17841			−0.407771
$106$		−	0.338096i		−	0.0328387i
$107$	−13.3341			−1.28906			−0.644530	−	0.764579i	$-0.722947\pi$
$107$	−13.3341			−1.28906			−0.644530	+	0.764579i	$0.722947\pi$
$108$	−1.70048			−0.163629
$109$			10.3491i			0.991268i	0.868531	+	0.495634i	$0.165064\pi$
$109$			10.3491i			0.991268i	−0.868531	+	0.495634i	$0.834936\pi$
$110$			0.522755i			0.0498427i
$111$			4.57944i			0.434661i
$112$		−	10.0289i		−	0.947641i
$113$	−2.19802			−0.206772			−0.103386	−	0.994641i	$-0.532968\pi$
$113$	−2.19802			−0.206772			−0.103386	+	0.994641i	$0.532968\pi$
$114$	4.36376			0.408703
$115$		−	5.88090i		−	0.548397i
$116$	10.5041			0.975283
$117$	−3.52768	+	0.745301i	−0.326134	+	0.0689031i
$118$	7.14500			0.657751
$119$		−	27.5817i		−	2.52841i
$120$	−1.93444			−0.176590
$121$	−1.00000			−0.0909091
$122$		−	0.487531i		−	0.0441390i
$123$		−	3.13233i		−	0.282433i
$124$			4.07324i			0.365787i
$125$			8.68031i			0.776390i
$126$	−2.39409			−0.213283
$127$	11.2742			1.00043			0.500213	−	0.865902i	$-0.333255\pi$
$127$	11.2742			1.00043			0.500213	+	0.865902i	$0.333255\pi$
$128$		−	11.5307i		−	1.01918i
$129$	5.21056			0.458764
$130$	−1.84411	+	0.389610i	−0.161739	+	0.0341710i
$131$	−13.1311			−1.14727			−0.573636	−	0.819110i	$-0.694468\pi$
$131$	−13.1311			−1.14727			−0.573636	+	0.819110i	$0.694468\pi$
$132$		−	1.70048i		−	0.148008i
$133$	−34.8798			−3.02446
$134$	1.82020			0.157241
$135$		−	0.955178i		−	0.0822086i
$136$		−	12.7693i		−	1.09496i
$137$		−	12.4741i		−	1.06573i	−0.846199	−	0.532867i	$-0.821115\pi$
$137$		−	12.4741i		−	1.06573i	0.846199	−	0.532867i	$-0.178885\pi$
$138$		−	3.36956i		−	0.286836i
$139$	−7.61482			−0.645880			−0.322940	−	0.946419i	$-0.604671\pi$
$139$	−7.61482			−0.645880			−0.322940	+	0.946419i	$0.604671\pi$
$140$	7.10530			0.600507
$141$			3.67401i			0.309407i
$142$	−0.994196			−0.0834311
$143$	−0.745301	−	3.52768i	−0.0623252	−	0.294999i
$144$	2.29259			0.191049
$145$			5.90028i			0.489992i
$146$	4.61083			0.381595
$147$	12.1361			1.00097
$148$		−	7.78724i		−	0.640107i
$149$			20.6278i			1.68989i	0.534849	+	0.844947i	$0.320368\pi$
$149$			20.6278i			1.68989i	−0.534849	+	0.844947i	$0.679632\pi$
$150$			2.23710i			0.182659i
$151$		−	4.38336i		−	0.356713i	−0.983966	−	0.178356i	$-0.942922\pi$
$151$		−	4.38336i		−	0.356713i	0.983966	−	0.178356i	$-0.0570780\pi$
$152$	−16.1480			−1.30977
$153$	6.30513			0.509740
$154$		−	2.39409i		−	0.192921i
$155$	−2.28798			−0.183775
$156$	5.99875	−	1.26737i	0.480284	−	0.101471i
$157$	12.3964			0.989344			0.494672	−	0.869080i	$-0.335288\pi$
$157$	12.3964			0.989344			0.494672	+	0.869080i	$0.335288\pi$
$158$		−	9.28440i		−	0.738627i
$159$	−0.617769			−0.0489922
$160$	5.06734			0.400609
$161$			26.9331i			2.12263i
$162$		−	0.547285i		−	0.0429988i
$163$		−	1.15407i		−	0.0903939i	−0.998978	−	0.0451970i	$-0.985608\pi$
$163$		−	1.15407i		−	0.0903939i	0.998978	−	0.0451970i	$-0.0143915\pi$
$164$			5.32647i			0.415927i
$165$	0.955178			0.0743605
$166$	6.50052			0.504538
$167$		−	11.6820i		−	0.903981i	−0.892023	−	0.451990i	$-0.850714\pi$
$167$		−	11.6820i		−	0.903981i	0.892023	−	0.451990i	$-0.149286\pi$
$168$	8.85928			0.683509
$169$	11.8891	−	5.25837i	0.914542	−	0.404490i
$170$	3.29604			0.252794
$171$		−	7.97346i		−	0.609746i
$172$	−8.86045			−0.675603
$173$	−9.14601			−0.695358			−0.347679	−	0.937614i	$-0.613030\pi$
$173$	−9.14601			−0.695358			−0.347679	+	0.937614i	$0.613030\pi$
$174$			3.38067i			0.256288i
$175$		−	17.8813i		−	1.35170i
$176$			2.29259i			0.172810i
$177$		−	13.0554i		−	0.981301i
$178$	5.50308			0.412473
$179$	14.1243			1.05570			0.527849	−	0.849338i	$-0.322999\pi$
$179$	14.1243			1.05570			0.527849	+	0.849338i	$0.322999\pi$
$180$			1.62426i			0.121065i
$181$	−2.52918			−0.187992			−0.0939961	−	0.995573i	$-0.529964\pi$
$181$	−2.52918			−0.187992			−0.0939961	+	0.995573i	$0.529964\pi$
$182$	8.44559	−	1.78432i	0.626029	−	0.132263i
$183$	−0.890818			−0.0658512
$184$			12.4690i			0.919226i
$185$	4.37418			0.321596
$186$	−1.31094			−0.0961226
$187$			6.30513i			0.461077i
$188$		−	6.24757i		−	0.455651i
$189$			4.37449i			0.318197i
$190$		−	4.16816i		−	0.302390i
$191$	2.92327			0.211520			0.105760	−	0.994392i	$-0.466272\pi$
$191$	2.92327			0.211520			0.105760	+	0.994392i	$0.466272\pi$
$192$	−1.68175			−0.121370
$193$			0.578869i			0.0416679i	0.999783	+	0.0208339i	$0.00663213\pi$
$193$			0.578869i			0.0416679i	−0.999783	+	0.0208339i	$0.993368\pi$
$194$	4.08739			0.293458
$195$	0.711895	+	3.36956i	0.0509799	+	0.241299i
$196$	−20.6372			−1.47409
$197$		−	13.9481i		−	0.993762i	−0.867819	−	0.496881i	$-0.834478\pi$
$197$		−	13.9481i		−	0.993762i	0.867819	−	0.496881i	$-0.165522\pi$
$198$	0.547285			0.0388939
$199$	−16.4750			−1.16788			−0.583942	−	0.811795i	$-0.698491\pi$
$199$	−16.4750			−1.16788			−0.583942	+	0.811795i	$0.698491\pi$
$200$		−	8.27835i		−	0.585368i
$201$		−	3.32587i		−	0.234589i
$202$			5.65372i			0.397794i
$203$		−	27.0219i		−	1.89656i
$204$	−10.7217			−0.750672
$205$	−2.99194			−0.208966
$206$		−	1.91923i		−	0.133719i
$207$	−6.15686			−0.427932
$208$	−8.08751	+	1.70867i	−0.560768	+	0.118475i
$209$	7.97346			0.551536
$210$			2.28678i			0.157803i
$211$	18.3150			1.26086			0.630428	−	0.776248i	$-0.282880\pi$
$211$	18.3150			1.26086			0.630428	+	0.776248i	$0.282880\pi$
$212$	1.05050			0.0721488
$213$			1.81660i			0.124471i
$214$			7.29758i			0.498852i
$215$		−	4.97701i		−	0.339429i
$216$			2.02522i			0.137799i
$217$	10.4784			0.711321
$218$	5.66393			0.383610
$219$		−	8.42492i		−	0.569303i
