LMFDB - Embedded newform 979.1.v.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [979,1,Mod(10,979)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(979, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([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("979.10");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 979 = 11 \cdot 89 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	979.v (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:	$0.488584647368$
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:	$\Z[a_1, \ldots, a_{4}]$
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			10.1
Root			$-0.755750 + 0.654861i$ of defining polynomial
Character	$\chi$	$=$	979.10
Dual form			979.1.v.a.98.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.0101786i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.368991 - 1.25667i) q^{5} +(-0.969672 + 0.139418i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.0101786i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.368991 - 1.25667i) q^{5} +(-0.969672 + 0.139418i) q^{9} +(-0.959493 - 0.281733i) q^{11} +(-0.100889 - 0.100889i) q^{12} +(-0.0653040 - 0.175087i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.708089 + 1.10181i) q^{20} +(-0.574406 + 0.767317i) q^{23} +(-0.601808 + 0.386758i) q^{25} +(-0.275997 + 0.0600395i) q^{27} +(-1.12299 - 1.50013i) q^{31} +(-0.139418 - 0.0303285i) q^{33} +(0.740365 + 0.641530i) q^{36} +(1.41061 - 1.41061i) q^{37} +(0.415415 + 0.909632i) q^{44} +(0.533002 + 1.16711i) q^{45} +(0.817178 - 0.708089i) q^{47} +(-0.0101786 + 0.142315i) q^{48} +(0.540641 + 0.841254i) q^{49} +(-1.45027 - 1.25667i) q^{53} +1.30972i q^{55} +(-1.19550 - 0.0855040i) q^{59} +(-0.0895567 + 0.164011i) q^{60} +(0.841254 - 0.540641i) q^{64} +(1.19136 - 1.37491i) q^{67} +(-0.0739364 + 0.115047i) q^{69} +(0.234072 - 0.797176i) q^{71} +(-0.0817095 + 0.0611670i) q^{75} +(1.29639 - 0.186393i) q^{80} +(0.901293 - 0.264644i) q^{81} +(0.959493 - 0.281733i) q^{89} +(0.956056 - 0.0683785i) q^{92} +(-0.175087 - 0.202061i) q^{93} +(-0.540641 + 0.158746i) q^{97} +(0.969672 + 0.139418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 2 q^{4} - 22 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 2 * q^4 - 22 * q^9	$ 20 q + 2 q^{3} - 2 q^{4} - 22 q^{9} - 2 q^{11} + 2 q^{12} + 4 q^{15} - 2 q^{16} - 2 q^{23} + 6 q^{25} + 2 q^{31} + 2 q^{33} + 2 q^{37} - 2 q^{44} - 4 q^{45} - 20 q^{48} - 2 q^{59} + 4 q^{60} - 2 q^{64} - 6 q^{75} + 20 q^{81} + 2 q^{89} - 2 q^{92} - 4 q^{93} + 22 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 2 * q^4 - 22 * q^9 - 2 * q^11 + 2 * q^12 + 4 * q^15 - 2 * q^16 - 2 * q^23 + 6 * q^25 + 2 * q^31 + 2 * q^33 + 2 * q^37 - 2 * q^44 - 4 * q^45 - 20 * q^48 - 2 * q^59 + 4 * q^60 - 2 * q^64 - 6 * q^75 + 20 * q^81 + 2 * q^89 - 2 * q^92 - 4 * q^93 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/979\mathbb{Z}\right)^\times$.

$n$	$90$	$804$
$\chi(n)$	$-1$	$e\left(\frac{43}{44}\right)$

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			0		0.415415	−	0.909632i	$-0.363636\pi$
$2$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$3$	0.142315	−	0.0101786i	0.142315	−	0.0101786i		−	1.00000i	$-0.5\pi$
$3$	0.142315	−	0.0101786i	0.142315	−	0.0101786i	0.142315	+	0.989821i	$0.454545\pi$
$4$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$5$	−0.368991	−	1.25667i	−0.368991	−	1.25667i	−0.909632	−	0.415415i	$-0.863636\pi$
$5$	−0.368991	−	1.25667i	−0.368991	−	1.25667i	0.540641	−	0.841254i	$-0.318182\pi$
$6$		0			0
$7$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$7$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$8$		0			0
$9$	−0.969672	+	0.139418i	−0.969672	+	0.139418i
$10$		0			0
$11$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$11$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$12$	−0.100889	−	0.100889i	−0.100889	−	0.100889i
$13$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$13$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$14$		0			0
$15$	−0.0653040	−	0.175087i	−0.0653040	−	0.175087i
$16$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$17$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$17$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$18$		0			0
$19$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$19$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$20$	−0.708089	+	1.10181i	−0.708089	+	1.10181i
$21$		0			0
$22$		0			0
$23$	−0.574406	+	0.767317i	−0.574406	+	0.767317i	−0.989821	−	0.142315i	$-0.954545\pi$
$23$	−0.574406	+	0.767317i	−0.574406	+	0.767317i	0.415415	+	0.909632i	$0.363636\pi$
$24$		0			0
$25$	−0.601808	+	0.386758i	−0.601808	+	0.386758i
$26$		0			0
$27$	−0.275997	+	0.0600395i	−0.275997	+	0.0600395i
$28$		0			0
$29$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$29$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$30$		0			0
$31$	−1.12299	−	1.50013i	−1.12299	−	1.50013i	−0.841254	−	0.540641i	$-0.818182\pi$
$31$	−1.12299	−	1.50013i	−1.12299	−	1.50013i	−0.281733	−	0.959493i	$-0.590909\pi$
$32$		0			0
$33$	−0.139418	−	0.0303285i	−0.139418	−	0.0303285i
$34$		0			0
$35$		0			0
$36$	0.740365	+	0.641530i	0.740365	+	0.641530i
$37$	1.41061	−	1.41061i	1.41061	−	1.41061i	0.654861	−	0.755750i	$-0.272727\pi$
$37$	1.41061	−	1.41061i	1.41061	−	1.41061i	0.755750	−	0.654861i	$-0.227273\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		0.0713392	−	0.997452i	$-0.477273\pi$
$41$		0			0		−0.0713392	+	0.997452i	$0.522727\pi$
$42$		0			0
