LMFDB - Embedded newform 819.2.fn.e.577.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(73,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("819.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fn (of order $12$, degree $4$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			577.3
Character	$\chi$	$=$	819.577
Dual form			819.2.fn.e.775.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.788958 - 0.211401i) q^{2} +(-1.15429 - 0.666428i) q^{4} +(-0.814012 + 3.03793i) q^{5} +(1.32595 + 2.28951i) q^{7} +(1.92491 + 1.92491i) q^{8} +O(q^{10})$	\(q+(-0.788958 - 0.211401i) q^{2} +(-1.15429 - 0.666428i) q^{4} +(-0.814012 + 3.03793i) q^{5} +(1.32595 + 2.28951i) q^{7} +(1.92491 + 1.92491i) q^{8} +(1.28444 - 2.22472i) q^{10} +(-0.491212 + 0.131620i) q^{11} +(1.73717 - 3.15947i) q^{13} +(-0.562115 - 2.08663i) q^{14} +(0.221107 + 0.382969i) q^{16} +(-0.606654 + 1.05076i) q^{17} +(-0.461325 + 1.72169i) q^{19} +(2.96417 - 2.96417i) q^{20} +0.415370 q^{22} +(-4.51168 + 2.60482i) q^{23} +(-4.23629 - 2.44583i) q^{25} +(-2.03847 + 2.12545i) q^{26} +(-0.00473432 - 3.52640i) q^{28} -1.64443 q^{29} +(-3.64327 + 0.976210i) q^{31} +(-1.50262 - 5.60785i) q^{32} +(0.700755 - 0.700755i) q^{34} +(-8.03472 + 2.16446i) q^{35} +(0.715128 - 2.66889i) q^{37} +(0.727931 - 1.26081i) q^{38} +(-7.41466 + 4.28086i) q^{40} +(-5.55629 - 5.55629i) q^{41} +7.46499i q^{43} +(0.654714 + 0.175430i) q^{44} +(4.11018 - 1.10132i) q^{46} +(4.73504 + 1.26875i) q^{47} +(-3.48371 + 6.07155i) q^{49} +(2.82521 + 2.82521i) q^{50} +(-4.11075 + 2.48924i) q^{52} +(-4.30982 + 7.46483i) q^{53} -1.59941i q^{55} +(-1.85477 + 6.95945i) q^{56} +(1.29738 + 0.347632i) q^{58} +(0.648171 + 2.41901i) q^{59} +(-9.09759 + 5.25249i) q^{61} +3.08076 q^{62} +3.85758i q^{64} +(8.18418 + 7.84924i) q^{65} +(-1.91620 - 7.15134i) q^{67} +(1.40051 - 0.808582i) q^{68} +(6.79662 - 0.00912470i) q^{70} +(-0.840390 + 0.840390i) q^{71} +(0.632677 + 2.36118i) q^{73} +(-1.12841 + 1.95447i) q^{74} +(1.67988 - 1.67988i) q^{76} +(-0.952667 - 0.950113i) q^{77} +(6.20571 + 10.7486i) q^{79} +(-1.34342 + 0.359968i) q^{80} +(3.20908 + 5.55828i) q^{82} +(-7.31472 - 7.31472i) q^{83} +(-2.69830 - 2.69830i) q^{85} +(1.57810 - 5.88956i) q^{86} +(-1.19890 - 0.692184i) q^{88} +(-9.42713 - 2.52599i) q^{89} +(9.53704 - 0.212040i) q^{91} +6.94369 q^{92} +(-3.46753 - 2.00198i) q^{94} +(-4.85484 - 2.80295i) q^{95} +(2.93184 + 2.93184i) q^{97} +(4.03203 - 4.05374i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	$ 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) $ 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.788958	−	0.211401i	−0.557877	−	0.149483i	−0.0311464	−	0.999515i	$-0.509916\pi$
$2$	−0.788958	−	0.211401i	−0.557877	−	0.149483i	−0.526731	+	0.850032i	$0.676582\pi$
$3$		0			0
$3$		0			0
$4$	−1.15429	−	0.666428i	−0.577143	−	0.333214i
$5$	−0.814012	+	3.03793i	−0.364037	+	1.35860i	0.504684	+	0.863304i	$0.331609\pi$
$5$	−0.814012	+	3.03793i	−0.364037	+	1.35860i	−0.868721	+	0.495301i	$0.835058\pi$
$6$		0			0
$7$	1.32595	+	2.28951i	0.501162	+	0.865353i
$7$	1.32595	+	2.28951i	0.501162	+	0.865353i
$8$	1.92491	+	1.92491i	0.680560	+	0.680560i
$9$		0			0
$10$	1.28444	−	2.22472i	0.406176	−	0.703518i
$11$	−0.491212	+	0.131620i	−0.148106	+	0.0396849i	−0.332110	−	0.943241i	$-0.607761\pi$
$11$	−0.491212	+	0.131620i	−0.148106	+	0.0396849i	0.184004	+	0.982925i	$0.441094\pi$
$12$		0			0
$13$	1.73717	−	3.15947i	0.481804	−	0.876279i
$13$	1.73717	−	3.15947i	0.481804	−	0.876279i
$14$	−0.562115	−	2.08663i	−0.150232	−	0.557676i
$15$		0			0
$16$	0.221107	+	0.382969i	0.0552768	+	0.0957423i
$17$	−0.606654	+	1.05076i	−0.147135	+	0.254846i	−0.930168	−	0.367135i	$-0.880339\pi$
$17$	−0.606654	+	1.05076i	−0.147135	+	0.254846i	0.783032	+	0.621981i	$0.213672\pi$
$18$		0			0
$19$	−0.461325	+	1.72169i	−0.105835	+	0.394982i	−0.998439	−	0.0558606i	$-0.982210\pi$
$19$	−0.461325	+	1.72169i	−0.105835	+	0.394982i	0.892603	+	0.450843i	$0.148876\pi$
$20$	2.96417	−	2.96417i	0.662808	−	0.662808i
$21$		0			0
$22$	0.415370			0.0885572
$23$	−4.51168	+	2.60482i	−0.940750	+	0.543142i	−0.890195	−	0.455579i	$-0.849432\pi$
$23$	−4.51168	+	2.60482i	−0.940750	+	0.543142i	−0.0505543	+	0.998721i	$0.516099\pi$
$24$		0			0
$25$	−4.23629	−	2.44583i	−0.847259	−	0.489165i
$26$	−2.03847	+	2.12545i	−0.399776	+	0.416835i
$27$		0			0
$28$	−0.00473432	−	3.52640i	−0.000894702	−	0.666427i
$29$	−1.64443			−0.305362			−0.152681	−	0.988276i	$-0.548791\pi$
$29$	−1.64443			−0.305362			−0.152681	+	0.988276i	$0.548791\pi$
$30$		0			0
$31$	−3.64327	+	0.976210i	−0.654350	+	0.175333i	−0.570695	−	0.821162i	$-0.693326\pi$
$31$	−3.64327	+	0.976210i	−0.654350	+	0.175333i	−0.0836552	+	0.996495i	$0.526659\pi$
$32$	−1.50262	−	5.60785i	−0.265628	−	0.991338i
$33$		0			0
$34$	0.700755	−	0.700755i	0.120178	−	0.120178i
$35$	−8.03472	+	2.16446i	−1.35811	+	0.365861i
$36$		0			0
$37$	0.715128	−	2.66889i	0.117566	−	0.438764i	−0.881900	−	0.471437i	$-0.843735\pi$
$37$	0.715128	−	2.66889i	0.117566	−	0.438764i	0.999466	+	0.0326734i	$0.0104021\pi$
$38$	0.727931	−	1.26081i	0.118086	−	0.204531i
$39$		0			0
$40$	−7.41466	+	4.28086i	−1.17236	+	0.676863i
$41$	−5.55629	−	5.55629i	−0.867747	−	0.867747i	0.124476	−	0.992223i	$-0.460275\pi$
$41$	−5.55629	−	5.55629i	−0.867747	−	0.867747i	−0.992223	+	0.124476i	$0.960275\pi$
$42$		0			0
$43$			7.46499i			1.13840i	0.822199	+	0.569200i	$0.192747\pi$
$43$			7.46499i			1.13840i	−0.822199	+	0.569200i	$0.807253\pi$
$44$	0.654714	+	0.175430i	0.0987019	+	0.0264471i
$45$		0			0
$46$	4.11018	−	1.10132i	0.606013	−	0.162381i
$47$	4.73504	+	1.26875i	0.690677	+	0.185066i	0.587051	−	0.809550i	$-0.300289\pi$
$47$	4.73504	+	1.26875i	0.690677	+	0.185066i	0.103626	+	0.994616i	$0.466956\pi$
$48$		0			0
$49$	−3.48371	+	6.07155i	−0.497673	+	0.867365i
$50$	2.82521	+	2.82521i	0.399545	+	0.399545i
$51$		0			0
$52$	−4.11075	+	2.48924i	−0.570058	+	0.345195i
$53$	−4.30982	+	7.46483i	−0.591999	+	1.02537i	0.401964	+	0.915656i	$0.368328\pi$
$53$	−4.30982	+	7.46483i	−0.591999	+	1.02537i	−0.993963	+	0.109717i	$0.965006\pi$
$54$		0			0
$55$		−	1.59941i		−	0.215664i
$56$	−1.85477	+	6.95945i	−0.247854	+	0.929996i
$57$		0			0
$58$	1.29738	+	0.347632i	0.170355	+	0.0456464i
$59$	0.648171	+	2.41901i	0.0843847	+	0.314928i	0.995197	−	0.0978928i	$-0.0312102\pi$
$59$	0.648171	+	2.41901i	0.0843847	+	0.314928i	−0.910812	+	0.412821i	$0.864544\pi$
$60$		0			0
$61$	−9.09759	+	5.25249i	−1.16483	+	0.672513i	−0.952456	−	0.304676i	$-0.901452\pi$
$61$	−9.09759	+	5.25249i	−1.16483	+	0.672513i	−0.212371	+	0.977189i	$0.568118\pi$
$62$	3.08076			0.391256
$63$		0			0
$64$			3.85758i			0.482198i
$65$	8.18418	+	7.84924i	1.01512	+	0.973579i
$66$		0			0
$67$	−1.91620	−	7.15134i	−0.234101	−	0.873675i	−0.978552	−	0.205999i	$-0.933956\pi$
$67$	−1.91620	−	7.15134i	−0.234101	−	0.873675i	0.744452	−	0.667676i	$-0.232711\pi$
$68$	1.40051	−	0.808582i	0.169836	−	0.0980550i
$69$		0			0
$70$	6.79662	−	0.00912470i	0.812351	−	0.00109061i
$71$	−0.840390	+	0.840390i	−0.0997360	+	0.0997360i	−0.755214	−	0.655478i	$-0.772467\pi$
$71$	−0.840390	+	0.840390i	−0.0997360	+	0.0997360i	0.655478	+	0.755214i	$0.272467\pi$
$72$		0			0
$73$	0.632677	+	2.36118i	0.0740492	+	0.276355i	0.993016	−	0.117979i	$-0.0376417\pi$
$73$	0.632677	+	2.36118i	0.0740492	+	0.276355i	−0.918967	+	0.394335i	$0.870975\pi$
$74$	−1.12841	+	1.95447i	−0.131175	+	0.227202i
$75$		0			0
$76$	1.67988	−	1.67988i	0.192695	−	0.192695i
$77$	−0.952667	−	0.950113i	−0.108567	−	0.108275i
$78$		0			0
$79$	6.20571	+	10.7486i	0.698197	+	1.20931i	0.969091	+	0.246704i	$0.0793474\pi$
$79$	6.20571	+	10.7486i	0.698197	+	1.20931i	−0.270894	+	0.962609i	$0.587319\pi$
