LMFDB - Embedded newform 135.2.q.a.2.14

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			2.14
Character	$\chi$	$=$	135.2
Dual form			135.2.q.a.68.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15565 + 1.65044i) q^{2} +(-0.352907 + 1.69572i) q^{3} +(-0.704386 + 1.93528i) q^{4} +(-2.13942 - 0.650308i) q^{5} +(-3.20652 + 1.37721i) q^{6} +(1.32708 + 0.618828i) q^{7} +(-0.115769 + 0.0310202i) q^{8} +(-2.75091 - 1.19686i) q^{9} +O(q^{10})$	\(q+(1.15565 + 1.65044i) q^{2} +(-0.352907 + 1.69572i) q^{3} +(-0.704386 + 1.93528i) q^{4} +(-2.13942 - 0.650308i) q^{5} +(-3.20652 + 1.37721i) q^{6} +(1.32708 + 0.618828i) q^{7} +(-0.115769 + 0.0310202i) q^{8} +(-2.75091 - 1.19686i) q^{9} +(-1.39912 - 4.28251i) q^{10} +(1.86051 - 2.21727i) q^{11} +(-3.03311 - 1.87741i) q^{12} +(5.02076 + 3.51558i) q^{13} +(0.512304 + 2.90542i) q^{14} +(1.85775 - 3.39835i) q^{15} +(2.97033 + 2.49240i) q^{16} +(-3.10881 - 0.833002i) q^{17} +(-1.20375 - 5.92337i) q^{18} +(-3.51741 - 2.03078i) q^{19} +(2.76550 - 3.68231i) q^{20} +(-1.51769 + 2.03197i) q^{21} +(5.80958 + 0.508272i) q^{22} +(-2.14034 - 4.58997i) q^{23} +(-0.0117458 - 0.207259i) q^{24} +(4.15420 + 2.78256i) q^{25} +12.3493i q^{26} +(3.00035 - 4.24239i) q^{27} +(-2.13239 + 2.13239i) q^{28} +(-0.368261 + 2.08851i) q^{29} +(7.75568 - 0.861192i) q^{30} +(-3.20394 - 1.16614i) q^{31} +(-0.701790 + 8.02150i) q^{32} +(3.10328 + 3.93739i) q^{33} +(-2.21787 - 6.09356i) q^{34} +(-2.43675 - 2.18694i) q^{35} +(4.25397 - 4.48075i) q^{36} +(3.04540 - 11.3656i) q^{37} +(-0.713220 - 8.15214i) q^{38} +(-7.73328 + 7.27312i) q^{39} +(0.267850 + 0.00892031i) q^{40} +(0.839107 - 0.147957i) q^{41} +(-5.10757 - 0.156621i) q^{42} +(-0.732994 + 0.0641287i) q^{43} +(2.98053 + 5.16243i) q^{44} +(5.10702 + 4.34952i) q^{45} +(5.10199 - 8.83690i) q^{46} +(-1.21825 + 2.61254i) q^{47} +(-5.27466 + 4.15725i) q^{48} +(-3.12132 - 3.71984i) q^{49} +(0.208362 + 10.0719i) q^{50} +(2.50966 - 4.97768i) q^{51} +(-10.3402 + 7.24028i) 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} +(4.68494 - 5.24785i) q^{57} +(-3.87255 + 1.80580i) q^{58} +(2.89613 - 2.43014i) q^{59} +(5.26819 + 5.98902i) q^{60} +(-4.21993 + 1.53593i) q^{61} +(-1.77799 - 6.63556i) q^{62} +(-2.91003 - 3.29067i) q^{63} +(-7.33402 + 4.23430i) q^{64} +(-8.45529 - 10.7863i) q^{65} +(-2.91213 + 9.67203i) q^{66} +(-2.55795 + 3.65313i) q^{67} +(3.80189 - 5.42967i) q^{68} +(8.53862 - 2.00957i) q^{69} +(0.793385 - 6.54906i) q^{70} +(-7.84988 + 4.53213i) q^{71} +(0.355597 + 0.0532255i) q^{72} +(2.15667 + 8.04880i) q^{73} +(22.2777 - 8.10840i) q^{74} +(-6.18448 + 6.06236i) q^{75} +(6.40774 - 5.37673i) q^{76} +(3.84116 - 1.79116i) q^{77} +(-20.9408 - 4.35814i) 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} +(-13.8441 + 9.69375i) q^{83} +(-2.86339 - 4.36846i) q^{84} +(6.10932 + 3.80382i) q^{85} +(-0.952926 - 1.13565i) q^{86} +(-3.41157 - 1.36152i) q^{87} +(-0.146609 + 0.314404i) q^{88} +(-3.05075 + 5.28406i) q^{89} +(-1.27670 + 13.4554i) q^{90} +(4.48742 + 7.77244i) q^{91} +(10.3905 - 0.909052i) q^{92} +(3.10813 - 5.02144i) q^{93} +(-5.71971 + 1.00854i) q^{94} +(6.20457 + 6.63207i) q^{95} +(-13.3545 - 4.02088i) q^{96} +(1.41304 + 16.1512i) q^{97} +(2.53222 - 9.45039i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.15565	+	1.65044i	0.817169	+	1.16704i	0.983489	+	0.180966i	$0.0579225\pi$
$2$	1.15565	+	1.65044i	0.817169	+	1.16704i	−0.166320	+	0.986072i	$0.553189\pi$
$3$	−0.352907	+	1.69572i	−0.203751	+	0.979023i
$3$	−0.352907	+	1.69572i	−0.203751	+	0.979023i
$4$	−0.704386	+	1.93528i	−0.352193	+	0.967642i
$5$	−2.13942	−	0.650308i	−0.956776	−	0.290826i
$5$	−2.13942	−	0.650308i	−0.956776	−	0.290826i
$6$	−3.20652	+	1.37721i	−1.30906	+	0.562242i
$7$	1.32708	+	0.618828i	0.501590	+	0.233895i	0.656910	−	0.753969i	$-0.271863\pi$
$7$	1.32708	+	0.618828i	0.501590	+	0.233895i	−0.155320	+	0.987864i	$0.549641\pi$
$8$	−0.115769	+	0.0310202i	−0.0409305	+	0.0109673i
$9$	−2.75091	−	1.19686i	−0.916971	−	0.398954i
$10$	−1.39912	−	4.28251i	−0.442442	−	1.35425i
$11$	1.86051	−	2.21727i	0.560965	−	0.668532i	−0.408785	−	0.912631i	$-0.634047\pi$
$11$	1.86051	−	2.21727i	0.560965	−	0.668532i	0.969751	+	0.244098i	$0.0784919\pi$
$12$	−3.03311	−	1.87741i	−0.875584	−	0.541963i
$13$	5.02076	+	3.51558i	1.39251	+	0.975045i	0.998433	+	0.0559675i	$0.0178243\pi$
$13$	5.02076	+	3.51558i	1.39251	+	0.975045i	0.394076	+	0.919078i	$0.371065\pi$
$14$	0.512304	+	2.90542i	0.136919	+	0.776506i
$15$	1.85775	−	3.39835i	0.479670	−	0.877449i
$16$	2.97033	+	2.49240i	0.742582	+	0.623101i
$17$	−3.10881	−	0.833002i	−0.753996	−	0.202033i	−0.138706	−	0.990334i	$-0.544294\pi$
$17$	−3.10881	−	0.833002i	−0.753996	−	0.202033i	−0.615290	+	0.788301i	$0.710961\pi$
$18$	−1.20375	−	5.92337i	−0.283726	−	1.39615i
$19$	−3.51741	−	2.03078i	−0.806949	−	0.465892i	0.0389464	−	0.999241i	$-0.487600\pi$
$19$	−3.51741	−	2.03078i	−0.806949	−	0.465892i	−0.845895	+	0.533349i	$0.820933\pi$
$20$	2.76550	−	3.68231i	0.618385	−	0.823389i
$21$	−1.51769	+	2.03197i	−0.331188	+	0.443411i
$22$	5.80958	+	0.508272i	1.23861	+	0.108364i
$23$	−2.14034	−	4.58997i	−0.446291	−	0.957074i	−0.992818	−	0.119633i	$-0.961828\pi$
$23$	−2.14034	−	4.58997i	−0.446291	−	0.957074i	0.546527	−	0.837441i	$-0.315949\pi$
$24$	−0.0117458	−	0.207259i	−0.00239760	−	0.0423065i
$25$	4.15420	+	2.78256i	0.830840	+	0.556511i
$26$			12.3493i			2.42189i
$27$	3.00035	−	4.24239i	0.577418	−	0.816448i
$28$	−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	$0.992466\pi$
$30$	7.75568	−	0.861192i	1.41599	−	0.157231i
$31$	−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	$0.710165\pi$
$32$	−0.701790	+	8.02150i	−0.124060	+	1.41801i
$33$	3.10328	+	3.93739i	0.540211	+	0.685412i
$34$	−2.21787	−	6.09356i	−0.380362	−	1.04504i
$35$	−2.43675	−	2.18694i	−0.411886	−	0.369661i
$36$	4.25397	−	4.48075i	0.708995	−	0.746791i
$37$	3.04540	−	11.3656i	0.500661	−	1.86849i	0.00497757	−	0.999988i	$-0.498416\pi$
$37$	3.04540	−	11.3656i	0.500661	−	1.86849i	0.495683	−	0.868503i	$-0.334918\pi$
$38$	−0.713220	−	8.15214i	−0.115700	−	1.32245i
$39$	−7.73328	+	7.27312i	−1.23832	+	1.16463i
$40$	0.267850	+	0.00892031i	0.0423509	+	0.00141043i
$41$	0.839107	−	0.147957i	0.131046	−	0.0231070i	−0.107740	−	0.994179i	$-0.534361\pi$
$41$	0.839107	−	0.147957i	0.131046	−	0.0231070i	0.238787	+	0.971072i	$0.423250\pi$
$42$	−5.10757	−	0.156621i	−0.788114	−	0.0241671i
$43$	−0.732994	+	0.0641287i	−0.111781	+	0.00977953i	−0.142909	−	0.989736i	$-0.545646\pi$
$43$	−0.732994	+	0.0641287i	−0.111781	+	0.00977953i	0.0311282	+	0.999515i	$0.490090\pi$
$44$	2.98053	+	5.16243i	0.449332	+	0.778266i
$45$	5.10702	+	4.34952i	0.761310	+	0.648389i
$46$	5.10199	−	8.83690i	0.752247	−	1.30293i
$47$	−1.21825	+	2.61254i	−0.177700	+	0.381078i	−0.974902	−	0.222634i	$-0.928535\pi$
$47$	−1.21825	+	2.61254i	−0.177700	+	0.381078i	0.797203	+	0.603712i	$0.206312\pi$
$48$	−5.27466	+	4.15725i	−0.761332	+	0.600048i
$49$	−3.12132	−	3.71984i	−0.445902	−	0.531406i
$50$	0.208362	+	10.0719i	0.0294668	+	1.42439i
$51$	2.50966	−	4.97768i	0.351422	−	0.697015i
$52$	−10.3402	+	7.24028i	−1.43393	+	1.00405i
$53$	0.0757900	+	0.0757900i	0.0104106	+	0.0104106i	0.712293	−	0.701882i	$-0.247657\pi$
$53$	0.0757900	+	0.0757900i	0.0104106	+	0.0104106i	−0.701882	+	0.712293i	$0.747657\pi$
$54$	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
$57$	4.68494	−	5.24785i	0.620536	−	0.695095i
$58$	−3.87255	+	1.80580i	−0.508491	+	0.237113i
$59$	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	$0.198629\pi$
$60$	5.26819	+	5.98902i	0.680120	+	0.773180i
$61$	−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	$0.481710\pi$
$62$	−1.77799	−	6.63556i	−0.225805	−	0.842717i
$63$	−2.91003	−	3.29067i	−0.366630	−	0.414586i
$64$	−7.33402	+	4.23430i	−0.916753	+	0.529287i
$65$	−8.45529	−	10.7863i	−1.04875	−	1.33788i
$66$	−2.91213	+	9.67203i	−0.358458	+	1.19054i
$67$	−2.55795	+	3.65313i	−0.312504	+	0.446301i	−0.944423	−	0.328733i	$-0.893378\pi$
$67$	−2.55795	+	3.65313i	−0.312504	+	0.446301i	0.631919	+	0.775034i	$0.282267\pi$
$68$	3.80189	−	5.42967i	0.461047	−	0.658444i
$69$	8.53862	−	2.00957i	1.02793	−	0.241924i
$70$	0.793385	−	6.54906i	0.0948277	−	0.782762i
$71$	−7.84988	+	4.53213i	−0.931609	+	0.537865i	−0.887320	−	0.461154i	$-0.847436\pi$
$71$	−7.84988	+	4.53213i	−0.931609	+	0.537865i	−0.0442890	+	0.999019i	$0.514102\pi$
$72$	0.355597	+	0.0532255i	0.0419075	+	0.00627268i
$73$	2.15667	+	8.04880i	0.252419	+	0.942041i	0.969508	+	0.245059i	$0.0788074\pi$
$73$	2.15667	+	8.04880i	0.252419	+	0.942041i	−0.717089	+	0.696982i	$0.754526\pi$
$74$	22.2777	−	8.10840i	2.58972	−	0.942583i
$75$	−6.18448	+	6.06236i	−0.714122	+	0.700022i
$76$	6.40774	−	5.37673i	0.735018	−	0.616754i
