LMFDB - Embedded newform 867.2.e.e.829.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(616,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("867.616");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.e (of order $4$, degree $2$, not 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:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			829.1
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	867.829
Dual form			867.2.e.e.616.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{3} +2.00000 q^{4} +(2.12132 + 2.12132i) q^{5} +(-2.82843 + 2.82843i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{3} +2.00000 q^{4} +(2.12132 + 2.12132i) q^{5} +(-2.82843 + 2.82843i) q^{7} +1.00000i q^{9} +(2.12132 - 2.12132i) q^{11} +(-1.41421 - 1.41421i) q^{12} +1.00000 q^{13} -3.00000i q^{15} +4.00000 q^{16} +1.00000i q^{19} +(4.24264 + 4.24264i) q^{20} +4.00000 q^{21} +(-6.36396 + 6.36396i) q^{23} +4.00000i q^{25} +(0.707107 - 0.707107i) q^{27} +(-5.65685 + 5.65685i) q^{28} +(4.24264 + 4.24264i) q^{29} +(-1.41421 - 1.41421i) q^{31} -3.00000 q^{33} -12.0000 q^{35} +2.00000i q^{36} +(2.82843 + 2.82843i) q^{37} +(-0.707107 - 0.707107i) q^{39} +(-2.12132 + 2.12132i) q^{41} -7.00000i q^{43} +(4.24264 - 4.24264i) q^{44} +(-2.12132 + 2.12132i) q^{45} +6.00000 q^{47} +(-2.82843 - 2.82843i) q^{48} -9.00000i q^{49} +2.00000 q^{52} +6.00000i q^{53} +9.00000 q^{55} +(0.707107 - 0.707107i) q^{57} +6.00000i q^{59} -6.00000i q^{60} +(5.65685 - 5.65685i) q^{61} +(-2.82843 - 2.82843i) q^{63} +8.00000 q^{64} +(2.12132 + 2.12132i) q^{65} -4.00000 q^{67} +9.00000 q^{69} +(-8.48528 - 8.48528i) q^{71} +(1.41421 + 1.41421i) q^{73} +(2.82843 - 2.82843i) q^{75} +2.00000i q^{76} +12.0000i q^{77} +(7.07107 - 7.07107i) q^{79} +(8.48528 + 8.48528i) q^{80} -1.00000 q^{81} +6.00000i q^{83} +8.00000 q^{84} -6.00000i q^{87} +(-2.82843 + 2.82843i) q^{91} +(-12.7279 + 12.7279i) q^{92} +2.00000i q^{93} +(-2.12132 + 2.12132i) q^{95} +(-11.3137 - 11.3137i) q^{97} +(2.12132 + 2.12132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{4}+O(q^{10}) $ 4 * q + 8 * q^4	$ 4 q + 8 q^{4} + 4 q^{13} + 16 q^{16} + 16 q^{21} - 12 q^{33} - 48 q^{35} + 24 q^{47} + 8 q^{52} + 36 q^{55} + 32 q^{64} - 16 q^{67} + 36 q^{69} - 4 q^{81} + 32 q^{84}+O(q^{100}) $ 4 * q + 8 * q^4 + 4 * q^13 + 16 * q^16 + 16 * q^21 - 12 * q^33 - 48 * q^35 + 24 * q^47 + 8 * q^52 + 36 * q^55 + 32 * q^64 - 16 * q^67 + 36 * q^69 - 4 * q^81 + 32 * q^84

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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		1.00000			$0$
$2$		0			0		−1.00000			$\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	2.00000			1.00000
$5$	2.12132	+	2.12132i	0.948683	+	0.948683i	0.998746	−	0.0500628i	$-0.0159421\pi$
$5$	2.12132	+	2.12132i	0.948683	+	0.948683i	−0.0500628	+	0.998746i	$0.515942\pi$
$6$		0			0
$7$	−2.82843	+	2.82843i	−1.06904	+	1.06904i	−0.0716124	+	0.997433i	$0.522814\pi$
$7$	−2.82843	+	2.82843i	−1.06904	+	1.06904i	−0.997433	+	0.0716124i	$0.977186\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	2.12132	−	2.12132i	0.639602	−	0.639602i	−0.310855	−	0.950457i	$-0.600615\pi$
$11$	2.12132	−	2.12132i	0.639602	−	0.639602i	0.950457	+	0.310855i	$0.100615\pi$
$12$	−1.41421	−	1.41421i	−0.408248	−	0.408248i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$		−	3.00000i		−	0.774597i
$16$	4.00000			1.00000
$17$		0			0
$17$		0			0
$18$		0			0
$19$			1.00000i			0.229416i	0.993399	+	0.114708i	$0.0365932\pi$
$19$			1.00000i			0.229416i	−0.993399	+	0.114708i	$0.963407\pi$
$20$	4.24264	+	4.24264i	0.948683	+	0.948683i
$21$	4.00000			0.872872
$22$		0			0
$23$	−6.36396	+	6.36396i	−1.32698	+	1.32698i	−0.418984	+	0.907994i	$0.637614\pi$
$23$	−6.36396	+	6.36396i	−1.32698	+	1.32698i	−0.907994	+	0.418984i	$0.862386\pi$
$24$		0			0
$25$			4.00000i			0.800000i
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−5.65685	+	5.65685i	−1.06904	+	1.06904i
$29$	4.24264	+	4.24264i	0.787839	+	0.787839i	0.981140	−	0.193301i	$-0.0619194\pi$
$29$	4.24264	+	4.24264i	0.787839	+	0.787839i	−0.193301	+	0.981140i	$0.561919\pi$
$30$		0			0
$31$	−1.41421	−	1.41421i	−0.254000	−	0.254000i	0.568608	−	0.822608i	$-0.307482\pi$
$31$	−1.41421	−	1.41421i	−0.254000	−	0.254000i	−0.822608	+	0.568608i	$0.807482\pi$
$32$		0			0
$33$	−3.00000			−0.522233
$34$		0			0
$35$	−12.0000			−2.02837
$36$			2.00000i			0.333333i
$37$	2.82843	+	2.82843i	0.464991	+	0.464991i	0.900287	−	0.435297i	$-0.143356\pi$
$37$	2.82843	+	2.82843i	0.464991	+	0.464991i	−0.435297	+	0.900287i	$0.643356\pi$
$38$		0			0
$39$	−0.707107	−	0.707107i	−0.113228	−	0.113228i
$40$		0			0
$41$	−2.12132	+	2.12132i	−0.331295	+	0.331295i	−0.853078	−	0.521783i	$-0.825267\pi$
$41$	−2.12132	+	2.12132i	−0.331295	+	0.331295i	0.521783	+	0.853078i	$0.325267\pi$
$42$		0			0
$43$		−	7.00000i		−	1.06749i	−0.845645	−	0.533745i	$-0.820784\pi$
$43$		−	7.00000i		−	1.06749i	0.845645	−	0.533745i	$-0.179216\pi$
$44$	4.24264	−	4.24264i	0.639602	−	0.639602i
$45$	−2.12132	+	2.12132i	−0.316228	+	0.316228i
$46$		0			0
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	−2.82843	−	2.82843i	−0.408248	−	0.408248i
$49$		−	9.00000i		−	1.28571i
$50$		0			0
$51$		0			0
$52$	2.00000			0.277350
$53$			6.00000i			0.824163i	0.911147	+	0.412082i	$0.135198\pi$
$53$			6.00000i			0.824163i	−0.911147	+	0.412082i	$0.864802\pi$
$54$		0			0
$55$	9.00000			1.21356
$56$		0			0
$57$	0.707107	−	0.707107i	0.0936586	−	0.0936586i
$58$		0			0
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		−	6.00000i		−	0.774597i
$61$	5.65685	−	5.65685i	0.724286	−	0.724286i	−0.245189	−	0.969475i	$-0.578850\pi$
$61$	5.65685	−	5.65685i	0.724286	−	0.724286i	0.969475	+	0.245189i	$0.0788501\pi$
$62$		0			0
$63$	−2.82843	−	2.82843i	−0.356348	−	0.356348i
$64$	8.00000			1.00000
$65$	2.12132	+	2.12132i	0.263117	+	0.263117i
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	9.00000			1.08347
$70$		0			0
$71$	−8.48528	−	8.48528i	−1.00702	−	1.00702i	−0.999975	−	0.00704243i	$-0.997758\pi$
$71$	−8.48528	−	8.48528i	−1.00702	−	1.00702i	−0.00704243	−	0.999975i	$-0.502242\pi$
$72$		0			0
$73$	1.41421	+	1.41421i	0.165521	+	0.165521i	0.785007	−	0.619486i	$-0.212659\pi$
$73$	1.41421	+	1.41421i	0.165521	+	0.165521i	−0.619486	+	0.785007i	$0.712659\pi$
$74$		0			0
$75$	2.82843	−	2.82843i	0.326599	−	0.326599i
$76$			2.00000i			0.229416i
$77$			12.0000i			1.36753i
$78$		0			0
$79$	7.07107	−	7.07107i	0.795557	−	0.795557i	−0.186834	−	0.982391i	$-0.559823\pi$
$79$	7.07107	−	7.07107i	0.795557	−	0.795557i	0.982391	+	0.186834i	$0.0598227\pi$
