LMFDB - Embedded newform 975.2.bc.k.751.1

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			751.1
Root			$2.36051i$ of defining polynomial
Character	$\chi$	$=$	975.751
Dual form			975.2.bc.k.901.1

$q$-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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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	$-0.980947\pi$
$2$	−2.04426	+	1.18025i	−1.44551	+	0.834565i	−0.447299	+	0.894384i	$0.647614\pi$
$3$	−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	$-0.00469555\pi$
$7$	3.93440	+	2.27152i	1.48706	+	0.858556i	0.487171	+	0.873307i	$0.338029\pi$
$8$			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	0.185677	−	0.982611i	$-0.440552\pi$
$11$	3.74607	−	2.16279i	1.12948	−	0.652106i	0.943804	+	0.330505i	$0.107219\pi$
$12$	−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	0.307795	+	0.951453i	$0.400409\pi$
$17$	−2.76283	+	4.78536i	−0.670085	+	1.16062i	−0.977880	+	0.209169i	$0.932924\pi$
$18$		−	2.36051i		−	0.556376i
$19$	3.41535	+	1.97185i	0.783535	+	0.452374i	0.837682	−	0.546159i	$-0.183910\pi$
$19$	3.41535	+	1.97185i	0.783535	+	0.452374i	−0.0541466	+	0.998533i	$0.517244\pi$
$20$		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	$-0.142483\pi$
$23$	0.364011	+	0.630486i	0.0759016	+	0.131465i	−0.825576	+	0.564290i	$0.809150\pi$
$24$	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	0.621769	−	0.783200i	$-0.286414\pi$
$29$	−1.97844	−	3.42676i	−0.367387	−	0.636333i	−0.989156	+	0.146868i	$0.953081\pi$
$30$		0			0
$31$			0.599343i			0.107645i	0.998551	+	0.0538226i	$0.0171405\pi$
$31$			0.599343i			0.107645i	−0.998551	+	0.0538226i	$0.982859\pi$
$32$	−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	$-0.545478\pi$
$37$	3.91499	−	2.26032i	0.643620	−	0.371594i	0.786008	+	0.618217i	$0.212145\pi$
$38$	−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	−0.994537	−	0.104382i	$-0.966714\pi$
$41$	−8.97339	+	5.18079i	−1.40141	+	0.809104i	−0.406871	+	0.913485i	$0.633380\pi$
$42$	5.36195	+	9.28716i	0.827366	+	1.43304i
$43$	5.45093	−	9.44128i	0.831258	−	1.43978i	−0.0657822	−	0.997834i	$-0.520954\pi$
$43$	5.45093	−	9.44128i	0.831258	−	1.43978i	0.897041	−	0.441948i	$-0.145712\pi$
$44$		−	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	$-0.517616\pi$
$53$	−0.805400			−0.110630			−0.0553151	+	0.998469i	$0.517616\pi$
$54$	−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	0.974011	−	0.226499i	$-0.0727282\pi$
$59$	9.71559	+	5.60930i	1.26486	+	0.730269i	0.290851	+	0.956768i	$0.406061\pi$
$60$		0			0
$61$	−6.20134	+	10.7410i	−0.794001	+	1.37525i	0.129471	+	0.991583i	$0.458672\pi$
$61$	−6.20134	+	10.7410i	−0.794001	+	1.37525i	−0.923472	+	0.383666i	$0.874661\pi$
$62$	−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	$-0.889095\pi$
$67$	−9.12013	+	5.26551i	−1.11420	+	0.643284i	−0.174287	+	0.984695i	$0.555762\pi$
$68$	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	0.552391	−	0.833585i	$-0.313716\pi$
$71$	0.898903	+	0.518982i	0.106680	+	0.0615918i	−0.445711	+	0.895177i	$0.647049\pi$
$72$	−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	−0.780420	−	0.625256i	$-0.784995\pi$
$89$	−5.93532	+	3.42676i	−0.629142	+	0.363235i	0.151278	+	0.988491i	$0.451661\pi$
$90$		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	$-0.523844\pi$
$97$	−9.61107	−	5.54895i	−0.975856	−	0.563411i	−0.901016	+	0.433785i	$0.857178\pi$
$98$	−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	0.971795	−	0.235826i	$-0.0757794\pi$
$101$	2.83072	+	4.90294i	0.281667	+	0.487861i	−0.690129	+	0.723687i	$0.742446\pi$
