LMFDB - Embedded newform 324.2.l.a.179.10

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			179.10
Character	$\chi$	$=$	324.179
Dual form			324.2.l.a.143.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.139573 - 1.40731i) q^{2} +(-1.96104 - 0.392845i) q^{4} +(2.42121 + 0.426924i) q^{5} +(2.49652 + 2.97523i) q^{7} +(-0.826562 + 2.70496i) q^{8} +O(q^{10})$	\(q+(0.139573 - 1.40731i) q^{2} +(-1.96104 - 0.392845i) q^{4} +(2.42121 + 0.426924i) q^{5} +(2.49652 + 2.97523i) q^{7} +(-0.826562 + 2.70496i) q^{8} +(0.938750 - 3.34780i) q^{10} +(-0.0101176 - 0.0573797i) q^{11} +(4.33551 - 1.57800i) q^{13} +(4.53552 - 3.09811i) q^{14} +(3.69135 + 1.54077i) q^{16} +(-1.79249 - 1.03489i) q^{17} +(-2.46167 + 1.42125i) q^{19} +(-4.58037 - 1.78837i) q^{20} +(-0.0821631 + 0.00622992i) q^{22} +(-4.37564 - 3.67159i) q^{23} +(0.981522 + 0.357245i) q^{25} +(-1.61561 - 6.32166i) q^{26} +(-3.72696 - 6.81529i) q^{28} +(-1.37208 + 3.76976i) q^{29} +(4.90230 - 5.84234i) q^{31} +(2.68355 - 4.97982i) q^{32} +(-1.70660 + 2.37814i) q^{34} +(4.77439 + 8.26948i) q^{35} +(2.41051 - 4.17513i) q^{37} +(1.65655 + 3.66270i) q^{38} +(-3.15609 + 6.19639i) q^{40} +(0.375295 + 1.03112i) q^{41} +(-9.50027 + 1.67515i) q^{43} +(-0.00270032 + 0.116498i) q^{44} +(-5.77779 + 5.64542i) q^{46} +(4.18449 - 3.51121i) q^{47} +(-1.40388 + 7.96178i) q^{49} +(0.639748 - 1.33144i) q^{50} +(-9.12202 + 1.39133i) q^{52} +10.5337i q^{53} -0.143248i q^{55} +(-10.1114 + 4.29376i) q^{56} +(5.11372 + 2.45710i) q^{58} +(0.277801 - 1.57549i) q^{59} +(-1.61738 + 1.35715i) q^{61} +(-7.53775 - 7.71449i) q^{62} +(-6.63359 - 4.47163i) q^{64} +(11.1709 - 1.96973i) q^{65} +(-2.58470 - 7.10142i) q^{67} +(3.10858 + 2.73363i) q^{68} +(12.3041 - 5.56484i) q^{70} +(-4.08357 + 7.07295i) q^{71} +(3.26625 + 5.65731i) q^{73} +(-5.53926 - 3.97507i) q^{74} +(5.38576 - 1.82006i) q^{76} +(0.145459 - 0.173352i) q^{77} +(-2.36993 + 6.51134i) q^{79} +(8.27973 + 5.30644i) q^{80} +(1.50348 - 0.384241i) q^{82} +(-10.7082 - 3.89747i) q^{83} +(-3.89816 - 3.27095i) q^{85} +(1.03148 + 13.6036i) q^{86} +(0.163572 + 0.0200602i) q^{88} +(1.85844 - 1.07297i) q^{89} +(15.5186 + 8.95967i) q^{91} +(7.13842 + 8.91908i) q^{92} +(-4.35731 - 6.37895i) q^{94} +(-6.56698 + 2.39019i) q^{95} +(-0.895047 - 5.07606i) q^{97} +(11.0087 + 3.08694i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	0.139573	−	1.40731i	0.0986930	−	0.995118i
$2$	0.139573	−	1.40731i	0.0986930	−	0.995118i
$3$		0			0
$3$		0			0
$4$	−1.96104	−	0.392845i	−0.980519	−	0.196422i
$5$	2.42121	+	0.426924i	1.08280	+	0.190926i	0.686452	−	0.727175i	$-0.259167\pi$
$5$	2.42121	+	0.426924i	1.08280	+	0.190926i	0.396345	+	0.918102i	$0.370278\pi$
$6$		0			0
$7$	2.49652	+	2.97523i	0.943595	+	1.12453i	0.992067	+	0.125708i	$0.0401202\pi$
$7$	2.49652	+	2.97523i	0.943595	+	1.12453i	−0.0484727	+	0.998825i	$0.515435\pi$
$8$	−0.826562	+	2.70496i	−0.292234	+	0.956347i
$9$		0			0
$10$	0.938750	−	3.34780i	0.296859	−	1.05867i
$11$	−0.0101176	−	0.0573797i	−0.00305057	−	0.0173006i	0.983244	−	0.182292i	$-0.0583515\pi$
$11$	−0.0101176	−	0.0573797i	−0.00305057	−	0.0173006i	−0.986295	+	0.164991i	$0.947240\pi$
$12$		0			0
$13$	4.33551	−	1.57800i	1.20246	−	0.437658i	0.338375	−	0.941011i	$-0.390123\pi$
$13$	4.33551	−	1.57800i	1.20246	−	0.437658i	0.864081	+	0.503353i	$0.167901\pi$
$14$	4.53552	−	3.09811i	1.21217	−	0.828004i
$15$		0			0
$16$	3.69135	+	1.54077i	0.922837	+	0.385192i
$17$	−1.79249	−	1.03489i	−0.434742	−	0.250998i	0.266623	−	0.963801i	$-0.414092\pi$
$17$	−1.79249	−	1.03489i	−0.434742	−	0.250998i	−0.701365	+	0.712803i	$0.747426\pi$
$18$		0			0
$19$	−2.46167	+	1.42125i	−0.564746	+	0.326056i	−0.755048	−	0.655669i	$-0.772387\pi$
$19$	−2.46167	+	1.42125i	−0.564746	+	0.326056i	0.190302	+	0.981726i	$0.439053\pi$
$20$	−4.58037	−	1.78837i	−1.02420	−	0.399893i
$21$		0			0
$22$	−0.0821631	+	0.00622992i	−0.0175172	+	0.00132822i
$23$	−4.37564	−	3.67159i	−0.912383	−	0.765580i	0.0601878	−	0.998187i	$-0.480830\pi$
$23$	−4.37564	−	3.67159i	−0.912383	−	0.765580i	−0.972571	+	0.232607i	$0.925274\pi$
$24$		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	0.744679	+	0.667423i	$0.232603\pi$
$29$	−1.37208	+	3.76976i	−0.254789	+	0.700028i	−0.999468	+	0.0326049i	$0.989620\pi$
$30$		0			0
$31$	4.90230	−	5.84234i	0.880479	−	1.04931i	−0.117935	−	0.993021i	$-0.537627\pi$
$31$	4.90230	−	5.84234i	0.880479	−	1.04931i	0.998414	−	0.0562932i	$-0.0179282\pi$
$32$	2.68355	−	4.97982i	0.474389	−	0.880315i
$33$		0			0
$34$	−1.70660	+	2.37814i	−0.292679	+	0.407848i
$35$	4.77439	+	8.26948i	0.807019	+	1.39780i
$36$		0			0
$37$	2.41051	−	4.17513i	0.396286	−	0.686387i	−0.596979	−	0.802257i	$-0.703632\pi$
$37$	2.41051	−	4.17513i	0.396286	−	0.686387i	0.993264	+	0.115870i	$0.0369656\pi$
$38$	1.65655	+	3.66270i	0.268728	+	0.594168i
$39$		0			0
$40$	−3.15609	+	6.19639i	−0.499022	+	0.979735i
$41$	0.375295	+	1.03112i	0.0586113	+	0.161033i	0.965542	−	0.260246i	$-0.0838036\pi$
$41$	0.375295	+	1.03112i	0.0586113	+	0.161033i	−0.906931	+	0.421279i	$0.861581\pi$
$42$		0			0
$43$	−9.50027	+	1.67515i	−1.44878	+	0.255459i	−0.842028	−	0.539434i	$-0.818638\pi$
$43$	−9.50027	+	1.67515i	−1.44878	+	0.255459i	−0.606750	+	0.794893i	$0.707527\pi$
$44$	−0.00270032	+	0.116498i	−0.000407088	+	0.0175628i
$45$		0			0
$46$	−5.77779	+	5.64542i	−0.851888	+	0.832371i
$47$	4.18449	−	3.51121i	0.610371	−	0.512162i	−0.284389	−	0.958709i	$-0.591791\pi$
$47$	4.18449	−	3.51121i	0.610371	−	0.512162i	0.894760	+	0.446547i	$0.147346\pi$
$48$		0			0
$49$	−1.40388	+	7.96178i	−0.200554	+	1.13740i
$50$	0.639748	−	1.33144i	0.0904740	−	0.188295i
$51$		0			0
$52$	−9.12202	+	1.39133i	−1.26500	+	0.192943i
$53$			10.5337i			1.44692i	0.690367	+	0.723459i	$0.257449\pi$
$53$			10.5337i			1.44692i	−0.690367	+	0.723459i	$0.742551\pi$
$54$		0			0
$55$		−	0.143248i		−	0.0193155i
$56$	−10.1114	+	4.29376i	−1.35119	+	0.573778i
$57$		0			0
$58$	5.11372	+	2.45710i	0.671464	+	0.322633i
$59$	0.277801	−	1.57549i	0.0361667	−	0.205111i	−0.961370	−	0.275260i	$-0.911236\pi$
$59$	0.277801	−	1.57549i	0.0361667	−	0.205111i	0.997537	+	0.0701484i	$0.0223473\pi$
$60$		0			0
$61$	−1.61738	+	1.35715i	−0.207085	+	0.173765i	−0.740431	−	0.672132i	$-0.765379\pi$
$61$	−1.61738	+	1.35715i	−0.207085	+	0.173765i	0.533346	+	0.845897i	$0.320934\pi$
$62$	−7.53775	−	7.71449i	−0.957295	−	0.979741i
$63$		0			0
$64$	−6.63359	−	4.47163i	−0.829199	−	0.558954i
$65$	11.1709	−	1.96973i	1.38558	−	0.244314i
$66$		0			0
$67$	−2.58470	−	7.10142i	−0.315772	−	0.867576i	−0.991463	−	0.130391i	$-0.958377\pi$
$67$	−2.58470	−	7.10142i	−0.315772	−	0.867576i	0.675691	−	0.737185i	$-0.263845\pi$
$68$	3.10858	+	2.73363i	0.376971	+	0.331502i
$69$		0			0
$70$	12.3041	−	5.56484i	1.47062	−	0.665126i
$71$	−4.08357	+	7.07295i	−0.484630	+	0.839404i	−0.999844	−	0.0176575i	$-0.994379\pi$
$71$	−4.08357	+	7.07295i	−0.484630	+	0.839404i	0.515214	+	0.857062i	$0.327712\pi$
$72$		0			0
$73$	3.26625	+	5.65731i	0.382286	+	0.662138i	0.991389	−	0.130953i	$-0.0418037\pi$
$73$	3.26625	+	5.65731i	0.382286	+	0.662138i	−0.609103	+	0.793091i	$0.708470\pi$
$74$	−5.53926	−	3.97507i	−0.643926	−	0.462093i
$75$		0			0
$76$	5.38576	−	1.82006i	0.617789	−	0.208776i
$77$	0.145459	−	0.173352i	0.0165766	−	0.0197552i
$78$		0			0
