LMFDB - Embedded newform 975.2.w.k.49.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(49,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("975.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.11
Character	$\chi$	$=$	975.49
Dual form			975.2.w.k.199.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18025 + 2.04426i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.78599 + 3.09343i) q^{4} +(2.04426 + 1.18025i) q^{6} +(2.27152 - 3.93440i) q^{7} -3.71068 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.18025 + 2.04426i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.78599 + 3.09343i) q^{4} +(2.04426 + 1.18025i) q^{6} +(2.27152 - 3.93440i) q^{7} -3.71068 q^{8} +(0.500000 - 0.866025i) q^{9} +(3.74607 - 2.16279i) q^{11} +3.57199i q^{12} +(-3.10021 - 1.84085i) q^{13} +10.7239 q^{14} +(-0.807554 - 1.39872i) q^{16} +(4.78536 + 2.76283i) q^{17} +2.36051 q^{18} +(-3.41535 - 1.97185i) q^{19} -4.54305i q^{21} +(8.84261 + 5.10528i) q^{22} +(-0.630486 + 0.364011i) q^{23} +(-3.21354 + 1.85534i) q^{24} +(0.104146 - 8.51029i) q^{26} -1.00000i q^{27} +(8.11385 + 14.0536i) q^{28} +(1.97844 + 3.42676i) q^{29} +0.599343i q^{31} +(-1.80444 + 3.12539i) q^{32} +(2.16279 - 3.74607i) q^{33} +13.0434i q^{34} +(1.78599 + 3.09343i) q^{36} +(-2.26032 - 3.91499i) q^{37} -9.30914i q^{38} +(-3.60528 - 0.0441204i) q^{39} +(-8.97339 + 5.18079i) q^{41} +(9.28716 - 5.36195i) q^{42} +(9.44128 + 5.45093i) q^{43} +15.4509i q^{44} +(-1.48827 - 0.859250i) q^{46} -1.42486 q^{47} +(-1.39872 - 0.807554i) q^{48} +(-6.81965 - 11.8120i) q^{49} +5.52566 q^{51} +(11.2315 - 6.30252i) q^{52} -0.805400i q^{53} +(2.04426 - 1.18025i) q^{54} +(-8.42890 + 14.5993i) q^{56} -3.94371 q^{57} +(-4.67012 + 8.08888i) q^{58} +(-9.71559 - 5.60930i) q^{59} +(-6.20134 + 10.7410i) q^{61} +(-1.22521 + 0.707376i) q^{62} +(-2.27152 - 3.93440i) q^{63} -11.7490 q^{64} +10.2106 q^{66} +(5.26551 + 9.12013i) q^{67} +(-17.0933 + 9.86879i) q^{68} +(-0.364011 + 0.630486i) q^{69} +(0.898903 + 0.518982i) q^{71} +(-1.85534 + 3.21354i) q^{72} -6.45306 q^{73} +(5.33550 - 9.24135i) q^{74} +(12.1996 - 7.04343i) q^{76} -19.6513i q^{77} +(-4.16495 - 7.42220i) q^{78} -4.22063 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-21.1817 - 12.2293i) q^{82} +7.69642 q^{83} +(14.0536 + 8.11385i) q^{84} +25.7339i q^{86} +(3.42676 + 1.97844i) q^{87} +(-13.9004 + 8.02543i) q^{88} +(5.93532 - 3.42676i) q^{89} +(-14.2848 + 8.01590i) q^{91} -2.60048i q^{92} +(0.299672 + 0.519046i) q^{93} +(-1.68170 - 2.91279i) q^{94} +3.60889i q^{96} +(-5.54895 + 9.61107i) q^{97} +(16.0978 - 27.8822i) q^{98} -4.32558i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 16 q^{4} + 12 q^{9}+O(q^{10}) $ 24 * q - 16 * q^4 + 12 * q^9	$ 24 q - 16 q^{4} + 12 q^{9} + 18 q^{11} - 20 q^{14} - 8 q^{16} + 18 q^{19} - 10 q^{26} + 32 q^{29} + 16 q^{36} + 6 q^{39} + 36 q^{41} - 90 q^{46} - 62 q^{49} + 50 q^{56} - 108 q^{59} - 22 q^{61} - 32 q^{64} + 60 q^{66} + 2 q^{69} - 66 q^{71} - 10 q^{74} - 54 q^{76} - 36 q^{79} - 12 q^{81} + 78 q^{84} + 96 q^{89} - 58 q^{91} + 60 q^{94}+O(q^{100}) $ 24 * q - 16 * q^4 + 12 * q^9 + 18 * q^11 - 20 * q^14 - 8 * q^16 + 18 * q^19 - 10 * q^26 + 32 * q^29 + 16 * q^36 + 6 * q^39 + 36 * q^41 - 90 * q^46 - 62 * q^49 + 50 * q^56 - 108 * q^59 - 22 * q^61 - 32 * q^64 + 60 * q^66 + 2 * q^69 - 66 * q^71 - 10 * q^74 - 54 * q^76 - 36 * q^79 - 12 * q^81 + 78 * q^84 + 96 * q^89 - 58 * q^91 + 60 * q^94

Display 100 coefficients 10 coefficients

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 $

$2$	1.18025	+	2.04426i	0.834565	+	1.44551i	0.894384	+	0.447299i	$0.147614\pi$
$2$	1.18025	+	2.04426i	0.834565	+	1.44551i	−0.0598198	+	0.998209i	$0.519053\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−1.78599	+	3.09343i	−0.892996	+	1.54671i
$5$		0			0
$5$		0			0
$6$	2.04426	+	1.18025i	0.834565	+	0.481836i
$7$	2.27152	−	3.93440i	0.858556	−	1.48706i	−0.0147510	−	0.999891i	$-0.504696\pi$
$7$	2.27152	−	3.93440i	0.858556	−	1.48706i	0.873307	−	0.487171i	$-0.161971\pi$
$8$	−3.71068			−1.31192
$9$	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	$0.107219\pi$
$12$			3.57199i			1.03114i
$13$	−3.10021	−	1.84085i	−0.859842	−	0.510560i
$13$	−3.10021	−	1.84085i	−0.859842	−	0.510560i
$14$	10.7239			2.86608
$15$		0			0
$16$	−0.807554	−	1.39872i	−0.201888	−	0.349681i
$17$	4.78536	+	2.76283i	1.16062	+	0.670085i	0.951453	−	0.307795i	$-0.0995909\pi$
$17$	4.78536	+	2.76283i	1.16062	+	0.670085i	0.209169	+	0.977880i	$0.432924\pi$
$18$	2.36051			0.556376
$19$	−3.41535	−	1.97185i	−0.783535	−	0.452374i	0.0541466	−	0.998533i	$-0.482756\pi$
$19$	−3.41535	−	1.97185i	−0.783535	−	0.452374i	−0.837682	+	0.546159i	$0.816090\pi$
$20$		0			0
$21$		−	4.54305i		−	0.991375i
$22$	8.84261	+	5.10528i	1.88525	+	1.08845i
$23$	−0.630486	+	0.364011i	−0.131465	+	0.0759016i	−0.564290	−	0.825576i	$-0.690850\pi$
$23$	−0.630486	+	0.364011i	−0.131465	+	0.0759016i	0.432825	+	0.901478i	$0.357517\pi$
$24$	−3.21354	+	1.85534i	−0.655962	+	0.378720i
$25$		0			0
$26$	0.104146	−	8.51029i	0.0204248	−	1.66900i
$27$		−	1.00000i		−	0.192450i
$28$	8.11385	+	14.0536i	1.53337	+	2.65588i
$29$	1.97844	+	3.42676i	0.367387	+	0.636333i	0.989156	−	0.146868i	$-0.0469192\pi$
$29$	1.97844	+	3.42676i	0.367387	+	0.636333i	−0.621769	+	0.783200i	$0.713586\pi$
$30$		0			0
$31$			0.599343i			0.107645i	0.998551	+	0.0538226i	$0.0171405\pi$
$31$			0.599343i			0.107645i	−0.998551	+	0.0538226i	$0.982859\pi$
$32$	−1.80444	+	3.12539i	−0.318984	+	0.552496i
$33$	2.16279	−	3.74607i	0.376494	−	0.652106i
$34$			13.0434i			2.23692i
$35$		0			0
$36$	1.78599	+	3.09343i	0.297665	+	0.515572i
$37$	−2.26032	−	3.91499i	−0.371594	−	0.643620i	0.618217	−	0.786008i	$-0.287855\pi$
$37$	−2.26032	−	3.91499i	−0.371594	−	0.643620i	−0.989811	+	0.142388i	$0.954522\pi$
$38$		−	9.30914i		−	1.51014i
$39$	−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	$0.633380\pi$
$42$	9.28716	−	5.36195i	1.43304	−	0.827366i
$43$	9.44128	+	5.45093i	1.43978	+	0.831258i	0.997834	−	0.0657822i	$-0.0209543\pi$
$43$	9.44128	+	5.45093i	1.43978	+	0.831258i	0.441948	+	0.897041i	$0.354288\pi$
$44$			15.4509i			2.32931i
$45$		0			0
$46$	−1.48827	−	0.859250i	−0.219433	−	0.126690i
$47$	−1.42486			−0.207838			−0.103919	−	0.994586i	$-0.533138\pi$
$47$	−1.42486			−0.207838			−0.103919	+	0.994586i	$0.533138\pi$
$48$	−1.39872	−	0.807554i	−0.201888	−	0.116560i
$49$	−6.81965	−	11.8120i	−0.974236	−	1.68743i
$50$		0			0
$51$	5.52566			0.773748
$52$	11.2315	−	6.30252i	1.55753	−	0.874003i
$53$		−	0.805400i		−	0.110630i	−0.998469	−	0.0553151i	$-0.982384\pi$
$53$		−	0.805400i		−	0.110630i	0.998469	−	0.0553151i	$-0.0176163\pi$
$54$	2.04426	−	1.18025i	0.278188	−	0.160612i
$55$		0			0
$56$	−8.42890	+	14.5993i	−1.12636	+	1.95091i
$57$	−3.94371			−0.522357
$58$	−4.67012	+	8.08888i	−0.613216	+	1.06212i
$59$	−9.71559	−	5.60930i	−1.26486	−	0.730269i	−0.290851	−	0.956768i	$-0.593939\pi$
$59$	−9.71559	−	5.60930i	−1.26486	−	0.730269i	−0.974011	+	0.226499i	$0.927272\pi$
$60$		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	$0.874661\pi$
$62$	−1.22521	+	0.707376i	−0.155602	+	0.0898369i
