LMFDB - Embedded newform 756.2.j.a.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(253,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("756.253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.j (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			253.2
Root			$0.500000 + 0.224437i$ of defining polynomial
Character	$\chi$	$=$	756.253
Dual form			756.2.j.a.505.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.555632 + 0.962383i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})$	$q+(-0.555632 + 0.962383i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.944368 - 1.63569i) q^{11} +(0.500000 - 0.866025i) q^{13} +5.87636 q^{17} +7.09888 q^{19} +(1.99381 - 3.45338i) q^{23} +(1.88255 + 3.26067i) q^{25} +(0.493810 + 0.855304i) q^{29} +(0.333104 - 0.576953i) q^{31} +1.11126 q^{35} -1.33379 q^{37} +(-0.944368 + 1.63569i) q^{41} +(5.43199 + 9.40848i) q^{43} +(-5.54944 - 9.61192i) q^{47} +(-0.500000 + 0.866025i) q^{49} +12.2101 q^{53} +2.09888 q^{55} +(2.38255 - 4.12669i) q^{59} +(-1.88255 - 3.26067i) q^{61} +(0.555632 + 0.962383i) q^{65} +(-2.04944 + 3.54974i) q^{67} +10.7651 q^{71} -3.09888 q^{73} +(-0.944368 + 1.63569i) q^{77} +(-3.21565 - 5.56967i) q^{79} +(-5.93818 - 10.2852i) q^{83} +(-3.26509 + 5.65531i) q^{85} -14.3090 q^{89} -1.00000 q^{91} +(-3.94437 + 6.83185i) q^{95} +(-0.382546 - 0.662589i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) $ 6 * q - 3 * q^5 - 3 * q^7	$ 6 q - 3 q^{5} - 3 q^{7} - 6 q^{11} + 3 q^{13} + 6 q^{19} - 6 q^{23} - 6 q^{25} - 15 q^{29} + 3 q^{31} + 6 q^{35} - 6 q^{37} - 6 q^{41} - 3 q^{43} - 15 q^{47} - 3 q^{49} + 36 q^{53} - 24 q^{55} - 3 q^{59} + 6 q^{61} + 3 q^{65} + 6 q^{67} + 30 q^{71} + 18 q^{73} - 6 q^{77} - 3 q^{79} - 18 q^{83} + 15 q^{85} - 12 q^{89} - 6 q^{91} - 24 q^{95} + 15 q^{97}+O(q^{100}) $ 6 * q - 3 * q^5 - 3 * q^7 - 6 * q^11 + 3 * q^13 + 6 * q^19 - 6 * q^23 - 6 * q^25 - 15 * q^29 + 3 * q^31 + 6 * q^35 - 6 * q^37 - 6 * q^41 - 3 * q^43 - 15 * q^47 - 3 * q^49 + 36 * q^53 - 24 * q^55 - 3 * q^59 + 6 * q^61 + 3 * q^65 + 6 * q^67 + 30 * q^71 + 18 * q^73 - 6 * q^77 - 3 * q^79 - 18 * q^83 + 15 * q^85 - 12 * q^89 - 6 * q^91 - 24 * q^95 + 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.555632	+	0.962383i	−0.248486	+	0.430391i	−0.963106	−	0.269122i	$-0.913266\pi$
$5$	−0.555632	+	0.962383i	−0.248486	+	0.430391i	0.714620	+	0.699513i	$0.246600\pi$
$6$		0			0
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.944368	−	1.63569i	−0.284738	−	0.493180i	0.687808	−	0.725893i	$-0.258573\pi$
$11$	−0.944368	−	1.63569i	−0.284738	−	0.493180i	−0.972546	+	0.232713i	$0.925240\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.87636			1.42523			0.712613	−	0.701557i	$-0.247512\pi$
$17$	5.87636			1.42523			0.712613	+	0.701557i	$0.247512\pi$
$18$		0			0
$19$	7.09888			1.62860			0.814298	−	0.580447i	$-0.197122\pi$
$19$	7.09888			1.62860			0.814298	+	0.580447i	$0.197122\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.99381	−	3.45338i	0.415738	−	0.720080i	−0.579767	−	0.814782i	$-0.696857\pi$
$23$	1.99381	−	3.45338i	0.415738	−	0.720080i	0.995506	+	0.0947024i	$0.0301899\pi$
$24$		0			0
$25$	1.88255	+	3.26067i	0.376509	+	0.652133i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.493810	+	0.855304i	0.0916982	+	0.158826i	0.908226	−	0.418480i	$-0.137437\pi$
$29$	0.493810	+	0.855304i	0.0916982	+	0.158826i	−0.816528	+	0.577306i	$0.804104\pi$
$30$		0			0
$31$	0.333104	−	0.576953i	0.0598272	−	0.103624i	−0.834561	−	0.550916i	$-0.814278\pi$
$31$	0.333104	−	0.576953i	0.0598272	−	0.103624i	0.894388	+	0.447292i	$0.147612\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.11126			0.187838
$36$		0			0
$37$	−1.33379			−0.219274			−0.109637	−	0.993972i	$-0.534969\pi$
$37$	−1.33379			−0.219274			−0.109637	+	0.993972i	$0.534969\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.944368	+	1.63569i	−0.147485	+	0.255452i	−0.930297	−	0.366806i	$-0.880451\pi$
$41$	−0.944368	+	1.63569i	−0.147485	+	0.255452i	0.782812	+	0.622258i	$0.213785\pi$
$42$		0			0
$43$	5.43199	+	9.40848i	0.828370	+	1.43478i	0.899316	+	0.437299i	$0.144065\pi$
$43$	5.43199	+	9.40848i	0.828370	+	1.43478i	−0.0709455	+	0.997480i	$0.522602\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.54944	−	9.61192i	−0.809469	−	1.40204i	−0.913232	−	0.407440i	$-0.866422\pi$
$47$	−5.54944	−	9.61192i	−0.809469	−	1.40204i	0.103763	−	0.994602i	$-0.466912\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	12.2101			1.67719			0.838596	−	0.544753i	$-0.183377\pi$
$53$	12.2101			1.67719			0.838596	+	0.544753i	$0.183377\pi$
$54$		0			0
$55$	2.09888			0.283014
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.38255	−	4.12669i	0.310181	−	0.537249i	−0.668220	−	0.743963i	$-0.732944\pi$
$59$	2.38255	−	4.12669i	0.310181	−	0.537249i	0.978401	+	0.206714i	$0.0662770\pi$
$60$		0			0
$61$	−1.88255	−	3.26067i	−0.241035	−	0.417485i	0.719974	−	0.694001i	$-0.244154\pi$
$61$	−1.88255	−	3.26067i	−0.241035	−	0.417485i	−0.961009	+	0.276515i	$0.910820\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.555632	+	0.962383i	0.0689177	+	0.119369i
$66$		0			0
$67$	−2.04944	+	3.54974i	−0.250379	+	0.433670i	−0.963630	−	0.267239i	$-0.913889\pi$
$67$	−2.04944	+	3.54974i	−0.250379	+	0.433670i	0.713251	+	0.700909i	$0.247222\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	10.7651			1.27758			0.638791	−	0.769381i	$-0.279435\pi$
$71$	10.7651			1.27758			0.638791	+	0.769381i	$0.279435\pi$
$72$		0			0
$73$	−3.09888			−0.362697			−0.181348	−	0.983419i	$-0.558046\pi$
$73$	−3.09888			−0.362697			−0.181348	+	0.983419i	$0.558046\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.944368	+	1.63569i	−0.107621	+	0.186405i
$78$		0			0
$79$	−3.21565	−	5.56967i	−0.361789	−	0.626637i	0.626466	−	0.779448i	$-0.284501\pi$
$79$	−3.21565	−	5.56967i	−0.361789	−	0.626637i	−0.988255	+	0.152812i	$0.951167\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.93818	−	10.2852i	−0.651800	−	1.12895i	−0.982686	−	0.185280i	$-0.940681\pi$
