LMFDB - Embedded newform 392.3.o.d.129.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(129,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("392.129");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} - 68 x^{14} + 568 x^{13} + 2134 x^{12} - 16640 x^{11} - 41092 x^{10} + 246584 x^{9} + \cdots + 24404548 $ x^16 - 8x^15 - 68x^14 + 568x^13 + 2134x^12 - 16640x^11 - 41092x^10 + 246584x^9 + 529107x^8 - 1796336x^7 - 4219324x^6 + 4315240x^5 + 15202946x^4 + 8033008x^3 + 2510160x^2 + 18662224*x + 24404548
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.4
Root			$-2.09236 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	392.129
Dual form			392.3.o.d.313.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16338 - 0.671680i) q^{3} +(-5.73452 + 3.31082i) q^{5} +(-3.59769 - 6.23139i) q^{9} +O(q^{10})$	\(q+(-1.16338 - 0.671680i) q^{3} +(-5.73452 + 3.31082i) q^{5} +(-3.59769 - 6.23139i) q^{9} +(6.26927 - 10.8587i) q^{11} +2.63066i q^{13} +8.89526 q^{15} +(22.9333 + 13.2406i) q^{17} +(-8.89479 + 5.13541i) q^{19} +(21.7478 + 37.6682i) q^{23} +(9.42312 - 16.3213i) q^{25} +21.7562i q^{27} +10.1226 q^{29} +(40.8522 + 23.5860i) q^{31} +(-14.5871 + 8.42188i) q^{33} +(-4.13235 - 7.15744i) q^{37} +(1.76696 - 3.06047i) q^{39} -66.9187i q^{41} +80.9734 q^{43} +(41.2621 + 23.8227i) q^{45} +(-24.1945 + 13.9687i) q^{47} +(-17.7868 - 30.8077i) q^{51} +(37.4267 - 64.8249i) q^{53} +83.0258i q^{55} +13.7974 q^{57} +(-61.1758 - 35.3199i) q^{59} +(-19.2802 + 11.1314i) q^{61} +(-8.70966 - 15.0856i) q^{65} +(-31.1659 + 53.9810i) q^{67} -58.4301i q^{69} +17.1596 q^{71} +(30.2230 + 17.4493i) q^{73} +(-21.9254 + 12.6586i) q^{75} +(54.7248 + 94.7861i) q^{79} +(-17.7660 + 30.7716i) q^{81} +10.8247i q^{83} -175.349 q^{85} +(-11.7764 - 6.79912i) q^{87} +(100.648 - 58.1090i) q^{89} +(-31.6845 - 54.8792i) q^{93} +(34.0049 - 58.8982i) q^{95} +55.5922i q^{97} -90.2196 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 64 q^{9}+O(q^{10}) $ 16 * q + 64 * q^9	$ 16 q + 64 q^{9} + 24 q^{11} + 80 q^{15} + 136 q^{23} + 80 q^{25} + 128 q^{29} + 64 q^{37} + 376 q^{39} + 272 q^{43} + 408 q^{51} + 104 q^{53} - 480 q^{57} - 224 q^{65} + 16 q^{67} + 704 q^{71} + 112 q^{79} - 584 q^{81} + 400 q^{85} - 784 q^{93} - 120 q^{95} - 1760 q^{99}+O(q^{100}) $ 16 * q + 64 * q^9 + 24 * q^11 + 80 * q^15 + 136 * q^23 + 80 * q^25 + 128 * q^29 + 64 * q^37 + 376 * q^39 + 272 * q^43 + 408 * q^51 + 104 * q^53 - 480 * q^57 - 224 * q^65 + 16 * q^67 + 704 * q^71 + 112 * q^79 - 584 * q^81 + 400 * q^85 - 784 * q^93 - 120 * q^95 - 1760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$	−1.16338	−	0.671680i	−0.387795	−	0.223893i	0.293410	−	0.955987i	$-0.405210\pi$
$3$	−1.16338	−	0.671680i	−0.387795	−	0.223893i	−0.681204	+	0.732094i	$0.738543\pi$
$4$		0			0
$5$	−5.73452	+	3.31082i	−1.14690	+	0.662165i	−0.948131	−	0.317881i	$-0.897029\pi$
$5$	−5.73452	+	3.31082i	−1.14690	+	0.662165i	−0.198773	+	0.980046i	$0.563696\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−3.59769	−	6.23139i	−0.399744	−	0.692376i
$10$		0			0
$11$	6.26927	−	10.8587i	0.569933	−	0.987153i	−0.426639	−	0.904422i	$-0.640302\pi$
$11$	6.26927	−	10.8587i	0.569933	−	0.987153i	0.996572	−	0.0827311i	$-0.0263643\pi$
$12$		0			0
$13$			2.63066i			0.202359i	0.994868	+	0.101179i	$0.0322616\pi$
$13$			2.63066i			0.202359i	−0.994868	+	0.101179i	$0.967738\pi$
$14$		0			0
$15$	8.89526			0.593017
$16$		0			0
$17$	22.9333	+	13.2406i	1.34902	+	0.778857i	0.988111	−	0.153745i	$-0.0491333\pi$
$17$	22.9333	+	13.2406i	1.34902	+	0.778857i	0.360909	+	0.932601i	$0.382467\pi$
$18$		0			0
$19$	−8.89479	+	5.13541i	−0.468147	+	0.270285i	−0.715464	−	0.698650i	$-0.753784\pi$
$19$	−8.89479	+	5.13541i	−0.468147	+	0.270285i	0.247317	+	0.968935i	$0.420451\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	21.7478	+	37.6682i	0.945555	+	1.63775i	0.754637	+	0.656143i	$0.227813\pi$
$23$	21.7478	+	37.6682i	0.945555	+	1.63775i	0.190918	+	0.981606i	$0.438854\pi$
$24$		0			0
$25$	9.42312	−	16.3213i	0.376925	−	0.652853i
$26$		0			0
$27$			21.7562i			0.805786i
$28$		0			0
$29$	10.1226			0.349054			0.174527	−	0.984652i	$-0.444160\pi$
$29$	10.1226			0.349054			0.174527	+	0.984652i	$0.444160\pi$
$30$		0			0
$31$	40.8522	+	23.5860i	1.31781	+	0.760840i	0.983377	−	0.181578i	$-0.0581205\pi$
$31$	40.8522	+	23.5860i	1.31781	+	0.760840i	0.334437	+	0.942418i	$0.391454\pi$
$32$		0			0
$33$	−14.5871	+	8.42188i	−0.442034	+	0.255208i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.13235	−	7.15744i	−0.111685	−	0.193444i	0.804765	−	0.593594i	$-0.202291\pi$
$37$	−4.13235	−	7.15744i	−0.111685	−	0.193444i	−0.916450	+	0.400150i	$0.868958\pi$
$38$		0			0
$39$	1.76696	−	3.06047i	0.0453067	−	0.0784735i
$40$		0			0
$41$		−	66.9187i		−	1.63216i	−0.577937	−	0.816081i	$-0.696142\pi$
$41$		−	66.9187i		−	1.63216i	0.577937	−	0.816081i	$-0.303858\pi$
$42$		0			0
$43$	80.9734			1.88310			0.941551	−	0.336870i	$-0.109368\pi$
$43$	80.9734			1.88310			0.941551	+	0.336870i	$0.109368\pi$
$44$		0			0
$45$	41.2621	+	23.8227i	0.916935	+	0.529392i
$46$		0			0
$47$	−24.1945	+	13.9687i	−0.514776	+	0.297206i	−0.734795	−	0.678290i	$-0.762722\pi$
$47$	−24.1945	+	13.9687i	−0.514776	+	0.297206i	0.220019	+	0.975496i	$0.429388\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−17.7868	−	30.8077i	−0.348761	−	0.604073i
$52$		0			0
$53$	37.4267	−	64.8249i	0.706164	−	1.22311i	−0.260106	−	0.965580i	$-0.583758\pi$
$53$	37.4267	−	64.8249i	0.706164	−	1.22311i	0.966270	−	0.257531i	$-0.0829090\pi$
$54$		0			0
$55$			83.0258i			1.50956i
$56$		0			0
$57$	13.7974			0.242060
$58$		0			0
$59$	−61.1758	−	35.3199i	−1.03688	−	0.598642i	−0.117931	−	0.993022i	$-0.537626\pi$
$59$	−61.1758	−	35.3199i	−1.03688	−	0.598642i	−0.918948	+	0.394380i	$0.870959\pi$
$60$		0			0
$61$	−19.2802	+	11.1314i	−0.316069	+	0.182482i	−0.649639	−	0.760243i	$-0.725080\pi$
$61$	−19.2802	+	11.1314i	−0.316069	+	0.182482i	0.333570	+	0.942725i	$0.391747\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.70966	−	15.0856i	−0.133995	−	0.232086i
$66$		0			0
$67$	−31.1659	+	53.9810i	−0.465163	+	0.805687i	−0.999209	−	0.0397691i	$-0.987338\pi$
$67$	−31.1659	+	53.9810i	−0.465163	+	0.805687i	0.534045	+	0.845456i	$0.320671\pi$
$68$		0			0
$69$		−	58.4301i		−	0.846813i
$70$		0			0
