LMFDB - Embedded newform 3584.2.m.b.2689.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3584,2,Mod(897,3584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3584, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("3584.897");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3584 = 2^{9} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3584.m (of order $4$, degree $2$, 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:	$28.6183840844$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2689.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	3584.2689
Dual form			3584.2.m.b.897.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{3} +(1.00000 - 1.00000i) q^{5} +1.00000i q^{7} +5.00000i q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{3} +(1.00000 - 1.00000i) q^{5} +1.00000i q^{7} +5.00000i q^{9} +(4.00000 - 4.00000i) q^{11} +(-1.00000 - 1.00000i) q^{13} -4.00000 q^{15} +4.00000 q^{17} +(2.00000 + 2.00000i) q^{19} +(2.00000 - 2.00000i) q^{21} -4.00000i q^{23} +3.00000i q^{25} +(4.00000 - 4.00000i) q^{27} +(7.00000 + 7.00000i) q^{29} -4.00000 q^{31} -16.0000 q^{33} +(1.00000 + 1.00000i) q^{35} +(5.00000 - 5.00000i) q^{37} +4.00000i q^{39} +12.0000i q^{41} +(5.00000 + 5.00000i) q^{45} +12.0000 q^{47} -1.00000 q^{49} +(-8.00000 - 8.00000i) q^{51} +(1.00000 - 1.00000i) q^{53} -8.00000i q^{55} -8.00000i q^{57} +(-2.00000 + 2.00000i) q^{59} +(3.00000 + 3.00000i) q^{61} -5.00000 q^{63} -2.00000 q^{65} +(4.00000 + 4.00000i) q^{67} +(-8.00000 + 8.00000i) q^{69} +6.00000i q^{73} +(6.00000 - 6.00000i) q^{75} +(4.00000 + 4.00000i) q^{77} +8.00000 q^{79} -1.00000 q^{81} +(10.0000 + 10.0000i) q^{83} +(4.00000 - 4.00000i) q^{85} -28.0000i q^{87} +10.0000i q^{89} +(1.00000 - 1.00000i) q^{91} +(8.00000 + 8.00000i) q^{93} +4.00000 q^{95} +4.00000 q^{97} +(20.0000 + 20.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{3} + 2 q^{5}+O(q^{10}) $ 2 * q - 4 * q^3 + 2 * q^5	$ 2 q - 4 q^{3} + 2 q^{5} + 8 q^{11} - 2 q^{13} - 8 q^{15} + 8 q^{17} + 4 q^{19} + 4 q^{21} + 8 q^{27} + 14 q^{29} - 8 q^{31} - 32 q^{33} + 2 q^{35} + 10 q^{37} + 10 q^{45} + 24 q^{47} - 2 q^{49} - 16 q^{51} + 2 q^{53} - 4 q^{59} + 6 q^{61} - 10 q^{63} - 4 q^{65} + 8 q^{67} - 16 q^{69} + 12 q^{75} + 8 q^{77} + 16 q^{79} - 2 q^{81} + 20 q^{83} + 8 q^{85} + 2 q^{91} + 16 q^{93} + 8 q^{95} + 8 q^{97} + 40 q^{99}+O(q^{100}) $ 2 * q - 4 * q^3 + 2 * q^5 + 8 * q^11 - 2 * q^13 - 8 * q^15 + 8 * q^17 + 4 * q^19 + 4 * q^21 + 8 * q^27 + 14 * q^29 - 8 * q^31 - 32 * q^33 + 2 * q^35 + 10 * q^37 + 10 * q^45 + 24 * q^47 - 2 * q^49 - 16 * q^51 + 2 * q^53 - 4 * q^59 + 6 * q^61 - 10 * q^63 - 4 * q^65 + 8 * q^67 - 16 * q^69 + 12 * q^75 + 8 * q^77 + 16 * q^79 - 2 * q^81 + 20 * q^83 + 8 * q^85 + 2 * q^91 + 16 * q^93 + 8 * q^95 + 8 * q^97 + 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$2$		0			0
$3$	−2.00000	−	2.00000i	−1.15470	−	1.15470i	−0.985599	−	0.169102i	$-0.945913\pi$
$3$	−2.00000	−	2.00000i	−1.15470	−	1.15470i	−0.169102	−	0.985599i	$-0.554087\pi$
$4$		0			0
$5$	1.00000	−	1.00000i	0.447214	−	0.447214i	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	1.00000	−	1.00000i	0.447214	−	0.447214i	0.894427	+	0.447214i	$0.147584\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$			5.00000i			1.66667i
$10$		0			0
$11$	4.00000	−	4.00000i	1.20605	−	1.20605i	0.233748	−	0.972297i	$-0.424901\pi$
$11$	4.00000	−	4.00000i	1.20605	−	1.20605i	0.972297	−	0.233748i	$-0.0750991\pi$
$12$		0			0
$13$	−1.00000	−	1.00000i	−0.277350	−	0.277350i	0.554700	−	0.832050i	$-0.312833\pi$
$13$	−1.00000	−	1.00000i	−0.277350	−	0.277350i	−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$	−4.00000			−1.03280
$16$		0			0
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$		0			0
$19$	2.00000	+	2.00000i	0.458831	+	0.458831i	0.898272	−	0.439440i	$-0.144823\pi$
$19$	2.00000	+	2.00000i	0.458831	+	0.458831i	−0.439440	+	0.898272i	$0.644823\pi$
$20$		0			0
$21$	2.00000	−	2.00000i	0.436436	−	0.436436i
$22$		0			0
$23$		−	4.00000i		−	0.834058i	−0.908893	−	0.417029i	$-0.863071\pi$
$23$		−	4.00000i		−	0.834058i	0.908893	−	0.417029i	$-0.136929\pi$
$24$		0			0
$25$			3.00000i			0.600000i
$26$		0			0
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$		0			0
$29$	7.00000	+	7.00000i	1.29987	+	1.29987i	0.928477	+	0.371391i	$0.121119\pi$
$29$	7.00000	+	7.00000i	1.29987	+	1.29987i	0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$	−16.0000			−2.78524
$34$		0			0
$35$	1.00000	+	1.00000i	0.169031	+	0.169031i
$36$		0			0
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	5.00000	−	5.00000i	0.821995	−	0.821995i	0.986394	+	0.164399i	$0.0525685\pi$
$38$		0			0
$39$			4.00000i			0.640513i
$40$		0			0
$41$			12.0000i			1.87409i	0.349215	+	0.937043i	$0.386448\pi$
$41$			12.0000i			1.87409i	−0.349215	+	0.937043i	$0.613552\pi$
$42$		0			0
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$		0			0
$45$	5.00000	+	5.00000i	0.745356	+	0.745356i
$46$		0			0
$47$	12.0000			1.75038			0.875190	−	0.483779i	$-0.160736\pi$
$47$	12.0000			1.75038			0.875190	+	0.483779i	$0.160736\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−8.00000	−	8.00000i	−1.12022	−	1.12022i
$52$		0			0
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	−0.635083	−	0.772444i	$-0.719034\pi$
$53$	1.00000	−	1.00000i	0.137361	−	0.137361i	0.772444	+	0.635083i	$0.219034\pi$
$54$		0			0
$55$		−	8.00000i		−	1.07872i
$56$		0			0
$57$		−	8.00000i		−	1.05963i
$58$		0			0
$59$	−2.00000	+	2.00000i	−0.260378	+	0.260378i	−0.825208	−	0.564830i	$-0.808942\pi$
$59$	−2.00000	+	2.00000i	−0.260378	+	0.260378i	0.564830	+	0.825208i	$0.308942\pi$
$60$		0			0
$61$	3.00000	+	3.00000i	0.384111	+	0.384111i	0.872581	−	0.488470i	$-0.162445\pi$
$61$	3.00000	+	3.00000i	0.384111	+	0.384111i	−0.488470	+	0.872581i	$0.662445\pi$
$62$		0			0
$63$	−5.00000			−0.629941
$64$		0			0
$65$	−2.00000			−0.248069
$66$		0			0
$67$	4.00000	+	4.00000i	0.488678	+	0.488678i	0.907889	−	0.419211i	$-0.137693\pi$
$67$	4.00000	+	4.00000i	0.488678	+	0.488678i	−0.419211	+	0.907889i	$0.637693\pi$