$83$	−5.93818	−	10.2852i	−0.651800	−	1.12895i	0.330886	−	0.943671i	$-0.392652\pi$
$84$		0			0
$85$	−3.26509	+	5.65531i	−0.354149	+	0.613404i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−14.3090			−1.51675			−0.758377	−	0.651816i	$-0.774007\pi$
$89$	−14.3090			−1.51675			−0.758377	+	0.651816i	$0.774007\pi$
$90$		0			0
$91$	−1.00000			−0.104828
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.94437	+	6.83185i	−0.404684	+	0.700933i
$96$		0			0
$97$	−0.382546	−	0.662589i	−0.0388417	−	0.0672757i	0.845951	−	0.533261i	$-0.179033\pi$
$97$	−0.382546	−	0.662589i	−0.0388417	−	0.0672757i	−0.884793	+	0.465985i	$0.845700\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.43818	+	7.68715i	0.441615	+	0.764900i	0.997810	−	0.0661523i	$-0.0210723\pi$
$101$	4.43818	+	7.68715i	0.441615	+	0.764900i	−0.556194	+	0.831052i	$0.687739\pi$
$102$		0			0
$103$	4.98143	−	8.62809i	0.490835	−	0.850151i	−0.509109	−	0.860702i	$-0.670025\pi$
$103$	4.98143	−	8.62809i	0.490835	−	0.850151i	0.999944	+	0.0105508i	$0.00335848\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.22253			0.504881			0.252440	−	0.967612i	$-0.418767\pi$
$107$	5.22253			0.504881			0.252440	+	0.967612i	$0.418767\pi$
$108$		0			0
$109$	−9.09888			−0.871515			−0.435758	−	0.900064i	$-0.643519\pi$
$109$	−9.09888			−0.871515			−0.435758	+	0.900064i	$0.643519\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.21015	+	10.7563i	−0.584202	+	1.01187i	0.410773	+	0.911738i	$0.365259\pi$
$113$	−6.21015	+	10.7563i	−0.584202	+	1.01187i	−0.994974	+	0.100129i	$0.968074\pi$
$114$		0			0
$115$	2.21565	+	3.83762i	0.206610	+	0.357860i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.93818	−	5.08907i	−0.269342	−	0.466515i
$120$		0			0
$121$	3.71634	−	6.43689i	0.337849	−	0.585172i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−9.74033			−0.871202
$126$		0			0
$127$	7.66621			0.680266			0.340133	−	0.940377i	$-0.389528\pi$
$127$	7.66621			0.680266			0.340133	+	0.940377i	$0.389528\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.27128	+	12.5942i	−0.635295	+	1.10036i	0.351158	+	0.936316i	$0.385788\pi$
$131$	−7.27128	+	12.5942i	−0.635295	+	1.10036i	−0.986453	+	0.164047i	$0.947545\pi$
$132$		0			0
$133$	−3.54944	−	6.14781i	−0.307776	−	0.533083i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.32072	+	4.01961i	0.198273	+	0.343419i	0.947969	−	0.318364i	$-0.103133\pi$
$137$	2.32072	+	4.01961i	0.198273	+	0.343419i	−0.749696	+	0.661783i	$0.769800\pi$
$138$		0			0
$139$	9.64833	−	16.7114i	0.818360	−	1.41744i	−0.0885293	−	0.996074i	$-0.528217\pi$
$139$	9.64833	−	16.7114i	0.818360	−	1.41744i	0.906890	−	0.421368i	$-0.138450\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.88874			−0.157944
$144$		0			0
$145$	−1.09751			−0.0911430
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−6.82072	+	11.8138i	−0.558775	+	0.967828i	0.438824	+	0.898573i	$0.355395\pi$
$149$	−6.82072	+	11.8138i	−0.558775	+	0.967828i	−0.997599	+	0.0692543i	$0.977938\pi$
$150$		0			0
$151$	−8.48143	−	14.6903i	−0.690209	−	1.19548i	−0.971769	−	0.235934i	$-0.924185\pi$
$151$	−8.48143	−	14.6903i	−0.690209	−	1.19548i	0.281560	−	0.959544i	$-0.409148\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.370166	+	0.641147i	0.0297325	+	0.0514981i
$156$		0			0
$157$	−11.3145	+	19.5973i	−0.902998	+	1.56404i	−0.0794160	+	0.996842i	$0.525306\pi$
$157$	−11.3145	+	19.5973i	−0.902998	+	1.56404i	−0.823582	+	0.567197i	$0.808028\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.98762			−0.314269
$162$		0			0
$163$	−18.0989			−1.41761			−0.708807	−	0.705402i	$-0.750766\pi$
$163$	−18.0989			−1.41761			−0.708807	+	0.705402i	$0.750766\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.61126	+	14.9151i	−0.666360	+	1.15417i	0.312555	+	0.949900i	$0.398815\pi$
$167$	−8.61126	+	14.9151i	−0.666360	+	1.15417i	−0.978915	+	0.204269i	$0.934518\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.431988	−	0.748226i	−0.0328435	−	0.0568865i	0.849136	−	0.528174i	$-0.177123\pi$
$173$	−0.431988	−	0.748226i	−0.0328435	−	0.0568865i	−0.881980	+	0.471287i	$0.843790\pi$
$174$		0			0
$175$	1.88255	−	3.26067i	0.142307	−	0.246483i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.67859			0.349694			0.174847	−	0.984596i	$-0.444057\pi$
$179$	4.67859			0.349694			0.174847	+	0.984596i	$0.444057\pi$
$180$		0			0
$181$	−16.8640			−1.25349			−0.626745	−	0.779225i	$-0.715613\pi$
$181$	−16.8640			−1.25349			−0.626745	+	0.779225i	$0.715613\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.741098	−	1.28362i	0.0544866	−	0.0943736i
$186$		0			0
$187$	−5.54944	−	9.61192i	−0.405815	−	0.702893i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.53087	−	14.7759i	−0.617272	−	1.06915i	−0.989981	−	0.141199i	$-0.954904\pi$
$191$	−8.53087	−	14.7759i	−0.617272	−	1.06915i	0.372709	−	0.927948i	$-0.378429\pi$
$192$		0			0
$193$	−3.71634	+	6.43689i	−0.267508	+	0.463337i	−0.968218	−	0.250109i	$-0.919533\pi$
$193$	−3.71634	+	6.43689i	−0.267508	+	0.463337i	0.700710	+	0.713446i	$0.252867\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	26.2953			1.87346			0.936730	−	0.350052i	$-0.113836\pi$
$197$	26.2953			1.87346			0.936730	+	0.350052i	$0.113836\pi$
$198$		0			0
$199$	10.4327			0.739553			0.369776	−	0.929121i	$-0.379434\pi$
$199$	10.4327			0.739553			0.369776	+	0.929121i	$0.379434\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.493810	−	0.855304i	0.0346587	−	0.0600306i
$204$		0			0
$205$	−1.04944	−	1.81769i	−0.0732962	−	0.126953i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.70396	−	11.6116i	−0.463723	−	0.803191i
$210$		0			0
$211$	−12.6978	+	21.9932i	−0.874150	+	1.51407i	−0.0164855	+	0.999864i	$0.505248\pi$
$211$	−12.6978	+	21.9932i	−0.874150	+	1.51407i	−0.857665	+	0.514209i	$0.828086\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−12.0727			−0.823355
$216$		0			0
$217$	−0.666208			−0.0452251
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.93818	−	5.08907i	0.197643	−	0.342328i
$222$		0			0