$220$	−1.62426			−0.109508
$221$	−22.2425	+	4.69922i	−1.49619	+	0.316104i
$222$	2.50626			0.168209
$223$			13.5671i			0.908518i	0.890870	+	0.454259i	$0.150096\pi$
$223$			13.5671i			0.908518i	−0.890870	+	0.454259i	$0.849904\pi$
$224$	−23.2072			−1.55060
$225$	4.08764			0.272509
$226$			1.20294i			0.0800185i
$227$		−	0.374486i		−	0.0248555i	−0.999923	−	0.0124278i	$-0.996044\pi$
$227$		−	0.374486i		−	0.0248555i	0.999923	−	0.0124278i	$-0.00395598\pi$
$228$			13.5587i			0.897947i
$229$		−	15.5719i		−	1.02902i	−0.857485	−	0.514509i	$-0.827974\pi$
$229$		−	15.5719i		−	1.02902i	0.857485	−	0.514509i	$-0.172026\pi$
$230$	−3.21853			−0.212224
$231$	−4.37449			−0.287820
$232$		−	12.5101i		−	0.821327i
$233$	13.8177			0.905227			0.452613	−	0.891707i	$-0.350492\pi$
$233$	13.8177			0.905227			0.452613	+	0.891707i	$0.350492\pi$
$234$	0.407892	+	1.93065i	0.0266648	+	0.126210i
$235$	3.50933			0.228923
$236$			22.2004i			1.44512i
$237$	−16.9645			−1.10196
$238$	−15.0951			−0.978468
$239$		−	10.7640i		−	0.696265i	−0.937445	−	0.348132i	$-0.886816\pi$
$239$		−	10.7640i		−	0.696265i	0.937445	−	0.348132i	$-0.113184\pi$
$240$		−	2.18983i		−	0.141353i
$241$			11.4930i			0.740326i	0.928967	+	0.370163i	$0.120698\pi$
$241$			11.4930i			0.740326i	−0.928967	+	0.370163i	$0.879302\pi$
$242$			0.547285i			0.0351808i
$243$	−1.00000			−0.0641500
$244$	1.51482			0.0969762
$245$		−	11.5922i		−	0.740596i
$246$	−1.71428			−0.109298
$247$	5.94263	+	28.1278i	0.378121	+	1.78973i
$248$	4.85110			0.308045
$249$		−	11.8778i		−	0.752722i
$250$	4.75060			0.300454
$251$	7.14001			0.450674			0.225337	−	0.974281i	$-0.427652\pi$
$251$	7.14001			0.450674			0.225337	+	0.974281i	$0.427652\pi$
$252$		−	7.43872i		−	0.468595i
$253$		−	6.15686i		−	0.387079i
$254$		−	6.17022i		−	0.387154i
$255$		−	6.02252i		−	0.377145i
$256$	−2.94706			−0.184191
$257$	−6.59154			−0.411169			−0.205584	−	0.978639i	$-0.565910\pi$
$257$	−6.59154			−0.411169			−0.205584	+	0.978639i	$0.565910\pi$
$258$		−	2.85166i		−	0.177537i
$259$	−20.0327			−1.24477
$260$	−1.21056	−	5.72987i	−0.0750759	−	0.355351i
$261$	6.17716			0.382356
$262$			7.18648i			0.443982i
$263$	31.2573			1.92741			0.963705	−	0.266968i	$-0.0860220\pi$
$263$	31.2573			1.92741			0.963705	+	0.266968i	$0.0860220\pi$
$264$	−2.02522			−0.124644
$265$			0.590079i			0.0362482i
$266$			19.0892i			1.17043i
$267$		−	10.0552i		−	0.615370i
$268$			5.65557i			0.345469i
$269$	−19.2067			−1.17105			−0.585525	−	0.810654i	$-0.699112\pi$
$269$	−19.2067			−1.17105			−0.585525	+	0.810654i	$0.699112\pi$
$270$	−0.522755			−0.0318138
$271$		−	10.6834i		−	0.648969i	−0.945891	−	0.324485i	$-0.894809\pi$
$271$		−	10.6834i		−	0.648969i	0.945891	−	0.324485i	$-0.105191\pi$
$272$	14.4551			0.876467
$273$	−3.26031	−	15.4318i	−0.197323	−	0.933974i
$274$	−6.82689			−0.412428
$275$			4.08764i			0.246494i
$276$	10.4696			0.630197
$277$	2.65933			0.159784			0.0798918	−	0.996804i	$-0.474543\pi$
$277$	2.65933			0.159784			0.0798918	+	0.996804i	$0.474543\pi$
$278$			4.16748i			0.249949i
$279$			2.39535i			0.143406i
$280$		−	8.46219i		−	0.505713i
$281$		−	33.4876i		−	1.99770i	−0.0479021	−	0.998852i	$-0.515254\pi$
$281$		−	33.4876i		−	1.99770i	0.0479021	−	0.998852i	$-0.484746\pi$
$282$	2.01073			0.119737
$283$	5.70923			0.339379			0.169689	−	0.985498i	$-0.445724\pi$
$283$	5.70923			0.339379			0.169689	+	0.985498i	$0.445724\pi$
$284$		−	3.08908i		−	0.183303i
$285$	−7.61607			−0.451137
$286$	−1.93065	+	0.407892i	−0.114162	+	0.0241192i
$287$	13.7024			0.808824
$288$		−	5.30513i		−	0.312608i
$289$	22.7547			1.33851
$290$	3.22914			0.189621
$291$		−	7.46849i		−	0.437811i
$292$			14.3264i			0.838389i
$293$			9.43872i			0.551416i	0.961241	+	0.275708i	$0.0889123\pi$
$293$			9.43872i			0.551416i	−0.961241	+	0.275708i	$0.911088\pi$
$294$		−	6.64192i		−	0.387365i
$295$	−12.4702			−0.726042
$296$	−9.27435			−0.539061
$297$		−	1.00000i		−	0.0580259i
$298$	11.2893			0.653971
$299$	21.7194	−	4.58872i	1.25607	−	0.265373i
$300$	−6.95094			−0.401313
$301$			22.7935i			1.31380i
$302$	−2.39895			−0.138044
$303$	10.3305			0.593470
$304$		−	18.2798i		−	1.04842i
$305$			0.850889i			0.0487218i
$306$		−	3.45071i		−	0.197264i
$307$			27.6352i			1.57722i	0.614891	+	0.788612i	$0.289200\pi$
$307$			27.6352i			1.57722i	−0.614891	+	0.788612i	$0.710800\pi$
$308$	7.43872			0.423861
$309$	−3.50682			−0.199496
$310$			1.25218i			0.0711189i
$311$	−2.04350			−0.115876			−0.0579381	−	0.998320i	$-0.518453\pi$
$311$	−2.04350			−0.115876			−0.0579381	+	0.998320i	$0.518453\pi$
$312$	−1.50940	−	7.14432i	−0.0854528	−	0.404467i
$313$	−8.31567			−0.470029			−0.235015	−	0.971992i	$-0.575514\pi$
$313$	−8.31567			−0.470029			−0.235015	+	0.971992i	$0.575514\pi$
$314$		−	6.78439i		−	0.382865i
$315$	4.17841			0.235427
$316$	28.8477			1.62281
$317$			15.1498i			0.850898i	0.904982	+	0.425449i	$0.139884\pi$
$317$			15.1498i			0.850898i	−0.904982	+	0.425449i	$0.860116\pi$
$318$			0.338096i			0.0189595i
$319$			6.17716i			0.345854i
$320$			1.60637i			0.0897989i
$321$	13.3341			0.744239
$322$	14.7401			0.821433
$323$		−	50.2737i		−	2.79731i
$324$	1.70048			0.0944711
$325$	−14.4199	+	3.04652i	−0.799871	+	0.168991i
$326$	−0.631607			−0.0349815
$327$		−	10.3491i		−	0.572309i
$328$	6.34366			0.350270
$329$	−16.0719			−0.886072
$330$		−	0.522755i		−	0.0287767i
$331$			25.9100i			1.42414i	0.702107	+	0.712071i	$0.252243\pi$
$331$			25.9100i			1.42414i	−0.702107	+	0.712071i	$0.747757\pi$
$332$			20.1979i			1.10850i
$333$		−	4.57944i		−	0.250952i