$43$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$43$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$44$	0.415415	+	0.909632i	0.415415	+	0.909632i
$45$	0.533002	+	1.16711i	0.533002	+	1.16711i
$46$		0			0
$47$	0.817178	−	0.708089i	0.817178	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$47$	0.817178	−	0.708089i	0.817178	−	0.708089i	0.959493	+	0.281733i	$0.0909091\pi$
$48$	−0.0101786	+	0.142315i	−0.0101786	+	0.142315i
$49$	0.540641	+	0.841254i	0.540641	+	0.841254i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.45027	−	1.25667i	−1.45027	−	1.25667i	−0.909632	−	0.415415i	$-0.863636\pi$
$53$	−1.45027	−	1.25667i	−1.45027	−	1.25667i	−0.540641	−	0.841254i	$-0.681818\pi$
$54$		0			0
$55$			1.30972i			1.30972i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.19550	−	0.0855040i	−1.19550	−	0.0855040i	−0.540641	−	0.841254i	$-0.681818\pi$
$59$	−1.19550	−	0.0855040i	−1.19550	−	0.0855040i	−0.654861	+	0.755750i	$0.727273\pi$
$60$	−0.0895567	+	0.164011i	−0.0895567	+	0.164011i
$61$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$61$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$62$		0			0
$63$		0			0
$64$	0.841254	−	0.540641i	0.841254	−	0.540641i
$65$		0			0
$66$		0			0
$67$	1.19136	−	1.37491i	1.19136	−	1.37491i	0.281733	−	0.959493i	$-0.409091\pi$
$67$	1.19136	−	1.37491i	1.19136	−	1.37491i	0.909632	−	0.415415i	$-0.136364\pi$
$68$		0			0
$69$	−0.0739364	+	0.115047i	−0.0739364	+	0.115047i
$70$		0			0
$71$	0.234072	−	0.797176i	0.234072	−	0.797176i	−0.755750	−	0.654861i	$-0.772727\pi$
$71$	0.234072	−	0.797176i	0.234072	−	0.797176i	0.989821	−	0.142315i	$-0.0454545\pi$
$72$		0			0
$73$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$73$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$74$		0			0
$75$	−0.0817095	+	0.0611670i	−0.0817095	+	0.0611670i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$79$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$80$	1.29639	−	0.186393i	1.29639	−	0.186393i
$81$	0.901293	−	0.264644i	0.901293	−	0.264644i
$82$		0			0
$83$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$83$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.959493	−	0.281733i	0.959493	−	0.281733i
$89$	0.959493	−	0.281733i	0.959493	−	0.281733i
$90$		0			0
$91$		0			0
$92$	0.956056	−	0.0683785i	0.956056	−	0.0683785i
$93$	−0.175087	−	0.202061i	−0.175087	−	0.202061i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.540641	+	0.158746i	−0.540641	+	0.158746i	−0.540641	−	0.841254i	$-0.681818\pi$
$97$	−0.540641	+	0.158746i	−0.540641	+	0.158746i			1.00000i	$0.5\pi$
$98$		0			0
$99$	0.969672	+	0.139418i	0.969672	+	0.139418i
$100$	0.686393	+	0.201543i	0.686393	+	0.201543i
$101$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$101$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$102$		0			0
$103$	−1.50013	+	1.12299i	−1.50013	+	1.12299i	−0.540641	+	0.841254i	$0.681818\pi$
$103$	−1.50013	+	1.12299i	−1.50013	+	1.12299i	−0.959493	+	0.281733i	$0.909091\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$107$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$108$	0.226115	+	0.169267i	0.226115	+	0.169267i
$109$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$109$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$110$		0			0
$111$	0.186393	−	0.215109i	0.186393	−	0.215109i
$112$		0			0
$113$	0.898064	−	0.334961i	0.898064	−	0.334961i	0.142315	−	0.989821i	$-0.454545\pi$
$113$	0.898064	−	0.334961i	0.898064	−	0.334961i	0.755750	+	0.654861i	$0.227273\pi$
$114$		0			0
$115$	1.17621	+	0.438705i	1.17621	+	0.438705i
$116$		0			0
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.841254	+	0.540641i	0.841254	+	0.540641i
$122$		0			0
$123$		0			0
$124$	−0.398326	+	1.83107i	−0.398326	+	1.83107i
$125$	−0.281733	−	0.244123i	−0.281733	−	0.244123i
$126$		0			0
$127$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$127$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$131$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$132$	0.0683785	+	0.125226i	0.0683785	+	0.125226i
$133$		0			0
$134$		0			0
$135$	0.177290	+	0.324683i	0.177290	+	0.324683i
$136$		0			0
$137$	−0.0303285	+	0.424047i	−0.0303285	+	0.424047i	0.959493	+	0.281733i	$0.0909091\pi$
$137$	−0.0303285	+	0.424047i	−0.0303285	+	0.424047i	−0.989821	+	0.142315i	$0.954545\pi$
$138$		0			0
$139$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$139$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$140$		0			0
$141$	0.109089	−	0.109089i	0.109089	−	0.109089i
$142$		0			0
$143$		0			0
$144$		−	0.979643i		−	0.979643i
$145$		0			0
$146$		0			0
$147$	0.0855040	+	0.114220i	0.0855040	+	0.114220i
$148$	−1.98982	−	0.142315i	−1.98982	−	0.142315i
$149$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$149$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$150$		0			0
$151$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$151$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.47080	+	1.96476i	−1.47080	+	1.96476i
$156$		0			0
$157$	1.37491	+	0.627899i	1.37491	+	0.627899i	0.959493	−	0.281733i	$-0.0909091\pi$
$157$	1.37491	+	0.627899i	1.37491	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$158$		0			0
$159$	−0.219186	−	0.164081i	−0.219186	−	0.164081i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	0.494217	+	1.32505i	0.494217	+	1.32505i	0.909632	+	0.415415i	$0.136364\pi$
$163$	0.494217	+	1.32505i	0.494217	+	1.32505i	−0.415415	+	0.909632i	$0.636364\pi$
$164$		0			0
$165$	0.0133311	+	0.186393i	0.0133311	+	0.186393i
$166$		0			0
$167$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$167$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$168$		0			0
