LMFDB - Embedded newform 975.2.bc.l.901.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(751,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.751"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,6,8,0,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 150x^{8} + 520x^{6} + 825x^{4} + 512x^{2} + 100 $ x^12 + 20x^10 + 150x^8 + 520x^6 + 825x^4 + 512*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.6
Root			$2.36051i$ of defining polynomial
Character	$\chi$	$=$	975.901
Dual form			975.2.bc.l.751.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.04426 + 1.18025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.78599 + 3.09343i) q^{4} +(2.04426 - 1.18025i) q^{6} +(-3.93440 + 2.27152i) q^{7} +3.71068i q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.74607 + 2.16279i) q^{11} +3.57199 q^{12} +(1.84085 + 3.10021i) q^{13} -10.7239 q^{14} +(-0.807554 + 1.39872i) q^{16} +(2.76283 + 4.78536i) q^{17} -2.36051i q^{18} +(3.41535 - 1.97185i) q^{19} +4.54305i q^{21} +(5.10528 + 8.84261i) q^{22} +(-0.364011 + 0.630486i) q^{23} +(3.21354 + 1.85534i) q^{24} +(0.104146 + 8.51029i) q^{26} -1.00000 q^{27} +(-14.0536 - 8.11385i) q^{28} +(-1.97844 + 3.42676i) q^{29} -0.599343i q^{31} +(3.12539 - 1.80444i) q^{32} +(3.74607 - 2.16279i) q^{33} +13.0434i q^{34} +(1.78599 - 3.09343i) q^{36} +(-3.91499 - 2.26032i) q^{37} +9.30914 q^{38} +(3.60528 - 0.0441204i) q^{39} +(-8.97339 - 5.18079i) q^{41} +(-5.36195 + 9.28716i) q^{42} +(-5.45093 - 9.44128i) q^{43} +15.4509i q^{44} +(-1.48827 + 0.859250i) q^{46} -1.42486i q^{47} +(0.807554 + 1.39872i) q^{48} +(6.81965 - 11.8120i) q^{49} +5.52566 q^{51} +(-6.30252 + 11.2315i) q^{52} +0.805400 q^{53} +(-2.04426 - 1.18025i) q^{54} +(-8.42890 - 14.5993i) q^{56} -3.94371i q^{57} +(-8.08888 + 4.67012i) q^{58} +(9.71559 - 5.60930i) q^{59} +(-6.20134 - 10.7410i) q^{61} +(0.707376 - 1.22521i) q^{62} +(3.93440 + 2.27152i) q^{63} +11.7490 q^{64} +10.2106 q^{66} +(9.12013 + 5.26551i) q^{67} +(-9.86879 + 17.0933i) q^{68} +(0.364011 + 0.630486i) q^{69} +(0.898903 - 0.518982i) q^{71} +(3.21354 - 1.85534i) q^{72} +6.45306i q^{73} +(-5.33550 - 9.24135i) q^{74} +(12.1996 + 7.04343i) q^{76} -19.6513 q^{77} +(7.42220 + 4.16495i) q^{78} +4.22063 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-12.2293 - 21.1817i) q^{82} -7.69642i q^{83} +(-14.0536 + 8.11385i) q^{84} -25.7339i q^{86} +(1.97844 + 3.42676i) q^{87} +(-8.02543 + 13.9004i) q^{88} +(-5.93532 - 3.42676i) q^{89} +(-14.2848 - 8.01590i) q^{91} -2.60048 q^{92} +(-0.519046 - 0.299672i) q^{93} +(1.68170 - 2.91279i) q^{94} -3.60889i q^{96} +(9.61107 - 5.54895i) q^{97} +(27.8822 - 16.0978i) q^{98} -4.32558i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9} + 9 q^{11} + 16 q^{12} - 3 q^{13} + 10 q^{14} - 4 q^{16} - 9 q^{19} + 15 q^{22} + q^{23} - 5 q^{26} - 12 q^{27} - 39 q^{28} - 16 q^{29} + 30 q^{32} + 9 q^{33}+ \cdots + 105 q^{98}+O(q^{100}) $ 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9 + 9 * q^11 + 16 * q^12 - 3 * q^13 + 10 * q^14 - 4 * q^16 - 9 * q^19 + 15 * q^22 + q^23 - 5 * q^26 - 12 * q^27 - 39 * q^28 - 16 * q^29 + 30 * q^32 + 9 * q^33 + 8 * q^36 - 15 * q^37 + 30 * q^38 - 3 * q^39 + 18 * q^41 + 5 * q^42 + q^43 - 45 * q^46 + 4 * q^48 + 31 * q^49 - 40 * q^52 - 16 * q^53 + 25 * q^56 - 30 * q^58 + 54 * q^59 - 11 * q^61 - 20 * q^62 + 3 * q^63 + 16 * q^64 + 30 * q^66 + 45 * q^67 - 30 * q^68 - q^69 - 33 * q^71 + 5 * q^74 - 27 * q^76 - 28 * q^77 + 20 * q^78 + 18 * q^79 - 6 * q^81 - 20 * q^82 - 39 * q^84 + 16 * q^87 - 5 * q^88 - 48 * q^89 - 29 * q^91 + 46 * q^92 - 12 * q^93 - 30 * q^94 - 9 * q^97 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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 $

$2$	2.04426	+	1.18025i	1.44551	+	0.834565i	0.998209	−	0.0598198i	$-0.0190526\pi$
$2$	2.04426	+	1.18025i	1.44551	+	0.834565i	0.447299	+	0.894384i	$0.352386\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.78599	+	3.09343i	0.892996	+	1.54671i
$5$		0			0
$5$		0			0
$6$	2.04426	−	1.18025i	0.834565	−	0.481836i
$7$	−3.93440	+	2.27152i	−1.48706	+	0.858556i	−0.999891	−	0.0147510i	$-0.995304\pi$
$7$	−3.93440	+	2.27152i	−1.48706	+	0.858556i	−0.487171	+	0.873307i	$0.661971\pi$
$8$			3.71068i			1.31192i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	3.74607	+	2.16279i	1.12948	+	0.652106i	0.943804	−	0.330505i	$-0.107219\pi$
$11$	3.74607	+	2.16279i	1.12948	+	0.652106i	0.185677	+	0.982611i	$0.440552\pi$
$12$	3.57199			1.03114
$13$	1.84085	+	3.10021i	0.510560	+	0.859842i
$13$	1.84085	+	3.10021i	0.510560	+	0.859842i
$14$	−10.7239			−2.86608
$15$		0			0
$16$	−0.807554	+	1.39872i	−0.201888	+	0.349681i
$17$	2.76283	+	4.78536i	0.670085	+	1.16062i	0.977880	+	0.209169i	$0.0670757\pi$
$17$	2.76283	+	4.78536i	0.670085	+	1.16062i	−0.307795	+	0.951453i	$0.599591\pi$
$18$		−	2.36051i		−	0.556376i
$19$	3.41535	−	1.97185i	0.783535	−	0.452374i	−0.0541466	−	0.998533i	$-0.517244\pi$
$19$	3.41535	−	1.97185i	0.783535	−	0.452374i	0.837682	+	0.546159i	$0.183910\pi$
$20$		0			0
$21$			4.54305i			0.991375i
$22$	5.10528	+	8.84261i	1.08845	+	1.88525i
$23$	−0.364011	+	0.630486i	−0.0759016	+	0.131465i	−0.901478	−	0.432825i	$-0.857517\pi$
$23$	−0.364011	+	0.630486i	−0.0759016	+	0.131465i	0.825576	+	0.564290i	$0.190850\pi$
$24$	3.21354	+	1.85534i	0.655962	+	0.378720i
$25$		0			0
$26$	0.104146	+	8.51029i	0.0204248	+	1.66900i
$27$	−1.00000			−0.192450
$28$	−14.0536	−	8.11385i	−2.65588	−	1.53337i
$29$	−1.97844	+	3.42676i	−0.367387	+	0.636333i	−0.989156	−	0.146868i	$-0.953081\pi$
$29$	−1.97844	+	3.42676i	−0.367387	+	0.636333i	0.621769	+	0.783200i	$0.286414\pi$
$30$		0			0
$31$		−	0.599343i		−	0.107645i	−0.998551	−	0.0538226i	$-0.982859\pi$
$31$		−	0.599343i		−	0.107645i	0.998551	−	0.0538226i	$-0.0171405\pi$
$32$	3.12539	−	1.80444i	0.552496	−	0.318984i
$33$	3.74607	−	2.16279i	0.652106	−	0.376494i
$34$			13.0434i			2.23692i
$35$		0			0
$36$	1.78599	−	3.09343i	0.297665	−	0.515572i
$37$	−3.91499	−	2.26032i	−0.643620	−	0.371594i	0.142388	−	0.989811i	$-0.454522\pi$
$37$	−3.91499	−	2.26032i	−0.643620	−	0.371594i	−0.786008	+	0.618217i	$0.787855\pi$
$38$	9.30914			1.51014
$39$	3.60528	−	0.0441204i	0.577307	−	0.00706491i
$40$		0			0
$41$	−8.97339	−	5.18079i	−1.40141	−	0.809104i	−0.406871	−	0.913485i	$-0.633380\pi$
$41$	−8.97339	−	5.18079i	−1.40141	−	0.809104i	−0.994537	+	0.104382i	$0.966714\pi$
$42$	−5.36195	+	9.28716i	−0.827366	+	1.43304i
$43$	−5.45093	−	9.44128i	−0.831258	−	1.43978i	−0.897041	−	0.441948i	$-0.854288\pi$
$43$	−5.45093	−	9.44128i	−0.831258	−	1.43978i	0.0657822	−	0.997834i	$-0.479046\pi$
$44$			15.4509i			2.32931i
$45$		0			0
$46$	−1.48827	+	0.859250i	−0.219433	+	0.126690i
$47$		−	1.42486i		−	0.207838i	−0.994586	−	0.103919i	$-0.966862\pi$
$47$		−	1.42486i		−	0.207838i	0.994586	−	0.103919i	$-0.0331382\pi$
$48$	0.807554	+	1.39872i	0.116560	+	0.201888i
$49$	6.81965	−	11.8120i	0.974236	−	1.68743i
$50$		0			0
$51$	5.52566			0.773748
$52$	−6.30252	+	11.2315i	−0.874003	+	1.55753i
$53$	0.805400			0.110630			0.0553151	−	0.998469i	$-0.482384\pi$
$53$	0.805400			0.110630			0.0553151	+	0.998469i	$0.482384\pi$
$54$	−2.04426	−	1.18025i	−0.278188	−	0.160612i
$55$		0			0
$56$	−8.42890	−	14.5993i	−1.12636	−	1.95091i
$57$		−	3.94371i		−	0.522357i
$58$	−8.08888	+	4.67012i	−1.06212	+	0.613216i
$59$	9.71559	−	5.60930i	1.26486	−	0.730269i	0.290851	−	0.956768i	$-0.406061\pi$
$59$	9.71559	−	5.60930i	1.26486	−	0.730269i	0.974011	+	0.226499i	$0.0727282\pi$
$60$		0			0
$61$	−6.20134	−	10.7410i	−0.794001	−	1.37525i	−0.923472	−	0.383666i	$-0.874661\pi$
$61$	−6.20134	−	10.7410i	−0.794001	−	1.37525i	0.129471	−	0.991583i	$-0.458672\pi$
$62$	0.707376	−	1.22521i	0.0898369	−	0.155602i
$63$	3.93440	+	2.27152i	0.495687	+	0.286185i
$64$	11.7490			1.46863
$65$		0			0
$66$	10.2106			1.25683
