LMFDB - Embedded newform 1617.2.c.a.538.3

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			538.3
Character	$\chi$	$=$	1617.538
Dual form			1617.2.c.a.538.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50303i q^{2} -1.00000i q^{3} -4.26518 q^{4} -0.980927i q^{5} -2.50303 q^{6} +5.66981i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.50303i q^{2} -1.00000i q^{3} -4.26518 q^{4} -0.980927i q^{5} -2.50303 q^{6} +5.66981i q^{8} -1.00000 q^{9} -2.45529 q^{10} +(-2.59661 - 2.06340i) q^{11} +4.26518i q^{12} +0.941338 q^{13} -0.980927 q^{15} +5.66137 q^{16} -5.17686 q^{17} +2.50303i q^{18} -2.54869 q^{19} +4.18383i q^{20} +(-5.16475 + 6.49940i) q^{22} -0.758182 q^{23} +5.66981 q^{24} +4.03778 q^{25} -2.35620i q^{26} +1.00000i q^{27} +8.74957i q^{29} +2.45529i q^{30} -6.36039i q^{31} -2.83098i q^{32} +(-2.06340 + 2.59661i) q^{33} +12.9578i q^{34} +4.26518 q^{36} +2.98848 q^{37} +6.37946i q^{38} -0.941338i q^{39} +5.56167 q^{40} -3.80891 q^{41} -6.73386i q^{43} +(11.0750 + 8.80076i) q^{44} +0.980927i q^{45} +1.89775i q^{46} +9.73275i q^{47} -5.66137i q^{48} -10.1067i q^{50} +5.17686i q^{51} -4.01497 q^{52} -4.49633 q^{53} +2.50303 q^{54} +(-2.02404 + 2.54709i) q^{55} +2.54869i q^{57} +21.9005 q^{58} +14.7090i q^{59} +4.18383 q^{60} -5.62667 q^{61} -15.9203 q^{62} +4.23671 q^{64} -0.923385i q^{65} +(6.49940 + 5.16475i) q^{66} +12.4252 q^{67} +22.0802 q^{68} +0.758182i q^{69} +10.4898 q^{71} -5.66981i q^{72} -10.2997 q^{73} -7.48027i q^{74} -4.03778i q^{75} +10.8706 q^{76} -2.35620 q^{78} -7.65664i q^{79} -5.55339i q^{80} +1.00000 q^{81} +9.53383i q^{82} -6.28891 q^{83} +5.07812i q^{85} -16.8551 q^{86} +8.74957 q^{87} +(11.6991 - 14.7223i) q^{88} +2.38421i q^{89} +2.45529 q^{90} +3.23378 q^{92} -6.36039 q^{93} +24.3614 q^{94} +2.50008i q^{95} -2.83098 q^{96} -7.30005i q^{97} +(2.59661 + 2.06340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	2.50303i		−	1.76991i	−0.465675	−	0.884956i	$-0.654188\pi$
$2$		−	2.50303i		−	1.76991i	0.465675	−	0.884956i	$-0.345812\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−4.26518			−2.13259
$5$		−	0.980927i		−	0.438684i	−0.975648	−	0.219342i	$-0.929609\pi$
$5$		−	0.980927i		−	0.438684i	0.975648	−	0.219342i	$-0.0703911\pi$
$6$	−2.50303			−1.02186
$7$		0			0
$7$		0			0
$8$			5.66981i			2.00458i
$9$	−1.00000			−0.333333
$10$	−2.45529			−0.776432
$11$	−2.59661	−	2.06340i	−0.782908	−	0.622138i
$11$	−2.59661	−	2.06340i	−0.782908	−	0.622138i
$12$			4.26518i			1.23125i
$13$	0.941338			0.261080			0.130540	−	0.991443i	$-0.458329\pi$
$13$	0.941338			0.261080			0.130540	+	0.991443i	$0.458329\pi$
$14$		0			0
$15$	−0.980927			−0.253274
$16$	5.66137			1.41534
$17$	−5.17686			−1.25557			−0.627786	−	0.778386i	$-0.716039\pi$
$17$	−5.17686			−1.25557			−0.627786	+	0.778386i	$0.716039\pi$
$18$			2.50303i			0.589971i
$19$	−2.54869			−0.584710			−0.292355	−	0.956310i	$-0.594439\pi$
$19$	−2.54869			−0.584710			−0.292355	+	0.956310i	$0.594439\pi$
$20$			4.18383i			0.935532i
$21$		0			0
$22$	−5.16475	+	6.49940i	−1.10113	+	1.38568i
$23$	−0.758182			−0.158092			−0.0790459	−	0.996871i	$-0.525187\pi$
$23$	−0.758182			−0.158092			−0.0790459	+	0.996871i	$0.525187\pi$
$24$	5.66981			1.15734
$25$	4.03778			0.807556
$26$		−	2.35620i		−	0.462089i
$27$			1.00000i			0.192450i
$28$		0			0
$29$			8.74957i			1.62475i	0.583132	+	0.812377i	$0.301827\pi$
$29$			8.74957i			1.62475i	−0.583132	+	0.812377i	$0.698173\pi$
$30$			2.45529i			0.448273i
