LMFDB - Embedded newform 738.2.u.c.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [738,2,Mod(289,738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(738, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 13]))

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

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

chi := DirichletCharacter("738.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 738 = 2 \cdot 3^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	738.u (of order $20$, degree $8$, 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:	$5.89295966917$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			289.3
Character	$\chi$	$=$	738.289
Dual form			738.2.u.c.595.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.04558 + 1.43911i) q^{5} +(1.54821 + 3.03854i) q^{7} +(0.587785 - 0.809017i) q^{8} +O(q^{10})$	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.04558 + 1.43911i) q^{5} +(1.54821 + 3.03854i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.43911 + 1.04558i) q^{10} +(-2.23077 + 0.353318i) q^{11} +(1.86784 + 0.951714i) q^{13} +(2.41140 + 2.41140i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.795170 + 5.02051i) q^{17} +(-5.44683 + 2.77530i) q^{19} +(1.69178 + 0.549692i) q^{20} +(-2.01240 + 1.02537i) q^{22} +(-1.80404 - 5.55226i) q^{23} +(0.567269 - 1.74588i) q^{25} +(2.07052 + 0.327938i) q^{26} +(3.03854 + 1.54821i) q^{28} +(0.885112 - 5.58838i) q^{29} +(8.04738 + 5.84677i) q^{31} -1.00000i q^{32} +(2.30767 + 4.52906i) q^{34} +(-2.75402 + 5.40507i) q^{35} +(5.41378 - 3.93334i) q^{37} +(-4.32263 + 4.32263i) q^{38} +1.77884 q^{40} +(-5.04886 + 3.93815i) q^{41} +(2.74873 - 0.893116i) q^{43} +(-1.59705 + 1.59705i) q^{44} +(-3.43149 - 4.72304i) q^{46} +(-1.35480 + 2.65894i) q^{47} +(-2.72124 + 3.74547i) q^{49} -1.83572i q^{50} +(2.07052 - 0.327938i) q^{52} +(1.48416 - 9.37059i) q^{53} +(-2.84090 - 2.84090i) q^{55} +(3.36824 + 0.533477i) q^{56} +(-0.885112 - 5.58838i) q^{58} +(-4.11085 - 12.6519i) q^{59} +(11.4753 + 3.72857i) q^{61} +(9.46027 + 3.07383i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(0.583350 + 3.68313i) q^{65} +(0.00693821 + 0.00109890i) q^{67} +(3.59429 + 3.59429i) q^{68} +(-0.948972 + 5.99157i) q^{70} +(-1.38782 + 0.219809i) q^{71} -3.50605i q^{73} +(3.93334 - 5.41378i) q^{74} +(-2.77530 + 5.44683i) q^{76} +(-4.52727 - 6.23125i) q^{77} +(7.14957 - 7.14957i) q^{79} +(1.69178 - 0.549692i) q^{80} +(-3.58479 + 5.30559i) q^{82} +3.14886 q^{83} +(-6.39367 + 6.39367i) q^{85} +(2.33821 - 1.69881i) q^{86} +(-1.02537 + 2.01240i) q^{88} +(-0.462708 - 0.908115i) q^{89} +7.14896i q^{91} +(-4.72304 - 3.43149i) q^{92} +(-0.466831 + 2.94745i) q^{94} +(-9.68905 - 4.93682i) q^{95} +(-6.32330 - 1.00151i) q^{97} +(-1.43064 + 4.40307i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{4}+O(q^{10}) $ 24 * q + 6 * q^4	$ 24 q + 6 q^{4} + 4 q^{10} - 4 q^{11} + 2 q^{13} - 6 q^{16} - 10 q^{17} - 8 q^{19} - 10 q^{20} + 4 q^{22} + 4 q^{23} + 6 q^{25} + 8 q^{26} + 14 q^{29} + 24 q^{31} + 20 q^{34} + 56 q^{37} - 8 q^{38} + 16 q^{40} - 4 q^{41} - 20 q^{43} + 4 q^{44} + 20 q^{46} + 12 q^{47} + 40 q^{49} + 8 q^{52} - 26 q^{53} - 4 q^{55} - 14 q^{58} + 8 q^{59} + 40 q^{61} + 6 q^{64} + 12 q^{65} + 8 q^{67} + 10 q^{68} - 60 q^{70} - 48 q^{71} + 10 q^{74} + 8 q^{76} + 20 q^{77} + 28 q^{79} - 10 q^{80} - 2 q^{82} + 80 q^{83} - 30 q^{85} + 8 q^{86} + 16 q^{88} - 58 q^{89} - 4 q^{92} - 8 q^{94} + 68 q^{95} - 86 q^{97} - 2 q^{98}+O(q^{100}) $ 24 * q + 6 * q^4 + 4 * q^10 - 4 * q^11 + 2 * q^13 - 6 * q^16 - 10 * q^17 - 8 * q^19 - 10 * q^20 + 4 * q^22 + 4 * q^23 + 6 * q^25 + 8 * q^26 + 14 * q^29 + 24 * q^31 + 20 * q^34 + 56 * q^37 - 8 * q^38 + 16 * q^40 - 4 * q^41 - 20 * q^43 + 4 * q^44 + 20 * q^46 + 12 * q^47 + 40 * q^49 + 8 * q^52 - 26 * q^53 - 4 * q^55 - 14 * q^58 + 8 * q^59 + 40 * q^61 + 6 * q^64 + 12 * q^65 + 8 * q^67 + 10 * q^68 - 60 * q^70 - 48 * q^71 + 10 * q^74 + 8 * q^76 + 20 * q^77 + 28 * q^79 - 10 * q^80 - 2 * q^82 + 80 * q^83 - 30 * q^85 + 8 * q^86 + 16 * q^88 - 58 * q^89 - 4 * q^92 - 8 * q^94 + 68 * q^95 - 86 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$2$	0.951057	−	0.309017i	0.672499	−	0.218508i
$3$		0			0
$3$		0			0
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	1.04558	+	1.43911i	0.467596	+	0.643591i	0.976062	−	0.217491i	$-0.0697873\pi$
$5$	1.04558	+	1.43911i	0.467596	+	0.643591i	−0.508466	+	0.861082i	$0.669787\pi$
$6$		0			0
$7$	1.54821	+	3.03854i	0.585169	+	1.14846i	0.973872	+	0.227096i	$0.0729230\pi$
$7$	1.54821	+	3.03854i	0.585169	+	1.14846i	−0.388704	+	0.921363i	$0.627077\pi$
$8$	0.587785	−	0.809017i	0.207813	−	0.286031i
$9$		0			0
$10$	1.43911	+	1.04558i	0.455088	+	0.330640i
$11$	−2.23077	+	0.353318i	−0.672601	+	0.106530i	−0.483388	−	0.875406i	$-0.660594\pi$
$11$	−2.23077	+	0.353318i	−0.672601	+	0.106530i	−0.189213	+	0.981936i	$0.560594\pi$
$12$		0			0
$13$	1.86784	+	0.951714i	0.518047	+	0.263958i	0.693407	−	0.720546i	$-0.256109\pi$
$13$	1.86784	+	0.951714i	0.518047	+	0.263958i	−0.175360	+	0.984504i	$0.556109\pi$
$14$	2.41140	+	2.41140i	0.644473	+	0.644473i
$15$		0			0
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	0.795170	+	5.02051i	0.192857	+	1.21765i	0.874156	+	0.485646i	$0.161416\pi$
$17$	0.795170	+	5.02051i	0.192857	+	1.21765i	−0.681299	+	0.732006i	$0.738584\pi$
$18$		0			0
$19$	−5.44683	+	2.77530i	−1.24959	+	0.636697i	−0.948463	−	0.316887i	$-0.897362\pi$
$19$	−5.44683	+	2.77530i	−1.24959	+	0.636697i	−0.301126	+	0.953584i	$0.597362\pi$
$20$	1.69178	+	0.549692i	0.378293	+	0.122915i
$21$		0			0
$22$	−2.01240	+	1.02537i	−0.429046	+	0.218610i
$23$	−1.80404	−	5.55226i	−0.376168	−	1.15773i	−0.942687	−	0.333678i	$-0.891710\pi$
$23$	−1.80404	−	5.55226i	−0.376168	−	1.15773i	0.566519	−	0.824049i	$-0.308290\pi$
$24$		0			0
$25$	0.567269	−	1.74588i	0.113454	−	0.349175i
$26$	2.07052	+	0.327938i	0.406062	+	0.0643140i
$27$		0			0
$28$	3.03854	+	1.54821i	0.574229	+	0.292584i
$29$	0.885112	−	5.58838i	0.164361	−	1.03774i	−0.758238	−	0.651977i	$-0.773940\pi$
$29$	0.885112	−	5.58838i	0.164361	−	1.03774i	0.922600	−	0.385759i	$-0.126060\pi$
$30$		0			0
$31$	8.04738	+	5.84677i	1.44535	+	1.05011i	0.986890	+	0.161397i	$0.0515999\pi$
$31$	8.04738	+	5.84677i	1.44535	+	1.05011i	0.458463	+	0.888713i	$0.348400\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	2.30767	+	4.52906i	0.395763	+	0.776728i
$35$	−2.75402	+	5.40507i	−0.465515	+	0.913624i
$36$		0			0
$37$	5.41378	−	3.93334i	0.890020	−	0.646637i	−0.0458635	−	0.998948i	$-0.514604\pi$
$37$	5.41378	−	3.93334i	0.890020	−	0.646637i	0.935883	+	0.352311i	$0.114604\pi$
$38$	−4.32263	+	4.32263i	−0.701223	+	0.701223i
$39$		0			0
$40$	1.77884			0.281260
$41$	−5.04886	+	3.93815i	−0.788499	+	0.615036i
$41$	−5.04886	+	3.93815i	−0.788499	+	0.615036i
$42$		0			0
$43$	2.74873	−	0.893116i	0.419177	−	0.136199i	−0.0918313	−	0.995775i	$-0.529272\pi$
$43$	2.74873	−	0.893116i	0.419177	−	0.136199i	0.511009	+	0.859576i	$0.329272\pi$
$44$	−1.59705	+	1.59705i	−0.240765	+	0.240765i
$45$		0			0
$46$	−3.43149	−	4.72304i	−0.505945	−	0.696374i
$47$	−1.35480	+	2.65894i	−0.197617	+	0.387846i	−0.968456	−	0.249185i	$-0.919837\pi$
$47$	−1.35480	+	2.65894i	−0.197617	+	0.387846i	0.770839	+	0.637030i	$0.219837\pi$
$48$		0			0
$49$	−2.72124	+	3.74547i	−0.388749	+	0.535067i
$50$		−	1.83572i		−	0.259610i
$51$		0			0
$52$	2.07052	−	0.327938i	0.287129	−	0.0454768i
$53$	1.48416	−	9.37059i	0.203864	−	1.28715i	−0.647294	−	0.762240i	$-0.724099\pi$
$53$	1.48416	−	9.37059i	0.203864	−	1.28715i	0.851158	−	0.524909i	$-0.175901\pi$
$54$		0			0
$55$	−2.84090	−	2.84090i	−0.383067	−	0.383067i
$56$	3.36824	+	0.533477i	0.450100	+	0.0712889i
$57$		0			0
$58$	−0.885112	−	5.58838i	−0.116221	−	0.733790i
$59$	−4.11085	−	12.6519i	−0.535187	−	1.64714i	−0.743244	−	0.669020i	$-0.766714\pi$
$59$	−4.11085	−	12.6519i	−0.535187	−	1.64714i	0.208057	−	0.978117i	$-0.433286\pi$