$223$	−7.26509	−	12.5835i	−0.486507	−	0.842654i	0.513373	−	0.858165i	$-0.328396\pi$
$223$	−7.26509	−	12.5835i	−0.486507	−	0.842654i	−0.999880	+	0.0155114i	$0.995062\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.70396	+	16.8077i	0.644074	+	1.11557i	0.984514	+	0.175303i	$0.0560906\pi$
$227$	9.70396	+	16.8077i	0.644074	+	1.11557i	−0.340440	+	0.940266i	$0.610576\pi$
$228$		0			0
$229$	5.26509	−	9.11941i	0.347927	−	0.602627i	−0.637954	−	0.770074i	$-0.720219\pi$
$229$	5.26509	−	9.11941i	0.347927	−	0.602627i	0.985881	+	0.167447i	$0.0535523\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−22.6414			−1.48329			−0.741645	−	0.670792i	$-0.765954\pi$
$233$	−22.6414			−1.48329			−0.741645	+	0.670792i	$0.765954\pi$
$234$		0			0
$235$	12.3338			0.804568
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.48762	−	4.30868i	0.160911	−	0.278706i	−0.774285	−	0.632837i	$-0.781890\pi$
$239$	2.48762	−	4.30868i	0.160911	−	0.278706i	0.935196	+	0.354132i	$0.115224\pi$
$240$		0			0
$241$	−0.117454	−	0.203436i	−0.00756588	−	0.0131045i	0.862218	−	0.506538i	$-0.169075\pi$
$241$	−0.117454	−	0.203436i	−0.00756588	−	0.0131045i	−0.869784	+	0.493433i	$0.835742\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.555632	−	0.962383i	−0.0354980	−	0.0614844i
$246$		0			0
$247$	3.54944	−	6.14781i	0.225846	−	0.391176i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	8.09888			0.511197			0.255599	−	0.966783i	$-0.417727\pi$
$251$	8.09888			0.511197			0.255599	+	0.966783i	$0.417727\pi$
$252$		0			0
$253$	−7.53156			−0.473505
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.8764	−	20.5705i	0.740827	−	1.28315i	−0.211293	−	0.977423i	$-0.567767\pi$
$257$	11.8764	−	20.5705i	0.740827	−	1.28315i	0.952119	−	0.305727i	$-0.0988994\pi$
$258$		0			0
$259$	0.666896	+	1.15510i	0.0414389	+	0.0717743i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.32691	−	5.76238i	−0.205146	−	0.355324i	0.745033	−	0.667028i	$-0.232434\pi$
$263$	−3.32691	−	5.76238i	−0.205146	−	0.355324i	−0.950179	+	0.311704i	$0.899100\pi$
$264$		0			0
$265$	−6.78435	+	11.7508i	−0.416759	+	0.721848i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−18.9876			−1.15770			−0.578848	−	0.815436i	$-0.696497\pi$
$269$	−18.9876			−1.15770			−0.578848	+	0.815436i	$0.696497\pi$
$270$		0			0
$271$	−22.3338			−1.35668			−0.678341	−	0.734748i	$-0.737301\pi$
$271$	−22.3338			−1.35668			−0.678341	+	0.734748i	$0.737301\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.55563	−	6.15854i	0.214413	−	0.371374i
$276$		0			0
$277$	15.9134	+	27.5628i	0.956145	+	1.65609i	0.731727	+	0.681598i	$0.238715\pi$
$277$	15.9134	+	27.5628i	0.956145	+	1.65609i	0.224418	+	0.974493i	$0.427952\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	9.92580	+	17.1920i	0.592123	+	1.02559i	0.993946	+	0.109870i	$0.0350436\pi$
$281$	9.92580	+	17.1920i	0.592123	+	1.02559i	−0.401822	+	0.915718i	$0.631623\pi$
$282$		0			0
$283$	1.56801	−	2.71588i	0.0932086	−	0.161442i	−0.815651	−	0.578544i	$-0.803621\pi$
$283$	1.56801	−	2.71588i	0.0932086	−	0.161442i	0.908860	+	0.417102i	$0.136954\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.88874			0.111489
$288$		0			0
$289$	17.5316			1.03127
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.93887	−	8.55437i	0.288532	−	0.499752i	−0.684928	−	0.728611i	$-0.740166\pi$
$293$	4.93887	−	8.55437i	0.288532	−	0.499752i	0.973459	+	0.228859i	$0.0734996\pi$
$294$		0			0
$295$	2.64764	+	4.58584i	0.154151	+	0.266998i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.99381	−	3.45338i	−0.115305	−	0.199714i
$300$		0			0
$301$	5.43199	−	9.40848i	0.313095	−	0.542296i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.18401			0.239576
$306$		0			0
$307$	15.4313			0.880711			0.440355	−	0.897824i	$-0.354852\pi$
$307$	15.4313			0.880711			0.440355	+	0.897824i	$0.354852\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	8.83310	−	15.2994i	0.500879	−	0.867549i	−0.499120	−	0.866533i	$-0.666343\pi$
$311$	8.83310	−	15.2994i	0.500879	−	0.867549i	0.999999	−	0.00101570i	$-0.000323307\pi$
$312$		0			0
$313$	−6.71634	−	11.6330i	−0.379630	−	0.657538i	0.611378	−	0.791338i	$-0.290615\pi$
$313$	−6.71634	−	11.6330i	−0.379630	−	0.657538i	−0.991008	+	0.133800i	$0.957282\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.93199	+	13.7386i	0.445505	+	0.771637i	0.998087	−	0.0618213i	$-0.0196909\pi$
$317$	7.93199	+	13.7386i	0.445505	+	0.771637i	−0.552582	+	0.833458i	$0.686358\pi$
$318$		0			0
$319$	0.932677	−	1.61544i	0.0522199	−	0.0904475i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	41.7156			2.32112
$324$		0			0
$325$	3.76509			0.208850
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.54944	+	9.61192i	−0.305951	+	0.529922i
$330$		0			0
$331$	9.04944	+	15.6741i	0.497402	+	0.861526i	0.999996	−	0.00299694i	$-0.000953957\pi$
$331$	9.04944	+	15.6741i	0.497402	+	0.861526i	−0.502593	+	0.864523i	$0.667621\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.27747	−	3.94470i	−0.124432	−	0.215522i
$336$		0			0
$337$	0.518570	−	0.898189i	0.0282483	−	0.0489275i	−0.851556	−	0.524264i	$-0.824340\pi$
$337$	0.518570	−	0.898189i	0.0282483	−	0.0489275i	0.879804	+	0.475337i	$0.157674\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.25829			−0.0681402
$342$		0			0
$343$	1.00000			0.0539949
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.9821	+	19.0216i	−0.589551	+	1.02113i	0.404740	+	0.914432i	$0.367362\pi$
$347$	−10.9821	+	19.0216i	−0.589551	+	1.02113i	−0.994291	+	0.106701i	$0.965971\pi$
$348$		0			0
$349$	−11.7651	−	20.3777i	−0.629771	−	1.09080i	−0.987597	−	0.157007i	$-0.949815\pi$
$349$	−11.7651	−	20.3777i	−0.629771	−	1.09080i	0.357827	−	0.933788i	$-0.383518\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	14.7713	+	25.5846i	0.786196	+	1.36173i	0.928282	+	0.371877i	$0.121286\pi$
$353$	14.7713	+	25.5846i	0.786196	+	1.36173i	−0.142086	+	0.989854i	$0.545381\pi$
$354$		0			0
$355$	−5.98143	+	10.3601i	−0.317461	+	0.549859i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−34.0741			−1.79836			−0.899182	−	0.437575i	$-0.855837\pi$
