LMFDB - Embedded newform 192.4.j.a.145.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,4,Mod(49,192)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("192.49"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	192.j (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.3283667211$
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			145.5
Character	$\chi$	$=$	192.145
Dual form			192.4.j.a.49.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.12132 - 2.12132i) q^{3} +(10.2951 - 10.2951i) q^{5} +32.8369i q^{7} +9.00000i q^{9} +(18.2226 - 18.2226i) q^{11} +(22.5535 + 22.5535i) q^{13} -43.6785 q^{15} +50.1440 q^{17} +(6.68982 + 6.68982i) q^{19} +(69.6576 - 69.6576i) q^{21} -186.886i q^{23} -86.9788i q^{25} +(19.0919 - 19.0919i) q^{27} +(118.332 + 118.332i) q^{29} +250.110 q^{31} -77.3118 q^{33} +(338.060 + 338.060i) q^{35} +(198.913 - 198.913i) q^{37} -95.6866i q^{39} +186.565i q^{41} +(-10.9329 + 10.9329i) q^{43} +(92.6560 + 92.6560i) q^{45} -23.1346 q^{47} -735.263 q^{49} +(-106.371 - 106.371i) q^{51} +(134.664 - 134.664i) q^{53} -375.207i q^{55} -28.3825i q^{57} +(-220.943 + 220.943i) q^{59} +(-453.845 - 453.845i) q^{61} -295.532 q^{63} +464.383 q^{65} +(184.273 + 184.273i) q^{67} +(-396.444 + 396.444i) q^{69} -18.8163i q^{71} +828.683i q^{73} +(-184.510 + 184.510i) q^{75} +(598.373 + 598.373i) q^{77} -1048.37 q^{79} -81.0000 q^{81} +(173.404 + 173.404i) q^{83} +(516.238 - 516.238i) q^{85} -502.041i q^{87} -335.168i q^{89} +(-740.589 + 740.589i) q^{91} +(-530.564 - 530.564i) q^{93} +137.745 q^{95} -687.122 q^{97} +(164.003 + 164.003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$4$		0			0
$5$	10.2951	−	10.2951i	0.920823	−	0.920823i	−0.0762646	−	0.997088i	$-0.524299\pi$
$5$	10.2951	−	10.2951i	0.920823	−	0.920823i	0.997088	+	0.0762646i	$0.0242994\pi$
$6$		0			0
$7$			32.8369i			1.77303i	0.462703	+	0.886513i	$0.346880\pi$
$7$			32.8369i			1.77303i	−0.462703	+	0.886513i	$0.653120\pi$
$8$		0			0
$9$			9.00000i			0.333333i
$10$		0			0
$11$	18.2226	−	18.2226i	0.499483	−	0.499483i	−0.411794	−	0.911277i	$-0.635098\pi$
$11$	18.2226	−	18.2226i	0.499483	−	0.499483i	0.911277	+	0.411794i	$0.135098\pi$
$12$		0			0
$13$	22.5535	+	22.5535i	0.481171	+	0.481171i	0.905506	−	0.424334i	$-0.139492\pi$
$13$	22.5535	+	22.5535i	0.481171	+	0.481171i	−0.424334	+	0.905506i	$0.639492\pi$
$14$		0			0
$15$	−43.6785			−0.751849
$16$		0			0
$17$	50.1440			0.715394			0.357697	−	0.933838i	$-0.383562\pi$
$17$	50.1440			0.715394			0.357697	+	0.933838i	$0.383562\pi$
$18$		0			0
$19$	6.68982	+	6.68982i	0.0807763	+	0.0807763i	0.746341	−	0.665564i	$-0.231809\pi$
$19$	6.68982	+	6.68982i	0.0807763	+	0.0807763i	−0.665564	+	0.746341i	$0.731809\pi$
$20$		0			0
$21$	69.6576	−	69.6576i	0.723835	−	0.723835i
$22$		0			0
$23$		−	186.886i		−	1.69428i	−0.531373	−	0.847138i	$-0.678324\pi$
$23$		−	186.886i		−	1.69428i	0.531373	−	0.847138i	$-0.321676\pi$
$24$		0			0
$25$		−	86.9788i		−	0.695830i
$26$		0			0
$27$	19.0919	−	19.0919i	0.136083	−	0.136083i
$28$		0			0
$29$	118.332	+	118.332i	0.757715	+	0.757715i	0.975906	−	0.218191i	$-0.0700156\pi$
$29$	118.332	+	118.332i	0.757715	+	0.757715i	−0.218191	+	0.975906i	$0.570016\pi$
$30$		0			0
$31$	250.110			1.44907			0.724534	−	0.689239i	$-0.242055\pi$
$31$	250.110			1.44907			0.724534	+	0.689239i	$0.242055\pi$
$32$		0			0
$33$	−77.3118			−0.407826
$34$		0			0
$35$	338.060	+	338.060i	1.63264	+	1.63264i
$36$		0			0
$37$	198.913	−	198.913i	0.883813	−	0.883813i	−0.110107	−	0.993920i	$-0.535119\pi$
$37$	198.913	−	198.913i	0.883813	−	0.883813i	0.993920	+	0.110107i	$0.0351194\pi$
$38$		0			0
$39$		−	95.6866i		−	0.392875i
$40$		0			0
$41$			186.565i			0.710647i	0.934743	+	0.355324i	$0.115629\pi$
$41$			186.565i			0.710647i	−0.934743	+	0.355324i	$0.884371\pi$
$42$		0			0
$43$	−10.9329	+	10.9329i	−0.0387734	+	0.0387734i	−0.726228	−	0.687454i	$-0.758728\pi$
$43$	−10.9329	+	10.9329i	−0.0387734	+	0.0387734i	0.687454	+	0.726228i	$0.258728\pi$
$44$		0			0
$45$	92.6560	+	92.6560i	0.306941	+	0.306941i
$46$		0			0
$47$	−23.1346			−0.0717983			−0.0358992	−	0.999355i	$-0.511430\pi$
$47$	−23.1346			−0.0717983			−0.0358992	+	0.999355i	$0.511430\pi$
$48$		0			0
$49$	−735.263			−2.14362
$50$		0			0
$51$	−106.371	−	106.371i	−0.292058	−	0.292058i
$52$		0			0
$53$	134.664	−	134.664i	0.349011	−	0.349011i	−0.510730	−	0.859741i	$-0.670625\pi$
$53$	134.664	−	134.664i	0.349011	−	0.349011i	0.859741	+	0.510730i	$0.170625\pi$
$54$		0			0
$55$		−	375.207i		−	0.919870i
$56$		0			0
$57$		−	28.3825i		−	0.0659536i
$58$		0			0
$59$	−220.943	+	220.943i	−0.487531	+	0.487531i	−0.907526	−	0.419995i	$-0.862032\pi$
$59$	−220.943	+	220.943i	−0.487531	+	0.487531i	0.419995	+	0.907526i	$0.362032\pi$
$60$		0			0
$61$	−453.845	−	453.845i	−0.952604	−	0.952604i	0.0463225	−	0.998927i	$-0.485250\pi$
$61$	−453.845	−	453.845i	−0.952604	−	0.952604i	−0.998927	+	0.0463225i	$0.985250\pi$
$62$		0			0
$63$	−295.532			−0.591009
$64$		0			0
$65$	464.383			0.886147
$66$		0			0
$67$	184.273	+	184.273i	0.336007	+	0.336007i	0.854862	−	0.518855i	$-0.173642\pi$
$67$	184.273	+	184.273i	0.336007	+	0.336007i	−0.518855	+	0.854862i	$0.673642\pi$
$68$		0			0
$69$	−396.444	+	396.444i	−0.691685	+	0.691685i
$70$		0			0
$71$		−	18.8163i		−	0.0314519i	−0.999876	−	0.0157259i	$-0.994994\pi$
$71$		−	18.8163i		−	0.0314519i	0.999876	−	0.0157259i	$-0.00500593\pi$
$72$		0			0
$73$			828.683i			1.32863i	0.747453	+	0.664315i	$0.231277\pi$
$73$			828.683i			1.32863i	−0.747453	+	0.664315i	$0.768723\pi$
$74$		0			0
$75$	−184.510	+	184.510i	−0.284071	+	0.284071i
$76$		0			0
$77$	598.373	+	598.373i	0.885596	+	0.885596i
$78$		0			0
$79$	−1048.37			−1.49304			−0.746522	−	0.665361i	$-0.768278\pi$
$79$	−1048.37			−1.49304			−0.746522	+	0.665361i	$0.768278\pi$
$80$		0			0
$81$	−81.0000			−0.111111
$82$		0			0
$83$	173.404	+	173.404i	0.229320	+	0.229320i	0.812409	−	0.583088i	$-0.198156\pi$
$83$	173.404	+	173.404i	0.229320	+	0.229320i	−0.583088	+	0.812409i	$0.698156\pi$
$84$		0			0
$85$	516.238	−	516.238i	0.658751	−	0.658751i
