LMFDB - Embedded newform 135.2.q.a.122.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			122.14
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65044 + 1.15565i) q^{2} +(-1.69572 + 0.352907i) q^{3} +(0.704386 + 1.93528i) q^{4} +(-0.268922 + 2.21984i) q^{5} +(-3.20652 - 1.37721i) q^{6} +(0.618828 + 1.32708i) q^{7} +(-0.0310202 + 0.115769i) q^{8} +(2.75091 - 1.19686i) q^{9} +O(q^{10})$	\(q+(1.65044 + 1.15565i) q^{2} +(-1.69572 + 0.352907i) q^{3} +(0.704386 + 1.93528i) q^{4} +(-0.268922 + 2.21984i) q^{5} +(-3.20652 - 1.37721i) q^{6} +(0.618828 + 1.32708i) q^{7} +(-0.0310202 + 0.115769i) q^{8} +(2.75091 - 1.19686i) q^{9} +(-3.00920 + 3.35293i) q^{10} +(1.86051 + 2.21727i) q^{11} +(-1.87741 - 3.03311i) q^{12} +(-3.51558 - 5.02076i) q^{13} +(-0.512304 + 2.90542i) q^{14} +(-0.327380 - 3.85912i) q^{15} +(2.97033 - 2.49240i) q^{16} +(-0.833002 - 3.10881i) q^{17} +(5.92337 + 1.20375i) q^{18} +(3.51741 - 2.03078i) q^{19} +(-4.48544 + 1.04318i) q^{20} +(-1.51769 - 2.03197i) q^{21} +(0.508272 + 5.80958i) q^{22} +(4.58997 + 2.14034i) q^{23} +(0.0117458 - 0.207259i) q^{24} +(-4.85536 - 1.19393i) q^{25} -12.3493i q^{26} +(-4.24239 + 3.00035i) q^{27} +(-2.13239 + 2.13239i) q^{28} +(0.368261 + 2.08851i) q^{29} +(3.91948 - 6.74759i) q^{30} +(-3.20394 + 1.16614i) q^{31} +(8.02150 - 0.701790i) q^{32} +(-3.93739 - 3.10328i) q^{33} +(2.21787 - 6.09356i) q^{34} +(-3.11232 + 1.01682i) q^{35} +(4.25397 + 4.48075i) q^{36} +(-11.3656 + 3.04540i) q^{37} +(8.15214 + 0.713220i) q^{38} +(7.73328 + 7.27312i) q^{39} +(-0.248646 - 0.0999926i) q^{40} +(0.839107 + 0.147957i) q^{41} +(-0.156621 - 5.10757i) q^{42} +(-0.0641287 + 0.732994i) q^{43} +(-2.98053 + 5.16243i) q^{44} +(1.91706 + 6.42844i) q^{45} +(5.10199 + 8.83690i) q^{46} +(2.61254 - 1.21825i) q^{47} +(-4.15725 + 5.27466i) q^{48} +(3.12132 - 3.71984i) q^{49} +(-6.63372 - 7.58161i) q^{50} +(2.50966 + 4.97768i) q^{51} +(7.24028 - 10.3402i) q^{52} +(-0.0757900 - 0.0757900i) q^{53} +(-10.4692 + 0.0491845i) q^{54} +(-5.42232 + 3.53376i) q^{55} +(-0.172831 + 0.0304748i) q^{56} +(-5.24785 + 4.68494i) q^{57} +(-1.80580 + 3.87255i) q^{58} +(-2.89613 - 2.43014i) q^{59} +(7.23789 - 3.35188i) q^{60} +(-4.21993 - 1.53593i) q^{61} +(-6.63556 - 1.77799i) q^{62} +(3.29067 + 2.91003i) q^{63} +(7.33402 + 4.23430i) q^{64} +(12.0907 - 6.45381i) q^{65} +(-2.91213 - 9.67203i) q^{66} +(3.65313 - 2.55795i) q^{67} +(5.42967 - 3.80189i) q^{68} +(-8.53862 - 2.00957i) q^{69} +(-6.31179 - 1.91856i) q^{70} +(-7.84988 - 4.53213i) q^{71} +(0.0532255 + 0.355597i) q^{72} +(-8.04880 - 2.15667i) q^{73} +(-22.2777 - 8.10840i) q^{74} +(8.65467 + 0.311072i) q^{75} +(6.40774 + 5.37673i) q^{76} +(-1.79116 + 3.84116i) q^{77} +(4.35814 + 20.9408i) q^{78} +(1.44073 - 0.254040i) q^{79} +(4.73394 + 7.26391i) q^{80} +(6.13505 - 6.58492i) q^{81} +(1.21391 + 1.21391i) q^{82} +(-9.69375 + 13.8441i) q^{83} +(2.86339 - 4.36846i) q^{84} +(7.12506 - 1.01310i) q^{85} +(-0.952926 + 1.13565i) q^{86} +(-1.36152 - 3.41157i) q^{87} +(-0.314404 + 0.146609i) q^{88} +(3.05075 + 5.28406i) q^{89} +(-4.26505 + 12.8252i) q^{90} +(4.48742 - 7.77244i) q^{91} +(-0.909052 + 10.3905i) q^{92} +(5.02144 - 3.10813i) q^{93} +(5.71971 + 1.00854i) q^{94} +(3.56209 + 8.35420i) q^{95} +(-13.3545 + 4.02088i) q^{96} +(16.1512 + 1.41304i) q^{97} +(9.45039 - 2.53222i) q^{98} +(7.77187 + 3.87275i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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	$-0.0531886\pi$
$2$	1.65044	+	1.15565i	1.16704	+	0.817169i	0.180966	+	0.983489i	$0.442077\pi$
$3$	−1.69572	+	0.352907i	−0.979023	+	0.203751i
$3$	−1.69572	+	0.352907i	−0.979023	+	0.203751i
$4$	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
$6$	−3.20652	−	1.37721i	−1.30906	−	0.562242i
$7$	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
$9$	2.75091	−	1.19686i	0.916971	−	0.398954i
$10$	−3.00920	+	3.35293i	−0.951592	+	1.06029i
$11$	1.86051	+	2.21727i	0.560965	+	0.668532i	0.969751	−	0.244098i	$-0.0784919\pi$
$11$	1.86051	+	2.21727i	0.560965	+	0.668532i	−0.408785	+	0.912631i	$0.634047\pi$
$12$	−1.87741	−	3.03311i	−0.541963	−	0.875584i
$13$	−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
$15$	−0.327380	−	3.85912i	−0.0845293	−	0.996421i
$16$	2.97033	−	2.49240i	0.742582	−	0.623101i
$17$	−0.833002	−	3.10881i	−0.202033	−	0.753996i	−0.990334	−	0.138706i	$-0.955706\pi$
$17$	−0.833002	−	3.10881i	−0.202033	−	0.753996i	0.788301	−	0.615290i	$-0.210961\pi$
$18$	5.92337	+	1.20375i	1.39615	+	0.283726i
$19$	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
$21$	−1.51769	−	2.03197i	−0.331188	−	0.443411i
$22$	0.508272	+	5.80958i	0.108364	+	1.23861i
$23$	4.58997	+	2.14034i	0.957074	+	0.446291i	0.837441	−	0.546527i	$-0.184051\pi$
$23$	4.58997	+	2.14034i	0.957074	+	0.446291i	0.119633	+	0.992818i	$0.461828\pi$
$24$	0.0117458	−	0.207259i	0.00239760	−	0.0423065i
$25$	−4.85536	−	1.19393i	−0.971072	−	0.238785i
$26$		−	12.3493i		−	2.42189i
$27$	−4.24239	+	3.00035i	−0.816448	+	0.577418i
$28$	−2.13239	+	2.13239i	−0.402983	+	0.402983i
$29$	0.368261	+	2.08851i	0.0683844	+	0.387827i	0.999720	+	0.0236650i	$0.00753352\pi$
$29$	0.368261	+	2.08851i	0.0683844	+	0.387827i	−0.931336	+	0.364162i	$0.881355\pi$
$30$	3.91948	−	6.74759i	0.715595	−	1.23194i
$31$	−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
$33$	−3.93739	−	3.10328i	−0.685412	−	0.540211i
$34$	2.21787	−	6.09356i	0.380362	−	1.04504i
$35$	−3.11232	+	1.01682i	−0.526079	+	0.171873i
$36$	4.25397	+	4.48075i	0.708995	+	0.746791i
$37$	−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
$39$	7.73328	+	7.27312i	1.23832	+	1.16463i
$40$	−0.248646	−	0.0999926i	−0.0393144	−	0.0158102i
$41$	0.839107	+	0.147957i	0.131046	+	0.0231070i	0.238787	−	0.971072i	$-0.423250\pi$
$41$	0.839107	+	0.147957i	0.131046	+	0.0231070i	−0.107740	+	0.994179i	$0.534361\pi$
$42$	−0.156621	−	5.10757i	−0.0241671	−	0.788114i
$43$	−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
$45$	1.91706	+	6.42844i	0.285778	+	0.958296i
$46$	5.10199	+	8.83690i	0.752247	+	1.30293i
$47$	2.61254	−	1.21825i	0.381078	−	0.177700i	−0.222634	−	0.974902i	$-0.571465\pi$
$47$	2.61254	−	1.21825i	0.381078	−	0.177700i	0.603712	+	0.797203i	$0.293688\pi$
$48$	−4.15725	+	5.27466i	−0.600048	+	0.761332i
$49$	3.12132	−	3.71984i	0.445902	−	0.531406i
$50$	−6.63372	−	7.58161i	−0.938150	−	1.07220i
$51$	2.50966	+	4.97768i	0.351422	+	0.697015i
$52$	7.24028	−	10.3402i	1.00405	−	1.43393i
$53$	−0.0757900	−	0.0757900i	−0.0104106	−	0.0104106i	0.701882	−	0.712293i	$-0.252343\pi$
$53$	−0.0757900	−	0.0757900i	−0.0104106	−	0.0104106i	−0.712293	+	0.701882i	$0.752343\pi$
$54$	−10.4692	+	0.0491845i	−1.42467	+	0.00669316i
$55$	−5.42232	+	3.53376i	−0.731145	+	0.476492i
$56$	−0.172831	+	0.0304748i	−0.0230955	+	0.00407236i
$57$	−5.24785	+	4.68494i	−0.695095	+	0.620536i
$58$	−1.80580	+	3.87255i	−0.237113	+	0.508491i
$59$	−2.89613	−	2.43014i	−0.377044	−	0.316377i	0.434497	−	0.900673i	$-0.356926\pi$
$59$	−2.89613	−	2.43014i	−0.377044	−	0.316377i	−0.811540	+	0.584296i	$0.801371\pi$
$60$	7.23789	−	3.35188i	0.934408	−	0.432726i
$61$	−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
$63$	3.29067	+	2.91003i	0.414586	+	0.366630i
$64$	7.33402	+	4.23430i	0.916753	+	0.529287i
$65$	12.0907	−	6.45381i	1.49967	−	0.800497i
$66$	−2.91213	−	9.67203i	−0.358458	−	1.19054i
$67$	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
$69$	−8.53862	−	2.00957i	−1.02793	−	0.241924i
$70$	−6.31179	−	1.91856i	−0.754403	−	0.229312i
$71$	−7.84988	−	4.53213i	−0.931609	−	0.537865i	−0.0442890	−	0.999019i	$-0.514102\pi$
$71$	−7.84988	−	4.53213i	−0.931609	−	0.537865i	−0.887320	+	0.461154i	$0.847436\pi$
$72$	0.0532255	+	0.355597i	0.00627268	+	0.0419075i
$73$	−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