$79$	−2.36993	+	6.51134i	−0.266638	+	0.732583i	0.732044	+	0.681258i	$0.238567\pi$
$79$	−2.36993	+	6.51134i	−0.266638	+	0.732583i	−0.998682	+	0.0513249i	$0.983656\pi$
$80$	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	$-0.603956\pi$
$83$	−10.7082	−	3.89747i	−1.17538	−	0.427803i	−0.854568	+	0.519340i	$0.826178\pi$
$84$		0			0
$85$	−3.89816	−	3.27095i	−0.422815	−	0.354784i
$86$	1.03148	+	13.6036i	0.111227	+	1.46692i
$87$		0			0
$88$	0.163572	+	0.0200602i	0.0174369	+	0.00213843i
$89$	1.85844	−	1.07297i	0.196995	−	0.113735i	−0.398258	−	0.917273i	$-0.630385\pi$
$89$	1.85844	−	1.07297i	0.196995	−	0.113735i	0.595253	+	0.803538i	$0.297052\pi$
$90$		0			0
$91$	15.5186	+	8.95967i	1.62679	+	0.939228i
$92$	7.13842	+	8.91908i	0.744232	+	0.929879i
$93$		0			0
$94$	−4.35731	−	6.37895i	−0.449422	−	0.657938i
$95$	−6.56698	+	2.39019i	−0.673758	+	0.245228i
$96$		0			0
$97$	−0.895047	−	5.07606i	−0.0908783	−	0.515396i	−0.995933	−	0.0901005i	$-0.971281\pi$
$97$	−0.895047	−	5.07606i	−0.0908783	−	0.515396i	0.905054	−	0.425296i	$-0.139830\pi$
$98$	11.0087	+	3.08694i	1.11205	+	0.311828i
$99$		0			0
$100$	−1.78446	−	1.08616i	−0.178446	−	0.108616i
$101$	−8.49605	−	10.1252i	−0.845389	−	1.00750i	−0.999810	−	0.0194902i	$-0.993796\pi$
$101$	−8.49605	−	10.1252i	−0.845389	−	1.00750i	0.154421	−	0.988005i	$-0.450649\pi$
$102$		0			0
$103$	1.02704	+	0.181095i	0.101197	+	0.0178438i	0.224017	−	0.974585i	$-0.428083\pi$
$103$	1.02704	+	0.181095i	0.101197	+	0.0178438i	−0.122820	+	0.992429i	$0.539194\pi$
$104$	0.684848	+	13.0317i	0.0671548	+	1.27786i
$105$		0			0
$106$	14.8242	+	1.47022i	1.43985	+	0.142801i
$107$	12.4850			1.20697			0.603485	−	0.797375i	$-0.293778\pi$
$107$	12.4850			1.20697			0.603485	+	0.797375i	$0.293778\pi$
$108$		0			0
$109$	−19.2545			−1.84425			−0.922123	−	0.386896i	$-0.873547\pi$
$109$	−19.2545			−1.84425			−0.922123	+	0.386896i	$0.873547\pi$
$110$	−0.201594	−	0.0199935i	−0.0192212	−	0.00190630i
$111$		0			0
$112$	4.63137	+	14.8292i	0.437623	+	1.40122i
$113$	−5.13364	−	0.905199i	−0.482932	−	0.0851540i	−0.0731186	−	0.997323i	$-0.523295\pi$
$113$	−5.13364	−	0.905199i	−0.482932	−	0.0851540i	−0.409814	+	0.912169i	$0.634406\pi$
$114$		0			0
$115$	−9.02683	−	10.7578i	−0.841756	−	1.00317i
$116$	4.17164	−	6.85364i	0.387327	−	0.636344i
$117$		0			0
$118$	−2.17843	−	0.610848i	−0.200541	−	0.0562331i
$119$	−1.39593	−	7.91669i	−0.127964	−	0.725722i
$120$		0			0
$121$	10.3334	−	3.76106i	0.939403	−	0.341915i
$122$	1.68418	+	2.46558i	0.152479	+	0.223223i
$123$		0			0
$124$	−11.9087	+	9.53120i	−1.06944	+	0.855927i
$125$	−8.42192	−	4.86240i	−0.753279	−	0.434906i
$126$		0			0
$127$	1.67801	−	0.968801i	0.148900	−	0.0859672i	−0.423699	−	0.905803i	$-0.639269\pi$
$127$	1.67801	−	0.968801i	0.148900	−	0.0859672i	0.572599	+	0.819836i	$0.305935\pi$
$128$	−7.21884	+	8.71140i	−0.638061	+	0.769986i
$129$		0			0
$130$	−1.21286	−	15.9958i	−0.106375	−	1.40292i
$131$	0.358293	+	0.300644i	0.0313042	+	0.0262674i	0.658306	−	0.752751i	$-0.271273\pi$
$131$	0.358293	+	0.300644i	0.0313042	+	0.0262674i	−0.627001	+	0.779018i	$0.715718\pi$
$132$		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	−0.987163	−	0.159715i	$-0.948942\pi$
$137$	−1.50159	+	4.12558i	−0.128289	+	0.352472i	0.858874	+	0.512187i	$0.171165\pi$
$138$		0			0
$139$	5.43008	−	6.47132i	0.460573	−	0.548890i	−0.484908	−	0.874565i	$-0.661147\pi$
$139$	5.43008	−	6.47132i	0.460573	−	0.548890i	0.945482	+	0.325675i	$0.105592\pi$
$140$	−6.11414	−	18.0924i	−0.516739	−	1.52908i
$141$		0			0
$142$	9.38387	+	6.73403i	0.787477	+	0.565108i
$143$	−0.134410	−	0.232805i	−0.0112399	−	0.0194681i
$144$		0			0
$145$	−4.93150	+	8.54161i	−0.409539	+	0.709342i
$146$	8.41747	−	3.80702i	0.696635	−	0.315071i
$147$		0			0
$148$	−6.36729	+	7.24063i	−0.523388	+	0.595177i
$149$	−3.47719	−	9.55350i	−0.284863	−	0.782653i	−0.996765	−	0.0803748i	$-0.974388\pi$
$149$	−3.47719	−	9.55350i	−0.284863	−	0.782653i	0.711902	−	0.702279i	$-0.247834\pi$
$150$		0			0
$151$	2.35013	−	0.414392i	0.191251	−	0.0337227i	−0.0772021	−	0.997015i	$-0.524599\pi$
$151$	2.35013	−	0.414392i	0.191251	−	0.0337227i	0.268453	+	0.963293i	$0.413488\pi$
$152$	−1.80969	−	7.83346i	−0.146785	−	0.635378i
$153$		0			0
$154$	−0.223657	−	0.228901i	−0.0180228	−	0.0184454i
$155$	14.3637	−	12.0526i	1.15372	−	0.968088i
$156$		0			0
$157$	−0.945663	+	5.36312i	−0.0754721	+	0.428024i	0.923537	+	0.383510i	$0.125285\pi$
$157$	−0.945663	+	5.36312i	−0.0754721	+	0.428024i	−0.999009	+	0.0445136i	$0.985826\pi$
$158$	8.83269	+	4.24403i	0.702691	+	0.337637i
$159$		0			0
$160$	8.62343	−	10.9115i	0.681742	−	0.862630i
$161$		−	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	$0.875112\pi$
$164$	−0.330901	−	2.16949i	−0.0258390	−	0.169409i
$165$		0			0
$166$	−6.97952	+	14.5258i	−0.541716	+	1.12742i
$167$	−0.806745	+	4.57528i	−0.0624278	+	0.354046i	0.937553	+	0.347843i	$0.113086\pi$
$167$	−0.806745	+	4.57528i	−0.0624278	+	0.354046i	−0.999981	+	0.00620306i	$0.998025\pi$
$168$		0			0
$169$	6.34803	−	5.32663i	0.488310	−	0.409741i
$170$	−5.14731	+	5.02939i	−0.394781	+	0.385736i
$171$		0			0
$172$	19.2885	+	0.447088i	1.47073	+	0.0340901i
$173$	−0.867796	+	0.153016i	−0.0659773	+	0.0116336i	−0.206539	−	0.978438i	$-0.566220\pi$
$173$	−0.867796	+	0.153016i	−0.0659773	+	0.0116336i	0.140562	+	0.990072i	$0.455109\pi$
$174$		0			0
$175$	1.38750	+	3.81213i	0.104885	+	0.288170i
$176$	0.0510612	−	0.227397i	0.00384888	−	0.0171407i
$177$		0			0
$178$	−1.25062	−	2.76516i	−0.0937377	−	0.207258i
$179$	6.34874	−	10.9963i	0.474527	−	0.821905i	−0.525047	−	0.851073i	$-0.675952\pi$
$179$	6.34874	−	10.9963i	0.474527	−	0.821905i	0.999575	+	0.0291678i	$0.00928571\pi$
$180$		0			0
$181$	−3.30529	−	5.72493i	−0.245680	−	0.425530i	0.716643	−	0.697441i	$-0.245678\pi$
$181$	−3.30529	−	5.72493i	−0.245680	−	0.425530i	−0.962323	+	0.271910i	$0.912345\pi$
$182$	14.7750	−	20.5889i	1.09520	−	1.52615i
$183$		0			0
$184$	13.5482	−	8.80111i	0.998789	−	0.648826i
$185$	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	$-0.0157949\pi$
$191$	23.9365	+	8.71219i	1.73199	+	0.630392i	0.733219	+	0.679993i	$0.238017\pi$
$192$		0			0
$193$	−15.7766	−	13.2381i	−1.13562	−	0.952899i	−0.136334	−	0.990663i	$-0.543532\pi$
$193$	−15.7766	−	13.2381i	−1.13562	−	0.952899i	−0.999287	+	0.0377638i	$0.987977\pi$
$194$	−7.26852	+	0.551127i	−0.521849	+	0.0395686i
$195$		0			0
$196$	5.88080	−	15.0619i	0.420057	−	1.07585i
$197$	−6.00833	+	3.46891i	−0.428076	+	0.247150i	−0.698526	−	0.715584i	$-0.746161\pi$
$197$	−6.00833	+	3.46891i	−0.428076	+	0.247150i	0.270451	+	0.962734i	$0.412827\pi$
$198$		0			0
$199$	−10.0244	−	5.78756i	−0.710608	−	0.410270i	0.100678	−	0.994919i	$-0.467899\pi$
$199$	−10.0244	−	5.78756i	−0.710608	−	0.410270i	−0.811286	+	0.584650i	$0.801232\pi$
$200$	−1.77762	+	2.35969i	−0.125697	+	0.166855i
$201$		0			0
$202$	−15.4351	+	10.5434i	−1.08601	+	0.741829i
$203$	−14.6413	+	5.32902i	−1.02762	+	0.374024i
$204$		0			0
$205$	0.468460	+	2.65677i	0.0327187	+	0.185557i
$206$	0.398203	−	1.42009i	0.0277441	−	0.0989421i
$207$		0			0
$208$	18.4352	+	0.855080i	1.27825	+	0.0592891i
$209$	0.106457	+	0.126870i	0.00736377	+	0.00877580i
$210$		0			0
$211$	−14.8845	−	2.62453i	−1.02469	−	0.180680i	−0.364046	−	0.931381i	$-0.618605\pi$
$211$	−14.8845	−	2.62453i	−1.02469	−	0.180680i	−0.660643	+	0.750701i	$0.729716\pi$