$86$		0			0
$87$		−	502.041i		−	0.618672i
$88$		0			0
$89$		−	335.168i		−	0.399188i	−0.979879	−	0.199594i	$-0.936038\pi$
$89$		−	335.168i		−	0.399188i	0.979879	−	0.199594i	$-0.0639623\pi$
$90$		0			0
$91$	−740.589	+	740.589i	−0.853130	+	0.853130i
$92$		0			0
$93$	−530.564	−	530.564i	−0.591579	−	0.591579i
$94$		0			0
$95$	137.745			0.148761
$96$		0			0
$97$	−687.122			−0.719244			−0.359622	−	0.933098i	$-0.617094\pi$
$97$	−687.122			−0.719244			−0.359622	+	0.933098i	$0.617094\pi$
$98$		0			0
$99$	164.003	+	164.003i	0.166494	+	0.166494i
$100$		0			0
$101$	51.6403	−	51.6403i	0.0508752	−	0.0508752i	−0.681211	−	0.732087i	$-0.738547\pi$
$101$	51.6403	−	51.6403i	0.0508752	−	0.0508752i	0.732087	+	0.681211i	$0.238547\pi$
$102$		0			0
$103$			116.260i			0.111218i	0.998453	+	0.0556089i	$0.0177100\pi$
$103$			116.260i			0.111218i	−0.998453	+	0.0556089i	$0.982290\pi$
$104$		0			0
$105$		−	1434.27i		−	1.33305i
$106$		0			0
$107$	330.891	−	330.891i	0.298958	−	0.298958i	−0.541648	−	0.840605i	$-0.682199\pi$
$107$	330.891	−	330.891i	0.298958	−	0.298958i	0.840605	+	0.541648i	$0.182199\pi$
$108$		0			0
$109$	508.212	+	508.212i	0.446586	+	0.446586i	0.894218	−	0.447632i	$-0.147732\pi$
$109$	508.212	+	508.212i	0.446586	+	0.446586i	−0.447632	+	0.894218i	$0.647732\pi$
$110$		0			0
$111$	−843.916			−0.721630
$112$		0			0
$113$	−1947.12			−1.62097			−0.810486	−	0.585758i	$-0.800797\pi$
$113$	−1947.12			−1.62097			−0.810486	+	0.585758i	$0.800797\pi$
$114$		0			0
$115$	−1924.01	−	1924.01i	−1.56013	−	1.56013i
$116$		0			0
$117$	−202.982	+	202.982i	−0.160390	+	0.160390i
$118$		0			0
$119$			1646.57i			1.26841i
$120$		0			0
$121$			666.876i			0.501034i
$122$		0			0
$123$	395.764	−	395.764i	0.290121	−	0.290121i
$124$		0			0
$125$	391.433	+	391.433i	0.280087	+	0.280087i
$126$		0			0
$127$	2298.87			1.60623			0.803117	−	0.595821i	$-0.203173\pi$
$127$	2298.87			1.60623			0.803117	+	0.595821i	$0.203173\pi$
$128$		0			0
$129$	46.3845			0.0316583
$130$		0			0
$131$	916.347	+	916.347i	0.611157	+	0.611157i	0.943248	−	0.332090i	$-0.107754\pi$
$131$	916.347	+	916.347i	0.611157	+	0.611157i	−0.332090	+	0.943248i	$0.607754\pi$
$132$		0			0
$133$	−219.673	+	219.673i	−0.143219	+	0.143219i
$134$		0			0
$135$		−	393.106i		−	0.250616i
$136$		0			0
$137$			867.840i			0.541201i	0.962692	+	0.270601i	$0.0872223\pi$
$137$			867.840i			0.541201i	−0.962692	+	0.270601i	$0.912778\pi$
$138$		0			0
$139$	241.394	−	241.394i	0.147300	−	0.147300i	−0.629611	−	0.776911i	$-0.716786\pi$
$139$	241.394	−	241.394i	0.147300	−	0.147300i	0.776911	+	0.629611i	$0.216786\pi$
$140$		0			0
$141$	49.0758	+	49.0758i	0.0293115	+	0.0293115i
$142$		0			0
$143$	821.967			0.480674
$144$		0			0
$145$	2436.49			1.39544
$146$		0			0
$147$	1559.73	+	1559.73i	0.875130	+	0.875130i
$148$		0			0
$149$	−1733.18	+	1733.18i	−0.952939	+	0.952939i	−0.998941	−	0.0460022i	$-0.985352\pi$
$149$	−1733.18	+	1733.18i	−0.952939	+	0.952939i	0.0460022	+	0.998941i	$0.485352\pi$
$150$		0			0
$151$			1719.99i			0.926959i	0.886108	+	0.463479i	$0.153399\pi$
$151$			1719.99i			0.926959i	−0.886108	+	0.463479i	$0.846601\pi$
$152$		0			0
$153$			451.296i			0.238465i
$154$		0			0
$155$	2574.91	−	2574.91i	1.33433	−	1.33433i
$156$		0			0
$157$	−1613.85	−	1613.85i	−0.820377	−	0.820377i	0.165785	−	0.986162i	$-0.446984\pi$
$157$	−1613.85	−	1613.85i	−0.820377	−	0.820377i	−0.986162	+	0.165785i	$0.946984\pi$
$158$		0			0
$159$	−571.332			−0.284966
$160$		0			0
$161$	6136.74			3.00400
$162$		0			0
$163$	−2582.38	−	2582.38i	−1.24090	−	1.24090i	−0.959626	−	0.281278i	$-0.909242\pi$
$163$	−2582.38	−	2582.38i	−1.24090	−	1.24090i	−0.281278	−	0.959626i	$-0.590758\pi$
$164$		0			0
$165$	−795.934	+	795.934i	−0.375536	+	0.375536i
$166$		0			0
$167$		−	1938.49i		−	0.898233i	−0.893473	−	0.449117i	$-0.851739\pi$
$167$		−	1938.49i		−	0.898233i	0.893473	−	0.449117i	$-0.148261\pi$
$168$		0			0
$169$		−	1179.68i		−	0.536948i
$170$		0			0
$171$	−60.2084	+	60.2084i	−0.0269254	+	0.0269254i
$172$		0			0
$173$	−2044.47	−	2044.47i	−0.898487	−	0.898487i	0.0968155	−	0.995302i	$-0.469134\pi$
$173$	−2044.47	−	2044.47i	−0.898487	−	0.898487i	−0.995302	+	0.0968155i	$0.969134\pi$
$174$		0			0
$175$	2856.11			1.23373
$176$		0			0
$177$	937.383			0.398068
$178$		0			0
$179$	676.126	+	676.126i	0.282324	+	0.282324i	0.834035	−	0.551711i	$-0.186025\pi$
$179$	676.126	+	676.126i	0.282324	+	0.282324i	−0.551711	+	0.834035i	$0.686025\pi$
$180$		0			0
$181$	1298.63	−	1298.63i	0.533295	−	0.533295i	−0.388257	−	0.921551i	$-0.626923\pi$
$181$	1298.63	−	1298.63i	0.533295	−	0.533295i	0.921551	+	0.388257i	$0.126923\pi$
$182$		0			0
$183$			1925.50i			0.777798i
$184$		0			0
$185$		−	4095.66i		−	1.62767i
$186$		0			0
$187$	913.752	−	913.752i	0.357327	−	0.357327i
$188$		0			0
$189$	626.918	+	626.918i	0.241278	+	0.241278i
$190$		0			0
$191$	−2290.42			−0.867692			−0.433846	−	0.900987i	$-0.642844\pi$
$191$	−2290.42			−0.867692			−0.433846	+	0.900987i	$0.642844\pi$
$192$		0			0
$193$	128.763			0.0480235			0.0240117	−	0.999712i	$-0.492356\pi$
$193$	128.763			0.0480235			0.0240117	+	0.999712i	$0.492356\pi$
$194$		0			0
$195$	−985.104	−	985.104i	−0.361768	−	0.361768i
$196$		0			0
$197$	725.669	−	725.669i	0.262446	−	0.262446i	−0.563601	−	0.826047i	$-0.690585\pi$
$197$	725.669	−	725.669i	0.262446	−	0.262446i	0.826047	+	0.563601i	$0.190585\pi$
$198$		0			0
$199$			2779.71i			0.990192i	0.868838	+	0.495096i	$0.164867\pi$
$199$			2779.71i			0.990192i	−0.868838	+	0.495096i	$0.835133\pi$
$200$		0			0
$201$		−	781.802i		−	0.274349i
$202$		0			0
$203$	−3885.66	+	3885.66i	−1.34345	+	1.34345i
$204$		0			0
$205$	1920.71	+	1920.71i	0.654381	+	0.654381i
$206$		0			0
$207$	1681.97			0.564758
$208$		0			0
$209$	243.811			0.0806928
$210$		0			0
$211$	−691.983	−	691.983i	−0.225773	−	0.225773i	0.585151	−	0.810924i	$-0.301035\pi$
$211$	−691.983	−	691.983i	−0.225773	−	0.225773i	−0.810924	+	0.585151i	$0.801035\pi$
$212$		0			0
$213$	−39.9154	+	39.9154i	−0.0128402	+	0.0128402i
$214$		0			0
$215$			225.111i			0.0714068i
$216$		0			0
