LMFDB - Embedded newform 712.1.y.a.603.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [712,1,Mod(99,712)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(712, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 22, 43]))

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

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

chi := DirichletCharacter("712.99");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 712 = 2^{3} \cdot 89 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	712.y (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:	$0.355334288995$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{44})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{44}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{44} - \cdots)$

Embedding invariants

Embedding label			603.1
Root			$0.755750 + 0.654861i$ of defining polynomial
Character	$\chi$	$=$	712.603
Dual form			712.1.y.a.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(0.956056 - 1.75089i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.59700 - 1.19550i) q^{6} +(-0.415415 + 0.909632i) q^{8} +(-1.61092 - 2.50664i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(0.956056 - 1.75089i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.59700 - 1.19550i) q^{6} +(-0.415415 + 0.909632i) q^{8} +(-1.61092 - 2.50664i) q^{9} +(0.755750 + 1.65486i) q^{11} +(-1.41061 + 1.41061i) q^{12} +(0.841254 + 0.540641i) q^{16} +(0.281733 - 0.0405070i) q^{17} +(-2.71038 + 1.23779i) q^{18} +(-0.682956 - 0.148568i) q^{19} +(1.74557 - 0.512546i) q^{22} +(1.19550 + 1.59700i) q^{24} +(0.654861 + 0.755750i) q^{25} +(-3.93914 + 0.281733i) q^{27} +(0.654861 - 0.755750i) q^{32} +(3.62001 + 0.258908i) q^{33} -0.284630i q^{34} +(0.839462 + 2.85895i) q^{36} +(-0.244250 + 0.654861i) q^{38} +(1.24123 - 0.677760i) q^{41} +(-1.12299 - 0.418852i) q^{43} +(-0.258908 - 1.80075i) q^{44} +(1.75089 - 0.956056i) q^{48} +(-0.755750 + 0.654861i) q^{49} +(0.841254 - 0.540641i) q^{50} +(0.198429 - 0.532008i) q^{51} +(-0.281733 + 3.93914i) q^{54} +(-0.913069 + 1.05374i) q^{57} +(0.767317 + 1.40524i) q^{59} +(-0.654861 - 0.755750i) q^{64} +(0.771454 - 3.54632i) q^{66} +(-1.03748 + 0.304632i) q^{67} +(-0.281733 - 0.0405070i) q^{68} +(2.94931 - 0.424047i) q^{72} +(-1.27155 - 0.817178i) q^{73} +(1.94931 - 0.424047i) q^{75} +(0.613435 + 0.334961i) q^{76} +(-2.03496 + 4.45595i) q^{81} +(-0.494217 - 1.32505i) q^{82} +(-0.767317 - 0.574406i) q^{83} +(-0.574406 + 1.05195i) q^{86} -1.81926 q^{88} +(0.654861 - 0.755750i) q^{89} +(-0.697148 - 1.86912i) q^{96} +(0.698939 - 1.53046i) q^{97} +(0.540641 + 0.841254i) q^{98} +(2.93068 - 4.56023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^8	$ 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8} - 2 q^{12} - 2 q^{16} - 2 q^{19} + 2 q^{24} + 2 q^{25} - 22 q^{27} + 2 q^{32} - 20 q^{38} + 2 q^{41} + 2 q^{43} - 2 q^{48} - 2 q^{50} + 4 q^{51} - 4 q^{57} - 2 q^{59} - 2 q^{64} + 22 q^{72} + 2 q^{75} - 2 q^{76} - 2 q^{81} - 2 q^{82} + 2 q^{83} - 2 q^{86} + 2 q^{89} + 2 q^{96} - 4 q^{97}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^8 - 2 * q^12 - 2 * q^16 - 2 * q^19 + 2 * q^24 + 2 * q^25 - 22 * q^27 + 2 * q^32 - 20 * q^38 + 2 * q^41 + 2 * q^43 - 2 * q^48 - 2 * q^50 + 4 * q^51 - 4 * q^57 - 2 * q^59 - 2 * q^64 + 22 * q^72 + 2 * q^75 - 2 * q^76 - 2 * q^81 - 2 * q^82 + 2 * q^83 - 2 * q^86 + 2 * q^89 + 2 * q^96 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/712\mathbb{Z}\right)^\times$.

$n$	$357$	$535$	$537$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{29}{44}\right)$

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 $

$2$	0.142315	−	0.989821i	0.142315	−	0.989821i
$2$	0.142315	−	0.989821i	0.142315	−	0.989821i
$3$	0.956056	−	1.75089i	0.956056	−	1.75089i	0.415415	−	0.909632i	$-0.363636\pi$
$3$	0.956056	−	1.75089i	0.956056	−	1.75089i	0.540641	−	0.841254i	$-0.318182\pi$
$4$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$5$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$5$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$6$	−1.59700	−	1.19550i	−1.59700	−	1.19550i
$7$		0			0		−0.349464	−	0.936950i	$-0.613636\pi$
$7$		0			0		0.349464	+	0.936950i	$0.386364\pi$
$8$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$9$	−1.61092	−	2.50664i	−1.61092	−	2.50664i
$10$		0			0
$11$	0.755750	+	1.65486i	0.755750	+	1.65486i	0.755750	+	0.654861i	$0.227273\pi$
$11$	0.755750	+	1.65486i	0.755750	+	1.65486i			1.00000i	$0.5\pi$
$12$	−1.41061	+	1.41061i	−1.41061	+	1.41061i
$13$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$13$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$14$		0			0
$15$		0			0
$16$	0.841254	+	0.540641i	0.841254	+	0.540641i
$17$	0.281733	−	0.0405070i	0.281733	−	0.0405070i		−	1.00000i	$-0.5\pi$
$17$	0.281733	−	0.0405070i	0.281733	−	0.0405070i	0.281733	+	0.959493i	$0.409091\pi$
$18$	−2.71038	+	1.23779i	−2.71038	+	1.23779i
$19$	−0.682956	−	0.148568i	−0.682956	−	0.148568i	−0.142315	−	0.989821i	$-0.545455\pi$
$19$	−0.682956	−	0.148568i	−0.682956	−	0.148568i	−0.540641	+	0.841254i	$0.681818\pi$
$20$		0			0
$21$		0			0
$22$	1.74557	−	0.512546i	1.74557	−	0.512546i
$23$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$23$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$24$	1.19550	+	1.59700i	1.19550	+	1.59700i
$25$	0.654861	+	0.755750i	0.654861	+	0.755750i
$26$		0			0
$27$	−3.93914	+	0.281733i	−3.93914	+	0.281733i
$28$		0			0
$29$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$29$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$30$		0			0
$31$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$31$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$32$	0.654861	−	0.755750i	0.654861	−	0.755750i
$33$	3.62001	+	0.258908i	3.62001	+	0.258908i
$34$		−	0.284630i		−	0.284630i
$35$		0			0
$36$	0.839462	+	2.85895i	0.839462	+	2.85895i
$37$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$37$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$38$	−0.244250	+	0.654861i	−0.244250	+	0.654861i
$39$		0			0
$40$		0			0
