LMFDB - Embedded newform 189.3.k.a.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,3,Mod(10,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("189.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	189.k (of order $6$, degree $2$, not 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:	$5.14987699641$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.2
Character	$\chi$	$=$	189.10
Dual form			189.3.k.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62718 + 2.81835i) q^{2} +(-3.29541 - 5.70782i) q^{4} -3.39483i q^{5} +(-6.91332 - 1.09817i) q^{7} +8.43145 q^{8} +O(q^{10})$	\(q+(-1.62718 + 2.81835i) q^{2} +(-3.29541 - 5.70782i) q^{4} -3.39483i q^{5} +(-6.91332 - 1.09817i) q^{7} +8.43145 q^{8} +(9.56782 + 5.52398i) q^{10} +18.7757 q^{11} +(6.13966 + 3.54474i) q^{13} +(14.3442 - 17.6973i) q^{14} +(-0.537814 + 0.931521i) q^{16} +(5.22522 + 3.01678i) q^{17} +(22.2011 - 12.8178i) q^{19} +(-19.3770 + 11.1873i) q^{20} +(-30.5514 + 52.9166i) q^{22} -1.98480 q^{23} +13.4752 q^{25} +(-19.9806 + 11.5358i) q^{26} +(16.5141 + 43.0789i) q^{28} +(-12.9572 - 22.4426i) q^{29} +(-6.84815 + 3.95378i) q^{31} +(15.1127 + 26.1759i) q^{32} +(-17.0047 + 9.81768i) q^{34} +(-3.72810 + 23.4695i) q^{35} +(-19.4790 - 33.7386i) q^{37} +83.4274i q^{38} -28.6233i q^{40} +(42.7546 + 24.6844i) q^{41} +(-18.6830 - 32.3599i) q^{43} +(-61.8737 - 107.168i) q^{44} +(3.22962 - 5.59387i) q^{46} +(-27.1575 - 15.6794i) q^{47} +(46.5880 + 15.1840i) q^{49} +(-21.9265 + 37.9778i) q^{50} -46.7254i q^{52} +(36.6033 - 63.3987i) q^{53} -63.7403i q^{55} +(-58.2893 - 9.25916i) q^{56} +84.3348 q^{58} +(45.9596 - 26.5348i) q^{59} +(34.8983 + 20.1485i) q^{61} -25.7340i q^{62} -102.666 q^{64} +(12.0338 - 20.8431i) q^{65} +(-38.1086 - 66.0061i) q^{67} -39.7661i q^{68} +(-60.0791 - 48.6962i) q^{70} +17.9011 q^{71} +(109.287 + 63.0970i) q^{73} +126.783 q^{74} +(-146.323 - 84.4799i) q^{76} +(-129.803 - 20.6189i) q^{77} +(-27.0552 + 46.8610i) q^{79} +(3.16235 + 1.82578i) q^{80} +(-139.139 + 80.3317i) q^{82} +(-114.768 + 66.2614i) q^{83} +(10.2415 - 17.7387i) q^{85} +121.602 q^{86} +158.306 q^{88} +(-50.0032 + 28.8694i) q^{89} +(-38.5527 - 31.2483i) q^{91} +(6.54073 + 11.3289i) q^{92} +(88.3801 - 51.0263i) q^{94} +(-43.5142 - 75.3689i) q^{95} +(-21.0909 + 12.1768i) q^{97} +(-118.601 + 106.595i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8	$ 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) $ 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.62718	+	2.81835i	−0.813588	+	1.40918i	0.0967485	+	0.995309i	$0.469156\pi$
$2$	−1.62718	+	2.81835i	−0.813588	+	1.40918i	−0.910337	+	0.413868i	$0.864178\pi$
$3$		0			0
$3$		0			0
$4$	−3.29541	−	5.70782i	−0.823852	−	1.42695i
$5$		−	3.39483i		−	0.678965i	−0.940612	−	0.339483i	$-0.889748\pi$
$5$		−	3.39483i		−	0.678965i	0.940612	−	0.339483i	$-0.110252\pi$
$6$		0			0
$7$	−6.91332	−	1.09817i	−0.987617	−	0.156881i
$7$	−6.91332	−	1.09817i	−0.987617	−	0.156881i
$8$	8.43145			1.05393
$9$		0			0
$10$	9.56782	+	5.52398i	0.956782	+	0.552398i
$11$	18.7757			1.70688			0.853441	−	0.521189i	$-0.174511\pi$
$11$	18.7757			1.70688			0.853441	+	0.521189i	$0.174511\pi$
$12$		0			0
$13$	6.13966	+	3.54474i	0.472282	+	0.272672i	0.717194	−	0.696873i	$-0.245426\pi$
$13$	6.13966	+	3.54474i	0.472282	+	0.272672i	−0.244913	+	0.969545i	$0.578759\pi$
$14$	14.3442	−	17.6973i	1.02459	−	1.26409i
$15$		0			0
$16$	−0.537814	+	0.931521i	−0.0336134	+	0.0582200i
$17$	5.22522	+	3.01678i	0.307366	+	0.177458i	0.645747	−	0.763551i	$-0.276546\pi$
$17$	5.22522	+	3.01678i	0.307366	+	0.177458i	−0.338381	+	0.941009i	$0.609879\pi$
$18$		0			0
$19$	22.2011	−	12.8178i	1.16848	−	0.674622i	0.215157	−	0.976579i	$-0.430974\pi$
$19$	22.2011	−	12.8178i	1.16848	−	0.674622i	0.953321	+	0.301958i	$0.0976402\pi$
$20$	−19.3770	+	11.1873i	−0.968852	+	0.559367i
$21$		0			0
$22$	−30.5514	+	52.9166i	−1.38870	+	2.40530i
$23$	−1.98480			−0.0862956			−0.0431478	−	0.999069i	$-0.513739\pi$
$23$	−1.98480			−0.0862956			−0.0431478	+	0.999069i	$0.513739\pi$
$24$		0			0
$25$	13.4752			0.539006
$26$	−19.9806	+	11.5358i	−0.768486	+	0.443686i
$27$		0			0
$28$	16.5141	+	43.0789i	0.589788	+	1.53853i
$29$	−12.9572	−	22.4426i	−0.446801	−	0.773882i	0.551375	−	0.834258i	$-0.314103\pi$
$29$	−12.9572	−	22.4426i	−0.446801	−	0.773882i	−0.998176	+	0.0603758i	$0.980770\pi$
$30$		0			0
$31$	−6.84815	+	3.95378i	−0.220908	+	0.127541i	−0.606371	−	0.795182i	$-0.707375\pi$
$31$	−6.84815	+	3.95378i	−0.220908	+	0.127541i	0.385463	+	0.922723i	$0.374042\pi$
$32$	15.1127	+	26.1759i	0.472270	+	0.817996i
$33$		0			0
$34$	−17.0047	+	9.81768i	−0.500139	+	0.288755i
$35$	−3.72810	+	23.4695i	−0.106517	+	0.670558i
$36$		0			0
$37$	−19.4790	−	33.7386i	−0.526460	−	0.911855i	−0.999525	−	0.0308275i	$-0.990186\pi$
$37$	−19.4790	−	33.7386i	−0.526460	−	0.911855i	0.473065	−	0.881028i	$-0.343148\pi$
$38$			83.4274i			2.19546i
$39$		0			0
$40$		−	28.6233i		−	0.715582i
$41$	42.7546	+	24.6844i	1.04279	+	0.602058i	0.920624	−	0.390451i	$-0.127681\pi$
$41$	42.7546	+	24.6844i	1.04279	+	0.602058i	0.122171	+	0.992509i	$0.461014\pi$
$42$		0			0
$43$	−18.6830	−	32.3599i	−0.434488	−	0.752556i	0.562765	−	0.826617i	$-0.309737\pi$
$43$	−18.6830	−	32.3599i	−0.434488	−	0.752556i	−0.997254	+	0.0740608i	$0.976404\pi$
$44$	−61.8737	−	107.168i	−1.40622	−	2.43564i
$45$		0			0
$46$	3.22962	−	5.59387i	0.0702091	−	0.121606i
$47$	−27.1575	−	15.6794i	−0.577819	−	0.333604i	0.182447	−	0.983216i	$-0.441598\pi$
$47$	−27.1575	−	15.6794i	−0.577819	−	0.333604i	−0.760266	+	0.649612i	$0.774932\pi$
$48$		0			0
$49$	46.5880	+	15.1840i	0.950776	+	0.309878i
$50$	−21.9265	+	37.9778i	−0.438529	+	0.759555i
$51$		0			0
$52$		−	46.7254i		−	0.898566i
$53$	36.6033	−	63.3987i	0.690628	−	1.19620i	−0.281005	−	0.959706i	$-0.590668\pi$
$53$	36.6033	−	63.3987i	0.690628	−	1.19620i	0.971633	−	0.236496i	$-0.0759990\pi$
$54$		0			0
$55$		−	63.7403i		−	1.15891i
$56$	−58.2893	−	9.25916i	−1.04088	−	0.165342i
$57$		0			0
$58$	84.3348			1.45405
$59$	45.9596	−	26.5348i	0.778976	−	0.449742i	−0.0570911	−	0.998369i	$-0.518183\pi$
$59$	45.9596	−	26.5348i	0.778976	−	0.449742i	0.836067	+	0.548627i	$0.184849\pi$
$60$		0			0
$61$	34.8983	+	20.1485i	0.572103	+	0.330304i	0.757989	−	0.652267i	$-0.226182\pi$
$61$	34.8983	+	20.1485i	0.572103	+	0.330304i	−0.185886	+	0.982571i	$0.559515\pi$
$62$		−	25.7340i		−	0.415065i
$63$		0			0
$64$	−102.666			−1.60416
$65$	12.0338	−	20.8431i	0.185135	−	0.320663i
$66$		0			0
$67$	−38.1086	−	66.0061i	−0.568785	−	0.985165i	−0.996686	−	0.0813395i	$-0.974080\pi$
$67$	−38.1086	−	66.0061i	−0.568785	−	0.985165i	0.427901	−	0.903826i	$-0.359253\pi$
$68$		−	39.7661i		−	0.584796i
$69$		0			0
$70$	−60.0791	−	48.6962i	−0.858273	−	0.695659i
$71$	17.9011			0.252128			0.126064	−	0.992022i	$-0.459766\pi$
$71$	17.9011			0.252128			0.126064	+	0.992022i	$0.459766\pi$
$72$		0			0
$73$	109.287	+	63.0970i	1.49709	+	0.864343i	0.999994	−	0.00335584i	$-0.00106820\pi$
$73$	109.287	+	63.0970i	1.49709	+	0.864343i	0.497091	+	0.867698i	$0.334402\pi$
$74$	126.783			1.71329
$75$		0			0
$76$	−146.323	−	84.4799i	−1.92531	−	1.11158i
$77$	−129.803	−	20.6189i	−1.68575	−	0.267778i
$78$		0			0
$79$	−27.0552	+	46.8610i	−0.342471	+	0.593177i	−0.984891	−	0.173176i	$-0.944597\pi$
$79$	−27.0552	+	46.8610i	−0.342471	+	0.593177i	0.642420	+	0.766353i	$0.277930\pi$
