LMFDB - Embedded newform 3525.1.bd.a.251.2

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			251.2
Root			$-0.398401 - 0.917211i$ of defining polynomial
Character	$\chi$	$=$	3525.251
Dual form			3525.1.bd.a.1601.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.211425 - 0.347674i) q^{2} +(0.816970 - 0.576680i) q^{3} +(0.383889 + 0.740871i) q^{4} +(-0.0277687 - 0.405963i) q^{6} +(0.744708 + 0.0509395i) q^{8} +(0.334880 - 0.942261i) q^{9} +O(q^{10})$	\(q+(0.211425 - 0.347674i) q^{2} +(0.816970 - 0.576680i) q^{3} +(0.383889 + 0.740871i) q^{4} +(-0.0277687 - 0.405963i) q^{6} +(0.744708 + 0.0509395i) q^{8} +(0.334880 - 0.942261i) q^{9} +(0.740871 + 0.383889i) q^{12} +(-0.306035 + 0.433553i) q^{16} +(-0.262234 + 1.90790i) q^{17} +(-0.256797 - 0.315646i) q^{18} +(-0.187206 - 0.900885i) q^{19} +(0.887885 + 1.46007i) q^{23} +(0.637780 - 0.387843i) q^{24} +(-0.269797 - 0.962917i) q^{27} +(1.14262 - 1.61872i) q^{31} +(0.383417 + 0.882715i) q^{32} +(0.607882 + 0.494549i) q^{34} +(0.826651 - 0.113621i) q^{36} +(-0.352794 - 0.125383i) q^{38} +0.695347 q^{46} +(0.730836 - 0.682553i) q^{47} +0.530684i q^{48} +(-0.854419 - 0.519584i) q^{49} +(0.886009 + 1.70992i) q^{51} +(-0.668198 + 0.0457060i) q^{53} +(-0.391823 - 0.109784i) q^{54} +(-0.672464 - 0.628038i) q^{57} +(-1.05893 - 1.13384i) q^{61} +(-0.321209 - 0.739496i) q^{62} +(-0.137780 - 0.0189375i) q^{64} +(-1.51418 + 0.538138i) q^{68} +(1.56737 + 0.680803i) q^{69} +(0.297386 - 0.684651i) q^{72} +(0.595574 - 0.484535i) q^{76} +(-1.81734 + 0.789381i) q^{79} +(-0.775711 - 0.631088i) q^{81} +(0.0185847 + 0.135214i) q^{83} +(-0.740871 + 1.21831i) q^{92} -1.98137i q^{93} +(-0.0827887 - 0.398401i) q^{94} +(0.822285 + 0.500042i) q^{96} +(-0.361291 + 0.187206i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times$.

$n$	$1552$	$2026$	$2351$
$\chi(n)$	$1$	$e\left(\frac{13}{23}\right)$	$-1$

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 $

$2$	0.211425	−	0.347674i	0.211425	−	0.347674i	−0.730836	−	0.682553i	$-0.760870\pi$
$2$	0.211425	−	0.347674i	0.211425	−	0.347674i	0.942261	+	0.334880i	$0.108696\pi$
$3$	0.816970	−	0.576680i	0.816970	−	0.576680i
$3$	0.816970	−	0.576680i	0.816970	−	0.576680i
$4$	0.383889	+	0.740871i	0.383889	+	0.740871i
$5$		0			0
$5$		0			0
$6$	−0.0277687	−	0.405963i	−0.0277687	−	0.405963i
$7$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$7$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$8$	0.744708	+	0.0509395i	0.744708	+	0.0509395i
$9$	0.334880	−	0.942261i	0.334880	−	0.942261i
$10$		0			0
$11$		0			0		0.990686	−	0.136167i	$-0.0434783\pi$
$11$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$12$	0.740871	+	0.383889i	0.740871	+	0.383889i
$13$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$13$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$14$		0			0
$15$		0			0
$16$	−0.306035	+	0.433553i	−0.306035	+	0.433553i
$17$	−0.262234	+	1.90790i	−0.262234	+	1.90790i	0.136167	+	0.990686i	$0.456522\pi$
$17$	−0.262234	+	1.90790i	−0.262234	+	1.90790i	−0.398401	+	0.917211i	$0.630435\pi$
$18$	−0.256797	−	0.315646i	−0.256797	−	0.315646i
$19$	−0.187206	−	0.900885i	−0.187206	−	0.900885i	−0.962917	−	0.269797i	$-0.913043\pi$
$19$	−0.187206	−	0.900885i	−0.187206	−	0.900885i	0.775711	−	0.631088i	$-0.217391\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.887885	+	1.46007i	0.887885	+	1.46007i	0.887885	+	0.460065i	$0.152174\pi$
$23$	0.887885	+	1.46007i	0.887885	+	1.46007i			1.00000i	$0.5\pi$
$24$	0.637780	−	0.387843i	0.637780	−	0.387843i
$25$		0			0
$26$		0			0
$27$	−0.269797	−	0.962917i	−0.269797	−	0.962917i
$28$		0			0
$29$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$29$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$30$		0			0
$31$	1.14262	−	1.61872i	1.14262	−	1.61872i	0.460065	−	0.887885i	$-0.347826\pi$
$31$	1.14262	−	1.61872i	1.14262	−	1.61872i	0.682553	−	0.730836i	$-0.260870\pi$
$32$	0.383417	+	0.882715i	0.383417	+	0.882715i
$33$		0			0
$34$	0.607882	+	0.494549i	0.607882	+	0.494549i
$35$		0			0
$36$	0.826651	−	0.113621i	0.826651	−	0.113621i
$37$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$37$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$38$	−0.352794	−	0.125383i	−0.352794	−	0.125383i
$39$		0			0
$40$		0			0
$41$		0			0		−0.0682424	−	0.997669i	$-0.521739\pi$
$41$		0			0		0.0682424	+	0.997669i	$0.478261\pi$
$42$		0			0
$43$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$43$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$44$		0			0
$45$		0			0
$46$	0.695347			0.695347
$47$	0.730836	−	0.682553i	0.730836	−	0.682553i
$47$	0.730836	−	0.682553i	0.730836	−	0.682553i
$48$			0.530684i			0.530684i
$49$	−0.854419	−	0.519584i	−0.854419	−	0.519584i
$50$		0			0
$51$	0.886009	+	1.70992i	0.886009	+	1.70992i
$52$		0			0
$53$	−0.668198	+	0.0457060i	−0.668198	+	0.0457060i	−0.398401	−	0.917211i	$-0.630435\pi$
$53$	−0.668198	+	0.0457060i	−0.668198	+	0.0457060i	−0.269797	+	0.962917i	$0.586957\pi$
$54$	−0.391823	−	0.109784i	−0.391823	−	0.109784i
$55$		0			0
$56$		0			0
$57$	−0.672464	−	0.628038i	−0.672464	−	0.628038i
$58$		0			0
$59$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$59$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$60$		0			0
$61$	−1.05893	−	1.13384i	−1.05893	−	1.13384i	−0.990686	−	0.136167i	$-0.956522\pi$
$61$	−1.05893	−	1.13384i	−1.05893	−	1.13384i	−0.0682424	−	0.997669i	$-0.521739\pi$
$62$	−0.321209	−	0.739496i	−0.321209	−	0.739496i
$63$		0			0
$64$	−0.137780	−	0.0189375i	−0.137780	−	0.0189375i
$65$		0			0
$66$		0			0
$67$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$67$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$68$	−1.51418	+	0.538138i	−1.51418	+	0.538138i
$69$	1.56737	+	0.680803i	1.56737	+	0.680803i
$70$		0			0
