LMFDB - Embedded newform 384.4.j.b.97.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,4,Mod(97,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("384.97");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	384.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$22.6567334422$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.10
Character	$\chi$	$=$	384.97
Dual form			384.4.j.b.289.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.12132 - 2.12132i) q^{3} +(-3.22588 - 3.22588i) q^{5} +24.6080i q^{7} -9.00000i q^{9} +O(q^{10})$	\(q+(2.12132 - 2.12132i) q^{3} +(-3.22588 - 3.22588i) q^{5} +24.6080i q^{7} -9.00000i q^{9} +(-23.7522 - 23.7522i) q^{11} +(18.6720 - 18.6720i) q^{13} -13.6863 q^{15} -3.55065 q^{17} +(109.089 - 109.089i) q^{19} +(52.2014 + 52.2014i) q^{21} -36.5653i q^{23} -104.187i q^{25} +(-19.0919 - 19.0919i) q^{27} +(-68.8087 + 68.8087i) q^{29} +306.914 q^{31} -100.772 q^{33} +(79.3824 - 79.3824i) q^{35} +(-92.9951 - 92.9951i) q^{37} -79.2188i q^{39} -385.594i q^{41} +(-150.610 - 150.610i) q^{43} +(-29.0329 + 29.0329i) q^{45} -114.406 q^{47} -262.553 q^{49} +(-7.53207 + 7.53207i) q^{51} +(-451.631 - 451.631i) q^{53} +153.243i q^{55} -462.824i q^{57} +(544.327 + 544.327i) q^{59} +(-179.921 + 179.921i) q^{61} +221.472 q^{63} -120.468 q^{65} +(283.133 - 283.133i) q^{67} +(-77.5666 - 77.5666i) q^{69} -930.296i q^{71} +701.187i q^{73} +(-221.015 - 221.015i) q^{75} +(584.494 - 584.494i) q^{77} +779.471 q^{79} -81.0000 q^{81} +(296.734 - 296.734i) q^{83} +(11.4540 + 11.4540i) q^{85} +291.931i q^{87} +865.485i q^{89} +(459.481 + 459.481i) q^{91} +(651.062 - 651.062i) q^{93} -703.813 q^{95} -542.420 q^{97} +(-213.770 + 213.770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q + 40 q^{11} + 120 q^{15} - 24 q^{19} - 400 q^{29} - 744 q^{31} + 456 q^{35} - 16 q^{37} - 1240 q^{43} - 1176 q^{49} - 744 q^{51} - 752 q^{53} + 1376 q^{59} + 912 q^{61} - 504 q^{63} + 976 q^{65} + 2256 q^{67} + 528 q^{69} - 1104 q^{75} - 1904 q^{77} + 5992 q^{79} - 1944 q^{81} - 2680 q^{83} + 240 q^{85} + 3496 q^{91} - 7728 q^{95} + 360 q^{99}+O(q^{100}) $ 24 * q + 40 * q^11 + 120 * q^15 - 24 * q^19 - 400 * q^29 - 744 * q^31 + 456 * q^35 - 16 * q^37 - 1240 * q^43 - 1176 * q^49 - 744 * q^51 - 752 * q^53 + 1376 * q^59 + 912 * q^61 - 504 * q^63 + 976 * q^65 + 2256 * q^67 + 528 * q^69 - 1104 * q^75 - 1904 * q^77 + 5992 * q^79 - 1944 * q^81 - 2680 * q^83 + 240 * q^85 + 3496 * q^91 - 7728 * q^95 + 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$3$	2.12132	−	2.12132i	0.408248	−	0.408248i
$4$		0			0
$5$	−3.22588	−	3.22588i	−0.288531	−	0.288531i	0.547968	−	0.836499i	$-0.315402\pi$
$5$	−3.22588	−	3.22588i	−0.288531	−	0.288531i	−0.836499	+	0.547968i	$0.815402\pi$
$6$		0			0
$7$			24.6080i			1.32871i	0.747419	+	0.664353i	$0.231293\pi$
$7$			24.6080i			1.32871i	−0.747419	+	0.664353i	$0.768707\pi$
$8$		0			0
$9$		−	9.00000i		−	0.333333i
$10$		0			0
$11$	−23.7522	−	23.7522i	−0.651051	−	0.651051i	0.302195	−	0.953246i	$-0.402280\pi$
$11$	−23.7522	−	23.7522i	−0.651051	−	0.651051i	−0.953246	+	0.302195i	$0.902280\pi$
$12$		0			0
$13$	18.6720	−	18.6720i	0.398361	−	0.398361i	−0.479294	−	0.877655i	$-0.659107\pi$
$13$	18.6720	−	18.6720i	0.398361	−	0.398361i	0.877655	+	0.479294i	$0.159107\pi$
$14$		0			0
$15$	−13.6863			−0.235585
$16$		0			0
$17$	−3.55065			−0.0506565			−0.0253282	−	0.999679i	$-0.508063\pi$
$17$	−3.55065			−0.0506565			−0.0253282	+	0.999679i	$0.508063\pi$
$18$		0			0
$19$	109.089	−	109.089i	1.31719	−	1.31719i	0.401202	−	0.915990i	$-0.368593\pi$
$19$	109.089	−	109.089i	1.31719	−	1.31719i	0.915990	−	0.401202i	$-0.131407\pi$
$20$		0			0
$21$	52.2014	+	52.2014i	0.542442	+	0.542442i
$22$		0			0
$23$		−	36.5653i		−	0.331495i	−0.986168	−	0.165747i	$-0.946996\pi$
$23$		−	36.5653i		−	0.331495i	0.986168	−	0.165747i	$-0.0530037\pi$
$24$		0			0
$25$		−	104.187i		−	0.833499i
$26$		0			0
$27$	−19.0919	−	19.0919i	−0.136083	−	0.136083i
$28$		0			0
$29$	−68.8087	+	68.8087i	−0.440602	+	0.440602i	−0.892214	−	0.451612i	$-0.850849\pi$
$29$	−68.8087	+	68.8087i	−0.440602	+	0.440602i	0.451612	+	0.892214i	$0.350849\pi$
$30$		0			0
$31$	306.914			1.77817			0.889086	−	0.457740i	$-0.151341\pi$
$31$	306.914			1.77817			0.889086	+	0.457740i	$0.151341\pi$
$32$		0			0
$33$	−100.772			−0.531581
$34$		0			0
$35$	79.3824	−	79.3824i	0.383374	−	0.383374i
$36$		0			0
$37$	−92.9951	−	92.9951i	−0.413197	−	0.413197i	0.469654	−	0.882851i	$-0.344379\pi$
$37$	−92.9951	−	92.9951i	−0.413197	−	0.413197i	−0.882851	+	0.469654i	$0.844379\pi$
$38$		0			0
$39$		−	79.2188i		−	0.325260i
$40$		0			0
$41$		−	385.594i		−	1.46877i	−0.678732	−	0.734386i	$-0.737470\pi$
$41$		−	385.594i		−	1.46877i	0.678732	−	0.734386i	$-0.262530\pi$
$42$		0			0
$43$	−150.610	−	150.610i	−0.534135	−	0.534135i	0.387665	−	0.921800i	$-0.373282\pi$
$43$	−150.610	−	150.610i	−0.534135	−	0.534135i	−0.921800	+	0.387665i	$0.873282\pi$
$44$		0			0
$45$	−29.0329	+	29.0329i	−0.0961772	+	0.0961772i
$46$		0			0
$47$	−114.406			−0.355060			−0.177530	−	0.984115i	$-0.556811\pi$
$47$	−114.406			−0.355060			−0.177530	+	0.984115i	$0.556811\pi$
$48$		0			0
$49$	−262.553			−0.765460
$50$		0			0
$51$	−7.53207	+	7.53207i	−0.0206804	+	0.0206804i
$52$		0			0
$53$	−451.631	−	451.631i	−1.17050	−	1.17050i	−0.982092	−	0.188404i	$-0.939669\pi$
$53$	−451.631	−	451.631i	−1.17050	−	1.17050i	−0.188404	−	0.982092i	$-0.560331\pi$
$54$		0			0
$55$			153.243i			0.375697i
$56$		0			0
$57$		−	462.824i		−	1.07548i
$58$		0			0
$59$	544.327	+	544.327i	1.20111	+	1.20111i	0.973830	+	0.227276i	$0.0729819\pi$
$59$	544.327	+	544.327i	1.20111	+	1.20111i	0.227276	+	0.973830i	$0.427018\pi$
$60$		0			0
$61$	−179.921	+	179.921i	−0.377647	+	0.377647i	−0.870253	−	0.492605i	$-0.836045\pi$
$61$	−179.921	+	179.921i	−0.377647	+	0.377647i	0.492605	+	0.870253i	$0.336045\pi$
$62$		0			0
$63$	221.472			0.442902
$64$		0			0
$65$	−120.468			−0.229879
$66$		0			0
$67$	283.133	−	283.133i	0.516272	−	0.516272i	−0.400170	−	0.916441i	$-0.631049\pi$
$67$	283.133	−	283.133i	0.516272	−	0.516272i	0.916441	+	0.400170i	$0.131049\pi$
$68$		0			0
$69$	−77.5666	−	77.5666i	−0.135332	−	0.135332i
$70$		0			0
$71$		−	930.296i		−	1.55501i	−0.628876	−	0.777505i	$-0.716485\pi$
