LMFDB - Embedded newform 384.4.j.b.289.2

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			289.2
Character	$\chi$	$=$	384.289
Dual form			384.4.j.b.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12132 - 2.12132i) q^{3} +(-10.2951 + 10.2951i) q^{5} -32.8369i q^{7} +9.00000i q^{9} +O(q^{10})$	\(q+(-2.12132 - 2.12132i) q^{3} +(-10.2951 + 10.2951i) q^{5} -32.8369i q^{7} +9.00000i q^{9} +(18.2226 - 18.2226i) q^{11} +(-22.5535 - 22.5535i) q^{13} +43.6785 q^{15} +50.1440 q^{17} +(6.68982 + 6.68982i) q^{19} +(-69.6576 + 69.6576i) q^{21} +186.886i q^{23} -86.9788i q^{25} +(19.0919 - 19.0919i) q^{27} +(-118.332 - 118.332i) q^{29} -250.110 q^{31} -77.3118 q^{33} +(338.060 + 338.060i) q^{35} +(-198.913 + 198.913i) q^{37} +95.6866i q^{39} +186.565i q^{41} +(-10.9329 + 10.9329i) q^{43} +(-92.6560 - 92.6560i) q^{45} +23.1346 q^{47} -735.263 q^{49} +(-106.371 - 106.371i) q^{51} +(-134.664 + 134.664i) q^{53} +375.207i q^{55} -28.3825i q^{57} +(-220.943 + 220.943i) q^{59} +(453.845 + 453.845i) q^{61} +295.532 q^{63} +464.383 q^{65} +(184.273 + 184.273i) q^{67} +(396.444 - 396.444i) q^{69} +18.8163i q^{71} +828.683i q^{73} +(-184.510 + 184.510i) q^{75} +(-598.373 - 598.373i) q^{77} +1048.37 q^{79} -81.0000 q^{81} +(173.404 + 173.404i) q^{83} +(-516.238 + 516.238i) q^{85} +502.041i q^{87} -335.168i q^{89} +(-740.589 + 740.589i) q^{91} +(530.564 + 530.564i) q^{93} -137.745 q^{95} -687.122 q^{97} +(164.003 + 164.003i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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
$5$	−10.2951	+	10.2951i	−0.920823	+	0.920823i	−0.997088	−	0.0762646i	$-0.975701\pi$
$5$	−10.2951	+	10.2951i	−0.920823	+	0.920823i	0.0762646	+	0.997088i	$0.475701\pi$
$6$		0			0
$7$		−	32.8369i		−	1.77303i	−0.462703	−	0.886513i	$-0.653120\pi$
$7$		−	32.8369i		−	1.77303i	0.462703	−	0.886513i	$-0.346880\pi$
$8$		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	0.424334	−	0.905506i	$-0.360508\pi$
$13$	−22.5535	−	22.5535i	−0.481171	−	0.481171i	−0.905506	+	0.424334i	$0.860508\pi$
$14$		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	$0.321676\pi$
$23$			186.886i			1.69428i	−0.531373	+	0.847138i	$0.678324\pi$
$24$		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	0.218191	−	0.975906i	$-0.429984\pi$
$29$	−118.332	−	118.332i	−0.757715	−	0.757715i	−0.975906	+	0.218191i	$0.929984\pi$
$30$		0			0
$31$	−250.110			−1.44907			−0.724534	−	0.689239i	$-0.757945\pi$
$31$	−250.110			−1.44907			−0.724534	+	0.689239i	$0.757945\pi$
$32$		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	−0.993920	−	0.110107i	$-0.964881\pi$
$37$	−198.913	+	198.913i	−0.883813	+	0.883813i	0.110107	+	0.993920i	$0.464881\pi$
$38$		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	$-0.488570\pi$
$47$	23.1346			0.0717983			0.0358992	+	0.999355i	$0.488570\pi$
$48$		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	−0.859741	−	0.510730i	$-0.829375\pi$
$53$	−134.664	+	134.664i	−0.349011	+	0.349011i	0.510730	+	0.859741i	$0.329375\pi$
$54$		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	0.998927	−	0.0463225i	$-0.0147502\pi$
$61$	453.845	+	453.845i	0.952604	+	0.952604i	−0.0463225	+	0.998927i	$0.514750\pi$
$62$		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	$0.00500593\pi$
$71$			18.8163i			0.0314519i	−0.999876	+	0.0157259i	$0.994994\pi$
$72$		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	$-0.231722\pi$
$79$	1048.37			1.49304			0.746522	+	0.665361i	$0.231722\pi$
