LMFDB - Embedded newform 3584.2.m.bc.2689.2

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:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2689.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	3584.2689
Dual form			3584.2.m.bc.897.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.73205 + 1.73205i) q^{3} +(-2.73205 + 2.73205i) q^{5} +1.00000i q^{7} +3.00000i q^{9} +O(q^{10})$	\(q+(1.73205 + 1.73205i) q^{3} +(-2.73205 + 2.73205i) q^{5} +1.00000i q^{7} +3.00000i q^{9} +(-2.00000 + 2.00000i) q^{11} +(4.73205 + 4.73205i) q^{13} -9.46410 q^{15} -3.46410 q^{17} +(1.73205 + 1.73205i) q^{19} +(-1.73205 + 1.73205i) q^{21} +9.46410i q^{23} -9.92820i q^{25} +(2.46410 + 2.46410i) q^{29} +7.46410 q^{31} -6.92820 q^{33} +(-2.73205 - 2.73205i) q^{35} +(-0.464102 + 0.464102i) q^{37} +16.3923i q^{39} +3.46410i q^{41} +(7.46410 - 7.46410i) q^{43} +(-8.19615 - 8.19615i) q^{45} -11.4641 q^{47} -1.00000 q^{49} +(-6.00000 - 6.00000i) q^{51} +(-1.00000 + 1.00000i) q^{53} -10.9282i q^{55} +6.00000i q^{57} +(2.26795 - 2.26795i) q^{59} +(-5.26795 - 5.26795i) q^{61} -3.00000 q^{63} -25.8564 q^{65} +(2.92820 + 2.92820i) q^{67} +(-16.3923 + 16.3923i) q^{69} -4.00000i q^{71} -6.00000i q^{73} +(17.1962 - 17.1962i) q^{75} +(-2.00000 - 2.00000i) q^{77} -4.00000 q^{79} +9.00000 q^{81} +(2.26795 + 2.26795i) q^{83} +(9.46410 - 9.46410i) q^{85} +8.53590i q^{87} -8.92820i q^{89} +(-4.73205 + 4.73205i) q^{91} +(12.9282 + 12.9282i) q^{93} -9.46410 q^{95} -2.39230 q^{97} +(-6.00000 - 6.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5}+O(q^{10}) $ 4 * q - 4 * q^5	$ 4 q - 4 q^{5} - 8 q^{11} + 12 q^{13} - 24 q^{15} - 4 q^{29} + 16 q^{31} - 4 q^{35} + 12 q^{37} + 16 q^{43} - 12 q^{45} - 32 q^{47} - 4 q^{49} - 24 q^{51} - 4 q^{53} + 16 q^{59} - 28 q^{61} - 12 q^{63} - 48 q^{65} - 16 q^{67} - 24 q^{69} + 48 q^{75} - 8 q^{77} - 16 q^{79} + 36 q^{81} + 16 q^{83} + 24 q^{85} - 12 q^{91} + 24 q^{93} - 24 q^{95} + 32 q^{97} - 24 q^{99}+O(q^{100}) $ 4 * q - 4 * q^5 - 8 * q^11 + 12 * q^13 - 24 * q^15 - 4 * q^29 + 16 * q^31 - 4 * q^35 + 12 * q^37 + 16 * q^43 - 12 * q^45 - 32 * q^47 - 4 * q^49 - 24 * q^51 - 4 * q^53 + 16 * q^59 - 28 * q^61 - 12 * q^63 - 48 * q^65 - 16 * q^67 - 24 * q^69 + 48 * q^75 - 8 * q^77 - 16 * q^79 + 36 * q^81 + 16 * q^83 + 24 * q^85 - 12 * q^91 + 24 * q^93 - 24 * q^95 + 32 * q^97 - 24 * 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
$3$	1.73205	+	1.73205i	1.00000	+	1.00000i	1.00000			$0$
$3$	1.73205	+	1.73205i	1.00000	+	1.00000i			1.00000i	$0.5\pi$
$4$		0			0
$5$	−2.73205	+	2.73205i	−1.22181	+	1.22181i	−0.254822	+	0.966988i	$0.582017\pi$
$5$	−2.73205	+	2.73205i	−1.22181	+	1.22181i	−0.966988	+	0.254822i	$0.917983\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$			3.00000i			1.00000i
$10$		0			0
$11$	−2.00000	+	2.00000i	−0.603023	+	0.603023i	−0.941113	−	0.338091i	$-0.890219\pi$
$11$	−2.00000	+	2.00000i	−0.603023	+	0.603023i	0.338091	+	0.941113i	$0.390219\pi$
$12$		0			0
$13$	4.73205	+	4.73205i	1.31243	+	1.31243i	0.919616	+	0.392819i	$0.128500\pi$
$13$	4.73205	+	4.73205i	1.31243	+	1.31243i	0.392819	+	0.919616i	$0.371500\pi$
$14$		0			0
$15$	−9.46410			−2.44362
$16$		0			0
$17$	−3.46410			−0.840168			−0.420084	−	0.907485i	$-0.637999\pi$
$17$	−3.46410			−0.840168			−0.420084	+	0.907485i	$0.637999\pi$
$18$		0			0
$19$	1.73205	+	1.73205i	0.397360	+	0.397360i	0.877301	−	0.479941i	$-0.159342\pi$
$19$	1.73205	+	1.73205i	0.397360	+	0.397360i	−0.479941	+	0.877301i	$0.659342\pi$
$20$		0			0
$21$	−1.73205	+	1.73205i	−0.377964	+	0.377964i
$22$		0			0
$23$			9.46410i			1.97340i	0.162547	+	0.986701i	$0.448029\pi$
$23$			9.46410i			1.97340i	−0.162547	+	0.986701i	$0.551971\pi$
$24$		0			0
$25$		−	9.92820i		−	1.98564i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.46410	+	2.46410i	0.457572	+	0.457572i	0.897858	−	0.440286i	$-0.145123\pi$
$29$	2.46410	+	2.46410i	0.457572	+	0.457572i	−0.440286	+	0.897858i	$0.645123\pi$
$30$		0			0
$31$	7.46410			1.34059			0.670296	−	0.742094i	$-0.266167\pi$
$31$	7.46410			1.34059			0.670296	+	0.742094i	$0.266167\pi$
$32$		0			0
$33$	−6.92820			−1.20605
$34$		0			0
$35$	−2.73205	−	2.73205i	−0.461801	−	0.461801i
$36$		0			0
$37$	−0.464102	+	0.464102i	−0.0762978	+	0.0762978i	−0.744226	−	0.667928i	$-0.767181\pi$
$37$	−0.464102	+	0.464102i	−0.0762978	+	0.0762978i	0.667928	+	0.744226i	$0.267181\pi$
$38$		0			0
$39$			16.3923i			2.62487i
$40$		0			0
$41$			3.46410i			0.541002i	0.962720	+	0.270501i	$0.0871893\pi$
$41$			3.46410i			0.541002i	−0.962720	+	0.270501i	$0.912811\pi$
$42$		0			0
$43$	7.46410	−	7.46410i	1.13826	−	1.13826i	0.149504	−	0.988761i	$-0.452232\pi$
$43$	7.46410	−	7.46410i	1.13826	−	1.13826i	0.988761	−	0.149504i	$-0.0477676\pi$
$44$		0			0
$45$	−8.19615	−	8.19615i	−1.22181	−	1.22181i
$46$		0			0
$47$	−11.4641			−1.67221			−0.836106	−	0.548569i	$-0.815173\pi$
$47$	−11.4641			−1.67221			−0.836106	+	0.548569i	$0.815173\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−6.00000	−	6.00000i	−0.840168	−	0.840168i
$52$		0			0
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	−0.772444	−	0.635083i	$-0.780966\pi$
$53$	−1.00000	+	1.00000i	−0.137361	+	0.137361i	0.635083	+	0.772444i	$0.280966\pi$
$54$		0			0
$55$		−	10.9282i		−	1.47356i
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$	2.26795	−	2.26795i	0.295262	−	0.295262i	−0.543893	−	0.839155i	$-0.683050\pi$
$59$	2.26795	−	2.26795i	0.295262	−	0.295262i	0.839155	+	0.543893i	$0.183050\pi$
$60$		0			0
$61$	−5.26795	−	5.26795i	−0.674492	−	0.674492i	0.284256	−	0.958748i	$-0.408253\pi$
$61$	−5.26795	−	5.26795i	−0.674492	−	0.674492i	−0.958748	+	0.284256i	$0.908253\pi$
$62$		0			0
$63$	−3.00000			−0.377964
$64$		0			0
$65$	−25.8564			−3.20709
$66$		0			0
$67$	2.92820	+	2.92820i	0.357737	+	0.357737i	0.862978	−	0.505241i	$-0.168596\pi$
$67$	2.92820	+	2.92820i	0.357737	+	0.357737i	−0.505241	+	0.862978i	$0.668596\pi$
$68$		0			0
$69$	−16.3923	+	16.3923i	−1.97340	+	1.97340i
$70$		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
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$		0			0
$75$	17.1962	−	17.1962i	1.98564	−	1.98564i
