LMFDB - Embedded newform 405.2.r.a.233.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [405,2,Mod(8,405)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("405.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(405, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([2, 27])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.23394128186$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			233.3
Character	$\chi$	$=$	405.233
Dual form			405.2.r.a.332.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.15565 + 1.65044i) q^{2} +(-0.704386 - 1.93528i) q^{4} +(2.13942 - 0.650308i) q^{5} +(1.32708 - 0.618828i) q^{7} +(0.115769 + 0.0310202i) q^{8} +(-1.39912 + 4.28251i) q^{10} +(-1.86051 - 2.21727i) q^{11} +(5.02076 - 3.51558i) q^{13} +(-0.512304 + 2.90542i) q^{14} +(2.97033 - 2.49240i) q^{16} +(3.10881 - 0.833002i) q^{17} +(-3.51741 + 2.03078i) q^{19} +(-2.76550 - 3.68231i) q^{20} +(5.80958 - 0.508272i) q^{22} +(2.14034 - 4.58997i) q^{23} +(4.15420 - 2.78256i) q^{25} +12.3493i q^{26} +(-2.13239 - 2.13239i) q^{28} +(0.368261 + 2.08851i) q^{29} +(-3.20394 + 1.16614i) q^{31} +(0.701790 + 8.02150i) q^{32} +(-2.21787 + 6.09356i) q^{34} +(2.43675 - 2.18694i) q^{35} +(3.04540 + 11.3656i) q^{37} +(0.713220 - 8.15214i) q^{38} +(0.267850 - 0.00892031i) q^{40} +(-0.839107 - 0.147957i) q^{41} +(-0.732994 - 0.0641287i) q^{43} +(-2.98053 + 5.16243i) q^{44} +(5.10199 + 8.83690i) q^{46} +(1.21825 + 2.61254i) q^{47} +(-3.12132 + 3.71984i) q^{49} +(-0.208362 + 10.0719i) q^{50} +(-10.3402 - 7.24028i) q^{52} +(-0.0757900 + 0.0757900i) q^{53} +(-5.42232 - 3.53376i) q^{55} +(0.172831 - 0.0304748i) q^{56} +(-3.87255 - 1.80580i) q^{58} +(-2.89613 - 2.43014i) q^{59} +(-4.21993 - 1.53593i) q^{61} +(1.77799 - 6.63556i) q^{62} +(-7.33402 - 4.23430i) q^{64} +(8.45529 - 10.7863i) q^{65} +(-2.55795 - 3.65313i) q^{67} +(-3.80189 - 5.42967i) q^{68} +(0.793385 + 6.54906i) q^{70} +(7.84988 + 4.53213i) q^{71} +(2.15667 - 8.04880i) q^{73} +(-22.2777 - 8.10840i) q^{74} +(6.40774 + 5.37673i) q^{76} +(-3.84116 - 1.79116i) q^{77} +(-1.44073 + 0.254040i) q^{79} +(4.73394 - 7.26391i) q^{80} +(1.21391 - 1.21391i) q^{82} +(13.8441 + 9.69375i) q^{83} +(6.10932 - 3.80382i) q^{85} +(0.952926 - 1.13565i) q^{86} +(-0.146609 - 0.314404i) q^{88} +(3.05075 + 5.28406i) q^{89} +(4.48742 - 7.77244i) q^{91} +(-10.3905 - 0.909052i) q^{92} +(-5.71971 - 1.00854i) q^{94} +(-6.20457 + 6.63207i) q^{95} +(1.41304 - 16.1512i) q^{97} +(-2.53222 - 9.45039i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Character values

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

$n$	$82$	$326$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{17}{18}\right)$

Coefficient data

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

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

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

$2$	−1.15565	+	1.65044i	−0.817169	+	1.16704i	0.166320	+	0.986072i	$0.446811\pi$
$2$	−1.15565	+	1.65044i	−0.817169	+	1.16704i	−0.983489	+	0.180966i	$0.942077\pi$
$3$		0			0
$3$		0			0
$4$	−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
$6$		0			0
$7$	1.32708	−	0.618828i	0.501590	−	0.233895i	−0.155320	−	0.987864i	$-0.549641\pi$
$7$	1.32708	−	0.618828i	0.501590	−	0.233895i	0.656910	+	0.753969i	$0.271863\pi$
$8$	0.115769	+	0.0310202i	0.0409305	+	0.0109673i
$9$		0			0
$10$	−1.39912	+	4.28251i	−0.442442	+	1.35425i
$11$	−1.86051	−	2.21727i	−0.560965	−	0.668532i	0.408785	−	0.912631i	$-0.365953\pi$
$11$	−1.86051	−	2.21727i	−0.560965	−	0.668532i	−0.969751	+	0.244098i	$0.921508\pi$
$12$		0			0
$13$	5.02076	−	3.51558i	1.39251	−	0.975045i	0.394076	−	0.919078i	$-0.371065\pi$
$13$	5.02076	−	3.51558i	1.39251	−	0.975045i	0.998433	−	0.0559675i	$-0.0178243\pi$
$14$	−0.512304	+	2.90542i	−0.136919	+	0.776506i
$15$		0			0
$16$	2.97033	−	2.49240i	0.742582	−	0.623101i
$17$	3.10881	−	0.833002i	0.753996	−	0.202033i	0.138706	−	0.990334i	$-0.455706\pi$
$17$	3.10881	−	0.833002i	0.753996	−	0.202033i	0.615290	+	0.788301i	$0.289039\pi$
$18$		0			0
$19$	−3.51741	+	2.03078i	−0.806949	+	0.465892i	−0.845895	−	0.533349i	$-0.820933\pi$
$19$	−3.51741	+	2.03078i	−0.806949	+	0.465892i	0.0389464	+	0.999241i	$0.487600\pi$
$20$	−2.76550	−	3.68231i	−0.618385	−	0.823389i
$21$		0			0
$22$	5.80958	−	0.508272i	1.23861	−	0.108364i
$23$	2.14034	−	4.58997i	0.446291	−	0.957074i	−0.546527	−	0.837441i	$-0.684051\pi$
$23$	2.14034	−	4.58997i	0.446291	−	0.957074i	0.992818	−	0.119633i	$-0.0381717\pi$
$24$		0			0
$25$	4.15420	−	2.78256i	0.830840	−	0.556511i
$26$			12.3493i			2.42189i
$27$		0			0
$28$	−2.13239	−	2.13239i	−0.402983	−	0.402983i
$29$	0.368261	+	2.08851i	0.0683844	+	0.387827i	0.999720	+	0.0236650i	$0.00753352\pi$
$29$	0.368261	+	2.08851i	0.0683844	+	0.387827i	−0.931336	+	0.364162i	$0.881355\pi$
$30$		0			0
$31$	−3.20394	+	1.16614i	−0.575445	+	0.209445i	−0.613316	−	0.789838i	$-0.710165\pi$
$31$	−3.20394	+	1.16614i	−0.575445	+	0.209445i	0.0378710	+	0.999283i	$0.487942\pi$
$32$	0.701790	+	8.02150i	0.124060	+	1.41801i
$33$		0			0
$34$	−2.21787	+	6.09356i	−0.380362	+	1.04504i
$35$	2.43675	−	2.18694i	0.411886	−	0.369661i
$36$		0			0
$37$	3.04540	+	11.3656i	0.500661	+	1.86849i	0.495683	+	0.868503i	$0.334918\pi$
$37$	3.04540	+	11.3656i	0.500661	+	1.86849i	0.00497757	+	0.999988i	$0.498416\pi$
$38$	0.713220	−	8.15214i	0.115700	−	1.32245i
$39$		0			0
$40$	0.267850	−	0.00892031i	0.0423509	−	0.00141043i
$41$	−0.839107	−	0.147957i	−0.131046	−	0.0231070i	0.107740	−	0.994179i	$-0.465639\pi$
$41$	−0.839107	−	0.147957i	−0.131046	−	0.0231070i	−0.238787	+	0.971072i	$0.576750\pi$
$42$		0			0
$43$	−0.732994	−	0.0641287i	−0.111781	−	0.00977953i	0.0311282	−	0.999515i	$-0.490090\pi$
$43$	−0.732994	−	0.0641287i	−0.111781	−	0.00977953i	−0.142909	+	0.989736i	$0.545646\pi$
$44$	−2.98053	+	5.16243i	−0.449332	+	0.778266i
$45$		0			0
$46$	5.10199	+	8.83690i	0.752247	+	1.30293i
$47$	1.21825	+	2.61254i	0.177700	+	0.381078i	0.974902	−	0.222634i	$-0.0714655\pi$
$47$	1.21825	+	2.61254i	0.177700	+	0.381078i	−0.797203	+	0.603712i	$0.793688\pi$
$48$		0			0
$49$	−3.12132	+	3.71984i	−0.445902	+	0.531406i
$50$	−0.208362	+	10.0719i	−0.0294668	+	1.42439i
$51$		0			0
$52$	−10.3402	−	7.24028i	−1.43393	−	1.00405i
$53$	−0.0757900	+	0.0757900i	−0.0104106	+	0.0104106i	−0.712293	−	0.701882i	$-0.752343\pi$
$53$	−0.0757900	+	0.0757900i	−0.0104106	+	0.0104106i	0.701882	+	0.712293i	$0.252343\pi$
$54$		0			0
$55$	−5.42232	−	3.53376i	−0.731145	−	0.476492i
$56$	0.172831	−	0.0304748i	0.0230955	−	0.00407236i
$57$		0			0
$58$	−3.87255	−	1.80580i	−0.508491	−	0.237113i
$59$	−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	$0.801371\pi$
$60$		0			0
$61$	−4.21993	−	1.53593i	−0.540306	−	0.196655i	0.0574282	−	0.998350i	$-0.481710\pi$
$61$	−4.21993	−	1.53593i	−0.540306	−	0.196655i	−0.597734	+	0.801694i	$0.703932\pi$
$62$	1.77799	−	6.63556i	0.225805	−	0.842717i
$63$		0			0
$64$	−7.33402	−	4.23430i	−0.916753	−	0.529287i
$65$	8.45529	−	10.7863i	1.04875	−	1.33788i
$66$		0			0
$67$	−2.55795	−	3.65313i	−0.312504	−	0.446301i	0.631919	−	0.775034i	$-0.282267\pi$
$67$	−2.55795	−	3.65313i	−0.312504	−	0.446301i	−0.944423	+	0.328733i	$0.893378\pi$
$68$	−3.80189	−	5.42967i	−0.461047	−	0.658444i
$69$		0			0
$70$	0.793385	+	6.54906i	0.0948277	+	0.782762i
$71$	7.84988	+	4.53213i	0.931609	+	0.537865i	0.887320	−	0.461154i	$-0.152564\pi$
$71$	7.84988	+	4.53213i	0.931609	+	0.537865i	0.0442890	+	0.999019i	$0.485898\pi$
$72$		0			0
$73$	2.15667	−	8.04880i	0.252419	−	0.942041i	−0.717089	−	0.696982i	$-0.754526\pi$
