LMFDB - Embedded newform 738.2.u.c.361.3

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			361.3
Character	$\chi$	$=$	738.361
Dual form			738.2.u.c.415.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(3.17802 - 1.03260i) q^{5} +(-0.0295159 + 0.186356i) q^{7} +(0.951057 + 0.309017i) q^{8} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(3.17802 - 1.03260i) q^{5} +(-0.0295159 + 0.186356i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.03260 + 3.17802i) q^{10} +(-1.66667 - 3.27102i) q^{11} +(5.44127 - 0.861812i) q^{13} +(-0.133416 - 0.133416i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-2.15110 + 1.09604i) q^{17} +(2.44120 + 0.386648i) q^{19} +(-1.96412 - 2.70338i) q^{20} +(3.62596 + 0.574295i) q^{22} +(-4.08088 - 2.96494i) q^{23} +(4.98846 - 3.62433i) q^{25} +(-2.50108 + 4.90864i) q^{26} +(0.186356 - 0.0295159i) q^{28} +(-0.824791 - 0.420252i) q^{29} +(0.894416 - 2.75273i) q^{31} -1.00000i q^{32} +(0.377670 - 2.38452i) q^{34} +(0.0986294 + 0.622721i) q^{35} +(-0.0598364 - 0.184157i) q^{37} +(-1.74771 + 1.74771i) q^{38} +3.34157 q^{40} +(0.312306 - 6.39550i) q^{41} +(-0.374552 + 0.515527i) q^{43} +(-2.59590 + 2.59590i) q^{44} +(4.79737 - 1.55876i) q^{46} +(-0.339165 - 2.14140i) q^{47} +(6.62354 + 2.15212i) q^{49} +6.16607i q^{50} +(-2.50108 - 4.90864i) q^{52} +(7.80894 + 3.97885i) q^{53} +(-8.67437 - 8.67437i) q^{55} +(-0.0856585 + 0.168114i) q^{56} +(0.824791 - 0.420252i) q^{58} +(-0.834669 - 0.606422i) q^{59} +(5.01958 + 6.90887i) q^{61} +(1.70128 + 2.34161i) q^{62} +(0.809017 + 0.587785i) q^{64} +(16.4025 - 8.35751i) q^{65} +(-5.92399 + 11.6265i) q^{67} +(1.70712 + 1.70712i) q^{68} +(-0.561765 - 0.286234i) q^{70} +(0.312899 + 0.614098i) q^{71} +6.55734i q^{73} +(0.184157 + 0.0598364i) q^{74} +(-0.386648 - 2.44120i) q^{76} +(0.658768 - 0.214047i) q^{77} +(10.1046 - 10.1046i) q^{79} +(-1.96412 + 2.70338i) q^{80} +(4.99050 + 4.01184i) q^{82} +13.1883 q^{83} +(-5.70447 + 5.70447i) q^{85} +(-0.196914 - 0.606038i) q^{86} +(-0.574295 - 3.62596i) q^{88} +(-2.07242 + 13.0848i) q^{89} +1.03945i q^{91} +(-1.55876 + 4.79737i) q^{92} +(1.93179 + 0.984294i) q^{94} +(8.15744 - 1.29201i) q^{95} +(-2.00053 + 3.92626i) q^{97} +(-5.63432 + 4.09357i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/738\mathbb{Z}\right)^\times$.

$n$	$83$	$703$
$\chi(n)$	$1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	3.17802	−	1.03260i	1.42125	−	0.461793i	0.505253	−	0.862971i	$-0.331399\pi$
$5$	3.17802	−	1.03260i	1.42125	−	0.461793i	0.916000	+	0.401178i	$0.131399\pi$
$6$		0			0
$7$	−0.0295159	+	0.186356i	−0.0111560	+	0.0704360i	−0.992638	−	0.121117i	$-0.961352\pi$
$7$	−0.0295159	+	0.186356i	−0.0111560	+	0.0704360i	0.981482	+	0.191553i	$0.0613524\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$		0			0
$10$	−1.03260	+	3.17802i	−0.326537	+	1.00498i
$11$	−1.66667	−	3.27102i	−0.502520	−	0.986251i	−0.993365	−	0.115004i	$-0.963312\pi$
$11$	−1.66667	−	3.27102i	−0.502520	−	0.986251i	0.490845	−	0.871247i	$-0.336688\pi$
$12$		0			0
$13$	5.44127	−	0.861812i	1.50914	−	0.239024i	0.653629	−	0.756815i	$-0.273246\pi$
$13$	5.44127	−	0.861812i	1.50914	−	0.239024i	0.855507	+	0.517792i	$0.173246\pi$
$14$	−0.133416	−	0.133416i	−0.0356570	−	0.0356570i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−2.15110	+	1.09604i	−0.521719	+	0.265829i	−0.694958	−	0.719051i	$-0.744577\pi$
$17$	−2.15110	+	1.09604i	−0.521719	+	0.265829i	0.173238	+	0.984880i	$0.444577\pi$
$18$		0			0
$19$	2.44120	+	0.386648i	0.560050	+	0.0887032i	0.430041	−	0.902810i	$-0.358499\pi$
$19$	2.44120	+	0.386648i	0.560050	+	0.0887032i	0.130009	+	0.991513i	$0.458499\pi$
$20$	−1.96412	−	2.70338i	−0.439191	−	0.604495i
$21$		0			0
$22$	3.62596	+	0.574295i	0.773057	+	0.122440i
$23$	−4.08088	−	2.96494i	−0.850923	−	0.618232i	0.0744774	−	0.997223i	$-0.476271\pi$
$23$	−4.08088	−	2.96494i	−0.850923	−	0.618232i	−0.925400	+	0.378991i	$0.876271\pi$
$24$		0			0
$25$	4.98846	−	3.62433i	0.997691	−	0.724865i
$26$	−2.50108	+	4.90864i	−0.490501	+	0.962663i
$27$		0			0
$28$	0.186356	−	0.0295159i	0.0352180	−	0.00557798i
$29$	−0.824791	−	0.420252i	−0.153160	−	0.0780389i	0.375731	−	0.926729i	$-0.377392\pi$
$29$	−0.824791	−	0.420252i	−0.153160	−	0.0780389i	−0.528891	+	0.848690i	$0.677392\pi$
$30$		0			0
$31$	0.894416	−	2.75273i	0.160642	−	0.494405i	−0.838047	−	0.545598i	$-0.816303\pi$
$31$	0.894416	−	2.75273i	0.160642	−	0.494405i	0.998689	+	0.0511934i	$0.0163025\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	0.377670	−	2.38452i	0.0647699	−	0.408941i
$35$	0.0986294	+	0.622721i	0.0166714	+	0.105259i
$36$		0			0
$37$	−0.0598364	−	0.184157i	−0.00983704	−	0.0302753i	0.946018	−	0.324115i	$-0.105067\pi$
$37$	−0.0598364	−	0.184157i	−0.00983704	−	0.0302753i	−0.955855	+	0.293840i	$0.905067\pi$
$38$	−1.74771	+	1.74771i	−0.283516	+	0.283516i
$39$		0			0
$40$	3.34157			0.528348
$41$	0.312306	−	6.39550i	0.0487740	−	0.998810i
$41$	0.312306	−	6.39550i	0.0487740	−	0.998810i
$42$		0			0
$43$	−0.374552	+	0.515527i	−0.0571186	+	0.0786171i	−0.836621	−	0.547782i	$-0.815472\pi$
$43$	−0.374552	+	0.515527i	−0.0571186	+	0.0786171i	0.779502	+	0.626400i	$0.215472\pi$
$44$	−2.59590	+	2.59590i	−0.391346	+	0.391346i
$45$		0			0
$46$	4.79737	−	1.55876i	0.707333	−	0.229826i
$47$	−0.339165	−	2.14140i	−0.0494722	−	0.312355i	−0.999999	−	0.00171134i	$-0.999455\pi$
$47$	−0.339165	−	2.14140i	−0.0494722	−	0.312355i	0.950526	−	0.310644i	$-0.100545\pi$
$48$		0			0
$49$	6.62354	+	2.15212i	0.946220	+	0.307445i
$50$			6.16607i			0.872014i
$51$		0			0
$52$	−2.50108	−	4.90864i	−0.346837	−	0.680705i
$53$	7.80894	+	3.97885i	1.07264	+	0.546538i	0.898855	−	0.438246i	$-0.144400\pi$
$53$	7.80894	+	3.97885i	1.07264	+	0.546538i	0.173785	+	0.984784i	$0.444400\pi$
$54$		0			0
$55$	−8.67437	−	8.67437i	−1.16965	−	1.16965i
$56$	−0.0856585	+	0.168114i	−0.0114466	+	0.0224652i
$57$		0			0
$58$	0.824791	−	0.420252i	0.108300	−	0.0551818i
$59$	−0.834669	−	0.606422i	−0.108665	−	0.0789495i	0.532126	−	0.846665i	$-0.321393\pi$
$59$	−0.834669	−	0.606422i	−0.108665	−	0.0789495i	−0.640791	+	0.767716i	$0.721393\pi$
$60$		0			0
$61$	5.01958	+	6.90887i	0.642692	+	0.884590i	0.998756	−	0.0498721i	$-0.0158814\pi$
$61$	5.01958	+	6.90887i	0.642692	+	0.884590i	−0.356064	+	0.934462i	$0.615881\pi$
$62$	1.70128	+	2.34161i	0.216063	+	0.297385i
$63$		0			0
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	16.4025	−	8.35751i	2.03448	−	1.03662i
$66$		0			0
$67$	−5.92399	+	11.6265i	−0.723730	+	1.42040i	0.176195	+	0.984355i	$0.443621\pi$
$67$	−5.92399	+	11.6265i	−0.723730	+	1.42040i	−0.899925	+	0.436045i	$0.856379\pi$
$68$	1.70712	+	1.70712i	0.207019	+	0.207019i
$69$		0			0
$70$	−0.561765	−	0.286234i	−0.0671438	−	0.0342115i
$71$	0.312899	+	0.614098i	0.0371342	+	0.0728800i	0.908828	−	0.417171i	$-0.136978\pi$
$71$	0.312899	+	0.614098i	0.0371342	+	0.0728800i	−0.871694	+	0.490051i	$0.836978\pi$
$72$		0			0
$73$			6.55734i			0.767478i	0.923442	+	0.383739i	$0.125364\pi$
$73$			6.55734i			0.767478i	−0.923442	+	0.383739i	$0.874636\pi$
$74$	0.184157	+	0.0598364i	0.0214079	+	0.00695584i
$75$		0			0
$76$	−0.386648	−	2.44120i	−0.0443516	−	0.280025i
$77$	0.658768	−	0.214047i	0.0750736	−	0.0243929i
$78$		0			0
$79$	10.1046	−	10.1046i	1.13685	−	1.13685i	0.147844	−	0.989011i	$-0.452767\pi$
$79$	10.1046	−	10.1046i	1.13685	−	1.13685i	0.989011	−	0.147844i	$-0.0472332\pi$
$80$	−1.96412	+	2.70338i	−0.219596	+	0.302248i
$81$		0			0
$82$	4.99050	+	4.01184i	0.551109	+	0.443034i
$83$	13.1883			1.44761			0.723804	−	0.690005i	$-0.242392\pi$