$60$		0			0
$61$	11.4753	+	3.72857i	1.46927	+	0.477394i	0.930887	−	0.365307i	$-0.119036\pi$
$61$	11.4753	+	3.72857i	1.46927	+	0.477394i	0.538381	+	0.842702i	$0.319036\pi$
$62$	9.46027	+	3.07383i	1.20146	+	0.390376i
$63$		0			0
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	0.583350	+	3.68313i	0.0723557	+	0.456836i
$66$		0			0
$67$	0.00693821	+	0.00109890i	0.000847637	+	0.000134253i	0.156858	−	0.987621i	$-0.449863\pi$
$67$	0.00693821	+	0.00109890i	0.000847637	+	0.000134253i	−0.156011	+	0.987755i	$0.549863\pi$
$68$	3.59429	+	3.59429i	0.435871	+	0.435871i
$69$		0			0
$70$	−0.948972	+	5.99157i	−0.113424	+	0.716130i
$71$	−1.38782	+	0.219809i	−0.164704	+	0.0260865i	−0.238242	−	0.971206i	$-0.576571\pi$
$71$	−1.38782	+	0.219809i	−0.164704	+	0.0260865i	0.0735378	+	0.997292i	$0.476571\pi$
$72$		0			0
$73$		−	3.50605i		−	0.410352i	−0.978725	−	0.205176i	$-0.934223\pi$
$73$		−	3.50605i		−	0.410352i	0.978725	−	0.205176i	$-0.0657766\pi$
$74$	3.93334	−	5.41378i	0.457241	−	0.629339i
$75$		0			0
$76$	−2.77530	+	5.44683i	−0.318349	+	0.624794i
$77$	−4.52727	−	6.23125i	−0.515930	−	0.710117i
$78$		0			0
$79$	7.14957	−	7.14957i	0.804389	−	0.804389i	−0.179389	−	0.983778i	$-0.557412\pi$
$79$	7.14957	−	7.14957i	0.804389	−	0.804389i	0.983778	+	0.179389i	$0.0574120\pi$
$80$	1.69178	−	0.549692i	0.189147	−	0.0614575i
$81$		0			0
$82$	−3.58479	+	5.30559i	−0.395874	+	0.585904i
$83$	3.14886			0.345632			0.172816	−	0.984954i	$-0.444713\pi$
$83$	3.14886			0.345632			0.172816	+	0.984954i	$0.444713\pi$
$84$		0			0
$85$	−6.39367	+	6.39367i	−0.693490	+	0.693490i
$86$	2.33821	−	1.69881i	0.252136	−	0.183187i
$87$		0			0
$88$	−1.02537	+	2.01240i	−0.109305	+	0.214523i
$89$	−0.462708	−	0.908115i	−0.0490469	−	0.0962600i	0.865182	−	0.501458i	$-0.167203\pi$
$89$	−0.462708	−	0.908115i	−0.0490469	−	0.0962600i	−0.914229	+	0.405198i	$0.867203\pi$
$90$		0			0
$91$			7.14896i			0.749415i
$92$	−4.72304	−	3.43149i	−0.492411	−	0.357757i
$93$		0			0
$94$	−0.466831	+	2.94745i	−0.0481499	+	0.304007i
$95$	−9.68905	−	4.93682i	−0.994076	−	0.506507i
$96$		0			0
$97$	−6.32330	−	1.00151i	−0.642034	−	0.101688i	−0.173076	−	0.984909i	$-0.555371\pi$
$97$	−6.32330	−	1.00151i	−0.642034	−	0.101688i	−0.468958	+	0.883220i	$0.655371\pi$
$98$	−1.43064	+	4.40307i	−0.144517	+	0.444777i
$99$		0			0
$100$	−0.567269	−	1.74588i	−0.0567269	−	0.174588i
$101$	−11.0309	+	5.62053i	−1.09762	+	0.559264i	−0.906458	−	0.422296i	$-0.861224\pi$
$101$	−11.0309	+	5.62053i	−1.09762	+	0.559264i	−0.191158	+	0.981559i	$0.561224\pi$
$102$		0			0
$103$	−14.6399	−	4.75679i	−1.44251	−	0.468701i	−0.519833	−	0.854268i	$-0.674006\pi$
$103$	−14.6399	−	4.75679i	−1.44251	−	0.468701i	−0.922680	+	0.385567i	$0.874006\pi$
$104$	1.86784	−	0.951714i	0.183157	−	0.0933232i
$105$		0			0
$106$	−1.48416	−	9.37059i	−0.144154	−	0.910152i
$107$	3.26026	−	10.0341i	0.315182	−	0.970029i	−0.660498	−	0.750828i	$-0.729655\pi$
$107$	3.26026	−	10.0341i	0.315182	−	0.970029i	0.975680	−	0.219202i	$-0.0703452\pi$
$108$		0			0
$109$	1.34871	+	1.34871i	0.129183	+	0.129183i	0.768742	−	0.639559i	$-0.220883\pi$
$109$	1.34871	+	1.34871i	0.129183	+	0.129183i	−0.639559	+	0.768742i	$0.720883\pi$
$110$	−3.57975	−	1.82397i	−0.341315	−	0.173909i
$111$		0			0
$112$	3.36824	−	0.533477i	0.318269	−	0.0504089i
$113$	6.65968	+	4.83854i	0.626490	+	0.455172i	0.855183	−	0.518327i	$-0.173445\pi$
$113$	6.65968	+	4.83854i	0.626490	+	0.455172i	−0.228692	+	0.973499i	$0.573445\pi$
$114$		0			0
$115$	6.10407	−	8.40153i	0.569208	−	0.783447i
$116$	−2.56870	−	5.04135i	−0.238497	−	0.468078i
$117$		0			0
$118$	−7.81930	−	10.7623i	−0.719825	−	0.990754i
$119$	−14.0239	+	10.1890i	−1.28557	+	0.934020i
$120$		0			0
$121$	−5.61014	+	1.82285i	−0.510013	+	0.165713i
$122$	12.0659			1.09239
$123$		0			0
$124$	9.94711			0.893277
$125$	11.5645	−	3.75754i	1.03436	−	0.336085i
$126$		0			0
$127$	−9.28024	+	6.74249i	−0.823488	+	0.598299i	−0.917709	−	0.397252i	$-0.869964\pi$
$127$	−9.28024	+	6.74249i	−0.823488	+	0.598299i	0.0942216	+	0.995551i	$0.469964\pi$
$128$	−0.587785	−	0.809017i	−0.0519534	−	0.0715077i
$129$		0			0
$130$	1.69295	+	3.32260i	0.148481	+	0.291411i
$131$	−8.75738	+	12.0535i	−0.765136	+	1.05312i	0.231633	+	0.972803i	$0.425593\pi$
$131$	−8.75738	+	12.0535i	−0.765136	+	1.05312i	−0.996769	+	0.0803164i	$0.974407\pi$
$132$		0			0
$133$	−16.8657	−	12.2536i	−1.46244	−	1.06253i
$134$	0.00693821	−	0.00109890i	0.000599370	−	9.49309e-5i
$135$		0			0
$136$	4.52906	+	2.30767i	0.388364	+	0.197881i
$137$	−3.95797	−	3.95797i	−0.338152	−	0.338152i	0.517519	−	0.855672i	$-0.326856\pi$
$137$	−3.95797	−	3.95797i	−0.338152	−	0.338152i	−0.855672	+	0.517519i	$0.826856\pi$
$138$		0			0
$139$	−3.08464	+	9.49356i	−0.261636	+	0.805233i	0.730813	+	0.682577i	$0.239141\pi$
$139$	−3.08464	+	9.49356i	−0.261636	+	0.805233i	−0.992449	+	0.122655i	$0.960859\pi$
$140$	0.948972	+	5.99157i	0.0802027	+	0.506380i
$141$		0			0
$142$	−1.25197	+	0.637911i	−0.105063	+	0.0535323i
$143$	−4.50298	−	1.46311i	−0.376558	−	0.122351i
$144$		0			0
$145$	8.96776	−	4.56930i	0.744732	−	0.379460i
$146$	−1.08343	−	3.33445i	−0.0896651	−	0.275961i
$147$		0			0
$148$	2.06788	−	6.36428i	0.169979	−	0.523140i
$149$	12.7704	+	2.02263i	1.04619	+	0.165700i	0.655788	−	0.754945i	$-0.272336\pi$
$149$	12.7704	+	2.02263i	1.04619	+	0.165700i	0.390401	+	0.920645i	$0.372336\pi$
$150$		0			0
$151$	−10.0785	−	5.13526i	−0.820177	−	0.417901i	−0.00704157	−	0.999975i	$-0.502241\pi$
$151$	−10.0785	−	5.13526i	−0.820177	−	0.417901i	−0.813136	+	0.582074i	$0.802241\pi$
$152$	−0.956303	+	6.03786i	−0.0775664	+	0.489735i
$153$		0			0
$154$	−6.23125	−	4.52727i	−0.502128	−	0.364818i
$155$			17.6943i			1.42124i
$156$		0			0
$157$	−5.36145	−	10.5224i	−0.427890	−	0.839782i	−0.999810	−	0.0194724i	$-0.993801\pi$
$157$	−5.36145	−	10.5224i	−0.427890	−	0.839782i	0.571920	−	0.820309i	$-0.306199\pi$
$158$	4.59031	−	9.00898i	0.365185	−	0.716716i
$159$		0			0
$160$	1.43911	−	1.04558i	0.113772	−	0.0826601i
$161$	14.0777	−	14.0777i	1.10948	−	1.10948i
$162$		0			0
$163$	7.53267			0.590004			0.295002	−	0.955497i	$-0.404680\pi$
$163$	7.53267			0.590004			0.295002	+	0.955497i	$0.404680\pi$
$164$	−1.76983	+	6.15368i	−0.138200	+	0.480521i
$165$		0			0
$166$	2.99474	−	0.973051i	0.232437	−	0.0755234i
$167$	−13.4892	+	13.4892i	−1.04382	+	1.04382i	−0.0448276	+	0.998995i	$0.514274\pi$
$167$	−13.4892	+	13.4892i	−1.04382	+	1.04382i	−0.998995	+	0.0448276i	$0.985726\pi$
$168$		0			0
$169$	−5.05813	−	6.96192i	−0.389087	−	0.535532i
$170$	−4.10499	+	8.05649i	−0.314838	+	0.617904i
$171$		0			0
$172$	1.69881	−	2.33821i	0.129533	−	0.178287i
$173$		−	5.56661i		−	0.423221i	−0.977354	−	0.211611i	$-0.932129\pi$
$173$		−	5.56661i		−	0.423221i	0.977354	−	0.211611i	$-0.0678709\pi$
$174$		0			0
$175$	6.18316	−	0.979316i	0.467403	−	0.0740293i
$176$	−0.353318	+	2.23077i	−0.0266324	+	0.168150i
$177$		0			0
$178$	−0.720684	−	0.720684i	−0.0540176	−	0.0540176i
$179$	−12.1892	−	1.93058i	−0.911062	−	0.144298i	−0.316728	−	0.948516i	$-0.602584\pi$
$179$	−12.1892	−	1.93058i	−0.911062	−	0.144298i	−0.594334	+	0.804218i	$0.702584\pi$
$180$		0			0
$181$	−1.96265	−	12.3917i	−0.145883	−	0.921068i	−0.946690	−	0.322146i	$-0.895596\pi$
$181$	−1.96265	−	12.3917i	−0.145883	−	0.921068i	0.800807	−	0.598922i	$-0.204404\pi$
$182$	2.20915	+	6.79907i	0.163753	+	0.503980i
$183$		0			0
$184$	−5.55226	−	1.80404i	−0.409318	−	0.132996i
$185$	11.3210	+	3.67843i	0.832340	+	0.270444i
$186$		0			0
$187$	−3.54768	−	10.9186i	−0.259432	−	0.798449i
$188$	0.466831	+	2.94745i	0.0340471	+	0.214965i
$189$		0			0
$190$	−10.7404	−	1.70111i	−0.779190	−	0.123412i
$191$	5.87753	+	5.87753i	0.425283	+	0.425283i	0.887018	−	0.461735i	$-0.152773\pi$
$191$	5.87753	+	5.87753i	0.425283	+	0.425283i	−0.461735	+	0.887018i	$0.652773\pi$
$192$		0			0
$193$	−0.103897	+	0.655981i	−0.00747868	+	0.0472185i	−0.991145	−	0.132781i	$-0.957609\pi$
