LMFDB - Embedded newform 3584.2.m.d.897.1

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:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			897.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	3584.897
Dual form			3584.2.m.d.2689.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 - 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 - 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{9} +(-2.00000 - 2.00000i) q^{11} +4.00000 q^{15} -2.00000 q^{17} +(3.00000 - 3.00000i) q^{19} +(1.00000 + 1.00000i) q^{21} +4.00000i q^{23} +3.00000i q^{25} +(-4.00000 - 4.00000i) q^{27} +(7.00000 - 7.00000i) q^{29} +6.00000 q^{31} +4.00000 q^{33} +(-2.00000 + 2.00000i) q^{35} +(3.00000 + 3.00000i) q^{37} -2.00000i q^{41} +(-6.00000 - 6.00000i) q^{43} +(2.00000 - 2.00000i) q^{45} -10.0000 q^{47} -1.00000 q^{49} +(2.00000 - 2.00000i) q^{51} +(5.00000 + 5.00000i) q^{53} +8.00000i q^{55} +6.00000i q^{57} +(-7.00000 - 7.00000i) q^{59} +(2.00000 - 2.00000i) q^{61} +1.00000 q^{63} +(-8.00000 + 8.00000i) q^{67} +(-4.00000 - 4.00000i) q^{69} -4.00000i q^{71} +14.0000i q^{73} +(-3.00000 - 3.00000i) q^{75} +(-2.00000 + 2.00000i) q^{77} +4.00000 q^{79} +5.00000 q^{81} +(-3.00000 + 3.00000i) q^{83} +(4.00000 + 4.00000i) q^{85} +14.0000i q^{87} -10.0000i q^{89} +(-6.00000 + 6.00000i) q^{93} -12.0000 q^{95} -6.00000 q^{97} +(2.00000 - 2.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 4 q^{5}+O(q^{10}) $ 2 * q - 2 * q^3 - 4 * q^5	$ 2 q - 2 q^{3} - 4 q^{5} - 4 q^{11} + 8 q^{15} - 4 q^{17} + 6 q^{19} + 2 q^{21} - 8 q^{27} + 14 q^{29} + 12 q^{31} + 8 q^{33} - 4 q^{35} + 6 q^{37} - 12 q^{43} + 4 q^{45} - 20 q^{47} - 2 q^{49} + 4 q^{51} + 10 q^{53} - 14 q^{59} + 4 q^{61} + 2 q^{63} - 16 q^{67} - 8 q^{69} - 6 q^{75} - 4 q^{77} + 8 q^{79} + 10 q^{81} - 6 q^{83} + 8 q^{85} - 12 q^{93} - 24 q^{95} - 12 q^{97} + 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 4 * q^5 - 4 * q^11 + 8 * q^15 - 4 * q^17 + 6 * q^19 + 2 * q^21 - 8 * q^27 + 14 * q^29 + 12 * q^31 + 8 * q^33 - 4 * q^35 + 6 * q^37 - 12 * q^43 + 4 * q^45 - 20 * q^47 - 2 * q^49 + 4 * q^51 + 10 * q^53 - 14 * q^59 + 4 * q^61 + 2 * q^63 - 16 * q^67 - 8 * q^69 - 6 * q^75 - 4 * q^77 + 8 * q^79 + 10 * q^81 - 6 * q^83 + 8 * q^85 - 12 * q^93 - 24 * q^95 - 12 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$2$		0			0
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	−0.934172	−	0.356822i	$-0.883860\pi$
$3$	−1.00000	+	1.00000i	−0.577350	+	0.577350i	0.356822	+	0.934172i	$0.383860\pi$
$4$		0			0
$5$	−2.00000	−	2.00000i	−0.894427	−	0.894427i	0.100509	−	0.994936i	$-0.467953\pi$
$5$	−2.00000	−	2.00000i	−0.894427	−	0.894427i	−0.994936	+	0.100509i	$0.967953\pi$
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	0.338091	−	0.941113i	$-0.390219\pi$
$11$	−2.00000	−	2.00000i	−0.603023	−	0.603023i	−0.941113	+	0.338091i	$0.890219\pi$
$12$		0			0
$13$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$13$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$14$		0			0
$15$	4.00000			1.03280
$16$		0			0
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	−0.273597	−	0.961844i	$-0.588214\pi$
$19$	3.00000	−	3.00000i	0.688247	−	0.688247i	0.961844	+	0.273597i	$0.0882135\pi$
$20$		0			0
$21$	1.00000	+	1.00000i	0.218218	+	0.218218i
$22$		0			0
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$		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	0.371391	−	0.928477i	$-0.378881\pi$
$29$	7.00000	−	7.00000i	1.29987	−	1.29987i	0.928477	−	0.371391i	$-0.121119\pi$
$30$		0			0
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$		0			0
$33$	4.00000			0.696311
$34$		0			0
$35$	−2.00000	+	2.00000i	−0.338062	+	0.338062i
$36$		0			0
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	0.909312	−	0.416115i	$-0.136609\pi$
$37$	3.00000	+	3.00000i	0.493197	+	0.493197i	−0.416115	+	0.909312i	$0.636609\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	2.00000i		−	0.312348i	−0.987730	−	0.156174i	$-0.950084\pi$
$41$		−	2.00000i		−	0.312348i	0.987730	−	0.156174i	$-0.0499160\pi$
$42$		0			0
$43$	−6.00000	−	6.00000i	−0.914991	−	0.914991i	0.0816682	−	0.996660i	$-0.473975\pi$
$43$	−6.00000	−	6.00000i	−0.914991	−	0.914991i	−0.996660	+	0.0816682i	$0.973975\pi$
$44$		0			0
$45$	2.00000	−	2.00000i	0.298142	−	0.298142i
$46$		0			0
$47$	−10.0000			−1.45865			−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000			−1.45865			−0.729325	+	0.684167i	$0.760166\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	2.00000	−	2.00000i	0.280056	−	0.280056i
$52$		0			0
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$		0			0
$55$			8.00000i			1.07872i
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$	−7.00000	−	7.00000i	−0.911322	−	0.911322i	0.0850540	−	0.996376i	$-0.472894\pi$
$59$	−7.00000	−	7.00000i	−0.911322	−	0.911322i	−0.996376	+	0.0850540i	$0.972894\pi$
$60$		0			0
$61$	2.00000	−	2.00000i	0.256074	−	0.256074i	−0.567381	−	0.823455i	$-0.692043\pi$
$61$	2.00000	−	2.00000i	0.256074	−	0.256074i	0.823455	+	0.567381i	$0.192043\pi$
$62$		0			0
$63$	1.00000			0.125988
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.00000	+	8.00000i	−0.977356	+	0.977356i	−0.999749	−	0.0223937i	$-0.992871\pi$
$67$	−8.00000	+	8.00000i	−0.977356	+	0.977356i	0.0223937	+	0.999749i	$0.492871\pi$
$68$		0			0
$69$	−4.00000	−	4.00000i	−0.481543	−	0.481543i
$70$		0			0
$71$		−	4.00000i		−	0.474713i	−0.971423	−	0.237356i	$-0.923719\pi$
$71$		−	4.00000i		−	0.474713i	0.971423	−	0.237356i	$-0.0762809\pi$
$72$		0			0
$73$			14.0000i			1.63858i	0.573382	+	0.819288i	$0.305631\pi$
$73$			14.0000i			1.63858i	−0.573382	+	0.819288i	$0.694369\pi$
$74$		0			0
$75$	−3.00000	−	3.00000i	−0.346410	−	0.346410i
$76$		0			0
$77$	−2.00000	+	2.00000i	−0.227921	+	0.227921i
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$		0			0