$31$		−	6.36039i		−	1.14236i	−0.820825	−	0.571179i	$-0.806486\pi$
$31$		−	6.36039i		−	1.14236i	0.820825	−	0.571179i	$-0.193514\pi$
$32$		−	2.83098i		−	0.500451i
$33$	−2.06340	+	2.59661i	−0.359192	+	0.452012i
$34$			12.9578i			2.22225i
$35$		0			0
$36$	4.26518			0.710863
$37$	2.98848			0.491304			0.245652	−	0.969358i	$-0.420998\pi$
$37$	2.98848			0.491304			0.245652	+	0.969358i	$0.420998\pi$
$38$			6.37946i			1.03488i
$39$		−	0.941338i		−	0.150735i
$40$	5.56167			0.879377
$41$	−3.80891			−0.594852			−0.297426	−	0.954745i	$-0.596128\pi$
$41$	−3.80891			−0.594852			−0.297426	+	0.954745i	$0.596128\pi$
$42$		0			0
$43$		−	6.73386i		−	1.02690i	−0.858118	−	0.513452i	$-0.828366\pi$
$43$		−	6.73386i		−	1.02690i	0.858118	−	0.513452i	$-0.171634\pi$
$44$	11.0750	+	8.80076i	1.66962	+	1.32676i
$45$			0.980927i			0.146228i
$46$			1.89775i			0.279808i
$47$			9.73275i			1.41967i	0.704369	+	0.709834i	$0.251230\pi$
$47$			9.73275i			1.41967i	−0.704369	+	0.709834i	$0.748770\pi$
$48$		−	5.66137i		−	0.817148i
$49$		0			0
$50$		−	10.1067i		−	1.42930i
$51$			5.17686i			0.724905i
$52$	−4.01497			−0.556777
$53$	−4.49633			−0.617618			−0.308809	−	0.951124i	$-0.599930\pi$
$53$	−4.49633			−0.617618			−0.308809	+	0.951124i	$0.599930\pi$
$54$	2.50303			0.340620
$55$	−2.02404	+	2.54709i	−0.272922	+	0.343449i
$56$		0			0
$57$			2.54869i			0.337582i
$58$	21.9005			2.87567
$59$			14.7090i			1.91494i	0.288526	+	0.957472i	$0.406835\pi$
$59$			14.7090i			1.91494i	−0.288526	+	0.957472i	$0.593165\pi$
$60$	4.18383			0.540130
$61$	−5.62667			−0.720421			−0.360211	−	0.932871i	$-0.617295\pi$
$61$	−5.62667			−0.720421			−0.360211	+	0.932871i	$0.617295\pi$
$62$	−15.9203			−2.02187
$63$		0			0
$64$	4.23671			0.529588
$65$		−	0.923385i		−	0.114532i
$66$	6.49940	+	5.16475i	0.800021	+	0.635737i
$67$	12.4252			1.51798			0.758991	−	0.651101i	$-0.225693\pi$
$67$	12.4252			1.51798			0.758991	+	0.651101i	$0.225693\pi$
$68$	22.0802			2.67762
$69$			0.758182i			0.0912743i
$70$		0			0
$71$	10.4898			1.24491			0.622455	−	0.782656i	$-0.286135\pi$
$71$	10.4898			1.24491			0.622455	+	0.782656i	$0.286135\pi$
$72$		−	5.66981i		−	0.668193i
$73$	−10.2997			−1.20549			−0.602743	−	0.797936i	$-0.705926\pi$
$73$	−10.2997			−1.20549			−0.602743	+	0.797936i	$0.705926\pi$
$74$		−	7.48027i		−	0.869564i
$75$		−	4.03778i		−	0.466243i
$76$	10.8706			1.24694
$77$		0			0
$78$	−2.35620			−0.266787
$79$		−	7.65664i		−	0.861439i	−0.902486	−	0.430719i	$-0.858260\pi$
$79$		−	7.65664i		−	0.861439i	0.902486	−	0.430719i	$-0.141740\pi$
$80$		−	5.55339i		−	0.620888i
$81$	1.00000			0.111111
$82$			9.53383i			1.05284i
$83$	−6.28891			−0.690297			−0.345149	−	0.938548i	$-0.612172\pi$
$83$	−6.28891			−0.690297			−0.345149	+	0.938548i	$0.612172\pi$
$84$		0			0
$85$			5.07812i			0.550799i
$86$	−16.8551			−1.81753
$87$	8.74957			0.938053
$88$	11.6991	−	14.7223i	1.24713	−	1.56940i
$89$			2.38421i			0.252725i	0.991984	+	0.126363i	$0.0403303\pi$
$89$			2.38421i			0.252725i	−0.991984	+	0.126363i	$0.959670\pi$
$90$	2.45529			0.258811
$91$		0			0
$92$	3.23378			0.337145
$93$	−6.36039			−0.659541
$94$	24.3614			2.51269
$95$			2.50008i			0.256503i
$96$	−2.83098			−0.288935
$97$		−	7.30005i		−	0.741208i	−0.928791	−	0.370604i	$-0.879151\pi$
$97$		−	7.30005i		−	0.741208i	0.928791	−	0.370604i	$-0.120849\pi$
$98$		0			0
$99$	2.59661	+	2.06340i	0.260969	+	0.207379i
$100$	−17.2218			−1.72218
$101$	−5.27998			−0.525378			−0.262689	−	0.964881i	$-0.584609\pi$