$71$		−	930.296i		−	1.55501i	0.628876	−	0.777505i	$-0.283515\pi$
$72$		0			0
$73$			701.187i			1.12422i	0.827064	+	0.562108i	$0.190009\pi$
$73$			701.187i			1.12422i	−0.827064	+	0.562108i	$0.809991\pi$
$74$		0			0
$75$	−221.015	−	221.015i	−0.340275	−	0.340275i
$76$		0			0
$77$	584.494	−	584.494i	0.865055	−	0.865055i
$78$		0			0
$79$	779.471			1.11009			0.555046	−	0.831819i	$-0.312701\pi$
$79$	779.471			1.11009			0.555046	+	0.831819i	$0.312701\pi$
$80$		0			0
$81$	−81.0000			−0.111111
$82$		0			0
$83$	296.734	−	296.734i	0.392419	−	0.392419i	−0.483129	−	0.875549i	$-0.660500\pi$
$83$	296.734	−	296.734i	0.392419	−	0.392419i	0.875549	+	0.483129i	$0.160500\pi$
$84$		0			0
$85$	11.4540	+	11.4540i	0.0146160	+	0.0146160i
$86$		0			0
$87$			291.931i			0.359750i
$88$		0			0
$89$			865.485i			1.03080i	0.856950	+	0.515400i	$0.172357\pi$
$89$			865.485i			1.03080i	−0.856950	+	0.515400i	$0.827643\pi$
$90$		0			0
$91$	459.481	+	459.481i	0.529305	+	0.529305i
$92$		0			0
$93$	651.062	−	651.062i	0.725936	−	0.725936i
$94$		0			0
$95$	−703.813			−0.760103
$96$		0			0
$97$	−542.420			−0.567778			−0.283889	−	0.958857i	$-0.591625\pi$
$97$	−542.420			−0.567778			−0.283889	+	0.958857i	$0.591625\pi$
$98$		0			0
$99$	−213.770	+	213.770i	−0.217017	+	0.217017i
$100$		0			0
$101$	−1109.76	−	1109.76i	−1.09331	−	1.09331i	−0.995172	−	0.0981421i	$-0.968710\pi$
$101$	−1109.76	−	1109.76i	−1.09331	−	1.09331i	−0.0981421	−	0.995172i	$-0.531290\pi$
$102$		0			0
$103$		−	806.968i		−	0.771970i	−0.922505	−	0.385985i	$-0.873862\pi$
$103$		−	806.968i		−	0.771970i	0.922505	−	0.385985i	$-0.126138\pi$
$104$		0			0
$105$		−	336.791i		−	0.313023i
$106$		0			0
$107$	−345.828	−	345.828i	−0.312453	−	0.312453i	0.533406	−	0.845859i	$-0.320912\pi$
$107$	−345.828	−	345.828i	−0.312453	−	0.312453i	−0.845859	+	0.533406i	$0.820912\pi$
$108$		0			0
$109$	−251.854	+	251.854i	−0.221314	+	0.221314i	−0.809052	−	0.587738i	$-0.800019\pi$
$109$	−251.854	+	251.854i	−0.221314	+	0.221314i	0.587738	+	0.809052i	$0.300019\pi$
$110$		0			0
$111$	−394.545			−0.337374
$112$		0			0
$113$	1692.35			1.40888			0.704439	−	0.709764i	$-0.251199\pi$
$113$	1692.35			1.40888			0.704439	+	0.709764i	$0.251199\pi$
$114$		0			0
$115$	−117.955	+	117.955i	−0.0956467	+	0.0956467i
$116$		0			0
$117$	−168.048	−	168.048i	−0.132787	−	0.132787i
$118$		0			0
$119$		−	87.3744i		−	0.0673076i
$120$		0			0
$121$		−	202.667i		−	0.152266i
$122$		0			0
$123$	−817.968	−	817.968i	−0.599624	−	0.599624i
$124$		0			0
$125$	−739.331	+	739.331i	−0.529022	+	0.529022i
$126$		0			0
$127$	507.618			0.354676			0.177338	−	0.984150i	$-0.443251\pi$
$127$	507.618			0.354676			0.177338	+	0.984150i	$0.443251\pi$
$128$		0			0
$129$	−638.984			−0.436119
$130$		0			0
$131$	−848.697	+	848.697i	−0.566038	+	0.566038i	−0.931016	−	0.364978i	$-0.881076\pi$
$131$	−848.697	+	848.697i	−0.566038	+	0.566038i	0.364978	+	0.931016i	$0.381076\pi$
$132$		0			0
$133$	2684.45	+	2684.45i	1.75016	+	1.75016i
$134$		0			0
$135$			123.176i			0.0785283i
$136$		0			0
$137$		−	784.731i		−	0.489373i	−0.969602	−	0.244687i	$-0.921315\pi$
$137$		−	784.731i		−	0.489373i	0.969602	−	0.244687i	$-0.0786851\pi$
$138$		0			0
$139$	1487.40	+	1487.40i	0.907623	+	0.907623i	0.996080	−	0.0884574i	$-0.0281937\pi$
$139$	1487.40	+	1487.40i	0.907623	+	0.907623i	−0.0884574	+	0.996080i	$0.528194\pi$
$140$		0			0
$141$	−242.692	+	242.692i	−0.144953	+	0.144953i
$142$		0			0
$143$	−887.004			−0.518706
$144$		0			0
$145$	443.937			0.254255
$146$		0			0
$147$	−556.959	+	556.959i	−0.312498	+	0.312498i
$148$		0			0
$149$	1440.83	+	1440.83i	0.792199	+	0.792199i	0.981851	−	0.189652i	$-0.0607360\pi$
$149$	1440.83	+	1440.83i	0.792199	+	0.792199i	−0.189652	+	0.981851i	$0.560736\pi$
$150$		0			0
$151$			1416.10i			0.763180i	0.924332	+	0.381590i	$0.124623\pi$
$151$			1416.10i			0.763180i	−0.924332	+	0.381590i	$0.875377\pi$
$152$		0			0
$153$			31.9559i			0.0168855i
$154$		0			0
$155$	−990.067	−	990.067i	−0.513059	−	0.513059i
$156$		0			0
$157$	−1700.27	+	1700.27i	−0.864309	+	0.864309i	−0.991835	−	0.127526i	$-0.959296\pi$
$157$	−1700.27	+	1700.27i	−0.864309	+	0.864309i	0.127526	+	0.991835i	$0.459296\pi$
$158$		0			0
$159$	−1916.11			−0.955706
$160$		0			0
$161$	899.797			0.440459
$162$		0			0
$163$	1041.45	−	1041.45i	0.500445	−	0.500445i	−0.411131	−	0.911576i	$-0.634866\pi$
$163$	1041.45	−	1041.45i	0.500445	−	0.500445i	0.911576	+	0.411131i	$0.134866\pi$
$164$		0			0
$165$	325.078	+	325.078i	0.153378	+	0.153378i
$166$		0			0
$167$			3044.20i			1.41058i	0.708917	+	0.705292i	$0.249184\pi$
$167$			3044.20i			1.41058i	−0.708917	+	0.705292i	$0.750816\pi$
$168$		0			0
$169$			1499.71i			0.682617i
$170$		0			0
$171$	−981.797	−	981.797i	−0.439064	−	0.439064i
$172$		0			0
$173$	1410.58	−	1410.58i	0.619912	−	0.619912i	−0.325597	−	0.945509i	$-0.605565\pi$
$173$	1410.58	−	1410.58i	0.619912	−	0.619912i	0.945509	+	0.325597i	$0.105565\pi$
$174$		0			0
$175$	2563.84			1.10748
$176$		0			0
$177$	2309.38			0.980699
$178$		0			0
$179$	−2160.33	+	2160.33i	−0.902069	+	0.902069i	−0.995615	−	0.0935459i	$-0.970180\pi$
$179$	−2160.33	+	2160.33i	−0.902069	+	0.902069i	0.0935459	+	0.995615i	$0.470180\pi$
$180$		0			0
$181$	214.307	+	214.307i	0.0880074	+	0.0880074i	0.749740	−	0.661733i	$-0.230179\pi$
$181$	214.307	+	214.307i	0.0880074	+	0.0880074i	−0.661733	+	0.749740i	$0.730179\pi$
$182$		0			0
$183$			763.339i			0.308348i
$184$		0			0
$185$			599.982i			0.238441i
$186$		0			0
$187$	84.3358	+	84.3358i	0.0329799	+	0.0329799i
$188$		0			0
$189$	469.813	−	469.813i	0.180814	−	0.180814i
$190$		0			0
$191$	−3267.16			−1.23772			−0.618858	−	0.785503i	$-0.712404\pi$
$191$	−3267.16			−1.23772			−0.618858	+	0.785503i	$0.712404\pi$
$192$		0			0
$193$	−694.819			−0.259141			−0.129570	−	0.991570i	$-0.541360\pi$
$193$	−694.819			−0.259141			−0.129570	+	0.991570i	$0.541360\pi$
$194$		0			0
$195$	−255.550	+	255.550i	−0.0938479	+	0.0938479i
$196$		0			0
$197$	597.455	+	597.455i	0.216076	+	0.216076i	0.806842	−	0.590767i	$-0.201175\pi$
$197$	597.455	+	597.455i	0.216076	+	0.216076i	−0.590767	+	0.806842i	$0.701175\pi$
$198$		0			0
$199$			3359.58i			1.19676i	0.801214	+	0.598378i	$0.204188\pi$
$199$			3359.58i			1.19676i	−0.801214	+	0.598378i	$0.795812\pi$