$63$	−2.27152	−	3.93440i	−0.286185	−	0.495687i
$64$	−11.7490			−1.46863
$65$		0			0
$66$	10.2106			1.25683
$67$	5.26551	+	9.12013i	0.643284	+	1.11420i	0.984695	+	0.174287i	$0.0557620\pi$
$67$	5.26551	+	9.12013i	0.643284	+	1.11420i	−0.341411	+	0.939914i	$0.610905\pi$
$68$	−17.0933	+	9.86879i	−2.07286	+	1.19677i
$69$	−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	$0.647049\pi$
$72$	−1.85534	+	3.21354i	−0.218654	+	0.378720i
$73$	−6.45306			−0.755274			−0.377637	−	0.925954i	$-0.623263\pi$
$73$	−6.45306			−0.755274			−0.377637	+	0.925954i	$0.623263\pi$
$74$	5.33550	−	9.24135i	0.620239	−	1.07429i
$75$		0			0
$76$	12.1996	−	7.04343i	1.39939	−	0.807937i
$77$		−	19.6513i		−	2.23948i
$78$	−4.16495	−	7.42220i	−0.471588	−	0.840398i
$79$	−4.22063			−0.474857			−0.237429	−	0.971405i	$-0.576305\pi$
$79$	−4.22063			−0.474857			−0.237429	+	0.971405i	$0.576305\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−21.1817	−	12.2293i	−2.33913	−	1.35050i
$83$	7.69642			0.844792			0.422396	−	0.906411i	$-0.361189\pi$
$83$	7.69642			0.844792			0.422396	+	0.906411i	$0.361189\pi$
$84$	14.0536	+	8.11385i	1.53337	+	0.885294i
$85$		0			0
$86$			25.7339i			2.77496i
$87$	3.42676	+	1.97844i	0.367387	+	0.212111i
$88$	−13.9004	+	8.02543i	−1.48179	+	0.855513i
$89$	5.93532	−	3.42676i	0.629142	−	0.363235i	−0.151278	−	0.988491i	$-0.548339\pi$
$89$	5.93532	−	3.42676i	0.629142	−	0.363235i	0.780420	+	0.625256i	$0.215005\pi$
$90$		0			0
$91$	−14.2848	+	8.01590i	−1.49746	+	0.840295i
$92$		−	2.60048i		−	0.271119i
$93$	0.299672	+	0.519046i	0.0310745	+	0.0538226i
$94$	−1.68170	−	2.91279i	−0.173454	−	0.300431i
$95$		0			0
$96$			3.60889i			0.368331i
$97$	−5.54895	+	9.61107i	−0.563411	+	0.975856i	0.433785	+	0.901016i	$0.357178\pi$
$97$	−5.54895	+	9.61107i	−0.563411	+	0.975856i	−0.997196	+	0.0748394i	$0.976156\pi$
$98$	16.0978	−	27.8822i	1.62613	−	2.81653i
$99$		−	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	$0.742446\pi$
$102$	6.52168	+	11.2959i	0.645742	+	1.11846i
$103$			3.25369i			0.320595i	0.987069	+	0.160298i	$0.0512454\pi$
$103$			3.25369i			0.320595i	−0.987069	+	0.160298i	$0.948755\pi$
$104$	11.5039	+	6.83080i	1.12805	+	0.669815i
$105$		0			0
$106$	1.64645	−	0.950576i	0.159917	−	0.0923281i
$107$	12.5709	−	7.25780i	1.21527	−	0.701638i	0.251370	−	0.967891i	$-0.419119\pi$
$107$	12.5709	−	7.25780i	1.21527	−	0.701638i	0.963903	+	0.266253i	$0.0857857\pi$
$108$	3.09343	+	1.78599i	0.297665	+	0.171857i
$109$			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
$112$	−7.33751			−0.693330
$113$	1.40150	+	0.809154i	0.131842	+	0.0761188i	0.564470	−	0.825453i	$-0.309081\pi$
$113$	1.40150	+	0.809154i	0.131842	+	0.0761188i	−0.432629	+	0.901572i	$0.642414\pi$
$114$	−4.65457	−	8.06195i	−0.435940	−	0.755071i
$115$		0			0
$116$	−14.1339			−1.31230
$117$	−3.14433	+	1.76443i	−0.290693	+	0.163122i
$118$		−	26.4816i		−	2.43783i
$119$	21.7401	−	12.5517i	1.99292	−	1.15061i
$120$		0			0
$121$	3.85534	−	6.67764i	0.350485	−	0.607058i
$122$	−29.2766			−2.65058
$123$	−5.18079	+	8.97339i	−0.467136	+	0.809104i
$124$	−1.85403	−	1.07042i	−0.166496	−	0.0961267i
$125$		0			0
$126$	5.36195	−	9.28716i	0.477680	−	0.827366i
$127$	16.1608	−	9.33047i	1.43404	−	0.827945i	0.436617	−	0.899648i	$-0.356177\pi$
$127$	16.1608	−	9.33047i	1.43404	−	0.827945i	0.997426	+	0.0717028i	$0.0228433\pi$
$128$	−10.2579	−	17.7672i	−0.906680	−	1.57042i
$129$	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	$0.364422\pi$
$132$	7.72546	+	13.3809i	0.672415	+	1.16466i
$133$	−15.5161	+	8.95823i	−1.34542	+	0.776777i
$134$	−12.4293	+	21.5281i	−1.07372	+	1.85975i
$135$		0			0
$136$	−17.7570	−	10.2520i	−1.52265	−	0.879100i
$137$	−1.14520	+	1.98355i	−0.0978414	+	0.169466i	−0.910791	−	0.412868i	$-0.864527\pi$
$137$	−1.14520	+	1.98355i	−0.0978414	+	0.169466i	0.812950	+	0.582334i	$0.197860\pi$
$138$	−1.71850			−0.146288
$139$	−4.18650	+	7.25122i	−0.355094	+	0.615041i	−0.987134	−	0.159895i	$-0.948884\pi$
$139$	−4.18650	+	7.25122i	−0.355094	+	0.615041i	0.632040	+	0.774936i	$0.282218\pi$
$140$		0			0
$141$	−1.23397	+	0.712432i	−0.103919	+	0.0599976i
$142$			2.45012i			0.205609i
$143$	−15.5949	−	0.190846i	−1.30411	−	0.0159594i
$144$	−1.61511			−0.134592
$145$		0			0
$146$	−7.61624	−	13.1917i	−0.630325	−	1.09175i
$147$	−11.8120	−	6.81965i	−0.974236	−	0.562475i
$148$	16.1477			1.32733
$149$	−19.7954	−	11.4289i	−1.62170	−	0.936291i	−0.986465	−	0.163974i	$-0.947569\pi$
$149$	−19.7954	−	11.4289i	−1.62170	−	0.936291i	−0.635238	−	0.772316i	$-0.719098\pi$
$150$		0			0
$151$		−	14.9011i		−	1.21263i	−0.795223	−	0.606317i	$-0.792646\pi$
$151$		−	14.9011i		−	1.21263i	0.795223	−	0.606317i	$-0.207354\pi$
$152$	12.6733	+	7.31692i	1.02794	+	0.593480i
$153$	4.78536	−	2.76283i	0.386874	−	0.223362i
$154$	40.1724	−	23.1935i	3.23718	−	1.86899i
$155$		0			0
$156$	6.57549	−	11.0739i	0.526460	−	0.886620i
$157$		−	0.495803i		−	0.0395694i	−0.999804	−	0.0197847i	$-0.993702\pi$
$157$		−	0.495803i		−	0.0395694i	0.999804	−	0.0197847i	$-0.00629807\pi$
$158$	−4.98140	−	8.62805i	−0.396299	−	0.686410i
$159$	−0.402700	−	0.697497i	−0.0319362	−	0.0553151i
$160$		0			0
$161$			3.30744i			0.260663i
$162$	1.18025	−	2.04426i	0.0927294	−	0.160612i
$163$	0.859509	−	1.48871i	0.0673220	−	0.116605i	−0.830400	−	0.557168i	$-0.811888\pi$
$163$	0.859509	−	1.48871i	0.0673220	−	0.116605i	0.897722	+	0.440563i	$0.145221\pi$
$164$		−	37.0114i		−	2.89011i
$165$		0			0
$166$	9.08372	+	15.7335i	0.705033	+	1.22115i
$167$	2.84214	+	4.92273i	0.219932	+	0.380933i	0.954787	−	0.297291i	$-0.0960833\pi$
$167$	2.84214	+	4.92273i	0.219932	+	0.380933i	−0.734855	+	0.678224i	$0.762750\pi$
$168$			16.8578i			1.30061i
$169$	6.22254	+	11.4140i	0.478657	+	0.878002i
$170$		0			0
$171$	−3.41535	+	1.97185i	−0.261178	+	0.150791i
$172$	−33.7241	+	19.4706i	−2.57144	+	1.48462i
$173$	5.95091	+	3.43576i	0.452439	+	0.261216i	0.708860	−	0.705349i	$-0.249210\pi$
$173$	5.95091	+	3.43576i	0.452439	+	0.261216i	−0.256421	+	0.966565i	$0.582543\pi$
$174$			9.34023i			0.708081i
$175$		0			0
$176$	−6.05030	−	3.49314i	−0.456058	−	0.263305i
$177$	−11.2186			−0.843242
$178$	14.0103	+	8.08888i	1.05012	+	0.606287i
$179$	−10.9566	−	18.9774i	−0.818937	−	1.41844i	−0.906466	−	0.422278i	$-0.861231\pi$
$179$	−10.9566	−	18.9774i	−0.818937	−	1.41844i	0.0875295	−	0.996162i	$-0.472103\pi$
$180$		0			0
$181$	−17.9404			−1.33350			−0.666750	−	0.745281i	$-0.732315\pi$
$181$	−17.9404			−1.33350			−0.666750	+	0.745281i	$0.732315\pi$
$182$	−33.2463	−	19.7411i	−2.46438	−	1.46331i
$183$			12.4027i			0.916833i
$184$	2.33953	−	1.35073i	0.172472	−	0.0995770i
$185$		0			0
$186$	−0.707376	+	1.22521i	−0.0518673	+	0.0898369i
$187$	23.9017			1.74787
$188$	2.54480	−	4.40772i	0.185598	−	0.321466i
$189$	−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	$0.137717\pi$
$192$	−10.1749	+	5.87451i	−0.734313	+	0.423956i
$193$	4.71197	+	8.16136i	0.339175	+	0.587468i	0.984278	−	0.176628i	$-0.0565189\pi$
$193$	4.71197	+	8.16136i	0.339175	+	0.587468i	−0.645103	+	0.764096i	$0.723186\pi$
$194$	−26.1967			−1.88081
$195$		0			0
$196$	48.7194			3.47996
$197$	−12.3309	−	21.3578i	−0.878542	−	1.52168i	−0.852941	−	0.522007i	$-0.825183\pi$