$101$	−5.27998			−0.525378			−0.262689	+	0.964881i	$0.584609\pi$
$102$	12.9578			1.28302
$103$		−	17.1646i		−	1.69128i	−0.533753	−	0.845641i	$-0.679219\pi$
$103$		−	17.1646i		−	1.69128i	0.533753	−	0.845641i	$-0.320781\pi$
$104$			5.33721i			0.523356i
$105$		0			0
$106$			11.2545i			1.09313i
$107$		−	12.7891i		−	1.23637i	−0.786033	−	0.618184i	$-0.787869\pi$
$107$		−	12.7891i		−	1.23637i	0.786033	−	0.618184i	$-0.212131\pi$
$108$		−	4.26518i		−	0.410417i
$109$		−	1.78172i		−	0.170658i	−0.996353	−	0.0853291i	$-0.972806\pi$
$109$		−	1.78172i		−	0.170658i	0.996353	−	0.0853291i	$-0.0271941\pi$
$110$	6.37544	+	5.06625i	0.607875	+	0.483048i
$111$		−	2.98848i		−	0.283654i
$112$		0			0
$113$	−15.0553			−1.41628			−0.708140	−	0.706073i	$-0.750465\pi$
$113$	−15.0553			−1.41628			−0.708140	+	0.706073i	$0.750465\pi$
$114$	6.37946			0.597491
$115$			0.743721i			0.0693523i
$116$		−	37.3185i		−	3.46493i
$117$	−0.941338			−0.0870268
$118$	36.8170			3.38928
$119$		0			0
$120$		−	5.56167i		−	0.507709i
$121$	2.48478	+	10.7157i	0.225889	+	0.974153i
$122$			14.0837i			1.27508i
$123$			3.80891i			0.343438i
$124$			27.1282i			2.43618i
$125$		−	8.86541i		−	0.792946i
$126$		0			0
$127$			5.11223i			0.453637i	0.973937	+	0.226818i	$0.0728324\pi$
$127$			5.11223i			0.453637i	−0.973937	+	0.226818i	$0.927168\pi$
$128$		−	16.2666i		−	1.43778i
$129$	−6.73386			−0.592883
$130$	−2.31126			−0.202711
$131$	−12.1916			−1.06519			−0.532593	−	0.846371i	$-0.678782\pi$
$131$	−12.1916			−1.06519			−0.532593	+	0.846371i	$0.678782\pi$
$132$	8.80076	−	11.0750i	0.766007	−	0.963955i
$133$		0			0
$134$		−	31.1007i		−	2.68669i
$135$	0.980927			0.0844248
$136$		−	29.3518i		−	2.51689i
$137$	3.02191			0.258179			0.129089	−	0.991633i	$-0.458795\pi$
$137$	3.02191			0.258179			0.129089	+	0.991633i	$0.458795\pi$
$138$	1.89775			0.161548
$139$	−11.6396			−0.987260			−0.493630	−	0.869672i	$-0.664330\pi$
$139$	−11.6396			−0.987260			−0.493630	+	0.869672i	$0.664330\pi$
$140$		0			0
$141$	9.73275			0.819646
$142$		−	26.2563i		−	2.20338i
$143$	−2.44429	−	1.94236i	−0.204402	−	0.162428i
$144$	−5.66137			−0.471781
$145$	8.58270			0.712754
$146$			25.7804i			2.13360i
$147$		0			0
$148$	−12.7464			−1.04775
$149$			1.27750i			0.104657i	0.998630	+	0.0523284i	$0.0166643\pi$
$149$			1.27750i			0.104657i	−0.998630	+	0.0523284i	$0.983336\pi$
$150$	−10.1067			−0.825209
$151$			22.7665i			1.85271i	0.376647	+	0.926357i	$0.377077\pi$
$151$			22.7665i			1.85271i	−0.376647	+	0.926357i	$0.622923\pi$
$152$		−	14.4506i		−	1.17210i
$153$	5.17686			0.418524
$154$		0			0
$155$	−6.23908			−0.501135
$156$			4.01497i			0.321455i
$157$			9.69954i			0.774107i	0.922057	+	0.387054i	$0.126507\pi$
$157$			9.69954i			0.774107i	−0.922057	+	0.387054i	$0.873493\pi$
$158$	−19.1648			−1.52467
$159$			4.49633i			0.356582i
$160$	−2.77698			−0.219540
$161$		0			0
$162$		−	2.50303i		−	0.196657i
$163$	−17.2853			−1.35389			−0.676943	−	0.736035i	$-0.736696\pi$
$163$	−17.2853			−1.35389			−0.676943	+	0.736035i	$0.736696\pi$
$164$	16.2457			1.26857
$165$	2.54709	+	2.02404i	0.198290	+	0.157572i
$166$			15.7413i			1.22177i
$167$	4.94196			0.382420			0.191210	−	0.981549i	$-0.438759\pi$
$167$	4.94196			0.382420			0.191210	+	0.981549i	$0.438759\pi$
$168$		0			0
$169$	−12.1139			−0.931837
$170$	12.7107			0.974866
$171$	2.54869			0.194903
$172$			28.7211i			2.18996i
$173$	−1.15936			−0.0881445			−0.0440722	−	0.999028i	$-0.514033\pi$
$173$	−1.15936			−0.0881445			−0.0440722	+	0.999028i	$0.514033\pi$
