LMFDB - Embedded newform 384.4.j.b.289.1

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			289.1
Character	$\chi$	$=$	384.289
Dual form			384.4.j.b.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.12132 - 2.12132i) q^{3} +(-14.6111 + 14.6111i) q^{5} +26.8889i q^{7} +9.00000i q^{9} +O(q^{10})$	\(q+(-2.12132 - 2.12132i) q^{3} +(-14.6111 + 14.6111i) q^{5} +26.8889i q^{7} +9.00000i q^{9} +(-23.1955 + 23.1955i) q^{11} +(-13.0684 - 13.0684i) q^{13} +61.9898 q^{15} -5.45837 q^{17} +(-4.68315 - 4.68315i) q^{19} +(57.0399 - 57.0399i) q^{21} +34.0741i q^{23} -301.971i q^{25} +(19.0919 - 19.0919i) q^{27} +(143.499 + 143.499i) q^{29} -97.8482 q^{31} +98.4101 q^{33} +(-392.877 - 392.877i) q^{35} +(268.672 - 268.672i) q^{37} +55.4446i q^{39} -115.423i q^{41} +(-73.4743 + 73.4743i) q^{43} +(-131.500 - 131.500i) q^{45} -583.126 q^{47} -380.010 q^{49} +(11.5790 + 11.5790i) q^{51} +(-163.300 + 163.300i) q^{53} -677.825i q^{55} +19.8689i q^{57} +(45.5102 - 45.5102i) q^{59} +(-187.762 - 187.762i) q^{61} -242.000 q^{63} +381.889 q^{65} +(223.276 + 223.276i) q^{67} +(72.2821 - 72.2821i) q^{69} +779.124i q^{71} +34.8164i q^{73} +(-640.577 + 640.577i) q^{75} +(-623.700 - 623.700i) q^{77} +234.796 q^{79} -81.0000 q^{81} +(-34.3162 - 34.3162i) q^{83} +(79.7531 - 79.7531i) q^{85} -608.813i q^{87} -1126.75i q^{89} +(351.395 - 351.395i) q^{91} +(207.567 + 207.567i) q^{93} +136.852 q^{95} +1339.63 q^{97} +(-208.759 - 208.759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−14.6111	+	14.6111i	−1.30686	+	1.30686i	−0.383191	+	0.923669i	$0.625175\pi$
$5$	−14.6111	+	14.6111i	−1.30686	+	1.30686i	−0.923669	+	0.383191i	$0.874825\pi$
$6$		0			0
$7$			26.8889i			1.45186i	0.687768	+	0.725931i	$0.258591\pi$
$7$			26.8889i			1.45186i	−0.687768	+	0.725931i	$0.741409\pi$
$8$		0			0
$9$			9.00000i			0.333333i
$10$		0			0
$11$	−23.1955	+	23.1955i	−0.635791	+	0.635791i	−0.949514	−	0.313723i	$-0.898424\pi$
$11$	−23.1955	+	23.1955i	−0.635791	+	0.635791i	0.313723	+	0.949514i	$0.398424\pi$
$12$		0			0
$13$	−13.0684	−	13.0684i	−0.278810	−	0.278810i	0.553824	−	0.832634i	$-0.313168\pi$
$13$	−13.0684	−	13.0684i	−0.278810	−	0.278810i	−0.832634	+	0.553824i	$0.813168\pi$
$14$		0			0
$15$	61.9898			1.06705
$16$		0			0
$17$	−5.45837			−0.0778735			−0.0389368	−	0.999242i	$-0.512397\pi$
$17$	−5.45837			−0.0778735			−0.0389368	+	0.999242i	$0.512397\pi$
$18$		0			0
$19$	−4.68315	−	4.68315i	−0.0565467	−	0.0565467i	0.678268	−	0.734815i	$-0.262731\pi$
$19$	−4.68315	−	4.68315i	−0.0565467	−	0.0565467i	−0.734815	+	0.678268i	$0.762731\pi$
$20$		0			0
$21$	57.0399	−	57.0399i	0.592720	−	0.592720i
$22$		0			0
$23$			34.0741i			0.308910i	0.988000	+	0.154455i	$0.0493622\pi$
$23$			34.0741i			0.308910i	−0.988000	+	0.154455i	$0.950638\pi$
$24$		0			0
$25$		−	301.971i		−	2.41577i
$26$		0			0
$27$	19.0919	−	19.0919i	0.136083	−	0.136083i
$28$		0			0
$29$	143.499	+	143.499i	0.918863	+	0.918863i	0.996947	−	0.0780836i	$-0.0248801\pi$
$29$	143.499	+	143.499i	0.918863	+	0.918863i	−0.0780836	+	0.996947i	$0.524880\pi$
$30$		0			0
$31$	−97.8482			−0.566905			−0.283452	−	0.958986i	$-0.591480\pi$
$31$	−97.8482			−0.566905			−0.283452	+	0.958986i	$0.591480\pi$
$32$		0			0
$33$	98.4101			0.519121
$34$		0			0
$35$	−392.877	−	392.877i	−1.89738	−	1.89738i
$36$		0			0
$37$	268.672	−	268.672i	1.19377	−	1.19377i	0.217765	−	0.976001i	$-0.430123\pi$
$37$	268.672	−	268.672i	1.19377	−	1.19377i	0.976001	−	0.217765i	$-0.0698766\pi$
$38$		0			0
$39$			55.4446i			0.227647i
$40$		0			0
$41$		−	115.423i		−	0.439661i	−0.975538	−	0.219830i	$-0.929450\pi$
$41$		−	115.423i		−	0.439661i	0.975538	−	0.219830i	$-0.0705504\pi$
$42$		0			0
$43$	−73.4743	+	73.4743i	−0.260575	+	0.260575i	−0.825288	−	0.564713i	$-0.808987\pi$
$43$	−73.4743	+	73.4743i	−0.260575	+	0.260575i	0.564713	+	0.825288i	$0.308987\pi$
$44$		0			0
$45$	−131.500	−	131.500i	−0.435620	−	0.435620i
$46$		0			0
$47$	−583.126			−1.80974			−0.904869	−	0.425690i	$-0.860031\pi$
$47$	−583.126			−1.80974			−0.904869	+	0.425690i	$0.860031\pi$
$48$		0			0
$49$	−380.010			−1.10790
$50$		0			0
$51$	11.5790	+	11.5790i	0.0317917	+	0.0317917i
$52$		0			0
$53$	−163.300	+	163.300i	−0.423225	+	0.423225i	−0.886313	−	0.463087i	$-0.846742\pi$
$53$	−163.300	+	163.300i	−0.423225	+	0.423225i	0.463087	+	0.886313i	$0.346742\pi$
$54$		0			0
$55$		−	677.825i		−	1.66178i
$56$		0			0
$57$			19.8689i			0.0461702i
$58$		0			0
$59$	45.5102	−	45.5102i	0.100422	−	0.100422i	−0.655111	−	0.755533i	$-0.727378\pi$
$59$	45.5102	−	45.5102i	0.100422	−	0.100422i	0.755533	+	0.655111i	$0.227378\pi$
$60$		0			0
$61$	−187.762	−	187.762i	−0.394106	−	0.394106i	0.482042	−	0.876148i	$-0.339895\pi$
$61$	−187.762	−	187.762i	−0.394106	−	0.394106i	−0.876148	+	0.482042i	$0.839895\pi$
$62$		0			0
$63$	−242.000			−0.483954
$64$		0			0
$65$	381.889			0.728731
$66$		0			0
$67$	223.276	+	223.276i	0.407128	+	0.407128i	0.880736	−	0.473608i	$-0.157049\pi$
$67$	223.276	+	223.276i	0.407128	+	0.407128i	−0.473608	+	0.880736i	$0.657049\pi$
$68$		0			0
$69$	72.2821	−	72.2821i	0.126112	−	0.126112i
$70$		0			0
$71$			779.124i			1.30232i	0.758939	+	0.651162i	$0.225718\pi$
$71$			779.124i			1.30232i	−0.758939	+	0.651162i	$0.774282\pi$
$72$		0			0
$73$			34.8164i			0.0558212i	0.999610	+	0.0279106i	$0.00888538\pi$
$73$			34.8164i			0.0558212i	−0.999610	+	0.0279106i	$0.991115\pi$
$74$		0			0
$75$	−640.577	+	640.577i	−0.986233	+	0.986233i
$76$		0			0
$77$	−623.700	−	623.700i	−0.923081	−	0.923081i
$78$		0			0
$79$	234.796			0.334388			0.167194	−	0.985924i	$-0.446529\pi$
$79$	234.796			0.334388			0.167194	+	0.985924i	$0.446529\pi$
$80$		0			0
$81$	−81.0000			−0.111111
$82$		0			0
$83$	−34.3162	−	34.3162i	−0.0453819	−	0.0453819i	0.684052	−	0.729434i	$-0.260216\pi$
$83$	−34.3162	−	34.3162i	−0.0453819	−	0.0453819i	−0.729434	+	0.684052i	$0.760216\pi$
$84$		0			0
$85$	79.7531	−	79.7531i	0.101770	−	0.101770i
$86$		0			0
$87$		−	608.813i		−	0.750249i
$88$		0			0
$89$		−	1126.75i		−	1.34196i	−0.741474	−	0.670982i	$-0.765873\pi$
