LMFDB - Embedded newform 3525.1.bd.a.551.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3525,1,Mod(101,3525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3525, base_ring=CyclotomicField(46))

chi = DirichletCharacter(H, H._module([23, 0, 32]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3525.101");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3525 = 3 \cdot 5^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3525.bd (of order $46$, degree $22$, 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:	$1.75920416953$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$2$ over $\Q(\zeta_{46})$
Coefficient field:	$\Q(\zeta_{92})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{44} - x^{42} + x^{40} - x^{38} + x^{36} - x^{34} + x^{32} - x^{30} + x^{28} - x^{26} + x^{24} + \cdots + 1 $ x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 705)
Projective image:	$D_{23}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{23} - \cdots)$

Embedding invariants

Embedding label			551.2
Root			$0.997669 + 0.0682424i$ of defining polynomial
Character	$\chi$	$=$	3525.551
Dual form			3525.1.bd.a.3026.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11525 - 0.787230i) q^{2} +(0.631088 + 0.775711i) q^{3} +(0.289174 - 0.813657i) q^{4} +(1.31448 + 0.368301i) q^{6} +(0.0502675 + 0.179407i) q^{8} +(-0.203456 + 0.979084i) q^{9} +O(q^{10})$	\(q+(1.11525 - 0.787230i) q^{2} +(0.631088 + 0.775711i) q^{3} +(0.289174 - 0.813657i) q^{4} +(1.31448 + 0.368301i) q^{6} +(0.0502675 + 0.179407i) q^{8} +(-0.203456 + 0.979084i) q^{9} +(0.813657 - 0.289174i) q^{12} +(0.867134 + 0.705466i) q^{16} +(0.478085 + 0.786177i) q^{17} +(0.543860 + 1.25209i) q^{18} +(0.457146 + 0.489484i) q^{19} +(-0.942261 - 0.665120i) q^{23} +(-0.107445 + 0.152215i) q^{24} +(-0.887885 + 0.460065i) q^{27} +(-1.32557 - 1.07843i) q^{31} +(1.33655 + 0.0914228i) q^{32} +(1.15209 + 0.500422i) q^{34} +(0.737804 + 0.448669i) q^{36} +(0.895169 + 0.186018i) q^{38} -1.57446 q^{46} +(-0.136167 - 0.990686i) q^{47} +1.11786i q^{48} +(0.576680 + 0.816970i) q^{49} +(-0.308133 + 0.867003i) q^{51} +(0.109784 - 0.391823i) q^{53} +(-0.628038 + 1.21206i) q^{54} +(-0.0911989 + 0.663521i) q^{57} +(1.81734 - 0.249787i) q^{61} +(-2.32731 - 0.159192i) q^{62} +(0.607445 - 0.369395i) q^{64} +(0.777928 - 0.161655i) q^{68} +(-0.0787081 - 1.15067i) q^{69} +(-0.185882 + 0.0127147i) q^{72} +(0.530467 - 0.230414i) q^{76} +(0.116615 - 1.70486i) q^{79} +(-0.917211 - 0.398401i) q^{81} +(1.00063 - 1.64547i) q^{83} +(-0.813657 + 0.574342i) q^{92} -1.70884i q^{93} +(-0.931758 - 0.997669i) q^{94} +(0.772565 + 1.09448i) q^{96} +(1.28629 + 0.457146i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) $ 44 * q + 6 * q^4 - 4 * q^6 + 2 * q^9	$ 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9} - 10 q^{16} + 4 q^{19} + 8 q^{24} - 4 q^{31} + 8 q^{34} - 6 q^{36} - 8 q^{46} + 2 q^{49} - 4 q^{51} + 4 q^{54} - 4 q^{61} + 14 q^{64} + 4 q^{69} + 34 q^{76} + 4 q^{79} - 2 q^{81} - 42 q^{94} + 34 q^{96}+O(q^{100}) $ 44 * q + 6 * q^4 - 4 * q^6 + 2 * q^9 - 10 * q^16 + 4 * q^19 + 8 * q^24 - 4 * q^31 + 8 * q^34 - 6 * q^36 - 8 * q^46 + 2 * q^49 - 4 * q^51 + 4 * q^54 - 4 * q^61 + 14 * q^64 + 4 * q^69 + 34 * q^76 + 4 * q^79 - 2 * q^81 - 42 * q^94 + 34 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$1$	$e\left(\frac{17}{23}\right)$	$-1$

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 $

$2$	1.11525	−	0.787230i	1.11525	−	0.787230i	0.136167	−	0.990686i	$-0.456522\pi$
$2$	1.11525	−	0.787230i	1.11525	−	0.787230i	0.979084	+	0.203456i	$0.0652174\pi$
$3$	0.631088	+	0.775711i	0.631088	+	0.775711i
$3$	0.631088	+	0.775711i	0.631088	+	0.775711i
$4$	0.289174	−	0.813657i	0.289174	−	0.813657i
$5$		0			0
$5$		0			0
$6$	1.31448	+	0.368301i	1.31448	+	0.368301i
$7$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$7$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$8$	0.0502675	+	0.179407i	0.0502675	+	0.179407i
$9$	−0.203456	+	0.979084i	−0.203456	+	0.979084i
$10$		0			0
$11$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$11$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$12$	0.813657	−	0.289174i	0.813657	−	0.289174i
$13$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$13$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$14$		0			0
$15$		0			0
$16$	0.867134	+	0.705466i	0.867134	+	0.705466i
$17$	0.478085	+	0.786177i	0.478085	+	0.786177i	0.997669	−	0.0682424i	$-0.0217391\pi$
$17$	0.478085	+	0.786177i	0.478085	+	0.786177i	−0.519584	+	0.854419i	$0.673913\pi$
$18$	0.543860	+	1.25209i	0.543860	+	1.25209i
$19$	0.457146	+	0.489484i	0.457146	+	0.489484i	0.917211	−	0.398401i	$-0.130435\pi$
$19$	0.457146	+	0.489484i	0.457146	+	0.489484i	−0.460065	+	0.887885i	$0.652174\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.942261	−	0.665120i	−0.942261	−	0.665120i		−	1.00000i	$-0.5\pi$
$23$	−0.942261	−	0.665120i	−0.942261	−	0.665120i	−0.942261	+	0.334880i	$0.891304\pi$
$24$	−0.107445	+	0.152215i	−0.107445	+	0.152215i
$25$		0			0
$26$		0			0
$27$	−0.887885	+	0.460065i	−0.887885	+	0.460065i
$28$		0			0
$29$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$29$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$30$		0			0
$31$	−1.32557	−	1.07843i	−1.32557	−	1.07843i	−0.990686	−	0.136167i	$-0.956522\pi$
$31$	−1.32557	−	1.07843i	−1.32557	−	1.07843i	−0.334880	−	0.942261i	$-0.608696\pi$
$32$	1.33655	+	0.0914228i	1.33655	+	0.0914228i
$33$		0			0
$34$	1.15209	+	0.500422i	1.15209	+	0.500422i
$35$		0			0
$36$	0.737804	+	0.448669i	0.737804	+	0.448669i
$37$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$37$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$38$	0.895169	+	0.186018i	0.895169	+	0.186018i
$39$		0			0
$40$		0			0
$41$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$41$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$42$		0			0
$43$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$43$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$44$		0			0
