LMFDB - Embedded newform 483.3.f.a.22.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,3,Mod(22,483)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	483.f (of order $2$, degree $1$, 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:	$13.1607967686$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			22.38
Character	$\chi$	$=$	483.22
Dual form			483.3.f.a.22.37

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.66763 q^{2} +1.73205 q^{3} +3.11624 q^{4} +3.30724i q^{5} +4.62047 q^{6} +2.64575i q^{7} -2.35753 q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+2.66763 q^{2} +1.73205 q^{3} +3.11624 q^{4} +3.30724i q^{5} +4.62047 q^{6} +2.64575i q^{7} -2.35753 q^{8} +3.00000 q^{9} +8.82249i q^{10} +17.1511i q^{11} +5.39749 q^{12} +21.0186 q^{13} +7.05788i q^{14} +5.72831i q^{15} -18.7540 q^{16} +24.3607i q^{17} +8.00289 q^{18} -31.1335i q^{19} +10.3062i q^{20} +4.58258i q^{21} +45.7526i q^{22} +(-18.7632 - 13.3020i) q^{23} -4.08337 q^{24} +14.0622 q^{25} +56.0698 q^{26} +5.19615 q^{27} +8.24481i q^{28} +57.3365 q^{29} +15.2810i q^{30} -4.60383 q^{31} -40.5986 q^{32} +29.7065i q^{33} +64.9854i q^{34} -8.75014 q^{35} +9.34873 q^{36} -15.4756i q^{37} -83.0525i q^{38} +36.4053 q^{39} -7.79693i q^{40} -29.9446 q^{41} +12.2246i q^{42} -29.6818i q^{43} +53.4469i q^{44} +9.92172i q^{45} +(-50.0533 - 35.4847i) q^{46} -56.0878 q^{47} -32.4829 q^{48} -7.00000 q^{49} +37.5126 q^{50} +42.1940i q^{51} +65.4990 q^{52} -39.8005i q^{53} +13.8614 q^{54} -56.7227 q^{55} -6.23745i q^{56} -53.9248i q^{57} +152.953 q^{58} -49.3743 q^{59} +17.8508i q^{60} -11.2627i q^{61} -12.2813 q^{62} +7.93725i q^{63} -33.2859 q^{64} +69.5135i q^{65} +79.2459i q^{66} +10.5712i q^{67} +75.9139i q^{68} +(-32.4988 - 23.0397i) q^{69} -23.3421 q^{70} +69.8410 q^{71} -7.07260 q^{72} +64.8502 q^{73} -41.2831i q^{74} +24.3564 q^{75} -97.0195i q^{76} -45.3774 q^{77} +97.1157 q^{78} -54.8428i q^{79} -62.0240i q^{80} +9.00000 q^{81} -79.8811 q^{82} -138.578i q^{83} +14.2804i q^{84} -80.5668 q^{85} -79.1801i q^{86} +99.3097 q^{87} -40.4342i q^{88} +83.7673i q^{89} +26.4675i q^{90} +55.6100i q^{91} +(-58.4707 - 41.4521i) q^{92} -7.97407 q^{93} -149.622 q^{94} +102.966 q^{95} -70.3188 q^{96} +124.766i q^{97} -18.6734 q^{98} +51.4532i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	$ 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) $ 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$-1$

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 $

$2$	2.66763			1.33381			0.666907	−	0.745141i	$-0.267618\pi$
$2$	2.66763			1.33381			0.666907	+	0.745141i	$0.267618\pi$
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$	3.11624			0.779061
$5$			3.30724i			0.661448i	0.943727	+	0.330724i	$0.107293\pi$
$5$			3.30724i			0.661448i	−0.943727	+	0.330724i	$0.892707\pi$
$6$	4.62047			0.770078
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$	−2.35753			−0.294692
$9$	3.00000			0.333333
$10$			8.82249i			0.882249i
$11$			17.1511i			1.55919i	0.626286	+	0.779593i	$0.284574\pi$
$11$			17.1511i			1.55919i	−0.626286	+	0.779593i	$0.715426\pi$
$12$	5.39749			0.449791
$13$	21.0186			1.61681			0.808407	−	0.588624i	$-0.200330\pi$
$13$	21.0186			1.61681			0.808407	+	0.588624i	$0.200330\pi$
$14$			7.05788i			0.504134i
$15$			5.72831i			0.381887i
$16$	−18.7540			−1.17213
$17$			24.3607i			1.43298i	0.697596	+	0.716492i	$0.254253\pi$
$17$			24.3607i			1.43298i	−0.697596	+	0.716492i	$0.745747\pi$
$18$	8.00289			0.444605
$19$		−	31.1335i		−	1.63860i	−0.573362	−	0.819302i	$-0.694361\pi$
$19$		−	31.1335i		−	1.63860i	0.573362	−	0.819302i	$-0.305639\pi$
$20$			10.3062i			0.515308i
$21$			4.58258i			0.218218i
$22$			45.7526i			2.07967i
$23$	−18.7632	−	13.3020i	−0.815792	−	0.578346i
$23$	−18.7632	−	13.3020i	−0.815792	−	0.578346i
$24$	−4.08337			−0.170140
$25$	14.0622			0.562486
$26$	56.0698			2.15653
$27$	5.19615			0.192450
$28$			8.24481i			0.294457i
$29$	57.3365			1.97712			0.988560	−	0.150825i	$-0.0481931\pi$
$29$	57.3365			1.97712			0.988560	+	0.150825i	$0.0481931\pi$
$30$			15.2810i			0.509367i
$31$	−4.60383			−0.148511			−0.0742553	−	0.997239i	$-0.523658\pi$
$31$	−4.60383			−0.148511			−0.0742553	+	0.997239i	$0.523658\pi$
$32$	−40.5986			−1.26871
$33$			29.7065i			0.900197i
$34$			64.9854i			1.91133i
$35$	−8.75014			−0.250004
$36$	9.34873			0.259687
$37$		−	15.4756i		−	0.418259i	−0.977888	−	0.209130i	$-0.932937\pi$
$37$		−	15.4756i		−	0.418259i	0.977888	−	0.209130i	$-0.0670631\pi$
$38$		−	83.0525i		−	2.18559i
$39$	36.4053			0.933468
$40$		−	7.79693i		−	0.194923i
$41$	−29.9446			−0.730356			−0.365178	−	0.930938i	$-0.618992\pi$
$41$	−29.9446			−0.730356			−0.365178	+	0.930938i	$0.618992\pi$
$42$			12.2246i			0.291062i
$43$		−	29.6818i		−	0.690275i	−0.938552	−	0.345137i	$-0.887832\pi$
$43$		−	29.6818i		−	0.690275i	0.938552	−	0.345137i	$-0.112168\pi$
$44$			53.4469i			1.21470i
$45$			9.92172i			0.220483i
$46$	−50.0533	−	35.4847i	−1.08811	−	0.771406i
$47$	−56.0878			−1.19336			−0.596679	−	0.802480i	$-0.703513\pi$
$47$	−56.0878			−1.19336			−0.596679	+	0.802480i	$0.703513\pi$
$48$	−32.4829			−0.676727
$49$	−7.00000			−0.142857
$50$	37.5126			0.750252
$51$			42.1940i			0.827333i
$52$	65.4990			1.25960
$53$		−	39.8005i		−	0.750954i	−0.926832	−	0.375477i	$-0.877479\pi$
$53$		−	39.8005i		−	0.750954i	0.926832	−	0.375477i	$-0.122521\pi$
$54$	13.8614			0.256693
$55$	−56.7227			−1.03132
$56$		−	6.23745i		−	0.111383i
$57$		−	53.9248i		−	0.946048i
$58$	152.953			2.63711
$59$	−49.3743			−0.836852			−0.418426	−	0.908251i	$-0.637418\pi$
$59$	−49.3743			−0.836852			−0.418426	+	0.908251i	$0.637418\pi$
$60$			17.8508i			0.297513i
$61$		−	11.2627i		−	0.184634i	−0.995730	−	0.0923172i	$-0.970573\pi$
$61$		−	11.2627i		−	0.184634i	0.995730	−	0.0923172i	$-0.0294274\pi$
$62$	−12.2813			−0.198086
$63$			7.93725i			0.125988i
$64$	−33.2859			−0.520093
$65$			69.5135i			1.06944i
$66$			79.2459i			1.20070i
$67$			10.5712i			0.157779i	0.996883	+	0.0788896i	$0.0251375\pi$
$67$			10.5712i			0.157779i	−0.996883	+	0.0788896i	$0.974863\pi$
$68$			75.9139i			1.11638i
$69$	−32.4988	−	23.0397i	−0.470998	−	0.333908i
$70$	−23.3421			−0.333459
$71$	69.8410			0.983676			0.491838	−	0.870687i	$-0.336325\pi$
$71$	69.8410			0.983676			0.491838	+	0.870687i	$0.336325\pi$
$72$	−7.07260			−0.0982306
$73$	64.8502			0.888359			0.444179	−	0.895938i	$-0.353495\pi$
$73$	64.8502			0.888359			0.444179	+	0.895938i	$0.353495\pi$
$74$		−	41.2831i		−	0.557880i
$75$	24.3564			0.324752
$76$		−	97.0195i		−	1.27657i
