LMFDB - Embedded newform 2300.1.bh.a.907.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2300,1,Mod(7,2300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2300, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 11, 38]))

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

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

chi := DirichletCharacter("2300.7");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2300 = 2^{2} \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2300.bh (of order $44$, degree $20$, 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:	$1.14784952906$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$2$ over $\Q(\zeta_{44})$
Coefficient field:	$\Q(\zeta_{88})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{22}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{22} - \cdots)$

Embedding invariants

Embedding label			907.1
Root			$0.997452 + 0.0713392i$ of defining polynomial
Character	$\chi$	$=$	2300.907
Dual form			2300.1.bh.a.743.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 - 0.0713392i) q^{2} +(-0.278401 - 1.27979i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.186393 + 1.29639i) q^{6} +(0.270040 + 0.494541i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.650724 + 0.297176i) q^{9} +O(q^{10})$	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.278401 - 1.27979i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.186393 + 1.29639i) q^{6} +(0.270040 + 0.494541i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.650724 + 0.297176i) q^{9} +(-0.0934345 - 1.30638i) q^{12} +(-0.234072 - 0.512546i) q^{14} +(0.959493 + 0.281733i) q^{16} +(0.670266 - 0.249996i) q^{18} +(0.557730 - 0.483276i) q^{21} +(0.0713392 - 0.997452i) q^{23} +1.30972i q^{24} +(-0.223402 - 0.298430i) q^{27} +(0.196911 + 0.527938i) q^{28} +(-0.822373 + 0.118239i) q^{29} +(-0.936950 - 0.349464i) q^{32} +(-0.686393 + 0.201543i) q^{36} +(0.797176 - 1.74557i) q^{41} +(-0.590785 + 0.442256i) q^{42} +(1.93440 - 0.420803i) q^{43} +(-0.142315 + 0.989821i) q^{46} +(0.587486 - 0.587486i) q^{47} +(0.0934345 - 1.30638i) q^{48} +(0.368991 - 0.574161i) q^{49} +(0.201543 + 0.313607i) q^{54} +(-0.158746 - 0.540641i) q^{56} +(0.828713 - 0.0592707i) q^{58} +(-1.07028 - 1.66538i) q^{61} +(-0.322687 - 0.241561i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-0.0771377 + 1.07853i) q^{67} +(-1.29639 + 0.186393i) q^{69} +(0.699022 - 0.152063i) q^{72} +(-0.788201 + 0.909632i) q^{81} +(-0.919672 + 1.68425i) q^{82} +(1.01311 + 0.377869i) q^{83} +(0.620830 - 0.398983i) q^{84} +(-1.95949 + 0.281733i) q^{86} +(0.380272 + 1.01955i) q^{87} +(1.27155 + 0.817178i) q^{89} +(0.212565 - 0.977147i) q^{92} +(-0.627899 + 0.544078i) q^{94} +(-0.186393 + 1.29639i) q^{96} +(-0.409011 + 0.546375i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{6}+O(q^{10}) $ 40 * q - 8 * q^6	$ 40 q - 8 q^{6} + 4 q^{16} - 12 q^{36} + 8 q^{41} - 4 q^{46} - 44 q^{56} + 20 q^{81} - 44 q^{86} + 8 q^{96}+O(q^{100}) $ 40 * q - 8 * q^6 + 4 * q^16 - 12 * q^36 + 8 * q^41 - 4 * q^46 - 44 * q^56 + 20 * q^81 - 44 * q^86 + 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2300\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.997452	−	0.0713392i	−0.997452	−	0.0713392i
$2$	−0.997452	−	0.0713392i	−0.997452	−	0.0713392i
$3$	−0.278401	−	1.27979i	−0.278401	−	1.27979i	−0.877679	−	0.479249i	$-0.840909\pi$
$3$	−0.278401	−	1.27979i	−0.278401	−	1.27979i	0.599278	−	0.800541i	$-0.295455\pi$
$4$	0.989821	+	0.142315i	0.989821	+	0.142315i
$5$		0			0
$5$		0			0
$6$	0.186393	+	1.29639i	0.186393	+	1.29639i
$7$	0.270040	+	0.494541i	0.270040	+	0.494541i	0.977147	−	0.212565i	$-0.0681818\pi$
$7$	0.270040	+	0.494541i	0.270040	+	0.494541i	−0.707107	+	0.707107i	$0.750000\pi$
$8$	−0.977147	−	0.212565i	−0.977147	−	0.212565i
$9$	−0.650724	+	0.297176i	−0.650724	+	0.297176i
$10$		0			0
$11$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$11$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$12$	−0.0934345	−	1.30638i	−0.0934345	−	1.30638i
$13$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$13$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$14$	−0.234072	−	0.512546i	−0.234072	−	0.512546i
$15$		0			0
$16$	0.959493	+	0.281733i	0.959493	+	0.281733i
$17$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$17$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$18$	0.670266	−	0.249996i	0.670266	−	0.249996i
$19$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$19$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$20$		0			0
$21$	0.557730	−	0.483276i	0.557730	−	0.483276i
$22$		0			0
$23$	0.0713392	−	0.997452i	0.0713392	−	0.997452i
$23$	0.0713392	−	0.997452i	0.0713392	−	0.997452i
$24$			1.30972i			1.30972i
$25$		0			0
$26$		0			0
$27$	−0.223402	−	0.298430i	−0.223402	−	0.298430i
$28$	0.196911	+	0.527938i	0.196911	+	0.527938i
$29$	−0.822373	+	0.118239i	−0.822373	+	0.118239i	−0.540641	−	0.841254i	$-0.681818\pi$
$29$	−0.822373	+	0.118239i	−0.822373	+	0.118239i	−0.281733	+	0.959493i	$0.590909\pi$
$30$		0			0
$31$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$31$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$32$	−0.936950	−	0.349464i	−0.936950	−	0.349464i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	−0.686393	+	0.201543i	−0.686393	+	0.201543i
$37$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$37$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$41$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$42$	−0.590785	+	0.442256i	−0.590785	+	0.442256i
$43$	1.93440	−	0.420803i	1.93440	−	0.420803i	0.936950	−	0.349464i	$-0.113636\pi$
$43$	1.93440	−	0.420803i	1.93440	−	0.420803i	0.997452	−	0.0713392i	$-0.0227273\pi$
$44$		0			0
$45$		0			0
$46$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$47$	0.587486	−	0.587486i	0.587486	−	0.587486i	−0.349464	−	0.936950i	$-0.613636\pi$
$47$	0.587486	−	0.587486i	0.587486	−	0.587486i	0.936950	+	0.349464i	$0.113636\pi$