$71$		0			0		0.854419	−	0.519584i	$-0.173913\pi$
$71$		0			0		−0.854419	+	0.519584i	$0.826087\pi$
$72$	0.297386	−	0.684651i	0.297386	−	0.684651i
$73$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$73$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$74$		0			0
$75$		0			0
$76$	0.595574	−	0.484535i	0.595574	−	0.484535i
$77$		0			0
$78$		0			0
$79$	−1.81734	+	0.789381i	−1.81734	+	0.789381i	−0.854419	+	0.519584i	$0.826087\pi$
$79$	−1.81734	+	0.789381i	−1.81734	+	0.789381i	−0.962917	+	0.269797i	$0.913043\pi$
$80$		0			0
$81$	−0.775711	−	0.631088i	−0.775711	−	0.631088i
$82$		0			0
$83$	0.0185847	+	0.135214i	0.0185847	+	0.135214i	0.997669	−	0.0682424i	$-0.0217391\pi$
$83$	0.0185847	+	0.135214i	0.0185847	+	0.135214i	−0.979084	+	0.203456i	$0.934783\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$89$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$90$		0			0
$91$		0			0
$92$	−0.740871	+	1.21831i	−0.740871	+	1.21831i
$93$		−	1.98137i		−	1.98137i
$94$	−0.0827887	−	0.398401i	−0.0827887	−	0.398401i
$95$		0			0
$96$	0.822285	+	0.500042i	0.822285	+	0.500042i
$97$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$97$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$98$	−0.361291	+	0.187206i	−0.361291	+	0.187206i
$99$		0			0
$100$		0			0
$101$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$101$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$102$	0.781818	+	0.0534778i	0.781818	+	0.0534778i
$103$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$103$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$104$		0			0
$105$		0			0
$106$	−0.125383	+	0.241978i	−0.125383	+	0.241978i
$107$	0.727872	−	0.894675i	0.727872	−	0.894675i	−0.269797	−	0.962917i	$-0.586957\pi$
$107$	0.727872	−	0.894675i	0.727872	−	0.894675i	0.997669	+	0.0682424i	$0.0217391\pi$
$108$	0.609826	−	0.569538i	0.609826	−	0.569538i
$109$	−0.125185	+	0.0543757i	−0.125185	+	0.0543757i	−0.460065	−	0.887885i	$-0.652174\pi$
$109$	−0.125185	+	0.0543757i	−0.125185	+	0.0543757i	0.334880	+	0.942261i	$0.391304\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.33655	+	0.277739i	−1.33655	+	0.277739i	−0.816970	−	0.576680i	$-0.804348\pi$
$113$	−1.33655	+	0.277739i	−1.33655	+	0.277739i	−0.519584	+	0.854419i	$0.673913\pi$
$114$	−0.360528	+	0.101015i	−0.360528	+	0.101015i
$115$		0			0
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.962917	−	0.269797i	0.962917	−	0.269797i
$122$	−0.618088	+	0.128440i	−0.618088	+	0.128440i
$123$		0			0
$124$	1.63790	+	0.225125i	1.63790	+	0.225125i
$125$		0			0
$126$		0			0
$127$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$127$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$128$	−0.643067	+	0.790436i	−0.643067	+	0.790436i
$129$		0			0
$130$		0			0
$131$		0			0		0.682553	−	0.730836i	$-0.260870\pi$
$131$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.292475	+	1.40747i	−0.292475	+	1.40747i
$137$	−0.121183	+	0.0627919i	−0.121183	+	0.0627919i	−0.519584	−	0.854419i	$-0.673913\pi$
$137$	−0.121183	+	0.0627919i	−0.121183	+	0.0627919i	0.398401	+	0.917211i	$0.369565\pi$
$138$	0.568078	−	0.400993i	0.568078	−	0.400993i
$139$	1.56737	+	0.953137i	1.56737	+	0.953137i	0.990686	+	0.136167i	$0.0434783\pi$
$139$	1.56737	+	0.953137i	1.56737	+	0.953137i	0.576680	+	0.816970i	$0.304348\pi$
$140$		0			0
$141$	0.203456	−	0.979084i	0.203456	−	0.979084i
$142$		0			0
$143$		0			0
$144$	0.306035	+	0.433553i	0.306035	+	0.433553i
$145$		0			0
$146$		0			0
$147$	−0.997669	+	0.0682424i	−0.997669	+	0.0682424i
$148$		0			0
$149$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$149$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$150$		0			0
$151$	−1.05893	+	1.13384i	−1.05893	+	1.13384i	−0.0682424	+	0.997669i	$0.521739\pi$
$151$	−1.05893	+	1.13384i	−1.05893	+	1.13384i	−0.990686	+	0.136167i	$0.956522\pi$
$152$	−0.0935233	−	0.680433i	−0.0935233	−	0.680433i
$153$	1.70992	+	0.886009i	1.70992	+	0.886009i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$157$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$158$	−0.109784	+	0.798735i	−0.109784	+	0.798735i
$159$	−0.519540	+	0.422677i	−0.519540	+	0.422677i
$160$		0			0
$161$		0			0
$162$	−0.383417	+	0.136267i	−0.383417	+	0.136267i
$163$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$163$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$164$		0			0
$165$		0			0
$166$	0.0509395	+	0.0221261i	0.0509395	+	0.0221261i
$167$	0.631088	−	0.224289i	0.631088	−	0.224289i		−	1.00000i	$-0.5\pi$
$167$	0.631088	−	0.224289i	0.631088	−	0.224289i	0.631088	+	0.775711i	$0.282609\pi$
$168$		0			0
$169$	−0.203456	−	0.979084i	−0.203456	−	0.979084i
$170$		0			0
$171$	−0.911560	−	0.125291i	−0.911560	−	0.125291i
$172$		0			0
$173$	−0.543860	−	1.25209i	−0.543860	−	1.25209i	−0.942261	−	0.334880i	$-0.891304\pi$
$173$	−0.543860	−	1.25209i	−0.543860	−	1.25209i	0.398401	−	0.917211i	$-0.369565\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$		0			0
$179$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$179$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$180$		0			0
$181$	1.31448	+	0.368301i	1.31448	+	0.368301i	0.854419	−	0.519584i	$-0.173913\pi$
$181$	1.31448	+	0.368301i	1.31448	+	0.368301i	0.460065	+	0.887885i	$0.347826\pi$
$182$		0			0
$183$	−1.51897	−	0.315646i	−1.51897	−	0.315646i
$184$	0.586841	+	1.13255i	0.586841	+	1.13255i
$185$		0			0
$186$	−0.688871	−	0.418911i	−0.688871	−	0.418911i
$187$		0			0
$188$	0.786244	+	0.279431i	0.786244	+	0.279431i
$189$		0			0
$190$		0			0
$191$		0			0		−0.576680	−	0.816970i	$-0.695652\pi$
$191$		0			0		0.576680	+	0.816970i	$0.304348\pi$
$192$	−0.123483	+	0.0639838i	−0.123483	+	0.0639838i
$193$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$193$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$194$		0			0