$359$	−34.0741			−1.79836			−0.899182	+	0.437575i	$0.855837\pi$
$360$		0			0
$361$	31.3942			1.65232
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.72184	−	2.98231i	0.0901252	−	0.156101i
$366$		0			0
$367$	13.5309	+	23.4362i	0.706306	+	1.22336i	0.966218	+	0.257725i	$0.0829730\pi$
$367$	13.5309	+	23.4362i	0.706306	+	1.22336i	−0.259912	+	0.965632i	$0.583694\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.10507	−	10.5743i	−0.316960	−	0.548990i
$372$		0			0
$373$	5.43199	−	9.40848i	0.281258	−	0.487153i	−0.690437	−	0.723392i	$-0.742582\pi$
$373$	5.43199	−	9.40848i	0.281258	−	0.487153i	0.971695	+	0.236240i	$0.0759151\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.987620			0.0508650
$378$		0			0
$379$	0.765092			0.0393001			0.0196501	−	0.999807i	$-0.493745\pi$
$379$	0.765092			0.0393001			0.0196501	+	0.999807i	$0.493745\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.87704	−	8.44729i	0.249205	−	0.431636i	−0.714100	−	0.700043i	$-0.753164\pi$
$383$	4.87704	−	8.44729i	0.249205	−	0.431636i	0.963306	+	0.268407i	$0.0864973\pi$
$384$		0			0
$385$	−1.04944	−	1.81769i	−0.0534845	−	0.0926379i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−12.3269	−	21.3508i	−0.624999	−	1.08253i	−0.988541	−	0.150953i	$-0.951766\pi$
$389$	−12.3269	−	21.3508i	−0.624999	−	1.08253i	0.363542	−	0.931578i	$-0.381567\pi$
$390$		0			0
$391$	11.7163	−	20.2933i	0.592521	−	1.02628i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	7.14687			0.359598
$396$		0			0
$397$	14.1964			0.712496			0.356248	−	0.934391i	$-0.384056\pi$
$397$	14.1964			0.712496			0.356248	+	0.934391i	$0.384056\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.4746	−	33.7309i	0.972513	−	1.68444i	0.284603	−	0.958646i	$-0.408138\pi$
$401$	19.4746	−	33.7309i	0.972513	−	1.68444i	0.687910	−	0.725796i	$-0.258528\pi$
$402$		0			0
$403$	−0.333104	−	0.576953i	−0.0165931	−	0.0287401i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.25959	+	2.18168i	0.0624356	+	0.108142i
$408$		0			0
$409$	4.09888	−	7.09948i	0.202677	−	0.351047i	−0.746713	−	0.665146i	$-0.768369\pi$
$409$	4.09888	−	7.09948i	0.202677	−	0.351047i	0.949390	+	0.314100i	$0.101703\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.76509			−0.234475
$414$		0			0
$415$	13.1978			0.647853
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−0.228718	+	0.396151i	−0.0111736	+	0.0193533i	−0.871558	−	0.490292i	$-0.836890\pi$
$419$	−0.228718	+	0.396151i	−0.0111736	+	0.0193533i	0.860385	+	0.509645i	$0.170223\pi$
$420$		0			0
$421$	9.31453	+	16.1332i	0.453963	+	0.786286i	0.998628	−	0.0523672i	$-0.0166766\pi$
$421$	9.31453	+	16.1332i	0.453963	+	0.786286i	−0.544665	+	0.838654i	$0.683343\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	11.0625	+	19.1608i	0.536611	+	0.929437i
$426$		0			0
$427$	−1.88255	+	3.26067i	−0.0911028	+	0.157795i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.5178			−0.506625			−0.253312	−	0.967385i	$-0.581520\pi$
$431$	−10.5178			−0.506625			−0.253312	+	0.967385i	$0.581520\pi$
$432$		0			0
$433$	−2.80223			−0.134667			−0.0673333	−	0.997731i	$-0.521449\pi$
$433$	−2.80223			−0.134667			−0.0673333	+	0.997731i	$0.521449\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	14.1538	−	24.5151i	0.677069	−	1.17272i
$438$		0			0
$439$	−2.14764	−	3.71982i	−0.102501	−	0.177537i	0.810213	−	0.586135i	$-0.199351\pi$
$439$	−2.14764	−	3.71982i	−0.102501	−	0.177537i	−0.912715	+	0.408598i	$0.866018\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	11.0989	+	19.2238i	0.527324	+	0.913352i	0.999493	+	0.0318437i	$0.0101379\pi$
$443$	11.0989	+	19.2238i	0.527324	+	0.913352i	−0.472169	+	0.881508i	$0.656529\pi$
$444$		0			0
$445$	7.95056	−	13.7708i	0.376893	−	0.652797i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−13.4313			−0.633862			−0.316931	−	0.948449i	$-0.602652\pi$
$449$	−13.4313			−0.633862			−0.316931	+	0.948449i	$0.602652\pi$
$450$		0			0
$451$	3.56732			0.167979
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.555632	−	0.962383i	0.0260484	−	0.0451172i
$456$		0			0
$457$	−7.45056	−	12.9047i	−0.348522	−	0.603658i	0.637465	−	0.770479i	$-0.279983\pi$
$457$	−7.45056	−	12.9047i	−0.348522	−	0.603658i	−0.985987	+	0.166821i	$0.946650\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.39561	+	5.88138i	0.158150	+	0.273923i	0.934201	−	0.356746i	$-0.116114\pi$
$461$	3.39561	+	5.88138i	0.158150	+	0.273923i	−0.776052	+	0.630669i	$0.782781\pi$
$462$		0			0
$463$	−2.21634	+	3.83881i	−0.103002	+	0.178405i	−0.912920	−	0.408138i	$-0.866178\pi$
$463$	−2.21634	+	3.83881i	−0.103002	+	0.178405i	0.809918	+	0.586543i	$0.199511\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	26.4189			1.22252			0.611261	−	0.791429i	$-0.290663\pi$
$467$	26.4189			1.22252			0.611261	+	0.791429i	$0.290663\pi$
$468$		0			0
$469$	4.09888			0.189269
$470$		0			0
$471$		0			0
$472$		0			0
$473$	10.2596	−	17.7701i	0.471736	−	0.817072i
$474$		0			0
$475$	13.3640	+	23.1471i	0.613181	+	1.06206i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.75959	−	4.77975i	−0.126089	−	0.218392i	0.796069	−	0.605206i	$-0.206909\pi$
$479$	−2.75959	−	4.77975i	−0.126089	−	0.218392i	−0.922158	+	0.386813i	$0.873576\pi$
$480$		0			0
$481$	−0.666896	+	1.15510i	−0.0304079	+	0.0526679i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.850219			0.0386065
$486$		0			0
$487$	−40.4930			−1.83492			−0.917458	−	0.397834i	$-0.869762\pi$
$487$	−40.4930			−1.83492			−0.917458	+	0.397834i	$0.869762\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.555632	−	0.962383i	0.0250753	−	0.0434317i	−0.853215	−	0.521559i	$-0.825351\pi$
$491$	0.555632	−	0.962383i	0.0250753	−	0.0434317i	0.878291	+	0.478127i	$0.158684\pi$
$492$		0			0
$493$	2.90180	+	5.02607i	0.130691	+	0.226363i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.38255	−	9.32284i	−0.241440	−	0.418187i
$498$		0			0
$499$	−1.33379	+	2.31020i	−0.0597088	+	0.103419i	−0.894335	−	0.447399i	$-0.852351\pi$
