LMFDB - Embedded newform 2300.1.bh.a.543.1

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			543.1
Root			$0.877679 + 0.479249i$ of defining polynomial
Character	$\chi$	$=$	2300.543
Dual form			2300.1.bh.a.1707.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.877679 - 0.479249i) q^{2} +(1.91410 + 0.136899i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-1.61435 - 1.03748i) q^{6} +(-0.635768 - 1.70456i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(2.65520 + 0.381761i) q^{9} +O(q^{10})$	\(q+(-0.877679 - 0.479249i) q^{2} +(1.91410 + 0.136899i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-1.61435 - 1.03748i) q^{6} +(-0.635768 - 1.70456i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(2.65520 + 0.381761i) q^{9} +(0.919672 + 1.68425i) q^{12} +(-0.258908 + 1.80075i) q^{14} +(-0.415415 + 0.909632i) q^{16} +(-2.14746 - 1.60757i) q^{18} +(-0.983568 - 3.34973i) q^{21} +(-0.479249 + 0.877679i) q^{23} -1.91899i q^{24} +(3.15492 + 0.686311i) q^{27} +(1.09024 - 1.45640i) q^{28} +(0.153882 - 0.239446i) q^{29} +(0.800541 - 0.599278i) q^{32} +(1.11435 + 2.44009i) q^{36} +(0.118239 + 0.822373i) q^{41} +(-0.742096 + 3.41136i) q^{42} +(0.0771377 - 1.07853i) q^{43} +(0.841254 - 0.540641i) q^{46} +(-0.201264 - 0.201264i) q^{47} +(-0.919672 + 1.68425i) q^{48} +(-1.74557 + 1.51255i) q^{49} +(-2.44009 - 2.11435i) q^{54} +(-1.65486 + 0.755750i) q^{56} +(-0.249813 + 0.136408i) q^{58} +(-0.817178 - 0.708089i) q^{61} +(-1.03736 - 4.76866i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(0.724384 - 1.32661i) q^{67} +(-1.03748 + 1.61435i) q^{69} +(0.191368 - 2.67567i) q^{72} +(3.37102 + 0.989821i) q^{81} +(0.290345 - 0.778446i) q^{82} +(-1.21002 + 0.905808i) q^{83} +(2.28621 - 2.63843i) q^{84} +(-0.584585 + 0.909632i) q^{86} +(0.327326 - 0.437256i) q^{87} +(-0.368991 - 0.425839i) q^{89} +(-0.997452 + 0.0713392i) q^{92} +(0.0801894 + 0.273100i) q^{94} +(1.61435 - 1.03748i) q^{96} +(2.25694 - 0.490967i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2300\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.877679	−	0.479249i	−0.877679	−	0.479249i
$2$	−0.877679	−	0.479249i	−0.877679	−	0.479249i
$3$	1.91410	+	0.136899i	1.91410	+	0.136899i	0.977147	−	0.212565i	$-0.0681818\pi$
$3$	1.91410	+	0.136899i	1.91410	+	0.136899i	0.936950	+	0.349464i	$0.113636\pi$
$4$	0.540641	+	0.841254i	0.540641	+	0.841254i
$5$		0			0
$5$		0			0
$6$	−1.61435	−	1.03748i	−1.61435	−	1.03748i
$7$	−0.635768	−	1.70456i	−0.635768	−	1.70456i	−0.707107	−	0.707107i	$-0.750000\pi$
$7$	−0.635768	−	1.70456i	−0.635768	−	1.70456i	0.0713392	−	0.997452i	$-0.477273\pi$
$8$	−0.0713392	−	0.997452i	−0.0713392	−	0.997452i
$9$	2.65520	+	0.381761i	2.65520	+	0.381761i
$10$		0			0
$11$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$11$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$12$	0.919672	+	1.68425i	0.919672	+	1.68425i
$13$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$13$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$14$	−0.258908	+	1.80075i	−0.258908	+	1.80075i
$15$		0			0
$16$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$17$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$17$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$18$	−2.14746	−	1.60757i	−2.14746	−	1.60757i
$19$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$19$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$20$		0			0
$21$	−0.983568	−	3.34973i	−0.983568	−	3.34973i
$22$		0			0
$23$	−0.479249	+	0.877679i	−0.479249	+	0.877679i
$23$	−0.479249	+	0.877679i	−0.479249	+	0.877679i
$24$		−	1.91899i		−	1.91899i
$25$		0			0
$26$		0			0
$27$	3.15492	+	0.686311i	3.15492	+	0.686311i
$28$	1.09024	−	1.45640i	1.09024	−	1.45640i
$29$	0.153882	−	0.239446i	0.153882	−	0.239446i	−0.755750	−	0.654861i	$-0.772727\pi$
$29$	0.153882	−	0.239446i	0.153882	−	0.239446i	0.909632	+	0.415415i	$0.136364\pi$
$30$		0			0
$31$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$31$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$32$	0.800541	−	0.599278i	0.800541	−	0.599278i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	1.11435	+	2.44009i	1.11435	+	2.44009i
$37$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$37$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.118239	+	0.822373i	0.118239	+	0.822373i	0.959493	+	0.281733i	$0.0909091\pi$
$41$	0.118239	+	0.822373i	0.118239	+	0.822373i	−0.841254	+	0.540641i	$0.818182\pi$
$42$	−0.742096	+	3.41136i	−0.742096	+	3.41136i
$43$	0.0771377	−	1.07853i	0.0771377	−	1.07853i	−0.800541	−	0.599278i	$-0.795455\pi$
$43$	0.0771377	−	1.07853i	0.0771377	−	1.07853i	0.877679	−	0.479249i	$-0.159091\pi$
$44$		0			0
$45$		0			0
$46$	0.841254	−	0.540641i	0.841254	−	0.540641i
$47$	−0.201264	−	0.201264i	−0.201264	−	0.201264i	0.599278	−	0.800541i	$-0.295455\pi$
$47$	−0.201264	−	0.201264i	−0.201264	−	0.201264i	−0.800541	+	0.599278i	$0.795455\pi$
$48$	−0.919672	+	1.68425i	−0.919672	+	1.68425i
$49$	−1.74557	+	1.51255i	−1.74557	+	1.51255i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$53$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$54$	−2.44009	−	2.11435i	−2.44009	−	2.11435i
$55$		0			0
$56$	−1.65486	+	0.755750i	−1.65486	+	0.755750i
$57$		0			0
$58$	−0.249813	+	0.136408i	−0.249813	+	0.136408i
$59$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$59$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$60$		0			0
$61$	−0.817178	−	0.708089i	−0.817178	−	0.708089i	0.142315	−	0.989821i	$-0.454545\pi$
$61$	−0.817178	−	0.708089i	−0.817178	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$62$		0			0
$63$	−1.03736	−	4.76866i	−1.03736	−	4.76866i
$64$	−0.989821	+	0.142315i	−0.989821	+	0.142315i
$65$		0			0
$66$		0			0
$67$	0.724384	−	1.32661i	0.724384	−	1.32661i	−0.212565	−	0.977147i	$-0.568182\pi$