$195$		0			0
$196$	0.0569430	−	0.832477i	0.0569430	−	0.832477i
$197$	−1.46184	−	0.519540i	−1.46184	−	0.519540i	−0.519584	−	0.854419i	$-0.673913\pi$
$197$	−1.46184	−	0.519540i	−1.46184	−	0.519540i	−0.942261	+	0.334880i	$0.891304\pi$
$198$		0			0
$199$	−0.663521	+	0.0911989i	−0.663521	+	0.0911989i	−0.460065	−	0.887885i	$-0.652174\pi$
$199$	−0.663521	+	0.0911989i	−0.663521	+	0.0911989i	−0.203456	+	0.979084i	$0.565217\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−0.926702	+	1.31284i	−0.926702	+	1.31284i
$205$		0			0
$206$		0			0
$207$	1.67310	−	0.347674i	1.67310	−	0.347674i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.985454	+	0.599268i	−0.985454	+	0.599268i	−0.917211	−	0.398401i	$-0.869565\pi$
$211$	−0.985454	+	0.599268i	−0.985454	+	0.599268i	−0.0682424	+	0.997669i	$0.521739\pi$
$212$	−0.290376	−	0.477503i	−0.290376	−	0.477503i
$213$		0			0
$214$	−0.157164	−	0.442218i	−0.157164	−	0.442218i
$215$		0			0
$216$	−0.151869	−	0.730836i	−0.151869	−	0.730836i
$217$		0			0
$218$	−0.00756233	+	0.0550200i	−0.00756233	+	0.0550200i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$223$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$224$		0			0
$225$		0			0
$226$	−0.186018	+	0.523405i	−0.186018	+	0.523405i
$227$	−1.54781	−	0.105873i	−1.54781	−	0.105873i	−0.730836	−	0.682553i	$-0.760870\pi$
$227$	−1.54781	−	0.105873i	−1.54781	−	0.105873i	−0.816970	+	0.576680i	$0.804348\pi$
$228$	0.207144	−	0.739306i	0.207144	−	0.739306i
$229$	−0.105873	−	1.54781i	−0.105873	−	1.54781i	−0.682553	−	0.730836i	$-0.739130\pi$
$229$	−0.105873	−	1.54781i	−0.105873	−	1.54781i	0.576680	−	0.816970i	$-0.304348\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.347996	−	0.572255i	0.347996	−	0.572255i	−0.631088	−	0.775711i	$-0.717391\pi$
$233$	0.347996	−	0.572255i	0.347996	−	0.572255i	0.979084	+	0.203456i	$0.0652174\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.02949	+	1.69292i	−1.02949	+	1.69292i
$238$		0			0
$239$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$239$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$240$		0			0
$241$	0.0457060	+	0.668198i	0.0457060	+	0.668198i	0.962917	+	0.269797i	$0.0869565\pi$
$241$	0.0457060	+	0.668198i	0.0457060	+	0.668198i	−0.917211	+	0.398401i	$0.869565\pi$
$242$	0.109784	−	0.391823i	0.109784	−	0.391823i
$243$	−0.997669	−	0.0682424i	−0.997669	−	0.0682424i
$244$	0.433516	−	1.21980i	0.433516	−	1.21980i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	0.933374	−	1.14727i	0.933374	−	1.14727i
$249$	0.0931581	+	0.0997480i	0.0931581	+	0.0997480i
$250$		0			0
$251$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$251$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.0922795	+	0.259650i	0.0922795	+	0.259650i
$257$	−0.767255	+	1.76640i	−0.767255	+	1.76640i	−0.136167	+	0.990686i	$0.543478\pi$
$257$	−0.767255	+	1.76640i	−0.767255	+	1.76640i	−0.631088	+	0.775711i	$0.717391\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.67310	+	0.347674i	−1.67310	+	0.347674i	−0.942261	−	0.334880i	$-0.891304\pi$
$263$	−1.67310	+	0.347674i	−1.67310	+	0.347674i	−0.730836	+	0.682553i	$0.760870\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$269$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$270$		0			0
$271$	−0.911560	+	0.125291i	−0.911560	+	0.125291i	−0.576680	−	0.816970i	$-0.695652\pi$
$271$	−0.911560	+	0.125291i	−0.911560	+	0.125291i	−0.334880	+	0.942261i	$0.608696\pi$
$272$	−0.746921	−	0.697575i	−0.746921	−	0.697575i
$273$		0			0
$274$	−0.00379000	+	0.0554078i	−0.00379000	+	0.0554078i
$275$		0			0
$276$	0.0973064	+	1.42257i	0.0973064	+	1.42257i
$277$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$277$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$278$	0.662761	−	0.343415i	0.662761	−	0.343415i
$279$	−1.14262	−	1.61872i	−1.14262	−	1.61872i
$280$		0			0
$281$		0			0		1.00000			$0$
$281$		0			0		−1.00000			$\pi$
$282$	−0.297386	−	0.277739i	−0.297386	−	0.277739i
$283$		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
$288$	0.960147	−	0.0656758i	0.960147	−	0.0656758i
$289$	−2.60839	−	0.730836i	−2.60839	−	0.730836i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−0.0554078	−	0.403122i	−0.0554078	−	0.403122i	−0.997669	−	0.0682424i	$-0.978261\pi$
$293$	−0.0554078	−	0.403122i	−0.0554078	−	0.403122i	0.942261	−	0.334880i	$-0.108696\pi$
$294$	−0.187206	+	0.361291i	−0.187206	+	0.361291i
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$		0			0
$302$	0.170321	+	0.607882i	0.170321	+	0.607882i
$303$		0			0
$304$	0.447872	+	0.194538i	0.447872	+	0.194538i
$305$		0			0
$306$	0.669562	−	0.407169i	0.669562	−	0.407169i
$307$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$307$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$311$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$312$		0			0
$313$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$313$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$314$		0			0
$315$		0			0
$316$	−1.28248	−	1.04338i	−1.28248	−	1.04338i
$317$	1.02405	+	0.530621i	1.02405	+	0.530621i	0.887885	−	0.460065i	$-0.152174\pi$
$317$	1.02405	+	0.530621i	1.02405	+	0.530621i	0.136167	+	0.990686i	$0.456522\pi$
$318$	0.0371099	+	0.269995i	0.0371099	+	0.269995i
$319$		0			0
$320$		0			0
$321$	0.0787081	−	1.15067i	0.0787081	−	1.15067i
$322$		0			0
$323$	1.76789	−	0.120927i	1.76789	−	0.120927i
$324$	0.169768	−	0.816970i	0.169768	−	0.816970i
$325$		0			0
$326$		0			0
$327$	−0.0709153	+	0.116615i	−0.0709153	+	0.116615i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.116615	−	0.0709153i	−0.116615	−	0.0709153i	0.460065	−	0.887885i	$-0.347826\pi$
$331$	−0.116615	−	0.0709153i	−0.116615	−	0.0709153i	−0.576680	+	0.816970i	$0.695652\pi$
$332$	−0.0930415	+	0.0656758i	−0.0930415	+	0.0656758i
$333$		0			0