$174$		−	21.9005i		−	1.66027i
$175$		0			0
$176$	−14.7004	−	11.6817i	−1.10808	−	0.880538i
$177$	14.7090			1.10559
$178$	5.96775			0.447302
$179$	19.2536			1.43908			0.719540	−	0.694451i	$-0.244353\pi$
$179$	19.2536			1.43908			0.719540	+	0.694451i	$0.244353\pi$
$180$		−	4.18383i		−	0.311844i
$181$		−	0.999542i		−	0.0742954i	−0.999310	−	0.0371477i	$-0.988173\pi$
$181$		−	0.999542i		−	0.0742954i	0.999310	−	0.0371477i	$-0.0118272\pi$
$182$		0			0
$183$			5.62667i			0.415935i
$184$		−	4.29874i		−	0.316908i
$185$		−	2.93149i		−	0.215527i
$186$			15.9203i			1.16733i
$187$	13.4423	+	10.6819i	0.982997	+	0.781139i
$188$		−	41.5119i		−	3.02757i
$189$		0			0
$190$	6.25778			0.453987
$191$	−22.1638			−1.60372			−0.801858	−	0.597514i	$-0.796155\pi$
$191$	−22.1638			−1.60372			−0.801858	+	0.597514i	$0.796155\pi$
$192$		−	4.23671i		−	0.305758i
$193$			12.0456i			0.867058i	0.901140	+	0.433529i	$0.142732\pi$
$193$			12.0456i			0.867058i	−0.901140	+	0.433529i	$0.857268\pi$
$194$	−18.2723			−1.31187
$195$	−0.923385			−0.0661249
$196$		0			0
$197$			0.892906i			0.0636169i	0.999494	+	0.0318085i	$0.0101267\pi$
$197$			0.892906i			0.0636169i	−0.999494	+	0.0318085i	$0.989873\pi$
$198$	5.16475	−	6.49940i	0.367043	−	0.461892i
$199$		−	10.2153i		−	0.724142i	−0.932151	−	0.362071i	$-0.882070\pi$
$199$		−	10.2153i		−	0.724142i	0.932151	−	0.362071i	$-0.117930\pi$
$200$			22.8934i			1.61881i
$201$		−	12.4252i		−	0.876407i
$202$			13.2160i			0.929872i
$203$		0			0
$204$		−	22.0802i		−	1.54592i
$205$			3.73627i			0.260952i
$206$	−42.9636			−2.99342
$207$	0.758182			0.0526973
$208$	5.32926			0.369518
$209$	6.61796	+	5.25896i	0.457774	+	0.363770i
$210$		0			0
$211$			5.90844i			0.406754i	0.979101	+	0.203377i	$0.0651917\pi$
$211$			5.90844i			0.406754i	−0.979101	+	0.203377i	$0.934808\pi$
$212$	19.1776			1.31712
$213$		−	10.4898i		−	0.718749i
$214$	−32.0115			−2.18826
$215$	−6.60543			−0.450486
$216$	−5.66981			−0.385782
$217$		0			0
$218$	−4.45971			−0.302050
$219$			10.2997i			0.695987i
$220$	8.63290	−	10.8638i	0.582030	−	0.732435i
$221$	−4.87317			−0.327805
$222$	−7.48027			−0.502043
$223$		−	13.1739i		−	0.882191i	−0.897460	−	0.441096i	$-0.854590\pi$
$223$		−	13.1739i		−	0.882191i	0.897460	−	0.441096i	$-0.145410\pi$
$224$		0			0
$225$	−4.03778			−0.269185
$226$			37.6838i			2.50669i
$227$	−26.4288			−1.75414			−0.877071	−	0.480361i	$-0.840506\pi$
$227$	−26.4288			−1.75414			−0.877071	+	0.480361i	$0.840506\pi$
$228$		−	10.8706i		−	0.719924i
$229$		−	11.0702i		−	0.731540i	−0.930705	−	0.365770i	$-0.880806\pi$
$229$		−	11.0702i		−	0.731540i	0.930705	−	0.365770i	$-0.119194\pi$
$230$	1.86156			0.122748
$231$		0			0
$232$	−49.6084			−3.25695
$233$		−	7.74230i		−	0.507215i	−0.967307	−	0.253607i	$-0.918383\pi$
$233$		−	7.74230i		−	0.507215i	0.967307	−	0.253607i	$-0.0816171\pi$
$234$			2.35620i			0.154030i
$235$	9.54712			0.622786
$236$		−	62.7363i		−	4.08379i
$237$	−7.65664			−0.497352
$238$		0			0
$239$			12.7580i			0.825249i	0.910901	+	0.412625i	$0.135388\pi$
$239$			12.7580i			0.825249i	−0.910901	+	0.412625i	$0.864612\pi$
$240$	−5.55339			−0.358470
$241$	−25.6106			−1.64972			−0.824861	−	0.565336i	$-0.808747\pi$
$241$	−25.6106			−1.64972			−0.824861	+	0.565336i	$0.808747\pi$
$242$	26.8217	−	6.21947i	1.72417	−	0.399803i
$243$		−	1.00000i		−	0.0641500i
$244$	23.9987			1.53636
$245$		0			0
$246$	9.53383			0.607855
$247$	−2.39918			−0.152656
$248$	36.0622			2.28995
$249$			6.28891i			0.398543i
