LMFDB - Embedded newform 1617.2.c.a.538.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(538,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1617.538");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.c (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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			538.1
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.a.538.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58645i q^{2} -1.00000i q^{3} -4.68975 q^{4} +1.50244i q^{5} -2.58645 q^{6} +6.95692i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.58645i q^{2} -1.00000i q^{3} -4.68975 q^{4} +1.50244i q^{5} -2.58645 q^{6} +6.95692i q^{8} -1.00000 q^{9} +3.88599 q^{10} +(-0.276211 + 3.30510i) q^{11} +4.68975i q^{12} +3.99370 q^{13} +1.50244 q^{15} +8.61425 q^{16} +2.76378 q^{17} +2.58645i q^{18} -4.91754 q^{19} -7.04606i q^{20} +(8.54850 + 0.714407i) q^{22} -0.0719444 q^{23} +6.95692 q^{24} +2.74268 q^{25} -10.3295i q^{26} +1.00000i q^{27} -5.06315i q^{29} -3.88599i q^{30} -10.2165i q^{31} -8.36654i q^{32} +(3.30510 + 0.276211i) q^{33} -7.14840i q^{34} +4.68975 q^{36} +7.81594 q^{37} +12.7190i q^{38} -3.99370i q^{39} -10.4523 q^{40} +2.98366 q^{41} +5.41033i q^{43} +(1.29536 - 15.5001i) q^{44} -1.50244i q^{45} +0.186081i q^{46} -5.18095i q^{47} -8.61425i q^{48} -7.09381i q^{50} -2.76378i q^{51} -18.7294 q^{52} +12.4643 q^{53} +2.58645 q^{54} +(-4.96572 - 0.414990i) q^{55} +4.91754i q^{57} -13.0956 q^{58} -6.37801i q^{59} -7.04606 q^{60} +1.37752 q^{61} -26.4246 q^{62} -4.41117 q^{64} +6.00028i q^{65} +(0.714407 - 8.54850i) q^{66} -4.55337 q^{67} -12.9614 q^{68} +0.0719444i q^{69} +9.59452 q^{71} -6.95692i q^{72} -8.96093 q^{73} -20.2156i q^{74} -2.74268i q^{75} +23.0620 q^{76} -10.3295 q^{78} +11.6546i q^{79} +12.9424i q^{80} +1.00000 q^{81} -7.71709i q^{82} +9.34449 q^{83} +4.15242i q^{85} +13.9936 q^{86} -5.06315 q^{87} +(-22.9933 - 1.92158i) q^{88} +13.6127i q^{89} -3.88599 q^{90} +0.337401 q^{92} -10.2165 q^{93} -13.4003 q^{94} -7.38830i q^{95} -8.36654 q^{96} -2.63550i q^{97} +(0.276211 - 3.30510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 24 * q^4 - 32 * q^9	$ 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) $ 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1617\mathbb{Z}\right)^\times$.

$n$	$199$	$442$	$1079$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	2.58645i		−	1.82890i	−0.404699	−	0.914450i	$-0.632624\pi$
$2$		−	2.58645i		−	1.82890i	0.404699	−	0.914450i	$-0.367376\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−4.68975			−2.34487
$5$			1.50244i			0.671911i	0.941878	+	0.335956i	$0.109059\pi$
$5$			1.50244i			0.671911i	−0.941878	+	0.335956i	$0.890941\pi$
$6$	−2.58645			−1.05592
$7$		0			0
$7$		0			0
$8$			6.95692i			2.45964i
$9$	−1.00000			−0.333333
$10$	3.88599			1.22886
$11$	−0.276211	+	3.30510i	−0.0832808	+	0.996526i
$11$	−0.276211	+	3.30510i	−0.0832808	+	0.996526i
$12$			4.68975i			1.35381i
$13$	3.99370			1.10765			0.553826	−	0.832632i	$-0.313167\pi$
$13$	3.99370			1.10765			0.553826	+	0.832632i	$0.313167\pi$
$14$		0			0
$15$	1.50244			0.387928
$16$	8.61425			2.15356
$17$	2.76378			0.670316			0.335158	−	0.942162i	$-0.391210\pi$
$17$	2.76378			0.670316			0.335158	+	0.942162i	$0.391210\pi$
$18$			2.58645i			0.609633i
$19$	−4.91754			−1.12816			−0.564080	−	0.825720i	$-0.690769\pi$
$19$	−4.91754			−1.12816			−0.564080	+	0.825720i	$0.690769\pi$
$20$		−	7.04606i		−	1.57555i
$21$		0			0
$22$	8.54850	+	0.714407i	1.82255	+	0.152312i
$23$	−0.0719444			−0.0150014			−0.00750072	−	0.999972i	$-0.502388\pi$
$23$	−0.0719444			−0.0150014			−0.00750072	+	0.999972i	$0.502388\pi$
$24$	6.95692			1.42007
$25$	2.74268			0.548535
$26$		−	10.3295i		−	2.02578i
$27$			1.00000i			0.192450i
$28$		0			0
$29$		−	5.06315i		−	0.940204i	−0.882612	−	0.470102i	$-0.844217\pi$
$29$		−	5.06315i		−	0.940204i	0.882612	−	0.470102i	$-0.155783\pi$
$30$		−	3.88599i		−	0.709482i
$31$		−	10.2165i		−	1.83495i	−0.397797	−	0.917473i	$-0.630225\pi$
$31$		−	10.2165i		−	1.83495i	0.397797	−	0.917473i	$-0.369775\pi$
$32$		−	8.36654i		−	1.47901i
$33$	3.30510	+	0.276211i	0.575345	+	0.0480822i
$34$		−	7.14840i		−	1.22594i
$35$		0			0
$36$	4.68975			0.781625
$37$	7.81594			1.28493			0.642467	−	0.766314i	$-0.277911\pi$
$37$	7.81594			1.28493			0.642467	+	0.766314i	$0.277911\pi$
$38$			12.7190i			2.06329i
$39$		−	3.99370i		−	0.639503i
$40$	−10.4523			−1.65266
$41$	2.98366			0.465969			0.232984	−	0.972480i	$-0.425151\pi$
$41$	2.98366			0.465969			0.232984	+	0.972480i	$0.425151\pi$
$42$		0			0
$43$			5.41033i			0.825068i	0.910942	+	0.412534i	$0.135356\pi$
$43$			5.41033i			0.825068i	−0.910942	+	0.412534i	$0.864644\pi$
$44$	1.29536	−	15.5001i	0.195283	−	2.33673i
$45$		−	1.50244i		−	0.223970i
$46$			0.186081i			0.0274361i
$47$		−	5.18095i		−	0.755719i	−0.925863	−	0.377860i	$-0.876660\pi$
$47$		−	5.18095i		−	0.755719i	0.925863	−	0.377860i	$-0.123340\pi$
$48$		−	8.61425i		−	1.24336i
$49$		0			0
$50$		−	7.09381i		−	1.00322i
$51$		−	2.76378i		−	0.387007i
$52$	−18.7294			−2.59731
$53$	12.4643			1.71210			0.856052	−	0.516890i	$-0.172910\pi$
$53$	12.4643			1.71210			0.856052	+	0.516890i	$0.172910\pi$
$54$	2.58645			0.351972
$55$	−4.96572	−	0.414990i	−0.669577	−	0.0559573i
$56$		0			0
$57$			4.91754i			0.651344i
$58$	−13.0956			−1.71954
$59$		−	6.37801i		−	0.830347i	−0.909742	−	0.415173i	$-0.863721\pi$
$59$		−	6.37801i		−	0.830347i	0.909742	−	0.415173i	$-0.136279\pi$
$60$	−7.04606			−0.909643
$61$	1.37752			0.176373			0.0881865	−	0.996104i	$-0.471893\pi$
$61$	1.37752			0.176373			0.0881865	+	0.996104i	$0.471893\pi$
$62$	−26.4246			−3.35593
$63$		0			0
$64$	−4.41117			−0.551397
$65$			6.00028i			0.744244i
$66$	0.714407	−	8.54850i	0.0879375	−	1.05225i
$67$	−4.55337			−0.556283			−0.278142	−	0.960540i	$-0.589718\pi$
$67$	−4.55337			−0.556283			−0.278142	+	0.960540i	$0.589718\pi$
$68$	−12.9614			−1.57181
$69$			0.0719444i			0.00866108i
$70$		0			0
$71$	9.59452			1.13866			0.569330	−	0.822109i	$-0.307203\pi$
$71$	9.59452			1.13866			0.569330	+	0.822109i	$0.307203\pi$
$72$		−	6.95692i		−	0.819880i
$73$	−8.96093			−1.04880			−0.524399	−	0.851473i	$-0.675710\pi$
$73$	−8.96093			−1.04880			−0.524399	+	0.851473i	$0.675710\pi$
$74$		−	20.2156i		−	2.35001i
$75$		−	2.74268i		−	0.316697i
$76$	23.0620			2.64539