$75$	8.65467	+	0.311072i	0.999355	+	0.0359195i
$76$	6.40774	+	5.37673i	0.735018	+	0.616754i
$77$	−1.79116	+	3.84116i	−0.204122	+	0.437741i
$78$	4.35814	+	20.9408i	0.493462	+	2.37108i
$79$	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
$81$	6.13505	−	6.58492i	0.681672	−	0.731658i
$82$	1.21391	+	1.21391i	0.134054	+	0.134054i
$83$	−9.69375	+	13.8441i	−1.06403	+	1.51959i	−0.225872	+	0.974157i	$0.572523\pi$
$83$	−9.69375	+	13.8441i	−1.06403	+	1.51959i	−0.838155	+	0.545431i	$0.816366\pi$
$84$	2.86339	−	4.36846i	0.312421	−	0.476638i
$85$	7.12506	−	1.01310i	0.772821	−	0.109886i
$86$	−0.952926	+	1.13565i	−0.102757	+	0.122461i
$87$	−1.36152	−	3.41157i	−0.145970	−	0.365758i
$88$	−0.314404	+	0.146609i	−0.0335156	+	0.0156286i
$89$	3.05075	+	5.28406i	0.323379	+	0.560109i	0.981183	−	0.193080i	$-0.0618477\pi$
$89$	3.05075	+	5.28406i	0.323379	+	0.560109i	−0.657804	+	0.753189i	$0.728514\pi$
$90$	−4.26505	+	12.8252i	−0.449576	+	1.35190i
$91$	4.48742	−	7.77244i	0.470410	−	0.814774i
$92$	−0.909052	+	10.3905i	−0.0947752	+	1.08329i
$93$	5.02144	−	3.10813i	0.520699	−	0.322299i
$94$	5.71971	+	1.00854i	0.589943	+	0.104023i
$95$	3.56209	+	8.35420i	0.365462	+	0.857123i
$96$	−13.3545	+	4.02088i	−1.36299	+	0.410379i
$97$	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
$99$	7.77187	+	3.87275i	0.781102	+	0.389226i
$100$	−1.10946	−	10.2375i	−0.110946	−	1.02375i
$101$	−1.88053	+	5.16673i	−0.187120	+	0.514108i	−0.997410	−	0.0719204i	$-0.977087\pi$
$101$	−1.88053	+	5.16673i	−0.187120	+	0.514108i	0.810290	+	0.586029i	$0.199309\pi$
$102$	−1.61043	+	11.1157i	−0.159456	+	1.10061i
$103$	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
$105$	4.91878	−	2.82259i	0.480023	−	0.275457i
$106$	−0.0375001	−	0.212674i	−0.00364233	−	0.0206567i
$107$	−10.5329	+	10.5329i	−1.01825	+	1.01825i	−0.0184189	+	0.999830i	$0.505863\pi$
$107$	−10.5329	+	10.5329i	−1.01825	+	1.01825i	−0.999830	+	0.0184189i	$0.994137\pi$
$108$	−8.79481	−	6.09682i	−0.846281	−	0.586667i
$109$		−	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
$111$	18.1981	−	9.17513i	1.72729	−	0.870865i
$112$	5.14574	+	2.39950i	0.486227	+	0.226731i
$113$	−1.32748	−	15.1732i	−0.124879	−	1.42737i	−0.757462	−	0.652879i	$-0.773561\pi$
$113$	−1.32748	−	15.1732i	−0.124879	−	1.42737i	0.632583	−	0.774492i	$-0.281995\pi$
$114$	−14.0754	+	1.66753i	−1.31829	+	0.156178i
$115$	−5.98554	+	9.61340i	−0.558155	+	0.896454i
$116$	−3.78247	+	2.18381i	−0.351193	+	0.202762i
$117$	−15.6802	−	9.60403i	−1.44963	−	0.887893i
$118$	−1.97149	−	7.35771i	−0.181491	−	0.677332i
$119$	3.61015	−	3.02928i	0.330942	−	0.277693i
$120$	0.456922	+	0.0818102i	0.0417111	+	0.00746822i
$121$	0.455341	−	2.58237i	0.0413946	−	0.234761i
$122$	−5.18974	−	7.41172i	−0.469857	−	0.671026i
$123$	−1.47510	+	0.0452332i	−0.133006	+	0.00407854i
$124$	−4.51362	−	5.37912i	−0.405335	−	0.483059i
$125$	3.95604	−	10.4570i	0.353839	−	0.935306i
$126$	2.06808	+	8.60571i	0.184239	+	0.766658i
$127$	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
$129$	−0.149935	−	1.26558i	−0.0132010	−	0.111428i
$130$	27.4133	+	3.32099i	2.40431	+	0.291270i
$131$	3.84111	+	10.5534i	0.335599	+	0.922051i	0.986627	+	0.162997i	$0.0521159\pi$
$131$	3.84111	+	10.5534i	0.335599	+	0.922051i	−0.651028	+	0.759054i	$0.725662\pi$
$132$	3.23228	−	9.80587i	0.281334	−	0.853492i
$133$	4.87168	+	3.41119i	0.422428	+	0.295787i
$134$	8.98538			0.776219
$135$	−5.51943	−	10.2243i	−0.475037	−	0.879966i
$136$	0.385743			0.0330772
$137$	16.1027	+	11.2752i	1.37574	+	0.963306i	0.999320	+	0.0368588i	$0.0117352\pi$
$137$	16.1027	+	11.2752i	1.37574	+	0.963306i	0.376424	+	0.926448i	$0.377154\pi$
$138$	−11.7701	−	13.1844i	−1.00194	−	1.12233i
$139$	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
$141$	−4.00020	+	2.98779i	−0.336878	+	0.251617i
$142$	−7.71820	−	16.5517i	−0.647697	−	1.38899i
$143$	4.59162	−	17.1362i	0.383971	−	1.43300i
$144$	5.18806	−	10.4115i	0.432338	−	0.867621i
$145$	−4.73520	+	0.255833i	−0.393237	+	0.0212458i
$146$	−10.7917	−	12.8611i	−0.893129	−	1.06439i
$147$	−3.98011	+	7.40933i	−0.328274	+	0.611111i
$148$	−13.8995	−	19.8505i	−1.14253	−	1.63170i
$149$	0.861743	−	4.88719i	0.0705968	−	0.400374i	−0.928948	−	0.370210i	$-0.879286\pi$
$149$	0.861743	−	4.88719i	0.0705968	−	0.400374i	0.999545	−	0.0301644i	$-0.00960308\pi$
$150$	13.9245	+	10.5152i	1.13693	+	0.858561i
$151$	−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
$153$	−6.01232	−	7.55507i	−0.486068	−	0.610791i
$154$	−7.39525	+	4.26965i	−0.595926	+	0.344058i
$155$	−1.72703	−	7.42583i	−0.138718	−	0.596457i
$156$	−8.62834	+	20.0892i	−0.690820	+	1.60842i
$157$	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
$159$	0.155265	+	0.101772i	0.0123133	+	0.00807101i
$160$	−0.599298	+	17.9951i	−0.0473787	+	1.42264i
$161$			7.41576i			0.584444i
$162$	17.7354	−	3.77805i	1.39343	−	0.296832i
$163$	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
$165$	7.94763	−	7.90583i	0.618722	−	0.615468i
$166$	−31.9979	+	11.6463i	−2.48352	+	0.903928i
$167$	−0.469806	+	0.0411027i	−0.0363547	+	0.00318063i	−0.105319	−	0.994439i	$-0.533586\pi$
$167$	−0.469806	+	0.0411027i	−0.0363547	+	0.00318063i	0.0689639	+	0.997619i	$0.478031\pi$
$168$	0.282318	−	0.112670i	0.0217813	−	0.00869266i
$169$	−8.40252	+	23.0857i	−0.646348	+	1.77583i
$170$	12.9303	+	6.56202i	0.991707	+	0.503284i
$171$	7.24553	−	9.79634i	0.554079	−	0.749145i
$172$	−1.46372	+	0.392203i	−0.111608	+	0.0299052i
$173$	−18.3690	−	1.60708i	−1.39657	−	0.122184i	−0.636125	−	0.771586i	$-0.719464\pi$
$173$	−18.3690	−	1.60708i	−1.39657	−	0.122184i	−0.760446	+	0.649402i	$0.775019\pi$
$174$	1.69548	−	7.20403i	0.128534	−	0.546136i
$175$	−1.42020	−	7.18230i	−0.107357	−	0.542931i
$176$	11.0527	+	1.94888i	0.833126	+	0.146903i
$177$	5.76862	+	3.09876i	0.433596	+	0.232917i
$178$	−1.07144	+	12.2466i	−0.0803080	+	0.917925i
$179$	−3.95796	+	6.85540i	−0.295832	+	0.512396i	−0.975178	−	0.221422i	$-0.928930\pi$
$179$	−3.95796	+	6.85540i	−0.295832	+	0.512396i	0.679346	+	0.733818i	$0.262264\pi$
$180$	−11.0905	+	8.23815i	−0.826638	+	0.614035i
$181$	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
$183$	7.69784	+	1.11526i	0.569041	+	0.0824421i
$184$	−0.390166	+	0.464982i	−0.0287634	+	0.0342789i
$185$	−3.70384	−	26.0487i	−0.272311	−	1.91514i
$186$	11.8795	+	0.673238i	0.871048	+	0.0493642i
$187$	5.34326	−	7.63096i	0.390738	−	0.558031i
$188$	4.19789	+	4.19789i	0.306162	+	0.306162i
$189$	−6.60703	−	3.77329i	−0.480590	−	0.274467i
$190$	−3.77553	+	17.9046i	−0.273905	+	1.29894i
$191$	−8.60644	+	1.51755i	−0.622740	+	0.109806i	−0.476110	−	0.879386i	$-0.657954\pi$
$191$	−8.60644	+	1.51755i	−0.622740	+	0.109806i	−0.146630	+	0.989191i	$0.546843\pi$
$192$	−13.9307	−	4.59195i	−1.00536	−	0.331395i
$193$	−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
$195$	−18.2248	+	15.2107i	−1.30511	+	1.08926i
$196$	9.39756	+	3.42043i	0.671254	+	0.244316i
$197$	1.93720	+	0.519071i	0.138020	+	0.0369822i	0.327167	−	0.944966i	$-0.393906\pi$
$197$	1.93720	+	0.519071i	0.138020	+	0.0369822i	−0.189148	+	0.981949i	$0.560573\pi$
$198$	8.35147	+	15.3733i	0.593513	+	1.09253i
$199$	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
$201$	−5.29196	+	5.62678i	−0.373266	+	0.396883i
$202$	−9.07464	+	6.35413i	−0.638490	+	0.447075i
$203$	−2.54374	+	1.78114i	−0.178535	+	0.125012i
$204$	−7.86546	+	8.36310i	−0.550693	+	0.585534i
$205$	−0.554096	+	1.82289i	−0.0386997	+	0.127316i
$206$	6.84718	+	3.95322i	0.477065	+	0.275434i
$207$	15.1883	+	0.394328i	1.05566	+	0.0274077i
$208$	−22.9562	−	6.15109i	−1.59172	−	0.426501i
$209$	11.0470	+	4.02077i	0.764134	+	0.278122i
$210$	11.3801	+	1.02587i	0.785301	+	0.0707914i
$211$	−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
$213$	14.9106	+	4.91493i	1.02166	+	0.336766i
$214$	−29.5562	+	5.21155i	−2.02042	+	0.356254i