$48$	0.0934345	−	1.30638i	0.0934345	−	1.30638i
$49$	0.368991	−	0.574161i	0.368991	−	0.574161i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$53$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$54$	0.201543	+	0.313607i	0.201543	+	0.313607i
$55$		0			0
$56$	−0.158746	−	0.540641i	−0.158746	−	0.540641i
$57$		0			0
$58$	0.828713	−	0.0592707i	0.828713	−	0.0592707i
$59$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$59$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$60$		0			0
$61$	−1.07028	−	1.66538i	−1.07028	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$61$	−1.07028	−	1.66538i	−1.07028	−	1.66538i	−0.415415	−	0.909632i	$-0.636364\pi$
$62$		0			0
$63$	−0.322687	−	0.241561i	−0.322687	−	0.241561i
$64$	0.909632	+	0.415415i	0.909632	+	0.415415i
$65$		0			0
$66$		0			0
$67$	−0.0771377	+	1.07853i	−0.0771377	+	1.07853i	0.800541	+	0.599278i	$0.204545\pi$
$67$	−0.0771377	+	1.07853i	−0.0771377	+	1.07853i	−0.877679	+	0.479249i	$0.840909\pi$
$68$		0			0
$69$	−1.29639	+	0.186393i	−1.29639	+	0.186393i
$70$		0			0
$71$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$71$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$72$	0.699022	−	0.152063i	0.699022	−	0.152063i
$73$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$73$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$79$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$80$		0			0
$81$	−0.788201	+	0.909632i	−0.788201	+	0.909632i
$82$	−0.919672	+	1.68425i	−0.919672	+	1.68425i
$83$	1.01311	+	0.377869i	1.01311	+	0.377869i	0.800541	−	0.599278i	$-0.204545\pi$
$83$	1.01311	+	0.377869i	1.01311	+	0.377869i	0.212565	+	0.977147i	$0.431818\pi$
$84$	0.620830	−	0.398983i	0.620830	−	0.398983i
$85$		0			0
$86$	−1.95949	+	0.281733i	−1.95949	+	0.281733i
$87$	0.380272	+	1.01955i	0.380272	+	1.01955i
$88$		0			0
$89$	1.27155	+	0.817178i	1.27155	+	0.817178i	0.989821	−	0.142315i	$-0.0454545\pi$
$89$	1.27155	+	0.817178i	1.27155	+	0.817178i	0.281733	+	0.959493i	$0.409091\pi$
$90$		0			0
$91$		0			0
$92$	0.212565	−	0.977147i	0.212565	−	0.977147i
$93$		0			0
$94$	−0.627899	+	0.544078i	−0.627899	+	0.544078i
$95$		0			0
$96$	−0.186393	+	1.29639i	−0.186393	+	1.29639i
$97$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$97$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$98$	−0.409011	+	0.546375i	−0.409011	+	0.546375i
$99$		0			0
$100$		0			0
$101$	−0.698939	−	1.53046i	−0.698939	−	1.53046i	−0.841254	−	0.540641i	$-0.818182\pi$
$101$	−0.698939	−	1.53046i	−0.698939	−	1.53046i	0.142315	−	0.989821i	$-0.454545\pi$
$102$		0			0
$103$	0.129785	+	1.81463i	0.129785	+	1.81463i	0.479249	+	0.877679i	$0.340909\pi$
$103$	0.129785	+	1.81463i	0.129785	+	1.81463i	−0.349464	+	0.936950i	$0.613636\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.77769	−	0.386712i	−1.77769	−	0.386712i	−0.800541	−	0.599278i	$-0.795455\pi$
$107$	−1.77769	−	0.386712i	−1.77769	−	0.386712i	−0.977147	+	0.212565i	$0.931818\pi$
$108$	−0.178657	−	0.327186i	−0.178657	−	0.327186i
$109$	−0.215109	−	1.49611i	−0.215109	−	1.49611i	−0.755750	−	0.654861i	$-0.772727\pi$
$109$	−0.215109	−	1.49611i	−0.215109	−	1.49611i	0.540641	−	0.841254i	$-0.318182\pi$
$110$		0			0
$111$		0			0
$112$	0.119773	+	0.550588i	0.119773	+	0.550588i
$113$		0			0		−0.997452	−	0.0713392i	$-0.977273\pi$
$113$		0			0		0.997452	+	0.0713392i	$0.0227273\pi$
$114$		0			0
$115$		0			0
$116$	−0.830830			−0.830830
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.142315	+	0.989821i	0.142315	+	0.989821i
$122$	0.948742	+	1.73749i	0.948742	+	1.73749i
$123$	−2.45590	−	0.534248i	−2.45590	−	0.534248i
$124$		0			0
$125$		0			0
$126$	0.304632	+	0.263965i	0.304632	+	0.263965i
$127$	−0.120029	−	1.67822i	−0.120029	−	1.67822i	−0.599278	−	0.800541i	$-0.704545\pi$
$127$	−0.120029	−	1.67822i	−0.120029	−	1.67822i	0.479249	−	0.877679i	$-0.340909\pi$
$128$	−0.877679	−	0.479249i	−0.877679	−	0.479249i
$129$	−1.07708	−	2.35848i	−1.07708	−	2.35848i
$130$		0			0
$131$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$131$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$132$		0			0
$133$		0			0
$134$	0.153882	−	1.07028i	0.153882	−	1.07028i
$135$		0			0
$136$		0			0
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$	1.30638	−	0.0934345i	1.30638	−	0.0934345i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	−0.915415	−	0.588302i	−0.915415	−	0.588302i
$142$		0			0
$143$		0			0
$144$	−0.708089	+	0.101808i	−0.708089	+	0.101808i
$145$		0			0
$146$		0			0
$147$	−0.837534	−	0.312384i	−0.837534	−	0.312384i
$148$		0			0
$149$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$149$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.909632	+	0.415415i	$0.863636\pi$
$150$		0			0
$151$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$151$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$157$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.512546	−	0.234072i	0.512546	−	0.234072i
$162$	0.851085	−	0.851085i	0.851085	−	0.851085i
$163$	−0.0203052	+	0.283904i	−0.0203052	+	0.283904i	0.977147	+	0.212565i	$0.0681818\pi$
$163$	−0.0203052	+	0.283904i	−0.0203052	+	0.283904i	−0.997452	+	0.0713392i	$0.977273\pi$
$164$	1.03748	−	1.61435i	1.03748	−	1.61435i
$165$		0			0
$166$	−0.983568	−	0.449181i	−0.983568	−	0.449181i
$167$	0.227858	+	0.170572i	0.227858	+	0.170572i	0.707107	−	0.707107i	$-0.250000\pi$
$167$	0.227858	+	0.170572i	0.227858	+	0.170572i	−0.479249	+	0.877679i	$0.659091\pi$
$168$	−0.647712	+	0.353677i	−0.647712	+	0.353677i
$169$	0.540641	+	0.841254i	0.540641	+	0.841254i
$170$		0			0
$171$		0			0
$172$	1.97460	−	0.141226i	1.97460	−	0.141226i
$173$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$173$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$174$	−0.306569	−	1.04408i	−0.306569	−	1.04408i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−1.21002	−	0.905808i	−1.21002	−	0.905808i