$77$		0			0
$78$	−10.3295			−1.16959
$79$			11.6546i			1.31125i	0.755088	+	0.655623i	$0.227594\pi$
$79$			11.6546i			1.31125i	−0.755088	+	0.655623i	$0.772406\pi$
$80$			12.9424i			1.44700i
$81$	1.00000			0.111111
$82$		−	7.71709i		−	0.852210i
$83$	9.34449			1.02569			0.512845	−	0.858481i	$-0.328591\pi$
$83$	9.34449			1.02569			0.512845	+	0.858481i	$0.328591\pi$
$84$		0			0
$85$			4.15242i			0.450393i
$86$	13.9936			1.50897
$87$	−5.06315			−0.542827
$88$	−22.9933	−	1.92158i	−2.45110	−	0.204841i
$89$			13.6127i			1.44294i	0.692446	+	0.721470i	$0.256533\pi$
$89$			13.6127i			1.44294i	−0.692446	+	0.721470i	$0.743467\pi$
$90$	−3.88599			−0.409619
$91$		0			0
$92$	0.337401			0.0351765
$93$	−10.2165			−1.05941
$94$	−13.4003			−1.38214
$95$		−	7.38830i		−	0.758024i
$96$	−8.36654			−0.853906
$97$		−	2.63550i		−	0.267594i	−0.991009	−	0.133797i	$-0.957283\pi$
$97$		−	2.63550i		−	0.267594i	0.991009	−	0.133797i	$-0.0427171\pi$
$98$		0			0
$99$	0.276211	−	3.30510i	0.0277603	−	0.332175i
$100$	−12.8625			−1.28625
$101$	6.36013			0.632857			0.316429	−	0.948616i	$-0.397516\pi$
$101$	6.36013			0.632857			0.316429	+	0.948616i	$0.397516\pi$
$102$	−7.14840			−0.707797
$103$		−	5.35515i		−	0.527659i	−0.964569	−	0.263829i	$-0.915014\pi$
$103$		−	5.35515i		−	0.527659i	0.964569	−	0.263829i	$-0.0849856\pi$
$104$			27.7838i			2.72443i
$105$		0			0
$106$		−	32.2384i		−	3.13127i
$107$			12.1243i			1.17210i	0.810274	+	0.586051i	$0.199318\pi$
$107$			12.1243i			1.17210i	−0.810274	+	0.586051i	$0.800682\pi$
$108$		−	4.68975i		−	0.451271i
$109$		−	18.8264i		−	1.80324i	−0.432527	−	0.901621i	$-0.642378\pi$
$109$		−	18.8264i		−	1.80324i	0.432527	−	0.901621i	$-0.357622\pi$
$110$	−1.07335	+	12.8436i	−0.102340	+	1.22459i
$111$		−	7.81594i		−	0.741857i
$112$		0			0
$113$	2.11831			0.199273			0.0996367	−	0.995024i	$-0.468232\pi$
$113$	2.11831			0.199273			0.0996367	+	0.995024i	$0.468232\pi$
$114$	12.7190			1.19124
$115$		−	0.108092i		−	0.0100796i
$116$			23.7449i			2.20466i
$117$	−3.99370			−0.369217
$118$	−16.4964			−1.51862
$119$		0			0
$120$			10.4523i			0.954164i
$121$	−10.8474	−	1.82581i	−0.986129	−	0.165983i
$122$		−	3.56288i		−	0.322568i
$123$		−	2.98366i		−	0.269027i
$124$			47.9131i			4.30272i
$125$			11.6329i			1.04048i
$126$		0			0
$127$			0.665478i			0.0590516i	0.999564	+	0.0295258i	$0.00939973\pi$
$127$			0.665478i			0.0590516i	−0.999564	+	0.0295258i	$0.990600\pi$
$128$		−	5.32377i		−	0.470560i
$129$	5.41033			0.476353
$130$	15.5195			1.36115
$131$	1.47488			0.128861			0.0644303	−	0.997922i	$-0.479477\pi$
$131$	1.47488			0.128861			0.0644303	+	0.997922i	$0.479477\pi$
$132$	−15.5001	−	1.29536i	−1.34911	−	0.112747i
$133$		0			0
$134$			11.7771i			1.01739i
$135$	−1.50244			−0.129309
$136$			19.2274i			1.64874i
$137$	18.8162			1.60758			0.803788	−	0.594916i	$-0.202815\pi$
$137$	18.8162			1.60758			0.803788	+	0.594916i	$0.202815\pi$
$138$	0.186081			0.0158403
$139$	6.54622			0.555243			0.277622	−	0.960691i	$-0.410454\pi$
$139$	6.54622			0.555243			0.277622	+	0.960691i	$0.410454\pi$
$140$		0			0
$141$	−5.18095			−0.436315
$142$		−	24.8158i		−	2.08250i
$143$	−1.10310	+	13.1996i	−0.0922461	+	1.10380i
$144$	−8.61425			−0.717854
$145$	7.60708			0.631734
$146$			23.1770i			1.91815i
$147$		0			0
$148$	−36.6548			−3.01301
$149$		−	12.7848i		−	1.04737i	−0.851911	−	0.523686i	$-0.824557\pi$
$149$		−	12.7848i		−	1.04737i	0.851911	−	0.523686i	$-0.175443\pi$
$150$	−7.09381			−0.579207
$151$			14.7551i			1.20075i	0.799718	+	0.600375i	$0.204982\pi$
$151$			14.7551i			1.20075i	−0.799718	+	0.600375i	$0.795018\pi$
$152$		−	34.2109i		−	2.77487i
$153$	−2.76378			−0.223439
$154$		0			0
$155$	15.3497			1.23292
$156$			18.7294i			1.49955i
$157$		−	17.3589i		−	1.38539i	−0.721230	−	0.692696i	$-0.756423\pi$
$157$		−	17.3589i		−	1.38539i	0.721230	−	0.692696i	$-0.243577\pi$
$158$	30.1441			2.39814
$159$		−	12.4643i		−	0.988484i
$160$	12.5702			0.993762
$161$		0			0
$162$		−	2.58645i		−	0.203211i
$163$	2.56883			0.201207			0.100603	−	0.994927i	$-0.467923\pi$
$163$	2.56883			0.201207			0.100603	+	0.994927i	$0.467923\pi$
$164$	−13.9926			−1.09264
$165$	−0.414990	+	4.96572i	−0.0323069	+	0.386580i
$166$		−	24.1691i		−	1.87589i
$167$	−0.481460			−0.0372565			−0.0186282	−	0.999826i	$-0.505930\pi$
$167$	−0.481460			−0.0372565			−0.0186282	+	0.999826i	$0.505930\pi$
$168$		0			0
$169$	2.94961			0.226893
$170$	10.7400			0.823723
$171$	4.91754			0.376053
$172$		−	25.3731i		−	1.93468i
$173$	1.91046			0.145250			0.0726248	−	0.997359i	$-0.476862\pi$
$173$	1.91046			0.145250			0.0726248	+	0.997359i	$0.476862\pi$
$174$			13.0956i			0.992776i
$175$		0			0
$176$	−2.37935	+	28.4710i	−0.179350	+	2.14608i
$177$	−6.37801			−0.479401
$178$	35.2085			2.63899
$179$	−13.6612			−1.02109			−0.510543	−	0.859852i	$-0.670556\pi$
$179$	−13.6612			−1.02109			−0.510543	+	0.859852i	$0.670556\pi$
$180$			7.04606i			0.525182i
$181$		−	15.6168i		−	1.16079i	−0.814337	−	0.580393i	$-0.802899\pi$
$181$		−	15.6168i		−	1.16079i	0.814337	−	0.580393i	$-0.197101\pi$
$182$		0			0
$183$		−	1.37752i		−	0.101829i
$184$		−	0.500511i		−	0.0368981i
$185$			11.7430i			0.863361i
$186$			26.4246i			1.93755i
$187$	−0.763387	+	9.13459i	−0.0558244	+	0.667987i
$188$			24.2974i			1.77207i
$189$		0			0
$190$	−19.1095			−1.38635
$191$	11.6860			0.845567			0.422784	−	0.906231i	$-0.361053\pi$
$191$	11.6860			0.845567			0.422784	+	0.906231i	$0.361053\pi$
$192$			4.41117i			0.318349i
$193$			17.7902i			1.28056i	0.768140	+	0.640282i	$0.221182\pi$
$193$			17.7902i			1.28056i	−0.768140	+	0.640282i	$0.778818\pi$
$194$	−6.81660			−0.489403
$195$	6.00028			0.429689
$196$		0			0
$197$			17.6962i			1.26080i	0.776270	+	0.630400i	$0.217109\pi$
$197$			17.6962i			1.26080i	−0.776270	+	0.630400i	$0.782891\pi$
$198$	−8.54850	−	0.714407i	−0.607515	−	0.0507707i
$199$		−	2.33496i		−	0.165521i	−0.996569	−	0.0827605i	$-0.973626\pi$
$199$		−	2.33496i		−	0.165521i	0.996569	−	0.0827605i	$-0.0263737\pi$
$200$			19.0806i			1.34920i
$201$			4.55337i			0.321170i
$202$		−	16.4502i		−	1.15743i
$203$		0			0
$204$			12.9614i			0.907483i
$205$			4.48276i			0.313090i
$206$	−13.8509			−0.965035
$207$	0.0719444			0.00500048
$208$	34.4027			2.38540
$209$	1.35828	−	16.2530i	0.0939541	−	1.12424i
$210$		0			0
$211$			11.1551i			0.767950i	0.923344	+	0.383975i	$0.125445\pi$