$77$	3.84116	−	1.79116i	0.437741	−	0.204122i
$78$	−20.9408	−	4.35814i	−2.37108	−	0.493462i
$79$	−1.44073	−	0.254040i	−0.162095	−	0.0285818i	0.0920115	−	0.995758i	$-0.470670\pi$
$79$	−1.44073	−	0.254040i	−0.162095	−	0.0285818i	−0.254107	+	0.967176i	$0.581781\pi$
$80$	−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
$83$	−13.8441	+	9.69375i	−1.51959	+	1.06403i	−0.545431	+	0.838155i	$0.683634\pi$
$83$	−13.8441	+	9.69375i	−1.51959	+	1.06403i	−0.974157	+	0.225872i	$0.927477\pi$
$84$	−2.86339	−	4.36846i	−0.312421	−	0.476638i
$85$	6.10932	+	3.80382i	0.662649	+	0.412582i
$86$	−0.952926	−	1.13565i	−0.102757	−	0.122461i
$87$	−3.41157	−	1.36152i	−0.365758	−	0.145970i
$88$	−0.146609	+	0.314404i	−0.0156286	+	0.0335156i
$89$	−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	$0.271486\pi$
$90$	−1.27670	+	13.4554i	−0.134576	+	1.41832i
$91$	4.48742	+	7.77244i	0.470410	+	0.814774i
$92$	10.3905	−	0.909052i	1.08329	−	0.0947752i
$93$	3.10813	−	5.02144i	0.322299	−	0.520699i
$94$	−5.71971	+	1.00854i	−0.589943	+	0.104023i
$95$	6.20457	+	6.63207i	0.636575	+	0.680436i
$96$	−13.3545	−	4.02088i	−1.36299	−	0.410379i
$97$	1.41304	+	16.1512i	0.143473	+	1.63990i	0.637496	+	0.770453i	$0.279970\pi$
$97$	1.41304	+	16.1512i	0.143473	+	1.63990i	−0.494023	+	0.869449i	$0.664474\pi$
$98$	2.53222	−	9.45039i	0.255793	−	0.954633i
$99$	−7.77187	+	3.87275i	−0.781102	+	0.389226i
$100$	−8.31119	+	6.07956i	−0.831119	+	0.607956i
$101$	−1.88053	−	5.16673i	−0.187120	−	0.514108i	0.810290	−	0.586029i	$-0.199309\pi$
$101$	−1.88053	−	5.16673i	−0.187120	−	0.514108i	−0.997410	+	0.0719204i	$0.977087\pi$
$102$	11.1157	−	1.61043i	1.10061	−	0.159456i
$103$	0.342012	−	3.90922i	0.0336994	−	0.385186i	−0.960551	−	0.278105i	$-0.910294\pi$
$103$	0.342012	−	3.90922i	0.0336994	−	0.385186i	0.994250	−	0.107082i	$-0.0341507\pi$
$104$	−0.690302	−	0.251249i	−0.0676897	−	0.0246370i
$105$	4.56838	−	3.36025i	0.445828	−	0.327927i
$106$	−0.0375001	+	0.212674i	−0.00364233	+	0.0206567i
$107$	10.5329	−	10.5329i	1.01825	−	1.01825i	0.0184189	−	0.999830i	$-0.494137\pi$
$107$	10.5329	−	10.5329i	1.01825	−	1.01825i	0.999830	−	0.0184189i	$-0.00586325\pi$
$108$	6.09682	+	8.79481i	0.586667	+	0.846281i
$109$		−	9.91447i		−	0.949634i	−0.880085	−	0.474817i	$-0.842514\pi$
$109$		−	9.91447i		−	0.949634i	0.880085	−	0.474817i	$-0.157486\pi$
$110$	−12.0986	−	4.86542i	−1.15355	−	0.463899i
$111$	18.1981	+	9.17513i	1.72729	+	0.870865i
$112$	2.39950	+	5.14574i	0.226731	+	0.486227i
$113$	15.1732	+	1.32748i	1.42737	+	0.124879i	0.774492	−	0.632583i	$-0.218005\pi$
$113$	15.1732	+	1.32748i	1.42737	+	0.124879i	0.652879	+	0.757462i	$0.273561\pi$
$114$	14.0754	+	1.66753i	1.31829	+	0.156178i
$115$	1.59418	+	11.2117i	0.148658	+	1.04550i
$116$	−3.78247	−	2.18381i	−0.351193	−	0.202762i
$117$	−9.60403	−	15.6802i	−0.887893	−	1.44963i
$118$	7.35771	+	1.97149i	0.677332	+	0.181491i
$119$	−3.61015	−	3.02928i	−0.330942	−	0.277693i
$120$	−0.109653	+	0.451051i	−0.0100099	+	0.0411751i
$121$	0.455341	+	2.58237i	0.0413946	+	0.234761i
$122$	−7.41172	−	5.18974i	−0.671026	−	0.469857i
$123$	−0.0452332	+	1.47510i	−0.00407854	+	0.133006i
$124$	4.51362	−	5.37912i	0.405335	−	0.483059i
$125$	−7.07804	−	8.65455i	−0.633080	−	0.774087i
$126$	2.06808	−	8.60571i	0.184239	−	0.766658i
$127$	−9.62937	+	2.58018i	−0.854468	+	0.228954i	−0.659360	−	0.751828i	$-0.729173\pi$
$127$	−9.62937	+	2.58018i	−0.854468	+	0.228954i	−0.195109	+	0.980782i	$0.562506\pi$
$128$	−0.868604	−	0.405037i	−0.0767745	−	0.0358005i
$129$	0.149935	−	1.26558i	0.0132010	−	0.111428i
$130$	8.03081	−	26.4202i	0.704349	−	2.31720i
$131$	3.84111	−	10.5534i	0.335599	−	0.922051i	−0.651028	−	0.759054i	$-0.725662\pi$
$131$	3.84111	−	10.5534i	0.335599	−	0.922051i	0.986627	−	0.162997i	$-0.0521159\pi$
$132$	−9.80587	+	3.23228i	−0.853492	+	0.281334i
$133$	−3.41119	−	4.87168i	−0.295787	−	0.422428i
$134$	−8.98538			−0.776219
$135$	−9.17786	+	7.12508i	−0.789905	+	0.613230i
$136$	0.385743			0.0330772
$137$	11.2752	+	16.1027i	0.963306	+	1.37574i	0.926448	+	0.376424i	$0.122846\pi$
$137$	11.2752	+	16.1027i	0.963306	+	1.37574i	0.0368588	+	0.999320i	$0.488265\pi$
$138$	13.1844	+	11.7701i	1.12233	+	1.00194i
$139$	−0.508611	+	1.39740i	−0.0431398	+	0.118526i	−0.959392	−	0.282076i	$-0.908977\pi$
$139$	−0.508611	+	1.39740i	−0.0431398	+	0.118526i	0.916252	+	0.400602i	$0.131199\pi$
$140$	5.94876	−	3.17535i	0.502762	−	0.268366i
$141$	−4.00020	−	2.98779i	−0.336878	−	0.251617i
$142$	−16.5517	−	7.71820i	−1.38899	−	0.647697i
$143$	17.1362	−	4.59162i	1.43300	−	0.383971i
$144$	−5.18806	−	10.4115i	−0.432338	−	0.867621i
$145$	2.14604	−	4.22872i	0.178219	−	0.351176i
$146$	−10.7917	+	12.8611i	−0.893129	+	1.06439i
$147$	7.40933	−	3.98011i	0.611111	−	0.328274i
$148$	19.8505	+	13.8995i	1.63170	+	1.14253i
$149$	−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	$-0.120714\pi$
$150$	−17.1527	−	3.20113i	−1.40051	−	0.261371i
$151$	−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	$-0.597383\pi$
$152$	0.470202	+	0.125990i	0.0381384	+	0.0102191i
$153$	7.55507	+	6.01232i	0.610791	+	0.486068i
$154$	7.39525	+	4.26965i	0.595926	+	0.344058i
$155$	6.09621	+	4.57840i	0.489659	+	0.367746i
$156$	−8.62834	−	20.0892i	−0.690820	−	1.60842i
$157$	6.76582	+	0.591932i	0.539971	+	0.0472413i	0.353879	−	0.935291i	$-0.384862\pi$
$157$	6.76582	+	0.591932i	0.539971	+	0.0472413i	0.186092	+	0.982532i	$0.440418\pi$
$158$	−1.24571	−	2.67143i	−0.0991032	−	0.212528i
$159$	−0.155265	+	0.101772i	−0.0123133	+	0.00807101i
$160$	6.71786	−	16.7049i	0.531093	−	1.32064i
$161$		−	7.41576i		−	0.584444i
$162$	−3.77805	+	17.7354i	−0.296832	+	1.39343i
$163$	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
$165$	−4.07869	−	10.4418i	−0.317525	−	0.812893i
$166$	−31.9979	−	11.6463i	−2.48352	−	0.903928i
$167$	0.0411027	−	0.469806i	0.00318063	−	0.0363547i	−0.994439	−	0.105319i	$-0.966414\pi$
$167$	0.0411027	−	0.469806i	0.00318063	−	0.0363547i	0.997619	+	0.0689639i	$0.0219693\pi$
$168$	0.112670	−	0.282318i	0.00869266	−	0.0217813i
$169$	8.40252	+	23.0857i	0.646348	+	1.77583i
$170$	0.782268	+	14.4790i	0.0599972	+	1.11049i
$171$	7.24553	+	9.79634i	0.554079	+	0.749145i
$172$	0.392203	−	1.46372i	0.0299052	−	0.111608i
$173$	1.60708	+	18.3690i	0.122184	+	1.39657i	0.771586	+	0.636125i	$0.219464\pi$
$173$	1.60708	+	18.3690i	0.122184	+	1.39657i	−0.649402	+	0.760446i	$0.724981\pi$
$174$	−1.69548	−	7.20403i	−0.128534	−	0.546136i
$175$	3.79104	+	6.26342i	0.286576	+	0.473470i
$176$	11.0527	−	1.94888i	0.833126	−	0.146903i
$177$	3.09876	+	5.76862i	0.232917	+	0.433596i
$178$	−12.2466	+	1.07144i	−0.917925	+	0.0803080i
$179$	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	$0.737736\pi$
$180$	−12.0149	+	6.81979i	−0.895536	+	0.508317i
$181$	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	$-0.0951998\pi$
$182$	−7.64207	+	16.3885i	−0.566468	+	1.21479i
$183$	−1.11526	−	7.69784i	−0.0824421	−	0.569041i
$184$	0.390166	+	0.464982i	0.0287634	+	0.0342789i
$185$	−13.9065	+	22.3353i	−1.02243	+	1.64212i
$186$	11.8795	−	0.673238i	0.871048	−	0.0493642i
$187$	−7.63096	+	5.34326i	−0.558031	+	0.390738i
$188$	−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	−0.146630	−	0.989191i	$-0.546843\pi$
$191$	−8.60644	−	1.51755i	−0.622740	−	0.109806i	−0.476110	+	0.879386i	$0.657954\pi$
$192$	−4.59195	−	13.9307i	−0.331395	−	1.00536i
$193$	−7.83132	+	3.65180i	−0.563711	+	0.262863i	−0.683517	−	0.729935i	$-0.739550\pi$
$193$	−7.83132	+	3.65180i	−0.563711	+	0.262863i	0.119806	+	0.992797i	$0.461773\pi$
$194$	−25.0236	+	20.9973i	−1.79659	+	1.50752i
$195$	21.2745	−	10.5312i	1.52350	−	0.754156i
$196$	9.39756	−	3.42043i	0.671254	−	0.244316i
$197$	0.519071	+	1.93720i	0.0369822	+	0.138020i	0.981949	−	0.189148i	$-0.0605725\pi$
$197$	0.519071	+	1.93720i	0.0369822	+	0.138020i	−0.944966	+	0.327167i	$0.893906\pi$
$198$	−15.3733	−	8.35147i	−1.09253	−	0.593513i
$199$	−15.5130	+	8.95641i	−1.09968	+	0.634903i	−0.936138	−	0.351633i	$-0.885627\pi$
$199$	−15.5130	+	8.95641i	−1.09968	+	0.634903i	−0.163546	+	0.986536i	$0.552293\pi$
$200$	−0.567243	−	0.193269i	−0.0401101	−	0.0136662i
$201$	−5.29196	−	5.62678i	−0.373266	−	0.396883i
$202$	6.35413	−	9.07464i	0.447075	−	0.638490i
$203$	−1.78114	+	2.54374i	−0.125012	+	0.178535i
$204$	7.86546	+	8.36310i	0.550693	+	0.585534i
$205$	−1.89142	−	0.229136i	−0.132102	−	0.0160035i
$206$	6.84718	−	3.95322i	0.477065	−	0.275434i
$207$	0.394328	+	15.1883i	0.0274077	+	1.05566i
$208$	6.15109	+	22.9562i	0.426501	+	1.59172i
$209$	−11.0470	+	4.02077i	−0.764134	+	0.278122i
$210$	10.8254	+	3.65656i	0.747020	+	0.252327i
$211$	−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	$0.397540\pi$
$212$	−0.200061	+	0.0932898i	−0.0137402	+	0.00640717i