$179$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$179$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$180$		0			0
$181$	−0.584585	+	0.909632i	−0.584585	+	0.909632i	0.415415	+	0.909632i	$0.363636\pi$
$181$	−0.584585	+	0.909632i	−0.584585	+	0.909632i	−1.00000			$1.00000\pi$
$182$		0			0
$183$	−1.83337	+	1.83337i	−1.83337	+	1.83337i
$184$	−0.281733	+	0.959493i	−0.281733	+	0.959493i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.665114	−	0.497898i	0.665114	−	0.497898i
$189$	0.0872586	−	0.191070i	0.0872586	−	0.191070i
$190$		0			0
$191$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$191$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$192$	0.278401	−	1.27979i	0.278401	−	1.27979i
$193$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$193$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$194$		0			0
$195$		0			0
$196$	0.446947	−	0.515804i	0.446947	−	0.515804i
$197$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$197$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$198$		0			0
$199$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$199$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$200$		0			0
$201$	1.40176	−	0.201543i	1.40176	−	0.201543i
$202$	0.587976	+	1.57642i	0.587976	+	1.57642i
$203$	−0.280548	−	0.374768i	−0.280548	−	0.374768i
$204$		0			0
$205$		0			0
$206$		−	1.81926i		−	1.81926i
$207$	0.249996	+	0.670266i	0.249996	+	0.670266i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$211$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$212$		0			0
$213$		0			0
$214$	1.74557	+	0.512546i	1.74557	+	0.512546i
$215$		0			0
$216$	0.154861	+	0.339098i	0.154861	+	0.339098i
$217$		0			0
$218$	0.107829	+	1.50765i	0.107829	+	1.50765i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	0.136408	+	0.249813i	0.136408	+	0.249813i	0.936950	−	0.349464i	$-0.113636\pi$
$223$	0.136408	+	0.249813i	0.136408	+	0.249813i	−0.800541	+	0.599278i	$0.795455\pi$
$224$	−0.0801894	−	0.557730i	−0.0801894	−	0.557730i
$225$		0			0
$226$		0			0
$227$	−0.386712	−	1.77769i	−0.386712	−	1.77769i	−0.599278	−	0.800541i	$-0.704545\pi$
$227$	−0.386712	−	1.77769i	−0.386712	−	1.77769i	0.212565	−	0.977147i	$-0.431818\pi$
$228$		0			0
$229$	1.51150			1.51150			0.755750	−	0.654861i	$-0.227273\pi$
$229$	1.51150			1.51150			0.755750	+	0.654861i	$0.227273\pi$
$230$		0			0
$231$		0			0
$232$	0.828713	+	0.0592707i	0.828713	+	0.0592707i
$233$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$233$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$239$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$240$		0			0
$241$	−0.425839	−	0.368991i	−0.425839	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$241$	−0.425839	−	0.368991i	−0.425839	−	0.368991i	−0.841254	+	0.540641i	$0.818182\pi$
$242$	−0.0713392	−	0.997452i	−0.0713392	−	0.997452i
$243$	1.05639	+	0.576832i	1.05639	+	0.576832i
$244$	−0.822373	−	1.80075i	−0.822373	−	1.80075i
$245$		0			0
$246$	2.41153	+	0.708089i	2.41153	+	0.708089i
$247$		0			0
$248$		0			0
$249$	0.201543	−	1.40176i	0.201543	−	1.40176i
$250$		0			0
$251$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$251$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$252$	−0.285025	−	0.285025i	−0.285025	−	0.285025i
$253$		0			0
$254$			1.68251i			1.68251i
$255$		0			0
$256$	0.841254	+	0.540641i	0.841254	+	0.540641i
$257$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$257$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$258$	0.906084	+	2.42931i	0.906084	+	2.42931i
$259$		0			0
$260$		0			0
$261$	0.500000	−	0.321330i	0.500000	−	0.321330i
$262$		0			0
$263$	−0.948742	+	1.73749i	−0.948742	+	1.73749i	−0.349464	+	0.936950i	$0.613636\pi$
$263$	−0.948742	+	1.73749i	−0.948742	+	1.73749i	−0.599278	+	0.800541i	$0.704545\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.691814	−	1.85483i	0.691814	−	1.85483i
$268$	−0.229843	+	1.05657i	−0.229843	+	1.05657i
$269$	−0.474017	+	1.61435i	−0.474017	+	1.61435i	0.281733	+	0.959493i	$0.409091\pi$
$269$	−0.474017	+	1.61435i	−0.474017	+	1.61435i	−0.755750	+	0.654861i	$0.772727\pi$
$270$		0			0
$271$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$271$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.30972			−1.30972
$277$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$277$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.80075	+	0.822373i	1.80075	+	0.822373i	0.959493	+	0.281733i	$0.0909091\pi$
$281$	1.80075	+	0.822373i	1.80075	+	0.822373i	0.841254	+	0.540641i	$0.181818\pi$
$282$	0.871114	+	0.652108i	0.871114	+	0.652108i
$283$	1.32661	−	0.724384i	1.32661	−	0.724384i	0.349464	−	0.936950i	$-0.386364\pi$
$283$	1.32661	−	0.724384i	1.32661	−	0.724384i	0.977147	+	0.212565i	$0.0681818\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.07853	−	0.0771377i	1.07853	−	0.0771377i
$288$	0.713548	−	0.0510339i	0.713548	−	0.0510339i
$289$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$293$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$294$	0.813115	+	0.371337i	0.813115	+	0.371337i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	1.28641	−	1.28641i	1.28641	−	1.28641i
$299$		0			0
$300$		0			0
$301$	0.730471	+	0.843008i	0.730471	+	0.843008i
$302$		0			0
$303$	−1.76409	+	1.32058i	−1.76409	+	1.32058i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−0.407910	+	1.87513i	−0.407910	+	1.87513i	0.0713392	+	0.997452i	$0.477273\pi$
$307$	−0.407910	+	1.87513i	−0.407910	+	1.87513i	−0.479249	+	0.877679i	$0.659091\pi$
$308$		0			0
$309$	2.28621	−	0.671292i	2.28621	−	0.671292i
$310$		0			0
$311$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$311$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$312$		0			0
$313$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$313$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.349464	−	0.936950i	$-0.613636\pi$
$317$		0			0		0.349464	+	0.936950i	$0.386364\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$			2.38273i			2.38273i