$76$		0			0
$77$	−2.00000	−	2.00000i	−0.227921	−	0.227921i
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$		0			0
$81$	9.00000			1.00000
$82$		0			0
$83$	2.26795	+	2.26795i	0.248940	+	0.248940i	0.820535	−	0.571596i	$-0.193675\pi$
$83$	2.26795	+	2.26795i	0.248940	+	0.248940i	−0.571596	+	0.820535i	$0.693675\pi$
$84$		0			0
$85$	9.46410	−	9.46410i	1.02653	−	1.02653i
$86$		0			0
$87$			8.53590i			0.915144i
$88$		0			0
$89$		−	8.92820i		−	0.946388i	−0.880958	−	0.473194i	$-0.843101\pi$
$89$		−	8.92820i		−	0.946388i	0.880958	−	0.473194i	$-0.156899\pi$
$90$		0			0
$91$	−4.73205	+	4.73205i	−0.496054	+	0.496054i
$92$		0			0
$93$	12.9282	+	12.9282i	1.34059	+	1.34059i
$94$		0			0
$95$	−9.46410			−0.970996
$96$		0			0
$97$	−2.39230			−0.242902			−0.121451	−	0.992597i	$-0.538755\pi$
$97$	−2.39230			−0.242902			−0.121451	+	0.992597i	$0.538755\pi$
$98$		0			0
$99$	−6.00000	−	6.00000i	−0.603023	−	0.603023i
$100$		0			0
$101$	1.26795	−	1.26795i	0.126166	−	0.126166i	−0.641204	−	0.767370i	$-0.721565\pi$
$101$	1.26795	−	1.26795i	0.126166	−	0.126166i	0.767370	+	0.641204i	$0.221565\pi$
$102$		0			0
$103$		−	15.4641i		−	1.52372i	−0.647740	−	0.761862i	$-0.724286\pi$
$103$		−	15.4641i		−	1.52372i	0.647740	−	0.761862i	$-0.275714\pi$
$104$		0			0
$105$		−	9.46410i		−	0.923602i
$106$		0			0
$107$	−1.46410	+	1.46410i	−0.141540	+	0.141540i	−0.774326	−	0.632786i	$-0.781911\pi$
$107$	−1.46410	+	1.46410i	−0.141540	+	0.141540i	0.632786	+	0.774326i	$0.281911\pi$
$108$		0			0
$109$	8.46410	+	8.46410i	0.810714	+	0.810714i	0.984741	−	0.174027i	$-0.0556780\pi$
$109$	8.46410	+	8.46410i	0.810714	+	0.810714i	−0.174027	+	0.984741i	$0.555678\pi$
$110$		0			0
$111$	−1.60770			−0.152596
$112$		0			0
$113$	13.8564			1.30350			0.651751	−	0.758433i	$-0.274035\pi$
$113$	13.8564			1.30350			0.651751	+	0.758433i	$0.274035\pi$
$114$		0			0
$115$	−25.8564	−	25.8564i	−2.41112	−	2.41112i
$116$		0			0
$117$	−14.1962	+	14.1962i	−1.31243	+	1.31243i
$118$		0			0
$119$		−	3.46410i		−	0.317554i
$120$		0			0
$121$			3.00000i			0.272727i
$122$		0			0
$123$	−6.00000	+	6.00000i	−0.541002	+	0.541002i
$124$		0			0
$125$	13.4641	+	13.4641i	1.20427	+	1.20427i
$126$		0			0
$127$	0.392305			0.0348114			0.0174057	−	0.999849i	$-0.494459\pi$
$127$	0.392305			0.0348114			0.0174057	+	0.999849i	$0.494459\pi$
$128$		0			0
$129$	25.8564			2.27653
$130$		0			0
$131$	−6.26795	−	6.26795i	−0.547633	−	0.547633i	0.378122	−	0.925756i	$-0.376570\pi$
$131$	−6.26795	−	6.26795i	−0.547633	−	0.547633i	−0.925756	+	0.378122i	$0.876570\pi$
$132$		0			0
$133$	−1.73205	+	1.73205i	−0.150188	+	0.150188i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	1.07180i		−	0.0915698i	−0.998951	−	0.0457849i	$-0.985421\pi$
$137$		−	1.07180i		−	0.0915698i	0.998951	−	0.0457849i	$-0.0145789\pi$
$138$		0			0
$139$	−1.19615	+	1.19615i	−0.101456	+	0.101456i	−0.756013	−	0.654557i	$-0.772855\pi$
$139$	−1.19615	+	1.19615i	−0.101456	+	0.101456i	0.654557	+	0.756013i	$0.272855\pi$
$140$		0			0
$141$	−19.8564	−	19.8564i	−1.67221	−	1.67221i
$142$		0			0
$143$	−18.9282			−1.58286
$144$		0			0
$145$	−13.4641			−1.11813
$146$		0			0
$147$	−1.73205	−	1.73205i	−0.142857	−	0.142857i
$148$		0			0
$149$	9.92820	−	9.92820i	0.813350	−	0.813350i	−0.171784	−	0.985135i	$-0.554953\pi$
$149$	9.92820	−	9.92820i	0.813350	−	0.813350i	0.985135	+	0.171784i	$0.0549533\pi$
$150$		0			0
$151$			8.39230i			0.682956i	0.939890	+	0.341478i	$0.110927\pi$
$151$			8.39230i			0.682956i	−0.939890	+	0.341478i	$0.889073\pi$
$152$		0			0
$153$		−	10.3923i		−	0.840168i
$154$		0			0
$155$	−20.3923	+	20.3923i	−1.63795	+	1.63795i
$156$		0			0
$157$	4.73205	+	4.73205i	0.377659	+	0.377659i	0.870257	−	0.492598i	$-0.163953\pi$
$157$	4.73205	+	4.73205i	0.377659	+	0.377659i	−0.492598	+	0.870257i	$0.663953\pi$
$158$		0			0
$159$	−3.46410			−0.274721
$160$		0			0
$161$	−9.46410			−0.745876
$162$		0			0
$163$	−6.00000	−	6.00000i	−0.469956	−	0.469956i	0.431944	−	0.901900i	$-0.357828\pi$
$163$	−6.00000	−	6.00000i	−0.469956	−	0.469956i	−0.901900	+	0.431944i	$0.857828\pi$
$164$		0			0
$165$	18.9282	−	18.9282i	1.47356	−	1.47356i
$166$		0			0
$167$		−	9.32051i		−	0.721243i	−0.932712	−	0.360621i	$-0.882565\pi$
$167$		−	9.32051i		−	0.721243i	0.932712	−	0.360621i	$-0.117435\pi$
$168$		0			0
$169$			31.7846i			2.44497i
$170$		0			0
$171$	−5.19615	+	5.19615i	−0.397360	+	0.397360i
$172$		0			0
$173$	4.73205	+	4.73205i	0.359771	+	0.359771i	0.863729	−	0.503957i	$-0.168123\pi$
$173$	4.73205	+	4.73205i	0.359771	+	0.359771i	−0.503957	+	0.863729i	$0.668123\pi$
$174$		0			0
$175$	9.92820			0.750502
$176$		0			0
$177$	7.85641			0.590524
$178$		0			0
$179$	13.8564	+	13.8564i	1.03568	+	1.03568i	0.999340	+	0.0363368i	$0.0115689\pi$
$179$	13.8564	+	13.8564i	1.03568	+	1.03568i	0.0363368	+	0.999340i	$0.488431\pi$
$180$		0			0
$181$	11.6603	−	11.6603i	0.866700	−	0.866700i	−0.125406	−	0.992106i	$-0.540023\pi$
$181$	11.6603	−	11.6603i	0.866700	−	0.866700i	0.992106	+	0.125406i	$0.0400232\pi$
$182$		0			0
$183$		−	18.2487i		−	1.34898i
$184$		0			0
$185$		−	2.53590i		−	0.186443i
$186$		0			0
$187$	6.92820	−	6.92820i	0.506640	−	0.506640i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−6.92820			−0.501307			−0.250654	−	0.968077i	$-0.580646\pi$
$191$	−6.92820			−0.501307			−0.250654	+	0.968077i	$0.580646\pi$
$192$		0			0
$193$	−10.0000			−0.719816			−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000			−0.719816			−0.359908	+	0.932988i	$0.617192\pi$
$194$		0			0
$195$	−44.7846	−	44.7846i	−3.20709	−	3.20709i
$196$		0			0
$197$	10.8564	−	10.8564i	0.773487	−	0.773487i	−0.205227	−	0.978714i	$-0.565793\pi$
$197$	10.8564	−	10.8564i	0.773487	−	0.773487i	0.978714	+	0.205227i	$0.0657934\pi$
$198$		0			0
$199$		−	14.3923i		−	1.02024i	−0.860102	−	0.510122i	$-0.829600\pi$
$199$		−	14.3923i		−	1.02024i	0.860102	−	0.510122i	$-0.170400\pi$
$200$		0			0
$201$			10.1436i			0.715474i
$202$		0			0
$203$	−2.46410	+	2.46410i	−0.172946	+	0.172946i
$204$		0			0
$205$	−9.46410	−	9.46410i	−0.661002	−	0.661002i
$206$		0			0
$207$	−28.3923			−1.97340
$208$		0			0
$209$	−6.92820			−0.479234