$71$	17.1596			0.241684			0.120842	−	0.992672i	$-0.461441\pi$
$71$	17.1596			0.241684			0.120842	+	0.992672i	$0.461441\pi$
$72$		0			0
$73$	30.2230	+	17.4493i	0.414014	+	0.239031i	0.692513	−	0.721406i	$-0.256504\pi$
$73$	30.2230	+	17.4493i	0.414014	+	0.239031i	−0.278499	+	0.960436i	$0.589837\pi$
$74$		0			0
$75$	−21.9254	+	12.6586i	−0.292339	+	0.168782i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	54.7248	+	94.7861i	0.692719	+	1.19982i	0.970944	+	0.239308i	$0.0769206\pi$
$79$	54.7248	+	94.7861i	0.692719	+	1.19982i	−0.278225	+	0.960516i	$0.589746\pi$
$80$		0			0
$81$	−17.7660	+	30.7716i	−0.219334	+	0.379897i
$82$		0			0
$83$			10.8247i			0.130418i	0.997872	+	0.0652088i	$0.0207713\pi$
$83$			10.8247i			0.130418i	−0.997872	+	0.0652088i	$0.979229\pi$
$84$		0			0
$85$	−175.349			−2.06293
$86$		0			0
$87$	−11.7764	−	6.79912i	−0.135361	−	0.0781508i
$88$		0			0
$89$	100.648	−	58.1090i	1.13087	−	0.652910i	0.186719	−	0.982413i	$-0.440215\pi$
$89$	100.648	−	58.1090i	1.13087	−	0.652910i	0.944154	+	0.329503i	$0.106881\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−31.6845	−	54.8792i	−0.340694	−	0.590099i
$94$		0			0
$95$	34.0049	−	58.8982i	0.357946	−	0.619981i
$96$		0			0
$97$			55.5922i			0.573116i	0.958063	+	0.286558i	$0.0925110\pi$
$97$			55.5922i			0.573116i	−0.958063	+	0.286558i	$0.907489\pi$
$98$		0			0
$99$	−90.2196			−0.911309
$100$		0			0
$101$	8.69261	+	5.01868i	0.0860654	+	0.0496899i	0.542415	−	0.840111i	$-0.317510\pi$
$101$	8.69261	+	5.01868i	0.0860654	+	0.0496899i	−0.456350	+	0.889801i	$0.650843\pi$
$102$		0			0
$103$	60.5802	−	34.9760i	0.588157	−	0.339573i	−0.176211	−	0.984352i	$-0.556384\pi$
$103$	60.5802	−	34.9760i	0.588157	−	0.339573i	0.764368	+	0.644780i	$0.223051\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	7.50760	+	13.0035i	0.0701645	+	0.121528i	0.898973	−	0.438004i	$-0.144314\pi$
$107$	7.50760	+	13.0035i	0.0701645	+	0.121528i	−0.828809	+	0.559532i	$0.810981\pi$
$108$		0			0
$109$	−61.8204	+	107.076i	−0.567160	+	0.982349i	0.429686	+	0.902979i	$0.358624\pi$
$109$	−61.8204	+	107.076i	−0.567160	+	0.982349i	−0.996845	+	0.0793707i	$0.974709\pi$
$110$		0			0
$111$			11.1025i			0.100022i
$112$		0			0
$113$	−87.6080			−0.775292			−0.387646	−	0.921808i	$-0.626712\pi$
$113$	−87.6080			−0.775292			−0.387646	+	0.921808i	$0.626712\pi$
$114$		0			0
$115$	−249.426	−	144.006i	−2.16892	−	1.25223i
$116$		0			0
$117$	16.3927	−	9.46431i	0.140108	−	0.0808915i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−18.1074	−	31.3629i	−0.149648	−	0.259197i
$122$		0			0
$123$	−44.9479	+	77.8521i	−0.365430	+	0.632944i
$124$		0			0
$125$		−	40.7480i		−	0.325984i
$126$		0			0
$127$	151.557			1.19336			0.596679	−	0.802480i	$-0.296486\pi$
$127$	151.557			1.19336			0.596679	+	0.802480i	$0.296486\pi$
$128$		0			0
$129$	−94.2031	−	54.3882i	−0.730257	−	0.421614i
$130$		0			0
$131$	107.502	−	62.0665i	0.820628	−	0.473790i	−0.0300049	−	0.999550i	$-0.509552\pi$
$131$	107.502	−	62.0665i	0.820628	−	0.473790i	0.850633	+	0.525760i	$0.176219\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−72.0311	−	124.761i	−0.533563	−	0.924159i
$136$		0			0
$137$	−54.6410	+	94.6410i	−0.398840	+	0.690810i	−0.993583	−	0.113105i	$-0.963920\pi$
$137$	−54.6410	+	94.6410i	−0.398840	+	0.690810i	0.594743	+	0.803916i	$0.297254\pi$
$138$		0			0
$139$		−	17.7902i		−	0.127987i	−0.997950	−	0.0639935i	$-0.979616\pi$
$139$		−	17.7902i		−	0.127987i	0.997950	−	0.0639935i	$-0.0203837\pi$
$140$		0			0
$141$	37.5299			0.266170
$142$		0			0
$143$	28.5655	+	16.4923i	0.199759	+	0.115331i
$144$		0			0
$145$	−58.0480	+	33.5140i	−0.400331	+	0.231131i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−54.1883	−	93.8568i	−0.363680	−	0.629912i	0.624884	−	0.780718i	$-0.285146\pi$
$149$	−54.1883	−	93.8568i	−0.363680	−	0.629912i	−0.988563	+	0.150806i	$0.951813\pi$
$150$		0			0
$151$	−27.6317	+	47.8595i	−0.182991	+	0.316950i	−0.942898	−	0.333082i	$-0.891911\pi$
$151$	−27.6317	+	47.8595i	−0.182991	+	0.316950i	0.759906	+	0.650033i	$0.225245\pi$
$152$		0			0
$153$		−	190.542i		−	1.24537i
$154$		0			0
$155$	−312.357			−2.01521
$156$		0			0
$157$	−190.916	−	110.226i	−1.21603	−	0.702074i	−0.251962	−	0.967737i	$-0.581076\pi$
$157$	−190.916	−	110.226i	−1.21603	−	0.702074i	−0.964066	+	0.265663i	$0.914409\pi$
$158$		0			0
$159$	−87.0831	+	50.2775i	−0.547693	+	0.316211i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	29.3447	+	50.8266i	0.180029	+	0.311819i	0.941890	−	0.335921i	$-0.109047\pi$
$163$	29.3447	+	50.8266i	0.180029	+	0.311819i	−0.761861	+	0.647740i	$0.775714\pi$
$164$		0			0
$165$	55.7667	−	96.5908i	0.337980	−	0.585399i
$166$		0			0
$167$		−	99.5134i		−	0.595888i	−0.954583	−	0.297944i	$-0.903699\pi$
$167$		−	99.5134i		−	0.595888i	0.954583	−	0.297944i	$-0.0963009\pi$
$168$		0			0
$169$	162.080			0.959051
$170$		0			0
$171$	64.0014	+	36.9512i	0.374277	+	0.216089i
$172$		0			0
$173$	123.428	−	71.2613i	0.713457	−	0.411915i	−0.0988824	−	0.995099i	$-0.531527\pi$
$173$	123.428	−	71.2613i	0.713457	−	0.411915i	0.812340	+	0.583184i	$0.198193\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	47.4473	+	82.1811i	0.268064	+	0.464300i
$178$		0			0
$179$	−136.649	+	236.683i	−0.763401	+	1.32225i	0.177687	+	0.984087i	$0.443138\pi$
$179$	−136.649	+	236.683i	−0.763401	+	1.32225i	−0.941088	+	0.338162i	$0.890195\pi$
$180$		0			0
$181$			289.628i			1.60015i	0.599898	+	0.800077i	$0.295208\pi$
$181$			289.628i			1.60015i	−0.599898	+	0.800077i	$0.704792\pi$
$182$		0			0
$183$	29.9070			0.163426
$184$		0			0
$185$	47.3940	+	27.3630i	0.256184	+	0.147908i
$186$		0			0
$187$	287.550	−	166.017i	1.53770	−	0.887792i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−34.7843	−	60.2482i	−0.182117	−	0.315436i	0.760484	−	0.649356i	$-0.224962\pi$
$191$	−34.7843	−	60.2482i	−0.182117	−	0.315436i	−0.942601	+	0.333921i	$0.891628\pi$
$192$		0			0
$193$	65.9026	−	114.147i	0.341464	−	0.591434i	−0.643240	−	0.765664i	$-0.722410\pi$
$193$	65.9026	−	114.147i	0.341464	−	0.591434i	0.984705	+	0.174230i	$0.0557438\pi$
$194$		0			0
$195$			23.4004i			0.120002i
$196$		0			0
$197$	39.1914			0.198941			0.0994706	−	0.995041i	$-0.468285\pi$
$197$	39.1914			0.198941			0.0994706	+	0.995041i	$0.468285\pi$
$198$		0			0
$199$	251.515	+	145.212i	1.26389	+	0.729709i	0.973825	−	0.227298i	$-0.0729890\pi$