$102$	−11.2959	+	6.52168i	−1.11846	+	0.645742i
$103$	3.25369			0.320595			0.160298	−	0.987069i	$-0.448755\pi$
$103$	3.25369			0.320595			0.160298	+	0.987069i	$0.448755\pi$
$104$	−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	0.967891	+	0.251370i	$0.0808809\pi$
$107$	7.25780	+	12.5709i	0.701638	+	1.21527i	−0.266253	+	0.963903i	$0.585786\pi$
$108$	1.78599	−	3.09343i	0.171857	−	0.297665i
$109$		−	2.24315i		−	0.214855i	−0.994213	−	0.107428i	$-0.965739\pi$
$109$		−	2.24315i		−	0.214855i	0.994213	−	0.107428i	$-0.0342614\pi$
$110$		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	$-0.809081\pi$
$113$	0.809154	−	1.40150i	0.0761188	−	0.131842i	0.901572	+	0.432629i	$0.142414\pi$
$114$	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	0.899648	+	0.436617i	$0.143823\pi$
$127$	9.33047	+	16.1608i	0.827945	+	1.43404i	−0.0717028	+	0.997426i	$0.522843\pi$
$128$	−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	$-0.364527\pi$
$137$	−1.98355	−	1.14520i	−0.169466	−	0.0978414i	−0.582334	+	0.812950i	$0.697860\pi$
$138$			1.71850i			0.146288i
$139$	4.18650	−	7.25122i	0.355094	−	0.615041i	−0.632040	−	0.774936i	$-0.717782\pi$
$139$	4.18650	−	7.25122i	0.355094	−	0.615041i	0.987134	+	0.159895i	$0.0511156\pi$
$140$		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	0.986465	+	0.163974i	$0.0524315\pi$
$149$	19.7954	+	11.4289i	1.62170	+	0.936291i	0.635238	+	0.772316i	$0.280902\pi$
$150$		0			0
$151$		−	14.9011i		−	1.21263i	−0.795223	−	0.606317i	$-0.792646\pi$
$151$		−	14.9011i		−	1.21263i	0.795223	−	0.606317i	$-0.207354\pi$
$152$	−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	$-0.493702\pi$
$157$	0.495803			0.0395694			0.0197847	+	0.999804i	$0.493702\pi$
$158$	−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	$-0.354779\pi$
$163$	−1.48871	−	0.859509i	−0.116605	−	0.0673220i	−0.557168	+	0.830400i	$0.688112\pi$
$164$			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	$-0.737250\pi$
$167$	−4.92273	+	2.84214i	−0.380933	+	0.219932i	0.297291	+	0.954787i	$0.403917\pi$
$168$	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	$-0.749210\pi$
$173$	3.43576	−	5.95091i	0.261216	−	0.452439i	0.966565	+	0.256421i	$0.0825432\pi$
$174$		−	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	0.906466	+	0.422278i	$0.138769\pi$
$179$	10.9566	+	18.9774i	0.818937	+	1.41844i	−0.0875295	+	0.996162i	$0.527897\pi$
$180$		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	−0.817034	−	0.576589i	$-0.804383\pi$
$191$	1.25521	−	2.17409i	0.0908239	−	0.157312i	0.907858	+	0.419278i	$0.137717\pi$
$192$	−5.87451	−	10.1749i	−0.423956	−	0.734313i
$193$	8.16136	−	4.71197i	0.587468	−	0.339175i	−0.176628	−	0.984278i	$-0.556519\pi$
$193$	8.16136	−	4.71197i	0.587468	−	0.339175i	0.764096	+	0.645103i	$0.223186\pi$
$194$	26.1967			1.88081
$195$		0			0
$196$	48.7194			3.47996
$197$	21.3578	−	12.3309i	1.52168	−	0.878542i	0.522007	−	0.852941i	$-0.325183\pi$
$197$	21.3578	−	12.3309i	1.52168	−	0.878542i	0.999672	−	0.0256008i	$-0.00814988\pi$
$198$	−5.10528	−	8.84261i	−0.362817	−	0.628417i
$199$	12.9766	−	22.4761i	0.919886	−	1.59329i	0.120300	−	0.992738i	$-0.461614\pi$
$199$	12.9766	−	22.4761i	0.919886	−	1.59329i	0.799586	−	0.600552i	$-0.205052\pi$
$200$		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	0.595994	−	0.802989i	$-0.296758\pi$
$211$	−5.77273	−	9.99866i	−0.397411	−	0.688336i	−0.993406	+	0.114652i	$0.963425\pi$
$212$	−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	$-0.754336\pi$
$223$	−7.03409	+	4.06113i	−0.471037	+	0.271954i	0.245636	+	0.969362i	$0.421003\pi$