$217$			8212.84i			2.56924i
$218$		0			0
$219$	1757.90	−	1757.90i	0.542411	−	0.542411i
$220$		0			0
$221$	1130.92	+	1130.92i	0.344227	+	0.344227i
$222$		0			0
$223$	2188.31			0.657130			0.328565	−	0.944481i	$-0.393435\pi$
$223$	2188.31			0.657130			0.328565	+	0.944481i	$0.393435\pi$
$224$		0			0
$225$	782.809			0.231943
$226$		0			0
$227$	−3063.77	−	3063.77i	−0.895814	−	0.895814i	0.0992483	−	0.995063i	$-0.468356\pi$
$227$	−3063.77	−	3063.77i	−0.895814	−	0.895814i	−0.995063	+	0.0992483i	$0.968356\pi$
$228$		0			0
$229$	3654.19	−	3654.19i	1.05448	−	1.05448i	0.0560514	−	0.998428i	$-0.482149\pi$
$229$	3654.19	−	3654.19i	1.05448	−	1.05448i	0.998428	−	0.0560514i	$-0.0178511\pi$
$230$		0			0
$231$		−	2538.68i		−	0.723086i
$232$		0			0
$233$		−	4142.40i		−	1.16471i	−0.812935	−	0.582355i	$-0.802131\pi$
$233$		−	4142.40i		−	1.16471i	0.812935	−	0.582355i	$-0.197869\pi$
$234$		0			0
$235$	−238.173	+	238.173i	−0.0661135	+	0.0661135i
$236$		0			0
$237$	2223.92	+	2223.92i	0.609533	+	0.609533i
$238$		0			0
$239$	−3081.29			−0.833942			−0.416971	−	0.908920i	$-0.636908\pi$
$239$	−3081.29			−0.833942			−0.416971	+	0.908920i	$0.636908\pi$
$240$		0			0
$241$	−5328.92			−1.42434			−0.712170	−	0.702007i	$-0.752287\pi$
$241$	−5328.92			−1.42434			−0.712170	+	0.702007i	$0.752287\pi$
$242$		0			0
$243$	171.827	+	171.827i	0.0453609	+	0.0453609i
$244$		0			0
$245$	−7569.61	+	7569.61i	−1.97390	+	1.97390i
$246$		0			0
$247$			301.758i			0.0777345i
$248$		0			0
$249$		−	735.692i		−	0.187239i
$250$		0			0
$251$	−360.857	+	360.857i	−0.0907455	+	0.0907455i	−0.751022	−	0.660277i	$-0.770439\pi$
$251$	−360.857	+	360.857i	−0.0907455	+	0.0907455i	0.660277	+	0.751022i	$0.270439\pi$
$252$		0			0
$253$	−3405.53	−	3405.53i	−0.846261	−	0.846261i
$254$		0			0
$255$	−2190.21			−0.537868
$256$		0			0
$257$	−4829.14			−1.17211			−0.586057	−	0.810270i	$-0.699321\pi$
$257$	−4829.14			−1.17211			−0.586057	+	0.810270i	$0.699321\pi$
$258$		0			0
$259$	6531.68	+	6531.68i	1.56702	+	1.56702i
$260$		0			0
$261$	−1064.99	+	1064.99i	−0.252572	+	0.252572i
$262$		0			0
$263$		−	2949.69i		−	0.691581i	−0.938312	−	0.345791i	$-0.887611\pi$
$263$		−	2949.69i		−	0.691581i	0.938312	−	0.345791i	$-0.112389\pi$
$264$		0			0
$265$		−	2772.77i		−	0.642754i
$266$		0			0
$267$	−710.999	+	710.999i	−0.162968	+	0.162968i
$268$		0			0
$269$	−2262.88	−	2262.88i	−0.512900	−	0.512900i	0.402514	−	0.915414i	$-0.368137\pi$
$269$	−2262.88	−	2262.88i	−0.512900	−	0.512900i	−0.915414	+	0.402514i	$0.868137\pi$
$270$		0			0
$271$	−1330.31			−0.298194			−0.149097	−	0.988823i	$-0.547637\pi$
$271$	−1330.31			−0.298194			−0.149097	+	0.988823i	$0.547637\pi$
$272$		0			0
$273$	3142.05			0.696577
$274$		0			0
$275$	−1584.98	−	1584.98i	−0.347555	−	0.347555i
$276$		0			0
$277$	−3226.46	+	3226.46i	−0.699853	+	0.699853i	−0.964379	−	0.264525i	$-0.914785\pi$
$277$	−3226.46	+	3226.46i	−0.699853	+	0.699853i	0.264525	+	0.964379i	$0.414785\pi$
$278$		0			0
$279$			2250.99i			0.483023i
$280$		0			0
$281$			6371.42i			1.35262i	0.736615	+	0.676312i	$0.236423\pi$
$281$			6371.42i			1.35262i	−0.736615	+	0.676312i	$0.763577\pi$
$282$		0			0
$283$	−2438.64	+	2438.64i	−0.512234	+	0.512234i	−0.915210	−	0.402976i	$-0.867976\pi$
$283$	−2438.64	+	2438.64i	−0.512234	+	0.512234i	0.402976	+	0.915210i	$0.367976\pi$
$284$		0			0
$285$	−292.201	−	292.201i	−0.0607316	−	0.0607316i
$286$		0			0
$287$	−6126.22			−1.26000
$288$		0			0
$289$	−2398.58			−0.488212
$290$		0			0
$291$	1457.61	+	1457.61i	0.293630	+	0.293630i
$292$		0			0
$293$	6920.93	−	6920.93i	1.37995	−	1.37995i	0.535265	−	0.844684i	$-0.320212\pi$
$293$	6920.93	−	6920.93i	1.37995	−	1.37995i	0.844684	−	0.535265i	$-0.179788\pi$
$294$		0			0
$295$			4549.27i			0.897860i
$296$		0			0
$297$		−	695.806i		−	0.135942i
$298$		0			0
$299$	4214.93	−	4214.93i	0.815237	−	0.815237i
$300$		0			0
$301$	−359.003	−	359.003i	−0.0687462	−	0.0687462i
$302$		0			0
$303$	−219.091			−0.0415394
$304$		0			0
$305$	−9344.76			−1.75436
$306$		0			0
$307$	−2964.65	−	2964.65i	−0.551146	−	0.551146i	0.375626	−	0.926771i	$-0.377428\pi$
$307$	−2964.65	−	2964.65i	−0.551146	−	0.551146i	−0.926771	+	0.375626i	$0.877428\pi$
$308$		0			0
$309$	246.625	−	246.625i	0.0454045	−	0.0454045i
$310$		0			0
$311$		−	3503.10i		−	0.638722i	−0.947633	−	0.319361i	$-0.896532\pi$
$311$		−	3503.10i		−	0.638722i	0.947633	−	0.319361i	$-0.103468\pi$
$312$		0			0
$313$		−	119.690i		−	0.0216144i	−0.999942	−	0.0108072i	$-0.996560\pi$
$313$		−	119.690i		−	0.0216144i	0.999942	−	0.0108072i	$-0.00344010\pi$
$314$		0			0
$315$	−3042.54	+	3042.54i	−0.544215	+	0.544215i
$316$		0			0
$317$	−1793.71	−	1793.71i	−0.317806	−	0.317806i	0.530118	−	0.847924i	$-0.322148\pi$
$317$	−1793.71	−	1793.71i	−0.317806	−	0.317806i	−0.847924	+	0.530118i	$0.822148\pi$
$318$		0			0
$319$	4312.63			0.756931
$320$		0			0
$321$	−1403.85			−0.244098
$322$		0			0
$323$	335.454	+	335.454i	0.0577869	+	0.0577869i
$324$		0			0
$325$	1961.68	−	1961.68i	0.334814	−	0.334814i
$326$		0			0
$327$		−	2156.16i		−	0.364636i
$328$		0			0
$329$		−	759.667i		−	0.127300i
$330$		0			0
$331$	1546.84	−	1546.84i	0.256864	−	0.256864i	−0.566913	−	0.823778i	$-0.691862\pi$
$331$	1546.84	−	1546.84i	0.256864	−	0.256864i	0.823778	+	0.566913i	$0.191862\pi$
$332$		0			0
$333$	1790.22	+	1790.22i	0.294604	+	0.294604i
$334$		0			0
$335$	3794.21			0.618806
$336$		0			0
$337$	2433.56			0.393367			0.196683	−	0.980467i	$-0.436983\pi$
$337$	2433.56			0.393367			0.196683	+	0.980467i	$0.436983\pi$
$338$		0			0
$339$	4130.47	+	4130.47i	0.661759	+	0.661759i
$340$		0			0
$341$	4557.65	−	4557.65i	0.723784	−	0.723784i
$342$		0			0
$343$		−	12880.7i		−	2.02767i
$344$		0			0
$345$			8162.88i			1.27384i
$346$		0			0
$347$	−1171.50	+	1171.50i	−0.181237	+	0.181237i	−0.791895	−	0.610658i	$-0.790905\pi$
$347$	−1171.50	+	1171.50i	−0.181237	+	0.181237i	0.610658	+	0.791895i	$0.290905\pi$
$348$		0			0
$349$	7672.16	+	7672.16i	1.17674	+	1.17674i	0.980571	+	0.196166i	$0.0628492\pi$
$349$	7672.16	+	7672.16i	1.17674	+	1.17674i	0.196166	+	0.980571i	$0.437151\pi$
