LMFDB - Embedded newform 552.2.n.b.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(91,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))

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

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

chi := DirichletCharacter("552.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.n (of order $2$, degree $1$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.4
Character	$\chi$	$=$	552.91
Dual form			552.2.n.b.91.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38507 + 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 - 0.791193i) q^{4} +2.03317 q^{5} +(1.38507 - 0.285614i) q^{6} -1.21988 q^{7} +(-2.31819 + 1.62049i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.38507 + 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 - 0.791193i) q^{4} +2.03317 q^{5} +(1.38507 - 0.285614i) q^{6} -1.21988 q^{7} +(-2.31819 + 1.62049i) q^{8} +1.00000 q^{9} +(-2.81608 + 0.580701i) q^{10} +1.88814i q^{11} +(-1.83685 + 0.791193i) q^{12} +3.19024i q^{13} +(1.68962 - 0.348415i) q^{14} -2.03317 q^{15} +(2.74803 - 2.90660i) q^{16} +5.91574i q^{17} +(-1.38507 + 0.285614i) q^{18} -6.08344i q^{19} +(3.73462 - 1.60863i) q^{20} +1.21988 q^{21} +(-0.539280 - 2.61521i) q^{22} +(3.96642 - 2.69583i) q^{23} +(2.31819 - 1.62049i) q^{24} -0.866240 q^{25} +(-0.911179 - 4.41871i) q^{26} -1.00000 q^{27} +(-2.24073 + 0.965159i) q^{28} +9.30575i q^{29} +(2.81608 - 0.580701i) q^{30} -3.55669i q^{31} +(-2.97605 + 4.81073i) q^{32} -1.88814i q^{33} +(-1.68962 - 8.19372i) q^{34} -2.48021 q^{35} +(1.83685 - 0.791193i) q^{36} +11.1137 q^{37} +(1.73752 + 8.42601i) q^{38} -3.19024i q^{39} +(-4.71327 + 3.29472i) q^{40} -2.52410 q^{41} +(-1.68962 + 0.348415i) q^{42} +11.6630i q^{43} +(1.49388 + 3.46823i) q^{44} +2.03317 q^{45} +(-4.72381 + 4.86679i) q^{46} +11.2078i q^{47} +(-2.74803 + 2.90660i) q^{48} -5.51190 q^{49} +(1.19980 - 0.247411i) q^{50} -5.91574i q^{51} +(2.52410 + 5.85999i) q^{52} +11.0682 q^{53} +(1.38507 - 0.285614i) q^{54} +3.83890i q^{55} +(2.82791 - 1.97680i) q^{56} +6.08344i q^{57} +(-2.65786 - 12.8891i) q^{58} +0.657857 q^{59} +(-3.73462 + 1.60863i) q^{60} +10.3789 q^{61} +(1.01584 + 4.92627i) q^{62} -1.21988 q^{63} +(2.74803 - 7.51321i) q^{64} +6.48629i q^{65} +(0.539280 + 2.61521i) q^{66} +2.45869i q^{67} +(4.68049 + 10.8663i) q^{68} +(-3.96642 + 2.69583i) q^{69} +(3.43528 - 0.708385i) q^{70} +4.84611i q^{71} +(-2.31819 + 1.62049i) q^{72} -7.87149 q^{73} +(-15.3933 + 3.17425i) q^{74} +0.866240 q^{75} +(-4.81318 - 11.1744i) q^{76} -2.30330i q^{77} +(0.911179 + 4.41871i) q^{78} -4.23131 q^{79} +(5.58719 - 5.90960i) q^{80} +1.00000 q^{81} +(3.49606 - 0.720918i) q^{82} +7.58314i q^{83} +(2.24073 - 0.965159i) q^{84} +12.0277i q^{85} +(-3.33113 - 16.1541i) q^{86} -9.30575i q^{87} +(-3.05971 - 4.37708i) q^{88} -3.85989i q^{89} +(-2.81608 + 0.580701i) q^{90} -3.89171i q^{91} +(5.15279 - 8.09004i) q^{92} +3.55669i q^{93} +(-3.20111 - 15.5236i) q^{94} -12.3686i q^{95} +(2.97605 - 4.81073i) q^{96} -3.03678i q^{97} +(7.63437 - 1.57428i) q^{98} +1.88814i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9	$ 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81} - 40 q^{82} + 40 q^{92} - 48 q^{94}+O(q^{100}) $ 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

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 $

$2$	−1.38507	+	0.285614i	−0.979394	+	0.201960i
$2$	−1.38507	+	0.285614i	−0.979394	+	0.201960i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.83685	−	0.791193i	0.918424	−	0.395596i
$5$	2.03317			0.909259			0.454630	−	0.890681i	$-0.349772\pi$
$5$	2.03317			0.909259			0.454630	+	0.890681i	$0.349772\pi$
$6$	1.38507	−	0.285614i	0.565453	−	0.116602i
$7$	−1.21988			−0.461071			−0.230535	−	0.973064i	$-0.574048\pi$
$7$	−1.21988			−0.461071			−0.230535	+	0.973064i	$0.574048\pi$
$8$	−2.31819	+	1.62049i	−0.819605	+	0.572930i
$9$	1.00000			0.333333
$10$	−2.81608	+	0.580701i	−0.890523	+	0.183634i
$11$			1.88814i			0.569296i	0.958632	+	0.284648i	$0.0918768\pi$
$11$			1.88814i			0.569296i	−0.958632	+	0.284648i	$0.908123\pi$
$12$	−1.83685	+	0.791193i	−0.530253	+	0.228398i
$13$			3.19024i			0.884814i	0.896814	+	0.442407i	$0.145875\pi$
$13$			3.19024i			0.884814i	−0.896814	+	0.442407i	$0.854125\pi$
$14$	1.68962	−	0.348415i	0.451570	−	0.0931178i
$15$	−2.03317			−0.524961
$16$	2.74803	−	2.90660i	0.687007	−	0.726651i
$17$			5.91574i			1.43478i	0.696673	+	0.717389i	$0.254663\pi$
$17$			5.91574i			1.43478i	−0.696673	+	0.717389i	$0.745337\pi$
$18$	−1.38507	+	0.285614i	−0.326465	+	0.0673199i
$19$		−	6.08344i		−	1.39564i	−0.716274	−	0.697819i	$-0.754154\pi$
$19$		−	6.08344i		−	1.39564i	0.716274	−	0.697819i	$-0.245846\pi$
$20$	3.73462	−	1.60863i	0.835086	−	0.359700i
$21$	1.21988			0.266199
$22$	−0.539280	−	2.61521i	−0.114975	−	0.557565i
$23$	3.96642	−	2.69583i	0.827056	−	0.562120i
$23$	3.96642	−	2.69583i	0.827056	−	0.562120i
$24$	2.31819	−	1.62049i	0.473199	−	0.330781i
$25$	−0.866240			−0.173248
$26$	−0.911179	−	4.41871i	−0.178697	−	0.866581i
$27$	−1.00000			−0.192450
$28$	−2.24073	+	0.965159i	−0.423459	+	0.182398i
$29$			9.30575i			1.72804i	0.503462	+	0.864018i	$0.332059\pi$
$29$			9.30575i			1.72804i	−0.503462	+	0.864018i	$0.667941\pi$
$30$	2.81608	−	0.580701i	0.514144	−	0.106021i
$31$		−	3.55669i		−	0.638800i	−0.947620	−	0.319400i	$-0.896519\pi$
$31$		−	3.55669i		−	0.638800i	0.947620	−	0.319400i	$-0.103481\pi$
$32$	−2.97605	+	4.81073i	−0.526096	+	0.850425i
$33$		−	1.88814i		−	0.328683i
$34$	−1.68962	−	8.19372i	−0.289767	−	1.40521i
$35$	−2.48021			−0.419233
$36$	1.83685	−	0.791193i	0.306141	−	0.131865i
$37$	11.1137			1.82709			0.913544	−	0.406739i	$-0.133334\pi$
$37$	11.1137			1.82709			0.913544	+	0.406739i	$0.133334\pi$
$38$	1.73752	+	8.42601i	0.281863	+	1.36688i
$39$		−	3.19024i		−	0.510848i
$40$	−4.71327	+	3.29472i	−0.745233	+	0.520941i
$41$	−2.52410			−0.394198			−0.197099	−	0.980384i	$-0.563152\pi$
$41$	−2.52410			−0.394198			−0.197099	+	0.980384i	$0.563152\pi$
$42$	−1.68962	+	0.348415i	−0.260714	+	0.0537616i
$43$			11.6630i			1.77859i	0.457330	+	0.889297i	$0.348806\pi$
$43$			11.6630i			1.77859i	−0.457330	+	0.889297i	$0.651194\pi$
$44$	1.49388	+	3.46823i	0.225212	+	0.522856i
$45$	2.03317			0.303086
$46$	−4.72381	+	4.86679i	−0.696487	+	0.717569i
$47$			11.2078i			1.63483i	0.576052	+	0.817413i	$0.304592\pi$
$47$			11.2078i			1.63483i	−0.576052	+	0.817413i	$0.695408\pi$
$48$	−2.74803	+	2.90660i	−0.396644	+	0.419532i
$49$	−5.51190			−0.787414
$50$	1.19980	−	0.247411i	0.169678	−	0.0349891i
$51$		−	5.91574i		−	0.828369i
$52$	2.52410	+	5.85999i	0.350029	+	0.812635i
$53$	11.0682			1.52034			0.760169	−	0.649725i	$-0.225116\pi$
$53$	11.0682			1.52034			0.760169	+	0.649725i	$0.225116\pi$
$54$	1.38507	−	0.285614i	0.188484	−	0.0388672i
$55$			3.83890i			0.517638i
$56$	2.82791	−	1.97680i	0.377896	−	0.264161i
$57$			6.08344i			0.805772i
$58$	−2.65786	−	12.8891i	−0.348994	−	1.69243i
$59$	0.657857			0.0856456			0.0428228	−	0.999083i	$-0.486365\pi$
$59$	0.657857			0.0856456			0.0428228	+	0.999083i	$0.486365\pi$
$60$	−3.73462	+	1.60863i	−0.482137	+	0.207673i
$61$	10.3789			1.32888			0.664441	−	0.747341i	$-0.268670\pi$
$61$	10.3789			1.32888			0.664441	+	0.747341i	$0.268670\pi$
$62$	1.01584	+	4.92627i	0.129012	+	0.625637i
$63$	−1.21988			−0.153690
$64$	2.74803	−	7.51321i	0.343503	−	0.939151i
$65$			6.48629i			0.804525i
$66$	0.539280	+	2.61521i	0.0663808	+	0.321910i
$67$			2.45869i			0.300377i	0.988657	+	0.150189i	$0.0479881\pi$
$67$			2.45869i			0.300377i	−0.988657	+	0.150189i	$0.952012\pi$
$68$	4.68049	+	10.8663i	0.567593	+	1.31773i
$69$	−3.96642	+	2.69583i	−0.477501	+	0.324540i
$70$	3.43528	−	0.708385i	0.410594	−	0.0846682i
$71$			4.84611i			0.575127i	0.957762	+	0.287564i	$0.0928453\pi$
$71$			4.84611i			0.575127i	−0.957762	+	0.287564i	$0.907155\pi$
$72$	−2.31819	+	1.62049i	−0.273202	+	0.190977i