$67$	0.724384	−	1.32661i	0.724384	−	1.32661i	0.936950	−	0.349464i	$-0.113636\pi$
$68$		0			0
$69$	−1.03748	+	1.61435i	−1.03748	+	1.61435i
$70$		0			0
$71$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$71$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$72$	0.191368	−	2.67567i	0.191368	−	2.67567i
$73$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$73$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$79$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$80$		0			0
$81$	3.37102	+	0.989821i	3.37102	+	0.989821i
$82$	0.290345	−	0.778446i	0.290345	−	0.778446i
$83$	−1.21002	+	0.905808i	−1.21002	+	0.905808i	−0.997452	−	0.0713392i	$-0.977273\pi$
$83$	−1.21002	+	0.905808i	−1.21002	+	0.905808i	−0.212565	+	0.977147i	$0.568182\pi$
$84$	2.28621	−	2.63843i	2.28621	−	2.63843i
$85$		0			0
$86$	−0.584585	+	0.909632i	−0.584585	+	0.909632i
$87$	0.327326	−	0.437256i	0.327326	−	0.437256i
$88$		0			0
$89$	−0.368991	−	0.425839i	−0.368991	−	0.425839i	0.540641	−	0.841254i	$-0.318182\pi$
$89$	−0.368991	−	0.425839i	−0.368991	−	0.425839i	−0.909632	+	0.415415i	$0.863636\pi$
$90$		0			0
$91$		0			0
$92$	−0.997452	+	0.0713392i	−0.997452	+	0.0713392i
$93$		0			0
$94$	0.0801894	+	0.273100i	0.0801894	+	0.273100i
$95$		0			0
$96$	1.61435	−	1.03748i	1.61435	−	1.03748i
$97$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$97$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$98$	2.25694	−	0.490967i	2.25694	−	0.490967i
$99$		0			0
$100$		0			0
$101$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$101$	−0.186393	+	1.29639i	−0.186393	+	1.29639i	−0.841254	+	0.540641i	$0.818182\pi$
$102$		0			0
$103$	0.948742	+	1.73749i	0.948742	+	1.73749i	0.599278	+	0.800541i	$0.295455\pi$
$103$	0.948742	+	1.73749i	0.948742	+	1.73749i	0.349464	+	0.936950i	$0.386364\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.141226	+	1.97460i	0.141226	+	1.97460i	0.212565	+	0.977147i	$0.431818\pi$
$107$	0.141226	+	1.97460i	0.141226	+	1.97460i	−0.0713392	+	0.997452i	$0.522727\pi$
$108$	1.12832	+	3.02514i	1.12832	+	3.02514i
$109$	0.474017	+	0.304632i	0.474017	+	0.304632i	0.755750	−	0.654861i	$-0.227273\pi$
$109$	0.474017	+	0.304632i	0.474017	+	0.304632i	−0.281733	+	0.959493i	$0.590909\pi$
$110$		0			0
$111$		0			0
$112$	1.81463	+	0.129785i	1.81463	+	0.129785i
$113$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$113$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$114$		0			0
$115$		0			0
$116$	0.284630			0.284630
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$122$	0.377869	+	1.01311i	0.377869	+	1.01311i
$123$	0.113740	+	1.59029i	0.113740	+	1.59029i
$124$		0			0
$125$		0			0
$126$	−1.37491	+	4.68251i	−1.37491	+	4.68251i
$127$	−0.627683	−	1.14952i	−0.627683	−	1.14952i	−0.977147	−	0.212565i	$-0.931818\pi$
$127$	−0.627683	−	1.14952i	−0.627683	−	1.14952i	0.349464	−	0.936950i	$-0.386364\pi$
$128$	0.936950	+	0.349464i	0.936950	+	0.349464i
$129$	0.295298	−	2.05384i	0.295298	−	2.05384i
$130$		0			0
$131$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$131$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$132$		0			0
$133$		0			0
$134$	−1.27155	+	0.817178i	−1.27155	+	0.817178i
$135$		0			0
$136$		0			0
$137$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$137$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$138$	1.68425	−	0.919672i	1.68425	−	0.919672i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	−0.357685	−	0.412791i	−0.357685	−	0.412791i
$142$		0			0
$143$		0			0
$144$	−1.45027	+	2.25667i	−1.45027	+	2.25667i
$145$		0			0
$146$		0			0
$147$	−3.54826	+	2.65619i	−3.54826	+	2.65619i
$148$		0			0
$149$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.989821	+	0.142315i	$0.0454545\pi$
$149$	1.89945	+	0.557730i	1.89945	+	0.557730i	0.909632	+	0.415415i	$0.136364\pi$
$150$		0			0
$151$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$151$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$157$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.80075	+	0.258908i	1.80075	+	0.258908i
$162$	−2.48430	−	2.48430i	−2.48430	−	2.48430i
$163$	−0.806340	+	1.47670i	−0.806340	+	1.47670i	0.0713392	+	0.997452i	$0.477273\pi$
$163$	−0.806340	+	1.47670i	−0.806340	+	1.47670i	−0.877679	+	0.479249i	$0.840909\pi$
$164$	−0.627899	+	0.544078i	−0.627899	+	0.544078i
$165$		0			0
$166$	1.49611	−	0.215109i	1.49611	−	0.215109i
$167$	0.357643	+	1.64406i	0.357643	+	1.64406i	0.707107	+	0.707107i	$0.250000\pi$
$167$	0.357643	+	1.64406i	0.357643	+	1.64406i	−0.349464	+	0.936950i	$0.613636\pi$
$168$	−3.27102	+	1.22003i	−3.27102	+	1.22003i
$169$	0.755750	+	0.654861i	0.755750	+	0.654861i
$170$		0			0
$171$		0			0
$172$	0.949018	−	0.518203i	0.949018	−	0.518203i
$173$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$173$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$174$	−0.496841	+	0.226900i	−0.496841	+	0.226900i
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.119773	+	0.550588i	0.119773	+	0.550588i
$179$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$179$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$180$		0			0
$181$	−1.14231	+	0.989821i	−1.14231	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$181$	−1.14231	+	0.989821i	−1.14231	+	0.989821i	−1.00000			$\pi$
$182$		0			0
$183$	−1.46722	−	1.46722i	−1.46722	−	1.46722i
$184$	0.909632	+	0.415415i	0.909632	+	0.415415i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.0605024	−	0.278125i	0.0605024	−	0.278125i
$189$	−0.835939	−	5.81408i	−0.835939	−	5.81408i
$190$		0			0
$191$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$191$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$192$	−1.91410	+	0.136899i	−1.91410	+	0.136899i
$193$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$193$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$194$		0			0