$499$	−1.33379	+	2.31020i	−0.0597088	+	0.103419i	0.834626	+	0.550817i	$0.185684\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.86398			−0.439813			−0.219906	−	0.975521i	$-0.570575\pi$
$503$	−9.86398			−0.439813			−0.219906	+	0.975521i	$0.570575\pi$
$504$		0			0
$505$	−9.86398			−0.438941
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.99381	−	8.64953i	0.221347	−	0.383384i	−0.733870	−	0.679289i	$-0.762288\pi$
$509$	4.99381	−	8.64953i	0.221347	−	0.383384i	0.955217	+	0.295906i	$0.0956214\pi$
$510$		0			0
$511$	1.54944	+	2.68371i	0.0685433	+	0.118720i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	5.53569	+	9.58809i	0.243931	+	0.422502i
$516$		0			0
$517$	−10.4814	+	18.1544i	−0.460973	+	0.798428i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−38.7527			−1.69779			−0.848894	−	0.528564i	$-0.822731\pi$
$521$	−38.7527			−1.69779			−0.848894	+	0.528564i	$0.822731\pi$
$522$		0			0
$523$	−19.6304			−0.858379			−0.429190	−	0.903214i	$-0.641201\pi$
$523$	−19.6304			−0.858379			−0.429190	+	0.903214i	$0.641201\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.95744	−	3.39038i	0.0852673	−	0.147687i
$528$		0			0
$529$	3.54944	+	6.14781i	0.154324	+	0.267296i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.944368	+	1.63569i	0.0409051	+	0.0708497i
$534$		0			0
$535$	−2.90180	+	5.02607i	−0.125456	+	0.217296i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.88874			0.0813536
$540$		0			0
$541$	−0.332415			−0.0142916			−0.00714582	−	0.999974i	$-0.502275\pi$
$541$	−0.332415			−0.0142916			−0.00714582	+	0.999974i	$0.502275\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.05563	−	8.75661i	0.216559	−	0.375092i
$546$		0			0
$547$	13.6476	+	23.6384i	0.583531	+	1.01071i	0.995057	+	0.0993071i	$0.0316626\pi$
$547$	13.6476	+	23.6384i	0.583531	+	1.01071i	−0.411526	+	0.911398i	$0.635004\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	3.50550	+	6.07171i	0.149339	+	0.258663i
$552$		0			0
$553$	−3.21565	+	5.56967i	−0.136743	+	0.236846i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	31.4079			1.33080			0.665398	−	0.746489i	$-0.268262\pi$
$557$	31.4079			1.33080			0.665398	+	0.746489i	$0.268262\pi$
$558$		0			0
$559$	10.8640			0.459497
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.8331	−	20.4955i	0.498706	−	0.863784i	−0.501293	−	0.865278i	$-0.667142\pi$
$563$	11.8331	−	20.4955i	0.498706	−	0.863784i	0.999999	+	0.00149369i	$0.000475458\pi$
$564$		0			0
$565$	−6.90112	−	11.9531i	−0.290332	−	0.502870i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.36398	−	4.09453i	−0.0991030	−	0.171652i	0.812211	−	0.583364i	$-0.198264\pi$
$569$	−2.36398	−	4.09453i	−0.0991030	−	0.171652i	−0.911314	+	0.411713i	$0.864931\pi$
$570$		0			0
$571$	−6.38255	+	11.0549i	−0.267101	+	0.462633i	−0.968112	−	0.250518i	$-0.919399\pi$
$571$	−6.38255	+	11.0549i	−0.267101	+	0.462633i	0.701011	+	0.713151i	$0.252732\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	15.0138			0.626117
$576$		0			0
$577$	−10.6304			−0.442551			−0.221276	−	0.975211i	$-0.571022\pi$
$577$	−10.6304			−0.442551			−0.221276	+	0.975211i	$0.571022\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−5.93818	+	10.2852i	−0.246357	+	0.426703i
$582$		0			0
$583$	−11.5309	−	19.9721i	−0.477560	−	0.827158i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.80834	+	3.13214i	0.0746384	+	0.129277i	0.900929	−	0.433967i	$-0.142886\pi$
$587$	1.80834	+	3.13214i	0.0746384	+	0.129277i	−0.826291	+	0.563244i	$0.809553\pi$
$588$		0			0
$589$	2.36467	−	4.09572i	0.0974343	−	0.168761i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−22.6786			−0.931298			−0.465649	−	0.884970i	$-0.654179\pi$
$593$	−22.6786			−0.931298			−0.465649	+	0.884970i	$0.654179\pi$
$594$		0			0
$595$	6.53018			0.267711
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−20.2953	+	35.1524i	−0.829242	+	1.43629i	0.0693908	+	0.997590i	$0.477894\pi$
$599$	−20.2953	+	35.1524i	−0.829242	+	1.43629i	−0.898633	+	0.438701i	$0.855439\pi$
$600$		0			0
$601$	−6.59957	−	11.4308i	−0.269202	−	0.466272i	0.699454	−	0.714678i	$-0.253427\pi$
$601$	−6.59957	−	11.4308i	−0.269202	−	0.466272i	−0.968656	+	0.248406i	$0.920093\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	4.12983	+	7.15308i	0.167902	+	0.290814i
$606$		0			0
$607$	0.833792	−	1.44417i	0.0338426	−	0.0586171i	−0.848608	−	0.529022i	$-0.822559\pi$
$607$	0.833792	−	1.44417i	0.0338426	−	0.0586171i	0.882451	+	0.470405i	$0.155892\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−11.0989			−0.449013
$612$		0			0
$613$	22.9257			0.925961			0.462981	−	0.886368i	$-0.346780\pi$
$613$	22.9257			0.925961			0.462981	+	0.886368i	$0.346780\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−5.37567	+	9.31093i	−0.216416	+	0.374844i	−0.953710	−	0.300729i	$-0.902770\pi$
$617$	−5.37567	+	9.31093i	−0.216416	+	0.374844i	0.737294	+	0.675573i	$0.236103\pi$
$618$		0			0
$619$	−12.9814	−	22.4845i	−0.521768	−	0.903728i	−0.999679	−	0.0253203i	$-0.991939\pi$
$619$	−12.9814	−	22.4845i	−0.521768	−	0.903728i	0.477912	−	0.878408i	$-0.341394\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	7.15452	+	12.3920i	0.286640	+	0.496474i
$624$		0			0
$625$	−4.00069	+	6.92940i	−0.160028	+	0.277176i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−7.83784			−0.312515
$630$		0			0
$631$	3.00138			0.119483			0.0597415	−	0.998214i	$-0.480972\pi$
$631$	3.00138			0.119483			0.0597415	+	0.998214i	$0.480972\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.25959	+	7.37783i	−0.169037	+	0.292780i
$636$		0			0
$637$	0.500000	+	0.866025i	0.0198107	+	0.0343132i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.77266	+	11.7306i	0.267504	+	0.463330i	0.968217	−	0.250113i	$-0.0804678\pi$
$641$	6.77266	+	11.7306i	0.267504	+	0.463330i	−0.700713	+	0.713444i	$0.747134\pi$
$642$		0			0
$643$	−17.4814	+	30.2787i	−0.689400	+	1.19408i	0.282632	+	0.959228i	$0.408793\pi$
$643$	−17.4814	+	30.2787i	−0.689400	+	1.19408i	−0.972032	+	0.234848i	$0.924541\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−25.9890			−1.02173			−0.510866	−	0.859660i	$-0.670675\pi$
