LMFDB - Embedded newform 252.2.bf.g.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(19,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("252.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bf (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.562828176.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 $ x^8 - 2x^7 + x^6 + 2x^5 - 6x^4 + 4x^3 + 4x^2 - 16x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.4
Root			$-1.33790 + 0.458297i$ of defining polynomial
Character	$\chi$	$=$	252.199
Dual form			252.2.bf.g.19.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06584 + 0.929502i) q^{2} +(0.272050 + 1.98141i) q^{4} +(-2.12403 + 1.22631i) q^{5} +(2.63169 + 0.272415i) q^{7} +(-1.55176 + 2.36475i) q^{8} +O(q^{10})$	\(q+(1.06584 + 0.929502i) q^{2} +(0.272050 + 1.98141i) q^{4} +(-2.12403 + 1.22631i) q^{5} +(2.63169 + 0.272415i) q^{7} +(-1.55176 + 2.36475i) q^{8} +(-3.40374 - 0.667235i) q^{10} +(1.09586 + 0.632697i) q^{11} +2.99744i q^{13} +(2.55176 + 2.73651i) q^{14} +(-3.85198 + 1.07809i) q^{16} +(-1.58759 - 0.916595i) q^{17} +(-2.07993 - 3.60254i) q^{19} +(-3.00766 - 3.87495i) q^{20} +(0.579927 + 1.69296i) q^{22} +(5.83564 - 3.36921i) q^{23} +(0.507662 - 0.879296i) q^{25} +(-2.78613 + 3.19481i) q^{26} +(0.176187 + 5.28857i) q^{28} +9.42323 q^{29} +(4.71989 - 8.17509i) q^{31} +(-5.10769 - 2.43135i) q^{32} +(-0.840146 - 2.45262i) q^{34} +(-5.92385 + 2.64865i) q^{35} +(-3.75572 - 6.50509i) q^{37} +(1.13169 - 5.77304i) q^{38} +(0.396078 - 6.92573i) q^{40} +1.08966i q^{41} +6.27176i q^{43} +(-0.955503 + 2.34348i) q^{44} +(9.35158 + 1.83319i) q^{46} +(-3.67579 - 6.36666i) q^{47} +(6.85158 + 1.43382i) q^{49} +(1.35840 - 0.465320i) q^{50} +(-5.93917 + 0.815456i) q^{52} +(-0.0358262 + 0.0620528i) q^{53} -3.10353 q^{55} +(-4.72795 + 5.80056i) q^{56} +(10.0437 + 8.75892i) q^{58} +(-1.68345 + 2.91583i) q^{59} +(-9.61496 + 5.55120i) q^{61} +(12.6294 - 4.32623i) q^{62} +(-3.18406 - 7.33906i) q^{64} +(-3.67579 - 6.36666i) q^{65} +(-2.43151 - 1.40383i) q^{67} +(1.38425 - 3.39503i) q^{68} +(-8.77582 - 2.68318i) q^{70} -2.92285i q^{71} +(7.01910 + 4.05248i) q^{73} +(2.04349 - 10.4244i) q^{74} +(6.57226 - 5.10126i) q^{76} +(2.71162 + 1.96359i) q^{77} +(-1.54471 + 0.891841i) q^{79} +(6.85964 - 7.01360i) q^{80} +(-1.01284 + 1.16141i) q^{82} +5.33626 q^{83} +4.49611 q^{85} +(-5.82962 + 6.68473i) q^{86} +(-3.19669 + 1.60964i) q^{88} +(-7.42323 + 4.28581i) q^{89} +(-0.816548 + 7.88834i) q^{91} +(8.26338 + 10.6462i) q^{92} +(2.00000 - 10.2025i) q^{94} +(8.83564 + 5.10126i) q^{95} -7.10394i q^{97} +(5.96998 + 7.89679i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8}+O(q^{10}) $ 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8	$ 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8} - 5 q^{10} - 6 q^{11} + 12 q^{14} - 17 q^{16} - 6 q^{19} - 22 q^{20} - 6 q^{22} + 2 q^{25} - 18 q^{26} + 13 q^{28} + 16 q^{29} + 6 q^{31} + 9 q^{32} - 28 q^{34} + 12 q^{35} + 6 q^{37} - 10 q^{38} - 17 q^{40} + 23 q^{44} + 24 q^{46} - 4 q^{47} + 4 q^{49} - 2 q^{50} + 16 q^{52} + 4 q^{53} - 8 q^{55} - 41 q^{56} + 37 q^{58} + 14 q^{59} + 12 q^{61} + 48 q^{62} + 2 q^{64} - 4 q^{65} + 42 q^{67} + 26 q^{68} + 3 q^{70} - 18 q^{73} + 10 q^{74} + 44 q^{76} - 8 q^{77} - 6 q^{79} + 39 q^{80} - 10 q^{82} - 4 q^{83} - 32 q^{85} - 36 q^{86} - 37 q^{88} - 34 q^{91} + 28 q^{92} + 16 q^{94} + 24 q^{95} + 53 q^{98}+O(q^{100}) $ 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8 - 5 * q^10 - 6 * q^11 + 12 * q^14 - 17 * q^16 - 6 * q^19 - 22 * q^20 - 6 * q^22 + 2 * q^25 - 18 * q^26 + 13 * q^28 + 16 * q^29 + 6 * q^31 + 9 * q^32 - 28 * q^34 + 12 * q^35 + 6 * q^37 - 10 * q^38 - 17 * q^40 + 23 * q^44 + 24 * q^46 - 4 * q^47 + 4 * q^49 - 2 * q^50 + 16 * q^52 + 4 * q^53 - 8 * q^55 - 41 * q^56 + 37 * q^58 + 14 * q^59 + 12 * q^61 + 48 * q^62 + 2 * q^64 - 4 * q^65 + 42 * q^67 + 26 * q^68 + 3 * q^70 - 18 * q^73 + 10 * q^74 + 44 * q^76 - 8 * q^77 - 6 * q^79 + 39 * q^80 - 10 * q^82 - 4 * q^83 - 32 * q^85 - 36 * q^86 - 37 * q^88 - 34 * q^91 + 28 * q^92 + 16 * q^94 + 24 * q^95 + 53 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.06584	+	0.929502i	0.753666	+	0.657257i
$2$	1.06584	+	0.929502i	0.753666	+	0.657257i
$3$		0			0
$3$		0			0
$4$	0.272050	+	1.98141i	0.136025	+	0.990705i
$5$	−2.12403	+	1.22631i	−0.949894	+	0.548422i	−0.893048	−	0.449961i	$-0.851438\pi$
$5$	−2.12403	+	1.22631i	−0.949894	+	0.548422i	−0.0568460	+	0.998383i	$0.518104\pi$
$6$		0			0
$7$	2.63169	+	0.272415i	0.994685	+	0.102963i
$7$	2.63169	+	0.272415i	0.994685	+	0.102963i
$8$	−1.55176	+	2.36475i	−0.548631	+	0.836065i
$9$		0			0
$10$	−3.40374	−	0.667235i	−1.07636	−	0.210998i
$11$	1.09586	+	0.632697i	0.330415	+	0.190765i	0.656025	−	0.754739i	$-0.272236\pi$
$11$	1.09586	+	0.632697i	0.330415	+	0.190765i	−0.325610	+	0.945504i	$0.605570\pi$
$12$		0			0
$13$			2.99744i			0.831342i	0.909515	+	0.415671i	$0.136453\pi$
$13$			2.99744i			0.831342i	−0.909515	+	0.415671i	$0.863547\pi$
$14$	2.55176	+	2.73651i	0.681987	+	0.731364i
$15$		0			0
$16$	−3.85198	+	1.07809i	−0.962994	+	0.269522i
$17$	−1.58759	−	0.916595i	−0.385047	−	0.222307i	0.294965	−	0.955508i	$-0.404692\pi$
$17$	−1.58759	−	0.916595i	−0.385047	−	0.222307i	−0.680012	+	0.733201i	$0.738025\pi$
$18$		0			0
$19$	−2.07993	−	3.60254i	−0.477168	−	0.826479i	0.522490	−	0.852646i	$-0.325003\pi$
$19$	−2.07993	−	3.60254i	−0.477168	−	0.826479i	−0.999658	+	0.0261665i	$0.991670\pi$
$20$	−3.00766	−	3.87495i	−0.672534	−	0.866466i
$21$		0			0
$22$	0.579927	+	1.69296i	0.123641	+	0.360941i
$23$	5.83564	−	3.36921i	1.21682	−	0.702529i	0.252580	−	0.967576i	$-0.418721\pi$
$23$	5.83564	−	3.36921i	1.21682	−	0.702529i	0.964236	+	0.265047i	$0.0853874\pi$
$24$		0			0
$25$	0.507662	−	0.879296i	0.101532	−	0.175859i
$26$	−2.78613	+	3.19481i	−0.546406	+	0.626554i
$27$		0			0
$28$	0.176187	+	5.28857i	0.0332962	+	0.999446i
$29$	9.42323			1.74985			0.874925	−	0.484258i	$-0.160910\pi$
$29$	9.42323			1.74985			0.874925	+	0.484258i	$0.160910\pi$
$30$		0			0
$31$	4.71989	−	8.17509i	0.847717	−	1.46829i	−0.0355228	−	0.999369i	$-0.511310\pi$
$31$	4.71989	−	8.17509i	0.847717	−	1.46829i	0.883240	−	0.468921i	$-0.155357\pi$
$32$	−5.10769	−	2.43135i	−0.902921	−	0.429806i
$33$		0			0
$34$	−0.840146	−	2.45262i	−0.144084	−	0.420620i
$35$	−5.92385	+	2.64865i	−1.00131	+	0.447703i
$36$		0			0
$37$	−3.75572	−	6.50509i	−0.617436	−	1.06943i	−0.989952	−	0.141405i	$-0.954838\pi$
$37$	−3.75572	−	6.50509i	−0.617436	−	1.06943i	0.372516	−	0.928026i	$-0.378495\pi$
$38$	1.13169	−	5.77304i	0.183584	−	0.936512i
$39$		0			0
$40$	0.396078	−	6.92573i	0.0626254	−	1.09505i
$41$			1.08966i			0.170176i	0.996373	+	0.0850880i	$0.0271171\pi$
$41$			1.08966i			0.170176i	−0.996373	+	0.0850880i	$0.972883\pi$
$42$		0			0
$43$			6.27176i			0.956435i	0.878241	+	0.478218i	$0.158717\pi$
$43$			6.27176i			0.956435i	−0.878241	+	0.478218i	$0.841283\pi$
$44$	−0.955503	+	2.34348i	−0.144047	+	0.353293i
$45$		0			0
$46$	9.35158	+	1.83319i	1.37882	+	0.270289i
$47$	−3.67579	−	6.36666i	−0.536169	−	0.928672i	−0.999106	−	0.0422808i	$-0.986538\pi$
$47$	−3.67579	−	6.36666i	−0.536169	−	0.928672i	0.462937	−	0.886391i	$-0.346796\pi$
$48$		0			0
$49$	6.85158	+	1.43382i	0.978797	+	0.204832i
$50$	1.35840	−	0.465320i	0.192106	−	0.0658063i
$51$		0			0
$52$	−5.93917	+	0.815456i	−0.823615	+	0.113083i
$53$	−0.0358262	+	0.0620528i	−0.00492111	+	0.00852361i	−0.868475	−	0.495732i	$-0.834900\pi$
$53$	−0.0358262	+	0.0620528i	−0.00492111	+	0.00852361i	0.863554	+	0.504256i	$0.168233\pi$
$54$		0			0
$55$	−3.10353			−0.418479
$56$	−4.72795	+	5.80056i	−0.631799	+	0.775132i
$57$		0			0
$58$	10.0437	+	8.75892i	1.31880	+	1.15010i
$59$	−1.68345	+	2.91583i	−0.219167	+	0.379608i	−0.954553	−	0.298040i	$-0.903667\pi$
$59$	−1.68345	+	2.91583i	−0.219167	+	0.379608i	0.735387	+	0.677648i	$0.237001\pi$
$60$		0			0
