LMFDB - Embedded newform 324.2.l.a.143.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(35,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("324.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.l (of order $18$, degree $6$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			143.11
Character	$\chi$	$=$	324.143
Dual form			324.2.l.a.179.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.797682 + 1.16778i) q^{2} +(-0.727407 + 1.86303i) q^{4} +(2.42121 - 0.426924i) q^{5} +(-2.49652 + 2.97523i) q^{7} +(-2.75584 + 0.636655i) q^{8} +O(q^{10})$	\(q+(0.797682 + 1.16778i) q^{2} +(-0.727407 + 1.86303i) q^{4} +(2.42121 - 0.426924i) q^{5} +(-2.49652 + 2.97523i) q^{7} +(-2.75584 + 0.636655i) q^{8} +(2.42991 + 2.48688i) q^{10} +(0.0101176 - 0.0573797i) q^{11} +(4.33551 + 1.57800i) q^{13} +(-5.46584 - 0.542086i) q^{14} +(-2.94176 - 2.71036i) q^{16} +(-1.79249 + 1.03489i) q^{17} +(2.46167 + 1.42125i) q^{19} +(-0.965832 + 4.82133i) q^{20} +(0.0750773 - 0.0339557i) q^{22} +(4.37564 - 3.67159i) q^{23} +(0.981522 - 0.357245i) q^{25} +(1.61561 + 6.32166i) q^{26} +(-3.72696 - 6.81529i) q^{28} +(-1.37208 - 3.76976i) q^{29} +(-4.90230 - 5.84234i) q^{31} +(0.818512 - 5.59732i) q^{32} +(-2.63836 - 1.26771i) q^{34} +(-4.77439 + 8.26948i) q^{35} +(2.41051 + 4.17513i) q^{37} +(0.303931 + 4.00838i) q^{38} +(-6.40067 + 2.71801i) q^{40} +(0.375295 - 1.03112i) q^{41} +(9.50027 + 1.67515i) q^{43} +(0.0995405 + 0.0605878i) q^{44} +(7.77797 + 2.18100i) q^{46} +(-4.18449 - 3.51121i) q^{47} +(-1.40388 - 7.96178i) q^{49} +(1.20013 + 0.861232i) q^{50} +(-6.09354 + 6.92934i) q^{52} -10.5337i q^{53} -0.143248i q^{55} +(4.98581 - 9.78869i) q^{56} +(3.30776 - 4.60936i) q^{58} +(-0.277801 - 1.57549i) q^{59} +(-1.61738 - 1.35715i) q^{61} +(2.91207 - 10.3851i) q^{62} +(7.18934 - 3.50904i) q^{64} +(11.1709 + 1.96973i) q^{65} +(2.58470 - 7.10142i) q^{67} +(-0.624168 - 4.09224i) q^{68} +(-13.4654 + 1.02099i) q^{70} +(4.08357 + 7.07295i) q^{71} +(3.26625 - 5.65731i) q^{73} +(-2.95280 + 6.14537i) q^{74} +(-4.43846 + 3.55234i) q^{76} +(0.145459 + 0.173352i) q^{77} +(2.36993 + 6.51134i) q^{79} +(-8.27973 - 5.30644i) q^{80} +(1.50348 - 0.384241i) q^{82} +(10.7082 - 3.89747i) q^{83} +(-3.89816 + 3.27095i) q^{85} +(5.62199 + 12.4304i) q^{86} +(0.00864860 + 0.164571i) q^{88} +(1.85844 + 1.07297i) q^{89} +(-15.5186 + 8.95967i) q^{91} +(3.65742 + 10.8227i) q^{92} +(0.762413 - 7.68738i) q^{94} +(6.56698 + 2.39019i) q^{95} +(-0.895047 + 5.07606i) q^{97} +(8.17774 - 7.99038i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	$ 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) $ 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.797682	+	1.16778i	0.564046	+	0.825743i
$2$	0.797682	+	1.16778i	0.564046	+	0.825743i
$3$		0			0
$3$		0			0
$4$	−0.727407	+	1.86303i	−0.363704	+	0.931515i
$5$	2.42121	−	0.426924i	1.08280	−	0.190926i	0.396345	−	0.918102i	$-0.370278\pi$
$5$	2.42121	−	0.426924i	1.08280	−	0.190926i	0.686452	+	0.727175i	$0.259167\pi$
$6$		0			0
$7$	−2.49652	+	2.97523i	−0.943595	+	1.12453i	0.0484727	+	0.998825i	$0.484565\pi$
$7$	−2.49652	+	2.97523i	−0.943595	+	1.12453i	−0.992067	+	0.125708i	$0.959880\pi$
$8$	−2.75584	+	0.636655i	−0.974338	+	0.225092i
$9$		0			0
$10$	2.42991	+	2.48688i	0.768404	+	0.786421i
$11$	0.0101176	−	0.0573797i	0.00305057	−	0.0173006i	−0.983244	−	0.182292i	$-0.941648\pi$
$11$	0.0101176	−	0.0573797i	0.00305057	−	0.0173006i	0.986295	+	0.164991i	$0.0527596\pi$
$12$		0			0
$13$	4.33551	+	1.57800i	1.20246	+	0.437658i	0.864081	−	0.503353i	$-0.167901\pi$
$13$	4.33551	+	1.57800i	1.20246	+	0.437658i	0.338375	+	0.941011i	$0.390123\pi$
$14$	−5.46584	−	0.542086i	−1.46081	−	0.144879i
$15$		0			0
$16$	−2.94176	−	2.71036i	−0.735439	−	0.677591i
$17$	−1.79249	+	1.03489i	−0.434742	+	0.250998i	−0.701365	−	0.712803i	$-0.747426\pi$
$17$	−1.79249	+	1.03489i	−0.434742	+	0.250998i	0.266623	+	0.963801i	$0.414092\pi$
$18$		0			0
$19$	2.46167	+	1.42125i	0.564746	+	0.326056i	0.755048	−	0.655669i	$-0.227613\pi$
$19$	2.46167	+	1.42125i	0.564746	+	0.326056i	−0.190302	+	0.981726i	$0.560947\pi$
$20$	−0.965832	+	4.82133i	−0.215967	+	1.07808i
$21$		0			0
$22$	0.0750773	−	0.0339557i	0.0160065	−	0.00723937i
$23$	4.37564	−	3.67159i	0.912383	−	0.765580i	−0.0601878	−	0.998187i	$-0.519170\pi$
$23$	4.37564	−	3.67159i	0.912383	−	0.765580i	0.972571	+	0.232607i	$0.0747255\pi$
$24$		0			0
$25$	0.981522	−	0.357245i	0.196304	−	0.0714490i
$26$	1.61561	+	6.32166i	0.316847	+	1.23978i
$27$		0			0
$28$	−3.72696	−	6.81529i	−0.704330	−	1.28797i
$29$	−1.37208	−	3.76976i	−0.254789	−	0.700028i	−0.999468	−	0.0326049i	$-0.989620\pi$
$29$	−1.37208	−	3.76976i	−0.254789	−	0.700028i	0.744679	−	0.667423i	$-0.232603\pi$
$30$		0			0
$31$	−4.90230	−	5.84234i	−0.880479	−	1.04931i	−0.998414	−	0.0562932i	$-0.982072\pi$
$31$	−4.90230	−	5.84234i	−0.880479	−	1.04931i	0.117935	−	0.993021i	$-0.462373\pi$
$32$	0.818512	−	5.59732i	0.144694	−	0.989476i
$33$		0			0
$34$	−2.63836	−	1.26771i	−0.452475	−	0.217410i
$35$	−4.77439	+	8.26948i	−0.807019	+	1.39780i
$36$		0			0
$37$	2.41051	+	4.17513i	0.396286	+	0.686387i	0.993264	−	0.115870i	$-0.0369656\pi$
$37$	2.41051	+	4.17513i	0.396286	+	0.686387i	−0.596979	+	0.802257i	$0.703632\pi$
$38$	0.303931	+	4.00838i	0.0493041	+	0.650246i
$39$		0			0
$40$	−6.40067	+	2.71801i	−1.01203	+	0.429755i
$41$	0.375295	−	1.03112i	0.0586113	−	0.161033i	−0.906931	−	0.421279i	$-0.861581\pi$
$41$	0.375295	−	1.03112i	0.0586113	−	0.161033i	0.965542	+	0.260246i	$0.0838036\pi$
$42$		0			0
$43$	9.50027	+	1.67515i	1.44878	+	0.255459i	0.842028	−	0.539434i	$-0.181362\pi$
$43$	9.50027	+	1.67515i	1.44878	+	0.255459i	0.606750	+	0.794893i	$0.292473\pi$
$44$	0.0995405	+	0.0605878i	0.0150063	+	0.00913395i
$45$		0			0
$46$	7.77797	+	2.18100i	1.14680	+	0.321571i
$47$	−4.18449	−	3.51121i	−0.610371	−	0.512162i	0.284389	−	0.958709i	$-0.408209\pi$
$47$	−4.18449	−	3.51121i	−0.610371	−	0.512162i	−0.894760	+	0.446547i	$0.852654\pi$
$48$		0			0
$49$	−1.40388	−	7.96178i	−0.200554	−	1.13740i
$50$	1.20013	+	0.861232i	0.169723	+	0.121797i
$51$		0			0
$52$	−6.09354	+	6.92934i	−0.845022	+	0.960927i
$53$		−	10.5337i		−	1.44692i	−0.690367	−	0.723459i	$-0.742551\pi$
$53$		−	10.5337i		−	1.44692i	0.690367	−	0.723459i	$-0.257449\pi$
$54$		0			0
$55$		−	0.143248i		−	0.0193155i
$56$	4.98581	−	9.78869i	0.666257	−	1.30807i
$57$		0			0
$58$	3.30776	−	4.60936i	0.434330	−	0.605238i
$59$	−0.277801	−	1.57549i	−0.0361667	−	0.205111i	0.961370	−	0.275260i	$-0.0887638\pi$
$59$	−0.277801	−	1.57549i	−0.0361667	−	0.205111i	−0.997537	+	0.0701484i	$0.977653\pi$
$60$		0			0
$61$	−1.61738	−	1.35715i	−0.207085	−	0.173765i	0.533346	−	0.845897i	$-0.320934\pi$
$61$	−1.61738	−	1.35715i	−0.207085	−	0.173765i	−0.740431	+	0.672132i	$0.765379\pi$
$62$	2.91207	−	10.3851i	0.369833	−	1.31891i
$63$		0			0
$64$	7.18934	−	3.50904i	0.898668	−	0.438630i
$65$	11.1709	+	1.96973i	1.38558	+	0.244314i
$66$		0			0
$67$	2.58470	−	7.10142i	0.315772	−	0.867576i	−0.675691	−	0.737185i	$-0.736155\pi$
$67$	2.58470	−	7.10142i	0.315772	−	0.867576i	0.991463	−	0.130391i	$-0.0416233\pi$
$68$	−0.624168	−	4.09224i	−0.0756915	−	0.496258i
$69$		0			0
$70$	−13.4654	+	1.02099i	−1.60942	+	0.122032i
$71$	4.08357	+	7.07295i	0.484630	+	0.839404i	0.999844	−	0.0176575i	$-0.00562084\pi$
$71$	4.08357	+	7.07295i	0.484630	+	0.839404i	−0.515214	+	0.857062i	$0.672288\pi$
$72$		0			0
$73$	3.26625	−	5.65731i	0.382286	−	0.662138i	−0.609103	−	0.793091i	$-0.708470\pi$
$73$	3.26625	−	5.65731i	0.382286	−	0.662138i	0.991389	+	0.130953i	$0.0418037\pi$
$74$	−2.95280	+	6.14537i	−0.343256	+	0.714384i
$75$		0			0
$76$	−4.43846	+	3.55234i	−0.509126	+	0.407481i
$77$	0.145459	+	0.173352i	0.0165766	+	0.0197552i
$78$		0			0
$79$	2.36993	+	6.51134i	0.266638	+	0.732583i	0.998682	+	0.0513249i	$0.0163444\pi$
$79$	2.36993	+	6.51134i	0.266638	+	0.732583i	−0.732044	+	0.681258i	$0.761433\pi$
$80$	−8.27973	−	5.30644i	−0.925702	−	0.593278i