$83$	−3.00000	+	3.00000i	−0.329293	+	0.329293i	−0.852318	−	0.523025i	$-0.824804\pi$
$83$	−3.00000	+	3.00000i	−0.329293	+	0.329293i	0.523025	+	0.852318i	$0.324804\pi$
$84$		0			0
$85$	4.00000	+	4.00000i	0.433861	+	0.433861i
$86$		0			0
$87$			14.0000i			1.50096i
$88$		0			0
$89$		−	10.0000i		−	1.06000i	−0.847998	−	0.529999i	$-0.822192\pi$
$89$		−	10.0000i		−	1.06000i	0.847998	−	0.529999i	$-0.177808\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−6.00000	+	6.00000i	−0.622171	+	0.622171i
$94$		0			0
$95$	−12.0000			−1.23117
$96$		0			0
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$		0			0
$99$	2.00000	−	2.00000i	0.201008	−	0.201008i
$100$		0			0
$101$	2.00000	+	2.00000i	0.199007	+	0.199007i	0.799574	−	0.600567i	$-0.205058\pi$
$101$	2.00000	+	2.00000i	0.199007	+	0.199007i	−0.600567	+	0.799574i	$0.705058\pi$
$102$		0			0
$103$			6.00000i			0.591198i	0.955312	+	0.295599i	$0.0955191\pi$
$103$			6.00000i			0.591198i	−0.955312	+	0.295599i	$0.904481\pi$
$104$		0			0
$105$		−	4.00000i		−	0.390360i
$106$		0			0
$107$	4.00000	+	4.00000i	0.386695	+	0.386695i	0.873507	−	0.486812i	$-0.161840\pi$
$107$	4.00000	+	4.00000i	0.386695	+	0.386695i	−0.486812	+	0.873507i	$0.661840\pi$
$108$		0			0
$109$	−3.00000	+	3.00000i	−0.287348	+	0.287348i	−0.836031	−	0.548683i	$-0.815129\pi$
$109$	−3.00000	+	3.00000i	−0.287348	+	0.287348i	0.548683	+	0.836031i	$0.315129\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		0			0
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$		0			0
$115$	8.00000	−	8.00000i	0.746004	−	0.746004i
$116$		0			0
$117$		0			0
$118$		0			0
$119$			2.00000i			0.183340i
$120$		0			0
$121$		−	3.00000i		−	0.272727i
$122$		0			0
$123$	2.00000	+	2.00000i	0.180334	+	0.180334i
$124$		0			0
$125$	−4.00000	+	4.00000i	−0.357771	+	0.357771i
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$	12.0000			1.05654
$130$		0			0
$131$	−9.00000	+	9.00000i	−0.786334	+	0.786334i	−0.980891	−	0.194557i	$-0.937673\pi$
$131$	−9.00000	+	9.00000i	−0.786334	+	0.786334i	0.194557	+	0.980891i	$0.437673\pi$
$132$		0			0
$133$	−3.00000	−	3.00000i	−0.260133	−	0.260133i
$134$		0			0
$135$			16.0000i			1.37706i
$136$		0			0
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$		0			0
$139$	−5.00000	−	5.00000i	−0.424094	−	0.424094i	0.462516	−	0.886611i	$-0.346947\pi$
$139$	−5.00000	−	5.00000i	−0.424094	−	0.424094i	−0.886611	+	0.462516i	$0.846947\pi$
$140$		0			0
$141$	10.0000	−	10.0000i	0.842152	−	0.842152i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	−28.0000			−2.32527
$146$		0			0
$147$	1.00000	−	1.00000i	0.0824786	−	0.0824786i
$148$		0			0
$149$	−7.00000	−	7.00000i	−0.573462	−	0.573462i	0.359632	−	0.933094i	$-0.382902\pi$
$149$	−7.00000	−	7.00000i	−0.573462	−	0.573462i	−0.933094	+	0.359632i	$0.882902\pi$
$150$		0			0
$151$			24.0000i			1.95309i	0.215308	+	0.976546i	$0.430924\pi$
$151$			24.0000i			1.95309i	−0.215308	+	0.976546i	$0.569076\pi$
$152$		0			0
$153$		−	2.00000i		−	0.161690i
$154$		0			0
$155$	−12.0000	−	12.0000i	−0.963863	−	0.963863i
$156$		0			0
$157$	8.00000	−	8.00000i	0.638470	−	0.638470i	−0.311708	−	0.950178i	$-0.600901\pi$
$157$	8.00000	−	8.00000i	0.638470	−	0.638470i	0.950178	+	0.311708i	$0.100901\pi$
$158$		0			0
$159$	−10.0000			−0.793052
$160$		0			0
$161$	4.00000			0.315244
$162$		0			0
$163$	−14.0000	+	14.0000i	−1.09656	+	1.09656i	−0.101755	+	0.994809i	$0.532446\pi$
$163$	−14.0000	+	14.0000i	−1.09656	+	1.09656i	−0.994809	+	0.101755i	$0.967554\pi$
$164$		0			0
$165$	−8.00000	−	8.00000i	−0.622799	−	0.622799i
$166$		0			0
$167$		−	14.0000i		−	1.08335i	−0.840587	−	0.541676i	$-0.817790\pi$
$167$		−	14.0000i		−	1.08335i	0.840587	−	0.541676i	$-0.182210\pi$
$168$		0			0
$169$			13.0000i			1.00000i
$170$		0			0
$171$	3.00000	+	3.00000i	0.229416	+	0.229416i
$172$		0			0
$173$	−8.00000	+	8.00000i	−0.608229	+	0.608229i	−0.942483	−	0.334254i	$-0.891516\pi$
$173$	−8.00000	+	8.00000i	−0.608229	+	0.608229i	0.334254	+	0.942483i	$0.391516\pi$
$174$		0			0
$175$	3.00000			0.226779
$176$		0			0
$177$	14.0000			1.05230
$178$		0			0
$179$	−8.00000	+	8.00000i	−0.597948	+	0.597948i	−0.939766	−	0.341818i	$-0.888957\pi$
$179$	−8.00000	+	8.00000i	−0.597948	+	0.597948i	0.341818	+	0.939766i	$0.388957\pi$
$180$		0			0
$181$	−4.00000	−	4.00000i	−0.297318	−	0.297318i	0.542645	−	0.839962i	$-0.317423\pi$
$181$	−4.00000	−	4.00000i	−0.297318	−	0.297318i	−0.839962	+	0.542645i	$0.817423\pi$
$182$		0			0
$183$			4.00000i			0.295689i
$184$		0			0
$185$		−	12.0000i		−	0.882258i
$186$		0			0
$187$	4.00000	+	4.00000i	0.292509	+	0.292509i
$188$		0			0
$189$	−4.00000	+	4.00000i	−0.290957	+	0.290957i
$190$		0			0
$191$	−20.0000			−1.44715			−0.723575	−	0.690246i	$-0.757502\pi$
$191$	−20.0000			−1.44715			−0.723575	+	0.690246i	$0.757502\pi$
$192$		0			0
$193$	18.0000			1.29567			0.647834	−	0.761781i	$-0.275675\pi$
$193$	18.0000			1.29567			0.647834	+	0.761781i	$0.275675\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.00000	+	7.00000i	0.498729	+	0.498729i	0.911042	−	0.412313i	$-0.135279\pi$
$197$	7.00000	+	7.00000i	0.498729	+	0.498729i	−0.412313	+	0.911042i	$0.635279\pi$
$198$		0			0
$199$			10.0000i			0.708881i	0.935079	+	0.354441i	$0.115329\pi$
$199$			10.0000i			0.708881i	−0.935079	+	0.354441i	$0.884671\pi$
$200$		0			0
$201$		−	16.0000i		−	1.12855i
$202$		0			0
$203$	−7.00000	−	7.00000i	−0.491304	−	0.491304i
$204$		0			0
$205$	−4.00000	+	4.00000i	−0.279372	+	0.279372i
$206$		0			0
$207$	−4.00000			−0.278019
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	−12.0000	+	12.0000i	−0.826114	+	0.826114i	−0.986977	−	0.160863i	$-0.948572\pi$
$211$	−12.0000	+	12.0000i	−0.826114	+	0.826114i	0.160863	+	0.986977i	$0.448572\pi$
$212$		0			0
$213$	4.00000	+	4.00000i	0.274075	+	0.274075i
$214$		0			0