$67$	9.12013	+	5.26551i	1.11420	+	0.643284i	0.939914	−	0.341411i	$-0.110905\pi$
$67$	9.12013	+	5.26551i	1.11420	+	0.643284i	0.174287	+	0.984695i	$0.444238\pi$
$68$	−9.86879	+	17.0933i	−1.19677	+	2.07286i
$69$	0.364011	+	0.630486i	0.0438218	+	0.0759016i
$70$		0			0
$71$	0.898903	−	0.518982i	0.106680	−	0.0615918i	−0.445711	−	0.895177i	$-0.647049\pi$
$71$	0.898903	−	0.518982i	0.106680	−	0.0615918i	0.552391	+	0.833585i	$0.313716\pi$
$72$	3.21354	−	1.85534i	0.378720	−	0.218654i
$73$			6.45306i			0.755274i	0.925954	+	0.377637i	$0.123263\pi$
$73$			6.45306i			0.755274i	−0.925954	+	0.377637i	$0.876737\pi$
$74$	−5.33550	−	9.24135i	−0.620239	−	1.07429i
$75$		0			0
$76$	12.1996	+	7.04343i	1.39939	+	0.807937i
$77$	−19.6513			−2.23948
$78$	7.42220	+	4.16495i	0.840398	+	0.471588i
$79$	4.22063			0.474857			0.237429	−	0.971405i	$-0.423695\pi$
$79$	4.22063			0.474857			0.237429	+	0.971405i	$0.423695\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−12.2293	−	21.1817i	−1.35050	−	2.33913i
$83$		−	7.69642i		−	0.844792i	−0.906411	−	0.422396i	$-0.861189\pi$
$83$		−	7.69642i		−	0.844792i	0.906411	−	0.422396i	$-0.138811\pi$
$84$	−14.0536	+	8.11385i	−1.53337	+	0.885294i
$85$		0			0
$86$		−	25.7339i		−	2.77496i
$87$	1.97844	+	3.42676i	0.212111	+	0.367387i
$88$	−8.02543	+	13.9004i	−0.855513	+	1.48179i
$89$	−5.93532	−	3.42676i	−0.629142	−	0.363235i	0.151278	−	0.988491i	$-0.451661\pi$
$89$	−5.93532	−	3.42676i	−0.629142	−	0.363235i	−0.780420	+	0.625256i	$0.784995\pi$
$90$		0			0
$91$	−14.2848	−	8.01590i	−1.49746	−	0.840295i
$92$	−2.60048			−0.271119
$93$	−0.519046	−	0.299672i	−0.0538226	−	0.0310745i
$94$	1.68170	−	2.91279i	0.173454	−	0.300431i
$95$		0			0
$96$		−	3.60889i		−	0.368331i
$97$	9.61107	−	5.54895i	0.975856	−	0.563411i	0.0748394	−	0.997196i	$-0.476156\pi$
$97$	9.61107	−	5.54895i	0.975856	−	0.563411i	0.901016	+	0.433785i	$0.142822\pi$
$98$	27.8822	−	16.0978i	2.81653	−	1.62613i
$99$		−	4.32558i		−	0.434737i
$100$		0			0
$101$	2.83072	−	4.90294i	0.281667	−	0.487861i	−0.690129	−	0.723687i	$-0.742446\pi$
$101$	2.83072	−	4.90294i	0.281667	−	0.487861i	0.971795	+	0.235826i	$0.0757794\pi$
$102$	11.2959	+	6.52168i	1.11846	+	0.645742i
$103$	−3.25369			−0.320595			−0.160298	−	0.987069i	$-0.551245\pi$
$103$	−3.25369			−0.320595			−0.160298	+	0.987069i	$0.551245\pi$
$104$	−11.5039	+	6.83080i	−1.12805	+	0.669815i
$105$		0			0
$106$	1.64645	+	0.950576i	0.159917	+	0.0923281i
$107$	−7.25780	+	12.5709i	−0.701638	+	1.21527i	0.266253	+	0.963903i	$0.414214\pi$
$107$	−7.25780	+	12.5709i	−0.701638	+	1.21527i	−0.967891	+	0.251370i	$0.919119\pi$
$108$	−1.78599	−	3.09343i	−0.171857	−	0.297665i
$109$			2.24315i			0.214855i	0.994213	+	0.107428i	$0.0342614\pi$
$109$			2.24315i			0.214855i	−0.994213	+	0.107428i	$0.965739\pi$
$110$		0			0
$111$	−3.91499	+	2.26032i	−0.371594	+	0.214540i
$112$		−	7.33751i		−	0.693330i
$113$	−0.809154	−	1.40150i	−0.0761188	−	0.131842i	0.825453	−	0.564470i	$-0.190919\pi$
$113$	−0.809154	−	1.40150i	−0.0761188	−	0.131842i	−0.901572	+	0.432629i	$0.857586\pi$
$114$	4.65457	−	8.06195i	0.435940	−	0.755071i
$115$		0			0
$116$	−14.1339			−1.31230
$117$	1.76443	−	3.14433i	0.163122	−	0.290693i
$118$	26.4816			2.43783
$119$	−21.7401	−	12.5517i	−1.99292	−	1.15061i
$120$		0			0
$121$	3.85534	+	6.67764i	0.350485	+	0.607058i
$122$		−	29.2766i		−	2.65058i
$123$	−8.97339	+	5.18079i	−0.809104	+	0.467136i
$124$	1.85403	−	1.07042i	0.166496	−	0.0961267i
$125$		0			0
$126$	5.36195	+	9.28716i	0.477680	+	0.827366i
$127$	−9.33047	+	16.1608i	−0.827945	+	1.43404i	0.0717028	+	0.997426i	$0.477157\pi$
$127$	−9.33047	+	16.1608i	−0.827945	+	1.43404i	−0.899648	+	0.436617i	$0.856177\pi$
$128$	17.7672	+	10.2579i	1.57042	+	0.906680i
$129$	−10.9019			−0.959855
$130$		0			0
$131$	9.45787			0.826338			0.413169	−	0.910654i	$-0.364422\pi$
$131$	9.45787			0.826338			0.413169	+	0.910654i	$0.364422\pi$
$132$	13.3809	+	7.72546i	1.16466	+	0.672415i
$133$	−8.95823	+	15.5161i	−0.776777	+	1.34542i
$134$	12.4293	+	21.5281i	1.07372	+	1.85975i
$135$		0			0
$136$	−17.7570	+	10.2520i	−1.52265	+	0.879100i
$137$	1.98355	−	1.14520i	0.169466	−	0.0978414i	−0.412868	−	0.910791i	$-0.635473\pi$
$137$	1.98355	−	1.14520i	0.169466	−	0.0978414i	0.582334	+	0.812950i	$0.302140\pi$
$138$			1.71850i			0.146288i
$139$	4.18650	+	7.25122i	0.355094	+	0.615041i	0.987134	−	0.159895i	$-0.0511156\pi$
$139$	4.18650	+	7.25122i	0.355094	+	0.615041i	−0.632040	+	0.774936i	$0.717782\pi$
$140$		0			0
$141$	−1.23397	−	0.712432i	−0.103919	−	0.0599976i
$142$	2.45012			0.205609
$143$	0.190846	+	15.5949i	0.0159594	+	1.30411i
$144$	1.61511			0.134592
$145$		0			0
$146$	−7.61624	+	13.1917i	−0.630325	+	1.09175i
$147$	−6.81965	−	11.8120i	−0.562475	−	0.974236i
$148$		−	16.1477i		−	1.32733i
$149$	19.7954	−	11.4289i	1.62170	−	0.936291i	0.635238	−	0.772316i	$-0.280902\pi$
$149$	19.7954	−	11.4289i	1.62170	−	0.936291i	0.986465	−	0.163974i	$-0.0524315\pi$
$150$		0			0
$151$			14.9011i			1.21263i	0.795223	+	0.606317i	$0.207354\pi$
$151$			14.9011i			1.21263i	−0.795223	+	0.606317i	$0.792646\pi$
$152$	7.31692	+	12.6733i	0.593480	+	1.02794i
$153$	2.76283	−	4.78536i	0.223362	−	0.386874i
$154$	−40.1724	−	23.1935i	−3.23718	−	1.86899i
$155$		0			0
$156$	6.57549	+	11.0739i	0.526460	+	0.886620i
$157$	−0.495803			−0.0395694			−0.0197847	−	0.999804i	$-0.506298\pi$
$157$	−0.495803			−0.0395694			−0.0197847	+	0.999804i	$0.506298\pi$
$158$	8.62805	+	4.98140i	0.686410	+	0.396299i
$159$	0.402700	−	0.697497i	0.0319362	−	0.0553151i
$160$		0			0
$161$		−	3.30744i		−	0.260663i
$162$	−2.04426	+	1.18025i	−0.160612	+	0.0927294i
$163$	1.48871	−	0.859509i	0.116605	−	0.0673220i	−0.440563	−	0.897722i	$-0.645221\pi$
$163$	1.48871	−	0.859509i	0.116605	−	0.0673220i	0.557168	+	0.830400i	$0.311888\pi$
$164$		−	37.0114i		−	2.89011i
$165$		0			0
$166$	9.08372	−	15.7335i	0.705033	−	1.22115i
$167$	4.92273	+	2.84214i	0.380933	+	0.219932i	0.678224	−	0.734855i	$-0.262750\pi$
$167$	4.92273	+	2.84214i	0.380933	+	0.219932i	−0.297291	+	0.954787i	$0.596083\pi$
$168$	−16.8578			−1.30061
$169$	−6.22254	+	11.4140i	−0.478657	+	0.878002i
$170$		0			0
$171$	−3.41535	−	1.97185i	−0.261178	−	0.150791i
$172$	19.4706	−	33.7241i	1.48462	−	2.57144i
$173$	−3.43576	−	5.95091i	−0.261216	−	0.452439i	0.705349	−	0.708860i	$-0.250790\pi$
$173$	−3.43576	−	5.95091i	−0.261216	−	0.452439i	−0.966565	+	0.256421i	$0.917457\pi$
$174$			9.34023i			0.708081i
$175$		0			0
$176$	−6.05030	+	3.49314i	−0.456058	+	0.263305i
$177$		−	11.2186i		−	0.843242i
$178$	−8.08888	−	14.0103i	−0.606287	−	1.05012i
$179$	10.9566	−	18.9774i	0.818937	−	1.41844i	−0.0875295	−	0.996162i	$-0.527897\pi$
$179$	10.9566	−	18.9774i	0.818937	−	1.41844i	0.906466	−	0.422278i	$-0.138769\pi$
$180$		0			0
$181$	−17.9404			−1.33350			−0.666750	−	0.745281i	$-0.732315\pi$
$181$	−17.9404			−1.33350			−0.666750	+	0.745281i	$0.732315\pi$
$182$	−19.7411	−	33.2463i	−1.46331	−	2.46438i
$183$	−12.4027			−0.916833
$184$	−2.33953	−	1.35073i	−0.172472	−	0.0995770i
$185$		0			0
$186$	−0.707376	−	1.22521i	−0.0518673	−	0.0898369i
$187$			23.9017i			1.74787i
$188$	4.40772	−	2.54480i	0.321466	−	0.185598i
$189$	3.93440	−	2.27152i	0.286185	−	0.165229i
$190$		0			0
$191$	1.25521	+	2.17409i	0.0908239	+	0.157312i	0.907858	−	0.419278i	$-0.137717\pi$
$191$	1.25521	+	2.17409i	0.0908239	+	0.157312i	−0.817034	+	0.576589i	$0.804383\pi$
$192$	5.87451	−	10.1749i	0.423956	−	0.734313i
$193$	−8.16136	−	4.71197i	−0.587468	−	0.339175i	0.176628	−	0.984278i	$-0.443481\pi$
$193$	−8.16136	−	4.71197i	−0.587468	−	0.339175i	−0.764096	+	0.645103i	$0.776814\pi$
$194$	26.1967			1.88081
$195$		0			0
$196$	48.7194			3.47996
$197$	−21.3578	−	12.3309i	−1.52168	−	0.878542i	−0.999672	−	0.0256008i	$-0.991850\pi$
$197$	−21.3578	−	12.3309i	−1.52168	−	0.878542i	−0.522007	−	0.852941i	$-0.674817\pi$
$198$	5.10528	−	8.84261i	0.362817	−	0.628417i