$73$	2.15667	−	8.04880i	0.252419	−	0.942041i	0.969508	−	0.245059i	$-0.0788074\pi$
$74$	−22.2777	−	8.10840i	−2.58972	−	0.942583i
$75$		0			0
$76$	6.40774	+	5.37673i	0.735018	+	0.616754i
$77$	−3.84116	−	1.79116i	−0.437741	−	0.204122i
$78$		0			0
$79$	−1.44073	+	0.254040i	−0.162095	+	0.0285818i	−0.254107	−	0.967176i	$-0.581781\pi$
$79$	−1.44073	+	0.254040i	−0.162095	+	0.0285818i	0.0920115	+	0.995758i	$0.470670\pi$
$80$	4.73394	−	7.26391i	0.529271	−	0.812130i
$81$		0			0
$82$	1.21391	−	1.21391i	0.134054	−	0.134054i
$83$	13.8441	+	9.69375i	1.51959	+	1.06403i	0.974157	+	0.225872i	$0.0725231\pi$
$83$	13.8441	+	9.69375i	1.51959	+	1.06403i	0.545431	+	0.838155i	$0.316366\pi$
$84$		0			0
$85$	6.10932	−	3.80382i	0.662649	−	0.412582i
$86$	0.952926	−	1.13565i	0.102757	−	0.122461i
$87$		0			0
$88$	−0.146609	−	0.314404i	−0.0156286	−	0.0335156i
$89$	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	$0.728514\pi$
$90$		0			0
$91$	4.48742	−	7.77244i	0.470410	−	0.814774i
$92$	−10.3905	−	0.909052i	−1.08329	−	0.0947752i
$93$		0			0
$94$	−5.71971	−	1.00854i	−0.589943	−	0.104023i
$95$	−6.20457	+	6.63207i	−0.636575	+	0.680436i
$96$		0			0
$97$	1.41304	−	16.1512i	0.143473	−	1.63990i	−0.494023	−	0.869449i	$-0.664474\pi$
$97$	1.41304	−	16.1512i	0.143473	−	1.63990i	0.637496	−	0.770453i	$-0.279970\pi$
$98$	−2.53222	−	9.45039i	−0.255793	−	0.954633i
$99$		0			0
$100$	−8.31119	−	6.07956i	−0.831119	−	0.607956i
$101$	1.88053	−	5.16673i	0.187120	−	0.514108i	−0.810290	−	0.586029i	$-0.800691\pi$
$101$	1.88053	−	5.16673i	0.187120	−	0.514108i	0.997410	+	0.0719204i	$0.0229128\pi$
$102$		0			0
$103$	0.342012	+	3.90922i	0.0336994	+	0.385186i	0.994250	+	0.107082i	$0.0341507\pi$
$103$	0.342012	+	3.90922i	0.0336994	+	0.385186i	−0.960551	+	0.278105i	$0.910294\pi$
$104$	0.690302	−	0.251249i	0.0676897	−	0.0246370i
$105$		0			0
$106$	−0.0375001	−	0.212674i	−0.00364233	−	0.0206567i
$107$	−10.5329	−	10.5329i	−1.01825	−	1.01825i	−0.999830	−	0.0184189i	$-0.994137\pi$
$107$	−10.5329	−	10.5329i	−1.01825	−	1.01825i	−0.0184189	−	0.999830i	$-0.505863\pi$
$108$		0			0
$109$			9.91447i			0.949634i	0.880085	+	0.474817i	$0.157486\pi$
$109$			9.91447i			0.949634i	−0.880085	+	0.474817i	$0.842514\pi$
$110$	12.0986	−	4.86542i	1.15355	−	0.463899i
$111$		0			0
$112$	2.39950	−	5.14574i	0.226731	−	0.486227i
$113$	−15.1732	+	1.32748i	−1.42737	+	0.124879i	−0.774492	−	0.632583i	$-0.781995\pi$
$113$	−15.1732	+	1.32748i	−1.42737	+	0.124879i	−0.652879	+	0.757462i	$0.726439\pi$
$114$		0			0
$115$	1.59418	−	11.2117i	0.148658	−	1.04550i
$116$	3.78247	−	2.18381i	0.351193	−	0.202762i
$117$		0			0
$118$	7.35771	−	1.97149i	0.677332	−	0.181491i
$119$	3.61015	−	3.02928i	0.330942	−	0.277693i
$120$		0			0
$121$	0.455341	−	2.58237i	0.0413946	−	0.234761i
$122$	7.41172	−	5.18974i	0.671026	−	0.469857i
$123$		0			0
$124$	4.51362	+	5.37912i	0.405335	+	0.483059i
$125$	7.07804	−	8.65455i	0.633080	−	0.774087i
$126$		0			0
$127$	−9.62937	−	2.58018i	−0.854468	−	0.228954i	−0.195109	−	0.980782i	$-0.562506\pi$
$127$	−9.62937	−	2.58018i	−0.854468	−	0.228954i	−0.659360	+	0.751828i	$0.729173\pi$
$128$	0.868604	−	0.405037i	0.0767745	−	0.0358005i
$129$		0			0
$130$	8.03081	+	26.4202i	0.704349	+	2.31720i
$131$	−3.84111	−	10.5534i	−0.335599	−	0.922051i	−0.986627	−	0.162997i	$-0.947884\pi$
$131$	−3.84111	−	10.5534i	−0.335599	−	0.922051i	0.651028	−	0.759054i	$-0.274338\pi$
$132$		0			0
$133$	−3.41119	+	4.87168i	−0.295787	+	0.422428i
$134$	8.98538			0.776219
$135$		0			0
$136$	0.385743			0.0330772
$137$	−11.2752	+	16.1027i	−0.963306	+	1.37574i	−0.0368588	+	0.999320i	$0.511735\pi$
$137$	−11.2752	+	16.1027i	−0.963306	+	1.37574i	−0.926448	+	0.376424i	$0.877154\pi$
$138$		0			0
$139$	−0.508611	−	1.39740i	−0.0431398	−	0.118526i	0.916252	−	0.400602i	$-0.131199\pi$
$139$	−0.508611	−	1.39740i	−0.0431398	−	0.118526i	−0.959392	+	0.282076i	$0.908977\pi$
$140$	−5.94876	−	3.17535i	−0.502762	−	0.268366i
$141$		0			0
$142$	−16.5517	+	7.71820i	−1.38899	+	0.647697i
$143$	−17.1362	−	4.59162i	−1.43300	−	0.383971i
$144$		0			0
$145$	2.14604	+	4.22872i	0.178219	+	0.351176i
$146$	10.7917	+	12.8611i	0.893129	+	1.06439i
$147$		0			0
$148$	19.8505	−	13.8995i	1.63170	−	1.14253i
$149$	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	$-0.00960308\pi$
$150$		0			0
$151$	−15.8833	+	13.3277i	−1.29257	+	1.08459i	−0.301186	+	0.953565i	$0.597383\pi$
$151$	−15.8833	+	13.3277i	−1.29257	+	1.08459i	−0.991379	+	0.131025i	$0.958173\pi$
$152$	−0.470202	+	0.125990i	−0.0381384	+	0.0102191i
$153$		0			0
$154$	7.39525	−	4.26965i	0.595926	−	0.344058i
$155$	−6.09621	+	4.57840i	−0.489659	+	0.367746i
$156$		0			0
$157$	6.76582	−	0.591932i	0.539971	−	0.0472413i	0.186092	−	0.982532i	$-0.440418\pi$
$157$	6.76582	−	0.591932i	0.539971	−	0.0472413i	0.353879	+	0.935291i	$0.384862\pi$
$158$	1.24571	−	2.67143i	0.0991032	−	0.212528i
$159$		0			0
$160$	6.71786	+	16.7049i	0.531093	+	1.32064i
$161$		−	7.41576i		−	0.584444i
$162$		0			0
$163$	14.3864	+	14.3864i	1.12683	+	1.12683i	0.990689	+	0.136142i	$0.0434702\pi$
$163$	14.3864	+	14.3864i	1.12683	+	1.12683i	0.136142	+	0.990689i	$0.456530\pi$
$164$	0.304716	+	1.72813i	0.0237943	+	0.134944i
$165$		0			0
$166$	−31.9979	+	11.6463i	−2.48352	+	0.903928i
$167$	−0.0411027	−	0.469806i	−0.00318063	−	0.0363547i	0.994439	−	0.105319i	$-0.0335862\pi$
$167$	−0.0411027	−	0.469806i	−0.00318063	−	0.0363547i	−0.997619	+	0.0689639i	$0.978031\pi$
$168$		0			0
$169$	8.40252	−	23.0857i	0.646348	−	1.77583i
$170$	−0.782268	+	14.4790i	−0.0599972	+	1.11049i
$171$		0			0
$172$	0.392203	+	1.46372i	0.0299052	+	0.111608i
$173$	−1.60708	+	18.3690i	−0.122184	+	1.39657i	0.649402	+	0.760446i	$0.275019\pi$
$173$	−1.60708	+	18.3690i	−0.122184	+	1.39657i	−0.771586	+	0.636125i	$0.780536\pi$
$174$		0			0
$175$	3.79104	−	6.26342i	0.286576	−	0.473470i
$176$	−11.0527	−	1.94888i	−0.833126	−	0.146903i
$177$		0			0
$178$	−12.2466	−	1.07144i	−0.917925	−	0.0803080i
$179$	−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	$0.262264\pi$
$180$		0			0
$181$	9.86110	+	17.0799i	0.732970	+	1.26954i	0.955608	+	0.294640i	$0.0951998\pi$
$181$	9.86110	+	17.0799i	0.732970	+	1.26954i	−0.222638	+	0.974901i	$0.571467\pi$
$182$	7.64207	+	16.3885i	0.566468	+	1.21479i
$183$		0			0
$184$	0.390166	−	0.464982i	0.0287634	−	0.0342789i
$185$	13.9065	+	22.3353i	1.02243	+	1.64212i
$186$		0			0
$187$	−7.63096	−	5.34326i	−0.558031	−	0.390738i
$188$	4.19789	−	4.19789i	0.306162	−	0.306162i
$189$		0			0
$190$	−3.77553	−	17.9046i	−0.273905	−	1.29894i
$191$	8.60644	−	1.51755i	0.622740	−	0.109806i	0.146630	−	0.989191i	$-0.453157\pi$
$191$	8.60644	−	1.51755i	0.622740	−	0.109806i	0.476110	+	0.879386i	$0.342046\pi$
$192$		0			0
$193$	−7.83132	−	3.65180i	−0.563711	−	0.262863i	0.119806	−	0.992797i	$-0.461773\pi$
$193$	−7.83132	−	3.65180i	−0.563711	−	0.262863i	−0.683517	+	0.729935i	$0.739550\pi$
$194$	25.0236	+	20.9973i	1.79659	+	1.50752i
$195$		0			0
$196$	9.39756	+	3.42043i	0.671254	+	0.244316i
$197$	−0.519071	+	1.93720i	−0.0369822	+	0.138020i	−0.981949	−	0.189148i	$-0.939427\pi$
$197$	−0.519071	+	1.93720i	−0.0369822	+	0.138020i	0.944966	+	0.327167i	$0.106094\pi$
$198$		0			0
$199$	−15.5130	−	8.95641i	−1.09968	−	0.634903i	−0.163546	−	0.986536i	$-0.552293\pi$
$199$	−15.5130	−	8.95641i	−1.09968	−	0.634903i	−0.936138	+	0.351633i	$0.885627\pi$
$200$	0.567243	−	0.193269i	0.0401101	−	0.0136662i
$201$		0			0
$202$	6.35413	+	9.07464i	0.447075	+	0.638490i
$203$	1.78114	+	2.54374i	0.125012	+	0.178535i
$204$		0			0