$45$		0			0
$46$	−1.57446			−1.57446
$47$	−0.136167	−	0.990686i	−0.136167	−	0.990686i
$47$	−0.136167	−	0.990686i	−0.136167	−	0.990686i
$48$			1.11786i			1.11786i
$49$	0.576680	+	0.816970i	0.576680	+	0.816970i
$50$		0			0
$51$	−0.308133	+	0.867003i	−0.308133	+	0.867003i
$52$		0			0
$53$	0.109784	−	0.391823i	0.109784	−	0.391823i	−0.887885	−	0.460065i	$-0.847826\pi$
$53$	0.109784	−	0.391823i	0.109784	−	0.391823i	0.997669	+	0.0682424i	$0.0217391\pi$
$54$	−0.628038	+	1.21206i	−0.628038	+	1.21206i
$55$		0			0
$56$		0			0
$57$	−0.0911989	+	0.663521i	−0.0911989	+	0.663521i
$58$		0			0
$59$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$59$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$60$		0			0
$61$	1.81734	−	0.249787i	1.81734	−	0.249787i	0.854419	−	0.519584i	$-0.173913\pi$
$61$	1.81734	−	0.249787i	1.81734	−	0.249787i	0.962917	+	0.269797i	$0.0869565\pi$
$62$	−2.32731	−	0.159192i	−2.32731	−	0.159192i
$63$		0			0
$64$	0.607445	−	0.369395i	0.607445	−	0.369395i
$65$		0			0
$66$		0			0
$67$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$67$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$68$	0.777928	−	0.161655i	0.777928	−	0.161655i
$69$	−0.0787081	−	1.15067i	−0.0787081	−	1.15067i
$70$		0			0
$71$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$71$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$72$	−0.185882	+	0.0127147i	−0.185882	+	0.0127147i
$73$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$73$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$74$		0			0
$75$		0			0
$76$	0.530467	−	0.230414i	0.530467	−	0.230414i
$77$		0			0
$78$		0			0
$79$	0.116615	−	1.70486i	0.116615	−	1.70486i	−0.460065	−	0.887885i	$-0.652174\pi$
$79$	0.116615	−	1.70486i	0.116615	−	1.70486i	0.576680	−	0.816970i	$-0.304348\pi$
$80$		0			0
$81$	−0.917211	−	0.398401i	−0.917211	−	0.398401i
$82$		0			0
$83$	1.00063	−	1.64547i	1.00063	−	1.64547i	0.269797	−	0.962917i	$-0.413043\pi$
$83$	1.00063	−	1.64547i	1.00063	−	1.64547i	0.730836	−	0.682553i	$-0.239130\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$89$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$90$		0			0
$91$		0			0
$92$	−0.813657	+	0.574342i	−0.813657	+	0.574342i
$93$		−	1.70884i		−	1.70884i
$94$	−0.931758	−	0.997669i	−0.931758	−	0.997669i
$95$		0			0
$96$	0.772565	+	1.09448i	0.772565	+	1.09448i
$97$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$97$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$98$	1.28629	+	0.457146i	1.28629	+	0.457146i
$99$		0			0
$100$		0			0
$101$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$101$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$102$	0.338885	+	1.20950i	0.338885	+	1.20950i
$103$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$103$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$104$		0			0
$105$		0			0
$106$	−0.186018	−	0.523405i	−0.186018	−	0.523405i
$107$	−0.618088	+	1.42298i	−0.618088	+	1.42298i	0.269797	+	0.962917i	$0.413043\pi$
$107$	−0.618088	+	1.42298i	−0.618088	+	1.42298i	−0.887885	+	0.460065i	$0.847826\pi$
$108$	0.117582	+	0.855472i	0.117582	+	0.855472i
$109$	0.131424	−	1.92135i	0.131424	−	1.92135i	−0.203456	−	0.979084i	$-0.565217\pi$
$109$	0.131424	−	1.92135i	0.131424	−	1.92135i	0.334880	−	0.942261i	$-0.391304\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.44806	+	1.35239i	−1.44806	+	1.35239i	−0.631088	+	0.775711i	$0.717391\pi$
$113$	−1.44806	+	1.35239i	−1.44806	+	1.35239i	−0.816970	+	0.576680i	$0.804348\pi$
$114$	0.420634	+	0.811787i	0.420634	+	0.811787i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.460065	+	0.887885i	0.460065	+	0.887885i
$122$	1.83015	−	1.70924i	1.83015	−	1.70924i
$123$		0			0
$124$	−1.26079	+	0.766702i	−1.26079	+	0.766702i
$125$		0			0
$126$		0			0
$127$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$127$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$128$	−0.147074	+	0.338599i	−0.147074	+	0.338599i
$129$		0			0
$130$		0			0
$131$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$131$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.117014	+	0.125291i	−0.117014	+	0.125291i
$137$	−1.81464	−	0.644923i	−1.81464	−	0.644923i	−0.997669	−	0.0682424i	$-0.978261\pi$
$137$	−1.81464	−	0.644923i	−1.81464	−	0.644923i	−0.816970	−	0.576680i	$-0.804348\pi$
$138$	−0.993623	−	1.22133i	−0.993623	−	1.22133i
$139$	−0.0787081	−	0.111504i	−0.0787081	−	0.111504i	0.775711	−	0.631088i	$-0.217391\pi$
$139$	−0.0787081	−	0.111504i	−0.0787081	−	0.111504i	−0.854419	+	0.519584i	$0.826087\pi$
$140$		0			0
$141$	0.682553	−	0.730836i	0.682553	−	0.730836i
$142$		0			0
$143$		0			0
$144$	−0.867134	+	0.705466i	−0.867134	+	0.705466i
$145$		0			0
$146$		0			0
$147$	−0.269797	+	0.962917i	−0.269797	+	0.962917i
$148$		0			0
$149$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$149$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$150$		0			0
$151$	1.81734	+	0.249787i	1.81734	+	0.249787i	0.962917	−	0.269797i	$-0.0869565\pi$
$151$	1.81734	+	0.249787i	1.81734	+	0.249787i	0.854419	+	0.519584i	$0.173913\pi$
$152$	−0.0648374	+	0.106620i	−0.0648374	+	0.106620i
$153$	−0.867003	+	0.308133i	−0.867003	+	0.308133i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$157$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$158$	−1.21206	−	1.99314i	−1.21206	−	1.99314i
$159$	0.373224	−	0.162114i	0.373224	−	0.162114i
$160$		0			0
$161$		0			0
$162$	−1.33655	+	0.277739i	−1.33655	+	0.277739i
$163$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$163$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$164$		0			0
$165$		0			0
$166$	−0.179407	−	2.62284i	−0.179407	−	2.62284i
$167$	−0.398401	+	0.0827887i	−0.398401	+	0.0827887i	−0.398401	−	0.917211i	$-0.630435\pi$
$167$	−0.398401	+	0.0827887i	−0.398401	+	0.0827887i			1.00000i	$0.5\pi$
$168$		0			0
$169$	−0.682553	−	0.730836i	−0.682553	−	0.730836i
$170$		0			0
$171$	−0.572255	+	0.347996i	−0.572255	+	0.347996i
$172$		0			0