$210$		0			0
$211$	−9.85641	−	9.85641i	−0.678543	−	0.678543i	0.281127	−	0.959670i	$-0.409292\pi$
$211$	−9.85641	−	9.85641i	−0.678543	−	0.678543i	−0.959670	+	0.281127i	$0.909292\pi$
$212$		0			0
$213$	6.92820	−	6.92820i	0.474713	−	0.474713i
$214$		0			0
$215$			40.7846i			2.78149i
$216$		0			0
$217$			7.46410i			0.506696i
$218$		0			0
$219$	10.3923	−	10.3923i	0.702247	−	0.702247i
$220$		0			0
$221$	−16.3923	−	16.3923i	−1.10267	−	1.10267i
$222$		0			0
$223$	−10.9282			−0.731807			−0.365903	−	0.930653i	$-0.619240\pi$
$223$	−10.9282			−0.731807			−0.365903	+	0.930653i	$0.619240\pi$
$224$		0			0
$225$	29.7846			1.98564
$226$		0			0
$227$	−13.1962	−	13.1962i	−0.875859	−	0.875859i	0.117244	−	0.993103i	$-0.462594\pi$
$227$	−13.1962	−	13.1962i	−0.875859	−	0.875859i	−0.993103	+	0.117244i	$0.962594\pi$
$228$		0			0
$229$	−16.7321	+	16.7321i	−1.10569	+	1.10569i	−0.111974	+	0.993711i	$0.535717\pi$
$229$	−16.7321	+	16.7321i	−1.10569	+	1.10569i	−0.993711	+	0.111974i	$0.964283\pi$
$230$		0			0
$231$		−	6.92820i		−	0.455842i
$232$		0			0
$233$			7.85641i			0.514690i	0.966320	+	0.257345i	$0.0828477\pi$
$233$			7.85641i			0.514690i	−0.966320	+	0.257345i	$0.917152\pi$
$234$		0			0
$235$	31.3205	−	31.3205i	2.04312	−	2.04312i
$236$		0			0
$237$	−6.92820	−	6.92820i	−0.450035	−	0.450035i
$238$		0			0
$239$	9.46410			0.612182			0.306091	−	0.952002i	$-0.400979\pi$
$239$	9.46410			0.612182			0.306091	+	0.952002i	$0.400979\pi$
$240$		0			0
$241$	13.3205			0.858049			0.429025	−	0.903293i	$-0.358857\pi$
$241$	13.3205			0.858049			0.429025	+	0.903293i	$0.358857\pi$
$242$		0			0
$243$	15.5885	+	15.5885i	1.00000	+	1.00000i
$244$		0			0
$245$	2.73205	−	2.73205i	0.174544	−	0.174544i
$246$		0			0
$247$			16.3923i			1.04302i
$248$		0			0
$249$			7.85641i			0.497880i
$250$		0			0
$251$	−5.73205	+	5.73205i	−0.361804	+	0.361804i	−0.864477	−	0.502673i	$-0.832350\pi$
$251$	−5.73205	+	5.73205i	−0.361804	+	0.361804i	0.502673	+	0.864477i	$0.332350\pi$
$252$		0			0
$253$	−18.9282	−	18.9282i	−1.19001	−	1.19001i
$254$		0			0
$255$	32.7846			2.05305
$256$		0			0
$257$	20.9282			1.30547			0.652733	−	0.757588i	$-0.273622\pi$
$257$	20.9282			1.30547			0.652733	+	0.757588i	$0.273622\pi$
$258$		0			0
$259$	−0.464102	−	0.464102i	−0.0288379	−	0.0288379i
$260$		0			0
$261$	−7.39230	+	7.39230i	−0.457572	+	0.457572i
$262$		0			0
$263$			12.7846i			0.788333i	0.919039	+	0.394166i	$0.128967\pi$
$263$			12.7846i			0.788333i	−0.919039	+	0.394166i	$0.871033\pi$
$264$		0			0
$265$		−	5.46410i		−	0.335657i
$266$		0			0
$267$	15.4641	−	15.4641i	0.946388	−	0.946388i
$268$		0			0
$269$	13.1244	+	13.1244i	0.800206	+	0.800206i	0.983128	−	0.182921i	$-0.0585554\pi$
$269$	13.1244	+	13.1244i	0.800206	+	0.800206i	−0.182921	+	0.983128i	$0.558555\pi$
$270$		0			0
$271$	2.92820			0.177876			0.0889378	−	0.996037i	$-0.471653\pi$
$271$	2.92820			0.177876			0.0889378	+	0.996037i	$0.471653\pi$
$272$		0			0
$273$	−16.3923			−0.992107
$274$		0			0
$275$	19.8564	+	19.8564i	1.19739	+	1.19739i
$276$		0			0
$277$	−3.00000	+	3.00000i	−0.180253	+	0.180253i	−0.791466	−	0.611213i	$-0.790682\pi$
$277$	−3.00000	+	3.00000i	−0.180253	+	0.180253i	0.611213	+	0.791466i	$0.290682\pi$
$278$		0			0
$279$			22.3923i			1.34059i
$280$		0			0
$281$			10.0000i			0.596550i	0.954480	+	0.298275i	$0.0964112\pi$
$281$			10.0000i			0.596550i	−0.954480	+	0.298275i	$0.903589\pi$
$282$		0			0
$283$	6.26795	−	6.26795i	0.372591	−	0.372591i	−0.495829	−	0.868420i	$-0.665136\pi$
$283$	6.26795	−	6.26795i	0.372591	−	0.372591i	0.868420	+	0.495829i	$0.165136\pi$
$284$		0			0
$285$	−16.3923	−	16.3923i	−0.970996	−	0.970996i
$286$		0			0
$287$	−3.46410			−0.204479
$288$		0			0
$289$	−5.00000			−0.294118
$290$		0			0
$291$	−4.14359	−	4.14359i	−0.242902	−	0.242902i
$292$		0			0
$293$	−17.2679	+	17.2679i	−1.00880	+	1.00880i	−0.00884347	+	0.999961i	$0.502815\pi$
$293$	−17.2679	+	17.2679i	−1.00880	+	1.00880i	−0.999961	+	0.00884347i	$0.997185\pi$
$294$		0			0
$295$			12.3923i			0.721508i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−44.7846	+	44.7846i	−2.58996	+	2.58996i
$300$		0			0
$301$	7.46410	+	7.46410i	0.430224	+	0.430224i
$302$		0			0
$303$	4.39230			0.252331
$304$		0			0
$305$	28.7846			1.64820
$306$		0			0
$307$	−1.73205	−	1.73205i	−0.0988534	−	0.0988534i	0.655951	−	0.754804i	$-0.272268\pi$
$307$	−1.73205	−	1.73205i	−0.0988534	−	0.0988534i	−0.754804	+	0.655951i	$0.772268\pi$
$308$		0			0
$309$	26.7846	−	26.7846i	1.52372	−	1.52372i
$310$		0			0
$311$		−	27.7128i		−	1.57145i	−0.618576	−	0.785725i	$-0.712290\pi$
$311$		−	27.7128i		−	1.57145i	0.618576	−	0.785725i	$-0.287710\pi$
$312$		0			0
$313$			32.2487i			1.82280i	0.411516	+	0.911402i	$0.364999\pi$
$313$			32.2487i			1.82280i	−0.411516	+	0.911402i	$0.635001\pi$
$314$		0			0
$315$	8.19615	−	8.19615i	0.461801	−	0.461801i
$316$		0			0
$317$	11.9282	+	11.9282i	0.669955	+	0.669955i	0.957705	−	0.287751i	$-0.0929075\pi$
$317$	11.9282	+	11.9282i	0.669955	+	0.669955i	−0.287751	+	0.957705i	$0.592907\pi$
$318$		0			0
$319$	−9.85641			−0.551853
$320$		0			0
$321$	−5.07180			−0.283080
$322$		0			0
$323$	−6.00000	−	6.00000i	−0.333849	−	0.333849i
$324$		0			0
$325$	46.9808	−	46.9808i	2.60602	−	2.60602i
$326$		0			0
$327$			29.3205i			1.62143i
$328$		0			0
$329$		−	11.4641i		−	0.632036i
$330$		0			0
$331$	8.53590	−	8.53590i	0.469175	−	0.469175i	−0.432472	−	0.901647i	$-0.642359\pi$
$331$	8.53590	−	8.53590i	0.469175	−	0.469175i	0.901647	+	0.432472i	$0.142359\pi$
$332$		0			0
$333$	−1.39230	−	1.39230i	−0.0762978	−	0.0762978i
$334$		0			0
$335$	−16.0000			−0.874173
$336$		0			0
$337$	20.0000			1.08947			0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000			1.08947			0.544735	+	0.838608i	$0.316630\pi$
$338$		0			0
$339$	24.0000	+	24.0000i	1.30350	+	1.30350i
$340$		0			0
$341$	−14.9282	+	14.9282i	−0.808408	+	0.808408i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$		−	89.5692i		−	4.82224i
$346$		0			0
$347$	22.3923	−	22.3923i	1.20208	−	1.20208i	0.228550	−	0.973532i	$-0.426602\pi$
$347$	22.3923	−	22.3923i	1.20208	−	1.20208i	0.973532	−	0.228550i	$-0.0733983\pi$