$197$	−12.3309	−	21.3578i	−0.878542	−	1.52168i	−0.0256008	−	0.999672i	$-0.508150\pi$
$198$	8.84261	−	5.10528i	0.628417	−	0.362817i
$199$	−12.9766	+	22.4761i	−0.919886	+	1.59329i	−0.120300	+	0.992738i	$0.538386\pi$
$199$	−12.9766	+	22.4761i	−0.919886	+	1.59329i	−0.799586	+	0.600552i	$0.794948\pi$
$200$		0			0
$201$	9.12013	+	5.26551i	0.643284	+	0.371400i
$202$	−6.68192	+	11.5734i	−0.470138	+	0.814303i
$203$	17.9763			1.26169
$204$	−9.86879	+	17.0933i	−0.690954	+	1.19677i
$205$		0			0
$206$	−6.65137	+	3.84017i	−0.463423	+	0.267557i
$207$			0.728022i			0.0506010i
$208$	−0.0712591	+	5.82292i	−0.00494093	+	0.403747i
$209$	−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	$0.963425\pi$
$212$	2.49145	+	1.43844i	0.171113	+	0.0987924i
$213$	1.03796			0.0711201
$214$	29.6736	+	17.1321i	2.02845	+	1.17112i
$215$		0			0
$216$			3.71068i			0.252480i
$217$	2.35805	+	1.36142i	0.160075	+	0.0924194i
$218$	−4.58558	+	2.64749i	−0.310575	+	0.179310i
$219$	−5.58852	+	3.22653i	−0.377637	+	0.218029i
$220$		0			0
$221$	−9.74965	−	17.3745i	−0.655833	−	1.16873i
$222$		−	10.6710i		−	0.716190i
$223$	−4.06113	−	7.03409i	−0.271954	−	0.471037i	0.697408	−	0.716674i	$-0.254336\pi$
$223$	−4.06113	−	7.03409i	−0.271954	−	0.471037i	−0.969362	+	0.245636i	$0.921003\pi$
$224$	8.19768	+	14.1988i	0.547730	+	0.948697i
$225$		0			0
$226$			3.82002i			0.254104i
$227$	−6.79346	+	11.7666i	−0.450898	+	0.780978i	−0.998442	−	0.0557990i	$-0.982229\pi$
$227$	−6.79346	+	11.7666i	−0.450898	+	0.780978i	0.547544	+	0.836777i	$0.315563\pi$
$228$	7.04343	−	12.1996i	0.466463	−	0.807937i
$229$		−	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
$232$	−7.34135	−	12.7156i	−0.481983	−	0.834820i
$233$			28.6851i			1.87922i	0.342240	+	0.939612i	$0.388814\pi$
$233$			28.6851i			1.87922i	−0.342240	+	0.939612i	$0.611186\pi$
$234$	−7.31805	−	4.34534i	−0.478396	−	0.284064i
$235$		0			0
$236$	34.7040	−	20.0363i	2.25904	−	1.30425i
$237$	−3.65517	+	2.11031i	−0.237429	+	0.137080i
$238$	51.3177	+	29.6283i	3.32643	+	1.92052i
$239$		−	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	0.994969	+	0.100188i	$0.0319445\pi$
$241$	24.5161	+	14.1544i	1.57922	+	0.911762i	0.584250	+	0.811574i	$0.301389\pi$
$242$	18.2011			1.17001
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−22.1511	−	38.3668i	−1.41808	−	2.45619i
$245$		0			0
$246$	−24.4586			−1.55942
$247$	6.95840	+	12.4003i	0.442752	+	0.789012i
$248$		−	2.22397i		−	0.141222i
$249$	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	$0.978177\pi$
$252$	16.2277			1.02225
$253$	−1.57456	+	2.72722i	−0.0989918	+	0.171459i
$254$	38.1477	+	22.0246i	2.39360	+	1.38195i
$255$		0			0
$256$	12.4649	−	21.5898i	0.779053	−	1.34936i
$257$	17.2822	−	9.97787i	1.07803	−	0.622402i	0.147668	−	0.989037i	$-0.452823\pi$
$257$	17.2822	−	9.97787i	1.07803	−	0.622402i	0.930365	+	0.366635i	$0.119490\pi$
$258$	12.8669	+	22.2862i	0.801061	+	1.38748i
$259$	−20.5375			−1.27614
$260$		0			0
$261$	3.95688			0.244925
$262$	11.1627	+	19.3343i	0.689633	+	1.19448i
$263$	2.94183	−	1.69847i	0.181401	−	0.104732i	−0.406550	−	0.913629i	$-0.633268\pi$
$263$	2.94183	−	1.69847i	0.181401	−	0.104732i	0.587951	+	0.808897i	$0.299935\pi$
$264$	−8.02543	+	13.9004i	−0.493931	+	0.855513i
$265$		0			0
$266$	−36.6258	−	21.1459i	−2.24567	−	1.29654i
$267$	3.42676	−	5.93532i	0.209714	−	0.363235i
$268$	−37.6166			−2.29780
$269$	7.66836	−	13.2820i	0.467548	−	0.809817i	−0.531765	−	0.846892i	$-0.678471\pi$
$269$	7.66836	−	13.2820i	0.467548	−	0.809817i	0.999312	+	0.0370755i	$0.0118042\pi$
$270$		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	$0.520946\pi$
$272$		−	8.92454i		−	0.541130i
$273$	−8.36307	+	14.0844i	−0.506156	+	0.852426i
$274$	−5.40652			−0.326620
$275$		0			0
$276$	−1.30024	−	2.25209i	−0.0782654	−	0.135560i
$277$	6.75572	+	3.90042i	0.405912	+	0.234353i	0.689032	−	0.724731i	$-0.258036\pi$
$277$	6.75572	+	3.90042i	0.405912	+	0.234353i	−0.283120	+	0.959085i	$0.591369\pi$
$278$	−19.7645			−1.18540
$279$	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	$-0.243621\pi$
$282$	−2.91279	−	1.68170i	−0.173454	−	0.100144i
$283$	6.79264	−	3.92173i	0.403780	−	0.233123i	−0.284333	−	0.958725i	$-0.591772\pi$
$283$	6.79264	−	3.92173i	0.403780	−	0.233123i	0.688114	+	0.725603i	$0.258439\pi$
$284$	−3.21087	+	1.85379i	−0.190530	+	0.110002i
$285$		0			0
$286$	−18.0158	−	32.1053i	−1.06530	−	1.89843i
$287$			47.0732i			2.77864i
$288$	1.80444	+	3.12539i	0.106328	+	0.184165i
$289$	6.76647	+	11.7199i	0.398028	+	0.689405i
$290$		0			0
$291$			11.0979i			0.650571i
$292$	11.5251	−	19.9621i	0.674457	−	1.16819i
$293$	5.14023	−	8.90314i	0.300296	−	0.520127i	−0.675907	−	0.736987i	$-0.736248\pi$
$293$	5.14023	−	8.90314i	0.300296	−	0.520127i	0.976203	+	0.216859i	$0.0695813\pi$
$294$		−	32.1956i		−	1.87769i
$295$		0			0
$296$	8.38732	+	14.5273i	0.487503	+	0.844380i
$297$	−2.16279	−	3.74607i	−0.125498	−	0.217369i
$298$		−	53.9559i		−	3.12558i
$299$	2.62473	+	0.0321206i	0.151792	+	0.00185758i
$300$		0			0
$301$	42.8922	−	24.7638i	2.47227	−	1.42736i
$302$	30.4617	−	17.5870i	1.75287	−	1.01202i
$303$	4.90294	+	2.83072i	0.281667	+	0.162620i
$304$			6.36951i			0.365317i
$305$		0			0
$306$	11.2959	+	6.52168i	0.645742	+	0.372820i
$307$	−33.8058			−1.92940			−0.964701	−	0.263348i	$-0.915173\pi$
$307$	−33.8058			−1.92940			−0.964701	+	0.263348i	$0.915173\pi$
$308$	60.7900	+	35.0971i	3.46383	+	1.99985i
$309$	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	$0.502588\pi$
$312$	13.3780	+	0.163716i	0.757383	+	0.00926862i
$313$		−	27.8341i		−	1.57328i	−0.617413	−	0.786639i	$-0.711819\pi$
$313$		−	27.8341i		−	1.57328i	0.617413	−	0.786639i	$-0.288181\pi$
$314$	1.01355	−	0.585173i	0.0571979	−	0.0330232i
$315$		0			0
$316$	7.53801	−	13.0562i	0.424046	−	0.734469i
$317$	−23.6134			−1.32626			−0.663130	−	0.748504i	$-0.730772\pi$
$317$	−23.6134			−1.32626			−0.663130	+	0.748504i	$0.730772\pi$
$318$	0.950576	−	1.64645i	0.0533056	−	0.0923281i
$319$	14.8227	+	8.55790i	0.829913	+	0.479151i
$320$		0			0
$321$	7.25780	−	12.5709i	0.405091	−	0.701638i
$322$	−6.76126	+	3.90362i	−0.376790	+	0.217540i
$323$	−10.8958	−	18.8721i	−0.606258	−	1.05007i
$324$	3.57199			0.198444
$325$		0			0
$326$	4.05775			0.224738
$327$	1.12158	+	1.94263i	0.0620233	+	0.107428i
$328$	33.2974	−	19.2243i	1.83854	−	1.06148i
$329$	−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	$0.620855\pi$
$332$	−13.7457	+	23.8083i	−0.754396	+	1.30665i
$333$	−4.52064			−0.247730
$334$	−6.70889	+	11.6201i	−0.367094	+	0.635826i
$335$		0			0
$336$	−6.35447	+	3.66876i	−0.346665	+	0.200147i
$337$		−	19.8753i		−	1.08268i	−0.840804	−	0.541339i	$-0.817918\pi$
$337$		−	19.8753i		−	1.08268i	0.840804	−	0.541339i	$-0.182082\pi$
$338$	−15.9890	+	26.1919i	−0.869689	+	1.42465i
$339$	1.61831			0.0878944
$340$		0			0
$341$	1.29625	+	2.24518i	0.0701961	+	0.121583i
$342$	−8.06195	−	4.65457i	−0.435940	−	0.251690i
$343$	−30.1627			−1.62863
$344$	−35.0336	−	20.2266i	−1.88888	−	1.09055i
$345$		0			0
$346$			16.2203i			0.872007i
$347$	1.48004	+	0.854503i	0.0794529	+	0.0458721i	0.539200	−	0.842178i	$-0.318727\pi$