$80$	−1.34342	+	0.359968i	−0.150199	+	0.0402456i
$81$		0			0
$82$	3.20908	+	5.55828i	0.354383	+	0.613809i
$83$	−7.31472	−	7.31472i	−0.802894	−	0.802894i	0.180653	−	0.983547i	$-0.442179\pi$
$83$	−7.31472	−	7.31472i	−0.802894	−	0.802894i	−0.983547	+	0.180653i	$0.942179\pi$
$84$		0			0
$85$	−2.69830	−	2.69830i	−0.292672	−	0.292672i
$86$	1.57810	−	5.88956i	0.170171	−	0.635088i
$87$		0			0
$88$	−1.19890	−	0.692184i	−0.127803	−	0.0737870i
$89$	−9.42713	−	2.52599i	−0.999273	−	0.267755i	−0.278132	−	0.960543i	$-0.589715\pi$
$89$	−9.42713	−	2.52599i	−0.999273	−	0.267755i	−0.721141	+	0.692788i	$0.756382\pi$
$90$		0			0
$91$	9.53704	−	0.212040i	0.999753	−	0.0222278i
$92$	6.94369			0.723930
$93$		0			0
$94$	−3.46753	−	2.00198i	−0.357649	−	0.206489i
$95$	−4.85484	−	2.80295i	−0.498097	−	0.287576i
$96$		0			0
$97$	2.93184	+	2.93184i	0.297683	+	0.297683i	0.840106	−	0.542423i	$-0.182493\pi$
$97$	2.93184	+	2.93184i	0.297683	+	0.297683i	−0.542423	+	0.840106i	$0.682493\pi$
$98$	4.03203	−	4.05374i	0.407297	−	0.409490i
$99$		0			0
$100$	3.25993	+	5.64637i	0.325993	+	0.564637i
$101$	7.72587	−	13.3816i	0.768753	−	1.33152i	−0.169487	−	0.985532i	$-0.554211\pi$
$101$	7.72587	−	13.3816i	0.768753	−	1.33152i	0.938240	−	0.345986i	$-0.112456\pi$
$102$		0			0
$103$	−8.75030	−	15.1560i	−0.862192	−	1.49336i	−0.869808	−	0.493390i	$-0.835758\pi$
$103$	−8.75030	−	15.1560i	−0.862192	−	1.49336i	0.00761617	−	0.999971i	$-0.497576\pi$
$104$	9.42561	−	2.73781i	0.924257	−	0.268464i
$105$		0			0
$106$	4.97833	−	4.97833i	0.483538	−	0.483538i
$107$	1.06208	+	1.83958i	0.102675	+	0.177839i	0.912786	−	0.408438i	$-0.133926\pi$
$107$	1.06208	+	1.83958i	0.102675	+	0.177839i	−0.810111	+	0.586277i	$0.800593\pi$
$108$		0			0
$109$	2.77172	+	10.3442i	0.265483	+	0.990796i	0.961954	+	0.273211i	$0.0880857\pi$
$109$	2.77172	+	10.3442i	0.265483	+	0.990796i	−0.696471	+	0.717585i	$0.745248\pi$
$110$	−0.338116	+	1.26187i	−0.0322381	+	0.120314i
$111$		0			0
$112$	−0.583634	+	1.01403i	−0.0551482	+	0.0958164i
$113$	−5.21100			−0.490210			−0.245105	−	0.969497i	$-0.578822\pi$
$113$	−5.21100			−0.490210			−0.245105	+	0.969497i	$0.578822\pi$
$114$		0			0
$115$	−4.24070	−	15.8265i	−0.395448	−	1.47583i
$116$	1.89814	+	1.09589i	0.176238	+	0.101751i
$117$		0			0
$118$		−	2.04552i		−	0.188305i
$119$	−3.21011	+	0.00430968i	−0.294270	+	0.000395068i
$120$		0			0
$121$	−9.30231	+	5.37069i	−0.845665	+	0.488245i
$122$	8.28799	−	2.22076i	0.750359	−	0.201058i
$123$		0			0
$124$	4.85595	+	1.30115i	0.436077	+	0.116846i
$125$	−0.240960	+	0.240960i	−0.0215521	+	0.0215521i
$126$		0			0
$127$		−	11.4359i		−	1.01477i	−0.861720	−	0.507384i	$-0.830613\pi$
$127$		−	11.4359i		−	1.01477i	0.861720	−	0.507384i	$-0.169387\pi$
$128$	−2.18974	+	8.17223i	−0.193548	+	0.722330i
$129$		0			0
$130$	−4.79764	−	7.92286i	−0.420781	−	0.694881i
$131$	−6.07972	+	3.51013i	−0.531188	+	0.306681i	−0.741500	−	0.670953i	$-0.765885\pi$
$131$	−6.07972	+	3.51013i	−0.531188	+	0.306681i	0.210312	+	0.977634i	$0.432552\pi$
$132$		0			0
$133$	−4.55351	+	1.22666i	−0.394840	+	0.106365i
$134$			6.04719i			0.522398i
$135$		0			0
$136$	−3.19037	+	0.854858i	−0.273572	+	0.0733034i
$137$	6.00784	−	1.60979i	0.513284	−	0.137534i	0.00712570	−	0.999975i	$-0.497732\pi$
$137$	6.00784	−	1.60979i	0.513284	−	0.137534i	0.506158	+	0.862441i	$0.331065\pi$
$138$		0			0
$139$		−	1.91666i		−	0.162569i	−0.996691	−	0.0812847i	$-0.974098\pi$
$139$		−	1.91666i		−	0.162569i	0.996691	−	0.0812847i	$-0.0259023\pi$
$140$	10.7168	+	2.85615i	0.905737	+	0.241389i
$141$		0			0
$142$	0.840691	−	0.485373i	0.0705493	−	0.0407316i
$143$	−0.437468	+	1.78061i	−0.0365829	+	0.148902i
$144$		0			0
$145$	1.33858	−	4.99565i	0.111163	−	0.414866i
$146$		−	1.99662i		−	0.165242i
$147$		0			0
$148$	−2.60409	+	2.60409i	−0.214055	+	0.214055i
$149$	1.07871	+	0.289039i	0.0883711	+	0.0236790i	0.302734	−	0.953075i	$-0.402101\pi$
$149$	1.07871	+	0.289039i	0.0883711	+	0.0236790i	−0.214363	+	0.976754i	$0.568767\pi$
$150$		0			0
$151$	12.7301	−	3.41102i	1.03596	−	0.277585i	0.299522	−	0.954089i	$-0.403173\pi$
$151$	12.7301	−	3.41102i	1.03596	−	0.277585i	0.736438	+	0.676505i	$0.236506\pi$
$152$	−4.20211	+	2.42609i	−0.340836	+	0.196782i
$153$		0			0
$154$	0.550760	+	0.950993i	0.0443815	+	0.0766332i
$155$		−	11.8626i		−	0.952831i
$156$		0			0
$157$	12.0413	+	6.95203i	0.960998	+	0.554833i	0.896480	−	0.443084i	$-0.146116\pi$
$157$	12.0413	+	6.95203i	0.960998	+	0.554833i	0.0645182	+	0.997917i	$0.479449\pi$
$158$	−2.62378	−	9.79209i	−0.208737	−	0.779017i
$159$		0			0
$160$	18.2594			1.44353
$161$	−11.9460	−	6.87567i	−0.941478	−	0.541879i
$162$		0			0
$163$	−2.11892	+	7.90791i	−0.165967	+	0.619396i	0.831948	+	0.554853i	$0.187226\pi$
$163$	−2.11892	+	7.90791i	−0.165967	+	0.619396i	−0.997915	+	0.0645426i	$0.979441\pi$
$164$	2.71069	+	10.1164i	0.211669	+	0.789959i
$165$		0			0
$166$	4.22467	+	7.31734i	0.327898	+	0.567936i
$167$	1.97146	−	1.97146i	0.152556	−	0.152556i	−0.626702	−	0.779259i	$-0.715596\pi$
$167$	1.97146	−	1.97146i	0.152556	−	0.152556i	0.779259	+	0.626702i	$0.215596\pi$
$168$		0			0
$169$	−6.96450	−	10.9771i	−0.535731	−	0.844389i
$170$	1.55842	+	2.69927i	0.119526	+	0.207024i
$171$		0			0
$172$	4.97487	−	8.61674i	0.379331	−	0.657020i
$173$	0.901884	+	1.56211i	0.0685690	+	0.118765i	0.898272	−	0.439441i	$-0.144823\pi$
$173$	0.901884	+	1.56211i	0.0685690	+	0.118765i	−0.829703	+	0.558206i	$0.811490\pi$
$174$		0			0
$175$	−0.0173752	−	12.9421i	−0.00131344	−	0.978329i
$176$	−0.159017	−	0.159017i	−0.0119863	−	0.0119863i
$177$		0			0
$178$	6.90361	+	3.98580i	0.517447	+	0.298748i
$179$	14.8199	+	8.55629i	1.10769	+	0.639527i	0.938231	−	0.346010i	$-0.112464\pi$
$179$	14.8199	+	8.55629i	1.10769	+	0.639527i	0.169462	+	0.985537i	$0.445797\pi$
$180$		0			0
$181$	−23.4682			−1.74438			−0.872190	−	0.489168i	$-0.837301\pi$
$181$	−23.4682			−1.74438			−0.872190	+	0.489168i	$0.837301\pi$
$182$	−7.56914	−	1.84884i	−0.561062	−	0.137045i
$183$		0			0
$184$	−13.6986	−	3.67054i	−1.00988	−	0.270596i
$185$	7.52580	+	4.34502i	0.553308	+	0.319452i
$186$		0			0
$187$	0.159695	−	0.595991i	0.0116781	−	0.0435832i
$188$	−4.62006	−	4.62006i	−0.336953	−	0.336953i
$189$		0			0
$190$	3.23772	+	3.23772i	0.234889	+	0.234889i
$191$	12.6234	+	21.8644i	0.913400	+	1.58206i	0.809227	+	0.587496i	$0.199886\pi$
$191$	12.6234	+	21.8644i	0.913400	+	1.58206i	0.104173	+	0.994559i	$0.466780\pi$
$192$		0			0
$193$	−5.15802	+	1.38209i	−0.371282	+	0.0994848i	−0.439635	−	0.898176i	$-0.644892\pi$
$193$	−5.15802	+	1.38209i	−0.371282	+	0.0994848i	0.0683529	+	0.997661i	$0.478226\pi$
$194$	−1.69330	−	2.93289i	−0.121572	−	0.210569i
$195$		0			0
$196$	8.06745	−	4.68667i	0.576247	−	0.334762i
$197$	10.7141	−	10.7141i	0.763345	−	0.763345i	−0.213580	−	0.976926i	$-0.568513\pi$
$197$	10.7141	−	10.7141i	0.763345	−	0.763345i	0.976926	+	0.213580i	$0.0685125\pi$
$198$		0			0
$199$	3.59015	−	6.21832i	0.254499	−	0.440805i	−0.710260	−	0.703939i	$-0.751423\pi$
$199$	3.59015	−	6.21832i	0.254499	−	0.440805i	0.964759	+	0.263134i	$0.0847561\pi$
$200$	−3.44650	−	12.8625i	−0.243704	−	0.909517i
$201$		0			0
$202$	−8.92426	+	8.92426i	−0.627909	+	0.627909i
$203$	−2.18043	−	3.76493i	−0.153036	−	0.264246i
$204$		0			0
$205$	21.4025	−	12.3568i	1.49482	−	0.863033i
$206$	3.69964	+	13.8072i	0.257766	+	0.961995i
$207$		0			0
$208$	1.59408	−	0.0333005i	0.110530	−	0.00230898i
$209$		−	0.906432i		−	0.0626992i
$210$		0			0
$211$	−2.72556			−0.187636			−0.0938178	−	0.995589i	$-0.529907\pi$
$211$	−2.72556			−0.187636			−0.0938178	+	0.995589i	$0.529907\pi$
$212$	9.94953	−	5.74437i	0.683337	−	0.394525i
$213$		0			0
$214$	−0.449049	−	1.67587i	−0.0306964	−	0.114560i
$215$	−22.6781	−	6.07659i	−1.54664	−	0.414420i
$216$		0			0