$348$		0			0
$349$	−4.33975	−	4.33975i	−0.232301	−	0.232301i	0.581351	−	0.813653i	$-0.302524\pi$
$349$	−4.33975	−	4.33975i	−0.232301	−	0.232301i	−0.813653	+	0.581351i	$0.802524\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	12.9282			0.688099			0.344049	−	0.938952i	$-0.388201\pi$
$353$	12.9282			0.688099			0.344049	+	0.938952i	$0.388201\pi$
$354$		0			0
$355$	10.9282	+	10.9282i	0.580009	+	0.580009i
$356$		0			0
$357$	6.00000	−	6.00000i	0.317554	−	0.317554i
$358$		0			0
$359$		−	29.4641i		−	1.55506i	−0.628848	−	0.777528i	$-0.716473\pi$
$359$		−	29.4641i		−	1.55506i	0.628848	−	0.777528i	$-0.283527\pi$
$360$		0			0
$361$		−	13.0000i		−	0.684211i
$362$		0			0
$363$	−5.19615	+	5.19615i	−0.272727	+	0.272727i
$364$		0			0
$365$	16.3923	+	16.3923i	0.858012	+	0.858012i
$366$		0			0
$367$	−21.0718			−1.09994			−0.549969	−	0.835185i	$-0.685361\pi$
$367$	−21.0718			−1.09994			−0.549969	+	0.835185i	$0.685361\pi$
$368$		0			0
$369$	−10.3923			−0.541002
$370$		0			0
$371$	−1.00000	−	1.00000i	−0.0519174	−	0.0519174i
$372$		0			0
$373$	−9.92820	+	9.92820i	−0.514063	+	0.514063i	−0.915769	−	0.401706i	$-0.868417\pi$
$373$	−9.92820	+	9.92820i	−0.514063	+	0.514063i	0.401706	+	0.915769i	$0.368417\pi$
$374$		0			0
$375$			46.6410i			2.40853i
$376$		0			0
$377$			23.3205i			1.20107i
$378$		0			0
$379$	−10.3923	+	10.3923i	−0.533817	+	0.533817i	−0.921706	−	0.387889i	$-0.873204\pi$
$379$	−10.3923	+	10.3923i	−0.533817	+	0.533817i	0.387889	+	0.921706i	$0.373204\pi$
$380$		0			0
$381$	0.679492	+	0.679492i	0.0348114	+	0.0348114i
$382$		0			0
$383$	−16.2487			−0.830270			−0.415135	−	0.909760i	$-0.636266\pi$
$383$	−16.2487			−0.830270			−0.415135	+	0.909760i	$0.636266\pi$
$384$		0			0
$385$	10.9282			0.556953
$386$		0			0
$387$	22.3923	+	22.3923i	1.13826	+	1.13826i
$388$		0			0
$389$	18.4641	−	18.4641i	0.936167	−	0.936167i	−0.0619144	−	0.998081i	$-0.519721\pi$
$389$	18.4641	−	18.4641i	0.936167	−	0.936167i	0.998081	+	0.0619144i	$0.0197206\pi$
$390$		0			0
$391$		−	32.7846i		−	1.65799i
$392$		0			0
$393$		−	21.7128i		−	1.09527i
$394$		0			0
$395$	10.9282	−	10.9282i	0.549858	−	0.549858i
$396$		0			0
$397$	25.5167	+	25.5167i	1.28064	+	1.28064i	0.940301	+	0.340343i	$0.110543\pi$
$397$	25.5167	+	25.5167i	1.28064	+	1.28064i	0.340343	+	0.940301i	$0.389457\pi$
$398$		0			0
$399$	−6.00000			−0.300376
$400$		0			0
$401$	11.0718			0.552899			0.276450	−	0.961028i	$-0.410842\pi$
$401$	11.0718			0.552899			0.276450	+	0.961028i	$0.410842\pi$
$402$		0			0
$403$	35.3205	+	35.3205i	1.75944	+	1.75944i
$404$		0			0
$405$	−24.5885	+	24.5885i	−1.22181	+	1.22181i
$406$		0			0
$407$		−	1.85641i		−	0.0920187i
$408$		0			0
$409$			33.3205i			1.64759i	0.566886	+	0.823797i	$0.308148\pi$
$409$			33.3205i			1.64759i	−0.566886	+	0.823797i	$0.691852\pi$
$410$		0			0
$411$	1.85641	−	1.85641i	0.0915698	−	0.0915698i
$412$		0			0
$413$	2.26795	+	2.26795i	0.111598	+	0.111598i
$414$		0			0
$415$	−12.3923			−0.608314
$416$		0			0
$417$	−4.14359			−0.202913
$418$		0			0
$419$	10.8038	+	10.8038i	0.527802	+	0.527802i	0.919917	−	0.392114i	$-0.128256\pi$
$419$	10.8038	+	10.8038i	0.527802	+	0.527802i	−0.392114	+	0.919917i	$0.628256\pi$
$420$		0			0
$421$	−13.0000	+	13.0000i	−0.633581	+	0.633581i	−0.948964	−	0.315383i	$-0.897867\pi$
$421$	−13.0000	+	13.0000i	−0.633581	+	0.633581i	0.315383	+	0.948964i	$0.397867\pi$
$422$		0			0
$423$		−	34.3923i		−	1.67221i
$424$		0			0
$425$			34.3923i			1.66827i
$426$		0			0
$427$	5.26795	−	5.26795i	0.254934	−	0.254934i
$428$		0			0
$429$	−32.7846	−	32.7846i	−1.58286	−	1.58286i
$430$		0			0
$431$	−18.2487			−0.879009			−0.439505	−	0.898240i	$-0.644846\pi$
$431$	−18.2487			−0.879009			−0.439505	+	0.898240i	$0.644846\pi$
$432$		0			0
$433$	14.3923			0.691650			0.345825	−	0.938299i	$-0.387599\pi$
$433$	14.3923			0.691650			0.345825	+	0.938299i	$0.387599\pi$
$434$		0			0
$435$	−23.3205	−	23.3205i	−1.11813	−	1.11813i
$436$		0			0
$437$	−16.3923	+	16.3923i	−0.784150	+	0.784150i
$438$		0			0
$439$			38.6410i			1.84424i	0.386910	+	0.922118i	$0.373542\pi$
$439$			38.6410i			1.84424i	−0.386910	+	0.922118i	$0.626458\pi$
$440$		0			0
$441$		−	3.00000i		−	0.142857i
$442$		0			0
$443$	−1.07180	+	1.07180i	−0.0509226	+	0.0509226i	−0.732110	−	0.681187i	$-0.761464\pi$
$443$	−1.07180	+	1.07180i	−0.0509226	+	0.0509226i	0.681187	+	0.732110i	$0.261464\pi$
$444$		0			0
$445$	24.3923	+	24.3923i	1.15631	+	1.15631i
$446$		0			0
$447$	34.3923			1.62670
$448$		0			0
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	−6.92820	−	6.92820i	−0.326236	−	0.326236i
$452$		0			0
$453$	−14.5359	+	14.5359i	−0.682956	+	0.682956i
$454$		0			0
$455$		−	25.8564i		−	1.21217i
$456$		0			0
$457$			3.85641i			0.180395i	0.995924	+	0.0901975i	$0.0287498\pi$
$457$			3.85641i			0.180395i	−0.995924	+	0.0901975i	$0.971250\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−18.1962	−	18.1962i	−0.847479	−	0.847479i	0.142339	−	0.989818i	$-0.454538\pi$
$461$	−18.1962	−	18.1962i	−0.847479	−	0.847479i	−0.989818	+	0.142339i	$0.954538\pi$
$462$		0			0
$463$	−13.8564			−0.643962			−0.321981	−	0.946746i	$-0.604349\pi$
$463$	−13.8564			−0.643962			−0.321981	+	0.946746i	$0.604349\pi$
$464$		0			0
$465$	−70.6410			−3.27590
$466$		0			0
$467$	−6.80385	−	6.80385i	−0.314845	−	0.314845i	0.531938	−	0.846783i	$-0.321464\pi$
$467$	−6.80385	−	6.80385i	−0.314845	−	0.314845i	−0.846783	+	0.531938i	$0.821464\pi$
$468$		0			0
$469$	−2.92820	+	2.92820i	−0.135212	+	0.135212i
$470$		0			0
$471$			16.3923i			0.755318i
$472$		0			0
$473$			29.8564i			1.37280i
$474$		0			0
$475$	17.1962	−	17.1962i	0.789014	−	0.789014i
$476$		0			0
$477$	−3.00000	−	3.00000i	−0.137361	−	0.137361i
$478$		0			0
$479$	−30.3923			−1.38866			−0.694330	−	0.719657i	$-0.744299\pi$
$479$	−30.3923			−1.38866			−0.694330	+	0.719657i	$0.744299\pi$
$480$		0			0
$481$	−4.39230			−0.200272
$482$		0			0
$483$	−16.3923	−	16.3923i	−0.745876	−	0.745876i
$484$		0			0
$485$	6.53590	−	6.53590i	0.296780	−	0.296780i
$486$		0			0
$487$			10.2487i			0.464413i	0.972666	+	0.232207i	$0.0745946\pi$
$487$			10.2487i			0.464413i	−0.972666	+	0.232207i	$0.925405\pi$