$169$	−0.989821	+	0.142315i	−0.989821	+	0.142315i
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.281733	−	0.959493i	$-0.590909\pi$
$173$		0			0		0.281733	+	0.959493i	$0.409091\pi$
$174$		0			0
$175$		0			0
$176$	0.415415	−	0.909632i	0.415415	−	0.909632i
$177$	−0.171008			−0.171008
$178$		0			0
$179$	−1.51150			−1.51150			−0.755750	−	0.654861i	$-0.772727\pi$
$179$	−1.51150			−1.51150			−0.755750	+	0.654861i	$0.772727\pi$
$180$	0.533002	−	1.16711i	0.533002	−	1.16711i
$181$	1.75089	−	0.125226i	1.75089	−	0.125226i	0.841254	−	0.540641i	$-0.181818\pi$
$181$	1.75089	−	0.125226i	1.75089	−	0.125226i	0.909632	+	0.415415i	$0.136364\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.29317	−	1.25217i	−2.29317	−	1.25217i
$186$		0			0
$187$		0			0
$188$	−1.07028	−	0.153882i	−1.07028	−	0.153882i
$189$		0			0
$190$		0			0
$191$	0.139418	+	1.94931i	0.139418	+	1.94931i	0.281733	+	0.959493i	$0.409091\pi$
$191$	0.139418	+	1.94931i	0.139418	+	1.94931i	−0.142315	+	0.989821i	$0.545455\pi$
$192$	0.114220	−	0.0855040i	0.114220	−	0.0855040i
$193$		0			0		−0.349464	−	0.936950i	$-0.613636\pi$
$193$		0			0		0.349464	+	0.936950i	$0.386364\pi$
$194$		0			0
$195$		0			0
$196$	0.281733	−	0.959493i	0.281733	−	0.959493i
$197$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$197$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$198$		0			0
$199$	0.258908	+	0.118239i	0.258908	+	0.118239i	0.540641	−	0.841254i	$-0.318182\pi$
$199$	0.258908	+	0.118239i	0.258908	+	0.118239i	−0.281733	+	0.959493i	$0.590909\pi$
$200$		0			0
$201$	0.155554	−	0.207796i	0.155554	−	0.207796i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.450008	−	0.824128i	0.450008	−	0.824128i
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$211$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$212$			1.91899i			1.91899i
$213$	0.0251978	−	0.115832i	0.0251978	−	0.115832i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.989821	−	0.857685i	0.989821	−	0.857685i
$221$		0			0
$222$		0			0
$223$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$223$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$224$		0			0
$225$	0.529635	−	0.458931i	0.529635	−	0.458931i
$226$		0			0
$227$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$227$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$228$		0			0
$229$	1.40524	−	0.767317i	1.40524	−	0.767317i	0.415415	−	0.909632i	$-0.363636\pi$
$229$	1.40524	−	0.767317i	1.40524	−	0.767317i	0.989821	+	0.142315i	$0.0454545\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	−1.19136	−	0.765644i	−1.19136	−	0.765644i
$236$	0.718267	+	0.959493i	0.718267	+	0.959493i
$237$		0			0
$238$		0			0
$239$		0			0		−0.212565	−	0.977147i	$-0.568182\pi$
$239$		0			0		0.212565	+	0.977147i	$0.431818\pi$
$240$	0.182598	−	0.0397218i	0.182598	−	0.0397218i
$241$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$241$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$242$		0			0
$243$	0.390217	−	0.145543i	0.390217	−	0.145543i
$244$		0			0
$245$	0.857685	−	0.989821i	0.857685	−	0.989821i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.118239	−	0.822373i	0.118239	−	0.822373i	−0.841254	−	0.540641i	$-0.818182\pi$
$251$	0.118239	−	0.822373i	0.118239	−	0.822373i	0.959493	−	0.281733i	$-0.0909091\pi$
$252$		0			0
$253$	0.767317	−	0.574406i	0.767317	−	0.574406i
$254$		0			0
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.959493	−	0.281733i
$257$	−1.95949	−	0.281733i	−1.95949	−	0.281733i	−0.959493	−	0.281733i	$-0.909091\pi$
$257$	−1.95949	−	0.281733i	−1.95949	−	0.281733i	−1.00000			$\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$263$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$264$		0			0
$265$	−1.04408	+	2.28621i	−1.04408	+	2.28621i
$266$		0			0
$267$	0.133682	−	0.0498610i	0.133682	−	0.0498610i
$268$	−1.81926			−1.81926
$269$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.142315	−	0.989821i	$-0.454545\pi$
$269$	0.797176	−	1.74557i	0.797176	−	1.74557i	0.654861	−	0.755750i	$-0.272727\pi$
$270$		0			0
$271$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$271$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.686393	−	0.201543i	0.686393	−	0.201543i
$276$	0.135365	−	0.0194625i	0.135365	−	0.0194625i
$277$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$277$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$278$		0			0
$279$	1.29807	+	1.29807i	1.29807	+	1.29807i
$280$		0			0
$281$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$281$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$282$		0			0
$283$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$283$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$284$	−0.755750	+	0.345139i	−0.755750	+	0.345139i
$285$		0			0
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.654861	−	0.755750i	0.654861	−	0.755750i
$290$		0			0
$291$	−0.0753254	+	0.0280949i	−0.0753254	+	0.0280949i
$292$		0			0
$293$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$293$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$294$		0			0
$295$	0.333679	+	1.53390i	0.333679	+	1.53390i
$296$		0			0
$297$	0.281733	+	0.0201499i	0.281733	+	0.0201499i
$298$		0			0
$299$		0			0
$300$	0.0997353	+	0.0216961i	0.0997353	+	0.0216961i
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$307$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$308$		0			0
$309$	−0.202061	+	0.175087i	−0.202061	+	0.175087i
$310$		0			0
$311$	0.234072	+	0.512546i	0.234072	+	0.512546i	0.989821	−	0.142315i	$-0.0454545\pi$