$217$	−7.06584	−	7.04689i	−0.479660	−	0.478374i
$218$		−	8.74709i		−	0.592428i
$219$		0			0
$220$	−1.06589	+	1.84618i	−0.0718623	+	0.124469i
$221$	2.26597	+	3.74204i	0.152426	+	0.251717i
$222$		0			0
$223$	15.3311	+	15.3311i	1.02665	+	1.02665i	0.999635	+	0.0270132i	$0.00859962\pi$
$223$	15.3311	+	15.3311i	1.02665	+	1.02665i	0.0270132	+	0.999635i	$0.491400\pi$
$224$	10.8468	−	10.8760i	0.724735	−	0.726683i
$225$		0			0
$226$	4.11126	+	1.10161i	0.273477	+	0.0732779i
$227$	17.4825	−	4.68443i	1.16036	−	0.310916i	0.373248	−	0.927732i	$-0.378244\pi$
$227$	17.4825	−	4.68443i	1.16036	−	0.310916i	0.787108	+	0.616815i	$0.211577\pi$
$228$		0			0
$229$	4.17546	+	1.11881i	0.275922	+	0.0739331i	0.394126	−	0.919056i	$-0.371047\pi$
$229$	4.17546	+	1.11881i	0.275922	+	0.0739331i	−0.118205	+	0.992989i	$0.537714\pi$
$230$			13.3829i			0.882445i
$231$		0			0
$232$	−3.16538	−	3.16538i	−0.207817	−	0.207817i
$233$	8.56327	−	4.94400i	0.560998	−	0.323892i	−0.192548	−	0.981288i	$-0.561675\pi$
$233$	8.56327	−	4.94400i	0.560998	−	0.323892i	0.753546	+	0.657395i	$0.228342\pi$
$234$		0			0
$235$	−7.70876	+	13.3520i	−0.502864	+	0.870986i
$236$	0.863919	−	3.22419i	0.0562363	−	0.209877i
$237$		0			0
$238$	2.53355	+	0.675219i	0.164226	+	0.0437679i
$239$	8.13735	−	8.13735i	0.526361	−	0.526361i	−0.393124	−	0.919485i	$-0.628606\pi$
$239$	8.13735	−	8.13735i	0.526361	−	0.526361i	0.919485	+	0.393124i	$0.128606\pi$
$240$		0			0
$241$	3.77210	+	14.0777i	0.242982	+	0.906822i	0.974387	+	0.224878i	$0.0721985\pi$
$241$	3.77210	+	14.0777i	0.242982	+	0.906822i	−0.731405	+	0.681944i	$0.761135\pi$
$242$	8.47450	−	2.27074i	0.544762	−	0.145968i
$243$		0			0
$244$	14.0016			0.896362
$245$	−15.6092	−	15.5256i	−0.997235	−	0.991894i
$246$		0			0
$247$	4.63822	+	4.44840i	0.295123	+	0.283045i
$248$	−8.89210	−	5.13386i	−0.564649	−	0.326000i
$249$		0			0
$250$	0.241046	−	0.139168i	0.0152451	−	0.00880177i
$251$	2.29786			0.145040			0.0725198	−	0.997367i	$-0.476896\pi$
$251$	2.29786			0.145040			0.0725198	+	0.997367i	$0.476896\pi$
$252$		0			0
$253$	1.87334	−	1.87334i	0.117776	−	0.117776i
$254$	−2.41755	+	9.02241i	−0.151690	+	0.566116i
$255$		0			0
$256$	7.31281	−	12.6662i	0.457051	−	0.791635i
$257$	9.02516	+	15.6320i	0.562974	+	0.975100i	0.997235	+	0.0743128i	$0.0236763\pi$
$257$	9.02516	+	15.6320i	0.562974	+	0.975100i	−0.434261	+	0.900787i	$0.642990\pi$
$258$		0			0
$259$	7.05869	−	1.90153i	0.438605	−	0.118155i
$260$	−4.21594	−	14.5144i	−0.261462	−	0.900148i
$261$		0			0
$262$	5.53869	−	1.48409i	0.342181	−	0.0916872i
$263$	3.98168	−	6.89647i	0.245521	−	0.425255i	−0.716757	−	0.697323i	$-0.754374\pi$
$263$	3.98168	−	6.89647i	0.245521	−	0.425255i	0.962278	+	0.272068i	$0.0877077\pi$
$264$		0			0
$265$	−19.1694	−	19.1694i	−1.17757	−	1.17757i
$266$	3.85185	−	0.00517124i	0.236172	−	0.000317069i
$267$		0			0
$268$	−2.55401	+	9.53170i	−0.156011	+	0.582241i
$269$	−6.97055	−	4.02445i	−0.425002	−	0.245375i	0.272213	−	0.962237i	$-0.412244\pi$
$269$	−6.97055	−	4.02445i	−0.425002	−	0.245375i	−0.697215	+	0.716862i	$0.745578\pi$
$270$		0			0
$271$	21.4521	+	5.74808i	1.30312	+	0.349171i	0.842631	−	0.538492i	$-0.181006\pi$
$271$	21.4521	+	5.74808i	1.30312	+	0.349171i	0.460494	+	0.887663i	$0.347672\pi$
$272$	−0.536543			−0.0325327
$273$		0			0
$274$	−5.08024			−0.306909
$275$	2.40284	+	0.643838i	0.144897	+	0.0388249i
$276$		0			0
$277$	1.27323	+	0.735098i	0.0765008	+	0.0441678i	0.537762	−	0.843096i	$-0.319270\pi$
$277$	1.27323	+	0.735098i	0.0765008	+	0.0441678i	−0.461262	+	0.887264i	$0.652603\pi$
$278$	−0.405184	+	1.51217i	−0.0243013	+	0.0906938i
$279$		0			0
$280$	−19.6325	−	11.2997i	−1.17327	−	0.675289i
$281$	13.2274	+	13.2274i	0.789081	+	0.789081i	0.981343	−	0.192263i	$-0.0615826\pi$
$281$	13.2274	+	13.2274i	0.789081	+	0.789081i	−0.192263	+	0.981343i	$0.561583\pi$
$282$		0			0
$283$	−2.39327	+	4.14527i	−0.142265	+	0.246411i	−0.928349	−	0.371709i	$-0.878772\pi$
$283$	−2.39327	+	4.14527i	−0.142265	+	0.246411i	0.786084	+	0.618120i	$0.212105\pi$
$284$	1.53011	−	0.409992i	0.0907954	−	0.0243285i
$285$		0			0
$286$	0.721567	−	1.31235i	0.0426671	−	0.0776008i
$287$	5.35381	−	20.0885i	0.316026	−	1.18579i
$288$		0			0
$289$	7.76394	+	13.4475i	0.456702	+	0.791032i
$290$	−2.11217	+	3.65838i	−0.124031	+	0.214828i
$291$		0			0
$292$	0.843267	−	3.14711i	0.0493484	−	0.184171i
$293$	−15.3136	+	15.3136i	−0.894628	+	0.894628i	−0.994955	−	0.100326i	$-0.968011\pi$
$293$	−15.3136	+	15.3136i	−0.894628	+	0.894628i	0.100326	+	0.994955i	$0.468011\pi$
$294$		0			0
$295$	−7.87640			−0.458582
$296$	6.51395	−	3.76083i	0.378616	−	0.218594i
$297$		0			0
$298$	−0.789951	−	0.456079i	−0.0457607	−	0.0264199i
$299$	0.392306	+	18.7795i	0.0226877	+	1.08605i
$300$		0			0
$301$	−17.0912	+	9.89820i	−0.985118	+	0.570523i
$302$	−10.7646			−0.619433
$303$		0			0
$304$	−0.761355	+	0.204004i	−0.0436667	+	0.0117005i
$305$	−8.55118	−	31.9134i	−0.489639	−	1.82736i
$306$		0			0
$307$	−9.36619	+	9.36619i	−0.534556	+	0.534556i	−0.921925	−	0.387369i	$-0.873384\pi$
$307$	−9.36619	+	9.36619i	−0.534556	+	0.534556i	0.387369	+	0.921925i	$0.373384\pi$
$308$	0.466470	+	1.73159i	0.0265796	+	0.0986663i
$309$		0			0
$310$	−2.50777	+	9.35913i	−0.142432	+	0.531563i
$311$	−2.71082	+	4.69528i	−0.153716	+	0.266245i	−0.932591	−	0.360935i	$-0.882458\pi$
$311$	−2.71082	+	4.69528i	−0.153716	+	0.266245i	0.778874	+	0.627180i	$0.215791\pi$
$312$		0			0
$313$	−18.2670	+	10.5464i	−1.03251	+	0.596120i	−0.917703	−	0.397268i	$-0.869958\pi$
$313$	−18.2670	+	10.5464i	−1.03251	+	0.596120i	−0.114807	+	0.993388i	$0.536625\pi$
$314$	−8.03039	−	8.03039i	−0.453181	−	0.453181i
$315$		0			0
$316$		−	16.5426i		−	0.930596i
$317$	−14.8840	−	3.98815i	−0.835968	−	0.223997i	−0.184652	−	0.982804i	$-0.559116\pi$
$317$	−14.8840	−	3.98815i	−0.835968	−	0.223997i	−0.651316	+	0.758807i	$0.725783\pi$
$318$		0			0
$319$	0.807761	−	0.216439i	0.0452259	−	0.0121183i
$320$	−11.7191	−	3.14012i	−0.655117	−	0.175538i
$321$		0			0
$322$	7.97138	+	7.95001i	0.444228	+	0.443036i
$323$	−1.52921	−	1.52921i	−0.0850874	−	0.0850874i
$324$		0			0
$325$	−15.0867	+	9.13564i	−0.836857	+	0.506754i
$326$	3.34348	−	5.79107i	0.185178	−	0.320738i
$327$		0			0
$328$		−	21.3908i		−	1.18111i
$329$	3.37361	+	12.5232i	0.185993	+	0.690428i
$330$		0			0
$331$	9.13594	+	2.44797i	0.502156	+	0.134552i	0.501001	−	0.865447i	$-0.332965\pi$
$331$	9.13594	+	2.44797i	0.502156	+	0.134552i	0.00115583	+	0.999999i	$0.499632\pi$
$332$	3.56855	+	13.3180i	0.195850	+	0.730921i
$333$		0			0
$334$	−1.97217	+	1.13863i	−0.107912	+	0.0623031i
$335$	23.2851			1.27220
$336$		0			0
$337$			30.8890i			1.68263i	0.540545	+	0.841315i	$0.318218\pi$
$337$			30.8890i			1.68263i	−0.540545	+	0.841315i	$0.681782\pi$
$338$	3.17414	+	10.1327i	0.172650	+	0.551148i
$339$		0			0
$340$	1.31639	+	4.91284i	0.0713913	+	0.266436i
$341$	1.66113	−	0.959052i	0.0899551	−	0.0519356i
$342$		0			0
$343$	−18.5201	+	0.0745920i	−0.999992	+	0.00402759i
$344$	−14.3695	+	14.3695i	−0.774750	+	0.774750i
$345$		0			0
$346$	−0.381318	−	1.42310i	−0.0204998	−	0.0765062i
$347$	5.48714	−	9.50400i	0.294565	−	0.510201i	−0.680319	−	0.732916i	$-0.738159\pi$
$347$	5.48714	−	9.50400i	0.294565	−	0.510201i	0.974884	+	0.222715i	$0.0714920\pi$
$348$		0			0
$349$	14.1593	−	14.1593i	0.757930	−	0.757930i	−0.218015	−	0.975945i	$-0.569958\pi$
$349$	14.1593	−	14.1593i	0.757930	−	0.757930i	0.975945	+	0.218015i	$0.0699582\pi$
$350$	−2.72226	+	10.2144i	−0.145511	+	0.545984i
$351$		0			0
$352$	1.47621	+	2.55687i	0.0786822	+	0.136282i
$353$	−18.4255	+	4.93709i	−0.980688	+	0.262775i	−0.713334	−	0.700824i	$-0.752816\pi$
$353$	−18.4255	+	4.93709i	−0.980688	+	0.262775i	−0.267354	+	0.963598i	$0.586149\pi$
$354$		0			0