$322$	−0.527938	+	0.196911i	−0.527938	+	0.196911i
$323$		0			0
$324$	−0.909632	+	0.788201i	−0.909632	+	0.788201i
$325$		0			0
$326$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$327$	−1.85483	+	0.691814i	−1.85483	+	0.691814i
$328$	−1.15001	+	1.53623i	−1.15001	+	1.53623i
$329$	0.449181	+	0.131891i	0.449181	+	0.131891i
$330$		0			0
$331$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$331$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$332$	0.949018	+	0.518203i	0.949018	+	0.518203i
$333$		0			0
$334$	−0.215109	−	0.186393i	−0.215109	−	0.186393i
$335$		0			0
$336$	0.671292	−	0.306569i	0.671292	−	0.306569i
$337$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$337$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$338$	−0.479249	−	0.877679i	−0.479249	−	0.877679i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.945619	+	0.0676320i	0.945619	+	0.0676320i
$344$	−1.97964			−1.97964
$345$		0			0
$346$		0			0
$347$	1.67822	+	0.120029i	1.67822	+	0.120029i	0.877679	−	0.479249i	$-0.159091\pi$
$347$	1.67822	+	0.120029i	1.67822	+	0.120029i	0.800541	+	0.599278i	$0.204545\pi$
$348$	0.231304	+	1.06329i	0.231304	+	1.06329i
$349$	−1.89945	−	0.273100i	−1.89945	−	0.273100i	−0.909632	−	0.415415i	$-0.863636\pi$
$349$	−1.89945	−	0.273100i	−1.89945	−	0.273100i	−0.989821	+	0.142315i	$0.954545\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$353$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$354$		0			0
$355$		0			0
$356$	1.14231	+	0.989821i	1.14231	+	0.989821i
$357$		0			0
$358$		0			0
$359$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$359$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$360$		0			0
$361$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$362$	0.647988	−	0.865611i	0.647988	−	0.865611i
$363$	1.22714	−	0.457701i	1.22714	−	0.457701i
$364$		0			0
$365$		0			0
$366$	1.95949	−	1.69791i	1.95949	−	1.69791i
$367$	0.764582	+	0.764582i	0.764582	+	0.764582i	0.977147	−	0.212565i	$-0.0681818\pi$
$367$	0.764582	+	0.764582i	0.764582	+	0.764582i	−0.212565	+	0.977147i	$0.568182\pi$
$368$	0.349464	−	0.936950i	0.349464	−	0.936950i
$369$			1.37279i			1.37279i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.349464	−	0.936950i	$-0.613636\pi$
$373$		0			0		0.349464	+	0.936950i	$0.386364\pi$
$374$		0			0
$375$		0			0
$376$	−0.698939	+	0.449181i	−0.698939	+	0.449181i
$377$		0			0
$378$	−0.100667	+	0.184358i	−0.100667	+	0.184358i
$379$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$379$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$380$		0			0
$381$	−2.11435	+	0.620830i	−2.11435	+	0.620830i
$382$		0			0
$383$	−0.119773	+	0.550588i	−0.119773	+	0.550588i	0.877679	+	0.479249i	$0.159091\pi$
$383$	−0.119773	+	0.550588i	−0.119773	+	0.550588i	−0.997452	+	0.0713392i	$0.977273\pi$
$384$	−0.368991	+	1.25667i	−0.368991	+	1.25667i
$385$		0			0
$386$		0			0
$387$	−1.13371	+	0.848684i	−1.13371	+	0.848684i
$388$		0			0
$389$	0.989821	+	1.14231i	0.989821	+	1.14231i	0.989821	+	0.142315i	$0.0454545\pi$
$389$	0.989821	+	1.14231i	0.989821	+	1.14231i			1.00000i	$0.500000\pi$
$390$		0			0
$391$		0			0
$392$	−0.482605	+	0.482605i	−0.482605	+	0.482605i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$397$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.304632	+	1.03748i	0.304632	+	1.03748i	0.959493	+	0.281733i	$0.0909091\pi$
$401$	0.304632	+	1.03748i	0.304632	+	1.03748i	−0.654861	+	0.755750i	$0.727273\pi$
$402$	−1.41257	+	0.101029i	−1.41257	+	0.101029i
$403$		0			0
$404$	−0.474017	−	1.61435i	−0.474017	−	1.61435i
$405$		0			0
$406$	0.253098	+	0.393828i	0.253098	+	0.393828i
$407$		0			0
$408$		0			0
$409$	0.755750	+	0.345139i	0.755750	+	0.345139i	0.755750	−	0.654861i	$-0.227273\pi$
$409$	0.755750	+	0.345139i	0.755750	+	0.345139i			1.00000i	$0.5\pi$
$410$		0			0
$411$		0			0
$412$	−0.129785	+	1.81463i	−0.129785	+	1.81463i
$413$		0			0
$414$	−0.201543	−	0.686393i	−0.201543	−	0.686393i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$419$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$420$		0			0
$421$	−0.158746	+	0.540641i	−0.158746	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$421$	−0.158746	+	0.540641i	−0.158746	+	0.540641i	−1.00000			$\pi$
$422$		0			0
$423$	−0.207704	+	0.556877i	−0.207704	+	0.556877i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.534583	−	0.979016i	0.534583	−	0.979016i
$428$	−1.70456	−	0.635768i	−1.70456	−	0.635768i
$429$		0			0
$430$		0			0
$431$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$431$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$432$	−0.130275	−	0.349281i	−0.130275	−	0.349281i
$433$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$433$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$434$		0			0
$435$		0			0
$436$		−	1.51150i		−	1.51150i
$437$		0			0
$438$		0			0
$439$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$439$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$440$		0			0
$441$	−0.0694846	+	0.483276i	−0.0694846	+	0.483276i
$442$		0			0
$443$	−0.170572	+	0.227858i	−0.170572	+	0.227858i	−0.877679	−	0.479249i	$-0.840909\pi$
$443$	−0.170572	+	0.227858i	−0.170572	+	0.227858i	0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$		0			0
$446$	−0.118239	−	0.258908i	−0.118239	−	0.258908i
$447$	2.09127	+	1.14192i	2.09127	+	1.14192i
$448$	0.0401971	+	0.562029i	0.0401971	+	0.562029i
$449$	0.989821	+	0.857685i	0.989821	+	0.857685i	0.989821	−	0.142315i	$-0.0454545\pi$
$449$	0.989821	+	0.857685i	0.989821	+	0.857685i			1.00000i	$0.5\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.258908	+	1.80075i	0.258908	+	1.80075i
$455$		0			0
$456$		0			0
$457$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$457$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$458$	−1.50765	−	0.107829i	−1.50765	−	0.107829i
$459$		0			0
$460$		0			0
$461$	1.30972			1.30972			0.654861	−	0.755750i	$-0.272727\pi$