$173$	−1.97675	−	0.135214i	−1.97675	−	0.135214i	−0.979084	−	0.203456i	$-0.934783\pi$
$173$	−1.97675	−	0.135214i	−1.97675	−	0.135214i	−0.997669	+	0.0682424i	$0.978261\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$179$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$180$		0			0
$181$	−0.911560	+	1.75923i	−0.911560	+	1.75923i	−0.334880	+	0.942261i	$0.608696\pi$
$181$	−0.911560	+	1.75923i	−0.911560	+	1.75923i	−0.576680	+	0.816970i	$0.695652\pi$
$182$		0			0
$183$	1.34066	+	1.25209i	1.34066	+	1.25209i
$184$	0.0719622	−	0.202482i	0.0719622	−	0.202482i
$185$		0			0
$186$	−1.34525	−	1.90578i	−1.34525	−	1.90578i
$187$		0			0
$188$	−0.845454	−	0.175687i	−0.845454	−	0.175687i
$189$		0			0
$190$		0			0
$191$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$191$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$192$	0.669895	+	0.238081i	0.669895	+	0.238081i
$193$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$193$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$194$		0			0
$195$		0			0
$196$	0.831494	−	0.232974i	0.831494	−	0.232974i
$197$	−1.79605	−	0.373224i	−1.79605	−	0.373224i	−0.816970	−	0.576680i	$-0.804348\pi$
$197$	−1.79605	−	0.373224i	−1.79605	−	0.373224i	−0.979084	+	0.203456i	$0.934783\pi$
$198$		0			0
$199$	−0.347674	−	0.211425i	−0.347674	−	0.211425i	0.334880	−	0.942261i	$-0.391304\pi$
$199$	−0.347674	−	0.211425i	−0.347674	−	0.211425i	−0.682553	+	0.730836i	$0.739130\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	0.616339	+	0.501429i	0.616339	+	0.501429i
$205$		0			0
$206$		0			0
$207$	0.842917	−	0.787230i	0.842917	−	0.787230i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.894675	−	1.26747i	0.894675	−	1.26747i	−0.0682424	−	0.997669i	$-0.521739\pi$
$211$	0.894675	−	1.26747i	0.894675	−	1.26747i	0.962917	−	0.269797i	$-0.0869565\pi$
$212$	−0.287063	−	0.202631i	−0.287063	−	0.202631i
$213$		0			0
$214$	0.430891	+	2.07356i	0.430891	+	2.07356i
$215$		0			0
$216$	−0.127171	−	0.136167i	−0.127171	−	0.136167i
$217$		0			0
$218$	−1.36597	−	2.24624i	−1.36597	−	2.24624i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$223$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$224$		0			0
$225$		0			0
$226$	−0.550304	+	2.64821i	−0.550304	+	2.64821i
$227$	−0.494921	−	1.76640i	−0.494921	−	1.76640i	−0.631088	−	0.775711i	$-0.717391\pi$
$227$	−0.494921	−	1.76640i	−0.494921	−	1.76640i	0.136167	−	0.990686i	$-0.456522\pi$
$228$	0.513506	+	0.266077i	0.513506	+	0.266077i
$229$	1.76640	+	0.494921i	1.76640	+	0.494921i	0.990686	−	0.136167i	$-0.0434783\pi$
$229$	1.76640	+	0.494921i	1.76640	+	0.494921i	0.775711	+	0.631088i	$0.217391\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.332435	+	0.234658i	−0.332435	+	0.234658i	−0.730836	−	0.682553i	$-0.760870\pi$
$233$	−0.332435	+	0.234658i	−0.332435	+	0.234658i	0.398401	+	0.917211i	$0.369565\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.39607	−	0.985454i	1.39607	−	0.985454i
$238$		0			0
$239$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$239$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$240$		0			0
$241$	0.391823	+	0.109784i	0.391823	+	0.109784i	0.460065	−	0.887885i	$-0.347826\pi$
$241$	0.391823	+	0.109784i	0.391823	+	0.109784i	−0.0682424	+	0.997669i	$0.521739\pi$
$242$	1.21206	+	0.628038i	1.21206	+	0.628038i
$243$	−0.269797	−	0.962917i	−0.269797	−	0.962917i
$244$	0.322285	−	1.55092i	0.322285	−	1.55092i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.126845	−	0.292026i	0.126845	−	0.292026i
$249$	1.90790	−	0.262234i	1.90790	−	0.262234i
$250$		0			0
$251$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$251$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.247177	+	1.18948i	0.247177	+	1.18948i
$257$	0.917985	−	0.0627919i	0.917985	−	0.0627919i	0.398401	−	0.917211i	$-0.369565\pi$
$257$	0.917985	−	0.0627919i	0.917985	−	0.0627919i	0.519584	+	0.854419i	$0.326087\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.842917	+	0.787230i	−0.842917	+	0.787230i	−0.979084	−	0.203456i	$-0.934783\pi$
$263$	−0.842917	+	0.787230i	−0.842917	+	0.787230i	0.136167	+	0.990686i	$0.456522\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$269$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$270$		0			0
$271$	−0.572255	−	0.347996i	−0.572255	−	0.347996i	0.203456	−	0.979084i	$-0.434783\pi$
$271$	−0.572255	−	0.347996i	−0.572255	−	0.347996i	−0.775711	+	0.631088i	$0.782609\pi$
$272$	−0.140057	+	1.01899i	−0.140057	+	1.01899i
$273$		0			0
$274$	−2.53148	+	0.709287i	−2.53148	+	0.709287i
$275$		0			0
$276$	−0.959012	−	0.268703i	−0.959012	−	0.268703i
$277$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$277$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$278$	−0.175559	−	0.0623935i	−0.175559	−	0.0623935i
$279$	1.32557	−	1.07843i	1.32557	−	1.07843i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	0.185882	−	1.35239i	0.185882	−	1.35239i
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.361441	+	1.29000i	−0.361441	+	1.29000i
$289$	0.0705559	−	0.136167i	0.0705559	−	0.136167i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	0.709287	−	1.16637i	0.709287	−	1.16637i	−0.269797	−	0.962917i	$-0.586957\pi$
$293$	0.709287	−	1.16637i	0.709287	−	1.16637i	0.979084	−	0.203456i	$-0.0652174\pi$
$294$	0.457146	+	1.28629i	0.457146	+	1.28629i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	2.22343	−	1.15209i	2.22343	−	1.15209i
$303$		0			0
$304$	0.0510927	+	0.746949i	0.0510927	+	0.746949i
$305$		0			0
$306$	−0.724354	+	1.02618i	−0.724354	+	1.02618i
$307$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$307$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$311$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$312$		0			0
$313$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$313$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$314$		0			0
$315$		0			0
$316$	−1.35344	−	0.587884i	−1.35344	−	0.587884i
$317$	−1.46184	+	0.519540i	−1.46184	+	0.519540i	−0.942261	−	0.334880i	$-0.891304\pi$