$488$		0			0
$489$		−	20.7846i		−	0.939913i
$490$		0			0
$491$	−13.0718	+	13.0718i	−0.589922	+	0.589922i	−0.937610	−	0.347688i	$-0.886967\pi$
$491$	−13.0718	+	13.0718i	−0.589922	+	0.589922i	0.347688	+	0.937610i	$0.386967\pi$
$492$		0			0
$493$	−8.53590	−	8.53590i	−0.384438	−	0.384438i
$494$		0			0
$495$	32.7846			1.47356
$496$		0			0
$497$	4.00000			0.179425
$498$		0			0
$499$	5.46410	+	5.46410i	0.244607	+	0.244607i	0.818753	−	0.574146i	$-0.194666\pi$
$499$	5.46410	+	5.46410i	0.244607	+	0.244607i	−0.574146	+	0.818753i	$0.694666\pi$
$500$		0			0
$501$	16.1436	−	16.1436i	0.721243	−	0.721243i
$502$		0			0
$503$		−	8.78461i		−	0.391686i	−0.980635	−	0.195843i	$-0.937256\pi$
$503$		−	8.78461i		−	0.391686i	0.980635	−	0.195843i	$-0.0627444\pi$
$504$		0			0
$505$			6.92820i			0.308301i
$506$		0			0
$507$	−55.0526	+	55.0526i	−2.44497	+	2.44497i
$508$		0			0
$509$	−8.73205	−	8.73205i	−0.387041	−	0.387041i	0.486589	−	0.873631i	$-0.338241\pi$
$509$	−8.73205	−	8.73205i	−0.387041	−	0.387041i	−0.873631	+	0.486589i	$0.838241\pi$
$510$		0			0
$511$	6.00000			0.265424
$512$		0			0
$513$		0			0
$514$		0			0
$515$	42.2487	+	42.2487i	1.86170	+	1.86170i
$516$		0			0
$517$	22.9282	−	22.9282i	1.00838	−	1.00838i
$518$		0			0
$519$			16.3923i			0.719542i
$520$		0			0
$521$		−	35.1769i		−	1.54113i	−0.637362	−	0.770564i	$-0.719975\pi$
$521$		−	35.1769i		−	1.54113i	0.637362	−	0.770564i	$-0.280025\pi$
$522$		0			0
$523$	25.7321	−	25.7321i	1.12518	−	1.12518i	0.134234	−	0.990950i	$-0.457142\pi$
$523$	25.7321	−	25.7321i	1.12518	−	1.12518i	0.990950	−	0.134234i	$-0.0428575\pi$
$524$		0			0
$525$	17.1962	+	17.1962i	0.750502	+	0.750502i
$526$		0			0
$527$	−25.8564			−1.12632
$528$		0			0
$529$	−66.5692			−2.89431
$530$		0			0
$531$	6.80385	+	6.80385i	0.295262	+	0.295262i
$532$		0			0
$533$	−16.3923	+	16.3923i	−0.710030	+	0.710030i
$534$		0			0
$535$		−	8.00000i		−	0.345870i
$536$		0			0
$537$			48.0000i			2.07135i
$538$		0			0
$539$	2.00000	−	2.00000i	0.0861461	−	0.0861461i
$540$		0			0
$541$	−0.856406	−	0.856406i	−0.0368198	−	0.0368198i	0.688457	−	0.725277i	$-0.258288\pi$
$541$	−0.856406	−	0.856406i	−0.0368198	−	0.0368198i	−0.725277	+	0.688457i	$0.758288\pi$
$542$		0			0
$543$	40.3923			1.73340
$544$		0			0
$545$	−46.2487			−1.98108
$546$		0			0
$547$	19.8564	+	19.8564i	0.848999	+	0.848999i	0.990008	−	0.141010i	$-0.0450348\pi$
$547$	19.8564	+	19.8564i	0.848999	+	0.848999i	−0.141010	+	0.990008i	$0.545035\pi$
$548$		0			0
$549$	15.8038	−	15.8038i	0.674492	−	0.674492i
$550$		0			0
$551$			8.53590i			0.363641i
$552$		0			0
$553$		−	4.00000i		−	0.170097i
$554$		0			0
$555$	4.39230	−	4.39230i	0.186443	−	0.186443i
$556$		0			0
$557$	26.7128	+	26.7128i	1.13186	+	1.13186i	0.989868	+	0.141990i	$0.0453501\pi$
$557$	26.7128	+	26.7128i	1.13186	+	1.13186i	0.141990	+	0.989868i	$0.454650\pi$
$558$		0			0
$559$	70.6410			2.98780
$560$		0			0
$561$	24.0000			1.01328
$562$		0			0
$563$	−11.5885	−	11.5885i	−0.488395	−	0.488395i	0.419404	−	0.907800i	$-0.362239\pi$
$563$	−11.5885	−	11.5885i	−0.488395	−	0.488395i	−0.907800	+	0.419404i	$0.862239\pi$
$564$		0			0
$565$	−37.8564	+	37.8564i	−1.59263	+	1.59263i
$566$		0			0
$567$			9.00000i			0.377964i
$568$		0			0
$569$			14.7846i			0.619803i	0.950769	+	0.309902i	$0.100296\pi$
$569$			14.7846i			0.619803i	−0.950769	+	0.309902i	$0.899704\pi$
$570$		0			0
$571$	−19.4641	+	19.4641i	−0.814547	+	0.814547i	−0.985312	−	0.170765i	$-0.945376\pi$
$571$	−19.4641	+	19.4641i	−0.814547	+	0.814547i	0.170765	+	0.985312i	$0.445376\pi$
$572$		0			0
$573$	−12.0000	−	12.0000i	−0.501307	−	0.501307i
$574$		0			0
$575$	93.9615			3.91847
$576$		0			0
$577$	−22.7846			−0.948536			−0.474268	−	0.880381i	$-0.657287\pi$
$577$	−22.7846			−0.948536			−0.474268	+	0.880381i	$0.657287\pi$
$578$		0			0
$579$	−17.3205	−	17.3205i	−0.719816	−	0.719816i
$580$		0			0
$581$	−2.26795	+	2.26795i	−0.0940904	+	0.0940904i
$582$		0			0
$583$		−	4.00000i		−	0.165663i
$584$		0			0
$585$		−	77.5692i		−	3.20709i
$586$		0			0
$587$	−26.5167	+	26.5167i	−1.09446	+	1.09446i	−0.0994135	+	0.995046i	$0.531697\pi$
$587$	−26.5167	+	26.5167i	−1.09446	+	1.09446i	−0.995046	+	0.0994135i	$0.968303\pi$
$588$		0			0
$589$	12.9282	+	12.9282i	0.532697	+	0.532697i
$590$		0			0
$591$	37.6077			1.54697
$592$		0			0
$593$	−28.6410			−1.17615			−0.588073	−	0.808808i	$-0.700113\pi$
$593$	−28.6410			−1.17615			−0.588073	+	0.808808i	$0.700113\pi$
$594$		0			0
$595$	9.46410	+	9.46410i	0.387990	+	0.387990i
$596$		0			0
$597$	24.9282	−	24.9282i	1.02024	−	1.02024i
$598$		0			0
$599$		−	16.7846i		−	0.685801i	−0.939372	−	0.342900i	$-0.888591\pi$
$599$		−	16.7846i		−	0.685801i	0.939372	−	0.342900i	$-0.111409\pi$
$600$		0			0
$601$		−	36.6410i		−	1.49462i	−0.664477	−	0.747309i	$-0.731345\pi$
$601$		−	36.6410i		−	1.49462i	0.664477	−	0.747309i	$-0.268655\pi$
$602$		0			0
$603$	−8.78461	+	8.78461i	−0.357737	+	0.357737i
$604$		0			0
$605$	−8.19615	−	8.19615i	−0.333221	−	0.333221i
$606$		0			0
$607$	−21.8564			−0.887124			−0.443562	−	0.896244i	$-0.646285\pi$
$607$	−21.8564			−0.887124			−0.443562	+	0.896244i	$0.646285\pi$
$608$		0			0
$609$	−8.53590			−0.345892
$610$		0			0
$611$	−54.2487	−	54.2487i	−2.19467	−	2.19467i
$612$		0			0
$613$	−12.4641	+	12.4641i	−0.503420	+	0.503420i	−0.912499	−	0.409079i	$-0.865850\pi$
$613$	−12.4641	+	12.4641i	−0.503420	+	0.503420i	0.409079	+	0.912499i	$0.365850\pi$
$614$		0			0
$615$		−	32.7846i		−	1.32200i
$616$		0			0
$617$			9.85641i			0.396804i	0.980121	+	0.198402i	$0.0635752\pi$
$617$			9.85641i			0.396804i	−0.980121	+	0.198402i	$0.936425\pi$
$618$		0			0
$619$	27.0526	−	27.0526i	1.08733	−	1.08733i	0.0915320	−	0.995802i	$-0.470824\pi$
$619$	27.0526	−	27.0526i	1.08733	−	1.08733i	0.995802	−	0.0915320i	$-0.0291764\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.92820			0.357701
$624$		0			0
$625$	−23.9282			−0.957128
$626$		0			0
$627$	−12.0000	−	12.0000i	−0.479234	−	0.479234i
$628$		0			0
$629$	1.60770	−	1.60770i	0.0641030	−	0.0641030i
$630$		0			0
$631$		−	31.7128i		−	1.26247i	−0.775593	−	0.631234i	$-0.782549\pi$