$224$	−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	$-0.482229\pi$
$227$	−11.7666	−	6.79346i	−0.780978	−	0.450898i	−0.836777	+	0.547544i	$0.815563\pi$
$228$	−12.1996	−	7.04343i	−0.807937	−	0.466463i
$229$			3.61042i			0.238583i	0.992859	+	0.119292i	$0.0380624\pi$
$229$			3.61042i			0.238583i	−0.992859	+	0.119292i	$0.961938\pi$
$230$		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	$-0.111186\pi$
$233$	28.6851			1.87922			0.939612	+	0.342240i	$0.111186\pi$
$234$	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	$0.0206459\pi$
$239$			2.00405i			0.129631i	−0.997897	+	0.0648157i	$0.979354\pi$
$240$		0			0
$241$	24.5161	+	14.1544i	1.57922	+	0.911762i	0.994969	+	0.100188i	$0.0319445\pi$
$241$	24.5161	+	14.1544i	1.57922	+	0.911762i	0.584250	+	0.811574i	$0.301389\pi$
$242$			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	0.439498	+	0.898243i	$0.355156\pi$
$251$	−8.84280	+	15.3162i	−0.558152	+	0.966748i	−0.997651	+	0.0685050i	$0.978177\pi$
$252$			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	0.989037	+	0.147668i	$0.0471766\pi$
$257$	9.97787	+	17.2822i	0.622402	+	1.07803i	−0.366635	+	0.930365i	$0.619490\pi$
$258$	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	$-0.200065\pi$
$263$	−1.69847	−	2.94183i	−0.104732	−	0.181401i	−0.913629	+	0.406550i	$0.866732\pi$
$264$	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	−0.999312	−	0.0370755i	$-0.988196\pi$
$269$	−7.66836	+	13.2820i	−0.467548	+	0.809817i	0.531765	+	0.846892i	$0.321529\pi$
$270$		0			0
$271$	−15.8495	+	9.15070i	−0.962787	+	0.555865i	−0.897030	−	0.441970i	$-0.854280\pi$
$271$	−15.8495	+	9.15070i	−0.962787	+	0.555865i	−0.0657572	+	0.997836i	$0.520946\pi$
$272$	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	$-0.908631\pi$
$277$	−3.90042	+	6.75572i	−0.234353	+	0.405912i	0.724731	+	0.689032i	$0.241964\pi$
$278$			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	$-0.756379\pi$
$281$		−	23.2268i		−	1.38559i	0.721134	−	0.692796i	$-0.243621\pi$
$282$	1.68170	−	2.91279i	0.100144	−	0.173454i
$283$	−3.92173	−	6.79264i	−0.233123	−	0.403780i	0.725603	−	0.688114i	$-0.241561\pi$
$283$	−3.92173	−	6.79264i	−0.233123	−	0.403780i	−0.958725	+	0.284333i	$0.908228\pi$
$284$	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	$-0.430419\pi$
$293$	−8.90314	−	5.14023i	−0.520127	−	0.300296i	−0.736987	+	0.675907i	$0.763752\pi$
$294$			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	$-0.788181\pi$
$313$	−27.8341			−1.57328			−0.786639	+	0.617413i	$0.788181\pi$
$314$	−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	0.619041	−	0.785359i	$-0.287522\pi$
$331$	4.51960	+	2.60939i	0.248420	+	0.143425i	−0.370621	+	0.928784i	$0.620855\pi$
$332$	−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	$-0.317918\pi$
$337$	19.8753			1.08268			0.541339	+	0.840804i	$0.317918\pi$
$338$	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	$-0.847940\pi$
$347$	−0.854503	+	1.48004i	−0.0458721	+	0.0794529i	0.842178	+	0.539200i	$0.181273\pi$
$348$	7.06695	+	12.2403i	0.378828	+	0.656150i
$349$	13.3270	−	7.69437i	0.713380	−	0.411870i	−0.0989311	−	0.995094i	$-0.531542\pi$
$349$	13.3270	−	7.69437i	0.713380	−	0.411870i	0.812311	+	0.583224i	$0.198209\pi$
$350$		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	$-0.499804\pi$
$353$	16.2885	−	9.40416i	0.866948	−	0.500533i	0.866333	+	0.499467i	$0.166471\pi$
$354$	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	$-0.851196\pi$
$359$		−	17.0768i		−	0.901280i	0.892706	−	0.450640i	$-0.148804\pi$
$360$		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	$-0.254331\pi$
