LMFDB - Embedded newform 192.4.j.a.145.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$11.3283667211$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 48)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			145.12
Character	$\chi$	$=$	192.145
Dual form			192.4.j.a.49.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.12132 + 2.12132i) q^{3} +(11.7911 - 11.7911i) q^{5} -12.5754i q^{7} +9.00000i q^{9} +(17.0042 - 17.0042i) q^{11} +(-49.2384 - 49.2384i) q^{13} +50.0252 q^{15} -51.8247 q^{17} +(11.6655 + 11.6655i) q^{19} +(26.6763 - 26.6763i) q^{21} -74.5524i q^{23} -153.058i q^{25} +(-19.0919 + 19.0919i) q^{27} +(211.183 + 211.183i) q^{29} +326.094 q^{31} +72.1427 q^{33} +(-148.277 - 148.277i) q^{35} +(110.757 - 110.757i) q^{37} -208.901i q^{39} -348.225i q^{41} +(-205.838 + 205.838i) q^{43} +(106.120 + 106.120i) q^{45} -254.983 q^{47} +184.861 q^{49} +(-109.937 - 109.937i) q^{51} +(-225.602 + 225.602i) q^{53} -400.995i q^{55} +49.4924i q^{57} +(-285.442 + 285.442i) q^{59} +(286.952 + 286.952i) q^{61} +113.178 q^{63} -1161.15 q^{65} +(627.335 + 627.335i) q^{67} +(158.150 - 158.150i) q^{69} +274.784i q^{71} -298.190i q^{73} +(324.686 - 324.686i) q^{75} +(-213.834 - 213.834i) q^{77} +175.664 q^{79} -81.0000 q^{81} +(-125.254 - 125.254i) q^{83} +(-611.068 + 611.068i) q^{85} +895.973i q^{87} +900.271i q^{89} +(-619.190 + 619.190i) q^{91} +(691.750 + 691.750i) q^{93} +275.096 q^{95} +5.27858 q^{97} +(153.038 + 153.038i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 40 q^{11} - 120 q^{15} - 24 q^{19} + 400 q^{29} + 744 q^{31} + 456 q^{35} + 16 q^{37} - 1240 q^{43} - 1176 q^{49} - 744 q^{51} + 752 q^{53} + 1376 q^{59} - 912 q^{61} + 504 q^{63} + 976 q^{65} + 2256 q^{67}+ \cdots + 360 q^{99}+O(q^{100}) $ 24 * q + 40 * q^11 - 120 * q^15 - 24 * q^19 + 400 * q^29 + 744 * q^31 + 456 * q^35 + 16 * q^37 - 1240 * q^43 - 1176 * q^49 - 744 * q^51 + 752 * q^53 + 1376 * q^59 - 912 * q^61 + 504 * q^63 + 976 * q^65 + 2256 * q^67 - 528 * q^69 - 1104 * q^75 + 1904 * q^77 - 5992 * q^79 - 1944 * q^81 - 2680 * q^83 - 240 * q^85 + 3496 * q^91 + 7728 * q^95 + 360 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$3$	2.12132	+	2.12132i	0.408248	+	0.408248i
$4$		0			0
$5$	11.7911	−	11.7911i	1.05462	−	1.05462i	0.0562056	−	0.998419i	$-0.482100\pi$
$5$	11.7911	−	11.7911i	1.05462	−	1.05462i	0.998419	−	0.0562056i	$-0.0179002\pi$
$6$		0			0
$7$		−	12.5754i		−	0.679005i	−0.940605	−	0.339503i	$-0.889741\pi$
$7$		−	12.5754i		−	0.679005i	0.940605	−	0.339503i	$-0.110259\pi$
$8$		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	$-0.983496\pi$
$13$	−49.2384	−	49.2384i	−1.05048	−	1.05048i	−0.0518270	−	0.998656i	$-0.516504\pi$
$14$		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	$-0.890270\pi$
$23$		−	74.5524i		−	0.675881i	0.941168	−	0.337940i	$-0.109730\pi$
$24$		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	$0.155437\pi$
$29$	211.183	+	211.183i	1.35227	+	1.35227i	0.469143	+	0.883122i	$0.344563\pi$
$30$		0			0
$31$	326.094			1.88930			0.944648	−	0.328084i	$-0.106403\pi$
$31$	326.094			1.88930			0.944648	+	0.328084i	$0.106403\pi$
$32$		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	−0.416855	−	0.908973i	$-0.636868\pi$
$37$	110.757	−	110.757i	0.492117	−	0.492117i	0.908973	+	0.416855i	$0.136868\pi$
$38$		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	$-0.629488\pi$
$47$	−254.983			−0.791342			−0.395671	+	0.918392i	$0.629488\pi$
$48$		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	−0.936189	−	0.351496i	$-0.885673\pi$
$53$	−225.602	+	225.602i	−0.584694	+	0.584694i	0.351496	+	0.936189i	$0.385673\pi$
$54$		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	0.940923	−	0.338621i	$-0.109961\pi$