$83$	13.1883			1.44761			0.723804	+	0.690005i	$0.242392\pi$
$84$		0			0
$85$	−5.70447	+	5.70447i	−0.618737	+	0.618737i
$86$	−0.196914	−	0.606038i	−0.0212337	−	0.0653507i
$87$		0			0
$88$	−0.574295	−	3.62596i	−0.0612201	−	0.386528i
$89$	−2.07242	+	13.0848i	−0.219676	+	1.38698i	0.593439	+	0.804879i	$0.297770\pi$
$89$	−2.07242	+	13.0848i	−0.219676	+	1.38698i	−0.813115	+	0.582103i	$0.802230\pi$
$90$		0			0
$91$			1.03945i			0.108964i
$92$	−1.55876	+	4.79737i	−0.162512	+	0.500160i
$93$		0			0
$94$	1.93179	+	0.984294i	0.199249	+	0.101522i
$95$	8.15744	−	1.29201i	0.836936	−	0.132558i
$96$		0			0
$97$	−2.00053	+	3.92626i	−0.203123	+	0.398651i	−0.969986	−	0.243159i	$-0.921816\pi$
$97$	−2.00053	+	3.92626i	−0.203123	+	0.398651i	0.766864	+	0.641810i	$0.221816\pi$
$98$	−5.63432	+	4.09357i	−0.569152	+	0.413513i
$99$		0			0
$100$	−4.98846	−	3.62433i	−0.498846	−	0.362433i
$101$	−9.05758	−	1.43458i	−0.901263	−	0.142746i	−0.311428	−	0.950270i	$-0.600807\pi$
$101$	−9.05758	−	1.43458i	−0.901263	−	0.142746i	−0.589835	+	0.807524i	$0.700807\pi$
$102$		0			0
$103$	6.41440	+	8.82866i	0.632029	+	0.869914i	0.998159	−	0.0606499i	$-0.0193173\pi$
$103$	6.41440	+	8.82866i	0.632029	+	0.869914i	−0.366130	+	0.930564i	$0.619317\pi$
$104$	5.44127	+	0.861812i	0.533560	+	0.0845076i
$105$		0			0
$106$	−7.80894	+	3.97885i	−0.758471	+	0.386460i
$107$	−11.9565	+	8.68692i	−1.15588	+	0.839797i	−0.989252	−	0.146223i	$-0.953288\pi$
$107$	−11.9565	+	8.68692i	−1.15588	+	0.839797i	−0.166629	+	0.986020i	$0.553288\pi$
$108$		0			0
$109$	−12.1467	−	12.1467i	−1.16345	−	1.16345i	−0.983716	−	0.179730i	$-0.942477\pi$
$109$	−12.1467	−	12.1467i	−1.16345	−	1.16345i	−0.179730	−	0.983716i	$-0.557523\pi$
$110$	12.1164	−	1.91905i	1.15525	−	0.182974i
$111$		0			0
$112$	−0.0856585	−	0.168114i	−0.00809397	−	0.0158853i
$113$	1.35334	−	4.16516i	0.127312	−	0.391826i	−0.867003	−	0.498302i	$-0.833957\pi$
$113$	1.35334	−	4.16516i	0.127312	−	0.391826i	0.994315	+	0.106477i	$0.0339570\pi$
$114$		0			0
$115$	−16.0307	−	5.20870i	−1.49487	−	0.485713i
$116$	−0.144809	+	0.914288i	−0.0134452	+	0.0848895i
$117$		0			0
$118$	0.981212	−	0.318815i	0.0903279	−	0.0293493i
$119$	−0.140762	−	0.433222i	−0.0129037	−	0.0397134i
$120$		0			0
$121$	−1.45617	+	2.00424i	−0.132379	+	0.182204i
$122$	−8.53983			−0.773160
$123$		0			0
$124$	−2.89439			−0.259924
$125$	2.29031	−	3.15234i	0.204852	−	0.281954i
$126$		0			0
$127$	−6.17483	−	19.0042i	−0.547928	−	1.68635i	−0.713926	−	0.700221i	$-0.753085\pi$
$127$	−6.17483	−	19.0042i	−0.547928	−	1.68635i	0.165998	−	0.986126i	$-0.446915\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$		0			0
$130$	−2.87980	+	18.1824i	−0.252575	+	1.59470i
$131$	−15.4172	−	5.00937i	−1.34701	−	0.437670i	−0.455325	−	0.890325i	$-0.650477\pi$
$131$	−15.4172	−	5.00937i	−1.34701	−	0.437670i	−0.891686	+	0.452655i	$0.850477\pi$
$132$		0			0
$133$	−0.144109	+	0.443521i	−0.0124958	+	0.0384581i
$134$	−5.92399	−	11.6265i	−0.511754	−	1.00437i
$135$		0			0
$136$	−2.38452	+	0.377670i	−0.204471	+	0.0323850i
$137$	5.57819	+	5.57819i	0.476577	+	0.476577i	0.904035	−	0.427458i	$-0.140591\pi$
$137$	5.57819	+	5.57819i	0.476577	+	0.476577i	−0.427458	+	0.904035i	$0.640591\pi$
$138$		0			0
$139$	−15.0914	+	10.9646i	−1.28004	+	0.930002i	−0.999554	−	0.0298566i	$-0.990495\pi$
$139$	−15.0914	+	10.9646i	−1.28004	+	0.930002i	−0.280484	+	0.959859i	$0.590495\pi$
$140$	0.561765	−	0.286234i	0.0474778	−	0.0241912i
$141$		0			0
$142$	−0.680733	−	0.107817i	−0.0571258	−	0.00904784i
$143$	−11.8878	−	16.3622i	−0.994108	−	1.36827i
$144$		0			0
$145$	−3.05516	−	0.483889i	−0.253717	−	0.0401848i
$146$	−5.30500	−	3.85431i	−0.439045	−	0.318985i
$147$		0			0
$148$	−0.156654	+	0.113816i	−0.0128769	+	0.00935558i
$149$	6.35880	−	12.4798i	0.520933	−	1.02239i	−0.469309	−	0.883034i	$-0.655497\pi$
$149$	6.35880	−	12.4798i	0.520933	−	1.02239i	0.990243	−	0.139355i	$-0.0445029\pi$
$150$		0			0
$151$	−1.05288	+	0.166760i	−0.0856823	+	0.0135707i	−0.199128	−	0.979973i	$-0.563811\pi$
$151$	−1.05288	+	0.166760i	−0.0856823	+	0.0135707i	0.113446	+	0.993544i	$0.463811\pi$
$152$	2.20224	+	1.12210i	0.178625	+	0.0910141i
$153$		0			0
$154$	−0.214047	+	0.658768i	−0.0172484	+	0.0530851i
$155$		−	9.67180i		−	0.776858i
$156$		0			0
$157$	0.799722	−	5.04925i	0.0638248	−	0.402974i	−0.935006	−	0.354632i	$-0.884606\pi$
$157$	0.799722	−	5.04925i	0.0638248	−	0.402974i	0.998831	−	0.0483421i	$-0.0153938\pi$
$158$	2.23545	+	14.1141i	0.177843	+	1.12286i
$159$		0			0
$160$	−1.03260	−	3.17802i	−0.0816343	−	0.251244i
$161$	0.672985	−	0.672985i	0.0530386	−	0.0530386i
$162$		0			0
$163$	21.5791			1.69020			0.845102	−	0.534604i	$-0.179539\pi$
$163$	21.5791			1.69020			0.845102	+	0.534604i	$0.179539\pi$
$164$	−6.17899	+	1.67930i	−0.482498	+	0.131131i
$165$		0			0
$166$	−7.75191	+	10.6696i	−0.601665	+	0.828121i
$167$	−9.92227	+	9.92227i	−0.767808	+	0.767808i	−0.977720	−	0.209912i	$-0.932682\pi$
$167$	−9.92227	+	9.92227i	−0.767808	+	0.767808i	0.209912	+	0.977720i	$0.432682\pi$
$168$		0			0
$169$	16.5009	−	5.36147i	1.26930	−	0.412421i
$170$	−1.26201	−	7.96802i	−0.0967918	−	0.611119i
$171$		0			0
$172$	0.606038	+	0.196914i	0.0462100	+	0.0150145i
$173$			8.84477i			0.672455i	0.941781	+	0.336228i	$0.109151\pi$
$173$			8.84477i			0.672455i	−0.941781	+	0.336228i	$0.890849\pi$
$174$		0			0
$175$	0.528176	+	1.03660i	0.0399264	+	0.0783599i
$176$	3.27102	+	1.66667i	0.246563	+	0.125630i
$177$		0			0
$178$	−9.36765	−	9.36765i	−0.702135	−	0.702135i
$179$	−2.14495	+	4.20971i	−0.160321	+	0.314648i	−0.957168	−	0.289533i	$-0.906500\pi$
$179$	−2.14495	+	4.20971i	−0.160321	+	0.314648i	0.796847	+	0.604182i	$0.206500\pi$
$180$		0			0
$181$	−21.1196	+	10.7610i	−1.56980	+	0.799855i	−0.999763	−	0.0217607i	$-0.993073\pi$
$181$	−21.1196	+	10.7610i	−1.56980	+	0.799855i	−0.570041	+	0.821616i	$0.693073\pi$
$182$	−0.840933	−	0.610973i	−0.0623341	−	0.0452884i
$183$		0			0
$184$	−2.96494	−	4.08088i	−0.218578	−	0.300847i
$185$	−0.380322	−	0.523469i	−0.0279619	−	0.0384862i
$186$		0			0
$187$	7.17036	+	5.20957i	0.524348	+	0.380961i
$188$	−1.93179	+	0.984294i	−0.140890	+	0.0717870i
$189$		0			0
$190$	−3.74956	+	7.35893i	−0.272022	+	0.533873i
$191$	−2.35072	−	2.35072i	−0.170092	−	0.170092i	0.616928	−	0.787020i	$-0.288377\pi$
$191$	−2.35072	−	2.35072i	−0.170092	−	0.170092i	−0.787020	+	0.616928i	$0.788377\pi$
$192$		0			0
$193$	−20.8129	−	10.6047i	−1.49815	−	0.763343i	−0.503240	−	0.864147i	$-0.667859\pi$
$193$	−20.8129	−	10.6047i	−1.49815	−	0.763343i	−0.994906	+	0.100803i	$0.967859\pi$
$194$	−2.00053	−	3.92626i	−0.143630	−	0.281889i
$195$		0			0
$196$		−	6.96440i		−	0.497457i
$197$	21.4788	+	6.97887i	1.53030	+	0.497224i	0.948680	−	0.316238i	$-0.102420\pi$
$197$	21.4788	+	6.97887i	1.53030	+	0.497224i	0.581618	+	0.813462i	$0.302420\pi$
$198$		0			0
$199$	0.570612	+	3.60270i	0.0404496	+	0.255389i	0.999624	−	0.0274272i	$-0.00873145\pi$
$199$	0.570612	+	3.60270i	0.0404496	+	0.255389i	−0.959174	+	0.282816i	$0.908731\pi$
$200$	5.86428	−	1.90542i	0.414667	−	0.134734i
$201$		0			0
$202$	6.48451	−	6.48451i	0.456249	−	0.456249i
$203$	0.102661	−	0.141301i	0.00720539	−	0.00991737i
$204$		0			0
$205$	−5.61149	−	20.6475i	−0.391923	−	1.44209i
$206$	−10.9128			−0.760333
$207$		0			0
$208$	−3.89552	+	3.89552i	−0.270105	+	0.270105i
$209$	−2.80394	−	8.62964i	−0.193953	−	0.596925i
$210$		0			0
$211$	3.26768	+	20.6313i	0.224956	+	1.42032i	0.798920	+	0.601438i	$0.205405\pi$
$211$	3.26768	+	20.6313i	0.224956	+	1.42032i	−0.573963	+	0.818881i	$0.694595\pi$