$200$		0			0
$201$		−	1201.23i		−	0.421534i
$202$		0			0
$203$	−1693.24	−	1693.24i	−0.585431	−	0.585431i
$204$		0			0
$205$	−1243.88	+	1243.88i	−0.423787	+	0.423787i
$206$		0			0
$207$	−329.087			−0.110498
$208$		0			0
$209$	−5182.19			−1.71512
$210$		0			0
$211$	−1339.88	+	1339.88i	−0.437161	+	0.437161i	−0.891055	−	0.453894i	$-0.850034\pi$
$211$	−1339.88	+	1339.88i	−0.437161	+	0.437161i	0.453894	+	0.891055i	$0.350034\pi$
$212$		0			0
$213$	−1973.45	−	1973.45i	−0.634831	−	0.634831i
$214$		0			0
$215$			971.699i			0.308230i
$216$		0			0
$217$			7552.53i			2.36267i
$218$		0			0
$219$	1487.44	+	1487.44i	0.458959	+	0.458959i
$220$		0			0
$221$	−66.2980	+	66.2980i	−0.0201796	+	0.0201796i
$222$		0			0
$223$	−2495.66			−0.749424			−0.374712	−	0.927141i	$-0.622258\pi$
$223$	−2495.66			−0.749424			−0.374712	+	0.927141i	$0.622258\pi$
$224$		0			0
$225$	−937.687			−0.277833
$226$		0			0
$227$	1729.68	−	1729.68i	0.505741	−	0.505741i	−0.407475	−	0.913216i	$-0.633591\pi$
$227$	1729.68	−	1729.68i	0.505741	−	0.505741i	0.913216	+	0.407475i	$0.133591\pi$
$228$		0			0
$229$	1283.18	+	1283.18i	0.370284	+	0.370284i	0.867581	−	0.497296i	$-0.165674\pi$
$229$	1283.18	+	1283.18i	0.370284	+	0.370284i	−0.497296	+	0.867581i	$0.665674\pi$
$230$		0			0
$231$		−	2479.80i		−	0.706314i
$232$		0			0
$233$		−	6515.45i		−	1.83194i	−0.401252	−	0.915968i	$-0.631425\pi$
$233$		−	6515.45i		−	1.83194i	0.401252	−	0.915968i	$-0.368575\pi$
$234$		0			0
$235$	369.060	+	369.060i	0.102446	+	0.102446i
$236$		0			0
$237$	1653.51	−	1653.51i	0.453193	−	0.453193i
$238$		0			0
$239$	761.174			0.206009			0.103005	−	0.994681i	$-0.467154\pi$
$239$	761.174			0.206009			0.103005	+	0.994681i	$0.467154\pi$
$240$		0			0
$241$	6225.86			1.66408			0.832040	−	0.554716i	$-0.187173\pi$
$241$	6225.86			1.66408			0.832040	+	0.554716i	$0.187173\pi$
$242$		0			0
$243$	−171.827	+	171.827i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	846.964	+	846.964i	0.220859	+	0.220859i
$246$		0			0
$247$		−	4073.81i		−	1.04944i
$248$		0			0
$249$		−	1258.94i		−	0.320409i
$250$		0			0
$251$	275.380	+	275.380i	0.0692502	+	0.0692502i	0.740884	−	0.671633i	$-0.234407\pi$
$251$	275.380	+	275.380i	0.0692502	+	0.0692502i	−0.671633	+	0.740884i	$0.734407\pi$
$252$		0			0
$253$	−868.505	+	868.505i	−0.215820	+	0.215820i
$254$		0			0
$255$	48.5951			0.0119339
$256$		0			0
$257$	1993.21			0.483786			0.241893	−	0.970303i	$-0.422232\pi$
$257$	1993.21			0.483786			0.241893	+	0.970303i	$0.422232\pi$
$258$		0			0
$259$	2288.42	−	2288.42i	0.549018	−	0.549018i
$260$		0			0
$261$	619.279	+	619.279i	0.146867	+	0.146867i
$262$		0			0
$263$		−	4385.21i		−	1.02815i	−0.857745	−	0.514075i	$-0.828135\pi$
$263$		−	4385.21i		−	1.02815i	0.857745	−	0.514075i	$-0.171865\pi$
$264$		0			0
$265$			2913.81i			0.675450i
$266$		0			0
$267$	1835.97	+	1835.97i	0.420823	+	0.420823i
$268$		0			0
$269$	1683.14	−	1683.14i	0.381498	−	0.381498i	−0.490144	−	0.871642i	$-0.663056\pi$
$269$	1683.14	−	1683.14i	0.381498	−	0.381498i	0.871642	+	0.490144i	$0.163056\pi$
$270$		0			0
$271$	2381.69			0.533866			0.266933	−	0.963715i	$-0.413990\pi$
$271$	2381.69			0.533866			0.266933	+	0.963715i	$0.413990\pi$
$272$		0			0
$273$	1949.41			0.432176
$274$		0			0
$275$	−2474.68	+	2474.68i	−0.542650	+	0.542650i
$276$		0			0
$277$	−5711.88	−	5711.88i	−1.23897	−	1.23897i	−0.960424	−	0.278543i	$-0.910148\pi$
$277$	−5711.88	−	5711.88i	−1.23897	−	1.23897i	−0.278543	−	0.960424i	$-0.589852\pi$
$278$		0			0
$279$		−	2762.22i		−	0.592724i
$280$		0			0
$281$			1996.19i			0.423781i	0.977293	+	0.211890i	$0.0679620\pi$
$281$			1996.19i			0.423781i	−0.977293	+	0.211890i	$0.932038\pi$
$282$		0			0
$283$	1457.11	+	1457.11i	0.306065	+	0.306065i	0.843381	−	0.537316i	$-0.180562\pi$
$283$	1457.11	+	1457.11i	0.306065	+	0.306065i	−0.537316	+	0.843381i	$0.680562\pi$
$284$		0			0
$285$	−1493.01	+	1493.01i	−0.310311	+	0.310311i
$286$		0			0
$287$	9488.69			1.95157
$288$		0			0
$289$	−4900.39			−0.997434
$290$		0			0
$291$	−1150.65	+	1150.65i	−0.231794	+	0.231794i
$292$		0			0
$293$	1542.07	+	1542.07i	0.307470	+	0.307470i	0.843927	−	0.536458i	$-0.180238\pi$
$293$	1542.07	+	1542.07i	0.307470	+	0.307470i	−0.536458	+	0.843927i	$0.680238\pi$
$294$		0			0
$295$		−	3511.86i		−	0.693114i
$296$		0			0
$297$			906.948i			0.177194i
$298$		0			0
$299$	−682.748	−	682.748i	−0.132055	−	0.132055i
$300$		0			0
$301$	3706.21	−	3706.21i	0.709708	−	0.709708i
$302$		0			0
$303$	−4708.29			−0.892688
$304$		0			0
$305$	1160.81			0.217926
$306$		0			0
$307$	3256.35	−	3256.35i	0.605373	−	0.605373i	−0.336360	−	0.941733i	$-0.609196\pi$
$307$	3256.35	−	3256.35i	0.605373	−	0.605373i	0.941733	+	0.336360i	$0.109196\pi$
$308$		0			0
$309$	−1711.84	−	1711.84i	−0.315156	−	0.315156i
$310$		0			0
$311$		−	1839.43i		−	0.335384i	−0.985839	−	0.167692i	$-0.946369\pi$
$311$		−	1839.43i		−	0.335384i	0.985839	−	0.167692i	$-0.0536314\pi$
$312$		0			0
$313$		−	3421.32i		−	0.617841i	−0.951088	−	0.308921i	$-0.900032\pi$
$313$		−	3421.32i		−	0.617841i	0.951088	−	0.308921i	$-0.0999678\pi$
$314$		0			0
$315$	−714.442	−	714.442i	−0.127791	−	0.127791i
$316$		0			0
$317$	−729.653	+	729.653i	−0.129279	+	0.129279i	−0.768786	−	0.639507i	$-0.779139\pi$
$317$	−729.653	+	729.653i	−0.129279	+	0.129279i	0.639507	+	0.768786i	$0.279139\pi$
$318$		0			0
$319$	3268.72			0.573708
$320$		0			0
$321$	−1467.22			−0.255117
$322$		0			0
$323$	−387.336	+	387.336i	−0.0667243	+	0.0667243i
$324$		0			0
$325$	−1945.39	−	1945.39i	−0.332034	−	0.332034i
$326$		0			0
$327$			1068.52i			0.180702i
$328$		0			0
$329$		−	2815.30i		−	0.471771i
$330$		0			0
$331$	2768.78	+	2768.78i	0.459776	+	0.459776i	0.898582	−	0.438806i	$-0.144598\pi$
$331$	2768.78	+	2768.78i	0.459776	+	0.459776i	−0.438806	+	0.898582i	$0.644598\pi$
$332$		0			0
$333$	−836.956	+	836.956i	−0.137732	+	0.137732i
$334$		0			0
$335$	−1826.71			−0.297921
$336$		0			0
$337$	−2334.75			−0.377394			−0.188697	−	0.982035i	$-0.560426\pi$
$337$	−2334.75			−0.377394			−0.188697	+	0.982035i	$0.560426\pi$
$338$		0			0
$339$	3590.03	−	3590.03i	0.575172	−	0.575172i
$340$		0			0
$341$	−7289.88	−	7289.88i	−1.15768	−	1.15768i
$342$		0			0
$343$			1979.64i			0.311634i
$344$		0			0
$345$			500.441i			0.0780952i
