LMFDB - Embedded newform 738.2.u.d.289.1

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			289.1
Character	$\chi$	$=$	738.289
Dual form			738.2.u.d.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-1.04558 - 1.43911i) q^{5} +(1.54821 + 3.03854i) q^{7} +(-0.587785 + 0.809017i) q^{8} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.809017 - 0.587785i) q^{4} +(-1.04558 - 1.43911i) q^{5} +(1.54821 + 3.03854i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(1.43911 + 1.04558i) q^{10} +(2.23077 - 0.353318i) q^{11} +(1.86784 + 0.951714i) q^{13} +(-2.41140 - 2.41140i) q^{14} +(0.309017 - 0.951057i) q^{16} +(-0.795170 - 5.02051i) q^{17} +(-5.44683 + 2.77530i) q^{19} +(-1.69178 - 0.549692i) q^{20} +(-2.01240 + 1.02537i) q^{22} +(1.80404 + 5.55226i) q^{23} +(0.567269 - 1.74588i) q^{25} +(-2.07052 - 0.327938i) q^{26} +(3.03854 + 1.54821i) q^{28} +(-0.885112 + 5.58838i) q^{29} +(8.04738 + 5.84677i) q^{31} +1.00000i q^{32} +(2.30767 + 4.52906i) q^{34} +(2.75402 - 5.40507i) q^{35} +(5.41378 - 3.93334i) q^{37} +(4.32263 - 4.32263i) q^{38} +1.77884 q^{40} +(5.04886 - 3.93815i) q^{41} +(2.74873 - 0.893116i) q^{43} +(1.59705 - 1.59705i) q^{44} +(-3.43149 - 4.72304i) q^{46} +(1.35480 - 2.65894i) q^{47} +(-2.72124 + 3.74547i) q^{49} +1.83572i q^{50} +(2.07052 - 0.327938i) q^{52} +(-1.48416 + 9.37059i) q^{53} +(-2.84090 - 2.84090i) q^{55} +(-3.36824 - 0.533477i) q^{56} +(-0.885112 - 5.58838i) q^{58} +(4.11085 + 12.6519i) q^{59} +(11.4753 + 3.72857i) q^{61} +(-9.46027 - 3.07383i) q^{62} +(-0.309017 - 0.951057i) q^{64} +(-0.583350 - 3.68313i) q^{65} +(0.00693821 + 0.00109890i) q^{67} +(-3.59429 - 3.59429i) q^{68} +(-0.948972 + 5.99157i) q^{70} +(1.38782 - 0.219809i) q^{71} -3.50605i q^{73} +(-3.93334 + 5.41378i) q^{74} +(-2.77530 + 5.44683i) q^{76} +(4.52727 + 6.23125i) q^{77} +(7.14957 - 7.14957i) q^{79} +(-1.69178 + 0.549692i) q^{80} +(-3.58479 + 5.30559i) q^{82} -3.14886 q^{83} +(-6.39367 + 6.39367i) q^{85} +(-2.33821 + 1.69881i) q^{86} +(-1.02537 + 2.01240i) q^{88} +(0.462708 + 0.908115i) q^{89} +7.14896i q^{91} +(4.72304 + 3.43149i) q^{92} +(-0.466831 + 2.94745i) q^{94} +(9.68905 + 4.93682i) q^{95} +(-6.32330 - 1.00151i) q^{97} +(1.43064 - 4.40307i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	0.508466	−	0.861082i	$-0.330213\pi$
$5$	−1.04558	−	1.43911i	−0.467596	−	0.643591i	−0.976062	+	0.217491i	$0.930213\pi$
$6$		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	0.189213	−	0.981936i	$-0.439406\pi$
$11$	2.23077	−	0.353318i	0.672601	−	0.106530i	0.483388	+	0.875406i	$0.339406\pi$
$12$		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	$-0.838584\pi$
$17$	−0.795170	−	5.02051i	−0.192857	−	1.21765i	0.681299	−	0.732006i	$-0.261416\pi$
$18$		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	$0.108290\pi$
$23$	1.80404	+	5.55226i	0.376168	+	1.15773i	−0.566519	+	0.824049i	$0.691710\pi$
$24$		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	$0.226060\pi$
$29$	−0.885112	+	5.58838i	−0.164361	+	1.03774i	−0.922600	+	0.385759i	$0.873940\pi$
$30$		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	−0.770839	−	0.637030i	$-0.780163\pi$
$47$	1.35480	−	2.65894i	0.197617	−	0.387846i	0.968456	+	0.249185i	$0.0801626\pi$
$48$		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	$0.275901\pi$
$53$	−1.48416	+	9.37059i	−0.203864	+	1.28715i	−0.851158	+	0.524909i	$0.824099\pi$
$54$		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	$0.233286\pi$
