LMFDB - Embedded newform 3525.1.bd.a.1001.1

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			1001.1
Root			$0.519584 + 0.854419i$ of defining polynomial
Character	$\chi$	$=$	3525.1001
Dual form			3525.1.bd.a.2951.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88555 - 0.391823i) q^{2} +(0.730836 + 0.682553i) q^{3} +(2.48458 + 1.07920i) q^{4} +(-1.11059 - 1.57335i) q^{6} +(-2.68860 - 1.89782i) q^{8} +(0.0682424 + 0.997669i) q^{9} +O(q^{10})$	\(q+(-1.88555 - 0.391823i) q^{2} +(0.730836 + 0.682553i) q^{3} +(2.48458 + 1.07920i) q^{4} +(-1.11059 - 1.57335i) q^{6} +(-2.68860 - 1.89782i) q^{8} +(0.0682424 + 0.997669i) q^{9} +(1.07920 + 2.48458i) q^{12} +(2.47696 + 2.65218i) q^{16} +(1.46184 - 0.519540i) q^{17} +(0.262234 - 1.90790i) q^{18} +(1.76640 - 0.494921i) q^{19} +(-0.398401 + 0.0827887i) q^{23} +(-0.669562 - 3.22211i) q^{24} +(-0.631088 + 0.775711i) q^{27} +(-0.457146 - 0.489484i) q^{31} +(-1.92135 - 3.15952i) q^{32} +(-2.95995 + 0.406836i) q^{34} +(-0.907135 + 2.55243i) q^{36} +(-3.52456 + 0.241086i) q^{38} +0.783645 q^{46} +(0.887885 - 0.460065i) q^{47} +3.62897i q^{48} +(-0.203456 + 0.979084i) q^{49} +(1.42298 + 0.618088i) q^{51} +(-0.111504 + 0.0787081i) q^{53} +(1.49389 - 1.21537i) q^{54} +(1.62876 + 0.843954i) q^{57} +(-0.911560 - 1.75923i) q^{61} +(0.670183 + 1.10207i) q^{62} +(1.16956 + 3.29083i) q^{64} +(4.19276 + 0.286792i) q^{68} +(-0.347674 - 0.211425i) q^{69} +(1.70992 - 2.81184i) q^{72} +(4.92287 + 0.676633i) q^{76} +(0.572255 - 0.347996i) q^{79} +(-0.990686 + 0.136167i) q^{81} +(1.08677 + 0.386237i) q^{83} +(-1.07920 - 0.224261i) q^{92} -0.669759i q^{93} +(-1.85442 + 0.519584i) q^{94} +(0.752350 - 3.62051i) q^{96} +(0.767255 - 1.76640i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$1$	$e\left(\frac{2}{23}\right)$	$-1$

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 $

$2$	−1.88555	−	0.391823i	−1.88555	−	0.391823i	−0.887885	−	0.460065i	$-0.847826\pi$
$2$	−1.88555	−	0.391823i	−1.88555	−	0.391823i	−0.997669	+	0.0682424i	$0.978261\pi$
$3$	0.730836	+	0.682553i	0.730836	+	0.682553i
$3$	0.730836	+	0.682553i	0.730836	+	0.682553i
$4$	2.48458	+	1.07920i	2.48458	+	1.07920i
$5$		0			0
$5$		0			0
$6$	−1.11059	−	1.57335i	−1.11059	−	1.57335i
$7$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$7$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$8$	−2.68860	−	1.89782i	−2.68860	−	1.89782i
$9$	0.0682424	+	0.997669i	0.0682424	+	0.997669i
$10$		0			0
$11$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$11$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$12$	1.07920	+	2.48458i	1.07920	+	2.48458i
$13$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$13$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$14$		0			0
$15$		0			0
$16$	2.47696	+	2.65218i	2.47696	+	2.65218i
$17$	1.46184	−	0.519540i	1.46184	−	0.519540i	0.519584	−	0.854419i	$-0.326087\pi$
$17$	1.46184	−	0.519540i	1.46184	−	0.519540i	0.942261	+	0.334880i	$0.108696\pi$
$18$	0.262234	−	1.90790i	0.262234	−	1.90790i
$19$	1.76640	−	0.494921i	1.76640	−	0.494921i	0.775711	−	0.631088i	$-0.217391\pi$
$19$	1.76640	−	0.494921i	1.76640	−	0.494921i	0.990686	+	0.136167i	$0.0434783\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.398401	+	0.0827887i	−0.398401	+	0.0827887i	−0.398401	−	0.917211i	$-0.630435\pi$
$23$	−0.398401	+	0.0827887i	−0.398401	+	0.0827887i			1.00000i	$0.5\pi$
$24$	−0.669562	−	3.22211i	−0.669562	−	3.22211i
$25$		0			0
$26$		0			0
$27$	−0.631088	+	0.775711i	−0.631088	+	0.775711i
$28$		0			0
$29$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$29$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$30$		0			0
$31$	−0.457146	−	0.489484i	−0.457146	−	0.489484i	0.460065	−	0.887885i	$-0.347826\pi$
$31$	−0.457146	−	0.489484i	−0.457146	−	0.489484i	−0.917211	+	0.398401i	$0.869565\pi$
$32$	−1.92135	−	3.15952i	−1.92135	−	3.15952i
$33$		0			0
$34$	−2.95995	+	0.406836i	−2.95995	+	0.406836i
$35$		0			0
$36$	−0.907135	+	2.55243i	−0.907135	+	2.55243i
$37$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$37$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$38$	−3.52456	+	0.241086i	−3.52456	+	0.241086i
$39$		0			0
$40$		0			0
$41$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$41$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$42$		0			0
$43$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$43$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$44$		0			0
$45$		0			0
$46$	0.783645			0.783645
$47$	0.887885	−	0.460065i	0.887885	−	0.460065i
$47$	0.887885	−	0.460065i	0.887885	−	0.460065i
$48$			3.62897i			3.62897i
$49$	−0.203456	+	0.979084i	−0.203456	+	0.979084i
$50$		0			0
$51$	1.42298	+	0.618088i	1.42298	+	0.618088i
$52$		0			0
$53$	−0.111504	+	0.0787081i	−0.111504	+	0.0787081i	−0.631088	−	0.775711i	$-0.717391\pi$
$53$	−0.111504	+	0.0787081i	−0.111504	+	0.0787081i	0.519584	+	0.854419i	$0.326087\pi$
$54$	1.49389	−	1.21537i	1.49389	−	1.21537i
$55$		0			0
$56$		0			0
$57$	1.62876	+	0.843954i	1.62876	+	0.843954i
$58$		0			0
$59$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$59$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$60$		0			0
$61$	−0.911560	−	1.75923i	−0.911560	−	1.75923i	−0.576680	−	0.816970i	$-0.695652\pi$
$61$	−0.911560	−	1.75923i	−0.911560	−	1.75923i	−0.334880	−	0.942261i	$-0.608696\pi$
$62$	0.670183	+	1.10207i	0.670183	+	1.10207i
$63$		0			0
$64$	1.16956	+	3.29083i	1.16956	+	3.29083i
$65$		0			0
$66$		0			0
$67$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$67$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$68$	4.19276	+	0.286792i	4.19276	+	0.286792i
$69$	−0.347674	−	0.211425i	−0.347674	−	0.211425i
$70$		0			0