$211$			11.1551i			0.767950i	−0.923344	+	0.383975i	$0.874555\pi$
$212$	−58.4545			−4.01467
$213$		−	9.59452i		−	0.657406i
$214$	31.3590			2.14366
$215$	−8.12870			−0.554372
$216$	−6.95692			−0.473358
$217$		0			0
$218$	−48.6936			−3.29795
$219$			8.96093i			0.605523i
$220$	23.2880	+	1.94620i	1.57007	+	0.131213i
$221$	11.0377			0.742477
$222$	−20.2156			−1.35678
$223$			18.8511i			1.26236i	0.775635	+	0.631182i	$0.217430\pi$
$223$			18.8511i			1.26236i	−0.775635	+	0.631182i	$0.782570\pi$
$224$		0			0
$225$	−2.74268			−0.182845
$226$		−	5.47890i		−	0.364451i
$227$	−1.26814			−0.0841692			−0.0420846	−	0.999114i	$-0.513400\pi$
$227$	−1.26814			−0.0841692			−0.0420846	+	0.999114i	$0.513400\pi$
$228$		−	23.0620i		−	1.52732i
$229$		−	27.1438i		−	1.79371i	−0.442320	−	0.896857i	$-0.645845\pi$
$229$		−	27.1438i		−	1.79371i	0.442320	−	0.896857i	$-0.354155\pi$
$230$	−0.279575			−0.0184346
$231$		0			0
$232$	35.2239			2.31256
$233$		−	0.316222i		−	0.0207164i	−0.999946	−	0.0103582i	$-0.996703\pi$
$233$		−	0.316222i		−	0.0207164i	0.999946	−	0.0103582i	$-0.00329718\pi$
$234$			10.3295i			0.675262i
$235$	7.78406			0.507776
$236$			29.9113i			1.94706i
$237$	11.6546			0.757048
$238$		0			0
$239$			0.351465i			0.0227344i	0.999935	+	0.0113672i	$0.00361837\pi$
$239$			0.351465i			0.0227344i	−0.999935	+	0.0113672i	$0.996382\pi$
$240$	12.9424			0.835427
$241$	20.3996			1.31405			0.657026	−	0.753868i	$-0.271814\pi$
$241$	20.3996			1.31405			0.657026	+	0.753868i	$0.271814\pi$
$242$	−4.72238	+	28.0564i	−0.303566	+	1.80353i
$243$		−	1.00000i		−	0.0641500i
$244$	−6.46021			−0.413572
$245$		0			0
$246$	−7.71709			−0.492024
$247$	−19.6392			−1.24961
$248$	71.0757			4.51331
$249$		−	9.34449i		−	0.592183i
$250$	30.0880			1.90293
$251$		−	21.9352i		−	1.38454i	−0.721639	−	0.692269i	$-0.756611\pi$
$251$		−	21.9352i		−	1.38454i	0.721639	−	0.692269i	$-0.243389\pi$
$252$		0			0
$253$	0.0198718	−	0.237784i	0.00124933	−	0.0149493i
$254$	1.72123			0.108000
$255$	4.15242			0.260034
$256$	−22.5920			−1.41200
$257$		−	1.11715i		−	0.0696860i	−0.999393	−	0.0348430i	$-0.988907\pi$
$257$		−	1.11715i		−	0.0696860i	0.999393	−	0.0348430i	$-0.0110931\pi$
$258$		−	13.9936i		−	0.871202i
$259$		0			0
$260$		−	28.1398i		−	1.74516i
$261$			5.06315i			0.313401i
$262$		−	3.81470i		−	0.235673i
$263$		−	1.22887i		−	0.0757753i	−0.999282	−	0.0378877i	$-0.987937\pi$
$263$		−	1.22887i		−	0.0757753i	0.999282	−	0.0378877i	$-0.0120629\pi$
$264$	−1.92158	+	22.9933i	−0.118265	+	1.41514i
$265$			18.7269i			1.15038i
$266$		0			0
$267$	13.6127			0.833082
$268$	21.3542			1.30441
$269$		−	6.22047i		−	0.379269i	−0.981855	−	0.189634i	$-0.939270\pi$
$269$		−	6.22047i		−	0.379269i	0.981855	−	0.189634i	$-0.0607303\pi$
$270$			3.88599i			0.236494i
$271$	−0.110951			−0.00673980			−0.00336990	−	0.999994i	$-0.501073\pi$
$271$	−0.110951			−0.00673980			−0.00336990	+	0.999994i	$0.501073\pi$
$272$	23.8079			1.44357
$273$		0			0
$274$		−	48.6672i		−	2.94010i
$275$	−0.757558	+	9.06483i	−0.0456825	+	0.546630i
$276$		−	0.337401i		−	0.0203092i
$277$			14.8386i			0.891567i	0.895141	+	0.445784i	$0.147075\pi$
$277$			14.8386i			0.891567i	−0.895141	+	0.445784i	$0.852925\pi$
$278$		−	16.9315i		−	1.01548i
$279$			10.2165i			0.611649i
$280$		0			0
$281$			4.77342i			0.284759i	0.989812	+	0.142379i	$0.0454753\pi$
$281$			4.77342i			0.284759i	−0.989812	+	0.142379i	$0.954525\pi$
$282$			13.4003i			0.797976i
$283$	−31.8574			−1.89372			−0.946862	−	0.321639i	$-0.895766\pi$
$283$	−31.8574			−1.89372			−0.946862	+	0.321639i	$0.895766\pi$
$284$	−44.9959			−2.67001
$285$	−7.38830			−0.437645
$286$	34.1401	+	2.85313i	2.01875	+	0.168709i
$287$		0			0
$288$			8.36654i			0.493003i
$289$	−9.36150			−0.550677
$290$		−	19.6754i		−	1.15538i
$291$	−2.63550			−0.154496
$292$	42.0245			2.45930
$293$	21.1094			1.23322			0.616611	−	0.787268i	$-0.288505\pi$
$293$	21.1094			1.23322			0.616611	+	0.787268i	$0.288505\pi$
$294$		0			0
$295$	9.58257			0.557919
$296$			54.3749i			3.16047i
$297$	−3.30510	−	0.276211i	−0.191782	−	0.0160274i
$298$	−33.0673			−1.91554
$299$	−0.287324			−0.0166164
$300$			12.8625i			0.742615i
$301$		0			0
$302$	38.1633			2.19605
$303$		−	6.36013i		−	0.365380i
$304$	−42.3609			−2.42956
$305$			2.06963i			0.118507i
$306$			7.14840i			0.408647i
$307$	−7.64034			−0.436057			−0.218029	−	0.975942i	$-0.569963\pi$
$307$	−7.64034			−0.436057			−0.218029	+	0.975942i	$0.569963\pi$
$308$		0			0
$309$	−5.35515			−0.304644
$310$		−	39.7014i		−	2.25489i
$311$			8.79797i			0.498887i	0.968389	+	0.249444i	$0.0802477\pi$
$311$			8.79797i			0.498887i	−0.968389	+	0.249444i	$0.919752\pi$
$312$	27.7838			1.57295
$313$			1.05676i			0.0597318i	0.999554	+	0.0298659i	$0.00950803\pi$
$313$			1.05676i			0.0597318i	−0.999554	+	0.0298659i	$0.990492\pi$
$314$	−44.8980			−2.53374
$315$		0			0
$316$		−	54.6572i		−	3.07471i
$317$	3.50457			0.196836			0.0984182	−	0.995145i	$-0.468622\pi$
$317$	3.50457			0.196836			0.0984182	+	0.995145i	$0.468622\pi$
$318$	−32.2384			−1.80784
$319$	16.7342	+	1.39850i	0.936938	+	0.0783009i
$320$		−	6.62752i		−	0.370490i
$321$	12.1243			0.676713
$322$		0			0
$323$	−13.5910			−0.756224
$324$	−4.68975			−0.260542
$325$	10.9534			0.607586
$326$		−	6.64418i		−	0.367987i
$327$	−18.8264			−1.04110
$328$			20.7570i			1.14612i
$329$		0			0
$330$	12.8436	+	1.07335i	0.707017	+	0.0590862i
$331$	5.59201			0.307365			0.153682	−	0.988120i	$-0.450887\pi$
$331$	5.59201			0.307365			0.153682	+	0.988120i	$0.450887\pi$
$332$	−43.8233			−2.40512
$333$	−7.81594			−0.428311
$334$			1.24527i			0.0681383i
$335$		−	6.84117i		−	0.373773i
$336$		0			0
$337$		−	0.965186i		−	0.0525770i	−0.999654	−	0.0262885i	$-0.991631\pi$
$337$		−	0.965186i		−	0.0525770i	0.999654	−	0.0262885i	$-0.00836886\pi$
$338$		−	7.62903i		−	0.414965i
$339$		−	2.11831i		−	0.115051i
$340$		−	19.4738i		−	1.05611i
$341$	33.7668	+	2.82192i	1.82857	+	0.152816i
$342$		−	12.7190i		−	0.687764i
$343$		0			0
$344$	−37.6392			−2.02937
$345$	−0.108092			−0.00581948
$346$		−	4.94132i		−	0.265647i
$347$		−	36.3907i		−	1.95356i	−0.214252	−	0.976778i	$-0.568732\pi$
$347$		−	36.3907i		−	1.95356i	0.214252	−	0.976778i	$-0.431268\pi$
$348$	23.7449			1.27286
$349$	−12.6498			−0.677128			−0.338564	−	0.940943i	$-0.609941\pi$
$349$	−12.6498			−0.677128			−0.338564	+	0.940943i	$0.609941\pi$