$89$		−	1126.75i		−	1.34196i	0.741474	−	0.670982i	$-0.234127\pi$
$90$		0			0
$91$	351.395	−	351.395i	0.404793	−	0.404793i
$92$		0			0
$93$	207.567	+	207.567i	0.231438	+	0.231438i
$94$		0			0
$95$	136.852			0.147797
$96$		0			0
$97$	1339.63			1.40225			0.701127	−	0.713037i	$-0.252681\pi$
$97$	1339.63			1.40225			0.701127	+	0.713037i	$0.252681\pi$
$98$		0			0
$99$	−208.759	−	208.759i	−0.211930	−	0.211930i
$100$		0			0
$101$	678.522	−	678.522i	0.668470	−	0.668470i	−0.288892	−	0.957362i	$-0.593287\pi$
$101$	678.522	−	678.522i	0.668470	−	0.668470i	0.957362	+	0.288892i	$0.0932868\pi$
$102$		0			0
$103$		−	878.610i		−	0.840505i	−0.907407	−	0.420253i	$-0.861941\pi$
$103$		−	878.610i		−	0.840505i	0.907407	−	0.420253i	$-0.138059\pi$
$104$		0			0
$105$			1666.84i			1.54920i
$106$		0			0
$107$	−174.580	+	174.580i	−0.157731	+	0.157731i	−0.781561	−	0.623829i	$-0.785576\pi$
$107$	−174.580	+	174.580i	−0.157731	+	0.157731i	0.623829	+	0.781561i	$0.285576\pi$
$108$		0			0
$109$	−1435.56	−	1435.56i	−1.26148	−	1.26148i	−0.950374	−	0.311110i	$-0.899299\pi$
$109$	−1435.56	−	1435.56i	−1.26148	−	1.26148i	−0.311110	−	0.950374i	$-0.600701\pi$
$110$		0			0
$111$	−1139.88			−0.974706
$112$		0			0
$113$	421.516			0.350911			0.175455	−	0.984487i	$-0.443860\pi$
$113$	421.516			0.350911			0.175455	+	0.984487i	$0.443860\pi$
$114$		0			0
$115$	−497.861	−	497.861i	−0.403703	−	0.403703i
$116$		0			0
$117$	117.616	−	117.616i	0.0929366	−	0.0929366i
$118$		0			0
$119$		−	146.769i		−	0.113062i
$120$		0			0
$121$			254.939i			0.191539i
$122$		0			0
$123$	−244.850	+	244.850i	−0.179491	+	0.179491i
$124$		0			0
$125$	2585.75	+	2585.75i	1.85021	+	1.85021i
$126$		0			0
$127$	353.404			0.246925			0.123463	−	0.992349i	$-0.460600\pi$
$127$	353.404			0.246925			0.123463	+	0.992349i	$0.460600\pi$
$128$		0			0
$129$	311.725			0.212759
$130$		0			0
$131$	1471.55	+	1471.55i	0.981450	+	0.981450i	0.999831	−	0.0183815i	$-0.00585134\pi$
$131$	1471.55	+	1471.55i	0.981450	+	0.981450i	−0.0183815	+	0.999831i	$0.505851\pi$
$132$		0			0
$133$	125.924	−	125.924i	0.0820980	−	0.0820980i
$134$		0			0
$135$			557.908i			0.355682i
$136$		0			0
$137$		−	348.474i		−	0.217315i	−0.994079	−	0.108657i	$-0.965345\pi$
$137$		−	348.474i		−	0.217315i	0.994079	−	0.108657i	$-0.0346552\pi$
$138$		0			0
$139$	1085.54	−	1085.54i	0.662404	−	0.662404i	−0.293542	−	0.955946i	$-0.594834\pi$
$139$	1085.54	−	1085.54i	0.662404	−	0.662404i	0.955946	+	0.293542i	$0.0948342\pi$
$140$		0			0
$141$	1237.00	+	1237.00i	0.738823	+	0.738823i
$142$		0			0
$143$	606.257			0.354530
$144$		0			0
$145$	−4193.36			−2.40165
$146$		0			0
$147$	806.124	+	806.124i	0.452299	+	0.452299i
$148$		0			0
$149$	−2136.62	+	2136.62i	−1.17476	+	1.17476i	−0.193694	+	0.981062i	$0.562047\pi$
$149$	−2136.62	+	2136.62i	−1.17476	+	1.17476i	−0.981062	+	0.193694i	$0.937953\pi$
$150$		0			0
$151$			2622.36i			1.41328i	0.707575	+	0.706639i	$0.249789\pi$
$151$			2622.36i			1.41328i	−0.707575	+	0.706639i	$0.750211\pi$
$152$		0			0
$153$		−	49.1254i		−	0.0259578i
$154$		0			0
$155$	1429.67	−	1429.67i	0.740866	−	0.740866i
$156$		0			0
$157$	−1174.74	−	1174.74i	−0.597162	−	0.597162i	0.342394	−	0.939556i	$-0.388762\pi$
$157$	−1174.74	−	1174.74i	−0.597162	−	0.597162i	−0.939556	+	0.342394i	$0.888762\pi$
$158$		0			0
$159$	692.822			0.345562
$160$		0			0
$161$	−916.213			−0.448495
$162$		0			0
$163$	1355.60	+	1355.60i	0.651403	+	0.651403i	0.953331	−	0.301928i	$-0.0976302\pi$
$163$	1355.60	+	1355.60i	0.651403	+	0.651403i	−0.301928	+	0.953331i	$0.597630\pi$
$164$		0			0
$165$	−1437.88	+	1437.88i	−0.678419	+	0.678419i
$166$		0			0
$167$			2044.59i			0.947398i	0.880687	+	0.473699i	$0.157081\pi$
$167$			2044.59i			0.947398i	−0.880687	+	0.473699i	$0.842919\pi$
$168$		0			0
$169$		−	1855.43i		−	0.844530i
$170$		0			0
$171$	42.1483	−	42.1483i	0.0188489	−	0.0188489i
$172$		0			0
$173$	408.164	+	408.164i	0.179376	+	0.179376i	0.791084	−	0.611708i	$-0.209517\pi$
$173$	408.164	+	408.164i	0.179376	+	0.179376i	−0.611708	+	0.791084i	$0.709517\pi$
$174$		0			0
$175$	8119.65			3.50736
$176$		0			0
$177$	−193.083			−0.0819946
$178$		0			0
$179$	−1927.19	−	1927.19i	−0.804719	−	0.804719i	0.179110	−	0.983829i	$-0.442678\pi$
$179$	−1927.19	−	1927.19i	−0.804719	−	0.804719i	−0.983829	+	0.179110i	$0.942678\pi$
$180$		0			0
$181$	205.719	−	205.719i	0.0844804	−	0.0844804i	−0.663604	−	0.748084i	$-0.730974\pi$
$181$	205.719	−	205.719i	0.0844804	−	0.0844804i	0.748084	+	0.663604i	$0.230974\pi$
$182$		0			0
$183$			796.607i			0.321786i
$184$		0			0
$185$			7851.20i			3.12017i
$186$		0			0
$187$	126.610	−	126.610i	0.0495113	−	0.0495113i
$188$		0			0
$189$	513.359	+	513.359i	0.197573	+	0.197573i
$190$		0			0
$191$	−1536.67			−0.582143			−0.291071	−	0.956701i	$-0.594012\pi$
$191$	−1536.67			−0.582143			−0.291071	+	0.956701i	$0.594012\pi$
$192$		0			0
$193$	127.730			0.0476385			0.0238192	−	0.999716i	$-0.492417\pi$
$193$	127.730			0.0476385			0.0238192	+	0.999716i	$0.492417\pi$
$194$		0			0
$195$	−810.109	−	810.109i	−0.297503	−	0.297503i
$196$		0			0
$197$	−2282.46	+	2282.46i	−0.825475	+	0.825475i	−0.986887	−	0.161412i	$-0.948395\pi$
$197$	−2282.46	+	2282.46i	−0.825475	+	0.825475i	0.161412	+	0.986887i	$0.448395\pi$
$198$		0			0
$199$		−	4155.43i		−	1.48026i	−0.672466	−	0.740128i	$-0.734765\pi$
$199$		−	4155.43i		−	1.48026i	0.672466	−	0.740128i	$-0.265235\pi$
$200$		0			0
$201$		−	947.282i		−	0.332418i
$202$		0			0
$203$	−3858.51	+	3858.51i	−1.33406	+	1.33406i
$204$		0			0
$205$	1686.47	+	1686.47i	0.574575	+	0.574575i
$206$		0			0
$207$	−306.667			−0.102970
$208$		0			0
$209$	217.256			0.0719038
$210$		0			0
$211$	−673.956	−	673.956i	−0.219891	−	0.219891i	0.588561	−	0.808453i	$-0.299695\pi$
$211$	−673.956	−	673.956i	−0.219891	−	0.219891i	−0.808453	+	0.588561i	$0.799695\pi$
$212$		0			0
$213$	1652.77	−	1652.77i	0.531671	−	0.531671i
$214$		0			0
$215$		−	2147.09i		−	0.681070i
$216$		0			0
$217$		−	2631.03i		−	0.823068i
$218$		0			0
$219$	73.8567	−	73.8567i	0.0227889	−	0.0227889i