$71$		0			0		−0.203456	−	0.979084i	$-0.565217\pi$
$71$		0			0		0.203456	+	0.979084i	$0.434783\pi$
$72$	1.70992	−	2.81184i	1.70992	−	2.81184i
$73$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$73$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$74$		0			0
$75$		0			0
$76$	4.92287	+	0.676633i	4.92287	+	0.676633i
$77$		0			0
$78$		0			0
$79$	0.572255	−	0.347996i	0.572255	−	0.347996i	−0.203456	−	0.979084i	$-0.565217\pi$
$79$	0.572255	−	0.347996i	0.572255	−	0.347996i	0.775711	+	0.631088i	$0.217391\pi$
$80$		0			0
$81$	−0.990686	+	0.136167i	−0.990686	+	0.136167i
$82$		0			0
$83$	1.08677	+	0.386237i	1.08677	+	0.386237i	0.816970	−	0.576680i	$-0.195652\pi$
$83$	1.08677	+	0.386237i	1.08677	+	0.386237i	0.269797	+	0.962917i	$0.413043\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$89$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$90$		0			0
$91$		0			0
$92$	−1.07920	−	0.224261i	−1.07920	−	0.224261i
$93$		−	0.669759i		−	0.669759i
$94$	−1.85442	+	0.519584i	−1.85442	+	0.519584i
$95$		0			0
$96$	0.752350	−	3.62051i	0.752350	−	3.62051i
$97$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$97$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$98$	0.767255	−	1.76640i	0.767255	−	1.76640i
$99$		0			0
$100$		0			0
$101$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$101$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$102$	−2.44093	−	1.72300i	−2.44093	−	1.72300i
$103$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$103$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$104$		0			0
$105$		0			0
$106$	0.241086	−	0.104719i	0.241086	−	0.104719i
$107$	0.185882	+	1.35239i	0.185882	+	1.35239i	0.816970	+	0.576680i	$0.195652\pi$
$107$	0.185882	+	1.35239i	0.185882	+	1.35239i	−0.631088	+	0.775711i	$0.717391\pi$
$108$	−2.40514	+	1.24624i	−2.40514	+	1.24624i
$109$	0.985454	−	0.599268i	0.985454	−	0.599268i	0.0682424	−	0.997669i	$-0.478261\pi$
$109$	0.985454	−	0.599268i	0.985454	−	0.599268i	0.917211	+	0.398401i	$0.130435\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.248248	+	0.886009i	0.248248	+	0.886009i	0.979084	+	0.203456i	$0.0652174\pi$
$113$	0.248248	+	0.886009i	0.248248	+	0.886009i	−0.730836	+	0.682553i	$0.760870\pi$
$114$	−2.74043	−	2.22950i	−2.74043	−	2.22950i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.775711	−	0.631088i	−0.775711	−	0.631088i
$122$	1.02949	+	3.67429i	1.02949	+	3.67429i
$123$		0			0
$124$	−0.607562	−	1.70952i	−0.607562	−	1.70952i
$125$		0			0
$126$		0			0
$127$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$127$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$128$	−0.412325	−	2.99989i	−0.412325	−	2.99989i
$129$		0			0
$130$		0			0
$131$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$131$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−4.91631	−	1.37749i	−4.91631	−	1.37749i
$137$	0.459500	−	1.05788i	0.459500	−	1.05788i	−0.519584	−	0.854419i	$-0.673913\pi$
$137$	0.459500	−	1.05788i	0.459500	−	1.05788i	0.979084	−	0.203456i	$-0.0652174\pi$
$138$	0.572716	+	0.534880i	0.572716	+	0.534880i
$139$	−0.347674	+	1.67310i	−0.347674	+	1.67310i	0.334880	+	0.942261i	$0.391304\pi$
$139$	−0.347674	+	1.67310i	−0.347674	+	1.67310i	−0.682553	+	0.730836i	$0.739130\pi$
$140$		0			0
$141$	0.962917	+	0.269797i	0.962917	+	0.269797i
$142$		0			0
$143$		0			0
$144$	−2.47696	+	2.65218i	−2.47696	+	2.65218i
$145$		0			0
$146$		0			0
$147$	−0.816970	+	0.576680i	−0.816970	+	0.576680i
$148$		0			0
$149$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$149$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$150$		0			0
$151$	−0.911560	+	1.75923i	−0.911560	+	1.75923i	−0.334880	+	0.942261i	$0.608696\pi$
$151$	−0.911560	+	1.75923i	−0.911560	+	1.75923i	−0.576680	+	0.816970i	$0.695652\pi$
$152$	−5.68841	−	2.02166i	−5.68841	−	2.02166i
$153$	0.618088	+	1.42298i	0.618088	+	1.42298i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$157$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$158$	−1.21537	+	0.431943i	−1.21537	+	0.431943i
$159$	−0.135214	−	0.0185847i	−0.135214	−	0.0185847i
$160$		0			0
$161$		0			0
$162$	1.92135	+	0.131424i	1.92135	+	0.131424i
$163$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$163$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$164$		0			0
$165$		0			0
$166$	−1.89782	−	1.15409i	−1.89782	−	1.15409i
$167$	−0.136167	−	0.00931405i	−0.136167	−	0.00931405i		−	1.00000i	$-0.5\pi$
$167$	−0.136167	−	0.00931405i	−0.136167	−	0.00931405i	−0.136167	+	0.990686i	$0.543478\pi$
$168$		0			0
$169$	−0.962917	+	0.269797i	−0.962917	+	0.269797i
$170$		0			0
$171$	0.614311	+	1.72850i	0.614311	+	1.72850i
$172$		0			0
$173$	0.478085	+	0.786177i	0.478085	+	0.786177i	0.997669	−	0.0682424i	$-0.0217391\pi$
$173$	0.478085	+	0.786177i	0.478085	+	0.786177i	−0.519584	+	0.854419i	$0.673913\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$179$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$180$		0			0
$181$	−0.713755	+	0.580683i	−0.713755	+	0.580683i	−0.917211	−	0.398401i	$-0.869565\pi$
$181$	−0.713755	+	0.580683i	−0.713755	+	0.580683i	0.203456	+	0.979084i	$0.434783\pi$
$182$		0			0
$183$	0.534568	−	1.90790i	0.534568	−	1.90790i
$184$	1.22826	+	0.533508i	1.22826	+	0.533508i
$185$		0			0
$186$	−0.262427	+	1.26287i	−0.262427	+	1.26287i
$187$		0			0
$188$	2.70252	−	0.184858i	2.70252	−	0.184858i
$189$		0			0
$190$		0			0
$191$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$191$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$192$	−1.39141	+	3.20335i	−1.39141	+	3.20335i
$193$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$193$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$194$		0			0
$195$		0			0
$196$	−1.56213	+	2.21304i	−1.56213	+	2.21304i