$59$	4.11085	+	12.6519i	0.535187	+	1.64714i	−0.208057	+	0.978117i	$0.566714\pi$
$60$		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	−0.0735378	−	0.997292i	$-0.523429\pi$
$71$	1.38782	−	0.219809i	0.164704	−	0.0260865i	0.238242	+	0.971206i	$0.423429\pi$
$72$		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	$-0.555287\pi$
$83$	−3.14886			−0.345632			−0.172816	+	0.984954i	$0.555287\pi$
$84$		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	0.914229	−	0.405198i	$-0.132797\pi$
$89$	0.462708	+	0.908115i	0.0490469	+	0.0962600i	−0.865182	+	0.501458i	$0.832797\pi$
$90$		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	0.191158	−	0.981559i	$-0.438776\pi$
$101$	11.0309	−	5.62053i	1.09762	−	0.559264i	0.906458	+	0.422296i	$0.138776\pi$
$102$		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	$0.270345\pi$
$107$	−3.26026	+	10.0341i	−0.315182	+	0.970029i	−0.975680	+	0.219202i	$0.929655\pi$
$108$		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	0.228692	−	0.973499i	$-0.426555\pi$
$113$	−6.65968	−	4.83854i	−0.626490	−	0.455172i	−0.855183	+	0.518327i	$0.826555\pi$
$114$		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	$-0.574407\pi$
$131$	8.75738	−	12.0535i	0.765136	−	1.05312i	0.996769	−	0.0803164i	$-0.0255931\pi$
$132$		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	0.855672	−	0.517519i	$-0.173144\pi$
$137$	3.95797	+	3.95797i	0.338152	+	0.338152i	−0.517519	+	0.855672i	$0.673144\pi$
$138$		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	−0.390401	−	0.920645i	$-0.627664\pi$
$149$	−12.7704	−	2.02263i	−1.04619	−	0.165700i	−0.655788	+	0.754945i	$0.727664\pi$
$150$		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	$-0.485726\pi$
$167$	13.4892	−	13.4892i	1.04382	−	1.04382i	0.998995	−	0.0448276i	$-0.0142739\pi$
$168$		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	$0.0678709\pi$
$173$			5.56661i			0.423221i	−0.977354	+	0.211611i	$0.932129\pi$
$174$		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	0.594334	−	0.804218i	$-0.297416\pi$
$179$	12.1892	+	1.93058i	0.911062	+	0.144298i	0.316728	+	0.948516i	$0.397416\pi$
$180$		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	0.461735	−	0.887018i	$-0.347227\pi$
$191$	−5.87753	−	5.87753i	−0.425283	−	0.425283i	−0.887018	+	0.461735i	$0.847227\pi$
$192$		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	$0.563472\pi$
$197$	−15.0053	+	20.6530i	−1.06908	+	1.47147i	−0.871000	+	0.491283i	$0.836528\pi$
$198$		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	−0.220388	−	0.975412i	$-0.570732\pi$
$227$	6.61717	−	3.37161i	0.439197	−	0.223782i	0.659585	+	0.751630i	$0.270732\pi$
$228$		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	−0.420395	−	0.907341i	$-0.638108\pi$
$233$	−21.3938	−	10.9007i	−1.40155	−	0.714126i	−0.981156	+	0.193215i	$0.938108\pi$
$234$		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	0.643060	−	0.765816i	$-0.277665\pi$
$239$	−5.48012	−	10.7553i	−0.354480	−	0.695705i	−0.997539	+	0.0701107i	$0.977665\pi$
$240$		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	0.876493	−	0.481415i	$-0.159877\pi$
$251$	2.34142	+	3.22269i	0.147789	+	0.203414i	−0.728704	+	0.684829i	$0.759877\pi$
$252$		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	−0.410872	−	0.911693i	$-0.634776\pi$
$257$	−8.33471	+	1.32009i	−0.519905	+	0.0823449i	−0.109033	+	0.994038i	$0.534776\pi$
$258$		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	$-0.874056\pi$
$263$	−2.66391	−	16.8193i	−0.164264	−	1.03712i	0.758477	−	0.651700i	$-0.225944\pi$