$367$	−5.20957	−	9.02325i	−0.271938	−	0.471010i	−0.969358	+	0.245653i	$0.920998\pi$
$368$	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	0.365437	+	0.930836i	$0.380920\pi$
$373$	−12.0400	+	20.8540i	−0.623410	+	1.07978i	−0.988846	+	0.148941i	$0.952414\pi$
$374$	−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	−0.683299	−	0.730139i	$-0.739455\pi$
$379$	−7.64369	+	4.41308i	−0.392630	+	0.226685i	0.290669	+	0.956824i	$0.406122\pi$
$380$		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	$-0.469295\pi$
$383$	−14.0423	−	8.10734i	−0.717529	−	0.414266i	−0.813843	+	0.581085i	$0.802628\pi$
$384$	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	$-0.393602\pi$
$397$	−6.49531	−	3.75007i	−0.325990	−	0.188211i	−0.654060	+	0.756443i	$0.726935\pi$
$398$			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	−0.424348	−	0.905499i	$-0.639497\pi$
$401$	2.95696	−	1.70720i	0.147664	−	0.0852536i	0.572011	+	0.820246i	$0.306163\pi$
$402$	−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	0.153375	−	0.988168i	$-0.450986\pi$
$409$	−12.6543	−	7.30598i	−0.625716	−	0.361257i	−0.779091	+	0.626911i	$0.784319\pi$
$410$		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	0.904613	−	0.426234i	$-0.140160\pi$
$419$	1.70258	+	2.94896i	0.0831765	+	0.144066i	−0.821436	+	0.570300i	$0.806827\pi$
$420$		0			0
$421$			14.9006i			0.726213i	0.931748	+	0.363107i	$0.118284\pi$
$421$			14.9006i			0.726213i	−0.931748	+	0.363107i	$0.881716\pi$
$422$	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	−0.379829	−	0.925057i	$-0.624017\pi$
$431$	4.80354	−	2.77332i	0.231378	−	0.133586i	0.611208	+	0.791470i	$0.290684\pi$
$432$	−0.807554	−	1.39872i	−0.0388535	−	0.0672962i
$433$	6.28072	−	10.8785i	0.301832	−	0.522789i	−0.674719	−	0.738075i	$-0.735735\pi$
$433$	6.28072	−	10.8785i	0.301832	−	0.522789i	0.976551	+	0.215286i	$0.0690684\pi$
$434$		−	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	−0.966308	−	0.257390i	$-0.917138\pi$
$439$	−14.7936	−	25.6233i	−0.706060	−	1.22293i	0.260248	−	0.965542i	$-0.416196\pi$
$440$		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	$-0.250755\pi$
$443$	29.6951			1.41086			0.705428	+	0.708781i	$0.250755\pi$
$444$	−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	0.257329	−	0.966324i	$-0.417158\pi$
$449$	−9.55371	−	5.51584i	−0.450867	−	0.260308i	−0.708196	+	0.706015i	$0.750491\pi$
$450$		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	$-0.558618\pi$
$457$	12.3287	−	7.11796i	0.576711	−	0.332964i	0.759825	+	0.650128i	$0.225285\pi$
$458$	−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	−0.0239731	−	0.999713i	$-0.507632\pi$
$461$	−19.3611	−	11.1781i	−0.901736	−	0.520618i	−0.877763	+	0.479095i	$0.840965\pi$
$462$	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	$-0.631560\pi$
$467$	−17.3591			−0.803282			−0.401641	+	0.915797i	$0.631560\pi$
$468$	−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	−0.688503	−	0.725233i	$-0.741732\pi$
$479$	−8.85694	+	5.11356i	−0.404684	+	0.233644i	0.283819	+	0.958878i	$0.408399\pi$
$480$		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	$-0.211584\pi$
$487$	14.2659	+	8.23642i	0.646449	+	0.373228i	−0.140645	+	0.990060i	$0.544918\pi$
$488$	−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	0.984317	+	0.176407i	$0.0564473\pi$
$491$	14.2907	+	24.7523i	0.644931	+	1.11705i	−0.339386	+	0.940647i	$0.610219\pi$
$492$	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	$0.106351\pi$
$499$			14.6508i			0.655858i	−0.944702	+	0.327929i	$0.893649\pi$
$500$		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	$-0.816126\pi$