$197$	1.97675	−	0.135214i	1.97675	−	0.135214i	0.979084	−	0.203456i	$-0.0652174\pi$
$197$	1.97675	−	0.135214i	1.97675	−	0.135214i	0.997669	+	0.0682424i	$0.0217391\pi$
$198$		0			0
$199$	−0.0457060	+	0.128604i	−0.0457060	+	0.128604i	−0.962917	−	0.269797i	$-0.913043\pi$
$199$	−0.0457060	+	0.128604i	−0.0457060	+	0.128604i	0.917211	+	0.398401i	$0.130435\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	2.86847	+	3.07138i	2.86847	+	3.07138i
$205$		0			0
$206$		0			0
$207$	−0.109784	−	0.391823i	−0.109784	−	0.391823i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	0.277739	+	1.33655i	0.277739	+	1.33655i	0.854419	+	0.519584i	$0.173913\pi$
$211$	0.277739	+	1.33655i	0.277739	+	1.33655i	−0.576680	+	0.816970i	$0.695652\pi$
$212$	−0.361982	+	0.0752208i	−0.361982	+	0.0752208i
$213$		0			0
$214$	0.179407	−	2.62284i	0.179407	−	2.62284i
$215$		0			0
$216$	3.16890	−	0.887885i	3.16890	−	0.887885i
$217$		0			0
$218$	−2.09293	+	0.743829i	−2.09293	+	0.743829i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$223$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$224$		0			0
$225$		0			0
$226$	−0.120927	−	1.76789i	−0.120927	−	1.76789i
$227$	−1.61872	−	1.14262i	−1.61872	−	1.14262i	−0.887885	−	0.460065i	$-0.847826\pi$
$227$	−1.61872	−	1.14262i	−1.61872	−	1.14262i	−0.730836	−	0.682553i	$-0.760870\pi$
$228$	3.13597	+	3.85463i	3.13597	+	3.85463i
$229$	−1.14262	−	1.61872i	−1.14262	−	1.61872i	−0.682553	−	0.730836i	$-0.739130\pi$
$229$	−1.14262	−	1.61872i	−1.14262	−	1.61872i	−0.460065	−	0.887885i	$-0.652174\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.133630	−	0.0277687i	−0.133630	−	0.0277687i	0.136167	−	0.990686i	$-0.456522\pi$
$233$	−0.133630	−	0.0277687i	−0.133630	−	0.0277687i	−0.269797	+	0.962917i	$0.586957\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	0.655751	+	0.136267i	0.655751	+	0.136267i
$238$		0			0
$239$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$239$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$240$		0			0
$241$	0.0787081	+	0.111504i	0.0787081	+	0.111504i	0.854419	−	0.519584i	$-0.173913\pi$
$241$	0.0787081	+	0.111504i	0.0787081	+	0.111504i	−0.775711	+	0.631088i	$0.782609\pi$
$242$	1.21537	+	1.49389i	1.21537	+	1.49389i
$243$	−0.816970	−	0.576680i	−0.816970	−	0.576680i
$244$	−0.366272	−	5.35470i	−0.366272	−	5.35470i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.300130	+	2.18361i	0.300130	+	2.18361i
$249$	0.530621	+	1.02405i	0.530621	+	1.02405i
$250$		0			0
$251$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$251$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.159627	+	2.33367i	−0.159627	+	2.33367i
$257$	−0.806094	+	1.32557i	−0.806094	+	1.32557i	0.136167	+	0.990686i	$0.456522\pi$
$257$	−0.806094	+	1.32557i	−0.806094	+	1.32557i	−0.942261	+	0.334880i	$0.891304\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.109784	+	0.391823i	0.109784	+	0.391823i	0.997669	−	0.0682424i	$-0.0217391\pi$
$263$	0.109784	+	0.391823i	0.109784	+	0.391823i	−0.887885	+	0.460065i	$0.847826\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$269$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$270$		0			0
$271$	0.614311	−	1.72850i	0.614311	−	1.72850i	−0.0682424	−	0.997669i	$-0.521739\pi$
$271$	0.614311	−	1.72850i	0.614311	−	1.72850i	0.682553	−	0.730836i	$-0.260870\pi$
$272$	4.99885	+	2.59020i	4.99885	+	2.59020i
$273$		0			0
$274$	−1.28091	+	1.81464i	−1.28091	+	1.81464i
$275$		0			0
$276$	−0.635651	−	0.900512i	−0.635651	−	0.900512i
$277$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$277$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$278$	1.31111	−	3.01849i	1.31111	−	3.01849i
$279$	0.457146	−	0.489484i	0.457146	−	0.489484i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−1.70992	−	0.886009i	−1.70992	−	0.886009i
$283$		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
$288$	3.02103	−	2.13248i	3.02103	−	2.13248i
$289$	1.09136	−	0.887885i	1.09136	−	0.887885i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.81464	−	0.644923i	−1.81464	−	0.644923i	−0.997669	−	0.0682424i	$-0.978261\pi$
$293$	−1.81464	−	0.644923i	−1.81464	−	0.644923i	−0.816970	−	0.576680i	$-0.804348\pi$
$294$	1.76640	−	0.767255i	1.76640	−	0.767255i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	2.40810	−	2.95995i	2.40810	−	2.95995i
$303$		0			0
$304$	5.68792	+	3.45890i	5.68792	+	3.45890i
$305$		0			0
$306$	−0.607882	−	2.92529i	−0.607882	−	2.92529i
$307$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$307$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$311$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$312$		0			0
$313$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$313$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$314$		0			0
$315$		0			0
$316$	1.79737	−	0.247043i	1.79737	−	0.247043i
$317$	0.543860	+	1.25209i	0.543860	+	1.25209i	0.942261	+	0.334880i	$0.108696\pi$
$317$	0.543860	+	1.25209i	0.543860	+	1.25209i	−0.398401	+	0.917211i	$0.630435\pi$
$318$	0.247671	+	0.0880222i	0.247671	+	0.0880222i
$319$		0			0
$320$		0			0
$321$	−0.787230	+	1.11525i	−0.787230	+	1.11525i
$322$		0			0
$323$	2.32507	−	1.64121i	2.32507	−	1.64121i
$324$	−2.60839	−	0.730836i	−2.60839	−	0.730836i
$325$		0			0
$326$		0			0
$327$	1.12924	+	0.234658i	1.12924	+	0.234658i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.234658	+	1.12924i	−0.234658	+	1.12924i	0.682553	+	0.730836i	$0.260870\pi$
$331$	−0.234658	+	1.12924i	−0.234658	+	1.12924i	−0.917211	+	0.398401i	$0.869565\pi$
$332$	2.28333	+	2.13248i	2.28333	+	2.13248i
$333$		0			0
$334$	0.253100	+	0.0709153i	0.253100	+	0.0709153i
$335$		0			0
$336$		0			0