$41$	1.24123	−	0.677760i	1.24123	−	0.677760i	0.281733	−	0.959493i	$-0.409091\pi$
$41$	1.24123	−	0.677760i	1.24123	−	0.677760i	0.959493	+	0.281733i	$0.0909091\pi$
$42$		0			0
$43$	−1.12299	−	0.418852i	−1.12299	−	0.418852i	−0.281733	−	0.959493i	$-0.590909\pi$
$43$	−1.12299	−	0.418852i	−1.12299	−	0.418852i	−0.841254	+	0.540641i	$0.818182\pi$
$44$	−0.258908	−	1.80075i	−0.258908	−	1.80075i
$45$		0			0
$46$		0			0
$47$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$47$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$48$	1.75089	−	0.956056i	1.75089	−	0.956056i
$49$	−0.755750	+	0.654861i	−0.755750	+	0.654861i
$50$	0.841254	−	0.540641i	0.841254	−	0.540641i
$51$	0.198429	−	0.532008i	0.198429	−	0.532008i
$52$		0			0
$53$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$53$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$54$	−0.281733	+	3.93914i	−0.281733	+	3.93914i
$55$		0			0
$56$		0			0
$57$	−0.913069	+	1.05374i	−0.913069	+	1.05374i
$58$		0			0
$59$	0.767317	+	1.40524i	0.767317	+	1.40524i	0.909632	+	0.415415i	$0.136364\pi$
$59$	0.767317	+	1.40524i	0.767317	+	1.40524i	−0.142315	+	0.989821i	$0.545455\pi$
$60$		0			0
$61$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$61$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$62$		0			0
$63$		0			0
$64$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$65$		0			0
$66$	0.771454	−	3.54632i	0.771454	−	3.54632i
$67$	−1.03748	+	0.304632i	−1.03748	+	0.304632i	−0.755750	−	0.654861i	$-0.772727\pi$
$67$	−1.03748	+	0.304632i	−1.03748	+	0.304632i	−0.281733	+	0.959493i	$0.590909\pi$
$68$	−0.281733	−	0.0405070i	−0.281733	−	0.0405070i
$69$		0			0
$70$		0			0
$71$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$71$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$72$	2.94931	−	0.424047i	2.94931	−	0.424047i
$73$	−1.27155	−	0.817178i	−1.27155	−	0.817178i	−0.281733	−	0.959493i	$-0.590909\pi$
$73$	−1.27155	−	0.817178i	−1.27155	−	0.817178i	−0.989821	+	0.142315i	$0.954545\pi$
$74$		0			0
$75$	1.94931	−	0.424047i	1.94931	−	0.424047i
$76$	0.613435	+	0.334961i	0.613435	+	0.334961i
$77$		0			0
$78$		0			0
$79$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$79$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$80$		0			0
$81$	−2.03496	+	4.45595i	−2.03496	+	4.45595i
$82$	−0.494217	−	1.32505i	−0.494217	−	1.32505i
$83$	−0.767317	−	0.574406i	−0.767317	−	0.574406i	0.142315	−	0.989821i	$-0.454545\pi$
$83$	−0.767317	−	0.574406i	−0.767317	−	0.574406i	−0.909632	+	0.415415i	$0.863636\pi$
$84$		0			0
$85$		0			0
$86$	−0.574406	+	1.05195i	−0.574406	+	1.05195i
$87$		0			0
$88$	−1.81926			−1.81926
$89$	0.654861	−	0.755750i	0.654861	−	0.755750i
$89$	0.654861	−	0.755750i	0.654861	−	0.755750i
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.697148	−	1.86912i	−0.697148	−	1.86912i
$97$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$97$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$98$	0.540641	+	0.841254i	0.540641	+	0.841254i
$99$	2.93068	−	4.56023i	2.93068	−	4.56023i
$100$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$101$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$101$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$102$	−0.498354	−	0.272122i	−0.498354	−	0.272122i
$103$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$103$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$107$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$108$	3.85895	+	0.839462i	3.85895	+	0.839462i
$109$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$109$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.574406	+	0.767317i	0.574406	+	0.767317i	0.989821	−	0.142315i	$-0.0454545\pi$
$113$	0.574406	+	0.767317i	0.574406	+	0.767317i	−0.415415	+	0.909632i	$0.636364\pi$
$114$	0.913069	+	1.05374i	0.913069	+	1.05374i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.50013	−	0.559521i	1.50013	−	0.559521i
$119$		0			0
$120$		0			0
$121$	−1.51255	+	1.74557i	−1.51255	+	1.74557i
$122$		0			0
$123$		−	2.82122i		−	2.82122i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$127$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$128$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$129$	−1.80700	+	1.56577i	−1.80700	+	1.56577i
$130$		0			0
$131$	−0.368991	+	1.25667i	−0.368991	+	1.25667i	0.540641	+	0.841254i	$0.318182\pi$
$131$	−0.368991	+	1.25667i	−0.368991	+	1.25667i	−0.909632	+	0.415415i	$0.863636\pi$
$132$	−3.40043	−	1.26830i	−3.40043	−	1.26830i
$133$		0			0
$134$	0.153882	+	1.07028i	0.153882	+	1.07028i
$135$		0			0
$136$	−0.0801894	+	0.273100i	−0.0801894	+	0.273100i
$137$	1.40524	−	0.767317i	1.40524	−	0.767317i	0.415415	−	0.909632i	$-0.363636\pi$
$137$	1.40524	−	0.767317i	1.40524	−	0.767317i	0.989821	+	0.142315i	$0.0454545\pi$
$138$		0			0
$139$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	−0.841254	−	0.540641i	$-0.818182\pi$
$139$	−0.698939	+	0.449181i	−0.698939	+	0.449181i	0.142315	+	0.989821i	$0.454545\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$		−	2.97964i		−	2.97964i
$145$		0			0
$146$	−0.989821	+	1.14231i	−0.989821	+	1.14231i
$147$	0.424047	+	1.94931i	0.424047	+	1.94931i
$148$		0			0
$149$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$149$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$150$	−0.142315	−	1.98982i	−0.142315	−	1.98982i
$151$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$151$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$152$	0.418852	−	0.559521i	0.418852	−	0.559521i
$153$	−0.555384	−	0.640947i	−0.555384	−	0.640947i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$157$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	4.12099	+	2.64840i	4.12099	+	2.64840i
$163$	0.114220	−	0.0855040i	0.114220	−	0.0855040i	−0.540641	−	0.841254i	$-0.681818\pi$
$163$	0.114220	−	0.0855040i	0.114220	−	0.0855040i	0.654861	+	0.755750i	$0.272727\pi$
$164$	−1.38189	+	0.300613i	−1.38189	+	0.300613i
$165$		0			0
$166$	−0.677760	+	0.677760i	−0.677760	+	0.677760i
$167$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$167$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$168$		0			0