$264$		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	$-0.927327\pi$
$269$	−5.23298	−	16.1055i	−0.319060	−	0.981967i	0.654990	−	0.755637i	$-0.272673\pi$
$270$		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	$0.463963\pi$
$281$	−12.6942	+	24.9137i	−0.757270	+	1.48623i	−0.870240	+	0.492627i	$0.836037\pi$
$282$		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	−0.992313	−	0.123749i	$-0.960508\pi$
$293$	−5.28804	+	10.3784i	−0.308931	+	0.606311i	0.683383	+	0.730060i	$0.260508\pi$
$294$		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	$-0.919519\pi$
$311$	−2.19891	−	13.8834i	−0.124689	−	0.787254i	0.843518	−	0.537101i	$-0.180481\pi$
$312$		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	0.656327	−	0.754476i	$-0.272109\pi$
$317$	26.9503	−	4.26850i	1.51368	−	0.239743i	0.857350	+	0.514733i	$0.172109\pi$
$318$		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	−0.0850719	−	0.996375i	$-0.527112\pi$
$347$	12.4995	−	6.36881i	0.671008	−	0.341896i	0.756080	+	0.654479i	$0.227112\pi$
$348$		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	$-0.751272\pi$
$353$	5.23026	−	16.0971i	0.278378	−	0.856761i	0.988306	−	0.152486i	$-0.0487278\pi$
$354$		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	0.474050	−	0.880498i	$-0.342792\pi$
$359$	−4.10898	−	2.98535i	−0.216864	−	0.157561i	−0.690914	+	0.722937i	$0.742792\pi$
$360$		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	0.563433	−	0.826162i	$-0.309480\pi$
$383$	−5.14171	−	5.14171i	−0.262729	−	0.262729i	−0.826162	+	0.563433i	$0.809480\pi$
$384$		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	−0.373762	−	0.927525i	$-0.621932\pi$
$389$	−24.0883	−	7.82678i	−1.22133	−	0.396833i	−0.847565	+	0.530691i	$0.821932\pi$
$390$		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	$-0.858444\pi$
$401$		−	17.2293i		−	0.860393i	0.902735	−	0.430196i	$-0.141556\pi$
$402$		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	$0.186845\pi$
$419$			22.6744i			1.10771i	−0.832611	+	0.553857i	$0.813155\pi$
$420$		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	0.998809	−	0.0487948i	$-0.0155381\pi$
$431$	36.9160	+	11.9947i	1.77818	+	0.577766i	0.779372	+	0.626561i	$0.215538\pi$
$432$		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	−0.988091	−	0.153872i	$-0.950826\pi$
$443$	−11.2902	+	15.5396i	−0.536413	+	0.738309i	0.451678	+	0.892181i	$0.350826\pi$
$444$		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	−0.382773	−	0.923842i	$-0.625031\pi$
$449$	−3.16621	+	1.02876i	−0.149423	+	0.0485504i	0.233351	+	0.972393i	$0.425031\pi$
$450$		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	0.0462323	−	0.998931i	$-0.485279\pi$
$461$	−19.0988	−	13.8761i	−0.889521	−	0.646275i	−0.935753	+	0.352656i	$0.885279\pi$
$462$		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	−0.946274	−	0.323366i	$-0.895185\pi$
$467$	0.202003	−	0.621701i	0.00934758	−	0.0287689i	0.955622	+	0.294597i	$0.0951855\pi$
$468$		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	0.931272	−	0.364325i	$-0.118700\pi$
$479$	25.9112	+	13.2024i	1.18392	+	0.603235i	0.252643	+	0.967560i	$0.418700\pi$
$480$		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	$-0.642366\pi$
$491$	−19.1668			−0.864987			−0.432493	+	0.901637i	$0.642366\pi$
$492$		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	−0.683940	−	0.729538i	$-0.739735\pi$
$503$	−24.8715	+	3.93926i	−1.10897	+	0.175643i	−0.425026	+	0.905181i	$0.639735\pi$