$250$	−22.1904			−1.40344
$251$			6.48260i			0.409178i	0.978848	+	0.204589i	$0.0655857\pi$
$251$			6.48260i			0.409178i	−0.978848	+	0.204589i	$0.934414\pi$
$252$		0			0
$253$	1.96870	+	1.56443i	0.123771	+	0.0983549i
$254$	12.7961			0.802897
$255$	5.07812			0.318004
$256$	−32.2424			−2.01515
$257$		−	16.0976i		−	1.00414i	−0.864826	−	0.502071i	$-0.832571\pi$
$257$		−	16.0976i		−	1.00414i	0.864826	−	0.502071i	$-0.167429\pi$
$258$			16.8551i			1.04935i
$259$		0			0
$260$			3.93840i			0.244249i
$261$		−	8.74957i		−	0.541585i
$262$			30.5160i			1.88529i
$263$			6.25530i			0.385719i	0.981226	+	0.192859i	$0.0617761\pi$
$263$			6.25530i			0.385719i	−0.981226	+	0.192859i	$0.938224\pi$
$264$	−14.7223	−	11.6991i	−0.906094	−	0.720028i
$265$			4.41057i			0.270939i
$266$		0			0
$267$	2.38421			0.145911
$268$	−52.9957			−3.23723
$269$		−	9.47772i		−	0.577867i	−0.957349	−	0.288933i	$-0.906699\pi$
$269$		−	9.47772i		−	0.577867i	0.957349	−	0.288933i	$-0.0933006\pi$
$270$		−	2.45529i		−	0.149424i
$271$	18.6738			1.13435			0.567177	−	0.823596i	$-0.308036\pi$
$271$	18.6738			1.13435			0.567177	+	0.823596i	$0.308036\pi$
$272$	−29.3081			−1.77706
$273$		0			0
$274$		−	7.56393i		−	0.456954i
$275$	−10.4845	−	8.33155i	−0.632242	−	0.502411i
$276$		−	3.23378i		−	0.194651i
$277$		−	17.6196i		−	1.05866i	−0.848416	−	0.529330i	$-0.822443\pi$
$277$		−	17.6196i		−	1.05866i	0.848416	−	0.529330i	$-0.177557\pi$
$278$			29.1344i			1.74736i
$279$			6.36039i			0.380786i
$280$		0			0
$281$		−	10.9532i		−	0.653414i	−0.945126	−	0.326707i	$-0.894061\pi$
$281$		−	10.9532i		−	0.653414i	0.945126	−	0.326707i	$-0.105939\pi$
$282$		−	24.3614i		−	1.45070i
$283$	27.6734			1.64501			0.822507	−	0.568755i	$-0.192575\pi$
$283$	27.6734			1.64501			0.822507	+	0.568755i	$0.192575\pi$
$284$	−44.7408			−2.65488
$285$	2.50008			0.148092
$286$	−4.86178	+	6.11814i	−0.287483	+	0.361773i
$287$		0			0
$288$			2.83098i			0.166817i
$289$	9.79984			0.576461
$290$		−	21.4828i		−	1.26151i
$291$	−7.30005			−0.427936
$292$	43.9299			2.57080
$293$	21.3408			1.24674			0.623370	−	0.781927i	$-0.285763\pi$
$293$	21.3408			1.24674			0.623370	+	0.781927i	$0.285763\pi$
$294$		0			0
$295$	14.4284			0.840056
$296$			16.9441i			0.984858i
$297$	2.06340	−	2.59661i	0.119731	−	0.150671i
$298$	3.19762			0.185233
$299$	−0.713705			−0.0412747
$300$			17.2218i			0.994304i
$301$		0			0
$302$	56.9854			3.27914
$303$			5.27998i			0.303327i
$304$	−14.4291			−0.827564
$305$			5.51935i			0.316037i
$306$		−	12.9578i		−	0.740751i
$307$	−24.9793			−1.42565			−0.712823	−	0.701344i	$-0.752584\pi$
$307$	−24.9793			−1.42565			−0.712823	+	0.701344i	$0.752584\pi$
$308$		0			0
$309$	−17.1646			−0.976462
$310$			15.6166i			0.886964i
$311$			24.1737i			1.37077i	0.728183	+	0.685383i	$0.240365\pi$
$311$			24.1737i			1.37077i	−0.728183	+	0.685383i	$0.759635\pi$
$312$	5.33721			0.302160
$313$			22.0736i			1.24768i	0.781554	+	0.623838i	$0.214427\pi$
$313$			22.0736i			1.24768i	−0.781554	+	0.623838i	$0.785573\pi$
$314$	24.2783			1.37010
$315$		0			0
$316$			32.6569i			1.83709i
$317$	−6.87207			−0.385974			−0.192987	−	0.981201i	$-0.561818\pi$
$317$	−6.87207			−0.385974			−0.192987	+	0.981201i	$0.561818\pi$
$318$	11.2545			0.631119
$319$	18.0539	−	22.7192i	1.01082	−	1.27203i
$320$		−	4.15590i		−	0.232322i
$321$	−12.7891			−0.713817
$322$		0			0
$323$	13.1942			0.734145
$324$	−4.26518			−0.236954
$325$	3.80092			0.210837
$326$			43.2656i			2.39626i
$327$	−1.78172			−0.0985295
$328$		−	21.5958i		−	1.19243i