$337$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$337$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$338$	1.92135	−	0.131424i	1.92135	−	0.131424i
$339$	−0.423320	+	0.816970i	−0.423320	+	0.816970i
$340$		0			0
$341$		0			0
$342$	−0.481049	−	3.49989i	−0.481049	−	3.49989i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.593413	−	1.66970i	−0.593413	−	1.66970i
$347$	−0.125291	+	0.911560i	−0.125291	+	0.911560i	0.816970	+	0.576680i	$0.195652\pi$
$347$	−0.125291	+	0.911560i	−0.125291	+	0.911560i	−0.942261	+	0.334880i	$0.891304\pi$
$348$		0			0
$349$	1.32557	+	1.07843i	1.32557	+	1.07843i	0.990686	+	0.136167i	$0.0434783\pi$
$349$	1.32557	+	1.07843i	1.32557	+	1.07843i	0.334880	+	0.942261i	$0.391304\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.79605	−	0.373224i	1.79605	−	0.373224i	0.816970	−	0.576680i	$-0.195652\pi$
$353$	1.79605	−	0.373224i	1.79605	−	0.373224i	0.979084	+	0.203456i	$0.0652174\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$359$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$360$		0			0
$361$	2.02079	−	1.22887i	2.02079	−	1.22887i
$362$	1.57335	−	0.815244i	1.57335	−	0.815244i
$363$	−0.136167	−	0.990686i	−0.136167	−	0.990686i
$364$		0			0
$365$		0			0
$366$	−1.75551	+	3.38799i	−1.75551	+	3.38799i
$367$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$367$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$368$	−1.20640	−	0.851567i	−1.20640	−	0.851567i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	0.722807	−	1.66407i	0.722807	−	1.66407i
$373$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$373$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$374$		0			0
$375$		0			0
$376$	−3.26029	−	0.448116i	−3.26029	−	0.448116i
$377$		0			0
$378$		0			0
$379$	−0.931758	+	0.997669i	−0.931758	+	0.997669i	0.0682424	+	0.997669i	$0.478261\pi$
$379$	−0.931758	+	0.997669i	−0.931758	+	0.997669i	−1.00000			$1.00000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.580683	−	0.713755i	−0.580683	−	0.713755i	0.398401	−	0.917211i	$-0.369565\pi$
$383$	−0.580683	−	0.713755i	−0.580683	−	0.713755i	−0.979084	+	0.203456i	$0.934783\pi$
$384$	1.74624	−	2.47386i	1.74624	−	2.47386i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$389$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$390$		0			0
$391$	−0.539389	+	0.328009i	−0.539389	+	0.328009i
$392$	2.40514	−	2.24624i	2.40514	−	2.24624i
$393$		0			0
$394$	−3.78025	−	0.519584i	−3.78025	−	0.519584i
$395$		0			0
$396$		0			0
$397$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$397$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$398$	0.136571	−	0.224582i	0.136571	−	0.224582i
$399$		0			0
$400$		0			0
$401$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$401$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−2.65281	−	4.36236i	−2.65281	−	4.36236i
$409$	−0.786177	−	1.51725i	−0.786177	−	1.51725i	−0.854419	−	0.519584i	$-0.826087\pi$
$409$	−0.786177	−	1.51725i	−0.786177	−	1.51725i	0.0682424	−	0.997669i	$-0.478261\pi$
$410$		0			0
$411$	1.05788	−	0.459500i	1.05788	−	0.459500i
$412$		0			0
$413$		0			0
$414$	0.0534778	+	0.781818i	0.0534778	+	0.781818i
$415$		0			0
$416$		0			0
$417$	−1.39607	+	0.985454i	−1.39607	+	0.985454i
$418$		0			0
$419$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$419$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$420$		0			0
$421$	0.277739	−	1.33655i	0.277739	−	1.33655i	−0.576680	−	0.816970i	$-0.695652\pi$
$421$	0.277739	−	1.33655i	0.277739	−	1.33655i	0.854419	−	0.519584i	$-0.173913\pi$
$422$		−	2.62897i		−	2.62897i
$423$	0.519584	+	0.854419i	0.519584	+	0.854419i
$424$	0.449163			0.449163
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−0.997669	+	3.56073i	−0.997669	+	3.56073i
$429$		0			0
$430$		0			0
$431$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$431$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$432$	−3.62051	+	0.247650i	−3.62051	+	0.247650i
$433$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$433$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$434$		0			0
$435$		0			0
$436$	3.09517	−	0.425421i	3.09517	−	0.425421i
$437$	−0.662761	+	0.343415i	−0.662761	+	0.343415i
$438$		0			0
$439$	0.787230	+	0.842917i	0.787230	+	0.842917i	0.990686	−	0.136167i	$-0.0434783\pi$
$439$	0.787230	+	0.842917i	0.787230	+	0.842917i	−0.203456	+	0.979084i	$0.565217\pi$
$440$		0			0
$441$	−0.990686	−	0.136167i	−0.990686	−	0.136167i
$442$		0			0
$443$	−0.727872	+	0.894675i	−0.727872	+	0.894675i	−0.997669	−	0.0682424i	$-0.978261\pi$
$443$	−0.727872	+	0.894675i	−0.727872	+	0.894675i	0.269797	+	0.962917i	$0.413043\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$449$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$450$		0			0
$451$		0			0
$452$	−0.339393	+	2.46927i	−0.339393	+	2.46927i
$453$	−1.86697	+	0.663521i	−1.86697	+	0.663521i
$454$	2.60448	+	2.78872i	2.60448	+	2.78872i
$455$		0			0
$456$	−2.77740	−	5.36014i	−2.77740	−	5.36014i
$457$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$457$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$458$	1.52022	+	3.49989i	1.52022	+	3.49989i
$459$	−0.519540	+	1.46184i	−0.519540	+	1.46184i
$460$		0			0
$461$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$461$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$462$		0			0
$463$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$463$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$464$		0			0
$465$		0			0
$466$	0.241086	+	0.104719i	0.241086	+	0.104719i
$467$	−1.24888	−	1.16637i	−1.24888	−	1.16637i	−0.979084	−	0.203456i	$-0.934783\pi$
$467$	−1.24888	−	1.16637i	−1.24888	−	1.16637i	−0.269797	−	0.962917i	$-0.586957\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	−1.18306	−	0.513876i	−1.18306	−	0.513876i