$169$	0.540641	+	0.841254i	0.540641	+	0.841254i
$170$		0			0
$171$	0.727779	+	1.95125i	0.727779	+	1.95125i
$172$	0.959493	+	0.718267i	0.959493	+	0.718267i
$173$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$173$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$174$		0			0
$175$		0			0
$176$	−0.258908	+	1.80075i	−0.258908	+	1.80075i
$177$	3.19401			3.19401
$178$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$179$	1.68251			1.68251			0.841254	−	0.540641i	$-0.181818\pi$
$179$	1.68251			1.68251			0.841254	+	0.540641i	$0.181818\pi$
$180$		0			0
$181$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$181$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.279953	+	0.435615i	0.279953	+	0.435615i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$191$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$192$	−1.94931	+	0.424047i	−1.94931	+	0.424047i
$193$	−0.340335	+	0.254771i	−0.340335	+	0.254771i	−0.755750	−	0.654861i	$-0.772727\pi$
$193$	−0.340335	+	0.254771i	−0.340335	+	0.254771i	0.415415	+	0.909632i	$0.363636\pi$
$194$	−1.41542	−	0.909632i	−1.41542	−	0.909632i
$195$		0			0
$196$	0.909632	−	0.415415i	0.909632	−	0.415415i
$197$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$197$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$198$	−4.09673	−	3.54984i	−4.09673	−	3.54984i
$199$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$199$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$200$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$201$	−0.458515	+	2.10776i	−0.458515	+	2.10776i
$202$		0			0
$203$		0			0
$204$	−0.340275	+	0.454554i	−0.340275	+	0.454554i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.270284	−	1.24248i	−0.270284	−	1.24248i
$210$		0			0
$211$	−1.19550	−	0.0855040i	−1.19550	−	0.0855040i	−0.540641	−	0.841254i	$-0.681818\pi$
$211$	−1.19550	−	0.0855040i	−1.19550	−	0.0855040i	−0.654861	+	0.755750i	$0.727273\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$	1.38010	−	3.70020i	1.38010	−	3.70020i
$217$		0			0
$218$		0			0
$219$	−2.64646	+	1.44508i	−2.64646	+	1.44508i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$223$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$224$		0			0
$225$	0.839462	−	2.85895i	0.839462	−	2.85895i
$226$	0.841254	−	0.459359i	0.841254	−	0.459359i
$227$	−1.14231	+	0.989821i	−1.14231	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$227$	−1.14231	+	0.989821i	−1.14231	+	0.989821i	−1.00000			$\pi$
$228$	1.17296	−	0.753813i	1.17296	−	0.753813i
$229$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$229$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			1.91899i			1.91899i	0.281733	+	0.959493i	$0.409091\pi$
$233$			1.91899i			1.91899i	−0.281733	+	0.959493i	$0.590909\pi$
$234$		0			0
$235$		0			0
$236$	−0.340335	−	1.56449i	−0.340335	−	1.56449i
$237$		0			0
$238$		0			0
$239$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$239$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$240$		0			0
$241$	1.05195	−	1.40524i	1.05195	−	1.40524i	0.142315	−	0.989821i	$-0.454545\pi$
$241$	1.05195	−	1.40524i	1.05195	−	1.40524i	0.909632	−	0.415415i	$-0.136364\pi$
$242$	1.51255	+	1.74557i	1.51255	+	1.74557i
$243$	3.48965	+	4.66163i	3.48965	+	4.66163i
$244$		0			0
$245$		0			0
$246$	−2.79250	−	0.401502i	−2.79250	−	0.401502i
$247$		0			0
$248$		0			0
$249$	−1.73932	+	0.794320i	−1.73932	+	0.794320i
$250$		0			0
$251$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.959493	−	0.281733i	$-0.909091\pi$
$251$	−1.61435	−	1.03748i	−1.61435	−	1.03748i	−0.654861	−	0.755750i	$-0.727273\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.415415	+	0.909632i	0.415415	+	0.909632i
$257$	0.449181	−	0.698939i	0.449181	−	0.698939i	−0.540641	−	0.841254i	$-0.681818\pi$
$257$	0.449181	−	0.698939i	0.449181	−	0.698939i	0.989821	+	0.142315i	$0.0454545\pi$
$258$	1.29267	+	2.01144i	1.29267	+	2.01144i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.19136	+	0.544078i	1.19136	+	0.544078i
$263$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$263$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$264$	−1.73932	+	3.18532i	−1.73932	+	3.18532i
$265$		0			0
$266$		0			0
$267$	−0.697148	−	1.86912i	−0.697148	−	1.86912i
$268$	1.08128			1.08128
$269$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$269$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$270$		0			0
$271$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$271$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$272$	0.258908	+	0.118239i	0.258908	+	0.118239i
$273$		0			0
$274$	−0.559521	−	1.50013i	−0.559521	−	1.50013i
$275$	−0.755750	+	1.65486i	−0.755750	+	1.65486i
$276$		0			0
$277$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$277$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$278$	0.345139	+	0.755750i	0.345139	+	0.755750i
$279$		0			0
$280$		0			0
$281$	−1.83107	+	0.398326i	−1.83107	+	0.398326i	−0.989821	−	0.142315i	$-0.954545\pi$
$281$	−1.83107	+	0.398326i	−1.83107	+	0.398326i	−0.841254	+	0.540641i	$0.818182\pi$
$282$		0			0
$283$	−0.474017	−	0.304632i	−0.474017	−	0.304632i	0.281733	−	0.959493i	$-0.409091\pi$
$283$	−0.474017	−	0.304632i	−0.474017	−	0.304632i	−0.755750	+	0.654861i	$0.772727\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.94931	−	0.424047i	−2.94931	−	0.424047i
$289$	−0.881761	+	0.258908i	−0.881761	+	0.258908i
$290$		0			0
$291$	−2.01144	−	2.68697i	−2.01144	−	2.68697i
$292$	0.989821	+	1.14231i	0.989821	+	1.14231i
$293$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$293$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$294$	1.98982	−	0.142315i	1.98982	−	0.142315i
$295$		0			0
$296$		0			0
$297$	−3.44323	−	6.30580i	−3.44323	−	6.30580i
$298$		0			0
$299$		0			0
$300$	−1.98982	−	0.142315i	−1.98982	−	0.142315i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.494217	−	0.494217i	−0.494217	−	0.494217i
$305$		0			0
$306$	−0.713463	+	0.458515i	−0.713463	+	0.458515i
$307$	1.45027	−	1.25667i	1.45027	−	1.25667i	0.540641	−	0.841254i	$-0.318182\pi$
