LMFDB - Embedded newform 3525.1.bd.a.776.2

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			776.2
Root			$0.631088 + 0.775711i$ of defining polynomial
Character	$\chi$	$=$	3525.776
Dual form			3525.1.bd.a.1976.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0911989 + 0.663521i) q^{2} +(0.519584 - 0.854419i) q^{3} +(0.530974 - 0.148772i) q^{4} +(0.614311 + 0.266833i) q^{6} +(0.413970 + 0.953056i) q^{8} +(-0.460065 - 0.887885i) q^{9} +O(q^{10})$	\(q+(0.0911989 + 0.663521i) q^{2} +(0.519584 - 0.854419i) q^{3} +(0.530974 - 0.148772i) q^{4} +(0.614311 + 0.266833i) q^{6} +(0.413970 + 0.953056i) q^{8} +(-0.460065 - 0.887885i) q^{9} +(0.148772 - 0.530974i) q^{12} +(-0.123473 + 0.0750854i) q^{16} +(-0.0997480 - 0.0931581i) q^{17} +(0.547173 - 0.386237i) q^{18} +(0.644923 + 1.81464i) q^{19} +(0.269797 - 1.96292i) q^{23} +(1.02940 + 0.141488i) q^{24} +(-0.997669 - 0.0682424i) q^{27} +(1.16637 - 0.709287i) q^{31} +(0.594669 + 0.730947i) q^{32} +(0.0527155 - 0.0746808i) q^{34} +(-0.376375 - 0.402999i) q^{36} +(-1.14523 + 0.593413i) q^{38} +1.32704 q^{46} +(-0.979084 + 0.203456i) q^{47} +0.144511i q^{48} +(0.990686 - 0.136167i) q^{49} +(-0.131424 + 0.0368232i) q^{51} +(-0.366581 + 0.843954i) q^{53} +(-0.0457060 - 0.668198i) q^{54} +(1.88555 + 0.391823i) q^{57} +(-0.234658 - 1.12924i) q^{61} +(0.576999 + 0.709227i) q^{62} +(-0.529402 + 0.566851i) q^{64} +(-0.0668230 - 0.0346249i) q^{68} +(-1.53697 - 1.25042i) q^{69} +(0.655751 - 0.806026i) q^{72} +(0.612405 + 0.867580i) q^{76} +(1.05893 - 0.861502i) q^{79} +(-0.576680 + 0.816970i) q^{81} +(-1.34066 + 1.25209i) q^{83} +(-0.148772 - 1.08240i) q^{92} -1.36511i q^{93} +(-0.224289 - 0.631088i) q^{94} +(0.933516 - 0.128309i) q^{96} +(0.180699 + 0.644923i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$1$	$e\left(\frac{14}{23}\right)$	$-1$

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 $

$2$	0.0911989	+	0.663521i	0.0911989	+	0.663521i	0.979084	+	0.203456i	$0.0652174\pi$
$2$	0.0911989	+	0.663521i	0.0911989	+	0.663521i	−0.887885	+	0.460065i	$0.847826\pi$
$3$	0.519584	−	0.854419i	0.519584	−	0.854419i
$3$	0.519584	−	0.854419i	0.519584	−	0.854419i
$4$	0.530974	−	0.148772i	0.530974	−	0.148772i
$5$		0			0
$5$		0			0
$6$	0.614311	+	0.266833i	0.614311	+	0.266833i
$7$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$7$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$8$	0.413970	+	0.953056i	0.413970	+	0.953056i
$9$	−0.460065	−	0.887885i	−0.460065	−	0.887885i
$10$		0			0
$11$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$11$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$12$	0.148772	−	0.530974i	0.148772	−	0.530974i
$13$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$13$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$14$		0			0
$15$		0			0
$16$	−0.123473	+	0.0750854i	−0.123473	+	0.0750854i
$17$	−0.0997480	−	0.0931581i	−0.0997480	−	0.0931581i	0.631088	−	0.775711i	$-0.282609\pi$
$17$	−0.0997480	−	0.0931581i	−0.0997480	−	0.0931581i	−0.730836	+	0.682553i	$0.760870\pi$
$18$	0.547173	−	0.386237i	0.547173	−	0.386237i
$19$	0.644923	+	1.81464i	0.644923	+	1.81464i	0.576680	+	0.816970i	$0.304348\pi$
$19$	0.644923	+	1.81464i	0.644923	+	1.81464i	0.0682424	+	0.997669i	$0.478261\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.269797	−	1.96292i	0.269797	−	1.96292i		−	1.00000i	$-0.5\pi$
$23$	0.269797	−	1.96292i	0.269797	−	1.96292i	0.269797	−	0.962917i	$-0.413043\pi$
$24$	1.02940	+	0.141488i	1.02940	+	0.141488i
$25$		0			0
$26$		0			0
$27$	−0.997669	−	0.0682424i	−0.997669	−	0.0682424i
$28$		0			0
$29$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$29$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$30$		0			0
$31$	1.16637	−	0.709287i	1.16637	−	0.709287i	0.203456	−	0.979084i	$-0.434783\pi$
$31$	1.16637	−	0.709287i	1.16637	−	0.709287i	0.962917	+	0.269797i	$0.0869565\pi$
$32$	0.594669	+	0.730947i	0.594669	+	0.730947i
$33$		0			0
$34$	0.0527155	−	0.0746808i	0.0527155	−	0.0746808i
$35$		0			0
$36$	−0.376375	−	0.402999i	−0.376375	−	0.402999i
$37$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$37$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$38$	−1.14523	+	0.593413i	−1.14523	+	0.593413i
$39$		0			0
$40$		0			0
$41$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$41$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$42$		0			0
$43$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$43$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$44$		0			0
$45$		0			0
$46$	1.32704			1.32704
$47$	−0.979084	+	0.203456i	−0.979084	+	0.203456i
$47$	−0.979084	+	0.203456i	−0.979084	+	0.203456i
$48$			0.144511i			0.144511i
$49$	0.990686	−	0.136167i	0.990686	−	0.136167i
$50$		0			0
$51$	−0.131424	+	0.0368232i	−0.131424	+	0.0368232i
$52$		0			0
$53$	−0.366581	+	0.843954i	−0.366581	+	0.843954i	0.631088	+	0.775711i	$0.282609\pi$
$53$	−0.366581	+	0.843954i	−0.366581	+	0.843954i	−0.997669	+	0.0682424i	$0.978261\pi$
$54$	−0.0457060	−	0.668198i	−0.0457060	−	0.668198i
$55$		0			0
$56$		0			0
$57$	1.88555	+	0.391823i	1.88555	+	0.391823i
$58$		0			0
$59$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$59$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$60$		0			0
$61$	−0.234658	−	1.12924i	−0.234658	−	1.12924i	−0.917211	−	0.398401i	$-0.869565\pi$
$61$	−0.234658	−	1.12924i	−0.234658	−	1.12924i	0.682553	−	0.730836i	$-0.260870\pi$
$62$	0.576999	+	0.709227i	0.576999	+	0.709227i
$63$		0			0
$64$	−0.529402	+	0.566851i	−0.529402	+	0.566851i
$65$		0			0
$66$		0			0
$67$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$67$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$68$	−0.0668230	−	0.0346249i	−0.0668230	−	0.0346249i
$69$	−1.53697	−	1.25042i	−1.53697	−	1.25042i
$70$		0			0
