LMFDB - Embedded newform 189.2.h.b.37.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(37,189)]

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, 2]))

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

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

chi := DirichletCharacter("189.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.h (of order $3$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.4
Root			$0.920620 - 1.59456i$ of defining polynomial
Character	$\chi$	$=$	189.37
Dual form			189.2.h.b.46.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.84124 q^{2} +1.39017 q^{4} +(0.667377 + 1.15593i) q^{5} +(1.90267 - 1.83844i) q^{7} -1.12285 q^{8} +O(q^{10})$	\(q+1.84124 q^{2} +1.39017 q^{4} +(0.667377 + 1.15593i) q^{5} +(1.90267 - 1.83844i) q^{7} -1.12285 q^{8} +(1.22880 + 2.12835i) q^{10} +(0.756508 - 1.31031i) q^{11} +(-2.58800 + 4.48254i) q^{13} +(3.50326 - 3.38501i) q^{14} -4.84777 q^{16} +(-0.774463 - 1.34141i) q^{17} +(-1.25211 + 2.16872i) q^{19} +(0.927765 + 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} +(-3.68039 - 6.37463i) q^{23} +(1.60922 - 2.78725i) q^{25} +(-4.76513 + 8.25344i) q^{26} +(2.64502 - 2.55574i) q^{28} +(0.0309713 + 0.0536439i) q^{29} -3.84777 q^{31} -6.68021 q^{32} +(-1.42597 - 2.46986i) q^{34} +(3.39490 + 0.972416i) q^{35} +(-0.281608 + 0.487760i) q^{37} +(-2.30543 + 3.99313i) q^{38} +(-0.749363 - 1.29794i) q^{40} +(-4.51188 + 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +(1.05167 - 1.82155i) q^{44} +(-6.77649 - 11.7372i) q^{46} +9.51851 q^{47} +(0.240269 - 6.99588i) q^{49} +(2.96296 - 5.13199i) q^{50} +(-3.59775 + 6.23148i) q^{52} +(-0.755374 - 1.30835i) q^{53} +2.01950 q^{55} +(-2.13641 + 2.06429i) q^{56} +(0.0570257 + 0.0987714i) q^{58} +8.44331 q^{59} +3.23917 q^{61} -7.08467 q^{62} -2.60434 q^{64} -6.90868 q^{65} +6.93339 q^{67} +(-1.07663 - 1.86478i) q^{68} +(6.25084 + 1.79045i) q^{70} +12.3304 q^{71} +(-1.37936 - 2.38912i) q^{73} +(-0.518508 + 0.898083i) q^{74} +(-1.74064 + 3.01488i) q^{76} +(-0.969547 - 3.88388i) q^{77} -5.91938 q^{79} +(-3.23529 - 5.60368i) q^{80} +(-8.30746 + 14.3889i) q^{82} +(-2.80111 - 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +(9.39010 + 16.2641i) q^{86} +(-0.849444 + 1.47128i) q^{88} +(-0.703287 + 1.21813i) q^{89} +(3.31680 + 13.2867i) q^{91} +(-5.11636 - 8.86180i) q^{92} +17.5259 q^{94} -3.34251 q^{95} +(-6.09713 - 10.5605i) q^{97} +(0.442393 - 12.8811i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	$ 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) $ 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.84124			1.30195			0.650977	−	0.759098i	$-0.274359\pi$
$2$	1.84124			1.30195			0.650977	+	0.759098i	$0.274359\pi$
$3$		0			0
$3$		0			0
$4$	1.39017			0.695084
$5$	0.667377	+	1.15593i	0.298460	+	0.516948i	0.975784	−	0.218737i	$-0.0701937\pi$
$5$	0.667377	+	1.15593i	0.298460	+	0.516948i	−0.677324	+	0.735685i	$0.736860\pi$
$6$		0			0
$7$	1.90267	−	1.83844i	0.719140	−	0.694865i
$7$	1.90267	−	1.83844i	0.719140	−	0.694865i
$8$	−1.12285			−0.396987
$9$		0			0
$10$	1.22880	+	2.12835i	0.388581	+	0.673042i
$11$	0.756508	−	1.31031i	0.228096	−	0.395073i	−0.729148	−	0.684356i	$-0.760083\pi$
$11$	0.756508	−	1.31031i	0.228096	−	0.395073i	0.957244	+	0.289283i	$0.0934167\pi$
$12$		0			0
$13$	−2.58800	+	4.48254i	−0.717781	+	1.24323i	0.244096	+	0.969751i	$0.421509\pi$
$13$	−2.58800	+	4.48254i	−0.717781	+	1.24323i	−0.961877	+	0.273482i	$0.911824\pi$
$14$	3.50326	−	3.38501i	0.936287	−	0.904683i
$15$		0			0
$16$	−4.84777			−1.21194
$17$	−0.774463	−	1.34141i	−0.187835	−	0.325340i	0.756693	−	0.653770i	$-0.226814\pi$
$17$	−0.774463	−	1.34141i	−0.187835	−	0.325340i	−0.944528	+	0.328430i	$0.893480\pi$
$18$		0			0
$19$	−1.25211	+	2.16872i	−0.287254	+	0.497538i	−0.973153	−	0.230158i	$-0.926076\pi$
$19$	−1.25211	+	2.16872i	−0.287254	+	0.497538i	0.685900	+	0.727696i	$0.259409\pi$
$20$	0.927765	+	1.60694i	0.207455	+	0.359322i
$21$		0			0
$22$	1.39291	−	2.41260i	0.296970	−	0.514367i
$23$	−3.68039	−	6.37463i	−0.767415	−	1.32920i	−0.938960	−	0.344025i	$-0.888209\pi$
$23$	−3.68039	−	6.37463i	−0.767415	−	1.32920i	0.171545	−	0.985176i	$-0.445124\pi$
$24$		0			0
$25$	1.60922	−	2.78725i	0.321843	−	0.557449i
$26$	−4.76513	+	8.25344i	−0.934518	+	1.61863i
$27$		0			0
$28$	2.64502	−	2.55574i	0.499862	−	0.482990i
$29$	0.0309713	+	0.0536439i	0.00575123	+	0.00996143i	0.868887	−	0.495011i	$-0.164836\pi$
$29$	0.0309713	+	0.0536439i	0.00575123	+	0.00996143i	−0.863135	+	0.504972i	$0.831503\pi$
$30$		0			0
$31$	−3.84777			−0.691080			−0.345540	−	0.938404i	$-0.612304\pi$
$31$	−3.84777			−0.691080			−0.345540	+	0.938404i	$0.612304\pi$
$32$	−6.68021			−1.18091
$33$		0			0
$34$	−1.42597	−	2.46986i	−0.244552	−	0.423577i
$35$	3.39490	+	0.972416i	0.573844	+	0.164368i
$36$		0			0
$37$	−0.281608	+	0.487760i	−0.0462961	+	0.0801872i	−0.888245	−	0.459370i	$-0.848075\pi$
$37$	−0.281608	+	0.487760i	−0.0462961	+	0.0801872i	0.841949	+	0.539557i	$0.181408\pi$
$38$	−2.30543	+	3.99313i	−0.373991	+	0.647771i
$39$		0			0
$40$	−0.749363	−	1.29794i	−0.118485	−	0.205222i
$41$	−4.51188	+	7.81481i	−0.704638	+	1.22047i	0.262185	+	0.965018i	$0.415557\pi$
$41$	−4.51188	+	7.81481i	−0.704638	+	1.22047i	−0.966822	+	0.255450i	$0.917776\pi$
$42$		0			0
$43$	5.09988	+	8.83325i	0.777724	+	1.34706i	0.933251	+	0.359226i	$0.116959\pi$
$43$	5.09988	+	8.83325i	0.777724	+	1.34706i	−0.155526	+	0.987832i	$0.549707\pi$
$44$	1.05167	−	1.82155i	0.158546	−	0.274609i
$45$		0			0
$46$	−6.77649	−	11.7372i	−0.999139	−	1.73056i
$47$	9.51851			1.38842			0.694209	−	0.719774i	$-0.255755\pi$
$47$	9.51851			1.38842			0.694209	+	0.719774i	$0.255755\pi$
$48$		0			0
$49$	0.240269	−	6.99588i	0.0343242	−	0.999411i
$50$	2.96296	−	5.13199i	0.419025	−	0.725773i
$51$		0			0
$52$	−3.59775	+	6.23148i	−0.498918	+	0.864151i
$53$	−0.755374	−	1.30835i	−0.103759	−	0.179715i	0.809472	−	0.587159i	$-0.199754\pi$
$53$	−0.755374	−	1.30835i	−0.103759	−	0.179715i	−0.913230	+	0.407444i	$0.866420\pi$
$54$		0			0
$55$	2.01950			0.272310
$56$	−2.13641	+	2.06429i	−0.285489	+	0.275853i
$57$		0			0
$58$	0.0570257	+	0.0987714i	0.00748784	+	0.0129693i
$59$	8.44331			1.09923			0.549613	−	0.835419i	$-0.314775\pi$
$59$	8.44331			1.09923			0.549613	+	0.835419i	$0.314775\pi$
$60$		0			0
$61$	3.23917			0.414733			0.207367	−	0.978263i	$-0.433511\pi$
$61$	3.23917			0.414733			0.207367	+	0.978263i	$0.433511\pi$
$62$	−7.08467			−0.899754
$63$		0			0
$64$	−2.60434			−0.325543
$65$	−6.90868			−0.856916
$66$		0			0
$67$	6.93339			0.847049			0.423524	−	0.905885i	$-0.360793\pi$
$67$	6.93339			0.847049			0.423524	+	0.905885i	$0.360793\pi$
$68$	−1.07663	−	1.86478i	−0.130561	−	0.226138i
$69$		0			0
$70$	6.25084	+	1.79045i	0.747118	+	0.214000i
$71$	12.3304			1.46335			0.731673	−	0.681656i	$-0.238740\pi$
$71$	12.3304			1.46335			0.731673	+	0.681656i	$0.238740\pi$
$72$		0			0
$73$	−1.37936	−	2.38912i	−0.161442	−	0.279625i	0.773944	−	0.633254i	$-0.218281\pi$
$73$	−1.37936	−	2.38912i	−0.161442	−	0.279625i	−0.935386	+	0.353629i	$0.884948\pi$
$74$	−0.518508	+	0.898083i	−0.0602754	+	0.104400i
$75$		0			0
$76$	−1.74064	+	3.01488i	−0.199665	+	0.345830i
$77$	−0.969547	−	3.88388i	−0.110490	−	0.442609i
$78$		0			0
$79$	−5.91938			−0.665982			−0.332991	−	0.942930i	$-0.608058\pi$
$79$	−5.91938			−0.665982			−0.332991	+	0.942930i	$0.608058\pi$
$80$	−3.23529	−	5.60368i	−0.361716	−	0.626511i
$81$		0			0
$82$	−8.30746	+	14.3889i	−0.917406	+	1.58899i
$83$	−2.80111	−	4.85167i	−0.307462	−	0.532540i	0.670344	−	0.742050i	$-0.266146\pi$