$215$			24.0000i			1.63679i
$216$		0			0
$217$		−	6.00000i		−	0.407307i
$218$		0			0
$219$	−14.0000	−	14.0000i	−0.946032	−	0.946032i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$		0			0
$227$	−1.00000	+	1.00000i	−0.0663723	+	0.0663723i	−0.739514	−	0.673141i	$-0.764945\pi$
$227$	−1.00000	+	1.00000i	−0.0663723	+	0.0663723i	0.673141	+	0.739514i	$0.264945\pi$
$228$		0			0
$229$	−4.00000	−	4.00000i	−0.264327	−	0.264327i	0.562482	−	0.826809i	$-0.309847\pi$
$229$	−4.00000	−	4.00000i	−0.264327	−	0.264327i	−0.826809	+	0.562482i	$0.809847\pi$
$230$		0			0
$231$		−	4.00000i		−	0.263181i
$232$		0			0
$233$		−	26.0000i		−	1.70332i	−0.524097	−	0.851658i	$-0.675597\pi$
$233$		−	26.0000i		−	1.70332i	0.524097	−	0.851658i	$-0.324403\pi$
$234$		0			0
$235$	20.0000	+	20.0000i	1.30466	+	1.30466i
$236$		0			0
$237$	−4.00000	+	4.00000i	−0.259828	+	0.259828i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$		0			0
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$		0			0
$245$	2.00000	+	2.00000i	0.127775	+	0.127775i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		−	6.00000i		−	0.380235i
$250$		0			0
$251$	−19.0000	−	19.0000i	−1.19927	−	1.19927i	−0.974386	−	0.224884i	$-0.927800\pi$
$251$	−19.0000	−	19.0000i	−1.19927	−	1.19927i	−0.224884	−	0.974386i	$-0.572200\pi$
$252$		0			0
$253$	8.00000	−	8.00000i	0.502956	−	0.502956i
$254$		0			0
$255$	−8.00000			−0.500979
$256$		0			0
$257$	−30.0000			−1.87135			−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000			−1.87135			−0.935674	+	0.352865i	$0.885208\pi$
$258$		0			0
$259$	3.00000	−	3.00000i	0.186411	−	0.186411i
$260$		0			0
$261$	7.00000	+	7.00000i	0.433289	+	0.433289i
$262$		0			0
$263$		−	4.00000i		−	0.246651i	−0.992366	−	0.123325i	$-0.960644\pi$
$263$		−	4.00000i		−	0.246651i	0.992366	−	0.123325i	$-0.0393559\pi$
$264$		0			0
$265$		−	20.0000i		−	1.22859i
$266$		0			0
$267$	10.0000	+	10.0000i	0.611990	+	0.611990i
$268$		0			0
$269$	−20.0000	+	20.0000i	−1.21942	+	1.21942i	−0.251587	+	0.967835i	$0.580952\pi$
$269$	−20.0000	+	20.0000i	−1.21942	+	1.21942i	−0.967835	+	0.251587i	$0.919048\pi$
$270$		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
$273$		0			0
$274$		0			0
$275$	6.00000	−	6.00000i	0.361814	−	0.361814i
$276$		0			0
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	0.791466	−	0.611213i	$-0.209318\pi$
$277$	3.00000	+	3.00000i	0.180253	+	0.180253i	−0.611213	+	0.791466i	$0.709318\pi$
$278$		0			0
$279$			6.00000i			0.359211i
$280$		0			0
$281$			22.0000i			1.31241i	0.754583	+	0.656205i	$0.227839\pi$
$281$			22.0000i			1.31241i	−0.754583	+	0.656205i	$0.772161\pi$
$282$		0			0
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	0.103022	−	0.994679i	$-0.467149\pi$
$283$	−15.0000	−	15.0000i	−0.891657	−	0.891657i	−0.994679	+	0.103022i	$0.967149\pi$
$284$		0			0
$285$	12.0000	−	12.0000i	0.710819	−	0.710819i
$286$		0			0
$287$	−2.00000			−0.118056
$288$		0			0
$289$	−13.0000			−0.764706
$290$		0			0
$291$	6.00000	−	6.00000i	0.351726	−	0.351726i
$292$		0			0
$293$	−2.00000	−	2.00000i	−0.116841	−	0.116841i	0.646269	−	0.763110i	$-0.276329\pi$
$293$	−2.00000	−	2.00000i	−0.116841	−	0.116841i	−0.763110	+	0.646269i	$0.776329\pi$
$294$		0			0
$295$			28.0000i			1.63022i
$296$		0			0
$297$			16.0000i			0.928414i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−6.00000	+	6.00000i	−0.345834	+	0.345834i
$302$		0			0
$303$	−4.00000			−0.229794
$304$		0			0
$305$	−8.00000			−0.458079
$306$		0			0
$307$	9.00000	−	9.00000i	0.513657	−	0.513657i	−0.401988	−	0.915645i	$-0.631681\pi$
$307$	9.00000	−	9.00000i	0.513657	−	0.513657i	0.915645	+	0.401988i	$0.131681\pi$
$308$		0			0
$309$	−6.00000	−	6.00000i	−0.341328	−	0.341328i
$310$		0			0
$311$		−	24.0000i		−	1.36092i	−0.732787	−	0.680458i	$-0.761781\pi$
$311$		−	24.0000i		−	1.36092i	0.732787	−	0.680458i	$-0.238219\pi$
$312$		0			0
$313$		−	22.0000i		−	1.24351i	−0.783210	−	0.621757i	$-0.786419\pi$
$313$		−	22.0000i		−	1.24351i	0.783210	−	0.621757i	$-0.213581\pi$
$314$		0			0
$315$	−2.00000	−	2.00000i	−0.112687	−	0.112687i
$316$		0			0
$317$	−21.0000	+	21.0000i	−1.17948	+	1.17948i	−0.199600	+	0.979877i	$0.563964\pi$
$317$	−21.0000	+	21.0000i	−1.17948	+	1.17948i	−0.979877	+	0.199600i	$0.936036\pi$
$318$		0			0
$319$	−28.0000			−1.56770
$320$		0			0
$321$	−8.00000			−0.446516
$322$		0			0
$323$	−6.00000	+	6.00000i	−0.333849	+	0.333849i
$324$		0			0
$325$		0			0
$326$		0			0
$327$		−	6.00000i		−	0.331801i
$328$		0			0
$329$			10.0000i			0.551318i
$330$		0			0
$331$	−10.0000	−	10.0000i	−0.549650	−	0.549650i	0.376690	−	0.926339i	$-0.377062\pi$
$331$	−10.0000	−	10.0000i	−0.549650	−	0.549650i	−0.926339	+	0.376690i	$0.877062\pi$
$332$		0			0
$333$	−3.00000	+	3.00000i	−0.164399	+	0.164399i
$334$		0			0
$335$	32.0000			1.74835
$336$		0			0
$337$	−16.0000			−0.871576			−0.435788	−	0.900049i	$-0.643530\pi$
$337$	−16.0000			−0.871576			−0.435788	+	0.900049i	$0.643530\pi$
$338$		0			0
$339$	−4.00000	+	4.00000i	−0.217250	+	0.217250i
$340$		0			0
$341$	−12.0000	−	12.0000i	−0.649836	−	0.649836i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			16.0000i			0.861411i
$346$		0			0
$347$	−10.0000	−	10.0000i	−0.536828	−	0.536828i	0.385768	−	0.922596i	$-0.373937\pi$
$347$	−10.0000	−	10.0000i	−0.536828	−	0.536828i	−0.922596	+	0.385768i	$0.873937\pi$
$348$		0			0
$349$	−20.0000	+	20.0000i	−1.07058	+	1.07058i	−0.0732628	+	0.997313i	$0.523341\pi$
$349$	−20.0000	+	20.0000i	−1.07058	+	1.07058i	−0.997313	+	0.0732628i	$0.976659\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−14.0000			−0.745145			−0.372572	−	0.928003i	$-0.621524\pi$
$353$	−14.0000			−0.745145			−0.372572	+	0.928003i	$0.621524\pi$
$354$		0			0
$355$	−8.00000	+	8.00000i	−0.424596	+	0.424596i
$356$		0			0
$357$	−2.00000	−	2.00000i	−0.105851	−	0.105851i