$71$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$71$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$72$	0.655751	−	0.806026i	0.655751	−	0.806026i
$73$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$73$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$74$		0			0
$75$		0			0
$76$	0.612405	+	0.867580i	0.612405	+	0.867580i
$77$		0			0
$78$		0			0
$79$	1.05893	−	0.861502i	1.05893	−	0.861502i	0.0682424	−	0.997669i	$-0.478261\pi$
$79$	1.05893	−	0.861502i	1.05893	−	0.861502i	0.990686	+	0.136167i	$0.0434783\pi$
$80$		0			0
$81$	−0.576680	+	0.816970i	−0.576680	+	0.816970i
$82$		0			0
$83$	−1.34066	+	1.25209i	−1.34066	+	1.25209i	−0.398401	+	0.917211i	$0.630435\pi$
$83$	−1.34066	+	1.25209i	−1.34066	+	1.25209i	−0.942261	+	0.334880i	$0.891304\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$89$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$90$		0			0
$91$		0			0
$92$	−0.148772	−	1.08240i	−0.148772	−	1.08240i
$93$		−	1.36511i		−	1.36511i
$94$	−0.224289	−	0.631088i	−0.224289	−	0.631088i
$95$		0			0
$96$	0.933516	−	0.128309i	0.933516	−	0.128309i
$97$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$97$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$98$	0.180699	+	0.644923i	0.180699	+	0.644923i
$99$		0			0
$100$		0			0
$101$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$101$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$102$	−0.0364186	−	0.0838441i	−0.0364186	−	0.0838441i
$103$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$103$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$104$		0			0
$105$		0			0
$106$	−0.593413	−	0.166266i	−0.593413	−	0.166266i
$107$	−1.39607	−	0.985454i	−1.39607	−	0.985454i	−0.997669	−	0.0682424i	$-0.978261\pi$
$107$	−1.39607	−	0.985454i	−1.39607	−	0.985454i	−0.398401	−	0.917211i	$-0.630435\pi$
$108$	−0.539889	+	0.112190i	−0.539889	+	0.112190i
$109$	−1.42298	+	1.15768i	−1.42298	+	1.15768i	−0.460065	+	0.887885i	$0.652174\pi$
$109$	−1.42298	+	1.15768i	−1.42298	+	1.15768i	−0.962917	+	0.269797i	$0.913043\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.383417	+	0.136267i	−0.383417	+	0.136267i	−0.519584	−	0.854419i	$-0.673913\pi$
$113$	−0.383417	+	0.136267i	−0.383417	+	0.136267i	0.136167	+	0.990686i	$0.456522\pi$
$114$	−0.0880222	+	1.28684i	−0.0880222	+	1.28684i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.0682424	+	0.997669i	−0.0682424	+	0.997669i
$122$	0.727872	−	0.258686i	0.727872	−	0.258686i
$123$		0			0
$124$	0.513792	−	0.550137i	0.513792	−	0.550137i
$125$		0			0
$126$		0			0
$127$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$127$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$128$	0.345426	+	0.243829i	0.345426	+	0.243829i
$129$		0			0
$130$		0			0
$131$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$131$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	0.0474922	−	0.133630i	0.0474922	−	0.133630i
$137$	−0.494921	−	1.76640i	−0.494921	−	1.76640i	−0.631088	−	0.775711i	$-0.717391\pi$
$137$	−0.494921	−	1.76640i	−0.494921	−	1.76640i	0.136167	−	0.990686i	$-0.456522\pi$
$138$	0.689510	−	1.13385i	0.689510	−	1.13385i
$139$	−1.53697	+	0.211252i	−1.53697	+	0.211252i	−0.854419	−	0.519584i	$-0.826087\pi$
$139$	−1.53697	+	0.211252i	−1.53697	+	0.211252i	−0.682553	+	0.730836i	$0.739130\pi$
$140$		0			0
$141$	−0.334880	+	0.942261i	−0.334880	+	0.942261i
$142$		0			0
$143$		0			0
$144$	0.123473	+	0.0750854i	0.123473	+	0.0750854i
$145$		0			0
$146$		0			0
$147$	0.398401	−	0.917211i	0.398401	−	0.917211i
$148$		0			0
$149$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$149$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$150$		0			0
$151$	−0.234658	+	1.12924i	−0.234658	+	1.12924i	0.682553	+	0.730836i	$0.260870\pi$
$151$	−0.234658	+	1.12924i	−0.234658	+	1.12924i	−0.917211	+	0.398401i	$0.869565\pi$
$152$	−1.46247	+	1.36585i	−1.46247	+	1.36585i
$153$	−0.0368232	+	0.131424i	−0.0368232	+	0.131424i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$157$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$158$	0.668198	+	0.624053i	0.668198	+	0.624053i
$159$	0.530621	+	0.751719i	0.530621	+	0.751719i
$160$		0			0
$161$		0			0
$162$	−0.594669	−	0.308133i	−0.594669	−	0.308133i
$163$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$163$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$164$		0			0
$165$		0			0
$166$	−0.953056	−	0.775368i	−0.953056	−	0.775368i
$167$	0.816970	+	0.423320i	0.816970	+	0.423320i	0.816970	−	0.576680i	$-0.195652\pi$
$167$	0.816970	+	0.423320i	0.816970	+	0.423320i			1.00000i	$0.5\pi$
$168$		0			0
$169$	0.334880	+	0.942261i	0.334880	+	0.942261i
$170$		0			0
$171$	1.31448	−	1.40747i	1.31448	−	1.40747i
$172$		0			0
$173$	0.256797	+	0.315646i	0.256797	+	0.315646i	0.887885	−	0.460065i	$-0.152174\pi$
$173$	0.256797	+	0.315646i	0.256797	+	0.315646i	−0.631088	+	0.775711i	$0.717391\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$179$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$180$		0			0
$181$	−0.0277687	−	0.405963i	−0.0277687	−	0.405963i	−0.990686	−	0.136167i	$-0.956522\pi$
$181$	−0.0277687	−	0.405963i	−0.0277687	−	0.405963i	0.962917	−	0.269797i	$-0.0869565\pi$
$182$		0			0
$183$	−1.08677	−	0.386237i	−1.08677	−	0.386237i
$184$	1.98246	−	0.555458i	1.98246	−	0.555458i
$185$		0			0
$186$	0.905777	−	0.124496i	0.905777	−	0.124496i
$187$		0			0
$188$	−0.489600	+	0.253690i	−0.489600	+	0.253690i
$189$		0			0
$190$		0			0
$191$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$191$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$192$	0.209260	+	0.746857i	0.209260	+	0.746857i
$193$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$193$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$194$		0			0
$195$		0			0