$347$	1.48004	+	0.854503i	0.0794529	+	0.0458721i	−0.459747	+	0.888050i	$0.652060\pi$
$348$	−12.2403	+	7.06695i	−0.656150	+	0.378828i
$349$	−13.3270	+	7.69437i	−0.713380	+	0.411870i	−0.812311	−	0.583224i	$-0.801791\pi$
$349$	−13.3270	+	7.69437i	−0.713380	+	0.411870i	0.0989311	+	0.995094i	$0.468458\pi$
$350$		0			0
$351$	−1.84085	+	3.10021i	−0.0982573	+	0.165477i
$352$			15.6105i			0.832045i
$353$	9.40416	+	16.2885i	0.500533	+	0.866948i	1.00000		0.000615369i	$0.000195878\pi$
$353$	9.40416	+	16.2885i	0.500533	+	0.866948i	−0.499467	+	0.866333i	$0.666471\pi$
$354$	−13.2408	−	22.9337i	−0.703740	−	1.21891i
$355$		0			0
$356$			24.4806i			1.29747i
$357$	12.5517	−	21.7401i	0.664305	−	1.15061i
$358$	25.8632	−	44.7963i	1.36691	−	2.36756i
$359$			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
$362$	−21.1742	−	36.6748i	−1.11289	−	1.92759i
$363$		−	7.71067i		−	0.404705i
$364$	0.715972	−	58.5054i	0.0375271	−	3.06652i
$365$		0			0
$366$	−25.3543	+	14.6383i	−1.32529	+	0.765156i
$367$	−9.02325	+	5.20957i	−0.471010	+	0.271938i	−0.716662	−	0.697420i	$-0.754331\pi$
$367$	−9.02325	+	5.20957i	−0.471010	+	0.271938i	0.245653	+	0.969358i	$0.420998\pi$
$368$	1.01830	+	0.587917i	0.0530827	+	0.0306473i
$369$			10.3616i			0.539402i
$370$		0			0
$371$	−3.16876	−	1.82949i	−0.164514	−	0.0949822i
$372$	−2.14084			−0.110998
$373$	−20.8540	−	12.0400i	−1.07978	−	0.623410i	−0.148941	−	0.988846i	$-0.547586\pi$
$373$	−20.8540	−	12.0400i	−1.07978	−	0.623410i	−0.930836	+	0.365437i	$0.880920\pi$
$374$	28.2101	+	48.8613i	1.45871	+	2.52656i
$375$		0			0
$376$	5.28721			0.272667
$377$	0.174579	−	14.2657i	0.00899127	−	0.734719i
$378$		−	10.7239i		−	0.551578i
$379$	7.64369	−	4.41308i	0.392630	−	0.226685i	−0.290669	−	0.956824i	$-0.593878\pi$
$379$	7.64369	−	4.41308i	0.392630	−	0.226685i	0.683299	+	0.730139i	$0.260545\pi$
$380$		0			0
$381$	9.33047	−	16.1608i	0.478014	−	0.827945i
$382$	5.92587			0.303194
$383$	8.10734	−	14.0423i	0.414266	−	0.717529i	−0.581085	−	0.813843i	$-0.697372\pi$
$383$	8.10734	−	14.0423i	0.414266	−	0.717529i	0.995351	+	0.0963135i	$0.0307051\pi$
$384$	−17.7672	−	10.2579i	−0.906680	−	0.523472i
$385$		0			0
$386$	−11.1226	+	19.2649i	−0.566126	+	0.980560i
$387$	9.44128	−	5.45093i	0.479927	−	0.277086i
$388$	−19.8208	−	34.3306i	−1.00625	−	1.74287i
$389$	33.1860			1.68259			0.841297	−	0.540573i	$-0.181792\pi$
$389$	33.1860			1.68259			0.841297	+	0.540573i	$0.181792\pi$
$390$		0			0
$391$	−4.02281			−0.203442
$392$	25.3055	+	43.8305i	1.27812	+	2.21377i
$393$	8.19076	−	4.72894i	0.413169	−	0.238543i
$394$	29.1072	−	50.4152i	1.46640	−	2.53988i
$395$		0			0
$396$	13.3809	+	7.72546i	0.672415	+	0.388219i
$397$	−3.75007	+	6.49531i	−0.188211	+	0.325990i	−0.944654	−	0.328069i	$-0.893602\pi$
$397$	−3.75007	+	6.49531i	−0.188211	+	0.325990i	0.756443	+	0.654060i	$0.226935\pi$
$398$	−61.2626			−3.07082
$399$	−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	$0.306163\pi$
$402$			24.8585i			1.23983i
$403$	1.10330	−	1.85809i	0.0549593	−	0.0925579i
$404$	−20.2225			−1.00611
$405$		0			0
$406$	21.2166	+	36.7482i	1.05296	+	1.82378i
$407$	−16.9346	−	9.77720i	−0.839417	−	0.484638i
$408$	−20.5040			−1.01510
$409$	12.6543	+	7.30598i	0.625716	+	0.361257i	0.779091	−	0.626911i	$-0.215681\pi$
$409$	12.6543	+	7.30598i	0.625716	+	0.361257i	−0.153375	+	0.988168i	$0.549014\pi$
$410$		0			0
$411$			2.29041i			0.112978i
$412$	−10.0650	−	5.81106i	−0.495869	−	0.286290i
$413$	−44.1384	+	25.4833i	−2.17191	+	1.25395i
$414$	−1.48827	+	0.859250i	−0.0731442	+	0.0422298i
$415$		0			0
$416$	11.3475	−	6.36764i	0.556358	−	0.312199i
$417$			8.37299i			0.410027i
$418$	−20.1337	−	34.8726i	−0.984773	−	1.70568i
$419$	−1.70258	−	2.94896i	−0.0831765	−	0.144066i	0.821436	−	0.570300i	$-0.193173\pi$
$419$	−1.70258	−	2.94896i	−0.0831765	−	0.144066i	−0.904613	+	0.426234i	$0.859840\pi$
$420$		0			0
$421$			14.9006i			0.726213i	0.931748	+	0.363107i	$0.118284\pi$
$421$			14.9006i			0.726213i	−0.931748	+	0.363107i	$0.881716\pi$
$422$	13.6266	−	23.6019i	0.663331	−	1.14892i
$423$	−0.712432	+	1.23397i	−0.0346396	+	0.0599976i
$424$			2.98858i			0.145138i
$425$		0			0
$426$	1.22506	+	2.12186i	0.0593543	+	0.102805i
$427$	28.1730	+	48.7971i	1.36339	+	2.36146i
$428$			51.8495i			2.50624i
$429$	−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	$0.290684\pi$
$432$	−1.39872	+	0.807554i	−0.0672962	+	0.0388535i
$433$	10.8785	+	6.28072i	0.522789	+	0.301832i	0.738075	−	0.674719i	$-0.235735\pi$
$433$	10.8785	+	6.28072i	0.522789	+	0.301832i	−0.215286	+	0.976551i	$0.569068\pi$
$434$			6.42729i			0.308520i
$435$		0			0
$436$	−6.93904	−	4.00625i	−0.332320	−	0.191865i
$437$	2.87111			0.137344
$438$	−13.1917	−	7.61624i	−0.630325	−	0.363918i
$439$	14.7936	+	25.6233i	0.706060	+	1.22293i	0.966308	+	0.257390i	$0.0828625\pi$
$439$	14.7936	+	25.6233i	0.706060	+	1.22293i	−0.260248	+	0.965542i	$0.583804\pi$
$440$		0			0
$441$	−13.6393			−0.649490
$442$	24.0109	−	40.4371i	1.14208	−	1.92340i
$443$			29.6951i			1.41086i	0.708781	+	0.705428i	$0.249245\pi$
$443$			29.6951i			1.41086i	−0.708781	+	0.705428i	$0.750755\pi$
$444$	13.9843	−	8.07383i	0.663665	−	0.383167i
$445$		0			0
$446$	9.58633	−	16.6040i	0.453926	−	0.786222i
$447$	−22.8578			−1.08114
$448$	−26.6882	+	46.2253i	−1.26090	+	2.18394i
$449$	9.55371	+	5.51584i	0.450867	+	0.260308i	0.708196	−	0.706015i	$-0.249509\pi$
$449$	9.55371	+	5.51584i	0.450867	+	0.260308i	−0.257329	+	0.966324i	$0.582842\pi$
$450$		0			0
$451$	−22.4099	+	38.8152i	−1.05524	+	1.82773i
$452$	−5.00612	+	2.89029i	−0.235468	+	0.135948i
$453$	−7.45054	−	12.9047i	−0.350057	−	0.606317i
$454$	−32.0720			−1.50521
$455$		0			0
$456$	14.6338			0.685292
$457$	−7.11796	−	12.3287i	−0.332964	−	0.576711i	0.650128	−	0.759825i	$-0.274715\pi$
$457$	−7.11796	−	12.3287i	−0.332964	−	0.576711i	−0.983092	+	0.183114i	$0.941382\pi$
$458$	7.38063	−	4.26121i	0.344874	−	0.199113i
$459$	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	$0.840965\pi$
$462$	23.1935	−	40.1724i	1.07906	−	1.86899i
$463$	−29.9717			−1.39290			−0.696451	−	0.717604i	$-0.745239\pi$
$463$	−29.9717			−1.39290			−0.696451	+	0.717604i	$0.745239\pi$
$464$	3.19539	−	5.53458i	0.148342	−	0.256936i
$465$		0			0
$466$	−58.6398	+	33.8557i	−2.71644	+	1.56833i
$467$			17.3591i			0.803282i	0.915797	+	0.401641i	$0.131560\pi$
$467$			17.3591i			0.803282i	−0.915797	+	0.401641i	$0.868440\pi$
$468$	0.157597	−	12.8780i	0.00728493	−	0.595286i
$469$	47.8429			2.20918
$470$		0			0
$471$	−0.247901	−	0.429378i	−0.0114227	−	0.0197847i
$472$	36.0515	+	20.8143i	1.65940	+	0.958057i
$473$	47.1569			2.16828
$474$	−8.62805	−	4.98140i	−0.396299	−	0.228803i
$475$		0			0
$476$			89.6688i			4.10996i
$477$	−0.697497	−	0.402700i	−0.0319362	−	0.0184384i
$478$	4.09680	−	2.36529i	0.187383	−	0.108186i
$479$	8.85694	−	5.11356i	0.404684	−	0.233644i	−0.283819	−	0.958878i	$-0.591601\pi$
$479$	8.85694	−	5.11356i	0.404684	−	0.233644i	0.688503	+	0.725233i	$0.258268\pi$
$480$		0			0
$481$	−0.199452	+	16.2982i	−0.00909424	+	0.743133i
$482$			66.8229i			3.04370i
$483$	1.65372	+	2.86433i	0.0752469	+	0.130331i
$484$	13.7712	+	23.8524i	0.625964	+	1.08420i