$77$	−45.3774			−0.589317
$78$	97.1157			1.24507
$79$		−	54.8428i		−	0.694213i	−0.937826	−	0.347106i	$-0.887164\pi$
$79$		−	54.8428i		−	0.694213i	0.937826	−	0.347106i	$-0.112836\pi$
$80$		−	62.0240i		−	0.775300i
$81$	9.00000			0.111111
$82$	−79.8811			−0.974159
$83$		−	138.578i		−	1.66961i	−0.550543	−	0.834807i	$-0.685579\pi$
$83$		−	138.578i		−	1.66961i	0.550543	−	0.834807i	$-0.314421\pi$
$84$			14.2804i			0.170005i
$85$	−80.5668			−0.947844
$86$		−	79.1801i		−	0.920699i
$87$	99.3097			1.14149
$88$		−	40.4342i		−	0.459480i
$89$			83.7673i			0.941206i	0.882345	+	0.470603i	$0.155964\pi$
$89$			83.7673i			0.941206i	−0.882345	+	0.470603i	$0.844036\pi$
$90$			26.4675i			0.294083i
$91$			55.6100i			0.611098i
$92$	−58.4707	−	41.4521i	−0.635551	−	0.450567i
$93$	−7.97407			−0.0857427
$94$	−149.622			−1.59172
$95$	102.966			1.08385
$96$	−70.3188			−0.732487
$97$			124.766i			1.28624i	0.765764	+	0.643122i	$0.222361\pi$
$97$			124.766i			1.28624i	−0.765764	+	0.643122i	$0.777639\pi$
$98$	−18.6734			−0.190545
$99$			51.4532i			0.519729i
$100$	43.8211			0.438211
$101$	−41.9712			−0.415556			−0.207778	−	0.978176i	$-0.566623\pi$
$101$	−41.9712			−0.415556			−0.207778	+	0.978176i	$0.566623\pi$
$102$			112.558i			1.10351i
$103$			39.8951i			0.387331i	0.981068	+	0.193666i	$0.0620377\pi$
$103$			39.8951i			0.387331i	−0.981068	+	0.193666i	$0.937962\pi$
$104$	−49.5520			−0.476462
$105$	−15.1557			−0.144340
$106$		−	106.173i		−	1.00163i
$107$		−	55.5065i		−	0.518753i	−0.965776	−	0.259376i	$-0.916483\pi$
$107$		−	55.5065i		−	0.518753i	0.965776	−	0.259376i	$-0.0835170\pi$
$108$	16.1925			0.149930
$109$		−	46.3487i		−	0.425218i	−0.977137	−	0.212609i	$-0.931804\pi$
$109$		−	46.3487i		−	0.425218i	0.977137	−	0.212609i	$-0.0681960\pi$
$110$	−151.315			−1.37559
$111$		−	26.8045i		−	0.241482i
$112$		−	49.6184i		−	0.443022i
$113$		−	56.0245i		−	0.495792i	−0.968787	−	0.247896i	$-0.920261\pi$
$113$		−	56.0245i		−	0.495792i	0.968787	−	0.247896i	$-0.0797391\pi$
$114$		−	143.851i		−	1.26185i
$115$	43.9928	−	62.0545i	0.382546	−	0.539604i
$116$	178.675			1.54030
$117$	63.0558			0.538938
$118$	−131.712			−1.11621
$119$	−64.4524			−0.541617
$120$		−	13.5047i		−	0.112539i
$121$	−173.159			−1.43106
$122$		−	30.0447i		−	0.246268i
$123$	−51.8656			−0.421671
$124$	−14.3467			−0.115699
$125$			129.188i			1.03350i
$126$			21.1736i			0.168045i
$127$	53.5586			0.421721			0.210861	−	0.977516i	$-0.432373\pi$
$127$	53.5586			0.421721			0.210861	+	0.977516i	$0.432373\pi$
$128$	73.5998			0.574998
$129$		−	51.4104i		−	0.398530i
$130$			185.436i			1.42643i
$131$	166.490			1.27092			0.635458	−	0.772136i	$-0.280811\pi$
$131$	166.490			1.27092			0.635458	+	0.772136i	$0.280811\pi$
$132$			92.5727i			0.701308i
$133$	82.3714			0.619334
$134$			28.2001i			0.210448i
$135$			17.1849i			0.127296i
$136$		−	57.4312i		−	0.422288i
$137$			22.5269i			0.164430i	0.996615	+	0.0822149i	$0.0261994\pi$
$137$			22.5269i			0.164430i	−0.996615	+	0.0822149i	$0.973801\pi$
$138$	−86.6948	−	61.4613i	−0.628223	−	0.445372i
$139$	−128.635			−0.925432			−0.462716	−	0.886507i	$-0.653125\pi$
$139$	−128.635			−0.925432			−0.462716	+	0.886507i	$0.653125\pi$
$140$	−27.2676			−0.194768
$141$	−97.1470			−0.688986
$142$	186.310			1.31204
$143$			360.491i			2.52092i
$144$	−56.2620			−0.390708
$145$			189.626i			1.30776i
$146$	172.996			1.18491
$147$	−12.1244			−0.0824786
$148$		−	48.2257i		−	0.325850i
$149$		−	233.418i		−	1.56656i	−0.621668	−	0.783281i	$-0.713545\pi$
$149$		−	233.418i		−	1.56656i	0.621668	−	0.783281i	$-0.286455\pi$
$150$	64.9737			0.433158
$151$	−96.7493			−0.640724			−0.320362	−	0.947295i	$-0.603805\pi$
$151$	−96.7493			−0.640724			−0.320362	+	0.947295i	$0.603805\pi$
$152$			73.3982i			0.482883i
$153$			73.0822i			0.477661i
$154$	−121.050			−0.786040
$155$		−	15.2260i		−	0.0982321i
$156$	113.448			0.727229
$157$		−	272.144i		−	1.73340i	−0.498827	−	0.866701i	$-0.666236\pi$
$157$		−	272.144i		−	1.73340i	0.498827	−	0.866701i	$-0.333764\pi$
$158$		−	146.300i		−	0.925951i
$159$		−	68.9366i		−	0.433563i
$160$		−	134.269i		−	0.839183i
$161$	35.1937	−	49.6428i	0.218594	−	0.308340i
$162$	24.0087			0.148202
$163$	245.749			1.50766			0.753830	−	0.657070i	$-0.228204\pi$
$163$	245.749			1.50766			0.753830	+	0.657070i	$0.228204\pi$
$164$	−93.3146			−0.568992
$165$	−98.2466			−0.595434
$166$		−	369.674i		−	2.22695i
$167$	−77.7797			−0.465747			−0.232873	−	0.972507i	$-0.574813\pi$
$167$	−77.7797			−0.465747			−0.232873	+	0.972507i	$0.574813\pi$
$168$		−	10.8036i		−	0.0643070i
$169$	272.781			1.61409
$170$	−214.922			−1.26425
$171$		−	93.4004i		−	0.546201i
$172$		−	92.4958i		−	0.537766i
$173$	−171.266			−0.989978			−0.494989	−	0.868899i	$-0.664828\pi$
$173$	−171.266			−0.989978			−0.494989	+	0.868899i	$0.664828\pi$
$174$	264.922			1.52254
$175$			37.2050i			0.212600i
$176$		−	321.651i		−	1.82756i
$177$	−85.5188			−0.483157
$178$			223.460i			1.25539i
$179$	72.6497			0.405864			0.202932	−	0.979193i	$-0.434953\pi$
$179$	72.6497			0.405864			0.202932	+	0.979193i	$0.434953\pi$
$180$			30.9185i			0.171769i
$181$		−	59.4183i		−	0.328278i	−0.986437	−	0.164139i	$-0.947515\pi$
$181$		−	59.4183i		−	0.328278i	0.986437	−	0.164139i	$-0.0524846\pi$
$182$			148.347i			0.815092i
$183$		−	19.5076i		−	0.106599i
$184$	44.2349	+	31.3598i	0.240407	+	0.170434i
$185$	51.1815			0.276657
$186$	−21.2719			−0.114365
$187$	−417.812			−2.23429
$188$	−174.783			−0.929699
$189$			13.7477i			0.0727393i
$190$	274.675			1.44566
$191$			338.489i			1.77219i	0.463502	+	0.886096i	$0.346593\pi$
$191$			338.489i			1.77219i	−0.463502	+	0.886096i	$0.653407\pi$
$192$	−57.6529			−0.300276
$193$	−248.328			−1.28667			−0.643337	−	0.765583i	$-0.722451\pi$
$193$	−248.328			−1.28667			−0.643337	+	0.765583i	$0.722451\pi$
$194$			332.828i			1.71561i
$195$			120.401i			0.617441i
$196$	−21.8137			−0.111294
$197$	322.716			1.63815			0.819075	−	0.573686i	$-0.194487\pi$
$197$	322.716			1.63815			0.819075	+	0.573686i	$0.194487\pi$
$198$			137.258i			0.693222i
$199$		−	221.503i		−	1.11308i	−0.830820	−	0.556541i	$-0.812128\pi$
$199$		−	221.503i		−	1.11308i	0.830820	−	0.556541i	$-0.187872\pi$
$200$	−33.1520			−0.165760
$201$			18.3099i			0.0910939i
$202$	−111.964			−0.554275
$203$			151.698i			0.747281i
$204$			131.487i			0.644543i
$205$		−	99.0340i		−	0.483093i
$206$			106.425i			0.516628i
$207$	−56.2896	−	39.9059i	−0.271931	−	0.192782i
$208$	−394.183			−1.89511
$209$	533.972			2.55489
$210$	−40.4297			−0.192523