$199$	12.9766	+	22.4761i	0.919886	+	1.59329i	0.799586	+	0.600552i	$0.205052\pi$
$199$	12.9766	+	22.4761i	0.919886	+	1.59329i	0.120300	+	0.992738i	$0.461614\pi$
$200$		0			0
$201$	9.12013	−	5.26551i	0.643284	−	0.371400i
$202$	11.5734	−	6.68192i	0.814303	−	0.470138i
$203$		−	17.9763i		−	1.26169i
$204$	9.86879	+	17.0933i	0.690954	+	1.19677i
$205$		0			0
$206$	−6.65137	−	3.84017i	−0.463423	−	0.267557i
$207$	0.728022			0.0506010
$208$	−5.82292	+	0.0712591i	−0.403747	+	0.00494093i
$209$	17.0588			1.17998
$210$		0			0
$211$	−5.77273	+	9.99866i	−0.397411	+	0.688336i	−0.993406	−	0.114652i	$-0.963425\pi$
$211$	−5.77273	+	9.99866i	−0.397411	+	0.688336i	0.595994	+	0.802989i	$0.296758\pi$
$212$	1.43844	+	2.49145i	0.0987924	+	0.171113i
$213$		−	1.03796i		−	0.0711201i
$214$	−29.6736	+	17.1321i	−2.02845	+	1.17112i
$215$		0			0
$216$		−	3.71068i		−	0.252480i
$217$	1.36142	+	2.35805i	0.0924194	+	0.160075i
$218$	−2.64749	+	4.58558i	−0.179310	+	0.310575i
$219$	5.58852	+	3.22653i	0.377637	+	0.218029i
$220$		0			0
$221$	−9.74965	+	17.3745i	−0.655833	+	1.16873i
$222$	−10.6710			−0.716190
$223$	7.03409	+	4.06113i	0.471037	+	0.271954i	0.716674	−	0.697408i	$-0.245664\pi$
$223$	7.03409	+	4.06113i	0.471037	+	0.271954i	−0.245636	+	0.969362i	$0.578997\pi$
$224$	−8.19768	+	14.1988i	−0.547730	+	0.948697i
$225$		0			0
$226$		−	3.82002i		−	0.254104i
$227$	11.7666	−	6.79346i	0.780978	−	0.450898i	−0.0557990	−	0.998442i	$-0.517771\pi$
$227$	11.7666	−	6.79346i	0.780978	−	0.450898i	0.836777	+	0.547544i	$0.184437\pi$
$228$	12.1996	−	7.04343i	0.807937	−	0.466463i
$229$		−	3.61042i		−	0.238583i	−0.992859	−	0.119292i	$-0.961938\pi$
$229$		−	3.61042i		−	0.238583i	0.992859	−	0.119292i	$-0.0380624\pi$
$230$		0			0
$231$	−9.82567	+	17.0186i	−0.646482	+	1.11974i
$232$	−12.7156	−	7.34135i	−0.834820	−	0.481983i
$233$	−28.6851			−1.87922			−0.939612	−	0.342240i	$-0.888814\pi$
$233$	−28.6851			−1.87922			−0.939612	+	0.342240i	$0.888814\pi$
$234$	7.31805	−	4.34534i	0.478396	−	0.284064i
$235$		0			0
$236$	34.7040	+	20.0363i	2.25904	+	1.30425i
$237$	2.11031	−	3.65517i	0.137080	−	0.237429i
$238$	−29.6283	−	51.3177i	−1.92052	−	3.32643i
$239$		−	2.00405i		−	0.129631i	−0.997897	−	0.0648157i	$-0.979354\pi$
$239$		−	2.00405i		−	0.129631i	0.997897	−	0.0648157i	$-0.0206459\pi$
$240$		0			0
$241$	24.5161	−	14.1544i	1.57922	−	0.911762i	0.584250	−	0.811574i	$-0.301389\pi$
$241$	24.5161	−	14.1544i	1.57922	−	0.911762i	0.994969	−	0.100188i	$-0.0319445\pi$
$242$			18.2011i			1.17001i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	22.1511	−	38.3668i	1.41808	−	2.45619i
$245$		0			0
$246$	−24.4586			−1.55942
$247$	12.4003	+	6.95840i	0.789012	+	0.442752i
$248$	2.22397			0.141222
$249$	−6.66530	−	3.84821i	−0.422396	−	0.243870i
$250$		0			0
$251$	−8.84280	−	15.3162i	−0.558152	−	0.966748i	−0.997651	−	0.0685050i	$-0.978177\pi$
$251$	−8.84280	−	15.3162i	−0.558152	−	0.966748i	0.439498	−	0.898243i	$-0.355156\pi$
$252$			16.2277i			1.02225i
$253$	−2.72722	+	1.57456i	−0.171459	+	0.0989918i
$254$	−38.1477	+	22.0246i	−2.39360	+	1.38195i
$255$		0			0
$256$	12.4649	+	21.5898i	0.779053	+	1.34936i
$257$	−9.97787	+	17.2822i	−0.622402	+	1.07803i	0.366635	+	0.930365i	$0.380510\pi$
$257$	−9.97787	+	17.2822i	−0.622402	+	1.07803i	−0.989037	+	0.147668i	$0.952823\pi$
$258$	−22.2862	−	12.8669i	−1.38748	−	0.801061i
$259$	20.5375			1.27614
$260$		0			0
$261$	3.95688			0.244925
$262$	19.3343	+	11.1627i	1.19448	+	0.689633i
$263$	1.69847	−	2.94183i	0.104732	−	0.181401i	−0.808897	−	0.587951i	$-0.799935\pi$
$263$	1.69847	−	2.94183i	0.104732	−	0.181401i	0.913629	+	0.406550i	$0.133268\pi$
$264$	8.02543	+	13.9004i	0.493931	+	0.855513i
$265$		0			0
$266$	−36.6258	+	21.1459i	−2.24567	+	1.29654i
$267$	−5.93532	+	3.42676i	−0.363235	+	0.209714i
$268$			37.6166i			2.29780i
$269$	−7.66836	−	13.2820i	−0.467548	−	0.809817i	0.531765	−	0.846892i	$-0.321529\pi$
$269$	−7.66836	−	13.2820i	−0.467548	−	0.809817i	−0.999312	+	0.0370755i	$0.988196\pi$
$270$		0			0
$271$	−15.8495	−	9.15070i	−0.962787	−	0.555865i	−0.0657572	−	0.997836i	$-0.520946\pi$
$271$	−15.8495	−	9.15070i	−0.962787	−	0.555865i	−0.897030	+	0.441970i	$0.854280\pi$
$272$	−8.92454			−0.541130
$273$	−14.0844	+	8.36307i	−0.852426	+	0.506156i
$274$	5.40652			0.326620
$275$		0			0
$276$	−1.30024	+	2.25209i	−0.0782654	+	0.135560i
$277$	3.90042	+	6.75572i	0.234353	+	0.405912i	0.959085	−	0.283120i	$-0.0913694\pi$
$277$	3.90042	+	6.75572i	0.234353	+	0.405912i	−0.724731	+	0.689032i	$0.758036\pi$
$278$			19.7645i			1.18540i
$279$	−0.519046	+	0.299672i	−0.0310745	+	0.0179409i
$280$		0			0
$281$			23.2268i			1.38559i	0.721134	+	0.692796i	$0.243621\pi$
$281$			23.2268i			1.38559i	−0.721134	+	0.692796i	$0.756379\pi$
$282$	−1.68170	−	2.91279i	−0.100144	−	0.173454i
$283$	3.92173	−	6.79264i	0.233123	−	0.403780i	−0.725603	−	0.688114i	$-0.758439\pi$
$283$	3.92173	−	6.79264i	0.233123	−	0.403780i	0.958725	+	0.284333i	$0.0917723\pi$
$284$	3.21087	+	1.85379i	0.190530	+	0.110002i
$285$		0			0
$286$	−18.0158	+	32.1053i	−1.06530	+	1.89843i
$287$	47.0732			2.77864
$288$	−3.12539	−	1.80444i	−0.184165	−	0.106328i
$289$	−6.76647	+	11.7199i	−0.398028	+	0.689405i
$290$		0			0
$291$		−	11.0979i		−	0.650571i
$292$	−19.9621	+	11.5251i	−1.16819	+	0.674457i
$293$	8.90314	−	5.14023i	0.520127	−	0.300296i	−0.216859	−	0.976203i	$-0.569581\pi$
$293$	8.90314	−	5.14023i	0.520127	−	0.300296i	0.736987	+	0.675907i	$0.236248\pi$
$294$		−	32.1956i		−	1.87769i
$295$		0			0
$296$	8.38732	−	14.5273i	0.487503	−	0.844380i
$297$	−3.74607	−	2.16279i	−0.217369	−	0.125498i
$298$	53.9559			3.12558
$299$	−2.62473	+	0.0321206i	−0.151792	+	0.00185758i
$300$		0			0
$301$	42.8922	+	24.7638i	2.47227	+	1.42736i
$302$	−17.5870	+	30.4617i	−1.01202	+	1.75287i
$303$	−2.83072	−	4.90294i	−0.162620	−	0.281667i
$304$			6.36951i			0.365317i
$305$		0			0
$306$	11.2959	−	6.52168i	0.645742	−	0.372820i
$307$		−	33.8058i		−	1.92940i	−0.263348	−	0.964701i	$-0.584827\pi$
$307$		−	33.8058i		−	1.92940i	0.263348	−	0.964701i	$-0.415173\pi$
$308$	−35.0971	−	60.7900i	−1.99985	−	3.46383i
$309$	−1.62684	+	2.81777i	−0.0925478	+	0.160298i
$310$		0			0
$311$	−0.286772			−0.0162613			−0.00813066	−	0.999967i	$-0.502588\pi$
$311$	−0.286772			−0.0162613			−0.00813066	+	0.999967i	$0.502588\pi$
$312$	0.163716	+	13.3780i	0.00926862	+	0.757383i
$313$	27.8341			1.57328			0.786639	−	0.617413i	$-0.211819\pi$
$313$	27.8341			1.57328			0.786639	+	0.617413i	$0.211819\pi$
$314$	−1.01355	−	0.585173i	−0.0571979	−	0.0330232i
$315$		0			0
$316$	7.53801	+	13.0562i	0.424046	+	0.734469i
$317$		−	23.6134i		−	1.32626i	−0.748504	−	0.663130i	$-0.769228\pi$
$317$		−	23.6134i		−	1.32626i	0.748504	−	0.663130i	$-0.230772\pi$
$318$	1.64645	−	0.950576i	0.0923281	−	0.0533056i
$319$	−14.8227	+	8.55790i	−0.829913	+	0.479151i
$320$		0			0
$321$	7.25780	+	12.5709i	0.405091	+	0.701638i
$322$	3.90362	−	6.76126i	0.217540	−	0.376790i
$323$	18.8721	+	10.8958i	1.05007	+	0.606258i
$324$	−3.57199			−0.198444
$325$		0			0
$326$	4.05775			0.224738
$327$	1.94263	+	1.12158i	0.107428	+	0.0620233i
$328$	19.2243	−	33.2974i	1.06148	−	1.83854i
$329$	3.23661	+	5.60598i	0.178440	+	0.309068i
$330$		0			0
$331$	4.51960	−	2.60939i	0.248420	−	0.143425i	−0.370621	−	0.928784i	$-0.620855\pi$
$331$	4.51960	−	2.60939i	0.248420	−	0.143425i	0.619041	+	0.785359i	$0.287522\pi$
$332$	23.8083	−	13.7457i	1.30665	−	0.754396i
$333$			4.52064i			0.247730i
$334$	6.70889	+	11.6201i	0.367094	+	0.635826i
$335$		0			0
$336$	−6.35447	−	3.66876i	−0.346665	−	0.200147i
$337$	−19.8753			−1.08268			−0.541339	−	0.840804i	$-0.682082\pi$
$337$	−19.8753			−1.08268			−0.541339	+	0.840804i	$0.682082\pi$
$338$	−26.1919	+	15.9890i	−1.42465	+	0.869689i
$339$	−1.61831			−0.0878944
$340$		0			0
$341$	1.29625	−	2.24518i	0.0701961	−	0.121583i
$342$	−4.65457	−	8.06195i	−0.251690	−	0.435940i
$343$			30.1627i			1.62863i