$212$	4.13812	−	20.6570i	0.284207	−	1.41873i
$213$		0			0
$214$	1.74257	−	17.5702i	0.119119	−	1.20108i
$215$	−23.7173			−1.61751
$216$		0			0
$217$	29.6210			2.01080
$218$	−2.68741	+	27.0970i	−0.182014	+	1.83524i
$219$		0			0
$220$	−0.0562741	+	0.280914i	−0.00379400	+	0.0189392i
$221$	−9.40441	−	1.65825i	−0.632609	−	0.111546i
$222$		0			0
$223$	−1.05516	−	1.25750i	−0.0706590	−	0.0842081i	0.729557	−	0.683920i	$-0.239726\pi$
$223$	−1.05516	−	1.25750i	−0.0706590	−	0.0842081i	−0.800216	+	0.599712i	$0.795282\pi$
$224$	21.5156	−	4.44802i	1.43757	−	0.297196i
$225$		0			0
$226$	−1.99041	+	7.09828i	−0.132400	+	0.472170i
$227$	4.74259	+	26.8966i	0.314777	+	1.78519i	0.573468	+	0.819228i	$0.305598\pi$
$227$	4.74259	+	26.8966i	0.314777	+	1.78519i	−0.258691	+	0.965960i	$0.583291\pi$
$228$		0			0
$229$	5.93639	−	2.16067i	0.392288	−	0.142781i	−0.138343	−	0.990384i	$-0.544178\pi$
$229$	5.93639	−	2.16067i	0.392288	−	0.142781i	0.530630	+	0.847603i	$0.321955\pi$
$230$	−16.3994	+	11.2021i	−1.08134	+	0.738641i
$231$		0			0
$232$	−9.06294	−	6.82737i	−0.595011	−	0.448239i
$233$	25.6785	+	14.8255i	1.68226	+	0.971251i	0.960157	+	0.279461i	$0.0901558\pi$
$233$	25.6785	+	14.8255i	1.68226	+	0.971251i	0.722099	+	0.691790i	$0.243178\pi$
$234$		0			0
$235$	11.6306	−	6.71490i	0.758693	−	0.438032i
$236$	−1.16370	+	2.98046i	−0.0757506	+	0.194012i
$237$		0			0
$238$	−11.3361	+	0.859544i	−0.734808	+	0.0557160i
$239$	7.12866	+	5.98165i	0.461114	+	0.386921i	0.843541	−	0.537065i	$-0.180467\pi$
$239$	7.12866	+	5.98165i	0.461114	+	0.386921i	−0.382426	+	0.923986i	$0.624911\pi$
$240$		0			0
$241$	13.2131	+	4.80918i	0.851132	+	0.309787i	0.730502	−	0.682911i	$-0.239286\pi$
$241$	13.2131	+	4.80918i	0.851132	+	0.309787i	0.120630	+	0.992697i	$0.461508\pi$
$242$	−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
$248$	11.7512	+	18.0896i	0.746203	+	1.14869i
$249$		0			0
$250$	−8.01837	+	11.1736i	−0.507126	+	0.706680i
$251$	−7.60386	−	13.1703i	−0.479951	−	0.831300i	0.519784	−	0.854298i	$-0.326012\pi$
$251$	−7.60386	−	13.1703i	−0.479951	−	0.831300i	−0.999736	+	0.0229974i	$0.992679\pi$
$252$		0			0
$253$	−0.166404	+	0.288220i	−0.0104617	+	0.0181203i
$254$	−1.12920	−	2.49670i	−0.0708521	−	0.156657i
$255$		0			0
$256$	11.2521	+	11.3750i	0.703255	+	0.710938i
$257$	2.42247	+	6.65567i	0.151109	+	0.415169i	0.992032	−	0.125986i	$-0.0402094\pi$
$257$	2.42247	+	6.65567i	0.151109	+	0.415169i	−0.840923	+	0.541155i	$0.817987\pi$
$258$		0			0
$259$	18.4399	−	3.25145i	1.14580	−	0.202035i
$260$	−22.6803	−	0.525707i	−1.40657	−	0.0326030i
$261$		0			0
$262$	0.473107	−	0.462268i	0.0292286	−	0.0285590i
$263$	−1.52299	+	1.27794i	−0.0939113	+	0.0788009i	−0.688535	−	0.725204i	$-0.741746\pi$
$263$	−1.52299	+	1.27794i	−0.0939113	+	0.0788009i	0.594623	+	0.804004i	$0.297301\pi$
$264$		0			0
$265$	−4.49710	+	25.5043i	−0.276255	+	1.56672i
$266$	−6.76178	+	14.0726i	−0.414591	+	0.862847i
$267$		0			0
$268$	2.27895	+	14.9415i	0.139209	+	0.912700i
$269$		−	1.18433i		−	0.0722097i	−0.999348	−	0.0361048i	$-0.988505\pi$
$269$		−	1.18433i		−	0.0722097i	0.999348	−	0.0361048i	$-0.0114950\pi$
$270$		0			0
$271$		−	10.9019i		−	0.662245i	−0.943588	−	0.331122i	$-0.892573\pi$
$271$		−	10.9019i		−	0.662245i	0.943588	−	0.331122i	$-0.107427\pi$
$272$	−5.02216	−	6.58195i	−0.304513	−	0.399089i
$273$		0			0
$274$	5.59639	+	2.68902i	0.338090	+	0.162450i
$275$	0.0105680	−	0.0599339i	0.000637272	−	0.00361415i
$276$		0			0
$277$	−4.33388	+	3.63656i	−0.260398	+	0.218500i	−0.763634	−	0.645649i	$-0.776587\pi$
$277$	−4.33388	+	3.63656i	−0.260398	+	0.218500i	0.503237	+	0.864149i	$0.332142\pi$
$278$	−8.34925	−	8.54502i	−0.500755	−	0.512496i
$279$		0			0
$280$	−26.3149	+	6.07928i	−1.57262	+	0.363306i
$281$	12.2002	−	2.15122i	0.727801	−	0.128331i	0.202542	−	0.979273i	$-0.435080\pi$
$281$	12.2002	−	2.15122i	0.727801	−	0.128331i	0.525259	+	0.850943i	$0.323969\pi$
$282$		0			0
$283$	7.70900	+	21.1803i	0.458252	+	1.25904i	0.926785	+	0.375592i	$0.122561\pi$
$283$	7.70900	+	21.1803i	0.458252	+	1.25904i	−0.468533	+	0.883446i	$0.655217\pi$
$284$	10.7866	−	12.2661i	0.640067	−	0.727860i
$285$		0			0
$286$	−0.346389	+	0.156663i	−0.0204824	+	0.00926369i
$287$	−2.13088	+	3.69079i	−0.125782	+	0.217860i
$288$		0			0
$289$	−6.35799	−	11.0124i	−0.374000	−	0.647786i
$290$	11.3324	+	8.13232i	0.665460	+	0.477546i
$291$		0			0
$292$	−4.18280	−	12.3773i	−0.244780	−	0.724329i
$293$	−16.1235	+	19.2153i	−0.941947	+	1.12257i	0.0503554	+	0.998731i	$0.483965\pi$
$293$	−16.1235	+	19.2153i	−0.941947	+	1.12257i	−0.992303	+	0.123838i	$0.960480\pi$
$294$		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
$302$	−0.255162	−	3.36520i	−0.0146829	−	0.193646i
$303$		0			0
$304$	−11.2767	+	1.45345i	−0.646762	+	0.0833611i
$305$	−4.49542	+	2.59543i	−0.257407	+	0.148614i
$306$		0			0
$307$	−7.99858	−	4.61798i	−0.456503	−	0.263562i	0.254070	−	0.967186i	$-0.418231\pi$
$307$	−7.99858	−	4.61798i	−0.456503	−	0.263562i	−0.710573	+	0.703624i	$0.751564\pi$
$308$	−0.353351	+	0.282806i	−0.0201341	+	0.0161144i
$309$		0			0
$310$	−14.9569	−	21.8964i	−0.849498	−	1.24363i
$311$	24.4624	−	8.90360i	1.38714	−	0.504877i	0.462803	−	0.886461i	$-0.346844\pi$
$311$	24.4624	−	8.90360i	1.38714	−	0.504877i	0.924334	+	0.381584i	$0.124621\pi$
$312$		0			0
$313$	3.88258	+	22.0192i	0.219456	+	1.24460i	0.873004	+	0.487713i	$0.162169\pi$
$313$	3.88258	+	22.0192i	0.219456	+	1.24460i	−0.653548	+	0.756885i	$0.726720\pi$
$314$	7.41558	+	2.07939i	0.418486	+	0.117347i
$315$		0			0
$316$	7.20547	−	11.8380i	0.405340	−	0.665938i
$317$	7.49063	+	8.92698i	0.420716	+	0.501389i	0.934220	−	0.356698i	$-0.116097\pi$
$317$	7.49063	+	8.92698i	0.420716	+	0.501389i	−0.513504	+	0.858087i	$0.671653\pi$
$318$		0			0
$319$	0.230190	+	0.0405887i	0.0128882	+	0.00227253i
$320$	−14.1523	−	13.6588i	−0.791135	−	0.763549i
$321$		0			0
$322$	−31.2208	−	3.09639i	−1.73987	−	0.172555i
$323$	5.88335			0.327358
$324$		0			0
$325$	4.81914			0.267318
$326$	13.7400	+	1.36269i	0.760986	+	0.0754724i
$327$		0			0
$328$	−3.09933	+	0.162877i	−0.171132	+	0.00899340i
$329$	20.8933	+	3.68406i	1.15189	+	0.203109i
$330$		0			0
$331$	2.82088	+	3.36179i	0.155050	+	0.184781i	0.837977	−	0.545705i	$-0.183738\pi$
$331$	2.82088	+	3.36179i	0.155050	+	0.184781i	−0.682928	+	0.730486i	$0.739294\pi$
$332$	19.4681	+	11.8498i	1.06845	+	0.650340i
$333$		0			0
$334$	6.32623	+	1.77392i	0.346156	+	0.0970648i
$335$	−3.22634	−	18.2975i	−0.176274	−	0.999698i
$336$		0			0
$337$	31.6135	−	11.5064i	1.72210	−	0.626793i	0.724081	−	0.689715i	$-0.242264\pi$
$337$	31.6135	−	11.5064i	1.72210	−	0.626793i	0.998018	+	0.0629227i	$0.0200421\pi$
$338$	−6.61020	−	9.67709i	−0.359548	−	0.526364i
$339$		0			0
$340$	6.35948	+	7.94583i	0.344891	+	0.430923i
$341$	−0.384831	−	0.222182i	−0.0208398	−	0.0120318i
$342$		0			0
$343$	−3.64812	+	2.10624i	−0.196980	+	0.113726i
$344$	3.32134	−	27.0824i	0.179075	−	1.46019i
$345$		0			0
$346$	0.0942197	+	1.24261i	0.00506528	+	0.0668033i
$347$	−11.4677	−	9.62251i	−0.615616	−	0.516563i	0.280806	−	0.959765i	$-0.409398\pi$
$347$	−11.4677	−	9.62251i	−0.615616	−	0.516563i	−0.896422	+	0.443201i	$0.853843\pi$
$348$		0			0
$349$	9.99580	+	3.63817i	0.535063	+	0.194747i	0.595398	−	0.803431i	$-0.296995\pi$
$349$	9.99580	+	3.63817i	0.535063	+	0.194747i	−0.0603346	+	0.998178i	$0.519217\pi$