$61$	286.952	+	286.952i	0.602301	+	0.602301i	−0.338621	+	0.940923i	$0.609961\pi$
$62$		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	$0.0737595\pi$
$71$			274.784i			0.459308i	−0.973272	+	0.229654i	$0.926241\pi$
$72$		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	$-0.460079\pi$
$79$	175.664			0.250174			0.125087	+	0.992146i	$0.460079\pi$
$80$		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	−0.896120	−	0.443812i	$-0.853626\pi$
$101$	−459.109	+	459.109i	−0.452307	+	0.452307i	0.443812	+	0.896120i	$0.353626\pi$
$102$		0			0
$103$		−	791.173i		−	0.756860i	−0.925630	−	0.378430i	$-0.876464\pi$
$103$		−	791.173i		−	0.756860i	0.925630	−	0.378430i	$-0.123536\pi$
$104$		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	0.501796	−	0.864986i	$-0.332673\pi$
$109$	−413.307	−	413.307i	−0.363189	−	0.363189i	−0.864986	+	0.501796i	$0.832673\pi$
$110$		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	$-0.519736\pi$
$127$	−177.367			−0.123927			−0.0619637	+	0.998078i	$0.519736\pi$
$128$		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	−0.0701033	−	0.997540i	$-0.522333\pi$
$149$	1686.80	−	1686.80i	0.927436	−	0.927436i	0.997540	+	0.0701033i	$0.0223329\pi$
$150$		0			0
$151$		−	1682.23i		−	0.906611i	−0.891355	−	0.453306i	$-0.850245\pi$
$151$		−	1682.23i		−	0.906611i	0.891355	−	0.453306i	$-0.149755\pi$
$152$		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	0.381903	−	0.924202i	$-0.375269\pi$
$157$	−1066.81	−	1066.81i	−0.542300	−	0.542300i	−0.924202	+	0.381903i	$0.875269\pi$
$158$		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	$0.0623448\pi$
$167$			839.991i			0.389224i	−0.980880	+	0.194612i	$0.937655\pi$
$168$		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	0.601208	−	0.799093i	$-0.294686\pi$
$173$	−450.278	−	450.278i	−0.197885	−	0.197885i	−0.799093	+	0.601208i	$0.794686\pi$
$174$		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	−0.845047	−	0.534691i	$-0.820428\pi$
$181$	−755.750	+	755.750i	−0.310356	+	0.310356i	0.534691	+	0.845047i	$0.320428\pi$
$182$		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	$-0.546012\pi$
$191$	−760.485			−0.288098			−0.144049	+	0.989571i	$0.546012\pi$
$192$		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	−0.691862	−	0.722029i	$-0.743210\pi$
$197$	83.4121	−	83.4121i	0.0301668	−	0.0301668i	0.722029	+	0.691862i	$0.243210\pi$
$198$		0			0
$199$		−	1734.18i		−	0.617754i	−0.951102	−	0.308877i	$-0.900047\pi$
$199$		−	1734.18i		−	0.617754i	0.951102	−	0.308877i	$-0.0999531\pi$
$200$		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	$-0.292708\pi$
$223$	4037.17			1.21233			0.606164	+	0.795340i	$0.292708\pi$
$224$		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	−0.999980	−	0.00625772i	$-0.998008\pi$
$229$	−3443.65	+	3443.65i	−0.993723	+	0.993723i	0.00625772	+	0.999980i	$0.498008\pi$
$230$		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	$-0.285913\pi$
$239$	4603.80			1.24600			0.623002	+	0.782220i	$0.285913\pi$
$240$		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	$-0.866337\pi$
$263$		−	3477.65i		−	0.815365i	0.913124	−	0.407683i	$-0.133663\pi$
$264$		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	0.990776	−	0.135510i	$-0.0432673\pi$
$269$	3773.37	+	3773.37i	0.855266	+	0.855266i	−0.135510	+	0.990776i	$0.543267\pi$
$270$		0			0
$271$	−8007.09			−1.79482			−0.897410	−	0.441198i	$-0.854554\pi$
$271$	−8007.09			−1.79482			−0.897410	+	0.441198i	$0.854554\pi$
$272$		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	−0.0128173	−	0.999918i	$-0.504080\pi$
$277$	4550.73	−	4550.73i	0.987101	−	0.987101i	0.999918	+	0.0128173i	$0.00407998\pi$