$213$	−4.91493	−	14.9106i	−0.336766	−	1.02166i
$214$	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
$218$	16.3632	−	11.4577i	1.10826	−	0.776011i
$219$	−14.4096	+	0.816623i	−0.973710	+	0.0551823i
$220$	−3.01943	−	12.9828i	−0.203570	−	0.875303i
$221$	−12.6801	−	15.1115i	−0.852955	−	1.01651i
$222$	5.88762	+	40.6381i	0.395151	+	2.72745i
$223$	5.05016	−	10.8301i	0.338184	−	0.725238i	−0.661511	−	0.749936i	$-0.730084\pi$
$223$	5.05016	−	10.8301i	0.338184	−	0.725238i	0.999695	+	0.0246975i	$0.00786226\pi$
$224$	−5.89526	+	10.2109i	−0.393894	+	0.682244i
$225$	−8.09751	−	12.6266i	−0.539834	−	0.841771i
$226$	15.3440	+	26.5765i	1.02067	+	1.76784i
$227$	−1.15273	+	0.100851i	−0.0765092	+	0.00669369i	−0.125346	−	0.992113i	$-0.540004\pi$
$227$	−1.15273	+	0.100851i	−0.0765092	+	0.00669369i	0.0488368	+	0.998807i	$0.484449\pi$
$228$	6.85608	+	12.7632i	0.454055	+	0.845264i
$229$	8.62548	−	1.52090i	0.569988	−	0.100504i	0.118776	−	0.992921i	$-0.462103\pi$
$229$	8.62548	−	1.52090i	0.569988	−	0.100504i	0.451212	+	0.892417i	$0.350992\pi$
$230$	−16.6620	+	15.5879i	−1.09866	+	1.02784i
$231$	1.68173	+	7.14564i	0.110650	+	0.470148i
$232$	−0.0221529	−	0.253208i	−0.00145441	−	0.0166240i
$233$	−4.23498	+	15.8052i	−0.277443	+	1.03543i	0.676743	+	0.736219i	$0.263391\pi$
$233$	−4.23498	+	15.8052i	−0.277443	+	1.03543i	−0.954186	+	0.299213i	$0.903276\pi$
$234$	14.7803	−	33.9717i	0.966221	−	2.22080i
$235$	4.30529	−	4.79707i	0.280846	−	0.312927i
$236$	2.66302	+	7.31658i	0.173348	+	0.476269i
$237$	0.939226	−	2.35343i	0.0610093	−	0.152871i
$238$	0.827567	−	9.45913i	0.0536432	−	0.613145i
$239$	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	$0.521507\pi$
$240$	13.9882	−	5.46394i	0.902933	−	0.352696i
$241$	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
$243$	−13.3313	+	8.07944i	−0.855201	+	0.518296i
$244$		−	9.24864i		−	0.592083i
$245$	4.25875	+	9.98810i	0.272082	+	0.638116i
$246$	−2.48684	+	1.63005i	−0.158555	+	0.103928i
$247$	−10.5207	−	22.5618i	−0.669417	−	1.43557i
$248$	0.407090	+	0.0356158i	0.0258503	+	0.00226161i
$249$	−11.5522	−	26.8967i	−0.732089	−	1.70451i
$250$	6.10408	−	21.6835i	0.386056	−	1.37139i
$251$	9.55376	+	5.51587i	0.603028	+	0.348158i	0.770232	−	0.637764i	$-0.220140\pi$
$251$	9.55376	+	5.51587i	0.603028	+	0.348158i	−0.167204	+	0.985922i	$0.553474\pi$
$252$	8.41818	−	3.31384i	0.530295	−	0.208752i
$253$	−14.1593	−	3.79398i	−0.890189	−	0.238525i
$254$	−15.3866	−	12.9109i	−0.965443	−	0.810103i
$255$	−8.60622	+	9.01729i	−0.538942	+	0.564684i
$256$	2.60580	+	14.7782i	0.162862	+	0.923639i
$257$	−4.73079	−	3.31253i	−0.295098	−	0.206630i	0.416646	−	0.909069i	$-0.363206\pi$
$257$	−4.73079	−	3.31253i	−0.295098	−	0.206630i	−0.711744	+	0.702439i	$0.752094\pi$
$258$	2.26204	−	1.21511i	0.140829	−	0.0756496i
$259$	11.0748	−	13.1985i	0.688157	−	0.820114i
$260$	26.8304	−	8.76566i	1.66395	−	0.543623i
$261$	3.51272	−	5.30456i	0.217432	−	0.328344i
$262$	21.8567	−	5.85647i	1.35031	−	0.361814i
$263$	−16.7213	−	7.79728i	−1.03108	−	0.480801i	−0.167958	−	0.985794i	$-0.553717\pi$
$263$	−16.7213	−	7.79728i	−1.03108	−	0.480801i	−0.863123	+	0.504993i	$0.831495\pi$
$264$	−0.481402	−	0.359563i	−0.0296282	−	0.0221296i
$265$	−0.112860	−	0.211433i	−0.00693291	−	0.0129882i
$266$	4.09828	−	11.2599i	0.251281	−	0.690390i
$267$	−7.88364	−	7.03800i	−0.482471	−	0.430719i
$268$	−5.26807	−	7.52358i	−0.321798	−	0.459576i
$269$	15.7262			0.958842			0.479421	−	0.877585i	$-0.340847\pi$
$269$	15.7262			0.958842			0.479421	+	0.877585i	$0.340847\pi$
$270$	−22.3659	−	6.91341i	−1.36115	−	0.420737i
$271$	−17.4326			−1.05895			−0.529477	−	0.848324i	$-0.677612\pi$
$271$	−17.4326			−1.05895			−0.529477	+	0.848324i	$0.677612\pi$
$272$	−7.15800	−	10.2227i	−0.434018	−	0.619841i
$273$	−14.7635	+	4.86645i	−0.893528	+	0.294531i
$274$	−13.5463	+	37.2181i	−0.818362	+	2.24843i
$275$	13.8986	−	4.03401i	0.838118	−	0.243260i
$276$	−2.12539	+	17.9402i	−0.127933	+	1.07987i
$277$	13.9179	+	6.49002i	0.836245	+	0.389947i	0.793078	−	0.609120i	$-0.208477\pi$
$277$	13.9179	+	6.49002i	0.836245	+	0.389947i	0.0431672	+	0.999068i	$0.486255\pi$
$278$	−2.89410	+	0.775471i	−0.173576	+	0.0465097i
$279$	7.41806	+	7.04262i	0.444107	+	0.421630i
$280$	0.349939	+	0.177591i	0.0209129	+	0.0106131i
$281$	4.76302	−	5.67634i	0.284138	−	0.338622i	−0.605031	−	0.796202i	$-0.706839\pi$
$281$	4.76302	−	5.67634i	0.284138	−	0.338622i	0.889168	+	0.457580i	$0.151284\pi$
$282$	0.308329	−	10.0549i	0.0183607	−	0.598763i
$283$	−11.7772	−	8.24647i	−0.700081	−	0.490202i	0.168530	−	0.985696i	$-0.446098\pi$
$283$	−11.7772	−	8.24647i	−0.700081	−	0.490202i	−0.868611	+	0.495495i	$0.834987\pi$
$284$	−3.24161	−	18.3841i	−0.192354	−	1.09090i
$285$	−13.4358	+	8.18069i	−0.795865	+	0.484582i
$286$	27.3816	+	22.9759i	1.61911	+	1.35859i
$287$	1.20512	+	0.322912i	0.0711362	+	0.0190609i
$288$	11.5312	−	21.2265i	0.679481	−	1.25078i
$289$	−5.75165	−	3.32072i	−0.338332	−	0.195336i
$290$	9.45932	−	1.34501i	0.555470	−	0.0789816i
$291$	−27.8865	−	3.30374i	−1.63473	−	0.193668i
$292$	−17.0958	−	1.49569i	−1.00046	−	0.0875288i
$293$	−8.51297	−	18.2561i	−0.497333	−	1.06653i	−0.981483	−	0.191549i	$-0.938649\pi$
$293$	−8.51297	−	18.2561i	−0.497333	−	1.06653i	0.484150	−	0.874985i	$-0.339129\pi$
$294$	15.1315	+	7.62904i	0.882490	+	0.444935i
$295$	−7.77636	+	3.31570i	−0.452757	+	0.193048i
$296$			1.41025i			0.0819691i
$297$	−3.82434	−	14.5456i	−0.221910	−	0.844022i
$298$	7.07014	−	7.07014i	0.409562	−	0.409562i
$299$	5.39025	−	30.5696i	0.311726	−	1.76789i
$300$	−7.37614	−	16.2390i	−0.425862	−	0.937557i
$301$	−1.01243	−	0.368493i	−0.0583553	−	0.0212396i
$302$	3.64098	−	41.6166i	0.209515	−	2.39477i
$303$	9.42496	−	1.36548i	0.541450	−	0.0784448i
$304$	−5.38635	−	14.7989i	−0.308928	−	0.848774i
$305$	10.0270	−	0.541738i	0.574144	−	0.0310198i
$306$	−1.19196	+	19.4173i	−0.0681401	+	1.11002i
$307$	−3.09276	+	11.5423i	−0.176513	+	0.658756i	0.819776	+	0.572684i	$0.194098\pi$
$307$	−3.09276	+	11.5423i	−0.176513	+	0.658756i	−0.996289	+	0.0860714i	$0.972569\pi$
$308$	0.760749	+	8.69540i	0.0433477	+	0.495467i
$309$	6.50822	+	1.95955i	0.370240	+	0.111475i
$310$	−0.511289	+	15.3525i	−0.0290392	+	0.871962i
$311$	2.38442	−	0.420438i	0.135208	−	0.0238408i	−0.105634	−	0.994405i	$-0.533687\pi$
$311$	2.38442	−	0.420438i	0.135208	−	0.0238408i	0.240843	+	0.970564i	$0.422576\pi$
$312$	0.669660	−	1.08189i	0.0379120	−	0.0612499i
$313$	12.2121	−	1.06842i	0.690267	−	0.0603905i	0.263375	−	0.964693i	$-0.415164\pi$
$313$	12.2121	−	1.06842i	0.690267	−	0.0603905i	0.426891	+	0.904303i	$0.359609\pi$
$314$	6.84198	+	11.8506i	0.386115	+	0.668771i
$315$	4.08582	+	8.93254i	0.230210	+	0.503292i
$316$	1.50647	−	2.60929i	0.0847457	−	0.146784i
$317$	−9.58656	+	20.5585i	−0.538435	+	1.15468i	0.429405	+	0.903112i	$0.358723\pi$
$317$	−9.58656	+	20.5585i	−0.538435	+	1.15468i	−0.967840	+	0.251566i	$0.919055\pi$
$318$	−0.347401	−	0.138644i	−0.0194813	−	0.00777475i
$319$	3.94565	+	4.70224i	0.220914	+	0.263275i
$320$	18.4441	−	4.28956i	1.03106	−	0.239794i
$321$	14.1436	+	21.5779i	0.789420	+	1.20436i
$322$	12.2393	−	8.57003i	0.682068	−	0.477589i
$323$	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
$327$	16.8121	+	3.49889i	0.929713	+	0.193489i
$328$	−0.0925528	+	0.0431581i	−0.00511038	+	0.00238301i
$329$	−3.23343	+	2.71317i	−0.178265	+	0.149582i
$330$	12.5200	−	18.7987i	0.689206	−	1.03484i
$331$	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	$0.240865\pi$
$332$	−9.00856	−	33.6204i	−0.494409	−	1.84516i
$333$	−21.9807	+	27.6208i	−1.20453	+	1.51361i
$334$	0.822888	−	0.475095i	0.0450264	−	0.0259960i
$335$	7.84818	−	6.15212i	0.428792	−	0.336126i
$336$	−9.57253	+	2.25290i	−0.522224	+	0.122906i
$337$	2.30026	−	3.28511i	0.125303	−	0.178951i	−0.751599	−	0.659620i	$-0.770717\pi$
$337$	2.30026	−	3.28511i	0.125303	−	0.178951i	0.876902	+	0.480669i	$0.159606\pi$
$338$	−28.3913	+	40.5469i	−1.54428	+	2.20546i
$339$	−7.60575	+	25.2609i	−0.413088	+	1.37198i
$340$	−11.6648	+	9.14391i	−0.632612	+	0.495898i
$341$	−8.54661	+	4.93439i	−0.462825	+	0.267212i
$342$	−7.79498	+	23.2795i	−0.421504	+	1.25881i
$343$	−4.49317	−	16.7687i	−0.242608	−	0.905427i
$344$	0.0828686	−	0.0301617i	0.00446798	−	0.00162621i
$345$	−19.5745	−	1.25342i	−1.05386	−	0.0674817i
$346$	−28.4598	+	23.8806i	−1.53001	+	1.28383i
$347$	11.2479	−	5.24496i	0.603816	−	0.281564i	−0.0965722	−	0.995326i	$-0.530788\pi$
$347$	11.2479	−	5.24496i	0.603816	−	0.281564i	0.700389	+	0.713762i	$0.253010\pi$
$348$	5.03798	−	5.64331i	0.270064	−	0.302513i
$349$	7.52479	+	1.32682i	0.402793	+	0.0710232i	0.371375	−	0.928483i	$-0.378887\pi$
$349$	7.52479	+	1.32682i	0.402793	+	0.0710232i	0.0314181	+	0.999506i	$0.489998\pi$