$350$	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	−0.798399	−	0.602129i	$-0.794319\pi$
$353$	3.76238	−	10.3371i	0.200252	−	0.550187i	0.998650	+	0.0519428i	$0.0165414\pi$
$354$		0			0
$355$	−12.9068	+	15.3817i	−0.685021	+	0.816376i
$356$	−4.06599	+	1.37406i	−0.215497	+	0.0728252i
$357$		0			0
$358$	−14.5891	−	10.4694i	−0.771060	−	0.553327i
$359$	−8.75833	−	15.1699i	−0.462247	−	0.800636i	0.536825	−	0.843693i	$-0.319623\pi$
$359$	−8.75833	−	15.1699i	−0.462247	−	0.800636i	−0.999073	+	0.0430578i	$0.986290\pi$
$360$		0			0
$361$	−5.46012	+	9.45721i	−0.287375	+	0.497748i
$362$	−8.51807	+	3.85252i	−0.447700	+	0.202484i
$363$		0			0
$364$	−26.9128	−	23.6666i	−1.41061	−	1.24047i
$365$	5.49303	+	15.0920i	0.287518	+	0.789950i
$366$		0			0
$367$	−5.12177	+	0.903106i	−0.267354	+	0.0471418i	−0.305718	−	0.952122i	$-0.598897\pi$
$367$	−5.12177	+	0.903106i	−0.267354	+	0.0471418i	0.0383639	+	0.999264i	$0.487785\pi$
$368$	−10.4949	−	20.2950i	−0.547085	−	1.05795i
$369$		0			0
$370$	−11.7146	−	11.9893i	−0.609015	−	0.623295i
$371$	−31.3403	+	26.2976i	−1.62711	+	1.36530i
$372$		0			0
$373$	−2.75601	+	15.6301i	−0.142701	+	0.809298i	0.826483	+	0.562961i	$0.190338\pi$
$373$	−2.75601	+	15.6301i	−0.142701	+	0.809298i	−0.969184	+	0.246336i	$0.920773\pi$
$374$	0.153724	+	0.0738630i	0.00794886	+	0.00381936i
$375$		0			0
$376$	6.03892	+	14.2211i	0.311434	+	0.733398i
$377$			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	$0.888544\pi$
$380$	13.8171	−	2.10744i	0.708801	−	0.108110i
$381$		0			0
$382$	15.6016	−	32.4701i	0.798249	−	1.66132i
$383$	−1.40419	+	7.96356i	−0.0717508	+	0.406919i	0.927686	+	0.373361i	$0.121795\pi$
$383$	−1.40419	+	7.96356i	−0.0717508	+	0.406919i	−0.999437	+	0.0335575i	$0.989316\pi$
$384$		0			0
$385$	0.426195	−	0.357620i	0.0217209	−	0.0182260i
$386$	−20.8321	+	20.3548i	−1.06032	+	1.03603i
$387$		0			0
$388$	−0.238882	+	10.3060i	−0.0121274	+	0.523207i
$389$	−19.3541	+	3.41265i	−0.981293	+	0.173028i	−0.641209	−	0.767367i	$-0.721567\pi$
$389$	−19.3541	+	3.41265i	−0.981293	+	0.173028i	−0.340084	+	0.940395i	$0.610456\pi$
$390$		0			0
$391$	4.04356	+	11.1096i	0.204492	+	0.561836i
$392$	−20.3759	−	10.3783i	−1.02914	−	0.524185i
$393$		0			0
$394$	4.04323	+	8.93974i	0.203695	+	0.450378i
$395$	−8.51795	+	14.7535i	−0.428585	+	0.742330i
$396$		0			0
$397$	12.3726	+	21.4299i	0.620961	+	1.07554i	0.989307	+	0.145848i	$0.0465910\pi$
$397$	12.3726	+	21.4299i	0.620961	+	1.07554i	−0.368346	+	0.929689i	$0.620076\pi$
$398$	−9.54402	+	13.2996i	−0.478399	+	0.666648i
$399$		0			0
$400$	3.07271	+	2.83101i	0.153635	+	0.141551i
$401$	7.82702	−	9.32788i	0.390863	−	0.465812i	−0.534349	−	0.845264i	$-0.679443\pi$
$401$	7.82702	−	9.32788i	0.390863	−	0.465812i	0.925211	+	0.379452i	$0.123888\pi$
$402$		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	0.999993	+	0.00381582i	$0.00121462\pi$
$409$	23.8114	+	19.9801i	1.17740	+	0.987954i	0.177405	+	0.984138i	$0.443230\pi$
$410$	3.80428	−	0.288455i	0.187880	−	0.0142458i
$411$		0			0
$412$	−1.94292	−	0.758600i	−0.0957209	−	0.0373736i
$413$	5.38099	−	3.10671i	0.264781	−	0.152871i
$414$		0			0
$415$	−24.2629	−	14.0082i	−1.19102	−	0.687635i
$416$	3.77642	−	25.8247i	0.185154	−	1.26616i
$417$		0			0
$418$	0.193404	−	0.132110i	0.00945971	−	0.00646171i
$419$	34.6419	−	12.6086i	1.69237	−	0.615971i	0.697446	−	0.716637i	$-0.254320\pi$
$419$	34.6419	−	12.6086i	1.69237	−	0.615971i	0.994920	+	0.100666i	$0.0320973\pi$
$420$		0			0
$421$	−6.39735	−	36.2812i	−0.311788	−	1.76824i	−0.589692	−	0.807628i	$-0.700751\pi$
$421$	−6.39735	−	36.2812i	−0.311788	−	1.76824i	0.277904	−	0.960609i	$-0.410360\pi$
$422$	−5.77100	+	20.5807i	−0.280928	+	1.00185i
$423$		0			0
$424$	−28.4933	−	8.70677i	−1.38376	−	0.422838i
$425$	−1.38966	−	1.65613i	−0.0674082	−	0.0803340i
$426$		0			0
$427$	−8.07565	−	1.42395i	−0.390808	−	0.0689100i
$428$	−24.4835	−	4.90466i	−1.18346	−	0.237076i
$429$		0			0
$430$	−3.31029	+	33.3776i	−0.159637	+	1.60961i
$431$	11.3781			0.548063			0.274032	−	0.961721i	$-0.411643\pi$
$431$	11.3781			0.548063			0.274032	+	0.961721i	$0.411643\pi$
$432$		0			0
$433$	−7.27646			−0.349684			−0.174842	−	0.984596i	$-0.555941\pi$
$433$	−7.27646			−0.349684			−0.174842	+	0.984596i	$0.555941\pi$
$434$	4.13429	−	41.6859i	0.198452	−	2.00099i
$435$		0			0
$436$	37.7588	+	7.56403i	1.80832	+	0.362251i
$437$	15.9896	+	2.81940i	0.764887	+	0.134870i
$438$		0			0
$439$	19.1310	+	22.7994i	0.913073	+	1.08816i	0.995797	+	0.0915858i	$0.0291936\pi$
$439$	19.1310	+	22.7994i	0.913073	+	1.08816i	−0.0827239	+	0.996573i	$0.526362\pi$
$440$	0.387479	+	0.118403i	0.0184723	+	0.00564464i
$441$		0			0
$442$	−3.64627	+	13.0035i	−0.173436	+	0.618512i
$443$	2.98686	+	16.9393i	0.141910	+	0.804811i	0.969797	+	0.243915i	$0.0784319\pi$
$443$	2.98686	+	16.9393i	0.141910	+	0.804811i	−0.827887	+	0.560895i	$0.810457\pi$
$444$		0			0
$445$	4.95776	−	1.80448i	0.235020	−	0.0855404i
$446$	−1.91696	+	1.30943i	−0.0907705	+	0.0620033i
$447$		0			0
$448$	−3.25673	−	30.9000i	−0.153866	−	1.45989i
$449$	−18.8763	−	10.8982i	−0.890826	−	0.514319i	−0.0166137	−	0.999862i	$-0.505289\pi$
$449$	−18.8763	−	10.8982i	−0.890826	−	0.514319i	−0.874213	+	0.485543i	$0.838622\pi$
$450$		0			0
$451$	0.0553680	−	0.0319667i	0.00260718	−	0.00150525i
$452$	9.71166	+	3.79185i	0.456798	+	0.178354i
$453$		0			0
$454$	38.5137	−	2.92026i	1.80754	−	0.137055i
$455$	33.7487	+	28.3185i	1.58216	+	1.32759i
$456$		0			0
$457$	−9.07489	−	3.30299i	−0.424505	−	0.154507i	0.120928	−	0.992661i	$-0.461413\pi$
$457$	−9.07489	−	3.30299i	−0.424505	−	0.154507i	−0.545434	+	0.838154i	$0.683635\pi$
$458$	−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	−0.345729	−	0.938334i	$-0.612368\pi$
$461$	11.2135	−	30.8088i	0.522264	−	1.43491i	0.867994	−	0.496575i	$-0.165409\pi$
$462$		0			0
$463$	24.6443	−	29.3699i	1.14532	−	1.36494i	0.224720	−	0.974423i	$-0.427853\pi$
$463$	24.6443	−	29.3699i	1.14532	−	1.36494i	0.920598	−	0.390512i	$-0.127702\pi$
$464$	−10.8732	+	11.8014i	−0.504774	+	0.547868i
$465$		0			0
$466$	24.4481	−	34.0684i	1.13254	−	1.57819i
$467$	5.79199	+	10.0320i	0.268021	+	0.464227i	0.968351	−	0.249593i	$-0.0802969\pi$
$467$	5.79199	+	10.0320i	0.268021	+	0.464227i	−0.700329	+	0.713820i	$0.746964\pi$
$468$		0			0
$469$	14.6756	−	25.4189i	0.677657	−	1.17374i
$470$	−7.82663	−	17.3050i	−0.361016	−	0.798220i
$471$		0			0
$472$	4.03201	+	2.05368i	0.185588	+	0.0945283i
$473$	0.192240	+	0.528174i	0.00883919	+	0.0242855i
$474$		0			0
$475$	−2.92392	+	0.515566i	−0.134159	+	0.0236558i
$476$	−0.372564	+	16.0733i	−0.0170764	+	0.736720i
$477$		0			0
$478$	9.41300	−	9.19735i	0.430541	−	0.420677i
$479$	−13.7316	+	11.5222i	−0.627412	+	0.526461i	−0.900124	−	0.435635i	$-0.856524\pi$
$479$	−13.7316	+	11.5222i	−0.627412	+	0.526461i	0.272712	+	0.962096i	$0.412080\pi$
$480$		0			0
$481$	3.86246	−	21.9051i	0.176113	−	0.998787i
$482$	8.61220	−	17.9237i	0.392275	−	0.816403i
$483$		0			0
$484$	−21.7418	+	3.31615i	−0.988262	+	0.150734i
$485$		−	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	$-0.171504\pi$
$488$	−2.33415	−	5.49672i	−0.105662	−	0.248825i
$489$		0			0
$490$	25.3366	+	12.1740i	1.14459	+	0.549966i
$491$	4.46394	−	25.3163i	0.201455	−	1.14251i	−0.701467	−	0.712702i	$-0.747471\pi$