$80$	3.16235	+	1.82578i	0.0395294	+	0.0228223i
$81$		0			0
$82$	−139.139	+	80.3317i	−1.69681	+	0.979655i
$83$	−114.768	+	66.2614i	−1.38275	+	0.798330i	−0.992484	−	0.122372i	$-0.960950\pi$
$83$	−114.768	+	66.2614i	−1.38275	+	0.798330i	−0.390265	+	0.920703i	$0.627616\pi$
$84$		0			0
$85$	10.2415	−	17.7387i	0.120488	−	0.208691i
$86$	121.602			1.41398
$87$		0			0
$88$	158.306			1.79894
$89$	−50.0032	+	28.8694i	−0.561834	+	0.324375i	−0.753881	−	0.657011i	$-0.771821\pi$
$89$	−50.0032	+	28.8694i	−0.561834	+	0.324375i	0.192047	+	0.981386i	$0.438487\pi$
$90$		0			0
$91$	−38.5527	−	31.2483i	−0.423656	−	0.343388i
$92$	6.54073	+	11.3289i	0.0710949	+	0.123140i
$93$		0			0
$94$	88.3801	−	51.0263i	0.940214	−	0.542833i
$95$	−43.5142	−	75.3689i	−0.458044	−	0.793356i
$96$		0			0
$97$	−21.0909	+	12.1768i	−0.217431	+	0.125534i	−0.604760	−	0.796407i	$-0.706731\pi$
$97$	−21.0909	+	12.1768i	−0.217431	+	0.125534i	0.387329	+	0.921942i	$0.373398\pi$
$98$	−118.601	+	106.595i	−1.21021	+	1.08770i
$99$		0			0
$100$	−44.4062	−	76.9137i	−0.444062	−	0.769137i
$101$		−	63.6272i		−	0.629972i	−0.949096	−	0.314986i	$-0.898000\pi$
$101$		−	63.6272i		−	0.629972i	0.949096	−	0.314986i	$-0.102000\pi$
$102$		0			0
$103$			130.316i			1.26520i	0.774478	+	0.632600i	$0.218012\pi$
$103$			130.316i			1.26520i	−0.774478	+	0.632600i	$0.781988\pi$
$104$	51.7662	+	29.8872i	0.497752	+	0.287377i
$105$		0			0
$106$	119.120	+	206.322i	1.12377	+	1.94643i
$107$	35.5021	+	61.4914i	0.331795	+	0.574686i	0.982864	−	0.184333i	$-0.0590124\pi$
$107$	35.5021	+	61.4914i	0.331795	+	0.574686i	−0.651069	+	0.759019i	$0.725679\pi$
$108$		0			0
$109$	39.3202	−	68.1045i	0.360736	−	0.624812i	−0.627347	−	0.778740i	$-0.715859\pi$
$109$	39.3202	−	68.1045i	0.360736	−	0.624812i	0.988082	+	0.153928i	$0.0491924\pi$
$110$	179.643	+	103.717i	1.63311	+	0.942879i
$111$		0			0
$112$	4.74105	−	5.84929i	0.0423308	−	0.0522258i
$113$	−16.0376	+	27.7779i	−0.141925	+	0.245822i	−0.928222	−	0.372028i	$-0.878663\pi$
$113$	−16.0376	+	27.7779i	−0.141925	+	0.245822i	0.786296	+	0.617850i	$0.211996\pi$
$114$		0			0
$115$			6.73805i			0.0585917i
$116$	−85.3987	+	147.915i	−0.736196	+	1.27513i
$117$		0			0
$118$			172.707i			1.46362i
$119$	−32.8107	−	26.5942i	−0.275720	−	0.223480i
$120$		0			0
$121$	231.527			1.91345
$122$	−113.571	+	65.5705i	−0.930913	+	0.537463i
$123$		0			0
$124$	45.1350	+	26.0587i	0.363992	+	0.210151i
$125$		−	130.616i		−	1.04493i
$126$		0			0
$127$	64.5210			0.508039			0.254020	−	0.967199i	$-0.418247\pi$
$127$	64.5210			0.508039			0.254020	+	0.967199i	$0.418247\pi$
$128$	106.606	−	184.647i	0.832857	−	1.44255i
$129$		0			0
$130$	39.1621	+	67.8308i	0.301247	+	0.521775i
$131$			71.3144i			0.544385i	0.962243	+	0.272192i	$0.0877487\pi$
$131$			71.3144i			0.544385i	−0.962243	+	0.272192i	$0.912251\pi$
$132$		0			0
$133$	−167.559	+	64.2331i	−1.25985	+	0.482955i
$134$	248.038			1.85103
$135$		0			0
$136$	44.0562	+	25.4358i	0.323942	+	0.187028i
$137$	14.1094			0.102988			0.0514942	−	0.998673i	$-0.483602\pi$
$137$	14.1094			0.102988			0.0514942	+	0.998673i	$0.483602\pi$
$138$		0			0
$139$	−143.293	−	82.7301i	−1.03088	−	0.595181i	−0.113646	−	0.993521i	$-0.536253\pi$
$139$	−143.293	−	82.7301i	−1.03088	−	0.595181i	−0.917238	+	0.398340i	$0.869586\pi$
$140$	146.245	−	56.0624i	1.04461	−	0.400446i
$141$		0			0
$142$	−29.1282	+	50.4516i	−0.205128	+	0.355293i
$143$	115.277	+	66.5549i	0.806130	+	0.465419i
$144$		0			0
$145$	−76.1886	+	43.9875i	−0.525439	+	0.303362i
$146$	−355.659	+	205.340i	−2.43602	+	1.40644i
$147$		0			0
$148$	−128.383	+	222.365i	−0.867450	+	1.50247i
$149$	67.9838			0.456267			0.228133	−	0.973630i	$-0.426738\pi$
$149$	67.9838			0.456267			0.228133	+	0.973630i	$0.426738\pi$
$150$		0			0
$151$	−159.533			−1.05651			−0.528254	−	0.849086i	$-0.677153\pi$
$151$	−159.533			−1.05651			−0.528254	+	0.849086i	$0.677153\pi$
$152$	187.187	−	108.073i	1.23150	−	0.711004i
$153$		0			0
$154$	269.323	−	332.279i	1.74885	−	2.15765i
$155$	13.4224	+	23.2483i	0.0865962	+	0.149989i
$156$		0			0
$157$	−141.606	+	81.7560i	−0.901946	+	0.520739i	−0.877831	−	0.478970i	$-0.841010\pi$
$157$	−141.606	+	81.7560i	−0.901946	+	0.520739i	−0.0241149	+	0.999709i	$0.507677\pi$
$158$	−88.0471	−	152.502i	−0.557260	−	0.965203i
$159$		0			0
$160$	88.8626	−	51.3048i	0.555391	−	0.320655i
$161$	13.7216	+	2.17965i	0.0852271	+	0.0135382i
$162$		0			0
$163$	−3.96702	−	6.87107i	−0.0243375	−	0.0421538i	0.853600	−	0.520929i	$-0.174414\pi$
$163$	−3.96702	−	6.87107i	−0.0243375	−	0.0421538i	−0.877938	+	0.478775i	$0.841081\pi$
$164$		−	325.380i		−	1.98403i
$165$		0			0
$166$		−	431.276i		−	2.59805i
$167$	−44.9655	−	25.9608i	−0.269254	−	0.155454i	0.359294	−	0.933224i	$-0.383017\pi$
$167$	−44.9655	−	25.9608i	−0.269254	−	0.155454i	−0.628549	+	0.777770i	$0.716351\pi$
$168$		0			0
$169$	−59.3697	−	102.831i	−0.351300	−	0.608469i
$170$	33.3293	+	57.7281i	0.196055	+	0.339577i
$171$		0			0
$172$	−123.136	+	213.278i	−0.715909	+	1.23999i
$173$	−55.3494	−	31.9560i	−0.319939	−	0.184717i	0.331427	−	0.943481i	$-0.392470\pi$
$173$	−55.3494	−	31.9560i	−0.319939	−	0.184717i	−0.651365	+	0.758764i	$0.725803\pi$
$174$		0			0
$175$	−93.1581	−	14.7980i	−0.532332	−	0.0845601i
$176$	−10.0978	+	17.4900i	−0.0573741	+	0.0993748i
$177$		0			0
$178$		−	187.902i		−	1.05563i
$179$	66.9142	−	115.899i	0.373823	−	0.647480i	−0.616328	−	0.787490i	$-0.711380\pi$
$179$	66.9142	−	115.899i	0.373823	−	0.647480i	0.990150	+	0.140010i	$0.0447136\pi$
$180$		0			0
$181$			105.015i			0.580192i	0.956998	+	0.290096i	$0.0936872\pi$
$181$			105.015i			0.580192i	−0.956998	+	0.290096i	$0.906313\pi$
$182$	150.801	−	57.8087i	0.828576	−	0.317630i
$183$		0			0
$184$	−16.7347			−0.0909496
$185$	−114.537	+	66.1278i	−0.619118	+	0.357448i
$186$		0			0
$187$	98.1073	+	56.6423i	0.524638	+	0.302900i
$188$			206.680i			1.09936i
$189$		0			0
$190$	283.221			1.49064
$191$	−112.536	+	194.918i	−0.589195	+	1.02052i	0.405143	+	0.914253i	$0.367222\pi$
$191$	−112.536	+	194.918i	−0.589195	+	1.02052i	−0.994338	+	0.106262i	$0.966112\pi$
$192$		0			0
$193$	111.008	+	192.272i	0.575173	+	0.996228i	0.996023	+	0.0890980i	$0.0283984\pi$
$193$	111.008	+	192.272i	0.575173	+	0.996228i	−0.420850	+	0.907130i	$0.638268\pi$
$194$		−	79.2553i		−	0.408532i
$195$		0			0
$196$	−66.8592	−	315.954i	−0.341118	−	1.61201i
$197$	46.6626			0.236866			0.118433	−	0.992962i	$-0.462213\pi$
$197$	46.6626			0.236866			0.118433	+	0.992962i	$0.462213\pi$
$198$		0			0
$199$	−63.3871	−	36.5966i	−0.318528	−	0.183902i	0.332208	−	0.943206i	$-0.392206\pi$
$199$	−63.3871	−	36.5966i	−0.318528	−	0.183902i	−0.650736	+	0.759304i	$0.725540\pi$
$200$	113.615			0.568075
$201$		0			0
$202$	179.324	+	103.533i	0.887742	+	0.512538i
$203$	64.9317	+	169.382i	0.319861	+	0.834394i
$204$		0			0
$205$	83.7991	−	145.144i	0.408776	−	0.708021i
$206$	−367.276	−	212.047i	−1.78289	−	1.02935i
$207$		0			0
$208$	−6.60399	+	3.81281i	−0.0317499	+	0.0183308i
$209$	416.841	−	240.663i	1.99446	−	1.15150i
$210$		0			0
$211$	52.4854	−	90.9074i	0.248746	−	0.430841i	−0.714432	−	0.699705i	$-0.753315\pi$
$211$	52.4854	−	90.9074i	0.248746	−	0.430841i	0.963178	+	0.268864i	$0.0866482\pi$
$212$	−482.491			−2.27590
$213$		0			0
$214$	−231.073			−1.07978
$215$	−109.856	+	63.4255i	−0.510959	+	0.295002i
$216$		0			0
$217$	51.6854	−	19.8133i	0.238182	−	0.0913057i
$218$	127.962	+	221.636i	0.586981	+	1.01668i