$346$		0			0
$347$	−1047.15	−	1047.15i	−0.161999	−	0.161999i	0.621453	−	0.783452i	$-0.286543\pi$
$347$	−1047.15	−	1047.15i	−0.161999	−	0.161999i	−0.783452	+	0.621453i	$0.786543\pi$
$348$		0			0
$349$	−692.953	+	692.953i	−0.106284	+	0.106284i	−0.758249	−	0.651965i	$-0.773945\pi$
$349$	−692.953	+	692.953i	−0.106284	+	0.106284i	0.651965	+	0.758249i	$0.273945\pi$
$350$		0			0
$351$	−712.969			−0.108420
$352$		0			0
$353$	−11254.7			−1.69695			−0.848477	−	0.529233i	$-0.822480\pi$
$353$	−11254.7			−1.69695			−0.848477	+	0.529233i	$0.822480\pi$
$354$		0			0
$355$	−3001.02	+	3001.02i	−0.448670	+	0.448670i
$356$		0			0
$357$	−185.349	−	185.349i	−0.0274782	−	0.0274782i
$358$		0			0
$359$			3855.05i			0.566746i	0.959010	+	0.283373i	$0.0914534\pi$
$359$			3855.05i			0.566746i	−0.959010	+	0.283373i	$0.908547\pi$
$360$		0			0
$361$		−	16941.6i		−	2.46999i
$362$		0			0
$363$	−429.921	−	429.921i	−0.0621625	−	0.0621625i
$364$		0			0
$365$	2261.95	−	2261.95i	0.324372	−	0.324372i
$366$		0			0
$367$	−1173.47			−0.166907			−0.0834534	−	0.996512i	$-0.526595\pi$
$367$	−1173.47			−0.166907			−0.0834534	+	0.996512i	$0.526595\pi$
$368$		0			0
$369$	−3470.35			−0.489591
$370$		0			0
$371$	11113.7	−	11113.7i	1.55525	−	1.55525i
$372$		0			0
$373$	−1645.82	−	1645.82i	−0.228464	−	0.228464i	0.583587	−	0.812051i	$-0.301649\pi$
$373$	−1645.82	−	1645.82i	−0.228464	−	0.228464i	−0.812051	+	0.583587i	$0.801649\pi$
$374$		0			0
$375$			3136.72i			0.431945i
$376$		0			0
$377$			2569.60i			0.351037i
$378$		0			0
$379$	−1829.15	−	1829.15i	−0.247908	−	0.247908i	0.572204	−	0.820111i	$-0.306089\pi$
$379$	−1829.15	−	1829.15i	−0.247908	−	0.247908i	−0.820111	+	0.572204i	$0.806089\pi$
$380$		0			0
$381$	1076.82	−	1076.82i	0.144796	−	0.144796i
$382$		0			0
$383$	3425.39			0.456995			0.228498	−	0.973544i	$-0.426619\pi$
$383$	3425.39			0.456995			0.228498	+	0.973544i	$0.426619\pi$
$384$		0			0
$385$	−3771.01			−0.499191
$386$		0			0
$387$	−1355.49	+	1355.49i	−0.178045	+	0.178045i
$388$		0			0
$389$	6327.26	+	6327.26i	0.824691	+	0.824691i	0.986777	−	0.162086i	$-0.0518221\pi$
$389$	6327.26	+	6327.26i	0.824691	+	0.824691i	−0.162086	+	0.986777i	$0.551822\pi$
$390$		0			0
$391$			129.831i			0.0167924i
$392$		0			0
$393$			3600.72i			0.462168i
$394$		0			0
$395$	−2514.48	−	2514.48i	−0.320297	−	0.320297i
$396$		0			0
$397$	536.835	−	536.835i	0.0678664	−	0.0678664i	−0.672359	−	0.740225i	$-0.734719\pi$
$397$	536.835	−	536.835i	0.0678664	−	0.0678664i	0.740225	+	0.672359i	$0.234719\pi$
$398$		0			0
$399$	11389.2			1.42900
$400$		0			0
$401$	8145.45			1.01437			0.507187	−	0.861836i	$-0.330685\pi$
$401$	8145.45			1.01437			0.507187	+	0.861836i	$0.330685\pi$
$402$		0			0
$403$	5730.71	−	5730.71i	0.708354	−	0.708354i
$404$		0			0
$405$	261.296	+	261.296i	0.0320591	+	0.0320591i
$406$		0			0
$407$			4417.67i			0.538025i
$408$		0			0
$409$			1931.84i			0.233554i	0.993158	+	0.116777i	$0.0372562\pi$
$409$			1931.84i			0.233554i	−0.993158	+	0.116777i	$0.962744\pi$
$410$		0			0
$411$	−1664.67	−	1664.67i	−0.199786	−	0.199786i
$412$		0			0
$413$	−13394.8	+	13394.8i	−1.59592	+	1.59592i
$414$		0			0
$415$	−1914.46			−0.226451
$416$		0			0
$417$	6310.50			0.741071
$418$		0			0
$419$	3381.69	−	3381.69i	0.394287	−	0.394287i	−0.481925	−	0.876212i	$-0.660062\pi$
$419$	3381.69	−	3381.69i	0.394287	−	0.394287i	0.876212	+	0.481925i	$0.160062\pi$
$420$		0			0
$421$	2730.44	+	2730.44i	0.316089	+	0.316089i	0.847263	−	0.531174i	$-0.178249\pi$
$421$	2730.44	+	2730.44i	0.316089	+	0.316089i	−0.531174	+	0.847263i	$0.678249\pi$
$422$		0			0
$423$			1029.65i			0.118353i
$424$		0			0
$425$			369.933i			0.0422221i
$426$		0			0
$427$	−4427.49	−	4427.49i	−0.501782	−	0.501782i
$428$		0			0
$429$	−1881.62	+	1881.62i	−0.211761	+	0.211761i
$430$		0			0
$431$	−6404.91			−0.715809			−0.357905	−	0.933758i	$-0.616509\pi$
$431$	−6404.91			−0.715809			−0.357905	+	0.933758i	$0.616509\pi$
$432$		0			0
$433$	5169.70			0.573764			0.286882	−	0.957966i	$-0.407381\pi$
$433$	5169.70			0.573764			0.286882	+	0.957966i	$0.407381\pi$
$434$		0			0
$435$	941.734	−	941.734i	0.103799	−	0.103799i
$436$		0			0
$437$	−3988.85	−	3988.85i	−0.436642	−	0.436642i
$438$		0			0
$439$		−	463.177i		−	0.0503559i	−0.999683	−	0.0251780i	$-0.991985\pi$
$439$		−	463.177i		−	0.0503559i	0.999683	−	0.0251780i	$-0.00801524\pi$
$440$		0			0
$441$			2362.98i			0.255153i
$442$		0			0
$443$	8274.66	+	8274.66i	0.887452	+	0.887452i	0.994278	−	0.106826i	$-0.0340688\pi$
$443$	8274.66	+	8274.66i	0.887452	+	0.887452i	−0.106826	+	0.994278i	$0.534069\pi$
$444$		0			0
$445$	2791.95	−	2791.95i	0.297418	−	0.297418i
$446$		0			0
$447$	6112.94			0.646828
$448$		0			0
$449$	−6245.19			−0.656412			−0.328206	−	0.944606i	$-0.606444\pi$
$449$	−6245.19			−0.656412			−0.328206	+	0.944606i	$0.606444\pi$
$450$		0			0
$451$	−9158.70	+	9158.70i	−0.956245	+	0.956245i
$452$		0			0
$453$	3003.99	+	3003.99i	0.311567	+	0.311567i
$454$		0			0
$455$		−	2964.46i		−	0.305442i
$456$		0			0
$457$		−	17086.8i		−	1.74899i	−0.485037	−	0.874494i	$-0.661194\pi$
$457$		−	17086.8i		−	1.74899i	0.485037	−	0.874494i	$-0.338806\pi$
$458$		0			0
$459$	67.7887	+	67.7887i	0.00689347	+	0.00689347i
$460$		0			0
$461$	9796.68	−	9796.68i	0.989755	−	0.989755i	−0.0101932	−	0.999948i	$-0.503245\pi$
$461$	9796.68	−	9796.68i	0.989755	−	0.989755i	0.999948	+	0.0101932i	$0.00324466\pi$
$462$		0			0
$463$	−10699.4			−1.07396			−0.536980	−	0.843595i	$-0.680435\pi$
$463$	−10699.4			−1.07396			−0.536980	+	0.843595i	$0.680435\pi$
$464$		0			0
$465$	−4200.50			−0.418911
$466$		0			0
$467$	−11145.1	+	11145.1i	−1.10435	+	1.10435i	−0.110473	+	0.993879i	$0.535236\pi$
$467$	−11145.1	+	11145.1i	−1.10435	+	1.10435i	−0.993879	+	0.110473i	$0.964764\pi$
$468$		0			0
$469$	6967.33	+	6967.33i	0.685973	+	0.685973i
$470$		0			0
$471$			7213.64i			0.705705i
$472$		0			0
$473$			7154.63i			0.695498i
$474$		0			0
$475$	−11365.7	−	11365.7i	−1.09788	−	1.09788i
$476$		0			0
$477$	−4064.68	+	4064.68i	−0.390165	+	0.390165i
$478$		0			0
$479$	2322.90			0.221579			0.110789	−	0.993844i	$-0.464662\pi$
$479$	2322.90			0.221579			0.110789	+	0.993844i	$0.464662\pi$
$480$		0			0
$481$	−3472.82			−0.329203
$482$		0			0
$483$	1908.76	−	1908.76i	0.179817	−	0.179817i
