LMFDB - Embedded newform 405.2.r.a.8.3

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			8.3
Character	$\chi$	$=$	405.8
Dual form			405.2.r.a.152.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{18}\right)$

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	−0.986072	−	0.166320i	$-0.946811\pi$
$2$	−1.65044	+	1.15565i	−1.16704	+	0.817169i	−0.180966	+	0.983489i	$0.557923\pi$
$3$		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	−0.753969	−	0.656910i	$-0.771863\pi$
$7$	0.618828	−	1.32708i	0.233895	−	0.501590i	0.987864	+	0.155320i	$0.0496410\pi$
$8$	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	−0.969751	−	0.244098i	$-0.921508\pi$
$11$	−1.86051	+	2.21727i	−0.560965	+	0.668532i	0.408785	+	0.912631i	$0.365953\pi$
$12$		0			0
$13$	−3.51558	+	5.02076i	−0.975045	+	1.39251i	−0.0559675	+	0.998433i	$0.517824\pi$
$13$	−3.51558	+	5.02076i	−0.975045	+	1.39251i	−0.919078	+	0.394076i	$0.871065\pi$
$14$	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	−0.788301	−	0.615290i	$-0.789039\pi$
$17$	0.833002	−	3.10881i	0.202033	−	0.753996i	0.990334	−	0.138706i	$-0.0442944\pi$
$18$		0			0
$19$	3.51741	+	2.03078i	0.806949	+	0.465892i	0.845895	−	0.533349i	$-0.179067\pi$
$19$	3.51741	+	2.03078i	0.806949	+	0.465892i	−0.0389464	+	0.999241i	$0.512400\pi$
$20$	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	−0.837441	−	0.546527i	$-0.815949\pi$
$23$	−4.58997	+	2.14034i	−0.957074	+	0.446291i	−0.119633	+	0.992818i	$0.538172\pi$
$24$		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	0.931336	+	0.364162i	$0.118645\pi$
$29$	−0.368261	+	2.08851i	−0.0683844	+	0.387827i	−0.999720	+	0.0236650i	$0.992466\pi$
$30$		0			0
$31$	−3.20394	−	1.16614i	−0.575445	−	0.209445i	0.0378710	−	0.999283i	$-0.487942\pi$
$31$	−3.20394	−	1.16614i	−0.575445	−	0.209445i	−0.613316	+	0.789838i	$0.710165\pi$
$32$	−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	−0.999988	−	0.00497757i	$-0.998416\pi$
$37$	−11.3656	−	3.04540i	−1.86849	−	0.500661i	−0.868503	−	0.495683i	$-0.834918\pi$
$38$	−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	−0.238787	−	0.971072i	$-0.576750\pi$
$41$	−0.839107	+	0.147957i	−0.131046	+	0.0231070i	0.107740	+	0.994179i	$0.465639\pi$
$42$		0			0
$43$	−0.0641287	−	0.732994i	−0.00977953	−	0.111781i	0.989736	−	0.142909i	$-0.0456455\pi$
$43$	−0.0641287	−	0.732994i	−0.00977953	−	0.111781i	−0.999515	+	0.0311282i	$0.990090\pi$
$44$	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	0.222634	−	0.974902i	$-0.428535\pi$
$47$	−2.61254	−	1.21825i	−0.381078	−	0.177700i	−0.603712	+	0.797203i	$0.706312\pi$
$48$		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	−0.701882	−	0.712293i	$-0.747657\pi$
$53$	0.0757900	−	0.0757900i	0.0104106	−	0.0104106i	0.712293	+	0.701882i	$0.247657\pi$
$54$		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	−0.434497	−	0.900673i	$-0.643074\pi$
$59$	2.89613	−	2.43014i	0.377044	−	0.316377i	0.811540	+	0.584296i	$0.198629\pi$
$60$		0			0
$61$	−4.21993	+	1.53593i	−0.540306	+	0.196655i	−0.597734	−	0.801694i	$-0.703932\pi$
$61$	−4.21993	+	1.53593i	−0.540306	+	0.196655i	0.0574282	+	0.998350i	$0.481710\pi$
$62$	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	0.775034	−	0.631919i	$-0.217733\pi$
$67$	3.65313	+	2.55795i	0.446301	+	0.312504i	−0.328733	+	0.944423i	$0.606622\pi$
$68$	−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	0.0442890	−	0.999019i	$-0.485898\pi$
$71$	7.84988	−	4.53213i	0.931609	−	0.537865i	0.887320	+	0.461154i	$0.152564\pi$
$72$		0			0
$73$	−8.04880	+	2.15667i	−0.942041	+	0.252419i	−0.696982	−	0.717089i	$-0.745474\pi$
$73$	−8.04880	+	2.15667i	−0.942041	+	0.252419i	−0.245059	+	0.969508i	$0.578807\pi$
$74$	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	0.254107	−	0.967176i	$-0.418219\pi$
$79$	1.44073	+	0.254040i	0.162095	+	0.0285818i	−0.0920115	+	0.995758i	$0.529330\pi$