$61$	−9.61496	+	5.55120i	−1.23107	+	0.710758i	−0.967253	−	0.253815i	$-0.918315\pi$
$61$	−9.61496	+	5.55120i	−1.23107	+	0.710758i	−0.263817	+	0.964573i	$0.584981\pi$
$62$	12.6294	−	4.32623i	1.60394	−	0.549432i
$63$		0			0
$64$	−3.18406	−	7.33906i	−0.398008	−	0.917382i
$65$	−3.67579	−	6.36666i	−0.455926	−	0.789686i
$66$		0			0
$67$	−2.43151	−	1.40383i	−0.297056	−	0.171505i	0.344064	−	0.938946i	$-0.388196\pi$
$67$	−2.43151	−	1.40383i	−0.297056	−	0.171505i	−0.641120	+	0.767441i	$0.721530\pi$
$68$	1.38425	−	3.39503i	0.167865	−	0.411707i
$69$		0			0
$70$	−8.77582	−	2.68318i	−1.04891	−	0.320702i
$71$		−	2.92285i		−	0.346878i	−0.984845	−	0.173439i	$-0.944512\pi$
$71$		−	2.92285i		−	0.346878i	0.984845	−	0.173439i	$-0.0554880\pi$
$72$		0			0
$73$	7.01910	+	4.05248i	0.821523	+	0.474307i	0.850941	−	0.525261i	$-0.176032\pi$
$73$	7.01910	+	4.05248i	0.821523	+	0.474307i	−0.0294183	+	0.999567i	$0.509365\pi$
$74$	2.04349	−	10.4244i	0.237551	−	1.21181i
$75$		0			0
$76$	6.57226	−	5.10126i	0.753890	−	0.585155i
$77$	2.71162	+	1.96359i	0.309017	+	0.223772i
$78$		0			0
$79$	−1.54471	+	0.891841i	−0.173794	+	0.100340i	−0.584374	−	0.811485i	$-0.698660\pi$
$79$	−1.54471	+	0.891841i	−0.173794	+	0.100340i	0.410580	+	0.911825i	$0.365326\pi$
$80$	6.85964	−	7.01360i	0.766931	−	0.784144i
$81$		0			0
$82$	−1.01284	+	1.16141i	−0.111849	+	0.128256i
$83$	5.33626			0.585730			0.292865	−	0.956154i	$-0.405391\pi$
$83$	5.33626			0.585730			0.292865	+	0.956154i	$0.405391\pi$
$84$		0			0
$85$	4.49611			0.487672
$86$	−5.82962	+	6.68473i	−0.628624	+	0.720833i
$87$		0			0
$88$	−3.19669	+	1.60964i	−0.340768	+	0.171589i
$89$	−7.42323	+	4.28581i	−0.786861	+	0.454294i	−0.838856	−	0.544353i	$-0.816775\pi$
$89$	−7.42323	+	4.28581i	−0.786861	+	0.454294i	0.0519952	+	0.998647i	$0.483442\pi$
$90$		0			0
$91$	−0.816548	+	7.88834i	−0.0855974	+	0.826923i
$92$	8.26338	+	10.6462i	0.861517	+	1.10994i
$93$		0			0
$94$	2.00000	−	10.2025i	0.206284	−	1.05231i
$95$	8.83564	+	5.10126i	0.906518	+	0.523378i
$96$		0			0
$97$		−	7.10394i		−	0.721296i	−0.932702	−	0.360648i	$-0.882556\pi$
$97$		−	7.10394i		−	0.721296i	0.932702	−	0.360648i	$-0.117444\pi$
$98$	5.96998	+	7.89679i	0.603059	+	0.797696i
$99$		0			0
$100$	1.88036	+	0.766674i	0.188036	+	0.0766674i
$101$	−0.808273	−	0.466657i	−0.0804262	−	0.0464341i	0.459248	−	0.888308i	$-0.348119\pi$
$101$	−0.808273	−	0.466657i	−0.0804262	−	0.0464341i	−0.539674	+	0.841874i	$0.681452\pi$
$102$		0			0
$103$	2.06460	+	3.57600i	0.203431	+	0.352353i	0.949632	−	0.313368i	$-0.101457\pi$
$103$	2.06460	+	3.57600i	0.203431	+	0.352353i	−0.746200	+	0.665721i	$0.768124\pi$
$104$	−7.08820	−	4.65132i	−0.695055	−	0.456100i
$105$		0			0
$106$	−0.0958634	+	0.0328381i	−0.00931108	+	0.00318952i
$107$	−11.9878	+	6.92118i	−1.15891	+	0.669096i	−0.951042	−	0.309062i	$-0.899985\pi$
$107$	−11.9878	+	6.92118i	−1.15891	+	0.669096i	−0.207866	+	0.978157i	$0.566652\pi$
$108$		0			0
$109$	0.492338	−	0.852754i	0.0471574	−	0.0816791i	−0.841483	−	0.540283i	$-0.818317\pi$
$109$	0.492338	−	0.852754i	0.0471574	−	0.0816791i	0.888641	+	0.458604i	$0.151650\pi$
$110$	−3.30788	−	2.88473i	−0.315394	−	0.275049i
$111$		0			0
$112$	−10.4309	+	1.78786i	−0.985627	+	0.168936i
$113$	−5.03187			−0.473359			−0.236679	−	0.971588i	$-0.576059\pi$
$113$	−5.03187			−0.473359			−0.236679	+	0.971588i	$0.576059\pi$
$114$		0			0
$115$	−8.26338	+	14.3126i	−0.770564	+	1.33466i
$116$	2.56359	+	18.6713i	0.238024	+	1.73359i
$117$		0			0
$118$	−4.50457	+	1.54304i	−0.414679	+	0.142049i
$119$	−3.92835	−	2.84468i	−0.360111	−	0.260771i
$120$		0			0
$121$	−4.69939	−	8.13958i	−0.427217	−	0.739962i
$122$	−15.4079	−	3.02041i	−1.39497	−	0.273455i
$123$		0			0
$124$	17.4823	+	7.12801i	1.56995	+	0.640114i
$125$		−	9.77288i		−	0.874113i
$126$		0			0
$127$			6.38337i			0.566433i	0.959056	+	0.283216i	$0.0914015\pi$
$127$			6.38337i			0.566433i	−0.959056	+	0.283216i	$0.908599\pi$
$128$	3.42795	−	10.7819i	0.302991	−	0.952993i
$129$		0			0
$130$	2.00000	−	10.2025i	0.175412	−	0.894820i
$131$	1.93601	+	3.35327i	0.169150	+	0.292976i	0.938121	−	0.346307i	$-0.112564\pi$
$131$	1.93601	+	3.35327i	0.169150	+	0.292976i	−0.768971	+	0.639283i	$0.779231\pi$
$132$		0			0
$133$	−4.49234	−	10.0474i	−0.389535	−	0.871217i
$134$	−1.28674	−	3.75636i	−0.111158	−	0.324500i
$135$		0			0
$136$	4.63108	−	2.33191i	0.397112	−	0.199960i
$137$	−7.35158	+	12.7333i	−0.628088	+	1.08788i	0.359847	+	0.933011i	$0.382829\pi$
$137$	−7.35158	+	12.7333i	−0.628088	+	1.08788i	−0.987935	+	0.154869i	$0.950504\pi$
$138$		0			0
$139$	2.01655			0.171041			0.0855207	−	0.996336i	$-0.472745\pi$
$139$	2.01655			0.171041			0.0855207	+	0.996336i	$0.472745\pi$
$140$	−6.85964	−	11.0170i	−0.579745	−	0.931107i
$141$		0			0
$142$	2.71679	−	3.11530i	0.227988	−	0.261430i
$143$	−1.89647	+	3.28479i	−0.158591	+	0.274688i
$144$		0			0
$145$	−20.0152	+	11.5558i	−1.66217	+	0.959656i
$146$	3.71448	+	10.8436i	0.307413	+	0.897421i
$147$		0			0
$148$	11.8675	−	9.21133i	0.975504	−	0.757167i
$149$	−0.248055	−	0.429644i	−0.0203215	−	0.0351978i	0.855686	−	0.517496i	$-0.173136\pi$
$149$	−0.248055	−	0.429644i	−0.0203215	−	0.0351978i	−0.876007	+	0.482298i	$0.839802\pi$
$150$		0			0
$151$	−11.4636	−	6.61849i	−0.932891	−	0.538605i	−0.0451665	−	0.998979i	$-0.514382\pi$
$151$	−11.4636	−	6.61849i	−0.932891	−	0.538605i	−0.887725	+	0.460374i	$0.847715\pi$
$152$	11.7466	+	0.671783i	0.952779	+	0.0544888i
$153$		0			0
$154$	1.06500	+	4.61334i	0.0858201	+	0.371753i
$155$			23.1522i			1.85963i
$156$		0			0
$157$	4.38345	+	2.53079i	0.349838	+	0.201979i	0.664614	−	0.747187i	$-0.268596\pi$
$157$	4.38345	+	2.53079i	0.349838	+	0.201979i	−0.314776	+	0.949166i	$0.601929\pi$
$158$	−2.47539	−	0.485251i	−0.196932	−	0.0386045i
$159$		0			0
$160$	13.8305	−	1.09935i	1.09339	−	0.0869115i
$161$	16.2754	−	7.27700i	1.28268	−	0.573508i
$162$		0			0
$163$	10.4232	−	6.01786i	0.816411	−	0.471355i	−0.0327665	−	0.999463i	$-0.510432\pi$
$163$	10.4232	−	6.01786i	0.816411	−	0.471355i	0.849177	+	0.528108i	$0.177098\pi$
$164$	−2.15906	+	0.296442i	−0.168594	+	0.0231482i
$165$		0			0
$166$	5.68762	+	4.96006i	0.441445	+	0.384976i
$167$	7.46424			0.577600			0.288800	−	0.957389i	$-0.406744\pi$
$167$	7.46424			0.577600			0.288800	+	0.957389i	$0.406744\pi$
$168$		0			0
$169$	4.01532			0.308871
$170$	4.79216	+	4.17915i	0.367542	+	0.320526i
$171$		0			0
$172$	−12.4269	+	1.70624i	−0.947545	+	0.130099i
$173$	−3.77932	+	2.18199i	−0.287336	+	0.165894i	−0.636740	−	0.771079i	$-0.719717\pi$
$173$	−3.77932	+	2.18199i	−0.287336	+	0.165894i	0.349404	+	0.936972i	$0.386384\pi$
$174$		0			0
$175$	1.57554	−	2.17574i	0.119100	−	0.164471i
$176$	−4.90334	−	1.25570i	−0.369603	−	0.0946518i
$177$		0			0
$178$	−11.8957	−	2.33191i	−0.891619	−	0.174784i
$179$	−21.2754	−	12.2834i	−1.59020	−	0.918102i	−0.993272	−	0.115808i	$-0.963054\pi$
$179$	−21.2754	−	12.2834i	−1.59020	−	0.918102i	−0.596928	−	0.802295i	$-0.703612\pi$
$180$		0			0
$181$			11.7182i			0.871011i	0.900186	+	0.435505i	$0.143430\pi$
$181$			11.7182i			0.871011i	−0.900186	+	0.435505i	$0.856570\pi$
$182$	−8.20255	+	7.64877i	−0.608013	+	0.566964i
$183$		0			0
$184$	−1.08820	+	19.0280i	−0.0802233	+	1.40277i
$185$	15.9545	+	9.21133i	1.17300	+	0.677231i
$186$		0			0
$187$	−1.15985	−	2.00893i	−0.0848169	−	0.146907i
$188$	11.6150	−	9.01530i	0.847108	−	0.657508i
$189$		0			0
$190$	4.67579	+	13.6499i	0.339217	+	0.990268i
$191$	13.7628	−	7.94594i	0.995839	−	0.574948i	0.0888244	−	0.996047i	$-0.471689\pi$
$191$	13.7628	−	7.94594i	0.995839	−	0.574948i	0.907014	+	0.421099i	$0.138356\pi$
$192$		0			0
$193$	−9.86690	+	17.0900i	−0.710235	+	1.23016i	0.254533	+	0.967064i	$0.418078\pi$
$193$	−9.86690	+	17.0900i	−0.710235	+	1.23016i	−0.964769	+	0.263100i	$0.915255\pi$
$194$	6.60313	−	7.57170i	0.474077	−	0.543616i
$195$		0			0
$196$	−0.977014	+	13.9659i	−0.0697867	+	0.997562i
$197$	−0.998775			−0.0711598			−0.0355799	−	0.999367i	$-0.511328\pi$