$215$	−1.60988	−	0.339474i	−0.109793	−	0.0231519i
$216$	−0.215748	−	0.584208i	−0.0146798	−	0.0397503i
$217$	−3.53025	−	3.53025i	−0.239649	−	0.239649i
$218$	11.4577	−	16.3632i	0.776011	−	1.10826i
$219$	14.4096	+	0.816623i	0.973710	+	0.0551823i
$220$	−10.6582	−	8.00459i	−0.718578	−	0.539669i
$221$	−12.6801	+	15.1115i	−0.852955	+	1.01651i
$222$	40.6381	+	5.88762i	2.72745	+	0.395151i
$223$	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
$225$	−14.7856	+	2.52680i	−0.985710	+	0.168453i
$226$	15.3440	−	26.5765i	1.02067	−	1.76784i
$227$	0.100851	−	1.15273i	0.00669369	−	0.0765092i	−0.992113	−	0.125346i	$-0.959996\pi$
$227$	0.100851	−	1.15273i	0.00669369	−	0.0765092i	0.998807	+	0.0488368i	$0.0155514\pi$
$228$	−12.7632	−	6.85608i	−0.845264	−	0.454055i
$229$	−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
$231$	1.68173	−	7.14564i	0.110650	−	0.470148i
$232$	−0.253208	−	0.0221529i	−0.0166240	−	0.00145441i
$233$	−15.8052	+	4.23498i	−1.03543	+	0.277443i	−0.736219	−	0.676743i	$-0.763391\pi$
$233$	−15.8052	+	4.23498i	−1.03543	+	0.277443i	−0.299213	+	0.954186i	$0.596724\pi$
$234$	−14.7803	−	33.9717i	−0.966221	−	2.22080i
$235$	2.00174	+	6.12703i	0.130579	+	0.399683i
$236$	2.66302	−	7.31658i	0.173348	−	0.476269i
$237$	−2.35343	+	0.939226i	−0.152871	+	0.0610093i
$238$	9.45913	−	0.827567i	0.613145	−	0.0536432i
$239$	−8.07123	+	2.93769i	−0.522085	+	0.190023i	−0.589601	−	0.807695i	$-0.700715\pi$
$239$	−8.07123	+	2.93769i	−0.522085	+	0.190023i	0.0675160	+	0.997718i	$0.478493\pi$
$240$	−10.5909	−	10.6469i	−0.683641	−	0.687254i
$241$	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
$243$	−8.07944	+	13.3313i	−0.518296	+	0.855201i
$244$		−	9.24864i		−	0.592083i
$245$	7.41805	+	7.92916i	0.473922	+	0.506576i
$246$	−2.48684	−	1.63005i	−0.158555	−	0.103928i
$247$	−22.5618	−	10.5207i	−1.43557	−	0.669417i
$248$	−0.0356158	−	0.407090i	−0.00226161	−	0.0258503i
$249$	11.5522	−	26.8967i	0.732089	−	1.70451i
$250$	18.6139	−	12.6869i	1.17725	−	0.802392i
$251$	9.55376	−	5.51587i	0.603028	−	0.348158i	−0.167204	−	0.985922i	$-0.553474\pi$
$251$	9.55376	−	5.51587i	0.603028	−	0.348158i	0.770232	+	0.637764i	$0.220140\pi$
$252$	−3.31384	+	8.41818i	−0.208752	+	0.530295i
$253$	3.79398	+	14.1593i	0.238525	+	0.890189i
$254$	15.3866	−	12.9109i	0.965443	−	0.810103i
$255$	−11.7246	+	4.23242i	−0.734220	+	0.265044i
$256$	2.60580	−	14.7782i	0.162862	−	0.923639i
$257$	−3.31253	−	4.73079i	−0.206630	−	0.295098i	0.702439	−	0.711744i	$-0.252094\pi$
$257$	−3.31253	−	4.73079i	−0.206630	−	0.295098i	−0.909069	+	0.416646i	$0.863206\pi$
$258$	1.21511	−	2.26204i	0.0756496	−	0.140829i
$259$	−11.0748	−	13.1985i	−0.688157	−	0.820114i
$260$	21.0065	+	18.8529i	1.30277	+	1.16921i
$261$	3.51272	+	5.30456i	0.217432	+	0.328344i
$262$	−5.85647	+	21.8567i	−0.361814	+	1.35031i
$263$	7.79728	+	16.7213i	0.480801	+	1.03108i	0.985794	+	0.167958i	$0.0537172\pi$
$263$	7.79728	+	16.7213i	0.480801	+	1.03108i	−0.504993	+	0.863123i	$0.668505\pi$
$264$	0.481402	−	0.359563i	0.0296282	−	0.0221296i
$265$	0.188623	−	0.147860i	0.0115870	−	0.00908296i
$266$	4.09828	+	11.2599i	0.251281	+	0.690390i
$267$	−7.03800	−	7.88364i	−0.430719	−	0.482471i
$268$	7.52358	+	5.26807i	0.459576	+	0.321798i
$269$	−15.7262			−0.958842			−0.479421	−	0.877585i	$-0.659153\pi$
$269$	−15.7262			−0.958842			−0.479421	+	0.877585i	$0.659153\pi$
$270$	2.70621	−	23.2531i	0.164695	−	1.41514i
$271$	−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
$273$	−4.86645	+	14.7635i	−0.294531	+	0.893528i
$274$	13.5463	+	37.2181i	0.818362	+	2.24843i
$275$	−6.38620	−	12.9870i	−0.385102	−	0.783144i
$276$	−2.12539	−	17.9402i	−0.127933	−	1.07987i
$277$	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
$279$	−7.41806	+	7.04262i	−0.444107	+	0.421630i
$280$	−0.0211709	−	0.391852i	−0.00126521	−	0.0234176i
$281$	4.76302	+	5.67634i	0.284138	+	0.338622i	0.889168	−	0.457580i	$-0.151284\pi$
$281$	4.76302	+	5.67634i	0.284138	+	0.338622i	−0.605031	+	0.796202i	$0.706839\pi$
$282$	−10.0549	+	0.308329i	−0.598763	+	0.0183607i
$283$	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
$285$	−8.98855	−	12.9093i	−0.532435	−	0.764679i
$286$	27.3816	−	22.9759i	1.61911	−	1.35859i
$287$	0.322912	+	1.20512i	0.0190609	+	0.0711362i
$288$	21.2265	−	11.5312i	1.25078	−	0.679481i
$289$	5.75165	−	3.32072i	0.338332	−	0.195336i
$290$	−8.11081	−	5.05000i	−0.476283	−	0.296546i
$291$	−27.8865	+	3.30374i	−1.63473	+	0.193668i
$292$	−1.49569	−	17.0958i	−0.0875288	−	1.00046i
$293$	18.2561	+	8.51297i	1.06653	+	0.497333i	0.874985	−	0.484150i	$-0.160871\pi$
$293$	18.2561	+	8.51297i	1.06653	+	0.497333i	0.191549	+	0.981483i	$0.438649\pi$
$294$	−15.1315	+	7.62904i	−0.882490	+	0.444935i
$295$	6.17335	−	5.77541i	0.359426	−	0.336258i
$296$		−	1.41025i		−	0.0819691i
$297$	−14.5456	−	3.82434i	−0.844022	−	0.221910i
$298$	7.07014	−	7.07014i	0.409562	−	0.409562i
$299$	−5.39025	−	30.5696i	−0.311726	−	1.76789i
$300$	5.49421	+	16.9683i	0.317208	+	0.979668i
$301$	−1.01243	+	0.368493i	−0.0583553	+	0.0212396i
$302$	−41.6166	+	3.64098i	−2.39477	+	0.209515i
$303$	1.36548	−	9.42496i	0.0784448	−	0.541450i
$304$	5.38635	−	14.7989i	0.308928	−	0.848774i
$305$	4.54434	−	8.95451i	0.260208	−	0.512733i
$306$	−1.19196	−	19.4173i	−0.0681401	−	1.11002i
$307$	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
$309$	−6.50822	+	1.95955i	−0.370240	+	0.111475i
$310$	5.73131	−	14.2517i	0.325516	−	0.809444i
$311$	2.38442	+	0.420438i	0.135208	+	0.0238408i	0.240843	−	0.970564i	$-0.422576\pi$
$311$	2.38442	+	0.420438i	0.135208	+	0.0238408i	−0.105634	+	0.994405i	$0.533687\pi$
$312$	−1.08189	+	0.669660i	−0.0612499	+	0.0379120i
$313$	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
$315$	−7.34474	+	6.52219i	−0.413829	+	0.367484i
$316$	1.50647	+	2.60929i	0.0847457	+	0.146784i
$317$	20.5585	−	9.58656i	1.15468	−	0.538435i	0.251566	−	0.967840i	$-0.419055\pi$
$317$	20.5585	−	9.58656i	1.15468	−	0.538435i	0.903112	+	0.429405i	$0.141277\pi$
$318$	0.138644	+	0.347401i	0.00777475	+	0.0194813i
$319$	−3.94565	+	4.70224i	−0.220914	+	0.263275i
$320$	−11.3717	+	15.1416i	−0.635700	+	0.846444i
$321$	14.1436	−	21.5779i	0.789420	−	1.20436i
$322$	−8.57003	+	12.2393i	−0.477589	+	0.682068i
$323$	−9.24330	−	9.24330i	−0.514311	−	0.514311i
$324$	17.0651	+	7.23473i	0.948063	+	0.401930i
$325$	11.0750	+	28.5750i	0.614329	+	1.58505i
$326$	40.3696	−	7.11825i	2.23587	−	0.394243i
$327$	3.49889	+	16.8121i	0.193489	+	0.929713i
$328$	−0.0431581	+	0.0925528i	−0.00238301	+	0.00511038i
$329$	3.23343	+	2.71317i	0.178265	+	0.149582i
$330$	22.2535	−	3.86343i	1.22501	−	0.212675i
$331$	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
$333$	−27.6208	+	21.9807i	−1.51361	+	1.20453i
$334$	−0.822888	−	0.475095i	−0.0450264	−	0.0259960i
$335$	4.69583	+	8.79726i	0.256561	+	0.480646i
$336$	−9.57253	−	2.25290i	−0.522224	−	0.122906i
$337$	−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
$339$	7.60575	+	25.2609i	0.413088	+	1.37198i
$340$	6.97943	+	13.0754i	0.378513	+	0.709113i
$341$	−8.54661	−	4.93439i	−0.462825	−	0.267212i
$342$	23.2795	−	7.79498i	1.25881	−	0.421504i
$343$	16.7687	+	4.49317i	0.905427	+	0.242608i
$344$	−0.0828686	−	0.0301617i	−0.00446798	−	0.00162621i
$345$	6.75715	−	18.4139i	0.363793	−	0.991373i
$346$	−28.4598	−	23.8806i	−1.53001	−	1.28383i
$347$	−5.24496	+	11.2479i	−0.281564	+	0.603816i	−0.995326	−	0.0965722i	$-0.969212\pi$
$347$	−5.24496	+	11.2479i	−0.281564	+	0.603816i	0.713762	+	0.700389i	$0.246990\pi$
$348$	5.64331	−	5.03798i	0.302513	−	0.270064i
$349$	−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
$351$	29.9785	+	10.7521i	1.60013	+	0.573902i
$352$	16.4801	+	16.4801i	0.878395	+	0.878395i
$353$	10.2693	−	14.6661i	0.546579	−	0.780595i	−0.446904	−	0.894582i	$-0.647473\pi$
