LMFDB - Embedded newform 972.2.l.c.755.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [972,2,Mod(107,972)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(972, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("972.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,3,0,3,6,0,0,-9,0,-3,0,0,6,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.76145907647$
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			755.15
Character	$\chi$	$=$	972.755
Dual form			972.2.l.c.215.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.28855 + 0.582781i) q^{2} +(1.32073 + 1.50189i) q^{4} +(1.58033 + 1.88337i) q^{5} +(1.32837 + 3.64966i) q^{7} +(0.826562 + 2.70496i) q^{8} +(0.938750 + 3.34780i) q^{10} +(0.0446335 + 0.0374519i) q^{11} +(-0.801171 - 4.54366i) q^{13} +(-0.415282 + 5.47693i) q^{14} +(-0.511330 + 3.96718i) q^{16} +(1.79249 - 1.03489i) q^{17} +(-2.46167 - 1.42125i) q^{19} +(-0.741407 + 4.86090i) q^{20} +(0.0356863 + 0.0742703i) q^{22} +(-5.36751 - 1.95361i) q^{23} +(-0.181378 + 1.02865i) q^{25} +(1.61561 - 6.32166i) q^{26} +(-3.72696 + 6.81529i) q^{28} +(-3.95075 - 0.696624i) q^{29} +(2.60846 - 7.16669i) q^{31} +(-2.97087 + 4.81393i) q^{32} +(2.91283 - 0.288886i) q^{34} +(-4.77439 + 8.26948i) q^{35} +(2.41051 + 4.17513i) q^{37} +(-2.34372 - 3.26596i) q^{38} +(-3.78818 + 5.83145i) q^{40} +(1.08062 - 0.190542i) q^{41} +(6.20086 - 7.38990i) q^{43} +(0.00270032 + 0.116498i) q^{44} +(-5.77779 - 5.64542i) q^{46} +(5.13304 - 1.86827i) q^{47} +(-6.19317 + 5.19668i) q^{49} +(-0.833190 + 1.21976i) q^{50} +(5.76594 - 7.20423i) q^{52} +10.5337i q^{53} +0.143248i q^{55} +(-8.77421 + 6.60985i) q^{56} +(-4.68477 - 3.20006i) q^{58} +(-1.22551 + 1.02833i) q^{59} +(1.98401 - 0.722122i) q^{61} +(7.53775 - 7.71449i) q^{62} +(-6.63359 + 4.47163i) q^{64} +(7.29127 - 8.68939i) q^{65} +(7.44236 - 1.31229i) q^{67} +(3.92169 + 1.32530i) q^{68} +(-10.9713 + 7.87324i) q^{70} +(4.08357 + 7.07295i) q^{71} +(3.26625 - 5.65731i) q^{73} +(0.672885 + 6.78467i) q^{74} +(-1.11666 - 5.57424i) q^{76} +(-0.0773972 + 0.212647i) q^{77} +(6.82395 + 1.20325i) q^{79} +(-8.27973 + 5.30644i) q^{80} +(1.50348 + 0.384241i) q^{82} +(-1.97880 + 11.2223i) q^{83} +(4.78181 + 1.74043i) q^{85} +(12.2968 - 5.90853i) q^{86} +(-0.0644136 + 0.151688i) q^{88} +(-1.85844 - 1.07297i) q^{89} +(15.5186 - 8.95967i) q^{91} +(-4.15494 - 10.6416i) q^{92} +(7.70299 + 0.584070i) q^{94} +(-1.21353 - 6.88226i) q^{95} +(-3.94848 - 3.31317i) q^{97} +(-11.0087 + 3.08694i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} - 12 q^{14} + 3 q^{16} - 18 q^{17} + 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 6 q^{29} - 57 q^{32} - 3 q^{34} - 6 q^{37} + 45 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) $ 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 - 12 * q^14 + 3 * q^16 - 18 * q^17 + 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 - 6 * q^29 - 57 * q^32 - 3 * q^34 - 6 * q^37 + 45 * q^38 - 12 * q^40 + 66 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 66 * q^50 - 24 * q^52 - 81 * q^56 - 24 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 - 42 * q^65 + 51 * q^68 - 30 * q^70 - 6 * q^73 - 96 * q^74 - 9 * q^76 + 30 * q^77 - 12 * q^82 + 66 * q^85 + 141 * q^86 - 45 * q^88 - 24 * q^92 - 51 * q^94 + 42 * q^97 - 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.28855	+	0.582781i	0.911144	+	0.412088i
$2$	1.28855	+	0.582781i	0.911144	+	0.412088i
$3$		0			0
$3$		0			0
$4$	1.32073	+	1.50189i	0.660366	+	0.750944i
$5$	1.58033	+	1.88337i	0.706746	+	0.842267i	0.993272	−	0.115806i	$-0.0369450\pi$
$5$	1.58033	+	1.88337i	0.706746	+	0.842267i	−0.286526	+	0.958072i	$0.592501\pi$
$6$		0			0
$7$	1.32837	+	3.64966i	0.502076	+	1.37944i	0.889244	+	0.457434i	$0.151231\pi$
$7$	1.32837	+	3.64966i	0.502076	+	1.37944i	−0.387168	+	0.922009i	$0.626547\pi$
$8$	0.826562	+	2.70496i	0.292234	+	0.956347i
$9$		0			0
$10$	0.938750	+	3.34780i	0.296859	+	1.05867i
$11$	0.0446335	+	0.0374519i	0.0134575	+	0.0112922i	0.649492	−	0.760369i	$-0.274982\pi$
$11$	0.0446335	+	0.0374519i	0.0134575	+	0.0112922i	−0.636034	+	0.771661i	$0.719426\pi$
$12$		0			0
$13$	−0.801171	−	4.54366i	−0.222205	−	1.26019i	−0.867957	−	0.496639i	$-0.834567\pi$
$13$	−0.801171	−	4.54366i	−0.222205	−	1.26019i	0.645752	−	0.763547i	$-0.276544\pi$
$14$	−0.415282	+	5.47693i	−0.110989	+	1.46377i
$15$		0			0
$16$	−0.511330	+	3.96718i	−0.127832	+	0.991796i
$17$	1.79249	−	1.03489i	0.434742	−	0.250998i	−0.266623	−	0.963801i	$-0.585908\pi$
$17$	1.79249	−	1.03489i	0.434742	−	0.250998i	0.701365	+	0.712803i	$0.252574\pi$
$18$		0			0
$19$	−2.46167	−	1.42125i	−0.564746	−	0.326056i	0.190302	−	0.981726i	$-0.439053\pi$
$19$	−2.46167	−	1.42125i	−0.564746	−	0.326056i	−0.755048	+	0.655669i	$0.772387\pi$
$20$	−0.741407	+	4.86090i	−0.165784	+	1.08693i
$21$		0			0
$22$	0.0356863	+	0.0742703i	0.00760834	+	0.0158345i
$23$	−5.36751	−	1.95361i	−1.11920	−	0.407357i	−0.284842	−	0.958574i	$-0.591941\pi$
$23$	−5.36751	−	1.95361i	−1.11920	−	0.407357i	−0.834361	+	0.551218i	$0.814163\pi$
$24$		0			0
$25$	−0.181378	+	1.02865i	−0.0362756	+	0.205729i
$26$	1.61561	−	6.32166i	0.316847	−	1.23978i
$27$		0			0
$28$	−3.72696	+	6.81529i	−0.704330	+	1.28797i
$29$	−3.95075	−	0.696624i	−0.733636	−	0.129360i	−0.205665	−	0.978622i	$-0.565936\pi$
$29$	−3.95075	−	0.696624i	−0.733636	−	0.129360i	−0.527971	+	0.849263i	$0.677047\pi$
$30$		0			0
$31$	2.60846	−	7.16669i	0.468493	−	1.28717i	−0.450456	−	0.892799i	$-0.648739\pi$
$31$	2.60846	−	7.16669i	0.468493	−	1.28717i	0.918949	−	0.394376i	$-0.129039\pi$
$32$	−2.97087	+	4.81393i	−0.525181	+	0.850990i
$33$		0			0
$34$	2.91283	−	0.288886i	0.499546	−	0.0495436i
$35$	−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	$0.703632\pi$
$38$	−2.34372	−	3.26596i	−0.380201	−	0.529809i
$39$		0			0
$40$	−3.78818	+	5.83145i	−0.598964	+	0.922033i
$41$	1.08062	−	0.190542i	0.168764	−	0.0297577i	−0.0886273	−	0.996065i	$-0.528248\pi$
$41$	1.08062	−	0.190542i	0.168764	−	0.0297577i	0.257392	+	0.966307i	$0.417137\pi$
$42$		0			0
$43$	6.20086	−	7.38990i	0.945622	−	1.12695i	−0.0461498	−	0.998935i	$-0.514695\pi$
$43$	6.20086	−	7.38990i	0.945622	−	1.12695i	0.991772	−	0.128014i	$-0.0408604\pi$
$44$	0.00270032	+	0.116498i	0.000407088	+	0.0175628i
$45$		0			0
$46$	−5.77779	−	5.64542i	−0.851888	−	0.832371i
$47$	5.13304	−	1.86827i	0.748731	−	0.272516i	0.0606593	−	0.998159i	$-0.480680\pi$
$47$	5.13304	−	1.86827i	0.748731	−	0.272516i	0.688072	+	0.725643i	$0.258457\pi$
$48$		0			0
$49$	−6.19317	+	5.19668i	−0.884738	+	0.742383i
$50$	−0.833190	+	1.21976i	−0.117831	+	0.172500i
$51$		0			0
$52$	5.76594	−	7.20423i	0.799592	−	0.999048i
$53$			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
$56$	−8.77421	+	6.60985i	−1.17250	+	0.883279i
$57$		0			0
$58$	−4.68477	−	3.20006i	−0.615140	−	0.420188i
$59$	−1.22551	+	1.02833i	−0.159548	+	0.133877i	−0.719067	−	0.694941i	$-0.755431\pi$
$59$	−1.22551	+	1.02833i	−0.159548	+	0.133877i	0.559519	+	0.828818i	$0.310986\pi$
$60$		0			0
$61$	1.98401	−	0.722122i	0.254027	−	0.0924583i	−0.211868	−	0.977298i	$-0.567955\pi$
$61$	1.98401	−	0.722122i	0.254027	−	0.0924583i	0.465895	+	0.884840i	$0.345732\pi$
$62$	7.53775	−	7.71449i	0.957295	−	0.979741i
$63$		0			0
$64$	−6.63359	+	4.47163i	−0.829199	+	0.558954i
$65$	7.29127	−	8.68939i	0.904370	−	1.07779i
$66$		0			0