$199$	251.515	+	145.212i	1.26389	+	0.729709i	0.290067	+	0.957006i	$0.406322\pi$
$200$		0			0
$201$	72.5159	−	41.8671i	0.360776	−	0.208294i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	221.556	+	383.746i	1.08076	+	1.87193i
$206$		0			0
$207$	156.483	−	271.037i	0.755959	−	1.30936i
$208$		0			0
$209$			128.781i			0.616177i
$210$		0			0
$211$	−114.121			−0.540860			−0.270430	−	0.962740i	$-0.587166\pi$
$211$	−114.121			−0.540860			−0.270430	+	0.962740i	$0.587166\pi$
$212$		0			0
$213$	−19.9632	−	11.5257i	−0.0937238	−	0.0541115i
$214$		0			0
$215$	−464.343	+	268.089i	−2.15974	+	1.24692i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−23.4406	−	40.6004i	−0.107035	−	0.185390i
$220$		0			0
$221$	−34.8314	+	60.3298i	−0.157608	+	0.272986i
$222$		0			0
$223$			28.6810i			0.128615i	0.997930	+	0.0643073i	$0.0204838\pi$
$223$			28.6810i			0.128615i	−0.997930	+	0.0643073i	$0.979516\pi$
$224$		0			0
$225$	−135.606			−0.602693
$226$		0			0
$227$	231.105	+	133.429i	1.01808	+	0.587791i	0.913548	−	0.406730i	$-0.133331\pi$
$227$	231.105	+	133.429i	1.01808	+	0.587791i	0.104535	+	0.994521i	$0.466664\pi$
$228$		0			0
$229$	−289.000	+	166.854i	−1.26201	+	0.728621i	−0.973463	−	0.228845i	$-0.926505\pi$
$229$	−289.000	+	166.854i	−1.26201	+	0.728621i	−0.288546	+	0.957466i	$0.593172\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−85.7246	−	148.479i	−0.367917	−	0.637251i	0.621323	−	0.783555i	$-0.286596\pi$
$233$	−85.7246	−	148.479i	−0.367917	−	0.637251i	−0.989240	+	0.146304i	$0.953262\pi$
$234$		0			0
$235$	92.4958	−	160.207i	0.393599	−	0.681733i
$236$		0			0
$237$		−	147.030i		−	0.620380i
$238$		0			0
$239$	143.422			0.600092			0.300046	−	0.953925i	$-0.402998\pi$
$239$	143.422			0.600092			0.300046	+	0.953925i	$0.402998\pi$
$240$		0			0
$241$	−115.758	−	66.8330i	−0.480324	−	0.277315i	0.240227	−	0.970717i	$-0.422778\pi$
$241$	−115.758	−	66.8330i	−0.480324	−	0.277315i	−0.720552	+	0.693401i	$0.756111\pi$
$242$		0			0
$243$	210.910	−	121.769i	0.867944	−	0.501108i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.5095	−	23.3992i	−0.0546944	−	0.0947335i
$248$		0			0
$249$	7.27071	−	12.5932i	0.0291996	−	0.0505752i
$250$		0			0
$251$		−	330.489i		−	1.31669i	−0.752716	−	0.658345i	$-0.771257\pi$
$251$		−	330.489i		−	1.31669i	0.752716	−	0.658345i	$-0.228743\pi$
$252$		0			0
$253$	545.370			2.15561
$254$		0			0
$255$	203.998	+	117.778i	0.799991	+	0.461875i
$256$		0			0
$257$	−272.585	+	157.377i	−1.06064	+	0.612363i	−0.925610	−	0.378478i	$-0.876447\pi$
$257$	−272.585	+	157.377i	−1.06064	+	0.612363i	−0.135033	+	0.990841i	$0.543114\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−36.4179	−	63.0776i	−0.139532	−	0.241677i
$262$		0			0
$263$	183.921	−	318.561i	0.699320	−	1.21126i	−0.269382	−	0.963033i	$-0.586819\pi$
$263$	183.921	−	318.561i	0.699320	−	1.21126i	0.968702	−	0.248225i	$-0.0798472\pi$
$264$		0			0
$265$			495.653i			1.87039i
$266$		0			0
$267$	−156.123			−0.584729
$268$		0			0
$269$	299.454	+	172.890i	1.11321	+	0.642713i	0.939659	−	0.342111i	$-0.111142\pi$
$269$	299.454	+	172.890i	1.11321	+	0.642713i	0.173553	+	0.984825i	$0.444475\pi$
$270$		0			0
$271$	−246.827	+	142.506i	−0.910800	+	0.525851i	−0.880689	−	0.473696i	$-0.842920\pi$
$271$	−246.827	+	142.506i	−0.910800	+	0.525851i	−0.0301118	+	0.999547i	$0.509586\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−118.152	−	204.645i	−0.429644	−	0.744165i
$276$		0			0
$277$	−22.1358	+	38.3403i	−0.0799126	+	0.138413i	−0.903212	−	0.429195i	$-0.858797\pi$
$277$	−22.1358	+	38.3403i	−0.0799126	+	0.138413i	0.823299	+	0.567607i	$0.192131\pi$
$278$		0			0
$279$		−	339.421i		−	1.21656i
$280$		0			0
$281$	328.085			1.16756			0.583781	−	0.811911i	$-0.301573\pi$
$281$	328.085			1.16756			0.583781	+	0.811911i	$0.301573\pi$
$282$		0			0
$283$	−426.374	−	246.167i	−1.50662	−	0.869849i	−0.999970	−	0.00769795i	$-0.997550\pi$
$283$	−426.374	−	246.167i	−1.50662	−	0.869849i	−0.506652	−	0.862151i	$-0.669117\pi$
$284$		0			0
$285$	−79.1214	+	45.6808i	−0.277619	+	0.160283i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	206.125	+	357.019i	0.713235	+	1.23536i
$290$		0			0
$291$	37.3402	−	64.6751i	0.128317	−	0.222251i
$292$		0			0
$293$			381.762i			1.30294i	0.758674	+	0.651470i	$0.225848\pi$
$293$			381.762i			1.30294i	−0.758674	+	0.651470i	$0.774152\pi$
$294$		0			0
$295$	467.752			1.58560
$296$		0			0
$297$	236.244	+	136.396i	0.795434	+	0.459244i
$298$		0			0
$299$	−99.0923	+	57.2110i	−0.331412	+	0.191341i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−6.74189	−	11.6773i	−0.0222505	−	0.0385389i
$304$		0			0
$305$	73.7084	−	127.667i	0.241667	−	0.418579i
$306$		0			0
$307$			121.613i			0.396134i	0.980188	+	0.198067i	$0.0634664\pi$
$307$			121.613i			0.396134i	−0.980188	+	0.198067i	$0.936534\pi$
$308$		0			0
$309$	−93.9706			−0.304112
$310$		0			0
$311$	462.740	+	267.163i	1.48791	+	0.859044i	0.999905	−	0.0137970i	$-0.00439185\pi$
$311$	462.740	+	267.163i	1.48791	+	0.859044i	0.488004	+	0.872841i	$0.337725\pi$
$312$		0			0
$313$	148.803	−	85.9117i	0.475410	−	0.274478i	−0.243092	−	0.970003i	$-0.578162\pi$
$313$	148.803	−	85.9117i	0.475410	−	0.274478i	0.718502	+	0.695525i	$0.244828\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−57.3696	−	99.3671i	−0.180977	−	0.313461i	0.761237	−	0.648474i	$-0.224593\pi$
$317$	−57.3696	−	99.3671i	−0.180977	−	0.313461i	−0.942213	+	0.335013i	$0.891259\pi$
$318$		0			0
$319$	63.4610	−	109.918i	0.198937	−	0.344570i
$320$		0			0
$321$		−	20.1708i		−	0.0628374i
$322$		0			0
$323$	−271.983			−0.842052
$324$		0			0
$325$	42.9359	+	24.7890i	0.132110	+	0.0762740i
$326$		0			0
$327$	143.842	−	83.0470i	0.439883	−	0.253966i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	42.0071	+	72.7583i	0.126910	+	0.219814i	0.922478	−	0.386050i	$-0.126161\pi$
$331$	42.0071	+	72.7583i	0.126910	+	0.219814i	−0.795568	+	0.605864i	$0.792828\pi$
$332$		0			0
$333$	−29.7338	+	51.5005i	−0.0892908	+	0.154656i
$334$		0			0
$335$		−	412.740i		−	1.23206i
$336$		0			0
$337$	2.76645			0.00820906			0.00410453	−	0.999992i	$-0.498693\pi$
$337$	2.76645			0.00820906			0.00410453	+	0.999992i	$0.498693\pi$
$338$		0			0
$339$	101.922	+	58.8446i	0.300654	+	0.173583i
$340$		0			0