$317$	−1.46184	+	0.519540i	−1.46184	+	0.519540i	−0.519584	+	0.854419i	$0.673913\pi$
$318$	0.288618	−	0.474611i	0.288618	−	0.474611i
$319$		0			0
$320$		0			0
$321$	−1.49389	+	0.418569i	−1.49389	+	0.418569i
$322$		0			0
$323$	−0.166266	+	0.593413i	−0.166266	+	0.593413i
$324$	−0.589395	+	0.631088i	−0.589395	+	0.631088i
$325$		0			0
$326$		0			0
$327$	1.57335	−	1.11059i	1.57335	−	1.11059i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−1.11059	−	1.57335i	−1.11059	−	1.57335i	−0.775711	−	0.631088i	$-0.782609\pi$
$331$	−1.11059	−	1.57335i	−1.11059	−	1.57335i	−0.334880	−	0.942261i	$-0.608696\pi$
$332$	−1.04949	−	1.29000i	−1.04949	−	1.29000i
$333$		0			0
$334$	−0.379143	+	0.405963i	−0.379143	+	0.405963i
$335$		0			0
$336$		0			0
$337$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$337$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$338$	−1.33655	−	0.277739i	−1.33655	−	0.277739i
$339$	−1.96292	−	0.269797i	−1.96292	−	0.269797i
$340$		0			0
$341$		0			0
$342$	−0.364255	+	0.838599i	−0.364255	+	0.838599i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−2.31102	+	1.40536i	−2.31102	+	1.40536i
$347$	0.789381	+	1.81734i	0.789381	+	1.81734i	0.519584	+	0.854419i	$0.326087\pi$
$347$	0.789381	+	1.81734i	0.789381	+	1.81734i	0.269797	+	0.962917i	$0.413043\pi$
$348$		0			0
$349$	0.0627919	+	0.121183i	0.0627919	+	0.121183i	0.917211	−	0.398401i	$-0.130435\pi$
$349$	0.0627919	+	0.121183i	0.0627919	+	0.121183i	−0.854419	+	0.519584i	$0.826087\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.547173	−	0.386237i	−0.547173	−	0.386237i	0.269797	−	0.962917i	$-0.413043\pi$
$353$	−0.547173	−	0.386237i	−0.547173	−	0.386237i	−0.816970	+	0.576680i	$0.804348\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$359$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$360$		0			0
$361$	0.0376304	−	0.550137i	0.0376304	−	0.550137i
$362$	0.368301	+	2.67959i	0.368301	+	2.67959i
$363$	−0.398401	+	0.917211i	−0.398401	+	0.917211i
$364$		0			0
$365$		0			0
$366$	2.48086	+	0.340986i	2.48086	+	0.340986i
$367$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$367$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$368$	−0.347847	−	1.24148i	−0.347847	−	1.24148i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−1.39041	−	0.494151i	−1.39041	−	0.494151i
$373$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$373$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$374$		0			0
$375$		0			0
$376$	0.170891	−	0.0742286i	0.170891	−	0.0742286i
$377$		0			0
$378$		0			0
$379$	−1.20346	+	0.979084i	−1.20346	+	0.979084i	−0.203456	+	0.979084i	$0.565217\pi$
$379$	−1.20346	+	0.979084i	−1.20346	+	0.979084i	−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.75923	+	0.911560i	1.75923	+	0.911560i	0.942261	+	0.334880i	$0.108696\pi$
$383$	1.75923	+	0.911560i	1.75923	+	0.911560i	0.816970	+	0.576680i	$0.195652\pi$
$384$	−0.355472	+	0.0995987i	−0.355472	+	0.0995987i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$389$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$390$		0			0
$391$	0.0724217	−	1.05877i	0.0724217	−	1.05877i
$392$	−0.117582	+	0.144528i	−0.117582	+	0.144528i
$393$		0			0
$394$	−2.29686	+	0.997669i	−2.29686	+	0.997669i
$395$		0			0
$396$		0			0
$397$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$397$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$398$	−0.554183	+	0.0379072i	−0.554183	+	0.0379072i
$399$		0			0
$400$		0			0
$401$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$401$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.171036	−	0.0116992i	−0.171036	−	0.0116992i
$409$	−0.135214	+	0.0185847i	−0.135214	+	0.0185847i	−0.203456	−	0.979084i	$-0.565217\pi$
$409$	−0.135214	+	0.0185847i	−0.135214	+	0.0185847i	0.0682424	+	0.997669i	$0.478261\pi$
$410$		0			0
$411$	−0.644923	−	1.81464i	−0.644923	−	1.81464i
$412$		0			0
$413$		0			0
$414$	0.320333	−	1.54153i	0.320333	−	1.54153i
$415$		0			0
$416$		0			0
$417$	0.0368232	−	0.131424i	0.0368232	−	0.131424i
$418$		0			0
$419$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$419$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$420$		0			0
$421$	0.894675	+	1.26747i	0.894675	+	1.26747i	0.962917	+	0.269797i	$0.0869565\pi$
$421$	0.894675	+	1.26747i	0.894675	+	1.26747i	−0.0682424	+	0.997669i	$0.521739\pi$
$422$		−	2.11786i		−	2.11786i
$423$	0.997669	+	0.0682424i	0.997669	+	0.0682424i
$424$	0.0758143			0.0758143
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.979084	+	0.914401i	0.979084	+	0.914401i
$429$		0			0
$430$		0			0
$431$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$431$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$432$	−1.09448	−	0.227435i	−1.09448	−	0.227435i
$433$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$433$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$434$		0			0
$435$		0			0
$436$	−1.52531	−	0.662536i	−1.52531	−	0.662536i
$437$	−0.105185	−	0.765279i	−0.105185	−	0.765279i
$438$		0			0
$439$	1.49389	+	1.21537i	1.49389	+	1.21537i	0.917211	+	0.398401i	$0.130435\pi$
$439$	1.49389	+	1.21537i	1.49389	+	1.21537i	0.576680	+	0.816970i	$0.304348\pi$
$440$		0			0
$441$	−0.917211	+	0.398401i	−0.917211	+	0.398401i
$442$		0			0
$443$	1.70992	−	0.886009i	1.70992	−	0.886009i	0.730836	−	0.682553i	$-0.239130\pi$
$443$	1.70992	−	0.886009i	1.70992	−	0.886009i	0.979084	−	0.203456i	$-0.0652174\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$449$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$450$		0			0
$451$		0			0
$452$	0.681642	+	1.56930i	0.681642	+	1.56930i
$453$	0.953137	+	1.56737i	0.953137	+	1.56737i
$454$	−1.94252	−	1.58036i	−1.94252	−	1.58036i
$455$		0			0
$456$	−0.123625	+	0.0169918i	−0.123625	+	0.0169918i
$457$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$457$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$458$	2.35959	−	0.838599i	2.35959	−	0.838599i
$459$	−0.786177	−	0.478085i	−0.786177	−	0.478085i
$460$		0			0