$631$		−	31.7128i		−	1.26247i	0.775593	−	0.631234i	$-0.217451\pi$
$632$		0			0
$633$		−	34.1436i		−	1.35709i
$634$		0			0
$635$	−1.07180	+	1.07180i	−0.0425330	+	0.0425330i
$636$		0			0
$637$	−4.73205	−	4.73205i	−0.187491	−	0.187491i
$638$		0			0
$639$	12.0000			0.474713
$640$		0			0
$641$	8.92820			0.352643			0.176321	−	0.984333i	$-0.443580\pi$
$641$	8.92820			0.352643			0.176321	+	0.984333i	$0.443580\pi$
$642$		0			0
$643$	10.8038	+	10.8038i	0.426062	+	0.426062i	0.887285	−	0.461222i	$-0.152589\pi$
$643$	10.8038	+	10.8038i	0.426062	+	0.426062i	−0.461222	+	0.887285i	$0.652589\pi$
$644$		0			0
$645$	−70.6410	+	70.6410i	−2.78149	+	2.78149i
$646$		0			0
$647$			45.3205i			1.78173i	0.454265	+	0.890867i	$0.349902\pi$
$647$			45.3205i			1.78173i	−0.454265	+	0.890867i	$0.650098\pi$
$648$		0			0
$649$			9.07180i			0.356099i
$650$		0			0
$651$	−12.9282	+	12.9282i	−0.506696	+	0.506696i
$652$		0			0
$653$	28.3205	+	28.3205i	1.10827	+	1.10827i	0.993378	+	0.114889i	$0.0366512\pi$
$653$	28.3205	+	28.3205i	1.10827	+	1.10827i	0.114889	+	0.993378i	$0.463349\pi$
$654$		0			0
$655$	34.2487			1.33821
$656$		0			0
$657$	18.0000			0.702247
$658$		0			0
$659$	−18.7846	−	18.7846i	−0.731745	−	0.731745i	0.239221	−	0.970965i	$-0.423108\pi$
$659$	−18.7846	−	18.7846i	−0.731745	−	0.731745i	−0.970965	+	0.239221i	$0.923108\pi$
$660$		0			0
$661$	−18.0526	+	18.0526i	−0.702163	+	0.702163i	−0.964874	−	0.262711i	$-0.915383\pi$
$661$	−18.0526	+	18.0526i	−0.702163	+	0.702163i	0.262711	+	0.964874i	$0.415383\pi$
$662$		0			0
$663$		−	56.7846i		−	2.20533i
$664$		0			0
$665$		−	9.46410i		−	0.367002i
$666$		0			0
$667$	−23.3205	+	23.3205i	−0.902974	+	0.902974i
$668$		0			0
$669$	−18.9282	−	18.9282i	−0.731807	−	0.731807i
$670$		0			0
$671$	21.0718			0.813468
$672$		0			0
$673$	9.07180			0.349692			0.174846	−	0.984596i	$-0.444057\pi$
$673$	9.07180			0.349692			0.174846	+	0.984596i	$0.444057\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	12.0526	−	12.0526i	0.463217	−	0.463217i	−0.436491	−	0.899709i	$-0.643779\pi$
$677$	12.0526	−	12.0526i	0.463217	−	0.463217i	0.899709	+	0.436491i	$0.143779\pi$
$678$		0			0
$679$		−	2.39230i		−	0.0918082i
$680$		0			0
$681$		−	45.7128i		−	1.75172i
$682$		0			0
$683$	−6.53590	+	6.53590i	−0.250089	+	0.250089i	−0.821007	−	0.570918i	$-0.806587\pi$
$683$	−6.53590	+	6.53590i	−0.250089	+	0.250089i	0.570918	+	0.821007i	$0.306587\pi$
$684$		0			0
$685$	2.92820	+	2.92820i	0.111881	+	0.111881i
$686$		0			0
$687$	−57.9615			−2.21137
$688$		0			0
$689$	−9.46410			−0.360554
$690$		0			0
$691$	36.1244	+	36.1244i	1.37424	+	1.37424i	0.854059	+	0.520176i	$0.174134\pi$
$691$	36.1244	+	36.1244i	1.37424	+	1.37424i	0.520176	+	0.854059i	$0.325866\pi$
$692$		0			0
$693$	6.00000	−	6.00000i	0.227921	−	0.227921i
$694$		0			0
$695$		−	6.53590i		−	0.247921i
$696$		0			0
$697$		−	12.0000i		−	0.454532i
$698$		0			0
$699$	−13.6077	+	13.6077i	−0.514690	+	0.514690i
$700$		0			0
$701$	−3.53590	−	3.53590i	−0.133549	−	0.133549i	0.637172	−	0.770721i	$-0.280104\pi$
$701$	−3.53590	−	3.53590i	−0.133549	−	0.133549i	−0.770721	+	0.637172i	$0.780104\pi$
$702$		0			0
$703$	−1.60770			−0.0606354
$704$		0			0
$705$	108.497			4.08625
$706$		0			0
$707$	1.26795	+	1.26795i	0.0476861	+	0.0476861i
$708$		0			0
$709$	−16.4641	+	16.4641i	−0.618322	+	0.618322i	−0.945101	−	0.326779i	$-0.894037\pi$
$709$	−16.4641	+	16.4641i	−0.618322	+	0.618322i	0.326779	+	0.945101i	$0.394037\pi$
$710$		0			0
$711$		−	12.0000i		−	0.450035i
$712$		0			0
$713$			70.6410i			2.64553i
$714$		0			0
$715$	51.7128	−	51.7128i	1.93395	−	1.93395i
$716$		0			0
$717$	16.3923	+	16.3923i	0.612182	+	0.612182i
$718$		0			0
$719$	11.4641			0.427539			0.213769	−	0.976884i	$-0.431426\pi$
$719$	11.4641			0.427539			0.213769	+	0.976884i	$0.431426\pi$
$720$		0			0
$721$	15.4641			0.575913
$722$		0			0
$723$	23.0718	+	23.0718i	0.858049	+	0.858049i
$724$		0			0
$725$	24.4641	−	24.4641i	0.908574	−	0.908574i
$726$		0			0
$727$		−	43.4641i		−	1.61199i	−0.591919	−	0.805997i	$-0.701630\pi$
$727$		−	43.4641i		−	1.61199i	0.591919	−	0.805997i	$-0.298370\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	−25.8564	+	25.8564i	−0.956334	+	0.956334i
$732$		0			0
$733$	16.1962	+	16.1962i	0.598219	+	0.598219i	0.939838	−	0.341620i	$-0.110975\pi$
$733$	16.1962	+	16.1962i	0.598219	+	0.598219i	−0.341620	+	0.939838i	$0.610975\pi$
$734$		0			0
$735$	9.46410			0.349089
$736$		0			0
$737$	−11.7128			−0.431447
$738$		0			0
$739$	16.9282	+	16.9282i	0.622714	+	0.622714i	0.946225	−	0.323511i	$-0.104863\pi$
$739$	16.9282	+	16.9282i	0.622714	+	0.622714i	−0.323511	+	0.946225i	$0.604863\pi$
$740$		0			0
$741$	−28.3923	+	28.3923i	−1.04302	+	1.04302i
$742$		0			0
$743$		−	4.67949i		−	0.171674i	−0.996309	−	0.0858370i	$-0.972644\pi$
$743$		−	4.67949i		−	0.171674i	0.996309	−	0.0858370i	$-0.0273564\pi$
$744$		0			0
$745$			54.2487i			1.98752i
$746$		0			0
$747$	−6.80385	+	6.80385i	−0.248940	+	0.248940i
$748$		0			0
$749$	−1.46410	−	1.46410i	−0.0534971	−	0.0534971i
$750$		0			0
$751$	−12.3923			−0.452202			−0.226101	−	0.974104i	$-0.572598\pi$
$751$	−12.3923			−0.452202			−0.226101	+	0.974104i	$0.572598\pi$
$752$		0			0
$753$	−19.8564			−0.723608
$754$		0			0
$755$	−22.9282	−	22.9282i	−0.834443	−	0.834443i
$756$		0			0
$757$	−34.3205	+	34.3205i	−1.24740	+	1.24740i	−0.290536	+	0.956864i	$0.593834\pi$
$757$	−34.3205	+	34.3205i	−1.24740	+	1.24740i	−0.956864	+	0.290536i	$0.906166\pi$
$758$		0			0
$759$		−	65.5692i		−	2.38001i
$760$		0			0
$761$		−	19.1769i		−	0.695163i	−0.937650	−	0.347581i	$-0.887003\pi$
$761$		−	19.1769i		−	0.695163i	0.937650	−	0.347581i	$-0.112997\pi$
$762$		0			0
$763$	−8.46410	+	8.46410i	−0.306421	+	0.306421i
$764$		0			0
$765$	28.3923	+	28.3923i	1.02653	+	1.02653i
$766$		0			0
$767$	21.4641			0.775024
$768$		0			0
$769$	−0.535898			−0.0193250			−0.00966250	−	0.999953i	$-0.503076\pi$
$769$	−0.535898			−0.0193250			−0.00966250	+	0.999953i	$0.503076\pi$
$770$		0			0
$771$	36.2487	+	36.2487i	1.30547	+	1.30547i
$772$		0			0
$773$	−10.0526	+	10.0526i	−0.361565	+	0.361565i	−0.864389	−	0.502824i	$-0.832295\pi$