$503$	1.21181	−	2.09892i	0.0540320	−	0.0935861i	0.891776	+	0.452477i	$0.149459\pi$
$504$	−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	−0.748816	−	0.662778i	$-0.769377\pi$
$509$	−12.3914	+	7.15420i	−0.549240	+	0.317104i	0.199575	+	0.979883i	$0.436044\pi$
$510$		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	$-0.0738407\pi$
$523$	6.57502	+	11.3883i	0.287505	+	0.497974i	−0.685708	+	0.727877i	$0.740507\pi$
$524$	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	$-0.865848\pi$
$541$		−	19.0301i		−	0.818169i	0.912496	−	0.409085i	$-0.134152\pi$
$542$	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	$-0.350944\pi$
$547$	21.1122			0.902694			0.451347	+	0.892348i	$0.350944\pi$
$548$	−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	$-0.735708\pi$
$557$	−8.79709	+	5.07900i	−0.372745	+	0.215204i	0.301912	+	0.953336i	$0.402375\pi$
$558$	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	$-0.935273\pi$
$563$	−7.46961	+	12.9377i	−0.314807	+	0.545261i	0.664590	+	0.747208i	$0.268606\pi$
$564$			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	−0.999986	−	0.00536121i	$-0.998293\pi$
$569$	−12.0374	−	20.8495i	−0.504636	−	0.874055i	0.495350	−	0.868694i	$-0.335040\pi$
$570$		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	$-0.457073\pi$
$587$	25.6779	−	14.8251i	1.05984	−	0.611898i	0.925388	+	0.379022i	$0.123739\pi$
$588$	−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	0.577740	−	0.816221i	$-0.303935\pi$
$601$	−10.2473	−	17.7489i	−0.417998	−	0.723993i	−0.995738	+	0.0922273i	$0.970601\pi$
$602$	−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	$-0.850677\pi$
$607$	−1.34177	+	2.32401i	−0.0544608	+	0.0943288i	0.837510	+	0.546422i	$0.184011\pi$
$608$	−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	$-0.598124\pi$
$613$	9.16309	−	5.29031i	0.370094	−	0.213674i	0.673499	+	0.739188i	$0.264790\pi$
$614$	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	$-0.450566\pi$
$617$	−15.4896	−	8.94290i	−0.623586	−	0.360028i	−0.778264	+	0.627937i	$0.783899\pi$
$618$	6.65137	+	3.84017i	0.267557	+	0.154474i
$619$		−	8.37677i		−	0.336691i	−0.985728	−	0.168345i	$-0.946158\pi$
$619$		−	8.37677i		−	0.336691i	0.985728	−	0.168345i	$-0.0538424\pi$
$620$		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	−0.250659	−	0.968076i	$-0.580647\pi$
$631$	−30.5045	−	17.6118i	−1.21437	−	0.701114i	−0.963707	+	0.266961i	$0.913980\pi$
$632$			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	−0.648449	−	0.761258i	$-0.724582\pi$
$641$	8.48264	−	14.6924i	0.335044	−	0.580313i	0.983493	+	0.180945i	$0.0579155\pi$
$642$			34.2642i			1.35230i
$643$	−39.8916	−	23.0314i	−1.57317	−	0.908272i	−0.995777	−	0.0918073i	$-0.970736\pi$
$643$	−39.8916	−	23.0314i	−1.57317	−	0.908272i	−0.577396	−	0.816464i	$-0.695931\pi$
$644$	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	$-0.156007\pi$
$647$	0.851665	+	1.47513i	0.0334824	+	0.0579932i	−0.848799	+	0.528716i	$0.822674\pi$
$648$	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	$-0.183832\pi$
$653$	−1.37739	−	2.38570i	−0.0539013	−	0.0933597i	−0.891717	+	0.452593i	$0.850499\pi$
$654$	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	−0.578121	−	0.815951i	$-0.696214\pi$
$659$	10.7195	−	18.5668i	0.417574	−	0.723260i	0.995695	+	0.0926917i	$0.0295471\pi$
$660$		0			0
$661$	−5.93927	+	3.42904i	−0.231011	+	0.133374i	−0.611038	−	0.791601i	$-0.709248\pi$
$661$	−5.93927	+	3.42904i	−0.231011	+	0.133374i	0.380027	+	0.924975i	$0.375915\pi$
$662$	−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	$-0.161144\pi$