$350$	−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
$353$	14.6661	−	10.2693i	0.780595	−	0.546579i	−0.113987	−	0.993482i	$-0.536362\pi$
$353$	14.6661	−	10.2693i	0.780595	−	0.546579i	0.894582	+	0.446904i	$0.147473\pi$
$354$	−5.93968	+	11.7808i	−0.315691	+	0.626145i
$355$	19.7414	−	4.59127i	1.04777	−	0.243680i
$356$	−8.07725	−	9.62609i	−0.428093	−	0.510182i
$357$	6.41085	−	5.05275i	0.339298	−	0.267420i
$358$	−6.74040	+	14.4548i	−0.356241	+	0.763962i
$359$	−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	$0.273940\pi$
$360$	−0.726157	−	0.345119i	−0.0382718	−	0.0181894i
$361$	−1.25189	−	2.16834i	−0.0658891	−	0.114123i
$362$	39.5854	−	3.46328i	2.08056	−	0.182026i
$363$	−4.53966	−	0.139206i	−0.238270	−	0.00730642i
$364$	−18.2028	+	3.20964i	−0.954084	+	0.168231i
$365$	0.620182	−	18.6222i	0.0324618	−	0.974732i
$366$	11.4160	−	10.7367i	0.596723	−	0.561215i
$367$	−1.19292	−	13.6352i	−0.0622701	−	0.711750i	−0.961596	−	0.274470i	$-0.911497\pi$
$367$	−1.19292	−	13.6352i	−0.0622701	−	0.711750i	0.899325	−	0.437280i	$-0.144058\pi$
$368$	5.08254	−	18.9683i	0.264946	−	0.988790i
$369$	−2.48539	−	0.597277i	−0.129384	−	0.0310930i
$370$	−52.9341	+	2.85992i	−2.75191	+	0.148680i
$371$	0.0536785	+	0.147481i	0.00278685	+	0.00765681i
$372$	7.52858	+	9.55215i	0.390339	+	0.495256i
$373$	−1.05518	+	12.0608i	−0.0546353	+	0.624485i	0.918678	+	0.395006i	$0.129258\pi$
$373$	−1.05518	+	12.0608i	−0.0546353	+	0.624485i	−0.973314	+	0.229478i	$0.926298\pi$
$374$	−17.6375	−	6.41951i	−0.912011	−	0.331945i
$375$	17.1736	−	8.94811i	0.886839	−	0.462078i
$376$	0.0599937	−	0.340241i	0.00309394	−	0.0175466i
$377$	−9.19128	+	9.19128i	−0.473375	+	0.473375i
$378$	13.8630	+	6.54389i	0.713037	+	0.336582i
$379$		−	22.5213i		−	1.15684i	−0.815738	−	0.578421i	$-0.803669\pi$
$379$		−	22.5213i		−	1.15684i	0.815738	−	0.578421i	$-0.196331\pi$
$380$	−17.2054	+	7.33607i	−0.882616	+	0.376332i
$381$	−0.976986	−	17.2393i	−0.0500525	−	0.883194i
$382$	−7.44142	−	15.9582i	−0.380736	−	0.816491i
$383$	−14.4118	−	1.26087i	−0.736410	−	0.0644275i	−0.287221	−	0.957864i	$-0.592731\pi$
$383$	−14.4118	−	1.26087i	−0.736410	−	0.0644275i	−0.449189	+	0.893437i	$0.648287\pi$
$384$	0.993364	−	1.32997i	0.0506924	−	0.0678695i
$385$	−9.38265	+	1.33411i	−0.478184	+	0.0679923i
$386$	−15.0774	−	8.70492i	−0.767417	−	0.443069i
$387$	2.09316	+	0.700880i	0.106401	+	0.0356277i
$388$	−32.2524	−	8.64201i	−1.63737	−	0.438731i
$389$	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	$0.618390\pi$
$390$	41.9670	+	22.9419i	2.12508	+	1.16171i
$391$	2.83044	+	16.0522i	0.143141	+	0.811795i
$392$	0.476742	+	0.333818i	0.0240791	+	0.0168604i
$393$	16.5399	+	10.2378i	0.834330	+	0.516428i
$394$	−2.59737	+	3.09542i	−0.130853	+	0.155945i
$395$	2.91713	+	1.48042i	0.146777	+	0.0744879i
$396$	−2.02047	−	17.7687i	−0.101532	−	0.892910i
$397$	−14.5205	+	3.89075i	−0.728761	+	0.195271i	−0.604077	−	0.796926i	$-0.706458\pi$
$397$	−14.5205	+	3.89075i	−0.728761	+	0.195271i	−0.124684	+	0.992197i	$0.539792\pi$
$398$	−32.7096	−	15.2527i	−1.63958	−	0.764550i
$399$	9.46482	−	4.06516i	0.473834	−	0.203512i
$400$	5.40409	+	18.6190i	0.270205	+	0.930952i
$401$	−8.96818	+	24.6399i	−0.447849	+	1.23046i	0.486369	+	0.873754i	$0.338321\pi$
$401$	−8.96818	+	24.6399i	−0.447849	+	1.23046i	−0.934218	+	0.356703i	$0.883901\pi$
$402$	3.17101	−	15.2367i	0.158155	−	0.759936i
$403$	−11.9866	−	17.1186i	−0.597094	−	0.852738i
$404$	11.3237			0.563375
$405$	−8.84319	−	18.0776i	−0.439422	−	0.898281i
$406$	−6.25667			−0.310513
$407$	−19.5346	−	27.8983i	−0.968294	−	1.38287i
$408$	−0.136131	+	0.654111i	−0.00673951	+	0.0323833i
$409$	2.57831	−	7.08384i	0.127489	−	0.350273i	−0.859483	−	0.511164i	$-0.829214\pi$
$409$	2.57831	−	7.08384i	0.127489	−	0.350273i	0.986972	+	0.160891i	$0.0514367\pi$
$410$	−1.80764	−	3.38647i	−0.0892731	−	0.167246i
$411$	−31.2847	+	13.4368i	−1.54316	+	0.662790i
$412$	7.32453	+	3.41549i	0.360854	+	0.168269i
$413$	5.34723	−	1.43279i	0.263120	−	0.0705028i
$414$	−24.6117	+	18.2032i	−1.20960	+	0.894637i
$415$	35.9222	−	11.7360i	1.76335	−	0.576099i
$416$	−31.7237	+	37.8068i	−1.55538	+	1.85363i
$417$	−2.19010	−	1.35561i	−0.107250	−	0.0663846i
$418$	−19.4025	−	13.5858i	−0.949006	−	0.664501i
$419$	−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	$-0.224384\pi$
$420$	3.28514	+	11.2080i	0.160298	+	0.546896i
$421$	−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	$0.775834\pi$
$422$	−20.7742	−	5.56643i	−1.01127	−	0.270969i
$423$	6.47814	−	5.72880i	0.314978	−	0.278544i
$424$	−0.0111251	−	0.00642311i	−0.000540285	−	0.000311934i
$425$	−10.5967	−	12.1109i	−0.514017	−	0.587464i
$426$	18.9291	−	25.3433i	0.917118	−	1.22788i
$427$	−6.55066	−	0.573108i	−0.317009	−	0.0277347i
$428$	12.9649	+	27.8032i	0.626680	+	1.34392i
$429$	1.73862	+	30.6785i	0.0839413	+	1.48117i
$430$	1.30018	+	3.04933i	0.0627003	+	0.147052i
$431$			2.91928i			0.140617i	0.997525	+	0.0703084i	$0.0223983\pi$
$431$			2.91928i			0.140617i	−0.997525	+	0.0703084i	$0.977602\pi$
$432$	19.4858	−	5.12321i	0.937510	−	0.246490i
$433$	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
$435$	6.41335	+	5.13142i	0.307497	+	0.246033i
$436$	19.1873	+	6.98361i	0.918905	+	0.334454i
$437$	−1.79276	+	20.4913i	−0.0857593	+	0.980233i
$438$	−18.0003	−	22.8385i	−0.860085	−	1.09126i
$439$	1.28129	+	3.52030i	0.0611524	+	0.168015i	0.966506	−	0.256643i	$-0.0826165\pi$
$439$	1.28129	+	3.52030i	0.0611524	+	0.168015i	−0.905354	+	0.424658i	$0.860394\pi$
$440$	0.518118	−	0.577301i	0.0247003	−	0.0275217i
$441$	4.13434	+	13.9687i	0.196873	+	0.665178i
$442$	10.2870	−	38.3914i	0.489300	−	1.82609i
$443$	2.43927	+	27.8809i	0.115893	+	1.32466i	0.802070	+	0.597229i	$0.203732\pi$
$443$	2.43927	+	27.8809i	0.115893	+	1.32466i	−0.686177	+	0.727434i	$0.740713\pi$
$444$	−30.5749	+	28.7556i	−1.45102	+	1.36468i
$445$	9.96310	−	9.32088i	0.472296	−	0.441852i
$446$	23.7107	−	4.18083i	1.12273	−	0.197968i
$447$	8.59141	+	0.263451i	0.406360	+	0.0124608i
$448$	−12.3531	+	1.08076i	−0.583631	+	0.0510611i
$449$	−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	$0.905647\pi$
$450$	11.4815	−	27.9564i	0.541244	−	1.31788i
$451$	1.23311	−	2.13580i	0.0580647	−	0.100571i
$452$	−13.2568	+	28.4293i	−0.623548	+	1.33720i
$453$	28.2053	−	22.2302i	1.32520	−	1.04446i
$454$	−1.49860	−	1.78596i	−0.0703328	−	0.0838193i
$455$	−4.54598	−	19.5467i	−0.213119	−	0.916363i
$456$	−0.379581	+	0.752866i	−0.0177755	+	0.0352562i
$457$	−29.0265	+	20.3246i	−1.35780	+	0.950745i	−0.357949	+	0.933741i	$0.616524\pi$
$457$	−29.0265	+	20.3246i	−1.35780	+	0.950745i	−0.999855	+	0.0170039i	$0.994587\pi$
$458$	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	0.710219	−	0.703981i	$-0.248596\pi$
$461$	24.4088	+	4.30393i	1.13683	+	0.200454i	0.426612	+	0.904435i	$0.359707\pi$
$462$	−9.84995	+	11.0335i	−0.458261	+	0.513323i
$463$	−4.90609	+	2.28775i	−0.228005	+	0.106321i	−0.533264	−	0.845949i	$-0.679035\pi$
$463$	−4.90609	+	2.28775i	−0.228005	+	0.106321i	0.305259	+	0.952269i	$0.401257\pi$
$464$	−6.29927	+	5.28572i	−0.292436	+	0.245383i
$465$	−9.91507	+	8.72170i	−0.459800	+	0.404459i
$466$	−30.9797	+	11.2757i	−1.43511	+	0.522336i
$467$	10.5998	+	39.5591i	0.490502	+	1.83058i	0.553891	+	0.832589i	$0.313143\pi$
$467$	10.5998	+	39.5591i	0.490502	+	1.83058i	−0.0633888	+	0.997989i	$0.520191\pi$
$468$	37.1106	−	7.54161i	1.71544	−	0.348611i
$469$	−5.65527	+	3.26507i	−0.261136	+	0.150767i
$470$	12.8927	+	1.56189i	0.594696	+	0.0720444i
$471$	−3.39145	+	11.2640i	−0.156270	+	0.519018i
$472$	−0.259898	+	0.371173i	−0.0119628	+	0.0170846i
$473$	−1.22155	+	1.74456i	−0.0561671	+	0.0802149i
$474$	4.96961	−	1.16960i	0.228262	−	0.0537216i
$475$	−8.96127	−	18.2236i	−0.411171	−	0.836158i
$476$	8.40545	−	4.85289i	0.385263	−	0.222432i
$477$	−0.117782	−	0.299202i	−0.00539285	−	0.0136995i
$478$	4.47905	+	16.7160i	0.204867	+	0.764574i
$479$	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	$0.171444\pi$
$480$	25.9561	+	17.2869i	1.18473	+	0.789034i
$481$	55.2468	−	46.3576i	2.51904	−	2.11372i
$482$	3.77382	−	1.75976i	0.171893	−	0.0801549i
$483$	12.5750	+	2.61707i	0.572184	+	0.119081i
$484$	−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	$0.388228\pi$
$488$	0.440891	−	0.308715i	0.0199582	−	0.0139749i
$489$	19.3182	+	29.4724i	0.873600	+	1.33279i
$490$	−11.5631	+	18.5716i	−0.522369	+	0.838979i
$491$	15.4259	+	18.3839i	0.696161	+	0.829652i	0.992086	−	0.125559i	$-0.0400724\pi$
$491$	15.4259	+	18.3839i	0.696161	+	0.829652i	−0.295925	+	0.955211i	$0.595628\pi$
$492$	−2.82288	−	1.12658i	−0.127265	−	0.0507902i
$493$	2.88459	−	6.18602i	0.129915	−	0.278604i
$494$	25.0786	−	43.4374i	1.12834	−	1.95434i
$495$	19.1457	−	3.23131i	0.860537	−	0.145237i
$496$	−6.61027	−	11.4493i	−0.296810	−	0.514090i