$80$		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	−0.732087	−	0.681211i	$-0.761453\pi$
$101$	−51.6403	+	51.6403i	−0.0508752	+	0.0508752i	0.681211	+	0.732087i	$0.261453\pi$
$102$		0			0
$103$		−	116.260i		−	0.111218i	−0.998453	−	0.0556089i	$-0.982290\pi$
$103$		−	116.260i		−	0.111218i	0.998453	−	0.0556089i	$-0.0177100\pi$
$104$		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	0.447632	−	0.894218i	$-0.352268\pi$
$109$	−508.212	−	508.212i	−0.446586	−	0.446586i	−0.894218	+	0.447632i	$0.852268\pi$
$110$		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	$-0.796827\pi$
$127$	−2298.87			−1.60623			−0.803117	+	0.595821i	$0.796827\pi$
$128$		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	−0.0460022	−	0.998941i	$-0.514648\pi$
$149$	1733.18	−	1733.18i	0.952939	−	0.952939i	0.998941	+	0.0460022i	$0.0146481\pi$
$150$		0			0
$151$		−	1719.99i		−	0.926959i	−0.886108	−	0.463479i	$-0.846601\pi$
$151$		−	1719.99i		−	0.926959i	0.886108	−	0.463479i	$-0.153399\pi$
$152$		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	0.986162	−	0.165785i	$-0.0530159\pi$
$157$	1613.85	+	1613.85i	0.820377	+	0.820377i	−0.165785	+	0.986162i	$0.553016\pi$
$158$		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	$0.148261\pi$
$167$			1938.49i			0.898233i	−0.893473	+	0.449117i	$0.851739\pi$
$168$		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	0.995302	−	0.0968155i	$-0.0308657\pi$
$173$	2044.47	+	2044.47i	0.898487	+	0.898487i	−0.0968155	+	0.995302i	$0.530866\pi$
$174$		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	−0.921551	−	0.388257i	$-0.873077\pi$
$181$	−1298.63	+	1298.63i	−0.533295	+	0.533295i	0.388257	+	0.921551i	$0.373077\pi$
$182$		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	$-0.357156\pi$
$191$	2290.42			0.867692			0.433846	+	0.900987i	$0.357156\pi$
$192$		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	−0.826047	−	0.563601i	$-0.809415\pi$
$197$	−725.669	+	725.669i	−0.262446	+	0.262446i	0.563601	+	0.826047i	$0.309415\pi$
$198$		0			0
$199$		−	2779.71i		−	0.990192i	−0.868838	−	0.495096i	$-0.835133\pi$
$199$		−	2779.71i		−	0.990192i	0.868838	−	0.495096i	$-0.164867\pi$
$200$		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	$-0.606565\pi$
$223$	−2188.31			−0.657130			−0.328565	+	0.944481i	$0.606565\pi$
$224$		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	$0.517851\pi$
$229$	−3654.19	+	3654.19i	−1.05448	+	1.05448i	−0.998428	+	0.0560514i	$0.982149\pi$
$230$		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	$-0.363092\pi$
$239$	3081.29			0.833942			0.416971	+	0.908920i	$0.363092\pi$
$240$		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	$0.112389\pi$
$263$			2949.69i			0.691581i	−0.938312	+	0.345791i	$0.887611\pi$
$264$		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	0.915414	−	0.402514i	$-0.131863\pi$
$269$	2262.88	+	2262.88i	0.512900	+	0.512900i	−0.402514	+	0.915414i	$0.631863\pi$
$270$		0			0
$271$	1330.31			0.298194			0.149097	−	0.988823i	$-0.452363\pi$
$271$	1330.31			0.298194			0.149097	+	0.988823i	$0.452363\pi$
$272$		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	−0.264525	−	0.964379i	$-0.585215\pi$
$277$	3226.46	−	3226.46i	0.699853	−	0.699853i	0.964379	+	0.264525i	$0.0852153\pi$
$278$		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	$0.679788\pi$
$293$	−6920.93	+	6920.93i	−1.37995	+	1.37995i	−0.844684	+	0.535265i	$0.820212\pi$