$491$	4.46394	−	25.3163i	0.201455	−	1.14251i	0.902922	−	0.429805i	$-0.141418\pi$
$492$		0			0
$493$	6.36074	−	5.33729i	0.286473	−	0.240380i
$494$	12.9617	+	13.2656i	0.583176	+	0.596850i
$495$		0			0
$496$	27.0978	−	14.0128i	1.21673	−	0.629192i
$497$	−31.2384	+	5.50816i	−1.40123	+	0.247075i
$498$		0			0
$499$	2.47255	+	6.79329i	0.110687	+	0.304109i	0.982652	−	0.185458i	$-0.0593769\pi$
$499$	2.47255	+	6.79329i	0.110687	+	0.304109i	−0.871965	+	0.489567i	$0.837155\pi$
$500$	14.6055	+	12.8439i	0.653180	+	0.574395i
$501$		0			0
$502$	−19.5959	+	8.86277i	−0.874610	+	0.395565i
$503$	19.3621	−	33.5362i	0.863314	−	1.49530i	−0.00539768	−	0.999985i	$-0.501718\pi$
$503$	19.3621	−	33.5362i	0.863314	−	1.49530i	0.868712	−	0.495318i	$-0.164949\pi$
$504$		0			0
$505$	−16.2480	−	28.1424i	−0.723027	−	1.25232i
$506$	0.382390	+	0.274410i	0.0169993	+	0.0121990i
$507$		0			0
$508$	−3.67124	+	1.24066i	−0.162885	+	0.0550453i
$509$	−12.2747	+	14.6284i	−0.544067	+	0.648394i	−0.966094	−	0.258189i	$-0.916874\pi$
$509$	−12.2747	+	14.6284i	−0.544067	+	0.648394i	0.422027	+	0.906583i	$0.361319\pi$
$510$		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
$518$	−2.00208	−	26.4044i	−0.0879665	−	1.16014i
$519$		0			0
$520$	−3.90539	+	31.8448i	−0.171263	+	1.39649i
$521$	19.0779	−	11.0146i	0.835817	−	0.482559i	−0.0200233	−	0.999800i	$-0.506374\pi$
$521$	19.0779	−	11.0146i	0.835817	−	0.482559i	0.855840	+	0.517240i	$0.173041\pi$
$522$		0			0
$523$	−3.75661	−	2.16888i	−0.164265	−	0.0948384i	0.415614	−	0.909541i	$-0.363567\pi$
$523$	−3.75661	−	2.16888i	−0.164265	−	0.0948384i	−0.579879	+	0.814703i	$0.696900\pi$
$524$	−0.584521	−	0.730328i	−0.0255349	−	0.0319045i
$525$		0			0
$526$	1.58588	+	2.32168i	0.0691478	+	0.101230i
$527$	−14.8335	+	5.39895i	−0.646158	+	0.235182i
$528$		0			0
$529$	1.67167	+	9.48053i	0.0726815	+	0.412197i
$530$	35.2648	+	9.88853i	1.53181	+	0.429530i
$531$		0			0
$532$	18.8608	+	11.4801i	0.817717	+	0.497724i
$533$	3.25420	+	3.87820i	0.140955	+	0.167984i
$534$		0			0
$535$	30.2288	+	5.33015i	1.30690	+	0.230442i
$536$	21.3455	−	1.12176i	0.921983	−	0.0484525i
$537$		0			0
$538$	−1.66671	−	0.165300i	−0.0718571	−	0.00712659i
$539$	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	$0.519774\pi$
$542$	−15.3424	−	1.52161i	−0.659012	−	0.0653589i
$543$		0			0
$544$	−9.96380	+	6.14907i	−0.427194	+	0.263639i
$545$	−46.6192	−	8.22022i	−1.99695	−	0.352115i
$546$		0			0
$547$	15.0106	+	17.8889i	0.641805	+	0.764874i	0.984654	−	0.174517i	$-0.0558364\pi$
$547$	15.0106	+	17.8889i	0.641805	+	0.764874i	−0.342849	+	0.939391i	$0.611392\pi$
$548$	4.56539	−	7.50054i	0.195024	−	0.320407i
$549$		0			0
$550$	−0.0828705	−	0.0232375i	−0.00353361	−	0.000990852i
$551$	−1.98015	−	11.2300i	−0.0843572	−	0.478413i
$552$		0			0
$553$	−25.2893	+	9.20456i	−1.07541	+	0.391418i
$554$	4.51287	+	6.60668i	0.191733	+	0.280691i
$555$		0			0
$556$	−13.1908	+	10.5573i	−0.559415	+	0.447730i
$557$	7.72227	+	4.45845i	0.327203	+	0.188911i	0.654599	−	0.755977i	$-0.272838\pi$
$557$	7.72227	+	4.45845i	0.327203	+	0.188911i	−0.327396	+	0.944887i	$0.606171\pi$
$558$		0			0
$559$	−38.5452	+	22.2541i	−1.63029	+	0.941247i
$560$	4.88257	+	37.8817i	0.206326	+	1.60080i
$561$		0			0
$562$	−1.32462	−	17.4697i	−0.0558756	−	0.736913i
$563$	−16.7813	−	14.0811i	−0.707246	−	0.593450i	0.216579	−	0.976265i	$-0.430510\pi$
$563$	−16.7813	−	14.0811i	−0.707246	−	0.593450i	−0.923825	+	0.382815i	$0.874955\pi$
$564$		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	−0.712757	−	0.701411i	$-0.752554\pi$
$569$	6.77697	−	18.6196i	0.284105	−	0.780573i	0.996862	−	0.0791612i	$-0.0252242\pi$
$570$		0			0
$571$	−17.6621	+	21.0489i	−0.739136	+	0.880869i	−0.996339	−	0.0854889i	$-0.972755\pi$
$571$	−17.6621	+	21.0489i	−0.739136	+	0.880869i	0.257203	+	0.966357i	$0.417199\pi$
$572$	0.172127	+	0.509342i	0.00719699	+	0.0212967i
$573$		0			0
$574$	4.89667	+	3.51394i	0.204383	+	0.146669i
$575$	−2.98313	−	5.16693i	−0.124405	−	0.215476i
$576$		0			0
$577$	1.20328	−	2.08414i	0.0500931	−	0.0867638i	−0.839892	−	0.542754i	$-0.817382\pi$
$577$	1.20328	−	2.08414i	0.0500931	−	0.0867638i	0.889985	+	0.455990i	$0.150715\pi$
$578$	−16.3852	+	7.41064i	−0.681535	+	0.308242i
$579$		0			0
$580$	13.0264	−	14.8131i	0.540891	−	0.615081i
$581$	−15.1373	−	41.5895i	−0.628003	−	1.72542i
$582$		0			0
$583$	0.604422	−	0.106576i	0.0250326	−	0.00441392i
$584$	−18.0025	+	4.15895i	−0.744951	+	0.172099i
$585$		0			0
$586$	24.7914	+	25.3727i	1.02412	+	1.04814i
$587$	−9.88712	+	8.29628i	−0.408085	+	0.342424i	−0.823609	−	0.567158i	$-0.808043\pi$
$587$	−9.88712	+	8.29628i	−0.408085	+	0.342424i	0.415524	+	0.909582i	$0.363598\pi$
$588$		0			0
$589$	−3.76445	+	21.3493i	−0.155112	+	0.879682i
$590$	−5.01364	−	2.40902i	−0.206408	−	0.0991776i
$591$		0			0
$592$	15.3309	−	11.6978i	0.630098	−	0.480777i
$593$			27.2738i			1.12000i	0.828493	+	0.560000i	$0.189199\pi$
$593$			27.2738i			1.12000i	−0.828493	+	0.560000i	$0.810801\pi$
$594$		0			0
$595$		−	19.7639i		−	0.810242i
$596$	3.06586	+	20.1008i	0.125583	+	0.823360i
$597$		0			0
$598$	−16.1412	+	33.5931i	−0.660064	+	1.37373i
$599$	−3.54790	+	20.1212i	−0.144963	+	0.822128i	0.822433	+	0.568862i	$0.192616\pi$
$599$	−3.54790	+	20.1212i	−0.144963	+	0.822128i	−0.967397	+	0.253267i	$0.918495\pi$
$600$		0			0
$601$	−33.6622	+	28.2459i	−1.37311	+	1.15217i	−0.401424	+	0.915892i	$0.631485\pi$
$601$	−33.6622	+	28.2459i	−1.37311	+	1.15217i	−0.971684	+	0.236282i	$0.924071\pi$
$602$	−37.8988	+	37.0306i	−1.54464	+	1.50925i
$603$		0			0
$604$	−4.77149	−	0.110598i	−0.194149	−	0.00450019i
$605$	26.6251	−	4.69472i	1.08246	−	0.190867i
$606$		0			0
$607$	−12.8907	−	35.4169i	−0.523217	−	1.43753i	−0.866920	−	0.498448i	$-0.833903\pi$
$607$	−12.8907	−	35.4169i	−0.523217	−	1.43753i	0.343703	−	0.939078i	$-0.388319\pi$
$608$	0.471535	+	16.0726i	0.0191233	+	0.651832i
$609$		0			0
$610$	3.02514	+	6.68870i	0.122484	+	0.270818i
$611$	12.6013	−	21.8260i	0.509792	−	0.882986i
$612$		0			0
$613$	1.70832	+	2.95890i	0.0689984	+	0.119509i	0.898461	−	0.439054i	$-0.144686\pi$
$613$	1.70832	+	2.95890i	0.0689984	+	0.119509i	−0.829462	+	0.558563i	$0.811353\pi$
$614$	−7.61532	+	10.6119i	−0.307329	+	0.428263i
$615$		0			0
$616$	0.348678	+	0.536747i	0.0140486	+	0.0216261i
$617$	18.5635	−	22.1231i	0.747336	−	0.890641i	−0.249641	−	0.968339i	$-0.580312\pi$
$617$	18.5635	−	22.1231i	0.747336	−	0.890641i	0.996977	+	0.0776977i	$0.0247569\pi$
$618$		0			0
$619$	6.14959	−	16.8958i	0.247173	−	0.679101i	−0.752614	−	0.658462i	$-0.771207\pi$
$619$	6.14959	−	16.8958i	0.247173	−	0.679101i	0.999787	−	0.0206398i	$-0.00657031\pi$
$620$	−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
$626$	31.5297	−	2.39070i	1.26018	−	0.0955517i
$627$		0			0
$628$	3.96136	−	10.1458i	0.158075	−	0.404861i
$629$	−8.64162	+	4.98924i	−0.344564	+	0.198934i
$630$		0			0
$631$	−10.4847	−	6.05333i	−0.417388	−	0.240979i	0.276571	−	0.960994i	$-0.410802\pi$
$631$	−10.4847	−	6.05333i	−0.417388	−	0.240979i	−0.693959	+	0.720014i	$0.744135\pi$
$632$	−15.6540	−	11.7926i	−0.622682	−	0.469084i
$633$		0			0
$634$	13.6085	−	9.29567i	0.540463	−	0.369178i
$635$	4.47642	−	1.62928i	0.177641	−	0.0646562i
$636$		0			0
$637$	6.47715	+	36.7337i	0.256634	+	1.45544i
$638$	0.0892492	−	0.318284i	0.00353341	−	0.0126010i
$639$		0			0