$80$	−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	0.838155	+	0.545431i	$0.183634\pi$
$83$	9.69375	+	13.8441i	1.06403	+	1.51959i	0.225872	+	0.974157i	$0.427477\pi$
$84$		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	−0.981183	−	0.193080i	$-0.938152\pi$
$89$	−3.05075	+	5.28406i	−0.323379	+	0.560109i	0.657804	+	0.753189i	$0.271486\pi$
$90$		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	0.770453	−	0.637496i	$-0.220030\pi$
$97$	16.1512	−	1.41304i	1.63990	−	0.143473i	0.869449	+	0.494023i	$0.164474\pi$
$98$	−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	0.997410	−	0.0719204i	$-0.0229128\pi$
$101$	1.88053	+	5.16673i	0.187120	+	0.514108i	−0.810290	+	0.586029i	$0.800691\pi$
$102$		0			0
$103$	3.90922	+	0.342012i	0.385186	+	0.0336994i	0.278105	−	0.960551i	$-0.410294\pi$
$103$	3.90922	+	0.342012i	0.385186	+	0.0336994i	0.107082	+	0.994250i	$0.465849\pi$
$104$	−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	0.999830	+	0.0184189i	$0.00586325\pi$
$107$	10.5329	+	10.5329i	1.01825	+	1.01825i	0.0184189	+	0.999830i	$0.494137\pi$
$108$		0			0
$109$			9.91447i			0.949634i	0.880085	+	0.474817i	$0.157486\pi$
$109$			9.91447i			0.949634i	−0.880085	+	0.474817i	$0.842514\pi$
$110$	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	−0.632583	−	0.774492i	$-0.718005\pi$
$113$	1.32748	−	15.1732i	0.124879	−	1.42737i	0.757462	−	0.652879i	$-0.226439\pi$
$114$		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	0.980782	+	0.195109i	$0.0625059\pi$
$127$	2.58018	+	9.62937i	0.228954	+	0.854468i	−0.751828	+	0.659360i	$0.770827\pi$
$128$	−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	0.651028	+	0.759054i	$0.274338\pi$
$131$	−3.84111	+	10.5534i	−0.335599	+	0.922051i	−0.986627	+	0.162997i	$0.947884\pi$
$132$		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	−0.376424	+	0.926448i	$0.622846\pi$
$137$	−16.1027	+	11.2752i	−1.37574	+	0.963306i	−0.999320	+	0.0368588i	$0.988265\pi$
$138$		0			0
$139$	0.508611	−	1.39740i	0.0431398	−	0.118526i	−0.916252	−	0.400602i	$-0.868801\pi$
$139$	0.508611	−	1.39740i	0.0431398	−	0.118526i	0.959392	+	0.282076i	$0.0910232\pi$
$140$	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	−0.999545	−	0.0301644i	$-0.990397\pi$
$149$	−0.861743	−	4.88719i	−0.0705968	−	0.400374i	0.928948	−	0.370210i	$-0.120714\pi$
$150$		0			0
$151$	−15.8833	−	13.3277i	−1.29257	−	1.08459i	−0.991379	−	0.131025i	$-0.958173\pi$
$151$	−15.8833	−	13.3277i	−1.29257	−	1.08459i	−0.301186	−	0.953565i	$-0.597383\pi$
$152$	−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	−0.935291	−	0.353879i	$-0.884862\pi$
$157$	0.591932	−	6.76582i	0.0472413	−	0.539971i	0.982532	−	0.186092i	$-0.0595821\pi$
$158$	−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	0.990689	+	0.136142i	$0.0434702\pi$
$163$	14.3864	+	14.3864i	1.12683	+	1.12683i	0.136142	+	0.990689i	$0.456530\pi$
$164$	−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	0.105319	−	0.994439i	$-0.466414\pi$
$167$	0.469806	+	0.0411027i	0.0363547	+	0.00318063i	−0.0689639	+	0.997619i	$0.521969\pi$
$168$		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	0.636125	−	0.771586i	$-0.280536\pi$
$173$	18.3690	−	1.60708i	1.39657	−	0.122184i	0.760446	+	0.649402i	$0.224981\pi$
$174$		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	0.975178	−	0.221422i	$-0.0710697\pi$
$179$	3.95796	+	6.85540i	0.295832	+	0.512396i	−0.679346	+	0.733818i	$0.737736\pi$
$180$		0			0
$181$	9.86110	−	17.0799i	0.732970	−	1.26954i	−0.222638	−	0.974901i	$-0.571467\pi$
$181$	9.86110	−	17.0799i	0.732970	−	1.26954i	0.955608	−	0.294640i	$-0.0951998\pi$
$182$	−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	0.476110	−	0.879386i	$-0.342046\pi$
$191$	8.60644	+	1.51755i	0.622740	+	0.109806i	0.146630	+	0.989191i	$0.453157\pi$
$192$		0			0