$334$	−6.39339			−0.349831
$335$	−3.17680			−0.173567
$336$			10.0289i			0.547121i
$337$	8.86485			0.482899			0.241449	−	0.970413i	$-0.422377\pi$
$337$	8.86485			0.482899			0.241449	+	0.970413i	$0.422377\pi$
$338$	−2.87783	−	6.50670i	−0.156533	−	0.353918i
$339$	2.19802			0.119380
$340$			10.2412i			0.555405i
$341$	−2.39535			−0.129715
$342$	−4.36376			−0.235965
$343$			22.4679i			1.21315i
$344$			10.5525i			0.568954i
$345$			5.88090i			0.316617i
$346$			5.00548i			0.269096i
$347$	11.7646			0.631558			0.315779	−	0.948833i	$-0.397734\pi$
$347$	11.7646			0.631558			0.315779	+	0.948833i	$0.397734\pi$
$348$	−10.5041			−0.563080
$349$		−	32.0398i		−	1.71505i	−0.514441	−	0.857526i	$-0.672001\pi$
$349$		−	32.0398i		−	1.71505i	0.514441	−	0.857526i	$-0.327999\pi$
$350$	−9.78617			−0.523093
$351$	3.52768	−	0.745301i	0.188294	−	0.0397812i
$352$	5.30513			0.282765
$353$		−	32.5832i		−	1.73423i	−0.498108	−	0.867115i	$-0.665972\pi$
$353$		−	32.5832i		−	1.73423i	0.498108	−	0.867115i	$-0.334028\pi$
$354$	−7.14500			−0.379753
$355$	1.73517			0.0920933
$356$			17.0987i			0.906230i
$357$			27.5817i			1.45978i
$358$		−	7.73000i		−	0.408543i
$359$		−	35.3920i		−	1.86792i	−0.357379	−	0.933959i	$-0.616330\pi$
$359$		−	35.3920i		−	1.86792i	0.357379	−	0.933959i	$-0.383670\pi$
$360$	1.93444			0.101954
$361$	−44.5761			−2.34611
$362$			1.38418i			0.0727509i
$363$	1.00000			0.0524864
$364$	5.54409	+	26.2414i	0.290589	+	1.37542i
$365$	−8.04730			−0.421215
$366$			0.487531i			0.0254837i
$367$	5.80933			0.303244			0.151622	−	0.988439i	$-0.451550\pi$
$367$	5.80933			0.303244			0.151622	+	0.988439i	$0.451550\pi$
$368$	−14.1151			−0.735803
$369$			3.13233i			0.163063i
$370$		−	2.39392i		−	0.124454i
$371$		−	2.70242i		−	0.140303i
$372$		−	4.07324i		−	0.211187i
$373$	3.47511			0.179934			0.0899672	−	0.995945i	$-0.471324\pi$
$373$	3.47511			0.179934			0.0899672	+	0.995945i	$0.471324\pi$
$374$	3.45071			0.178432
$375$		−	8.68031i		−	0.448249i
$376$	−7.44066			−0.383723
$377$	−21.7910	+	4.60384i	−1.12230	+	0.237110i
$378$	2.39409			0.123139
$379$		−	10.2421i		−	0.526102i	−0.964782	−	0.263051i	$-0.915271\pi$
$379$		−	10.2421i		−	0.526102i	0.964782	−	0.263051i	$-0.0847288\pi$
$380$	12.9510			0.664371
$381$	−11.2742			−0.577597
$382$		−	1.59986i		−	0.0818560i
$383$			23.2952i			1.19033i	0.803604	+	0.595164i	$0.202913\pi$
$383$			23.2952i			1.19033i	−0.803604	+	0.595164i	$0.797087\pi$
$384$			11.5307i			0.588422i
$385$			4.17841i			0.212952i
$386$	0.316806			0.0161250
$387$	−5.21056			−0.264868
$388$			12.7000i			0.644745i
$389$	−2.88009			−0.146026			−0.0730131	−	0.997331i	$-0.523262\pi$
$389$	−2.88009			−0.146026			−0.0730131	+	0.997331i	$0.523262\pi$
$390$	1.84411	−	0.389610i	0.0933802	−	0.0197287i
$391$	−38.8199			−1.96320
$392$			24.5783i			1.24139i
$393$	13.1311			0.662378
$394$	−7.63360			−0.384575
$395$			16.2041i			0.815315i
$396$			1.70048i			0.0854523i
$397$		−	10.6070i		−	0.532352i	−0.963924	−	0.266176i	$-0.914240\pi$
$397$		−	10.6070i		−	0.532352i	0.963924	−	0.266176i	$-0.0857602\pi$
$398$			9.01655i			0.451959i
$399$	34.8798			1.74617
$400$	9.37126			0.468563
$401$			28.5679i			1.42661i	0.700853	+	0.713305i	$0.252803\pi$
$401$			28.5679i			1.42661i	−0.700853	+	0.713305i	$0.747197\pi$
$402$	−1.82020			−0.0907833
$403$	−1.78525	−	8.45001i	−0.0889299	−	0.420925i
$404$	−17.5668			−0.873979
$405$			0.955178i			0.0474632i
$406$	−14.7887			−0.733950
$407$	4.57944			0.226994
$408$			12.7693i			0.632173i
$409$			1.20414i			0.0595409i	0.999557	+	0.0297704i	$0.00947763\pi$
$409$			1.20414i			0.0595409i	−0.999557	+	0.0297704i	$0.990522\pi$
$410$			1.63744i			0.0808675i
$411$			12.4741i			0.615302i
$412$	5.96327			0.293789
$413$	57.1105			2.81022
$414$			3.36956i			0.165605i
$415$	−11.3454			−0.556922
$416$	3.95392	+	18.7148i	0.193857	+	0.917569i
$417$	7.61482			0.372899
$418$		−	4.36376i		−	0.213438i
$419$	4.27522			0.208858			0.104429	−	0.994532i	$-0.466698\pi$
$419$	4.27522			0.208858			0.104429	+	0.994532i	$0.466698\pi$
$420$	−7.10530			−0.346703
$421$			16.5321i			0.805725i	0.915261	+	0.402862i	$0.131985\pi$
$421$			16.5321i			0.805725i	−0.915261	+	0.402862i	$0.868015\pi$
$422$		−	10.0235i		−	0.487937i
$423$		−	3.67401i		−	0.178636i
$424$		−	1.25112i		−	0.0607595i
$425$	25.7731			1.25018
$426$	0.994196			0.0481689
$427$		−	3.89687i		−	0.188583i
$428$	−22.6744			−1.09601
$429$	0.745301	+	3.52768i	0.0359835	+	0.170318i
$430$	−2.72385			−0.131355
$431$			17.3415i			0.835310i	0.908606	+	0.417655i	$0.137148\pi$
$431$			17.3415i			0.835310i	−0.908606	+	0.417655i	$0.862852\pi$
$432$	−2.29259			−0.110302
$433$	5.31382			0.255366			0.127683	−	0.991815i	$-0.459246\pi$
$433$	5.31382			0.255366			0.127683	+	0.991815i	$0.459246\pi$
$434$		−	5.73468i		−	0.275273i
$435$		−	5.90028i		−	0.282897i
$436$			17.5985i			0.842815i
$437$			49.0915i			2.34837i
$438$	−4.61083			−0.220314
$439$	−32.9098			−1.57070			−0.785349	−	0.619054i	$-0.787516\pi$
$439$	−32.9098			−1.57070			−0.785349	+	0.619054i	$0.787516\pi$
$440$			1.93444i			0.0922209i
$441$	−12.1361			−0.577911
$442$	2.57182	+	12.1730i	0.122329	+	0.579010i
$443$	−14.6797			−0.697451			−0.348726	−	0.937225i	$-0.613385\pi$
$443$	−14.6797			−0.697451			−0.348726	+	0.937225i	$0.613385\pi$
$444$			7.78724i			0.369566i
$445$	−9.60454			−0.455299
$446$	7.42505			0.351586
$447$		−	20.6278i		−	0.975661i
$448$		−	7.35680i		−	0.347576i
$449$			24.7121i			1.16623i	0.812388	+	0.583117i	$0.198167\pi$
$449$			24.7121i			1.16623i	−0.812388	+	0.583117i	$0.801833\pi$