$497$	−13.2220	+	1.15678i	−0.593089	+	0.0518886i
$498$	31.0411	−	50.1494i	1.39099	−	2.24725i
$499$	31.1017	−	5.48406i	1.39230	−	0.245500i	0.573325	−	0.819328i	$-0.305653\pi$
$499$	31.1017	−	5.48406i	1.39230	−	0.245500i	0.818976	+	0.573828i	$0.194542\pi$
$500$	21.7347	−	7.60188i	0.972005	−	0.339966i
$501$	0.782153	+	0.235497i	0.0349440	+	0.0105212i
$502$	1.93720	+	22.1423i	0.0864616	+	0.988261i
$503$	−0.730168	+	2.72503i	−0.0325566	+	0.121503i	−0.980292	−	0.197555i	$-0.936700\pi$
$503$	−0.730168	+	2.72503i	−0.0325566	+	0.121503i	0.947735	+	0.319058i	$0.103366\pi$
$504$	0.438969	+	0.290688i	0.0195532	+	0.0129483i
$505$	0.663284	+	12.2767i	0.0295158	+	0.546306i
$506$	−10.1015	−	27.7536i	−0.449066	−	1.23380i
$507$	−42.1122	+	6.10118i	−1.87027	+	0.270963i
$508$	1.78941	−	20.4530i	0.0793920	−	0.907455i
$509$	−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	$0.773972\pi$
$510$	−24.8283	−	3.78322i	−1.09942	−	0.167524i
$511$	−2.11875	+	12.0160i	−0.0937279	+	0.531557i
$512$	−22.7346	+	22.7346i	−1.00474	+	1.00474i
$513$	−19.1688	+	8.82917i	−0.846324	+	0.389817i
$514$		−	11.6360i		−	0.513243i
$515$	−3.27390	+	8.14102i	−0.144265	+	0.358736i
$516$	2.34365	+	1.18162i	0.103173	+	0.0520181i
$517$	3.52615	+	7.56184i	0.155080	+	0.332569i
$518$	34.5820	+	3.02553i	1.51944	+	0.132934i
$519$	−31.7158	−	3.75740i	−1.39217	−	0.164932i
$520$	1.31345	+	0.986435i	0.0575987	+	0.0432581i
$521$	−7.62484	−	4.40220i	−0.334050	−	0.192864i	0.323588	−	0.946198i	$-0.395111\pi$
$521$	−7.62484	−	4.40220i	−0.334050	−	0.192864i	−0.657638	+	0.753334i	$0.728444\pi$
$522$	12.8143	−	0.332694i	0.560868	−	0.0145616i
$523$	1.24254	+	0.332937i	0.0543324	+	0.0145583i	0.285883	−	0.958265i	$-0.407713\pi$
$523$	1.24254	+	0.332937i	0.0543324	+	0.0145583i	−0.231550	+	0.972823i	$0.574380\pi$
$524$	17.7181	+	14.8673i	0.774019	+	0.649479i
$525$	−11.9589	+	4.21812i	−0.521928	+	0.184094i
$526$	−6.45507	−	36.6085i	−0.281454	−	1.59621i
$527$	8.98903	+	6.29419i	0.391568	+	0.274179i
$528$	−0.595809	+	19.4300i	−0.0259293	+	0.845581i
$529$	−1.70263	+	2.02911i	−0.0740274	+	0.0882224i
$530$	0.218532	−	0.430611i	0.00949241	−	0.0187046i
$531$	−10.8755	+	3.21884i	−0.471958	+	0.139686i
$532$	11.8309	−	3.17007i	0.512933	−	0.137440i
$533$	4.73311	+	2.20709i	0.205014	+	0.0955995i
$534$	2.50506	−	21.1450i	0.108405	−	0.915032i
$535$	−29.3837	+	15.6846i	−1.27037	+	0.678103i
$536$	0.182810	−	0.502268i	0.00789621	−	0.0216947i
$537$	−13.0216	+	4.29227i	−0.561924	+	0.185225i
$538$	18.1740	+	25.9551i	0.783535	+	1.11900i
$539$	−14.0551			−0.605398
$540$	−7.32430	−	22.7806i	−0.315188	−	0.980320i
$541$	−9.16794			−0.394160			−0.197080	−	0.980387i	$-0.563146\pi$
$541$	−9.16794			−0.394160			−0.197080	+	0.980387i	$0.563146\pi$
$542$	−20.1460	−	28.7714i	−0.865344	−	1.23584i
$543$	25.4827	+	22.7493i	1.09357	+	0.976265i
$544$	8.86365	−	24.3527i	0.380026	−	1.04411i
$545$	−6.44745	+	21.2112i	−0.276179	+	0.908587i
$546$	−25.0933	−	18.7424i	−1.07389	−	0.802100i
$547$	4.18752	+	1.95267i	0.179046	+	0.0834904i	0.510074	−	0.860130i	$-0.329618\pi$
$547$	4.18752	+	1.95267i	0.179046	+	0.0834904i	−0.331029	+	0.943621i	$0.607396\pi$
$548$	−39.1053	+	10.4782i	−1.67050	+	0.447608i
$549$	13.4469	+	0.825461i	0.573901	+	0.0352298i
$550$	22.7199	+	18.2769i	0.968778	+	0.779331i
$551$	5.53663	−	6.59830i	0.235868	−	0.281097i
$552$	−0.926170	+	0.497516i	−0.0394204	+	0.0211757i
$553$	−1.75476	−	1.22870i	−0.0746202	−	0.0522496i
$554$	5.37283	+	30.4709i	0.228270	+	1.29458i
$555$	−32.9666	−	31.4638i	−1.39935	−	1.33556i
$556$	−2.34610	−	1.96861i	−0.0994968	−	0.0834878i
$557$	9.73354	+	2.60809i	0.412423	+	0.110509i	0.459064	−	0.888403i	$-0.348185\pi$
$557$	9.73354	+	2.60809i	0.412423	+	0.110509i	−0.0466405	+	0.998912i	$0.514852\pi$
$558$	−3.05074	+	20.3819i	−0.129148	+	0.862833i
$559$	−3.90564	−	2.25492i	−0.165191	−	0.0953730i
$560$	−1.78721	−	12.5693i	−0.0755235	−	0.531150i
$561$	−6.36763	−	14.8256i	−0.268842	−	0.625938i
$562$	14.8729	+	1.30121i	0.627373	+	0.0548881i
$563$	6.99817	+	15.0076i	0.294938	+	0.632496i	0.996810	−	0.0798064i	$-0.0254302\pi$
$563$	6.99817	+	15.0076i	0.294938	+	0.632496i	−0.701873	+	0.712302i	$0.747652\pi$
$564$	8.59990	−	5.63697i	0.362121	−	0.237359i
$565$	−31.5984	−	12.7073i	−1.32936	−	0.534598i
$566$		−	28.9676i		−	1.21760i
$567$	4.06677	+	12.5353i	0.170788	+	0.526432i
$568$	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	$0.981964\pi$
$570$	−29.0288	−	12.7209i	−1.21588	−	0.532820i
$571$	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	$0.500816\pi$
$572$	−3.18438	+	36.3976i	−0.133146	+	1.52186i
$573$	5.61060	−	14.0585i	0.234386	−	0.587304i
$574$	0.859755	+	2.36216i	0.0358855	+	0.0985946i
$575$	3.88045	−	25.0232i	0.161826	−	1.04354i
$576$	25.2431	−	2.87039i	1.05180	−	0.119599i
$577$	−4.56140	+	17.0234i	−0.189894	+	0.708693i	0.803636	+	0.595121i	$0.202896\pi$
$577$	−4.56140	+	17.0234i	−0.189894	+	0.708693i	−0.993530	+	0.113572i	$0.963771\pi$
$578$	−1.16625	−	13.3304i	−0.0485098	−	0.554469i
$579$	−3.42870	−	14.5684i	−0.142492	−	0.605444i
$580$	6.67212	+	7.13184i	0.277045	+	0.296134i
$581$	−24.3710	+	4.29727i	−1.01108	+	0.178281i
$582$	−26.7744	−	49.8430i	−1.10984	−	2.06606i
$583$	0.309055	−	0.0270388i	0.0127998	−	0.00111983i
$584$	−0.499351	−	0.864901i	−0.0206633	−	0.0357898i
$585$	10.3501	+	39.7920i	0.427922	+	1.64520i
$586$	20.2926	−	35.1479i	0.838280	−	1.45194i
$587$	3.45411	−	7.40736i	0.142566	−	0.305734i	−0.822040	−	0.569430i	$-0.807164\pi$
$587$	3.45411	−	7.40736i	0.142566	−	0.305734i	0.964606	+	0.263696i	$0.0849416\pi$
$588$	2.48362	+	17.1427i	0.102423	+	0.706953i
$589$	8.90140	+	10.6083i	0.366776	+	0.437106i
$590$	−14.4591	−	9.00262i	−0.595273	−	0.370632i
$591$	−3.46812	+	0.196546i	−0.142660	+	0.00808483i
$592$	37.3735	−	26.1692i	1.53604	−	1.07555i
$593$	−28.1239	−	28.1239i	−1.15491	−	1.15491i	−0.985555	−	0.169357i	$-0.945831\pi$
$593$	−28.1239	−	28.1239i	−1.15491	−	1.15491i	−0.169357	−	0.985555i	$-0.554169\pi$
$594$	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
$597$	−9.71291	−	29.4664i	−0.397523	−	1.20598i
$598$	56.6826	−	26.4315i	2.31793	−	1.08087i
$599$	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	$0.0145035\pi$
$600$	0.527914	−	0.893677i	0.0215520	−	0.0364842i
$601$	−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	$0.543126\pi$
$602$	−0.561836	−	2.09680i	−0.0228987	−	0.0854593i
$603$	11.4090	−	6.98794i	0.464610	−	0.284571i
$604$	36.9808	−	21.3509i	1.50473	−	0.868755i
$605$	0.705169	−	5.82087i	0.0286692	−	0.236652i
$606$	13.1456	+	13.9773i	0.534004	+	0.567790i
$607$	4.90539	−	7.00562i	0.199104	−	0.284349i	−0.707168	−	0.707046i	$-0.750027\pi$
$607$	4.90539	−	7.00562i	0.199104	−	0.284349i	0.906271	+	0.422696i	$0.138916\pi$
$608$	18.7583	−	26.7897i	0.760751	−	1.08647i
$609$	−3.68488	−	3.91802i	−0.149319	−	0.158766i
$610$	12.4818	+	15.9229i	0.505374	+	0.644700i
$611$	−15.3011	+	8.83410i	−0.619017	+	0.357389i
$612$	−16.9572	+	10.3862i	−0.685456	+	0.419837i
$613$	9.58796	+	35.7827i	0.387254	+	1.44525i	0.834583	+	0.550882i	$0.185709\pi$
$613$	9.58796	+	35.7827i	0.387254	+	1.44525i	−0.447329	+	0.894369i	$0.647625\pi$
$614$	−22.6241	+	8.23450i	−0.913034	+	0.332317i
$615$	1.05604	−	3.12644i	0.0425838	−	0.126070i
$616$	−0.389125	+	0.326514i	−0.0156783	+	0.0131556i
$617$	11.1077	−	5.17963i	0.447181	−	0.208524i	−0.185965	−	0.982556i	$-0.559541\pi$
$617$	11.1077	−	5.17963i	0.447181	−	0.208524i	0.633146	+	0.774032i	$0.281763\pi$
$618$	4.28712	+	13.0060i	0.172453	+	0.523178i
$619$	−8.63834	−	1.52317i	−0.347204	−	0.0612215i	−0.00267331	−	0.999996i	$-0.500851\pi$
$619$	−8.63834	−	1.52317i	−0.347204	−	0.0612215i	−0.344531	+	0.938775i	$0.611962\pi$
$620$	−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
$623$	−7.31853	+	5.12449i	−0.293211	+	0.205308i
$624$	−41.0979	+	2.32911i	−1.64523	+	0.0932391i
$625$	9.51476	+	23.1186i	0.380590	+	0.924744i
$626$	15.8763	+	18.9206i	0.634543	+	0.756218i
$627$	−2.91953	−	20.1515i	−0.116595	−	0.804773i
$628$	−5.91130	+	12.6768i	−0.235887	+	0.505860i
$629$	−18.9351	+	32.7966i	−0.754992	+	1.30769i
$630$	−10.0208	+	17.0663i	−0.399240	+	0.679938i
$631$	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	$0.610989\pi$
$632$	0.174673	−	0.0152819i	0.00694810	−	0.000607880i
$633$	−8.74923	−	16.2875i	−0.347751	−	0.647368i
$634$	−45.0092	+	7.93634i	−1.78755	+	0.315192i
$635$	22.2791	+	0.741969i	0.884121	+	0.0294442i
$636$	−0.0875903	−	0.372169i	−0.00347318	−	0.0147575i
$637$	−2.59401	−	29.6497i	−0.102778	−	1.17476i
$638$	−3.20098	+	11.9462i	−0.126728	+	0.472955i
$639$	27.0187	−	3.07228i	1.06884	−	0.121538i
$640$	1.59491	+	1.43140i	0.0630442	+	0.0565811i
$641$	−3.35944	−	9.23000i	−0.132690	−	0.364563i	0.855499	−	0.517805i	$-0.173251\pi$