$294$		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	$0.103468\pi$
$311$			3503.10i			0.638722i	−0.947633	+	0.319361i	$0.896532\pi$
$312$		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	0.847924	−	0.530118i	$-0.177852\pi$
$317$	1793.71	+	1793.71i	0.317806	+	0.317806i	−0.530118	+	0.847924i	$0.677852\pi$
$318$		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	$-0.937151\pi$
$349$	−7672.16	−	7672.16i	−1.17674	−	1.17674i	−0.196166	−	0.980571i	$-0.562849\pi$
$350$		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	$-0.889630\pi$
$359$		−	4623.13i		−	0.679664i	0.940486	−	0.339832i	$-0.110370\pi$
$360$		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	$-0.218511\pi$
$367$	10876.3			1.54697			0.773487	+	0.633813i	$0.218511\pi$
$368$		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	−0.662688	−	0.748895i	$-0.730585\pi$
$373$	621.022	−	621.022i	0.0862073	−	0.0862073i	0.748895	+	0.662688i	$0.230585\pi$
$374$		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	$-0.577365\pi$
$383$	−3607.79			−0.481330			−0.240665	+	0.970608i	$0.577365\pi$
$384$		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	−0.894704	−	0.446659i	$-0.852614\pi$
$389$	−3437.52	+	3437.52i	−0.448045	+	0.448045i	0.446659	+	0.894704i	$0.352614\pi$
$390$		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	0.600197	−	0.799852i	$-0.295089\pi$
$397$	−1579.30	−	1579.30i	−0.199655	−	0.199655i	−0.799852	+	0.600197i	$0.795089\pi$
$398$		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	−0.656944	−	0.753939i	$-0.728151\pi$
$421$	837.867	−	837.867i	0.0969956	−	0.0969956i	0.753939	+	0.656944i	$0.228151\pi$
$422$		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	$-0.621961\pi$
$431$	−6690.20			−0.747693			−0.373846	+	0.927491i	$0.621961\pi$
$432$		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	$-0.893495\pi$
$439$		−	6041.06i		−	0.656775i	0.944543	−	0.328387i	$-0.106505\pi$
$440$		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	0.222321	−	0.974974i	$-0.428637\pi$
$461$	−7449.82	−	7449.82i	−0.752653	−	0.752653i	−0.974974	+	0.222321i	$0.928637\pi$
$462$		0			0
$463$	6924.56			0.695058			0.347529	−	0.937669i	$-0.387021\pi$
$463$	6924.56			0.695058			0.347529	+	0.937669i	$0.387021\pi$
$464$		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	$-0.657523\pi$
$479$	−9957.56			−0.949839			−0.474919	+	0.880029i	$0.657523\pi$
$480$		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	$-0.883824\pi$
$487$		−	7671.90i		−	0.713854i	0.934132	−	0.356927i	$-0.116176\pi$
$488$		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	$-0.980027\pi$
$503$		−	1414.75i		−	0.125409i	0.998032	−	0.0627045i	$-0.0199726\pi$
$504$		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	0.996786	−	0.0801087i	$-0.0255268\pi$
$509$	10526.7	+	10526.7i	0.916677	+	0.916677i	−0.0801087	+	0.996786i	$0.525527\pi$
$510$		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	$0.0225601\pi$
$541$	13442.8	+	13442.8i	1.06830	+	1.06830i	0.0708153	+	0.997489i	$0.477440\pi$
$542$		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	0.357151	−	0.934046i	$-0.383748\pi$
$557$	−7583.67	−	7583.67i	−0.576895	−	0.576895i	−0.934046	+	0.357151i	$0.883748\pi$
$558$		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	$-0.809148\pi$
$599$		−	16545.3i		−	1.12859i	0.825574	−	0.564294i	$-0.190852\pi$
$600$		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	$-0.590347\pi$