$450$		−	2.23710i		−	0.105458i
$451$	−3.13233			−0.147496
$452$	−3.73768			−0.175806
$453$			4.38336i			0.205948i
$454$	−0.204951			−0.00961881
$455$	−14.7401	+	3.11418i	−0.691026	+	0.145995i
$456$	16.1480			0.756199
$457$			19.1273i			0.894735i	0.894350	+	0.447368i	$0.147638\pi$
$457$			19.1273i			0.894735i	−0.894350	+	0.447368i	$0.852362\pi$
$458$	−8.52225			−0.398219
$459$	−6.30513			−0.294298
$460$		−	10.0003i		−	0.466268i
$461$		−	33.9286i		−	1.58021i	−0.612970	−	0.790106i	$-0.710025\pi$
$461$		−	33.9286i		−	1.58021i	0.612970	−	0.790106i	$-0.289975\pi$
$462$			2.39409i			0.111383i
$463$		−	30.9206i		−	1.43700i	−0.695527	−	0.718500i	$-0.744829\pi$
$463$		−	30.9206i		−	1.43700i	0.695527	−	0.718500i	$-0.255171\pi$
$464$	14.1617			0.657439
$465$	2.28798			0.106103
$466$		−	7.56222i		−	0.350313i
$467$	−17.2553			−0.798481			−0.399240	−	0.916846i	$-0.630726\pi$
$467$	−17.2553			−0.798481			−0.399240	+	0.916846i	$0.630726\pi$
$468$	−5.99875	+	1.26737i	−0.277292	+	0.0585842i
$469$	14.5490			0.671809
$470$		−	1.92060i		−	0.0885908i
$471$	−12.3964			−0.571198
$472$	26.4399			1.21700
$473$		−	5.21056i		−	0.239582i
$474$			9.28440i			0.426447i
$475$		−	32.5926i		−	1.49545i
$476$		−	46.9021i		−	2.14976i
$477$	0.617769			0.0282857
$478$	−5.89097			−0.269447
$479$			30.2952i			1.38422i	0.721791	+	0.692111i	$0.243319\pi$
$479$			30.2952i			1.38422i	−0.721791	+	0.692111i	$0.756681\pi$
$480$	−5.06734			−0.231292
$481$	3.41306	+	16.1548i	0.155622	+	0.736595i
$482$	6.28992			0.286498
$483$		−	26.9331i		−	1.22550i
$484$	−1.70048			−0.0772945
$485$	−7.13373			−0.323926
$486$			0.547285i			0.0248254i
$487$		−	0.563260i		−	0.0255237i	−0.999919	−	0.0127619i	$-0.995938\pi$
$487$		−	0.563260i		−	0.0255237i	0.999919	−	0.0127619i	$-0.00406234\pi$
$488$		−	1.80410i		−	0.0816678i
$489$			1.15407i			0.0521890i
$490$	−6.34422			−0.286602
$491$	−7.33979			−0.331240			−0.165620	−	0.986190i	$-0.552963\pi$
$491$	−7.33979			−0.331240			−0.165620	+	0.986190i	$0.552963\pi$
$492$		−	5.32647i		−	0.240136i
$493$	38.9478			1.75412
$494$	15.3939	−	3.25231i	0.692606	−	0.146329i
$495$	−0.955178			−0.0429320
$496$			5.49154i			0.246577i
$497$	−7.94667			−0.356457
$498$	−6.50052			−0.291295
$499$			33.8165i			1.51383i	0.653511	+	0.756917i	$0.273295\pi$
$499$			33.8165i			1.51383i	−0.653511	+	0.756917i	$0.726705\pi$
$500$			14.7607i			0.660118i
$501$			11.6820i			0.521913i
$502$		−	3.90762i		−	0.174406i
$503$	−15.1318			−0.674692			−0.337346	−	0.941381i	$-0.609529\pi$
$503$	−15.1318			−0.674692			−0.337346	+	0.941381i	$0.609529\pi$
$504$	−8.85928			−0.394624
$505$		−	9.86744i		−	0.439095i
$506$	−3.36956			−0.149795
$507$	−11.8891	+	5.25837i	−0.528011	+	0.233532i
$508$	19.1716			0.850602
$509$		−	7.59020i		−	0.336430i	−0.985750	−	0.168215i	$-0.946200\pi$
$509$		−	7.59020i		−	0.336430i	0.985750	−	0.168215i	$-0.0538003\pi$
$510$	−3.29604			−0.145951
$511$	36.8547			1.63036
$512$		−	21.4484i		−	0.947896i
$513$			7.97346i			0.352037i
$514$			3.60745i			0.159118i
$515$			3.34964i			0.147603i
$516$	8.86045			0.390060
$517$	3.67401			0.161583
$518$			10.9636i			0.481713i
$519$	9.14601			0.401465
$520$	−6.82409	+	1.44174i	−0.299256	+	0.0632246i
$521$	26.6667			1.16829			0.584144	−	0.811650i	$-0.301430\pi$
$521$	26.6667			1.16829			0.584144	+	0.811650i	$0.301430\pi$
$522$		−	3.38067i		−	0.147968i
$523$	38.5709			1.68659			0.843293	−	0.537454i	$-0.180614\pi$
$523$	38.5709			1.68659			0.843293	+	0.537454i	$0.180614\pi$
$524$	−22.3292			−0.975457
$525$			17.8813i			0.780404i
$526$		−	17.1067i		−	0.745887i
$527$			15.1030i			0.657896i
$528$		−	2.29259i		−	0.0997720i
$529$	14.9070			0.648130
$530$	0.322941			0.0140277
$531$			13.0554i			0.566554i
$532$	−59.3124			−2.57152
$533$	−2.33453	−	11.0499i	−0.101120	−	0.478623i
$534$	−5.50308			−0.238142
$535$		−	12.7365i		−	0.550646i
$536$	6.73561			0.290934
$537$	−14.1243			−0.609507
$538$			10.5115i			0.453184i
$539$		−	12.1361i		−	0.522740i
$540$		−	1.62426i		−	0.0698970i
$541$		−	22.1465i		−	0.952154i	−0.879404	−	0.476077i	$-0.842058\pi$
$541$		−	22.1465i		−	0.952154i	0.879404	−	0.476077i	$-0.157942\pi$
$542$	−5.84686			−0.251144
$543$	2.52918			0.108537
$544$		−	33.4496i		−	1.43414i
$545$	−9.88527			−0.423438
$546$	−8.44559	+	1.78432i	−0.361438	+	0.0763618i
$547$	−36.0573			−1.54170			−0.770849	−	0.637018i	$-0.780168\pi$
$547$	−36.0573			−1.54170			−0.770849	+	0.637018i	$0.780168\pi$
$548$		−	21.2119i		−	0.906129i
$549$	0.890818			0.0380192
$550$	2.23710			0.0953904
$551$		−	49.2533i		−	2.09826i
$552$		−	12.4690i		−	0.530715i
$553$		−	74.2108i		−	3.15576i
$554$		−	1.45541i		−	0.0618345i
$555$	−4.37418			−0.185673
$556$	−12.9488			−0.549153
$557$			20.9181i			0.886326i	0.896441	+	0.443163i	$0.146144\pi$
$557$			20.9181i			0.886326i	−0.896441	+	0.443163i	$0.853856\pi$
$558$	1.31094			0.0554964
$559$	18.3812	−	3.88344i	0.777442	−	0.164252i
$560$	9.57937			0.404802
$561$		−	6.30513i		−	0.266203i
$562$	−18.3273			−0.773090
$563$	−22.2118			−0.936117			−0.468059	−	0.883697i	$-0.655046\pi$
$563$	−22.2118			−0.936117			−0.468059	+	0.883697i	$0.655046\pi$
$564$			6.24757i			0.263070i
$565$		−	2.09950i		−	0.0883265i
$566$		−	3.12458i		−	0.131336i
$567$		−	4.37449i		−	0.183711i
$568$	−3.67900			−0.154367
$569$	−9.66437			−0.405152			−0.202576	−	0.979267i	$-0.564931\pi$
$569$	−9.66437			−0.405152			−0.202576	+	0.979267i	$0.564931\pi$
$570$			4.16816i			0.174585i
$571$	27.9479			1.16958			0.584792	−	0.811183i	$-0.301176\pi$
$571$	27.9479			1.16958			0.584792	+	0.811183i	$0.301176\pi$