$67$	7.44236	−	1.31229i	0.909229	−	0.160322i	0.300576	−	0.953758i	$-0.402821\pi$
$67$	7.44236	−	1.31229i	0.909229	−	0.160322i	0.608653	+	0.793436i	$0.291710\pi$
$68$	3.92169	+	1.32530i	0.475575	+	0.160716i
$69$		0			0
$70$	−10.9713	+	7.87324i	−1.31133	+	0.941032i
$71$	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	$0.0418037\pi$
$74$	0.672885	+	6.78467i	0.0782212	+	0.788702i
$75$		0			0
$76$	−1.11666	−	5.57424i	−0.128089	−	0.639409i
$77$	−0.0773972	+	0.212647i	−0.00882023	+	0.0242334i
$78$		0			0
$79$	6.82395	+	1.20325i	0.767754	+	0.135376i	0.543790	−	0.839222i	$-0.316989\pi$
$79$	6.82395	+	1.20325i	0.767754	+	0.135376i	0.223965	+	0.974597i	$0.428100\pi$
$80$	−8.27973	+	5.30644i	−0.925702	+	0.593278i
$81$		0			0
$82$	1.50348	+	0.384241i	0.166032	+	0.0424323i
$83$	−1.97880	+	11.2223i	−0.217201	+	1.23181i	0.659844	+	0.751402i	$0.270622\pi$
$83$	−1.97880	+	11.2223i	−0.217201	+	1.23181i	−0.877046	+	0.480407i	$0.840489\pi$
$84$		0			0
$85$	4.78181	+	1.74043i	0.518660	+	0.188777i
$86$	12.2968	−	5.90853i	1.32600	−	0.637133i
$87$		0			0
$88$	−0.0644136	+	0.151688i	−0.00686651	+	0.0161700i
$89$	−1.85844	−	1.07297i	−0.196995	−	0.113735i	0.398258	−	0.917273i	$-0.369615\pi$
$89$	−1.85844	−	1.07297i	−0.196995	−	0.113735i	−0.595253	+	0.803538i	$0.702948\pi$
$90$		0			0
$91$	15.5186	−	8.95967i	1.62679	−	0.939228i
$92$	−4.15494	−	10.6416i	−0.433182	−	1.10946i
$93$		0			0
$94$	7.70299	+	0.584070i	0.794502	+	0.0602422i
$95$	−1.21353	−	6.88226i	−0.124505	−	0.706105i
$96$		0			0
$97$	−3.94848	−	3.31317i	−0.400907	−	0.336401i	0.419937	−	0.907553i	$-0.362052\pi$
$97$	−3.94848	−	3.31317i	−0.400907	−	0.336401i	−0.820844	+	0.571152i	$0.806497\pi$
$98$	−11.0087	+	3.08694i	−1.11205	+	0.311828i
$99$		0			0
$100$	−1.78446	+	1.08616i	−0.178446	+	0.108616i
$101$	4.52066	+	12.4204i	0.449822	+	1.23588i	0.932848	+	0.360270i	$0.117315\pi$
$101$	4.52066	+	12.4204i	0.449822	+	1.23588i	−0.483026	+	0.875606i	$0.660462\pi$
$102$		0			0
$103$	−0.670352	−	0.798895i	−0.0660518	−	0.0787174i	0.732007	−	0.681297i	$-0.238584\pi$
$103$	−0.670352	−	0.798895i	−0.0660518	−	0.0787174i	−0.798059	+	0.602580i	$0.794139\pi$
$104$	11.6282	−	5.92275i	1.14024	−	0.580774i
$105$		0			0
$106$	−6.13885	+	13.5733i	−0.596258	+	1.31835i
$107$	−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	$0.873547\pi$
$110$	−0.0834820	+	0.184582i	−0.00795970	+	0.0175992i
$111$		0			0
$112$	−15.1581	+	3.40370i	−1.43231	+	0.321619i
$113$	−3.35075	−	3.99326i	−0.315212	−	0.375655i	0.585055	−	0.810994i	$-0.301073\pi$
$113$	−3.35075	−	3.99326i	−0.315212	−	0.375655i	−0.900267	+	0.435339i	$0.856628\pi$
$114$		0			0
$115$	−4.80308	−	13.1963i	−0.447889	−	1.23057i
$116$	−4.17164	−	6.85364i	−0.387327	−	0.636344i
$117$		0			0
$118$	−2.17843	+	0.610848i	−0.200541	+	0.0562331i
$119$	6.15809	+	5.16725i	0.564512	+	0.473681i
$120$		0			0
$121$	−1.90954	−	10.8295i	−0.173595	−	0.984504i
$122$	2.97734	+	0.225754i	0.269556	+	0.0204388i
$123$		0			0
$124$	14.2086	−	5.54766i	1.27597	−	0.498195i
$125$	8.42192	−	4.86240i	0.753279	−	0.434906i
$126$		0			0
$127$	1.67801	+	0.968801i	0.148900	+	0.0859672i	0.572599	−	0.819836i	$-0.305935\pi$
$127$	1.67801	+	0.968801i	0.148900	+	0.0859672i	−0.423699	+	0.905803i	$0.639269\pi$
$128$	−11.1537	+	1.89600i	−0.985858	+	0.167584i
$129$		0			0
$130$	14.4592	−	6.94752i	1.26815	−	0.609338i
$131$	0.439512	+	0.159969i	0.0384003	+	0.0139766i	0.361149	−	0.932508i	$-0.382385\pi$
$131$	0.439512	+	0.159969i	0.0384003	+	0.0139766i	−0.322749	+	0.946485i	$0.604607\pi$
$132$		0			0
$133$	1.91706	−	10.8722i	0.166230	−	0.942740i
$134$	10.3546	+	2.64631i	0.894505	+	0.228607i
$135$		0			0
$136$	4.28094	+	3.99320i	0.367088	+	0.342414i
$137$	−4.32365	−	0.762377i	−0.369395	−	0.0651343i	−0.0141305	−	0.999900i	$-0.504498\pi$
$137$	−4.32365	−	0.762377i	−0.369395	−	0.0651343i	−0.355264	+	0.934766i	$0.615609\pi$
$138$		0			0
$139$	2.88929	−	7.93825i	0.245066	−	0.673313i	−0.754784	−	0.655974i	$-0.772258\pi$
$139$	2.88929	−	7.93825i	0.245066	−	0.673313i	0.999850	−	0.0173395i	$-0.00551960\pi$
$140$	−18.7255	+	3.75118i	−1.58260	+	0.317033i
$141$		0			0
$142$	1.13991	+	11.4937i	0.0956592	+	0.964528i
$143$	0.134410	−	0.232805i	0.0112399	−	0.0194681i
$144$		0			0
$145$	−4.93150	−	8.54161i	−0.409539	−	0.709342i
$146$	7.50571	−	5.38623i	0.621177	−	0.445768i
$147$		0			0
$148$	−3.08693	+	9.13455i	−0.253744	+	0.750855i
$149$	−10.0122	+	1.76542i	−0.820229	+	0.144629i	−0.567989	−	0.823036i	$-0.692278\pi$
$149$	−10.0122	+	1.76542i	−0.820229	+	0.144629i	−0.252240	+	0.967665i	$0.581167\pi$
$150$		0			0
$151$	−1.53394	+	1.82808i	−0.124830	+	0.148767i	−0.824840	−	0.565367i	$-0.808735\pi$
$151$	−1.53394	+	1.82808i	−0.124830	+	0.148767i	0.700009	+	0.714134i	$0.253179\pi$
$152$	1.80969	−	7.83346i	0.146785	−	0.635378i
$153$		0			0
$154$	−0.223657	+	0.228901i	−0.0180228	+	0.0184454i
$155$	17.6197	−	6.41305i	1.41525	−	0.515109i
$156$		0			0
$157$	−4.17177	+	3.50053i	−0.332943	+	0.279373i	−0.793898	−	0.608051i	$-0.791952\pi$
$157$	−4.17177	+	3.50053i	−0.332943	+	0.279373i	0.460954	+	0.887424i	$0.347507\pi$
$158$	8.09178	+	5.52731i	0.643748	+	0.439729i
$159$		0			0
$160$	−13.7614	+	2.01236i	−1.08793	+	0.159091i
$161$		−	22.1847i		−	1.74840i
$162$		0			0
$163$		−	9.76328i		−	0.764719i	−0.924014	−	0.382360i	$-0.875112\pi$
$163$		−	9.76328i		−	0.764719i	0.924014	−	0.382360i	$-0.124888\pi$
$164$	1.71338	+	1.37131i	0.133793	+	0.107082i
$165$		0			0
$166$	−9.08994	+	13.3073i	−0.705516	+	1.03285i
$167$	3.55893	−	2.98630i	0.275399	−	0.231087i	−0.494618	−	0.869110i	$-0.664692\pi$
$167$	3.55893	−	2.98630i	0.275399	−	0.231087i	0.770017	+	0.638023i	$0.220248\pi$
$168$		0			0
$169$	−7.78701	+	2.83424i	−0.599001	+	0.218018i
$170$	5.14731	+	5.02939i	0.394781	+	0.385736i
$171$		0			0
$172$	19.2885	−	0.447088i	1.47073	−	0.0340901i
$173$	−0.566413	+	0.675025i	−0.0430636	+	0.0513212i	−0.787146	−	0.616766i	$-0.788442\pi$
$173$	−0.566413	+	0.675025i	−0.0430636	+	0.0513212i	0.744083	+	0.668087i	$0.232887\pi$
$174$		0			0
$175$	−3.99515	+	0.704452i	−0.302005	+	0.0532516i
$176$	−0.171401	+	0.157919i	−0.0129198	+	0.0119036i
$177$		0			0
$178$	−1.76939	−	2.46565i	−0.132622	−	0.184808i
$179$	−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	$0.245678\pi$
$182$	25.2180	−	2.50105i	1.86929	−	0.185390i
$183$		0			0
$184$	0.847864	−	16.1337i	0.0625054	−	1.18939i
$185$	−4.05389	+	11.1380i	−0.298048	+	0.818880i
$186$		0			0
$187$	0.118764	+	0.0209412i	0.00868486	+	0.00153138i
$188$	9.58531	+	5.24176i	0.699081	+	0.382294i
$189$		0			0
$190$	2.44716	−	9.57538i	0.177535	−	0.694671i
$191$	4.42330	−	25.0858i	0.320058	−	1.81514i	−0.222282	−	0.974982i	$-0.571350\pi$
$191$	4.42330	−	25.0858i	0.320058	−	1.81514i	0.542340	−	0.840159i	$-0.317538\pi$
$192$		0			0
$193$	19.3528	+	7.04384i	1.39305	+	0.507027i	0.926106	−	0.377263i	$-0.123135\pi$
$193$	19.3528	+	7.04384i	1.39305	+	0.507027i	0.466939	+	0.884290i	$0.345357\pi$
$194$	−3.15697	−	6.57028i	−0.226657	−	0.471719i
$195$		0			0
$196$	−15.9844	−	2.43801i	−1.14174	−	0.174143i
$197$	6.00833	+	3.46891i	0.428076	+	0.247150i	0.698526	−	0.715584i	$-0.253839\pi$
$197$	6.00833	+	3.46891i	0.428076	+	0.247150i	−0.270451	+	0.962734i	$0.587173\pi$
$198$		0			0
$199$	−10.0244	+	5.78756i	−0.710608	+	0.410270i	−0.811286	−	0.584650i	$-0.801232\pi$