$205$	−1.89142	+	0.229136i	−0.132102	+	0.0160035i
$206$	−6.84718	−	3.95322i	−0.477065	−	0.275434i
$207$		0			0
$208$	6.15109	−	22.9562i	0.426501	−	1.59172i
$209$	11.0470	+	4.02077i	0.764134	+	0.278122i
$210$		0			0
$211$	−8.17709	−	6.86139i	−0.562934	−	0.472358i	0.316359	−	0.948640i	$-0.397540\pi$
$211$	−8.17709	−	6.86139i	−0.562934	−	0.472358i	−0.879293	+	0.476282i	$0.841984\pi$
$212$	0.200061	+	0.0932898i	0.0137402	+	0.00640717i
$213$		0			0
$214$	29.5562	−	5.21155i	2.02042	−	0.356254i
$215$	−1.60988	+	0.339474i	−0.109793	+	0.0231519i
$216$		0			0
$217$	−3.53025	+	3.53025i	−0.239649	+	0.239649i
$218$	−16.3632	−	11.4577i	−1.10826	−	0.776011i
$219$		0			0
$220$	−3.01943	+	12.9828i	−0.203570	+	0.875303i
$221$	12.6801	−	15.1115i	0.852955	−	1.01651i
$222$		0			0
$223$	5.05016	+	10.8301i	0.338184	+	0.725238i	0.999695	−	0.0246975i	$-0.00786226\pi$
$223$	5.05016	+	10.8301i	0.338184	+	0.725238i	−0.661511	+	0.749936i	$0.730084\pi$
$224$	5.89526	+	10.2109i	0.393894	+	0.682244i
$225$		0			0
$226$	15.3440	−	26.5765i	1.02067	−	1.76784i
$227$	1.15273	+	0.100851i	0.0765092	+	0.00669369i	0.125346	−	0.992113i	$-0.459996\pi$
$227$	1.15273	+	0.100851i	0.0765092	+	0.00669369i	−0.0488368	+	0.998807i	$0.515551\pi$
$228$		0			0
$229$	8.62548	+	1.52090i	0.569988	+	0.100504i	0.451212	−	0.892417i	$-0.350992\pi$
$229$	8.62548	+	1.52090i	0.569988	+	0.100504i	0.118776	+	0.992921i	$0.462103\pi$
$230$	16.6620	+	15.5879i	1.09866	+	1.02784i
$231$		0			0
$232$	−0.0221529	+	0.253208i	−0.00145441	+	0.0166240i
$233$	4.23498	+	15.8052i	0.277443	+	1.03543i	0.954186	+	0.299213i	$0.0967240\pi$
$233$	4.23498	+	15.8052i	0.277443	+	1.03543i	−0.676743	+	0.736219i	$0.736609\pi$
$234$		0			0
$235$	4.30529	+	4.79707i	0.280846	+	0.312927i
$236$	−2.66302	+	7.31658i	−0.173348	+	0.476269i
$237$		0			0
$238$	0.827567	+	9.45913i	0.0536432	+	0.613145i
$239$	−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	$0.478493\pi$
$240$		0			0
$241$	0.358872	+	2.03527i	0.0231170	+	0.131103i	0.994182	−	0.107712i	$-0.0343523\pi$
$241$	0.358872	+	2.03527i	0.0231170	+	0.131103i	−0.971065	+	0.238815i	$0.923241\pi$
$242$	3.73583	+	3.73583i	0.240148	+	0.240148i
$243$		0			0
$244$			9.24864i			0.592083i
$245$	−4.25875	+	9.98810i	−0.272082	+	0.638116i
$246$		0			0
$247$	−10.5207	+	22.5618i	−0.669417	+	1.43557i
$248$	−0.407090	+	0.0356158i	−0.0258503	+	0.00226161i
$249$		0			0
$250$	6.10408	+	21.6835i	0.386056	+	1.37139i
$251$	−9.55376	+	5.51587i	−0.603028	+	0.348158i	−0.770232	−	0.637764i	$-0.779860\pi$
$251$	−9.55376	+	5.51587i	−0.603028	+	0.348158i	0.167204	+	0.985922i	$0.446526\pi$
$252$		0			0
$253$	−14.1593	+	3.79398i	−0.890189	+	0.238525i
$254$	15.3866	−	12.9109i	0.965443	−	0.810103i
$255$		0			0
$256$	2.60580	−	14.7782i	0.162862	−	0.923639i
$257$	4.73079	−	3.31253i	0.295098	−	0.206630i	−0.416646	−	0.909069i	$-0.636794\pi$
$257$	4.73079	−	3.31253i	0.295098	−	0.206630i	0.711744	+	0.702439i	$0.247906\pi$
$258$		0			0
$259$	11.0748	+	13.1985i	0.688157	+	0.820114i
$260$	−26.8304	−	8.76566i	−1.66395	−	0.543623i
$261$		0			0
$262$	21.8567	+	5.85647i	1.35031	+	0.361814i
$263$	16.7213	−	7.79728i	1.03108	−	0.480801i	0.167958	−	0.985794i	$-0.446283\pi$
$263$	16.7213	−	7.79728i	1.03108	−	0.480801i	0.863123	+	0.504993i	$0.168505\pi$
$264$		0			0
$265$	−0.112860	+	0.211433i	−0.00693291	+	0.0129882i
$266$	−4.09828	−	11.2599i	−0.251281	−	0.690390i
$267$		0			0
$268$	−5.26807	+	7.52358i	−0.321798	+	0.459576i
$269$	−15.7262			−0.958842			−0.479421	−	0.877585i	$-0.659153\pi$
$269$	−15.7262			−0.958842			−0.479421	+	0.877585i	$0.659153\pi$
$270$		0			0
$271$	−17.4326			−1.05895			−0.529477	−	0.848324i	$-0.677612\pi$
$271$	−17.4326			−1.05895			−0.529477	+	0.848324i	$0.677612\pi$
$272$	7.15800	−	10.2227i	0.434018	−	0.619841i
$273$		0			0
$274$	−13.5463	−	37.2181i	−0.818362	−	2.24843i
$275$	−13.8986	−	4.03401i	−0.838118	−	0.243260i
$276$		0			0
$277$	13.9179	−	6.49002i	0.836245	−	0.389947i	0.0431672	−	0.999068i	$-0.486255\pi$
$277$	13.9179	−	6.49002i	0.836245	−	0.389947i	0.793078	+	0.609120i	$0.208477\pi$
$278$	2.89410	+	0.775471i	0.173576	+	0.0465097i
$279$		0			0
$280$	0.349939	−	0.177591i	0.0209129	−	0.0106131i
$281$	−4.76302	−	5.67634i	−0.284138	−	0.338622i	0.605031	−	0.796202i	$-0.293161\pi$
$281$	−4.76302	−	5.67634i	−0.284138	−	0.338622i	−0.889168	+	0.457580i	$0.848716\pi$
$282$		0			0
$283$	−11.7772	+	8.24647i	−0.700081	+	0.490202i	−0.868611	−	0.495495i	$-0.834987\pi$
$283$	−11.7772	+	8.24647i	−0.700081	+	0.490202i	0.168530	+	0.985696i	$0.446098\pi$
$284$	3.24161	−	18.3841i	0.192354	−	1.09090i
$285$		0			0
$286$	27.3816	−	22.9759i	1.61911	−	1.35859i
$287$	−1.20512	+	0.322912i	−0.0711362	+	0.0190609i
$288$		0			0
$289$	−5.75165	+	3.32072i	−0.338332	+	0.195336i
$290$	−9.45932	−	1.34501i	−0.555470	−	0.0789816i
$291$		0			0
$292$	−17.0958	+	1.49569i	−1.00046	+	0.0875288i
$293$	8.51297	−	18.2561i	0.497333	−	1.06653i	−0.484150	−	0.874985i	$-0.660871\pi$
$293$	8.51297	−	18.2561i	0.497333	−	1.06653i	0.981483	−	0.191549i	$-0.0613510\pi$
$294$		0			0
$295$	−7.77636	−	3.31570i	−0.452757	−	0.193048i
$296$			1.41025i			0.0819691i
$297$		0			0
$298$	7.07014	+	7.07014i	0.409562	+	0.409562i
$299$	−5.39025	−	30.5696i	−0.311726	−	1.76789i
$300$		0			0
$301$	−1.01243	+	0.368493i	−0.0583553	+	0.0212396i
$302$	−3.64098	−	41.6166i	−0.209515	−	2.39477i
$303$		0			0
$304$	−5.38635	+	14.7989i	−0.308928	+	0.848774i
$305$	−10.0270	−	0.541738i	−0.574144	−	0.0310198i
$306$		0			0
$307$	−3.09276	−	11.5423i	−0.176513	−	0.658756i	−0.996289	−	0.0860714i	$-0.972569\pi$
$307$	−3.09276	−	11.5423i	−0.176513	−	0.658756i	0.819776	−	0.572684i	$-0.194098\pi$
$308$	−0.760749	+	8.69540i	−0.0433477	+	0.495467i
$309$		0			0
$310$	−0.511289	−	15.3525i	−0.0290392	−	0.871962i
$311$	−2.38442	−	0.420438i	−0.135208	−	0.0238408i	0.105634	−	0.994405i	$-0.466313\pi$
$311$	−2.38442	−	0.420438i	−0.135208	−	0.0238408i	−0.240843	+	0.970564i	$0.577424\pi$
$312$		0			0
$313$	12.2121	+	1.06842i	0.690267	+	0.0603905i	0.426891	−	0.904303i	$-0.359609\pi$
$313$	12.2121	+	1.06842i	0.690267	+	0.0603905i	0.263375	+	0.964693i	$0.415164\pi$
$314$	−6.84198	+	11.8506i	−0.386115	+	0.668771i
$315$		0			0
$316$	1.50647	+	2.60929i	0.0847457	+	0.146784i
$317$	9.58656	+	20.5585i	0.538435	+	1.15468i	0.967840	+	0.251566i	$0.0809455\pi$
$317$	9.58656	+	20.5585i	0.538435	+	1.15468i	−0.429405	+	0.903112i	$0.641277\pi$
$318$		0			0
$319$	3.94565	−	4.70224i	0.220914	−	0.263275i
$320$	−18.4441	−	4.28956i	−1.03106	−	0.239794i
$321$		0			0
$322$	12.2393	+	8.57003i	0.682068	+	0.477589i
$323$	−9.24330	+	9.24330i	−0.514311	+	0.514311i
$324$		0			0
$325$	11.0750	−	28.5750i	0.614329	−	1.58505i
$326$	−40.3696	+	7.11825i	−2.23587	+	0.394243i
$327$		0			0
$328$	−0.0925528	−	0.0431581i	−0.00511038	−	0.00238301i
$329$	3.23343	+	2.71317i	0.178265	+	0.149582i
$330$		0			0
$331$	15.3336	+	5.58098i	0.842812	+	0.306758i	0.727106	−	0.686525i	$-0.240865\pi$
$331$	15.3336	+	5.58098i	0.842812	+	0.306758i	0.115706	+	0.993284i	$0.463087\pi$
$332$	9.00856	−	33.6204i	0.494409	−	1.84516i
$333$		0			0
$334$	0.822888	+	0.475095i	0.0450264	+	0.0259960i
$335$	−7.84818	−	6.15212i	−0.428792	−	0.336126i
$336$		0			0
$337$	2.30026	+	3.28511i	0.125303	+	0.178951i	0.876902	−	0.480669i	$-0.159606\pi$
$337$	2.30026	+	3.28511i	0.125303	+	0.178951i	−0.751599	+	0.659620i	$0.770717\pi$
$338$	28.3913	+	40.5469i	1.54428	+	2.20546i
$339$		0			0
$340$	−11.6648	−	9.14391i	−0.632612	−	0.495898i
$341$	8.54661	+	4.93439i	0.462825	+	0.267212i
$342$		0			0
$343$	−4.49317	+	16.7687i	−0.242608	+	0.905427i