$195$		0			0
$196$	−2.21616	−	0.650724i	−2.21616	−	0.650724i
$197$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$197$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$198$		0			0
$199$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$199$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$200$		0			0
$201$	1.56815	−	2.44009i	1.56815	−	2.44009i
$202$	0.784887	−	1.04849i	0.784887	−	1.04849i
$203$	−0.505983	−	0.110070i	−0.505983	−	0.110070i
$204$		0			0
$205$		0			0
$206$		−	1.97964i		−	1.97964i
$207$	−1.60757	+	2.14746i	−1.60757	+	2.14746i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$211$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$212$		0			0
$213$		0			0
$214$	0.822373	−	1.80075i	0.822373	−	1.80075i
$215$		0			0
$216$	0.459493	−	3.19584i	0.459493	−	3.19584i
$217$		0			0
$218$	−0.270040	−	0.494541i	−0.270040	−	0.494541i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−0.587976	−	1.57642i	−0.587976	−	1.57642i	−0.800541	−	0.599278i	$-0.795455\pi$
$223$	−0.587976	−	1.57642i	−0.587976	−	1.57642i	0.212565	−	0.977147i	$-0.431818\pi$
$224$	−1.53046	−	0.983568i	−1.53046	−	0.983568i
$225$		0			0
$226$		0			0
$227$	−1.97460	−	0.141226i	−1.97460	−	0.141226i	−0.977147	−	0.212565i	$-0.931818\pi$
$227$	−1.97460	−	0.141226i	−1.97460	−	0.141226i	−0.997452	+	0.0713392i	$0.977273\pi$
$228$		0			0
$229$	0.563465			0.563465			0.281733	−	0.959493i	$-0.409091\pi$
$229$	0.563465			0.563465			0.281733	+	0.959493i	$0.409091\pi$
$230$		0			0
$231$		0			0
$232$	−0.249813	−	0.136408i	−0.249813	−	0.136408i
$233$		0			0		−0.997452	−	0.0713392i	$-0.977273\pi$
$233$		0			0		0.997452	+	0.0713392i	$0.0227273\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$239$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$240$		0			0
$241$	0.512546	−	1.74557i	0.512546	−	1.74557i	−0.142315	−	0.989821i	$-0.545455\pi$
$241$	0.512546	−	1.74557i	0.512546	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$242$	0.479249	+	0.877679i	0.479249	+	0.877679i
$243$	3.29182	+	1.22779i	3.29182	+	1.22779i
$244$	0.153882	−	1.07028i	0.153882	−	1.07028i
$245$		0			0
$246$	0.662317	−	1.45027i	0.662317	−	1.45027i
$247$		0			0
$248$		0			0
$249$	−2.44009	+	1.56815i	−2.44009	+	1.56815i
$250$		0			0
$251$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$251$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$252$	3.45081	−	3.45081i	3.45081	−	3.45081i
$253$		0			0
$254$			1.30972i			1.30972i
$255$		0			0
$256$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$257$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$257$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$258$	−1.24348	+	1.66109i	−1.24348	+	1.66109i
$259$		0			0
$260$		0			0
$261$	0.500000	−	0.577031i	0.500000	−	0.577031i
$262$		0			0
$263$	−0.377869	+	1.01311i	−0.377869	+	1.01311i	0.599278	+	0.800541i	$0.295455\pi$
$263$	−0.377869	+	1.01311i	−0.377869	+	1.01311i	−0.977147	+	0.212565i	$0.931818\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.647988	−	0.865611i	−0.647988	−	0.865611i
$268$	1.50765	−	0.107829i	1.50765	−	0.107829i
$269$	−1.19136	−	0.544078i	−1.19136	−	0.544078i	−0.281733	−	0.959493i	$-0.590909\pi$
$269$	−1.19136	−	0.544078i	−1.19136	−	0.544078i	−0.909632	+	0.415415i	$0.863636\pi$
$270$		0			0
$271$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$271$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−1.91899			−1.91899
$277$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$277$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.07028	+	0.153882i	−1.07028	+	0.153882i	−0.654861	−	0.755750i	$-0.727273\pi$
$281$	−1.07028	+	0.153882i	−1.07028	+	0.153882i	−0.415415	+	0.909632i	$0.636364\pi$
$282$	0.116103	+	0.533718i	0.116103	+	0.533718i
$283$	−0.527938	+	0.196911i	−0.527938	+	0.196911i	−0.599278	−	0.800541i	$-0.704545\pi$
$283$	−0.527938	+	0.196911i	−0.527938	+	0.196911i	0.0713392	+	0.997452i	$0.477273\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.32661	−	0.724384i	1.32661	−	0.724384i
$288$	2.35438	−	1.28559i	2.35438	−	1.28559i
$289$	0.909632	−	0.415415i	0.909632	−	0.415415i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$293$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$294$	4.38721	−	0.630785i	4.38721	−	0.630785i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.39982	−	1.39982i	−1.39982	−	1.39982i
$299$		0			0
$300$		0			0
$301$	−1.88745	+	0.554206i	−1.88745	+	0.554206i
$302$		0			0
$303$	−0.534248	+	2.45590i	−0.534248	+	2.45590i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−0.828713	+	0.0592707i	−0.828713	+	0.0592707i	−0.479249	−	0.877679i	$-0.659091\pi$
$307$	−0.828713	+	0.0592707i	−0.828713	+	0.0592707i	−0.349464	+	0.936950i	$0.613636\pi$
$308$		0			0
$309$	1.57812	+	3.45561i	1.57812	+	3.45561i
$310$		0			0
$311$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$311$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$312$		0			0
$313$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$313$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$317$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$			3.79891i			3.79891i
$322$	−1.45640	−	1.09024i	−1.45640	−	1.09024i
$323$		0			0
$324$	0.989821	+	3.37102i	0.989821	+	3.37102i
$325$		0			0
$326$	1.41542	−	0.909632i	1.41542	−	0.909632i
$327$	0.865611	+	0.647988i	0.865611	+	0.647988i
$328$	0.811843	−	0.176606i	0.811843	−	0.176606i
$329$	−0.215109	+	0.471022i	−0.215109	+	0.471022i
$330$		0			0
$331$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$331$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$332$	−1.41620	−	0.528215i	−1.41620	−	0.528215i
$333$		0			0
$334$	0.474017	−	1.61435i	0.474017	−	1.61435i
$335$		0			0
$336$	3.45561	+	0.496841i	3.45561	+	0.496841i