$344$	35.0336	−	20.2266i	1.88888	−	1.09055i
$345$		0			0
$346$		−	16.2203i		−	0.872007i
$347$	0.854503	+	1.48004i	0.0458721	+	0.0794529i	0.888050	−	0.459747i	$-0.152060\pi$
$347$	0.854503	+	1.48004i	0.0458721	+	0.0794529i	−0.842178	+	0.539200i	$0.818727\pi$
$348$	−7.06695	+	12.2403i	−0.378828	+	0.656150i
$349$	13.3270	+	7.69437i	0.713380	+	0.411870i	0.812311	−	0.583224i	$-0.198209\pi$
$349$	13.3270	+	7.69437i	0.713380	+	0.411870i	−0.0989311	+	0.995094i	$0.531542\pi$
$350$		0			0
$351$	−1.84085	−	3.10021i	−0.0982573	−	0.165477i
$352$	15.6105			0.832045
$353$	−16.2885	−	9.40416i	−0.866948	−	0.500533i	−0.000615369	−	1.00000i	$-0.500196\pi$
$353$	−16.2885	−	9.40416i	−0.866948	−	0.500533i	−0.866333	+	0.499467i	$0.833529\pi$
$354$	13.2408	−	22.9337i	0.703740	−	1.21891i
$355$		0			0
$356$		−	24.4806i		−	1.29747i
$357$	−21.7401	+	12.5517i	−1.15061	+	0.664305i
$358$	44.7963	−	25.8632i	2.36756	−	1.36691i
$359$			17.0768i			0.901280i	0.892706	+	0.450640i	$0.148804\pi$
$359$			17.0768i			0.901280i	−0.892706	+	0.450640i	$0.851196\pi$
$360$		0			0
$361$	−1.72359	+	2.98534i	−0.0907152	+	0.157123i
$362$	−36.6748	−	21.1742i	−1.92759	−	1.11289i
$363$	7.71067			0.404705
$364$	−0.715972	−	58.5054i	−0.0375271	−	3.06652i
$365$		0			0
$366$	−25.3543	−	14.6383i	−1.32529	−	0.765156i
$367$	5.20957	−	9.02325i	0.271938	−	0.471010i	−0.697420	−	0.716662i	$-0.745669\pi$
$367$	5.20957	−	9.02325i	0.271938	−	0.471010i	0.969358	+	0.245653i	$0.0790023\pi$
$368$	−0.587917	−	1.01830i	−0.0306473	−	0.0530827i
$369$			10.3616i			0.539402i
$370$		0			0
$371$	−3.16876	+	1.82949i	−0.164514	+	0.0949822i
$372$		−	2.14084i		−	0.110998i
$373$	12.0400	+	20.8540i	0.623410	+	1.07978i	0.988846	+	0.148941i	$0.0475864\pi$
$373$	12.0400	+	20.8540i	0.623410	+	1.07978i	−0.365437	+	0.930836i	$0.619080\pi$
$374$	−28.2101	+	48.8613i	−1.45871	+	2.52656i
$375$		0			0
$376$	5.28721			0.272667
$377$	−14.2657	+	0.174579i	−0.734719	+	0.00899127i
$378$	10.7239			0.551578
$379$	−7.64369	−	4.41308i	−0.392630	−	0.226685i	0.290669	−	0.956824i	$-0.406122\pi$
$379$	−7.64369	−	4.41308i	−0.392630	−	0.226685i	−0.683299	+	0.730139i	$0.739455\pi$
$380$		0			0
$381$	9.33047	+	16.1608i	0.478014	+	0.827945i
$382$			5.92587i			0.303194i
$383$	14.0423	−	8.10734i	0.717529	−	0.414266i	−0.0963135	−	0.995351i	$-0.530705\pi$
$383$	14.0423	−	8.10734i	0.717529	−	0.414266i	0.813843	+	0.581085i	$0.197372\pi$
$384$	17.7672	−	10.2579i	0.906680	−	0.523472i
$385$		0			0
$386$	−11.1226	−	19.2649i	−0.566126	−	0.980560i
$387$	−5.45093	+	9.44128i	−0.277086	+	0.479927i
$388$	34.3306	+	19.8208i	1.74287	+	1.00625i
$389$	−33.1860			−1.68259			−0.841297	−	0.540573i	$-0.818208\pi$
$389$	−33.1860			−1.68259			−0.841297	+	0.540573i	$0.818208\pi$
$390$		0			0
$391$	−4.02281			−0.203442
$392$	43.8305	+	25.3055i	2.21377	+	1.27812i
$393$	4.72894	−	8.19076i	0.238543	−	0.413169i
$394$	−29.1072	−	50.4152i	−1.46640	−	2.53988i
$395$		0			0
$396$	13.3809	−	7.72546i	0.672415	−	0.388219i
$397$	6.49531	−	3.75007i	0.325990	−	0.188211i	−0.328069	−	0.944654i	$-0.606398\pi$
$397$	6.49531	−	3.75007i	0.325990	−	0.188211i	0.654060	+	0.756443i	$0.273065\pi$
$398$			61.2626i			3.07082i
$399$	8.95823	+	15.5161i	0.448472	+	0.776777i
$400$		0			0
$401$	2.95696	+	1.70720i	0.147664	+	0.0852536i	0.572011	−	0.820246i	$-0.306163\pi$
$401$	2.95696	+	1.70720i	0.147664	+	0.0852536i	−0.424348	+	0.905499i	$0.639497\pi$
$402$	24.8585			1.23983
$403$	1.85809	−	1.10330i	0.0925579	−	0.0549593i
$404$	20.2225			1.00611
$405$		0			0
$406$	21.2166	−	36.7482i	1.05296	−	1.82378i
$407$	−9.77720	−	16.9346i	−0.484638	−	0.839417i
$408$			20.5040i			1.01510i
$409$	−12.6543	+	7.30598i	−0.625716	+	0.361257i	−0.779091	−	0.626911i	$-0.784319\pi$
$409$	−12.6543	+	7.30598i	−0.625716	+	0.361257i	0.153375	+	0.988168i	$0.450986\pi$
$410$		0			0
$411$		−	2.29041i		−	0.112978i
$412$	−5.81106	−	10.0650i	−0.286290	−	0.495869i
$413$	−25.4833	+	44.1384i	−1.25395	+	2.17191i
$414$	1.48827	+	0.859250i	0.0731442	+	0.0422298i
$415$		0			0
$416$	11.3475	+	6.36764i	0.556358	+	0.312199i
$417$	8.37299			0.410027
$418$	34.8726	+	20.1337i	1.70568	+	0.984773i
$419$	1.70258	−	2.94896i	0.0831765	−	0.144066i	−0.821436	−	0.570300i	$-0.806827\pi$
$419$	1.70258	−	2.94896i	0.0831765	−	0.144066i	0.904613	+	0.426234i	$0.140160\pi$
$420$		0			0
$421$		−	14.9006i		−	0.726213i	−0.931748	−	0.363107i	$-0.881716\pi$
$421$		−	14.9006i		−	0.726213i	0.931748	−	0.363107i	$-0.118284\pi$
$422$	−23.6019	+	13.6266i	−1.14892	+	0.663331i
$423$	−1.23397	+	0.712432i	−0.0599976	+	0.0346396i
$424$			2.98858i			0.145138i
$425$		0			0
$426$	1.22506	−	2.12186i	0.0593543	−	0.102805i
$427$	48.7971	+	28.1730i	2.36146	+	1.36339i
$428$	−51.8495			−2.50624
$429$	13.6010	+	7.63219i	0.656664	+	0.368486i
$430$		0			0
$431$	4.80354	+	2.77332i	0.231378	+	0.133586i	0.611208	−	0.791470i	$-0.290684\pi$
$431$	4.80354	+	2.77332i	0.231378	+	0.133586i	−0.379829	+	0.925057i	$0.624017\pi$
$432$	0.807554	−	1.39872i	0.0388535	−	0.0672962i
$433$	−6.28072	−	10.8785i	−0.301832	−	0.522789i	0.674719	−	0.738075i	$-0.264265\pi$
$433$	−6.28072	−	10.8785i	−0.301832	−	0.522789i	−0.976551	+	0.215286i	$0.930932\pi$
$434$			6.42729i			0.308520i
$435$		0			0
$436$	−6.93904	+	4.00625i	−0.332320	+	0.191865i
$437$			2.87111i			0.137344i
$438$	7.61624	+	13.1917i	0.363918	+	0.630325i
$439$	−14.7936	+	25.6233i	−0.706060	+	1.22293i	0.260248	+	0.965542i	$0.416196\pi$
$439$	−14.7936	+	25.6233i	−0.706060	+	1.22293i	−0.966308	+	0.257390i	$0.917138\pi$
$440$		0			0
$441$	−13.6393			−0.649490
$442$	−40.4371	+	24.0109i	−1.92340	+	1.14208i
$443$	−29.6951			−1.41086			−0.705428	−	0.708781i	$-0.749245\pi$
$443$	−29.6951			−1.41086			−0.705428	+	0.708781i	$0.749245\pi$
$444$	−13.9843	−	8.07383i	−0.663665	−	0.383167i
$445$		0			0
$446$	9.58633	+	16.6040i	0.453926	+	0.786222i
$447$		−	22.8578i		−	1.08114i
$448$	−46.2253	+	26.6882i	−2.18394	+	1.26090i
$449$	−9.55371	+	5.51584i	−0.450867	+	0.260308i	−0.708196	−	0.706015i	$-0.750491\pi$
$449$	−9.55371	+	5.51584i	−0.450867	+	0.260308i	0.257329	+	0.966324i	$0.417158\pi$
$450$		0			0
$451$	−22.4099	−	38.8152i	−1.05524	−	1.82773i
$452$	2.89029	−	5.00612i	0.135948	−	0.235468i
$453$	12.9047	+	7.45054i	0.606317	+	0.350057i
$454$	32.0720			1.50521
$455$		0			0
$456$	14.6338			0.685292
$457$	−12.3287	−	7.11796i	−0.576711	−	0.332964i	0.183114	−	0.983092i	$-0.441382\pi$
$457$	−12.3287	−	7.11796i	−0.576711	−	0.332964i	−0.759825	+	0.650128i	$0.774715\pi$
$458$	4.26121	−	7.38063i	0.199113	−	0.344874i
$459$	−2.76283	−	4.78536i	−0.128958	−	0.223362i
$460$		0			0
$461$	−19.3611	+	11.1781i	−0.901736	+	0.520618i	−0.877763	−	0.479095i	$-0.840965\pi$
$461$	−19.3611	+	11.1781i	−0.901736	+	0.520618i	−0.0239731	+	0.999713i	$0.507632\pi$
$462$	−40.1724	+	23.1935i	−1.86899	+	1.07906i
$463$			29.9717i			1.39290i	0.717604	+	0.696451i	$0.245239\pi$
$463$			29.9717i			1.39290i	−0.717604	+	0.696451i	$0.754761\pi$
$464$	−3.19539	−	5.53458i	−0.148342	−	0.256936i
$465$		0			0
$466$	−58.6398	−	33.8557i	−2.71644	−	1.56833i
$467$	17.3591			0.803282			0.401641	−	0.915797i	$-0.368440\pi$
$467$	17.3591			0.803282			0.401641	+	0.915797i	$0.368440\pi$
$468$	12.8780	−	0.157597i	0.595286	−	0.00728493i
$469$	−47.8429			−2.20918
$470$		0			0
$471$	−0.247901	+	0.429378i	−0.0114227	+	0.0197847i
$472$	20.8143	+	36.0515i	0.958057	+	1.65940i
$473$		−	47.1569i		−	2.16828i
$474$	8.62805	−	4.98140i	0.396299	−	0.228803i
$475$		0			0
$476$		−	89.6688i		−	4.10996i
$477$	−0.402700	−	0.697497i	−0.0184384	−	0.0319362i
$478$	2.36529	−	4.09680i	0.108186	−	0.187383i
$479$	−8.85694	−	5.11356i	−0.404684	−	0.233644i	0.283819	−	0.958878i	$-0.408399\pi$
$479$	−8.85694	−	5.11356i	−0.404684	−	0.233644i	−0.688503	+	0.725233i	$0.741732\pi$
$480$		0			0
$481$	−0.199452	−	16.2982i	−0.00909424	−	0.743133i
$482$	66.8229			3.04370