$344$	−0.0828686	−	0.0301617i	−0.00446798	−	0.00162621i
$345$		0			0
$346$	−28.4598	−	23.8806i	−1.53001	−	1.28383i
$347$	−11.2479	−	5.24496i	−0.603816	−	0.281564i	0.0965722	−	0.995326i	$-0.469212\pi$
$347$	−11.2479	−	5.24496i	−0.603816	−	0.281564i	−0.700389	+	0.713762i	$0.746990\pi$
$348$		0			0
$349$	7.52479	−	1.32682i	0.402793	−	0.0710232i	0.0314181	−	0.999506i	$-0.489998\pi$
$349$	7.52479	−	1.32682i	0.402793	−	0.0710232i	0.371375	+	0.928483i	$0.378887\pi$
$350$	5.95628	+	13.4952i	0.318377	+	0.721349i
$351$		0			0
$352$	16.4801	−	16.4801i	0.878395	−	0.878395i
$353$	−14.6661	−	10.2693i	−0.780595	−	0.546579i	0.113987	−	0.993482i	$-0.463638\pi$
$353$	−14.6661	−	10.2693i	−0.780595	−	0.546579i	−0.894582	+	0.446904i	$0.852527\pi$
$354$		0			0
$355$	19.7414	+	4.59127i	1.04777	+	0.243680i
$356$	8.07725	−	9.62609i	0.428093	−	0.510182i
$357$		0			0
$358$	−6.74040	−	14.4548i	−0.356241	−	0.763962i
$359$	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			0
$361$	−1.25189	+	2.16834i	−0.0658891	+	0.114123i
$362$	−39.5854	−	3.46328i	−2.08056	−	0.182026i
$363$		0			0
$364$	−18.2028	−	3.20964i	−0.954084	−	0.168231i
$365$	−0.620182	−	18.6222i	−0.0324618	−	0.974732i
$366$		0			0
$367$	−1.19292	+	13.6352i	−0.0622701	+	0.711750i	0.899325	+	0.437280i	$0.144058\pi$
$367$	−1.19292	+	13.6352i	−0.0622701	+	0.711750i	−0.961596	+	0.274470i	$0.911497\pi$
$368$	−5.08254	−	18.9683i	−0.264946	−	0.988790i
$369$		0			0
$370$	−52.9341	−	2.85992i	−2.75191	−	0.148680i
$371$	−0.0536785	+	0.147481i	−0.00278685	+	0.00765681i
$372$		0			0
$373$	−1.05518	−	12.0608i	−0.0546353	−	0.624485i	−0.973314	−	0.229478i	$-0.926298\pi$
$373$	−1.05518	−	12.0608i	−0.0546353	−	0.624485i	0.918678	−	0.395006i	$-0.129258\pi$
$374$	17.6375	−	6.41951i	0.912011	−	0.331945i
$375$		0			0
$376$	0.0599937	+	0.340241i	0.00309394	+	0.0175466i
$377$	9.19128	+	9.19128i	0.473375	+	0.473375i
$378$		0			0
$379$			22.5213i			1.15684i	0.815738	+	0.578421i	$0.196331\pi$
$379$			22.5213i			1.15684i	−0.815738	+	0.578421i	$0.803669\pi$
$380$	17.2054	+	7.33607i	0.882616	+	0.376332i
$381$		0			0
$382$	−7.44142	+	15.9582i	−0.380736	+	0.816491i
$383$	14.4118	−	1.26087i	0.736410	−	0.0644275i	0.287221	−	0.957864i	$-0.407269\pi$
$383$	14.4118	−	1.26087i	0.736410	−	0.0644275i	0.449189	+	0.893437i	$0.351713\pi$
$384$		0			0
$385$	−9.38265	−	1.33411i	−0.478184	−	0.0679923i
$386$	15.0774	−	8.70492i	0.767417	−	0.443069i
$387$		0			0
$388$	−32.2524	+	8.64201i	−1.63737	+	0.438731i
$389$	−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	$0.381610\pi$
$390$		0			0
$391$	2.83044	−	16.0522i	0.143141	−	0.811795i
$392$	−0.476742	+	0.333818i	−0.0240791	+	0.0168604i
$393$		0			0
$394$	−2.59737	−	3.09542i	−0.130853	−	0.155945i
$395$	−2.91713	+	1.48042i	−0.146777	+	0.0744879i
$396$		0			0
$397$	−14.5205	−	3.89075i	−0.728761	−	0.195271i	−0.124684	−	0.992197i	$-0.539792\pi$
$397$	−14.5205	−	3.89075i	−0.728761	−	0.195271i	−0.604077	+	0.796926i	$0.706458\pi$
$398$	32.7096	−	15.2527i	1.63958	−	0.764550i
$399$		0			0
$400$	5.40409	−	18.6190i	0.270205	−	0.930952i
$401$	8.96818	+	24.6399i	0.447849	+	1.23046i	0.934218	+	0.356703i	$0.116099\pi$
$401$	8.96818	+	24.6399i	0.447849	+	1.23046i	−0.486369	+	0.873754i	$0.661679\pi$
$402$		0			0
$403$	−11.9866	+	17.1186i	−0.597094	+	0.852738i
$404$	−11.3237			−0.563375
$405$		0			0
$406$	−6.25667			−0.310513
$407$	19.5346	−	27.8983i	0.968294	−	1.38287i
$408$		0			0
$409$	2.57831	+	7.08384i	0.127489	+	0.350273i	0.986972	−	0.160891i	$-0.0514367\pi$
$409$	2.57831	+	7.08384i	0.127489	+	0.350273i	−0.859483	+	0.511164i	$0.829214\pi$
$410$	1.80764	−	3.38647i	0.0892731	−	0.167246i
$411$		0			0
$412$	7.32453	−	3.41549i	0.360854	−	0.168269i
$413$	−5.34723	−	1.43279i	−0.263120	−	0.0705028i
$414$		0			0
$415$	35.9222	+	11.7360i	1.76335	+	0.576099i
$416$	31.7237	+	37.8068i	1.55538	+	1.85363i
$417$		0			0
$418$	−19.4025	+	13.5858i	−0.949006	+	0.664501i
$419$	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	$-0.113273\pi$
$420$		0			0
$421$	−5.26964	+	4.42176i	−0.256827	+	0.215503i	−0.762105	−	0.647453i	$-0.775834\pi$
$421$	−5.26964	+	4.42176i	−0.256827	+	0.215503i	0.505279	+	0.862956i	$0.331390\pi$
$422$	20.7742	−	5.56643i	1.01127	−	0.270969i
$423$		0			0
$424$	−0.0111251	+	0.00642311i	−0.000540285	+	0.000311934i
$425$	10.5967	−	12.1109i	0.514017	−	0.587464i
$426$		0			0
$427$	−6.55066	+	0.573108i	−0.317009	+	0.0277347i
$428$	−12.9649	+	27.8032i	−0.626680	+	1.34392i
$429$		0			0
$430$	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	$0.977602\pi$
$432$		0			0
$433$	3.01763	+	3.01763i	0.145018	+	0.145018i	0.775888	−	0.630870i	$-0.217302\pi$
$433$	3.01763	+	3.01763i	0.145018	+	0.145018i	−0.630870	+	0.775888i	$0.717302\pi$
$434$	−1.74673	−	9.90621i	−0.0838458	−	0.475513i
$435$		0			0
$436$	19.1873	−	6.98361i	0.918905	−	0.334454i
$437$	1.79276	+	20.4913i	0.0857593	+	0.980233i
$438$		0			0
$439$	1.28129	−	3.52030i	0.0611524	−	0.168015i	−0.905354	−	0.424658i	$-0.860394\pi$
$439$	1.28129	−	3.52030i	0.0611524	−	0.168015i	0.966506	+	0.256643i	$0.0826165\pi$
$440$	−0.518118	−	0.577301i	−0.0247003	−	0.0275217i
$441$		0			0
$442$	10.2870	+	38.3914i	0.489300	+	1.82609i
$443$	−2.43927	+	27.8809i	−0.115893	+	1.32466i	0.686177	+	0.727434i	$0.259287\pi$
$443$	−2.43927	+	27.8809i	−0.115893	+	1.32466i	−0.802070	+	0.597229i	$0.796268\pi$
$444$		0			0
$445$	9.96310	+	9.32088i	0.472296	+	0.441852i
$446$	−23.7107	−	4.18083i	−1.12273	−	0.197968i
$447$		0			0
$448$	−12.3531	−	1.08076i	−0.583631	−	0.0510611i
$449$	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	$0.0943530\pi$
$450$		0			0
$451$	1.23311	+	2.13580i	0.0580647	+	0.100571i
$452$	13.2568	+	28.4293i	0.623548	+	1.33720i
$453$		0			0
$454$	−1.49860	+	1.78596i	−0.0703328	+	0.0838193i
$455$	4.54598	−	19.5467i	0.213119	−	0.916363i
$456$		0			0
$457$	−29.0265	−	20.3246i	−1.35780	−	0.950745i	−0.999855	−	0.0170039i	$-0.994587\pi$
$457$	−29.0265	−	20.3246i	−1.35780	−	0.950745i	−0.357949	−	0.933741i	$-0.616524\pi$
$458$	−12.4782	+	12.4782i	−0.583068	+	0.583068i
$459$		0			0
$460$	−22.8208	+	4.81219i	−1.06402	+	0.224369i
$461$	−24.4088	+	4.30393i	−1.13683	+	0.200454i	−0.710219	−	0.703981i	$-0.751404\pi$
$461$	−24.4088	+	4.30393i	−1.13683	+	0.200454i	−0.426612	+	0.904435i	$0.640293\pi$
$462$		0			0
$463$	−4.90609	−	2.28775i	−0.228005	−	0.106321i	0.305259	−	0.952269i	$-0.401257\pi$
$463$	−4.90609	−	2.28775i	−0.228005	−	0.106321i	−0.533264	+	0.845949i	$0.679035\pi$
$464$	6.29927	+	5.28572i	0.292436	+	0.245383i
$465$		0			0
$466$	−30.9797	−	11.2757i	−1.43511	−	0.522336i
$467$	−10.5998	+	39.5591i	−0.490502	+	1.83058i	0.0633888	+	0.997989i	$0.479809\pi$
$467$	−10.5998	+	39.5591i	−0.490502	+	1.83058i	−0.553891	+	0.832589i	$0.686857\pi$
$468$		0			0
$469$	−5.65527	−	3.26507i	−0.261136	−	0.150767i
$470$	−12.8927	+	1.56189i	−0.594696	+	0.0720444i
$471$		0			0
$472$	−0.259898	−	0.371173i	−0.0119628	−	0.0170846i
$473$	1.22155	+	1.74456i	0.0561671	+	0.0802149i
$474$		0			0
$475$	−8.96127	+	18.2236i	−0.411171	+	0.836158i
$476$	−8.40545	−	4.85289i	−0.385263	−	0.222432i
$477$		0			0
$478$	4.47905	−	16.7160i	0.204867	−	0.764574i
$479$	−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	$0.828556\pi$
$480$		0			0
$481$	55.2468	+	46.3576i	2.51904	+	2.11372i
$482$	−3.77382	−	1.75976i	−0.171893	−	0.0801549i
$483$		0			0
$484$	−5.31835	+	0.937769i	−0.241743	+	0.0426258i
$485$	−7.48013	−	35.4730i	−0.339655	−	1.61074i
$486$		0			0
$487$	28.3122	−	28.3122i	1.28295	−	1.28295i	0.343969	−	0.938981i	$-0.388228\pi$