$73$	−7.87149			−0.921288			−0.460644	−	0.887585i	$-0.652382\pi$
$73$	−7.87149			−0.921288			−0.460644	+	0.887585i	$0.652382\pi$
$74$	−15.3933	+	3.17425i	−1.78944	+	0.368999i
$75$	0.866240			0.100025
$76$	−4.81318	−	11.1744i	−0.552109	−	1.28179i
$77$		−	2.30330i		−	0.262486i
$78$	0.911179	+	4.41871i	0.103171	+	0.500321i
$79$	−4.23131			−0.476060			−0.238030	−	0.971258i	$-0.576502\pi$
$79$	−4.23131			−0.476060			−0.238030	+	0.971258i	$0.576502\pi$
$80$	5.58719	−	5.90960i	0.624667	−	0.660714i
$81$	1.00000			0.111111
$82$	3.49606	−	0.720918i	0.386075	−	0.0796121i
$83$			7.58314i			0.832358i	0.909283	+	0.416179i	$0.136631\pi$
$83$			7.58314i			0.832358i	−0.909283	+	0.416179i	$0.863369\pi$
$84$	2.24073	−	0.965159i	0.244484	−	0.105307i
$85$			12.0277i			1.30458i
$86$	−3.33113	−	16.1541i	−0.359205	−	1.74194i
$87$		−	9.30575i		−	0.997681i
$88$	−3.05971	−	4.37708i	−0.326167	−	0.466598i
$89$		−	3.85989i		−	0.409147i	−0.978851	−	0.204574i	$-0.934419\pi$
$89$		−	3.85989i		−	0.409147i	0.978851	−	0.204574i	$-0.0655808\pi$
$90$	−2.81608	+	0.580701i	−0.296841	+	0.0612113i
$91$		−	3.89171i		−	0.407962i
$92$	5.15279	−	8.09004i	0.537215	−	0.843445i
$93$			3.55669i			0.368811i
$94$	−3.20111	−	15.5236i	−0.330169	−	1.60114i
$95$		−	12.3686i		−	1.26900i
$96$	2.97605	−	4.81073i	0.303742	−	0.490993i
$97$		−	3.03678i		−	0.308338i	−0.988044	−	0.154169i	$-0.950730\pi$
$97$		−	3.03678i		−	0.308338i	0.988044	−	0.154169i	$-0.0492701\pi$
$98$	7.63437	−	1.57428i	0.771188	−	0.159026i
$99$			1.88814i			0.189765i
$100$	−1.59115	+	0.685363i	−0.159115	+	0.0685363i
$101$		−	7.00245i		−	0.696770i	−0.937352	−	0.348385i	$-0.886730\pi$
$101$		−	7.00245i		−	0.696770i	0.937352	−	0.348385i	$-0.113270\pi$
$102$	1.68962	+	8.19372i	0.167297	+	0.811299i
$103$	−3.05695			−0.301210			−0.150605	−	0.988594i	$-0.548122\pi$
$103$	−3.05695			−0.301210			−0.150605	+	0.988594i	$0.548122\pi$
$104$	−5.16975	−	7.39559i	−0.506936	−	0.725198i
$105$	2.48021			0.242044
$106$	−15.3303	+	3.16124i	−1.48901	+	0.307047i
$107$		−	4.21095i		−	0.407088i	−0.979066	−	0.203544i	$-0.934754\pi$
$107$		−	4.21095i		−	0.407088i	0.979066	−	0.203544i	$-0.0652459\pi$
$108$	−1.83685	+	0.791193i	−0.176751	+	0.0761326i
$109$	3.18091			0.304676			0.152338	−	0.988328i	$-0.451320\pi$
$109$	3.18091			0.304676			0.152338	+	0.988328i	$0.451320\pi$
$110$	−1.09645	−	5.31716i	−0.104542	−	0.506971i
$111$	−11.1137			−1.05487
$112$	−3.35226	+	3.54570i	−0.316759	+	0.335037i
$113$		−	18.9194i		−	1.77979i	−0.456169	−	0.889893i	$-0.650779\pi$
$113$		−	18.9194i		−	1.77979i	0.456169	−	0.889893i	$-0.349221\pi$
$114$	−1.73752	−	8.42601i	−0.162734	−	0.789168i
$115$	8.06438	−	5.48108i	0.752008	−	0.511113i
$116$	7.36265	+	17.0933i	0.683604	+	1.58707i
$117$			3.19024i			0.294938i
$118$	−0.911179	+	0.187893i	−0.0838808	+	0.0172970i
$119$		−	7.21648i		−	0.661534i
$120$	4.71327	−	3.29472i	0.430260	−	0.300766i
$121$	7.43492			0.675902
$122$	−14.3755	+	2.96436i	−1.30150	+	0.268381i
$123$	2.52410			0.227590
$124$	−2.81403	−	6.53310i	−0.252707	−	0.586690i
$125$	−11.9270			−1.06679
$126$	1.68962	−	0.348415i	0.150523	−	0.0310393i
$127$		−	7.44653i		−	0.660773i	−0.943846	−	0.330386i	$-0.892821\pi$
$127$		−	7.44653i		−	0.660773i	0.943846	−	0.330386i	$-0.107179\pi$
$128$	−1.66034	+	11.1912i	−0.146754	+	0.989173i
$129$		−	11.6630i		−	1.02687i
$130$	−1.85258	−	8.98398i	−0.162482	−	0.787947i
$131$	1.82236			0.159220			0.0796101	−	0.996826i	$-0.474632\pi$
$131$	1.82236			0.159220			0.0796101	+	0.996826i	$0.474632\pi$
$132$	−1.49388	−	3.46823i	−0.130026	−	0.301871i
$133$			7.42106i			0.643488i
$134$	−0.702238	−	3.40547i	−0.0606641	−	0.294187i
$135$	−2.03317			−0.174987
$136$	−9.58639	−	13.7138i	−0.822026	−	1.17595i
$137$		−	0.220739i		−	0.0188590i	−0.999956	−	0.00942952i	$-0.996998\pi$
$137$		−	0.220739i		−	0.0188590i	0.999956	−	0.00942952i	$-0.00300155\pi$
$138$	4.72381	−	4.86679i	0.402117	−	0.414289i
$139$	21.9828			1.86456			0.932279	−	0.361741i	$-0.117817\pi$
$139$	21.9828			1.86456			0.932279	+	0.361741i	$0.117817\pi$
$140$	−4.55578	+	1.96233i	−0.385034	+	0.165847i
$141$		−	11.2078i		−	0.943867i
$142$	−1.38412	−	6.71221i	−0.116153	−	0.563276i
$143$	−6.02363			−0.503721
$144$	2.74803	−	2.90660i	0.229002	−	0.242217i
$145$			18.9201i			1.57123i
$146$	10.9026	−	2.24821i	0.902304	−	0.186063i
$147$	5.51190			0.454614
$148$	20.4143	−	8.79312i	1.67804	−	0.722790i
$149$	−14.3997			−1.17967			−0.589835	−	0.807524i	$-0.700807\pi$
$149$	−14.3997			−1.17967			−0.589835	+	0.807524i	$0.700807\pi$
$150$	−1.19980	+	0.247411i	−0.0979636	+	0.0202010i
$151$			4.90495i			0.399160i	0.979882	+	0.199580i	$0.0639577\pi$
$151$			4.90495i			0.399160i	−0.979882	+	0.199580i	$0.936042\pi$
$152$	9.85816	+	14.1026i	0.799602	+	1.14387i
$153$			5.91574i			0.478259i
$154$	0.657857	+	3.19024i	0.0530116	+	0.257077i
$155$		−	7.23133i		−	0.580835i
$156$	−2.52410	−	5.85999i	−0.202089	−	0.469175i
$157$	−5.78202			−0.461455			−0.230728	−	0.973018i	$-0.574111\pi$
$157$	−5.78202			−0.461455			−0.230728	+	0.973018i	$0.574111\pi$
$158$	5.86067	−	1.20852i	0.466250	−	0.0961450i
$159$	−11.0682			−0.877768
$160$	−6.05080	+	9.78101i	−0.478358	+	0.773257i
$161$	−4.83855	+	3.28859i	−0.381331	+	0.259177i
$162$	−1.38507	+	0.285614i	−0.108822	+	0.0224400i
$163$	−11.2880			−0.884146			−0.442073	−	0.896979i	$-0.645757\pi$
$163$	−11.2880			−0.884146			−0.442073	+	0.896979i	$0.645757\pi$
$164$	−4.63638	+	1.99705i	−0.362041	+	0.155943i
$165$		−	3.83890i		−	0.298858i
$166$	−2.16585	−	10.5032i	−0.168103	−	0.815206i
$167$			0.358139i			0.0277136i	0.999904	+	0.0138568i	$0.00441090\pi$
$167$			0.358139i			0.0277136i	−0.999904	+	0.0138568i	$0.995589\pi$
$168$	−2.82791	+	1.97680i	−0.218178	+	0.152513i
$169$	2.82236			0.217104
$170$	−3.43528	−	16.6592i	−0.263474	−	1.27770i
$171$		−	6.08344i		−	0.465213i
$172$	9.22770	+	21.4232i	0.703605	+	1.63350i
$173$		−	10.1430i		−	0.771157i	−0.922675	−	0.385578i	$-0.874002\pi$
$173$		−	10.1430i		−	0.771157i	0.922675	−	0.385578i	$-0.125998\pi$
$174$	2.65786	+	12.8891i	0.201492	+	0.977123i
$175$	1.05671			0.0798796
$176$	5.48808	+	5.18867i	0.413680	+	0.391110i
$177$	−0.657857			−0.0494475
$178$	1.10244	+	5.34622i	0.0826313	+	0.400716i
$179$	−11.8262			−0.883931			−0.441966	−	0.897032i	$-0.645719\pi$
$179$	−11.8262			−0.883931			−0.441966	+	0.897032i	$0.645719\pi$
$180$	3.73462	−	1.60863i	0.278362	−	0.119900i
$181$	20.2209			1.50301			0.751506	−	0.659727i	$-0.229328\pi$
$181$	20.2209			1.50301			0.751506	+	0.659727i	$0.229328\pi$
$182$	1.11153	+	5.39029i	0.0823919	+	0.399555i
$183$	−10.3789			−0.767230
$184$	−4.82635	+	12.6770i	−0.355803	+	0.934561i
$185$	22.5961			1.66130
$186$	−1.01584	−	4.92627i	−0.0744851	−	0.361212i
$187$	−11.1698			−0.816813
$188$	8.86753	+	20.5870i	0.646731	+	1.50146i
$189$	1.21988			0.0887331
$190$	3.53266	+	17.1315i	0.256286	+	1.24285i
$191$	4.20470			0.304241			0.152121	−	0.988362i	$-0.451390\pi$
$191$	4.20470			0.304241			0.152121	+	0.988362i	$0.451390\pi$
$192$	−2.74803	+	7.51321i	−0.198322	+	0.542219i
$193$	−6.30116			−0.453567			−0.226784	−	0.973945i	$-0.572821\pi$
$193$	−6.30116			−0.453567			−0.226784	+	0.973945i	$0.572821\pi$
$194$	0.867348	+	4.20616i	0.0622719	+	0.301985i
$195$		−	6.48629i		−	0.464493i
$196$	−10.1245	+	4.36097i	−0.723180	+	0.311498i
$197$		−	11.6091i		−	0.827111i	−0.910479	−	0.413556i	$-0.864287\pi$
$197$		−	11.6091i		−	0.827111i	0.910479	−	0.413556i	$-0.135713\pi$
$198$	−0.539280	−	2.61521i	−0.0383250	−	0.185855i
$199$	−8.61769			−0.610892			−0.305446	−	0.952209i	$-0.598806\pi$
$199$	−8.61769			−0.610892			−0.305446	+	0.952209i	$0.598806\pi$
$200$	2.00811	−	1.40373i	0.141995	−	0.0992589i
$201$		−	2.45869i		−	0.173423i
$202$	2.00000	+	9.69890i	0.140720	+	0.682412i
$203$		−	11.3519i		−	0.796746i
$204$	−4.68049	−	10.8663i	−0.327700	−	0.760794i
$205$	−5.13190			−0.358428
