LMFDB - Embedded newform 384.4.j.b.289.7

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			289.7
Character	$\chi$	$=$	384.289
Dual form			384.4.j.b.97.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.12132 + 2.12132i) q^{3} +(-11.7911 + 11.7911i) q^{5} +12.5754i q^{7} +9.00000i q^{9} +O(q^{10})$	\(q+(2.12132 + 2.12132i) q^{3} +(-11.7911 + 11.7911i) q^{5} +12.5754i q^{7} +9.00000i q^{9} +(17.0042 - 17.0042i) q^{11} +(49.2384 + 49.2384i) q^{13} -50.0252 q^{15} -51.8247 q^{17} +(11.6655 + 11.6655i) q^{19} +(-26.6763 + 26.6763i) q^{21} +74.5524i q^{23} -153.058i q^{25} +(-19.0919 + 19.0919i) q^{27} +(-211.183 - 211.183i) q^{29} -326.094 q^{31} +72.1427 q^{33} +(-148.277 - 148.277i) q^{35} +(-110.757 + 110.757i) q^{37} +208.901i q^{39} -348.225i q^{41} +(-205.838 + 205.838i) q^{43} +(-106.120 - 106.120i) q^{45} +254.983 q^{47} +184.861 q^{49} +(-109.937 - 109.937i) q^{51} +(225.602 - 225.602i) q^{53} +400.995i q^{55} +49.4924i q^{57} +(-285.442 + 285.442i) q^{59} +(-286.952 - 286.952i) q^{61} -113.178 q^{63} -1161.15 q^{65} +(627.335 + 627.335i) q^{67} +(-158.150 + 158.150i) q^{69} -274.784i q^{71} -298.190i q^{73} +(324.686 - 324.686i) q^{75} +(213.834 + 213.834i) q^{77} -175.664 q^{79} -81.0000 q^{81} +(-125.254 - 125.254i) q^{83} +(611.068 - 611.068i) q^{85} -895.973i q^{87} +900.271i q^{89} +(-619.190 + 619.190i) q^{91} +(-691.750 - 691.750i) q^{93} -275.096 q^{95} +5.27858 q^{97} +(153.038 + 153.038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−11.7911	+	11.7911i	−1.05462	+	1.05462i	−0.0562056	+	0.998419i	$0.517900\pi$
$5$	−11.7911	+	11.7911i	−1.05462	+	1.05462i	−0.998419	+	0.0562056i	$0.982100\pi$
$6$		0			0
$7$			12.5754i			0.679005i	0.940605	+	0.339503i	$0.110259\pi$
$7$			12.5754i			0.679005i	−0.940605	+	0.339503i	$0.889741\pi$
$8$		0			0
$9$			9.00000i			0.333333i
$10$		0			0
$11$	17.0042	−	17.0042i	0.466087	−	0.466087i	−0.434557	−	0.900644i	$-0.643095\pi$
$11$	17.0042	−	17.0042i	0.466087	−	0.466087i	0.900644	+	0.434557i	$0.143095\pi$
$12$		0			0
$13$	49.2384	+	49.2384i	1.05048	+	1.05048i	0.998656	+	0.0518270i	$0.0165045\pi$
$13$	49.2384	+	49.2384i	1.05048	+	1.05048i	0.0518270	+	0.998656i	$0.483496\pi$
$14$		0			0
$15$	−50.0252			−0.861098
$16$		0			0
$17$	−51.8247			−0.739372			−0.369686	−	0.929157i	$-0.620535\pi$
$17$	−51.8247			−0.739372			−0.369686	+	0.929157i	$0.620535\pi$
$18$		0			0
$19$	11.6655	+	11.6655i	0.140855	+	0.140855i	0.774018	−	0.633163i	$-0.218244\pi$
$19$	11.6655	+	11.6655i	0.140855	+	0.140855i	−0.633163	+	0.774018i	$0.718244\pi$
$20$		0			0
$21$	−26.6763	+	26.6763i	−0.277203	+	0.277203i
$22$		0			0
$23$			74.5524i			0.675881i	0.941168	+	0.337940i	$0.109730\pi$
$23$			74.5524i			0.675881i	−0.941168	+	0.337940i	$0.890270\pi$
$24$		0			0
$25$		−	153.058i		−	1.22447i
$26$		0			0
$27$	−19.0919	+	19.0919i	−0.136083	+	0.136083i
$28$		0			0
$29$	−211.183	−	211.183i	−1.35227	−	1.35227i	−0.883122	−	0.469143i	$-0.844563\pi$
$29$	−211.183	−	211.183i	−1.35227	−	1.35227i	−0.469143	−	0.883122i	$-0.655437\pi$
$30$		0			0
$31$	−326.094			−1.88930			−0.944648	−	0.328084i	$-0.893597\pi$
$31$	−326.094			−1.88930			−0.944648	+	0.328084i	$0.893597\pi$
$32$		0			0
$33$	72.1427			0.380558
$34$		0			0
$35$	−148.277	−	148.277i	−0.716096	−	0.716096i
$36$		0			0
$37$	−110.757	+	110.757i	−0.492117	+	0.492117i	−0.908973	−	0.416855i	$-0.863132\pi$
$37$	−110.757	+	110.757i	−0.492117	+	0.492117i	0.416855	+	0.908973i	$0.363132\pi$
$38$		0			0
$39$			208.901i			0.857716i
$40$		0			0
$41$		−	348.225i		−	1.32643i	−0.748430	−	0.663214i	$-0.769192\pi$
$41$		−	348.225i		−	1.32643i	0.748430	−	0.663214i	$-0.230808\pi$
$42$		0			0
$43$	−205.838	+	205.838i	−0.729998	+	0.729998i	−0.970619	−	0.240621i	$-0.922649\pi$
$43$	−205.838	+	205.838i	−0.729998	+	0.729998i	0.240621	+	0.970619i	$0.422649\pi$
$44$		0			0
$45$	−106.120	−	106.120i	−0.351542	−	0.351542i
$46$		0			0
$47$	254.983			0.791342			0.395671	−	0.918392i	$-0.370512\pi$
$47$	254.983			0.791342			0.395671	+	0.918392i	$0.370512\pi$
$48$		0			0
$49$	184.861			0.538952
$50$		0			0
$51$	−109.937	−	109.937i	−0.301848	−	0.301848i
$52$		0			0
$53$	225.602	−	225.602i	0.584694	−	0.584694i	−0.351496	−	0.936189i	$-0.614327\pi$
$53$	225.602	−	225.602i	0.584694	−	0.584694i	0.936189	+	0.351496i	$0.114327\pi$
$54$		0			0
$55$			400.995i			0.983094i
$56$		0			0
$57$			49.4924i			0.115007i
$58$		0			0
$59$	−285.442	+	285.442i	−0.629854	+	0.629854i	−0.948031	−	0.318177i	$-0.896929\pi$
$59$	−285.442	+	285.442i	−0.629854	+	0.629854i	0.318177	+	0.948031i	$0.396929\pi$
$60$		0			0
$61$	−286.952	−	286.952i	−0.602301	−	0.602301i	0.338621	−	0.940923i	$-0.390039\pi$
$61$	−286.952	−	286.952i	−0.602301	−	0.602301i	−0.940923	+	0.338621i	$0.890039\pi$
$62$		0			0
$63$	−113.178			−0.226335
$64$		0			0
$65$	−1161.15			−2.21573
$66$		0			0
$67$	627.335	+	627.335i	1.14390	+	1.14390i	0.987731	+	0.156168i	$0.0499141\pi$
$67$	627.335	+	627.335i	1.14390	+	1.14390i	0.156168	+	0.987731i	$0.450086\pi$
$68$		0			0
$69$	−158.150	+	158.150i	−0.275927	+	0.275927i
$70$		0			0
$71$		−	274.784i		−	0.459308i	−0.973272	−	0.229654i	$-0.926241\pi$
$71$		−	274.784i		−	0.459308i	0.973272	−	0.229654i	$-0.0737595\pi$
$72$		0			0
$73$		−	298.190i		−	0.478089i	−0.971009	−	0.239044i	$-0.923166\pi$
$73$		−	298.190i		−	0.478089i	0.971009	−	0.239044i	$-0.0768341\pi$
$74$		0			0
$75$	324.686	−	324.686i	0.499887	−	0.499887i
$76$		0			0
$77$	213.834	+	213.834i	0.316475	+	0.316475i
$78$		0			0
$79$	−175.664			−0.250174			−0.125087	−	0.992146i	$-0.539921\pi$
$79$	−175.664			−0.250174			−0.125087	+	0.992146i	$0.539921\pi$
$80$		0			0
$81$	−81.0000			−0.111111
$82$		0			0
$83$	−125.254	−	125.254i	−0.165644	−	0.165644i	0.619418	−	0.785062i	$-0.287369\pi$
$83$	−125.254	−	125.254i	−0.165644	−	0.165644i	−0.785062	+	0.619418i	$0.787369\pi$
$84$		0			0
$85$	611.068	−	611.068i	0.779760	−	0.779760i
$86$		0			0
$87$		−	895.973i		−	1.10412i
$88$		0			0
$89$			900.271i			1.07223i	0.844145	+	0.536116i	$0.180109\pi$