$193$	−0.103897	+	0.655981i	−0.00747868	+	0.0472185i	0.983667	+	0.179999i	$0.0576095\pi$
$194$	−6.32330	+	1.00151i	−0.453987	+	0.0719044i
$195$		0			0
$196$			4.62966i			0.330690i
$197$	15.0053	−	20.6530i	1.06908	−	1.47147i	0.198085	−	0.980185i	$-0.436528\pi$
$197$	15.0053	−	20.6530i	1.06908	−	1.47147i	0.871000	−	0.491283i	$-0.163472\pi$
$198$		0			0
$199$	5.46979	−	10.7351i	0.387743	−	0.760989i	−0.611806	−	0.791008i	$-0.709557\pi$
$199$	5.46979	−	10.7351i	0.387743	−	0.760989i	0.999549	+	0.0300189i	$0.00955674\pi$
$200$	−1.07901	−	1.48513i	−0.0762976	−	0.105015i
$201$		0			0
$202$	−8.75418	+	8.75418i	−0.615942	+	0.615942i
$203$	18.3508	−	5.96255i	1.28798	−	0.418489i
$204$		0			0
$205$	−10.9464	−	3.14824i	−0.764531	−	0.219883i
$206$	−15.3933			−1.07250
$207$		0			0
$208$	1.48233	−	1.48233i	0.102781	−	0.102781i
$209$	11.1700	−	8.11551i	0.772648	−	0.561361i
$210$		0			0
$211$	−5.80762	+	11.3981i	−0.399813	+	0.784677i	−0.999883	−	0.0152702i	$-0.995139\pi$
$211$	−5.80762	+	11.3981i	−0.399813	+	0.784677i	0.600071	+	0.799947i	$0.295139\pi$
$212$	−4.30719	−	8.45333i	−0.295819	−	0.580577i
$213$		0			0
$214$		−	10.5504i		−	0.721213i
$215$	4.15930	+	3.02191i	0.283662	+	0.206093i
$216$		0			0
$217$	−5.30656	+	33.5043i	−0.360233	+	2.27442i
$218$	1.69947	+	0.865922i	0.115102	+	0.0586476i
$219$		0			0
$220$	−3.96818	−	0.628498i	−0.267535	−	0.0423733i
$221$	−3.29283	+	10.1343i	−0.221500	+	0.681706i
$222$		0			0
$223$	−4.73643	−	14.5772i	−0.317175	−	0.976165i	−0.974850	−	0.222863i	$-0.928460\pi$
$223$	−4.73643	−	14.5772i	−0.317175	−	0.976165i	0.657675	−	0.753302i	$-0.271540\pi$
$224$	3.03854	−	1.54821i	0.203021	−	0.103444i
$225$		0			0
$226$	7.82893	+	2.54377i	0.520772	+	0.169209i
$227$	−6.61717	+	3.37161i	−0.439197	+	0.223782i	−0.659585	−	0.751630i	$-0.729268\pi$
$227$	−6.61717	+	3.37161i	−0.439197	+	0.223782i	0.220388	+	0.975412i	$0.429268\pi$
$228$		0			0
$229$	0.587329	+	3.70825i	0.0388118	+	0.245048i	0.999465	−	0.0327021i	$-0.0104113\pi$
$229$	0.587329	+	3.70825i	0.0388118	+	0.245048i	−0.960653	+	0.277750i	$0.910411\pi$
$230$	3.20910	−	9.87659i	0.211602	−	0.651243i
$231$		0			0
$232$	−4.00084	−	4.00084i	−0.262668	−	0.262668i
$233$	21.3938	+	10.9007i	1.40155	+	0.714126i	0.981156	−	0.193215i	$-0.0618916\pi$
$233$	21.3938	+	10.9007i	1.40155	+	0.714126i	0.420395	+	0.907341i	$0.361892\pi$
$234$		0			0
$235$	−5.24305	+	0.830418i	−0.342019	+	0.0541705i
$236$	−10.7623	−	7.81930i	−0.700569	−	0.508993i
$237$		0			0
$238$	−10.1890	+	14.0239i	−0.660452	+	0.909034i
$239$	5.48012	+	10.7553i	0.354480	+	0.695705i	0.997539	−	0.0701107i	$-0.0223352\pi$
$239$	5.48012	+	10.7553i	0.354480	+	0.695705i	−0.643060	+	0.765816i	$0.722335\pi$
$240$		0			0
$241$	1.43523	+	1.97543i	0.0924514	+	0.127248i	0.852737	−	0.522341i	$-0.174941\pi$
$241$	1.43523	+	1.97543i	0.0924514	+	0.127248i	−0.760286	+	0.649589i	$0.774941\pi$
$242$	−4.77227	+	3.46726i	−0.306773	+	0.222884i
$243$		0			0
$244$	11.4753	−	3.72857i	0.734634	−	0.238697i
$245$	−8.23543			−0.526142
$246$		0			0
$247$	−12.8151			−0.815406
$248$	9.46027	−	3.07383i	0.600728	−	0.195188i
$249$		0			0
$250$	9.83738	−	7.14727i	0.622170	−	0.452033i
$251$	−2.34142	−	3.22269i	−0.147789	−	0.203414i	0.728704	−	0.684829i	$-0.240123\pi$
$251$	−2.34142	−	3.22269i	−0.147789	−	0.203414i	−0.876493	+	0.481415i	$0.840123\pi$
$252$		0			0
$253$	5.98610	+	11.7484i	0.376343	+	0.738615i
$254$	−6.74249	+	9.28024i	−0.423061	+	0.582294i
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	8.33471	−	1.32009i	0.519905	−	0.0823449i	0.109033	−	0.994038i	$-0.465224\pi$
$257$	8.33471	−	1.32009i	0.519905	−	0.0823449i	0.410872	+	0.911693i	$0.365224\pi$
$258$		0			0
$259$	20.3333	+	10.3603i	1.26345	+	0.643759i
$260$	2.63683	+	2.63683i	0.163529	+	0.163529i
$261$		0			0
$262$	−4.60403	+	14.1697i	−0.284438	+	0.875410i
$263$	2.66391	+	16.8193i	0.164264	+	1.03712i	0.922741	+	0.385421i	$0.125944\pi$
$263$	2.66391	+	16.8193i	0.164264	+	1.03712i	−0.758477	+	0.651700i	$0.774056\pi$
$264$		0			0
$265$	15.0371	−	7.66180i	0.923724	−	0.470661i
$266$	−19.8268	−	6.44212i	−1.21566	−	0.394992i
$267$		0			0
$268$	0.00625905	−	0.00318914i	0.000382332	−	0.000194808i
$269$	5.23298	+	16.1055i	0.319060	+	0.981967i	0.974051	+	0.226330i	$0.0726727\pi$
$269$	5.23298	+	16.1055i	0.319060	+	0.981967i	−0.654990	+	0.755637i	$0.727327\pi$
$270$		0			0
$271$	5.53888	−	17.0469i	0.336463	−	1.03553i	−0.629534	−	0.776973i	$-0.716754\pi$
$271$	5.53888	−	17.0469i	0.336463	−	1.03553i	0.965997	−	0.258554i	$-0.0832459\pi$
$272$	5.02051	+	0.795170i	0.304413	+	0.0482143i
$273$		0			0
$274$	−4.98733	−	2.54117i	−0.301296	−	0.153518i
$275$	−0.648595	+	4.09506i	−0.0391117	+	0.246942i
$276$		0			0
$277$	3.48140	+	2.52939i	0.209177	+	0.151976i	0.687441	−	0.726240i	$-0.258734\pi$
$277$	3.48140	+	2.52939i	0.209177	+	0.151976i	−0.478264	+	0.878216i	$0.658734\pi$
$278$			9.98212i			0.598688i
$279$		0			0
$280$	2.75402	+	5.40507i	0.164584	+	0.323015i
$281$	12.6942	−	24.9137i	0.757270	−	1.48623i	−0.112971	−	0.993598i	$-0.536037\pi$
$281$	12.6942	−	24.9137i	0.757270	−	1.48623i	0.870240	−	0.492627i	$-0.163963\pi$
$282$		0			0
$283$	−18.1015	+	13.1515i	−1.07602	+	0.781777i	−0.976985	−	0.213307i	$-0.931577\pi$
$283$	−18.1015	+	13.1515i	−1.07602	+	0.781777i	−0.0990379	+	0.995084i	$0.531577\pi$
$284$	−0.993569	+	0.993569i	−0.0589575	+	0.0589575i
$285$		0			0
$286$	−4.73471			−0.279969
$287$	−19.7829	−	9.24405i	−1.16775	−	0.545659i
$288$		0			0
$289$	−8.40522	+	2.73102i	−0.494425	+	0.160648i
$290$	7.11686	−	7.11686i	0.417916	−	0.417916i
$291$		0			0
$292$	−2.06080	−	2.83645i	−0.120599	−	0.165991i
$293$	5.28804	−	10.3784i	0.308931	−	0.606311i	−0.683383	−	0.730060i	$-0.739492\pi$
$293$	5.28804	−	10.3784i	0.308931	−	0.606311i	0.992313	+	0.123749i	$0.0394919\pi$
$294$		0			0
$295$	13.9093	−	19.1445i	0.809831	−	1.11464i
$296$		−	6.69180i		−	0.388953i
$297$		0			0
$298$	12.7704	−	2.02263i	0.739768	−	0.117168i
$299$	1.91450	−	12.0877i	0.110718	−	0.699049i
$300$		0			0
$301$	6.96938	+	6.96938i	0.401708	+	0.401708i
$302$	−11.1721	−	1.76949i	−0.642883	−	0.101823i
$303$		0			0
$304$	0.956303	+	6.03786i	0.0548477	+	0.346295i
$305$	6.63253	+	20.4128i	0.379778	+	1.16884i
$306$		0			0
$307$	5.17127	+	1.68025i	0.295140	+	0.0958967i	0.452844	−	0.891590i	$-0.350409\pi$
$307$	5.17127	+	1.68025i	0.295140	+	0.0958967i	−0.157704	+	0.987486i	$0.550409\pi$
$308$	−7.32527	−	2.38012i	−0.417396	−	0.135620i
$309$		0			0
$310$	5.46785	+	16.8283i	0.310553	+	0.955784i
$311$	2.19891	+	13.8834i	0.124689	+	0.787254i	0.968206	+	0.250152i	$0.0804807\pi$
$311$	2.19891	+	13.8834i	0.124689	+	0.787254i	−0.843518	+	0.537101i	$0.819519\pi$
$312$		0			0
$313$	25.6343	+	4.06008i	1.44894	+	0.229489i	0.830796	−	0.556577i	$-0.187886\pi$
$313$	25.6343	+	4.06008i	1.44894	+	0.229489i	0.618142	+	0.786066i	$0.287886\pi$
$314$	−8.35065	−	8.35065i	−0.471254	−	0.471254i
$315$		0			0
$316$	1.58171	−	9.98653i	0.0889782	−	0.561786i
$317$	−26.9503	+	4.26850i	−1.51368	+	0.239743i	−0.857350	−	0.514733i	$-0.827891\pi$
$317$	−26.9503	+	4.26850i	−1.51368	+	0.239743i	−0.656327	+	0.754476i	$0.727891\pi$
$318$		0			0
$319$			12.7791i			0.715492i
$320$	1.04558	−	1.43911i	0.0584495	−	0.0804489i
$321$		0			0
$322$	9.03845	−	17.7390i	0.503693	−	0.988553i
$323$	−18.2646	−	25.1390i	−1.01627	−	1.39877i
$324$		0			0
$325$	2.72114	−	2.72114i	0.150942	−	0.150942i
$326$	7.16399	−	2.32772i	0.396777	−	0.128921i
$327$		0			0
$328$	0.218386	+	6.39940i	0.0120584	+	0.353348i
$329$	−10.1768			−0.561064
$330$		0			0
$331$	20.7213	−	20.7213i	1.13895	−	1.13895i	0.150305	−	0.988640i	$-0.451974\pi$
$331$	20.7213	−	20.7213i	1.13895	−	1.13895i	0.988640	−	0.150305i	$-0.0480257\pi$
$332$	2.54748	−	1.85085i	0.139811	−	0.101579i
$333$		0			0
$334$	−8.66057	+	16.9973i	−0.473885	+	0.930053i
$335$	0.00567298	+	0.0111339i	0.000309948	+	0.000608308i