$196$	0.505771	−	0.219687i	0.505771	−	0.219687i
$197$	1.02405	−	0.530621i	1.02405	−	0.530621i	0.136167	−	0.990686i	$-0.456522\pi$
$197$	1.02405	−	0.530621i	1.02405	−	0.530621i	0.887885	+	0.460065i	$0.152174\pi$
$198$		0			0
$199$	−0.628038	−	0.672464i	−0.628038	−	0.672464i	0.334880	−	0.942261i	$-0.391304\pi$
$199$	−0.628038	−	0.672464i	−0.628038	−	0.672464i	−0.962917	+	0.269797i	$0.913043\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.0643043	+	0.0391043i	−0.0643043	+	0.0391043i
$205$		0			0
$206$		0			0
$207$	−1.86697	+	0.663521i	−1.86697	+	0.663521i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−1.69292	−	0.232687i	−1.69292	−	0.232687i	−0.775711	−	0.631088i	$-0.782609\pi$
$211$	−1.69292	−	0.232687i	−1.69292	−	0.232687i	−0.917211	+	0.398401i	$0.869565\pi$
$212$	−0.0690883	+	0.502655i	−0.0690883	+	0.502655i
$213$		0			0
$214$	0.526549	−	1.01619i	0.526549	−	1.01619i
$215$		0			0
$216$	−0.347967	−	0.979084i	−0.347967	−	0.979084i
$217$		0			0
$218$	−0.897921	−	0.838599i	−0.897921	−	0.838599i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$223$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$224$		0			0
$225$		0			0
$226$	−0.125383	−	0.241978i	−0.125383	−	0.241978i
$227$	0.459500	+	1.05788i	0.459500	+	1.05788i	0.979084	+	0.203456i	$0.0652174\pi$
$227$	0.459500	+	1.05788i	0.459500	+	1.05788i	−0.519584	+	0.854419i	$0.673913\pi$
$228$	1.05947	−	0.0724699i	1.05947	−	0.0724699i
$229$	−1.05788	−	0.459500i	−1.05788	−	0.459500i	−0.203456	−	0.979084i	$-0.565217\pi$
$229$	−1.05788	−	0.459500i	−1.05788	−	0.459500i	−0.854419	+	0.519584i	$0.826087\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.125291	+	0.911560i	0.125291	+	0.911560i	0.942261	+	0.334880i	$0.108696\pi$
$233$	0.125291	+	0.911560i	0.125291	+	0.911560i	−0.816970	+	0.576680i	$0.804348\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.185882	−	1.35239i	−0.185882	−	1.35239i
$238$		0			0
$239$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$239$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$240$		0			0
$241$	−0.843954	−	0.366581i	−0.843954	−	0.366581i	−0.0682424	−	0.997669i	$-0.521739\pi$
$241$	−0.843954	−	0.366581i	−0.843954	−	0.366581i	−0.775711	+	0.631088i	$0.782609\pi$
$242$	−0.668198	+	0.0457060i	−0.668198	+	0.0457060i
$243$	0.398401	+	0.917211i	0.398401	+	0.917211i
$244$	−0.292596	−	0.564685i	−0.292596	−	0.564685i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	1.15883	+	0.817995i	1.15883	+	0.817995i
$249$	0.373224	+	1.79605i	0.373224	+	1.79605i
$250$		0			0
$251$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$251$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.487118	+	0.940096i	−0.487118	+	0.940096i
$257$	−0.0861339	+	0.105873i	−0.0861339	+	0.105873i	−0.816970	−	0.576680i	$-0.804348\pi$
$257$	−0.0861339	+	0.105873i	−0.0861339	+	0.105873i	0.730836	+	0.682553i	$0.239130\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.86697	−	0.663521i	1.86697	−	0.663521i	0.887885	−	0.460065i	$-0.152174\pi$
$263$	1.86697	−	0.663521i	1.86697	−	0.663521i	0.979084	−	0.203456i	$-0.0652174\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$269$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$270$		0			0
$271$	1.31448	+	1.40747i	1.31448	+	1.40747i	0.854419	+	0.519584i	$0.173913\pi$
$271$	1.31448	+	1.40747i	1.31448	+	1.40747i	0.460065	+	0.887885i	$0.347826\pi$
$272$	0.0193110	+	0.00401286i	0.0193110	+	0.00401286i
$273$		0			0
$274$	1.12691	−	0.489484i	1.12691	−	0.489484i
$275$		0			0
$276$	−1.00212	−	0.435282i	−1.00212	−	0.435282i
$277$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$277$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$278$	−0.280340	−	1.00055i	−0.280340	−	1.00055i
$279$	−1.16637	−	0.709287i	−1.16637	−	0.709287i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−0.655751	−	0.136267i	−0.655751	−	0.136267i
$283$		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
$288$	0.375410	−	0.864281i	0.375410	−	0.864281i
$289$	−0.0669712	−	0.979084i	−0.0669712	−	0.979084i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.489484	+	0.457146i	−0.489484	+	0.457146i	−0.887885	−	0.460065i	$-0.847826\pi$
$293$	−0.489484	+	0.457146i	−0.489484	+	0.457146i	0.398401	+	0.917211i	$0.369565\pi$
$294$	0.644923	+	0.180699i	0.644923	+	0.180699i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	−0.770673	−	0.0527155i	−0.770673	−	0.0527155i
$303$		0			0
$304$	−0.215883	−	0.175634i	−0.215883	−	0.175634i
$305$		0			0
$306$	−0.0905606	−	0.0124473i	−0.0905606	−	0.0124473i
$307$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$307$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$311$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$312$		0			0
$313$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$313$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$314$		0			0
$315$		0			0
$316$	0.434096	−	0.614974i	0.434096	−	0.614974i
$317$	−0.461039	+	1.64547i	−0.461039	+	1.64547i	0.269797	+	0.962917i	$0.413043\pi$
$317$	−0.461039	+	1.64547i	−0.461039	+	1.64547i	−0.730836	+	0.682553i	$0.760870\pi$
$318$	−0.450389	+	0.420634i	−0.450389	+	0.420634i
$319$		0			0
$320$		0			0
$321$	−1.56737	+	0.680803i	−1.56737	+	0.680803i
$322$		0			0
$323$	0.104719	−	0.241086i	0.104719	−	0.241086i
$324$	−0.184660	+	0.519584i	−0.184660	+	0.519584i
$325$		0			0
$326$		0			0
$327$	0.249787	+	1.81734i	0.249787	+	1.81734i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.81734	−	0.249787i	1.81734	−	0.249787i	0.854419	−	0.519584i	$-0.173913\pi$
$331$	1.81734	−	0.249787i	1.81734	−	0.249787i	0.962917	+	0.269797i	$0.0869565\pi$
$332$	−0.525581	+	0.864281i	−0.525581	+	0.864281i
$333$		0			0
$334$	−0.206375	+	0.580683i	−0.206375	+	0.580683i
$335$		0			0
$336$		0			0