$337$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$337$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$338$	−0.349464	−	0.936950i	−0.349464	−	0.936950i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	2.09127	+	1.14192i	2.09127	+	1.14192i
$344$	−1.08128			−1.08128
$345$		0			0
$346$		0			0
$347$	−1.14952	−	0.627683i	−1.14952	−	0.627683i	−0.212565	−	0.977147i	$-0.568182\pi$
$347$	−1.14952	−	0.627683i	−1.14952	−	0.627683i	−0.936950	+	0.349464i	$0.886364\pi$
$348$	0.544809	+	0.0389655i	0.544809	+	0.0389655i
$349$	0.449181	+	0.698939i	0.449181	+	0.698939i	0.989821	−	0.142315i	$-0.0454545\pi$
$349$	0.449181	+	0.698939i	0.449181	+	0.698939i	−0.540641	+	0.841254i	$0.681818\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$353$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$354$		0			0
$355$		0			0
$356$	0.158746	−	0.540641i	0.158746	−	0.540641i
$357$		0			0
$358$		0			0
$359$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$359$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$360$		0			0
$361$	0.415415	−	0.909632i	0.415415	−	0.909632i
$362$	1.47696	−	0.321292i	1.47696	−	0.321292i
$363$	−1.53623	−	1.15001i	−1.53623	−	1.15001i
$364$		0			0
$365$		0			0
$366$	0.584585	+	1.99091i	0.584585	+	1.99091i
$367$	1.06879	−	1.06879i	1.06879	−	1.06879i	0.0713392	−	0.997452i	$-0.477273\pi$
$367$	1.06879	−	1.06879i	1.06879	−	1.06879i	0.997452	−	0.0713392i	$-0.0227273\pi$
$368$	−0.599278	−	0.800541i	−0.599278	−	0.800541i
$369$			2.22871i			2.22871i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$373$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$374$		0			0
$375$		0			0
$376$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$377$		0			0
$378$	−2.05271	+	5.50352i	−2.05271	+	5.50352i
$379$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$379$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$380$		0			0
$381$	−1.04408	−	2.28621i	−1.04408	−	2.28621i
$382$		0			0
$383$	−1.81463	+	0.129785i	−1.81463	+	0.129785i	−0.936950	−	0.349464i	$-0.886364\pi$
$383$	−1.81463	+	0.129785i	−1.81463	+	0.129785i	−0.877679	+	0.479249i	$0.840909\pi$
$384$	1.74557	+	0.797176i	1.74557	+	0.797176i
$385$		0			0
$386$		0			0
$387$	0.616555	−	2.83426i	0.616555	−	2.83426i
$388$		0			0
$389$	0.540641	−	0.158746i	0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$389$	0.540641	−	0.158746i	0.540641	−	0.158746i	0.540641	+	0.841254i	$0.318182\pi$
$390$		0			0
$391$		0			0
$392$	1.63322	+	1.63322i	1.63322	+	1.63322i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$397$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.37491	+	0.627899i	−1.37491	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$401$	−1.37491	+	0.627899i	−1.37491	+	0.627899i	−0.415415	+	0.909632i	$0.636364\pi$
$402$	−2.54575	+	1.39008i	−2.54575	+	1.39008i
$403$		0			0
$404$	−1.19136	+	0.544078i	−1.19136	+	0.544078i
$405$		0			0
$406$	0.391340	+	0.339098i	0.391340	+	0.339098i
$407$		0			0
$408$		0			0
$409$	0.281733	−	0.0405070i	0.281733	−	0.0405070i		−	1.00000i	$-0.5\pi$
$409$	0.281733	−	0.0405070i	0.281733	−	0.0405070i	0.281733	+	0.959493i	$0.409091\pi$
$410$		0			0
$411$		0			0
$412$	−0.948742	+	1.73749i	−0.948742	+	1.73749i
$413$		0			0
$414$	2.44009	−	1.11435i	2.44009	−	1.11435i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$419$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$420$		0			0
$421$	−1.65486	−	0.755750i	−1.65486	−	0.755750i	−0.654861	−	0.755750i	$-0.727273\pi$
$421$	−1.65486	−	0.755750i	−1.65486	−	0.755750i	−1.00000			$\pi$
$422$		0			0
$423$	−0.457561	−	0.611230i	−0.457561	−	0.611230i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.687444	+	1.84311i	−0.687444	+	1.84311i
$428$	−1.58479	+	1.18636i	−1.58479	+	1.18636i
$429$		0			0
$430$		0			0
$431$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$431$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$432$	−1.93489	+	2.58471i	−1.93489	+	2.58471i
$433$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$433$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$434$		0			0
$435$		0			0
$436$			0.563465i			0.563465i
$437$		0			0
$438$		0			0
$439$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$439$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$440$		0			0
$441$	−5.21228	+	3.34973i	−5.21228	+	3.34973i
$442$		0			0
$443$	1.64406	−	0.357643i	1.64406	−	0.357643i	0.707107	−	0.707107i	$-0.250000\pi$
$443$	1.64406	−	0.357643i	1.64406	−	0.357643i	0.936950	+	0.349464i	$0.113636\pi$
$444$		0			0
$445$		0			0
$446$	−0.239446	+	1.66538i	−0.239446	+	1.66538i
$447$	3.55938	+	1.32758i	3.55938	+	1.32758i
$448$	0.871880	+	1.59673i	0.871880	+	1.59673i
$449$	0.540641	−	1.84125i	0.540641	−	1.84125i		−	1.00000i	$-0.5\pi$
$449$	0.540641	−	1.84125i	0.540641	−	1.84125i	0.540641	−	0.841254i	$-0.318182\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$		0			0
$454$	1.66538	+	1.07028i	1.66538	+	1.07028i
$455$		0			0
$456$		0			0
$457$		0			0		−0.997452	−	0.0713392i	$-0.977273\pi$
$457$		0			0		0.997452	+	0.0713392i	$0.0227273\pi$
$458$	−0.494541	−	0.270040i	−0.494541	−	0.270040i
$459$		0			0
$460$		0			0
$461$	1.91899			1.91899			0.959493	−	0.281733i	$-0.0909091\pi$
$461$	1.91899			1.91899			0.959493	+	0.281733i	$0.0909091\pi$
$462$		0			0
$463$	−0.828713	−	0.0592707i	−0.828713	−	0.0592707i	−0.349464	−	0.936950i	$-0.613636\pi$
$463$	−0.828713	−	0.0592707i	−0.828713	−	0.0592707i	−0.479249	+	0.877679i	$0.659091\pi$
$464$	0.153882	+	0.239446i	0.153882	+	0.239446i
$465$		0			0
$466$		0			0
$467$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$467$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$468$		0			0
$469$	−2.72183	−	0.391340i	−2.72183	−	0.391340i
$470$		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		0.841254	−	0.540641i	$-0.181818\pi$