$311$	0.234072	+	0.512546i	0.234072	+	0.512546i	−0.755750	+	0.654861i	$0.772727\pi$
$312$		0			0
$313$	−0.841254	−	1.54064i	−0.841254	−	1.54064i	−0.841254	−	0.540641i	$-0.818182\pi$
$313$	−0.841254	−	1.54064i	−0.841254	−	1.54064i		−	1.00000i	$-0.5\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$317$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$318$		0			0
$319$		0			0
$320$	−0.989821	−	0.857685i	−0.989821	−	0.857685i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.790226	−	0.507847i	−0.790226	−	0.507847i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.53046	−	0.983568i	1.53046	−	0.983568i	0.540641	−	0.841254i	$-0.318182\pi$
$331$	1.53046	−	0.983568i	1.53046	−	0.983568i	0.989821	−	0.142315i	$-0.0454545\pi$
$332$		0			0
$333$	−1.17116	+	1.56449i	−1.17116	+	1.56449i
$334$		0			0
$335$	−2.16741	−	0.989821i	−2.16741	−	0.989821i
$336$		0			0
$337$		0			0		−0.800541	−	0.599278i	$-0.795455\pi$
$337$		0			0		0.800541	+	0.599278i	$0.204545\pi$
$338$		0			0
$339$	0.124398	−	0.0568109i	0.124398	−	0.0568109i
$340$		0			0
$341$	0.654861	+	1.75575i	0.654861	+	1.75575i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	0.171858	+	0.0504621i	0.171858	+	0.0504621i
$346$		0			0
$347$		0			0		0.989821	−	0.142315i	$-0.0454545\pi$
$347$		0			0		−0.989821	+	0.142315i	$0.954545\pi$
$348$		0			0
$349$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$349$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.94931	+	0.139418i	−1.94931	+	0.139418i	−0.989821	−	0.142315i	$-0.954545\pi$
$353$	−1.94931	+	0.139418i	−1.94931	+	0.139418i	−0.959493	+	0.281733i	$0.909091\pi$
$354$		0			0
$355$	−1.08816			−1.08816
$356$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$357$		0			0
$358$		0			0
$359$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$359$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$360$		0			0
$361$	0.281733	+	0.959493i	0.281733	+	0.959493i
$362$		0			0
$363$	0.125226	+	0.0683785i	0.125226	+	0.0683785i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.654861	−	0.755750i	$-0.727273\pi$
$367$	−1.61435	−	0.474017i	−1.61435	−	0.474017i	−0.959493	+	0.281733i	$0.909091\pi$
$368$	−0.677760	−	0.677760i	−0.677760	−	0.677760i
$369$		0			0
$370$		0			0
$371$		0			0
$372$	−0.0380500	+	0.264644i	−0.0380500	+	0.264644i
$373$		0			0		0.909632	−	0.415415i	$-0.136364\pi$
$373$		0			0		−0.909632	+	0.415415i	$0.863636\pi$
$374$		0			0
$375$	−0.0425795	−	0.0318746i	−0.0425795	−	0.0318746i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.17116	+	1.56449i	−1.17116	+	1.56449i	−0.415415	+	0.909632i	$0.636364\pi$
$379$	−1.17116	+	1.56449i	−1.17116	+	1.56449i	−0.755750	+	0.654861i	$0.772727\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.56449	−	0.340335i	1.56449	−	0.340335i	0.654861	−	0.755750i	$-0.272727\pi$
$383$	1.56449	−	0.340335i	1.56449	−	0.340335i	0.909632	+	0.415415i	$0.136364\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		0			0
$388$	0.474017	+	0.304632i	0.474017	+	0.304632i
$389$	0.682956	+	0.148568i	0.682956	+	0.148568i	0.540641	−	0.841254i	$-0.318182\pi$
$389$	0.682956	+	0.148568i	0.682956	+	0.148568i	0.142315	+	0.989821i	$0.454545\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−0.529635	−	0.824128i	−0.529635	−	0.824128i
$397$	0.0855040	−	1.19550i	0.0855040	−	1.19550i	−0.755750	−	0.654861i	$-0.772727\pi$
$397$	0.0855040	−	1.19550i	0.0855040	−	1.19550i	0.841254	−	0.540641i	$-0.181818\pi$
$398$		0			0
$399$		0			0
$400$	−0.297176	−	0.650724i	−0.297176	−	0.650724i
$401$	0.544078	+	1.19136i	0.544078	+	1.19136i	0.959493	+	0.281733i	$0.0909091\pi$
$401$	0.544078	+	1.19136i	0.544078	+	1.19136i	−0.415415	+	0.909632i	$0.636364\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.665138	−	1.03498i	−0.665138	−	1.03498i
$406$		0			0
$407$	−1.75089	+	0.956056i	−1.75089	+	0.956056i
$408$		0			0
$409$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$409$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$410$		0			0
$411$			0.0606569i			0.0606569i
$412$	1.83107	+	0.398326i	1.83107	+	0.398326i
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$	1.64468	+	0.613435i	1.64468	+	0.613435i	0.989821	−	0.142315i	$-0.0454545\pi$
$419$	1.64468	+	0.613435i	1.64468	+	0.613435i	0.654861	+	0.755750i	$0.272727\pi$
$420$		0			0
$421$	−0.654861	+	0.244250i	−0.654861	+	0.244250i	−0.654861	−	0.755750i	$-0.727273\pi$
$421$	−0.654861	+	0.244250i	−0.654861	+	0.244250i			1.00000i	$0.5\pi$
$422$		0			0
$423$	−0.693674	+	0.800543i	−0.693674	+	0.800543i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$431$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$432$	−0.0201499	−	0.281733i	−0.0201499	−	0.281733i
$433$	−0.847507	−	0.847507i	−0.847507	−	0.847507i	0.142315	−	0.989821i	$-0.454545\pi$
$433$	−0.847507	−	0.847507i	−0.847507	−	0.847507i	−0.989821	+	0.142315i	$0.954545\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		0.349464	−	0.936950i	$-0.386364\pi$
$439$		0			0		−0.349464	+	0.936950i	$0.613636\pi$
$440$		0			0
$441$	−0.641530	−	0.740365i	−0.641530	−	0.740365i
$442$		0			0
$443$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$443$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$444$	−0.284630			−0.284630
$445$	−0.708089	−	1.10181i	−0.708089	−	1.10181i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$449$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$450$		0			0
$451$		0			0
$452$	−0.841254	−	0.459359i	−0.841254	−	0.459359i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$457$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$458$		0			0
$459$		0			0