$212$	1.37102	−	8.65628i	0.0941620	−	0.594515i
$213$		0			0
$214$		−	14.7791i		−	1.01028i
$215$	−0.658000	+	2.02512i	−0.0448752	+	0.138112i
$216$		0			0
$217$	0.486588	+	0.247929i	0.0330318	+	0.0168305i
$218$	16.9666	−	2.68724i	1.14912	−	0.182003i
$219$		0			0
$220$	−5.56929	+	10.9303i	−0.375481	+	0.736924i
$221$	−10.7601	+	7.81770i	−0.723805	+	0.525875i
$222$		0			0
$223$	−10.2913	−	7.47706i	−0.689156	−	0.500701i	0.187227	−	0.982317i	$-0.440050\pi$
$223$	−10.2913	−	7.47706i	−0.689156	−	0.500701i	−0.876382	+	0.481616i	$0.840050\pi$
$224$	0.186356	+	0.0295159i	0.0124514	+	0.00197211i
$225$		0			0
$226$	2.57421	+	3.54310i	0.171234	+	0.235684i
$227$	−21.8290	−	3.45738i	−1.44884	−	0.229474i	−0.618087	−	0.786109i	$-0.712092\pi$
$227$	−21.8290	−	3.45738i	−1.44884	−	0.229474i	−0.830757	+	0.556635i	$0.812092\pi$
$228$		0			0
$229$	−6.21657	+	3.16750i	−0.410803	+	0.209314i	−0.647164	−	0.762351i	$-0.724045\pi$
$229$	−6.21657	+	3.16750i	−0.410803	+	0.209314i	0.236361	+	0.971665i	$0.424045\pi$
$230$	13.6365	−	9.90753i	0.899167	−	0.653283i
$231$		0			0
$232$	−0.654558	−	0.654558i	−0.0429739	−	0.0429739i
$233$	2.71839	−	0.430551i	0.178088	−	0.0282063i	−0.0667535	−	0.997769i	$-0.521264\pi$
$233$	2.71839	−	0.430551i	0.178088	−	0.0282063i	0.244841	+	0.969563i	$0.421264\pi$
$234$		0			0
$235$	−3.28908	−	6.45519i	−0.214556	−	0.421090i
$236$	−0.318815	+	0.981212i	−0.0207531	+	0.0638715i
$237$		0			0
$238$	0.433222	+	0.140762i	0.0280816	+	0.00912426i
$239$	−3.21128	+	20.2752i	−0.207721	+	1.31150i	0.634735	+	0.772730i	$0.281109\pi$
$239$	−3.21128	+	20.2752i	−0.207721	+	1.31150i	−0.842455	+	0.538766i	$0.818891\pi$
$240$		0			0
$241$	−27.1757	+	8.82991i	−1.75054	+	0.568784i	−0.996152	−	0.0876466i	$-0.972065\pi$
$241$	−27.1757	+	8.82991i	−1.75054	+	0.568784i	−0.754386	+	0.656431i	$0.772065\pi$
$242$	−0.765553	−	2.35613i	−0.0492116	−	0.151458i
$243$		0			0
$244$	5.01958	−	6.90887i	0.321346	−	0.442295i
$245$	23.2720			1.48679
$246$		0			0
$247$	13.6164			0.866394
$248$	1.70128	−	2.34161i	0.108031	−	0.148692i
$249$		0			0
$250$	1.20409	+	3.70580i	0.0761532	+	0.234375i
$251$	16.6877	−	5.42218i	1.05332	−	0.342245i	0.269350	−	0.963042i	$-0.413191\pi$
$251$	16.6877	−	5.42218i	1.05332	−	0.342245i	0.783971	+	0.620798i	$0.213191\pi$
$252$		0			0
$253$	−2.89689	+	18.2902i	−0.182126	+	1.14990i
$254$	19.0042	+	6.17483i	1.19243	+	0.387443i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	5.63128	+	11.0520i	0.351270	+	0.689406i	0.997263	−	0.0739376i	$-0.0235566\pi$
$257$	5.63128	+	11.0520i	0.351270	+	0.689406i	−0.645993	+	0.763343i	$0.723557\pi$
$258$		0			0
$259$	0.0360850	−	0.00571530i	0.00224221	−	0.000355132i
$260$	−13.0171	−	13.0171i	−0.807288	−	0.807288i
$261$		0			0
$262$	13.1147	−	9.52838i	0.810228	−	0.588665i
$263$	−8.64227	+	4.40346i	−0.532905	+	0.271529i	−0.699668	−	0.714468i	$-0.746669\pi$
$263$	−8.64227	+	4.40346i	−0.532905	+	0.271529i	0.166763	+	0.985997i	$0.446669\pi$
$264$		0			0
$265$	28.9255	+	4.58135i	1.77688	+	0.281430i
$266$	−0.274111	−	0.377281i	−0.0168068	−	0.0231326i
$267$		0			0
$268$	12.8880	+	2.04127i	0.787263	+	0.124690i
$269$	−1.80972	−	1.31484i	−0.110341	−	0.0801671i	0.531247	−	0.847217i	$-0.321724\pi$
$269$	−1.80972	−	1.31484i	−0.110341	−	0.0801671i	−0.641587	+	0.767050i	$0.721724\pi$
$270$		0			0
$271$	−1.01376	+	0.736538i	−0.0615814	+	0.0447415i	−0.618150	−	0.786060i	$-0.712118\pi$
$271$	−1.01376	+	0.736538i	−0.0615814	+	0.0447415i	0.556569	+	0.830802i	$0.312118\pi$
$272$	1.09604	−	2.15110i	0.0664573	−	0.130430i
$273$		0			0
$274$	−7.79163	+	1.23407i	−0.470710	+	0.0745531i
$275$	−20.1694	−	10.2768i	−1.21626	−	0.619715i
$276$		0			0
$277$	6.16373	−	18.9700i	0.370343	−	1.13980i	−0.576225	−	0.817291i	$-0.695475\pi$
$277$	6.16373	−	18.9700i	0.370343	−	1.13980i	0.946567	−	0.322506i	$-0.104525\pi$
$278$		−	18.6540i		−	1.11879i
$279$		0			0
$280$	−0.0986294	+	0.622721i	−0.00589423	+	0.0372147i
$281$	1.49711	+	9.45238i	0.0893101	+	0.563882i	0.991248	+	0.132015i	$0.0421448\pi$
$281$	1.49711	+	9.45238i	0.0893101	+	0.563882i	−0.901938	+	0.431866i	$0.857855\pi$
$282$		0			0
$283$	4.98294	+	15.3359i	0.296205	+	0.911625i	0.982814	+	0.184599i	$0.0590985\pi$
$283$	4.98294	+	15.3359i	0.296205	+	0.911625i	−0.686609	+	0.727027i	$0.740902\pi$
$284$	0.487351	−	0.487351i	0.0289190	−	0.0289190i
$285$		0			0
$286$	20.2247			1.19591
$287$	1.18262	+	0.246969i	0.0698080	+	0.0145781i
$288$		0			0
$289$	−6.56641	+	9.03789i	−0.386260	+	0.531641i
$290$	2.18725	−	2.18725i	0.128440	−	0.128440i
$291$		0			0
$292$	6.23640	−	2.02633i	0.364958	−	0.118582i
$293$	2.59359	+	16.3753i	0.151519	+	0.956653i	0.939896	+	0.341461i	$0.110922\pi$
$293$	2.59359	+	16.3753i	0.151519	+	0.956653i	−0.788377	+	0.615192i	$0.789078\pi$
$294$		0			0
$295$	−3.27879	−	1.06534i	−0.190898	−	0.0620266i
$296$		−	0.193635i		−	0.0112548i
$297$		0			0
$298$	6.35880	+	12.4798i	0.368355	+	0.722938i
$299$	−24.7604	−	12.6160i	−1.43193	−	0.729605i
$300$		0			0
$301$	−0.0850163	−	0.0850163i	−0.00490026	−	0.00490026i
$302$	0.483956	−	0.949818i	0.0278486	−	0.0546559i
$303$		0			0
$304$	−2.20224	+	1.12210i	−0.126307	+	0.0643567i
$305$	23.0864	+	16.7733i	1.32193	+	0.960435i
$306$		0			0
$307$	15.5549	+	21.4095i	0.887766	+	1.22191i	0.974209	+	0.225648i	$0.0724500\pi$
$307$	15.5549	+	21.4095i	0.887766	+	1.22191i	−0.0864429	+	0.996257i	$0.527550\pi$
$308$	−0.407141	−	0.560382i	−0.0231990	−	0.0319307i
$309$		0			0
$310$	7.82465	+	5.68494i	0.444410	+	0.322883i
$311$	−8.61374	+	4.38892i	−0.488440	+	0.248873i	−0.680824	−	0.732447i	$-0.738378\pi$
$311$	−8.61374	+	4.38892i	−0.488440	+	0.248873i	0.192384	+	0.981320i	$0.438378\pi$
$312$		0			0
$313$	−1.78085	+	3.49511i	−0.100660	+	0.197555i	−0.935844	−	0.352414i	$-0.885361\pi$
$313$	−1.78085	+	3.49511i	−0.100660	+	0.197555i	0.835185	+	0.549970i	$0.185361\pi$
$314$	3.61486	+	3.61486i	0.203998	+	0.203998i
$315$		0			0
$316$	−12.7325	−	6.48754i	−0.716260	−	0.364953i
$317$	−11.4931	−	22.5564i	−0.645516	−	1.26690i	−0.949365	−	0.314176i	$-0.898272\pi$
$317$	−11.4931	−	22.5564i	−0.645516	−	1.26690i	0.303849	−	0.952720i	$-0.401728\pi$
$318$		0			0
$319$			3.39833i			0.190270i
$320$	3.17802	+	1.03260i	0.177657	+	0.0577242i
$321$		0			0
$322$	0.148886	+	0.940027i	0.00829707	+	0.0523856i
$323$	−5.67506	+	1.84394i	−0.315769	+	0.102599i
$324$		0			0
$325$	24.0200	−	24.0200i	1.33239	−	1.33239i
$326$	−12.6839	+	17.4579i	−0.702495	+	0.966901i
$327$		0			0
$328$	2.27334	−	5.98598i	0.125524	−	0.330520i
$329$	0.409074			0.0225530
$330$		0			0
$331$	−3.65359	+	3.65359i	−0.200820	+	0.200820i	−0.800351	−	0.599532i	$-0.795354\pi$
$331$	−3.65359	+	3.65359i	−0.200820	+	0.200820i	0.599532	+	0.800351i	$0.295354\pi$
$332$	−4.07542	−	12.5429i	−0.223668	−	0.688379i
$333$		0			0
$334$	−2.19512	−	13.8594i	−0.120112	−	0.758355i
$335$	−6.82103	+	43.0663i	−0.372673	+	2.35296i
$336$		0			0
$337$		−	24.1672i		−	1.31647i	−0.752811	−	0.658237i	$-0.771303\pi$
$337$		−	24.1672i		−	1.31647i	0.752811	−	0.658237i	$-0.228697\pi$
$338$	−5.36147	+	16.5009i	−0.291626	+	0.897531i
$339$		0			0
$340$	7.18806	+	3.66250i	0.389827	+	0.198627i
$341$	−10.4949	+	1.66223i	−0.568333	+	0.0900151i
$342$		0			0
$343$	−1.19617	+	2.34761i	−0.0645871	+	0.126759i
$344$	−0.515527	+	0.374552i	−0.0277953	+	0.0201945i
$345$		0			0
$346$	−7.15557	−	5.19882i	−0.384686	−	0.279490i
$347$	−7.08501	−	1.12215i	−0.380343	−	0.0602404i	−0.0366642	−	0.999328i	$-0.511673\pi$
$347$	−7.08501	−	1.12215i	−0.380343	−	0.0602404i	−0.343679	+	0.939087i	$0.611673\pi$
$348$		0			0