$355$	−1.86896	−	3.23714i	−0.0991942	−	0.171809i
$356$	9.19822	+	9.19822i	0.487504	+	0.487504i
$357$		0			0
$358$	−9.88349	−	9.88349i	−0.522359	−	0.522359i
$359$	7.25413	−	27.0728i	0.382858	−	1.42885i	−0.458657	−	0.888613i	$-0.651669\pi$
$359$	7.25413	−	27.0728i	0.382858	−	1.42885i	0.841515	−	0.540233i	$-0.181664\pi$
$360$		0			0
$361$	13.7031	+	7.91149i	0.721216	+	0.416394i
$362$	18.5154	+	4.96120i	0.973150	+	0.260755i
$363$		0			0
$364$	−11.1498	−	6.11099i	−0.584407	−	0.320303i
$365$	−7.68812			−0.402414
$366$		0			0
$367$	14.4837	+	8.36218i	0.756044	+	0.436502i	0.827874	−	0.560915i	$-0.189550\pi$
$367$	14.4837	+	8.36218i	0.756044	+	0.436502i	−0.0718297	+	0.997417i	$0.522884\pi$
$368$	−1.99513	−	1.15189i	−0.104003	−	0.0600463i
$369$		0			0
$370$	−5.01900	−	5.01900i	−0.260925	−	0.260925i
$371$	−22.8054	+	0.0306170i	−1.18400	+	0.00158956i
$372$		0			0
$373$	−8.19490	−	14.1940i	−0.424316	−	0.734937i	0.572040	−	0.820226i	$-0.306152\pi$
$373$	−8.19490	−	14.1940i	−0.424316	−	0.734937i	−0.996356	+	0.0852887i	$0.972819\pi$
$374$	−0.251986	+	0.436452i	−0.0130299	+	0.0225684i
$375$		0			0
$376$	6.67231	+	11.5568i	0.344098	+	0.595996i
$377$	−2.85664	+	5.19551i	−0.147125	+	0.267582i
$378$		0			0
$379$	2.80924	−	2.80924i	0.144301	−	0.144301i	−0.631266	−	0.775567i	$-0.717464\pi$
$379$	2.80924	−	2.80924i	0.144301	−	0.144301i	0.775567	+	0.631266i	$0.217464\pi$
$380$	3.73592	+	6.47081i	0.191649	+	0.331945i
$381$		0			0
$382$	−5.33721	−	19.9187i	−0.273075	−	1.01913i
$383$	−10.0367	+	37.4573i	−0.512849	+	1.91398i	−0.125342	+	0.992114i	$0.540003\pi$
$383$	−10.0367	+	37.4573i	−0.512849	+	1.91398i	−0.387508	+	0.921867i	$0.626664\pi$
$384$		0			0
$385$	3.66186	−	2.12074i	0.186626	−	0.108083i
$386$	4.36163			0.222001
$387$		0			0
$388$	−1.43032	−	5.33804i	−0.0726137	−	0.270998i
$389$	4.22632	+	2.44006i	0.214283	+	0.123716i	0.603300	−	0.797514i	$-0.293852\pi$
$389$	4.22632	+	2.44006i	0.214283	+	0.123716i	−0.389017	+	0.921230i	$0.627185\pi$
$390$		0			0
$391$		−	6.32089i		−	0.319661i
$392$	−18.3931	+	4.98138i	−0.928990	+	0.251598i
$393$		0			0
$394$	−10.7179	+	6.18798i	−0.539960	+	0.311746i
$395$	−37.7051	+	10.1030i	−1.89715	+	0.508339i
$396$		0			0
$397$	−30.5778	−	8.19329i	−1.53466	−	0.411210i	−0.610121	−	0.792308i	$-0.708879\pi$
$397$	−30.5778	−	8.19329i	−1.53466	−	0.411210i	−0.924534	+	0.381099i	$0.875546\pi$
$398$	−4.14703	+	4.14703i	−0.207872	+	0.207872i
$399$		0			0
$400$		−	2.16316i		−	0.108158i
$401$	−2.50381	+	9.34436i	−0.125035	+	0.466635i	−0.999841	−	0.0178375i	$-0.994322\pi$
$401$	−2.50381	+	9.34436i	−0.125035	+	0.466635i	0.874806	+	0.484473i	$0.160989\pi$
$402$		0			0
$403$	−3.24466	+	13.2066i	−0.161628	+	0.657869i
$404$	−17.8357	+	10.2975i	−0.887361	+	0.512318i
$405$		0			0
$406$	0.924356	+	3.43131i	0.0458750	+	0.170293i
$407$			1.40512i			0.0696491i
$408$		0			0
$409$	11.5530	−	3.09562i	0.571259	−	0.153068i	0.0383851	−	0.999263i	$-0.487779\pi$
$409$	11.5530	−	3.09562i	0.571259	−	0.153068i	0.532874	+	0.846195i	$0.321112\pi$
$410$	−19.4979	+	5.22445i	−0.962933	+	0.258017i
$411$		0			0
$412$			23.3258i			1.14918i
$413$	−4.67890	+	4.69148i	−0.230234	+	0.230853i
$414$		0			0
$415$	28.1759	−	16.2674i	1.38310	−	0.798533i
$416$	−20.3281	−	4.99430i	−0.996669	−	0.244866i
$417$		0			0
$418$	−0.191620	+	0.715137i	−0.00937246	+	0.0349785i
$419$		−	18.5355i		−	0.905516i	−0.891633	−	0.452758i	$-0.850440\pi$
$419$		−	18.5355i		−	0.905516i	0.891633	−	0.452758i	$-0.149560\pi$
$420$		0			0
$421$	19.2884	−	19.2884i	0.940060	−	0.940060i	−0.0582422	−	0.998302i	$-0.518550\pi$
$421$	19.2884	−	19.2884i	0.940060	−	0.940060i	0.998302	+	0.0582422i	$0.0185496\pi$
$422$	2.15036	+	0.576186i	0.104678	+	0.0280483i
$423$		0			0
$424$	−22.6652	+	6.07312i	−1.10072	+	0.294937i
$425$	5.13993	−	2.96754i	0.249323	−	0.143947i
$426$		0			0
$427$	−24.0886	−	13.8645i	−1.16573	−	0.670948i
$428$		−	2.83120i		−	0.136851i
$429$		0			0
$430$	16.6075	+	9.58834i	0.800884	+	0.462391i
$431$	2.37115	+	8.84924i	0.114214	+	0.426253i	0.999227	−	0.0393138i	$-0.0125172\pi$
$431$	2.37115	+	8.84924i	0.114214	+	0.426253i	−0.885013	+	0.465567i	$0.845851\pi$
$432$		0			0
$433$	−23.6700			−1.13751			−0.568755	−	0.822507i	$-0.692575\pi$
$433$	−23.6700			−1.13751			−0.568755	+	0.822507i	$0.692575\pi$
$434$	4.08493	+	7.05342i	0.196083	+	0.338575i
$435$		0			0
$436$	3.69431	−	13.7873i	0.176925	−	0.660294i
$437$	−2.40333	−	8.96936i	−0.114967	−	0.429063i
$438$		0			0
$439$	5.64906	+	9.78446i	0.269615	+	0.466987i	0.968762	−	0.247991i	$-0.0797703\pi$
$439$	5.64906	+	9.78446i	0.269615	+	0.466987i	−0.699148	+	0.714977i	$0.746437\pi$
$440$	3.07872	−	3.07872i	0.146772	−	0.146772i
$441$		0			0
$442$	−0.996685	−	3.43134i	−0.0474075	−	0.163212i
$443$	19.5144	+	33.7999i	0.927157	+	1.60588i	0.788054	+	0.615606i	$0.211089\pi$
$443$	19.5144	+	33.7999i	0.927157	+	1.60588i	0.139103	+	0.990278i	$0.455578\pi$
$444$		0			0
$445$	15.3476	−	26.5828i	0.727545	−	1.26015i
$446$	−8.85460	−	15.3366i	−0.419278	−	0.726210i
$447$		0			0
$448$	−8.83198	+	5.11497i	−0.417272	+	0.241659i
$449$	8.82288	+	8.82288i	0.416378	+	0.416378i	0.883953	−	0.467576i	$-0.154872\pi$
$449$	8.82288	+	8.82288i	0.416378	+	0.416378i	−0.467576	+	0.883953i	$0.654872\pi$
$450$		0			0
$451$	3.46063	+	1.99800i	0.162955	+	0.0940820i
$452$	6.01499	+	3.47276i	0.282921	+	0.163345i
$453$		0			0
$454$	−14.7833			−0.693813
$455$	−7.11910	+	29.1455i	−0.333748	+	1.36636i
$456$		0			0
$457$	−22.0825	−	5.91700i	−1.03298	−	0.276786i	−0.297777	−	0.954635i	$-0.596245\pi$
$457$	−22.0825	−	5.91700i	−1.03298	−	0.276786i	−0.735200	+	0.677850i	$0.762912\pi$
$458$	−3.05774	−	1.76539i	−0.142879	−	0.0824912i
$459$		0			0
$460$	−5.65224	+	21.0945i	−0.263537	+	0.983534i
$461$	−7.67189	−	7.67189i	−0.357316	−	0.357316i	0.505507	−	0.862823i	$-0.331306\pi$
$461$	−7.67189	−	7.67189i	−0.357316	−	0.357316i	−0.862823	+	0.505507i	$0.831306\pi$
$462$		0			0
$463$	14.0571	+	14.0571i	0.653289	+	0.653289i	0.953783	−	0.300495i	$-0.0971518\pi$
$463$	14.0571	+	14.0571i	0.653289	+	0.653289i	−0.300495	+	0.953783i	$0.597152\pi$
$464$	−0.363594	−	0.629764i	−0.0168794	−	0.0292361i
$465$		0			0
$466$	−7.80122	+	2.09033i	−0.361385	+	0.0968327i
$467$	4.96276	+	8.59575i	0.229649	+	0.397764i	0.957704	−	0.287755i	$-0.0929088\pi$
$467$	4.96276	+	8.59575i	0.229649	+	0.397764i	−0.728055	+	0.685519i	$0.759576\pi$
$468$		0			0
$469$	13.8323	−	13.8695i	0.638715	−	0.640433i
$470$	8.90450	−	8.90450i	0.410734	−	0.410734i
$471$		0			0
$472$	−3.40871	+	5.90406i	−0.156899	+	0.271756i
$473$	−0.982540	−	3.66689i	−0.0451772	−	0.168604i
$474$		0			0
$475$	6.16525	−	6.16525i	0.282881	−	0.282881i
$476$	3.70826	+	2.13433i	0.169968	+	0.0978269i
$477$		0			0
$478$	−8.14026	+	4.69978i	−0.372327	+	0.214963i
$479$	−5.45991	−	20.3767i	−0.249470	−	0.931034i	−0.971084	−	0.238738i	$-0.923266\pi$
$479$	−5.45991	−	20.3767i	−0.249470	−	0.931034i	0.721614	−	0.692295i	$-0.243400\pi$
$480$		0			0
$481$	−7.19000	−	6.89574i	−0.327836	−	0.314419i
$482$		−	11.9041i		−	0.542217i
$483$		0			0
$484$	14.3167			0.650760
$485$	−11.2933	+	6.52018i	−0.512801	+	0.296066i
$486$		0			0
$487$	11.3470	+	42.3475i	0.514181	+	1.91895i	0.368544	+	0.929610i	$0.379856\pi$
$487$	11.3470	+	42.3475i	0.514181	+	1.91895i	0.145637	+	0.989338i	$0.453477\pi$
$488$	−27.6227	−	7.40147i	−1.25042	−	0.335049i
$489$		0			0
$490$	9.03287	+	15.5488i	0.408064	+	0.702424i
$491$			37.1276i			1.67554i	0.546021	+	0.837772i	$0.316142\pi$
$491$			37.1276i			1.67554i	−0.546021	+	0.837772i	$0.683858\pi$
$492$		0			0
$493$	0.997597	−	1.72789i	0.0449295	−	0.0778202i
$494$	−2.71896	−	4.49012i	−0.122332	−	0.202020i
$495$		0			0
$496$	−1.17941	−	1.17941i	−0.0529571	−	0.0529571i