$336$		0			0
$337$			19.3728i			1.05531i	0.849460	+	0.527653i	$0.176928\pi$
$337$			19.3728i			1.05531i	−0.849460	+	0.527653i	$0.823072\pi$
$338$	−6.96192	−	5.05813i	−0.378678	−	0.275126i
$339$		0			0
$340$	−1.41448	+	8.93069i	−0.0767110	+	0.484334i
$341$	−20.0176	−	10.1995i	−1.08401	−	0.552332i
$342$		0			0
$343$	7.98389	+	1.26452i	0.431090	+	0.0682779i
$344$	0.893116	−	2.74873i	0.0481536	−	0.148202i
$345$		0			0
$346$	−1.72018	−	5.29416i	−0.0924773	−	0.284616i
$347$	−12.4995	+	6.36881i	−0.671008	+	0.341896i	−0.756080	−	0.654479i	$-0.772888\pi$
$347$	−12.4995	+	6.36881i	−0.671008	+	0.341896i	0.0850719	+	0.996375i	$0.472888\pi$
$348$		0			0
$349$	32.2349	+	10.4738i	1.72550	+	0.560648i	0.992787	−	0.119893i	$-0.0382550\pi$
$349$	32.2349	+	10.4738i	1.72550	+	0.560648i	0.732710	+	0.680541i	$0.238255\pi$
$350$	5.57791	−	2.84209i	0.298152	−	0.151916i
$351$		0			0
$352$	0.353318	+	2.23077i	0.0188319	+	0.118900i
$353$	−5.23026	+	16.0971i	−0.278378	+	0.856761i	0.709927	+	0.704275i	$0.248728\pi$
$353$	−5.23026	+	16.0971i	−0.278378	+	0.856761i	−0.988306	+	0.152486i	$0.951272\pi$
$354$		0			0
$355$	−1.76740	−	1.76740i	−0.0938040	−	0.0938040i
$356$	−0.908115	−	0.462708i	−0.0481300	−	0.0245235i
$357$		0			0
$358$	−12.1892	+	1.93058i	−0.644218	+	0.102034i
$359$	4.10898	+	2.98535i	0.216864	+	0.157561i	0.690914	−	0.722937i	$-0.257208\pi$
$359$	4.10898	+	2.98535i	0.216864	+	0.157561i	−0.474050	+	0.880498i	$0.657208\pi$
$360$		0			0
$361$	10.7978	−	14.8619i	0.568304	−	0.782203i
$362$	−5.69584	−	11.1787i	−0.299367	−	0.587540i
$363$		0			0
$364$	4.20205	+	5.78363i	0.220247	+	0.303145i
$365$	5.04560	−	3.66584i	0.264099	−	0.191879i
$366$		0			0
$367$	−29.5961	+	9.61636i	−1.54490	+	0.501970i	−0.952724	−	0.303836i	$-0.901732\pi$
$367$	−29.5961	+	9.61636i	−1.54490	+	0.501970i	−0.592180	+	0.805806i	$0.701732\pi$
$368$	−5.83799			−0.304326
$369$		0			0
$370$	11.9036			0.618841
$371$	30.7707	−	9.99799i	1.59753	−	0.519070i
$372$		0			0
$373$	−30.8719	+	22.4297i	−1.59849	+	1.16137i	−0.708153	+	0.706059i	$0.750471\pi$
$373$	−30.8719	+	22.4297i	−1.59849	+	1.16137i	−0.890333	+	0.455310i	$0.849529\pi$
$374$	−6.74808	−	9.28793i	−0.348935	−	0.480268i
$375$		0			0
$376$	1.35480	+	2.65894i	0.0698683	+	0.137124i
$377$	6.97179	−	9.59584i	0.359065	−	0.494211i
$378$		0			0
$379$	2.00548	+	1.45707i	0.103015	+	0.0748447i	0.638100	−	0.769953i	$-0.279721\pi$
$379$	2.00548	+	1.45707i	0.103015	+	0.0748447i	−0.535085	+	0.844798i	$0.679721\pi$
$380$	−10.7404	+	1.70111i	−0.550971	+	0.0872652i
$381$		0			0
$382$	7.40612	+	3.77361i	0.378930	+	0.193074i
$383$	5.14171	+	5.14171i	0.262729	+	0.262729i	0.826162	−	0.563433i	$-0.190520\pi$
$383$	5.14171	+	5.14171i	0.262729	+	0.262729i	−0.563433	+	0.826162i	$0.690520\pi$
$384$		0			0
$385$	4.23387	−	13.0305i	0.215778	−	0.664096i
$386$	0.103897	+	0.655981i	0.00528823	+	0.0333885i
$387$		0			0
$388$	−5.70433	+	2.90650i	−0.289594	+	0.147555i
$389$	24.0883	+	7.82678i	1.22133	+	0.396833i	0.847565	−	0.530691i	$-0.178068\pi$
$389$	24.0883	+	7.82678i	1.22133	+	0.396833i	0.373762	+	0.927525i	$0.378068\pi$
$390$		0			0
$391$	26.4406	−	13.4722i	1.33716	−	0.681318i
$392$	1.43064	+	4.40307i	0.0722584	+	0.222388i
$393$		0			0
$394$	7.88876	−	24.2791i	0.397430	−	1.22316i
$395$	17.7645	+	2.81361i	0.893827	+	0.141568i
$396$		0			0
$397$	16.2797	+	8.29492i	0.817054	+	0.416310i	0.811986	−	0.583677i	$-0.198387\pi$
$397$	16.2797	+	8.29492i	0.817054	+	0.416310i	0.00506853	+	0.999987i	$0.498387\pi$
$398$	1.88476	−	11.8999i	0.0944746	−	0.596489i
$399$		0			0
$400$	−1.48513	−	1.07901i	−0.0742565	−	0.0539505i
$401$			17.2293i			0.860393i	0.902735	+	0.430196i	$0.141556\pi$
$401$			17.2293i			0.860393i	−0.902735	+	0.430196i	$0.858444\pi$
$402$		0			0
$403$	9.46680	+	18.5796i	0.471575	+	0.925518i
$404$	−5.62053	+	11.0309i	−0.279632	+	0.548808i
$405$		0			0
$406$	15.6102	−	11.3414i	0.774719	−	0.562866i
$407$	−10.6871	+	10.6871i	−0.529742	+	0.529742i
$408$		0			0
$409$	−38.5484			−1.90610			−0.953048	−	0.302819i	$-0.902072\pi$
$409$	−38.5484			−1.90610			−0.953048	+	0.302819i	$0.902072\pi$
$410$	−11.3835	+	0.388474i	−0.562192	+	0.0191854i
$411$		0			0
$412$	−14.6399	+	4.75679i	−0.721257	+	0.234350i
$413$	32.0788	−	32.0788i	1.57849	−	1.57849i
$414$		0			0
$415$	3.29237	+	4.53156i	0.161616	+	0.222446i
$416$	0.951714	−	1.86784i	0.0466616	−	0.0915785i
$417$		0			0
$418$	8.11551	−	11.1700i	0.396942	−	0.546344i
$419$		−	22.6744i		−	1.10771i	−0.832611	−	0.553857i	$-0.813155\pi$
$419$		−	22.6744i		−	1.10771i	0.832611	−	0.553857i	$-0.186845\pi$
$420$		0			0
$421$	−13.6345	+	2.15949i	−0.664505	+	0.105247i	−0.479570	−	0.877504i	$-0.659207\pi$
$421$	−13.6345	+	2.15949i	−0.664505	+	0.105247i	−0.184935	+	0.982751i	$0.559207\pi$
$422$	−2.00117	+	12.6349i	−0.0974154	+	0.615056i
$423$		0			0
$424$	−6.70860	−	6.70860i	−0.325798	−	0.325798i
$425$	9.21625	+	1.45971i	0.447054	+	0.0708064i
$426$		0			0
$427$	6.43688	+	40.6409i	0.311503	+	1.96675i
$428$	−3.26026	−	10.0341i	−0.157591	−	0.485015i
$429$		0			0
$430$	4.88955	+	1.58871i	0.235795	+	0.0766145i
$431$	−36.9160	−	11.9947i	−1.77818	−	0.577766i	−0.779372	−	0.626561i	$-0.784462\pi$
$431$	−36.9160	−	11.9947i	−1.77818	−	0.577766i	−0.998809	+	0.0487948i	$0.984462\pi$
$432$		0			0
$433$	−7.79697	−	23.9966i	−0.374698	−	1.15320i	−0.943682	−	0.330854i	$-0.892663\pi$
$433$	−7.79697	−	23.9966i	−0.374698	−	1.15320i	0.568984	−	0.822349i	$-0.307337\pi$
$434$	5.30656	+	33.5043i	0.254723	+	1.60826i
$435$		0			0
$436$	1.88387	+	0.298376i	0.0902212	+	0.0142896i
$437$	25.2355	+	25.2355i	1.20718	+	1.20718i
$438$		0			0
$439$	−5.06670	+	31.9899i	−0.241820	+	1.52679i	0.505791	+	0.862656i	$0.331201\pi$
$439$	−5.06670	+	31.9899i	−0.241820	+	1.52679i	−0.747611	+	0.664137i	$0.768799\pi$
$440$	−3.96818	+	0.628498i	−0.189175	+	0.0299625i
$441$		0			0
$442$			10.6558i			0.506846i
$443$	11.2902	−	15.5396i	0.536413	−	0.738309i	−0.451678	−	0.892181i	$-0.649174\pi$
$443$	11.2902	−	15.5396i	0.536413	−	0.738309i	0.988091	+	0.153872i	$0.0491743\pi$
$444$		0			0
$445$	0.823084	−	1.61539i	0.0390179	−	0.0765770i
$446$	−9.00923	−	12.4001i	−0.426600	−	0.587164i
$447$		0			0
$448$	2.41140	−	2.41140i	0.113928	−	0.113928i
$449$	3.16621	−	1.02876i	0.149423	−	0.0485504i	−0.233351	−	0.972393i	$-0.574969\pi$
$449$	3.16621	−	1.02876i	0.149423	−	0.0485504i	0.382773	+	0.923842i	$0.374969\pi$
$450$		0			0
$451$	9.87140	−	10.5689i	0.464826	−	0.497672i
$452$	8.23182			0.387192
$453$		0			0
$454$	−5.25141	+	5.25141i	−0.246461	+	0.246461i
$455$	−10.2882	+	7.47479i	−0.482317	+	0.350424i
$456$		0			0
$457$	3.48344	−	6.83663i	0.162948	−	0.319804i	−0.795067	−	0.606522i	$-0.792564\pi$
$457$	3.48344	−	6.83663i	0.162948	−	0.319804i	0.958015	+	0.286718i	$0.0925642\pi$
$458$	1.70450	+	3.34526i	0.0796458	+	0.156314i
$459$		0			0
$460$		−	10.3849i		−	0.484197i
$461$	19.0988	+	13.8761i	0.889521	+	0.646275i	0.935753	−	0.352656i	$-0.114721\pi$
$461$	19.0988	+	13.8761i	0.889521	+	0.646275i	−0.0462323	+	0.998931i	$0.514721\pi$
$462$		0			0
$463$	−2.93227	+	18.5136i	−0.136274	+	0.860400i	0.820939	+	0.571016i	$0.193451\pi$
$463$	−2.93227	+	18.5136i	−0.136274	+	0.860400i	−0.957213	+	0.289384i	$0.906549\pi$
$464$	−5.04135	−	2.56870i	−0.234039	−	0.119249i
$465$		0			0
$466$	23.7152	+	3.75611i	1.09858	+	0.173999i
$467$	−0.202003	+	0.621701i	−0.00934758	+	0.0287689i	−0.955622	−	0.294597i	$-0.904815\pi$
$467$	−0.202003	+	0.621701i	−0.00934758	+	0.0287689i	0.946274	+	0.323366i	$0.104815\pi$
$468$		0			0
$469$	0.00740275	+	0.0227833i	0.000341827	+	0.00105204i
$470$	−4.72983	+	2.40997i	−0.218171	+	0.111164i
$471$		0			0
$472$	−12.6519	−	4.11085i	−0.582351	−	0.189217i
$473$	−5.81622	+	2.96351i	−0.267430	+	0.136262i
$474$		0			0
$475$	1.75551	+	11.0838i	0.0805482	+	0.508561i
$476$	−5.35665	+	16.4861i	−0.245522	+	0.755638i
$477$		0			0
$478$	8.53549	+	8.53549i	0.390404	+	0.390404i