$307$	1.45027	−	1.25667i	1.45027	−	1.25667i	0.909632	−	0.415415i	$-0.136364\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$311$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$312$		0			0
$313$	−0.398326	−	0.148568i	−0.398326	−	0.148568i	0.142315	−	0.989821i	$-0.454545\pi$
$313$	−0.398326	−	0.148568i	−0.398326	−	0.148568i	−0.540641	+	0.841254i	$0.681818\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$317$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.198429	−	0.0141919i	−0.198429	−	0.0141919i
$324$	3.20792	−	3.70214i	3.20792	−	3.70214i
$325$		0			0
$326$	−0.0683785	−	0.125226i	−0.0683785	−	0.125226i
$327$		0			0
$328$	0.100889	+	1.41061i	0.100889	+	1.41061i
$329$		0			0
$330$		0			0
$331$	0.544078	+	0.627899i	0.544078	+	0.627899i	0.959493	−	0.281733i	$-0.0909091\pi$
$331$	0.544078	+	0.627899i	0.544078	+	0.627899i	−0.415415	+	0.909632i	$0.636364\pi$
$332$	0.574406	+	0.767317i	0.574406	+	0.767317i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.83107	−	0.398326i	−1.83107	−	0.398326i	−0.841254	−	0.540641i	$-0.818182\pi$
$337$	−1.83107	−	0.398326i	−1.83107	−	0.398326i	−0.989821	+	0.142315i	$0.954545\pi$
$338$	0.909632	−	0.415415i	0.909632	−	0.415415i
$339$	1.89265	−	0.272122i	1.89265	−	0.272122i
$340$		0			0
$341$		0			0
$342$	2.03496	−	0.442679i	2.03496	−	0.442679i
$343$		0			0
$344$	0.847507	−	0.847507i	0.847507	−	0.847507i
$345$		0			0
$346$		0			0
$347$	0.304632	+	0.474017i	0.304632	+	0.474017i	0.959493	−	0.281733i	$-0.0909091\pi$
$347$	0.304632	+	0.474017i	0.304632	+	0.474017i	−0.654861	+	0.755750i	$0.727273\pi$
$348$		0			0
$349$		0			0		−0.349464	−	0.936950i	$-0.613636\pi$
$349$		0			0		0.349464	+	0.936950i	$0.386364\pi$
$350$		0			0
$351$		0			0
$352$	1.74557	+	0.512546i	1.74557	+	0.512546i
$353$	0.203743	−	0.373128i	0.203743	−	0.373128i	−0.755750	−	0.654861i	$-0.772727\pi$
$353$	0.203743	−	0.373128i	0.203743	−	0.373128i	0.959493	+	0.281733i	$0.0909091\pi$
$354$	0.454554	−	3.16150i	0.454554	−	3.16150i
$355$		0			0
$356$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$357$		0			0
$358$	0.239446	−	1.66538i	0.239446	−	1.66538i
$359$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$359$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$360$		0			0
$361$	−0.465276	−	0.212484i	−0.465276	−	0.212484i
$362$		0			0
$363$	1.61022	+	4.31716i	1.61022	+	4.31716i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$367$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$368$		0			0
$369$	−3.69841	−	2.01948i	−3.69841	−	2.01948i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$373$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$374$	0.471022	−	0.215109i	0.471022	−	0.215109i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.415415	−	1.90963i	0.415415	−	1.90963i		−	1.00000i	$-0.5\pi$
$379$	0.415415	−	1.90963i	0.415415	−	1.90963i	0.415415	−	0.909632i	$-0.363636\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$383$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$384$	0.142315	+	1.98982i	0.142315	+	1.98982i
$385$		0			0
$386$	0.203743	+	0.373128i	0.203743	+	0.373128i
$387$	0.759127	+	3.48965i	0.759127	+	3.48965i
$388$	−1.10181	+	1.27155i	−1.10181	+	1.27155i
$389$		0			0		−0.997452	−	0.0713392i	$-0.977273\pi$
$389$		0			0		0.997452	+	0.0713392i	$0.0227273\pi$
$390$		0			0
$391$		0			0
$392$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$393$	1.84751	+	1.84751i	1.84751	+	1.84751i
$394$		0			0
$395$		0			0
$396$	−4.09673	+	3.54984i	−4.09673	+	3.54984i
$397$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$397$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$398$		0			0
$399$		0			0
$400$	0.142315	+	0.989821i	0.142315	+	0.989821i
$401$	−0.153882	−	1.07028i	−0.153882	−	1.07028i	−0.909632	−	0.415415i	$-0.863636\pi$
$401$	−0.153882	−	1.07028i	−0.153882	−	1.07028i	0.755750	−	0.654861i	$-0.227273\pi$
$402$	2.02105	+	0.753813i	2.02105	+	0.753813i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.401502	+	0.401502i	0.401502	+	0.401502i
$409$	0.474017	+	1.61435i	0.474017	+	1.61435i	0.755750	+	0.654861i	$0.227273\pi$
$409$	0.474017	+	1.61435i	0.474017	+	1.61435i	−0.281733	+	0.959493i	$0.590909\pi$
$410$		0			0
$411$		−	3.19401i		−	3.19401i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.118239	+	1.65320i	0.118239	+	1.65320i
$418$	−1.26830	+	0.0907103i	−1.26830	+	0.0907103i
$419$	−0.254771	+	0.340335i	−0.254771	+	0.340335i	−0.909632	−	0.415415i	$-0.863636\pi$
$419$	−0.254771	+	0.340335i	−0.254771	+	0.340335i	0.654861	+	0.755750i	$0.272727\pi$
$420$		0			0
$421$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$421$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$422$	−0.254771	+	1.17116i	−0.254771	+	1.17116i
$423$		0			0
$424$		0			0
$425$	0.215109	+	0.186393i	0.215109	+	0.186393i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$431$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$432$	−3.46613	−	1.89265i	−3.46613	−	1.89265i
$433$	0.100889	−	0.100889i	0.100889	−	0.100889i	−0.654861	−	0.755750i	$-0.727273\pi$
$433$	0.100889	−	0.100889i	0.100889	−	0.100889i	0.755750	+	0.654861i	$0.227273\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.05374	+	2.82518i	1.05374	+	2.82518i
$439$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$439$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$440$		0			0
$441$	2.85895	+	0.839462i	2.85895	+	0.839462i
$442$		0			0
$443$	−0.0801894	+	0.557730i	−0.0801894	+	0.557730i	0.909632	+	0.415415i	$0.136364\pi$
$443$	−0.0801894	+	0.557730i	−0.0801894	+	0.557730i	−0.989821	+	0.142315i	$0.954545\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.540641	−	0.158746i	−0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$449$	−0.540641	−	0.158746i	−0.540641	−	0.158746i	−0.540641	+	0.841254i	$0.681818\pi$
$450$	−2.71038	−	1.23779i	−2.71038	−	1.23779i
$451$	2.05965	+	1.54184i	2.05965	+	1.54184i
$452$	−0.334961	−	0.898064i	−0.334961	−	0.898064i
$453$		0			0
$454$	0.817178	+	1.27155i	0.817178	+	1.27155i
$455$		0			0
$456$	−0.579211	−	1.26830i	−0.579211	−	1.26830i