$80$	8.48528	+	8.48528i	0.948683	+	0.948683i
$81$	−1.00000			−0.111111
$82$		0			0
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	8.00000			0.872872
$85$		0			0
$86$		0			0
$87$		−	6.00000i		−	0.643268i
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$		0			0
$91$	−2.82843	+	2.82843i	−0.296500	+	0.296500i
$92$	−12.7279	+	12.7279i	−1.32698	+	1.32698i
$93$			2.00000i			0.207390i
$94$		0			0
$95$	−2.12132	+	2.12132i	−0.217643	+	0.217643i
$96$		0			0
$97$	−11.3137	−	11.3137i	−1.14873	−	1.14873i	−0.986802	−	0.161931i	$-0.948228\pi$
$97$	−11.3137	−	11.3137i	−1.14873	−	1.14873i	−0.161931	−	0.986802i	$-0.551772\pi$
$98$		0			0
$99$	2.12132	+	2.12132i	0.213201	+	0.213201i
$100$			8.00000i			0.800000i
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$		0			0
$103$	5.00000			0.492665			0.246332	−	0.969185i	$-0.420775\pi$
$103$	5.00000			0.492665			0.246332	+	0.969185i	$0.420775\pi$
$104$		0			0
$105$	8.48528	+	8.48528i	0.828079	+	0.828079i
$106$		0			0
$107$	6.36396	+	6.36396i	0.615227	+	0.615227i	0.944303	−	0.329076i	$-0.106737\pi$
$107$	6.36396	+	6.36396i	0.615227	+	0.615227i	−0.329076	+	0.944303i	$0.606737\pi$
$108$	1.41421	−	1.41421i	0.136083	−	0.136083i
$109$	14.1421	−	14.1421i	1.35457	−	1.35457i	0.474100	−	0.880471i	$-0.342774\pi$
$109$	14.1421	−	14.1421i	1.35457	−	1.35457i	0.880471	−	0.474100i	$-0.157226\pi$
$110$		0			0
$111$		−	4.00000i		−	0.379663i
$112$	−11.3137	+	11.3137i	−1.06904	+	1.06904i
$113$	6.36396	−	6.36396i	0.598671	−	0.598671i	−0.341288	−	0.939959i	$-0.610863\pi$
$113$	6.36396	−	6.36396i	0.598671	−	0.598671i	0.939959	+	0.341288i	$0.110863\pi$
$114$		0			0
$115$	−27.0000			−2.51776
$116$	8.48528	+	8.48528i	0.787839	+	0.787839i
$117$			1.00000i			0.0924500i
$118$		0			0
$119$		0			0
$120$		0			0
$121$			2.00000i			0.181818i
$122$		0			0
$123$	3.00000			0.270501
$124$	−2.82843	−	2.82843i	−0.254000	−	0.254000i
$125$	2.12132	−	2.12132i	0.189737	−	0.189737i
$126$		0			0
$127$		−	13.0000i		−	1.15356i	−0.816898	−	0.576782i	$-0.804308\pi$
$127$		−	13.0000i		−	1.15356i	0.816898	−	0.576782i	$-0.195692\pi$
$128$		0			0
$129$	−4.94975	+	4.94975i	−0.435801	+	0.435801i
$130$		0			0
$131$	2.12132	+	2.12132i	0.185341	+	0.185341i	0.793678	−	0.608338i	$-0.208163\pi$
$131$	2.12132	+	2.12132i	0.185341	+	0.185341i	−0.608338	+	0.793678i	$0.708163\pi$
$132$	−6.00000			−0.522233
$133$	−2.82843	−	2.82843i	−0.245256	−	0.245256i
$134$		0			0
$135$	3.00000			0.258199
$136$		0			0
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		0			0
$139$	−1.41421	−	1.41421i	−0.119952	−	0.119952i	0.644583	−	0.764535i	$-0.277031\pi$
$139$	−1.41421	−	1.41421i	−0.119952	−	0.119952i	−0.764535	+	0.644583i	$0.777031\pi$
$140$	−24.0000			−2.02837
$141$	−4.24264	−	4.24264i	−0.357295	−	0.357295i
$142$		0			0
$143$	2.12132	−	2.12132i	0.177394	−	0.177394i
$144$			4.00000i			0.333333i
$145$			18.0000i			1.49482i
$146$		0			0
$147$	−6.36396	+	6.36396i	−0.524891	+	0.524891i
$148$	5.65685	+	5.65685i	0.464991	+	0.464991i
$149$	18.0000			1.47462			0.737309	−	0.675556i	$-0.236096\pi$
$149$	18.0000			1.47462			0.737309	+	0.675556i	$0.236096\pi$
$150$		0			0
$151$		−	8.00000i		−	0.651031i	−0.945537	−	0.325515i	$-0.894462\pi$
$151$		−	8.00000i		−	0.651031i	0.945537	−	0.325515i	$-0.105538\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	6.00000i		−	0.481932i
$156$	−1.41421	−	1.41421i	−0.113228	−	0.113228i
$157$	−11.0000			−0.877896			−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−11.0000			−0.877896			−0.438948	+	0.898513i	$0.644649\pi$
$158$		0			0
$159$	4.24264	−	4.24264i	0.336463	−	0.336463i
$160$		0			0
$161$		−	36.0000i		−	2.83720i
$162$		0			0
$163$	1.41421	−	1.41421i	0.110770	−	0.110770i	−0.649550	−	0.760319i	$-0.725042\pi$
$163$	1.41421	−	1.41421i	0.110770	−	0.110770i	0.760319	+	0.649550i	$0.225042\pi$
$164$	−4.24264	+	4.24264i	−0.331295	+	0.331295i
$165$	−6.36396	−	6.36396i	−0.495434	−	0.495434i
$166$		0			0
$167$	−14.8492	−	14.8492i	−1.14907	−	1.14907i	−0.986736	−	0.162333i	$-0.948098\pi$
$167$	−14.8492	−	14.8492i	−1.14907	−	1.14907i	−0.162333	−	0.986736i	$-0.551902\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−1.00000			−0.0764719
$172$		−	14.0000i		−	1.06749i
$173$	−10.6066	−	10.6066i	−0.806405	−	0.806405i	0.177683	−	0.984088i	$-0.443140\pi$
$173$	−10.6066	−	10.6066i	−0.806405	−	0.806405i	−0.984088	+	0.177683i	$0.943140\pi$
$174$		0			0
$175$	−11.3137	−	11.3137i	−0.855236	−	0.855236i
$176$	8.48528	−	8.48528i	0.639602	−	0.639602i
$177$	4.24264	−	4.24264i	0.318896	−	0.318896i
$178$		0			0
$179$		−	6.00000i		−	0.448461i	−0.974536	−	0.224231i	$-0.928013\pi$
$179$		−	6.00000i		−	0.448461i	0.974536	−	0.224231i	$-0.0719869\pi$
$180$	−4.24264	+	4.24264i	−0.316228	+	0.316228i
$181$	−9.89949	+	9.89949i	−0.735824	+	0.735824i	−0.971767	−	0.235943i	$-0.924182\pi$
$181$	−9.89949	+	9.89949i	−0.735824	+	0.735824i	0.235943	+	0.971767i	$0.424182\pi$
$182$		0			0
$183$	−8.00000			−0.591377
$184$		0			0
$185$			12.0000i			0.882258i
$186$		0			0
$187$		0			0
$188$	12.0000			0.875190
$189$			4.00000i			0.290957i
$190$		0			0
$191$	−18.0000			−1.30243			−0.651217	−	0.758891i	$-0.725741\pi$
$191$	−18.0000			−1.30243			−0.651217	+	0.758891i	$0.725741\pi$
$192$	−5.65685	−	5.65685i	−0.408248	−	0.408248i
$193$	15.5563	−	15.5563i	1.11977	−	1.11977i	0.127996	−	0.991775i	$-0.459146\pi$
$193$	15.5563	−	15.5563i	1.11977	−	1.11977i	0.991775	−	0.127996i	$-0.0408544\pi$
$194$		0			0
$195$		−	3.00000i		−	0.214834i
$196$		−	18.0000i		−	1.28571i
$197$	2.12132	−	2.12132i	0.151138	−	0.151138i	−0.627488	−	0.778626i	$-0.715917\pi$
$197$	2.12132	−	2.12132i	0.151138	−	0.151138i	0.778626	+	0.627488i	$0.215917\pi$
$198$		0			0
$199$	−11.3137	−	11.3137i	−0.802008	−	0.802008i	0.181402	−	0.983409i	$-0.441937\pi$
$199$	−11.3137	−	11.3137i	−0.802008	−	0.802008i	−0.983409	+	0.181402i	$0.941937\pi$
$200$		0			0
$201$	2.82843	+	2.82843i	0.199502	+	0.199502i
$202$		0			0
$203$	−24.0000			−1.68447
$204$		0			0
$205$	−9.00000			−0.628587
$206$		0			0
$207$	−6.36396	−	6.36396i	−0.442326	−	0.442326i
$208$	4.00000			0.277350
$209$	2.12132	+	2.12132i	0.146735	+	0.146735i
$210$		0			0
$211$	1.41421	−	1.41421i	0.0973585	−	0.0973585i	−0.656750	−	0.754108i	$-0.728069\pi$
$211$	1.41421	−	1.41421i	0.0973585	−	0.0973585i	0.754108	+	0.656750i	$0.228069\pi$
$212$			12.0000i			0.824163i
$213$			12.0000i			0.822226i
$214$		0			0
$215$	14.8492	−	14.8492i	1.01271	−	1.01271i
$216$		0			0
$217$	8.00000			0.543075
$218$		0			0