$206$	4.23410	−	0.873109i	0.295004	−	0.0608324i
$207$	3.96642	−	2.69583i	0.275685	−	0.187373i
$208$	9.27277	+	8.76687i	0.642951	+	0.607873i
$209$	11.4864			0.794531
$210$	−3.43528	+	0.708385i	−0.237057	+	0.0488832i
$211$	−19.6552			−1.35312			−0.676561	−	0.736387i	$-0.736530\pi$
$211$	−19.6552			−1.35312			−0.676561	+	0.736387i	$0.736530\pi$
$212$	20.3307	−	8.75710i	1.39632	−	0.601440i
$213$		−	4.84611i		−	0.332050i
$214$	1.20271	+	5.83246i	0.0822153	+	0.398699i
$215$			23.7128i			1.61720i
$216$	2.31819	−	1.62049i	0.157733	−	0.110260i
$217$			4.33873i			0.294532i
$218$	−4.40579	+	0.908513i	−0.298398	+	0.0615323i
$219$	7.87149			0.531906
$220$	3.03731	+	7.05149i	0.204776	+	0.475411i
$221$	−18.8726			−1.26951
$222$	15.3933	−	3.17425i	1.03313	−	0.213041i
$223$		−	14.8511i		−	0.994501i	−0.867607	−	0.497250i	$-0.834343\pi$
$223$		−	14.8511i		−	0.994501i	0.867607	−	0.497250i	$-0.165657\pi$
$224$	3.63042	−	5.86851i	0.242567	−	0.392106i
$225$	−0.866240			−0.0577493
$226$	5.40365	+	26.2047i	0.359445	+	1.74311i
$227$		−	17.2433i		−	1.14448i	−0.820086	−	0.572240i	$-0.806074\pi$
$227$		−	17.2433i		−	1.14448i	0.820086	−	0.572240i	$-0.193926\pi$
$228$	4.81318	+	11.1744i	0.318760	+	0.740041i
$229$	2.59033			0.171174			0.0855869	−	0.996331i	$-0.472723\pi$
$229$	2.59033			0.171174			0.0855869	+	0.996331i	$0.472723\pi$
$230$	−9.60428	+	9.89499i	−0.633287	+	0.652456i
$231$			2.30330i			0.151546i
$232$	−15.0799	−	21.5725i	−0.990042	−	1.41631i
$233$	−22.1288			−1.44970			−0.724852	−	0.688905i	$-0.758092\pi$
$233$	−22.1288			−1.44970			−0.724852	+	0.688905i	$0.758092\pi$
$234$	−0.911179	−	4.41871i	−0.0595656	−	0.288860i
$235$			22.7873i			1.48648i
$236$	1.20838	−	0.520491i	0.0786590	−	0.0338811i
$237$	4.23131			0.274853
$238$	2.06113	+	9.99535i	0.133603	+	0.647902i
$239$		−	20.5586i		−	1.32983i	−0.746920	−	0.664914i	$-0.768468\pi$
$239$		−	20.5586i		−	1.32983i	0.746920	−	0.664914i	$-0.231532\pi$
$240$	−5.58719	+	5.90960i	−0.360652	+	0.381463i
$241$		−	13.5001i		−	0.869619i	−0.900522	−	0.434810i	$-0.856816\pi$
$241$		−	13.5001i		−	0.869619i	0.900522	−	0.434810i	$-0.143184\pi$
$242$	−10.2979	+	2.12352i	−0.661974	+	0.136505i
$243$	−1.00000			−0.0641500
$244$	19.0645	−	8.21171i	1.22048	−	0.525701i
$245$	−11.2066			−0.715963
$246$	−3.49606	+	0.720918i	−0.222900	+	0.0459641i
$247$	19.4077			1.23488
$248$	5.76358	+	8.24509i	0.365987	+	0.523563i
$249$		−	7.58314i		−	0.480562i
$250$	16.5198	−	3.40653i	1.04480	−	0.215448i
$251$			25.0872i			1.58349i	0.610853	+	0.791744i	$0.290827\pi$
$251$			25.0872i			1.58349i	−0.610853	+	0.791744i	$0.709173\pi$
$252$	−2.24073	+	0.965159i	−0.141153	+	0.0607993i
$253$	5.09012	+	7.48916i	0.320013	+	0.470840i
$254$	2.12684	+	10.3140i	0.133450	+	0.647157i
$255$		−	12.0277i		−	0.753202i
$256$	−0.896688	−	15.9749i	−0.0560430	−	0.998428i
$257$	−12.4382			−0.775875			−0.387937	−	0.921686i	$-0.626812\pi$
$257$	−12.4382			−0.775875			−0.387937	+	0.921686i	$0.626812\pi$
$258$	3.33113	+	16.1541i	0.207387	+	1.00571i
$259$	−13.5574			−0.842417
$260$	5.13190	+	11.9143i	0.318267	+	0.738895i
$261$			9.30575i			0.576012i
$262$	−2.52410	+	0.520491i	−0.155939	+	0.0321561i
$263$	10.3726			0.639602			0.319801	−	0.947485i	$-0.396384\pi$
$263$	10.3726			0.639602			0.319801	+	0.947485i	$0.396384\pi$
$264$	3.05971	+	4.37708i	0.188312	+	0.269390i
$265$	22.5035			1.38238
$266$	−2.11956	−	10.2787i	−0.129959	−	0.630228i
$267$			3.85989i			0.236221i
$268$	1.94530	+	4.51625i	0.118828	+	0.275874i
$269$		−	17.9895i		−	1.09684i	−0.836202	−	0.548421i	$-0.815229\pi$
$269$		−	17.9895i		−	1.09684i	0.836202	−	0.548421i	$-0.184771\pi$
$270$	2.81608	−	0.580701i	0.171381	−	0.0353403i
$271$			7.39559i			0.449250i	0.974445	+	0.224625i	$0.0721158\pi$
$271$			7.39559i			0.449250i	−0.974445	+	0.224625i	$0.927884\pi$
$272$	17.1947	+	16.2566i	1.04258	+	0.985702i
$273$			3.89171i			0.235537i
$274$	0.0630463	+	0.305740i	0.00380877	+	0.0184704i
$275$		−	1.63558i		−	0.0986294i
$276$	−5.15279	+	8.09004i	−0.310161	+	0.486963i
$277$			30.0768i			1.80714i	0.428441	+	0.903570i	$0.359063\pi$
$277$			30.0768i			1.80714i	−0.428441	+	0.903570i	$0.640937\pi$
$278$	−30.4478	+	6.27861i	−1.82614	+	0.376566i
$279$		−	3.55669i		−	0.212933i
$280$	5.74961	−	4.01916i	0.343605	−	0.240191i
$281$			6.06727i			0.361943i	0.983488	+	0.180971i	$0.0579242\pi$
$281$			6.06727i			0.361943i	−0.983488	+	0.180971i	$0.942076\pi$
$282$	3.20111	+	15.5236i	0.190623	+	0.924418i
$283$		−	25.5734i		−	1.52018i	−0.649818	−	0.760090i	$-0.725155\pi$
$283$		−	25.5734i		−	1.52018i	0.649818	−	0.760090i	$-0.274845\pi$
$284$	3.83421	+	8.90157i	0.227518	+	0.528211i
$285$			12.3686i			0.732655i
$286$	8.34316	−	1.72044i	0.493341	−	0.101731i
$287$	3.07909			0.181753
$288$	−2.97605	+	4.81073i	−0.175365	+	0.283475i
$289$	−17.9960			−1.05859
$290$	−5.40386	−	26.2057i	−0.317326	−	1.53885i
$291$			3.03678i			0.178019i
$292$	−14.4587	+	6.22787i	−0.846134	+	0.364458i
$293$	−19.4122			−1.13407			−0.567035	−	0.823694i	$-0.691910\pi$
$293$	−19.4122			−1.13407			−0.567035	+	0.823694i	$0.691910\pi$
$294$	−7.63437	+	1.57428i	−0.445246	+	0.0918137i
$295$	1.33753			0.0778741
$296$	−25.7638	+	18.0097i	−1.49749	+	1.04679i
$297$		−	1.88814i		−	0.109561i
$298$	19.9446	−	4.11276i	1.15536	−	0.238246i
$299$	8.60036	+	12.6538i	0.497372	+	0.731790i
$300$	1.59115	−	0.685363i	0.0918652	−	0.0395694i
$301$		−	14.2275i		−	0.820058i
$302$	−1.40093	−	6.79371i	−0.0806142	−	0.390934i
$303$			7.00245i			0.402280i
$304$	−17.6822	−	16.7175i	−1.01414	−	0.958813i
$305$	21.1020			1.20830
$306$	−1.68962	−	8.19372i	−0.0965891	−	0.468404i
$307$	2.20932			0.126093			0.0630464	−	0.998011i	$-0.479918\pi$
$307$	2.20932			0.126093			0.0630464	+	0.998011i	$0.479918\pi$
$308$	−1.82236	−	4.23082i	−0.103838	−	0.241073i
$309$	3.05695			0.173904
$310$	2.06537	+	10.0159i	0.117305	+	0.568866i
$311$			18.3744i			1.04192i	0.853583	+	0.520958i	$0.174425\pi$
$311$			18.3744i			1.04192i	−0.853583	+	0.520958i	$0.825575\pi$
$312$	5.16975	+	7.39559i	0.292680	+	0.418693i
$313$			14.6786i			0.829684i	0.909893	+	0.414842i	$0.136163\pi$
$313$			14.6786i			0.829684i	−0.909893	+	0.414842i	$0.863837\pi$
$314$	8.00851	−	1.65143i	0.451947	−	0.0931955i
$315$	−2.48021			−0.139744
$316$	−7.77228	+	3.34778i	−0.437225	+	0.188328i
$317$		−	1.06596i		−	0.0598705i	−0.999552	−	0.0299353i	$-0.990470\pi$
$317$		−	1.06596i		−	0.0598705i	0.999552	−	0.0299353i	$-0.00953011\pi$
$318$	15.3303	−	3.16124i	0.859680	−	0.177274i
$319$	−17.5706			−0.983764
$320$	5.58719	−	15.2756i	0.312334	−	0.853932i
$321$			4.21095i			0.235032i
$322$	5.76247	−	5.93689i	0.321130	−	0.330850i
$323$	35.9881			2.00243
$324$	1.83685	−	0.791193i	0.102047	−	0.0439552i
$325$		−	2.76351i		−	0.153292i
$326$	15.6347	−	3.22402i	0.865927	−	0.178562i
$327$	−3.18091			−0.175905
$328$	5.85134	−	4.09027i	0.323086	−	0.225847i
$329$		−	13.6722i		−	0.753770i
$330$	1.09645	+	5.31716i	0.0603574	+	0.292700i
$331$	11.3481			0.623748			0.311874	−	0.950124i	$-0.399043\pi$
$331$	11.3481			0.623748			0.311874	+	0.950124i	$0.399043\pi$
$332$	5.99973	+	13.9291i	0.329278	+	0.764458i
$333$	11.1137			0.609030
$334$	−0.102290	−	0.496048i	−0.00559703	−	0.0271425i
$335$			4.99893i			0.273121i
$336$	3.35226	−	3.54570i	0.182881	−	0.193434i
$337$			9.38843i			0.511420i	0.966754	+	0.255710i	$0.0823093\pi$
$337$			9.38843i			0.511420i	−0.966754	+	0.255710i	$0.917691\pi$
$338$	−3.90917	+	0.806106i	−0.212631	+	0.0438464i
$339$			18.9194i			1.02756i
$340$	9.51621	+	22.0930i	0.516089	+	1.19816i
$341$	6.71553			0.363666
$342$	1.73752	+	8.42601i	0.0939543	+	0.455626i
$343$	15.2630			0.824124
$344$	−18.8998	−	27.0371i	−1.01901	−	1.45774i
$345$	−8.06438	+	5.48108i	−0.434172	+	0.295091i
$346$	2.89698	+	14.0488i	0.155743	+	0.755266i
$347$	4.53959			0.243698			0.121849	−	0.992549i	$-0.461118\pi$
$347$	4.53959			0.243698			0.121849	+	0.992549i	$0.461118\pi$