$278$		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	−0.908351	−	0.418208i	$-0.862658\pi$
$293$	−2458.24	+	2458.24i	−0.490143	+	0.490143i	0.418208	+	0.908351i	$0.362658\pi$
$294$		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	$-0.865218\pi$
$311$		−	4507.09i		−	0.821779i	0.911685	−	0.410890i	$-0.134782\pi$
$312$		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	0.613990	−	0.789314i	$-0.289563\pi$
$317$	−989.530	−	989.530i	−0.175323	−	0.175323i	−0.789314	+	0.613990i	$0.789563\pi$
$318$		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	$0.0389990\pi$
$349$	7267.79	+	7267.79i	1.11472	+	1.11472i	0.122213	+	0.992504i	$0.461001\pi$
$350$		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	$-0.884525\pi$
$359$		−	4827.70i		−	0.709738i	0.934916	−	0.354869i	$-0.115475\pi$
$360$		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	$-0.441808\pi$
$367$	2556.37			0.363600			0.181800	+	0.983336i	$0.441808\pi$
$368$		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	−0.623420	−	0.781887i	$-0.714257\pi$
$373$	1141.57	−	1141.57i	0.158468	−	0.158468i	0.781887	+	0.623420i	$0.214257\pi$
$374$		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	$-0.492125\pi$
$383$	370.858			0.0494777			0.0247388	+	0.999694i	$0.492125\pi$
$384$		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	−0.989077	−	0.147403i	$-0.952909\pi$
$389$	−6457.55	+	6457.55i	−0.841673	+	0.841673i	0.147403	+	0.989077i	$0.452909\pi$
$390$		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	0.692267	−	0.721641i	$-0.256612\pi$
$397$	−232.353	−	232.353i	−0.0293739	−	0.0293739i	−0.721641	+	0.692267i	$0.756612\pi$
$398$		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	$-0.406437\pi$
$421$	10770.4	−	10770.4i	1.24683	−	1.24683i	0.957110	−	0.289723i	$-0.0935632\pi$
$422$		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	$-0.638574\pi$
$431$	−7546.94			−0.843442			−0.421721	+	0.906726i	$0.638574\pi$
$432$		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	$-0.872016\pi$
$439$		−	7198.92i		−	0.782656i	0.920251	−	0.391328i	$-0.127984\pi$
$440$		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	$-0.949602\pi$
$461$	−11334.9	−	11334.9i	−1.14516	−	1.14516i	−0.157670	−	0.987492i	$-0.550398\pi$
$462$		0			0
$463$	−3013.37			−0.302469			−0.151234	−	0.988498i	$-0.548325\pi$
$463$	−3013.37			−0.302469			−0.151234	+	0.988498i	$0.548325\pi$
$464$		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	$-0.668177\pi$
$479$	−10569.4			−1.00821			−0.504103	+	0.863644i	$0.668177\pi$
$480$		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	$0.0234061\pi$
$487$			1579.10i			0.146932i	−0.997298	+	0.0734661i	$0.976594\pi$
$488$		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	$-0.953417\pi$
$503$		−	3290.09i		−	0.291646i	0.989311	−	0.145823i	$-0.0465830\pi$
$504$		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	0.765140	−	0.643864i	$-0.222670\pi$
$509$	1392.67	+	1392.67i	0.121275	+	0.121275i	−0.643864	+	0.765140i	$0.722670\pi$
$510$		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	0.812686	−	0.582702i	$-0.198004\pi$
$541$	2893.97	+	2893.97i	0.229984	+	0.229984i	−0.582702	+	0.812686i	$0.698004\pi$
$542$		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	0.306602	−	0.951838i	$-0.400808\pi$
$557$	−8482.07	−	8482.07i	−0.645236	−	0.645236i	−0.951838	+	0.306602i	$0.900808\pi$
$558$		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	$-0.922857\pi$
$599$		−	7036.50i		−	0.479973i	0.970776	−	0.239986i	$-0.0771430\pi$
$600$		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	$-0.619096\pi$
$607$	−10931.5			−0.730967			−0.365484	+	0.930818i	$0.619096\pi$