$197$	−0.998775			−0.0711598			−0.0355799	+	0.999367i	$0.511328\pi$
$198$		0			0
$199$	−1.35158	+	2.34101i	−0.0958110	+	0.165950i	−0.909947	−	0.414725i	$-0.863878\pi$
$199$	−1.35158	+	2.34101i	−0.0958110	+	0.165950i	0.814136	+	0.580675i	$0.197211\pi$
$200$	1.29154	+	2.56495i	0.0913259	+	0.181370i
$201$		0			0
$202$	−0.427735	−	1.24868i	−0.0300953	−	0.0878565i
$203$	24.7990	+	2.56703i	1.74055	+	0.180170i
$204$		0			0
$205$	−1.33626	−	2.31446i	−0.0933282	−	0.161649i
$206$	−1.12335	+	5.73051i	−0.0782676	+	0.399264i
$207$		0			0
$208$	−3.23151	−	11.5461i	−0.224065	−	0.800577i
$209$		−	5.26385i		−	0.364108i
$210$		0			0
$211$		−	18.1798i		−	1.25155i	−0.780004	−	0.625774i	$-0.784783\pi$
$211$		−	18.1798i		−	1.25155i	0.780004	−	0.625774i	$-0.215217\pi$
$212$	−0.132699	−	0.0541049i	−0.00911378	−	0.00371594i
$213$		0			0
$214$	−19.2104	−	3.76582i	−1.31320	−	0.257426i
$215$	−7.69111	−	13.3214i	−0.524530	−	0.908512i
$216$		0			0
$217$	14.6483	−	20.2285i	0.994392	−	1.37320i
$218$	1.31739	−	0.451274i	0.0892251	−	0.0305642i
$219$		0			0
$220$	−0.844315	−	6.14936i	−0.0569237	−	0.414590i
$221$	2.74744	−	4.75871i	0.184813	−	0.320106i
$222$		0			0
$223$	11.5996			0.776769			0.388385	−	0.921497i	$-0.373033\pi$
$223$	11.5996			0.776769			0.388385	+	0.921497i	$0.373033\pi$
$224$	−12.7795	−	7.78997i	−0.853868	−	0.520489i
$225$		0			0
$226$	−5.36320	−	4.67714i	−0.356754	−	0.311119i
$227$	5.08054	−	8.79975i	0.337207	−	0.584060i	−0.646699	−	0.762745i	$-0.723851\pi$
$227$	5.08054	−	8.79975i	0.337207	−	0.584060i	0.983906	+	0.178685i	$0.0571844\pi$
$228$		0			0
$229$	20.0025	−	11.5485i	1.32181	−	0.763145i	0.337789	−	0.941222i	$-0.390321\pi$
$229$	20.0025	−	11.5485i	1.32181	−	0.763145i	0.984017	+	0.178077i	$0.0569876\pi$
$230$	−22.1111	+	7.57417i	−1.45796	+	0.499426i
$231$		0			0
$232$	−14.6226	+	22.2836i	−0.960022	+	1.46299i
$233$	−3.42774	−	5.93701i	−0.224558	−	0.388947i	0.731628	−	0.681704i	$-0.238761\pi$
$233$	−3.42774	−	5.93701i	−0.224558	−	0.388947i	−0.956187	+	0.292757i	$0.905427\pi$
$234$		0			0
$235$	15.6150	+	9.01530i	1.01861	+	0.588093i
$236$	−6.23543	−	2.54236i	−0.405892	−	0.165494i
$237$		0			0
$238$	−1.54288	−	6.68339i	−0.100010	−	0.433220i
$239$		−	22.2257i		−	1.43766i	−0.695184	−	0.718832i	$-0.744677\pi$
$239$		−	22.2257i		−	1.43766i	0.695184	−	0.718832i	$-0.255323\pi$
$240$		0			0
$241$	13.3605	+	7.71367i	0.860623	+	0.496881i	0.864221	−	0.503112i	$-0.167812\pi$
$241$	13.3605	+	7.71367i	0.860623	+	0.496881i	−0.00359762	+	0.999994i	$0.501145\pi$
$242$	2.55694	−	13.0436i	0.164366	−	0.838476i
$243$		0			0
$244$	−13.6150	−	17.5410i	−0.871608	−	1.12295i
$245$	−16.3113	+	5.35667i	−1.04209	+	0.342225i
$246$		0			0
$247$	10.7984	−	6.23447i	0.687087	−	0.396690i
$248$	12.0079	+	23.8472i	0.762501	+	1.51430i
$249$		0			0
$250$	9.08392	−	10.4164i	0.574517	−	0.658789i
$251$	−22.2954			−1.40727			−0.703636	−	0.710561i	$-0.748441\pi$
$251$	−22.2954			−1.40727			−0.703636	+	0.710561i	$0.748441\pi$
$252$		0			0
$253$	8.52676			0.536073
$254$	−5.93336	+	6.80369i	−0.372292	+	0.426901i
$255$		0			0
$256$	13.6755	−	8.30553i	0.854716	−	0.519096i
$257$	−2.48529	+	1.43488i	−0.155028	+	0.0895055i	−0.575507	−	0.817797i	$-0.695195\pi$
$257$	−2.48529	+	1.43488i	−0.155028	+	0.0895055i	0.420479	+	0.907302i	$0.361862\pi$
$258$		0			0
$259$	−8.11180	−	18.1425i	−0.504043	−	1.12732i
$260$	11.6150	−	9.01530i	0.720329	−	0.559105i
$261$		0			0
$262$	−1.05338	+	5.37359i	−0.0650783	+	0.331981i
$263$	−8.98186	−	5.18568i	−0.553845	−	0.319763i	0.196826	−	0.980438i	$-0.436937\pi$
$263$	−8.98186	−	5.18568i	−0.553845	−	0.319763i	−0.750672	+	0.660676i	$0.770270\pi$
$264$		0			0
$265$		−	0.175736i		−	0.0107954i
$266$	4.55092	−	14.8846i	0.279035	−	0.912632i
$267$		0			0
$268$	2.12007	−	5.19973i	0.129504	−	0.317624i
$269$	−4.48011	−	2.58659i	−0.273157	−	0.157707i	0.357164	−	0.934042i	$-0.383744\pi$
$269$	−4.48011	−	2.58659i	−0.273157	−	0.157707i	−0.630322	+	0.776334i	$0.717077\pi$
$270$		0			0
$271$	−12.1195	−	20.9916i	−0.736209	−	1.27515i	−0.954191	−	0.299198i	$-0.903281\pi$
$271$	−12.1195	−	20.9916i	−0.736209	−	1.27515i	0.217982	−	0.975953i	$-0.430053\pi$
$272$	7.10353	+	1.81914i	0.430714	+	0.110302i
$273$		0			0
$274$	−19.6713	+	6.73842i	−1.18839	+	0.407083i
$275$	1.11266	−	0.642393i	0.0670957	−	0.0387377i
$276$		0			0
$277$	1.50766	−	2.61135i	0.0905866	−	0.156901i	−0.817171	−	0.576395i	$-0.804459\pi$
$277$	1.50766	−	2.61135i	0.0905866	−	0.156901i	0.907758	+	0.419494i	$0.137792\pi$
$278$	2.14933	+	1.87439i	0.128908	+	0.112418i
$279$		0			0
$280$	2.92902	−	18.1185i	0.175043	−	1.08279i
$281$	6.91922			0.412766			0.206383	−	0.978471i	$-0.433831\pi$
$281$	6.91922			0.412766			0.206383	+	0.978471i	$0.433831\pi$
$282$		0			0
$283$	−10.2870	+	17.8176i	−0.611497	+	1.05914i	0.379491	+	0.925195i	$0.376099\pi$
$283$	−10.2870	+	17.8176i	−0.611497	+	1.05914i	−0.990988	+	0.133949i	$0.957234\pi$
$284$	5.79136	−	0.795162i	0.343654	−	0.0471842i
$285$		0			0
$286$	−5.07457	+	1.73830i	−0.300066	+	0.102788i
$287$	−0.296839	+	2.86764i	−0.0175218	+	0.169272i
$288$		0			0
$289$	−6.81971	−	11.8121i	−0.401159	−	0.694828i
$290$	−32.0742	−	6.28751i	−1.88346	−	0.369215i
$291$		0			0
$292$	−6.12007	+	15.0102i	−0.358150	+	0.878405i
$293$			28.3113i			1.65396i	0.562229	+	0.826982i	$0.309944\pi$
$293$			28.3113i			1.65396i	−0.562229	+	0.826982i	$0.690056\pi$
$294$		0			0
$295$		−	8.25772i		−	0.480783i
$296$	21.2109	+	1.21304i	1.23286	+	0.0705063i
$297$		0			0
$298$	0.134967	−	0.688502i	0.00781843	−	0.0398838i
$299$	10.0990	+	17.4920i	0.584042	+	1.01159i
$300$		0			0
$301$	−1.70852	+	16.5053i	−0.0984775	+	0.951352i
$302$	−6.06647	−	17.7097i	−0.349086	−	1.01908i
$303$		0			0
$304$	11.8957	+	11.6346i	0.682264	+	0.667288i
$305$	13.6150	−	23.5818i	0.779590	−	1.35029i
$306$		0			0
$307$	−8.65596			−0.494022			−0.247011	−	0.969013i	$-0.579448\pi$
$307$	−8.65596			−0.494022			−0.247011	+	0.969013i	$0.579448\pi$
$308$	−3.15298	+	5.90702i	−0.179658	+	0.336584i
$309$		0			0
$310$	−21.5200	+	24.6766i	−1.22225	+	1.40154i
$311$	4.67129	−	8.09091i	0.264884	−	0.458793i	−0.702649	−	0.711537i	$-0.748000\pi$
$311$	4.67129	−	8.09091i	0.264884	−	0.458793i	0.967533	+	0.252743i	$0.0813329\pi$
$312$		0			0
$313$	−6.38734	+	3.68773i	−0.361034	+	0.208443i	−0.669534	−	0.742781i	$-0.733506\pi$
$313$	−6.38734	+	3.68773i	−0.361034	+	0.208443i	0.308500	+	0.951224i	$0.400173\pi$
$314$	2.31971	+	6.77186i	0.130909	+	0.382158i
$315$		0			0
$316$	−2.18734	−	2.81809i	−0.123048	−	0.158530i
$317$	−1.81514	−	3.14392i	−0.101949	−	0.176580i	0.810539	−	0.585685i	$-0.199174\pi$
$317$	−1.81514	−	3.14392i	−0.101949	−	0.176580i	−0.912487	+	0.409105i	$0.865841\pi$
$318$		0			0
$319$	10.3266	+	5.96205i	0.578177	+	0.333811i
$320$	15.7630	+	11.6837i	0.881178	+	0.653139i
$321$		0			0
$322$	24.1111	+	7.37189i	1.34366	+	0.410820i
$323$			7.62580i			0.424311i
$324$		0			0
$325$	2.63564	+	1.52169i	0.146199	+	0.0844081i
$326$	16.7032	+	3.27432i	0.925103	+	0.181348i
$327$		0			0
$328$	−2.57677	−	1.69089i	−0.142278	−	0.0933638i
$329$	−7.93917	−	17.7564i	−0.437701	−	0.978942i
$330$		0			0
$331$	−0.544164	+	0.314173i	−0.0299100	+	0.0172685i	−0.514880	−	0.857262i	$-0.672164\pi$
$331$	−0.544164	+	0.314173i	−0.0299100	+	0.0172685i	0.484970	+	0.874531i	$0.338830\pi$
$332$	1.45173	+	10.5733i	0.0796741	+	0.580286i
$333$		0			0
$334$	7.95572	+	6.93803i	0.435318	+	0.379632i
$335$	6.88612			0.376229
$336$		0			0
$337$	−22.3119			−1.21541			−0.607704	−	0.794164i	$-0.707909\pi$
$337$	−22.3119			−1.21541			−0.607704	+	0.794164i	$0.707909\pi$
$338$	4.27971	+	3.73225i	0.232786	+	0.203008i
$339$		0			0
$340$	1.22317	+	8.90864i	0.0663356	+	0.483139i
$341$	10.3447	−	5.97252i	0.560198	−	0.323430i
$342$		0			0
$343$	17.6406	+	5.63984i	0.952505	+	0.304523i
$344$	−14.8311	−	9.73229i	−0.799642	−	0.524730i
$345$		0			0
$346$	−6.05633	−	1.18722i	−0.325590	−	0.0638254i