$348$	−7.36265	−	17.0933i	−0.394679	−	0.916295i
$349$		−	35.2981i		−	1.88946i	−0.327847	−	0.944731i	$-0.606323\pi$
$349$		−	35.2981i		−	1.88946i	0.327847	−	0.944731i	$-0.393677\pi$
$350$	−1.46362	+	0.301811i	−0.0782336	+	0.0161325i
$351$		−	3.19024i		−	0.170283i
$352$	−9.08334	−	5.61920i	−0.484144	−	0.299505i
$353$	31.1526			1.65808			0.829042	−	0.559187i	$-0.188886\pi$
$353$	31.1526			1.65808			0.829042	+	0.559187i	$0.188886\pi$
$354$	0.911179	−	0.187893i	0.0484286	−	0.00998642i
$355$			9.85294i			0.522940i
$356$	−3.05392	−	7.09003i	−0.161857	−	0.375771i
$357$			7.21648i			0.381937i
$358$	16.3801	−	3.37773i	0.865717	−	0.178519i
$359$	24.9684			1.31778			0.658891	−	0.752239i	$-0.271026\pi$
$359$	24.9684			1.31778			0.658891	+	0.752239i	$0.271026\pi$
$360$	−4.71327	+	3.29472i	−0.248411	+	0.173647i
$361$	−18.0083			−0.947805
$362$	−28.0075	+	5.77539i	−1.47204	+	0.303548i
$363$	−7.43492			−0.390232
$364$	−3.07909	−	7.14848i	−0.161388	−	0.374682i
$365$	−16.0040			−0.837690
$366$	14.3755	−	2.96436i	0.751421	−	0.154950i
$367$	−25.0550			−1.30786			−0.653931	−	0.756554i	$-0.726881\pi$
$367$	−25.0550			−1.30786			−0.653931	+	0.756554i	$0.726881\pi$
$368$	3.06411	−	18.9370i	0.159728	−	0.987161i
$369$	−2.52410			−0.131399
$370$	−31.2972	+	6.45377i	−1.62706	+	0.335515i
$371$	−13.5019			−0.700983
$372$	2.81403	+	6.53310i	0.145900	+	0.338725i
$373$	17.3417			0.897918			0.448959	−	0.893552i	$-0.351795\pi$
$373$	17.3417			0.897918			0.448959	+	0.893552i	$0.351795\pi$
$374$	15.4709	−	3.19024i	0.799982	−	0.164963i
$375$	11.9270			0.615909
$376$	−18.1621	−	25.9818i	−0.936640	−	1.33991i
$377$	−29.6876			−1.52899
$378$	−1.68962	+	0.348415i	−0.0869046	+	0.0179205i
$379$		−	16.9340i		−	0.869841i	−0.900469	−	0.434920i	$-0.856777\pi$
$379$		−	16.9340i		−	0.869841i	0.900469	−	0.434920i	$-0.143223\pi$
$380$	−9.78599	−	22.7193i	−0.502010	−	1.16548i
$381$			7.44653i			0.381497i
$382$	−5.82381	+	1.20092i	−0.297972	+	0.0614445i
$383$	−29.5868			−1.51182			−0.755908	−	0.654677i	$-0.772804\pi$
$383$	−29.5868			−1.51182			−0.755908	+	0.654677i	$0.772804\pi$
$384$	1.66034	−	11.1912i	0.0847286	−	0.571099i
$385$		−	4.68300i		−	0.238668i
$386$	8.72756	−	1.79970i	0.444221	−	0.0916024i
$387$			11.6630i			0.592865i
$388$	−2.40268	−	5.57811i	−0.121978	−	0.283185i
$389$	−9.18306			−0.465600			−0.232800	−	0.972525i	$-0.574789\pi$
$389$	−9.18306			−0.465600			−0.232800	+	0.972525i	$0.574789\pi$
$390$	1.85258	+	8.98398i	0.0938089	+	0.454921i
$391$	15.9478	+	23.4643i	0.806517	+	1.18664i
$392$	12.7776	−	8.93197i	0.645368	−	0.451133i
$393$	−1.82236			−0.0919258
$394$	3.31571	+	16.0794i	0.167043	+	0.810067i
$395$	−8.60296			−0.432862
$396$	1.49388	+	3.46823i	0.0750705	+	0.174285i
$397$			12.2452i			0.614568i	0.951618	+	0.307284i	$0.0994202\pi$
$397$			12.2452i			0.614568i	−0.951618	+	0.307284i	$0.900580\pi$
$398$	11.9361	−	2.46134i	0.598304	−	0.123376i
$399$		−	7.42106i		−	0.371518i
$400$	−2.38045	+	2.51782i	−0.119023	+	0.125891i
$401$		−	8.99372i		−	0.449125i	−0.974460	−	0.224563i	$-0.927905\pi$
$401$		−	8.99372i		−	0.449125i	0.974460	−	0.224563i	$-0.0720953\pi$
$402$	0.702238	+	3.40547i	0.0350244	+	0.169849i
$403$	11.3467			0.565219
$404$	−5.54029	−	12.8624i	−0.275640	−	0.639930i
$405$	2.03317			0.101029
$406$	3.24226	+	15.7232i	0.160911	+	0.780328i
$407$			20.9843i			1.04015i
$408$	9.58639	+	13.7138i	0.474597	+	0.678935i
$409$	29.6011			1.46368			0.731840	−	0.681477i	$-0.238662\pi$
$409$	29.6011			1.46368			0.731840	+	0.681477i	$0.238662\pi$
$410$	7.10806	−	1.46575i	0.351042	−	0.0723880i
$411$			0.220739i			0.0108883i
$412$	−5.61516	+	2.41864i	−0.276639	+	0.119158i
$413$	−0.802505			−0.0394887
$414$	−4.72381	+	4.86679i	−0.232162	+	0.239190i
$415$			15.4178i			0.756829i
$416$	−15.3474	−	9.49431i	−0.752468	−	0.465497i
$417$	−21.9828			−1.07650
$418$	−15.9095	+	3.28068i	−0.778159	+	0.160463i
$419$		−	13.6353i		−	0.666126i	−0.942905	−	0.333063i	$-0.891918\pi$
$419$		−	13.6353i		−	0.666126i	0.942905	−	0.333063i	$-0.108082\pi$
$420$	4.55578	−	1.96233i	0.222299	−	0.0957518i
$421$	4.56033			0.222257			0.111128	−	0.993806i	$-0.464553\pi$
$421$	4.56033			0.222257			0.111128	+	0.993806i	$0.464553\pi$
$422$	27.2239	−	5.61381i	1.32524	−	0.273276i
$423$			11.2078i			0.544942i
$424$	−25.6583	+	17.9359i	−1.24608	+	0.871047i
$425$		−	5.12445i		−	0.248572i
$426$	1.38412	+	6.71221i	0.0670608	+	0.325208i
$427$	−12.6610			−0.612709
$428$	−3.33167	−	7.73487i	−0.161042	−	0.373879i
$429$	6.02363			0.290824
$430$	−6.77273	−	32.8440i	−0.326610	−	1.58388i
$431$	30.0775			1.44878			0.724392	−	0.689389i	$-0.242121\pi$
$431$	30.0775			1.44878			0.724392	+	0.689389i	$0.242121\pi$
$432$	−2.74803	+	2.90660i	−0.132215	+	0.139844i
$433$		−	17.0843i		−	0.821018i	−0.911857	−	0.410509i	$-0.865351\pi$
$433$		−	17.0843i		−	0.821018i	0.911857	−	0.410509i	$-0.134649\pi$
$434$	−1.23920	−	6.00945i	−0.0594836	−	0.288463i
$435$		−	18.9201i		−	0.907151i
$436$	5.84285	−	2.51671i	0.279822	−	0.120529i
$437$	−16.4000	−	24.1295i	−0.784516	−	1.15427i
$438$	−10.9026	+	2.24821i	−0.520946	+	0.107424i
$439$		−	17.2515i		−	0.823371i	−0.911326	−	0.411685i	$-0.864940\pi$
$439$		−	17.2515i		−	0.823371i	0.911326	−	0.411685i	$-0.135060\pi$
$440$	−6.22090	−	8.89932i	−0.296570	−	0.424258i
$441$	−5.51190			−0.262471
$442$	26.1400	−	5.39029i	1.24335	−	0.256390i
$443$	−19.0033			−0.902875			−0.451437	−	0.892303i	$-0.649089\pi$
$443$	−19.0033			−0.902875			−0.451437	+	0.892303i	$0.649089\pi$
$444$	−20.4143	+	8.79312i	−0.968819	+	0.417303i
$445$		−	7.84779i		−	0.372021i
$446$	4.24168	+	20.5698i	0.200849	+	0.974008i
$447$	14.3997			0.681083
$448$	−3.35226	+	9.16520i	−0.158379	+	0.433015i
$449$	9.95996			0.470039			0.235020	−	0.971991i	$-0.424485\pi$
$449$	9.95996			0.470039			0.235020	+	0.971991i	$0.424485\pi$
$450$	1.19980	−	0.247411i	0.0565593	−	0.0116630i
$451$		−	4.76585i		−	0.224415i
$452$	−14.9689	−	34.7520i	−0.704077	−	1.63460i
$453$		−	4.90495i		−	0.230455i
$454$	4.92495	+	23.8833i	0.231139	+	1.12090i
$455$		−	7.91248i		−	0.370943i
$456$	−9.85816	−	14.1026i	−0.461651	−	0.660414i
$457$		−	11.2976i		−	0.528478i	−0.964457	−	0.264239i	$-0.914879\pi$
$457$		−	11.2976i		−	0.528478i	0.964457	−	0.264239i	$-0.0851207\pi$
$458$	−3.58779	+	0.739835i	−0.167647	+	0.0345702i
$459$		−	5.91574i		−	0.276123i
$460$	10.4765	−	16.4484i	0.488468	−	0.766910i
$461$			7.73780i			0.360385i	0.983631	+	0.180193i	$0.0576721\pi$
$461$			7.73780i			0.360385i	−0.983631	+	0.180193i	$0.942328\pi$
$462$	−0.657857	−	3.19024i	−0.0306063	−	0.148423i
$463$		−	15.8063i		−	0.734581i	−0.930106	−	0.367290i	$-0.880286\pi$
$463$		−	15.8063i		−	0.734581i	0.930106	−	0.367290i	$-0.119714\pi$
$464$	27.0481	+	25.5725i	1.25568	+	1.18717i
$465$			7.23133i			0.335345i
$466$	30.6499	−	6.32029i	1.41983	−	0.292782i
$467$			32.5241i			1.50504i	0.658572	+	0.752518i	$0.271161\pi$
$467$			32.5241i			1.50504i	−0.658572	+	0.752518i	$0.728839\pi$
$468$	2.52410	+	5.85999i	0.116676	+	0.270878i
$469$		−	2.99931i		−	0.138495i
$470$	−6.50838	−	31.5621i	−0.300209	−	1.45585i
$471$	5.78202			0.266421
$472$	−1.52504	+	1.06605i	−0.0701956	+	0.0490689i
$473$	−22.0214			−1.01255
$474$	−5.86067	+	1.20852i	−0.269190	+	0.0555093i
$475$			5.26972i			0.241791i
$476$	−5.70963	−	13.2556i	−0.261700	−	0.607569i
$477$	11.0682			0.506779
$478$	5.87184	+	28.4752i	0.268572	+	1.30243i
$479$	−16.2098			−0.740643			−0.370322	−	0.928904i	$-0.620753\pi$
$479$	−16.2098			−0.740643			−0.370322	+	0.928904i	$0.620753\pi$
$480$	6.05080	−	9.78101i	0.276180	−	0.446440i
$481$			35.4555i			1.61663i
$482$	3.85583	+	18.6986i	0.175628	+	0.851700i
$483$	4.83855	−	3.28859i	0.220162	−	0.149636i
$484$	13.6568	−	5.88246i	0.620765	−	0.267384i
$485$		−	6.17427i		−	0.280359i
$486$	1.38507	−	0.285614i	0.0628281	−	0.0129557i
$487$		−	15.4990i		−	0.702327i	−0.936314	−	0.351164i	$-0.885786\pi$