$641$	−3.35944	−	9.23000i	−0.132690	−	0.364563i	−0.988189	+	0.153242i	$0.951029\pi$
$642$	−19.2679	+	48.2797i	−0.760443	+	1.90545i
$643$	1.62110	−	18.5293i	0.0639299	−	0.730723i	−0.894812	−	0.446444i	$-0.852690\pi$
$643$	1.62110	−	18.5293i	0.0639299	−	0.730723i	0.958742	−	0.284279i	$-0.0917541\pi$
$644$	14.3516	+	5.22355i	0.565532	+	0.205837i
$645$	−1.14379	+	2.61010i	−0.0450367	+	0.102773i
$646$	−4.57349	+	25.9375i	−0.179942	+	1.02050i
$647$	14.2018	−	14.2018i	0.558331	−	0.558331i	−0.370501	−	0.928832i	$-0.620814\pi$
$647$	14.2018	−	14.2018i	0.558331	−	0.558331i	0.928832	+	0.370501i	$0.120814\pi$
$648$	−0.914513	−	0.572019i	−0.0359255	−	0.0224710i
$649$		−	10.9428i		−	0.429542i
$650$	−34.3625	+	51.3013i	−1.34781	+	2.01220i
$651$	7.23215	−	4.74045i	0.283450	−	0.185793i
$652$	17.7082	+	37.9754i	0.693507	+	1.48723i
$653$	−19.8693	−	1.73834i	−0.777546	−	0.0680265i	−0.308528	−	0.951215i	$-0.599836\pi$
$653$	−19.8693	−	1.73834i	−0.777546	−	0.0680265i	−0.469018	+	0.883189i	$0.655392\pi$
$654$	13.6543	+	31.7909i	0.533924	+	1.24312i
$655$	−15.0806	+	20.0801i	−0.589250	+	0.784595i
$656$	2.86119	+	1.65191i	0.111711	+	0.0644963i
$657$	3.70048	−	24.7228i	0.144370	−	0.964528i
$658$	−8.21463	−	2.20110i	−0.320240	−	0.0858080i
$659$	−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	$0.728820\pi$
$660$	23.0808	−	0.538356i	0.898420	−	0.0209555i
$661$	−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	$-0.279756\pi$
$662$	26.9314	+	18.8576i	1.04672	+	0.732920i
$663$	30.0998	−	16.1689i	1.16898	−	0.627947i
$664$	1.30202	−	1.55168i	0.0505280	−	0.0602169i
$665$	4.12986	+	12.6409i	0.160149	+	0.490192i
$666$	−70.9885	−	4.35774i	−2.75075	−	0.168859i
$667$	10.3744	−	2.77981i	0.401699	−	0.107635i
$668$	0.880256	+	0.410470i	0.0340581	+	0.0158816i
$669$	16.5826	+	12.3857i	0.641119	+	0.478858i
$670$	19.2235	+	5.84326i	0.742668	+	0.225745i
$671$	−4.44565	+	12.2143i	−0.171622	+	0.471529i
$672$	−15.2343	−	13.6002i	−0.587676	−	0.524639i
$673$	14.0367	+	20.0466i	0.541077	+	0.772738i	0.992847	−	0.119397i	$-0.0380961\pi$
$673$	14.0367	+	20.0466i	0.541077	+	0.772738i	−0.451770	+	0.892135i	$0.649207\pi$
$674$	8.08017			0.311236
$675$	24.2688	−	9.27508i	0.934105	−	0.356998i
$676$	−50.5961			−1.94600
$677$	−11.7412	−	16.7682i	−0.451252	−	0.644455i	0.527487	−	0.849563i	$-0.323134\pi$
$677$	−11.7412	−	16.7682i	−0.451252	−	0.644455i	−0.978739	+	0.205108i	$0.934245\pi$
$678$	−50.4813	+	16.6400i	−1.93872	+	0.639055i
$679$	−8.11957	+	22.3083i	−0.311601	+	0.856115i
$680$	−0.825265	−	0.250852i	−0.0316474	−	0.00961972i
$681$	0.235792	−	1.99029i	0.00903556	−	0.0762681i
$682$	−18.0208	−	8.40325i	−0.690053	−	0.321777i
$683$	−21.3380	+	5.71751i	−0.816477	+	0.218774i	−0.642806	−	0.766029i	$-0.722230\pi$
$683$	−21.3380	+	5.71751i	−0.816477	+	0.218774i	−0.173671	+	0.984804i	$0.555563\pi$
$684$	−24.0623	+	7.12175i	−0.920047	+	0.272307i
$685$	−13.6507	−	41.7827i	−0.521566	−	1.59643i
$686$	22.4833	−	26.7945i	0.858416	−	1.02302i
$687$	−0.464968	+	15.1631i	−0.0177396	+	0.578509i
$688$	−2.33707	−	1.63643i	−0.0890999	−	0.0623884i
$689$	0.114078	+	0.646969i	0.00434603	+	0.0246476i
$690$	−20.5526	−	33.7551i	−0.782425	−	1.28503i
$691$	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	$0.611402\pi$
$692$	−36.6813	−	9.82872i	−1.39441	−	0.373632i
$693$	−12.7105	+	0.329998i	−0.482831	+	0.0125356i
$694$	21.6551	+	12.5026i	0.822016	+	0.474591i
$695$	1.99687	−	2.65886i	0.0757455	−	0.100856i
$696$	0.437188	+	0.0517940i	0.0165716	+	0.00196325i
$697$	−2.73187	−	0.239008i	−0.103477	−	0.00905306i
$698$	6.50619	+	13.9526i	0.246263	+	0.528112i
$699$	−25.3066	−	12.7591i	−0.957182	−	0.482593i
$700$	−14.7918	+	2.92487i	−0.559079	+	0.110550i
$701$			11.4005i			0.430590i	0.976549	+	0.215295i	$0.0690713\pi$
$701$			11.4005i			0.430590i	−0.976549	+	0.215295i	$0.930929\pi$
$702$	52.3903	+	37.0521i	1.97735	+	1.39844i
$703$	−33.7929	+	33.7929i	−1.27452	+	1.27452i
$704$	−4.25644	+	24.1395i	−0.160421	+	0.909791i
$705$	6.61511	+	8.99348i	0.249139	+	0.338714i
$706$	33.8977	+	12.3377i	1.27576	+	0.464337i
$707$	0.701693	−	8.02039i	0.0263899	−	0.301638i
$708$	−13.3466	+	1.93365i	−0.501598	+	0.0726711i
$709$	−5.28444	−	14.5189i	−0.198461	−	0.545268i	0.800043	−	0.599943i	$-0.204810\pi$
$709$	−5.28444	−	14.5189i	−0.198461	−	0.545268i	−0.998504	+	0.0546749i	$0.982588\pi$
$710$	30.3918	+	27.2762i	1.14059	+	1.02366i
$711$	3.65928	+	2.42320i	0.137234	+	0.0908772i
$712$	0.189270	−	0.706365i	0.00709319	−	0.0264722i
$713$	1.50497	+	17.2019i	0.0563616	+	0.644216i
$714$	15.7480	+	4.74151i	0.589353	+	0.177447i
$715$	−39.6474	−	1.32039i	−1.48273	−	0.0493798i
$716$	−16.0551	+	2.83094i	−0.600006	+	0.105797i
$717$	−7.82988	+	12.6498i	−0.292412	+	0.472415i
$718$	−25.1504	+	2.20038i	−0.938606	+	0.0821174i
$719$	−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	$0.889556\pi$
$720$	4.32877	+	25.6483i	0.161324	+	0.955854i
$721$	2.87301	−	4.97620i	0.106997	−	0.185323i
$722$	2.13197	−	4.57202i	0.0793437	−	0.170153i
$723$	3.32459	+	1.32681i	0.123643	+	0.0493444i
$724$	26.1085	+	31.1149i	0.970315	+	1.15638i
$725$	−7.34124	+	7.65140i	−0.272647	+	0.284166i
$726$	−5.01651	−	7.65331i	−0.186180	−	0.284041i
$727$	35.1712	−	24.6272i	1.30443	−	0.913371i	0.305186	−	0.952293i	$-0.401281\pi$
$727$	35.1712	−	24.6272i	1.30443	−	0.913371i	0.999242	+	0.0389219i	$0.0123924\pi$
$728$	−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
$732$	15.6831	+	3.26391i	0.579663	+	0.120638i
$733$	0.567513	−	0.264636i	0.0209616	−	0.00977454i	−0.412109	−	0.911134i	$-0.635208\pi$
$733$	0.567513	−	0.264636i	0.0209616	−	0.00977454i	0.433071	+	0.901360i	$0.357430\pi$
$734$	21.1255	−	17.7264i	0.779755	−	0.654292i
$735$	−18.4399	+	3.69677i	−0.680167	+	0.136357i
$736$	38.3205	−	13.9475i	1.41251	−	0.514112i
$737$	3.34089	+	12.4684i	0.123063	+	0.459278i
$738$	−1.88648	−	4.79224i	−0.0694423	−	0.176405i
$739$	−23.6846	+	13.6743i	−0.871251	+	0.503017i	−0.867764	−	0.496977i	$-0.834443\pi$
$739$	−23.6846	+	13.6743i	−0.871251	+	0.503017i	−0.00348723	+	0.999994i	$0.501110\pi$
$740$	−33.4295	−	42.6457i	−1.22889	−	1.56769i
$741$	41.9712	−	9.87796i	1.54185	−	0.362876i
$742$	−0.181374	+	0.259029i	−0.00665846	+	0.00950927i
$743$	20.5718	−	29.3796i	0.754706	−	1.07783i	−0.239558	−	0.970882i	$-0.577003\pi$
$743$	20.5718	−	29.3796i	0.754706	−	1.07783i	0.994264	−	0.106950i	$-0.0341086\pi$
$744$	−0.204059	+	0.677741i	−0.00748118	+	0.0248472i
$745$	−1.33455	+	11.0161i	−0.0488941	+	0.403600i
$746$	−21.1251	+	12.1966i	−0.773444	+	0.446548i
$747$	49.6860	−	10.0972i	1.81792	−	0.369437i
$748$	−4.96558	−	18.5318i	−0.181559	−	0.677589i
$749$	20.4960	−	7.45993i	0.748907	−	0.272580i
$750$	34.6150	+	18.0031i	1.26396	+	0.657379i
$751$	−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	$0.501046\pi$
$752$	−10.1301	+	4.72374i	−0.369407	+	0.172257i
$753$	−12.7249	+	14.2539i	−0.463723	+	0.519441i
$754$	−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	$0.984328\pi$
$758$	37.1701	−	26.0268i	1.35008	−	0.945336i
$759$	11.4304	−	22.6713i	0.414899	−	0.822915i
$760$	−0.924024	−	0.575321i	−0.0335179	−	0.0208691i
$761$	5.19201	+	6.18759i	0.188210	+	0.224300i	0.851896	−	0.523712i	$-0.175453\pi$
$761$	5.19201	+	6.18759i	0.188210	+	0.224300i	−0.663685	+	0.748012i	$0.731009\pi$
$762$	27.3233	−	21.5350i	0.989819	−	0.780132i
$763$	6.13535	−	13.1573i	0.222115	−	0.476326i
$764$	8.99914	−	15.5870i	0.325577	−	0.563917i
$765$	−12.2536	−	17.7760i	−0.443029	−	0.642692i
$766$	−14.5740	−	25.2430i	−0.526582	−	0.912066i
$767$	23.0841	−	2.01960i	0.833519	−	0.0729234i
$768$	−25.9793	−	0.796640i	−0.937447	−	0.0287463i
$769$	16.0619	−	2.83215i	0.579208	−	0.102130i	0.123634	−	0.992328i	$-0.460545\pi$
$769$	16.0619	−	2.83215i	0.579208	−	0.102130i	0.455574	+	0.890198i	$0.349434\pi$
$770$	−13.0449	−	13.9437i	−0.470107	−	0.502498i
$771$	7.28665	−	6.85306i	0.262422	−	0.246807i
$772$	−1.55101	−	17.7281i	−0.0558220	−	0.638048i
$773$	3.06271	−	11.4302i	0.110158	−	0.411116i	−0.888721	−	0.458448i	$-0.848405\pi$
$773$	3.06271	−	11.4302i	0.110158	−	0.411116i	0.998879	+	0.0473325i	$0.0150720\pi$
$774$	1.26220	+	4.26460i	0.0453688	+	0.153288i
$775$	−10.0650	−	13.7595i	−0.361544	−	0.494256i
$776$	−0.664599	−	1.82597i	−0.0238577	−	0.0655485i
$777$	18.4725	+	23.4376i	0.662697	+	0.840820i
$778$	−2.21968	+	25.3711i	−0.0795795	+	0.909598i
$779$	−3.25195	−	1.18361i	−0.116513	−	0.0424073i
$780$	5.39546	+	48.5902i	0.193188	+	1.73981i
$781$	−4.55583	+	25.8374i	−0.163020	+	0.924534i
$782$	−23.2222	+	23.2222i	−0.830425	+	0.830425i
$783$	7.75538	+	7.82859i	0.277154	+	0.279771i
$784$		−	18.8287i		−	0.672455i
$785$	−14.0900	−	5.66625i	−0.502892	−	0.202237i
$786$	2.21756	+	39.1295i	0.0790976	+	1.39570i