$219$		0			0
$220$	−363.818	+	210.050i	−1.65372	+	0.954774i
$221$	21.3874	+	37.0441i	0.0967755	+	0.167620i
$222$		0			0
$223$	25.3354	−	14.6274i	0.113612	−	0.0655937i	−0.442117	−	0.896957i	$-0.645773\pi$
$223$	25.3354	−	14.6274i	0.113612	−	0.0655937i	0.555729	+	0.831364i	$0.312439\pi$
$224$	−75.7331	−	197.559i	−0.338094	−	0.881958i
$225$		0			0
$226$	−52.1919	−	90.3991i	−0.230938	−	0.399996i
$227$		−	232.404i		−	1.02381i	−0.859043	−	0.511903i	$-0.828941\pi$
$227$		−	232.404i		−	1.02381i	0.859043	−	0.511903i	$-0.171059\pi$
$228$		0			0
$229$			217.885i			0.951461i	0.879591	+	0.475731i	$0.157816\pi$
$229$			217.885i			0.951461i	−0.879591	+	0.475731i	$0.842184\pi$
$230$	−18.9902	−	10.9640i	−0.0825661	−	0.0476695i
$231$		0			0
$232$	−109.248	−	189.223i	−0.470897	−	0.815618i
$233$	−0.185875	−	0.321945i	−0.000797747	−	0.00138174i	0.865626	−	0.500691i	$-0.166921\pi$
$233$	−0.185875	−	0.321945i	−0.000797747	−	0.00138174i	−0.866424	+	0.499309i	$0.833587\pi$
$234$		0			0
$235$	−53.2288	+	92.1950i	−0.226506	+	0.392319i
$236$	−302.911	−	174.886i	−1.28352	−	0.741042i
$237$		0			0
$238$	128.341	−	49.1987i	0.539246	−	0.206717i
$239$	−215.408	+	373.097i	−0.901288	+	1.56108i	−0.0754646	+	0.997148i	$0.524044\pi$
$239$	−215.408	+	373.097i	−0.901288	+	1.56108i	−0.825824	+	0.563929i	$0.809289\pi$
$240$		0			0
$241$		−	281.470i		−	1.16792i	−0.811781	−	0.583962i	$-0.801502\pi$
$241$		−	281.470i		−	1.16792i	0.811781	−	0.583962i	$-0.198498\pi$
$242$	−376.736	+	652.526i	−1.55676	+	2.69639i
$243$		0			0
$244$		−	265.591i		−	1.08849i
$245$	51.5470	−	158.158i	0.210396	−	0.645544i
$246$		0			0
$247$	181.743			0.735801
$248$	−57.7398	+	33.3361i	−0.232822	+	0.134420i
$249$		0			0
$250$	368.123	+	212.536i	1.47249	+	0.850144i
$251$			277.192i			1.10435i	0.833729	+	0.552175i	$0.186202\pi$
$251$			277.192i			1.10435i	−0.833729	+	0.552175i	$0.813798\pi$
$252$		0			0
$253$	−37.2660			−0.147297
$254$	−104.987	+	181.843i	−0.413335	+	0.715917i
$255$		0			0
$256$	141.600	+	245.258i	0.553125	+	0.958041i
$257$			114.798i			0.446684i	0.974740	+	0.223342i	$0.0716967\pi$
$257$			114.798i			0.446684i	−0.974740	+	0.223342i	$0.928303\pi$
$258$		0			0
$259$	97.6139	+	254.637i	0.376888	+	0.983156i
$260$	−158.625			−0.610095
$261$		0			0
$262$	−200.989	−	116.041i	−0.767134	−	0.442905i
$263$	−157.185			−0.597663			−0.298832	−	0.954306i	$-0.596597\pi$
$263$	−157.185			−0.597663			−0.298832	+	0.954306i	$0.596597\pi$
$264$		0			0
$265$	−215.228	−	124.262i	−0.812180	−	0.468912i
$266$	91.6174	−	576.760i	0.344426	−	2.16827i
$267$		0			0
$268$	−251.167	+	435.034i	−0.937190	+	1.62326i
$269$	363.512	+	209.874i	1.35135	+	0.780200i	0.988438	−	0.151624i	$-0.0484504\pi$
$269$	363.512	+	209.874i	1.35135	+	0.780200i	0.362908	+	0.931825i	$0.381784\pi$
$270$		0			0
$271$	−64.2582	+	37.0995i	−0.237115	+	0.136899i	−0.613850	−	0.789423i	$-0.710380\pi$
$271$	−64.2582	+	37.0995i	−0.237115	+	0.136899i	0.376735	+	0.926321i	$0.377047\pi$
$272$	−5.62039	+	3.24493i	−0.0206632	+	0.0119299i
$273$		0			0
$274$	−22.9585	+	39.7653i	−0.0837902	+	0.145129i
$275$	253.006			0.920021
$276$		0			0
$277$	469.006			1.69316			0.846580	−	0.532261i	$-0.178657\pi$
$277$	469.006			1.69316			0.846580	+	0.532261i	$0.178657\pi$
$278$	466.326	−	269.233i	1.67743	−	0.968465i
$279$		0			0
$280$	−31.4332	+	197.882i	−0.112262	+	0.706721i
$281$	113.700	+	196.934i	0.404626	+	0.700832i	0.994278	−	0.106825i	$-0.0340685\pi$
$281$	113.700	+	196.934i	0.404626	+	0.700832i	−0.589652	+	0.807657i	$0.700735\pi$
$282$		0			0
$283$	−30.6689	+	17.7067i	−0.108371	+	0.0625678i	−0.553206	−	0.833045i	$-0.686596\pi$
$283$	−30.6689	+	17.7067i	−0.108371	+	0.0625678i	0.444835	+	0.895613i	$0.353262\pi$
$284$	−58.9914	−	102.176i	−0.207716	−	0.359775i
$285$		0			0
$286$	−375.151	+	216.593i	−1.31172	+	0.757319i
$287$	−268.469	−	217.603i	−0.935431	−	0.758198i
$288$		0			0
$289$	−126.298	−	218.755i	−0.437017	−	0.756936i
$290$		−	286.302i		−	0.987248i
$291$		0			0
$292$		−	831.722i		−	2.84836i
$293$	29.8882	+	17.2560i	0.102007	+	0.0588940i	0.550136	−	0.835075i	$-0.314576\pi$
$293$	29.8882	+	17.2560i	0.102007	+	0.0588940i	−0.448128	+	0.893969i	$0.647909\pi$
$294$		0			0
$295$	−90.0810	−	156.025i	−0.305359	−	0.528898i
$296$	−164.236	−	284.465i	−0.554852	−	0.961032i
$297$		0			0
$298$	−110.622	+	191.602i	−0.371214	+	0.642961i
$299$	−12.1860	−	7.03559i	−0.0407558	−	0.0235304i
$300$		0			0
$301$	93.6249	+	244.232i	0.311046	+	0.811401i
$302$	259.588	−	449.620i	0.859563	−	1.48881i
$303$		0			0
$304$			27.5744i			0.0907052i
$305$	68.4008	−	118.474i	0.224265	−	0.388438i
$306$		0			0
$307$			281.940i			0.918370i	0.888341	+	0.459185i	$0.151859\pi$
$307$			281.940i			0.918370i	−0.888341	+	0.459185i	$0.848141\pi$
$308$	310.064	+	808.837i	1.00670	+	2.62609i
$309$		0			0
$310$	−87.3625			−0.281815
$311$	41.5484	−	23.9880i	0.133596	−	0.0771318i	−0.431712	−	0.902011i	$-0.642090\pi$
$311$	41.5484	−	23.9880i	0.133596	−	0.0771318i	0.565309	+	0.824880i	$0.308757\pi$
$312$		0			0
$313$	43.5506	+	25.1440i	0.139139	+	0.0803322i	0.567954	−	0.823060i	$-0.307735\pi$
$313$	43.5506	+	25.1440i	0.139139	+	0.0803322i	−0.428814	+	0.903393i	$0.641069\pi$
$314$		−	532.126i		−	1.69467i
$315$		0			0
$316$	356.632			1.12858
$317$	113.389	−	196.395i	0.357693	−	0.619542i	−0.629882	−	0.776691i	$-0.716897\pi$
$317$	113.389	−	196.395i	0.357693	−	0.619542i	0.987575	+	0.157149i	$0.0502302\pi$
$318$		0			0
$319$	−243.281	−	421.375i	−0.762637	−	1.32093i
$320$			348.534i			1.08917i
$321$		0			0
$322$	−28.4704	+	35.1255i	−0.0884174	+	0.109085i
$323$	154.674			0.478867
$324$		0			0
$325$	82.7329	+	47.7659i	0.254563	+	0.146972i
$326$	25.8202			0.0792029
$327$		0			0
$328$	360.483	+	208.125i	1.09903	+	0.634527i
$329$	170.530	+	138.220i	0.518328	+	0.420122i
$330$		0			0
$331$	6.39312	−	11.0732i	0.0193146	−	0.0334538i	−0.856207	−	0.516634i	$-0.827185\pi$
$331$	6.39312	−	11.0732i	0.0193146	−	0.0334538i	0.875521	+	0.483180i	$0.160518\pi$
$332$	756.416	+	436.717i	2.27836	+	1.31541i
$333$		0			0
$334$	146.334	−	84.4857i	0.438125	−	0.252951i
$335$	−224.079	+	129.372i	−0.668893	+	0.386185i
$336$		0			0
$337$	202.622	−	350.952i	0.601252	−	1.04140i	−0.391379	−	0.920229i	$-0.628002\pi$
$337$	202.622	−	350.952i	0.601252	−	1.04140i	0.992632	−	0.121170i	$-0.0386647\pi$
$338$	386.420			1.14325
$339$		0			0
$340$	−134.999			−0.397056
$341$	−128.579	+	74.2351i	−0.377064	+	0.217698i
$342$		0			0
$343$	−305.404	−	156.133i	−0.890389	−	0.455200i
$344$	−157.525	−	272.841i	−0.457921	−	0.793142i
$345$		0			0
$346$	180.126	−	103.996i	0.520597	−	0.300567i
$347$	−169.575	−	293.713i	−0.488690	−	0.846435i	0.511226	−	0.859446i	$-0.329192\pi$
$347$	−169.575	−	293.713i	−0.488690	−	0.846435i	−0.999915	+	0.0130114i	$0.995858\pi$
$348$		0			0
$349$	294.743	−	170.170i	0.844535	−	0.487593i	−0.0142680	−	0.999898i	$-0.504542\pi$
$349$	294.743	−	170.170i	0.844535	−	0.487593i	0.858803	+	0.512306i	$0.171208\pi$
$350$	193.291	−	238.473i	0.552259	−	0.681353i
$351$		0			0
$352$	283.751	+	491.471i	0.806110	+	1.39622i
$353$			292.484i			0.828567i	0.910148	+	0.414284i	$0.135968\pi$
$353$			292.484i			0.828567i	−0.910148	+	0.414284i	$0.864032\pi$
$354$		0			0
$355$		−	60.7710i		−	0.171186i
$356$	329.562	+	190.273i	0.925737	+	0.534475i
$357$		0			0
$358$	217.763	+	377.176i	0.608275	+	1.05356i