$497$	−3.03840	−	0.809766i	−0.136291	−	0.0363230i
$498$		0			0
$499$	5.17328	+	1.38618i	0.231588	+	0.0620538i	0.372747	−	0.927933i	$-0.378416\pi$
$499$	5.17328	+	1.38618i	0.231588	+	0.0620538i	−0.141159	+	0.989987i	$0.545083\pi$
$500$	0.438720	−	0.117555i	0.0196201	−	0.00525720i
$501$		0			0
$502$	−1.81292	−	0.485769i	−0.0809144	−	0.0216809i
$503$			27.7355i			1.23666i	0.785917	+	0.618332i	$0.212191\pi$
$503$			27.7355i			1.23666i	−0.785917	+	0.618332i	$0.787809\pi$
$504$		0			0
$505$	34.3634	+	34.3634i	1.52915	+	1.52915i
$506$	−1.87401	+	1.08196i	−0.0833101	+	0.0480991i
$507$		0			0
$508$	−7.62117	+	13.2003i	−0.338135	+	0.585667i
$509$	7.83435	−	29.2382i	0.347252	−	1.29596i	−0.542708	−	0.839921i	$-0.682601\pi$
$509$	7.83435	−	29.2382i	0.347252	−	1.29596i	0.889960	−	0.456039i	$-0.150732\pi$
$510$		0			0
$511$	−4.56705	+	4.57933i	−0.202034	+	0.202578i
$512$	3.51784	−	3.51784i	0.155468	−	0.155468i
$513$		0			0
$514$	−3.81585	−	14.2409i	−0.168310	−	0.628141i
$515$	53.1656	−	14.2457i	2.34276	−	0.627740i
$516$		0			0
$517$	−2.49290			−0.109638
$518$	−5.97099	+	0.00801626i	−0.262350	+	0.000352214i
$519$		0			0
$520$	0.644732	+	30.8630i	0.0282733	+	1.35343i
$521$	36.7196	+	21.2001i	1.60872	+	0.928792i	0.989658	+	0.143446i	$0.0458183\pi$
$521$	36.7196	+	21.2001i	1.60872	+	0.928792i	0.619057	+	0.785346i	$0.287515\pi$
$522$		0			0
$523$	−3.60227	+	2.07977i	−0.157516	+	0.0909420i	−0.576686	−	0.816966i	$-0.695654\pi$
$523$	−3.60227	+	2.07977i	−0.157516	+	0.0909420i	0.419170	+	0.907908i	$0.362321\pi$
$524$	9.35699			0.408762
$525$		0			0
$526$	−4.59929	+	4.59929i	−0.200539	+	0.200539i
$527$	1.18444	−	4.42040i	0.0515952	−	0.192556i
$528$		0			0
$529$	2.07015	−	3.58560i	0.0900064	−	0.155896i
$530$	11.0714	+	19.1763i	0.480912	+	0.832964i
$531$		0			0
$532$	6.07354	+	1.61866i	0.263321	+	0.0701780i
$533$	−27.2071	+	7.90273i	−1.17847	+	0.342305i
$534$		0			0
$535$	−6.45306	+	1.72909i	−0.278990	+	0.0747552i
$536$	10.0772	−	17.4542i	0.435269	−	0.753908i
$537$		0			0
$538$	4.64870	+	4.64870i	0.200420	+	0.200420i
$539$	0.912103	−	3.44094i	0.0392870	−	0.148212i
$540$		0			0
$541$	10.8361	−	40.4410i	0.465882	−	1.73869i	−0.188068	−	0.982156i	$-0.560223\pi$
$541$	10.8361	−	40.4410i	0.465882	−	1.73869i	0.653950	−	0.756538i	$-0.273111\pi$
$542$	−15.7097	−	9.06999i	−0.674789	−	0.389589i
$543$		0			0
$544$	6.80405	+	1.82314i	0.291721	+	0.0781665i
$545$	−33.6812			−1.44275
$546$		0			0
$547$	−13.4403			−0.574667			−0.287334	−	0.957831i	$-0.592769\pi$
$547$	−13.4403			−0.574667			−0.287334	+	0.957831i	$0.592769\pi$
$548$	−8.00758	−	2.14562i	−0.342067	−	0.0916565i
$549$		0			0
$550$	−1.75963	−	1.01592i	−0.0750308	−	0.0433191i
$551$	0.758614	−	2.83118i	0.0323180	−	0.120613i
$552$		0			0
$553$	−16.3806	+	28.4602i	−0.696573	+	1.21025i
$554$	−0.849123	−	0.849123i	−0.0360758	−	0.0360758i
$555$		0			0
$556$	−1.27732	+	2.21238i	−0.0541704	+	0.0938258i
$557$	20.1649	−	5.40317i	0.854415	−	0.228940i	0.195078	−	0.980788i	$-0.437504\pi$
$557$	20.1649	−	5.40317i	0.854415	−	0.228940i	0.659337	+	0.751848i	$0.270837\pi$
$558$		0			0
$559$	23.5854	+	12.9679i	0.997556	+	0.548485i
$560$	−2.60546	−	2.59847i	−0.110101	−	0.109805i
$561$		0			0
$562$	−7.63958	−	13.2321i	−0.322256	−	0.558164i
$563$	13.5788	−	23.5192i	0.572278	−	0.991215i	−0.424053	−	0.905637i	$-0.639393\pi$
$563$	13.5788	−	23.5192i	0.572278	−	0.991215i	0.996331	−	0.0855779i	$-0.0272737\pi$
$564$		0			0
$565$	4.24181	−	15.8307i	0.178454	−	0.666001i
$566$	2.76450	−	2.76450i	0.116201	−	0.116201i
$567$		0			0
$568$	−3.23536			−0.135753
$569$	−10.6066	+	6.12370i	−0.444650	+	0.256719i	−0.705568	−	0.708642i	$-0.749308\pi$
$569$	−10.6066	+	6.12370i	−0.444650	+	0.256719i	0.260918	+	0.965361i	$0.415975\pi$
$570$		0			0
$571$	4.06355	+	2.34609i	0.170054	+	0.0981809i	0.582611	−	0.812751i	$-0.302031\pi$
$571$	4.06355	+	2.34609i	0.170054	+	0.0981809i	−0.412557	+	0.910932i	$0.635364\pi$
$572$	1.69161	−	1.76380i	0.0707300	−	0.0737481i
$573$		0			0
$574$	−8.47066	+	14.7172i	−0.353559	+	0.614285i
$575$	25.4837			1.06274
$576$		0			0
$577$	−16.4860	+	4.41741i	−0.686321	+	0.183899i	−0.585095	−	0.810964i	$-0.698943\pi$
$577$	−16.4860	+	4.41741i	−0.686321	+	0.183899i	−0.101225	+	0.994864i	$0.532276\pi$
$578$	−3.28260	−	12.2508i	−0.136538	−	0.509568i
$579$		0			0
$580$	−4.87435	+	4.87435i	−0.202396	+	0.202396i
$581$	7.04816	−	26.4461i	0.292407	−	1.09717i
$582$		0			0
$583$	1.13452	−	4.23407i	0.0469868	−	0.175357i
$584$	−3.32722	+	5.76292i	−0.137682	+	0.238471i
$585$		0			0
$586$	15.3191	−	8.84446i	0.632824	−	0.365361i
$587$	−6.21734	−	6.21734i	−0.256617	−	0.256617i	0.567060	−	0.823677i	$-0.308081\pi$
$587$	−6.21734	−	6.21734i	−0.256617	−	0.256617i	−0.823677	+	0.567060i	$0.808081\pi$
$588$		0			0
$589$		−	6.72291i		−	0.277013i
$590$	6.21415	+	1.66508i	0.255833	+	0.0685501i
$591$		0			0
$592$	1.18022	−	0.316240i	0.0485069	−	0.0129974i
$593$	−37.5829	−	10.0703i	−1.54334	−	0.413538i	−0.615999	−	0.787747i	$-0.711248\pi$
$593$	−37.5829	−	10.0703i	−1.54334	−	0.413538i	−0.927344	+	0.374209i	$0.877914\pi$
$594$		0			0
$595$	2.59997	−	9.75560i	0.106589	−	0.399941i
$596$	−1.05251	−	1.05251i	−0.0431127	−	0.0431127i
$597$		0			0
$598$	3.66049	−	14.8992i	0.149688	−	0.609272i
$599$	−17.4902	+	30.2939i	−0.714629	+	1.23777i	0.248474	+	0.968639i	$0.420071\pi$
$599$	−17.4902	+	30.2939i	−0.714629	+	1.23777i	−0.963103	+	0.269135i	$0.913262\pi$
$600$		0			0
$601$		−	11.7882i		−	0.480852i	−0.970667	−	0.240426i	$-0.922713\pi$
$601$		−	11.7882i		−	0.480852i	0.970667	−	0.240426i	$-0.0772872\pi$
$602$	15.5767	−	4.19618i	0.634859	−	0.171024i
$603$		0			0
$604$	−16.9674	−	4.54639i	−0.690393	−	0.184990i
$605$	−8.74361	−	32.6316i	−0.355478	−	1.32666i
$606$		0			0
$607$	16.5407	−	9.54978i	0.671366	−	0.387614i	−0.125228	−	0.992128i	$-0.539966\pi$
$607$	16.5407	−	9.54978i	0.671366	−	0.387614i	0.796594	+	0.604514i	$0.206633\pi$
$608$	10.3482			0.419673
$609$		0			0
$610$			26.9861i			1.09263i
$611$	12.2341	−	12.7562i	0.494940	−	0.516060i
$612$		0			0
$613$	−6.57860	−	24.5517i	−0.265707	−	0.991632i	−0.961816	−	0.273696i	$-0.911754\pi$
$613$	−6.57860	−	24.5517i	−0.265707	−	0.991632i	0.696109	−	0.717936i	$-0.254913\pi$
$614$	9.36954	−	5.40951i	0.378124	−	0.218310i
$615$		0			0
$616$	−0.00491729	−	3.66269i	−0.000198123	−	0.147574i
$617$	10.4089	−	10.4089i	0.419046	−	0.419046i	−0.465829	−	0.884875i	$-0.654244\pi$
$617$	10.4089	−	10.4089i	0.419046	−	0.419046i	0.884875	+	0.465829i	$0.154244\pi$
$618$		0			0
$619$	−8.22887	−	30.7106i	−0.330746	−	1.23436i	−0.908408	−	0.418085i	$-0.862701\pi$
$619$	−8.22887	−	30.7106i	−0.330746	−	1.23436i	0.577661	−	0.816276i	$-0.303965\pi$
$620$	−7.90560	+	13.6929i	−0.317496	+	0.549920i
$621$		0			0
$622$	3.13131	−	3.13131i	0.125554	−	0.125554i
$623$	−6.71662	−	24.9328i	−0.269096	−	0.998913i
$624$		0			0
$625$	−12.7650	−	22.1096i	−0.510600	−	0.884385i
$626$	16.6414	−	4.45905i	0.665124	−	0.178219i
$627$		0			0
$628$	−9.26606	−	16.0493i	−0.369756	−	0.640436i
$629$	2.37052	+	2.37052i	0.0945188	+	0.0945188i
$630$		0			0
$631$	26.3103	+	26.3103i	1.04739	+	1.04739i	0.998820	+	0.0485754i	$0.0154681\pi$
$631$	26.3103	+	26.3103i	1.04739	+	1.04739i	0.0485754	+	0.998820i	$0.484532\pi$
$632$	−8.74469	+	32.6356i	−0.347845	+	1.29817i
$633$		0			0
$634$	10.8997	+	6.29297i	0.432884	+	0.249926i
$635$	34.7414	+	9.30892i	1.37867	+	0.369413i
$636$		0			0
$637$	13.1311	+	21.5540i	0.520273	+	0.854000i
$638$	−0.683045			−0.0270420
$639$		0			0
$640$	−23.0442	−	13.3046i	−0.910903	−	0.525910i
$641$	−20.0412	−	11.5708i	−0.791579	−	0.457018i	0.0489393	−	0.998802i	$-0.484416\pi$
$641$	−20.0412	−	11.5708i	−0.791579	−	0.457018i	−0.840518	+	0.541784i	$0.817749\pi$
$642$		0			0