$487$		−	15.4990i		−	0.702327i	0.936314	−	0.351164i	$-0.114214\pi$
$488$	−24.0603	+	16.8189i	−1.08916	+	0.761356i
$489$	11.2880			0.510462
$490$	15.5219	−	3.20076i	0.701210	−	0.144596i
$491$	25.3264			1.14296			0.571481	−	0.820615i	$-0.306369\pi$
$491$	25.3264			1.14296			0.571481	+	0.820615i	$0.306369\pi$
$492$	4.63638	−	1.99705i	0.209024	−	0.0900338i
$493$	−55.0504			−2.47935
$494$	−26.8810	+	5.54311i	−1.20943	+	0.249396i
$495$			3.83890i			0.172546i
$496$	−10.3379	−	9.77388i	−0.464185	−	0.438860i
$497$		−	5.91166i		−	0.265174i
$498$	2.16585	+	10.5032i	0.0970542	+	0.470659i
$499$	1.02051			0.0456842			0.0228421	−	0.999739i	$-0.492729\pi$
$499$	1.02051			0.0456842			0.0228421	+	0.999739i	$0.492729\pi$
$500$	−21.9082	+	9.43658i	−0.979763	+	0.422017i
$501$		−	0.358139i		−	0.0160005i
$502$	−7.16526	−	34.7476i	−0.319801	−	1.55086i
$503$	14.2820			0.636805			0.318403	−	0.947956i	$-0.396854\pi$
$503$	14.2820			0.636805			0.318403	+	0.947956i	$0.396854\pi$
$504$	2.82791	−	1.97680i	0.125965	−	0.0880537i
$505$		−	14.2371i		−	0.633544i
$506$	−9.18919	−	8.91922i	−0.408509	−	0.396508i
$507$	−2.82236			−0.125345
$508$	−5.89164	−	13.6782i	−0.261399	−	0.606870i
$509$		−	16.0929i		−	0.713307i	−0.934237	−	0.356654i	$-0.883918\pi$
$509$		−	16.0929i		−	0.713307i	0.934237	−	0.356654i	$-0.116082\pi$
$510$	3.43528	+	16.6592i	0.152117	+	0.737681i
$511$	9.60226			0.424779
$512$	5.80462	+	21.8702i	0.256531	+	0.966536i
$513$			6.08344i			0.268591i
$514$	17.2278	−	3.55253i	0.759887	−	0.156695i
$515$	−6.21529			−0.273878
$516$	−9.22770	−	21.4232i	−0.406227	−	0.943104i
$517$	−21.1619			−0.930700
$518$	18.7780	−	3.87219i	0.825058	−	0.170134i
$519$			10.1430i			0.445227i
$520$	−10.5110	−	15.0365i	−0.460936	−	0.659392i
$521$		−	40.0850i		−	1.75615i	−0.478519	−	0.878077i	$-0.658826\pi$
$521$		−	40.0850i		−	1.75615i	0.478519	−	0.878077i	$-0.341174\pi$
$522$	−2.65786	−	12.8891i	−0.116331	−	0.564142i
$523$		−	3.67778i		−	0.160818i	−0.996762	−	0.0804091i	$-0.974377\pi$
$523$		−	3.67778i		−	0.160818i	0.996762	−	0.0804091i	$-0.0256227\pi$
$524$	3.34740	−	1.44184i	0.146232	−	0.0629869i
$525$	−1.05671			−0.0461185
$526$	−14.3668	+	2.96256i	−0.626422	+	0.129174i
$527$	21.0404			0.916536
$528$	−5.48808	−	5.18867i	−0.238838	−	0.225808i
$529$	8.46496	−	21.3856i	0.368042	−	0.929809i
$530$	−31.1690	+	6.42733i	−1.35390	+	0.279185i
$531$	0.657857			0.0285485
$532$	5.87149	+	13.6314i	0.254561	+	0.590995i
$533$		−	8.05248i		−	0.348792i
$534$	−1.10244	−	5.34622i	−0.0477072	−	0.231354i
$535$		−	8.56155i		−	0.370148i
$536$	−3.98429	−	5.69972i	−0.172095	−	0.246190i
$537$	11.8262			0.510338
$538$	5.13807	+	24.9168i	0.221518	+	1.07424i
$539$		−	10.4072i		−	0.448272i
$540$	−3.73462	+	1.60863i	−0.160712	+	0.0692242i
$541$			39.3379i			1.69127i	0.533761	+	0.845635i	$0.320778\pi$
$541$			39.3379i			1.69127i	−0.533761	+	0.845635i	$0.679222\pi$
$542$	−2.11229	−	10.2434i	−0.0907305	−	0.439993i
$543$	−20.2209			−0.867764
$544$	−28.4590	−	17.6055i	−1.22017	−	0.754831i
$545$	6.46731			0.277029
$546$	−1.11153	−	5.39029i	−0.0475690	−	0.230683i
$547$	14.0964			0.602718			0.301359	−	0.953511i	$-0.402560\pi$
$547$	14.0964			0.602718			0.301359	+	0.953511i	$0.402560\pi$
$548$	−0.174647	−	0.405465i	−0.00746057	−	0.0173206i
$549$	10.3789			0.442961
$550$	0.467146	+	2.26540i	0.0199192	+	0.0965970i
$551$	56.6110			2.41171
$552$	4.82635	−	12.6770i	0.205423	−	0.539569i
$553$	5.16169			0.219497
$554$	−8.59036	−	41.6585i	−0.364970	−	1.76990i
$555$	−22.5961			−0.959150
$556$	40.3791	−	17.3926i	1.71246	−	0.737612i
$557$	−10.4485			−0.442715			−0.221358	−	0.975193i	$-0.571049\pi$
$557$	−10.4485			−0.442715			−0.221358	+	0.975193i	$0.571049\pi$
$558$	1.01584	+	4.92627i	0.0430040	+	0.208546i
$559$	−37.2079			−1.57372
$560$	−6.81570	+	7.20900i	−0.288016	+	0.304636i
$561$	11.1698			0.471587
$562$	−1.73290	−	8.40361i	−0.0730979	−	0.354485i
$563$			19.6672i			0.828873i	0.910078	+	0.414436i	$0.136021\pi$
$563$			19.6672i			0.828873i	−0.910078	+	0.414436i	$0.863979\pi$
$564$	−8.86753	−	20.5870i	−0.373390	−	0.866871i
$565$		−	38.4662i		−	1.61829i
$566$	7.30412	+	35.4210i	0.307015	+	1.48885i
$567$	−1.21988			−0.0512301
$568$	−7.85307	−	11.2342i	−0.329507	−	0.471377i
$569$		−	1.07567i		−	0.0450943i	−0.999746	−	0.0225471i	$-0.992822\pi$
$569$		−	1.07567i		−	0.0450943i	0.999746	−	0.0225471i	$-0.00717759\pi$
$570$	−3.53266	−	17.1315i	−0.147967	−	0.717558i
$571$			28.5359i			1.19419i	0.802170	+	0.597096i	$0.203679\pi$
$571$			28.5359i			1.19419i	−0.802170	+	0.597096i	$0.796321\pi$
$572$	−11.0645	+	4.76585i	−0.462630	+	0.199270i
$573$	−4.20470			−0.175654
$574$	−4.26476	+	0.879433i	−0.178008	+	0.0367068i
$575$	−3.43587	+	2.33524i	−0.143286	+	0.0973862i
$576$	2.74803	−	7.51321i	0.114501	−	0.313050i
$577$	4.04788			0.168515			0.0842577	−	0.996444i	$-0.473148\pi$
$577$	4.04788			0.168515			0.0842577	+	0.996444i	$0.473148\pi$
$578$	24.9257	−	5.13990i	1.03677	−	0.213792i
$579$	6.30116			0.261867
$580$	14.9695	+	34.7534i	0.621574	+	1.44306i
$581$		−	9.25051i		−	0.383776i
$582$	−0.867348	−	4.20616i	−0.0359527	−	0.174351i
$583$			20.8984i			0.865523i
$584$	18.2476	−	12.7557i	0.755092	−	0.527833i
$585$			6.48629i			0.268175i
$586$	26.8872	−	5.54439i	1.11070	−	0.229037i
$587$	−15.3197			−0.632312			−0.316156	−	0.948707i	$-0.602392\pi$
$587$	−15.3197			−0.632312			−0.316156	+	0.948707i	$0.602392\pi$
$588$	10.1245	−	4.36097i	0.417528	−	0.179844i
$589$	−21.6369			−0.891534
$590$	−1.85258	+	0.382018i	−0.0762694	+	0.0157274i
$591$			11.6091i			0.477533i
$592$	30.5409	−	32.3033i	1.25522	−	1.32766i
$593$	2.25798			0.0927240			0.0463620	−	0.998925i	$-0.485237\pi$
$593$	2.25798			0.0927240			0.0463620	+	0.998925i	$0.485237\pi$
$594$	0.539280	+	2.61521i	0.0221269	+	0.107303i
$595$		−	14.6723i		−	0.601506i
$596$	−26.4501	+	11.3929i	−1.08344	+	0.466673i
$597$	8.61769			0.352699
$598$	−15.5262	−	15.0701i	−0.634915	−	0.616262i
$599$			22.8436i			0.933362i	0.884426	+	0.466681i	$0.154550\pi$
$599$			22.8436i			0.933362i	−0.884426	+	0.466681i	$0.845450\pi$
$600$	−2.00811	+	1.40373i	−0.0819808	+	0.0573071i
$601$	−9.74798			−0.397628			−0.198814	−	0.980037i	$-0.563709\pi$
$601$	−9.74798			−0.397628			−0.198814	+	0.980037i	$0.563709\pi$
$602$	4.06357	+	19.7061i	0.165619	+	0.803159i
$603$			2.45869i			0.100126i
$604$	3.88076	+	9.00966i	0.157906	+	0.366598i
$605$	15.1164			0.614570
$606$	−2.00000	−	9.69890i	−0.0812444	−	0.393991i
$607$			27.7790i			1.12752i	0.825940	+	0.563758i	$0.190645\pi$
$607$			27.7790i			1.12752i	−0.825940	+	0.563758i	$0.809355\pi$
$608$	29.2658	+	18.1046i	1.18689	+	0.734240i
$609$			11.3519i			0.460002i
$610$	−29.2278	+	6.02704i	−1.18340	+	0.244028i
$611$	−35.7556			−1.44652
$612$	4.68049	+	10.8663i	0.189198	+	0.439245i
$613$	13.1317			0.530386			0.265193	−	0.964195i	$-0.414564\pi$
$613$	13.1317			0.530386			0.265193	+	0.964195i	$0.414564\pi$
$614$	−3.06007	+	0.631015i	−0.123495	+	0.0254657i
$615$	5.13190			0.206938
$616$	3.73248	+	5.33950i	0.150386	+	0.215135i
$617$			26.8543i			1.08111i	0.841307	+	0.540557i	$0.181787\pi$
$617$			26.8543i			1.08111i	−0.841307	+	0.540557i	$0.818213\pi$
$618$	−4.23410	+	0.873109i	−0.170320	+	0.0351216i
$619$		−	37.7150i		−	1.51589i	−0.652317	−	0.757946i	$-0.726203\pi$
$619$		−	37.7150i		−	1.51589i	0.652317	−	0.757946i	$-0.273797\pi$
$620$	−5.72138	−	13.2829i	−0.229776	−	0.533453i
$621$	−3.96642	+	2.69583i	−0.159167	+	0.108180i
$622$	−5.24799	−	25.4498i	−0.210425	−	1.02045i
$623$			4.70859i			0.188646i
$624$	−9.27277	−	8.76687i	−0.371208	−	0.350956i
$625$	−19.9184			−0.796737
$626$	−4.19242	−	20.3309i	−0.167563	−	0.812588i
$627$	−11.4864			−0.458723
$628$	−10.6207	+	4.57469i	−0.423812	+	0.182550i
$629$			65.7460i			2.62147i
$630$	3.43528	−	0.708385i	0.136865	−	0.0282227i
$631$	38.4398			1.53027			0.765133	−	0.643872i	$-0.222673\pi$
$631$	38.4398			1.53027			0.765133	+	0.643872i	$0.222673\pi$