$220$		0			0
$221$	71.3323	+	71.3323i	0.0217119	+	0.0217119i
$222$		0			0
$223$	−2979.58			−0.894741			−0.447371	−	0.894349i	$-0.647639\pi$
$223$	−2979.58			−0.894741			−0.447371	+	0.894349i	$0.647639\pi$
$224$		0			0
$225$	2717.74			0.805256
$226$		0			0
$227$	−1929.35	−	1929.35i	−0.564120	−	0.564120i	0.366355	−	0.930475i	$-0.380606\pi$
$227$	−1929.35	−	1929.35i	−0.564120	−	0.564120i	−0.930475	+	0.366355i	$0.880606\pi$
$228$		0			0
$229$	−3209.50	+	3209.50i	−0.926156	+	0.926156i	−0.997455	−	0.0712994i	$-0.977285\pi$
$229$	−3209.50	+	3209.50i	−0.926156	+	0.926156i	0.0712994	+	0.997455i	$0.477285\pi$
$230$		0			0
$231$			2646.14i			0.753692i
$232$		0			0
$233$			294.276i			0.0827412i	0.999144	+	0.0413706i	$0.0131724\pi$
$233$			294.276i			0.0827412i	−0.999144	+	0.0413706i	$0.986828\pi$
$234$		0			0
$235$	8520.14	−	8520.14i	2.36507	−	2.36507i
$236$		0			0
$237$	−498.079	−	498.079i	−0.136513	−	0.136513i
$238$		0			0
$239$	−1922.58			−0.520339			−0.260170	−	0.965563i	$-0.583778\pi$
$239$	−1922.58			−0.520339			−0.260170	+	0.965563i	$0.583778\pi$
$240$		0			0
$241$	3843.86			1.02741			0.513703	−	0.857968i	$-0.328273\pi$
$241$	3843.86			1.02741			0.513703	+	0.857968i	$0.328273\pi$
$242$		0			0
$243$	171.827	+	171.827i	0.0453609	+	0.0453609i
$244$		0			0
$245$	5552.38	−	5552.38i	1.44787	−	1.44787i
$246$		0			0
$247$			122.403i			0.0315316i
$248$		0			0
$249$			145.591i			0.0370542i
$250$		0			0
$251$	−2843.24	+	2843.24i	−0.714995	+	0.714995i	−0.967576	−	0.252580i	$-0.918721\pi$
$251$	−2843.24	+	2843.24i	−0.714995	+	0.714995i	0.252580	+	0.967576i	$0.418721\pi$
$252$		0			0
$253$	−790.365	−	790.365i	−0.196403	−	0.196403i
$254$		0			0
$255$	−338.364			−0.0830947
$256$		0			0
$257$	−666.774			−0.161837			−0.0809187	−	0.996721i	$-0.525785\pi$
$257$	−666.774			−0.161837			−0.0809187	+	0.996721i	$0.525785\pi$
$258$		0			0
$259$	7224.27	+	7224.27i	1.73318	+	1.73318i
$260$		0			0
$261$	−1291.49	+	1291.49i	−0.306288	+	0.306288i
$262$		0			0
$263$		−	2105.93i		−	0.493753i	−0.969047	−	0.246876i	$-0.920596\pi$
$263$		−	2105.93i		−	0.493753i	0.969047	−	0.246876i	$-0.0794042\pi$
$264$		0			0
$265$		−	4771.99i		−	1.10619i
$266$		0			0
$267$	−2390.19	+	2390.19i	−0.547854	+	0.547854i
$268$		0			0
$269$	−4501.90	−	4501.90i	−1.02039	−	1.02039i	−0.999788	−	0.0206059i	$-0.993440\pi$
$269$	−4501.90	−	4501.90i	−1.02039	−	1.02039i	−0.0206059	−	0.999788i	$-0.506560\pi$
$270$		0			0
$271$	−1153.92			−0.258656			−0.129328	−	0.991602i	$-0.541282\pi$
$271$	−1153.92			−0.258656			−0.129328	+	0.991602i	$0.541282\pi$
$272$		0			0
$273$	−1490.84			−0.330512
$274$		0			0
$275$	7004.36	+	7004.36i	1.53592	+	1.53592i
$276$		0			0
$277$	5285.17	−	5285.17i	1.14641	−	1.14641i	0.159156	−	0.987253i	$-0.449123\pi$
$277$	5285.17	−	5285.17i	1.14641	−	1.14641i	0.987253	−	0.159156i	$-0.0508772\pi$
$278$		0			0
$279$		−	880.634i		−	0.188968i
$280$		0			0
$281$			5520.01i			1.17187i	0.810357	+	0.585936i	$0.199273\pi$
$281$			5520.01i			1.17187i	−0.810357	+	0.585936i	$0.800727\pi$
$282$		0			0
$283$	−4233.41	+	4233.41i	−0.889223	+	0.889223i	−0.994448	−	0.105226i	$-0.966444\pi$
$283$	−4233.41	+	4233.41i	−0.889223	+	0.889223i	0.105226	+	0.994448i	$0.466444\pi$
$284$		0			0
$285$	−290.308	−	290.308i	−0.0603380	−	0.0603380i
$286$		0			0
$287$	3103.60			0.638326
$288$		0			0
$289$	−4883.21			−0.993936
$290$		0			0
$291$	−2841.78	−	2841.78i	−0.572468	−	0.572468i
$292$		0			0
$293$	1434.65	−	1434.65i	0.286052	−	0.286052i	−0.549465	−	0.835517i	$-0.685168\pi$
$293$	1434.65	−	1434.65i	0.286052	−	0.286052i	0.835517	+	0.549465i	$0.185168\pi$
$294$		0			0
$295$			1329.91i			0.262476i
$296$		0			0
$297$			885.691i			0.173040i
$298$		0			0
$299$	445.295	−	445.295i	0.0861273	−	0.0861273i
$300$		0			0
$301$	−1975.64	−	1975.64i	−0.378319	−	0.378319i
$302$		0			0
$303$	−2878.73			−0.545803
$304$		0			0
$305$	5486.84			1.03008
$306$		0			0
$307$	−6589.97	−	6589.97i	−1.22511	−	1.22511i	−0.965791	−	0.259321i	$-0.916501\pi$
$307$	−6589.97	−	6589.97i	−1.22511	−	1.22511i	−0.259321	−	0.965791i	$-0.583499\pi$
$308$		0			0
$309$	−1863.81	+	1863.81i	−0.343135	+	0.343135i
$310$		0			0
$311$		−	1906.34i		−	0.347585i	−0.984782	−	0.173792i	$-0.944398\pi$
$311$		−	1906.34i		−	0.347585i	0.984782	−	0.173792i	$-0.0556022\pi$
$312$		0			0
$313$			5657.11i			1.02159i	0.859702	+	0.510797i	$0.170649\pi$
$313$			5657.11i			1.02159i	−0.859702	+	0.510797i	$0.829351\pi$
$314$		0			0
$315$	3535.89	−	3535.89i	0.632460	−	0.632460i
$316$		0			0
$317$	−587.024	−	587.024i	−0.104008	−	0.104008i	0.653188	−	0.757196i	$-0.273431\pi$
$317$	−587.024	−	587.024i	−0.104008	−	0.104008i	−0.757196	+	0.653188i	$0.773431\pi$
$318$		0			0
$319$	−6657.04			−1.16841
$320$		0			0
$321$	740.678			0.128787
$322$		0			0
$323$	25.5624	+	25.5624i	0.00440349	+	0.00440349i
$324$		0			0
$325$	−3946.28	+	3946.28i	−0.673540	+	0.673540i
$326$		0			0
$327$			6090.57i			1.03000i
$328$		0			0
$329$		−	15679.6i		−	2.62749i
$330$		0			0
$331$	−7738.24	+	7738.24i	−1.28499	+	1.28499i	−0.347200	+	0.937791i	$0.612867\pi$
$331$	−7738.24	+	7738.24i	−1.28499	+	1.28499i	−0.937791	+	0.347200i	$0.887133\pi$
$332$		0			0
$333$	2418.04	+	2418.04i	0.397922	+	0.397922i
$334$		0			0
$335$	−6524.65			−1.06412
$336$		0			0
$337$	−5948.81			−0.961579			−0.480789	−	0.876836i	$-0.659650\pi$
$337$	−5948.81			−0.961579			−0.480789	+	0.876836i	$0.659650\pi$
$338$		0			0
$339$	−894.171	−	894.171i	−0.143259	−	0.143259i
$340$		0			0
$341$	2269.64	−	2269.64i	0.360433	−	0.360433i
$342$		0			0
$343$		−	995.165i		−	0.156658i
$344$		0			0
$345$			2112.25i			0.329622i
$346$		0			0
$347$	4649.48	−	4649.48i	0.719300	−	0.719300i	−0.249162	−	0.968462i	$-0.580155\pi$
$347$	4649.48	−	4649.48i	0.719300	−	0.719300i	0.968462	+	0.249162i	$0.0801551\pi$
$348$		0			0
$349$	2080.00	+	2080.00i	0.319025	+	0.319025i	0.848393	−	0.529367i	$-0.177571\pi$
$349$	2080.00	+	2080.00i	0.319025	+	0.319025i	−0.529367	+	0.848393i	$0.677571\pi$
$350$		0			0
$351$	−499.001			−0.0758824
$352$		0			0
