LMFDB - Embedded newform 405.2.r.a.152.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [405,2,Mod(8,405)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(405, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 27]))

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

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

chi := DirichletCharacter("405.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 405 = 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	405.r (of order $36$, degree $12$, 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:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			152.3
Character	$\chi$	$=$	405.152
Dual form			405.2.r.a.8.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.65044 - 1.15565i) q^{2} +(0.704386 + 1.93528i) q^{4} +(0.268922 - 2.21984i) q^{5} +(0.618828 + 1.32708i) q^{7} +(0.0310202 - 0.115769i) q^{8} +(-3.00920 + 3.35293i) q^{10} +(-1.86051 - 2.21727i) q^{11} +(-3.51558 - 5.02076i) q^{13} +(0.512304 - 2.90542i) q^{14} +(2.97033 - 2.49240i) q^{16} +(0.833002 + 3.10881i) q^{17} +(3.51741 - 2.03078i) q^{19} +(4.48544 - 1.04318i) q^{20} +(0.508272 + 5.80958i) q^{22} +(-4.58997 - 2.14034i) q^{23} +(-4.85536 - 1.19393i) q^{25} +12.3493i q^{26} +(-2.13239 + 2.13239i) q^{28} +(-0.368261 - 2.08851i) q^{29} +(-3.20394 + 1.16614i) q^{31} +(-8.02150 + 0.701790i) q^{32} +(2.21787 - 6.09356i) q^{34} +(3.11232 - 1.01682i) q^{35} +(-11.3656 + 3.04540i) q^{37} +(-8.15214 - 0.713220i) q^{38} +(-0.248646 - 0.0999926i) q^{40} +(-0.839107 - 0.147957i) q^{41} +(-0.0641287 + 0.732994i) q^{43} +(2.98053 - 5.16243i) q^{44} +(5.10199 + 8.83690i) q^{46} +(-2.61254 + 1.21825i) q^{47} +(3.12132 - 3.71984i) q^{49} +(6.63372 + 7.58161i) q^{50} +(7.24028 - 10.3402i) q^{52} +(0.0757900 + 0.0757900i) q^{53} +(-5.42232 + 3.53376i) q^{55} +(0.172831 - 0.0304748i) q^{56} +(-1.80580 + 3.87255i) q^{58} +(2.89613 + 2.43014i) q^{59} +(-4.21993 - 1.53593i) q^{61} +(6.63556 + 1.77799i) q^{62} +(7.33402 + 4.23430i) q^{64} +(-12.0907 + 6.45381i) q^{65} +(3.65313 - 2.55795i) q^{67} +(-5.42967 + 3.80189i) q^{68} +(-6.31179 - 1.91856i) q^{70} +(7.84988 + 4.53213i) q^{71} +(-8.04880 - 2.15667i) q^{73} +(22.2777 + 8.10840i) q^{74} +(6.40774 + 5.37673i) q^{76} +(1.79116 - 3.84116i) q^{77} +(1.44073 - 0.254040i) q^{79} +(-4.73394 - 7.26391i) q^{80} +(1.21391 + 1.21391i) q^{82} +(9.69375 - 13.8441i) q^{83} +(7.12506 - 1.01310i) q^{85} +(0.952926 - 1.13565i) q^{86} +(-0.314404 + 0.146609i) q^{88} +(-3.05075 - 5.28406i) q^{89} +(4.48742 - 7.77244i) q^{91} +(0.909052 - 10.3905i) q^{92} +(5.71971 + 1.00854i) q^{94} +(-3.56209 - 8.35420i) q^{95} +(16.1512 + 1.41304i) q^{97} +(-9.45039 + 2.53222i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/405\mathbb{Z}\right)^\times$.

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−1.65044	−	1.15565i	−1.16704	−	0.817169i	−0.180966	−	0.983489i	$-0.557923\pi$
$2$	−1.65044	−	1.15565i	−1.16704	−	0.817169i	−0.986072	+	0.166320i	$0.946811\pi$
$3$		0			0
$3$		0			0
$4$	0.704386	+	1.93528i	0.352193	+	0.967642i
$5$	0.268922	−	2.21984i	0.120266	−	0.992742i
$5$	0.268922	−	2.21984i	0.120266	−	0.992742i
$6$		0			0
$7$	0.618828	+	1.32708i	0.233895	+	0.501590i	0.987864	−	0.155320i	$-0.0496410\pi$
$7$	0.618828	+	1.32708i	0.233895	+	0.501590i	−0.753969	+	0.656910i	$0.771863\pi$
$8$	0.0310202	−	0.115769i	0.0109673	−	0.0409305i
$9$		0			0
$10$	−3.00920	+	3.35293i	−0.951592	+	1.06029i
$11$	−1.86051	−	2.21727i	−0.560965	−	0.668532i	0.408785	−	0.912631i	$-0.365953\pi$
$11$	−1.86051	−	2.21727i	−0.560965	−	0.668532i	−0.969751	+	0.244098i	$0.921508\pi$
$12$		0			0
$13$	−3.51558	−	5.02076i	−0.975045	−	1.39251i	−0.919078	−	0.394076i	$-0.871065\pi$
$13$	−3.51558	−	5.02076i	−0.975045	−	1.39251i	−0.0559675	−	0.998433i	$-0.517824\pi$
$14$	0.512304	−	2.90542i	0.136919	−	0.776506i
$15$		0			0
$16$	2.97033	−	2.49240i	0.742582	−	0.623101i
$17$	0.833002	+	3.10881i	0.202033	+	0.753996i	0.990334	+	0.138706i	$0.0442944\pi$
$17$	0.833002	+	3.10881i	0.202033	+	0.753996i	−0.788301	+	0.615290i	$0.789039\pi$
$18$		0			0
$19$	3.51741	−	2.03078i	0.806949	−	0.465892i	−0.0389464	−	0.999241i	$-0.512400\pi$
$19$	3.51741	−	2.03078i	0.806949	−	0.465892i	0.845895	+	0.533349i	$0.179067\pi$
$20$	4.48544	−	1.04318i	1.00298	−	0.233262i
$21$		0			0
$22$	0.508272	+	5.80958i	0.108364	+	1.23861i
$23$	−4.58997	−	2.14034i	−0.957074	−	0.446291i	−0.119633	−	0.992818i	$-0.538172\pi$
$23$	−4.58997	−	2.14034i	−0.957074	−	0.446291i	−0.837441	+	0.546527i	$0.815949\pi$
$24$		0			0
$25$	−4.85536	−	1.19393i	−0.971072	−	0.238785i
$26$			12.3493i			2.42189i
$27$		0			0
$28$	−2.13239	+	2.13239i	−0.402983	+	0.402983i
$29$	−0.368261	−	2.08851i	−0.0683844	−	0.387827i	−0.999720	−	0.0236650i	$-0.992466\pi$
$29$	−0.368261	−	2.08851i	−0.0683844	−	0.387827i	0.931336	−	0.364162i	$-0.118645\pi$
$30$		0			0
$31$	−3.20394	+	1.16614i	−0.575445	+	0.209445i	−0.613316	−	0.789838i	$-0.710165\pi$
$31$	−3.20394	+	1.16614i	−0.575445	+	0.209445i	0.0378710	+	0.999283i	$0.487942\pi$
$32$	−8.02150	+	0.701790i	−1.41801	+	0.124060i
$33$		0			0
$34$	2.21787	−	6.09356i	0.380362	−	1.04504i
$35$	3.11232	−	1.01682i	0.526079	−	0.171873i
$36$		0			0
$37$	−11.3656	+	3.04540i	−1.86849	+	0.500661i	−0.868503	+	0.495683i	$0.834918\pi$
$37$	−11.3656	+	3.04540i	−1.86849	+	0.500661i	−0.999988	+	0.00497757i	$0.998416\pi$
$38$	−8.15214	−	0.713220i	−1.32245	−	0.115700i
$39$		0			0
$40$	−0.248646	−	0.0999926i	−0.0393144	−	0.0158102i
$41$	−0.839107	−	0.147957i	−0.131046	−	0.0231070i	0.107740	−	0.994179i	$-0.465639\pi$
$41$	−0.839107	−	0.147957i	−0.131046	−	0.0231070i	−0.238787	+	0.971072i	$0.576750\pi$
$42$		0			0
$43$	−0.0641287	+	0.732994i	−0.00977953	+	0.111781i	−0.999515	−	0.0311282i	$-0.990090\pi$
$43$	−0.0641287	+	0.732994i	−0.00977953	+	0.111781i	0.989736	+	0.142909i	$0.0456455\pi$
$44$	2.98053	−	5.16243i	0.449332	−	0.778266i
$45$		0			0
$46$	5.10199	+	8.83690i	0.752247	+	1.30293i
$47$	−2.61254	+	1.21825i	−0.381078	+	0.177700i	−0.603712	−	0.797203i	$-0.706312\pi$
$47$	−2.61254	+	1.21825i	−0.381078	+	0.177700i	0.222634	+	0.974902i	$0.428535\pi$
$48$		0			0
$49$	3.12132	−	3.71984i	0.445902	−	0.531406i
$50$	6.63372	+	7.58161i	0.938150	+	1.07220i
$51$		0			0
$52$	7.24028	−	10.3402i	1.00405	−	1.43393i
$53$	0.0757900	+	0.0757900i	0.0104106	+	0.0104106i	0.712293	−	0.701882i	$-0.247657\pi$
$53$	0.0757900	+	0.0757900i	0.0104106	+	0.0104106i	−0.701882	+	0.712293i	$0.747657\pi$
$54$		0			0
$55$	−5.42232	+	3.53376i	−0.731145	+	0.476492i
$56$	0.172831	−	0.0304748i	0.0230955	−	0.00407236i
$57$		0			0
$58$	−1.80580	+	3.87255i	−0.237113	+	0.508491i
$59$	2.89613	+	2.43014i	0.377044	+	0.316377i	0.811540	−	0.584296i	$-0.198629\pi$
$59$	2.89613	+	2.43014i	0.377044	+	0.316377i	−0.434497	+	0.900673i	$0.643074\pi$
$60$		0			0
$61$	−4.21993	−	1.53593i	−0.540306	−	0.196655i	0.0574282	−	0.998350i	$-0.481710\pi$
$61$	−4.21993	−	1.53593i	−0.540306	−	0.196655i	−0.597734	+	0.801694i	$0.703932\pi$
$62$	6.63556	+	1.77799i	0.842717	+	0.225805i
$63$		0			0
$64$	7.33402	+	4.23430i	0.916753	+	0.529287i
$65$	−12.0907	+	6.45381i	−1.49967	+	0.800497i
$66$		0			0
$67$	3.65313	−	2.55795i	0.446301	−	0.312504i	−0.328733	−	0.944423i	$-0.606622\pi$
$67$	3.65313	−	2.55795i	0.446301	−	0.312504i	0.775034	+	0.631919i	$0.217733\pi$
$68$	−5.42967	+	3.80189i	−0.658444	+	0.461047i
$69$		0			0
$70$	−6.31179	−	1.91856i	−0.754403	−	0.229312i
$71$	7.84988	+	4.53213i	0.931609	+	0.537865i	0.887320	−	0.461154i	$-0.152564\pi$
$71$	7.84988	+	4.53213i	0.931609	+	0.537865i	0.0442890	+	0.999019i	$0.485898\pi$
$72$		0			0
$73$	−8.04880	−	2.15667i	−0.942041	−	0.252419i	−0.245059	−	0.969508i	$-0.578807\pi$
$73$	−8.04880	−	2.15667i	−0.942041	−	0.252419i	−0.696982	+	0.717089i	$0.745474\pi$