$483$	−2.86433	−	1.65372i	−0.130331	−	0.0752469i
$484$	−13.7712	+	23.8524i	−0.625964	+	1.08420i
$485$		0			0
$486$			2.36051i			0.107075i
$487$	−14.2659	+	8.23642i	−0.646449	+	0.373228i	−0.787095	−	0.616832i	$-0.788416\pi$
$487$	−14.2659	+	8.23642i	−0.646449	+	0.373228i	0.140645	+	0.990060i	$0.455082\pi$
$488$	39.8566	−	23.0112i	1.80422	−	1.04167i
$489$		−	1.71902i		−	0.0777367i
$490$		0			0
$491$	14.2907	−	24.7523i	0.644931	−	1.11705i	−0.339386	−	0.940647i	$-0.610219\pi$
$491$	14.2907	−	24.7523i	0.644931	−	1.11705i	0.984317	−	0.176407i	$-0.0564473\pi$
$492$	−32.0528	−	18.5057i	−1.44505	−	0.834302i
$493$	−21.8644			−0.984722
$494$	17.1367	+	28.8602i	0.771018	+	1.29848i
$495$		0			0
$496$	0.838316	+	0.484002i	0.0376415	+	0.0217323i
$497$	−2.35776	+	4.08376i	−0.105760	+	0.183182i
$498$	−9.08372	−	15.7335i	−0.407051	−	0.705033i
$499$		−	14.6508i		−	0.655858i	−0.944702	−	0.327929i	$-0.893649\pi$
$499$		−	14.6508i		−	0.655858i	0.944702	−	0.327929i	$-0.106351\pi$
$500$		0			0
$501$	4.92273	−	2.84214i	0.219932	−	0.126978i
$502$		−	41.7469i		−	1.86326i
$503$	−1.21181	−	2.09892i	−0.0540320	−	0.0935861i	0.837744	−	0.546063i	$-0.183874\pi$
$503$	−1.21181	−	2.09892i	−0.0540320	−	0.0935861i	−0.891776	+	0.452477i	$0.850541\pi$
$504$	−8.42890	+	14.5993i	−0.375453	+	0.650304i
$505$		0			0
$506$	−7.43352			−0.330460
$507$	6.77356	+	11.0959i	0.300825	+	0.492786i
$508$	−66.6566			−2.95741
$509$	−12.3914	−	7.15420i	−0.549240	−	0.317104i	0.199575	−	0.979883i	$-0.436044\pi$
$509$	−12.3914	−	7.15420i	−0.549240	−	0.317104i	−0.748816	+	0.662778i	$0.769377\pi$
$510$		0			0
$511$	−14.6583	−	25.3889i	−0.648445	−	1.12314i
$512$			17.8150i			0.787321i
$513$	−3.41535	+	1.97185i	−0.150791	+	0.0870595i
$514$	−40.7947	+	23.5528i	−1.79938	+	1.03887i
$515$		0			0
$516$	−19.4706	−	33.7241i	−0.857147	−	1.48462i
$517$	3.08169	−	5.33764i	0.135532	−	0.234749i
$518$	41.9839	+	24.2394i	1.84467	+	1.06502i
$519$	−6.87152			−0.301626
$520$		0			0
$521$	−34.9071			−1.52931			−0.764654	−	0.644441i	$-0.777090\pi$
$521$	−34.9071			−1.52931			−0.764654	+	0.644441i	$0.777090\pi$
$522$	8.08888	+	4.67012i	0.354041	+	0.204405i
$523$	−6.57502	+	11.3883i	−0.287505	+	0.497974i	−0.973214	−	0.229902i	$-0.926159\pi$
$523$	−6.57502	+	11.3883i	−0.287505	+	0.497974i	0.685708	+	0.727877i	$0.259493\pi$
$524$	16.8917	+	29.2573i	0.737917	+	1.27811i
$525$		0			0
$526$	6.94420	−	4.00924i	0.302782	−	0.174811i
$527$	2.86807	−	1.65588i	0.124935	−	0.0721314i
$528$			6.98628i			0.304039i
$529$	11.2350	+	19.4596i	0.488478	+	0.846069i
$530$		0			0
$531$	−9.71559	−	5.60930i	−0.421621	−	0.243423i
$532$	−63.9973			−2.77464
$533$	−0.457157	−	37.3564i	−0.0198017	−	1.61809i
$534$	−16.1778			−0.700080
$535$		0			0
$536$	−19.5386	+	33.8419i	−0.843940	+	1.46175i
$537$	−10.9566	−	18.9774i	−0.472813	−	0.818937i
$538$		−	36.2024i		−	1.56080i
$539$	51.0937	−	29.4990i	2.20076	−	1.27061i
$540$		0			0
$541$			19.0301i			0.818169i	0.912496	+	0.409085i	$0.134152\pi$
$541$			19.0301i			0.818169i	−0.912496	+	0.409085i	$0.865848\pi$
$542$	−21.6003	−	37.4128i	−0.927811	−	1.60702i
$543$	−8.97021	+	15.5369i	−0.384948	+	0.666750i
$544$	17.2698	+	9.97075i	0.740439	+	0.427492i
$545$		0			0
$546$	−38.6627	+	0.473142i	−1.65461	+	0.0202486i
$547$	−21.1122			−0.902694			−0.451347	−	0.892348i	$-0.649056\pi$
$547$	−21.1122			−0.902694			−0.451347	+	0.892348i	$0.649056\pi$
$548$	7.08522	+	4.09065i	0.302666	+	0.174744i
$549$	−6.20134	+	10.7410i	−0.264667	+	0.458416i
$550$		0			0
$551$			15.6048i			0.664785i
$552$	−2.33953	+	1.35073i	−0.0995770	+	0.0574908i
$553$	−16.6056	+	9.58726i	−0.706143	+	0.407692i
$554$			18.4139i			0.782332i
$555$		0			0
$556$	−14.9541	+	25.9013i	−0.634195	+	1.09846i
$557$	8.79709	+	5.07900i	0.372745	+	0.215204i	0.674657	−	0.738132i	$-0.264292\pi$
$557$	8.79709	+	5.07900i	0.372745	+	0.215204i	−0.301912	+	0.953336i	$0.597625\pi$
$558$	−1.41475			−0.0598912
$559$	19.2356	−	34.2790i	0.813578	−	1.44985i
$560$		0			0
$561$	20.6995	+	11.9509i	0.873933	+	0.504566i
$562$	−27.4134	+	47.4815i	−1.15637	+	2.00288i
$563$	7.46961	+	12.9377i	0.314807	+	0.545261i	0.979396	−	0.201947i	$-0.0647270\pi$
$563$	7.46961	+	12.9377i	0.314807	+	0.545261i	−0.664590	+	0.747208i	$0.731394\pi$
$564$		−	5.08959i		−	0.214311i
$565$		0			0
$566$	16.0341	−	9.25727i	0.673962	−	0.389112i
$567$		−	4.54305i		−	0.190790i
$568$	1.92577	+	3.33554i	0.0808037	+	0.139956i
$569$	−12.0374	+	20.8495i	−0.504636	+	0.874055i	0.495350	+	0.868694i	$0.335040\pi$
$569$	−12.0374	+	20.8495i	−0.504636	+	0.874055i	−0.999986	+	0.00536121i	$0.998293\pi$
$570$		0			0
$571$	1.95913			0.0819868			0.0409934	−	0.999159i	$-0.486948\pi$
$571$	1.95913			0.0819868			0.0409934	+	0.999159i	$0.486948\pi$
$572$	−47.9010	+	28.4428i	−2.00284	+	1.18925i
$573$	2.51042			0.104874
$574$	96.2297	+	55.5583i	4.01655	+	2.31896i
$575$		0			0
$576$	−5.87451	−	10.1749i	−0.244771	−	0.423956i
$577$		−	1.22118i		−	0.0508382i	−0.999677	−	0.0254191i	$-0.991908\pi$
$577$		−	1.22118i		−	0.0508382i	0.999677	−	0.0254191i	$-0.00809202\pi$
$578$	−27.6648	+	15.9723i	−1.15071	+	0.664360i
$579$	−8.16136	+	4.71197i	−0.339175	+	0.195823i
$580$		0			0
$581$	17.4826	+	30.2808i	0.725301	+	1.25626i
$582$	13.0983	−	22.6870i	0.542943	−	0.940405i
$583$	3.01708	+	1.74191i	0.124955	+	0.0721427i
$584$	−23.9452			−0.990861
$585$		0			0
$586$	24.2671			1.00246
$587$	−25.6779	−	14.8251i	−1.05984	−	0.611898i	−0.134451	−	0.990920i	$-0.542927\pi$
$587$	−25.6779	−	14.8251i	−1.05984	−	0.611898i	−0.925388	+	0.379022i	$0.876261\pi$
$588$	24.3597	−	42.1922i	1.00458	−	1.73998i
$589$	−1.18182	−	2.04697i	−0.0486959	−	0.0843438i
$590$		0			0
$591$	−21.3578	+	12.3309i	−0.878542	+	0.507226i
$592$	6.32313	−	3.65066i	0.259879	−	0.150041i
$593$			10.2794i			0.422126i	0.977473	+	0.211063i	$0.0676925\pi$
$593$			10.2794i			0.422126i	−0.977473	+	0.211063i	$0.932308\pi$
$594$	−5.10528	−	8.84261i	−0.209472	−	0.362817i
$595$		0			0
$596$	70.7089	+	40.8238i	2.89635	+	1.67221i
$597$	25.9532			1.06219
$598$	−5.40352	−	3.03218i	−0.220967	−	0.123995i
$599$	−15.0591			−0.615296			−0.307648	−	0.951500i	$-0.599542\pi$
$599$	−15.0591			−0.615296			−0.307648	+	0.951500i	$0.599542\pi$
$600$		0			0
$601$	−10.2473	+	17.7489i	−0.417998	+	0.723993i	−0.995738	−	0.0922273i	$-0.970601\pi$
$601$	−10.2473	+	17.7489i	−0.417998	+	0.723993i	0.577740	+	0.816221i	$0.303935\pi$
$602$	58.4551	+	101.247i	2.38245	+	4.12653i
$603$		−	10.5310i		−	0.428856i
$604$	−46.0955	+	26.6132i	−1.87560	+	1.08288i
$605$		0			0
$606$		−	13.3638i		−	0.542869i
$607$	1.34177	+	2.32401i	0.0544608	+	0.0943288i	0.891971	−	0.452094i	$-0.149323\pi$
$607$	1.34177	+	2.32401i	0.0544608	+	0.0943288i	−0.837510	+	0.546422i	$0.815989\pi$
$608$	7.11620	−	12.3256i	0.288600	−	0.499870i
$609$	−15.5679	−	8.98815i	−0.630844	−	0.364218i
$610$		0			0
$611$	4.41737	−	2.62296i	0.178708	−	0.106114i
$612$	19.7376			0.797845
$613$	−9.16309	−	5.29031i	−0.370094	−	0.213674i	0.303406	−	0.952862i	$-0.401876\pi$
$613$	−9.16309	−	5.29031i	−0.370094	−	0.213674i	−0.673499	+	0.739188i	$0.735210\pi$
$614$	39.8994	−	69.1079i	1.61021	−	2.78897i
$615$		0			0
$616$		−	72.9198i		−	2.93802i
$617$	15.4896	−	8.94290i	0.623586	−	0.360028i	−0.154678	−	0.987965i	$-0.549434\pi$
$617$	15.4896	−	8.94290i	0.623586	−	0.360028i	0.778264	+	0.627937i	$0.216101\pi$
$618$	−6.65137	+	3.84017i	−0.267557	+	0.154474i
$619$			8.37677i			0.336691i	0.985728	+	0.168345i	$0.0538424\pi$
$619$			8.37677i			0.336691i	−0.985728	+	0.168345i	$0.946158\pi$
$620$		0			0
$621$	0.364011	−	0.630486i	0.0146073	−	0.0253005i
$622$	−0.586235	−	0.338463i	−0.0235059	−	0.0135711i
$623$	31.1358			1.24743
$624$	−2.84975	+	5.07842i	−0.114081	+	0.203300i
$625$		0			0
$626$	56.9001	+	32.8513i	2.27419	+	1.31300i
$627$	8.52942	−	14.7734i	0.340632	−	0.589992i
$628$	−0.885500	−	1.53373i	−0.0353353	−	0.0612025i