$219$		−	2.00000i		−	0.135147i
$220$	18.0000			1.21356
$221$		0			0
$222$		0			0
$223$			1.00000i			0.0669650i	0.999439	+	0.0334825i	$0.0106598\pi$
$223$			1.00000i			0.0669650i	−0.999439	+	0.0334825i	$0.989340\pi$
$224$		0			0
$225$	−4.00000			−0.266667
$226$		0			0
$227$	−2.12132	+	2.12132i	−0.140797	+	0.140797i	−0.773992	−	0.633195i	$-0.781743\pi$
$227$	−2.12132	+	2.12132i	−0.140797	+	0.140797i	0.633195	+	0.773992i	$0.281743\pi$
$228$	1.41421	−	1.41421i	0.0936586	−	0.0936586i
$229$			14.0000i			0.925146i	0.886581	+	0.462573i	$0.153074\pi$
$229$			14.0000i			0.925146i	−0.886581	+	0.462573i	$0.846926\pi$
$230$		0			0
$231$	8.48528	−	8.48528i	0.558291	−	0.558291i
$232$		0			0
$233$	14.8492	+	14.8492i	0.972806	+	0.972806i	0.999640	−	0.0268337i	$-0.00854246\pi$
$233$	14.8492	+	14.8492i	0.972806	+	0.972806i	−0.0268337	+	0.999640i	$0.508542\pi$
$234$		0			0
$235$	12.7279	+	12.7279i	0.830278	+	0.830278i
$236$			12.0000i			0.781133i
$237$	−10.0000			−0.649570
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		−	12.0000i		−	0.774597i
$241$	−5.65685	−	5.65685i	−0.364390	−	0.364390i	0.501036	−	0.865426i	$-0.332952\pi$
$241$	−5.65685	−	5.65685i	−0.364390	−	0.364390i	−0.865426	+	0.501036i	$0.832952\pi$
$242$		0			0
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	11.3137	−	11.3137i	0.724286	−	0.724286i
$245$	19.0919	−	19.0919i	1.21974	−	1.21974i
$246$		0			0
$247$			1.00000i			0.0636285i
$248$		0			0
$249$	4.24264	−	4.24264i	0.268866	−	0.268866i
$250$		0			0
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$	−5.65685	−	5.65685i	−0.356348	−	0.356348i
$253$			27.0000i			1.69748i
$254$		0			0
$255$		0			0
$256$	16.0000			1.00000
$257$		−	12.0000i		−	0.748539i	−0.927320	−	0.374270i	$-0.877893\pi$
$257$		−	12.0000i		−	0.748539i	0.927320	−	0.374270i	$-0.122107\pi$
$258$		0			0
$259$	−16.0000			−0.994192
$260$	4.24264	+	4.24264i	0.263117	+	0.263117i
$261$	−4.24264	+	4.24264i	−0.262613	+	0.262613i
$262$		0			0
$263$			12.0000i			0.739952i	0.929041	+	0.369976i	$0.120634\pi$
$263$			12.0000i			0.739952i	−0.929041	+	0.369976i	$0.879366\pi$
$264$		0			0
$265$	−12.7279	+	12.7279i	−0.781870	+	0.781870i
$266$		0			0
$267$		0			0
$268$	−8.00000			−0.488678
$269$	10.6066	+	10.6066i	0.646696	+	0.646696i	0.952193	−	0.305497i	$-0.0988226\pi$
$269$	10.6066	+	10.6066i	0.646696	+	0.646696i	−0.305497	+	0.952193i	$0.598823\pi$
$270$		0			0
$271$	11.0000			0.668202			0.334101	−	0.942537i	$-0.391567\pi$
$271$	11.0000			0.668202			0.334101	+	0.942537i	$0.391567\pi$
$272$		0			0
$273$	4.00000			0.242091
$274$		0			0
$275$	8.48528	+	8.48528i	0.511682	+	0.511682i
$276$	18.0000			1.08347
$277$	1.41421	+	1.41421i	0.0849719	+	0.0849719i	0.748315	−	0.663343i	$-0.230863\pi$
$277$	1.41421	+	1.41421i	0.0849719	+	0.0849719i	−0.663343	+	0.748315i	$0.730863\pi$
$278$		0			0
$279$	1.41421	−	1.41421i	0.0846668	−	0.0846668i
$280$		0			0
$281$			12.0000i			0.715860i	0.933748	+	0.357930i	$0.116517\pi$
$281$			12.0000i			0.715860i	−0.933748	+	0.357930i	$0.883483\pi$
$282$		0			0
$283$	7.07107	−	7.07107i	0.420331	−	0.420331i	−0.464986	−	0.885318i	$-0.653941\pi$
$283$	7.07107	−	7.07107i	0.420331	−	0.420331i	0.885318	+	0.464986i	$0.153941\pi$
$284$	−16.9706	−	16.9706i	−1.00702	−	1.00702i
$285$	3.00000			0.177705
$286$		0			0
$287$		−	12.0000i		−	0.708338i
$288$		0			0
$289$		0			0
$290$		0			0
$291$			16.0000i			0.937937i
$292$	2.82843	+	2.82843i	0.165521	+	0.165521i
$293$	24.0000			1.40209			0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000			1.40209			0.701047	+	0.713115i	$0.252716\pi$
$294$		0			0
$295$	−12.7279	+	12.7279i	−0.741048	+	0.741048i
$296$		0			0
$297$		−	3.00000i		−	0.174078i
$298$		0			0
$299$	−6.36396	+	6.36396i	−0.368037	+	0.368037i
$300$	5.65685	−	5.65685i	0.326599	−	0.326599i
$301$	19.7990	+	19.7990i	1.14119	+	1.14119i
$302$		0			0
$303$		0			0
$304$			4.00000i			0.229416i
$305$	24.0000			1.37424
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$			24.0000i			1.36753i
$309$	−3.53553	−	3.53553i	−0.201129	−	0.201129i
$310$		0			0
$311$	−16.9706	−	16.9706i	−0.962312	−	0.962312i	0.0370028	−	0.999315i	$-0.488219\pi$
$311$	−16.9706	−	16.9706i	−0.962312	−	0.962312i	−0.999315	+	0.0370028i	$0.988219\pi$
$312$		0			0
$313$	−11.3137	+	11.3137i	−0.639489	+	0.639489i	−0.950429	−	0.310941i	$-0.899356\pi$
$313$	−11.3137	+	11.3137i	−0.639489	+	0.639489i	0.310941	+	0.950429i	$0.399356\pi$
$314$		0			0
$315$		−	12.0000i		−	0.676123i
$316$	14.1421	−	14.1421i	0.795557	−	0.795557i
$317$	4.24264	−	4.24264i	0.238290	−	0.238290i	−0.577851	−	0.816142i	$-0.696109\pi$
$317$	4.24264	−	4.24264i	0.238290	−	0.238290i	0.816142	+	0.577851i	$0.196109\pi$
$318$		0			0
$319$	18.0000			1.00781
$320$	16.9706	+	16.9706i	0.948683	+	0.948683i
$321$		−	9.00000i		−	0.502331i
$322$		0			0
$323$		0			0
$324$	−2.00000			−0.111111
$325$			4.00000i			0.221880i
$326$		0			0
$327$	−20.0000			−1.10600
$328$		0			0
$329$	−16.9706	+	16.9706i	−0.935617	+	0.935617i
$330$		0			0
$331$		−	13.0000i		−	0.714545i	−0.934000	−	0.357272i	$-0.883707\pi$
$331$		−	13.0000i		−	0.714545i	0.934000	−	0.357272i	$-0.116293\pi$
$332$			12.0000i			0.658586i
$333$	−2.82843	+	2.82843i	−0.154997	+	0.154997i
$334$		0			0
$335$	−8.48528	−	8.48528i	−0.463600	−	0.463600i
$336$	16.0000			0.872872
$337$	−9.89949	−	9.89949i	−0.539260	−	0.539260i	0.384052	−	0.923312i	$-0.374528\pi$
$337$	−9.89949	−	9.89949i	−0.539260	−	0.539260i	−0.923312	+	0.384052i	$0.874528\pi$
$338$		0			0
$339$	−9.00000			−0.488813
$340$		0			0
$341$	−6.00000			−0.324918
$342$		0			0
$343$	5.65685	+	5.65685i	0.305441	+	0.305441i
$344$		0			0
$345$	19.0919	+	19.0919i	1.02787	+	1.02787i
$346$		0			0
$347$	−8.48528	+	8.48528i	−0.455514	+	0.455514i	−0.897180	−	0.441666i	$-0.854388\pi$
$347$	−8.48528	+	8.48528i	−0.455514	+	0.455514i	0.441666	+	0.897180i	$0.354388\pi$
$348$		−	12.0000i		−	0.643268i
$349$		−	19.0000i		−	1.01705i	−0.861048	−	0.508523i	$-0.830192\pi$
$349$		−	19.0000i		−	1.01705i	0.861048	−	0.508523i	$-0.169808\pi$
$350$		0			0
$351$	0.707107	−	0.707107i	0.0377426	−	0.0377426i
$352$		0			0
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$		−	36.0000i		−	1.91068i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$		0			0
$361$	18.0000			0.947368
$362$		0			0
$363$	1.41421	−	1.41421i	0.0742270	−	0.0742270i
$364$	−5.65685	+	5.65685i	−0.296500	+	0.296500i
$365$			6.00000i			0.314054i
$366$		0			0
$367$	5.65685	−	5.65685i	0.295285	−	0.295285i	−0.543879	−	0.839164i	$-0.683045\pi$
$367$	5.65685	−	5.65685i	0.295285	−	0.295285i	0.839164	+	0.543879i	$0.183045\pi$