$68$		0			0
$69$	−8.00000	+	8.00000i	−0.963087	+	0.963087i
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$		0			0
$75$	6.00000	−	6.00000i	0.692820	−	0.692820i
$76$		0			0
$77$	4.00000	+	4.00000i	0.455842	+	0.455842i
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	10.0000	+	10.0000i	1.09764	+	1.09764i	0.994686	+	0.102957i	$0.0328303\pi$
$83$	10.0000	+	10.0000i	1.09764	+	1.09764i	0.102957	+	0.994686i	$0.467170\pi$
$84$		0			0
$85$	4.00000	−	4.00000i	0.433861	−	0.433861i
$86$		0			0
$87$		−	28.0000i		−	3.00192i
$88$		0			0
$89$			10.0000i			1.06000i	0.847998	+	0.529999i	$0.177808\pi$
$89$			10.0000i			1.06000i	−0.847998	+	0.529999i	$0.822192\pi$
$90$		0			0
$91$	1.00000	−	1.00000i	0.104828	−	0.104828i
$92$		0			0
$93$	8.00000	+	8.00000i	0.829561	+	0.829561i
$94$		0			0
$95$	4.00000			0.410391
$96$		0			0
$97$	4.00000			0.406138			0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000			0.406138			0.203069	+	0.979164i	$0.434908\pi$
$98$		0			0
$99$	20.0000	+	20.0000i	2.01008	+	2.01008i
$100$		0			0
$101$	−9.00000	+	9.00000i	−0.895533	+	0.895533i	−0.995037	−	0.0995037i	$-0.968274\pi$
$101$	−9.00000	+	9.00000i	−0.895533	+	0.895533i	0.0995037	+	0.995037i	$0.468274\pi$
$102$		0			0
$103$		−	12.0000i		−	1.18240i	−0.806527	−	0.591198i	$-0.798655\pi$
$103$		−	12.0000i		−	1.18240i	0.806527	−	0.591198i	$-0.201345\pi$
$104$		0			0
$105$		−	4.00000i		−	0.390360i
$106$		0			0
$107$	8.00000	−	8.00000i	0.773389	−	0.773389i	−0.205308	−	0.978697i	$-0.565820\pi$
$107$	8.00000	−	8.00000i	0.773389	−	0.773389i	0.978697	+	0.205308i	$0.0658197\pi$
$108$		0			0
$109$	−1.00000	−	1.00000i	−0.0957826	−	0.0957826i	0.657592	−	0.753374i	$-0.271575\pi$
$109$	−1.00000	−	1.00000i	−0.0957826	−	0.0957826i	−0.753374	+	0.657592i	$0.771575\pi$
$110$		0			0
$111$	−20.0000			−1.89832
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$	−4.00000	−	4.00000i	−0.373002	−	0.373002i
$116$		0			0
$117$	5.00000	−	5.00000i	0.462250	−	0.462250i
$118$		0			0
$119$			4.00000i			0.366679i
$120$		0			0
$121$		−	21.0000i		−	1.90909i
$122$		0			0
$123$	24.0000	−	24.0000i	2.16401	−	2.16401i
$124$		0			0
$125$	8.00000	+	8.00000i	0.715542	+	0.715542i
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.00000	−	2.00000i	−0.174741	−	0.174741i	0.614318	−	0.789059i	$-0.289431\pi$
$131$	−2.00000	−	2.00000i	−0.174741	−	0.174741i	−0.789059	+	0.614318i	$0.789431\pi$
$132$		0			0
$133$	−2.00000	+	2.00000i	−0.173422	+	0.173422i
$134$		0			0
$135$		−	8.00000i		−	0.688530i
$136$		0			0
$137$			16.0000i			1.36697i	0.729964	+	0.683486i	$0.239537\pi$
$137$			16.0000i			1.36697i	−0.729964	+	0.683486i	$0.760463\pi$
$138$		0			0
$139$	−14.0000	+	14.0000i	−1.18746	+	1.18746i	−0.209698	+	0.977766i	$0.567248\pi$
$139$	−14.0000	+	14.0000i	−1.18746	+	1.18746i	−0.977766	+	0.209698i	$0.932752\pi$
$140$		0			0
$141$	−24.0000	−	24.0000i	−2.02116	−	2.02116i
$142$		0			0
$143$	−8.00000			−0.668994
$144$		0			0
$145$	14.0000			1.16264
$146$		0			0
$147$	2.00000	+	2.00000i	0.164957	+	0.164957i
$148$		0			0
$149$	15.0000	−	15.0000i	1.22885	−	1.22885i	0.264448	−	0.964400i	$-0.414810\pi$
$149$	15.0000	−	15.0000i	1.22885	−	1.22885i	0.964400	−	0.264448i	$-0.0851897\pi$
$150$		0			0
$151$			4.00000i			0.325515i	0.986666	+	0.162758i	$0.0520389\pi$
$151$			4.00000i			0.325515i	−0.986666	+	0.162758i	$0.947961\pi$
$152$		0			0
$153$			20.0000i			1.61690i
$154$		0			0
$155$	−4.00000	+	4.00000i	−0.321288	+	0.321288i
$156$		0			0
$157$	−9.00000	−	9.00000i	−0.718278	−	0.718278i	0.249974	−	0.968252i	$-0.419578\pi$
$157$	−9.00000	−	9.00000i	−0.718278	−	0.718278i	−0.968252	+	0.249974i	$0.919578\pi$
$158$		0			0
$159$	−4.00000			−0.317221
$160$		0			0
$161$	4.00000			0.315244
$162$		0			0
$163$	4.00000	+	4.00000i	0.313304	+	0.313304i	0.846188	−	0.532884i	$-0.178892\pi$
$163$	4.00000	+	4.00000i	0.313304	+	0.313304i	−0.532884	+	0.846188i	$0.678892\pi$
$164$		0			0
$165$	−16.0000	+	16.0000i	−1.24560	+	1.24560i
$166$		0			0
$167$			4.00000i			0.309529i	0.987951	+	0.154765i	$0.0494619\pi$
$167$			4.00000i			0.309529i	−0.987951	+	0.154765i	$0.950538\pi$
$168$		0			0
$169$		−	11.0000i		−	0.846154i
$170$		0			0
$171$	−10.0000	+	10.0000i	−0.764719	+	0.764719i
$172$		0			0
$173$	−9.00000	−	9.00000i	−0.684257	−	0.684257i	0.276699	−	0.960957i	$-0.410759\pi$
$173$	−9.00000	−	9.00000i	−0.684257	−	0.684257i	−0.960957	+	0.276699i	$0.910759\pi$
$174$		0			0
$175$	−3.00000			−0.226779
$176$		0			0
$177$	8.00000			0.601317
$178$		0			0
$179$	−12.0000	−	12.0000i	−0.896922	−	0.896922i	0.0982406	−	0.995163i	$-0.468679\pi$
$179$	−12.0000	−	12.0000i	−0.896922	−	0.896922i	−0.995163	+	0.0982406i	$0.968679\pi$
$180$		0			0
$181$	−3.00000	+	3.00000i	−0.222988	+	0.222988i	−0.809756	−	0.586767i	$-0.800400\pi$
$181$	−3.00000	+	3.00000i	−0.222988	+	0.222988i	0.586767	+	0.809756i	$0.300400\pi$
$182$		0			0
$183$		−	12.0000i		−	0.887066i
$184$		0			0
$185$		−	10.0000i		−	0.735215i
$186$		0			0
$187$	16.0000	−	16.0000i	1.17004	−	1.17004i
$188$		0			0
$189$	4.00000	+	4.00000i	0.290957	+	0.290957i
$190$		0			0
$191$	−24.0000			−1.73658			−0.868290	−	0.496058i	$-0.834780\pi$
$191$	−24.0000			−1.73658			−0.868290	+	0.496058i	$0.834780\pi$
$192$		0			0
$193$	16.0000			1.15171			0.575853	−	0.817554i	$-0.304670\pi$
$193$	16.0000			1.15171			0.575853	+	0.817554i	$0.304670\pi$
$194$		0			0
$195$	4.00000	+	4.00000i	0.286446	+	0.286446i
$196$		0			0
$197$	15.0000	−	15.0000i	1.06871	−	1.06871i	0.0712470	−	0.997459i	$-0.477302\pi$
$197$	15.0000	−	15.0000i	1.06871	−	1.06871i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		0			0
$199$		−	12.0000i		−	0.850657i	−0.905039	−	0.425329i	$-0.860158\pi$
$199$		−	12.0000i		−	0.850657i	0.905039	−	0.425329i	$-0.139842\pi$
$200$		0			0
$201$		−	16.0000i		−	1.12855i
$202$		0			0
$203$	−7.00000	+	7.00000i	−0.491304	+	0.491304i
$204$		0			0
$205$	12.0000	+	12.0000i	0.838116	+	0.838116i
$206$		0			0
$207$	20.0000			1.39010
$208$		0			0
$209$	16.0000			1.10674
$210$		0			0