$193$	−3.65180	−	7.83132i	−0.262863	−	0.563711i	0.729935	−	0.683517i	$-0.239550\pi$
$193$	−3.65180	−	7.83132i	−0.262863	−	0.563711i	−0.992797	+	0.119806i	$0.961773\pi$
$194$	−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	−0.327167	−	0.944966i	$-0.606094\pi$
$197$	−1.93720	+	0.519071i	−0.138020	+	0.0369822i	0.189148	+	0.981949i	$0.439427\pi$
$198$		0			0
$199$	15.5130	−	8.95641i	1.09968	−	0.634903i	0.163546	−	0.986536i	$-0.447707\pi$
$199$	15.5130	−	8.95641i	1.09968	−	0.634903i	0.936138	+	0.351633i	$0.114373\pi$
$200$	−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	−0.879293	−	0.476282i	$-0.841984\pi$
$211$	−8.17709	+	6.86139i	−0.562934	+	0.472358i	0.316359	+	0.948640i	$0.397540\pi$
$212$	−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	0.749936	−	0.661511i	$-0.230084\pi$
$223$	10.8301	+	5.05016i	0.725238	+	0.338184i	−0.0246975	+	0.999695i	$0.507862\pi$
$224$	−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	0.992113	−	0.125346i	$-0.0400041\pi$
$227$	−0.100851	−	1.15273i	−0.00669369	−	0.0765092i	−0.998807	+	0.0488368i	$0.984449\pi$
$228$		0			0
$229$	−8.62548	+	1.52090i	−0.569988	+	0.100504i	−0.451212	−	0.892417i	$-0.649008\pi$
$229$	−8.62548	+	1.52090i	−0.569988	+	0.100504i	−0.118776	+	0.992921i	$0.537897\pi$
$230$	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	0.736219	−	0.676743i	$-0.236609\pi$
$233$	15.8052	+	4.23498i	1.03543	+	0.277443i	0.299213	+	0.954186i	$0.403276\pi$
$234$		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	0.589601	−	0.807695i	$-0.299285\pi$
$239$	8.07123	+	2.93769i	0.522085	+	0.190023i	−0.0675160	+	0.997718i	$0.521507\pi$
$240$		0			0
$241$	0.358872	−	2.03527i	0.0231170	−	0.131103i	−0.971065	−	0.238815i	$-0.923241\pi$
$241$	0.358872	−	2.03527i	0.0231170	−	0.131103i	0.994182	+	0.107712i	$0.0343523\pi$
$242$	−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	0.167204	−	0.985922i	$-0.446526\pi$
$251$	−9.55376	−	5.51587i	−0.603028	−	0.348158i	−0.770232	+	0.637764i	$0.779860\pi$
$252$		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	−0.702439	−	0.711744i	$-0.747906\pi$
$257$	3.31253	−	4.73079i	0.206630	−	0.295098i	0.909069	+	0.416646i	$0.136794\pi$
$258$		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	0.504993	+	0.863123i	$0.331495\pi$
$263$	−7.79728	+	16.7213i	−0.480801	+	1.03108i	−0.985794	+	0.167958i	$0.946283\pi$
$264$		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	−0.609120	−	0.793078i	$-0.708477\pi$
$277$	6.49002	−	13.9179i	0.389947	−	0.836245i	0.999068	−	0.0431672i	$-0.0137448\pi$
$278$	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	−0.889168	−	0.457580i	$-0.848716\pi$
$281$	−4.76302	+	5.67634i	−0.284138	+	0.338622i	0.605031	+	0.796202i	$0.293161\pi$
$282$		0			0
$283$	8.24647	−	11.7772i	0.490202	−	0.700081i	−0.495495	−	0.868611i	$-0.665013\pi$
$283$	8.24647	−	11.7772i	0.490202	−	0.700081i	0.985696	+	0.168530i	$0.0539021\pi$
$284$	−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	−0.874985	−	0.484150i	$-0.839129\pi$
$293$	−18.2561	+	8.51297i	−1.06653	+	0.497333i	−0.191549	+	0.981483i	$0.561351\pi$
$294$		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	0.572684	−	0.819776i	$-0.305902\pi$
$307$	11.5423	+	3.09276i	0.658756	+	0.176513i	0.0860714	+	0.996289i	$0.472569\pi$
$308$	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	−0.240843	−	0.970564i	$-0.577424\pi$
$311$	−2.38442	+	0.420438i	−0.135208	+	0.0238408i	0.105634	+	0.994405i	$0.466313\pi$
$312$		0			0
$313$	1.06842	+	12.2121i	0.0603905	+	0.690267i	0.964693	+	0.263375i	$0.0848358\pi$
$313$	1.06842	+	12.2121i	0.0603905	+	0.690267i	−0.904303	+	0.426891i	$0.859609\pi$
$314$	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	−0.251566	−	0.967840i	$-0.580945\pi$
$317$	−20.5585	−	9.58656i	−1.15468	−	0.538435i	−0.903112	+	0.429405i	$0.858723\pi$