$358$		0			0
$359$		−	24.0000i		−	1.26667i	−0.773877	−	0.633336i	$-0.781685\pi$
$359$		−	24.0000i		−	1.26667i	0.773877	−	0.633336i	$-0.218315\pi$
$360$		0			0
$361$			1.00000i			0.0526316i
$362$		0			0
$363$	3.00000	+	3.00000i	0.157459	+	0.157459i
$364$		0			0
$365$	28.0000	−	28.0000i	1.46559	−	1.46559i
$366$		0			0
$367$	32.0000			1.67039			0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000			1.67039			0.835193	+	0.549957i	$0.185356\pi$
$368$		0			0
$369$	2.00000			0.104116
$370$		0			0
$371$	5.00000	−	5.00000i	0.259587	−	0.259587i
$372$		0			0
$373$	−1.00000	−	1.00000i	−0.0517780	−	0.0517780i	0.680744	−	0.732522i	$-0.261657\pi$
$373$	−1.00000	−	1.00000i	−0.0517780	−	0.0517780i	−0.732522	+	0.680744i	$0.761657\pi$
$374$		0			0
$375$		−	8.00000i		−	0.413118i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−10.0000	−	10.0000i	−0.513665	−	0.513665i	0.401982	−	0.915648i	$-0.368321\pi$
$379$	−10.0000	−	10.0000i	−0.513665	−	0.513665i	−0.915648	+	0.401982i	$0.868321\pi$
$380$		0			0
$381$	16.0000	−	16.0000i	0.819705	−	0.819705i
$382$		0			0
$383$	2.00000			0.102195			0.0510976	−	0.998694i	$-0.483728\pi$
$383$	2.00000			0.102195			0.0510976	+	0.998694i	$0.483728\pi$
$384$		0			0
$385$	8.00000			0.407718
$386$		0			0
$387$	6.00000	−	6.00000i	0.304997	−	0.304997i
$388$		0			0
$389$	11.0000	+	11.0000i	0.557722	+	0.557722i	0.928658	−	0.370936i	$-0.120963\pi$
$389$	11.0000	+	11.0000i	0.557722	+	0.557722i	−0.370936	+	0.928658i	$0.620963\pi$
$390$		0			0
$391$		−	8.00000i		−	0.404577i
$392$		0			0
$393$		−	18.0000i		−	0.907980i
$394$		0			0
$395$	−8.00000	−	8.00000i	−0.402524	−	0.402524i
$396$		0			0
$397$	12.0000	−	12.0000i	0.602263	−	0.602263i	−0.338650	−	0.940913i	$-0.609970\pi$
$397$	12.0000	−	12.0000i	0.602263	−	0.602263i	0.940913	+	0.338650i	$0.109970\pi$
$398$		0			0
$399$	6.00000			0.300376
$400$		0			0
$401$	34.0000			1.69788			0.848939	−	0.528490i	$-0.177242\pi$
$401$	34.0000			1.69788			0.848939	+	0.528490i	$0.177242\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−10.0000	−	10.0000i	−0.496904	−	0.496904i
$406$		0			0
$407$		−	12.0000i		−	0.594818i
$408$		0			0
$409$			14.0000i			0.692255i	0.938187	+	0.346128i	$0.112504\pi$
$409$			14.0000i			0.692255i	−0.938187	+	0.346128i	$0.887496\pi$
$410$		0			0
$411$	−12.0000	−	12.0000i	−0.591916	−	0.591916i
$412$		0			0
$413$	−7.00000	+	7.00000i	−0.344447	+	0.344447i
$414$		0			0
$415$	12.0000			0.589057
$416$		0			0
$417$	10.0000			0.489702
$418$		0			0
$419$	3.00000	−	3.00000i	0.146560	−	0.146560i	−0.630020	−	0.776579i	$-0.716953\pi$
$419$	3.00000	−	3.00000i	0.146560	−	0.146560i	0.776579	+	0.630020i	$0.216953\pi$
$420$		0			0
$421$	−3.00000	−	3.00000i	−0.146211	−	0.146211i	0.630212	−	0.776423i	$-0.282968\pi$
$421$	−3.00000	−	3.00000i	−0.146211	−	0.146211i	−0.776423	+	0.630212i	$0.782968\pi$
$422$		0			0
$423$		−	10.0000i		−	0.486217i
$424$		0			0
$425$		−	6.00000i		−	0.291043i
$426$		0			0
$427$	−2.00000	−	2.00000i	−0.0967868	−	0.0967868i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−36.0000			−1.73406			−0.867029	−	0.498257i	$-0.833974\pi$
$431$	−36.0000			−1.73406			−0.867029	+	0.498257i	$0.833974\pi$
$432$		0			0
$433$	10.0000			0.480569			0.240285	−	0.970702i	$-0.422759\pi$
$433$	10.0000			0.480569			0.240285	+	0.970702i	$0.422759\pi$
$434$		0			0
$435$	28.0000	−	28.0000i	1.34250	−	1.34250i
$436$		0			0
$437$	12.0000	+	12.0000i	0.574038	+	0.574038i
$438$		0			0
$439$		0			0		1.00000			$0$
$439$		0			0		−1.00000			$\pi$
$440$		0			0
$441$		−	1.00000i		−	0.0476190i
$442$		0			0
$443$	20.0000	+	20.0000i	0.950229	+	0.950229i	0.998819	−	0.0485901i	$-0.0154728\pi$
$443$	20.0000	+	20.0000i	0.950229	+	0.950229i	−0.0485901	+	0.998819i	$0.515473\pi$
$444$		0			0
$445$	−20.0000	+	20.0000i	−0.948091	+	0.948091i
$446$		0			0
$447$	14.0000			0.662177
$448$		0			0
$449$	16.0000			0.755087			0.377543	−	0.925992i	$-0.376769\pi$
$449$	16.0000			0.755087			0.377543	+	0.925992i	$0.376769\pi$
$450$		0			0
$451$	−4.00000	+	4.00000i	−0.188353	+	0.188353i
$452$		0			0
$453$	−24.0000	−	24.0000i	−1.12762	−	1.12762i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			22.0000i			1.02912i	0.857455	+	0.514558i	$0.172044\pi$
$457$			22.0000i			1.02912i	−0.857455	+	0.514558i	$0.827956\pi$
$458$		0			0
$459$	8.00000	+	8.00000i	0.373408	+	0.373408i
$460$		0			0
$461$	20.0000	−	20.0000i	0.931493	−	0.931493i	−0.0663064	−	0.997799i	$-0.521121\pi$
$461$	20.0000	−	20.0000i	0.931493	−	0.931493i	0.997799	+	0.0663064i	$0.0211215\pi$
$462$		0			0
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$		0			0
$465$	24.0000			1.11297
$466$		0			0
$467$	−19.0000	+	19.0000i	−0.879215	+	0.879215i	−0.993453	−	0.114238i	$-0.963557\pi$
$467$	−19.0000	+	19.0000i	−0.879215	+	0.879215i	0.114238	+	0.993453i	$0.463557\pi$
$468$		0			0
$469$	8.00000	+	8.00000i	0.369406	+	0.369406i
$470$		0			0
$471$			16.0000i			0.737241i
$472$		0			0
$473$			24.0000i			1.10352i
$474$		0			0
$475$	9.00000	+	9.00000i	0.412948	+	0.412948i
$476$		0			0
$477$	−5.00000	+	5.00000i	−0.228934	+	0.228934i
$478$		0			0
$479$	−18.0000			−0.822441			−0.411220	−	0.911536i	$-0.634897\pi$
$479$	−18.0000			−0.822441			−0.411220	+	0.911536i	$0.634897\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−4.00000	+	4.00000i	−0.182006	+	0.182006i
$484$		0			0
$485$	12.0000	+	12.0000i	0.544892	+	0.544892i
$486$		0			0
$487$			20.0000i			0.906287i	0.891438	+	0.453143i	$0.149697\pi$
$487$			20.0000i			0.906287i	−0.891438	+	0.453143i	$0.850303\pi$
$488$		0			0
$489$		−	28.0000i		−	1.26620i
$490$		0			0
$491$	16.0000	+	16.0000i	0.722070	+	0.722070i	0.969027	−	0.246957i	$-0.0794305\pi$
$491$	16.0000	+	16.0000i	0.722070	+	0.722070i	−0.246957	+	0.969027i	$0.579431\pi$
$492$		0			0
$493$	−14.0000	+	14.0000i	−0.630528	+	0.630528i