$81$		0			0
$82$	1.50348	−	0.384241i	0.166032	−	0.0424323i
$83$	10.7082	−	3.89747i	1.17538	−	0.427803i	0.320811	−	0.947143i	$-0.396044\pi$
$83$	10.7082	−	3.89747i	1.17538	−	0.427803i	0.854568	+	0.519340i	$0.173822\pi$
$84$		0			0
$85$	−3.89816	+	3.27095i	−0.422815	+	0.354784i
$86$	5.62199	+	12.4304i	0.606234	+	1.34041i
$87$		0			0
$88$	0.00864860	+	0.164571i	0.000921944	+	0.0175433i
$89$	1.85844	+	1.07297i	0.196995	+	0.113735i	0.595253	−	0.803538i	$-0.297052\pi$
$89$	1.85844	+	1.07297i	0.196995	+	0.113735i	−0.398258	+	0.917273i	$0.630385\pi$
$90$		0			0
$91$	−15.5186	+	8.95967i	−1.62679	+	0.939228i
$92$	3.65742	+	10.8227i	0.381312	+	1.12834i
$93$		0			0
$94$	0.762413	−	7.68738i	0.0786369	−	0.792893i
$95$	6.56698	+	2.39019i	0.673758	+	0.245228i
$96$		0			0
$97$	−0.895047	+	5.07606i	−0.0908783	+	0.515396i	0.905054	+	0.425296i	$0.139830\pi$
$97$	−0.895047	+	5.07606i	−0.0908783	+	0.515396i	−0.995933	+	0.0901005i	$0.971281\pi$
$98$	8.17774	−	7.99038i	0.826076	−	0.807151i
$99$		0			0
$100$	−0.0484086	+	2.08847i	−0.00484086	+	0.208847i
$101$	−8.49605	+	10.1252i	−0.845389	+	1.00750i	0.154421	+	0.988005i	$0.450649\pi$
$101$	−8.49605	+	10.1252i	−0.845389	+	1.00750i	−0.999810	+	0.0194902i	$0.993796\pi$
$102$		0			0
$103$	−1.02704	+	0.181095i	−0.101197	+	0.0178438i	−0.224017	−	0.974585i	$-0.571917\pi$
$103$	−1.02704	+	0.181095i	−0.101197	+	0.0178438i	0.122820	+	0.992429i	$0.460806\pi$
$104$	−12.9526	−	1.58849i	−1.27011	−	0.155764i
$105$		0			0
$106$	12.3010	−	8.40256i	1.19478	−	0.816129i
$107$	−12.4850			−1.20697			−0.603485	−	0.797375i	$-0.706222\pi$
$107$	−12.4850			−1.20697			−0.603485	+	0.797375i	$0.706222\pi$
$108$		0			0
$109$	−19.2545			−1.84425			−0.922123	−	0.386896i	$-0.873547\pi$
$109$	−19.2545			−1.84425			−0.922123	+	0.386896i	$0.873547\pi$
$110$	0.167281	−	0.114266i	0.0159496	−	0.0108948i
$111$		0			0
$112$	15.4081	−	1.98595i	1.45593	−	0.187655i
$113$	−5.13364	+	0.905199i	−0.482932	+	0.0851540i	−0.409814	−	0.912169i	$-0.634406\pi$
$113$	−5.13364	+	0.905199i	−0.482932	+	0.0851540i	−0.0731186	+	0.997323i	$0.523295\pi$
$114$		0			0
$115$	9.02683	−	10.7578i	0.841756	−	1.00317i
$116$	8.02124	+	0.185925i	0.744754	+	0.0172627i
$117$		0			0
$118$	1.61822	−	1.58115i	0.148970	−	0.145557i
$119$	1.39593	−	7.91669i	0.127964	−	0.725722i
$120$		0			0
$121$	10.3334	+	3.76106i	0.939403	+	0.341915i
$122$	0.294686	−	2.97131i	0.0266797	−	0.269010i
$123$		0			0
$124$	14.4504	−	4.88338i	1.29769	−	0.438540i
$125$	−8.42192	+	4.86240i	−0.753279	+	0.434906i
$126$		0			0
$127$	−1.67801	−	0.968801i	−0.148900	−	0.0859672i	0.423699	−	0.905803i	$-0.360731\pi$
$127$	−1.67801	−	0.968801i	−0.148900	−	0.0859672i	−0.572599	+	0.819836i	$0.694065\pi$
$128$	9.83259	+	5.59645i	0.869086	+	0.494661i
$129$		0			0
$130$	6.61060	+	14.6163i	0.579788	+	1.28193i
$131$	−0.358293	+	0.300644i	−0.0313042	+	0.0262674i	−0.658306	−	0.752751i	$-0.728727\pi$
$131$	−0.358293	+	0.300644i	−0.0313042	+	0.0262674i	0.627001	+	0.779018i	$0.284282\pi$
$132$		0			0
$133$	−10.3741	+	3.77588i	−0.899552	+	0.327410i
$134$	10.3546	−	2.64631i	0.894505	−	0.228607i
$135$		0			0
$136$	4.28094	−	3.99320i	0.367088	−	0.342414i
$137$	−1.50159	−	4.12558i	−0.128289	−	0.352472i	0.858874	−	0.512187i	$-0.171165\pi$
$137$	−1.50159	−	4.12558i	−0.128289	−	0.352472i	−0.987163	+	0.159715i	$0.948942\pi$
$138$		0			0
$139$	−5.43008	−	6.47132i	−0.460573	−	0.548890i	0.484908	−	0.874565i	$-0.338853\pi$
$139$	−5.43008	−	6.47132i	−0.460573	−	0.548890i	−0.945482	+	0.325675i	$0.894408\pi$
$140$	−11.9334	−	14.9101i	−1.00855	−	1.26013i
$141$		0			0
$142$	−5.00224	+	10.4107i	−0.419778	+	0.873643i
$143$	0.134410	−	0.232805i	0.0112399	−	0.0194681i
$144$		0			0
$145$	−4.93150	−	8.54161i	−0.409539	−	0.709342i
$146$	9.21191	−	0.698482i	0.762383	−	0.0578068i
$147$		0			0
$148$	−9.53181	+	1.45384i	−0.783510	+	0.119505i
$149$	−3.47719	+	9.55350i	−0.284863	+	0.782653i	0.711902	+	0.702279i	$0.247834\pi$
$149$	−3.47719	+	9.55350i	−0.284863	+	0.782653i	−0.996765	+	0.0803748i	$0.974388\pi$
$150$		0			0
$151$	−2.35013	−	0.414392i	−0.191251	−	0.0337227i	0.0772021	−	0.997015i	$-0.475401\pi$
$151$	−2.35013	−	0.414392i	−0.191251	−	0.0337227i	−0.268453	+	0.963293i	$0.586512\pi$
$152$	−7.68882	−	2.34950i	−0.623646	−	0.190569i
$153$		0			0
$154$	−0.0864058	+	0.308143i	−0.00696278	+	0.0248309i
$155$	−14.3637	−	12.0526i	−1.15372	−	0.968088i
$156$		0			0
$157$	−0.945663	−	5.36312i	−0.0754721	−	0.428024i	−0.999009	−	0.0445136i	$-0.985826\pi$
$157$	−0.945663	−	5.36312i	−0.0754721	−	0.428024i	0.923537	−	0.383510i	$-0.125285\pi$
$158$	−5.71334	+	7.96153i	−0.454529	+	0.633385i
$159$		0			0
$160$	−0.407845	−	13.9017i	−0.0322430	−	1.09903i
$161$			22.1847i			1.74840i
$162$		0			0
$163$			9.76328i			0.764719i	0.924014	+	0.382360i	$0.124888\pi$
$163$			9.76328i			0.764719i	−0.924014	+	0.382360i	$0.875112\pi$
$164$	1.64801	+	1.44923i	0.128688	+	0.113166i
$165$		0			0
$166$	13.0931	+	9.39586i	1.01622	+	0.729260i
$167$	0.806745	+	4.57528i	0.0624278	+	0.354046i	0.999981	+	0.00620306i	$0.00197451\pi$
$167$	0.806745	+	4.57528i	0.0624278	+	0.354046i	−0.937553	+	0.347843i	$0.886914\pi$
$168$		0			0
$169$	6.34803	+	5.32663i	0.488310	+	0.409741i
$170$	−6.92923	−	1.94301i	−0.531448	−	0.149022i
$171$		0			0
$172$	−10.0314	+	16.4808i	−0.764889	+	1.25665i
$173$	−0.867796	−	0.153016i	−0.0659773	−	0.0116336i	0.140562	−	0.990072i	$-0.455109\pi$
$173$	−0.867796	−	0.153016i	−0.0659773	−	0.0116336i	−0.206539	+	0.978438i	$0.566220\pi$
$174$		0			0
$175$	−1.38750	+	3.81213i	−0.104885	+	0.288170i
$176$	−0.185283	+	0.141375i	−0.0139662	+	0.0106565i
$177$		0			0
$178$	0.229454	+	3.02614i	0.0171983	+	0.226819i
$179$	−6.34874	−	10.9963i	−0.474527	−	0.821905i	0.525047	−	0.851073i	$-0.324048\pi$
$179$	−6.34874	−	10.9963i	−0.474527	−	0.821905i	−0.999575	+	0.0291678i	$0.990714\pi$
$180$		0			0
$181$	−3.30529	+	5.72493i	−0.245680	+	0.425530i	−0.962323	−	0.271910i	$-0.912345\pi$
$181$	−3.30529	+	5.72493i	−0.245680	+	0.425530i	0.716643	+	0.697441i	$0.245678\pi$
$182$	−22.8418	−	10.9753i	−1.69315	−	0.813543i
$183$		0			0
$184$	−9.72102	+	12.9041i	−0.716643	+	0.951303i
$185$	7.61882	+	9.07975i	0.560147	+	0.667557i
$186$		0			0
$187$	0.0412462	+	0.113323i	0.00301622	+	0.00828700i
$188$	9.58531	−	5.24176i	0.699081	−	0.382294i
$189$		0			0
$190$	2.44716	+	9.57538i	0.177535	+	0.694671i
$191$	−23.9365	+	8.71219i	−1.73199	+	0.630392i	−0.998769	−	0.0496008i	$-0.984205\pi$
$191$	−23.9365	+	8.71219i	−1.73199	+	0.630392i	−0.733219	+	0.679993i	$0.761983\pi$
$192$		0			0
$193$	−15.7766	+	13.2381i	−1.13562	+	0.952899i	−0.999287	−	0.0377638i	$-0.987977\pi$
$193$	−15.7766	+	13.2381i	−1.13562	+	0.952899i	−0.136334	+	0.990663i	$0.543532\pi$
$194$	−6.64168	+	3.00387i	−0.476845	+	0.215665i
$195$		0			0
$196$	15.8542	+	3.17599i	1.13244	+	0.226857i
$197$	−6.00833	−	3.46891i	−0.428076	−	0.247150i	0.270451	−	0.962734i	$-0.412827\pi$
$197$	−6.00833	−	3.46891i	−0.428076	−	0.247150i	−0.698526	+	0.715584i	$0.746161\pi$
$198$		0			0
$199$	10.0244	−	5.78756i	0.710608	−	0.410270i	−0.100678	−	0.994919i	$-0.532101\pi$
$199$	10.0244	−	5.78756i	0.710608	−	0.410270i	0.811286	+	0.584650i	$0.198768\pi$
$200$	−2.47748	+	1.60940i	−0.175184	+	0.113802i
$201$		0			0
$202$	−18.6011	−	1.84481i	−1.30877	−	0.129800i
$203$	14.6413	+	5.32902i	1.02762	+	0.374024i
$204$		0			0
$205$	0.468460	−	2.65677i	0.0327187	−	0.185557i
$206$	−1.03073	−	1.05490i	−0.0718143	−	0.0734981i
$207$		0			0
$208$	−8.47709	−	16.3929i	−0.587780	−	1.13664i
$209$	0.106457	−	0.126870i	0.00736377	−	0.00877580i
$210$		0			0
$211$	14.8845	−	2.62453i	1.02469	−	0.180680i	0.364046	−	0.931381i	$-0.381395\pi$
$211$	14.8845	−	2.62453i	1.02469	−	0.180680i	0.660643	+	0.750701i	$0.270284\pi$
$212$	19.6246	+	7.66231i	1.34783	+	0.526249i
$213$		0			0
$214$	−9.95905	−	14.5797i	−0.680787	−	0.996647i
$215$	23.7173			1.61751
$216$		0			0
$217$	29.6210			2.01080
$218$	−15.3590	−	22.4850i	−1.04024	−	1.52287i