$484$		0			0
$485$	1749.78	+	1749.78i	0.163822	+	0.163822i
$486$		0			0
$487$		−	6238.14i		−	0.580446i	−0.956959	−	0.290223i	$-0.906271\pi$
$487$		−	6238.14i		−	0.580446i	0.956959	−	0.290223i	$-0.0937295\pi$
$488$		0			0
$489$		−	4418.49i		−	0.408612i
$490$		0			0
$491$	7481.69	+	7481.69i	0.687666	+	0.687666i	0.961716	−	0.274049i	$-0.0883632\pi$
$491$	7481.69	+	7481.69i	0.687666	+	0.687666i	−0.274049	+	0.961716i	$0.588363\pi$
$492$		0			0
$493$	244.316	−	244.316i	0.0223194	−	0.0223194i
$494$		0			0
$495$	1379.19			0.125232
$496$		0			0
$497$	22892.7			2.06615
$498$		0			0
$499$	−14385.4	+	14385.4i	−1.29054	+	1.29054i	−0.356084	+	0.934454i	$0.615888\pi$
$499$	−14385.4	+	14385.4i	−1.29054	+	1.29054i	−0.934454	+	0.356084i	$0.884112\pi$
$500$		0			0
$501$	6457.73	+	6457.73i	0.575868	+	0.575868i
$502$		0			0
$503$		−	10411.3i		−	0.922892i	−0.887168	−	0.461446i	$-0.847331\pi$
$503$		−	10411.3i		−	0.922892i	0.887168	−	0.461446i	$-0.152669\pi$
$504$		0			0
$505$			7159.87i			0.630911i
$506$		0			0
$507$	3181.36	+	3181.36i	0.278677	+	0.278677i
$508$		0			0
$509$	2836.55	−	2836.55i	0.247010	−	0.247010i	−0.572733	−	0.819742i	$-0.694117\pi$
$509$	2836.55	−	2836.55i	0.247010	−	0.247010i	0.819742	+	0.572733i	$0.194117\pi$
$510$		0			0
$511$	−17254.8			−1.49375
$512$		0			0
$513$	−4165.41			−0.358494
$514$		0			0
$515$	−2603.18	+	2603.18i	−0.222738	+	0.222738i
$516$		0			0
$517$	2717.39	+	2717.39i	0.231162	+	0.231162i
$518$		0			0
$519$		−	5984.60i		−	0.506156i
$520$		0			0
$521$			9858.27i			0.828980i	0.910054	+	0.414490i	$0.136040\pi$
$521$			9858.27i			0.828980i	−0.910054	+	0.414490i	$0.863960\pi$
$522$		0			0
$523$	174.291	+	174.291i	0.0145721	+	0.0145721i	0.714355	−	0.699783i	$-0.246720\pi$
$523$	174.291	+	174.291i	0.0145721	+	0.0145721i	−0.699783	+	0.714355i	$0.746720\pi$
$524$		0			0
$525$	5438.73	−	5438.73i	0.452125	−	0.452125i
$526$		0			0
$527$	−1089.74			−0.0900759
$528$		0			0
$529$	10830.0			0.890111
$530$		0			0
$531$	4898.94	−	4898.94i	0.400369	−	0.400369i
$532$		0			0
$533$	−7199.83	−	7199.83i	−0.585101	−	0.585101i
$534$		0			0
$535$			2231.20i			0.180305i
$536$		0			0
$537$			9165.49i			0.736536i
$538$		0			0
$539$	6236.21	+	6236.21i	0.498353	+	0.498353i
$540$		0			0
$541$	−4401.08	+	4401.08i	−0.349755	+	0.349755i	−0.860018	−	0.510263i	$-0.829548\pi$
$541$	−4401.08	+	4401.08i	−0.349755	+	0.349755i	0.510263	+	0.860018i	$0.329548\pi$
$542$		0			0
$543$	909.229			0.0718577
$544$		0			0
$545$	1624.90			0.127712
$546$		0			0
$547$	873.908	−	873.908i	0.0683101	−	0.0683101i	−0.672126	−	0.740436i	$-0.734619\pi$
$547$	873.908	−	873.908i	0.0683101	−	0.0683101i	0.740436	+	0.672126i	$0.234619\pi$
$548$		0			0
$549$	1619.29	+	1619.29i	0.125882	+	0.125882i
$550$		0			0
$551$			15012.5i			1.16071i
$552$		0			0
$553$			19181.2i			1.47499i
$554$		0			0
$555$	1272.75	+	1272.75i	0.0973431	+	0.0973431i
$556$		0			0
$557$	−11487.1	+	11487.1i	−0.873830	+	0.873830i	−0.992887	−	0.119057i	$-0.962013\pi$
$557$	−11487.1	+	11487.1i	−0.873830	+	0.873830i	0.119057	+	0.992887i	$0.462013\pi$
$558$		0			0
$559$	−5624.39			−0.425557
$560$		0			0
$561$	357.807			0.0269280
$562$		0			0
$563$	4674.36	−	4674.36i	0.349912	−	0.349912i	−0.510164	−	0.860077i	$-0.670415\pi$
$563$	4674.36	−	4674.36i	0.349912	−	0.349912i	0.860077	+	0.510164i	$0.170415\pi$
$564$		0			0
$565$	−5459.33	−	5459.33i	−0.406506	−	0.406506i
$566$		0			0
$567$		−	1993.25i		−	0.147634i
$568$		0			0
$569$			21013.7i			1.54823i	0.633048	+	0.774113i	$0.281804\pi$
$569$			21013.7i			1.54823i	−0.633048	+	0.774113i	$0.718196\pi$
$570$		0			0
$571$	−6974.02	−	6974.02i	−0.511127	−	0.511127i	0.403745	−	0.914872i	$-0.367708\pi$
$571$	−6974.02	−	6974.02i	−0.511127	−	0.511127i	−0.914872	+	0.403745i	$0.867708\pi$
$572$		0			0
$573$	−6930.70	+	6930.70i	−0.505295	+	0.505295i
$574$		0			0
$575$	−3809.64			−0.276301
$576$		0			0
$577$	−1772.18			−0.127863			−0.0639315	−	0.997954i	$-0.520364\pi$
$577$	−1772.18			−0.127863			−0.0639315	+	0.997954i	$0.520364\pi$
$578$		0			0
$579$	−1473.93	+	1473.93i	−0.105794	+	0.105794i
$580$		0			0
$581$	7302.03	+	7302.03i	0.521410	+	0.521410i
$582$		0			0
$583$			21454.4i			1.52410i
$584$		0			0
$585$			1084.21i			0.0766265i
$586$		0			0
$587$	707.518	+	707.518i	0.0497485	+	0.0497485i	0.731543	−	0.681795i	$-0.238800\pi$
$587$	707.518	+	707.518i	0.0497485	+	0.0497485i	−0.681795	+	0.731543i	$0.738800\pi$
$588$		0			0
$589$	33480.8	−	33480.8i	2.34219	−	2.34219i
$590$		0			0
$591$	2534.79			0.176425
$592$		0			0
$593$	7025.73			0.486530			0.243265	−	0.969960i	$-0.421782\pi$
$593$	7025.73			0.486530			0.243265	+	0.969960i	$0.421782\pi$
$594$		0			0
$595$	−281.859	+	281.859i	−0.0194204	+	0.0194204i
$596$		0			0
$597$	7126.75	+	7126.75i	0.488574	+	0.488574i
$598$		0			0
$599$		−	25562.9i		−	1.74369i	−0.489781	−	0.871846i	$-0.662923\pi$
$599$		−	25562.9i		−	1.74369i	0.489781	−	0.871846i	$-0.337077\pi$
$600$		0			0
$601$		−	6395.84i		−	0.434096i	−0.976161	−	0.217048i	$-0.930357\pi$
$601$		−	6395.84i		−	0.434096i	0.976161	−	0.217048i	$-0.0696428\pi$
$602$		0			0
$603$	−2548.20	−	2548.20i	−0.172091	−	0.172091i
$604$		0			0
$605$	−653.778	+	653.778i	−0.0439337	+	0.0439337i
$606$		0			0
$607$	9420.38			0.629920			0.314960	−	0.949105i	$-0.398009\pi$
$607$	9420.38			0.629920			0.314960	+	0.949105i	$0.398009\pi$
$608$		0			0
$609$	−7183.83			−0.478002
$610$		0			0
$611$	−2136.19	+	2136.19i	−0.141442	+	0.141442i
$612$		0			0
$613$	−10149.0	−	10149.0i	−0.668700	−	0.668700i	0.288715	−	0.957415i	$-0.406772\pi$
$613$	−10149.0	−	10149.0i	−0.668700	−	0.668700i	−0.957415	+	0.288715i	$0.906772\pi$
$614$		0			0
$615$			5277.33i			0.346021i
$616$		0			0
$617$			9621.85i			0.627814i	0.949454	+	0.313907i	$0.101638\pi$
$617$			9621.85i			0.627814i	−0.949454	+	0.313907i	$0.898362\pi$
$618$		0			0
$619$	−3235.21	−	3235.21i	−0.210071	−	0.210071i	0.594227	−	0.804298i	$-0.297458\pi$
$619$	−3235.21	−	3235.21i	−0.210071	−	0.210071i	−0.804298	+	0.594227i	$0.797458\pi$
$620$		0			0
$621$	−698.100	+	698.100i	−0.0451107	+	0.0451107i
$622$		0			0
$623$	−21297.8			−1.36963
$624$		0			0
$625$	−8253.44			−0.528220
$626$		0			0
$627$	−10993.1	+	10993.1i	−0.700193	+	0.700193i
$628$		0			0