$359$	−5.84920	−	10.1311i	−0.0162930	−	0.0282203i	0.857764	−	0.514044i	$-0.171853\pi$
$359$	−5.84920	−	10.1311i	−0.0162930	−	0.0282203i	−0.874057	+	0.485823i	$0.838520\pi$
$360$		0			0
$361$	148.092	−	256.504i	0.410228	−	0.710536i
$362$	−295.968	−	170.877i	−0.817592	−	0.472037i
$363$		0			0
$364$	−51.3125	+	323.028i	−0.140968	+	0.887439i
$365$	214.203	−	371.011i	0.586858	−	1.01647i
$366$		0			0
$367$			663.222i			1.80715i	0.428435	+	0.903573i	$0.359065\pi$
$367$			663.222i			1.80715i	−0.428435	+	0.903573i	$0.640935\pi$
$368$	1.06745	−	1.84888i	0.00290068	−	0.00502413i
$369$		0			0
$370$		−	430.407i		−	1.16326i
$371$	−322.673	+	398.099i	−0.869738	+	1.07304i
$372$		0			0
$373$	87.6682			0.235035			0.117518	−	0.993071i	$-0.462506\pi$
$373$	87.6682			0.235035			0.117518	+	0.993071i	$0.462506\pi$
$374$	−319.276	+	184.334i	−0.853678	+	0.492871i
$375$		0			0
$376$	−228.977	−	132.200i	−0.608981	−	0.351596i
$377$		−	183.720i		−	0.487320i
$378$		0			0
$379$	−649.363			−1.71336			−0.856679	−	0.515850i	$-0.827476\pi$
$379$	−649.363			−1.71336			−0.856679	+	0.515850i	$0.827476\pi$
$380$	−286.794	+	496.743i	−0.754722	+	1.30722i
$381$		0			0
$382$	−366.233	−	634.334i	−0.958724	−	1.66056i
$383$			464.806i			1.21359i	0.794858	+	0.606796i	$0.207545\pi$
$383$			464.806i			1.21359i	−0.794858	+	0.606796i	$0.792455\pi$
$384$		0			0
$385$	−69.9976	+	440.657i	−0.181812	+	1.14456i
$386$	−722.521			−1.87182
$387$		0			0
$388$	139.006	+	80.2552i	0.358263	+	0.206843i
$389$	152.669			0.392466			0.196233	−	0.980557i	$-0.437129\pi$
$389$	152.669			0.392466			0.196233	+	0.980557i	$0.437129\pi$
$390$		0			0
$391$	−10.3710	−	5.98771i	−0.0265243	−	0.0153138i
$392$	392.805	+	128.023i	1.00205	+	0.326590i
$393$		0			0
$394$	−75.9282	+	131.512i	−0.192711	+	0.333786i
$395$	159.085	+	91.8476i	0.402746	+	0.232526i
$396$		0			0
$397$	−373.946	+	215.898i	−0.941929	+	0.543823i	−0.890564	−	0.454857i	$-0.849690\pi$
$397$	−373.946	+	215.898i	−0.941929	+	0.543823i	−0.0513642	+	0.998680i	$0.516357\pi$
$398$	206.284	−	119.098i	0.518302	−	0.299242i
$399$		0			0
$400$	−7.24712	+	12.5524i	−0.0181178	+	0.0313810i
$401$	−79.7371			−0.198846			−0.0994229	−	0.995045i	$-0.531700\pi$
$401$	−79.7371			−0.198846			−0.0994229	+	0.995045i	$0.531700\pi$
$402$		0			0
$403$	−56.0605			−0.139108
$404$	−363.172	+	209.678i	−0.898942	+	0.519004i
$405$		0			0
$406$	−583.034	−	92.6139i	−1.43604	−	0.228113i
$407$	−365.732	−	633.467i	−0.898605	−	1.55643i
$408$		0			0
$409$	5.57267	−	3.21739i	0.0136251	−	0.00786647i	−0.493172	−	0.869932i	$-0.664163\pi$
$409$	5.57267	−	3.21739i	0.0136251	−	0.00786647i	0.506797	+	0.862065i	$0.330829\pi$
$410$	272.712	+	472.351i	0.665151	+	1.15208i
$411$		0			0
$412$	743.818	−	429.443i	1.80538	−	1.04234i
$413$	−346.873	+	132.972i	−0.839887	+	0.321966i
$414$		0			0
$415$	224.946	+	389.618i	0.542039	+	0.938838i
$416$			214.281i			0.515100i
$417$		0			0
$418$			1566.41i			3.74739i
$419$	−347.531	−	200.647i	−0.829429	−	0.478871i	0.0242282	−	0.999706i	$-0.492287\pi$
$419$	−347.531	−	200.647i	−0.829429	−	0.478871i	−0.853657	+	0.520835i	$0.825621\pi$
$420$		0			0
$421$	46.9188	+	81.2658i	0.111446	+	0.193030i	0.916354	−	0.400370i	$-0.131118\pi$
$421$	46.9188	+	81.2658i	0.111446	+	0.193030i	−0.804907	+	0.593400i	$0.797785\pi$
$422$	170.806	+	295.845i	0.404754	+	0.701054i
$423$		0			0
$424$	308.618	−	534.543i	0.727874	−	1.26071i
$425$	70.4107	+	40.6516i	0.165672	+	0.0956509i
$426$		0			0
$427$	−219.137	−	177.618i	−0.513201	−	0.415966i
$428$	233.988	−	405.279i	0.546700	−	0.946913i
$429$		0			0
$430$		−	412.818i		−	0.960042i
$431$	358.936	−	621.695i	0.832798	−	1.44245i	−0.0630126	−	0.998013i	$-0.520071\pi$
$431$	358.936	−	621.695i	0.832798	−	1.44245i	0.895811	−	0.444436i	$-0.146596\pi$
$432$		0			0
$433$			481.797i			1.11269i	0.830950	+	0.556347i	$0.187797\pi$
$433$			481.797i			1.11269i	−0.830950	+	0.556347i	$0.812203\pi$
$434$	−28.2603	+	177.908i	−0.0651160	+	0.409925i
$435$		0			0
$436$	−518.304			−1.18877
$437$	−44.0647	+	25.4408i	−0.100835	+	0.0582169i
$438$		0			0
$439$	−500.912	−	289.201i	−1.14103	−	0.658773i	−0.194344	−	0.980934i	$-0.562258\pi$
$439$	−500.912	−	289.201i	−1.14103	−	0.658773i	−0.946685	+	0.322160i	$0.895591\pi$
$440$		−	537.423i		−	1.22141i
$441$		0			0
$442$	−139.204			−0.314942
$443$	63.7290	−	110.382i	0.143858	−	0.249169i	−0.785088	−	0.619384i	$-0.787383\pi$
$443$	63.7290	−	110.382i	0.143858	−	0.249169i	0.928946	+	0.370215i	$0.120716\pi$
$444$		0			0
$445$	98.0065	+	169.752i	0.220239	+	0.381466i
$446$			95.2054i			0.213465i
$447$		0			0
$448$	709.766	+	112.745i	1.58430	+	0.251663i
$449$	−769.390			−1.71356			−0.856782	−	0.515679i	$-0.827540\pi$
$449$	−769.390			−1.71356			−0.856782	+	0.515679i	$0.827540\pi$
$450$		0			0
$451$	802.748	+	463.467i	1.77993	+	1.02764i
$452$	211.401			0.467702
$453$		0			0
$454$	654.997	+	378.163i	1.44272	+	0.832957i
$455$	−106.082	+	130.880i	−0.233148	+	0.287648i
$456$		0			0
$457$	60.5441	−	104.865i	0.132482	−	0.229465i	−0.792151	−	0.610325i	$-0.791039\pi$
$457$	60.5441	−	104.865i	0.132482	−	0.229465i	0.924633	+	0.380860i	$0.124372\pi$
$458$	−614.076	−	354.537i	−1.34078	−	0.774098i
$459$		0			0
$460$	38.4595	−	22.2046i	0.0836077	−	0.0482709i
$461$	173.351	−	100.084i	0.376033	−	0.217103i	−0.300058	−	0.953921i	$-0.597006\pi$
$461$	173.351	−	100.084i	0.376033	−	0.217103i	0.676091	+	0.736818i	$0.263673\pi$
$462$		0			0
$463$	30.3643	−	52.5925i	0.0655816	−	0.113591i	−0.831370	−	0.555719i	$-0.812443\pi$
$463$	30.3643	−	52.5925i	0.0655816	−	0.113591i	0.896952	+	0.442128i	$0.145776\pi$
$464$	27.8743			0.0600739
$465$		0			0
$466$	1.20981			0.00259615
$467$	56.9687	−	32.8909i	0.121989	−	0.0704302i	−0.437764	−	0.899090i	$-0.644229\pi$
$467$	56.9687	−	32.8909i	0.121989	−	0.0704302i	0.559753	+	0.828660i	$0.310896\pi$
$468$		0			0
$469$	190.971	+	498.171i	0.407188	+	1.06220i
$470$	−173.225	−	300.035i	−0.368565	−	0.638373i
$471$		0			0
$472$	387.506	−	223.727i	0.820987	−	0.473997i
$473$	−350.787	−	607.580i	−0.741621	−	1.28452i
$474$		0			0
$475$	299.163	−	172.722i	0.629817	−	0.363625i
$476$	−43.6700	+	274.916i	−0.0917437	+	0.577555i
$477$		0			0
$478$	−701.014	−	1214.19i	−1.46656	−	2.54015i
$479$			531.170i			1.10891i	0.832212	+	0.554457i	$0.187074\pi$
$479$			531.170i			1.10891i	−0.832212	+	0.554457i	$0.812926\pi$
$480$		0			0
$481$		−	276.192i		−	0.574203i
$482$	793.281	+	458.001i	1.64581	+	0.950210i
$483$		0			0
$484$	−762.978	−	1321.52i	−1.57640	−	2.73040i
$485$	41.3381	+	71.5998i	0.0852333	+	0.147628i
$486$		0			0
$487$	438.744	−	759.927i	0.900911	−	1.56042i	0.0745980	−	0.997214i	$-0.476233\pi$
$487$	438.744	−	759.927i	0.900911	−	1.56042i	0.826313	−	0.563211i	$-0.190434\pi$
$488$	294.243	+	169.881i	0.602957	+	0.348117i
$489$		0			0
$490$	361.870	+	402.629i	0.738510	+	0.821692i
$491$	112.081	−	194.130i	0.228271	−	0.395377i	−0.729025	−	0.684487i	$-0.760026\pi$
$491$	112.081	−	194.130i	0.228271	−	0.395377i	0.957296	+	0.289110i	$0.0933594\pi$
$492$		0			0
$493$		−	156.357i		−	0.317153i
$494$	−295.728	+	512.216i	−0.598640	+	1.03687i
$495$		0			0
$496$		−	8.50560i		−	0.0171484i
$497$	−123.756	−	19.6584i	−0.249006	−	0.0395542i
$498$		0			0
$499$	−804.278			−1.61178			−0.805889	−	0.592066i	$-0.798312\pi$
$499$	−804.278			−1.61178			−0.805889	+	0.592066i	$0.798312\pi$
$500$	−745.535	+	430.435i	−1.49107	+	0.860870i