$350$		0			0
$351$	861.179			0.130958
$352$		0			0
$353$	−2040.98			−0.307734			−0.153867	−	0.988092i	$-0.549173\pi$
$353$	−2040.98			−0.307734			−0.153867	+	0.988092i	$0.549173\pi$
$354$		0			0
$355$	−193.716	−	193.716i	−0.0289616	−	0.0289616i
$356$		0			0
$357$	3492.91	−	3492.91i	0.517827	−	0.517827i
$358$		0			0
$359$			4623.13i			0.679664i	0.940486	+	0.339832i	$0.110370\pi$
$359$			4623.13i			0.679664i	−0.940486	+	0.339832i	$0.889630\pi$
$360$		0			0
$361$		−	6769.49i		−	0.986950i
$362$		0			0
$363$	1414.66	−	1414.66i	0.204546	−	0.204546i
$364$		0			0
$365$	8531.38	+	8531.38i	1.22343	+	1.22343i
$366$		0			0
$367$	−10876.3			−1.54697			−0.773487	−	0.633813i	$-0.781489\pi$
$367$	−10876.3			−1.54697			−0.773487	+	0.633813i	$0.781489\pi$
$368$		0			0
$369$	−1679.08			−0.236882
$370$		0			0
$371$	4421.96	+	4421.96i	0.618805	+	0.618805i
$372$		0			0
$373$	−621.022	+	621.022i	−0.0862073	+	0.0862073i	−0.748895	−	0.662688i	$-0.769415\pi$
$373$	−621.022	+	621.022i	−0.0862073	+	0.0862073i	0.662688	+	0.748895i	$0.269415\pi$
$374$		0			0
$375$		−	1660.71i		−	0.228690i
$376$		0			0
$377$			5337.62i			0.729181i
$378$		0			0
$379$	−8642.89	+	8642.89i	−1.17139	+	1.17139i	−0.189507	+	0.981879i	$0.560689\pi$
$379$	−8642.89	+	8642.89i	−1.17139	+	1.17139i	−0.981879	+	0.189507i	$0.939311\pi$
$380$		0			0
$381$	−4876.64	−	4876.64i	−0.655742	−	0.655742i
$382$		0			0
$383$	3607.79			0.481330			0.240665	−	0.970608i	$-0.422635\pi$
$383$	3607.79			0.481330			0.240665	+	0.970608i	$0.422635\pi$
$384$		0			0
$385$	12320.6			1.63095
$386$		0			0
$387$	−98.3963	−	98.3963i	−0.0129245	−	0.0129245i
$388$		0			0
$389$	3437.52	−	3437.52i	0.448045	−	0.448045i	−0.446659	−	0.894704i	$-0.647386\pi$
$389$	3437.52	−	3437.52i	0.448045	−	0.448045i	0.894704	+	0.446659i	$0.147386\pi$
$390$		0			0
$391$		−	9371.18i		−	1.21207i
$392$		0			0
$393$		−	3887.73i		−	0.499008i
$394$		0			0
$395$	−10793.1	+	10793.1i	−1.37483	+	1.37483i
$396$		0			0
$397$	1579.30	+	1579.30i	0.199655	+	0.199655i	0.799852	−	0.600197i	$-0.204911\pi$
$397$	1579.30	+	1579.30i	0.199655	+	0.199655i	−0.600197	+	0.799852i	$0.704911\pi$
$398$		0			0
$399$	931.994			0.116937
$400$		0			0
$401$	2316.77			0.288513			0.144257	−	0.989540i	$-0.453921\pi$
$401$	2316.77			0.288513			0.144257	+	0.989540i	$0.453921\pi$
$402$		0			0
$403$	5640.87	+	5640.87i	0.697250	+	0.697250i
$404$		0			0
$405$	−833.904	+	833.904i	−0.102314	+	0.102314i
$406$		0			0
$407$		−	7249.40i		−	0.882898i
$408$		0			0
$409$			669.173i			0.0809009i	0.999182	+	0.0404504i	$0.0128793\pi$
$409$			669.173i			0.0809009i	−0.999182	+	0.0404504i	$0.987121\pi$
$410$		0			0
$411$	1840.97	−	1840.97i	0.220945	−	0.220945i
$412$		0			0
$413$	−7255.09	−	7255.09i	−0.864406	−	0.864406i
$414$		0			0
$415$	3570.44			0.422327
$416$		0			0
$417$	−1024.15			−0.120270
$418$		0			0
$419$	3656.45	+	3656.45i	0.426323	+	0.426323i	0.887374	−	0.461051i	$-0.152527\pi$
$419$	3656.45	+	3656.45i	0.426323	+	0.426323i	−0.461051	+	0.887374i	$0.652527\pi$
$420$		0			0
$421$	−837.867	+	837.867i	−0.0969956	+	0.0969956i	−0.753939	−	0.656944i	$-0.771849\pi$
$421$	−837.867	+	837.867i	−0.0969956	+	0.0969956i	0.656944	+	0.753939i	$0.271849\pi$
$422$		0			0
$423$		−	208.211i		−	0.0239328i
$424$		0			0
$425$		−	4361.46i		−	0.497793i
$426$		0			0
$427$	14902.9	−	14902.9i	1.68899	−	1.68899i
$428$		0			0
$429$	−1743.66	−	1743.66i	−0.196234	−	0.196234i
$430$		0			0
$431$	6690.20			0.747693			0.373846	−	0.927491i	$-0.378039\pi$
$431$	6690.20			0.747693			0.373846	+	0.927491i	$0.378039\pi$
$432$		0			0
$433$	−7836.97			−0.869794			−0.434897	−	0.900480i	$-0.643215\pi$
$433$	−7836.97			−0.869794			−0.434897	+	0.900480i	$0.643215\pi$
$434$		0			0
$435$	−5168.57	−	5168.57i	−0.569687	−	0.569687i
$436$		0			0
$437$	1250.23	−	1250.23i	0.136857	−	0.136857i
$438$		0			0
$439$			6041.06i			0.656775i	0.944543	+	0.328387i	$0.106505\pi$
$439$			6041.06i			0.656775i	−0.944543	+	0.328387i	$0.893495\pi$
$440$		0			0
$441$		−	6617.36i		−	0.714541i
$442$		0			0
$443$	8281.65	−	8281.65i	0.888201	−	0.888201i	−0.106149	−	0.994350i	$-0.533852\pi$
$443$	8281.65	−	8281.65i	0.888201	−	0.888201i	0.994350	+	0.106149i	$0.0338521\pi$
$444$		0			0
$445$	−3450.59	−	3450.59i	−0.367581	−	0.367581i
$446$		0			0
$447$	7353.28			0.778072
$448$		0			0
$449$	15502.7			1.62944			0.814718	−	0.579858i	$-0.196892\pi$
$449$	15502.7			1.62944			0.814718	+	0.579858i	$0.196892\pi$
$450$		0			0
$451$	3399.69	+	3399.69i	0.354956	+	0.354956i
$452$		0			0
$453$	3648.65	−	3648.65i	0.378429	−	0.378429i
$454$		0			0
$455$			15248.9i			1.57116i
$456$		0			0
$457$			4866.06i			0.498085i	0.968493	+	0.249043i	$0.0801159\pi$
$457$			4866.06i			0.498085i	−0.968493	+	0.249043i	$0.919884\pi$
$458$		0			0
$459$	957.343	−	957.343i	0.0973528	−	0.0973528i
$460$		0			0
$461$	7449.82	+	7449.82i	0.752653	+	0.752653i	0.974974	−	0.222321i	$-0.0713633\pi$
$461$	7449.82	+	7449.82i	0.752653	+	0.752653i	−0.222321	+	0.974974i	$0.571363\pi$
$462$		0			0
$463$	−6924.56			−0.695058			−0.347529	−	0.937669i	$-0.612979\pi$
$463$	−6924.56			−0.695058			−0.347529	+	0.937669i	$0.612979\pi$
$464$		0			0
$465$	−10924.4			−1.08948
$466$		0			0
$467$	−4040.04	−	4040.04i	−0.400323	−	0.400323i	0.478024	−	0.878347i	$-0.341353\pi$
$467$	−4040.04	−	4040.04i	−0.400323	−	0.400323i	−0.878347	+	0.478024i	$0.841353\pi$
$468$		0			0
$469$	−6050.94	+	6050.94i	−0.595750	+	0.595750i
$470$		0			0
$471$			6846.98i			0.669835i
$472$		0			0
$473$			398.452i			0.0387333i
$474$		0			0
$475$	581.872	−	581.872i	0.0562066	−	0.0562066i
$476$		0			0
$477$	1211.98	+	1211.98i	0.116337	+	0.116337i
$478$		0			0
$479$	9957.56			0.949839			0.474919	−	0.880029i	$-0.342477\pi$
$479$	9957.56			0.949839			0.474919	+	0.880029i	$0.342477\pi$
$480$		0			0
$481$	8972.38			0.850531
$482$		0			0
$483$	−13018.0	−	13018.0i	−1.22638	−	1.22638i
$484$		0			0
$485$	−7074.00	+	7074.00i	−0.662296	+	0.662296i
$486$		0			0
$487$			7671.90i			0.713854i	0.934132	+	0.356927i	$0.116176\pi$