$347$	5.97104	+	3.44738i	0.320542	+	0.185065i	0.651634	−	0.758533i	$-0.274084\pi$
$347$	5.97104	+	3.44738i	0.320542	+	0.185065i	−0.331092	+	0.943598i	$0.607417\pi$
$348$		0			0
$349$			13.4768i			0.721399i	0.932682	+	0.360699i	$0.117462\pi$
$349$			13.4768i			0.721399i	−0.932682	+	0.360699i	$0.882538\pi$
$350$	3.70164	−	0.854532i	0.197861	−	0.0456766i
$351$		0			0
$352$	−4.05903	−	5.89605i	−0.216347	−	0.314260i
$353$	24.7550	+	14.2923i	1.31758	+	0.760702i	0.983338	−	0.181787i	$-0.0581881\pi$
$353$	24.7550	+	14.2923i	1.31758	+	0.760702i	0.334237	+	0.942489i	$0.391521\pi$
$354$		0			0
$355$	3.58431	+	6.20821i	0.190236	+	0.329498i
$356$	−10.5114	−	13.5425i	−0.557105	−	0.717752i
$357$		0			0
$358$	−11.2589	−	32.8677i	−0.595050	−	1.73711i
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	−0.649906	−	0.760014i	$-0.725192\pi$
$359$	−6.00000	+	3.46410i	−0.316668	+	0.182828i	0.333238	+	0.942843i	$0.391859\pi$
$360$		0			0
$361$	0.847808	−	1.46845i	0.0446215	−	0.0772867i
$362$	−10.8921	+	12.4898i	−0.572478	+	0.656451i
$363$		0			0
$364$	−15.8522	+	0.528111i	−0.830881	+	0.0276805i
$365$	−19.8783			−1.04048
$366$		0			0
$367$	6.47184	−	11.2095i	0.337827	−	0.585134i	−0.646197	−	0.763171i	$-0.723641\pi$
$367$	6.47184	−	11.2095i	0.337827	−	0.585134i	0.984024	+	0.178037i	$0.0569748\pi$
$368$	−18.8465	+	19.2695i	−0.982440	+	1.00449i
$369$		0			0
$370$	8.44306	+	24.6476i	0.438934	+	1.28137i
$371$	−0.111188	+	0.153544i	−0.00577257	+	0.00797162i
$372$		0			0
$373$	−1.53954	−	2.66655i	−0.0797141	−	0.138069i	0.823412	−	0.567443i	$-0.192067\pi$
$373$	−1.53954	−	2.66655i	−0.0797141	−	0.138069i	−0.903127	+	0.429374i	$0.858734\pi$
$374$	0.631077	−	3.21929i	0.0326322	−	0.166466i
$375$		0			0
$376$	20.7595	+	1.18722i	1.07059	+	0.0612263i
$377$			28.2456i			1.45472i
$378$		0			0
$379$		−	5.21020i		−	0.267630i	−0.991006	−	0.133815i	$-0.957277\pi$
$379$		−	5.21020i		−	0.267630i	0.991006	−	0.133815i	$-0.0427228\pi$
$380$	−7.70395	+	18.8948i	−0.395205	+	0.969285i
$381$		0			0
$382$	22.0547	+	4.32339i	1.12842	+	0.221204i
$383$	19.4353	+	33.6629i	0.993096	+	1.72009i	0.598134	+	0.801396i	$0.295909\pi$
$383$	19.4353	+	33.6629i	0.993096	+	1.72009i	0.394963	+	0.918697i	$0.370758\pi$
$384$		0			0
$385$	−8.16752	−	0.845446i	−0.416255	−	0.0430879i
$386$	−26.4018	+	9.04395i	−1.34381	+	0.460325i
$387$		0			0
$388$	14.0758	−	1.93263i	0.714592	−	0.0981144i
$389$	−1.86752	+	3.23463i	−0.0946869	+	0.164002i	−0.909478	−	0.415752i	$-0.863518\pi$
$389$	−1.86752	+	3.23463i	−0.0946869	+	0.164002i	0.814791	+	0.579755i	$0.196852\pi$
$390$		0			0
$391$	−12.3528			−0.624708
$392$	−14.0227	+	13.9773i	−0.708251	+	0.705961i
$393$		0			0
$394$	−1.06454	−	0.928364i	−0.0536307	−	0.0467703i
$395$	2.18734	−	3.78859i	0.110057	−	0.190625i
$396$		0			0
$397$	−5.81082	+	3.35488i	−0.291637	+	0.168377i	−0.638680	−	0.769473i	$-0.720519\pi$
$397$	−5.81082	+	3.35488i	−0.291637	+	0.168377i	0.347043	+	0.937849i	$0.387186\pi$
$398$	−3.61655	+	1.23885i	−0.181281	+	0.0620980i
$399$		0			0
$400$	−1.00754	+	3.93433i	−0.0503772	+	0.196717i
$401$	2.92385	+	5.06425i	0.146010	+	0.252897i	0.929749	−	0.368193i	$-0.120024\pi$
$401$	2.92385	+	5.06425i	0.146010	+	0.252897i	−0.783739	+	0.621090i	$0.786690\pi$
$402$		0			0
$403$	24.5044	+	14.1476i	1.22065	+	0.704743i
$404$	0.704748	−	1.72848i	0.0350625	−	0.0859949i
$405$		0			0
$406$	24.0459	+	25.7868i	1.19338	+	1.27978i
$407$		−	9.50492i		−	0.471142i
$408$		0			0
$409$	−26.7299	−	15.4325i	−1.32171	−	0.763089i	−0.337708	−	0.941251i	$-0.609652\pi$
$409$	−26.7299	−	15.4325i	−1.32171	−	0.763089i	−0.984001	+	0.178162i	$0.942985\pi$
$410$	0.727058	−	3.70891i	0.0359068	−	0.183170i
$411$		0			0
$412$	−6.52384	+	5.06368i	−0.321407	+	0.249469i
$413$	−5.22464	+	7.21495i	−0.257088	+	0.355024i
$414$		0			0
$415$	−11.3344	+	6.54389i	−0.556382	+	0.321227i
$416$	7.28783	−	15.3100i	0.357315	−	0.750636i
$417$		0			0
$418$	4.89277	−	5.61045i	0.239313	−	0.274416i
$419$	−29.0866			−1.42097			−0.710487	−	0.703710i	$-0.751525\pi$
$419$	−29.0866			−1.42097			−0.710487	+	0.703710i	$0.751525\pi$
$420$		0			0
$421$	13.8642			0.675702			0.337851	−	0.941200i	$-0.390300\pi$
$421$	13.8642			0.675702			0.337851	+	0.941200i	$0.390300\pi$
$422$	16.8982	−	19.3768i	0.822590	−	0.943250i
$423$		0			0
$424$	−0.0911455	−	0.181011i	−0.00442642	−	0.00879068i
$425$	−1.61192	+	0.930641i	−0.0781895	+	0.0451427i
$426$		0			0
$427$	−26.8158	+	11.9898i	−1.29771	+	0.580226i
$428$	−16.9750	−	21.8699i	−0.820517	−	1.05712i
$429$		0			0
$430$	4.18474	−	21.3475i	0.201806	−	1.02947i
$431$	27.6258	+	15.9498i	1.33069	+	0.768273i	0.985405	−	0.170226i	$-0.0544499\pi$
$431$	27.6258	+	15.9498i	1.33069	+	0.768273i	0.345282	+	0.938499i	$0.387783\pi$
$432$		0			0
$433$			9.82239i			0.472034i	0.971749	+	0.236017i	$0.0758421\pi$
$433$			9.82239i			0.472034i	−0.971749	+	0.236017i	$0.924158\pi$
$434$	34.4153	−	7.94485i	1.65199	−	0.381365i
$435$		0			0
$436$	1.82360	+	0.743532i	0.0873345	+	0.0356087i
$437$	−24.2754	−	14.0154i	−1.16125	−	0.670449i
$438$		0			0
$439$	8.51989	+	14.7569i	0.406632	+	0.704308i	0.994510	−	0.104642i	$-0.0333697\pi$
$439$	8.51989	+	14.7569i	0.406632	+	0.704308i	−0.587878	+	0.808950i	$0.700036\pi$
$440$	4.81594	−	7.33906i	0.229591	−	0.349876i
$441$		0			0
$442$	7.35158	−	2.51829i	0.349679	−	0.119783i
$443$	−7.30000	+	4.21466i	−0.346833	+	0.200244i	−0.663290	−	0.748363i	$-0.730840\pi$
$443$	−7.30000	+	4.21466i	−0.346833	+	0.200244i	0.316456	+	0.948607i	$0.397507\pi$
$444$		0			0
$445$	10.5114	−	18.2063i	0.498290	−	0.863063i
$446$	12.3634	+	10.7819i	0.585425	+	0.510537i
$447$		0			0
$448$	−6.38020	−	20.1815i	−0.301436	−	0.953486i
$449$	−9.64064			−0.454970			−0.227485	−	0.973782i	$-0.573050\pi$
$449$	−9.64064			−0.454970			−0.227485	+	0.973782i	$0.573050\pi$
$450$		0			0
$451$	−0.689424	+	1.19412i	−0.0324637	+	0.0562288i
$452$	−1.36892	−	9.97021i	−0.0643887	−	0.468959i
$453$		0			0
$454$	13.5945	−	4.65680i	0.638020	−	0.218554i
$455$	−7.93917	−	17.7564i	−0.372194	−	0.832433i
$456$		0			0
$457$	14.5229	+	25.1543i	0.679351	+	1.17667i	0.975177	+	0.221429i	$0.0710720\pi$
$457$	14.5229	+	25.1543i	0.679351	+	1.17667i	−0.295825	+	0.955242i	$0.595595\pi$
$458$	32.0539	+	6.28353i	1.49778	+	0.293610i
$459$		0			0
$460$	−30.6072	−	12.4794i	−1.42707	−	0.581855i
$461$		−	23.9796i		−	1.11684i	−0.829559	−	0.558420i	$-0.811408\pi$
$461$		−	23.9796i		−	1.11684i	0.829559	−	0.558420i	$-0.188592\pi$
$462$		0			0
$463$			28.4975i			1.32439i	0.749331	+	0.662196i	$0.230375\pi$
$463$			28.4975i			1.32439i	−0.749331	+	0.662196i	$0.769625\pi$
$464$	−36.2981	+	10.1591i	−1.68510	+	0.471623i
$465$		0			0
$466$	1.86503	−	9.51402i	0.0863960	−	0.440729i
$467$	−9.29075	−	16.0921i	−0.429925	−	0.744651i	0.566942	−	0.823758i	$-0.308127\pi$
$467$	−9.29075	−	16.0921i	−0.429925	−	0.744651i	−0.996866	+	0.0791067i	$0.974793\pi$
$468$		0			0
$469$	−6.01655	−	4.35683i	−0.277818	−	0.201180i
$470$	8.26338	+	24.1231i	0.381161	+	1.11271i
$471$		0			0
$472$	−4.28287	−	8.50561i	−0.197135	−	0.391502i
$473$	−3.96813	+	6.87300i	−0.182455	+	0.316021i
$474$		0			0
$475$	−4.22360			−0.193792
$476$	4.56776	−	8.55757i	0.209363	−	0.392235i
$477$		0			0
$478$	20.6589	−	23.6892i	0.944915	−	1.08352i
$479$	−14.1707	+	24.5443i	−0.647475	+	1.12146i	0.336249	+	0.941773i	$0.390842\pi$
$479$	−14.1707	+	24.5443i	−0.647475	+	1.12146i	−0.983724	+	0.179686i	$0.942492\pi$
$480$		0			0
$481$	19.4987	−	11.2576i	0.889062	−	0.513300i
$482$	7.07031	+	20.6402i	0.322044	+	0.940134i
$483$		0			0
$484$	14.8494	−	11.5258i	0.674972	−	0.523900i
$485$	8.71162	+	15.0890i	0.395574	+	0.685154i
$486$		0			0
$487$	−35.9498	−	20.7556i	−1.62904	−	0.940528i	−0.984379	−	0.176060i	$-0.943665\pi$
$487$	−35.9498	−	20.7556i	−1.62904	−	0.940528i	−0.644662	−	0.764468i	$-0.723002\pi$
$488$	1.79295	−	31.3511i	0.0811630	−	1.41920i
$489$		0			0