$487$	28.3122	−	28.3122i	1.28295	−	1.28295i	0.938981	−	0.343969i	$-0.111772\pi$
$488$	−0.440891	−	0.308715i	−0.0199582	−	0.0139749i
$489$		0			0
$490$	−11.5631	−	18.5716i	−0.522369	−	0.838979i
$491$	−15.4259	+	18.3839i	−0.696161	+	0.829652i	−0.992086	−	0.125559i	$-0.959928\pi$
$491$	−15.4259	+	18.3839i	−0.696161	+	0.829652i	0.295925	+	0.955211i	$0.404372\pi$
$492$		0			0
$493$	2.88459	+	6.18602i	0.129915	+	0.278604i
$494$	−25.0786	−	43.4374i	−1.12834	−	1.95434i
$495$		0			0
$496$	−6.61027	+	11.4493i	−0.296810	+	0.514090i
$497$	13.2220	+	1.15678i	0.593089	+	0.0518886i
$498$		0			0
$499$	31.1017	+	5.48406i	1.39230	+	0.245500i	0.818976	−	0.573828i	$-0.194542\pi$
$499$	31.1017	+	5.48406i	1.39230	+	0.245500i	0.573325	+	0.819328i	$0.305653\pi$
$500$	−21.7347	−	7.60188i	−0.972005	−	0.339966i
$501$		0			0
$502$	1.93720	−	22.1423i	0.0864616	−	0.988261i
$503$	0.730168	+	2.72503i	0.0325566	+	0.121503i	0.980292	−	0.197555i	$-0.0633002\pi$
$503$	0.730168	+	2.72503i	0.0325566	+	0.121503i	−0.947735	+	0.319058i	$0.896634\pi$
$504$		0			0
$505$	0.663284	−	12.2767i	0.0295158	−	0.546306i
$506$	10.1015	−	27.7536i	0.449066	−	1.23380i
$507$		0			0
$508$	1.78941	+	20.4530i	0.0793920	+	0.907455i
$509$	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	$0.226028\pi$
$510$		0			0
$511$	−2.11875	−	12.0160i	−0.0937279	−	0.531557i
$512$	22.7346	+	22.7346i	1.00474	+	1.00474i
$513$		0			0
$514$			11.6360i			0.513243i
$515$	3.27390	+	8.14102i	0.144265	+	0.358736i
$516$		0			0
$517$	3.52615	−	7.56184i	0.155080	−	0.332569i
$518$	−34.5820	+	3.02553i	−1.51944	+	0.132934i
$519$		0			0
$520$	1.31345	−	0.986435i	0.0575987	−	0.0432581i
$521$	7.62484	−	4.40220i	0.334050	−	0.192864i	−0.323588	−	0.946198i	$-0.604889\pi$
$521$	7.62484	−	4.40220i	0.334050	−	0.192864i	0.657638	+	0.753334i	$0.271556\pi$
$522$		0			0
$523$	1.24254	−	0.332937i	0.0543324	−	0.0145583i	−0.231550	−	0.972823i	$-0.574380\pi$
$523$	1.24254	−	0.332937i	0.0543324	−	0.0145583i	0.285883	+	0.958265i	$0.407713\pi$
$524$	−17.7181	+	14.8673i	−0.774019	+	0.649479i
$525$		0			0
$526$	−6.45507	+	36.6085i	−0.281454	+	1.59621i
$527$	−8.98903	+	6.29419i	−0.391568	+	0.274179i
$528$		0			0
$529$	−1.70263	−	2.02911i	−0.0740274	−	0.0882224i
$530$	−0.218532	−	0.430611i	−0.00949241	−	0.0187046i
$531$		0			0
$532$	11.8309	+	3.17007i	0.512933	+	0.137440i
$533$	−4.73311	+	2.20709i	−0.205014	+	0.0955995i
$534$		0			0
$535$	−29.3837	−	15.6846i	−1.27037	−	0.678103i
$536$	−0.182810	−	0.502268i	−0.00789621	−	0.0216947i
$537$		0			0
$538$	18.1740	−	25.9551i	0.783535	−	1.11900i
$539$	14.0551			0.605398
$540$		0			0
$541$	−9.16794			−0.394160			−0.197080	−	0.980387i	$-0.563146\pi$
$541$	−9.16794			−0.394160			−0.197080	+	0.980387i	$0.563146\pi$
$542$	20.1460	−	28.7714i	0.865344	−	1.23584i
$543$		0			0
$544$	8.86365	+	24.3527i	0.380026	+	1.04411i
$545$	6.44745	+	21.2112i	0.276179	+	0.908587i
$546$		0			0
$547$	4.18752	−	1.95267i	0.179046	−	0.0834904i	−0.331029	−	0.943621i	$-0.607396\pi$
$547$	4.18752	−	1.95267i	0.179046	−	0.0834904i	0.510074	+	0.860130i	$0.329618\pi$
$548$	39.1053	+	10.4782i	1.67050	+	0.447608i
$549$		0			0
$550$	22.7199	−	18.2769i	0.968778	−	0.779331i
$551$	−5.53663	−	6.59830i	−0.235868	−	0.281097i
$552$		0			0
$553$	−1.75476	+	1.22870i	−0.0746202	+	0.0522496i
$554$	−5.37283	+	30.4709i	−0.228270	+	1.29458i
$555$		0			0
$556$	−2.34610	+	1.96861i	−0.0994968	+	0.0834878i
$557$	−9.73354	+	2.60809i	−0.412423	+	0.110509i	−0.459064	−	0.888403i	$-0.651815\pi$
$557$	−9.73354	+	2.60809i	−0.412423	+	0.110509i	0.0466405	+	0.998912i	$0.485148\pi$
$558$		0			0
$559$	−3.90564	+	2.25492i	−0.165191	+	0.0953730i
$560$	1.78721	−	12.5693i	0.0755235	−	0.531150i
$561$		0			0
$562$	14.8729	−	1.30121i	0.627373	−	0.0548881i
$563$	−6.99817	+	15.0076i	−0.294938	+	0.632496i	−0.996810	−	0.0798064i	$-0.974570\pi$
$563$	−6.99817	+	15.0076i	−0.294938	+	0.632496i	0.701873	+	0.712302i	$0.252348\pi$
$564$		0			0
$565$	−31.5984	+	12.7073i	−1.32936	+	0.534598i
$566$		−	28.9676i		−	1.21760i
$567$		0			0
$568$	0.768184	+	0.768184i	0.0322323	+	0.0322323i
$569$	1.89828	+	10.7657i	0.0795799	+	0.451320i	0.998395	+	0.0566320i	$0.0180362\pi$
$569$	1.89828	+	10.7657i	0.0795799	+	0.451320i	−0.918815	+	0.394688i	$0.870853\pi$
$570$		0			0
$571$	15.2515	−	5.55110i	0.638256	−	0.232306i	−0.00256475	−	0.999997i	$-0.500816\pi$
$571$	15.2515	−	5.55110i	0.638256	−	0.232306i	0.640821	+	0.767691i	$0.278594\pi$
$572$	3.18438	+	36.3976i	0.133146	+	1.52186i
$573$		0			0
$574$	0.859755	−	2.36216i	0.0358855	−	0.0985946i
$575$	−3.88045	−	25.0232i	−0.161826	−	1.04354i
$576$		0			0
$577$	−4.56140	−	17.0234i	−0.189894	−	0.708693i	−0.993530	−	0.113572i	$-0.963771\pi$
$577$	−4.56140	−	17.0234i	−0.189894	−	0.708693i	0.803636	−	0.595121i	$-0.202896\pi$
$578$	1.16625	−	13.3304i	0.0485098	−	0.554469i
$579$		0			0
$580$	6.67212	−	7.13184i	0.277045	−	0.296134i
$581$	24.3710	+	4.29727i	1.01108	+	0.178281i
$582$		0			0
$583$	0.309055	+	0.0270388i	0.0127998	+	0.00111983i
$584$	0.499351	−	0.864901i	0.0206633	−	0.0357898i
$585$		0			0
$586$	20.2926	+	35.1479i	0.838280	+	1.45194i
$587$	−3.45411	−	7.40736i	−0.142566	−	0.305734i	0.822040	−	0.569430i	$-0.192836\pi$
$587$	−3.45411	−	7.40736i	−0.142566	−	0.305734i	−0.964606	+	0.263696i	$0.915058\pi$
$588$		0			0
$589$	8.90140	−	10.6083i	0.366776	−	0.437106i
$590$	14.4591	−	9.00262i	0.595273	−	0.370632i
$591$		0			0
$592$	37.3735	+	26.1692i	1.53604	+	1.07555i
$593$	28.1239	−	28.1239i	1.15491	−	1.15491i	0.169357	−	0.985555i	$-0.445831\pi$
$593$	28.1239	−	28.1239i	1.15491	−	1.15491i	0.985555	−	0.169357i	$-0.0541692\pi$
$594$		0			0
$595$	5.75366	−	8.82860i	0.235877	−	0.361937i
$596$	−10.0651	+	1.77475i	−0.412282	+	0.0726965i
$597$		0			0
$598$	56.6826	+	26.4315i	2.31793	+	1.08087i
$599$	−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			0
$601$	−21.4617	−	7.81141i	−0.875440	−	0.318634i	−0.135072	−	0.990836i	$-0.543126\pi$
$601$	−21.4617	−	7.81141i	−0.875440	−	0.318634i	−0.740368	+	0.672202i	$0.765349\pi$
$602$	0.561836	−	2.09680i	0.0228987	−	0.0854593i
$603$		0			0
$604$	36.9808	+	21.3509i	1.50473	+	0.868755i
$605$	−0.705169	−	5.82087i	−0.0286692	−	0.236652i
$606$		0			0
$607$	4.90539	+	7.00562i	0.199104	+	0.284349i	0.906271	−	0.422696i	$-0.138916\pi$
$607$	4.90539	+	7.00562i	0.199104	+	0.284349i	−0.707168	+	0.707046i	$0.750027\pi$
$608$	−18.7583	−	26.7897i	−0.760751	−	1.08647i
$609$		0			0
$610$	12.4818	−	15.9229i	0.505374	−	0.644700i
$611$	15.3011	+	8.83410i	0.619017	+	0.357389i
$612$		0			0
$613$	9.58796	−	35.7827i	0.387254	−	1.44525i	−0.447329	−	0.894369i	$-0.647625\pi$
$613$	9.58796	−	35.7827i	0.387254	−	1.44525i	0.834583	−	0.550882i	$-0.185709\pi$
$614$	22.6241	+	8.23450i	0.913034	+	0.332317i
$615$		0			0
$616$	−0.389125	−	0.326514i	−0.0156783	−	0.0131556i
$617$	−11.1077	−	5.17963i	−0.447181	−	0.208524i	0.185965	−	0.982556i	$-0.440459\pi$
$617$	−11.1077	−	5.17963i	−0.447181	−	0.208524i	−0.633146	+	0.774032i	$0.718237\pi$
$618$		0			0
$619$	−8.63834	+	1.52317i	−0.347204	+	0.0612215i	−0.344531	−	0.938775i	$-0.611962\pi$
$619$	−8.63834	+	1.52317i	−0.347204	+	0.0612215i	−0.00267331	+	0.999996i	$0.500851\pi$
$620$	13.1546	+	8.57294i	0.528301	+	0.344297i
$621$		0			0
$622$	3.44947	−	3.44947i	0.138311	−	0.138311i
$623$	7.31853	+	5.12449i	0.293211	+	0.205308i
$624$		0			0
$625$	9.51476	−	23.1186i	0.380590	−	0.924744i
$626$	−15.8763	+	18.9206i	−0.634543	+	0.756218i
$627$		0			0
$628$	−5.91130	−	12.6768i	−0.235887	−	0.505860i
$629$	18.9351	+	32.7966i	0.754992	+	1.30769i