$337$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$337$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$338$	−0.594669	+	0.308133i	−0.594669	+	0.308133i
$339$	−0.0827887	+	0.398401i	−0.0827887	+	0.398401i
$340$		0			0
$341$		0			0
$342$	1.05376	+	0.743829i	1.05376	+	0.743829i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.186018	+	0.199177i	−0.186018	+	0.199177i
$347$	0.332435	−	0.234658i	0.332435	−	0.234658i	−0.398401	−	0.917211i	$-0.630435\pi$
$347$	0.332435	−	0.234658i	0.332435	−	0.234658i	0.730836	+	0.682553i	$0.239130\pi$
$348$		0			0
$349$	−0.105873	+	1.54781i	−0.105873	+	1.54781i	0.576680	+	0.816970i	$0.304348\pi$
$349$	−0.105873	+	1.54781i	−0.105873	+	1.54781i	−0.682553	+	0.730836i	$0.739130\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.262234	+	1.90790i	−0.262234	+	1.90790i	0.136167	+	0.990686i	$0.456522\pi$
$353$	−0.262234	+	1.90790i	−0.262234	+	1.90790i	−0.398401	+	0.917211i	$0.630435\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$359$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$360$		0			0
$361$	−2.10128	+	1.70952i	−2.10128	+	1.70952i
$362$	0.266833	−	0.0554485i	0.266833	−	0.0554485i
$363$	0.816970	+	0.576680i	0.816970	+	0.576680i
$364$		0			0
$365$		0			0
$366$	0.157164	−	0.756317i	0.157164	−	0.756317i
$367$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$367$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$368$	0.114074	+	0.262624i	0.114074	+	0.262624i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.203090	−	0.724836i	−0.203090	−	0.724836i
$373$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$373$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$374$		0			0
$375$		0			0
$376$	−0.599217	−	0.848897i	−0.599217	−	0.848897i
$377$		0			0
$378$		0			0
$379$	−1.46007	−	0.887885i	−1.46007	−	0.887885i	−0.460065	−	0.887885i	$-0.652174\pi$
$379$	−1.46007	−	0.887885i	−1.46007	−	0.887885i	−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.405963	+	0.0277687i	−0.405963	+	0.0277687i	−0.269797	−	0.962917i	$-0.586957\pi$
$383$	−0.405963	+	0.0277687i	−0.405963	+	0.0277687i	−0.136167	+	0.990686i	$0.543478\pi$
$384$	0.387810	−	0.168450i	0.387810	−	0.168450i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$389$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$390$		0			0
$391$	−0.209773	+	0.170663i	−0.209773	+	0.170663i
$392$	0.539889	+	0.887810i	0.539889	+	0.887810i
$393$		0			0
$394$	0.445471	+	0.631088i	0.445471	+	0.631088i
$395$		0			0
$396$		0			0
$397$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$397$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$398$	0.388918	−	0.478044i	0.388918	−	0.478044i
$399$		0			0
$400$		0			0
$401$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$401$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.0895000	−	0.110010i	−0.0895000	−	0.110010i
$409$	0.315646	+	1.51897i	0.315646	+	1.51897i	0.775711	+	0.631088i	$0.217391\pi$
$409$	0.315646	+	1.51897i	0.315646	+	1.51897i	−0.460065	+	0.887885i	$0.652174\pi$
$410$		0			0
$411$	−1.76640	−	0.494921i	−1.76640	−	0.494921i
$412$		0			0
$413$		0			0
$414$	−0.610526	−	1.17826i	−0.610526	−	1.17826i
$415$		0			0
$416$		0			0
$417$	−0.618088	+	1.42298i	−0.618088	+	1.42298i
$418$		0			0
$419$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$419$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$420$		0			0
$421$	−1.69292	+	0.232687i	−1.69292	+	0.232687i	−0.917211	−	0.398401i	$-0.869565\pi$
$421$	−1.69292	+	0.232687i	−1.69292	+	0.232687i	−0.775711	+	0.631088i	$0.782609\pi$
$422$		−	1.14451i		−	1.14451i
$423$	0.631088	+	0.775711i	0.631088	+	0.775711i
$424$	−0.956088			−0.956088
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.887885	−	0.315554i	−0.887885	−	0.315554i
$429$		0			0
$430$		0			0
$431$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$431$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$432$	0.128309	−	0.0664843i	0.128309	−	0.0664843i
$433$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$433$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$434$		0			0
$435$		0			0
$436$	−0.583336	+	0.826399i	−0.583336	+	0.826399i
$437$	3.73598	−	0.776346i	3.73598	−	0.776346i
$438$		0			0
$439$	1.56737	−	0.953137i	1.56737	−	0.953137i	0.576680	−	0.816970i	$-0.304348\pi$
$439$	1.56737	−	0.953137i	1.56737	−	0.953137i	0.990686	−	0.136167i	$-0.0434783\pi$
$440$		0			0
$441$	−0.576680	−	0.816970i	−0.576680	−	0.816970i
$442$		0			0
$443$	−1.83015	−	0.125185i	−1.83015	−	0.125185i	−0.887885	−	0.460065i	$-0.847826\pi$
$443$	−1.83015	−	0.125185i	−1.83015	−	0.125185i	−0.942261	+	0.334880i	$0.891304\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$449$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$450$		0			0
$451$		0			0
$452$	−0.183312	+	0.129396i	−0.183312	+	0.129396i
$453$	0.842917	+	0.787230i	0.842917	+	0.787230i
$454$	−0.660017	+	0.401365i	−0.660017	+	0.401365i
$455$		0			0
$456$	0.407135	+	1.95924i	0.407135	+	1.95924i
$457$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$457$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$458$	0.208411	−	0.743829i	0.208411	−	0.743829i
$459$	0.0931581	+	0.0997480i	0.0931581	+	0.0997480i
$460$		0			0
$461$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$461$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$462$		0			0
$463$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$463$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$464$		0			0
$465$		0			0
$466$	−0.593413	+	0.166266i	−0.593413	+	0.166266i
$467$	0.806094	−	1.32557i	0.806094	−	1.32557i	−0.136167	−	0.990686i	$-0.543478\pi$
$467$	0.806094	−	1.32557i	0.806094	−	1.32557i	0.942261	−	0.334880i	$-0.108696\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.880388	−	0.246673i	0.880388	−	0.246673i