$89$			900.271i			1.07223i	−0.844145	+	0.536116i	$0.819891\pi$
$90$		0			0
$91$	−619.190	+	619.190i	−0.713283	+	0.713283i
$92$		0			0
$93$	−691.750	−	691.750i	−0.771302	−	0.771302i
$94$		0			0
$95$	−275.096			−0.297098
$96$		0			0
$97$	5.27858			0.00552534			0.00276267	−	0.999996i	$-0.499121\pi$
$97$	5.27858			0.00552534			0.00276267	+	0.999996i	$0.499121\pi$
$98$		0			0
$99$	153.038	+	153.038i	0.155362	+	0.155362i
$100$		0			0
$101$	459.109	−	459.109i	0.452307	−	0.452307i	−0.443812	−	0.896120i	$-0.646374\pi$
$101$	459.109	−	459.109i	0.452307	−	0.452307i	0.896120	+	0.443812i	$0.146374\pi$
$102$		0			0
$103$			791.173i			0.756860i	0.925630	+	0.378430i	$0.123536\pi$
$103$			791.173i			0.756860i	−0.925630	+	0.378430i	$0.876464\pi$
$104$		0			0
$105$		−	629.085i		−	0.584690i
$106$		0			0
$107$	−1525.81	+	1525.81i	−1.37855	+	1.37855i	−0.531487	+	0.847067i	$0.678366\pi$
$107$	−1525.81	+	1525.81i	−1.37855	+	1.37855i	−0.847067	+	0.531487i	$0.821634\pi$
$108$		0			0
$109$	413.307	+	413.307i	0.363189	+	0.363189i	0.864986	−	0.501796i	$-0.167327\pi$
$109$	413.307	+	413.307i	0.363189	+	0.363189i	−0.501796	+	0.864986i	$0.667327\pi$
$110$		0			0
$111$	−469.902			−0.401812
$112$		0			0
$113$	210.248			0.175031			0.0875154	−	0.996163i	$-0.472107\pi$
$113$	210.248			0.175031			0.0875154	+	0.996163i	$0.472107\pi$
$114$		0			0
$115$	−879.053	−	879.053i	−0.712801	−	0.712801i
$116$		0			0
$117$	−443.146	+	443.146i	−0.350161	+	0.350161i
$118$		0			0
$119$		−	651.714i		−	0.502038i
$120$		0			0
$121$			752.715i			0.565526i
$122$		0			0
$123$	738.696	−	738.696i	0.541512	−	0.541512i
$124$		0			0
$125$	330.838	+	330.838i	0.236729	+	0.236729i
$126$		0			0
$127$	177.367			0.123927			0.0619637	−	0.998078i	$-0.480264\pi$
$127$	177.367			0.123927			0.0619637	+	0.998078i	$0.480264\pi$
$128$		0			0
$129$	−873.295			−0.596041
$130$		0			0
$131$	−938.828	−	938.828i	−0.626151	−	0.626151i	0.320946	−	0.947097i	$-0.395999\pi$
$131$	−938.828	−	938.828i	−0.626151	−	0.626151i	−0.947097	+	0.320946i	$0.895999\pi$
$132$		0			0
$133$	−146.697	+	146.697i	−0.0956411	+	0.0956411i
$134$		0			0
$135$		−	450.227i		−	0.287033i
$136$		0			0
$137$			307.429i			0.191718i	0.995395	+	0.0958592i	$0.0305598\pi$
$137$			307.429i			0.191718i	−0.995395	+	0.0958592i	$0.969440\pi$
$138$		0			0
$139$	1253.43	−	1253.43i	0.764852	−	0.764852i	−0.212343	−	0.977195i	$-0.568109\pi$
$139$	1253.43	−	1253.43i	0.764852	−	0.764852i	0.977195	+	0.212343i	$0.0681095\pi$
$140$		0			0
$141$	540.901	+	540.901i	0.323064	+	0.323064i
$142$		0			0
$143$	1674.52			0.979233
$144$		0			0
$145$	4980.14			2.85226
$146$		0			0
$147$	392.148	+	392.148i	0.220026	+	0.220026i
$148$		0			0
$149$	−1686.80	+	1686.80i	−0.927436	+	0.927436i	−0.997540	−	0.0701033i	$-0.977667\pi$
$149$	−1686.80	+	1686.80i	−0.927436	+	0.927436i	0.0701033	+	0.997540i	$0.477667\pi$
$150$		0			0
$151$			1682.23i			0.906611i	0.891355	+	0.453306i	$0.149755\pi$
$151$			1682.23i			0.906611i	−0.891355	+	0.453306i	$0.850245\pi$
$152$		0			0
$153$		−	466.422i		−	0.246457i
$154$		0			0
$155$	3844.99	−	3844.99i	1.99250	−	1.99250i
$156$		0			0
$157$	1066.81	+	1066.81i	0.542300	+	0.542300i	0.924202	−	0.381903i	$-0.124731\pi$
$157$	1066.81	+	1066.81i	0.542300	+	0.542300i	−0.381903	+	0.924202i	$0.624731\pi$
$158$		0			0
$159$	957.147			0.477400
$160$		0			0
$161$	−937.523			−0.458927
$162$		0			0
$163$	2379.54	+	2379.54i	1.14343	+	1.14343i	0.987817	+	0.155618i	$0.0497367\pi$
$163$	2379.54	+	2379.54i	1.14343	+	1.14343i	0.155618	+	0.987817i	$0.450263\pi$
$164$		0			0
$165$	−850.639	+	850.639i	−0.401346	+	0.401346i
$166$		0			0
$167$		−	839.991i		−	0.389224i	−0.980880	−	0.194612i	$-0.937655\pi$
$167$		−	839.991i		−	0.389224i	0.980880	−	0.194612i	$-0.0623448\pi$
$168$		0			0
$169$			2651.84i			1.20703i
$170$		0			0
$171$	−104.989	+	104.989i	−0.0469516	+	0.0469516i
$172$		0			0
$173$	450.278	+	450.278i	0.197885	+	0.197885i	0.799093	−	0.601208i	$-0.205314\pi$
$173$	450.278	+	450.278i	0.197885	+	0.197885i	−0.601208	+	0.799093i	$0.705314\pi$
$174$		0			0
$175$	1924.76			0.831419
$176$		0			0
$177$	−1211.03			−0.514274
$178$		0			0
$179$	647.759	+	647.759i	0.270479	+	0.270479i	0.829293	−	0.558814i	$-0.188743\pi$
$179$	647.759	+	647.759i	0.270479	+	0.270479i	−0.558814	+	0.829293i	$0.688743\pi$
$180$		0			0
$181$	755.750	−	755.750i	0.310356	−	0.310356i	−0.534691	−	0.845047i	$-0.679572\pi$
$181$	755.750	−	755.750i	0.310356	−	0.310356i	0.845047	+	0.534691i	$0.179572\pi$
$182$		0			0
$183$		−	1217.43i		−	0.491777i
$184$		0			0
$185$		−	2611.89i		−	1.03800i
$186$		0			0
$187$	−881.237	+	881.237i	−0.344612	+	0.344612i
$188$		0			0
$189$	−240.087	−	240.087i	−0.0924009	−	0.0924009i
$190$		0			0
$191$	760.485			0.288098			0.144049	−	0.989571i	$-0.453988\pi$
$191$	760.485			0.288098			0.144049	+	0.989571i	$0.453988\pi$
$192$		0			0
$193$	2184.99			0.814915			0.407458	−	0.913224i	$-0.366415\pi$
$193$	2184.99			0.814915			0.407458	+	0.913224i	$0.366415\pi$
$194$		0			0
$195$	−2463.16	−	2463.16i	−0.904568	−	0.904568i
$196$		0			0
$197$	−83.4121	+	83.4121i	−0.0301668	+	0.0301668i	−0.722029	−	0.691862i	$-0.756790\pi$
$197$	−83.4121	+	83.4121i	−0.0301668	+	0.0301668i	0.691862	+	0.722029i	$0.256790\pi$
$198$		0			0
$199$			1734.18i			0.617754i	0.951102	+	0.308877i	$0.0999531\pi$
$199$			1734.18i			0.617754i	−0.951102	+	0.308877i	$0.900047\pi$
$200$		0			0
$201$			2661.56i			0.933989i
$202$		0			0
$203$	2655.70	−	2655.70i	0.918195	−	0.918195i
$204$		0			0
$205$	4105.94	+	4105.94i	1.39888	+	1.39888i
$206$		0			0
$207$	−670.972			−0.225294
$208$		0			0
$209$	396.723			0.131301
$210$		0			0
$211$	365.900	+	365.900i	0.119382	+	0.119382i	0.764274	−	0.644892i	$-0.223098\pi$
$211$	365.900	+	365.900i	0.119382	+	0.119382i	−0.644892	+	0.764274i	$0.723098\pi$
$212$		0			0
$213$	582.905	−	582.905i	0.187512	−	0.187512i
$214$		0			0
$215$		−	4854.09i		−	1.53975i
$216$		0			0
$217$		−	4100.75i		−	1.28284i
$218$		0			0
$219$	632.556	−	632.556i	0.195179	−	0.195179i