$219$		0			0
$220$	0.266875	+	0.104199i	0.0179927	+	0.00702512i
$221$	−9.40441	+	1.65825i	−0.632609	+	0.111546i
$222$		0			0
$223$	1.05516	−	1.25750i	0.0706590	−	0.0842081i	−0.729557	−	0.683920i	$-0.760274\pi$
$223$	1.05516	−	1.25750i	0.0706590	−	0.0842081i	0.800216	+	0.599712i	$0.204718\pi$
$224$	14.6099	+	16.4091i	0.976166	+	1.09638i
$225$		0			0
$226$	−5.15208	−	5.27289i	−0.342711	−	0.350747i
$227$	−4.74259	+	26.8966i	−0.314777	+	1.78519i	0.258691	+	0.965960i	$0.416709\pi$
$227$	−4.74259	+	26.8966i	−0.314777	+	1.78519i	−0.573468	+	0.819228i	$0.694402\pi$
$228$		0			0
$229$	5.93639	+	2.16067i	0.392288	+	0.142781i	0.530630	−	0.847603i	$-0.321955\pi$
$229$	5.93639	+	2.16067i	0.392288	+	0.142781i	−0.138343	+	0.990384i	$0.544178\pi$
$230$	19.7632	+	1.96006i	1.30315	+	0.129242i
$231$		0			0
$232$	6.18128	+	9.51533i	0.405821	+	0.624712i
$233$	25.6785	−	14.8255i	1.68226	−	0.971251i	0.722099	−	0.691790i	$-0.243178\pi$
$233$	25.6785	−	14.8255i	1.68226	−	0.971251i	0.960157	−	0.279461i	$-0.0901558\pi$
$234$		0			0
$235$	−11.6306	−	6.71490i	−0.758693	−	0.438032i
$236$	3.13726	+	0.628471i	0.204218	+	0.0409100i
$237$		0			0
$238$	10.3584	−	4.68487i	0.671438	−	0.303675i
$239$	−7.12866	+	5.98165i	−0.461114	+	0.386921i	−0.843541	−	0.537065i	$-0.819533\pi$
$239$	−7.12866	+	5.98165i	−0.461114	+	0.386921i	0.382426	+	0.923986i	$0.375089\pi$
$240$		0			0
$241$	13.2131	−	4.80918i	0.851132	−	0.309787i	0.120630	−	0.992697i	$-0.461508\pi$
$241$	13.2131	−	4.80918i	0.851132	−	0.309787i	0.730502	+	0.682911i	$0.239286\pi$
$242$	3.85071	+	15.0673i	0.247533	+	0.968561i
$243$		0			0
$244$	3.70490	−	2.02604i	0.237182	−	0.129704i
$245$	−6.79816	−	18.6778i	−0.434318	−	1.19328i
$246$		0			0
$247$	8.42988	+	10.0463i	0.536381	+	0.639234i
$248$	17.2295	+	12.9795i	1.09408	+	0.824198i
$249$		0			0
$250$	−12.3962	−	5.95628i	−0.784005	−	0.376708i
$251$	7.60386	−	13.1703i	0.479951	−	0.831300i	−0.519784	−	0.854298i	$-0.673988\pi$
$251$	7.60386	−	13.1703i	0.479951	−	0.831300i	0.999736	+	0.0229974i	$0.00732094\pi$
$252$		0			0
$253$	−0.166404	−	0.288220i	−0.0104617	−	0.0181203i
$254$	−0.207176	−	2.73234i	−0.0129994	−	0.171442i
$255$		0			0
$256$	1.30787	+	15.9465i	0.0817422	+	0.996654i
$257$	2.42247	−	6.65567i	0.151109	−	0.415169i	−0.840923	−	0.541155i	$-0.817987\pi$
$257$	2.42247	−	6.65567i	0.151109	−	0.415169i	0.992032	+	0.125986i	$0.0402094\pi$
$258$		0			0
$259$	−18.4399	−	3.25145i	−1.14580	−	0.202035i
$260$	−11.7954	+	19.3789i	−0.731521	+	1.20183i
$261$		0			0
$262$	−0.636889	−	0.178589i	−0.0393471	−	0.0110332i
$263$	1.52299	+	1.27794i	0.0939113	+	0.0788009i	0.688535	−	0.725204i	$-0.258254\pi$
$263$	1.52299	+	1.27794i	0.0939113	+	0.0788009i	−0.594623	+	0.804004i	$0.702699\pi$
$264$		0			0
$265$	−4.49710	−	25.5043i	−0.276255	−	1.56672i
$266$	−12.6846	−	9.10273i	−0.777746	−	0.558124i
$267$		0			0
$268$	11.3500	+	9.98100i	0.693313	+	0.609687i
$269$			1.18433i			0.0722097i	0.999348	+	0.0361048i	$0.0114950\pi$
$269$			1.18433i			0.0722097i	−0.999348	+	0.0361048i	$0.988505\pi$
$270$		0			0
$271$		−	10.9019i		−	0.662245i	−0.943588	−	0.331122i	$-0.892573\pi$
$271$		−	10.9019i		−	0.662245i	0.943588	−	0.331122i	$-0.107427\pi$
$272$	8.07800	+	1.81388i	0.489800	+	0.109983i
$273$		0			0
$274$	3.61997	−	5.04443i	0.218690	−	0.304745i
$275$	−0.0105680	−	0.0599339i	−0.000637272	−	0.00361415i
$276$		0			0
$277$	−4.33388	−	3.63656i	−0.260398	−	0.218500i	0.503237	−	0.864149i	$-0.332142\pi$
$277$	−4.33388	−	3.63656i	−0.260398	−	0.218500i	−0.763634	+	0.645649i	$0.776587\pi$
$278$	3.22558	−	11.5032i	0.193457	−	0.689915i
$279$		0			0
$280$	7.89265	−	25.8290i	0.471676	−	1.54358i
$281$	12.2002	+	2.15122i	0.727801	+	0.128331i	0.525259	−	0.850943i	$-0.323969\pi$
$281$	12.2002	+	2.15122i	0.727801	+	0.128331i	0.202542	+	0.979273i	$0.435080\pi$
$282$		0			0
$283$	−7.70900	+	21.1803i	−0.458252	+	1.25904i	0.468533	+	0.883446i	$0.344783\pi$
$283$	−7.70900	+	21.1803i	−0.458252	+	1.25904i	−0.926785	+	0.375592i	$0.877439\pi$
$284$	−16.1475	+	2.46289i	−0.958179	+	0.146146i
$285$		0			0
$286$	0.379081	−	0.0287434i	0.0224155	−	0.00169963i
$287$	2.13088	+	3.69079i	0.125782	+	0.217860i
$288$		0			0
$289$	−6.35799	+	11.0124i	−0.374000	+	0.647786i
$290$	6.04093	−	12.5724i	0.354735	−	0.738276i
$291$		0			0
$292$	8.16385	+	10.2003i	0.477753	+	0.596927i
$293$	−16.1235	−	19.2153i	−0.941947	−	1.12257i	−0.992303	−	0.123838i	$-0.960480\pi$
$293$	−16.1235	−	19.2153i	−0.941947	−	1.12257i	0.0503554	−	0.998731i	$-0.483965\pi$
$294$		0			0
$295$	−1.34523	−	3.69599i	−0.0783223	−	0.215189i
$296$	−9.30111	−	9.97134i	−0.540616	−	0.579572i
$297$		0			0
$298$	−13.9301	+	3.56007i	−0.806946	+	0.206229i
$299$	24.7644	−	9.01350i	1.43216	−	0.521264i
$300$		0			0
$301$	−28.7016	+	24.0835i	−1.65433	+	1.38815i
$302$	−1.39074	−	3.07498i	−0.0800281	−	0.176945i
$303$		0			0
$304$	−3.38955	−	10.8530i	−0.194404	−	0.622461i
$305$	−4.49542	−	2.59543i	−0.257407	−	0.148614i
$306$		0			0
$307$	7.99858	−	4.61798i	0.456503	−	0.263562i	−0.254070	−	0.967186i	$-0.581769\pi$
$307$	7.99858	−	4.61798i	0.456503	−	0.263562i	0.710573	+	0.703624i	$0.248436\pi$
$308$	−0.428767	+	0.144898i	−0.0244313	+	0.00825631i
$309$		0			0
$310$	2.61706	−	26.3878i	0.148639	−	1.49873i
$311$	−24.4624	−	8.90360i	−1.38714	−	0.504877i	−0.462803	−	0.886461i	$-0.653156\pi$
$311$	−24.4624	−	8.90360i	−1.38714	−	0.504877i	−0.924334	+	0.381584i	$0.875379\pi$
$312$		0			0
$313$	3.88258	−	22.0192i	0.219456	−	1.24460i	−0.653548	−	0.756885i	$-0.726720\pi$
$313$	3.88258	−	22.0192i	0.219456	−	1.24460i	0.873004	−	0.487713i	$-0.162169\pi$
$314$	5.50859	−	5.38239i	0.310868	−	0.303746i
$315$		0			0
$316$	−13.8547	−	0.321139i	−0.779389	−	0.0180655i
$317$	7.49063	−	8.92698i	0.420716	−	0.501389i	−0.513504	−	0.858087i	$-0.671653\pi$
$317$	7.49063	−	8.92698i	0.420716	−	0.501389i	0.934220	+	0.356698i	$0.116097\pi$
$318$		0			0
$319$	−0.230190	+	0.0405887i	−0.0128882	+	0.00227253i
$320$	15.9088	−	11.5654i	0.889329	−	0.646527i
$321$		0			0
$322$	−25.9068	+	17.6964i	−1.44373	+	0.986179i
$323$	−5.88335			−0.327358
$324$		0			0
$325$	4.81914			0.267318
$326$	−11.4013	+	7.78799i	−0.631462	+	0.431337i
$327$		0			0
$328$	−0.377790	+	3.08053i	−0.0208600	+	0.170094i
$329$	20.8933	−	3.68406i	1.15189	−	0.203109i
$330$		0			0
$331$	−2.82088	+	3.36179i	−0.155050	+	0.184781i	−0.837977	−	0.545705i	$-0.816262\pi$
$331$	−2.82088	+	3.36179i	−0.155050	+	0.184781i	0.682928	+	0.730486i	$0.260706\pi$
$332$	−0.528128	+	22.7848i	−0.0289848	+	1.25048i
$333$		0			0
$334$	−4.69938	+	4.59171i	−0.257139	+	0.251247i
$335$	3.22634	−	18.2975i	0.176274	−	0.999698i
$336$		0			0
$337$	31.6135	+	11.5064i	1.72210	+	0.626793i	0.998018	−	0.0629227i	$-0.0200421\pi$
$337$	31.6135	+	11.5064i	1.72210	+	0.626793i	0.724081	+	0.689715i	$0.242264\pi$
$338$	−1.15661	+	11.6620i	−0.0629112	+	0.634331i
$339$		0			0
$340$	−3.25832	−	9.64170i	−0.176707	−	0.522895i
$341$	−0.384831	+	0.222182i	−0.0208398	+	0.0120318i
$342$		0			0
$343$	3.64812	+	2.10624i	0.196980	+	0.113726i
$344$	−27.2477	+	1.43194i	−1.46910	+	0.0772048i
$345$		0			0
$346$	−0.513536	−	1.13545i	−0.0276079	−	0.0610422i
$347$	11.4677	−	9.62251i	0.615616	−	0.516563i	−0.280806	−	0.959765i	$-0.590602\pi$
$347$	11.4677	−	9.62251i	0.615616	−	0.516563i	0.896422	+	0.443201i	$0.146157\pi$
$348$		0			0
$349$	9.99580	−	3.63817i	0.535063	−	0.194747i	−0.0603346	−	0.998178i	$-0.519217\pi$
$349$	9.99580	−	3.63817i	0.535063	−	0.194747i	0.595398	+	0.803431i	$0.296995\pi$
$350$	−5.55850	+	1.42057i	−0.297114	+	0.0759328i
$351$		0			0
$352$	−0.312891	−	0.103597i	−0.0166772	−	0.00552176i
$353$	3.76238	+	10.3371i	0.200252	+	0.550187i	0.998650	−	0.0519428i	$-0.0165414\pi$
$353$	3.76238	+	10.3371i	0.200252	+	0.550187i	−0.798399	+	0.602129i	$0.794319\pi$
$354$		0			0
$355$	12.9068	+	15.3817i	0.685021	+	0.816376i
$356$	−3.35083	+	2.68185i	−0.177593	+	0.142138i
$357$		0			0
$358$	7.77700	−	16.1855i	0.411027	−	0.855430i