$572$	−1.26737	−	5.99875i	−0.0529914	−	0.250820i
$573$	−2.92327			−0.122121
$574$		−	7.49909i		−	0.313006i
$575$	−25.1670			−1.04954
$576$	1.68175			0.0700730
$577$			1.39111i			0.0579125i	0.999581	+	0.0289563i	$0.00921836\pi$
$577$			1.39111i			0.0579125i	−0.999581	+	0.0289563i	$0.990782\pi$
$578$		−	12.4533i		−	0.517989i
$579$		−	0.578869i		−	0.0240570i
$580$			10.0333i			0.416610i
$581$	51.9591			2.15563
$582$	−4.08739			−0.169428
$583$			0.617769i			0.0255854i
$584$	17.0623			0.706043
$585$	−0.711895	−	3.36956i	−0.0294332	−	0.139314i
$586$	5.16567			0.213392
$587$		−	17.9218i		−	0.739713i	−0.929089	−	0.369856i	$-0.879407\pi$
$587$		−	17.9218i		−	0.739713i	0.929089	−	0.369856i	$-0.120593\pi$
$588$	20.6372			0.851065
$589$	19.0992			0.786969
$590$			6.82475i			0.280970i
$591$			13.9481i			0.573749i
$592$		−	10.4988i		−	0.431496i
$593$			11.1399i			0.457462i	0.973490	+	0.228731i	$0.0734576\pi$
$593$			11.1399i			0.457462i	−0.973490	+	0.228731i	$0.926542\pi$
$594$	−0.547285			−0.0224554
$595$	26.3454			1.08006
$596$			35.0771i			1.43682i
$597$	16.4750			0.674279
$598$	−2.51134	−	11.8867i	−0.102696	−	0.486085i
$599$	−13.5965			−0.555537			−0.277768	−	0.960648i	$-0.589595\pi$
$599$	−13.5965			−0.555537			−0.277768	+	0.960648i	$0.589595\pi$
$600$			8.27835i			0.337962i
$601$	25.3091			1.03238			0.516189	−	0.856475i	$-0.327350\pi$
$601$	25.3091			1.03238			0.516189	+	0.856475i	$0.327350\pi$
$602$	12.4746			0.508425
$603$			3.32587i			0.135440i
$604$		−	7.45381i		−	0.303291i
$605$		−	0.955178i		−	0.0388335i
$606$		−	5.65372i		−	0.229666i
$607$	−37.7004			−1.53021			−0.765107	−	0.643903i	$-0.777314\pi$
$607$	−37.7004			−1.53021			−0.765107	+	0.643903i	$0.777314\pi$
$608$	−42.3003			−1.71550
$609$			27.0219i			1.09498i
$610$	0.465679			0.0188548
$611$	2.73824	+	12.9607i	0.110777	+	0.524335i
$612$	10.7217			0.433401
$613$			3.16757i			0.127937i	0.997952	+	0.0639686i	$0.0203757\pi$
$613$			3.16757i			0.127937i	−0.997952	+	0.0639686i	$0.979624\pi$
$614$	15.1243			0.610369
$615$	2.99194			0.120646
$616$		−	8.85928i		−	0.356951i
$617$			23.0775i			0.929065i	0.885556	+	0.464533i	$0.153778\pi$
$617$			23.0775i			0.929065i	−0.885556	+	0.464533i	$0.846222\pi$
$618$			1.91923i			0.0772028i
$619$			28.0983i			1.12937i	0.825307	+	0.564684i	$0.191002\pi$
$619$			28.0983i			1.12937i	−0.825307	+	0.564684i	$0.808998\pi$
$620$	−3.89066			−0.156253
$621$	6.15686			0.247066
$622$			1.11838i			0.0448428i
$623$	43.9865			1.76228
$624$	8.08751	−	1.70867i	0.323760	−	0.0684015i
$625$	12.1469			0.485878
$626$			4.55104i			0.181896i
$627$	−7.97346			−0.318429
$628$	21.0799			0.841179
$629$		−	28.8740i		−	1.15128i
$630$		−	2.28678i		−	0.0911076i
$631$		−	47.0147i		−	1.87162i	−0.352499	−	0.935812i	$-0.614668\pi$
$631$		−	47.0147i		−	1.87162i	0.352499	−	0.935812i	$-0.385332\pi$
$632$		−	34.3567i		−	1.36664i
$633$	−18.3150			−0.727955
$634$	8.29126			0.329288
$635$			10.7689i			0.427351i
$636$	−1.05050			−0.0416551
$637$	42.8124	−	9.04507i	1.69629	−	0.358379i
$638$	3.38067			0.133842
$639$		−	1.81660i		−	0.0718634i
$640$	11.0138			0.435360
$641$	−43.5686			−1.72085			−0.860427	−	0.509573i	$-0.829803\pi$
$641$	−43.5686			−1.72085			−0.860427	+	0.509573i	$0.829803\pi$
$642$		−	7.29758i		−	0.288013i
$643$			4.29183i			0.169253i	0.996413	+	0.0846267i	$0.0269698\pi$
$643$			4.29183i			0.169253i	−0.996413	+	0.0846267i	$0.973030\pi$
$644$			45.7992i			1.80474i
$645$			4.97701i			0.195970i
$646$	−27.5141			−1.08253
$647$	34.9754			1.37503			0.687513	−	0.726173i	$-0.258703\pi$
$647$	34.9754			1.37503			0.687513	+	0.726173i	$0.258703\pi$
$648$		−	2.02522i		−	0.0795580i
$649$	−13.0554			−0.512468
$650$	1.66732	+	7.89178i	0.0653975	+	0.309541i
$651$	−10.4784			−0.410681
$652$		−	1.96248i		−	0.0768565i
$653$	−26.6555			−1.04311			−0.521555	−	0.853218i	$-0.674648\pi$
$653$	−26.6555			−1.04311			−0.521555	+	0.853218i	$0.674648\pi$
$654$	−5.66393			−0.221477
$655$		−	12.5426i		−	0.490079i
$656$			7.18115i			0.280377i
$657$			8.42492i			0.328687i
$658$			8.79591i			0.342900i
$659$	−38.0227			−1.48115			−0.740577	−	0.671971i	$-0.765448\pi$
$659$	−38.0227			−1.48115			−0.740577	+	0.671971i	$0.765448\pi$
$660$	1.62426			0.0632242
$661$		−	7.43138i		−	0.289047i	−0.989501	−	0.144524i	$-0.953835\pi$
$661$		−	7.43138i		−	0.289047i	0.989501	−	0.144524i	$-0.0461650\pi$
$662$	14.1802			0.551128
$663$	22.2425	−	4.69922i	0.863827	−	0.182503i
$664$	24.0550			0.933517
$665$		−	33.3164i		−	1.29195i
$666$	−2.50626			−0.0971155
$667$	−38.0319			−1.47260
$668$		−	19.8650i		−	0.768600i
$669$		−	13.5671i		−	0.524533i
$670$			1.73861i			0.0671685i
$671$			0.890818i			0.0343896i
$672$	23.2072			0.895238
$673$	−30.2624			−1.16653			−0.583265	−	0.812282i	$-0.698225\pi$
$673$	−30.2624			−1.16653			−0.583265	+	0.812282i	$0.698225\pi$
$674$		−	4.85160i		−	0.186877i
$675$	−4.08764			−0.157333
$676$	20.2171	−	8.94175i	0.777580	−	0.343913i
$677$	−1.58564			−0.0609412			−0.0304706	−	0.999536i	$-0.509701\pi$
$677$	−1.58564			−0.0609412			−0.0304706	+	0.999536i	$0.509701\pi$
$678$		−	1.20294i		−	0.0461987i
$679$	32.6708			1.25379
$680$	12.1969			0.467730
$681$			0.374486i			0.0143503i
$682$			1.31094i			0.0501984i
$683$		−	7.72684i		−	0.295659i	−0.989013	−	0.147830i	$-0.952771\pi$
$683$		−	7.72684i		−	0.295659i	0.989013	−	0.147830i	$-0.0472287\pi$
$684$		−	13.5587i		−	0.518430i
$685$	11.9150			0.455248
$686$	12.2964			0.469477
$687$			15.5719i			0.594104i
$688$	−11.9457			−0.455424