$220$		0			0
$221$	−2551.77	−	2551.77i	−0.776698	−	0.776698i
$222$		0			0
$223$	−4037.17			−1.21233			−0.606164	−	0.795340i	$-0.707292\pi$
$223$	−4037.17			−1.21233			−0.606164	+	0.795340i	$0.707292\pi$
$224$		0			0
$225$	1377.53			0.408156
$226$		0			0
$227$	1502.81	+	1502.81i	0.439407	+	0.439407i	0.891812	−	0.452406i	$-0.149434\pi$
$227$	1502.81	+	1502.81i	0.439407	+	0.439407i	−0.452406	+	0.891812i	$0.649434\pi$
$228$		0			0
$229$	3443.65	−	3443.65i	0.993723	−	0.993723i	−0.00625772	−	0.999980i	$-0.501992\pi$
$229$	3443.65	−	3443.65i	0.993723	−	0.993723i	0.999980	+	0.00625772i	$0.00199191\pi$
$230$		0			0
$231$			907.219i			0.258401i
$232$		0			0
$233$			1139.00i			0.320250i	0.987097	+	0.160125i	$0.0511898\pi$
$233$			1139.00i			0.320250i	−0.987097	+	0.160125i	$0.948810\pi$
$234$		0			0
$235$	−3006.52	+	3006.52i	−0.834569	+	0.834569i
$236$		0			0
$237$	−372.640	−	372.640i	−0.102133	−	0.102133i
$238$		0			0
$239$	−4603.80			−1.24600			−0.623002	−	0.782220i	$-0.714087\pi$
$239$	−4603.80			−1.24600			−0.623002	+	0.782220i	$0.714087\pi$
$240$		0			0
$241$	−4681.58			−1.25132			−0.625658	−	0.780097i	$-0.715170\pi$
$241$	−4681.58			−1.25132			−0.625658	+	0.780097i	$0.715170\pi$
$242$		0			0
$243$	−171.827	−	171.827i	−0.0453609	−	0.0453609i
$244$		0			0
$245$	−2179.70	+	2179.70i	−0.568392	+	0.568392i
$246$		0			0
$247$			1148.78i			0.295931i
$248$		0			0
$249$		−	531.408i		−	0.135248i
$250$		0			0
$251$	476.440	−	476.440i	0.119811	−	0.119811i	−0.644659	−	0.764470i	$-0.723001\pi$
$251$	476.440	−	476.440i	0.119811	−	0.119811i	0.764470	+	0.644659i	$0.223001\pi$
$252$		0			0
$253$	1267.70	+	1267.70i	0.315019	+	0.315019i
$254$		0			0
$255$	2592.54			0.636672
$256$		0			0
$257$	925.326			0.224592			0.112296	−	0.993675i	$-0.464179\pi$
$257$	925.326			0.224592			0.112296	+	0.993675i	$0.464179\pi$
$258$		0			0
$259$	−1392.81	−	1392.81i	−0.334150	−	0.334150i
$260$		0			0
$261$	1900.65	−	1900.65i	0.450755	−	0.450755i
$262$		0			0
$263$			3477.65i			0.815365i	0.913124	+	0.407683i	$0.133663\pi$
$263$			3477.65i			0.815365i	−0.913124	+	0.407683i	$0.866337\pi$
$264$		0			0
$265$			5320.17i			1.23327i
$266$		0			0
$267$	−1909.76	+	1909.76i	−0.437737	+	0.437737i
$268$		0			0
$269$	−3773.37	−	3773.37i	−0.855266	−	0.855266i	0.135510	−	0.990776i	$-0.456733\pi$
$269$	−3773.37	−	3773.37i	−0.855266	−	0.855266i	−0.990776	+	0.135510i	$0.956733\pi$
$270$		0			0
$271$	8007.09			1.79482			0.897410	−	0.441198i	$-0.145446\pi$
$271$	8007.09			1.79482			0.897410	+	0.441198i	$0.145446\pi$
$272$		0			0
$273$	−2627.00			−0.582394
$274$		0			0
$275$	−2602.63	−	2602.63i	−0.570708	−	0.570708i
$276$		0			0
$277$	−4550.73	+	4550.73i	−0.987101	+	0.987101i	−0.999918	−	0.0128173i	$-0.995920\pi$
$277$	−4550.73	+	4550.73i	−0.987101	+	0.987101i	0.0128173	+	0.999918i	$0.495920\pi$
$278$		0			0
$279$		−	2934.85i		−	0.629766i
$280$		0			0
$281$			3333.05i			0.707592i	0.935323	+	0.353796i	$0.115109\pi$
$281$			3333.05i			0.707592i	−0.935323	+	0.353796i	$0.884891\pi$
$282$		0			0
$283$	−6242.23	+	6242.23i	−1.31117	+	1.31117i	−0.390621	+	0.920552i	$0.627740\pi$
$283$	−6242.23	+	6242.23i	−1.31117	+	1.31117i	−0.920552	+	0.390621i	$0.872260\pi$
$284$		0			0
$285$	−583.568	−	583.568i	−0.121290	−	0.121290i
$286$		0			0
$287$	4379.05			0.900651
$288$		0			0
$289$	−2227.20			−0.453329
$290$		0			0
$291$	11.1976	+	11.1976i	0.00225571	+	0.00225571i
$292$		0			0
$293$	2458.24	−	2458.24i	0.490143	−	0.490143i	−0.418208	−	0.908351i	$-0.637342\pi$
$293$	2458.24	−	2458.24i	0.490143	−	0.490143i	0.908351	+	0.418208i	$0.137342\pi$
$294$		0			0
$295$		−	6731.33i		−	1.32852i
$296$		0			0
$297$			649.284i			0.126853i
$298$		0			0
$299$	−3670.84	+	3670.84i	−0.710001	+	0.710001i
$300$		0			0
$301$	−2588.48	−	2588.48i	−0.495673	−	0.495673i
$302$		0			0
$303$	1947.83			0.369307
$304$		0			0
$305$	6766.93			1.27040
$306$		0			0
$307$	3008.49	+	3008.49i	0.559295	+	0.559295i	0.929107	−	0.369812i	$-0.120578\pi$
$307$	3008.49	+	3008.49i	0.559295	+	0.559295i	−0.369812	+	0.929107i	$0.620578\pi$
$308$		0			0
$309$	−1678.33	+	1678.33i	−0.308987	+	0.308987i
$310$		0			0
$311$			4507.09i			0.821779i	0.911685	+	0.410890i	$0.134782\pi$
$311$			4507.09i			0.821779i	−0.911685	+	0.410890i	$0.865218\pi$
$312$		0			0
$313$		−	5237.61i		−	0.945837i	−0.881106	−	0.472919i	$-0.843200\pi$
$313$		−	5237.61i		−	0.945837i	0.881106	−	0.472919i	$-0.156800\pi$
$314$		0			0
$315$	1334.49	−	1334.49i	0.238699	−	0.238699i
$316$		0			0
$317$	989.530	+	989.530i	0.175323	+	0.175323i	0.789314	−	0.613990i	$-0.210437\pi$
$317$	989.530	+	989.530i	0.175323	+	0.175323i	−0.613990	+	0.789314i	$0.710437\pi$
$318$		0			0
$319$	−7181.99			−1.26055
$320$		0			0
$321$	−6473.45			−1.12558
$322$		0			0
$323$	−604.559	−	604.559i	−0.104144	−	0.104144i
$324$		0			0
$325$	7536.35	−	7536.35i	1.28628	−	1.28628i
$326$		0			0
$327$			1753.51i			0.296543i
$328$		0			0
$329$			3206.50i			0.537325i
$330$		0			0
$331$	5652.55	−	5652.55i	0.938647	−	0.938647i	−0.0595765	−	0.998224i	$-0.518975\pi$
$331$	5652.55	−	5652.55i	0.938647	−	0.938647i	0.998224	+	0.0595765i	$0.0189750\pi$
$332$		0			0
$333$	−996.813	−	996.813i	−0.164039	−	0.164039i
$334$		0			0
$335$	−14793.9			−2.41277
$336$		0			0
$337$	291.315			0.0470888			0.0235444	−	0.999723i	$-0.492505\pi$
$337$	291.315			0.0470888			0.0235444	+	0.999723i	$0.492505\pi$
$338$		0			0
$339$	446.004	+	446.004i	0.0714560	+	0.0714560i
$340$		0			0
$341$	−5544.96	+	5544.96i	−0.880577	+	0.880577i
$342$		0			0
$343$			6638.03i			1.04496i
$344$		0			0
$345$		−	3729.50i		−	0.581999i
$346$		0			0
$347$	−6530.87	+	6530.87i	−1.01036	+	1.01036i	−0.0104158	+	0.999946i	$0.503316\pi$
$347$	−6530.87	+	6530.87i	−1.01036	+	1.01036i	−0.999946	+	0.0104158i	$0.996684\pi$
$348$		0			0
$349$	−7267.79	−	7267.79i	−1.11472	−	1.11472i	−0.992504	−	0.122213i	$-0.961001\pi$
$349$	−7267.79	−	7267.79i	−1.11472	−	1.11472i	−0.122213	−	0.992504i	$-0.538999\pi$
$350$		0			0
$351$	−1880.11			−0.285905
$352$		0			0