$673$	0.450047	+	0.779505i	0.0173481	+	0.0300477i	−0.857221	+	0.514949i	$0.827811\pi$
$674$	−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	$-0.217825\pi$
$677$	40.3221			1.54970			0.774851	+	0.632144i	$0.217825\pi$
$678$	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	$-0.382174\pi$
$683$	−6.91828	−	3.99427i	−0.264721	−	0.152837i	−0.626486	+	0.779433i	$0.715507\pi$
$684$			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	0.167402	−	0.985889i	$-0.446462\pi$
$691$	29.0446	−	16.7689i	1.10491	−	0.637919i	0.937506	+	0.347970i	$0.113129\pi$
$692$	−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	−0.167411	−	0.985887i	$-0.553541\pi$
$709$	−29.4208	−	16.9861i	−1.10492	−	0.637926i	−0.937509	+	0.347961i	$0.886874\pi$
$710$		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	−0.550677	−	0.834719i	$-0.685630\pi$
$719$	12.0007	−	20.7858i	0.447549	−	0.775178i	0.998226	+	0.0595406i	$0.0189636\pi$
$720$		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	$-0.661485\pi$
$727$	−26.1991			−0.971672			−0.485836	+	0.874050i	$0.661485\pi$
$728$	−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	−0.478612	−	0.878027i	$-0.658860\pi$
$739$	1.15468	−	0.666653i	0.0424755	−	0.0245232i	0.521087	+	0.853503i	$0.325527\pi$
$740$		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	$-0.851027\pi$
$743$	−25.8413	+	14.9195i	−0.948025	+	0.547342i	−0.0555581	+	0.998455i	$0.517694\pi$
$744$	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	0.761569	−	0.648084i	$-0.224429\pi$
$751$	−4.94574	−	8.56627i	−0.180473	−	0.312588i	−0.942042	+	0.335496i	$0.891096\pi$
$752$	−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	0.849989	+	0.526800i	$0.176608\pi$
$757$	24.2455	+	41.9944i	0.881217	+	1.52631i	0.0312280	+	0.999512i	$0.490058\pi$
$758$	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	0.837559	−	0.546347i	$-0.183982\pi$
$761$	21.6052	+	12.4738i	0.783188	+	0.452174i	−0.0543707	+	0.998521i	$0.517315\pi$
$762$			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	−0.362852	−	0.931847i	$-0.618197\pi$
$769$	7.28560	−	4.20634i	0.262725	−	0.151685i	0.625577	+	0.780162i	$0.284864\pi$
$770$		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	$-0.567457\pi$
$773$	−32.3114	−	18.6550i	−1.16216	−	0.670973i	−0.951821	+	0.306655i	$0.900790\pi$
$774$	−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	$-0.214415\pi$
$787$	17.7335	+	10.2385i	0.632133	+	0.364962i	−0.149445	+	0.988770i	$0.547749\pi$
$788$		−	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	$-0.690264\pi$
$797$	12.2660	−	21.2453i	0.434484	−	0.752548i	0.997253	+	0.0740660i	$0.0235975\pi$
$798$			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	0.680055	−	0.733161i	$-0.261956\pi$
$809$	−8.38808	−	14.5286i	−0.294909	−	0.510798i	−0.974964	+	0.222364i	$0.928623\pi$
$810$		0			0
$811$		−	50.7808i		−	1.78315i	−0.452869	−	0.891577i	$-0.649600\pi$
$811$		−	50.7808i		−	1.78315i	0.452869	−	0.891577i	$-0.350400\pi$
$812$	−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	−0.379977	−	0.924996i	$-0.624068\pi$
$821$	6.62188	−	3.82315i	0.231105	−	0.133429i	0.611082	+	0.791567i	$0.290735\pi$
$822$	−2.70326	−	4.68219i	−0.0942871	−	0.163310i
$823$	2.54563	−	4.40916i	0.0887351	−	0.153694i	−0.818242	−	0.574874i	$-0.805051\pi$
$823$	2.54563	−	4.40916i	0.0887351	−	0.153694i	0.906977	+	0.421181i	$0.138384\pi$
$824$			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	0.947900	−	0.318568i	$-0.103202\pi$
$829$	5.70266	+	9.87730i	0.198062	+	0.343053i	−0.749838	+	0.661621i	$0.769869\pi$