$632$	9.80899	−	6.85680i	0.390181	−	0.272749i
$633$	19.6552			0.781225
$634$	0.304455	+	1.47644i	0.0120914	+	0.0586368i
$635$		−	15.1400i		−	0.600814i
$636$	−20.3307	+	8.75710i	−0.806163	+	0.347242i
$637$		−	17.5843i		−	0.696715i
$638$	24.3365	−	5.01841i	0.963492	−	0.198681i
$639$			4.84611i			0.191709i
$640$	−3.37574	+	22.7536i	−0.133438	+	0.899414i
$641$			45.0011i			1.77744i	0.458455	+	0.888718i	$0.348403\pi$
$641$			45.0011i			1.77744i	−0.458455	+	0.888718i	$0.651597\pi$
$642$	−1.20271	−	5.83246i	−0.0474670	−	0.230189i
$643$			25.2162i			0.994430i	0.867627	+	0.497215i	$0.165644\pi$
$643$			25.2162i			0.994430i	−0.867627	+	0.497215i	$0.834356\pi$
$644$	−6.28577	+	9.86887i	−0.247694	+	0.388888i
$645$		−	23.7128i		−	0.933692i
$646$	−49.8461	+	10.2787i	−1.96117	+	0.404410i
$647$			18.2382i			0.717017i	0.933527	+	0.358508i	$0.116715\pi$
$647$			18.2382i			0.717017i	−0.933527	+	0.358508i	$0.883285\pi$
$648$	−2.31819	+	1.62049i	−0.0910672	+	0.0636588i
$649$			1.24213i			0.0487577i
$650$	0.789299	+	3.82767i	0.0309589	+	0.150133i
$651$		−	4.33873i		−	0.170048i
$652$	−20.7344	+	8.93100i	−0.812021	+	0.349765i
$653$		−	12.8376i		−	0.502373i	−0.967939	−	0.251186i	$-0.919179\pi$
$653$		−	12.8376i		−	0.502373i	0.967939	−	0.251186i	$-0.0808207\pi$
$654$	4.40579	−	0.908513i	0.172280	−	0.0355257i
$655$	3.70515			0.144772
$656$	−6.93629	+	7.33655i	−0.270817	+	0.286444i
$657$	−7.87149			−0.307096
$658$	3.90496	+	18.9369i	0.152231	+	0.738238i
$659$		−	6.88484i		−	0.268195i	−0.990968	−	0.134098i	$-0.957186\pi$
$659$		−	6.88484i		−	0.268195i	0.990968	−	0.134098i	$-0.0428136\pi$
$660$	−3.03731	−	7.05149i	−0.118227	−	0.274479i
$661$	−11.3609			−0.441888			−0.220944	−	0.975287i	$-0.570914\pi$
$661$	−11.3609			−0.441888			−0.220944	+	0.975287i	$0.570914\pi$
$662$	−15.7179	+	3.24118i	−0.610895	+	0.125972i
$663$	18.8726			0.732952
$664$	−12.2884	−	17.5792i	−0.476882	−	0.682204i
$665$			15.0882i			0.585097i
$666$	−15.3933	+	3.17425i	−0.596480	+	0.123000i
$667$	25.0868	+	36.9105i	0.971363	+	1.42918i
$668$	0.283357	+	0.657846i	0.0109634	+	0.0254528i
$669$			14.8511i			0.574175i
$670$	−1.42777	−	6.92388i	−0.0551594	−	0.267493i
$671$			19.5968i			0.756527i
$672$	−3.63042	+	5.86851i	−0.140046	+	0.226383i
$673$	1.24484			0.0479849			0.0239925	−	0.999712i	$-0.492362\pi$
$673$	1.24484			0.0479849			0.0239925	+	0.999712i	$0.492362\pi$
$674$	−2.68147	−	13.0036i	−0.103286	−	0.500882i
$675$	0.866240			0.0333416
$676$	5.18424	−	2.23303i	0.199394	−	0.0858857i
$677$	18.1961			0.699333			0.349667	−	0.936874i	$-0.386295\pi$
$677$	18.1961			0.699333			0.349667	+	0.936874i	$0.386295\pi$
$678$	−5.40365	−	26.2047i	−0.207526	−	1.00639i
$679$			3.70450i			0.142166i
$680$	−19.4907	−	27.8824i	−0.747435	−	1.06924i
$681$			17.2433i			0.660766i
$682$	−9.30150	+	1.91805i	−0.356173	+	0.0734460i
$683$	22.9048			0.876428			0.438214	−	0.898871i	$-0.355611\pi$
$683$	22.9048			0.876428			0.438214	+	0.898871i	$0.355611\pi$
$684$	−4.81318	−	11.1744i	−0.184036	−	0.427263i
$685$		−	0.448799i		−	0.0171477i
$686$	−21.1403	+	4.35933i	−0.807142	+	0.166440i
$687$	−2.59033			−0.0988272
$688$	33.8998	+	32.0503i	1.29242	+	1.22191i
$689$			35.3103i			1.34522i
$690$	9.60428	−	9.89499i	0.365629	−	0.376696i
$691$	39.6585			1.50868			0.754340	−	0.656484i	$-0.227957\pi$
$691$	39.6585			1.50868			0.754340	+	0.656484i	$0.227957\pi$
$692$	−8.02505	−	18.6311i	−0.305067	−	0.708249i
$693$		−	2.30330i		−	0.0874953i
$694$	−6.28766	+	1.29657i	−0.238676	+	0.0492172i
$695$	44.6947			1.69537
$696$	15.0799	+	21.5725i	0.571601	+	0.817704i
$697$		−	14.9319i		−	0.565586i
$698$	10.0816	+	48.8904i	0.381595	+	1.85053i
$699$	22.1288			0.836987
$700$	1.94101	−	0.836059i	0.0733633	−	0.0316001i
$701$	22.9169			0.865560			0.432780	−	0.901499i	$-0.357533\pi$
$701$	22.9169			0.865560			0.432780	+	0.901499i	$0.357533\pi$
$702$	0.911179	+	4.41871i	0.0343902	+	0.166774i
$703$		−	67.6099i		−	2.54995i
$704$	14.1860	+	5.18867i	0.534655	+	0.195555i
$705$		−	22.7873i		−	0.858220i
$706$	−43.1485	+	8.89762i	−1.62392	+	0.334866i
$707$			8.54214i			0.321260i
$708$	−1.20838	+	0.520491i	−0.0454138	+	0.0195613i
$709$	−5.57334			−0.209311			−0.104656	−	0.994509i	$-0.533374\pi$
$709$	−5.57334			−0.209311			−0.104656	+	0.994509i	$0.533374\pi$
$710$	−2.81414	−	13.6470i	−0.105613	−	0.512164i
$711$	−4.23131			−0.158687
$712$	6.25491	+	8.94796i	0.234413	+	0.335339i
$713$	−9.58824	−	14.1073i	−0.359082	−	0.528323i
$714$	−2.06113	−	9.99535i	−0.0771359	−	0.374066i
$715$	−12.2470			−0.458013
$716$	−21.7229	+	9.35680i	−0.811824	+	0.349680i
$717$			20.5586i			0.767776i
$718$	−34.5830	+	7.13133i	−1.29063	+	0.266139i
$719$			3.83953i			0.143190i	0.997434	+	0.0715952i	$0.0228090\pi$
$719$			3.83953i			0.143190i	−0.997434	+	0.0715952i	$0.977191\pi$
$720$	5.58719	−	5.90960i	0.208222	−	0.220238i
$721$	3.72911			0.138879
$722$	24.9428	−	5.14343i	0.928274	−	0.191419i
$723$			13.5001i			0.502075i
$724$	37.1428	−	15.9987i	1.38040	−	0.594586i
$725$		−	8.06101i		−	0.299379i
$726$	10.2979	−	2.12352i	0.382191	−	0.0788112i
$727$	12.5993			0.467281			0.233641	−	0.972323i	$-0.424936\pi$
$727$	12.5993			0.467281			0.233641	+	0.972323i	$0.424936\pi$
$728$	6.30647	+	9.02172i	0.233733	+	0.334367i
$729$	1.00000			0.0370370
$730$	22.1668	−	4.57098i	0.820428	−	0.169180i
$731$	−68.9954			−2.55189
$732$	−19.0645	+	8.21171i	−0.704643	+	0.303514i
$733$	5.84348			0.215834			0.107917	−	0.994160i	$-0.465582\pi$
$733$	5.84348			0.215834			0.107917	+	0.994160i	$0.465582\pi$
$734$	34.7030	−	7.15608i	1.28091	−	0.264136i
$735$	11.2066			0.413361
$736$	1.16468	+	27.1043i	0.0429305	+	0.999078i
$737$	−4.64236			−0.171004
$738$	3.49606	−	0.720918i	0.128692	−	0.0265374i
$739$	−22.0429			−0.810861			−0.405430	−	0.914126i	$-0.632878\pi$
$739$	−22.0429			−0.810861			−0.405430	+	0.914126i	$0.632878\pi$
$740$	41.5056	−	17.8779i	1.52578	−	0.657203i
$741$	−19.4077			−0.712958
$742$	18.7011	−	3.85633i	0.686539	−	0.141570i
$743$	−27.7944			−1.01968			−0.509839	−	0.860270i	$-0.670295\pi$
$743$	−27.7944			−1.01968			−0.509839	+	0.860270i	$0.670295\pi$
$744$	−5.76358	−	8.24509i	−0.211303	−	0.302280i
$745$	−29.2770			−1.07263
$746$	−24.0195	+	4.95303i	−0.879415	+	0.181343i
$747$			7.58314i			0.277453i
$748$	−20.5171	+	8.83743i	−0.750181	+	0.323128i
$749$			5.13684i			0.187696i
$750$	−16.5198	+	3.40653i	−0.603218	+	0.124389i
$751$	38.5857			1.40801			0.704005	−	0.710195i	$-0.251393\pi$
$751$	38.5857			1.40801			0.704005	+	0.710195i	$0.251393\pi$
$752$	32.5766	+	30.7993i	1.18795	+	1.12314i
$753$		−	25.0872i		−	0.914228i
$754$	41.1195	−	8.47921i	1.49748	−	0.308794i
$755$			9.97258i			0.362939i
$756$	2.24073	−	0.965159i	0.0814946	−	0.0351025i
$757$	38.4124			1.39612			0.698060	−	0.716039i	$-0.254047\pi$
$757$	38.4124			1.39612			0.698060	+	0.716039i	$0.254047\pi$
$758$	4.83659	+	23.4548i	0.175673	+	0.851916i
$759$	−5.09012	−	7.48916i	−0.184760	−	0.271839i
$760$	20.0433	+	28.6729i	0.727046	+	1.04008i
$761$	26.4292			0.958056			0.479028	−	0.877800i	$-0.340989\pi$
$761$	26.4292			0.958056			0.479028	+	0.877800i	$0.340989\pi$
$762$	−2.12684	−	10.3140i	−0.0770472	−	0.373636i
$763$	−3.88032			−0.140477
$764$	7.72339	−	3.32673i	0.279423	−	0.120357i
$765$			12.0277i			0.434861i
$766$	40.9799	−	8.45043i	1.48066	−	0.305326i
$767$			2.09872i			0.0757804i
$768$	0.896688	+	15.9749i	0.0323564	+	0.576443i
$769$		−	31.7255i		−	1.14405i	−0.820236	−	0.572025i	$-0.806158\pi$
$769$		−	31.7255i		−	1.14405i	0.820236	−	0.572025i	$-0.193842\pi$
$770$	1.33753	+	6.48629i	0.0482013	+	0.233750i
$771$	12.4382			0.447951
$772$	−11.5743	+	4.98543i	−0.416567	+	0.179430i
$773$	−21.0369			−0.756645			−0.378322	−	0.925674i	$-0.623499\pi$
$773$	−21.0369			−0.756645			−0.378322	+	0.925674i	$0.623499\pi$
$774$	−3.33113	−	16.1541i	−0.119735	−	0.580648i
$775$			3.08095i			0.110671i
$776$	4.92107	+	7.03984i	0.176656	+	0.252715i