$643$	−11.9385	−	11.9385i	−0.470808	−	0.470808i	0.431368	−	0.902176i	$-0.358031\pi$
$643$	−11.9385	−	11.9385i	−0.470808	−	0.470808i	−0.902176	+	0.431368i	$0.858031\pi$
$644$	9.20699	+	15.8976i	0.362806	+	0.626455i
$645$		0			0
$646$	0.883205	+	1.52976i	0.0347492	+	0.0601874i
$647$	10.2367	−	17.7305i	0.402446	−	0.697056i	−0.591575	−	0.806250i	$-0.701494\pi$
$647$	10.2367	−	17.7305i	0.402446	−	0.697056i	0.994020	+	0.109194i	$0.0348269\pi$
$648$		0			0
$649$	−0.636779	−	1.10293i	−0.0249958	−	0.0432939i
$650$	13.8340	−	4.01830i	0.542615	−	0.157611i
$651$		0			0
$652$	7.71589	−	7.71589i	0.302178	−	0.302178i
$653$	−20.9319	−	36.2552i	−0.819130	−	1.41878i	−0.906324	−	0.422584i	$-0.861123\pi$
$653$	−20.9319	−	36.2552i	−0.819130	−	1.41878i	0.0871932	−	0.996191i	$-0.472210\pi$
$654$		0			0
$655$	−5.71457	−	21.3271i	−0.223287	−	0.833318i
$656$	0.899351	−	3.35642i	0.0351138	−	0.131046i
$657$		0			0
$658$	−0.0142221	−	10.5935i	−0.000554436	−	0.412977i
$659$	36.8332			1.43482			0.717410	−	0.696651i	$-0.245328\pi$
$659$	36.8332			1.43482			0.717410	+	0.696651i	$0.245328\pi$
$660$		0			0
$661$	1.87935	+	7.01384i	0.0730983	+	0.272807i	0.992795	−	0.119822i	$-0.0382324\pi$
$661$	1.87935	+	7.01384i	0.0730983	+	0.272807i	−0.919697	+	0.392629i	$0.871566\pi$
$662$	−6.69037	−	3.86268i	−0.260028	−	0.150128i
$663$		0			0
$664$		−	28.1604i		−	1.09284i
$665$	−0.0199122	−	14.8318i	−0.000772161	−	0.575152i
$666$		0			0
$667$	7.41911	−	4.28343i	0.287269	−	0.165855i
$668$	−3.58947	+	0.961794i	−0.138881	+	0.0372129i
$669$		0			0
$670$	−18.3710	−	4.92248i	−0.709732	−	0.190172i
$671$	3.77751	−	3.77751i	0.145829	−	0.145829i
$672$		0			0
$673$		−	28.4985i		−	1.09854i	−0.835646	−	0.549269i	$-0.814906\pi$
$673$		−	28.4985i		−	1.09854i	0.835646	−	0.549269i	$-0.185094\pi$
$674$	6.52995	−	24.3701i	0.251524	−	0.938701i
$675$		0			0
$676$	0.723616	+	17.3120i	0.0278314	+	0.665846i
$677$	−13.1864	+	7.61318i	−0.506795	+	0.292598i	−0.731515	−	0.681825i	$-0.761186\pi$
$677$	−13.1864	+	7.61318i	−0.506795	+	0.292598i	0.224720	+	0.974423i	$0.427853\pi$
$678$		0			0
$679$	−2.82500	+	10.5999i	−0.108414	+	0.406788i
$680$		−	10.3880i		−	0.398362i
$681$		0			0
$682$	−1.51330	+	0.405488i	−0.0579474	+	0.0155270i
$683$	−41.7404	+	11.1843i	−1.59715	+	0.427956i	−0.944182	−	0.329426i	$-0.893145\pi$
$683$	−41.7404	+	11.1843i	−1.59715	+	0.427956i	−0.652972	+	0.757382i	$0.726478\pi$
$684$		0			0
$685$			19.5618i			0.747418i
$686$	14.6274	+	3.85631i	0.558475	+	0.147235i
$687$		0			0
$688$	−2.85886	+	1.65056i	−0.108993	+	0.0629271i
$689$	16.0980	+	26.5844i	0.613286	+	1.01278i
$690$		0			0
$691$	2.59802	−	9.69593i	0.0988332	−	0.368851i	−0.898739	−	0.438483i	$-0.855516\pi$
$691$	2.59802	−	9.69593i	0.0988332	−	0.368851i	0.997573	+	0.0696323i	$0.0221826\pi$
$692$		−	2.40416i		−	0.0913926i
$693$		0			0
$694$	−6.33827	+	6.33827i	−0.240597	+	0.240597i
$695$	5.82270	+	1.56019i	0.220868	+	0.0591813i
$696$		0			0
$697$	9.20905	−	2.46756i	0.348818	−	0.0934654i
$698$	−14.1644	+	8.17781i	−0.536130	+	0.309535i
$699$		0			0
$700$	−8.60490	+	14.9504i	−0.325235	+	0.565074i
$701$			24.4239i			0.922479i	0.887276	+	0.461239i	$0.152595\pi$
$701$			24.4239i			0.922479i	−0.887276	+	0.461239i	$0.847405\pi$
$702$		0			0
$703$	4.26509	+	2.46245i	0.160861	+	0.0928732i
$704$	−0.507735	−	1.89489i	−0.0191360	−	0.0714164i
$705$		0			0
$706$	15.5806			0.586384
$707$	40.8814	−	0.0548847i	1.53750	−	0.00206415i
$708$		0			0
$709$	7.20208	−	26.8785i	0.270480	−	1.00944i	−0.688330	−	0.725397i	$-0.741656\pi$
$709$	7.20208	−	26.8785i	0.270480	−	1.00944i	0.958810	−	0.284047i	$-0.0916773\pi$
$710$	0.790199	+	2.94906i	0.0296556	+	0.110676i
$711$		0			0
$712$	−13.2841	−	23.0087i	−0.497843	−	0.862289i
$713$	13.8944	−	13.8944i	0.520349	−	0.520349i
$714$		0			0
$715$	−5.05328	−	2.77844i	−0.188982	−	0.103908i
$716$	−11.4043	−	19.7528i	−0.426199	−	0.738197i
$717$		0			0
$718$	−11.4464	+	19.8258i	−0.427176	+	0.739890i
$719$	−6.94803	−	12.0343i	−0.259118	−	0.448805i	0.706888	−	0.707325i	$-0.250098\pi$
$719$	−6.94803	−	12.0343i	−0.259118	−	0.448805i	−0.966006	+	0.258520i	$0.916765\pi$
$720$		0			0
$721$	23.0972	−	40.1299i	0.860187	−	1.49452i
$722$	−9.13867	−	9.13867i	−0.340106	−	0.340106i
$723$		0			0
$724$	27.0891	+	15.6399i	1.00676	+	0.581251i
$725$	6.96627	+	4.02198i	0.258721	+	0.149372i
$726$		0			0
$727$	−14.0631			−0.521572			−0.260786	−	0.965397i	$-0.583982\pi$
$727$	−14.0631			−0.521572			−0.260786	+	0.965397i	$0.583982\pi$
$728$	18.7661	+	17.9498i	0.695519	+	0.665265i
$729$		0			0
$730$	6.06560	+	1.62527i	0.224498	+	0.0601540i
$731$	−7.84388	−	4.52866i	−0.290116	−	0.167499i
$732$		0			0
$733$	−5.86099	+	21.8735i	−0.216481	+	0.807917i	0.769159	+	0.639057i	$0.220675\pi$
$733$	−5.86099	+	21.8735i	−0.216481	+	0.807917i	−0.985640	+	0.168860i	$0.945991\pi$
$734$	−9.65927	−	9.65927i	−0.356530	−	0.356530i
$735$		0			0
$736$	21.3868	+	21.3868i	0.788327	+	0.788327i
$737$	1.88252	+	3.26061i	0.0693434	+	0.120106i
$738$		0			0
$739$	−0.964923	+	0.258550i	−0.0354953	+	0.00951093i	−0.276523	−	0.961007i	$-0.589182\pi$
$739$	−0.964923	+	0.258550i	−0.0354953	+	0.00951093i	0.241028	+	0.970518i	$0.422516\pi$
$740$	−5.79129	−	10.0308i	−0.212892	−	0.368740i
$741$		0			0
$742$	17.9990	+	4.79692i	0.660763	+	0.176100i
$743$	7.54553	−	7.54553i	0.276819	−	0.276819i	−0.555019	−	0.831838i	$-0.687289\pi$
$743$	7.54553	−	7.54553i	0.276819	−	0.276819i	0.831838	+	0.555019i	$0.187289\pi$
$744$		0			0
$745$	−1.75616	+	3.04176i	−0.0643407	+	0.111441i
$746$	3.46481	+	12.9309i	0.126856	+	0.473433i
$747$		0			0
$748$	−0.581519	+	0.581519i	−0.0212625	+	0.0212625i
$749$	−2.80347	+	4.87084i	−0.102436	+	0.177976i
$750$		0			0
$751$	−36.8341	+	21.2662i	−1.34409	+	0.776013i	−0.987405	−	0.158210i	$-0.949428\pi$
$751$	−36.8341	+	21.2662i	−1.34409	+	0.776013i	−0.356689	+	0.934223i	$0.616094\pi$
$752$	0.561060	+	2.09390i	0.0204598	+	0.0763568i
$753$		0			0
$754$	3.35210	−	3.49514i	0.122076	−	0.127286i
$755$			41.4498i			1.50851i
$756$		0			0
$757$	44.6260			1.62196			0.810979	−	0.585075i	$-0.198935\pi$
$757$	44.6260			1.62196			0.810979	+	0.585075i	$0.198935\pi$
$758$	−2.81025	+	1.62250i	−0.102073	+	0.0589317i
$759$		0			0
$760$	−3.94973	−	14.7406i	−0.143272	−	0.534697i
$761$	45.7257	+	12.2522i	1.65756	+	0.444141i	0.961714	−	0.274054i	$-0.0883649\pi$
$761$	45.7257	+	12.2522i	1.65756	+	0.444141i	0.695842	+	0.718195i	$0.255032\pi$
$762$		0			0
$763$	−20.0080	+	20.0618i	−0.724338	+	0.726286i
$764$		−	33.6504i		−	1.21743i
$765$		0			0
$766$	15.8370	−	27.4305i	0.572214	−	0.991104i
$767$	8.76877	+	2.15434i	0.316622	+	0.0777889i
$768$		0			0
$769$	17.0724	+	17.0724i	0.615648	+	0.615648i	0.944412	−	0.328764i	$-0.106632\pi$
$769$	17.0724	+	17.0724i	0.615648	+	0.615648i	−0.328764	+	0.944412i	$0.606632\pi$
$770$	−3.33738	+	0.899052i	−0.120271	+	0.0323996i
$771$		0			0
$772$	6.87490	+	1.84212i	0.247433	+	0.0662994i
$773$	38.0617	−	10.1986i	1.36898	−	0.366818i	0.501876	−	0.864939i	$-0.332643\pi$
$773$	38.0617	−	10.1986i	1.36898	−	0.366818i	0.867107	+	0.498121i	$0.165977\pi$
$774$		0			0
$775$	17.8216	+	4.77528i	0.640170	+	0.171533i
$776$			11.2871i			0.405182i
$777$		0			0
$778$	−2.81855	−	2.81855i	−0.101050	−	0.101050i
$779$	12.1294	−	7.00294i	0.434582	−	0.250906i
$780$		0			0
$781$	0.302198	−	0.523422i	0.0108135	−	0.0187295i
$782$	−1.33624	+	4.98692i	−0.0477839	+	0.178332i
$783$		0			0
$784$	−3.09549	+	0.00831162i	−0.110553	+	0.000296844i
$785$	−30.9215	+	30.9215i	−1.10364	+	1.10364i
$786$		0			0
$787$	3.76475	+	14.0502i	0.134199	+	0.500837i	1.00000		0.000448541i	$0.000142775\pi$
$787$	3.76475	+	14.0502i	0.134199	+	0.500837i	−0.865801	+	0.500388i	$0.833191\pi$
$788$	−19.5072	+	5.22695i	−0.694917	+	0.186202i