$461$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$461$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$462$		0			0
$463$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$463$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$464$		0			0
$465$		0			0
$466$	−0.186018	+	0.523405i	−0.186018	+	0.523405i
$467$	0.0861339	+	0.105873i	0.0861339	+	0.105873i	0.816970	−	0.576680i	$-0.195652\pi$
$467$	0.0861339	+	0.105873i	0.0861339	+	0.105873i	−0.730836	+	0.682553i	$0.760870\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.781189	−	2.19806i	0.781189	−	2.19806i
$475$		0			0
$476$		0			0
$477$	0.361291	+	0.187206i	0.361291	+	0.187206i
$478$		0			0
$479$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$479$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$480$		0			0
$481$		0			0
$482$	0.523405	−	0.186018i	0.523405	−	0.186018i
$483$		0			0
$484$	0.855472	−	0.117582i	0.855472	−	0.117582i
$485$		0			0
$486$	−1.05893	−	0.861502i	−1.05893	−	0.861502i
$487$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$487$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$488$	0.136167	+	0.313487i	0.136167	+	0.313487i
$489$		0			0
$490$		0			0
$491$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$491$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.388649	−	1.87028i	−0.388649	−	1.87028i
$497$		0			0
$498$	1.92135	−	1.79441i	1.92135	−	1.79441i
$499$	−1.05788	+	0.459500i	−1.05788	+	0.459500i	−0.854419	−	0.519584i	$-0.826087\pi$
$499$	−1.05788	+	0.459500i	−1.05788	+	0.459500i	−0.203456	+	0.979084i	$0.565217\pi$
$500$		0			0
$501$	−0.315646	−	0.256797i	−0.315646	−	0.256797i
$502$		0			0
$503$	0.185882	+	1.35239i	0.185882	+	1.35239i	0.816970	+	0.576680i	$0.195652\pi$
$503$	0.185882	+	1.35239i	0.185882	+	1.35239i	−0.631088	+	0.775711i	$0.717391\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.136167	−	0.990686i	0.136167	−	0.990686i
$508$		0			0
$509$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$509$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$510$		0			0
$511$		0			0
$512$	0.942261	+	0.880010i	0.942261	+	0.880010i
$513$	−0.631088	−	0.224289i	−0.631088	−	0.224289i
$514$	0.974352	−	0.792694i	0.974352	−	0.792694i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.14262	−	1.61872i	−1.14262	−	1.61872i
$520$		0			0
$521$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$521$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$522$		0			0
$523$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$523$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$524$		0			0
$525$		0			0
$526$	−0.320333	+	1.54153i	−0.320333	+	1.54153i
$527$	0.214102	−	1.55771i	0.214102	−	1.55771i
$528$		0			0
$529$	0.110591	+	0.311173i	0.110591	+	0.311173i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−0.985454	+	1.39607i	−0.985454	+	1.39607i	−0.0682424	+	0.997669i	$0.521739\pi$
$541$	−0.985454	+	1.39607i	−0.985454	+	1.39607i	−0.917211	+	0.398401i	$0.869565\pi$
$542$	−0.912161	+	0.0623935i	−0.912161	+	0.0623935i
$543$	−1.93993	+	0.403122i	−1.93993	+	0.403122i
$544$	0.567112	+	1.09448i	0.567112	+	1.09448i
$545$		0			0
$546$		0			0
$547$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$547$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$548$	−1.04949	+	1.29000i	−1.04949	+	1.29000i
$549$	−0.125185	+	1.83015i	−0.125185	+	1.83015i
$550$		0			0
$551$		0			0
$552$	0.202482	−	0.0719622i	0.202482	−	0.0719622i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.113486	+	0.0317974i	−0.113486	+	0.0317974i
$557$	0.816970	+	0.423320i	0.816970	+	0.423320i	0.816970	−	0.576680i	$-0.195652\pi$
$557$	0.816970	+	0.423320i	0.816970	+	0.423320i			1.00000i	$0.5\pi$
$558$	0.629368	−	2.24624i	0.629368	−	2.24624i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	0.920130i		−	0.920130i	−0.887885	−	0.460065i	$-0.847826\pi$
$563$		−	0.920130i		−	0.920130i	0.887885	−	0.460065i	$-0.152174\pi$
$564$	−0.397273	−	0.766702i	−0.397273	−	0.766702i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$569$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$570$		0			0
$571$	−0.308133	+	0.594669i	−0.308133	+	0.594669i	−0.990686	−	0.136167i	$-0.956522\pi$
$571$	−0.308133	+	0.594669i	−0.308133	+	0.594669i	0.682553	+	0.730836i	$0.260870\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.238081	+	0.669895i	0.238081	+	0.669895i
$577$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$577$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$578$	−0.0285070	−	0.207404i	−0.0285070	−	0.207404i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.127171	−	1.85917i	−0.127171	−	1.85917i
$587$	0.547173	+	0.386237i	0.547173	+	0.386237i	0.816970	−	0.576680i	$-0.195652\pi$
$587$	0.547173	+	0.386237i	0.547173	+	0.386237i	−0.269797	+	0.962917i	$0.586957\pi$
$588$	0.705466	+	0.497972i	0.705466	+	0.497972i
$589$	−0.0781042	−	1.14184i	−0.0781042	−	1.14184i
$590$		0			0
$591$	−0.843954	−	1.62876i	−0.843954	−	1.62876i
$592$		0			0
$593$	0.543860	+	1.25209i	0.543860	+	1.25209i	0.942261	+	0.334880i	$0.108696\pi$
$593$	0.543860	+	1.25209i	0.543860	+	1.25209i	−0.398401	+	0.917211i	$0.630435\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.0554078	−	0.403122i	−0.0554078	−	0.403122i
$598$		0			0
$599$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$599$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$600$		0			0
$601$	1.96292	+	0.269797i	1.96292	+	0.269797i	1.00000			$0$
$601$	1.96292	+	0.269797i	1.96292	+	0.269797i	0.962917	+	0.269797i	$0.0869565\pi$
$602$		0			0
$603$		0			0
$604$	0.728767	−	1.40646i	0.728767	−	1.40646i
$605$		0			0
$606$		0			0
$607$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$607$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$608$	0.566251	+	0.696015i	0.566251	+	0.696015i
$609$		0			0
$610$		0			0
$611$		0			0
$612$			0.794546i			0.794546i
$613$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$613$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.461039	+	1.64547i	−0.461039	+	1.64547i	0.269797	+	0.962917i	$0.413043\pi$