$341$	512.227	−	295.734i	1.50213	−	0.867256i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	193.452	+	335.068i	0.560730	+	0.971213i
$346$		0			0
$347$	−220.301	+	381.573i	−0.634875	+	1.09963i	0.351667	+	0.936125i	$0.385615\pi$
$347$	−220.301	+	381.573i	−0.634875	+	1.09963i	−0.986542	+	0.163510i	$0.947718\pi$
$348$		0			0
$349$		−	400.441i		−	1.14740i	−0.819067	−	0.573698i	$-0.805508\pi$
$349$		−	400.441i		−	1.14740i	0.819067	−	0.573698i	$-0.194492\pi$
$350$		0			0
$351$	−57.2333			−0.163058
$352$		0			0
$353$	−81.5977	−	47.1105i	−0.231155	−	0.133457i	0.379950	−	0.925007i	$-0.375941\pi$
$353$	−81.5977	−	47.1105i	−0.231155	−	0.133457i	−0.611105	+	0.791550i	$0.709275\pi$
$354$		0			0
$355$	−98.4019	+	56.8124i	−0.277189	+	0.160035i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	184.581	+	319.703i	0.514153	+	0.890539i	0.999865	+	0.0164200i	$0.00522690\pi$
$359$	184.581	+	319.703i	0.514153	+	0.890539i	−0.485712	+	0.874119i	$0.661440\pi$
$360$		0			0
$361$	−127.755	+	221.278i	−0.353892	+	0.612960i
$362$		0			0
$363$			48.6494i			0.134020i
$364$		0			0
$365$	−231.086			−0.633112
$366$		0			0
$367$	231.876	+	133.874i	0.631815	+	0.364779i	0.781455	−	0.623962i	$-0.214478\pi$
$367$	231.876	+	133.874i	0.631815	+	0.364779i	−0.149640	+	0.988741i	$0.547811\pi$
$368$		0			0
$369$	−416.996	+	240.753i	−1.13007	+	0.652447i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	52.9580	+	91.7260i	0.141979	+	0.245914i	0.928242	−	0.371978i	$-0.121320\pi$
$373$	52.9580	+	91.7260i	0.141979	+	0.245914i	−0.786263	+	0.617892i	$0.787987\pi$
$374$		0			0
$375$	−27.3696	+	47.4056i	−0.0729856	+	0.126415i
$376$		0			0
$377$			26.6290i			0.0706340i
$378$		0			0
$379$	8.04037			0.0212147			0.0106074	−	0.999944i	$-0.496624\pi$
$379$	8.04037			0.0212147			0.0106074	+	0.999944i	$0.496624\pi$
$380$		0			0
$381$	−176.318	−	101.797i	−0.462778	−	0.267185i
$382$		0			0
$383$	275.283	−	158.935i	0.718754	−	0.414973i	−0.0955396	−	0.995426i	$-0.530458\pi$
$383$	275.283	−	158.935i	0.718754	−	0.414973i	0.814294	+	0.580453i	$0.197124\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−291.317	−	504.577i	−0.752758	−	1.30382i
$388$		0			0
$389$	196.672	−	340.647i	0.505584	−	0.875698i	−0.494395	−	0.869238i	$-0.664610\pi$
$389$	196.672	−	340.647i	0.505584	−	0.875698i	0.999979	−	0.00646042i	$-0.00205643\pi$
$390$		0			0
$391$			1151.81i			2.94581i
$392$		0			0
$393$	−166.755			−0.424313
$394$		0			0
$395$	−627.640	−	362.368i	−1.58896	−	0.917388i
$396$		0			0
$397$	−62.5331	+	36.1035i	−0.157514	+	0.0909408i	−0.576685	−	0.816966i	$-0.695654\pi$
$397$	−62.5331	+	36.1035i	−0.157514	+	0.0909408i	0.419171	+	0.907907i	$0.362321\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−240.128	−	415.914i	−0.598824	−	1.03719i	−0.992995	−	0.118156i	$-0.962302\pi$
$401$	−240.128	−	415.914i	−0.598824	−	1.03719i	0.394171	−	0.919037i	$-0.371032\pi$
$402$		0			0
$403$	−62.0469	+	107.468i	−0.153962	+	0.266671i
$404$		0			0
$405$		−	235.281i		−	0.580940i
$406$		0			0
$407$	−103.627			−0.254612
$408$		0			0
$409$	−623.302	−	359.863i	−1.52397	−	0.879862i	−0.999597	−	0.0283699i	$-0.990968\pi$
$409$	−623.302	−	359.863i	−1.52397	−	0.879862i	−0.524368	−	0.851492i	$-0.675698\pi$
$410$		0			0
$411$	127.137	−	73.4025i	0.309336	−	0.178595i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−35.8386	−	62.0742i	−0.0863580	−	0.149576i
$416$		0			0
$417$	−11.9493	+	20.6968i	−0.0286554	+	0.0496326i
$418$		0			0
$419$		−	473.040i		−	1.12897i	−0.825442	−	0.564487i	$-0.809074\pi$
$419$		−	473.040i		−	1.12897i	0.825442	−	0.564487i	$-0.190926\pi$
$420$		0			0
$421$	179.357			0.426027			0.213014	−	0.977049i	$-0.431672\pi$
$421$	179.357			0.426027			0.213014	+	0.977049i	$0.431672\pi$
$422$		0			0
$423$	174.089	+	100.510i	0.411557	+	0.237612i
$424$		0			0
$425$	432.207	−	249.535i	1.01696	−	0.587141i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−22.1551	−	38.3738i	−0.0516436	−	0.0894494i
$430$		0			0
$431$	−29.1068	+	50.4145i	−0.0675333	+	0.116971i	−0.897815	−	0.440373i	$-0.854846\pi$
$431$	−29.1068	+	50.4145i	−0.0675333	+	0.116971i	0.830282	+	0.557344i	$0.188180\pi$
$432$		0			0
$433$		−	241.364i		−	0.557422i	−0.960375	−	0.278711i	$-0.910093\pi$
$433$		−	241.364i		−	0.557422i	0.960375	−	0.278711i	$-0.0899071\pi$
$434$		0			0
$435$	90.0428			0.206995
$436$		0			0
$437$	−386.883	−	223.367i	−0.885316	−	0.511138i
$438$		0			0
$439$	−187.023	+	107.978i	−0.426021	+	0.245964i	−0.697650	−	0.716438i	$-0.745771\pi$
$439$	−187.023	+	107.978i	−0.426021	+	0.245964i	0.271629	+	0.962402i	$0.412438\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−106.909	−	185.172i	−0.241329	−	0.417994i	0.719764	−	0.694219i	$-0.244250\pi$
$443$	−106.909	−	185.172i	−0.241329	−	0.417994i	−0.961093	+	0.276224i	$0.910917\pi$
$444$		0			0
$445$	−384.777	+	666.454i	−0.864668	+	1.49765i
$446$		0			0
$447$			145.589i			0.325702i
$448$		0			0
$449$	−625.904			−1.39400			−0.696998	−	0.717073i	$-0.745481\pi$
$449$	−625.904			−1.39400			−0.696998	+	0.717073i	$0.745481\pi$
$450$		0			0
$451$	−726.649	−	419.531i	−1.61119	−	0.930224i
$452$		0			0
$453$	64.2926	−	37.1193i	0.141926	−	0.0819411i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−303.041	−	524.882i	−0.663108	−	1.14854i	−0.979794	−	0.200007i	$-0.935903\pi$
$457$	−303.041	−	524.882i	−0.663108	−	1.14854i	0.316686	−	0.948530i	$-0.397430\pi$
$458$		0			0
$459$	−288.065	+	498.943i	−0.627592	+	1.08702i
$460$		0			0
$461$		−	268.244i		−	0.581874i	−0.956742	−	0.290937i	$-0.906033\pi$
$461$		−	268.244i		−	0.581874i	0.956742	−	0.290937i	$-0.0939670\pi$
$462$		0			0
$463$	−417.587			−0.901916			−0.450958	−	0.892545i	$-0.648918\pi$
$463$	−417.587			−0.901916			−0.450958	+	0.892545i	$0.648918\pi$
$464$		0			0
$465$	363.391	+	209.804i	0.781486	+	0.451191i
$466$		0			0
$467$	−204.395	+	118.008i	−0.437677	+	0.252693i	−0.702612	−	0.711573i	$-0.747983\pi$
$467$	−204.395	+	118.008i	−0.437677	+	0.252693i	0.264935	+	0.964266i	$0.414650\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	148.073	+	256.469i	0.314379	+	0.544521i
$472$		0			0
$473$	507.644	−	879.265i	1.07324	−	1.85891i
$474$		0			0
$475$			193.566i			0.407508i
$476$		0			0
$477$	−538.599			−1.12914
$478$		0			0
$479$	−494.073	−	285.253i	−1.03147	−	0.595519i	−0.114063	−	0.993473i	$-0.536387\pi$
$479$	−494.073	−	285.253i	−1.03147	−	0.595519i	−0.917405	+	0.397955i	$0.869720\pi$