$353$	10.2693	−	14.6661i	0.546579	−	0.780595i	0.993482	+	0.113987i	$0.0363622\pi$
$354$	5.93968	+	11.7808i	0.315691	+	0.626145i
$355$	12.1716	−	16.2067i	0.646001	−	0.860161i
$356$	−8.07725	+	9.62609i	−0.428093	+	0.510182i
$357$	−5.05275	+	6.41085i	−0.267420	+	0.339298i
$358$	−14.4548	+	6.74040i	−0.763962	+	0.356241i
$359$	6.26521	+	10.8517i	0.330665	+	0.572729i	0.982642	−	0.185510i	$-0.0593936\pi$
$359$	6.26521	+	10.8517i	0.330665	+	0.572729i	−0.651977	+	0.758239i	$0.726060\pi$
$360$	−0.803681	+	0.0225239i	−0.0423577	+	0.00118712i
$361$	−1.25189	+	2.16834i	−0.0658891	+	0.114123i
$362$	−3.46328	+	39.5854i	−0.182026	+	2.08056i
$363$	0.139206	+	4.53966i	0.00730642	+	0.238270i
$364$	18.2028	+	3.20964i	0.954084	+	0.168231i
$365$	6.95196	−	17.2871i	0.363882	−	0.904846i
$366$	11.4160	+	10.7367i	0.596723	+	0.561215i
$367$	−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
$369$	2.48539	−	0.597277i	0.129384	−	0.0310930i
$370$	23.9903	−	47.2723i	1.24720	−	2.45757i
$371$	0.0536785	−	0.147481i	0.00278685	−	0.00765681i
$372$	9.55215	+	7.52858i	0.495256	+	0.390339i
$373$	−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
$375$	−3.01796	+	19.1283i	−0.155847	+	0.987781i
$376$	0.0599937	+	0.340241i	0.00309394	+	0.0175466i
$377$	9.19128	−	9.19128i	0.473375	−	0.473375i
$378$	−6.54389	−	13.8630i	−0.336582	−	0.713037i
$379$		−	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
$381$	−0.976986	+	17.2393i	−0.0500525	+	0.883194i
$382$	−15.9582	−	7.44142i	−0.816491	−	0.380736i
$383$	1.26087	+	14.4118i	0.0644275	+	0.736410i	0.957864	+	0.287221i	$0.0927314\pi$
$383$	1.26087	+	14.4118i	0.0644275	+	0.736410i	−0.893437	+	0.449189i	$0.851713\pi$
$384$	−0.993364	−	1.32997i	−0.0506924	−	0.0678695i
$385$	−8.04507	−	5.00906i	−0.410015	−	0.255286i
$386$	−15.0774	+	8.70492i	−0.767417	+	0.443069i
$387$	0.700880	+	2.09316i	0.0356277	+	0.106401i
$388$	8.64201	+	32.2524i	0.438731	+	1.63737i
$389$	−9.68308	+	8.12507i	−0.490951	+	0.411957i	−0.854367	−	0.519670i	$-0.826055\pi$
$389$	−9.68308	+	8.12507i	−0.490951	+	0.411957i	0.363416	+	0.931627i	$0.381610\pi$
$390$	−47.6573	+	4.04290i	−2.41322	+	0.204720i
$391$	2.83044	−	16.0522i	0.143141	−	0.811795i
$392$	0.333818	+	0.476742i	0.0168604	+	0.0240791i
$393$	−10.2378	−	16.5399i	−0.516428	−	0.834330i
$394$	2.59737	+	3.09542i	0.130853	+	0.155945i
$395$	0.176483	+	3.26651i	0.00887982	+	0.164356i
$396$	−2.02047	+	17.7687i	−0.101532	+	0.892910i
$397$	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
$399$	−9.46482	−	4.06516i	−0.473834	−	0.203512i
$400$	−17.3978	+	8.55516i	−0.869889	+	0.427758i
$401$	−8.96818	−	24.6399i	−0.447849	−	1.23046i	−0.934218	−	0.356703i	$-0.883901\pi$
$401$	−8.96818	−	24.6399i	−0.447849	−	1.23046i	0.486369	−	0.873754i	$-0.338321\pi$
$402$	−15.2367	+	3.17101i	−0.759936	+	0.158155i
$403$	17.1186	+	11.9866i	0.852738	+	0.597094i
$404$	−11.3237			−0.563375
$405$	12.9676	+	15.3896i	0.644366	+	0.764718i
$406$	−6.25667			−0.310513
$407$	−27.8983	−	19.5346i	−1.38287	−	0.968294i
$408$	−0.654111	+	0.136131i	−0.0323833	+	0.00673951i
$409$	−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
$411$	−31.2847	−	13.4368i	−1.54316	−	0.662790i
$412$	3.41549	+	7.32453i	0.168269	+	0.360854i
$413$	1.43279	−	5.34723i	0.0705028	−	0.263120i
$414$	24.6117	+	18.2032i	1.20960	+	0.894637i
$415$	−28.1248	−	25.2415i	−1.38059	−	1.23906i
$416$	−31.7237	−	37.8068i	−1.55538	−	1.85363i
$417$	−1.35561	−	2.19010i	−0.0663846	−	0.107250i
$418$	13.5858	+	19.4025i	0.664501	+	0.949006i
$419$	3.59622	−	20.3952i	0.175687	−	0.996370i	−0.761661	−	0.647975i	$-0.775616\pi$
$419$	3.59622	−	20.3952i	0.175687	−	0.996370i	0.937348	−	0.348394i	$-0.113273\pi$
$420$	8.92724	+	7.53103i	0.435604	+	0.367477i
$421$	−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
$423$	5.72880	−	6.47814i	0.278544	−	0.314978i
$424$	0.0111251	−	0.00642311i	0.000540285	−	0.000311934i
$425$	0.332837	+	16.0889i	0.0161450	+	0.780427i
$426$	18.9291	+	25.3433i	0.917118	+	1.22788i
$427$	−0.573108	−	6.55066i	−0.0277347	−	0.317009i
$428$	−27.8032	−	12.9649i	−1.34392	−	0.626680i
$429$	−1.73862	+	30.6785i	−0.0839413	+	1.48117i
$430$	−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	$-0.0223983\pi$
$432$	−5.12321	+	19.4858i	−0.246490	+	0.937510i
$433$	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
$435$	7.93927	−	2.10490i	0.380659	−	0.100922i
$436$	19.1873	−	6.98361i	0.918905	−	0.334454i
$437$	20.4913	−	1.79276i	0.980233	−	0.0857593i
$438$	22.8385	+	18.0003i	1.09126	+	0.860085i
$439$	−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
$441$	4.13434	−	13.9687i	0.196873	−	0.665178i
$442$	−38.3914	+	10.2870i	−1.82609	+	0.489300i
$443$	−27.8809	−	2.43927i	−1.32466	−	0.115893i	−0.597229	−	0.802070i	$-0.703732\pi$
$443$	−27.8809	−	2.43927i	−1.32466	−	0.115893i	−0.727434	+	0.686177i	$0.759287\pi$
$444$	30.5749	+	28.7556i	1.45102	+	1.36468i
$445$	−12.5502	+	5.35118i	−0.594935	+	0.253670i
$446$	23.7107	+	4.18083i	1.12273	+	0.197968i
$447$	0.263451	+	8.59141i	0.0124608	+	0.406360i
$448$	−1.08076	+	12.3531i	−0.0510611	+	0.583631i
$449$	4.77256	−	8.26631i	0.225231	−	0.390111i	−0.731158	−	0.682208i	$-0.761020\pi$
$449$	4.77256	−	8.26631i	0.225231	−	0.390111i	0.956389	+	0.292097i	$0.0943530\pi$
$450$	−27.3229	−	12.9167i	−1.28802	−	0.608900i
$451$	1.23311	+	2.13580i	0.0580647	+	0.100571i
$452$	28.4293	−	13.2568i	1.33720	−	0.623548i
$453$	22.2302	−	28.2053i	1.04446	−	1.32520i
$454$	1.49860	−	1.78596i	0.0703328	−	0.0838193i
$455$	16.0468	+	12.0515i	0.752286	+	0.564985i
$456$	−0.379581	−	0.752866i	−0.0177755	−	0.0352562i
$457$	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
$459$	12.8614	+	10.6895i	0.600321	+	0.498942i
$460$	−22.8208	−	4.81219i	−1.06402	−	0.224369i
$461$	24.4088	−	4.30393i	1.13683	−	0.200454i	0.426612	−	0.904435i	$-0.359707\pi$
$461$	24.4088	−	4.30393i	1.13683	−	0.200454i	0.710219	+	0.703981i	$0.248596\pi$
$462$	11.0335	−	9.84995i	0.513323	−	0.458261i
$463$	−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
$465$	5.54918	+	11.9826i	0.257337	+	0.555681i
$466$	−30.9797	−	11.2757i	−1.43511	−	0.522336i
$467$	39.5591	+	10.5998i	1.83058	+	0.490502i	0.997989	−	0.0633888i	$-0.0201908\pi$
$467$	39.5591	+	10.5998i	1.83058	+	0.490502i	0.832589	+	0.553891i	$0.186857\pi$
$468$	7.54161	−	37.1106i	0.348611	−	1.71544i
$469$	5.65527	+	3.26507i	0.261136	+	0.150767i
$470$	−3.77695	+	12.4256i	−0.174218	+	0.573151i
$471$	−3.39145	−	11.2640i	−0.156270	−	0.519018i
$472$	0.371173	−	0.259898i	0.0170846	−	0.0119628i
$473$	−1.74456	+	1.22155i	−0.0802149	+	0.0561671i
$474$	−4.96961	−	1.16960i	−0.228262	−	0.0537216i
$475$	−19.5029	+	5.66062i	−0.894854	+	0.259727i
$476$	8.40545	+	4.85289i	0.385263	+	0.222432i
$477$	−0.299202	−	0.117782i	−0.0136995	−	0.00539285i
$478$	−16.7160	−	4.47905i	−0.764574	−	0.204867i
$479$	−25.9636	−	9.44996i	−1.18631	−	0.431780i	−0.327880	−	0.944719i	$-0.606334\pi$
$479$	−25.9636	−	9.44996i	−1.18631	−	0.431780i	−0.858425	+	0.512940i	$0.828556\pi$
$480$	−5.33437	−	30.7262i	−0.243480	−	1.40245i
$481$	55.2468	+	46.3576i	2.51904	+	2.11372i
$482$	−1.75976	+	3.77382i	−0.0801549	+	0.171893i
$483$	−2.61707	−	12.5750i	−0.119081	−	0.572184i
$484$	5.31835	−	0.937769i	0.241743	−	0.0426258i
$485$	−7.48013	+	35.4730i	−0.339655	+	1.61074i
$486$	−28.7409	+	12.6655i	−1.30372	+	0.574517i
$487$	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
$489$	−19.3182	+	29.4724i	−0.873600	+	1.33279i
$490$	3.07971	+	21.6593i	0.139127	+	0.978467i
$491$	15.4259	−	18.3839i	0.696161	−	0.829652i	−0.295925	−	0.955211i	$-0.595628\pi$
$491$	15.4259	−	18.3839i	0.696161	−	0.829652i	0.992086	+	0.125559i	$0.0400724\pi$
$492$	−1.12658	−	2.82288i	−0.0507902	−	0.127265i
$493$	6.18602	−	2.88459i	0.278604	−	0.129915i
$494$	−25.0786	−	43.4374i	−1.12834	−	1.95434i