$629$		−	24.9795i		−	0.995999i
$630$		0			0
$631$	−30.5045	+	17.6118i	−1.21437	+	0.701114i	−0.963707	−	0.266961i	$-0.913980\pi$
$631$	−30.5045	+	17.6118i	−1.21437	+	0.701114i	−0.250659	+	0.968076i	$0.580647\pi$
$632$			15.6614i			0.622977i
$633$	5.77273	+	9.99866i	0.229445	+	0.397411i
$634$	27.8698	−	48.2719i	1.10685	−	1.91712i
$635$		0			0
$636$	2.87688			0.114076
$637$	49.1735	−	0.601771i	1.94833	−	0.0238430i
$638$	−40.4019			−1.59953
$639$	−0.898903	−	0.518982i	−0.0355600	−	0.0205306i
$640$		0			0
$641$	8.48264	+	14.6924i	0.335044	+	0.580313i	0.983493	−	0.180945i	$-0.0579155\pi$
$641$	8.48264	+	14.6924i	0.335044	+	0.580313i	−0.648449	+	0.761258i	$0.724582\pi$
$642$			34.2642i			1.35230i
$643$	39.8916	−	23.0314i	1.57317	−	0.908272i	0.577396	−	0.816464i	$-0.304069\pi$
$643$	39.8916	−	23.0314i	1.57317	−	0.908272i	0.995777	−	0.0918073i	$-0.0292644\pi$
$644$	10.2313	−	5.90707i	0.403171	−	0.232771i
$645$		0			0
$646$	25.7196	+	44.5476i	1.01192	+	1.75270i
$647$	−0.851665	+	1.47513i	−0.0334824	+	0.0579932i	−0.882281	−	0.470723i	$-0.843993\pi$
$647$	−0.851665	+	1.47513i	−0.0334824	+	0.0579932i	0.848799	+	0.528716i	$0.177326\pi$
$648$	−3.21354	−	1.85534i	−0.126240	−	0.0728846i
$649$	48.5270			1.90485
$650$		0			0
$651$	2.72285			0.106717
$652$	5.31766	+	3.07015i	0.208256	+	0.120237i
$653$	1.37739	−	2.38570i	0.0539013	−	0.0933597i	−0.837816	−	0.545953i	$-0.816168\pi$
$653$	1.37739	−	2.38570i	0.0539013	−	0.0933597i	0.891717	+	0.452593i	$0.149501\pi$
$654$	2.64749	+	4.58558i	0.103525	+	0.179310i
$655$		0			0
$656$	14.4930	−	8.36754i	0.565857	−	0.326697i
$657$	5.58852	−	3.22653i	0.218029	−	0.125879i
$658$			15.2801i			0.595680i
$659$	10.7195	+	18.5668i	0.417574	+	0.723260i	0.995695	−	0.0926917i	$-0.0295471\pi$
$659$	10.7195	+	18.5668i	0.417574	+	0.723260i	−0.578121	+	0.815951i	$0.696214\pi$
$660$		0			0
$661$	−5.93927	−	3.42904i	−0.231011	−	0.133374i	0.380027	−	0.924975i	$-0.375915\pi$
$661$	−5.93927	−	3.42904i	−0.231011	−	0.133374i	−0.611038	+	0.791601i	$0.709248\pi$
$662$	12.3190			0.478791
$663$	10.1719	+	17.1307i	0.395045	+	0.665301i
$664$	28.5589			1.10830
$665$		0			0
$666$	−5.33550	+	9.24135i	−0.206746	+	0.358095i
$667$	−1.44035	−	2.49476i	−0.0557705	−	0.0965973i
$668$			20.3042i			0.785592i
$669$	7.03409	−	4.06113i	0.271954	−	0.157012i
$670$		0			0
$671$		−	53.6489i		−	2.07109i
$672$	8.19768	+	14.1988i	0.316232	+	0.547730i
$673$	−0.450047	+	0.779505i	−0.0173481	+	0.0300477i	−0.874569	−	0.484901i	$-0.838856\pi$
$673$	−0.450047	+	0.779505i	−0.0173481	+	0.0300477i	0.857221	+	0.514949i	$0.172189\pi$
$674$	−40.6303	−	23.4579i	−1.56502	−	0.903565i
$675$		0			0
$676$	−46.4219	+	1.13636i	−1.78546	+	0.0437063i
$677$	−40.3221			−1.54970			−0.774851	−	0.632144i	$-0.782175\pi$
$677$	−40.3221			−1.54970			−0.774851	+	0.632144i	$0.782175\pi$
$678$	−3.30824	−	1.91001i	−0.127052	−	0.0733536i
$679$	−25.2092	+	43.6635i	−0.967439	+	1.67565i
$680$		0			0
$681$		−	13.5869i		−	0.520652i
$682$	5.29975	−	3.05981i	0.202938	−	0.117166i
$683$	6.91828	−	3.99427i	0.264721	−	0.152837i	−0.361765	−	0.932269i	$-0.617826\pi$
$683$	6.91828	−	3.99427i	0.264721	−	0.152837i	0.626486	+	0.779433i	$0.284493\pi$
$684$		−	14.0869i		−	0.538625i
$685$		0			0
$686$	−35.5996	+	61.6603i	−1.35920	+	2.35420i
$687$	−3.12672	−	1.80521i	−0.119292	−	0.0688731i
$688$	17.6077			0.671286
$689$	1.48262	+	2.49691i	0.0564834	+	0.0951246i
$690$		0			0
$691$	29.0446	+	16.7689i	1.10491	+	0.637919i	0.937506	−	0.347970i	$-0.113129\pi$
$691$	29.0446	+	16.7689i	1.10491	+	0.637919i	0.167402	+	0.985889i	$0.446462\pi$
$692$	12.2725	−	21.2566i	0.466530	−	0.808053i
$693$	9.82567	+	17.0186i	0.373246	+	0.646482i
$694$			4.03412i			0.153133i
$695$		0			0
$696$	−12.7156	+	7.34135i	−0.481983	+	0.278273i
$697$		−	57.2546i		−	2.16867i
$698$	18.1626	+	31.4586i	0.687465	+	1.19072i
$699$	−14.3426	+	24.8420i	−0.542486	+	0.939612i
$700$		0			0
$701$	5.96325			0.225229			0.112614	−	0.993639i	$-0.464078\pi$
$701$	5.96325			0.225229			0.112614	+	0.993639i	$0.464078\pi$
$702$	−0.104146	−	8.51029i	−0.00393075	−	0.321200i
$703$	−17.8281			−0.672399
$704$	44.0126	+	25.4107i	1.65879	+	0.957701i
$705$		0			0
$706$	−22.1986	−	38.4490i	−0.835454	−	1.44705i
$707$			25.7202i			0.967306i
$708$	34.7040	−	20.0363i	1.30425	−	0.753012i
$709$	−29.4208	+	16.9861i	−1.10492	+	0.637926i	−0.937509	−	0.347961i	$-0.886874\pi$
$709$	−29.4208	+	16.9861i	−1.10492	+	0.637926i	−0.167411	+	0.985887i	$0.553541\pi$
$710$		0			0
$711$	−2.11031	−	3.65517i	−0.0791429	−	0.137080i
$712$	12.7156	−	22.0241i	0.476537	−	0.825386i
$713$	0.377877	+	0.218168i	0.0141516	+	0.00817044i
$714$	−59.2566			−2.21762
$715$		0			0
$716$	78.2738			2.92523
$717$	−1.73556	−	1.00203i	−0.0648157	−	0.0374213i
$718$	−20.1550	+	34.9094i	−0.752177	+	1.30281i
$719$	12.0007	+	20.7858i	0.447549	+	0.775178i	0.998226	−	0.0595406i	$-0.0189636\pi$
$719$	12.0007	+	20.7858i	0.447549	+	0.775178i	−0.550677	+	0.834719i	$0.685630\pi$
$720$		0			0
$721$	12.8013	−	7.39083i	0.476745	−	0.275249i
$722$	−7.04692	+	4.06854i	−0.262259	+	0.151415i
$723$		−	28.3087i		−	1.05281i
$724$	−32.0414	−	55.4974i	−1.19081	−	2.06255i
$725$		0			0
$726$	15.7626	+	9.10054i	0.585005	+	0.337753i
$727$	26.1991			0.971672			0.485836	−	0.874050i	$-0.338515\pi$
$727$	26.1991			0.971672			0.485836	+	0.874050i	$0.338515\pi$
$728$	29.7444	−	53.0064i	1.10240	−	1.96455i
$729$	1.00000			0.0370370
$730$		0			0
$731$	30.1200	−	52.1693i	1.11403	−	1.92955i
$732$	−22.1511	−	38.3668i	−0.818728	−	1.41808i
$733$		−	49.2273i		−	1.81825i	−0.416520	−	0.909127i	$-0.636750\pi$
$733$		−	49.2273i		−	1.81825i	0.416520	−	0.909127i	$-0.363250\pi$
$734$	21.2994	−	12.2972i	0.786176	−	0.453899i
$735$		0			0
$736$			2.62735i			0.0968455i
$737$	22.7764	+	39.4499i	0.838979	+	1.45315i
$738$	−12.2293	+	21.1817i	−0.450166	+	0.779711i
$739$	1.15468	+	0.666653i	0.0424755	+	0.0245232i	0.521087	−	0.853503i	$-0.325527\pi$
$739$	1.15468	+	0.666653i	0.0424755	+	0.0245232i	−0.478612	+	0.878027i	$0.658860\pi$
$740$		0			0
$741$	12.2263	−	7.25977i	0.449144	−	0.266694i
$742$	−8.63703			−0.317075
$743$	25.8413	+	14.9195i	0.948025	+	0.547342i	0.892467	−	0.451113i	$-0.148973\pi$
$743$	25.8413	+	14.9195i	0.948025	+	0.547342i	0.0555581	+	0.998455i	$0.482306\pi$
$744$	1.11198	−	1.92601i	0.0407673	−	0.0706111i
$745$		0			0
$746$			56.8412i			2.08110i
$747$	−6.66530	+	3.84821i	−0.243870	+	0.140799i
$748$	−73.9383	+	42.6883i	−2.70345	+	1.56084i
$749$		−	65.9451i		−	2.40958i
$750$		0			0
$751$	−4.94574	+	8.56627i	−0.180473	+	0.312588i	−0.942042	−	0.335496i	$-0.891096\pi$
$751$	−4.94574	+	8.56627i	−0.180473	+	0.312588i	0.761569	+	0.648084i	$0.224429\pi$
$752$	1.99299	+	1.15065i	0.0726770	+	0.0419601i
$753$	−17.6856			−0.644499
$754$	−29.3687	−	16.4802i	−1.06955	−	0.600173i
$755$		0			0
$756$	14.0536	+	8.11385i	0.511125	+	0.295098i
$757$	−24.2455	+	41.9944i	−0.881217	+	1.52631i	−0.0312280	+	0.999512i	$0.509942\pi$
$757$	−24.2455	+	41.9944i	−0.881217	+	1.52631i	−0.849989	+	0.526800i	$0.823392\pi$
$758$	−10.4171	−	18.0430i	−0.378366	−	0.655350i
$759$			3.14912i			0.114306i
$760$		0			0
$761$	21.6052	−	12.4738i	0.783188	−	0.452174i	−0.0543707	−	0.998521i	$-0.517315\pi$
$761$	21.6052	−	12.4738i	0.783188	−	0.452174i	0.837559	+	0.546347i	$0.183982\pi$
$762$			44.0492i			1.59574i
$763$	−5.09538	−	8.82545i	−0.184465	−	0.319503i
$764$	−4.48360	+	7.76582i	−0.162211	+	0.280957i
$765$		0			0
$766$	38.2748			1.38293
$767$	35.2749	+	19.7945i	1.27370	+	0.714736i
$768$	24.9297			0.899573
$769$	7.28560	+	4.20634i	0.262725	+	0.151685i	0.625577	−	0.780162i	$-0.284864\pi$
$769$	7.28560	+	4.20634i	0.262725	+	0.151685i	−0.362852	+	0.931847i	$0.618197\pi$
$770$		0			0
$771$	9.97787	+	17.2822i	0.359344	+	0.622402i
$772$		−	33.6621i		−	1.21153i
$773$	32.3114	−	18.6550i	1.16216	−	0.670973i	0.210339	−	0.977628i	$-0.432543\pi$