$689$	−2.17929	+	0.460424i	−0.0830243	+	0.0175407i
$690$	3.21853			0.122527
$691$			38.7247i			1.47316i	0.676353	+	0.736578i	$0.263559\pi$
$691$			38.7247i			1.47316i	−0.676353	+	0.736578i	$0.736441\pi$
$692$	−15.5526			−0.591221
$693$	4.37449			0.166173
$694$		−	6.43861i		−	0.244406i
$695$		−	7.27350i		−	0.275900i
$696$			12.5101i			0.474194i
$697$			19.7498i			0.748076i
$698$	−17.5349			−0.663706
$699$	−13.8177			−0.522633
$700$		−	30.4068i		−	1.14927i
$701$	−30.1810			−1.13992			−0.569960	−	0.821673i	$-0.693041\pi$
$701$	−30.1810			−1.13992			−0.569960	+	0.821673i	$0.693041\pi$
$702$	−0.407892	−	1.93065i	−0.0153949	−	0.0728676i
$703$	−36.5140			−1.37715
$704$			1.68175i			0.0633834i
$705$	−3.50933			−0.132169
$706$	−17.8323			−0.671128
$707$			45.1905i			1.69956i
$708$		−	22.2004i		−	0.834341i
$709$		−	5.86817i		−	0.220384i	−0.993910	−	0.110192i	$-0.964853\pi$
$709$		−	5.86817i		−	0.220384i	0.993910	−	0.110192i	$-0.0351465\pi$
$710$		−	0.949634i		−	0.0356391i
$711$	16.9645			0.636217
$712$	20.3640			0.763175
$713$		−	14.7478i		−	0.552310i
$714$	15.0951			0.564919
$715$	3.36956	−	0.711895i	0.126014	−	0.0266234i
$716$	24.0180			0.897596
$717$			10.7640i			0.401989i
$718$	−19.3695			−0.722864
$719$	12.9294			0.482185			0.241093	−	0.970502i	$-0.422494\pi$
$719$	12.9294			0.482185			0.241093	+	0.970502i	$0.422494\pi$
$720$			2.18983i			0.0816100i
$721$		−	15.3405i		−	0.571311i
$722$			24.3958i			0.907918i
$723$		−	11.4930i		−	0.427427i
$724$	−4.30081			−0.159838
$725$	25.2500			0.937760
$726$		−	0.547285i		−	0.0203117i
$727$	−35.9583			−1.33362			−0.666809	−	0.745228i	$-0.732340\pi$
$727$	−35.9583			−1.33362			−0.666809	+	0.745228i	$0.732340\pi$
$728$	31.2527	−	6.60284i	1.15830	−	0.244717i
$729$	1.00000			0.0370370
$730$			4.40417i			0.163005i
$731$	−32.8533			−1.21512
$732$	−1.51482			−0.0559892
$733$			10.2262i			0.377712i	0.982005	+	0.188856i	$0.0604780\pi$
$733$			10.2262i			0.377712i	−0.982005	+	0.188856i	$0.939522\pi$
$734$		−	3.17936i		−	0.117352i
$735$			11.5922i			0.427583i
$736$			32.6630i			1.20397i
$737$	−3.32587			−0.122510
$738$	1.71428			0.0631035
$739$		−	41.5569i		−	1.52870i	−0.644803	−	0.764348i	$-0.723061\pi$
$739$		−	41.5569i		−	1.52870i	0.644803	−	0.764348i	$-0.276939\pi$
$740$	7.43819			0.273433
$741$	−5.94263	−	28.1278i	−0.218308	−	1.03330i
$742$	−1.47899			−0.0542956
$743$			10.9762i			0.402678i	0.979522	+	0.201339i	$0.0645293\pi$
$743$			10.9762i			0.402678i	−0.979522	+	0.201339i	$0.935471\pi$
$744$	−4.85110			−0.177850
$745$	−19.7032			−0.721870
$746$		−	1.90188i		−	0.0696327i
$747$			11.8778i			0.434585i
$748$			10.7217i			0.392026i
$749$			58.3300i			2.13133i
$750$	−4.75060			−0.173467
$751$	5.26951			0.192287			0.0961435	−	0.995367i	$-0.469349\pi$
$751$	5.26951			0.192287			0.0961435	+	0.995367i	$0.469349\pi$
$752$		−	8.42298i		−	0.307154i
$753$	−7.14001			−0.260196
$754$	2.51962	+	11.9259i	0.0917590	+	0.434316i
$755$	4.18689			0.152376
$756$			7.43872i			0.270544i
$757$	−35.5804			−1.29319			−0.646596	−	0.762833i	$-0.723808\pi$
$757$	−35.5804			−1.29319			−0.646596	+	0.762833i	$0.723808\pi$
$758$	−5.60536			−0.203596
$759$			6.15686i			0.223480i
$760$		−	15.4242i		−	0.559494i
$761$		−	21.0809i		−	0.764181i	−0.924125	−	0.382091i	$-0.875204\pi$
$761$		−	21.0809i		−	0.764181i	0.924125	−	0.382091i	$-0.124796\pi$
$762$			6.17022i			0.223524i
$763$	45.2722			1.63896
$764$	4.97096			0.179843
$765$			6.02252i			0.217745i
$766$	12.7491			0.460644
$767$	−9.73018	−	46.0551i	−0.351336	−	1.66295i
$768$	2.94706			0.106343
$769$		−	39.0584i		−	1.40848i	−0.709960	−	0.704242i	$-0.751287\pi$
$769$		−	39.0584i		−	1.40848i	0.709960	−	0.704242i	$-0.248713\pi$
$770$	2.28678			0.0824099
$771$	6.59154			0.237389
$772$			0.984354i			0.0354277i
$773$			1.22434i			0.0440366i	0.999758	+	0.0220183i	$0.00700921\pi$
$773$			1.22434i			0.0440366i	−0.999758	+	0.0220183i	$0.992991\pi$
$774$			2.85166i			0.102501i
$775$			9.79130i			0.351714i
$776$	15.1253			0.542967
$777$	20.0327			0.718669
$778$			1.57623i			0.0565106i
$779$	24.9755			0.894842
$780$	1.21056	+	5.72987i	0.0433451	+	0.205162i
$781$	1.81660			0.0650029
$782$			21.2455i			0.759739i
$783$	−6.17716			−0.220754
$784$	−27.8231			−0.993683
$785$			11.8408i			0.422616i
$786$		−	7.18648i		−	0.256333i
$787$		−	18.5952i		−	0.662849i	−0.943482	−	0.331424i	$-0.892471\pi$
$787$		−	18.5952i		−	0.662849i	0.943482	−	0.331424i	$-0.107529\pi$
$788$		−	23.7185i		−	0.844936i
$789$	−31.2573			−1.11279
$790$	8.86825			0.315518
$791$			9.61519i			0.341877i
$792$	2.02522			0.0719630
$793$	−3.14252	+	0.663928i	−0.111594	+	0.0235768i
$794$	−5.80508			−0.206014
$795$		−	0.590079i		−	0.0209279i
$796$	−28.0155			−0.992982
$797$	43.4546			1.53924			0.769621	−	0.638501i	$-0.220445\pi$
$797$	43.4546			1.53924			0.769621	+	0.638501i	$0.220445\pi$
$798$		−	19.0892i		−	0.675750i
$799$		−	23.1651i		−	0.819522i
$800$		−	21.6855i		−	0.766697i
$801$			10.0552i			0.355284i
$802$	15.6348			0.552083
$803$	−8.42492			−0.297309
$804$		−	5.65557i		−	0.199457i
$805$	−25.7259			−0.906719
$806$	−4.62457	+	0.977043i	−0.162893	+	0.0344149i
$807$	19.2067			0.676107
$808$			20.9215i			0.736014i
$809$	−16.7906			−0.590325			−0.295162	−	0.955447i	$-0.595374\pi$
$809$	−16.7906			−0.590325			−0.295162	+	0.955447i	$0.595374\pi$
$810$	0.522755			0.0183677
$811$			41.8130i			1.46825i	0.679013	+	0.734126i	$0.262408\pi$
$811$			41.8130i			1.46825i	−0.679013	+	0.734126i	$0.737592\pi$
$812$		−	45.9501i		−	1.61253i
$813$			10.6834i			0.374683i