$629$	330.193	+	330.193i	0.0209311	+	0.0209311i
$630$		0			0
$631$			371.400i			0.0234314i	0.999931	+	0.0117157i	$0.00372930\pi$
$631$			371.400i			0.0234314i	−0.999931	+	0.0117157i	$0.996271\pi$
$632$		0			0
$633$			5684.62i			0.356941i
$634$		0			0
$635$	−1637.52	−	1637.52i	−0.102335	−	0.102335i
$636$		0			0
$637$	−4902.40	+	4902.40i	−0.304930	+	0.304930i
$638$		0			0
$639$	−8372.66			−0.518337
$640$		0			0
$641$	−9470.43			−0.583556			−0.291778	−	0.956486i	$-0.594247\pi$
$641$	−9470.43			−0.583556			−0.291778	+	0.956486i	$0.594247\pi$
$642$		0			0
$643$	−6234.89	+	6234.89i	−0.382395	+	0.382395i	−0.871964	−	0.489569i	$-0.837154\pi$
$643$	−6234.89	+	6234.89i	−0.382395	+	0.382395i	0.489569	+	0.871964i	$0.337154\pi$
$644$		0			0
$645$	2061.29	+	2061.29i	0.125834	+	0.125834i
$646$		0			0
$647$			27954.8i			1.69863i	0.527884	+	0.849316i	$0.322986\pi$
$647$			27954.8i			1.69863i	−0.527884	+	0.849316i	$0.677014\pi$
$648$		0			0
$649$		−	25857.9i		−	1.56396i
$650$		0			0
$651$	16021.3	+	16021.3i	0.964555	+	0.964555i
$652$		0			0
$653$	−15041.2	+	15041.2i	−0.901387	+	0.901387i	−0.995556	−	0.0941690i	$-0.969981\pi$
$653$	−15041.2	+	15041.2i	−0.901387	+	0.901387i	0.0941690	+	0.995556i	$0.469981\pi$
$654$		0			0
$655$	5475.59			0.326640
$656$		0			0
$657$	6310.69			0.374739
$658$		0			0
$659$	−17971.9	+	17971.9i	−1.06234	+	1.06234i	−0.0644201	+	0.997923i	$0.520520\pi$
$659$	−17971.9	+	17971.9i	−1.06234	+	1.06234i	−0.997923	+	0.0644201i	$0.979480\pi$
$660$		0			0
$661$	−18445.8	−	18445.8i	−1.08541	−	1.08541i	−0.995994	−	0.0894197i	$-0.971499\pi$
$661$	−18445.8	−	18445.8i	−1.08541	−	1.08541i	−0.0894197	−	0.995994i	$-0.528501\pi$
$662$		0			0
$663$			281.278i			0.0164765i
$664$		0			0
$665$		−	17319.4i		−	1.00995i
$666$		0			0
$667$	2516.01	+	2516.01i	0.146057	+	0.146057i
$668$		0			0
$669$	−5294.09	+	5294.09i	−0.305951	+	0.305951i
$670$		0			0
$671$	8547.02			0.491735
$672$		0			0
$673$	8934.70			0.511749			0.255875	−	0.966710i	$-0.417637\pi$
$673$	8934.70			0.511749			0.255875	+	0.966710i	$0.417637\pi$
$674$		0			0
$675$	−1989.13	+	1989.13i	−0.113425	+	0.113425i
$676$		0			0
$677$	16188.7	+	16188.7i	0.919030	+	0.919030i	0.996959	−	0.0779287i	$-0.0248306\pi$
$677$	16188.7	+	16188.7i	0.919030	+	0.919030i	−0.0779287	+	0.996959i	$0.524831\pi$
$678$		0			0
$679$		−	13347.9i		−	0.754410i
$680$		0			0
$681$		−	7338.43i		−	0.412936i
$682$		0			0
$683$	4013.46	+	4013.46i	0.224848	+	0.224848i	0.810536	−	0.585689i	$-0.199176\pi$
$683$	4013.46	+	4013.46i	0.224848	+	0.224848i	−0.585689	+	0.810536i	$0.699176\pi$
$684$		0			0
$685$	−2531.45	+	2531.45i	−0.141200	+	0.141200i
$686$		0			0
$687$	5444.09			0.302336
$688$		0			0
$689$	−16865.7			−0.932560
$690$		0			0
$691$	5748.83	−	5748.83i	0.316492	−	0.316492i	−0.530926	−	0.847418i	$-0.678156\pi$
$691$	5748.83	−	5748.83i	0.316492	−	0.316492i	0.847418	+	0.530926i	$0.178156\pi$
$692$		0			0
$693$	−5260.44	−	5260.44i	−0.288352	−	0.288352i
$694$		0			0
$695$		−	9596.34i		−	0.523755i
$696$		0			0
$697$			1369.11i			0.0744028i
$698$		0			0
$699$	−13821.3	−	13821.3i	−0.747885	−	0.747885i
$700$		0			0
$701$	12548.7	−	12548.7i	0.676119	−	0.676119i	−0.283001	−	0.959120i	$-0.591330\pi$
$701$	12548.7	−	12548.7i	0.676119	−	0.676119i	0.959120	+	0.283001i	$0.0913300\pi$
$702$		0			0
$703$	−20289.4			−1.08852
$704$		0			0
$705$	1565.79			0.0836468
$706$		0			0
$707$	27308.8	−	27308.8i	1.45269	−	1.45269i
$708$		0			0
$709$	18950.0	+	18950.0i	1.00378	+	1.00378i	0.999993	+	0.00379062i	$0.00120660\pi$
$709$	18950.0	+	18950.0i	1.00378	+	1.00378i	0.00379062	+	0.999993i	$0.498793\pi$
$710$		0			0
$711$		−	7015.24i		−	0.370031i
$712$		0			0
$713$		−	11222.4i		−	0.589455i
$714$		0			0
$715$	2861.37	+	2861.37i	0.149663	+	0.149663i
$716$		0			0
$717$	1614.69	−	1614.69i	0.0841029	−	0.0841029i
$718$		0			0
$719$	33244.6			1.72436			0.862180	−	0.506603i	$-0.169099\pi$
$719$	33244.6			1.72436			0.862180	+	0.506603i	$0.169099\pi$
$720$		0			0
$721$	19857.9			1.02572
$722$		0			0
$723$	13207.1	−	13207.1i	0.679358	−	0.679358i
$724$		0			0
$725$	7169.00	+	7169.00i	0.367242	+	0.367242i
$726$		0			0
$727$			25543.7i			1.30312i	0.758599	+	0.651558i	$0.225884\pi$
$727$			25543.7i			1.30312i	−0.758599	+	0.651558i	$0.774116\pi$
$728$		0			0
$729$			729.000i			0.0370370i
$730$		0			0
$731$	534.764	+	534.764i	0.0270574	+	0.0270574i
$732$		0			0
$733$	−17290.1	+	17290.1i	−0.871246	+	0.871246i	−0.992608	−	0.121363i	$-0.961274\pi$
$733$	−17290.1	+	17290.1i	−0.871246	+	0.871246i	0.121363	+	0.992608i	$0.461274\pi$
$734$		0			0
$735$	3593.37			0.180331
$736$		0			0
$737$	−13450.1			−0.672238
$738$		0			0
$739$	2931.71	−	2931.71i	0.145933	−	0.145933i	−0.630365	−	0.776299i	$-0.717095\pi$
$739$	2931.71	−	2931.71i	0.145933	−	0.145933i	0.776299	+	0.630365i	$0.217095\pi$
$740$		0			0
$741$	−8641.86	−	8641.86i	−0.428430	−	0.428430i
$742$		0			0
$743$		−	23349.2i		−	1.15289i	−0.817135	−	0.576446i	$-0.804439\pi$
$743$		−	23349.2i		−	1.15289i	0.817135	−	0.576446i	$-0.195561\pi$
$744$		0			0
$745$		−	9295.91i		−	0.457149i
$746$		0			0
$747$	−2670.61	−	2670.61i	−0.130806	−	0.130806i
$748$		0			0
$749$	8510.13	−	8510.13i	0.415158	−	0.415158i
$750$		0			0
$751$	18998.3			0.923115			0.461557	−	0.887110i	$-0.347291\pi$
$751$	18998.3			0.923115			0.461557	+	0.887110i	$0.347291\pi$
$752$		0			0
$753$	1168.34			0.0565426
$754$		0			0
$755$	4568.15	−	4568.15i	0.220201	−	0.220201i
$756$		0			0
$757$	2302.76	+	2302.76i	0.110562	+	0.110562i	0.760224	−	0.649662i	$-0.225089\pi$
$757$	2302.76	+	2302.76i	0.110562	+	0.110562i	−0.649662	+	0.760224i	$0.725089\pi$
$758$		0			0
$759$			3684.75i			0.176216i
$760$		0			0
$761$		−	23935.6i		−	1.14016i	−0.821588	−	0.570082i	$-0.806912\pi$
$761$		−	23935.6i		−	1.14016i	0.821588	−	0.570082i	$-0.193088\pi$
$762$		0			0
$763$	−6197.61	−	6197.61i	−0.294061	−	0.294061i
$764$		0			0
$765$	103.086	−	103.086i	0.00487200	−	0.00487200i
$766$		0			0
$767$	20327.4			0.956948
$768$		0			0
$769$	−10382.5			−0.486867			−0.243434	−	0.969918i	$-0.578274\pi$
$769$	−10382.5			−0.486867			−0.243434	+	0.969918i	$0.578274\pi$
$770$		0			0
$771$	4228.23	−	4228.23i	0.197505	−	0.197505i
$772$		0			0
$773$	−12250.4	−	12250.4i	−0.570009	−	0.570009i	0.362122	−	0.932131i	$-0.382052\pi$