$334$	0.0554485	−	0.266833i	0.0554485	−	0.266833i
$335$		0			0
$336$		0			0
$337$		0			0		−0.997669	−	0.0682424i	$-0.978261\pi$
$337$		0			0		0.997669	+	0.0682424i	$0.0217391\pi$
$338$	−0.383417	−	0.136267i	−0.383417	−	0.136267i
$339$	−0.931758	+	0.997669i	−0.931758	+	0.997669i
$340$		0			0
$341$		0			0
$342$	−0.236287	+	0.290436i	−0.236287	+	0.290436i
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.550304	−	0.0756376i	−0.550304	−	0.0756376i
$347$	0.861502	+	1.05893i	0.861502	+	1.05893i	0.997669	+	0.0682424i	$0.0217391\pi$
$347$	0.861502	+	1.05893i	0.861502	+	1.05893i	−0.136167	+	0.990686i	$0.543478\pi$
$348$		0			0
$349$	1.76640	−	0.494921i	1.76640	−	0.494921i	0.775711	−	0.631088i	$-0.217391\pi$
$349$	1.76640	−	0.494921i	1.76640	−	0.494921i	0.990686	+	0.136167i	$0.0434783\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.478085	+	0.786177i	0.478085	+	0.786177i	0.997669	−	0.0682424i	$-0.0217391\pi$
$353$	0.478085	+	0.786177i	0.478085	+	0.786177i	−0.519584	+	0.854419i	$0.673913\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$359$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$360$		0			0
$361$	0.140664	−	0.0610990i	0.140664	−	0.0610990i
$362$	0.405963	−	0.379143i	0.405963	−	0.379143i
$363$	0.631088	−	0.775711i	0.631088	−	0.775711i
$364$		0			0
$365$		0			0
$366$	−0.430891	+	0.461371i	−0.430891	+	0.461371i
$367$		0			0		−0.942261	−	0.334880i	$-0.891304\pi$
$367$		0			0		0.942261	+	0.334880i	$0.108696\pi$
$368$	−0.904739	−	0.0618858i	−0.904739	−	0.0618858i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	1.46794	−	0.760626i	1.46794	−	0.760626i
$373$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$373$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$374$		0			0
$375$		0			0
$376$	0.579029	−	0.471075i	0.579029	−	0.471075i
$377$		0			0
$378$		0			0
$379$	−0.665120	−	0.942261i	−0.665120	−	0.942261i	0.334880	−	0.942261i	$-0.391304\pi$
$379$	−0.665120	−	0.942261i	−0.665120	−	0.942261i	−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.368301	+	1.31448i	−0.368301	+	1.31448i	0.519584	+	0.854419i	$0.326087\pi$
$383$	−0.368301	+	1.31448i	−0.368301	+	1.31448i	−0.887885	+	0.460065i	$0.847826\pi$
$384$	−0.0695378	+	1.01661i	−0.0695378	+	1.01661i
$385$		0			0
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		−0.775711	−	0.631088i	$-0.782609\pi$
$389$		0			0		0.775711	+	0.631088i	$0.217391\pi$
$390$		0			0
$391$	−3.01849	+	1.31111i	−3.01849	+	1.31111i
$392$	−0.609826	−	0.430462i	−0.609826	−	0.430462i
$393$		0			0
$394$	−0.489701	+	0.398401i	−0.489701	+	0.398401i
$395$		0			0
$396$		0			0
$397$		0			0		0.942261	−	0.334880i	$-0.108696\pi$
$397$		0			0		−0.942261	+	0.334880i	$0.891304\pi$
$398$	−0.108577	+	0.249970i	−0.108577	+	0.249970i
$399$		0			0
$400$		0			0
$401$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$401$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.572716	+	1.31852i	0.572716	+	1.31852i
$409$	1.25209	+	1.34066i	1.25209	+	1.34066i	0.917211	+	0.398401i	$0.130435\pi$
$409$	1.25209	+	1.34066i	1.25209	+	1.34066i	0.334880	+	0.942261i	$0.391304\pi$
$410$		0			0
$411$	−0.0627919	+	0.121183i	−0.0627919	+	0.121183i
$412$		0			0
$413$		0			0
$414$	0.232858	−	0.655198i	0.232858	−	0.655198i
$415$		0			0
$416$		0			0
$417$	1.83015	−	0.125185i	1.83015	−	0.125185i
$418$		0			0
$419$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$419$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$420$		0			0
$421$	−0.985454	−	0.599268i	−0.985454	−	0.599268i	−0.0682424	−	0.997669i	$-0.521739\pi$
$421$	−0.985454	−	0.599268i	−0.985454	−	0.599268i	−0.917211	+	0.398401i	$0.869565\pi$
$422$			0.469316i			0.469316i
$423$	−0.398401	−	0.917211i	−0.398401	−	0.917211i
$424$	−0.499941			−0.499941
$425$		0			0
$426$		0			0
$427$		0			0
$428$	0.942261	+	0.195804i	0.942261	+	0.195804i
$429$		0			0
$430$		0			0
$431$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$431$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$432$	0.500042	+	0.177715i	0.500042	+	0.177715i
$433$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$433$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$434$		0			0
$435$		0			0
$436$	−0.0883427	−	0.0718721i	−0.0883427	−	0.0718721i
$437$	1.14913	−	1.07322i	1.14913	−	1.07322i
$438$		0			0
$439$	−0.0787081	+	0.111504i	−0.0787081	+	0.111504i	−0.854419	−	0.519584i	$-0.826087\pi$
$439$	−0.0787081	+	0.111504i	−0.0787081	+	0.111504i	0.775711	+	0.631088i	$0.217391\pi$
$440$		0			0
$441$	−0.775711	+	0.631088i	−0.775711	+	0.631088i
$442$		0			0
$443$	−0.0368232	−	0.131424i	−0.0368232	−	0.131424i	0.942261	−	0.334880i	$-0.108696\pi$
$443$	−0.0368232	−	0.131424i	−0.0368232	−	0.131424i	−0.979084	+	0.203456i	$0.934783\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$449$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$450$		0			0
$451$		0			0
$452$	−0.718857	−	0.883594i	−0.718857	−	0.883594i
$453$	−0.211252	+	1.53697i	−0.211252	+	1.53697i
$454$	−0.364054	+	0.515747i	−0.364054	+	0.515747i
$455$		0			0
$456$	−0.468798	−	0.501960i	−0.468798	−	0.501960i
$457$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$457$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$458$	−0.560515	−	0.290436i	−0.560515	−	0.290436i
$459$	1.90790	−	0.262234i	1.90790	−	0.262234i
$460$		0			0
$461$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$461$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$462$		0			0
$463$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$463$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$464$		0			0
$465$		0			0
$466$	−0.125383	−	0.241978i	−0.125383	−	0.241978i
$467$	1.49867	−	1.05788i	1.49867	−	1.05788i	0.519584	−	0.854419i	$-0.326087\pi$