$461$	1.30972			1.30972			0.654861	+	0.755750i	$0.272727\pi$
$462$		0			0
$463$	−0.407910	−	1.87513i	−0.407910	−	1.87513i	−0.479249	−	0.877679i	$-0.659091\pi$
$463$	−0.407910	−	1.87513i	−0.407910	−	1.87513i	0.0713392	−	0.997452i	$-0.477273\pi$
$464$	−0.822373	−	0.118239i	−0.822373	−	0.118239i
$465$		0			0
$466$		0			0
$467$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$467$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$468$		0			0
$469$	−0.554206	+	0.253098i	−0.554206	+	0.253098i
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$479$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$480$		0			0
$481$		0			0
$482$	0.398430	+	0.398430i	0.398430	+	0.398430i
$483$	−0.442256	−	0.590785i	−0.442256	−	0.590785i
$484$			1.00000i			1.00000i
$485$		0			0
$486$	−1.01255	−	0.650724i	−1.01255	−	0.650724i
$487$	1.15001	+	1.53623i	1.15001	+	1.53623i	0.800541	+	0.599278i	$0.204545\pi$
$487$	1.15001	+	1.53623i	1.15001	+	1.53623i	0.349464	+	0.936950i	$0.386364\pi$
$488$	0.691814	+	1.85483i	0.691814	+	1.85483i
$489$	0.368991	−	0.0530529i	0.368991	−	0.0530529i
$490$		0			0
$491$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$491$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$492$	−2.35487	−	0.878321i	−2.35487	−	0.878321i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.301030	+	1.38381i	−0.301030	+	1.38381i
$499$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$499$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$500$		0			0
$501$	0.154861	−	0.339098i	0.154861	−	0.339098i
$502$		0			0
$503$	1.47696	−	0.321292i	1.47696	−	0.321292i	0.599278	−	0.800541i	$-0.295455\pi$
$503$	1.47696	−	0.321292i	1.47696	−	0.321292i	0.877679	+	0.479249i	$0.159091\pi$
$504$	0.263965	+	0.304632i	0.263965	+	0.304632i
$505$		0			0
$506$		0			0
$507$	0.926113	−	0.926113i	0.926113	−	0.926113i
$508$	0.120029	−	1.67822i	0.120029	−	1.67822i
$509$	−0.153882	+	0.239446i	−0.153882	+	0.239446i	−0.909632	−	0.415415i	$-0.863636\pi$
$509$	−0.153882	+	0.239446i	−0.153882	+	0.239446i	0.755750	+	0.654861i	$0.227273\pi$
$510$		0			0
$511$		0			0
$512$	−0.800541	−	0.599278i	−0.800541	−	0.599278i
$513$		0			0
$514$		0			0
$515$		0			0
$516$	−0.730471	−	2.48775i	−0.730471	−	2.48775i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.983568	−	1.53046i	−0.983568	−	1.53046i	−0.841254	−	0.540641i	$-0.818182\pi$
$521$	−0.983568	−	1.53046i	−0.983568	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$522$	−0.521650	+	0.284842i	−0.521650	+	0.284842i
$523$	−0.865611	−	0.647988i	−0.865611	−	0.647988i	0.0713392	−	0.997452i	$-0.477273\pi$
$523$	−0.865611	−	0.647988i	−0.865611	−	0.647988i	−0.936950	+	0.349464i	$0.886364\pi$
$524$		0			0
$525$		0			0
$526$	1.07028	−	1.66538i	1.07028	−	1.66538i
$527$		0			0
$528$		0			0
$529$	−0.989821	−	0.142315i	−0.989821	−	0.142315i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.822373	+	1.80075i	−0.822373	+	1.80075i
$535$		0			0
$536$	0.304632	−	1.03748i	0.304632	−	1.03748i
$537$		0			0
$538$	0.587976	−	1.57642i	0.587976	−	1.57642i
$539$		0			0
$540$		0			0
$541$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.142315	+	0.989821i	$0.545455\pi$
$541$	−1.10181	+	1.27155i	−1.10181	+	1.27155i	−0.959493	+	0.281733i	$0.909091\pi$
$542$		0			0
$543$	1.32689	+	0.494903i	1.32689	+	0.494903i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.290345	+	0.778446i	0.290345	+	0.778446i	0.997452	+	0.0713392i	$0.0227273\pi$
$547$	0.290345	+	0.778446i	0.290345	+	0.778446i	−0.707107	+	0.707107i	$0.750000\pi$
$548$		0			0
$549$	1.19136	+	0.765644i	1.19136	+	0.765644i
$550$		0			0
$551$		0			0
$552$	1.30638	+	0.0934345i	1.30638	+	0.0934345i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$557$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−1.73749	−	0.948742i	−1.73749	−	0.948742i
$563$	−0.0401971	−	0.562029i	−0.0401971	−	0.562029i	−0.977147	−	0.212565i	$-0.931818\pi$
$563$	−0.0401971	−	0.562029i	−0.0401971	−	0.562029i	0.936950	−	0.349464i	$-0.113636\pi$
$564$	−0.822373	−	0.712591i	−0.822373	−	0.712591i
$565$		0			0
$566$	−1.37491	+	0.627899i	−1.37491	+	0.627899i
$567$	−0.662697	−	0.144161i	−0.662697	−	0.144161i
$568$		0			0
$569$	0.153882	+	1.07028i	0.153882	+	1.07028i	0.909632	+	0.415415i	$0.136364\pi$
$569$	0.153882	+	1.07028i	0.153882	+	1.07028i	−0.755750	+	0.654861i	$0.772727\pi$
$570$		0			0
$571$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$571$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$572$		0			0
$573$		0			0
$574$	−1.08128			−1.08128
$575$		0			0
$576$	−0.715370			−0.715370
$577$		0			0		−0.997452	−	0.0713392i	$-0.977273\pi$
$577$		0			0		0.997452	+	0.0713392i	$0.0227273\pi$
$578$	0.212565	+	0.977147i	0.212565	+	0.977147i
$579$		0			0
$580$		0			0
$581$	0.0867074	+	0.603063i	0.0867074	+	0.603063i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.0203052	−	0.283904i	−0.0203052	−	0.283904i	−0.997452	−	0.0713392i	$-0.977273\pi$
$587$	−0.0203052	−	0.283904i	−0.0203052	−	0.283904i	0.977147	−	0.212565i	$-0.0681818\pi$
$588$	−0.784552	−	0.428398i	−0.784552	−	0.428398i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$593$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$594$		0			0
$595$		0			0
$596$	−1.37491	+	1.19136i	−1.37491	+	1.19136i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$601$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$602$	−0.668470	−	0.892971i	−0.668470	−	0.892971i
$603$	−0.270316	−	0.724746i	−0.270316	−	0.724746i
$604$		0			0
$605$		0			0
$606$	1.85380	−	1.19136i	1.85380	−	1.19136i
$607$	0.266684	+	0.0994679i	0.266684	+	0.0994679i	0.479249	−	0.877679i	$-0.340909\pi$
$607$	0.266684	+	0.0994679i	0.266684	+	0.0994679i	−0.212565	+	0.977147i	$0.568182\pi$
$608$		0			0
$609$	−0.401520	+	0.463379i	−0.401520	+	0.463379i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$613$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$614$	0.540641	−	1.84125i	0.540641	−	1.84125i
$615$		0			0