$359$	8.75833	−	15.1699i	0.462247	−	0.800636i	−0.536825	−	0.843693i	$-0.680377\pi$
$359$	8.75833	−	15.1699i	0.462247	−	0.800636i	0.999073	+	0.0430578i	$0.0137100\pi$
$360$		0			0
$361$	−5.46012	−	9.45721i	−0.287375	−	0.497748i
$362$	−9.32201	+	0.706830i	−0.489954	+	0.0371502i
$363$		0			0
$364$	−5.40378	−	35.4289i	−0.283235	−	1.85698i
$365$	5.49303	−	15.0920i	0.287518	−	0.789950i
$366$		0			0
$367$	5.12177	+	0.903106i	0.267354	+	0.0471418i	0.305718	−	0.952122i	$-0.401103\pi$
$367$	5.12177	+	0.903106i	0.267354	+	0.0471418i	−0.0383639	+	0.999264i	$0.512215\pi$
$368$	−22.8234	−	1.05862i	−1.18975	−	0.0551842i
$369$		0			0
$370$	−4.52574	+	16.1398i	−0.235282	+	0.839070i
$371$	31.3403	+	26.2976i	1.62711	+	1.36530i
$372$		0			0
$373$	−2.75601	−	15.6301i	−0.142701	−	0.809298i	−0.969184	−	0.246336i	$-0.920773\pi$
$373$	−2.75601	−	15.6301i	−0.142701	−	0.809298i	0.826483	−	0.562961i	$-0.190338\pi$
$374$	−0.0994346	+	0.138562i	−0.00514164	+	0.00716487i
$375$		0			0
$376$	13.7672	+	7.01225i	0.709991	+	0.361629i
$377$		−	18.5090i		−	0.953262i
$378$		0			0
$379$			13.3564i			0.686073i	0.939322	+	0.343037i	$0.111456\pi$
$379$			13.3564i			0.686073i	−0.939322	+	0.343037i	$0.888544\pi$
$380$	−9.22986	+	10.4958i	−0.473482	+	0.538425i
$381$		0			0
$382$	−29.2676	−	21.0030i	−1.49746	−	1.07461i
$383$	1.40419	+	7.96356i	0.0717508	+	0.406919i	0.999437	+	0.0335575i	$0.0106837\pi$
$383$	1.40419	+	7.96356i	0.0717508	+	0.406919i	−0.927686	+	0.373361i	$0.878205\pi$
$384$		0			0
$385$	0.426195	+	0.357620i	0.0217209	+	0.0182260i
$386$	−28.0438	−	7.86371i	−1.42739	−	0.400252i
$387$		0			0
$388$	−8.80579	−	5.35987i	−0.447046	−	0.272106i
$389$	−19.3541	−	3.41265i	−0.981293	−	0.173028i	−0.340084	−	0.940395i	$-0.610456\pi$
$389$	−19.3541	−	3.41265i	−0.981293	−	0.173028i	−0.641209	+	0.767367i	$0.721567\pi$
$390$		0			0
$391$	−4.04356	+	11.1096i	−0.204492	+	0.561836i
$392$	8.93777	+	21.0476i	0.451426	+	1.06307i
$393$		0			0
$394$	−0.741821	−	9.78348i	−0.0373724	−	0.492884i
$395$	8.51795	+	14.7535i	0.428585	+	0.742330i
$396$		0			0
$397$	12.3726	−	21.4299i	0.620961	−	1.07554i	−0.368346	−	0.929689i	$-0.620076\pi$
$397$	12.3726	−	21.4299i	0.620961	−	1.07554i	0.989307	−	0.145848i	$-0.0465910\pi$
$398$	14.7548	+	7.08958i	0.739593	+	0.355368i
$399$		0			0
$400$	−3.85566	−	1.60935i	−0.192783	−	0.0804677i
$401$	7.82702	+	9.32788i	0.390863	+	0.465812i	0.925211	−	0.379452i	$-0.123888\pi$
$401$	7.82702	+	9.32788i	0.390863	+	0.465812i	−0.534349	+	0.845264i	$0.679443\pi$
$402$		0			0
$403$	−12.0348	−	33.0654i	−0.599496	−	1.64710i
$404$	−12.6835	−	23.1935i	−0.631026	−	1.15392i
$405$		0			0
$406$	5.45604	+	21.3487i	0.270779	+	1.05952i
$407$	0.263956	−	0.0960722i	0.0130838	−	0.00476212i
$408$		0			0
$409$	23.8114	−	19.9801i	1.17740	−	0.987954i	0.177405	−	0.984138i	$-0.443230\pi$
$409$	23.8114	−	19.9801i	1.17740	−	0.987954i	0.999993	−	0.00381582i	$-0.00121462\pi$
$410$	3.47620	−	1.57220i	0.171677	−	0.0776454i
$411$		0			0
$412$	0.409691	−	2.04513i	0.0201840	−	0.100756i
$413$	5.38099	+	3.10671i	0.264781	+	0.152871i
$414$		0			0
$415$	24.2629	−	14.0082i	1.19102	−	0.687635i
$416$	12.3812	−	22.9757i	0.607040	−	1.12647i
$417$		0			0
$418$	0.233075	+	0.0231157i	0.0114001	+	0.00113063i
$419$	−34.6419	−	12.6086i	−1.69237	−	0.615971i	−0.697446	−	0.716637i	$-0.745680\pi$
$419$	−34.6419	−	12.6086i	−1.69237	−	0.615971i	−0.994920	+	0.100666i	$0.967903\pi$
$420$		0			0
$421$	−6.39735	+	36.2812i	−0.311788	+	1.76824i	0.277904	+	0.960609i	$0.410360\pi$
$421$	−6.39735	+	36.2812i	−0.311788	+	1.76824i	−0.589692	+	0.807628i	$0.700751\pi$
$422$	14.9379	+	15.2882i	0.727167	+	0.744218i
$423$		0			0
$424$	6.70635	+	29.0293i	0.325689	+	1.40979i
$425$	−1.38966	+	1.65613i	−0.0674082	+	0.0803340i
$426$		0			0
$427$	8.07565	−	1.42395i	0.390808	−	0.0689100i
$428$	9.08167	−	23.2599i	0.438979	−	1.12431i
$429$		0			0
$430$	18.9189	+	27.6965i	0.912348	+	1.33564i
$431$	−11.3781			−0.548063			−0.274032	−	0.961721i	$-0.588357\pi$
$431$	−11.3781			−0.548063			−0.274032	+	0.961721i	$0.588357\pi$
$432$		0			0
$433$	−7.27646			−0.349684			−0.174842	−	0.984596i	$-0.555941\pi$
$433$	−7.27646			−0.349684			−0.174842	+	0.984596i	$0.555941\pi$
$434$	23.6281	+	34.5907i	1.13419	+	1.66041i
$435$		0			0
$436$	14.0059	−	35.8717i	0.670759	−	1.71794i
$437$	15.9896	−	2.81940i	0.764887	−	0.134870i
$438$		0			0
$439$	−19.1310	+	22.7994i	−0.913073	+	1.08816i	0.0827239	+	0.996573i	$0.473638\pi$
$439$	−19.1310	+	22.7994i	−0.913073	+	1.08816i	−0.995797	+	0.0915858i	$0.970806\pi$
$440$	0.0911994	+	0.394768i	0.00434776	+	0.0188198i
$441$		0			0
$442$	−9.43820	−	9.65950i	−0.448929	−	0.459456i
$443$	−2.98686	+	16.9393i	−0.141910	+	0.804811i	0.827887	+	0.560895i	$0.189543\pi$
$443$	−2.98686	+	16.9393i	−0.141910	+	0.804811i	−0.969797	+	0.243915i	$0.921568\pi$
$444$		0			0
$445$	4.95776	+	1.80448i	0.235020	+	0.0855404i
$446$	2.31016	+	0.229115i	0.109389	+	0.0108489i
$447$		0			0
$448$	−7.50808	+	30.1503i	−0.354724	+	1.42447i
$449$	−18.8763	+	10.8982i	−0.890826	+	0.514319i	−0.874213	−	0.485543i	$-0.838622\pi$
$449$	−18.8763	+	10.8982i	−0.890826	+	0.514319i	−0.0166137	+	0.999862i	$0.505289\pi$
$450$		0			0
$451$	−0.0553680	−	0.0319667i	−0.00260718	−	0.00150525i
$452$	2.04783	−	10.2226i	0.0963220	−	0.480829i
$453$		0			0
$454$	−35.1923	+	15.9166i	−1.65166	+	0.747004i
$455$	−33.7487	+	28.3185i	−1.58216	+	1.32759i
$456$		0			0
$457$	−9.07489	+	3.30299i	−0.424505	+	0.154507i	−0.545434	−	0.838154i	$-0.683635\pi$
$457$	−9.07489	+	3.30299i	−0.424505	+	0.154507i	0.120928	+	0.992661i	$0.461413\pi$
$458$	2.21217	+	8.65590i	0.103368	+	0.404464i
$459$		0			0
$460$	13.4758	+	24.6425i	0.628314	+	1.14896i
$461$	11.2135	+	30.8088i	0.522264	+	1.43491i	0.867994	+	0.496575i	$0.165409\pi$
$461$	11.2135	+	30.8088i	0.522264	+	1.43491i	−0.345729	+	0.938334i	$0.612368\pi$
$462$		0			0
$463$	−24.6443	−	29.3699i	−1.14532	−	1.36494i	−0.920598	−	0.390512i	$-0.872298\pi$
$463$	−24.6443	−	29.3699i	−1.14532	−	1.36494i	−0.224720	−	0.974423i	$-0.572147\pi$
$464$	−6.18109	+	14.8086i	−0.286950	+	0.687471i
$465$		0			0
$466$	37.7962	+	18.1608i	1.75087	+	0.841281i
$467$	−5.79199	+	10.0320i	−0.268021	+	0.464227i	−0.968351	−	0.249593i	$-0.919703\pi$
$467$	−5.79199	+	10.0320i	−0.268021	+	0.464227i	0.700329	+	0.713820i	$0.253036\pi$
$468$		0			0
$469$	14.6756	+	25.4189i	0.677657	+	1.17374i
$470$	−1.43597	−	18.9382i	−0.0662364	−	0.873556i
$471$		0			0
$472$	1.76862	+	4.16494i	0.0814074	+	0.191707i
$473$	0.192240	−	0.528174i	0.00883919	−	0.0242855i
$474$		0			0
$475$	2.92392	+	0.515566i	0.134159	+	0.0236558i
$476$	13.7336	+	8.35931i	0.629480	+	0.383148i
$477$		0			0
$478$	−12.6716	−	3.55323i	−0.579587	−	0.162521i
$479$	13.7316	+	11.5222i	0.627412	+	0.526461i	0.900124	−	0.435635i	$-0.143476\pi$
$479$	13.7316	+	11.5222i	0.627412	+	0.526461i	−0.272712	+	0.962096i	$0.587920\pi$
$480$		0			0
$481$	3.86246	+	21.9051i	0.176113	+	0.998787i
$482$	16.1559	+	11.5938i	0.735882	+	0.528083i
$483$		0			0
$484$	−14.5236	+	16.5157i	−0.660163	+	0.750712i
$485$			12.6723i			0.575421i
$486$		0			0
$487$		−	22.6464i		−	1.02621i	−0.858327	−	0.513104i	$-0.828496\pi$
$487$		−	22.6464i		−	1.02621i	0.858327	−	0.513104i	$-0.171504\pi$
$488$	5.32129	+	2.71036i	0.240883	+	0.122692i
$489$		0			0
$490$	16.3887	−	22.8377i	0.740367	−	1.03170i
$491$	−4.46394	−	25.3163i	−0.201455	−	1.14251i	−0.902922	−	0.429805i	$-0.858582\pi$
$491$	−4.46394	−	25.3163i	−0.201455	−	1.14251i	0.701467	−	0.712702i	$-0.252529\pi$
$492$		0			0
$493$	6.36074	+	5.33729i	0.286473	+	0.240380i
$494$	−5.00753	+	17.8580i	−0.225299	+	0.803470i
$495$		0			0
$496$	−1.41346	+	30.4737i	−0.0634663	+	1.36831i
$497$	−31.2384	−	5.50816i	−1.40123	−	0.247075i
$498$		0			0
$499$	−2.47255	+	6.79329i	−0.110687	+	0.304109i	−0.982652	−	0.185458i	$-0.940623\pi$
$499$	−2.47255	+	6.79329i	−0.110687	+	0.304109i	0.871965	+	0.489567i	$0.162845\pi$
$500$	−2.93263	−	19.2272i	−0.131151	−	0.859868i