$457$	1.38189	−	1.38189i	1.38189	−	1.38189i	0.540641	−	0.841254i	$-0.318182\pi$
$457$	1.38189	−	1.38189i	1.38189	−	1.38189i	0.841254	−	0.540641i	$-0.181818\pi$
$458$		0			0
$459$	−1.09837	+	0.238936i	−1.09837	+	0.238936i
$460$		0			0
$461$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$461$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$462$		0			0
$463$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$463$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$464$		0			0
$465$		0			0
$466$	1.89945	+	0.273100i	1.89945	+	0.273100i
$467$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	−0.415415	−	0.909632i	$-0.636364\pi$
$467$	−0.273100	+	0.0801894i	−0.273100	+	0.0801894i	0.142315	+	0.989821i	$0.454545\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.59700	+	0.114220i	−1.59700	+	0.114220i
$473$	−0.155554	−	2.17493i	−0.155554	−	2.17493i
$474$		0			0
$475$	−0.334961	−	0.613435i	−0.334961	−	0.613435i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		0			0
$482$	−1.24123	−	1.24123i	−1.24123	−	1.24123i
$483$		0			0
$484$	1.94306	−	1.24873i	1.94306	−	1.24873i
$485$		0			0
$486$	5.11081	−	2.79071i	5.11081	−	2.79071i
$487$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$487$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$488$		0			0
$489$	−0.0405070	−	0.281733i	−0.0405070	−	0.281733i
$490$		0			0
$491$	1.75575	+	0.654861i	1.75575	+	0.654861i	1.00000			$0$
$491$	1.75575	+	0.654861i	1.75575	+	0.654861i	0.755750	+	0.654861i	$0.227273\pi$
$492$	−0.794830	+	2.70694i	−0.794830	+	2.70694i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.538704	+	1.83466i	0.538704	+	1.83466i
$499$	−0.125226	+	1.75089i	−0.125226	+	1.75089i	0.415415	+	0.909632i	$0.363636\pi$
$499$	−0.125226	+	1.75089i	−0.125226	+	1.75089i	−0.540641	+	0.841254i	$0.681818\pi$
$500$		0			0
$501$		0			0
$502$	−1.25667	+	1.45027i	−1.25667	+	1.45027i
$503$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$503$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.98982	−	0.142315i	1.98982	−	0.142315i
$508$		0			0
$509$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$509$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$510$		0			0
$511$		0			0
$512$	0.959493	−	0.281733i	0.959493	−	0.281733i
$513$	2.73211	+	0.392818i	2.73211	+	0.392818i
$514$	−0.627899	−	0.544078i	−0.627899	−	0.544078i
$515$		0			0
$516$	2.17493	−	0.993259i	2.17493	−	0.993259i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.05195	+	0.574406i	1.05195	+	0.574406i	0.909632	−	0.415415i	$-0.136364\pi$
$521$	1.05195	+	0.574406i	1.05195	+	0.574406i	0.142315	+	0.989821i	$0.454545\pi$
$522$		0			0
$523$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	−0.909632	−	0.415415i	$-0.863636\pi$
$523$	−0.627899	−	1.37491i	−0.627899	−	1.37491i	0.281733	−	0.959493i	$-0.409091\pi$
$524$	0.708089	−	1.10181i	0.708089	−	1.10181i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	2.90537	+	2.17493i	2.90537	+	2.17493i
$529$	−0.909632	−	0.415415i	−0.909632	−	0.415415i
$530$		0			0
$531$	2.28633	−	4.18710i	2.28633	−	4.18710i
$532$		0			0
$533$		0			0
$534$	−1.94931	+	0.424047i	−1.94931	+	0.424047i
$535$		0			0
$536$	0.153882	−	1.07028i	0.153882	−	1.07028i
$537$	1.60857	−	2.94588i	1.60857	−	2.94588i
$538$		0			0
$539$	−1.65486	−	0.755750i	−1.65486	−	0.755750i
$540$		0			0
$541$		0			0		−0.349464	−	0.936950i	$-0.613636\pi$
$541$		0			0		0.349464	+	0.936950i	$0.386364\pi$
$542$		0			0
$543$		0			0
$544$	0.153882	−	0.239446i	0.153882	−	0.239446i
$545$		0			0
$546$		0			0
$547$	−1.64468	−	0.898064i	−1.64468	−	0.898064i	−0.989821	−	0.142315i	$-0.954545\pi$
$547$	−1.64468	−	0.898064i	−1.64468	−	0.898064i	−0.654861	−	0.755750i	$-0.727273\pi$
$548$	−1.56449	+	0.340335i	−1.56449	+	0.340335i
$549$		0			0
$550$	1.53046	+	0.983568i	1.53046	+	0.983568i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.797176	−	0.234072i	0.797176	−	0.234072i
$557$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$557$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.03036	−	0.0736930i	1.03036	−	0.0736930i
$562$	0.133682	+	1.86912i	0.133682	+	1.86912i
$563$	1.75575	−	0.654861i	1.75575	−	0.654861i	0.755750	−	0.654861i	$-0.227273\pi$
$563$	1.75575	−	0.654861i	1.75575	−	0.654861i	1.00000			$0$
$564$		0			0
$565$		0			0
$566$	−0.368991	+	0.425839i	−0.368991	+	0.425839i
$567$		0			0
$568$		0			0
$569$	0.139418	−	1.94931i	0.139418	−	1.94931i	−0.142315	−	0.989821i	$-0.545455\pi$
$569$	0.139418	−	1.94931i	0.139418	−	1.94931i	0.281733	−	0.959493i	$-0.409091\pi$
$570$		0			0
$571$	−1.00000	−	1.00000i	−1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$571$	−1.00000	−	1.00000i	−1.00000	−	1.00000i	−1.00000			$\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.839462	+	2.85895i	−0.839462	+	2.85895i
$577$	0.654861	+	0.244250i	0.654861	+	0.244250i	0.654861	−	0.755750i	$-0.272727\pi$
$577$	0.654861	+	0.244250i	0.654861	+	0.244250i			1.00000i	$0.5\pi$
$578$	0.130785	+	0.909632i	0.130785	+	0.909632i
$579$	0.120696	+	0.839462i	0.120696	+	0.839462i
$580$		0			0
$581$		0			0
$582$	−2.94588	+	1.60857i	−2.94588	+	1.60857i
$583$		0			0
$584$	1.27155	−	0.817178i	1.27155	−	0.817178i
$585$		0			0
$586$		0			0
$587$	−0.234072	−	0.797176i	−0.234072	−	0.797176i	−0.989821	−	0.142315i	$-0.954545\pi$
$587$	−0.234072	−	0.797176i	−0.234072	−	0.797176i	0.755750	−	0.654861i	$-0.227273\pi$
$588$	0.142315	−	1.98982i	0.142315	−	1.98982i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.936593	−	1.71524i	−0.936593	−	1.71524i	−0.654861	−	0.755750i	$-0.727273\pi$
$593$	−0.936593	−	1.71524i	−0.936593	−	1.71524i	−0.281733	−	0.959493i	$-0.590909\pi$
$594$	−6.73164	+	2.51077i	−6.73164	+	2.51077i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$599$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$600$	−0.424047	+	1.94931i	−0.424047	+	1.94931i
$601$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.415415	−	0.909632i	$-0.363636\pi$
$601$	1.25667	−	0.368991i	1.25667	−	0.368991i	0.841254	+	0.540641i	$0.181818\pi$
$602$		0			0