$353$	−8253.63			−1.24447			−0.622233	−	0.782832i	$-0.713774\pi$
$353$	−8253.63			−1.24447			−0.622233	+	0.782832i	$0.713774\pi$
$354$		0			0
$355$	3240.00	+	3240.00i	0.484398	+	0.484398i
$356$		0			0
$357$	1382.49	−	1382.49i	0.204956	−	0.204956i
$358$		0			0
$359$			4827.70i			0.709738i	0.934916	+	0.354869i	$0.115475\pi$
$359$			4827.70i			0.709738i	−0.934916	+	0.354869i	$0.884525\pi$
$360$		0			0
$361$		−	6586.83i		−	0.960320i
$362$		0			0
$363$	−1596.75	+	1596.75i	−0.230875	+	0.230875i
$364$		0			0
$365$	3515.97	+	3515.97i	0.504204	+	0.504204i
$366$		0			0
$367$	−2556.37			−0.363600			−0.181800	−	0.983336i	$-0.558192\pi$
$367$	−2556.37			−0.363600			−0.181800	+	0.983336i	$0.558192\pi$
$368$		0			0
$369$	3134.02			0.442143
$370$		0			0
$371$	2837.02	+	2837.02i	0.397010	+	0.397010i
$372$		0			0
$373$	−1141.57	+	1141.57i	−0.158468	+	0.158468i	−0.781887	−	0.623420i	$-0.785743\pi$
$373$	−1141.57	+	1141.57i	−0.158468	+	0.158468i	0.623420	+	0.781887i	$0.285743\pi$
$374$		0			0
$375$			1403.63i			0.193288i
$376$		0			0
$377$		−	20796.6i		−	2.84106i
$378$		0			0
$379$	2602.11	−	2602.11i	0.352668	−	0.352668i	−0.508433	−	0.861101i	$-0.669775\pi$
$379$	2602.11	−	2602.11i	0.352668	−	0.352668i	0.861101	+	0.508433i	$0.169775\pi$
$380$		0			0
$381$	376.252	+	376.252i	0.0505931	+	0.0505931i
$382$		0			0
$383$	−370.858			−0.0494777			−0.0247388	−	0.999694i	$-0.507875\pi$
$383$	−370.858			−0.0494777			−0.0247388	+	0.999694i	$0.507875\pi$
$384$		0			0
$385$	−5042.65			−0.667526
$386$		0			0
$387$	−1852.54	−	1852.54i	−0.243333	−	0.243333i
$388$		0			0
$389$	6457.55	−	6457.55i	0.841673	−	0.841673i	−0.147403	−	0.989077i	$-0.547091\pi$
$389$	6457.55	−	6457.55i	0.841673	−	0.841673i	0.989077	+	0.147403i	$0.0470914\pi$
$390$		0			0
$391$		−	3863.66i		−	0.499728i
$392$		0			0
$393$		−	3983.11i		−	0.511250i
$394$		0			0
$395$	2071.27	−	2071.27i	0.263840	−	0.263840i
$396$		0			0
$397$	232.353	+	232.353i	0.0293739	+	0.0293739i	0.721641	−	0.692267i	$-0.243388\pi$
$397$	232.353	+	232.353i	0.0293739	+	0.0293739i	−0.692267	+	0.721641i	$0.743388\pi$
$398$		0			0
$399$	−622.384			−0.0780906
$400$		0			0
$401$	−119.615			−0.0148960			−0.00744801	−	0.999972i	$-0.502371\pi$
$401$	−119.615			−0.0148960			−0.00744801	+	0.999972i	$0.502371\pi$
$402$		0			0
$403$	−16056.4	−	16056.4i	−1.98467	−	1.98467i
$404$		0			0
$405$	955.076	−	955.076i	0.117181	−	0.117181i
$406$		0			0
$407$			3766.67i			0.458739i
$408$		0			0
$409$		−	626.952i		−	0.0757965i	−0.999282	−	0.0378983i	$-0.987934\pi$
$409$		−	626.952i		−	0.0757965i	0.999282	−	0.0378983i	$-0.0120663\pi$
$410$		0			0
$411$	−652.155	+	652.155i	−0.0782687	+	0.0782687i
$412$		0			0
$413$	−3589.54	−	3589.54i	−0.427674	−	0.427674i
$414$		0			0
$415$	2953.76			0.349384
$416$		0			0
$417$	5317.85			0.624499
$418$		0			0
$419$	4981.58	+	4981.58i	0.580826	+	0.580826i	0.935130	−	0.354304i	$-0.115282\pi$
$419$	4981.58	+	4981.58i	0.580826	+	0.580826i	−0.354304	+	0.935130i	$0.615282\pi$
$420$		0			0
$421$	−10770.4	+	10770.4i	−1.24683	+	1.24683i	−0.289723	+	0.957110i	$0.593563\pi$
$421$	−10770.4	+	10770.4i	−1.24683	+	1.24683i	−0.957110	+	0.289723i	$0.906437\pi$
$422$		0			0
$423$			2294.85i			0.263781i
$424$		0			0
$425$			7932.20i			0.905337i
$426$		0			0
$427$	3608.52	−	3608.52i	0.408966	−	0.408966i
$428$		0			0
$429$	3552.19	+	3552.19i	0.399770	+	0.399770i
$430$		0			0
$431$	7546.94			0.843442			0.421721	−	0.906726i	$-0.361426\pi$
$431$	7546.94			0.843442			0.421721	+	0.906726i	$0.361426\pi$
$432$		0			0
$433$	5614.17			0.623094			0.311547	−	0.950231i	$-0.399153\pi$
$433$	5614.17			0.623094			0.311547	+	0.950231i	$0.399153\pi$
$434$		0			0
$435$	10564.5	+	10564.5i	1.16443	+	1.16443i
$436$		0			0
$437$	−869.689	+	869.689i	−0.0952010	+	0.0952010i
$438$		0			0
$439$			7198.92i			0.782656i	0.920251	+	0.391328i	$0.127984\pi$
$439$			7198.92i			0.782656i	−0.920251	+	0.391328i	$0.872016\pi$
$440$		0			0
$441$			1663.74i			0.179651i
$442$		0			0
$443$	5582.95	−	5582.95i	0.598767	−	0.598767i	−0.341217	−	0.939984i	$-0.610839\pi$
$443$	5582.95	−	5582.95i	0.598767	−	0.598767i	0.939984	+	0.341217i	$0.110839\pi$
$444$		0			0
$445$	−10615.2	−	10615.2i	−1.13080	−	1.13080i
$446$		0			0
$447$	−7156.49			−0.757249
$448$		0			0
$449$	1224.53			0.128706			0.0643530	−	0.997927i	$-0.479502\pi$
$449$	1224.53			0.128706			0.0643530	+	0.997927i	$0.479502\pi$
$450$		0			0
$451$	−5921.28	−	5921.28i	−0.618231	−	0.618231i
$452$		0			0
$453$	−3568.56	+	3568.56i	−0.370123	+	0.370123i
$454$		0			0
$455$		−	14601.8i		−	1.50449i
$456$		0			0
$457$			11182.3i			1.14461i	0.820040	+	0.572307i	$0.193951\pi$
$457$			11182.3i			1.14461i	−0.820040	+	0.572307i	$0.806049\pi$
$458$		0			0
$459$	989.431	−	989.431i	0.100616	−	0.100616i
$460$		0			0
$461$	11334.9	+	11334.9i	1.14516	+	1.14516i	0.987492	+	0.157670i	$0.0503982\pi$
$461$	11334.9	+	11334.9i	1.14516	+	1.14516i	0.157670	+	0.987492i	$0.449602\pi$
$462$		0			0
$463$	3013.37			0.302469			0.151234	−	0.988498i	$-0.451675\pi$
$463$	3013.37			0.302469			0.151234	+	0.988498i	$0.451675\pi$
$464$		0			0
$465$	16312.9			1.62687
$466$		0			0
$467$	843.917	+	843.917i	0.0836228	+	0.0836228i	0.747681	−	0.664058i	$-0.231167\pi$
$467$	843.917	+	843.917i	0.0836228	+	0.0836228i	−0.664058	+	0.747681i	$0.731167\pi$
$468$		0			0
$469$	−7888.96	+	7888.96i	−0.776713	+	0.776713i
$470$		0			0
$471$			4526.11i			0.442786i
$472$		0			0
$473$			7000.20i			0.680485i
$474$		0			0
$475$	1785.50	−	1785.50i	0.172472	−	0.172472i
$476$		0			0
$477$	2030.41	+	2030.41i	0.194898	+	0.194898i
$478$		0			0
$479$	10569.4			1.00821			0.504103	−	0.863644i	$-0.331823\pi$
$479$	10569.4			1.00821			0.504103	+	0.863644i	$0.331823\pi$
$480$		0			0
$481$	−10907.0			−1.03392
$482$		0			0
$483$	−1988.79	−	1988.79i	−0.187356	−	0.187356i
$484$		0			0
$485$	−62.2400	+	62.2400i	−0.00582716	+	0.00582716i
$486$		0			0
$487$		−	1579.10i		−	0.146932i	−0.997298	−	0.0734661i	$-0.976594\pi$
$487$		−	1579.10i		−	0.146932i	0.997298	−	0.0734661i	$-0.0234061\pi$