$504$		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	$-0.977900\pi$
$509$	−1.58521	−	10.0086i	−0.0702632	−	0.443624i	0.927328	−	0.374251i	$-0.122100\pi$
$510$		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	$-0.846793\pi$
$521$	2.27512	−	14.3646i	0.0996750	−	0.629323i	0.986062	−	0.166378i	$-0.0532072\pi$
$522$		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	0.962585	−	0.270979i	$-0.0873474\pi$
$557$	−0.864378	−	5.45747i	−0.0366249	−	0.231240i	−0.999210	+	0.0397388i	$0.987347\pi$
$558$		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	0.0593375	−	0.998238i	$-0.481101\pi$
$563$	10.0663	−	1.59434i	0.424243	−	0.0671936i	0.364906	+	0.931044i	$0.381101\pi$
$564$		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	0.997998	−	0.0632488i	$-0.0201462\pi$
$569$	15.0146	+	20.6659i	0.629446	+	0.866359i	−0.368551	+	0.929607i	$0.620146\pi$
$570$		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	−0.380388	−	0.924827i	$-0.624209\pi$
$587$	−32.7606	−	16.6924i	−1.35217	−	0.688967i	−0.971787	+	0.235860i	$0.924209\pi$
$588$		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	0.345430	−	0.938444i	$-0.387733\pi$
$593$	31.8443	−	16.2255i	1.30769	−	0.666300i	0.962256	+	0.272145i	$0.0877329\pi$
$594$		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	$0.384020\pi$
$599$	−11.7757	+	36.2418i	−0.481141	+	1.48080i	−0.837493	+	0.546448i	$0.815980\pi$
$600$		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	−0.399999	−	0.916516i	$-0.630990\pi$
$617$	−4.59259	+	1.49222i	−0.184891	+	0.0600746i	0.215108	+	0.976590i	$0.430990\pi$
$618$		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	0.942457	−	0.334327i	$-0.108509\pi$
$641$	43.9387	+	6.95921i	1.73547	+	0.274872i	0.793017	+	0.609199i	$0.208509\pi$
$642$		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	$-0.853874\pi$
$647$		−	22.5423i		−	0.886229i	0.896465	−	0.443114i	$-0.146126\pi$
$648$		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	−0.00983760	−	0.999952i	$-0.503131\pi$
$653$	25.3012	−	25.3012i	0.990114	−	0.990114i	0.999952	+	0.00983760i	$0.00313146\pi$
$654$		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	−0.821298	−	0.570500i	$-0.806750\pi$
$659$	−6.43824	+	6.43824i	−0.250798	+	0.250798i	0.570500	+	0.821298i	$0.306750\pi$
$660$		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	0.778703	−	0.627392i	$-0.215878\pi$
$677$	27.0578	+	8.79161i	1.03992	+	0.337889i	0.261212	+	0.965281i	$0.415878\pi$
$678$		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	$-0.824404\pi$
$683$	−35.9543	−	35.9543i	−1.37575	−	1.37575i	−0.524095	−	0.851660i	$-0.675596\pi$
$684$		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	−0.512760	−	0.858532i	$-0.671377\pi$
$701$	3.84706	−	2.79505i	0.145302	−	0.105568i	0.658061	+	0.752964i	$0.271377\pi$
$702$		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	−0.0705784	−	0.997506i	$-0.522484\pi$
$719$	18.6341	−	9.49457i	0.694936	−	0.354088i	0.765515	+	0.643419i	$0.222484\pi$
$720$		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	$-0.964026\pi$
$743$	−21.6382	−	29.7825i	−0.793830	−	1.09261i	0.199791	−	0.979839i	$-0.435974\pi$
$744$		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	$0.201273\pi$
$761$	13.8331	+	42.5738i	0.501449	+	1.54330i	−0.305212	+	0.952284i	$0.598727\pi$
$762$		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	−0.998118	−	0.0613212i	$-0.980469\pi$
$773$	−10.0599	+	19.7436i	−0.361829	+	0.710130i	0.636289	+	0.771451i	$0.280469\pi$