$479$	−25.9112	−	13.2024i	−1.18392	−	0.603235i	−0.252643	−	0.967560i	$-0.581300\pi$
$479$	−25.9112	−	13.2024i	−1.18392	−	0.603235i	−0.931272	+	0.364325i	$0.881300\pi$
$480$		0			0
$481$	13.8555	−	2.19450i	0.631757	−	0.100060i
$482$	1.97543	+	1.43523i	0.0899783	+	0.0653730i
$483$		0			0
$484$	−3.46726	+	4.77227i	−0.157603	+	0.216921i
$485$	−5.17021	−	10.1471i	−0.234767	−	0.460756i
$486$		0			0
$487$	−10.2172	−	14.0627i	−0.462984	−	0.637243i	0.512140	−	0.858902i	$-0.328853\pi$
$487$	−10.2172	−	14.0627i	−0.462984	−	0.637243i	−0.975124	+	0.221659i	$0.928853\pi$
$488$	9.76152	−	7.09216i	0.441883	−	0.321047i
$489$		0			0
$490$	−7.83236	+	2.54489i	−0.353830	+	0.114966i
$491$	19.1668			0.864987			0.432493	−	0.901637i	$-0.357634\pi$
$491$	19.1668			0.864987			0.432493	+	0.901637i	$0.357634\pi$
$492$		0			0
$493$	28.7603			1.29530
$494$	−12.1879	+	3.96009i	−0.548360	+	0.178173i
$495$		0			0
$496$	8.04738	−	5.84677i	0.361338	−	0.262528i
$497$	−2.81654	−	3.87663i	−0.126339	−	0.173891i
$498$		0			0
$499$	−8.26750	−	16.2259i	−0.370104	−	0.726370i	0.628575	−	0.777749i	$-0.283638\pi$
$499$	−8.26750	−	16.2259i	−0.370104	−	0.726370i	−0.998679	+	0.0513787i	$0.983638\pi$
$500$	7.14727	−	9.83738i	0.319636	−	0.439941i
$501$		0			0
$502$	−3.22269	−	2.34142i	−0.143835	−	0.104503i
$503$	24.8715	−	3.93926i	1.10897	−	0.175643i	0.425026	−	0.905181i	$-0.360265\pi$
$503$	24.8715	−	3.93926i	1.10897	−	0.175643i	0.683940	+	0.729538i	$0.260265\pi$
$504$		0			0
$505$	−19.6222	−	9.99803i	−0.873178	−	0.444907i
$506$	9.32358	+	9.32358i	0.414484	+	0.414484i
$507$		0			0
$508$	−3.54474	+	10.9096i	−0.157272	+	0.484034i
$509$	1.58521	+	10.0086i	0.0702632	+	0.443624i	0.997591	+	0.0693735i	$0.0221000\pi$
$509$	1.58521	+	10.0086i	0.0702632	+	0.443624i	−0.927328	+	0.374251i	$0.877900\pi$
$510$		0			0
$511$	10.6532	−	5.42810i	0.471272	−	0.240125i
$512$	−0.951057	−	0.309017i	−0.0420312	−	0.0136568i
$513$		0			0
$514$	7.51885	−	3.83105i	0.331642	−	0.168980i
$515$	−8.46158	−	26.0421i	−0.372862	−	1.14755i
$516$		0			0
$517$	2.08278	−	6.41014i	0.0916006	−	0.281918i
$518$	22.5396	+	3.56992i	0.990333	+	0.156853i
$519$		0			0
$520$	3.32260	+	1.69295i	0.145706	+	0.0742407i
$521$	−2.27512	+	14.3646i	−0.0996750	+	0.629323i	0.886387	+	0.462945i	$0.153207\pi$
$521$	−2.27512	+	14.3646i	−0.0996750	+	0.629323i	−0.986062	+	0.166378i	$0.946793\pi$
$522$		0			0
$523$	−8.47530	−	6.15766i	−0.370599	−	0.269256i	0.386860	−	0.922138i	$-0.373560\pi$
$523$	−8.47530	−	6.15766i	−0.370599	−	0.269256i	−0.757459	+	0.652882i	$0.773560\pi$
$524$			14.8990i			0.650864i
$525$		0			0
$526$	7.73098	+	15.1729i	0.337087	+	0.661570i
$527$	−22.9547	+	45.0511i	−0.999922	+	1.96246i
$528$		0			0
$529$	−8.96566	+	6.51393i	−0.389811	+	0.283215i
$530$	11.9335	−	11.9335i	0.518360	−	0.518360i
$531$		0			0
$532$	−20.8471			−0.903838
$533$	−13.1785	+	2.55078i	−0.570823	+	0.110487i
$534$		0			0
$535$	17.8490	−	5.79949i	0.771680	−	0.250734i
$536$	0.00496721	−	0.00496721i	0.000214551	−	0.000214551i
$537$		0			0
$538$	9.95372	+	13.7001i	0.429135	+	0.590654i
$539$	4.74711	−	9.31673i	0.204473	−	0.401300i
$540$		0			0
$541$	8.26920	−	11.3816i	0.355521	−	0.489332i	−0.593373	−	0.804927i	$-0.702204\pi$
$541$	8.26920	−	11.3816i	0.355521	−	0.489332i	0.948894	+	0.315595i	$0.102204\pi$
$542$		−	17.9242i		−	0.769910i
$543$		0			0
$544$	5.02051	−	0.795170i	0.215252	−	0.0340926i
$545$	−0.530764	+	3.35111i	−0.0227355	+	0.143546i
$546$		0			0
$547$	−15.2993	−	15.2993i	−0.654151	−	0.654151i	0.299839	−	0.953990i	$-0.403067\pi$
$547$	−15.2993	−	15.2993i	−0.654151	−	0.654151i	−0.953990	+	0.299839i	$0.903067\pi$
$548$	−5.52850	−	0.875629i	−0.236166	−	0.0374050i
$549$		0			0
$550$	0.648595	+	4.09506i	0.0276562	+	0.174614i
$551$	10.6884	+	32.8954i	0.455340	+	1.40139i
$552$		0			0
$553$	32.7933	+	10.6552i	1.39451	+	0.453104i
$554$	4.09263	+	1.32978i	0.173879	+	0.0564968i
$555$		0			0
$556$	3.08464	+	9.49356i	0.130818	+	0.402616i
$557$	0.864378	+	5.45747i	0.0366249	+	0.231240i	0.999210	−	0.0397388i	$-0.0126526\pi$
$557$	0.864378	+	5.45747i	0.0366249	+	0.231240i	−0.962585	+	0.270979i	$0.912653\pi$
$558$		0			0
$559$	5.98419	+	0.947802i	0.253104	+	0.0400878i
$560$	4.28949	+	4.28949i	0.181264	+	0.181264i
$561$		0			0
$562$	4.37411	−	27.6170i	0.184511	−	1.16495i
$563$	−10.0663	+	1.59434i	−0.424243	+	0.0671936i	−0.364906	−	0.931044i	$-0.618899\pi$
$563$	−10.0663	+	1.59434i	−0.424243	+	0.0671936i	−0.0593375	+	0.998238i	$0.518899\pi$
$564$		0			0
$565$			14.6431i			0.616040i
$566$	−13.1515	+	18.1015i	−0.552800	+	0.760863i
$567$		0			0
$568$	−0.637911	+	1.25197i	−0.0267661	+	0.0525315i
$569$	−15.0146	−	20.6659i	−0.629446	−	0.866359i	0.368551	−	0.929607i	$-0.379854\pi$
$569$	−15.0146	−	20.6659i	−0.629446	−	0.866359i	−0.997998	+	0.0632488i	$0.979854\pi$
$570$		0			0
$571$	7.69816	−	7.69816i	0.322158	−	0.322158i	−0.527436	−	0.849595i	$-0.676847\pi$
$571$	7.69816	−	7.69816i	0.322158	−	0.322158i	0.849595	+	0.527436i	$0.176847\pi$
$572$	−4.50298	+	1.46311i	−0.188279	+	0.0611755i
$573$		0			0
$574$	−21.6712	−	2.67836i	−0.904540	−	0.111792i
$575$	−10.7169			−0.446927
$576$		0			0
$577$	6.80472	−	6.80472i	0.283284	−	0.283284i	−0.551133	−	0.834417i	$-0.685804\pi$
$577$	6.80472	−	6.80472i	0.283284	−	0.283284i	0.834417	+	0.551133i	$0.185804\pi$
$578$	−7.14991	+	5.19471i	−0.297397	+	0.216072i
$579$		0			0
$580$	4.56930	−	8.96776i	0.189730	−	0.372366i
$581$	4.87510	+	9.56792i	0.202253	+	0.396944i
$582$		0			0
$583$			21.4280i			0.887456i
$584$	−2.83645	−	2.06080i	−0.117373	−	0.0852766i
$585$		0			0
$586$	1.82214	−	11.5045i	0.0752717	−	0.475247i
$587$	32.7606	+	16.6924i	1.35217	+	0.688967i	0.971787	−	0.235860i	$-0.0757906\pi$
$587$	32.7606	+	16.6924i	1.35217	+	0.688967i	0.380388	+	0.924827i	$0.375791\pi$
$588$		0			0
$589$	−60.0593	−	9.51245i	−2.47470	−	0.391954i
$590$	7.31255	−	22.5057i	0.301053	−	0.926546i
$591$		0			0
$592$	−2.06788	−	6.36428i	−0.0849893	−	0.261570i
$593$	−31.8443	+	16.2255i	−1.30769	+	0.666300i	−0.962256	−	0.272145i	$-0.912267\pi$
$593$	−31.8443	+	16.2255i	−1.30769	+	0.666300i	−0.345430	+	0.938444i	$0.612267\pi$
$594$		0			0
$595$	−29.3261	−	9.52864i	−1.20225	−	0.390636i
$596$	11.5203	−	5.86990i	0.471891	−	0.240440i
$597$		0			0
$598$	−1.91450	−	12.0877i	−0.0782898	−	0.494302i
$599$	11.7757	−	36.2418i	0.481141	−	1.48080i	−0.356352	−	0.934352i	$-0.615980\pi$
$599$	11.7757	−	36.2418i	0.481141	−	1.48080i	0.837493	−	0.546448i	$-0.184020\pi$
$600$		0			0
$601$	−1.66359	−	1.66359i	−0.0678592	−	0.0678592i	0.672363	−	0.740222i	$-0.265280\pi$
$601$	−1.66359	−	1.66359i	−0.0678592	−	0.0678592i	−0.740222	+	0.672363i	$0.765280\pi$
$602$	8.78193	+	4.47462i	0.357925	+	0.182372i
$603$		0			0
$604$	−11.1721	+	1.76949i	−0.454587	+	0.0719995i
$605$	−8.48912	−	6.16770i	−0.345132	−	0.250753i
$606$		0			0
$607$	5.03466	−	6.92961i	0.204350	−	0.281264i	−0.694525	−	0.719469i	$-0.744385\pi$
$607$	5.03466	−	6.92961i	0.204350	−	0.281264i	0.898875	+	0.438204i	$0.144385\pi$
$608$	2.77530	+	5.44683i	0.112553	+	0.220898i
$609$		0			0
$610$	12.6158	+	17.3642i	0.510800	+	0.703056i
$611$	−5.06109	+	3.67710i	−0.204750	+	0.148760i
$612$		0			0
$613$	−8.33321	+	2.70762i	−0.336575	+	0.109360i	−0.472428	−	0.881369i	$-0.656622\pi$
$613$	−8.33321	+	2.70762i	−0.336575	+	0.109360i	0.135853	+	0.990729i	$0.456622\pi$
$614$	5.43739			0.219435
$615$		0			0
$616$	−7.70225			−0.310332
$617$	4.59259	−	1.49222i	0.184891	−	0.0600746i	−0.215108	−	0.976590i	$-0.569010\pi$
$617$	4.59259	−	1.49222i	0.184891	−	0.0600746i	0.399999	+	0.916516i	$0.369010\pi$
$618$		0			0
$619$	8.31099	−	6.03829i	0.334047	−	0.242699i	−0.408099	−	0.912938i	$-0.633808\pi$
$619$	8.31099	−	6.03829i	0.334047	−	0.242699i	0.742146	+	0.670238i	$0.233808\pi$
$620$	10.4005	+	14.3150i	0.417693	+	0.574905i
$621$		0			0
$622$	6.38148	+	12.5244i	0.255874	+	0.502181i