$603$	2.43490	+	2.10985i	2.43490	+	2.10985i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$607$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$608$	−0.559521	+	0.418852i	−0.559521	+	0.418852i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.352311	+	0.771454i	0.352311	+	0.771454i
$613$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$613$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$614$	−1.03748	−	1.61435i	−1.03748	−	1.61435i
$615$		0			0
$616$		0			0
$617$	−0.114220	−	0.0855040i	−0.114220	−	0.0855040i	0.540641	−	0.841254i	$-0.318182\pi$
$617$	−0.114220	−	0.0855040i	−0.114220	−	0.0855040i	−0.654861	+	0.755750i	$0.727273\pi$
$618$		0			0
$619$	−1.25667	−	0.368991i	−1.25667	−	0.368991i	−0.415415	−	0.909632i	$-0.636364\pi$
$619$	−1.25667	−	0.368991i	−1.25667	−	0.368991i	−0.841254	+	0.540641i	$0.818182\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$626$	−0.203743	+	0.373128i	−0.203743	+	0.373128i
$627$	−2.43384	−	0.714640i	−2.43384	−	0.714640i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$631$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$632$		0			0
$633$	−1.29267	+	2.01144i	−1.29267	+	2.01144i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.19136	+	0.544078i	−1.19136	+	0.544078i	−0.909632	−	0.415415i	$-0.863636\pi$
$641$	−1.19136	+	0.544078i	−1.19136	+	0.544078i	−0.281733	+	0.959493i	$0.590909\pi$
$642$		0			0
$643$	1.27155	+	1.10181i	1.27155	+	1.10181i	0.989821	+	0.142315i	$0.0454545\pi$
$643$	1.27155	+	1.10181i	1.27155	+	1.10181i	0.281733	+	0.959493i	$0.409091\pi$
$644$		0			0
$645$		0			0
$646$	−0.0422868	+	0.194389i	−0.0422868	+	0.194389i
$647$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$647$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$648$	−3.20792	−	3.70214i	−3.20792	−	3.70214i
$649$	−1.74557	+	2.33181i	−1.74557	+	2.33181i
$650$		0			0
$651$		0			0
$652$	−0.133682	+	0.0498610i	−0.133682	+	0.0498610i
$653$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$653$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$654$		0			0
$655$		0			0
$656$	1.41061	+	0.100889i	1.41061	+	0.100889i
$657$			4.50373i			4.50373i
$658$		0			0
$659$	−0.368991	−	1.25667i	−0.368991	−	1.25667i	−0.909632	−	0.415415i	$-0.863636\pi$
$659$	−0.368991	−	1.25667i	−0.368991	−	1.25667i	0.540641	−	0.841254i	$-0.318182\pi$
$660$		0			0
$661$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$661$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$662$	0.698939	−	0.449181i	0.698939	−	0.449181i
$663$		0			0
$664$	0.841254	−	0.459359i	0.841254	−	0.459359i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$673$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$674$	−0.654861	+	1.75575i	−0.654861	+	1.75575i
$675$	−2.79250	−	2.79250i	−2.79250	−	2.79250i
$676$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$677$		0			0		0.0713392	−	0.997452i	$-0.477273\pi$
$677$		0			0		−0.0713392	+	0.997452i	$0.522727\pi$
$678$		−	1.91211i		−	1.91211i
$679$		0			0
$680$		0			0
$681$	0.640947	+	2.94639i	0.640947	+	2.94639i
$682$		0			0
$683$	0.133682	−	0.0498610i	0.133682	−	0.0498610i	−0.281733	−	0.959493i	$-0.590909\pi$
$683$	0.133682	−	0.0498610i	0.133682	−	0.0498610i	0.415415	+	0.909632i	$0.363636\pi$
$684$	−0.148568	−	2.07725i	−0.148568	−	2.07725i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.718267	−	0.959493i	−0.718267	−	0.959493i
$689$		0			0
$690$		0			0
$691$	1.89945	+	0.273100i	1.89945	+	0.273100i	0.989821	−	0.142315i	$-0.0454545\pi$
$691$	1.89945	+	0.273100i	1.89945	+	0.273100i	0.909632	+	0.415415i	$0.136364\pi$
$692$		0			0
$693$		0			0
$694$	0.512546	−	0.234072i	0.512546	−	0.234072i
$695$		0			0
$696$		0			0
$697$	0.322240	−	0.241226i	0.322240	−	0.241226i
$698$		0			0
$699$	3.35992	+	1.83466i	3.35992	+	1.83466i
$700$		0			0
$701$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$701$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$702$		0			0
$703$		0			0
$704$	0.755750	−	1.65486i	0.755750	−	1.65486i
$705$		0			0
$706$	−0.340335	−	0.254771i	−0.340335	−	0.254771i
$707$		0			0
$708$	−3.06463	−	0.899856i	−3.06463	−	0.899856i
$709$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$709$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$710$		0			0
$711$		0			0
$712$	0.415415	+	0.909632i	0.415415	+	0.909632i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$717$		0			0
$718$		0			0
$719$		0			0		−0.349464	−	0.936950i	$-0.613636\pi$
$719$		0			0		0.349464	+	0.936950i	$0.386364\pi$
$720$		0			0
$721$		0			0
$722$	−0.276537	+	0.430300i	−0.276537	+	0.430300i
$723$	−1.45469	−	3.18532i	−1.45469	−	3.18532i
$724$		0			0
$725$		0			0
$726$	4.50237	−	0.979431i	4.50237	−	0.979431i
$727$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$727$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$728$		0			0
$729$	6.64951	−	0.956056i	6.64951	−	0.956056i
$730$		0			0
$731$	−0.333348	−	0.0725155i	−0.333348	−	0.0725155i
$732$		0			0
$733$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$733$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.28820	−	1.48666i	−1.28820	−	1.48666i
$738$	−2.52527	+	3.37336i	−2.52527	+	3.37336i
$739$	0.424047	−	0.0303285i	0.424047	−	0.0303285i	0.142315	−	0.989821i	$-0.454545\pi$
$739$	0.424047	−	0.0303285i	0.424047	−	0.0303285i	0.281733	+	0.959493i	$0.409091\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$743$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.203743	+	2.84870i	−0.203743	+	2.84870i
$748$	−0.145886	−	0.496841i	−0.145886	−	0.496841i
$749$		0			0
$750$		0			0
$751$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$751$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$752$		0			0
$753$	−3.35992	+	1.83466i	−3.35992	+	1.83466i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$757$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$758$	−1.83107	−	0.682956i	−1.83107	−	0.682956i
$759$		0			0
$760$		0			0
$761$	−1.37491	+	1.19136i	−1.37491	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$761$	−1.37491	+	1.19136i	−1.37491	+	1.19136i	−0.959493	+	0.281733i	$0.909091\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.98982	+	0.142315i	1.98982	+	0.142315i