$467$	1.49867	−	1.05788i	1.49867	−	1.05788i	0.979084	−	0.203456i	$-0.0652174\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$	0.370925	+	0.715852i	0.370925	+	0.715852i
$475$		0			0
$476$		0			0
$477$	−0.180699	+	0.644923i	−0.180699	+	0.644923i
$478$		0			0
$479$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$479$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$480$		0			0
$481$		0			0
$482$	0.241978	+	0.125383i	0.241978	+	0.125383i
$483$		0			0
$484$	0.569538	+	0.609826i	0.569538	+	0.609826i
$485$		0			0
$486$	−0.234658	+	0.332435i	−0.234658	+	0.332435i
$487$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$487$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$488$	−0.730836	−	0.898318i	−0.730836	−	0.898318i
$489$		0			0
$490$		0			0
$491$		0			0		−0.334880	−	0.942261i	$-0.608696\pi$
$491$		0			0		0.334880	+	0.942261i	$0.391304\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	0.352120	+	0.990770i	0.352120	+	0.990770i
$497$		0			0
$498$	0.0543757	−	0.0112994i	0.0543757	−	0.0112994i
$499$	1.32557	−	1.07843i	1.32557	−	1.07843i	0.334880	−	0.942261i	$-0.391304\pi$
$499$	1.32557	−	1.07843i	1.32557	−	1.07843i	0.990686	−	0.136167i	$-0.0434783\pi$
$500$		0			0
$501$	0.386237	−	0.547173i	0.386237	−	0.547173i
$502$		0			0
$503$	−0.297386	+	0.277739i	−0.297386	+	0.277739i	−0.816970	−	0.576680i	$-0.804348\pi$
$503$	−0.297386	+	0.277739i	−0.297386	+	0.277739i	0.519584	+	0.854419i	$0.326087\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.730836	−	0.682553i	−0.730836	−	0.682553i
$508$		0			0
$509$		0			0		0.0682424	−	0.997669i	$-0.478261\pi$
$509$		0			0		−0.0682424	+	0.997669i	$0.521739\pi$
$510$		0			0
$511$		0			0
$512$	−0.887885	−	0.184505i	−0.887885	−	0.184505i
$513$	−0.816970	+	0.423320i	−0.816970	+	0.423320i
$514$	0.451913	+	0.640215i	0.451913	+	0.640215i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.16637	−	0.709287i	−1.16637	−	0.709287i
$520$		0			0
$521$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$521$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$522$		0			0
$523$		0			0		0.997669	−	0.0682424i	$-0.0217391\pi$
$523$		0			0		−0.997669	+	0.0682424i	$0.978261\pi$
$524$		0			0
$525$		0			0
$526$	−0.232858	+	0.655198i	−0.232858	+	0.655198i
$527$	2.78872	+	2.60448i	2.78872	+	2.60448i
$528$		0			0
$529$	−0.883385	+	1.70486i	−0.883385	+	1.70486i
$530$		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
$541$	−1.69292	+	1.02949i	−1.69292	+	1.02949i	−0.775711	+	0.631088i	$0.782609\pi$
$541$	−1.69292	+	1.02949i	−1.69292	+	1.02949i	−0.917211	+	0.398401i	$0.869565\pi$
$542$	−0.149166	+	0.343415i	−0.149166	+	0.343415i
$543$	1.28629	−	0.457146i	1.28629	−	0.457146i
$544$	−1.78468	+	0.500042i	−1.78468	+	0.500042i
$545$		0			0
$546$		0			0
$547$		0			0		0.136167	−	0.990686i	$-0.456522\pi$
$547$		0			0		−0.136167	+	0.990686i	$0.543478\pi$
$548$	−0.0930415	−	0.0656758i	−0.0930415	−	0.0656758i
$549$	−1.42298	+	0.618088i	−1.42298	+	0.618088i
$550$		0			0
$551$		0			0
$552$	1.13255	+	0.586841i	1.13255	+	0.586841i
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.104458	+	1.52712i	−0.104458	+	1.52712i
$557$	0.519584	−	1.85442i	0.519584	−	1.85442i		−	1.00000i	$-0.5\pi$
$557$	0.519584	−	1.85442i	0.519584	−	1.85442i	0.519584	−	0.854419i	$-0.326087\pi$
$558$	−0.804365	+	0.0550200i	−0.804365	+	0.0550200i
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$			1.92583i			1.92583i	0.269797	+	0.962917i	$0.413043\pi$
$563$			1.92583i			1.92583i	−0.269797	+	0.962917i	$0.586957\pi$
$564$	0.803480	−	0.225125i	0.803480	−	0.225125i
$565$		0			0
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.203456	−	0.979084i	$-0.434783\pi$
$569$		0			0		−0.203456	+	0.979084i	$0.565217\pi$
$570$		0			0
$571$	0.886009	+	0.248248i	0.886009	+	0.248248i	0.682553	−	0.730836i	$-0.260870\pi$
$571$	0.886009	+	0.248248i	0.886009	+	0.248248i	0.203456	+	0.979084i	$0.434783\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.0639838	+	0.123483i	−0.0639838	+	0.123483i
$577$		0			0		0.631088	−	0.775711i	$-0.282609\pi$
$577$		0			0		−0.631088	+	0.775711i	$0.717391\pi$
$578$	−0.805571	+	0.752350i	−0.805571	+	0.752350i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$	−0.151869	−	0.0659662i	−0.151869	−	0.0659662i
$587$	−0.478085	−	0.786177i	−0.478085	−	0.786177i	0.519584	−	0.854419i	$-0.326087\pi$
$587$	−0.478085	−	0.786177i	−0.478085	−	0.786177i	−0.997669	+	0.0682424i	$0.978261\pi$
$588$	−0.433553	−	0.712947i	−0.433553	−	0.712947i
$589$	−1.67219	−	0.726333i	−1.67219	−	0.726333i
$590$		0			0
$591$	−1.49389	+	0.418569i	−1.49389	+	0.418569i
$592$		0			0
$593$	−0.256797	−	0.315646i	−0.256797	−	0.315646i	0.631088	−	0.775711i	$-0.282609\pi$
$593$	−0.256797	−	0.315646i	−0.256797	−	0.315646i	−0.887885	+	0.460065i	$0.847826\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.489484	+	0.457146i	−0.489484	+	0.457146i
$598$		0			0
$599$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$599$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$600$		0			0
$601$	0.931758	−	0.997669i	0.931758	−	0.997669i	−0.0682424	−	0.997669i	$-0.521739\pi$
$601$	0.931758	−	0.997669i	0.931758	−	0.997669i	1.00000			$0$
$602$		0			0
$603$		0			0
$604$	−1.24654	−	0.349263i	−1.24654	−	0.349263i
$605$		0			0
$606$		0			0
$607$		0			0		0.887885	−	0.460065i	$-0.152174\pi$
$607$		0			0		−0.887885	+	0.460065i	$0.847826\pi$
$608$	0.723447	−	0.510664i	0.723447	−	0.510664i
$609$		0			0
$610$		0			0
$611$		0			0
$612$			1.60696i			1.60696i
$613$		0			0		0.519584	−	0.854419i	$-0.326087\pi$
$613$		0			0		−0.519584	+	0.854419i	$0.673913\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.97675	−	0.135214i	1.97675	−	0.135214i	0.979084	−	0.203456i	$-0.0652174\pi$
$617$	1.97675	−	0.135214i	1.97675	−	0.135214i	0.997669	+	0.0682424i	$0.0217391\pi$
$618$		0			0