$608$		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	−0.776390	−	0.630253i	$-0.782951\pi$
$613$	−2217.95	+	2217.95i	−0.146137	+	0.146137i	0.630253	+	0.776390i	$0.282951\pi$
$614$		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	$0.185126\pi$
$631$			17415.1i			1.09871i	−0.835590	+	0.549354i	$0.814874\pi$
$632$		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	$-0.957324\pi$
$647$		−	4399.67i		−	0.267340i	0.991026	−	0.133670i	$-0.0426762\pi$
$648$		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	$-0.826242\pi$
$653$	−22924.8	−	22924.8i	−1.37384	−	1.37384i	−0.519167	−	0.854673i	$-0.673758\pi$
$654$		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	−0.339861	−	0.940476i	$-0.610380\pi$
$661$	10207.0	−	10207.0i	0.600615	−	0.600615i	0.940476	+	0.339861i	$0.110380\pi$
$662$		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	−0.346876	−	0.937911i	$-0.612758\pi$
$677$	10411.1	−	10411.1i	0.591035	−	0.591035i	0.937911	+	0.346876i	$0.112758\pi$
$678$		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	0.776971	−	0.629536i	$-0.216755\pi$
$701$	2736.38	+	2736.38i	0.147435	+	0.147435i	−0.629536	+	0.776971i	$0.716755\pi$
$702$		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	−0.727543	−	0.686062i	$-0.759338\pi$
$709$	−783.090	+	783.090i	−0.0414803	+	0.0414803i	0.686062	+	0.727543i	$0.259338\pi$
$710$		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	$-0.407729\pi$
$719$	11021.5			0.571671			0.285835	+	0.958279i	$0.407729\pi$
$720$		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	$-0.812893\pi$
$727$		−	21740.4i		−	1.10909i	0.832154	−	0.554544i	$-0.187107\pi$
$728$		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	0.956528	−	0.291642i	$-0.0942015\pi$
$733$	13194.8	+	13194.8i	0.664886	+	0.664886i	−0.291642	+	0.956528i	$0.594202\pi$
$734$		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	$0.0586268\pi$
$743$			7418.24i			0.366284i	−0.983086	+	0.183142i	$0.941373\pi$
$744$		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	$-0.427291\pi$
$751$	9320.68			0.452885			0.226442	+	0.974025i	$0.427291\pi$
$752$		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	−0.654758	−	0.755839i	$-0.727229\pi$
$757$	2105.29	−	2105.29i	0.101081	−	0.101081i	0.755839	+	0.654758i	$0.227229\pi$
$758$		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	$0.501822\pi$
$773$	−21614.3	+	21614.3i	−1.00571	+	1.00571i	−0.999984	+	0.00572318i	$0.998178\pi$
$774$		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	0.741269	−	0.671208i	$-0.234224\pi$
$797$	1576.38	+	1576.38i	0.0700603	+	0.0700603i	−0.671208	+	0.741269i	$0.734224\pi$
$798$		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	−0.362240	−	0.932085i	$-0.617988\pi$
$821$	13405.1	−	13405.1i	0.569844	−	0.569844i	0.932085	+	0.362240i	$0.117988\pi$
$822$		0			0
$823$			17203.4i			0.728643i	0.931273	+	0.364321i	$0.118699\pi$
$823$			17203.4i			0.728643i	−0.931273	+	0.364321i	$0.881301\pi$
$824$		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	0.576271	−	0.817259i	$-0.304507\pi$
$829$	−5752.09	−	5752.09i	−0.240987	−	0.240987i	−0.817259	+	0.576271i	$0.804507\pi$
$830$		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	$0.392844\pi$
$839$			45875.9i			1.88774i	−0.330318	+	0.943870i	$0.607156\pi$
$840$		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	$0.531697\pi$
$853$	−27266.2	+	27266.2i	−1.09446	+	1.09446i	−0.995046	+	0.0994157i	$0.968303\pi$
$854$		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	$-0.788179\pi$
$863$	−39885.9			−1.57327			−0.786635	+	0.617418i	$0.788179\pi$
$864$		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	0.856731	−	0.515763i	$-0.172491\pi$