$494$		0			0
$495$	−8.00000			−0.359573
$496$		0			0
$497$	−4.00000			−0.179425
$498$		0			0
$499$	8.00000	−	8.00000i	0.358129	−	0.358129i	−0.504994	−	0.863123i	$-0.668505\pi$
$499$	8.00000	−	8.00000i	0.358129	−	0.358129i	0.863123	+	0.504994i	$0.168505\pi$
$500$		0			0
$501$	14.0000	+	14.0000i	0.625474	+	0.625474i
$502$		0			0
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$		0			0
$505$		−	8.00000i		−	0.355995i
$506$		0			0
$507$	−13.0000	−	13.0000i	−0.577350	−	0.577350i
$508$		0			0
$509$	28.0000	−	28.0000i	1.24108	−	1.24108i	0.281524	−	0.959554i	$-0.409160\pi$
$509$	28.0000	−	28.0000i	1.24108	−	1.24108i	0.959554	−	0.281524i	$-0.0908399\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$		0			0
$513$	−24.0000			−1.05963
$514$		0			0
$515$	12.0000	−	12.0000i	0.528783	−	0.528783i
$516$		0			0
$517$	20.0000	+	20.0000i	0.879599	+	0.879599i
$518$		0			0
$519$		−	16.0000i		−	0.702322i
$520$		0			0
$521$			14.0000i			0.613351i	0.951814	+	0.306676i	$0.0992167\pi$
$521$			14.0000i			0.613351i	−0.951814	+	0.306676i	$0.900783\pi$
$522$		0			0
$523$	27.0000	+	27.0000i	1.18063	+	1.18063i	0.979582	+	0.201046i	$0.0644340\pi$
$523$	27.0000	+	27.0000i	1.18063	+	1.18063i	0.201046	+	0.979582i	$0.435566\pi$
$524$		0			0
$525$	−3.00000	+	3.00000i	−0.130931	+	0.130931i
$526$		0			0
$527$	−12.0000			−0.522728
$528$		0			0
$529$	7.00000			0.304348
$530$		0			0
$531$	7.00000	−	7.00000i	0.303774	−	0.303774i
$532$		0			0
$533$		0			0
$534$		0			0
$535$		−	16.0000i		−	0.691740i
$536$		0			0
$537$		−	16.0000i		−	0.690451i
$538$		0			0
$539$	2.00000	+	2.00000i	0.0861461	+	0.0861461i
$540$		0			0
$541$	−13.0000	+	13.0000i	−0.558914	+	0.558914i	−0.928998	−	0.370084i	$-0.879329\pi$
$541$	−13.0000	+	13.0000i	−0.558914	+	0.558914i	0.370084	+	0.928998i	$0.379329\pi$
$542$		0			0
$543$	8.00000			0.343313
$544$		0			0
$545$	12.0000			0.514024
$546$		0			0
$547$	6.00000	−	6.00000i	0.256541	−	0.256541i	−0.567104	−	0.823646i	$-0.691936\pi$
$547$	6.00000	−	6.00000i	0.256541	−	0.256541i	0.823646	+	0.567104i	$0.191936\pi$
$548$		0			0
$549$	2.00000	+	2.00000i	0.0853579	+	0.0853579i
$550$		0			0
$551$		−	42.0000i		−	1.78926i
$552$		0			0
$553$		−	4.00000i		−	0.170097i
$554$		0			0
$555$	12.0000	+	12.0000i	0.509372	+	0.509372i
$556$		0			0
$557$	−3.00000	+	3.00000i	−0.127114	+	0.127114i	−0.767802	−	0.640688i	$-0.778649\pi$
$557$	−3.00000	+	3.00000i	−0.127114	+	0.127114i	0.640688	+	0.767802i	$0.278649\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−8.00000			−0.337760
$562$		0			0
$563$	−7.00000	+	7.00000i	−0.295015	+	0.295015i	−0.839058	−	0.544043i	$-0.816893\pi$
$563$	−7.00000	+	7.00000i	−0.295015	+	0.295015i	0.544043	+	0.839058i	$0.316893\pi$
$564$		0			0
$565$	−8.00000	−	8.00000i	−0.336563	−	0.336563i
$566$		0			0
$567$		−	5.00000i		−	0.209980i
$568$		0			0
$569$			22.0000i			0.922288i	0.887325	+	0.461144i	$0.152561\pi$
$569$			22.0000i			0.922288i	−0.887325	+	0.461144i	$0.847439\pi$
$570$		0			0
$571$	18.0000	+	18.0000i	0.753277	+	0.753277i	0.975089	−	0.221813i	$-0.0711974\pi$
$571$	18.0000	+	18.0000i	0.753277	+	0.753277i	−0.221813	+	0.975089i	$0.571197\pi$
$572$		0			0
$573$	20.0000	−	20.0000i	0.835512	−	0.835512i
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	10.0000			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$578$		0			0
$579$	−18.0000	+	18.0000i	−0.748054	+	0.748054i
$580$		0			0
$581$	3.00000	+	3.00000i	0.124461	+	0.124461i
$582$		0			0
$583$		−	20.0000i		−	0.828315i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.0000	−	19.0000i	−0.784214	−	0.784214i	0.196325	−	0.980539i	$-0.437099\pi$
$587$	−19.0000	−	19.0000i	−0.784214	−	0.784214i	−0.980539	+	0.196325i	$0.937099\pi$
$588$		0			0
$589$	18.0000	−	18.0000i	0.741677	−	0.741677i
$590$		0			0
$591$	−14.0000			−0.575883
$592$		0			0
$593$	−46.0000			−1.88899			−0.944497	−	0.328521i	$-0.893450\pi$
$593$	−46.0000			−1.88899			−0.944497	+	0.328521i	$0.893450\pi$
$594$		0			0
$595$	4.00000	−	4.00000i	0.163984	−	0.163984i
$596$		0			0
$597$	−10.0000	−	10.0000i	−0.409273	−	0.409273i
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$		0			0
$601$			22.0000i			0.897399i	0.893683	+	0.448699i	$0.148113\pi$
$601$			22.0000i			0.897399i	−0.893683	+	0.448699i	$0.851887\pi$
$602$		0			0
$603$	−8.00000	−	8.00000i	−0.325785	−	0.325785i
$604$		0			0
$605$	−6.00000	+	6.00000i	−0.243935	+	0.243935i
$606$		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
$609$	14.0000			0.567309
$610$		0			0
$611$		0			0
$612$		0			0
$613$	3.00000	+	3.00000i	0.121169	+	0.121169i	0.765091	−	0.643922i	$-0.222694\pi$
$613$	3.00000	+	3.00000i	0.121169	+	0.121169i	−0.643922	+	0.765091i	$0.722694\pi$
$614$		0			0
$615$		−	8.00000i		−	0.322591i
$616$		0			0
$617$		−	8.00000i		−	0.322068i	−0.986949	−	0.161034i	$-0.948517\pi$
$617$		−	8.00000i		−	0.322068i	0.986949	−	0.161034i	$-0.0514829\pi$
$618$		0			0
$619$	21.0000	+	21.0000i	0.844061	+	0.844061i	0.989384	−	0.145323i	$-0.0464221\pi$
$619$	21.0000	+	21.0000i	0.844061	+	0.844061i	−0.145323	+	0.989384i	$0.546422\pi$
$620$		0			0
$621$	16.0000	−	16.0000i	0.642058	−	0.642058i
$622$		0			0
$623$	−10.0000			−0.400642
$624$		0			0
$625$	31.0000			1.24000
$626$		0			0
$627$	12.0000	−	12.0000i	0.479234	−	0.479234i
$628$		0			0
$629$	−6.00000	−	6.00000i	−0.239236	−	0.239236i
$630$		0			0
$631$		−	20.0000i		−	0.796187i	−0.917345	−	0.398094i	$-0.869672\pi$
$631$		−	20.0000i		−	0.796187i	0.917345	−	0.398094i	$-0.130328\pi$
$632$		0			0
$633$		−	24.0000i		−	0.953914i
$634$		0			0
$635$	32.0000	+	32.0000i	1.26988	+	1.26988i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	4.00000			0.158238
$640$		0			0
$641$	42.0000			1.65890			0.829450	−	0.558581i	$-0.188654\pi$
$641$	42.0000			1.65890			0.829450	+	0.558581i	$0.188654\pi$