$460$	−0.438705	−	1.17621i	−0.438705	−	1.17621i
$461$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$461$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$462$		0			0
$463$	−0.540641	+	1.84125i	−0.540641	+	1.84125i			1.00000i	$0.5\pi$
$463$	−0.540641	+	1.84125i	−0.540641	+	1.84125i	−0.540641	+	0.841254i	$0.681818\pi$
$464$		0			0
$465$	−0.189318	+	0.294585i	−0.189318	+	0.294585i
$466$		0			0
$467$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.281733	+	0.959493i	$0.590909\pi$
$467$	−1.19136	+	1.37491i	−1.19136	+	1.37491i	−0.909632	+	0.415415i	$0.863636\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	0.202061	+	0.0753648i	0.202061	+	0.0753648i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.58149	+	1.01636i	1.58149	+	1.01636i
$478$		0			0
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$485$	0.398983	+	0.620830i	0.398983	+	0.620830i
$486$		0			0
$487$	1.14231	−	0.989821i	1.14231	−	0.989821i	0.142315	−	0.989821i	$-0.454545\pi$
$487$	1.14231	−	0.989821i	1.14231	−	0.989821i	1.00000			$0$
$488$		0			0
$489$	0.0838215	+	0.183543i	0.0838215	+	0.183543i
$490$		0			0
$491$		0			0		−0.479249	−	0.877679i	$-0.659091\pi$
$491$		0			0		0.479249	+	0.877679i	$0.340909\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−0.182598	−	1.27000i	−0.182598	−	1.27000i
$496$	1.64468	−	0.898064i	1.64468	−	0.898064i
$497$		0			0
$498$		0			0
$499$	−0.254771	+	1.17116i	−0.254771	+	1.17116i	0.654861	+	0.755750i	$0.272727\pi$
$499$	−0.254771	+	1.17116i	−0.254771	+	1.17116i	−0.909632	+	0.415415i	$0.863636\pi$
$500$			0.372786i			0.372786i
$501$		0			0
$502$		0			0
$503$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$503$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.139418	+	0.0303285i	−0.139418	+	0.0303285i
$508$		0			0
$509$	1.27155	−	0.817178i	1.27155	−	0.817178i	0.281733	−	0.959493i	$-0.409091\pi$
$509$	1.27155	−	0.817178i	1.27155	−	0.817178i	0.989821	+	0.142315i	$0.0454545\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.96476	+	1.47080i	1.96476	+	1.47080i
$516$		0			0
$517$	−0.983568	+	0.449181i	−0.983568	+	0.449181i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.142315	−	1.98982i	−0.142315	−	1.98982i	−0.142315	−	0.989821i	$-0.545455\pi$
$521$	−0.142315	−	1.98982i	−0.142315	−	1.98982i		−	1.00000i	$-0.5\pi$
$522$		0			0
$523$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$523$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.0498610	−	0.133682i	0.0498610	−	0.133682i
$529$	0.0228997	+	0.0779892i	0.0228997	+	0.0779892i
$530$		0			0
$531$	1.17116	−	0.0837633i	1.17116	−	0.0837633i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−0.215109	+	0.0153849i	−0.215109	+	0.0153849i
$538$		0			0
$539$	−0.281733	−	0.959493i	−0.281733	−	0.959493i
$540$	0.129279	−	0.346609i	0.129279	−	0.346609i
$541$		0			0		−0.877679	−	0.479249i	$-0.840909\pi$
$541$		0			0		0.877679	+	0.479249i	$0.159091\pi$
$542$		0			0
$543$	0.247902	−	0.0356430i	0.247902	−	0.0356430i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$547$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$548$	0.340335	−	0.254771i	0.340335	−	0.254771i
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−0.339098	−	0.154861i	−0.339098	−	0.154861i
$556$		0			0
$557$		0			0		0.599278	−	0.800541i	$-0.295455\pi$
$557$		0			0		−0.599278	+	0.800541i	$0.704545\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$563$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$564$	−0.153882	−	0.0110059i	−0.153882	−	0.0110059i
$565$	−0.752312	−	1.00497i	−0.752312	−	1.00497i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$569$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$570$		0			0
$571$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$571$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$572$		0			0
$573$	0.0396824	+	0.275997i	0.0396824	+	0.275997i
$574$		0			0
$575$	0.0489159	−	0.683934i	0.0489159	−	0.683934i
$576$	−0.740365	+	0.641530i	−0.740365	+	0.641530i
$577$	0.334961	+	0.613435i	0.334961	+	0.613435i	0.989821	−	0.142315i	$-0.0454545\pi$
$577$	0.334961	+	0.613435i	0.334961	+	0.613435i	−0.654861	+	0.755750i	$0.727273\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	1.03748	+	1.61435i	1.03748	+	1.61435i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.425839	+	0.368991i	0.425839	+	0.368991i	0.841254	−	0.540641i	$-0.181818\pi$
$587$	0.425839	+	0.368991i	0.425839	+	0.368991i	−0.415415	+	0.909632i	$0.636364\pi$
$588$	0.0303285	−	0.139418i	0.0303285	−	0.139418i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.19550	+	1.59700i	1.19550	+	1.59700i
$593$		0			0		−0.997452	−	0.0713392i	$-0.977273\pi$
$593$		0			0		0.997452	+	0.0713392i	$0.0227273\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.0380500	+	0.0141919i	0.0380500	+	0.0141919i
$598$		0			0
$599$	1.86912	−	0.697148i	1.86912	−	0.697148i	0.909632	−	0.415415i	$-0.136364\pi$
$599$	1.86912	−	0.697148i	1.86912	−	0.697148i	0.959493	−	0.281733i	$-0.0909091\pi$
$600$		0			0
$601$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$601$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$602$		0			0
$603$	−0.963546	+	1.49931i	−0.963546	+	1.49931i
$604$		0			0
$605$	0.368991	−	1.25667i	0.368991	−	1.25667i
$606$		0			0
$607$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$607$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$613$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.682956	+	1.83107i	−0.682956	+	1.83107i	−0.142315	+	0.989821i	$0.545455\pi$
$617$	−0.682956	+	1.83107i	−0.682956	+	1.83107i	−0.540641	+	0.841254i	$0.681818\pi$