$329$		0			0
$330$	5.06625	−	6.37544i	0.278888	−	0.350957i
$331$	−4.77568			−0.262495			−0.131248	−	0.991350i	$-0.541898\pi$
$331$	−4.77568			−0.262495			−0.131248	+	0.991350i	$0.541898\pi$
$332$	26.8233			1.47212
$333$	−2.98848			−0.163768
$334$		−	12.3699i		−	0.676850i
$335$		−	12.1882i		−	0.665914i
$336$		0			0
$337$			16.3128i			0.888613i	0.895875	+	0.444306i	$0.146550\pi$
$337$			16.3128i			0.888613i	−0.895875	+	0.444306i	$0.853450\pi$
$338$			30.3214i			1.64927i
$339$			15.0553i			0.817689i
$340$		−	21.6591i		−	1.17463i
$341$	−13.1240	+	16.5154i	−0.710705	+	0.894361i
$342$		−	6.37946i		−	0.344962i
$343$		0			0
$344$	38.1797			2.05851
$345$	0.743721			0.0400406
$346$			2.90192i			0.156008i
$347$		−	11.6514i		−	0.625478i	−0.949839	−	0.312739i	$-0.898753\pi$
$347$		−	11.6514i		−	0.625478i	0.949839	−	0.312739i	$-0.101247\pi$
$348$	−37.3185			−2.00048
$349$	−12.3693			−0.662111			−0.331056	−	0.943611i	$-0.607405\pi$
$349$	−12.3693			−0.662111			−0.331056	+	0.943611i	$0.607405\pi$
$350$		0			0
$351$			0.941338i			0.0502449i
$352$	−5.84143	+	7.35095i	−0.311349	+	0.391807i
$353$			13.4303i			0.714821i	0.933947	+	0.357411i	$0.116340\pi$
$353$			13.4303i			0.714821i	−0.933947	+	0.357411i	$0.883660\pi$
$354$		−	36.8170i		−	1.95680i
$355$		−	10.2897i		−	0.546122i
$356$		−	10.1691i		−	0.538959i
$357$		0			0
$358$		−	48.1924i		−	2.54704i
$359$			1.97877i			0.104436i	0.998636	+	0.0522178i	$0.0166290\pi$
$359$			1.97877i			0.104436i	−0.998636	+	0.0522178i	$0.983371\pi$
$360$	−5.56167			−0.293126
$361$	−12.5042			−0.658114
$362$	−2.50189			−0.131496
$363$	10.7157	−	2.48478i	0.562428	−	0.130417i
$364$		0			0
$365$			10.1032i			0.528827i
$366$	14.0837			0.736169
$367$			12.1135i			0.632320i	0.948706	+	0.316160i	$0.102394\pi$
$367$			12.1135i			0.632320i	−0.948706	+	0.316160i	$0.897606\pi$
$368$	−4.29235			−0.223754
$369$	3.80891			0.198284
$370$	−7.33761			−0.381464
$371$		0			0
$372$	27.1282			1.40653
$373$			15.1073i			0.782228i	0.920342	+	0.391114i	$0.127910\pi$
$373$			15.1073i			0.782228i	−0.920342	+	0.391114i	$0.872090\pi$
$374$	26.7372	−	33.6465i	1.38255	−	1.73982i
$375$	−8.86541			−0.457808
$376$	−55.1828			−2.84584
$377$			8.23631i			0.424192i
$378$		0			0
$379$	−0.0566884			−0.00291189			−0.00145594	−	0.999999i	$-0.500463\pi$
$379$	−0.0566884			−0.00291189			−0.00145594	+	0.999999i	$0.500463\pi$
$380$		−	10.6633i		−	0.547015i
$381$	5.11223			0.261907
$382$			55.4767i			2.83844i
$383$			9.64881i			0.493031i	0.969139	+	0.246516i	$0.0792856\pi$
$383$			9.64881i			0.493031i	−0.969139	+	0.246516i	$0.920714\pi$
$384$	−16.2666			−0.830100
$385$		0			0
$386$	30.1504			1.53462
$387$			6.73386i			0.342301i
$388$			31.1360i			1.58069i
$389$	9.01841			0.457251			0.228626	−	0.973514i	$-0.426577\pi$
$389$	9.01841			0.457251			0.228626	+	0.973514i	$0.426577\pi$
$390$			2.31126i			0.117035i
$391$	3.92500			0.198496
$392$		0			0
$393$			12.1916i			0.614986i
$394$	2.23497			0.112596
$395$	−7.51060			−0.377899
$396$	−11.0750	−	8.80076i	−0.556540	−	0.442255i
$397$			14.6144i			0.733478i	0.930324	+	0.366739i	$0.119526\pi$
$397$			14.6144i			0.733478i	−0.930324	+	0.366739i	$0.880474\pi$
$398$	−25.5692			−1.28167
$399$		0			0
$400$	22.8594			1.14297
$401$	−14.2245			−0.710339			−0.355169	−	0.934802i	$-0.615577\pi$
$401$	−14.2245			−0.710339			−0.355169	+	0.934802i	$0.615577\pi$
$402$	−31.1007			−1.55116
$403$		−	5.98728i		−	0.298247i
$404$	22.5200			1.12041