$777$	13.5574			0.486370
$778$	12.7192	−	2.62281i	0.456006	−	0.0940325i
$779$			15.3552i			0.550157i
$780$	−5.13190	−	11.9143i	−0.183752	−	0.426601i
$781$	−9.15014			−0.327418
$782$	−28.7907	−	27.9448i	−1.02955	−	0.999304i
$783$		−	9.30575i		−	0.332560i
$784$	−15.1468	+	16.0209i	−0.540959	+	0.572175i
$785$	−11.7558			−0.419583
$786$	2.52410	−	0.520491i	0.0900315	−	0.0185653i
$787$		−	26.6770i		−	0.950934i	−0.879734	−	0.475467i	$-0.842279\pi$
$787$		−	26.6770i		−	0.950934i	0.879734	−	0.475467i	$-0.157721\pi$
$788$	−9.18500	−	21.3241i	−0.327202	−	0.759639i
$789$	−10.3726			−0.369274
$790$	11.9157	−	2.45713i	0.423942	−	0.0874207i
$791$			23.0793i			0.820607i
$792$	−3.05971	−	4.37708i	−0.108722	−	0.155533i
$793$			33.1112i			1.17581i
$794$	−3.49740	−	16.9605i	−0.124118	−	0.601904i
$795$	−22.5035			−0.798118
$796$	−15.8294	+	6.81826i	−0.561058	+	0.241667i
$797$	25.5900			0.906443			0.453222	−	0.891398i	$-0.350275\pi$
$797$	25.5900			0.906443			0.453222	+	0.891398i	$0.350275\pi$
$798$	2.11956	+	10.2787i	0.0750317	+	0.363862i
$799$	−66.3024			−2.34561
$800$	2.57797	−	4.16725i	0.0911451	−	0.147334i
$801$		−	3.85989i		−	0.136382i
$802$	2.56874	+	12.4570i	0.0907052	+	0.439870i
$803$		−	14.8625i		−	0.524486i
$804$	−1.94530	−	4.51625i	−0.0686054	−	0.159276i
$805$	−9.83757	+	6.68625i	−0.346729	+	0.235659i
$806$	−15.7160	+	3.24078i	−0.553572	+	0.114152i
$807$			17.9895i			0.633262i
$808$	11.3474	+	16.2330i	0.399200	+	0.571076i
$809$	−34.2026			−1.20250			−0.601250	−	0.799061i	$-0.705331\pi$
$809$	−34.2026			−1.20250			−0.601250	+	0.799061i	$0.705331\pi$
$810$	−2.81608	+	0.580701i	−0.0989470	+	0.0204038i
$811$	−52.9847			−1.86054			−0.930272	−	0.366869i	$-0.880430\pi$
$811$	−52.9847			−1.86054			−0.930272	+	0.366869i	$0.880430\pi$
$812$	−8.98153	−	20.8517i	−0.315190	−	0.731751i
$813$		−	7.39559i		−	0.259375i
$814$	−5.99343	−	29.0648i	−0.210070	−	1.01872i
$815$	−22.9504			−0.803918
$816$	−17.1947	−	16.2566i	−0.601935	−	0.569095i
$817$	70.9513			2.48227
$818$	−40.9996	+	8.45450i	−1.43352	+	0.295605i
$819$		−	3.89171i		−	0.135987i
$820$	−9.42653	+	4.06033i	−0.329189	+	0.141793i
$821$			31.4859i			1.09886i	0.835538	+	0.549432i	$0.185156\pi$
$821$			31.4859i			1.09886i	−0.835538	+	0.549432i	$0.814844\pi$
$822$	−0.0630463	−	0.305740i	−0.00219899	−	0.0106639i
$823$			48.2371i			1.68144i	0.541469	+	0.840720i	$0.317868\pi$
$823$			48.2371i			1.68144i	−0.541469	+	0.840720i	$0.682132\pi$
$824$	7.08660	−	4.95376i	0.246873	−	0.172572i
$825$			1.63558i			0.0569437i
$826$	1.11153	−	0.229207i	0.0386750	−	0.00797513i
$827$			1.17993i			0.0410300i	0.999790	+	0.0205150i	$0.00653059\pi$
$827$			1.17993i			0.0410300i	−0.999790	+	0.0205150i	$0.993469\pi$
$828$	5.15279	−	8.09004i	0.179072	−	0.281148i
$829$		−	26.1335i		−	0.907654i	−0.891090	−	0.453827i	$-0.850058\pi$
$829$		−	26.1335i		−	0.907654i	0.891090	−	0.453827i	$-0.149942\pi$
$830$	−4.40354	−	21.3547i	−0.152849	−	0.741233i
$831$		−	30.0768i		−	1.04335i
$832$	23.9690	+	8.76687i	0.830974	+	0.303937i
$833$		−	32.6069i		−	1.12976i
$834$	30.4478	−	6.27861i	1.05432	−	0.217410i
$835$			0.728155i			0.0251988i
$836$	21.0988	−	9.08796i	0.729717	−	0.314314i
$837$			3.55669i			0.122937i
$838$	3.89443	+	18.8858i	0.134531	+	0.652400i
$839$	20.5929			0.710946			0.355473	−	0.934687i	$-0.384320\pi$
$839$	20.5929			0.710946			0.355473	+	0.934687i	$0.384320\pi$
$840$	−5.74961	+	4.01916i	−0.198380	+	0.138674i
$841$	−57.5970			−1.98610
$842$	−6.31639	+	1.30250i	−0.217677	+	0.0448870i
$843$		−	6.06727i		−	0.208968i
$844$	−36.1037	+	15.5511i	−1.24274	+	0.535290i
$845$	5.73832			0.197404
$846$	−3.20111	−	15.5236i	−0.110056	−	0.533713i
$847$	−9.06970			−0.311639
$848$	30.4158	−	32.1710i	1.04448	−	1.10476i
$849$			25.5734i			0.877676i
$850$	1.46362	+	7.09773i	0.0502016	+	0.243450i
$851$	44.0818	−	29.9608i	1.51110	−	1.02704i
$852$	−3.83421	−	8.90157i	−0.131358	−	0.304963i
$853$		−	13.1368i		−	0.449794i	−0.974383	−	0.224897i	$-0.927795\pi$
$853$		−	13.1368i		−	0.449794i	0.974383	−	0.224897i	$-0.0722045\pi$
$854$	17.5364	−	3.61616i	0.600083	−	0.123743i
$855$		−	12.3686i		−	0.422999i
$856$	6.82379	+	9.76178i	0.233232	+	0.333651i
$857$	31.3190			1.06984			0.534918	−	0.844904i	$-0.320342\pi$
$857$	31.3190			1.06984			0.534918	+	0.844904i	$0.320342\pi$
$858$	−8.34316	+	1.72044i	−0.284831	+	0.0587347i
$859$	10.4517			0.356606			0.178303	−	0.983976i	$-0.442939\pi$
$859$	10.4517			0.356606			0.178303	+	0.983976i	$0.442939\pi$
$860$	18.7614	+	43.5569i	0.639760	+	1.48528i
$861$	−3.07909			−0.104935
$862$	−41.6595	+	8.59057i	−1.41893	+	0.292596i
$863$		−	31.2021i		−	1.06213i	−0.847331	−	0.531066i	$-0.821792\pi$
$863$		−	31.2021i		−	1.06213i	0.847331	−	0.531066i	$-0.178208\pi$
$864$	2.97605	−	4.81073i	0.101247	−	0.163664i
$865$		−	20.6224i		−	0.701181i
$866$	4.87951	+	23.6630i	0.165813	+	0.804100i
$867$	17.9960			0.611175
$868$	3.43277	+	7.96959i	0.116516	+	0.270505i
$869$		−	7.98932i		−	0.271019i
$870$	5.40386	+	26.2057i	0.183208	+	0.888458i
$871$	−7.84382			−0.265778
$872$	−7.37396	+	5.15463i	−0.249714	+	0.174558i
$873$		−	3.03678i		−	0.102779i
$874$	29.6068	+	28.7370i	1.00147	+	0.972044i
$875$	14.5495			0.491864
$876$	14.4587	−	6.22787i	0.488516	−	0.210420i
$877$		−	33.3576i		−	1.12641i	−0.826318	−	0.563203i	$-0.809569\pi$
$877$		−	33.3576i		−	1.12641i	0.826318	−	0.563203i	$-0.190431\pi$
$878$	4.92728	+	23.8946i	0.166288	+	0.806404i
$879$	19.4122			0.654756
$880$	11.1582	+	10.5494i	0.376142	+	0.355621i
$881$			3.93660i			0.132627i	0.997799	+	0.0663137i	$0.0211238\pi$
$881$			3.93660i			0.132627i	−0.997799	+	0.0663137i	$0.978876\pi$
$882$	7.63437	−	1.57428i	0.257063	−	0.0530087i
$883$	25.8164			0.868790			0.434395	−	0.900722i	$-0.356962\pi$
$883$	25.8164			0.868790			0.434395	+	0.900722i	$0.356962\pi$
$884$	−34.6662	+	14.9319i	−1.16595	+	0.502214i
$885$	−1.33753			−0.0449606
$886$	26.3210	−	5.42762i	0.884270	−	0.182344i
$887$		−	50.2556i		−	1.68742i	−0.536800	−	0.843709i	$-0.680367\pi$
$887$		−	50.2556i		−	1.68742i	0.536800	−	0.843709i	$-0.319633\pi$
$888$	25.7638	−	18.0097i	0.864576	−	0.604366i
$889$			9.08387i			0.304663i
$890$	2.24144	+	10.8698i	0.0751333	+	0.364355i
$891$			1.88814i			0.0632551i
$892$	−11.7501	−	27.2792i	−0.393421	−	0.913374i
$893$	68.1820			2.28162
$894$	−19.9446	+	4.11276i	−0.667048	+	0.137551i
$895$	−24.0446			−0.803723
$896$	2.02541	−	13.6519i	0.0676641	−	0.456079i
$897$	−8.60036	−	12.6538i	−0.287158	−	0.422499i
$898$	−13.7953	+	2.84471i	−0.460354	+	0.0949291i
$899$	33.0977			1.10387
$900$	−1.59115	+	0.685363i	−0.0530384	+	0.0228454i
$901$			65.4767i			2.18135i
$902$	1.36120	+	6.60105i	0.0453229	+	0.219791i
$903$			14.2275i			0.473460i
$904$	30.6587	+	43.8588i	1.01969	+	1.45872i
$905$	41.1125			1.36663
$906$	1.40093	+	6.79371i	0.0465426	+	0.225706i
$907$		−	18.7971i		−	0.624147i	−0.950058	−	0.312074i	$-0.898976\pi$
$907$		−	18.7971i		−	0.624147i	0.950058	−	0.312074i	$-0.101024\pi$
$908$	−13.6428	−	31.6734i	−0.452753	−	1.05112i
$909$		−	7.00245i		−	0.232257i
$910$	2.25992	+	10.9594i	0.0749156	+	0.363299i
$911$	5.60263			0.185623			0.0928117	−	0.995684i	$-0.470415\pi$
$911$	5.60263			0.185623			0.0928117	+	0.995684i	$0.470415\pi$
$912$	17.6822	+	16.7175i	0.585515	+	0.553571i
$913$	−14.3180			−0.473858
$914$	3.22675	+	15.6479i	0.106731	+	0.517588i
$915$	−21.1020			−0.697611
$916$	4.75804	−	2.04945i	0.157210	−	0.0677157i
$917$	−2.22305			−0.0734117
$918$	1.68962	+	8.19372i	0.0557658	+	0.270433i
$919$	−29.5139			−0.973572			−0.486786	−	0.873521i	$-0.661831\pi$
$919$	−29.5139			−0.973572			−0.486786	+	0.873521i	$0.661831\pi$
$920$	−9.81277	+	25.7744i	−0.323517	+	0.849758i
$921$	−2.20932			−0.0727997
$922$	−2.21003	−	10.7174i	−0.0727833	−	0.352959i
$923$	−15.4603			−0.508881
$924$	1.82236	+	4.23082i	0.0599512	+	0.139184i
$925$	−9.62717			−0.316539
$926$	4.51450	+	21.8929i	0.148356	+	0.719444i