$368$	−25.4558	+	25.4558i	−1.32698	+	1.32698i
$369$	−2.12132	−	2.12132i	−0.110432	−	0.110432i
$370$		0			0
$371$	−16.9706	−	16.9706i	−0.881068	−	0.881068i
$372$			4.00000i			0.207390i
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$	−3.00000			−0.154919
$376$		0			0
$377$	4.24264	+	4.24264i	0.218507	+	0.218507i
$378$		0			0
$379$	22.6274	+	22.6274i	1.16229	+	1.16229i	0.983973	+	0.178320i	$0.0570661\pi$
$379$	22.6274	+	22.6274i	1.16229	+	1.16229i	0.178320	+	0.983973i	$0.442934\pi$
$380$	−4.24264	+	4.24264i	−0.217643	+	0.217643i
$381$	−9.19239	+	9.19239i	−0.470940	+	0.470940i
$382$		0			0
$383$		−	12.0000i		−	0.613171i	−0.951843	−	0.306586i	$-0.900813\pi$
$383$		−	12.0000i		−	0.613171i	0.951843	−	0.306586i	$-0.0991866\pi$
$384$		0			0
$385$	−25.4558	+	25.4558i	−1.29735	+	1.29735i
$386$		0			0
$387$	7.00000			0.355830
$388$	−22.6274	−	22.6274i	−1.14873	−	1.14873i
$389$		−	36.0000i		−	1.82527i	−0.408773	−	0.912636i	$-0.634043\pi$
$389$		−	36.0000i		−	1.82527i	0.408773	−	0.912636i	$-0.365957\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		−	3.00000i		−	0.151330i
$394$		0			0
$395$	30.0000			1.50946
$396$	4.24264	+	4.24264i	0.213201	+	0.213201i
$397$	−14.1421	+	14.1421i	−0.709773	+	0.709773i	−0.966487	−	0.256714i	$-0.917360\pi$
$397$	−14.1421	+	14.1421i	−0.709773	+	0.709773i	0.256714	+	0.966487i	$0.417360\pi$
$398$		0			0
$399$			4.00000i			0.200250i
$400$			16.0000i			0.800000i
$401$	−10.6066	+	10.6066i	−0.529668	+	0.529668i	−0.920473	−	0.390805i	$-0.872197\pi$
$401$	−10.6066	+	10.6066i	−0.529668	+	0.529668i	0.390805	+	0.920473i	$0.372197\pi$
$402$		0			0
$403$	−1.41421	−	1.41421i	−0.0704470	−	0.0704470i
$404$		0			0
$405$	−2.12132	−	2.12132i	−0.105409	−	0.105409i
$406$		0			0
$407$	12.0000			0.594818
$408$		0			0
$409$	−19.0000			−0.939490			−0.469745	−	0.882802i	$-0.655654\pi$
$409$	−19.0000			−0.939490			−0.469745	+	0.882802i	$0.655654\pi$
$410$		0			0
$411$	4.24264	+	4.24264i	0.209274	+	0.209274i
$412$	10.0000			0.492665
$413$	−16.9706	−	16.9706i	−0.835067	−	0.835067i
$414$		0			0
$415$	−12.7279	+	12.7279i	−0.624789	+	0.624789i
$416$		0			0
$417$			2.00000i			0.0979404i
$418$		0			0
$419$	−8.48528	+	8.48528i	−0.414533	+	0.414533i	−0.883314	−	0.468781i	$-0.844693\pi$
$419$	−8.48528	+	8.48528i	−0.414533	+	0.414533i	0.468781	+	0.883314i	$0.344693\pi$
$420$	16.9706	+	16.9706i	0.828079	+	0.828079i
$421$	25.0000			1.21843			0.609213	−	0.793007i	$-0.291486\pi$
$421$	25.0000			1.21843			0.609213	+	0.793007i	$0.291486\pi$
$422$		0			0
$423$			6.00000i			0.291730i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			32.0000i			1.54859i
$428$	12.7279	+	12.7279i	0.615227	+	0.615227i
$429$	−3.00000			−0.144841
$430$		0			0
$431$	16.9706	−	16.9706i	0.817443	−	0.817443i	−0.168294	−	0.985737i	$-0.553826\pi$
$431$	16.9706	−	16.9706i	0.817443	−	0.817443i	0.985737	+	0.168294i	$0.0538257\pi$
$432$	2.82843	−	2.82843i	0.136083	−	0.136083i
$433$		−	1.00000i		−	0.0480569i	−0.999711	−	0.0240285i	$-0.992351\pi$
$433$		−	1.00000i		−	0.0480569i	0.999711	−	0.0240285i	$-0.00764923\pi$
$434$		0			0
$435$	12.7279	−	12.7279i	0.610257	−	0.610257i
$436$	28.2843	−	28.2843i	1.35457	−	1.35457i
$437$	−6.36396	−	6.36396i	−0.304430	−	0.304430i
$438$		0			0
$439$	19.7990	+	19.7990i	0.944954	+	0.944954i	0.998562	−	0.0536078i	$-0.0170721\pi$
$439$	19.7990	+	19.7990i	0.944954	+	0.944954i	−0.0536078	+	0.998562i	$0.517072\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$		0			0
$443$	6.00000			0.285069			0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000			0.285069			0.142534	+	0.989790i	$0.454475\pi$
$444$		−	8.00000i		−	0.379663i
$445$		0			0
$446$		0			0
$447$	−12.7279	−	12.7279i	−0.602010	−	0.602010i
$448$	−22.6274	+	22.6274i	−1.06904	+	1.06904i
$449$	−4.24264	+	4.24264i	−0.200223	+	0.200223i	−0.800095	−	0.599873i	$-0.795218\pi$
$449$	−4.24264	+	4.24264i	−0.200223	+	0.200223i	0.599873	+	0.800095i	$0.295218\pi$
$450$		0			0
$451$			9.00000i			0.423793i
$452$	12.7279	−	12.7279i	0.598671	−	0.598671i
$453$	−5.65685	+	5.65685i	−0.265782	+	0.265782i
$454$		0			0
$455$	−12.0000			−0.562569
$456$		0			0
$457$			19.0000i			0.888783i	0.895833	+	0.444391i	$0.146580\pi$
$457$			19.0000i			0.888783i	−0.895833	+	0.444391i	$0.853420\pi$
$458$		0			0
$459$		0			0
$460$	−54.0000			−2.51776
$461$		−	30.0000i		−	1.39724i	−0.715493	−	0.698620i	$-0.753798\pi$
$461$		−	30.0000i		−	1.39724i	0.715493	−	0.698620i	$-0.246202\pi$
$462$		0			0
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	16.9706	+	16.9706i	0.787839	+	0.787839i
$465$	−4.24264	+	4.24264i	−0.196748	+	0.196748i
$466$		0			0
$467$			42.0000i			1.94353i	0.235954	+	0.971764i	$0.424178\pi$
$467$			42.0000i			1.94353i	−0.235954	+	0.971764i	$0.575822\pi$
$468$			2.00000i			0.0924500i
$469$	11.3137	−	11.3137i	0.522419	−	0.522419i
$470$		0			0
$471$	7.77817	+	7.77817i	0.358399	+	0.358399i
$472$		0			0
$473$	−14.8492	−	14.8492i	−0.682769	−	0.682769i
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−6.00000			−0.274721
$478$		0			0
$479$	19.0919	+	19.0919i	0.872330	+	0.872330i	0.992726	−	0.120396i	$-0.0384163\pi$
$479$	19.0919	+	19.0919i	0.872330	+	0.872330i	−0.120396	+	0.992726i	$0.538416\pi$
$480$		0			0
$481$	2.82843	+	2.82843i	0.128965	+	0.128965i
$482$		0			0
$483$	−25.4558	+	25.4558i	−1.15828	+	1.15828i
$484$			4.00000i			0.181818i
$485$		−	48.0000i		−	2.17957i
$486$		0			0
$487$	15.5563	−	15.5563i	0.704925	−	0.704925i	−0.260538	−	0.965464i	$-0.583900\pi$
$487$	15.5563	−	15.5563i	0.704925	−	0.704925i	0.965464	+	0.260538i	$0.0839000\pi$
$488$		0			0
$489$	−2.00000			−0.0904431
$490$		0			0
$491$			6.00000i			0.270776i	0.990793	+	0.135388i	$0.0432281\pi$
$491$			6.00000i			0.270776i	−0.990793	+	0.135388i	$0.956772\pi$
$492$	6.00000			0.270501
$493$		0			0
$494$		0			0
$495$			9.00000i			0.404520i
$496$	−5.65685	−	5.65685i	−0.254000	−	0.254000i
$497$	48.0000			2.15309
$498$		0			0
$499$	15.5563	−	15.5563i	0.696398	−	0.696398i	−0.267234	−	0.963632i	$-0.586110\pi$
$499$	15.5563	−	15.5563i	0.696398	−	0.696398i	0.963632	+	0.267234i	$0.0861096\pi$
$500$	4.24264	−	4.24264i	0.189737	−	0.189737i
$501$			21.0000i			0.938211i
$502$		0			0
$503$	10.6066	−	10.6066i	0.472925	−	0.472925i	−0.429935	−	0.902860i	$-0.641463\pi$
$503$	10.6066	−	10.6066i	0.472925	−	0.472925i	0.902860	+	0.429935i	$0.141463\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	8.48528	+	8.48528i	0.376845	+	0.376845i
$508$		−	26.0000i		−	1.15356i