$211$	−154.277			−0.731171			−0.365585	−	0.930778i	$-0.619131\pi$
$211$	−154.277			−0.731171			−0.365585	+	0.930778i	$0.619131\pi$
$212$		−	124.028i		−	0.585039i
$213$	120.968			0.567926
$214$		−	148.071i		−	0.691920i
$215$	98.1649			0.456581
$216$	−12.2501			−0.0567135
$217$		−	12.1806i		−	0.0561318i
$218$		−	123.641i		−	0.567161i
$219$	112.324			0.512894
$220$	−176.762			−0.803462
$221$			512.028i			2.31687i
$222$		−	71.5045i		−	0.322092i
$223$	10.1487			0.0455098			0.0227549	−	0.999741i	$-0.492756\pi$
$223$	10.1487			0.0455098			0.0227549	+	0.999741i	$0.492756\pi$
$224$		−	107.414i		−	0.479526i
$225$	42.1865			0.187495
$226$		−	149.453i		−	0.661295i
$227$			41.5659i			0.183110i	0.995800	+	0.0915549i	$0.0291837\pi$
$227$			41.5659i			0.183110i	−0.995800	+	0.0915549i	$0.970816\pi$
$228$		−	168.043i		−	0.737029i
$229$			364.068i			1.58982i	0.606729	+	0.794909i	$0.292481\pi$
$229$			364.068i			1.58982i	−0.606729	+	0.794909i	$0.707519\pi$
$230$	117.356	−	165.538i	0.510245	−	0.719732i
$231$	−78.5960			−0.340242
$232$	−135.173			−0.582641
$233$	−92.1517			−0.395501			−0.197750	−	0.980252i	$-0.563364\pi$
$233$	−92.1517			−0.395501			−0.197750	+	0.980252i	$0.563364\pi$
$234$	168.209			0.718844
$235$		−	185.496i		−	0.789345i
$236$	−153.862			−0.651959
$237$		−	94.9906i		−	0.400804i
$238$	−171.935			−0.722416
$239$	293.133			1.22650			0.613249	−	0.789890i	$-0.289862\pi$
$239$	293.133			1.22650			0.613249	+	0.789890i	$0.289862\pi$
$240$		−	107.429i		−	0.447620i
$241$		−	158.817i		−	0.658990i	−0.944157	−	0.329495i	$-0.893122\pi$
$241$		−	158.817i		−	0.658990i	0.944157	−	0.329495i	$-0.106878\pi$
$242$	−461.923			−1.90877
$243$	15.5885			0.0641500
$244$		−	35.0973i		−	0.143841i
$245$		−	23.1507i		−	0.0944926i
$246$	−138.358			−0.562431
$247$		−	654.382i		−	2.64932i
$248$	10.8537			0.0437649
$249$		−	240.024i		−	0.963952i
$250$			344.626i			1.37850i
$251$			282.700i			1.12630i	0.826356	+	0.563148i	$0.190410\pi$
$251$			282.700i			1.12630i	−0.826356	+	0.563148i	$0.809590\pi$
$252$			24.7344i			0.0981524i
$253$	228.143	−	321.809i	0.901749	−	1.27197i
$254$	142.875			0.562498
$255$	−139.546			−0.547238
$256$	329.481			1.28703
$257$	141.422			0.550279			0.275139	−	0.961404i	$-0.411276\pi$
$257$	141.422			0.550279			0.275139	+	0.961404i	$0.411276\pi$
$258$		−	137.144i		−	0.531566i
$259$	40.9446			0.158087
$260$			216.621i			0.833158i
$261$	172.010			0.659040
$262$	444.133			1.69517
$263$			363.490i			1.38209i	0.722810	+	0.691047i	$0.242850\pi$
$263$			363.490i			1.38209i	−0.722810	+	0.691047i	$0.757150\pi$
$264$		−	70.0341i		−	0.265281i
$265$	131.630			0.496717
$266$	219.736			0.826077
$267$			145.089i			0.543406i
$268$			32.9425i			0.122920i
$269$	−449.648			−1.67156			−0.835778	−	0.549068i	$-0.814983\pi$
$269$	−449.648			−1.67156			−0.835778	+	0.549068i	$0.814983\pi$
$270$			45.8430i			0.169789i
$271$	−292.096			−1.07784			−0.538922	−	0.842355i	$-0.681168\pi$
$271$	−292.096			−1.07784			−0.538922	+	0.842355i	$0.681168\pi$
$272$		−	456.861i		−	1.67964i
$273$			96.3193i			0.352818i
$274$			60.0933i			0.219319i
$275$			241.181i			0.877021i
$276$	−101.274	−	71.7972i	−0.366936	−	0.260135i
$277$	193.987			0.700316			0.350158	−	0.936691i	$-0.386128\pi$
$277$	193.987			0.700316			0.350158	+	0.936691i	$0.386128\pi$
$278$	−343.150			−1.23435
$279$	−13.8115			−0.0495036
$280$	20.6288			0.0736741
$281$		−	316.930i		−	1.12787i	−0.825821	−	0.563933i	$-0.809288\pi$
$281$		−	316.930i		−	1.12787i	0.825821	−	0.563933i	$-0.190712\pi$
$282$	−259.152			−0.918979
$283$			69.6696i			0.246182i	0.992395	+	0.123091i	$0.0392808\pi$
$283$			69.6696i			0.246182i	−0.992395	+	0.123091i	$0.960719\pi$
$284$	217.642			0.766344
$285$	178.342			0.625762
$286$			961.656i			3.36243i
$287$		−	79.2259i		−	0.276049i
$288$	−121.796			−0.422902
$289$	−304.445			−1.05344
$290$			505.851i			1.74431i
$291$			216.100i			0.742613i
$292$	202.089			0.692086
$293$			336.092i			1.14707i	0.819181	+	0.573535i	$0.194428\pi$
$293$			336.092i			1.14707i	−0.819181	+	0.573535i	$0.805572\pi$
$294$	−32.3433			−0.110011
$295$		−	163.293i		−	0.553534i
$296$			36.4843i			0.123258i
$297$			89.1195i			0.300066i
$298$		−	622.672i		−	2.08950i
$299$	−394.376	−	279.588i	−1.31898	−	0.935078i
$300$	75.9004			0.253001
$301$	78.5307			0.260899
$302$	−258.091			−0.854607
$303$	−72.6962			−0.239921
$304$			583.877i			1.92065i
$305$	37.2485			0.122126
$306$			194.956i			0.637111i
$307$	−414.074			−1.34878			−0.674388	−	0.738377i	$-0.735592\pi$
$307$	−414.074			−1.34878			−0.674388	+	0.738377i	$0.735592\pi$
$308$	−141.407			−0.459114
$309$			69.1004i			0.223626i
$310$		−	40.6173i		−	0.131023i
$311$	177.346			0.570244			0.285122	−	0.958491i	$-0.407966\pi$
$311$	177.346			0.570244			0.285122	+	0.958491i	$0.407966\pi$
$312$	−85.8267			−0.275085
$313$			114.945i			0.367237i	0.982998	+	0.183619i	$0.0587812\pi$
$313$			114.945i			0.367237i	−0.982998	+	0.183619i	$0.941219\pi$
$314$		−	725.980i		−	2.31204i
$315$	−26.2504			−0.0833347
$316$		−	170.904i		−	0.540834i
$317$	164.436			0.518726			0.259363	−	0.965780i	$-0.416487\pi$
$317$	164.436			0.518726			0.259363	+	0.965780i	$0.416487\pi$
$318$		−	183.897i		−	0.578293i
$319$			983.381i			3.08270i
$320$		−	110.085i		−	0.344014i
$321$		−	96.1401i		−	0.299502i
$322$	93.8836	−	132.429i	0.291564	−	0.411269i
$323$	758.434			2.34809
$324$	28.0462			0.0865623
$325$	295.567			0.909436
$326$	655.566			2.01094
$327$		−	80.2783i		−	0.245499i
$328$	70.5954			0.215230
$329$		−	148.394i		−	0.451047i
$330$	−262.085			−0.794198
$331$	258.374			0.780587			0.390293	−	0.920691i	$-0.372374\pi$
$331$	258.374			0.780587			0.390293	+	0.920691i	$0.372374\pi$
$332$		−	431.842i		−	1.30073i
$333$		−	46.4268i		−	0.139420i
$334$	−207.487			−0.621220
$335$	−34.9615			−0.104363
$336$		−	85.9416i		−	0.255779i
$337$		−	177.779i		−	0.527536i	−0.964586	−	0.263768i	$-0.915035\pi$
$337$		−	177.779i		−	0.527536i	0.964586	−	0.263768i	$-0.0849653\pi$
$338$	727.679			2.15290
$339$		−	97.0373i		−	0.286246i
$340$	−251.066			−0.738428
$341$		−	78.9605i		−	0.231556i
$342$		−	249.158i		−	0.728531i
$343$		−	18.5203i		−	0.0539949i
$344$			69.9759i			0.203418i
$345$	76.1977	−	107.481i	0.220863	−	0.311540i
$346$	−456.875			−1.32045
$347$	−413.847			−1.19264			−0.596321	−	0.802746i	$-0.703371\pi$
$347$	−413.847			−1.19264			−0.596321	+	0.802746i	$0.703371\pi$
$348$	309.473			0.889291
$349$	28.7100			0.0822637			0.0411319	−	0.999154i	$-0.486904\pi$
$349$	28.7100			0.0822637			0.0411319	+	0.999154i	$0.486904\pi$
$350$			99.2490i			0.283569i