$349$	0.00688816	+	0.00948074i	0.000368715	+	0.000507492i	0.809201	−	0.587531i	$-0.199900\pi$
$349$	0.00688816	+	0.00948074i	0.000368715	+	0.000507492i	−0.808833	+	0.588039i	$0.799900\pi$
$350$	−1.14909	−	0.181997i	−0.0614212	−	0.00972816i
$351$		0			0
$352$	−3.27102	+	1.66667i	−0.174346	+	0.0888338i
$353$	14.4588	−	10.5049i	0.769563	−	0.559120i	−0.132266	−	0.991214i	$-0.542225\pi$
$353$	14.4588	−	10.5049i	0.769563	−	0.559120i	0.901829	+	0.432094i	$0.142225\pi$
$354$		0			0
$355$	1.62852	+	1.62852i	0.0864327	+	0.0864327i
$356$	13.0848	−	2.07242i	0.693491	−	0.109838i
$357$		0			0
$358$	−2.14495	−	4.20971i	−0.113364	−	0.222490i
$359$	−4.08702	+	12.5786i	−0.215705	+	0.663871i	0.783398	+	0.621520i	$0.213485\pi$
$359$	−4.08702	+	12.5786i	−0.215705	+	0.663871i	−0.999103	+	0.0423509i	$0.986515\pi$
$360$		0			0
$361$	−12.2601	−	3.98355i	−0.645269	−	0.209661i
$362$	3.70797	−	23.4112i	0.194887	−	1.23047i
$363$		0			0
$364$	0.988576	−	0.321208i	0.0518155	−	0.0168359i
$365$	6.77111	+	20.8393i	0.354416	+	1.09078i
$366$		0			0
$367$	7.87957	−	10.8453i	0.411310	−	0.566120i	−0.552227	−	0.833694i	$-0.686222\pi$
$367$	7.87957	−	10.8453i	0.411310	−	0.566120i	0.963537	+	0.267574i	$0.0862218\pi$
$368$	5.04425			0.262950
$369$		0			0
$370$	0.647043			0.0336382
$371$	−0.971971	+	1.33780i	−0.0504622	+	0.0694553i
$372$		0			0
$373$	2.59411	+	7.98386i	0.134318	+	0.413389i	0.995483	−	0.0949365i	$-0.0302648\pi$
$373$	2.59411	+	7.98386i	0.134318	+	0.413389i	−0.861165	+	0.508325i	$0.830265\pi$
$374$	−8.42926	+	2.73883i	−0.435867	+	0.141622i
$375$		0			0
$376$	0.339165	−	2.14140i	0.0174911	−	0.110434i
$377$	−4.85009	−	1.57589i	−0.249792	−	0.0811624i
$378$		0			0
$379$	6.33795	−	19.5062i	0.325558	−	1.00197i	−0.645630	−	0.763651i	$-0.723405\pi$
$379$	6.33795	−	19.5062i	0.325558	−	1.00197i	0.971188	−	0.238315i	$-0.0765950\pi$
$380$	−3.74956	−	7.35893i	−0.192349	−	0.377505i
$381$		0			0
$382$	3.28349	−	0.520053i	0.167998	−	0.0266083i
$383$	9.35955	+	9.35955i	0.478251	+	0.478251i	0.904572	−	0.426321i	$-0.140191\pi$
$383$	9.35955	+	9.35955i	0.478251	+	0.478251i	−0.426321	+	0.904572i	$0.640191\pi$
$384$		0			0
$385$	1.87255	−	1.36049i	0.0954342	−	0.0693370i
$386$	20.8129	−	10.6047i	1.05935	−	0.539765i
$387$		0			0
$388$	4.35229	+	0.689335i	0.220954	+	0.0349957i
$389$	5.08926	+	7.00477i	0.258036	+	0.355156i	0.918305	−	0.395873i	$-0.129558\pi$
$389$	5.08926	+	7.00477i	0.258036	+	0.355156i	−0.660269	+	0.751029i	$0.729558\pi$
$390$		0			0
$391$	12.0281	+	1.90506i	0.608287	+	0.0963432i
$392$	5.63432	+	4.09357i	0.284576	+	0.206757i
$393$		0			0
$394$	−18.2709	+	13.2746i	−0.920476	+	0.668765i
$395$	21.6786	−	42.5466i	1.09077	−	2.14075i
$396$		0			0
$397$	36.4796	−	5.77780i	1.83086	−	0.289979i	0.856694	−	0.515825i	$-0.172515\pi$
$397$	36.4796	−	5.77780i	1.83086	−	0.289979i	0.974163	+	0.225846i	$0.0725145\pi$
$398$	−3.25004	−	1.65598i	−0.162910	−	0.0830068i
$399$		0			0
$400$	−1.90542	+	5.86428i	−0.0952710	+	0.293214i
$401$			21.7437i			1.08583i	0.839788	+	0.542915i	$0.182679\pi$
$401$			21.7437i			1.08583i	−0.839788	+	0.542915i	$0.817321\pi$
$402$		0			0
$403$	2.49442	−	15.7491i	0.124256	−	0.784521i
$404$	1.43458	+	9.05758i	0.0713730	+	0.450631i
$405$		0			0
$406$	0.0539721	+	0.166109i	0.00267859	+	0.00824385i
$407$	−0.502656	+	0.502656i	−0.0249157	+	0.0249157i
$408$		0			0
$409$	28.3303			1.40084			0.700421	−	0.713729i	$-0.252995\pi$
$409$	28.3303			1.40084			0.700421	+	0.713729i	$0.252995\pi$
$410$	20.0025	+	7.59652i	0.987855	+	0.375165i
$411$		0			0
$412$	6.41440	−	8.82866i	0.316015	−	0.434957i
$413$	0.137647	−	0.137647i	0.00677314	−	0.00677314i
$414$		0			0
$415$	41.9128	−	13.6183i	2.05742	−	0.668496i
$416$	−0.861812	−	5.44127i	−0.0422538	−	0.266780i
$417$		0			0
$418$	8.62964	+	2.80394i	0.422090	+	0.137145i
$419$		−	36.1746i		−	1.76725i	−0.468199	−	0.883623i	$-0.655097\pi$
$419$		−	36.1746i		−	1.76725i	0.468199	−	0.883623i	$-0.344903\pi$
$420$		0			0
$421$	8.03166	+	15.7630i	0.391439	+	0.768243i	0.999674	−	0.0255140i	$-0.00812224\pi$
$421$	8.03166	+	15.7630i	0.391439	+	0.768243i	−0.608235	+	0.793757i	$0.708122\pi$
$422$	−18.6118	−	9.48318i	−0.906008	−	0.461634i
$423$		0			0
$424$	6.19721	+	6.19721i	0.300963	+	0.300963i
$425$	−6.75827	+	13.2639i	−0.327824	+	0.643391i
$426$		0			0
$427$	−1.43567	+	0.731509i	−0.0694768	+	0.0354002i
$428$	11.9565	+	8.68692i	0.577940	+	0.419898i
$429$		0			0
$430$	−1.25159	−	1.72267i	−0.0603571	−	0.0830744i
$431$	23.3523	+	32.1417i	1.12484	+	1.54821i	0.797516	+	0.603298i	$0.206147\pi$
$431$	23.3523	+	32.1417i	1.12484	+	1.54821i	0.327325	+	0.944912i	$0.393853\pi$
$432$		0			0
$433$	3.78342	+	2.74881i	0.181820	+	0.132100i	0.674972	−	0.737843i	$-0.264156\pi$
$433$	3.78342	+	2.74881i	0.181820	+	0.132100i	−0.493153	+	0.869943i	$0.664156\pi$
$434$	−0.486588	+	0.247929i	−0.0233570	+	0.0119010i
$435$		0			0
$436$	−7.79868	+	15.3058i	−0.373489	+	0.733014i
$437$	−8.81587	−	8.81587i	−0.421720	−	0.421720i
$438$		0			0
$439$	−6.56624	−	3.34567i	−0.313390	−	0.159680i	0.290220	−	0.956960i	$-0.406271\pi$
$439$	−6.56624	−	3.34567i	−0.313390	−	0.159680i	−0.603610	+	0.797280i	$0.706271\pi$
$440$	−5.56929	−	10.9303i	−0.265505	−	0.521084i
$441$		0			0
$442$		−	13.3003i		−	0.632629i
$443$	27.4050	+	8.90444i	1.30205	+	0.423063i	0.876295	−	0.481775i	$-0.160008\pi$
$443$	27.4050	+	8.90444i	1.30205	+	0.423063i	0.425758	+	0.904837i	$0.360008\pi$
$444$		0			0
$445$	6.92514	+	43.7236i	0.328283	+	2.07270i
$446$	12.0981	−	3.93092i	0.572863	−	0.186135i
$447$		0			0
$448$	−0.133416	+	0.133416i	−0.00630332	+	0.00630332i
$449$	2.46964	−	3.39917i	0.116549	−	0.160417i	−0.746756	−	0.665098i	$-0.768390\pi$
$449$	2.46964	−	3.39917i	0.116549	−	0.160417i	0.863306	+	0.504681i	$0.168390\pi$
$450$		0			0
$451$	−21.4404	+	9.63763i	−1.00959	+	0.453818i
$452$	−4.37951			−0.205995
$453$		0			0
$454$	15.6279	−	15.6279i	0.733452	−	0.733452i
$455$	1.07334	+	3.30339i	0.0503188	+	0.154865i
$456$		0			0
$457$	−5.01200	−	31.6445i	−0.234451	−	1.48027i	−0.771236	−	0.636549i	$-0.780361\pi$
$457$	−5.01200	−	31.6445i	−0.234451	−	1.48027i	0.536785	−	0.843719i	$-0.319639\pi$
$458$	1.09145	−	6.89112i	0.0510000	−	0.322001i
$459$		0			0
$460$			16.8557i			0.785901i
$461$	2.10166	−	6.46826i	0.0978842	−	0.301257i	−0.890110	−	0.455745i	$-0.849373\pi$
$461$	2.10166	−	6.46826i	0.0978842	−	0.301257i	0.987995	+	0.154488i	$0.0493729\pi$
$462$		0			0
$463$	−11.0090	−	5.60935i	−0.511631	−	0.260689i	0.179061	−	0.983838i	$-0.442694\pi$
$463$	−11.0090	−	5.60935i	−0.511631	−	0.260689i	−0.690692	+	0.723149i	$0.742694\pi$
$464$	0.914288	−	0.144809i	0.0424448	−	0.00672259i
$465$		0			0
$466$	−1.24951	+	2.45230i	−0.0578824	+	0.113601i
$467$	1.85811	−	1.35000i	0.0859832	−	0.0624705i	−0.543963	−	0.839109i	$-0.683077\pi$
$467$	1.85811	−	1.35000i	0.0859832	−	0.0624705i	0.629946	+	0.776639i	$0.283077\pi$
$468$		0			0
$469$	−1.99181	−	1.44714i	−0.0919734	−	0.0668226i
$470$	7.15564	+	1.13334i	0.330065	+	0.0522771i
$471$		0			0
$472$	−0.606422	−	0.834669i	−0.0279129	−	0.0384187i
$473$	2.31055	+	0.365956i	0.106239	+	0.0168267i
$474$		0			0
$475$	13.5792	−	6.91893i	0.623055	−	0.317462i
$476$	−0.368520	+	0.267746i	−0.0168911	+	0.0122721i
$477$		0			0
$478$	−14.5155	−	14.5155i	−0.663922	−	0.663922i
$479$	−34.0388	+	5.39122i	−1.55527	+	0.246331i	−0.874084	−	0.485775i	$-0.838537\pi$
$479$	−34.0388	+	5.39122i	−1.55527	+	0.246331i	−0.681190	+	0.732107i	$0.738537\pi$
$480$		0			0
$481$	−0.484295	−	0.950482i	−0.0220819	−	0.0433382i
$482$	8.82991	−	27.1757i	0.402191	−	1.23782i
$483$		0			0