$616$		0			0
$617$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$617$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$618$	−2.32828	+	0.506486i	−2.32828	+	0.506486i
$619$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$619$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$620$		0			0
$621$	−0.313607	+	0.201543i	−0.313607	+	0.201543i
$622$		0			0
$623$	−0.0607579	+	0.849507i	−0.0607579	+	0.849507i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$631$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.983568	+	1.53046i	−0.983568	+	1.53046i	−0.142315	+	0.989821i	$0.545455\pi$
$641$	−0.983568	+	1.53046i	−0.983568	+	1.53046i	−0.841254	+	0.540641i	$0.818182\pi$
$642$	0.169982	−	2.37666i	0.169982	−	2.37666i
$643$	1.39982	−	1.39982i	1.39982	−	1.39982i	0.599278	−	0.800541i	$-0.295455\pi$
$643$	1.39982	−	1.39982i	1.39982	−	1.39982i	0.800541	−	0.599278i	$-0.204545\pi$
$644$	0.540641	−	0.158746i	0.540641	−	0.158746i
$645$		0			0
$646$		0			0
$647$	−1.64406	+	0.357643i	−1.64406	+	0.357643i	−0.936950	−	0.349464i	$-0.886364\pi$
$647$	−1.64406	+	0.357643i	−1.64406	+	0.357643i	−0.707107	+	0.707107i	$0.750000\pi$
$648$	0.963544	−	0.721300i	0.963544	−	0.721300i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.0605024	+	0.278125i	−0.0605024	+	0.278125i
$653$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$653$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$654$	1.89945	−	0.557730i	1.89945	−	0.557730i
$655$		0			0
$656$	1.25667	−	1.45027i	1.25667	−	1.45027i
$657$		0			0
$658$	−0.438627	−	0.163599i	−0.438627	−	0.163599i
$659$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$659$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$660$		0			0
$661$	1.80075	−	0.258908i	1.80075	−	0.258908i	0.841254	−	0.540641i	$-0.181818\pi$
$661$	1.80075	−	0.258908i	1.80075	−	0.258908i	0.959493	+	0.281733i	$0.0909091\pi$
$662$		0			0
$663$		0			0
$664$	−0.909632	−	0.584585i	−0.909632	−	0.584585i
$665$		0			0
$666$		0			0
$667$	0.0592707	+	0.828713i	0.0592707	+	0.828713i
$668$	0.201264	+	0.201264i	0.201264	+	0.201264i
$669$	0.281733	−	0.244123i	0.281733	−	0.244123i
$670$		0			0
$671$		0			0
$672$	−0.691452	+	0.257898i	−0.691452	+	0.257898i
$673$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$673$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$674$		0			0
$675$		0			0
$676$	0.415415	+	0.909632i	0.415415	+	0.909632i
$677$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$677$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.16741	+	0.989821i	−2.16741	+	0.989821i
$682$		0			0
$683$	−0.919672	−	1.68425i	−0.919672	−	1.68425i	−0.707107	−	0.707107i	$-0.750000\pi$
$683$	−0.919672	−	1.68425i	−0.919672	−	1.68425i	−0.212565	−	0.977147i	$-0.568182\pi$
$684$		0			0
$685$		0			0
$686$	−0.938384	−	0.134919i	−0.938384	−	0.134919i
$687$	−0.420803	−	1.93440i	−0.420803	−	1.93440i
$688$	1.97460	+	0.141226i	1.97460	+	0.141226i
$689$		0			0
$690$		0			0
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	−1.66538	−	0.239446i	−1.66538	−	0.239446i
$695$		0			0
$696$	−0.154861	−	1.07708i	−0.154861	−	1.07708i
$697$		0			0
$698$	1.87513	+	0.407910i	1.87513	+	0.407910i
$699$		0			0
$700$		0			0
$701$	1.49611	+	1.29639i	1.49611	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$701$	1.49611	+	1.29639i	1.49611	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.568136	−	0.758940i	0.568136	−	0.758940i
$708$		0			0
$709$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$709$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$710$		0			0
$711$		0			0
$712$	−1.06879	−	1.06879i	−1.06879	−	1.06879i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$719$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$720$		0			0
$721$	−0.862362	+	0.554206i	−0.862362	+	0.554206i
$722$	0.936950	+	0.349464i	0.936950	+	0.349464i
$723$	−0.353677	+	0.647712i	−0.353677	+	0.647712i
$724$	−0.708089	+	0.817178i	−0.708089	+	0.817178i
$725$		0			0
$726$	−1.25667	+	0.368991i	−1.25667	+	0.368991i
$727$	0.635768	−	1.70456i	0.635768	−	1.70456i	−0.0713392	−	0.997452i	$-0.522727\pi$
$727$	0.635768	−	1.70456i	0.635768	−	1.70456i	0.707107	−	0.707107i	$-0.250000\pi$
$728$		0			0
$729$	0.105026	−	0.357685i	0.105026	−	0.357685i
$730$		0			0
$731$		0			0
$732$	−2.07563	+	1.55380i	−2.07563	+	1.55380i
$733$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$733$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$734$	−0.708089	−	0.817178i	−0.708089	−	0.817178i
$735$		0			0
$736$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$737$		0			0
$738$	0.0979334	−	1.36929i	0.0979334	−	1.36929i
$739$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$739$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.59673	−	0.871880i	1.59673	−	0.871880i	0.599278	−	0.800541i	$-0.295455\pi$
$743$	1.59673	−	0.871880i	1.59673	−	0.871880i	0.997452	−	0.0713392i	$-0.0227273\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.771546	+	0.0551821i	−0.771546	+	0.0551821i
$748$		0			0
$749$	−0.288802	−	0.983568i	−0.288802	−	0.983568i
$750$		0			0
$751$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$751$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$752$	0.729202	−	0.398174i	0.729202	−	0.398174i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.113563	−	0.176707i	0.113563	−	0.176707i
$757$		0			0		0.0713392	−	0.997452i	$-0.477273\pi$
$757$		0			0		−0.0713392	+	0.997452i	$0.522727\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$761$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$762$	2.15326	−	0.468412i	2.15326	−	0.468412i
$763$	0.681803	−	0.510391i	0.681803	−	0.510391i
$764$		0			0
$765$		0			0
$766$	0.158746	−	0.540641i	0.158746	−	0.540641i
$767$		0			0
$768$	0.457701	−	1.22714i	0.457701	−	1.22714i
$769$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.909632	−	0.415415i	$-0.136364\pi$