$617$	−0.461039	+	1.64547i	−0.461039	+	1.64547i	−0.730836	+	0.682553i	$0.760870\pi$
$618$		0			0
$619$	1.76640	−	0.494921i	1.76640	−	0.494921i	0.775711	−	0.631088i	$-0.217391\pi$
$619$	1.76640	−	0.494921i	1.76640	−	0.494921i	0.990686	+	0.136167i	$0.0434783\pi$
$620$		0			0
$621$	1.14262	+	0.157049i	1.14262	+	0.157049i
$622$		0			0
$623$		0			0
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	−0.530621	−	1.02405i	−0.530621	−	1.02405i	−0.990686	−	0.136167i	$-0.956522\pi$
$631$	−0.530621	−	1.02405i	−0.530621	−	1.02405i	0.460065	−	0.887885i	$-0.347826\pi$
$632$	0.311725	−	0.0647772i	0.311725	−	0.0647772i
$633$	1.54781	−	0.105873i	1.54781	−	0.105873i
$634$	−1.22133	+	1.73023i	−1.22133	+	1.73023i
$635$		0			0
$636$	−0.0239787	−	0.350556i	−0.0239787	−	0.350556i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$641$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$642$	−1.33655	+	1.64285i	−1.33655	+	1.64285i
$643$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$643$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$644$		0			0
$645$		0			0
$646$	0.281724	+	0.792694i	0.281724	+	0.792694i
$647$	−0.211425	+	0.347674i	−0.211425	+	0.347674i	−0.942261	−	0.334880i	$-0.891304\pi$
$647$	−0.211425	+	0.347674i	−0.211425	+	0.347674i	0.730836	+	0.682553i	$0.239130\pi$
$648$	0.0253701	−	0.184581i	0.0253701	−	0.184581i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.489484	+	0.457146i	0.489484	+	0.457146i	0.887885	−	0.460065i	$-0.152174\pi$
$653$	0.489484	+	0.457146i	0.489484	+	0.457146i	−0.398401	+	0.917211i	$0.630435\pi$
$654$	0.880388	−	2.47717i	0.880388	−	2.47717i
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		1.00000			$0$
$659$		0			0		−1.00000			$\pi$
$660$		0			0
$661$	−0.713755	+	0.580683i	−0.713755	+	0.580683i	−0.917211	−	0.398401i	$-0.869565\pi$
$661$	−0.713755	+	0.580683i	−0.713755	+	0.580683i	0.203456	+	0.979084i	$0.434783\pi$
$662$	−2.47717	−	0.880388i	−2.47717	−	0.880388i
$663$		0			0
$664$	0.345509	+	0.0968070i	0.345509	+	0.0968070i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.0478455	+	0.348102i	−0.0478455	+	0.348102i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$673$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$674$		0			0
$675$		0			0
$676$	−0.792026	+	0.344025i	−0.792026	+	0.344025i
$677$	0.0997480	−	0.0931581i	0.0997480	−	0.0931581i	−0.631088	−	0.775711i	$-0.717391\pi$
$677$	0.0997480	−	0.0931581i	0.0997480	−	0.0931581i	0.730836	+	0.682553i	$0.239130\pi$
$678$	−2.40154	+	1.24438i	−2.40154	+	1.24438i
$679$		0			0
$680$		0			0
$681$	1.05788	−	1.49867i	1.05788	−	1.49867i
$682$		0			0
$683$	1.15067	−	0.0787081i	1.15067	−	0.0787081i	0.519584	−	0.854419i	$-0.326087\pi$
$683$	1.15067	−	0.0787081i	1.15067	−	0.0787081i	0.631088	+	0.775711i	$0.282609\pi$
$684$	0.117668	+	0.566251i	0.117668	+	0.566251i
$685$		0			0
$686$		0			0
$687$	0.730836	+	1.68255i	0.730836	+	1.68255i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.911560	+	0.125291i	−0.911560	+	0.125291i	−0.576680	−	0.816970i	$-0.695652\pi$
$691$	−0.911560	+	0.125291i	−0.911560	+	0.125291i	−0.334880	+	0.942261i	$0.608696\pi$
$692$	−0.681642	+	1.56930i	−0.681642	+	1.56930i
$693$		0			0
$694$	2.31102	+	1.40536i	2.31102	+	1.40536i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.165427	+	0.0857176i	0.165427	+	0.0857176i
$699$	−0.391823	−	0.109784i	−0.391823	−	0.109784i
$700$		0			0
$701$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$701$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.914293			−0.914293
$707$		0			0
$708$		0			0
$709$	−0.386237	+	1.08677i	−0.386237	+	1.08677i	0.576680	+	0.816970i	$0.304348\pi$
$709$	−0.386237	+	1.08677i	−0.386237	+	1.08677i	−0.962917	+	0.269797i	$0.913043\pi$
$710$		0			0
$711$	1.64547	+	0.461039i	1.64547	+	0.461039i
$712$		0			0
$713$	0.531744	+	1.89782i	0.531744	+	1.89782i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$719$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$720$		0			0
$721$		0			0
$722$	−0.391117	−	0.643165i	−0.391117	−	0.643165i
$723$	0.162114	+	0.373224i	0.162114	+	0.373224i
$724$	1.16781	+	1.25042i	1.16781	+	1.25042i
$725$		0			0
$726$	0.277739	+	1.33655i	0.277739	+	1.33655i
$727$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$727$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$728$		0			0
$729$	0.576680	−	0.816970i	0.576680	−	0.816970i
$730$		0			0
$731$		0			0
$732$	1.40646	−	0.728767i	1.40646	−	0.728767i
$733$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$733$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$734$		0			0
$735$		0			0
$736$	−1.19858	−	0.975113i	−1.19858	−	0.975113i
$737$		0			0
$738$		0			0
$739$	−1.81734	−	0.789381i	−1.81734	−	0.789381i	−0.962917	−	0.269797i	$-0.913043\pi$
$739$	−1.81734	−	0.789381i	−1.81734	−	0.789381i	−0.854419	−	0.519584i	$-0.826087\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.655751	+	0.136267i	0.655751	+	0.136267i	0.519584	−	0.854419i	$-0.326087\pi$
$743$	0.655751	+	0.136267i	0.655751	+	0.136267i	0.136167	+	0.990686i	$0.456522\pi$
$744$	0.306578	−	0.0858991i	0.306578	−	0.0858991i
$745$		0			0
$746$		0			0
$747$	1.40747	+	1.31448i	1.40747	+	1.31448i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.55142			−1.55142			−0.775711	−	0.631088i	$-0.782609\pi$
$751$	−1.55142			−1.55142			−0.775711	+	0.631088i	$0.782609\pi$
$752$	0.580820	−	0.955118i	0.580820	−	0.955118i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$757$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$758$	−0.571391	+	2.03932i	−0.571391	+	2.03932i
$759$		0			0
$760$		0			0
$761$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$761$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	2.67959	−	0.368301i	2.67959	−	0.368301i
$767$		0			0
$768$	−0.766702	+	0.942404i	−0.766702	+	0.942404i
$769$	−0.786177	+	0.478085i	−0.786177	+	0.478085i	−0.854419	−	0.519584i	$-0.826087\pi$
$769$	−0.786177	+	0.478085i	−0.786177	+	0.478085i	0.0682424	+	0.997669i	$0.478261\pi$