$814$		−	2.50626i		−	0.0878443i
$815$	1.10234			0.0386134
$816$	−14.4551			−0.506028
$817$			41.5462i			1.45352i
$818$	0.659008			0.0230417
$819$	3.26031	+	15.4318i	0.113924	+	0.539230i
$820$	−5.08772			−0.177671
$821$		−	26.6996i		−	0.931822i	−0.884832	−	0.465911i	$-0.845727\pi$
$821$		−	26.6996i		−	0.931822i	0.884832	−	0.465911i	$-0.154273\pi$
$822$	6.82689			0.238115
$823$	−24.2092			−0.843878			−0.421939	−	0.906624i	$-0.638650\pi$
$823$	−24.2092			−0.843878			−0.421939	+	0.906624i	$0.638650\pi$
$824$		−	7.10207i		−	0.247412i
$825$		−	4.08764i		−	0.142313i
$826$		−	31.2557i		−	1.08753i
$827$			11.6768i			0.406043i	0.979174	+	0.203022i	$0.0650762\pi$
$827$			11.6768i			0.406043i	−0.979174	+	0.203022i	$0.934924\pi$
$828$	−10.4696			−0.363844
$829$	47.7326			1.65782			0.828911	−	0.559380i	$-0.188961\pi$
$829$	47.7326			1.65782			0.828911	+	0.559380i	$0.188961\pi$
$830$			6.20915i			0.215523i
$831$	−2.65933			−0.0922510
$832$	−5.93268	+	1.25341i	−0.205679	+	0.0434543i
$833$	−76.5199			−2.65126
$834$		−	4.16748i		−	0.144308i
$835$	11.1584			0.386152
$836$	13.5587			0.468937
$837$		−	2.39535i		−	0.0827953i
$838$		−	2.33977i		−	0.0808259i
$839$		−	16.9518i		−	0.585243i	−0.956228	−	0.292621i	$-0.905472\pi$
$839$		−	16.9518i		−	0.585243i	0.956228	−	0.292621i	$-0.0945275\pi$
$840$			8.46219i			0.291973i
$841$	9.15726			0.315768
$842$	9.04777			0.311807
$843$			33.4876i			1.15337i
$844$	31.1442			1.07203
$845$	5.02268	+	11.3562i	0.172785	+	0.390664i
$846$	−2.01073			−0.0691303
$847$			4.37449i			0.150309i
$848$	1.41629			0.0486355
$849$	−5.70923			−0.195940
$850$		−	14.1052i		−	0.483805i
$851$			28.1950i			0.966511i
$852$			3.08908i			0.105830i
$853$		−	25.0979i		−	0.859336i	−0.902987	−	0.429668i	$-0.858631\pi$
$853$		−	25.0979i		−	0.859336i	0.902987	−	0.429668i	$-0.141369\pi$
$854$	−2.13270			−0.0729795
$855$	7.61607			0.260464
$856$			27.0045i			0.922996i
$857$	−21.5163			−0.734983			−0.367492	−	0.930027i	$-0.619783\pi$
$857$	−21.5163			−0.734983			−0.367492	+	0.930027i	$0.619783\pi$
$858$	1.93065	−	0.407892i	0.0659112	−	0.0139252i
$859$	−11.0033			−0.375428			−0.187714	−	0.982224i	$-0.560108\pi$
$859$	−11.0033			−0.375428			−0.187714	+	0.982224i	$0.560108\pi$
$860$		−	8.46331i		−	0.288596i
$861$	−13.7024			−0.466975
$862$	9.49074			0.323256
$863$			37.6567i			1.28185i	0.767604	+	0.640924i	$0.221449\pi$
$863$			37.6567i			1.28185i	−0.767604	+	0.640924i	$0.778551\pi$
$864$			5.30513i			0.180484i
$865$		−	8.73606i		−	0.297035i
$866$		−	2.90818i		−	0.0988238i
$867$	−22.7547			−0.772790
$868$	17.8183			0.604793
$869$			16.9645i			0.575480i
$870$	−3.22914			−0.109478
$871$	−2.47877	−	11.7326i	−0.0839901	−	0.397544i
$872$	20.9593			0.709770
$873$			7.46849i			0.252770i
$874$	26.8671			0.908792
$875$	37.9719			1.28368
$876$		−	14.3264i		−	0.484044i
$877$		−	10.2307i		−	0.345466i	−0.984969	−	0.172733i	$-0.944740\pi$
$877$		−	10.2307i		−	0.345466i	0.984969	−	0.172733i	$-0.0552598\pi$
$878$			18.0110i			0.607843i
$879$		−	9.43872i		−	0.318360i
$880$	−2.18983			−0.0738191
$881$	33.1131			1.11561			0.557805	−	0.829972i	$-0.311644\pi$
$881$	33.1131			1.11561			0.557805	+	0.829972i	$0.311644\pi$
$882$			6.64192i			0.223645i
$883$	5.00333			0.168375			0.0841877	−	0.996450i	$-0.473170\pi$
$883$	5.00333			0.168375			0.0841877	+	0.996450i	$0.473170\pi$
$884$	−37.8229	+	7.99093i	−1.27212	+	0.268764i
$885$	12.4702			0.419181
$886$			8.03396i			0.269906i
$887$	2.24511			0.0753835			0.0376917	−	0.999289i	$-0.488000\pi$
$887$	2.24511			0.0753835			0.0376917	+	0.999289i	$0.488000\pi$
$888$	9.27435			0.311227
$889$		−	49.3190i		−	1.65411i
$890$			5.25642i			0.176196i
$891$			1.00000i			0.0335013i
$892$			23.0705i			0.772458i
$893$	−29.2946			−0.980305
$894$	−11.2893			−0.377570
$895$			13.4912i			0.450961i
$896$	−50.4407			−1.68511
$897$	−21.7194	+	4.58872i	−0.725191	+	0.153213i
$898$	13.5245			0.451320
$899$			14.7964i			0.493488i
$900$	6.95094			0.231698
$901$	3.89511			0.129765
$902$			1.71428i			0.0570793i
$903$		−	22.7935i		−	0.758521i
$904$			4.45146i			0.148053i
$905$		−	2.41581i		−	0.0803044i
$906$	2.39895			0.0796997
$907$	14.8281			0.492360			0.246180	−	0.969224i	$-0.420825\pi$
$907$	14.8281			0.492360			0.246180	+	0.969224i	$0.420825\pi$
$908$		−	0.636806i		−	0.0211331i
$909$	−10.3305			−0.342640
$910$	1.70434	+	8.06704i	0.0564984	+	0.267420i
$911$	43.6416			1.44591			0.722956	−	0.690895i	$-0.242783\pi$
$911$	43.6416			1.44591			0.722956	+	0.690895i	$0.242783\pi$
$912$			18.2798i			0.605306i
$913$	−11.8778			−0.393096
$914$	10.4681			0.346253
$915$		−	0.850889i		−	0.0281295i
$916$		−	26.4796i		−	0.874912i
$917$			57.4420i			1.89690i
$918$			3.45071i			0.113890i
$919$	−19.5795			−0.645868			−0.322934	−	0.946422i	$-0.604669\pi$
$919$	−19.5795			−0.645868			−0.322934	+	0.946422i	$0.604669\pi$
$920$	−11.9101			−0.392664
$921$		−	27.6352i		−	0.910611i
$922$	−18.5686			−0.611525
$923$	1.35391	+	6.40837i	0.0445645	+	0.210934i
$924$	−7.43872			−0.244716
$925$		−	18.7191i		−	0.615479i
$926$	−16.9224			−0.556104
$927$	3.50682			0.115179
$928$		−	32.7706i		−	1.07575i
$929$			20.4642i			0.671410i	0.941967	+	0.335705i	$0.108975\pi$
$929$			20.4642i			0.671410i	−0.941967	+	0.335705i	$0.891025\pi$
$930$		−	1.25218i		−	0.0410605i
$931$			96.7669i			3.17141i
$932$	23.4967			0.769660
$933$	2.04350			0.0669012
$934$			9.44358i			0.309003i
$935$	−6.02252			−0.196958
$936$	1.50940	+	7.14432i	0.0493362	+	0.233519i
$937$	−4.95499			−0.161872			−0.0809362	−	0.996719i	$-0.525791\pi$