$485$		0			0
$486$		−	2.36051i		−	0.107075i
$487$	8.23642	−	14.2659i	0.373228	−	0.646449i	−0.616832	−	0.787095i	$-0.711584\pi$
$487$	8.23642	−	14.2659i	0.373228	−	0.646449i	0.990060	+	0.140645i	$0.0449177\pi$
$488$	23.0112	−	39.8566i	1.04167	−	1.80422i
$489$		−	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	$0.610219\pi$
$492$	−18.5057	−	32.0528i	−0.834302	−	1.44505i
$493$			21.8644i			0.984722i
$494$	−17.1367	+	28.8602i	−0.771018	+	1.29848i
$495$		0			0
$496$	0.838316	−	0.484002i	0.0376415	−	0.0217323i
$497$	4.08376	−	2.35776i	0.183182	−	0.105760i
$498$	15.7335	+	9.08372i	0.705033	+	0.407051i
$499$		−	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
$502$	−41.7469			−1.86326
$503$	2.09892	+	1.21181i	0.0935861	+	0.0540320i	0.546063	−	0.837744i	$-0.316126\pi$
$503$	2.09892	+	1.21181i	0.0935861	+	0.0540320i	−0.452477	+	0.891776i	$0.649459\pi$
$504$	8.42890	+	14.5993i	0.375453	+	0.650304i
$505$		0			0
$506$	−7.43352			−0.330460
$507$	11.0959	+	6.77356i	0.492786	+	0.300825i
$508$			66.6566i			2.95741i
$509$	12.3914	−	7.15420i	0.549240	−	0.317104i	−0.199575	−	0.979883i	$-0.563956\pi$
$509$	12.3914	−	7.15420i	0.549240	−	0.317104i	0.748816	+	0.662778i	$0.230623\pi$
$510$		0			0
$511$	−14.6583	+	25.3889i	−0.648445	+	1.12314i
$512$	17.8150			0.787321
$513$	−1.97185	+	3.41535i	−0.0870595	+	0.150791i
$514$	40.7947	+	23.5528i	1.79938	+	1.03887i
$515$		0			0
$516$	−19.4706	+	33.7241i	−0.857147	+	1.48462i
$517$	−5.33764	+	3.08169i	−0.234749	+	0.135532i
$518$	−24.2394	−	41.9839i	−1.06502	−	1.84467i
$519$	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	$0.777090\pi$
$522$	4.67012	+	8.08888i	0.204405	+	0.354041i
$523$	−11.3883	+	6.57502i	−0.497974	+	0.287505i	−0.727877	−	0.685708i	$-0.759493\pi$
$523$	−11.3883	+	6.57502i	−0.497974	+	0.287505i	0.229902	+	0.973214i	$0.426159\pi$
$524$	−16.8917	+	29.2573i	−0.737917	+	1.27811i
$525$		0			0
$526$	6.94420	+	4.00924i	0.302782	+	0.174811i
$527$	−1.65588	+	2.86807i	−0.0721314	+	0.124935i
$528$	−6.98628			−0.304039
$529$	−11.2350	+	19.4596i	−0.488478	+	0.846069i
$530$		0			0
$531$	−9.71559	+	5.60930i	−0.421621	+	0.243423i
$532$		−	63.9973i		−	2.77464i
$533$	37.3564	+	0.457157i	1.61809	+	0.0198017i
$534$	16.1778			0.700080
$535$		0			0
$536$	−19.5386	−	33.8419i	−0.843940	−	1.46175i
$537$	−18.9774	−	10.9566i	−0.818937	−	0.472813i
$538$	36.2024			1.56080
$539$	−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	$-0.134152\pi$
$542$	−37.4128	−	21.6003i	−1.60702	−	0.927811i
$543$	−15.5369	+	8.97021i	−0.666750	+	0.384948i
$544$	−17.2698	+	9.97075i	−0.740439	+	0.427492i
$545$		0			0
$546$	−38.6627	−	0.473142i	−1.65461	−	0.0202486i
$547$		−	21.1122i		−	0.902694i	−0.892348	−	0.451347i	$-0.850944\pi$
$547$		−	21.1122i		−	0.902694i	0.892348	−	0.451347i	$-0.149056\pi$
$548$	−4.09065	−	7.08522i	−0.174744	−	0.302666i
$549$	6.20134	+	10.7410i	0.264667	+	0.458416i
$550$		0			0
$551$		−	15.6048i		−	0.664785i
$552$	1.35073	−	2.33953i	0.0574908	−	0.0995770i
$553$	−9.58726	+	16.6056i	−0.407692	+	0.706143i
$554$			18.4139i			0.782332i
$555$		0			0
$556$	−14.9541	−	25.9013i	−0.634195	−	1.09846i
$557$	5.07900	+	8.79709i	0.215204	+	0.372745i	0.953336	−	0.301912i	$-0.0976250\pi$
$557$	5.07900	+	8.79709i	0.215204	+	0.372745i	−0.738132	+	0.674657i	$0.764292\pi$
$558$			1.41475i			0.0598912i
$559$	−19.2356	−	34.2790i	−0.813578	−	1.44985i
$560$		0			0
$561$	20.6995	−	11.9509i	0.873933	−	0.504566i
$562$	47.4815	−	27.4134i	2.00288	−	1.15637i
$563$	−12.9377	−	7.46961i	−0.545261	−	0.314807i	0.201947	−	0.979396i	$-0.435273\pi$
$563$	−12.9377	−	7.46961i	−0.545261	−	0.314807i	−0.747208	+	0.664590i	$0.768606\pi$
$564$		−	5.08959i		−	0.214311i
$565$		0			0
$566$	16.0341	+	9.25727i	0.673962	+	0.389112i
$567$	−4.54305			−0.190790
$568$	−3.33554	−	1.92577i	−0.139956	−	0.0808037i
$569$	12.0374	+	20.8495i	0.504636	+	0.874055i	0.999986	+	0.00536121i	$0.00170654\pi$
$569$	12.0374	+	20.8495i	0.504636	+	0.874055i	−0.495350	+	0.868694i	$0.664960\pi$
$570$		0			0
$571$	1.95913			0.0819868			0.0409934	−	0.999159i	$-0.486948\pi$
$571$	1.95913			0.0819868			0.0409934	+	0.999159i	$0.486948\pi$
$572$	28.4428	−	47.9010i	1.18925	−	2.00284i
$573$		−	2.51042i		−	0.104874i
$574$	−96.2297	+	55.5583i	−4.01655	+	2.31896i
$575$		0			0
$576$	−5.87451	+	10.1749i	−0.244771	+	0.423956i
$577$	−1.22118			−0.0508382			−0.0254191	−	0.999677i	$-0.508092\pi$
$577$	−1.22118			−0.0508382			−0.0254191	+	0.999677i	$0.508092\pi$
$578$	−15.9723	+	27.6648i	−0.664360	+	1.15071i
$579$	8.16136	+	4.71197i	0.339175	+	0.195823i
$580$		0			0
$581$	17.4826	−	30.2808i	0.725301	−	1.25626i
$582$	−22.6870	+	13.0983i	−0.940405	+	0.542943i
$583$	−1.74191	−	3.01708i	−0.0721427	−	0.124955i
$584$	23.9452			0.990861
$585$		0			0
$586$	24.2671			1.00246
$587$	−14.8251	−	25.6779i	−0.611898	−	1.05984i	−0.990920	−	0.134451i	$-0.957073\pi$
$587$	−14.8251	−	25.6779i	−0.611898	−	1.05984i	0.379022	−	0.925388i	$-0.376261\pi$
$588$	42.1922	−	24.3597i	1.73998	−	1.00458i
$589$	1.18182	−	2.04697i	0.0486959	−	0.0843438i
$590$		0			0
$591$	−21.3578	−	12.3309i	−0.878542	−	0.507226i
$592$	−3.65066	+	6.32313i	−0.150041	+	0.259879i
$593$	−10.2794			−0.422126			−0.211063	−	0.977473i	$-0.567692\pi$
$593$	−10.2794			−0.422126			−0.211063	+	0.977473i	$0.567692\pi$
$594$	5.10528	−	8.84261i	0.209472	−	0.362817i
$595$		0			0
$596$	70.7089	−	40.8238i	2.89635	−	1.67221i
$597$			25.9532i			1.06219i
$598$	3.03218	+	5.40352i	0.123995	+	0.220967i
$599$	15.0591			0.615296			0.307648	−	0.951500i	$-0.400458\pi$
$599$	15.0591			0.615296			0.307648	+	0.951500i	$0.400458\pi$
$600$		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	$0.970601\pi$
$602$	101.247	+	58.4551i	4.12653	+	2.38245i
$603$	10.5310			0.428856
$604$	46.0955	+	26.6132i	1.87560	+	1.08288i
$605$		0			0
$606$			13.3638i			0.542869i
$607$	2.32401	+	1.34177i	0.0943288	+	0.0544608i	0.546422	−	0.837510i	$-0.315989\pi$
$607$	2.32401	+	1.34177i	0.0943288	+	0.0544608i	−0.452094	+	0.891971i	$0.649323\pi$
$608$	12.3256	−	7.11620i	0.499870	−	0.288600i
$609$	15.5679	−	8.98815i	0.630844	−	0.364218i
$610$		0			0
$611$	4.41737	+	2.62296i	0.178708	+	0.106114i
$612$			19.7376i			0.797845i
$613$	5.29031	+	9.16309i	0.213674	+	0.370094i	0.952862	−	0.303406i	$-0.0981237\pi$
$613$	5.29031	+	9.16309i	0.213674	+	0.370094i	−0.739188	+	0.673499i	$0.764790\pi$
$614$	−39.8994	−	69.1079i	−1.61021	−	2.78897i
$615$		0			0
$616$			72.9198i			2.93802i
$617$	−8.94290	+	15.4896i	−0.360028	+	0.623586i	−0.987965	−	0.154678i	$-0.950566\pi$
$617$	−8.94290	+	15.4896i	−0.360028	+	0.623586i	0.627937	+	0.778264i	$0.283899\pi$
$618$	−3.84017	+	6.65137i	−0.154474	+	0.267557i
$619$			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
$622$	−0.338463	−	0.586235i	−0.0135711	−	0.0235059i
$623$		−	31.1358i		−	1.24743i
$624$	2.84975	+	5.07842i	0.114081	+	0.203300i
$625$		0			0
$626$	56.9001	−	32.8513i	2.27419	−	1.31300i
$627$	−14.7734	+	8.52942i	−0.589992	+	0.340632i
$628$	1.53373	+	0.885500i	0.0612025	+	0.0353353i
$629$		−	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	$0.913980\pi$
$632$	15.6614			0.622977