$350$		0			0
$351$			3.99370i			0.213168i
$352$	27.6523	+	2.31093i	1.47387	+	0.123173i
$353$		−	1.82732i		−	0.0972584i	−0.998817	−	0.0486292i	$-0.984515\pi$
$353$		−	1.82732i		−	0.0972584i	0.998817	−	0.0486292i	$-0.0154853\pi$
$354$			16.4964i			0.876776i
$355$			14.4152i			0.765078i
$356$		−	63.8400i		−	3.38351i
$357$		0			0
$358$			35.3341i			1.86746i
$359$			16.9902i			0.896706i	0.893856	+	0.448353i	$0.147989\pi$
$359$			16.9902i			0.896706i	−0.893856	+	0.448353i	$0.852011\pi$
$360$	10.4523			0.550887
$361$	5.18217			0.272746
$362$	−40.3921			−2.12296
$363$	−1.82581	+	10.8474i	−0.0958303	+	0.569342i
$364$		0			0
$365$		−	13.4632i		−	0.704699i
$366$	−3.56288			−0.186235
$367$		−	11.8701i		−	0.619614i	−0.950800	−	0.309807i	$-0.899736\pi$
$367$		−	11.8701i		−	0.619614i	0.950800	−	0.309807i	$-0.100264\pi$
$368$	−0.619747			−0.0323065
$369$	−2.98366			−0.155323
$370$	30.3727			1.57900
$371$		0			0
$372$	47.9131			2.48418
$373$		−	14.7762i		−	0.765081i	−0.923939	−	0.382541i	$-0.875049\pi$
$373$		−	14.7762i		−	0.765081i	0.923939	−	0.382541i	$-0.124951\pi$
$374$	23.6262	+	1.97447i	1.22168	+	0.102097i
$375$	11.6329			0.600720
$376$	36.0434			1.85880
$377$		−	20.2207i		−	1.04142i
$378$		0			0
$379$	−19.7260			−1.01326			−0.506628	−	0.862165i	$-0.669108\pi$
$379$	−19.7260			−1.01326			−0.506628	+	0.862165i	$0.669108\pi$
$380$			34.6493i			1.77747i
$381$	0.665478			0.0340935
$382$		−	30.2252i		−	1.54646i
$383$		−	12.6323i		−	0.645480i	−0.946488	−	0.322740i	$-0.895396\pi$
$383$		−	12.6323i		−	0.645480i	0.946488	−	0.322740i	$-0.104604\pi$
$384$	−5.32377			−0.271678
$385$		0			0
$386$	46.0134			2.34202
$387$		−	5.41033i		−	0.275023i
$388$			12.3598i			0.627475i
$389$	−28.7619			−1.45829			−0.729144	−	0.684360i	$-0.760082\pi$
$389$	−28.7619			−1.45829			−0.729144	+	0.684360i	$0.760082\pi$
$390$		−	15.5195i		−	0.785859i
$391$	−0.198839			−0.0100557
$392$		0			0
$393$		−	1.47488i		−	0.0743977i
$394$	45.7704			2.30588
$395$	−17.5103			−0.881041
$396$	−1.29536	+	15.5001i	−0.0650943	+	0.778910i
$397$		−	22.3947i		−	1.12396i	−0.827151	−	0.561980i	$-0.810040\pi$
$397$		−	22.3947i		−	1.12396i	0.827151	−	0.561980i	$-0.189960\pi$
$398$	−6.03927			−0.302721
$399$		0			0
$400$	23.6261			1.18131
$401$	15.7166			0.784851			0.392425	−	0.919784i	$-0.371636\pi$
$401$	15.7166			0.784851			0.392425	+	0.919784i	$0.371636\pi$
$402$	11.7771			0.587388
$403$		−	40.8018i		−	2.03248i
$404$	−29.8274			−1.48397
$405$			1.50244i			0.0746568i
$406$		0			0
$407$	−2.15885	+	25.8325i	−0.107010	+	1.28047i
$408$	19.2274			0.951898
$409$	5.71393			0.282535			0.141268	−	0.989971i	$-0.454882\pi$
$409$	5.71393			0.282535			0.141268	+	0.989971i	$0.454882\pi$
$410$	11.5945			0.572610
$411$		−	18.8162i		−	0.928134i
$412$			25.1143i			1.23729i
$413$		0			0
$414$		−	0.186081i		−	0.00914537i
$415$			14.0395i			0.689173i
$416$		−	33.4134i		−	1.63823i
$417$		−	6.54622i		−	0.320570i
$418$	−42.0376	−	3.51313i	−2.05612	−	0.171833i
$419$			7.07742i			0.345755i	0.984943	+	0.172877i	$0.0553064\pi$
$419$			7.07742i			0.345755i	−0.984943	+	0.172877i	$0.944694\pi$
$420$		0			0
$421$	12.8275			0.625173			0.312586	−	0.949889i	$-0.398805\pi$
$421$	12.8275			0.625173			0.312586	+	0.949889i	$0.398805\pi$
$422$	28.8522			1.40450
$423$			5.18095i			0.251906i
$424$			86.7131i			4.21116i
$425$	7.58017			0.367692
$426$	−24.8158			−1.20233
$427$		0			0
$428$		−	56.8600i		−	2.74843i
$429$	13.1996	+	1.10310i	0.637282	+	0.0532583i
$430$			21.0245i			1.01389i
$431$			11.1146i			0.535369i	0.963507	+	0.267685i	$0.0862586\pi$
$431$			11.1146i			0.535369i	−0.963507	+	0.267685i	$0.913741\pi$
$432$			8.61425i			0.414453i
$433$		−	10.6990i		−	0.514162i	−0.966390	−	0.257081i	$-0.917239\pi$
$433$		−	10.6990i		−	0.514162i	0.966390	−	0.257081i	$-0.0827607\pi$
$434$		0			0
$435$		−	7.60708i		−	0.364732i
$436$			88.2911i			4.22838i
$437$	0.353789			0.0169240
$438$	23.1770			1.10744
$439$	−3.84329			−0.183430			−0.0917152	−	0.995785i	$-0.529235\pi$
$439$	−3.84329			−0.183430			−0.0917152	+	0.995785i	$0.529235\pi$
$440$	2.88705	−	34.5461i	0.137635	−	1.64692i
$441$		0			0
$442$		−	28.5485i		−	1.35792i
$443$	41.1812			1.95658			0.978289	−	0.207246i	$-0.0664501\pi$
$443$	41.1812			1.95658			0.978289	+	0.207246i	$0.0664501\pi$
$444$			36.6548i			1.73956i
$445$	−20.4522			−0.969527
$446$	48.7576			2.30874
$447$	−12.7848			−0.604700
$448$		0			0
$449$	−4.60643			−0.217391			−0.108695	−	0.994075i	$-0.534667\pi$
$449$	−4.60643			−0.217391			−0.108695	+	0.994075i	$0.534667\pi$
$450$			7.09381i			0.334405i
$451$	−0.824119	+	9.86129i	−0.0388062	+	0.464350i
$452$	−9.93432			−0.467271
$453$	14.7551			0.693254
$454$			3.27998i			0.153937i
$455$		0			0
$456$	−34.2109			−1.60207
$457$		−	11.1016i		−	0.519313i	−0.965701	−	0.259656i	$-0.916391\pi$
$457$		−	11.1016i		−	0.519313i	0.965701	−	0.259656i	$-0.0836093\pi$
$458$	−70.2063			−3.28052
$459$			2.76378i			0.129002i
$460$			0.506924i			0.0236355i
$461$	−36.8801			−1.71768			−0.858838	−	0.512247i	$-0.828813\pi$
$461$	−36.8801			−1.71768			−0.858838	+	0.512247i	$0.828813\pi$
$462$		0			0
$463$	−8.86148			−0.411828			−0.205914	−	0.978570i	$-0.566017\pi$
$463$	−8.86148			−0.411828			−0.205914	+	0.978570i	$0.566017\pi$
$464$		−	43.6153i		−	2.02479i
$465$		−	15.3497i		−	0.711827i
$466$	−0.817894			−0.0378882
$467$			30.3094i			1.40255i	0.712890	+	0.701276i	$0.247386\pi$
$467$			30.3094i			1.40255i	−0.712890	+	0.701276i	$0.752614\pi$
$468$	18.7294			0.865768
$469$		0			0
$470$		−	20.1331i		−	0.928672i
$471$	−17.3589			−0.799856
$472$	44.3713			2.04235
$473$	−17.8817	−	1.49439i	−0.822202	−	0.0687123i
$474$		−	30.1441i		−	1.38457i
$475$	−13.4872			−0.618836
$476$		0			0
$477$	−12.4643			−0.570701
$478$	0.909049			0.0415789
$479$	16.2610			0.742985			0.371493	−	0.928436i	$-0.378846\pi$
$479$	16.2610			0.742985			0.371493	+	0.928436i	$0.378846\pi$
$480$		−	12.5702i		−	0.573749i
$481$	31.2145			1.42326
$482$		−	52.7626i		−	2.40327i
$483$		0			0
$484$	50.8717	+	8.56260i	2.31235	+	0.389209i
$485$	3.95968			0.179800
$486$	−2.58645			−0.117324
$487$	12.2233			0.553891			0.276945	−	0.960886i	$-0.410678\pi$
$487$	12.2233			0.553891			0.276945	+	0.960886i	$0.410678\pi$
$488$			9.58327i			0.433814i
$489$		−	2.56883i		−	0.116167i
$490$		0			0
$491$			0.0272318i			0.00122895i	1.00000		0.000614476i	$0.000195594\pi$