$773$	−10.0526	+	10.0526i	−0.361565	+	0.361565i	0.502824	+	0.864389i	$0.332295\pi$
$774$		0			0
$775$		−	74.1051i		−	2.66193i
$776$		0			0
$777$		−	1.60770i		−	0.0576757i
$778$		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
$783$		0			0
$784$		0			0
$785$	−25.8564			−0.922855
$786$		0			0
$787$	−7.58846	−	7.58846i	−0.270499	−	0.270499i	0.558802	−	0.829301i	$-0.311261\pi$
$787$	−7.58846	−	7.58846i	−0.270499	−	0.270499i	−0.829301	+	0.558802i	$0.811261\pi$
$788$		0			0
$789$	−22.1436	+	22.1436i	−0.788333	+	0.788333i
$790$		0			0
$791$			13.8564i			0.492677i
$792$		0			0
$793$		−	49.8564i		−	1.77045i
$794$		0			0
$795$	9.46410	−	9.46410i	0.335657	−	0.335657i
$796$		0			0
$797$	−15.2679	−	15.2679i	−0.540819	−	0.540819i	0.382950	−	0.923769i	$-0.374908\pi$
$797$	−15.2679	−	15.2679i	−0.540819	−	0.540819i	−0.923769	+	0.382950i	$0.874908\pi$
$798$		0			0
$799$	39.7128			1.40494
$800$		0			0
$801$	26.7846			0.946388
$802$		0			0
$803$	12.0000	+	12.0000i	0.423471	+	0.423471i
$804$		0			0
$805$	25.8564	−	25.8564i	0.911319	−	0.911319i
$806$		0			0
$807$			45.4641i			1.60041i
$808$		0			0
$809$		−	30.0000i		−	1.05474i	−0.849635	−	0.527372i	$-0.823177\pi$
$809$		−	30.0000i		−	1.05474i	0.849635	−	0.527372i	$-0.176823\pi$
$810$		0			0
$811$	−23.5885	+	23.5885i	−0.828303	+	0.828303i	−0.987282	−	0.158979i	$-0.949180\pi$
$811$	−23.5885	+	23.5885i	−0.828303	+	0.828303i	0.158979	+	0.987282i	$0.449180\pi$
$812$		0			0
$813$	5.07180	+	5.07180i	0.177876	+	0.177876i
$814$		0			0
$815$	32.7846			1.14839
$816$		0			0
$817$	25.8564			0.904601
$818$		0			0
$819$	−14.1962	−	14.1962i	−0.496054	−	0.496054i
$820$		0			0
$821$	37.7846	−	37.7846i	1.31869	−	1.31869i	0.403880	−	0.914812i	$-0.367661\pi$
$821$	37.7846	−	37.7846i	1.31869	−	1.31869i	0.914812	−	0.403880i	$-0.132339\pi$
$822$		0			0
$823$			22.6410i			0.789216i	0.918850	+	0.394608i	$0.129120\pi$
$823$			22.6410i			0.789216i	−0.918850	+	0.394608i	$0.870880\pi$
$824$		0			0
$825$			68.7846i			2.39477i
$826$		0			0
$827$	5.46410	−	5.46410i	0.190005	−	0.190005i	−0.605693	−	0.795698i	$-0.707104\pi$
$827$	5.46410	−	5.46410i	0.190005	−	0.190005i	0.795698	+	0.605693i	$0.207104\pi$
$828$		0			0
$829$	5.66025	+	5.66025i	0.196589	+	0.196589i	0.798536	−	0.601947i	$-0.205608\pi$
$829$	5.66025	+	5.66025i	0.196589	+	0.196589i	−0.601947	+	0.798536i	$0.705608\pi$
$830$		0			0
$831$	−10.3923			−0.360505
$832$		0			0
$833$	3.46410			0.120024
$834$		0			0
$835$	25.4641	+	25.4641i	0.881222	+	0.881222i
$836$		0			0
$837$		0			0
$838$		0			0
$839$			22.3923i			0.773068i	0.922275	+	0.386534i	$0.126328\pi$
$839$			22.3923i			0.773068i	−0.922275	+	0.386534i	$0.873672\pi$
$840$		0			0
$841$		−	16.8564i		−	0.581255i
$842$		0			0
$843$	−17.3205	+	17.3205i	−0.596550	+	0.596550i
$844$		0			0
$845$	−86.8372	−	86.8372i	−2.98729	−	2.98729i
$846$		0			0
$847$	−3.00000			−0.103081
$848$		0			0
$849$	21.7128			0.745182
$850$		0			0
$851$	−4.39230	−	4.39230i	−0.150566	−	0.150566i
$852$		0			0
$853$	10.5885	−	10.5885i	0.362542	−	0.362542i	−0.502206	−	0.864748i	$-0.667478\pi$
$853$	10.5885	−	10.5885i	0.362542	−	0.362542i	0.864748	+	0.502206i	$0.167478\pi$
$854$		0			0
$855$		−	28.3923i		−	0.970996i
$856$		0			0
$857$		−	47.4641i		−	1.62134i	−0.585501	−	0.810671i	$-0.699102\pi$
$857$		−	47.4641i		−	1.62134i	0.585501	−	0.810671i	$-0.300898\pi$
$858$		0			0
$859$	22.8038	−	22.8038i	0.778057	−	0.778057i	−0.201443	−	0.979500i	$-0.564563\pi$
$859$	22.8038	−	22.8038i	0.778057	−	0.778057i	0.979500	+	0.201443i	$0.0645631\pi$
$860$		0			0
$861$	−6.00000	−	6.00000i	−0.204479	−	0.204479i
$862$		0			0
$863$	33.8564			1.15249			0.576243	−	0.817279i	$-0.304518\pi$
$863$	33.8564			1.15249			0.576243	+	0.817279i	$0.304518\pi$
$864$		0			0
$865$	−25.8564			−0.879144
$866$		0			0
$867$	−8.66025	−	8.66025i	−0.294118	−	0.294118i
$868$		0			0
$869$	8.00000	−	8.00000i	0.271381	−	0.271381i
$870$		0			0
$871$			27.7128i			0.939013i
$872$		0			0
$873$		−	7.17691i		−	0.242902i
$874$		0			0
$875$	−13.4641	+	13.4641i	−0.455170	+	0.455170i
$876$		0			0
$877$	7.39230	+	7.39230i	0.249620	+	0.249620i	0.820815	−	0.571194i	$-0.193520\pi$
$877$	7.39230	+	7.39230i	0.249620	+	0.249620i	−0.571194	+	0.820815i	$0.693520\pi$
$878$		0			0
$879$	−59.8179			−2.01761
$880$		0			0
$881$	−3.07180			−0.103491			−0.0517457	−	0.998660i	$-0.516479\pi$
$881$	−3.07180			−0.103491			−0.0517457	+	0.998660i	$0.516479\pi$
$882$		0			0
$883$	7.60770	+	7.60770i	0.256019	+	0.256019i	0.823433	−	0.567414i	$-0.192056\pi$
$883$	7.60770	+	7.60770i	0.256019	+	0.256019i	−0.567414	+	0.823433i	$0.692056\pi$
$884$		0			0
$885$	−21.4641	+	21.4641i	−0.721508	+	0.721508i
$886$		0			0
$887$		−	13.6077i		−	0.456902i	−0.973555	−	0.228451i	$-0.926634\pi$
$887$		−	13.6077i		−	0.456902i	0.973555	−	0.228451i	$-0.0733660\pi$
$888$		0			0
$889$			0.392305i			0.0131575i
$890$		0			0
$891$	−18.0000	+	18.0000i	−0.603023	+	0.603023i
$892$		0			0
$893$	−19.8564	−	19.8564i	−0.664469	−	0.664469i
$894$		0			0
$895$	−75.7128			−2.53080
$896$		0			0
$897$	−155.138			−5.17992
$898$		0			0
$899$	18.3923	+	18.3923i	0.613418	+	0.613418i
$900$		0			0
$901$	3.46410	−	3.46410i	0.115406	−	0.115406i
$902$		0			0
$903$			25.8564i			0.860447i
$904$		0			0
$905$			63.7128i			2.11789i
$906$		0			0
$907$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$907$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$908$		0			0
$909$	3.80385	+	3.80385i	0.126166	+	0.126166i
$910$		0			0
$911$	−46.2487			−1.53229			−0.766144	−	0.642669i	$-0.777827\pi$
$911$	−46.2487			−1.53229			−0.766144	+	0.642669i	$0.777827\pi$
$912$		0			0
$913$	−9.07180			−0.300233
$914$		0			0
$915$	49.8564	+	49.8564i	1.64820	+	1.64820i
$916$		0			0
$917$	6.26795	−	6.26795i	0.206986	−	0.206986i
$918$		0			0
$919$		−	37.8564i		−	1.24877i	−0.781118	−	0.624384i	$-0.785350\pi$
$919$		−	37.8564i		−	1.24877i	0.781118	−	0.624384i	$-0.214650\pi$
$920$		0			0
$921$		−	6.00000i		−	0.197707i
$922$		0			0
$923$	18.9282	−	18.9282i	0.623029	−	0.623029i
$924$		0			0
$925$	4.60770	+	4.60770i	0.151500	+	0.151500i
$926$		0			0
$927$	46.3923			1.52372
$928$		0			0