$74$	22.2777	+	8.10840i	2.58972	+	0.942583i
$75$		0			0
$76$	6.40774	+	5.37673i	0.735018	+	0.616754i
$77$	1.79116	−	3.84116i	0.204122	−	0.437741i
$78$		0			0
$79$	1.44073	−	0.254040i	0.162095	−	0.0285818i	−0.0920115	−	0.995758i	$-0.529330\pi$
$79$	1.44073	−	0.254040i	0.162095	−	0.0285818i	0.254107	+	0.967176i	$0.418219\pi$
$80$	−4.73394	−	7.26391i	−0.529271	−	0.812130i
$81$		0			0
$82$	1.21391	+	1.21391i	0.134054	+	0.134054i
$83$	9.69375	−	13.8441i	1.06403	−	1.51959i	0.225872	−	0.974157i	$-0.427477\pi$
$83$	9.69375	−	13.8441i	1.06403	−	1.51959i	0.838155	−	0.545431i	$-0.183634\pi$
$84$		0			0
$85$	7.12506	−	1.01310i	0.772821	−	0.109886i
$86$	0.952926	−	1.13565i	0.102757	−	0.122461i
$87$		0			0
$88$	−0.314404	+	0.146609i	−0.0335156	+	0.0156286i
$89$	−3.05075	−	5.28406i	−0.323379	−	0.560109i	0.657804	−	0.753189i	$-0.271486\pi$
$89$	−3.05075	−	5.28406i	−0.323379	−	0.560109i	−0.981183	+	0.193080i	$0.938152\pi$
$90$		0			0
$91$	4.48742	−	7.77244i	0.470410	−	0.814774i
$92$	0.909052	−	10.3905i	0.0947752	−	1.08329i
$93$		0			0
$94$	5.71971	+	1.00854i	0.589943	+	0.104023i
$95$	−3.56209	−	8.35420i	−0.365462	−	0.857123i
$96$		0			0
$97$	16.1512	+	1.41304i	1.63990	+	0.143473i	0.869449	−	0.494023i	$-0.164474\pi$
$97$	16.1512	+	1.41304i	1.63990	+	0.143473i	0.770453	+	0.637496i	$0.220030\pi$
$98$	−9.45039	+	2.53222i	−0.954633	+	0.255793i
$99$		0			0
$100$	−1.10946	−	10.2375i	−0.110946	−	1.02375i
$101$	1.88053	−	5.16673i	0.187120	−	0.514108i	−0.810290	−	0.586029i	$-0.800691\pi$
$101$	1.88053	−	5.16673i	0.187120	−	0.514108i	0.997410	+	0.0719204i	$0.0229128\pi$
$102$		0			0
$103$	3.90922	−	0.342012i	0.385186	−	0.0336994i	0.107082	−	0.994250i	$-0.465849\pi$
$103$	3.90922	−	0.342012i	0.385186	−	0.0336994i	0.278105	+	0.960551i	$0.410294\pi$
$104$	−0.690302	+	0.251249i	−0.0676897	+	0.0246370i
$105$		0			0
$106$	−0.0375001	−	0.212674i	−0.00364233	−	0.0206567i
$107$	10.5329	−	10.5329i	1.01825	−	1.01825i	0.0184189	−	0.999830i	$-0.494137\pi$
$107$	10.5329	−	10.5329i	1.01825	−	1.01825i	0.999830	−	0.0184189i	$-0.00586325\pi$
$108$		0			0
$109$		−	9.91447i		−	0.949634i	−0.880085	−	0.474817i	$-0.842514\pi$
$109$		−	9.91447i		−	0.949634i	0.880085	−	0.474817i	$-0.157486\pi$
$110$	13.0330	+	0.434043i	1.24265	+	0.0413843i
$111$		0			0
$112$	5.14574	+	2.39950i	0.486227	+	0.226731i
$113$	1.32748	+	15.1732i	0.124879	+	1.42737i	0.757462	+	0.652879i	$0.226439\pi$
$113$	1.32748	+	15.1732i	0.124879	+	1.42737i	−0.632583	+	0.774492i	$0.718005\pi$
$114$		0			0
$115$	−5.98554	+	9.61340i	−0.558155	+	0.896454i
$116$	3.78247	−	2.18381i	0.351193	−	0.202762i
$117$		0			0
$118$	−1.97149	−	7.35771i	−0.181491	−	0.677332i
$119$	−3.61015	+	3.02928i	−0.330942	+	0.277693i
$120$		0			0
$121$	0.455341	−	2.58237i	0.0413946	−	0.234761i
$122$	5.18974	+	7.41172i	0.469857	+	0.671026i
$123$		0			0
$124$	−4.51362	−	5.37912i	−0.405335	−	0.483059i
$125$	−3.95604	+	10.4570i	−0.353839	+	0.935306i
$126$		0			0
$127$	2.58018	−	9.62937i	0.228954	−	0.854468i	−0.751828	−	0.659360i	$-0.770827\pi$
$127$	2.58018	−	9.62937i	0.228954	−	0.854468i	0.980782	−	0.195109i	$-0.0625059\pi$
$128$	−0.405037	−	0.868604i	−0.0358005	−	0.0767745i
$129$		0			0
$130$	27.4133	+	3.32099i	2.40431	+	0.291270i
$131$	−3.84111	−	10.5534i	−0.335599	−	0.922051i	−0.986627	−	0.162997i	$-0.947884\pi$
$131$	−3.84111	−	10.5534i	−0.335599	−	0.922051i	0.651028	−	0.759054i	$-0.274338\pi$
$132$		0			0
$133$	4.87168	+	3.41119i	0.422428	+	0.295787i
$134$	−8.98538			−0.776219
$135$		0			0
$136$	0.385743			0.0330772
$137$	−16.1027	−	11.2752i	−1.37574	−	0.963306i	−0.999320	−	0.0368588i	$-0.988265\pi$
$137$	−16.1027	−	11.2752i	−1.37574	−	0.963306i	−0.376424	−	0.926448i	$-0.622846\pi$
$138$		0			0
$139$	0.508611	+	1.39740i	0.0431398	+	0.118526i	0.959392	−	0.282076i	$-0.0910232\pi$
$139$	0.508611	+	1.39740i	0.0431398	+	0.118526i	−0.916252	+	0.400602i	$0.868801\pi$
$140$	4.16010	+	5.30700i	0.351593	+	0.448523i
$141$		0			0
$142$	−7.71820	−	16.5517i	−0.647697	−	1.38899i
$143$	−4.59162	+	17.1362i	−0.383971	+	1.43300i
$144$		0			0
$145$	−4.73520	+	0.255833i	−0.393237	+	0.0212458i
$146$	10.7917	+	12.8611i	0.893129	+	1.06439i
$147$		0			0
$148$	−13.8995	−	19.8505i	−1.14253	−	1.63170i
$149$	−0.861743	+	4.88719i	−0.0705968	+	0.400374i	0.928948	+	0.370210i	$0.120714\pi$
$149$	−0.861743	+	4.88719i	−0.0705968	+	0.400374i	−0.999545	+	0.0301644i	$0.990397\pi$
$150$		0			0
$151$	−15.8833	+	13.3277i	−1.29257	+	1.08459i	−0.301186	+	0.953565i	$0.597383\pi$
$151$	−15.8833	+	13.3277i	−1.29257	+	1.08459i	−0.991379	+	0.131025i	$0.958173\pi$
$152$	−0.125990	−	0.470202i	−0.0102191	−	0.0381384i
$153$		0			0
$154$	−7.39525	+	4.26965i	−0.595926	+	0.344058i
$155$	1.72703	+	7.42583i	0.138718	+	0.596457i
$156$		0			0
$157$	0.591932	+	6.76582i	0.0472413	+	0.539971i	0.982532	+	0.186092i	$0.0595821\pi$
$157$	0.591932	+	6.76582i	0.0472413	+	0.539971i	−0.935291	+	0.353879i	$0.884862\pi$
$158$	−2.67143	−	1.24571i	−0.212528	−	0.0991032i
$159$		0			0
$160$	−0.599298	+	17.9951i	−0.0473787	+	1.42264i
$161$		−	7.41576i		−	0.584444i
$162$		0			0
$163$	14.3864	−	14.3864i	1.12683	−	1.12683i	0.136142	−	0.990689i	$-0.456530\pi$
$163$	14.3864	−	14.3864i	1.12683	−	1.12683i	0.990689	−	0.136142i	$-0.0434702\pi$
$164$	−0.304716	−	1.72813i	−0.0237943	−	0.134944i
$165$		0			0
$166$	−31.9979	+	11.6463i	−2.48352	+	0.903928i
$167$	0.469806	−	0.0411027i	0.0363547	−	0.00318063i	−0.0689639	−	0.997619i	$-0.521969\pi$
$167$	0.469806	−	0.0411027i	0.0363547	−	0.00318063i	0.105319	+	0.994439i	$0.466414\pi$
$168$		0			0
$169$	−8.40252	+	23.0857i	−0.646348	+	1.77583i
$170$	−12.9303	−	6.56202i	−0.991707	−	0.503284i
$171$		0			0
$172$	−1.46372	+	0.392203i	−0.111608	+	0.0299052i
$173$	18.3690	+	1.60708i	1.39657	+	0.122184i	0.760446	−	0.649402i	$-0.224981\pi$
$173$	18.3690	+	1.60708i	1.39657	+	0.122184i	0.636125	+	0.771586i	$0.280536\pi$
$174$		0			0
$175$	−1.42020	−	7.18230i	−0.107357	−	0.542931i
$176$	−11.0527	−	1.94888i	−0.833126	−	0.146903i
$177$		0			0
$178$	−1.07144	+	12.2466i	−0.0803080	+	0.917925i
$179$	3.95796	−	6.85540i	0.295832	−	0.512396i	−0.679346	−	0.733818i	$-0.737736\pi$
$179$	3.95796	−	6.85540i	0.295832	−	0.512396i	0.975178	+	0.221422i	$0.0710697\pi$
$180$		0			0
$181$	9.86110	+	17.0799i	0.732970	+	1.26954i	0.955608	+	0.294640i	$0.0951998\pi$
$181$	9.86110	+	17.0799i	0.732970	+	1.26954i	−0.222638	+	0.974901i	$0.571467\pi$
$182$	−16.3885	+	7.64207i	−1.21479	+	0.566468i
$183$		0			0
$184$	−0.390166	+	0.464982i	−0.0287634	+	0.0342789i
$185$	3.70384	+	26.0487i	0.272311	+	1.91514i
$186$		0			0
$187$	5.34326	−	7.63096i	0.390738	−	0.558031i
$188$	−4.19789	−	4.19789i	−0.306162	−	0.306162i
$189$		0			0
$190$	−3.77553	+	17.9046i	−0.273905	+	1.29894i
$191$	8.60644	−	1.51755i	0.622740	−	0.109806i	0.146630	−	0.989191i	$-0.453157\pi$
$191$	8.60644	−	1.51755i	0.622740	−	0.109806i	0.476110	+	0.879386i	$0.342046\pi$
$192$		0			0
$193$	−3.65180	+	7.83132i	−0.262863	+	0.563711i	−0.992797	−	0.119806i	$-0.961773\pi$
$193$	−3.65180	+	7.83132i	−0.262863	+	0.563711i	0.729935	+	0.683517i	$0.239550\pi$
$194$	−25.0236	−	20.9973i	−1.79659	−	1.50752i
$195$		0			0
$196$	9.39756	+	3.42043i	0.671254	+	0.244316i
$197$	−1.93720	−	0.519071i	−0.138020	−	0.0369822i	0.189148	−	0.981949i	$-0.439427\pi$
$197$	−1.93720	−	0.519071i	−0.138020	−	0.0369822i	−0.327167	+	0.944966i	$0.606094\pi$
$198$		0			0
$199$	15.5130	+	8.95641i	1.09968	+	0.634903i	0.936138	−	0.351633i	$-0.114373\pi$
$199$	15.5130	+	8.95641i	1.09968	+	0.634903i	0.163546	+	0.986536i	$0.447707\pi$
$200$	−0.288834	+	0.525064i	−0.0204236	+	0.0371276i
$201$		0			0
$202$	−9.07464	+	6.35413i	−0.638490	+	0.447075i
$203$	2.54374	−	1.78114i	0.178535	−	0.125012i
$204$		0			0
$205$	−0.554096	+	1.82289i	−0.0386997	+	0.127316i