$488$		0			0
$489$			10095.5i			0.933611i
$490$		0			0
$491$	−8650.50	+	8650.50i	−0.795095	+	0.795095i	−0.982318	−	0.187222i	$-0.940052\pi$
$491$	−8650.50	+	8650.50i	−0.795095	+	0.795095i	0.187222	+	0.982318i	$0.440052\pi$
$492$		0			0
$493$	10944.5	+	10944.5i	0.999828	+	0.999828i
$494$		0			0
$495$	−3608.95			−0.327698
$496$		0			0
$497$	3455.51			0.311873
$498$		0			0
$499$	11942.3	+	11942.3i	1.07137	+	1.07137i	0.997250	+	0.0741168i	$0.0236137\pi$
$499$	11942.3	+	11942.3i	1.07137	+	1.07137i	0.0741168	+	0.997250i	$0.476386\pi$
$500$		0			0
$501$	1781.89	−	1781.89i	0.158900	−	0.158900i
$502$		0			0
$503$			3290.09i			0.291646i	0.989311	+	0.145823i	$0.0465830\pi$
$503$			3290.09i			0.291646i	−0.989311	+	0.145823i	$0.953417\pi$
$504$		0			0
$505$			10826.8i			0.954029i
$506$		0			0
$507$	−5625.41	+	5625.41i	−0.492768	+	0.492768i
$508$		0			0
$509$	−1392.67	−	1392.67i	−0.121275	−	0.121275i	0.643864	−	0.765140i	$-0.277330\pi$
$509$	−1392.67	−	1392.67i	−0.121275	−	0.121275i	−0.765140	+	0.643864i	$0.777330\pi$
$510$		0			0
$511$	3749.84			0.324625
$512$		0			0
$513$	−445.431			−0.0383358
$514$		0			0
$515$	−9328.77	−	9328.77i	−0.798203	−	0.798203i
$516$		0			0
$517$	4335.78	−	4335.78i	0.368834	−	0.368834i
$518$		0			0
$519$			1910.37i			0.161572i
$520$		0			0
$521$		−	1175.72i		−	0.0988661i	−0.998777	−	0.0494331i	$-0.984259\pi$
$521$		−	1175.72i		−	0.0988661i	0.998777	−	0.0494331i	$-0.0157414\pi$
$522$		0			0
$523$	9451.05	−	9451.05i	0.790183	−	0.790183i	−0.191341	−	0.981524i	$-0.561284\pi$
$523$	9451.05	−	9451.05i	0.790183	−	0.790183i	0.981524	+	0.191341i	$0.0612836\pi$
$524$		0			0
$525$	4083.04	+	4083.04i	0.339426	+	0.339426i
$526$		0			0
$527$	16899.7			1.39689
$528$		0			0
$529$	6608.93			0.543185
$530$		0			0
$531$	−2568.98	−	2568.98i	−0.209951	−	0.209951i
$532$		0			0
$533$	17146.0	−	17146.0i	1.39339	−	1.39339i
$534$		0			0
$535$		−	35981.7i		−	2.90771i
$536$		0			0
$537$			2748.21i			0.220845i
$538$		0			0
$539$	3143.40	−	3143.40i	0.251198	−	0.251198i
$540$		0			0
$541$	−2893.97	−	2893.97i	−0.229984	−	0.229984i	0.582702	−	0.812686i	$-0.301996\pi$
$541$	−2893.97	−	2893.97i	−0.229984	−	0.229984i	−0.812686	+	0.582702i	$0.801996\pi$
$542$		0			0
$543$	3206.38			0.253405
$544$		0			0
$545$	−9746.66			−0.766057
$546$		0			0
$547$	956.857	+	956.857i	0.0747939	+	0.0747939i	0.743514	−	0.668720i	$-0.233158\pi$
$547$	956.857	+	956.857i	0.0747939	+	0.0747939i	−0.668720	+	0.743514i	$0.733158\pi$
$548$		0			0
$549$	2582.56	−	2582.56i	0.200767	−	0.200767i
$550$		0			0
$551$		−	4927.09i		−	0.380946i
$552$		0			0
$553$		−	2209.04i		−	0.169870i
$554$		0			0
$555$	5540.65	−	5540.65i	0.423761	−	0.423761i
$556$		0			0
$557$	8482.07	+	8482.07i	0.645236	+	0.645236i	0.951838	−	0.306602i	$-0.0991919\pi$
$557$	8482.07	+	8482.07i	0.645236	+	0.645236i	−0.306602	+	0.951838i	$0.599192\pi$
$558$		0			0
$559$	−20270.2			−1.53370
$560$		0			0
$561$	−3738.77			−0.281374
$562$		0			0
$563$	−9461.78	−	9461.78i	−0.708289	−	0.708289i	0.257886	−	0.966175i	$-0.416974\pi$
$563$	−9461.78	−	9461.78i	−0.708289	−	0.708289i	−0.966175	+	0.257886i	$0.916974\pi$
$564$		0			0
$565$	−2479.05	+	2479.05i	−0.184592	+	0.184592i
$566$		0			0
$567$		−	1018.60i		−	0.0754450i
$568$		0			0
$569$			7197.61i			0.530298i	0.964207	+	0.265149i	$0.0854211\pi$
$569$			7197.61i			0.530298i	−0.964207	+	0.265149i	$0.914579\pi$
$570$		0			0
$571$	−990.936	+	990.936i	−0.0726259	+	0.0726259i	−0.742487	−	0.669861i	$-0.766354\pi$
$571$	−990.936	+	990.936i	−0.0726259	+	0.0726259i	0.669861	+	0.742487i	$0.266354\pi$
$572$		0			0
$573$	1613.23	+	1613.23i	0.117616	+	0.117616i
$574$		0			0
$575$	11410.9			0.827594
$576$		0			0
$577$	−14836.1			−1.07043			−0.535214	−	0.844717i	$-0.679769\pi$
$577$	−14836.1			−1.07043			−0.535214	+	0.844717i	$0.679769\pi$
$578$		0			0
$579$	4635.05	+	4635.05i	0.332688	+	0.332688i
$580$		0			0
$581$	1575.11	−	1575.11i	0.112473	−	0.112473i
$582$		0			0
$583$		−	7672.35i		−	0.545036i
$584$		0			0
$585$		−	10450.3i		−	0.738577i
$586$		0			0
$587$	−4038.29	+	4038.29i	−0.283949	+	0.283949i	−0.834682	−	0.550733i	$-0.814348\pi$
$587$	−4038.29	+	4038.29i	−0.283949	+	0.283949i	0.550733	+	0.834682i	$0.314348\pi$
$588$		0			0
$589$	−3804.04	−	3804.04i	−0.266116	−	0.266116i
$590$		0			0
$591$	−353.888			−0.0246311
$592$		0			0
$593$	11081.1			0.767361			0.383681	−	0.923466i	$-0.374656\pi$
$593$	11081.1			0.767361			0.383681	+	0.923466i	$0.374656\pi$
$594$		0			0
$595$	7684.40	+	7684.40i	0.529461	+	0.529461i
$596$		0			0
$597$	−3678.76	+	3678.76i	−0.252197	+	0.252197i
$598$		0			0
$599$			7036.50i			0.479973i	0.970776	+	0.239986i	$0.0771430\pi$
$599$			7036.50i			0.479973i	−0.970776	+	0.239986i	$0.922857\pi$
$600$		0			0
$601$		−	24290.7i		−	1.64865i	−0.566117	−	0.824325i	$-0.691555\pi$
$601$		−	24290.7i		−	1.64865i	0.566117	−	0.824325i	$-0.308445\pi$
$602$		0			0
$603$	−5646.02	+	5646.02i	−0.381299	+	0.381299i
$604$		0			0
$605$	−8875.31	−	8875.31i	−0.596418	−	0.596418i
$606$		0			0
$607$	10931.5			0.730967			0.365484	−	0.930818i	$-0.380904\pi$
$607$	10931.5			0.730967			0.365484	+	0.930818i	$0.380904\pi$
$608$		0			0
$609$	11267.2			0.749703
$610$		0			0
$611$	12555.0	+	12555.0i	0.831292	+	0.831292i
$612$		0			0
$613$	2217.95	−	2217.95i	0.146137	−	0.146137i	−0.630253	−	0.776390i	$-0.717049\pi$
$613$	2217.95	−	2217.95i	0.146137	−	0.146137i	0.776390	+	0.630253i	$0.217049\pi$
$614$		0			0
$615$			17420.0i			1.14218i
$616$		0			0
$617$			26271.5i			1.71418i	0.515164	+	0.857092i	$0.327731\pi$
$617$			26271.5i			1.71418i	−0.515164	+	0.857092i	$0.672269\pi$
$618$		0			0
$619$	11171.8	−	11171.8i	0.725417	−	0.725417i	−0.244287	−	0.969703i	$-0.578554\pi$
$619$	11171.8	−	11171.8i	0.725417	−	0.725417i	0.969703	+	0.244287i	$0.0785538\pi$
$620$		0			0
$621$	−1423.35	−	1423.35i	−0.0919757	−	0.0919757i
$622$		0			0
$623$	−11321.2			−0.728050
$624$		0			0
$625$	11330.4			0.725148
$626$		0			0
$627$	841.578	+	841.578i	0.0536035	+	0.0536035i
$628$		0			0