$642$		0			0
$643$	−33.0000	+	33.0000i	−1.30139	+	1.30139i	−0.373940	+	0.927453i	$0.621993\pi$
$643$	−33.0000	+	33.0000i	−1.30139	+	1.30139i	−0.927453	+	0.373940i	$0.878007\pi$
$644$		0			0
$645$	−24.0000	−	24.0000i	−0.944999	−	0.944999i
$646$		0			0
$647$		−	38.0000i		−	1.49393i	−0.664861	−	0.746967i	$-0.731509\pi$
$647$		−	38.0000i		−	1.49393i	0.664861	−	0.746967i	$-0.268491\pi$
$648$		0			0
$649$			28.0000i			1.09910i
$650$		0			0
$651$	6.00000	+	6.00000i	0.235159	+	0.235159i
$652$		0			0
$653$	−5.00000	+	5.00000i	−0.195665	+	0.195665i	−0.798139	−	0.602474i	$-0.794182\pi$
$653$	−5.00000	+	5.00000i	−0.195665	+	0.195665i	0.602474	+	0.798139i	$0.294182\pi$
$654$		0			0
$655$	36.0000			1.40664
$656$		0			0
$657$	−14.0000			−0.546192
$658$		0			0
$659$	−10.0000	+	10.0000i	−0.389545	+	0.389545i	−0.874525	−	0.484980i	$-0.838827\pi$
$659$	−10.0000	+	10.0000i	−0.389545	+	0.389545i	0.484980	+	0.874525i	$0.338827\pi$
$660$		0			0
$661$	−18.0000	−	18.0000i	−0.700119	−	0.700119i	0.264317	−	0.964436i	$-0.414853\pi$
$661$	−18.0000	−	18.0000i	−0.700119	−	0.700119i	−0.964436	+	0.264317i	$0.914853\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			12.0000i			0.465340i
$666$		0			0
$667$	28.0000	+	28.0000i	1.08416	+	1.08416i
$668$		0			0
$669$	−8.00000	+	8.00000i	−0.309298	+	0.309298i
$670$		0			0
$671$	−8.00000			−0.308837
$672$		0			0
$673$	−44.0000			−1.69608			−0.848038	−	0.529936i	$-0.822216\pi$
$673$	−44.0000			−1.69608			−0.848038	+	0.529936i	$0.822216\pi$
$674$		0			0
$675$	12.0000	−	12.0000i	0.461880	−	0.461880i
$676$		0			0
$677$	16.0000	+	16.0000i	0.614930	+	0.614930i	0.944227	−	0.329297i	$-0.106812\pi$
$677$	16.0000	+	16.0000i	0.614930	+	0.614930i	−0.329297	+	0.944227i	$0.606812\pi$
$678$		0			0
$679$			6.00000i			0.230259i
$680$		0			0
$681$		−	2.00000i		−	0.0766402i
$682$		0			0
$683$	28.0000	+	28.0000i	1.07139	+	1.07139i	0.997248	+	0.0741426i	$0.0236220\pi$
$683$	28.0000	+	28.0000i	1.07139	+	1.07139i	0.0741426	+	0.997248i	$0.476378\pi$
$684$		0			0
$685$	24.0000	−	24.0000i	0.916993	−	0.916993i
$686$		0			0
$687$	8.00000			0.305219
$688$		0			0
$689$		0			0
$690$		0			0
$691$	33.0000	−	33.0000i	1.25538	−	1.25538i	0.302104	−	0.953275i	$-0.402311\pi$
$691$	33.0000	−	33.0000i	1.25538	−	1.25538i	0.953275	−	0.302104i	$-0.0976891\pi$
$692$		0			0
$693$	−2.00000	−	2.00000i	−0.0759737	−	0.0759737i
$694$		0			0
$695$			20.0000i			0.758643i
$696$		0			0
$697$			4.00000i			0.151511i
$698$		0			0
$699$	26.0000	+	26.0000i	0.983410	+	0.983410i
$700$		0			0
$701$	−11.0000	+	11.0000i	−0.415464	+	0.415464i	−0.883637	−	0.468173i	$-0.844913\pi$
$701$	−11.0000	+	11.0000i	−0.415464	+	0.415464i	0.468173	+	0.883637i	$0.344913\pi$
$702$		0			0
$703$	18.0000			0.678883
$704$		0			0
$705$	−40.0000			−1.50649
$706$		0			0
$707$	2.00000	−	2.00000i	0.0752177	−	0.0752177i
$708$		0			0
$709$	27.0000	+	27.0000i	1.01401	+	1.01401i	0.999901	+	0.0141058i	$0.00449016\pi$
$709$	27.0000	+	27.0000i	1.01401	+	1.01401i	0.0141058	+	0.999901i	$0.495510\pi$
$710$		0			0
$711$			4.00000i			0.150012i
$712$		0			0
$713$			24.0000i			0.898807i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−12.0000	+	12.0000i	−0.448148	+	0.448148i
$718$		0			0
$719$	−30.0000			−1.11881			−0.559406	−	0.828894i	$-0.688971\pi$
$719$	−30.0000			−1.11881			−0.559406	+	0.828894i	$0.688971\pi$
$720$		0			0
$721$	6.00000			0.223452
$722$		0			0
$723$	−14.0000	+	14.0000i	−0.520666	+	0.520666i
$724$		0			0
$725$	21.0000	+	21.0000i	0.779920	+	0.779920i
$726$		0			0
$727$		−	22.0000i		−	0.815935i	−0.912996	−	0.407967i	$-0.866238\pi$
$727$		−	22.0000i		−	0.815935i	0.912996	−	0.407967i	$-0.133762\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$		0			0
$731$	12.0000	+	12.0000i	0.443836	+	0.443836i
$732$		0			0
$733$	30.0000	−	30.0000i	1.10808	−	1.10808i	0.114672	−	0.993403i	$-0.463418\pi$
$733$	30.0000	−	30.0000i	1.10808	−	1.10808i	0.993403	−	0.114672i	$-0.0365817\pi$
$734$		0			0
$735$	−4.00000			−0.147542
$736$		0			0
$737$	32.0000			1.17874
$738$		0			0
$739$	−34.0000	+	34.0000i	−1.25071	+	1.25071i	−0.295308	+	0.955402i	$0.595422\pi$
$739$	−34.0000	+	34.0000i	−1.25071	+	1.25071i	−0.955402	+	0.295308i	$0.904578\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$			28.0000i			1.02584i
$746$		0			0
$747$	−3.00000	−	3.00000i	−0.109764	−	0.109764i
$748$		0			0
$749$	4.00000	−	4.00000i	0.146157	−	0.146157i
$750$		0			0
$751$	−4.00000			−0.145962			−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000			−0.145962			−0.0729810	+	0.997333i	$0.523251\pi$
$752$		0			0
$753$	38.0000			1.38480
$754$		0			0
$755$	48.0000	−	48.0000i	1.74690	−	1.74690i
$756$		0			0
$757$	11.0000	+	11.0000i	0.399802	+	0.399802i	0.878163	−	0.478361i	$-0.158769\pi$
$757$	11.0000	+	11.0000i	0.399802	+	0.399802i	−0.478361	+	0.878163i	$0.658769\pi$
$758$		0			0
$759$			16.0000i			0.580763i
$760$		0			0
$761$			6.00000i			0.217500i	0.994069	+	0.108750i	$0.0346848\pi$
$761$			6.00000i			0.217500i	−0.994069	+	0.108750i	$0.965315\pi$
$762$		0			0
$763$	3.00000	+	3.00000i	0.108607	+	0.108607i
$764$		0			0
$765$	−4.00000	+	4.00000i	−0.144620	+	0.144620i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−42.0000			−1.51456			−0.757279	−	0.653091i	$-0.773472\pi$
$769$	−42.0000			−1.51456			−0.757279	+	0.653091i	$0.773472\pi$
$770$		0			0
$771$	30.0000	−	30.0000i	1.08042	−	1.08042i
$772$		0			0
$773$	30.0000	+	30.0000i	1.07903	+	1.07903i	0.996597	+	0.0824280i	$0.0262674\pi$
$773$	30.0000	+	30.0000i	1.07903	+	1.07903i	0.0824280	+	0.996597i	$0.473733\pi$
$774$		0			0
$775$			18.0000i			0.646579i
$776$		0			0
$777$			6.00000i			0.215249i
$778$		0			0
$779$	−6.00000	−	6.00000i	−0.214972	−	0.214972i
$780$		0			0
$781$	−8.00000	+	8.00000i	−0.286263	+	0.286263i
$782$		0			0
$783$	−56.0000			−2.00128