$787$	−20.1245	−	43.1572i	−0.717361	−	1.53839i	−0.837988	−	0.545689i	$-0.816268\pi$
$787$	−20.1245	−	43.1572i	−0.717361	−	1.53839i	0.120627	−	0.992698i	$-0.461510\pi$
$788$	−4.11465	−	0.359985i	−0.146578	−	0.0128240i
$789$	19.1231	−	25.6029i	0.680799	−	0.911488i
$790$	0.927837	+	6.52539i	0.0330110	+	0.232163i
$791$	19.3145	+	11.1513i	0.686746	+	0.396493i
$792$	0.779608	−	0.689429i	0.0277022	−	0.0244978i
$793$	−26.5869	−	7.12394i	−0.944129	−	0.252979i
$794$	−23.2020	−	19.4688i	−0.823409	−	0.690922i
$795$	0.398360	−	0.116762i	0.0141284	−	0.00414111i
$796$	−6.40609	−	36.3307i	−0.227058	−	1.28771i
$797$	13.5475	+	9.48608i	0.479878	+	0.336014i	0.788358	−	0.615216i	$-0.210931\pi$
$797$	13.5475	+	9.48608i	0.479878	+	0.336014i	−0.308480	+	0.951231i	$0.599820\pi$
$798$	17.6473	+	10.9232i	0.624709	+	0.386678i
$799$	5.96354	−	7.10708i	0.210975	−	0.251430i
$800$	−25.2356	+	31.3701i	−0.892215	+	1.10910i
$801$	14.7166	−	10.8847i	0.519987	−	0.384591i
$802$	−51.0307	+	13.6736i	−1.80196	+	0.482833i
$803$	21.8589	+	10.1930i	0.771383	+	0.359702i
$804$	14.6170	−	6.27803i	0.515502	−	0.221409i
$805$	−4.82252	+	15.8654i	−0.169972	+	0.559182i
$806$	14.4009	−	39.5663i	0.507252	−	1.39366i
$807$	−5.54988	+	26.6671i	−0.195365	+	0.938728i
$808$	0.377980	+	0.539812i	0.0132973	+	0.0189905i
$809$	21.1013			0.741881			0.370941	−	0.928657i	$-0.379035\pi$
$809$	21.1013			0.741881			0.370941	+	0.928657i	$0.379035\pi$
$810$	19.6163	−	35.4865i	0.689246	−	1.24687i
$811$	3.03312			0.106507			0.0532537	−	0.998581i	$-0.483041\pi$
$811$	3.03312			0.106507			0.0532537	+	0.998581i	$0.483041\pi$
$812$	−3.66824	−	5.23879i	−0.128730	−	0.183845i
$813$	6.15208	−	29.5607i	0.215763	−	1.03674i
$814$	23.4693	−	64.4814i	0.822599	−	2.26007i
$815$	−40.1341	+	21.4229i	−1.40584	+	0.750412i
$816$	19.8609	−	8.53029i	0.695270	−	0.298620i
$817$	2.70847	+	1.26298i	0.0947574	+	0.0441861i
$818$	14.6711	−	3.93110i	0.512962	−	0.137448i
$819$	−3.04198	−	26.7521i	−0.106295	−	0.934795i
$820$	1.77573	−	3.49903i	0.0620111	−	0.122191i
$821$	7.72326	−	9.20422i	0.269544	−	0.321230i	−0.614246	−	0.789115i	$-0.710540\pi$
$821$	7.72326	−	9.20422i	0.269544	−	0.321230i	0.883789	+	0.467885i	$0.154984\pi$
$822$	−58.3309	−	36.1052i	−2.03452	−	1.25931i
$823$	−19.4859	−	13.6442i	−0.679237	−	0.475607i	0.182339	−	0.983236i	$-0.441633\pi$
$823$	−19.4859	−	13.6442i	−0.679237	−	0.475607i	−0.861576	+	0.507629i	$0.830522\pi$
$824$	0.0816702	+	0.463175i	0.00284512	+	0.0161355i
$825$	1.93562	+	24.9918i	0.0673897	+	0.870101i
$826$	8.54427	+	7.16949i	0.297293	+	0.249459i
$827$	−44.8353	−	12.0136i	−1.55907	−	0.417753i	−0.626704	−	0.779257i	$-0.715597\pi$
$827$	−44.8353	−	12.0136i	−1.55907	−	0.417753i	−0.932370	+	0.361504i	$0.882263\pi$
$828$	−29.6714	−	9.93527i	−1.03115	−	0.345275i
$829$	27.8169	+	16.0601i	0.966123	+	0.557791i	0.898052	−	0.439889i	$-0.144982\pi$
$829$	27.8169	+	16.0601i	0.966123	+	0.557791i	0.0680706	+	0.997681i	$0.478316\pi$
$830$	60.8832	+	45.7248i	2.11329	+	1.58713i
$831$	−15.9170	+	21.3104i	−0.552153	+	0.739251i
$832$	−51.7084	−	4.52390i	−1.79267	−	0.156838i
$833$	6.60493	+	14.1643i	0.228847	+	0.490765i
$834$	−0.293632	−	5.18124i	−0.0101677	−	0.179412i
$835$	−0.393455	+	0.978382i	−0.0136161	+	0.0338583i
$836$		−	24.2112i		−	0.837361i
$837$	−14.5602	+	10.0935i	−0.503273	+	0.348884i
$838$	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	$0.717960\pi$
$840$	−0.424641	+	0.530725i	−0.0146515	+	0.0183117i
$841$	23.0248	+	8.38035i	0.793959	+	0.288977i
$842$	1.20798	−	13.8072i	0.0416296	−	0.475829i
$843$	7.94457	+	10.0799i	0.273625	+	0.347172i
$844$	−7.51891	−	20.6580i	−0.258812	−	0.711079i
$845$	−2.96366	−	54.8542i	−0.101953	−	1.88704i
$846$	16.9415	+	4.07129i	0.582461	+	0.139974i
$847$	−0.993767	+	3.70879i	−0.0341463	+	0.127436i
$848$	0.0362221	+	0.414021i	0.00124387	+	0.0142175i
$849$	18.1399	−	17.0605i	0.622561	−	0.585516i
$850$	7.74218	−	31.4852i	0.265555	−	1.07993i
$851$	−58.6858	+	10.3479i	−2.01172	+	0.354721i
$852$	32.3182	+	0.991020i	1.10720	+	0.0339518i
$853$	50.7794	−	4.44262i	1.73865	−	0.152112i	0.826763	−	0.562550i	$-0.190180\pi$
$853$	50.7794	−	4.44262i	1.73865	−	0.152112i	0.911889	+	0.410438i	$0.134624\pi$
$854$	−6.62440	−	11.4738i	−0.226682	−	0.392625i
$855$	−9.13056	−	25.6703i	−0.312259	−	0.877905i
$856$	−0.892646	+	1.54611i	−0.0305100	+	0.0528449i
$857$	4.25654	−	9.12817i	0.145400	−	0.311812i	−0.820097	−	0.572224i	$-0.806081\pi$
$857$	4.25654	−	9.12817i	0.145400	−	0.311812i	0.965498	+	0.260412i	$0.0838584\pi$
$858$	−48.6238	+	38.3232i	−1.65999	+	1.30833i
$859$	8.01487	+	9.55175i	0.273464	+	0.325902i	0.885245	−	0.465126i	$-0.153991\pi$
$859$	8.01487	+	9.55175i	0.273464	+	0.325902i	−0.611781	+	0.791027i	$0.709547\pi$
$860$	−1.79096	+	2.87646i	−0.0610711	+	0.0980864i
$861$	−0.972864	+	1.92959i	−0.0331551	+	0.0657603i
$862$	−4.81810	+	3.37367i	−0.164105	+	0.114908i
$863$	−23.9621	−	23.9621i	−0.815678	−	0.815678i	0.169800	−	0.985479i	$-0.445688\pi$
$863$	−23.9621	−	23.9621i	−0.815678	−	0.815678i	−0.985479	+	0.169800i	$0.945688\pi$
$864$	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
$867$	7.66079	−	8.58127i	0.260174	−	0.291435i
$868$	9.31869	−	4.34538i	0.316297	−	0.147492i
$869$	−3.24378	+	2.72185i	−0.110038	+	0.0923326i
$870$	−1.05751	+	16.5150i	−0.0358529	+	0.559911i
$871$	−25.6857	+	9.34885i	−0.870328	+	0.316774i
$872$	0.307549	+	1.14779i	0.0104149	+	0.0388690i
$873$	15.4435	−	46.1217i	0.522685	−	1.56098i
$874$	−35.8915	+	20.7220i	−1.21405	+	0.700932i
$875$	−4.03746	−	15.8654i	−0.136491	−	0.536348i
$876$	8.56951	−	28.4619i	0.289537	−	0.961637i
$877$	−26.9320	+	38.4629i	−0.909430	+	1.29880i	0.0445739	+	0.999006i	$0.485807\pi$
$877$	−26.9320	+	38.4629i	−0.909430	+	1.29880i	−0.954004	+	0.299794i	$0.903082\pi$
$878$	−4.32933	+	6.18293i	−0.146108	+	0.208664i
$879$	33.9615	−	7.99287i	1.14549	−	0.269593i
$880$	−24.9136	−	3.01816i	−0.839838	−	0.101742i
$881$	20.2756	−	11.7061i	0.683103	−	0.394390i	−0.117920	−	0.993023i	$-0.537623\pi$
$881$	20.2756	−	11.7061i	0.683103	−	0.394390i	0.801023	+	0.598633i	$0.204289\pi$
$882$	−18.2767	+	22.9665i	−0.615409	+	0.773321i
$883$	−1.63802	−	6.11319i	−0.0551239	−	0.205725i	0.932871	−	0.360210i	$-0.117295\pi$
$883$	−1.63802	−	6.11319i	−0.0551239	−	0.205725i	−0.987995	+	0.154485i	$0.950628\pi$
$884$	38.1768	−	13.8952i	1.28402	−	0.467347i
$885$	−2.87817	−	14.3566i	−0.0967485	−	0.482593i
$886$	−43.1969	+	36.2465i	−1.45123	+	1.21773i
$887$	29.6855	−	13.8426i	0.996741	−	0.464788i	0.145384	−	0.989375i	$-0.453558\pi$
$887$	29.6855	−	13.8426i	0.996741	−	0.464788i	0.851357	+	0.524587i	$0.175780\pi$
$888$	−2.39139	−	0.497687i	−0.0802497	−	0.0167013i
$889$	−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
$893$	9.59056	−	6.71538i	0.320936	−	0.224722i
$894$	9.49386	+	14.4841i	0.317522	+	0.484420i
$895$	−4.00962	−	17.2404i	−0.134027	−	0.576284i
$896$	−0.902060	−	1.07503i	−0.0301357	−	0.0359143i
$897$	49.9352	+	19.9286i	1.66729	+	0.665396i
$898$	8.12765	−	17.4298i	0.271223	−	0.581640i
$899$	3.61538	−	6.26203i	0.120580	−	0.208850i
$900$	30.1398	−	6.77701i	1.00466	−	0.225900i
$901$	−0.172483	−	0.298750i	−0.00574625	−	0.00995280i
$902$	4.95006	−	0.433074i	0.164819	−	0.0144198i
$903$	0.982153	−	1.58675i	0.0326840	−	0.0528036i
$904$	−1.79776	+	0.316994i	−0.0597926	+	0.0105430i
$905$	−32.2042	+	30.1283i	−1.07050	+	1.00150i
$906$	69.2851	+	20.8609i	2.30184	+	0.693056i
$907$	2.49616	+	28.5313i	0.0828837	+	0.947365i	0.917814	+	0.397010i	$0.129952\pi$
$907$	2.49616	+	28.5313i	0.0828837	+	0.947365i	−0.834931	+	0.550355i	$0.814492\pi$
$908$	0.616790	−	2.30189i	0.0204689	−	0.0763910i
$909$	−1.01067	+	16.4640i	−0.0335217	+	0.546075i
$910$	27.0071	−	30.0920i	0.895277	−	0.997542i
$911$	−6.61616	−	18.1777i	−0.219203	−	0.602255i	0.780536	−	0.625111i	$-0.214946\pi$
$911$	−6.61616	−	18.1777i	−0.219203	−	0.602255i	−0.999739	+	0.0228557i	$0.992724\pi$
$912$	26.9956	−	3.91110i	0.893913	−	0.129509i
$913$	−4.26345	+	48.7315i	−0.141100	+	1.61278i
$914$	−67.0891	−	24.4184i	−2.21911	−	0.807690i
$915$	−2.61996	+	17.1941i	−0.0866134	+	0.568421i
$916$	−3.13228	+	17.7641i	−0.103493	+	0.586941i
$917$	11.6282	−	11.6282i	0.383996	−	0.383996i
$918$	−32.5057	−	8.87375i	−1.07285	−	0.292877i
$919$			44.6775i			1.47377i	0.676016	+	0.736887i	$0.263705\pi$
$919$			44.6775i			1.47377i	−0.676016	+	0.736887i	$0.736295\pi$
$920$	−0.532346	−	1.24852i	−0.0175509	−	0.0411624i
$921$	−18.4811	−	9.31782i	−0.608972	−	0.307032i
$922$	21.1047	+	45.2591i	0.695046	+	1.49053i
$923$	−55.3454	−	4.84210i	−1.82172	−	0.159380i
$924$	−15.0134	−	1.77865i	−0.493905	−	0.0585134i
$925$	44.2766	−	38.7409i	1.45581	−	1.27379i
$926$	−9.44552	−	5.45337i	−0.310399	−	0.179209i