$495$	−10.6869	+	16.2108i	−0.480340	+	0.728623i
$496$	−6.61027	+	11.4493i	−0.296810	+	0.514090i
$497$	1.15678	−	13.2220i	0.0518886	−	0.593089i
$498$	50.1494	−	31.0411i	2.24725	−	1.39099i
$499$	−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
$501$	0.782153	−	0.235497i	0.0349440	−	0.0105212i
$502$	22.1423	+	1.93720i	0.988261	+	0.0864616i
$503$	−2.72503	+	0.730168i	−0.121503	+	0.0325566i	−0.319058	−	0.947735i	$-0.603366\pi$
$503$	−2.72503	+	0.730168i	−0.121503	+	0.0325566i	0.197555	+	0.980292i	$0.436700\pi$
$504$	−0.438969	+	0.290688i	−0.0195532	+	0.0129483i
$505$	−10.9636	−	5.56393i	−0.487873	−	0.247592i
$506$	−10.1015	+	27.7536i	−0.449066	+	1.23380i
$507$	6.10118	−	42.1122i	0.270963	−	1.87027i
$508$	20.4530	−	1.78941i	0.907455	−	0.0793920i
$509$	20.7599	−	7.55598i	0.920166	−	0.334913i	0.161861	−	0.986814i	$-0.448250\pi$
$509$	20.7599	−	7.55598i	0.920166	−	0.334913i	0.758304	+	0.651901i	$0.226028\pi$
$510$	−24.2419	−	6.56414i	−1.07345	−	0.290665i
$511$	−2.11875	−	12.0160i	−0.0937279	−	0.531557i
$512$	22.7346	−	22.7346i	1.00474	−	1.00474i
$513$	−8.82917	+	19.1688i	−0.389817	+	0.846324i
$514$		−	11.6360i		−	0.513243i
$515$	−0.292064	+	8.76980i	−0.0128699	+	0.386444i
$516$	2.34365	−	1.18162i	0.103173	−	0.0520181i
$517$	7.56184	+	3.52615i	0.332569	+	0.155080i
$518$	−3.02553	−	34.5820i	−0.132934	−	1.51944i
$519$	31.7158	−	3.75740i	1.39217	−	0.164932i
$520$	0.372095	+	1.59992i	0.0163175	+	0.0701614i
$521$	−7.62484	+	4.40220i	−0.334050	+	0.192864i	−0.657638	−	0.753334i	$-0.728444\pi$
$521$	−7.62484	+	4.40220i	−0.334050	+	0.192864i	0.323588	+	0.946198i	$0.395111\pi$
$522$	−0.332694	+	12.8143i	−0.0145616	+	0.560868i
$523$	−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
$525$	4.94293	+	11.6779i	0.215727	+	0.509667i
$526$	−6.45507	+	36.6085i	−0.281454	+	1.59621i
$527$	6.29419	+	8.98903i	0.274179	+	0.391568i
$528$	−19.4300	+	0.595809i	−0.845581	+	0.0259293i
$529$	1.70263	+	2.02911i	0.0740274	+	0.0882224i
$530$	0.482186	−	0.0260515i	0.0209448	−	0.00113161i
$531$	−10.8755	−	3.21884i	−0.471958	−	0.139686i
$532$	−3.17007	+	11.8309i	−0.137440	+	0.512933i
$533$	−2.20709	−	4.73311i	−0.0955995	−	0.205014i
$534$	−2.50506	−	21.1450i	−0.108405	−	0.915032i
$535$	−20.5487	−	26.2137i	−0.888398	−	1.13332i
$536$	0.182810	+	0.502268i	0.00789621	+	0.0216947i
$537$	4.29227	−	13.0216i	0.185225	−	0.561924i
$538$	−25.9551	−	18.1740i	−1.11900	−	0.783535i
$539$	14.0551			0.605398
$540$	15.8991	−	17.8835i	0.684187	−	0.769583i
$541$	−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
$543$	−22.7493	−	25.4827i	−0.976265	−	1.09357i
$544$	−8.86365	−	24.3527i	−0.380026	−	1.04411i
$545$	22.0085	+	2.66622i	0.942741	+	0.114208i
$546$	−25.0933	+	18.7424i	−1.07389	+	0.802100i
$547$	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
$549$	−13.4469	+	0.825461i	−0.573901	+	0.0352298i
$550$	4.46837	−	28.8144i	0.190532	−	1.22865i
$551$	5.53663	+	6.59830i	0.235868	+	0.281097i
$552$	0.497516	−	0.926170i	0.0211757	−	0.0394204i
$553$	1.22870	+	1.75476i	0.0522496	+	0.0746202i
$554$	−5.37283	+	30.4709i	−0.228270	+	1.29458i
$555$	15.4734	+	42.8642i	0.656811	+	1.81948i
$556$	−2.34610	+	1.96861i	−0.0994968	+	0.0834878i
$557$	2.60809	+	9.73354i	0.110509	+	0.412423i	0.998912	−	0.0466405i	$-0.0148515\pi$
$557$	2.60809	+	9.73354i	0.110509	+	0.412423i	−0.888403	+	0.459064i	$0.848185\pi$
$558$	−20.3819	+	3.05074i	−0.862833	+	0.129148i
$559$	3.90564	−	2.25492i	0.165191	−	0.0953730i
$560$	−6.71031	+	10.7774i	−0.283562	+	0.455430i
$561$	−6.36763	+	14.8256i	−0.268842	+	0.625938i
$562$	1.30121	+	14.8729i	0.0548881	+	0.627373i
$563$	−15.0076	−	6.99817i	−0.632496	−	0.294938i	0.0798064	−	0.996810i	$-0.474570\pi$
$563$	−15.0076	−	6.99817i	−0.632496	−	0.294938i	−0.712302	+	0.701873i	$0.752348\pi$
$564$	−8.59990	−	5.63697i	−0.362121	−	0.237359i
$565$	34.0390	+	1.13361i	1.43203	+	0.0476914i
$566$			28.9676i			1.21760i
$567$	12.5353	+	4.06677i	0.526432	+	0.170788i
$568$	0.768184	−	0.768184i	0.0322323	−	0.0322323i
$569$	1.89828	+	10.7657i	0.0795799	+	0.451320i	0.998395	+	0.0566320i	$0.0180362\pi$
$569$	1.89828	+	10.7657i	0.0795799	+	0.451320i	−0.918815	+	0.394688i	$0.870853\pi$
$570$	0.0835511	−	31.6936i	0.00349957	−	1.32750i
$571$	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
$573$	14.0585	−	5.61060i	0.587304	−	0.234386i
$574$	−0.859755	+	2.36216i	−0.0358855	+	0.0985946i
$575$	−19.7305	−	15.8722i	−0.822820	−	0.661916i
$576$	25.2431	+	2.87039i	1.05180	+	0.119599i
$577$	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
$579$	3.42870	−	14.5684i	0.142492	−	0.605444i
$580$	−3.83051	−	8.98374i	−0.159053	−	0.373030i
$581$	−24.3710	−	4.29727i	−1.01108	−	0.178281i
$582$	−49.8430	−	26.7744i	−2.06606	−	1.10984i
$583$	0.0270388	−	0.309055i	0.00111983	−	0.0127998i
$584$	0.499351	−	0.864901i	0.0206633	−	0.0357898i
$585$	25.5361	−	32.2248i	1.05579	−	1.33233i
$586$	20.2926	+	35.1479i	0.838280	+	1.45194i
$587$	−7.40736	+	3.45411i	−0.305734	+	0.142566i	−0.569430	−	0.822040i	$-0.692836\pi$
$587$	−7.40736	+	3.45411i	−0.305734	+	0.142566i	0.263696	+	0.964606i	$0.415058\pi$
$588$	−17.1427	−	2.48362i	−0.706953	−	0.102423i
$589$	−8.90140	+	10.6083i	−0.366776	+	0.437106i
$590$	16.8631	−	2.39774i	0.694243	−	0.0987135i
$591$	−3.46812	−	0.196546i	−0.142660	−	0.00808483i
$592$	−26.1692	+	37.3735i	−1.07555	+	1.53604i
$593$	28.1239	+	28.1239i	1.15491	+	1.15491i	0.985555	+	0.169357i	$0.0541692\pi$
$593$	28.1239	+	28.1239i	1.15491	+	1.15491i	0.169357	+	0.985555i	$0.445831\pi$
$594$	−19.5871	−	23.1215i	−0.803668	−	0.948687i
$595$	5.75366	+	8.82860i	0.235877	+	0.361937i
$596$	10.0651	−	1.77475i	0.412282	−	0.0726965i
$597$	−29.4664	−	9.71291i	−1.20598	−	0.397523i
$598$	26.4315	−	56.6826i	1.08087	−	2.31793i
$599$	−27.5968	−	23.1564i	−1.12757	−	0.946147i	−0.128612	−	0.991695i	$-0.541052\pi$
$599$	−27.5968	−	23.1564i	−1.12757	−	0.946147i	−0.998962	+	0.0455483i	$0.985496\pi$
$600$	−0.304482	+	0.992292i	−0.0124304	+	0.0405101i
$601$	−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
$603$	6.98794	−	11.4090i	0.284571	−	0.464610i
$604$	−36.9808	−	21.3509i	−1.50473	−	0.868755i
$605$	5.60999	+	1.70524i	0.228078	+	0.0693279i
$606$	13.1456	−	13.9773i	0.534004	−	0.567790i
$607$	−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
$609$	3.68488	−	3.91802i	0.149319	−	0.158766i
$610$	17.8485	−	9.52721i	0.722663	−	0.385745i
$611$	−15.3011	−	8.83410i	−0.619017	−	0.357389i
$612$	10.3862	−	16.9572i	0.419837	−	0.685456i
$613$	−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
$615$	0.296278	−	3.28665i	0.0119471	−	0.132531i
$616$	−0.389125	−	0.326514i	−0.0156783	−	0.0131556i
$617$	−5.17963	+	11.1077i	−0.208524	+	0.447181i	−0.982556	−	0.185965i	$-0.940459\pi$
$617$	−5.17963	+	11.1077i	−0.208524	+	0.447181i	0.774032	+	0.633146i	$0.218237\pi$
$618$	−13.0060	−	4.28712i	−0.523178	−	0.172453i
$619$	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
$621$	−25.8942	+	4.69138i	−1.03910	+	0.188259i
$622$	3.44947	+	3.44947i	0.138311	+	0.138311i
$623$	−5.12449	+	7.31853i	−0.205308	+	0.293211i
$624$	41.0979	+	2.32911i	1.64523	+	0.0932391i
$625$	22.1491	+	11.5939i	0.885963	+	0.463756i
$626$	15.8763	−	18.9206i	0.634543	−	0.756218i
$627$	−20.1515	−	2.91953i	−0.804773	−	0.116595i
$628$	−12.6768	+	5.91130i	−0.505860	+	0.235887i
$629$	18.9351	+	32.7966i	0.754992	+	1.30769i
$630$	−19.6594	+	2.27653i	−0.783251	+	0.0906993i
$631$	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
$633$	16.2875	+	8.74923i	0.647368	+	0.347751i
$634$	45.0092	+	7.93634i	1.78755	+	0.315192i
$635$	20.6818	+	8.31714i	0.820731	+	0.330056i
$636$	−0.0875903	+	0.372169i	−0.00347318	+	0.0147575i
$637$	−29.6497	−	2.59401i	−1.17476	−	0.102778i
$638$	−11.9462	+	3.20098i	−0.472955	+	0.126728i
$639$	−27.0187	−	3.07228i	−1.06884	−	0.121538i