$487$			7671.90i			0.713854i	−0.934132	+	0.356927i	$0.883824\pi$
$488$		0			0
$489$			10956.1i			1.01319i
$490$		0			0
$491$	13794.0	−	13794.0i	1.26785	−	1.26785i	0.320656	−	0.947196i	$-0.396097\pi$
$491$	13794.0	−	13794.0i	1.26785	−	1.26785i	0.947196	−	0.320656i	$-0.103903\pi$
$492$		0			0
$493$	5933.64	+	5933.64i	0.542065	+	0.542065i
$494$		0			0
$495$	3376.86			0.306623
$496$		0			0
$497$	617.869			0.0557650
$498$		0			0
$499$	−2138.01	−	2138.01i	−0.191805	−	0.191805i	0.604671	−	0.796476i	$-0.293305\pi$
$499$	−2138.01	−	2138.01i	−0.191805	−	0.191805i	−0.796476	+	0.604671i	$0.793305\pi$
$500$		0			0
$501$	−4112.16	+	4112.16i	−0.366702	+	0.366702i
$502$		0			0
$503$			1414.75i			0.125409i	0.998032	+	0.0627045i	$0.0199726\pi$
$503$			1414.75i			0.125409i	−0.998032	+	0.0627045i	$0.980027\pi$
$504$		0			0
$505$		−	1063.28i		−	0.0936942i
$506$		0			0
$507$	−2502.47	+	2502.47i	−0.219208	+	0.219208i
$508$		0			0
$509$	−10526.7	−	10526.7i	−0.916677	−	0.916677i	0.0801087	−	0.996786i	$-0.474473\pi$
$509$	−10526.7	−	10526.7i	−0.916677	−	0.916677i	−0.996786	+	0.0801087i	$0.974473\pi$
$510$		0			0
$511$	−27211.4			−2.35570
$512$		0			0
$513$	255.443			0.0219845
$514$		0			0
$515$	1196.91	+	1196.91i	0.102412	+	0.102412i
$516$		0			0
$517$	−421.571	+	421.571i	−0.0358620	+	0.0358620i
$518$		0			0
$519$			8673.95i			0.733611i
$520$		0			0
$521$		−	2004.13i		−	0.168527i	−0.996444	−	0.0842636i	$-0.973146\pi$
$521$		−	2004.13i		−	0.168527i	0.996444	−	0.0842636i	$-0.0268538\pi$
$522$		0			0
$523$	−1006.02	+	1006.02i	−0.0841110	+	0.0841110i	−0.747911	−	0.663800i	$-0.768943\pi$
$523$	−1006.02	+	1006.02i	−0.0841110	+	0.0841110i	0.663800	+	0.747911i	$0.268943\pi$
$524$		0			0
$525$	−6058.73	−	6058.73i	−0.503666	−	0.503666i
$526$		0			0
$527$	12541.5			1.03665
$528$		0			0
$529$	−22759.2			−1.87057
$530$		0			0
$531$	−1988.49	−	1988.49i	−0.162510	−	0.162510i
$532$		0			0
$533$	−4207.70	+	4207.70i	−0.341943	+	0.341943i
$534$		0			0
$535$		−	6813.12i		−	0.550574i
$536$		0			0
$537$		−	2868.56i		−	0.230517i
$538$		0			0
$539$	−13398.4	+	13398.4i	−1.07070	+	1.07070i
$540$		0			0
$541$	−13442.8	−	13442.8i	−1.06830	−	1.06830i	−0.997489	−	0.0708153i	$-0.977440\pi$
$541$	−13442.8	−	13442.8i	−1.06830	−	1.06830i	−0.0708153	−	0.997489i	$-0.522560\pi$
$542$		0			0
$543$	−5509.61			−0.435433
$544$		0			0
$545$	10464.2			0.822454
$546$		0			0
$547$	−10996.4	−	10996.4i	−0.859546	−	0.859546i	0.131739	−	0.991284i	$-0.457944\pi$
$547$	−10996.4	−	10996.4i	−0.859546	−	0.859546i	−0.991284	+	0.131739i	$0.957944\pi$
$548$		0			0
$549$	4084.60	−	4084.60i	0.317535	−	0.317535i
$550$		0			0
$551$			1583.24i			0.122411i
$552$		0			0
$553$		−	34425.1i		−	2.64721i
$554$		0			0
$555$	−8688.21	+	8688.21i	−0.664494	+	0.664494i
$556$		0			0
$557$	7583.67	+	7583.67i	0.576895	+	0.576895i	0.934046	−	0.357151i	$-0.116252\pi$
$557$	7583.67	+	7583.67i	0.576895	+	0.576895i	−0.357151	+	0.934046i	$0.616252\pi$
$558$		0			0
$559$	−493.152			−0.0373133
$560$		0			0
$561$	−3876.72			−0.291756
$562$		0			0
$563$	−7263.00	−	7263.00i	−0.543693	−	0.543693i	0.380917	−	0.924609i	$-0.375608\pi$
$563$	−7263.00	−	7263.00i	−0.543693	−	0.543693i	−0.924609	+	0.380917i	$0.875608\pi$
$564$		0			0
$565$	−20045.8	+	20045.8i	−1.49263	+	1.49263i
$566$		0			0
$567$		−	2659.79i		−	0.197003i
$568$		0			0
$569$			26176.3i			1.92859i	0.264835	+	0.964294i	$0.414682\pi$
$569$			26176.3i			1.92859i	−0.264835	+	0.964294i	$0.585318\pi$
$570$		0			0
$571$	3443.57	−	3443.57i	0.252380	−	0.252380i	−0.569566	−	0.821946i	$-0.692889\pi$
$571$	3443.57	−	3443.57i	0.252380	−	0.252380i	0.821946	+	0.569566i	$0.192889\pi$
$572$		0			0
$573$	4858.72	+	4858.72i	0.354234	+	0.354234i
$574$		0			0
$575$	−16255.1			−1.17893
$576$		0			0
$577$	20621.2			1.48782			0.743909	−	0.668281i	$-0.232970\pi$
$577$	20621.2			1.48782			0.743909	+	0.668281i	$0.232970\pi$
$578$		0			0
$579$	−273.147	−	273.147i	−0.0196055	−	0.0196055i
$580$		0			0
$581$	−5694.06	+	5694.06i	−0.406591	+	0.406591i
$582$		0			0
$583$		−	4907.86i		−	0.348650i
$584$		0			0
$585$			4179.44i			0.295382i
$586$		0			0
$587$	−16989.3	+	16989.3i	−1.19459	+	1.19459i	−0.218823	+	0.975765i	$0.570222\pi$
$587$	−16989.3	+	16989.3i	−1.19459	+	1.19459i	−0.975765	+	0.218823i	$0.929778\pi$
$588$		0			0
$589$	1673.19	+	1673.19i	0.117050	+	0.117050i
$590$		0			0
$591$	−3078.75			−0.214286
$592$		0			0
$593$	2210.09			0.153048			0.0765239	−	0.997068i	$-0.475618\pi$
$593$	2210.09			0.153048			0.0765239	+	0.997068i	$0.475618\pi$
$594$		0			0
$595$	16951.7	+	16951.7i	1.16798	+	1.16798i
$596$		0			0
$597$	5896.65	−	5896.65i	0.404244	−	0.404244i
$598$		0			0
$599$			16545.3i			1.12859i	0.825574	+	0.564294i	$0.190852\pi$
$599$			16545.3i			1.12859i	−0.825574	+	0.564294i	$0.809148\pi$
$600$		0			0
$601$		−	19182.8i		−	1.30197i	−0.759092	−	0.650983i	$-0.774357\pi$
$601$		−	19182.8i		−	1.30197i	0.759092	−	0.650983i	$-0.225643\pi$
$602$		0			0
$603$	−1658.45	+	1658.45i	−0.112002	+	0.112002i
$604$		0			0
$605$	6865.57	+	6865.57i	0.461364	+	0.461364i
$606$		0			0
$607$	8375.82			0.560073			0.280036	−	0.959989i	$-0.409653\pi$
$607$	8375.82			0.560073			0.280036	+	0.959989i	$0.409653\pi$
$608$		0			0
$609$	16485.5			1.09692
$610$		0			0
$611$	−521.766	−	521.766i	−0.0345473	−	0.0345473i
$612$		0			0
$613$	−9161.47	+	9161.47i	−0.603635	+	0.603635i	−0.941275	−	0.337640i	$-0.890371\pi$
$613$	−9161.47	+	9161.47i	−0.603635	+	0.603635i	0.337640	+	0.941275i	$0.390371\pi$
$614$		0			0
$615$		−	8148.87i		−	0.534299i
$616$		0			0
$617$			7849.67i			0.512181i	0.966653	+	0.256091i	$0.0824346\pi$
$617$			7849.67i			0.512181i	−0.966653	+	0.256091i	$0.917565\pi$
$618$		0			0
$619$	−19459.4	+	19459.4i	−1.26355	+	1.26355i	−0.314190	+	0.949360i	$0.601733\pi$
$619$	−19459.4	+	19459.4i	−1.26355	+	1.26355i	−0.949360	+	0.314190i	$0.898267\pi$
$620$		0			0
$621$	−3568.00	−	3568.00i	−0.230562	−	0.230562i
$622$		0			0
$623$	11005.9			0.707771
$624$		0			0
$625$	18932.0			1.21165
$626$		0			0
$627$	−517.202	−	517.202i	−0.0329427	−	0.0329427i
$628$		0			0