$206$	−6.84718	−	3.95322i	−0.477065	−	0.275434i
$207$		0			0
$208$	−22.9562	−	6.15109i	−1.59172	−	0.426501i
$209$	−11.0470	−	4.02077i	−0.764134	−	0.278122i
$210$		0			0
$211$	−8.17709	−	6.86139i	−0.562934	−	0.472358i	0.316359	−	0.948640i	$-0.397540\pi$
$211$	−8.17709	−	6.86139i	−0.562934	−	0.472358i	−0.879293	+	0.476282i	$0.841984\pi$
$212$	−0.0932898	+	0.200061i	−0.00640717	+	0.0137402i
$213$		0			0
$214$	−29.5562	+	5.21155i	−2.02042	+	0.356254i
$215$	1.60988	+	0.339474i	0.109793	+	0.0231519i
$216$		0			0
$217$	−3.53025	−	3.53025i	−0.239649	−	0.239649i
$218$	−11.4577	+	16.3632i	−0.776011	+	1.10826i
$219$		0			0
$220$	−10.6582	−	8.00459i	−0.718578	−	0.539669i
$221$	12.6801	−	15.1115i	0.852955	−	1.01651i
$222$		0			0
$223$	10.8301	−	5.05016i	0.725238	−	0.338184i	−0.0246975	−	0.999695i	$-0.507862\pi$
$223$	10.8301	−	5.05016i	0.725238	−	0.338184i	0.749936	+	0.661511i	$0.230084\pi$
$224$	−5.89526	−	10.2109i	−0.393894	−	0.682244i
$225$		0			0
$226$	15.3440	−	26.5765i	1.02067	−	1.76784i
$227$	−0.100851	+	1.15273i	−0.00669369	+	0.0765092i	−0.998807	−	0.0488368i	$-0.984449\pi$
$227$	−0.100851	+	1.15273i	−0.00669369	+	0.0765092i	0.992113	+	0.125346i	$0.0400041\pi$
$228$		0			0
$229$	−8.62548	−	1.52090i	−0.569988	−	0.100504i	−0.118776	−	0.992921i	$-0.537897\pi$
$229$	−8.62548	−	1.52090i	−0.569988	−	0.100504i	−0.451212	+	0.892417i	$0.649008\pi$
$230$	20.9885	−	8.94914i	1.38394	−	0.590089i
$231$		0			0
$232$	−0.253208	−	0.0221529i	−0.0166240	−	0.00145441i
$233$	15.8052	−	4.23498i	1.03543	−	0.277443i	0.299213	−	0.954186i	$-0.403276\pi$
$233$	15.8052	−	4.23498i	1.03543	−	0.277443i	0.736219	+	0.676743i	$0.236609\pi$
$234$		0			0
$235$	2.00174	+	6.12703i	0.130579	+	0.399683i
$236$	−2.66302	+	7.31658i	−0.173348	+	0.476269i
$237$		0			0
$238$	9.45913	−	0.827567i	0.613145	−	0.0536432i
$239$	8.07123	−	2.93769i	0.522085	−	0.190023i	−0.0675160	−	0.997718i	$-0.521507\pi$
$239$	8.07123	−	2.93769i	0.522085	−	0.190023i	0.589601	+	0.807695i	$0.299285\pi$
$240$		0			0
$241$	0.358872	+	2.03527i	0.0231170	+	0.131103i	0.994182	−	0.107712i	$-0.0343523\pi$
$241$	0.358872	+	2.03527i	0.0231170	+	0.131103i	−0.971065	+	0.238815i	$0.923241\pi$
$242$	−3.73583	+	3.73583i	−0.240148	+	0.240148i
$243$		0			0
$244$		−	9.24864i		−	0.592083i
$245$	−7.41805	−	7.92916i	−0.473922	−	0.506576i
$246$		0			0
$247$	−22.5618	−	10.5207i	−1.43557	−	0.669417i
$248$	0.0356158	+	0.407090i	0.00226161	+	0.0258503i
$249$		0			0
$250$	18.6139	−	12.6869i	1.17725	−	0.802392i
$251$	−9.55376	+	5.51587i	−0.603028	+	0.348158i	−0.770232	−	0.637764i	$-0.779860\pi$
$251$	−9.55376	+	5.51587i	−0.603028	+	0.348158i	0.167204	+	0.985922i	$0.446526\pi$
$252$		0			0
$253$	3.79398	+	14.1593i	0.238525	+	0.890189i
$254$	−15.3866	+	12.9109i	−0.965443	+	0.810103i
$255$		0			0
$256$	2.60580	−	14.7782i	0.162862	−	0.923639i
$257$	3.31253	+	4.73079i	0.206630	+	0.295098i	0.909069	−	0.416646i	$-0.136794\pi$
$257$	3.31253	+	4.73079i	0.206630	+	0.295098i	−0.702439	+	0.711744i	$0.747906\pi$
$258$		0			0
$259$	−11.0748	−	13.1985i	−0.688157	−	0.820114i
$260$	−21.0065	−	18.8529i	−1.30277	−	1.16921i
$261$		0			0
$262$	−5.85647	+	21.8567i	−0.361814	+	1.35031i
$263$	−7.79728	−	16.7213i	−0.480801	−	1.03108i	−0.985794	−	0.167958i	$-0.946283\pi$
$263$	−7.79728	−	16.7213i	−0.480801	−	1.03108i	0.504993	−	0.863123i	$-0.331495\pi$
$264$		0			0
$265$	0.188623	−	0.147860i	0.0115870	−	0.00908296i
$266$	−4.09828	−	11.2599i	−0.251281	−	0.690390i
$267$		0			0
$268$	7.52358	+	5.26807i	0.459576	+	0.321798i
$269$	15.7262			0.958842			0.479421	−	0.877585i	$-0.340847\pi$
$269$	15.7262			0.958842			0.479421	+	0.877585i	$0.340847\pi$
$270$		0			0
$271$	−17.4326			−1.05895			−0.529477	−	0.848324i	$-0.677612\pi$
$271$	−17.4326			−1.05895			−0.529477	+	0.848324i	$0.677612\pi$
$272$	10.2227	+	7.15800i	0.619841	+	0.434018i
$273$		0			0
$274$	13.5463	+	37.2181i	0.818362	+	2.24843i
$275$	6.38620	+	12.9870i	0.385102	+	0.783144i
$276$		0			0
$277$	6.49002	+	13.9179i	0.389947	+	0.836245i	0.999068	+	0.0431672i	$0.0137448\pi$
$277$	6.49002	+	13.9179i	0.389947	+	0.836245i	−0.609120	+	0.793078i	$0.708477\pi$
$278$	0.775471	−	2.89410i	0.0465097	−	0.173576i
$279$		0			0
$280$	−0.0211709	−	0.391852i	−0.00126521	−	0.0234176i
$281$	−4.76302	−	5.67634i	−0.284138	−	0.338622i	0.605031	−	0.796202i	$-0.293161\pi$
$281$	−4.76302	−	5.67634i	−0.284138	−	0.338622i	−0.889168	+	0.457580i	$0.848716\pi$
$282$		0			0
$283$	8.24647	+	11.7772i	0.490202	+	0.700081i	0.985696	−	0.168530i	$-0.0539021\pi$
$283$	8.24647	+	11.7772i	0.490202	+	0.700081i	−0.495495	+	0.868611i	$0.665013\pi$
$284$	−3.24161	+	18.3841i	−0.192354	+	1.09090i
$285$		0			0
$286$	27.3816	−	22.9759i	1.61911	−	1.35859i
$287$	−0.322912	−	1.20512i	−0.0190609	−	0.0711362i
$288$		0			0
$289$	5.75165	−	3.32072i	0.338332	−	0.195336i
$290$	8.11081	+	5.05000i	0.476283	+	0.296546i
$291$		0			0
$292$	−1.49569	−	17.0958i	−0.0875288	−	1.00046i
$293$	−18.2561	−	8.51297i	−1.06653	−	0.497333i	−0.191549	−	0.981483i	$-0.561351\pi$
$293$	−18.2561	−	8.51297i	−1.06653	−	0.497333i	−0.874985	+	0.484150i	$0.839129\pi$
$294$		0			0
$295$	6.17335	−	5.77541i	0.359426	−	0.336258i
$296$			1.41025i			0.0819691i
$297$		0			0
$298$	7.07014	−	7.07014i	0.409562	−	0.409562i
$299$	5.39025	+	30.5696i	0.311726	+	1.76789i
$300$		0			0
$301$	−1.01243	+	0.368493i	−0.0583553	+	0.0212396i
$302$	41.6166	−	3.64098i	2.39477	−	0.209515i
$303$		0			0
$304$	5.38635	−	14.7989i	0.308928	−	0.848774i
$305$	−4.54434	+	8.95451i	−0.260208	+	0.512733i
$306$		0			0
$307$	11.5423	−	3.09276i	0.658756	−	0.176513i	0.0860714	−	0.996289i	$-0.472569\pi$
$307$	11.5423	−	3.09276i	0.658756	−	0.176513i	0.572684	+	0.819776i	$0.305902\pi$
$308$	8.69540	+	0.760749i	0.495467	+	0.0433477i
$309$		0			0
$310$	5.73131	−	14.2517i	0.325516	−	0.809444i
$311$	−2.38442	−	0.420438i	−0.135208	−	0.0238408i	0.105634	−	0.994405i	$-0.466313\pi$
$311$	−2.38442	−	0.420438i	−0.135208	−	0.0238408i	−0.240843	+	0.970564i	$0.577424\pi$
$312$		0			0
$313$	1.06842	−	12.2121i	0.0603905	−	0.690267i	−0.904303	−	0.426891i	$-0.859609\pi$
$313$	1.06842	−	12.2121i	0.0603905	−	0.690267i	0.964693	−	0.263375i	$-0.0848358\pi$
$314$	6.84198	−	11.8506i	0.386115	−	0.668771i
$315$		0			0
$316$	1.50647	+	2.60929i	0.0847457	+	0.146784i
$317$	−20.5585	+	9.58656i	−1.15468	+	0.538435i	−0.903112	−	0.429405i	$-0.858723\pi$
$317$	−20.5585	+	9.58656i	−1.15468	+	0.538435i	−0.251566	+	0.967840i	$0.580945\pi$
$318$		0			0
$319$	−3.94565	+	4.70224i	−0.220914	+	0.263275i
$320$	11.3717	−	15.1416i	0.635700	−	0.846444i
$321$		0			0
$322$	−8.57003	+	12.2393i	−0.477589	+	0.682068i
$323$	9.24330	+	9.24330i	0.514311	+	0.514311i
$324$		0			0
$325$	11.0750	+	28.5750i	0.614329	+	1.58505i
$326$	−40.3696	+	7.11825i	−2.23587	+	0.394243i
$327$		0			0
$328$	−0.0431581	+	0.0925528i	−0.00238301	+	0.00511038i
$329$	−3.23343	−	2.71317i	−0.178265	−	0.149582i
$330$		0			0
$331$	15.3336	+	5.58098i	0.842812	+	0.306758i	0.727106	−	0.686525i	$-0.240865\pi$
$331$	15.3336	+	5.58098i	0.842812	+	0.306758i	0.115706	+	0.993284i	$0.463087\pi$
$332$	33.6204	+	9.00856i	1.84516	+	0.494409i
$333$		0			0
$334$	−0.822888	−	0.475095i	−0.0450264	−	0.0259960i
$335$	−4.69583	−	8.79726i	−0.256561	−	0.480646i
$336$		0			0
$337$	−3.28511	+	2.30026i	−0.178951	+	0.125303i	−0.659620	−	0.751599i	$-0.729283\pi$
$337$	−3.28511	+	2.30026i	−0.178951	+	0.125303i	0.480669	+	0.876902i	$0.340394\pi$
$338$	40.5469	−	28.3913i	2.20546	−	1.54428i
$339$		0			0
$340$	6.97943	+	13.0754i	0.378513	+	0.709113i
$341$	8.54661	+	4.93439i	0.462825	+	0.267212i
$342$		0			0
$343$	16.7687	+	4.49317i	0.905427	+	0.242608i
$344$	0.0828686	+	0.0301617i	0.00446798	+	0.00162621i
$345$		0			0
$346$	−28.4598	−	23.8806i	−1.53001	−	1.28383i