$83$	−2.80111	−	4.85167i	−0.307462	−	0.532540i	−0.977806	+	0.209510i	$0.932813\pi$
$84$		0			0
$85$	1.03372	−	1.79045i	0.112122	−	0.194202i
$86$	9.39010	+	16.2641i	1.01256	+	1.75381i
$87$		0			0
$88$	−0.849444	+	1.47128i	−0.0905511	+	0.156839i
$89$	−0.703287	+	1.21813i	−0.0745483	+	0.129121i	−0.900890	−	0.434048i	$-0.857085\pi$
$89$	−0.703287	+	1.21813i	−0.0745483	+	0.129121i	0.826341	+	0.563169i	$0.190418\pi$
$90$		0			0
$91$	3.31680	+	13.2867i	0.347695	+	1.39282i
$92$	−5.11636	−	8.86180i	−0.533418	−	0.923906i
$93$		0			0
$94$	17.5259			1.80765
$95$	−3.34251			−0.342935
$96$		0			0
$97$	−6.09713	−	10.5605i	−0.619070	−	1.07226i	−0.989656	−	0.143462i	$-0.954176\pi$
$97$	−6.09713	−	10.5605i	−0.619070	−	1.07226i	0.370586	−	0.928798i	$-0.379157\pi$
$98$	0.442393	−	12.8811i	0.0446885	−	1.30119i
$99$		0			0
$100$	2.23708	−	3.87474i	0.223708	−	0.387474i
$101$	0.559336	−	0.968798i	0.0556560	−	0.0963990i	−0.836855	−	0.547425i	$-0.815608\pi$
$101$	0.559336	−	0.968798i	0.0556560	−	0.0963990i	0.892511	+	0.451025i	$0.148942\pi$
$102$		0			0
$103$	−0.965224	−	1.67182i	−0.0951063	−	0.164729i	0.814547	−	0.580098i	$-0.196986\pi$
$103$	−0.965224	−	1.67182i	−0.0951063	−	0.164729i	−0.909653	+	0.415369i	$0.863652\pi$
$104$	2.90593	−	5.03322i	0.284950	−	0.493548i
$105$		0			0
$106$	−1.39082	−	2.40898i	−0.135089	−	0.233981i
$107$	−2.88969	+	5.00509i	−0.279357	+	0.483860i	−0.971225	−	0.238163i	$-0.923455\pi$
$107$	−2.88969	+	5.00509i	−0.279357	+	0.483860i	0.691868	+	0.722024i	$0.256788\pi$
$108$		0			0
$109$	−4.12106	−	7.13788i	−0.394726	−	0.683685i	0.598340	−	0.801242i	$-0.295827\pi$
$109$	−4.12106	−	7.13788i	−0.394726	−	0.683685i	−0.993066	+	0.117557i	$0.962494\pi$
$110$	3.71839			0.354535
$111$		0			0
$112$	−9.22368	+	8.91234i	−0.871556	+	0.842137i
$113$	−7.25105	+	12.5592i	−0.682121	+	1.18147i	0.292211	+	0.956354i	$0.405609\pi$
$113$	−7.25105	+	12.5592i	−0.682121	+	1.18147i	−0.974332	+	0.225115i	$0.927724\pi$
$114$		0			0
$115$	4.91242	−	8.50856i	0.458085	−	0.793427i
$116$	0.0430553	+	0.0745740i	0.00399759	+	0.00692403i
$117$		0			0
$118$	15.5462			1.43114
$119$	−3.93965	−	1.12845i	−0.361147	−	0.103445i
$120$		0			0
$121$	4.35539	+	7.54376i	0.395945	+	0.685796i
$122$	5.96409			0.539963
$123$		0			0
$124$	−5.34904			−0.480358
$125$	10.9696			0.981149
$126$		0			0
$127$	8.50004			0.754257			0.377128	−	0.926161i	$-0.376912\pi$
$127$	8.50004			0.754257			0.377128	+	0.926161i	$0.376912\pi$
$128$	8.56521			0.757065
$129$		0			0
$130$	−12.7205			−1.11566
$131$	−1.00673	−	1.74371i	−0.0879585	−	0.152349i	0.818690	−	0.574236i	$-0.194701\pi$
$131$	−1.00673	−	1.74371i	−0.0879585	−	0.152349i	−0.906648	+	0.421888i	$0.861368\pi$
$132$		0			0
$133$	1.60471	+	6.42827i	0.139146	+	0.557402i
$134$	12.7660			1.10282
$135$		0			0
$136$	0.869605	+	1.50620i	0.0745680	+	0.129156i
$137$	1.10870	−	1.92032i	0.0947225	−	0.164064i	−0.814770	−	0.579784i	$-0.803137\pi$
$137$	1.10870	−	1.92032i	0.0947225	−	0.164064i	0.909493	+	0.415720i	$0.136470\pi$
$138$		0			0
$139$	0.377669	−	0.654143i	0.0320335	−	0.0554836i	−0.849564	−	0.527485i	$-0.823135\pi$
$139$	0.377669	−	0.654143i	0.0320335	−	0.0554836i	0.881598	+	0.472002i	$0.156468\pi$
$140$	4.71948	+	1.35182i	0.398869	+	0.114250i
$141$		0			0
$142$	22.7032			1.90521
$143$	3.91568	+	6.78216i	0.327446	+	0.567153i
$144$		0			0
$145$	−0.0413391	+	0.0716014i	−0.00343303	+	0.00594618i
$146$	−2.53973	−	4.39894i	−0.210189	−	0.364059i
$147$		0			0
$148$	−0.391482	+	0.678068i	−0.0321797	+	0.0557368i
$149$	3.29249	+	5.70277i	0.269732	+	0.467189i	0.968792	−	0.247873i	$-0.0797317\pi$
$149$	3.29249	+	5.70277i	0.269732	+	0.467189i	−0.699061	+	0.715062i	$0.746398\pi$
$150$		0			0
$151$	−6.33356	+	10.9700i	−0.515417	+	0.892729i	0.484422	+	0.874834i	$0.339030\pi$
$151$	−6.33356	+	10.9700i	−0.515417	+	0.892729i	−0.999840	+	0.0178950i	$0.994304\pi$
$152$	1.40593	−	2.43514i	0.114036	−	0.197516i
$153$		0			0
$154$	−1.78517	−	7.15115i	−0.143853	−	0.576256i
$155$	−2.56791	−	4.44775i	−0.206260	−	0.357252i
$156$		0			0
$157$	−17.3074			−1.38128			−0.690642	−	0.723197i	$-0.742672\pi$
$157$	−17.3074			−1.38128			−0.690642	+	0.723197i	$0.742672\pi$
$158$	−10.8990			−0.867078
$159$		0			0
$160$	−4.45822	−	7.72186i	−0.352453	−	0.610467i
$161$	−18.7219	−	5.36260i	−1.47549	−	0.422632i
$162$		0			0
$163$	6.10963	−	10.5822i	0.478543	−	0.828861i	−0.521154	−	0.853463i	$-0.674498\pi$
$163$	6.10963	−	10.5822i	0.478543	−	0.828861i	0.999697	+	0.0246014i	$0.00783167\pi$
$164$	−6.27227	+	10.8639i	−0.489782	+	0.848327i
$165$		0			0
$166$	−5.15752	−	8.93309i	−0.400301	−	0.693342i
$167$	−1.76248	+	3.05270i	−0.136385	+	0.236225i	−0.926126	−	0.377215i	$-0.876882\pi$
$167$	−1.76248	+	3.05270i	−0.136385	+	0.236225i	0.789741	+	0.613440i	$0.210215\pi$
$168$		0			0
$169$	−6.89546	−	11.9433i	−0.530420	−	0.918714i
$170$	1.90332	−	3.29665i	0.145978	−	0.252842i
$171$		0			0
$172$	7.08968	+	12.2797i	0.540583	+	0.936318i
$173$	−10.1409			−0.770999			−0.385500	−	0.922708i	$-0.625971\pi$
$173$	−10.1409			−0.770999			−0.385500	+	0.922708i	$0.625971\pi$
$174$		0			0
$175$	−2.06239	−	8.26164i	−0.155902	−	0.624522i
$176$	−3.66738	+	6.35208i	−0.276439	+	0.478806i
$177$		0			0
$178$	−1.29492	+	2.24287i	−0.0970584	+	0.168110i
$179$	−0.850579	−	1.47325i	−0.0635752	−	0.110116i	0.832486	−	0.554046i	$-0.186917\pi$
$179$	−0.850579	−	1.47325i	−0.0635752	−	0.110116i	−0.896061	+	0.443931i	$0.853584\pi$
$180$		0			0
$181$	−16.9941			−1.26316			−0.631581	−	0.775310i	$-0.717594\pi$
$181$	−16.9941			−1.26316			−0.631581	+	0.775310i	$0.717594\pi$
$182$	6.10702	+	24.4639i	0.452683	+	1.81339i
$183$		0			0
$184$	4.13252	+	7.15774i	0.304654	+	0.527676i
$185$	−0.751755			−0.0552701
$186$		0			0
$187$	−2.34355			−0.171377
$188$	13.2323			0.965066
$189$		0			0
$190$	−6.15437			−0.446485
$191$	−22.6939			−1.64208			−0.821038	−	0.570873i	$-0.806605\pi$
$191$	−22.6939			−1.64208			−0.821038	+	0.570873i	$0.806605\pi$
$192$		0			0
$193$	6.18698			0.445348			0.222674	−	0.974893i	$-0.428521\pi$
$193$	6.18698			0.445348			0.222674	+	0.974893i	$0.428521\pi$
$194$	−11.2263	−	19.4445i	−0.806001	−	1.39603i
$195$		0			0
$196$	0.334014	−	9.72544i	0.0238582	−	0.694674i
$197$	−9.77010			−0.696091			−0.348045	−	0.937478i	$-0.613154\pi$
$197$	−9.77010			−0.696091			−0.348045	+	0.937478i	$0.613154\pi$
$198$		0			0
$199$	−4.33973	−	7.51664i	−0.307636	−	0.532840i	0.670209	−	0.742172i	$-0.266204\pi$
$199$	−4.33973	−	7.51664i	−0.307636	−	0.532840i	−0.977845	+	0.209332i	$0.932871\pi$
$200$	−1.80691	+	3.12965i	−0.127768	+	0.221300i
$201$		0			0
$202$	1.02987	−	1.78379i	0.0724615	−	0.125507i
$203$	0.157549	+	0.0451275i	0.0110578	+	0.00316733i
$204$		0			0
$205$	−12.0445			−0.841224
$206$	−1.77721	−	3.07822i	−0.123824	−	0.214470i
$207$		0			0
$208$	12.5460	−	21.7303i	0.869909	−	1.50673i
$209$	1.89446	+	3.28130i	0.131043	+	0.226973i
$210$		0			0
$211$	−2.84219	+	4.92283i	−0.195665	+	0.338901i	−0.947118	−	0.320885i	$-0.896020\pi$
$211$	−2.84219	+	4.92283i	−0.195665	+	0.338901i	0.751453	+	0.659786i	$0.229353\pi$
$212$	−1.05010	−	1.81882i	−0.0721209	−	0.124917i
$213$		0			0
$214$	−5.32062	+	9.21558i	−0.363710	+	0.629964i
$215$	−6.80708	+	11.7902i	−0.464239	+	0.804086i
$216$		0			0
$217$	−7.32102	+	7.07390i	−0.496983	+	0.480207i
$218$	−7.58786	−	13.1426i	−0.513915	−	0.890126i
$219$		0			0
$220$	2.80745			0.189278
$221$	8.01723			0.539298
$222$		0			0
$223$	5.86133	+	10.1521i	0.392503	+	0.679836i	0.992779	−	0.119957i	$-0.0382758\pi$
$223$	5.86133	+	10.1521i	0.392503	+	0.679836i	−0.600276	+	0.799793i	$0.704942\pi$