$318$		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	0.115706	−	0.993284i	$-0.463087\pi$
$331$	15.3336	−	5.58098i	0.842812	−	0.306758i	0.727106	+	0.686525i	$0.240865\pi$
$332$	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	0.480669	−	0.876902i	$-0.340394\pi$
$337$	−3.28511	−	2.30026i	−0.178951	−	0.125303i	−0.659620	+	0.751599i	$0.729283\pi$
$338$	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	0.995326	−	0.0965722i	$-0.0307879\pi$
$347$	5.24496	+	11.2479i	0.281564	+	0.603816i	−0.713762	+	0.700389i	$0.753010\pi$
$348$		0			0
$349$	−7.52479	−	1.32682i	−0.402793	−	0.0710232i	−0.0314181	−	0.999506i	$-0.510002\pi$
$349$	−7.52479	−	1.32682i	−0.402793	−	0.0710232i	−0.371375	+	0.928483i	$0.621113\pi$
$350$	−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	0.446904	−	0.894582i	$-0.352527\pi$
$353$	−10.2693	−	14.6661i	−0.546579	−	0.780595i	−0.993482	+	0.113987i	$0.963638\pi$
$354$		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	−0.982642	−	0.185510i	$-0.940606\pi$
$359$	−6.26521	+	10.8517i	−0.330665	+	0.572729i	0.651977	+	0.758239i	$0.273940\pi$
$360$		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	−0.437280	−	0.899325i	$-0.644058\pi$
$367$	−13.6352	+	1.19292i	−0.711750	+	0.0622701i	−0.274470	+	0.961596i	$0.588503\pi$
$368$	−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	−0.229478	−	0.973314i	$-0.573702\pi$
$373$	−12.0608	−	1.05518i	−0.624485	−	0.0546353i	−0.395006	+	0.918678i	$0.629258\pi$
$374$	−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	$0.196331\pi$
$379$			22.5213i			1.15684i	−0.815738	+	0.578421i	$0.803669\pi$
$380$	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	0.893437	+	0.449189i	$0.148287\pi$
$383$	−1.26087	+	14.4118i	−0.0644275	+	0.736410i	−0.957864	+	0.287221i	$0.907269\pi$
$384$		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	0.854367	−	0.519670i	$-0.173945\pi$
$389$	9.68308	+	8.12507i	0.490951	+	0.411957i	−0.363416	+	0.931627i	$0.618390\pi$
$390$		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	0.992197	+	0.124684i	$0.0397916\pi$
$397$	3.89075	+	14.5205i	0.195271	+	0.728761i	−0.796926	+	0.604077i	$0.793542\pi$
$398$	−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	−0.486369	−	0.873754i	$-0.661679\pi$
$401$	8.96818	−	24.6399i	0.447849	−	1.23046i	0.934218	−	0.356703i	$-0.116099\pi$
$402$		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	−0.986972	−	0.160891i	$-0.948563\pi$
$409$	−2.57831	+	7.08384i	−0.127489	+	0.350273i	0.859483	+	0.511164i	$0.170786\pi$
$410$	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	−0.937348	−	0.348394i	$-0.886727\pi$
$419$	−3.59622	−	20.3952i	−0.175687	−	0.996370i	0.761661	−	0.647975i	$-0.224384\pi$
$420$		0			0
$421$	−5.26964	−	4.42176i	−0.256827	−	0.215503i	0.505279	−	0.862956i	$-0.331390\pi$
$421$	−5.26964	−	4.42176i	−0.256827	−	0.215503i	−0.762105	+	0.647453i	$0.775834\pi$
$422$	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	$-0.977602\pi$
$431$		−	2.91928i		−	0.140617i	0.997525	−	0.0703084i	$-0.0223983\pi$
$432$		0			0
$433$	3.01763	+	3.01763i	0.145018	+	0.145018i	0.775888	−	0.630870i	$-0.217302\pi$
$433$	3.01763	+	3.01763i	0.145018	+	0.145018i	−0.630870	+	0.775888i	$0.717302\pi$
$434$	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	0.905354	−	0.424658i	$-0.139606\pi$
$439$	−1.28129	−	3.52030i	−0.0611524	−	0.168015i	−0.966506	+	0.256643i	$0.917383\pi$
$440$	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	0.597229	−	0.802070i	$-0.296268\pi$
$443$	27.8809	−	2.43927i	1.32466	−	0.115893i	0.727434	+	0.686177i	$0.240713\pi$
$444$		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	0.731158	−	0.682208i	$-0.238980\pi$
$449$	−4.77256	−	8.26631i	−0.225231	−	0.390111i	−0.956389	+	0.292097i	$0.905647\pi$
$450$		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	0.933741	+	0.357949i	$0.116524\pi$