$629$	9974.28	−	9974.28i	0.632274	−	0.632274i
$630$		0			0
$631$			27115.0i			1.71067i	0.518078	+	0.855334i	$0.326648\pi$
$631$			27115.0i			1.71067i	−0.518078	+	0.855334i	$0.673352\pi$
$632$		0			0
$633$			2935.83i			0.184343i
$634$		0			0
$635$	23667.1	−	23667.1i	1.47906	−	1.47906i
$636$		0			0
$637$	−16582.8	−	16582.8i	−1.03145	−	1.03145i
$638$		0			0
$639$	169.347			0.0104840
$640$		0			0
$641$	−22843.0			−1.40755			−0.703777	−	0.710421i	$-0.748505\pi$
$641$	−22843.0			−1.40755			−0.703777	+	0.710421i	$0.748505\pi$
$642$		0			0
$643$	−10235.4	−	10235.4i	−0.627754	−	0.627754i	0.319749	−	0.947502i	$-0.396402\pi$
$643$	−10235.4	−	10235.4i	−0.627754	−	0.627754i	−0.947502	+	0.319749i	$0.896402\pi$
$644$		0			0
$645$	477.533	−	477.533i	0.0291517	−	0.0291517i
$646$		0			0
$647$		−	3376.19i		−	0.205149i	−0.994725	−	0.102575i	$-0.967292\pi$
$647$		−	3376.19i		−	0.205149i	0.994725	−	0.102575i	$-0.0327080\pi$
$648$		0			0
$649$			8052.30i			0.487027i
$650$		0			0
$651$	17422.1	−	17422.1i	1.04889	−	1.04889i
$652$		0			0
$653$	2226.27	+	2226.27i	0.133416	+	0.133416i	0.770661	−	0.637245i	$-0.219926\pi$
$653$	2226.27	+	2226.27i	0.133416	+	0.133416i	−0.637245	+	0.770661i	$0.719926\pi$
$654$		0			0
$655$	18867.8			1.12554
$656$		0			0
$657$	−7458.14			−0.442877
$658$		0			0
$659$	−18279.8	−	18279.8i	−1.08055	−	1.08055i	−0.996458	−	0.0840908i	$-0.973201\pi$
$659$	−18279.8	−	18279.8i	−1.08055	−	1.08055i	−0.0840908	−	0.996458i	$-0.526799\pi$
$660$		0			0
$661$	2202.71	−	2202.71i	0.129615	−	0.129615i	−0.639323	−	0.768938i	$-0.720785\pi$
$661$	2202.71	−	2202.71i	0.129615	−	0.129615i	0.768938	+	0.639323i	$0.220785\pi$
$662$		0			0
$663$		−	4798.10i		−	0.281060i
$664$		0			0
$665$			4523.12i			0.263758i
$666$		0			0
$667$	22114.6	−	22114.6i	1.28378	−	1.28378i
$668$		0			0
$669$	−4642.10	−	4642.10i	−0.268272	−	0.268272i
$670$		0			0
$671$	−16540.4			−0.951619
$672$		0			0
$673$	−9151.57			−0.524171			−0.262086	−	0.965045i	$-0.584410\pi$
$673$	−9151.57			−0.524171			−0.262086	+	0.965045i	$0.584410\pi$
$674$		0			0
$675$	−1660.59	−	1660.59i	−0.0946905	−	0.0946905i
$676$		0			0
$677$	17555.1	−	17555.1i	0.996597	−	0.996597i	−0.00339762	−	0.999994i	$-0.501081\pi$
$677$	17555.1	−	17555.1i	0.996597	−	0.996597i	0.999994	+	0.00339762i	$0.00108150\pi$
$678$		0			0
$679$		−	22563.0i		−	1.27524i
$680$		0			0
$681$			12998.5i			0.731429i
$682$		0			0
$683$	933.246	−	933.246i	0.0522836	−	0.0522836i	−0.680482	−	0.732765i	$-0.738229\pi$
$683$	933.246	−	933.246i	0.0522836	−	0.0522836i	0.732765	+	0.680482i	$0.238229\pi$
$684$		0			0
$685$	8934.52	+	8934.52i	0.498351	+	0.498351i
$686$		0			0
$687$	−15503.4			−0.860979
$688$		0			0
$689$	6074.31			0.335868
$690$		0			0
$691$	14135.0	+	14135.0i	0.778175	+	0.778175i	0.979520	−	0.201345i	$-0.0645313\pi$
$691$	14135.0	+	14135.0i	0.778175	+	0.778175i	−0.201345	+	0.979520i	$0.564531\pi$
$692$		0			0
$693$	−5385.35	+	5385.35i	−0.295199	+	0.295199i
$694$		0			0
$695$		−	4970.35i		−	0.271275i
$696$		0			0
$697$			9355.10i			0.508393i
$698$		0			0
$699$	−8787.35	+	8787.35i	−0.475491	+	0.475491i
$700$		0			0
$701$	−22882.9	−	22882.9i	−1.23292	−	1.23292i	−0.962839	−	0.270077i	$-0.912951\pi$
$701$	−22882.9	−	22882.9i	−1.23292	−	1.23292i	−0.270077	−	0.962839i	$-0.587049\pi$
$702$		0			0
$703$	2661.38			0.142782
$704$		0			0
$705$	1010.48			0.0539815
$706$		0			0
$707$	1695.71	+	1695.71i	0.0902031	+	0.0902031i
$708$		0			0
$709$	−5612.43	+	5612.43i	−0.297291	+	0.297291i	−0.839952	−	0.542661i	$-0.817417\pi$
$709$	−5612.43	+	5612.43i	−0.297291	+	0.297291i	0.542661	+	0.839952i	$0.317417\pi$
$710$		0			0
$711$		−	9435.30i		−	0.497681i
$712$		0			0
$713$		−	46742.0i		−	2.45512i
$714$		0			0
$715$	8462.24	−	8462.24i	0.442615	−	0.442615i
$716$		0			0
$717$	6536.41	+	6536.41i	0.340455	+	0.340455i
$718$		0			0
$719$	29244.9			1.51690			0.758450	−	0.651732i	$-0.225957\pi$
$719$	29244.9			1.51690			0.758450	+	0.651732i	$0.225957\pi$
$720$		0			0
$721$	−3817.62			−0.197192
$722$		0			0
$723$	11304.3	+	11304.3i	0.581484	+	0.581484i
$724$		0			0
$725$	10292.4	−	10292.4i	0.527241	−	0.527241i
$726$		0			0
$727$			3308.71i			0.168794i	0.996432	+	0.0843971i	$0.0268964\pi$
$727$			3308.71i			0.168794i	−0.996432	+	0.0843971i	$0.973104\pi$
$728$		0			0
$729$		−	729.000i		−	0.0370370i
$730$		0			0
$731$	−548.220	+	548.220i	−0.0277382	+	0.0277382i
$732$		0			0
$733$	25116.9	+	25116.9i	1.26564	+	1.26564i	0.948318	+	0.317323i	$0.102784\pi$
$733$	25116.9	+	25116.9i	1.26564	+	1.26564i	0.317323	+	0.948318i	$0.397216\pi$
$734$		0			0
$735$	32115.2			1.61168
$736$		0			0
$737$	6715.84			0.335660
$738$		0			0
$739$	17503.6	+	17503.6i	0.871286	+	0.871286i	0.992613	−	0.121327i	$-0.0387150\pi$
$739$	17503.6	+	17503.6i	0.871286	+	0.871286i	−0.121327	+	0.992613i	$0.538715\pi$
$740$		0			0
$741$	640.126	−	640.126i	0.0317350	−	0.0317350i
$742$		0			0
$743$			14568.9i			0.719356i	0.933077	+	0.359678i	$0.117113\pi$
$743$			14568.9i			0.719356i	−0.933077	+	0.359678i	$0.882887\pi$
$744$		0			0
$745$			35686.6i			1.75498i
$746$		0			0
$747$	−1560.64	+	1560.64i	−0.0764402	+	0.0764402i
$748$		0			0
$749$	10865.4	+	10865.4i	0.530060	+	0.530060i
$750$		0			0
$751$	−10015.9			−0.486665			−0.243333	−	0.969943i	$-0.578241\pi$
$751$	−10015.9			−0.486665			−0.243333	+	0.969943i	$0.578241\pi$
$752$		0			0
$753$	1530.99			0.0740934
$754$		0			0
$755$	17707.5	+	17707.5i	0.853565	+	0.853565i
$756$		0			0
$757$	1632.84	−	1632.84i	0.0783971	−	0.0783971i	−0.666821	−	0.745218i	$-0.732345\pi$
$757$	1632.84	−	1632.84i	0.0783971	−	0.0783971i	0.745218	+	0.666821i	$0.232345\pi$
$758$		0			0
$759$			14448.5i			0.690970i
$760$		0			0
$761$			5379.15i			0.256234i	0.991759	+	0.128117i	$0.0408933\pi$
$761$			5379.15i			0.256234i	−0.991759	+	0.128117i	$0.959107\pi$
$762$		0			0
$763$	−16688.1	+	16688.1i	−0.791809	+	0.791809i
$764$		0			0
$765$	4646.14	+	4646.14i	0.219584	+	0.219584i
$766$		0			0
$767$	−9966.11			−0.469172
$768$		0			0
$769$	1737.59			0.0814812			0.0407406	−	0.999170i	$-0.487028\pi$