$633$	−9.99866	−	5.77273i	−0.397411	−	0.229445i
$634$	−27.8698	−	48.2719i	−1.10685	−	1.91712i
$635$		0			0
$636$	2.87688			0.114076
$637$	−0.601771	+	49.1735i	−0.0238430	+	1.94833i
$638$			40.4019i			1.59953i
$639$	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	$0.0579155\pi$
$642$	34.2642			1.35230
$643$	23.0314	−	39.8916i	0.908272	−	1.57317i	0.0918073	−	0.995777i	$-0.470736\pi$
$643$	23.0314	−	39.8916i	0.908272	−	1.57317i	0.816464	−	0.577396i	$-0.195931\pi$
$644$	−10.2313	−	5.90707i	−0.403171	−	0.232771i
$645$		0			0
$646$	25.7196	−	44.5476i	1.01192	−	1.75270i
$647$	1.47513	−	0.851665i	0.0579932	−	0.0334824i	−0.470723	−	0.882281i	$-0.656007\pi$
$647$	1.47513	−	0.851665i	0.0579932	−	0.0334824i	0.528716	+	0.848799i	$0.322674\pi$
$648$	1.85534	+	3.21354i	0.0728846	+	0.126240i
$649$	−48.5270			−1.90485
$650$		0			0
$651$	2.72285			0.106717
$652$	3.07015	+	5.31766i	0.120237	+	0.208256i
$653$	2.38570	−	1.37739i	0.0933597	−	0.0539013i	−0.452593	−	0.891717i	$-0.649501\pi$
$653$	2.38570	−	1.37739i	0.0933597	−	0.0539013i	0.545953	+	0.837816i	$0.316168\pi$
$654$	−2.64749	+	4.58558i	−0.103525	+	0.179310i
$655$		0			0
$656$	14.4930	+	8.36754i	0.565857	+	0.326697i
$657$	−3.22653	+	5.58852i	−0.125879	+	0.218029i
$658$	−15.2801			−0.595680
$659$	−10.7195	+	18.5668i	−0.417574	+	0.723260i	−0.995695	−	0.0926917i	$-0.970453\pi$
$659$	−10.7195	+	18.5668i	−0.417574	+	0.723260i	0.578121	+	0.815951i	$0.303786\pi$
$660$		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	$0.375915\pi$
$662$			12.3190i			0.478791i
$663$	−17.1307	−	10.1719i	−0.665301	−	0.395045i
$664$	−28.5589			−1.10830
$665$		0			0
$666$	−5.33550	−	9.24135i	−0.206746	−	0.358095i
$667$	−2.49476	−	1.44035i	−0.0965973	−	0.0557705i
$668$	−20.3042			−0.785592
$669$	−7.03409	−	4.06113i	−0.271954	−	0.157012i
$670$		0			0
$671$			53.6489i			2.07109i
$672$	14.1988	+	8.19768i	0.547730	+	0.316232i
$673$	−0.779505	+	0.450047i	−0.0300477	+	0.0173481i	−0.514949	−	0.857221i	$-0.672189\pi$
$673$	−0.779505	+	0.450047i	−0.0300477	+	0.0173481i	0.484901	+	0.874569i	$0.338856\pi$
$674$	40.6303	−	23.4579i	1.56502	−	0.903565i
$675$		0			0
$676$	−46.4219	−	1.13636i	−1.78546	−	0.0437063i
$677$		−	40.3221i		−	1.54970i	−0.632144	−	0.774851i	$-0.717825\pi$
$677$		−	40.3221i		−	1.54970i	0.632144	−	0.774851i	$-0.282175\pi$
$678$	1.91001	+	3.30824i	0.0733536	+	0.127052i
$679$	25.2092	+	43.6635i	0.967439	+	1.67565i
$680$		0			0
$681$			13.5869i			0.520652i
$682$	−3.05981	+	5.29975i	−0.117166	+	0.202938i
$683$	3.99427	−	6.91828i	0.152837	−	0.264721i	−0.779433	−	0.626486i	$-0.784493\pi$
$683$	3.99427	−	6.91828i	0.152837	−	0.264721i	0.932269	+	0.361765i	$0.117826\pi$
$684$		−	14.0869i		−	0.538625i
$685$		0			0
$686$	−35.5996	−	61.6603i	−1.35920	−	2.35420i
$687$	−1.80521	−	3.12672i	−0.0688731	−	0.119292i
$688$		−	17.6077i		−	0.671286i
$689$	−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	$0.113129\pi$
$692$	−21.2566	+	12.2725i	−0.808053	+	0.466530i
$693$	−17.0186	−	9.82567i	−0.646482	−	0.373246i
$694$			4.03412i			0.153133i
$695$		0			0
$696$	−12.7156	−	7.34135i	−0.481983	−	0.278273i
$697$	−57.2546			−2.16867
$698$	−31.4586	−	18.1626i	−1.19072	−	0.687465i
$699$	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	$0.464078\pi$
$702$	−8.51029	−	0.104146i	−0.321200	−	0.00393075i
$703$			17.8281i			0.672399i
$704$	−44.0126	+	25.4107i	−1.65879	+	0.957701i
$705$		0			0
$706$	−22.1986	+	38.4490i	−0.835454	+	1.44705i
$707$	25.7202			0.967306
$708$	20.0363	−	34.7040i	0.753012	−	1.30425i
$709$	29.4208	+	16.9861i	1.10492	+	0.637926i	0.937509	−	0.347961i	$-0.113126\pi$
$709$	29.4208	+	16.9861i	1.10492	+	0.637926i	0.167411	+	0.985887i	$0.446459\pi$
$710$		0			0
$711$	−2.11031	+	3.65517i	−0.0791429	+	0.137080i
$712$	−22.0241	+	12.7156i	−0.825386	+	0.476537i
$713$	−0.218168	−	0.377877i	−0.00817044	−	0.0141516i
$714$	59.2566			2.21762
$715$		0			0
$716$	78.2738			2.92523
$717$	−1.00203	−	1.73556i	−0.0374213	−	0.0648157i
$718$	−34.9094	+	20.1550i	−1.30281	+	0.752177i
$719$	−12.0007	+	20.7858i	−0.447549	+	0.775178i	−0.998226	−	0.0595406i	$-0.981036\pi$
$719$	−12.0007	+	20.7858i	−0.447549	+	0.775178i	0.550677	+	0.834719i	$0.314370\pi$
$720$		0			0
$721$	12.8013	+	7.39083i	0.476745	+	0.275249i
$722$	4.06854	−	7.04692i	0.151415	−	0.262259i
$723$	28.3087			1.05281
$724$	32.0414	−	55.4974i	1.19081	−	2.06255i
$725$		0			0
$726$	15.7626	−	9.10054i	0.585005	−	0.337753i
$727$			26.1991i			0.971672i	0.874050	+	0.485836i	$0.161485\pi$
$727$			26.1991i			0.971672i	−0.874050	+	0.485836i	$0.838515\pi$
$728$	53.0064	−	29.7444i	1.96455	−	1.10240i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	30.1200	+	52.1693i	1.11403	+	1.92955i
$732$	−38.3668	−	22.1511i	−1.41808	−	0.818728i
$733$	49.2273			1.81825			0.909127	−	0.416520i	$-0.136750\pi$
$733$	49.2273			1.81825			0.909127	+	0.416520i	$0.136750\pi$
$734$	−21.2994	−	12.2972i	−0.786176	−	0.453899i
$735$		0			0
$736$		−	2.62735i		−	0.0968455i
$737$	39.4499	+	22.7764i	1.45315	+	0.838979i
$738$	−21.1817	+	12.2293i	−0.779711	+	0.450166i
$739$	−1.15468	+	0.666653i	−0.0424755	+	0.0245232i	−0.521087	−	0.853503i	$-0.674473\pi$
$739$	−1.15468	+	0.666653i	−0.0424755	+	0.0245232i	0.478612	+	0.878027i	$0.341140\pi$
$740$		0			0
$741$	12.2263	+	7.25977i	0.449144	+	0.266694i
$742$		−	8.63703i		−	0.317075i
$743$	−14.9195	−	25.8413i	−0.547342	−	0.948025i	−0.998455	−	0.0555581i	$-0.982306\pi$
$743$	−14.9195	−	25.8413i	−0.547342	−	0.948025i	0.451113	−	0.892467i	$-0.351027\pi$
$744$	−1.11198	−	1.92601i	−0.0407673	−	0.0706111i
$745$		0			0
$746$		−	56.8412i		−	2.08110i
$747$	3.84821	−	6.66530i	0.140799	−	0.243870i
$748$	−42.6883	+	73.9383i	−1.56084	+	2.70345i
$749$		−	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	$0.891096\pi$
$752$	1.15065	+	1.99299i	0.0419601	+	0.0726770i
$753$			17.6856i			0.644499i
$754$	29.3687	−	16.4802i	1.06955	−	0.600173i
$755$		0			0
$756$	14.0536	−	8.11385i	0.511125	−	0.295098i
$757$	41.9944	−	24.2455i	1.52631	−	0.881217i	0.526800	−	0.849989i	$-0.323392\pi$
$757$	41.9944	−	24.2455i	1.52631	−	0.881217i	0.999512	−	0.0312280i	$-0.00994180\pi$
$758$	18.0430	+	10.4171i	0.655350	+	0.378366i
$759$			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	$0.517315\pi$
$762$	44.0492			1.59574
$763$	8.82545	+	5.09538i	0.319503	+	0.184465i
$764$	4.48360	+	7.76582i	0.162211	+	0.280957i
$765$		0			0
$766$	38.2748			1.38293
$767$	19.7945	+	35.2749i	0.714736	+	1.27370i
$768$		−	24.9297i		−	0.899573i
$769$	−7.28560	+	4.20634i	−0.262725	+	0.151685i	−0.625577	−	0.780162i	$-0.715136\pi$
$769$	−7.28560	+	4.20634i	−0.262725	+	0.151685i	0.362852	+	0.931847i	$0.381803\pi$
$770$		0			0
$771$	9.97787	−	17.2822i	0.359344	−	0.622402i
$772$	−33.6621			−1.21153
$773$	18.6550	−	32.3114i	0.670973	−	1.16216i	−0.306655	−	0.951821i	$-0.599210\pi$
$773$	18.6550	−	32.3114i	0.670973	−	1.16216i	0.977628	−	0.210339i	$-0.0674569\pi$
$774$	22.2862	+	12.8669i	0.801061	+	0.462493i
$775$		0			0
$776$	20.5904	−	35.6636i	0.739151	−	1.28025i
$777$	−17.7860	+	10.2687i	−0.638069	+	0.368389i
$778$	39.1678	+	67.8406i	1.40423	+	2.43220i
$779$	40.8630			1.46407