$490$	−22.3643	−	9.45197i	−1.01032	−	0.426996i
$491$		−	1.72728i		−	0.0779509i	−0.999240	−	0.0389755i	$-0.987591\pi$
$491$		−	1.72728i		−	0.0779509i	0.999240	−	0.0389755i	$-0.0124094\pi$
$492$		0			0
$493$	−14.9602	−	8.63729i	−0.673774	−	0.389004i
$494$	17.3044	+	3.39218i	0.778561	+	0.152621i
$495$		0			0
$496$	−9.36745	+	36.5787i	−0.420611	+	1.64243i
$497$	0.796226	−	7.69203i	0.0357156	−	0.345035i
$498$		0			0
$499$	−36.6216	+	21.1435i	−1.63941	+	0.946514i	−0.658373	+	0.752691i	$0.728755\pi$
$499$	−36.6216	+	21.1435i	−1.63941	+	0.946514i	−0.981037	+	0.193822i	$0.937911\pi$
$500$	19.3641	−	2.65872i	0.865988	−	0.118901i
$501$		0			0
$502$	−23.7634	−	20.7236i	−1.06061	−	0.924940i
$503$	−4.23770			−0.188950			−0.0944748	−	0.995527i	$-0.530117\pi$
$503$	−4.23770			−0.188950			−0.0944748	+	0.995527i	$0.530117\pi$
$504$		0			0
$505$	2.28906			0.101862
$506$	9.08820	+	7.92564i	0.404020	+	0.352338i
$507$		0			0
$508$	−12.6481	+	1.73660i	−0.561168	+	0.0770491i
$509$	36.1788	−	20.8878i	1.60360	−	0.925836i	0.612836	−	0.790210i	$-0.290029\pi$
$509$	36.1788	−	20.8878i	1.60360	−	0.925836i	0.990760	−	0.135626i	$-0.0433046\pi$
$510$		0			0
$511$	17.3681	+	12.5770i	0.768321	+	0.556372i
$512$	22.2959	+	3.85896i	0.985350	+	0.170544i
$513$		0			0
$514$	−3.98266	−	0.780720i	−0.175668	−	0.0344361i
$515$	−8.77055	−	5.06368i	−0.386476	−	0.223132i
$516$		0			0
$517$		−	9.30265i		−	0.409130i
$518$	8.21758	−	26.8770i	0.361060	−	1.18091i
$519$		0			0
$520$	20.7595	+	1.18722i	0.910364	+	0.0520631i
$521$	−30.2681	−	17.4753i	−1.32607	−	0.765607i	−0.341381	−	0.939925i	$-0.610895\pi$
$521$	−30.2681	−	17.4753i	−1.32607	−	0.765607i	−0.984689	+	0.174318i	$0.944228\pi$
$522$		0			0
$523$	6.13503	+	10.6262i	0.268266	+	0.464651i	0.968414	−	0.249347i	$-0.0802160\pi$
$523$	6.13503	+	10.6262i	0.268266	+	0.464651i	−0.700148	+	0.713998i	$0.746883\pi$
$524$	−6.11751	+	4.74829i	−0.267245	+	0.207430i
$525$		0			0
$526$	−4.75317	−	13.8758i	−0.207248	−	0.605014i
$527$	−14.9865	+	8.65246i	−0.652822	+	0.376907i
$528$		0			0
$529$	11.2032	−	19.4044i	0.487094	−	0.843671i
$530$	0.163347	−	0.187307i	0.00709534	−	0.00813610i
$531$		0			0
$532$	18.6858	−	11.6346i	0.810133	−	0.504422i
$533$	−3.26619			−0.141474
$534$		0			0
$535$	16.9750	−	29.4016i	0.733893	−	1.27114i
$536$	7.09283	−	3.57149i	0.306364	−	0.154265i
$537$		0			0
$538$	−2.37086	−	6.92118i	−0.102215	−	0.298393i
$539$	6.60122	+	5.90625i	0.284335	+	0.254400i
$540$		0			0
$541$	0.467883	+	0.810397i	0.0201158	+	0.0348417i	0.875908	−	0.482478i	$-0.160263\pi$
$541$	0.467883	+	0.810397i	0.0201158	+	0.0348417i	−0.855792	+	0.517320i	$0.826930\pi$
$542$	6.59424	−	33.6390i	0.283247	−	1.44492i
$543$		0			0
$544$	5.88036	+	8.54167i	0.252118	+	0.366221i
$545$			2.41503i			0.103449i
$546$		0			0
$547$		−	7.13048i		−	0.304877i	−0.988313	−	0.152439i	$-0.951287\pi$
$547$		−	7.13048i		−	0.304877i	0.988313	−	0.152439i	$-0.0487127\pi$
$548$	−27.2299	−	11.1024i	−1.16320	−	0.474271i
$549$		0			0
$550$	1.78302	+	0.349526i	0.0760284	+	0.0149038i
$551$	−19.5996	−	33.9476i	−0.834973	−	1.44621i
$552$		0			0
$553$	−4.30816	+	1.92625i	−0.183201	+	0.0819123i
$554$	4.03419	−	1.38192i	0.171396	−	0.0587120i
$555$		0			0
$556$	0.548603	+	3.99561i	0.0232659	+	0.169452i
$557$	4.97622	−	8.61907i	0.210849	−	0.365202i	−0.741131	−	0.671360i	$-0.765710\pi$
$557$	4.97622	−	8.61907i	0.210849	−	0.365202i	0.951981	+	0.306159i	$0.0990438\pi$
$558$		0			0
$559$	−18.7993			−0.795124
$560$	19.9630	−	16.5889i	0.843593	−	0.701011i
$561$		0			0
$562$	7.37481	+	6.43143i	0.311088	+	0.271293i
$563$	−0.844531	+	1.46277i	−0.0355927	+	0.0616484i	−0.883273	−	0.468859i	$-0.844665\pi$
$563$	−0.844531	+	1.46277i	−0.0355927	+	0.0616484i	0.847680	+	0.530507i	$0.177999\pi$
$564$		0			0
$565$	10.6878	−	6.17063i	0.449641	−	0.259600i
$566$	−27.5258	+	9.42899i	−1.15700	+	0.396330i
$567$		0			0
$568$	6.91180	+	4.53557i	0.290013	+	0.190308i
$569$	−6.96935	−	12.0713i	−0.292170	−	0.506054i	0.682152	−	0.731210i	$-0.261044\pi$
$569$	−6.96935	−	12.0713i	−0.292170	−	0.506054i	−0.974323	+	0.225156i	$0.927711\pi$
$570$		0			0
$571$	−16.1591	−	9.32947i	−0.676238	−	0.390426i	0.122198	−	0.992506i	$-0.461006\pi$
$571$	−16.1591	−	9.32947i	−0.676238	−	0.390426i	−0.798436	+	0.602079i	$0.794339\pi$
$572$	−7.02446	−	2.86407i	−0.293707	−	0.119753i
$573$		0			0
$574$	−2.98186	+	2.78055i	−0.124461	+	0.116058i
$575$		−	6.84168i		−	0.285318i
$576$		0			0
$577$	29.4591	+	17.0082i	1.22640	+	0.708062i	0.966275	−	0.257513i	$-0.0829031\pi$
$577$	29.4591	+	17.0082i	1.22640	+	0.708062i	0.260125	+	0.965575i	$0.416236\pi$
$578$	3.71061	−	18.9288i	0.154341	−	0.787333i
$579$		0			0
$580$	−28.3419	−	36.5146i	−1.17683	−	1.51619i
$581$	14.0434	+	1.45367i	0.582617	+	0.0603086i
$582$		0			0
$583$	−0.0785213	+	0.0453343i	−0.00325202	+	0.00187755i
$584$	−20.4751	+	10.3099i	−0.847264	+	0.426627i
$585$		0			0
$586$	−26.3154	+	30.1755i	−1.08708	+	1.24654i
$587$	41.9153			1.73003			0.865015	−	0.501746i	$-0.167309\pi$
$587$	41.9153			1.73003			0.865015	+	0.501746i	$0.167309\pi$
$588$		0			0
$589$	−39.2681			−1.61801
$590$	7.67557	−	8.80145i	0.315998	−	0.362350i
$591$		0			0
$592$	21.4800	+	21.0085i	0.882822	+	0.863443i
$593$	−21.1354	+	12.2025i	−0.867927	+	0.501098i	−0.866659	−	0.498901i	$-0.833737\pi$
$593$	−21.1354	+	12.2025i	−0.867927	+	0.501098i	−0.00126806	+	0.999999i	$0.500404\pi$
$594$		0			0
$595$	11.8324	+	1.22481i	0.485080	+	0.0502121i
$596$	0.783818	−	0.608384i	0.0321064	−	0.0249204i
$597$		0			0
$598$	−5.49489	+	28.0308i	−0.224703	+	1.14627i
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	0.820416	−	0.571767i	$-0.193742\pi$
$599$	18.0000	+	10.3923i	0.735460	+	0.424618i	−0.0849563	+	0.996385i	$0.527075\pi$
$600$		0			0
$601$		−	10.6623i		−	0.434924i	−0.976069	−	0.217462i	$-0.930222\pi$
$601$		−	10.6623i		−	0.434924i	0.976069	−	0.217462i	$-0.0697778\pi$
$602$	−17.1628	+	16.0041i	−0.699502	+	0.652277i
$603$		0			0
$604$	9.99528	−	24.5146i	0.406702	−	0.997484i
$605$	19.9633	+	11.5258i	0.811622	+	0.468590i
$606$		0			0
$607$	20.0215	+	34.6782i	0.812646	+	1.40754i	0.911006	+	0.412393i	$0.135307\pi$
$607$	20.0215	+	34.6782i	0.812646	+	1.40754i	−0.0983597	+	0.995151i	$0.531360\pi$
$608$	1.86460	+	23.4577i	0.0756196	+	0.951335i
$609$		0			0
$610$	36.4308	−	12.4794i	1.47504	−	0.505276i
$611$	19.0837	−	11.0180i	0.772044	−	0.445740i
$612$		0			0
$613$	−11.2481	+	19.4822i	−0.454305	+	0.786879i	−0.998648	−	0.0519838i	$-0.983446\pi$
$613$	−11.2481	+	19.4822i	−0.454305	+	0.786879i	0.544343	+	0.838863i	$0.316779\pi$
$614$	−9.22591	−	8.04574i	−0.372328	−	0.324700i
$615$		0			0
$616$	−8.85118	+	3.36526i	−0.356624	+	0.135590i
$617$	18.0820			0.727954			0.363977	−	0.931408i	$-0.381419\pi$
$617$	18.0820			0.727954			0.363977	+	0.931408i	$0.381419\pi$
$618$		0			0
$619$	16.0465	−	27.7933i	0.644962	−	1.11711i	−0.339348	−	0.940661i	$-0.610207\pi$
$619$	16.0465	−	27.7933i	0.644962	−	1.11711i	0.984310	−	0.176446i	$-0.0564601\pi$
$620$	−45.8739	+	6.29855i	−1.84234	+	0.252956i
$621$		0			0
$622$	12.4994	−	4.28168i	0.501180	−	0.171680i
$623$	−20.7032	+	9.25671i	−0.829455	+	0.370862i
$624$		0			0
$625$	14.5229	+	25.1543i	0.580915	+	1.00617i
$626$	−10.2357	−	2.00650i	−0.409100	−	0.0801958i
$627$		0			0
$628$	−3.82201	+	9.37392i	−0.152515	+	0.374060i
$629$			13.7699i			0.549041i
$630$		0			0
$631$			2.95509i			0.117640i	0.998269	+	0.0588201i	$0.0187338\pi$
$631$			2.95509i			0.117640i	−0.998269	+	0.0588201i	$0.981266\pi$
$632$	0.288050	−	5.03678i	0.0114580	−	0.200352i
$633$		0			0
$634$	0.987620	−	5.03811i	0.0392234	−	0.200089i
$635$	−7.82798	−	13.5585i	−0.310644	−	0.538051i
$636$		0			0
$637$	−4.29780	+	20.5372i	−0.170285	+	0.813715i
$638$	5.46479	+	15.9532i	0.216353	+	0.631593i
$639$		0			0
$640$	5.94085	+	27.1048i	0.234833	+	1.07141i
$641$	−20.7459	+	35.9329i	−0.819412	+	1.41926i	0.0867040	+	0.996234i	$0.472367\pi$