$501$		0			0
$502$	21.4454	−	1.62607i	0.957155	−	0.0725752i
$503$	−19.3621	−	33.5362i	−0.863314	−	1.49530i	−0.868712	−	0.495318i	$-0.835051\pi$
$503$	−19.3621	−	33.5362i	−0.863314	−	1.49530i	0.00539768	−	0.999985i	$-0.498282\pi$
$504$		0			0
$505$	−16.2480	+	28.1424i	−0.723027	+	1.25232i
$506$	0.203840	−	0.424231i	0.00906177	−	0.0188594i
$507$		0			0
$508$	3.02550	−	2.42147i	0.134235	−	0.107436i
$509$	−12.2747	−	14.6284i	−0.544067	−	0.648394i	0.422027	−	0.906583i	$-0.361319\pi$
$509$	−12.2747	−	14.6284i	−0.544067	−	0.648394i	−0.966094	+	0.258189i	$0.916874\pi$
$510$		0			0
$511$	8.67757	+	23.8414i	0.383873	+	1.05468i
$512$	−17.5786	+	14.2475i	−0.776873	+	0.629657i
$513$		0			0
$514$	9.70469	−	2.48021i	0.428056	−	0.109397i
$515$	−2.40936	+	0.876936i	−0.106169	+	0.0386424i
$516$		0			0
$517$	−0.243809	+	0.204580i	−0.0107227	+	0.00899742i
$518$	−10.9122	−	24.1273i	−0.479454	−	1.06009i
$519$		0			0
$520$	−32.0392	+	1.68374i	−1.40501	+	0.0738368i
$521$	19.0779	+	11.0146i	0.835817	+	0.482559i	0.855840	−	0.517240i	$-0.173041\pi$
$521$	19.0779	+	11.0146i	0.835817	+	0.482559i	−0.0200233	+	0.999800i	$0.506374\pi$
$522$		0			0
$523$	3.75661	−	2.16888i	0.164265	−	0.0948384i	−0.415614	−	0.909541i	$-0.636433\pi$
$523$	3.75661	−	2.16888i	0.164265	−	0.0948384i	0.579879	+	0.814703i	$0.303100\pi$
$524$	−0.299483	−	0.886202i	−0.0130830	−	0.0387139i
$525$		0			0
$526$	−0.277487	+	2.79789i	−0.0120990	+	0.121994i
$527$	14.8335	+	5.39895i	0.646158	+	0.235182i
$528$		0			0
$529$	1.67167	−	9.48053i	0.0726815	−	0.412197i
$530$	26.1961	−	25.5960i	1.13789	−	1.11182i
$531$		0			0
$532$	0.511652	−	22.0739i	0.0221829	−	0.957026i
$533$	3.25420	−	3.87820i	0.140955	−	0.167984i
$534$		0			0
$535$	−30.2288	+	5.33015i	−1.30690	+	0.230442i
$536$	−2.60188	+	21.2160i	−0.112384	+	0.916390i
$537$		0			0
$538$	−1.38303	+	0.944716i	−0.0596266	+	0.0407296i
$539$	−0.471048			−0.0202895
$540$		0			0
$541$	−2.88802			−0.124166			−0.0620829	−	0.998071i	$-0.519774\pi$
$541$	−2.88802			−0.124166			−0.0620829	+	0.998071i	$0.519774\pi$
$542$	12.7310	−	8.69627i	0.546844	−	0.373537i
$543$		0			0
$544$	4.32546	+	10.8802i	0.185452	+	0.466485i
$545$	−46.6192	+	8.22022i	−1.99695	+	0.352115i
$546$		0			0
$547$	−15.0106	+	17.8889i	−0.641805	+	0.764874i	−0.984654	−	0.174517i	$-0.944164\pi$
$547$	−15.0106	+	17.8889i	−0.641805	+	0.764874i	0.342849	+	0.939391i	$0.388608\pi$
$548$	8.77835	+	0.203474i	0.374993	+	0.00869196i
$549$		0			0
$550$	0.0615596	−	0.0601492i	0.00262491	−	0.00256477i
$551$	1.98015	−	11.2300i	0.0843572	−	0.478413i
$552$		0			0
$553$	−25.2893	−	9.20456i	−1.07541	−	0.391418i
$554$	0.789631	−	7.96183i	0.0335482	−	0.338266i
$555$		0			0
$556$	16.0061	−	5.40912i	0.678811	−	0.229398i
$557$	7.72227	−	4.45845i	0.327203	−	0.188911i	−0.327396	−	0.944887i	$-0.606171\pi$
$557$	7.72227	−	4.45845i	0.327203	−	0.188911i	0.654599	+	0.755977i	$0.272838\pi$
$558$		0			0
$559$	38.5452	+	22.2541i	1.63029	+	0.941247i
$560$	36.4584	−	11.3865i	1.54065	−	0.481167i
$561$		0			0
$562$	7.21971	+	15.9631i	0.304545	+	0.673362i
$563$	16.7813	−	14.0811i	0.707246	−	0.593450i	−0.216579	−	0.976265i	$-0.569490\pi$
$563$	16.7813	−	14.0811i	0.707246	−	0.593450i	0.923825	+	0.382815i	$0.125045\pi$
$564$		0			0
$565$	−12.0432	+	4.38335i	−0.506660	+	0.184409i
$566$	−30.8832	+	7.89275i	−1.29812	+	0.331757i
$567$		0			0
$568$	−15.7567	−	16.8921i	−0.661136	−	0.708777i
$569$	6.77697	+	18.6196i	0.284105	+	0.780573i	0.996862	+	0.0791612i	$0.0252242\pi$
$569$	6.77697	+	18.6196i	0.284105	+	0.780573i	−0.712757	+	0.701411i	$0.752554\pi$
$570$		0			0
$571$	17.6621	+	21.0489i	0.739136	+	0.880869i	0.996339	−	0.0854889i	$-0.0272452\pi$
$571$	17.6621	+	21.0489i	0.739136	+	0.880869i	−0.257203	+	0.966357i	$0.582801\pi$
$572$	0.335952	+	0.419754i	0.0140468	+	0.0175508i
$573$		0			0
$574$	−2.61026	+	5.43246i	−0.108950	+	0.226747i
$575$	2.98313	−	5.16693i	0.124405	−	0.215476i
$576$		0			0
$577$	1.20328	+	2.08414i	0.0500931	+	0.0867638i	0.889985	−	0.455990i	$-0.150715\pi$
$577$	1.20328	+	2.08414i	0.0500931	+	0.0867638i	−0.839892	+	0.542754i	$0.817382\pi$
$578$	−17.9316	+	1.35965i	−0.745858	+	0.0565538i
$579$		0			0
$580$	19.5005	−	2.97430i	0.809713	−	0.123501i
$581$	−15.1373	+	41.5895i	−0.628003	+	1.72542i
$582$		0			0
$583$	−0.604422	−	0.106576i	−0.0250326	−	0.00441392i
$584$	−5.39952	+	17.6701i	−0.223434	+	0.731196i
$585$		0			0
$586$	9.57772	−	34.1564i	0.395652	−	1.41099i
$587$	9.88712	+	8.29628i	0.408085	+	0.342424i	0.823609	−	0.567158i	$-0.191957\pi$
$587$	9.88712	+	8.29628i	0.408085	+	0.342424i	−0.415524	+	0.909582i	$0.636402\pi$
$588$		0			0
$589$	−3.76445	−	21.3493i	−0.155112	−	0.879682i
$590$	3.24303	−	4.51915i	0.133513	−	0.186051i
$591$		0			0
$592$	4.22497	−	18.8156i	0.173645	−	0.773316i
$593$		−	27.2738i		−	1.12000i	−0.828493	−	0.560000i	$-0.810801\pi$
$593$		−	27.2738i		−	1.12000i	0.828493	−	0.560000i	$-0.189199\pi$
$594$		0			0
$595$		−	19.7639i		−	0.810242i
$596$	−15.2691	−	13.4274i	−0.625448	−	0.550008i
$597$		0			0
$598$	30.2799	+	21.7294i	1.23824	+	0.888581i
$599$	3.54790	+	20.1212i	0.144963	+	0.822128i	0.967397	+	0.253267i	$0.0815050\pi$
$599$	3.54790	+	20.1212i	0.144963	+	0.822128i	−0.822433	+	0.568862i	$0.807384\pi$
$600$		0			0
$601$	−33.6622	−	28.2459i	−1.37311	−	1.15217i	−0.971684	−	0.236282i	$-0.924071\pi$
$601$	−33.6622	−	28.2459i	−1.37311	−	1.15217i	−0.401424	−	0.915892i	$-0.631485\pi$
$602$	−51.0188	−	14.3061i	−2.07937	−	0.583072i
$603$		0			0
$604$	2.48153	−	4.07693i	0.100972	−	0.165888i
$605$	26.6251	+	4.69472i	1.08246	+	0.190867i
$606$		0			0
$607$	12.8907	−	35.4169i	0.523217	−	1.43753i	−0.343703	−	0.939078i	$-0.611681\pi$
$607$	12.8907	−	35.4169i	0.523217	−	1.43753i	0.866920	−	0.498448i	$-0.166097\pi$
$608$	9.97008	−	12.6155i	0.404340	−	0.511624i
$609$		0			0
$610$	−0.555029	−	7.31998i	−0.0224725	−	0.296377i
$611$	−12.6013	−	21.8260i	−0.509792	−	0.882986i
$612$		0			0
$613$	1.70832	−	2.95890i	0.0689984	−	0.119509i	−0.829462	−	0.558563i	$-0.811353\pi$
$613$	1.70832	−	2.95890i	0.0689984	−	0.119509i	0.898461	+	0.439054i	$0.144686\pi$
$614$	11.7731	+	5.65688i	0.475124	+	0.228293i
$615$		0			0
$616$	−0.511228	−	0.385122i	−0.0205980	−	0.0155170i
$617$	18.5635	+	22.1231i	0.747336	+	0.890641i	0.996977	−	0.0776977i	$-0.0247569\pi$
$617$	18.5635	+	22.1231i	0.747336	+	0.890641i	−0.249641	+	0.968339i	$0.580312\pi$
$618$		0			0
$619$	−6.14959	−	16.8958i	−0.247173	−	0.679101i	−0.999787	−	0.0206398i	$-0.993430\pi$
$619$	−6.14959	−	16.8958i	−0.247173	−	0.679101i	0.752614	−	0.658462i	$-0.228793\pi$
$620$	32.9026	−	17.9929i	1.32140	−	0.722612i
$621$		0			0
$622$	−9.11582	−	35.6689i	−0.365511	−	1.43019i
$623$	−7.83198	+	2.85061i	−0.313782	+	0.114207i
$624$		0			0
$625$	−22.3161	+	18.7254i	−0.892643	+	0.749016i
$626$	28.8106	−	13.0303i	1.15150	−	0.520796i
$627$		0			0
$628$	10.6795	+	2.13938i	0.426160	+	0.0853704i
$629$	−8.64162	−	4.98924i	−0.344564	−	0.198934i
$630$		0			0
$631$	10.4847	−	6.05333i	0.417388	−	0.240979i	−0.276571	−	0.960994i	$-0.589198\pi$
$631$	10.4847	−	6.05333i	0.417388	−	0.240979i	0.693959	+	0.720014i	$0.255865\pi$
$632$	−10.6766	−	16.4354i	−0.424694	−	0.653765i
$633$		0			0
$634$	16.3999	+	1.62649i	0.651322	+	0.0645963i
$635$	−4.47642	−	1.62928i	−0.177641	−	0.0646562i
$636$		0			0
$637$	6.47715	−	36.7337i	0.256634	−	1.45544i
$638$	−0.231017	−	0.236434i	−0.00914605	−	0.00936050i
$639$		0			0
$640$	26.1960	+	9.35239i	1.03549	+	0.369686i
$641$	−12.3621	+	14.7326i	−0.488275	+	0.581904i	−0.952778	−	0.303668i	$-0.901789\pi$
$641$	−12.3621	+	14.7326i	−0.488275	+	0.581904i	0.464503	+	0.885572i	$0.346233\pi$
$642$		0			0
$643$	2.81767	−	0.496831i	0.111118	−	0.0195931i	−0.117813	−	0.993036i	$-0.537588\pi$
$643$	2.81767	−	0.496831i	0.111118	−	0.0195931i	0.228931	+	0.973443i	$0.426477\pi$
$644$	−41.3308	−	16.1373i	−1.62866	−	0.635900i
$645$		0			0
$646$	−4.69304	−	6.87044i	−0.184645	−	0.270314i