$773$	−12250.4	−	12250.4i	−0.570009	−	0.570009i	−0.932131	+	0.362122i	$0.882052\pi$
$774$		0			0
$775$		−	31976.5i		−	1.48211i
$776$		0			0
$777$		−	9708.95i		−	0.448271i
$778$		0			0
$779$	−42063.9	−	42063.9i	−1.93465	−	1.93465i
$780$		0			0
$781$	−22096.6	+	22096.6i	−1.01239	+	1.01239i
$782$		0			0
$783$	2627.38			0.119917
$784$		0			0
$785$	10969.7			0.498761
$786$		0			0
$787$	16691.8	−	16691.8i	0.756033	−	0.756033i	−0.219565	−	0.975598i	$-0.570464\pi$
$787$	16691.8	−	16691.8i	0.756033	−	0.756033i	0.975598	+	0.219565i	$0.0704639\pi$
$788$		0			0
$789$	−9302.43	−	9302.43i	−0.419741	−	0.419741i
$790$		0			0
$791$			41645.4i			1.87199i
$792$		0			0
$793$			6718.97i			0.300880i
$794$		0			0
$795$	6181.13	+	6181.13i	0.275751	+	0.275751i
$796$		0			0
$797$	6753.90	−	6753.90i	0.300170	−	0.300170i	−0.540910	−	0.841080i	$-0.681920\pi$
$797$	6753.90	−	6753.90i	0.300170	−	0.300170i	0.841080	+	0.540910i	$0.181920\pi$
$798$		0			0
$799$	406.216			0.0179861
$800$		0			0
$801$	7789.37			0.343600
$802$		0			0
$803$	16654.7	−	16654.7i	0.731921	−	0.731921i
$804$		0			0
$805$	−2902.64	−	2902.64i	−0.127086	−	0.127086i
$806$		0			0
$807$		−	7140.97i		−	0.311492i
$808$		0			0
$809$		−	13717.0i		−	0.596125i	−0.954546	−	0.298063i	$-0.903660\pi$
$809$		−	13717.0i		−	0.596125i	0.954546	−	0.298063i	$-0.0963404\pi$
$810$		0			0
$811$	4025.22	+	4025.22i	0.174284	+	0.174284i	0.788859	−	0.614574i	$-0.210672\pi$
$811$	4025.22	+	4025.22i	0.174284	+	0.174284i	−0.614574	+	0.788859i	$0.710672\pi$
$812$		0			0
$813$	5052.34	−	5052.34i	0.217950	−	0.217950i
$814$		0			0
$815$	−6719.18			−0.288788
$816$		0			0
$817$	−32859.7			−1.40712
$818$		0			0
$819$	4135.33	−	4135.33i	0.176435	−	0.176435i
$820$		0			0
$821$	−1800.87	−	1800.87i	−0.0765539	−	0.0765539i	0.667793	−	0.744347i	$-0.267239\pi$
$821$	−1800.87	−	1800.87i	−0.0765539	−	0.0765539i	−0.744347	+	0.667793i	$0.767239\pi$
$822$		0			0
$823$		−	35700.7i		−	1.51209i	−0.654522	−	0.756043i	$-0.727130\pi$
$823$		−	35700.7i		−	1.51209i	0.654522	−	0.756043i	$-0.272870\pi$
$824$		0			0
$825$			10499.2i			0.443072i
$826$		0			0
$827$	20857.1	+	20857.1i	0.876994	+	0.876994i	0.993222	−	0.116229i	$-0.0370805\pi$
$827$	20857.1	+	20857.1i	0.876994	+	0.876994i	−0.116229	+	0.993222i	$0.537080\pi$
$828$		0			0
$829$	9907.55	−	9907.55i	0.415083	−	0.415083i	−0.468422	−	0.883505i	$-0.655177\pi$
$829$	9907.55	−	9907.55i	0.415083	−	0.415083i	0.883505	+	0.468422i	$0.155177\pi$
$830$		0			0
$831$	−24233.5			−1.01161
$832$		0			0
$833$	932.235			0.0387755
$834$		0			0
$835$	9820.23	−	9820.23i	0.406998	−	0.406998i
$836$		0			0
$837$	−5859.56	−	5859.56i	−0.241979	−	0.241979i
$838$		0			0
$839$			15663.0i			0.644513i	0.946652	+	0.322257i	$0.104441\pi$
$839$			15663.0i			0.644513i	−0.946652	+	0.322257i	$0.895559\pi$
$840$		0			0
$841$			14919.7i			0.611740i
$842$		0			0
$843$	4234.55	+	4234.55i	0.173008	+	0.173008i
$844$		0			0
$845$	4837.88	−	4837.88i	0.196957	−	0.196957i
$846$		0			0
$847$	4987.22			0.202317
$848$		0			0
$849$	6182.00			0.249901
$850$		0			0
$851$	−3400.39	+	3400.39i	−0.136973	+	0.136973i
$852$		0			0
$853$	−4808.17	−	4808.17i	−0.192999	−	0.192999i	0.603991	−	0.796991i	$-0.293576\pi$
$853$	−4808.17	−	4808.17i	−0.192999	−	0.192999i	−0.796991	+	0.603991i	$0.793576\pi$
$854$		0			0
$855$			6334.32i			0.253368i
$856$		0			0
$857$		−	19827.2i		−	0.790298i	−0.918617	−	0.395149i	$-0.870693\pi$
$857$		−	19827.2i		−	0.790298i	0.918617	−	0.395149i	$-0.129307\pi$
$858$		0			0
$859$	25818.2	+	25818.2i	1.02550	+	1.02550i	0.999666	+	0.0258367i	$0.00822499\pi$
$859$	25818.2	+	25818.2i	1.02550	+	1.02550i	0.0258367	+	0.999666i	$0.491775\pi$
$860$		0			0
$861$	20128.5	−	20128.5i	0.796724	−	0.796724i
$862$		0			0
$863$	−633.059			−0.0249706			−0.0124853	−	0.999922i	$-0.503974\pi$
$863$	−633.059			−0.0249706			−0.0124853	+	0.999922i	$0.503974\pi$
$864$		0			0
$865$	−9100.75			−0.357728
$866$		0			0
$867$	−10395.3	+	10395.3i	−0.407201	+	0.407201i
$868$		0			0
$869$	−18514.1	−	18514.1i	−0.722726	−	0.722726i
$870$		0			0
$871$		−	10573.3i		−	0.411325i
$872$		0			0
$873$			4881.78i			0.189259i
$874$		0			0
$875$	−18193.4	−	18193.4i	−0.702915	−	0.702915i
$876$		0			0
$877$	22480.1	−	22480.1i	0.865563	−	0.865563i	−0.126415	−	0.991977i	$-0.540347\pi$
$877$	22480.1	−	22480.1i	0.865563	−	0.865563i	0.991977	+	0.126415i	$0.0403470\pi$
$878$		0			0
$879$	6542.45			0.251048
$880$		0			0
$881$	−37603.1			−1.43800			−0.719001	−	0.695009i	$-0.755400\pi$
$881$	−37603.1			−1.43800			−0.719001	+	0.695009i	$0.755400\pi$
$882$		0			0
$883$	11054.8	−	11054.8i	0.421316	−	0.421316i	−0.464341	−	0.885657i	$-0.653709\pi$
$883$	11054.8	−	11054.8i	0.421316	−	0.421316i	0.885657	+	0.464341i	$0.153709\pi$
$884$		0			0
$885$	−7449.79	−	7449.79i	−0.282963	−	0.282963i
$886$		0			0
$887$		−	20920.6i		−	0.791935i	−0.918264	−	0.395968i	$-0.870409\pi$
$887$		−	20920.6i		−	0.791935i	0.918264	−	0.395968i	$-0.129591\pi$
$888$		0			0
$889$			12491.5i			0.471260i
$890$		0			0
$891$	1923.93	+	1923.93i	0.0723389	+	0.0723389i
$892$		0			0
$893$	−12480.4	+	12480.4i	−0.467682	+	0.467682i
$894$		0			0
$895$	13937.9			0.520551
$896$		0			0
$897$	−2896.65			−0.107822
$898$		0			0
$899$	−21118.3	+	21118.3i	−0.783467	+	0.783467i
$900$		0			0
$901$	1603.58	+	1603.58i	0.0592932	+	0.0592932i
$902$		0			0
$903$		−	15724.1i		−	0.579475i
$904$		0			0
$905$		−	1382.66i		−	0.0507858i
$906$		0			0
$907$	32396.8	+	32396.8i	1.18602	+	1.18602i	0.978159	+	0.207859i	$0.0666494\pi$
$907$	32396.8	+	32396.8i	1.18602	+	1.18602i	0.207859	+	0.978159i	$0.433351\pi$
$908$		0			0
$909$	−9987.80	+	9987.80i	−0.364438	+	0.364438i
$910$		0			0
$911$	11273.7			0.410006			0.205003	−	0.978761i	$-0.434280\pi$
$911$	11273.7			0.410006			0.205003	+	0.978761i	$0.434280\pi$
$912$		0			0
$913$	−14096.2			−0.510970
$914$		0			0
$915$	2462.44	−	2462.44i	0.0889680	−	0.0889680i
$916$		0			0
$917$	−20884.7	−	20884.7i	−0.752098	−	0.752098i
$918$		0			0
$919$			44241.7i			1.58803i	0.607898	+	0.794015i	$0.292013\pi$
$919$			44241.7i			1.58803i	−0.607898	+	0.794015i	$0.707987\pi$
$920$		0			0
$921$		−	13815.5i		−	0.494285i
$922$		0			0
$923$	−17370.5	−	17370.5i	−0.619456	−	0.619456i