$457$	20.3246	+	29.0265i	0.950745	+	1.35780i	0.0170039	+	0.999855i	$0.494587\pi$
$458$	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	−0.426612	−	0.904435i	$-0.640293\pi$
$461$	−24.4088	−	4.30393i	−1.13683	−	0.200454i	−0.710219	+	0.703981i	$0.751404\pi$
$462$		0			0
$463$	−2.28775	−	4.90609i	−0.106321	−	0.228005i	0.845949	−	0.533264i	$-0.179035\pi$
$463$	−2.28775	−	4.90609i	−0.106321	−	0.228005i	−0.952269	+	0.305259i	$0.901257\pi$
$464$	−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	−0.997989	−	0.0633888i	$-0.979809\pi$
$467$	−39.5591	+	10.5998i	−1.83058	+	0.490502i	−0.832589	+	0.553891i	$0.813143\pi$
$468$		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	0.327880	−	0.944719i	$-0.393666\pi$
$479$	25.9636	−	9.44996i	1.18631	−	0.431780i	0.858425	+	0.512940i	$0.171444\pi$
$480$		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	0.343969	−	0.938981i	$-0.388228\pi$
$487$	28.3122	−	28.3122i	1.28295	−	1.28295i	0.938981	−	0.343969i	$-0.111772\pi$
$488$	−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	0.295925	−	0.955211i	$-0.404372\pi$
$491$	−15.4259	−	18.3839i	−0.696161	−	0.829652i	−0.992086	+	0.125559i	$0.959928\pi$
$492$		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	−0.818976	−	0.573828i	$-0.805458\pi$
$499$	−31.1017	+	5.48406i	−1.39230	+	0.245500i	−0.573325	+	0.819328i	$0.694347\pi$
$500$	−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	0.319058	−	0.947735i	$-0.396634\pi$
$503$	2.72503	+	0.730168i	0.121503	+	0.0325566i	−0.197555	+	0.980292i	$0.563300\pi$
$504$		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	−0.161861	−	0.986814i	$-0.551750\pi$
$509$	−20.7599	−	7.55598i	−0.920166	−	0.334913i	−0.758304	+	0.651901i	$0.773972\pi$
$510$		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	0.657638	−	0.753334i	$-0.271556\pi$
$521$	7.62484	+	4.40220i	0.334050	+	0.192864i	−0.323588	+	0.946198i	$0.604889\pi$
$522$		0			0
$523$	−0.332937	+	1.24254i	−0.0145583	+	0.0543324i	−0.972823	−	0.231550i	$-0.925620\pi$
$523$	−0.332937	+	1.24254i	−0.0145583	+	0.0543324i	0.958265	+	0.285883i	$0.0922868\pi$
$524$	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	−0.860130	−	0.510074i	$-0.829618\pi$
$547$	1.95267	−	4.18752i	0.0834904	−	0.179046i	0.943621	+	0.331029i	$0.107396\pi$
$548$	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	−0.998912	−	0.0466405i	$-0.985148\pi$
$557$	−2.60809	+	9.73354i	−0.110509	+	0.412423i	0.888403	+	0.459064i	$0.151815\pi$
$558$		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	−0.0798064	−	0.996810i	$-0.525430\pi$
$563$	15.0076	−	6.99817i	0.632496	−	0.294938i	0.712302	+	0.701873i	$0.247652\pi$
$564$		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	0.918815	+	0.394688i	$0.129147\pi$
$569$	−1.89828	+	10.7657i	−0.0795799	+	0.451320i	−0.998395	+	0.0566320i	$0.981964\pi$
$570$		0			0
$571$	15.2515	+	5.55110i	0.638256	+	0.232306i	0.640821	−	0.767691i	$-0.278594\pi$
$571$	15.2515	+	5.55110i	0.638256	+	0.232306i	−0.00256475	+	0.999997i	$0.500816\pi$
$572$	−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	0.595121	−	0.803636i	$-0.297104\pi$
$577$	17.0234	+	4.56140i	0.708693	+	0.189894i	0.113572	+	0.993530i	$0.463771\pi$
$578$	−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	0.569430	−	0.822040i	$-0.307164\pi$
$587$	7.40736	+	3.45411i	0.305734	+	0.142566i	−0.263696	+	0.964606i	$0.584942\pi$
$588$		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	−0.169357	+	0.985555i	$0.554169\pi$
$593$	−28.1239	+	28.1239i	−1.15491	+	1.15491i	−0.985555	+	0.169357i	$0.945831\pi$
$594$		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	0.128612	−	0.991695i	$-0.458948\pi$
$599$	27.5968	−	23.1564i	1.12757	−	0.946147i	0.998962	+	0.0455483i	$0.0145035\pi$
$600$		0			0