$647$	36.4238			1.43197			0.715984	−	0.698117i	$-0.245978\pi$
$647$	36.4238			1.43197			0.715984	+	0.698117i	$0.245978\pi$
$648$		0			0
$649$	−0.0932118			−0.00365888
$650$	3.84414	+	5.62768i	0.150779	+	0.220736i
$651$		0			0
$652$	−18.1893	−	7.10188i	−0.712347	−	0.278131i
$653$	21.4999	−	3.79102i	0.841357	−	0.148354i	0.263671	−	0.964613i	$-0.415067\pi$
$653$	21.4999	−	3.79102i	0.841357	−	0.148354i	0.577686	+	0.816259i	$0.303956\pi$
$654$		0			0
$655$	−0.739151	+	0.880886i	−0.0288810	+	0.0344190i
$656$	−3.89872	+	2.01611i	−0.152220	+	0.0787157i
$657$		0			0
$658$	20.9684	+	21.4600i	0.817432	+	0.836599i
$659$	−0.0574639	+	0.325894i	−0.00223847	+	0.0126950i	−0.985907	−	0.167297i	$-0.946496\pi$
$659$	−0.0574639	+	0.325894i	−0.00223847	+	0.0126950i	0.983668	+	0.179992i	$0.0576072\pi$
$660$		0			0
$661$	−22.2519	−	8.09903i	−0.865498	−	0.315016i	−0.129156	−	0.991624i	$-0.541227\pi$
$661$	−22.2519	−	8.09903i	−0.865498	−	0.315016i	−0.736343	+	0.676609i	$0.763449\pi$
$662$	−6.17599	−	0.612517i	−0.240037	−	0.0238062i
$663$		0			0
$664$	−27.0288	+	17.5583i	−1.04892	+	0.681392i
$665$	−23.5059	+	13.5712i	−0.911521	+	0.526267i
$666$		0			0
$667$	−19.8448	−	11.4574i	−0.768393	−	0.443632i
$668$	−9.11071	−	1.82510i	−0.352504	−	0.0706153i
$669$		0			0
$670$	23.9410	−	10.8279i	0.924921	−	0.418319i
$671$	−0.0942366	+	0.0790739i	−0.00363796	+	0.00305261i
$672$		0			0
$673$	−3.46425	+	1.26088i	−0.133537	+	0.0486035i	−0.407924	−	0.913016i	$-0.633747\pi$
$673$	−3.46425	+	1.26088i	−0.133537	+	0.0486035i	0.274387	+	0.961619i	$0.411525\pi$
$674$	11.7806	+	46.0960i	0.453774	+	1.77555i
$675$		0			0
$676$	−14.5413	+	7.95194i	−0.559280	+	0.305844i
$677$	3.26640	+	8.97437i	0.125538	+	0.344913i	0.986501	−	0.163754i	$-0.0523605\pi$
$677$	3.26640	+	8.97437i	0.125538	+	0.344913i	−0.860963	+	0.508668i	$0.830138\pi$
$678$		0			0
$679$	−12.8680	−	15.3355i	−0.493828	−	0.588521i
$680$	8.66026	−	11.4960i	0.332106	−	0.440852i
$681$		0			0
$682$	−0.566432	−	0.272166i	−0.0216898	−	0.0104218i
$683$	−14.0206	+	24.2843i	−0.536482	+	0.929214i	0.462608	+	0.886563i	$0.346914\pi$
$683$	−14.0206	+	24.2843i	−0.536482	+	0.929214i	−0.999090	+	0.0426510i	$0.986420\pi$
$684$		0			0
$685$	−5.39697	−	9.34783i	−0.206208	−	0.357162i
$686$	0.450417	+	5.94030i	0.0171970	+	0.226802i
$687$		0			0
$688$	−23.4072	−	30.6771i	−0.892392	−	1.16955i
$689$	16.6222	−	45.6691i	0.633255	−	1.73985i
$690$		0			0
$691$	−39.8542	−	7.02737i	−1.51613	−	0.267334i	−0.647217	−	0.762306i	$-0.724067\pi$
$691$	−39.8542	−	7.02737i	−1.51613	−	0.267334i	−0.868909	+	0.494972i	$0.835178\pi$
$692$	0.916314	−	1.50542i	0.0348330	−	0.0572276i
$693$		0			0
$694$	20.3845	+	5.71597i	0.773785	+	0.216975i
$695$	−15.9101	−	13.3502i	−0.603505	−	0.506401i
$696$		0			0
$697$	0.394382	+	2.23665i	0.0149383	+	0.0847192i
$698$	12.2220	+	8.77076i	0.462611	+	0.331978i
$699$		0			0
$700$	−6.09282	−	5.35792i	−0.230287	−	0.202510i
$701$			13.2691i			0.501165i	0.968095	+	0.250583i	$0.0806222\pi$
$701$			13.2691i			0.501165i	−0.968095	+	0.250583i	$0.919378\pi$
$702$		0			0
$703$			13.7037i			0.516846i
$704$	−0.128609	−	0.448025i	−0.00484714	−	0.0168856i
$705$		0			0
$706$	−9.07020	+	12.6393i	−0.341362	+	0.475687i
$707$	−8.91429	−	50.5555i	−0.335257	−	1.90133i
$708$		0			0
$709$	10.1345	+	8.50383i	0.380608	+	0.319368i	0.812941	−	0.582346i	$-0.197865\pi$
$709$	10.1345	+	8.50383i	0.380608	+	0.319368i	−0.432333	+	0.901714i	$0.642310\pi$
$710$	−7.66689	+	27.3419i	−0.287733	+	1.02612i
$711$		0			0
$712$	−5.80469	−	1.77376i	−0.217540	−	0.0664744i
$713$	−42.9014	−	7.56467i	−1.60667	−	0.283299i
$714$		0			0
$715$	0.226045	−	0.621052i	0.00845359	−	0.0232260i
$716$	25.1046	−	3.82907i	0.938204	−	0.143099i
$717$		0			0
$718$	24.7014	−	1.87296i	0.921848	−	0.0698981i
$719$	20.7715	+	35.9773i	0.774647	+	1.34173i	0.934992	+	0.354668i	$0.115406\pi$
$719$	20.7715	+	35.9773i	0.774647	+	1.34173i	−0.160345	+	0.987061i	$0.551261\pi$
$720$		0			0
$721$	2.02522	−	3.50779i	0.0754232	−	0.130637i
$722$	6.68847	−	13.9200i	0.248919	−	0.518050i
$723$		0			0
$724$	−8.26142	−	10.3222i	−0.307033	−	0.383622i
$725$	−2.69346	−	3.20994i	−0.100033	−	0.119214i
$726$		0			0
$727$	11.7278	+	32.2219i	0.434960	+	1.19504i	0.942732	+	0.333552i	$0.108247\pi$
$727$	11.7278	+	32.2219i	0.434960	+	1.19504i	−0.507772	+	0.861492i	$0.669531\pi$
$728$	37.0626	−	34.5714i	1.37363	−	1.28130i
$729$		0			0
$730$	22.0058	−	5.62396i	0.814470	−	0.208152i
$731$	−18.7627	+	6.82907i	−0.693964	+	0.252582i
$732$		0			0
$733$	16.7604	−	14.0636i	0.619059	−	0.519452i	−0.278449	−	0.960451i	$-0.589820\pi$
$733$	16.7604	−	14.0636i	0.619059	−	0.519452i	0.897507	+	0.440999i	$0.145376\pi$
$734$	3.03092	+	6.70148i	0.111873	+	0.247356i
$735$		0			0
$736$	−16.9696	−	27.4971i	−0.625507	−	1.01356i
$737$	−0.381326	−	0.220159i	−0.0140463	−	0.00810965i
$738$		0			0
$739$	−23.8855	+	13.7903i	−0.878644	+	0.507285i	−0.870211	−	0.492679i	$-0.836018\pi$
$739$	−23.8855	+	13.7903i	−0.878644	+	0.507285i	−0.00843293	+	0.999964i	$0.502684\pi$
$740$	−22.4578	+	7.58940i	−0.825566	+	0.278992i
$741$		0			0
$742$	−5.71018	+	57.5756i	−0.209627	+	2.11367i
$743$	19.8494	+	7.22459i	0.728204	+	0.265045i	0.679404	−	0.733764i	$-0.262238\pi$
$743$	19.8494	+	7.22459i	0.728204	+	0.265045i	0.0487995	+	0.998809i	$0.484460\pi$
$744$		0			0
$745$	−4.34038	+	24.6155i	−0.159019	+	0.901843i
$746$	16.0541	−	15.6863i	0.587782	−	0.574316i
$747$		0			0
$748$	−0.241127	−	0.00558908i	−0.00881647	−	0.000204357i
$749$	31.1690	−	37.1457i	1.13889	−	1.35728i
$750$		0			0
$751$	15.0474	−	2.65327i	0.549088	−	0.0968191i	0.107780	−	0.994175i	$-0.465626\pi$
$751$	15.0474	−	2.65327i	0.549088	−	0.0968191i	0.441308	+	0.897356i	$0.354515\pi$
$752$	2.79312	+	21.6706i	0.101855	+	0.790246i
$753$		0			0
$754$	21.6144	−	14.7643i	0.787150	−	0.537684i
$755$	−5.86707			−0.213525
$756$		0			0
$757$	−29.8309			−1.08422			−0.542112	−	0.840306i	$-0.682375\pi$
$757$	−29.8309			−1.08422			−0.542112	+	0.840306i	$0.682375\pi$
$758$	−15.5973	+	10.6542i	−0.566520	+	0.386977i
$759$		0			0
$760$	−19.6193	−	2.40607i	−0.711667	−	0.0872774i
$761$	9.36641	−	1.65155i	0.339532	−	0.0598687i	−0.00128248	−	0.999999i	$-0.500408\pi$
$761$	9.36641	−	1.65155i	0.339532	−	0.0598687i	0.340815	+	0.940130i	$0.389297\pi$
$762$		0			0
$763$	48.0692	−	57.2866i	1.74022	−	2.07392i
$764$	1.18055	−	50.9318i	0.0427108	−	1.84265i
$765$		0			0
$766$	−8.17956	+	7.99217i	−0.295540	+	0.288769i
$767$	1.28171	−	7.26893i	0.0462798	−	0.262466i
$768$		0			0
$769$	−5.24113	−	1.90762i	−0.189000	−	0.0687904i	0.245786	−	0.969324i	$-0.420954\pi$
$769$	−5.24113	−	1.90762i	−0.189000	−	0.0687904i	−0.434786	+	0.900534i	$0.643176\pi$
$770$	−0.0776525	+	0.782968i	−0.00279840	+	0.0282162i
$771$		0			0
$772$	−13.1870	−	39.0217i	−0.474610	−	1.40442i
$773$	−15.2614	+	8.81115i	−0.548913	+	0.316915i	−0.748683	−	0.662928i	$-0.769314\pi$
$773$	−15.2614	+	8.81115i	−0.548913	+	0.316915i	0.199770	+	0.979843i	$0.435980\pi$
$774$		0			0
$775$	−6.89886	−	3.98306i	−0.247815	−	0.143076i
$776$	−0.765094	−	14.5587i	−0.0274653	−	0.522626i
$777$		0			0
$778$	−11.4532	−	25.3235i	−0.410618	−	0.907892i
$779$	2.38932	−	2.00488i	0.0856063	−	0.0718323i
$780$		0			0
$781$	0.447159	−	0.162753i	0.0160006	−	0.00582375i
$782$	−16.1990	+	4.13994i	−0.579275	+	0.148044i
$783$		0			0
$784$	−17.4494	+	27.2266i	−0.623194	+	0.972380i
$785$	−4.57930	−	12.5815i	−0.163442	−	0.449053i
$786$		0			0
$787$	24.8613	+	29.6285i	0.886209	+	1.05614i	0.998050	+	0.0624168i	$0.0198808\pi$
$787$	24.8613	+	29.6285i	0.886209	+	1.05614i	−0.111841	+	0.993726i	$0.535675\pi$
$788$	10.8332	−	8.67038i	0.385916	−	0.308870i
$789$		0			0
$790$	−10.4342	+	21.7157i	−0.371233	+	0.772609i
$791$	10.1230	−	17.5336i	0.359934	−	0.623424i
$792$		0			0
$793$	−4.87062	−	8.43615i	−0.172961	−	0.299577i
$794$	34.8947	−	2.64585i	1.23837	−	0.0938978i
$795$		0			0
$796$	3.49061	+	22.8856i	0.123722	+	0.811158i
$797$	1.14049	−	3.13346i	0.0403981	−	0.110993i	−0.917853	−	0.396920i	$-0.870079\pi$