$937$	−4.95499			−0.161872			−0.0809362	+	0.996719i	$0.525791\pi$
$938$		−	7.96243i		−	0.259983i
$939$	8.31567			0.271372
$940$	5.96754			0.194640
$941$			23.7965i			0.775744i	0.921713	+	0.387872i	$0.126790\pi$
$941$			23.7965i			0.775744i	−0.921713	+	0.387872i	$0.873210\pi$
$942$			6.78439i			0.221047i
$943$		−	19.2854i		−	0.628018i
$944$			29.9305i			0.974156i
$945$	−4.17841			−0.135924
$946$	−2.85166			−0.0927156
$947$			40.0504i			1.30146i	0.759308	+	0.650731i	$0.225538\pi$
$947$			40.0504i			1.30146i	−0.759308	+	0.650731i	$0.774462\pi$
$948$	−28.8477			−0.936930
$949$	−6.27911	−	29.7204i	−0.203828	−	0.964766i
$950$	−17.8374			−0.578723
$951$		−	15.1498i		−	0.491266i
$952$	−55.8590			−1.81040
$953$	−28.4952			−0.923049			−0.461524	−	0.887128i	$-0.652697\pi$
$953$	−28.4952			−0.923049			−0.461524	+	0.887128i	$0.652697\pi$
$954$		−	0.338096i		−	0.0109462i
$955$			2.79224i			0.0903548i
$956$		−	18.3039i		−	0.591992i
$957$		−	6.17716i		−	0.199679i
$958$	16.5801			0.535679
$959$	−54.5678			−1.76209
$960$		−	1.60637i		−	0.0518454i
$961$	25.2623			0.814913
$962$	8.84128	−	1.86792i	0.285054	−	0.0602241i
$963$	−13.3341			−0.429687
$964$			19.5435i			0.629454i
$965$	−0.552923			−0.0177992
$966$	−14.7401			−0.474255
$967$			18.4660i			0.593826i	0.954904	+	0.296913i	$0.0959572\pi$
$967$			18.4660i			0.593826i	−0.954904	+	0.296913i	$0.904043\pi$
$968$			2.02522i			0.0650929i
$969$			50.2737i			1.61502i
$970$			3.90419i			0.125356i
$971$	−36.8905			−1.18387			−0.591936	−	0.805985i	$-0.701636\pi$
$971$	−36.8905			−1.18387			−0.591936	+	0.805985i	$0.701636\pi$
$972$	−1.70048			−0.0545429
$973$			33.3109i			1.06790i
$974$	−0.308264			−0.00987741
$975$	14.4199	−	3.04652i	0.461805	−	0.0975667i
$976$	2.04228			0.0653717
$977$		−	0.0175455i		−	0.000561330i	−1.00000		0.000280665i	$-0.999911\pi$
$977$		−	0.0175455i		−	0.000561330i	1.00000		0.000280665i	$-8.93385e-5\pi$
$978$	0.631607			0.0201966
$979$	−10.0552			−0.321367
$980$		−	19.7122i		−	0.629684i
$981$			10.3491i			0.330423i
$982$			4.01696i			0.128186i
$983$		−	3.04897i		−	0.0972470i	−0.998817	−	0.0486235i	$-0.984517\pi$
$983$		−	3.04897i		−	0.0972470i	0.998817	−	0.0486235i	$-0.0154834\pi$
$984$	−6.34366			−0.202228
$985$	13.3229			0.424504
$986$		−	21.3155i		−	0.678825i
$987$	16.0719			0.511574
$988$	10.1053	+	47.8308i	0.321493	+	1.52170i
$989$	32.0807			1.02011
$990$			0.522755i			0.0166142i
$991$	33.7339			1.07159			0.535796	−	0.844348i	$-0.320012\pi$
$991$	33.7339			1.07159			0.535796	+	0.844348i	$0.320012\pi$
$992$	12.7076			0.403468
$993$		−	25.9100i		−	0.822229i
$994$			4.34910i			0.137945i
$995$		−	15.7366i		−	0.498884i
$996$		−	20.1979i		−	0.639994i
$997$	14.5802			0.461758			0.230879	−	0.972982i	$-0.425840\pi$
$997$	14.5802			0.461758			0.230879	+	0.972982i	$0.425840\pi$
$998$	18.5073			0.585837
$999$			4.57944i			0.144887i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.b.a.298.4	✓	10
3.2	odd	2		1287.2.b.a.298.7		10
13.5	odd	4		5577.2.a.t.1.2		5
13.8	odd	4		5577.2.a.q.1.4		5
13.12	even	2	inner	429.2.b.a.298.7	yes	10
39.38	odd	2		1287.2.b.a.298.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.b.a.298.4	✓	10	1.1	even	1	trivial
429.2.b.a.298.7	yes	10	13.12	even	2	inner
1287.2.b.a.298.4		10	39.38	odd	2
1287.2.b.a.298.7		10	3.2	odd	2
5577.2.a.q.1.4		5	13.8	odd	4
5577.2.a.t.1.2		5	13.5	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)

\(f(q)\)	\(=\)	\(q-0.547285i q^{2} -1.00000 q^{3} +1.70048 q^{4} +0.955178i q^{5} +0.547285i q^{6} -4.37449i q^{7} -2.02522i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.547285i q^{2} -1.00000 q^{3} +1.70048 q^{4} +0.955178i q^{5} +0.547285i q^{6} -4.37449i q^{7} -2.02522i q^{8} +1.00000 q^{9} +0.522755 q^{10} +1.00000i q^{11} -1.70048 q^{12} +(-3.52768 + 0.745301i) q^{13} -2.39409 q^{14} -0.955178i q^{15} +2.29259 q^{16} +6.30513 q^{17} -0.547285i q^{18} -7.97346i q^{19} +1.62426i q^{20} +4.37449i q^{21} +0.547285 q^{22} -6.15686 q^{23} +2.02522i q^{24} +4.08764 q^{25} +(0.407892 + 1.93065i) q^{26} -1.00000 q^{27} -7.43872i q^{28} +6.17716 q^{29} -0.522755 q^{30} +2.39535i q^{31} -5.30513i q^{32} -1.00000i q^{33} -3.45071i q^{34} +4.17841 q^{35} +1.70048 q^{36} -4.57944i q^{37} -4.36376 q^{38} +(3.52768 - 0.745301i) q^{39} +1.93444 q^{40} +3.13233i q^{41} +2.39409 q^{42} -5.21056 q^{43} +1.70048i q^{44} +0.955178i q^{45} +3.36956i q^{46} -3.67401i q^{47} -2.29259 q^{48} -12.1361 q^{49} -2.23710i q^{50} -6.30513 q^{51} +(-5.99875 + 1.26737i) q^{52} +0.617769 q^{53} +0.547285i q^{54} -0.955178 q^{55} -8.85928 q^{56} +7.97346i q^{57} -3.38067i q^{58} +13.0554i q^{59} -1.62426i q^{60} +0.890818 q^{61} +1.31094 q^{62} -4.37449i q^{63} +1.68175 q^{64} +(-0.711895 - 3.36956i) q^{65} -0.547285 q^{66} +3.32587i q^{67} +10.7217 q^{68} +6.15686 q^{69} -2.28678i q^{70} -1.81660i q^{71} -2.02522i q^{72} +8.42492i q^{73} -2.50626 q^{74} -4.08764 q^{75} -13.5587i q^{76} +4.37449 q^{77} +(-0.407892 - 1.93065i) q^{78} +16.9645 q^{79} +2.18983i q^{80} +1.00000 q^{81} +1.71428 q^{82} +11.8778i q^{83} +7.43872i q^{84} +6.02252i q^{85} +2.85166i q^{86} -6.17716 q^{87} +2.02522 q^{88} +10.0552i q^{89} +0.522755 q^{90} +(3.26031 + 15.4318i) q^{91} -10.4696 q^{92} -2.39535i q^{93} -2.01073 q^{94} +7.61607 q^{95} +5.30513i q^{96} +7.46849i q^{97} +6.64192i q^{98} +1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{3} - 6 q^{4} + 10 q^{9}+O(q^{10}) \) 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

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