$491$			0.0272318i			0.00122895i	−1.00000		0.000614476i	$0.999804\pi$
$492$			13.9926i			0.630835i
$493$		−	13.9935i		−	0.630234i
$494$			50.7958i			2.28541i
$495$	4.96572	+	0.414990i	0.223192	+	0.0186524i
$496$		−	88.0079i		−	3.95167i
$497$		0			0
$498$	−24.1691			−1.08304
$499$	−14.5163			−0.649841			−0.324921	−	0.945741i	$-0.605338\pi$
$499$	−14.5163			−0.649841			−0.324921	+	0.945741i	$0.605338\pi$
$500$		−	54.5554i		−	2.43979i
$501$			0.481460i			0.0215100i
$502$	−56.7345			−2.53218
$503$	11.2845			0.503153			0.251577	−	0.967837i	$-0.419051\pi$
$503$	11.2845			0.503153			0.251577	+	0.967837i	$0.419051\pi$
$504$		0			0
$505$			9.55571i			0.425224i
$506$	−0.615016	−	0.0513976i	−0.0273408	−	0.00228490i
$507$		−	2.94961i		−	0.130997i
$508$		−	3.12093i		−	0.138469i
$509$			40.7374i			1.80565i	0.430004	+	0.902827i	$0.358512\pi$
$509$			40.7374i			1.80565i	−0.430004	+	0.902827i	$0.641488\pi$
$510$		−	10.7400i		−	0.475577i
$511$		0			0
$512$			47.7858i			2.11185i
$513$		−	4.91754i		−	0.217115i
$514$	−2.88946			−0.127449
$515$	8.04579			0.354540
$516$	−25.3731			−1.11699
$517$	17.1236	+	1.43104i	0.753094	+	0.0629369i
$518$		0			0
$519$		−	1.91046i		−	0.0838599i
$520$	−41.7435			−1.83057
$521$			22.4367i			0.982969i	0.870886	+	0.491484i	$0.163546\pi$
$521$			22.4367i			0.982969i	−0.870886	+	0.491484i	$0.836454\pi$
$522$	13.0956			0.573180
$523$	−35.6549			−1.55908			−0.779539	−	0.626354i	$-0.784547\pi$
$523$	−35.6549			−1.55908			−0.779539	+	0.626354i	$0.784547\pi$
$524$	−6.91680			−0.302162
$525$		0			0
$526$	−3.17841			−0.138585
$527$		−	28.2363i		−	1.22999i
$528$	28.4710	+	2.37935i	1.23904	+	0.103548i
$529$	−22.9948			−0.999775
$530$	48.4362			2.10393
$531$			6.37801i			0.276782i
$532$		0			0
$533$	11.9158			0.516131
$534$		−	35.2085i		−	1.52362i
$535$	−18.2160			−0.787548
$536$		−	31.6774i		−	1.36826i
$537$			13.6612i			0.589524i
$538$	−16.0890			−0.693644
$539$		0			0
$540$	7.04606			0.303214
$541$			10.3288i			0.444071i	0.975039	+	0.222035i	$0.0712700\pi$
$541$			10.3288i			0.444071i	−0.975039	+	0.222035i	$0.928730\pi$
$542$			0.286970i			0.0123264i
$543$	−15.6168			−0.670180
$544$		−	23.1233i		−	0.991403i
$545$	28.2855			1.21162
$546$		0			0
$547$		−	21.7253i		−	0.928908i	−0.885597	−	0.464454i	$-0.846251\pi$
$547$		−	21.7253i		−	0.928908i	0.885597	−	0.464454i	$-0.153749\pi$
$548$	−88.2432			−3.76956
$549$	−1.37752			−0.0587910
$550$	23.4458	+	1.95939i	0.999731	+	0.0835486i
$551$			24.8982i			1.06070i
$552$	−0.500511			−0.0213032
$553$		0			0
$554$	38.3795			1.63059
$555$	11.7430			0.498462
$556$	−30.7001			−1.30198
$557$			10.9141i			0.462446i	0.972901	+	0.231223i	$0.0742726\pi$
$557$			10.9141i			0.462446i	−0.972901	+	0.231223i	$0.925727\pi$
$558$	26.4246			1.11864
$559$			21.6072i			0.913888i
$560$		0			0
$561$	9.13459	+	0.763387i	0.385663	+	0.0322302i
$562$	12.3462			0.520795
$563$	32.4568			1.36789			0.683945	−	0.729533i	$-0.260263\pi$
$563$	32.4568			1.36789			0.683945	+	0.729533i	$0.260263\pi$
$564$	24.2974			1.02310
$565$			3.18262i			0.133894i
$566$			82.3977i			3.46343i
$567$		0			0
$568$			66.7483i			2.80069i
$569$		−	6.05638i		−	0.253897i	−0.991909	−	0.126948i	$-0.959482\pi$
$569$		−	6.05638i		−	0.253897i	0.991909	−	0.126948i	$-0.0405182\pi$
$570$			19.1095i			0.800409i
$571$			14.1113i			0.590538i	0.955414	+	0.295269i	$0.0954093\pi$
$571$			14.1113i			0.590538i	−0.955414	+	0.295269i	$0.904591\pi$
$572$	5.17328	−	61.9027i	0.216306	−	2.58828i
$573$		−	11.6860i		−	0.488188i
$574$		0			0
$575$	−0.197320			−0.00822882
$576$	4.41117			0.183799
$577$			44.7126i			1.86141i	0.365773	+	0.930704i	$0.380805\pi$
$577$			44.7126i			1.86141i	−0.365773	+	0.930704i	$0.619195\pi$
$578$			24.2131i			1.00713i
$579$	17.7902			0.739334
$580$	−35.6753			−1.48134
$581$		0			0
$582$			6.81660i			0.282557i
$583$	−3.44278	+	41.1958i	−0.142585	+	1.70616i
$584$		−	62.3404i		−	2.57966i
$585$		−	6.00028i		−	0.248081i
$586$		−	54.5984i		−	2.25544i
$587$			24.7377i			1.02103i	0.859868	+	0.510517i	$0.170546\pi$
$587$			24.7377i			1.02103i	−0.859868	+	0.510517i	$0.829454\pi$
$588$		0			0
$589$			50.2403i			2.07011i
$590$		−	24.7849i		−	1.02038i
$591$	17.6962			0.727924
$592$	67.3285			2.76718
$593$	−11.1781			−0.459030			−0.229515	−	0.973305i	$-0.573714\pi$
$593$	−11.1781			−0.459030			−0.229515	+	0.973305i	$0.573714\pi$
$594$	−0.714407	+	8.54850i	−0.0293125	+	0.350749i
$595$		0			0
$596$			59.9575i			2.45596i
$597$	−2.33496			−0.0955636
$598$			0.743150i			0.0303897i
$599$	−27.7998			−1.13587			−0.567935	−	0.823073i	$-0.692257\pi$
$599$	−27.7998			−1.13587			−0.567935	+	0.823073i	$0.692257\pi$
$600$	19.0806			0.778961
$601$	27.1607			1.10791			0.553955	−	0.832547i	$-0.313118\pi$
$601$	27.1607			1.10791			0.553955	+	0.832547i	$0.313118\pi$
$602$		0			0
$603$	4.55337			0.185428
$604$		−	69.1976i		−	2.81561i
$605$	2.74317	−	16.2976i	0.111526	−	0.662591i
$606$	−16.4502			−0.668244
$607$	12.8095			0.519920			0.259960	−	0.965619i	$-0.416291\pi$
$607$	12.8095			0.519920			0.259960	+	0.965619i	$0.416291\pi$
$608$			41.1428i			1.66856i
$609$		0			0
$610$	5.35302			0.216737
$611$		−	20.6911i		−	0.837074i
$612$	12.9614			0.523936
$613$			42.8807i			1.73194i	0.500100	+	0.865968i	$0.333297\pi$
$613$			42.8807i			1.73194i	−0.500100	+	0.865968i	$0.666703\pi$
$614$			19.7614i			0.797505i
$615$	4.48276			0.180762
$616$		0			0
$617$	−13.3792			−0.538627			−0.269313	−	0.963053i	$-0.586797\pi$
$617$	−13.3792			−0.538627			−0.269313	+	0.963053i	$0.586797\pi$
$618$			13.8509i			0.557163i
$619$			29.4806i			1.18493i	0.805598	+	0.592463i	$0.201844\pi$
$619$			29.4806i			1.18493i	−0.805598	+	0.592463i	$0.798156\pi$
$620$	−71.9864			−2.89105
$621$		−	0.0719444i		−	0.00288703i
$622$	22.7555			0.912414
$623$		0			0
$624$		−	34.4027i		−	1.37721i
$625$	−3.76433			−0.150573
$626$	2.73327			0.109243
$627$	−16.2530	−	1.35828i	−0.649081	−	0.0542444i
$628$			81.4089i			3.24857i
$629$	21.6016			0.861311
$630$		0			0
$631$	−14.9445			−0.594932			−0.297466	−	0.954732i	$-0.596142\pi$
$631$	−14.9445			−0.594932			−0.297466	+	0.954732i	$0.596142\pi$
$632$	−81.0801			−3.22519
$633$	11.1551			0.443376
$634$		−	9.06442i		−	0.359994i
$635$	−0.999840			−0.0396775
$636$			58.4545i			2.31787i
$637$		0			0
$638$	3.61716	−	43.2824i	0.143205	−	1.71357i