$484$	2.35613	+	0.765553i	0.107097	+	0.0347979i
$485$	−2.30346	+	14.5435i	−0.104595	+	0.660385i
$486$		0			0
$487$	16.4793	−	5.35445i	0.746748	−	0.242633i	0.0891666	−	0.996017i	$-0.471580\pi$
$487$	16.4793	−	5.35445i	0.746748	−	0.242633i	0.657581	+	0.753384i	$0.271580\pi$
$488$	2.63895	+	8.12186i	0.119460	+	0.367659i
$489$		0			0
$490$	−13.6789	+	18.8275i	−0.617952	+	0.850538i
$491$	−30.4472			−1.37406			−0.687031	−	0.726628i	$-0.741086\pi$
$491$	−30.4472			−1.37406			−0.687031	+	0.726628i	$0.741086\pi$
$492$		0			0
$493$	2.23483			0.100651
$494$	−8.00355	+	11.0159i	−0.360097	+	0.495630i
$495$		0			0
$496$	0.894416	+	2.75273i	0.0401605	+	0.123601i
$497$	−0.123676	+	0.0401849i	−0.00554764	+	0.00180254i
$498$		0			0
$499$	0.862810	−	5.44757i	0.0386247	−	0.243867i	−0.960821	−	0.277171i	$-0.910603\pi$
$499$	0.862810	−	5.44757i	0.0386247	−	0.243867i	0.999445	+	0.0333044i	$0.0106031\pi$
$500$	−3.70580	−	1.20409i	−0.165728	−	0.0538484i
$501$		0			0
$502$	−5.42218	+	16.6877i	−0.242004	+	0.744810i
$503$	4.95912	+	9.73283i	0.221116	+	0.433965i	0.974741	−	0.223340i	$-0.0716961\pi$
$503$	4.95912	+	9.73283i	0.221116	+	0.433965i	−0.753624	+	0.657306i	$0.771696\pi$
$504$		0			0
$505$	−30.2665	+	4.79374i	−1.34684	+	0.213319i
$506$	−13.0944	−	13.0944i	−0.582115	−	0.582115i
$507$		0			0
$508$	−16.1659	+	11.7452i	−0.717246	+	0.521110i
$509$	26.4370	−	13.4703i	1.17180	−	0.597061i	0.243866	−	0.969809i	$-0.421584\pi$
$509$	26.4370	−	13.4703i	1.17180	−	0.597061i	0.927933	+	0.372748i	$0.121584\pi$
$510$		0			0
$511$	−1.22200	−	0.193546i	−0.0540581	−	0.00856196i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$		0			0
$514$	−12.2513	−	1.94041i	−0.540379	−	0.0855877i
$515$	29.5016	+	21.4341i	1.29999	+	0.944501i
$516$		0			0
$517$	−6.43930	+	4.67842i	−0.283200	+	0.205757i
$518$	−0.0165864	+	0.0325527i	−0.000728767	+	0.00143029i
$519$		0			0
$520$	18.1824	−	2.87980i	0.797349	−	0.126288i
$521$	−30.6711	−	15.6277i	−1.34372	−	0.684662i	−0.373673	−	0.927561i	$-0.621902\pi$
$521$	−30.6711	−	15.6277i	−1.34372	−	0.684662i	−0.970052	+	0.242899i	$0.921902\pi$
$522$		0			0
$523$	9.10779	−	28.0309i	0.398256	−	1.22570i	−0.528141	−	0.849156i	$-0.677111\pi$
$523$	9.10779	−	28.0309i	0.398256	−	1.22570i	0.926397	−	0.376548i	$-0.122889\pi$
$524$			16.2106i			0.708166i
$525$		0			0
$526$	1.51733	−	9.58003i	0.0661586	−	0.417709i
$527$	1.09313	+	6.90172i	0.0476173	+	0.300644i
$528$		0			0
$529$	0.755376	+	2.32481i	0.0328424	+	0.101079i
$530$	−20.7084	+	20.7084i	−0.899515	+	0.899515i
$531$		0			0
$532$	0.466345			0.0202186
$533$	−3.81238	−	35.0688i	−0.165132	−	1.51900i
$534$		0			0
$535$	−29.0279	+	39.9535i	−1.25499	+	1.72734i
$536$	−9.22682	+	9.22682i	−0.398538	+	0.398538i
$537$		0			0
$538$	2.12745	−	0.691251i	0.0917210	−	0.0298020i
$539$	−3.99962	−	25.2526i	−0.172276	−	1.08771i
$540$		0			0
$541$	4.64295	+	1.50859i	0.199616	+	0.0648592i	0.407119	−	0.913375i	$-0.366534\pi$
$541$	4.64295	+	1.50859i	0.199616	+	0.0648592i	−0.207503	+	0.978234i	$0.566534\pi$
$542$		−	1.25307i		−	0.0538241i
$543$		0			0
$544$	1.09604	+	2.15110i	0.0469924	+	0.0922278i
$545$	−51.1453	−	26.0598i	−2.19082	−	1.11628i
$546$		0			0
$547$	−17.3535	−	17.3535i	−0.741980	−	0.741980i	0.230978	−	0.972959i	$-0.425807\pi$
$547$	−17.3535	−	17.3535i	−0.741980	−	0.741980i	−0.972959	+	0.230978i	$0.925807\pi$
$548$	3.58142	−	7.02893i	0.152991	−	0.300261i
$549$		0			0
$550$	20.1694	−	10.2768i	0.860025	−	0.438204i
$551$	−1.85099	−	1.34482i	−0.0788549	−	0.0572915i
$552$		0			0
$553$	1.58480	+	2.18130i	0.0673927	+	0.0927582i
$554$	11.7241	+	16.1369i	0.498110	+	0.685589i
$555$		0			0
$556$	15.0914	+	10.9646i	0.640019	+	0.465001i
$557$	9.87211	−	5.03009i	0.418295	−	0.213132i	−0.232159	−	0.972678i	$-0.574579\pi$
$557$	9.87211	−	5.03009i	0.418295	−	0.213132i	0.650454	+	0.759546i	$0.274579\pi$
$558$		0			0
$559$	−1.59375	+	3.12791i	−0.0674084	+	0.132297i
$560$	−0.445819	−	0.445819i	−0.0188393	−	0.0188393i
$561$		0			0
$562$	−8.52711	−	4.34478i	−0.359695	−	0.183274i
$563$	−13.3810	−	26.2618i	−0.563944	−	1.10680i	−0.980284	−	0.197593i	$-0.936688\pi$
$563$	−13.3810	−	26.2618i	−0.563944	−	1.10680i	0.416340	−	0.909209i	$-0.363312\pi$
$564$		0			0
$565$		−	14.6344i		−	0.615675i
$566$	−15.3359	−	4.98294i	−0.644617	−	0.209449i
$567$		0			0
$568$	0.107817	+	0.680733i	0.00452392	+	0.0285629i
$569$	−12.0321	+	3.90946i	−0.504411	+	0.163893i	−0.550159	−	0.835060i	$-0.685433\pi$
$569$	−12.0321	+	3.90946i	−0.504411	+	0.163893i	0.0457478	+	0.998953i	$0.485433\pi$
$570$		0			0
$571$	−12.9232	+	12.9232i	−0.540818	+	0.540818i	−0.923769	−	0.382951i	$-0.874908\pi$
$571$	−12.9232	+	12.9232i	−0.540818	+	0.540818i	0.382951	+	0.923769i	$0.374908\pi$
$572$	−11.8878	+	16.3622i	−0.497054	+	0.684136i
$573$		0			0
$574$	−0.894931	+	0.811597i	−0.0373537	+	0.0338754i
$575$	−31.1032			−1.29709
$576$		0			0
$577$	−21.7134	+	21.7134i	−0.903941	+	0.903941i	−0.995774	−	0.0918333i	$-0.970727\pi$
$577$	−21.7134	+	21.7134i	−0.903941	+	0.903941i	0.0918333	+	0.995774i	$0.470727\pi$
$578$	−3.45217	−	10.6247i	−0.143591	−	0.441928i
$579$		0			0
$580$	0.483889	+	3.05516i	0.0200924	+	0.126858i
$581$	−0.389266	+	2.45773i	−0.0161495	+	0.101964i
$582$		0			0
$583$		−	32.1747i		−	1.33254i
$584$	−2.02633	+	6.23640i	−0.0838501	+	0.258064i
$585$		0			0
$586$	−14.7723	−	7.52688i	−0.610240	−	0.310933i
$587$	−14.8919	+	2.35865i	−0.614656	+	0.0973519i	−0.455997	−	0.889981i	$-0.650717\pi$
$587$	−14.8919	+	2.35865i	−0.614656	+	0.0973519i	−0.158659	+	0.987333i	$0.550717\pi$
$588$		0			0
$589$	3.24779	−	6.37414i	0.133823	−	0.262642i
$590$	2.78910	−	2.02640i	0.114826	−	0.0834256i
$591$		0			0
$592$	0.156654	+	0.113816i	0.00643843	+	0.00467779i
$593$	43.2237	+	6.84596i	1.77498	+	0.281130i	0.956145	−	0.292893i	$-0.0946180\pi$
$593$	43.2237	+	6.84596i	1.77498	+	0.281130i	0.818839	+	0.574023i	$0.194618\pi$
$594$		0			0
$595$	−0.894691	−	1.23144i	−0.0366787	−	0.0504840i
$596$	−13.8340	−	2.19109i	−0.566663	−	0.0897506i
$597$		0			0
$598$	24.7604	−	12.6160i	1.01253	−	0.515908i
$599$	24.6062	−	17.8774i	1.00538	−	0.730452i	0.0421457	−	0.999111i	$-0.486581\pi$
$599$	24.6062	−	17.8774i	1.00538	−	0.730452i	0.963235	+	0.268659i	$0.0865806\pi$
$600$		0			0
$601$	4.67274	+	4.67274i	0.190605	+	0.190605i	0.795957	−	0.605353i	$-0.206968\pi$
$601$	4.67274	+	4.67274i	0.190605	+	0.190605i	−0.605353	+	0.795957i	$0.706968\pi$
$602$	0.118751	−	0.0188083i	0.00483993	−	0.000766569i
$603$		0			0
$604$	0.483956	+	0.949818i	0.0196919	+	0.0386475i
$605$	−2.55815	+	7.87317i	−0.104003	+	0.320090i
$606$		0			0
$607$	1.26069	+	0.409622i	0.0511697	+	0.0166260i	0.334490	−	0.942399i	$-0.391436\pi$
$607$	1.26069	+	0.409622i	0.0511697	+	0.0166260i	−0.283320	+	0.959025i	$0.591436\pi$
$608$	0.386648	−	2.44120i	0.0156807	−	0.0990038i
$609$		0			0
$610$	−27.1397	+	8.81823i	−1.09886	+	0.357040i
$611$	−3.69097	−	11.3596i	−0.149321	−	0.459562i
$612$		0			0
$613$	−13.7949	+	18.9870i	−0.557170	+	0.766879i	−0.990963	−	0.134134i	$-0.957175\pi$
$613$	−13.7949	+	18.9870i	−0.557170	+	0.766879i	0.433793	+	0.901012i	$0.357175\pi$
$614$	−26.4636			−1.06798
$615$		0			0
$616$	0.692670			0.0279085
$617$	9.71209	−	13.3675i	0.390994	−	0.538157i	−0.567461	−	0.823400i	$-0.692074\pi$
$617$	9.71209	−	13.3675i	0.390994	−	0.538157i	0.958455	+	0.285243i	$0.0920743\pi$
$618$		0			0
$619$	4.36790	+	13.4430i	0.175561	+	0.540320i	0.999659	−	0.0261273i	$-0.00831752\pi$
$619$	4.36790	+	13.4430i	0.175561	+	0.540320i	−0.824098	+	0.566447i	$0.808318\pi$
$620$	−9.19843	+	2.98875i	−0.369418	+	0.120031i