$224$	−12.7102	+	12.2812i	−0.849236	+	0.820571i
$225$		0			0
$226$	−13.3509	+	23.1245i	−0.888091	+	1.53822i
$227$	5.59154	−	9.68482i	0.371123	−	0.642804i	−0.618615	−	0.785694i	$-0.712306\pi$
$227$	5.59154	−	9.68482i	0.371123	−	0.642804i	0.989739	+	0.142890i	$0.0456394\pi$
$228$		0			0
$229$	4.82824	+	8.36275i	0.319059	+	0.552626i	0.980292	−	0.197554i	$-0.0632999\pi$
$229$	4.82824	+	8.36275i	0.319059	+	0.552626i	−0.661233	+	0.750181i	$0.729967\pi$
$230$	9.04494	−	15.6663i	0.596406	−	1.03301i
$231$		0			0
$232$	−0.0347761	−	0.0602340i	−0.00228317	−	0.00395456i
$233$	9.64492	−	16.7055i	0.631860	−	1.09441i	−0.355311	−	0.934748i	$-0.615625\pi$
$233$	9.64492	−	16.7055i	0.631860	−	1.09441i	0.987171	−	0.159666i	$-0.0510416\pi$
$234$		0			0
$235$	6.35243	+	11.0027i	0.414387	+	0.717739i
$236$	11.7376			0.764054
$237$		0			0
$238$	−7.25384	−	2.07775i	−0.470197	−	0.134680i
$239$	0.194641	−	0.337128i	0.0125903	−	0.0218070i	−0.859662	−	0.510864i	$-0.829326\pi$
$239$	0.194641	−	0.337128i	0.0125903	−	0.0218070i	0.872252	+	0.489057i	$0.162659\pi$
$240$		0			0
$241$	−5.31807	+	9.21117i	−0.342567	+	0.593344i	−0.984909	−	0.173075i	$-0.944630\pi$
$241$	−5.31807	+	9.21117i	−0.342567	+	0.593344i	0.642342	+	0.766419i	$0.277963\pi$
$242$	8.01932	+	13.8899i	0.515502	+	0.892875i
$243$		0			0
$244$	4.50299			0.288274
$245$	8.24709	−	4.39115i	0.526888	−	0.280540i
$246$		0			0
$247$	−6.48091	−	11.2253i	−0.412370	−	0.714247i
$248$	4.32046			0.274350
$249$		0			0
$250$	20.1976			1.27741
$251$	3.26628			0.206166			0.103083	−	0.994673i	$-0.467129\pi$
$251$	3.26628			0.206166			0.103083	+	0.994673i	$0.467129\pi$
$252$		0			0
$253$	−11.1370			−0.700176
$254$	15.6506			0.982007
$255$		0			0
$256$	20.9793			1.31121
$257$	−2.34787	−	4.06663i	−0.146456	−	0.253669i	0.783459	−	0.621443i	$-0.213453\pi$
$257$	−2.34787	−	4.06663i	−0.146456	−	0.253669i	−0.929915	+	0.367774i	$0.880120\pi$
$258$		0			0
$259$	0.360911	+	1.44576i	0.0224259	+	0.0898354i
$260$	−9.60421			−0.595628
$261$		0			0
$262$	−1.85363	−	3.21059i	−0.114518	−	0.198351i
$263$	9.77491	−	16.9306i	0.602747	−	1.04399i	−0.389656	−	0.920960i	$-0.627406\pi$
$263$	9.77491	−	16.9306i	0.602747	−	1.04399i	0.992403	−	0.123028i	$-0.0392605\pi$
$264$		0			0
$265$	1.00824	−	1.74632i	0.0619355	−	0.107276i
$266$	2.95466	+	11.8360i	0.181162	+	0.725711i
$267$		0			0
$268$	9.63858			0.588770
$269$	−7.88365	−	13.6549i	−0.480675	−	0.832553i	0.519079	−	0.854726i	$-0.326275\pi$
$269$	−7.88365	−	13.6549i	−0.480675	−	0.832553i	−0.999754	+	0.0221730i	$0.992942\pi$
$270$		0			0
$271$	7.39882	−	12.8151i	0.449446	−	0.778464i	−0.548904	−	0.835886i	$-0.684955\pi$
$271$	7.39882	−	12.8151i	0.449446	−	0.778464i	0.998350	+	0.0574218i	$0.0182880\pi$
$272$	3.75442	+	6.50285i	0.227645	+	0.394293i
$273$		0			0
$274$	2.04138	−	3.53578i	0.123324	−	0.213604i
$275$	−2.43477	−	4.21715i	−0.146822	−	0.254304i
$276$		0			0
$277$	3.72561	−	6.45295i	0.223850	−	0.387720i	−0.732124	−	0.681172i	$-0.761471\pi$
$277$	3.72561	−	6.45295i	0.223850	−	0.387720i	0.955974	+	0.293452i	$0.0948040\pi$
$278$	0.695380	−	1.20443i	0.0417061	−	0.0722371i
$279$		0			0
$280$	−3.81196	−	1.09188i	−0.227808	−	0.0652521i
$281$	12.9938	+	22.5060i	0.775146	+	1.34259i	0.934712	+	0.355406i	$0.115657\pi$
$281$	12.9938	+	22.5060i	0.775146	+	1.34259i	−0.159566	+	0.987187i	$0.551009\pi$
$282$		0			0
$283$	18.7554			1.11489			0.557445	−	0.830214i	$-0.311782\pi$
$283$	18.7554			1.11489			0.557445	+	0.830214i	$0.311782\pi$
$284$	17.1413			1.01715
$285$		0			0
$286$	7.20971	+	12.4876i	0.426319	+	0.738406i
$287$	5.78246	+	23.1638i	0.341328	+	1.36732i
$288$		0			0
$289$	7.30041	−	12.6447i	0.429436	−	0.743805i
$290$	−0.0761152	+	0.131835i	−0.00446964	+	0.00774165i
$291$		0			0
$292$	−1.91754	−	3.32127i	−0.112215	−	0.194363i
$293$	1.23089	−	2.13196i	0.0719093	−	0.124551i	−0.827829	−	0.560981i	$-0.810424\pi$
$293$	1.23089	−	2.13196i	0.0719093	−	0.124551i	0.899738	+	0.436430i	$0.143757\pi$
$294$		0			0
$295$	5.63487	+	9.75988i	0.328075	+	0.568242i
$296$	0.316203	−	0.547680i	0.0183790	−	0.0318333i
$297$		0			0
$298$	6.06227	+	10.5002i	0.351178	+	0.608258i
$299$	38.0994			2.20334
$300$		0			0
$301$	25.9428	+	7.43089i	1.49532	+	0.428309i
$302$	−11.6616	+	20.1985i	−0.671050	+	1.16229i
$303$		0			0
$304$	6.06994	−	10.5134i	0.348135	−	0.602987i
$305$	2.16175	+	3.74425i	0.123781	+	0.214395i
$306$		0			0
$307$	−4.66277			−0.266118			−0.133059	−	0.991108i	$-0.542480\pi$
$307$	−4.66277			−0.266118			−0.133059	+	0.991108i	$0.542480\pi$
$308$	−1.34783	−	5.39924i	−0.0767999	−	0.307650i
$309$		0			0
$310$	−4.72814	−	8.18938i	−0.268541	−	0.465126i
$311$	−27.4821			−1.55837			−0.779183	−	0.626797i	$-0.784366\pi$
$311$	−27.4821			−1.55837			−0.779183	+	0.626797i	$0.784366\pi$
$312$		0			0
$313$	5.49332			0.310501			0.155250	−	0.987875i	$-0.450382\pi$
$313$	5.49332			0.310501			0.155250	+	0.987875i	$0.450382\pi$
$314$	−31.8671			−1.79837
$315$		0			0
$316$	−8.22893			−0.462914
$317$	−9.87758			−0.554780			−0.277390	−	0.960757i	$-0.589469\pi$
$317$	−9.87758			−0.554780			−0.277390	+	0.960757i	$0.589469\pi$
$318$		0			0
$319$	0.0937203			0.00524733
$320$	−1.73808	−	3.01044i	−0.0971614	−	0.168288i
$321$		0			0
$322$	−34.4716	−	9.87383i	−1.92103	−	0.550247i
$323$	3.87885			0.215825
$324$		0			0
$325$	8.32930	+	14.4268i	0.462026	+	0.800253i
$326$	11.2493	−	19.4844i	0.623041	−	1.07914i
$327$		0			0
$328$	5.06616	−	8.77485i	0.279732	−	0.484510i
$329$	18.1105	−	17.4992i	0.998466	−	0.964763i
$330$		0			0
$331$	−20.6942			−1.13746			−0.568729	−	0.822525i	$-0.692565\pi$
$331$	−20.6942			−1.13746			−0.568729	+	0.822525i	$0.692565\pi$
$332$	−3.89401	−	6.74463i	−0.213712	−	0.370160i
$333$		0			0
$334$	−3.24514	+	5.62076i	−0.177566	+	0.307554i
$335$	4.62718	+	8.01452i	0.252810	+	0.437880i
$336$		0			0
$337$	0.748747	−	1.29687i	0.0407869	−	0.0706449i	−0.844911	−	0.534906i	$-0.820347\pi$
$337$	0.748747	−	1.29687i	0.0407869	−	0.0706449i	0.885698	+	0.464261i	$0.153680\pi$
$338$	−12.6962	−	21.9905i	−0.690582	−	1.19612i
$339$		0			0
$340$	1.43704	−	2.48903i	0.0779344	−	0.134986i
$341$	−2.91087	+	5.04177i	−0.157632	+	0.273027i
$342$		0			0
$343$	−12.4044	−	13.7525i	−0.669772	−	0.742567i
$344$	−5.72639	−	9.91840i	−0.308746	−	0.534764i
$345$		0			0
$346$	−18.6719			−1.00381
$347$	29.5388			1.58572			0.792862	−	0.609401i	$-0.208590\pi$
$347$	29.5388			1.58572			0.792862	+	0.609401i	$0.208590\pi$
$348$		0			0
$349$	18.0006	+	31.1780i	0.963551	+	1.66892i	0.713458	+	0.700698i	$0.247128\pi$
$349$	18.0006	+	31.1780i	0.963551	+	1.66892i	0.250094	+	0.968222i	$0.419539\pi$
$350$	−3.79735	−	15.2117i	−0.202977	−	0.813098i
$351$		0			0
$352$	−5.05363	+	8.75315i	−0.269360	+	0.466545i
$353$	−14.7465	+	25.5417i	−0.784877	+	1.35945i	0.144196	+	0.989549i	$0.453940\pi$
$353$	−14.7465	+	25.5417i	−0.784877	+	1.35945i	−0.929073	+	0.369897i	$0.879393\pi$
$354$		0			0
$355$	8.22900	+	14.2530i	0.436750	+	0.756473i
$356$	−0.977687	+	1.69340i	−0.0518173	+	0.0897502i
$357$		0			0
$358$	−1.56612	−	2.71260i	−0.0827720	−	0.143365i
$359$	−2.70535	+	4.68580i	−0.142783	+	0.247307i	−0.928544	−	0.371224i	$-0.878938\pi$
$359$	−2.70535	+	4.68580i	−0.142783	+	0.247307i	0.785761	+	0.618531i	$0.212272\pi$
$360$		0			0
$361$	6.36444	+	11.0235i	0.334971	+	0.580186i
$362$	−31.2902			−1.64458
$363$		0			0
$364$	4.61090	+	18.4707i	0.241677	+	0.968126i
$365$	1.84110	−	3.18888i	0.0963676	−	0.166914i
$366$		0			0
$367$	11.5422	−	19.9916i	0.602496	−	1.04355i	−0.389946	−	0.920838i	$-0.627506\pi$