$797$	1.14049	−	3.13346i	0.0403981	−	0.110993i	0.958251	+	0.285927i	$0.0923014\pi$
$798$		0			0
$799$	11.1344	+	1.96329i	0.393906	+	0.0694562i
$800$	−1.19623	−	5.78631i	−0.0422930	−	0.204577i
$801$		0			0
$802$	−4.64941	+	16.5809i	−0.164176	+	0.585492i
$803$	−0.291568	−	0.244655i	−0.0102892	−	0.00863368i
$804$		0			0
$805$	9.47120	+	53.7139i	0.333816	+	1.89316i
$806$	29.0130	−	40.4296i	1.02194	−	1.42407i
$807$		0			0
$808$	16.9675	−	33.3125i	0.596915	−	1.17193i
$809$			5.26208i			0.185005i	0.995712	+	0.0925025i	$0.0294866\pi$
$809$			5.26208i			0.185005i	−0.995712	+	0.0925025i	$0.970513\pi$
$810$		0			0
$811$		−	3.33372i		−	0.117063i	−0.998286	−	0.0585314i	$-0.981358\pi$
$811$		−	3.33372i		−	0.117063i	0.998286	−	0.0585314i	$-0.0186418\pi$
$812$	−20.5783	+	23.4009i	−0.722158	+	0.821211i
$813$		0			0
$814$	0.322744	+	0.231607i	0.0113122	+	0.00811782i
$815$	4.16818	+	23.6389i	0.146005	+	0.828036i
$816$		0			0
$817$	21.0057	+	17.6259i	0.734897	+	0.616652i
$818$	42.3263	+	11.8686i	1.47990	+	0.414976i
$819$		0			0
$820$	4.60888	+	2.80531i	0.160949	+	0.0979656i
$821$	−25.8625	−	4.56026i	−0.902608	−	0.159154i	−0.296963	−	0.954889i	$-0.595974\pi$
$821$	−25.8625	−	4.56026i	−0.902608	−	0.159154i	−0.605645	+	0.795735i	$0.707085\pi$
$822$		0			0
$823$	−13.1732	+	36.1930i	−0.459188	+	1.26161i	0.466903	+	0.884308i	$0.345370\pi$
$823$	−13.1732	+	36.1930i	−0.459188	+	1.26161i	−0.926091	+	0.377300i	$0.876853\pi$
$824$	2.71506	−	1.15294i	0.0945837	−	0.0401645i
$825$		0			0
$826$	0.664366	+	8.76196i	0.0231162	+	0.304868i
$827$	16.3619	+	28.3397i	0.568960	+	0.985467i	0.996669	+	0.0815507i	$0.0259873\pi$
$827$	16.3619	+	28.3397i	0.568960	+	0.985467i	−0.427710	+	0.903916i	$0.640679\pi$
$828$		0			0
$829$	13.4083	−	23.2238i	0.465688	−	0.806595i	−0.533544	−	0.845772i	$-0.679140\pi$
$829$	13.4083	−	23.2238i	0.465688	−	0.806595i	0.999232	+	0.0391769i	$0.0124736\pi$
$830$	35.7125	+	17.1596i	1.23960	+	0.595617i
$831$		0			0
$832$	36.7068	−	3.86874i	1.27258	−	0.134125i
$833$	10.7560	+	12.8185i	0.372674	+	0.444136i
$834$		0			0
$835$	3.90659	+	10.7333i	0.135193	+	0.371440i
$836$	0.158926	+	0.290619i	0.00549656	+	0.0100513i
$837$		0			0
$838$	−12.9091	−	50.5117i	−0.445939	−	1.74490i
$839$	−5.91646	+	2.15341i	−0.204259	+	0.0743441i	−0.442124	−	0.896954i	$-0.645775\pi$
$839$	−5.91646	+	2.15341i	−0.204259	+	0.0743441i	0.237865	+	0.971298i	$0.423552\pi$
$840$		0			0
$841$	9.88678	−	8.29599i	0.340923	−	0.286069i
$842$	−47.4714	+	21.4702i	−1.63597	+	0.739911i
$843$		0			0
$844$	−5.93748	+	29.6393i	−0.204377	+	1.02023i
$845$	17.6440	+	10.1867i	0.606971	+	0.350435i
$846$		0			0
$847$	−36.9876	+	21.3548i	−1.27091	+	0.733760i
$848$	−28.5502	+	30.9877i	−0.980418	+	1.06412i
$849$		0			0
$850$	−3.04249	−	0.301746i	−0.104357	−	0.0103498i
$851$	25.8769	+	9.41842i	0.887049	+	0.322859i
$852$		0			0
$853$	0.124811	−	0.707838i	0.00427344	−	0.0242359i	−0.982596	−	0.185753i	$-0.940528\pi$
$853$	0.124811	−	0.707838i	0.00427344	−	0.0242359i	0.986870	+	0.161517i	$0.0516387\pi$
$854$	8.10466	+	8.29470i	0.277336	+	0.283839i
$855$		0			0
$856$	34.4067	−	7.94863i	1.17600	−	0.271679i
$857$	35.0599	−	41.7827i	1.19762	−	1.42727i	0.320337	−	0.947304i	$-0.396204\pi$
$857$	35.0599	−	41.7827i	1.19762	−	1.42727i	0.877286	−	0.479968i	$-0.159352\pi$
$858$		0			0
$859$	29.9885	−	5.28779i	1.02320	−	0.180417i	0.363220	−	0.931704i	$-0.381677\pi$
$859$	29.9885	−	5.28779i	1.02320	−	0.180417i	0.659976	+	0.751286i	$0.270566\pi$
$860$	−17.2521	+	44.1860i	−0.588293	+	1.50673i
$861$		0			0
$862$	−9.07610	−	13.2871i	−0.309133	−	0.452560i
$863$	−30.5772			−1.04086			−0.520430	−	0.853904i	$-0.674228\pi$
$863$	−30.5772			−1.04086			−0.520430	+	0.853904i	$0.674228\pi$
$864$		0			0
$865$	−2.16644			−0.0736612
$866$	−5.80430	−	8.49728i	−0.197238	−	0.288749i
$867$		0			0
$868$	−21.5465	+	55.1848i	−0.731337	+	1.87309i
$869$	0.397596	−	0.0701070i	0.0134875	−	0.00237822i
$870$		0			0
$871$	22.4120	−	26.7096i	0.759403	−	0.905022i
$872$	53.0624	−	12.2585i	1.79692	−	0.415125i
$873$		0			0
$874$	16.0471	+	16.4233i	0.542800	+	0.555527i
$875$	6.55870	−	37.1962i	0.221725	−	1.25746i
$876$		0			0
$877$	31.7998	+	11.5742i	1.07380	+	0.390832i	0.817597	−	0.575790i	$-0.195306\pi$
$877$	31.7998	+	11.5742i	1.07380	+	0.390832i	0.256205	+	0.966622i	$0.417528\pi$
$878$	−41.8851	−	4.15405i	−1.41355	−	0.140192i
$879$		0			0
$880$	−0.388253	+	0.421400i	−0.0130880	+	0.0142054i
$881$	10.3117	−	5.95348i	0.347411	−	0.200578i	−0.316133	−	0.948715i	$-0.602385\pi$
$881$	10.3117	−	5.95348i	0.347411	−	0.200578i	0.663544	+	0.748137i	$0.269051\pi$
$882$		0			0
$883$	10.5936	+	6.11620i	0.356502	+	0.205827i	0.667545	−	0.744569i	$-0.267345\pi$
$883$	10.5936	+	6.11620i	0.356502	+	0.205827i	−0.311043	+	0.950396i	$0.600678\pi$
$884$	3.75147	−	18.7269i	0.126175	−	0.629854i
$885$		0			0
$886$	−22.1639	+	10.0242i	−0.744611	+	0.336769i
$887$	−10.2202	+	8.57573i	−0.343159	+	0.287945i	−0.798036	−	0.602609i	$-0.794128\pi$
$887$	−10.2202	+	8.57573i	−0.343159	+	0.287945i	0.454877	+	0.890554i	$0.349683\pi$
$888$		0			0
$889$	7.07159	−	2.57385i	0.237174	−	0.0863241i
$890$	1.84749	+	7.22896i	0.0619279	+	0.242315i
$891$		0			0
$892$	1.57522	+	2.88051i	0.0527422	+	0.0964467i
$893$	−5.31055	−	14.5906i	−0.177711	−	0.488257i
$894$		0			0
$895$	−20.0662	−	23.9140i	−0.670740	−	0.799357i
$896$	−41.1980	+	15.2826i	−1.37633	+	0.510556i
$897$		0			0
$898$	−27.7840	−	13.3500i	−0.927163	−	0.445494i
$899$	−15.2979	+	26.4967i	−0.510212	+	0.883714i
$900$		0			0
$901$	10.9013	+	18.8816i	0.363174	+	0.629036i
$902$	−0.00683603	−	0.0901568i	−0.000227615	−	0.00300189i
$903$		0			0
$904$	13.5712	−	5.76295i	0.451372	−	0.191673i
$905$	−5.55868	+	15.2723i	−0.184777	+	0.507670i
$906$		0			0
$907$	19.8590	+	3.50168i	0.659407	+	0.116271i	0.493331	−	0.869842i	$-0.335779\pi$
$907$	19.8590	+	3.50168i	0.659407	+	0.116271i	0.166076	+	0.986113i	$0.446890\pi$
$908$	−46.6593	−	28.4003i	−1.54844	−	0.942499i
$909$		0			0
$910$	−59.9904	−	16.8218i	−1.98866	−	0.557636i
$911$	−24.2137	−	20.3177i	−0.802237	−	0.673157i	0.146505	−	0.989210i	$-0.453198\pi$
$911$	−24.2137	−	20.3177i	−0.802237	−	0.673157i	−0.948741	+	0.316053i	$0.897642\pi$
$912$		0			0
$913$	−0.115294	−	0.653867i	−0.00381569	−	0.0216398i
$914$	−11.0960	−	7.96271i	−0.367024	−	0.263383i
$915$		0			0
$916$	−8.34356	+	9.48798i	−0.275679	+	0.313492i
$917$		−	1.81657i		−	0.0599884i
$918$		0			0
$919$		−	3.86720i		−	0.127567i	−0.997964	−	0.0637835i	$-0.979683\pi$
$919$		−	3.86720i		−	0.127567i	0.997964	−	0.0637835i	$-0.0203167\pi$
$920$	−18.0275	+	35.3937i	−0.594351	+	1.16689i
$921$		0			0
$922$	−27.0330	+	37.6705i	−0.890286	+	1.24061i
$923$	6.54327	+	37.1087i	0.215374	+	1.22145i
$924$		0			0
$925$	3.85752	+	3.23684i	0.126834	+	0.106427i
$926$	14.6392	−	52.2069i	0.481075	−	1.71562i
$927$		0			0
$928$	−22.2237	+	4.59439i	−0.729527	+	0.150818i
$929$	49.6909	+	8.76185i	1.63031	+	0.287467i	0.912593	−	0.408870i	$-0.134077\pi$
$929$	49.6909	+	8.76185i	1.63031	+	0.287467i	0.717715	+	0.696337i	$0.245188\pi$
$930$		0			0
$931$	7.85977	−	21.5945i	0.257593	−	0.707732i
$932$	8.94160	+	58.6240i	0.292892	+	1.92029i
$933$		0			0
$934$	−16.3353	+	1.23861i	−0.534509	+	0.0405285i
$935$	0.148246	+	0.256770i	0.00484816	+	0.00839726i
$936$		0			0
$937$	24.0457	−	41.6483i	0.785538	−	1.36059i	−0.143139	−	0.989703i	$-0.545720\pi$
$937$	24.0457	−	41.6483i	0.785538	−	1.36059i	0.928677	−	0.370890i	$-0.120947\pi$
$938$	−17.9771	+	37.4140i	−0.586975	+	1.22161i
$939$		0			0
$940$	20.9702	−	16.7836i	0.683973	−	0.547420i
$941$	−4.71969	−	5.62470i	−0.153857	−	0.183360i	0.683610	−	0.729848i	$-0.260409\pi$
$941$	−4.71969	−	5.62470i	−0.153857	−	0.183360i	−0.837467	+	0.546488i	$0.815965\pi$
$942$		0			0
$943$	−2.14368	−	5.88972i	−0.0698079	−	0.191796i
$944$	−3.45292	+	5.38765i	−0.112383	+	0.175353i
$945$		0			0
$946$	0.770136	−	0.196822i	0.0250393	−	0.00639923i