$509$	36.0000			1.59567			0.797836	−	0.602875i	$-0.205978\pi$
$509$	36.0000			1.59567			0.797836	+	0.602875i	$0.205978\pi$
$510$		0			0
$511$	−8.00000			−0.353899
$512$		0			0
$513$	0.707107	+	0.707107i	0.0312195	+	0.0312195i
$514$		0			0
$515$	10.6066	+	10.6066i	0.467383	+	0.467383i
$516$	−9.89949	+	9.89949i	−0.435801	+	0.435801i
$517$	12.7279	−	12.7279i	0.559773	−	0.559773i
$518$		0			0
$519$			15.0000i			0.658427i
$520$		0			0
$521$	−14.8492	+	14.8492i	−0.650557	+	0.650557i	−0.953127	−	0.302570i	$-0.902155\pi$
$521$	−14.8492	+	14.8492i	−0.650557	+	0.650557i	0.302570	+	0.953127i	$0.402155\pi$
$522$		0			0
$523$	−20.0000			−0.874539			−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000			−0.874539			−0.437269	+	0.899331i	$0.644054\pi$
$524$	4.24264	+	4.24264i	0.185341	+	0.185341i
$525$			16.0000i			0.698297i
$526$		0			0
$527$		0			0
$528$	−12.0000			−0.522233
$529$		−	58.0000i		−	2.52174i
$530$		0			0
$531$	−6.00000			−0.260378
$532$	−5.65685	−	5.65685i	−0.245256	−	0.245256i
$533$	−2.12132	+	2.12132i	−0.0918846	+	0.0918846i
$534$		0			0
$535$			27.0000i			1.16731i
$536$		0			0
$537$	−4.24264	+	4.24264i	−0.183083	+	0.183083i
$538$		0			0
$539$	−19.0919	−	19.0919i	−0.822346	−	0.822346i
$540$	6.00000			0.258199
$541$	11.3137	+	11.3137i	0.486414	+	0.486414i	0.907173	−	0.420758i	$-0.138236\pi$
$541$	11.3137	+	11.3137i	0.486414	+	0.486414i	−0.420758	+	0.907173i	$0.638236\pi$
$542$		0			0
$543$	14.0000			0.600798
$544$		0			0
$545$	60.0000			2.57012
$546$		0			0
$547$	−5.65685	−	5.65685i	−0.241870	−	0.241870i	0.575754	−	0.817623i	$-0.304709\pi$
$547$	−5.65685	−	5.65685i	−0.241870	−	0.241870i	−0.817623	+	0.575754i	$0.804709\pi$
$548$	−12.0000			−0.512615
$549$	5.65685	+	5.65685i	0.241429	+	0.241429i
$550$		0			0
$551$	−4.24264	+	4.24264i	−0.180743	+	0.180743i
$552$		0			0
$553$			40.0000i			1.70097i
$554$		0			0
$555$	8.48528	−	8.48528i	0.360180	−	0.360180i
$556$	−2.82843	−	2.82843i	−0.119952	−	0.119952i
$557$	30.0000			1.27114			0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000			1.27114			0.635570	+	0.772043i	$0.280765\pi$
$558$		0			0
$559$		−	7.00000i		−	0.296068i
$560$	−48.0000			−2.02837
$561$		0			0
$562$		0			0
$563$			30.0000i			1.26435i	0.774826	+	0.632175i	$0.217837\pi$
$563$			30.0000i			1.26435i	−0.774826	+	0.632175i	$0.782163\pi$
$564$	−8.48528	−	8.48528i	−0.357295	−	0.357295i
$565$	27.0000			1.13590
$566$		0			0
$567$	2.82843	−	2.82843i	0.118783	−	0.118783i
$568$		0			0
$569$		−	24.0000i		−	1.00613i	−0.864248	−	0.503066i	$-0.832205\pi$
$569$		−	24.0000i		−	1.00613i	0.864248	−	0.503066i	$-0.167795\pi$
$570$		0			0
$571$	5.65685	−	5.65685i	0.236732	−	0.236732i	−0.578763	−	0.815495i	$-0.696465\pi$
$571$	5.65685	−	5.65685i	0.236732	−	0.236732i	0.815495	+	0.578763i	$0.196465\pi$
$572$	4.24264	−	4.24264i	0.177394	−	0.177394i
$573$	12.7279	+	12.7279i	0.531717	+	0.531717i
$574$		0			0
$575$	−25.4558	−	25.4558i	−1.06158	−	1.06158i
$576$			8.00000i			0.333333i
$577$	−7.00000			−0.291414			−0.145707	−	0.989328i	$-0.546546\pi$
$577$	−7.00000			−0.291414			−0.145707	+	0.989328i	$0.546546\pi$
$578$		0			0
$579$	−22.0000			−0.914289
$580$			36.0000i			1.49482i
$581$	−16.9706	−	16.9706i	−0.704058	−	0.704058i
$582$		0			0
$583$	12.7279	+	12.7279i	0.527137	+	0.527137i
$584$		0			0
$585$	−2.12132	+	2.12132i	−0.0877058	+	0.0877058i
$586$		0			0
$587$		−	36.0000i		−	1.48588i	−0.669359	−	0.742940i	$-0.733431\pi$
$587$		−	36.0000i		−	1.48588i	0.669359	−	0.742940i	$-0.266569\pi$
$588$	−12.7279	+	12.7279i	−0.524891	+	0.524891i
$589$	1.41421	−	1.41421i	0.0582717	−	0.0582717i
$590$		0			0
$591$	−3.00000			−0.123404
$592$	11.3137	+	11.3137i	0.464991	+	0.464991i
$593$			18.0000i			0.739171i	0.929197	+	0.369586i	$0.120500\pi$
$593$			18.0000i			0.739171i	−0.929197	+	0.369586i	$0.879500\pi$
$594$		0			0
$595$		0			0
$596$	36.0000			1.47462
$597$			16.0000i			0.654836i
$598$		0			0
$599$	6.00000			0.245153			0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000			0.245153			0.122577	+	0.992459i	$0.460884\pi$
$600$		0			0
$601$	−26.8701	+	26.8701i	−1.09605	+	1.09605i	−0.101185	+	0.994868i	$0.532263\pi$
$601$	−26.8701	+	26.8701i	−1.09605	+	1.09605i	−0.994868	+	0.101185i	$0.967737\pi$
$602$		0			0
$603$		−	4.00000i		−	0.162893i
$604$		−	16.0000i		−	0.651031i
$605$	−4.24264	+	4.24264i	−0.172488	+	0.172488i
$606$		0			0
$607$	26.8701	+	26.8701i	1.09062	+	1.09062i	0.995462	+	0.0951600i	$0.0303363\pi$
$607$	26.8701	+	26.8701i	1.09062	+	1.09062i	0.0951600	+	0.995462i	$0.469664\pi$
$608$		0			0
$609$	16.9706	+	16.9706i	0.687682	+	0.687682i
$610$		0			0
$611$	6.00000			0.242734
$612$		0			0
$613$	11.0000			0.444286			0.222143	−	0.975014i	$-0.428695\pi$
$613$	11.0000			0.444286			0.222143	+	0.975014i	$0.428695\pi$
$614$		0			0
$615$	6.36396	+	6.36396i	0.256620	+	0.256620i
$616$		0			0
$617$	−4.24264	−	4.24264i	−0.170802	−	0.170802i	0.616530	−	0.787332i	$-0.288538\pi$
$617$	−4.24264	−	4.24264i	−0.170802	−	0.170802i	−0.787332	+	0.616530i	$0.788538\pi$
$618$		0			0
$619$	−7.07107	+	7.07107i	−0.284210	+	0.284210i	−0.834786	−	0.550575i	$-0.814408\pi$
$619$	−7.07107	+	7.07107i	−0.284210	+	0.284210i	0.550575	+	0.834786i	$0.314408\pi$
$620$		−	12.0000i		−	0.481932i
$621$			9.00000i			0.361158i
$622$		0			0
$623$		0			0
$624$	−2.82843	−	2.82843i	−0.113228	−	0.113228i
$625$	29.0000			1.16000
$626$		0			0
$627$		−	3.00000i		−	0.119808i
$628$	−22.0000			−0.877896
$629$		0			0
$630$		0			0
$631$			37.0000i			1.47295i	0.676467	+	0.736473i	$0.263510\pi$
$631$			37.0000i			1.47295i	−0.676467	+	0.736473i	$0.736490\pi$
$632$		0			0
$633$	−2.00000			−0.0794929
$634$		0			0
$635$	27.5772	−	27.5772i	1.09437	−	1.09437i
$636$	8.48528	−	8.48528i	0.336463	−	0.336463i
$637$		−	9.00000i		−	0.356593i
$638$		0			0
$639$	8.48528	−	8.48528i	0.335673	−	0.335673i
$640$		0			0
$641$	−23.3345	−	23.3345i	−0.921658	−	0.921658i	0.0754884	−	0.997147i	$-0.475948\pi$
$641$	−23.3345	−	23.3345i	−0.921658	−	0.921658i	−0.997147	+	0.0754884i	$0.975948\pi$
$642$		0			0
$643$	−22.6274	−	22.6274i	−0.892338	−	0.892338i	0.102405	−	0.994743i	$-0.467346\pi$
$643$	−22.6274	−	22.6274i	−0.892338	−	0.892338i	−0.994743	+	0.102405i	$0.967346\pi$
$644$		−	72.0000i		−	2.83720i
$645$	−21.0000			−0.826874
$646$		0			0
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$		0			0
$649$	12.7279	+	12.7279i	0.499615	+	0.499615i
$650$		0			0
$651$	−5.65685	−	5.65685i	−0.221710	−	0.221710i
$652$	2.82843	−	2.82843i	0.110770	−	0.110770i
$653$	19.0919	−	19.0919i	0.747123	−	0.747123i	−0.226815	−	0.973938i	$-0.572831\pi$