$769$	1.89945	−	0.557730i	1.89945	−	0.557730i	0.989821	−	0.142315i	$-0.0454545\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$773$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$774$	1.19136	−	0.765644i	1.19136	−	0.765644i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.905808	−	1.21002i	−0.905808	−	1.21002i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.219006	+	0.219006i	0.219006	+	0.219006i
$784$	0.515804	−	0.446947i	0.515804	−	0.446947i
$785$		0			0
$786$		0			0
$787$	−1.41620	+	0.528215i	−1.41620	+	0.528215i	−0.936950	−	0.349464i	$-0.886364\pi$
$787$	−1.41620	+	0.528215i	−1.41620	+	0.528215i	−0.479249	+	0.877679i	$0.659091\pi$
$788$		0			0
$789$	2.48775	+	0.730471i	2.48775	+	0.730471i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$797$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−1.07028	−	0.153882i	−1.07028	−	0.153882i
$802$	−0.229843	−	1.05657i	−0.229843	−	1.05657i
$803$		0			0
$804$	1.41618			1.41618
$805$		0			0
$806$		0			0
$807$	2.19800	+	0.157204i	2.19800	+	0.157204i
$808$	0.357643	+	1.64406i	0.357643	+	1.64406i
$809$	−1.29639	−	0.186393i	−1.29639	−	0.186393i	−0.540641	−	0.841254i	$-0.681818\pi$
$809$	−1.29639	−	0.186393i	−1.29639	−	0.186393i	−0.755750	+	0.654861i	$0.772727\pi$
$810$		0			0
$811$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$811$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$812$	−0.224357	−	0.410880i	−0.224357	−	0.410880i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.729202	−	0.398174i	−0.729202	−	0.398174i
$819$		0			0
$820$		0			0
$821$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.142315	−	0.989821i	$-0.545455\pi$
$821$	−0.797176	−	0.234072i	−0.797176	−	0.234072i	−0.654861	+	0.755750i	$0.727273\pi$
$822$		0			0
$823$	−1.79799	+	0.670617i	−1.79799	+	0.670617i	−0.800541	+	0.599278i	$0.795455\pi$
$823$	−1.79799	+	0.670617i	−1.79799	+	0.670617i	−0.997452	+	0.0713392i	$0.977273\pi$
$824$	0.258908	−	1.80075i	0.258908	−	1.80075i
$825$		0			0
$826$		0			0
$827$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$827$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$828$	0.152063	+	0.699022i	0.152063	+	0.699022i
$829$		−	1.91899i		−	1.91899i	−0.281733	−	0.959493i	$-0.590909\pi$
$829$		−	1.91899i		−	1.91899i	0.281733	−	0.959493i	$-0.409091\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$839$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$840$		0			0
$841$	−0.297176	+	0.0872586i	−0.297176	+	0.0872586i
$842$	0.196911	−	0.527938i	0.196911	−	0.527938i
$843$	0.551135	−	2.53353i	0.551135	−	2.53353i
$844$		0			0
$845$		0			0
$846$	0.246902	−	0.540641i	0.246902	−	0.540641i
$847$	−0.451077	+	0.337672i	−0.451077	+	0.337672i
$848$		0			0
$849$	−1.29639	−	1.49611i	−1.29639	−	1.49611i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.0713392	−	0.997452i	$-0.477273\pi$
$853$		0			0		−0.0713392	+	0.997452i	$0.522727\pi$
$854$	−0.603063	+	0.938384i	−0.603063	+	0.938384i
$855$		0			0
$856$	1.65486	+	0.755750i	1.65486	+	0.755750i
$857$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$857$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$858$		0			0
$859$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$859$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$860$		0			0
$861$	−0.398983	−	1.35881i	−0.398983	−	1.35881i
$862$		0			0
$863$	−1.91410	+	0.136899i	−1.91410	+	0.136899i	−0.977147	−	0.212565i	$-0.931818\pi$
$863$	−1.91410	+	0.136899i	−1.91410	+	0.136899i	−0.936950	+	0.349464i	$0.886364\pi$
$864$	0.105026	+	0.357685i	0.105026	+	0.357685i
$865$		0			0
$866$		0			0
$867$	−1.14952	+	0.627683i	−1.14952	+	0.627683i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	−0.107829	+	1.50765i	−0.107829	+	1.50765i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$877$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.304632	−	1.03748i	0.304632	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$881$	0.304632	−	1.03748i	0.304632	−	1.03748i	0.959493	−	0.281733i	$-0.0909091\pi$
$882$	0.103784	−	0.477087i	0.103784	−	0.477087i
$883$	−0.457701	+	1.22714i	−0.457701	+	1.22714i	0.479249	+	0.877679i	$0.340909\pi$
$883$	−0.457701	+	1.22714i	−0.457701	+	1.22714i	−0.936950	+	0.349464i	$0.886364\pi$
$884$		0			0
$885$		0			0
$886$	0.186393	−	0.215109i	0.186393	−	0.215109i
$887$	−0.627683	+	1.14952i	−0.627683	+	1.14952i	0.349464	+	0.936950i	$0.386364\pi$
$887$	−0.627683	+	1.14952i	−0.627683	+	1.14952i	−0.977147	+	0.212565i	$0.931818\pi$
$888$		0			0
$889$	0.797537	−	0.512546i	0.797537	−	0.512546i
$890$		0			0
$891$		0			0
$892$	0.0994679	+	0.266684i	0.0994679	+	0.266684i
$893$		0			0
$894$	−2.00448	−	1.28820i	−2.00448	−	1.28820i
$895$		0			0
$896$		−	0.563465i		−	0.563465i
$897$		0			0
$898$	−0.926113	−	0.926113i	−0.926113	−	0.926113i
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	0.875510	−	1.16954i	0.875510	−	1.16954i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1.32661	−	0.724384i	−1.32661	−	0.724384i	−0.349464	−	0.936950i	$-0.613636\pi$
$907$	−1.32661	−	0.724384i	−1.32661	−	0.724384i	−0.977147	+	0.212565i	$0.931818\pi$
$908$	−0.129785	−	1.81463i	−0.129785	−	1.81463i
$909$	0.909632	+	0.788201i	0.909632	+	0.788201i
$910$		0			0
$911$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$911$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	1.49611	+	0.215109i	1.49611	+	0.215109i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	2.51334			2.51334
$922$	−1.30638	−	0.0934345i	−1.30638	−	0.0934345i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.273100	+	1.89945i	0.273100	+	1.89945i
$927$	−0.623717	−	1.14225i	−0.623717	−	1.14225i
$928$	0.811843	+	0.176606i	0.811843	+	0.176606i
$929$	0.755750	−	0.345139i	0.755750	−	0.345139i		−	1.00000i	$-0.5\pi$
$929$	0.755750	−	0.345139i	0.755750	−	0.345139i	0.755750	+	0.654861i	$0.227273\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$937$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$938$	0.570850	−	0.212916i	0.570850	−	0.212916i