$769$	0.368991	−	0.425839i	0.368991	−	0.425839i	−0.540641	−	0.841254i	$-0.681818\pi$
$769$	0.368991	−	0.425839i	0.368991	−	0.425839i	0.909632	+	0.415415i	$0.136364\pi$
$770$		0			0
$771$	−0.794320	−	1.45469i	−0.794320	−	1.45469i
$772$	0.398326	−	0.148568i	0.398326	−	0.148568i
$773$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$773$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$774$	3.56217	−	0.254771i	3.56217	−	0.254771i
$775$		0			0
$776$	1.10181	+	1.27155i	1.10181	+	1.27155i
$777$		0			0
$778$		0			0
$779$	−0.948395	+	0.278474i	−0.948395	+	0.278474i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.989821	+	0.142315i	−0.989821	+	0.142315i
$785$		0			0
$786$	2.09163	−	1.56577i	2.09163	−	1.56577i
$787$	1.71524	−	0.373128i	1.71524	−	0.373128i	0.755750	−	0.654861i	$-0.227273\pi$
$787$	1.71524	−	0.373128i	1.71524	−	0.373128i	0.959493	+	0.281733i	$0.0909091\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	2.93068	+	4.56023i	2.93068	+	4.56023i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$797$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$798$		0			0
$799$		0			0
$800$	1.00000			1.00000
$801$	−2.94931	−	0.424047i	−2.94931	−	0.424047i
$802$	−1.08128			−1.08128
$803$	0.391340	−	2.72183i	0.391340	−	2.72183i
$804$	1.03377	−	1.89320i	1.03377	−	1.89320i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$809$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$810$		0			0
$811$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$811$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.454554	−	0.340275i	0.454554	−	0.340275i
$817$	0.704722	+	0.452897i	0.704722	+	0.452897i
$818$	1.66538	−	0.239446i	1.66538	−	0.239446i
$819$		0			0
$820$		0			0
$821$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$821$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$822$	−3.16150	−	0.454554i	−3.16150	−	0.454554i
$823$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$823$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$824$		0			0
$825$	2.17493	+	2.90537i	2.17493	+	2.90537i
$826$		0			0
$827$	1.05195	−	1.40524i	1.05195	−	1.40524i	0.142315	−	0.989821i	$-0.454545\pi$
$827$	1.05195	−	1.40524i	1.05195	−	1.40524i	0.909632	−	0.415415i	$-0.136364\pi$
$828$		0			0
$829$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$829$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.186393	+	0.215109i	−0.186393	+	0.215109i
$834$	1.65320	+	0.118239i	1.65320	+	0.118239i
$835$		0			0
$836$	−0.0907103	+	1.26830i	−0.0907103	+	1.26830i
$837$		0			0
$838$	0.300613	+	0.300613i	0.300613	+	0.300613i
$839$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$839$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$840$		0			0
$841$	0.755750	−	0.654861i	0.755750	−	0.654861i
$842$		0			0
$843$	−1.05319	+	3.58682i	−1.05319	+	3.58682i
$844$	1.12299	+	0.418852i	1.12299	+	0.418852i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.986563	+	0.538704i	−0.986563	+	0.538704i
$850$	0.215109	−	0.186393i	0.215109	−	0.186393i
$851$		0			0
$852$		0			0
$853$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$853$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.697148	−	0.0498610i	−0.697148	−	0.0498610i	−0.281733	−	0.959493i	$-0.590909\pi$
$857$	−0.697148	−	0.0498610i	−0.697148	−	0.0498610i	−0.415415	+	0.909632i	$0.636364\pi$
$858$		0			0
$859$	−0.203743	−	0.936593i	−0.203743	−	0.936593i	−0.959493	−	0.281733i	$-0.909091\pi$
$859$	−0.203743	−	0.936593i	−0.203743	−	0.936593i	0.755750	−	0.654861i	$-0.227273\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$863$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$864$	−2.36667	+	3.16150i	−2.36667	+	3.16150i
$865$		0			0
$866$	−0.0855040	−	0.114220i	−0.0855040	−	0.114220i
$867$	−0.389694	+	1.79139i	−0.389694	+	1.79139i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−4.96224	+	0.713463i	−4.96224	+	0.713463i
$874$		0			0
$875$		0			0
$876$	2.94639	−	0.640947i	2.94639	−	0.640947i
$877$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$877$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.07028	−	1.66538i	−1.07028	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$881$	−1.07028	−	1.66538i	−1.07028	−	1.66538i	−0.415415	−	0.909632i	$-0.636364\pi$
$882$	1.23779	−	2.71038i	1.23779	−	2.71038i
$883$	−0.613435	−	1.64468i	−0.613435	−	1.64468i	−0.755750	−	0.654861i	$-0.772727\pi$
$883$	−0.613435	−	1.64468i	−0.613435	−	1.64468i	0.142315	−	0.989821i	$-0.454545\pi$
$884$		0			0
$885$		0			0
$886$	0.540641	+	0.158746i	0.540641	+	0.158746i
$887$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$887$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−8.91190			−8.91190
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.234072	+	0.512546i	−0.234072	+	0.512546i
$899$		0			0
$900$	−1.61092	+	2.50664i	−1.61092	+	2.50664i
$901$		0			0
$902$	1.81926	−	1.81926i	1.81926	−	1.81926i
$903$		0			0
$904$	−0.936593	+	0.203743i	−0.936593	+	0.203743i
$905$		0			0
$906$		0			0
$907$	−1.95949	+	0.281733i	−1.95949	+	0.281733i	−0.959493	+	0.281733i	$0.909091\pi$
$907$	−1.95949	+	0.281733i	−1.95949	+	0.281733i	−1.00000			$\pi$
$908$	1.37491	−	0.627899i	1.37491	−	0.627899i
$909$		0			0
$910$		0			0
$911$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$911$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$912$	−1.33782	+	0.392818i	−1.33782	+	0.392818i
$913$	0.370663	−	1.70391i	0.370663	−	1.70391i
$914$	−1.17116	−	1.56449i	−1.17116	−	1.56449i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.0801894	+	1.12119i	0.0801894	+	1.12119i
$919$		0			0		0.936950	−	0.349464i	$-0.113636\pi$
$919$		0			0		−0.936950	+	0.349464i	$0.886364\pi$
$920$		0			0
$921$	−0.813741	−	3.74071i	−0.813741	−	3.74071i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.61435	−	1.03748i	1.61435	−	1.03748i	0.654861	−	0.755750i	$-0.272727\pi$
$929$	1.61435	−	1.03748i	1.61435	−	1.03748i	0.959493	−	0.281733i	$-0.0909091\pi$
$930$		0			0