$639$	−9.59452			−0.379553
$640$	7.99864			0.316174
$641$	13.6708			0.539962			0.269981	−	0.962866i	$-0.412983\pi$
$641$	13.6708			0.539962			0.269981	+	0.962866i	$0.412983\pi$
$642$		−	31.3590i		−	1.23764i
$643$		−	31.9795i		−	1.26115i	−0.776129	−	0.630574i	$-0.782819\pi$
$643$		−	31.9795i		−	1.26115i	0.776129	−	0.630574i	$-0.217181\pi$
$644$		0			0
$645$			8.12870i			0.320067i
$646$			35.1525i			1.38306i
$647$		−	0.830590i		−	0.0326539i	−0.999867	−	0.0163269i	$-0.994803\pi$
$647$		−	0.830590i		−	0.0326539i	0.999867	−	0.0163269i	$-0.00519725\pi$
$648$			6.95692i			0.273293i
$649$	21.0800	+	1.76168i	0.827462	+	0.0691519i
$650$		−	28.3305i		−	1.11121i
$651$		0			0
$652$	−12.0472			−0.471804
$653$	19.4719			0.761994			0.380997	−	0.924576i	$-0.375581\pi$
$653$	19.4719			0.761994			0.380997	+	0.924576i	$0.375581\pi$
$654$			48.6936i			1.90407i
$655$			2.21591i			0.0865829i
$656$	25.7020			1.00349
$657$	8.96093			0.349599
$658$		0			0
$659$			8.85133i			0.344799i	0.985027	+	0.172399i	$0.0551520\pi$
$659$			8.85133i			0.344799i	−0.985027	+	0.172399i	$0.944848\pi$
$660$	1.94620	−	23.2880i	0.0757557	−	0.906483i
$661$			3.22906i			0.125596i	0.998026	+	0.0627980i	$0.0200024\pi$
$661$			3.22906i			0.125596i	−0.998026	+	0.0627980i	$0.979998\pi$
$662$		−	14.4635i		−	0.562139i
$663$		−	11.0377i		−	0.428669i
$664$			65.0088i			2.52283i
$665$		0			0
$666$			20.2156i			0.783338i
$667$			0.364265i			0.0141044i
$668$	2.25792			0.0873617
$669$	18.8511			0.728826
$670$	−17.6944			−0.683593
$671$	−0.380485	+	4.55284i	−0.0146885	+	0.175760i
$672$		0			0
$673$		−	3.90455i		−	0.150509i	−0.997164	−	0.0752547i	$-0.976023\pi$
$673$		−	3.90455i		−	0.150509i	0.997164	−	0.0752547i	$-0.0239770\pi$
$674$	−2.49641			−0.0961581
$675$			2.74268i			0.105566i
$676$	−13.8329			−0.532036
$677$	−42.2879			−1.62526			−0.812628	−	0.582782i	$-0.801964\pi$
$677$	−42.2879			−1.62526			−0.812628	+	0.582782i	$0.801964\pi$
$678$	−5.47890			−0.210416
$679$		0			0
$680$	−28.8880			−1.10780
$681$			1.26814i			0.0485951i
$682$	7.29878	−	87.3362i	0.279485	−	3.34428i
$683$	13.8525			0.530049			0.265025	−	0.964242i	$-0.414620\pi$
$683$	13.8525			0.530049			0.265025	+	0.964242i	$0.414620\pi$
$684$	−23.0620			−0.881798
$685$			28.2702i			1.08015i
$686$		0			0
$687$	−27.1438			−1.03560
$688$			46.6060i			1.77684i
$689$	49.7787			1.89642
$690$			0.279575i			0.0106432i
$691$			27.4904i			1.04578i	0.852399	+	0.522891i	$0.175147\pi$
$691$			27.4904i			1.04578i	−0.852399	+	0.522891i	$0.824853\pi$
$692$	−8.95958			−0.340592
$693$		0			0
$694$	−94.1230			−3.57286
$695$			9.83529i			0.373074i
$696$		−	35.2239i		−	1.33516i
$697$	8.24618			0.312346
$698$			32.7181i			1.23840i
$699$	−0.316222			−0.0119606
$700$		0			0
$701$		−	26.9901i		−	1.01940i	−0.860352	−	0.509700i	$-0.829756\pi$
$701$		−	26.9901i		−	1.01940i	0.860352	−	0.509700i	$-0.170244\pi$
$702$	10.3295			0.389862
$703$	−38.4352			−1.44961
$704$	1.21841	−	14.5794i	0.0459207	−	0.549481i
$705$		−	7.78406i		−	0.293165i
$706$	−4.72628			−0.177876
$707$		0			0
$708$	29.9113			1.12413
$709$	15.7845			0.592799			0.296400	−	0.955064i	$-0.404214\pi$
$709$	15.7845			0.592799			0.296400	+	0.955064i	$0.404214\pi$
$710$	37.2842			1.39925
$711$		−	11.6546i		−	0.437082i
$712$	−94.7021			−3.54911
$713$			0.735023i			0.0275268i
$714$		0			0
$715$	−19.8316	−	1.65734i	−0.741658	−	0.0619812i
$716$	64.0676			2.39432
$717$	0.351465			0.0131257
$718$	43.9443			1.63999
$719$			37.4774i			1.39767i	0.715282	+	0.698836i	$0.246298\pi$
$719$			37.4774i			1.39767i	−0.715282	+	0.698836i	$0.753702\pi$
$720$		−	12.9424i		−	0.482334i
$721$		0			0
$722$		−	13.4035i		−	0.498825i
$723$		−	20.3996i		−	0.758668i
$724$			73.2388i			2.72190i
$725$		−	13.8866i		−	0.515735i
$726$	28.0564	+	4.72238i	1.04127	+	0.175264i
$727$			4.00301i			0.148464i	0.997241	+	0.0742318i	$0.0236505\pi$
$727$			4.00301i			0.148464i	−0.997241	+	0.0742318i	$0.976350\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−34.8221			−1.28882
$731$			14.9530i			0.553056i
$732$			6.46021i			0.238776i
$733$	−0.288896			−0.0106706			−0.00533530	−	0.999986i	$-0.501698\pi$
$733$	−0.288896			−0.0106706			−0.00533530	+	0.999986i	$0.501698\pi$
$734$	−30.7014			−1.13321
$735$		0			0
$736$			0.601925i			0.0221873i
$737$	1.25769	−	15.0494i	0.0463277	−	0.554351i
$738$			7.71709i			0.284070i
$739$		−	4.10187i		−	0.150890i	−0.997150	−	0.0754449i	$-0.975962\pi$
$739$		−	4.10187i		−	0.150890i	0.997150	−	0.0754449i	$-0.0240377\pi$
$740$		−	55.0716i		−	2.02447i
$741$			19.6392i			0.721462i
$742$		0			0
$743$		−	23.5527i		−	0.864063i	−0.901858	−	0.432032i	$-0.857797\pi$
$743$		−	23.5527i		−	0.864063i	0.901858	−	0.432032i	$-0.142203\pi$
$744$		−	71.0757i		−	2.60576i
$745$	19.2084			0.703741
$746$	−38.2179			−1.39926
$747$	−9.34449			−0.341897
$748$	3.58010	−	42.8389i	0.130901	−	1.56635i
$749$		0			0
$750$		−	30.0880i		−	1.09866i
$751$	14.4308			0.526587			0.263294	−	0.964716i	$-0.415191\pi$
$751$	14.4308			0.526587			0.263294	+	0.964716i	$0.415191\pi$
$752$		−	44.6300i		−	1.62749i
$753$	−21.9352			−0.799364
$754$	−52.2999			−1.90465
$755$	−22.1686			−0.806798
$756$		0			0
$757$	13.1686			0.478620			0.239310	−	0.970943i	$-0.423079\pi$
$757$	13.1686			0.478620			0.239310	+	0.970943i	$0.423079\pi$
$758$			51.0204i			1.85314i
$759$	−0.237784	−	0.0198718i	−0.00863100	−	0.000721302i
$760$	51.3998			1.86447
$761$	−30.1166			−1.09173			−0.545863	−	0.837874i	$-0.683798\pi$
$761$	−30.1166			−1.09173			−0.545863	+	0.837874i	$0.683798\pi$
$762$		−	1.72123i		−	0.0623536i
$763$		0			0
$764$	−54.8043			−1.98275
$765$		−	4.15242i		−	0.150131i
$766$	−32.6729			−1.18052
$767$		−	25.4718i		−	0.919735i
$768$			22.5920i			0.815220i
$769$	−26.3978			−0.951930			−0.475965	−	0.879464i	$-0.657901\pi$
$769$	−26.3978			−0.951930			−0.475965	+	0.879464i	$0.657901\pi$
$770$		0			0
$771$	−1.11715			−0.0402332
$772$		−	83.4314i		−	3.00276i
$773$			32.7360i			1.17743i	0.808340	+	0.588716i	$0.200366\pi$
$773$			32.7360i			1.17743i	−0.808340	+	0.588716i	$0.799634\pi$
$774$	−13.9936			−0.502989
$775$		−	28.0207i		−	1.00653i
$776$	18.3349			0.658186
$777$		0			0
$778$			74.3914i			2.66706i
$779$	−14.6722			−0.525688
$780$	−28.1398			−1.00757
$781$	−2.65011	+	31.7109i	−0.0948285	+	1.13470i
$782$			0.514287i			0.0183909i