$780$		0			0
$781$	4.48980			0.160658
$782$	−4.74793	−	8.22365i	−0.169786	−	0.294077i
$783$	3.42676	−	1.97844i	0.122462	−	0.0707036i
$784$	−11.0145	+	19.0776i	−0.393374	+	0.681344i
$785$		0			0
$786$	19.3343	+	11.1627i	0.689633	+	0.398160i
$787$	10.2385	−	17.7335i	0.364962	−	0.632133i	−0.623808	−	0.781578i	$-0.714415\pi$
$787$	10.2385	−	17.7335i	0.364962	−	0.632133i	0.988770	+	0.149445i	$0.0477486\pi$
$788$	88.0918			3.13814
$789$	1.69847	−	2.94183i	0.0604670	−	0.104732i
$790$		0			0
$791$	6.36706	−	3.67603i	0.226387	−	0.130704i
$792$			16.0509i			0.570342i
$793$	38.9981	−	21.8837i	1.38486	−	0.777113i
$794$	−17.7041			−0.628296
$795$		0			0
$796$	−46.3522	−	80.2843i	−1.64291	−	2.84560i
$797$	−21.2453	−	12.2660i	−0.752548	−	0.434484i	0.0740660	−	0.997253i	$-0.476402\pi$
$797$	−21.2453	−	12.2660i	−0.752548	−	0.434484i	−0.826614	+	0.562770i	$0.809736\pi$
$798$	−42.2919			−1.49712
$799$	−6.81850	−	3.93666i	−0.241221	−	0.139269i
$800$		0			0
$801$		−	6.85351i		−	0.242157i
$802$	6.97992	+	4.02986i	0.246470	+	0.142299i
$803$	−24.1736	+	13.9566i	−0.853067	+	0.492519i
$804$	−32.5770	+	18.8083i	−1.14890	+	0.663318i
$805$		0			0
$806$	5.10058	+	0.0624194i	0.179660	+	0.00219863i
$807$		−	15.3367i		−	0.539878i
$808$	−10.5039	−	18.1932i	−0.369525	−	0.640036i
$809$	8.38808	+	14.5286i	0.294909	+	0.510798i	0.974964	−	0.222364i	$-0.0713773\pi$
$809$	8.38808	+	14.5286i	0.294909	+	0.510798i	−0.680055	+	0.733161i	$0.738044\pi$
$810$		0			0
$811$		−	50.7808i		−	1.78315i	−0.452869	−	0.891577i	$-0.649600\pi$
$811$		−	50.7808i		−	1.78315i	0.452869	−	0.891577i	$-0.350400\pi$
$812$	−32.1055	+	55.6084i	−1.12668	+	1.95147i
$813$	−9.15070	+	15.8495i	−0.320929	+	0.555865i
$814$		−	46.1583i		−	1.61785i
$815$		0			0
$816$	−4.46227	−	7.72888i	−0.156211	−	0.270565i
$817$	−21.4969	−	37.2336i	−0.752080	−	1.30264i
$818$			34.4916i			1.20597i
$819$	−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	$0.290735\pi$
$822$	−4.68219	+	2.70326i	−0.163310	+	0.0942871i
$823$	4.40916	+	2.54563i	0.153694	+	0.0887351i	0.574874	−	0.818242i	$-0.305051\pi$
$823$	4.40916	+	2.54563i	0.153694	+	0.0887351i	−0.421181	+	0.906977i	$0.638384\pi$
$824$		−	12.0734i		−	0.420596i
$825$		0			0
$826$	−104.189	−	60.1535i	−3.62520	−	2.09301i
$827$	47.2400			1.64270			0.821349	−	0.570426i	$-0.193222\pi$
$827$	47.2400			1.64270			0.821349	+	0.570426i	$0.193222\pi$
$828$	−2.25209	−	1.30024i	−0.0782654	−	0.0451865i
$829$	−5.70266	−	9.87730i	−0.198062	−	0.343053i	0.749838	−	0.661621i	$-0.230131\pi$
$829$	−5.70266	−	9.87730i	−0.198062	−	0.343053i	−0.947900	+	0.318568i	$0.896798\pi$
$830$		0			0
$831$	7.80083			0.270608
$832$	36.4244	+	21.6282i	1.26279	+	0.749822i
$833$		−	75.3662i		−	2.61128i
$834$	−17.1165	+	9.88224i	−0.592698	+	0.342194i
$835$		0			0
$836$	30.4669	−	52.7703i	1.05372	−	1.82510i
$837$	0.599343			0.0207163
$838$	4.01895	−	6.96103i	0.138832	−	0.240465i
$839$	−23.5533	−	13.5985i	−0.813151	−	0.469473i	0.0348977	−	0.999391i	$-0.488889\pi$
$839$	−23.5533	−	13.5985i	−0.813151	−	0.469473i	−0.848049	+	0.529918i	$0.822223\pi$
$840$		0			0
$841$	6.67156	−	11.5555i	0.230054	−	0.398465i
$842$	−30.4608	+	17.5865i	−1.04975	+	0.606072i
$843$	−11.6134	−	20.1150i	−0.399986	−	0.692796i
$844$	41.2402			1.41955
$845$		0			0
$846$	−3.36340			−0.115636
$847$	−17.5150	−	30.3368i	−0.601822	−	1.04239i
$848$	−1.12653	+	0.650404i	−0.0386853	+	0.0223350i
$849$	3.92173	−	6.79264i	0.134593	−	0.233123i
$850$		0			0
$851$	2.85020	+	1.64556i	0.0977036	+	0.0564092i
$852$	−1.85379	+	3.21087i	−0.0635100	+	0.110002i
$853$	−29.5962			−1.01335			−0.506677	−	0.862136i	$-0.669126\pi$
$853$	−29.5962			−1.01335			−0.506677	+	0.862136i	$0.669126\pi$
$854$	−66.5025	+	115.186i	−2.27567	+	3.94158i
$855$		0			0
$856$	−46.6465	+	26.9314i	−1.59434	+	0.920495i
$857$		−	23.3137i		−	0.796382i	−0.917302	−	0.398191i	$-0.869638\pi$
$857$		−	23.3137i		−	0.796382i	0.917302	−	0.398191i	$-0.130362\pi$
$858$	−31.6548	−	18.7961i	−1.08068	−	0.641689i
$859$	−46.6719			−1.59242			−0.796212	−	0.605018i	$-0.793166\pi$
$859$	−46.6719			−1.59242			−0.796212	+	0.605018i	$0.793166\pi$
$860$		0			0
$861$	23.5366	+	40.7666i	0.802125	+	1.38932i
$862$	11.3388	+	6.54645i	0.386200	+	0.222973i
$863$	52.3597			1.78234			0.891172	−	0.453665i	$-0.149884\pi$
$863$	52.3597			1.78234			0.891172	+	0.453665i	$0.149884\pi$
$864$	3.12539	+	1.80444i	0.106328	+	0.0613884i
$865$		0			0
$866$			29.6514i			1.00759i
$867$	11.7199	+	6.76647i	0.398028	+	0.229802i
$868$	−8.42293	+	4.86298i	−0.285893	+	0.165060i
$869$	−15.8107	+	9.12833i	−0.536343	+	0.309658i
$870$		0			0
$871$	0.464632	−	37.9673i	0.0157435	−	1.28647i
$872$		−	8.32362i		−	0.281873i
$873$	5.54895	+	9.61107i	0.187804	+	0.325285i
$874$	3.38863	+	5.86928i	0.114622	+	0.198531i
$875$		0			0
$876$		−	23.0502i		−	0.778795i
$877$	7.90738	−	13.6960i	0.267013	−	0.462480i	−0.701076	−	0.713087i	$-0.747297\pi$
$877$	7.90738	−	13.6960i	0.267013	−	0.462480i	0.968089	+	0.250606i	$0.0806300\pi$
$878$	−34.9204	+	60.4839i	−1.17851	+	2.04123i
$879$		−	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	$0.576861\pi$
$882$	−16.0978	−	27.8822i	−0.542042	−	0.938844i
$883$			18.5133i			0.623024i	0.950242	+	0.311512i	$0.100835\pi$
$883$			18.5133i			0.623024i	−0.950242	+	0.311512i	$0.899165\pi$
$884$	71.1595	+	0.870829i	2.39335	+	0.0292892i
$885$		0			0
$886$	−60.7044	+	35.0477i	−2.03941	+	1.17745i
$887$	28.9164	−	16.6949i	0.970919	−	0.560560i	0.0714024	−	0.997448i	$-0.477253\pi$
$887$	28.9164	−	16.6949i	0.970919	−	0.560560i	0.899516	+	0.436888i	$0.143919\pi$
$888$	14.5273	+	8.38732i	0.487503	+	0.281460i
$889$		−	84.7775i		−	2.84335i
$890$		0			0
$891$	−3.74607	−	2.16279i	−0.125498	−	0.0724562i
$892$	29.0126			0.971414
$893$	4.86641	+	2.80962i	0.162848	+	0.0940205i
$894$	−26.9779	−	46.7272i	−0.902277	−	1.56279i
$895$		0			0
$896$	−93.2045			−3.11374
$897$	2.28914	−	1.28455i	0.0764321	−	0.0428897i
$898$			26.0403i			0.868977i
$899$	−2.05380	+	1.18576i	−0.0684981	+	0.0395474i
$900$		0			0
$901$	2.22519	−	3.85413i	0.0741317	−	0.128400i
$902$	−105.798			−3.52267
$903$	24.7638	−	42.8922i	0.824089	−	1.42736i
$904$	−5.20050	−	3.00251i	−0.172966	−	0.0998620i
$905$		0			0
$906$	17.5870	−	30.4617i	0.584291	−	1.01202i
$907$	−28.6130	+	16.5197i	−0.950078	+	0.548528i	−0.893105	−	0.449848i	$-0.851478\pi$
$907$	−28.6130	+	16.5197i	−0.950078	+	0.548528i	−0.0569728	+	0.998376i	$0.518145\pi$
$908$	−24.2661	−	42.0302i	−0.805300	−	1.39482i
$909$	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	$0.537032\pi$
$912$	3.18476	+	5.51616i	0.105458	+	0.182658i
$913$	28.8313	−	16.6458i	0.954176	−	0.550894i
$914$	16.8020	−	29.1019i	0.555760	−	0.962604i
$915$		0			0
$916$	11.1686	+	6.44819i	0.369021	+	0.213054i
$917$	21.4838	−	37.2110i	0.709458	−	1.22882i
$918$	13.0434			0.430495
$919$	5.28827	−	9.15956i	0.174444	−	0.302146i	−0.765525	−	0.643406i	$-0.777521\pi$
$919$	5.28827	−	9.15956i	0.174444	−	0.302146i	0.939969	+	0.341261i	$0.110854\pi$
$920$		0			0
$921$	−29.2767	+	16.9029i	−0.964701	+	0.556970i
$922$		−	52.7721i		−	1.73796i
$923$	−1.83141	−	3.26369i	−0.0602818	−	0.107426i
$924$	70.1943			2.30922