$211$	−12.0000	−	12.0000i	−0.826114	−	0.826114i	0.160863	−	0.986977i	$-0.448572\pi$
$211$	−12.0000	−	12.0000i	−0.826114	−	0.826114i	−0.986977	+	0.160863i	$0.948572\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	4.00000i		−	0.271538i
$218$		0			0
$219$	12.0000	−	12.0000i	0.810885	−	0.810885i
$220$		0			0
$221$	−4.00000	−	4.00000i	−0.269069	−	0.269069i
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$	−15.0000			−1.00000
$226$		0			0
$227$	2.00000	+	2.00000i	0.132745	+	0.132745i	0.770357	−	0.637613i	$-0.220078\pi$
$227$	2.00000	+	2.00000i	0.132745	+	0.132745i	−0.637613	+	0.770357i	$0.720078\pi$
$228$		0			0
$229$	21.0000	−	21.0000i	1.38772	−	1.38772i	0.557628	−	0.830091i	$-0.311711\pi$
$229$	21.0000	−	21.0000i	1.38772	−	1.38772i	0.830091	−	0.557628i	$-0.188289\pi$
$230$		0			0
$231$		−	16.0000i		−	1.05272i
$232$		0			0
$233$		−	10.0000i		−	0.655122i	−0.944830	−	0.327561i	$-0.893773\pi$
$233$		−	10.0000i		−	0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$		0			0
$235$	12.0000	−	12.0000i	0.782794	−	0.782794i
$236$		0			0
$237$	−16.0000	−	16.0000i	−1.03931	−	1.03931i
$238$		0			0
$239$	−28.0000			−1.81117			−0.905585	−	0.424165i	$-0.860568\pi$
$239$	−28.0000			−1.81117			−0.905585	+	0.424165i	$0.860568\pi$
$240$		0			0
$241$	−4.00000			−0.257663			−0.128831	−	0.991667i	$-0.541123\pi$
$241$	−4.00000			−0.257663			−0.128831	+	0.991667i	$0.541123\pi$
$242$		0			0
$243$	−10.0000	−	10.0000i	−0.641500	−	0.641500i
$244$		0			0
$245$	−1.00000	+	1.00000i	−0.0638877	+	0.0638877i
$246$		0			0
$247$		−	4.00000i		−	0.254514i
$248$		0			0
$249$		−	40.0000i		−	2.53490i
$250$		0			0
$251$	10.0000	−	10.0000i	0.631194	−	0.631194i	−0.317173	−	0.948368i	$-0.602734\pi$
$251$	10.0000	−	10.0000i	0.631194	−	0.631194i	0.948368	+	0.317173i	$0.102734\pi$
$252$		0			0
$253$	−16.0000	−	16.0000i	−1.00591	−	1.00591i
$254$		0			0
$255$	−16.0000			−1.00196
$256$		0			0
$257$	−14.0000			−0.873296			−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000			−0.873296			−0.436648	+	0.899632i	$0.643834\pi$
$258$		0			0
$259$	5.00000	+	5.00000i	0.310685	+	0.310685i
$260$		0			0
$261$	−35.0000	+	35.0000i	−2.16645	+	2.16645i
$262$		0			0
$263$			24.0000i			1.47990i	0.672660	+	0.739952i	$0.265152\pi$
$263$			24.0000i			1.47990i	−0.672660	+	0.739952i	$0.734848\pi$
$264$		0			0
$265$		−	2.00000i		−	0.122859i
$266$		0			0
$267$	20.0000	−	20.0000i	1.22398	−	1.22398i
$268$		0			0
$269$	−7.00000	−	7.00000i	−0.426798	−	0.426798i	0.460738	−	0.887536i	$-0.347585\pi$
$269$	−7.00000	−	7.00000i	−0.426798	−	0.426798i	−0.887536	+	0.460738i	$0.847585\pi$
$270$		0			0
$271$	16.0000			0.971931			0.485965	−	0.873978i	$-0.338468\pi$
$271$	16.0000			0.971931			0.485965	+	0.873978i	$0.338468\pi$
$272$		0			0
$273$	−4.00000			−0.242091
$274$		0			0
$275$	12.0000	+	12.0000i	0.723627	+	0.723627i
$276$		0			0
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	−0.995545	−	0.0942828i	$-0.969944\pi$
$277$	−15.0000	+	15.0000i	−0.901263	+	0.901263i	0.0942828	+	0.995545i	$0.469944\pi$
$278$		0			0
$279$		−	20.0000i		−	1.19737i
$280$		0			0
$281$		−	10.0000i		−	0.596550i	−0.954480	−	0.298275i	$-0.903589\pi$
$281$		−	10.0000i		−	0.596550i	0.954480	−	0.298275i	$-0.0964112\pi$
$282$		0			0
$283$	−6.00000	+	6.00000i	−0.356663	+	0.356663i	−0.862581	−	0.505918i	$-0.831154\pi$
$283$	−6.00000	+	6.00000i	−0.356663	+	0.356663i	0.505918	+	0.862581i	$0.331154\pi$
$284$		0			0
$285$	−8.00000	−	8.00000i	−0.473879	−	0.473879i
$286$		0			0
$287$	−12.0000			−0.708338
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$	−8.00000	−	8.00000i	−0.468968	−	0.468968i
$292$		0			0
$293$	1.00000	−	1.00000i	0.0584206	−	0.0584206i	−0.677293	−	0.735714i	$-0.736847\pi$
$293$	1.00000	−	1.00000i	0.0584206	−	0.0584206i	0.735714	+	0.677293i	$0.236847\pi$
$294$		0			0
$295$			4.00000i			0.232889i
$296$		0			0
$297$		−	32.0000i		−	1.85683i
$298$		0			0
$299$	−4.00000	+	4.00000i	−0.231326	+	0.231326i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	36.0000			2.06815
$304$		0			0
$305$	6.00000			0.343559
$306$		0			0
$307$	10.0000	+	10.0000i	0.570730	+	0.570730i	0.932332	−	0.361602i	$-0.117770\pi$
$307$	10.0000	+	10.0000i	0.570730	+	0.570730i	−0.361602	+	0.932332i	$0.617770\pi$
$308$		0			0
$309$	−24.0000	+	24.0000i	−1.36531	+	1.36531i
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		0			0
$313$			20.0000i			1.13047i	0.824931	+	0.565233i	$0.191214\pi$
$313$			20.0000i			1.13047i	−0.824931	+	0.565233i	$0.808786\pi$
$314$		0			0
$315$	−5.00000	+	5.00000i	−0.281718	+	0.281718i
$316$		0			0
$317$	−13.0000	−	13.0000i	−0.730153	−	0.730153i	0.240497	−	0.970650i	$-0.422690\pi$
$317$	−13.0000	−	13.0000i	−0.730153	−	0.730153i	−0.970650	+	0.240497i	$0.922690\pi$
$318$		0			0
$319$	56.0000			3.13540
$320$		0			0
$321$	−32.0000			−1.78607
$322$		0			0
$323$	8.00000	+	8.00000i	0.445132	+	0.445132i
$324$		0			0
$325$	3.00000	−	3.00000i	0.166410	−	0.166410i
$326$		0			0
$327$			4.00000i			0.221201i
$328$		0			0
$329$			12.0000i			0.661581i
$330$		0			0
$331$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$331$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$332$		0			0
$333$	25.0000	+	25.0000i	1.36999	+	1.36999i
$334$		0			0
$335$	8.00000			0.437087
$336$		0			0
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$		0			0
$339$	12.0000	+	12.0000i	0.651751	+	0.651751i
$340$		0			0
$341$	−16.0000	+	16.0000i	−0.866449	+	0.866449i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$			16.0000i			0.861411i
$346$		0			0
$347$	24.0000	−	24.0000i	1.28839	−	1.28839i	0.352621	−	0.935766i	$-0.385290\pi$
$347$	24.0000	−	24.0000i	1.28839	−	1.28839i	0.935766	−	0.352621i	$-0.114710\pi$
$348$		0			0
$349$	−23.0000	−	23.0000i	−1.23116	−	1.23116i	−0.963518	−	0.267644i	$-0.913755\pi$
$349$	−23.0000	−	23.0000i	−1.23116	−	1.23116i	−0.267644	−	0.963518i	$-0.586245\pi$
$350$		0			0
$351$	−8.00000			−0.427008
$352$		0			0
$353$	30.0000			1.59674			0.798369	−	0.602168i	$-0.205696\pi$