$367$	11.5422	−	19.9916i	0.602496	−	1.04355i	0.992442	−	0.122715i	$-0.0391602\pi$
$368$	17.8417	+	30.9027i	0.930063	+	1.61092i
$369$		0			0
$370$	−1.38416			−0.0719591
$371$	−3.84254	−	1.10063i	−0.199495	−	0.0571421i
$372$		0			0
$373$	−10.7515	−	18.6222i	−0.556692	−	0.964219i	−0.997770	−	0.0667498i	$-0.978737\pi$
$373$	−10.7515	−	18.6222i	−0.556692	−	0.964219i	0.441078	−	0.897469i	$-0.354596\pi$
$374$	−4.31504			−0.223125
$375$		0			0
$376$	−10.6878			−0.551184
$377$	−0.320615			−0.0165125
$378$		0			0
$379$	5.72168			0.293903			0.146952	−	0.989144i	$-0.453054\pi$
$379$	5.72168			0.293903			0.146952	+	0.989144i	$0.453054\pi$
$380$	−4.64665			−0.238368
$381$		0			0
$382$	−41.7850			−2.13791
$383$	−17.4604	−	30.2424i	−0.892187	−	1.54531i	−0.837248	−	0.546823i	$-0.815837\pi$
$383$	−17.4604	−	30.2424i	−0.892187	−	1.54531i	−0.0549390	−	0.998490i	$-0.517496\pi$
$384$		0			0
$385$	3.84244	−	3.71274i	0.195829	−	0.189219i
$386$	11.3917			0.579823
$387$		0			0
$388$	−8.47603	−	14.6809i	−0.430305	−	0.745311i
$389$	−14.4411	+	25.0127i	−0.732192	+	1.26819i	0.223752	+	0.974646i	$0.428169\pi$
$389$	−14.4411	+	25.0127i	−0.732192	+	1.26819i	−0.955944	+	0.293548i	$0.905164\pi$
$390$		0			0
$391$	−5.70066	+	9.87383i	−0.288295	+	0.499341i
$392$	−0.269786	+	7.85531i	−0.0136262	+	0.396753i
$393$		0			0
$394$	−17.9891			−0.906278
$395$	−3.95046	−	6.84239i	−0.198769	−	0.344278i
$396$		0			0
$397$	5.59226	−	9.68607i	0.280667	−	0.486130i	−0.690882	−	0.722968i	$-0.742778\pi$
$397$	5.59226	−	9.68607i	0.280667	−	0.486130i	0.971549	+	0.236838i	$0.0761109\pi$
$398$	−7.99049	−	13.8399i	−0.400527	−	0.693734i
$399$		0			0
$400$	−7.80111	+	13.5119i	−0.390056	+	0.675596i
$401$	−0.541061	−	0.937146i	−0.0270193	−	0.0467988i	0.852200	−	0.523217i	$-0.175268\pi$
$401$	−0.541061	−	0.937146i	−0.0270193	−	0.0467988i	−0.879219	+	0.476418i	$0.841935\pi$
$402$		0			0
$403$	9.95802	−	17.2478i	0.496044	−	0.859174i
$404$	0.777570	−	1.34679i	0.0386856	−	0.0670054i
$405$		0			0
$406$	0.290086	+	0.0830905i	0.0143967	+	0.00412371i
$407$	0.426078	+	0.737988i	0.0211199	+	0.0365807i
$408$		0			0
$409$	−21.7349			−1.07472			−0.537360	−	0.843353i	$-0.680578\pi$
$409$	−21.7349			−1.07472			−0.537360	+	0.843353i	$0.680578\pi$
$410$	−22.1768			−1.09524
$411$		0			0
$412$	−1.34182	−	2.32410i	−0.0661069	−	0.114500i
$413$	16.0648	−	15.5225i	0.790497	−	0.763814i
$414$		0			0
$415$	3.73879	−	6.47578i	0.183530	−	0.317884i
$416$	17.2884	−	29.9443i	0.847632	−	1.46814i
$417$		0			0
$418$	3.48816	+	6.04167i	0.170611	+	0.295508i
$419$	−12.5906	+	21.8075i	−0.615090	+	1.06537i	0.375279	+	0.926912i	$0.377547\pi$
$419$	−12.5906	+	21.8075i	−0.615090	+	1.06537i	−0.990369	+	0.138455i	$0.955787\pi$
$420$		0			0
$421$	−14.8304	−	25.6869i	−0.722788	−	1.25191i	−0.959878	−	0.280418i	$-0.909527\pi$
$421$	−14.8304	−	25.6869i	−0.722788	−	1.25191i	0.237090	−	0.971488i	$-0.423806\pi$
$422$	−5.23316	+	9.06411i	−0.254746	+	0.441234i
$423$		0			0
$424$	0.848171	+	1.46907i	0.0411908	+	0.0713446i
$425$	−4.98512			−0.241814
$426$		0			0
$427$	6.16305	−	5.95502i	0.298251	−	0.288184i
$428$	−4.01715	+	6.95791i	−0.194176	+	0.336323i
$429$		0			0
$430$	−12.5335	+	21.7086i	−0.604418	+	1.04688i
$431$	−2.44517	−	4.23516i	−0.117780	−	0.204000i	0.801108	−	0.598520i	$-0.204244\pi$
$431$	−2.44517	−	4.23516i	−0.117780	−	0.204000i	−0.918887	+	0.394520i	$0.870911\pi$
$432$		0			0
$433$	9.71430			0.466839			0.233420	−	0.972376i	$-0.425008\pi$
$433$	9.71430			0.466839			0.233420	+	0.972376i	$0.425008\pi$
$434$	−13.4798	+	13.0247i	−0.647049	+	0.625208i
$435$		0			0
$436$	−5.72896	−	9.92285i	−0.274367	−	0.475218i
$437$	18.4330			0.881771
$438$		0			0
$439$	−14.8235			−0.707488			−0.353744	−	0.935342i	$-0.615092\pi$
$439$	−14.8235			−0.707488			−0.353744	+	0.935342i	$0.615092\pi$
$440$	−2.26760			−0.108103
$441$		0			0
$442$	14.7617			0.702141
$443$	21.9020			1.04059			0.520297	−	0.853986i	$-0.325821\pi$
$443$	21.9020			1.04059			0.520297	+	0.853986i	$0.325821\pi$
$444$		0			0
$445$	−1.87743			−0.0889987
$446$	10.7921	+	18.6925i	0.511021	+	0.885115i
$447$		0			0
$448$	−4.95519	+	4.78793i	−0.234111	+	0.226208i
$449$	−21.4952			−1.01442			−0.507212	−	0.861822i	$-0.669324\pi$
$449$	−21.4952			−1.01442			−0.507212	+	0.861822i	$0.669324\pi$
$450$		0			0
$451$	6.82655	+	11.8239i	0.321450	+	0.556767i
$452$	−10.0802	+	17.4594i	−0.474131	+	0.821220i
$453$		0			0
$454$	10.2954	−	17.8321i	0.483185	−	0.836902i
$455$	−13.1449	+	12.7012i	−0.616242	+	0.595441i
$456$		0			0
$457$	40.6255			1.90038			0.950190	−	0.311670i	$-0.100888\pi$
$457$	40.6255			1.90038			0.950190	+	0.311670i	$0.100888\pi$
$458$	8.88995	+	15.3978i	0.415400	+	0.719494i
$459$		0			0
$460$	6.82908	−	11.8283i	0.318408	−	0.551498i
$461$	−1.41541	−	2.45155i	−0.0659220	−	0.114180i	0.831181	−	0.556003i	$-0.187666\pi$
$461$	−1.41541	−	2.45155i	−0.0659220	−	0.114180i	−0.897103	+	0.441822i	$0.854332\pi$
$462$		0			0
$463$	−13.9324	+	24.1317i	−0.647494	+	1.12149i	0.336225	+	0.941782i	$0.390850\pi$
$463$	−13.9324	+	24.1317i	−0.647494	+	1.12149i	−0.983719	+	0.179711i	$0.942484\pi$
$464$	−0.150142	−	0.260053i	−0.00697016	−	0.0120727i
$465$		0			0
$466$	17.7586	−	30.7588i	0.822653	−	1.42488i
$467$	13.3219	−	23.0742i	0.616464	−	1.06775i	−0.373661	−	0.927565i	$-0.621898\pi$
$467$	13.3219	−	23.0742i	0.616464	−	1.06775i	0.990126	−	0.140182i	$-0.0447689\pi$
$468$		0			0
$469$	13.1919	−	12.7466i	0.609146	−	0.588585i
$470$	11.6964	+	20.2587i	0.539513	+	0.934463i
$471$		0			0
$472$	−9.48056			−0.436378
$473$	15.4324			0.709582
$474$		0			0
$475$	4.02983	+	6.97987i	0.184901	+	0.320258i
$476$	−5.47677	−	1.56873i	−0.251027	−	0.0719027i
$477$		0			0
$478$	0.358381	−	0.620734i	0.0163920	−	0.0283917i
$479$	−15.7895	+	27.3483i	−0.721443	+	1.24958i	0.238979	+	0.971025i	$0.423187\pi$
$479$	−15.7895	+	27.3483i	−0.721443	+	1.24958i	−0.960422	+	0.278551i	$0.910146\pi$
$480$		0			0
$481$	−1.45760	−	2.52464i	−0.0664609	−	0.115114i
$482$	−9.79185	+	16.9600i	−0.446007	+	0.772506i
$483$		0			0
$484$	6.05472	+	10.4871i	0.275215	+	0.476686i
$485$	8.13817	−	14.0957i	0.369535	−	0.640054i
$486$		0			0
$487$	−0.153087	−	0.265154i	−0.00693703	−	0.0120153i	0.862536	−	0.505996i	$-0.168875\pi$
$487$	−0.153087	−	0.265154i	−0.00693703	−	0.0120153i	−0.869473	+	0.493980i	$0.835541\pi$
$488$	−3.63710			−0.164644
$489$		0			0
$490$	15.1849	−	8.08516i	0.685983	−	0.365250i
$491$	9.06981	−	15.7094i	0.409315	−	0.708954i	−0.585498	−	0.810674i	$-0.699101\pi$
$491$	9.06981	−	15.7094i	0.409315	−	0.708954i	0.994813	+	0.101720i	$0.0324345\pi$
$492$		0			0
$493$	0.0479723	−	0.0830905i	0.00216057	−	0.00374221i
$494$	−11.9329	−	20.6684i	−0.536887	−	0.929916i
$495$		0			0
$496$	18.6531			0.837549
$497$	23.4606	−	22.6687i	1.05235	−	1.01683i
$498$		0			0
$499$	10.6546	+	18.4543i	0.476964	+	0.826126i	0.999652	−	0.0263983i	$-0.00840381\pi$
$499$	10.6546	+	18.4543i	0.476964	+	0.826126i	−0.522687	+	0.852524i	$0.675070\pi$
$500$	15.2496			0.681981
$501$		0			0
$502$	6.01401			0.268418
$503$	17.0738			0.761285			0.380642	−	0.924722i	$-0.375703\pi$
$503$	17.0738			0.761285			0.380642	+	0.924722i	$0.375703\pi$
$504$		0			0
$505$	1.49315			0.0664443
$506$	−20.5059			−0.911597
$507$		0			0
$508$	11.8165			0.524271
$509$	18.3868	+	31.8468i	0.814979	+	1.41159i	0.909343	+	0.416048i	$0.136585\pi$
$509$	18.3868	+	31.8468i	0.814979	+	1.41159i	−0.0943635	+	0.995538i	$0.530082\pi$
$510$		0			0
$511$	−7.01670	−	2.00982i	−0.310401	−	0.0889093i
$512$	21.4975			0.950065
$513$		0			0
$514$	−4.32299	−	7.48764i	−0.190679	−	0.330265i
$515$	1.28834	−	2.23146i	0.0567709	−	0.0983300i