$629$	5739.95	−	5739.95i	0.363858	−	0.363858i
$630$		0			0
$631$		−	17415.1i		−	1.09871i	−0.835590	−	0.549354i	$-0.814874\pi$
$631$		−	17415.1i		−	1.09871i	0.835590	−	0.549354i	$-0.185126\pi$
$632$		0			0
$633$			1552.38i			0.0974749i
$634$		0			0
$635$	−2091.34	+	2091.34i	−0.130697	+	0.130697i
$636$		0			0
$637$	9102.24	+	9102.24i	0.566160	+	0.566160i
$638$		0			0
$639$	2473.06			0.153103
$640$		0			0
$641$	−2727.28			−0.168051			−0.0840257	−	0.996464i	$-0.526778\pi$
$641$	−2727.28			−0.168051			−0.0840257	+	0.996464i	$0.526778\pi$
$642$		0			0
$643$	−11681.7	−	11681.7i	−0.716458	−	0.716458i	0.251420	−	0.967878i	$-0.419103\pi$
$643$	−11681.7	−	11681.7i	−0.716458	−	0.716458i	−0.967878	+	0.251420i	$0.919103\pi$
$644$		0			0
$645$	10297.1	−	10297.1i	0.628600	−	0.628600i
$646$		0			0
$647$			4399.67i			0.267340i	0.991026	+	0.133670i	$0.0426762\pi$
$647$			4399.67i			0.267340i	−0.991026	+	0.133670i	$0.957324\pi$
$648$		0			0
$649$			9707.43i			0.587134i
$650$		0			0
$651$	8699.00	−	8699.00i	0.523718	−	0.523718i
$652$		0			0
$653$	22924.8	+	22924.8i	1.37384	+	1.37384i	0.854673	+	0.519167i	$0.173758\pi$
$653$	22924.8	+	22924.8i	1.37384	+	1.37384i	0.519167	+	0.854673i	$0.326242\pi$
$654$		0			0
$655$	22139.6			1.32071
$656$		0			0
$657$	2683.71			0.159363
$658$		0			0
$659$	11508.4	+	11508.4i	0.680276	+	0.680276i	0.960062	−	0.279786i	$-0.0902636\pi$
$659$	11508.4	+	11508.4i	0.680276	+	0.680276i	−0.279786	+	0.960062i	$0.590264\pi$
$660$		0			0
$661$	−10207.0	+	10207.0i	−0.600615	+	0.600615i	−0.940476	−	0.339861i	$-0.889620\pi$
$661$	−10207.0	+	10207.0i	−0.600615	+	0.600615i	0.339861	+	0.940476i	$0.389620\pi$
$662$		0			0
$663$		−	10826.2i		−	0.634171i
$664$		0			0
$665$		−	3459.43i		−	0.201731i
$666$		0			0
$667$	15744.2	−	15744.2i	0.913970	−	0.913970i
$668$		0			0
$669$	−8564.13	−	8564.13i	−0.494930	−	0.494930i
$670$		0			0
$671$	−9758.76			−0.561450
$672$		0			0
$673$	−23908.4			−1.36939			−0.684695	−	0.728830i	$-0.740065\pi$
$673$	−23908.4			−1.36939			−0.684695	+	0.728830i	$0.740065\pi$
$674$		0			0
$675$	2922.17	+	2922.17i	0.166629	+	0.166629i
$676$		0			0
$677$	−10411.1	+	10411.1i	−0.591035	+	0.591035i	−0.937911	−	0.346876i	$-0.887242\pi$
$677$	−10411.1	+	10411.1i	−0.591035	+	0.591035i	0.346876	+	0.937911i	$0.387242\pi$
$678$		0			0
$679$			66.3800i			0.00375174i
$680$		0			0
$681$			6375.90i			0.358774i
$682$		0			0
$683$	−11126.8	+	11126.8i	−0.623358	+	0.623358i	−0.946389	−	0.323030i	$-0.895298\pi$
$683$	−11126.8	+	11126.8i	−0.623358	+	0.623358i	0.323030	+	0.946389i	$0.395298\pi$
$684$		0			0
$685$	−3624.91	−	3624.91i	−0.202191	−	0.202191i
$686$		0			0
$687$	14610.2			0.811371
$688$		0			0
$689$	22216.5			1.22842
$690$		0			0
$691$	−2722.85	−	2722.85i	−0.149901	−	0.149901i	0.628173	−	0.778074i	$-0.283803\pi$
$691$	−2722.85	−	2722.85i	−0.149901	−	0.149901i	−0.778074	+	0.628173i	$0.783803\pi$
$692$		0			0
$693$	−1924.50	+	1924.50i	−0.105492	+	0.105492i
$694$		0			0
$695$			29558.5i			1.61326i
$696$		0			0
$697$			18046.6i			0.980724i
$698$		0			0
$699$	−2416.18	+	2416.18i	−0.130742	+	0.130742i
$700$		0			0
$701$	−2736.38	−	2736.38i	−0.147435	−	0.147435i	0.629536	−	0.776971i	$-0.283245\pi$
$701$	−2736.38	−	2736.38i	−0.147435	−	0.147435i	−0.776971	+	0.629536i	$0.783245\pi$
$702$		0			0
$703$	−2584.06			−0.138634
$704$		0			0
$705$	−12755.6			−0.681423
$706$		0			0
$707$	5773.45	+	5773.45i	0.307119	+	0.307119i
$708$		0			0
$709$	783.090	−	783.090i	0.0414803	−	0.0414803i	−0.686062	−	0.727543i	$-0.740662\pi$
$709$	783.090	−	783.090i	0.0414803	−	0.0414803i	0.727543	+	0.686062i	$0.240662\pi$
$710$		0			0
$711$		−	1580.98i		−	0.0833915i
$712$		0			0
$713$		−	24311.1i		−	1.27694i
$714$		0			0
$715$	−19744.4	+	19744.4i	−1.03272	+	1.03272i
$716$		0			0
$717$	−9766.14	−	9766.14i	−0.508679	−	0.508679i
$718$		0			0
$719$	−11021.5			−0.571671			−0.285835	−	0.958279i	$-0.592271\pi$
$719$	−11021.5			−0.571671			−0.285835	+	0.958279i	$0.592271\pi$
$720$		0			0
$721$	−9949.27			−0.513912
$722$		0			0
$723$	−9931.14	−	9931.14i	−0.510848	−	0.510848i
$724$		0			0
$725$	−32323.3	+	32323.3i	−1.65580	+	1.65580i
$726$		0			0
$727$			21740.4i			1.10909i	0.832154	+	0.554544i	$0.187107\pi$
$727$			21740.4i			1.10909i	−0.832154	+	0.554544i	$0.812893\pi$
$728$		0			0
$729$		−	729.000i		−	0.0370370i
$730$		0			0
$731$	10667.5	−	10667.5i	0.539741	−	0.539741i
$732$		0			0
$733$	−13194.8	−	13194.8i	−0.664886	−	0.664886i	0.291642	−	0.956528i	$-0.405798\pi$
$733$	−13194.8	−	13194.8i	−0.664886	−	0.664886i	−0.956528	+	0.291642i	$0.905798\pi$
$734$		0			0
$735$	−9247.69			−0.464090
$736$		0			0
$737$	21334.7			1.06631
$738$		0			0
$739$	−21786.6	−	21786.6i	−1.08448	−	1.08448i	−0.996085	−	0.0883973i	$-0.971825\pi$
$739$	−21786.6	−	21786.6i	−1.08448	−	1.08448i	−0.0883973	−	0.996085i	$-0.528175\pi$
$740$		0			0
$741$	−2436.93	+	2436.93i	−0.120813	+	0.120813i
$742$		0			0
$743$		−	7418.24i		−	0.366284i	−0.983086	−	0.183142i	$-0.941373\pi$
$743$		−	7418.24i		−	0.366284i	0.983086	−	0.183142i	$-0.0586268\pi$
$744$		0			0
$745$		−	39778.3i		−	1.95619i
$746$		0			0
$747$	1127.29	−	1127.29i	0.0552146	−	0.0552146i
$748$		0			0
$749$	−19187.5	−	19187.5i	−0.936045	−	0.936045i
$750$		0			0
$751$	−9320.68			−0.452885			−0.226442	−	0.974025i	$-0.572709\pi$
$751$	−9320.68			−0.452885			−0.226442	+	0.974025i	$0.572709\pi$
$752$		0			0
$753$	2021.36			0.0978255
$754$		0			0
$755$	−19835.3	−	19835.3i	−0.956135	−	0.956135i
$756$		0			0
$757$	−2105.29	+	2105.29i	−0.101081	+	0.101081i	−0.755839	−	0.654758i	$-0.772771\pi$
$757$	−2105.29	+	2105.29i	−0.101081	+	0.101081i	0.654758	+	0.755839i	$0.272771\pi$
$758$		0			0
$759$			5378.41i			0.257212i
$760$		0			0
$761$		−	13011.0i		−	0.619776i	−0.950773	−	0.309888i	$-0.899708\pi$
$761$		−	13011.0i		−	0.619776i	0.950773	−	0.309888i	$-0.100292\pi$
$762$		0			0
$763$	−5197.48	+	5197.48i	−0.246607	+	0.246607i
$764$		0			0
$765$	5499.61	+	5499.61i	0.259920	+	0.259920i
$766$		0			0
$767$	−28109.4			−1.32330
$768$		0			0