$783$	5.06315			0.180942
$784$		0			0
$785$	26.0807			0.930860
$786$	−3.81470			−0.136066
$787$	−17.1176			−0.610178			−0.305089	−	0.952324i	$-0.598686\pi$
$787$	−17.1176			−0.610178			−0.305089	+	0.952324i	$0.598686\pi$
$788$		−	82.9907i		−	2.95642i
$789$	−1.22887			−0.0437489
$790$			45.2897i			1.61134i
$791$		0			0
$792$	22.9933	+	1.92158i	0.817032	+	0.0682803i
$793$	5.50138			0.195360
$794$	−57.9230			−2.05561
$795$	18.7269			0.664173
$796$			10.9504i			0.388126i
$797$			45.0372i			1.59530i	0.603121	+	0.797650i	$0.293924\pi$
$797$			45.0372i			1.59530i	−0.603121	+	0.797650i	$0.706076\pi$
$798$		0			0
$799$		−	14.3190i		−	0.506571i
$800$		−	22.9467i		−	0.811289i
$801$		−	13.6127i		−	0.480980i
$802$		−	40.6503i		−	1.43541i
$803$	2.47511	−	29.6168i	0.0873446	−	1.04515i
$804$		−	21.3542i		−	0.753104i
$805$		0			0
$806$	−105.532			−3.71721
$807$	−6.22047			−0.218971
$808$			44.2469i			1.55660i
$809$			4.11315i			0.144611i	0.997383	+	0.0723053i	$0.0230356\pi$
$809$			4.11315i			0.144611i	−0.997383	+	0.0723053i	$0.976964\pi$
$810$	3.88599			0.136540
$811$	24.9774			0.877076			0.438538	−	0.898713i	$-0.355496\pi$
$811$	24.9774			0.877076			0.438538	+	0.898713i	$0.355496\pi$
$812$		0			0
$813$			0.110951i			0.00389122i
$814$	66.8146	+	5.58377i	2.34185	+	0.195711i
$815$			3.85952i			0.135193i
$816$		−	23.8079i		−	0.833444i
$817$		−	26.6055i		−	0.930809i
$818$		−	14.7788i		−	0.516729i
$819$		0			0
$820$		−	21.0230i		−	0.734156i
$821$		−	4.98896i		−	0.174116i	−0.996203	−	0.0870580i	$-0.972253\pi$
$821$		−	4.98896i		−	0.174116i	0.996203	−	0.0870580i	$-0.0277465\pi$
$822$	−48.6672			−1.69746
$823$	−46.1744			−1.60954			−0.804769	−	0.593588i	$-0.797711\pi$
$823$	−46.1744			−1.60954			−0.804769	+	0.593588i	$0.797711\pi$
$824$	37.2553			1.29785
$825$	9.06483	+	0.757558i	0.315597	+	0.0263748i
$826$		0			0
$827$		−	35.2177i		−	1.22464i	−0.790611	−	0.612319i	$-0.790237\pi$
$827$		−	35.2177i		−	1.22464i	0.790611	−	0.612319i	$-0.209763\pi$
$828$	−0.337401			−0.0117255
$829$			19.9434i			0.692661i	0.938112	+	0.346331i	$0.112573\pi$
$829$			19.9434i			0.692661i	−0.938112	+	0.346331i	$0.887427\pi$
$830$	36.3126			1.26043
$831$	14.8386			0.514747
$832$	−17.6169			−0.610756
$833$		0			0
$834$	−16.9315			−0.586290
$835$		−	0.723364i		−	0.0250330i
$836$	−6.36998	+	76.2223i	−0.220311	+	2.63620i
$837$	10.2165			0.353136
$838$	18.3054			0.632350
$839$		−	41.5888i		−	1.43580i	−0.696144	−	0.717902i	$-0.745103\pi$
$839$		−	41.5888i		−	1.43580i	0.696144	−	0.717902i	$-0.254897\pi$
$840$		0			0
$841$	3.36447			0.116016
$842$		−	33.1777i		−	1.14338i
$843$	4.77342			0.164405
$844$		−	52.3147i		−	1.80075i
$845$			4.43161i			0.152452i
$846$	13.4003			0.460712
$847$		0			0
$848$	107.371			3.68712
$849$			31.8574i			1.09334i
$850$		−	19.6058i		−	0.672472i
$851$	−0.562313			−0.0192758
$852$			44.9959i			1.54153i
$853$	−45.8254			−1.56903			−0.784516	−	0.620108i	$-0.787089\pi$
$853$	−45.8254			−1.56903			−0.784516	+	0.620108i	$0.787089\pi$
$854$		0			0
$855$			7.38830i			0.252675i
$856$	−84.3478			−2.88295
$857$	32.7545			1.11887			0.559437	−	0.828873i	$-0.311017\pi$
$857$	32.7545			1.11887			0.559437	+	0.828873i	$0.311017\pi$
$858$	2.85313	−	34.1401i	0.0974041	−	1.16552i
$859$		−	19.6981i		−	0.672089i	−0.941846	−	0.336045i	$-0.890911\pi$
$859$		−	19.6981i		−	0.672089i	0.941846	−	0.336045i	$-0.109089\pi$
$860$	38.1215			1.29993
$861$		0			0
$862$	28.7473			0.979137
$863$	5.35830			0.182399			0.0911993	−	0.995833i	$-0.470930\pi$
$863$	5.35830			0.182399			0.0911993	+	0.995833i	$0.470930\pi$
$864$	8.36654			0.284635
$865$			2.87035i			0.0975949i
$866$	−27.6725			−0.940350
$867$			9.36150i			0.317933i
$868$		0			0
$869$	−38.5197	−	3.21913i	−1.30669	−	0.109202i
$870$	−19.6754			−0.667057
$871$	−18.1848			−0.616168
$872$	130.974			4.43533
$873$			2.63550i			0.0891981i
$874$		−	0.915059i		−	0.0309523i
$875$		0			0
$876$		−	42.0245i		−	1.41988i
$877$		−	1.05455i		−	0.0356098i	−0.999841	−	0.0178049i	$-0.994332\pi$
$877$		−	1.05455i		−	0.0356098i	0.999841	−	0.0178049i	$-0.00566777\pi$
$878$			9.94050i			0.335476i
$879$		−	21.1094i		−	0.712001i
$880$	−42.7759	−	3.57483i	−1.44198	−	0.120507i
$881$		−	24.1996i		−	0.815304i	−0.913137	−	0.407652i	$-0.866348\pi$
$881$		−	24.1996i		−	0.815304i	0.913137	−	0.407652i	$-0.133652\pi$
$882$		0			0
$883$	−14.1892			−0.477506			−0.238753	−	0.971080i	$-0.576739\pi$
$883$	−14.1892			−0.477506			−0.238753	+	0.971080i	$0.576739\pi$
$884$	−51.7641			−1.74101
$885$		−	9.58257i		−	0.322115i
$886$		−	106.513i		−	3.57838i
$887$	3.49941			0.117499			0.0587494	−	0.998273i	$-0.481289\pi$
$887$	3.49941			0.117499			0.0587494	+	0.998273i	$0.481289\pi$
$888$	54.3749			1.82470
$889$		0			0
$890$			52.8987i			1.77317i
$891$	−0.276211	+	3.30510i	−0.00925342	+	0.110725i
$892$		−	88.4070i		−	2.96008i
$893$			25.4775i			0.852573i
$894$			33.0673i			1.10594i
$895$		−	20.5251i		−	0.686079i
$896$		0			0
$897$			0.287324i			0.00959347i
$898$			11.9143i			0.397586i
$899$	−51.7280			−1.72522
$900$	12.8625			0.428749
$901$	34.4486			1.14765
$902$	25.5058	+	2.13155i	0.849250	+	0.0709727i
$903$		0			0
$904$			14.7369i			0.490141i
$905$	23.4633			0.779945
$906$		−	38.1633i		−	1.26789i
$907$	12.8890			0.427972			0.213986	−	0.976837i	$-0.431355\pi$
$907$	12.8890			0.427972			0.213986	+	0.976837i	$0.431355\pi$
$908$	5.94724			0.197366
$909$	−6.36013			−0.210952
$910$		0			0
$911$	−48.9915			−1.62316			−0.811581	−	0.584240i	$-0.801393\pi$
$911$	−48.9915			−1.62316			−0.811581	+	0.584240i	$0.801393\pi$
$912$			42.3609i			1.40271i
$913$	−2.58105	+	30.8845i	−0.0854203	+	1.02213i
$914$	−28.7139			−0.949771
$915$	2.06963			0.0684200
$916$			127.298i			4.20604i
$917$		0			0
$918$	7.14840			0.235932
$919$			8.99250i			0.296635i	0.988940	+	0.148318i	$0.0473858\pi$
$919$			8.99250i			0.296635i	−0.988940	+	0.148318i	$0.952614\pi$
$920$	0.751987			0.0247923
$921$			7.64034i			0.251758i
$922$			95.3887i			3.14146i
$923$	38.3176			1.26124
$924$		0			0
$925$	21.4366			0.704831
$926$			22.9198i			0.753192i
$927$			5.35515i			0.175886i
$928$	−42.3611			−1.39057
$929$		−	26.2858i		−	0.862408i	−0.902254	−	0.431204i	$-0.858089\pi$
$929$		−	26.2858i		−	0.862408i	0.902254	−	0.431204i	$-0.141911\pi$
$930$	−39.7014			−1.30186
$931$		0			0
$932$			1.48300i			0.0485773i
$933$	8.79797			0.288033