$647$	−25.9890			−1.02173			−0.510866	+	0.859660i	$0.670675\pi$
$648$		0			0
$649$	−9.00000			−0.353281
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.93818	+	5.08907i	−0.114980	+	0.199151i	−0.917772	−	0.397108i	$-0.870014\pi$
$653$	−2.93818	+	5.08907i	−0.114980	+	0.199151i	0.802792	+	0.596259i	$0.203347\pi$
$654$		0			0
$655$	−8.08031	−	13.9955i	−0.315724	−	0.546850i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−20.6359	−	35.7425i	−0.803862	−	1.39233i	−0.917056	−	0.398758i	$-0.869441\pi$
$659$	−20.6359	−	35.7425i	−0.803862	−	1.39233i	0.113194	−	0.993573i	$-0.463892\pi$
$660$		0			0
$661$	18.4814	−	32.0108i	0.718844	−	1.24507i	−0.242614	−	0.970123i	$-0.578005\pi$
$661$	18.4814	−	32.0108i	0.718844	−	1.24507i	0.961458	−	0.274952i	$-0.0886619\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	7.88874			0.305912
$666$		0			0
$667$	3.93825			0.152490
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−3.55563	+	6.15854i	−0.137264	+	0.237748i
$672$		0			0
$673$	−22.6971	−	39.3125i	−0.874908	−	1.51539i	−0.856861	−	0.515548i	$-0.827588\pi$
$673$	−22.6971	−	39.3125i	−0.874908	−	1.51539i	−0.0180476	−	0.999837i	$-0.505745\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.14764	+	1.98777i	0.0441073	+	0.0763961i	0.887236	−	0.461315i	$-0.152622\pi$
$677$	1.14764	+	1.98777i	0.0441073	+	0.0763961i	−0.843129	+	0.537711i	$0.819289\pi$
$678$		0			0
$679$	−0.382546	+	0.662589i	−0.0146808	+	0.0254278i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−32.1483			−1.23012			−0.615059	−	0.788481i	$-0.710868\pi$
$683$	−32.1483			−1.23012			−0.615059	+	0.788481i	$0.710868\pi$
$684$		0			0
$685$	−5.15787			−0.197072
$686$		0			0
$687$		0			0
$688$		0			0
$689$	6.10507	−	10.5743i	0.232585	−	0.402849i
$690$		0			0
$691$	3.40180	+	5.89210i	0.129411	+	0.224146i	0.923448	−	0.383723i	$-0.125358\pi$
$691$	3.40180	+	5.89210i	0.129411	+	0.224146i	−0.794038	+	0.607869i	$0.792025\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	10.7218	+	18.5708i	0.406703	+	0.704429i
$696$		0			0
$697$	−5.54944	+	9.61192i	−0.210200	+	0.364077i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−42.5933			−1.60873			−0.804363	−	0.594137i	$-0.797493\pi$
$701$	−42.5933			−1.60873			−0.804363	+	0.594137i	$0.797493\pi$
$702$		0			0
$703$	−9.46844			−0.357109
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.43818	−	7.68715i	0.166915	−	0.289105i
$708$		0			0
$709$	2.56732	+	4.44673i	0.0964178	+	0.167001i	0.910199	−	0.414170i	$-0.135928\pi$
$709$	2.56732	+	4.44673i	0.0964178	+	0.167001i	−0.813782	+	0.581171i	$0.802595\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.32829	−	2.30067i	−0.0497449	−	0.0861607i
$714$		0			0
$715$	1.04944	−	1.81769i	0.0392469	−	0.0679776i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−23.6057			−0.880344			−0.440172	−	0.897914i	$-0.645082\pi$
$719$	−23.6057			−0.880344			−0.440172	+	0.897914i	$0.645082\pi$
$720$		0			0
$721$	−9.96286			−0.371036
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.85924	+	3.22030i	−0.0690505	+	0.119599i
$726$		0			0
$727$	−0.000688709	−	0.00119288i	−2.55428e−5	−	4.42414e-5i	0.866013	−	0.500022i	$-0.166675\pi$
$727$	−0.000688709	−	0.00119288i	−2.55428e−5	−	4.42414e-5i	−0.866038	+	0.499978i	$0.833341\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	31.9203	+	55.2876i	1.18061	+	2.04488i
$732$		0			0
$733$	10.6978	−	18.5291i	0.395131	−	0.684387i	−0.597987	−	0.801506i	$-0.704032\pi$
$733$	10.6978	−	18.5291i	0.395131	−	0.684387i	0.993118	+	0.117119i	$0.0373658\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.74171			0.285170
$738$		0			0
$739$	−32.0232			−1.17799			−0.588997	−	0.808135i	$-0.700477\pi$
$739$	−32.0232			−1.17799			−0.588997	+	0.808135i	$0.700477\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−25.2596	+	43.7509i	−0.926685	+	1.60506i	−0.137855	+	0.990452i	$0.544021\pi$
$743$	−25.2596	+	43.7509i	−0.926685	+	1.60506i	−0.788829	+	0.614612i	$0.789312\pi$
$744$		0			0
$745$	−7.57963	−	13.1283i	−0.277696	−	0.480984i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.61126	−	4.52284i	−0.0954135	−	0.165261i
$750$		0			0
$751$	−20.3145	+	35.1858i	−0.741288	+	1.28395i	0.210621	+	0.977568i	$0.432451\pi$
$751$	−20.3145	+	35.1858i	−0.741288	+	1.28395i	−0.951909	+	0.306381i	$0.900882\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	18.8502			0.686030
$756$		0			0
$757$	−7.90112			−0.287171			−0.143585	−	0.989638i	$-0.545863\pi$
$757$	−7.90112			−0.287171			−0.143585	+	0.989638i	$0.545863\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	11.0124	−	19.0740i	0.399198	−	0.691432i	−0.594429	−	0.804148i	$-0.702622\pi$
$761$	11.0124	−	19.0740i	0.399198	−	0.691432i	0.993627	+	0.112716i	$0.0359551\pi$
$762$		0			0
$763$	4.54944	+	7.87987i	0.164701	+	0.285270i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.38255	−	4.12669i	−0.0860287	−	0.149006i
$768$		0			0
$769$	24.4127	−	42.2841i	0.880346	−	1.52480i	0.0293884	−	0.999568i	$-0.490644\pi$
$769$	24.4127	−	42.2841i	0.880346	−	1.52480i	0.850957	−	0.525235i	$-0.176023\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−34.4807			−1.24018			−0.620092	−	0.784529i	$-0.712905\pi$
$773$	−34.4807			−1.24018			−0.620092	+	0.784529i	$0.712905\pi$
$774$		0			0
$775$	2.50833			0.0901020
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−6.70396	+	11.6116i	−0.240194	+	0.416029i
$780$		0			0
$781$	−10.1662	−	17.6084i	−0.363776	−	0.630078i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−12.5734	−	21.7778i	−0.448765	−	0.777284i
$786$		0			0
$787$	−5.86329	+	10.1555i	−0.209004	+	0.362005i	−0.951401	−	0.307955i	$-0.900355\pi$
$787$	−5.86329	+	10.1555i	−0.209004	+	0.362005i	0.742397	+	0.669960i	$0.233689\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	12.4203			0.441615
$792$		0			0
$793$	−3.76509			−0.133702
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−26.1236	+	45.2473i	−0.925344	+	1.60274i	−0.134338	+	0.990936i	$0.542891\pi$