$641$	−20.7459	+	35.9329i	−0.819412	+	1.41926i	−0.906116	+	0.423029i	$0.860967\pi$
$642$		0			0
$643$	16.7686			0.661290			0.330645	−	0.943755i	$-0.392734\pi$
$643$	16.7686			0.661290			0.330645	+	0.943755i	$0.392734\pi$
$644$	18.8465	+	30.2686i	0.742655	+	1.19275i
$645$		0			0
$646$	−7.08820	+	8.12792i	−0.278882	+	0.319789i
$647$	−9.31180	+	16.1285i	−0.366085	+	0.634077i	−0.988950	−	0.148252i	$-0.952635\pi$
$647$	−9.31180	+	16.1285i	−0.366085	+	0.634077i	0.622865	+	0.782329i	$0.285969\pi$
$648$		0			0
$649$	−3.68967	+	2.13023i	−0.144832	+	0.0836189i
$650$	1.39477	+	4.07172i	0.0547075	+	0.159706i
$651$		0			0
$652$	14.7595	+	19.0155i	0.578026	+	0.744706i
$653$	12.8305	+	22.2230i	0.502095	+	0.869654i	0.999997	+	0.00242072i	$0.000770540\pi$
$653$	12.8305	+	22.2230i	0.502095	+	0.869654i	−0.497902	+	0.867233i	$0.665896\pi$
$654$		0			0
$655$	−8.22428	−	4.74829i	−0.321349	−	0.185531i
$656$	−1.17475	−	4.19734i	−0.0458661	−	0.163879i
$657$		0			0
$658$	8.04270	−	26.3050i	0.313537	−	1.02548i
$659$		−	27.7044i		−	1.07921i	−0.841919	−	0.539604i	$-0.818574\pi$
$659$		−	27.7044i		−	1.07921i	0.841919	−	0.539604i	$-0.181426\pi$
$660$		0			0
$661$	−29.5472	−	17.0591i	−1.14925	−	0.663522i	−0.200548	−	0.979684i	$-0.564272\pi$
$661$	−29.5472	−	17.0591i	−1.14925	−	0.663522i	−0.948705	+	0.316162i	$0.897606\pi$
$662$	−0.872019	−	0.170942i	−0.0338920	−	0.00664385i
$663$		0			0
$664$	−8.28060	+	12.6189i	−0.321350	+	0.489708i
$665$	21.8630	+	15.8319i	0.847811	+	0.613935i
$666$		0			0
$667$	54.9906	−	31.7489i	2.12925	−	1.22932i
$668$	2.03065	+	14.7897i	0.0785681	+	0.572231i
$669$		0			0
$670$	7.33953	+	6.40066i	0.283551	+	0.247279i
$671$	−14.0489			−0.542352
$672$		0			0
$673$	−17.7032			−0.682407			−0.341203	−	0.939990i	$-0.610834\pi$
$673$	−17.7032			−0.682407			−0.341203	+	0.939990i	$0.610834\pi$
$674$	−23.7811	−	20.7390i	−0.916012	−	0.798836i
$675$		0			0
$676$	1.09237	+	7.95601i	0.0420142	+	0.306000i
$677$	35.5808	−	20.5426i	1.36748	−	0.789516i	0.376876	−	0.926264i	$-0.376998\pi$
$677$	35.5808	−	20.5426i	1.36748	−	0.789516i	0.990606	+	0.136747i	$0.0436649\pi$
$678$		0			0
$679$	1.93522	−	18.6954i	0.0742668	−	0.717462i
$680$	−6.97690	+	10.6322i	−0.267552	+	0.407725i
$681$		0			0
$682$	16.5773	+	3.24965i	0.634779	+	0.124436i
$683$	18.3842	+	10.6141i	0.703450	+	0.406137i	0.808631	−	0.588316i	$-0.200209\pi$
$683$	18.3842	+	10.6141i	0.703450	+	0.406137i	−0.105181	+	0.994453i	$0.533542\pi$
$684$		0			0
$685$		−	36.0612i		−	1.37783i
$686$	13.5599	+	22.4082i	0.517721	+	0.855550i
$687$		0			0
$688$	−6.76151	−	24.1587i	−0.257780	−	0.921042i
$689$	−0.186000	−	0.107387i	−0.00708603	−	0.00409112i
$690$		0			0
$691$	−19.4878	−	33.7539i	−0.741352	−	1.28406i	−0.951880	−	0.306472i	$-0.900851\pi$
$691$	−19.4878	−	33.7539i	−0.741352	−	1.28406i	0.210528	−	0.977588i	$-0.432482\pi$
$692$	−5.35158	−	6.89477i	−0.203437	−	0.262100i
$693$		0			0
$694$	3.15985	+	9.22447i	0.119946	+	0.350156i
$695$	−4.28321	+	2.47291i	−0.162471	+	0.0938028i
$696$		0			0
$697$	0.998775	−	1.72993i	0.0378313	−	0.0655257i
$698$	−12.5268	+	14.3642i	−0.474145	+	0.543694i
$699$		0			0
$700$	4.73966	+	2.52989i	0.179142	+	0.0956207i
$701$	−4.28115			−0.161697			−0.0808485	−	0.996726i	$-0.525763\pi$
$701$	−4.28115			−0.161697			−0.0808485	+	0.996726i	$0.525763\pi$
$702$		0			0
$703$	−15.6232	+	27.0602i	−0.589241	+	1.02060i
$704$	1.15410	−	10.0572i	0.0434967	−	0.379043i
$705$		0			0
$706$	13.1002	+	38.2432i	0.493034	+	1.43930i
$707$	−2.00000	−	1.44828i	−0.0752177	−	0.0544682i
$708$		0			0
$709$	21.8796	+	37.8965i	0.821704	+	1.42323i	0.904412	+	0.426660i	$0.140310\pi$
$709$	21.8796	+	37.8965i	0.821704	+	1.42323i	−0.0827080	+	0.996574i	$0.526357\pi$
$710$	−1.95023	+	9.94861i	−0.0731907	+	0.373365i
$711$		0			0
$712$	1.38425	−	24.2046i	0.0518768	−	0.907107i
$713$		−	63.6092i		−	2.38218i
$714$		0			0
$715$		−	9.30265i		−	0.347899i
$716$	18.5504	−	45.4971i	0.693262	−	1.70030i
$717$		0			0
$718$	−9.61496	−	1.88482i	−0.358827	−	0.0703409i
$719$	20.7657	+	35.9672i	0.774429	+	1.34135i	0.935115	+	0.354345i	$0.115296\pi$
$719$	20.7657	+	35.9672i	0.774429	+	1.34135i	−0.160685	+	0.987006i	$0.551370\pi$
$720$		0			0
$721$	4.45924	+	9.97334i	0.166071	+	0.371427i
$722$	2.26856	−	0.777097i	0.0844270	−	0.0289205i
$723$		0			0
$724$	−23.2187	+	3.18795i	−0.862915	+	0.118479i
$725$	4.78382	−	8.28582i	0.177667	−	0.307727i
$726$		0			0
$727$	−7.19963			−0.267020			−0.133510	−	0.991047i	$-0.542625\pi$
$727$	−7.19963			−0.267020			−0.133510	+	0.991047i	$0.542625\pi$
$728$	−17.3869	−	14.1718i	−0.644400	−	0.525241i
$729$		0			0
$730$	−21.1872	−	18.4770i	−0.784174	−	0.683863i
$731$	5.74867	−	9.95698i	0.212622	−	0.368272i
$732$		0			0
$733$	20.9219	−	12.0793i	0.772768	−	0.446158i	−0.0610934	−	0.998132i	$-0.519459\pi$
$733$	20.9219	−	12.0793i	0.772768	−	0.446158i	0.833861	+	0.551974i	$0.186125\pi$
$734$	17.3173	−	5.93205i	0.639192	−	0.218956i
$735$		0			0
$736$	−37.9984	+	3.02041i	−1.40064	+	0.111334i
$737$	−1.77640	−	3.07682i	−0.0654345	−	0.113336i
$738$		0			0
$739$	8.16690	+	4.71516i	0.300424	+	0.173450i	0.642634	−	0.766174i	$-0.277842\pi$
$739$	8.16690	+	4.71516i	0.300424	+	0.173450i	−0.342209	+	0.939624i	$0.611175\pi$
$740$	−13.9110	+	34.1184i	−0.511379	+	1.25422i
$741$		0			0
$742$	−0.261228	+	0.0603051i	−0.00958999	+	0.00221387i
$743$			2.32851i			0.0854248i	0.999087	+	0.0427124i	$0.0135999\pi$
$743$			2.32851i			0.0854248i	−0.999087	+	0.0427124i	$0.986400\pi$
$744$		0			0
$745$	1.05375	+	0.608384i	0.0386065	+	0.0222895i
$746$	0.837662	−	4.27313i	0.0306690	−	0.156451i
$747$		0			0
$748$	3.66497	−	2.84468i	0.134005	−	0.104012i
$749$	−33.4337	+	14.9487i	−1.22164	+	0.546215i
$750$		0			0
$751$	−26.9834	+	15.5789i	−0.984638	+	0.568481i	−0.903667	−	0.428235i	$-0.859135\pi$
$751$	−26.9834	+	15.5789i	−0.984638	+	0.568481i	−0.0809709	+	0.996716i	$0.525802\pi$
$752$	21.0229	+	20.5614i	0.766625	+	0.749797i
$753$		0			0
$754$	−26.2544	+	30.1054i	−0.956128	+	1.09638i
$755$	32.4652			1.18153
$756$		0			0
$757$	−0.559856			−0.0203483			−0.0101742	−	0.999948i	$-0.503239\pi$
$757$	−0.559856			−0.0203483			−0.0101742	+	0.999948i	$0.503239\pi$
$758$	4.84289	−	5.55326i	0.175902	−	0.201704i
$759$		0			0
$760$	−25.7740	+	12.9781i	−0.934922	+	0.470766i
$761$	−39.6196	+	22.8744i	−1.43621	+	0.829196i	−0.997584	−	0.0694744i	$-0.977868\pi$
$761$	−39.6196	+	22.8744i	−1.43621	+	0.829196i	−0.438625	+	0.898670i	$0.644534\pi$
$762$		0			0
$763$	1.52798	−	2.11006i	0.0553167	−	0.0763895i
$764$	19.4883	+	25.1080i	0.705063	+	0.908376i
$765$		0			0
$766$	−10.5747	+	53.9446i	−0.382081	+	1.94910i
$767$	−8.74002	−	5.04606i	−0.315584	−	0.182203i
$768$		0			0
$769$		−	8.33377i		−	0.300524i	−0.988646	−	0.150262i	$-0.951988\pi$
$769$		−	8.33377i		−	0.300524i	0.988646	−	0.150262i	$-0.0480117\pi$
$770$	−7.91946	−	8.49284i	−0.285398	−	0.306061i
$771$		0			0
$772$	−36.5466	−	14.9011i	−1.31534	−	0.536301i
$773$	−26.5674	−	15.3387i	−0.955563	−	0.551695i	−0.0607584	−	0.998153i	$-0.519352\pi$
$773$	−26.5674	−	15.3387i	−0.955563	−	0.551695i	−0.894805	+	0.446458i	$0.852685\pi$
$774$		0			0
$775$	−4.79222	−	8.30037i	−0.172142	−	0.298158i
$776$	16.7990	+	11.0236i	0.603050	+	0.395725i
$777$		0			0
$778$	−4.99708	+	1.71176i	−0.179154	+	0.0613695i
$779$	3.92554	−	2.26641i	0.140647	−	0.0812025i
$780$		0			0
$781$	1.84928	−	3.20304i	0.0661723	−	0.114614i
$782$	−13.1662	−	11.4820i	−0.470821	−	0.410594i
$783$		0			0
$784$	−27.9379	+	1.86355i	−0.997783	+	0.0665555i
$785$	−12.4141			−0.443078
$786$		0			0
$787$	11.0792	−	19.1897i	0.394931	−	0.684040i	−0.598162	−	0.801375i	$-0.704102\pi$
$787$	11.0792	−	19.1897i	0.394931	−	0.684040i	0.993092	+	0.117335i	$0.0374353\pi$
$788$	−0.271717	−	1.97898i	−0.00967952	−	0.0704984i
$789$		0			0
$790$	5.85287	−	2.00491i	0.208236	−	0.0713314i
$791$	−13.2423	−	1.37076i	−0.470843	−	0.0487385i
$792$		0			0
$793$	−16.6394	−	28.8203i	−0.590883	−	1.02344i