$351$	109.216			0.311156
$352$		−	696.308i		−	1.97815i
$353$	−226.500			−0.641643			−0.320822	−	0.947140i	$-0.603959\pi$
$353$	−226.500			−0.641643			−0.320822	+	0.947140i	$0.603959\pi$
$354$	−228.132			−0.644442
$355$			230.981i			0.650651i
$356$			261.039i			0.733257i
$357$	−111.635			−0.312703
$358$	193.802			0.541347
$359$			186.105i			0.518398i	0.965824	+	0.259199i	$0.0834586\pi$
$359$			186.105i			0.518398i	−0.965824	+	0.259199i	$0.916541\pi$
$360$		−	23.3908i		−	0.0649745i
$361$	−608.293			−1.68502
$362$		−	158.506i		−	0.437862i
$363$	−299.920			−0.826225
$364$			173.294i			0.476083i
$365$			214.475i			0.587603i
$366$		−	52.0390i		−	0.142183i
$367$		−	9.64565i		−	0.0262824i	−0.999914	−	0.0131412i	$-0.995817\pi$
$367$		−	9.64565i		−	0.0262824i	0.999914	−	0.0131412i	$-0.00418310\pi$
$368$	351.885	+	249.465i	0.956210	+	0.677894i
$369$	−89.8338			−0.243452
$370$	136.533			0.369009
$371$	105.302			0.283834
$372$	−24.8491			−0.0667988
$373$			290.646i			0.779211i	0.920982	+	0.389606i	$0.127389\pi$
$373$			290.646i			0.779211i	−0.920982	+	0.389606i	$0.872611\pi$
$374$	−1114.57			−2.98013
$375$			223.760i			0.596694i
$376$	132.229			0.351673
$377$	1205.13			3.19664
$378$			36.6738i			0.0970207i
$379$		−	155.531i		−	0.410372i	−0.978723	−	0.205186i	$-0.934220\pi$
$379$		−	155.531i		−	0.410372i	0.978723	−	0.205186i	$-0.0657800\pi$
$380$	320.867			0.844386
$381$	92.7663			0.243481
$382$			902.962i			2.36378i
$383$			217.453i			0.567763i	0.958859	+	0.283882i	$0.0916223\pi$
$383$			217.453i			0.567763i	−0.958859	+	0.283882i	$0.908378\pi$
$384$	127.479			0.331976
$385$		−	150.074i		−	0.389803i
$386$	−662.448			−1.71619
$387$		−	89.0455i		−	0.230092i
$388$			388.800i			1.00206i
$389$		−	35.0187i		−	0.0900223i	−0.998986	−	0.0450112i	$-0.985668\pi$
$389$		−	35.0187i		−	0.0900223i	0.998986	−	0.0450112i	$-0.0143323\pi$
$390$			321.185i			0.823552i
$391$	324.045	−	457.085i	0.828760	−	1.16902i
$392$	16.5027			0.0420988
$393$	288.369			0.733764
$394$	860.886			2.18499
$395$	181.378			0.459186
$396$			160.341i			0.404900i
$397$	134.300			0.338286			0.169143	−	0.985591i	$-0.445900\pi$
$397$	134.300			0.338286			0.169143	+	0.985591i	$0.445900\pi$
$398$		−	590.889i		−	1.48465i
$399$	142.671			0.357573
$400$	−263.722			−0.659304
$401$			641.220i			1.59905i	0.600631	+	0.799526i	$0.294916\pi$
$401$			641.220i			1.59905i	−0.600631	+	0.799526i	$0.705084\pi$
$402$			48.8439i			0.121502i
$403$	−96.7660			−0.240114
$404$	−130.792			−0.323744
$405$			29.7652i			0.0734943i
$406$			404.674i			0.996735i
$407$	265.423			0.652144
$408$		−	99.4738i		−	0.243808i
$409$	−96.8273			−0.236742			−0.118371	−	0.992969i	$-0.537767\pi$
$409$	−96.8273			−0.236742			−0.118371	+	0.992969i	$0.537767\pi$
$410$		−	264.186i		−	0.644356i
$411$			39.0177i			0.0949335i
$412$			124.323i			0.301755i
$413$		−	130.632i		−	0.316300i
$414$	−150.160	−	106.454i	−0.362705	−	0.257135i
$415$	458.311			1.10436
$416$	−853.325			−2.05126
$417$	−222.802			−0.534298
$418$	1424.44			3.40775
$419$		−	500.242i		−	1.19390i	−0.802280	−	0.596948i	$-0.796380\pi$
$419$		−	500.242i		−	1.19390i	0.802280	−	0.596948i	$-0.203620\pi$
$420$	−47.2288			−0.112450
$421$			535.578i			1.27216i	0.771624	+	0.636079i	$0.219445\pi$
$421$			535.578i			1.27216i	−0.771624	+	0.636079i	$0.780555\pi$
$422$	−411.554			−0.975246
$423$	−168.264			−0.397786
$424$			93.8312i			0.221300i
$425$			342.564i			0.806033i
$426$	322.698			0.757508
$427$	29.7983			0.0697853
$428$		−	172.972i		−	0.404140i
$429$			624.389i			1.45545i
$430$	261.868			0.608995
$431$		−	656.357i		−	1.52287i	−0.648241	−	0.761435i	$-0.724495\pi$
$431$		−	656.357i		−	1.52287i	0.648241	−	0.761435i	$-0.275505\pi$
$432$	−97.4486			−0.225576
$433$			773.991i			1.78751i	0.448557	+	0.893754i	$0.351938\pi$
$433$			773.991i			1.78751i	−0.448557	+	0.893754i	$0.648062\pi$
$434$		−	32.4933i		−	0.0748693i
$435$			328.441i			0.755037i
$436$		−	144.434i		−	0.331270i
$437$	−414.136	+	584.164i	−0.947680	+	1.33676i
$438$	299.638			0.684106
$439$	526.837			1.20008			0.600042	−	0.799968i	$-0.295150\pi$
$439$	526.837			1.20008			0.600042	+	0.799968i	$0.295150\pi$
$440$	133.726			0.303922
$441$	−21.0000			−0.0476190
$442$			1365.90i			3.09027i
$443$	−241.984			−0.546240			−0.273120	−	0.961980i	$-0.588056\pi$
$443$	−241.984			−0.546240			−0.273120	+	0.961980i	$0.588056\pi$
$444$		−	83.5294i		−	0.188129i
$445$	−277.039			−0.622559
$446$	27.0729			0.0607016
$447$		−	404.291i		−	0.904455i
$448$		−	88.0663i		−	0.196577i
$449$	194.789			0.433828			0.216914	−	0.976191i	$-0.430401\pi$
$449$	194.789			0.433828			0.216914	+	0.976191i	$0.430401\pi$
$450$	112.538			0.250084
$451$		−	513.581i		−	1.13876i
$452$		−	174.586i		−	0.386252i
$453$	−167.575			−0.369922
$454$			110.882i			0.244235i
$455$	−183.916			−0.404210
$456$			127.129i			0.278793i
$457$			498.166i			1.09008i	0.838410	+	0.545040i	$0.183485\pi$
$457$			498.166i			1.09008i	−0.838410	+	0.545040i	$0.816515\pi$
$458$			971.199i			2.12052i
$459$			126.582i			0.275778i
$460$	137.092	−	193.377i	0.298027	−	0.420384i
$461$	−740.448			−1.60618			−0.803089	−	0.595860i	$-0.796811\pi$
$461$	−740.448			−1.60618			−0.803089	+	0.595860i	$0.796811\pi$
$462$	−209.665			−0.453820
$463$	152.783			0.329984			0.164992	−	0.986295i	$-0.447240\pi$
$463$	152.783			0.329984			0.164992	+	0.986295i	$0.447240\pi$
$464$	−1075.29			−2.31743
$465$		−	26.3722i		−	0.0567143i
$466$	−245.826			−0.527525
$467$		−	113.927i		−	0.243956i	−0.992533	−	0.121978i	$-0.961076\pi$
$467$		−	113.927i		−	0.243956i	0.992533	−	0.121978i	$-0.0389237\pi$
$468$	196.497			0.419866
$469$	−27.9688			−0.0596350
$470$		−	494.835i		−	1.05284i
$471$		−	471.368i		−	1.00078i
$472$	116.402			0.246613
$473$	509.074			1.07627
$474$		−	253.400i		−	0.534598i
$475$		−	437.804i		−	0.921692i
$476$	−200.849			−0.421952
$477$		−	119.402i		−	0.250318i
$478$	781.970			1.63592
$479$			493.979i			1.03127i	0.856808	+	0.515636i	$0.172444\pi$
$479$			493.979i			1.03127i	−0.856808	+	0.515636i	$0.827556\pi$
$480$		−	232.561i		−	0.484503i
$481$		−	325.275i		−	0.676248i
$482$		−	423.664i		−	0.878970i
$483$	60.9572	−	85.9838i	0.126205	−	0.178020i
$484$	−539.605			−1.11489
$485$	−412.630			−0.850784
$486$	41.5842			0.0855642
$487$	−734.795			−1.50882			−0.754410	−	0.656403i	$-0.772077\pi$
$487$	−734.795			−1.50882			−0.754410	+	0.656403i	$0.772077\pi$
$488$			26.5522i			0.0544103i
$489$	425.649			0.870448
$490$		−	61.7574i		−	0.126036i
$491$	−788.696			−1.60631			−0.803153	−	0.595773i	$-0.796846\pi$