$480$		0			0
$481$	18.8288	−	10.8708i	0.0391451	−	0.0226004i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−184.056	−	318.794i	−0.379497	−	0.657308i
$486$		0			0
$487$	−28.0172	+	48.5273i	−0.0575303	+	0.0996453i	−0.893356	−	0.449349i	$-0.851656\pi$
$487$	−28.0172	+	48.5273i	−0.0575303	+	0.0996453i	0.835826	+	0.548995i	$0.184989\pi$
$488$		0			0
$489$		−	78.8411i		−	0.161229i
$490$		0			0
$491$	−70.3733			−0.143326			−0.0716632	−	0.997429i	$-0.522831\pi$
$491$	−70.3733			−0.143326			−0.0716632	+	0.997429i	$0.522831\pi$
$492$		0			0
$493$	232.144	+	134.028i	0.470880	+	0.271863i
$494$		0			0
$495$	517.366	−	298.701i	1.04518	−	0.603437i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	358.323	+	620.634i	0.718083	+	1.24376i	0.961759	+	0.273899i	$0.0883133\pi$
$499$	358.323	+	620.634i	0.718083	+	1.24376i	−0.243676	+	0.969857i	$0.578353\pi$
$500$		0			0
$501$	−66.8411	+	115.772i	−0.133415	+	0.231082i
$502$		0			0
$503$		−	46.1333i		−	0.0917164i	−0.998948	−	0.0458582i	$-0.985398\pi$
$503$		−	46.1333i		−	0.0917164i	0.998948	−	0.0458582i	$-0.0146022\pi$
$504$		0			0
$505$	−66.4639			−0.131612
$506$		0			0
$507$	−188.561	−	108.866i	−0.371915	−	0.214725i
$508$		0			0
$509$	−291.749	+	168.441i	−0.573181	+	0.330926i	−0.758419	−	0.651768i	$-0.774028\pi$
$509$	−291.749	+	168.441i	−0.573181	+	0.330926i	0.185238	+	0.982694i	$0.440694\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−111.727	−	193.517i	−0.217792	−	0.377226i
$514$		0			0
$515$	−231.599	+	401.141i	−0.449706	+	0.778914i
$516$		0			0
$517$			350.294i			0.677551i
$518$		0			0
$519$	−191.459			−0.368900
$520$		0			0
$521$	206.008	+	118.939i	0.395408	+	0.228289i	0.684501	−	0.729012i	$-0.260020\pi$
$521$	206.008	+	118.939i	0.395408	+	0.228289i	−0.289093	+	0.957301i	$0.593354\pi$
$522$		0			0
$523$	734.124	−	423.847i	1.40368	−	0.810415i	0.408912	−	0.912574i	$-0.365908\pi$
$523$	734.124	−	423.847i	1.40368	−	0.810415i	0.994768	+	0.102159i	$0.0325751\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	624.585	+	1081.81i	1.18517	+	2.05278i
$528$		0			0
$529$	−681.430	+	1180.27i	−1.28815	+	2.23114i
$530$		0			0
$531$			508.280i			0.957213i
$532$		0			0
$533$	176.040			0.330282
$534$		0			0
$535$	−86.1049	−	49.7127i	−0.160944	−	0.0929209i
$536$		0			0
$537$	317.950	−	183.568i	0.592085	−	0.341841i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	22.4415	+	38.8698i	0.0414815	+	0.0718480i	0.886021	−	0.463646i	$-0.153459\pi$
$541$	22.4415	+	38.8698i	0.0414815	+	0.0718480i	−0.844539	+	0.535494i	$0.820126\pi$
$542$		0			0
$543$	194.537	−	336.948i	0.358264	−	0.620531i
$544$		0			0
$545$		−	818.706i		−	1.50221i
$546$		0			0
$547$	400.295			0.731800			0.365900	−	0.930654i	$-0.380761\pi$
$547$	400.295			0.731800			0.365900	+	0.930654i	$0.380761\pi$
$548$		0			0
$549$	138.728	+	80.0949i	0.252693	+	0.145892i
$550$		0			0
$551$	−90.0380	+	51.9835i	−0.163408	+	0.0943439i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−36.7583	−	63.6672i	−0.0662312	−	0.114716i
$556$		0			0
$557$	92.9162	−	160.936i	0.166815	−	0.288933i	−0.770483	−	0.637460i	$-0.779985\pi$
$557$	92.9162	−	160.936i	0.166815	−	0.288933i	0.937298	+	0.348528i	$0.113318\pi$
$558$		0			0
$559$			213.014i			0.381062i
$560$		0			0
$561$	−446.042			−0.795083
$562$		0			0
$563$	63.8853	+	36.8842i	0.113473	+	0.0655136i	0.555662	−	0.831408i	$-0.312465\pi$
$563$	63.8853	+	36.8842i	0.113473	+	0.0655136i	−0.442189	+	0.896922i	$0.645798\pi$
$564$		0			0
$565$	502.390	−	290.055i	0.889186	−	0.513372i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−64.0638	−	110.962i	−0.112590	−	0.195012i	0.804224	−	0.594327i	$-0.202581\pi$
$569$	−64.0638	−	110.962i	−0.112590	−	0.195012i	−0.916814	+	0.399315i	$0.869248\pi$
$570$		0			0
$571$	569.991	−	987.253i	0.998232	−	1.72899i	0.447648	−	0.894210i	$-0.352262\pi$
$571$	569.991	−	987.253i	0.998232	−	1.72899i	0.550585	−	0.834779i	$-0.314405\pi$
$572$		0			0
$573$			93.4557i			0.163099i
$574$		0			0
$575$	819.727			1.42561
$576$		0			0
$577$	249.294	+	143.930i	0.432051	+	0.249445i	0.700220	−	0.713927i	$-0.253085\pi$
$577$	249.294	+	143.930i	0.432051	+	0.249445i	−0.268169	+	0.963372i	$0.586419\pi$
$578$		0			0
$579$	−153.340	+	88.5310i	−0.264836	+	0.152903i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−469.275	−	812.809i	−0.804932	−	1.39418i
$584$		0			0
$585$	−62.6693	+	108.546i	−0.107127	+	0.185550i
$586$		0			0
$587$			11.5536i			0.0196825i	0.999952	+	0.00984123i	$0.00313261\pi$
$587$			11.5536i			0.0196825i	−0.999952	+	0.00984123i	$0.996867\pi$
$588$		0			0
$589$	−484.496			−0.822573
$590$		0			0
$591$	−45.5946	−	26.3241i	−0.0771483	−	0.0445416i
$592$		0			0
$593$	111.095	−	64.1405i	0.187343	−	0.108163i	−0.403395	−	0.915026i	$-0.632170\pi$
$593$	111.095	−	64.1405i	0.187343	−	0.108163i	0.590738	+	0.806863i	$0.298837\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−195.072	−	337.875i	−0.326754	−	0.565954i
$598$		0			0
$599$	−316.766	+	548.654i	−0.528824	+	0.915950i	0.470611	+	0.882341i	$0.344034\pi$
$599$	−316.766	+	548.654i	−0.528824	+	0.915950i	−0.999435	+	0.0336093i	$0.989300\pi$
$600$		0			0
$601$		−	323.899i		−	0.538933i	−0.963010	−	0.269467i	$-0.913153\pi$
$601$		−	323.899i		−	0.538933i	0.963010	−	0.269467i	$-0.0868474\pi$
$602$		0			0
$603$	448.502			0.743784
$604$		0			0
$605$	207.674	+	119.901i	0.343263	+	0.198183i
$606$		0			0
$607$	−553.107	+	319.337i	−0.911214	+	0.526090i	−0.880822	−	0.473448i	$-0.843009\pi$
$607$	−553.107	+	319.337i	−0.911214	+	0.526090i	−0.0303927	+	0.999538i	$0.509676\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−36.7469	−	63.6475i	−0.0601422	−	0.104169i
$612$		0			0
$613$	490.636	−	849.807i	0.800386	−	1.38631i	−0.118977	−	0.992897i	$-0.537961\pi$
$613$	490.636	−	849.807i	0.800386	−	1.38631i	0.919362	−	0.393412i	$-0.128705\pi$
$614$		0			0
$615$		−	595.259i		−	0.967900i
$616$		0			0
$617$	208.446			0.337837			0.168919	−	0.985630i	$-0.445972\pi$
$617$	208.446			0.337837			0.168919	+	0.985630i	$0.445972\pi$
$618$		0			0
$619$	368.572	+	212.795i	0.595431	+	0.343772i	0.767242	−	0.641358i	$-0.221628\pi$
$619$	368.572	+	212.795i	0.595431	+	0.343772i	−0.171811	+	0.985130i	$0.554962\pi$
$620$		0			0
$621$	−819.518	+	473.149i	−1.31968	+	0.761915i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	370.488	+	641.703i	0.592780	+	1.02673i