$621$		0			0
$622$	1.51232	−	9.54840i	0.0606384	−	0.382856i
$623$	−2.37725	−	0.772417i	−0.0952427	−	0.0309462i
$624$		0			0
$625$	−5.50357	+	16.9382i	−0.220143	+	0.677530i
$626$	−1.78085	−	3.49511i	−0.0711770	−	0.139693i
$627$		0			0
$628$	−5.04925	+	0.799722i	−0.201487	+	0.0319124i
$629$	0.330558	+	0.330558i	0.0131802	+	0.0131802i
$630$		0			0
$631$	−34.3090	+	24.9269i	−1.36582	+	0.992326i	−0.367769	+	0.929917i	$0.619878\pi$
$631$	−34.3090	+	24.9269i	−1.36582	+	0.992326i	−0.998051	+	0.0624085i	$0.980122\pi$
$632$	12.7325	−	6.48754i	0.506472	−	0.258061i
$633$		0			0
$634$	25.0040	+	3.96025i	0.993036	+	0.157281i
$635$	−39.2475	−	54.0195i	−1.55749	−	2.14370i
$636$		0			0
$637$	37.8951	+	6.00200i	1.50146	+	0.237808i
$638$	−2.74931	−	1.99749i	−0.108846	−	0.0790814i
$639$		0			0
$640$	−2.70338	+	1.96412i	−0.106861	+	0.0776388i
$641$	15.5004	−	30.4213i	0.612230	−	1.20157i	−0.351875	−	0.936047i	$-0.614456\pi$
$641$	15.5004	−	30.4213i	0.612230	−	1.20157i	0.964105	−	0.265522i	$-0.0855442\pi$
$642$		0			0
$643$	−10.2584	+	1.62477i	−0.404552	+	0.0640747i	−0.355395	−	0.934716i	$-0.615654\pi$
$643$	−10.2584	+	1.62477i	−0.404552	+	0.0640747i	−0.0491571	+	0.998791i	$0.515654\pi$
$644$	−0.848010	−	0.432083i	−0.0334163	−	0.0170264i
$645$		0			0
$646$	1.84394	−	5.67506i	0.0725488	−	0.223282i
$647$			35.8164i			1.40809i	0.710156	+	0.704044i	$0.248624\pi$
$647$			35.8164i			1.40809i	−0.710156	+	0.704044i	$0.751376\pi$
$648$		0			0
$649$	−0.592505	+	3.74093i	−0.0232578	+	0.146844i
$650$	5.31399	+	33.5512i	0.208432	+	1.31599i
$651$		0			0
$652$	−6.66831	−	20.5229i	−0.261151	−	0.803740i
$653$	−22.2976	+	22.2976i	−0.872573	+	0.872573i	−0.992752	−	0.120179i	$-0.961653\pi$
$653$	−22.2976	+	22.2976i	−0.872573	+	0.872573i	0.120179	+	0.992752i	$0.461653\pi$
$654$		0			0
$655$	−54.1690			−2.11656
$656$	3.50652	+	5.35764i	0.136907	+	0.209181i
$657$		0			0
$658$	−0.240448	+	0.330948i	−0.00937362	+	0.0129017i
$659$	23.7601	−	23.7601i	0.925562	−	0.925562i	−0.0718533	−	0.997415i	$-0.522891\pi$
$659$	23.7601	−	23.7601i	0.925562	−	0.925562i	0.997415	+	0.0718533i	$0.0228913\pi$
$660$		0			0
$661$	−41.6593	+	13.5359i	−1.62036	+	0.526487i	−0.972027	−	0.234871i	$-0.924533\pi$
$661$	−41.6593	+	13.5359i	−1.62036	+	0.526487i	−0.648332	+	0.761357i	$0.724533\pi$
$662$	−0.808290	−	5.10335i	−0.0314151	−	0.198347i
$663$		0			0
$664$	12.5429	+	4.07542i	0.486757	+	0.158157i
$665$			1.55832i			0.0604292i
$666$		0			0
$667$	2.11986	+	4.16045i	0.0820812	+	0.161093i
$668$	12.5028	+	6.37049i	0.483747	+	0.246482i
$669$		0			0
$670$	−30.8321	−	30.8321i	−1.19115	−	1.19115i
$671$	14.2331	−	27.9340i	0.549462	−	1.07838i
$672$		0			0
$673$	−15.9149	+	8.10903i	−0.613473	+	0.312580i	−0.732977	−	0.680254i	$-0.761870\pi$
$673$	−15.9149	+	8.10903i	−0.613473	+	0.312580i	0.119504	+	0.992834i	$0.461870\pi$
$674$	19.5517	+	14.2051i	0.753104	+	0.547162i
$675$		0			0
$676$	−10.1981	−	14.0365i	−0.392236	−	0.539866i
$677$	24.8457	+	34.1972i	0.954899	+	1.31431i	0.949316	+	0.314322i	$0.101777\pi$
$677$	24.8457	+	34.1972i	0.954899	+	1.31431i	0.00558305	+	0.999984i	$0.498223\pi$
$678$		0			0
$679$	−0.672634	−	0.488698i	−0.0258133	−	0.0187545i
$680$	−7.18806	+	3.66250i	−0.275649	+	0.140450i
$681$		0			0
$682$	4.82399	−	9.46762i	0.184720	−	0.362534i
$683$	21.7524	+	21.7524i	0.832332	+	0.832332i	0.987835	−	0.155503i	$-0.0496999\pi$
$683$	21.7524	+	21.7524i	0.832332	+	0.832332i	−0.155503	+	0.987835i	$0.549700\pi$
$684$		0			0
$685$	23.4876	+	11.9676i	0.897417	+	0.457257i
$686$	−1.19617	−	2.34761i	−0.0456700	−	0.0896323i
$687$		0			0
$688$		−	0.637226i		−	0.0242940i
$689$	45.9195	+	14.9202i	1.74939	+	0.568413i
$690$		0			0
$691$	2.72449	+	17.2018i	0.103645	+	0.654386i	0.983741	+	0.179592i	$0.0574776\pi$
$691$	2.72449	+	17.2018i	0.103645	+	0.654386i	−0.880097	+	0.474795i	$0.842522\pi$
$692$	8.41187	−	2.73318i	0.319771	−	0.103900i
$693$		0			0
$694$	5.07231	−	5.07231i	0.192542	−	0.192542i
$695$	−36.6388	+	50.4290i	−1.38979	+	1.91288i
$696$		0			0
$697$	6.33794	+	14.0997i	0.240066	+	0.534064i
$698$	−0.0117188			−0.000443565
$699$		0			0
$700$	0.822654	−	0.822654i	0.0310934	−	0.0310934i
$701$	4.19956	+	12.9249i	0.158615	+	0.488167i	0.998509	−	0.0545831i	$-0.0173830\pi$
$701$	4.19956	+	12.9249i	0.158615	+	0.488167i	−0.839894	+	0.542750i	$0.817383\pi$
$702$		0			0
$703$	−0.0748685	−	0.472701i	−0.00282372	−	0.0178283i
$704$	0.574295	−	3.62596i	0.0216446	−	0.136658i
$705$		0			0
$706$			17.8720i			0.672623i
$707$	0.534685	−	1.64559i	0.0201089	−	0.0618889i
$708$		0			0
$709$	−23.8743	−	12.1645i	−0.896617	−	0.456849i	−0.0559697	−	0.998432i	$-0.517825\pi$
$709$	−23.8743	−	12.1645i	−0.896617	−	0.456849i	−0.840647	+	0.541583i	$0.817825\pi$
$710$	−2.27471	+	0.360279i	−0.0853685	+	0.0135210i
$711$		0			0
$712$	−6.01440	+	11.8039i	−0.225399	+	0.442371i
$713$	−11.8117	+	8.58168i	−0.442351	+	0.321386i
$714$		0			0
$715$	−54.6752	−	39.7239i	−2.04474	−	1.48559i
$716$	4.66649	+	0.739100i	0.174395	+	0.0276215i
$717$		0			0
$718$	−7.77398	−	10.7000i	−0.290122	−	0.399319i
$719$	3.27883	+	0.519316i	0.122280	+	0.0193672i	0.217274	−	0.976111i	$-0.430283\pi$
$719$	3.27883	+	0.519316i	0.122280	+	0.0193672i	−0.0949946	+	0.995478i	$0.530283\pi$
$720$		0			0
$721$	−1.83460	+	0.934776i	−0.0683241	+	0.0348129i
$722$	10.4291	−	7.57716i	0.388130	−	0.281993i
$723$		0			0
$724$	16.7606	+	16.7606i	0.622902	+	0.622902i
$725$	−5.63757	+	0.892903i	−0.209374	+	0.0331616i
$726$		0			0
$727$	0.223503	+	0.438650i	0.00828928	+	0.0162686i	0.895114	−	0.445837i	$-0.147094\pi$
$727$	0.223503	+	0.438650i	0.00828928	+	0.0162686i	−0.886825	+	0.462106i	$0.847094\pi$
$728$	−0.321208	+	0.988576i	−0.0119048	+	0.0366391i
$729$		0			0
$730$	−20.8393	−	6.77111i	−0.771299	−	0.250610i
$731$	0.240661	−	1.51948i	0.00890118	−	0.0561998i
$732$		0			0
$733$	22.4451	−	7.29286i	0.829029	−	0.269368i	0.136393	−	0.990655i	$-0.456449\pi$
$733$	22.4451	−	7.29286i	0.829029	−	0.269368i	0.692636	+	0.721287i	$0.256449\pi$
$734$	4.14254	+	12.7494i	0.152904	+	0.470590i
$735$		0			0
$736$	−2.96494	+	4.08088i	−0.109289	+	0.150423i
$737$	47.9038			1.76456
$738$		0			0
$739$	−18.2730			−0.672182			−0.336091	−	0.941830i	$-0.609105\pi$
$739$	−18.2730			−0.672182			−0.336091	+	0.941830i	$0.609105\pi$
$740$	−0.380322	+	0.523469i	−0.0139809	+	0.0192431i
$741$		0			0
$742$	−0.510996	−	1.57268i	−0.0187592	−	0.0577350i
$743$	51.5726	−	16.7569i	1.89201	−	0.614752i	0.914205	−	0.405252i	$-0.132816\pi$
$743$	51.5726	−	16.7569i	1.89201	−	0.614752i	0.977809	−	0.209500i	$-0.0671837\pi$
$744$		0			0
$745$	7.32168	−	46.2273i	0.268246	−	1.69364i
$746$	−7.98386	−	2.59411i	−0.292310	−	0.0949773i
$747$		0			0
$748$	2.73883	−	8.42926i	0.100142	−	0.308204i
$749$	−1.26595	−	2.48457i	−0.0462569	−	0.0907844i
$750$		0			0
$751$	1.31559	−	0.208368i	0.0480064	−	0.00760347i	−0.132385	−	0.991198i	$-0.542264\pi$
$751$	1.31559	−	0.208368i	0.0480064	−	0.00760347i	0.180391	+	0.983595i	$0.442264\pi$
$752$	1.53307	+	1.53307i	0.0559055	+	0.0559055i
$753$		0			0
$754$	4.12573	−	2.99752i	0.150250	−	0.109163i
$755$	−3.17388	+	1.61717i	−0.115509	+	0.0588549i
$756$		0			0
$757$	−17.0784	−	2.70495i	−0.620723	−	0.0983129i	−0.161851	−	0.986815i	$-0.551746\pi$
$757$	−17.0784	−	2.70495i	−0.620723	−	0.0983129i	−0.458872	+	0.888502i	$0.651746\pi$
$758$	12.0555	+	16.5930i	0.437875	+	0.602683i
$759$		0			0
$760$	8.15744	+	1.29201i	0.295901	+	0.0468662i
$761$	−14.3315	−	10.4125i	−0.519517	−	0.377451i	0.296905	−	0.954907i	$-0.404046\pi$