$347$	5.24496	−	11.2479i	0.281564	−	0.603816i	−0.713762	−	0.700389i	$-0.753010\pi$
$347$	5.24496	−	11.2479i	0.281564	−	0.603816i	0.995326	+	0.0965722i	$0.0307879\pi$
$348$		0			0
$349$	−7.52479	+	1.32682i	−0.402793	+	0.0710232i	−0.371375	−	0.928483i	$-0.621113\pi$
$349$	−7.52479	+	1.32682i	−0.402793	+	0.0710232i	−0.0314181	+	0.999506i	$0.510002\pi$
$350$	−5.95628	+	13.4952i	−0.318377	+	0.721349i
$351$		0			0
$352$	16.4801	+	16.4801i	0.878395	+	0.878395i
$353$	−10.2693	+	14.6661i	−0.546579	+	0.780595i	−0.993482	−	0.113987i	$-0.963638\pi$
$353$	−10.2693	+	14.6661i	−0.546579	+	0.780595i	0.446904	+	0.894582i	$0.352527\pi$
$354$		0			0
$355$	12.1716	−	16.2067i	0.646001	−	0.860161i
$356$	8.07725	−	9.62609i	0.428093	−	0.510182i
$357$		0			0
$358$	−14.4548	+	6.74040i	−0.763962	+	0.356241i
$359$	−6.26521	−	10.8517i	−0.330665	−	0.572729i	0.651977	−	0.758239i	$-0.273940\pi$
$359$	−6.26521	−	10.8517i	−0.330665	−	0.572729i	−0.982642	+	0.185510i	$0.940606\pi$
$360$		0			0
$361$	−1.25189	+	2.16834i	−0.0658891	+	0.114123i
$362$	3.46328	−	39.5854i	0.182026	−	2.08056i
$363$		0			0
$364$	18.2028	+	3.20964i	0.954084	+	0.168231i
$365$	−6.95196	+	17.2871i	−0.363882	+	0.904846i
$366$		0			0
$367$	−13.6352	−	1.19292i	−0.711750	−	0.0622701i	−0.274470	−	0.961596i	$-0.588503\pi$
$367$	−13.6352	−	1.19292i	−0.711750	−	0.0622701i	−0.437280	+	0.899325i	$0.644058\pi$
$368$	−18.9683	+	5.08254i	−0.988790	+	0.264946i
$369$		0			0
$370$	23.9903	−	47.2723i	1.24720	−	2.45757i
$371$	−0.0536785	+	0.147481i	−0.00278685	+	0.00765681i
$372$		0			0
$373$	−12.0608	+	1.05518i	−0.624485	+	0.0546353i	−0.395006	−	0.918678i	$-0.629258\pi$
$373$	−12.0608	+	1.05518i	−0.624485	+	0.0546353i	−0.229478	+	0.973314i	$0.573702\pi$
$374$	−17.6375	+	6.41951i	−0.912011	+	0.331945i
$375$		0			0
$376$	0.0599937	+	0.340241i	0.00309394	+	0.0175466i
$377$	−9.19128	+	9.19128i	−0.473375	+	0.473375i
$378$		0			0
$379$		−	22.5213i		−	1.15684i	−0.815738	−	0.578421i	$-0.803669\pi$
$379$		−	22.5213i		−	1.15684i	0.815738	−	0.578421i	$-0.196331\pi$
$380$	13.6587	−	12.7782i	0.700674	−	0.655509i
$381$		0			0
$382$	−15.9582	−	7.44142i	−0.816491	−	0.380736i
$383$	−1.26087	−	14.4118i	−0.0644275	−	0.736410i	−0.957864	−	0.287221i	$-0.907269\pi$
$383$	−1.26087	−	14.4118i	−0.0644275	−	0.736410i	0.893437	−	0.449189i	$-0.148287\pi$
$384$		0			0
$385$	−8.04507	−	5.00906i	−0.410015	−	0.255286i
$386$	15.0774	−	8.70492i	0.767417	−	0.443069i
$387$		0			0
$388$	8.64201	+	32.2524i	0.438731	+	1.63737i
$389$	9.68308	−	8.12507i	0.490951	−	0.411957i	−0.363416	−	0.931627i	$-0.618390\pi$
$389$	9.68308	−	8.12507i	0.490951	−	0.411957i	0.854367	+	0.519670i	$0.173945\pi$
$390$		0			0
$391$	2.83044	−	16.0522i	0.143141	−	0.811795i
$392$	−0.333818	−	0.476742i	−0.0168604	−	0.0240791i
$393$		0			0
$394$	2.59737	+	3.09542i	0.130853	+	0.155945i
$395$	−0.176483	−	3.26651i	−0.00887982	−	0.164356i
$396$		0			0
$397$	3.89075	−	14.5205i	0.195271	−	0.728761i	−0.796926	−	0.604077i	$-0.793542\pi$
$397$	3.89075	−	14.5205i	0.195271	−	0.728761i	0.992197	−	0.124684i	$-0.0397916\pi$
$398$	−15.2527	−	32.7096i	−0.764550	−	1.63958i
$399$		0			0
$400$	−17.3978	+	8.55516i	−0.869889	+	0.427758i
$401$	8.96818	+	24.6399i	0.447849	+	1.23046i	0.934218	+	0.356703i	$0.116099\pi$
$401$	8.96818	+	24.6399i	0.447849	+	1.23046i	−0.486369	+	0.873754i	$0.661679\pi$
$402$		0			0
$403$	17.1186	+	11.9866i	0.852738	+	0.597094i
$404$	11.3237			0.563375
$405$		0			0
$406$	−6.25667			−0.310513
$407$	27.8983	+	19.5346i	1.38287	+	0.968294i
$408$		0			0
$409$	−2.57831	−	7.08384i	−0.127489	−	0.350273i	0.859483	−	0.511164i	$-0.170786\pi$
$409$	−2.57831	−	7.08384i	−0.127489	−	0.350273i	−0.986972	+	0.160891i	$0.948563\pi$
$410$	3.02113	−	2.36824i	0.149203	−	0.116959i
$411$		0			0
$412$	3.41549	+	7.32453i	0.168269	+	0.360854i
$413$	−1.43279	+	5.34723i	−0.0705028	+	0.263120i
$414$		0			0
$415$	−28.1248	−	25.2415i	−1.38059	−	1.23906i
$416$	31.7237	+	37.8068i	1.55538	+	1.85363i
$417$		0			0
$418$	13.5858	+	19.4025i	0.664501	+	0.949006i
$419$	−3.59622	+	20.3952i	−0.175687	+	0.996370i	0.761661	+	0.647975i	$0.224384\pi$
$419$	−3.59622	+	20.3952i	−0.175687	+	0.996370i	−0.937348	+	0.348394i	$0.886727\pi$
$420$		0			0
$421$	−5.26964	+	4.42176i	−0.256827	+	0.215503i	−0.762105	−	0.647453i	$-0.775834\pi$
$421$	−5.26964	+	4.42176i	−0.256827	+	0.215503i	0.505279	+	0.862956i	$0.331390\pi$
$422$	5.56643	+	20.7742i	0.270969	+	1.01127i
$423$		0			0
$424$	0.0111251	−	0.00642311i	0.000540285	−	0.000311934i
$425$	−0.332837	−	16.0889i	−0.0161450	−	0.780427i
$426$		0			0
$427$	−0.573108	−	6.55066i	−0.0277347	−	0.317009i
$428$	27.8032	+	12.9649i	1.34392	+	0.626680i
$429$		0			0
$430$	−2.26470	−	2.42074i	−0.109214	−	0.116739i
$431$			2.91928i			0.140617i	0.997525	+	0.0703084i	$0.0223983\pi$
$431$			2.91928i			0.140617i	−0.997525	+	0.0703084i	$0.977602\pi$
$432$		0			0
$433$	3.01763	−	3.01763i	0.145018	−	0.145018i	−0.630870	−	0.775888i	$-0.717302\pi$
$433$	3.01763	−	3.01763i	0.145018	−	0.145018i	0.775888	+	0.630870i	$0.217302\pi$
$434$	1.74673	+	9.90621i	0.0838458	+	0.475513i
$435$		0			0
$436$	19.1873	−	6.98361i	0.918905	−	0.334454i
$437$	−20.4913	+	1.79276i	−0.980233	+	0.0857593i
$438$		0			0
$439$	−1.28129	+	3.52030i	−0.0611524	+	0.168015i	−0.966506	−	0.256643i	$-0.917383\pi$
$439$	−1.28129	+	3.52030i	−0.0611524	+	0.168015i	0.905354	+	0.424658i	$0.139606\pi$
$440$	0.240898	+	0.737353i	0.0114844	+	0.0351519i
$441$		0			0
$442$	−38.3914	+	10.2870i	−1.82609	+	0.489300i
$443$	27.8809	+	2.43927i	1.32466	+	0.115893i	0.727434	−	0.686177i	$-0.240713\pi$
$443$	27.8809	+	2.43927i	1.32466	+	0.115893i	0.597229	+	0.802070i	$0.296268\pi$
$444$		0			0
$445$	−12.5502	+	5.35118i	−0.594935	+	0.253670i
$446$	−23.7107	−	4.18083i	−1.12273	−	0.197968i
$447$		0			0
$448$	−1.08076	+	12.3531i	−0.0510611	+	0.583631i
$449$	−4.77256	+	8.26631i	−0.225231	+	0.390111i	−0.956389	−	0.292097i	$-0.905647\pi$
$449$	−4.77256	+	8.26631i	−0.225231	+	0.390111i	0.731158	+	0.682208i	$0.238980\pi$
$450$		0			0
$451$	1.23311	+	2.13580i	0.0580647	+	0.100571i
$452$	−28.4293	+	13.2568i	−1.33720	+	0.623548i
$453$		0			0
$454$	1.49860	−	1.78596i	0.0703328	−	0.0838193i
$455$	−16.0468	−	12.0515i	−0.752286	−	0.564985i
$456$		0			0
$457$	20.3246	−	29.0265i	0.950745	−	1.35780i	0.0170039	−	0.999855i	$-0.494587\pi$
$457$	20.3246	−	29.0265i	0.950745	−	1.35780i	0.933741	−	0.357949i	$-0.116524\pi$
$458$	12.4782	+	12.4782i	0.583068	+	0.583068i
$459$		0			0
$460$	−22.8208	−	4.81219i	−1.06402	−	0.224369i
$461$	−24.4088	+	4.30393i	−1.13683	+	0.200454i	−0.710219	−	0.703981i	$-0.751404\pi$
$461$	−24.4088	+	4.30393i	−1.13683	+	0.200454i	−0.426612	+	0.904435i	$0.640293\pi$
$462$		0			0
$463$	−2.28775	+	4.90609i	−0.106321	+	0.228005i	−0.952269	−	0.305259i	$-0.901257\pi$
$463$	−2.28775	+	4.90609i	−0.106321	+	0.228005i	0.845949	+	0.533264i	$0.179035\pi$
$464$	−6.29927	−	5.28572i	−0.292436	−	0.245383i
$465$		0			0
$466$	−30.9797	−	11.2757i	−1.43511	−	0.522336i
$467$	−39.5591	−	10.5998i	−1.83058	−	0.490502i	−0.832589	−	0.553891i	$-0.813143\pi$
$467$	−39.5591	−	10.5998i	−1.83058	−	0.490502i	−0.997989	+	0.0633888i	$0.979809\pi$
$468$		0			0
$469$	5.65527	+	3.26507i	0.261136	+	0.150767i
$470$	3.77695	−	12.4256i	0.174218	−	0.573151i
$471$		0			0
$472$	0.371173	−	0.259898i	0.0170846	−	0.0119628i
$473$	1.74456	−	1.22155i	0.0802149	−	0.0561671i
$474$		0			0
$475$	−19.5029	+	5.66062i	−0.894854	+	0.259727i
$476$	−8.40545	−	4.85289i	−0.385263	−	0.222432i
$477$		0			0
$478$	−16.7160	−	4.47905i	−0.764574	−	0.204867i
$479$	25.9636	+	9.44996i	1.18631	+	0.431780i	0.858425	−	0.512940i	$-0.171444\pi$
$479$	25.9636	+	9.44996i	1.18631	+	0.431780i	0.327880	+	0.944719i	$0.393666\pi$
$480$		0			0
$481$	55.2468	+	46.3576i	2.51904	+	2.11372i