$618$		0			0
$619$	−0.708089	−	0.817178i	−0.708089	−	0.817178i	0.281733	−	0.959493i	$-0.409091\pi$
$619$	−0.708089	−	0.817178i	−0.708089	−	0.817178i	−0.989821	+	0.142315i	$0.954545\pi$
$620$	2.44803	−	0.175087i	2.44803	−	0.175087i
$621$	0.112465	−	0.246265i	0.112465	−	0.246265i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.500000	+	1.09485i	−0.500000	+	1.09485i
$626$		0			0
$627$		0			0
$628$	−0.425839	−	1.45027i	−0.425839	−	1.45027i
$629$		0			0
$630$		0			0
$631$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.654861	−	0.755750i	$-0.272727\pi$
$631$	1.61435	−	0.474017i	1.61435	−	0.474017i	0.959493	+	0.281733i	$0.0909091\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$		0			0
$636$	0.0195325	+	0.273100i	0.0195325	+	0.273100i
$637$		0			0
$638$		0			0
$639$	−0.115832	+	0.805632i	−0.115832	+	0.805632i
$640$		0			0
$641$	−0.158746	+	0.540641i	−0.158746	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$641$	−0.158746	+	0.540641i	−0.158746	+	0.540641i	−1.00000			$\pi$
$642$		0			0
$643$	−0.449181	+	0.698939i	−0.449181	+	0.698939i	−0.989821	−	0.142315i	$-0.954545\pi$
$643$	−0.449181	+	0.698939i	−0.449181	+	0.698939i	0.540641	+	0.841254i	$0.318182\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.50013	+	0.559521i	−1.50013	+	0.559521i	−0.959493	−	0.281733i	$-0.909091\pi$
$647$	−1.50013	+	0.559521i	−1.50013	+	0.559521i	−0.540641	+	0.841254i	$0.681818\pi$
$648$		0			0
$649$	1.12299	+	0.418852i	1.12299	+	0.418852i
$650$		0			0
$651$		0			0
$652$	0.677760	−	1.24123i	0.677760	−	1.24123i
$653$	1.75089	+	0.125226i	1.75089	+	0.125226i	0.909632	−	0.415415i	$-0.136364\pi$
$653$	1.75089	+	0.125226i	1.75089	+	0.125226i	0.841254	+	0.540641i	$0.181818\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		−0.755750	−	0.654861i	$-0.772727\pi$
$659$		0			0		0.755750	+	0.654861i	$0.227273\pi$
$660$	0.132136	−	0.132136i	0.132136	−	0.132136i
$661$	0.125226	−	0.0683785i	0.125226	−	0.0683785i	−0.415415	−	0.909632i	$-0.636364\pi$
$661$	0.125226	−	0.0683785i	0.125226	−	0.0683785i	0.540641	+	0.841254i	$0.318182\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		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		−0.142315	−	0.989821i	$-0.545455\pi$
$673$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$674$		0			0
$675$	0.142877	−	0.142877i	0.142877	−	0.142877i
$676$	0.755750	+	0.654861i	0.755750	+	0.654861i
$677$		0			0		0.212565	−	0.977147i	$-0.431818\pi$
$677$		0			0		−0.212565	+	0.977147i	$0.568182\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.0683785	+	0.125226i	−0.0683785	+	0.125226i	−0.909632	−	0.415415i	$-0.863636\pi$
$683$	−0.0683785	+	0.125226i	−0.0683785	+	0.125226i	0.841254	+	0.540641i	$0.181818\pi$
$684$		0			0
$685$	0.544078	−	0.118357i	0.544078	−	0.118357i
$686$		0			0
$687$	0.192176	−	0.123504i	0.192176	−	0.123504i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	−0.983568	−	0.449181i	−0.983568	−	0.449181i	−0.142315	−	0.989821i	$-0.545455\pi$
$691$	−0.983568	−	0.449181i	−0.983568	−	0.449181i	−0.841254	+	0.540641i	$0.818182\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$		0			0
$701$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$701$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$702$		0			0
$703$		0			0
$704$	−0.959493	+	0.281733i	−0.959493	+	0.281733i
$705$	−0.177342	−	0.0968361i	−0.177342	−	0.0968361i
$706$		0			0
$707$		0			0
$708$	0.111986	+	0.129239i	0.111986	+	0.129239i
$709$	−0.424047	+	0.0303285i	−0.424047	+	0.0303285i	−0.281733	−	0.959493i	$-0.590909\pi$
$709$	−0.424047	+	0.0303285i	−0.424047	+	0.0303285i	−0.142315	+	0.989821i	$0.545455\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.79613			1.79613
$714$		0			0
$715$		0			0
$716$	0.989821	+	1.14231i	0.989821	+	1.14231i
$717$		0			0
$718$		0			0
$719$	1.64468	+	0.898064i	1.64468	+	0.898064i	0.989821	+	0.142315i	$0.0454545\pi$
$719$	1.64468	+	0.898064i	1.64468	+	0.898064i	0.654861	+	0.755750i	$0.272727\pi$
$720$	−1.23109	+	0.361480i	−1.23109	+	0.361480i
$721$		0			0
$722$		0			0
$723$		0			0
$724$	−1.24123	−	1.24123i	−1.24123	−	1.24123i
$725$		0			0
$726$		0			0
$727$	−0.613435	−	1.64468i	−0.613435	−	1.64468i	−0.755750	−	0.654861i	$-0.772727\pi$
$727$	−0.613435	−	1.64468i	−0.613435	−	1.64468i	0.142315	−	0.989821i	$-0.454545\pi$
$728$		0			0
$729$	−0.800404	+	0.365532i	−0.800404	+	0.365532i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.909632	−	0.415415i	$-0.863636\pi$
$733$		0			0		0.909632	+	0.415415i	$0.136364\pi$
$734$		0			0
$735$	0.111986	−	0.149596i	0.111986	−	0.149596i
$736$		0			0
$737$	−1.53046	+	0.983568i	−1.53046	+	0.983568i
$738$		0			0
$739$		0			0		0.977147	−	0.212565i	$-0.0681818\pi$
$739$		0			0		−0.977147	+	0.212565i	$0.931818\pi$
$740$	0.555384	+	2.55306i	0.555384	+	2.55306i
$741$		0			0
$742$		0			0
$743$		0			0		−0.599278	−	0.800541i	$-0.704545\pi$
$743$		0			0		0.599278	+	0.800541i	$0.295455\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	−0.654861	−	0.755750i	$-0.727273\pi$
$751$	−0.239446	−	1.66538i	−0.239446	−	1.66538i	0.415415	−	0.909632i	$-0.363636\pi$
$752$	0.584585	+	0.909632i	0.584585	+	0.909632i
$753$	0.00845665	−	0.118239i	0.00845665	−	0.118239i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	0.755750	+	1.65486i	0.755750	+	1.65486i	0.755750	+	0.654861i	$0.227273\pi$
$757$	0.755750	+	1.65486i	0.755750	+	1.65486i			1.00000i	$0.5\pi$
$758$		0			0
$759$	0.103354	−	0.0895567i	0.103354	−	0.0895567i
$760$		0			0
$761$		0			0		−0.540641	−	0.841254i	$-0.681818\pi$
$761$		0			0		0.540641	+	0.841254i	$0.318182\pi$