$479$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$480$		0			0
$481$		0			0
$482$	−1.28641	+	1.28641i	−1.28641	+	1.28641i
$483$	3.41136	+	0.742096i	3.41136	+	0.742096i
$484$		−	1.00000i		−	1.00000i
$485$		0			0
$486$	−2.30075	−	2.65520i	−2.30075	−	2.65520i
$487$	−0.811843	−	0.176606i	−0.811843	−	0.176606i	−0.212565	−	0.977147i	$-0.568182\pi$
$487$	−0.811843	−	0.176606i	−0.811843	−	0.176606i	−0.599278	+	0.800541i	$0.704545\pi$
$488$	−0.647988	+	0.865611i	−0.647988	+	0.865611i
$489$	−1.74557	+	2.71616i	−1.74557	+	2.71616i
$490$		0			0
$491$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$491$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$492$	−1.27634	+	0.955459i	−1.27634	+	0.955459i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.89316	−	0.206923i	2.89316	−	0.206923i
$499$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$499$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$500$		0			0
$501$	0.459493	+	3.19584i	0.459493	+	3.19584i
$502$		0			0
$503$	0.0401971	−	0.562029i	0.0401971	−	0.562029i	−0.936950	−	0.349464i	$-0.886364\pi$
$503$	0.0401971	−	0.562029i	0.0401971	−	0.562029i	0.977147	−	0.212565i	$-0.0681818\pi$
$504$	−4.68251	+	1.37491i	−4.68251	+	1.37491i
$505$		0			0
$506$		0			0
$507$	1.35693	+	1.35693i	1.35693	+	1.35693i
$508$	0.627683	−	1.14952i	0.627683	−	1.14952i
$509$	1.27155	−	1.10181i	1.27155	−	1.10181i	0.281733	−	0.959493i	$-0.409091\pi$
$509$	1.27155	−	1.10181i	1.27155	−	1.10181i	0.989821	−	0.142315i	$-0.0454545\pi$
$510$		0			0
$511$		0			0
$512$	0.212565	+	0.977147i	0.212565	+	0.977147i
$513$		0			0
$514$		0			0
$515$		0			0
$516$	1.88745	−	0.861971i	1.88745	−	0.861971i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.49611	+	1.29639i	1.49611	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$521$	1.49611	+	1.29639i	1.49611	+	1.29639i	0.654861	+	0.755750i	$0.272727\pi$
$522$	−0.715381	+	0.266823i	−0.715381	+	0.266823i
$523$	0.321292	+	1.47696i	0.321292	+	1.47696i	0.800541	+	0.599278i	$0.204545\pi$
$523$	0.321292	+	1.47696i	0.321292	+	1.47696i	−0.479249	+	0.877679i	$0.659091\pi$
$524$		0			0
$525$		0			0
$526$	0.817178	−	0.708089i	0.817178	−	0.708089i
$527$		0			0
$528$		0			0
$529$	−0.540641	−	0.841254i	−0.540641	−	0.841254i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.153882	+	1.07028i	0.153882	+	1.07028i
$535$		0			0
$536$	−1.37491	−	0.627899i	−1.37491	−	0.627899i
$537$		0			0
$538$	0.784887	+	1.04849i	0.784887	+	1.04849i
$539$		0			0
$540$		0			0
$541$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$541$	1.25667	+	0.368991i	1.25667	+	0.368991i	0.415415	+	0.909632i	$0.363636\pi$
$542$		0			0
$543$	−2.32201	+	1.73823i	−2.32201	+	1.73823i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.170572	−	0.227858i	0.170572	−	0.227858i	−0.707107	−	0.707107i	$-0.750000\pi$
$547$	0.170572	−	0.227858i	0.170572	−	0.227858i	0.877679	+	0.479249i	$0.159091\pi$
$548$		0			0
$549$	−1.89945	−	2.19209i	−1.89945	−	2.19209i
$550$		0			0
$551$		0			0
$552$	1.68425	+	0.919672i	1.68425	+	0.919672i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$557$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.01311	+	0.377869i	1.01311	+	0.377869i
$563$	−0.871880	−	1.59673i	−0.871880	−	1.59673i	−0.800541	−	0.599278i	$-0.795455\pi$
$563$	−0.871880	−	1.59673i	−0.871880	−	1.59673i	−0.0713392	−	0.997452i	$-0.522727\pi$
$564$	0.153882	−	0.524075i	0.153882	−	0.524075i
$565$		0			0
$566$	0.557730	+	0.0801894i	0.557730	+	0.0801894i
$567$	−0.455978	−	6.37540i	−0.455978	−	6.37540i
$568$		0			0
$569$	−1.27155	−	0.817178i	−1.27155	−	0.817178i	−0.281733	−	0.959493i	$-0.590909\pi$
$569$	−1.27155	−	0.817178i	−1.27155	−	0.817178i	−0.989821	+	0.142315i	$0.954545\pi$
$570$		0			0
$571$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$571$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$572$		0			0
$573$		0			0
$574$	−1.51150			−1.51150
$575$		0			0
$576$	−2.68251			−2.68251
$577$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$577$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$578$	−0.997452	−	0.0713392i	−0.997452	−	0.0713392i
$579$		0			0
$580$		0			0
$581$	2.31329	+	1.48666i	2.31329	+	1.48666i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.806340	−	1.47670i	−0.806340	−	1.47670i	−0.877679	−	0.479249i	$-0.840909\pi$
$587$	−0.806340	−	1.47670i	−0.806340	−	1.47670i	0.0713392	−	0.997452i	$-0.477273\pi$
$588$	−4.15286	−	1.54894i	−4.15286	−	1.54894i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$593$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$594$		0			0
$595$		0			0
$596$	0.557730	+	1.89945i	0.557730	+	1.89945i
$597$		0			0
$598$		0			0
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.841254	+	0.540641i	$0.181818\pi$
$601$	1.25667	+	1.45027i	1.25667	+	1.45027i	0.415415	+	0.909632i	$0.363636\pi$
$602$	1.92218	+	0.418145i	1.92218	+	0.418145i
$603$	2.42984	−	3.24588i	2.42984	−	3.24588i
$604$		0			0
$605$		0			0
$606$	1.64589	−	1.89945i	1.64589	−	1.89945i
$607$	1.34692	−	1.00829i	1.34692	−	1.00829i	0.349464	−	0.936950i	$-0.386364\pi$
$607$	1.34692	−	1.00829i	1.34692	−	1.00829i	0.997452	−	0.0713392i	$-0.0227273\pi$
$608$		0			0
$609$	−0.953431	−	0.279953i	−0.953431	−	0.279953i
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$613$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$614$	0.755750	+	0.345139i	0.755750	+	0.345139i
$615$		0			0
$616$		0			0
$617$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$617$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$618$	0.271011	−	3.78923i	0.271011	−	3.78923i
$619$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$619$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$620$		0			0
$621$	−2.11435	+	2.44009i	−2.11435	+	2.44009i