$623$	2.04297	−	2.81191i	0.0818499	−	0.112657i
$624$		0			0
$625$	10.0735	+	7.31882i	0.402939	+	0.292753i
$626$	25.6343	−	4.06008i	1.02455	−	0.162273i
$627$		0			0
$628$	−10.5224	−	5.36145i	−0.419891	−	0.213945i
$629$	24.0522	+	24.0522i	0.959025	+	0.959025i
$630$		0			0
$631$	−5.28253	+	16.2580i	−0.210294	+	0.647220i	0.789160	+	0.614188i	$0.210516\pi$
$631$	−5.28253	+	16.2580i	−0.210294	+	0.647220i	−0.999454	+	0.0330318i	$0.989484\pi$
$632$	−1.58171	−	9.98653i	−0.0629171	−	0.397243i
$633$		0			0
$634$	−24.3122	+	12.3877i	−0.965560	+	0.491977i
$635$	−19.4064	−	6.30552i	−0.770120	−	0.250227i
$636$		0			0
$637$	−8.64747	+	4.40611i	−0.342625	+	0.174576i
$638$	3.94896	+	12.1536i	0.156341	+	0.481167i
$639$		0			0
$640$	0.549692	−	1.69178i	0.0217285	−	0.0668734i
$641$	−43.9387	−	6.95921i	−1.73547	−	0.274872i	−0.793017	−	0.609199i	$-0.791491\pi$
$641$	−43.9387	−	6.95921i	−1.73547	−	0.274872i	−0.942457	+	0.334327i	$0.891491\pi$
$642$		0			0
$643$	−12.1424	−	6.18688i	−0.478851	−	0.243987i	0.197867	−	0.980229i	$-0.436599\pi$
$643$	−12.1424	−	6.18688i	−0.478851	−	0.243987i	−0.676718	+	0.736242i	$0.736599\pi$
$644$	3.11444	−	19.6638i	0.122726	−	0.774861i
$645$		0			0
$646$	−25.1390	−	18.2646i	−0.989081	−	0.718610i
$647$			22.5423i			0.886229i	0.896465	+	0.443114i	$0.146126\pi$
$647$			22.5423i			0.886229i	−0.896465	+	0.443114i	$0.853874\pi$
$648$		0			0
$649$	13.6405	+	26.7710i	0.535436	+	1.05085i
$650$	1.74708	−	3.42884i	0.0685262	−	0.134490i
$651$		0			0
$652$	6.09406	−	4.42759i	0.238662	−	0.173398i
$653$	−25.3012	+	25.3012i	−0.990114	+	0.990114i	−0.999952	−	0.00983760i	$-0.996869\pi$
$653$	−25.3012	+	25.3012i	−0.990114	+	0.990114i	0.00983760	+	0.999952i	$0.496869\pi$
$654$		0			0
$655$	−26.5029			−1.03555
$656$	2.18522	+	6.01871i	0.0853185	+	0.234991i
$657$		0			0
$658$	−9.67870	+	3.14480i	−0.377315	+	0.122597i
$659$	6.43824	−	6.43824i	0.250798	−	0.250798i	−0.570500	−	0.821298i	$-0.693250\pi$
$659$	6.43824	−	6.43824i	0.250798	−	0.250798i	0.821298	+	0.570500i	$0.193250\pi$
$660$		0			0
$661$	−13.0749	−	17.9961i	−0.508555	−	0.699966i	0.475120	−	0.879921i	$-0.342405\pi$
$661$	−13.0749	−	17.9961i	−0.508555	−	0.699966i	−0.983675	+	0.179955i	$0.942405\pi$
$662$	13.3039	−	26.1103i	0.517070	−	1.01481i
$663$		0			0
$664$	1.85085	−	2.54748i	0.0718270	−	0.0988614i
$665$		−	37.0838i		−	1.43805i
$666$		0			0
$667$	−32.6249	+	5.16728i	−1.26324	+	0.200078i
$668$	−2.98423	+	18.8417i	−0.115463	+	0.729007i
$669$		0			0
$670$	0.00883588	+	0.00883588i	0.000341360	+	0.000341360i
$671$	−26.9162	−	4.26310i	−1.03909	−	0.164575i
$672$		0			0
$673$	−4.64345	−	29.3176i	−0.178992	−	1.13011i	−0.899583	−	0.436749i	$-0.856130\pi$
$673$	−4.64345	−	29.3176i	−0.178992	−	1.13011i	0.720592	−	0.693360i	$-0.243870\pi$
$674$	5.98653	+	18.4247i	0.230593	+	0.709691i
$675$		0			0
$676$	−8.18422	−	2.65922i	−0.314778	−	0.102278i
$677$	−27.0578	−	8.79161i	−1.03992	−	0.337889i	−0.261212	−	0.965281i	$-0.584122\pi$
$677$	−27.0578	−	8.79161i	−1.03992	−	0.337889i	−0.778703	+	0.627392i	$0.784122\pi$
$678$		0			0
$679$	−6.74668	−	20.7641i	−0.258914	−	0.796854i
$680$	1.41448	+	8.93069i	0.0542429	+	0.342476i
$681$		0			0
$682$	−22.1897	−	3.51450i	−0.849687	−	0.134577i
$683$	35.9543	+	35.9543i	1.37575	+	1.37575i	0.851660	+	0.524095i	$0.175596\pi$
$683$	35.9543	+	35.9543i	1.37575	+	1.37575i	0.524095	+	0.851660i	$0.324404\pi$
$684$		0			0
$685$	1.55761	−	9.83433i	0.0595130	−	0.375751i
$686$	7.98389	−	1.26452i	0.304826	−	0.0482798i
$687$		0			0
$688$		−	2.89019i		−	0.110187i
$689$	11.6903	−	16.0903i	0.445364	−	0.612992i
$690$		0			0
$691$	14.1551	−	27.7809i	0.538484	−	1.05683i	−0.448162	−	0.893952i	$-0.647921\pi$
$691$	14.1551	−	27.7809i	0.538484	−	1.05683i	0.986646	−	0.162881i	$-0.0520787\pi$
$692$	−3.27197	−	4.50348i	−0.124382	−	0.171197i
$693$		0			0
$694$	−9.91966	+	9.91966i	−0.376545	+	0.376545i
$695$	−16.8875	+	5.48709i	−0.640581	+	0.208137i
$696$		0			0
$697$	−23.7862	−	22.2163i	−0.900967	−	0.841503i
$698$	33.8938			1.28290
$699$		0			0
$700$	4.42665	−	4.42665i	0.167312	−	0.167312i
$701$	−3.84706	+	2.79505i	−0.145302	+	0.105568i	−0.658061	−	0.752964i	$-0.728623\pi$
$701$	−3.84706	+	2.79505i	−0.145302	+	0.105568i	0.512760	+	0.858532i	$0.328623\pi$
$702$		0			0
$703$	−18.5717	+	36.4491i	−0.700447	+	1.37470i
$704$	1.02537	+	2.01240i	0.0386451	+	0.0758453i
$705$		0			0
$706$			16.9255i			0.636998i
$707$	−34.1564	−	24.8160i	−1.28458	−	0.933303i
$708$		0			0
$709$	6.93858	−	43.8085i	0.260584	−	1.64526i	−0.416340	−	0.909209i	$-0.636687\pi$
$709$	6.93858	−	43.8085i	0.260584	−	1.64526i	0.676924	−	0.736053i	$-0.263313\pi$
$710$	−2.22706	−	1.13474i	−0.0835799	−	0.0425861i
$711$		0			0
$712$	−1.00665	−	0.159438i	−0.0377259	−	0.00597520i
$713$	17.9450	−	55.2290i	0.672045	−	2.06834i
$714$		0			0
$715$	−2.60263	−	8.01008i	−0.0973330	−	0.299560i
$716$	−10.9960	+	5.60275i	−0.410940	+	0.209385i
$717$		0			0
$718$	4.83039	+	1.56949i	0.180269	+	0.0585728i
$719$	−18.6341	+	9.49457i	−0.694936	+	0.354088i	−0.765515	−	0.643419i	$-0.777516\pi$
$719$	−18.6341	+	9.49457i	−0.694936	+	0.354088i	0.0705784	+	0.997506i	$0.477516\pi$
$720$		0			0
$721$	−8.21198	−	51.8484i	−0.305830	−	1.93094i
$722$	5.67672	−	17.4712i	0.211266	−	0.650209i
$723$		0			0
$724$	−8.87148	−	8.87148i	−0.329706	−	0.329706i
$725$	−9.25452	−	4.71541i	−0.343704	−	0.175126i
$726$		0			0
$727$	−9.19619	+	1.45653i	−0.341068	+	0.0540198i	−0.324619	−	0.945845i	$-0.605236\pi$
$727$	−9.19619	+	1.45653i	−0.341068	+	0.0540198i	−0.0164488	+	0.999865i	$0.505236\pi$
$728$	5.78363	+	4.20205i	0.214356	+	0.155739i
$729$		0			0
$730$	3.66584	−	5.04560i	0.135679	−	0.186746i
$731$	6.66960	+	13.0898i	0.246684	+	0.484145i
$732$		0			0
$733$	−3.74503	−	5.15459i	−0.138326	−	0.190389i	0.734234	−	0.678897i	$-0.237542\pi$
$733$	−3.74503	−	5.15459i	−0.138326	−	0.190389i	−0.872560	+	0.488507i	$0.837542\pi$
$734$	−25.1760	+	18.2914i	−0.929261	+	0.675148i
$735$		0			0
$736$	−5.55226	+	1.80404i	−0.204659	+	0.0664978i
$737$	−0.0158658			−0.000584423
$738$		0			0
$739$	28.7896			1.05904			0.529521	−	0.848297i	$-0.322372\pi$
$739$	28.7896			1.05904			0.529521	+	0.848297i	$0.322372\pi$
$740$	11.3210	−	3.67843i	0.416170	−	0.135222i
$741$		0			0
$742$	26.1751	−	19.0173i	0.960917	−	0.698147i
$743$	21.6382	+	29.7825i	0.793830	+	1.09261i	0.993621	+	0.112775i	$0.0359738\pi$
$743$	21.6382	+	29.7825i	0.793830	+	1.09261i	−0.199791	+	0.979839i	$0.564026\pi$
$744$		0			0
$745$	10.4416	+	20.4928i	0.382551	+	0.750799i
$746$	−22.4297	+	30.8719i	−0.821211	+	1.13030i
$747$		0			0
$748$	−9.28793	−	6.74808i	−0.339601	−	0.246734i
$749$	35.5364	−	5.62842i	1.29847	−	0.205658i
$750$		0			0
$751$	24.5643	+	12.5161i	0.896365	+	0.456721i	0.840558	−	0.541721i	$-0.182227\pi$
$751$	24.5643	+	12.5161i	0.896365	+	0.456721i	0.0558065	+	0.998442i	$0.482227\pi$
$752$	2.11014	+	2.11014i	0.0769490	+	0.0769490i
$753$		0			0
$754$	3.66529	−	11.2806i	0.133482	−	0.410815i
$755$	−3.14764	−	19.8734i	−0.114554	−	0.723268i
$756$		0			0
$757$	−16.0280	+	8.16668i	−0.582548	+	0.296823i	−0.720321	−	0.693641i	$-0.756006\pi$
$757$	−16.0280	+	8.16668i	−0.582548	+	0.296823i	0.137773	+	0.990464i	$0.456006\pi$
$758$	2.35759	+	0.766027i	0.0856315	+	0.0278234i
$759$		0			0
$760$	−9.68905	+	4.93682i	−0.351459	+	0.179077i
$761$	−13.8331	−	42.5738i	−0.501449	−	1.54330i	−0.806660	−	0.591015i	$-0.798727\pi$
$761$	−13.8331	−	42.5738i	−0.501449	−	1.54330i	0.305212	−	0.952284i	$-0.401273\pi$
$762$		0			0
$763$	−2.01001	+	6.18617i	−0.0727672	+	0.223954i
$764$	8.20975	+	1.30030i	0.297018	+	0.0470431i
$765$		0			0
$766$	6.47894	+	3.30118i	0.234093	+	0.119277i
$767$	4.36256	−	27.5441i	0.157523	−	0.994560i
$768$		0			0
$769$	−10.7023	−	7.77569i	−0.385936	−	0.280399i	0.377852	−	0.925866i	$-0.376663\pi$
$769$	−10.7023	−	7.77569i	−0.385936	−	0.280399i	−0.763788	+	0.645467i	$0.776663\pi$
$770$		−	13.7011i		−	0.493753i
$771$		0			0