$405$		−	0.980927i		−	0.0487427i
$406$		0			0
$407$	−7.75993	−	6.16643i	−0.384645	−	0.305659i
$408$	−29.3518			−1.45313
$409$	−3.58626			−0.177329			−0.0886646	−	0.996062i	$-0.528260\pi$
$409$	−3.58626			−0.177329			−0.0886646	+	0.996062i	$0.528260\pi$
$410$	9.35200			0.461862
$411$		−	3.02191i		−	0.149060i
$412$			73.2101i			3.60680i
$413$		0			0
$414$		−	1.89775i		−	0.0932695i
$415$			6.16896i			0.302822i
$416$		−	2.66491i		−	0.130658i
$417$			11.6396i			0.569995i
$418$	13.1634	−	16.5650i	0.643841	−	0.810219i
$419$		−	29.6711i		−	1.44953i	−0.688997	−	0.724764i	$-0.741949\pi$
$419$		−	29.6711i		−	1.44953i	0.688997	−	0.724764i	$-0.258051\pi$
$420$		0			0
$421$	−6.62829			−0.323043			−0.161521	−	0.986869i	$-0.551640\pi$
$421$	−6.62829			−0.323043			−0.161521	+	0.986869i	$0.551640\pi$
$422$	14.7890			0.719918
$423$		−	9.73275i		−	0.473223i
$424$		−	25.4933i		−	1.23806i
$425$	−20.9030			−1.01395
$426$	−26.2563			−1.27212
$427$		0			0
$428$			54.5477i			2.63666i
$429$	−1.94236	+	2.44429i	−0.0937778	+	0.118011i
$430$			16.5336i			0.797321i
$431$		−	35.9728i		−	1.73275i	−0.499393	−	0.866375i	$-0.666444\pi$
$431$		−	35.9728i		−	1.73275i	0.499393	−	0.866375i	$-0.333556\pi$
$432$			5.66137i			0.272383i
$433$		−	17.4731i		−	0.839702i	−0.907593	−	0.419851i	$-0.862082\pi$
$433$		−	17.4731i		−	0.839702i	0.907593	−	0.419851i	$-0.137918\pi$
$434$		0			0
$435$		−	8.58270i		−	0.411509i
$436$			7.59936i			0.363943i
$437$	1.93237			0.0924378
$438$	25.7804			1.23184
$439$	−32.5404			−1.55307			−0.776533	−	0.630076i	$-0.783024\pi$
$439$	−32.5404			−1.55307			−0.776533	+	0.630076i	$0.783024\pi$
$440$	−14.4415	−	11.4759i	−0.688471	−	0.547094i
$441$		0			0
$442$			12.1977i			0.580186i
$443$	2.66126			0.126440			0.0632201	−	0.998000i	$-0.479863\pi$
$443$	2.66126			0.126440			0.0632201	+	0.998000i	$0.479863\pi$
$444$			12.7464i			0.604918i
$445$	2.33873			0.110867
$446$	−32.9748			−1.56140
$447$	1.27750			0.0604236
$448$		0			0
$449$	−40.5312			−1.91278			−0.956392	−	0.292086i	$-0.905651\pi$
$449$	−40.5312			−1.91278			−0.956392	+	0.292086i	$0.905651\pi$
$450$			10.1067i			0.476434i
$451$	9.89026	+	7.85930i	0.465714	+	0.370080i
$452$	64.2133			3.02034
$453$	22.7665			1.06966
$454$			66.1522i			3.10468i
$455$		0			0
$456$	−14.4506			−0.676711
$457$			14.7399i			0.689505i	0.938694	+	0.344752i	$0.112037\pi$
$457$			14.7399i			0.689505i	−0.938694	+	0.344752i	$0.887963\pi$
$458$	−27.7091			−1.29476
$459$		−	5.17686i		−	0.241635i
$460$		−	3.17210i		−	0.147900i
$461$	−5.02966			−0.234255			−0.117127	−	0.993117i	$-0.537369\pi$
$461$	−5.02966			−0.234255			−0.117127	+	0.993117i	$0.537369\pi$
$462$		0			0
$463$	2.81117			0.130646			0.0653230	−	0.997864i	$-0.479192\pi$
$463$	2.81117			0.130646			0.0653230	+	0.997864i	$0.479192\pi$
$464$			49.5346i			2.29958i
$465$			6.23908i			0.289330i
$466$	−19.3792			−0.897726
$467$			14.0664i			0.650914i	0.945557	+	0.325457i	$0.105518\pi$
$467$			14.0664i			0.650914i	−0.945557	+	0.325457i	$0.894482\pi$
$468$	4.01497			0.185592
$469$		0			0
$470$		−	23.8968i		−	1.10228i
$471$	9.69954			0.446931
$472$	−83.3970			−3.83866
$473$	−13.8946	+	17.4852i	−0.638876	+	0.803971i
$474$			19.1648i			0.880269i
$475$	−10.2911			−0.472186
$476$		0			0
$477$	4.49633			0.205873
$478$	31.9338			1.46062
$479$	40.1260			1.83341			0.916703	−	0.399570i	$-0.130841\pi$
$479$	40.1260			1.83341			0.916703	+	0.399570i	$0.130841\pi$
$480$			2.77698i			0.126751i
$481$	2.81317			0.128270
$482$			64.1041i			2.91986i