$784$		0			0
$785$	−32.0000			−1.14213
$786$		0			0
$787$	−19.0000	+	19.0000i	−0.677277	+	0.677277i	−0.959383	−	0.282106i	$-0.908967\pi$
$787$	−19.0000	+	19.0000i	−0.677277	+	0.677277i	0.282106	+	0.959383i	$0.408967\pi$
$788$		0			0
$789$	4.00000	+	4.00000i	0.142404	+	0.142404i
$790$		0			0
$791$		−	4.00000i		−	0.142224i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	20.0000	+	20.0000i	0.709327	+	0.709327i
$796$		0			0
$797$	12.0000	−	12.0000i	0.425062	−	0.425062i	−0.461880	−	0.886942i	$-0.652825\pi$
$797$	12.0000	−	12.0000i	0.425062	−	0.425062i	0.886942	+	0.461880i	$0.152825\pi$
$798$		0			0
$799$	20.0000			0.707549
$800$		0			0
$801$	10.0000			0.353333
$802$		0			0
$803$	28.0000	−	28.0000i	0.988099	−	0.988099i
$804$		0			0
$805$	−8.00000	−	8.00000i	−0.281963	−	0.281963i
$806$		0			0
$807$		−	40.0000i		−	1.40807i
$808$		0			0
$809$		−	6.00000i		−	0.210949i	−0.994422	−	0.105474i	$-0.966364\pi$
$809$		−	6.00000i		−	0.210949i	0.994422	−	0.105474i	$-0.0336361\pi$
$810$		0			0
$811$	9.00000	+	9.00000i	0.316033	+	0.316033i	0.847241	−	0.531208i	$-0.178262\pi$
$811$	9.00000	+	9.00000i	0.316033	+	0.316033i	−0.531208	+	0.847241i	$0.678262\pi$
$812$		0			0
$813$	−16.0000	+	16.0000i	−0.561144	+	0.561144i
$814$		0			0
$815$	56.0000			1.96159
$816$		0			0
$817$	−36.0000			−1.25948
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−37.0000	−	37.0000i	−1.29131	−	1.29131i	−0.933978	−	0.357331i	$-0.883687\pi$
$821$	−37.0000	−	37.0000i	−1.29131	−	1.29131i	−0.357331	−	0.933978i	$-0.616313\pi$
$822$		0			0
$823$		−	16.0000i		−	0.557725i	−0.960331	−	0.278862i	$-0.910043\pi$
$823$		−	16.0000i		−	0.557725i	0.960331	−	0.278862i	$-0.0899574\pi$
$824$		0			0
$825$			12.0000i			0.417786i
$826$		0			0
$827$	8.00000	+	8.00000i	0.278187	+	0.278187i	0.832385	−	0.554198i	$-0.186975\pi$
$827$	8.00000	+	8.00000i	0.278187	+	0.278187i	−0.554198	+	0.832385i	$0.686975\pi$
$828$		0			0
$829$	−6.00000	+	6.00000i	−0.208389	+	0.208389i	−0.803582	−	0.595194i	$-0.797075\pi$
$829$	−6.00000	+	6.00000i	−0.208389	+	0.208389i	0.595194	+	0.803582i	$0.297075\pi$
$830$		0			0
$831$	−6.00000			−0.208138
$832$		0			0
$833$	2.00000			0.0692959
$834$		0			0
$835$	−28.0000	+	28.0000i	−0.968980	+	0.968980i
$836$		0			0
$837$	−24.0000	−	24.0000i	−0.829561	−	0.829561i
$838$		0			0
$839$		−	18.0000i		−	0.621429i	−0.950503	−	0.310715i	$-0.899432\pi$
$839$		−	18.0000i		−	0.621429i	0.950503	−	0.310715i	$-0.100568\pi$
$840$		0			0
$841$		−	69.0000i		−	2.37931i
$842$		0			0
$843$	−22.0000	−	22.0000i	−0.757720	−	0.757720i
$844$		0			0
$845$	26.0000	−	26.0000i	0.894427	−	0.894427i
$846$		0			0
$847$	−3.00000			−0.103081
$848$		0			0
$849$	30.0000			1.02960
$850$		0			0
$851$	−12.0000	+	12.0000i	−0.411355	+	0.411355i
$852$		0			0
$853$	24.0000	+	24.0000i	0.821744	+	0.821744i	0.986358	−	0.164614i	$-0.0526378\pi$
$853$	24.0000	+	24.0000i	0.821744	+	0.821744i	−0.164614	+	0.986358i	$0.552638\pi$
$854$		0			0
$855$		−	12.0000i		−	0.410391i
$856$		0			0
$857$		−	42.0000i		−	1.43469i	−0.696717	−	0.717346i	$-0.745357\pi$
$857$		−	42.0000i		−	1.43469i	0.696717	−	0.717346i	$-0.254643\pi$
$858$		0			0
$859$	7.00000	+	7.00000i	0.238837	+	0.238837i	0.816368	−	0.577531i	$-0.195984\pi$
$859$	7.00000	+	7.00000i	0.238837	+	0.238837i	−0.577531	+	0.816368i	$0.695984\pi$
$860$		0			0
$861$	2.00000	−	2.00000i	0.0681598	−	0.0681598i
$862$		0			0
$863$	4.00000			0.136162			0.0680808	−	0.997680i	$-0.478312\pi$
$863$	4.00000			0.136162			0.0680808	+	0.997680i	$0.478312\pi$
$864$		0			0
$865$	32.0000			1.08803
$866$		0			0
$867$	13.0000	−	13.0000i	0.441503	−	0.441503i
$868$		0			0
$869$	−8.00000	−	8.00000i	−0.271381	−	0.271381i
$870$		0			0
$871$		0			0
$872$		0			0
$873$		−	6.00000i		−	0.203069i
$874$		0			0
$875$	4.00000	+	4.00000i	0.135225	+	0.135225i
$876$		0			0
$877$	−7.00000	+	7.00000i	−0.236373	+	0.236373i	−0.815347	−	0.578973i	$-0.803454\pi$
$877$	−7.00000	+	7.00000i	−0.236373	+	0.236373i	0.578973	+	0.815347i	$0.303454\pi$
$878$		0			0
$879$	4.00000			0.134917
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$	−24.0000	+	24.0000i	−0.807664	+	0.807664i	−0.984280	−	0.176616i	$-0.943485\pi$
$883$	−24.0000	+	24.0000i	−0.807664	+	0.807664i	0.176616	+	0.984280i	$0.443485\pi$
$884$		0			0
$885$	−28.0000	−	28.0000i	−0.941210	−	0.941210i
$886$		0			0
$887$			2.00000i			0.0671534i	0.999436	+	0.0335767i	$0.0106898\pi$
$887$			2.00000i			0.0671534i	−0.999436	+	0.0335767i	$0.989310\pi$
$888$		0			0
$889$			16.0000i			0.536623i
$890$		0			0
$891$	−10.0000	−	10.0000i	−0.335013	−	0.335013i
$892$		0			0
$893$	−30.0000	+	30.0000i	−1.00391	+	1.00391i
$894$		0			0
$895$	32.0000			1.06964
$896$		0			0
$897$		0			0
$898$		0			0
$899$	42.0000	−	42.0000i	1.40078	−	1.40078i
$900$		0			0
$901$	−10.0000	−	10.0000i	−0.333148	−	0.333148i
$902$		0			0
$903$		−	12.0000i		−	0.399335i
$904$		0			0
$905$			16.0000i			0.531858i
$906$		0			0
$907$	−24.0000	−	24.0000i	−0.796907	−	0.796907i	0.185700	−	0.982607i	$-0.440545\pi$
$907$	−24.0000	−	24.0000i	−0.796907	−	0.796907i	−0.982607	+	0.185700i	$0.940545\pi$
$908$		0			0
$909$	−2.00000	+	2.00000i	−0.0663358	+	0.0663358i
$910$		0			0
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$		0			0
$913$	12.0000			0.397142
$914$		0			0
$915$	8.00000	−	8.00000i	0.264472	−	0.264472i
$916$		0			0
$917$	9.00000	+	9.00000i	0.297206	+	0.297206i
$918$		0			0
$919$		−	32.0000i		−	1.05558i	−0.849374	−	0.527791i	$-0.823020\pi$
$919$		−	32.0000i		−	1.05558i	0.849374	−	0.527791i	$-0.176980\pi$
$920$		0			0
$921$			18.0000i			0.593120i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−9.00000	+	9.00000i	−0.295918	+	0.295918i
$926$		0			0
$927$	−6.00000			−0.197066
$928$		0			0
$929$	−38.0000			−1.24674			−0.623370	−	0.781927i	$-0.714237\pi$