$491$	−788.696			−1.60631			−0.803153	+	0.595773i	$0.796846\pi$
$492$	−161.626			−0.328507
$493$			1396.76i			2.83318i
$494$		−	1745.65i		−	3.53370i
$495$	−170.168			−0.343774
$496$	86.3402			0.174073
$497$			184.782i			0.371795i
$498$		−	640.295i		−	1.28573i
$499$	268.640			0.538356			0.269178	−	0.963090i	$-0.413248\pi$
$499$	268.640			0.538356			0.269178	+	0.963090i	$0.413248\pi$
$500$			402.581i			0.805162i
$501$	−134.718			−0.268899
$502$			754.139i			1.50227i
$503$		−	390.653i		−	0.776645i	−0.921523	−	0.388323i	$-0.873055\pi$
$503$		−	390.653i		−	0.776645i	0.921523	−	0.388323i	$-0.126945\pi$
$504$		−	18.7123i		−	0.0371277i
$505$		−	138.809i		−	0.274869i
$506$	608.600	−	858.466i	1.20277	−	1.69657i
$507$	472.471			0.931895
$508$	166.902			0.328547
$509$	−6.02049			−0.0118281			−0.00591404	−	0.999983i	$-0.501883\pi$
$509$	−6.02049			−0.0118281			−0.00591404	+	0.999983i	$0.501883\pi$
$510$	−372.256			−0.729914
$511$			171.578i			0.335768i
$512$	584.533			1.14167
$513$		−	161.774i		−	0.315349i
$514$	377.260			0.733969
$515$	−131.943			−0.256200
$516$		−	160.207i		−	0.310479i
$517$		−	961.966i		−	1.86067i
$518$	109.225			0.210859
$519$	−296.642			−0.571564
$520$		−	163.881i		−	0.315155i
$521$		−	334.884i		−	0.642771i	−0.946948	−	0.321386i	$-0.895851\pi$
$521$		−	334.884i		−	0.642771i	0.946948	−	0.321386i	$-0.104149\pi$
$522$	458.858			0.879037
$523$		−	793.375i		−	1.51697i	−0.651691	−	0.758484i	$-0.725940\pi$
$523$		−	793.375i		−	1.51697i	0.651691	−	0.758484i	$-0.274060\pi$
$524$	518.823			0.990121
$525$			64.4409i			0.122745i
$526$			969.658i			1.84346i
$527$		−	112.153i		−	0.212813i
$528$		−	557.116i		−	1.05514i
$529$	175.116	+	499.175i	0.331032	+	0.943620i
$530$	351.140			0.662528
$531$	−148.123			−0.278951
$532$	256.689			0.482499
$533$	−629.393			−1.18085
$534$			387.044i			0.724802i
$535$	183.573			0.343128
$536$		−	24.9220i		−	0.0464963i
$537$	125.833			0.234326
$538$	−1199.49			−2.22954
$539$		−	120.057i		−	0.222741i
$540$			53.5524i			0.0991712i
$541$	104.322			0.192832			0.0964162	−	0.995341i	$-0.469262\pi$
$541$	104.322			0.192832			0.0964162	+	0.995341i	$0.469262\pi$
$542$	−779.204			−1.43765
$543$		−	102.916i		−	0.189531i
$544$		−	989.010i		−	1.81803i
$545$	153.286			0.281259
$546$			256.944i			0.470594i
$547$	−7.79813			−0.0142562			−0.00712809	−	0.999975i	$-0.502269\pi$
$547$	−7.79813			−0.0142562			−0.00712809	+	0.999975i	$0.502269\pi$
$548$			70.1992i			0.128101i
$549$		−	33.7881i		−	0.0615448i
$550$			643.381i			1.16978i
$551$		−	1785.08i		−	3.23972i
$552$	76.6171	+	54.3168i	0.138799	+	0.0984000i
$553$	145.100			0.262388
$554$	517.487			0.934091
$555$	88.6490			0.159728
$556$	−400.858			−0.720968
$557$			259.779i			0.466390i	0.972430	+	0.233195i	$0.0749181\pi$
$557$			259.779i			0.466390i	−0.972430	+	0.233195i	$0.925082\pi$
$558$	−36.8439			−0.0660286
$559$		−	623.870i		−	1.11605i
$560$	164.100			0.293036
$561$	−723.672			−1.28997
$562$		−	845.452i		−	1.50436i
$563$		−	661.112i		−	1.17427i	−0.809490	−	0.587133i	$-0.800257\pi$
$563$		−	661.112i		−	1.17427i	0.809490	−	0.587133i	$-0.199743\pi$
$564$	−302.734			−0.536762
$565$	185.287			0.327941
$566$			185.853i			0.328362i
$567$			23.8118i			0.0419961i
$568$	−164.653			−0.289881
$569$		−	564.844i		−	0.992697i	−0.868123	−	0.496348i	$-0.834674\pi$
$569$		−	564.844i		−	0.992697i	0.868123	−	0.496348i	$-0.165326\pi$
$570$	475.751			0.834650
$571$		−	334.883i		−	0.586484i	−0.956038	−	0.293242i	$-0.905266\pi$
$571$		−	334.883i		−	0.586484i	0.956038	−	0.293242i	$-0.0947342\pi$
$572$			1123.38i			1.96395i
$573$			586.280i			1.02318i
$574$		−	211.345i		−	0.368198i
$575$	−263.851	−	187.054i	−0.458871	−	0.325312i
$576$	−99.8578			−0.173364
$577$	−597.995			−1.03639			−0.518193	−	0.855264i	$-0.673395\pi$
$577$	−597.995			−1.03639			−0.518193	+	0.855264i	$0.673395\pi$
$578$	−812.145			−1.40510
$579$	−430.117			−0.742862
$580$			590.920i			1.01883i
$581$	366.643			0.631054
$582$			576.476i			0.990508i
$583$	682.621			1.17088
$584$	−152.887			−0.261792
$585$			208.541i			0.356480i
$586$			896.568i			1.52998i
$587$	185.002			0.315166			0.157583	−	0.987506i	$-0.449630\pi$
$587$	185.002			0.315166			0.157583	+	0.987506i	$0.449630\pi$
$588$	−37.7824			−0.0642559
$589$			143.333i			0.243350i
$590$		−	435.604i		−	0.738312i
$591$	558.960			0.945787
$592$			290.229i			0.490252i
$593$	−251.997			−0.424953			−0.212477	−	0.977166i	$-0.568153\pi$
$593$	−251.997			−0.424953			−0.212477	+	0.977166i	$0.568153\pi$
$594$			237.738i			0.400232i
$595$		−	213.160i		−	0.358251i
$596$		−	727.386i		−	1.22045i
$597$		−	383.655i		−	0.642638i
$598$	−1052.05	−	745.838i	−1.75928	−	1.24722i
$599$	−874.357			−1.45970			−0.729848	−	0.683610i	$-0.760409\pi$
$599$	−874.357			−1.45970			−0.729848	+	0.683610i	$0.760409\pi$
$600$	−57.4210			−0.0957016
$601$	−595.195			−0.990341			−0.495170	−	0.868796i	$-0.664894\pi$
$601$	−595.195			−0.990341			−0.495170	+	0.868796i	$0.664894\pi$
$602$	209.491			0.347991
$603$			31.7136i			0.0525931i
$604$	−301.495			−0.499163
$605$		−	572.677i		−	0.946574i
$606$	−193.926			−0.320011
$607$	−650.911			−1.07234			−0.536171	−	0.844110i	$-0.680130\pi$
$607$	−650.911			−1.07234			−0.536171	+	0.844110i	$0.680130\pi$
$608$			1263.97i			2.07891i
$609$			262.749i			0.431443i
$610$	99.3651			0.162894
$611$	−1178.89			−1.92944
$612$			227.742i			0.372127i
$613$		−	966.710i		−	1.57701i	−0.615025	−	0.788507i	$-0.710854\pi$
$613$		−	966.710i		−	1.57701i	0.615025	−	0.788507i	$-0.289146\pi$
$614$	−1104.60			−1.79902
$615$		−	171.532i		−	0.278914i
$616$	106.979			0.173667
$617$		−	1169.78i		−	1.89592i	−0.318386	−	0.947961i	$-0.603141\pi$
$617$		−	1169.78i		−	1.89592i	0.318386	−	0.947961i	$-0.396859\pi$
$618$			184.334i			0.298275i
$619$		−	502.353i		−	0.811556i	−0.913972	−	0.405778i	$-0.867001\pi$
$619$		−	502.353i		−	0.811556i	0.913972	−	0.405778i	$-0.132999\pi$
$620$		−	47.4479i		−	0.0765288i
$621$	−97.4965	−	69.1190i	−0.156999	−	0.111303i
$622$	473.093			0.760599
$623$	−221.628			−0.355742
$624$	−682.744			−1.09414
$625$	−75.7020			−0.121123
$626$			306.631i			0.489827i
$627$	924.866			1.47507
$628$		−	848.068i		−	1.35043i
$629$	376.997			0.599359
$630$	−70.0264			−0.111153
$631$		−	983.032i		−	1.55789i	−0.627089	−	0.778947i	$-0.715754\pi$
$631$		−	983.032i		−	1.55789i	0.627089	−	0.778947i	$-0.284246\pi$
$632$			129.294i			0.204579i
$633$	−267.216			−0.422142
$634$	438.655			0.691885
$635$			177.131i			0.278947i
$636$		−	214.823i		−	0.337772i