$761$	−14.3315	−	10.4125i	−0.519517	−	0.377451i	−0.816422	+	0.577456i	$0.804046\pi$
$762$		0			0
$763$	2.62214	−	1.90510i	0.0949278	−	0.0689691i
$764$	−1.50925	+	2.96208i	−0.0546029	+	0.107164i
$765$		0			0
$766$	−13.0734	+	2.07063i	−0.472363	+	0.0748149i
$767$	−5.06428	−	2.58038i	−0.182860	−	0.0931720i
$768$		0			0
$769$	10.1379	−	31.2014i	0.365583	−	1.12515i	−0.584032	−	0.811731i	$-0.698526\pi$
$769$	10.1379	−	31.2014i	0.365583	−	1.12515i	0.949615	−	0.313419i	$-0.101474\pi$
$770$			2.31460i			0.0834125i
$771$		0			0
$772$	−3.65413	+	23.0713i	−0.131515	+	0.830354i
$773$	−3.80592	−	24.0296i	−0.136889	−	0.864285i	−0.956578	−	0.291476i	$-0.905854\pi$
$773$	−3.80592	−	24.0296i	−0.136889	−	0.864285i	0.819689	−	0.572809i	$-0.194146\pi$
$774$		0			0
$775$	−5.51503	−	16.9735i	−0.198106	−	0.609707i
$776$	−3.11589	+	3.11589i	−0.111854	+	0.111854i
$777$		0			0
$778$	−8.65837			−0.310418
$779$	3.23521	−	15.4920i	0.115914	−	0.555057i
$780$		0			0
$781$	1.48723	−	2.04700i	0.0532173	−	0.0732473i
$782$	−8.61116	+	8.61116i	−0.307935	+	0.307935i
$783$		0			0
$784$	−6.62354	+	2.15212i	−0.236555	+	0.0768614i
$785$	−2.67233	−	16.8724i	−0.0953794	−	0.602202i
$786$		0			0
$787$	−2.52782	−	0.821338i	−0.0901070	−	0.0292776i	0.263617	−	0.964628i	$-0.415085\pi$
$787$	−2.52782	−	0.821338i	−0.0901070	−	0.0292776i	−0.353724	+	0.935350i	$0.615085\pi$
$788$		−	22.5841i		−	0.804525i
$789$		0			0
$790$	21.6786	+	42.5466i	0.771288	+	1.51374i
$791$	0.736259	+	0.375142i	0.0261783	+	0.0133385i
$792$		0			0
$793$	33.2670	+	33.2670i	1.18135	+	1.18135i
$794$	−16.7678	+	32.9087i	−0.595068	+	1.16789i
$795$		0			0
$796$	3.25004	−	1.65598i	0.115195	−	0.0586946i
$797$	16.8491	+	12.2416i	0.596827	+	0.433620i	0.844751	−	0.535159i	$-0.179748\pi$
$797$	16.8491	+	12.2416i	0.596827	+	0.433620i	−0.247924	+	0.968779i	$0.579748\pi$
$798$		0			0
$799$	3.07664	+	4.23464i	0.108844	+	0.149811i
$800$	−3.62433	−	4.98846i	−0.128139	−	0.176369i
$801$		0			0
$802$	−17.5910	−	12.7806i	−0.621161	−	0.451300i
$803$	21.4492	−	10.9289i	0.756926	−	0.385673i
$804$		0			0
$805$	1.44383	−	2.83368i	0.0508884	−	0.0998742i
$806$	11.2751	+	11.2751i	0.397150	+	0.397150i
$807$		0			0
$808$	−8.17096	−	4.16331i	−0.287453	−	0.146465i
$809$	−15.3881	−	30.2008i	−0.541015	−	1.06180i	−0.986075	−	0.166301i	$-0.946818\pi$
$809$	−15.3881	−	30.2008i	−0.541015	−	1.06180i	0.445060	−	0.895501i	$-0.353182\pi$
$810$		0			0
$811$		−	2.85031i		−	0.100088i	−0.998747	−	0.0500440i	$-0.984064\pi$
$811$		−	2.85031i		−	0.100088i	0.998747	−	0.0500440i	$-0.0159362\pi$
$812$	−0.166109	−	0.0539721i	−0.00582928	−	0.00189405i
$813$		0			0
$814$	−0.111203	−	0.702111i	−0.00389768	−	0.0246090i
$815$	68.5788	−	22.2826i	2.40221	−	0.780525i
$816$		0			0
$817$	−1.11368	+	1.11368i	−0.0389629	+	0.0389629i
$818$	−16.6521	+	22.9197i	−0.582228	+	0.801368i
$819$		0			0
$820$	−17.9029	+	11.7173i	−0.625197	+	0.409185i
$821$	−16.9213			−0.590557			−0.295278	−	0.955411i	$-0.595412\pi$
$821$	−16.9213			−0.590557			−0.295278	+	0.955411i	$0.595412\pi$
$822$		0			0
$823$	13.6211	−	13.6211i	0.474802	−	0.474802i	−0.428663	−	0.903465i	$-0.641015\pi$
$823$	13.6211	−	13.6211i	0.474802	−	0.474802i	0.903465	+	0.428663i	$0.141015\pi$
$824$	3.37225	+	10.3787i	0.117478	+	0.361560i
$825$		0			0
$826$	0.0304518	+	0.192265i	0.00105955	+	0.00668975i
$827$	−8.04493	+	50.7937i	−0.279750	+	1.76627i	0.302393	+	0.953183i	$0.402214\pi$
$827$	−8.04493	+	50.7937i	−0.279750	+	1.76627i	−0.582143	+	0.813086i	$0.697786\pi$
$828$		0			0
$829$		−	28.2684i		−	0.981804i	−0.871215	−	0.490902i	$-0.836667\pi$
$829$		−	28.2684i		−	0.981804i	0.871215	−	0.490902i	$-0.163333\pi$
$830$	−13.6183	+	41.9128i	−0.472698	+	1.45481i
$831$		0			0
$832$	4.90864	+	2.50108i	0.170176	+	0.0867092i
$833$	−16.6067	+	2.63025i	−0.575389	+	0.0911326i
$834$		0			0
$835$	−21.2874	+	41.7789i	−0.736681	+	1.44582i
$836$	−7.34081	+	5.33341i	−0.253887	+	0.184460i
$837$		0			0
$838$	29.2659	+	21.2629i	1.01097	+	0.734515i
$839$	7.01571	+	1.11118i	0.242209	+	0.0383622i	0.276359	−	0.961055i	$-0.410872\pi$
$839$	7.01571	+	1.11118i	0.242209	+	0.0383622i	−0.0341495	+	0.999417i	$0.510872\pi$
$840$		0			0
$841$	−16.5421	−	22.7683i	−0.570417	−	0.785112i
$842$	−17.4734	−	2.76752i	−0.602175	−	0.0953751i
$843$		0			0
$844$	18.6118	−	9.48318i	0.640644	−	0.326424i
$845$	46.9040	−	34.0777i	1.61355	−	1.17231i
$846$		0			0
$847$	−0.330523	−	0.330523i	−0.0113569	−	0.0113569i
$848$	−8.65628	+	1.37102i	−0.297258	+	0.0470810i
$849$		0			0
$850$	−6.75827	−	13.2639i	−0.231807	−	0.454946i
$851$	−0.301830	+	0.928936i	−0.0103466	+	0.0318435i
$852$		0			0
$853$	−5.49384	−	1.78506i	−0.188106	−	0.0611192i	0.213449	−	0.976954i	$-0.431530\pi$
$853$	−5.49384	−	1.78506i	−0.188106	−	0.0611192i	−0.401555	+	0.915835i	$0.631530\pi$
$854$	0.252061	−	1.59145i	0.00862534	−	0.0544583i
$855$		0			0
$856$	−14.0557	+	4.56699i	−0.480415	+	0.156096i
$857$	0.513931	+	1.58172i	0.0175555	+	0.0540304i	0.959451	−	0.281877i	$-0.0909570\pi$
$857$	0.513931	+	1.58172i	0.0175555	+	0.0540304i	−0.941895	+	0.335908i	$0.890957\pi$
$858$		0			0
$859$	22.1239	−	30.4510i	0.754859	−	1.03897i	−0.242765	−	0.970085i	$-0.578055\pi$
$859$	22.1239	−	30.4510i	0.754859	−	1.03897i	0.997624	−	0.0688892i	$-0.0219455\pi$
$860$	2.12933			0.0726097
$861$		0			0
$862$	−39.7293			−1.35319
$863$	−1.42739	+	1.96464i	−0.0485891	+	0.0668771i	−0.832620	−	0.553844i	$-0.813160\pi$
$863$	−1.42739	+	1.96464i	−0.0485891	+	0.0668771i	0.784031	+	0.620722i	$0.213160\pi$
$864$		0			0
$865$	9.13312	+	28.1088i	0.310535	+	0.955729i
$866$	−4.44768	+	1.44514i	−0.151138	+	0.0491078i
$867$		0			0
$868$	0.0854306	−	0.539387i	0.00289970	−	0.0183080i
$869$	−49.8933	−	16.2113i	−1.69252	−	0.549932i
$870$		0			0
$871$	−22.2141	+	68.3681i	−0.752698	+	2.31656i
$872$	−7.79868	−	15.3058i	−0.264097	−	0.518319i
$873$		0			0
$874$	12.3140	−	1.95035i	0.416528	−	0.0659716i
$875$	0.519857	+	0.519857i	0.0175744	+	0.0175744i
$876$		0			0
$877$	18.6352	−	13.5393i	0.629266	−	0.457189i	−0.226880	−	0.973923i	$-0.572852\pi$
$877$	18.6352	−	13.5393i	0.629266	−	0.457189i	0.856146	+	0.516734i	$0.172852\pi$
$878$	6.56624	−	3.34567i	0.221600	−	0.112911i
$879$		0			0
$880$	12.1164	+	1.91905i	0.408443	+	0.0646910i
$881$	3.71080	+	5.10748i	0.125020	+	0.172075i	0.866939	−	0.498414i	$-0.166084\pi$
$881$	3.71080	+	5.10748i	0.125020	+	0.172075i	−0.741919	+	0.670490i	$0.766084\pi$
$882$		0			0
$883$	1.91690	+	0.303607i	0.0645088	+	0.0102172i	0.188605	−	0.982053i	$-0.439603\pi$
$883$	1.91690	+	0.303607i	0.0645088	+	0.0102172i	−0.124097	+	0.992270i	$0.539603\pi$
$884$	10.7601	+	7.81770i	0.361903	+	0.262938i
$885$		0			0
$886$	−23.3121	+	16.9372i	−0.783186	+	0.569018i
$887$	−15.0643	+	29.5653i	−0.505809	+	0.992706i	0.487046	+	0.873376i	$0.338074\pi$
$887$	−15.0643	+	29.5653i	−0.505809	+	0.992706i	−0.992855	+	0.119329i	$0.961926\pi$
$888$		0			0
$889$	3.72380	−	0.589792i	0.124892	−	0.0197810i
$890$	−39.4436	−	20.0975i	−1.32215	−	0.673671i
$891$		0			0
$892$	−3.93092	+	12.0981i	−0.131617	+	0.405076i
$893$		−	5.35873i		−	0.179323i
$894$		0			0
$895$	−2.46975	+	15.5934i	−0.0825547	+	0.521230i
$896$	−0.0295159	−	0.186356i	−0.000986057	−	0.00622572i
$897$		0			0
$898$	1.29837	+	3.99596i	0.0433270	+	0.133347i
$899$	−1.89455	+	1.89455i	−0.0631867	+	0.0631867i
$900$		0			0
$901$	−21.1588			−0.704902
$902$	4.80532	−	23.0105i	0.160000	−	0.766165i
$903$		0			0
$904$	2.57421	−	3.54310i	0.0856171	−	0.117842i
$905$	−56.0066	+	56.0066i	−1.86172	+	1.86172i
$906$		0			0
$907$	39.6329	−	12.8775i	1.31599	−	0.427591i	0.434874	−	0.900491i	$-0.356793\pi$