$199$	−10.0244	+	5.78756i	−0.710608	+	0.410270i	0.100678	+	0.994919i	$0.467899\pi$
$200$	−2.93236	+	0.359619i	−0.207349	+	0.0254289i
$201$		0			0
$202$	−1.41327	+	18.6389i	−0.0994375	+	1.31143i
$203$	−2.70561	−	15.3443i	−0.189897	−	1.07696i
$204$		0			0
$205$	2.06660	+	1.73408i	0.144338	+	0.121114i
$206$	−0.398203	−	1.42009i	−0.0277441	−	0.0989421i
$207$		0			0
$208$	18.4352	−	0.855080i	1.27825	−	0.0592891i
$209$	−0.0566445	−	0.155629i	−0.00391818	−	0.0107651i
$210$		0			0
$211$	9.71514	+	11.5781i	0.668818	+	0.797066i	0.988623	−	0.150417i	$-0.0480617\pi$
$211$	9.71514	+	11.5781i	0.668818	+	0.797066i	−0.319805	+	0.947484i	$0.603617\pi$
$212$	−15.8205	+	13.9122i	−1.08655	+	0.955496i
$213$		0			0
$214$	−16.0876	−	7.27601i	−1.09972	−	0.497378i
$215$	23.7173			1.61751
$216$		0			0
$217$	29.6210			2.01080
$218$	−24.8104	−	11.2212i	−1.68037	−	0.759993i
$219$		0			0
$220$	−0.215142	+	0.189192i	−0.0145049	+	0.0127553i
$221$	−6.13829	−	7.31533i	−0.412906	−	0.492083i
$222$		0			0
$223$	−0.561441	−	1.54255i	−0.0375969	−	0.103297i	0.919474	−	0.393151i	$-0.128615\pi$
$223$	−0.561441	−	1.54255i	−0.0375969	−	0.103297i	−0.957071	+	0.289855i	$0.906393\pi$
$224$	−21.5156	−	4.44802i	−1.43757	−	0.297196i
$225$		0			0
$226$	−1.99041	−	7.09828i	−0.132400	−	0.472170i
$227$	−20.9218	−	17.5555i	−1.38863	−	1.16520i	−0.965892	−	0.258947i	$-0.916625\pi$
$227$	−20.9218	−	17.5555i	−1.38863	−	1.16520i	−0.422738	−	0.906252i	$-0.638931\pi$
$228$		0			0
$229$	−1.09700	−	6.22140i	−0.0724918	−	0.411121i	−0.999361	−	0.0357375i	$-0.988622\pi$
$229$	−1.09700	−	6.22140i	−0.0724918	−	0.411121i	0.926869	−	0.375384i	$-0.122489\pi$
$230$	1.50156	−	19.8033i	0.0990102	−	1.30579i
$231$		0			0
$232$	−1.38120	−	11.2624i	−0.0906803	−	0.739414i
$233$	−25.6785	+	14.8255i	−1.68226	+	0.971251i	−0.722099	+	0.691790i	$0.756822\pi$
$233$	−25.6785	+	14.8255i	−1.68226	+	0.971251i	−0.960157	+	0.279461i	$0.909844\pi$
$234$		0			0
$235$	11.6306	+	6.71490i	0.758693	+	0.438032i
$236$	−3.16301	−	0.482437i	−0.205894	−	0.0314040i
$237$		0			0
$238$	4.92365	+	10.2471i	0.319153	+	0.664221i
$239$	8.74459	+	3.18277i	0.565641	+	0.205876i	0.608982	−	0.793184i	$-0.291578\pi$
$239$	8.74459	+	3.18277i	0.565641	+	0.205876i	−0.0433415	+	0.999060i	$0.513800\pi$
$240$		0			0
$241$	−2.44169	+	13.8475i	−0.157283	+	0.891996i	0.799386	+	0.600818i	$0.205158\pi$
$241$	−2.44169	+	13.8475i	−0.157283	+	0.891996i	−0.956669	+	0.291178i	$0.905953\pi$
$242$	3.85071	−	15.0673i	0.247533	−	0.968561i
$243$		0			0
$244$	3.70490	+	2.02604i	0.237182	+	0.129704i
$245$	−19.5745	−	3.45151i	−1.25057	−	0.220509i
$246$		0			0
$247$	−4.48545	+	12.3237i	−0.285402	+	0.784136i
$248$	21.5416	+	1.13207i	1.36790	+	0.0718863i
$249$		0			0
$250$	13.6858	−	1.35732i	0.865566	−	0.0858444i
$251$	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
$254$	1.59761	+	2.22626i	0.100243	+	0.139688i
$255$		0			0
$256$	−15.4771	−	4.05708i	−0.967318	−	0.253567i
$257$	6.97521	−	1.22992i	0.435102	−	0.0767202i	0.0481926	−	0.998838i	$-0.484654\pi$
$257$	6.97521	−	1.22992i	0.435102	−	0.0767202i	0.386909	+	0.922118i	$0.373543\pi$
$258$		0			0
$259$	−12.0358	+	14.3437i	−0.747866	+	0.891272i
$260$	22.6803	−	0.525707i	1.40657	−	0.0326030i
$261$		0			0
$262$	0.473107	+	0.462268i	0.0292286	+	0.0285590i
$263$	−1.86822	+	0.679976i	−0.115199	+	0.0419291i	−0.398977	−	0.916961i	$-0.630635\pi$
$263$	−1.86822	+	0.679976i	−0.115199	+	0.0419291i	0.283777	+	0.958890i	$0.408412\pi$
$264$		0			0
$265$	−19.8389	+	16.6468i	−1.21869	+	1.02260i
$266$	8.80635	−	12.8922i	0.539952	−	0.790470i
$267$		0			0
$268$	11.8003	+	9.44440i	0.720817	+	0.576909i
$269$		−	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	$0.107427\pi$
$271$			10.9019i			0.662245i	−0.943588	+	0.331122i	$0.892573\pi$
$272$	3.18906	+	7.64030i	0.193365	+	0.463261i
$273$		0			0
$274$	−5.12696	−	3.50211i	−0.309731	−	0.211570i
$275$	−0.0466203	+	0.0391191i	−0.00281131	+	0.00235897i
$276$		0			0
$277$	5.31629	−	1.93497i	0.319425	−	0.116261i	−0.177331	−	0.984151i	$-0.556746\pi$
$277$	5.31629	−	1.93497i	0.319425	−	0.116261i	0.496756	+	0.867890i	$0.334524\pi$
$278$	8.34925	−	8.54502i	0.500755	−	0.512496i
$279$		0			0
$280$	−26.3149	−	6.07928i	−1.57262	−	0.363306i
$281$	7.96310	−	9.49005i	0.475039	−	0.566129i	−0.474308	−	0.880359i	$-0.657302\pi$
$281$	7.96310	−	9.49005i	0.475039	−	0.566129i	0.949347	+	0.314230i	$0.101746\pi$
$282$		0			0
$283$	−22.1972	+	3.91396i	−1.31949	+	0.232661i	−0.788665	−	0.614824i	$-0.789227\pi$
$283$	−22.1972	+	3.91396i	−1.31949	+	0.232661i	−0.530820	+	0.847484i	$0.678116\pi$
$284$	−5.22946	+	15.4745i	−0.310312	+	0.918244i
$285$		0			0
$286$	0.308869	−	0.221650i	0.0182638	−	0.0131064i
$287$	2.13088	+	3.69079i	0.125782	+	0.217860i
$288$		0			0
$289$	−6.35799	+	11.0124i	−0.374000	+	0.647786i
$290$	−1.37661	−	13.8803i	−0.0808372	−	0.815079i
$291$		0			0
$292$	12.8105	−	2.56626i	0.749677	−	0.150179i
$293$	8.57916	−	23.5710i	0.501200	−	1.37703i	−0.388905	−	0.921278i	$-0.627147\pi$
$293$	8.57916	−	23.5710i	0.501200	−	1.37703i	0.890104	−	0.455757i	$-0.150631\pi$
$294$		0			0
$295$	−3.87344	−	0.682991i	−0.225520	−	0.0397653i
$296$	−9.30111	+	9.97134i	−0.540616	+	0.579572i
$297$		0			0
$298$	−13.9301	−	3.56007i	−0.806946	−	0.206229i
$299$	−4.57628	+	25.9534i	−0.264653	+	1.50092i
$300$		0			0
$301$	35.2077	+	12.8145i	2.02934	+	0.738618i
$302$	−3.04193	+	1.46162i	−0.175043	+	0.0841070i
$303$		0			0
$304$	6.89707	−	9.03917i	0.395574	−	0.518432i
$305$	4.49542	+	2.59543i	0.257407	+	0.148614i
$306$		0			0
$307$	−7.99858	+	4.61798i	−0.456503	+	0.263562i	−0.710573	−	0.703624i	$-0.751564\pi$
$307$	−7.99858	+	4.61798i	−0.456503	+	0.263562i	0.254070	+	0.967186i	$0.418231\pi$
$308$	−0.421593	+	0.164608i	−0.0240225	+	0.00937942i
$309$		0			0
$310$	26.4413	+	2.00488i	1.50177	+	0.113870i
$311$	4.52048	+	25.6369i	0.256333	+	1.45373i	0.792629	+	0.609705i	$0.208712\pi$
$311$	4.52048	+	25.6369i	0.256333	+	1.45373i	−0.536296	+	0.844030i	$0.680177\pi$
$312$		0			0
$313$	17.1279	+	14.3720i	0.968125	+	0.812354i	0.982256	−	0.187547i	$-0.0600536\pi$
$313$	17.1279	+	14.3720i	0.968125	+	0.812354i	−0.0141304	+	0.999900i	$0.504498\pi$
$314$	−7.41558	+	2.07939i	−0.418486	+	0.117347i
$315$		0			0
$316$	7.20547	+	11.8380i	0.405340	+	0.665938i
$317$	−3.98568	−	10.9506i	−0.223858	−	0.615045i	0.776019	−	0.630709i	$-0.217236\pi$
$317$	−3.98568	−	10.9506i	−0.223858	−	0.615045i	−0.999877	+	0.0156642i	$0.995014\pi$
$318$		0			0
$319$	−0.150246	−	0.179056i	−0.00841215	−	0.0100252i
$320$	−18.9050	−	5.42682i	−1.05682	−	0.303369i
$321$		0			0
$322$	12.9288	−	28.5862i	0.720496	−	1.59305i
$323$	−5.88335			−0.327358
$324$		0			0
$325$	4.81914			0.267318
$326$	5.68986	−	12.5805i	0.315132	−	0.696769i
$327$		0			0
$328$	1.40861	+	2.76554i	0.0777774	+	0.152701i
$329$	13.6371	+	16.2521i	0.751840	+	0.896008i
$330$		0			0
$331$	1.50096	+	4.12385i	0.0825001	+	0.226667i	0.974083	−	0.226190i	$-0.0726270\pi$
$331$	1.50096	+	4.12385i	0.0825001	+	0.226667i	−0.891583	+	0.452857i	$0.850405\pi$
$332$	−19.4681	+	11.8498i	−1.06845	+	0.650340i
$333$		0			0
$334$	6.32623	−	1.77392i	0.346156	−	0.0970648i
$335$	14.2329	+	11.9428i	0.777627	+	0.652507i
$336$		0			0
$337$	−5.84195	−	33.1313i	−0.318231	−	1.80478i	−0.553502	−	0.832848i	$-0.686709\pi$
$337$	−5.84195	−	33.1313i	−0.318231	−	1.80478i	0.235271	−	0.971930i	$-0.424402\pi$