$637$	−147.130			−0.230974
$638$			2623.30i			4.11175i
$639$	209.523			0.327892
$640$			243.412i			0.380332i
$641$		−	788.720i		−	1.23045i	−0.788350	−	0.615227i	$-0.789065\pi$
$641$		−	788.720i		−	1.23045i	0.788350	−	0.615227i	$-0.210935\pi$
$642$		−	256.466i		−	0.399480i
$643$			884.399i			1.37543i	0.725983	+	0.687713i	$0.241385\pi$
$643$			884.399i			1.37543i	−0.725983	+	0.687713i	$0.758615\pi$
$644$	109.672	−	154.699i	0.170298	−	0.240216i
$645$	170.027			0.263607
$646$	2023.22			3.13192
$647$	−303.858			−0.469642			−0.234821	−	0.972039i	$-0.575450\pi$
$647$	−303.858			−0.469642			−0.234821	+	0.972039i	$0.575450\pi$
$648$	−21.2178			−0.0327435
$649$		−	846.821i		−	1.30481i
$650$	788.462			1.21302
$651$		−	21.0974i		−	0.0324077i
$652$	765.812			1.17456
$653$	665.838			1.01966			0.509830	−	0.860275i	$-0.329708\pi$
$653$	665.838			1.01966			0.509830	+	0.860275i	$0.329708\pi$
$654$		−	214.153i		−	0.327451i
$655$			550.622i			0.840645i
$656$	561.581			0.856068
$657$	194.551			0.296120
$658$		−	395.861i		−	0.601613i
$659$			172.630i			0.261958i	0.991385	+	0.130979i	$0.0418120\pi$
$659$			172.630i			0.261958i	−0.991385	+	0.130979i	$0.958188\pi$
$660$	−306.160			−0.463879
$661$		−	602.867i		−	0.912053i	−0.889966	−	0.456027i	$-0.849272\pi$
$661$		−	602.867i		−	0.912053i	0.889966	−	0.456027i	$-0.150728\pi$
$662$	689.246			1.04116
$663$			886.858i			1.33764i
$664$			326.702i			0.492021i
$665$			272.422i			0.409657i
$666$		−	123.849i		−	0.185960i
$667$	−1075.82	−	762.688i	−1.61292	−	1.14346i
$668$	−242.381			−0.362845
$669$	17.5780			0.0262751
$670$	−93.2644			−0.139201
$671$	193.167			0.287880
$672$		−	186.046i		−	0.276854i
$673$	−1222.90			−1.81709			−0.908546	−	0.417785i	$-0.862806\pi$
$673$	−1222.90			−1.81709			−0.908546	+	0.417785i	$0.862806\pi$
$674$		−	474.250i		−	0.703634i
$675$	73.0691			0.108251
$676$	850.052			1.25747
$677$			1157.48i			1.70972i	0.518855	+	0.854862i	$0.326358\pi$
$677$			1157.48i			1.70972i	−0.518855	+	0.854862i	$0.673642\pi$
$678$		−	258.859i		−	0.381799i
$679$	−330.099			−0.486155
$680$	189.939			0.279322
$681$			71.9943i			0.105719i
$682$		−	210.637i		−	0.308853i
$683$	462.003			0.676432			0.338216	−	0.941068i	$-0.390176\pi$
$683$	462.003			0.676432			0.338216	+	0.941068i	$0.390176\pi$
$684$		−	291.058i		−	0.425524i
$685$	−74.5018			−0.108762
$686$		−	49.4052i		−	0.0720192i
$687$			630.585i			0.917882i
$688$			556.653i			0.809088i
$689$		−	836.551i		−	1.21415i
$690$	203.267	−	286.721i	0.294590	−	0.415537i
$691$	5.66096			0.00819241			0.00409621	−	0.999992i	$-0.498696\pi$
$691$	5.66096			0.00819241			0.00409621	+	0.999992i	$0.498696\pi$
$692$	−533.707			−0.771254
$693$	−136.132			−0.196439
$694$	−1103.99			−1.59076
$695$		−	425.427i		−	0.612125i
$696$	−234.126			−0.336388
$697$		−	729.472i		−	1.04659i
$698$	76.5877			0.109725
$699$	−159.611			−0.228342
$700$			115.940i			0.165628i
$701$			525.141i			0.749132i	0.927200	+	0.374566i	$0.122208\pi$
$701$			525.141i			0.749132i	−0.927200	+	0.374566i	$0.877792\pi$
$702$	291.347			0.415024
$703$	−481.809			−0.685361
$704$		−	570.889i		−	0.810921i
$705$		−	321.289i		−	0.455728i
$706$	−604.218			−0.855833
$707$		−	111.045i		−	0.157065i
$708$	−266.497			−0.376409
$709$			505.452i			0.712908i	0.934313	+	0.356454i	$0.116014\pi$
$709$			505.452i			0.712908i	−0.934313	+	0.356454i	$0.883986\pi$
$710$			616.172i			0.867848i
$711$		−	164.528i		−	0.231404i
$712$		−	197.484i		−	0.277366i
$713$	86.3826	+	61.2400i	0.121154	+	0.0858905i
$714$	−297.800			−0.417087
$715$	−1192.23			−1.66746
$716$	226.394			0.316193
$717$	507.721			0.708119
$718$			496.459i			0.691447i
$719$	−417.257			−0.580329			−0.290165	−	0.956977i	$-0.593710\pi$
$719$	−417.257			−0.580329			−0.290165	+	0.956977i	$0.593710\pi$
$720$		−	186.072i		−	0.258433i
$721$	−105.553			−0.146398
$722$	−1622.70			−2.24751
$723$		−	275.078i		−	0.380468i
$724$		−	185.162i		−	0.255749i
$725$	806.275			1.11210
$726$	−800.074			−1.10203
$727$			720.650i			0.991266i	0.868532	+	0.495633i	$0.165064\pi$
$727$			720.650i			0.991266i	−0.868532	+	0.495633i	$0.834936\pi$
$728$		−	131.102i		−	0.180086i
$729$	27.0000			0.0370370
$730$			572.140i			0.783754i
$731$	723.070			0.989152
$732$		−	60.7903i		−	0.0830469i
$733$			635.738i			0.867310i	0.901079	+	0.433655i	$0.142776\pi$
$733$			635.738i			0.867310i	−0.901079	+	0.433655i	$0.857224\pi$
$734$		−	25.7310i		−	0.0350559i
$735$		−	40.0982i		−	0.0545553i
$736$	761.759	+	540.041i	1.03500	+	0.733751i
$737$	−181.307			−0.246007
$738$	−239.643			−0.324720
$739$	−218.765			−0.296029			−0.148014	−	0.988985i	$-0.547288\pi$
$739$	−218.765			−0.296029			−0.148014	+	0.988985i	$0.547288\pi$
$740$	159.494			0.215533
$741$		−	1133.42i		−	1.52958i
$742$	280.908			0.378582
$743$			653.288i			0.879257i	0.898180	+	0.439629i	$0.144890\pi$
$743$			653.288i			0.879257i	−0.898180	+	0.439629i	$0.855110\pi$
$744$	18.7991			0.0252677
$745$	771.969			1.03620
$746$			775.335i			1.03932i
$747$		−	415.734i		−	0.556538i
$748$	−1302.00			−1.74065
$749$	146.856			0.196070
$750$			596.909i			0.795879i
$751$			669.748i			0.891808i	0.895081	+	0.445904i	$0.147118\pi$
$751$			669.748i			0.891808i	−0.895081	+	0.445904i	$0.852882\pi$
$752$	1051.87			1.39877
$753$			489.651i			0.650267i
$754$	3214.85			4.26372
$755$		−	319.973i		−	0.423806i
$756$			42.8413i			0.0566683i
$757$		−	236.104i		−	0.311895i	−0.987765	−	0.155947i	$-0.950157\pi$
$757$		−	236.104i		−	0.311895i	0.987765	−	0.155947i	$-0.0498430\pi$
$758$		−	414.899i		−	0.547361i
$759$	395.155	−	557.389i	0.520625	−	0.734373i
$760$	−242.746			−0.319402
$761$	392.505			0.515775			0.257887	−	0.966175i	$-0.416974\pi$
$761$	392.505			0.515775			0.257887	+	0.966175i	$0.416974\pi$
$762$	247.466			0.324758
$763$	122.627			0.160717
$764$			1054.81i			1.38065i
$765$	−241.700			−0.315948
$766$			580.085i			0.757291i
$767$	−1037.78			−1.35303
$768$	570.677			0.743069
$769$			69.1111i			0.0898714i	0.998990	+	0.0449357i	$0.0143083\pi$
$769$			69.1111i			0.0898714i	−0.998990	+	0.0449357i	$0.985692\pi$
$770$		−	400.342i		−	0.519925i
$771$	244.949			0.317703
$772$	−773.851			−1.00240
$773$			275.781i			0.356767i	0.983961	+	0.178383i	$0.0570867\pi$
$773$			275.781i			0.356767i	−0.983961	+	0.178383i	$0.942913\pi$
$774$		−	237.540i		−	0.306900i
$775$	−64.7398			−0.0835352
$776$		−	294.139i		−	0.379046i
$777$	70.9181			0.0912717
$778$		−	93.4168i		−	0.120073i
$779$			932.279i			1.19676i
$780$			375.199i			0.481024i
$781$			1197.85i			1.53374i