$773$	32.3114	−	18.6550i	1.16216	−	0.670973i	0.951821	+	0.306655i	$0.0992098\pi$
$774$	−22.2862	+	12.8669i	−0.801061	+	0.462493i
$775$		0			0
$776$	20.5904	+	35.6636i	0.739151	+	1.28025i
$777$	10.2687	−	17.7860i	0.368389	−	0.638069i
$778$	−67.8406	−	39.1678i	−2.43220	−	1.40423i
$779$	−40.8630			−1.46407
$780$		0			0
$781$	4.48980			0.160658
$782$	−8.22365	−	4.74793i	−0.294077	−	0.169786i
$783$	1.97844	−	3.42676i	0.0707036	−	0.122462i
$784$	11.0145	+	19.0776i	0.393374	+	0.681344i
$785$		0			0
$786$	19.3343	−	11.1627i	0.689633	−	0.398160i
$787$	−17.7335	+	10.2385i	−0.632133	+	0.364962i	−0.781578	−	0.623808i	$-0.785585\pi$
$787$	−17.7335	+	10.2385i	−0.632133	+	0.364962i	0.149445	+	0.988770i	$0.452251\pi$
$788$		−	88.0918i		−	3.13814i
$789$	−1.69847	−	2.94183i	−0.0604670	−	0.104732i
$790$		0			0
$791$	6.36706	+	3.67603i	0.226387	+	0.130704i
$792$	16.0509			0.570342
$793$	21.8837	−	38.9981i	0.777113	−	1.38486i
$794$	17.7041			0.628296
$795$		0			0
$796$	−46.3522	+	80.2843i	−1.64291	+	2.84560i
$797$	−12.2660	−	21.2453i	−0.434484	−	0.752548i	0.562770	−	0.826614i	$-0.309736\pi$
$797$	−12.2660	−	21.2453i	−0.434484	−	0.752548i	−0.997253	+	0.0740660i	$0.976402\pi$
$798$			42.2919i			1.49712i
$799$	6.81850	−	3.93666i	0.241221	−	0.139269i
$800$		0			0
$801$			6.85351i			0.242157i
$802$	4.02986	+	6.97992i	0.142299	+	0.246470i
$803$	−13.9566	+	24.1736i	−0.492519	+	0.853067i
$804$	32.5770	+	18.8083i	1.14890	+	0.663318i
$805$		0			0
$806$	5.10058	−	0.0624194i	0.179660	−	0.00219863i
$807$	−15.3367			−0.539878
$808$	18.1932	+	10.5039i	0.640036	+	0.369525i
$809$	−8.38808	+	14.5286i	−0.294909	+	0.510798i	−0.974964	−	0.222364i	$-0.928623\pi$
$809$	−8.38808	+	14.5286i	−0.294909	+	0.510798i	0.680055	+	0.733161i	$0.261956\pi$
$810$		0			0
$811$			50.7808i			1.78315i	0.452869	+	0.891577i	$0.350400\pi$
$811$			50.7808i			1.78315i	−0.452869	+	0.891577i	$0.649600\pi$
$812$	55.6084	−	32.1055i	1.95147	−	1.12668i
$813$	−15.8495	+	9.15070i	−0.555865	+	0.320929i
$814$		−	46.1583i		−	1.61785i
$815$		0			0
$816$	−4.46227	+	7.72888i	−0.156211	+	0.270565i
$817$	−37.2336	−	21.4969i	−1.30264	−	0.752080i
$818$	−34.4916			−1.20597
$819$	0.200441	+	16.3790i	0.00700397	+	0.572328i
$820$		0			0
$821$	6.62188	+	3.82315i	0.231105	+	0.133429i	0.611082	−	0.791567i	$-0.290735\pi$
$821$	6.62188	+	3.82315i	0.231105	+	0.133429i	−0.379977	+	0.924996i	$0.624068\pi$
$822$	2.70326	−	4.68219i	0.0942871	−	0.163310i
$823$	−2.54563	−	4.40916i	−0.0887351	−	0.153694i	0.818242	−	0.574874i	$-0.194949\pi$
$823$	−2.54563	−	4.40916i	−0.0887351	−	0.153694i	−0.906977	+	0.421181i	$0.861616\pi$
$824$		−	12.0734i		−	0.420596i
$825$		0			0
$826$	−104.189	+	60.1535i	−3.62520	+	2.09301i
$827$			47.2400i			1.64270i	0.570426	+	0.821349i	$0.306778\pi$
$827$			47.2400i			1.64270i	−0.570426	+	0.821349i	$0.693222\pi$
$828$	1.30024	+	2.25209i	0.0451865	+	0.0782654i
$829$	5.70266	−	9.87730i	0.198062	−	0.343053i	−0.749838	−	0.661621i	$-0.769869\pi$
$829$	5.70266	−	9.87730i	0.198062	−	0.343053i	0.947900	+	0.318568i	$0.103202\pi$
$830$		0			0
$831$	7.80083			0.270608
$832$	21.6282	+	36.4244i	0.749822	+	1.26279i
$833$	75.3662			2.61128
$834$	17.1165	+	9.88224i	0.592698	+	0.342194i
$835$		0			0
$836$	30.4669	+	52.7703i	1.05372	+	1.82510i
$837$			0.599343i			0.0207163i
$838$	6.96103	−	4.01895i	0.240465	−	0.138832i
$839$	23.5533	−	13.5985i	0.813151	−	0.469473i	−0.0348977	−	0.999391i	$-0.511111\pi$
$839$	23.5533	−	13.5985i	0.813151	−	0.469473i	0.848049	+	0.529918i	$0.177777\pi$
$840$		0			0
$841$	6.67156	+	11.5555i	0.230054	+	0.398465i
$842$	17.5865	−	30.4608i	0.606072	−	1.04975i
$843$	20.1150	+	11.6134i	0.692796	+	0.399986i
$844$	−41.2402			−1.41955
$845$		0			0
$846$	−3.36340			−0.115636
$847$	−30.3368	−	17.5150i	−1.04239	−	0.601822i
$848$	−0.650404	+	1.12653i	−0.0223350	+	0.0386853i
$849$	−3.92173	−	6.79264i	−0.134593	−	0.233123i
$850$		0			0
$851$	2.85020	−	1.64556i	0.0977036	−	0.0564092i
$852$	3.21087	−	1.85379i	0.110002	−	0.0635100i
$853$			29.5962i			1.01335i	0.862136	+	0.506677i	$0.169126\pi$
$853$			29.5962i			1.01335i	−0.862136	+	0.506677i	$0.830874\pi$
$854$	66.5025	+	115.186i	2.27567	+	3.94158i
$855$		0			0
$856$	−46.6465	−	26.9314i	−1.59434	−	0.920495i
$857$	−23.3137			−0.796382			−0.398191	−	0.917302i	$-0.630362\pi$
$857$	−23.3137			−0.796382			−0.398191	+	0.917302i	$0.630362\pi$
$858$	18.7961	+	31.6548i	0.641689	+	1.08068i
$859$	46.6719			1.59242			0.796212	−	0.605018i	$-0.206834\pi$
$859$	46.6719			1.59242			0.796212	+	0.605018i	$0.206834\pi$
$860$		0			0
$861$	23.5366	−	40.7666i	0.802125	−	1.38932i
$862$	6.54645	+	11.3388i	0.222973	+	0.386200i
$863$		−	52.3597i		−	1.78234i	−0.453665	−	0.891172i	$-0.649884\pi$
$863$		−	52.3597i		−	1.78234i	0.453665	−	0.891172i	$-0.350116\pi$
$864$	−3.12539	+	1.80444i	−0.106328	+	0.0613884i
$865$		0			0
$866$		−	29.6514i		−	1.00759i
$867$	6.76647	+	11.7199i	0.229802	+	0.398028i
$868$	−4.86298	+	8.42293i	−0.165060	+	0.285893i
$869$	15.8107	+	9.12833i	0.536343	+	0.309658i
$870$		0			0
$871$	0.464632	+	37.9673i	0.0157435	+	1.28647i
$872$	−8.32362			−0.281873
$873$	−9.61107	−	5.54895i	−0.325285	−	0.187804i
$874$	−3.38863	+	5.86928i	−0.114622	+	0.198531i
$875$		0			0
$876$			23.0502i			0.778795i
$877$	−13.6960	+	7.90738i	−0.462480	+	0.267013i	−0.713087	−	0.701076i	$-0.752703\pi$
$877$	−13.6960	+	7.90738i	−0.462480	+	0.267013i	0.250606	+	0.968089i	$0.419370\pi$
$878$	−60.4839	+	34.9204i	−2.04123	+	1.17851i
$879$		−	10.2805i		−	0.346751i
$880$		0			0
$881$	21.4105	−	37.0841i	0.721338	−	1.24939i	−0.239126	−	0.970989i	$-0.576861\pi$
$881$	21.4105	−	37.0841i	0.721338	−	1.24939i	0.960464	−	0.278406i	$-0.0898059\pi$
$882$	−27.8822	−	16.0978i	−0.938844	−	0.542042i
$883$	−18.5133			−0.623024			−0.311512	−	0.950242i	$-0.600835\pi$
$883$	−18.5133			−0.623024			−0.311512	+	0.950242i	$0.600835\pi$
$884$	−71.1595	+	0.870829i	−2.39335	+	0.0292892i
$885$		0			0
$886$	−60.7044	−	35.0477i	−2.03941	−	1.17745i
$887$	−16.6949	+	28.9164i	−0.560560	+	0.970919i	0.436888	+	0.899516i	$0.356081\pi$
$887$	−16.6949	+	28.9164i	−0.560560	+	0.970919i	−0.997448	+	0.0714024i	$0.977253\pi$
$888$	−8.38732	−	14.5273i	−0.281460	−	0.487503i
$889$		−	84.7775i		−	2.84335i
$890$		0			0
$891$	−3.74607	+	2.16279i	−0.125498	+	0.0724562i
$892$			29.0126i			0.971414i
$893$	−2.80962	−	4.86641i	−0.0940205	−	0.162848i
$894$	26.9779	−	46.7272i	0.902277	−	1.56279i
$895$		0			0
$896$	−93.2045			−3.11374
$897$	−1.28455	+	2.28914i	−0.0428897	+	0.0764321i
$898$	−26.0403			−0.868977
$899$	2.05380	+	1.18576i	0.0684981	+	0.0395474i
$900$		0			0
$901$	2.22519	+	3.85413i	0.0741317	+	0.128400i
$902$		−	105.798i		−	3.52267i
$903$	42.8922	−	24.7638i	1.42736	−	0.824089i
$904$	5.20050	−	3.00251i	0.172966	−	0.0998620i
$905$		0			0
$906$	17.5870	+	30.4617i	0.584291	+	1.01202i
$907$	16.5197	−	28.6130i	0.548528	−	0.950078i	−0.449848	−	0.893105i	$-0.648522\pi$
$907$	16.5197	−	28.6130i	0.548528	−	0.950078i	0.998376	−	0.0569728i	$-0.0181448\pi$
$908$	42.0302	+	24.2661i	1.39482	+	0.805300i
$909$	−5.66143			−0.187778
$910$		0			0
$911$	−7.00701			−0.232153			−0.116076	−	0.993240i	$-0.537032\pi$
$911$	−7.00701			−0.232153			−0.116076	+	0.993240i	$0.537032\pi$
$912$	5.51616	+	3.18476i	0.182658	+	0.105458i
$913$	16.6458	−	28.8313i	0.550894	−	0.954176i
$914$	−16.8020	−	29.1019i	−0.555760	−	0.962604i
$915$		0			0
$916$	11.1686	−	6.44819i	0.369021	−	0.213054i
$917$	−37.2110	+	21.4838i	−1.22882	+	0.709458i
$918$		−	13.0434i		−	0.430495i
$919$	−5.28827	−	9.15956i	−0.174444	−	0.302146i	0.765525	−	0.643406i	$-0.222479\pi$
$919$	−5.28827	−	9.15956i	−0.174444	−	0.302146i	−0.939969	+	0.341261i	$0.889146\pi$
$920$		0			0
$921$	−29.2767	−	16.9029i	−0.964701	−	0.556970i
$922$	−52.7721			−1.73796
$923$	3.26369	+	1.83141i	0.107426	+	0.0602818i
$924$	−70.1943			−2.30922