$877$	8855.51	+	8855.51i	0.340968	+	0.340968i	−0.515763	+	0.856731i	$0.672491\pi$
$878$		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	$-0.753782\pi$
$887$		−	36912.9i		−	1.39731i	0.715459	−	0.698655i	$-0.246218\pi$
$888$		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	$-0.869255\pi$
$911$	−50418.8			−1.83365			−0.916823	+	0.399295i	$0.869255\pi$
$912$		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	$0.405673\pi$
$919$			53290.4i			1.91283i	−0.292018	+	0.956413i	$0.594327\pi$
$920$		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	0.967682	−	0.252175i	$-0.0811458\pi$
$941$	20653.7	+	20653.7i	0.715507	+	0.715507i	−0.252175	+	0.967682i	$0.581146\pi$
$942$		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	$0.0344786\pi$
$967$			6501.58i			0.216212i	−0.994139	+	0.108106i	$0.965521\pi$
$968$		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	$0.196591\pi$
$983$			35694.8i			1.15818i	−0.815265	+	0.579088i	$0.803409\pi$
$984$		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	$-0.768922\pi$
$991$	−46662.2			−1.49573			−0.747867	+	0.663849i	$0.768922\pi$
$992$		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	−0.966798	−	0.255543i	$-0.917746\pi$
$997$	−22390.7	+	22390.7i	−0.711255	+	0.711255i	0.255543	+	0.966798i	$0.417746\pi$
$998$		0			0
$999$			4229.12i			0.133937i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.12	✓	24	4.3	odd	2
48.4.j.a.37.12	yes	24	16.11	odd	4
144.4.k.b.37.1		24	48.11	even	4
144.4.k.b.109.1		24	12.11	even	2
192.4.j.a.49.12		24	16.5	even	4	inner
192.4.j.a.145.12		24	1.1	even	1	trivial
384.4.j.a.97.6		24	16.13	even	4
384.4.j.a.289.6		24	8.5	even	2
384.4.j.b.97.7		24	16.3	odd	4
384.4.j.b.289.7		24	8.3	odd	2
576.4.k.b.145.2		24	3.2	odd	2
576.4.k.b.433.2		24	48.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(2.12132 + 2.12132i) q^{3} +(11.7911 - 11.7911i) q^{5} -12.5754i q^{7} +9.00000i q^{9} +(17.0042 - 17.0042i) q^{11} +(-49.2384 - 49.2384i) q^{13} +50.0252 q^{15} -51.8247 q^{17} +(11.6655 + 11.6655i) q^{19} +(26.6763 - 26.6763i) q^{21} -74.5524i q^{23} -153.058i q^{25} +(-19.0919 + 19.0919i) q^{27} +(211.183 + 211.183i) q^{29} +326.094 q^{31} +72.1427 q^{33} +(-148.277 - 148.277i) q^{35} +(110.757 - 110.757i) q^{37} -208.901i q^{39} -348.225i q^{41} +(-205.838 + 205.838i) q^{43} +(106.120 + 106.120i) q^{45} -254.983 q^{47} +184.861 q^{49} +(-109.937 - 109.937i) q^{51} +(-225.602 + 225.602i) q^{53} -400.995i q^{55} +49.4924i q^{57} +(-285.442 + 285.442i) q^{59} +(286.952 + 286.952i) q^{61} +113.178 q^{63} -1161.15 q^{65} +(627.335 + 627.335i) q^{67} +(158.150 - 158.150i) q^{69} +274.784i q^{71} -298.190i q^{73} +(324.686 - 324.686i) q^{75} +(-213.834 - 213.834i) q^{77} +175.664 q^{79} -81.0000 q^{81} +(-125.254 - 125.254i) q^{83} +(-611.068 + 611.068i) q^{85} +895.973i q^{87} +900.271i q^{89} +(-619.190 + 619.190i) q^{91} +(691.750 + 691.750i) q^{93} +275.096 q^{95} +5.27858 q^{97} +(153.038 + 153.038i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 40 q^{11} - 120 q^{15} - 24 q^{19} + 400 q^{29} + 744 q^{31} + 456 q^{35} + 16 q^{37} - 1240 q^{43} - 1176 q^{49} - 744 q^{51} + 752 q^{53} + 1376 q^{59} - 912 q^{61} + 504 q^{63} + 976 q^{65} + 2256 q^{67}+ \cdots + 360 q^{99}+O(q^{100}) \) 24 * q + 40 * q^11 - 120 * q^15 - 24 * q^19 + 400 * q^29 + 744 * q^31 + 456 * q^35 + 16 * q^37 - 1240 * q^43 - 1176 * q^49 - 744 * q^51 + 752 * q^53 + 1376 * q^59 - 912 * q^61 + 504 * q^63 + 976 * q^65 + 2256 * q^67 - 528 * q^69 - 1104 * q^75 + 1904 * q^77 - 5992 * q^79 - 1944 * q^81 - 2680 * q^83 - 240 * q^85 + 3496 * q^91 + 7728 * q^95 + 360 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more