$939$		0			0
$940$		0			0
$941$	−1.49611	+	1.29639i	−1.49611	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$941$	−1.49611	+	1.29639i	−1.49611	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$942$		0			0
$943$	−1.68425	−	0.919672i	−1.68425	−	0.919672i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.784887	−	1.04849i	−0.784887	−	1.04849i	−0.997452	−	0.0713392i	$-0.977273\pi$
$947$	−0.784887	−	1.04849i	−0.784887	−	1.04849i	0.212565	−	0.977147i	$-0.431818\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$953$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.415415	−	0.909632i	0.415415	−	0.909632i
$962$		0			0
$963$	1.27171	−	0.276643i	1.27171	−	0.276643i
$964$	−0.368991	−	0.425839i	−0.368991	−	0.425839i
$965$		0			0
$966$	0.398983	+	0.620830i	0.398983	+	0.620830i
$967$	−0.926113	+	0.926113i	−0.926113	+	0.926113i	−0.997452	−	0.0713392i	$-0.977273\pi$
$967$	−0.926113	+	0.926113i	−0.926113	+	0.926113i	0.0713392	+	0.997452i	$0.477273\pi$
$968$	0.0713392	−	0.997452i	0.0713392	−	0.997452i
$969$		0			0
$970$		0			0
$971$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$971$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$972$	0.963544	+	0.721300i	0.963544	+	0.721300i
$973$		0			0
$974$	−1.03748	−	1.61435i	−1.03748	−	1.61435i
$975$		0			0
$976$	−0.557730	−	1.89945i	−0.557730	−	1.89945i
$977$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$977$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$978$	−0.371836	+	0.0265942i	−0.371836	+	0.0265942i
$979$		0			0
$980$		0			0
$981$	0.584585	+	0.909632i	0.584585	+	0.909632i
$982$		0			0
$983$	1.21002	+	0.905808i	1.21002	+	0.905808i	0.997452	−	0.0713392i	$-0.0227273\pi$
$983$	1.21002	+	0.905808i	1.21002	+	0.905808i	0.212565	+	0.977147i	$0.431818\pi$
$984$	2.28621	+	1.04408i	2.28621	+	1.04408i
$985$		0			0
$986$		0			0
$987$	0.0437408	−	0.611576i	0.0437408	−	0.611576i
$988$		0			0
$989$	−0.281733	−	1.95949i	−0.281733	−	1.95949i
$990$		0			0
$991$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$991$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.398983	−	1.35881i	0.398983	−	1.35881i
$997$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$997$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2300.1.bh.a.907.1	yes	40
4.3	odd	2	inner	2300.1.bh.a.907.2	yes	40
5.2	odd	4	inner	2300.1.bh.a.1643.2	yes	40
5.3	odd	4	inner	2300.1.bh.a.1643.1	yes	40
5.4	even	2	inner	2300.1.bh.a.907.2	yes	40
20.3	even	4	inner	2300.1.bh.a.1643.2	yes	40
20.7	even	4	inner	2300.1.bh.a.1643.1	yes	40
20.19	odd	2	CM	2300.1.bh.a.907.1	yes	40
23.7	odd	22	inner	2300.1.bh.a.7.2	yes	40
92.7	even	22	inner	2300.1.bh.a.7.1	✓	40
115.7	even	44	inner	2300.1.bh.a.743.1	yes	40
115.53	even	44	inner	2300.1.bh.a.743.2	yes	40
115.99	odd	22	inner	2300.1.bh.a.7.1	✓	40
460.7	odd	44	inner	2300.1.bh.a.743.2	yes	40
460.99	even	22	inner	2300.1.bh.a.7.2	yes	40
460.283	odd	44	inner	2300.1.bh.a.743.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2300.1.bh.a.7.1	✓	40	92.7	even	22	inner
2300.1.bh.a.7.1	✓	40	115.99	odd	22	inner
2300.1.bh.a.7.2	yes	40	23.7	odd	22	inner
2300.1.bh.a.7.2	yes	40	460.99	even	22	inner
2300.1.bh.a.743.1	yes	40	115.7	even	44	inner
2300.1.bh.a.743.1	yes	40	460.283	odd	44	inner
2300.1.bh.a.743.2	yes	40	115.53	even	44	inner
2300.1.bh.a.743.2	yes	40	460.7	odd	44	inner
2300.1.bh.a.907.1	yes	40	1.1	even	1	trivial
2300.1.bh.a.907.1	yes	40	20.19	odd	2	CM
2300.1.bh.a.907.2	yes	40	4.3	odd	2	inner
2300.1.bh.a.907.2	yes	40	5.4	even	2	inner
2300.1.bh.a.1643.1	yes	40	5.3	odd	4	inner
2300.1.bh.a.1643.1	yes	40	20.7	even	4	inner
2300.1.bh.a.1643.2	yes	40	5.2	odd	4	inner
2300.1.bh.a.1643.2	yes	40	20.3	even	4	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:	\( N \)	\(=\)	\( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2300.bh (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.278401 - 1.27979i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.186393 + 1.29639i) q^{6} +(0.270040 + 0.494541i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.650724 + 0.297176i) q^{9} +O(q^{10})\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(-0.278401 - 1.27979i) q^{3} +(0.989821 + 0.142315i) q^{4} +(0.186393 + 1.29639i) q^{6} +(0.270040 + 0.494541i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.650724 + 0.297176i) q^{9} +(-0.0934345 - 1.30638i) q^{12} +(-0.234072 - 0.512546i) q^{14} +(0.959493 + 0.281733i) q^{16} +(0.670266 - 0.249996i) q^{18} +(0.557730 - 0.483276i) q^{21} +(0.0713392 - 0.997452i) q^{23} +1.30972i q^{24} +(-0.223402 - 0.298430i) q^{27} +(0.196911 + 0.527938i) q^{28} +(-0.822373 + 0.118239i) q^{29} +(-0.936950 - 0.349464i) q^{32} +(-0.686393 + 0.201543i) q^{36} +(0.797176 - 1.74557i) q^{41} +(-0.590785 + 0.442256i) q^{42} +(1.93440 - 0.420803i) q^{43} +(-0.142315 + 0.989821i) q^{46} +(0.587486 - 0.587486i) q^{47} +(0.0934345 - 1.30638i) q^{48} +(0.368991 - 0.574161i) q^{49} +(0.201543 + 0.313607i) q^{54} +(-0.158746 - 0.540641i) q^{56} +(0.828713 - 0.0592707i) q^{58} +(-1.07028 - 1.66538i) q^{61} +(-0.322687 - 0.241561i) q^{63} +(0.909632 + 0.415415i) q^{64} +(-0.0771377 + 1.07853i) q^{67} +(-1.29639 + 0.186393i) q^{69} +(0.699022 - 0.152063i) q^{72} +(-0.788201 + 0.909632i) q^{81} +(-0.919672 + 1.68425i) q^{82} +(1.01311 + 0.377869i) q^{83} +(0.620830 - 0.398983i) q^{84} +(-1.95949 + 0.281733i) q^{86} +(0.380272 + 1.01955i) q^{87} +(1.27155 + 0.817178i) q^{89} +(0.212565 - 0.977147i) q^{92} +(-0.627899 + 0.544078i) q^{94} +(-0.186393 + 1.29639i) q^{96} +(-0.409011 + 0.546375i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{6}+O(q^{10}) \) 40 * q - 8 * q^6	\( 40 q - 8 q^{6} + 4 q^{16} - 12 q^{36} + 8 q^{41} - 4 q^{46} - 44 q^{56} + 20 q^{81} - 44 q^{86} + 8 q^{96}+O(q^{100}) \) 40 * q - 8 * q^6 + 4 * q^16 - 12 * q^36 + 8 * q^41 - 4 * q^46 - 44 * q^56 + 20 * q^81 - 44 * q^86 + 8 * q^96

Introduction

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