$516$		0			0
$517$	7.20083	−	12.4722i	0.316692	−	0.548527i
$518$	0.664525	+	2.66200i	0.0291975	+	0.116961i
$519$		0			0
$520$	7.75740			0.340184
$521$	9.57535	+	16.5850i	0.419504	+	0.726602i	0.995890	−	0.0905758i	$-0.0288707\pi$
$521$	9.57535	+	16.5850i	0.419504	+	0.726602i	−0.576386	+	0.817178i	$0.695537\pi$
$522$		0			0
$523$	−20.9715	+	36.3236i	−0.917018	+	1.58832i	−0.113097	+	0.993584i	$0.536077\pi$
$523$	−20.9715	+	36.3236i	−0.917018	+	1.58832i	−0.803920	+	0.594737i	$0.797256\pi$
$524$	−1.39952	−	2.42405i	−0.0611385	−	0.105895i
$525$		0			0
$526$	17.9980	−	31.1734i	0.784749	−	1.35922i
$527$	2.97996	+	5.16144i	0.129809	+	0.224836i
$528$		0			0
$529$	−15.5906	+	27.0037i	−0.677851	+	1.17407i
$530$	1.85641	−	3.21539i	0.0806372	−	0.139668i
$531$		0			0
$532$	2.23082	+	8.93637i	0.0967183	+	0.387441i
$533$	−23.3535	−	40.4494i	−1.01155	−	1.75206i
$534$		0			0
$535$	−7.71405			−0.333507
$536$	−7.78515			−0.336267
$537$		0			0
$538$	−14.5157	−	25.1419i	−0.625816	−	1.08395i
$539$	−8.98500	−	5.60726i	−0.387011	−	0.241522i
$540$		0			0
$541$	−1.44272	+	2.49886i	−0.0620273	+	0.107434i	−0.895371	−	0.445320i	$-0.853090\pi$
$541$	−1.44272	+	2.49886i	−0.0620273	+	0.107434i	0.833344	+	0.552754i	$0.186423\pi$
$542$	13.6230	−	23.5957i	0.585158	−	1.01352i
$543$		0			0
$544$	5.17358	+	8.96090i	0.221815	+	0.384196i
$545$	5.50059	−	9.52731i	0.235620	−	0.408105i
$546$		0			0
$547$	1.38738	+	2.40301i	0.0593201	+	0.102745i	0.894160	−	0.447747i	$-0.147773\pi$
$547$	1.38738	+	2.40301i	0.0593201	+	0.102745i	−0.834840	+	0.550492i	$0.814440\pi$
$548$	1.54128	−	2.66957i	0.0658401	−	0.114038i
$549$		0			0
$550$	−4.48300	−	7.76478i	−0.191156	−	0.331091i
$551$	−0.155118			−0.00660825
$552$		0			0
$553$	−11.2626	+	10.8824i	−0.478935	+	0.462768i
$554$	6.85975	−	11.8814i	0.291443	−	0.504794i
$555$		0			0
$556$	0.525024	−	0.909368i	0.0222660	−	0.0385658i
$557$	−15.5344	−	26.9064i	−0.658214	−	1.14006i	−0.981078	−	0.193614i	$-0.937979\pi$
$557$	−15.5344	−	26.9064i	−0.658214	−	1.14006i	0.322864	−	0.946445i	$-0.395354\pi$
$558$		0			0
$559$	−52.7939			−2.23294
$560$	−16.4577	−	4.71405i	−0.695465	−	0.199205i
$561$		0			0
$562$	23.9248	+	41.4389i	1.00920	+	1.74799i
$563$	−0.288041			−0.0121395			−0.00606973	−	0.999982i	$-0.501932\pi$
$563$	−0.288041			−0.0121395			−0.00606973	+	0.999982i	$0.501932\pi$
$564$		0			0
$565$	−19.3567			−0.814344
$566$	34.5331			1.45154
$567$		0			0
$568$	−13.8451			−0.580929
$569$	16.0801			0.674112			0.337056	−	0.941485i	$-0.390569\pi$
$569$	16.0801			0.674112			0.337056	+	0.941485i	$0.390569\pi$
$570$		0			0
$571$	−15.2858			−0.639690			−0.319845	−	0.947470i	$-0.603631\pi$
$571$	−15.2858			−0.639690			−0.319845	+	0.947470i	$0.603631\pi$
$572$	5.44345	+	9.42834i	0.227602	+	0.394218i
$573$		0			0
$574$	10.6469	+	42.6501i	0.444393	+	1.78018i
$575$	−23.6902			−0.987950
$576$		0			0
$577$	12.0812	+	20.9253i	0.502949	+	0.871133i	0.999994	+	0.00340833i	$0.00108491\pi$
$577$	12.0812	+	20.9253i	0.502949	+	0.871133i	−0.497045	+	0.867725i	$0.665582\pi$
$578$	13.4418	−	23.2819i	0.559106	−	0.968400i
$579$		0			0
$580$	−0.0574683	+	0.0995380i	−0.00238624	+	0.00413309i
$581$	−14.2491	−	4.08142i	−0.591152	−	0.169326i
$582$		0			0
$583$	−2.28579			−0.0946676
$584$	1.54881	+	2.68262i	0.0640902	+	0.111007i
$585$		0			0
$586$	2.26636	−	3.92546i	0.0936226	−	0.162159i
$587$	−18.0145	−	31.2020i	−0.743537	−	1.28784i	−0.950875	−	0.309574i	$-0.899814\pi$
$587$	−18.0145	−	31.2020i	−0.743537	−	1.28784i	0.207339	−	0.978269i	$-0.433520\pi$
$588$		0			0
$589$	4.81783	−	8.34472i	0.198515	−	0.343838i
$590$	10.3752	+	17.9703i	0.427138	+	0.739825i
$591$		0			0
$592$	1.36517	−	2.36455i	0.0561082	−	0.0971823i
$593$	−12.4668	+	21.5932i	−0.511951	+	0.886726i	0.487953	+	0.872870i	$0.337744\pi$
$593$	−12.4668	+	21.5932i	−0.511951	+	0.886726i	−0.999904	+	0.0138558i	$0.995589\pi$
$594$		0			0
$595$	−1.32482	−	5.30706i	−0.0543124	−	0.217568i
$596$	4.57712	+	7.92780i	0.187486	+	0.324735i
$597$		0			0
$598$	70.1501			2.86865
$599$	−39.5283			−1.61508			−0.807542	−	0.589810i	$-0.799203\pi$
$599$	−39.5283			−1.61508			−0.807542	+	0.589810i	$0.799203\pi$
$600$		0			0
$601$	1.86447	+	3.22936i	0.0760534	+	0.131728i	0.901544	−	0.432688i	$-0.142435\pi$
$601$	1.86447	+	3.22936i	0.0760534	+	0.131728i	−0.825490	+	0.564416i	$0.809101\pi$
$602$	47.7669	+	13.6821i	1.94683	+	0.557639i
$603$		0			0
$604$	−8.80470	+	15.2502i	−0.358258	+	0.620521i
$605$	−5.81337	+	10.0691i	−0.236347	+	0.409365i
$606$		0			0
$607$	−11.8264	−	20.4839i	−0.480018	−	0.831415i	0.519719	−	0.854337i	$-0.326036\pi$
$607$	−11.8264	−	20.4839i	−0.480018	−	0.831415i	−0.999737	+	0.0229218i	$0.992703\pi$
$608$	8.36436	−	14.4875i	0.339219	−	0.587545i
$609$		0			0
$610$	3.98029	+	6.89407i	0.161157	+	0.279133i
$611$	−24.6339	+	42.6671i	−0.996580	+	1.72613i
$612$		0			0
$613$	1.89952	+	3.29006i	0.0767208	+	0.132884i	0.901833	−	0.432084i	$-0.142222\pi$
$613$	1.89952	+	3.29006i	0.0767208	+	0.132884i	−0.825113	+	0.564968i	$0.808888\pi$
$614$	−8.58528			−0.346474
$615$		0			0
$616$	1.08865	+	4.36101i	0.0438631	+	0.175710i
$617$	17.5615	−	30.4174i	0.706999	−	1.22456i	−0.258966	−	0.965886i	$-0.583382\pi$
$617$	17.5615	−	30.4174i	0.706999	−	1.22456i	0.965965	−	0.258672i	$-0.0832849\pi$
$618$		0			0
$619$	10.5816	−	18.3279i	0.425311	−	0.736660i	−0.571138	−	0.820854i	$-0.693498\pi$
$619$	10.5816	−	18.3279i	0.425311	−	0.736660i	0.996449	+	0.0841934i	$0.0268314\pi$
$620$	−3.56983	−	6.18312i	−0.143368	−	0.248320i
$621$		0			0
$622$	−50.6011			−2.02892
$623$	0.901339	+	3.61064i	0.0361114	+	0.144657i
$624$		0			0
$625$	−0.725240	−	1.25615i	−0.0290096	−	0.0502461i
$626$	10.1145			0.404257
$627$		0			0
$628$	−24.0602			−0.960107
$629$	0.872381			0.0347841
$630$		0			0
$631$	4.74845			0.189033			0.0945164	−	0.995523i	$-0.469870\pi$
$631$	4.74845			0.189033			0.0945164	+	0.995523i	$0.469870\pi$
$632$	6.64657			0.264386
$633$		0			0
$634$	−18.1870			−0.722298
$635$	5.67273	+	9.82546i	0.225115	+	0.389911i
$636$		0			0
$637$	30.7375	+	19.1823i	1.21786	+	0.760031i
$638$	0.172562			0.00683178
$639$		0			0
$640$	5.71622	+	9.90078i	0.225953	+	0.391363i
$641$	−4.93735	+	8.55174i	−0.195013	+	0.337773i	−0.946905	−	0.321514i	$-0.895808\pi$
$641$	−4.93735	+	8.55174i	−0.195013	+	0.337773i	0.751891	+	0.659287i	$0.229142\pi$
$642$		0			0
$643$	21.9748	−	38.0615i	0.866602	−	1.50100i	0.00115462	−	0.999999i	$-0.499632\pi$
$643$	21.9748	−	38.0615i	0.866602	−	1.50100i	0.865448	−	0.501000i	$-0.167034\pi$
$644$	−26.0266	−	7.45491i	−1.02559	−	0.293764i
$645$		0			0
$646$	7.14190			0.280994
$647$	−22.1936	−	38.4404i	−0.872521	−	1.51125i	−0.859381	−	0.511336i	$-0.829151\pi$
$647$	−22.1936	−	38.4404i	−0.872521	−	1.51125i	−0.0131398	−	0.999914i	$-0.504183\pi$
$648$		0			0
$649$	6.38743	−	11.0634i	0.250729	−	0.434275i
$650$	15.3362	+	26.5631i	0.601537	+	1.04189i
$651$		0			0
$652$	8.49341	−	14.7110i	0.332628	−	0.576128i
$653$	20.9956	+	36.3655i	0.821622	+	1.42309i	0.904474	+	0.426529i	$0.140264\pi$
$653$	20.9956	+	36.3655i	0.821622	+	1.42309i	−0.0828523	+	0.996562i	$0.526403\pi$
$654$		0			0
$655$	1.34374	−	2.32742i	0.0525042	−	0.0909399i
$656$	21.8726	−	37.8844i	0.853980	−	1.47914i
$657$		0			0
$658$	33.3459	−	32.2203i	1.29996	−	1.25608i
$659$	19.6365	+	34.0114i	0.764928	+	1.32489i	0.940284	+	0.340390i	$0.110559\pi$
$659$	19.6365	+	34.0114i	0.764928	+	1.32489i	−0.175356	+	0.984505i	$0.556108\pi$
$660$		0			0
$661$	−0.186739			−0.00726330			−0.00363165	−	0.999993i	$-0.501156\pi$
$661$	−0.186739			−0.00726330			−0.00363165	+	0.999993i	$0.501156\pi$