$353$	30.0000			1.59674			0.798369	+	0.602168i	$0.205696\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	8.00000	−	8.00000i	0.423405	−	0.423405i
$358$		0			0
$359$			4.00000i			0.211112i	0.994413	+	0.105556i	$0.0336622\pi$
$359$			4.00000i			0.211112i	−0.994413	+	0.105556i	$0.966338\pi$
$360$		0			0
$361$		−	11.0000i		−	0.578947i
$362$		0			0
$363$	−42.0000	+	42.0000i	−2.20443	+	2.20443i
$364$		0			0
$365$	6.00000	+	6.00000i	0.314054	+	0.314054i
$366$		0			0
$367$	−8.00000			−0.417597			−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000			−0.417597			−0.208798	+	0.977959i	$0.566955\pi$
$368$		0			0
$369$	−60.0000			−3.12348
$370$		0			0
$371$	1.00000	+	1.00000i	0.0519174	+	0.0519174i
$372$		0			0
$373$	9.00000	−	9.00000i	0.466002	−	0.466002i	−0.434614	−	0.900617i	$-0.643115\pi$
$373$	9.00000	−	9.00000i	0.466002	−	0.466002i	0.900617	+	0.434614i	$0.143115\pi$
$374$		0			0
$375$		−	32.0000i		−	1.65247i
$376$		0			0
$377$		−	14.0000i		−	0.721037i
$378$		0			0
$379$	−24.0000	+	24.0000i	−1.23280	+	1.23280i	−0.269912	+	0.962885i	$0.586995\pi$
$379$	−24.0000	+	24.0000i	−1.23280	+	1.23280i	−0.962885	+	0.269912i	$0.913005\pi$
$380$		0			0
$381$	8.00000	+	8.00000i	0.409852	+	0.409852i
$382$		0			0
$383$	−20.0000			−1.02195			−0.510976	−	0.859595i	$-0.670716\pi$
$383$	−20.0000			−1.02195			−0.510976	+	0.859595i	$0.670716\pi$
$384$		0			0
$385$	8.00000			0.407718
$386$		0			0
$387$		0			0
$388$		0			0
$389$	21.0000	−	21.0000i	1.06474	−	1.06474i	0.0669885	−	0.997754i	$-0.478661\pi$
$389$	21.0000	−	21.0000i	1.06474	−	1.06474i	0.997754	−	0.0669885i	$-0.0213391\pi$
$390$		0			0
$391$		−	16.0000i		−	0.809155i
$392$		0			0
$393$			8.00000i			0.403547i
$394$		0			0
$395$	8.00000	−	8.00000i	0.402524	−	0.402524i
$396$		0			0
$397$	−15.0000	−	15.0000i	−0.752828	−	0.752828i	0.222178	−	0.975006i	$-0.428683\pi$
$397$	−15.0000	−	15.0000i	−0.752828	−	0.752828i	−0.975006	+	0.222178i	$0.928683\pi$
$398$		0			0
$399$	8.00000			0.400501
$400$		0			0
$401$	24.0000			1.19850			0.599251	−	0.800561i	$-0.295465\pi$
$401$	24.0000			1.19850			0.599251	+	0.800561i	$0.295465\pi$
$402$		0			0
$403$	4.00000	+	4.00000i	0.199254	+	0.199254i
$404$		0			0
$405$	−1.00000	+	1.00000i	−0.0496904	+	0.0496904i
$406$		0			0
$407$		−	40.0000i		−	1.98273i
$408$		0			0
$409$			20.0000i			0.988936i	0.869196	+	0.494468i	$0.164637\pi$
$409$			20.0000i			0.988936i	−0.869196	+	0.494468i	$0.835363\pi$
$410$		0			0
$411$	32.0000	−	32.0000i	1.57844	−	1.57844i
$412$		0			0
$413$	−2.00000	−	2.00000i	−0.0984136	−	0.0984136i
$414$		0			0
$415$	20.0000			0.981761
$416$		0			0
$417$	56.0000			2.74233
$418$		0			0
$419$	−18.0000	−	18.0000i	−0.879358	−	0.879358i	0.114111	−	0.993468i	$-0.463598\pi$
$419$	−18.0000	−	18.0000i	−0.879358	−	0.879358i	−0.993468	+	0.114111i	$0.963598\pi$
$420$		0			0
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	−0.891552	−	0.452919i	$-0.850383\pi$
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	0.452919	+	0.891552i	$0.350383\pi$
$422$		0			0
$423$			60.0000i			2.91730i
$424$		0			0
$425$			12.0000i			0.582086i
$426$		0			0
$427$	−3.00000	+	3.00000i	−0.145180	+	0.145180i
$428$		0			0
$429$	16.0000	+	16.0000i	0.772487	+	0.772487i
$430$		0			0
$431$	36.0000			1.73406			0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000			1.73406			0.867029	+	0.498257i	$0.166026\pi$
$432$		0			0
$433$	−36.0000			−1.73005			−0.865025	−	0.501729i	$-0.832697\pi$
$433$	−36.0000			−1.73005			−0.865025	+	0.501729i	$0.832697\pi$
$434$		0			0
$435$	−28.0000	−	28.0000i	−1.34250	−	1.34250i
$436$		0			0
$437$	8.00000	−	8.00000i	0.382692	−	0.382692i
$438$		0			0
$439$			32.0000i			1.52728i	0.645644	+	0.763638i	$0.276589\pi$
$439$			32.0000i			1.52728i	−0.645644	+	0.763638i	$0.723411\pi$
$440$		0			0
$441$		−	5.00000i		−	0.238095i
$442$		0			0
$443$	4.00000	−	4.00000i	0.190046	−	0.190046i	−0.605670	−	0.795716i	$-0.707095\pi$
$443$	4.00000	−	4.00000i	0.190046	−	0.190046i	0.795716	+	0.605670i	$0.207095\pi$
$444$		0			0
$445$	10.0000	+	10.0000i	0.474045	+	0.474045i
$446$		0			0
$447$	−60.0000			−2.83790
$448$		0			0
$449$	8.00000			0.377543			0.188772	−	0.982021i	$-0.439549\pi$
$449$	8.00000			0.377543			0.188772	+	0.982021i	$0.439549\pi$
$450$		0			0
$451$	48.0000	+	48.0000i	2.26023	+	2.26023i
$452$		0			0
$453$	8.00000	−	8.00000i	0.375873	−	0.375873i
$454$		0			0
$455$		−	2.00000i		−	0.0937614i
$456$		0			0
$457$			16.0000i			0.748448i	0.927338	+	0.374224i	$0.122091\pi$
$457$			16.0000i			0.748448i	−0.927338	+	0.374224i	$0.877909\pi$
$458$		0			0
$459$	16.0000	−	16.0000i	0.746816	−	0.746816i
$460$		0			0
$461$	9.00000	+	9.00000i	0.419172	+	0.419172i	0.884918	−	0.465746i	$-0.154214\pi$
$461$	9.00000	+	9.00000i	0.419172	+	0.419172i	−0.465746	+	0.884918i	$0.654214\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$		0			0
$465$	16.0000			0.741982
$466$		0			0
$467$	6.00000	+	6.00000i	0.277647	+	0.277647i	0.832169	−	0.554522i	$-0.187099\pi$
$467$	6.00000	+	6.00000i	0.277647	+	0.277647i	−0.554522	+	0.832169i	$0.687099\pi$
$468$		0			0
$469$	−4.00000	+	4.00000i	−0.184703	+	0.184703i
$470$		0			0
$471$			36.0000i			1.65879i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	−6.00000	+	6.00000i	−0.275299	+	0.275299i
$476$		0			0
$477$	5.00000	+	5.00000i	0.228934	+	0.228934i
$478$		0			0
$479$	−12.0000			−0.548294			−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000			−0.548294			−0.274147	+	0.961688i	$0.588395\pi$
$480$		0			0
$481$	−10.0000			−0.455961
$482$		0			0
$483$	−8.00000	−	8.00000i	−0.364013	−	0.364013i
$484$		0			0
$485$	4.00000	−	4.00000i	0.181631	−	0.181631i
$486$		0			0
$487$			4.00000i			0.181257i	0.995885	+	0.0906287i	$0.0288876\pi$
$487$			4.00000i			0.181257i	−0.995885	+	0.0906287i	$0.971112\pi$
$488$		0			0
$489$		−	16.0000i		−	0.723545i
$490$		0			0
$491$	−20.0000	+	20.0000i	−0.902587	+	0.902587i	−0.995659	−	0.0930720i	$-0.970331\pi$
$491$	−20.0000	+	20.0000i	−0.902587	+	0.902587i	0.0930720	+	0.995659i	$0.470331\pi$
$492$		0			0
$493$	28.0000	+	28.0000i	1.26106	+	1.26106i
$494$		0			0
$495$	40.0000			1.79787