$653$	19.0919	−	19.0919i	0.747123	−	0.747123i	0.973938	+	0.226815i	$0.0728312\pi$
$654$		0			0
$655$			9.00000i			0.351659i
$656$	−8.48528	+	8.48528i	−0.331295	+	0.331295i
$657$	−1.41421	+	1.41421i	−0.0551737	+	0.0551737i
$658$		0			0
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$	−12.7279	−	12.7279i	−0.495434	−	0.495434i
$661$			31.0000i			1.20576i	0.797832	+	0.602880i	$0.205980\pi$
$661$			31.0000i			1.20576i	−0.797832	+	0.602880i	$0.794020\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	12.0000i		−	0.465340i
$666$		0			0
$667$	−54.0000			−2.09089
$668$	−29.6985	−	29.6985i	−1.14907	−	1.14907i
$669$	0.707107	−	0.707107i	0.0273383	−	0.0273383i
$670$		0			0
$671$		−	24.0000i		−	0.926510i
$672$		0			0
$673$	−15.5563	+	15.5563i	−0.599653	+	0.599653i	−0.940220	−	0.340567i	$-0.889381\pi$
$673$	−15.5563	+	15.5563i	−0.599653	+	0.599653i	0.340567	+	0.940220i	$0.389381\pi$
$674$		0			0
$675$	2.82843	+	2.82843i	0.108866	+	0.108866i
$676$	−24.0000			−0.923077
$677$	19.0919	+	19.0919i	0.733761	+	0.733761i	0.971363	−	0.237602i	$-0.0763614\pi$
$677$	19.0919	+	19.0919i	0.733761	+	0.733761i	−0.237602	+	0.971363i	$0.576361\pi$
$678$		0			0
$679$	64.0000			2.45609
$680$		0			0
$681$	3.00000			0.114960
$682$		0			0
$683$	−2.12132	−	2.12132i	−0.0811701	−	0.0811701i	0.665356	−	0.746526i	$-0.268280\pi$
$683$	−2.12132	−	2.12132i	−0.0811701	−	0.0811701i	−0.746526	+	0.665356i	$0.768280\pi$
$684$	−2.00000			−0.0764719
$685$	−12.7279	−	12.7279i	−0.486309	−	0.486309i
$686$		0			0
$687$	9.89949	−	9.89949i	0.377689	−	0.377689i
$688$		−	28.0000i		−	1.06749i
$689$			6.00000i			0.228582i
$690$		0			0
$691$	−14.1421	+	14.1421i	−0.537992	+	0.537992i	−0.922939	−	0.384947i	$-0.874220\pi$
$691$	−14.1421	+	14.1421i	−0.537992	+	0.537992i	0.384947	+	0.922939i	$0.374220\pi$
$692$	−21.2132	−	21.2132i	−0.806405	−	0.806405i
$693$	−12.0000			−0.455842
$694$		0			0
$695$		−	6.00000i		−	0.227593i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		−	21.0000i		−	0.794293i
$700$	−22.6274	−	22.6274i	−0.855236	−	0.855236i
$701$	−24.0000			−0.906467			−0.453234	−	0.891392i	$-0.649730\pi$
$701$	−24.0000			−0.906467			−0.453234	+	0.891392i	$0.649730\pi$
$702$		0			0
$703$	−2.82843	+	2.82843i	−0.106676	+	0.106676i
$704$	16.9706	−	16.9706i	0.639602	−	0.639602i
$705$		−	18.0000i		−	0.677919i
$706$		0			0
$707$		0			0
$708$	8.48528	−	8.48528i	0.318896	−	0.318896i
$709$	9.89949	+	9.89949i	0.371783	+	0.371783i	0.868126	−	0.496343i	$-0.165324\pi$
$709$	9.89949	+	9.89949i	0.371783	+	0.371783i	−0.496343	+	0.868126i	$0.665324\pi$
$710$		0			0
$711$	7.07107	+	7.07107i	0.265186	+	0.265186i
$712$		0			0
$713$	18.0000			0.674105
$714$		0			0
$715$	9.00000			0.336581
$716$		−	12.0000i		−	0.448461i
$717$	8.48528	+	8.48528i	0.316889	+	0.316889i
$718$		0			0
$719$	2.12132	+	2.12132i	0.0791119	+	0.0791119i	0.745555	−	0.666444i	$-0.232184\pi$
$719$	2.12132	+	2.12132i	0.0791119	+	0.0791119i	−0.666444	+	0.745555i	$0.732184\pi$
$720$	−8.48528	+	8.48528i	−0.316228	+	0.316228i
$721$	−14.1421	+	14.1421i	−0.526681	+	0.526681i
$722$		0			0
$723$			8.00000i			0.297523i
$724$	−19.7990	+	19.7990i	−0.735824	+	0.735824i
$725$	−16.9706	+	16.9706i	−0.630271	+	0.630271i
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		0			0
$732$	−16.0000			−0.591377
$733$		−	2.00000i		−	0.0738717i	−0.999318	−	0.0369358i	$-0.988240\pi$
$733$		−	2.00000i		−	0.0738717i	0.999318	−	0.0369358i	$-0.0117597\pi$
$734$		0			0
$735$	−27.0000			−0.995910
$736$		0			0
$737$	−8.48528	+	8.48528i	−0.312559	+	0.312559i
$738$		0			0
$739$		−	1.00000i		−	0.0367856i	−0.999831	−	0.0183928i	$-0.994145\pi$
$739$		−	1.00000i		−	0.0367856i	0.999831	−	0.0183928i	$-0.00585494\pi$
$740$			24.0000i			0.882258i
$741$	0.707107	−	0.707107i	0.0259762	−	0.0259762i
$742$		0			0
$743$	16.9706	+	16.9706i	0.622590	+	0.622590i	0.946193	−	0.323603i	$-0.104894\pi$
$743$	16.9706	+	16.9706i	0.622590	+	0.622590i	−0.323603	+	0.946193i	$0.604894\pi$
$744$		0			0
$745$	38.1838	+	38.1838i	1.39894	+	1.39894i
$746$		0			0
$747$	−6.00000			−0.219529
$748$		0			0
$749$	−36.0000			−1.31541
$750$		0			0
$751$	32.5269	+	32.5269i	1.18692	+	1.18692i	0.977913	+	0.209010i	$0.0670243\pi$
$751$	32.5269	+	32.5269i	1.18692	+	1.18692i	0.209010	+	0.977913i	$0.432976\pi$
$752$	24.0000			0.875190
$753$	16.9706	+	16.9706i	0.618442	+	0.618442i
$754$		0			0
$755$	16.9706	−	16.9706i	0.617622	−	0.617622i
$756$			8.00000i			0.290957i
$757$		−	43.0000i		−	1.56286i	−0.623992	−	0.781431i	$-0.714490\pi$
$757$		−	43.0000i		−	1.56286i	0.623992	−	0.781431i	$-0.285510\pi$
$758$		0			0
$759$	19.0919	−	19.0919i	0.692991	−	0.692991i
$760$		0			0
$761$	−30.0000			−1.08750			−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000			−1.08750			−0.543750	+	0.839248i	$0.682996\pi$
$762$		0			0
$763$			80.0000i			2.89619i
$764$	−36.0000			−1.30243
$765$		0			0
$766$		0			0
$767$			6.00000i			0.216647i
$768$	−11.3137	−	11.3137i	−0.408248	−	0.408248i
$769$	−41.0000			−1.47850			−0.739249	−	0.673432i	$-0.764819\pi$
$769$	−41.0000			−1.47850			−0.739249	+	0.673432i	$0.764819\pi$
$770$		0			0
$771$	−8.48528	+	8.48528i	−0.305590	+	0.305590i
$772$	31.1127	−	31.1127i	1.11977	−	1.11977i
$773$			24.0000i			0.863220i	0.902060	+	0.431610i	$0.142054\pi$
$773$			24.0000i			0.863220i	−0.902060	+	0.431610i	$0.857946\pi$
$774$		0			0
$775$	5.65685	−	5.65685i	0.203200	−	0.203200i
$776$		0			0
$777$	11.3137	+	11.3137i	0.405877	+	0.405877i
$778$		0			0
$779$	−2.12132	−	2.12132i	−0.0760042	−	0.0760042i
$780$		−	6.00000i		−	0.214834i
$781$	−36.0000			−1.28818
$782$		0			0
$783$	6.00000			0.214423
$784$		−	36.0000i		−	1.28571i
$785$	−23.3345	−	23.3345i	−0.832845	−	0.832845i
$786$		0			0
$787$	−28.2843	−	28.2843i	−1.00823	−	1.00823i	−0.999966	−	0.00825949i	$-0.997371\pi$
$787$	−28.2843	−	28.2843i	−1.00823	−	1.00823i	−0.00825949	−	0.999966i	$-0.502629\pi$
$788$	4.24264	−	4.24264i	0.151138	−	0.151138i
$789$	8.48528	−	8.48528i	0.302084	−	0.302084i
$790$		0			0
$791$			36.0000i			1.28001i
$792$		0			0
$793$	5.65685	−	5.65685i	0.200881	−	0.200881i
$794$		0			0
$795$	18.0000			0.638394
$796$	−22.6274	−	22.6274i	−0.802008	−	0.802008i
$797$			48.0000i			1.70025i	0.526583	+	0.850124i	$0.323473\pi$
$797$			48.0000i			1.70025i	−0.526583	+	0.850124i	$0.676527\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.00000			0.211735
$804$	5.65685	+	5.65685i	0.199502	+	0.199502i
$805$	76.3675	−	76.3675i	2.69160	−	2.69160i
$806$		0			0
$807$		−	15.0000i		−	0.528025i
$808$		0			0