$789$		0			0
$790$	31.8835			1.13436
$791$	−6.90953	−	11.9306i	−0.245675	−	0.424205i
$792$		0			0
$793$	0.791068	+	37.8680i	0.0280916	+	1.34473i
$794$	22.3925	+	12.9283i	0.794681	+	0.458809i
$795$		0			0
$796$	−8.28813	+	4.78515i	−0.293765	+	0.169605i
$797$	−2.90737			−0.102984			−0.0514922	−	0.998673i	$-0.516398\pi$
$797$	−2.90737			−0.102984			−0.0514922	+	0.998673i	$0.516398\pi$
$798$		0			0
$799$	−4.20568	+	4.20568i	−0.148786	+	0.148786i
$800$	−7.35029	+	27.4317i	−0.259872	+	0.969856i
$801$		0			0
$802$	3.95081	−	6.84300i	0.139508	−	0.241635i
$803$	−0.621557	−	1.07657i	−0.0219343	−	0.0379912i
$804$		0			0
$805$	30.6120	−	30.6943i	1.07893	−	1.08183i
$806$	5.35179	−	9.73355i	0.188509	−	0.342850i
$807$		0			0
$808$	40.6301	−	10.8868i	1.42936	−	0.382996i
$809$	0.931766	−	1.61387i	0.0327591	−	0.0567405i	−0.849181	−	0.528102i	$-0.822904\pi$
$809$	0.931766	−	1.61387i	0.0327591	−	0.0567405i	0.881940	+	0.471361i	$0.156237\pi$
$810$		0			0
$811$	12.4905	+	12.4905i	0.438602	+	0.438602i	0.891541	−	0.452940i	$-0.149625\pi$
$811$	12.4905	+	12.4905i	0.438602	+	0.438602i	−0.452940	+	0.891541i	$0.649625\pi$
$812$	0.00778523	+	5.79890i	0.000273208	+	0.203502i
$813$		0			0
$814$	0.297043	−	1.10858i	0.0104113	−	0.0388557i
$815$	−22.2989	−	12.8743i	−0.781096	−	0.450966i
$816$		0			0
$817$	−12.8524	−	3.44378i	−0.449647	−	0.120483i
$818$	−9.76924			−0.341574
$819$		0			0
$820$	−32.9395			−1.15030
$821$	−24.8464	−	6.65758i	−0.867147	−	0.232351i	−0.202293	−	0.979325i	$-0.564839\pi$
$821$	−24.8464	−	6.65758i	−0.867147	−	0.232351i	−0.664853	+	0.746974i	$0.731506\pi$
$822$		0			0
$823$	−14.7104	−	8.49308i	−0.512774	−	0.296050i	0.221199	−	0.975229i	$-0.429003\pi$
$823$	−14.7104	−	8.49308i	−0.512774	−	0.296050i	−0.733973	+	0.679178i	$0.762336\pi$
$824$	12.3303	−	46.0175i	0.429548	−	1.60310i
$825$		0			0
$826$	4.68324	−	2.71226i	0.162951	−	0.0943715i
$827$	10.3024	+	10.3024i	0.358251	+	0.358251i	0.863168	−	0.504917i	$-0.168477\pi$
$827$	10.3024	+	10.3024i	0.358251	+	0.358251i	−0.504917	+	0.863168i	$0.668477\pi$
$828$		0			0
$829$	−2.24299	+	3.88497i	−0.0779023	+	0.134931i	−0.902345	−	0.431015i	$-0.858156\pi$
$829$	−2.24299	+	3.88497i	−0.0779023	+	0.134931i	0.824442	+	0.565946i	$0.191489\pi$
$830$	−25.6685	+	6.87786i	−0.890967	+	0.238734i
$831$		0			0
$832$	12.1879	+	6.70127i	0.422540	+	0.232325i
$833$	−4.26631	−	7.34386i	−0.147819	−	0.254450i
$834$		0			0
$835$	4.38437	+	7.59395i	0.151727	+	0.262800i
$836$	−0.604072	+	1.04628i	−0.0208923	+	0.0361864i
$837$		0			0
$838$	−3.91841	+	14.6237i	−0.135359	+	0.505167i
$839$	3.77561	−	3.77561i	0.130348	−	0.130348i	−0.638923	−	0.769271i	$-0.720620\pi$
$839$	3.77561	−	3.77561i	0.130348	−	0.130348i	0.769271	+	0.638923i	$0.220620\pi$
$840$		0			0
$841$	−26.2959			−0.906754
$842$	−19.2953	+	11.1402i	−0.664961	+	0.383916i
$843$		0			0
$844$	3.14608	+	1.81639i	0.108293	+	0.0625228i
$845$	39.0167	−	12.2222i	1.34222	−	0.420458i
$846$		0			0
$847$	−24.6307	−	14.1765i	−0.846320	−	0.487109i
$848$	−3.81173			−0.130895
$849$		0			0
$850$	−4.68253	+	1.25468i	−0.160609	+	0.0430351i
$851$	3.72556	+	13.9040i	0.127710	+	0.476622i
$852$		0			0
$853$	−18.5441	+	18.5441i	−0.634938	+	0.634938i	−0.949302	−	0.314364i	$-0.898209\pi$
$853$	−18.5441	+	18.5441i	−0.634938	+	0.634938i	0.314364	+	0.949302i	$0.398209\pi$
$854$	16.0739	+	16.0308i	0.550038	+	0.548563i
$855$		0			0
$856$	−1.49662	+	5.58545i	−0.0511533	+	0.190907i
$857$	−23.3241	+	40.3984i	−0.796734	+	1.37998i	0.124997	+	0.992157i	$0.460108\pi$
$857$	−23.3241	+	40.3984i	−0.796734	+	1.37998i	−0.921732	+	0.387828i	$0.873226\pi$
$858$		0			0
$859$	2.09313	−	1.20847i	0.0714165	−	0.0412323i	−0.463867	−	0.885905i	$-0.653538\pi$
$859$	2.09313	−	1.20847i	0.0714165	−	0.0412323i	0.535283	+	0.844673i	$0.320205\pi$
$860$	22.1275	+	22.1275i	0.754540	+	0.754540i
$861$		0			0
$862$		−	7.48294i		−	0.254870i
$863$	53.3502	+	14.2951i	1.81606	+	0.486612i	0.996288	−	0.0860781i	$-0.0274335\pi$
$863$	53.3502	+	14.2951i	1.81606	+	0.486612i	0.819772	+	0.572690i	$0.194100\pi$
$864$		0			0
$865$	−5.47973	+	1.46829i	−0.186316	+	0.0499233i
$866$	18.6747	+	5.00386i	0.634591	+	0.170038i
$867$		0			0
$868$	3.45976	+	12.8430i	0.117432	+	0.435920i
$869$	−4.46305	−	4.46305i	−0.151399	−	0.151399i
$870$		0			0
$871$	−25.9232	−	6.36891i	−0.878374	−	0.215802i
$872$	−14.5764	+	25.2470i	−0.493619	+	0.854973i
$873$		0			0
$874$			7.58451i			0.256550i
$875$	−0.871182	−	0.232179i	−0.0294513	−	0.00784909i
$876$		0			0
$877$	24.8229	+	6.65127i	0.838208	+	0.224597i	0.652292	−	0.757968i	$-0.273808\pi$
$877$	24.8229	+	6.65127i	0.838208	+	0.224597i	0.185917	+	0.982565i	$0.440474\pi$
$878$	−2.38843	−	8.91374i	−0.0806056	−	0.300824i
$879$		0			0
$880$	0.612524	−	0.353641i	0.0206482	−	0.0119212i
$881$	−14.0101			−0.472014			−0.236007	−	0.971751i	$-0.575839\pi$
$881$	−14.0101			−0.472014			−0.236007	+	0.971751i	$0.575839\pi$
$882$		0			0
$883$		−	26.0607i		−	0.877012i	−0.898728	−	0.438506i	$-0.855508\pi$
$883$		−	26.0607i		−	0.877012i	0.898728	−	0.438506i	$-0.144492\pi$
$884$	−0.121779	−	5.82950i	−0.00409587	−	0.196067i
$885$		0			0
$886$	−8.25071	−	30.7921i	−0.277188	−	1.03448i
$887$	19.8272	−	11.4472i	0.665731	−	0.384360i	−0.128726	−	0.991680i	$-0.541089\pi$
$887$	19.8272	−	11.4472i	0.665731	−	0.384360i	0.794457	+	0.607320i	$0.207756\pi$
$888$		0			0
$889$	26.1825	−	15.1634i	0.878133	−	0.508563i
$890$	−17.7282	+	17.7282i	−0.594251	+	0.594251i
$891$		0			0
$892$	−7.47943	−	27.9136i	−0.250430	−	0.934617i
$893$	−4.36878	+	7.56695i	−0.146196	+	0.253218i
$894$		0			0
$895$	−38.0570	+	38.0570i	−1.27211	+	1.27211i
$896$	−21.6139	+	5.82254i	−0.722070	+	0.194517i
$897$		0			0
$898$	−5.09572	−	8.82605i	−0.170046	−	0.294529i
$899$	5.99108	−	1.60530i	0.199814	−	0.0535399i
$900$		0			0
$901$	−5.22914	−	9.05713i	−0.174208	−	0.301737i
$902$	−2.30792	−	2.30792i	−0.0768452	−	0.0768452i
$903$		0			0
$904$	−10.0307	−	10.0307i	−0.333617	−	0.333617i
$905$	19.1034	−	71.2949i	0.635019	−	2.36992i
$906$		0			0
$907$	19.6282	+	11.3323i	0.651742	+	0.376284i	0.789123	−	0.614235i	$-0.210535\pi$
$907$	19.6282	+	11.3323i	0.651742	+	0.376284i	−0.137381	+	0.990518i	$0.543868\pi$
$908$	−23.3017	−	6.24367i	−0.773293	−	0.207203i
$909$		0			0
$910$	11.7780	−	21.4896i	0.390438	−	0.712372i
$911$	5.46179			0.180957			0.0904786	−	0.995898i	$-0.471160\pi$
$911$	5.46179			0.180957			0.0904786	+	0.995898i	$0.471160\pi$
$912$		0			0
$913$	4.55584	+	2.63031i	0.150776	+	0.0870507i
$914$	16.1713	+	9.33653i	0.534900	+	0.308825i
$915$		0			0
$916$	−4.07407	−	4.07407i	−0.134611	−	0.134611i
$917$	−16.0979	−	9.26532i	−0.531599	−	0.305968i
$918$		0			0
$919$	10.9646	+	18.9912i	0.361688	+	0.626461i	0.988239	−	0.152919i	$-0.0488674\pi$
$919$	10.9646	+	18.9912i	0.361688	+	0.626461i	−0.626551	+	0.779380i	$0.715534\pi$
$920$	22.3017	−	38.6277i	0.735266	−	1.27352i
$921$		0			0
$922$	4.43096	+	7.67464i	0.145926	+	0.252751i
$923$	1.19529	+	4.11509i	0.0393434	+	0.135450i
$924$		0			0
$925$	−9.55714	+	9.55714i	−0.314237	+	0.314237i
$926$	−8.11878	−	14.0621i	−0.266800	−	0.462110i
$927$		0			0
$928$	2.47095	+	9.22169i	0.0811128	+	0.302717i
$929$	2.40562	−	8.97788i	0.0789257	−	0.294555i	−0.915169	−	0.403070i	$-0.867943\pi$
$929$	2.40562	−	8.97788i	0.0789257	−	0.294555i	0.994095	+	0.108515i	$0.0346097\pi$
$930$		0			0
$931$	−8.84619	−	8.79881i	−0.289922	−	0.288369i
$932$	−13.1793			−0.431702
$933$		0			0
$934$	−2.09826	−	7.83081i	−0.0686572	−	0.256232i
$935$	1.68059	+	0.970288i	0.0549611	+	0.0317318i
$936$		0			0
$937$			3.37326i			0.110200i	0.998481	+	0.0550998i	$0.0175477\pi$
$937$			3.37326i			0.110200i	−0.998481	+	0.0550998i	$0.982452\pi$
$938$	−13.8451	+	8.01827i	−0.452058	+	0.261806i