$338$	−11.6857	−	0.886055i	−0.635619	−	0.0481951i
$339$		0			0
$340$	3.70155	+	9.48038i	0.200745	+	0.514146i
$341$	0.384831	−	0.222182i	0.0208398	−	0.0120318i
$342$		0			0
$343$	−3.64812	−	2.10624i	−0.196980	−	0.113726i
$344$	25.1148	+	10.6649i	1.35410	+	0.575011i
$345$		0			0
$346$	−1.12324	+	0.539710i	−0.0603860	+	0.0290150i
$347$	−14.0672	−	5.12003i	−0.755165	−	0.274858i	−0.0643876	−	0.997925i	$-0.520509\pi$
$347$	−14.0672	−	5.12003i	−0.755165	−	0.274858i	−0.690778	+	0.723067i	$0.742732\pi$
$348$		0			0
$349$	−1.84715	+	10.4757i	−0.0988756	+	0.560752i	0.894615	+	0.446838i	$0.147450\pi$
$349$	−1.84715	+	10.4757i	−0.0988756	+	0.560752i	−0.993491	+	0.113914i	$0.963661\pi$
$350$	−5.55850	−	1.42057i	−0.297114	−	0.0759328i
$351$		0			0
$352$	−0.312891	+	0.103597i	−0.0166772	+	0.00552176i
$353$	10.8334	+	1.91021i	0.576601	+	0.101670i	0.454341	−	0.890828i	$-0.349875\pi$
$353$	10.8334	+	1.91021i	0.576601	+	0.101670i	0.122260	+	0.992498i	$0.460986\pi$
$354$		0			0
$355$	−6.86755	+	18.8684i	−0.364492	+	1.00143i
$356$	−0.843023	−	4.20828i	−0.0446802	−	0.223039i
$357$		0			0
$358$	−1.77223	−	17.8693i	−0.0936650	−	0.944421i
$359$	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
$362$	−7.59541	+	5.45061i	−0.399206	+	0.286477i
$363$		0			0
$364$	33.9523	+	11.4739i	1.77959	+	0.601393i
$365$	15.8165	−	2.78888i	0.827876	−	0.145977i
$366$		0			0
$367$	3.34300	−	3.98403i	0.174503	−	0.207965i	−0.671703	−	0.740821i	$-0.734437\pi$
$367$	3.34300	−	3.98403i	0.174503	−	0.207965i	0.846206	+	0.532856i	$0.178881\pi$
$368$	10.4949	−	20.2950i	0.547085	−	1.05795i
$369$		0			0
$370$	−11.7146	+	11.9893i	−0.609015	+	0.623295i
$371$	−38.4445	+	13.9927i	−1.99594	+	0.726463i
$372$		0			0
$373$	−12.1581	+	10.2018i	−0.629522	+	0.528232i	−0.900780	−	0.434275i	$-0.857005\pi$
$373$	−12.1581	+	10.2018i	−0.629522	+	0.528232i	0.271259	+	0.962507i	$0.412560\pi$
$374$	0.140829	+	0.0961971i	0.00728209	+	0.00497423i
$375$		0			0
$376$	9.29638	+	12.3404i	0.479424	+	0.636408i
$377$			18.5090i			0.953262i
$378$		0			0
$379$		−	13.3564i		−	0.686073i	−0.939322	−	0.343037i	$-0.888544\pi$
$379$		−	13.3564i		−	0.686073i	0.939322	−	0.343037i	$-0.111456\pi$
$380$	8.73364	−	10.9122i	0.448026	−	0.559785i
$381$		0			0
$382$	20.3191	−	29.7465i	1.03962	−	1.52196i
$383$	6.19455	−	5.19784i	0.316527	−	0.265597i	−0.470657	−	0.882316i	$-0.655983\pi$
$383$	6.19455	−	5.19784i	0.316527	−	0.265597i	0.787183	+	0.616719i	$0.211539\pi$
$384$		0			0
$385$	−0.522806	+	0.190286i	−0.0266446	+	0.00969786i
$386$	20.8321	+	20.3548i	1.06032	+	1.03603i
$387$		0			0
$388$	−0.238882	−	10.3060i	−0.0121274	−	0.523207i
$389$	−12.6325	+	15.0548i	−0.640493	+	0.763310i	−0.984448	−	0.175676i	$-0.943789\pi$
$389$	−12.6325	+	15.0548i	−0.640493	+	0.763310i	0.343955	+	0.938986i	$0.388233\pi$
$390$		0			0
$391$	−11.6430	+	2.05297i	−0.588811	+	0.103823i
$392$	−19.1758	−	12.4569i	−0.968526	−	0.629167i
$393$		0			0
$394$	5.72043	+	7.97141i	0.288191	+	0.401594i
$395$	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	$-0.0465910\pi$
$398$	−16.2898	+	1.61557i	−0.816533	+	0.0809814i
$399$		0			0
$400$	−3.98808	−	1.24554i	−0.199404	−	0.0622769i
$401$	−4.16467	+	11.4423i	−0.207974	+	0.571403i	−0.999195	−	0.0401276i	$-0.987224\pi$
$401$	−4.16467	+	11.4423i	−0.207974	+	0.571403i	0.791221	+	0.611530i	$0.209446\pi$
$402$		0			0
$403$	−34.6528	−	6.11023i	−1.72618	−	0.304372i
$404$	−12.6835	+	23.1935i	−0.631026	+	1.15392i
$405$		0			0
$406$	5.45604	−	21.3487i	0.270779	−	1.05952i
$407$	−0.0487771	+	0.276629i	−0.00241779	+	0.0137120i
$408$		0			0
$409$	−29.2090	−	10.6312i	−1.44429	−	0.525679i	−0.503301	−	0.864111i	$-0.667881\pi$
$409$	−29.2090	−	10.6312i	−1.44429	−	0.525679i	−0.940991	+	0.338432i	$0.890104\pi$
$410$	1.65233	+	3.43883i	0.0816028	+	0.169832i
$411$		0			0
$412$	0.314493	−	2.06192i	0.0154940	−	0.101583i
$413$	−5.38099	−	3.10671i	−0.264781	−	0.152871i
$414$		0			0
$415$	−24.2629	+	14.0082i	−1.19102	+	0.687635i
$416$	24.2531	+	9.64188i	1.18910	+	0.472732i
$417$		0			0
$418$	0.0177085	−	0.233548i	0.000866151	−	0.0114232i
$419$	6.40156	+	36.3051i	0.312737	+	1.77362i	0.584639	+	0.811293i	$0.301236\pi$
$419$	6.40156	+	36.3051i	0.312737	+	1.77362i	−0.271903	+	0.962325i	$0.587653\pi$
$420$		0			0
$421$	−28.2218	−	23.6809i	−1.37544	−	1.15413i	−0.970864	−	0.239632i	$-0.922973\pi$
$421$	−28.2218	−	23.6809i	−1.37544	−	1.15413i	−0.404580	−	0.914502i	$-0.632582\pi$
$422$	5.77100	+	20.5807i	0.280928	+	1.00185i
$423$		0			0
$424$	−28.4933	+	8.70677i	−1.38376	+	0.422838i
$425$	0.739420	+	2.03154i	0.0358672	+	0.0985442i
$426$		0			0
$427$	5.27101	+	6.28174i	0.255082	+	0.303995i
$428$	−16.4893	−	18.7510i	−0.797042	−	0.906366i
$429$		0			0
$430$	30.5610	+	13.8220i	1.47378	+	0.666556i
$431$	−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	$0.555941\pi$
$434$	38.1682	+	17.2625i	1.83213	+	0.828629i
$435$		0			0
$436$	−25.4301	−	28.9181i	−1.21788	−	1.38493i
$437$	10.4365	+	12.4377i	0.499244	+	0.594976i
$438$		0			0
$439$	10.1794	+	27.9677i	0.485836	+	1.33482i	0.904419	+	0.426645i	$0.140305\pi$
$439$	10.1794	+	27.9677i	0.485836	+	1.33482i	−0.418583	+	0.908179i	$0.637473\pi$
$440$	−0.387479	+	0.118403i	−0.0184723	+	0.00564464i
$441$		0			0
$442$	−3.64627	−	13.0035i	−0.173436	−	0.618512i
$443$	−13.1764	−	11.0563i	−0.626032	−	0.525303i	0.273661	−	0.961826i	$-0.411765\pi$
$443$	−13.1764	−	11.0563i	−0.626032	−	0.525303i	−0.899693	+	0.436523i	$0.856210\pi$
$444$		0			0
$445$	−0.916157	−	5.19578i	−0.0434300	−	0.246304i
$446$	0.175521	−	2.31485i	0.00831114	−	0.109611i
$447$		0			0
$448$	−25.1318	−	18.2704i	−1.18737	−	0.863195i
$449$	18.8763	−	10.8982i	0.890826	−	0.514319i	0.0166137	−	0.999862i	$-0.494711\pi$
$449$	18.8763	−	10.8982i	0.890826	−	0.514319i	0.874213	+	0.485543i	$0.161378\pi$
$450$		0			0
$451$	0.0553680	+	0.0319667i	0.00260718	+	0.00150525i
$452$	1.57199	−	10.3065i	0.0739402	−	0.484776i
$453$		0			0
$454$	−16.7278	−	34.8140i	−0.785077	−	1.63390i
$455$	41.3989	+	15.0680i	1.94081	+	0.706396i
$456$		0			0
$457$	1.67697	−	9.51058i	0.0784454	−	0.444886i	−0.920134	−	0.391604i	$-0.871920\pi$
$457$	1.67697	−	9.51058i	0.0784454	−	0.444886i	0.998579	−	0.0532825i	$-0.0169684\pi$
$458$	2.21217	−	8.65590i	0.103368	−	0.404464i
$459$		0			0
$460$	13.4758	−	24.6425i	0.628314	−	1.14896i
$461$	32.2880	+	5.69324i	1.50380	+	0.265161i	0.864044	−	0.503417i	$-0.167924\pi$
$461$	32.2880	+	5.69324i	1.50380	+	0.265161i	0.639757	+	0.768578i	$0.279035\pi$
$462$		0			0
$463$	13.1130	−	36.0275i	0.609411	−	1.67434i	−0.122105	−	0.992517i	$-0.538965\pi$
$463$	13.1130	−	36.0275i	0.609411	−	1.67434i	0.731516	−	0.681825i	$-0.238813\pi$
$464$	4.78377	−	15.3172i	0.222081	−	0.711081i
$465$		0			0
$466$	−41.7281	+	4.13848i	−1.93302	+	0.191711i
$467$	−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
$470$	11.0733	+	15.4306i	0.510771	+	0.711759i
$471$		0			0
$472$	−3.79455	−	2.46499i	−0.174658	−	0.113460i
$473$	0.553532	−	0.0976026i	0.0254514	−	0.00448777i
$474$		0			0
$475$	1.90845	−	2.27440i	0.0875658	−	0.104357i
$476$	0.372564	+	16.0733i	0.0170764	+	0.736720i
$477$		0			0
$478$	9.41300	+	9.19735i	0.430541	+	0.420677i
$479$	−16.8443	+	6.13082i	−0.769635	+	0.280124i	−0.696844	−	0.717223i	$-0.745413\pi$
$479$	−16.8443	+	6.13082i	−0.769635	+	0.280124i	−0.0727912	+	0.997347i	$0.523191\pi$
$480$		0			0