$353$	3582.84			0.540213			0.270106	−	0.962830i	$-0.412941\pi$
$353$	3582.84			0.540213			0.270106	+	0.962830i	$0.412941\pi$
$354$		0			0
$355$	−11383.9	−	11383.9i	−1.70195	−	1.70195i
$356$		0			0
$357$	−311.345	+	311.345i	−0.0461572	+	0.0461572i
$358$		0			0
$359$		−	7283.18i		−	1.07073i	−0.844621	−	0.535364i	$-0.820174\pi$
$359$		−	7283.18i		−	1.07073i	0.844621	−	0.535364i	$-0.179826\pi$
$360$		0			0
$361$		−	6815.14i		−	0.993605i
$362$		0			0
$363$	540.806	−	540.806i	0.0781955	−	0.0781955i
$364$		0			0
$365$	−508.707	−	508.707i	−0.0729506	−	0.0729506i
$366$		0			0
$367$	−4603.82			−0.654816			−0.327408	−	0.944883i	$-0.606175\pi$
$367$	−4603.82			−0.654816			−0.327408	+	0.944883i	$0.606175\pi$
$368$		0			0
$369$	1038.81			0.146554
$370$		0			0
$371$	−4390.94	−	4390.94i	−0.614465	−	0.614465i
$372$		0			0
$373$	7197.92	−	7197.92i	0.999180	−	0.999180i	−0.000819708	−	1.00000i	$-0.500261\pi$
$373$	7197.92	−	7197.92i	0.999180	−	0.999180i	1.00000		0.000819708i	$0.000260921\pi$
$374$		0			0
$375$		−	10970.4i		−	1.51069i
$376$		0			0
$377$		−	3750.60i		−	0.512376i
$378$		0			0
$379$	−2684.91	+	2684.91i	−0.363891	+	0.363891i	−0.865243	−	0.501352i	$-0.832836\pi$
$379$	−2684.91	+	2684.91i	−0.363891	+	0.363891i	0.501352	+	0.865243i	$0.332836\pi$
$380$		0			0
$381$	−749.682	−	749.682i	−0.100807	−	0.100807i
$382$		0			0
$383$	12844.4			1.71363			0.856814	−	0.515625i	$-0.172440\pi$
$383$	12844.4			1.71363			0.856814	+	0.515625i	$0.172440\pi$
$384$		0			0
$385$	18225.9			2.41268
$386$		0			0
$387$	−661.269	−	661.269i	−0.0868584	−	0.0868584i
$388$		0			0
$389$	1921.42	−	1921.42i	0.250437	−	0.250437i	−0.570713	−	0.821150i	$-0.693333\pi$
$389$	1921.42	−	1921.42i	0.250437	−	0.250437i	0.821150	+	0.570713i	$0.193333\pi$
$390$		0			0
$391$		−	185.989i		−	0.0240560i
$392$		0			0
$393$		−	6243.26i		−	0.801350i
$394$		0			0
$395$	−3430.64	+	3430.64i	−0.436999	+	0.436999i
$396$		0			0
$397$	−6960.80	−	6960.80i	−0.879982	−	0.879982i	0.113551	−	0.993532i	$-0.463778\pi$
$397$	−6960.80	−	6960.80i	−0.879982	−	0.879982i	−0.993532	+	0.113551i	$0.963778\pi$
$398$		0			0
$399$	−534.252			−0.0670328
$400$		0			0
$401$	−13711.0			−1.70747			−0.853737	−	0.520705i	$-0.825669\pi$
$401$	−13711.0			−1.70747			−0.853737	+	0.520705i	$0.825669\pi$
$402$		0			0
$403$	1278.72	+	1278.72i	0.158059	+	0.158059i
$404$		0			0
$405$	1183.50	−	1183.50i	0.145207	−	0.145207i
$406$		0			0
$407$			12463.9i			1.51797i
$408$		0			0
$409$			1491.35i			0.180299i	0.995928	+	0.0901496i	$0.0287345\pi$
$409$			1491.35i			0.180299i	−0.995928	+	0.0901496i	$0.971265\pi$
$410$		0			0
$411$	−739.225	+	739.225i	−0.0887184	+	0.0887184i
$412$		0			0
$413$	1223.72	+	1223.72i	0.145799	+	0.145799i
$414$		0			0
$415$	1002.80			0.118616
$416$		0			0
$417$	−4605.55			−0.540850
$418$		0			0
$419$	−7971.51	−	7971.51i	−0.929436	−	0.929436i	0.0682334	−	0.997669i	$-0.478264\pi$
$419$	−7971.51	−	7971.51i	−0.929436	−	0.929436i	−0.997669	+	0.0682334i	$0.978264\pi$
$420$		0			0
$421$	−6869.92	+	6869.92i	−0.795296	+	0.795296i	−0.982350	−	0.187054i	$-0.940106\pi$
$421$	−6869.92	+	6869.92i	−0.795296	+	0.795296i	0.187054	+	0.982350i	$0.440106\pi$
$422$		0			0
$423$		−	5248.14i		−	0.603246i
$424$		0			0
$425$			1648.27i			0.188124i
$426$		0			0
$427$	5048.71	−	5048.71i	0.572187	−	0.572187i
$428$		0			0
$429$	−1286.06	−	1286.06i	−0.144736	−	0.144736i
$430$		0			0
$431$	−7332.75			−0.819504			−0.409752	−	0.912197i	$-0.634385\pi$
$431$	−7332.75			−0.819504			−0.409752	+	0.912197i	$0.634385\pi$
$432$		0			0
$433$	−1171.84			−0.130058			−0.0650288	−	0.997883i	$-0.520714\pi$
$433$	−1171.84			−0.130058			−0.0650288	+	0.997883i	$0.520714\pi$
$434$		0			0
$435$	8895.46	+	8895.46i	0.980470	+	0.980470i
$436$		0			0
$437$	159.574	−	159.574i	0.0174679	−	0.0174679i
$438$		0			0
$439$			14740.0i			1.60251i	0.598326	+	0.801253i	$0.295833\pi$
$439$			14740.0i			1.60251i	−0.598326	+	0.801253i	$0.704167\pi$
$440$		0			0
$441$		−	3420.09i		−	0.369301i
$442$		0			0
$443$	5856.74	−	5856.74i	0.628131	−	0.628131i	−0.319466	−	0.947598i	$-0.603504\pi$
$443$	5856.74	−	5856.74i	0.628131	−	0.628131i	0.947598	+	0.319466i	$0.103504\pi$
$444$		0			0
$445$	16463.0	+	16463.0i	1.75376	+	1.75376i
$446$		0			0
$447$	9064.90			0.959184
$448$		0			0
$449$	1619.32			0.170201			0.0851005	−	0.996372i	$-0.472879\pi$
$449$	1619.32			0.170201			0.0851005	+	0.996372i	$0.472879\pi$
$450$		0			0
$451$	2677.30	+	2677.30i	0.279532	+	0.279532i
$452$		0			0
$453$	5562.87	−	5562.87i	0.576968	−	0.576968i
$454$		0			0
$455$			10268.6i			1.05802i
$456$		0			0
$457$			14520.4i			1.48629i	0.669131	+	0.743145i	$0.266667\pi$
$457$			14520.4i			1.48629i	−0.669131	+	0.743145i	$0.733333\pi$
$458$		0			0
$459$	−104.211	+	104.211i	−0.0105972	+	0.0105972i
$460$		0			0
$461$	2585.41	+	2585.41i	0.261203	+	0.261203i	0.825543	−	0.564339i	$-0.190869\pi$
$461$	2585.41	+	2585.41i	0.261203	+	0.261203i	−0.564339	+	0.825543i	$0.690869\pi$
$462$		0			0
$463$	6446.14			0.647036			0.323518	−	0.946222i	$-0.395134\pi$
$463$	6446.14			0.647036			0.323518	+	0.946222i	$0.395134\pi$
$464$		0			0
$465$	−6065.59			−0.604914
$466$		0			0
$467$	2471.47	+	2471.47i	0.244895	+	0.244895i	0.818871	−	0.573977i	$-0.194600\pi$
$467$	2471.47	+	2471.47i	0.244895	+	0.244895i	−0.573977	+	0.818871i	$0.694600\pi$
$468$		0			0
$469$	−6003.65	+	6003.65i	−0.591093	+	0.591093i
$470$		0			0
$471$			4984.00i			0.487581i
$472$		0			0
$473$		−	3408.55i		−	0.331343i
$474$		0			0
$475$	−1414.17	+	1414.17i	−0.136604	+	0.136604i
$476$		0			0
$477$	−1469.70	−	1469.70i	−0.141075	−	0.141075i
$478$		0			0
$479$	−4936.05			−0.470843			−0.235422	−	0.971893i	$-0.575647\pi$
$479$	−4936.05			−0.470843			−0.235422	+	0.971893i	$0.575647\pi$
$480$		0			0
$481$	−7022.23			−0.665667
$482$		0			0
$483$	1943.58	+	1943.58i	0.183097	+	0.183097i
$484$		0			0
$485$	−19573.5	+	19573.5i	−1.83255	+	1.83255i
$486$		0			0
$487$		−	2236.98i		−	0.208146i	−0.994570	−	0.104073i	$-0.966812\pi$
$487$		−	2236.98i		−	0.208146i	0.994570	−	0.104073i	$-0.0331876\pi$