$925$		0			0
$926$	−35.3742	+	61.2698i	−1.16247	+	2.01345i
$927$	1.62684	+	2.81777i	0.0534325	+	0.0925478i
$928$			14.2799i			0.468762i
$929$	−12.6230	+	7.28788i	−0.414147	+	0.239108i	−0.692570	−	0.721351i	$-0.743522\pi$
$929$	−12.6230	+	7.28788i	−0.414147	+	0.239108i	0.278423	+	0.960459i	$0.410188\pi$
$930$		0			0
$931$		−	53.7894i		−	1.76288i
$932$	−51.2314	−	88.7354i	−1.67814	−	2.90663i
$933$	−0.143386	+	0.248351i	−0.00469424	+	0.00813066i
$934$	35.4864	+	20.4881i	1.16115	+	0.670391i
$935$		0			0
$936$	11.6676	+	6.54724i	0.381367	+	0.214003i
$937$	−2.03451			−0.0664644			−0.0332322	−	0.999448i	$-0.510580\pi$
$937$	−2.03451			−0.0664644			−0.0332322	+	0.999448i	$0.510580\pi$
$938$	−97.8033	−	56.4668i	−3.19339	−	1.84370i
$939$	13.9171	−	24.1051i	0.454166	−	0.786639i
$940$		0			0
$941$		−	15.6270i		−	0.509424i	−0.967017	−	0.254712i	$-0.918019\pi$
$941$		−	15.6270i		−	0.509424i	0.967017	−	0.254712i	$-0.0819807\pi$
$942$	−1.01355	+	0.585173i	−0.0330232	+	0.0190660i
$943$	6.53283	−	3.77173i	0.212738	−	0.122824i
$944$			18.1192i			0.589731i
$945$		0			0
$946$	55.6570	−	96.4008i	1.80957	−	3.13426i
$947$	30.4622	+	17.5874i	0.989890	+	0.571513i	0.905241	−	0.424898i	$-0.139690\pi$
$947$	30.4622	+	17.5874i	0.989890	+	0.571513i	0.0846485	+	0.996411i	$0.473023\pi$
$948$	15.0760			0.489646
$949$	−20.0058	+	11.8791i	−0.649416	+	0.385612i
$950$		0			0
$951$	−20.4498	−	11.8067i	−0.663130	−	0.382858i
$952$	46.5753	−	80.6707i	1.50951	−	2.61455i
$953$	1.59492	+	2.76248i	0.0516645	+	0.0894855i	0.890701	−	0.454589i	$-0.150214\pi$
$953$	1.59492	+	2.76248i	0.0516645	+	0.0894855i	−0.839037	+	0.544075i	$0.816881\pi$
$954$		−	1.90115i		−	0.0615521i
$955$		0			0
$956$	6.19939	−	3.57922i	0.200503	−	0.115760i
$957$			17.1158i			0.553275i
$958$	−12.0706	−	20.9069i	−0.389983	−	0.675470i
$959$	−5.20272	+	9.01138i	−0.168005	+	0.290993i
$960$		0			0
$961$	30.6408			0.988413
$962$	18.8282	−	33.5531i	0.607047	−	1.08179i
$963$	14.5156			0.467759
$964$	87.5710	+	50.5591i	2.82047	+	1.62840i
$965$		0			0
$966$	−3.90362	−	6.76126i	−0.125597	−	0.217540i
$967$		−	19.5885i		−	0.629925i	−0.949104	−	0.314962i	$-0.898008\pi$
$967$		−	19.5885i		−	0.629925i	0.949104	−	0.314962i	$-0.101992\pi$
$968$	−24.7786	+	14.3059i	−0.796414	+	0.459810i
$969$	18.8721	−	10.8958i	0.606258	−	0.350023i
$970$		0			0
$971$	9.75194	+	16.8909i	0.312955	+	0.542053i	0.979001	−	0.203857i	$-0.0653479\pi$
$971$	9.75194	+	16.8909i	0.312955	+	0.542053i	−0.666046	+	0.745911i	$0.732015\pi$
$972$	−1.78599	+	3.09343i	−0.0572857	+	0.0992218i
$973$	−32.9427	−	19.0195i	−1.05609	−	0.609736i
$974$	−38.8842			−1.24593
$975$		0			0
$976$	20.0317			0.641198
$977$	9.84958	+	5.68666i	0.315116	+	0.181932i	0.649213	−	0.760606i	$-0.275098\pi$
$977$	9.84958	+	5.68666i	0.315116	+	0.181932i	−0.334098	+	0.942538i	$0.608432\pi$
$978$	2.02888	−	3.51412i	0.0648763	−	0.112369i
$979$	−14.8227	−	25.6737i	−0.473736	−	0.820535i
$980$		0			0
$981$	1.94263	−	1.12158i	0.0620233	−	0.0358092i
$982$	58.4278	−	33.7333i	1.86451	−	1.07647i
$983$		−	29.0243i		−	0.925732i	−0.886428	−	0.462866i	$-0.846821\pi$
$983$		−	29.0243i		−	0.925732i	0.886428	−	0.462866i	$-0.153179\pi$
$984$	−19.2243	−	33.2974i	−0.612847	−	1.06148i
$985$		0			0
$986$	−44.6964	−	25.8055i	−1.42342	−	0.821814i
$987$	6.47323			0.206045
$988$	0.621517	+	50.7871i	0.0197731	+	1.61575i
$989$	7.93679			0.252375
$990$		0			0
$991$	5.12446	−	8.87583i	0.162784	−	0.281950i	−0.773082	−	0.634306i	$-0.781286\pi$
$991$	5.12446	−	8.87583i	0.162784	−	0.281950i	0.935866	+	0.352356i	$0.114619\pi$
$992$	−1.08148	−	1.87318i	−0.0343371	−	0.0594735i
$993$		−	5.21879i		−	0.165613i
$994$	−9.63973	+	5.56550i	−0.305754	+	0.176527i
$995$		0			0
$996$		−	27.4915i		−	0.871101i
$997$	7.24112	+	12.5420i	0.229328	+	0.397209i	0.957609	−	0.288070i	$-0.0930137\pi$
$997$	7.24112	+	12.5420i	0.229328	+	0.397209i	−0.728281	+	0.685279i	$0.759680\pi$
$998$	17.2916	−	29.9499i	0.547356	−	0.948048i
$999$	3.91499	+	2.26032i	0.123865	+	0.0715134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bc.l.901.6	yes	12
5.2	odd	4		975.2.w.k.199.2		24
5.3	odd	4		975.2.w.k.199.11		24
5.4	even	2		975.2.bc.k.901.1	yes	12
13.10	even	6	inner	975.2.bc.l.751.6	yes	12
65.23	odd	12		975.2.w.k.49.2		24
65.49	even	6		975.2.bc.k.751.1	✓	12
65.62	odd	12		975.2.w.k.49.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.w.k.49.2		24	65.23	odd	12
975.2.w.k.49.11		24	65.62	odd	12
975.2.w.k.199.2		24	5.2	odd	4
975.2.w.k.199.11		24	5.3	odd	4
975.2.bc.k.751.1	✓	12	65.49	even	6
975.2.bc.k.901.1	yes	12	5.4	even	2
975.2.bc.l.751.6	yes	12	13.10	even	6	inner
975.2.bc.l.901.6	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.04426 + 1.18025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(1.78599 + 3.09343i) q^{4} +(2.04426 - 1.18025i) q^{6} +(-3.93440 + 2.27152i) q^{7} +3.71068i q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.74607 + 2.16279i) q^{11} +3.57199 q^{12} +(1.84085 + 3.10021i) q^{13} -10.7239 q^{14} +(-0.807554 + 1.39872i) q^{16} +(2.76283 + 4.78536i) q^{17} -2.36051i q^{18} +(3.41535 - 1.97185i) q^{19} +4.54305i q^{21} +(5.10528 + 8.84261i) q^{22} +(-0.364011 + 0.630486i) q^{23} +(3.21354 + 1.85534i) q^{24} +(0.104146 + 8.51029i) q^{26} -1.00000 q^{27} +(-14.0536 - 8.11385i) q^{28} +(-1.97844 + 3.42676i) q^{29} -0.599343i q^{31} +(3.12539 - 1.80444i) q^{32} +(3.74607 - 2.16279i) q^{33} +13.0434i q^{34} +(1.78599 - 3.09343i) q^{36} +(-3.91499 - 2.26032i) q^{37} +9.30914 q^{38} +(3.60528 - 0.0441204i) q^{39} +(-8.97339 - 5.18079i) q^{41} +(-5.36195 + 9.28716i) q^{42} +(-5.45093 - 9.44128i) q^{43} +15.4509i q^{44} +(-1.48827 + 0.859250i) q^{46} -1.42486i q^{47} +(0.807554 + 1.39872i) q^{48} +(6.81965 - 11.8120i) q^{49} +5.52566 q^{51} +(-6.30252 + 11.2315i) q^{52} +0.805400 q^{53} +(-2.04426 - 1.18025i) q^{54} +(-8.42890 - 14.5993i) q^{56} -3.94371i q^{57} +(-8.08888 + 4.67012i) q^{58} +(9.71559 - 5.60930i) q^{59} +(-6.20134 - 10.7410i) q^{61} +(0.707376 - 1.22521i) q^{62} +(3.93440 + 2.27152i) q^{63} +11.7490 q^{64} +10.2106 q^{66} +(9.12013 + 5.26551i) q^{67} +(-9.86879 + 17.0933i) q^{68} +(0.364011 + 0.630486i) q^{69} +(0.898903 - 0.518982i) q^{71} +(3.21354 - 1.85534i) q^{72} +6.45306i q^{73} +(-5.33550 - 9.24135i) q^{74} +(12.1996 + 7.04343i) q^{76} -19.6513 q^{77} +(7.42220 + 4.16495i) q^{78} +4.22063 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-12.2293 - 21.1817i) q^{82} -7.69642i q^{83} +(-14.0536 + 8.11385i) q^{84} -25.7339i q^{86} +(1.97844 + 3.42676i) q^{87} +(-8.02543 + 13.9004i) q^{88} +(-5.93532 - 3.42676i) q^{89} +(-14.2848 - 8.01590i) q^{91} -2.60048 q^{92} +(-0.519046 - 0.299672i) q^{93} +(1.68170 - 2.91279i) q^{94} -3.60889i q^{96} +(9.61107 - 5.54895i) q^{97} +(27.8822 - 16.0978i) q^{98} -4.32558i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 8 q^{4} - 3 q^{7} - 6 q^{9} + 9 q^{11} + 16 q^{12} - 3 q^{13} + 10 q^{14} - 4 q^{16} - 9 q^{19} + 15 q^{22} + q^{23} - 5 q^{26} - 12 q^{27} - 39 q^{28} - 16 q^{29} + 30 q^{32} + 9 q^{33}+ \cdots + 105 q^{98}+O(q^{100}) \) 12 * q + 6 * q^3 + 8 * q^4 - 3 * q^7 - 6 * q^9 + 9 * q^11 + 16 * q^12 - 3 * q^13 + 10 * q^14 - 4 * q^16 - 9 * q^19 + 15 * q^22 + q^23 - 5 * q^26 - 12 * q^27 - 39 * q^28 - 16 * q^29 + 30 * q^32 + 9 * q^33 + 8 * q^36 - 15 * q^37 + 30 * q^38 - 3 * q^39 + 18 * q^41 + 5 * q^42 + q^43 - 45 * q^46 + 4 * q^48 + 31 * q^49 - 40 * q^52 - 16 * q^53 + 25 * q^56 - 30 * q^58 + 54 * q^59 - 11 * q^61 - 20 * q^62 + 3 * q^63 + 16 * q^64 + 30 * q^66 + 45 * q^67 - 30 * q^68 - q^69 - 33 * q^71 + 5 * q^74 - 27 * q^76 - 28 * q^77 + 20 * q^78 + 18 * q^79 - 6 * q^81 - 20 * q^82 - 39 * q^84 + 16 * q^87 - 5 * q^88 - 48 * q^89 - 29 * q^91 + 46 * q^92 - 12 * q^93 - 30 * q^94 - 9 * q^97 + 105 * q^98

Introduction

L-functions

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