$475$		0			0
$476$		0			0
$477$	−0.0861339	−	0.105873i	−0.0861339	−	0.105873i
$478$		0			0
$479$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$479$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$480$		0			0
$481$		0			0
$482$	−0.104719	−	0.241086i	−0.104719	−	0.241086i
$483$		0			0
$484$	−1.24624	−	2.40514i	−1.24624	−	2.40514i
$485$		0			0
$486$	1.31448	+	1.40747i	1.31448	+	1.40747i
$487$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$487$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$488$	−0.887885	+	6.45984i	−0.887885	+	6.45984i
$489$		0			0
$490$		0			0
$491$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$491$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.165866	−	2.42487i	0.165866	−	2.42487i
$497$		0			0
$498$	−0.599268	−	2.13881i	−0.599268	−	2.13881i
$499$	0.403122	+	0.0554078i	0.403122	+	0.0554078i	0.334880	−	0.942261i	$-0.391304\pi$
$499$	0.403122	+	0.0554078i	0.403122	+	0.0554078i	0.0682424	+	0.997669i	$0.478261\pi$
$500$		0			0
$501$	−0.0931581	−	0.0997480i	−0.0931581	−	0.0997480i
$502$		0			0
$503$	−1.70992	+	0.886009i	−1.70992	+	0.886009i	−0.730836	+	0.682553i	$0.760870\pi$
$503$	−1.70992	+	0.886009i	−1.70992	+	0.886009i	−0.979084	+	0.203456i	$0.934783\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.887885	−	0.460065i	−0.887885	−	0.460065i
$508$		0			0
$509$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$509$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$510$		0			0
$511$		0			0
$512$	0.398401	−	1.42191i	0.398401	−	1.42191i
$513$	−0.730836	+	1.68255i	−0.730836	+	1.68255i
$514$	2.03932	−	2.18358i	2.03932	−	2.18358i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.187206	+	0.900885i	−0.187206	+	0.900885i
$520$		0			0
$521$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$521$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$522$		0			0
$523$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$523$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$524$		0			0
$525$		0			0
$526$	−0.0534778	−	0.781818i	−0.0534778	−	0.781818i
$527$	−0.922583	−	0.478044i	−0.922583	−	0.478044i
$528$		0			0
$529$	−0.765342	+	0.332435i	−0.765342	+	0.332435i
$530$		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
$541$	−0.136267	−	0.655751i	−0.136267	−	0.655751i	−0.990686	−	0.136167i	$-0.956522\pi$
$541$	−0.136267	−	0.655751i	−0.136267	−	0.655751i	0.854419	−	0.519584i	$-0.173913\pi$
$542$	−1.83558	+	3.01849i	−1.83558	+	3.01849i
$543$	−0.917985	−	0.0627919i	−0.917985	−	0.0627919i
$544$	−4.45020	−	3.62051i	−4.45020	−	3.62051i
$545$		0			0
$546$		0			0
$547$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$547$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$548$	2.28333	−	2.13248i	2.28333	−	2.13248i
$549$	1.69292	−	1.02949i	1.69292	−	1.02949i
$550$		0			0
$551$		0			0
$552$	0.533508	+	1.22826i	0.533508	+	1.22826i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−2.66944	+	3.78173i	−2.66944	+	3.78173i
$557$	−0.979084	−	1.20346i	−0.979084	−	1.20346i	−0.979084	−	0.203456i	$-0.934783\pi$
$557$	−0.979084	−	1.20346i	−0.979084	−	1.20346i		−	1.00000i	$-0.5\pi$
$558$	−1.05376	+	0.743829i	−1.05376	+	0.743829i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	1.55142i		−	1.55142i	−0.631088	−	0.775711i	$-0.717391\pi$
$563$		−	1.55142i		−	1.55142i	0.631088	−	0.775711i	$-0.282609\pi$
$564$	2.10128	+	1.70952i	2.10128	+	1.70952i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$569$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$570$		0			0
$571$	1.42298	−	1.15768i	1.42298	−	1.15768i	0.460065	−	0.887885i	$-0.347826\pi$
$571$	1.42298	−	1.15768i	1.42298	−	1.15768i	0.962917	−	0.269797i	$-0.0869565\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−3.20335	+	1.39141i	−3.20335	+	1.39141i
$577$		0			0		−0.136167	−	0.990686i	$-0.543478\pi$
$577$		0			0		0.136167	+	0.990686i	$0.456522\pi$
$578$	−2.40571	+	1.24654i	−2.40571	+	1.24654i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	3.16890	+	1.92705i	3.16890	+	1.92705i
$587$	−1.79605	+	0.373224i	−1.79605	+	0.373224i	−0.979084	−	0.203456i	$-0.934783\pi$
$587$	−1.79605	+	0.373224i	−1.79605	+	0.373224i	−0.816970	+	0.576680i	$0.804348\pi$
$588$	−2.65218	+	0.551130i	−2.65218	+	0.551130i
$589$	−1.04976	−	0.638372i	−1.04976	−	0.638372i
$590$		0			0
$591$	1.53697	+	1.25042i	1.53697	+	1.25042i
$592$		0			0
$593$	0.262234	−	1.90790i	0.262234	−	1.90790i	−0.136167	−	0.990686i	$-0.543478\pi$
$593$	0.262234	−	1.90790i	0.262234	−	1.90790i	0.398401	−	0.917211i	$-0.369565\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.121183	+	0.0627919i	−0.121183	+	0.0627919i
$598$		0			0
$599$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$599$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$600$		0			0
$601$	0.423320	−	0.816970i	0.423320	−	0.816970i	−0.576680	−	0.816970i	$-0.695652\pi$
$601$	0.423320	−	0.816970i	0.423320	−	0.816970i	1.00000			$0$
$602$		0			0
$603$		0			0
$604$	−4.16341	+	3.38719i	−4.16341	+	3.38719i
$605$		0			0
$606$		0			0
$607$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$607$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$608$	−4.95757	−	4.63005i	−4.95757	−	4.63005i
$609$		0			0
$610$		0			0
$611$		0			0
$612$			4.20255i			4.20255i
$613$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$613$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.547173	−	0.386237i	0.547173	−	0.386237i	−0.269797	−	0.962917i	$-0.586957\pi$
$617$	0.547173	−	0.386237i	0.547173	−	0.386237i	0.816970	+	0.576680i	$0.195652\pi$
$618$		0			0
$619$	−1.14262	+	1.61872i	−1.14262	+	1.61872i	−0.460065	+	0.887885i	$0.652174\pi$