$769$	26438.9			1.23981			0.619904	−	0.784677i	$-0.287171\pi$
$769$	26438.9			1.23981			0.619904	+	0.784677i	$0.287171\pi$
$770$		0			0
$771$	1962.91	+	1962.91i	0.0916895	+	0.0916895i
$772$		0			0
$773$	21614.3	−	21614.3i	1.00571	−	1.00571i	0.00572318	−	0.999984i	$-0.498178\pi$
$773$	21614.3	−	21614.3i	1.00571	−	1.00571i	0.999984	−	0.00572318i	$-0.00182175\pi$
$774$		0			0
$775$			49911.4i			2.31338i
$776$		0			0
$777$		−	5909.19i		−	0.272833i
$778$		0			0
$779$	4062.20	−	4062.20i	0.186834	−	0.186834i
$780$		0			0
$781$	−4672.48	−	4672.48i	−0.214077	−	0.214077i
$782$		0			0
$783$	8063.76			0.368040
$784$		0			0
$785$	−25157.8			−1.14385
$786$		0			0
$787$	20949.4	+	20949.4i	0.948874	+	0.948874i	0.998755	−	0.0498808i	$-0.0158842\pi$
$787$	20949.4	+	20949.4i	0.948874	+	0.948874i	−0.0498808	+	0.998755i	$0.515884\pi$
$788$		0			0
$789$	−7377.21	+	7377.21i	−0.332871	+	0.332871i
$790$		0			0
$791$			2643.94i			0.118847i
$792$		0			0
$793$		−	28258.1i		−	1.26541i
$794$		0			0
$795$	−11285.8	+	11285.8i	−0.503478	+	0.503478i
$796$		0			0
$797$	−1576.38	−	1576.38i	−0.0700603	−	0.0700603i	0.671208	−	0.741269i	$-0.265776\pi$
$797$	−1576.38	−	1576.38i	−0.0700603	−	0.0700603i	−0.741269	+	0.671208i	$0.765776\pi$
$798$		0			0
$799$	−13214.4			−0.585097
$800$		0			0
$801$	−8102.44			−0.357410
$802$		0			0
$803$	−5070.48	−	5070.48i	−0.222831	−	0.222831i
$804$		0			0
$805$	11054.4	−	11054.4i	0.483995	−	0.483995i
$806$		0			0
$807$		−	16009.1i		−	0.698322i
$808$		0			0
$809$		−	8102.89i		−	0.352142i	−0.984378	−	0.176071i	$-0.943661\pi$
$809$		−	8102.89i		−	0.352142i	0.984378	−	0.176071i	$-0.0563388\pi$
$810$		0			0
$811$	−20649.6	+	20649.6i	−0.894090	+	0.894090i	−0.994905	−	0.100816i	$-0.967855\pi$
$811$	−20649.6	+	20649.6i	−0.894090	+	0.894090i	0.100816	+	0.994905i	$0.467855\pi$
$812$		0			0
$813$	16985.6	+	16985.6i	0.732732	+	0.732732i
$814$		0			0
$815$	−56114.6			−2.41179
$816$		0			0
$817$	−4802.38			−0.205647
$818$		0			0
$819$	−5572.71	−	5572.71i	−0.237761	−	0.237761i
$820$		0			0
$821$	−13405.1	+	13405.1i	−0.569844	+	0.569844i	−0.932085	−	0.362240i	$-0.882012\pi$
$821$	−13405.1	+	13405.1i	−0.569844	+	0.569844i	0.362240	+	0.932085i	$0.382012\pi$
$822$		0			0
$823$		−	17203.4i		−	0.728643i	−0.931273	−	0.364321i	$-0.881301\pi$
$823$		−	17203.4i		−	0.728643i	0.931273	−	0.364321i	$-0.118699\pi$
$824$		0			0
$825$		−	11042.0i		−	0.465981i
$826$		0			0
$827$	11127.2	−	11127.2i	0.467872	−	0.467872i	−0.433353	−	0.901224i	$-0.642670\pi$
$827$	11127.2	−	11127.2i	0.467872	−	0.467872i	0.901224	+	0.433353i	$0.142670\pi$
$828$		0			0
$829$	5752.09	+	5752.09i	0.240987	+	0.240987i	0.817259	−	0.576271i	$-0.195493\pi$
$829$	5752.09	+	5752.09i	0.240987	+	0.240987i	−0.576271	+	0.817259i	$0.695493\pi$
$830$		0			0
$831$	−19307.1			−0.805964
$832$		0			0
$833$	−9580.34			−0.398486
$834$		0			0
$835$	9904.39	+	9904.39i	0.410486	+	0.410486i
$836$		0			0
$837$	6225.75	−	6225.75i	0.257101	−	0.257101i
$838$		0			0
$839$		−	45875.9i		−	1.88774i	−0.330318	−	0.943870i	$-0.607156\pi$
$839$		−	45875.9i		−	1.88774i	0.330318	−	0.943870i	$-0.392844\pi$
$840$		0			0
$841$			64807.5i			2.65724i
$842$		0			0
$843$	−7070.47	+	7070.47i	−0.288873	+	0.288873i
$844$		0			0
$845$	−31268.1	−	31268.1i	−1.27296	−	1.27296i
$846$		0			0
$847$	−9465.66			−0.383995
$848$		0			0
$849$	−26483.5			−1.07057
$850$		0			0
$851$	−8257.21	−	8257.21i	−0.332613	−	0.332613i
$852$		0			0
$853$	27266.2	−	27266.2i	1.09446	−	1.09446i	0.0994157	−	0.995046i	$-0.468303\pi$
$853$	27266.2	−	27266.2i	1.09446	−	1.09446i	0.995046	−	0.0994157i	$-0.0316973\pi$
$854$		0			0
$855$		−	2475.87i		−	0.0990326i
$856$		0			0
$857$		−	28960.0i		−	1.15432i	−0.816629	−	0.577162i	$-0.804160\pi$
$857$		−	28960.0i		−	1.15432i	0.816629	−	0.577162i	$-0.195840\pi$
$858$		0			0
$859$	−17255.5	+	17255.5i	−0.685388	+	0.685388i	−0.961209	−	0.275821i	$-0.911050\pi$
$859$	−17255.5	+	17255.5i	−0.685388	+	0.685388i	0.275821	+	0.961209i	$0.411050\pi$
$860$		0			0
$861$	9289.36	+	9289.36i	0.367689	+	0.367689i
$862$		0			0
$863$	39885.9			1.57327			0.786635	−	0.617418i	$-0.211821\pi$
$863$	39885.9			1.57327			0.786635	+	0.617418i	$0.211821\pi$
$864$		0			0
$865$	−10618.5			−0.417388
$866$		0			0
$867$	−4724.61	−	4724.61i	−0.185071	−	0.185071i
$868$		0			0
$869$	−2987.03	+	2987.03i	−0.116603	+	0.116603i
$870$		0			0
$871$			61778.0i			2.40329i
$872$		0			0
$873$			47.5072i			0.00184178i
$874$		0			0
$875$	−4160.41	+	4160.41i	−0.160740	+	0.160740i
$876$		0			0
$877$	−8855.51	−	8855.51i	−0.340968	−	0.340968i	0.515763	−	0.856731i	$-0.327509\pi$
$877$	−8855.51	−	8855.51i	−0.340968	−	0.340968i	−0.856731	+	0.515763i	$0.827509\pi$
$878$		0			0
$879$	10429.4			0.400200
$880$		0			0
$881$	−43343.8			−1.65753			−0.828767	−	0.559593i	$-0.810957\pi$
$881$	−43343.8			−1.65753			−0.828767	+	0.559593i	$0.810957\pi$
$882$		0			0
$883$	−11229.3	−	11229.3i	−0.427968	−	0.427968i	0.459968	−	0.887936i	$-0.347861\pi$
$883$	−11229.3	−	11229.3i	−0.427968	−	0.427968i	−0.887936	+	0.459968i	$0.847861\pi$
$884$		0			0
$885$	14279.3	−	14279.3i	0.542366	−	0.542366i
$886$		0			0
$887$			36912.9i			1.39731i	0.715459	+	0.698655i	$0.246218\pi$
$887$			36912.9i			1.39731i	−0.715459	+	0.698655i	$0.753782\pi$
$888$		0			0
$889$			2230.45i			0.0841473i
$890$		0			0
$891$	−1377.34	+	1377.34i	−0.0517874	+	0.0517874i
$892$		0			0
$893$	2974.49	+	2974.49i	0.111464	+	0.111464i
$894$		0			0
$895$	−15275.5			−0.570508
$896$		0			0
$897$	−15574.1			−0.579714
$898$		0			0
$899$	68865.5	+	68865.5i	2.55483	+	2.55483i
$900$		0			0
$901$	−11691.7	+	11691.7i	−0.432306	+	0.432306i
$902$		0			0
$903$		−	10982.0i		−	0.404715i
$904$		0			0
$905$			17822.2i			0.654618i
$906$		0			0
$907$	−14588.0	+	14588.0i	−0.534053	+	0.534053i	−0.921776	−	0.387723i	$-0.873262\pi$
$907$	−14588.0	+	14588.0i	−0.534053	+	0.534053i	0.387723	+	0.921776i	$0.373262\pi$
$908$		0			0
$909$	4131.98	+	4131.98i	0.150769	+	0.150769i
$910$		0			0
$911$	50418.8			1.83365			0.916823	−	0.399295i	$-0.130745\pi$