$640$	−2.03708	+	0.665529i	−0.0805228	+	0.0263073i
$641$	−3.35944	+	9.23000i	−0.132690	+	0.364563i	−0.988189	−	0.153242i	$-0.951029\pi$
$641$	−3.35944	+	9.23000i	−0.132690	+	0.364563i	0.855499	+	0.517805i	$0.173251\pi$
$642$	48.2797	−	19.2679i	1.90545	−	0.760443i
$643$	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
$645$	2.84971	+	0.00751244i	0.112207	+	0.000295802i
$646$	−4.57349	−	25.9375i	−0.179942	−	1.02050i
$647$	−14.2018	+	14.2018i	−0.558331	+	0.558331i	−0.928832	−	0.370501i	$-0.879186\pi$
$647$	−14.2018	+	14.2018i	−0.558331	+	0.558331i	0.370501	+	0.928832i	$0.379186\pi$
$648$	0.572019	+	0.914513i	0.0224710	+	0.0359255i
$649$		−	10.9428i		−	0.429542i
$650$	−14.7441	+	59.9601i	−0.578312	+	2.35183i
$651$	7.23215	+	4.74045i	0.283450	+	0.185793i
$652$	37.9754	+	17.7082i	1.48723	+	0.693507i
$653$	1.73834	+	19.8693i	0.0680265	+	0.777546i	0.951215	+	0.308528i	$0.0998365\pi$
$653$	1.73834	+	19.8693i	0.0680265	+	0.777546i	−0.883189	+	0.469018i	$0.844608\pi$
$654$	−13.6543	+	31.7909i	−0.533924	+	1.24312i
$655$	−24.4597	+	5.68860i	−0.955719	+	0.222272i
$656$	2.86119	−	1.65191i	0.111711	−	0.0644963i
$657$	−24.7228	+	3.70048i	−0.964528	+	0.144370i
$658$	2.20110	+	8.21463i	0.0858080	+	0.320240i
$659$	0.815140	−	0.683983i	0.0317533	−	0.0266442i	−0.626773	−	0.779202i	$-0.715625\pi$
$659$	0.815140	−	0.683983i	0.0317533	−	0.0266442i	0.658526	+	0.752558i	$0.271180\pi$
$660$	20.8982	+	9.81215i	0.813462	+	0.381938i
$661$	−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
$663$	16.1689	−	30.0998i	0.627947	−	1.16898i
$664$	−1.30202	−	1.55168i	−0.0505280	−	0.0602169i
$665$	−8.88238	+	9.89699i	−0.344444	+	0.383789i
$666$	−70.9885	+	4.35774i	−2.75075	+	0.168859i
$667$	−2.77981	+	10.3744i	−0.107635	+	0.401699i
$668$	−0.410470	−	0.880256i	−0.0158816	−	0.0340581i
$669$	−16.5826	+	12.3857i	−0.641119	+	0.478858i
$670$	−2.41637	+	19.9461i	−0.0933525	+	0.770585i
$671$	−4.44565	−	12.2143i	−0.171622	−	0.471529i
$672$	−13.6002	−	15.2343i	−0.524639	−	0.587676i
$673$	−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
$675$	24.1805	−	9.50270i	0.930710	−	0.365759i
$676$	−50.5961			−1.94600
$677$	−16.7682	−	11.7412i	−0.644455	−	0.451252i	0.205108	−	0.978739i	$-0.434245\pi$
$677$	−16.7682	−	11.7412i	−0.644455	−	0.451252i	−0.849563	+	0.527487i	$0.823134\pi$
$678$	−16.6400	+	50.4813i	−0.639055	+	1.93872i
$679$	8.11957	+	22.3083i	0.311601	+	0.856115i
$680$	−0.103735	+	0.856287i	−0.00397805	+	0.0328371i
$681$	0.235792	+	1.99029i	0.00903556	+	0.0762681i
$682$	−8.40325	−	18.0208i	−0.321777	−	0.690053i
$683$	−5.71751	+	21.3380i	−0.218774	+	0.816477i	0.766029	+	0.642806i	$0.222230\pi$
$683$	−5.71751	+	21.3380i	−0.218774	+	0.816477i	−0.984804	+	0.173671i	$0.944437\pi$
$684$	24.0623	+	7.12175i	0.920047	+	0.272307i
$685$	−29.3595	+	32.7132i	−1.12177	+	1.24991i
$686$	22.4833	+	26.7945i	0.858416	+	1.02302i
$687$	15.1631	−	0.464968i	0.578509	−	0.0177396i
$688$	1.63643	+	2.33707i	0.0623884	+	0.0890999i
$689$	−0.114078	+	0.646969i	−0.00434603	+	0.0246476i
$690$	32.4324	−	22.5822i	1.23468	−	0.859690i
$691$	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
$693$	−0.329998	+	12.7105i	−0.0125356	+	0.482831i
$694$	−21.6551	+	12.5026i	−0.822016	+	0.474591i
$695$	−3.23877	+	0.753243i	−0.122854	+	0.0285721i
$696$	0.437188	−	0.0517940i	0.0165716	−	0.00196325i
$697$	−0.239008	−	2.73187i	−0.00905306	−	0.103477i
$698$	−13.9526	−	6.50619i	−0.528112	−	0.246263i
$699$	25.3066	−	12.7591i	0.957182	−	0.482593i
$700$	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	$-0.0690713\pi$
$702$	37.0521	+	52.3903i	1.39844	+	1.97735i
$703$	−33.7929	+	33.7929i	−1.27452	+	1.27452i
$704$	4.25644	+	24.1395i	0.160421	+	0.909791i
$705$	−5.55666	−	9.68328i	−0.209276	−	0.364693i
$706$	33.8977	−	12.3377i	1.27576	−	0.464337i
$707$	−8.02039	+	0.701693i	−0.301638	+	0.0263899i
$708$	−1.93365	+	13.3466i	−0.0726711	+	0.501598i
$709$	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
$711$	3.65928	−	2.42320i	0.137234	−	0.0908772i
$712$	−0.706365	+	0.189270i	−0.0264722	+	0.00709319i
$713$	−17.2019	−	1.50497i	−0.644216	−	0.0563616i
$714$	−15.7480	+	4.74151i	−0.589353	+	0.177447i
$715$	36.8047	+	14.8010i	1.37642	+	0.553524i
$716$	−16.0551	−	2.83094i	−0.600006	−	0.105797i
$717$	12.6498	−	7.82988i	0.472415	−	0.292412i
$718$	−2.20038	+	25.1504i	−0.0821174	+	0.938606i
$719$	4.71157	−	8.16068i	0.175712	−	0.304342i	−0.764695	−	0.644392i	$-0.777111\pi$
$719$	4.71157	−	8.16068i	0.175712	−	0.304342i	0.940407	+	0.340050i	$0.110444\pi$
$720$	21.7166	+	14.3165i	0.809328	+	0.533545i
$721$	2.87301	+	4.97620i	0.106997	+	0.185323i
$722$	−4.57202	+	2.13197i	−0.170153	+	0.0793437i
$723$	−1.32681	−	3.32459i	−0.0493444	−	0.123643i
$724$	−26.1085	+	31.1149i	−0.970315	+	1.15638i
$725$	0.705492	−	10.5802i	0.0262013	−	0.392938i
$726$	−5.01651	+	7.65331i	−0.186180	+	0.284041i
$727$	−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
$729$	8.99575	−	25.4573i	0.333176	−	0.942865i
$730$	31.4516	−	20.4972i	1.16408	−	0.758636i
$731$	2.33216	−	0.411222i	0.0862579	−	0.0152096i
$732$	3.26391	+	15.6831i	0.120638	+	0.579663i
$733$	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
$735$	−15.3772	−	10.8277i	−0.567196	−	0.399387i
$736$	38.3205	+	13.9475i	1.41251	+	0.514112i
$737$	12.4684	+	3.34089i	0.459278	+	0.123063i
$738$	4.79224	+	1.88648i	0.176405	+	0.0694423i
$739$	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
$741$	41.9712	+	9.87796i	1.54185	+	0.362876i
$742$	0.259029	−	0.181374i	0.00950927	−	0.00665846i
$743$	29.3796	−	20.5718i	1.07783	−	0.754706i	0.106950	−	0.994264i	$-0.465891\pi$
$743$	29.3796	−	20.5718i	1.07783	−	0.754706i	0.970882	+	0.239558i	$0.0770025\pi$
$744$	0.204059	+	0.677741i	0.00748118	+	0.0248472i
$745$	10.6170	+	3.22720i	0.388978	+	0.118236i
$746$	−21.1251	−	12.1966i	−0.773444	−	0.446548i
$747$	−10.0972	+	49.6860i	−0.369437	+	1.81792i
$748$	18.5318	+	4.96558i	0.677589	+	0.181559i
$749$	−20.4960	−	7.45993i	−0.748907	−	0.272580i
$750$	−27.0866	+	28.0824i	−0.989063	+	1.02543i
$751$	−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
$753$	−14.2539	+	12.7249i	−0.519441	+	0.463723i
$754$	25.7916	−	4.54775i	0.939274	−	0.165619i
$755$	−25.3139	−	38.8425i	−0.921267	−	1.41362i
$756$	2.64850	−	15.4443i	0.0963250	−	0.561705i
$757$	−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
$759$	−11.4304	−	22.6713i	−0.414899	−	0.822915i
$760$	−1.07765	+	0.153230i	−0.0390906	+	0.00555824i
$761$	5.19201	−	6.18759i	0.188210	−	0.224300i	−0.663685	−	0.748012i	$-0.731009\pi$
$761$	5.19201	−	6.18759i	0.188210	−	0.224300i	0.851896	+	0.523712i	$0.175453\pi$
$762$	−21.5350	+	27.3233i	−0.780132	+	0.989819i
$763$	13.1573	−	6.13535i	0.476326	−	0.222115i
$764$	−8.99914	−	15.5870i	−0.325577	−	0.563917i
$765$	18.3879	−	11.3147i	0.664815	−	0.409082i
$766$	−14.5740	+	25.2430i	−0.526582	+	0.912066i
$767$	−2.01960	+	23.0841i	−0.0729234	+	0.833519i
$768$	0.796640	+	25.9793i	0.0287463	+	0.937447i
$769$	−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
$771$	7.28665	+	6.85306i	0.262422	+	0.246807i
$772$	−17.7281	−	1.55101i	−0.638048	−	0.0558220i
$773$	11.4302	−	3.06271i	0.411116	−	0.110158i	−0.0473325	−	0.998879i	$-0.515072\pi$
$773$	11.4302	−	3.06271i	0.411116	−	0.110158i	0.458448	+	0.888721i	$0.348405\pi$
$774$	−1.26220	+	4.26460i	−0.0453688	+	0.153288i
$775$	16.9486	−	1.83675i	0.608811	−	0.0659781i
$776$	−0.664599	+	1.82597i	−0.0238577	+	0.0655485i
$777$	23.4376	+	18.4725i	0.840820	+	0.662697i
$778$	−25.3711	+	2.21968i	−0.909598	+	0.0795795i
$779$	3.25195	−	1.18361i	0.116513	−	0.0424073i
$780$	−42.2744	−	24.5559i	−1.51367	−	0.879244i
$781$	−4.55583	−	25.8374i	−0.163020	−	0.924534i
$782$	23.2222	−	23.2222i	0.830425	−	0.830425i
$783$	−7.82859	−	7.75538i	−0.279771	−	0.277154i
$784$		−	18.8287i		−	0.672455i