$607$	−8375.82			−0.560073			−0.280036	+	0.959989i	$0.590347\pi$
$608$		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	−0.337640	−	0.941275i	$-0.609629\pi$
$613$	9161.47	−	9161.47i	0.603635	−	0.603635i	0.941275	+	0.337640i	$0.109629\pi$
$614$		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	$-0.673352\pi$
$631$		−	27115.0i		−	1.71067i	0.518078	−	0.855334i	$-0.326648\pi$
$632$		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	$0.0327080\pi$
$647$			3376.19i			0.205149i	−0.994725	+	0.102575i	$0.967292\pi$
$648$		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	0.637245	−	0.770661i	$-0.280074\pi$
$653$	−2226.27	−	2226.27i	−0.133416	−	0.133416i	−0.770661	+	0.637245i	$0.780074\pi$
$654$		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	−0.768938	−	0.639323i	$-0.779215\pi$
$661$	−2202.71	+	2202.71i	−0.129615	+	0.129615i	0.639323	+	0.768938i	$0.279215\pi$
$662$		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	−0.999994	−	0.00339762i	$-0.998919\pi$
$677$	−17555.1	+	17555.1i	−0.996597	+	0.996597i	0.00339762	+	0.999994i	$0.498919\pi$
$678$		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	$0.0870491\pi$
$701$	22882.9	+	22882.9i	1.23292	+	1.23292i	0.270077	+	0.962839i	$0.412951\pi$
$702$		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	−0.542661	−	0.839952i	$-0.682583\pi$
$709$	5612.43	−	5612.43i	0.297291	−	0.297291i	0.839952	+	0.542661i	$0.182583\pi$
$710$		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	$-0.774043\pi$
$719$	−29244.9			−1.51690			−0.758450	+	0.651732i	$0.774043\pi$
$720$		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	$-0.973104\pi$
$727$		−	3308.71i		−	0.168794i	0.996432	−	0.0843971i	$-0.0268964\pi$
$728$		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	$-0.897216\pi$
$733$	−25116.9	−	25116.9i	−1.26564	−	1.26564i	−0.317323	−	0.948318i	$-0.602784\pi$
$734$		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	$-0.882887\pi$
$743$		−	14568.9i		−	0.719356i	0.933077	−	0.359678i	$-0.117113\pi$
$744$		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	$-0.421759\pi$
$751$	10015.9			0.486665			0.243333	+	0.969943i	$0.421759\pi$
$752$		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	−0.745218	−	0.666821i	$-0.767655\pi$
$757$	−1632.84	+	1632.84i	−0.0783971	+	0.0783971i	0.666821	+	0.745218i	$0.267655\pi$
$758$		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	−0.645239	−	0.763980i	$-0.723242\pi$
$773$	2551.94	−	2551.94i	0.118741	−	0.118741i	0.763980	+	0.645239i	$0.223242\pi$
$774$		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	0.526236	−	0.850339i	$-0.323603\pi$
$797$	−7292.39	−	7292.39i	−0.324102	−	0.324102i	−0.850339	+	0.526236i	$0.823603\pi$
$798$		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	−0.451096	−	0.892475i	$-0.648967\pi$
$821$	10383.1	−	10383.1i	0.441380	−	0.441380i	0.892475	+	0.451096i	$0.148967\pi$
$822$		0			0
$823$			13572.9i			0.574876i	0.957799	+	0.287438i	$0.0928035\pi$
$823$			13572.9i			0.574876i	−0.957799	+	0.287438i	$0.907196\pi$
$824$		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	$-0.900950\pi$
$829$	−30030.7	−	30030.7i	−1.25815	−	1.25815i	−0.306177	−	0.951975i	$-0.599050\pi$
$830$		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	$-0.961758\pi$
$839$		−	5825.32i		−	0.239705i	0.992792	−	0.119852i	$-0.0382421\pi$
$840$		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	−0.953118	−	0.302598i	$-0.902146\pi$