$782$	864.432	−	1219.33i	1.10541	−	1.55925i
$783$	297.929			0.380497
$784$	131.278			0.167446
$785$	900.047			1.14656
$786$	769.262			0.978704
$787$		−	538.317i		−	0.684011i	−0.939698	−	0.342005i	$-0.888894\pi$
$787$		−	538.317i		−	0.684011i	0.939698	−	0.342005i	$-0.111106\pi$
$788$	1005.66			1.27622
$789$			629.584i			0.797952i
$790$	483.850			0.612469
$791$	148.227			0.187392
$792$		−	121.303i		−	0.153160i
$793$		−	236.726i		−	0.298520i
$794$	358.262			0.451211
$795$	227.990			0.286780
$796$		−	690.259i		−	0.867159i
$797$		−	740.010i		−	0.928494i	−0.885706	−	0.464247i	$-0.846325\pi$
$797$		−	740.010i		−	0.928494i	0.885706	−	0.464247i	$-0.153675\pi$
$798$	380.595			0.476936
$799$		−	1366.34i		−	1.71006i
$800$	−570.903			−0.713629
$801$			251.302i			0.313735i
$802$			1710.54i			2.13284i
$803$			1112.25i			1.38512i
$804$			57.0580i			0.0709677i
$805$	164.181	+	116.394i	0.203951	+	0.144589i
$806$	−258.136			−0.320268
$807$	−778.814			−0.965073
$808$	98.9485			0.122461
$809$	−88.7120			−0.109656			−0.0548282	−	0.998496i	$-0.517461\pi$
$809$	−88.7120			−0.109656			−0.0548282	+	0.998496i	$0.517461\pi$
$810$			79.4024i			0.0980277i
$811$	−436.124			−0.537761			−0.268881	−	0.963174i	$-0.586654\pi$
$811$	−436.124			−0.537761			−0.268881	+	0.963174i	$0.586654\pi$
$812$			472.728i			0.582178i
$813$	−505.925			−0.622294
$814$	708.050			0.869840
$815$			812.750i			0.997239i
$816$		−	791.306i		−	0.969738i
$817$	−924.098			−1.13109
$818$	−258.299			−0.315769
$819$			166.830i			0.203699i
$820$		−	308.614i		−	0.376359i
$821$	−568.009			−0.691850			−0.345925	−	0.938262i	$-0.612435\pi$
$821$	−568.009			−0.691850			−0.345925	+	0.938262i	$0.612435\pi$
$822$			104.085i			0.126624i
$823$	−911.468			−1.10749			−0.553747	−	0.832685i	$-0.686803\pi$
$823$	−911.468			−1.10749			−0.553747	+	0.832685i	$0.686803\pi$
$824$		−	94.0542i		−	0.114143i
$825$			417.737i			0.506348i
$826$		−	348.478i		−	0.421886i
$827$		−	1370.09i		−	1.65670i	−0.560212	−	0.828350i	$-0.689280\pi$
$827$		−	1370.09i		−	1.65670i	0.560212	−	0.828350i	$-0.310720\pi$
$828$	−175.412	−	124.356i	−0.211850	−	0.150189i
$829$	−622.156			−0.750489			−0.375245	−	0.926926i	$-0.622441\pi$
$829$	−622.156			−0.750489			−0.375245	+	0.926926i	$0.622441\pi$
$830$	1222.60			1.47301
$831$	335.996			0.404328
$832$	−699.623			−0.840893
$833$		−	170.525i		−	0.204712i
$834$	−594.354			−0.712655
$835$		−	257.236i		−	0.308067i
$836$	1663.99			1.99041
$837$	−23.9222			−0.0285809
$838$		−	1334.46i		−	1.59243i
$839$		−	27.8410i		−	0.0331836i	−0.999862	−	0.0165918i	$-0.994718\pi$
$839$		−	27.8410i		−	0.0331836i	0.999862	−	0.0165918i	$-0.00528158\pi$
$840$	35.7300			0.0425358
$841$	2446.47			2.90901
$842$			1428.72i			1.69682i
$843$		−	548.939i		−	0.651174i
$844$	−480.765			−0.569627
$845$			902.153i			1.06764i
$846$	−448.865			−0.530573
$847$		−	458.135i		−	0.540891i
$848$			746.420i			0.880212i
$849$			120.671i			0.142133i
$850$			913.834i			1.07510i
$851$	−205.856	+	290.372i	−0.241899	+	0.341212i
$852$	376.966			0.442449
$853$	1449.97			1.69984			0.849922	−	0.526909i	$-0.176649\pi$
$853$	1449.97			1.69984			0.849922	+	0.526909i	$0.176649\pi$
$854$	79.4908			0.0930806
$855$	308.898			0.361284
$856$			130.859i			0.152872i
$857$	863.288			1.00734			0.503669	−	0.863897i	$-0.331983\pi$
$857$	863.288			1.00734			0.503669	+	0.863897i	$0.331983\pi$
$858$			1665.64i			1.94130i
$859$	−540.665			−0.629412			−0.314706	−	0.949189i	$-0.601906\pi$
$859$	−540.665			−0.629412			−0.314706	+	0.949189i	$0.601906\pi$
$860$	305.906			0.355705
$861$		−	137.223i		−	0.159377i
$862$		−	1750.92i		−	2.03123i
$863$	−759.238			−0.879766			−0.439883	−	0.898055i	$-0.644980\pi$
$863$	−759.238			−0.879766			−0.439883	+	0.898055i	$0.644980\pi$
$864$	−210.956			−0.244162
$865$		−	566.419i		−	0.654820i
$866$			2064.72i			2.38420i
$867$	−527.313			−0.608205
$868$		−	37.9577i		−	0.0437301i
$869$	940.612			1.08241
$870$			876.159i			1.00708i
$871$			222.192i			0.255100i
$872$			109.269i			0.125308i
$873$			374.297i			0.428748i
$874$	−1104.76	+	1558.33i	−1.26403	+	1.78299i
$875$	−341.799			−0.390628
$876$	350.028			0.399576
$877$	−1172.25			−1.33666			−0.668331	−	0.743864i	$-0.732991\pi$
$877$	−1172.25			−1.33666			−0.668331	+	0.743864i	$0.732991\pi$
$878$	1405.41			1.60069
$879$			582.128i			0.662261i
$880$	1063.78			1.20884
$881$			790.744i			0.897553i	0.893644	+	0.448776i	$0.148140\pi$
$881$			790.744i			0.897553i	−0.893644	+	0.448776i	$0.851860\pi$
$882$	−56.0202			−0.0635150
$883$	911.520			1.03230			0.516149	−	0.856499i	$-0.327365\pi$
$883$	911.520			1.03230			0.516149	+	0.856499i	$0.327365\pi$
$884$			1595.60i			1.80498i
$885$		−	282.831i		−	0.319583i
$886$	−645.524			−0.728583
$887$	906.065			1.02149			0.510747	−	0.859731i	$-0.329369\pi$
$887$	906.065			1.02149			0.510747	+	0.859731i	$0.329369\pi$
$888$			63.1926i			0.0711628i
$889$			141.703i			0.159396i
$890$	−739.037			−0.830378
$891$			154.359i			0.173243i
$892$	31.6258			0.0354549
$893$			1746.21i			1.95544i
$894$		−	1078.50i		−	1.20637i
$895$			240.270i			0.268458i
$896$			194.727i			0.217329i
$897$	−683.080	−	484.261i	−0.761516	−	0.539868i
$898$	519.625			0.578647
$899$	−263.968			−0.293624
$900$	131.463			0.146070
$901$	969.570			1.07610
$902$		−	1370.04i		−	1.51890i
$903$	136.019			0.150630
$904$			132.080i			0.146106i
$905$	196.511			0.217139
$906$	−447.027			−0.493408
$907$		−	1143.69i		−	1.26096i	−0.776204	−	0.630482i	$-0.782857\pi$
$907$		−	1143.69i		−	1.26096i	0.776204	−	0.630482i	$-0.217143\pi$
$908$			129.530i			0.142654i
$909$	−125.914			−0.138519
$910$	−490.618			−0.539141
$911$			1598.63i			1.75481i	0.479754	+	0.877403i	$0.340726\pi$
$911$			1598.63i			1.75481i	−0.479754	+	0.877403i	$0.659274\pi$
$912$			1011.30i			1.10889i
$913$	2376.76			2.60324
$914$			1328.92i			1.45396i
$915$	64.5163			0.0705096
$916$			1134.53i			1.23857i
$917$			440.491i			0.480361i
$918$			337.674i			0.367836i
$919$		−	68.1826i		−	0.0741922i	−0.999312	−	0.0370961i	$-0.988189\pi$
$919$		−	68.1826i		−	0.0741922i	0.999312	−	0.0370961i	$-0.0118108\pi$
$920$	−103.714	+	146.296i	−0.112733	+	0.159017i
$921$	−717.198			−0.778716
$922$	−1975.24			−2.14234
$923$	1467.96			1.59042
$924$	−244.924			−0.265070
$925$		−	217.620i		−	0.235265i
$926$	407.568			0.440138
$927$			119.685i			0.129110i
$928$	−2327.78			−2.50838
$929$	−760.307			−0.818414			−0.409207	−	0.912442i	$-0.634195\pi$
$929$	−760.307			−0.818414			−0.409207	+	0.912442i	$0.634195\pi$
$930$		−	70.3512i		−	0.0756464i
$931$			217.934i			0.234086i