$622$		0			0
$623$	−0.491274	+	0.899702i	−0.491274	+	0.899702i
$624$		0			0
$625$		0			0
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$631$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$632$		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
$641$	1.49611	−	1.29639i	1.49611	−	1.29639i	0.654861	−	0.755750i	$-0.272727\pi$
$641$	1.49611	−	1.29639i	1.49611	−	1.29639i	0.841254	−	0.540641i	$-0.181818\pi$
$642$	1.82062	−	3.33422i	1.82062	−	3.33422i
$643$	0.764582	+	0.764582i	0.764582	+	0.764582i	0.977147	−	0.212565i	$-0.0681818\pi$
$643$	0.764582	+	0.764582i	0.764582	+	0.764582i	−0.212565	+	0.977147i	$0.568182\pi$
$644$	0.755750	+	1.65486i	0.755750	+	1.65486i
$645$		0			0
$646$		0			0
$647$	0.0934345	−	1.30638i	0.0934345	−	1.30638i	−0.707107	−	0.707107i	$-0.750000\pi$
$647$	0.0934345	−	1.30638i	0.0934345	−	1.30638i	0.800541	−	0.599278i	$-0.204545\pi$
$648$	0.746814	−	3.43305i	0.746814	−	3.43305i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−1.67822	+	0.120029i	−1.67822	+	0.120029i
$653$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$653$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$654$	−0.449181	−	0.983568i	−0.449181	−	0.983568i
$655$		0			0
$656$	−0.797176	−	0.234072i	−0.797176	−	0.234072i
$657$		0			0
$658$	0.414533	−	0.310316i	0.414533	−	0.310316i
$659$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$659$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$660$		0			0
$661$	−1.07028	+	1.66538i	−1.07028	+	1.66538i	−0.415415	+	0.909632i	$0.636364\pi$
$661$	−1.07028	+	1.66538i	−1.07028	+	1.66538i	−0.654861	+	0.755750i	$0.727273\pi$
$662$		0			0
$663$		0			0
$664$	0.989821	+	1.14231i	0.989821	+	1.14231i
$665$		0			0
$666$		0			0
$667$	0.136408	+	0.249813i	0.136408	+	0.249813i
$668$	−1.18971	+	1.18971i	−1.18971	+	1.18971i
$669$	−0.909632	−	3.09792i	−0.909632	−	3.09792i
$670$		0			0
$671$		0			0
$672$	−2.79480	−	2.09216i	−2.79480	−	2.09216i
$673$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$673$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$674$		0			0
$675$		0			0
$676$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$677$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$677$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−3.76024	−	0.540641i	−3.76024	−	0.540641i
$682$		0			0
$683$	0.290345	+	0.778446i	0.290345	+	0.778446i	0.997452	+	0.0713392i	$0.0227273\pi$
$683$	0.290345	+	0.778446i	0.290345	+	0.778446i	−0.707107	+	0.707107i	$0.750000\pi$
$684$		0			0
$685$		0			0
$686$	−1.28820	−	2.00448i	−1.28820	−	2.00448i
$687$	1.07853	+	0.0771377i	1.07853	+	0.0771377i
$688$	0.949018	+	0.518203i	0.949018	+	0.518203i
$689$		0			0
$690$		0			0
$691$		0			0		1.00000			$0$
$691$		0			0		−1.00000			$\pi$
$692$		0			0
$693$		0			0
$694$	0.708089	+	1.10181i	0.708089	+	1.10181i
$695$		0			0
$696$	−0.459493	−	0.295298i	−0.459493	−	0.295298i
$697$		0			0
$698$	−0.0592707	−	0.828713i	−0.0592707	−	0.828713i
$699$		0			0
$700$		0			0
$701$	0.304632	−	1.03748i	0.304632	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$701$	0.304632	−	1.03748i	0.304632	−	1.03748i	0.959493	−	0.281733i	$-0.0909091\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$	2.32828	−	0.506486i	2.32828	−	0.506486i
$708$		0			0
$709$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$709$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$710$		0			0
$711$		0			0
$712$	−0.398430	+	0.398430i	−0.398430	+	0.398430i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$719$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$720$		0			0
$721$	2.35848	−	2.72183i	2.35848	−	2.72183i
$722$	−0.800541	+	0.599278i	−0.800541	+	0.599278i
$723$	1.22003	−	3.27102i	1.22003	−	3.27102i
$724$	−1.45027	−	0.425839i	−1.45027	−	0.425839i
$725$		0			0
$726$	0.797176	+	1.74557i	0.797176	+	1.74557i
$727$	1.18636	+	1.58479i	1.18636	+	1.58479i	0.707107	+	0.707107i	$0.250000\pi$
$727$	1.18636	+	1.58479i	1.18636	+	1.58479i	0.479249	+	0.877679i	$0.340909\pi$
$728$		0			0
$729$	2.93694	+	1.34125i	2.93694	+	1.34125i
$730$		0			0
$731$		0			0
$732$	0.441065	−	2.02754i	0.441065	−	2.02754i
$733$		0			0		0.0713392	−	0.997452i	$-0.477273\pi$
$733$		0			0		−0.0713392	+	0.997452i	$0.522727\pi$
$734$	−1.45027	+	0.425839i	−1.45027	+	0.425839i
$735$		0			0
$736$	0.142315	+	0.989821i	0.142315	+	0.989821i
$737$		0			0
$738$	1.06811	−	1.95609i	1.06811	−	1.95609i
$739$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$739$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.85483	−	0.691814i	1.85483	−	0.691814i	0.877679	−	0.479249i	$-0.159091\pi$
$743$	1.85483	−	0.691814i	1.85483	−	0.691814i	0.977147	−	0.212565i	$-0.0681818\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.55864	+	1.94317i	−3.55864	+	1.94317i
$748$		0			0
$749$	3.27603	−	1.49611i	3.27603	−	1.49611i
$750$		0			0
$751$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$751$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$752$	0.266684	−	0.0994679i	0.266684	−	0.0994679i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	4.43918	−	3.84657i	4.43918	−	3.84657i
$757$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$757$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.654861	−	0.755750i	$-0.727273\pi$
$761$	−0.797176	+	0.234072i	−0.797176	+	0.234072i	−0.142315	+	0.989821i	$0.545455\pi$
$762$	−0.179299	+	2.50693i	−0.179299	+	2.50693i
$763$	0.217899	−	1.00167i	0.217899	−	1.00167i
$764$		0			0
$765$		0			0
$766$	1.65486	+	0.755750i	1.65486	+	0.755750i
$767$		0			0
$768$	−1.15001	−	1.53623i	−1.15001	−	1.53623i
$769$	−0.449181	−	0.983568i	−0.449181	−	0.983568i	−0.989821	−	0.142315i	$-0.954545\pi$