$762$		0			0
$763$		0			0
$764$	1.38189	−	1.38189i	1.38189	−	1.38189i
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.139418	−	0.0303285i	−0.139418	−	0.0303285i
$769$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$769$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$770$		0			0
$771$	−0.281733	−	0.0201499i	−0.281733	−	0.0201499i
$772$		0			0
$773$	0.148568	+	0.682956i	0.148568	+	0.682956i	0.989821	+	0.142315i	$0.0454545\pi$
$773$	0.148568	+	0.682956i	0.148568	+	0.682956i	−0.841254	+	0.540641i	$0.818182\pi$
$774$		0			0
$775$	1.25601	+	0.468468i	1.25601	+	0.468468i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$	−0.449181	+	0.698939i	−0.449181	+	0.698939i
$782$		0			0
$783$		0			0
$784$	−0.909632	+	0.415415i	−0.909632	+	0.415415i
$785$	0.281733	−	1.95949i	0.281733	−	1.95949i
$786$		0			0
$787$		0			0		0.800541	−	0.599278i	$-0.204545\pi$
$787$		0			0		−0.800541	+	0.599278i	$0.795455\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−0.125317	+	0.335989i	−0.125317	+	0.335989i
$796$	−0.0801894	−	0.273100i	−0.0801894	−	0.273100i
$797$	0.857685	+	0.989821i	0.857685	+	0.989821i	1.00000			$0$
$797$	0.857685	+	0.989821i	0.857685	+	0.989821i	−0.142315	+	0.989821i	$0.545455\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$	−0.891115	+	0.406958i	−0.891115	+	0.406958i
$802$		0			0
$803$		0			0
$804$	−0.258908	+	0.0185175i	−0.258908	+	0.0185175i
$805$		0			0
$806$		0			0
$807$	0.0956825	−	0.256535i	0.0956825	−	0.256535i
$808$		0			0
$809$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$809$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$810$		0			0
$811$		0			0		−0.989821	−	0.142315i	$-0.954545\pi$
$811$		0			0		0.989821	+	0.142315i	$0.0454545\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.48278	−	1.11000i	1.48278	−	1.11000i
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.540641	−	0.841254i	$-0.318182\pi$
$821$		0			0		−0.540641	+	0.841254i	$0.681818\pi$
$822$		0			0
$823$	0.989821	−	1.14231i	0.989821	−	1.14231i		−	1.00000i	$-0.5\pi$
$823$	0.989821	−	1.14231i	0.989821	−	1.14231i	0.989821	−	0.142315i	$-0.0454545\pi$
$824$		0			0
$825$	0.0956325	−	0.0356691i	0.0956325	−	0.0356691i
$826$		0			0
$827$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$827$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$828$	−0.917527	+	0.199596i	−0.917527	+	0.199596i
$829$	0.0903680	+	0.415415i	0.0903680	+	0.415415i	1.00000			$0$
$829$	0.0903680	+	0.415415i	0.0903680	+	0.415415i	−0.909632	+	0.415415i	$0.863636\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.400008	+	0.346609i	0.400008	+	0.346609i
$838$		0			0
$839$	0.373128	−	0.203743i	0.373128	−	0.203743i	−0.281733	−	0.959493i	$-0.590909\pi$
$839$	0.373128	−	0.203743i	0.373128	−	0.203743i	0.654861	+	0.755750i	$0.272727\pi$
$840$		0			0
$841$	−0.540641	−	0.841254i	−0.540641	−	0.841254i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.544078	+	1.19136i	0.544078	+	1.19136i
$846$		0			0
$847$		0			0
$848$	1.45027	−	1.25667i	1.45027	−	1.25667i
$849$		0			0
$850$		0			0
$851$	0.272122	+	1.89265i	0.272122	+	1.89265i
$852$	−0.104041	+	0.0568109i	−0.104041	+	0.0568109i
$853$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$853$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		0			0		−0.977147	−	0.212565i	$-0.931818\pi$
$857$		0			0		0.977147	+	0.212565i	$0.0681818\pi$
$858$		0			0
$859$	−1.19550	−	1.59700i	−1.19550	−	1.59700i	−0.654861	−	0.755750i	$-0.727273\pi$
$859$	−1.19550	−	1.59700i	−1.19550	−	1.59700i	−0.540641	−	0.841254i	$-0.681818\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.83107	+	0.398326i	−1.83107	+	0.398326i	−0.989821	−	0.142315i	$-0.954545\pi$
$863$	−1.83107	+	0.398326i	−1.83107	+	0.398326i	−0.841254	+	0.540641i	$0.818182\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	0.0855040	−	0.114220i	0.0855040	−	0.114220i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.502112	−	0.229307i	0.502112	−	0.229307i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.0713392	−	0.997452i	$-0.522727\pi$
$877$		0			0		0.0713392	+	0.997452i	$0.477273\pi$
$878$		0			0
$879$		0			0
$880$	−1.29639	−	0.186393i	−1.29639	−	0.186393i
$881$	1.66538	−	0.239446i	1.66538	−	0.239446i	0.755750	−	0.654861i	$-0.227273\pi$
$881$	1.66538	−	0.239446i	1.66538	−	0.239446i	0.909632	+	0.415415i	$0.136364\pi$
$882$		0			0
$883$	−1.40524	−	0.767317i	−1.40524	−	0.767317i	−0.415415	−	0.909632i	$-0.636364\pi$
$883$	−1.40524	−	0.767317i	−1.40524	−	0.767317i	−0.989821	+	0.142315i	$0.954545\pi$
$884$		0			0
$885$	0.0631004	+	0.214900i	0.0631004	+	0.214900i
$886$		0			0
$887$		0			0		0.997452	−	0.0713392i	$-0.0227273\pi$
$887$		0			0		−0.997452	+	0.0713392i	$0.977273\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.939343			−0.939343
$892$		0			0
$893$		0			0
$894$		0			0
$895$	0.557730	+	1.89945i	0.557730	+	1.89945i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.693674	−	0.0997353i	−0.693674	−	0.0997353i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.803429	−	2.15408i	−0.803429	−	2.15408i
$906$		0			0
$907$	1.53046	−	0.698939i	1.53046	−	0.698939i	0.540641	−	0.841254i	$-0.318182\pi$
$907$	1.53046	−	0.698939i	1.53046	−	0.698939i	0.989821	+	0.142315i	$0.0454545\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.258908	−	0.118239i	−0.258908	−	0.118239i	0.281733	−	0.959493i	$-0.409091\pi$
$911$	−0.258908	−	0.118239i	−0.258908	−	0.118239i	−0.540641	+	0.841254i	$0.681818\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−1.50013	−	0.559521i	−1.50013	−	0.559521i