$929$	−38.0000			−1.24674			−0.623370	+	0.781927i	$0.714237\pi$
$930$		0			0
$931$	−3.00000	+	3.00000i	−0.0983210	+	0.0983210i
$932$		0			0
$933$	24.0000	+	24.0000i	0.785725	+	0.785725i
$934$		0			0
$935$		−	16.0000i		−	0.523256i
$936$		0			0
$937$		−	26.0000i		−	0.849383i	−0.905338	−	0.424691i	$-0.860383\pi$
$937$		−	26.0000i		−	0.849383i	0.905338	−	0.424691i	$-0.139617\pi$
$938$		0			0
$939$	22.0000	+	22.0000i	0.717943	+	0.717943i
$940$		0			0
$941$	−18.0000	+	18.0000i	−0.586783	+	0.586783i	−0.936759	−	0.349976i	$-0.886190\pi$
$941$	−18.0000	+	18.0000i	−0.586783	+	0.586783i	0.349976	+	0.936759i	$0.386190\pi$
$942$		0			0
$943$	8.00000			0.260516
$944$		0			0
$945$	16.0000			0.520480
$946$		0			0
$947$	14.0000	−	14.0000i	0.454939	−	0.454939i	−0.442051	−	0.896990i	$-0.645749\pi$
$947$	14.0000	−	14.0000i	0.454939	−	0.454939i	0.896990	+	0.442051i	$0.145749\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		−	42.0000i		−	1.36194i
$952$		0			0
$953$		−	48.0000i		−	1.55487i	−0.628962	−	0.777436i	$-0.716520\pi$
$953$		−	48.0000i		−	1.55487i	0.628962	−	0.777436i	$-0.283480\pi$
$954$		0			0
$955$	40.0000	+	40.0000i	1.29437	+	1.29437i
$956$		0			0
$957$	28.0000	−	28.0000i	0.905111	−	0.905111i
$958$		0			0
$959$	12.0000			0.387500
$960$		0			0
$961$	5.00000			0.161290
$962$		0			0
$963$	−4.00000	+	4.00000i	−0.128898	+	0.128898i
$964$		0			0
$965$	−36.0000	−	36.0000i	−1.15888	−	1.15888i
$966$		0			0
$967$		−	20.0000i		−	0.643157i	−0.946883	−	0.321578i	$-0.895787\pi$
$967$		−	20.0000i		−	0.643157i	0.946883	−	0.321578i	$-0.104213\pi$
$968$		0			0
$969$		−	12.0000i		−	0.385496i
$970$		0			0
$971$	−25.0000	−	25.0000i	−0.802288	−	0.802288i	0.181165	−	0.983453i	$-0.442013\pi$
$971$	−25.0000	−	25.0000i	−0.802288	−	0.802288i	−0.983453	+	0.181165i	$0.942013\pi$
$972$		0			0
$973$	−5.00000	+	5.00000i	−0.160293	+	0.160293i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$		0			0
$979$	−20.0000	+	20.0000i	−0.639203	+	0.639203i
$980$		0			0
$981$	−3.00000	−	3.00000i	−0.0957826	−	0.0957826i
$982$		0			0
$983$		−	6.00000i		−	0.191370i	−0.995412	−	0.0956851i	$-0.969496\pi$
$983$		−	6.00000i		−	0.191370i	0.995412	−	0.0956851i	$-0.0305042\pi$
$984$		0			0
$985$		−	28.0000i		−	0.892154i
$986$		0			0
$987$	−10.0000	−	10.0000i	−0.318304	−	0.318304i
$988$		0			0
$989$	24.0000	−	24.0000i	0.763156	−	0.763156i
$990$		0			0
$991$	16.0000			0.508257			0.254128	−	0.967170i	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		0			0
$993$	20.0000			0.634681
$994$		0			0
$995$	20.0000	−	20.0000i	0.634043	−	0.634043i
$996$		0			0
$997$	6.00000	+	6.00000i	0.190022	+	0.190022i	0.795706	−	0.605684i	$-0.207100\pi$
$997$	6.00000	+	6.00000i	0.190022	+	0.190022i	−0.605684	+	0.795706i	$0.707100\pi$
$998$		0			0
$999$		−	24.0000i		−	0.759326i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3584.2.m.d.897.1	✓	2
4.3	odd	2		3584.2.m.s.897.1	yes	2
8.3	odd	2		3584.2.m.j.897.1	yes	2
8.5	even	2		3584.2.m.y.897.1	yes	2
16.3	odd	4		3584.2.m.s.2689.1	yes	2
16.5	even	4		3584.2.m.y.2689.1	yes	2
16.11	odd	4		3584.2.m.j.2689.1	yes	2
16.13	even	4	inner	3584.2.m.d.2689.1	yes	2
32.3	odd	8		7168.2.a.p.1.2		2
32.13	even	8		7168.2.a.d.1.2		2
32.19	odd	8		7168.2.a.p.1.1		2
32.29	even	8		7168.2.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3584.2.m.d.897.1	✓	2	1.1	even	1	trivial
3584.2.m.d.2689.1	yes	2	16.13	even	4	inner
3584.2.m.j.897.1	yes	2	8.3	odd	2
3584.2.m.j.2689.1	yes	2	16.11	odd	4
3584.2.m.s.897.1	yes	2	4.3	odd	2
3584.2.m.s.2689.1	yes	2	16.3	odd	4
3584.2.m.y.897.1	yes	2	8.5	even	2
3584.2.m.y.2689.1	yes	2	16.5	even	4
7168.2.a.d.1.1		2	32.29	even	8
7168.2.a.d.1.2		2	32.13	even	8
7168.2.a.p.1.1		2	32.19	odd	8
7168.2.a.p.1.2		2	32.3	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 - 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{3} +(-2.00000 - 2.00000i) q^{5} -1.00000i q^{7} +1.00000i q^{9} +(-2.00000 - 2.00000i) q^{11} +4.00000 q^{15} -2.00000 q^{17} +(3.00000 - 3.00000i) q^{19} +(1.00000 + 1.00000i) q^{21} +4.00000i q^{23} +3.00000i q^{25} +(-4.00000 - 4.00000i) q^{27} +(7.00000 - 7.00000i) q^{29} +6.00000 q^{31} +4.00000 q^{33} +(-2.00000 + 2.00000i) q^{35} +(3.00000 + 3.00000i) q^{37} -2.00000i q^{41} +(-6.00000 - 6.00000i) q^{43} +(2.00000 - 2.00000i) q^{45} -10.0000 q^{47} -1.00000 q^{49} +(2.00000 - 2.00000i) q^{51} +(5.00000 + 5.00000i) q^{53} +8.00000i q^{55} +6.00000i q^{57} +(-7.00000 - 7.00000i) q^{59} +(2.00000 - 2.00000i) q^{61} +1.00000 q^{63} +(-8.00000 + 8.00000i) q^{67} +(-4.00000 - 4.00000i) q^{69} -4.00000i q^{71} +14.0000i q^{73} +(-3.00000 - 3.00000i) q^{75} +(-2.00000 + 2.00000i) q^{77} +4.00000 q^{79} +5.00000 q^{81} +(-3.00000 + 3.00000i) q^{83} +(4.00000 + 4.00000i) q^{85} +14.0000i q^{87} -10.0000i q^{89} +(-6.00000 + 6.00000i) q^{93} -12.0000 q^{95} -6.00000 q^{97} +(2.00000 - 2.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 4 q^{5}+O(q^{10}) \) 2 * q - 2 * q^3 - 4 * q^5	\( 2 q - 2 q^{3} - 4 q^{5} - 4 q^{11} + 8 q^{15} - 4 q^{17} + 6 q^{19} + 2 q^{21} - 8 q^{27} + 14 q^{29} + 12 q^{31} + 8 q^{33} - 4 q^{35} + 6 q^{37} - 12 q^{43} + 4 q^{45} - 20 q^{47} - 2 q^{49} + 4 q^{51} + 10 q^{53} - 14 q^{59} + 4 q^{61} + 2 q^{63} - 16 q^{67} - 8 q^{69} - 6 q^{75} - 4 q^{77} + 8 q^{79} + 10 q^{81} - 6 q^{83} + 8 q^{85} - 12 q^{93} - 24 q^{95} - 12 q^{97} + 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 4 * q^5 - 4 * q^11 + 8 * q^15 - 4 * q^17 + 6 * q^19 + 2 * q^21 - 8 * q^27 + 14 * q^29 + 12 * q^31 + 8 * q^33 - 4 * q^35 + 6 * q^37 - 12 * q^43 + 4 * q^45 - 20 * q^47 - 2 * q^49 + 4 * q^51 + 10 * q^53 - 14 * q^59 + 4 * q^61 + 2 * q^63 - 16 * q^67 - 8 * q^69 - 6 * q^75 - 4 * q^77 + 8 * q^79 + 10 * q^81 - 6 * q^83 + 8 * q^85 - 12 * q^93 - 24 * q^95 - 12 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more