$794$	−9.31180	−	1.82539i	−0.330463	−	0.0647807i
$795$		0			0
$796$	−5.00619	−	2.04116i	−0.177440	−	0.0723472i
$797$		−	24.1705i		−	0.856164i	−0.903740	−	0.428082i	$-0.859189\pi$
$797$		−	24.1705i		−	0.856164i	0.903740	−	0.428082i	$-0.140811\pi$
$798$		0			0
$799$			13.4768i			0.476776i
$800$	−4.73086	+	3.25687i	−0.167261	+	0.115148i
$801$		0			0
$802$	−1.59087	+	8.11542i	−0.0561754	+	0.286566i
$803$	5.12798	+	8.88192i	0.180963	+	0.313436i
$804$		0			0
$805$	−25.6456	+	35.4152i	−0.903889	+	1.24822i
$806$	12.9676	+	37.8560i	0.456765	+	1.33342i
$807$		0			0
$808$	2.35777	−	1.18722i	0.0829462	−	0.0417663i
$809$	7.61046	−	13.1817i	0.267569	−	0.463444i	−0.700664	−	0.713491i	$-0.747113\pi$
$809$	7.61046	−	13.1817i	0.267569	−	0.463444i	0.968234	+	0.250047i	$0.0804462\pi$
$810$		0			0
$811$	48.4574			1.70157			0.850785	−	0.525515i	$-0.176127\pi$
$811$	48.4574			1.70157			0.850785	+	0.525515i	$0.176127\pi$
$812$	1.66025	+	49.8354i	0.0582634	+	1.74888i
$813$		0			0
$814$	8.83485	−	10.1308i	0.309661	−	0.355083i
$815$	−14.7595	+	25.5642i	−0.517002	+	0.895474i
$816$		0			0
$817$	22.5943	−	13.0448i	0.790474	−	0.456380i
$818$	−14.1454	−	41.2942i	−0.494581	−	1.44382i
$819$		0			0
$820$	4.22238	−	3.27732i	0.147452	−	0.114449i
$821$	25.7647	+	44.6257i	0.899193	+	1.55745i	0.828528	+	0.559948i	$0.189179\pi$
$821$	25.7647	+	44.6257i	0.899193	+	1.55745i	0.0706654	+	0.997500i	$0.477488\pi$
$822$		0			0
$823$	1.90279	+	1.09858i	0.0663272	+	0.0382941i	0.532797	−	0.846243i	$-0.321141\pi$
$823$	1.90279	+	1.09858i	0.0663272	+	0.0382941i	−0.466470	+	0.884537i	$0.654474\pi$
$824$	−11.6601	−	0.666834i	−0.406199	−	0.0232303i
$825$		0			0
$826$	−12.2750	+	2.83370i	−0.427101	+	0.0985971i
$827$			10.2864i			0.357693i	0.983877	+	0.178846i	$0.0572365\pi$
$827$			10.2864i			0.357693i	−0.983877	+	0.178846i	$0.942763\pi$
$828$		0			0
$829$	0.662548	+	0.382522i	0.0230112	+	0.0132855i	0.511461	−	0.859306i	$-0.329104\pi$
$829$	0.662548	+	0.382522i	0.0230112	+	0.0132855i	−0.488450	+	0.872592i	$0.662438\pi$
$830$	−18.1632	−	3.56054i	−0.630455	−	0.123588i
$831$		0			0
$832$	21.9984	−	9.54406i	0.762658	−	0.330881i
$833$	−9.56326	−	8.55644i	−0.331347	−	0.296463i
$834$		0			0
$835$	−15.8542	+	9.15345i	−0.548659	+	0.316768i
$836$	10.4299	−	1.43203i	0.360724	−	0.0495279i
$837$		0			0
$838$	−31.0018	−	27.0361i	−1.07094	−	0.933946i
$839$	3.50389			0.120968			0.0604839	−	0.998169i	$-0.480736\pi$
$839$	3.50389			0.120968			0.0604839	+	0.998169i	$0.480736\pi$
$840$		0			0
$841$	59.7973			2.06198
$842$	14.7771	+	12.8868i	0.509253	+	0.444110i
$843$		0			0
$844$	36.0216	−	4.94582i	1.23992	−	0.170242i
$845$	−8.52866	+	4.92402i	−0.293395	+	0.169392i
$846$		0			0
$847$	−10.1500	−	22.7010i	−0.348758	−	0.780017i
$848$	0.0711034	−	0.277650i	0.00244170	−	0.00953453i
$849$		0			0
$850$	−2.58309	−	0.506362i	−0.0885991	−	0.0173681i
$851$	−43.8341	−	25.3076i	−1.50261	−	0.867534i
$852$		0			0
$853$		−	25.3974i		−	0.869589i	−0.900530	−	0.434795i	$-0.856821\pi$
$853$		−	25.3974i		−	0.869589i	0.900530	−	0.434795i	$-0.143179\pi$
$854$	−39.7260	−	12.1461i	−1.35940	−	0.415632i
$855$		0			0
$856$	2.23543	−	39.0882i	0.0764055	−	1.33601i
$857$	25.0609	+	14.4689i	0.856065	+	0.494249i	0.862693	−	0.505729i	$-0.168776\pi$
$857$	25.0609	+	14.4689i	0.856065	+	0.494249i	−0.00662744	+	0.999978i	$0.502110\pi$
$858$		0			0
$859$	2.34404	+	4.05999i	0.0799775	+	0.138525i	0.903240	−	0.429136i	$-0.141182\pi$
$859$	2.34404	+	4.05999i	0.0799775	+	0.138525i	−0.823263	+	0.567661i	$0.807848\pi$
$860$	24.3028	−	18.8633i	0.828718	−	0.643235i
$861$		0			0
$862$	14.6195	+	42.6782i	0.497941	+	1.45363i
$863$	37.6419	−	21.7325i	1.28134	−	0.739784i	0.304250	−	0.952592i	$-0.401594\pi$
$863$	37.6419	−	21.7325i	1.28134	−	0.739784i	0.977094	+	0.212808i	$0.0682609\pi$
$864$		0			0
$865$	5.35158	−	9.26921i	0.181959	−	0.315163i
$866$	−9.12993	+	10.4691i	−0.310248	+	0.355756i
$867$		0			0
$868$	44.0661	+	23.5211i	1.49570	+	0.798359i
$869$	−2.25706			−0.0765655
$870$		0			0
$871$	4.20791	−	7.28831i	0.142580	−	0.246955i
$872$	1.25256	+	2.48753i	0.0424169	+	0.0842383i
$873$		0			0
$874$	−12.8465	−	37.5023i	−0.434538	−	1.26854i
$875$	2.66227	−	25.7192i	0.0900013	−	0.869467i
$876$		0			0
$877$	23.0063	+	39.8481i	0.776868	+	1.34558i	0.933738	+	0.357956i	$0.116526\pi$
$877$	23.0063	+	39.8481i	0.776868	+	1.34558i	−0.156870	+	0.987619i	$0.550140\pi$
$878$	−4.63568	+	23.6478i	−0.156447	+	0.798075i
$879$		0			0
$880$	11.9547	−	3.34587i	0.402993	−	0.112789i
$881$			40.8047i			1.37475i	0.726304	+	0.687373i	$0.241236\pi$
$881$			40.8047i			1.37475i	−0.726304	+	0.687373i	$0.758764\pi$
$882$		0			0
$883$			6.06234i			0.204014i	0.994784	+	0.102007i	$0.0325264\pi$
$883$			6.06234i			0.204014i	−0.994784	+	0.102007i	$0.967474\pi$
$884$	10.1764	+	4.14920i	0.342269	+	0.139553i
$885$		0			0
$886$	−11.6982	−	2.29320i	−0.393009	−	0.0770415i
$887$	−22.1276	−	38.3262i	−0.742973	−	1.28687i	−0.951136	−	0.308772i	$-0.900082\pi$
$887$	−22.1276	−	38.3262i	−0.742973	−	1.28687i	0.208163	−	0.978094i	$-0.433251\pi$
$888$		0			0
$889$	−1.73892	+	16.7991i	−0.0583216	+	0.563422i
$890$	28.1264	−	9.63473i	0.942799	−	0.322957i
$891$		0			0
$892$	3.15568	+	22.9836i	0.105660	+	0.769549i
$893$	−15.2908	+	26.4844i	−0.511685	+	0.886265i
$894$		0			0
$895$	60.2528			2.01403
$896$	11.9584	−	27.4408i	0.399504	−	0.916732i
$897$		0			0
$898$	−10.2754	−	8.96100i	−0.342895	−	0.299032i
$899$	44.4766	−	77.0358i	1.48338	−	2.56929i
$900$		0			0
$901$	0.113755	−	0.0656762i	0.00378971	−	0.00218799i
$902$	−1.84475	+	0.631922i	−0.0614236	+	0.0210407i
$903$		0			0
$904$	7.80827	−	11.8991i	0.259699	−	0.395759i
$905$	−14.3702	−	24.8899i	−0.477681	−	0.827368i
$906$		0			0
$907$	−5.54526	−	3.20156i	−0.184127	−	0.106306i	0.405103	−	0.914271i	$-0.367236\pi$
$907$	−5.54526	−	3.20156i	−0.184127	−	0.106306i	−0.589230	+	0.807965i	$0.700569\pi$
$908$	18.8181	+	7.67266i	0.624500	+	0.254626i
$909$		0			0
$910$	8.04270	−	26.3050i	0.266613	−	0.872004i
$911$			48.9687i			1.62241i	0.584765	+	0.811203i	$0.301187\pi$
$911$			48.9687i			1.62241i	−0.584765	+	0.811203i	$0.698813\pi$
$912$		0			0
$913$	5.84781	+	3.37623i	0.193534	+	0.111737i
$914$	−7.90190	+	40.3097i	−0.261372	+	1.33333i
$915$		0			0
$916$	28.3240	+	36.4915i	0.935850	+	1.20571i
$917$	4.18150	+	9.35216i	0.138085	+	0.308835i
$918$		0			0
$919$	−21.2676	+	12.2789i	−0.701554	+	0.405042i	−0.807926	−	0.589284i	$-0.799410\pi$
$919$	−21.2676	+	12.2789i	−0.701554	+	0.405042i	0.106372	+	0.994326i	$0.466077\pi$
$920$	−21.0229	−	41.7506i	−0.693103	−	1.37648i
$921$		0			0
$922$	22.2891	−	25.5585i	0.734051	−	0.841724i
$923$	8.76108			0.288374
$924$		0			0
$925$	−7.62654			−0.250759
$926$	−26.4885	+	30.3739i	−0.870466	+	0.998149i
$927$		0			0
$928$	−48.1310	−	22.9112i	−1.57998	−	0.752096i
$929$	8.51680	−	4.91718i	0.279427	−	0.161327i	−0.353737	−	0.935345i	$-0.615089\pi$
$929$	8.51680	−	4.91718i	0.279427	−	0.161327i	0.633164	+	0.774018i	$0.281756\pi$
$930$		0			0
$931$	−9.08539	−	27.6653i	−0.297762	−	0.906695i
$932$	10.8311	−	8.40692i	0.354786	−	0.275378i
$933$		0			0
$934$	5.05510	−	25.7874i	0.165408	−	0.843790i
$935$	4.92712	+	2.84468i	0.161134	+	0.0930308i
$936$		0			0
$937$			38.1447i			1.24613i	0.782168	+	0.623067i	$0.214114\pi$
$937$			38.1447i			1.24613i	−0.782168	+	0.623067i	$0.785886\pi$
$938$	−2.36303	−	10.2361i	−0.0771555	−	0.334220i
$939$		0			0
$940$	−13.6150	+	33.3923i	−0.444071	+	1.08914i
$941$	−29.7788	−	17.1928i	−0.970760	−	0.560469i	−0.0712922	−	0.997455i	$-0.522712\pi$
$941$	−29.7788	−	17.1928i	−0.970760	−	0.560469i	−0.899468	+	0.436987i	$0.856046\pi$
$942$		0			0
$943$	3.67129	+	6.35886i	0.119554	+	0.207073i
$944$	3.34111	−	13.0466i	0.108744	−	0.424631i
$945$		0			0
$946$	−10.6179	+	3.63716i	−0.345217	+	0.118254i
$947$	−14.2630	+	8.23476i	−0.463486	+	0.267594i	−0.713509	−	0.700646i	$-0.752895\pi$