$626$		0			0
$627$	86.4995	−	149.822i	0.137958	−	0.238950i
$628$		0			0
$629$		−	218.858i		−	0.347947i
$630$		0			0
$631$	575.230			0.911616			0.455808	−	0.890078i	$-0.349350\pi$
$631$	575.230			0.911616			0.455808	+	0.890078i	$0.349350\pi$
$632$		0			0
$633$	132.767	+	76.6530i	0.209742	+	0.121095i
$634$		0			0
$635$	−869.104	+	501.777i	−1.36867	+	0.790200i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−61.7349	−	106.928i	−0.0966118	−	0.167336i
$640$		0			0
$641$	99.5830	−	172.483i	0.155356	−	0.269084i	−0.777833	−	0.628471i	$-0.783681\pi$
$641$	99.5830	−	172.483i	0.155356	−	0.269084i	0.933188	+	0.359387i	$0.117014\pi$
$642$		0			0
$643$			898.859i			1.39791i	0.715164	+	0.698957i	$0.246352\pi$
$643$			898.859i			1.39791i	−0.715164	+	0.698957i	$0.753648\pi$
$644$		0			0
$645$	720.279			1.11671
$646$		0			0
$647$	−334.425	−	193.080i	−0.516885	−	0.298424i	0.218774	−	0.975776i	$-0.429794\pi$
$647$	−334.425	−	193.080i	−0.516885	−	0.298424i	−0.735659	+	0.677352i	$0.763128\pi$
$648$		0			0
$649$	−767.055	+	442.859i	−1.18190	+	0.682372i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−71.7744	−	124.317i	−0.109915	−	0.190378i	0.805821	−	0.592160i	$-0.201724\pi$
$653$	−71.7744	−	124.317i	−0.109915	−	0.190378i	−0.915736	+	0.401781i	$0.868391\pi$
$654$		0			0
$655$	−410.982	+	711.843i	−0.627454	+	1.08678i
$656$		0			0
$657$		−	251.108i		−	0.382204i
$658$		0			0
$659$	−251.484			−0.381614			−0.190807	−	0.981628i	$-0.561110\pi$
$659$	−251.484			−0.381614			−0.190807	+	0.981628i	$0.561110\pi$
$660$		0			0
$661$	317.590	+	183.361i	0.480469	+	0.277399i	0.720612	−	0.693339i	$-0.243861\pi$
$661$	317.590	+	183.361i	0.480469	+	0.277399i	−0.240143	+	0.970737i	$0.577194\pi$
$662$		0			0
$663$	81.0446	−	46.7911i	0.122239	−	0.0705749i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	220.143	+	381.299i	0.330049	+	0.571662i
$668$		0			0
$669$	19.2645	−	33.3671i	0.0287959	−	0.0498760i
$670$		0			0
$671$			279.144i			0.416011i
$672$		0			0
$673$	1082.98			1.60919			0.804593	−	0.593827i	$-0.202383\pi$
$673$	1082.98			1.60919			0.804593	+	0.593827i	$0.202383\pi$
$674$		0			0
$675$	355.090	+	205.012i	0.526060	+	0.303721i
$676$		0			0
$677$	825.842	−	476.800i	1.21986	−	0.704284i	0.254969	−	0.966949i	$-0.417935\pi$
$677$	825.842	−	476.800i	1.21986	−	0.704284i	0.964887	+	0.262665i	$0.0846015\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−179.242	−	310.457i	−0.263205	−	0.455884i
$682$		0			0
$683$	86.9047	−	150.523i	0.127240	−	0.220386i	−0.795367	−	0.606129i	$-0.792722\pi$
$683$	86.9047	−	150.523i	0.127240	−	0.220386i	0.922606	+	0.385743i	$0.126055\pi$
$684$		0			0
$685$		−	723.627i		−	1.05639i
$686$		0			0
$687$	448.291			0.652534
$688$		0			0
$689$	170.532	+	98.4569i	0.247507	+	0.142898i
$690$		0			0
$691$	183.198	−	105.770i	0.265120	−	0.153067i	−0.361548	−	0.932354i	$-0.617752\pi$
$691$	183.198	−	105.770i	0.265120	−	0.153067i	0.626668	+	0.779286i	$0.284418\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	58.9002	+	102.018i	0.0847485	+	0.146789i
$696$		0			0
$697$	886.041	−	1534.67i	1.27122	−	2.20182i
$698$		0			0
$699$			230.318i			0.329496i
$700$		0			0
$701$	−757.766			−1.08098			−0.540489	−	0.841351i	$-0.681761\pi$
$701$	−757.766			−1.08098			−0.540489	+	0.841351i	$0.681761\pi$
$702$		0			0
$703$	73.5127	+	42.4426i	0.104570	+	0.0603735i
$704$		0			0
$705$	−215.216	+	124.255i	−0.305271	+	0.176248i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	231.371	+	400.747i	0.326334	+	0.565228i	0.981782	−	0.190013i	$-0.0608531\pi$
$709$	231.371	+	400.747i	0.326334	+	0.565228i	−0.655447	+	0.755241i	$0.727520\pi$
$710$		0			0
$711$	393.766	−	682.022i	0.553820	−	0.959244i
$712$		0			0
$713$			2051.77i			2.87766i
$714$		0			0
$715$	−218.413			−0.305472
$716$		0			0
$717$	−166.855	−	96.3336i	−0.232712	−	0.134356i
$718$		0			0
$719$	−1087.26	+	627.728i	−1.51218	+	0.873057i	−0.512280	+	0.858818i	$0.671199\pi$
$719$	−1087.26	+	627.728i	−1.51218	+	0.873057i	−0.999899	+	0.0142386i	$0.995468\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	89.7808	+	155.505i	0.124178	+	0.215083i
$724$		0			0
$725$	95.3861	−	165.214i	0.131567	−	0.227881i
$726$		0			0
$727$		−	190.560i		−	0.262118i	−0.991375	−	0.131059i	$-0.958162\pi$
$727$		−	190.560i		−	0.262118i	0.991375	−	0.131059i	$-0.0418377\pi$
$728$		0			0
$729$	−7.37128			−0.0101115
$730$		0			0
$731$	1856.99	+	1072.13i	2.54034	+	1.46667i
$732$		0			0
$733$	−772.778	+	446.164i	−1.05427	+	0.608681i	−0.923841	−	0.382777i	$-0.874968\pi$
$733$	−772.778	+	446.164i	−1.05427	+	0.608681i	−0.130426	+	0.991458i	$0.541635\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	390.775	+	676.842i	0.530224	+	0.918375i
$738$		0			0
$739$	−12.7104	+	22.0151i	−0.0171995	+	0.0297903i	−0.874497	−	0.485031i	$-0.838808\pi$
$739$	−12.7104	+	22.0151i	−0.0171995	+	0.0297903i	0.857298	+	0.514821i	$0.172142\pi$
$740$		0			0
$741$			36.2963i			0.0489828i
$742$		0			0
$743$	−662.948			−0.892258			−0.446129	−	0.894969i	$-0.647198\pi$
$743$	−662.948			−0.892258			−0.446129	+	0.894969i	$0.647198\pi$
$744$		0			0
$745$	621.487	+	358.816i	0.834211	+	0.481632i
$746$		0			0
$747$	67.4527	−	38.9438i	0.0902981	−	0.0521336i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−581.617	−	1007.39i	−0.774457	−	1.34140i	−0.935099	−	0.354386i	$-0.884690\pi$
$751$	−581.617	−	1007.39i	−0.774457	−	1.34140i	0.160642	−	0.987013i	$-0.448643\pi$
$752$		0			0
$753$	−221.983	+	384.486i	−0.294798	+	0.510605i
$754$		0			0
$755$		−	365.935i		−	0.484682i
$756$		0			0
$757$	−670.569			−0.885825			−0.442912	−	0.896565i	$-0.646055\pi$
$757$	−670.569			−0.885825			−0.442912	+	0.896565i	$0.646055\pi$
$758$		0			0
$759$	−634.474	−	366.314i	−0.835934	−	0.482627i
$760$		0			0
$761$	1176.90	−	679.484i	1.54652	−	0.892883i	0.548116	−	0.836403i	$-0.315345\pi$
$761$	1176.90	−	679.484i	1.54652	−	0.892883i	0.998404	−	0.0564807i	$-0.0179880\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	630.851	+	1092.67i	0.824642	+	1.42832i
$766$		0			0
$767$	92.9146	−	160.933i	0.121140	−	0.209821i
$768$		0			0
$769$		−	1174.06i		−	1.52674i	−0.645961	−	0.763370i	$-0.723543\pi$
$769$		−	1174.06i		−	1.52674i	0.645961	−	0.763370i	$-0.276457\pi$
$770$		0			0