$934$	78.3939			2.56513
$935$	−13.7242	−	1.14694i	−0.448828	−	0.0375090i
$936$		−	27.7838i		−	0.908142i
$937$	8.07052			0.263653			0.131826	−	0.991273i	$-0.457916\pi$
$937$	8.07052			0.263653			0.131826	+	0.991273i	$0.457916\pi$
$938$		0			0
$939$	1.05676			0.0344862
$940$	−36.5053			−1.19067
$941$	−57.9088			−1.88777			−0.943887	−	0.330269i	$-0.892861\pi$
$941$	−57.9088			−1.88777			−0.943887	+	0.330269i	$0.892861\pi$
$942$			44.8980i			1.46286i
$943$	−0.214657			−0.00699020
$944$		−	54.9418i		−	1.78820i
$945$		0			0
$946$	−3.86518	+	46.2502i	−0.125668	+	1.50373i
$947$	−35.7633			−1.16215			−0.581075	−	0.813850i	$-0.697368\pi$
$947$	−35.7633			−1.16215			−0.581075	+	0.813850i	$0.697368\pi$
$948$	−54.6572			−1.77518
$949$	−35.7872			−1.16170
$950$			34.8841i			1.13179i
$951$		−	3.50457i		−	0.113644i
$952$		0			0
$953$			26.3682i			0.854148i	0.904217	+	0.427074i	$0.140456\pi$
$953$			26.3682i			0.854148i	−0.904217	+	0.427074i	$0.859544\pi$
$954$			32.2384i			1.04376i
$955$			17.5575i			0.568146i
$956$		−	1.64828i		−	0.0533093i
$957$	1.39850	−	16.7342i	0.0452071	−	0.540941i
$958$		−	42.0584i		−	1.35885i
$959$		0			0
$960$	−6.62752			−0.213902
$961$	−73.3779			−2.36703
$962$		−	80.7349i		−	2.60300i
$963$		−	12.1243i		−	0.390700i
$964$	−95.6689			−3.08129
$965$	−26.7286			−0.860425
$966$		0			0
$967$		0	0.000437698i		0	1.40754e-5i	1.00000		7.03771e-6i	$2.24017e-6\pi$
$967$		0	0.000437698i		0	1.40754e-5i	−1.00000		7.03771e-6i	$0.999998\pi$
$968$	12.7020	−	75.4645i	0.408258	−	2.42552i
$969$			13.5910i			0.436606i
$970$		−	10.2415i		−	0.328836i
$971$		−	13.2147i		−	0.424081i	−0.977261	−	0.212041i	$-0.931989\pi$
$971$		−	13.2147i		−	0.424081i	0.977261	−	0.212041i	$-0.0680109\pi$
$972$			4.68975i			0.150424i
$973$		0			0
$974$		−	31.6150i		−	1.01301i
$975$		−	10.9534i		−	0.350790i
$976$	11.8663			0.379830
$977$	−43.8898			−1.40416			−0.702079	−	0.712099i	$-0.747745\pi$
$977$	−43.8898			−1.40416			−0.702079	+	0.712099i	$0.747745\pi$
$978$	−6.64418			−0.212457
$979$	−44.9913	−	3.75997i	−1.43793	−	0.120169i
$980$		0			0
$981$			18.8264i			0.601081i
$982$	0.0704337			0.00224763
$983$			24.8211i			0.791669i	0.918322	+	0.395834i	$0.129545\pi$
$983$			24.8211i			0.791669i	−0.918322	+	0.395834i	$0.870455\pi$
$984$	20.7570			0.661711
$985$	−26.5874			−0.847146
$986$	−36.1935			−1.15263
$987$		0			0
$988$	92.1027			2.93018
$989$		−	0.389243i		−	0.0123772i
$990$	1.07335	−	12.8436i	0.0341134	−	0.408196i
$991$	9.88481			0.314001			0.157001	−	0.987598i	$-0.449818\pi$
$991$	9.88481			0.314001			0.157001	+	0.987598i	$0.449818\pi$
$992$	−85.4771			−2.71390
$993$		−	5.59201i		−	0.177457i
$994$		0			0
$995$	3.50814			0.111215
$996$			43.8233i			1.38859i
$997$	−33.1351			−1.04940			−0.524699	−	0.851288i	$-0.675822\pi$
$997$	−33.1351			−1.04940			−0.524699	+	0.851288i	$0.675822\pi$
$998$			37.5459i			1.18849i
$999$			7.81594i			0.247286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.a.538.1		32
7.4	even	3		231.2.p.a.208.16	yes	32
7.5	odd	6		231.2.p.a.10.1	✓	32
7.6	odd	2	inner	1617.2.c.a.538.2		32
11.10	odd	2	inner	1617.2.c.a.538.31		32
21.5	even	6		693.2.bg.b.10.16		32
21.11	odd	6		693.2.bg.b.208.1		32
77.32	odd	6		231.2.p.a.208.1	yes	32
77.54	even	6		231.2.p.a.10.16	yes	32
77.76	even	2	inner	1617.2.c.a.538.32		32
231.32	even	6		693.2.bg.b.208.16		32
231.131	odd	6		693.2.bg.b.10.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.1	✓	32	7.5	odd	6
231.2.p.a.10.16	yes	32	77.54	even	6
231.2.p.a.208.1	yes	32	77.32	odd	6
231.2.p.a.208.16	yes	32	7.4	even	3
693.2.bg.b.10.1		32	231.131	odd	6
693.2.bg.b.10.16		32	21.5	even	6
693.2.bg.b.208.1		32	21.11	odd	6
693.2.bg.b.208.16		32	231.32	even	6
1617.2.c.a.538.1		32	1.1	even	1	trivial
1617.2.c.a.538.2		32	7.6	odd	2	inner
1617.2.c.a.538.31		32	11.10	odd	2	inner
1617.2.c.a.538.32		32	77.76	even	2	inner

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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.58645i q^{2} -1.00000i q^{3} -4.68975 q^{4} +1.50244i q^{5} -2.58645 q^{6} +6.95692i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.58645i q^{2} -1.00000i q^{3} -4.68975 q^{4} +1.50244i q^{5} -2.58645 q^{6} +6.95692i q^{8} -1.00000 q^{9} +3.88599 q^{10} +(-0.276211 + 3.30510i) q^{11} +4.68975i q^{12} +3.99370 q^{13} +1.50244 q^{15} +8.61425 q^{16} +2.76378 q^{17} +2.58645i q^{18} -4.91754 q^{19} -7.04606i q^{20} +(8.54850 + 0.714407i) q^{22} -0.0719444 q^{23} +6.95692 q^{24} +2.74268 q^{25} -10.3295i q^{26} +1.00000i q^{27} -5.06315i q^{29} -3.88599i q^{30} -10.2165i q^{31} -8.36654i q^{32} +(3.30510 + 0.276211i) q^{33} -7.14840i q^{34} +4.68975 q^{36} +7.81594 q^{37} +12.7190i q^{38} -3.99370i q^{39} -10.4523 q^{40} +2.98366 q^{41} +5.41033i q^{43} +(1.29536 - 15.5001i) q^{44} -1.50244i q^{45} +0.186081i q^{46} -5.18095i q^{47} -8.61425i q^{48} -7.09381i q^{50} -2.76378i q^{51} -18.7294 q^{52} +12.4643 q^{53} +2.58645 q^{54} +(-4.96572 - 0.414990i) q^{55} +4.91754i q^{57} -13.0956 q^{58} -6.37801i q^{59} -7.04606 q^{60} +1.37752 q^{61} -26.4246 q^{62} -4.41117 q^{64} +6.00028i q^{65} +(0.714407 - 8.54850i) q^{66} -4.55337 q^{67} -12.9614 q^{68} +0.0719444i q^{69} +9.59452 q^{71} -6.95692i q^{72} -8.96093 q^{73} -20.2156i q^{74} -2.74268i q^{75} +23.0620 q^{76} -10.3295 q^{78} +11.6546i q^{79} +12.9424i q^{80} +1.00000 q^{81} -7.71709i q^{82} +9.34449 q^{83} +4.15242i q^{85} +13.9936 q^{86} -5.06315 q^{87} +(-22.9933 - 1.92158i) q^{88} +13.6127i q^{89} -3.88599 q^{90} +0.337401 q^{92} -10.2165 q^{93} -13.4003 q^{94} -7.38830i q^{95} -8.36654 q^{96} -2.63550i q^{97} +(0.276211 - 3.30510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 24 * q^4 - 32 * q^9	\( 32 q - 24 q^{4} - 32 q^{9} - 4 q^{11} + 8 q^{15} + 40 q^{16} + 8 q^{22} - 48 q^{23} + 24 q^{36} + 64 q^{37} + 56 q^{44} - 72 q^{53} - 24 q^{58} + 8 q^{64} - 40 q^{67} + 72 q^{71} - 48 q^{78} + 32 q^{81} - 128 q^{86} - 48 q^{88} - 16 q^{92} - 32 q^{93} + 4 q^{99}+O(q^{100}) \) 32 * q - 24 * q^4 - 32 * q^9 - 4 * q^11 + 8 * q^15 + 40 * q^16 + 8 * q^22 - 48 * q^23 + 24 * q^36 + 64 * q^37 + 56 * q^44 - 72 * q^53 - 24 * q^58 + 8 * q^64 - 40 * q^67 + 72 * q^71 - 48 * q^78 + 32 * q^81 - 128 * q^86 - 48 * q^88 - 16 * q^92 - 32 * q^93 + 4 * q^99

Introduction

L-functions

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