$481$	17.0392	−	14.2976i	0.776919	−	0.651912i
$482$	−11.2163	+	16.4202i	−0.510888	+	0.747922i
$483$		0			0
$484$	13.7428	−	17.1708i	0.624671	−	0.780493i
$485$		−	12.6723i		−	0.575421i
$486$		0			0
$487$			22.6464i			1.02621i	0.858327	+	0.513104i	$0.171504\pi$
$487$			22.6464i			1.02621i	−0.858327	+	0.513104i	$0.828496\pi$
$488$	3.59322	+	4.76980i	0.162657	+	0.215919i
$489$		0			0
$490$	−23.2113	−	15.8551i	−1.04858	−	0.716261i
$491$	−19.6925	+	16.5240i	−0.888712	+	0.745718i	−0.967951	−	0.251137i	$-0.919195\pi$
$491$	−19.6925	+	16.5240i	−0.888712	+	0.745718i	0.0792391	+	0.996856i	$0.474751\pi$
$492$		0			0
$493$	−7.80260	+	2.83992i	−0.351412	+	0.127903i
$494$	−12.9617	+	13.2656i	−0.583176	+	0.596850i
$495$		0			0
$496$	27.0978	+	14.0128i	1.21673	+	0.629192i
$497$	−20.3894	+	24.2991i	−0.914589	+	1.08996i
$498$		0			0
$499$	−7.11944	+	1.25535i	−0.318710	+	0.0561971i	−0.330715	−	0.943731i	$-0.607290\pi$
$499$	−7.11944	+	1.25535i	−0.318710	+	0.0561971i	0.0120049	+	0.999928i	$0.496179\pi$
$500$	18.4259	+	6.22685i	0.824030	+	0.278473i
$501$		0			0
$502$	17.4734	−	12.5392i	0.779874	−	0.559652i
$503$	−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
$506$	−0.0464510	−	0.468364i	−0.00206500	−	0.0208213i
$507$		0			0
$508$	0.761176	+	3.79971i	0.0337717	+	0.168585i
$509$	6.53124	−	17.9444i	0.289492	−	0.795373i	−0.706646	−	0.707567i	$-0.749793\pi$
$509$	6.53124	−	17.9444i	0.289492	−	0.795373i	0.996138	−	0.0878050i	$-0.0279852\pi$
$510$		0			0
$511$	24.9861	+	4.40572i	1.10532	+	0.194898i
$512$	−17.5786	−	14.2475i	−0.776873	−	0.629657i
$513$		0			0
$514$	9.70469	+	2.48021i	0.428056	+	0.109397i
$515$	0.445232	−	2.52504i	0.0196193	−	0.111266i
$516$		0			0
$517$	0.299076	+	0.108855i	0.0131533	+	0.00478743i
$518$	−23.8679	+	11.4683i	−1.04870	+	0.503890i
$519$		0			0
$520$	29.5311	+	12.5402i	1.29503	+	0.549926i
$521$	−19.0779	−	11.0146i	−0.835817	−	0.482559i	0.0200233	−	0.999800i	$-0.493626\pi$
$521$	−19.0779	−	11.0146i	−0.835817	−	0.482559i	−0.855840	+	0.517240i	$0.826959\pi$
$522$		0			0
$523$	−3.75661	+	2.16888i	−0.164265	+	0.0948384i	−0.579879	−	0.814703i	$-0.696900\pi$
$523$	−3.75661	+	2.16888i	−0.164265	+	0.0948384i	0.415614	+	0.909541i	$0.363567\pi$
$524$	0.340222	+	0.871374i	0.0148627	+	0.0380661i
$525$		0			0
$526$	−2.80357	−	0.212578i	−0.122242	−	0.00926883i
$527$	−2.74112	−	15.5457i	−0.119405	−	0.677180i
$528$		0			0
$529$	7.37455	+	6.18798i	0.320632	+	0.269043i
$530$	−35.2648	+	9.88853i	−1.53181	+	0.429530i
$531$		0			0
$532$	18.8608	−	11.4801i	0.817717	−	0.497724i
$533$	−1.73152	−	4.75732i	−0.0750005	−	0.206062i
$534$		0			0
$535$	−19.7304	−	23.5138i	−0.853021	−	1.01659i
$536$	9.70126	+	19.0466i	0.419030	+	0.822687i
$537$		0			0
$538$	0.690203	−	1.52607i	0.0297568	−	0.0657934i
$539$	−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	$0.519774\pi$
$542$	−6.35344	+	14.0477i	−0.272903	+	0.603400i
$543$		0			0
$544$	−0.343352	+	11.7034i	−0.0147211	+	0.501781i
$545$	−30.4285	−	36.2633i	−1.30341	−	1.55335i
$546$		0			0
$547$	7.98695	+	21.9440i	0.341497	+	0.938256i	0.984961	+	0.172779i	$0.0552747\pi$
$547$	7.98695	+	21.9440i	0.341497	+	0.938256i	−0.643463	+	0.765477i	$0.722503\pi$
$548$	−4.56539	−	7.50054i	−0.195024	−	0.320407i
$549$		0			0
$550$	−0.0828705	+	0.0232375i	−0.00353361	+	0.000990852i
$551$	8.73537	+	7.32985i	0.372139	+	0.312262i
$552$		0			0
$553$	4.67328	+	26.5035i	0.198728	+	1.12704i
$554$	7.97799	+	0.604922i	0.338952	+	0.0257007i
$555$		0			0
$556$	15.7383	−	6.14492i	0.667454	−	0.260603i
$557$	−7.72227	+	4.45845i	−0.327203	+	0.188911i	−0.654599	−	0.755977i	$-0.727162\pi$
$557$	−7.72227	+	4.45845i	−0.327203	+	0.188911i	0.327396	+	0.944887i	$0.393829\pi$
$558$		0			0
$559$	−38.5452	−	22.2541i	−1.63029	−	0.941247i
$560$	−30.3653	−	23.1693i	−1.28317	−	0.979082i
$561$		0			0
$562$	15.7915	−	7.58768i	0.666124	−	0.320067i
$563$	−20.5853	−	7.49242i	−0.867565	−	0.315768i	−0.130385	−	0.991463i	$-0.541621\pi$
$563$	−20.5853	−	7.49242i	−0.867565	−	0.315768i	−0.737181	+	0.675696i	$0.763843\pi$
$564$		0			0
$565$	2.22549	−	12.6214i	0.0936269	−	0.530985i
$566$	−30.8832	−	7.89275i	−1.29812	−	0.331757i
$567$		0			0
$568$	−15.7567	+	16.8921i	−0.661136	+	0.708777i
$569$	19.5135	+	3.44076i	0.818048	+	0.144244i	0.566986	−	0.823727i	$-0.308109\pi$
$569$	19.5135	+	3.44076i	0.818048	+	0.144244i	0.251062	+	0.967971i	$0.419220\pi$
$570$		0			0
$571$	−9.39781	+	25.8203i	−0.393286	+	1.08055i	0.572205	+	0.820111i	$0.306088\pi$
$571$	−9.39781	+	25.8203i	−0.393286	+	1.08055i	−0.965491	+	0.260435i	$0.916134\pi$
$572$	0.527166	−	0.105604i	0.0220419	−	0.00441555i
$573$		0			0
$574$	0.594826	+	5.99761i	0.0248275	+	0.250335i
$575$	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	$0.817382\pi$
$578$	−14.6104	+	10.4847i	−0.607713	+	0.436106i
$579$		0			0
$580$	6.31534	−	18.6877i	0.262230	−	0.775966i
$581$	−43.5863	+	7.68543i	−1.80826	+	0.318845i
$582$		0			0
$583$	−0.394508	+	0.470157i	−0.0163389	+	0.0194719i
$584$	18.0025	+	4.15895i	0.744951	+	0.172099i
$585$		0			0
$586$	24.7914	−	25.3727i	1.02412	−	1.04814i
$587$	−12.1284	+	4.41436i	−0.500591	+	0.182200i	−0.579960	−	0.814645i	$-0.696932\pi$
$587$	−12.1284	+	4.41436i	−0.500591	+	0.182200i	0.0793690	+	0.996845i	$0.474709\pi$
$588$		0			0
$589$	−16.6068	+	13.9348i	−0.684271	+	0.574172i
$590$	−4.59309	−	3.13743i	−0.189095	−	0.129166i
$591$		0			0
$592$	−17.7961	+	7.42808i	−0.731414	+	0.305292i
$593$			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
$596$	−15.8749	−	12.7055i	−0.650260	−	0.520438i
$597$		0			0
$598$	−21.0219	+	30.7753i	−0.859649	+	1.25849i
$599$	15.6515	−	13.1332i	0.639502	−	0.536606i	−0.264363	−	0.964423i	$-0.585162\pi$
$599$	15.6515	−	13.1332i	0.639502	−	0.536606i	0.903865	+	0.427817i	$0.140717\pi$
$600$		0			0
$601$	41.2928	−	15.0293i	1.68437	−	0.613059i	0.690469	−	0.723362i	$-0.257404\pi$
$601$	41.2928	−	15.0293i	1.68437	−	0.613059i	0.993898	+	0.110303i	$0.0351822\pi$
$602$	37.8988	+	37.0306i	1.54464	+	1.50925i
$603$		0			0
$604$	−4.77149	+	0.110598i	−0.194149	+	0.00450019i
$605$	17.3783	−	20.7106i	0.706528	−	0.842007i
$606$		0			0
$607$	37.1173	−	6.54477i	1.50654	−	0.265644i	0.641414	−	0.767195i	$-0.278348\pi$
$607$	37.1173	−	6.54477i	1.50654	−	0.265644i	0.865128	+	0.501550i	$0.167237\pi$
$608$	14.1551	−	7.62796i	0.574065	−	0.309355i
$609$		0			0
$610$	4.28002	+	5.96419i	0.173293	+	0.241483i
$611$	−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	$0.144686\pi$
$614$	−12.9979	+	1.28909i	−0.524551	+	0.0520235i
$615$		0			0
$616$	−0.639175	−	0.0335902i	−0.0257531	−	0.00135339i
$617$	−9.87741	+	27.1380i	−0.397649	+	1.09253i	0.565777	+	0.824559i	$0.308576\pi$
$617$	−9.87741	+	27.1380i	−0.397649	+	1.09253i	−0.963426	+	0.267974i	$0.913646\pi$
$618$		0			0
$619$	−17.7070	−	3.12223i	−0.711705	−	0.125493i	−0.193937	−	0.981014i	$-0.562126\pi$
$619$	−17.7070	−	3.12223i	−0.711705	−	0.125493i	−0.517768	+	0.855521i	$0.673237\pi$
$620$	32.9026	+	17.9929i	1.32140	+	0.722612i
$621$		0			0
$622$	−9.11582	+	35.6689i	−0.365511	+	1.43019i
$623$	1.44729	−	8.20800i	0.0579845	−	0.328847i
$624$		0			0
$625$	27.3747	+	9.96358i	1.09499	+	0.398543i
$626$	13.6944	+	28.5009i	0.547340	+	1.13912i
$627$		0			0
$628$	−10.7672	−	1.64226i	−0.429658	−	0.0655334i
$629$	8.64162	+	4.98924i	0.344564	+	0.198934i
$630$		0			0