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−8.00000	−	8.00000i	−0.358129	−	0.358129i	0.504994	−	0.863123i	$-0.331495\pi$
$499$	−8.00000	−	8.00000i	−0.358129	−	0.358129i	−0.863123	+	0.504994i	$0.831495\pi$
$500$		0			0
$501$	8.00000	−	8.00000i	0.357414	−	0.357414i
$502$		0			0
$503$			16.0000i			0.713405i	0.934218	+	0.356702i	$0.116099\pi$
$503$			16.0000i			0.713405i	−0.934218	+	0.356702i	$0.883901\pi$
$504$		0			0
$505$			18.0000i			0.800989i
$506$		0			0
$507$	−22.0000	+	22.0000i	−0.977054	+	0.977054i
$508$		0			0
$509$	−25.0000	−	25.0000i	−1.10811	−	1.10811i	−0.993399	−	0.114706i	$-0.963407\pi$
$509$	−25.0000	−	25.0000i	−1.10811	−	1.10811i	−0.114706	−	0.993399i	$-0.536593\pi$
$510$		0			0
$511$	−6.00000			−0.265424
$512$		0			0
$513$	16.0000			0.706417
$514$		0			0
$515$	−12.0000	−	12.0000i	−0.528783	−	0.528783i
$516$		0			0
$517$	48.0000	−	48.0000i	2.11104	−	2.11104i
$518$		0			0
$519$			36.0000i			1.58022i
$520$		0			0
$521$		−	12.0000i		−	0.525730i	−0.964833	−	0.262865i	$-0.915333\pi$
$521$		−	12.0000i		−	0.525730i	0.964833	−	0.262865i	$-0.0846673\pi$
$522$		0			0
$523$	2.00000	−	2.00000i	0.0874539	−	0.0874539i	−0.662027	−	0.749480i	$-0.730303\pi$
$523$	2.00000	−	2.00000i	0.0874539	−	0.0874539i	0.749480	+	0.662027i	$0.230303\pi$
$524$		0			0
$525$	6.00000	+	6.00000i	0.261861	+	0.261861i
$526$		0			0
$527$	−16.0000			−0.696971
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$	−10.0000	−	10.0000i	−0.433963	−	0.433963i
$532$		0			0
$533$	12.0000	−	12.0000i	0.519778	−	0.519778i
$534$		0			0
$535$		−	16.0000i		−	0.691740i
$536$		0			0
$537$			48.0000i			2.07135i
$538$		0			0
$539$	−4.00000	+	4.00000i	−0.172292	+	0.172292i
$540$		0			0
$541$	21.0000	+	21.0000i	0.902861	+	0.902861i	0.995683	−	0.0928222i	$-0.0295888\pi$
$541$	21.0000	+	21.0000i	0.902861	+	0.902861i	−0.0928222	+	0.995683i	$0.529589\pi$
$542$		0			0
$543$	12.0000			0.514969
$544$		0			0
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	4.00000	+	4.00000i	0.171028	+	0.171028i	0.787431	−	0.616403i	$-0.211411\pi$
$547$	4.00000	+	4.00000i	0.171028	+	0.171028i	−0.616403	+	0.787431i	$0.711411\pi$
$548$		0			0
$549$	−15.0000	+	15.0000i	−0.640184	+	0.640184i
$550$		0			0
$551$			28.0000i			1.19284i
$552$		0			0
$553$			8.00000i			0.340195i
$554$		0			0
$555$	−20.0000	+	20.0000i	−0.848953	+	0.848953i
$556$		0			0
$557$	5.00000	+	5.00000i	0.211857	+	0.211857i	0.805056	−	0.593199i	$-0.202135\pi$
$557$	5.00000	+	5.00000i	0.211857	+	0.211857i	−0.593199	+	0.805056i	$0.702135\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−64.0000			−2.70208
$562$		0			0
$563$	−10.0000	−	10.0000i	−0.421450	−	0.421450i	0.464253	−	0.885703i	$-0.346323\pi$
$563$	−10.0000	−	10.0000i	−0.421450	−	0.421450i	−0.885703	+	0.464253i	$0.846323\pi$
$564$		0			0
$565$	−6.00000	+	6.00000i	−0.252422	+	0.252422i
$566$		0			0
$567$		−	1.00000i		−	0.0419961i
$568$		0			0
$569$			8.00000i			0.335377i	0.985840	+	0.167689i	$0.0536304\pi$
$569$			8.00000i			0.335377i	−0.985840	+	0.167689i	$0.946370\pi$
$570$		0			0
$571$	−24.0000	+	24.0000i	−1.00437	+	1.00437i	−0.00437833	+	0.999990i	$0.501394\pi$
$571$	−24.0000	+	24.0000i	−1.00437	+	1.00437i	−0.999990	+	0.00437833i	$0.998606\pi$
$572$		0			0
$573$	48.0000	+	48.0000i	2.00523	+	2.00523i
$574$		0			0
$575$	12.0000			0.500435
$576$		0			0
$577$	−2.00000			−0.0832611			−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000			−0.0832611			−0.0416305	+	0.999133i	$0.513255\pi$
$578$		0			0
$579$	−32.0000	−	32.0000i	−1.32987	−	1.32987i
$580$		0			0
$581$	−10.0000	+	10.0000i	−0.414870	+	0.414870i
$582$		0			0
$583$		−	8.00000i		−	0.331326i
$584$		0			0
$585$		−	10.0000i		−	0.413449i
$586$		0			0
$587$	14.0000	−	14.0000i	0.577842	−	0.577842i	−0.356466	−	0.934308i	$-0.616019\pi$
$587$	14.0000	−	14.0000i	0.577842	−	0.577842i	0.934308	+	0.356466i	$0.116019\pi$
$588$		0			0
$589$	−8.00000	−	8.00000i	−0.329634	−	0.329634i
$590$		0			0
$591$	−60.0000			−2.46807
$592$		0			0
$593$	2.00000			0.0821302			0.0410651	−	0.999156i	$-0.486925\pi$
$593$	2.00000			0.0821302			0.0410651	+	0.999156i	$0.486925\pi$
$594$		0			0
$595$	4.00000	+	4.00000i	0.163984	+	0.163984i
$596$		0			0
$597$	−24.0000	+	24.0000i	−0.982255	+	0.982255i
$598$		0			0
$599$			32.0000i			1.30748i	0.756717	+	0.653742i	$0.226802\pi$
$599$			32.0000i			1.30748i	−0.756717	+	0.653742i	$0.773198\pi$
$600$		0			0
$601$		−	22.0000i		−	0.897399i	−0.893683	−	0.448699i	$-0.851887\pi$
$601$		−	22.0000i		−	0.897399i	0.893683	−	0.448699i	$-0.148113\pi$
$602$		0			0
$603$	−20.0000	+	20.0000i	−0.814463	+	0.814463i
$604$		0			0
$605$	−21.0000	−	21.0000i	−0.853771	−	0.853771i
$606$		0			0
$607$	−8.00000			−0.324710			−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000			−0.324710			−0.162355	+	0.986732i	$0.551909\pi$
$608$		0			0
$609$	28.0000			1.13462
$610$		0			0
$611$	−12.0000	−	12.0000i	−0.485468	−	0.485468i
$612$		0			0
$613$	19.0000	−	19.0000i	0.767403	−	0.767403i	−0.210246	−	0.977649i	$-0.567426\pi$
$613$	19.0000	−	19.0000i	0.767403	−	0.767403i	0.977649	+	0.210246i	$0.0674264\pi$
$614$		0			0
$615$		−	48.0000i		−	1.93555i
$616$		0			0
$617$			18.0000i			0.724653i	0.932051	+	0.362326i	$0.118017\pi$
$617$			18.0000i			0.724653i	−0.932051	+	0.362326i	$0.881983\pi$
$618$		0			0
$619$	−6.00000	+	6.00000i	−0.241160	+	0.241160i	−0.817330	−	0.576170i	$-0.804547\pi$
$619$	−6.00000	+	6.00000i	−0.241160	+	0.241160i	0.576170	+	0.817330i	$0.304547\pi$
$620$		0			0
$621$	−16.0000	−	16.0000i	−0.642058	−	0.642058i
$622$		0			0
$623$	−10.0000			−0.400642
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−32.0000	−	32.0000i	−1.27796	−	1.27796i
$628$		0			0
$629$	20.0000	−	20.0000i	0.797452	−	0.797452i
$630$		0			0
$631$		−	40.0000i		−	1.59237i	−0.605050	−	0.796187i	$-0.706847\pi$
$631$		−	40.0000i		−	1.59237i	0.605050	−	0.796187i	$-0.293153\pi$
$632$		0			0
$633$			48.0000i			1.90783i
$634$		0			0
$635$	−4.00000	+	4.00000i	−0.158735	+	0.158735i
$636$		0			0