$630$		0			0
$631$	16.1540	−	27.9796i	0.643083	−	1.11385i	−0.341658	−	0.939824i	$-0.610989\pi$
$631$	16.1540	−	27.9796i	0.643083	−	1.11385i	0.984741	−	0.174027i	$-0.0556781\pi$
$632$	−0.174673	−	0.0152819i	−0.00694810	−	0.000607880i
$633$		0			0
$634$	−45.0092	−	7.93634i	−1.78755	−	0.315192i
$635$	−22.2791	+	0.741969i	−0.884121	+	0.0294442i
$636$		0			0
$637$	−2.59401	+	29.6497i	−0.102778	+	1.17476i
$638$	3.20098	+	11.9462i	0.126728	+	0.472955i
$639$		0			0
$640$	1.59491	−	1.43140i	0.0630442	−	0.0565811i
$641$	3.35944	−	9.23000i	0.132690	−	0.364563i	−0.855499	−	0.517805i	$-0.826749\pi$
$641$	3.35944	−	9.23000i	0.132690	−	0.364563i	0.988189	+	0.153242i	$0.0489715\pi$
$642$		0			0
$643$	1.62110	+	18.5293i	0.0639299	+	0.730723i	0.958742	+	0.284279i	$0.0917541\pi$
$643$	1.62110	+	18.5293i	0.0639299	+	0.730723i	−0.894812	+	0.446444i	$0.852690\pi$
$644$	−14.3516	+	5.22355i	−0.565532	+	0.205837i
$645$		0			0
$646$	−4.57349	−	25.9375i	−0.179942	−	1.02050i
$647$	−14.2018	−	14.2018i	−0.558331	−	0.558331i	0.370501	−	0.928832i	$-0.379186\pi$
$647$	−14.2018	−	14.2018i	−0.558331	−	0.558331i	−0.928832	+	0.370501i	$0.879186\pi$
$648$		0			0
$649$			10.9428i			0.429542i
$650$	34.3625	+	51.3013i	1.34781	+	2.01220i
$651$		0			0
$652$	17.7082	−	37.9754i	0.693507	−	1.48723i
$653$	19.8693	−	1.73834i	0.777546	−	0.0680265i	0.308528	−	0.951215i	$-0.400164\pi$
$653$	19.8693	−	1.73834i	0.777546	−	0.0680265i	0.469018	+	0.883189i	$0.344608\pi$
$654$		0			0
$655$	−15.0806	−	20.0801i	−0.589250	−	0.784595i
$656$	−2.86119	+	1.65191i	−0.111711	+	0.0644963i
$657$		0			0
$658$	−8.21463	+	2.20110i	−0.320240	+	0.0858080i
$659$	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	$0.271180\pi$
$660$		0			0
$661$	−5.78183	+	32.7904i	−0.224887	+	1.27540i	0.638014	+	0.770025i	$0.279756\pi$
$661$	−5.78183	+	32.7904i	−0.224887	+	1.27540i	−0.862901	+	0.505373i	$0.831355\pi$
$662$	−26.9314	+	18.8576i	−1.04672	+	0.732920i
$663$		0			0
$664$	1.30202	+	1.55168i	0.0505280	+	0.0602169i
$665$	−4.12986	+	12.6409i	−0.160149	+	0.490192i
$666$		0			0
$667$	10.3744	+	2.77981i	0.401699	+	0.107635i
$668$	−0.880256	+	0.410470i	−0.0340581	+	0.0158816i
$669$		0			0
$670$	19.2235	−	5.84326i	0.742668	−	0.225745i
$671$	4.44565	+	12.2143i	0.171622	+	0.471529i
$672$		0			0
$673$	14.0367	−	20.0466i	0.541077	−	0.772738i	−0.451770	−	0.892135i	$-0.649207\pi$
$673$	14.0367	−	20.0466i	0.541077	−	0.772738i	0.992847	+	0.119397i	$0.0380961\pi$
$674$	−8.08017			−0.311236
$675$		0			0
$676$	−50.5961			−1.94600
$677$	11.7412	−	16.7682i	0.451252	−	0.644455i	−0.527487	−	0.849563i	$-0.676866\pi$
$677$	11.7412	−	16.7682i	0.451252	−	0.644455i	0.978739	+	0.205108i	$0.0657546\pi$
$678$		0			0
$679$	−8.11957	−	22.3083i	−0.311601	−	0.856115i
$680$	0.825265	−	0.250852i	0.0316474	−	0.00961972i
$681$		0			0
$682$	−18.0208	+	8.40325i	−0.690053	+	0.321777i
$683$	21.3380	+	5.71751i	0.816477	+	0.218774i	0.642806	−	0.766029i	$-0.277770\pi$
$683$	21.3380	+	5.71751i	0.816477	+	0.218774i	0.173671	+	0.984804i	$0.444437\pi$
$684$		0			0
$685$	−13.6507	+	41.7827i	−0.521566	+	1.59643i
$686$	−22.4833	−	26.7945i	−0.858416	−	1.02302i
$687$		0			0
$688$	−2.33707	+	1.63643i	−0.0890999	+	0.0623884i
$689$	−0.114078	+	0.646969i	−0.00434603	+	0.0246476i
$690$		0			0
$691$	13.7398	−	11.5291i	0.522688	−	0.438587i	−0.342880	−	0.939379i	$-0.611402\pi$
$691$	13.7398	−	11.5291i	0.522688	−	0.438587i	0.865568	+	0.500792i	$0.166958\pi$
$692$	36.6813	−	9.82872i	1.39441	−	0.373632i
$693$		0			0
$694$	21.6551	−	12.5026i	0.822016	−	0.474591i
$695$	−1.99687	−	2.65886i	−0.0757455	−	0.100856i
$696$		0			0
$697$	−2.73187	+	0.239008i	−0.103477	+	0.00905306i
$698$	−6.50619	+	13.9526i	−0.246263	+	0.528112i
$699$		0			0
$700$	−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	$0.930929\pi$
$702$		0			0
$703$	−33.7929	−	33.7929i	−1.27452	−	1.27452i
$704$	4.25644	+	24.1395i	0.160421	+	0.909791i
$705$		0			0
$706$	33.8977	−	12.3377i	1.27576	−	0.464337i
$707$	−0.701693	−	8.02039i	−0.0263899	−	0.301638i
$708$		0			0
$709$	−5.28444	+	14.5189i	−0.198461	+	0.545268i	−0.998504	−	0.0546749i	$-0.982588\pi$
$709$	−5.28444	+	14.5189i	−0.198461	+	0.545268i	0.800043	+	0.599943i	$0.204810\pi$
$710$	−30.3918	+	27.2762i	−1.14059	+	1.02366i
$711$		0			0
$712$	0.189270	+	0.706365i	0.00709319	+	0.0264722i
$713$	−1.50497	+	17.2019i	−0.0563616	+	0.644216i
$714$		0			0
$715$	−39.6474	+	1.32039i	−1.48273	+	0.0493798i
$716$	16.0551	+	2.83094i	0.600006	+	0.105797i
$717$		0			0
$718$	−25.1504	−	2.20038i	−0.938606	−	0.0821174i
$719$	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	$0.110444\pi$
$720$		0			0
$721$	2.87301	+	4.97620i	0.106997	+	0.185323i
$722$	−2.13197	−	4.57202i	−0.0793437	−	0.170153i
$723$		0			0
$724$	26.1085	−	31.1149i	0.970315	−	1.15638i
$725$	7.34124	+	7.65140i	0.272647	+	0.284166i
$726$		0			0
$727$	35.1712	+	24.6272i	1.30443	+	0.913371i	0.999242	−	0.0389219i	$-0.0123924\pi$
$727$	35.1712	+	24.6272i	1.30443	+	0.913371i	0.305186	+	0.952293i	$0.401281\pi$
$728$	0.760607	−	0.760607i	0.0281900	−	0.0281900i
$729$		0			0
$730$	31.4516	+	20.4972i	1.16408	+	0.758636i
$731$	−2.33216	+	0.411222i	−0.0862579	+	0.0152096i
$732$		0			0
$733$	0.567513	+	0.264636i	0.0209616	+	0.00977454i	0.433071	−	0.901360i	$-0.357430\pi$
$733$	0.567513	+	0.264636i	0.0209616	+	0.00977454i	−0.412109	+	0.911134i	$0.635208\pi$
$734$	−21.1255	−	17.7264i	−0.779755	−	0.654292i
$735$		0			0
$736$	38.3205	+	13.9475i	1.41251	+	0.514112i
$737$	−3.34089	+	12.4684i	−0.123063	+	0.459278i
$738$		0			0
$739$	−23.6846	−	13.6743i	−0.871251	−	0.503017i	−0.00348723	−	0.999994i	$-0.501110\pi$
$739$	−23.6846	−	13.6743i	−0.871251	−	0.503017i	−0.867764	+	0.496977i	$0.834443\pi$
$740$	33.4295	−	42.6457i	1.22889	−	1.56769i
$741$		0			0
$742$	−0.181374	−	0.259029i	−0.00665846	−	0.00950927i
$743$	−20.5718	−	29.3796i	−0.754706	−	1.07783i	−0.994264	−	0.106950i	$-0.965891\pi$
$743$	−20.5718	−	29.3796i	−0.754706	−	1.07783i	0.239558	−	0.970882i	$-0.422997\pi$
$744$		0			0
$745$	−1.33455	−	11.0161i	−0.0488941	−	0.403600i
$746$	21.1251	+	12.1966i	0.773444	+	0.446548i
$747$		0			0
$748$	−4.96558	+	18.5318i	−0.181559	+	0.677589i
$749$	−20.4960	−	7.45993i	−0.748907	−	0.272580i
$750$		0			0
$751$	−27.0935	−	22.7342i	−0.988657	−	0.829582i	−0.00328459	−	0.999995i	$-0.501046\pi$
$751$	−27.0935	−	22.7342i	−0.988657	−	0.829582i	−0.985373	+	0.170413i	$0.945490\pi$
$752$	10.1301	+	4.72374i	0.369407	+	0.172257i
$753$		0			0
$754$	−25.7916	+	4.54775i	−0.939274	+	0.165619i
$755$	−25.3139	+	38.8425i	−0.921267	+	1.41362i
$756$		0			0
$757$	−26.1262	+	26.1262i	−0.949573	+	0.949573i	−0.998788	−	0.0492153i	$-0.984328\pi$
$757$	−26.1262	+	26.1262i	−0.949573	+	0.949573i	0.0492153	+	0.998788i	$0.484328\pi$
$758$	−37.1701	−	26.0268i	−1.35008	−	0.945336i
$759$		0			0
$760$	−0.924024	+	0.575321i	−0.0335179	+	0.0208691i
$761$	−5.19201	+	6.18759i	−0.188210	+	0.224300i	−0.851896	−	0.523712i	$-0.824547\pi$
$761$	−5.19201	+	6.18759i	−0.188210	+	0.224300i	0.663685	+	0.748012i	$0.268991\pi$
$762$		0			0
$763$	6.13535	+	13.1573i	0.222115	+	0.476326i
$764$	−8.99914	−	15.5870i	−0.325577	−	0.563917i
$765$		0			0
$766$	−14.5740	+	25.2430i	−0.526582	+	0.912066i
$767$	−23.0841	−	2.01960i	−0.833519	−	0.0729234i
$768$		0			0
$769$	16.0619	+	2.83215i	0.579208	+	0.102130i	0.455574	−	0.890198i	$-0.349434\pi$
$769$	16.0619	+	2.83215i	0.579208	+	0.102130i	0.123634	+	0.992328i	$0.460545\pi$
$770$	13.0449	−	13.9437i	0.470107	−	0.502498i
$771$		0			0
$772$	−1.55101	+	17.7281i	−0.0558220	+	0.638048i