$482$	1.75976	−	3.77382i	0.0801549	−	0.171893i
$483$		0			0
$484$	5.31835	−	0.937769i	0.241743	−	0.0426258i
$485$	7.48013	−	35.4730i	0.339655	−	1.61074i
$486$		0			0
$487$	28.3122	+	28.3122i	1.28295	+	1.28295i	0.938981	+	0.343969i	$0.111772\pi$
$487$	28.3122	+	28.3122i	1.28295	+	1.28295i	0.343969	+	0.938981i	$0.388228\pi$
$488$	−0.308715	+	0.440891i	−0.0139749	+	0.0199582i
$489$		0			0
$490$	3.07971	+	21.6593i	0.139127	+	0.978467i
$491$	−15.4259	+	18.3839i	−0.696161	+	0.829652i	−0.992086	−	0.125559i	$-0.959928\pi$
$491$	−15.4259	+	18.3839i	−0.696161	+	0.829652i	0.295925	+	0.955211i	$0.404372\pi$
$492$		0			0
$493$	6.18602	−	2.88459i	0.278604	−	0.129915i
$494$	25.0786	+	43.4374i	1.12834	+	1.95434i
$495$		0			0
$496$	−6.61027	+	11.4493i	−0.296810	+	0.514090i
$497$	−1.15678	+	13.2220i	−0.0518886	+	0.593089i
$498$		0			0
$499$	−31.1017	−	5.48406i	−1.39230	−	0.245500i	−0.573325	−	0.819328i	$-0.694347\pi$
$499$	−31.1017	−	5.48406i	−1.39230	−	0.245500i	−0.818976	+	0.573828i	$0.805458\pi$
$500$	−23.0239	−	0.290269i	−1.02966	−	0.0129812i
$501$		0			0
$502$	22.1423	+	1.93720i	0.988261	+	0.0864616i
$503$	2.72503	−	0.730168i	0.121503	−	0.0325566i	−0.197555	−	0.980292i	$-0.563300\pi$
$503$	2.72503	−	0.730168i	0.121503	−	0.0325566i	0.319058	+	0.947735i	$0.396634\pi$
$504$		0			0
$505$	−10.9636	−	5.56393i	−0.487873	−	0.247592i
$506$	10.1015	−	27.7536i	0.449066	−	1.23380i
$507$		0			0
$508$	20.4530	−	1.78941i	0.907455	−	0.0793920i
$509$	−20.7599	+	7.55598i	−0.920166	+	0.334913i	−0.758304	−	0.651901i	$-0.773972\pi$
$509$	−20.7599	+	7.55598i	−0.920166	+	0.334913i	−0.161861	+	0.986814i	$0.551750\pi$
$510$		0			0
$511$	−2.11875	−	12.0160i	−0.0937279	−	0.531557i
$512$	−22.7346	+	22.7346i	−1.00474	+	1.00474i
$513$		0			0
$514$		−	11.6360i		−	0.513243i
$515$	0.292064	−	8.76980i	0.0128699	−	0.386444i
$516$		0			0
$517$	7.56184	+	3.52615i	0.332569	+	0.155080i
$518$	3.02553	+	34.5820i	0.132934	+	1.51944i
$519$		0			0
$520$	0.372095	+	1.59992i	0.0163175	+	0.0701614i
$521$	7.62484	−	4.40220i	0.334050	−	0.192864i	−0.323588	−	0.946198i	$-0.604889\pi$
$521$	7.62484	−	4.40220i	0.334050	−	0.192864i	0.657638	+	0.753334i	$0.271556\pi$
$522$		0			0
$523$	−0.332937	−	1.24254i	−0.0145583	−	0.0543324i	0.958265	−	0.285883i	$-0.0922868\pi$
$523$	−0.332937	−	1.24254i	−0.0145583	−	0.0543324i	−0.972823	+	0.231550i	$0.925620\pi$
$524$	17.7181	−	14.8673i	0.774019	−	0.649479i
$525$		0			0
$526$	−6.45507	+	36.6085i	−0.281454	+	1.59621i
$527$	−6.29419	−	8.98903i	−0.274179	−	0.391568i
$528$		0			0
$529$	1.70263	+	2.02911i	0.0740274	+	0.0882224i
$530$	−0.482186	+	0.0260515i	−0.0209448	+	0.00113161i
$531$		0			0
$532$	−3.17007	+	11.8309i	−0.137440	+	0.512933i
$533$	2.20709	+	4.73311i	0.0955995	+	0.205014i
$534$		0			0
$535$	−20.5487	−	26.2137i	−0.888398	−	1.13332i
$536$	−0.182810	−	0.502268i	−0.00789621	−	0.0216947i
$537$		0			0
$538$	−25.9551	−	18.1740i	−1.11900	−	0.783535i
$539$	−14.0551			−0.605398
$540$		0			0
$541$	−9.16794			−0.394160			−0.197080	−	0.980387i	$-0.563146\pi$
$541$	−9.16794			−0.394160			−0.197080	+	0.980387i	$0.563146\pi$
$542$	28.7714	+	20.1460i	1.23584	+	0.865344i
$543$		0			0
$544$	−8.86365	−	24.3527i	−0.380026	−	1.04411i
$545$	−22.0085	−	2.66622i	−0.942741	−	0.114208i
$546$		0			0
$547$	1.95267	+	4.18752i	0.0834904	+	0.179046i	0.943621	−	0.331029i	$-0.107396\pi$
$547$	1.95267	+	4.18752i	0.0834904	+	0.179046i	−0.860130	+	0.510074i	$0.829618\pi$
$548$	10.4782	−	39.1053i	0.447608	−	1.67050i
$549$		0			0
$550$	4.46837	−	28.8144i	0.190532	−	1.22865i
$551$	−5.53663	−	6.59830i	−0.235868	−	0.281097i
$552$		0			0
$553$	1.22870	+	1.75476i	0.0522496	+	0.0746202i
$554$	5.37283	−	30.4709i	0.228270	−	1.29458i
$555$		0			0
$556$	−2.34610	+	1.96861i	−0.0994968	+	0.0834878i
$557$	−2.60809	−	9.73354i	−0.110509	−	0.412423i	0.888403	−	0.459064i	$-0.151815\pi$
$557$	−2.60809	−	9.73354i	−0.110509	−	0.412423i	−0.998912	+	0.0466405i	$0.985148\pi$
$558$		0			0
$559$	3.90564	−	2.25492i	0.165191	−	0.0953730i
$560$	6.71031	−	10.7774i	0.283562	−	0.455430i
$561$		0			0
$562$	1.30121	+	14.8729i	0.0548881	+	0.627373i
$563$	15.0076	+	6.99817i	0.632496	+	0.294938i	0.712302	−	0.701873i	$-0.247652\pi$
$563$	15.0076	+	6.99817i	0.632496	+	0.294938i	−0.0798064	+	0.996810i	$0.525430\pi$
$564$		0			0
$565$	34.0390	+	1.13361i	1.43203	+	0.0476914i
$566$		−	28.9676i		−	1.21760i
$567$		0			0
$568$	0.768184	−	0.768184i	0.0322323	−	0.0322323i
$569$	−1.89828	−	10.7657i	−0.0795799	−	0.451320i	−0.998395	−	0.0566320i	$-0.981964\pi$
$569$	−1.89828	−	10.7657i	−0.0795799	−	0.451320i	0.918815	−	0.394688i	$-0.129147\pi$
$570$		0			0
$571$	15.2515	−	5.55110i	0.638256	−	0.232306i	−0.00256475	−	0.999997i	$-0.500816\pi$
$571$	15.2515	−	5.55110i	0.638256	−	0.232306i	0.640821	+	0.767691i	$0.278594\pi$
$572$	−36.3976	+	3.18438i	−1.52186	+	0.133146i
$573$		0			0
$574$	−0.859755	+	2.36216i	−0.0358855	+	0.0985946i
$575$	19.7305	+	15.8722i	0.822820	+	0.661916i
$576$		0			0
$577$	17.0234	−	4.56140i	0.708693	−	0.189894i	0.113572	−	0.993530i	$-0.463771\pi$
$577$	17.0234	−	4.56140i	0.708693	−	0.189894i	0.595121	+	0.803636i	$0.297104\pi$
$578$	−13.3304	−	1.16625i	−0.554469	−	0.0485098i
$579$		0			0
$580$	−3.83051	−	8.98374i	−0.159053	−	0.373030i
$581$	24.3710	+	4.29727i	1.01108	+	0.178281i
$582$		0			0
$583$	0.0270388	−	0.309055i	0.00111983	−	0.0127998i
$584$	−0.499351	+	0.864901i	−0.0206633	+	0.0357898i
$585$		0			0
$586$	20.2926	+	35.1479i	0.838280	+	1.45194i
$587$	7.40736	−	3.45411i	0.305734	−	0.142566i	−0.263696	−	0.964606i	$-0.584942\pi$
$587$	7.40736	−	3.45411i	0.305734	−	0.142566i	0.569430	+	0.822040i	$0.307164\pi$
$588$		0			0
$589$	−8.90140	+	10.6083i	−0.366776	+	0.437106i
$590$	−16.8631	+	2.39774i	−0.694243	+	0.0987135i
$591$		0			0
$592$	−26.1692	+	37.3735i	−1.07555	+	1.53604i
$593$	−28.1239	−	28.1239i	−1.15491	−	1.15491i	−0.985555	−	0.169357i	$-0.945831\pi$
$593$	−28.1239	−	28.1239i	−1.15491	−	1.15491i	−0.169357	−	0.985555i	$-0.554169\pi$
$594$		0			0
$595$	5.75366	+	8.82860i	0.235877	+	0.361937i
$596$	−10.0651	+	1.77475i	−0.412282	+	0.0726965i
$597$		0			0
$598$	26.4315	−	56.6826i	1.08087	−	2.31793i
$599$	27.5968	+	23.1564i	1.12757	+	0.946147i	0.998962	−	0.0455483i	$-0.0145035\pi$
$599$	27.5968	+	23.1564i	1.12757	+	0.946147i	0.128612	+	0.991695i	$0.458948\pi$
$600$		0			0
$601$	−21.4617	−	7.81141i	−0.875440	−	0.318634i	−0.135072	−	0.990836i	$-0.543126\pi$
$601$	−21.4617	−	7.81141i	−0.875440	−	0.318634i	−0.740368	+	0.672202i	$0.765349\pi$
$602$	2.09680	+	0.561836i	0.0854593	+	0.0228987i
$603$		0			0
$604$	−36.9808	−	21.3509i	−1.50473	−	0.868755i
$605$	−5.60999	−	1.70524i	−0.228078	−	0.0693279i
$606$		0			0
$607$	−7.00562	+	4.90539i	−0.284349	+	0.199104i	−0.707046	−	0.707168i	$-0.749973\pi$
$607$	−7.00562	+	4.90539i	−0.284349	+	0.199104i	0.422696	+	0.906271i	$0.361084\pi$
$608$	−26.7897	+	18.7583i	−1.08647	+	0.760751i
$609$		0			0
$610$	17.8485	−	9.52721i	0.722663	−	0.385745i
$611$	15.3011	+	8.83410i	0.619017	+	0.357389i
$612$		0			0
$613$	−35.7827	−	9.58796i	−1.44525	−	0.387254i	−0.550882	−	0.834583i	$-0.685709\pi$
$613$	−35.7827	−	9.58796i	−1.44525	−	0.387254i	−0.894369	+	0.447329i	$0.852375\pi$
$614$	−22.6241	−	8.23450i	−0.913034	−	0.332317i
$615$		0			0
$616$	−0.389125	−	0.326514i	−0.0156783	−	0.0131556i
$617$	5.17963	−	11.1077i	0.208524	−	0.447181i	−0.774032	−	0.633146i	$-0.781763\pi$
$617$	5.17963	−	11.1077i	0.208524	−	0.447181i	0.982556	+	0.185965i	$0.0595411\pi$
$618$		0			0
$619$	8.63834	−	1.52317i	0.347204	−	0.0612215i	0.00267331	−	0.999996i	$-0.499149\pi$
$619$	8.63834	−	1.52317i	0.347204	−	0.0612215i	0.344531	+	0.938775i	$0.388038\pi$
$620$	−13.1546	+	8.57294i	−0.528301	+	0.344297i
$621$		0			0