$488$		0			0
$489$		−	5751.32i		−	0.531868i
$490$		0			0
$491$	339.268	−	339.268i	0.0311832	−	0.0311832i	−0.691343	−	0.722526i	$-0.742981\pi$
$491$	339.268	−	339.268i	0.0311832	−	0.0311832i	0.722526	+	0.691343i	$0.242981\pi$
$492$		0			0
$493$	−783.269	−	783.269i	−0.0715551	−	0.0715551i
$494$		0			0
$495$	6100.43			0.553927
$496$		0			0
$497$	−20949.7			−1.89079
$498$		0			0
$499$	11481.3	+	11481.3i	1.03001	+	1.03001i	0.999536	+	0.0304745i	$0.00970184\pi$
$499$	11481.3	+	11481.3i	1.03001	+	1.03001i	0.0304745	+	0.999536i	$0.490298\pi$
$500$		0			0
$501$	4337.24	−	4337.24i	0.386774	−	0.386774i
$502$		0			0
$503$		−	14599.0i		−	1.29411i	−0.762444	−	0.647054i	$-0.776001\pi$
$503$		−	14599.0i		−	1.29411i	0.762444	−	0.647054i	$-0.223999\pi$
$504$		0			0
$505$			19828.0i			1.74719i
$506$		0			0
$507$	−3935.97	+	3935.97i	−0.344778	+	0.344778i
$508$		0			0
$509$	9776.63	+	9776.63i	0.851359	+	0.851359i	0.990301	−	0.138942i	$-0.0443701\pi$
$509$	9776.63	+	9776.63i	0.851359	+	0.851359i	−0.138942	+	0.990301i	$0.544370\pi$
$510$		0			0
$511$	−936.173			−0.0810447
$512$		0			0
$513$	−178.820			−0.0153901
$514$		0			0
$515$	12837.5	+	12837.5i	1.09842	+	1.09842i
$516$		0			0
$517$	13525.9	−	13525.9i	1.15062	−	1.15062i
$518$		0			0
$519$		−	1731.69i		−	0.146460i
$520$		0			0
$521$			7529.46i			0.633151i	0.948567	+	0.316575i	$0.102533\pi$
$521$			7529.46i			0.633151i	−0.948567	+	0.316575i	$0.897467\pi$
$522$		0			0
$523$	−6097.66	+	6097.66i	−0.509813	+	0.509813i	−0.914469	−	0.404656i	$-0.867391\pi$
$523$	−6097.66	+	6097.66i	−0.509813	+	0.509813i	0.404656	+	0.914469i	$0.367391\pi$
$524$		0			0
$525$	−17224.4	−	17224.4i	−1.43187	−	1.43187i
$526$		0			0
$527$	534.092			0.0441469
$528$		0			0
$529$	11006.0			0.904574
$530$		0			0
$531$	409.592	+	409.592i	0.0334741	+	0.0334741i
$532$		0			0
$533$	−1508.40	+	1508.40i	−0.122582	+	0.122582i
$534$		0			0
$535$		−	5101.61i		−	0.412265i
$536$		0			0
$537$			8176.37i			0.657051i
$538$		0			0
$539$	8814.52	−	8814.52i	0.704394	−	0.704394i
$540$		0			0
$541$	4747.68	+	4747.68i	0.377299	+	0.377299i	0.870127	−	0.492828i	$-0.164037\pi$
$541$	4747.68	+	4747.68i	0.377299	+	0.377299i	−0.492828	+	0.870127i	$0.664037\pi$
$542$		0			0
$543$	−872.791			−0.0689780
$544$		0			0
$545$	41950.4			3.29717
$546$		0			0
$547$	6489.70	+	6489.70i	0.507275	+	0.507275i	0.913689	−	0.406414i	$-0.133221\pi$
$547$	6489.70	+	6489.70i	0.507275	+	0.507275i	−0.406414	+	0.913689i	$0.633221\pi$
$548$		0			0
$549$	1689.86	−	1689.86i	0.131369	−	0.131369i
$550$		0			0
$551$		−	1344.05i		−	0.103917i
$552$		0			0
$553$			6313.41i			0.485485i
$554$		0			0
$555$	16654.9	−	16654.9i	1.27380	−	1.27380i
$556$		0			0
$557$	−13178.1	−	13178.1i	−1.00247	−	1.00247i	−0.999997	−	0.00247058i	$-0.999214\pi$
$557$	−13178.1	−	13178.1i	−1.00247	−	1.00247i	−0.00247058	−	0.999997i	$-0.500786\pi$
$558$		0			0
$559$	1920.39			0.145302
$560$		0			0
$561$	−537.159			−0.0404258
$562$		0			0
$563$	−13912.9	−	13912.9i	−1.04149	−	1.04149i	−0.999101	−	0.0423880i	$-0.986503\pi$
$563$	−13912.9	−	13912.9i	−1.04149	−	1.04149i	−0.0423880	−	0.999101i	$-0.513497\pi$
$564$		0			0
$565$	−6158.84	+	6158.84i	−0.458591	+	0.458591i
$566$		0			0
$567$		−	2178.00i		−	0.161318i
$568$		0			0
$569$		−	8207.75i		−	0.604722i	−0.953193	−	0.302361i	$-0.902225\pi$
$569$		−	8207.75i		−	0.604722i	0.953193	−	0.302361i	$-0.0977749\pi$
$570$		0			0
$571$	−17905.9	+	17905.9i	−1.31233	+	1.31233i	−0.392632	+	0.919695i	$0.628436\pi$
$571$	−17905.9	+	17905.9i	−1.31233	+	1.31233i	−0.919695	+	0.392632i	$0.871564\pi$
$572$		0			0
$573$	3259.76	+	3259.76i	0.237659	+	0.237659i
$574$		0			0
$575$	10289.4			0.746256
$576$		0			0
$577$	19888.0			1.43492			0.717458	−	0.696602i	$-0.245305\pi$
$577$	19888.0			1.43492			0.717458	+	0.696602i	$0.245305\pi$
$578$		0			0
$579$	−270.957	−	270.957i	−0.0194483	−	0.0194483i
$580$		0			0
$581$	922.724	−	922.724i	0.0658882	−	0.0658882i
$582$		0			0
$583$		−	7575.64i		−	0.538166i
$584$		0			0
$585$			3437.00i			0.242910i
$586$		0			0
$587$	12662.0	−	12662.0i	0.890315	−	0.890315i	−0.104237	−	0.994552i	$-0.533240\pi$
$587$	12662.0	−	12662.0i	0.890315	−	0.890315i	0.994552	+	0.104237i	$0.0332401\pi$
$588$		0			0
$589$	458.238	+	458.238i	0.0320566	+	0.0320566i
$590$		0			0
$591$	9683.66			0.673997
$592$		0			0
$593$	−13327.0			−0.922889			−0.461445	−	0.887169i	$-0.652669\pi$
$593$	−13327.0			−0.922889			−0.461445	+	0.887169i	$0.652669\pi$
$594$		0			0
$595$	2144.47	+	2144.47i	0.147756	+	0.147756i
$596$		0			0
$597$	−8815.01	+	8815.01i	−0.604312	+	0.604312i
$598$		0			0
$599$			16403.3i			1.11890i	0.828863	+	0.559451i	$0.188988\pi$
$599$			16403.3i			1.11890i	−0.828863	+	0.559451i	$0.811012\pi$
$600$		0			0
$601$			7619.35i			0.517137i	0.965993	+	0.258569i	$0.0832508\pi$
$601$			7619.35i			0.517137i	−0.965993	+	0.258569i	$0.916749\pi$
$602$		0			0
$603$	−2009.49	+	2009.49i	−0.135709	+	0.135709i
$604$		0			0
$605$	−3724.94	−	3724.94i	−0.250315	−	0.250315i
$606$		0			0
$607$	−9012.16			−0.602623			−0.301312	−	0.953526i	$-0.597424\pi$
$607$	−9012.16			−0.602623			−0.301312	+	0.953526i	$0.597424\pi$
$608$		0			0
$609$	16370.3			1.08926
$610$		0			0
$611$	7620.54	+	7620.54i	0.504573	+	0.504573i
$612$		0			0
$613$	−4092.45	+	4092.45i	−0.269645	+	0.269645i	−0.828957	−	0.559312i	$-0.811065\pi$
$613$	−4092.45	+	4092.45i	−0.269645	+	0.269645i	0.559312	+	0.828957i	$0.311065\pi$
$614$		0			0
$615$		−	7155.07i		−	0.469138i
$616$		0			0
$617$		−	1667.40i		−	0.108796i	−0.998519	−	0.0543978i	$-0.982676\pi$
$617$		−	1667.40i		−	0.108796i	0.998519	−	0.0543978i	$-0.0173239\pi$
$618$		0			0
$619$	7367.45	−	7367.45i	0.478389	−	0.478389i	−0.426227	−	0.904616i	$-0.640158\pi$
$619$	7367.45	−	7367.45i	0.478389	−	0.478389i	0.904616	+	0.426227i	$0.140158\pi$
$620$		0			0
$621$	650.539	+	650.539i	0.0420374	+	0.0420374i
$622$		0			0
$623$	30296.9			1.94834
$624$		0			0
$625$	−37815.1			−2.42016
$626$		0			0
$627$	−460.869	−	460.869i	−0.0293546	−	0.0293546i