$601$	−21.4617	+	7.81141i	−0.875440	+	0.318634i	−0.740368	−	0.672202i	$-0.765349\pi$
$601$	−21.4617	+	7.81141i	−0.875440	+	0.318634i	−0.135072	+	0.990836i	$0.543126\pi$
$602$	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	0.422696	−	0.906271i	$-0.361084\pi$
$607$	−7.00562	−	4.90539i	−0.284349	−	0.199104i	−0.707046	+	0.707168i	$0.749973\pi$
$608$	−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	−0.894369	−	0.447329i	$-0.852375\pi$
$613$	−35.7827	+	9.58796i	−1.44525	+	0.387254i	−0.550882	+	0.834583i	$0.685709\pi$
$614$	−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	0.982556	−	0.185965i	$-0.0595411\pi$
$617$	5.17963	+	11.1077i	0.208524	+	0.447181i	−0.774032	+	0.633146i	$0.781763\pi$
$618$		0			0
$619$	8.63834	+	1.52317i	0.347204	+	0.0612215i	0.344531	−	0.938775i	$-0.388038\pi$
$619$	8.63834	+	1.52317i	0.347204	+	0.0612215i	0.00267331	+	0.999996i	$0.499149\pi$
$620$	−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	0.984741	+	0.174027i	$0.0556781\pi$
$631$	16.1540	+	27.9796i	0.643083	+	1.11385i	−0.341658	+	0.939824i	$0.610989\pi$
$632$	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	0.988189	−	0.153242i	$-0.0489715\pi$
$641$	3.35944	+	9.23000i	0.132690	+	0.364563i	−0.855499	+	0.517805i	$0.826749\pi$
$642$		0			0
$643$	18.5293	+	1.62110i	0.730723	+	0.0639299i	0.446444	−	0.894812i	$-0.352690\pi$
$643$	18.5293	+	1.62110i	0.730723	+	0.0639299i	0.284279	+	0.958742i	$0.408246\pi$
$644$	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	0.928832	−	0.370501i	$-0.120814\pi$
$647$	14.2018	+	14.2018i	0.558331	+	0.558331i	−0.370501	+	0.928832i	$0.620814\pi$
$648$		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	0.883189	+	0.469018i	$0.155392\pi$
$653$	−1.73834	+	19.8693i	−0.0680265	+	0.777546i	−0.951215	+	0.308528i	$0.900164\pi$
$654$		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	0.626773	−	0.779202i	$-0.284375\pi$
$659$	−0.815140	−	0.683983i	−0.0317533	−	0.0266442i	−0.658526	+	0.752558i	$0.728820\pi$
$660$		0			0
$661$	−5.78183	−	32.7904i	−0.224887	−	1.27540i	−0.862901	−	0.505373i	$-0.831355\pi$
$661$	−5.78183	−	32.7904i	−0.224887	−	1.27540i	0.638014	−	0.770025i	$-0.279756\pi$
$662$	−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	−0.892135	−	0.451770i	$-0.850793\pi$
$673$	−20.0466	+	14.0367i	−0.772738	+	0.541077i	0.119397	+	0.992847i	$0.461904\pi$
$674$	8.08017			0.311236
$675$		0			0
$676$	−50.5961			−1.94600
$677$	16.7682	−	11.7412i	0.644455	−	0.451252i	−0.205108	−	0.978739i	$-0.565755\pi$
$677$	16.7682	−	11.7412i	0.644455	−	0.451252i	0.849563	+	0.527487i	$0.176866\pi$
$678$		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	0.984804	+	0.173671i	$0.0555630\pi$
$683$	5.71751	+	21.3380i	0.218774	+	0.816477i	−0.766029	+	0.642806i	$0.777770\pi$
$684$		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	0.865568	−	0.500792i	$-0.166958\pi$
$691$	13.7398	+	11.5291i	0.522688	+	0.438587i	−0.342880	+	0.939379i	$0.611402\pi$
$692$	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	$-0.930929\pi$
$701$		−	11.4005i		−	0.430590i	0.976549	−	0.215295i	$-0.0690713\pi$
$702$		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	0.998504	−	0.0546749i	$-0.0174122\pi$
$709$	5.28444	+	14.5189i	0.198461	+	0.545268i	−0.800043	+	0.599943i	$0.795190\pi$
$710$	−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	0.764695	−	0.644392i	$-0.222889\pi$
$719$	−4.71157	−	8.16068i	−0.175712	−	0.304342i	−0.940407	+	0.340050i	$0.889556\pi$
$720$		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	−0.952293	−	0.305186i	$-0.901281\pi$
$727$	−24.6272	−	35.1712i	−0.913371	−	1.30443i	0.0389219	−	0.999242i	$-0.487608\pi$
$728$	−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	0.911134	−	0.412109i	$-0.135208\pi$
$733$	0.264636	+	0.567513i	0.00977454	+	0.0209616i	−0.901360	+	0.433071i	$0.857430\pi$