$622$	3.44947	+	3.44947i	0.138311	+	0.138311i
$623$	5.12449	−	7.31853i	0.205308	−	0.293211i
$624$		0			0
$625$	22.1491	+	11.5939i	0.885963	+	0.463756i
$626$	−15.8763	+	18.9206i	−0.634543	+	0.756218i
$627$		0			0
$628$	−12.6768	+	5.91130i	−0.505860	+	0.235887i
$629$	−18.9351	−	32.7966i	−0.754992	−	1.30769i
$630$		0			0
$631$	16.1540	−	27.9796i	0.643083	−	1.11385i	−0.341658	−	0.939824i	$-0.610989\pi$
$631$	16.1540	−	27.9796i	0.643083	−	1.11385i	0.984741	−	0.174027i	$-0.0556781\pi$
$632$	0.0152819	−	0.174673i	0.000607880	−	0.00694810i
$633$		0			0
$634$	45.0092	+	7.93634i	1.78755	+	0.315192i
$635$	−20.6818	−	8.31714i	−0.820731	−	0.330056i
$636$		0			0
$637$	−29.6497	−	2.59401i	−1.17476	−	0.102778i
$638$	11.9462	−	3.20098i	0.472955	−	0.126728i
$639$		0			0
$640$	−2.03708	+	0.665529i	−0.0805228	+	0.0263073i
$641$	3.35944	−	9.23000i	0.132690	−	0.364563i	−0.855499	−	0.517805i	$-0.826749\pi$
$641$	3.35944	−	9.23000i	0.132690	−	0.364563i	0.988189	+	0.153242i	$0.0489715\pi$
$642$		0			0
$643$	18.5293	−	1.62110i	0.730723	−	0.0639299i	0.284279	−	0.958742i	$-0.408246\pi$
$643$	18.5293	−	1.62110i	0.730723	−	0.0639299i	0.446444	+	0.894812i	$0.352690\pi$
$644$	14.3516	−	5.22355i	0.565532	−	0.205837i
$645$		0			0
$646$	−4.57349	−	25.9375i	−0.179942	−	1.02050i
$647$	14.2018	−	14.2018i	0.558331	−	0.558331i	−0.370501	−	0.928832i	$-0.620814\pi$
$647$	14.2018	−	14.2018i	0.558331	−	0.558331i	0.928832	+	0.370501i	$0.120814\pi$
$648$		0			0
$649$		−	10.9428i		−	0.429542i
$650$	14.7441	−	59.9601i	0.578312	−	2.35183i
$651$		0			0
$652$	37.9754	+	17.7082i	1.48723	+	0.693507i
$653$	−1.73834	−	19.8693i	−0.0680265	−	0.777546i	−0.951215	−	0.308528i	$-0.900164\pi$
$653$	−1.73834	−	19.8693i	−0.0680265	−	0.777546i	0.883189	−	0.469018i	$-0.155392\pi$
$654$		0			0
$655$	−24.4597	+	5.68860i	−0.955719	+	0.222272i
$656$	−2.86119	+	1.65191i	−0.111711	+	0.0644963i
$657$		0			0
$658$	2.20110	+	8.21463i	0.0858080	+	0.320240i
$659$	−0.815140	+	0.683983i	−0.0317533	+	0.0266442i	−0.658526	−	0.752558i	$-0.728820\pi$
$659$	−0.815140	+	0.683983i	−0.0317533	+	0.0266442i	0.626773	+	0.779202i	$0.284375\pi$
$660$		0			0
$661$	−5.78183	+	32.7904i	−0.224887	+	1.27540i	0.638014	+	0.770025i	$0.279756\pi$
$661$	−5.78183	+	32.7904i	−0.224887	+	1.27540i	−0.862901	+	0.505373i	$0.831355\pi$
$662$	−18.8576	−	26.9314i	−0.732920	−	1.04672i
$663$		0			0
$664$	−1.30202	−	1.55168i	−0.0505280	−	0.0602169i
$665$	8.88238	−	9.89699i	0.344444	−	0.383789i
$666$		0			0
$667$	−2.77981	+	10.3744i	−0.107635	+	0.401699i
$668$	0.410470	+	0.880256i	0.0158816	+	0.0340581i
$669$		0			0
$670$	−2.41637	+	19.9461i	−0.0933525	+	0.770585i
$671$	4.44565	+	12.2143i	0.171622	+	0.471529i
$672$		0			0
$673$	−20.0466	−	14.0367i	−0.772738	−	0.541077i	0.119397	−	0.992847i	$-0.461904\pi$
$673$	−20.0466	−	14.0367i	−0.772738	−	0.541077i	−0.892135	+	0.451770i	$0.850793\pi$
$674$	8.08017			0.311236
$675$		0			0
$676$	−50.5961			−1.94600
$677$	16.7682	+	11.7412i	0.644455	+	0.451252i	0.849563	−	0.527487i	$-0.176866\pi$
$677$	16.7682	+	11.7412i	0.644455	+	0.451252i	−0.205108	+	0.978739i	$0.565755\pi$
$678$		0			0
$679$	8.11957	+	22.3083i	0.311601	+	0.856115i
$680$	0.103735	−	0.856287i	0.00397805	−	0.0328371i
$681$		0			0
$682$	−8.40325	−	18.0208i	−0.321777	−	0.690053i
$683$	5.71751	−	21.3380i	0.218774	−	0.816477i	−0.766029	−	0.642806i	$-0.777770\pi$
$683$	5.71751	−	21.3380i	0.218774	−	0.816477i	0.984804	−	0.173671i	$-0.0555630\pi$
$684$		0			0
$685$	−29.3595	+	32.7132i	−1.12177	+	1.24991i
$686$	−22.4833	−	26.7945i	−0.858416	−	1.02302i
$687$		0			0
$688$	1.63643	+	2.33707i	0.0623884	+	0.0890999i
$689$	0.114078	−	0.646969i	0.00434603	−	0.0246476i
$690$		0			0
$691$	13.7398	−	11.5291i	0.522688	−	0.438587i	−0.342880	−	0.939379i	$-0.611402\pi$
$691$	13.7398	−	11.5291i	0.522688	−	0.438587i	0.865568	+	0.500792i	$0.166958\pi$
$692$	9.82872	+	36.6813i	0.373632	+	1.39441i
$693$		0			0
$694$	−21.6551	+	12.5026i	−0.822016	+	0.474591i
$695$	3.23877	−	0.753243i	0.122854	−	0.0285721i
$696$		0			0
$697$	−0.239008	−	2.73187i	−0.00905306	−	0.103477i
$698$	13.9526	+	6.50619i	0.528112	+	0.246263i
$699$		0			0
$700$	12.8994	−	7.80759i	0.487552	−	0.295099i
$701$			11.4005i			0.430590i	0.976549	+	0.215295i	$0.0690713\pi$
$701$			11.4005i			0.430590i	−0.976549	+	0.215295i	$0.930929\pi$
$702$		0			0
$703$	−33.7929	+	33.7929i	−1.27452	+	1.27452i
$704$	−4.25644	−	24.1395i	−0.160421	−	0.909791i
$705$		0			0
$706$	33.8977	−	12.3377i	1.27576	−	0.464337i
$707$	8.02039	−	0.701693i	0.301638	−	0.0263899i
$708$		0			0
$709$	5.28444	−	14.5189i	0.198461	−	0.545268i	−0.800043	−	0.599943i	$-0.795190\pi$
$709$	5.28444	−	14.5189i	0.198461	−	0.545268i	0.998504	+	0.0546749i	$0.0174122\pi$
$710$	−38.8178	+	12.6820i	−1.45680	+	0.475948i
$711$		0			0
$712$	−0.706365	+	0.189270i	−0.0264722	+	0.00709319i
$713$	17.2019	+	1.50497i	0.644216	+	0.0563616i
$714$		0			0
$715$	36.8047	+	14.8010i	1.37642	+	0.553524i
$716$	16.0551	+	2.83094i	0.600006	+	0.105797i
$717$		0			0
$718$	−2.20038	+	25.1504i	−0.0821174	+	0.938606i
$719$	−4.71157	+	8.16068i	−0.175712	+	0.304342i	−0.940407	−	0.340050i	$-0.889556\pi$
$719$	−4.71157	+	8.16068i	−0.175712	+	0.304342i	0.764695	+	0.644392i	$0.222889\pi$
$720$		0			0
$721$	2.87301	+	4.97620i	0.106997	+	0.185323i
$722$	4.57202	−	2.13197i	0.170153	−	0.0793437i
$723$		0			0
$724$	−26.1085	+	31.1149i	−0.970315	+	1.15638i
$725$	−0.705492	+	10.5802i	−0.0262013	+	0.392938i
$726$		0			0
$727$	−24.6272	+	35.1712i	−0.913371	+	1.30443i	0.0389219	+	0.999242i	$0.487608\pi$
$727$	−24.6272	+	35.1712i	−0.913371	+	1.30443i	−0.952293	+	0.305186i	$0.901281\pi$
$728$	−0.760607	−	0.760607i	−0.0281900	−	0.0281900i
$729$		0			0
$730$	31.4516	−	20.4972i	1.16408	−	0.758636i
$731$	−2.33216	+	0.411222i	−0.0862579	+	0.0152096i
$732$		0			0
$733$	0.264636	−	0.567513i	0.00977454	−	0.0209616i	−0.901360	−	0.433071i	$-0.857430\pi$
$733$	0.264636	−	0.567513i	0.00977454	−	0.0209616i	0.911134	+	0.412109i	$0.135208\pi$
$734$	21.1255	+	17.7264i	0.779755	+	0.654292i
$735$		0			0
$736$	38.3205	+	13.9475i	1.41251	+	0.514112i
$737$	−12.4684	−	3.34089i	−0.459278	−	0.123063i
$738$		0			0
$739$	23.6846	+	13.6743i	0.871251	+	0.503017i	0.867764	−	0.496977i	$-0.165557\pi$
$739$	23.6846	+	13.6743i	0.871251	+	0.503017i	0.00348723	+	0.999994i	$0.498890\pi$
$740$	−47.8028	+	25.5163i	−1.75726	+	0.937999i
$741$		0			0
$742$	0.259029	−	0.181374i	0.00950927	−	0.00665846i
$743$	−29.3796	+	20.5718i	−1.07783	+	0.754706i	−0.970882	−	0.239558i	$-0.922997\pi$
$743$	−29.3796	+	20.5718i	−1.07783	+	0.754706i	−0.106950	+	0.994264i	$0.534109\pi$
$744$		0			0
$745$	10.6170	+	3.22720i	0.388978	+	0.118236i
$746$	21.1251	+	12.1966i	0.773444	+	0.446548i
$747$		0			0
$748$	18.5318	+	4.96558i	0.677589	+	0.181559i
$749$	20.4960	+	7.45993i	0.748907	+	0.272580i
$750$		0			0
$751$	−27.0935	−	22.7342i	−0.988657	−	0.829582i	−0.00328459	−	0.999995i	$-0.501046\pi$
$751$	−27.0935	−	22.7342i	−0.988657	−	0.829582i	−0.985373	+	0.170413i	$0.945490\pi$
$752$	−4.72374	+	10.1301i	−0.172257	+	0.369407i
$753$		0			0
$754$	25.7916	−	4.54775i	0.939274	−	0.165619i
$755$	25.3139	+	38.8425i	0.921267	+	1.41362i
$756$		0			0
$757$	−26.1262	−	26.1262i	−0.949573	−	0.949573i	0.0492153	−	0.998788i	$-0.484328\pi$
$757$	−26.1262	−	26.1262i	−0.949573	−	0.949573i	−0.998788	+	0.0492153i	$0.984328\pi$
$758$	−26.0268	+	37.1701i	−0.945336	+	1.35008i
$759$		0			0
$760$	−1.07765	+	0.153230i	−0.0390906	+	0.00555824i
$761$	−5.19201	+	6.18759i	−0.188210	+	0.224300i	−0.851896	−	0.523712i	$-0.824547\pi$
$761$	−5.19201	+	6.18759i	−0.188210	+	0.224300i	0.663685	+	0.748012i	$0.268991\pi$
$762$		0			0
$763$	13.1573	−	6.13535i	0.476326	−	0.222115i
$764$	8.99914	+	15.5870i	0.325577	+	0.563917i
$765$		0			0