$947$	−29.9257	+	10.8921i	−0.972454	+	0.353944i	−0.778902	−	0.627146i	$-0.784223\pi$
$947$	−29.9257	+	10.8921i	−0.972454	+	0.353944i	−0.193552	+	0.981090i	$0.562001\pi$
$948$		0			0
$949$	23.0881	−	19.3732i	0.749472	−	0.628881i
$950$	1.73029	+	3.82574i	0.0561380	+	0.124123i
$951$		0			0
$952$	1.19325	+	22.7059i	0.0386735	+	0.735902i
$953$	−13.1967	−	7.61912i	−0.427483	−	0.246807i	0.270791	−	0.962638i	$-0.412715\pi$
$953$	−13.1967	−	7.61912i	−0.427483	−	0.246807i	−0.698274	+	0.715831i	$0.746048\pi$
$954$		0			0
$955$	−54.2359	+	31.3131i	−1.75503	+	1.01327i
$956$	−5.95856	−	17.6320i	−0.192714	−	0.570259i
$957$		0			0
$958$	−2.50189	+	25.2265i	−0.0808323	+	0.815030i
$959$	16.0233	+	5.83201i	0.517420	+	0.188325i
$960$		0			0
$961$	−4.71723	+	26.7528i	−0.152169	+	0.862992i
$962$	−22.4993	+	21.9838i	−0.725406	+	0.708787i
$963$		0			0
$964$	−0.651671	+	28.1147i	−0.0209889	+	0.905513i
$965$	−32.5466	+	38.7876i	−1.04771	+	1.24862i
$966$		0			0
$967$	−42.5027	+	7.49437i	−1.36680	+	0.241003i	−0.808430	−	0.588592i	$-0.799682\pi$
$967$	−42.5027	+	7.49437i	−1.36680	+	0.241003i	−0.558365	+	0.829595i	$0.688571\pi$
$968$	−30.8718	−	3.78606i	−0.992257	−	0.121689i
$969$		0			0
$970$	−14.7985	+	10.1085i	−0.475150	+	0.324564i
$971$	−32.9105			−1.05615			−0.528074	−	0.849198i	$-0.677086\pi$
$971$	−32.9105			−1.05615			−0.528074	+	0.849198i	$0.677086\pi$
$972$		0			0
$973$	32.8100			1.05184
$974$	26.4460	−	18.0646i	0.847384	−	0.578829i
$975$		0			0
$976$	1.07959	+	8.37609i	0.0345569	+	0.268112i
$977$	−55.9116	+	9.85873i	−1.78877	+	0.315409i	−0.967070	−	0.254510i	$-0.918086\pi$
$977$	−55.9116	+	9.85873i	−1.78877	+	0.315409i	−0.821701	+	0.569919i	$0.806975\pi$
$978$		0			0
$979$	0.0803698	−	0.0957811i	0.00256863	−	0.00306118i
$980$	39.7423	+	0.921187i	1.26952	+	0.0294262i
$981$		0			0
$982$	26.0029	−	25.4072i	0.829787	−	0.810776i
$983$	5.63075	−	31.9336i	0.179593	−	1.01852i	−0.753114	−	0.657890i	$-0.771449\pi$
$983$	5.63075	−	31.9336i	0.179593	−	1.01852i	0.932707	−	0.360634i	$-0.117440\pi$
$984$		0			0
$985$	−16.0284	−	5.83385i	−0.510707	−	0.185882i
$986$	−1.15892	+	11.6854i	−0.0369077	+	0.372139i
$987$		0			0
$988$	−24.8486	+	8.39734i	−0.790539	+	0.267155i
$989$	47.7202	−	27.5513i	1.51741	−	0.876080i
$990$		0			0
$991$	−36.6324	−	21.1497i	−1.16367	−	0.671843i	−0.211486	−	0.977381i	$-0.567830\pi$
$991$	−36.6324	−	21.1497i	−1.16367	−	0.671843i	−0.952180	+	0.305539i	$0.901164\pi$
$992$	−36.7140	+	22.6577i	−1.16567	+	0.719384i
$993$		0			0
$994$	−18.4860	−	40.8732i	−0.586339	−	1.29642i
$995$	21.8002	−	18.2925i	0.691113	−	0.579912i
$996$		0			0
$997$	31.7692	−	11.5630i	1.00614	−	0.366205i	0.214191	−	0.976792i	$-0.431288\pi$
$997$	31.7692	−	11.5630i	1.00614	−	0.366205i	0.791950	+	0.610586i	$0.209066\pi$
$998$	−9.90536	+	2.53149i	−0.313549	+	0.0801329i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.l.a.143.11		96
3.2	odd	2		108.2.l.a.47.6	yes	96
4.3	odd	2	inner	324.2.l.a.143.10		96
9.2	odd	6		972.2.l.d.107.6		96
9.4	even	3		972.2.l.b.755.1		96
9.5	odd	6		972.2.l.c.755.16		96
9.7	even	3		972.2.l.a.107.11		96
12.11	even	2		108.2.l.a.47.7	yes	96
27.4	even	9		108.2.l.a.23.7	yes	96
27.5	odd	18		972.2.l.b.215.2		96
27.13	even	9		972.2.l.d.863.4		96
27.14	odd	18		972.2.l.a.863.13		96
27.22	even	9		972.2.l.c.215.15		96
27.23	odd	18	inner	324.2.l.a.179.10		96
36.7	odd	6		972.2.l.a.107.13		96
36.11	even	6		972.2.l.d.107.4		96
36.23	even	6		972.2.l.c.755.15		96
36.31	odd	6		972.2.l.b.755.2		96
108.23	even	18	inner	324.2.l.a.179.11		96
108.31	odd	18		108.2.l.a.23.6	✓	96
108.59	even	18		972.2.l.b.215.1		96
108.67	odd	18		972.2.l.d.863.6		96
108.95	even	18		972.2.l.a.863.11		96
108.103	odd	18		972.2.l.c.215.16		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.6	✓	96	108.31	odd	18
108.2.l.a.23.7	yes	96	27.4	even	9
108.2.l.a.47.6	yes	96	3.2	odd	2
108.2.l.a.47.7	yes	96	12.11	even	2
324.2.l.a.143.10		96	4.3	odd	2	inner
324.2.l.a.143.11		96	1.1	even	1	trivial
324.2.l.a.179.10		96	27.23	odd	18	inner
324.2.l.a.179.11		96	108.23	even	18	inner
972.2.l.a.107.11		96	9.7	even	3
972.2.l.a.107.13		96	36.7	odd	6
972.2.l.a.863.11		96	108.95	even	18
972.2.l.a.863.13		96	27.14	odd	18
972.2.l.b.215.1		96	108.59	even	18
972.2.l.b.215.2		96	27.5	odd	18
972.2.l.b.755.1		96	9.4	even	3
972.2.l.b.755.2		96	36.31	odd	6
972.2.l.c.215.15		96	27.22	even	9
972.2.l.c.215.16		96	108.103	odd	18
972.2.l.c.755.15		96	36.23	even	6
972.2.l.c.755.16		96	9.5	odd	6
972.2.l.d.107.4		96	36.11	even	6
972.2.l.d.107.6		96	9.2	odd	6
972.2.l.d.863.4		96	27.13	even	9
972.2.l.d.863.6		96	108.67	odd	18

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.797682 + 1.16778i) q^{2} +(-0.727407 + 1.86303i) q^{4} +(2.42121 - 0.426924i) q^{5} +(-2.49652 + 2.97523i) q^{7} +(-2.75584 + 0.636655i) q^{8} +O(q^{10})\)	\(q+(0.797682 + 1.16778i) q^{2} +(-0.727407 + 1.86303i) q^{4} +(2.42121 - 0.426924i) q^{5} +(-2.49652 + 2.97523i) q^{7} +(-2.75584 + 0.636655i) q^{8} +(2.42991 + 2.48688i) q^{10} +(0.0101176 - 0.0573797i) q^{11} +(4.33551 + 1.57800i) q^{13} +(-5.46584 - 0.542086i) q^{14} +(-2.94176 - 2.71036i) q^{16} +(-1.79249 + 1.03489i) q^{17} +(2.46167 + 1.42125i) q^{19} +(-0.965832 + 4.82133i) q^{20} +(0.0750773 - 0.0339557i) q^{22} +(4.37564 - 3.67159i) q^{23} +(0.981522 - 0.357245i) q^{25} +(1.61561 + 6.32166i) q^{26} +(-3.72696 - 6.81529i) q^{28} +(-1.37208 - 3.76976i) q^{29} +(-4.90230 - 5.84234i) q^{31} +(0.818512 - 5.59732i) q^{32} +(-2.63836 - 1.26771i) q^{34} +(-4.77439 + 8.26948i) q^{35} +(2.41051 + 4.17513i) q^{37} +(0.303931 + 4.00838i) q^{38} +(-6.40067 + 2.71801i) q^{40} +(0.375295 - 1.03112i) q^{41} +(9.50027 + 1.67515i) q^{43} +(0.0995405 + 0.0605878i) q^{44} +(7.77797 + 2.18100i) q^{46} +(-4.18449 - 3.51121i) q^{47} +(-1.40388 - 7.96178i) q^{49} +(1.20013 + 0.861232i) q^{50} +(-6.09354 + 6.92934i) q^{52} -10.5337i q^{53} -0.143248i q^{55} +(4.98581 - 9.78869i) q^{56} +(3.30776 - 4.60936i) q^{58} +(-0.277801 - 1.57549i) q^{59} +(-1.61738 - 1.35715i) q^{61} +(2.91207 - 10.3851i) q^{62} +(7.18934 - 3.50904i) q^{64} +(11.1709 + 1.96973i) q^{65} +(2.58470 - 7.10142i) q^{67} +(-0.624168 - 4.09224i) q^{68} +(-13.4654 + 1.02099i) q^{70} +(4.08357 + 7.07295i) q^{71} +(3.26625 - 5.65731i) q^{73} +(-2.95280 + 6.14537i) q^{74} +(-4.43846 + 3.55234i) q^{76} +(0.145459 + 0.173352i) q^{77} +(2.36993 + 6.51134i) q^{79} +(-8.27973 - 5.30644i) q^{80} +(1.50348 - 0.384241i) q^{82} +(10.7082 - 3.89747i) q^{83} +(-3.89816 + 3.27095i) q^{85} +(5.62199 + 12.4304i) q^{86} +(0.00864860 + 0.164571i) q^{88} +(1.85844 + 1.07297i) q^{89} +(-15.5186 + 8.95967i) q^{91} +(3.65742 + 10.8227i) q^{92} +(0.762413 - 7.68738i) q^{94} +(6.56698 + 2.39019i) q^{95} +(-0.895047 + 5.07606i) q^{97} +(8.17774 - 7.99038i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8} - 3 q^{10} - 12 q^{13} + 21 q^{14} - 6 q^{16} + 18 q^{17} + 27 q^{20} - 6 q^{22} - 12 q^{25} - 12 q^{28} + 24 q^{29} - 24 q^{32} - 12 q^{34} - 6 q^{37} - 18 q^{38} - 21 q^{40} + 42 q^{41} - 63 q^{44} - 3 q^{46} - 12 q^{49} - 87 q^{50} - 33 q^{52} - 99 q^{56} - 33 q^{58} - 12 q^{61} - 90 q^{62} - 3 q^{64} - 12 q^{65} - 51 q^{68} - 21 q^{70} - 6 q^{73} - 21 q^{74} - 18 q^{76} - 12 q^{77} - 12 q^{82} - 42 q^{85} + 30 q^{86} + 18 q^{88} + 123 q^{92} + 21 q^{94} - 30 q^{97} + 180 q^{98}+O(q^{100}) \) 96 * q + 6 * q^2 - 6 * q^4 + 12 * q^5 + 9 * q^8 - 3 * q^10 - 12 * q^13 + 21 * q^14 - 6 * q^16 + 18 * q^17 + 27 * q^20 - 6 * q^22 - 12 * q^25 - 12 * q^28 + 24 * q^29 - 24 * q^32 - 12 * q^34 - 6 * q^37 - 18 * q^38 - 21 * q^40 + 42 * q^41 - 63 * q^44 - 3 * q^46 - 12 * q^49 - 87 * q^50 - 33 * q^52 - 99 * q^56 - 33 * q^58 - 12 * q^61 - 90 * q^62 - 3 * q^64 - 12 * q^65 - 51 * q^68 - 21 * q^70 - 6 * q^73 - 21 * q^74 - 18 * q^76 - 12 * q^77 - 12 * q^82 - 42 * q^85 + 30 * q^86 + 18 * q^88 + 123 * q^92 + 21 * q^94 - 30 * q^97 + 180 * q^98

Introduction

L-functions

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