$631$	−10.4847	+	6.05333i	−0.417388	+	0.240979i	−0.693959	−	0.720014i	$-0.744135\pi$
$631$	−10.4847	+	6.05333i	−0.417388	+	0.240979i	0.276571	+	0.960994i	$0.410802\pi$
$632$	2.38569	+	19.4530i	0.0948975	+	0.773801i
$633$		0			0
$634$	1.24602	−	16.4332i	0.0494860	−	0.652644i
$635$	0.827209	+	4.69134i	0.0328268	+	0.186170i
$636$		0			0
$637$	28.5738	+	23.9762i	1.13213	+	0.949973i
$638$	−0.0892492	−	0.318284i	−0.00353341	−	0.0126010i
$639$		0			0
$640$	−21.1974	−	18.0102i	−0.837901	−	0.711916i
$641$	6.57776	+	18.0722i	0.259806	+	0.713811i	0.999179	+	0.0405147i	$0.0128998\pi$
$641$	6.57776	+	18.0722i	0.259806	+	0.713811i	−0.739373	+	0.673296i	$0.764878\pi$
$642$		0			0
$643$	1.83910	+	2.19176i	0.0725272	+	0.0864345i	0.801088	−	0.598547i	$-0.204255\pi$
$643$	1.83910	+	2.19176i	0.0725272	+	0.0864345i	−0.728561	+	0.684981i	$0.759810\pi$
$644$	33.3190	−	29.3001i	1.31295	−	1.15459i
$645$		0			0
$646$	−7.58100	−	3.42870i	−0.298270	−	0.134901i
$647$	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
$650$	6.20971	+	2.80850i	0.243565	+	0.110158i
$651$		0			0
$652$	14.6633	−	12.8947i	0.574261	−	0.504995i
$653$	14.0331	+	16.7240i	0.549157	+	0.654459i	0.967214	−	0.253961i	$-0.0817335\pi$
$653$	14.0331	+	16.7240i	0.549157	+	0.654459i	−0.418058	+	0.908420i	$0.637289\pi$
$654$		0			0
$655$	0.393294	+	1.08057i	0.0153673	+	0.0422212i
$656$	0.203364	+	4.38445i	0.00794001	+	0.171184i
$657$		0			0
$658$	8.10075	+	28.8892i	0.315800	+	1.12622i
$659$	−0.253500	−	0.212712i	−0.00987497	−	0.00828609i	0.637837	−	0.770172i	$-0.279829\pi$
$659$	−0.253500	−	0.212712i	−0.00987497	−	0.00828609i	−0.647712	+	0.761885i	$0.724274\pi$
$660$		0			0
$661$	4.11198	+	23.3202i	0.159938	+	0.907052i	0.954132	+	0.299387i	$0.0967822\pi$
$661$	4.11198	+	23.3202i	0.159938	+	0.907052i	−0.794194	+	0.607664i	$0.792107\pi$
$662$	−0.469238	+	6.18852i	−0.0182374	+	0.240524i
$663$		0			0
$664$	−31.9915	+	3.92338i	−1.24151	+	0.152257i
$665$	23.5059	−	13.5712i	0.911521	−	0.526267i
$666$		0			0
$667$	19.8448	+	11.4574i	0.768393	+	0.443632i
$668$	9.18549	+	1.40101i	0.355397	+	0.0542068i
$669$		0			0
$670$	11.3798	+	23.6836i	0.439640	+	0.914979i
$671$	0.115598	+	0.0420744i	0.00446262	+	0.00162426i
$672$		0			0
$673$	0.640167	−	3.63057i	0.0246766	−	0.139948i	−0.969980	−	0.243183i	$-0.921808\pi$
$673$	0.640167	−	3.63057i	0.0246766	−	0.139948i	0.994657	+	0.103235i	$0.0329194\pi$
$674$	11.7806	−	46.0960i	0.453774	−	1.77555i
$675$		0			0
$676$	−14.5413	−	7.95194i	−0.559280	−	0.305844i
$677$	9.40523	+	1.65840i	0.361473	+	0.0637374i	0.351435	−	0.936212i	$-0.385694\pi$
$677$	9.40523	+	1.65840i	0.361473	+	0.0637374i	0.0100375	+	0.999950i	$0.496805\pi$
$678$		0			0
$679$	6.84691	−	18.8117i	0.262760	−	0.721928i
$680$	−0.755345	+	14.3732i	−0.0289662	+	0.551185i
$681$		0			0
$682$	0.625358	−	0.0620213i	0.0239462	−	0.00237492i
$683$	−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
$686$	−3.47331	−	4.84006i	−0.132612	−	0.184794i
$687$		0			0
$688$	26.1464	+	28.3786i	0.996822	+	1.08193i
$689$	47.8617	−	8.43931i	1.82339	−	0.321512i
$690$		0			0
$691$	−26.0130	+	31.0011i	−0.989581	+	1.17934i	−0.00579604	+	0.999983i	$0.501845\pi$
$691$	−26.0130	+	31.0011i	−0.989581	+	1.17934i	−0.983785	+	0.179353i	$0.942599\pi$
$692$	−1.76189	+	0.0408389i	−0.0669771	+	0.00155246i
$693$		0			0
$694$	−15.1424	−	14.7955i	−0.574798	−	0.561630i
$695$	19.5166	−	7.10348i	0.740309	−	0.269450i
$696$		0			0
$697$	1.73981	−	1.45987i	0.0658998	−	0.0552965i
$698$	−8.48519	+	12.4220i	−0.321169	+	0.470180i
$699$		0			0
$700$	−6.33453	−	5.06987i	−0.239423	−	0.191623i
$701$		−	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
$704$	−0.463551	−	0.0488565i	−0.0174708	−	0.00184135i
$705$		0			0
$706$	12.8461	+	8.77488i	0.483470	+	0.330247i
$707$	−39.3252	+	32.9977i	−1.47898	+	1.24101i
$708$		0			0
$709$	−12.4318	+	4.52479i	−0.466885	+	0.169932i	−0.564741	−	0.825268i	$-0.691024\pi$
$709$	−12.4318	+	4.52479i	−0.466885	+	0.169932i	0.0978558	+	0.995201i	$0.468802\pi$
$710$	−19.8454	+	20.3107i	−0.744784	+	0.762247i
$711$		0			0
$712$	1.36623	−	5.91389i	0.0512016	−	0.221632i
$713$	−28.0019	+	33.3713i	−1.04868	+	1.24977i
$714$		0			0
$715$	0.650869	−	0.114766i	0.0243411	−	0.00429200i
$716$	8.13027	−	24.0583i	0.303843	−	0.899102i
$717$		0			0
$718$	20.1263	−	14.4430i	0.751106	−	0.539008i
$719$	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
$722$	−1.52417	−	15.3682i	−0.0567237	−	0.571944i
$723$		0			0
$724$	−12.9636	+	2.59693i	−0.481788	+	0.0965141i
$725$	1.43316	−	3.93757i	0.0532262	−	0.146238i
$726$		0			0
$727$	33.7689	+	5.95436i	1.25242	+	0.220835i	0.760230	−	0.649654i	$-0.225086\pi$
$727$	33.7689	+	5.95436i	1.25242	+	0.220835i	0.492188	+	0.870489i	$0.336197\pi$
$728$	37.0626	+	34.5714i	1.37363	+	1.28130i
$729$		0			0
$730$	22.0058	+	5.62396i	0.814470	+	0.208152i
$731$	3.46721	−	19.6635i	0.128239	−	0.727282i
$732$		0			0
$733$	−20.5596	−	7.48310i	−0.759388	−	0.276395i	−0.0668372	−	0.997764i	$-0.521291\pi$
$733$	−20.5596	−	7.48310i	−0.759388	−	0.276395i	−0.692551	+	0.721369i	$0.743513\pi$
$734$	6.62944	−	3.18539i	0.244697	−	0.117575i
$735$		0			0
$736$	25.3508	−	20.0349i	0.934441	−	0.738495i
$737$	0.381326	+	0.220159i	0.0140463	+	0.00810965i
$738$		0			0
$739$	23.8855	−	13.7903i	0.878644	−	0.507285i	0.00843293	−	0.999964i	$-0.497316\pi$
$739$	23.8855	−	13.7903i	0.878644	−	0.507285i	0.870211	+	0.492679i	$0.163982\pi$
$740$	−22.0821	+	8.62179i	−0.811753	+	0.316943i
$741$		0			0
$742$	−57.6925	−	4.37446i	−2.11796	−	0.160592i
$743$	−3.66802	−	20.8024i	−0.134567	−	0.763165i	−0.975161	−	0.221499i	$-0.928905\pi$
$743$	−3.66802	−	20.8024i	−0.134567	−	0.763165i	0.840594	−	0.541666i	$-0.182206\pi$
$744$		0			0
$745$	−19.1475	−	16.0666i	−0.701509	−	0.588636i
$746$	−21.6118	+	6.06011i	−0.791263	+	0.221876i
$747$		0			0
$748$	0.125404	+	0.206027i	0.00458521	+	0.00753311i
$749$	−16.5847	−	45.5660i	−0.605991	−	1.66495i
$750$		0			0
$751$	9.82151	+	11.7048i	0.358392	+	0.427115i	0.914871	−	0.403747i	$-0.132292\pi$
$751$	9.82151	+	11.7048i	0.358392	+	0.427115i	−0.556479	+	0.830862i	$0.687848\pi$
$752$	4.78711	+	21.3190i	0.174568	+	0.777425i
$753$		0			0
$754$	−10.7867	+	23.8498i	−0.392828	+	0.868559i
$755$	−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	$0.682375\pi$
$758$	7.78387	−	17.2104i	0.282723	−	0.625112i
$759$		0			0
$760$	17.6132	−	8.97116i	0.638897	−	0.325418i
$761$	6.11349	+	7.28578i	0.221614	+	0.264109i	0.865383	−	0.501110i	$-0.167075\pi$
$761$	6.11349	+	7.28578i	0.221614	+	0.264109i	−0.643770	+	0.765219i	$0.722630\pi$
$762$		0			0
$763$	−25.5771	−	70.2725i	−0.925953	−	2.54403i
$764$	43.5180	−	26.4883i	1.57442	−	0.958313i
$765$		0			0
$766$	11.0112	−	3.08763i	0.397851	−	0.111560i
$767$	5.65422	+	4.74446i	0.204162	+	0.171312i
$768$		0			0
$769$	0.968522	+	5.49276i	0.0349258	+	0.198074i	0.997278	−	0.0737309i	$-0.0234906\pi$
$769$	0.968522	+	5.49276i	0.0349258	+	0.198074i	−0.962352	+	0.271805i	$0.912379\pi$
$770$	−0.784557	−	0.0594881i	−0.0282735	−	0.00214380i
$771$		0			0
$772$	14.9808	+	38.3688i	0.539172	+	1.38092i
$773$	15.2614	−	8.81115i	0.548913	−	0.316915i	−0.199770	−	0.979843i	$-0.564020\pi$
$773$	15.2614	−	8.81115i	0.548913	−	0.316915i	0.748683	+	0.662928i	$0.230686\pi$
$774$		0			0
$775$	6.89886	+	3.98306i	0.247815	+	0.143076i
$776$	5.69831	−	13.4190i	0.204558	−	0.481714i
$777$		0			0