$771$	422.828			0.548416
$772$		0			0
$773$	993.811	+	573.777i	1.28565	+	0.742273i	0.977876	−	0.209185i	$-0.0670812\pi$
$773$	993.811	+	573.777i	1.28565	+	0.742273i	0.307778	+	0.951458i	$0.400415\pi$
$774$		0			0
$775$	769.911	−	444.508i	0.993434	−	0.573559i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	343.655	+	595.227i	0.441148	+	0.764091i
$780$		0			0
$781$	107.578	−	186.331i	0.137744	−	0.238579i
$782$		0			0
$783$			220.229i			0.281263i
$784$		0			0
$785$	1459.75			1.85956
$786$		0			0
$787$	788.426	+	455.198i	1.00181	+	0.578397i	0.908784	−	0.417267i	$-0.137012\pi$
$787$	788.426	+	455.198i	1.00181	+	0.578397i	0.0930283	+	0.995663i	$0.470345\pi$
$788$		0			0
$789$	−427.942	+	247.072i	−0.542385	+	0.313146i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−29.2830	−	50.7197i	−0.0369269	−	0.0639592i
$794$		0			0
$795$	332.920	−	576.634i	0.418767	−	0.725326i
$796$		0			0
$797$			1079.02i			1.35386i	0.736050	+	0.676928i	$0.236689\pi$
$797$			1079.02i			1.35386i	−0.736050	+	0.676928i	$0.763311\pi$
$798$		0			0
$799$	−739.813			−0.925924
$800$		0			0
$801$	−724.199	−	418.117i	−0.904119	−	0.521993i
$802$		0			0
$803$	378.952	−	218.788i	0.471920	−	0.272463i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−232.253	−	402.274i	−0.287798	−	0.498481i
$808$		0			0
$809$	−513.659	+	889.683i	−0.634930	+	1.09973i	0.351599	+	0.936151i	$0.385638\pi$
$809$	−513.659	+	889.683i	−0.634930	+	1.09973i	−0.986530	+	0.163581i	$0.947695\pi$
$810$		0			0
$811$		−	984.329i		−	1.21372i	−0.794808	−	0.606861i	$-0.792428\pi$
$811$		−	984.329i		−	1.21372i	0.794808	−	0.606861i	$-0.207572\pi$
$812$		0			0
$813$	382.872			0.470938
$814$		0			0
$815$	−336.556	−	194.311i	−0.412952	−	0.238418i
$816$		0			0
$817$	−720.241	+	415.831i	−0.881568	+	0.508974i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−559.469	−	969.029i	−0.681449	−	1.18030i	−0.974539	−	0.224219i	$-0.928017\pi$
$821$	−559.469	−	969.029i	−0.681449	−	1.18030i	0.293090	−	0.956085i	$-0.405316\pi$
$822$		0			0
$823$	−55.3452	+	95.8607i	−0.0672481	+	0.116477i	−0.897689	−	0.440630i	$-0.854755\pi$
$823$	−55.3452	+	95.8607i	−0.0672481	+	0.116477i	0.830441	+	0.557107i	$0.188089\pi$
$824$		0			0
$825$			317.442i			0.384778i
$826$		0			0
$827$	600.694			0.726353			0.363177	−	0.931720i	$-0.381692\pi$
$827$	600.694			0.726353			0.363177	+	0.931720i	$0.381692\pi$
$828$		0			0
$829$	−910.860	−	525.886i	−1.09875	−	0.634361i	−0.162855	−	0.986650i	$-0.552070\pi$
$829$	−910.860	−	525.886i	−1.09875	−	0.634361i	−0.935891	+	0.352289i	$0.885403\pi$
$830$		0			0
$831$	51.5048	−	29.7363i	0.0619794	−	0.0357838i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	329.471	+	570.661i	0.394576	+	0.683426i
$836$		0			0
$837$	−513.143	+	888.790i	−0.613074	+	1.06188i
$838$		0			0
$839$		−	147.774i		−	0.176131i	−0.996115	−	0.0880656i	$-0.971931\pi$
$839$		−	147.774i		−	0.176131i	0.996115	−	0.0880656i	$-0.0280685\pi$
$840$		0			0
$841$	−738.534			−0.878161
$842$		0			0
$843$	−381.689	−	220.368i	−0.452774	−	0.261409i
$844$		0			0
$845$	−929.448	+	536.617i	−1.09994	+	0.635050i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	330.691	+	572.774i	0.389507	+	0.674645i
$850$		0			0
$851$	179.739	−	311.316i	0.211209	−	0.365824i
$852$		0			0
$853$			773.138i			0.906376i	0.891415	+	0.453188i	$0.149713\pi$
$853$			773.138i			0.906376i	−0.891415	+	0.453188i	$0.850287\pi$
$854$		0			0
$855$	−489.356			−0.572346
$856$		0			0
$857$	−815.454	−	470.803i	−0.951521	−	0.549361i	−0.0579682	−	0.998318i	$-0.518462\pi$
$857$	−815.454	−	470.803i	−0.951521	−	0.549361i	−0.893553	+	0.448957i	$0.851796\pi$
$858$		0			0
$859$	−635.569	+	366.946i	−0.739894	+	0.427178i	−0.822031	−	0.569443i	$-0.807159\pi$
$859$	−635.569	+	366.946i	−0.739894	+	0.427178i	0.0821366	+	0.996621i	$0.473826\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−369.973	−	640.812i	−0.428706	−	0.742540i	0.568053	−	0.822992i	$-0.307697\pi$
$863$	−369.973	−	640.812i	−0.428706	−	0.742540i	−0.996758	+	0.0804519i	$0.974364\pi$
$864$		0			0
$865$	−471.867	+	817.298i	−0.545511	+	0.944853i
$866$		0			0
$867$		−	553.800i		−	0.638754i
$868$		0			0
$869$	1372.34			1.57921
$870$		0			0
$871$	−142.006	−	81.9871i	−0.163038	−	0.0941298i
$872$		0			0
$873$	346.416	−	200.004i	0.396812	−	0.229099i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−253.496	−	439.068i	−0.289049	−	0.500647i	0.684534	−	0.728981i	$-0.260006\pi$
$877$	−253.496	−	439.068i	−0.289049	−	0.500647i	−0.973583	+	0.228334i	$0.926672\pi$
$878$		0			0
$879$	256.422	−	444.135i	0.291720	−	0.505273i
$880$		0			0
$881$			112.813i			0.128052i	0.997948	+	0.0640258i	$0.0203940\pi$
$881$			112.813i			0.128052i	−0.997948	+	0.0640258i	$0.979606\pi$
$882$		0			0
$883$	133.113			0.150751			0.0753754	−	0.997155i	$-0.475984\pi$
$883$	133.113			0.150751			0.0753754	+	0.997155i	$0.475984\pi$
$884$		0			0
$885$	−544.175	−	314.179i	−0.614887	−	0.355005i
$886$		0			0
$887$	423.968	−	244.778i	0.477979	−	0.275962i	−0.241595	−	0.970377i	$-0.577670\pi$
$887$	423.968	−	244.778i	0.477979	−	0.275962i	0.719574	+	0.694416i	$0.244337\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	222.760	+	385.831i	0.250011	+	0.433032i
$892$		0			0
$893$	143.470	−	248.497i	0.160660	−	0.278272i
$894$		0			0
$895$		−	1809.68i		−	2.02199i
$896$		0			0
$897$	153.710			0.171360
$898$		0			0
$899$	413.529	+	238.751i	0.459988	+	0.265574i
$900$		0			0
$901$	1716.64	−	991.100i	1.90526	−	1.10000i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−958.907	−	1660.88i	−1.05957	−	1.83522i
$906$		0			0
$907$	129.603	−	224.480i	0.142892	−	0.247497i	−0.785692	−	0.618617i	$-0.787693\pi$
$907$	129.603	−	224.480i	0.142892	−	0.247497i	0.928585	+	0.371121i	$0.121026\pi$
$908$		0			0
$909$		−	72.2227i		−	0.0794529i
$910$		0			0
$911$	−752.359			−0.825860			−0.412930	−	0.910763i	$-0.635495\pi$
$911$	−752.359			−0.825860			−0.412930	+	0.910763i	$0.635495\pi$
$912$		0			0
$913$	117.542	+	67.8627i	0.128742	+	0.0743293i
$914$		0			0
$915$	−171.502	+	99.0169i	−0.187434	+	0.108215i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−165.480	−	286.619i	−0.180065	−	0.311881i	0.761838	−	0.647768i	$-0.224297\pi$
$919$	−165.480	−	286.619i	−0.180065	−	0.311881i	−0.941902	+	0.335887i	$0.890964\pi$
$920$		0			0
$921$	81.6851	−	141.483i	0.0886918	−	0.153619i