$785$	−15.1782	−	0.505485i	−0.541733	−	0.0180415i
$786$	2.21756	−	39.1295i	0.0790976	−	1.39570i
$787$	−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
$789$	−19.1231	−	25.6029i	−0.680799	−	0.911488i
$790$	−3.48368	+	5.59514i	−0.123944	+	0.199066i
$791$	19.3145	−	11.1513i	0.686746	−	0.396493i
$792$	−0.689429	+	0.779608i	−0.0244978	+	0.0277022i
$793$	7.12394	+	26.5869i	0.252979	+	0.944129i
$794$	23.2020	−	19.4688i	0.823409	−	0.690922i
$795$	−0.267671	+	0.317295i	−0.00949330	+	0.0112533i
$796$	−6.40609	+	36.3307i	−0.227058	+	1.28771i
$797$	9.48608	+	13.5475i	0.336014	+	0.479878i	0.951231	−	0.308480i	$-0.0998203\pi$
$797$	9.48608	+	13.5475i	0.336014	+	0.479878i	−0.615216	+	0.788358i	$0.710931\pi$
$798$	−10.9232	−	17.6473i	−0.386678	−	0.624709i
$799$	−5.96354	−	7.10708i	−0.210975	−	0.251430i
$800$	−39.7851	−	6.16964i	−1.40662	−	0.218130i
$801$	14.7166	+	10.8847i	0.519987	+	0.384591i
$802$	13.6736	−	51.0307i	0.482833	−	1.80196i
$803$	−10.1930	−	21.8589i	−0.359702	−	0.771383i
$804$	−14.6170	−	6.27803i	−0.515502	−	0.221409i
$805$	−16.4618	−	1.99426i	−0.580202	−	0.0702885i
$806$	14.4009	+	39.5663i	0.507252	+	1.39366i
$807$	26.6671	−	5.54988i	0.938728	−	0.195365i
$808$	−0.539812	−	0.377980i	−0.0189905	−	0.0132973i
$809$	−21.1013			−0.741881			−0.370941	−	0.928657i	$-0.620965\pi$
$809$	−21.1013			−0.741881			−0.370941	+	0.928657i	$0.620965\pi$
$810$	3.61721	+	40.3857i	0.127096	+	1.41901i
$811$	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
$813$	29.5607	−	6.15208i	1.03674	−	0.215763i
$814$	−23.4693	−	64.4814i	−0.822599	−	2.26007i
$815$	28.0667	+	35.8043i	0.983133	+	1.25417i
$816$	19.8609	+	8.53029i	0.695270	+	0.298620i
$817$	1.26298	+	2.70847i	0.0441861	+	0.0947574i
$818$	3.93110	−	14.6711i	0.137448	−	0.512962i
$819$	3.04198	−	26.7521i	0.106295	−	0.934795i
$820$	−3.91811	+	0.211687i	−0.136826	+	0.00739244i
$821$	7.72326	+	9.20422i	0.269544	+	0.321230i	0.883789	−	0.467885i	$-0.154984\pi$
$821$	7.72326	+	9.20422i	0.269544	+	0.321230i	−0.614246	+	0.789115i	$0.710540\pi$
$822$	−36.1052	−	58.3309i	−1.25931	−	2.03452i
$823$	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
$825$	15.4124	+	19.7685i	0.536590	+	0.688251i
$826$	8.54427	−	7.16949i	0.297293	−	0.249459i
$827$	−12.0136	−	44.8353i	−0.417753	−	1.55907i	−0.779257	−	0.626704i	$-0.784403\pi$
$827$	−12.0136	−	44.8353i	−0.417753	−	1.55907i	0.361504	−	0.932370i	$-0.382263\pi$
$828$	9.93527	+	29.6714i	0.345275	+	1.03115i
$829$	−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
$831$	−15.9170	−	21.3104i	−0.552153	−	0.739251i
$832$	−4.52390	−	51.7084i	−0.156838	−	1.79267i
$833$	−14.1643	−	6.60493i	−0.490765	−	0.228847i
$834$	0.293632	−	5.18124i	0.0101677	−	0.179412i
$835$	0.0351000	−	1.05395i	0.00121468	−	0.0364734i
$836$			24.2112i			0.837361i
$837$	10.0935	−	14.5602i	0.348884	−	0.503273i
$838$	29.5051	−	29.5051i	1.01924	−	1.01924i
$839$	8.77845	+	49.7851i	0.303066	+	1.71877i	0.632472	+	0.774583i	$0.282040\pi$
$839$	8.77845	+	49.7851i	0.303066	+	1.71877i	−0.329406	+	0.944188i	$0.606849\pi$
$840$	0.174187	+	0.656999i	0.00601003	+	0.0226686i
$841$	23.0248	−	8.38035i	0.793959	−	0.288977i
$842$	−13.8072	+	1.20798i	−0.475829	+	0.0416296i
$843$	−10.0799	−	7.94457i	−0.347172	−	0.273625i
$844$	7.51891	−	20.6580i	0.258812	−	0.711079i
$845$	−48.9870	−	24.8605i	−1.68520	−	0.855227i
$846$	16.9415	−	4.07129i	0.582461	−	0.139974i
$847$	3.70879	−	0.993767i	0.127436	−	0.0341463i
$848$	−0.414021	−	0.0362221i	−0.0142175	−	0.00124387i
$849$	−18.1399	−	17.0605i	−0.622561	−	0.585516i
$850$	−18.0439	+	26.9385i	−0.618899	+	0.923982i
$851$	−58.6858	−	10.3479i	−2.01172	−	0.354721i
$852$	0.991020	+	32.3182i	0.0339518	+	1.10720i
$853$	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
$855$	19.7978	+	18.7184i	0.677071	+	0.640154i
$856$	−0.892646	−	1.54611i	−0.0305100	−	0.0528449i
$857$	−9.12817	+	4.25654i	−0.311812	+	0.145400i	−0.572224	−	0.820097i	$-0.693919\pi$
$857$	−9.12817	+	4.25654i	−0.311812	+	0.145400i	0.260412	+	0.965498i	$0.416142\pi$
$858$	−38.3232	+	48.6238i	−1.30833	+	1.65999i
$859$	−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
$861$	−0.972864	−	1.92959i	−0.0331551	−	0.0657603i
$862$	3.37367	−	4.81810i	0.114908	−	0.164105i
$863$	23.9621	+	23.9621i	0.815678	+	0.815678i	0.985479	−	0.169800i	$-0.0543122\pi$
$863$	23.9621	+	23.9621i	0.815678	+	0.815678i	−0.169800	+	0.985479i	$0.554312\pi$
$864$	−31.9247	+	27.0446i	−1.08610	+	0.920076i
$865$	8.50730	−	40.3441i	0.289257	−	1.37174i
$866$	8.46774	−	1.49309i	0.287745	−	0.0507373i
$867$	−8.58127	+	7.66079i	−0.291435	+	0.260174i
$868$	4.34538	−	9.31869i	0.147492	−	0.316297i
$869$	3.24378	+	2.72185i	0.110038	+	0.0923326i
$870$	15.5358	+	5.70100i	0.526714	+	0.193282i
$871$	−25.6857	−	9.34885i	−0.870328	−	0.316774i
$872$	1.14779	+	0.307549i	0.0388690	+	0.0104149i
$873$	46.1217	−	15.4435i	1.56098	−	0.522685i
$874$	35.8915	+	20.7220i	1.21405	+	0.700932i
$875$	16.3255	−	1.22113i	0.551901	−	0.0412816i
$876$	8.56951	+	28.4619i	0.289537	+	0.961637i
$877$	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
$879$	−33.9615	−	7.99287i	−1.14549	−	0.269593i
$880$	−7.29851	+	24.0110i	−0.246033	+	0.809412i
$881$	20.2756	+	11.7061i	0.683103	+	0.394390i	0.801023	−	0.598633i	$-0.204289\pi$
$881$	20.2756	+	11.7061i	0.683103	+	0.394390i	−0.117920	+	0.993023i	$0.537623\pi$
$882$	22.9665	−	18.2767i	0.773321	−	0.615409i
$883$	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
$885$	−8.43007	+	11.9721i	−0.283374	+	0.402437i
$886$	−43.1969	−	36.2465i	−1.45123	−	1.21773i
$887$	−13.8426	+	29.6855i	−0.464788	+	0.996741i	0.524587	+	0.851357i	$0.324220\pi$
$887$	−13.8426	+	29.6855i	−0.464788	+	0.996741i	−0.989375	+	0.145384i	$0.953558\pi$
$888$	0.497687	+	2.39139i	0.0167013	+	0.0802497i
$889$	14.3756	−	2.53481i	0.482144	−	0.0850149i
$890$	−26.8974	−	5.67182i	−0.901604	−	0.190120i
$891$	26.0149	+	1.35174i	0.871531	+	0.0452851i
$892$	17.4021	+	17.4021i	0.582665	+	0.582665i
$893$	6.71538	−	9.59056i	0.224722	−	0.320936i
$894$	−9.49386	+	14.4841i	−0.317522	+	0.484420i
$895$	−14.1535	−	10.6296i	−0.473099	−	0.355309i
$896$	−0.902060	+	1.07503i	−0.0301357	+	0.0359143i
$897$	19.9286	+	49.9352i	0.665396	+	1.66729i
$898$	17.4298	−	8.12765i	0.581640	−	0.271223i
$899$	−3.61538	−	6.26203i	−0.120580	−	0.208850i
$900$	−15.3049	−	26.8346i	−0.510162	−	0.894486i
$901$	−0.172483	+	0.298750i	−0.00574625	+	0.00995280i
$902$	−0.433074	+	4.95006i	−0.0144198	+	0.164819i
$903$	1.58675	−	0.982153i	0.0528036	−	0.0326840i
$904$	1.79776	+	0.316994i	0.0597926	+	0.0105430i
$905$	−40.5666	+	17.2969i	−1.34848	+	0.574968i
$906$	69.2851	−	20.8609i	2.30184	−	0.693056i
$907$	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
$909$	1.01067	+	16.4640i	0.0335217	+	0.546075i
$910$	12.5569	+	38.4349i	0.416258	+	1.27410i
$911$	−6.61616	+	18.1777i	−0.219203	+	0.602255i	−0.999739	−	0.0228557i	$-0.992724\pi$
$911$	−6.61616	+	18.1777i	−0.219203	+	0.602255i	0.780536	+	0.625111i	$0.214946\pi$
$912$	−3.91110	+	26.9956i	−0.129509	+	0.893913i
$913$	−48.7315	+	4.26345i	−1.61278	+	0.141100i
$914$	67.0891	−	24.4184i	2.21911	−	0.807690i
$915$	−4.54581	+	16.7880i	−0.150280	+	0.554995i
$916$	−3.13228	−	17.7641i	−0.103493	−	0.586941i
$917$	−11.6282	+	11.6282i	−0.383996	+	0.383996i
$918$	8.87375	+	32.5057i	0.292877	+	1.07285i
$919$			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
$921$	−18.4811	+	9.31782i	−0.608972	+	0.307032i
$922$	45.2591	+	21.1047i	1.49053	+	0.695046i
$923$	4.84210	+	55.3454i	0.159380	+	1.82172i
$924$	15.0134	−	1.77865i	0.493905	−	0.0585134i
$925$	58.8200	−	1.21683i	1.93399	−	0.0400092i
$926$	−9.44552	+	5.45337i	−0.310399	+	0.179209i
$927$	10.3446	−	5.61963i	0.339760	−	0.184573i
$928$	4.41970	+	16.4946i	0.145084	+	0.541461i