$619$	−1.14262	+	1.61872i	−1.14262	+	1.61872i	−0.682553	+	0.730836i	$0.739130\pi$
$620$		0			0
$621$	0.187206	−	0.361291i	0.187206	−	0.361291i
$622$		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
$631$	−0.315646	−	0.256797i	−0.315646	−	0.256797i	0.460065	−	0.887885i	$-0.347826\pi$
$631$	−0.315646	−	0.256797i	−0.315646	−	0.256797i	−0.775711	+	0.631088i	$0.782609\pi$
$632$	−2.19900	−	0.150416i	−2.19900	−	0.150416i
$633$	−0.709287	+	1.16637i	−0.709287	+	1.16637i
$634$	−0.534880	−	2.57398i	−0.534880	−	2.57398i
$635$		0			0
$636$	−0.315892	−	0.192098i	−0.315892	−	0.192098i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$641$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$642$	1.92135	−	1.79441i	1.92135	−	1.79441i
$643$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$643$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$644$		0			0
$645$		0			0
$646$	−5.02710	+	2.18358i	−5.02710	+	2.18358i
$647$	−0.128604	−	0.0457060i	−0.128604	−	0.0457060i	0.269797	−	0.962917i	$-0.413043\pi$
$647$	−0.128604	−	0.0457060i	−0.128604	−	0.0457060i	−0.398401	+	0.917211i	$0.630435\pi$
$648$	2.92198	+	1.51405i	2.92198	+	1.51405i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.494921	−	1.76640i	0.494921	−	1.76640i	−0.136167	−	0.990686i	$-0.543478\pi$
$653$	0.494921	−	1.76640i	0.494921	−	1.76640i	0.631088	−	0.775711i	$-0.282609\pi$
$654$	−2.03729	−	0.884921i	−2.03729	−	0.884921i
$655$		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
$661$	−1.05893	+	1.13384i	−1.05893	+	1.13384i	−0.0682424	+	0.997669i	$0.521739\pi$
$661$	−1.05893	+	1.13384i	−1.05893	+	1.13384i	−0.990686	+	0.136167i	$0.956522\pi$
$662$	0.884921	−	2.03729i	0.884921	−	2.03729i
$663$		0			0
$664$	−2.18887	−	3.10092i	−2.18887	−	3.10092i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	−0.328265	−	0.170093i	−0.328265	−	0.170093i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$673$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$674$		0			0
$675$		0			0
$676$	−2.68361	−	0.368854i	−2.68361	−	0.368854i
$677$	−0.461039	−	1.64547i	−0.461039	−	1.64547i	−0.730836	−	0.682553i	$-0.760870\pi$
$677$	−0.461039	−	1.64547i	−0.461039	−	1.64547i	0.269797	−	0.962917i	$-0.413043\pi$
$678$	1.11830	−	1.37457i	1.11830	−	1.37457i
$679$		0			0
$680$		0			0
$681$	−0.403122	−	1.93993i	−0.403122	−	1.93993i
$682$		0			0
$683$	−0.211425	+	0.347674i	−0.211425	+	0.347674i	−0.942261	−	0.334880i	$-0.891304\pi$
$683$	−0.211425	+	0.347674i	−0.211425	+	0.347674i	0.730836	+	0.682553i	$0.239130\pi$
$684$	−0.339107	+	4.95757i	−0.339107	+	4.95757i
$685$		0			0
$686$		0			0
$687$	0.269797	−	1.96292i	0.269797	−	1.96292i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.713755	−	1.37749i	−0.713755	−	1.37749i	−0.917211	−	0.398401i	$-0.869565\pi$
$691$	−0.713755	−	1.37749i	−0.713755	−	1.37749i	0.203456	−	0.979084i	$-0.434783\pi$
$692$	0.339393	+	2.46927i	0.339393	+	2.46927i
$693$		0			0
$694$	0.593413	−	1.66970i	0.593413	−	1.66970i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−2.07687	−	2.55282i	−2.07687	−	2.55282i
$699$	−0.0787081	−	0.111504i	−0.0787081	−	0.111504i
$700$		0			0
$701$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$701$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−3.53279			−3.53279
$707$		0			0
$708$		0			0
$709$	0.373224	+	0.162114i	0.373224	+	0.162114i	0.576680	−	0.816970i	$-0.304348\pi$
$709$	0.373224	+	0.162114i	0.373224	+	0.162114i	−0.203456	+	0.979084i	$0.565217\pi$
$710$		0			0
$711$	0.386237	+	0.547173i	0.386237	+	0.547173i
$712$		0			0
$713$	0.222651	+	0.157164i	0.222651	+	0.157164i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$719$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$720$		0			0
$721$		0			0
$722$	−4.29181	+	1.52531i	−4.29181	+	1.52531i
$723$	−0.0185847	+	0.135214i	−0.0185847	+	0.135214i
$724$	−2.40006	+	0.672464i	−2.40006	+	0.672464i
$725$		0			0
$726$	−0.131424	+	1.92135i	−0.131424	+	1.92135i
$727$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$727$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$728$		0			0
$729$	−0.203456	−	0.979084i	−0.203456	−	0.979084i
$730$		0			0
$731$		0			0
$732$	3.38719	−	4.16341i	3.38719	−	4.16341i
$733$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$733$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$734$		0			0
$735$		0			0
$736$	1.02704	+	1.09969i	1.02704	+	1.09969i
$737$		0			0
$738$		0			0
$739$	0.911560	−	0.125291i	0.911560	−	0.125291i	0.334880	−	0.942261i	$-0.391304\pi$
$739$	0.911560	−	0.125291i	0.911560	−	0.125291i	0.576680	+	0.816970i	$0.304348\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.83015	+	0.125185i	−1.83015	+	0.125185i	−0.942261	−	0.334880i	$-0.891304\pi$
$743$	−1.83015	+	0.125185i	−1.83015	+	0.125185i	−0.887885	+	0.460065i	$0.847826\pi$
$744$	−1.27108	+	1.80071i	−1.27108	+	1.80071i
$745$		0			0
$746$		0			0
$747$	−0.311173	+	1.11059i	−0.311173	+	1.11059i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1.36511			1.36511			0.682553	−	0.730836i	$-0.260870\pi$
$751$	1.36511			1.36511			0.682553	+	0.730836i	$0.260870\pi$
$752$	3.41944	+	1.21527i	3.41944	+	1.21527i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$757$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$758$	2.14779	−	1.51607i	2.14779	−	1.51607i
$759$		0			0
$760$		0			0
$761$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$761$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.815244	+	1.57335i	0.815244	+	1.57335i
$767$		0			0
$768$	−1.70952	+	1.59658i	−1.70952	+	1.59658i
$769$	−0.519540	−	1.46184i	−0.519540	−	1.46184i	−0.854419	−	0.519584i	$-0.826087\pi$
$769$	−0.519540	−	1.46184i	−0.519540	−	1.46184i	0.334880	−	0.942261i	$-0.391304\pi$