$809$	−36.0624	+	36.0624i	−1.26789	+	1.26789i	−0.320711	+	0.947177i	$0.603922\pi$
$809$	−36.0624	+	36.0624i	−1.26789	+	1.26789i	−0.947177	+	0.320711i	$0.896078\pi$
$810$		0			0
$811$	−7.07107	−	7.07107i	−0.248299	−	0.248299i	0.571973	−	0.820272i	$-0.306178\pi$
$811$	−7.07107	−	7.07107i	−0.248299	−	0.248299i	−0.820272	+	0.571973i	$0.806178\pi$
$812$	−48.0000			−1.68447
$813$	−7.77817	−	7.77817i	−0.272792	−	0.272792i
$814$		0			0
$815$	6.00000			0.210171
$816$		0			0
$817$	7.00000			0.244899
$818$		0			0
$819$	−2.82843	−	2.82843i	−0.0988332	−	0.0988332i
$820$	−18.0000			−0.628587
$821$	−14.8492	−	14.8492i	−0.518242	−	0.518242i	0.398797	−	0.917039i	$-0.369428\pi$
$821$	−14.8492	−	14.8492i	−0.518242	−	0.518242i	−0.917039	+	0.398797i	$0.869428\pi$
$822$		0			0
$823$	−19.7990	+	19.7990i	−0.690149	+	0.690149i	−0.962265	−	0.272115i	$-0.912277\pi$
$823$	−19.7990	+	19.7990i	−0.690149	+	0.690149i	0.272115	+	0.962265i	$0.412277\pi$
$824$		0			0
$825$		−	12.0000i		−	0.417786i
$826$		0			0
$827$	14.8492	−	14.8492i	0.516359	−	0.516359i	−0.400109	−	0.916468i	$-0.631028\pi$
$827$	14.8492	−	14.8492i	0.516359	−	0.516359i	0.916468	+	0.400109i	$0.131028\pi$
$828$	−12.7279	−	12.7279i	−0.442326	−	0.442326i
$829$	−14.0000			−0.486240			−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000			−0.486240			−0.243120	+	0.969996i	$0.578171\pi$
$830$		0			0
$831$		−	2.00000i		−	0.0693792i
$832$	8.00000			0.277350
$833$		0			0
$834$		0			0
$835$		−	63.0000i		−	2.18020i
$836$	4.24264	+	4.24264i	0.146735	+	0.146735i
$837$	−2.00000			−0.0691301
$838$		0			0
$839$	40.3051	−	40.3051i	1.39149	−	1.39149i	0.569483	−	0.822003i	$-0.307143\pi$
$839$	40.3051	−	40.3051i	1.39149	−	1.39149i	0.822003	−	0.569483i	$-0.192857\pi$
$840$		0			0
$841$			7.00000i			0.241379i
$842$		0			0
$843$	8.48528	−	8.48528i	0.292249	−	0.292249i
$844$	2.82843	−	2.82843i	0.0973585	−	0.0973585i
$845$	−25.4558	−	25.4558i	−0.875708	−	0.875708i
$846$		0			0
$847$	−5.65685	−	5.65685i	−0.194372	−	0.194372i
$848$			24.0000i			0.824163i
$849$	−10.0000			−0.343199
$850$		0			0
$851$	−36.0000			−1.23406
$852$			24.0000i			0.822226i
$853$	−18.3848	−	18.3848i	−0.629483	−	0.629483i	0.318455	−	0.947938i	$-0.396836\pi$
$853$	−18.3848	−	18.3848i	−0.629483	−	0.629483i	−0.947938	+	0.318455i	$0.896836\pi$
$854$		0			0
$855$	−2.12132	−	2.12132i	−0.0725476	−	0.0725476i
$856$		0			0
$857$	−12.7279	+	12.7279i	−0.434778	+	0.434778i	−0.890250	−	0.455472i	$-0.849470\pi$
$857$	−12.7279	+	12.7279i	−0.434778	+	0.434778i	0.455472	+	0.890250i	$0.349470\pi$
$858$		0			0
$859$			20.0000i			0.682391i	0.939992	+	0.341196i	$0.110832\pi$
$859$			20.0000i			0.682391i	−0.939992	+	0.341196i	$0.889168\pi$
$860$	29.6985	−	29.6985i	1.01271	−	1.01271i
$861$	−8.48528	+	8.48528i	−0.289178	+	0.289178i
$862$		0			0
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$		−	45.0000i		−	1.53005i
$866$		0			0
$867$		0			0
$868$	16.0000			0.543075
$869$		−	30.0000i		−	1.01768i
$870$		0			0
$871$	−4.00000			−0.135535
$872$		0			0
$873$	11.3137	−	11.3137i	0.382911	−	0.382911i
$874$		0			0
$875$			12.0000i			0.405674i
$876$		−	4.00000i		−	0.135147i
$877$	9.89949	−	9.89949i	0.334282	−	0.334282i	−0.519928	−	0.854210i	$-0.674041\pi$
$877$	9.89949	−	9.89949i	0.334282	−	0.334282i	0.854210	+	0.519928i	$0.174041\pi$
$878$		0			0
$879$	−16.9706	−	16.9706i	−0.572403	−	0.572403i
$880$	36.0000			1.21356
$881$	−12.7279	−	12.7279i	−0.428815	−	0.428815i	0.459410	−	0.888224i	$-0.348061\pi$
$881$	−12.7279	−	12.7279i	−0.428815	−	0.428815i	−0.888224	+	0.459410i	$0.848061\pi$
$882$		0			0
$883$	11.0000			0.370179			0.185090	−	0.982722i	$-0.440742\pi$
$883$	11.0000			0.370179			0.185090	+	0.982722i	$0.440742\pi$
$884$		0			0
$885$	18.0000			0.605063
$886$		0			0
$887$	−27.5772	−	27.5772i	−0.925951	−	0.925951i	0.0714907	−	0.997441i	$-0.477224\pi$
$887$	−27.5772	−	27.5772i	−0.925951	−	0.925951i	−0.997441	+	0.0714907i	$0.977224\pi$
$888$		0			0
$889$	36.7696	+	36.7696i	1.23321	+	1.23321i
$890$		0			0
$891$	−2.12132	+	2.12132i	−0.0710669	+	0.0710669i
$892$			2.00000i			0.0669650i
$893$			6.00000i			0.200782i
$894$		0			0
$895$	12.7279	−	12.7279i	0.425448	−	0.425448i
$896$		0			0
$897$	9.00000			0.300501
$898$		0			0
$899$		−	12.0000i		−	0.400222i
$900$	−8.00000			−0.266667
$901$		0			0
$902$		0			0
$903$		−	28.0000i		−	0.931782i
$904$		0			0
$905$	−42.0000			−1.39613
$906$		0			0
$907$	−1.41421	+	1.41421i	−0.0469582	+	0.0469582i	−0.730196	−	0.683238i	$-0.760571\pi$
$907$	−1.41421	+	1.41421i	−0.0469582	+	0.0469582i	0.683238	+	0.730196i	$0.260571\pi$
$908$	−4.24264	+	4.24264i	−0.140797	+	0.140797i
$909$		0			0
$910$		0			0
$911$	−19.0919	+	19.0919i	−0.632542	+	0.632542i	−0.948705	−	0.316163i	$-0.897605\pi$
$911$	−19.0919	+	19.0919i	−0.632542	+	0.632542i	0.316163	+	0.948705i	$0.397605\pi$
$912$	2.82843	−	2.82843i	0.0936586	−	0.0936586i
$913$	12.7279	+	12.7279i	0.421233	+	0.421233i
$914$		0			0
$915$	−16.9706	−	16.9706i	−0.561029	−	0.561029i
$916$			28.0000i			0.925146i
$917$	−12.0000			−0.396275
$918$		0			0
$919$	11.0000			0.362857			0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000			0.362857			0.181428	+	0.983404i	$0.441928\pi$
$920$		0			0
$921$	−14.1421	−	14.1421i	−0.465999	−	0.465999i
$922$		0			0
$923$	−8.48528	−	8.48528i	−0.279296	−	0.279296i
$924$	16.9706	−	16.9706i	0.558291	−	0.558291i
$925$	−11.3137	+	11.3137i	−0.371992	+	0.371992i
$926$		0			0
$927$			5.00000i			0.164222i
$928$		0			0
$929$	−10.6066	+	10.6066i	−0.347991	+	0.347991i	−0.859361	−	0.511370i	$-0.829138\pi$
$929$	−10.6066	+	10.6066i	−0.347991	+	0.347991i	0.511370	+	0.859361i	$0.329138\pi$
$930$		0			0
$931$	9.00000			0.294963
$932$	29.6985	+	29.6985i	0.972806	+	0.972806i
$933$			24.0000i			0.785725i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			22.0000i			0.718709i	0.933201	+	0.359354i	$0.117003\pi$
$937$			22.0000i			0.718709i	−0.933201	+	0.359354i	$0.882997\pi$
$938$		0			0
$939$	16.0000			0.522140
$940$	25.4558	+	25.4558i	0.830278	+	0.830278i
$941$	−12.7279	+	12.7279i	−0.414918	+	0.414918i	−0.883448	−	0.468529i	$-0.844784\pi$
$941$	−12.7279	+	12.7279i	−0.414918	+	0.414918i	0.468529	+	0.883448i	$0.344784\pi$
$942$		0			0
$943$		−	27.0000i		−	0.879241i
$944$			24.0000i			0.781133i
$945$	−8.48528	+	8.48528i	−0.276026	+	0.276026i
$946$		0			0
$947$	25.4558	+	25.4558i	0.827204	+	0.827204i	0.987129	−	0.159925i	$-0.0511253\pi$
$947$	25.4558	+	25.4558i	0.827204	+	0.827204i	−0.159925	+	0.987129i	$0.551125\pi$
$948$	−20.0000			−0.649570
$949$	1.41421	+	1.41421i	0.0459073	+	0.0459073i