$619$	−0.105873	+	1.54781i	−0.105873	+	1.54781i	0.576680	+	0.816970i	$0.304348\pi$
$619$	−0.105873	+	1.54781i	−0.105873	+	1.54781i	−0.682553	+	0.730836i	$0.739130\pi$
$620$		0			0
$621$	1.16637	−	1.24888i	1.16637	−	1.24888i
$622$		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
$631$	1.64547	−	0.461039i	1.64547	−	0.461039i	0.682553	−	0.730836i	$-0.260870\pi$
$631$	1.64547	−	0.461039i	1.64547	−	0.461039i	0.962917	+	0.269797i	$0.0869565\pi$
$632$	−1.39360	+	0.495284i	−1.39360	+	0.495284i
$633$	−0.459500	+	1.05788i	−0.459500	+	1.05788i
$634$	0.400993	−	0.243849i	0.400993	−	0.243849i
$635$		0			0
$636$	−0.512595	−	0.222651i	−0.512595	−	0.222651i
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$		0			0		−0.990686	−	0.136167i	$-0.956522\pi$
$641$		0			0		0.990686	+	0.136167i	$0.0434783\pi$
$642$	−0.383417	−	0.270645i	−0.383417	−	0.270645i
$643$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$643$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$644$		0			0
$645$		0			0
$646$	0.331732	−	0.640215i	0.331732	−	0.640215i
$647$	−0.0911989	−	0.663521i	−0.0911989	−	0.663521i	−0.979084	−	0.203456i	$-0.934783\pi$
$647$	−0.0911989	−	0.663521i	−0.0911989	−	0.663521i	0.887885	−	0.460065i	$-0.152174\pi$
$648$	−0.545531	−	0.509491i	−0.545531	−	0.509491i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.900885	+	0.187206i	0.900885	+	0.187206i	0.631088	−	0.775711i	$-0.282609\pi$
$653$	0.900885	+	0.187206i	0.900885	+	0.187206i	0.269797	+	0.962917i	$0.413043\pi$
$654$	0.0255508	+	0.0493108i	0.0255508	+	0.0493108i
$655$		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
$661$	−1.11059	−	1.57335i	−1.11059	−	1.57335i	−0.775711	−	0.631088i	$-0.782609\pi$
$661$	−1.11059	−	1.57335i	−1.11059	−	1.57335i	−0.334880	−	0.942261i	$-0.608696\pi$
$662$	−0.0493108	+	0.0255508i	−0.0493108	+	0.0255508i
$663$		0			0
$664$	0.00695246	+	0.101641i	0.00695246	+	0.101641i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	0.408437	+	0.381453i	0.408437	+	0.381453i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.398401	−	0.917211i	$-0.630435\pi$
$673$		0			0		0.398401	+	0.917211i	$0.369565\pi$
$674$		0			0
$675$		0			0
$676$	0.647271	−	0.526594i	0.647271	−	0.526594i
$677$	−1.79605	+	0.373224i	−1.79605	+	0.373224i	−0.979084	−	0.203456i	$-0.934783\pi$
$677$	−1.79605	+	0.373224i	−1.79605	+	0.373224i	−0.816970	+	0.576680i	$0.804348\pi$
$678$	0.149866	+	0.534880i	0.149866	+	0.534880i
$679$		0			0
$680$		0			0
$681$	−1.32557	+	0.806094i	−1.32557	+	0.806094i
$682$		0			0
$683$	0.680803	−	1.56737i	0.680803	−	1.56737i	−0.136167	−	0.990686i	$-0.543478\pi$
$683$	0.680803	−	1.56737i	0.680803	−	1.56737i	0.816970	−	0.576680i	$-0.195652\pi$
$684$	−0.257113	−	0.723447i	−0.257113	−	0.723447i
$685$		0			0
$686$		0			0
$687$	−0.979084	−	1.20346i	−0.979084	−	1.20346i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	1.31448	+	1.40747i	1.31448	+	1.40747i	0.854419	+	0.519584i	$0.173913\pi$
$691$	1.31448	+	1.40747i	1.31448	+	1.40747i	0.460065	+	0.887885i	$0.347826\pi$
$692$	0.718857	−	0.883594i	0.718857	−	0.883594i
$693$		0			0
$694$	0.550304	−	0.0756376i	0.550304	−	0.0756376i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	0.201389	−	0.718768i	0.201389	−	0.718768i
$699$	−0.0457060	−	0.668198i	−0.0457060	−	0.668198i
$700$		0			0
$701$		0			0		−0.460065	−	0.887885i	$-0.652174\pi$
$701$		0			0		0.460065	+	0.887885i	$0.347826\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.374412			0.374412
$707$		0			0
$708$		0			0
$709$	−0.786177	−	1.51725i	−0.786177	−	1.51725i	−0.854419	−	0.519584i	$-0.826087\pi$
$709$	−0.786177	−	1.51725i	−0.786177	−	1.51725i	0.0682424	−	0.997669i	$-0.478261\pi$
$710$		0			0
$711$	0.135214	+	1.97675i	0.135214	+	1.97675i
$712$		0			0
$713$	3.37795	+	0.231058i	3.37795	+	0.231058i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.682553	−	0.730836i	$-0.739130\pi$
$719$		0			0		0.682553	+	0.730836i	$0.260870\pi$
$720$		0			0
$721$		0			0
$722$	0.00849738	−	0.0618231i	0.00849738	−	0.0618231i
$723$	0.422677	+	0.519540i	0.422677	+	0.519540i
$724$	0.231752	+	1.11525i	0.231752	+	1.11525i
$725$		0			0
$726$	−0.136267	−	0.383417i	−0.136267	−	0.383417i
$727$		0			0		0.398401	−	0.917211i	$-0.369565\pi$
$727$		0			0		−0.398401	+	0.917211i	$0.630435\pi$
$728$		0			0
$729$	−0.854419	+	0.519584i	−0.854419	+	0.519584i
$730$		0			0
$731$		0			0
$732$	−0.349263	−	1.24654i	−0.349263	−	1.24654i
$733$		0			0		0.979084	−	0.203456i	$-0.0652174\pi$
$733$		0			0		−0.979084	+	0.203456i	$0.934783\pi$
$734$		0			0
$735$		0			0
$736$	−0.948391	+	1.34356i	−0.948391	+	1.34356i
$737$		0			0
$738$		0			0
$739$	1.05893	+	0.861502i	1.05893	+	0.861502i	0.990686	−	0.136167i	$-0.0434783\pi$
$739$	1.05893	+	0.861502i	1.05893	+	0.861502i	0.0682424	+	0.997669i	$0.478261\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.867003	−	0.308133i	−0.867003	−	0.308133i	−0.136167	−	0.990686i	$-0.543478\pi$
$743$	−0.867003	−	0.308133i	−0.867003	−	0.308133i	−0.730836	+	0.682553i	$0.760870\pi$
$744$	0.100930	−	1.47554i	0.100930	−	1.47554i
$745$		0			0
$746$		0			0
$747$	0.133630	+	0.0277687i	0.133630	+	0.0277687i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−1.15336			−1.15336			−0.576680	−	0.816970i	$-0.695652\pi$
$751$	−1.15336			−1.15336			−0.576680	+	0.816970i	$0.695652\pi$
$752$	0.0722614	+	0.525741i	0.0722614	+	0.525741i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.979084	−	0.203456i	$-0.934783\pi$
$757$		0			0		0.979084	+	0.203456i	$0.0652174\pi$
$758$	−0.468222	+	0.0320273i	−0.468222	+	0.0320273i
$759$		0			0
$760$		0			0
$761$		0			0		0.334880	−	0.942261i	$-0.391304\pi$
$761$		0			0		−0.334880	+	0.942261i	$0.608696\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.379143	+	0.405963i	0.379143	+	0.405963i
$767$		0			0
$768$	0.225125	+	0.158910i	0.225125	+	0.158910i