$947$	−14.2630	+	8.23476i	−0.463486	+	0.267594i	0.250023	+	0.968240i	$0.419562\pi$
$948$		0			0
$949$	−12.1471	+	21.0394i	−0.394311	+	0.682966i
$950$	−4.50170	−	3.92585i	−0.146055	−	0.127371i
$951$		0			0
$952$	12.8228	−	4.87529i	0.415589	−	0.158009i
$953$	52.4540			1.69915			0.849576	−	0.527466i	$-0.176858\pi$
$953$	52.4540			1.69915			0.849576	+	0.527466i	$0.176858\pi$
$954$		0			0
$955$	−19.4883	+	33.7548i	−0.630628	+	1.09228i
$956$	44.0383	−	6.04652i	1.42430	−	0.195558i
$957$		0			0
$958$	−37.9178	+	12.9888i	−1.22507	+	0.419648i
$959$	−22.8158	+	31.5074i	−0.736761	+	1.01743i
$960$		0			0
$961$	−29.0547	−	50.3243i	−0.937250	−	1.62336i
$962$	31.2465	+	6.12524i	1.00743	+	0.197486i
$963$		0			0
$964$	−11.6492	+	28.5711i	−0.375196	+	0.920213i
$965$		−	48.3995i		−	1.55803i
$966$		0			0
$967$		−	16.3573i		−	0.526016i	−0.964794	−	0.263008i	$-0.915285\pi$
$967$		−	16.3573i		−	0.526016i	0.964794	−	0.263008i	$-0.0847146\pi$
$968$	26.5404	+	1.51783i	0.853040	+	0.0487848i
$969$		0			0
$970$	−4.74000	+	24.1800i	−0.152192	+	0.776372i
$971$	11.6591	+	20.1942i	0.374159	+	0.648063i	0.990201	−	0.139651i	$-0.0445981\pi$
$971$	11.6591	+	20.1942i	0.374159	+	0.648063i	−0.616042	+	0.787714i	$0.711265\pi$
$972$		0			0
$973$	5.30693	+	0.549337i	0.170132	+	0.0176109i
$974$	−19.0245	−	55.5377i	−0.609585	−	1.77954i
$975$		0			0
$976$	31.0519	−	31.7489i	0.993948	−	1.01626i
$977$	19.9922	−	34.6275i	0.639608	−	1.10783i	−0.345911	−	0.938267i	$-0.612430\pi$
$977$	19.9922	−	34.6275i	0.639608	−	1.10783i	0.985519	−	0.169566i	$-0.0542366\pi$
$978$		0			0
$979$	−10.8465			−0.346655
$980$	−15.0512	−	30.8620i	−0.480795	−	0.985851i
$981$		0			0
$982$	1.60551	−	1.84101i	0.0512338	−	0.0587490i
$983$	−10.7628	+	18.6417i	−0.343279	+	0.594577i	−0.985040	−	0.172328i	$-0.944871\pi$
$983$	−10.7628	+	18.6417i	−0.343279	+	0.594577i	0.641761	+	0.766905i	$0.278204\pi$
$984$		0			0
$985$	2.12143	−	1.22481i	0.0675943	−	0.0390256i
$986$	−7.91689	−	23.1116i	−0.252125	−	0.736022i
$987$		0			0
$988$	15.2908	+	19.7000i	0.486464	+	0.626741i
$989$	21.1309	+	36.5998i	0.671923	+	1.16381i
$990$		0			0
$991$	9.69666	+	5.59837i	0.308025	+	0.177838i	0.646042	−	0.763302i	$-0.276423\pi$
$991$	9.69666	+	5.59837i	0.308025	+	0.177838i	−0.338018	+	0.941140i	$0.609756\pi$
$992$	−43.9843	+	30.2802i	−1.39650	+	0.961396i
$993$		0			0
$994$	7.99841	−	7.45841i	0.253694	−	0.236567i
$995$		−	6.62982i		−	0.210179i
$996$		0			0
$997$	−49.1699	−	28.3883i	−1.55723	−	0.899066i	−0.997521	−	0.0703755i	$-0.977580\pi$
$997$	−49.1699	−	28.3883i	−1.55723	−	0.899066i	−0.559707	−	0.828690i	$-0.689086\pi$
$998$	−58.6859	−	11.5042i	−1.85767	−	0.364159i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bf.g.199.4		8
3.2	odd	2		84.2.o.a.31.1	yes	8
4.3	odd	2		252.2.bf.f.199.3		8
7.3	odd	6		1764.2.b.j.1567.2		8
7.4	even	3		1764.2.b.i.1567.2		8
7.5	odd	6		252.2.bf.f.19.3		8
12.11	even	2		84.2.o.b.31.2	yes	8
21.2	odd	6		588.2.o.b.19.2		8
21.5	even	6		84.2.o.b.19.2	yes	8
21.11	odd	6		588.2.b.b.391.7		8
21.17	even	6		588.2.b.a.391.7		8
21.20	even	2		588.2.o.d.31.1		8
24.5	odd	2		1344.2.bl.j.703.1		8
24.11	even	2		1344.2.bl.i.703.1		8
28.3	even	6		1764.2.b.i.1567.1		8
28.11	odd	6		1764.2.b.j.1567.1		8
28.19	even	6	inner	252.2.bf.g.19.4		8
84.11	even	6		588.2.b.a.391.8		8
84.23	even	6		588.2.o.d.19.1		8
84.47	odd	6		84.2.o.a.19.1	✓	8
84.59	odd	6		588.2.b.b.391.8		8
84.83	odd	2		588.2.o.b.31.2		8
168.5	even	6		1344.2.bl.i.1279.1		8
168.131	odd	6		1344.2.bl.j.1279.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.o.a.19.1	✓	8	84.47	odd	6
84.2.o.a.31.1	yes	8	3.2	odd	2
84.2.o.b.19.2	yes	8	21.5	even	6
84.2.o.b.31.2	yes	8	12.11	even	2
252.2.bf.f.19.3		8	7.5	odd	6
252.2.bf.f.199.3		8	4.3	odd	2
252.2.bf.g.19.4		8	28.19	even	6	inner
252.2.bf.g.199.4		8	1.1	even	1	trivial
588.2.b.a.391.7		8	21.17	even	6
588.2.b.a.391.8		8	84.11	even	6
588.2.b.b.391.7		8	21.11	odd	6
588.2.b.b.391.8		8	84.59	odd	6
588.2.o.b.19.2		8	21.2	odd	6
588.2.o.b.31.2		8	84.83	odd	2
588.2.o.d.19.1		8	84.23	even	6
588.2.o.d.31.1		8	21.20	even	2
1344.2.bl.i.703.1		8	24.11	even	2
1344.2.bl.i.1279.1		8	168.5	even	6
1344.2.bl.j.703.1		8	24.5	odd	2
1344.2.bl.j.1279.1		8	168.131	odd	6
1764.2.b.i.1567.1		8	28.3	even	6
1764.2.b.i.1567.2		8	7.4	even	3
1764.2.b.j.1567.1		8	28.11	odd	6
1764.2.b.j.1567.2		8	7.3	odd	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bf (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06584 + 0.929502i) q^{2} +(0.272050 + 1.98141i) q^{4} +(-2.12403 + 1.22631i) q^{5} +(2.63169 + 0.272415i) q^{7} +(-1.55176 + 2.36475i) q^{8} +O(q^{10})\)	\(q+(1.06584 + 0.929502i) q^{2} +(0.272050 + 1.98141i) q^{4} +(-2.12403 + 1.22631i) q^{5} +(2.63169 + 0.272415i) q^{7} +(-1.55176 + 2.36475i) q^{8} +(-3.40374 - 0.667235i) q^{10} +(1.09586 + 0.632697i) q^{11} +2.99744i q^{13} +(2.55176 + 2.73651i) q^{14} +(-3.85198 + 1.07809i) q^{16} +(-1.58759 - 0.916595i) q^{17} +(-2.07993 - 3.60254i) q^{19} +(-3.00766 - 3.87495i) q^{20} +(0.579927 + 1.69296i) q^{22} +(5.83564 - 3.36921i) q^{23} +(0.507662 - 0.879296i) q^{25} +(-2.78613 + 3.19481i) q^{26} +(0.176187 + 5.28857i) q^{28} +9.42323 q^{29} +(4.71989 - 8.17509i) q^{31} +(-5.10769 - 2.43135i) q^{32} +(-0.840146 - 2.45262i) q^{34} +(-5.92385 + 2.64865i) q^{35} +(-3.75572 - 6.50509i) q^{37} +(1.13169 - 5.77304i) q^{38} +(0.396078 - 6.92573i) q^{40} +1.08966i q^{41} +6.27176i q^{43} +(-0.955503 + 2.34348i) q^{44} +(9.35158 + 1.83319i) q^{46} +(-3.67579 - 6.36666i) q^{47} +(6.85158 + 1.43382i) q^{49} +(1.35840 - 0.465320i) q^{50} +(-5.93917 + 0.815456i) q^{52} +(-0.0358262 + 0.0620528i) q^{53} -3.10353 q^{55} +(-4.72795 + 5.80056i) q^{56} +(10.0437 + 8.75892i) q^{58} +(-1.68345 + 2.91583i) q^{59} +(-9.61496 + 5.55120i) q^{61} +(12.6294 - 4.32623i) q^{62} +(-3.18406 - 7.33906i) q^{64} +(-3.67579 - 6.36666i) q^{65} +(-2.43151 - 1.40383i) q^{67} +(1.38425 - 3.39503i) q^{68} +(-8.77582 - 2.68318i) q^{70} -2.92285i q^{71} +(7.01910 + 4.05248i) q^{73} +(2.04349 - 10.4244i) q^{74} +(6.57226 - 5.10126i) q^{76} +(2.71162 + 1.96359i) q^{77} +(-1.54471 + 0.891841i) q^{79} +(6.85964 - 7.01360i) q^{80} +(-1.01284 + 1.16141i) q^{82} +5.33626 q^{83} +4.49611 q^{85} +(-5.82962 + 6.68473i) q^{86} +(-3.19669 + 1.60964i) q^{88} +(-7.42323 + 4.28581i) q^{89} +(-0.816548 + 7.88834i) q^{91} +(8.26338 + 10.6462i) q^{92} +(2.00000 - 10.2025i) q^{94} +(8.83564 + 5.10126i) q^{95} -7.10394i q^{97} +(5.96998 + 7.89679i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8	\( 8 q - q^{2} - q^{4} + 2 q^{7} - 4 q^{8} - 5 q^{10} - 6 q^{11} + 12 q^{14} - 17 q^{16} - 6 q^{19} - 22 q^{20} - 6 q^{22} + 2 q^{25} - 18 q^{26} + 13 q^{28} + 16 q^{29} + 6 q^{31} + 9 q^{32} - 28 q^{34} + 12 q^{35} + 6 q^{37} - 10 q^{38} - 17 q^{40} + 23 q^{44} + 24 q^{46} - 4 q^{47} + 4 q^{49} - 2 q^{50} + 16 q^{52} + 4 q^{53} - 8 q^{55} - 41 q^{56} + 37 q^{58} + 14 q^{59} + 12 q^{61} + 48 q^{62} + 2 q^{64} - 4 q^{65} + 42 q^{67} + 26 q^{68} + 3 q^{70} - 18 q^{73} + 10 q^{74} + 44 q^{76} - 8 q^{77} - 6 q^{79} + 39 q^{80} - 10 q^{82} - 4 q^{83} - 32 q^{85} - 36 q^{86} - 37 q^{88} - 34 q^{91} + 28 q^{92} + 16 q^{94} + 24 q^{95} + 53 q^{98}+O(q^{100}) \) 8 * q - q^2 - q^4 + 2 * q^7 - 4 * q^8 - 5 * q^10 - 6 * q^11 + 12 * q^14 - 17 * q^16 - 6 * q^19 - 22 * q^20 - 6 * q^22 + 2 * q^25 - 18 * q^26 + 13 * q^28 + 16 * q^29 + 6 * q^31 + 9 * q^32 - 28 * q^34 + 12 * q^35 + 6 * q^37 - 10 * q^38 - 17 * q^40 + 23 * q^44 + 24 * q^46 - 4 * q^47 + 4 * q^49 - 2 * q^50 + 16 * q^52 + 4 * q^53 - 8 * q^55 - 41 * q^56 + 37 * q^58 + 14 * q^59 + 12 * q^61 + 48 * q^62 + 2 * q^64 - 4 * q^65 + 42 * q^67 + 26 * q^68 + 3 * q^70 - 18 * q^73 + 10 * q^74 + 44 * q^76 - 8 * q^77 - 6 * q^79 + 39 * q^80 - 10 * q^82 - 4 * q^83 - 32 * q^85 - 36 * q^86 - 37 * q^88 - 34 * q^91 + 28 * q^92 + 16 * q^94 + 24 * q^95 + 53 * q^98

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