$501$		0			0
$502$	−781.224	−	451.040i	−1.55622	−	0.898486i
$503$		−	391.146i		−	0.777625i	−0.921317	−	0.388813i	$-0.872885\pi$
$503$		−	391.146i		−	0.777625i	0.921317	−	0.388813i	$-0.127115\pi$
$504$		0			0
$505$	−216.003			−0.427729
$506$	60.6384	−	105.029i	0.119839	−	0.207567i
$507$		0			0
$508$	−212.623	−	368.274i	−0.418550	−	0.724949i
$509$		−	606.648i		−	1.19184i	−0.803043	−	0.595921i	$-0.796787\pi$
$509$		−	606.648i		−	1.19184i	0.803043	−	0.595921i	$-0.203213\pi$
$510$		0			0
$511$	−686.247	−	556.226i	−1.34295	−	1.08850i
$512$	−68.7875			−0.134351
$513$		0			0
$514$	−323.541	−	186.796i	−0.629457	−	0.363417i
$515$	442.399			0.859027
$516$		0			0
$517$	−509.902	−	294.392i	−0.986270	−	0.569423i
$518$	−876.493	−	139.229i	−1.69207	−	0.268783i
$519$		0			0
$520$	101.462	−	175.737i	0.195119	−	0.337956i
$521$	224.671	+	129.714i	0.431231	+	0.248971i	0.699871	−	0.714269i	$-0.253241\pi$
$521$	224.671	+	129.714i	0.431231	+	0.248971i	−0.268640	+	0.963241i	$0.586574\pi$
$522$		0			0
$523$	855.360	−	493.842i	1.63549	−	0.944249i	0.653127	−	0.757248i	$-0.273457\pi$
$523$	855.360	−	493.842i	1.63549	−	0.944249i	0.982360	−	0.187000i	$-0.0598765\pi$
$524$	407.050	−	235.010i	0.776812	−	0.448493i
$525$		0			0
$526$	255.768	−	443.004i	0.486252	−	0.842213i
$527$	−47.7108			−0.0905329
$528$		0			0
$529$	−525.061			−0.992553
$530$	700.427	−	404.392i	1.32156	−	0.763003i
$531$		0			0
$532$	918.808	+	744.725i	1.72708	+	1.39986i
$533$	174.999	+	303.107i	0.328329	+	0.568682i
$534$		0			0
$535$	208.753	−	120.523i	0.390192	−	0.225277i
$536$	−321.311	−	556.526i	−0.599460	−	1.03830i
$537$		0			0
$538$	−1183.00	+	683.004i	−2.19888	+	1.26952i
$539$	874.724	+	285.090i	1.62286	+	0.528925i
$540$		0			0
$541$	−88.7497	−	153.719i	−0.164048	−	0.284139i	0.772269	−	0.635296i	$-0.219122\pi$
$541$	−88.7497	−	153.719i	−0.164048	−	0.284139i	−0.936317	+	0.351157i	$0.885788\pi$
$542$		−	241.470i		−	0.445516i
$543$		0			0
$544$			182.366i			0.335232i
$545$	−231.203	−	133.485i	−0.424226	−	0.244927i
$546$		0			0
$547$	340.323	+	589.457i	0.622163	+	1.07762i	0.989082	+	0.147365i	$0.0470792\pi$
$547$	340.323	+	589.457i	0.622163	+	1.07762i	−0.366919	+	0.930253i	$0.619587\pi$
$548$	−46.4963	−	80.5339i	−0.0848472	−	0.146960i
$549$		0			0
$550$	−411.685	+	713.059i	−0.748518	+	1.29647i
$551$	−575.329	−	332.166i	−1.04415	−	0.602843i
$552$		0			0
$553$	238.502	−	294.254i	0.431288	−	0.532104i
$554$	−763.155	+	1321.82i	−1.37754	+	2.38596i
$555$		0			0
$556$			1090.52i			1.96137i
$557$	−368.817	+	638.810i	−0.662150	+	1.14688i	0.317900	+	0.948124i	$0.397022\pi$
$557$	−368.817	+	638.810i	−0.662150	+	1.14688i	−0.980050	+	0.198753i	$0.936311\pi$
$558$		0			0
$559$		−	264.905i		−	0.473891i
$560$	−19.8573	−	16.0950i	−0.0354595	−	0.0287411i
$561$		0			0
$562$	−740.039			−1.31680
$563$	372.871	−	215.277i	0.662293	−	0.382375i	−0.130857	−	0.991401i	$-0.541773\pi$
$563$	372.871	−	215.277i	0.662293	−	0.382375i	0.793150	+	0.609026i	$0.208440\pi$
$564$		0			0
$565$	94.3011	+	54.4447i	0.166905	+	0.0963624i
$566$		−	115.248i		−	0.203618i
$567$		0			0
$568$	150.932			0.265725
$569$	−171.284	+	296.673i	−0.301026	+	0.521393i	−0.976369	−	0.216111i	$-0.930663\pi$
$569$	−171.284	+	296.673i	−0.301026	+	0.521393i	0.675342	+	0.737504i	$0.263996\pi$
$570$		0			0
$571$	277.709	+	481.007i	0.486356	+	0.842394i	0.999877	−	0.0156833i	$-0.00499235\pi$
$571$	277.709	+	481.007i	0.486356	+	0.842394i	−0.513521	+	0.858077i	$0.671659\pi$
$572$		−	877.303i		−	1.53375i
$573$		0			0
$574$	1050.13	−	402.561i	1.82949	−	0.701326i
$575$	−26.7455			−0.0465139
$576$		0			0
$577$	−342.152	−	197.542i	−0.592984	−	0.342360i	0.173292	−	0.984870i	$-0.444559\pi$
$577$	−342.152	−	197.542i	−0.592984	−	0.342360i	−0.766277	+	0.642511i	$0.777893\pi$
$578$	822.037			1.42221
$579$		0			0
$580$	502.145	+	289.914i	0.865768	+	0.499851i
$581$	866.196	−	332.052i	1.49087	−	0.571517i
$582$		0			0
$583$	687.252	−	1190.36i	1.17882	−	2.04178i
$584$	921.449	+	531.999i	1.57782	+	0.910957i
$585$		0			0
$586$	−97.2667	+	56.1570i	−0.165984	+	0.0958310i
$587$	−635.345	+	366.816i	−1.08236	+	0.624900i	−0.931532	−	0.363660i	$-0.881527\pi$
$587$	−635.345	+	366.816i	−1.08236	+	0.624900i	−0.150827	+	0.988560i	$0.548194\pi$
$588$		0			0
$589$	−101.358	+	175.557i	−0.172084	+	0.298059i
$590$	586.311			0.993747
$591$		0			0
$592$	41.9043			0.0707843
$593$	−217.935	+	125.825i	−0.367512	+	0.212183i	−0.672371	−	0.740214i	$-0.734724\pi$
$593$	−217.935	+	125.825i	−0.367512	+	0.212183i	0.304859	+	0.952398i	$0.401391\pi$
$594$		0			0
$595$	−90.2826	+	111.387i	−0.151735	+	0.187204i
$596$	−224.034	−	388.039i	−0.375897	−	0.651072i
$597$		0			0
$598$	39.6575	−	22.8963i	0.0663170	−	0.0382881i
$599$	365.743	+	633.485i	0.610589	+	1.05757i	0.991141	+	0.132811i	$0.0424004\pi$
$599$	365.743	+	633.485i	0.610589	+	1.05757i	−0.380553	+	0.924759i	$0.624266\pi$
$600$		0			0
$601$	480.584	−	277.465i	0.799640	−	0.461672i	−0.0437053	−	0.999044i	$-0.513916\pi$
$601$	480.584	−	277.465i	0.799640	−	0.461672i	0.843345	+	0.537372i	$0.180583\pi$
$602$	−840.675	−	133.540i	−1.39647	−	0.221827i
$603$		0			0
$604$	525.726	+	910.584i	0.870407	+	1.50759i
$605$		−	785.995i		−	1.29917i
$606$		0			0
$607$			926.256i			1.52596i	0.646424	+	0.762978i	$0.276264\pi$
$607$			926.256i			1.52596i	−0.646424	+	0.762978i	$0.723736\pi$
$608$	671.035	+	387.422i	1.10368	+	0.637208i
$609$		0			0
$610$	222.600	+	385.555i	0.364919	+	0.632058i
$611$	−111.159	−	192.532i	−0.181929	−	0.315110i
$612$		0			0
$613$	−54.0715	+	93.6546i	−0.0882080	+	0.152781i	−0.906754	−	0.421661i	$-0.861447\pi$
$613$	−54.0715	+	93.6546i	−0.0882080	+	0.152781i	0.818546	+	0.574441i	$0.194781\pi$
$614$	−794.606	−	458.766i	−1.29415	−	0.747175i
$615$		0			0
$616$	−1094.42	−	173.847i	−1.77666	−	0.282220i
$617$	−380.105	+	658.361i	−0.616053	+	1.06704i	0.374145	+	0.927370i	$0.377936\pi$
$617$	−380.105	+	658.361i	−0.616053	+	1.06704i	−0.990199	+	0.139666i	$0.955397\pi$
$618$		0			0
$619$			1085.17i			1.75310i	0.481307	+	0.876552i	$0.340162\pi$
$619$			1085.17i			1.75310i	−0.481307	+	0.876552i	$0.659838\pi$
$620$	88.4647	−	153.225i	0.142685	−	0.247138i
$621$		0			0
$622$			156.131i			0.251014i
$623$	377.392	−	144.671i	0.605766	−	0.232217i
$624$		0			0
$625$	−106.541			−0.170466
$626$	−141.729	+	81.8274i	−0.226404	+	0.130715i
$627$		0			0
$628$	933.296	+	538.839i	1.48614	+	0.858024i
$629$		−	235.056i		−	0.373698i
$630$		0			0
$631$	−117.683			−0.186502			−0.0932508	−	0.995643i	$-0.529726\pi$
$631$	−117.683			−0.186502			−0.0932508	+	0.995643i	$0.529726\pi$
$632$	−228.114	+	395.106i	−0.360940	+	0.625167i
$633$		0			0
$634$	369.007	+	639.138i	0.582029	+	1.00810i
$635$		−	219.038i		−	0.344941i
$636$		0			0
$637$	232.212	+	258.367i	0.364539	+	0.405600i
$638$	1583.45			2.48189
$639$		0			0
$640$	−626.843	−	361.908i	−0.979442	−	0.565481i
$641$	435.002			0.678630			0.339315	−	0.940673i	$-0.389805\pi$
$641$	435.002			0.678630			0.339315	+	0.940673i	$0.389805\pi$
$642$		0			0
$643$	313.239	+	180.849i	0.487153	+	0.281258i	0.723392	−	0.690437i	$-0.242582\pi$
$643$	313.239	+	180.849i	0.487153	+	0.281258i	−0.236240	+	0.971695i	$0.575915\pi$
$644$	−32.7771	−	85.5030i	−0.0508962	−	0.132769i
$645$		0			0
$646$	−251.682	+	435.927i	−0.389601	+	0.674809i
$647$	−549.009	−	316.970i	−0.848545	−	0.489908i	0.0116145	−	0.999933i	$-0.496303\pi$