$637$	1.00000	+	1.00000i	0.0396214	+	0.0396214i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−24.0000			−0.947943			−0.473972	−	0.880540i	$-0.657180\pi$
$641$	−24.0000			−0.947943			−0.473972	+	0.880540i	$0.657180\pi$
$642$		0			0
$643$	10.0000	+	10.0000i	0.394362	+	0.394362i	0.876239	−	0.481877i	$-0.160045\pi$
$643$	10.0000	+	10.0000i	0.394362	+	0.394362i	−0.481877	+	0.876239i	$0.660045\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	12.0000i		−	0.471769i	−0.971781	−	0.235884i	$-0.924201\pi$
$647$		−	12.0000i		−	0.471769i	0.971781	−	0.235884i	$-0.0757987\pi$
$648$		0			0
$649$			16.0000i			0.628055i
$650$		0			0
$651$	−8.00000	+	8.00000i	−0.313545	+	0.313545i
$652$		0			0
$653$	−1.00000	−	1.00000i	−0.0391330	−	0.0391330i	0.687270	−	0.726403i	$-0.258809\pi$
$653$	−1.00000	−	1.00000i	−0.0391330	−	0.0391330i	−0.726403	+	0.687270i	$0.758809\pi$
$654$		0			0
$655$	−4.00000			−0.156293
$656$		0			0
$657$	−30.0000			−1.17041
$658$		0			0
$659$	−12.0000	−	12.0000i	−0.467454	−	0.467454i	0.433635	−	0.901089i	$-0.357231\pi$
$659$	−12.0000	−	12.0000i	−0.467454	−	0.467454i	−0.901089	+	0.433635i	$0.857231\pi$
$660$		0			0
$661$	9.00000	−	9.00000i	0.350059	−	0.350059i	−0.510072	−	0.860132i	$-0.670381\pi$
$661$	9.00000	−	9.00000i	0.350059	−	0.350059i	0.860132	+	0.510072i	$0.170381\pi$
$662$		0			0
$663$			16.0000i			0.621389i
$664$		0			0
$665$			4.00000i			0.155113i
$666$		0			0
$667$	28.0000	−	28.0000i	1.08416	−	1.08416i
$668$		0			0
$669$	32.0000	+	32.0000i	1.23719	+	1.23719i
$670$		0			0
$671$	24.0000			0.926510
$672$		0			0
$673$	−16.0000			−0.616755			−0.308377	−	0.951264i	$-0.599786\pi$
$673$	−16.0000			−0.616755			−0.308377	+	0.951264i	$0.599786\pi$
$674$		0			0
$675$	12.0000	+	12.0000i	0.461880	+	0.461880i
$676$		0			0
$677$	−5.00000	+	5.00000i	−0.192166	+	0.192166i	−0.796631	−	0.604466i	$-0.793387\pi$
$677$	−5.00000	+	5.00000i	−0.192166	+	0.192166i	0.604466	+	0.796631i	$0.293387\pi$
$678$		0			0
$679$			4.00000i			0.153506i
$680$		0			0
$681$		−	8.00000i		−	0.306561i
$682$		0			0
$683$	16.0000	−	16.0000i	0.612223	−	0.612223i	−0.331302	−	0.943525i	$-0.607488\pi$
$683$	16.0000	−	16.0000i	0.612223	−	0.612223i	0.943525	+	0.331302i	$0.107488\pi$
$684$		0			0
$685$	16.0000	+	16.0000i	0.611329	+	0.611329i
$686$		0			0
$687$	−84.0000			−3.20480
$688$		0			0
$689$	−2.00000			−0.0761939
$690$		0			0
$691$	18.0000	+	18.0000i	0.684752	+	0.684752i	0.961067	−	0.276315i	$-0.0891133\pi$
$691$	18.0000	+	18.0000i	0.684752	+	0.684752i	−0.276315	+	0.961067i	$0.589113\pi$
$692$		0			0
$693$	−20.0000	+	20.0000i	−0.759737	+	0.759737i
$694$		0			0
$695$			28.0000i			1.06210i
$696$		0			0
$697$			48.0000i			1.81813i
$698$		0			0
$699$	−20.0000	+	20.0000i	−0.756469	+	0.756469i
$700$		0			0
$701$	−23.0000	−	23.0000i	−0.868698	−	0.868698i	0.123630	−	0.992328i	$-0.460546\pi$
$701$	−23.0000	−	23.0000i	−0.868698	−	0.868698i	−0.992328	+	0.123630i	$0.960546\pi$
$702$		0			0
$703$	20.0000			0.754314
$704$		0			0
$705$	−48.0000			−1.80778
$706$		0			0
$707$	−9.00000	−	9.00000i	−0.338480	−	0.338480i
$708$		0			0
$709$	−11.0000	+	11.0000i	−0.413114	+	0.413114i	−0.882822	−	0.469708i	$-0.844359\pi$
$709$	−11.0000	+	11.0000i	−0.413114	+	0.413114i	0.469708	+	0.882822i	$0.344359\pi$
$710$		0			0
$711$			40.0000i			1.50012i
$712$		0			0
$713$			16.0000i			0.599205i
$714$		0			0
$715$	−8.00000	+	8.00000i	−0.299183	+	0.299183i
$716$		0			0
$717$	56.0000	+	56.0000i	2.09136	+	2.09136i
$718$		0			0
$719$	−4.00000			−0.149175			−0.0745874	−	0.997214i	$-0.523764\pi$
$719$	−4.00000			−0.149175			−0.0745874	+	0.997214i	$0.523764\pi$
$720$		0			0
$721$	12.0000			0.446903
$722$		0			0
$723$	8.00000	+	8.00000i	0.297523	+	0.297523i
$724$		0			0
$725$	−21.0000	+	21.0000i	−0.779920	+	0.779920i
$726$		0			0
$727$			20.0000i			0.741759i	0.928681	+	0.370879i	$0.120944\pi$
$727$			20.0000i			0.741759i	−0.928681	+	0.370879i	$0.879056\pi$
$728$		0			0
$729$			43.0000i			1.59259i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−3.00000	−	3.00000i	−0.110808	−	0.110808i	0.649529	−	0.760337i	$-0.274966\pi$
$733$	−3.00000	−	3.00000i	−0.110808	−	0.110808i	−0.760337	+	0.649529i	$0.774966\pi$
$734$		0			0
$735$	4.00000			0.147542
$736$		0			0
$737$	32.0000			1.17874
$738$		0			0
$739$	−4.00000	−	4.00000i	−0.147142	−	0.147142i	0.629698	−	0.776840i	$-0.283179\pi$
$739$	−4.00000	−	4.00000i	−0.147142	−	0.147142i	−0.776840	+	0.629698i	$0.783179\pi$
$740$		0			0
$741$	−8.00000	+	8.00000i	−0.293887	+	0.293887i
$742$		0			0
$743$			28.0000i			1.02722i	0.858024	+	0.513610i	$0.171692\pi$
$743$			28.0000i			1.02722i	−0.858024	+	0.513610i	$0.828308\pi$
$744$		0			0
$745$		−	30.0000i		−	1.09911i
$746$		0			0
$747$	−50.0000	+	50.0000i	−1.82940	+	1.82940i
$748$		0			0
$749$	8.00000	+	8.00000i	0.292314	+	0.292314i
$750$		0			0
$751$	20.0000			0.729810			0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000			0.729810			0.364905	+	0.931045i	$0.381101\pi$
$752$		0			0
$753$	−40.0000			−1.45768
$754$		0			0
$755$	4.00000	+	4.00000i	0.145575	+	0.145575i
$756$		0			0
$757$	3.00000	−	3.00000i	0.109037	−	0.109037i	−0.650484	−	0.759520i	$-0.725434\pi$
$757$	3.00000	−	3.00000i	0.109037	−	0.109037i	0.759520	+	0.650484i	$0.225434\pi$
$758$		0			0
$759$			64.0000i			2.32305i
$760$		0			0
$761$		−	4.00000i		−	0.145000i	−0.997368	−	0.0724999i	$-0.976902\pi$
$761$		−	4.00000i		−	0.145000i	0.997368	−	0.0724999i	$-0.0230977\pi$
$762$		0			0
$763$	1.00000	−	1.00000i	0.0362024	−	0.0362024i
$764$		0			0
$765$	20.0000	+	20.0000i	0.723102	+	0.723102i
$766$		0			0
$767$	4.00000			0.144432
$768$		0			0
$769$	44.0000			1.58668			0.793340	−	0.608778i	$-0.208340\pi$
$769$	44.0000			1.58668			0.793340	+	0.608778i	$0.208340\pi$
$770$		0			0
$771$	28.0000	+	28.0000i	1.00840	+	1.00840i
$772$		0			0
$773$	−9.00000	+	9.00000i	−0.323708	+	0.323708i	−0.850188	−	0.526480i	$-0.823511\pi$
$773$	−9.00000	+	9.00000i	−0.323708	+	0.323708i	0.526480	+	0.850188i	$0.323511\pi$
$774$		0			0
$775$		−	12.0000i		−	0.431053i
$776$		0			0
$777$		−	20.0000i		−	0.717496i
$778$		0			0