$769$	−0.449181	−	0.983568i	−0.449181	−	0.983568i	0.540641	−	0.841254i	$-0.318182\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$773$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$774$	−1.89945	+	2.19209i	−1.89945	+	2.19209i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.550588	−	0.119773i	−0.550588	−	0.119773i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	0.649821	−	0.649821i	0.649821	−	0.649821i
$784$	−0.650724	−	2.21616i	−0.650724	−	2.21616i
$785$		0			0
$786$		0			0
$787$	0.451077	+	0.337672i	0.451077	+	0.337672i	0.800541	−	0.599278i	$-0.204545\pi$
$787$	0.451077	+	0.337672i	0.451077	+	0.337672i	−0.349464	+	0.936950i	$0.613636\pi$
$788$		0			0
$789$	−0.861971	+	1.88745i	−0.861971	+	1.88745i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$797$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−0.817178	−	1.27155i	−0.817178	−	1.27155i
$802$	1.50765	+	0.107829i	1.50765	+	0.107829i
$803$		0			0
$804$	2.90055			2.90055
$805$		0			0
$806$		0			0
$807$	−2.20590	−	1.20451i	−2.20590	−	1.20451i
$808$	1.30638	+	0.0934345i	1.30638	+	0.0934345i
$809$	−1.03748	−	1.61435i	−1.03748	−	1.61435i	−0.755750	−	0.654861i	$-0.772727\pi$
$809$	−1.03748	−	1.61435i	−1.03748	−	1.61435i	−0.281733	−	0.959493i	$-0.590909\pi$
$810$		0			0
$811$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$811$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$812$	−0.180958	−	0.485168i	−0.180958	−	0.485168i
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.266684	−	0.0994679i	−0.266684	−	0.0994679i
$819$		0			0
$820$		0			0
$821$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$821$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$822$		0			0
$823$	−0.665114	−	0.497898i	−0.665114	−	0.497898i	0.212565	−	0.977147i	$-0.431818\pi$
$823$	−0.665114	−	0.497898i	−0.665114	−	0.497898i	−0.877679	+	0.479249i	$0.840909\pi$
$824$	1.66538	−	1.07028i	1.66538	−	1.07028i
$825$		0			0
$826$		0			0
$827$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$827$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$828$	−2.67567	−	0.191368i	−2.67567	−	0.191368i
$829$		−	0.830830i		−	0.830830i	−0.909632	−	0.415415i	$-0.863636\pi$
$829$		−	0.830830i		−	0.830830i	0.909632	−	0.415415i	$-0.136364\pi$
$830$		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		−0.959493	−	0.281733i	$-0.909091\pi$
$839$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$840$		0			0
$841$	0.381761	+	0.835939i	0.381761	+	0.835939i
$842$	1.09024	+	1.45640i	1.09024	+	1.45640i
$843$	−2.06968	+	0.148026i	−2.06968	+	0.148026i
$844$		0			0
$845$		0			0
$846$	0.108660	+	0.755750i	0.108660	+	0.755750i
$847$	−0.386712	+	1.77769i	−0.386712	+	1.77769i
$848$		0			0
$849$	−1.03748	+	0.304632i	−1.03748	+	0.304632i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$853$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$854$	1.48666	−	1.28820i	1.48666	−	1.28820i
$855$		0			0
$856$	1.95949	−	0.281733i	1.95949	−	0.281733i
$857$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$857$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$858$		0			0
$859$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$859$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$860$		0			0
$861$	2.63843	−	1.20493i	2.63843	−	1.20493i
$862$		0			0
$863$	0.729202	−	0.398174i	0.729202	−	0.398174i	−0.0713392	−	0.997452i	$-0.522727\pi$
$863$	0.729202	−	0.398174i	0.729202	−	0.398174i	0.800541	+	0.599278i	$0.204545\pi$
$864$	2.93694	−	1.34125i	2.93694	−	1.34125i
$865$		0			0
$866$		0			0
$867$	1.79799	−	0.670617i	1.79799	−	0.670617i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	0.270040	−	0.494541i	0.270040	−	0.494541i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		0.0713392	−	0.997452i	$-0.477273\pi$
$877$		0			0		−0.0713392	+	0.997452i	$0.522727\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.37491	−	0.627899i	−1.37491	−	0.627899i	−0.415415	−	0.909632i	$-0.636364\pi$
$881$	−1.37491	−	0.627899i	−1.37491	−	0.627899i	−0.959493	+	0.281733i	$0.909091\pi$
$882$	6.18006	−	0.442006i	6.18006	−	0.442006i
$883$	1.15001	+	1.53623i	1.15001	+	1.53623i	0.800541	+	0.599278i	$0.204545\pi$
$883$	1.15001	+	1.53623i	1.15001	+	1.53623i	0.349464	+	0.936950i	$0.386364\pi$
$884$		0			0
$885$		0			0
$886$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$887$	−0.670617	+	1.79799i	−0.670617	+	1.79799i	−0.0713392	+	0.997452i	$0.522727\pi$
$887$	−0.670617	+	1.79799i	−0.670617	+	1.79799i	−0.599278	+	0.800541i	$0.704545\pi$
$888$		0			0
$889$	−1.56036	+	1.80075i	−1.56036	+	1.80075i
$890$		0			0
$891$		0			0
$892$	1.00829	−	1.34692i	1.00829	−	1.34692i
$893$		0			0
$894$	−2.48775	−	2.87102i	−2.48775	−	2.87102i
$895$		0			0
$896$		−	1.81926i		−	1.81926i
$897$		0			0
$898$	−1.35693	+	1.35693i	−1.35693	+	1.35693i
$899$		0			0
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−3.68864	+	0.802414i	−3.68864	+	0.802414i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.527938	+	0.196911i	0.527938	+	0.196911i	0.599278	−	0.800541i	$-0.295455\pi$
$907$	0.527938	+	0.196911i	0.527938	+	0.196911i	−0.0713392	+	0.997452i	$0.522727\pi$
$908$	−0.948742	−	1.73749i	−0.948742	−	1.73749i
$909$	−0.989821	+	3.37102i	−0.989821	+	3.37102i
$910$		0			0
$911$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$911$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.304632	+	0.474017i	0.304632	+	0.474017i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$	−1.59435			−1.59435
$922$	−1.68425	−	0.919672i	−1.68425	−	0.919672i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	0.698939	+	0.449181i	0.698939	+	0.449181i
$927$	1.85580	+	4.97558i	1.85580	+	4.97558i
$928$	−0.0203052	−	0.283904i	−0.0203052	−	0.283904i
$929$	0.281733	+	0.0405070i	0.281733	+	0.0405070i	0.281733	−	0.959493i	$-0.409091\pi$