$778$	−25.0513	+	12.0370i	−0.898133	+	0.431546i
$779$	−2.93094	−	1.06677i	−0.105012	−	0.0382211i
$780$		0			0
$781$	−0.0826317	+	0.468628i	−0.00295679	+	0.0167688i
$782$	−16.1990	−	4.13994i	−0.579275	−	0.148044i
$783$		0			0
$784$	−17.4494	−	27.2266i	−0.623194	−	0.972380i
$785$	−13.1856	−	2.32497i	−0.470613	−	0.0829817i
$786$		0			0
$787$	−13.2284	+	36.3448i	−0.471542	+	1.29555i	0.444971	+	0.895545i	$0.353214\pi$
$787$	−13.2284	+	36.3448i	−0.471542	+	1.29555i	−0.916513	+	0.400006i	$0.869008\pi$
$788$	2.72548	+	13.6053i	0.0970914	+	0.484670i
$789$		0			0
$790$	2.37775	+	23.9748i	0.0845966	+	0.852984i
$791$	10.1230	−	17.5336i	0.359934	−	0.623424i
$792$		0			0
$793$	−4.87062	−	8.43615i	−0.172961	−	0.299577i
$794$	28.4316	−	20.4031i	1.00900	−	0.724078i
$795$		0			0
$796$	−21.9318	−	7.41162i	−0.777351	−	0.262698i
$797$	3.28390	−	0.579040i	0.116322	−	0.0205107i	−0.115184	−	0.993344i	$-0.536746\pi$
$797$	3.28390	−	0.579040i	0.116322	−	0.0205107i	0.231506	+	0.972833i	$0.425635\pi$
$798$		0			0
$799$	7.26745	−	8.66100i	0.257104	−	0.306404i
$800$	−4.41298	−	3.92912i	−0.156022	−	0.138915i
$801$		0			0
$802$	−12.0348	+	12.3170i	−0.424962	+	0.434927i
$803$	0.357661	−	0.130178i	0.0126216	−	0.00459389i
$804$		0			0
$805$	41.7820	−	35.0592i	1.47262	−	1.23568i
$806$	−41.0911	−	28.0684i	−1.44737	−	0.988666i
$807$		0			0
$808$	−29.8601	+	22.4944i	−1.05047	+	0.791351i
$809$		−	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	$0.0186418\pi$
$811$			3.33372i			0.117063i	−0.998286	+	0.0585314i	$0.981358\pi$
$812$	19.4720	−	24.3292i	0.683333	−	0.853789i
$813$		0			0
$814$	−0.224066	+	0.328024i	−0.00785351	+	0.0114972i
$815$	18.3878	−	15.4292i	0.644098	−	0.540462i
$816$		0			0
$817$	−25.7673	+	9.37854i	−0.901485	+	0.328114i
$818$	−31.4416	−	30.7213i	−1.09933	−	1.07415i
$819$		0			0
$820$	0.125029	+	5.39406i	0.00436620	+	0.188369i
$821$	−16.8806	+	20.1175i	−0.589135	+	0.702104i	−0.975440	−	0.220267i	$-0.929307\pi$
$821$	−16.8806	+	20.1175i	−0.589135	+	0.702104i	0.386304	+	0.922371i	$0.373752\pi$
$822$		0			0
$823$	−37.9306	+	6.68820i	−1.32218	+	0.233136i	−0.789797	−	0.613368i	$-0.789814\pi$
$823$	−37.9306	+	6.68820i	−1.32218	+	0.233136i	−0.532382	+	0.846504i	$0.678703\pi$
$824$	1.60689	−	2.47361i	0.0559786	−	0.0861723i
$825$		0			0
$826$	−5.12315	−	7.13910i	−0.178257	−	0.248401i
$827$	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	$0.0124736\pi$
$830$	−39.4277	+	3.91033i	−1.36856	+	0.135729i
$831$		0			0
$832$	25.6322	+	26.5583i	0.888637	+	0.920743i
$833$	−5.72316	+	15.7243i	−0.198296	+	0.544813i
$834$		0			0
$835$	11.2486	+	1.98343i	0.389274	+	0.0686394i
$836$	0.158926	−	0.290619i	0.00549656	−	0.0100513i
$837$		0			0
$838$	−12.9091	+	50.5117i	−0.445939	+	1.74490i
$839$	1.09332	−	6.20051i	0.0377455	−	0.214065i	−0.960101	−	0.279652i	$-0.909781\pi$
$839$	1.09332	−	6.20051i	0.0377455	−	0.214065i	0.997847	+	0.0655869i	$0.0208920\pi$
$840$		0			0
$841$	−12.1279	−	4.41421i	−0.418204	−	0.152214i
$842$	−22.5644	−	46.9611i	−0.777622	−	1.61839i
$843$		0			0
$844$	−4.55783	+	29.8826i	−0.156887	+	1.02860i
$845$	−17.6440	−	10.1867i	−0.606971	−	0.350435i
$846$		0			0
$847$	36.9876	−	21.3548i	1.27091	−	0.733760i
$848$	−41.7892	−	5.38621i	−1.43505	−	0.184963i
$849$		0			0
$850$	−0.231162	+	3.04867i	−0.00792878	+	0.104568i
$851$	−4.78186	−	27.1193i	−0.163920	−	0.929637i
$852$		0			0
$853$	0.550600	+	0.462008i	0.0188522	+	0.0158189i	0.652165	−	0.758077i	$-0.273861\pi$
$853$	0.550600	+	0.462008i	0.0188522	+	0.0158189i	−0.633313	+	0.773896i	$0.718305\pi$
$854$	3.13109	+	11.1662i	0.107144	+	0.382099i
$855$		0			0
$856$	−10.3196	−	33.7714i	−0.352717	−	1.15428i
$857$	−18.6550	−	51.2541i	−0.637242	−	1.75081i	−0.660221	−	0.751072i	$-0.729537\pi$
$857$	−18.6550	−	51.2541i	−0.637242	−	1.75081i	0.0229789	−	0.999736i	$-0.492685\pi$
$858$		0			0
$859$	19.5736	+	23.3269i	0.667844	+	0.795905i	0.988489	−	0.151294i	$-0.0483441\pi$
$859$	19.5736	+	23.3269i	0.667844	+	0.795905i	−0.320645	+	0.947199i	$0.603900\pi$
$860$	31.3242	+	35.6207i	1.06815	+	1.21466i
$861$		0			0
$862$	−14.6613	−	6.63093i	−0.499365	−	0.225850i
$863$	−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
$866$	−9.37609	−	4.24058i	−0.318613	−	0.144101i
$867$		0			0
$868$	39.1214	+	44.4874i	1.32787	+	1.51000i
$869$	0.259513	+	0.309275i	0.00880336	+	0.0104914i
$870$		0			0
$871$	−11.9252	−	32.7642i	−0.404070	−	1.11017i
$872$	−15.9150	−	52.0826i	−0.538951	−	1.76374i
$873$		0			0
$874$	6.19948	+	22.1088i	0.209701	+	0.747842i
$875$	28.9335	+	24.2781i	0.978132	+	0.820750i
$876$		0			0
$877$	−5.87636	−	33.3265i	−0.198431	−	1.12536i	−0.907448	−	0.420165i	$-0.861972\pi$
$877$	−5.87636	−	33.3265i	−0.198431	−	1.12536i	0.709017	−	0.705191i	$-0.249139\pi$
$878$	−3.18234	+	41.9701i	−0.107399	+	1.41642i
$879$		0			0
$880$	−0.568290	−	0.0732468i	−0.0191570	−	0.00246915i
$881$	−10.3117	+	5.95348i	−0.347411	+	0.200578i	−0.663544	−	0.748137i	$-0.730949\pi$
$881$	−10.3117	+	5.95348i	−0.347411	+	0.200578i	0.316133	+	0.948715i	$0.397615\pi$
$882$		0			0
$883$	−10.5936	−	6.11620i	−0.356502	−	0.205827i	0.311043	−	0.950396i	$-0.399322\pi$
$883$	−10.5936	−	6.11620i	−0.356502	−	0.205827i	−0.667545	+	0.744569i	$0.732655\pi$
$884$	2.87976	−	18.8806i	0.0968568	−	0.635024i
$885$		0			0
$886$	−10.5351	−	21.9257i	−0.353934	−	0.736607i
$887$	12.5369	+	4.56305i	0.420947	+	0.153212i	0.543804	−	0.839212i	$-0.316983\pi$
$887$	12.5369	+	4.56305i	0.420947	+	0.153212i	−0.122857	+	0.992424i	$0.539206\pi$
$888$		0			0
$889$	−1.30678	+	7.41110i	−0.0438279	+	0.248560i
$890$	1.84749	−	7.22896i	0.0619279	−	0.242315i
$891$		0			0
$892$	1.57522	−	2.88051i	0.0527422	−	0.0964467i
$893$	−15.2911	−	2.69624i	−0.511698	−	0.0902262i
$894$		0			0
$895$	10.6770	−	29.3349i	0.356893	−	0.980557i
$896$	−21.7360	−	38.1887i	−0.726148	−	1.27579i
$897$		0			0
$898$	30.6743	−	3.04219i	1.02362	−	0.101519i
$899$	−15.2979	+	26.4967i	−0.510212	+	0.883714i
$900$		0			0
$901$	10.9013	+	18.8816i	0.363174	+	0.629036i
$902$	0.0527150	+	0.0734582i	0.00175522	+	0.00244589i
$903$		0			0
$904$	8.03201	−	12.3643i	0.267141	−	0.411231i
$905$	−16.0056	+	2.82222i	−0.532043	+	0.0938136i
$906$		0			0
$907$	12.9620	−	15.4476i	0.430398	−	0.512928i	−0.506639	−	0.862158i	$-0.669112\pi$
$907$	12.9620	−	15.4476i	0.430398	−	0.512928i	0.937037	+	0.349230i	$0.113557\pi$
$908$	−1.26577	−	54.6083i	−0.0420060	−	1.81224i
$909$		0			0
$910$	44.5633	+	43.5423i	1.47726	+	1.44341i
$911$	29.7025	−	10.8108i	0.984089	−	0.358179i	0.200660	−	0.979661i	$-0.435691\pi$
$911$	29.7025	−	10.8108i	0.984089	−	0.358179i	0.783429	+	0.621482i	$0.213469\pi$
$912$		0			0
$913$	−0.508618	+	0.426781i	−0.0168328	+	0.0141244i
$914$	7.70345	−	11.2776i	0.254807	−	0.373029i
$915$		0			0
$916$	7.89499	−	9.86437i	0.260858	−	0.325928i
$917$			1.81657i			0.0599884i
$918$		0			0
$919$			3.86720i			0.127567i	0.997964	+	0.0637835i	$0.0203167\pi$
$919$			3.86720i			0.127567i	−0.997964	+	0.0637835i	$0.979683\pi$
$920$	31.7255	−	23.8997i	1.04596	−	0.787950i
$921$		0			0
$922$	38.2868	+	26.1528i	1.26091	+	0.861298i
$923$	28.8655	−	24.2210i	0.950118	−	0.797244i
$924$		0			0
$925$	−4.73194	+	1.72229i	−0.155585	+	0.0566284i
$926$	37.8929	−	38.7814i	1.24524	−	1.27444i
$927$		0			0
$928$	15.0907	−	16.9491i	0.495376	−	0.556380i
$929$	32.4335	−	38.6527i	1.06411	−	1.26815i	0.102204	−	0.994763i	$-0.467410\pi$