$766$	−14.5740	+	25.2430i	−0.526582	+	0.912066i
$767$	2.01960	−	23.0841i	0.0729234	−	0.833519i
$768$		0			0
$769$	−16.0619	−	2.83215i	−0.579208	−	0.102130i	−0.123634	−	0.992328i	$-0.539455\pi$
$769$	−16.0619	−	2.83215i	−0.579208	−	0.102130i	−0.455574	+	0.890198i	$0.650566\pi$
$770$	7.48918	+	17.5645i	0.269891	+	0.632979i
$771$		0			0
$772$	−17.7281	−	1.55101i	−0.638048	−	0.0558220i
$773$	−11.4302	+	3.06271i	−0.411116	+	0.110158i	−0.458448	−	0.888721i	$-0.651595\pi$
$773$	−11.4302	+	3.06271i	−0.411116	+	0.110158i	0.0473325	+	0.998879i	$0.484928\pi$
$774$		0			0
$775$	16.9486	−	1.83675i	0.608811	−	0.0659781i
$776$	0.664599	−	1.82597i	0.0238577	−	0.0655485i
$777$		0			0
$778$	−25.3711	+	2.21968i	−0.909598	+	0.0795795i
$779$	−3.25195	+	1.18361i	−0.116513	+	0.0424073i
$780$		0			0
$781$	−4.55583	−	25.8374i	−0.163020	−	0.924534i
$782$	−23.2222	+	23.2222i	−0.830425	+	0.830425i
$783$		0			0
$784$		−	18.8287i		−	0.672455i
$785$	15.1782	+	0.505485i	0.541733	+	0.0180415i
$786$		0			0
$787$	−43.1572	−	20.1245i	−1.53839	−	0.717361i	−0.545689	−	0.837988i	$-0.683732\pi$
$787$	−43.1572	−	20.1245i	−1.53839	−	0.717361i	−0.992698	+	0.120627i	$0.961510\pi$
$788$	−0.359985	−	4.11465i	−0.0128240	−	0.146578i
$789$		0			0
$790$	−3.48368	+	5.59514i	−0.123944	+	0.199066i
$791$	−19.3145	+	11.1513i	−0.686746	+	0.396493i
$792$		0			0
$793$	7.12394	+	26.5869i	0.252979	+	0.944129i
$794$	−23.2020	+	19.4688i	−0.823409	+	0.690922i
$795$		0			0
$796$	−6.40609	+	36.3307i	−0.227058	+	1.28771i
$797$	−9.48608	−	13.5475i	−0.336014	−	0.479878i	0.615216	−	0.788358i	$-0.289069\pi$
$797$	−9.48608	−	13.5475i	−0.336014	−	0.479878i	−0.951231	+	0.308480i	$0.900180\pi$
$798$		0			0
$799$	−5.96354	−	7.10708i	−0.210975	−	0.251430i
$800$	39.7851	+	6.16964i	1.40662	+	0.218130i
$801$		0			0
$802$	13.6736	−	51.0307i	0.482833	−	1.80196i
$803$	10.1930	+	21.8589i	0.359702	+	0.771383i
$804$		0			0
$805$	−16.4618	−	1.99426i	−0.580202	−	0.0702885i
$806$	−14.4009	−	39.5663i	−0.507252	−	1.39366i
$807$		0			0
$808$	−0.539812	−	0.377980i	−0.0189905	−	0.0132973i
$809$	21.1013			0.741881			0.370941	−	0.928657i	$-0.379035\pi$
$809$	21.1013			0.741881			0.370941	+	0.928657i	$0.379035\pi$
$810$		0			0
$811$	3.03312			0.106507			0.0532537	−	0.998581i	$-0.483041\pi$
$811$	3.03312			0.106507			0.0532537	+	0.998581i	$0.483041\pi$
$812$	5.23879	+	3.66824i	0.183845	+	0.128730i
$813$		0			0
$814$	−23.4693	−	64.4814i	−0.822599	−	2.26007i
$815$	−28.0667	−	35.8043i	−0.983133	−	1.25417i
$816$		0			0
$817$	1.26298	+	2.70847i	0.0441861	+	0.0947574i
$818$	−3.93110	+	14.6711i	−0.137448	+	0.512962i
$819$		0			0
$820$	−3.91811	+	0.211687i	−0.136826	+	0.00739244i
$821$	−7.72326	−	9.20422i	−0.269544	−	0.321230i	0.614246	−	0.789115i	$-0.289460\pi$
$821$	−7.72326	−	9.20422i	−0.269544	−	0.321230i	−0.883789	+	0.467885i	$0.845016\pi$
$822$		0			0
$823$	13.6442	+	19.4859i	0.475607	+	0.679237i	0.983236	−	0.182339i	$-0.0583668\pi$
$823$	13.6442	+	19.4859i	0.475607	+	0.679237i	−0.507629	+	0.861576i	$0.669478\pi$
$824$	0.0816702	−	0.463175i	0.00284512	−	0.0161355i
$825$		0			0
$826$	8.54427	−	7.16949i	0.297293	−	0.249459i
$827$	12.0136	+	44.8353i	0.417753	+	1.55907i	0.779257	+	0.626704i	$0.215597\pi$
$827$	12.0136	+	44.8353i	0.417753	+	1.55907i	−0.361504	+	0.932370i	$0.617737\pi$
$828$		0			0
$829$	−27.8169	+	16.0601i	−0.966123	+	0.557791i	−0.898052	−	0.439889i	$-0.855018\pi$
$829$	−27.8169	+	16.0601i	−0.966123	+	0.557791i	−0.0680706	+	0.997681i	$0.521684\pi$
$830$	17.2479	+	74.1622i	0.598684	+	2.57421i
$831$		0			0
$832$	−4.52390	−	51.7084i	−0.156838	−	1.79267i
$833$	14.1643	+	6.60493i	0.490765	+	0.228847i
$834$		0			0
$835$	0.0351000	−	1.05395i	0.00121468	−	0.0364734i
$836$		−	24.2112i		−	0.837361i
$837$		0			0
$838$	29.5051	−	29.5051i	1.01924	−	1.01924i
$839$	−8.77845	−	49.7851i	−0.303066	−	1.71877i	−0.632472	−	0.774583i	$-0.717960\pi$
$839$	−8.77845	−	49.7851i	−0.303066	−	1.71877i	0.329406	−	0.944188i	$-0.393151\pi$
$840$		0			0
$841$	23.0248	−	8.38035i	0.793959	−	0.288977i
$842$	13.8072	−	1.20798i	0.475829	−	0.0416296i
$843$		0			0
$844$	7.51891	−	20.6580i	0.258812	−	0.711079i
$845$	48.9870	+	24.8605i	1.68520	+	0.855227i
$846$		0			0
$847$	3.70879	−	0.993767i	0.127436	−	0.0341463i
$848$	0.414021	+	0.0362221i	0.0142175	+	0.00124387i
$849$		0			0
$850$	−18.0439	+	26.9385i	−0.618899	+	0.923982i
$851$	58.6858	+	10.3479i	2.01172	+	0.354721i
$852$		0			0
$853$	4.44262	−	50.7794i	0.152112	−	1.73865i	−0.410438	−	0.911889i	$-0.634624\pi$
$853$	4.44262	−	50.7794i	0.152112	−	1.73865i	0.562550	−	0.826763i	$-0.309820\pi$
$854$	−6.62440	+	11.4738i	−0.226682	+	0.392625i
$855$		0			0
$856$	−0.892646	−	1.54611i	−0.0305100	−	0.0528449i
$857$	9.12817	−	4.25654i	0.311812	−	0.145400i	−0.260412	−	0.965498i	$-0.583858\pi$
$857$	9.12817	−	4.25654i	0.311812	−	0.145400i	0.572224	+	0.820097i	$0.306081\pi$
$858$		0			0
$859$	−8.01487	+	9.55175i	−0.273464	+	0.325902i	−0.885245	−	0.465126i	$-0.846009\pi$
$859$	−8.01487	+	9.55175i	−0.273464	+	0.325902i	0.611781	+	0.791027i	$0.290453\pi$
$860$	0.477000	+	3.35470i	0.0162656	+	0.114394i
$861$		0			0
$862$	3.37367	−	4.81810i	0.114908	−	0.164105i
$863$	−23.9621	−	23.9621i	−0.815678	−	0.815678i	0.169800	−	0.985479i	$-0.445688\pi$
$863$	−23.9621	−	23.9621i	−0.815678	−	0.815678i	−0.985479	+	0.169800i	$0.945688\pi$
$864$		0			0
$865$	8.50730	−	40.3441i	0.289257	−	1.37174i
$866$	−8.46774	+	1.49309i	−0.287745	+	0.0507373i
$867$		0			0
$868$	4.34538	−	9.31869i	0.147492	−	0.316297i
$869$	−3.24378	−	2.72185i	−0.110038	−	0.0923326i
$870$		0			0
$871$	−25.6857	−	9.34885i	−0.870328	−	0.316774i
$872$	−1.14779	−	0.307549i	−0.0388690	−	0.0104149i
$873$		0			0
$874$	35.8915	+	20.7220i	1.21405	+	0.700932i
$875$	−16.3255	+	1.22113i	−0.551901	+	0.0412816i
$876$		0			0
$877$	38.4629	−	26.9320i	1.29880	−	0.909430i	0.299794	−	0.954004i	$-0.403082\pi$
$877$	38.4629	−	26.9320i	1.29880	−	0.909430i	0.999006	+	0.0445739i	$0.0141930\pi$
$878$	6.18293	−	4.32933i	0.208664	−	0.146108i
$879$		0			0
$880$	−7.29851	+	24.0110i	−0.246033	+	0.809412i
$881$	−20.2756	−	11.7061i	−0.683103	−	0.394390i	0.117920	−	0.993023i	$-0.462377\pi$
$881$	−20.2756	−	11.7061i	−0.683103	−	0.394390i	−0.801023	+	0.598633i	$0.795711\pi$
$882$		0			0
$883$	6.11319	+	1.63802i	0.205725	+	0.0551239i	0.360210	−	0.932871i	$-0.382705\pi$
$883$	6.11319	+	1.63802i	0.205725	+	0.0551239i	−0.154485	+	0.987995i	$0.549372\pi$
$884$	38.1768	+	13.8952i	1.28402	+	0.467347i
$885$		0			0
$886$	−43.1969	−	36.2465i	−1.45123	−	1.21773i
$887$	13.8426	−	29.6855i	0.464788	−	0.996741i	−0.524587	−	0.851357i	$-0.675780\pi$
$887$	13.8426	−	29.6855i	0.464788	−	0.996741i	0.989375	−	0.145384i	$-0.0464419\pi$
$888$		0			0
$889$	14.3756	−	2.53481i	0.482144	−	0.0850149i
$890$	26.8974	+	5.67182i	0.901604	+	0.190120i
$891$		0			0
$892$	17.4021	+	17.4021i	0.582665	+	0.582665i
$893$	−6.71538	+	9.59056i	−0.224722	+	0.320936i
$894$		0			0
$895$	−14.1535	−	10.6296i	−0.473099	−	0.355309i
$896$	0.902060	−	1.07503i	0.0301357	−	0.0359143i
$897$		0			0
$898$	17.4298	−	8.12765i	0.581640	−	0.271223i
$899$	3.61538	+	6.26203i	0.120580	+	0.208850i
$900$		0			0
$901$	−0.172483	+	0.298750i	−0.00574625	+	0.00995280i
$902$	0.433074	−	4.95006i	0.0144198	−	0.164819i
$903$		0			0
$904$	1.79776	+	0.316994i	0.0597926	+	0.0105430i
$905$	40.5666	−	17.2969i	1.34848	−	0.574968i
$906$		0			0
$907$	28.5313	+	2.49616i	0.947365	+	0.0828837i	0.550355	−	0.834931i	$-0.314492\pi$
$907$	28.5313	+	2.49616i	0.947365	+	0.0828837i	0.397010	+	0.917814i	$0.370048\pi$
$908$	−2.30189	+	0.616790i	−0.0763910	+	0.0204689i
$909$		0			0
$910$	12.5569	+	38.4349i	0.416258	+	1.27410i
$911$	6.61616	−	18.1777i	0.219203	−	0.602255i	−0.780536	−	0.625111i	$-0.785054\pi$