$925$		0			0
$926$	−35.3742	−	61.2698i	−1.16247	−	2.01345i
$927$	2.81777	+	1.62684i	0.0925478	+	0.0534325i
$928$	−14.2799			−0.468762
$929$	12.6230	+	7.28788i	0.414147	+	0.239108i	0.692570	−	0.721351i	$-0.256478\pi$
$929$	12.6230	+	7.28788i	0.414147	+	0.239108i	−0.278423	+	0.960459i	$0.589812\pi$
$930$		0			0
$931$			53.7894i			1.76288i
$932$	−88.7354	−	51.2314i	−2.90663	−	1.67814i
$933$	−0.248351	+	0.143386i	−0.00813066	+	0.00469424i
$934$	−35.4864	+	20.4881i	−1.16115	+	0.670391i
$935$		0			0
$936$	11.6676	−	6.54724i	0.381367	−	0.214003i
$937$		−	2.03451i		−	0.0664644i	−0.999448	−	0.0332322i	$-0.989420\pi$
$937$		−	2.03451i		−	0.0664644i	0.999448	−	0.0332322i	$-0.0105801\pi$
$938$	56.4668	+	97.8033i	1.84370	+	3.19339i
$939$	−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	$0.918019\pi$
$942$	0.585173	−	1.01355i	0.0190660	−	0.0330232i
$943$	3.77173	−	6.53283i	0.122824	−	0.212738i
$944$			18.1192i			0.589731i
$945$		0			0
$946$	55.6570	+	96.4008i	1.80957	+	3.13426i
$947$	17.5874	+	30.4622i	0.571513	+	0.989890i	0.996411	+	0.0846485i	$0.0269767\pi$
$947$	17.5874	+	30.4622i	0.571513	+	0.989890i	−0.424898	+	0.905241i	$0.639690\pi$
$948$		−	15.0760i		−	0.489646i
$949$	20.0058	+	11.8791i	0.649416	+	0.385612i
$950$		0			0
$951$	−20.4498	+	11.8067i	−0.663130	+	0.382858i
$952$	−80.6707	+	46.5753i	−2.61455	+	1.50951i
$953$	−2.76248	−	1.59492i	−0.0894855	−	0.0516645i	0.454589	−	0.890701i	$-0.349786\pi$
$953$	−2.76248	−	1.59492i	−0.0894855	−	0.0516645i	−0.544075	+	0.839037i	$0.683119\pi$
$954$		−	1.90115i		−	0.0615521i
$955$		0			0
$956$	6.19939	+	3.57922i	0.200503	+	0.115760i
$957$	17.1158			0.553275
$958$	20.9069	+	12.0706i	0.675470	+	0.389983i
$959$	5.20272	+	9.01138i	0.168005	+	0.290993i
$960$		0			0
$961$	30.6408			0.988413
$962$	−33.5531	+	18.8282i	−1.08179	+	0.607047i
$963$		−	14.5156i		−	0.467759i
$964$	−87.5710	+	50.5591i	−2.82047	+	1.62840i
$965$		0			0
$966$	−3.90362	+	6.76126i	−0.125597	+	0.217540i
$967$	−19.5885			−0.629925			−0.314962	−	0.949104i	$-0.601992\pi$
$967$	−19.5885			−0.629925			−0.314962	+	0.949104i	$0.601992\pi$
$968$	−14.3059	+	24.7786i	−0.459810	+	0.796414i
$969$	−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	$0.0653479\pi$
$972$	3.09343	−	1.78599i	0.0992218	−	0.0572857i
$973$	19.0195	+	32.9427i	0.609736	+	1.05609i
$974$	38.8842			1.24593
$975$		0			0
$976$	20.0317			0.641198
$977$	5.68666	+	9.84958i	0.181932	+	0.315116i	0.942538	−	0.334098i	$-0.108432\pi$
$977$	5.68666	+	9.84958i	0.181932	+	0.315116i	−0.760606	+	0.649213i	$0.775098\pi$
$978$	3.51412	−	2.02888i	0.112369	−	0.0648763i
$979$	14.8227	−	25.6737i	0.473736	−	0.820535i
$980$		0			0
$981$	1.94263	+	1.12158i	0.0620233	+	0.0358092i
$982$	−33.7333	+	58.4278i	−1.07647	+	1.86451i
$983$	29.0243			0.925732			0.462866	−	0.886428i	$-0.346821\pi$
$983$	29.0243			0.925732			0.462866	+	0.886428i	$0.346821\pi$
$984$	19.2243	−	33.2974i	0.612847	−	1.06148i
$985$		0			0
$986$	−44.6964	+	25.8055i	−1.42342	+	0.821814i
$987$			6.47323i			0.206045i
$988$	−50.7871	−	0.621517i	−1.61575	−	0.0197731i
$989$	−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	$0.781286\pi$
$992$	−1.87318	−	1.08148i	−0.0594735	−	0.0343371i
$993$	5.21879			0.165613
$994$	9.63973	+	5.56550i	0.305754	+	0.176527i
$995$		0			0
$996$			27.4915i			0.871101i
$997$	12.5420	+	7.24112i	0.397209	+	0.229328i	0.685279	−	0.728281i	$-0.259680\pi$
$997$	12.5420	+	7.24112i	0.397209	+	0.229328i	−0.288070	+	0.957609i	$0.593014\pi$
$998$	29.9499	−	17.2916i	0.948048	−	0.547356i
$999$	−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.w.k.49.11		24
5.2	odd	4		975.2.bc.k.751.1	✓	12
5.3	odd	4		975.2.bc.l.751.6	yes	12
5.4	even	2	inner	975.2.w.k.49.2		24
13.4	even	6	inner	975.2.w.k.199.2		24
65.4	even	6	inner	975.2.w.k.199.11		24
65.17	odd	12		975.2.bc.k.901.1	yes	12
65.43	odd	12		975.2.bc.l.901.6	yes	12

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.18025 + 2.04426i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.78599 + 3.09343i) q^{4} +(2.04426 + 1.18025i) q^{6} +(2.27152 - 3.93440i) q^{7} -3.71068 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.18025 + 2.04426i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-1.78599 + 3.09343i) q^{4} +(2.04426 + 1.18025i) q^{6} +(2.27152 - 3.93440i) q^{7} -3.71068 q^{8} +(0.500000 - 0.866025i) q^{9} +(3.74607 - 2.16279i) q^{11} +3.57199i q^{12} +(-3.10021 - 1.84085i) q^{13} +10.7239 q^{14} +(-0.807554 - 1.39872i) q^{16} +(4.78536 + 2.76283i) q^{17} +2.36051 q^{18} +(-3.41535 - 1.97185i) q^{19} -4.54305i q^{21} +(8.84261 + 5.10528i) q^{22} +(-0.630486 + 0.364011i) q^{23} +(-3.21354 + 1.85534i) q^{24} +(0.104146 - 8.51029i) q^{26} -1.00000i q^{27} +(8.11385 + 14.0536i) q^{28} +(1.97844 + 3.42676i) q^{29} +0.599343i q^{31} +(-1.80444 + 3.12539i) q^{32} +(2.16279 - 3.74607i) q^{33} +13.0434i q^{34} +(1.78599 + 3.09343i) q^{36} +(-2.26032 - 3.91499i) q^{37} -9.30914i q^{38} +(-3.60528 - 0.0441204i) q^{39} +(-8.97339 + 5.18079i) q^{41} +(9.28716 - 5.36195i) q^{42} +(9.44128 + 5.45093i) q^{43} +15.4509i q^{44} +(-1.48827 - 0.859250i) q^{46} -1.42486 q^{47} +(-1.39872 - 0.807554i) q^{48} +(-6.81965 - 11.8120i) q^{49} +5.52566 q^{51} +(11.2315 - 6.30252i) q^{52} -0.805400i q^{53} +(2.04426 - 1.18025i) q^{54} +(-8.42890 + 14.5993i) q^{56} -3.94371 q^{57} +(-4.67012 + 8.08888i) q^{58} +(-9.71559 - 5.60930i) q^{59} +(-6.20134 + 10.7410i) q^{61} +(-1.22521 + 0.707376i) q^{62} +(-2.27152 - 3.93440i) q^{63} -11.7490 q^{64} +10.2106 q^{66} +(5.26551 + 9.12013i) q^{67} +(-17.0933 + 9.86879i) q^{68} +(-0.364011 + 0.630486i) q^{69} +(0.898903 + 0.518982i) q^{71} +(-1.85534 + 3.21354i) q^{72} -6.45306 q^{73} +(5.33550 - 9.24135i) q^{74} +(12.1996 - 7.04343i) q^{76} -19.6513i q^{77} +(-4.16495 - 7.42220i) q^{78} -4.22063 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-21.1817 - 12.2293i) q^{82} +7.69642 q^{83} +(14.0536 + 8.11385i) q^{84} +25.7339i q^{86} +(3.42676 + 1.97844i) q^{87} +(-13.9004 + 8.02543i) q^{88} +(5.93532 - 3.42676i) q^{89} +(-14.2848 + 8.01590i) q^{91} -2.60048i q^{92} +(0.299672 + 0.519046i) q^{93} +(-1.68170 - 2.91279i) q^{94} +3.60889i q^{96} +(-5.54895 + 9.61107i) q^{97} +(16.0978 - 27.8822i) q^{98} -4.32558i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 16 q^{4} + 12 q^{9}+O(q^{10}) \) 24 * q - 16 * q^4 + 12 * q^9	\( 24 q - 16 q^{4} + 12 q^{9} + 18 q^{11} - 20 q^{14} - 8 q^{16} + 18 q^{19} - 10 q^{26} + 32 q^{29} + 16 q^{36} + 6 q^{39} + 36 q^{41} - 90 q^{46} - 62 q^{49} + 50 q^{56} - 108 q^{59} - 22 q^{61} - 32 q^{64} + 60 q^{66} + 2 q^{69} - 66 q^{71} - 10 q^{74} - 54 q^{76} - 36 q^{79} - 12 q^{81} + 78 q^{84} + 96 q^{89} - 58 q^{91} + 60 q^{94}+O(q^{100}) \) 24 * q - 16 * q^4 + 12 * q^9 + 18 * q^11 - 20 * q^14 - 8 * q^16 + 18 * q^19 - 10 * q^26 + 32 * q^29 + 16 * q^36 + 6 * q^39 + 36 * q^41 - 90 * q^46 - 62 * q^49 + 50 * q^56 - 108 * q^59 - 22 * q^61 - 32 * q^64 + 60 * q^66 + 2 * q^69 - 66 * q^71 - 10 * q^74 - 54 * q^76 - 36 * q^79 - 12 * q^81 + 78 * q^84 + 96 * q^89 - 58 * q^91 + 60 * q^94

Introduction

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