$950$		0			0
$951$	−6.00000			−0.194563
$952$		0			0
$953$	36.0000			1.16615			0.583077	−	0.812417i	$-0.301849\pi$
$953$	36.0000			1.16615			0.583077	+	0.812417i	$0.301849\pi$
$954$		0			0
$955$	−38.1838	−	38.1838i	−1.23560	−	1.23560i
$956$	−24.0000			−0.776215
$957$	−12.7279	−	12.7279i	−0.411435	−	0.411435i
$958$		0			0
$959$	16.9706	−	16.9706i	0.548008	−	0.548008i
$960$		−	24.0000i		−	0.774597i
$961$		−	27.0000i		−	0.870968i
$962$		0			0
$963$	−6.36396	+	6.36396i	−0.205076	+	0.205076i
$964$	−11.3137	−	11.3137i	−0.364390	−	0.364390i
$965$	66.0000			2.12462
$966$		0			0
$967$		−	41.0000i		−	1.31847i	−0.751936	−	0.659236i	$-0.770880\pi$
$967$		−	41.0000i		−	1.31847i	0.751936	−	0.659236i	$-0.229120\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	6.00000i		−	0.192549i	−0.995355	−	0.0962746i	$-0.969307\pi$
$971$		−	6.00000i		−	0.192549i	0.995355	−	0.0962746i	$-0.0306927\pi$
$972$	1.41421	+	1.41421i	0.0453609	+	0.0453609i
$973$	8.00000			0.256468
$974$		0			0
$975$	2.82843	−	2.82843i	0.0905822	−	0.0905822i
$976$	22.6274	−	22.6274i	0.724286	−	0.724286i
$977$		−	30.0000i		−	0.959785i	−0.877327	−	0.479893i	$-0.840676\pi$
$977$		−	30.0000i		−	0.959785i	0.877327	−	0.479893i	$-0.159324\pi$
$978$		0			0
$979$		0			0
$980$	38.1838	−	38.1838i	1.21974	−	1.21974i
$981$	14.1421	+	14.1421i	0.451524	+	0.451524i
$982$		0			0
$983$	6.36396	+	6.36396i	0.202979	+	0.202979i	0.801275	−	0.598296i	$-0.204155\pi$
$983$	6.36396	+	6.36396i	0.202979	+	0.202979i	−0.598296	+	0.801275i	$0.704155\pi$
$984$		0			0
$985$	9.00000			0.286764
$986$		0			0
$987$	24.0000			0.763928
$988$			2.00000i			0.0636285i
$989$	44.5477	+	44.5477i	1.41654	+	1.41654i
$990$		0			0
$991$	−36.7696	−	36.7696i	−1.16802	−	1.16802i	−0.982672	−	0.185351i	$-0.940658\pi$
$991$	−36.7696	−	36.7696i	−1.16802	−	1.16802i	−0.185351	−	0.982672i	$-0.559342\pi$
$992$		0			0
$993$	−9.19239	+	9.19239i	−0.291712	+	0.291712i
$994$		0			0
$995$		−	48.0000i		−	1.52170i
$996$	8.48528	−	8.48528i	0.268866	−	0.268866i
$997$	−43.8406	+	43.8406i	−1.38845	+	1.38845i	−0.559857	+	0.828589i	$0.689144\pi$
$997$	−43.8406	+	43.8406i	−1.38845	+	1.38845i	−0.828589	+	0.559857i	$0.810856\pi$
$998$		0			0
$999$	4.00000			0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.e.e.829.1		4
17.2	even	8		867.2.a.c.1.1		1
17.3	odd	16		867.2.h.c.712.1		8
17.4	even	4	inner	867.2.e.e.616.1		4
17.5	odd	16		867.2.h.c.733.2		8
17.6	odd	16		867.2.h.c.757.1		8
17.7	odd	16		867.2.h.c.688.1		8
17.8	even	8		867.2.d.a.577.2		2
17.9	even	8		867.2.d.a.577.1		2
17.10	odd	16		867.2.h.c.688.2		8
17.11	odd	16		867.2.h.c.757.2		8
17.12	odd	16		867.2.h.c.733.1		8
17.13	even	4	inner	867.2.e.e.616.2		4
17.14	odd	16		867.2.h.c.712.2		8
17.15	even	8		51.2.a.a.1.1	✓	1
17.16	even	2	inner	867.2.e.e.829.2		4
51.2	odd	8		2601.2.a.f.1.1		1
51.32	odd	8		153.2.a.b.1.1		1
68.15	odd	8		816.2.a.g.1.1		1
85.32	odd	8		1275.2.b.b.1174.1		2
85.49	even	8		1275.2.a.d.1.1		1
85.83	odd	8		1275.2.b.b.1174.2		2
119.83	odd	8		2499.2.a.d.1.1		1
136.83	odd	8		3264.2.a.r.1.1		1
136.117	even	8		3264.2.a.a.1.1		1
187.32	odd	8		6171.2.a.e.1.1		1
204.83	even	8		2448.2.a.c.1.1		1
221.168	even	8		8619.2.a.g.1.1		1
255.134	odd	8		3825.2.a.i.1.1		1
357.83	even	8		7497.2.a.j.1.1		1
408.83	even	8		9792.2.a.cd.1.1		1
408.389	odd	8		9792.2.a.by.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.a.1.1	✓	1	17.15	even	8
153.2.a.b.1.1		1	51.32	odd	8
816.2.a.g.1.1		1	68.15	odd	8
867.2.a.c.1.1		1	17.2	even	8
867.2.d.a.577.1		2	17.9	even	8
867.2.d.a.577.2		2	17.8	even	8
867.2.e.e.616.1		4	17.4	even	4	inner
867.2.e.e.616.2		4	17.13	even	4	inner
867.2.e.e.829.1		4	1.1	even	1	trivial
867.2.e.e.829.2		4	17.16	even	2	inner
867.2.h.c.688.1		8	17.7	odd	16
867.2.h.c.688.2		8	17.10	odd	16
867.2.h.c.712.1		8	17.3	odd	16
867.2.h.c.712.2		8	17.14	odd	16
867.2.h.c.733.1		8	17.12	odd	16
867.2.h.c.733.2		8	17.5	odd	16
867.2.h.c.757.1		8	17.6	odd	16
867.2.h.c.757.2		8	17.11	odd	16
1275.2.a.d.1.1		1	85.49	even	8
1275.2.b.b.1174.1		2	85.32	odd	8
1275.2.b.b.1174.2		2	85.83	odd	8
2448.2.a.c.1.1		1	204.83	even	8
2499.2.a.d.1.1		1	119.83	odd	8
2601.2.a.f.1.1		1	51.2	odd	8
3264.2.a.a.1.1		1	136.117	even	8
3264.2.a.r.1.1		1	136.83	odd	8
3825.2.a.i.1.1		1	255.134	odd	8
6171.2.a.e.1.1		1	187.32	odd	8
7497.2.a.j.1.1		1	357.83	even	8
8619.2.a.g.1.1		1	221.168	even	8
9792.2.a.by.1.1		1	408.389	odd	8
9792.2.a.cd.1.1		1	408.83	even	8

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{3} +2.00000 q^{4} +(2.12132 + 2.12132i) q^{5} +(-2.82843 + 2.82843i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{3} +2.00000 q^{4} +(2.12132 + 2.12132i) q^{5} +(-2.82843 + 2.82843i) q^{7} +1.00000i q^{9} +(2.12132 - 2.12132i) q^{11} +(-1.41421 - 1.41421i) q^{12} +1.00000 q^{13} -3.00000i q^{15} +4.00000 q^{16} +1.00000i q^{19} +(4.24264 + 4.24264i) q^{20} +4.00000 q^{21} +(-6.36396 + 6.36396i) q^{23} +4.00000i q^{25} +(0.707107 - 0.707107i) q^{27} +(-5.65685 + 5.65685i) q^{28} +(4.24264 + 4.24264i) q^{29} +(-1.41421 - 1.41421i) q^{31} -3.00000 q^{33} -12.0000 q^{35} +2.00000i q^{36} +(2.82843 + 2.82843i) q^{37} +(-0.707107 - 0.707107i) q^{39} +(-2.12132 + 2.12132i) q^{41} -7.00000i q^{43} +(4.24264 - 4.24264i) q^{44} +(-2.12132 + 2.12132i) q^{45} +6.00000 q^{47} +(-2.82843 - 2.82843i) q^{48} -9.00000i q^{49} +2.00000 q^{52} +6.00000i q^{53} +9.00000 q^{55} +(0.707107 - 0.707107i) q^{57} +6.00000i q^{59} -6.00000i q^{60} +(5.65685 - 5.65685i) q^{61} +(-2.82843 - 2.82843i) q^{63} +8.00000 q^{64} +(2.12132 + 2.12132i) q^{65} -4.00000 q^{67} +9.00000 q^{69} +(-8.48528 - 8.48528i) q^{71} +(1.41421 + 1.41421i) q^{73} +(2.82843 - 2.82843i) q^{75} +2.00000i q^{76} +12.0000i q^{77} +(7.07107 - 7.07107i) q^{79} +(8.48528 + 8.48528i) q^{80} -1.00000 q^{81} +6.00000i q^{83} +8.00000 q^{84} -6.00000i q^{87} +(-2.82843 + 2.82843i) q^{91} +(-12.7279 + 12.7279i) q^{92} +2.00000i q^{93} +(-2.12132 + 2.12132i) q^{95} +(-11.3137 - 11.3137i) q^{97} +(2.12132 + 2.12132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{4}+O(q^{10}) \) 4 * q + 8 * q^4	\( 4 q + 8 q^{4} + 4 q^{13} + 16 q^{16} + 16 q^{21} - 12 q^{33} - 48 q^{35} + 24 q^{47} + 8 q^{52} + 36 q^{55} + 32 q^{64} - 16 q^{67} + 36 q^{69} - 4 q^{81} + 32 q^{84}+O(q^{100}) \) 4 * q + 8 * q^4 + 4 * q^13 + 16 * q^16 + 16 * q^21 - 12 * q^33 - 48 * q^35 + 24 * q^47 + 8 * q^52 + 36 * q^55 + 32 * q^64 - 16 * q^67 + 36 * q^69 - 4 * q^81 + 32 * q^84

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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