$772$	0.301521	+	0.591769i	0.0108520	+	0.0212982i
$773$	10.0599	−	19.7436i	0.361829	−	0.710130i	−0.636289	−	0.771451i	$-0.719531\pi$
$773$	10.0599	−	19.7436i	0.361829	−	0.710130i	0.998118	+	0.0613212i	$0.0195314\pi$
$774$		0			0
$775$	14.7728	−	10.7330i	0.530653	−	0.385542i
$776$	−4.52698	+	4.52698i	−0.162509	+	0.162509i
$777$		0			0
$778$	25.3280			0.908052
$779$	16.5707	−	35.4625i	0.593708	−	1.27058i
$780$		0			0
$781$	3.01824	−	0.980685i	0.108001	−	0.0350917i
$782$	20.9834	−	20.9834i	0.750365	−	0.750365i
$783$		0			0
$784$	2.72124	+	3.74547i	0.0971873	+	0.133767i
$785$	9.53717	−	18.7177i	0.340396	−	0.668065i
$786$		0			0
$787$	−3.94765	+	5.43347i	−0.140718	+	0.193682i	−0.873559	−	0.486718i	$-0.838194\pi$
$787$	−3.94765	+	5.43347i	−0.140718	+	0.193682i	0.732841	+	0.680400i	$0.238194\pi$
$788$		−	25.5286i		−	0.909417i
$789$		0			0
$790$	17.7645	−	2.81361i	0.632031	−	0.100104i
$791$	−4.39149	+	27.7268i	−0.156143	+	0.985850i
$792$		0			0
$793$	17.8856	+	17.8856i	0.635137	+	0.635137i
$794$	18.0462	+	2.85823i	0.640435	+	0.101435i
$795$		0			0
$796$	−1.88476	−	11.8999i	−0.0668036	−	0.421781i
$797$	10.9411	+	33.6732i	0.387553	+	1.19276i	0.934611	+	0.355671i	$0.115747\pi$
$797$	10.9411	+	33.6732i	0.387553	+	1.19276i	−0.547059	+	0.837094i	$0.684253\pi$
$798$		0			0
$799$	−14.4265	−	4.68745i	−0.510373	−	0.165830i
$800$	−1.74588	−	0.567269i	−0.0617260	−	0.0200560i
$801$		0			0
$802$	5.32416	+	16.3861i	0.188003	+	0.578613i
$803$	1.23875	+	7.82117i	0.0437146	+	0.276003i
$804$		0			0
$805$	34.9788	+	5.54009i	1.23284	+	0.195263i
$806$	14.7449	+	14.7449i	0.519367	+	0.519367i
$807$		0			0
$808$	−1.93670	+	12.2279i	−0.0681330	+	0.430175i
$809$	−42.6095	+	6.74868i	−1.49807	+	0.237271i	−0.851003	−	0.525162i	$-0.824005\pi$
$809$	−42.6095	+	6.74868i	−1.49807	+	0.237271i	−0.647068	+	0.762433i	$0.724005\pi$
$810$		0			0
$811$		−	32.7241i		−	1.14910i	−0.818470	−	0.574549i	$-0.805177\pi$
$811$		−	32.7241i		−	1.14910i	0.818470	−	0.574549i	$-0.194823\pi$
$812$	11.3414	−	15.6102i	0.398006	−	0.547809i
$813$		0			0
$814$	−6.86157	+	13.4666i	−0.240498	+	0.472004i
$815$	7.87598	+	10.8404i	0.275884	+	0.379721i
$816$		0			0
$817$	−12.4932	+	12.4932i	−0.437082	+	0.437082i
$818$	−36.6617	+	11.9121i	−1.28185	+	0.416497i
$819$		0			0
$820$	−10.7063	+	3.88716i	−0.373881	+	0.135746i
$821$	23.3134			0.813645			0.406822	−	0.913507i	$-0.366637\pi$
$821$	23.3134			0.813645			0.406822	+	0.913507i	$0.366637\pi$
$822$		0			0
$823$	8.04389	−	8.04389i	0.280392	−	0.280392i	−0.552873	−	0.833265i	$-0.686469\pi$
$823$	8.04389	−	8.04389i	0.280392	−	0.280392i	0.833265	+	0.552873i	$0.186469\pi$
$824$	−12.4534	+	9.04796i	−0.433836	+	0.315201i
$825$		0			0
$826$	20.5958	−	40.4216i	0.716621	−	1.40645i
$827$	−17.9249	−	35.1797i	−0.623311	−	1.22332i	−0.959549	−	0.281540i	$-0.909155\pi$
$827$	−17.9249	−	35.1797i	−0.623311	−	1.22332i	0.336238	−	0.941777i	$-0.390845\pi$
$828$		0			0
$829$			33.6575i			1.16897i	0.811403	+	0.584487i	$0.198704\pi$
$829$			33.6575i			1.16897i	−0.811403	+	0.584487i	$0.801296\pi$
$830$	4.53156	+	3.29237i	0.157293	+	0.114280i
$831$		0			0
$832$	0.327938	−	2.07052i	0.0113692	−	0.0717824i
$833$	−20.9680	−	10.6837i	−0.726499	−	0.370170i
$834$		0			0
$835$	−33.5164	−	5.30847i	−1.15988	−	0.183707i
$836$	4.26657	−	13.1312i	0.147563	−	0.454151i
$837$		0			0
$838$	−7.00676	−	21.5646i	−0.242045	−	0.744937i
$839$	−26.0813	+	13.2891i	−0.900427	+	0.458790i	−0.841985	−	0.539500i	$-0.818613\pi$
$839$	−26.0813	+	13.2891i	−0.900427	+	0.458790i	−0.0584415	+	0.998291i	$0.518613\pi$
$840$		0			0
$841$	−2.86593	−	0.931196i	−0.0988251	−	0.0321102i
$842$	−12.2999	+	6.26709i	−0.423881	+	0.215978i
$843$		0			0
$844$	2.00117	+	12.6349i	0.0688831	+	0.434911i
$845$	4.73032	−	14.5584i	0.162728	−	0.500826i
$846$		0			0
$847$	−14.2245	−	14.2245i	−0.488758	−	0.488758i
$848$	−8.45333	−	4.30719i	−0.290289	−	0.147909i
$849$		0			0
$850$	9.21625	−	1.45971i	0.316115	−	0.0500677i
$851$	−31.6056	−	22.9628i	−1.08343	−	0.787155i
$852$		0			0
$853$	15.4626	−	21.2825i	0.529430	−	0.728699i	−0.457613	−	0.889151i	$-0.651295\pi$
$853$	15.4626	−	21.2825i	0.529430	−	0.728699i	0.987043	+	0.160453i	$0.0512955\pi$
$854$	18.6806	+	36.6627i	0.639235	+	1.25457i
$855$		0			0
$856$	−6.20139	−	8.53548i	−0.211959	−	0.291737i
$857$	−43.3328	+	31.4832i	−1.48022	+	1.07544i	−0.502737	+	0.864440i	$0.667674\pi$
$857$	−43.3328	+	31.4832i	−1.48022	+	1.07544i	−0.977485	+	0.211005i	$0.932326\pi$
$858$		0			0
$859$	−32.4890	+	10.5563i	−1.10851	+	0.360177i	−0.805372	−	0.592770i	$-0.798034\pi$
$859$	−32.4890	+	10.5563i	−1.10851	+	0.360177i	−0.303138	+	0.952947i	$0.598034\pi$
$860$	5.14118			0.175313
$861$		0			0
$862$	−38.8158			−1.32207
$863$	−20.6558	+	6.71148i	−0.703132	+	0.228462i	−0.638695	−	0.769460i	$-0.720525\pi$
$863$	−20.6558	+	6.71148i	−0.703132	+	0.228462i	−0.0644375	+	0.997922i	$0.520525\pi$
$864$		0			0
$865$	8.01098	−	5.82032i	0.272381	−	0.197897i
$866$	−14.8307	−	20.4127i	−0.503968	−	0.693652i
$867$		0			0
$868$	15.4002	+	30.2247i	0.522718	+	1.02589i
$869$	−13.4229	+	18.4751i	−0.455342	+	0.626724i
$870$		0			0
$871$	0.0119136	+	0.00865577i	0.000403678	+	0.000293290i
$872$	1.88387	−	0.298376i	0.0637960	−	0.0101043i
$873$		0			0
$874$	31.7986	+	16.2022i	1.07560	+	0.548047i
$875$	29.3218	+	29.3218i	0.991257	+	0.991257i
$876$		0			0
$877$	−16.9023	+	52.0199i	−0.570750	+	1.75659i	0.0794659	+	0.996838i	$0.474679\pi$
$877$	−16.9023	+	52.0199i	−0.570750	+	1.75659i	−0.650216	+	0.759750i	$0.725321\pi$
$878$	5.06670	+	31.9899i	0.170993	+	1.07961i
$879$		0			0
$880$	−3.57975	+	1.82397i	−0.120673	+	0.0614861i
$881$	−35.4552	−	11.5201i	−1.19452	−	0.388122i	−0.356775	−	0.934190i	$-0.616124\pi$
$881$	−35.4552	−	11.5201i	−1.19452	−	0.388122i	−0.837740	+	0.546069i	$0.816124\pi$
$882$		0			0
$883$	−35.7781	+	18.2299i	−1.20403	+	0.613483i	−0.936704	−	0.350123i	$-0.886140\pi$
$883$	−35.7781	+	18.2299i	−1.20403	+	0.613483i	−0.267325	+	0.963606i	$0.586140\pi$
$884$	3.29283	+	10.1343i	0.110750	+	0.340853i
$885$		0			0
$886$	5.93560	−	18.2679i	0.199411	−	0.613722i
$887$	−22.8530	−	3.61956i	−0.767328	−	0.121533i	−0.239514	−	0.970893i	$-0.576988\pi$
$887$	−22.8530	−	3.61956i	−0.767328	−	0.121533i	−0.527814	+	0.849360i	$0.676988\pi$
$888$		0			0
$889$	−34.8551	−	17.7595i	−1.16900	−	0.595636i
$890$	0.283615	−	1.79068i	0.00950681	−	0.0600236i
$891$		0			0
$892$	−12.4001	−	9.00923i	−0.415188	−	0.301651i
$893$		−	18.2427i		−	0.610470i
$894$		0			0
$895$	−9.96641	−	19.5602i	−0.333140	−	0.653824i
$896$	1.54821	−	3.03854i	0.0517221	−	0.101510i
$897$		0			0
$898$	2.69334	−	1.95683i	0.0898780	−	0.0653002i
$899$	39.7968	−	39.7968i	1.32730	−	1.32730i
$900$		0			0
$901$	48.2253			1.60662
$902$	6.12227	−	13.1021i	0.203849	−	0.436252i
$903$		0			0
$904$	7.82893	−	2.54377i	0.260386	−	0.0846046i
$905$	15.7810	−	15.7810i	0.524577	−	0.524577i
$906$		0			0
$907$	14.2547	+	19.6199i	0.473320	+	0.651469i	0.977204	−	0.212303i	$-0.0680962\pi$
$907$	14.2547	+	19.6199i	0.473320	+	0.651469i	−0.503884	+	0.863771i	$0.668096\pi$
$908$	−3.37161	+	6.61717i	−0.111891	+	0.219598i
$909$		0			0
$910$	−7.47479	+	10.2882i	−0.247787	+	0.341049i
$911$			11.7055i			0.387822i	0.981019	+	0.193911i	$0.0621173\pi$
$911$			11.7055i			0.387822i	−0.981019	+	0.193911i	$0.937883\pi$
$912$		0			0
$913$	−7.02436	+	1.11255i	−0.232473	+	0.0368200i
$914$	1.20031	−	7.57847i	0.0397028	−	0.250673i
$915$		0			0
$916$	2.65481	+	2.65481i	0.0877175	+	0.0877175i
$917$	−50.1833	−	7.94825i	−1.65720	−	0.262474i
$918$		0			0
$919$	1.95978	+	12.3736i	0.0646472	+	0.408166i	0.998697	+	0.0510246i	$0.0162487\pi$
$919$	1.95978	+	12.3736i	0.0646472	+	0.408166i	−0.934050	+	0.357142i	$0.883751\pi$
$920$	−3.20910	−	9.87659i	−0.105801	−	0.325622i
$921$		0			0
$922$	22.4520	+	7.29510i	0.739418	+	0.240251i
$923$	−2.80142	−	0.910238i	−0.0922100	−	0.0299608i
$924$		0			0