$770$		0			0
$771$	0.628038	+	0.672464i	0.628038	+	0.672464i
$772$		0			0
$773$	−0.133630	+	0.0277687i	−0.133630	+	0.0277687i	−0.269797	−	0.962917i	$-0.586957\pi$
$773$	−0.133630	+	0.0277687i	−0.133630	+	0.0277687i	0.136167	+	0.990686i	$0.456522\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.752725	−	1.23780i	−0.752725	−	1.23780i
$783$		0			0
$784$	−0.0762852	+	1.11525i	−0.0762852	+	1.11525i
$785$		0			0
$786$		0			0
$787$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$787$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$788$	−0.823048	+	1.35344i	−0.823048	+	1.35344i
$789$	−1.14262	−	0.157049i	−1.14262	−	0.157049i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.272565	+	0.221748i	−0.272565	+	0.221748i
$797$	−0.111504	+	0.0787081i	−0.111504	+	0.0787081i	−0.631088	−	0.775711i	$-0.717391\pi$
$797$	−0.111504	+	0.0787081i	−0.111504	+	0.0787081i	0.519584	+	0.854419i	$0.326087\pi$
$798$		0			0
$799$	0.713755	−	0.580683i	0.713755	−	0.580683i
$800$		0			0
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$809$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$810$		0			0
$811$	0.663521	+	1.86697i	0.663521	+	1.86697i	0.460065	+	0.887885i	$0.347826\pi$
$811$	0.663521	+	1.86697i	0.663521	+	1.86697i	0.203456	+	0.979084i	$0.434783\pi$
$812$		0			0
$813$	−0.0911989	−	0.663521i	−0.0911989	−	0.663521i
$814$		0			0
$815$		0			0
$816$	−0.878833	+	0.534430i	−0.878833	+	0.534430i
$817$		0			0
$818$	−0.136167	+	0.127171i	−0.136167	+	0.127171i
$819$		0			0
$820$		0			0
$821$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$821$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$822$	−2.14779	−	1.51607i	−2.14779	−	1.51607i
$823$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$823$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.0997480	−	0.0931581i	0.0997480	−	0.0931581i	−0.631088	−	0.775711i	$-0.717391\pi$
$827$	0.0997480	−	0.0931581i	0.0997480	−	0.0931581i	0.730836	+	0.682553i	$0.239130\pi$
$828$	−0.396785	−	0.913491i	−0.396785	−	0.913491i
$829$	−1.16637	+	0.709287i	−1.16637	+	0.709287i	−0.962917	−	0.269797i	$-0.913043\pi$
$829$	−1.16637	+	0.709287i	−1.16637	+	0.709287i	−0.203456	+	0.979084i	$0.565217\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.366581	+	0.843954i	−0.366581	+	0.843954i
$834$	−0.0623935	−	0.175559i	−0.0623935	−	0.175559i
$835$		0			0
$836$		0			0
$837$	1.67310	+	0.347674i	1.67310	+	0.347674i
$838$		0			0
$839$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$839$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$840$		0			0
$841$	0.682553	−	0.730836i	0.682553	−	0.730836i
$842$	1.99557	+	0.709227i	1.99557	+	0.709227i
$843$		0			0
$844$	−0.772565	−	1.09448i	−0.772565	−	1.09448i
$845$		0			0
$846$	1.16637	−	0.709287i	1.16637	−	0.709287i
$847$		0			0
$848$	0.371615	−	0.262314i	0.371615	−	0.262314i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$853$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$854$		0			0
$855$		0			0
$856$	−0.286363	−	0.0393597i	−0.286363	−	0.0393597i
$857$	0.806094	−	1.32557i	0.806094	−	1.32557i	−0.136167	−	0.990686i	$-0.543478\pi$
$857$	0.806094	−	1.32557i	0.806094	−	1.32557i	0.942261	−	0.334880i	$-0.108696\pi$
$858$		0			0
$859$	1.25209	+	0.543860i	1.25209	+	0.543860i	0.917211	−	0.398401i	$-0.130435\pi$
$859$	1.25209	+	0.543860i	1.25209	+	0.543860i	0.334880	+	0.942261i	$0.391304\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.887885	−	1.46007i	−0.887885	−	1.46007i	−0.887885	−	0.460065i	$-0.847826\pi$
$863$	−0.887885	−	1.46007i	−0.887885	−	1.46007i		−	1.00000i	$-0.5\pi$
$864$	−1.22877	+	0.533729i	−1.22877	+	0.533729i
$865$		0			0
$866$		0			0
$867$	0.150153	−	0.0312021i	0.150153	−	0.0312021i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.351309	−	0.0730029i	0.351309	−	0.0730029i
$873$		0			0
$874$	−0.719758	−	0.770673i	−0.719758	−	0.770673i
$875$		0			0
$876$		0			0
$877$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$877$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$878$	2.62284	+	0.179407i	2.62284	+	0.179407i
$879$	1.35239	−	0.185882i	1.35239	−	0.185882i
$880$		0			0
$881$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$881$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$882$	−0.709287	+	1.16637i	−0.709287	+	1.16637i
$883$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$883$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$884$		0			0
$885$		0			0
$886$	1.20950	−	2.33422i	1.20950	−	2.33422i
$887$	0.180699	−	0.644923i	0.180699	−	0.644923i	−0.816970	−	0.576680i	$-0.804348\pi$
$887$	0.180699	−	0.644923i	0.180699	−	0.644923i	0.997669	−	0.0682424i	$-0.0217391\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	0.422677	−	0.519540i	0.422677	−	0.519540i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.360528	−	0.101015i	0.360528	−	0.101015i
$902$		0			0
$903$		0			0
$904$	−0.315419	−	0.191811i	−0.315419	−	0.191811i
$905$		0			0
$906$	2.29686	+	0.997669i	2.29686	+	0.997669i
$907$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$907$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$908$	−1.58036	−	0.108100i	−1.58036	−	0.108100i
$909$		0			0
$910$		0			0
$911$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$911$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$912$	−0.547173	+	0.511024i	−0.547173	+	0.511024i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.913491	−	1.29412i	0.913491	−	1.29412i
$917$		0			0
$918$	−1.25315	+	0.0857176i	−1.25315	+	0.0857176i
$919$	0.234658	+	1.12924i	0.234658	+	1.12924i	0.917211	+	0.398401i	$0.130435\pi$
$919$	0.234658	+	1.12924i	0.234658	+	1.12924i	−0.682553	+	0.730836i	$0.739130\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$929$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$930$		0			0
$931$	−0.136267	+	0.655751i	−0.136267	+	0.655751i
$932$	0.0947998	+	0.338345i	0.0947998	+	0.338345i
$933$		0			0
$934$	0.179407	+	0.0502675i	0.179407	+	0.0502675i