$640$	−21.1974	+	18.0102i	−0.837901	+	0.711916i
$641$	−12.3621	−	14.7326i	−0.488275	−	0.581904i	0.464503	−	0.885572i	$-0.346233\pi$
$641$	−12.3621	−	14.7326i	−0.488275	−	0.581904i	−0.952778	+	0.303668i	$0.901789\pi$
$642$		0			0
$643$	−2.81767	−	0.496831i	−0.111118	−	0.0195931i	0.117813	−	0.993036i	$-0.462412\pi$
$643$	−2.81767	−	0.496831i	−0.111118	−	0.0195931i	−0.228931	+	0.973443i	$0.573523\pi$
$644$	−8.71515	+	43.5051i	−0.343425	+	1.71434i
$645$		0			0
$646$	0.821156	−	8.27969i	0.0323080	−	0.325760i
$647$	−36.4238			−1.43197			−0.715984	−	0.698117i	$-0.754022\pi$
$647$	−36.4238			−1.43197			−0.715984	+	0.698117i	$0.754022\pi$
$648$		0			0
$649$	−0.0932118			−0.00365888
$650$	0.672621	−	6.78202i	0.0263824	−	0.266013i
$651$		0			0
$652$	3.83545	−	19.1462i	0.150208	−	0.749822i
$653$	21.4999	+	3.79102i	0.841357	+	0.148354i	0.577686	−	0.816259i	$-0.303956\pi$
$653$	21.4999	+	3.79102i	0.841357	+	0.148354i	0.263671	+	0.964613i	$0.415067\pi$
$654$		0			0
$655$	0.739151	+	0.880886i	0.0288810	+	0.0344190i
$656$	−0.203364	+	4.38445i	−0.00794001	+	0.171184i
$657$		0			0
$658$	8.10075	−	28.8892i	0.315800	−	1.12622i
$659$	0.0574639	+	0.325894i	0.00223847	+	0.0126950i	0.985907	−	0.167297i	$-0.0535039\pi$
$659$	0.0574639	+	0.325894i	0.00223847	+	0.0126950i	−0.983668	+	0.179992i	$0.942393\pi$
$660$		0			0
$661$	−22.2519	+	8.09903i	−0.865498	+	0.315016i	−0.736343	−	0.676609i	$-0.763449\pi$
$661$	−22.2519	+	8.09903i	−0.865498	+	0.315016i	−0.129156	+	0.991624i	$0.541227\pi$
$662$	5.12480	−	3.50063i	0.199181	−	0.136056i
$663$		0			0
$664$	19.3935	−	25.7438i	0.752613	−	0.999051i
$665$	−23.5059	−	13.5712i	−0.911521	−	0.526267i
$666$		0			0
$667$	19.8448	−	11.4574i	0.768393	−	0.443632i
$668$	3.37943	−	8.65537i	0.130754	−	0.334886i
$669$		0			0
$670$	−26.2005	+	1.98662i	−1.01221	+	0.0767500i
$671$	0.0942366	+	0.0790739i	0.00363796	+	0.00305261i
$672$		0			0
$673$	−3.46425	−	1.26088i	−0.133537	−	0.0486035i	0.274387	−	0.961619i	$-0.411525\pi$
$673$	−3.46425	−	1.26088i	−0.133537	−	0.0486035i	−0.407924	+	0.913016i	$0.633747\pi$
$674$	−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	−0.860963	−	0.508668i	$-0.830138\pi$
$677$	3.26640	−	8.97437i	0.125538	−	0.344913i	0.986501	+	0.163754i	$0.0523605\pi$
$678$		0			0
$679$	12.8680	−	15.3355i	0.493828	−	0.588521i
$680$	12.0698	−	7.84073i	0.462857	−	0.300678i
$681$		0			0
$682$	−0.366391	+	0.510566i	−0.0140298	+	0.0195506i
$683$	14.0206	+	24.2843i	0.536482	+	0.929214i	0.999090	+	0.0426510i	$0.0135804\pi$
$683$	14.0206	+	24.2843i	0.536482	+	0.929214i	−0.462608	+	0.886563i	$0.653086\pi$
$684$		0			0
$685$	−5.39697	+	9.34783i	−0.206208	+	0.357162i
$686$	2.45496	+	5.42801i	0.0937307	+	0.207242i
$687$		0			0
$688$	−37.6498	−	8.45413i	−1.43539	−	0.322311i
$689$	16.6222	+	45.6691i	0.633255	+	1.73985i
$690$		0			0
$691$	39.8542	−	7.02737i	1.51613	−	0.267334i	0.647217	−	0.762306i	$-0.275933\pi$
$691$	39.8542	−	7.02737i	1.51613	−	0.267334i	0.868909	+	0.494972i	$0.164822\pi$
$692$	1.76189	+	0.0408389i	0.0669771	+	0.00155246i
$693$		0			0
$694$	−15.1424	+	14.7955i	−0.574798	+	0.561630i
$695$	15.9101	−	13.3502i	0.603505	−	0.506401i
$696$		0			0
$697$	0.394382	−	2.23665i	0.0149383	−	0.0847192i
$698$	6.51518	−	13.5594i	0.246603	−	0.513231i
$699$		0			0
$700$	−1.22337	−	8.02080i	−0.0462390	−	0.303158i
$701$		−	13.2691i		−	0.501165i	−0.968095	−	0.250583i	$-0.919378\pi$
$701$		−	13.2691i		−	0.501165i	0.968095	−	0.250583i	$-0.0806222\pi$
$702$		0			0
$703$			13.7037i			0.516846i
$704$	−0.189465	+	0.425876i	−0.00714072	+	0.0160508i
$705$		0			0
$706$	−14.0223	−	6.73761i	−0.527737	−	0.253573i
$707$	8.91429	−	50.5555i	0.335257	−	1.90133i
$708$		0			0
$709$	10.1345	−	8.50383i	0.380608	−	0.319368i	−0.432333	−	0.901714i	$-0.642310\pi$
$709$	10.1345	−	8.50383i	0.380608	−	0.319368i	0.812941	+	0.582346i	$0.197865\pi$
$710$	19.8454	+	20.3107i	0.744784	+	0.762247i
$711$		0			0
$712$	1.36623	+	5.91389i	0.0512016	+	0.221632i
$713$	−42.9014	+	7.56467i	−1.60667	+	0.283299i
$714$		0			0
$715$	−0.226045	−	0.621052i	−0.00845359	−	0.0232260i
$716$	−16.7700	+	19.0702i	−0.626724	+	0.712686i
$717$		0			0
$718$	−22.5711	+	10.2084i	−0.842347	+	0.380973i
$719$	−20.7715	+	35.9773i	−0.774647	+	1.34173i	0.160345	+	0.987061i	$0.448739\pi$
$719$	−20.7715	+	35.9773i	−0.774647	+	1.34173i	−0.934992	+	0.354668i	$0.884594\pi$
$720$		0			0
$721$	2.02522	+	3.50779i	0.0754232	+	0.130637i
$722$	12.5471	+	9.00405i	0.466956	+	0.335096i
$723$		0			0
$724$	4.23279	+	12.5253i	0.157310	+	0.465498i
$725$	−2.69346	+	3.20994i	−0.100033	+	0.119214i
$726$		0			0
$727$	−11.7278	+	32.2219i	−0.434960	+	1.19504i	0.507772	+	0.861492i	$0.330469\pi$
$727$	−11.7278	+	32.2219i	−0.434960	+	1.19504i	−0.942732	+	0.333552i	$0.891753\pi$
$728$	−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	0.897507	−	0.440999i	$-0.145376\pi$
$733$	16.7604	+	14.0636i	0.619059	+	0.519452i	−0.278449	+	0.960451i	$0.589820\pi$
$734$	0.556089	+	7.33396i	0.0205256	+	0.270702i
$735$		0			0
$736$	−30.0261	+	11.9370i	−1.10678	+	0.440002i
$737$	−0.381326	+	0.220159i	−0.0140463	+	0.00810965i
$738$		0			0
$739$	23.8855	+	13.7903i	0.878644	+	0.507285i	0.870211	−	0.492679i	$-0.163982\pi$
$739$	23.8855	+	13.7903i	0.878644	+	0.507285i	0.00843293	+	0.999964i	$0.497316\pi$
$740$	−18.5077	+	14.8127i	−0.680358	+	0.544527i
$741$		0			0
$742$	32.6346	+	47.7759i	1.19805	+	1.75391i
$743$	−19.8494	+	7.22459i	−0.728204	+	0.265045i	−0.679404	−	0.733764i	$-0.737762\pi$
$743$	−19.8494	+	7.22459i	−0.728204	+	0.265045i	−0.0487995	+	0.998809i	$0.515540\pi$
$744$		0			0
$745$	−4.34038	−	24.6155i	−0.159019	−	0.901843i
$746$	21.6118	+	6.06011i	0.791263	+	0.221876i
$747$		0			0
$748$	0.125404	−	0.206027i	0.00458521	−	0.00753311i
$749$	31.1690	+	37.1457i	1.13889	+	1.35728i
$750$		0			0
$751$	−15.0474	−	2.65327i	−0.549088	−	0.0968191i	−0.107780	−	0.994175i	$-0.534374\pi$
$751$	−15.0474	−	2.65327i	−0.549088	−	0.0968191i	−0.441308	+	0.897356i	$0.645485\pi$
$752$	20.8564	−	6.51375i	0.760553	−	0.237532i
$753$		0			0
$754$	26.0479	+	2.58336i	0.948608	+	0.0940803i
$755$	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	$0.682375\pi$
$758$	18.7966	+	1.86420i	0.682724	+	0.0677106i
$759$		0			0
$760$	−1.03734	−	19.7390i	−0.0376281	−	0.716010i
$761$	9.36641	+	1.65155i	0.339532	+	0.0598687i	0.340815	−	0.940130i	$-0.389297\pi$
$761$	9.36641	+	1.65155i	0.339532	+	0.0598687i	−0.00128248	+	0.999999i	$0.500408\pi$
$762$		0			0
$763$	−48.0692	−	57.2866i	−1.74022	−	2.07392i
$764$	−43.5180	−	26.4883i	−1.57442	−	0.958313i
$765$		0			0
$766$	11.0112	+	3.08763i	0.397851	+	0.111560i
$767$	−1.28171	−	7.26893i	−0.0462798	−	0.262466i
$768$		0			0
$769$	−5.24113	+	1.90762i	−0.189000	+	0.0687904i	−0.434786	−	0.900534i	$-0.643176\pi$
$769$	−5.24113	+	1.90762i	−0.189000	+	0.0687904i	0.245786	+	0.969324i	$0.420954\pi$
$770$	−0.443797	−	0.649702i	−0.0159933	−	0.0234136i
$771$		0			0
$772$	25.7379	+	32.1582i	0.926328	+	1.15740i
$773$	−15.2614	−	8.81115i	−0.548913	−	0.316915i	0.199770	−	0.979843i	$-0.435980\pi$
$773$	−15.2614	−	8.81115i	−0.548913	−	0.316915i	−0.748683	+	0.662928i	$0.769314\pi$
$774$		0			0
$775$	6.89886	−	3.98306i	0.247815	−	0.143076i
$776$	14.4704	+	1.77462i	0.519455	+	0.0637050i
$777$		0			0
$778$	2.10135	+	27.7135i	0.0753370	+	0.993579i