$773$	−3.06271	−	11.4302i	−0.110158	−	0.411116i	0.888721	−	0.458448i	$-0.151595\pi$
$773$	−3.06271	−	11.4302i	−0.110158	−	0.411116i	−0.998879	+	0.0473325i	$0.984928\pi$
$774$		0			0
$775$	−10.0650	+	13.7595i	−0.361544	+	0.494256i
$776$	0.664599	−	1.82597i	0.0238577	−	0.0655485i
$777$		0			0
$778$	−2.21968	−	25.3711i	−0.0795795	−	0.909598i
$779$	3.25195	−	1.18361i	0.116513	−	0.0424073i
$780$		0			0
$781$	−4.55583	−	25.8374i	−0.163020	−	0.924534i
$782$	23.2222	+	23.2222i	0.830425	+	0.830425i
$783$		0			0
$784$			18.8287i			0.672455i
$785$	14.0900	−	5.66625i	0.502892	−	0.202237i
$786$		0			0
$787$	−20.1245	+	43.1572i	−0.717361	+	1.53839i	0.120627	+	0.992698i	$0.461510\pi$
$787$	−20.1245	+	43.1572i	−0.717361	+	1.53839i	−0.837988	+	0.545689i	$0.816268\pi$
$788$	4.11465	−	0.359985i	0.146578	−	0.0128240i
$789$		0			0
$790$	0.927837	−	6.52539i	0.0330110	−	0.232163i
$791$	−19.3145	+	11.1513i	−0.686746	+	0.396493i
$792$		0			0
$793$	−26.5869	+	7.12394i	−0.944129	+	0.252979i
$794$	23.2020	−	19.4688i	0.823409	−	0.690922i
$795$		0			0
$796$	−6.40609	+	36.3307i	−0.227058	+	1.28771i
$797$	−13.5475	+	9.48608i	−0.479878	+	0.336014i	−0.788358	−	0.615216i	$-0.789069\pi$
$797$	−13.5475	+	9.48608i	−0.479878	+	0.336014i	0.308480	+	0.951231i	$0.400180\pi$
$798$		0			0
$799$	5.96354	+	7.10708i	0.210975	+	0.251430i
$800$	25.2356	+	31.3701i	0.892215	+	1.10910i
$801$		0			0
$802$	−51.0307	−	13.6736i	−1.80196	−	0.482833i
$803$	−21.8589	+	10.1930i	−0.771383	+	0.359702i
$804$		0			0
$805$	−4.82252	−	15.8654i	−0.169972	−	0.559182i
$806$	−14.4009	−	39.5663i	−0.507252	−	1.39366i
$807$		0			0
$808$	0.377980	−	0.539812i	0.0132973	−	0.0189905i
$809$	−21.1013			−0.741881			−0.370941	−	0.928657i	$-0.620965\pi$
$809$	−21.1013			−0.741881			−0.370941	+	0.928657i	$0.620965\pi$
$810$		0			0
$811$	3.03312			0.106507			0.0532537	−	0.998581i	$-0.483041\pi$
$811$	3.03312			0.106507			0.0532537	+	0.998581i	$0.483041\pi$
$812$	3.66824	−	5.23879i	0.128730	−	0.183845i
$813$		0			0
$814$	23.4693	+	64.4814i	0.822599	+	2.26007i
$815$	40.1341	+	21.4229i	1.40584	+	0.750412i
$816$		0			0
$817$	2.70847	−	1.26298i	0.0947574	−	0.0441861i
$818$	−14.6711	−	3.93110i	−0.512962	−	0.137448i
$819$		0			0
$820$	1.77573	+	3.49903i	0.0620111	+	0.122191i
$821$	−7.72326	−	9.20422i	−0.269544	−	0.321230i	0.614246	−	0.789115i	$-0.289460\pi$
$821$	−7.72326	−	9.20422i	−0.269544	−	0.321230i	−0.883789	+	0.467885i	$0.845016\pi$
$822$		0			0
$823$	−19.4859	+	13.6442i	−0.679237	+	0.475607i	−0.861576	−	0.507629i	$-0.830522\pi$
$823$	−19.4859	+	13.6442i	−0.679237	+	0.475607i	0.182339	+	0.983236i	$0.441633\pi$
$824$	−0.0816702	+	0.463175i	−0.00284512	+	0.0161355i
$825$		0			0
$826$	8.54427	−	7.16949i	0.297293	−	0.249459i
$827$	44.8353	−	12.0136i	1.55907	−	0.417753i	0.626704	−	0.779257i	$-0.284403\pi$
$827$	44.8353	−	12.0136i	1.55907	−	0.417753i	0.932370	+	0.361504i	$0.117737\pi$
$828$		0			0
$829$	27.8169	−	16.0601i	0.966123	−	0.557791i	0.0680706	−	0.997681i	$-0.478316\pi$
$829$	27.8169	−	16.0601i	0.966123	−	0.557791i	0.898052	+	0.439889i	$0.144982\pi$
$830$	−60.8832	+	45.7248i	−2.11329	+	1.58713i
$831$		0			0
$832$	−51.7084	+	4.52390i	−1.79267	+	0.156838i
$833$	−6.60493	+	14.1643i	−0.228847	+	0.490765i
$834$		0			0
$835$	−0.393455	−	0.978382i	−0.0136161	−	0.0338583i
$836$		−	24.2112i		−	0.837361i
$837$		0			0
$838$	29.5051	+	29.5051i	1.01924	+	1.01924i
$839$	8.77845	+	49.7851i	0.303066	+	1.71877i	0.632472	+	0.774583i	$0.282040\pi$
$839$	8.77845	+	49.7851i	0.303066	+	1.71877i	−0.329406	+	0.944188i	$0.606849\pi$
$840$		0			0
$841$	23.0248	−	8.38035i	0.793959	−	0.288977i
$842$	−1.20798	−	13.8072i	−0.0416296	−	0.475829i
$843$		0			0
$844$	−7.51891	+	20.6580i	−0.258812	+	0.711079i
$845$	2.96366	−	54.8542i	0.101953	−	1.88704i
$846$		0			0
$847$	−0.993767	−	3.70879i	−0.0341463	−	0.127436i
$848$	−0.0362221	+	0.414021i	−0.00124387	+	0.0142175i
$849$		0			0
$850$	7.74218	+	31.4852i	0.265555	+	1.07993i
$851$	58.6858	+	10.3479i	2.01172	+	0.354721i
$852$		0			0
$853$	50.7794	+	4.44262i	1.73865	+	0.152112i	0.911889	−	0.410438i	$-0.134624\pi$
$853$	50.7794	+	4.44262i	1.73865	+	0.152112i	0.826763	+	0.562550i	$0.190180\pi$
$854$	6.62440	−	11.4738i	0.226682	−	0.392625i
$855$		0			0
$856$	−0.892646	−	1.54611i	−0.0305100	−	0.0528449i
$857$	−4.25654	−	9.12817i	−0.145400	−	0.311812i	0.820097	−	0.572224i	$-0.193919\pi$
$857$	−4.25654	−	9.12817i	−0.145400	−	0.311812i	−0.965498	+	0.260412i	$0.916142\pi$
$858$		0			0
$859$	8.01487	−	9.55175i	0.273464	−	0.325902i	−0.611781	−	0.791027i	$-0.709547\pi$
$859$	8.01487	−	9.55175i	0.273464	−	0.325902i	0.885245	+	0.465126i	$0.153991\pi$
$860$	1.79096	+	2.87646i	0.0610711	+	0.0980864i
$861$		0			0
$862$	−4.81810	−	3.37367i	−0.164105	−	0.114908i
$863$	23.9621	−	23.9621i	0.815678	−	0.815678i	−0.169800	−	0.985479i	$-0.554312\pi$
$863$	23.9621	−	23.9621i	0.815678	−	0.815678i	0.985479	+	0.169800i	$0.0543122\pi$
$864$		0			0
$865$	8.50730	+	40.3441i	0.289257	+	1.37174i
$866$	−8.46774	+	1.49309i	−0.287745	+	0.0507373i
$867$		0			0
$868$	9.31869	+	4.34538i	0.316297	+	0.147492i
$869$	3.24378	+	2.72185i	0.110038	+	0.0923326i
$870$		0			0
$871$	−25.6857	−	9.34885i	−0.870328	−	0.316774i
$872$	−0.307549	+	1.14779i	−0.0104149	+	0.0388690i
$873$		0			0
$874$	−35.8915	−	20.7220i	−1.21405	−	0.700932i
$875$	4.03746	−	15.8654i	0.136491	−	0.536348i
$876$		0			0
$877$	−26.9320	−	38.4629i	−0.909430	−	1.29880i	−0.954004	−	0.299794i	$-0.903082\pi$
$877$	−26.9320	−	38.4629i	−0.909430	−	1.29880i	0.0445739	−	0.999006i	$-0.485807\pi$
$878$	4.32933	+	6.18293i	0.146108	+	0.208664i
$879$		0			0
$880$	−24.9136	+	3.01816i	−0.839838	+	0.101742i
$881$	−20.2756	−	11.7061i	−0.683103	−	0.394390i	0.117920	−	0.993023i	$-0.462377\pi$
$881$	−20.2756	−	11.7061i	−0.683103	−	0.394390i	−0.801023	+	0.598633i	$0.795711\pi$
$882$		0			0
$883$	−1.63802	+	6.11319i	−0.0551239	+	0.205725i	−0.987995	−	0.154485i	$-0.950628\pi$
$883$	−1.63802	+	6.11319i	−0.0551239	+	0.205725i	0.932871	+	0.360210i	$0.117295\pi$
$884$	−38.1768	−	13.8952i	−1.28402	−	0.467347i
$885$		0			0
$886$	−43.1969	−	36.2465i	−1.45123	−	1.21773i
$887$	−29.6855	−	13.8426i	−0.996741	−	0.464788i	−0.145384	−	0.989375i	$-0.546442\pi$
$887$	−29.6855	−	13.8426i	−0.996741	−	0.464788i	−0.851357	+	0.524587i	$0.824220\pi$
$888$		0			0
$889$	−14.3756	+	2.53481i	−0.482144	+	0.0850149i
$890$	−26.8974	+	5.67182i	−0.901604	+	0.190120i
$891$		0			0
$892$	17.4021	−	17.4021i	0.582665	−	0.582665i
$893$	−9.59056	−	6.71538i	−0.320936	−	0.224722i
$894$		0			0
$895$	−4.00962	+	17.2404i	−0.134027	+	0.576284i
$896$	0.902060	−	1.07503i	0.0301357	−	0.0359143i
$897$		0			0
$898$	8.12765	+	17.4298i	0.271223	+	0.581640i
$899$	−3.61538	−	6.26203i	−0.120580	−	0.208850i
$900$		0			0
$901$	−0.172483	+	0.298750i	−0.00574625	+	0.00995280i
$902$	−4.95006	−	0.433074i	−0.164819	−	0.0144198i
$903$		0			0
$904$	−1.79776	−	0.316994i	−0.0597926	−	0.0105430i
$905$	32.2042	+	30.1283i	1.07050	+	1.00150i
$906$		0			0
$907$	2.49616	−	28.5313i	0.0828837	−	0.947365i	−0.834931	−	0.550355i	$-0.814492\pi$
$907$	2.49616	−	28.5313i	0.0828837	−	0.947365i	0.917814	−	0.397010i	$-0.129952\pi$
$908$	−0.616790	−	2.30189i	−0.0204689	−	0.0763910i
$909$		0			0
$910$	27.0071	+	30.0920i	0.895277	+	0.997542i
$911$	6.61616	−	18.1777i	0.219203	−	0.602255i	−0.780536	−	0.625111i	$-0.785054\pi$
$911$	6.61616	−	18.1777i	0.219203	−	0.602255i	0.999739	+	0.0228557i	$0.00727584\pi$
$912$		0			0
$913$	−4.26345	−	48.7315i	−0.141100	−	1.61278i