$647$	−549.009	−	316.970i	−0.848545	−	0.489908i	−0.860160	+	0.510025i	$0.829636\pi$
$648$		0			0
$649$	862.924	−	498.210i	1.32962	−	0.767657i
$650$	−269.242	+	155.447i	−0.414219	+	0.239149i
$651$		0			0
$652$	−26.1459	+	45.2860i	−0.0401011	+	0.0694571i
$653$	−1031.45			−1.57955			−0.789775	−	0.613396i	$-0.789803\pi$
$653$	−1031.45			−1.57955			−0.789775	+	0.613396i	$0.789803\pi$
$654$		0			0
$655$	242.100			0.369618
$656$	−45.9880	+	26.5512i	−0.0701037	+	0.0404744i
$657$		0			0
$658$	−667.036	+	255.705i	−1.01373	+	0.388609i
$659$	−484.360	−	838.936i	−0.734993	−	1.27304i	−0.954727	−	0.297485i	$-0.903852\pi$
$659$	−484.360	−	838.936i	−0.734993	−	1.27304i	0.219734	−	0.975560i	$-0.429481\pi$
$660$		0			0
$661$	398.504	−	230.076i	0.602880	−	0.348073i	−0.167294	−	0.985907i	$-0.553503\pi$
$661$	398.504	−	230.076i	0.602880	−	0.348073i	0.770174	+	0.637834i	$0.220169\pi$
$662$	20.8055	+	36.0362i	0.0314282	+	0.0544353i
$663$		0			0
$664$	−967.661	+	558.680i	−1.45732	+	0.841385i
$665$	218.060	+	568.835i	0.327910	+	0.855391i
$666$		0			0
$667$	25.7175	+	44.5440i	0.0385570	+	0.0667826i
$668$			342.206i			0.512285i
$669$		0			0
$670$		−	842.045i		−	1.25678i
$671$	655.240	+	378.303i	0.976513	+	0.563790i
$672$		0			0
$673$	214.421	+	371.388i	0.318605	+	0.551840i	0.980197	−	0.198024i	$-0.0634524\pi$
$673$	214.421	+	371.388i	0.318605	+	0.551840i	−0.661592	+	0.749864i	$0.730119\pi$
$674$	659.404	+	1142.12i	0.978344	+	1.69454i
$675$		0			0
$676$	−391.295	+	677.743i	−0.578839	+	1.00258i
$677$	989.574	+	571.331i	1.46170	+	0.843916i	0.999090	−	0.0426437i	$-0.0135780\pi$
$677$	989.574	+	571.331i	1.46170	+	0.843916i	0.462615	+	0.886559i	$0.346911\pi$
$678$		0			0
$679$	159.180	−	61.0209i	0.234433	−	0.0898687i
$680$	86.3502	−	149.563i	0.126986	−	0.219946i
$681$		0			0
$682$		−	483.175i		−	0.708467i
$683$	−159.780	+	276.748i	−0.233939	+	0.405194i	−0.958964	−	0.283529i	$-0.908495\pi$
$683$	−159.780	+	276.748i	−0.233939	+	0.405194i	0.725025	+	0.688723i	$0.241828\pi$
$684$		0			0
$685$		−	47.8990i		−	0.0699255i
$686$	936.985	−	606.678i	1.36587	−	0.884371i
$687$		0			0
$688$	40.1919			0.0584184
$689$	449.463	−	259.498i	0.652342	−	0.376630i
$690$		0			0
$691$	−1069.32	−	617.370i	−1.54749	−	0.893444i	−0.998333	−	0.0577249i	$-0.981615\pi$
$691$	−1069.32	−	617.370i	−1.54749	−	0.893444i	−0.549157	−	0.835719i	$-0.685051\pi$
$692$			421.232i			0.608717i
$693$		0			0
$694$	1103.72			1.59037
$695$	−280.854	+	486.454i	−0.404107	+	0.699934i
$696$		0			0
$697$	148.935	+	257.963i	0.213680	+	0.370104i
$698$			1107.59i			1.58680i
$699$		0			0
$700$	222.530	+	580.495i	0.317900	+	0.829279i
$701$	632.317			0.902022			0.451011	−	0.892518i	$-0.351064\pi$
$701$	632.317			0.902022			0.451011	+	0.892518i	$0.351064\pi$
$702$		0			0
$703$	−864.911	−	499.357i	−1.23031	−	0.710322i
$704$	−1927.63			−2.73812
$705$		0			0
$706$	−824.324	−	475.924i	−1.16760	−	0.674113i
$707$	−69.8735	+	439.875i	−0.0988309	+	0.622172i
$708$		0			0
$709$	−577.728	+	1000.65i	−0.814849	+	1.41136i	0.0945866	+	0.995517i	$0.469847\pi$
$709$	−577.728	+	1000.65i	−0.814849	+	1.41136i	−0.909436	+	0.415844i	$0.863486\pi$
$710$	171.274	+	98.8852i	0.241231	+	0.139275i
$711$		0			0
$712$	−421.600	+	243.411i	−0.592134	+	0.341869i
$713$	13.5922	−	7.84747i	0.0190634	−	0.0110063i
$714$		0			0
$715$	225.942	−	391.344i	0.316003	−	0.547334i
$716$	−882.039			−1.23190
$717$		0			0
$718$	38.0707			0.0530233
$719$	−663.637	+	383.151i	−0.923001	+	0.532895i	−0.884591	−	0.466367i	$-0.845562\pi$
$719$	−663.637	+	383.151i	−0.923001	+	0.532895i	−0.0384095	+	0.999262i	$0.512229\pi$
$720$		0			0
$721$	143.109	−	900.914i	0.198486	−	1.24953i
$722$	481.945	+	834.754i	0.667514	+	1.15617i
$723$		0			0
$724$	599.405	−	346.066i	0.827907	−	0.477992i
$725$	−174.601	−	302.417i	−0.240829	−	0.417127i
$726$		0			0
$727$	906.479	−	523.356i	1.24688	−	0.719884i	0.276391	−	0.961045i	$-0.410862\pi$
$727$	906.479	−	523.356i	1.24688	−	0.719884i	0.970485	+	0.241161i	$0.0775282\pi$
$728$	−325.055	−	263.468i	−0.446505	−	0.361907i
$729$		0			0
$730$	697.094	+	1207.40i	0.954923	+	1.65397i
$731$		−	225.450i		−	0.308413i
$732$		0			0
$733$		−	1000.80i		−	1.36534i	−0.730726	−	0.682671i	$-0.760818\pi$
$733$		−	1000.80i		−	1.36534i	0.730726	−	0.682671i	$-0.239182\pi$
$734$	−1869.19	−	1079.18i	−2.54659	−	1.47027i
$735$		0			0
$736$	−29.9956	−	51.9539i	−0.0407549	−	0.0705895i
$737$	−715.516	−	1239.31i	−0.970850	−	1.68156i
$738$		0			0
$739$	−136.733	+	236.828i	−0.185024	+	0.320471i	−0.943585	−	0.331132i	$-0.892570\pi$
$739$	−136.733	+	236.828i	−0.185024	+	0.320471i	0.758561	+	0.651602i	$0.225903\pi$
$740$	754.891	+	435.837i	1.02012	+	0.588969i
$741$		0			0
$742$	−596.938	−	1557.18i	−0.804499	−	2.09863i
$743$	236.316	−	409.311i	0.318056	−	0.550889i	−0.662026	−	0.749481i	$-0.730303\pi$
$743$	236.316	−	409.311i	0.318056	−	0.550889i	0.980082	+	0.198591i	$0.0636367\pi$
$744$		0			0
$745$		−	230.793i		−	0.309789i
$746$	−142.652	+	247.080i	−0.191222	+	0.331206i
$747$		0			0
$748$		−	746.638i		−	0.998179i
$749$	−177.909	−	464.097i	−0.237529	−	0.619622i
$750$		0			0
$751$	446.482			0.594517			0.297258	−	0.954797i	$-0.403928\pi$
$751$	446.482			0.594517			0.297258	+	0.954797i	$0.403928\pi$
$752$	29.2114	−	16.8652i	0.0388449	−	0.0224271i
$753$		0			0
$754$	517.787	+	298.945i	0.686720	+	0.396478i
$755$			541.586i			0.717333i
$756$		0			0
$757$	−799.955			−1.05674			−0.528372	−	0.849013i	$-0.677197\pi$
$757$	−799.955			−1.05674			−0.528372	+	0.849013i	$0.677197\pi$
$758$	1056.63	−	1830.13i	1.39397	−	2.41442i
$759$		0			0
$760$	−366.888	−	635.468i	−0.482747	−	0.836143i
$761$		−	947.724i		−	1.24537i	−0.782474	−	0.622683i	$-0.786042\pi$
$761$		−	947.724i		−	1.24537i	0.782474	−	0.622683i	$-0.213958\pi$
$762$		0			0
$763$	−346.623	+	427.648i	−0.454290	+	0.560483i
$764$	1483.41			1.94164
$765$		0			0
$766$	−1309.99	−	756.321i	−1.71016	−	0.987364i
$767$	376.235			0.490528
$768$		0			0
$769$	1014.90	+	585.954i	1.31977	+	0.761968i	0.983691	−	0.179866i	$-0.0575665\pi$
$769$	1014.90	+	585.954i	1.31977	+	0.761968i	0.336077	+	0.941835i	$0.390900\pi$
$770$	−1128.03	−	914.305i	−1.46497	−	1.18741i
$771$		0			0
$772$	731.636	−	1267.23i	0.947715	−	1.64149i
$773$	18.1610	+	10.4853i	0.0234942	+	0.0135644i	0.511701	−	0.859164i	$-0.329016\pi$
$773$	18.1610	+	10.4853i	0.0234942	+	0.0135644i	−0.488207	+	0.872728i	$0.662349\pi$
$774$		0			0
$775$	−92.2800	+	53.2779i	−0.119071	+	0.0687456i
$776$	−177.826	+	102.668i	−0.229158	+	0.132304i
$777$		0			0
$778$	−248.420	+	430.276i	−0.319306	+	0.553054i
$779$	1265.60			1.62464
$780$		0			0
$781$	336.106			0.430353
$782$	33.7510	−	19.4861i	0.0431598	−	0.0249183i
$783$		0			0
$784$	−39.1999	+	35.2316i	−0.0499999	+	0.0449382i
$785$	277.547	+	480.726i	0.353563	+	0.612390i
$786$		0			0
$787$	−308.826	+	178.301i	−0.392410	+	0.226558i	−0.683204	−	0.730228i	$-0.739414\pi$
$787$	−308.826	+	178.301i	−0.392410	+	0.226558i	0.290794	+	0.956786i	$0.406081\pi$
$788$	−153.772	−	266.341i	−0.195142	−	0.337997i
$789$		0			0
$790$	−517.718	+	298.905i	−0.655339	+	0.378360i
$791$	141.378	−	174.425i	0.178733	−	0.220513i
$792$		0			0
$793$	142.842	+	247.410i	0.180129	+	0.311993i
$794$		−	1405.21i		−	1.76979i
$795$		0			0
$796$			482.403i			0.606034i
$797$	−437.476	−	252.577i	−0.548904	−	0.316910i	0.199776	−	0.979842i	$-0.435979\pi$