$830$		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	0.848049	−	0.529918i	$-0.177777\pi$
$839$	23.5533	+	13.5985i	0.813151	+	0.469473i	−0.0348977	+	0.999391i	$0.511111\pi$
$840$		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	$-0.369638\pi$
$857$	23.3137			0.796382			0.398191	+	0.917302i	$0.369638\pi$
$858$	−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	$-0.247297\pi$
$877$	13.6960	+	7.90738i	0.462480	+	0.267013i	−0.250606	+	0.968089i	$0.580630\pi$
$878$	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	0.960464	+	0.278406i	$0.0898059\pi$
$881$	21.4105	+	37.0841i	0.721338	+	1.24939i	−0.239126	+	0.970989i	$0.576861\pi$
$882$	27.8822	−	16.0978i	0.938844	−	0.542042i
$883$	18.5133			0.623024			0.311512	−	0.950242i	$-0.399165\pi$
$883$	18.5133			0.623024			0.311512	+	0.950242i	$0.399165\pi$
$884$	−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	0.997448	+	0.0714024i	$0.0227474\pi$
$887$	16.6949	+	28.9164i	0.560560	+	0.970919i	−0.436888	+	0.899516i	$0.643919\pi$
$888$	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	−0.998376	−	0.0569728i	$-0.981855\pi$
$907$	−16.5197	−	28.6130i	−0.548528	−	0.950078i	0.449848	−	0.893105i	$-0.351478\pi$
$908$	−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	−0.939969	−	0.341261i	$-0.889146\pi$
$919$	−5.28827	+	9.15956i	−0.174444	+	0.302146i	0.765525	+	0.643406i	$0.222479\pi$
$920$		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	0.278423	−	0.960459i	$-0.410188\pi$
$929$	−12.6230	−	7.28788i	−0.414147	−	0.239108i	−0.692570	+	0.721351i	$0.743522\pi$
$930$		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	$-0.489420\pi$
$937$	2.03451			0.0664644			0.0332322	+	0.999448i	$0.489420\pi$
$938$	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	$0.0819807\pi$
$941$			15.6270i			0.509424i	−0.967017	+	0.254712i	$0.918019\pi$
$942$	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	$-0.860310\pi$
$947$	−30.4622	+	17.5874i	−0.989890	+	0.571513i	−0.0846485	+	0.996411i	$0.526977\pi$
$948$	−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	$-0.849786\pi$
$953$	−1.59492	+	2.76248i	−0.0516645	+	0.0894855i	0.839037	+	0.544075i	$0.183119\pi$
$954$			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	−0.666046	−	0.745911i	$-0.732015\pi$
$971$	9.75194	−	16.8909i	0.312955	−	0.542053i	0.979001	+	0.203857i	$0.0653479\pi$
$972$	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	$-0.724902\pi$
$977$	−9.84958	+	5.68666i	−0.315116	+	0.181932i	0.334098	+	0.942538i	$0.391568\pi$
$978$	−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	0.935866	−	0.352356i	$-0.114619\pi$
$991$	5.12446	+	8.87583i	0.162784	+	0.281950i	−0.773082	+	0.634306i	$0.781286\pi$
$992$	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	$-0.906986\pi$
$997$	−7.24112	+	12.5420i	−0.229328	+	0.397209i	0.728281	+	0.685279i	$0.240320\pi$
$998$	−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.k.751.1	✓	12
5.2	odd	4		975.2.w.k.49.2		24
5.3	odd	4		975.2.w.k.49.11		24
5.4	even	2		975.2.bc.l.751.6	yes	12
13.4	even	6	inner	975.2.bc.k.901.1	yes	12
65.4	even	6		975.2.bc.l.901.6	yes	12
65.17	odd	12		975.2.w.k.199.11		24
65.43	odd	12		975.2.w.k.199.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.w.k.49.2		24	5.2	odd	4
975.2.w.k.49.11		24	5.3	odd	4
975.2.w.k.199.2		24	65.43	odd	12
975.2.w.k.199.11		24	65.17	odd	12
975.2.bc.k.751.1	✓	12	1.1	even	1	trivial
975.2.bc.k.901.1	yes	12	13.4	even	6	inner
975.2.bc.l.751.6	yes	12	5.4	even	2
975.2.bc.l.901.6	yes	12	65.4	even	6

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

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