$475$		0			0
$476$		0			0
$477$	0.917985	−	0.0627919i	0.917985	−	0.0627919i
$478$		0			0
$479$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$479$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$480$		0			0
$481$		0			0
$482$	0.166266	−	0.593413i	0.166266	−	0.593413i
$483$		0			0
$484$	0.112190	+	0.539889i	0.112190	+	0.539889i
$485$		0			0
$486$	−0.572255	+	0.347996i	−0.572255	+	0.347996i
$487$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$487$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$488$	0.979084	−	0.691113i	0.979084	−	0.691113i
$489$		0			0
$490$		0			0
$491$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$491$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.0907581	+	0.175155i	−0.0907581	+	0.175155i
$497$		0			0
$498$	−1.15768	+	0.411440i	−1.15768	+	0.411440i
$499$	−1.14262	−	1.61872i	−1.14262	−	1.61872i	−0.682553	−	0.730836i	$-0.739130\pi$
$499$	−1.14262	−	1.61872i	−1.14262	−	1.61872i	−0.460065	−	0.887885i	$-0.652174\pi$
$500$		0			0
$501$	0.786177	−	0.478085i	0.786177	−	0.478085i
$502$		0			0
$503$	−0.655751	+	0.136267i	−0.655751	+	0.136267i	−0.519584	−	0.854419i	$-0.673913\pi$
$503$	−0.655751	+	0.136267i	−0.655751	+	0.136267i	−0.136167	+	0.990686i	$0.543478\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.979084	+	0.203456i	0.979084	+	0.203456i
$508$		0			0
$509$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$509$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$510$		0			0
$511$		0			0
$512$	−0.269797	−	0.0958858i	−0.269797	−	0.0958858i
$513$	−0.519584	−	1.85442i	−0.519584	−	1.85442i
$514$	−0.0781042	−	0.0474962i	−0.0781042	−	0.0474962i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	0.403122	−	0.0554078i	0.403122	−	0.0554078i
$520$		0			0
$521$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$521$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$522$		0			0
$523$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$523$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$524$		0			0
$525$		0			0
$526$	0.610526	+	1.17826i	0.610526	+	1.17826i
$527$	−0.182419	−	0.0379072i	−0.182419	−	0.0379072i
$528$		0			0
$529$	−2.81734	−	0.789381i	−2.81734	−	0.789381i
$530$		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
$541$	−1.35239	−	0.185882i	−1.35239	−	0.185882i	−0.576680	−	0.816970i	$-0.695652\pi$
$541$	−1.35239	−	0.185882i	−1.35239	−	0.185882i	−0.775711	+	0.631088i	$0.782609\pi$
$542$	−0.814006	+	1.00055i	−0.814006	+	1.00055i
$543$	−0.361291	−	0.187206i	−0.361291	−	0.187206i
$544$	0.00877656	−	0.128309i	0.00877656	−	0.128309i
$545$		0			0
$546$		0			0
$547$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$547$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$548$	−0.525581	−	0.864281i	−0.525581	−	0.864281i
$549$	−0.894675	+	0.727872i	−0.894675	+	0.727872i
$550$		0			0
$551$		0			0
$552$	0.555458	−	1.98246i	0.555458	−	1.98246i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.784665	+	0.340828i	−0.784665	+	0.340828i
$557$	−0.136167	+	0.00931405i	−0.136167	+	0.00931405i	−0.136167	−	0.990686i	$-0.543478\pi$
$557$	−0.136167	+	0.00931405i	−0.136167	+	0.00931405i			1.00000i	$0.5\pi$
$558$	0.364255	−	0.838599i	0.364255	−	0.838599i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$			0.136485i			0.136485i	0.997669	+	0.0682424i	$0.0217391\pi$
$563$			0.136485i			0.136485i	−0.997669	+	0.0682424i	$0.978261\pi$
$564$	−0.0376304	+	0.550137i	−0.0376304	+	0.550137i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$569$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$570$		0			0
$571$	−0.131424	−	1.92135i	−0.131424	−	1.92135i	−0.334880	−	0.942261i	$-0.608696\pi$
$571$	−0.131424	−	1.92135i	−0.131424	−	1.92135i	0.203456	−	0.979084i	$-0.434783\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.746857	+	0.209260i	0.746857	+	0.209260i
$577$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$577$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$578$	0.643535	−	0.133728i	0.643535	−	0.133728i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.347967	−	0.283092i	−0.347967	−	0.283092i
$587$	0.262234	−	1.90790i	0.262234	−	1.90790i	−0.136167	−	0.990686i	$-0.543478\pi$
$587$	0.262234	−	1.90790i	0.262234	−	1.90790i	0.398401	−	0.917211i	$-0.369565\pi$
$588$	0.0750854	−	0.546287i	0.0750854	−	0.546287i
$589$	2.03932	+	1.65911i	2.03932	+	1.65911i
$590$		0			0
$591$	0.0787081	−	1.15067i	0.0787081	−	1.15067i
$592$		0			0
$593$	0.547173	−	0.386237i	0.547173	−	0.386237i	−0.269797	−	0.962917i	$-0.586957\pi$
$593$	0.547173	−	0.386237i	0.547173	−	0.386237i	0.816970	+	0.576680i	$0.195652\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.900885	+	0.187206i	−0.900885	+	0.187206i
$598$		0			0
$599$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$599$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$600$		0			0
$601$	0.0827887	−	0.398401i	0.0827887	−	0.398401i	−0.917211	−	0.398401i	$-0.869565\pi$
$601$	0.0827887	−	0.398401i	0.0827887	−	0.398401i	1.00000			$0$
$602$		0			0
$603$		0			0
$604$	0.0434014	+	0.634506i	0.0434014	+	0.634506i
$605$		0			0
$606$		0			0
$607$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$607$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$608$	−0.942889	+	1.55051i	−0.942889	+	1.55051i
$609$		0			0
$610$		0			0
$611$		0			0
$612$			0.0752608i			0.0752608i
$613$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$613$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.543860	−	1.25209i	0.543860	−	1.25209i	−0.398401	−	0.917211i	$-0.630435\pi$
$617$	0.543860	−	1.25209i	0.543860	−	1.25209i	0.942261	−	0.334880i	$-0.108696\pi$
$618$		0			0
$619$	−1.05788	+	0.459500i	−1.05788	+	0.459500i	−0.854419	−	0.519584i	$-0.826087\pi$