$935$		0			0
$936$		0			0
$937$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$937$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.121183	−	0.0627919i	−0.121183	−	0.0627919i	0.398401	−	0.917211i	$-0.369565\pi$
$947$	−0.121183	−	0.0627919i	−0.121183	−	0.0627919i	−0.519584	+	0.854419i	$0.673913\pi$
$948$	−0.398114	−	1.42089i	−0.398114	−	1.42089i
$949$		0			0
$950$		0			0
$951$	−1.32557	−	0.806094i	−1.32557	−	0.806094i
$952$		0			0
$953$	−0.543860	+	1.25209i	−0.543860	+	1.25209i	0.398401	+	0.917211i	$0.369565\pi$
$953$	−0.543860	+	1.25209i	−0.543860	+	1.25209i	−0.942261	+	0.334880i	$0.891304\pi$
$954$	0.550304	−	0.0756376i	0.550304	−	0.0756376i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.390662	+	1.87997i	0.390662	+	1.87997i
$962$		0			0
$963$	−1.26747	−	0.894675i	−1.26747	−	0.894675i
$964$	0.202631	−	0.287063i	0.202631	−	0.287063i
$965$		0			0
$966$		0			0
$967$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$967$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$968$	−0.136167	+	0.127171i	−0.136167	+	0.127171i
$969$	−0.565246	+	0.245521i	−0.565246	+	0.245521i
$970$		0			0
$971$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$971$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$972$	−0.861502	−	0.0589284i	−0.861502	−	0.0589284i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	1.75209	+	1.06547i	1.75209	+	1.06547i
$977$	−0.269797	+	1.96292i	−0.269797	+	1.96292i			1.00000i	$0.5\pi$
$977$	−0.269797	+	1.96292i	−0.269797	+	1.96292i	−0.269797	+	0.962917i	$0.586957\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.85442	+	0.519584i	1.85442	+	0.519584i
$982$		0			0
$983$	−1.72850	−	0.614311i	−1.72850	−	0.614311i	−0.730836	−	0.682553i	$-0.760870\pi$
$983$	−1.72850	−	0.614311i	−1.72850	−	0.614311i	−0.997669	+	0.0682424i	$0.978261\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.519540	−	1.46184i	0.519540	−	1.46184i	−0.334880	−	0.942261i	$-0.608696\pi$
$991$	0.519540	−	1.46184i	0.519540	−	1.46184i	0.854419	−	0.519584i	$-0.173913\pi$
$992$	−1.67310	−	1.56256i	−1.67310	−	1.56256i
$993$	0.519584	−	1.85442i	0.519584	−	1.85442i
$994$		0			0
$995$		0			0
$996$	0.338345	−	1.62820i	0.338345	−	1.62820i
$997$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$997$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$998$	−0.818064	+	1.34525i	−0.818064	+	1.34525i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bd.a.551.2		44
3.2	odd	2	inner	3525.1.bd.a.551.1		44
5.2	odd	4		705.1.p.b.269.1	yes	22
5.3	odd	4		705.1.p.a.269.1	✓	22
5.4	even	2	inner	3525.1.bd.a.551.1		44
15.2	even	4		705.1.p.a.269.1	✓	22
15.8	even	4		705.1.p.b.269.1	yes	22
15.14	odd	2	CM	3525.1.bd.a.551.2		44
47.18	even	23	inner	3525.1.bd.a.3026.1		44
141.65	odd	46	inner	3525.1.bd.a.3026.2		44
235.18	odd	92		705.1.p.a.629.1	yes	22
235.112	odd	92		705.1.p.b.629.1	yes	22
235.159	even	46	inner	3525.1.bd.a.3026.2		44
705.347	even	92		705.1.p.a.629.1	yes	22
705.488	even	92		705.1.p.b.629.1	yes	22
705.629	odd	46	inner	3525.1.bd.a.3026.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.1.p.a.269.1	✓	22	5.3	odd	4
705.1.p.a.269.1	✓	22	15.2	even	4
705.1.p.a.629.1	yes	22	235.18	odd	92
705.1.p.a.629.1	yes	22	705.347	even	92
705.1.p.b.269.1	yes	22	5.2	odd	4
705.1.p.b.269.1	yes	22	15.8	even	4
705.1.p.b.629.1	yes	22	235.112	odd	92
705.1.p.b.629.1	yes	22	705.488	even	92
3525.1.bd.a.551.1		44	3.2	odd	2	inner
3525.1.bd.a.551.1		44	5.4	even	2	inner
3525.1.bd.a.551.2		44	1.1	even	1	trivial
3525.1.bd.a.551.2		44	15.14	odd	2	CM
3525.1.bd.a.3026.1		44	47.18	even	23	inner
3525.1.bd.a.3026.1		44	705.629	odd	46	inner
3525.1.bd.a.3026.2		44	141.65	odd	46	inner
3525.1.bd.a.3026.2		44	235.159	even	46	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3525.bd (of order \(46\), degree \(22\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11525 - 0.787230i) q^{2} +(0.631088 + 0.775711i) q^{3} +(0.289174 - 0.813657i) q^{4} +(1.31448 + 0.368301i) q^{6} +(0.0502675 + 0.179407i) q^{8} +(-0.203456 + 0.979084i) q^{9} +O(q^{10})\)	\(q+(1.11525 - 0.787230i) q^{2} +(0.631088 + 0.775711i) q^{3} +(0.289174 - 0.813657i) q^{4} +(1.31448 + 0.368301i) q^{6} +(0.0502675 + 0.179407i) q^{8} +(-0.203456 + 0.979084i) q^{9} +(0.813657 - 0.289174i) q^{12} +(0.867134 + 0.705466i) q^{16} +(0.478085 + 0.786177i) q^{17} +(0.543860 + 1.25209i) q^{18} +(0.457146 + 0.489484i) q^{19} +(-0.942261 - 0.665120i) q^{23} +(-0.107445 + 0.152215i) q^{24} +(-0.887885 + 0.460065i) q^{27} +(-1.32557 - 1.07843i) q^{31} +(1.33655 + 0.0914228i) q^{32} +(1.15209 + 0.500422i) q^{34} +(0.737804 + 0.448669i) q^{36} +(0.895169 + 0.186018i) q^{38} -1.57446 q^{46} +(-0.136167 - 0.990686i) q^{47} +1.11786i q^{48} +(0.576680 + 0.816970i) q^{49} +(-0.308133 + 0.867003i) q^{51} +(0.109784 - 0.391823i) q^{53} +(-0.628038 + 1.21206i) q^{54} +(-0.0911989 + 0.663521i) q^{57} +(1.81734 - 0.249787i) q^{61} +(-2.32731 - 0.159192i) q^{62} +(0.607445 - 0.369395i) q^{64} +(0.777928 - 0.161655i) q^{68} +(-0.0787081 - 1.15067i) q^{69} +(-0.185882 + 0.0127147i) q^{72} +(0.530467 - 0.230414i) q^{76} +(0.116615 - 1.70486i) q^{79} +(-0.917211 - 0.398401i) q^{81} +(1.00063 - 1.64547i) q^{83} +(-0.813657 + 0.574342i) q^{92} -1.70884i q^{93} +(-0.931758 - 0.997669i) q^{94} +(0.772565 + 1.09448i) q^{96} +(1.28629 + 0.457146i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 44 * q + 6 * q^4 - 4 * q^6 + 2 * q^9	\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9} - 10 q^{16} + 4 q^{19} + 8 q^{24} - 4 q^{31} + 8 q^{34} - 6 q^{36} - 8 q^{46} + 2 q^{49} - 4 q^{51} + 4 q^{54} - 4 q^{61} + 14 q^{64} + 4 q^{69} + 34 q^{76} + 4 q^{79} - 2 q^{81} - 42 q^{94} + 34 q^{96}+O(q^{100}) \) 44 * q + 6 * q^4 - 4 * q^6 + 2 * q^9 - 10 * q^16 + 4 * q^19 + 8 * q^24 - 4 * q^31 + 8 * q^34 - 6 * q^36 - 8 * q^46 + 2 * q^49 - 4 * q^51 + 4 * q^54 - 4 * q^61 + 14 * q^64 + 4 * q^69 + 34 * q^76 + 4 * q^79 - 2 * q^81 - 42 * q^94 + 34 * q^96

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