$797$	−26.1236	+	45.2473i	−0.925344	+	1.60274i	−0.791007	+	0.611808i	$0.790443\pi$
$798$		0			0
$799$	−32.6105	−	56.4830i	−1.15368	−	1.99823i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.92649	+	5.06882i	0.103273	+	0.178875i
$804$		0			0
$805$	2.21565	−	3.83762i	0.0780914	−	0.135258i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	30.5439			1.07387			0.536934	−	0.843624i	$-0.319582\pi$
$809$	30.5439			1.07387			0.536934	+	0.843624i	$0.319582\pi$
$810$		0			0
$811$	−27.9629			−0.981909			−0.490954	−	0.871185i	$-0.663352\pi$
$811$	−27.9629			−0.981909			−0.490954	+	0.871185i	$0.663352\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.0563	−	17.4181i	0.352258	−	0.610128i
$816$		0			0
$817$	38.5611	+	66.7897i	1.34908	+	2.33668i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.78435	−	6.55469i	−0.132075	−	0.228760i	0.792401	−	0.610000i	$-0.208831\pi$
$821$	−3.78435	−	6.55469i	−0.132075	−	0.228760i	−0.924476	+	0.381240i	$0.875497\pi$
$822$		0			0
$823$	18.1978	−	31.5195i	0.634334	−	1.09870i	−0.352321	−	0.935879i	$-0.614608\pi$
$823$	18.1978	−	31.5195i	0.634334	−	1.09870i	0.986656	−	0.162820i	$-0.0520591\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.36955			0.0823975			0.0411987	−	0.999151i	$-0.486882\pi$
$827$	2.36955			0.0823975			0.0411987	+	0.999151i	$0.486882\pi$
$828$		0			0
$829$	−22.2335			−0.772202			−0.386101	−	0.922456i	$-0.626178\pi$
$829$	−22.2335			−0.772202			−0.386101	+	0.922456i	$0.626178\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.93818	+	5.08907i	−0.101802	+	0.176326i
$834$		0			0
$835$	−9.56939	−	16.5747i	−0.331162	−	0.573590i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−6.05494	−	10.4875i	−0.209040	−	0.362068i	0.742372	−	0.669987i	$-0.233701\pi$
$839$	−6.05494	−	10.4875i	−0.209040	−	0.362068i	−0.951412	+	0.307920i	$0.900367\pi$
$840$		0			0
$841$	14.0123	−	24.2700i	0.483183	−	0.836897i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−13.3352			−0.458744
$846$		0			0
$847$	−7.43268			−0.255390
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.65933	+	4.60609i	−0.0911606	+	0.157895i
$852$		0			0
$853$	16.5494	+	28.6645i	0.566642	+	0.981453i	0.996895	+	0.0787444i	$0.0250911\pi$
$853$	16.5494	+	28.6645i	0.566642	+	0.981453i	−0.430253	+	0.902708i	$0.641576\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.77128	+	15.1923i	0.299621	+	0.518959i	0.976049	−	0.217549i	$-0.0698063\pi$
$857$	8.77128	+	15.1923i	0.299621	+	0.518959i	−0.676428	+	0.736509i	$0.736473\pi$
$858$		0			0
$859$	−6.93130	+	12.0054i	−0.236493	+	0.409618i	−0.959705	−	0.281008i	$-0.909331\pi$
$859$	−6.93130	+	12.0054i	−0.236493	+	0.409618i	0.723213	+	0.690625i	$0.242665\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.9890			0.374070			0.187035	−	0.982353i	$-0.440112\pi$
$863$	10.9890			0.374070			0.187035	+	0.982353i	$0.440112\pi$
$864$		0			0
$865$	0.960106			0.0326446
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.07351	+	10.5196i	−0.206030	+	0.356854i
$870$		0			0
$871$	2.04944	+	3.54974i	0.0694427	+	0.120278i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.87017	+	8.43538i	0.164642	+	0.285168i
$876$		0			0
$877$	−12.2472	+	21.2128i	−0.413559	+	0.716305i	−0.995276	−	0.0970861i	$-0.969048\pi$
$877$	−12.2472	+	21.2128i	−0.413559	+	0.716305i	0.581717	+	0.813391i	$0.302381\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	19.9243			0.671268			0.335634	−	0.941992i	$-0.391049\pi$
$881$	19.9243			0.671268			0.335634	+	0.941992i	$0.391049\pi$
$882$		0			0
$883$	39.5316			1.33034			0.665171	−	0.746691i	$-0.268358\pi$
$883$	39.5316			1.33034			0.665171	+	0.746691i	$0.268358\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−20.5378	+	35.5724i	−0.689590	+	1.19441i	0.282380	+	0.959303i	$0.408876\pi$
$887$	−20.5378	+	35.5724i	−0.689590	+	1.19441i	−0.971971	+	0.235103i	$0.924457\pi$
$888$		0			0
$889$	−3.83310	−	6.63913i	−0.128558	−	0.222669i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−39.3948	−	68.2339i	−1.31830	−	2.28336i
$894$		0			0
$895$	−2.59957	+	4.50259i	−0.0868941	+	0.150505i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.657960			0.0219442
$900$		0			0
$901$	71.7512			2.39038
$902$		0			0
$903$		0			0
$904$		0			0
$905$	9.37017	−	16.2296i	0.311475	−	0.539490i
$906$		0			0
$907$	5.83242	+	10.1020i	0.193662	+	0.335433i	0.946461	−	0.322818i	$-0.104630\pi$
$907$	5.83242	+	10.1020i	0.193662	+	0.335433i	−0.752799	+	0.658250i	$0.771297\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−20.8028	−	36.0316i	−0.689229	−	1.19378i	−0.972088	−	0.234618i	$-0.924616\pi$
$911$	−20.8028	−	36.0316i	−0.689229	−	1.19378i	0.282859	−	0.959162i	$-0.408717\pi$
$912$		0			0
$913$	−11.2156	+	19.4261i	−0.371184	+	0.642909i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.5426			0.480238
$918$		0			0
$919$	−28.3338			−0.934646			−0.467323	−	0.884087i	$-0.654781\pi$
$919$	−28.3338			−0.934646			−0.467323	+	0.884087i	$0.654781\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.38255	−	9.32284i	0.177169	−	0.306865i
$924$		0			0
$925$	−2.51093	−	4.34905i	−0.0825587	−	0.142996i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	14.9127	+	25.8296i	0.489271	+	0.847442i	0.999924	−	0.0123450i	$-0.00392964\pi$
$929$	14.9127	+	25.8296i	0.489271	+	0.847442i	−0.510653	+	0.859787i	$0.670596\pi$
$930$		0			0
$931$	−3.54944	+	6.14781i	−0.116328	+	0.201486i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	12.3338			0.403358
$936$		0			0
$937$	−2.56870			−0.0839158			−0.0419579	−	0.999119i	$-0.513360\pi$
$937$	−2.56870			−0.0839158			−0.0419579	+	0.999119i	$0.513360\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.33448	−	4.04344i	0.0761019	−	0.131812i	−0.825463	−	0.564456i	$-0.809086\pi$
$941$	2.33448	−	4.04344i	0.0761019	−	0.131812i	0.901565	+	0.432644i	$0.142419\pi$
$942$		0			0
$943$	3.76578	+	6.52252i	0.122631	+	0.212403i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	15.8454	+	27.4450i	0.514907	+	0.891844i	0.999850	+	0.0172990i	$0.00550671\pi$