$779$	−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	0.111841	+	0.993726i	$0.464325\pi$
$787$	−24.8613	+	29.6285i	−0.886209	+	1.05614i	−0.998050	+	0.0624168i	$0.980119\pi$
$788$	13.1453	−	4.44233i	0.468282	−	0.158251i
$789$		0			0
$790$	19.5739	+	14.0466i	0.696408	+	0.499755i
$791$	−10.1230	−	17.5336i	−0.359934	−	0.623424i
$792$		0			0
$793$	−4.87062	+	8.43615i	−0.172961	+	0.299577i
$794$	31.8854	−	14.4210i	1.13157	−	0.511782i
$795$		0			0
$796$	17.3845	+	15.2877i	0.616178	+	0.541856i
$797$	1.14049	+	3.13346i	0.0403981	+	0.110993i	0.958251	−	0.285927i	$-0.0923014\pi$
$797$	1.14049	+	3.13346i	0.0403981	+	0.110993i	−0.917853	+	0.396920i	$0.870079\pi$
$798$		0			0
$799$	−11.1344	+	1.96329i	−0.393906	+	0.0694562i
$800$	4.41298	−	3.92912i	0.156022	−	0.138915i
$801$		0			0
$802$	−12.0348	−	12.3170i	−0.424962	−	0.434927i
$803$	0.291568	−	0.244655i	0.0102892	−	0.00863368i
$804$		0			0
$805$	9.47120	−	53.7139i	0.333816	−	1.89316i
$806$	−44.8534	−	21.5517i	−1.57990	−	0.759127i
$807$		0			0
$808$	34.4108	−	14.6124i	1.21057	−	0.514061i
$809$		−	5.26208i		−	0.185005i	−0.995712	−	0.0925025i	$-0.970513\pi$
$809$		−	5.26208i		−	0.185005i	0.995712	−	0.0925025i	$-0.0294866\pi$
$810$		0			0
$811$		−	3.33372i		−	0.117063i	−0.998286	−	0.0585314i	$-0.981358\pi$
$811$		−	3.33372i		−	0.117063i	0.998286	−	0.0585314i	$-0.0186418\pi$
$812$	30.8057	−	4.69863i	1.08107	−	0.164890i
$813$		0			0
$814$	−0.172044	+	0.358059i	−0.00603016	+	0.0125500i
$815$	−4.16818	+	23.6389i	−0.146005	+	0.828036i
$816$		0			0
$817$	21.0057	−	17.6259i	0.734897	−	0.616652i
$818$	31.4416	−	30.7213i	1.09933	−	1.07415i
$819$		0			0
$820$	0.125029	−	5.39406i	0.00436620	−	0.188369i
$821$	−25.8625	+	4.56026i	−0.902608	+	0.159154i	−0.605645	−	0.795735i	$-0.707085\pi$
$821$	−25.8625	+	4.56026i	−0.902608	+	0.159154i	−0.296963	+	0.954889i	$0.595974\pi$
$822$		0			0
$823$	13.1732	+	36.1930i	0.459188	+	1.26161i	0.926091	+	0.377300i	$0.123147\pi$
$823$	13.1732	+	36.1930i	0.459188	+	1.26161i	−0.466903	+	0.884308i	$0.654630\pi$
$824$	−1.33876	+	2.62841i	−0.0466381	+	0.0915650i
$825$		0			0
$826$	−3.62107	−	8.00632i	−0.125993	−	0.278576i
$827$	−16.3619	+	28.3397i	−0.568960	+	0.985467i	0.427710	+	0.903916i	$0.359321\pi$
$827$	−16.3619	+	28.3397i	−0.568960	+	0.985467i	−0.996669	+	0.0815507i	$0.974013\pi$
$828$		0			0
$829$	13.4083	+	23.2238i	0.465688	+	0.806595i	0.999232	−	0.0391769i	$-0.0124736\pi$
$829$	13.4083	+	23.2238i	0.465688	+	0.806595i	−0.533544	+	0.845772i	$0.679140\pi$
$830$	−23.1003	+	32.1902i	−0.801823	+	1.11734i
$831$		0			0
$832$	−35.8163	−	8.91902i	−1.24171	−	0.309211i
$833$	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	$-0.354225\pi$
$839$	5.91646	+	2.15341i	0.204259	+	0.0743441i	−0.237865	+	0.971298i	$0.576448\pi$
$840$		0			0
$841$	9.88678	+	8.29599i	0.340923	+	0.286069i
$842$	−51.9518	+	3.93918i	−1.79038	+	0.135753i
$843$		0			0
$844$	28.1580	+	10.9941i	0.969237	+	0.378432i
$845$	17.6440	−	10.1867i	0.606971	−	0.350435i
$846$		0			0
$847$	36.9876	+	21.3548i	1.27091	+	0.733760i
$848$	−16.2300	+	38.8836i	−0.557341	+	1.33527i
$849$		0			0
$850$	−2.52464	+	1.72452i	−0.0865945	+	0.0591507i
$851$	−25.8769	+	9.41842i	−0.887049	+	0.322859i
$852$		0			0
$853$	0.124811	+	0.707838i	0.00427344	+	0.0242359i	0.986870	−	0.161517i	$-0.0516387\pi$
$853$	0.124811	+	0.707838i	0.00427344	+	0.0242359i	−0.982596	+	0.185753i	$0.940528\pi$
$854$	−3.13109	+	11.1662i	−0.107144	+	0.382099i
$855$		0			0
$856$	−10.3196	+	33.7714i	−0.352717	+	1.15428i
$857$	35.0599	+	41.7827i	1.19762	+	1.42727i	0.877286	+	0.479968i	$0.159352\pi$
$857$	35.0599	+	41.7827i	1.19762	+	1.42727i	0.320337	+	0.947304i	$0.396204\pi$
$858$		0			0
$859$	−29.9885	−	5.28779i	−1.02320	−	0.180417i	−0.363220	−	0.931704i	$-0.618323\pi$
$859$	−29.9885	−	5.28779i	−1.02320	−	0.180417i	−0.659976	+	0.751286i	$0.729434\pi$
$860$	46.5105	+	9.31721i	1.58600	+	0.317714i
$861$		0			0
$862$	1.58807	−	16.0125i	0.0540900	−	0.545388i
$863$	30.5772			1.04086			0.520430	−	0.853904i	$-0.325772\pi$
$863$	30.5772			1.04086			0.520430	+	0.853904i	$0.325772\pi$
$864$		0			0
$865$	−2.16644			−0.0736612
$866$	−1.01560	+	10.2402i	−0.0345114	+	0.347977i
$867$		0			0
$868$	−58.0879	−	11.6364i	−1.97163	−	0.394967i
$869$	0.397596	+	0.0701070i	0.0134875	+	0.00237822i
$870$		0			0
$871$	−22.4120	−	26.7096i	−0.759403	−	0.905022i
$872$	15.9150	−	52.0826i	0.538951	−	1.76374i
$873$		0			0
$874$	6.19948	−	22.1088i	0.209701	−	0.747842i
$875$	−6.55870	−	37.1962i	−0.221725	−	1.25746i
$876$		0			0
$877$	31.7998	−	11.5742i	1.07380	−	0.390832i	0.256205	−	0.966622i	$-0.417528\pi$
$877$	31.7998	−	11.5742i	1.07380	−	0.390832i	0.817597	+	0.575790i	$0.195306\pi$
$878$	34.7560	−	23.7411i	1.17296	−	0.801222i
$879$		0			0
$880$	0.220711	−	0.528777i	0.00744017	−	0.0178251i
$881$	10.3117	+	5.95348i	0.347411	+	0.200578i	0.663544	−	0.748137i	$-0.269051\pi$
$881$	10.3117	+	5.95348i	0.347411	+	0.200578i	−0.316133	+	0.948715i	$0.602385\pi$
$882$		0			0
$883$	−10.5936	+	6.11620i	−0.356502	+	0.205827i	−0.667545	−	0.744569i	$-0.732655\pi$
$883$	−10.5936	+	6.11620i	−0.356502	+	0.205827i	0.311043	+	0.950396i	$0.399322\pi$
$884$	17.7910	+	6.94637i	0.598375	+	0.233632i
$885$		0			0
$886$	24.2557	−	1.83916i	0.814887	−	0.0617879i
$887$	10.2202	+	8.57573i	0.343159	+	0.287945i	0.798036	−	0.602609i	$-0.205872\pi$
$887$	10.2202	+	8.57573i	0.343159	+	0.287945i	−0.454877	+	0.890554i	$0.650317\pi$
$888$		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
$896$	−43.9404	+	0.270431i	−1.46794	+	0.00903448i
$897$		0			0
$898$	−17.9718	+	25.0437i	−0.599726	+	0.835718i
$899$	15.2979	+	26.4967i	0.510212	+	0.883714i
$900$		0			0
$901$	10.9013	−	18.8816i	0.363174	−	0.629036i
$902$	−0.0372592	−	0.0823816i	−0.00124060	−	0.00274301i
$903$		0			0
$904$	6.69180	−	13.1381i	0.222566	−	0.436966i
$905$	−5.55868	−	15.2723i	−0.184777	−	0.507670i
$906$		0			0
$907$	−19.8590	+	3.50168i	−0.659407	+	0.116271i	−0.493331	−	0.869842i	$-0.664221\pi$
$907$	−19.8590	+	3.50168i	−0.659407	+	0.116271i	−0.166076	+	0.986113i	$0.553110\pi$
$908$	1.26577	−	54.6083i	0.0420060	−	1.81224i
$909$		0			0
$910$	44.5633	−	43.5423i	1.47726	−	1.44341i
$911$	24.2137	−	20.3177i	0.802237	−	0.673157i	−0.146505	−	0.989210i	$-0.546802\pi$
$911$	24.2137	−	20.3177i	0.802237	−	0.673157i	0.948741	+	0.316053i	$0.102358\pi$
$912$		0			0
$913$	−0.115294	+	0.653867i	−0.00381569	+	0.0216398i
$914$	−5.91494	+	12.3102i	−0.195649	+	0.407184i
$915$		0			0
$916$	−12.4903	+	1.90508i	−0.412691	+	0.0629455i
$917$			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	$-0.0203167\pi$
$920$	36.5605	−	15.5252i	1.20536	−	0.511852i
$921$		0			0
$922$	−41.7924	−	20.0809i	−1.37636	−	0.661330i
$923$	−6.54327	+	37.1087i	−0.215374	+	1.22145i
$924$		0			0
$925$	3.85752	−	3.23684i	0.126834	−	0.106427i
$926$	−37.8929	−	38.7814i	−1.24524	−	1.27444i
$927$		0			0
$928$	15.0907	+	16.9491i	0.495376	+	0.556380i
$929$	49.6909	−	8.76185i	1.63031	−	0.287467i	0.717715	−	0.696337i	$-0.245188\pi$
$929$	49.6909	−	8.76185i	1.63031	−	0.287467i	0.912593	+	0.408870i	$0.134077\pi$
$930$		0			0
$931$	−7.85977	−	21.5945i	−0.257593	−	0.707732i
$932$	−44.5325	−	39.1611i	−1.45871	−	1.28276i
$933$		0			0
$934$	14.9266	−	6.75093i	0.488412	−	0.220897i
$935$	−0.148246	+	0.256770i	−0.00484816	+	0.00839726i