$779$	−24.0000	+	24.0000i	−0.859889	+	0.859889i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	56.0000			2.00128
$784$		0			0
$785$	−18.0000			−0.642448
$786$		0			0
$787$	−18.0000	−	18.0000i	−0.641631	−	0.641631i	0.309326	−	0.950956i	$-0.399897\pi$
$787$	−18.0000	−	18.0000i	−0.641631	−	0.641631i	−0.950956	+	0.309326i	$0.899897\pi$
$788$		0			0
$789$	48.0000	−	48.0000i	1.70885	−	1.70885i
$790$		0			0
$791$		−	6.00000i		−	0.213335i
$792$		0			0
$793$		−	6.00000i		−	0.213066i
$794$		0			0
$795$	−4.00000	+	4.00000i	−0.141865	+	0.141865i
$796$		0			0
$797$	−17.0000	−	17.0000i	−0.602171	−	0.602171i	0.338717	−	0.940888i	$-0.390007\pi$
$797$	−17.0000	−	17.0000i	−0.602171	−	0.602171i	−0.940888	+	0.338717i	$0.890007\pi$
$798$		0			0
$799$	48.0000			1.69812
$800$		0			0
$801$	−50.0000			−1.76666
$802$		0			0
$803$	24.0000	+	24.0000i	0.846942	+	0.846942i
$804$		0			0
$805$	4.00000	−	4.00000i	0.140981	−	0.140981i
$806$		0			0
$807$			28.0000i			0.985647i
$808$		0			0
$809$		−	48.0000i		−	1.68759i	−0.536666	−	0.843795i	$-0.680316\pi$
$809$		−	48.0000i		−	1.68759i	0.536666	−	0.843795i	$-0.319684\pi$
$810$		0			0
$811$	−22.0000	+	22.0000i	−0.772524	+	0.772524i	−0.978547	−	0.206023i	$-0.933948\pi$
$811$	−22.0000	+	22.0000i	−0.772524	+	0.772524i	0.206023	+	0.978547i	$0.433948\pi$
$812$		0			0
$813$	−32.0000	−	32.0000i	−1.12229	−	1.12229i
$814$		0			0
$815$	8.00000			0.280228
$816$		0			0
$817$		0			0
$818$		0			0
$819$	5.00000	+	5.00000i	0.174714	+	0.174714i
$820$		0			0
$821$	−31.0000	+	31.0000i	−1.08191	+	1.08191i	−0.0855758	+	0.996332i	$0.527273\pi$
$821$	−31.0000	+	31.0000i	−1.08191	+	1.08191i	−0.996332	+	0.0855758i	$0.972727\pi$
$822$		0			0
$823$		−	24.0000i		−	0.836587i	−0.908312	−	0.418294i	$-0.862628\pi$
$823$		−	24.0000i		−	0.836587i	0.908312	−	0.418294i	$-0.137372\pi$
$824$		0			0
$825$		−	48.0000i		−	1.67115i
$826$		0			0
$827$	−40.0000	+	40.0000i	−1.39094	+	1.39094i	−0.567702	+	0.823234i	$0.692168\pi$
$827$	−40.0000	+	40.0000i	−1.39094	+	1.39094i	−0.823234	+	0.567702i	$0.807832\pi$
$828$		0			0
$829$	−13.0000	−	13.0000i	−0.451509	−	0.451509i	0.444346	−	0.895855i	$-0.353436\pi$
$829$	−13.0000	−	13.0000i	−0.451509	−	0.451509i	−0.895855	+	0.444346i	$0.853436\pi$
$830$		0			0
$831$	60.0000			2.08138
$832$		0			0
$833$	−4.00000			−0.138592
$834$		0			0
$835$	4.00000	+	4.00000i	0.138426	+	0.138426i
$836$		0			0
$837$	−16.0000	+	16.0000i	−0.553041	+	0.553041i
$838$		0			0
$839$			44.0000i			1.51905i	0.650479	+	0.759524i	$0.274568\pi$
$839$			44.0000i			1.51905i	−0.650479	+	0.759524i	$0.725432\pi$
$840$		0			0
$841$			69.0000i			2.37931i
$842$		0			0
$843$	−20.0000	+	20.0000i	−0.688837	+	0.688837i
$844$		0			0
$845$	−11.0000	−	11.0000i	−0.378412	−	0.378412i
$846$		0			0
$847$	21.0000			0.721569
$848$		0			0
$849$	24.0000			0.823678
$850$		0			0
$851$	−20.0000	−	20.0000i	−0.685591	−	0.685591i
$852$		0			0
$853$	−13.0000	+	13.0000i	−0.445112	+	0.445112i	−0.893726	−	0.448614i	$-0.851918\pi$
$853$	−13.0000	+	13.0000i	−0.445112	+	0.445112i	0.448614	+	0.893726i	$0.351918\pi$
$854$		0			0
$855$			20.0000i			0.683986i
$856$		0			0
$857$		−	12.0000i		−	0.409912i	−0.978771	−	0.204956i	$-0.934295\pi$
$857$		−	12.0000i		−	0.409912i	0.978771	−	0.204956i	$-0.0657052\pi$
$858$		0			0
$859$	6.00000	−	6.00000i	0.204717	−	0.204717i	−0.597300	−	0.802018i	$-0.703760\pi$
$859$	6.00000	−	6.00000i	0.204717	−	0.204717i	0.802018	+	0.597300i	$0.203760\pi$
$860$		0			0
$861$	24.0000	+	24.0000i	0.817918	+	0.817918i
$862$		0			0
$863$	−32.0000			−1.08929			−0.544646	−	0.838666i	$-0.683336\pi$
$863$	−32.0000			−1.08929			−0.544646	+	0.838666i	$0.683336\pi$
$864$		0			0
$865$	−18.0000			−0.612018
$866$		0			0
$867$	2.00000	+	2.00000i	0.0679236	+	0.0679236i
$868$		0			0
$869$	32.0000	−	32.0000i	1.08553	−	1.08553i
$870$		0			0
$871$		−	8.00000i		−	0.271070i
$872$		0			0
$873$			20.0000i			0.676897i
$874$		0			0
$875$	−8.00000	+	8.00000i	−0.270449	+	0.270449i
$876$		0			0
$877$	−9.00000	−	9.00000i	−0.303908	−	0.303908i	0.538632	−	0.842541i	$-0.318941\pi$
$877$	−9.00000	−	9.00000i	−0.303908	−	0.303908i	−0.842541	+	0.538632i	$0.818941\pi$
$878$		0			0
$879$	−4.00000			−0.134917
$880$		0			0
$881$	14.0000			0.471672			0.235836	−	0.971793i	$-0.424217\pi$
$881$	14.0000			0.471672			0.235836	+	0.971793i	$0.424217\pi$
$882$		0			0
$883$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$883$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$884$		0			0
$885$	8.00000	−	8.00000i	0.268917	−	0.268917i
$886$		0			0
$887$		−	28.0000i		−	0.940148i	−0.882627	−	0.470074i	$-0.844227\pi$
$887$		−	28.0000i		−	0.940148i	0.882627	−	0.470074i	$-0.155773\pi$
$888$		0			0
$889$		−	4.00000i		−	0.134156i
$890$		0			0
$891$	−4.00000	+	4.00000i	−0.134005	+	0.134005i
$892$		0			0
$893$	24.0000	+	24.0000i	0.803129	+	0.803129i
$894$		0			0
$895$	−24.0000			−0.802232
$896$		0			0
$897$	16.0000			0.534224
$898$		0			0
$899$	−28.0000	−	28.0000i	−0.933852	−	0.933852i
$900$		0			0
$901$	4.00000	−	4.00000i	0.133259	−	0.133259i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			6.00000i			0.199447i
$906$		0			0
$907$	4.00000	−	4.00000i	0.132818	−	0.132818i	−0.637573	−	0.770390i	$-0.720061\pi$
$907$	4.00000	−	4.00000i	0.132818	−	0.132818i	0.770390	+	0.637573i	$0.220061\pi$
$908$		0			0
$909$	−45.0000	−	45.0000i	−1.49256	−	1.49256i
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$		0			0
$913$	80.0000			2.64761
$914$		0			0
$915$	−12.0000	−	12.0000i	−0.396708	−	0.396708i
$916$		0			0
$917$	2.00000	−	2.00000i	0.0660458	−	0.0660458i
$918$		0			0
$919$		−	16.0000i		−	0.527791i	−0.964551	−	0.263896i	$-0.914993\pi$
$919$		−	16.0000i		−	0.527791i	0.964551	−	0.263896i	$-0.0850075\pi$
$920$		0			0
$921$		−	40.0000i		−	1.31804i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	15.0000	+	15.0000i	0.493197	+	0.493197i
$926$		0			0
$927$	60.0000			1.97066
$928$		0			0
$929$	12.0000			0.393707			0.196854	−	0.980433i	$-0.436928\pi$
$929$	12.0000			0.393707			0.196854	+	0.980433i	$0.436928\pi$
$930$		0			0