$929$	32.4335	−	38.6527i	1.06411	−	1.26815i	0.961903	−	0.273390i	$-0.0881451\pi$
$930$		0			0
$931$	22.6313	−	3.99051i	0.741711	−	0.130784i
$932$	−56.1807	−	18.9857i	−1.84026	−	0.621898i
$933$		0			0
$934$	−13.3098	+	9.55132i	−0.435509	+	0.312529i
$935$	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	$-0.120947\pi$
$938$	4.09664	+	41.3062i	0.133760	+	1.34870i
$939$		0			0
$940$	5.27583	+	26.3364i	0.172078	+	0.858997i
$941$	2.51129	−	6.89972i	0.0818658	−	0.224924i	−0.892006	−	0.452024i	$-0.850702\pi$
$941$	2.51129	−	6.89972i	0.0818658	−	0.224924i	0.973872	+	0.227100i	$0.0729243\pi$
$942$		0			0
$943$	−6.17249	−	1.08838i	−0.201004	−	0.0354424i
$944$	−3.45292	−	5.38765i	−0.112383	−	0.175353i
$945$		0			0
$946$	0.770136	+	0.196822i	0.0250393	+	0.00639923i
$947$	5.53004	−	31.3624i	0.179702	−	1.01914i	−0.752873	−	0.658166i	$-0.771332\pi$
$947$	5.53004	−	31.3624i	0.179702	−	1.01914i	0.932575	−	0.360976i	$-0.117556\pi$
$948$		0			0
$949$	−28.3218	−	10.3083i	−0.919363	−	0.334621i
$950$	3.78462	−	1.81848i	0.122789	−	0.0589992i
$951$		0			0
$952$	−8.88716	+	20.9284i	−0.288034	+	0.678295i
$953$	13.1967	+	7.61912i	0.427483	+	0.246807i	0.698274	−	0.715831i	$-0.253952\pi$
$953$	13.1967	+	7.61912i	0.427483	+	0.246807i	−0.270791	+	0.962638i	$0.587285\pi$
$954$		0			0
$955$	54.2359	−	31.3131i	1.75503	−	1.01327i
$956$	6.76910	+	17.3370i	0.218929	+	0.560718i
$957$		0			0
$958$	−25.2777	−	1.91665i	−0.816684	−	0.0619241i
$959$	−2.96099	−	16.7926i	−0.0956153	−	0.542261i
$960$		0			0
$961$	−20.8099	−	17.4616i	−0.671289	−	0.563278i
$962$	30.2882	−	8.49304i	0.976530	−	0.273827i
$963$		0			0
$964$	−24.0222	+	14.6217i	−0.773703	+	0.470933i
$965$	17.3177	+	47.5800i	0.557477	+	1.53165i
$966$		0			0
$967$	−27.7417	−	33.0612i	−0.892112	−	1.06318i	−0.997633	−	0.0687608i	$-0.978095\pi$
$967$	−27.7417	−	33.0612i	−0.892112	−	1.06318i	0.105521	−	0.994417i	$-0.466349\pi$
$968$	27.7151	−	14.1165i	0.890797	−	0.453722i
$969$		0			0
$970$	7.38519	−	16.3290i	0.237124	−	0.524291i
$971$	−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
$974$	−13.1979	+	29.1811i	−0.422888	+	0.935023i
$975$		0			0
$976$	1.85031	+	8.24019i	0.0592268	+	0.263762i
$977$	−36.4937	−	43.4915i	−1.16754	−	1.39142i	−0.904415	−	0.426654i	$-0.859692\pi$
$977$	−36.4937	−	43.4915i	−1.16754	−	1.39142i	−0.263123	−	0.964762i	$-0.584752\pi$
$978$		0			0
$979$	−0.0427639	−	0.117493i	−0.00136674	−	0.00375509i
$980$	−20.6689	−	33.9572i	−0.660244	−	1.08472i
$981$		0			0
$982$	−35.0048	+	9.81561i	−1.11705	+	0.313229i
$983$	24.8399	+	20.8432i	0.792271	+	0.664794i	0.946306	−	0.323271i	$-0.104783\pi$
$983$	24.8399	+	20.8432i	0.792271	+	0.664794i	−0.154036	+	0.988065i	$0.549227\pi$
$984$		0			0
$985$	2.96192	+	16.7979i	0.0943748	+	0.535226i
$986$	−11.7091	−	0.887830i	−0.372894	−	0.0282743i
$987$		0			0
$988$	−24.4328	+	9.53963i	−0.777312	+	0.303496i
$989$	−47.7202	+	27.5513i	−1.51741	+	0.876080i
$990$		0			0
$991$	36.6324	+	21.1497i	1.16367	+	0.671843i	0.952180	−	0.305539i	$-0.0988365\pi$
$991$	36.6324	+	21.1497i	1.16367	+	0.671843i	0.211486	+	0.977381i	$0.432170\pi$
$992$	26.7505	+	33.8483i	0.849330	+	1.07468i
$993$		0			0
$994$	−40.4338	+	19.4281i	−1.28248	+	0.616223i
$995$	−26.7419	−	9.73326i	−0.847775	−	0.308565i
$996$		0			0
$997$	−5.87071	+	33.2945i	−0.185927	+	1.05445i	0.738831	+	0.673891i	$0.235378\pi$
$997$	−5.87071	+	33.2945i	−0.185927	+	1.05445i	−0.924758	+	0.380555i	$0.875733\pi$
$998$	−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	972.2.l.c.755.15		96
3.2	odd	2		972.2.l.b.755.2		96
4.3	odd	2	inner	972.2.l.c.755.16		96
9.2	odd	6		324.2.l.a.143.10		96
9.4	even	3		972.2.l.d.107.4		96
9.5	odd	6		972.2.l.a.107.13		96
9.7	even	3		108.2.l.a.47.7	yes	96
12.11	even	2		972.2.l.b.755.1		96
27.4	even	9		972.2.l.a.863.11		96
27.5	odd	18		108.2.l.a.23.6	✓	96
27.13	even	9		972.2.l.b.215.1		96
27.14	odd	18	inner	972.2.l.c.215.16		96
27.22	even	9		324.2.l.a.179.11		96
27.23	odd	18		972.2.l.d.863.6		96
36.7	odd	6		108.2.l.a.47.6	yes	96
36.11	even	6		324.2.l.a.143.11		96
36.23	even	6		972.2.l.a.107.11		96
36.31	odd	6		972.2.l.d.107.6		96
108.23	even	18		972.2.l.d.863.4		96
108.31	odd	18		972.2.l.a.863.13		96
108.59	even	18		108.2.l.a.23.7	yes	96
108.67	odd	18		972.2.l.b.215.2		96
108.95	even	18	inner	972.2.l.c.215.15		96
108.103	odd	18		324.2.l.a.179.10		96

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

Level:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.28855 + 0.582781i) q^{2} +(1.32073 + 1.50189i) q^{4} +(1.58033 + 1.88337i) q^{5} +(1.32837 + 3.64966i) q^{7} +(0.826562 + 2.70496i) q^{8} +(0.938750 + 3.34780i) q^{10} +(0.0446335 + 0.0374519i) q^{11} +(-0.801171 - 4.54366i) q^{13} +(-0.415282 + 5.47693i) q^{14} +(-0.511330 + 3.96718i) q^{16} +(1.79249 - 1.03489i) q^{17} +(-2.46167 - 1.42125i) q^{19} +(-0.741407 + 4.86090i) q^{20} +(0.0356863 + 0.0742703i) q^{22} +(-5.36751 - 1.95361i) q^{23} +(-0.181378 + 1.02865i) q^{25} +(1.61561 - 6.32166i) q^{26} +(-3.72696 + 6.81529i) q^{28} +(-3.95075 - 0.696624i) q^{29} +(2.60846 - 7.16669i) q^{31} +(-2.97087 + 4.81393i) q^{32} +(2.91283 - 0.288886i) q^{34} +(-4.77439 + 8.26948i) q^{35} +(2.41051 + 4.17513i) q^{37} +(-2.34372 - 3.26596i) q^{38} +(-3.78818 + 5.83145i) q^{40} +(1.08062 - 0.190542i) q^{41} +(6.20086 - 7.38990i) q^{43} +(0.00270032 + 0.116498i) q^{44} +(-5.77779 - 5.64542i) q^{46} +(5.13304 - 1.86827i) q^{47} +(-6.19317 + 5.19668i) q^{49} +(-0.833190 + 1.21976i) q^{50} +(5.76594 - 7.20423i) q^{52} +10.5337i q^{53} +0.143248i q^{55} +(-8.77421 + 6.60985i) q^{56} +(-4.68477 - 3.20006i) q^{58} +(-1.22551 + 1.02833i) q^{59} +(1.98401 - 0.722122i) q^{61} +(7.53775 - 7.71449i) q^{62} +(-6.63359 + 4.47163i) q^{64} +(7.29127 - 8.68939i) q^{65} +(7.44236 - 1.31229i) q^{67} +(3.92169 + 1.32530i) q^{68} +(-10.9713 + 7.87324i) q^{70} +(4.08357 + 7.07295i) q^{71} +(3.26625 - 5.65731i) q^{73} +(0.672885 + 6.78467i) q^{74} +(-1.11666 - 5.57424i) q^{76} +(-0.0773972 + 0.212647i) q^{77} +(6.82395 + 1.20325i) q^{79} +(-8.27973 + 5.30644i) q^{80} +(1.50348 + 0.384241i) q^{82} +(-1.97880 + 11.2223i) q^{83} +(4.78181 + 1.74043i) q^{85} +(12.2968 - 5.90853i) q^{86} +(-0.0644136 + 0.151688i) q^{88} +(-1.85844 - 1.07297i) q^{89} +(15.5186 - 8.95967i) q^{91} +(-4.15494 - 10.6416i) q^{92} +(7.70299 + 0.584070i) q^{94} +(-1.21353 - 6.88226i) q^{95} +(-3.94848 - 3.31317i) q^{97} +(-11.0087 + 3.08694i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} - 12 q^{14} + 3 q^{16} - 18 q^{17} + 45 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} - 6 q^{29} - 57 q^{32} - 3 q^{34} - 6 q^{37} + 45 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) \) 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 - 12 * q^14 + 3 * q^16 - 18 * q^17 + 45 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 - 6 * q^29 - 57 * q^32 - 3 * q^34 - 6 * q^37 + 45 * q^38 - 12 * q^40 + 66 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 66 * q^50 - 24 * q^52 - 81 * q^56 - 24 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 - 42 * q^65 + 51 * q^68 - 30 * q^70 - 6 * q^73 - 96 * q^74 - 9 * q^76 + 30 * q^77 - 12 * q^82 + 66 * q^85 + 141 * q^86 - 45 * q^88 - 24 * q^92 - 51 * q^94 + 42 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

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