$925$	−3.79605	−	11.6830i	−0.124813	−	0.384136i
$926$	2.93227	+	18.5136i	0.0963603	+	0.608395i
$927$		0			0
$928$	−5.58838	−	0.885112i	−0.183448	−	0.0290552i
$929$	31.9483	+	31.9483i	1.04819	+	1.04819i	0.998779	+	0.0494113i	$0.0157345\pi$
$929$	31.9483	+	31.9483i	1.04819	+	1.04819i	0.0494113	+	0.998779i	$0.484265\pi$
$930$		0			0
$931$	4.42735	−	27.9532i	0.145101	−	0.916130i
$932$	23.7152	−	3.75611i	0.776816	−	0.123036i
$933$		0			0
$934$			0.653695i			0.0213896i
$935$	12.0038	−	16.5218i	0.392565	−	0.540319i
$936$		0			0
$937$	−19.3593	+	37.9948i	−0.632441	+	1.24124i	0.323096	+	0.946366i	$0.395276\pi$
$937$	−19.3593	+	37.9948i	−0.632441	+	1.24124i	−0.955537	+	0.294870i	$0.904724\pi$
$938$	0.0140809	+	0.0193807i	0.000459757	+	0.000632801i
$939$		0			0
$940$	−3.75361	+	3.75361i	−0.122429	+	0.122429i
$941$	−45.0498	+	14.6376i	−1.46858	+	0.477171i	−0.930679	−	0.365836i	$-0.880783\pi$
$941$	−45.0498	+	14.6376i	−1.46858	+	0.477171i	−0.537902	+	0.843007i	$0.680783\pi$
$942$		0			0
$943$	30.9740	+	20.9280i	1.00865	+	0.681510i
$944$	−13.3030			−0.432976
$945$		0			0
$946$	−4.61577	+	4.61577i	−0.150072	+	0.150072i
$947$	27.4149	−	19.9181i	0.890864	−	0.647250i	−0.0452393	−	0.998976i	$-0.514405\pi$
$947$	27.4149	−	19.9181i	0.890864	−	0.647250i	0.936103	+	0.351726i	$0.114405\pi$
$948$		0			0
$949$	3.33675	−	6.54874i	0.108316	−	0.212581i
$950$	5.09468	+	9.99887i	0.165293	+	0.324406i
$951$		0			0
$952$			17.3345i			0.561814i
$953$	−5.51549	−	4.00724i	−0.178664	−	0.129807i	0.494859	−	0.868973i	$-0.335220\pi$
$953$	−5.51549	−	4.00724i	−0.178664	−	0.129807i	−0.673523	+	0.739166i	$0.735220\pi$
$954$		0			0
$955$	−2.31302	+	14.6038i	−0.0748476	+	0.472569i
$956$	10.7553	+	5.48012i	0.347853	+	0.177240i
$957$		0			0
$958$	−28.7228	−	4.54925i	−0.927993	−	0.146980i
$959$	5.89866	−	18.1542i	0.190478	−	0.586230i
$960$		0			0
$961$	20.9962	+	64.6196i	0.677296	+	2.08450i
$962$	12.4992	−	6.36868i	0.402991	−	0.205334i
$963$		0			0
$964$	2.32225	+	0.754546i	0.0747948	+	0.0243023i
$965$	−1.05266	+	0.536359i	−0.0338864	+	0.0172660i
$966$		0			0
$967$	6.66846	+	42.1030i	0.214443	+	1.35394i	0.826415	+	0.563062i	$0.190377\pi$
$967$	6.66846	+	42.1030i	0.214443	+	1.35394i	−0.611972	+	0.790880i	$0.709623\pi$
$968$	−1.82285	+	5.61014i	−0.0585885	+	0.180317i
$969$		0			0
$970$	−8.05279	−	8.05279i	−0.258559	−	0.258559i
$971$	−10.4282	−	5.31345i	−0.334658	−	0.170517i	0.278584	−	0.960412i	$-0.410135\pi$
$971$	−10.4282	−	5.31345i	−0.334658	−	0.170517i	−0.613242	+	0.789895i	$0.710135\pi$
$972$		0			0
$973$	−33.6222	+	5.32523i	−1.07788	+	0.170719i
$974$	−14.0627	−	10.2172i	−0.450599	−	0.327379i
$975$		0			0
$976$	7.09216	−	9.76152i	0.227014	−	0.312458i
$977$	25.0815	+	49.2252i	0.802427	+	1.57485i	0.818170	+	0.574976i	$0.194989\pi$
$977$	25.0815	+	49.2252i	0.802427	+	1.57485i	−0.0157428	+	0.999876i	$0.505011\pi$
$978$		0			0
$979$	1.35305	+	1.86231i	0.0432436	+	0.0595197i
$980$	−6.66260	+	4.84066i	−0.212829	+	0.154629i
$981$		0			0
$982$	18.2287	−	5.92288i	0.581702	−	0.189007i
$983$	36.6332			1.16842			0.584209	−	0.811603i	$-0.301405\pi$
$983$	36.6332			1.16842			0.584209	+	0.811603i	$0.301405\pi$
$984$		0			0
$985$	45.4113			1.44692
$986$	27.3527	−	8.88742i	0.871087	−	0.283033i
$987$		0			0
$988$	−10.3676	+	7.53254i	−0.329839	+	0.239642i
$989$	−9.91763	−	13.6504i	−0.315362	−	0.434059i
$990$		0			0
$991$	1.79439	+	3.52169i	0.0570008	+	0.111870i	0.917749	−	0.397160i	$-0.130004\pi$
$991$	1.79439	+	3.52169i	0.0570008	+	0.111870i	−0.860749	+	0.509030i	$0.830004\pi$
$992$	5.84677	−	8.04738i	0.185635	−	0.255505i
$993$		0			0
$994$	−3.87663	−	2.81654i	−0.122959	−	0.0893351i
$995$	21.1681	−	3.35269i	0.671073	−	0.106287i
$996$		0			0
$997$	−37.4675	−	19.0907i	−1.18661	−	0.604608i	−0.254601	−	0.967046i	$-0.581944\pi$
$997$	−37.4675	−	19.0907i	−1.18661	−	0.604608i	−0.932008	+	0.362439i	$0.881944\pi$
$998$	−12.8769	−	12.8769i	−0.407612	−	0.407612i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.u.c.289.3	✓	24
3.2	odd	2		738.2.u.d.289.1	yes	24
41.21	even	20	inner	738.2.u.c.595.3	yes	24
123.62	odd	20		738.2.u.d.595.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.u.c.289.3	✓	24	1.1	even	1	trivial
738.2.u.c.595.3	yes	24	41.21	even	20	inner
738.2.u.d.289.1	yes	24	3.2	odd	2
738.2.u.d.595.1	yes	24	123.62	odd	20

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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	738.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.04558 + 1.43911i) q^{5} +(1.54821 + 3.03854i) q^{7} +(0.587785 - 0.809017i) q^{8} +O(q^{10})\)	\(q+(0.951057 - 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(1.04558 + 1.43911i) q^{5} +(1.54821 + 3.03854i) q^{7} +(0.587785 - 0.809017i) q^{8} +(1.43911 + 1.04558i) q^{10} +(-2.23077 + 0.353318i) q^{11} +(1.86784 + 0.951714i) q^{13} +(2.41140 + 2.41140i) q^{14} +(0.309017 - 0.951057i) q^{16} +(0.795170 + 5.02051i) q^{17} +(-5.44683 + 2.77530i) q^{19} +(1.69178 + 0.549692i) q^{20} +(-2.01240 + 1.02537i) q^{22} +(-1.80404 - 5.55226i) q^{23} +(0.567269 - 1.74588i) q^{25} +(2.07052 + 0.327938i) q^{26} +(3.03854 + 1.54821i) q^{28} +(0.885112 - 5.58838i) q^{29} +(8.04738 + 5.84677i) q^{31} -1.00000i q^{32} +(2.30767 + 4.52906i) q^{34} +(-2.75402 + 5.40507i) q^{35} +(5.41378 - 3.93334i) q^{37} +(-4.32263 + 4.32263i) q^{38} +1.77884 q^{40} +(-5.04886 + 3.93815i) q^{41} +(2.74873 - 0.893116i) q^{43} +(-1.59705 + 1.59705i) q^{44} +(-3.43149 - 4.72304i) q^{46} +(-1.35480 + 2.65894i) q^{47} +(-2.72124 + 3.74547i) q^{49} -1.83572i q^{50} +(2.07052 - 0.327938i) q^{52} +(1.48416 - 9.37059i) q^{53} +(-2.84090 - 2.84090i) q^{55} +(3.36824 + 0.533477i) q^{56} +(-0.885112 - 5.58838i) q^{58} +(-4.11085 - 12.6519i) q^{59} +(11.4753 + 3.72857i) q^{61} +(9.46027 + 3.07383i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(0.583350 + 3.68313i) q^{65} +(0.00693821 + 0.00109890i) q^{67} +(3.59429 + 3.59429i) q^{68} +(-0.948972 + 5.99157i) q^{70} +(-1.38782 + 0.219809i) q^{71} -3.50605i q^{73} +(3.93334 - 5.41378i) q^{74} +(-2.77530 + 5.44683i) q^{76} +(-4.52727 - 6.23125i) q^{77} +(7.14957 - 7.14957i) q^{79} +(1.69178 - 0.549692i) q^{80} +(-3.58479 + 5.30559i) q^{82} +3.14886 q^{83} +(-6.39367 + 6.39367i) q^{85} +(2.33821 - 1.69881i) q^{86} +(-1.02537 + 2.01240i) q^{88} +(-0.462708 - 0.908115i) q^{89} +7.14896i q^{91} +(-4.72304 - 3.43149i) q^{92} +(-0.466831 + 2.94745i) q^{94} +(-9.68905 - 4.93682i) q^{95} +(-6.32330 - 1.00151i) q^{97} +(-1.43064 + 4.40307i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4}+O(q^{10}) \) 24 * q + 6 * q^4	\( 24 q + 6 q^{4} + 4 q^{10} - 4 q^{11} + 2 q^{13} - 6 q^{16} - 10 q^{17} - 8 q^{19} - 10 q^{20} + 4 q^{22} + 4 q^{23} + 6 q^{25} + 8 q^{26} + 14 q^{29} + 24 q^{31} + 20 q^{34} + 56 q^{37} - 8 q^{38} + 16 q^{40} - 4 q^{41} - 20 q^{43} + 4 q^{44} + 20 q^{46} + 12 q^{47} + 40 q^{49} + 8 q^{52} - 26 q^{53} - 4 q^{55} - 14 q^{58} + 8 q^{59} + 40 q^{61} + 6 q^{64} + 12 q^{65} + 8 q^{67} + 10 q^{68} - 60 q^{70} - 48 q^{71} + 10 q^{74} + 8 q^{76} + 20 q^{77} + 28 q^{79} - 10 q^{80} - 2 q^{82} + 80 q^{83} - 30 q^{85} + 8 q^{86} + 16 q^{88} - 58 q^{89} - 4 q^{92} - 8 q^{94} + 68 q^{95} - 86 q^{97} - 2 q^{98}+O(q^{100}) \) 24 * q + 6 * q^4 + 4 * q^10 - 4 * q^11 + 2 * q^13 - 6 * q^16 - 10 * q^17 - 8 * q^19 - 10 * q^20 + 4 * q^22 + 4 * q^23 + 6 * q^25 + 8 * q^26 + 14 * q^29 + 24 * q^31 + 20 * q^34 + 56 * q^37 - 8 * q^38 + 16 * q^40 - 4 * q^41 - 20 * q^43 + 4 * q^44 + 20 * q^46 + 12 * q^47 + 40 * q^49 + 8 * q^52 - 26 * q^53 - 4 * q^55 - 14 * q^58 + 8 * q^59 + 40 * q^61 + 6 * q^64 + 12 * q^65 + 8 * q^67 + 10 * q^68 - 60 * q^70 - 48 * q^71 + 10 * q^74 + 8 * q^76 + 20 * q^77 + 28 * q^79 - 10 * q^80 - 2 * q^82 + 80 * q^83 - 30 * q^85 + 8 * q^86 + 16 * q^88 - 58 * q^89 - 4 * q^92 - 8 * q^94 + 68 * q^95 - 86 * q^97 - 2 * q^98

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