$628$		0			0
$629$	−1466.51	+	1466.51i	−0.0929628	+	0.0929628i
$630$		0			0
$631$		−	10707.1i		−	0.675502i	−0.941236	−	0.337751i	$-0.890334\pi$
$631$		−	10707.1i		−	0.675502i	0.941236	−	0.337751i	$-0.109666\pi$
$632$		0			0
$633$			2859.35i			0.179540i
$634$		0			0
$635$	−5163.63	+	5163.63i	−0.322697	+	0.322697i
$636$		0			0
$637$	4966.13	+	4966.13i	0.308894	+	0.308894i
$638$		0			0
$639$	−7012.11			−0.434108
$640$		0			0
$641$	−17229.7			−1.06167			−0.530837	−	0.847474i	$-0.678122\pi$
$641$	−17229.7			−1.06167			−0.530837	+	0.847474i	$0.678122\pi$
$642$		0			0
$643$	−15204.3	−	15204.3i	−0.932505	−	0.932505i	0.0653574	−	0.997862i	$-0.479181\pi$
$643$	−15204.3	−	15204.3i	−0.932505	−	0.932505i	−0.997862	+	0.0653574i	$0.979181\pi$
$644$		0			0
$645$	−4554.66	+	4554.66i	−0.278046	+	0.278046i
$646$		0			0
$647$		−	15349.4i		−	0.932687i	−0.884604	−	0.466343i	$-0.845571\pi$
$647$		−	15349.4i		−	0.932687i	0.884604	−	0.466343i	$-0.154429\pi$
$648$		0			0
$649$			2111.26i			0.127695i
$650$		0			0
$651$	−5581.25	+	5581.25i	−0.336016	+	0.336016i
$652$		0			0
$653$	1800.83	+	1800.83i	0.107920	+	0.107920i	0.759005	−	0.651085i	$-0.225686\pi$
$653$	1800.83	+	1800.83i	0.107920	+	0.107920i	−0.651085	+	0.759005i	$0.725686\pi$
$654$		0			0
$655$	−43002.0			−2.56523
$656$		0			0
$657$	−313.348			−0.0186071
$658$		0			0
$659$	8640.80	+	8640.80i	0.510771	+	0.510771i	0.914763	−	0.403992i	$-0.132378\pi$
$659$	8640.80	+	8640.80i	0.510771	+	0.510771i	−0.403992	+	0.914763i	$0.632378\pi$
$660$		0			0
$661$	−10455.9	+	10455.9i	−0.615258	+	0.615258i	−0.944311	−	0.329053i	$-0.893271\pi$
$661$	−10455.9	+	10455.9i	−0.615258	+	0.615258i	0.329053	+	0.944311i	$0.393271\pi$
$662$		0			0
$663$		−	302.637i		−	0.0177277i
$664$		0			0
$665$			3679.80i			0.214581i
$666$		0			0
$667$	−4889.59	+	4889.59i	−0.283846	+	0.283846i
$668$		0			0
$669$	6320.64	+	6320.64i	0.365277	+	0.365277i
$670$		0			0
$671$	8710.47			0.501138
$672$		0			0
$673$	−13498.3			−0.773139			−0.386569	−	0.922260i	$-0.626340\pi$
$673$	−13498.3			−0.773139			−0.386569	+	0.922260i	$0.626340\pi$
$674$		0			0
$675$	−5765.19	−	5765.19i	−0.328744	−	0.328744i
$676$		0			0
$677$	−1664.87	+	1664.87i	−0.0945141	+	0.0945141i	−0.752783	−	0.658269i	$-0.771289\pi$
$677$	−1664.87	+	1664.87i	−0.0945141	+	0.0945141i	0.658269	+	0.752783i	$0.271289\pi$
$678$		0			0
$679$			36021.1i			2.03588i
$680$		0			0
$681$			8185.52i			0.460602i
$682$		0			0
$683$	−1119.87	+	1119.87i	−0.0627388	+	0.0627388i	−0.737780	−	0.675041i	$-0.764126\pi$
$683$	−1119.87	+	1119.87i	−0.0627388	+	0.0627388i	0.675041	+	0.737780i	$0.264126\pi$
$684$		0			0
$685$	5091.60	+	5091.60i	0.284000	+	0.284000i
$686$		0			0
$687$	13616.7			0.756203
$688$		0			0
$689$	4268.14			0.235999
$690$		0			0
$691$	6727.79	+	6727.79i	0.370387	+	0.370387i	0.867618	−	0.497231i	$-0.165650\pi$
$691$	6727.79	+	6727.79i	0.370387	+	0.370387i	−0.497231	+	0.867618i	$0.665650\pi$
$692$		0			0
$693$	5613.30	−	5613.30i	0.307694	−	0.307694i
$694$		0			0
$695$			31721.9i			1.73134i
$696$		0			0
$697$			630.023i			0.0342379i
$698$		0			0
$699$	624.255	−	624.255i	0.0337789	−	0.0337789i
$700$		0			0
$701$	−4997.17	−	4997.17i	−0.269244	−	0.269244i	0.559551	−	0.828796i	$-0.310973\pi$
$701$	−4997.17	−	4997.17i	−0.269244	−	0.269244i	−0.828796	+	0.559551i	$0.810973\pi$
$702$		0			0
$703$	−2516.46			−0.135007
$704$		0			0
$705$	−36147.9			−1.93108
$706$		0			0
$707$	18244.7	+	18244.7i	0.970526	+	0.970526i
$708$		0			0
$709$	−13706.1	+	13706.1i	−0.726014	+	0.726014i	−0.969823	−	0.243809i	$-0.921603\pi$
$709$	−13706.1	+	13706.1i	−0.726014	+	0.726014i	0.243809	+	0.969823i	$0.421603\pi$
$710$		0			0
$711$			2113.17i			0.111463i
$712$		0			0
$713$		−	3334.09i		−	0.175123i
$714$		0			0
$715$	−8858.10	+	8858.10i	−0.463321	+	0.463321i
$716$		0			0
$717$	4078.40	+	4078.40i	0.212428	+	0.212428i
$718$		0			0
$719$	−15019.2			−0.779029			−0.389515	−	0.921020i	$-0.627357\pi$
$719$	−15019.2			−0.779029			−0.389515	+	0.921020i	$0.627357\pi$
$720$		0			0
$721$	23624.8			1.22030
$722$		0			0
$723$	−8154.06	−	8154.06i	−0.419437	−	0.419437i
$724$		0			0
$725$	43332.4	−	43332.4i	2.21976	−	2.21976i
$726$		0			0
$727$		−	11712.1i		−	0.597494i	−0.954332	−	0.298747i	$-0.903431\pi$
$727$		−	11712.1i		−	0.597494i	0.954332	−	0.298747i	$-0.0965687\pi$
$728$		0			0
$729$		−	729.000i		−	0.0370370i
$730$		0			0
$731$	401.050	−	401.050i	0.0202919	−	0.0202919i
$732$		0			0
$733$	18107.1	+	18107.1i	0.912418	+	0.912418i	0.996462	−	0.0840439i	$-0.0267836\pi$
$733$	18107.1	+	18107.1i	0.912418	+	0.912418i	−0.0840439	+	0.996462i	$0.526784\pi$
$734$		0			0
$735$	−23556.8			−1.18218
$736$		0			0
$737$	−10358.0			−0.517697
$738$		0			0
$739$	−5930.06	−	5930.06i	−0.295184	−	0.295184i	0.543940	−	0.839124i	$-0.316932\pi$
$739$	−5930.06	−	5930.06i	−0.295184	−	0.295184i	−0.839124	+	0.543940i	$0.816932\pi$
$740$		0			0
$741$	259.655	−	259.655i	0.0128727	−	0.0128727i
$742$		0			0
$743$		−	37209.5i		−	1.83726i	−0.395118	−	0.918630i	$-0.629296\pi$
$743$		−	37209.5i		−	1.83726i	0.395118	−	0.918630i	$-0.370704\pi$
$744$		0			0
$745$		−	62436.9i		−	3.07048i
$746$		0			0
$747$	308.846	−	308.846i	0.0151273	−	0.0151273i
$748$		0			0
$749$	−4694.24	−	4694.24i	−0.229004	−	0.229004i
$750$		0			0
$751$	38763.9			1.88351			0.941753	−	0.336304i	$-0.109177\pi$
$751$	38763.9			1.88351			0.941753	+	0.336304i	$0.109177\pi$
$752$		0			0
$753$	12062.9			0.583791
$754$		0			0
$755$	−38315.7	−	38315.7i	−1.84696	−	1.84696i
$756$		0			0
$757$	20356.8	−	20356.8i	0.977384	−	0.977384i	−0.0223658	−	0.999750i	$-0.507120\pi$
$757$	20356.8	−	20356.8i	0.977384	−	0.977384i	0.999750	+	0.0223658i	$0.00711984\pi$
$758$		0			0
$759$			3353.24i			0.160362i
$760$		0			0
$761$		−	21557.8i		−	1.02690i	−0.858121	−	0.513448i	$-0.828368\pi$
$761$		−	21557.8i		−	1.02690i	0.858121	−	0.513448i	$-0.171632\pi$
$762$		0			0
$763$	38600.6	−	38600.6i	1.83150	−	1.83150i
$764$		0			0
$765$	717.778	+	717.778i	0.0339233	+	0.0339233i
$766$		0			0
$767$	−1189.49			−0.0559975