$922$		0			0
$923$			45.1411i			0.0489069i
$924$		0			0
$925$	−155.759			−0.168388
$926$		0			0
$927$	−435.898	−	251.666i	−0.470224	−	0.271484i
$928$		0			0
$929$	−198.797	+	114.775i	−0.213990	+	0.123547i	−0.603164	−	0.797617i	$-0.706094\pi$
$929$	−198.797	+	114.775i	−0.213990	+	0.123547i	0.389174	+	0.921164i	$0.372760\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−358.896	−	621.626i	−0.384669	−	0.666265i
$934$		0			0
$935$	−1099.31	+	1904.06i	−1.17573	+	2.03642i
$936$		0			0
$937$			503.860i			0.537738i	0.963177	+	0.268869i	$0.0866499\pi$
$937$			503.860i			0.537738i	−0.963177	+	0.268869i	$0.913350\pi$
$938$		0			0
$939$	−230.820			−0.245815
$940$		0			0
$941$	−1101.65	−	636.037i	−1.17072	−	0.675916i	−0.216871	−	0.976200i	$-0.569585\pi$
$941$	−1101.65	−	636.037i	−1.17072	−	0.675916i	−0.953850	+	0.300284i	$0.902919\pi$
$942$		0			0
$943$	2520.71	−	1455.33i	2.67307	−	1.54330i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−486.273	−	842.249i	−0.513488	−	0.889387i	−0.999878	−	0.0156447i	$-0.995020\pi$
$947$	−486.273	−	842.249i	−0.513488	−	0.889387i	0.486390	−	0.873742i	$-0.338313\pi$
$948$		0			0
$949$	−45.9031	+	79.5065i	−0.0483700	+	0.0837792i
$950$		0			0
$951$			154.136i			0.162078i
$952$		0			0
$953$	−345.615			−0.362660			−0.181330	−	0.983422i	$-0.558040\pi$
$953$	−345.615			−0.362660			−0.181330	+	0.983422i	$0.558040\pi$
$954$		0			0
$955$	398.942	+	230.330i	0.417741	+	0.241183i
$956$		0			0
$957$	−147.659	+	85.2510i	−0.154294	+	0.0890815i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	632.103	+	1094.83i	0.657755	+	1.13927i
$962$		0			0
$963$	54.0201	−	93.5655i	0.0560956	−	0.0971604i
$964$		0			0
$965$			872.768i			0.904423i
$966$		0			0
$967$	−1385.34			−1.43261			−0.716306	−	0.697786i	$-0.754169\pi$
$967$	−1385.34			−1.43261			−0.716306	+	0.697786i	$0.754169\pi$
$968$		0			0
$969$	316.420	+	182.685i	0.326543	+	0.188530i
$970$		0			0
$971$	−971.573	+	560.938i	−1.00059	+	0.577691i	−0.908423	−	0.418053i	$-0.862713\pi$
$971$	−971.573	+	560.938i	−1.00059	+	0.577691i	−0.0921670	+	0.995744i	$0.529379\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−33.3006	−	57.6783i	−0.0341545	−	0.0591573i
$976$		0			0
$977$	−324.424	+	561.919i	−0.332061	+	0.575147i	−0.982916	−	0.184055i	$-0.941077\pi$
$977$	−324.424	+	561.919i	−0.332061	+	0.575147i	0.650855	+	0.759202i	$0.274411\pi$
$978$		0			0
$979$		−	1457.20i		−	1.48846i
$980$		0			0
$981$	889.643			0.906874
$982$		0			0
$983$	−1657.11	−	956.731i	−1.68576	−	0.973276i	−0.957701	−	0.287767i	$-0.907087\pi$
$983$	−1657.11	−	956.731i	−1.68576	−	0.973276i	−0.728064	−	0.685510i	$-0.759579\pi$
$984$		0			0
$985$	−224.744	+	129.756i	−0.228166	+	0.131732i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1760.99	+	3050.12i	1.78058	+	3.08405i
$990$		0			0
$991$	−121.984	+	211.283i	−0.123092	+	0.213202i	−0.920986	−	0.389597i	$-0.872614\pi$
$991$	−121.984	+	211.283i	−0.123092	+	0.213202i	0.797894	+	0.602798i	$0.205948\pi$
$992$		0			0
$993$		−	112.861i		−	0.113657i
$994$		0			0
$995$	−1923.09			−1.93275
$996$		0			0
$997$	−333.075	−	192.301i	−0.334077	−	0.192880i	0.323573	−	0.946203i	$-0.395116\pi$
$997$	−333.075	−	192.301i	−0.334077	−	0.192880i	−0.657650	+	0.753324i	$0.728449\pi$
$998$		0			0
$999$	155.719	−	89.9043i	0.155875	−	0.0899943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.o.d.129.4		16
4.3	odd	2		784.3.s.k.129.5		16
7.2	even	3	inner	392.3.o.d.313.5		16
7.3	odd	6		392.3.c.b.97.4	✓	8
7.4	even	3		392.3.c.b.97.5	yes	8
7.5	odd	6	inner	392.3.o.d.313.4		16
7.6	odd	2	inner	392.3.o.d.129.5		16
21.11	odd	6		3528.3.f.e.2449.7		8
21.17	even	6		3528.3.f.e.2449.2		8
28.3	even	6		784.3.c.g.97.5		8
28.11	odd	6		784.3.c.g.97.4		8
28.19	even	6		784.3.s.k.705.5		16
28.23	odd	6		784.3.s.k.705.4		16
28.27	even	2		784.3.s.k.129.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.3.c.b.97.4	✓	8	7.3	odd	6
392.3.c.b.97.5	yes	8	7.4	even	3
392.3.o.d.129.4		16	1.1	even	1	trivial
392.3.o.d.129.5		16	7.6	odd	2	inner
392.3.o.d.313.4		16	7.5	odd	6	inner
392.3.o.d.313.5		16	7.2	even	3	inner
784.3.c.g.97.4		8	28.11	odd	6
784.3.c.g.97.5		8	28.3	even	6
784.3.s.k.129.4		16	28.27	even	2
784.3.s.k.129.5		16	4.3	odd	2
784.3.s.k.705.4		16	28.23	odd	6
784.3.s.k.705.5		16	28.19	even	6
3528.3.f.e.2449.2		8	21.17	even	6
3528.3.f.e.2449.7		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.16338 - 0.671680i) q^{3} +(-5.73452 + 3.31082i) q^{5} +(-3.59769 - 6.23139i) q^{9} +O(q^{10})\)	\(q+(-1.16338 - 0.671680i) q^{3} +(-5.73452 + 3.31082i) q^{5} +(-3.59769 - 6.23139i) q^{9} +(6.26927 - 10.8587i) q^{11} +2.63066i q^{13} +8.89526 q^{15} +(22.9333 + 13.2406i) q^{17} +(-8.89479 + 5.13541i) q^{19} +(21.7478 + 37.6682i) q^{23} +(9.42312 - 16.3213i) q^{25} +21.7562i q^{27} +10.1226 q^{29} +(40.8522 + 23.5860i) q^{31} +(-14.5871 + 8.42188i) q^{33} +(-4.13235 - 7.15744i) q^{37} +(1.76696 - 3.06047i) q^{39} -66.9187i q^{41} +80.9734 q^{43} +(41.2621 + 23.8227i) q^{45} +(-24.1945 + 13.9687i) q^{47} +(-17.7868 - 30.8077i) q^{51} +(37.4267 - 64.8249i) q^{53} +83.0258i q^{55} +13.7974 q^{57} +(-61.1758 - 35.3199i) q^{59} +(-19.2802 + 11.1314i) q^{61} +(-8.70966 - 15.0856i) q^{65} +(-31.1659 + 53.9810i) q^{67} -58.4301i q^{69} +17.1596 q^{71} +(30.2230 + 17.4493i) q^{73} +(-21.9254 + 12.6586i) q^{75} +(54.7248 + 94.7861i) q^{79} +(-17.7660 + 30.7716i) q^{81} +10.8247i q^{83} -175.349 q^{85} +(-11.7764 - 6.79912i) q^{87} +(100.648 - 58.1090i) q^{89} +(-31.6845 - 54.8792i) q^{93} +(34.0049 - 58.8982i) q^{95} +55.5922i q^{97} -90.2196 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 64 q^{9}+O(q^{10}) \) 16 * q + 64 * q^9	\( 16 q + 64 q^{9} + 24 q^{11} + 80 q^{15} + 136 q^{23} + 80 q^{25} + 128 q^{29} + 64 q^{37} + 376 q^{39} + 272 q^{43} + 408 q^{51} + 104 q^{53} - 480 q^{57} - 224 q^{65} + 16 q^{67} + 704 q^{71} + 112 q^{79} - 584 q^{81} + 400 q^{85} - 784 q^{93} - 120 q^{95} - 1760 q^{99}+O(q^{100}) \) 16 * q + 64 * q^9 + 24 * q^11 + 80 * q^15 + 136 * q^23 + 80 * q^25 + 128 * q^29 + 64 * q^37 + 376 * q^39 + 272 * q^43 + 408 * q^51 + 104 * q^53 - 480 * q^57 - 224 * q^65 + 16 * q^67 + 704 * q^71 + 112 * q^79 - 584 * q^81 + 400 * q^85 - 784 * q^93 - 120 * q^95 - 1760 * q^99

Introduction

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