$769$	1.90790	+	0.262234i	1.90790	+	0.262234i	0.990686	−	0.136167i	$-0.0434783\pi$
$769$	1.90790	+	0.262234i	1.90790	+	0.262234i	0.917211	+	0.398401i	$0.130435\pi$
$770$		0			0
$771$	0.391823	+	1.88555i	0.391823	+	1.88555i
$772$		0			0
$773$	−1.72850	+	0.614311i	−1.72850	+	0.614311i	−0.997669	−	0.0682424i	$-0.978261\pi$
$773$	−1.72850	+	0.614311i	−1.72850	+	0.614311i	−0.730836	+	0.682553i	$0.760870\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−0.182344	+	1.32665i	−0.182344	+	1.32665i
$783$		0			0
$784$	0.486749	−	0.211425i	0.486749	−	0.211425i
$785$		0			0
$786$		0			0
$787$		0			0		−0.887885	−	0.460065i	$-0.847826\pi$
$787$		0			0		0.887885	+	0.460065i	$0.152174\pi$
$788$	−0.176273	−	1.28248i	−0.176273	−	1.28248i
$789$	−1.16637	+	1.24888i	−1.16637	+	1.24888i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	−0.322285	−	0.456574i	−0.322285	−	0.456574i
$797$	−0.953137	+	1.56737i	−0.953137	+	1.56737i	−0.136167	+	0.990686i	$0.543478\pi$
$797$	−0.953137	+	1.56737i	−0.953137	+	1.56737i	−0.816970	+	0.576680i	$0.804348\pi$
$798$		0			0
$799$	1.11059	+	1.57335i	1.11059	+	1.57335i
$800$		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		0.682553	−	0.730836i	$-0.260870\pi$
$809$		0			0		−0.682553	+	0.730836i	$0.739130\pi$
$810$		0			0
$811$	0.628038	−	1.21206i	0.628038	−	1.21206i	−0.334880	−	0.942261i	$-0.608696\pi$
$811$	0.628038	−	1.21206i	0.628038	−	1.21206i	0.962917	−	0.269797i	$-0.0869565\pi$
$812$		0			0
$813$	−0.672464	+	0.628038i	−0.672464	+	0.628038i
$814$		0			0
$815$		0			0
$816$	−1.01249	−	0.139164i	−1.01249	−	0.139164i
$817$		0			0
$818$	0.730836	−	0.151869i	0.730836	−	0.151869i
$819$		0			0
$820$		0			0
$821$		0			0		−0.917211	−	0.398401i	$-0.869565\pi$
$821$		0			0		0.917211	+	0.398401i	$0.130435\pi$
$822$	0.0288563	+	0.0474522i	0.0288563	+	0.0474522i
$823$		0			0		−0.519584	−	0.854419i	$-0.673913\pi$
$823$		0			0		0.519584	+	0.854419i	$0.326087\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.79605	+	0.373224i	−1.79605	+	0.373224i	−0.979084	−	0.203456i	$-0.934783\pi$
$827$	−1.79605	+	0.373224i	−1.79605	+	0.373224i	−0.816970	+	0.576680i	$0.804348\pi$
$828$	0.899864	+	1.10608i	0.899864	+	1.10608i
$829$	0.403122	+	0.0554078i	0.403122	+	0.0554078i	0.334880	−	0.942261i	$-0.391304\pi$
$829$	0.403122	+	0.0554078i	0.403122	+	0.0554078i	0.0682424	+	0.997669i	$0.478261\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.21537	−	1.49389i	1.21537	−	1.49389i
$834$	0.343415	−	0.662761i	0.343415	−	0.662761i
$835$		0			0
$836$		0			0
$837$	−1.86697	−	0.663521i	−1.86697	−	0.663521i
$838$		0			0
$839$		0			0		−0.962917	−	0.269797i	$-0.913043\pi$
$839$		0			0		0.962917	+	0.269797i	$0.0869565\pi$
$840$		0			0
$841$	0.203456	−	0.979084i	0.203456	−	0.979084i
$842$	−0.416699	+	0.215916i	−0.416699	+	0.215916i
$843$		0			0
$844$	−0.822285	−	0.500042i	−0.822285	−	0.500042i
$845$		0			0
$846$	−0.403122	−	0.0554078i	−0.403122	−	0.0554078i
$847$		0			0
$848$	0.184676	−	0.303687i	0.184676	−	0.303687i
$849$		0			0
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.269797	−	0.962917i	$-0.413043\pi$
$853$		0			0		−0.269797	+	0.962917i	$0.586957\pi$
$854$		0			0
$855$		0			0
$856$	0.587627	−	0.629195i	0.587627	−	0.629195i
$857$	−0.157049	−	1.14262i	−0.157049	−	1.14262i	−0.887885	−	0.460065i	$-0.847826\pi$
$857$	−0.157049	−	1.14262i	−0.157049	−	1.14262i	0.730836	−	0.682553i	$-0.239130\pi$
$858$		0			0
$859$	0.315646	+	0.256797i	0.315646	+	0.256797i	0.775711	−	0.631088i	$-0.217391\pi$
$859$	0.315646	+	0.256797i	0.315646	+	0.256797i	−0.460065	+	0.887885i	$0.652174\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−0.269797	+	1.96292i	−0.269797	+	1.96292i			1.00000i	$0.5\pi$
$863$	−0.269797	+	1.96292i	−0.269797	+	1.96292i	−0.269797	+	0.962917i	$0.586957\pi$
$864$	0.746537	−	0.607353i	0.746537	−	0.607353i
$865$		0			0
$866$		0			0
$867$	−2.55243	+	0.907135i	−2.55243	+	0.907135i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.0959965	+	0.0341172i	−0.0959965	+	0.0341172i
$873$		0			0
$874$	−0.130173	−	0.626428i	−0.130173	−	0.626428i
$875$		0			0
$876$		0			0
$877$		0			0		−0.816970	−	0.576680i	$-0.804348\pi$
$877$		0			0		0.816970	+	0.576680i	$0.195652\pi$
$878$	0.0221261	+	0.0509395i	0.0221261	+	0.0509395i
$879$	−0.277739	−	0.297386i	−0.277739	−	0.297386i
$880$		0			0
$881$		0			0		0.460065	−	0.887885i	$-0.347826\pi$
$881$		0			0		−0.460065	+	0.887885i	$0.652174\pi$
$882$	0.0554078	+	0.403122i	0.0554078	+	0.403122i
$883$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$883$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$884$		0			0
$885$		0			0
$886$	−0.0534778	−	0.0149838i	−0.0534778	−	0.0149838i
$887$	−0.917985	+	0.0627919i	−0.917985	+	0.0627919i	−0.519584	−	0.854419i	$-0.673913\pi$
$887$	−0.917985	+	0.0627919i	−0.917985	+	0.0627919i	−0.398401	+	0.917211i	$0.630435\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.751719	−	0.530621i	−0.751719	−	0.530621i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	0.0880222	−	1.28684i	0.0880222	−	1.28684i
$902$		0			0
$903$		0			0
$904$	−1.00949	+	0.138751i	−1.00949	+	0.138751i
$905$		0			0
$906$	0.489701	+	0.398401i	0.489701	+	0.398401i
$907$		0			0		0.730836	−	0.682553i	$-0.239130\pi$
$907$		0			0		−0.730836	+	0.682553i	$0.760870\pi$
$908$	−0.515747	−	1.18737i	−0.515747	−	1.18737i
$909$		0			0
$910$		0			0
$911$		0			0		0.775711	−	0.631088i	$-0.217391\pi$
$911$		0			0		−0.775711	+	0.631088i	$0.782609\pi$
$912$	0.478085	−	0.0993472i	0.478085	−	0.0993472i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	1.10608	−	0.672623i	1.10608	−	0.672623i
$917$		0			0
$918$	0.312205	−	0.718768i	0.312205	−	0.718768i
$919$	0.572255	+	1.61017i	0.572255	+	1.61017i	0.775711	+	0.631088i	$0.217391\pi$