$929$	−7.46410			−0.244889			−0.122445	−	0.992475i	$-0.539073\pi$
$929$	−7.46410			−0.244889			−0.122445	+	0.992475i	$0.539073\pi$
$930$		0			0
$931$	−1.73205	−	1.73205i	−0.0567657	−	0.0567657i
$932$		0			0
$933$	48.0000	−	48.0000i	1.57145	−	1.57145i
$934$		0			0
$935$			37.8564i			1.23804i
$936$		0			0
$937$			32.6410i			1.06634i	0.846010	+	0.533168i	$0.178999\pi$
$937$			32.6410i			1.06634i	−0.846010	+	0.533168i	$0.821001\pi$
$938$		0			0
$939$	−55.8564	+	55.8564i	−1.82280	+	1.82280i
$940$		0			0
$941$	−4.19615	−	4.19615i	−0.136791	−	0.136791i	0.635396	−	0.772187i	$-0.280837\pi$
$941$	−4.19615	−	4.19615i	−0.136791	−	0.136791i	−0.772187	+	0.635396i	$0.780837\pi$
$942$		0			0
$943$	−32.7846			−1.06761
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.78461	+	6.78461i	0.220470	+	0.220470i	0.808696	−	0.588226i	$-0.200174\pi$
$947$	6.78461	+	6.78461i	0.220470	+	0.220470i	−0.588226	+	0.808696i	$0.700174\pi$
$948$		0			0
$949$	28.3923	−	28.3923i	0.921653	−	0.921653i
$950$		0			0
$951$			41.3205i			1.33991i
$952$		0			0
$953$			26.1436i			0.846874i	0.905926	+	0.423437i	$0.139177\pi$
$953$			26.1436i			0.846874i	−0.905926	+	0.423437i	$0.860823\pi$
$954$		0			0
$955$	18.9282	−	18.9282i	0.612502	−	0.612502i
$956$		0			0
$957$	−17.0718	−	17.0718i	−0.551853	−	0.551853i
$958$		0			0
$959$	1.07180			0.0346101
$960$		0			0
$961$	24.7128			0.797188
$962$		0			0
$963$	−4.39230	−	4.39230i	−0.141540	−	0.141540i
$964$		0			0
$965$	27.3205	−	27.3205i	0.879478	−	0.879478i
$966$		0			0
$967$		−	46.5359i		−	1.49649i	−0.663420	−	0.748247i	$-0.730896\pi$
$967$		−	46.5359i		−	1.49649i	0.663420	−	0.748247i	$-0.269104\pi$
$968$		0			0
$969$		−	20.7846i		−	0.667698i
$970$		0			0
$971$	21.7321	−	21.7321i	0.697415	−	0.697415i	−0.266437	−	0.963852i	$-0.585847\pi$
$971$	21.7321	−	21.7321i	0.697415	−	0.697415i	0.963852	+	0.266437i	$0.0858466\pi$
$972$		0			0
$973$	−1.19615	−	1.19615i	−0.0383469	−	0.0383469i
$974$		0			0
$975$	162.746			5.21205
$976$		0			0
$977$	−9.07180			−0.290232			−0.145116	−	0.989415i	$-0.546356\pi$
$977$	−9.07180			−0.290232			−0.145116	+	0.989415i	$0.546356\pi$
$978$		0			0
$979$	17.8564	+	17.8564i	0.570693	+	0.570693i
$980$		0			0
$981$	−25.3923	+	25.3923i	−0.810714	+	0.810714i
$982$		0			0
$983$			29.3205i			0.935179i	0.883946	+	0.467589i	$0.154877\pi$
$983$			29.3205i			0.935179i	−0.883946	+	0.467589i	$0.845123\pi$
$984$		0			0
$985$			59.3205i			1.89011i
$986$		0			0
$987$	19.8564	−	19.8564i	0.632036	−	0.632036i
$988$		0			0
$989$	70.6410	+	70.6410i	2.24625	+	2.24625i
$990$		0			0
$991$	11.7128			0.372070			0.186035	−	0.982543i	$-0.440436\pi$
$991$	11.7128			0.372070			0.186035	+	0.982543i	$0.440436\pi$
$992$		0			0
$993$	29.5692			0.938351
$994$		0			0
$995$	39.3205	+	39.3205i	1.24654	+	1.24654i
$996$		0			0
$997$	25.6603	−	25.6603i	0.812668	−	0.812668i	−0.172365	−	0.985033i	$-0.555141\pi$
$997$	25.6603	−	25.6603i	0.812668	−	0.812668i	0.985033	+	0.172365i	$0.0551408\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3584.2.m.bc.2689.2	yes	4
4.3	odd	2		3584.2.m.bd.2689.1	yes	4
8.3	odd	2		3584.2.m.be.2689.2	yes	4
8.5	even	2		3584.2.m.bf.2689.1	yes	4
16.3	odd	4		3584.2.m.be.897.2	yes	4
16.5	even	4	inner	3584.2.m.bc.897.2	✓	4
16.11	odd	4		3584.2.m.bd.897.1	yes	4
16.13	even	4		3584.2.m.bf.897.1	yes	4
32.5	even	8		7168.2.a.u.1.1		4
32.11	odd	8		7168.2.a.v.1.2		4
32.21	even	8		7168.2.a.u.1.4		4
32.27	odd	8		7168.2.a.v.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3584.2.m.bc.897.2	✓	4	16.5	even	4	inner
3584.2.m.bc.2689.2	yes	4	1.1	even	1	trivial
3584.2.m.bd.897.1	yes	4	16.11	odd	4
3584.2.m.bd.2689.1	yes	4	4.3	odd	2
3584.2.m.be.897.2	yes	4	16.3	odd	4
3584.2.m.be.2689.2	yes	4	8.3	odd	2
3584.2.m.bf.897.1	yes	4	16.13	even	4
3584.2.m.bf.2689.1	yes	4	8.5	even	2
7168.2.a.u.1.1		4	32.5	even	8
7168.2.a.u.1.4		4	32.21	even	8
7168.2.a.v.1.2		4	32.11	odd	8
7168.2.a.v.1.3		4	32.27	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)

\(f(q)\)	\(=\)	\(q+(1.73205 + 1.73205i) q^{3} +(-2.73205 + 2.73205i) q^{5} +1.00000i q^{7} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.73205 + 1.73205i) q^{3} +(-2.73205 + 2.73205i) q^{5} +1.00000i q^{7} +3.00000i q^{9} +(-2.00000 + 2.00000i) q^{11} +(4.73205 + 4.73205i) q^{13} -9.46410 q^{15} -3.46410 q^{17} +(1.73205 + 1.73205i) q^{19} +(-1.73205 + 1.73205i) q^{21} +9.46410i q^{23} -9.92820i q^{25} +(2.46410 + 2.46410i) q^{29} +7.46410 q^{31} -6.92820 q^{33} +(-2.73205 - 2.73205i) q^{35} +(-0.464102 + 0.464102i) q^{37} +16.3923i q^{39} +3.46410i q^{41} +(7.46410 - 7.46410i) q^{43} +(-8.19615 - 8.19615i) q^{45} -11.4641 q^{47} -1.00000 q^{49} +(-6.00000 - 6.00000i) q^{51} +(-1.00000 + 1.00000i) q^{53} -10.9282i q^{55} +6.00000i q^{57} +(2.26795 - 2.26795i) q^{59} +(-5.26795 - 5.26795i) q^{61} -3.00000 q^{63} -25.8564 q^{65} +(2.92820 + 2.92820i) q^{67} +(-16.3923 + 16.3923i) q^{69} -4.00000i q^{71} -6.00000i q^{73} +(17.1962 - 17.1962i) q^{75} +(-2.00000 - 2.00000i) q^{77} -4.00000 q^{79} +9.00000 q^{81} +(2.26795 + 2.26795i) q^{83} +(9.46410 - 9.46410i) q^{85} +8.53590i q^{87} -8.92820i q^{89} +(-4.73205 + 4.73205i) q^{91} +(12.9282 + 12.9282i) q^{93} -9.46410 q^{95} -2.39230 q^{97} +(-6.00000 - 6.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5}+O(q^{10}) \) 4 * q - 4 * q^5	\( 4 q - 4 q^{5} - 8 q^{11} + 12 q^{13} - 24 q^{15} - 4 q^{29} + 16 q^{31} - 4 q^{35} + 12 q^{37} + 16 q^{43} - 12 q^{45} - 32 q^{47} - 4 q^{49} - 24 q^{51} - 4 q^{53} + 16 q^{59} - 28 q^{61} - 12 q^{63} - 48 q^{65} - 16 q^{67} - 24 q^{69} + 48 q^{75} - 8 q^{77} - 16 q^{79} + 36 q^{81} + 16 q^{83} + 24 q^{85} - 12 q^{91} + 24 q^{93} - 24 q^{95} + 32 q^{97} - 24 q^{99}+O(q^{100}) \) 4 * q - 4 * q^5 - 8 * q^11 + 12 * q^13 - 24 * q^15 - 4 * q^29 + 16 * q^31 - 4 * q^35 + 12 * q^37 + 16 * q^43 - 12 * q^45 - 32 * q^47 - 4 * q^49 - 24 * q^51 - 4 * q^53 + 16 * q^59 - 28 * q^61 - 12 * q^63 - 48 * q^65 - 16 * q^67 - 24 * q^69 + 48 * q^75 - 8 * q^77 - 16 * q^79 + 36 * q^81 + 16 * q^83 + 24 * q^85 - 12 * q^91 + 24 * q^93 - 24 * q^95 + 32 * q^97 - 24 * q^99

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