$619$	−1.05788	+	0.459500i	−1.05788	+	0.459500i	−0.203456	+	0.979084i	$0.565217\pi$
$620$		0			0
$621$	−0.403122	+	1.93993i	−0.403122	+	1.93993i
$622$		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
$631$	0.135214	−	1.97675i	0.135214	−	1.97675i	−0.0682424	−	0.997669i	$-0.521739\pi$
$631$	0.135214	−	1.97675i	0.135214	−	1.97675i	0.203456	−	0.979084i	$-0.434783\pi$
$632$	1.25942	+	0.652581i	1.25942	+	0.652581i
$633$	−1.07843	+	1.32557i	−1.07843	+	1.32557i
$634$	−1.13385	−	0.155844i	−1.13385	−	0.155844i
$635$		0			0
$636$	0.393581	+	0.320202i	0.393581	+	0.320202i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$641$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$642$	−0.594669	−	0.977892i	−0.594669	−	0.977892i
$643$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$643$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$644$		0			0
$645$		0			0
$646$	0.169516	+	0.0474962i	0.169516	+	0.0474962i
$647$	−0.672464	+	0.628038i	−0.672464	+	0.628038i	−0.942261	−	0.334880i	$-0.891304\pi$
$647$	−0.672464	+	0.628038i	−0.672464	+	0.628038i	0.269797	+	0.962917i	$0.413043\pi$
$648$	−1.01735	−	0.211407i	−1.01735	−	0.211407i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.81464	+	0.644923i	1.81464	+	0.644923i	0.997669	+	0.0682424i	$0.0217391\pi$
$653$	1.81464	+	0.644923i	1.81464	+	0.644923i	0.816970	+	0.576680i	$0.195652\pi$
$654$	−1.18306	+	0.331478i	−1.18306	+	0.331478i
$655$		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
$661$	−0.116615	−	0.0709153i	−0.116615	−	0.0709153i	0.460065	−	0.887885i	$-0.347826\pi$
$661$	−0.116615	−	0.0709153i	−0.116615	−	0.0709153i	−0.576680	+	0.816970i	$0.695652\pi$
$662$	0.331478	+	1.18306i	0.331478	+	1.18306i
$663$		0			0
$664$	−1.74831	−	0.759397i	−1.74831	−	0.759397i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.496768	+	0.103230i	0.496768	+	0.103230i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$673$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$674$		0			0
$675$		0			0
$676$	0.317995	+	0.450496i	0.317995	+	0.450496i
$677$	−1.46184	+	0.519540i	−1.46184	+	0.519540i	−0.942261	−	0.334880i	$-0.891304\pi$
$677$	−1.46184	+	0.519540i	−1.46184	+	0.519540i	−0.519584	+	0.854419i	$0.673913\pi$
$678$	−0.271898	−	0.0185983i	−0.271898	−	0.0185983i
$679$		0			0
$680$		0			0
$681$	1.14262	+	0.157049i	1.14262	+	0.157049i
$682$		0			0
$683$	1.25042	−	1.53697i	1.25042	−	1.53697i	0.519584	−	0.854419i	$-0.326087\pi$
$683$	1.25042	−	1.53697i	1.25042	−	1.53697i	0.730836	−	0.682553i	$-0.239130\pi$
$684$	0.488565	−	0.942889i	0.488565	−	0.942889i
$685$		0			0
$686$		0			0
$687$	−0.942261	+	0.665120i	−0.942261	+	0.665120i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.0277687	−	0.133630i	−0.0277687	−	0.133630i	0.962917	−	0.269797i	$-0.0869565\pi$
$691$	−0.0277687	−	0.133630i	−0.0277687	−	0.133630i	−0.990686	+	0.136167i	$0.956522\pi$
$692$	0.183312	+	0.129396i	0.183312	+	0.129396i
$693$		0			0
$694$	0.186018	+	0.199177i	0.186018	+	0.199177i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−1.03666	+	0.0709093i	−1.03666	+	0.0709093i
$699$	0.843954	+	0.366581i	0.843954	+	0.366581i
$700$		0			0
$701$		0			0		0.962917	−	0.269797i	$-0.0869565\pi$
$701$		0			0		−0.962917	+	0.269797i	$0.913043\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−1.28985			−1.28985
$707$		0			0
$708$		0			0
$709$	1.90790	−	0.534568i	1.90790	−	0.534568i	0.917211	−	0.398401i	$-0.130435\pi$
$709$	1.90790	−	0.534568i	1.90790	−	0.534568i	0.990686	−	0.136167i	$-0.0434783\pi$
$710$		0			0
$711$	−1.25209	−	0.543860i	−1.25209	−	0.543860i
$712$		0			0
$713$	−1.07759	−	2.48086i	−1.07759	−	2.48086i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$719$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$720$		0			0
$721$		0			0
$722$	−1.32593	−	1.23834i	−1.32593	−	1.23834i
$723$	−0.751719	+	0.530621i	−0.751719	+	0.530621i
$724$	−0.0751404	−	0.211425i	−0.0751404	−	0.211425i
$725$		0			0
$726$	−0.308133	+	0.594669i	−0.308133	+	0.594669i
$727$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$727$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$728$		0			0
$729$	0.990686	+	0.136167i	0.990686	+	0.136167i
$730$		0			0
$731$		0			0
$732$	−0.634506	−	0.0434014i	−0.634506	−	0.0434014i
$733$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$733$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$734$		0			0
$735$		0			0
$736$	1.59523	−	0.970080i	1.59523	−	0.970080i
$737$		0			0
$738$		0			0
$739$	0.234658	−	0.332435i	0.234658	−	0.332435i	−0.682553	−	0.730836i	$-0.739130\pi$
$739$	0.234658	−	0.332435i	0.234658	−	0.332435i	0.917211	+	0.398401i	$0.130435\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.70992	−	0.886009i	1.70992	−	0.886009i	0.730836	−	0.682553i	$-0.239130\pi$
$743$	1.70992	−	0.886009i	1.70992	−	0.886009i	0.979084	−	0.203456i	$-0.0652174\pi$
$744$	1.30102	−	0.565114i	1.30102	−	0.565114i
$745$		0			0
$746$		0			0
$747$	1.72850	+	0.614311i	1.72850	+	0.614311i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.70884			1.70884			0.854419	−	0.519584i	$-0.173913\pi$
$751$	1.70884			1.70884			0.854419	+	0.519584i	$0.173913\pi$
$752$	0.105614	−	0.0986361i	0.105614	−	0.0986361i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$757$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$758$	0.455974	−	1.04976i	0.455974	−	1.04976i
$759$		0			0
$760$		0			0
$761$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$761$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	−0.0554485	−	0.266833i	−0.0554485	−	0.266833i
$767$		0			0
$768$	0.550137	+	0.904662i	0.550137	+	0.904662i
$769$	0.0931581	−	0.0997480i	0.0931581	−	0.0997480i	−0.682553	−	0.730836i	$-0.739130\pi$
$769$	0.0931581	−	0.0997480i	0.0931581	−	0.0997480i	0.775711	+	0.631088i	$0.217391\pi$