$769$	1737.59			0.0814812			0.0407406	+	0.999170i	$0.487028\pi$
$770$		0			0
$771$	10244.1	+	10244.1i	0.478514	+	0.478514i
$772$		0			0
$773$	−2551.94	+	2551.94i	−0.118741	+	0.118741i	−0.763980	−	0.645239i	$-0.776758\pi$
$773$	−2551.94	+	2551.94i	−0.118741	+	0.118741i	0.645239	+	0.763980i	$0.276758\pi$
$774$		0			0
$775$		−	21754.3i		−	1.00831i
$776$		0			0
$777$		−	27711.6i		−	1.27947i
$778$		0			0
$779$	−1248.09	+	1248.09i	−0.0574035	+	0.0574035i
$780$		0			0
$781$	−342.881	−	342.881i	−0.0157097	−	0.0157097i
$782$		0			0
$783$	4518.37			0.206224
$784$		0			0
$785$	−33229.5			−1.51084
$786$		0			0
$787$	12908.2	+	12908.2i	0.584658	+	0.584658i	0.936180	−	0.351522i	$-0.114336\pi$
$787$	12908.2	+	12908.2i	0.584658	+	0.584658i	−0.351522	+	0.936180i	$0.614336\pi$
$788$		0			0
$789$	−6257.24	+	6257.24i	−0.282337	+	0.282337i
$790$		0			0
$791$		−	63937.5i		−	2.87403i
$792$		0			0
$793$		−	20471.6i		−	0.916732i
$794$		0			0
$795$	−5881.93	+	5881.93i	−0.262403	+	0.262403i
$796$		0			0
$797$	7292.39	+	7292.39i	0.324102	+	0.324102i	0.850339	−	0.526236i	$-0.176397\pi$
$797$	7292.39	+	7292.39i	0.324102	+	0.324102i	−0.526236	+	0.850339i	$0.676397\pi$
$798$		0			0
$799$	−1160.06			−0.0513641
$800$		0			0
$801$	3016.51			0.133063
$802$		0			0
$803$	15100.7	+	15100.7i	0.663628	+	0.663628i
$804$		0			0
$805$	63178.5	−	63178.5i	2.76615	−	2.76615i
$806$		0			0
$807$			9600.59i			0.418781i
$808$		0			0
$809$			13623.8i			0.592073i	0.955177	+	0.296036i	$0.0956650\pi$
$809$			13623.8i			0.592073i	−0.955177	+	0.296036i	$0.904335\pi$
$810$		0			0
$811$	−6432.57	+	6432.57i	−0.278518	+	0.278518i	−0.832517	−	0.553999i	$-0.813101\pi$
$811$	−6432.57	+	6432.57i	−0.278518	+	0.278518i	0.553999	+	0.832517i	$0.313101\pi$
$812$		0			0
$813$	2822.01	+	2822.01i	0.121737	+	0.121737i
$814$		0			0
$815$	−53171.7			−2.28531
$816$		0			0
$817$	−146.279			−0.00626394
$818$		0			0
$819$	−6665.30	−	6665.30i	−0.284377	−	0.284377i
$820$		0			0
$821$	−10383.1	+	10383.1i	−0.441380	+	0.441380i	−0.892475	−	0.451096i	$-0.851033\pi$
$821$	−10383.1	+	10383.1i	−0.441380	+	0.441380i	0.451096	+	0.892475i	$0.351033\pi$
$822$		0			0
$823$		−	13572.9i		−	0.574876i	−0.957799	−	0.287438i	$-0.907196\pi$
$823$		−	13572.9i		−	0.574876i	0.957799	−	0.287438i	$-0.0928035\pi$
$824$		0			0
$825$			6724.49i			0.283778i
$826$		0			0
$827$	−14405.3	+	14405.3i	−0.605708	+	0.605708i	−0.941821	−	0.336114i	$-0.890887\pi$
$827$	−14405.3	+	14405.3i	−0.605708	+	0.605708i	0.336114	+	0.941821i	$0.390887\pi$
$828$		0			0
$829$	30030.7	+	30030.7i	1.25815	+	1.25815i	0.951975	+	0.306177i	$0.0990500\pi$
$829$	30030.7	+	30030.7i	1.25815	+	1.25815i	0.306177	+	0.951975i	$0.400950\pi$
$830$		0			0
$831$	13688.7			0.571428
$832$		0			0
$833$	−36869.0			−1.53353
$834$		0			0
$835$	−19957.0	−	19957.0i	−0.827114	−	0.827114i
$836$		0			0
$837$	4775.07	−	4775.07i	0.197193	−	0.197193i
$838$		0			0
$839$			5825.32i			0.239705i	0.992792	+	0.119852i	$0.0382421\pi$
$839$			5825.32i			0.239705i	−0.992792	+	0.119852i	$0.961758\pi$
$840$		0			0
$841$			3616.01i			0.148264i
$842$		0			0
$843$	13515.8	−	13515.8i	0.552206	−	0.552206i
$844$		0			0
$845$	−12144.9	−	12144.9i	−0.494434	−	0.494434i
$846$		0			0
$847$	−21898.2			−0.888346
$848$		0			0
$849$	10346.3			0.418237
$850$		0			0
$851$	−37173.9	−	37173.9i	−1.49742	−	1.49742i
$852$		0			0
$853$	16206.3	−	16206.3i	0.650521	−	0.650521i	−0.302598	−	0.953118i	$-0.597854\pi$
$853$	16206.3	−	16206.3i	0.650521	−	0.650521i	0.953118	+	0.302598i	$0.0978539\pi$
$854$		0			0
$855$			1239.70i			0.0495871i
$856$		0			0
$857$		−	2342.64i		−	0.0933759i	−0.998910	−	0.0466879i	$-0.985133\pi$
$857$		−	2342.64i		−	0.0933759i	0.998910	−	0.0466879i	$-0.0148666\pi$
$858$		0			0
$859$	12182.8	−	12182.8i	0.483904	−	0.483904i	−0.422472	−	0.906376i	$-0.638838\pi$
$859$	12182.8	−	12182.8i	0.483904	−	0.483904i	0.906376	+	0.422472i	$0.138838\pi$
$860$		0			0
$861$	12995.7	+	12995.7i	0.514391	+	0.514391i
$862$		0			0
$863$	29827.9			1.17654			0.588269	−	0.808665i	$-0.299810\pi$
$863$	29827.9			1.17654			0.588269	+	0.808665i	$0.299810\pi$
$864$		0			0
$865$	−42096.1			−1.65469
$866$		0			0
$867$	5088.16	+	5088.16i	0.199312	+	0.199312i
$868$		0			0
$869$	−19103.9	+	19103.9i	−0.745750	+	0.745750i
$870$		0			0
$871$			8312.00i			0.323354i
$872$		0			0
$873$		−	6184.10i		−	0.239748i
$874$		0			0
$875$	−12853.4	+	12853.4i	−0.496601	+	0.496601i
$876$		0			0
$877$	−26406.8	−	26406.8i	−1.01675	−	1.01675i	−0.999857	−	0.0168967i	$-0.994621\pi$
$877$	−26406.8	−	26406.8i	−1.01675	−	1.01675i	−0.0168967	−	0.999857i	$-0.505379\pi$
$878$		0			0
$879$	−29363.0			−1.12672
$880$		0			0
$881$	30799.2			1.17781			0.588906	−	0.808202i	$-0.299559\pi$
$881$	30799.2			1.17781			0.588906	+	0.808202i	$0.299559\pi$
$882$		0			0
$883$	−31934.4	−	31934.4i	−1.21708	−	1.21708i	−0.968651	−	0.248424i	$-0.920087\pi$
$883$	−31934.4	−	31934.4i	−1.21708	−	1.21708i	−0.248424	−	0.968651i	$-0.579913\pi$
$884$		0			0
$885$	9650.46	−	9650.46i	0.366550	−	0.366550i
$886$		0			0
$887$			8071.18i			0.305528i	0.988263	+	0.152764i	$0.0488175\pi$
$887$			8071.18i			0.305528i	−0.988263	+	0.152764i	$0.951183\pi$
$888$		0			0
$889$			75487.8i			2.84790i
$890$		0			0
$891$	−1476.03	+	1476.03i	−0.0554981	+	0.0554981i
$892$		0			0
$893$	−154.766	−	154.766i	−0.00579960	−	0.00579960i
$894$		0			0
$895$	13921.6			0.519941
$896$		0			0
$897$	−17882.4			−0.665638
$898$		0			0
$899$	29596.1	+	29596.1i	1.09798	+	1.09798i
$900$		0			0
$901$	6752.60	−	6752.60i	0.249680	−	0.249680i
$902$		0			0
$903$			1523.12i			0.0561311i
$904$		0			0
$905$		−	26739.1i		−	0.982140i
$906$		0			0
$907$	−5166.14	+	5166.14i	−0.189128	+	0.189128i	−0.795319	−	0.606191i	$-0.792697\pi$
$907$	−5166.14	+	5166.14i	−0.189128	+	0.189128i	0.606191	+	0.795319i	$0.292697\pi$
$908$		0			0
$909$	464.762	+	464.762i	0.0169584	+	0.0169584i
$910$		0			0
$911$	−31180.6			−1.13398			−0.566992	−	0.823723i	$-0.691893\pi$
$911$	−31180.6			−1.13398			−0.566992	+	0.823723i	$0.691893\pi$
$912$		0			0
$913$	6319.74			0.229083
$914$		0			0