$924$		0			0
$925$	−9688.92	+	9688.92i	−0.344400	+	0.344400i
$926$		0			0
$927$	−7262.71			−0.257323
$928$		0			0
$929$	7271.46			0.256802			0.128401	−	0.991722i	$-0.459016\pi$
$929$	7271.46			0.256802			0.128401	+	0.991722i	$0.459016\pi$
$930$		0			0
$931$	−28641.5	+	28641.5i	−1.00826	+	1.00826i
$932$		0			0
$933$	−3902.02	−	3902.02i	−0.136920	−	0.136920i
$934$		0			0
$935$		−	544.114i		−	0.0190315i
$936$		0			0
$937$			26357.3i			0.918948i	0.888191	+	0.459474i	$0.151962\pi$
$937$			26357.3i			0.918948i	−0.888191	+	0.459474i	$0.848038\pi$
$938$		0			0
$939$	−7257.71	−	7257.71i	−0.252233	−	0.252233i
$940$		0			0
$941$	19843.2	−	19843.2i	0.687427	−	0.687427i	−0.274235	−	0.961663i	$-0.588425\pi$
$941$	19843.2	−	19843.2i	0.687427	−	0.687427i	0.961663	+	0.274235i	$0.0884247\pi$
$942$		0			0
$943$	−14099.3			−0.486890
$944$		0			0
$945$	−3031.12			−0.104341
$946$		0			0
$947$	−24241.9	+	24241.9i	−0.831845	+	0.831845i	−0.987769	−	0.155924i	$-0.950164\pi$
$947$	−24241.9	+	24241.9i	−0.831845	+	0.831845i	0.155924	+	0.987769i	$0.450164\pi$
$948$		0			0
$949$	13092.6	+	13092.6i	0.447844	+	0.447844i
$950$		0			0
$951$			3095.66i			0.105556i
$952$		0			0
$953$			42596.4i			1.44788i	0.689861	+	0.723942i	$0.257672\pi$
$953$			42596.4i			1.44788i	−0.689861	+	0.723942i	$0.742328\pi$
$954$		0			0
$955$	10539.5	+	10539.5i	0.357120	+	0.357120i
$956$		0			0
$957$	6934.00	−	6934.00i	0.234216	−	0.234216i
$958$		0			0
$959$	19310.7			0.650233
$960$		0			0
$961$	64405.1			2.16190
$962$		0			0
$963$	−3112.45	+	3112.45i	−0.104151	+	0.104151i
$964$		0			0
$965$	2241.40	+	2241.40i	0.0747703	+	0.0747703i
$966$		0			0
$967$		−	38631.7i		−	1.28471i	−0.766409	−	0.642353i	$-0.777958\pi$
$967$		−	38631.7i		−	1.28471i	0.766409	−	0.642353i	$-0.222042\pi$
$968$		0			0
$969$			1643.33i			0.0544802i
$970$		0			0
$971$	1713.62	+	1713.62i	0.0566351	+	0.0566351i	0.734857	−	0.678222i	$-0.237249\pi$
$971$	1713.62	+	1713.62i	0.0566351	+	0.0566351i	−0.678222	+	0.734857i	$0.737249\pi$
$972$		0			0
$973$	−36601.9	+	36601.9i	−1.20596	+	1.20596i
$974$		0			0
$975$	−8253.60			−0.271104
$976$		0			0
$977$	26738.5			0.875579			0.437789	−	0.899078i	$-0.355762\pi$
$977$	26738.5			0.875579			0.437789	+	0.899078i	$0.355762\pi$
$978$		0			0
$979$	20557.2	−	20557.2i	0.671103	−	0.671103i
$980$		0			0
$981$	2266.68	+	2266.68i	0.0737713	+	0.0737713i
$982$		0			0
$983$		−	35262.6i		−	1.14415i	−0.820201	−	0.572076i	$-0.806138\pi$
$983$		−	35262.6i		−	1.14415i	0.820201	−	0.572076i	$-0.193862\pi$
$984$		0			0
$985$		−	3854.64i		−	0.124689i
$986$		0			0
$987$	−5972.15	−	5972.15i	−0.192600	−	0.192600i
$988$		0			0
$989$	−5507.09	+	5507.09i	−0.177063	+	0.177063i
$990$		0			0
$991$	48515.7			1.55515			0.777574	−	0.628791i	$-0.216450\pi$
$991$	48515.7			1.55515			0.777574	+	0.628791i	$0.216450\pi$
$992$		0			0
$993$	11746.9			0.375406
$994$		0			0
$995$	10837.6	−	10837.6i	0.345302	−	0.345302i
$996$		0			0
$997$	−11465.5	−	11465.5i	−0.364208	−	0.364208i	0.501151	−	0.865360i	$-0.332910\pi$
$997$	−11465.5	−	11465.5i	−0.364208	−	0.364208i	−0.865360	+	0.501151i	$0.832910\pi$
$998$		0			0
$999$			3550.90i			0.112458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.4.j.b.97.10		24
4.3	odd	2		384.4.j.a.97.3		24
8.3	odd	2		192.4.j.a.49.11		24
8.5	even	2		48.4.j.a.37.4	yes	24
16.3	odd	4		384.4.j.a.289.3		24
16.5	even	4		48.4.j.a.13.4	✓	24
16.11	odd	4		192.4.j.a.145.11		24
16.13	even	4	inner	384.4.j.b.289.10		24
24.5	odd	2		144.4.k.b.37.9		24
24.11	even	2		576.4.k.b.433.4		24
48.5	odd	4		144.4.k.b.109.9		24
48.11	even	4		576.4.k.b.145.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.4	✓	24	16.5	even	4
48.4.j.a.37.4	yes	24	8.5	even	2
144.4.k.b.37.9		24	24.5	odd	2
144.4.k.b.109.9		24	48.5	odd	4
192.4.j.a.49.11		24	8.3	odd	2
192.4.j.a.145.11		24	16.11	odd	4
384.4.j.a.97.3		24	4.3	odd	2
384.4.j.a.289.3		24	16.3	odd	4
384.4.j.b.97.10		24	1.1	even	1	trivial
384.4.j.b.289.10		24	16.13	even	4	inner
576.4.k.b.145.4		24	48.11	even	4
576.4.k.b.433.4		24	24.11	even	2

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	384.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.12132 - 2.12132i) q^{3} +(-3.22588 - 3.22588i) q^{5} +24.6080i q^{7} -9.00000i q^{9} +O(q^{10})\)	\(q+(2.12132 - 2.12132i) q^{3} +(-3.22588 - 3.22588i) q^{5} +24.6080i q^{7} -9.00000i q^{9} +(-23.7522 - 23.7522i) q^{11} +(18.6720 - 18.6720i) q^{13} -13.6863 q^{15} -3.55065 q^{17} +(109.089 - 109.089i) q^{19} +(52.2014 + 52.2014i) q^{21} -36.5653i q^{23} -104.187i q^{25} +(-19.0919 - 19.0919i) q^{27} +(-68.8087 + 68.8087i) q^{29} +306.914 q^{31} -100.772 q^{33} +(79.3824 - 79.3824i) q^{35} +(-92.9951 - 92.9951i) q^{37} -79.2188i q^{39} -385.594i q^{41} +(-150.610 - 150.610i) q^{43} +(-29.0329 + 29.0329i) q^{45} -114.406 q^{47} -262.553 q^{49} +(-7.53207 + 7.53207i) q^{51} +(-451.631 - 451.631i) q^{53} +153.243i q^{55} -462.824i q^{57} +(544.327 + 544.327i) q^{59} +(-179.921 + 179.921i) q^{61} +221.472 q^{63} -120.468 q^{65} +(283.133 - 283.133i) q^{67} +(-77.5666 - 77.5666i) q^{69} -930.296i q^{71} +701.187i q^{73} +(-221.015 - 221.015i) q^{75} +(584.494 - 584.494i) q^{77} +779.471 q^{79} -81.0000 q^{81} +(296.734 - 296.734i) q^{83} +(11.4540 + 11.4540i) q^{85} +291.931i q^{87} +865.485i q^{89} +(459.481 + 459.481i) q^{91} +(651.062 - 651.062i) q^{93} -703.813 q^{95} -542.420 q^{97} +(-213.770 + 213.770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q + 40 q^{11} + 120 q^{15} - 24 q^{19} - 400 q^{29} - 744 q^{31} + 456 q^{35} - 16 q^{37} - 1240 q^{43} - 1176 q^{49} - 744 q^{51} - 752 q^{53} + 1376 q^{59} + 912 q^{61} - 504 q^{63} + 976 q^{65} + 2256 q^{67} + 528 q^{69} - 1104 q^{75} - 1904 q^{77} + 5992 q^{79} - 1944 q^{81} - 2680 q^{83} + 240 q^{85} + 3496 q^{91} - 7728 q^{95} + 360 q^{99}+O(q^{100}) \) 24 * q + 40 * q^11 + 120 * q^15 - 24 * q^19 - 400 * q^29 - 744 * q^31 + 456 * q^35 - 16 * q^37 - 1240 * q^43 - 1176 * q^49 - 744 * q^51 - 752 * q^53 + 1376 * q^59 + 912 * q^61 - 504 * q^63 + 976 * q^65 + 2256 * q^67 + 528 * q^69 - 1104 * q^75 - 1904 * q^77 + 5992 * q^79 - 1944 * q^81 - 2680 * q^83 + 240 * q^85 + 3496 * q^91 - 7728 * q^95 + 360 * q^99

Introduction

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