$768$		0			0
$769$	22834.1			1.07076			0.535382	−	0.844610i	$-0.320168\pi$
$769$	22834.1			1.07076			0.535382	+	0.844610i	$0.320168\pi$
$770$		0			0
$771$	1414.44	+	1414.44i	0.0660698	+	0.0660698i
$772$		0			0
$773$	2123.96	−	2123.96i	0.0988275	−	0.0988275i	−0.655964	−	0.754792i	$-0.727738\pi$
$773$	2123.96	−	2123.96i	0.0988275	−	0.0988275i	0.754792	+	0.655964i	$0.227738\pi$
$774$		0			0
$775$			29547.3i			1.36951i
$776$		0			0
$777$		−	30650.0i		−	1.41514i
$778$		0			0
$779$	−540.544	+	540.544i	−0.0248614	+	0.0248614i
$780$		0			0
$781$	−18072.2	−	18072.2i	−0.828006	−	0.828006i
$782$		0			0
$783$	5479.32			0.250083
$784$		0			0
$785$	34328.6			1.56082
$786$		0			0
$787$	−17766.3	−	17766.3i	−0.804703	−	0.804703i	0.179124	−	0.983827i	$-0.442674\pi$
$787$	−17766.3	−	17766.3i	−0.804703	−	0.804703i	−0.983827	+	0.179124i	$0.942674\pi$
$788$		0			0
$789$	−4467.34	+	4467.34i	−0.201574	+	0.201574i
$790$		0			0
$791$			11334.1i			0.509474i
$792$		0			0
$793$			4907.51i			0.219761i
$794$		0			0
$795$	−10122.9	+	10122.9i	−0.451601	+	0.451601i
$796$		0			0
$797$	−11229.8	−	11229.8i	−0.499097	−	0.499097i	0.412059	−	0.911157i	$-0.364810\pi$
$797$	−11229.8	−	11229.8i	−0.499097	−	0.499097i	−0.911157	+	0.412059i	$0.864810\pi$
$798$		0			0
$799$	3182.92			0.140931
$800$		0			0
$801$	10140.7			0.447321
$802$		0			0
$803$	−807.583	−	807.583i	−0.0354907	−	0.0354907i
$804$		0			0
$805$	13386.9	−	13386.9i	0.586121	−	0.586121i
$806$		0			0
$807$			19100.0i			0.833148i
$808$		0			0
$809$			1902.91i			0.0826981i	0.999145	+	0.0413491i	$0.0131656\pi$
$809$			1902.91i			0.0826981i	−0.999145	+	0.0413491i	$0.986834\pi$
$810$		0			0
$811$	−25145.5	+	25145.5i	−1.08875	+	1.08875i	−0.0930971	+	0.995657i	$0.529677\pi$
$811$	−25145.5	+	25145.5i	−1.08875	+	1.08875i	−0.995657	+	0.0930971i	$0.970323\pi$
$812$		0			0
$813$	2447.84	+	2447.84i	0.105596	+	0.105596i
$814$		0			0
$815$	−39613.7			−1.70258
$816$		0			0
$817$	688.182			0.0294693
$818$		0			0
$819$	3162.55	+	3162.55i	0.134931	+	0.134931i
$820$		0			0
$821$	−1370.67	+	1370.67i	−0.0582662	+	0.0582662i	−0.735639	−	0.677373i	$-0.763118\pi$
$821$	−1370.67	+	1370.67i	−0.0582662	+	0.0582662i	0.677373	+	0.735639i	$0.263118\pi$
$822$		0			0
$823$		−	42263.7i		−	1.79006i	−0.446003	−	0.895031i	$-0.647153\pi$
$823$		−	42263.7i		−	1.79006i	0.446003	−	0.895031i	$-0.352847\pi$
$824$		0			0
$825$		−	29717.0i		−	1.25408i
$826$		0			0
$827$	−17377.6	+	17377.6i	−0.730686	+	0.730686i	−0.970756	−	0.240070i	$-0.922830\pi$
$827$	−17377.6	+	17377.6i	−0.730686	+	0.730686i	0.240070	+	0.970756i	$0.422830\pi$
$828$		0			0
$829$	−17427.0	−	17427.0i	−0.730113	−	0.730113i	0.240529	−	0.970642i	$-0.422679\pi$
$829$	−17427.0	−	17427.0i	−0.730113	−	0.730113i	−0.970642	+	0.240529i	$0.922679\pi$
$830$		0			0
$831$	−22423.1			−0.936039
$832$		0			0
$833$	2074.24			0.0862762
$834$		0			0
$835$	−29873.9	−	29873.9i	−1.23812	−	1.23812i
$836$		0			0
$837$	−1868.11	+	1868.11i	−0.0771460	+	0.0771460i
$838$		0			0
$839$		−	31608.4i		−	1.30065i	−0.759658	−	0.650323i	$-0.774634\pi$
$839$		−	31608.4i		−	1.30065i	0.759658	−	0.650323i	$-0.225366\pi$
$840$		0			0
$841$			16794.7i			0.688619i
$842$		0			0
$843$	11709.7	−	11709.7i	0.478415	−	0.478415i
$844$		0			0
$845$	27110.0	+	27110.0i	1.10368	+	1.10368i
$846$		0			0
$847$	−6855.01			−0.278088
$848$		0			0
$849$	17960.8			0.726047
$850$		0			0
$851$	9154.74	+	9154.74i	0.368767	+	0.368767i
$852$		0			0
$853$	12042.1	−	12042.1i	0.483367	−	0.483367i	−0.422838	−	0.906205i	$-0.638966\pi$
$853$	12042.1	−	12042.1i	0.483367	−	0.483367i	0.906205	+	0.422838i	$0.138966\pi$
$854$		0			0
$855$			1231.67i			0.0492658i
$856$		0			0
$857$			30191.5i			1.20341i	0.798718	+	0.601705i	$0.205512\pi$
$857$			30191.5i			1.20341i	−0.798718	+	0.601705i	$0.794488\pi$
$858$		0			0
$859$	12486.8	−	12486.8i	0.495978	−	0.495978i	−0.414206	−	0.910183i	$-0.635941\pi$
$859$	12486.8	−	12486.8i	0.495978	−	0.495978i	0.910183	+	0.414206i	$0.135941\pi$
$860$		0			0
$861$	−6583.73	−	6583.73i	−0.260596	−	0.260596i
$862$		0			0
$863$	−21201.2			−0.836267			−0.418133	−	0.908386i	$-0.637316\pi$
$863$	−21201.2			−0.836267			−0.418133	+	0.908386i	$0.637316\pi$
$864$		0			0
$865$	−11927.5			−0.468840
$866$		0			0
$867$	10358.8	+	10358.8i	0.405773	+	0.405773i
$868$		0			0
$869$	−5446.22	+	5446.22i	−0.212601	+	0.212601i
$870$		0			0
$871$		−	5835.74i		−	0.227022i
$872$		0			0
$873$			12056.6i			0.467418i
$874$		0			0
$875$	−69527.8	+	69527.8i	−2.68625	+	2.68625i
$876$		0			0
$877$	5223.37	+	5223.37i	0.201118	+	0.201118i	0.800479	−	0.599361i	$-0.204579\pi$
$877$	5223.37	+	5223.37i	0.201118	+	0.201118i	−0.599361	+	0.800479i	$0.704579\pi$
$878$		0			0
$879$	−6086.72			−0.233561
$880$		0			0
$881$	−40623.3			−1.55350			−0.776749	−	0.629810i	$-0.783133\pi$
$881$	−40623.3			−1.55350			−0.776749	+	0.629810i	$0.783133\pi$
$882$		0			0
$883$	30217.0	+	30217.0i	1.15162	+	1.15162i	0.986227	+	0.165398i	$0.0528908\pi$
$883$	30217.0	+	30217.0i	1.15162	+	1.15162i	0.165398	+	0.986227i	$0.447109\pi$
$884$		0			0
$885$	2821.17	−	2821.17i	0.107155	−	0.107155i
$886$		0			0
$887$		−	26591.6i		−	1.00660i	−0.864111	−	0.503302i	$-0.832118\pi$
$887$		−	26591.6i		−	1.00660i	0.864111	−	0.503302i	$-0.167882\pi$
$888$		0			0
$889$			9502.62i			0.358501i
$890$		0			0
$891$	1878.83	−	1878.83i	0.0706435	−	0.0706435i
$892$		0			0
$893$	2730.87	+	2730.87i	0.102335	+	0.102335i
$894$		0			0
$895$	56316.8			2.10331
$896$		0			0
$897$	−1889.22			−0.0703226
$898$		0			0
$899$	−14041.1	−	14041.1i	−0.520908	−	0.520908i
$900$		0			0
$901$	891.351	−	891.351i	0.0329581	−	0.0329581i
$902$		0			0
$903$			8381.93i			0.308896i
$904$		0			0
$905$			6011.57i			0.220808i
$906$		0			0
$907$	17765.7	−	17765.7i	0.650387	−	0.650387i	−0.302699	−	0.953086i	$-0.597888\pi$
$907$	17765.7	−	17765.7i	0.650387	−	0.650387i	0.953086	+	0.302699i	$0.0978878\pi$
$908$		0			0
$909$	6106.70	+	6106.70i	0.222823	+	0.222823i
$910$		0			0
$911$	−32406.1			−1.17855			−0.589277	−	0.807931i	$-0.700587\pi$