$662$	−38.1030			−1.48092
$663$		0			0
$664$	3.14522	+	5.44769i	0.122058	+	0.211411i
$665$	−6.35969	+	6.14502i	−0.246618	+	0.238293i
$666$		0			0
$667$	0.227973	−	0.394862i	0.00882717	−	0.0152891i
$668$	−2.45014	+	4.24376i	−0.0947987	+	0.164196i
$669$		0			0
$670$	8.51976	+	14.7567i	0.329147	+	0.570099i
$671$	2.45046	−	4.24432i	0.0945989	−	0.163850i
$672$		0			0
$673$	−5.43382	−	9.41166i	−0.209458	−	0.362793i	0.742086	−	0.670305i	$-0.233837\pi$
$673$	−5.43382	−	9.41166i	−0.209458	−	0.362793i	−0.951544	+	0.307512i	$0.900503\pi$
$674$	1.37862	−	2.38785i	0.0531026	−	0.0919764i
$675$		0			0
$676$	−9.58584	−	16.6032i	−0.368686	−	0.638583i
$677$	−28.3901			−1.09112			−0.545560	−	0.838072i	$-0.683683\pi$
$677$	−28.3901			−1.09112			−0.545560	+	0.838072i	$0.683683\pi$
$678$		0			0
$679$	−31.0157	−	8.88396i	−1.19027	−	0.340935i
$680$	−1.16071	+	2.01041i	−0.0445111	+	0.0770956i
$681$		0			0
$682$	−5.35961	+	9.28312i	−0.205230	+	0.355469i
$683$	−5.92034	−	10.2543i	−0.226536	−	0.392371i	0.730243	−	0.683187i	$-0.239407\pi$
$683$	−5.92034	−	10.2543i	−0.226536	−	0.392371i	−0.956779	+	0.290816i	$0.906073\pi$
$684$		0			0
$685$	2.95968			0.113083
$686$	−22.8394	−	25.3217i	−0.872012	−	0.966788i
$687$		0			0
$688$	−24.7230	−	42.8216i	−0.942557	−	1.63256i
$689$	7.81962			0.297904
$690$		0			0
$691$	11.9083			0.453014			0.226507	−	0.974010i	$-0.427269\pi$
$691$	11.9083			0.453014			0.226507	+	0.974010i	$0.427269\pi$
$692$	−14.0976			−0.535909
$693$		0			0
$694$	54.3880			2.06454
$695$	1.00819			0.0382429
$696$		0			0
$697$	13.9771			0.529422
$698$	33.1435	+	57.4062i	1.25450	+	2.17286i
$699$		0			0
$700$	−2.86706	−	11.4851i	−0.108365	−	0.434095i
$701$	31.3902			1.18559			0.592795	−	0.805353i	$-0.298024\pi$
$701$	31.3902			1.18559			0.592795	+	0.805353i	$0.298024\pi$
$702$		0			0
$703$	−0.705208	−	1.22146i	−0.0265974	−	0.0460681i
$704$	−1.97020	+	3.41249i	−0.0742549	+	0.128613i
$705$		0			0
$706$	−27.1518	+	47.0284i	−1.02187	+	1.76994i
$707$	−0.716849	−	2.87160i	−0.0269599	−	0.107998i
$708$		0			0
$709$	0.625218			0.0234806			0.0117403	−	0.999931i	$-0.496263\pi$
$709$	0.625218			0.0234806			0.0117403	+	0.999931i	$0.496263\pi$
$710$	15.1516	+	26.2433i	0.568628	+	0.984893i
$711$		0			0
$712$	0.789685	−	1.36777i	0.0295947	−	0.0512595i
$713$	14.1613	+	24.5281i	0.530345	+	0.918584i
$714$		0			0
$715$	−5.22647	+	9.05251i	−0.195459	+	0.338545i
$716$	−1.18245	−	2.04806i	−0.0441901	−	0.0765395i
$717$		0			0
$718$	−4.98119	+	8.62768i	−0.185897	+	0.321982i
$719$	−12.1969	+	21.1257i	−0.454869	+	0.787857i	−0.998681	−	0.0513506i	$-0.983647\pi$
$719$	−12.1969	+	21.1257i	−0.454869	+	0.787857i	0.543811	+	0.839208i	$0.316981\pi$
$720$		0			0
$721$	−4.91003	−	1.40640i	−0.182859	−	0.0523771i
$722$	11.7185	+	20.2970i	0.436116	+	0.755376i
$723$		0			0
$724$	−23.6246			−0.878003
$725$	0.199358			0.00740399
$726$		0			0
$727$	−18.9253	−	32.7796i	−0.701900	−	1.21573i	−0.967799	−	0.251726i	$-0.919002\pi$
$727$	−18.9253	−	32.7796i	−0.701900	−	1.21573i	0.265899	−	0.964001i	$-0.414331\pi$
$728$	−3.72426	−	14.9189i	−0.138030	−	0.552932i
$729$		0			0
$730$	3.38991	−	5.87150i	0.125466	−	0.217314i
$731$	7.89934	−	13.6821i	0.292168	−	0.506049i
$732$		0			0
$733$	−1.20077	−	2.07980i	−0.0443516	−	0.0768193i	0.842997	−	0.537918i	$-0.180789\pi$
$733$	−1.20077	−	2.07980i	−0.0443516	−	0.0768193i	−0.887349	+	0.461098i	$0.847456\pi$
$734$	21.2519	−	36.8093i	0.784421	−	1.35866i
$735$		0			0
$736$	24.5858	+	42.5839i	0.906245	+	1.56966i
$737$	5.24517	−	9.08490i	0.193208	−	0.334646i
$738$		0			0
$739$	−15.1940	−	26.3167i	−0.558920	−	0.968077i	−0.997587	−	0.0694277i	$-0.977883\pi$
$739$	−15.1940	−	26.3167i	−0.558920	−	0.968077i	0.438667	−	0.898650i	$-0.355451\pi$
$740$	−1.04507			−0.0384174
$741$		0			0
$742$	−7.07504	−	2.02653i	−0.259733	−	0.0743963i
$743$	2.54785	−	4.41300i	0.0934715	−	0.161897i	−0.815498	−	0.578760i	$-0.803537\pi$
$743$	2.54785	−	4.41300i	0.0934715	−	0.161897i	0.908970	+	0.416862i	$0.136870\pi$
$744$		0			0
$745$	−4.39467	+	7.61179i	−0.161008	+	0.278874i
$746$	−19.7961	−	34.2879i	−0.724787	−	1.25537i
$747$		0			0
$748$	−3.25793			−0.119122
$749$	3.70345	+	14.8355i	0.135321	+	0.542079i
$750$		0			0
$751$	0.487506	+	0.844384i	0.0177893	+	0.0308120i	0.874783	−	0.484515i	$-0.161004\pi$
$751$	0.487506	+	0.844384i	0.0177893	+	0.0308120i	−0.856994	+	0.515327i	$0.827671\pi$
$752$	−46.1435			−1.68268
$753$		0			0
$754$	−0.590329			−0.0214985
$755$	−16.9075			−0.615326
$756$		0			0
$757$	11.6346			0.422865			0.211433	−	0.977393i	$-0.432187\pi$
$757$	11.6346			0.422865			0.211433	+	0.977393i	$0.432187\pi$
$758$	10.5350			0.382648
$759$		0			0
$760$	3.75314			0.136141
$761$	−27.0875	−	46.9169i	−0.981920	−	1.70073i	−0.654897	−	0.755718i	$-0.727288\pi$
$761$	−27.0875	−	46.9169i	−0.981920	−	1.70073i	−0.327023	−	0.945016i	$-0.606045\pi$
$762$		0			0
$763$	−20.9636	−	6.00468i	−0.758932	−	0.217384i
$764$	−31.5484			−1.14138
$765$		0			0
$766$	−32.1489	−	55.6835i	−1.16159	−	2.01193i
$767$	−21.8513	+	37.8475i	−0.789004	+	1.36659i
$768$		0			0
$769$	−10.4326	+	18.0698i	−0.376208	+	0.651612i	−0.990507	−	0.137462i	$-0.956106\pi$
$769$	−10.4326	+	18.0698i	−0.376208	+	0.651612i	0.614299	+	0.789074i	$0.289439\pi$
$770$	7.07485	−	6.83604i	0.254960	−	0.246354i
$771$		0			0
$772$	8.60094			0.309554
$773$	27.4972	+	47.6266i	0.989007	+	1.71301i	0.622561	+	0.782572i	$0.286092\pi$
$773$	27.4972	+	47.6266i	0.989007	+	1.71301i	0.366447	+	0.930439i	$0.380574\pi$
$774$		0			0
$775$	−6.19189	+	10.7247i	−0.222419	+	0.385242i
$776$	6.84616	+	11.8579i	0.245763	+	0.425674i
$777$		0			0
$778$	−26.5895	+	46.0544i	−0.953281	+	1.65113i
$779$	−11.2987	−	19.5700i	−0.404819	−	0.701168i
$780$		0			0
$781$	9.32802	−	16.1566i	0.333783	−	0.578129i
$782$	−10.4963	+	18.1801i	−0.375346	+	0.650119i
$783$		0			0
$784$	−1.16477	+	33.9144i	−0.0415989	+	1.21123i
$785$	−11.5506	−	20.0062i	−0.412258	−	0.714051i
$786$		0			0
$787$	9.18949			0.327570			0.163785	−	0.986496i	$-0.447630\pi$
$787$	9.18949			0.327570			0.163785	+	0.986496i	$0.447630\pi$
$788$	−13.5821			−0.483841
$789$		0			0
$790$	−7.27374	−	12.5985i	−0.258788	−	0.448234i
$791$	9.29301	+	37.2266i	0.330421	+	1.32362i
$792$		0			0
$793$	−8.38296	+	14.5197i	−0.297688	+	0.515610i
$794$	10.2967	−	17.8344i	0.365416	−	0.632919i
$795$		0			0
$796$	−6.03296	−	10.4494i	−0.213832	−	0.370369i
$797$	−3.53774	+	6.12754i	−0.125313	+	0.217049i	−0.921855	−	0.387534i	$-0.873327\pi$
$797$	−3.53774	+	6.12754i	−0.125313	+	0.217049i	0.796542	+	0.604583i	$0.206660\pi$
$798$		0			0
$799$	−7.37174	−	12.7682i	−0.260793	−	0.451707i
$800$	−10.7499	+	18.6194i	−0.380067	+	0.658295i
$801$		0			0
$802$	−0.996224	−	1.72551i	−0.0351779	−	0.0609299i
$803$	−4.17398			−0.147297
$804$		0			0
$805$	−6.29579	−	25.2201i	−0.221898	−	0.888892i
$806$	18.3351	−	31.7573i	0.645827	−	1.11860i
$807$		0			0
$808$	−0.628050	+	1.08781i	−0.0220947	+	0.0382692i
$809$	2.97060	+	5.14522i	0.104441	+	0.180896i	0.913510	−	0.406817i	$-0.133361\pi$
$809$	2.97060	+	5.14522i	0.104441	+	0.180896i	−0.809069	+	0.587714i	$0.800028\pi$
$810$		0			0
$811$	44.4139			1.55958			0.779791	−	0.626039i	$-0.215325\pi$
$811$	44.4139			1.55958			0.779791	+	0.626039i	$0.215325\pi$
$812$	0.219020	+	0.0627347i	0.00768609	+	0.00220156i
$813$		0			0
$814$	0.784512	+	1.35881i	0.0274971	+	0.0476264i
$815$	16.3097			0.571304
$816$		0			0
$817$	−25.5424			−0.893616
$818$	−40.0191			−1.39924
$819$		0			0
$820$	−16.7439			−0.584721
$821$	−6.35522			−0.221799			−0.110899	−	0.993832i	$-0.535373\pi$