$770$		0			0
$771$	−1.49389	+	0.418569i	−1.49389	+	0.418569i
$772$		0			0
$773$	−1.70486	−	0.116615i	−1.70486	−	0.116615i	−0.816970	−	0.576680i	$-0.804348\pi$
$773$	−1.70486	−	0.116615i	−1.70486	−	0.116615i	−0.887885	+	0.460065i	$0.847826\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	1.14557	−	0.407135i	1.14557	−	0.407135i
$783$		0			0
$784$	−3.10066	+	1.88555i	−3.10066	+	1.88555i
$785$		0			0
$786$		0			0
$787$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$787$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$788$	5.05732	+	1.79737i	5.05732	+	1.79737i
$789$	−0.187206	+	0.361291i	−0.187206	+	0.361291i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.252350	+	0.270201i	−0.252350	+	0.270201i
$797$	−1.67310	−	0.347674i	−1.67310	−	0.347674i	−0.730836	−	0.682553i	$-0.760870\pi$
$797$	−1.67310	−	0.347674i	−1.67310	−	0.347674i	−0.942261	+	0.334880i	$0.891304\pi$
$798$		0			0
$799$	1.05893	−	1.13384i	1.05893	−	1.13384i
$800$		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		0.460065	−	0.887885i	$-0.347826\pi$
$809$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$810$		0			0
$811$	−0.843954	+	0.366581i	−0.843954	+	0.366581i	−0.775711	−	0.631088i	$-0.782609\pi$
$811$	−0.843954	+	0.366581i	−0.843954	+	0.366581i	−0.0682424	+	0.997669i	$0.521739\pi$
$812$		0			0
$813$	1.62876	−	0.843954i	1.62876	−	0.843954i
$814$		0			0
$815$		0			0
$816$	1.88539	+	5.30499i	1.88539	+	5.30499i
$817$		0			0
$818$	0.887885	+	3.16890i	0.887885	+	3.16890i
$819$		0			0
$820$		0			0
$821$		0			0		−0.854419	−	0.519584i	$-0.826087\pi$
$821$		0			0		0.854419	+	0.519584i	$0.173913\pi$
$822$	−2.17472	+	0.451913i	−2.17472	+	0.451913i
$823$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$823$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−0.461039	−	1.64547i	−0.461039	−	1.64547i	−0.730836	−	0.682553i	$-0.760870\pi$
$827$	−0.461039	−	1.64547i	−0.461039	−	1.64547i	0.269797	−	0.962917i	$-0.413043\pi$
$828$	0.150091	−	1.09199i	0.150091	−	1.09199i
$829$	0.644923	+	1.81464i	0.644923	+	1.81464i	0.576680	+	0.816970i	$0.304348\pi$
$829$	0.644923	+	1.81464i	0.644923	+	1.81464i	0.0682424	+	0.997669i	$0.478261\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.211252	+	1.53697i	0.211252	+	1.53697i
$834$	3.01849	−	1.31111i	3.01849	−	1.31111i
$835$		0			0
$836$		0			0
$837$	0.668198	−	0.0457060i	0.668198	−	0.0457060i
$838$		0			0
$839$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$839$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$840$		0			0
$841$	0.962917	+	0.269797i	0.962917	+	0.269797i
$842$	−1.04738	+	2.41132i	−1.04738	+	2.41132i
$843$		0			0
$844$	−0.752350	+	3.62051i	−0.752350	+	3.62051i
$845$		0			0
$846$	−0.644923	−	1.81464i	−0.644923	−	1.81464i
$847$		0			0
$848$	−0.484940	−	0.100772i	−0.484940	−	0.100772i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.631088	−	0.775711i	$-0.717391\pi$
$853$		0			0		0.631088	+	0.775711i	$0.282609\pi$
$854$		0			0
$855$		0			0
$856$	2.06683	−	3.98881i	2.06683	−	3.98881i
$857$	1.28629	+	0.457146i	1.28629	+	0.457146i	0.887885	−	0.460065i	$-0.152174\pi$
$857$	1.28629	+	0.457146i	1.28629	+	0.457146i	0.398401	+	0.917211i	$0.369565\pi$
$858$		0			0
$859$	1.90790	−	0.262234i	1.90790	−	0.262234i	0.917211	−	0.398401i	$-0.130435\pi$
$859$	1.90790	−	0.262234i	1.90790	−	0.262234i	0.990686	+	0.136167i	$0.0434783\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.631088	+	0.224289i	−0.631088	+	0.224289i	−0.631088	−	0.775711i	$-0.717391\pi$
$863$	−0.631088	+	0.224289i	−0.631088	+	0.224289i			1.00000i	$0.5\pi$
$864$	3.66341	+	0.503524i	3.66341	+	0.503524i
$865$		0			0
$866$		0			0
$867$	1.40363	+	0.0960111i	1.40363	+	0.0960111i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−3.78679	−	0.259024i	−3.78679	−	0.259024i
$873$		0			0
$874$	1.38423	−	0.387843i	1.38423	−	0.387843i
$875$		0			0
$876$		0			0
$877$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$877$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$878$	−1.15409	−	1.89782i	−1.15409	−	1.89782i
$879$	−0.886009	−	1.70992i	−0.886009	−	1.70992i
$880$		0			0
$881$		0			0		0.917211	−	0.398401i	$-0.130435\pi$
$881$		0			0		−0.917211	+	0.398401i	$0.869565\pi$
$882$	1.81464	+	0.644923i	1.81464	+	0.644923i
$883$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$883$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$884$		0			0
$885$		0			0
$886$	1.72300	−	1.40176i	1.72300	−	1.40176i
$887$	1.49867	−	1.05788i	1.49867	−	1.05788i	0.519584	−	0.854419i	$-0.326087\pi$
$887$	1.49867	−	1.05788i	1.49867	−	1.05788i	0.979084	−	0.203456i	$-0.0652174\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.34066	−	1.25209i	1.34066	−	1.25209i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−0.122110	+	0.172990i	−0.122110	+	0.172990i
$902$		0			0
$903$		0			0
$904$	1.01405	−	2.85325i	1.01405	−	2.85325i
$905$		0			0
$906$	3.78025	−	0.519584i	3.78025	−	0.519584i
$907$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$907$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$908$	−2.78872	−	4.58585i	−2.78872	−	4.58585i
$909$		0			0
$910$		0			0
$911$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$911$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$912$	1.79605	+	6.41020i	1.79605	+	6.41020i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.09199	−	5.25496i	−1.09199	−	5.25496i
$917$		0			0
$918$	1.55240	−	2.55282i	1.55240	−	2.55282i
$919$	0.0277687	−	0.405963i	0.0277687	−	0.405963i	−0.962917	−	0.269797i	$-0.913043\pi$
$919$	0.0277687	−	0.405963i	0.0277687	−	0.405963i	0.990686	−	0.136167i	$-0.0434783\pi$
$920$		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		0.334880	−	0.942261i	$-0.391304\pi$