$915$	19823.2	+	19823.2i	0.716214	+	0.716214i
$916$		0			0
$917$	−30090.0	+	30090.0i	−1.08360	+	1.08360i
$918$		0			0
$919$			27889.6i			1.00108i	0.865713	+	0.500541i	$0.166866\pi$
$919$			27889.6i			1.00108i	−0.865713	+	0.500541i	$0.833134\pi$
$920$		0			0
$921$			12578.0i			0.450009i
$922$		0			0
$923$	424.374	−	424.374i	0.0151337	−	0.0151337i
$924$		0			0
$925$	−17301.2	−	17301.2i	−0.614984	−	0.614984i
$926$		0			0
$927$	−1046.34			−0.0370726
$928$		0			0
$929$	17906.3			0.632385			0.316192	−	0.948695i	$-0.397595\pi$
$929$	17906.3			0.632385			0.316192	+	0.948695i	$0.397595\pi$
$930$		0			0
$931$	−4918.78	−	4918.78i	−0.173154	−	0.173154i
$932$		0			0
$933$	−7431.19	+	7431.19i	−0.260757	+	0.260757i
$934$		0			0
$935$		−	18814.4i		−	0.658070i
$936$		0			0
$937$		−	10815.1i		−	0.377070i	−0.982067	−	0.188535i	$-0.939626\pi$
$937$		−	10815.1i		−	0.377070i	0.982067	−	0.188535i	$-0.0603738\pi$
$938$		0			0
$939$	−253.901	+	253.901i	−0.00882402	+	0.00882402i
$940$		0			0
$941$	−29716.3	−	29716.3i	−1.02946	−	1.02946i	−0.999553	−	0.0299093i	$-0.990478\pi$
$941$	−29716.3	−	29716.3i	−1.02946	−	1.02946i	−0.0299093	−	0.999553i	$-0.509522\pi$
$942$		0			0
$943$	34866.3			1.20403
$944$		0			0
$945$	12908.4			0.444349
$946$		0			0
$947$	15362.1	+	15362.1i	0.527138	+	0.527138i	0.919718	−	0.392580i	$-0.128417\pi$
$947$	15362.1	+	15362.1i	0.527138	+	0.527138i	−0.392580	+	0.919718i	$0.628417\pi$
$948$		0			0
$949$	−18689.7	+	18689.7i	−0.639299	+	0.639299i
$950$		0			0
$951$			7610.05i			0.259488i
$952$		0			0
$953$		−	24261.6i		−	0.824671i	−0.911032	−	0.412336i	$-0.864713\pi$
$953$		−	24261.6i		−	0.824671i	0.911032	−	0.412336i	$-0.135287\pi$
$954$		0			0
$955$	−23580.2	+	23580.2i	−0.798991	+	0.798991i
$956$		0			0
$957$	−9148.47	−	9148.47i	−0.309016	−	0.309016i
$958$		0			0
$959$	−28497.2			−0.959565
$960$		0			0
$961$	32764.1			1.09980
$962$		0			0
$963$	2978.02	+	2978.02i	0.0996525	+	0.0996525i
$964$		0			0
$965$	1325.63	−	1325.63i	0.0442211	−	0.0442211i
$966$		0			0
$967$		−	6229.01i		−	0.207147i	−0.994622	−	0.103574i	$-0.966972\pi$
$967$		−	6229.01i		−	0.207147i	0.994622	−	0.103574i	$-0.0330277\pi$
$968$		0			0
$969$		−	1423.21i		−	0.0471828i
$970$		0			0
$971$	1224.70	−	1224.70i	0.0404762	−	0.0404762i	−0.686579	−	0.727055i	$-0.740888\pi$
$971$	1224.70	−	1224.70i	0.0404762	−	0.0404762i	0.727055	+	0.686579i	$0.240888\pi$
$972$		0			0
$973$	7926.62	+	7926.62i	0.261167	+	0.261167i
$974$		0			0
$975$	−8322.70			−0.273374
$976$		0			0
$977$	−35749.1			−1.17064			−0.585320	−	0.810802i	$-0.699031\pi$
$977$	−35749.1			−1.17064			−0.585320	+	0.810802i	$0.699031\pi$
$978$		0			0
$979$	−6107.62	−	6107.62i	−0.199387	−	0.199387i
$980$		0			0
$981$	−4573.91	+	4573.91i	−0.148862	+	0.148862i
$982$		0			0
$983$		−	53895.9i		−	1.74874i	−0.485259	−	0.874371i	$-0.661275\pi$
$983$		−	53895.9i		−	1.74874i	0.485259	−	0.874371i	$-0.338725\pi$
$984$		0			0
$985$		−	14941.7i		−	0.483332i
$986$		0			0
$987$	−1611.50	+	1611.50i	−0.0519701	+	0.0519701i
$988$		0			0
$989$	2043.21	+	2043.21i	0.0656928	+	0.0656928i
$990$		0			0
$991$	9898.33			0.317286			0.158643	−	0.987336i	$-0.449288\pi$
$991$	9898.33			0.317286			0.158643	+	0.987336i	$0.449288\pi$
$992$		0			0
$993$	−6562.70			−0.209729
$994$		0			0
$995$	28617.4	+	28617.4i	0.911791	+	0.911791i
$996$		0			0
$997$	−37538.1	+	37538.1i	−1.19242	+	1.19242i	−0.216034	+	0.976386i	$0.569312\pi$
$997$	−37538.1	+	37538.1i	−1.19242	+	1.19242i	−0.976386	+	0.216034i	$0.930688\pi$
$998$		0			0
$999$		−	7595.24i		−	0.240543i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.4.j.a.145.5		24
3.2	odd	2		576.4.k.b.145.3		24
4.3	odd	2		48.4.j.a.13.7	✓	24
8.3	odd	2		384.4.j.b.289.2		24
8.5	even	2		384.4.j.a.289.11		24
12.11	even	2		144.4.k.b.109.6		24
16.3	odd	4		384.4.j.b.97.2		24
16.5	even	4	inner	192.4.j.a.49.5		24
16.11	odd	4		48.4.j.a.37.7	yes	24
16.13	even	4		384.4.j.a.97.11		24
48.5	odd	4		576.4.k.b.433.3		24
48.11	even	4		144.4.k.b.37.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.7	✓	24	4.3	odd	2
48.4.j.a.37.7	yes	24	16.11	odd	4
144.4.k.b.37.6		24	48.11	even	4
144.4.k.b.109.6		24	12.11	even	2
192.4.j.a.49.5		24	16.5	even	4	inner
192.4.j.a.145.5		24	1.1	even	1	trivial
384.4.j.a.97.11		24	16.13	even	4
384.4.j.a.289.11		24	8.5	even	2
384.4.j.b.97.2		24	16.3	odd	4
384.4.j.b.289.2		24	8.3	odd	2
576.4.k.b.145.3		24	3.2	odd	2
576.4.k.b.433.3		24	48.5	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	192.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.12132 - 2.12132i) q^{3} +(10.2951 - 10.2951i) q^{5} +32.8369i q^{7} +9.00000i q^{9} +(18.2226 - 18.2226i) q^{11} +(22.5535 + 22.5535i) q^{13} -43.6785 q^{15} +50.1440 q^{17} +(6.68982 + 6.68982i) q^{19} +(69.6576 - 69.6576i) q^{21} -186.886i q^{23} -86.9788i q^{25} +(19.0919 - 19.0919i) q^{27} +(118.332 + 118.332i) q^{29} +250.110 q^{31} -77.3118 q^{33} +(338.060 + 338.060i) q^{35} +(198.913 - 198.913i) q^{37} -95.6866i q^{39} +186.565i q^{41} +(-10.9329 + 10.9329i) q^{43} +(92.6560 + 92.6560i) q^{45} -23.1346 q^{47} -735.263 q^{49} +(-106.371 - 106.371i) q^{51} +(134.664 - 134.664i) q^{53} -375.207i q^{55} -28.3825i q^{57} +(-220.943 + 220.943i) q^{59} +(-453.845 - 453.845i) q^{61} -295.532 q^{63} +464.383 q^{65} +(184.273 + 184.273i) q^{67} +(-396.444 + 396.444i) q^{69} -18.8163i q^{71} +828.683i q^{73} +(-184.510 + 184.510i) q^{75} +(598.373 + 598.373i) q^{77} -1048.37 q^{79} -81.0000 q^{81} +(173.404 + 173.404i) q^{83} +(516.238 - 516.238i) q^{85} -502.041i q^{87} -335.168i q^{89} +(-740.589 + 740.589i) q^{91} +(-530.564 - 530.564i) q^{93} +137.745 q^{95} -687.122 q^{97} +(164.003 + 164.003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 40 q^{11} - 120 q^{15} - 24 q^{19} + 400 q^{29} + 744 q^{31} + 456 q^{35} + 16 q^{37} - 1240 q^{43} - 1176 q^{49} - 744 q^{51} + 752 q^{53} + 1376 q^{59} - 912 q^{61} + 504 q^{63} + 976 q^{65} + 2256 q^{67}+ \cdots + 360 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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