$931$	0.613435	−	0.334961i	0.613435	−	0.334961i
$932$	0.540641	−	1.84125i	0.540641	−	1.84125i
$933$		0			0
$934$	0.0405070	+	0.281733i	0.0405070	+	0.281733i
$935$		0			0
$936$		0			0
$937$	−0.557730	+	1.89945i	−0.557730	+	1.89945i	−0.142315	+	0.989821i	$0.545455\pi$
$937$	−0.557730	+	1.89945i	−0.557730	+	1.89945i	−0.415415	+	0.909632i	$0.636364\pi$
$938$		0			0
$939$	−0.640947	+	0.555384i	−0.640947	+	0.555384i
$940$		0			0
$941$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$941$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$942$		0			0
$943$		0			0
$944$	−0.114220	+	1.59700i	−0.114220	+	1.59700i
$945$		0			0
$946$	−2.17493	−	0.155554i	−2.17493	−	0.155554i
$947$	0.708089	−	0.817178i	0.708089	−	0.817178i	−0.281733	−	0.959493i	$-0.590909\pi$
$947$	0.708089	−	0.817178i	0.708089	−	0.817178i	0.989821	+	0.142315i	$0.0454545\pi$
$948$		0			0
$949$		0			0
$950$	−0.654861	+	0.244250i	−0.654861	+	0.244250i
$951$		0			0
$952$		0			0
$953$	0.0855040	−	0.114220i	0.0855040	−	0.114220i	−0.755750	−	0.654861i	$-0.772727\pi$
$953$	0.0855040	−	0.114220i	0.0855040	−	0.114220i	0.841254	+	0.540641i	$0.181818\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.909632	+	0.415415i	−0.909632	+	0.415415i
$962$		0			0
$963$		0			0
$964$	−1.40524	+	1.05195i	−1.40524	+	1.05195i
$965$		0			0
$966$		0			0
$967$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$967$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$968$	−0.959493	−	2.10100i	−0.959493	−	2.10100i
$969$	−0.214558	+	0.333858i	−0.214558	+	0.333858i
$970$		0			0
$971$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$971$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$972$	−2.03496	−	5.45595i	−2.03496	−	5.45595i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	0.540641	+	0.841254i	$0.318182\pi$
$977$	−0.215109	+	1.49611i	−0.215109	+	1.49611i	−0.755750	+	0.654861i	$0.772727\pi$
$978$	−0.284630			−0.284630
$979$	1.74557	+	0.512546i	1.74557	+	0.512546i
$980$		0			0
$981$		0			0
$982$	0.898064	−	1.64468i	0.898064	−	1.64468i
$983$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$983$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$984$	2.56627	+	1.17198i	2.56627	+	1.17198i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$991$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$992$		0			0
$993$	1.61955	−	0.352311i	1.61955	−	0.352311i
$994$		0			0
$995$		0			0
$996$	1.89265	−	0.272122i	1.89265	−	0.272122i
$997$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$997$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$998$	1.71524	+	0.373128i	1.71524	+	0.373128i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	712.1.y.a.603.1	yes	20
4.3	odd	2		2848.1.cc.a.2383.1		20
8.3	odd	2	CM	712.1.y.a.603.1	yes	20
8.5	even	2		2848.1.cc.a.2383.1		20
89.40	even	44	inner	712.1.y.a.307.1	✓	20
356.307	odd	44		2848.1.cc.a.2799.1		20
712.307	odd	44	inner	712.1.y.a.307.1	✓	20
712.485	even	44		2848.1.cc.a.2799.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
712.1.y.a.307.1	✓	20	89.40	even	44	inner
712.1.y.a.307.1	✓	20	712.307	odd	44	inner
712.1.y.a.603.1	yes	20	1.1	even	1	trivial
712.1.y.a.603.1	yes	20	8.3	odd	2	CM
2848.1.cc.a.2383.1		20	4.3	odd	2
2848.1.cc.a.2383.1		20	8.5	even	2
2848.1.cc.a.2799.1		20	356.307	odd	44
2848.1.cc.a.2799.1		20	712.485	even	44

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:	\( N \)	\(=\)	\( 712 = 2^{3} \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	712.y (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(0.956056 - 1.75089i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.59700 - 1.19550i) q^{6} +(-0.415415 + 0.909632i) q^{8} +(-1.61092 - 2.50664i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(0.956056 - 1.75089i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-1.59700 - 1.19550i) q^{6} +(-0.415415 + 0.909632i) q^{8} +(-1.61092 - 2.50664i) q^{9} +(0.755750 + 1.65486i) q^{11} +(-1.41061 + 1.41061i) q^{12} +(0.841254 + 0.540641i) q^{16} +(0.281733 - 0.0405070i) q^{17} +(-2.71038 + 1.23779i) q^{18} +(-0.682956 - 0.148568i) q^{19} +(1.74557 - 0.512546i) q^{22} +(1.19550 + 1.59700i) q^{24} +(0.654861 + 0.755750i) q^{25} +(-3.93914 + 0.281733i) q^{27} +(0.654861 - 0.755750i) q^{32} +(3.62001 + 0.258908i) q^{33} -0.284630i q^{34} +(0.839462 + 2.85895i) q^{36} +(-0.244250 + 0.654861i) q^{38} +(1.24123 - 0.677760i) q^{41} +(-1.12299 - 0.418852i) q^{43} +(-0.258908 - 1.80075i) q^{44} +(1.75089 - 0.956056i) q^{48} +(-0.755750 + 0.654861i) q^{49} +(0.841254 - 0.540641i) q^{50} +(0.198429 - 0.532008i) q^{51} +(-0.281733 + 3.93914i) q^{54} +(-0.913069 + 1.05374i) q^{57} +(0.767317 + 1.40524i) q^{59} +(-0.654861 - 0.755750i) q^{64} +(0.771454 - 3.54632i) q^{66} +(-1.03748 + 0.304632i) q^{67} +(-0.281733 - 0.0405070i) q^{68} +(2.94931 - 0.424047i) q^{72} +(-1.27155 - 0.817178i) q^{73} +(1.94931 - 0.424047i) q^{75} +(0.613435 + 0.334961i) q^{76} +(-2.03496 + 4.45595i) q^{81} +(-0.494217 - 1.32505i) q^{82} +(-0.767317 - 0.574406i) q^{83} +(-0.574406 + 1.05195i) q^{86} -1.81926 q^{88} +(0.654861 - 0.755750i) q^{89} +(-0.697148 - 1.86912i) q^{96} +(0.698939 - 1.53046i) q^{97} +(0.540641 + 0.841254i) q^{98} +(2.93068 - 4.56023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^8	\( 20 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{6} + 2 q^{8} - 2 q^{12} - 2 q^{16} - 2 q^{19} + 2 q^{24} + 2 q^{25} - 22 q^{27} + 2 q^{32} - 20 q^{38} + 2 q^{41} + 2 q^{43} - 2 q^{48} - 2 q^{50} + 4 q^{51} - 4 q^{57} - 2 q^{59} - 2 q^{64} + 22 q^{72} + 2 q^{75} - 2 q^{76} - 2 q^{81} - 2 q^{82} + 2 q^{83} - 2 q^{86} + 2 q^{89} + 2 q^{96} - 4 q^{97}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 + 2 * q^6 + 2 * q^8 - 2 * q^12 - 2 * q^16 - 2 * q^19 + 2 * q^24 + 2 * q^25 - 22 * q^27 + 2 * q^32 - 20 * q^38 + 2 * q^41 + 2 * q^43 - 2 * q^48 - 2 * q^50 + 4 * q^51 - 4 * q^57 - 2 * q^59 - 2 * q^64 + 22 * q^72 + 2 * q^75 - 2 * q^76 - 2 * q^81 - 2 * q^82 + 2 * q^83 - 2 * q^86 + 2 * q^89 + 2 * q^96 - 4 * q^97

Introduction

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