$797$	−437.476	−	252.577i	−0.548904	−	0.316910i	−0.748680	+	0.662932i	$0.769312\pi$
$798$		0			0
$799$	−94.6027	−	163.857i	−0.118401	−	0.205077i
$800$	203.645	+	352.724i	0.254557	+	0.440905i
$801$		0			0
$802$	129.746	−	224.727i	0.161779	−	0.280209i
$803$	2051.95	+	1184.69i	2.55535	+	1.47533i
$804$		0			0
$805$	7.39952	−	46.5823i	0.00919195	−	0.0578662i
$806$	91.2203	−	157.998i	0.113177	−	0.196028i
$807$		0			0
$808$		−	536.469i		−	0.663947i
$809$	−175.890	+	304.651i	−0.217417	+	0.376577i	−0.954018	−	0.299751i	$-0.903096\pi$
$809$	−175.890	+	304.651i	−0.217417	+	0.376577i	0.736601	+	0.676328i	$0.236430\pi$
$810$		0			0
$811$		−	390.065i		−	0.480968i	−0.970653	−	0.240484i	$-0.922694\pi$
$811$		−	390.065i		−	0.480968i	0.970653	−	0.240484i	$-0.0773062\pi$
$812$	752.825	−	928.801i	0.927124	−	1.14384i
$813$		0			0
$814$	2380.44			2.92438
$815$	−23.3261	+	13.4673i	−0.0286210	+	0.0165243i
$816$		0			0
$817$	−829.566	−	478.950i	−1.01538	−	0.586230i
$818$			20.9410i			0.0256003i
$819$		0			0
$820$	−1104.61			−1.34709
$821$	−95.8864	+	166.080i	−0.116792	+	0.202290i	−0.918495	−	0.395433i	$-0.870594\pi$
$821$	−95.8864	+	166.080i	−0.116792	+	0.202290i	0.801703	+	0.597723i	$0.203928\pi$
$822$		0			0
$823$	213.073	+	369.054i	0.258898	+	0.448425i	0.965947	−	0.258740i	$-0.0833072\pi$
$823$	213.073	+	369.054i	0.258898	+	0.448425i	−0.707049	+	0.707165i	$0.749974\pi$
$824$			1098.75i			1.33343i
$825$		0			0
$826$	189.662	−	1193.98i	0.229615	−	1.44550i
$827$	−153.677			−0.185825			−0.0929125	−	0.995674i	$-0.529618\pi$
$827$	−153.677			−0.185825			−0.0929125	+	0.995674i	$0.529618\pi$
$828$		0			0
$829$	698.756	+	403.427i	0.842890	+	0.486643i	0.858246	−	0.513239i	$-0.171555\pi$
$829$	698.756	+	403.427i	0.842890	+	0.486643i	−0.0153554	+	0.999882i	$0.504888\pi$
$830$	−1464.11			−1.76399
$831$		0			0
$832$	−630.337	−	363.925i	−0.757616	−	0.437410i
$833$	197.626	+	219.886i	0.237246	+	0.263969i
$834$		0			0
$835$	−88.1325	+	152.650i	−0.105548	+	0.182814i
$836$	−2747.33	−	1586.17i	−3.28628	−	1.89733i
$837$		0			0
$838$	1130.99	−	652.976i	1.34963	−	0.779208i
$839$	5.26538	−	3.03997i	0.00627578	−	0.00362333i	−0.496859	−	0.867831i	$-0.665513\pi$
$839$	5.26538	−	3.03997i	0.00627578	−	0.00362333i	0.503135	+	0.864208i	$0.332180\pi$
$840$		0			0
$841$	84.7206	−	146.740i	0.100738	−	0.174483i
$842$	−305.381			−0.362685
$843$		0			0
$844$	−691.844			−0.819720
$845$	−349.094	+	201.550i	−0.413130	+	0.238520i
$846$		0			0
$847$	−1600.62	−	254.256i	−1.88976	−	0.300185i
$848$	39.3715	+	68.1934i	0.0464286	+	0.0804167i
$849$		0			0
$850$	−229.141	+	132.295i	−0.269578	+	0.155641i
$851$	38.6619	+	66.9644i	0.0454312	+	0.0786891i
$852$		0			0
$853$	−1300.52	+	750.858i	−1.52465	+	0.880256i	−0.525074	+	0.851056i	$0.675963\pi$
$853$	−1300.52	+	750.858i	−1.52465	+	0.880256i	−0.999574	+	0.0291996i	$0.990704\pi$
$854$	857.163	−	328.589i	1.00370	−	0.384765i
$855$		0			0
$856$	299.334	+	518.461i	0.349689	+	0.605679i
$857$			843.652i			0.984425i	0.870475	+	0.492213i	$0.163812\pi$
$857$			843.652i			0.984425i	−0.870475	+	0.492213i	$0.836188\pi$
$858$		0			0
$859$			1478.11i			1.72073i	0.509675	+	0.860367i	$0.329766\pi$
$859$			1478.11i			1.72073i	−0.509675	+	0.860367i	$0.670234\pi$
$860$	724.043	+	418.026i	0.841910	+	0.486077i
$861$		0			0
$862$	1168.10	+	2023.22i	1.35511	+	2.34712i
$863$	−722.464	−	1251.34i	−0.837154	−	1.44999i	−0.892265	−	0.451512i	$-0.850885\pi$
$863$	−722.464	−	1251.34i	−0.837154	−	1.44999i	0.0551113	−	0.998480i	$-0.482449\pi$
$864$		0			0
$865$	−108.485	+	187.901i	−0.125416	+	0.217227i
$866$	−1357.87	−	783.968i	−1.56798	−	0.905275i
$867$		0			0
$868$	−283.416	−	229.718i	−0.326516	−	0.264652i
$869$	−507.980	+	879.848i	−0.584557	+	1.01248i
$870$		0			0
$871$		−	540.340i		−	0.620367i
$872$	331.526	−	574.220i	0.380190	−	0.658509i
$873$		0			0
$874$		−	165.587i		−	0.189458i
$875$	−143.439	+	902.994i	−0.163930	+	1.03199i
$876$		0			0
$877$	−1400.86			−1.59734			−0.798668	−	0.601772i	$-0.794462\pi$
$877$	−1400.86			−1.59734			−0.798668	+	0.601772i	$0.794462\pi$
$878$	1630.14	−	941.164i	1.85666	−	1.07194i
$879$		0			0
$880$	59.3754	+	34.2804i	0.0674720	+	0.0389550i
$881$			1699.22i			1.92874i	0.264560	+	0.964369i	$0.414773\pi$
$881$			1699.22i			1.92874i	−0.264560	+	0.964369i	$0.585227\pi$
$882$		0			0
$883$	618.373			0.700309			0.350154	−	0.936692i	$-0.386129\pi$
$883$	618.373			0.700309			0.350154	+	0.936692i	$0.386129\pi$
$884$	140.960	−	244.151i	0.159458	−	0.276189i
$885$		0			0
$886$	207.397	+	359.222i	0.234082	+	0.405442i
$887$			234.087i			0.263909i	0.991256	+	0.131955i	$0.0421253\pi$
$887$			234.087i			0.263909i	−0.991256	+	0.131955i	$0.957875\pi$
$888$		0			0
$889$	−446.055	−	70.8550i	−0.501749	−	0.0797019i
$890$	−637.896			−0.716737
$891$		0			0
$892$	−166.981	−	96.4065i	−0.187198	−	0.108079i
$893$	−803.902			−0.900226
$894$		0			0
$895$	−393.456	−	227.162i	−0.439616	−	0.253812i
$896$	−939.773	+	1159.45i	−1.04885	+	1.29403i
$897$		0			0
$898$	1251.93	−	2168.41i	1.39414	−	2.41471i
$899$	177.466	+	102.460i	0.197404	+	0.113971i
$900$		0			0
$901$	382.520	−	220.848i	0.424551	−	0.245115i
$902$	−2612.43	+	1508.28i	−2.89626	+	1.67216i
$903$		0			0
$904$	−135.220	+	234.208i	−0.149579	+	0.259079i
$905$	356.506			0.393930
$906$		0			0
$907$	376.511			0.415117			0.207559	−	0.978223i	$-0.433448\pi$
$907$	376.511			0.415117			0.207559	+	0.978223i	$0.433448\pi$
$908$	−1326.52	+	765.867i	−1.46093	+	0.843466i
$909$		0			0
$910$	−196.251	−	511.943i	−0.215660	−	0.562574i
$911$	336.249	+	582.401i	0.369099	+	0.639298i	0.989425	−	0.145046i	$-0.0463330\pi$
$911$	336.249	+	582.401i	0.369099	+	0.639298i	−0.620326	+	0.784344i	$0.713000\pi$
$912$		0			0
$913$	−2154.85	+	1244.11i	−2.36019	+	1.36266i
$914$	197.032	+	341.269i	0.215571	+	0.373380i
$915$		0			0
$916$	1243.65	−	718.019i	1.35769	−	0.783864i
$917$	78.3153	−	493.019i	0.0854038	−	0.537644i
$918$		0			0
$919$	438.864	+	760.135i	0.477545	+	0.827132i	0.999669	−	0.0257374i	$-0.00819336\pi$
$919$	438.864	+	760.135i	0.477545	+	0.827132i	−0.522124	+	0.852870i	$0.674860\pi$
$920$			56.8115i			0.0617516i
$921$		0			0
$922$			651.420i			0.706529i
$923$	109.907	+	63.4546i	0.119075	+	0.0687482i
$924$		0			0
$925$	−262.483	−	454.634i	−0.283765	−	0.491496i
$926$	98.8162	+	171.155i	0.106713	+	0.184832i
$927$		0			0
$928$	391.636	−	678.334i	0.422022	−	0.730963i
$929$	−771.822	−	445.612i	−0.830809	−	0.479668i	0.0233204	−	0.999728i	$-0.492576\pi$
$929$	−771.822	−	445.612i	−0.830809	−	0.479668i	−0.854130	+	0.520060i	$0.825910\pi$
$930$		0			0
$931$	1228.93	−	260.055i	1.32001	−	0.279329i
$932$	−1.22507	+	2.12188i	−0.00131445	+	0.00227670i
$933$		0			0
$934$			214.077i			0.229205i
$935$	192.291	−	333.057i	0.205658	−	0.356211i
$936$		0			0
$937$			869.077i			0.927510i	0.885963	+	0.463755i	$0.153498\pi$
$937$			869.077i			0.927510i	−0.885963	+	0.463755i	$0.846502\pi$
$938$	−1714.77	−	272.388i	−1.82811	−	0.290392i
$939$		0			0
$940$	701.643			0.746429
$941$	−1295.61	+	748.022i	−1.37685	+	0.794922i	−0.991779	−	0.127966i	$-0.959155\pi$
$941$	−1295.61	+	748.022i	−1.37685	+	0.794922i	−0.385067	+	0.922888i	$0.625822\pi$
$942$		0			0
$943$	−84.8593	−	48.9935i	−0.0899886	−	0.0519550i
$944$			57.0831i			0.0604694i
$945$		0			0
$946$	2283.17			2.41350
$947$	−51.3155	+	88.8810i	−0.0541874	+	0.0938553i	−0.891847	−	0.452338i	$-0.850590\pi$