$911$	6.61616	−	18.1777i	0.219203	−	0.602255i	0.999739	+	0.0228557i	$0.00727584\pi$
$912$		0			0
$913$	−48.7315	+	4.26345i	−1.61278	+	0.141100i
$914$	−67.0891	+	24.4184i	−2.21911	+	0.807690i
$915$		0			0
$916$	−3.13228	−	17.7641i	−0.103493	−	0.586941i
$917$	11.6282	−	11.6282i	0.383996	−	0.383996i
$918$		0			0
$919$			44.6775i			1.47377i	0.676016	+	0.736887i	$0.263705\pi$
$919$			44.6775i			1.47377i	−0.676016	+	0.736887i	$0.736295\pi$
$920$	0.927260	+	0.991149i	0.0305708	+	0.0326772i
$921$		0			0
$922$	45.2591	+	21.1047i	1.49053	+	0.695046i
$923$	−4.84210	−	55.3454i	−0.159380	−	1.82172i
$924$		0			0
$925$	58.8200	−	1.21683i	1.93399	−	0.0400092i
$926$	9.44552	−	5.45337i	0.310399	−	0.179209i
$927$		0			0
$928$	4.41970	+	16.4946i	0.145084	+	0.541461i
$929$	−40.3230	+	33.8350i	−1.32296	+	1.11009i	−0.337286	+	0.941402i	$0.609509\pi$
$929$	−40.3230	+	33.8350i	−1.32296	+	1.11009i	−0.985669	+	0.168689i	$0.946047\pi$
$930$		0			0
$931$	3.42478	−	19.4229i	0.112243	−	0.636560i
$932$	19.3288	+	27.6044i	0.633137	+	0.904213i
$933$		0			0
$934$	53.0403	+	63.2110i	1.73553	+	2.06833i
$935$	−15.5026	−	13.9133i	−0.506988	−	0.455013i
$936$		0			0
$937$	3.71263	−	13.8557i	0.121286	−	0.452647i	−0.878394	−	0.477938i	$-0.841384\pi$
$937$	3.71263	−	13.8557i	0.121286	−	0.452647i	0.999680	+	0.0252908i	$0.00805116\pi$
$938$	−5.56041	−	11.9243i	−0.181554	−	0.389343i
$939$		0			0
$940$	−10.4475	+	8.18973i	−0.340761	+	0.267119i
$941$	0.0906224	+	0.248983i	0.00295420	+	0.00811661i	0.941161	−	0.337959i	$-0.109736\pi$
$941$	0.0906224	+	0.248983i	0.00295420	+	0.00811661i	−0.938207	+	0.346075i	$0.887514\pi$
$942$		0			0
$943$	3.53479	+	2.47509i	0.115109	+	0.0806000i
$944$	14.6593			0.477121
$945$		0			0
$946$	−4.29098			−0.139512
$947$	27.9252	+	19.5534i	0.907446	+	0.635401i	0.931276	−	0.364315i	$-0.118697\pi$
$947$	27.9252	+	19.5534i	0.907446	+	0.635401i	−0.0238294	+	0.999716i	$0.507586\pi$
$948$		0			0
$949$	17.4680	+	47.9930i	0.567037	+	1.55792i
$950$	38.7301	+	13.1960i	1.25657	+	0.428135i
$951$		0			0
$952$	0.238709	+	0.511912i	0.00773659	+	0.0165912i
$953$	−6.91874	+	25.8211i	−0.224120	+	0.836427i	0.758635	+	0.651516i	$0.225867\pi$
$953$	−6.91874	+	25.8211i	−0.224120	+	0.836427i	−0.982755	+	0.184912i	$0.940800\pi$
$954$		0			0
$955$	−1.05425	−	19.5130i	−0.0341146	−	0.631426i
$956$	11.3705	+	13.5509i	0.367749	+	0.438266i
$957$		0			0
$958$	−31.9305	−	45.6014i	−1.03163	−	1.47331i
$959$	4.99834	−	28.3470i	0.161405	−	0.915372i
$960$		0			0
$961$	−14.8420	+	12.4539i	−0.478775	+	0.401740i
$962$	−37.6084	−	140.356i	−1.21254	−	4.52528i
$963$		0			0
$964$	−3.68603	+	2.12813i	−0.118719	+	0.0685425i
$965$	16.4022	+	10.2124i	0.528006	+	0.328750i
$966$		0			0
$967$	−1.77416	−	20.2788i	−0.0570532	−	0.652121i	−0.969849	−	0.243706i	$-0.921637\pi$
$967$	−1.77416	−	20.2788i	−0.0570532	−	0.652121i	0.912796	−	0.408416i	$-0.133919\pi$
$968$	−0.284833	−	0.132820i	−0.00915488	−	0.00426899i
$969$		0			0
$970$	−53.3399	+	49.9016i	−1.71264	+	1.60224i
$971$			40.5268i			1.30057i	0.759692	+	0.650284i	$0.225350\pi$
$971$			40.5268i			1.30057i	−0.759692	+	0.650284i	$0.774650\pi$
$972$		0			0
$973$	−1.53972	+	1.53972i	−0.0493610	+	0.0493610i
$974$	−14.0086	−	79.4468i	−0.448865	−	2.54564i
$975$		0			0
$976$	−16.3627	+	5.95554i	−0.523758	+	0.190632i
$977$	35.4680	−	3.10305i	1.13472	−	0.0992752i	0.495721	−	0.868482i	$-0.334904\pi$
$977$	35.4680	−	3.10305i	1.13472	−	0.0992752i	0.639000	+	0.769207i	$0.279348\pi$
$978$		0			0
$979$	−6.04024	+	16.5954i	−0.193047	+	0.530392i
$980$	10.1200	−	19.9412i	0.323272	−	0.636999i
$981$		0			0
$982$	46.7049	−	12.5145i	1.49041	−	0.399355i
$983$	−36.5814	−	3.20046i	−1.16677	−	0.102079i	−0.512735	−	0.858547i	$-0.671368\pi$
$983$	−36.5814	−	3.20046i	−1.16677	−	0.102079i	−0.654030	+	0.756468i	$0.726923\pi$
$984$		0			0
$985$	−1.67321	+	4.16068i	−0.0533128	+	0.132570i
$986$	−13.5432	−	2.38804i	−0.431305	−	0.0760507i
$987$		0			0
$988$	4.46840	−	51.0740i	0.142159	−	1.62488i
$989$	1.86320	−	3.22716i	0.0592464	−	0.102618i
$990$		0			0
$991$	6.40763	+	11.0983i	0.203545	+	0.352550i	0.949668	−	0.313258i	$-0.101420\pi$
$991$	6.40763	+	11.0983i	0.203545	+	0.352550i	−0.746123	+	0.665808i	$0.768087\pi$
$992$	24.8820	−	11.6027i	0.790005	−	0.368385i
$993$		0			0
$994$	17.1893	−	20.4854i	0.545210	−	0.649756i
$995$	24.0536	−	32.0277i	0.762549	−	1.01535i
$996$		0			0
$997$	31.6947	−	45.2647i	1.00378	−	1.43355i	0.105349	−	0.994435i	$-0.466404\pi$
$997$	31.6947	−	45.2647i	1.00378	−	1.43355i	0.898432	−	0.439113i	$-0.144707\pi$
$998$	44.9938	+	44.9938i	1.42425	+	1.42425i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	405.2.r.a.152.3		192
3.2	odd	2		135.2.q.a.122.14	yes	192
5.3	odd	4	inner	405.2.r.a.233.3		192
15.2	even	4		675.2.ba.b.68.3		192
15.8	even	4		135.2.q.a.68.14	yes	192
15.14	odd	2		675.2.ba.b.257.3		192
27.2	odd	18	inner	405.2.r.a.332.3		192
27.25	even	9		135.2.q.a.2.14	✓	192
135.52	odd	36		675.2.ba.b.218.3		192
135.79	even	18		675.2.ba.b.407.3		192
135.83	even	36	inner	405.2.r.a.8.3		192
135.133	odd	36		135.2.q.a.83.14	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.14	✓	192	27.25	even	9
135.2.q.a.68.14	yes	192	15.8	even	4
135.2.q.a.83.14	yes	192	135.133	odd	36
135.2.q.a.122.14	yes	192	3.2	odd	2
405.2.r.a.8.3		192	135.83	even	36	inner
405.2.r.a.152.3		192	1.1	even	1	trivial
405.2.r.a.233.3		192	5.3	odd	4	inner
405.2.r.a.332.3		192	27.2	odd	18	inner
675.2.ba.b.68.3		192	15.2	even	4
675.2.ba.b.218.3		192	135.52	odd	36
675.2.ba.b.257.3		192	15.14	odd	2
675.2.ba.b.407.3		192	135.79	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 405 = 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	405.r (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.65044 - 1.15565i) q^{2} +(0.704386 + 1.93528i) q^{4} +(0.268922 - 2.21984i) q^{5} +(0.618828 + 1.32708i) q^{7} +(0.0310202 - 0.115769i) q^{8} +(-3.00920 + 3.35293i) q^{10} +(-1.86051 - 2.21727i) q^{11} +(-3.51558 - 5.02076i) q^{13} +(0.512304 - 2.90542i) q^{14} +(2.97033 - 2.49240i) q^{16} +(0.833002 + 3.10881i) q^{17} +(3.51741 - 2.03078i) q^{19} +(4.48544 - 1.04318i) q^{20} +(0.508272 + 5.80958i) q^{22} +(-4.58997 - 2.14034i) q^{23} +(-4.85536 - 1.19393i) q^{25} +12.3493i q^{26} +(-2.13239 + 2.13239i) q^{28} +(-0.368261 - 2.08851i) q^{29} +(-3.20394 + 1.16614i) q^{31} +(-8.02150 + 0.701790i) q^{32} +(2.21787 - 6.09356i) q^{34} +(3.11232 - 1.01682i) q^{35} +(-11.3656 + 3.04540i) q^{37} +(-8.15214 - 0.713220i) q^{38} +(-0.248646 - 0.0999926i) q^{40} +(-0.839107 - 0.147957i) q^{41} +(-0.0641287 + 0.732994i) q^{43} +(2.98053 - 5.16243i) q^{44} +(5.10199 + 8.83690i) q^{46} +(-2.61254 + 1.21825i) q^{47} +(3.12132 - 3.71984i) q^{49} +(6.63372 + 7.58161i) q^{50} +(7.24028 - 10.3402i) q^{52} +(0.0757900 + 0.0757900i) q^{53} +(-5.42232 + 3.53376i) q^{55} +(0.172831 - 0.0304748i) q^{56} +(-1.80580 + 3.87255i) q^{58} +(2.89613 + 2.43014i) q^{59} +(-4.21993 - 1.53593i) q^{61} +(6.63556 + 1.77799i) q^{62} +(7.33402 + 4.23430i) q^{64} +(-12.0907 + 6.45381i) q^{65} +(3.65313 - 2.55795i) q^{67} +(-5.42967 + 3.80189i) q^{68} +(-6.31179 - 1.91856i) q^{70} +(7.84988 + 4.53213i) q^{71} +(-8.04880 - 2.15667i) q^{73} +(22.2777 + 8.10840i) q^{74} +(6.40774 + 5.37673i) q^{76} +(1.79116 - 3.84116i) q^{77} +(1.44073 - 0.254040i) q^{79} +(-4.73394 - 7.26391i) q^{80} +(1.21391 + 1.21391i) q^{82} +(9.69375 - 13.8441i) q^{83} +(7.12506 - 1.01310i) q^{85} +(0.952926 - 1.13565i) q^{86} +(-0.314404 + 0.146609i) q^{88} +(-3.05075 - 5.28406i) q^{89} +(4.48742 - 7.77244i) q^{91} +(0.909052 - 10.3905i) q^{92} +(5.71971 + 1.00854i) q^{94} +(-3.56209 - 8.35420i) q^{95} +(16.1512 + 1.41304i) q^{97} +(-9.45039 + 2.53222i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

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