$734$	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	0.00348723	−	0.999994i	$-0.498890\pi$
$739$	23.6846	−	13.6743i	0.871251	−	0.503017i	0.867764	+	0.496977i	$0.165557\pi$
$740$	−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	−0.106950	−	0.994264i	$-0.534109\pi$
$743$	−29.3796	−	20.5718i	−1.07783	−	0.754706i	−0.970882	+	0.239558i	$0.922997\pi$
$744$		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	−0.985373	−	0.170413i	$-0.945490\pi$
$751$	−27.0935	+	22.7342i	−0.988657	+	0.829582i	−0.00328459	+	0.999995i	$0.501046\pi$
$752$	−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	−0.998788	−	0.0492153i	$-0.984328\pi$
$757$	−26.1262	+	26.1262i	−0.949573	+	0.949573i	0.0492153	+	0.998788i	$0.484328\pi$
$758$	−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	0.663685	−	0.748012i	$-0.268991\pi$
$761$	−5.19201	−	6.18759i	−0.188210	−	0.224300i	−0.851896	+	0.523712i	$0.824547\pi$
$762$		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	−0.455574	−	0.890198i	$-0.650566\pi$
$769$	−16.0619	+	2.83215i	−0.579208	+	0.102130i	−0.123634	+	0.992328i	$0.539455\pi$
$770$	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	0.0473325	−	0.998879i	$-0.484928\pi$
$773$	−11.4302	−	3.06271i	−0.411116	−	0.110158i	−0.458448	+	0.888721i	$0.651595\pi$
$774$		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	−0.992698	−	0.120627i	$-0.961510\pi$
$787$	−43.1572	+	20.1245i	−1.53839	+	0.717361i	−0.545689	+	0.837988i	$0.683732\pi$
$788$	−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	−0.951231	−	0.308480i	$-0.900180\pi$
$797$	−9.48608	+	13.5475i	−0.336014	+	0.479878i	0.615216	+	0.788358i	$0.289069\pi$
$798$		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	−0.883789	−	0.467885i	$-0.845016\pi$
$821$	−7.72326	+	9.20422i	−0.269544	+	0.321230i	0.614246	+	0.789115i	$0.289460\pi$
$822$		0			0
$823$	13.6442	−	19.4859i	0.475607	−	0.679237i	−0.507629	−	0.861576i	$-0.669478\pi$
$823$	13.6442	−	19.4859i	0.475607	−	0.679237i	0.983236	+	0.182339i	$0.0583668\pi$
$824$	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	−0.361504	−	0.932370i	$-0.617737\pi$
$827$	12.0136	−	44.8353i	0.417753	−	1.55907i	0.779257	−	0.626704i	$-0.215597\pi$
$828$		0			0
$829$	−27.8169	−	16.0601i	−0.966123	−	0.557791i	−0.0680706	−	0.997681i	$-0.521684\pi$
$829$	−27.8169	−	16.0601i	−0.966123	−	0.557791i	−0.898052	+	0.439889i	$0.855018\pi$
$830$	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	0.329406	+	0.944188i	$0.393151\pi$
$839$	−8.77845	+	49.7851i	−0.303066	+	1.71877i	−0.632472	+	0.774583i	$0.717960\pi$
$840$		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	0.562550	+	0.826763i	$0.309820\pi$
$853$	4.44262	+	50.7794i	0.152112	+	1.73865i	−0.410438	+	0.911889i	$0.634624\pi$
$854$	−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	0.572224	−	0.820097i	$-0.306081\pi$
$857$	9.12817	+	4.25654i	0.311812	+	0.145400i	−0.260412	+	0.965498i	$0.583858\pi$
$858$		0			0
$859$	−8.01487	−	9.55175i	−0.273464	−	0.325902i	0.611781	−	0.791027i	$-0.290453\pi$
$859$	−8.01487	−	9.55175i	−0.273464	−	0.325902i	−0.885245	+	0.465126i	$0.846009\pi$
$860$	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	−0.985479	−	0.169800i	$-0.945688\pi$
$863$	−23.9621	+	23.9621i	−0.815678	+	0.815678i	0.169800	+	0.985479i	$0.445688\pi$
$864$		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	0.999006	−	0.0445739i	$-0.0141930\pi$
$877$	38.4629	+	26.9320i	1.29880	+	0.909430i	0.299794	+	0.954004i	$0.403082\pi$
$878$	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	−0.801023	−	0.598633i	$-0.795711\pi$
$881$	−20.2756	+	11.7061i	−0.683103	+	0.394390i	0.117920	+	0.993023i	$0.462377\pi$
$882$		0			0
$883$	6.11319	−	1.63802i	0.205725	−	0.0551239i	−0.154485	−	0.987995i	$-0.549372\pi$
$883$	6.11319	−	1.63802i	0.205725	−	0.0551239i	0.360210	+	0.932871i	$0.382705\pi$