$927$	−3.05695			−0.100403
$928$	−44.7675	−	27.6944i	−1.46956	−	0.909112i
$929$	−59.0986			−1.93896			−0.969481	−	0.245165i	$-0.921158\pi$
$929$	−59.0986			−1.93896			−0.969481	+	0.245165i	$0.921158\pi$
$930$	−2.06537	−	10.0159i	−0.0677262	−	0.328435i
$931$			33.5313i			1.09894i
$932$	−40.6472	+	17.5081i	−1.33144	+	0.573498i
$933$		−	18.3744i		−	0.601550i
$934$	−9.28935	−	45.0482i	−0.303957	−	1.47402i
$935$	−22.7100			−0.742695
$936$	−5.16975	−	7.39559i	−0.168979	−	0.241733i
$937$			13.5151i			0.441518i	0.975328	+	0.220759i	$0.0708535\pi$
$937$			13.5151i			0.441518i	−0.975328	+	0.220759i	$0.929147\pi$
$938$	0.856645	+	4.15426i	0.0279704	+	0.135641i
$939$		−	14.6786i		−	0.479018i
$940$	18.0292	+	41.8568i	0.588046	+	1.36522i
$941$	−13.6282			−0.444267			−0.222133	−	0.975016i	$-0.571302\pi$
$941$	−13.6282			−0.444267			−0.222133	+	0.975016i	$0.571302\pi$
$942$	−8.00851	+	1.65143i	−0.260931	+	0.0538064i
$943$	−10.0116	+	6.80454i	−0.326023	+	0.221586i
$944$	1.80781	−	1.91213i	0.0588391	−	0.0622345i
$945$	2.48021			0.0806814
$946$	30.5013	−	6.28964i	0.991682	−	0.204494i
$947$	5.13751			0.166947			0.0834733	−	0.996510i	$-0.473399\pi$
$947$	5.13751			0.166947			0.0834733	+	0.996510i	$0.473399\pi$
$948$	7.77228	−	3.34778i	0.252432	−	0.108731i
$949$		−	25.1120i		−	0.815169i
$950$	−1.50511	−	7.29894i	−0.0488322	−	0.236809i
$951$			1.06596i			0.0345663i
$952$	11.6942	+	16.7292i	0.379012	+	0.542196i
$953$			20.0968i			0.651000i	0.945542	+	0.325500i	$0.105533\pi$
$953$			20.0968i			0.651000i	−0.945542	+	0.325500i	$0.894467\pi$
$954$	−15.3303	+	3.16124i	−0.496337	+	0.102349i
$955$	8.54884			0.276634
$956$	−16.2658	−	37.7631i	−0.526075	−	1.22135i
$957$	17.5706			0.567976
$958$	22.4517	−	4.62974i	0.725381	−	0.149580i
$959$			0.269275i			0.00869535i
$960$	−5.58719	+	15.2756i	−0.180326	+	0.493018i
$961$	18.3500			0.591935
$962$	−10.1266	−	49.1085i	−0.326495	−	1.58332i
$963$		−	4.21095i		−	0.135696i
$964$	−10.6812	−	24.7977i	−0.344018	−	0.798680i
$965$	−12.8113			−0.412410
$966$	−5.76247	+	5.93689i	−0.185404	+	0.191016i
$967$		−	4.12341i		−	0.132600i	−0.997800	−	0.0663000i	$-0.978881\pi$
$967$		−	4.12341i		−	0.132600i	0.997800	−	0.0663000i	$-0.0211194\pi$
$968$	−17.2356	+	12.0482i	−0.553972	+	0.387244i
$969$	−35.9881			−1.15610
$970$	1.76346	+	8.55181i	0.0566213	+	0.274582i
$971$			29.8517i			0.957987i	0.877818	+	0.478993i	$0.158998\pi$
$971$			29.8517i			0.957987i	−0.877818	+	0.478993i	$0.841002\pi$
$972$	−1.83685	+	0.791193i	−0.0589170	+	0.0253775i
$973$	−26.8164			−0.859693
$974$	4.42674	+	21.4672i	0.141842	+	0.687855i
$975$			2.76351i			0.0885033i
$976$	28.5215	−	30.1673i	0.912951	−	0.965633i
$977$		−	27.9916i		−	0.895531i	−0.894151	−	0.447766i	$-0.852220\pi$
$977$		−	27.9916i		−	0.895531i	0.894151	−	0.447766i	$-0.147780\pi$
$978$	−15.6347	+	3.22402i	−0.499943	+	0.103093i
$979$	7.28802			0.232926
$980$	−20.5848	+	8.86658i	−0.657558	+	0.283232i
$981$	3.18091			0.101559
$982$	−35.0788	+	7.23357i	−1.11941	+	0.230833i
$983$	−23.2880			−0.742773			−0.371386	−	0.928478i	$-0.621118\pi$
$983$	−23.2880			−0.742773			−0.371386	+	0.928478i	$0.621118\pi$
$984$	−5.85134	+	4.09027i	−0.186534	+	0.130393i
$985$		−	23.6031i		−	0.752058i
$986$	76.2488	−	15.7232i	2.42826	−	0.500728i
$987$			13.6722i			0.435189i
$988$	35.6489	−	15.3552i	1.13414	−	0.488514i
$989$	31.4416	+	46.2604i	0.999784	+	1.47100i
$990$	−1.09645	−	5.31716i	−0.0348473	−	0.168990i
$991$			20.0895i			0.638164i	0.947727	+	0.319082i	$0.103374\pi$
$991$			20.0895i			0.638164i	−0.947727	+	0.319082i	$0.896626\pi$
$992$	17.1103	+	10.5849i	0.543252	+	0.336070i
$993$	−11.3481			−0.360121
$994$	1.68846	+	8.18808i	0.0535546	+	0.259710i
$995$	−17.5212			−0.555459
$996$	−5.99973	−	13.9291i	−0.190109	−	0.441360i
$997$		−	28.4733i		−	0.901758i	−0.892585	−	0.450879i	$-0.851111\pi$
$997$		−	28.4733i		−	0.901758i	0.892585	−	0.450879i	$-0.148889\pi$
$998$	−1.41348	+	0.291471i	−0.0447428	+	0.00922637i
$999$	−11.1137			−0.351623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.n.b.91.4	yes	24
4.3	odd	2		2208.2.n.b.367.17		24
8.3	odd	2	inner	552.2.n.b.91.1	✓	24
8.5	even	2		2208.2.n.b.367.7		24
23.22	odd	2	inner	552.2.n.b.91.3	yes	24
92.91	even	2		2208.2.n.b.367.8		24
184.45	odd	2		2208.2.n.b.367.18		24
184.91	even	2	inner	552.2.n.b.91.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.n.b.91.1	✓	24	8.3	odd	2	inner
552.2.n.b.91.2	yes	24	184.91	even	2	inner
552.2.n.b.91.3	yes	24	23.22	odd	2	inner
552.2.n.b.91.4	yes	24	1.1	even	1	trivial
2208.2.n.b.367.7		24	8.5	even	2
2208.2.n.b.367.8		24	92.91	even	2
2208.2.n.b.367.17		24	4.3	odd	2
2208.2.n.b.367.18		24	184.45	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38507 + 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 - 0.791193i) q^{4} +2.03317 q^{5} +(1.38507 - 0.285614i) q^{6} -1.21988 q^{7} +(-2.31819 + 1.62049i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.38507 + 0.285614i) q^{2} -1.00000 q^{3} +(1.83685 - 0.791193i) q^{4} +2.03317 q^{5} +(1.38507 - 0.285614i) q^{6} -1.21988 q^{7} +(-2.31819 + 1.62049i) q^{8} +1.00000 q^{9} +(-2.81608 + 0.580701i) q^{10} +1.88814i q^{11} +(-1.83685 + 0.791193i) q^{12} +3.19024i q^{13} +(1.68962 - 0.348415i) q^{14} -2.03317 q^{15} +(2.74803 - 2.90660i) q^{16} +5.91574i q^{17} +(-1.38507 + 0.285614i) q^{18} -6.08344i q^{19} +(3.73462 - 1.60863i) q^{20} +1.21988 q^{21} +(-0.539280 - 2.61521i) q^{22} +(3.96642 - 2.69583i) q^{23} +(2.31819 - 1.62049i) q^{24} -0.866240 q^{25} +(-0.911179 - 4.41871i) q^{26} -1.00000 q^{27} +(-2.24073 + 0.965159i) q^{28} +9.30575i q^{29} +(2.81608 - 0.580701i) q^{30} -3.55669i q^{31} +(-2.97605 + 4.81073i) q^{32} -1.88814i q^{33} +(-1.68962 - 8.19372i) q^{34} -2.48021 q^{35} +(1.83685 - 0.791193i) q^{36} +11.1137 q^{37} +(1.73752 + 8.42601i) q^{38} -3.19024i q^{39} +(-4.71327 + 3.29472i) q^{40} -2.52410 q^{41} +(-1.68962 + 0.348415i) q^{42} +11.6630i q^{43} +(1.49388 + 3.46823i) q^{44} +2.03317 q^{45} +(-4.72381 + 4.86679i) q^{46} +11.2078i q^{47} +(-2.74803 + 2.90660i) q^{48} -5.51190 q^{49} +(1.19980 - 0.247411i) q^{50} -5.91574i q^{51} +(2.52410 + 5.85999i) q^{52} +11.0682 q^{53} +(1.38507 - 0.285614i) q^{54} +3.83890i q^{55} +(2.82791 - 1.97680i) q^{56} +6.08344i q^{57} +(-2.65786 - 12.8891i) q^{58} +0.657857 q^{59} +(-3.73462 + 1.60863i) q^{60} +10.3789 q^{61} +(1.01584 + 4.92627i) q^{62} -1.21988 q^{63} +(2.74803 - 7.51321i) q^{64} +6.48629i q^{65} +(0.539280 + 2.61521i) q^{66} +2.45869i q^{67} +(4.68049 + 10.8663i) q^{68} +(-3.96642 + 2.69583i) q^{69} +(3.43528 - 0.708385i) q^{70} +4.84611i q^{71} +(-2.31819 + 1.62049i) q^{72} -7.87149 q^{73} +(-15.3933 + 3.17425i) q^{74} +0.866240 q^{75} +(-4.81318 - 11.1744i) q^{76} -2.30330i q^{77} +(0.911179 + 4.41871i) q^{78} -4.23131 q^{79} +(5.58719 - 5.90960i) q^{80} +1.00000 q^{81} +(3.49606 - 0.720918i) q^{82} +7.58314i q^{83} +(2.24073 - 0.965159i) q^{84} +12.0277i q^{85} +(-3.33113 - 16.1541i) q^{86} -9.30575i q^{87} +(-3.05971 - 4.37708i) q^{88} -3.85989i q^{89} +(-2.81608 + 0.580701i) q^{90} -3.89171i q^{91} +(5.15279 - 8.09004i) q^{92} +3.55669i q^{93} +(-3.20111 - 15.5236i) q^{94} -12.3686i q^{95} +(2.97605 - 4.81073i) q^{96} -3.03678i q^{97} +(7.63437 - 1.57428i) q^{98} +1.88814i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9	\( 24 q - 24 q^{3} + 4 q^{4} + 24 q^{9} - 4 q^{12} + 4 q^{16} + 24 q^{25} - 24 q^{27} + 4 q^{36} - 44 q^{46} - 4 q^{48} + 56 q^{49} - 40 q^{50} - 48 q^{58} - 40 q^{62} + 4 q^{64} + 32 q^{73} - 24 q^{75} + 24 q^{81} - 40 q^{82} + 40 q^{92} - 48 q^{94}+O(q^{100}) \) 24 * q - 24 * q^3 + 4 * q^4 + 24 * q^9 - 4 * q^12 + 4 * q^16 + 24 * q^25 - 24 * q^27 + 4 * q^36 - 44 * q^46 - 4 * q^48 + 56 * q^49 - 40 * q^50 - 48 * q^58 - 40 * q^62 + 4 * q^64 + 32 * q^73 - 24 * q^75 + 24 * q^81 - 40 * q^82 + 40 * q^92 - 48 * q^94

Introduction

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