$914$	67.0891	−	24.4184i	2.21911	−	0.807690i
$915$		0			0
$916$	−3.13228	−	17.7641i	−0.103493	−	0.586941i
$917$	−11.6282	−	11.6282i	−0.383996	−	0.383996i
$918$		0			0
$919$		−	44.6775i		−	1.47377i	−0.676016	−	0.736887i	$-0.736295\pi$
$919$		−	44.6775i		−	1.47377i	0.676016	−	0.736887i	$-0.263705\pi$
$920$	0.532346	−	1.24852i	0.0175509	−	0.0411624i
$921$		0			0
$922$	21.1047	−	45.2591i	0.695046	−	1.49053i
$923$	55.3454	−	4.84210i	1.82172	−	0.159380i
$924$		0			0
$925$	44.2766	+	38.7409i	1.45581	+	1.27379i
$926$	9.44552	−	5.45337i	0.310399	−	0.179209i
$927$		0			0
$928$	−16.4946	+	4.41970i	−0.541461	+	0.145084i
$929$	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	$-0.0539535\pi$
$930$		0			0
$931$	3.42478	−	19.4229i	0.112243	−	0.636560i
$932$	27.6044	−	19.3288i	0.904213	−	0.633137i
$933$		0			0
$934$	−53.0403	−	63.2110i	−1.73553	−	2.06833i
$935$	−19.8006	−	6.46898i	−0.647547	−	0.211558i
$936$		0			0
$937$	−13.8557	−	3.71263i	−0.452647	−	0.121286i	0.0252908	−	0.999680i	$-0.491949\pi$
$937$	−13.8557	−	3.71263i	−0.452647	−	0.121286i	−0.477938	+	0.878394i	$0.658616\pi$
$938$	11.9243	−	5.56041i	0.389343	−	0.181554i
$939$		0			0
$940$	6.25111	−	11.7109i	0.203889	−	0.381969i
$941$	0.0906224	+	0.248983i	0.00295420	+	0.00811661i	0.941161	−	0.337959i	$-0.109736\pi$
$941$	0.0906224	+	0.248983i	0.00295420	+	0.00811661i	−0.938207	+	0.346075i	$0.887514\pi$
$942$		0			0
$943$	−2.47509	+	3.53479i	−0.0806000	+	0.115109i
$944$	−14.6593			−0.477121
$945$		0			0
$946$	−4.29098			−0.139512
$947$	19.5534	−	27.9252i	0.635401	−	0.907446i	−0.364315	−	0.931276i	$-0.618697\pi$
$947$	19.5534	−	27.9252i	0.635401	−	0.907446i	0.999716	+	0.0238294i	$0.00758584\pi$
$948$		0			0
$949$	−17.4680	−	47.9930i	−0.567037	−	1.55792i
$950$	−19.7209	−	35.8502i	−0.639832	−	1.16313i
$951$		0			0
$952$	0.511912	−	0.238709i	0.0165912	−	0.00773659i
$953$	−25.8211	−	6.91874i	−0.836427	−	0.224120i	−0.184912	−	0.982755i	$-0.559200\pi$
$953$	−25.8211	−	6.91874i	−0.836427	−	0.224120i	−0.651516	+	0.758635i	$0.725867\pi$
$954$		0			0
$955$	17.4259	−	8.84350i	0.563888	−	0.286169i
$956$	11.3705	+	13.5509i	0.367749	+	0.438266i
$957$		0			0
$958$	45.6014	−	31.9305i	1.47331	−	1.03163i
$959$	−4.99834	+	28.3470i	−0.161405	+	0.915372i
$960$		0			0
$961$	−14.8420	+	12.4539i	−0.478775	+	0.401740i
$962$	−140.356	+	37.6084i	−4.52528	+	1.21254i
$963$		0			0
$964$	3.68603	−	2.12813i	0.118719	−	0.0685425i
$965$	−19.1292	−	2.71996i	−0.615792	−	0.0875587i
$966$		0			0
$967$	−20.2788	+	1.77416i	−0.652121	+	0.0570532i	−0.408416	−	0.912796i	$-0.633919\pi$
$967$	−20.2788	+	1.77416i	−0.652121	+	0.0570532i	−0.243706	+	0.969849i	$0.578363\pi$
$968$	0.132820	−	0.284833i	0.00426899	−	0.00915488i
$969$		0			0
$970$	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	$0.774650\pi$
$972$		0			0
$973$	−1.53972	−	1.53972i	−0.0493610	−	0.0493610i
$974$	14.0086	+	79.4468i	0.448865	+	2.54564i
$975$		0			0
$976$	−16.3627	+	5.95554i	−0.523758	+	0.190632i
$977$	−3.10305	−	35.4680i	−0.0992752	−	1.13472i	−0.868482	−	0.495721i	$-0.834904\pi$
$977$	−3.10305	−	35.4680i	−0.0992752	−	1.13472i	0.769207	−	0.639000i	$-0.220652\pi$
$978$		0			0
$979$	6.04024	−	16.5954i	0.193047	−	0.530392i
$980$	22.3296	+	1.20642i	0.713293	+	0.0385377i
$981$		0			0
$982$	−12.5145	−	46.7049i	−0.399355	−	1.49041i
$983$	3.20046	−	36.5814i	0.102079	−	1.16677i	−0.756468	−	0.654030i	$-0.773077\pi$
$983$	3.20046	−	36.5814i	0.102079	−	1.16677i	0.858547	−	0.512735i	$-0.171368\pi$
$984$		0			0
$985$	0.149266	+	4.48203i	0.00475602	+	0.142809i
$986$	−13.5432	−	2.38804i	−0.431305	−	0.0760507i
$987$		0			0
$988$	51.0740	+	4.46840i	1.62488	+	0.142159i
$989$	−1.86320	+	3.22716i	−0.0592464	+	0.102618i
$990$		0			0
$991$	6.40763	+	11.0983i	0.203545	+	0.352550i	0.949668	−	0.313258i	$-0.101420\pi$
$991$	6.40763	+	11.0983i	0.203545	+	0.352550i	−0.746123	+	0.665808i	$0.768087\pi$
$992$	−11.6027	−	24.8820i	−0.368385	−	0.790005i
$993$		0			0
$994$	−17.1893	+	20.4854i	−0.545210	+	0.649756i
$995$	−39.0131	−	9.07329i	−1.23680	−	0.287643i
$996$		0			0
$997$	−45.2647	−	31.6947i	−1.43355	−	1.00378i	−0.994435	−	0.105349i	$-0.966404\pi$
$997$	−45.2647	−	31.6947i	−1.43355	−	1.00378i	−0.439113	−	0.898432i	$-0.644707\pi$
$998$	−44.9938	+	44.9938i	−1.42425	+	1.42425i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.14	✓	192	135.52	odd	36
135.2.q.a.68.14	yes	192	3.2	odd	2
135.2.q.a.83.14	yes	192	27.25	even	9
135.2.q.a.122.14	yes	192	15.2	even	4
405.2.r.a.8.3		192	27.2	odd	18	inner
405.2.r.a.152.3		192	5.2	odd	4	inner
405.2.r.a.233.3		192	1.1	even	1	trivial
405.2.r.a.332.3		192	135.2	even	36	inner
675.2.ba.b.68.3		192	15.14	odd	2
675.2.ba.b.218.3		192	135.79	even	18
675.2.ba.b.257.3		192	15.8	even	4
675.2.ba.b.407.3		192	135.133	odd	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.15565 + 1.65044i) q^{2} +(-0.704386 - 1.93528i) q^{4} +(2.13942 - 0.650308i) q^{5} +(1.32708 - 0.618828i) q^{7} +(0.115769 + 0.0310202i) q^{8} +(-1.39912 + 4.28251i) q^{10} +(-1.86051 - 2.21727i) q^{11} +(5.02076 - 3.51558i) q^{13} +(-0.512304 + 2.90542i) q^{14} +(2.97033 - 2.49240i) q^{16} +(3.10881 - 0.833002i) q^{17} +(-3.51741 + 2.03078i) q^{19} +(-2.76550 - 3.68231i) q^{20} +(5.80958 - 0.508272i) q^{22} +(2.14034 - 4.58997i) q^{23} +(4.15420 - 2.78256i) q^{25} +12.3493i q^{26} +(-2.13239 - 2.13239i) q^{28} +(0.368261 + 2.08851i) q^{29} +(-3.20394 + 1.16614i) q^{31} +(0.701790 + 8.02150i) q^{32} +(-2.21787 + 6.09356i) q^{34} +(2.43675 - 2.18694i) q^{35} +(3.04540 + 11.3656i) q^{37} +(0.713220 - 8.15214i) q^{38} +(0.267850 - 0.00892031i) q^{40} +(-0.839107 - 0.147957i) q^{41} +(-0.732994 - 0.0641287i) q^{43} +(-2.98053 + 5.16243i) q^{44} +(5.10199 + 8.83690i) q^{46} +(1.21825 + 2.61254i) q^{47} +(-3.12132 + 3.71984i) q^{49} +(-0.208362 + 10.0719i) q^{50} +(-10.3402 - 7.24028i) q^{52} +(-0.0757900 + 0.0757900i) q^{53} +(-5.42232 - 3.53376i) q^{55} +(0.172831 - 0.0304748i) q^{56} +(-3.87255 - 1.80580i) q^{58} +(-2.89613 - 2.43014i) q^{59} +(-4.21993 - 1.53593i) q^{61} +(1.77799 - 6.63556i) q^{62} +(-7.33402 - 4.23430i) q^{64} +(8.45529 - 10.7863i) q^{65} +(-2.55795 - 3.65313i) q^{67} +(-3.80189 - 5.42967i) q^{68} +(0.793385 + 6.54906i) q^{70} +(7.84988 + 4.53213i) q^{71} +(2.15667 - 8.04880i) q^{73} +(-22.2777 - 8.10840i) q^{74} +(6.40774 + 5.37673i) q^{76} +(-3.84116 - 1.79116i) q^{77} +(-1.44073 + 0.254040i) q^{79} +(4.73394 - 7.26391i) q^{80} +(1.21391 - 1.21391i) q^{82} +(13.8441 + 9.69375i) q^{83} +(6.10932 - 3.80382i) q^{85} +(0.952926 - 1.13565i) q^{86} +(-0.146609 - 0.314404i) q^{88} +(3.05075 + 5.28406i) q^{89} +(4.48742 - 7.77244i) q^{91} +(-10.3905 - 0.909052i) q^{92} +(-5.71971 - 1.00854i) q^{94} +(-6.20457 + 6.63207i) q^{95} +(1.41304 - 16.1512i) q^{97} +(-2.53222 - 9.45039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^5 - 12 * q^7 + 18 * q^8 - 6 * q^10 + 36 * q^11 - 12 * q^13 - 24 * q^16 + 18 * q^17 - 36 * q^20 - 12 * q^22 + 36 * q^23 - 30 * q^25 - 24 * q^28 - 24 * q^31 + 48 * q^32 - 36 * q^35 - 6 * q^37 - 12 * q^38 - 36 * q^40 - 24 * q^41 - 12 * q^43 - 12 * q^46 + 6 * q^47 - 36 * q^50 + 12 * q^52 - 24 * q^55 - 180 * q^56 - 12 * q^58 - 60 * q^61 + 18 * q^62 + 84 * q^65 + 24 * q^67 + 60 * q^68 - 12 * q^70 + 36 * q^71 - 6 * q^73 - 72 * q^76 - 132 * q^77 - 24 * q^82 - 48 * q^83 - 12 * q^85 - 12 * q^86 - 48 * q^88 - 12 * q^91 - 258 * q^92 - 18 * q^95 + 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

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Database

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