$770$		0			0
$771$	0.0457060	+	0.128604i	0.0457060	+	0.128604i
$772$		0			0
$773$	1.37749	+	0.713755i	1.37749	+	0.713755i	0.979084	−	0.203456i	$-0.0652174\pi$
$773$	1.37749	+	0.713755i	1.37749	+	0.713755i	0.398401	+	0.917211i	$0.369565\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.132370	−	0.123625i	−0.132370	−	0.123625i
$783$		0			0
$784$	−0.112098	+	0.0911989i	−0.112098	+	0.0911989i
$785$		0			0
$786$		0			0
$787$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$787$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$788$	0.464804	−	0.434096i	0.464804	−	0.434096i
$789$	0.403122	−	1.93993i	0.403122	−	1.93993i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.433516	−	0.263627i	−0.433516	−	0.263627i
$797$	0.211252	+	1.53697i	0.211252	+	1.53697i	0.730836	+	0.682553i	$0.239130\pi$
$797$	0.211252	+	1.53697i	0.211252	+	1.53697i	−0.519584	+	0.854419i	$0.673913\pi$
$798$		0			0
$799$	0.116615	+	0.0709153i	0.116615	+	0.0709153i
$800$		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		0.203456	−	0.979084i	$-0.434783\pi$
$809$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$810$		0			0
$811$	0.391823	+	0.109784i	0.391823	+	0.109784i	0.460065	−	0.887885i	$-0.347826\pi$
$811$	0.391823	+	0.109784i	0.391823	+	0.109784i	−0.0682424	+	0.997669i	$0.521739\pi$
$812$		0			0
$813$	1.88555	−	0.391823i	1.88555	−	0.391823i
$814$		0			0
$815$		0			0
$816$	0.0134623	−	0.0144146i	0.0134623	−	0.0144146i
$817$		0			0
$818$	−0.979084	+	0.347967i	−0.979084	+	0.347967i
$819$		0			0
$820$		0			0
$821$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$821$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$822$	0.167297	−	1.21718i	0.167297	−	1.21718i
$823$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$823$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.46184	+	0.519540i	−1.46184	+	0.519540i	−0.942261	−	0.334880i	$-0.891304\pi$
$827$	−1.46184	+	0.519540i	−1.46184	+	0.519540i	−0.519584	+	0.854419i	$0.673913\pi$
$828$	−0.892599	+	0.630065i	−0.892599	+	0.630065i
$829$	0.457146	−	0.489484i	0.457146	−	0.489484i	−0.460065	−	0.887885i	$-0.652174\pi$
$829$	0.457146	−	0.489484i	0.457146	−	0.489484i	0.917211	+	0.398401i	$0.130435\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.111504	−	0.0787081i	−0.111504	−	0.0787081i
$834$	−1.00055	−	0.280340i	−1.00055	−	0.280340i
$835$		0			0
$836$		0			0
$837$	−1.21206	+	0.628038i	−1.21206	+	0.628038i
$838$		0			0
$839$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$839$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$840$		0			0
$841$	−0.334880	+	0.942261i	−0.334880	+	0.942261i
$842$	−0.308785	−	1.10207i	−0.308785	−	1.10207i
$843$		0			0
$844$	−0.933516	+	0.128309i	−0.933516	+	0.128309i
$845$		0			0
$846$	−0.457146	+	0.489484i	−0.457146	+	0.489484i
$847$		0			0
$848$	−0.0181059	−	0.131730i	−0.0181059	−	0.131730i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$853$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$854$		0			0
$855$		0			0
$856$	0.361260	−	1.73848i	0.361260	−	1.73848i
$857$	−1.24888	+	1.16637i	−1.24888	+	1.16637i	−0.269797	+	0.962917i	$0.586957\pi$
$857$	−1.24888	+	1.16637i	−1.24888	+	1.16637i	−0.979084	+	0.203456i	$0.934783\pi$
$858$		0			0
$859$	−0.386237	+	0.547173i	−0.386237	+	0.547173i	−0.962917	−	0.269797i	$-0.913043\pi$
$859$	−0.386237	+	0.547173i	−0.386237	+	0.547173i	0.576680	+	0.816970i	$0.304348\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.997669	−	0.931758i	−0.997669	−	0.931758i		−	1.00000i	$-0.5\pi$
$863$	−0.997669	−	0.931758i	−0.997669	−	0.931758i	−0.997669	+	0.0682424i	$0.978261\pi$
$864$	−0.543401	−	0.769824i	−0.543401	−	0.769824i
$865$		0			0
$866$		0			0
$867$	−0.871346	−	0.451495i	−0.871346	−	0.451495i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−1.69241	−	0.876935i	−1.69241	−	0.876935i
$873$		0			0
$874$	0.855840	+	2.40810i	0.855840	+	2.40810i
$875$		0			0
$876$		0			0
$877$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$877$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$878$	0.775368	+	0.953056i	0.775368	+	0.953056i
$879$	0.136267	+	0.655751i	0.136267	+	0.655751i
$880$		0			0
$881$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$881$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$882$	0.489484	−	0.457146i	0.489484	−	0.457146i
$883$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$883$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$884$		0			0
$885$		0			0
$886$	−0.0838441	−	1.22576i	−0.0838441	−	1.22576i
$887$	0.767255	−	1.76640i	0.767255	−	1.76640i	0.136167	−	0.990686i	$-0.456522\pi$
$887$	0.767255	−	1.76640i	0.767255	−	1.76640i	0.631088	−	0.775711i	$-0.282609\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.00063	−	1.64547i	−1.00063	−	1.64547i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.115187	−	0.0500327i	0.115187	−	0.0500327i
$902$		0			0
$903$		0			0
$904$	−0.288593	−	0.309008i	−0.288593	−	0.309008i
$905$		0			0
$906$	−0.445471	+	0.631088i	−0.445471	+	0.631088i
$907$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$907$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$908$	0.401365	+	0.493344i	0.401365	+	0.493344i
$909$		0			0
$910$		0			0
$911$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$911$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$912$	−0.262234	+	0.0931981i	−0.262234	+	0.0931981i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−0.630065	−	0.0866005i	−0.630065	−	0.0866005i
$917$		0			0
$918$	−0.0576890	+	0.0709093i	−0.0576890	+	0.0709093i
$919$	0.911560	−	1.75923i	0.911560	−	1.75923i	0.334880	−	0.942261i	$-0.391304\pi$
$919$	0.911560	−	1.75923i	0.911560	−	1.75923i	0.576680	−	0.816970i	$-0.304348\pi$