$947$	15.8454	+	27.4450i	0.514907	+	0.891844i	−0.484944	+	0.874545i	$0.661160\pi$
$948$		0			0
$949$	−1.54944	+	2.68371i	−0.0502970	+	0.0871170i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−13.0604			−0.423067			−0.211533	−	0.977371i	$-0.567846\pi$
$953$	−13.0604			−0.423067			−0.211533	+	0.977371i	$0.567846\pi$
$954$		0			0
$955$	18.9601			0.613535
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.32072	−	4.01961i	0.0749401	−	0.129800i
$960$		0			0
$961$	15.2781	+	26.4624i	0.492841	+	0.853626i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.12983	−	7.15308i	−0.132944	−	0.230266i
$966$		0			0
$967$	4.48074	−	7.76087i	0.144091	−	0.249573i	−0.784942	−	0.619569i	$-0.787308\pi$
$967$	4.48074	−	7.76087i	0.144091	−	0.249573i	0.929033	+	0.369996i	$0.120641\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.543941			−0.0174559			−0.00872795	−	0.999962i	$-0.502778\pi$
$971$	−0.543941			−0.0174559			−0.00872795	+	0.999962i	$0.502778\pi$
$972$		0			0
$973$	−19.2967			−0.618622
$974$		0			0
$975$		0			0
$976$		0			0
$977$	18.2280	−	31.5717i	0.583164	−	1.01007i	−0.411938	−	0.911212i	$-0.635148\pi$
$977$	18.2280	−	31.5717i	0.583164	−	1.01007i	0.995102	−	0.0988575i	$-0.0315188\pi$
$978$		0			0
$979$	13.5130	+	23.4052i	0.431877	+	0.748033i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−18.1916	−	31.5087i	−0.580221	−	1.00497i	−0.995453	−	0.0952569i	$-0.969633\pi$
$983$	−18.1916	−	31.5087i	−0.580221	−	1.00497i	0.415231	−	0.909716i	$-0.363701\pi$
$984$		0			0
$985$	−14.6105	+	25.3061i	−0.465529	+	0.806320i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	43.3214			1.37754
$990$		0			0
$991$	−31.9642			−1.01538			−0.507689	−	0.861541i	$-0.669500\pi$
$991$	−31.9642			−1.01538			−0.507689	+	0.861541i	$0.669500\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.79673	+	10.0402i	−0.183769	+	0.318297i
$996$		0			0
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.j.a.253.2		6
3.2	odd	2		252.2.j.b.85.3	✓	6
4.3	odd	2		3024.2.r.i.1009.2		6
7.2	even	3		5292.2.l.g.361.2		6
7.3	odd	6		5292.2.i.g.1549.2		6
7.4	even	3		5292.2.i.d.1549.2		6
7.5	odd	6		5292.2.l.d.361.2		6
7.6	odd	2		5292.2.j.e.1765.2		6
9.2	odd	6		252.2.j.b.169.3	yes	6
9.4	even	3		2268.2.a.j.1.2		3
9.5	odd	6		2268.2.a.g.1.2		3
9.7	even	3	inner	756.2.j.a.505.2		6
12.11	even	2		1008.2.r.g.337.1		6
21.2	odd	6		1764.2.l.d.949.3		6
21.5	even	6		1764.2.l.g.949.1		6
21.11	odd	6		1764.2.i.f.373.1		6
21.17	even	6		1764.2.i.e.373.3		6
21.20	even	2		1764.2.j.d.589.1		6
36.7	odd	6		3024.2.r.i.2017.2		6
36.11	even	6		1008.2.r.g.673.1		6
36.23	even	6		9072.2.a.bt.1.2		3
36.31	odd	6		9072.2.a.bz.1.2		3
63.2	odd	6		1764.2.i.f.1537.1		6
63.11	odd	6		1764.2.l.d.961.3		6
63.16	even	3		5292.2.i.d.2125.2		6
63.20	even	6		1764.2.j.d.1177.1		6
63.25	even	3		5292.2.l.g.3313.2		6
63.34	odd	6		5292.2.j.e.3529.2		6
63.38	even	6		1764.2.l.g.961.1		6
63.47	even	6		1764.2.i.e.1537.3		6
63.52	odd	6		5292.2.l.d.3313.2		6
63.61	odd	6		5292.2.i.g.2125.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.j.b.85.3	✓	6	3.2	odd	2
252.2.j.b.169.3	yes	6	9.2	odd	6
756.2.j.a.253.2		6	1.1	even	1	trivial
756.2.j.a.505.2		6	9.7	even	3	inner
1008.2.r.g.337.1		6	12.11	even	2
1008.2.r.g.673.1		6	36.11	even	6
1764.2.i.e.373.3		6	21.17	even	6
1764.2.i.e.1537.3		6	63.47	even	6
1764.2.i.f.373.1		6	21.11	odd	6
1764.2.i.f.1537.1		6	63.2	odd	6
1764.2.j.d.589.1		6	21.20	even	2
1764.2.j.d.1177.1		6	63.20	even	6
1764.2.l.d.949.3		6	21.2	odd	6
1764.2.l.d.961.3		6	63.11	odd	6
1764.2.l.g.949.1		6	21.5	even	6
1764.2.l.g.961.1		6	63.38	even	6
2268.2.a.g.1.2		3	9.5	odd	6
2268.2.a.j.1.2		3	9.4	even	3
3024.2.r.i.1009.2		6	4.3	odd	2
3024.2.r.i.2017.2		6	36.7	odd	6
5292.2.i.d.1549.2		6	7.4	even	3
5292.2.i.d.2125.2		6	63.16	even	3
5292.2.i.g.1549.2		6	7.3	odd	6
5292.2.i.g.2125.2		6	63.61	odd	6
5292.2.j.e.1765.2		6	7.6	odd	2
5292.2.j.e.3529.2		6	63.34	odd	6
5292.2.l.d.361.2		6	7.5	odd	6
5292.2.l.d.3313.2		6	63.52	odd	6
5292.2.l.g.361.2		6	7.2	even	3
5292.2.l.g.3313.2		6	63.25	even	3
9072.2.a.bt.1.2		3	36.23	even	6
9072.2.a.bz.1.2		3	36.31	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.j (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.555632 + 0.962383i) q^{5} +(-0.500000 - 0.866025i) q^{7} +O(q^{10})\)	\(q+(-0.555632 + 0.962383i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(-0.944368 - 1.63569i) q^{11} +(0.500000 - 0.866025i) q^{13} +5.87636 q^{17} +7.09888 q^{19} +(1.99381 - 3.45338i) q^{23} +(1.88255 + 3.26067i) q^{25} +(0.493810 + 0.855304i) q^{29} +(0.333104 - 0.576953i) q^{31} +1.11126 q^{35} -1.33379 q^{37} +(-0.944368 + 1.63569i) q^{41} +(5.43199 + 9.40848i) q^{43} +(-5.54944 - 9.61192i) q^{47} +(-0.500000 + 0.866025i) q^{49} +12.2101 q^{53} +2.09888 q^{55} +(2.38255 - 4.12669i) q^{59} +(-1.88255 - 3.26067i) q^{61} +(0.555632 + 0.962383i) q^{65} +(-2.04944 + 3.54974i) q^{67} +10.7651 q^{71} -3.09888 q^{73} +(-0.944368 + 1.63569i) q^{77} +(-3.21565 - 5.56967i) q^{79} +(-5.93818 - 10.2852i) q^{83} +(-3.26509 + 5.65531i) q^{85} -14.3090 q^{89} -1.00000 q^{91} +(-3.94437 + 6.83185i) q^{95} +(-0.382546 - 0.662589i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{5} - 3 q^{7}+O(q^{10}) \) 6 * q - 3 * q^5 - 3 * q^7	\( 6 q - 3 q^{5} - 3 q^{7} - 6 q^{11} + 3 q^{13} + 6 q^{19} - 6 q^{23} - 6 q^{25} - 15 q^{29} + 3 q^{31} + 6 q^{35} - 6 q^{37} - 6 q^{41} - 3 q^{43} - 15 q^{47} - 3 q^{49} + 36 q^{53} - 24 q^{55} - 3 q^{59} + 6 q^{61} + 3 q^{65} + 6 q^{67} + 30 q^{71} + 18 q^{73} - 6 q^{77} - 3 q^{79} - 18 q^{83} + 15 q^{85} - 12 q^{89} - 6 q^{91} - 24 q^{95} + 15 q^{97}+O(q^{100}) \) 6 * q - 3 * q^5 - 3 * q^7 - 6 * q^11 + 3 * q^13 + 6 * q^19 - 6 * q^23 - 6 * q^25 - 15 * q^29 + 3 * q^31 + 6 * q^35 - 6 * q^37 - 6 * q^41 - 3 * q^43 - 15 * q^47 - 3 * q^49 + 36 * q^53 - 24 * q^55 - 3 * q^59 + 6 * q^61 + 3 * q^65 + 6 * q^67 + 30 * q^71 + 18 * q^73 - 6 * q^77 - 3 * q^79 - 18 * q^83 + 15 * q^85 - 12 * q^89 - 6 * q^91 - 24 * q^95 + 15 * q^97

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