$947$	−51.3155	+	88.8810i	−0.0541874	+	0.0938553i	0.837659	+	0.546193i	$0.183924\pi$
$948$		0			0
$949$	447.324	+	774.789i	0.471364	+	0.816426i
$950$			1124.20i			1.18337i
$951$		0			0
$952$	−276.642	−	224.227i	−0.290590	−	0.235533i
$953$	−483.292			−0.507127			−0.253564	−	0.967319i	$-0.581603\pi$
$953$	−483.292			−0.507127			−0.253564	+	0.967319i	$0.581603\pi$
$954$		0			0
$955$	661.714	+	382.041i	0.692894	+	0.400043i
$956$	2839.43			2.97011
$957$		0			0
$958$	−1497.02	−	864.307i	−1.56266	−	0.902200i
$959$	−97.5429	−	15.4945i	−0.101713	−	0.0161570i
$960$		0			0
$961$	−449.235	+	778.098i	−0.467466	+	0.809676i
$962$	778.406	+	449.413i	0.809154	+	0.467165i
$963$		0			0
$964$	−1606.58	+	927.558i	−1.66657	+	0.962198i
$965$	652.730	−	376.854i	0.676404	−	0.390522i
$966$		0			0
$967$	33.8027	−	58.5480i	0.0349562	−	0.0605460i	−0.848018	−	0.529967i	$-0.822204\pi$
$967$	33.8027	−	58.5480i	0.0349562	−	0.0605460i	0.882974	+	0.469421i	$0.155537\pi$
$968$	1952.11			2.01664
$969$		0			0
$970$	−269.058			−0.277379
$971$	1493.78	−	862.435i	1.53840	−	0.888193i	0.539462	−	0.842010i	$-0.318628\pi$
$971$	1493.78	−	862.435i	1.53840	−	0.888193i	0.998933	−	0.0461830i	$-0.0147057\pi$
$972$		0			0
$973$	899.778	+	729.300i	0.924746	+	0.749538i
$974$	1427.83	+	2473.07i	1.46594	+	2.53909i
$975$		0			0
$976$	−37.5376	+	21.6723i	−0.0384606	+	0.0222052i
$977$	124.443	+	215.542i	0.127373	+	0.220616i	0.922658	−	0.385619i	$-0.126012\pi$
$977$	124.443	+	215.542i	0.127373	+	0.220616i	−0.795285	+	0.606236i	$0.792679\pi$
$978$		0			0
$979$	−938.847	+	542.043i	−0.958985	+	0.553670i
$980$	−1072.61	+	226.975i	−1.09450	+	0.231607i
$981$		0			0
$982$	364.752	+	631.768i	0.371437	+	0.643349i
$983$		−	1687.42i		−	1.71660i	−0.513150	−	0.858299i	$-0.671522\pi$
$983$		−	1687.42i		−	1.71660i	0.513150	−	0.858299i	$-0.328478\pi$
$984$		0			0
$985$		−	158.411i		−	0.160824i
$986$	440.668	+	254.420i	0.446925	+	0.258032i
$987$		0			0
$988$	−598.918	−	1037.36i	−0.606192	−	1.04996i
$989$	37.0820	+	64.2279i	0.0374944	+	0.0649423i
$990$		0			0
$991$	−87.9010	+	152.249i	−0.0886993	+	0.153632i	−0.906962	−	0.421213i	$-0.861604\pi$
$991$	−87.9010	+	152.249i	−0.0886993	+	0.153632i	0.818262	+	0.574845i	$0.194938\pi$
$992$	−206.988	−	119.504i	−0.208657	−	0.120468i
$993$		0			0
$994$	256.777	−	316.800i	0.258327	−	0.318712i
$995$	−124.239	+	215.188i	−0.124863	+	0.216270i
$996$		0			0
$997$		−	1604.74i		−	1.60957i	−0.593566	−	0.804785i	$-0.702281\pi$
$997$		−	1604.74i		−	1.60957i	0.593566	−	0.804785i	$-0.297719\pi$
$998$	1308.70	−	2266.74i	1.31132	−	2.27128i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.3.k.a.10.2		28
3.2	odd	2		63.3.k.a.31.13	✓	28
7.5	odd	6		189.3.t.a.145.13		28
9.2	odd	6		63.3.t.a.52.2	yes	28
9.7	even	3		189.3.t.a.73.13		28
21.2	odd	6		441.3.t.a.166.2		28
21.5	even	6		63.3.t.a.40.2	yes	28
21.11	odd	6		441.3.l.a.391.13		28
21.17	even	6		441.3.l.b.391.13		28
21.20	even	2		441.3.k.b.31.13		28
63.2	odd	6		441.3.k.b.313.13		28
63.11	odd	6		441.3.l.b.97.13		28
63.20	even	6		441.3.t.a.178.2		28
63.38	even	6		441.3.l.a.97.13		28
63.47	even	6		63.3.k.a.61.13	yes	28
63.61	odd	6	inner	189.3.k.a.19.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.k.a.31.13	✓	28	3.2	odd	2
63.3.k.a.61.13	yes	28	63.47	even	6
63.3.t.a.40.2	yes	28	21.5	even	6
63.3.t.a.52.2	yes	28	9.2	odd	6
189.3.k.a.10.2		28	1.1	even	1	trivial
189.3.k.a.19.2		28	63.61	odd	6	inner
189.3.t.a.73.13		28	9.7	even	3
189.3.t.a.145.13		28	7.5	odd	6
441.3.k.b.31.13		28	21.20	even	2
441.3.k.b.313.13		28	63.2	odd	6
441.3.l.a.97.13		28	63.38	even	6
441.3.l.a.391.13		28	21.11	odd	6
441.3.l.b.97.13		28	63.11	odd	6
441.3.l.b.391.13		28	21.17	even	6
441.3.t.a.166.2		28	21.2	odd	6
441.3.t.a.178.2		28	63.20	even	6

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	189.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.62718 + 2.81835i) q^{2} +(-3.29541 - 5.70782i) q^{4} -3.39483i q^{5} +(-6.91332 - 1.09817i) q^{7} +8.43145 q^{8} +O(q^{10})\)	\(q+(-1.62718 + 2.81835i) q^{2} +(-3.29541 - 5.70782i) q^{4} -3.39483i q^{5} +(-6.91332 - 1.09817i) q^{7} +8.43145 q^{8} +(9.56782 + 5.52398i) q^{10} +18.7757 q^{11} +(6.13966 + 3.54474i) q^{13} +(14.3442 - 17.6973i) q^{14} +(-0.537814 + 0.931521i) q^{16} +(5.22522 + 3.01678i) q^{17} +(22.2011 - 12.8178i) q^{19} +(-19.3770 + 11.1873i) q^{20} +(-30.5514 + 52.9166i) q^{22} -1.98480 q^{23} +13.4752 q^{25} +(-19.9806 + 11.5358i) q^{26} +(16.5141 + 43.0789i) q^{28} +(-12.9572 - 22.4426i) q^{29} +(-6.84815 + 3.95378i) q^{31} +(15.1127 + 26.1759i) q^{32} +(-17.0047 + 9.81768i) q^{34} +(-3.72810 + 23.4695i) q^{35} +(-19.4790 - 33.7386i) q^{37} +83.4274i q^{38} -28.6233i q^{40} +(42.7546 + 24.6844i) q^{41} +(-18.6830 - 32.3599i) q^{43} +(-61.8737 - 107.168i) q^{44} +(3.22962 - 5.59387i) q^{46} +(-27.1575 - 15.6794i) q^{47} +(46.5880 + 15.1840i) q^{49} +(-21.9265 + 37.9778i) q^{50} -46.7254i q^{52} +(36.6033 - 63.3987i) q^{53} -63.7403i q^{55} +(-58.2893 - 9.25916i) q^{56} +84.3348 q^{58} +(45.9596 - 26.5348i) q^{59} +(34.8983 + 20.1485i) q^{61} -25.7340i q^{62} -102.666 q^{64} +(12.0338 - 20.8431i) q^{65} +(-38.1086 - 66.0061i) q^{67} -39.7661i q^{68} +(-60.0791 - 48.6962i) q^{70} +17.9011 q^{71} +(109.287 + 63.0970i) q^{73} +126.783 q^{74} +(-146.323 - 84.4799i) q^{76} +(-129.803 - 20.6189i) q^{77} +(-27.0552 + 46.8610i) q^{79} +(3.16235 + 1.82578i) q^{80} +(-139.139 + 80.3317i) q^{82} +(-114.768 + 66.2614i) q^{83} +(10.2415 - 17.7387i) q^{85} +121.602 q^{86} +158.306 q^{88} +(-50.0032 + 28.8694i) q^{89} +(-38.5527 - 31.2483i) q^{91} +(6.54073 + 11.3289i) q^{92} +(88.3801 - 51.0263i) q^{94} +(-43.5142 - 75.3689i) q^{95} +(-21.0909 + 12.1768i) q^{97} +(-118.601 + 106.595i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8}+O(q^{10}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8	\( 28 q - q^{2} - 23 q^{4} + 16 q^{8} - 6 q^{10} + 14 q^{11} + 15 q^{13} + 11 q^{14} - 27 q^{16} + 33 q^{17} - 6 q^{19} - 108 q^{20} - 10 q^{22} + 68 q^{23} - 62 q^{25} - 54 q^{26} - 16 q^{28} - 70 q^{29} + 45 q^{31} - 153 q^{32} + 12 q^{34} - 18 q^{35} + 9 q^{37} + 234 q^{41} + 30 q^{43} - 51 q^{44} - 22 q^{46} + 111 q^{47} + 34 q^{49} - 241 q^{50} - 148 q^{53} + 412 q^{56} - 34 q^{58} - 42 q^{59} + 120 q^{61} - 48 q^{64} - 114 q^{65} - 34 q^{67} + 264 q^{70} + 350 q^{71} - 6 q^{73} + 718 q^{74} + 72 q^{76} + 32 q^{77} - 82 q^{79} + 609 q^{80} - 18 q^{82} - 738 q^{83} + 3 q^{85} + 34 q^{86} - 50 q^{88} - 21 q^{89} + 39 q^{91} - 288 q^{92} - 3 q^{94} - 507 q^{95} - 57 q^{97} - 811 q^{98}+O(q^{100}) \) 28 * q - q^2 - 23 * q^4 + 16 * q^8 - 6 * q^10 + 14 * q^11 + 15 * q^13 + 11 * q^14 - 27 * q^16 + 33 * q^17 - 6 * q^19 - 108 * q^20 - 10 * q^22 + 68 * q^23 - 62 * q^25 - 54 * q^26 - 16 * q^28 - 70 * q^29 + 45 * q^31 - 153 * q^32 + 12 * q^34 - 18 * q^35 + 9 * q^37 + 234 * q^41 + 30 * q^43 - 51 * q^44 - 22 * q^46 + 111 * q^47 + 34 * q^49 - 241 * q^50 - 148 * q^53 + 412 * q^56 - 34 * q^58 - 42 * q^59 + 120 * q^61 - 48 * q^64 - 114 * q^65 - 34 * q^67 + 264 * q^70 + 350 * q^71 - 6 * q^73 + 718 * q^74 + 72 * q^76 + 32 * q^77 - 82 * q^79 + 609 * q^80 - 18 * q^82 - 738 * q^83 + 3 * q^85 + 34 * q^86 - 50 * q^88 - 21 * q^89 + 39 * q^91 - 288 * q^92 - 3 * q^94 - 507 * q^95 - 57 * q^97 - 811 * q^98

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