$932$	−287.167			−0.308119
$933$	307.172			0.329230
$934$		−	303.916i		−	0.325392i
$935$		−	1381.81i		−	1.47787i
$936$	−148.656			−0.158821
$937$			24.3750i			0.0260139i	0.999915	+	0.0130070i	$0.00414036\pi$
$937$			24.3750i			0.0260139i	−0.999915	+	0.0130070i	$0.995860\pi$
$938$	−74.6104			−0.0795420
$939$			199.091i			0.212025i
$940$		−	578.051i		−	0.614948i
$941$			19.0976i			0.0202950i	0.999949	+	0.0101475i	$0.00323010\pi$
$941$			19.0976i			0.0202950i	−0.999949	+	0.0101475i	$0.996770\pi$
$942$		−	1257.43i		−	1.33486i
$943$	561.857	+	398.322i	0.595818	+	0.422398i
$944$	925.965			0.980895
$945$	−45.4671			−0.0481133
$946$	1358.02			1.43554
$947$	−1001.13			−1.05716			−0.528578	−	0.848885i	$-0.677275\pi$
$947$	−1001.13			−1.05716			−0.528578	+	0.848885i	$0.677275\pi$
$948$		−	296.014i		−	0.312251i
$949$	1363.06			1.43631
$950$		−	1167.90i		−	1.22937i
$951$	284.812			0.299487
$952$	151.949			0.159610
$953$		−	1248.05i		−	1.30960i	−0.755801	−	0.654801i	$-0.772752\pi$
$953$		−	1248.05i		−	1.30960i	0.755801	−	0.654801i	$-0.227248\pi$
$954$		−	318.519i		−	0.333878i
$955$	−1119.46			−1.17221
$956$	913.474			0.955517
$957$			1703.27i			1.77980i
$958$			1317.75i			1.37552i
$959$	−59.6005			−0.0621486
$960$		−	190.672i		−	0.198617i
$961$	−939.805			−0.977945
$962$		−	867.714i		−	0.901989i
$963$		−	166.520i		−	0.172918i
$964$		−	494.911i		−	0.513393i
$965$		−	821.281i		−	0.851069i
$966$	162.611	−	229.373i	0.168335	−	0.237446i
$967$	783.250			0.809980			0.404990	−	0.914321i	$-0.367275\pi$
$967$	783.250			0.809980			0.404990	+	0.914321i	$0.367275\pi$
$968$	408.227			0.421723
$969$	1313.65			1.35567
$970$	−1100.74			−1.13479
$971$		−	315.064i		−	0.324474i	−0.986752	−	0.162237i	$-0.948129\pi$
$971$		−	315.064i		−	0.324474i	0.986752	−	0.162237i	$-0.0518709\pi$
$972$	48.5774			0.0499768
$973$		−	340.336i		−	0.349780i
$974$	−1960.16			−2.01249
$975$	511.936			0.525063
$976$			211.221i			0.216415i
$977$		−	90.4011i		−	0.0925292i	−0.998929	−	0.0462646i	$-0.985268\pi$
$977$		−	90.4011i		−	0.0925292i	0.998929	−	0.0462646i	$-0.0147317\pi$
$978$	1135.47			1.16102
$979$	−1436.70			−1.46752
$980$		−	72.1432i		−	0.0736155i
$981$		−	139.046i		−	0.141739i
$982$	−2103.95			−2.14251
$983$			804.697i			0.818613i	0.912397	+	0.409307i	$0.134229\pi$
$983$			804.697i			0.818613i	−0.912397	+	0.409307i	$0.865771\pi$
$984$	122.275			0.124263
$985$			1067.30i			1.08355i
$986$			3726.03i			3.77894i
$987$		−	257.027i		−	0.260412i
$988$		−	2039.21i		−	2.06398i
$989$	−394.826	+	556.926i	−0.399218	+	0.563120i
$990$	−453.945			−0.458530
$991$	238.112			0.240275			0.120137	−	0.992757i	$-0.461667\pi$
$991$	238.112			0.240275			0.120137	+	0.992757i	$0.461667\pi$
$992$	186.909			0.188416
$993$	447.517			0.450672
$994$			492.930i			0.495905i
$995$	732.565			0.736246
$996$		−	747.973i		−	0.750977i
$997$	1291.91			1.29580			0.647898	−	0.761727i	$-0.275648\pi$
$997$	1291.91			1.29580			0.647898	+	0.761727i	$0.275648\pi$
$998$	716.631			0.718067
$999$		−	80.4136i		−	0.0804941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.3.f.a.22.38	yes	48
23.22	odd	2	inner	483.3.f.a.22.37	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.3.f.a.22.37	✓	48	23.22	odd	2	inner
483.3.f.a.22.38	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	483.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.66763 q^{2} +1.73205 q^{3} +3.11624 q^{4} +3.30724i q^{5} +4.62047 q^{6} +2.64575i q^{7} -2.35753 q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+2.66763 q^{2} +1.73205 q^{3} +3.11624 q^{4} +3.30724i q^{5} +4.62047 q^{6} +2.64575i q^{7} -2.35753 q^{8} +3.00000 q^{9} +8.82249i q^{10} +17.1511i q^{11} +5.39749 q^{12} +21.0186 q^{13} +7.05788i q^{14} +5.72831i q^{15} -18.7540 q^{16} +24.3607i q^{17} +8.00289 q^{18} -31.1335i q^{19} +10.3062i q^{20} +4.58258i q^{21} +45.7526i q^{22} +(-18.7632 - 13.3020i) q^{23} -4.08337 q^{24} +14.0622 q^{25} +56.0698 q^{26} +5.19615 q^{27} +8.24481i q^{28} +57.3365 q^{29} +15.2810i q^{30} -4.60383 q^{31} -40.5986 q^{32} +29.7065i q^{33} +64.9854i q^{34} -8.75014 q^{35} +9.34873 q^{36} -15.4756i q^{37} -83.0525i q^{38} +36.4053 q^{39} -7.79693i q^{40} -29.9446 q^{41} +12.2246i q^{42} -29.6818i q^{43} +53.4469i q^{44} +9.92172i q^{45} +(-50.0533 - 35.4847i) q^{46} -56.0878 q^{47} -32.4829 q^{48} -7.00000 q^{49} +37.5126 q^{50} +42.1940i q^{51} +65.4990 q^{52} -39.8005i q^{53} +13.8614 q^{54} -56.7227 q^{55} -6.23745i q^{56} -53.9248i q^{57} +152.953 q^{58} -49.3743 q^{59} +17.8508i q^{60} -11.2627i q^{61} -12.2813 q^{62} +7.93725i q^{63} -33.2859 q^{64} +69.5135i q^{65} +79.2459i q^{66} +10.5712i q^{67} +75.9139i q^{68} +(-32.4988 - 23.0397i) q^{69} -23.3421 q^{70} +69.8410 q^{71} -7.07260 q^{72} +64.8502 q^{73} -41.2831i q^{74} +24.3564 q^{75} -97.0195i q^{76} -45.3774 q^{77} +97.1157 q^{78} -54.8428i q^{79} -62.0240i q^{80} +9.00000 q^{81} -79.8811 q^{82} -138.578i q^{83} +14.2804i q^{84} -80.5668 q^{85} -79.1801i q^{86} +99.3097 q^{87} -40.4342i q^{88} +83.7673i q^{89} +26.4675i q^{90} +55.6100i q^{91} +(-58.4707 - 41.4521i) q^{92} -7.97407 q^{93} -149.622 q^{94} +102.966 q^{95} -70.3188 q^{96} +124.766i q^{97} -18.6734 q^{98} +51.4532i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9}+O(q^{10}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9	\( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36} + 96 q^{39} - 24 q^{41} - 148 q^{46} - 408 q^{47} - 96 q^{48} - 336 q^{49} + 236 q^{50} - 32 q^{52} - 72 q^{54} - 24 q^{55} - 56 q^{58} + 136 q^{59} + 184 q^{62} + 716 q^{64} - 48 q^{69} - 112 q^{70} + 48 q^{71} - 12 q^{72} - 224 q^{73} - 48 q^{75} + 224 q^{77} - 96 q^{78} + 432 q^{81} + 640 q^{82} - 424 q^{85} + 312 q^{87} + 1060 q^{92} + 192 q^{93} + 216 q^{94} + 624 q^{95} + 48 q^{96} - 28 q^{98}+O(q^{100}) \) 48 * q + 4 * q^2 + 116 * q^4 - 24 * q^6 - 4 * q^8 + 144 * q^9 + 16 * q^13 + 324 * q^16 + 12 * q^18 - 4 * q^23 - 24 * q^24 - 176 * q^25 + 136 * q^26 - 128 * q^29 - 8 * q^31 - 252 * q^32 - 56 * q^35 + 348 * q^36 + 96 * q^39 - 24 * q^41 - 148 * q^46 - 408 * q^47 - 96 * q^48 - 336 * q^49 + 236 * q^50 - 32 * q^52 - 72 * q^54 - 24 * q^55 - 56 * q^58 + 136 * q^59 + 184 * q^62 + 716 * q^64 - 48 * q^69 - 112 * q^70 + 48 * q^71 - 12 * q^72 - 224 * q^73 - 48 * q^75 + 224 * q^77 - 96 * q^78 + 432 * q^81 + 640 * q^82 - 424 * q^85 + 312 * q^87 + 1060 * q^92 + 192 * q^93 + 216 * q^94 + 624 * q^95 + 48 * q^96 - 28 * q^98

Introduction

L-functions

Modular forms

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