$927$	−5.61963	+	10.3446i	−0.184573	+	0.339760i
$928$	−16.4946	−	4.41970i	−0.541461	−	0.145084i
$929$	−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	$-0.609509\pi$
$930$	−25.8530	−	6.28500i	−0.847754	−	0.206093i
$931$	3.42478	+	19.4229i	0.112243	+	0.636560i
$932$	−27.6044	−	19.3288i	−0.904213	−	0.633137i
$933$	−0.128535	+	4.19168i	−0.00420806	+	0.137229i
$934$	−53.0403	+	63.2110i	−1.73553	+	2.06833i
$935$	19.8006	−	6.46898i	0.647547	−	0.211558i
$936$	1.59825	+	1.51736i	0.0522404	+	0.0495965i
$937$	−13.8557	+	3.71263i	−0.452647	+	0.121286i	−0.477938	−	0.878394i	$-0.658616\pi$
$937$	−13.8557	+	3.71263i	−0.452647	+	0.121286i	0.0252908	+	0.999680i	$0.491949\pi$
$938$	−11.9243	−	5.56041i	−0.389343	−	0.181554i
$939$	−2.49799	+	21.0853i	−0.0815188	+	0.688092i
$940$	6.25111	+	11.7109i	0.203889	+	0.381969i
$941$	−0.0906224	+	0.248983i	−0.00295420	+	0.00811661i	−0.941161	−	0.337959i	$-0.890264\pi$
$941$	−0.0906224	+	0.248983i	−0.00295420	+	0.00811661i	0.938207	+	0.346075i	$0.112486\pi$
$942$	−22.5099	+	7.41988i	−0.733413	+	0.241753i
$943$	−2.47509	−	3.53479i	−0.0806000	−	0.115109i
$944$	14.6593			0.477121
$945$	−16.5890	+	3.77604i	−0.539639	+	0.122835i
$946$	−4.29098			−0.139512
$947$	−19.5534	−	27.9252i	−0.635401	−	0.907446i	0.364315	−	0.931276i	$-0.381303\pi$
$947$	−19.5534	−	27.9252i	−0.635401	−	0.907446i	−0.999716	+	0.0238294i	$0.992414\pi$
$948$	3.89297	+	3.47539i	0.126438	+	0.112875i
$949$	−17.4680	+	47.9930i	−0.567037	+	1.55792i
$950$	19.7209	−	35.8502i	0.639832	−	1.16313i
$951$	−31.4782	−	23.5113i	−1.02075	−	0.762407i
$952$	0.511912	+	0.238709i	0.0165912	+	0.00773659i
$953$	25.8211	−	6.91874i	0.836427	−	0.224120i	0.184912	−	0.982755i	$-0.440800\pi$
$953$	25.8211	−	6.91874i	0.836427	−	0.224120i	0.651516	+	0.758635i	$0.274133\pi$
$954$	0.357701	−	0.540165i	0.0115810	−	0.0174885i
$955$	17.4259	+	8.84350i	0.563888	+	0.286169i
$956$	−11.3705	+	13.5509i	−0.367749	+	0.438266i
$957$	−9.36611	+	5.03125i	−0.302763	+	0.162637i
$958$	45.6014	+	31.9305i	1.47331	+	1.03163i
$959$	4.99834	+	28.3470i	0.161405	+	0.915372i
$960$	0.764818	+	32.7898i	0.0246844	+	1.05829i
$961$	−14.8420	−	12.4539i	−0.478775	−	0.401740i
$962$	140.356	+	37.6084i	4.52528	+	1.21254i
$963$	−41.5813	+	16.3686i	−1.33994	+	0.527471i
$964$	3.68603	+	2.12813i	0.118719	+	0.0685425i
$965$	19.1292	−	2.71996i	0.615792	−	0.0875587i
$966$	10.2130	+	23.7788i	0.328599	+	0.765069i
$967$	−20.2788	−	1.77416i	−0.652121	−	0.0570532i	−0.243706	−	0.969849i	$-0.578363\pi$
$967$	−20.2788	−	1.77416i	−0.652121	−	0.0570532i	−0.408416	+	0.912796i	$0.633919\pi$
$968$	−0.132820	−	0.284833i	−0.00426899	−	0.00915488i
$969$	−18.9360	+	12.4120i	−0.608313	+	0.398731i
$970$	67.1905	−	28.6489i	2.15736	−	0.919859i
$971$			40.5268i			1.30057i	0.759692	+	0.650284i	$0.225350\pi$
$971$			40.5268i			1.30057i	−0.759692	+	0.650284i	$0.774650\pi$
$972$	−6.24566	−	31.4908i	−0.200329	−	1.01007i
$973$	−1.53972	+	1.53972i	−0.0493610	+	0.0493610i
$974$	−14.0086	+	79.4468i	−0.448865	+	2.54564i
$975$	−52.3635	+	8.69570i	−1.67697	+	0.278485i
$976$	−16.3627	−	5.95554i	−0.523758	−	0.190632i
$977$	3.10305	−	35.4680i	0.0992752	−	1.13472i	−0.769207	−	0.639000i	$-0.779348\pi$
$977$	3.10305	−	35.4680i	0.0992752	−	1.13472i	0.868482	−	0.495721i	$-0.165096\pi$
$978$	−26.3173	+	65.9434i	−0.841533	+	2.10864i
$979$	6.04024	+	16.5954i	0.193047	+	0.530392i
$980$	−22.3296	+	1.20642i	−0.713293	+	0.0385377i
$981$	−11.8662	+	27.2738i	−0.378860	+	0.870787i
$982$	−12.5145	+	46.7049i	−0.399355	+	1.49041i
$983$	−3.20046	−	36.5814i	−0.102079	−	1.16677i	−0.858547	−	0.512735i	$-0.828632\pi$
$983$	−3.20046	−	36.5814i	−0.102079	−	1.16677i	0.756468	−	0.654030i	$-0.226923\pi$
$984$	−0.0405214	−	0.172174i	−0.00129177	−	0.00548871i
$985$	0.149266	−	4.48203i	0.00475602	−	0.142809i
$986$	13.5432	−	2.38804i	0.431305	−	0.0760507i
$987$	−3.45966	−	6.44047i	−0.110122	−	0.205002i
$988$	51.0740	−	4.46840i	1.62488	−	0.142159i
$989$	1.86320	+	3.22716i	0.0592464	+	0.102618i
$990$	27.4589	+	27.8646i	0.872701	+	0.885597i
$991$	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	$0.101420\pi$
$992$	11.6027	−	24.8820i	0.368385	−	0.790005i
$993$	4.05242	+	27.9710i	0.128600	+	0.887634i
$994$	−17.1893	−	20.4854i	−0.545210	−	0.649756i
$995$	39.0131	−	9.07329i	1.23680	−	0.287643i
$996$	60.1899	−	3.41109i	1.90719	−	0.108085i
$997$	−45.2647	+	31.6947i	−1.43355	+	1.00378i	−0.439113	+	0.898432i	$0.644707\pi$
$997$	−45.2647	+	31.6947i	−1.43355	+	1.00378i	−0.994435	+	0.105349i	$0.966404\pi$
$998$	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.2.14	✓	192
3.2	odd	2		405.2.r.a.332.3		192
5.2	odd	4		675.2.ba.b.218.3		192
5.3	odd	4	inner	135.2.q.a.83.14	yes	192
5.4	even	2		675.2.ba.b.407.3		192
15.8	even	4		405.2.r.a.8.3		192
27.13	even	9		405.2.r.a.152.3		192
27.14	odd	18	inner	135.2.q.a.122.14	yes	192
135.13	odd	36		405.2.r.a.233.3		192
135.14	odd	18		675.2.ba.b.257.3		192
135.68	even	36	inner	135.2.q.a.68.14	yes	192
135.122	even	36		675.2.ba.b.68.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.14	✓	192	1.1	even	1	trivial
135.2.q.a.68.14	yes	192	135.68	even	36	inner
135.2.q.a.83.14	yes	192	5.3	odd	4	inner
135.2.q.a.122.14	yes	192	27.14	odd	18	inner
405.2.r.a.8.3		192	15.8	even	4
405.2.r.a.152.3		192	27.13	even	9
405.2.r.a.233.3		192	135.13	odd	36
405.2.r.a.332.3		192	3.2	odd	2
675.2.ba.b.68.3		192	135.122	even	36
675.2.ba.b.218.3		192	5.2	odd	4
675.2.ba.b.257.3		192	135.14	odd	18
675.2.ba.b.407.3		192	5.4	even	2

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)

\(f(q)\)	\(=\)	\(q+(1.15565 + 1.65044i) q^{2} +(-0.352907 + 1.69572i) q^{3} +(-0.704386 + 1.93528i) q^{4} +(-2.13942 - 0.650308i) q^{5} +(-3.20652 + 1.37721i) q^{6} +(1.32708 + 0.618828i) q^{7} +(-0.115769 + 0.0310202i) q^{8} +(-2.75091 - 1.19686i) q^{9} +O(q^{10})\)	\(q+(1.15565 + 1.65044i) q^{2} +(-0.352907 + 1.69572i) q^{3} +(-0.704386 + 1.93528i) q^{4} +(-2.13942 - 0.650308i) q^{5} +(-3.20652 + 1.37721i) q^{6} +(1.32708 + 0.618828i) q^{7} +(-0.115769 + 0.0310202i) q^{8} +(-2.75091 - 1.19686i) q^{9} +(-1.39912 - 4.28251i) q^{10} +(1.86051 - 2.21727i) q^{11} +(-3.03311 - 1.87741i) q^{12} +(5.02076 + 3.51558i) q^{13} +(0.512304 + 2.90542i) q^{14} +(1.85775 - 3.39835i) q^{15} +(2.97033 + 2.49240i) q^{16} +(-3.10881 - 0.833002i) q^{17} +(-1.20375 - 5.92337i) q^{18} +(-3.51741 - 2.03078i) q^{19} +(2.76550 - 3.68231i) q^{20} +(-1.51769 + 2.03197i) q^{21} +(5.80958 + 0.508272i) q^{22} +(-2.14034 - 4.58997i) q^{23} +(-0.0117458 - 0.207259i) q^{24} +(4.15420 + 2.78256i) q^{25} +12.3493i q^{26} +(3.00035 - 4.24239i) q^{27} +(-2.13239 + 2.13239i) q^{28} +(-0.368261 + 2.08851i) q^{29} +(7.75568 - 0.861192i) q^{30} +(-3.20394 - 1.16614i) q^{31} +(-0.701790 + 8.02150i) q^{32} +(3.10328 + 3.93739i) q^{33} +(-2.21787 - 6.09356i) q^{34} +(-2.43675 - 2.18694i) q^{35} +(4.25397 - 4.48075i) q^{36} +(3.04540 - 11.3656i) q^{37} +(-0.713220 - 8.15214i) q^{38} +(-7.73328 + 7.27312i) q^{39} +(0.267850 + 0.00892031i) q^{40} +(0.839107 - 0.147957i) q^{41} +(-5.10757 - 0.156621i) q^{42} +(-0.732994 + 0.0641287i) q^{43} +(2.98053 + 5.16243i) q^{44} +(5.10702 + 4.34952i) q^{45} +(5.10199 - 8.83690i) q^{46} +(-1.21825 + 2.61254i) q^{47} +(-5.27466 + 4.15725i) q^{48} +(-3.12132 - 3.71984i) q^{49} +(0.208362 + 10.0719i) q^{50} +(2.50966 - 4.97768i) q^{51} +(-10.3402 + 7.24028i) 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} +(4.68494 - 5.24785i) q^{57} +(-3.87255 + 1.80580i) q^{58} +(2.89613 - 2.43014i) q^{59} +(5.26819 + 5.98902i) q^{60} +(-4.21993 + 1.53593i) q^{61} +(-1.77799 - 6.63556i) q^{62} +(-2.91003 - 3.29067i) q^{63} +(-7.33402 + 4.23430i) q^{64} +(-8.45529 - 10.7863i) q^{65} +(-2.91213 + 9.67203i) q^{66} +(-2.55795 + 3.65313i) q^{67} +(3.80189 - 5.42967i) q^{68} +(8.53862 - 2.00957i) q^{69} +(0.793385 - 6.54906i) q^{70} +(-7.84988 + 4.53213i) q^{71} +(0.355597 + 0.0532255i) q^{72} +(2.15667 + 8.04880i) q^{73} +(22.2777 - 8.10840i) q^{74} +(-6.18448 + 6.06236i) q^{75} +(6.40774 - 5.37673i) q^{76} +(3.84116 - 1.79116i) q^{77} +(-20.9408 - 4.35814i) 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} +(-13.8441 + 9.69375i) q^{83} +(-2.86339 - 4.36846i) q^{84} +(6.10932 + 3.80382i) q^{85} +(-0.952926 - 1.13565i) q^{86} +(-3.41157 - 1.36152i) q^{87} +(-0.146609 + 0.314404i) q^{88} +(-3.05075 + 5.28406i) q^{89} +(-1.27670 + 13.4554i) q^{90} +(4.48742 + 7.77244i) q^{91} +(10.3905 - 0.909052i) q^{92} +(3.10813 - 5.02144i) q^{93} +(-5.71971 + 1.00854i) q^{94} +(6.20457 + 6.63207i) q^{95} +(-13.3545 - 4.02088i) q^{96} +(1.41304 + 16.1512i) q^{97} +(2.53222 - 9.45039i) 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

Properties

Related objects

Downloads

Learn more