$920$		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		−0.682553	−	0.730836i	$-0.739130\pi$
$929$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$930$		0			0
$931$	0.886009	+	1.70992i	0.886009	+	1.70992i
$932$	0.202141	+	0.465375i	0.202141	+	0.465375i
$933$		0			0
$934$	0.953056	+	0.413970i	0.953056	+	0.413970i
$935$		0			0
$936$		0			0
$937$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$937$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$938$		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
$947$	−1.54781	+	0.105873i	−1.54781	+	0.105873i	−0.816970	−	0.576680i	$-0.804348\pi$
$947$	−1.54781	+	0.105873i	−1.54781	+	0.105873i	−0.730836	+	0.682553i	$0.760870\pi$
$948$	−0.299897	−	0.690431i	−0.299897	−	0.690431i
$949$		0			0
$950$		0			0
$951$	1.16637	+	1.24888i	1.16637	+	1.24888i
$952$		0			0
$953$	−0.547173	−	0.386237i	−0.547173	−	0.386237i	0.269797	−	0.962917i	$-0.413043\pi$
$953$	−0.547173	−	0.386237i	−0.547173	−	0.386237i	−0.816970	+	0.576680i	$0.804348\pi$
$954$	0.125383	+	0.603376i	0.125383	+	0.603376i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.397273	−	0.766702i	0.397273	−	0.766702i
$962$		0			0
$963$	−0.232687	+	1.69292i	−0.232687	+	1.69292i
$964$	−0.502655	−	0.0690883i	−0.502655	−	0.0690883i
$965$		0			0
$966$		0			0
$967$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$967$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$968$	−0.979084	+	0.347967i	−0.979084	+	0.347967i
$969$	−0.151579	−	0.214738i	−0.151579	−	0.214738i
$970$		0			0
$971$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$971$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$972$	0.347996	+	0.427745i	0.347996	+	0.427745i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.113763	+	0.121810i	0.113763	+	0.121810i
$977$	0.398401	+	0.0827887i	0.398401	+	0.0827887i	0.398401	−	0.917211i	$-0.369565\pi$
$977$	0.398401	+	0.0827887i	0.398401	+	0.0827887i			1.00000i	$0.5\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	1.68255	+	0.730836i	1.68255	+	0.730836i
$982$		0			0
$983$	0.311173	+	1.11059i	0.311173	+	1.11059i	0.942261	+	0.334880i	$0.108696\pi$
$983$	0.311173	+	1.11059i	0.311173	+	1.11059i	−0.631088	+	0.775711i	$0.717391\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	1.64547	−	0.461039i	1.64547	−	0.461039i	0.682553	−	0.730836i	$-0.260870\pi$
$991$	1.64547	−	0.461039i	1.64547	−	0.461039i	0.962917	+	0.269797i	$0.0869565\pi$
$992$	1.21206	+	0.430765i	1.21206	+	0.430765i
$993$	0.730836	−	1.68255i	0.730836	−	1.68255i
$994$		0			0
$995$		0			0
$996$	0.465375	+	0.898133i	0.465375	+	0.898133i
$997$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$997$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$998$	0.969850	−	0.905777i	0.969850	−	0.905777i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bd.a.776.2		44
3.2	odd	2	inner	3525.1.bd.a.776.1		44
5.2	odd	4		705.1.p.b.494.1	yes	22
5.3	odd	4		705.1.p.a.494.1	yes	22
5.4	even	2	inner	3525.1.bd.a.776.1		44
15.2	even	4		705.1.p.a.494.1	yes	22
15.8	even	4		705.1.p.b.494.1	yes	22
15.14	odd	2	CM	3525.1.bd.a.776.2		44
47.2	even	23	inner	3525.1.bd.a.1976.1		44
141.2	odd	46	inner	3525.1.bd.a.1976.2		44
235.2	odd	92		705.1.p.b.284.1	yes	22
235.49	even	46	inner	3525.1.bd.a.1976.2		44
235.143	odd	92		705.1.p.a.284.1	✓	22
705.2	even	92		705.1.p.a.284.1	✓	22
705.143	even	92		705.1.p.b.284.1	yes	22
705.284	odd	46	inner	3525.1.bd.a.1976.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.1.p.a.284.1	✓	22	235.143	odd	92
705.1.p.a.284.1	✓	22	705.2	even	92
705.1.p.a.494.1	yes	22	5.3	odd	4
705.1.p.a.494.1	yes	22	15.2	even	4
705.1.p.b.284.1	yes	22	235.2	odd	92
705.1.p.b.284.1	yes	22	705.143	even	92
705.1.p.b.494.1	yes	22	5.2	odd	4
705.1.p.b.494.1	yes	22	15.8	even	4
3525.1.bd.a.776.1		44	3.2	odd	2	inner
3525.1.bd.a.776.1		44	5.4	even	2	inner
3525.1.bd.a.776.2		44	1.1	even	1	trivial
3525.1.bd.a.776.2		44	15.14	odd	2	CM
3525.1.bd.a.1976.1		44	47.2	even	23	inner
3525.1.bd.a.1976.1		44	705.284	odd	46	inner
3525.1.bd.a.1976.2		44	141.2	odd	46	inner
3525.1.bd.a.1976.2		44	235.49	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)

\(f(q)\)	\(=\)	\(q+(0.0911989 + 0.663521i) q^{2} +(0.519584 - 0.854419i) q^{3} +(0.530974 - 0.148772i) q^{4} +(0.614311 + 0.266833i) q^{6} +(0.413970 + 0.953056i) q^{8} +(-0.460065 - 0.887885i) q^{9} +O(q^{10})\)	\(q+(0.0911989 + 0.663521i) q^{2} +(0.519584 - 0.854419i) q^{3} +(0.530974 - 0.148772i) q^{4} +(0.614311 + 0.266833i) q^{6} +(0.413970 + 0.953056i) q^{8} +(-0.460065 - 0.887885i) q^{9} +(0.148772 - 0.530974i) q^{12} +(-0.123473 + 0.0750854i) q^{16} +(-0.0997480 - 0.0931581i) q^{17} +(0.547173 - 0.386237i) q^{18} +(0.644923 + 1.81464i) q^{19} +(0.269797 - 1.96292i) q^{23} +(1.02940 + 0.141488i) q^{24} +(-0.997669 - 0.0682424i) q^{27} +(1.16637 - 0.709287i) q^{31} +(0.594669 + 0.730947i) q^{32} +(0.0527155 - 0.0746808i) q^{34} +(-0.376375 - 0.402999i) q^{36} +(-1.14523 + 0.593413i) q^{38} +1.32704 q^{46} +(-0.979084 + 0.203456i) q^{47} +0.144511i q^{48} +(0.990686 - 0.136167i) q^{49} +(-0.131424 + 0.0368232i) q^{51} +(-0.366581 + 0.843954i) q^{53} +(-0.0457060 - 0.668198i) q^{54} +(1.88555 + 0.391823i) q^{57} +(-0.234658 - 1.12924i) q^{61} +(0.576999 + 0.709227i) q^{62} +(-0.529402 + 0.566851i) q^{64} +(-0.0668230 - 0.0346249i) q^{68} +(-1.53697 - 1.25042i) q^{69} +(0.655751 - 0.806026i) q^{72} +(0.612405 + 0.867580i) q^{76} +(1.05893 - 0.861502i) q^{79} +(-0.576680 + 0.816970i) q^{81} +(-1.34066 + 1.25209i) q^{83} +(-0.148772 - 1.08240i) q^{92} -1.36511i q^{93} +(-0.224289 - 0.631088i) q^{94} +(0.933516 - 0.128309i) q^{96} +(0.180699 + 0.644923i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 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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