$939$		0			0
$940$	17.7962	−	10.2747i	0.580449	−	0.335122i
$941$	1.07944	−	0.289236i	0.0351888	−	0.00942881i	−0.241182	−	0.970480i	$-0.577535\pi$
$941$	1.07944	−	0.289236i	0.0351888	−	0.00942881i	0.276371	+	0.961051i	$0.410868\pi$
$942$		0			0
$943$	39.5413	+	10.5951i	1.28764	+	0.345023i
$944$	−0.783090	+	0.783090i	−0.0254874	+	0.0254874i
$945$		0			0
$946$			3.10073i			0.100813i
$947$	−3.07530	+	11.4772i	−0.0999338	+	0.372958i	−0.997721	−	0.0674710i	$-0.978507\pi$
$947$	−3.07530	+	11.4772i	−0.0999338	+	0.372958i	0.897787	+	0.440429i	$0.145174\pi$
$948$		0			0
$949$	8.55915	+	2.10284i	0.277842	+	0.0682612i
$950$	−6.16746	+	3.56078i	−0.200099	+	0.115527i
$951$		0			0
$952$	−6.18748	−	6.17089i	−0.200537	−	0.200000i
$953$			27.4279i			0.888478i	0.895908	+	0.444239i	$0.146526\pi$
$953$			27.4279i			0.888478i	−0.895908	+	0.444239i	$0.853474\pi$
$954$		0			0
$955$	−76.6983	+	20.5513i	−2.48190	+	0.665023i
$956$	−14.8158	+	3.96988i	−0.479177	+	0.128395i
$957$		0			0
$958$			17.2306i			0.556694i
$959$	11.6517	+	11.6205i	0.376254	+	0.375245i
$960$		0			0
$961$	−14.5264	+	8.38681i	−0.468593	+	0.270542i
$962$	4.21484	+	6.96042i	0.135892	+	0.224413i
$963$		0			0
$964$	5.02766	−	18.7635i	0.161930	−	0.604331i
$965$		−	16.7948i		−	0.540642i
$966$		0			0
$967$	−1.22569	+	1.22569i	−0.0394155	+	0.0394155i	−0.726540	−	0.687124i	$-0.758873\pi$
$967$	−1.22569	+	1.22569i	−0.0394155	+	0.0394155i	0.687124	+	0.726540i	$0.258873\pi$
$968$	−28.2443	−	7.56803i	−0.907806	−	0.243246i
$969$		0			0
$970$	10.2883	−	2.75674i	0.330337	−	0.0885135i
$971$	10.7056	−	6.18087i	0.343559	−	0.198354i	−0.318286	−	0.947995i	$-0.603107\pi$
$971$	10.7056	−	6.18087i	0.343559	−	0.198354i	0.661845	+	0.749641i	$0.269774\pi$
$972$		0			0
$973$	4.38822	−	2.54140i	0.140680	−	0.0814736i
$974$		−	35.8091i		−	1.14740i
$975$		0			0
$976$	−4.02309	−	2.32273i	−0.128776	−	0.0743488i
$977$	0.0433889	+	0.161930i	0.00138813	+	0.00518058i	0.966616	−	0.256228i	$-0.0824797\pi$
$977$	0.0433889	+	0.161930i	0.00138813	+	0.00518058i	−0.965228	+	0.261408i	$0.915813\pi$
$978$		0			0
$979$	4.96319			0.158624
$980$	7.67080	+	28.3234i	0.245035	+	0.904757i
$981$		0			0
$982$	7.84879	−	29.2921i	0.250465	−	0.934748i
$983$	3.00899	+	11.2297i	0.0959718	+	0.358172i	0.997165	−	0.0752459i	$-0.0239742\pi$
$983$	3.00899	+	11.2297i	0.0959718	+	0.358172i	−0.901193	+	0.433418i	$0.857307\pi$
$984$		0			0
$985$	23.8272	+	41.2700i	0.759199	+	1.31497i
$986$	−1.15234	+	1.15234i	−0.0366979	+	0.0366979i
$987$		0			0
$988$	−2.38930	−	8.22576i	−0.0760137	−	0.261696i
$989$	−19.4449	−	33.6796i	−0.618313	−	1.07095i
$990$		0			0
$991$	−4.59806	+	7.96408i	−0.146062	+	0.252987i	−0.929769	−	0.368144i	$-0.879993\pi$
$991$	−4.59806	+	7.96408i	−0.146062	+	0.252987i	0.783707	+	0.621131i	$0.213327\pi$
$992$	10.9489	+	18.9640i	0.347628	+	0.602109i
$993$		0			0
$994$	2.22598	+	1.28119i	0.0706039	+	0.0406369i
$995$	15.9684	+	15.9684i	0.506233	+	0.506233i
$996$		0			0
$997$	−25.9655	−	14.9912i	−0.822337	−	0.474776i	0.0288849	−	0.999583i	$-0.490804\pi$
$997$	−25.9655	−	14.9912i	−0.822337	−	0.474776i	−0.851222	+	0.524806i	$0.824138\pi$
$998$	−3.78846	−	2.18727i	−0.119922	−	0.0692368i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fn.e.577.3		32
3.2	odd	2		91.2.bb.a.31.6	yes	32
7.5	odd	6	inner	819.2.fn.e.460.6		32
13.8	odd	4	inner	819.2.fn.e.73.6		32
21.2	odd	6		637.2.bc.b.460.3		32
21.5	even	6		91.2.bb.a.5.3	✓	32
21.11	odd	6		637.2.i.a.538.6		32
21.17	even	6		637.2.i.a.538.5		32
21.20	even	2		637.2.bc.b.31.6		32
39.8	even	4		91.2.bb.a.73.3	yes	32
91.47	even	12	inner	819.2.fn.e.775.3		32
273.47	odd	12		91.2.bb.a.47.6	yes	32
273.86	even	12		637.2.bc.b.411.6		32
273.125	odd	4		637.2.bc.b.619.3		32
273.164	odd	12		637.2.i.a.489.5		32
273.242	even	12		637.2.i.a.489.6		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.bb.a.5.3	✓	32	21.5	even	6
91.2.bb.a.31.6	yes	32	3.2	odd	2
91.2.bb.a.47.6	yes	32	273.47	odd	12
91.2.bb.a.73.3	yes	32	39.8	even	4
637.2.i.a.489.5		32	273.164	odd	12
637.2.i.a.489.6		32	273.242	even	12
637.2.i.a.538.5		32	21.17	even	6
637.2.i.a.538.6		32	21.11	odd	6
637.2.bc.b.31.6		32	21.20	even	2
637.2.bc.b.411.6		32	273.86	even	12
637.2.bc.b.460.3		32	21.2	odd	6
637.2.bc.b.619.3		32	273.125	odd	4
819.2.fn.e.73.6		32	13.8	odd	4	inner
819.2.fn.e.460.6		32	7.5	odd	6	inner
819.2.fn.e.577.3		32	1.1	even	1	trivial
819.2.fn.e.775.3		32	91.47	even	12	inner

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.788958 - 0.211401i) q^{2} +(-1.15429 - 0.666428i) q^{4} +(-0.814012 + 3.03793i) q^{5} +(1.32595 + 2.28951i) q^{7} +(1.92491 + 1.92491i) q^{8} +O(q^{10})\)	\(q+(-0.788958 - 0.211401i) q^{2} +(-1.15429 - 0.666428i) q^{4} +(-0.814012 + 3.03793i) q^{5} +(1.32595 + 2.28951i) q^{7} +(1.92491 + 1.92491i) q^{8} +(1.28444 - 2.22472i) q^{10} +(-0.491212 + 0.131620i) q^{11} +(1.73717 - 3.15947i) q^{13} +(-0.562115 - 2.08663i) q^{14} +(0.221107 + 0.382969i) q^{16} +(-0.606654 + 1.05076i) q^{17} +(-0.461325 + 1.72169i) q^{19} +(2.96417 - 2.96417i) q^{20} +0.415370 q^{22} +(-4.51168 + 2.60482i) q^{23} +(-4.23629 - 2.44583i) q^{25} +(-2.03847 + 2.12545i) q^{26} +(-0.00473432 - 3.52640i) q^{28} -1.64443 q^{29} +(-3.64327 + 0.976210i) q^{31} +(-1.50262 - 5.60785i) q^{32} +(0.700755 - 0.700755i) q^{34} +(-8.03472 + 2.16446i) q^{35} +(0.715128 - 2.66889i) q^{37} +(0.727931 - 1.26081i) q^{38} +(-7.41466 + 4.28086i) q^{40} +(-5.55629 - 5.55629i) q^{41} +7.46499i q^{43} +(0.654714 + 0.175430i) q^{44} +(4.11018 - 1.10132i) q^{46} +(4.73504 + 1.26875i) q^{47} +(-3.48371 + 6.07155i) q^{49} +(2.82521 + 2.82521i) q^{50} +(-4.11075 + 2.48924i) q^{52} +(-4.30982 + 7.46483i) q^{53} -1.59941i q^{55} +(-1.85477 + 6.95945i) q^{56} +(1.29738 + 0.347632i) q^{58} +(0.648171 + 2.41901i) q^{59} +(-9.09759 + 5.25249i) q^{61} +3.08076 q^{62} +3.85758i q^{64} +(8.18418 + 7.84924i) q^{65} +(-1.91620 - 7.15134i) q^{67} +(1.40051 - 0.808582i) q^{68} +(6.79662 - 0.00912470i) q^{70} +(-0.840390 + 0.840390i) q^{71} +(0.632677 + 2.36118i) q^{73} +(-1.12841 + 1.95447i) q^{74} +(1.67988 - 1.67988i) q^{76} +(-0.952667 - 0.950113i) q^{77} +(6.20571 + 10.7486i) q^{79} +(-1.34342 + 0.359968i) q^{80} +(3.20908 + 5.55828i) q^{82} +(-7.31472 - 7.31472i) q^{83} +(-2.69830 - 2.69830i) q^{85} +(1.57810 - 5.88956i) q^{86} +(-1.19890 - 0.692184i) q^{88} +(-9.42713 - 2.52599i) q^{89} +(9.53704 - 0.212040i) q^{91} +6.94369 q^{92} +(-3.46753 - 2.00198i) q^{94} +(-4.85484 - 2.80295i) q^{95} +(2.93184 + 2.93184i) q^{97} +(4.03203 - 4.05374i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8}+O(q^{10}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8	\( 32 q + 2 q^{2} + 6 q^{5} - 6 q^{7} + 16 q^{8} + 10 q^{11} - 28 q^{14} + 12 q^{16} + 12 q^{19} - 8 q^{22} - 24 q^{26} - 6 q^{28} - 16 q^{29} + 24 q^{31} - 4 q^{32} - 28 q^{35} - 8 q^{37} - 132 q^{40} + 42 q^{44} + 12 q^{46} - 30 q^{47} - 88 q^{50} + 36 q^{52} + 12 q^{53} + 26 q^{58} + 54 q^{59} - 48 q^{61} + 8 q^{65} + 16 q^{67} + 48 q^{68} + 50 q^{70} + 36 q^{71} + 66 q^{73} - 12 q^{74} - 32 q^{79} - 138 q^{80} - 84 q^{85} - 42 q^{86} + 60 q^{89} - 48 q^{92} - 72 q^{94} + 86 q^{98}+O(q^{100}) \) 32 * q + 2 * q^2 + 6 * q^5 - 6 * q^7 + 16 * q^8 + 10 * q^11 - 28 * q^14 + 12 * q^16 + 12 * q^19 - 8 * q^22 - 24 * q^26 - 6 * q^28 - 16 * q^29 + 24 * q^31 - 4 * q^32 - 28 * q^35 - 8 * q^37 - 132 * q^40 + 42 * q^44 + 12 * q^46 - 30 * q^47 - 88 * q^50 + 36 * q^52 + 12 * q^53 + 26 * q^58 + 54 * q^59 - 48 * q^61 + 8 * q^65 + 16 * q^67 + 48 * q^68 + 50 * q^70 + 36 * q^71 + 66 * q^73 - 12 * q^74 - 32 * q^79 - 138 * q^80 - 84 * q^85 - 42 * q^86 + 60 * q^89 - 48 * q^92 - 72 * q^94 + 86 * q^98

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