$919$	0.572255	+	1.61017i	0.572255	+	1.61017i	−0.203456	+	0.979084i	$0.565217\pi$
$920$		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		0.990686	−	0.136167i	$-0.0434783\pi$
$929$		0			0		−0.990686	+	0.136167i	$0.956522\pi$
$930$		0			0
$931$	−0.308133	+	0.867003i	−0.308133	+	0.867003i
$932$	0.557559	+	0.0381381i	0.557559	+	0.0381381i
$933$		0			0
$934$	−0.0509395	−	0.744708i	−0.0509395	−	0.744708i
$935$		0			0
$936$		0			0
$937$		0			0		0.816970	−	0.576680i	$-0.195652\pi$
$937$		0			0		−0.816970	+	0.576680i	$0.804348\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.494921	+	1.76640i	−0.494921	+	1.76640i	0.136167	+	0.990686i	$0.456522\pi$
$947$	−0.494921	+	1.76640i	−0.494921	+	1.76640i	−0.631088	+	0.775711i	$0.717391\pi$
$948$	−1.64945	−	0.112825i	−1.64945	−	0.112825i
$949$		0			0
$950$		0			0
$951$	1.14262	−	0.157049i	1.14262	−	0.157049i
$952$		0			0
$953$	0.256797	−	0.315646i	0.256797	−	0.315646i	−0.631088	−	0.775711i	$-0.717391\pi$
$953$	0.256797	−	0.315646i	0.256797	−	0.315646i	0.887885	+	0.460065i	$0.152174\pi$
$954$	0.186018	+	0.199177i	0.186018	+	0.199177i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.979802	−	2.75690i	−0.979802	−	2.75690i
$962$		0			0
$963$	−0.599268	−	0.985454i	−0.599268	−	0.985454i
$964$	−0.477503	+	0.290376i	−0.477503	+	0.290376i
$965$		0			0
$966$		0			0
$967$		0			0		−0.269797	−	0.962917i	$-0.586957\pi$
$967$		0			0		0.269797	+	0.962917i	$0.413043\pi$
$968$	0.730836	−	0.151869i	0.730836	−	0.151869i
$969$	1.37457	−	1.11830i	1.37457	−	1.11830i
$970$		0			0
$971$		0			0		0.576680	−	0.816970i	$-0.304348\pi$
$971$		0			0		−0.576680	+	0.816970i	$0.695652\pi$
$972$	−0.332435	−	0.765342i	−0.332435	−	0.765342i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	0.815646	−	0.112108i	0.815646	−	0.112108i
$977$	−0.997669	−	0.931758i	−0.997669	−	0.931758i		−	1.00000i	$-0.5\pi$
$977$	−0.997669	−	0.931758i	−0.997669	−	0.931758i	−0.997669	+	0.0682424i	$0.978261\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.00931405	+	0.136167i	0.00931405	+	0.136167i
$982$		0			0
$983$	1.37749	−	0.713755i	1.37749	−	0.713755i	0.398401	−	0.917211i	$-0.369565\pi$
$983$	1.37749	−	0.713755i	1.37749	−	0.713755i	0.979084	+	0.203456i	$0.0652174\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.530621	−	1.02405i	−0.530621	−	1.02405i	−0.990686	−	0.136167i	$-0.956522\pi$
$991$	−0.530621	−	1.02405i	−0.530621	−	1.02405i	0.460065	−	0.887885i	$-0.347826\pi$
$992$	1.86697	+	0.387961i	1.86697	+	0.387961i
$993$	−0.136167	+	0.00931405i	−0.136167	+	0.00931405i
$994$		0			0
$995$		0			0
$996$	−0.0381381	+	0.107310i	−0.0381381	+	0.107310i
$997$		0			0		−0.730836	−	0.682553i	$-0.760870\pi$
$997$		0			0		0.730836	+	0.682553i	$0.239130\pi$
$998$	−0.0946831	−	0.688871i	−0.0946831	−	0.688871i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3525.1.bd.a.251.2		44
3.2	odd	2	inner	3525.1.bd.a.251.1		44
5.2	odd	4		705.1.p.a.674.1	yes	22
5.3	odd	4		705.1.p.b.674.1	yes	22
5.4	even	2	inner	3525.1.bd.a.251.1		44
15.2	even	4		705.1.p.b.674.1	yes	22
15.8	even	4		705.1.p.a.674.1	yes	22
15.14	odd	2	CM	3525.1.bd.a.251.2		44
47.3	even	23	inner	3525.1.bd.a.1601.1		44
141.50	odd	46	inner	3525.1.bd.a.1601.2		44
235.3	odd	92		705.1.p.b.614.1	yes	22
235.97	odd	92		705.1.p.a.614.1	✓	22
235.144	even	46	inner	3525.1.bd.a.1601.2		44
705.332	even	92		705.1.p.b.614.1	yes	22
705.473	even	92		705.1.p.a.614.1	✓	22
705.614	odd	46	inner	3525.1.bd.a.1601.1		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
705.1.p.a.614.1	✓	22	235.97	odd	92
705.1.p.a.614.1	✓	22	705.473	even	92
705.1.p.a.674.1	yes	22	5.2	odd	4
705.1.p.a.674.1	yes	22	15.8	even	4
705.1.p.b.614.1	yes	22	235.3	odd	92
705.1.p.b.614.1	yes	22	705.332	even	92
705.1.p.b.674.1	yes	22	5.3	odd	4
705.1.p.b.674.1	yes	22	15.2	even	4
3525.1.bd.a.251.1		44	3.2	odd	2	inner
3525.1.bd.a.251.1		44	5.4	even	2	inner
3525.1.bd.a.251.2		44	1.1	even	1	trivial
3525.1.bd.a.251.2		44	15.14	odd	2	CM
3525.1.bd.a.1601.1		44	47.3	even	23	inner
3525.1.bd.a.1601.1		44	705.614	odd	46	inner
3525.1.bd.a.1601.2		44	141.50	odd	46	inner
3525.1.bd.a.1601.2		44	235.144	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)

\(f(q)\)	\(=\)	\(q+(0.211425 - 0.347674i) q^{2} +(0.816970 - 0.576680i) q^{3} +(0.383889 + 0.740871i) q^{4} +(-0.0277687 - 0.405963i) q^{6} +(0.744708 + 0.0509395i) q^{8} +(0.334880 - 0.942261i) q^{9} +O(q^{10})\)	\(q+(0.211425 - 0.347674i) q^{2} +(0.816970 - 0.576680i) q^{3} +(0.383889 + 0.740871i) q^{4} +(-0.0277687 - 0.405963i) q^{6} +(0.744708 + 0.0509395i) q^{8} +(0.334880 - 0.942261i) q^{9} +(0.740871 + 0.383889i) q^{12} +(-0.306035 + 0.433553i) q^{16} +(-0.262234 + 1.90790i) q^{17} +(-0.256797 - 0.315646i) q^{18} +(-0.187206 - 0.900885i) q^{19} +(0.887885 + 1.46007i) q^{23} +(0.637780 - 0.387843i) q^{24} +(-0.269797 - 0.962917i) q^{27} +(1.14262 - 1.61872i) q^{31} +(0.383417 + 0.882715i) q^{32} +(0.607882 + 0.494549i) q^{34} +(0.826651 - 0.113621i) q^{36} +(-0.352794 - 0.125383i) q^{38} +0.695347 q^{46} +(0.730836 - 0.682553i) q^{47} +0.530684i q^{48} +(-0.854419 - 0.519584i) q^{49} +(0.886009 + 1.70992i) q^{51} +(-0.668198 + 0.0457060i) q^{53} +(-0.391823 - 0.109784i) q^{54} +(-0.672464 - 0.628038i) q^{57} +(-1.05893 - 1.13384i) q^{61} +(-0.321209 - 0.739496i) q^{62} +(-0.137780 - 0.0189375i) q^{64} +(-1.51418 + 0.538138i) q^{68} +(1.56737 + 0.680803i) q^{69} +(0.297386 - 0.684651i) q^{72} +(0.595574 - 0.484535i) q^{76} +(-1.81734 + 0.789381i) q^{79} +(-0.775711 - 0.631088i) q^{81} +(0.0185847 + 0.135214i) q^{83} +(-0.740871 + 1.21831i) q^{92} -1.98137i q^{93} +(-0.0827887 - 0.398401i) q^{94} +(0.822285 + 0.500042i) q^{96} +(-0.361291 + 0.187206i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 6 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more