$929$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$930$		0			0
$931$	0.125185	+	1.83015i	0.125185	+	1.83015i
$932$	−0.302046	−	0.213208i	−0.302046	−	0.213208i
$933$		0			0
$934$	1.89782	+	2.68860i	1.89782	+	2.68860i
$935$		0			0
$936$		0			0
$937$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$937$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$938$		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
$947$	1.07843	+	1.32557i	1.07843	+	1.32557i	0.942261	+	0.334880i	$0.108696\pi$
$947$	1.07843	+	1.32557i	1.07843	+	1.32557i	0.136167	+	0.990686i	$0.456522\pi$
$948$	1.48220	+	1.04625i	1.48220	+	1.04625i
$949$		0			0
$950$		0			0
$951$	−0.457146	+	1.28629i	−0.457146	+	1.28629i
$952$		0			0
$953$	−0.262234	−	1.90790i	−0.262234	−	1.90790i	−0.398401	−	0.917211i	$-0.630435\pi$
$953$	−0.262234	−	1.90790i	−0.262234	−	1.90790i	0.136167	−	0.990686i	$-0.456522\pi$
$954$	0.120927	+	0.233378i	0.120927	+	0.233378i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.0376304	−	0.550137i	0.0376304	−	0.550137i
$962$		0			0
$963$	−1.33655	+	0.277739i	−1.33655	+	0.277739i
$964$	0.0752208	+	0.361982i	0.0752208	+	0.361982i
$965$		0			0
$966$		0			0
$967$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$967$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$968$	0.887885	+	3.16890i	0.887885	+	3.16890i
$969$	2.81946	+	0.387525i	2.81946	+	0.387525i
$970$		0			0
$971$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$971$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$972$	−1.40747	−	2.31448i	−1.40747	−	2.31448i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	2.40790	−	6.77517i	2.40790	−	6.77517i
$977$	−0.816970	−	0.423320i	−0.816970	−	0.423320i		−	1.00000i	$-0.5\pi$
$977$	−0.816970	−	0.423320i	−0.816970	−	0.423320i	−0.816970	+	0.576680i	$0.804348\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.665120	+	0.942261i	0.665120	+	0.942261i
$982$		0			0
$983$	−0.789381	+	1.81734i	−0.789381	+	1.81734i	−0.269797	+	0.962917i	$0.586957\pi$
$983$	−0.789381	+	1.81734i	−0.789381	+	1.81734i	−0.519584	+	0.854419i	$0.673913\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−1.25209	−	0.543860i	−1.25209	−	0.543860i	−0.334880	−	0.942261i	$-0.608696\pi$
$991$	−1.25209	−	0.543860i	−1.25209	−	0.543860i	−0.917211	+	0.398401i	$0.869565\pi$
$992$	−0.668198	+	2.38483i	−0.668198	+	2.38483i
$993$	−0.942261	+	0.665120i	−0.942261	+	0.665120i
$994$		0			0
$995$		0			0
$996$	0.213208	+	3.11698i	0.213208	+	3.11698i
$997$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$997$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$998$	−0.738398	−	0.262427i	−0.738398	−	0.262427i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bd.a.1001.1		44
3.2	odd	2	inner	3525.1.bd.a.1001.2		44
5.2	odd	4		705.1.p.a.14.1	✓	22
5.3	odd	4		705.1.p.b.14.1	yes	22
5.4	even	2	inner	3525.1.bd.a.1001.2		44
15.2	even	4		705.1.p.b.14.1	yes	22
15.8	even	4		705.1.p.a.14.1	✓	22
15.14	odd	2	CM	3525.1.bd.a.1001.1		44
47.37	even	23	inner	3525.1.bd.a.2951.2		44
141.131	odd	46	inner	3525.1.bd.a.2951.1		44
235.37	odd	92		705.1.p.a.554.1	yes	22
235.84	even	46	inner	3525.1.bd.a.2951.1		44
235.178	odd	92		705.1.p.b.554.1	yes	22
705.272	even	92		705.1.p.b.554.1	yes	22
705.413	even	92		705.1.p.a.554.1	yes	22
705.554	odd	46	inner	3525.1.bd.a.2951.2		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.1.p.a.14.1	✓	22	5.2	odd	4
705.1.p.a.14.1	✓	22	15.8	even	4
705.1.p.a.554.1	yes	22	235.37	odd	92
705.1.p.a.554.1	yes	22	705.413	even	92
705.1.p.b.14.1	yes	22	5.3	odd	4
705.1.p.b.14.1	yes	22	15.2	even	4
705.1.p.b.554.1	yes	22	235.178	odd	92
705.1.p.b.554.1	yes	22	705.272	even	92
3525.1.bd.a.1001.1		44	1.1	even	1	trivial
3525.1.bd.a.1001.1		44	15.14	odd	2	CM
3525.1.bd.a.1001.2		44	3.2	odd	2	inner
3525.1.bd.a.1001.2		44	5.4	even	2	inner
3525.1.bd.a.2951.1		44	141.131	odd	46	inner
3525.1.bd.a.2951.1		44	235.84	even	46	inner
3525.1.bd.a.2951.2		44	47.37	even	23	inner
3525.1.bd.a.2951.2		44	705.554	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.88555 - 0.391823i) q^{2} +(0.730836 + 0.682553i) q^{3} +(2.48458 + 1.07920i) q^{4} +(-1.11059 - 1.57335i) q^{6} +(-2.68860 - 1.89782i) q^{8} +(0.0682424 + 0.997669i) q^{9} +O(q^{10})\)	\(q+(-1.88555 - 0.391823i) q^{2} +(0.730836 + 0.682553i) q^{3} +(2.48458 + 1.07920i) q^{4} +(-1.11059 - 1.57335i) q^{6} +(-2.68860 - 1.89782i) q^{8} +(0.0682424 + 0.997669i) q^{9} +(1.07920 + 2.48458i) q^{12} +(2.47696 + 2.65218i) q^{16} +(1.46184 - 0.519540i) q^{17} +(0.262234 - 1.90790i) q^{18} +(1.76640 - 0.494921i) q^{19} +(-0.398401 + 0.0827887i) q^{23} +(-0.669562 - 3.22211i) q^{24} +(-0.631088 + 0.775711i) q^{27} +(-0.457146 - 0.489484i) q^{31} +(-1.92135 - 3.15952i) q^{32} +(-2.95995 + 0.406836i) q^{34} +(-0.907135 + 2.55243i) q^{36} +(-3.52456 + 0.241086i) q^{38} +0.783645 q^{46} +(0.887885 - 0.460065i) q^{47} +3.62897i q^{48} +(-0.203456 + 0.979084i) q^{49} +(1.42298 + 0.618088i) q^{51} +(-0.111504 + 0.0787081i) q^{53} +(1.49389 - 1.21537i) q^{54} +(1.62876 + 0.843954i) q^{57} +(-0.911560 - 1.75923i) q^{61} +(0.670183 + 1.10207i) q^{62} +(1.16956 + 3.29083i) q^{64} +(4.19276 + 0.286792i) q^{68} +(-0.347674 - 0.211425i) q^{69} +(1.70992 - 2.81184i) q^{72} +(4.92287 + 0.676633i) q^{76} +(0.572255 - 0.347996i) q^{79} +(-0.990686 + 0.136167i) q^{81} +(1.08677 + 0.386237i) q^{83} +(-1.07920 - 0.224261i) q^{92} -0.669759i q^{93} +(-1.85442 + 0.519584i) q^{94} +(0.752350 - 3.62051i) q^{96} +(0.767255 - 1.76640i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 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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