$929$	0.281733	+	0.0405070i	0.281733	+	0.0405070i			1.00000i	$0.5\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$937$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$938$	2.20134	+	1.64790i	2.20134	+	1.64790i
$939$		0			0
$940$		0			0
$941$	−0.304632	−	1.03748i	−0.304632	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$941$	−0.304632	−	1.03748i	−0.304632	−	1.03748i	0.654861	−	0.755750i	$-0.272727\pi$
$942$		0			0
$943$	−0.778446	−	0.290345i	−0.778446	−	0.290345i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.87513	−	0.407910i	−1.87513	−	0.407910i	−0.877679	−	0.479249i	$-0.840909\pi$
$947$	−1.87513	−	0.407910i	−1.87513	−	0.407910i	−0.997452	+	0.0713392i	$0.977273\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$953$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$962$		0			0
$963$	−0.378840	+	5.29688i	−0.378840	+	5.29688i
$964$	1.74557	−	0.512546i	1.74557	−	0.512546i
$965$		0			0
$966$	−2.63843	−	2.28621i	−2.63843	−	2.28621i
$967$	−1.35693	−	1.35693i	−1.35693	−	1.35693i	−0.877679	−	0.479249i	$-0.840909\pi$
$967$	−1.35693	−	1.35693i	−1.35693	−	1.35693i	−0.479249	−	0.877679i	$-0.659091\pi$
$968$	−0.479249	+	0.877679i	−0.479249	+	0.877679i
$969$		0			0
$970$		0			0
$971$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$971$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$972$	0.746814	+	3.43305i	0.746814	+	3.43305i
$973$		0			0
$974$	0.627899	+	0.544078i	0.627899	+	0.544078i
$975$		0			0
$976$	0.983568	−	0.449181i	0.983568	−	0.449181i
$977$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$977$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$978$	2.83377	−	1.54735i	2.83377	−	1.54735i
$979$		0			0
$980$		0			0
$981$	1.14231	+	0.989821i	1.14231	+	0.989821i
$982$		0			0
$983$	−0.119773	−	0.550588i	−0.119773	−	0.550588i	−0.997452	−	0.0713392i	$-0.977273\pi$
$983$	−0.119773	−	0.550588i	−0.119773	−	0.550588i	0.877679	−	0.479249i	$-0.159091\pi$
$984$	1.57812	−	0.226900i	1.57812	−	0.226900i
$985$		0			0
$986$		0			0
$987$	−0.476221	+	0.872134i	−0.476221	+	0.872134i
$988$		0			0
$989$	0.909632	+	0.584585i	0.909632	+	0.584585i
$990$		0			0
$991$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$991$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	−2.63843	−	1.20493i	−2.63843	−	1.20493i
$997$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$997$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$998$		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.543.1	yes	40
4.3	odd	2	inner	2300.1.bh.a.543.2	yes	40
5.2	odd	4	inner	2300.1.bh.a.2107.2	yes	40
5.3	odd	4	inner	2300.1.bh.a.2107.1	yes	40
5.4	even	2	inner	2300.1.bh.a.543.2	yes	40
20.3	even	4	inner	2300.1.bh.a.2107.2	yes	40
20.7	even	4	inner	2300.1.bh.a.2107.1	yes	40
20.19	odd	2	CM	2300.1.bh.a.543.1	yes	40
23.5	odd	22	inner	2300.1.bh.a.143.1	✓	40
92.51	even	22	inner	2300.1.bh.a.143.2	yes	40
115.28	even	44	inner	2300.1.bh.a.1707.1	yes	40
115.74	odd	22	inner	2300.1.bh.a.143.2	yes	40
115.97	even	44	inner	2300.1.bh.a.1707.2	yes	40
460.143	odd	44	inner	2300.1.bh.a.1707.2	yes	40
460.327	odd	44	inner	2300.1.bh.a.1707.1	yes	40
460.419	even	22	inner	2300.1.bh.a.143.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2300.1.bh.a.143.1	✓	40	23.5	odd	22	inner
2300.1.bh.a.143.1	✓	40	460.419	even	22	inner
2300.1.bh.a.143.2	yes	40	92.51	even	22	inner
2300.1.bh.a.143.2	yes	40	115.74	odd	22	inner
2300.1.bh.a.543.1	yes	40	1.1	even	1	trivial
2300.1.bh.a.543.1	yes	40	20.19	odd	2	CM
2300.1.bh.a.543.2	yes	40	4.3	odd	2	inner
2300.1.bh.a.543.2	yes	40	5.4	even	2	inner
2300.1.bh.a.1707.1	yes	40	115.28	even	44	inner
2300.1.bh.a.1707.1	yes	40	460.327	odd	44	inner
2300.1.bh.a.1707.2	yes	40	115.97	even	44	inner
2300.1.bh.a.1707.2	yes	40	460.143	odd	44	inner
2300.1.bh.a.2107.1	yes	40	5.3	odd	4	inner
2300.1.bh.a.2107.1	yes	40	20.7	even	4	inner
2300.1.bh.a.2107.2	yes	40	5.2	odd	4	inner
2300.1.bh.a.2107.2	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)

\(f(q)\)	\(=\)	\(q+(-0.877679 - 0.479249i) q^{2} +(1.91410 + 0.136899i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-1.61435 - 1.03748i) q^{6} +(-0.635768 - 1.70456i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(2.65520 + 0.381761i) q^{9} +O(q^{10})\)	\(q+(-0.877679 - 0.479249i) q^{2} +(1.91410 + 0.136899i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-1.61435 - 1.03748i) q^{6} +(-0.635768 - 1.70456i) q^{7} +(-0.0713392 - 0.997452i) q^{8} +(2.65520 + 0.381761i) q^{9} +(0.919672 + 1.68425i) q^{12} +(-0.258908 + 1.80075i) q^{14} +(-0.415415 + 0.909632i) q^{16} +(-2.14746 - 1.60757i) q^{18} +(-0.983568 - 3.34973i) q^{21} +(-0.479249 + 0.877679i) q^{23} -1.91899i q^{24} +(3.15492 + 0.686311i) q^{27} +(1.09024 - 1.45640i) q^{28} +(0.153882 - 0.239446i) q^{29} +(0.800541 - 0.599278i) q^{32} +(1.11435 + 2.44009i) q^{36} +(0.118239 + 0.822373i) q^{41} +(-0.742096 + 3.41136i) q^{42} +(0.0771377 - 1.07853i) q^{43} +(0.841254 - 0.540641i) q^{46} +(-0.201264 - 0.201264i) q^{47} +(-0.919672 + 1.68425i) q^{48} +(-1.74557 + 1.51255i) q^{49} +(-2.44009 - 2.11435i) q^{54} +(-1.65486 + 0.755750i) q^{56} +(-0.249813 + 0.136408i) q^{58} +(-0.817178 - 0.708089i) q^{61} +(-1.03736 - 4.76866i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(0.724384 - 1.32661i) q^{67} +(-1.03748 + 1.61435i) q^{69} +(0.191368 - 2.67567i) q^{72} +(3.37102 + 0.989821i) q^{81} +(0.290345 - 0.778446i) q^{82} +(-1.21002 + 0.905808i) q^{83} +(2.28621 - 2.63843i) q^{84} +(-0.584585 + 0.909632i) q^{86} +(0.327326 - 0.437256i) q^{87} +(-0.368991 - 0.425839i) q^{89} +(-0.997452 + 0.0713392i) q^{92} +(0.0801894 + 0.273100i) q^{94} +(1.61435 - 1.03748i) q^{96} +(2.25694 - 0.490967i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{6}+O(q^{10}) \) 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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