$884$	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	0.989375	+	0.145384i	$0.0464419\pi$
$887$	13.8426	+	29.6855i	0.464788	+	0.996741i	−0.524587	+	0.851357i	$0.675780\pi$
$888$		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	0.397010	−	0.917814i	$-0.370048\pi$
$907$	28.5313	−	2.49616i	0.947365	−	0.0828837i	0.550355	+	0.834931i	$0.314492\pi$
$908$	−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	0.999739	−	0.0228557i	$-0.00727584\pi$
$911$	6.61616	+	18.1777i	0.219203	+	0.602255i	−0.780536	+	0.625111i	$0.785054\pi$
$912$		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	$-0.736295\pi$
$919$		−	44.6775i		−	1.47377i	0.676016	−	0.736887i	$-0.263705\pi$
$920$	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	−0.985669	−	0.168689i	$-0.946047\pi$
$929$	−40.3230	−	33.8350i	−1.32296	−	1.11009i	−0.337286	−	0.941402i	$-0.609509\pi$
$930$		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	0.999680	−	0.0252908i	$-0.00805116\pi$
$937$	3.71263	+	13.8557i	0.121286	+	0.452647i	−0.878394	+	0.477938i	$0.841384\pi$
$938$	−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	−0.938207	−	0.346075i	$-0.887514\pi$
$941$	0.0906224	−	0.248983i	0.00295420	−	0.00811661i	0.941161	+	0.337959i	$0.109736\pi$
$942$		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	−0.0238294	−	0.999716i	$-0.507586\pi$
$947$	27.9252	−	19.5534i	0.907446	−	0.635401i	0.931276	+	0.364315i	$0.118697\pi$
$948$		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	−0.982755	−	0.184912i	$-0.940800\pi$
$953$	−6.91874	−	25.8211i	−0.224120	−	0.836427i	0.758635	−	0.651516i	$-0.225867\pi$
$954$		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	0.912796	+	0.408416i	$0.133919\pi$
$967$	−1.77416	+	20.2788i	−0.0570532	+	0.652121i	−0.969849	+	0.243706i	$0.921637\pi$
$968$	−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	$-0.774650\pi$
$971$		−	40.5268i		−	1.30057i	0.759692	−	0.650284i	$-0.225350\pi$
$972$		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	0.639000	−	0.769207i	$-0.279348\pi$
$977$	35.4680	+	3.10305i	1.13472	+	0.0992752i	0.495721	+	0.868482i	$0.334904\pi$
$978$		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	−0.654030	−	0.756468i	$-0.726923\pi$
$983$	−36.5814	+	3.20046i	−1.16677	+	0.102079i	−0.512735	+	0.858547i	$0.671368\pi$
$984$		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	−0.746123	−	0.665808i	$-0.768087\pi$
$991$	6.40763	−	11.0983i	0.203545	−	0.352550i	0.949668	+	0.313258i	$0.101420\pi$
$992$	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	0.898432	+	0.439113i	$0.144707\pi$
$997$	31.6947	+	45.2647i	1.00378	+	1.43355i	0.105349	+	0.994435i	$0.466404\pi$
$998$	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.8.3		192
3.2	odd	2		135.2.q.a.83.14	yes	192
5.2	odd	4	inner	405.2.r.a.332.3		192
15.2	even	4		135.2.q.a.2.14	✓	192
15.8	even	4		675.2.ba.b.407.3		192
15.14	odd	2		675.2.ba.b.218.3		192
27.13	even	9		135.2.q.a.68.14	yes	192
27.14	odd	18	inner	405.2.r.a.233.3		192
135.13	odd	36		675.2.ba.b.257.3		192
135.67	odd	36		135.2.q.a.122.14	yes	192
135.94	even	18		675.2.ba.b.68.3		192
135.122	even	36	inner	405.2.r.a.152.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.14	✓	192	15.2	even	4
135.2.q.a.68.14	yes	192	27.13	even	9
135.2.q.a.83.14	yes	192	3.2	odd	2
135.2.q.a.122.14	yes	192	135.67	odd	36
405.2.r.a.8.3		192	1.1	even	1	trivial
405.2.r.a.152.3		192	135.122	even	36	inner
405.2.r.a.233.3		192	27.14	odd	18	inner
405.2.r.a.332.3		192	5.2	odd	4	inner
675.2.ba.b.68.3		192	135.94	even	18
675.2.ba.b.218.3		192	15.14	odd	2
675.2.ba.b.257.3		192	135.13	odd	36
675.2.ba.b.407.3		192	15.8	even	4

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)

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

L-functions

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