$821$	−6.35522			−0.221799			−0.110899	+	0.993832i	$0.535373\pi$
$822$		0			0
$823$	−9.46433			−0.329906			−0.164953	−	0.986301i	$-0.552747\pi$
$823$	−9.46433			−0.329906			−0.164953	+	0.986301i	$0.552747\pi$
$824$	1.08380	+	1.87720i	0.0377560	+	0.0653953i
$825$		0			0
$826$	29.5792	−	28.5807i	1.02919	−	0.994450i
$827$	4.86261			0.169090			0.0845448	−	0.996420i	$-0.473056\pi$
$827$	4.86261			0.169090			0.0845448	+	0.996420i	$0.473056\pi$
$828$		0			0
$829$	20.3926	+	35.3211i	0.708266	+	1.22675i	0.965500	+	0.260403i	$0.0838555\pi$
$829$	20.3926	+	35.3211i	0.708266	+	1.22675i	−0.257234	+	0.966349i	$0.582811\pi$
$830$	6.88402	−	11.9235i	0.238948	−	0.413870i
$831$		0			0
$832$	6.74003	−	11.6741i	0.233668	−	0.404725i
$833$	−9.57041	+	5.09575i	−0.331595	+	0.176557i
$834$		0			0
$835$	−4.70494			−0.162821
$836$	2.63362	+	4.56156i	0.0910856	+	0.157765i
$837$		0			0
$838$	−23.1823	+	40.1529i	−0.800818	+	1.38706i
$839$	−9.60171	−	16.6307i	−0.331488	−	0.574154i	0.651316	−	0.758807i	$-0.274217\pi$
$839$	−9.60171	−	16.6307i	−0.331488	−	0.574154i	−0.982804	+	0.184653i	$0.940884\pi$
$840$		0			0
$841$	14.4981	−	25.1114i	0.499934	−	0.865911i
$842$	−27.3063	−	47.2959i	−0.941036	−	1.62992i
$843$		0			0
$844$	−3.95113	+	6.84355i	−0.136003	+	0.235565i
$845$	9.20374	−	15.9413i	0.316618	−	0.548399i
$846$		0			0
$847$	22.1556	+	6.34612i	0.761276	+	0.218055i
$848$	3.66188	+	6.34256i	0.125749	+	0.217804i
$849$		0			0
$850$	−9.17880			−0.314830
$851$	4.14571			0.142113
$852$		0			0
$853$	−6.95055	−	12.0387i	−0.237982	−	0.412198i	0.722153	−	0.691734i	$-0.243153\pi$
$853$	−6.95055	−	12.0387i	−0.237982	−	0.412198i	−0.960135	+	0.279536i	$0.909819\pi$
$854$	11.3477	−	10.9646i	0.388309	−	0.375202i
$855$		0			0
$856$	3.24469	−	5.61996i	0.110901	−	0.192086i
$857$	28.4919	−	49.3494i	0.973265	−	1.68574i	0.287718	−	0.957715i	$-0.407103\pi$
$857$	28.4919	−	49.3494i	0.973265	−	1.68574i	0.685547	−	0.728029i	$-0.259563\pi$
$858$		0			0
$859$	10.0501	+	17.4073i	0.342905	+	0.593929i	0.984971	−	0.172721i	$-0.0552557\pi$
$859$	10.0501	+	17.4073i	0.342905	+	0.593929i	−0.642066	+	0.766650i	$0.721922\pi$
$860$	−9.46298	+	16.3904i	−0.322685	+	0.558907i
$861$		0			0
$862$	−4.50214	−	7.79794i	−0.153344	−	0.265599i
$863$	3.08893	−	5.35018i	0.105148	−	0.182122i	−0.808650	−	0.588289i	$-0.799802\pi$
$863$	3.08893	−	5.35018i	0.105148	−	0.182122i	0.913799	+	0.406167i	$0.133135\pi$
$864$		0			0
$865$	−6.76781	−	11.7222i	−0.230112	−	0.398566i
$866$	17.8864			0.607803
$867$		0			0
$868$	−10.1774	+	9.83390i	−0.345445	+	0.333784i
$869$	−4.47806	+	7.75623i	−0.151908	+	0.263112i
$870$		0			0
$871$	−17.9436	+	31.0792i	−0.607996	+	1.05308i
$872$	4.62732	+	8.01476i	0.156701	+	0.271414i
$873$		0			0
$874$	33.9396			1.14802
$875$	20.8714	−	20.1669i	0.705583	−	0.681767i
$876$		0			0
$877$	18.6287	+	32.2658i	0.629046	+	1.08954i	0.987743	+	0.156086i	$0.0498877\pi$
$877$	18.6287	+	32.2658i	0.629046	+	1.08954i	−0.358697	+	0.933454i	$0.616779\pi$
$878$	−27.2937			−0.921117
$879$		0			0
$880$	−9.79009			−0.330024
$881$	11.7848			0.397041			0.198520	−	0.980097i	$-0.436386\pi$
$881$	11.7848			0.397041			0.198520	+	0.980097i	$0.436386\pi$
$882$		0			0
$883$	−29.2308			−0.983693			−0.491847	−	0.870682i	$-0.663678\pi$
$883$	−29.2308			−0.983693			−0.491847	+	0.870682i	$0.663678\pi$
$884$	11.1453			0.374857
$885$		0			0
$886$	40.3268			1.35480
$887$	14.2581	+	24.6957i	0.478739	+	0.829201i	0.999703	−	0.0243782i	$-0.00776058\pi$
$887$	14.2581	+	24.6957i	0.478739	+	0.829201i	−0.520964	+	0.853579i	$0.674427\pi$
$888$		0			0
$889$	16.1727	−	15.6268i	0.542416	−	0.524107i
$890$	−3.45680			−0.115872
$891$		0			0
$892$	8.14822	+	14.1131i	0.272823	+	0.472543i
$893$	−11.9182	+	20.6430i	−0.398828	+	0.690790i
$894$		0			0
$895$	1.13531	−	1.96642i	0.0379493	−	0.0657301i
$896$	16.2967	−	15.7466i	0.544435	−	0.526058i
$897$		0			0
$898$	−39.5779			−1.32073
$899$	−0.119171	−	0.206410i	−0.00397456	−	0.00688414i
$900$		0			0
$901$	−1.17002	+	2.02653i	−0.0389790	+	0.0675135i
$902$	12.5693	+	21.7707i	0.418513	+	0.724885i
$903$		0			0
$904$	8.14183	−	14.1021i	0.270793	−	0.469028i
$905$	−11.3415	−	19.6440i	−0.377003	−	0.652989i
$906$		0			0
$907$	3.94577	−	6.83428i	0.131017	−	0.226929i	−0.793052	−	0.609154i	$-0.791509\pi$
$907$	3.94577	−	6.83428i	0.131017	−	0.226929i	0.924069	+	0.382226i	$0.124842\pi$
$908$	7.77317	−	13.4635i	0.257962	−	0.446803i
$909$		0			0
$910$	−24.2029	+	23.3860i	−0.802319	+	0.775237i
$911$	14.2206	+	24.6308i	0.471150	+	0.816055i	0.999455	−	0.0329991i	$-0.0105058\pi$
$911$	14.2206	+	24.6308i	0.471150	+	0.816055i	−0.528306	+	0.849054i	$0.677173\pi$
$912$		0			0
$913$	−8.47625			−0.280523
$914$	74.8013			2.47421
$915$		0			0
$916$	6.71206	+	11.6256i	0.221773	+	0.384121i
$917$	−5.12118	−	1.46688i	−0.169116	−	0.0484406i
$918$		0			0
$919$	3.99271	−	6.91558i	0.131707	−	0.228124i	−0.792627	−	0.609706i	$-0.791287\pi$
$919$	3.99271	−	6.91558i	0.131707	−	0.228124i	0.924335	+	0.381582i	$0.124621\pi$
$920$	−5.51590	+	9.55382i	−0.181854	+	0.314980i
$921$		0			0
$922$	−2.60610	−	4.51390i	−0.0858274	−	0.148657i
$923$	−31.9110	+	55.2714i	−1.05036	+	1.81928i
$924$		0			0
$925$	0.906337	+	1.56982i	0.0298002	+	0.0516154i
$926$	−25.6529	+	44.4322i	−0.843008	+	1.46013i
$927$		0			0
$928$	−0.206895	−	0.358353i	−0.00679167	−	0.0117635i
$929$	−18.8006			−0.616829			−0.308414	−	0.951252i	$-0.599798\pi$
$929$	−18.8006			−0.616829			−0.308414	+	0.951252i	$0.599798\pi$
$930$		0			0
$931$	14.8712	+	9.28068i	0.487385	+	0.304162i
$932$	13.4081	−	23.2234i	0.439196	−	0.760709i
$933$		0			0
$934$	24.5288	−	42.4852i	0.802608	−	1.39016i
$935$	−1.56403	−	2.70898i	−0.0511493	−	0.0885932i
$936$		0			0
$937$	48.5788			1.58700			0.793500	−	0.608570i	$-0.208256\pi$
$937$	48.5788			1.58700			0.793500	+	0.608570i	$0.208256\pi$
$938$	24.2895	−	23.4696i	0.793081	−	0.766310i
$939$		0			0
$940$	8.83094	+	15.2956i	0.288034	+	0.498889i
$941$	−20.4851			−0.667795			−0.333898	−	0.942609i	$-0.608364\pi$
$941$	−20.4851			−0.667795			−0.333898	+	0.942609i	$0.608364\pi$
$942$		0			0
$943$	66.4220			2.16300
$944$	−40.9312			−1.33220
$945$		0			0
$946$	28.4148			0.923843
$947$	14.8505			0.482576			0.241288	−	0.970454i	$-0.422430\pi$
$947$	14.8505			0.482576			0.241288	+	0.970454i	$0.422430\pi$
$948$		0			0
$949$	14.2791			0.463519
$950$	7.41989	+	12.8516i	0.240733	+	0.416962i
$951$		0			0
$952$	4.42363	+	1.26708i	0.143371	+	0.0410662i
$953$	−46.4678			−1.50524			−0.752620	−	0.658456i	$-0.771210\pi$
$953$	−46.4678			−1.50524			−0.752620	+	0.658456i	$0.771210\pi$
$954$		0			0
$955$	−15.1454	−	26.2326i	−0.490094	−	0.848868i
$956$	0.270584	−	0.468665i	0.00875130	−	0.0151577i
$957$		0			0
$958$	−29.0724	+	50.3548i	−0.939285	+	1.62689i
$959$	−1.42092	−	5.69201i	−0.0458838	−	0.183804i
$960$		0			0
$961$	−16.1947			−0.522409
$962$	−2.68380	−	4.64847i	−0.0865291	−	0.149873i
$963$		0			0
$964$	−7.39301	+	12.8051i	−0.238113	+	0.412423i
$965$	4.12905	+	7.15172i	0.132919	+	0.230222i
$966$		0			0
$967$	0.863670	−	1.49592i	0.0277738	−	0.0481056i	−0.851804	−	0.523860i	$-0.824492\pi$
$967$	0.863670	−	1.49592i	0.0277738	−	0.0481056i	0.879578	+	0.475754i	$0.157825\pi$
$968$	−4.89045	−	8.47050i	−0.157185	−	0.272252i
$969$		0			0
$970$	14.9843	−	25.9536i	0.481118	−	0.833320i
$971$	3.78085	−	6.54863i	0.121333	−	0.210156i	−0.798960	−	0.601384i	$-0.794616\pi$
$971$	3.78085	−	6.54863i	0.121333	−	0.210156i	0.920294	+	0.391228i	$0.127950\pi$
$972$		0			0
$973$	−0.484024	−	1.93894i	−0.0155171	−	0.0621595i