$911$	50418.8			1.83365			0.916823	+	0.399295i	$0.130745\pi$
$912$		0			0
$913$	−4259.69			−0.154409
$914$		0			0
$915$	14354.8	+	14354.8i	0.518640	+	0.518640i
$916$		0			0
$917$	11806.1	−	11806.1i	0.425160	−	0.425160i
$918$		0			0
$919$		−	53290.4i		−	1.91283i	−0.292018	−	0.956413i	$-0.594327\pi$
$919$		−	53290.4i		−	1.91283i	0.292018	−	0.956413i	$-0.405673\pi$
$920$		0			0
$921$			12763.9i			0.456662i
$922$		0			0
$923$	13529.9	−	13529.9i	0.482495	−	0.482495i
$924$		0			0
$925$	16952.3	+	16952.3i	0.602581	+	0.602581i
$926$		0			0
$927$	−7120.55			−0.252287
$928$		0			0
$929$	44859.2			1.58427			0.792133	−	0.610349i	$-0.208971\pi$
$929$	44859.2			1.58427			0.792133	+	0.610349i	$0.208971\pi$
$930$		0			0
$931$	2156.48	+	2156.48i	0.0759140	+	0.0759140i
$932$		0			0
$933$	−9560.97	+	9560.97i	−0.335490	+	0.335490i
$934$		0			0
$935$		−	20781.4i		−	0.726872i
$936$		0			0
$937$			22463.9i			0.783204i	0.920135	+	0.391602i	$0.128079\pi$
$937$			22463.9i			0.783204i	−0.920135	+	0.391602i	$0.871921\pi$
$938$		0			0
$939$	11110.6	−	11110.6i	0.386136	−	0.386136i
$940$		0			0
$941$	−20653.7	−	20653.7i	−0.715507	−	0.715507i	0.252175	−	0.967682i	$-0.418854\pi$
$941$	−20653.7	−	20653.7i	−0.715507	−	0.715507i	−0.967682	+	0.252175i	$0.918854\pi$
$942$		0			0
$943$	25961.0			0.896507
$944$		0			0
$945$	5661.77			0.194897
$946$		0			0
$947$	−33123.2	−	33123.2i	−1.13660	−	1.13660i	−0.989055	−	0.147544i	$-0.952863\pi$
$947$	−33123.2	−	33123.2i	−1.13660	−	1.13660i	−0.147544	−	0.989055i	$-0.547137\pi$
$948$		0			0
$949$	14682.4	−	14682.4i	0.502224	−	0.502224i
$950$		0			0
$951$			4198.22i			0.143151i
$952$		0			0
$953$		−	10871.9i		−	0.369544i	−0.982781	−	0.184772i	$-0.940845\pi$
$953$		−	10871.9i		−	0.369544i	0.982781	−	0.184772i	$-0.0591546\pi$
$954$		0			0
$955$	−8966.93	+	8966.93i	−0.303836	+	0.303836i
$956$		0			0
$957$	−15235.3	−	15235.3i	−0.514616	−	0.514616i
$958$		0			0
$959$	−3866.02			−0.130178
$960$		0			0
$961$	76546.3			2.56944
$962$		0			0
$963$	−13732.3	−	13732.3i	−0.459518	−	0.459518i
$964$		0			0
$965$	−25763.3	+	25763.3i	−0.859430	+	0.859430i
$966$		0			0
$967$		−	6501.58i		−	0.216212i	−0.994139	−	0.108106i	$-0.965521\pi$
$967$		−	6501.58i		−	0.216212i	0.994139	−	0.108106i	$-0.0344786\pi$
$968$		0			0
$969$		−	2564.93i		−	0.0850333i
$970$		0			0
$971$	16761.7	−	16761.7i	0.553975	−	0.553975i	−0.373611	−	0.927586i	$-0.621880\pi$
$971$	16761.7	−	16761.7i	0.553975	−	0.553975i	0.927586	+	0.373611i	$0.121880\pi$
$972$		0			0
$973$	15762.3	+	15762.3i	0.519338	+	0.519338i
$974$		0			0
$975$	31974.0			1.05024
$976$		0			0
$977$	−7407.34			−0.242561			−0.121280	−	0.992618i	$-0.538700\pi$
$977$	−7407.34			−0.242561			−0.121280	+	0.992618i	$0.538700\pi$
$978$		0			0
$979$	15308.4	+	15308.4i	0.499753	+	0.499753i
$980$		0			0
$981$	−3719.76	+	3719.76i	−0.121063	+	0.121063i
$982$		0			0
$983$		−	35694.8i		−	1.15818i	−0.815265	−	0.579088i	$-0.803409\pi$
$983$		−	35694.8i		−	1.15818i	0.815265	−	0.579088i	$-0.196591\pi$
$984$		0			0
$985$		−	1967.04i		−	0.0636294i
$986$		0			0
$987$	−6802.01	+	6802.01i	−0.219362	+	0.219362i
$988$		0			0
$989$	−15345.7	−	15345.7i	−0.493392	−	0.493392i
$990$		0			0
$991$	46662.2			1.49573			0.747867	−	0.663849i	$-0.231078\pi$
$991$	46662.2			1.49573			0.747867	+	0.663849i	$0.231078\pi$
$992$		0			0
$993$	23981.7			0.766402
$994$		0			0
$995$	−20447.9	−	20447.9i	−0.651498	−	0.651498i
$996$		0			0
$997$	22390.7	−	22390.7i	0.711255	−	0.711255i	−0.255543	−	0.966798i	$-0.582254\pi$
$997$	22390.7	−	22390.7i	0.711255	−	0.711255i	0.966798	+	0.255543i	$0.0822542\pi$
$998$		0			0
$999$		−	4229.12i		−	0.133937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.4.j.b.289.7		24
4.3	odd	2		384.4.j.a.289.6		24
8.3	odd	2		192.4.j.a.145.12		24
8.5	even	2		48.4.j.a.13.12	✓	24
16.3	odd	4		192.4.j.a.49.12		24
16.5	even	4	inner	384.4.j.b.97.7		24
16.11	odd	4		384.4.j.a.97.6		24
16.13	even	4		48.4.j.a.37.12	yes	24
24.5	odd	2		144.4.k.b.109.1		24
24.11	even	2		576.4.k.b.145.2		24
48.29	odd	4		144.4.k.b.37.1		24
48.35	even	4		576.4.k.b.433.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.12	✓	24	8.5	even	2
48.4.j.a.37.12	yes	24	16.13	even	4
144.4.k.b.37.1		24	48.29	odd	4
144.4.k.b.109.1		24	24.5	odd	2
192.4.j.a.49.12		24	16.3	odd	4
192.4.j.a.145.12		24	8.3	odd	2
384.4.j.a.97.6		24	16.11	odd	4
384.4.j.a.289.6		24	4.3	odd	2
384.4.j.b.97.7		24	16.5	even	4	inner
384.4.j.b.289.7		24	1.1	even	1	trivial
576.4.k.b.145.2		24	24.11	even	2
576.4.k.b.433.2		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)

\(f(q)\)	\(=\)	\(q+(2.12132 + 2.12132i) q^{3} +(-11.7911 + 11.7911i) q^{5} +12.5754i q^{7} +9.00000i q^{9} +O(q^{10})\)	\(q+(2.12132 + 2.12132i) q^{3} +(-11.7911 + 11.7911i) q^{5} +12.5754i q^{7} +9.00000i q^{9} +(17.0042 - 17.0042i) q^{11} +(49.2384 + 49.2384i) q^{13} -50.0252 q^{15} -51.8247 q^{17} +(11.6655 + 11.6655i) q^{19} +(-26.6763 + 26.6763i) q^{21} +74.5524i q^{23} -153.058i q^{25} +(-19.0919 + 19.0919i) q^{27} +(-211.183 - 211.183i) q^{29} -326.094 q^{31} +72.1427 q^{33} +(-148.277 - 148.277i) q^{35} +(-110.757 + 110.757i) q^{37} +208.901i q^{39} -348.225i q^{41} +(-205.838 + 205.838i) q^{43} +(-106.120 - 106.120i) q^{45} +254.983 q^{47} +184.861 q^{49} +(-109.937 - 109.937i) q^{51} +(225.602 - 225.602i) q^{53} +400.995i q^{55} +49.4924i q^{57} +(-285.442 + 285.442i) q^{59} +(-286.952 - 286.952i) q^{61} -113.178 q^{63} -1161.15 q^{65} +(627.335 + 627.335i) q^{67} +(-158.150 + 158.150i) q^{69} -274.784i q^{71} -298.190i q^{73} +(324.686 - 324.686i) q^{75} +(213.834 + 213.834i) q^{77} -175.664 q^{79} -81.0000 q^{81} +(-125.254 - 125.254i) q^{83} +(611.068 - 611.068i) q^{85} -895.973i q^{87} +900.271i q^{89} +(-619.190 + 619.190i) q^{91} +(-691.750 - 691.750i) q^{93} -275.096 q^{95} +5.27858 q^{97} +(153.038 + 153.038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 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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