$929$	40.3230	−	33.8350i	1.32296	−	1.11009i	0.337286	−	0.941402i	$-0.390491\pi$
$929$	40.3230	−	33.8350i	1.32296	−	1.11009i	0.985669	−	0.168689i	$-0.0539535\pi$
$930$	−4.68914	+	26.1895i	−0.153763	+	0.858789i
$931$	3.42478	−	19.4229i	0.112243	−	0.636560i
$932$	−19.3288	−	27.6044i	−0.633137	−	0.904213i
$933$	−4.19168	+	0.128535i	−0.137229	+	0.00420806i
$934$	53.0403	+	63.2110i	1.73553	+	2.06833i
$935$	15.5026	+	13.9133i	0.506988	+	0.455013i
$936$	1.59825	−	1.51736i	0.0522404	−	0.0495965i
$937$	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
$939$	2.49799	+	21.0853i	0.0815188	+	0.688092i
$940$	−10.4475	+	8.18973i	−0.340761	+	0.267119i
$941$	−0.0906224	−	0.248983i	−0.00295420	−	0.00811661i	0.938207	−	0.346075i	$-0.112486\pi$
$941$	−0.0906224	−	0.248983i	−0.00295420	−	0.00811661i	−0.941161	+	0.337959i	$0.890264\pi$
$942$	7.41988	−	22.5099i	0.241753	−	0.733413i
$943$	3.53479	+	2.47509i	0.115109	+	0.0806000i
$944$	−14.6593			−0.477121
$945$	10.1529	−	13.6518i	0.330273	−	0.444093i
$946$	−4.29098			−0.139512
$947$	−27.9252	−	19.5534i	−0.907446	−	0.635401i	0.0238294	−	0.999716i	$-0.492414\pi$
$947$	−27.9252	−	19.5534i	−0.907446	−	0.635401i	−0.931276	+	0.364315i	$0.881303\pi$
$948$	−3.47539	−	3.89297i	−0.112875	−	0.126438i
$949$	17.4680	+	47.9930i	0.567037	+	1.55792i
$950$	−38.7301	−	13.1960i	−1.25657	−	0.428135i
$951$	−31.4782	+	23.5113i	−1.02075	+	0.762407i
$952$	0.238709	+	0.511912i	0.00773659	+	0.0165912i
$953$	6.91874	−	25.8211i	0.224120	−	0.836427i	−0.758635	−	0.651516i	$-0.774133\pi$
$953$	6.91874	−	25.8211i	0.224120	−	0.836427i	0.982755	−	0.184912i	$-0.0591999\pi$
$954$	−0.357701	−	0.540165i	−0.0115810	−	0.0174885i
$955$	−1.05425	−	19.5130i	−0.0341146	−	0.631426i
$956$	−11.3705	−	13.5509i	−0.367749	−	0.438266i
$957$	5.03125	−	9.36611i	0.162637	−	0.302763i
$958$	−31.9305	−	45.6014i	−1.03163	−	1.47331i
$959$	−4.99834	+	28.3470i	−0.161405	+	0.915372i
$960$	13.9397	−	29.6891i	0.449901	−	0.958212i
$961$	−14.8420	+	12.4539i	−0.478775	+	0.401740i
$962$	37.6084	+	140.356i	1.21254	+	4.52528i
$963$	−16.3686	+	41.5813i	−0.527471	+	1.33994i
$964$	−3.68603	+	2.12813i	−0.118719	+	0.0685425i
$965$	−16.4022	−	10.2124i	−0.528006	−	0.328750i
$966$	10.2130	−	23.7788i	0.328599	−	0.765069i
$967$	−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
$969$	18.9360	+	12.4120i	0.608313	+	0.398731i
$970$	−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	$-0.225350\pi$
$972$	−31.4908	−	6.24566i	−1.01007	−	0.200329i
$973$	−1.53972	+	1.53972i	−0.0493610	+	0.0493610i
$974$	14.0086	+	79.4468i	0.448865	+	2.54564i
$975$	−28.8643	−	44.5466i	−0.924398	−	1.42663i
$976$	−16.3627	+	5.95554i	−0.523758	+	0.190632i
$977$	−35.4680	+	3.10305i	−1.13472	+	0.0992752i	−0.639000	−	0.769207i	$-0.720652\pi$
$977$	−35.4680	+	3.10305i	−1.13472	+	0.0992752i	−0.495721	+	0.868482i	$0.665096\pi$
$978$	−65.9434	+	26.3173i	−2.10864	+	0.841533i
$979$	−6.04024	+	16.5954i	−0.193047	+	0.530392i
$980$	−10.1200	+	19.9412i	−0.323272	+	0.636999i
$981$	−11.8662	−	27.2738i	−0.378860	−	0.870787i
$982$	46.7049	−	12.5145i	1.49041	−	0.399355i
$983$	36.5814	+	3.20046i	1.16677	+	0.102079i	0.654030	−	0.756468i	$-0.273077\pi$
$983$	36.5814	+	3.20046i	1.16677	+	0.102079i	0.512735	+	0.858547i	$0.328632\pi$
$984$	0.0405214	−	0.172174i	0.00129177	−	0.00548871i
$985$	−1.67321	+	4.16068i	−0.0533128	+	0.132570i
$986$	13.5432	+	2.38804i	0.431305	+	0.0760507i
$987$	−6.44047	−	3.45966i	−0.205002	−	0.110122i
$988$	4.46840	−	51.0740i	0.142159	−	1.62488i
$989$	−1.86320	+	3.22716i	−0.0592464	+	0.102618i
$990$	−36.3722	+	14.4047i	−1.15598	+	0.457811i
$991$	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
$993$	−27.9710	−	4.05242i	−0.887634	−	0.128600i
$994$	17.1893	−	20.4854i	0.545210	−	0.649756i
$995$	−24.0536	+	32.0277i	−0.762549	+	1.01535i
$996$	60.1899	+	3.41109i	1.90719	+	0.108085i
$997$	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
$999$	39.0800	−	47.0206i	1.23644	−	1.48766i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.14	✓	192	27.2	odd	18	inner
135.2.q.a.68.14	yes	192	5.3	odd	4	inner
135.2.q.a.83.14	yes	192	135.83	even	36	inner
135.2.q.a.122.14	yes	192	1.1	even	1	trivial
405.2.r.a.8.3		192	135.133	odd	36
405.2.r.a.152.3		192	3.2	odd	2
405.2.r.a.233.3		192	15.8	even	4
405.2.r.a.332.3		192	27.25	even	9
675.2.ba.b.68.3		192	5.2	odd	4
675.2.ba.b.218.3		192	135.2	even	36
675.2.ba.b.257.3		192	5.4	even	2
675.2.ba.b.407.3		192	135.29	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.65044 + 1.15565i) q^{2} +(-1.69572 + 0.352907i) q^{3} +(0.704386 + 1.93528i) q^{4} +(-0.268922 + 2.21984i) q^{5} +(-3.20652 - 1.37721i) q^{6} +(0.618828 + 1.32708i) q^{7} +(-0.0310202 + 0.115769i) q^{8} +(2.75091 - 1.19686i) q^{9} +O(q^{10})\)	\(q+(1.65044 + 1.15565i) q^{2} +(-1.69572 + 0.352907i) q^{3} +(0.704386 + 1.93528i) q^{4} +(-0.268922 + 2.21984i) q^{5} +(-3.20652 - 1.37721i) q^{6} +(0.618828 + 1.32708i) q^{7} +(-0.0310202 + 0.115769i) q^{8} +(2.75091 - 1.19686i) q^{9} +(-3.00920 + 3.35293i) q^{10} +(1.86051 + 2.21727i) q^{11} +(-1.87741 - 3.03311i) q^{12} +(-3.51558 - 5.02076i) q^{13} +(-0.512304 + 2.90542i) q^{14} +(-0.327380 - 3.85912i) q^{15} +(2.97033 - 2.49240i) q^{16} +(-0.833002 - 3.10881i) q^{17} +(5.92337 + 1.20375i) q^{18} +(3.51741 - 2.03078i) q^{19} +(-4.48544 + 1.04318i) q^{20} +(-1.51769 - 2.03197i) q^{21} +(0.508272 + 5.80958i) q^{22} +(4.58997 + 2.14034i) q^{23} +(0.0117458 - 0.207259i) q^{24} +(-4.85536 - 1.19393i) q^{25} -12.3493i q^{26} +(-4.24239 + 3.00035i) q^{27} +(-2.13239 + 2.13239i) q^{28} +(0.368261 + 2.08851i) q^{29} +(3.91948 - 6.74759i) q^{30} +(-3.20394 + 1.16614i) q^{31} +(8.02150 - 0.701790i) q^{32} +(-3.93739 - 3.10328i) q^{33} +(2.21787 - 6.09356i) q^{34} +(-3.11232 + 1.01682i) q^{35} +(4.25397 + 4.48075i) q^{36} +(-11.3656 + 3.04540i) q^{37} +(8.15214 + 0.713220i) q^{38} +(7.73328 + 7.27312i) q^{39} +(-0.248646 - 0.0999926i) q^{40} +(0.839107 + 0.147957i) q^{41} +(-0.156621 - 5.10757i) q^{42} +(-0.0641287 + 0.732994i) q^{43} +(-2.98053 + 5.16243i) q^{44} +(1.91706 + 6.42844i) q^{45} +(5.10199 + 8.83690i) q^{46} +(2.61254 - 1.21825i) q^{47} +(-4.15725 + 5.27466i) q^{48} +(3.12132 - 3.71984i) q^{49} +(-6.63372 - 7.58161i) q^{50} +(2.50966 + 4.97768i) q^{51} +(7.24028 - 10.3402i) q^{52} +(-0.0757900 - 0.0757900i) q^{53} +(-10.4692 + 0.0491845i) q^{54} +(-5.42232 + 3.53376i) q^{55} +(-0.172831 + 0.0304748i) q^{56} +(-5.24785 + 4.68494i) q^{57} +(-1.80580 + 3.87255i) q^{58} +(-2.89613 - 2.43014i) q^{59} +(7.23789 - 3.35188i) q^{60} +(-4.21993 - 1.53593i) q^{61} +(-6.63556 - 1.77799i) q^{62} +(3.29067 + 2.91003i) q^{63} +(7.33402 + 4.23430i) q^{64} +(12.0907 - 6.45381i) q^{65} +(-2.91213 - 9.67203i) q^{66} +(3.65313 - 2.55795i) q^{67} +(5.42967 - 3.80189i) q^{68} +(-8.53862 - 2.00957i) q^{69} +(-6.31179 - 1.91856i) q^{70} +(-7.84988 - 4.53213i) q^{71} +(0.0532255 + 0.355597i) q^{72} +(-8.04880 - 2.15667i) q^{73} +(-22.2777 - 8.10840i) q^{74} +(8.65467 + 0.311072i) q^{75} +(6.40774 + 5.37673i) q^{76} +(-1.79116 + 3.84116i) q^{77} +(4.35814 + 20.9408i) q^{78} +(1.44073 - 0.254040i) q^{79} +(4.73394 + 7.26391i) q^{80} +(6.13505 - 6.58492i) q^{81} +(1.21391 + 1.21391i) q^{82} +(-9.69375 + 13.8441i) q^{83} +(2.86339 - 4.36846i) q^{84} +(7.12506 - 1.01310i) q^{85} +(-0.952926 + 1.13565i) q^{86} +(-1.36152 - 3.41157i) q^{87} +(-0.314404 + 0.146609i) q^{88} +(3.05075 + 5.28406i) q^{89} +(-4.26505 + 12.8252i) q^{90} +(4.48742 - 7.77244i) q^{91} +(-0.909052 + 10.3905i) q^{92} +(5.02144 - 3.10813i) q^{93} +(5.71971 + 1.00854i) q^{94} +(3.56209 + 8.35420i) q^{95} +(-13.3545 + 4.02088i) q^{96} +(16.1512 + 1.41304i) q^{97} +(9.45039 - 2.53222i) q^{98} +(7.77187 + 3.87275i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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