$974$	−0.281870	−	0.488213i	−0.00903169	−	0.0156434i
$975$		0			0
$976$	−15.7027			−0.502633
$977$	56.6202			1.81144			0.905721	−	0.423875i	$-0.139330\pi$
$977$	56.6202			1.81144			0.905721	+	0.423875i	$0.139330\pi$
$978$		0			0
$979$	1.06408	+	1.84305i	0.0340083	+	0.0589041i
$980$	11.4648	−	6.10443i	0.366231	−	0.194999i
$981$		0			0
$982$	16.6997	−	28.9247i	0.532909	−	0.923025i
$983$	16.1486	−	27.9702i	0.515061	−	0.892112i	−0.484786	−	0.874633i	$-0.661103\pi$
$983$	16.1486	−	27.9702i	0.515061	−	0.892112i	0.999847	−	0.0174790i	$-0.00556402\pi$
$984$		0			0
$985$	−6.52033	−	11.2936i	−0.207755	−	0.359842i
$986$	0.0883286	−	0.152990i	0.00281296	−	0.00487218i
$987$		0			0
$988$	−9.00955	−	15.6050i	−0.286632	−	0.496461i
$989$	37.5391	−	65.0197i	1.19367	−	2.06750i
$990$		0			0
$991$	−7.15502	−	12.3929i	−0.227287	−	0.393672i	0.729716	−	0.683750i	$-0.239652\pi$
$991$	−7.15502	−	12.3929i	−0.227287	−	0.393672i	−0.957003	+	0.290078i	$0.906319\pi$
$992$	25.7039			0.816100
$993$		0			0
$994$	43.1965	−	41.7384i	1.37011	−	1.32386i
$995$	5.79247	−	10.0329i	0.183634	−	0.318063i
$996$		0			0
$997$	−28.1262	+	48.7160i	−0.890765	+	1.54285i	−0.0518058	+	0.998657i	$0.516498\pi$
$997$	−28.1262	+	48.7160i	−0.890765	+	1.54285i	−0.838960	+	0.544194i	$0.816836\pi$
$998$	19.6176	+	33.9787i	0.620985	+	1.07558i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.h.b.37.4		10
3.2	odd	2		63.2.h.b.58.2	yes	10
4.3	odd	2		3024.2.q.i.2305.4		10
7.2	even	3		1323.2.f.e.442.2		10
7.3	odd	6		1323.2.g.f.361.2		10
7.4	even	3		189.2.g.b.172.2		10
7.5	odd	6		1323.2.f.f.442.2		10
7.6	odd	2		1323.2.h.f.226.4		10
9.2	odd	6		63.2.g.b.16.4	yes	10
9.4	even	3		567.2.e.e.163.2		10
9.5	odd	6		567.2.e.f.163.4		10
9.7	even	3		189.2.g.b.100.2		10
12.11	even	2		1008.2.q.i.625.2		10
21.2	odd	6		441.2.f.e.148.4		10
21.5	even	6		441.2.f.f.148.4		10
21.11	odd	6		63.2.g.b.4.4	✓	10
21.17	even	6		441.2.g.f.67.4		10
21.20	even	2		441.2.h.f.373.2		10
28.11	odd	6		3024.2.t.i.1873.2		10
36.7	odd	6		3024.2.t.i.289.2		10
36.11	even	6		1008.2.t.i.961.5		10
63.2	odd	6		441.2.f.e.295.4		10
63.4	even	3		567.2.e.e.487.2		10
63.5	even	6		3969.2.a.ba.1.2		5
63.11	odd	6		63.2.h.b.25.2	yes	10
63.16	even	3		1323.2.f.e.883.2		10
63.20	even	6		441.2.g.f.79.4		10
63.23	odd	6		3969.2.a.z.1.2		5
63.25	even	3	inner	189.2.h.b.46.4		10
63.32	odd	6		567.2.e.f.487.4		10
63.34	odd	6		1323.2.g.f.667.2		10
63.38	even	6		441.2.h.f.214.2		10
63.40	odd	6		3969.2.a.bb.1.4		5
63.47	even	6		441.2.f.f.295.4		10
63.52	odd	6		1323.2.h.f.802.4		10
63.58	even	3		3969.2.a.bc.1.4		5
63.61	odd	6		1323.2.f.f.883.2		10
84.11	even	6		1008.2.t.i.193.5		10
252.11	even	6		1008.2.q.i.529.2		10
252.151	odd	6		3024.2.q.i.2881.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	21.11	odd	6
63.2.g.b.16.4	yes	10	9.2	odd	6
63.2.h.b.25.2	yes	10	63.11	odd	6
63.2.h.b.58.2	yes	10	3.2	odd	2
189.2.g.b.100.2		10	9.7	even	3
189.2.g.b.172.2		10	7.4	even	3
189.2.h.b.37.4		10	1.1	even	1	trivial
189.2.h.b.46.4		10	63.25	even	3	inner
441.2.f.e.148.4		10	21.2	odd	6
441.2.f.e.295.4		10	63.2	odd	6
441.2.f.f.148.4		10	21.5	even	6
441.2.f.f.295.4		10	63.47	even	6
441.2.g.f.67.4		10	21.17	even	6
441.2.g.f.79.4		10	63.20	even	6
441.2.h.f.214.2		10	63.38	even	6
441.2.h.f.373.2		10	21.20	even	2
567.2.e.e.163.2		10	9.4	even	3
567.2.e.e.487.2		10	63.4	even	3
567.2.e.f.163.4		10	9.5	odd	6
567.2.e.f.487.4		10	63.32	odd	6
1008.2.q.i.529.2		10	252.11	even	6
1008.2.q.i.625.2		10	12.11	even	2
1008.2.t.i.193.5		10	84.11	even	6
1008.2.t.i.961.5		10	36.11	even	6
1323.2.f.e.442.2		10	7.2	even	3
1323.2.f.e.883.2		10	63.16	even	3
1323.2.f.f.442.2		10	7.5	odd	6
1323.2.f.f.883.2		10	63.61	odd	6
1323.2.g.f.361.2		10	7.3	odd	6
1323.2.g.f.667.2		10	63.34	odd	6
1323.2.h.f.226.4		10	7.6	odd	2
1323.2.h.f.802.4		10	63.52	odd	6
3024.2.q.i.2305.4		10	4.3	odd	2
3024.2.q.i.2881.4		10	252.151	odd	6
3024.2.t.i.289.2		10	36.7	odd	6
3024.2.t.i.1873.2		10	28.11	odd	6
3969.2.a.z.1.2		5	63.23	odd	6
3969.2.a.ba.1.2		5	63.5	even	6
3969.2.a.bb.1.4		5	63.40	odd	6
3969.2.a.bc.1.4		5	63.58	even	3

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.84124 q^{2} +1.39017 q^{4} +(0.667377 + 1.15593i) q^{5} +(1.90267 - 1.83844i) q^{7} -1.12285 q^{8} +O(q^{10})\)	\(q+1.84124 q^{2} +1.39017 q^{4} +(0.667377 + 1.15593i) q^{5} +(1.90267 - 1.83844i) q^{7} -1.12285 q^{8} +(1.22880 + 2.12835i) q^{10} +(0.756508 - 1.31031i) q^{11} +(-2.58800 + 4.48254i) q^{13} +(3.50326 - 3.38501i) q^{14} -4.84777 q^{16} +(-0.774463 - 1.34141i) q^{17} +(-1.25211 + 2.16872i) q^{19} +(0.927765 + 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} +(-3.68039 - 6.37463i) q^{23} +(1.60922 - 2.78725i) q^{25} +(-4.76513 + 8.25344i) q^{26} +(2.64502 - 2.55574i) q^{28} +(0.0309713 + 0.0536439i) q^{29} -3.84777 q^{31} -6.68021 q^{32} +(-1.42597 - 2.46986i) q^{34} +(3.39490 + 0.972416i) q^{35} +(-0.281608 + 0.487760i) q^{37} +(-2.30543 + 3.99313i) q^{38} +(-0.749363 - 1.29794i) q^{40} +(-4.51188 + 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +(1.05167 - 1.82155i) q^{44} +(-6.77649 - 11.7372i) q^{46} +9.51851 q^{47} +(0.240269 - 6.99588i) q^{49} +(2.96296 - 5.13199i) q^{50} +(-3.59775 + 6.23148i) q^{52} +(-0.755374 - 1.30835i) q^{53} +2.01950 q^{55} +(-2.13641 + 2.06429i) q^{56} +(0.0570257 + 0.0987714i) q^{58} +8.44331 q^{59} +3.23917 q^{61} -7.08467 q^{62} -2.60434 q^{64} -6.90868 q^{65} +6.93339 q^{67} +(-1.07663 - 1.86478i) q^{68} +(6.25084 + 1.79045i) q^{70} +12.3304 q^{71} +(-1.37936 - 2.38912i) q^{73} +(-0.518508 + 0.898083i) q^{74} +(-1.74064 + 3.01488i) q^{76} +(-0.969547 - 3.88388i) q^{77} -5.91938 q^{79} +(-3.23529 - 5.60368i) q^{80} +(-8.30746 + 14.3889i) q^{82} +(-2.80111 - 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +(9.39010 + 16.2641i) q^{86} +(-0.849444 + 1.47128i) q^{88} +(-0.703287 + 1.21813i) q^{89} +(3.31680 + 13.2867i) q^{91} +(-5.11636 - 8.86180i) q^{92} +17.5259 q^{94} -3.34251 q^{95} +(-6.09713 - 10.5605i) q^{97} +(0.442393 - 12.8811i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8	\( 10 q + 4 q^{2} + 8 q^{4} - 4 q^{5} - 4 q^{7} + 6 q^{8} - 7 q^{10} - 4 q^{11} - 8 q^{13} + 20 q^{14} - 4 q^{16} - 12 q^{17} + q^{19} - 5 q^{20} - q^{22} - 3 q^{23} - q^{25} - 11 q^{26} - 2 q^{28} - 7 q^{29} + 6 q^{31} - 4 q^{32} + 3 q^{34} - 5 q^{35} - 20 q^{38} - 3 q^{40} - 5 q^{41} - 7 q^{43} + 10 q^{44} + 3 q^{46} + 54 q^{47} - 8 q^{49} - 19 q^{50} - 10 q^{52} + 21 q^{53} + 4 q^{55} - 18 q^{56} - 10 q^{58} + 60 q^{59} + 28 q^{61} + 12 q^{62} - 50 q^{64} - 22 q^{65} + 4 q^{67} - 27 q^{68} + 40 q^{70} + 6 q^{71} + 15 q^{73} + 36 q^{74} + 5 q^{76} - 11 q^{77} + 8 q^{79} - 20 q^{80} - 5 q^{82} - 9 q^{83} - 6 q^{85} + 8 q^{86} - 18 q^{88} - 28 q^{89} - 4 q^{91} - 27 q^{92} + 6 q^{94} - 28 q^{95} - 12 q^{97} - 59 q^{98}+O(q^{100}) \) 10 * q + 4 * q^2 + 8 * q^4 - 4 * q^5 - 4 * q^7 + 6 * q^8 - 7 * q^10 - 4 * q^11 - 8 * q^13 + 20 * q^14 - 4 * q^16 - 12 * q^17 + q^19 - 5 * q^20 - q^22 - 3 * q^23 - q^25 - 11 * q^26 - 2 * q^28 - 7 * q^29 + 6 * q^31 - 4 * q^32 + 3 * q^34 - 5 * q^35 - 20 * q^38 - 3 * q^40 - 5 * q^41 - 7 * q^43 + 10 * q^44 + 3 * q^46 + 54 * q^47 - 8 * q^49 - 19 * q^50 - 10 * q^52 + 21 * q^53 + 4 * q^55 - 18 * q^56 - 10 * q^58 + 60 * q^59 + 28 * q^61 + 12 * q^62 - 50 * q^64 - 22 * q^65 + 4 * q^67 - 27 * q^68 + 40 * q^70 + 6 * q^71 + 15 * q^73 + 36 * q^74 + 5 * q^76 - 11 * q^77 + 8 * q^79 - 20 * q^80 - 5 * q^82 - 9 * q^83 - 6 * q^85 + 8 * q^86 - 18 * q^88 - 28 * q^89 - 4 * q^91 - 27 * q^92 + 6 * q^94 - 28 * q^95 - 12 * q^97 - 59 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more