$853$	−16206.3	+	16206.3i	−0.650521	+	0.650521i	0.302598	+	0.953118i	$0.402146\pi$
$854$		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	$-0.700190\pi$
$863$	−29827.9			−1.17654			−0.588269	+	0.808665i	$0.700190\pi$
$864$		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	$0.00537863\pi$
$877$	26406.8	+	26406.8i	1.01675	+	1.01675i	0.0168967	+	0.999857i	$0.494621\pi$
$878$		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	$-0.951183\pi$
$887$		−	8071.18i		−	0.305528i	0.988263	−	0.152764i	$-0.0488175\pi$
$888$		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	$-0.308107\pi$
$911$	31180.6			1.13398			0.566992	+	0.823723i	$0.308107\pi$
$912$		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	$-0.833134\pi$
$919$		−	27889.6i		−	1.00108i	0.865713	−	0.500541i	$-0.166866\pi$
$920$		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	$0.00952183\pi$
$941$	29716.3	+	29716.3i	1.02946	+	1.02946i	0.0299093	+	0.999553i	$0.490478\pi$
$942$		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	$0.0330277\pi$
$967$			6229.01i			0.207147i	−0.994622	+	0.103574i	$0.966972\pi$
$968$		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	$0.338725\pi$
$983$			53895.9i			1.74874i	−0.485259	+	0.874371i	$0.661275\pi$
$984$		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	$-0.550712\pi$
$991$	−9898.33			−0.317286			−0.158643	+	0.987336i	$0.550712\pi$
$992$		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	$-0.430688\pi$
$997$	37538.1	−	37538.1i	1.19242	−	1.19242i	0.976386	−	0.216034i	$-0.0693124\pi$
$998$		0			0
$999$			7595.24i			0.240543i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.7	✓	24	8.5	even	2
48.4.j.a.37.7	yes	24	16.13	even	4
144.4.k.b.37.6		24	48.29	odd	4
144.4.k.b.109.6		24	24.5	odd	2
192.4.j.a.49.5		24	16.3	odd	4
192.4.j.a.145.5		24	8.3	odd	2
384.4.j.a.97.11		24	16.11	odd	4
384.4.j.a.289.11		24	4.3	odd	2
384.4.j.b.97.2		24	16.5	even	4	inner
384.4.j.b.289.2		24	1.1	even	1	trivial
576.4.k.b.145.3		24	24.11	even	2
576.4.k.b.433.3		24	48.35	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-2.12132 - 2.12132i) q^{3} +(-10.2951 + 10.2951i) q^{5} -32.8369i q^{7} +9.00000i q^{9} +O(q^{10})\)	\(q+(-2.12132 - 2.12132i) q^{3} +(-10.2951 + 10.2951i) q^{5} -32.8369i q^{7} +9.00000i q^{9} +(18.2226 - 18.2226i) q^{11} +(-22.5535 - 22.5535i) q^{13} +43.6785 q^{15} +50.1440 q^{17} +(6.68982 + 6.68982i) q^{19} +(-69.6576 + 69.6576i) q^{21} +186.886i q^{23} -86.9788i q^{25} +(19.0919 - 19.0919i) q^{27} +(-118.332 - 118.332i) q^{29} -250.110 q^{31} -77.3118 q^{33} +(338.060 + 338.060i) q^{35} +(-198.913 + 198.913i) q^{37} +95.6866i q^{39} +186.565i q^{41} +(-10.9329 + 10.9329i) q^{43} +(-92.6560 - 92.6560i) q^{45} +23.1346 q^{47} -735.263 q^{49} +(-106.371 - 106.371i) q^{51} +(-134.664 + 134.664i) q^{53} +375.207i q^{55} -28.3825i q^{57} +(-220.943 + 220.943i) q^{59} +(453.845 + 453.845i) q^{61} +295.532 q^{63} +464.383 q^{65} +(184.273 + 184.273i) q^{67} +(396.444 - 396.444i) q^{69} +18.8163i q^{71} +828.683i q^{73} +(-184.510 + 184.510i) q^{75} +(-598.373 - 598.373i) q^{77} +1048.37 q^{79} -81.0000 q^{81} +(173.404 + 173.404i) q^{83} +(-516.238 + 516.238i) q^{85} +502.041i q^{87} -335.168i q^{89} +(-740.589 + 740.589i) q^{91} +(530.564 + 530.564i) q^{93} -137.745 q^{95} -687.122 q^{97} +(164.003 + 164.003i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 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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