$907$	39.6329	−	12.8775i	1.31599	−	0.427591i	0.881116	+	0.472900i	$0.156793\pi$
$908$	3.45738	+	21.8290i	0.114737	+	0.724422i
$909$		0			0
$910$	−3.30339	−	1.07334i	−0.109506	−	0.0355808i
$911$		−	32.0723i		−	1.06260i	−0.847183	−	0.531301i	$-0.821703\pi$
$911$		−	32.0723i		−	1.06260i	0.847183	−	0.531301i	$-0.178297\pi$
$912$		0			0
$913$	−21.9806	−	43.1394i	−0.727452	−	1.42770i
$914$	28.5469	+	14.5454i	0.944249	+	0.481119i
$915$		0			0
$916$	4.93350	+	4.93350i	0.163007	+	0.163007i
$917$	1.38858	−	2.72524i	0.0458549	−	0.0899954i
$918$		0			0
$919$	26.4568	−	13.4804i	0.872728	−	0.444677i	0.0405447	−	0.999178i	$-0.487091\pi$
$919$	26.4568	−	13.4804i	0.872728	−	0.444677i	0.832183	+	0.554501i	$0.187091\pi$
$920$	−13.6365	−	9.90753i	−0.449584	−	0.326642i
$921$		0			0
$922$	3.99760	+	5.50223i	0.131654	+	0.181206i
$923$	2.23180	+	3.07181i	0.0734606	+	0.101110i
$924$		0			0
$925$	−0.965938	−	0.701795i	−0.0317598	−	0.0230749i
$926$	11.0090	−	5.60935i	0.361777	−	0.184335i
$927$		0			0
$928$	−0.420252	+	0.824791i	−0.0137955	+	0.0270751i
$929$	−32.7111	−	32.7111i	−1.07322	−	1.07322i	−0.997099	−	0.0761188i	$-0.975747\pi$
$929$	−32.7111	−	32.7111i	−1.07322	−	1.07322i	−0.0761188	−	0.997099i	$-0.524253\pi$
$930$		0			0
$931$	15.3373	+	7.81473i	0.502659	+	0.256118i
$932$	−1.24951	−	2.45230i	−0.0409290	−	0.0803277i
$933$		0			0
$934$			2.29675i			0.0751521i
$935$	28.1669	+	9.15199i	0.921157	+	0.299302i
$936$		0			0
$937$	3.07185	+	19.3949i	0.100353	+	0.633603i	0.985679	+	0.168632i	$0.0539351\pi$
$937$	3.07185	+	19.3949i	0.100353	+	0.633603i	−0.885326	+	0.464971i	$0.846065\pi$
$938$	2.34152	−	0.760805i	0.0764532	−	0.0248412i
$939$		0			0
$940$	−5.12287	+	5.12287i	−0.167090	+	0.167090i
$941$	9.06491	−	12.4768i	0.295507	−	0.406731i	−0.635286	−	0.772277i	$-0.719118\pi$
$941$	9.06491	−	12.4768i	0.295507	−	0.406731i	0.930793	+	0.365546i	$0.119118\pi$
$942$		0			0
$943$	−20.2367	+	25.1733i	−0.658999	+	0.819757i
$944$	1.03171			0.0335792
$945$		0			0
$946$	−1.65417	+	1.65417i	−0.0537818	+	0.0537818i
$947$	−9.69981	−	29.8529i	−0.315201	−	0.970090i	−0.975671	−	0.219238i	$-0.929643\pi$
$947$	−9.69981	−	29.8529i	−0.315201	−	0.970090i	0.660470	−	0.750852i	$-0.270357\pi$
$948$		0			0
$949$	5.65119	+	35.6802i	0.183445	+	1.15823i
$950$	−2.38410	+	15.0526i	−0.0773505	+	0.488372i
$951$		0			0
$952$		−	0.455516i		−	0.0147634i
$953$	−11.3377	+	34.8939i	−0.367265	+	1.13032i	0.581286	+	0.813699i	$0.302550\pi$
$953$	−11.3377	+	34.8939i	−0.367265	+	1.13032i	−0.948551	+	0.316625i	$0.897450\pi$
$954$		0			0
$955$	−9.89798	−	5.04327i	−0.320291	−	0.163197i
$956$	20.2752	−	3.21128i	0.655748	−	0.103860i
$957$		0			0
$958$	15.6459	−	30.7069i	0.505497	−	0.992094i
$959$	−1.20418	+	0.874884i	−0.0388848	+	0.0282515i
$960$		0			0
$961$	18.3020	+	13.2972i	0.590387	+	0.428941i
$962$	1.05362	+	0.166877i	0.0339700	+	0.00538032i
$963$		0			0
$964$	16.7955	+	23.1170i	0.540946	+	0.744548i
$965$	−77.0943	−	12.2105i	−2.48175	−	0.393071i
$966$		0			0
$967$	40.0388	−	20.4008i	1.28756	−	0.656045i	0.329920	−	0.944009i	$-0.392978\pi$
$967$	40.0388	−	20.4008i	1.28756	−	0.656045i	0.957641	+	0.287964i	$0.0929783\pi$
$968$	−2.00424	+	1.45617i	−0.0644189	+	0.0468030i
$969$		0			0
$970$	−10.4120	−	10.4120i	−0.334308	−	0.334308i
$971$	57.9014	−	9.17068i	1.85814	−	0.294301i	0.875983	−	0.482342i	$-0.160214\pi$
$971$	57.9014	−	9.17068i	1.85814	−	0.294301i	0.982161	+	0.188041i	$0.0602138\pi$
$972$		0			0
$973$	−1.59788	−	3.13601i	−0.0512256	−	0.100536i
$974$	−5.35445	+	16.4793i	−0.171567	+	0.528030i
$975$		0			0
$976$	−8.12186	−	2.63895i	−0.259974	−	0.0844708i
$977$	−1.44366	+	9.11491i	−0.0461868	+	0.291612i	−0.999960	−	0.00891457i	$-0.997162\pi$
$977$	−1.44366	+	9.11491i	−0.0461868	+	0.291612i	0.953773	+	0.300526i	$0.0971624\pi$
$978$		0			0
$979$	46.2546	−	15.0290i	1.47830	−	0.480330i
$980$	−7.19145	−	22.1330i	−0.229722	−	0.707013i
$981$		0			0
$982$	17.8964	−	24.6323i	0.571097	−	0.786048i
$983$	−3.57723			−0.114096			−0.0570480	−	0.998371i	$-0.518169\pi$
$983$	−3.57723			−0.114096			−0.0570480	+	0.998371i	$0.518169\pi$
$984$		0			0
$985$	75.4663			2.40456
$986$	−1.31360	+	1.80801i	−0.0418335	+	0.0575788i
$987$		0			0
$988$	−4.20771	−	12.9500i	−0.133865	−	0.411995i
$989$	3.05701	−	0.993281i	0.0972071	−	0.0315845i
$990$		0			0
$991$	−5.73604	+	36.2160i	−0.182211	+	1.15044i	0.711796	+	0.702386i	$0.247882\pi$
$991$	−5.73604	+	36.2160i	−0.182211	+	1.15044i	−0.894008	+	0.448052i	$0.852118\pi$
$992$	−2.75273	−	0.894416i	−0.0873992	−	0.0283977i
$993$		0			0
$994$	0.0401849	−	0.123676i	0.00127459	−	0.00392278i
$995$	5.53357	+	10.8602i	0.175426	+	0.344293i
$996$		0			0
$997$	−51.3631	+	8.13511i	−1.62668	+	0.257642i	−0.902095	−	0.431538i	$-0.857971\pi$
$997$	−51.3631	+	8.13511i	−1.62668	+	0.257642i	−0.724590	+	0.689180i	$0.757971\pi$
$998$	3.90003	+	3.90003i	0.123453	+	0.123453i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	738.2.u.c.361.3	✓	24
3.2	odd	2		738.2.u.d.361.1	yes	24
41.5	even	20	inner	738.2.u.c.415.3	yes	24
123.5	odd	20		738.2.u.d.415.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
738.2.u.c.361.3	✓	24	1.1	even	1	trivial
738.2.u.c.415.3	yes	24	41.5	even	20	inner
738.2.u.d.361.1	yes	24	3.2	odd	2
738.2.u.d.415.1	yes	24	123.5	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)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(3.17802 - 1.03260i) q^{5} +(-0.0295159 + 0.186356i) q^{7} +(0.951057 + 0.309017i) q^{8} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.309017 - 0.951057i) q^{4} +(3.17802 - 1.03260i) q^{5} +(-0.0295159 + 0.186356i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.03260 + 3.17802i) q^{10} +(-1.66667 - 3.27102i) q^{11} +(5.44127 - 0.861812i) q^{13} +(-0.133416 - 0.133416i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-2.15110 + 1.09604i) q^{17} +(2.44120 + 0.386648i) q^{19} +(-1.96412 - 2.70338i) q^{20} +(3.62596 + 0.574295i) q^{22} +(-4.08088 - 2.96494i) q^{23} +(4.98846 - 3.62433i) q^{25} +(-2.50108 + 4.90864i) q^{26} +(0.186356 - 0.0295159i) q^{28} +(-0.824791 - 0.420252i) q^{29} +(0.894416 - 2.75273i) q^{31} -1.00000i q^{32} +(0.377670 - 2.38452i) q^{34} +(0.0986294 + 0.622721i) q^{35} +(-0.0598364 - 0.184157i) q^{37} +(-1.74771 + 1.74771i) q^{38} +3.34157 q^{40} +(0.312306 - 6.39550i) q^{41} +(-0.374552 + 0.515527i) q^{43} +(-2.59590 + 2.59590i) q^{44} +(4.79737 - 1.55876i) q^{46} +(-0.339165 - 2.14140i) q^{47} +(6.62354 + 2.15212i) q^{49} +6.16607i q^{50} +(-2.50108 - 4.90864i) q^{52} +(7.80894 + 3.97885i) q^{53} +(-8.67437 - 8.67437i) q^{55} +(-0.0856585 + 0.168114i) q^{56} +(0.824791 - 0.420252i) q^{58} +(-0.834669 - 0.606422i) q^{59} +(5.01958 + 6.90887i) q^{61} +(1.70128 + 2.34161i) q^{62} +(0.809017 + 0.587785i) q^{64} +(16.4025 - 8.35751i) q^{65} +(-5.92399 + 11.6265i) q^{67} +(1.70712 + 1.70712i) q^{68} +(-0.561765 - 0.286234i) q^{70} +(0.312899 + 0.614098i) q^{71} +6.55734i q^{73} +(0.184157 + 0.0598364i) q^{74} +(-0.386648 - 2.44120i) q^{76} +(0.658768 - 0.214047i) q^{77} +(10.1046 - 10.1046i) q^{79} +(-1.96412 + 2.70338i) q^{80} +(4.99050 + 4.01184i) q^{82} +13.1883 q^{83} +(-5.70447 + 5.70447i) q^{85} +(-0.196914 - 0.606038i) q^{86} +(-0.574295 - 3.62596i) q^{88} +(-2.07242 + 13.0848i) q^{89} +1.03945i q^{91} +(-1.55876 + 4.79737i) q^{92} +(1.93179 + 0.984294i) q^{94} +(8.15744 - 1.29201i) q^{95} +(-2.00053 + 3.92626i) q^{97} +(-5.63432 + 4.09357i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{4}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more