$911$	−32406.1			−1.17855			−0.589277	+	0.807931i	$0.700587\pi$
$912$		0			0
$913$	1591.96			0.0577068
$914$		0			0
$915$	−11639.3	−	11639.3i	−0.420530	−	0.420530i
$916$		0			0
$917$	−39568.3	+	39568.3i	−1.42493	+	1.42493i
$918$		0			0
$919$			28632.2i			1.02774i	0.857870	+	0.513868i	$0.171788\pi$
$919$			28632.2i			1.02774i	−0.857870	+	0.513868i	$0.828212\pi$
$920$		0			0
$921$			27958.9i			1.00030i
$922$		0			0
$923$	10181.9	−	10181.9i	0.363100	−	0.363100i
$924$		0			0
$925$	−81131.0	−	81131.0i	−2.88386	−	2.88386i
$926$		0			0
$927$	7907.49			0.280168
$928$		0			0
$929$	−5285.59			−0.186668			−0.0933340	−	0.995635i	$-0.529752\pi$
$929$	−5285.59			−0.186668			−0.0933340	+	0.995635i	$0.529752\pi$
$930$		0			0
$931$	1779.64	+	1779.64i	0.0626482	+	0.0626482i
$932$		0			0
$933$	−4043.97	+	4043.97i	−0.141901	+	0.141901i
$934$		0			0
$935$			3699.82i			0.129409i
$936$		0			0
$937$		−	41589.1i		−	1.45001i	−0.688746	−	0.725003i	$-0.741838\pi$
$937$		−	41589.1i		−	1.45001i	0.688746	−	0.725003i	$-0.258162\pi$
$938$		0			0
$939$	12000.5	−	12000.5i	0.417064	−	0.417064i
$940$		0			0
$941$	−13190.1	−	13190.1i	−0.456945	−	0.456945i	0.440707	−	0.897651i	$-0.354728\pi$
$941$	−13190.1	−	13190.1i	−0.456945	−	0.456945i	−0.897651	+	0.440707i	$0.854728\pi$
$942$		0			0
$943$	3932.94			0.135816
$944$		0			0
$945$	−15001.5			−0.516401
$946$		0			0
$947$	8427.73	+	8427.73i	0.289192	+	0.289192i	0.836761	−	0.547569i	$-0.184447\pi$
$947$	8427.73	+	8427.73i	0.289192	+	0.289192i	−0.547569	+	0.836761i	$0.684447\pi$
$948$		0			0
$949$	454.995	−	454.995i	0.0155635	−	0.0155635i
$950$		0			0
$951$			2490.53i			0.0849222i
$952$		0			0
$953$			49459.8i			1.68118i	0.541675	+	0.840588i	$0.317790\pi$
$953$			49459.8i			1.68118i	−0.541675	+	0.840588i	$0.682210\pi$
$954$		0			0
$955$	22452.4	−	22452.4i	0.760779	−	0.760779i
$956$		0			0
$957$	14121.7	+	14121.7i	0.477002	+	0.477002i
$958$		0			0
$959$	9370.06			0.315511
$960$		0			0
$961$	−20216.7			−0.678619
$962$		0			0
$963$	−1571.22	−	1571.22i	−0.0525771	−	0.0525771i
$964$		0			0
$965$	−1866.29	+	1866.29i	−0.0622568	+	0.0622568i
$966$		0			0
$967$			32986.2i			1.09696i	0.836163	+	0.548482i	$0.184794\pi$
$967$			32986.2i			1.09696i	−0.836163	+	0.548482i	$0.815206\pi$
$968$		0			0
$969$		−	108.452i		−	0.00359544i
$970$		0			0
$971$	29353.0	−	29353.0i	0.970117	−	0.970117i	−0.0294494	−	0.999566i	$-0.509375\pi$
$971$	29353.0	−	29353.0i	0.970117	−	0.970117i	0.999566	+	0.0294494i	$0.00937539\pi$
$972$		0			0
$973$	29188.9	+	29188.9i	0.961718	+	0.961718i
$974$		0			0
$975$	16742.7			0.549943
$976$		0			0
$977$	44894.0			1.47010			0.735050	−	0.678013i	$-0.237159\pi$
$977$	44894.0			1.47010			0.735050	+	0.678013i	$0.237159\pi$
$978$		0			0
$979$	26135.4	+	26135.4i	0.853208	+	0.853208i
$980$		0			0
$981$	12920.0	−	12920.0i	0.420495	−	0.420495i
$982$		0			0
$983$		−	2200.38i		−	0.0713949i	−0.999363	−	0.0356974i	$-0.988635\pi$
$983$		−	2200.38i		−	0.0713949i	0.999363	−	0.0356974i	$-0.0113653\pi$
$984$		0			0
$985$		−	66698.7i		−	2.15756i
$986$		0			0
$987$	−33261.4	+	33261.4i	−1.07267	+	1.07267i
$988$		0			0
$989$	−2503.57	−	2503.57i	−0.0804944	−	0.0804944i
$990$		0			0
$991$	−40976.5			−1.31348			−0.656741	−	0.754116i	$-0.728065\pi$
$991$	−40976.5			−1.31348			−0.656741	+	0.754116i	$0.728065\pi$
$992$		0			0
$993$	32830.6			1.04919
$994$		0			0
$995$	60715.6	+	60715.6i	1.93449	+	1.93449i
$996$		0			0
$997$	−22095.1	+	22095.1i	−0.701864	+	0.701864i	−0.964810	−	0.262946i	$-0.915306\pi$
$997$	−22095.1	+	22095.1i	−0.701864	+	0.701864i	0.262946	+	0.964810i	$0.415306\pi$
$998$		0			0
$999$		−	10258.9i		−	0.324902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.4.j.b.289.1		24
4.3	odd	2		384.4.j.a.289.12		24
8.3	odd	2		192.4.j.a.145.6		24
8.5	even	2		48.4.j.a.13.2	✓	24
16.3	odd	4		192.4.j.a.49.6		24
16.5	even	4	inner	384.4.j.b.97.1		24
16.11	odd	4		384.4.j.a.97.12		24
16.13	even	4		48.4.j.a.37.2	yes	24
24.5	odd	2		144.4.k.b.109.11		24
24.11	even	2		576.4.k.b.145.1		24
48.29	odd	4		144.4.k.b.37.11		24
48.35	even	4		576.4.k.b.433.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.2	✓	24	8.5	even	2
48.4.j.a.37.2	yes	24	16.13	even	4
144.4.k.b.37.11		24	48.29	odd	4
144.4.k.b.109.11		24	24.5	odd	2
192.4.j.a.49.6		24	16.3	odd	4
192.4.j.a.145.6		24	8.3	odd	2
384.4.j.a.97.12		24	16.11	odd	4
384.4.j.a.289.12		24	4.3	odd	2
384.4.j.b.97.1		24	16.5	even	4	inner
384.4.j.b.289.1		24	1.1	even	1	trivial
576.4.k.b.145.1		24	24.11	even	2
576.4.k.b.433.1		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)

\(f(q)\)	\(=\)	\(q+(-2.12132 - 2.12132i) q^{3} +(-14.6111 + 14.6111i) q^{5} +26.8889i q^{7} +9.00000i q^{9} +O(q^{10})\)	\(q+(-2.12132 - 2.12132i) q^{3} +(-14.6111 + 14.6111i) q^{5} +26.8889i q^{7} +9.00000i q^{9} +(-23.1955 + 23.1955i) q^{11} +(-13.0684 - 13.0684i) q^{13} +61.9898 q^{15} -5.45837 q^{17} +(-4.68315 - 4.68315i) q^{19} +(57.0399 - 57.0399i) q^{21} +34.0741i q^{23} -301.971i q^{25} +(19.0919 - 19.0919i) q^{27} +(143.499 + 143.499i) q^{29} -97.8482 q^{31} +98.4101 q^{33} +(-392.877 - 392.877i) q^{35} +(268.672 - 268.672i) q^{37} +55.4446i q^{39} -115.423i q^{41} +(-73.4743 + 73.4743i) q^{43} +(-131.500 - 131.500i) q^{45} -583.126 q^{47} -380.010 q^{49} +(11.5790 + 11.5790i) q^{51} +(-163.300 + 163.300i) q^{53} -677.825i q^{55} +19.8689i q^{57} +(45.5102 - 45.5102i) q^{59} +(-187.762 - 187.762i) q^{61} -242.000 q^{63} +381.889 q^{65} +(223.276 + 223.276i) q^{67} +(72.2821 - 72.2821i) q^{69} +779.124i q^{71} +34.8164i q^{73} +(-640.577 + 640.577i) q^{75} +(-623.700 - 623.700i) q^{77} +234.796 q^{79} -81.0000 q^{81} +(-34.3162 - 34.3162i) q^{83} +(79.7531 - 79.7531i) q^{85} -608.813i q^{87} -1126.75i q^{89} +(351.395 - 351.395i) q^{91} +(207.567 + 207.567i) q^{93} +136.852 q^{95} +1339.63 q^{97} +(-208.759 - 208.759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 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

L-functions

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