$917$		0			0
$918$		0			0
$919$		0			0		0.479249	−	0.877679i	$-0.340909\pi$
$919$		0			0		−0.479249	+	0.877679i	$0.659091\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−0.303351	+	1.39448i	−0.303351	+	1.39448i
$926$		0			0
$927$	1.29807	−	1.29807i	1.29807	−	1.29807i
$928$		0			0
$929$	−0.153882	−	1.07028i	−0.153882	−	1.07028i	−0.909632	−	0.415415i	$-0.863636\pi$
$929$	−0.153882	−	1.07028i	−0.153882	−	1.07028i	0.755750	−	0.654861i	$-0.227273\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	0.0385289	+	0.0705604i	0.0385289	+	0.0705604i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.755750	−	0.654861i	$-0.227273\pi$
$937$		0			0		−0.755750	+	0.654861i	$0.772727\pi$
$938$		0			0
$939$	−0.135404	−	0.210693i	−0.135404	−	0.210693i
$940$	0.201543	+	1.40176i	0.201543	+	1.40176i
$941$		0			0		0.877679	−	0.479249i	$-0.159091\pi$
$941$		0			0		−0.877679	+	0.479249i	$0.840909\pi$
$942$		0			0
$943$		0			0
$944$	0.254771	−	1.17116i	0.254771	−	1.17116i
$945$		0			0
$946$		0			0
$947$	0.239446	+	0.153882i	0.239446	+	0.153882i	0.654861	−	0.755750i	$-0.272727\pi$
$947$	0.239446	+	0.153882i	0.239446	+	0.153882i	−0.415415	+	0.909632i	$0.636364\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−0.0510279	−	0.234571i	−0.0510279	−	0.234571i
$952$		0			0
$953$		0			0		−0.936950	−	0.349464i	$-0.886364\pi$
$953$		0			0		0.936950	+	0.349464i	$0.113636\pi$
$954$		0			0
$955$	2.39820	−	0.894482i	2.39820	−	0.894482i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	−0.149596	−	0.111986i	−0.149596	−	0.111986i
$961$	−0.707571	+	2.40977i	−0.707571	+	2.40977i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$967$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	0.540641	−	0.158746i	0.540641	−	0.158746i		−	1.00000i	$-0.5\pi$
$971$	0.540641	−	0.158746i	0.540641	−	0.158746i	0.540641	+	0.841254i	$0.318182\pi$
$972$	−0.365532	−	0.199596i	−0.365532	−	0.199596i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	−0.959493	−	0.281733i	$-0.909091\pi$
$977$	−0.118239	+	0.258908i	−0.118239	+	0.258908i	0.841254	+	0.540641i	$0.181818\pi$
$978$		0			0
$979$	−1.00000			−1.00000
$980$	−1.30972			−1.30972
$981$		0			0
$982$		0			0
$983$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.841254	−	0.540641i	$-0.818182\pi$
$983$	−1.25667	−	1.45027i	−1.25667	−	1.45027i	−0.415415	−	0.909632i	$-0.636364\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.100889	+	0.100889i	0.100889	+	0.100889i	0.755750	−	0.654861i	$-0.227273\pi$
$991$	0.100889	+	0.100889i	0.100889	+	0.100889i	−0.654861	+	0.755750i	$0.727273\pi$
$992$		0			0
$993$	0.207796	−	0.155554i	0.207796	−	0.155554i
$994$		0			0
$995$	0.0530529	−	0.368991i	0.0530529	−	0.368991i
$996$		0			0
$997$		0			0		0.281733	−	0.959493i	$-0.409091\pi$
$997$		0			0		−0.281733	+	0.959493i	$0.590909\pi$
$998$		0			0
$999$	−0.304632	+	0.474017i	−0.304632	+	0.474017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	979.1.v.a.10.1	✓	20
11.10	odd	2	CM	979.1.v.a.10.1	✓	20
89.9	even	44	inner	979.1.v.a.98.1	yes	20
979.98	odd	44	inner	979.1.v.a.98.1	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
979.1.v.a.10.1	✓	20	1.1	even	1	trivial
979.1.v.a.10.1	✓	20	11.10	odd	2	CM
979.1.v.a.98.1	yes	20	89.9	even	44	inner
979.1.v.a.98.1	yes	20	979.98	odd	44	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:	\( N \)	\(=\)	\( 979 = 11 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	979.v (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.0101786i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.368991 - 1.25667i) q^{5} +(-0.969672 + 0.139418i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.0101786i) q^{3} +(-0.654861 - 0.755750i) q^{4} +(-0.368991 - 1.25667i) q^{5} +(-0.969672 + 0.139418i) q^{9} +(-0.959493 - 0.281733i) q^{11} +(-0.100889 - 0.100889i) q^{12} +(-0.0653040 - 0.175087i) q^{15} +(-0.142315 + 0.989821i) q^{16} +(-0.708089 + 1.10181i) q^{20} +(-0.574406 + 0.767317i) q^{23} +(-0.601808 + 0.386758i) q^{25} +(-0.275997 + 0.0600395i) q^{27} +(-1.12299 - 1.50013i) q^{31} +(-0.139418 - 0.0303285i) q^{33} +(0.740365 + 0.641530i) q^{36} +(1.41061 - 1.41061i) q^{37} +(0.415415 + 0.909632i) q^{44} +(0.533002 + 1.16711i) q^{45} +(0.817178 - 0.708089i) q^{47} +(-0.0101786 + 0.142315i) q^{48} +(0.540641 + 0.841254i) q^{49} +(-1.45027 - 1.25667i) q^{53} +1.30972i q^{55} +(-1.19550 - 0.0855040i) q^{59} +(-0.0895567 + 0.164011i) q^{60} +(0.841254 - 0.540641i) q^{64} +(1.19136 - 1.37491i) q^{67} +(-0.0739364 + 0.115047i) q^{69} +(0.234072 - 0.797176i) q^{71} +(-0.0817095 + 0.0611670i) q^{75} +(1.29639 - 0.186393i) q^{80} +(0.901293 - 0.264644i) q^{81} +(0.959493 - 0.281733i) q^{89} +(0.956056 - 0.0683785i) q^{92} +(-0.175087 - 0.202061i) q^{93} +(-0.540641 + 0.158746i) q^{97} +(0.969672 + 0.139418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 2 q^{4} - 22 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 2 * q^4 - 22 * q^9	\( 20 q + 2 q^{3} - 2 q^{4} - 22 q^{9} - 2 q^{11} + 2 q^{12} + 4 q^{15} - 2 q^{16} - 2 q^{23} + 6 q^{25} + 2 q^{31} + 2 q^{33} + 2 q^{37} - 2 q^{44} - 4 q^{45} - 20 q^{48} - 2 q^{59} + 4 q^{60} - 2 q^{64} - 6 q^{75} + 20 q^{81} + 2 q^{89} - 2 q^{92} - 4 q^{93} + 22 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 2 * q^4 - 22 * q^9 - 2 * q^11 + 2 * q^12 + 4 * q^15 - 2 * q^16 - 2 * q^23 + 6 * q^25 + 2 * q^31 + 2 * q^33 + 2 * q^37 - 2 * q^44 - 4 * q^45 - 20 * q^48 - 2 * q^59 + 4 * q^60 - 2 * q^64 - 6 * q^75 + 20 * q^81 + 2 * q^89 - 2 * q^92 - 4 * q^93 + 22 * q^99

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