$936$		0			0
$937$	24.0457	+	41.6483i	0.785538	+	1.36059i	0.928677	+	0.370890i	$0.120947\pi$
$937$	24.0457	+	41.6483i	0.785538	+	1.36059i	−0.143139	+	0.989703i	$0.545720\pi$
$938$	−33.7239	−	24.2009i	−1.10113	−	0.790188i
$939$		0			0
$940$	−25.4459	+	8.59918i	−0.829953	+	0.280474i
$941$	−4.71969	+	5.62470i	−0.153857	+	0.183360i	−0.837467	−	0.546488i	$-0.815965\pi$
$941$	−4.71969	+	5.62470i	−0.153857	+	0.183360i	0.683610	+	0.729848i	$0.260409\pi$
$942$		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	$-0.215777\pi$
$947$	29.9257	+	10.8921i	0.972454	+	0.353944i	0.193552	+	0.981090i	$0.437999\pi$
$948$		0			0
$949$	23.0881	+	19.3732i	0.749472	+	0.628881i
$950$	0.317460	+	4.18681i	0.0102998	+	0.135838i
$951$		0			0
$952$	22.5681	+	2.76771i	0.731438	+	0.0897021i
$953$	−13.1967	+	7.61912i	−0.427483	+	0.246807i	−0.698274	−	0.715831i	$-0.746048\pi$
$953$	−13.1967	+	7.61912i	−0.427483	+	0.246807i	0.270791	+	0.962638i	$0.412715\pi$
$954$		0			0
$955$	54.2359	+	31.3131i	1.75503	+	1.01327i
$956$	−11.6297	−	14.5307i	−0.376132	−	0.469957i
$957$		0			0
$958$	14.2987	+	20.9328i	0.461970	+	0.676307i
$959$	−16.0233	+	5.83201i	−0.517420	+	0.188325i
$960$		0			0
$961$	−4.71723	−	26.7528i	−0.152169	−	0.862992i
$962$	−30.2882	−	8.49304i	−0.976530	−	0.273827i
$963$		0			0
$964$	−24.0222	−	14.6217i	−0.773703	−	0.470933i
$965$	−32.5466	−	38.7876i	−1.04771	−	1.24862i
$966$		0			0
$967$	42.5027	+	7.49437i	1.36680	+	0.241003i	0.808430	−	0.588592i	$-0.200318\pi$
$967$	42.5027	+	7.49437i	1.36680	+	0.241003i	0.558365	+	0.829595i	$0.311429\pi$
$968$	1.63229	+	31.0602i	0.0524638	+	0.998314i
$969$		0			0
$970$	−17.8339	−	1.76871i	−0.572612	−	0.0567900i
$971$	32.9105			1.05615			0.528074	−	0.849198i	$-0.322914\pi$
$971$	32.9105			1.05615			0.528074	+	0.849198i	$0.322914\pi$
$972$		0			0
$973$	32.8100			1.05184
$974$	−31.8705	−	3.16083i	−1.02120	−	0.101279i
$975$		0			0
$976$	−8.06137	+	2.51768i	−0.258038	+	0.0805891i
$977$	−55.9116	−	9.85873i	−1.78877	−	0.315409i	−0.821701	−	0.569919i	$-0.806975\pi$
$977$	−55.9116	−	9.85873i	−1.78877	−	0.315409i	−0.967070	+	0.254510i	$0.918086\pi$
$978$		0			0
$979$	−0.0803698	−	0.0957811i	−0.00256863	−	0.00306118i
$980$	20.6689	−	33.9572i	0.660244	−	1.08472i
$981$		0			0
$982$	−35.0048	−	9.81561i	−1.11705	−	0.313229i
$983$	−5.63075	−	31.9336i	−0.179593	−	1.01852i	−0.932707	−	0.360634i	$-0.882560\pi$
$983$	−5.63075	−	31.9336i	−0.179593	−	1.01852i	0.753114	−	0.657890i	$-0.228551\pi$
$984$		0			0
$985$	−16.0284	+	5.83385i	−0.510707	+	0.185882i
$986$	−6.62344	−	9.69647i	−0.210933	−	0.308799i
$987$		0			0
$988$	20.4780	−	16.3896i	0.651491	−	0.521424i
$989$	47.7202	+	27.5513i	1.51741	+	0.876080i
$990$		0			0
$991$	36.6324	−	21.1497i	1.16367	−	0.671843i	0.211486	−	0.977381i	$-0.432170\pi$
$991$	36.6324	−	21.1497i	1.16367	−	0.671843i	0.952180	+	0.305539i	$0.0988365\pi$
$992$	−15.9382	−	40.0908i	−0.506038	−	1.27288i
$993$		0			0
$994$	3.39166	+	44.7308i	0.107577	+	1.41878i
$995$	−21.8002	−	18.2925i	−0.691113	−	0.579912i
$996$		0			0
$997$	31.7692	+	11.5630i	1.00614	+	0.366205i	0.791950	−	0.610586i	$-0.209066\pi$
$997$	31.7692	+	11.5630i	1.00614	+	0.366205i	0.214191	+	0.976792i	$0.431288\pi$
$998$	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.179.10		96
3.2	odd	2		108.2.l.a.23.7	yes	96
4.3	odd	2	inner	324.2.l.a.179.11		96
9.2	odd	6		972.2.l.c.215.15		96
9.4	even	3		972.2.l.a.863.13		96
9.5	odd	6		972.2.l.d.863.4		96
9.7	even	3		972.2.l.b.215.2		96
12.11	even	2		108.2.l.a.23.6	✓	96
27.2	odd	18		972.2.l.a.107.11		96
27.7	even	9		108.2.l.a.47.6	yes	96
27.11	odd	18		972.2.l.b.755.1		96
27.16	even	9		972.2.l.c.755.16		96
27.20	odd	18	inner	324.2.l.a.143.11		96
27.25	even	9		972.2.l.d.107.6		96
36.7	odd	6		972.2.l.b.215.1		96
36.11	even	6		972.2.l.c.215.16		96
36.23	even	6		972.2.l.d.863.6		96
36.31	odd	6		972.2.l.a.863.11		96
108.7	odd	18		108.2.l.a.47.7	yes	96
108.11	even	18		972.2.l.b.755.2		96
108.43	odd	18		972.2.l.c.755.15		96
108.47	even	18	inner	324.2.l.a.143.10		96
108.79	odd	18		972.2.l.d.107.4		96
108.83	even	18		972.2.l.a.107.13		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.6	✓	96	12.11	even	2
108.2.l.a.23.7	yes	96	3.2	odd	2
108.2.l.a.47.6	yes	96	27.7	even	9
108.2.l.a.47.7	yes	96	108.7	odd	18
324.2.l.a.143.10		96	108.47	even	18	inner
324.2.l.a.143.11		96	27.20	odd	18	inner
324.2.l.a.179.10		96	1.1	even	1	trivial
324.2.l.a.179.11		96	4.3	odd	2	inner
972.2.l.a.107.11		96	27.2	odd	18
972.2.l.a.107.13		96	108.83	even	18
972.2.l.a.863.11		96	36.31	odd	6
972.2.l.a.863.13		96	9.4	even	3
972.2.l.b.215.1		96	36.7	odd	6
972.2.l.b.215.2		96	9.7	even	3
972.2.l.b.755.1		96	27.11	odd	18
972.2.l.b.755.2		96	108.11	even	18
972.2.l.c.215.15		96	9.2	odd	6
972.2.l.c.215.16		96	36.11	even	6
972.2.l.c.755.15		96	108.43	odd	18
972.2.l.c.755.16		96	27.16	even	9
972.2.l.d.107.4		96	108.79	odd	18
972.2.l.d.107.6		96	27.25	even	9
972.2.l.d.863.4		96	9.5	odd	6
972.2.l.d.863.6		96	36.23	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.139573 - 1.40731i) q^{2} +(-1.96104 - 0.392845i) q^{4} +(2.42121 + 0.426924i) q^{5} +(2.49652 + 2.97523i) q^{7} +(-0.826562 + 2.70496i) q^{8} +O(q^{10})\)	\(q+(0.139573 - 1.40731i) q^{2} +(-1.96104 - 0.392845i) q^{4} +(2.42121 + 0.426924i) q^{5} +(2.49652 + 2.97523i) q^{7} +(-0.826562 + 2.70496i) q^{8} +(0.938750 - 3.34780i) q^{10} +(-0.0101176 - 0.0573797i) q^{11} +(4.33551 - 1.57800i) q^{13} +(4.53552 - 3.09811i) q^{14} +(3.69135 + 1.54077i) q^{16} +(-1.79249 - 1.03489i) q^{17} +(-2.46167 + 1.42125i) q^{19} +(-4.58037 - 1.78837i) q^{20} +(-0.0821631 + 0.00622992i) q^{22} +(-4.37564 - 3.67159i) q^{23} +(0.981522 + 0.357245i) q^{25} +(-1.61561 - 6.32166i) q^{26} +(-3.72696 - 6.81529i) q^{28} +(-1.37208 + 3.76976i) q^{29} +(4.90230 - 5.84234i) q^{31} +(2.68355 - 4.97982i) q^{32} +(-1.70660 + 2.37814i) q^{34} +(4.77439 + 8.26948i) q^{35} +(2.41051 - 4.17513i) q^{37} +(1.65655 + 3.66270i) q^{38} +(-3.15609 + 6.19639i) q^{40} +(0.375295 + 1.03112i) q^{41} +(-9.50027 + 1.67515i) q^{43} +(-0.00270032 + 0.116498i) q^{44} +(-5.77779 + 5.64542i) q^{46} +(4.18449 - 3.51121i) q^{47} +(-1.40388 + 7.96178i) q^{49} +(0.639748 - 1.33144i) q^{50} +(-9.12202 + 1.39133i) q^{52} +10.5337i q^{53} -0.143248i q^{55} +(-10.1114 + 4.29376i) q^{56} +(5.11372 + 2.45710i) q^{58} +(0.277801 - 1.57549i) q^{59} +(-1.61738 + 1.35715i) q^{61} +(-7.53775 - 7.71449i) q^{62} +(-6.63359 - 4.47163i) q^{64} +(11.1709 - 1.96973i) q^{65} +(-2.58470 - 7.10142i) q^{67} +(3.10858 + 2.73363i) q^{68} +(12.3041 - 5.56484i) q^{70} +(-4.08357 + 7.07295i) q^{71} +(3.26625 + 5.65731i) q^{73} +(-5.53926 - 3.97507i) q^{74} +(5.38576 - 1.82006i) q^{76} +(0.145459 - 0.173352i) q^{77} +(-2.36993 + 6.51134i) q^{79} +(8.27973 + 5.30644i) q^{80} +(1.50348 - 0.384241i) q^{82} +(-10.7082 - 3.89747i) q^{83} +(-3.89816 - 3.27095i) q^{85} +(1.03148 + 13.6036i) q^{86} +(0.163572 + 0.0200602i) q^{88} +(1.85844 - 1.07297i) q^{89} +(15.5186 + 8.95967i) q^{91} +(7.13842 + 8.91908i) q^{92} +(-4.35731 - 6.37895i) q^{94} +(-6.56698 + 2.39019i) q^{95} +(-0.895047 - 5.07606i) q^{97} +(11.0087 + 3.08694i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 6 q^{2} - 6 q^{4} + 12 q^{5} + 9 q^{8}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more