$774$		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	$-0.884253\pi$
$797$	−10.9411	−	33.6732i	−0.387553	−	1.19276i	0.547059	−	0.837094i	$-0.315747\pi$
$798$		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	0.647068	−	0.762433i	$-0.275995\pi$
$809$	42.6095	−	6.74868i	1.49807	−	0.237271i	0.851003	+	0.525162i	$0.175995\pi$
$810$		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	$-0.633363\pi$
$821$	−23.3134			−0.813645			−0.406822	+	0.913507i	$0.633363\pi$
$822$		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	$0.0908453\pi$
$827$	17.9249	+	35.1797i	0.623311	+	1.22332i	−0.336238	+	0.941777i	$0.609155\pi$
$828$		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	0.0584415	−	0.998291i	$-0.481387\pi$
$839$	26.0813	−	13.2891i	0.900427	−	0.458790i	0.841985	+	0.539500i	$0.181387\pi$
$840$		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	$-0.332326\pi$
$857$	43.3328	−	31.4832i	1.48022	−	1.07544i	0.977485	−	0.211005i	$-0.0676735\pi$
$858$		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	0.0644375	−	0.997922i	$-0.479475\pi$
$863$	20.6558	−	6.71148i	0.703132	−	0.228462i	0.638695	+	0.769460i	$0.279475\pi$
$864$		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	0.837740	−	0.546069i	$-0.183876\pi$
$881$	35.4552	+	11.5201i	1.19452	+	0.388122i	0.356775	+	0.934190i	$0.383876\pi$
$882$		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	0.527814	−	0.849360i	$-0.323012\pi$
$887$	22.8530	+	3.61956i	0.767328	+	0.121533i	0.239514	+	0.970893i	$0.423012\pi$
$888$		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	$-0.937883\pi$
$911$		−	11.7055i		−	0.387822i	0.981019	−	0.193911i	$-0.0621173\pi$
$912$		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	$-0.984265\pi$
$929$	−31.9483	−	31.9483i	−1.04819	−	1.04819i	−0.0494113	−	0.998779i	$-0.515735\pi$
$930$		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	0.537902	−	0.843007i	$-0.319217\pi$
$941$	45.0498	−	14.6376i	1.46858	−	0.477171i	0.930679	+	0.365836i	$0.119217\pi$
$942$		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	−0.936103	−	0.351726i	$-0.885595\pi$
$947$	−27.4149	+	19.9181i	−0.890864	+	0.647250i	0.0452393	+	0.998976i	$0.485595\pi$
$948$		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	0.673523	−	0.739166i	$-0.264780\pi$
$953$	5.51549	+	4.00724i	0.178664	+	0.129807i	−0.494859	+	0.868973i	$0.664780\pi$
$954$		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	0.613242	−	0.789895i	$-0.289865\pi$
$971$	10.4282	+	5.31345i	0.334658	+	0.170517i	−0.278584	+	0.960412i	$0.589865\pi$
$972$		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	$-0.805011\pi$
$977$	−25.0815	−	49.2252i	−0.802427	−	1.57485i	0.0157428	−	0.999876i	$-0.494989\pi$
$978$		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	$-0.698595\pi$
$983$	−36.6332			−1.16842			−0.584209	+	0.811603i	$0.698595\pi$
$984$		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.d.289.1	yes	24
3.2	odd	2		738.2.u.c.289.3	✓	24
41.21	even	20	inner	738.2.u.d.595.1	yes	24
123.62	odd	20		738.2.u.c.595.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.u.c.289.3	✓	24	3.2	odd	2
738.2.u.c.595.3	yes	24	123.62	odd	20
738.2.u.d.289.1	yes	24	1.1	even	1	trivial
738.2.u.d.595.1	yes	24	41.21	even	20	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:	\( N \)	\(=\)	\( 738 = 2 \cdot 3^{2} \cdot 41 \)
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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