$931$	−2.00000	−	2.00000i	−0.0655474	−	0.0655474i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	32.0000i		−	1.04651i
$936$		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
$939$	40.0000	−	40.0000i	1.30535	−	1.30535i
$940$		0			0
$941$	29.0000	+	29.0000i	0.945373	+	0.945373i	0.998583	−	0.0532103i	$-0.0169454\pi$
$941$	29.0000	+	29.0000i	0.945373	+	0.945373i	−0.0532103	+	0.998583i	$0.516945\pi$
$942$		0			0
$943$	48.0000			1.56310
$944$		0			0
$945$	8.00000			0.260240
$946$		0			0
$947$	12.0000	+	12.0000i	0.389948	+	0.389948i	0.874669	−	0.484721i	$-0.161079\pi$
$947$	12.0000	+	12.0000i	0.389948	+	0.389948i	−0.484721	+	0.874669i	$0.661079\pi$
$948$		0			0
$949$	6.00000	−	6.00000i	0.194768	−	0.194768i
$950$		0			0
$951$			52.0000i			1.68622i
$952$		0			0
$953$		−	24.0000i		−	0.777436i	−0.921357	−	0.388718i	$-0.872918\pi$
$953$		−	24.0000i		−	0.777436i	0.921357	−	0.388718i	$-0.127082\pi$
$954$		0			0
$955$	−24.0000	+	24.0000i	−0.776622	+	0.776622i
$956$		0			0
$957$	−112.000	−	112.000i	−3.62045	−	3.62045i
$958$		0			0
$959$	−16.0000			−0.516667
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	40.0000	+	40.0000i	1.28898	+	1.28898i
$964$		0			0
$965$	16.0000	−	16.0000i	0.515058	−	0.515058i
$966$		0			0
$967$			28.0000i			0.900419i	0.892923	+	0.450210i	$0.148651\pi$
$967$			28.0000i			0.900419i	−0.892923	+	0.450210i	$0.851349\pi$
$968$		0			0
$969$		−	32.0000i		−	1.02799i
$970$		0			0
$971$	26.0000	−	26.0000i	0.834380	−	0.834380i	−0.153733	−	0.988112i	$-0.549129\pi$
$971$	26.0000	−	26.0000i	0.834380	−	0.834380i	0.988112	+	0.153733i	$0.0491295\pi$
$972$		0			0
$973$	−14.0000	−	14.0000i	−0.448819	−	0.448819i
$974$		0			0
$975$	−12.0000			−0.384308
$976$		0			0
$977$	48.0000			1.53566			0.767828	−	0.640656i	$-0.221338\pi$
$977$	48.0000			1.53566			0.767828	+	0.640656i	$0.221338\pi$
$978$		0			0
$979$	40.0000	+	40.0000i	1.27841	+	1.27841i
$980$		0			0
$981$	5.00000	−	5.00000i	0.159638	−	0.159638i
$982$		0			0
$983$		−	60.0000i		−	1.91370i	−0.290578	−	0.956851i	$-0.593847\pi$
$983$		−	60.0000i		−	1.91370i	0.290578	−	0.956851i	$-0.406153\pi$
$984$		0			0
$985$		−	30.0000i		−	0.955879i
$986$		0			0
$987$	24.0000	−	24.0000i	0.763928	−	0.763928i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−56.0000			−1.77890			−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000			−1.77890			−0.889449	+	0.457034i	$0.848912\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.0000	−	12.0000i	−0.380426	−	0.380426i
$996$		0			0
$997$	23.0000	−	23.0000i	0.728417	−	0.728417i	−0.241887	−	0.970304i	$-0.577766\pi$
$997$	23.0000	−	23.0000i	0.728417	−	0.728417i	0.970304	+	0.241887i	$0.0777664\pi$
$998$		0			0
$999$		−	40.0000i		−	1.26554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3584.2.m.b.2689.1	yes	2
4.3	odd	2		3584.2.m.bb.2689.1	yes	2
8.3	odd	2		3584.2.m.a.2689.1	yes	2
8.5	even	2		3584.2.m.ba.2689.1	yes	2
16.3	odd	4		3584.2.m.a.897.1	✓	2
16.5	even	4	inner	3584.2.m.b.897.1	yes	2
16.11	odd	4		3584.2.m.bb.897.1	yes	2
16.13	even	4		3584.2.m.ba.897.1	yes	2
32.5	even	8		7168.2.a.h.1.2		2
32.11	odd	8		7168.2.a.r.1.2		2
32.21	even	8		7168.2.a.h.1.1		2
32.27	odd	8		7168.2.a.r.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3584.2.m.a.897.1	✓	2	16.3	odd	4
3584.2.m.a.2689.1	yes	2	8.3	odd	2
3584.2.m.b.897.1	yes	2	16.5	even	4	inner
3584.2.m.b.2689.1	yes	2	1.1	even	1	trivial
3584.2.m.ba.897.1	yes	2	16.13	even	4
3584.2.m.ba.2689.1	yes	2	8.5	even	2
3584.2.m.bb.897.1	yes	2	16.11	odd	4
3584.2.m.bb.2689.1	yes	2	4.3	odd	2
7168.2.a.h.1.1		2	32.21	even	8
7168.2.a.h.1.2		2	32.5	even	8
7168.2.a.r.1.1		2	32.27	odd	8
7168.2.a.r.1.2		2	32.11	odd	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:	\( N \)	\(=\)	\( 3584 = 2^{9} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3584.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{3} +(1.00000 - 1.00000i) q^{5} +1.00000i q^{7} +5.00000i q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{3} +(1.00000 - 1.00000i) q^{5} +1.00000i q^{7} +5.00000i q^{9} +(4.00000 - 4.00000i) q^{11} +(-1.00000 - 1.00000i) q^{13} -4.00000 q^{15} +4.00000 q^{17} +(2.00000 + 2.00000i) q^{19} +(2.00000 - 2.00000i) q^{21} -4.00000i q^{23} +3.00000i q^{25} +(4.00000 - 4.00000i) q^{27} +(7.00000 + 7.00000i) q^{29} -4.00000 q^{31} -16.0000 q^{33} +(1.00000 + 1.00000i) q^{35} +(5.00000 - 5.00000i) q^{37} +4.00000i q^{39} +12.0000i q^{41} +(5.00000 + 5.00000i) q^{45} +12.0000 q^{47} -1.00000 q^{49} +(-8.00000 - 8.00000i) q^{51} +(1.00000 - 1.00000i) q^{53} -8.00000i q^{55} -8.00000i q^{57} +(-2.00000 + 2.00000i) q^{59} +(3.00000 + 3.00000i) q^{61} -5.00000 q^{63} -2.00000 q^{65} +(4.00000 + 4.00000i) q^{67} +(-8.00000 + 8.00000i) q^{69} +6.00000i q^{73} +(6.00000 - 6.00000i) q^{75} +(4.00000 + 4.00000i) q^{77} +8.00000 q^{79} -1.00000 q^{81} +(10.0000 + 10.0000i) q^{83} +(4.00000 - 4.00000i) q^{85} -28.0000i q^{87} +10.0000i q^{89} +(1.00000 - 1.00000i) q^{91} +(8.00000 + 8.00000i) q^{93} +4.00000 q^{95} +4.00000 q^{97} +(20.0000 + 20.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{3} + 2 q^{5}+O(q^{10}) \) 2 * q - 4 * q^3 + 2 * q^5	\( 2 q - 4 q^{3} + 2 q^{5} + 8 q^{11} - 2 q^{13} - 8 q^{15} + 8 q^{17} + 4 q^{19} + 4 q^{21} + 8 q^{27} + 14 q^{29} - 8 q^{31} - 32 q^{33} + 2 q^{35} + 10 q^{37} + 10 q^{45} + 24 q^{47} - 2 q^{49} - 16 q^{51} + 2 q^{53} - 4 q^{59} + 6 q^{61} - 10 q^{63} - 4 q^{65} + 8 q^{67} - 16 q^{69} + 12 q^{75} + 8 q^{77} + 16 q^{79} - 2 q^{81} + 20 q^{83} + 8 q^{85} + 2 q^{91} + 16 q^{93} + 8 q^{95} + 8 q^{97} + 40 q^{99}+O(q^{100}) \) 2 * q - 4 * q^3 + 2 * q^5 + 8 * q^11 - 2 * q^13 - 8 * q^15 + 8 * q^17 + 4 * q^19 + 4 * q^21 + 8 * q^27 + 14 * q^29 - 8 * q^31 - 32 * q^33 + 2 * q^35 + 10 * q^37 + 10 * q^45 + 24 * q^47 - 2 * q^49 - 16 * q^51 + 2 * q^53 - 4 * q^59 + 6 * q^61 - 10 * q^63 - 4 * q^65 + 8 * q^67 - 16 * q^69 + 12 * q^75 + 8 * q^77 + 16 * q^79 - 2 * q^81 + 20 * q^83 + 8 * q^85 + 2 * q^91 + 16 * q^93 + 8 * q^95 + 8 * q^97 + 40 * q^99

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