$483$		0			0
$484$	−10.5980	−	45.7043i	−0.481727	−	2.07747i
$485$	−7.16082			−0.325156
$486$	−2.50303			−0.113540
$487$	2.60141			0.117881			0.0589405	−	0.998261i	$-0.481228\pi$
$487$	2.60141			0.117881			0.0589405	+	0.998261i	$0.481228\pi$
$488$		−	31.9021i		−	1.44414i
$489$			17.2853i			0.781667i
$490$		0			0
$491$		−	20.4535i		−	0.923052i	−0.887127	−	0.461526i	$-0.847302\pi$
$491$		−	20.4535i		−	0.923052i	0.887127	−	0.461526i	$-0.152698\pi$
$492$		−	16.2457i		−	0.732412i
$493$		−	45.2953i		−	2.04000i
$494$			6.00523i			0.270188i
$495$	2.02404	−	2.54709i	0.0909740	−	0.114483i
$496$		−	36.0085i		−	1.61683i
$497$		0			0
$498$	15.7413			0.705387
$499$	33.7200			1.50952			0.754758	−	0.656003i	$-0.227754\pi$
$499$	33.7200			1.50952			0.754758	+	0.656003i	$0.227754\pi$
$500$			37.8125i			1.69103i
$501$		−	4.94196i		−	0.220790i
$502$	16.2262			0.724209
$503$	−13.4051			−0.597705			−0.298852	−	0.954299i	$-0.596604\pi$
$503$	−13.4051			−0.597705			−0.298852	+	0.954299i	$0.596604\pi$
$504$		0			0
$505$			5.17928i			0.230475i
$506$	3.91582	−	4.92773i	0.174079	−	0.219064i
$507$			12.1139i			0.537996i
$508$		−	21.8046i		−	0.967421i
$509$			7.65294i			0.339210i	0.985512	+	0.169605i	$0.0542492\pi$
$509$			7.65294i			0.339210i	−0.985512	+	0.169605i	$0.945751\pi$
$510$		−	12.7107i		−	0.562839i
$511$		0			0
$512$			48.1706i			2.12886i
$513$		−	2.54869i		−	0.112527i
$514$	−40.2929			−1.77724
$515$	−16.8373			−0.741938
$516$	28.7211			1.26438
$517$	20.0825	−	25.2722i	0.883229	−	1.11147i
$518$		0			0
$519$			1.15936i			0.0508902i
$520$	5.23541			0.229588
$521$		−	8.91023i		−	0.390364i	−0.980767	−	0.195182i	$-0.937470\pi$
$521$		−	8.91023i		−	0.390364i	0.980767	−	0.195182i	$-0.0625298\pi$
$522$	−21.9005			−0.958558
$523$	10.2546			0.448401			0.224200	−	0.974543i	$-0.428023\pi$
$523$	10.2546			0.448401			0.224200	+	0.974543i	$0.428023\pi$
$524$	51.9994			2.27160
$525$		0			0
$526$	15.6572			0.682688
$527$			32.9268i			1.43431i
$528$	−11.6817	+	14.7004i	−0.508379	+	0.639752i
$529$	−22.4252			−0.975007
$530$	11.0398			0.479538
$531$		−	14.7090i		−	0.638315i
$532$		0			0
$533$	−3.58548			−0.155304
$534$		−	5.96775i		−	0.258250i
$535$	−12.5452			−0.542375
$536$			70.4486i			3.04292i
$537$		−	19.2536i		−	0.830853i
$538$	−23.7230			−1.02277
$539$		0			0
$540$	−4.18383			−0.180043
$541$		−	8.81266i		−	0.378886i	−0.981892	−	0.189443i	$-0.939332\pi$
$541$		−	8.81266i		−	0.378886i	0.981892	−	0.189443i	$-0.0606682\pi$
$542$		−	46.7412i		−	2.00771i
$543$	−0.999542			−0.0428944
$544$			14.6556i			0.628352i
$545$	−1.74774			−0.0748650
$546$		0			0
$547$			1.13200i			0.0484007i	0.999707	+	0.0242004i	$0.00770397\pi$
$547$			1.13200i			0.0484007i	−0.999707	+	0.0242004i	$0.992296\pi$
$548$	−12.8890			−0.550589
$549$	5.62667			0.240140
$550$	−20.8541	+	26.2432i	−0.889224	+	1.11901i
$551$		−	22.3000i		−	0.950010i
$552$	−4.29874			−0.182967
$553$		0			0
$554$	−44.1025			−1.87373
$555$	−2.93149			−0.124435
$556$	49.6450			2.10542
$557$			7.53621i			0.319319i	0.987172	+	0.159660i	$0.0510397\pi$
$557$			7.53621i			0.319319i	−0.987172	+	0.159660i	$0.948960\pi$
$558$	15.9203			0.673958
$559$		−	6.33884i		−	0.268104i
$560$		0			0
$561$	10.6819	−	13.4423i	0.450991	−	0.567534i
$562$	−27.4163			−1.15649
$563$	4.77290			0.201154			0.100577	−	0.994929i	$-0.467931\pi$
$563$	4.77290			0.201154			0.100577	+	0.994929i	$0.467931\pi$
$564$	−41.5119			−1.74797
$565$			14.7681i			0.621299i
$566$		−	69.2675i		−	2.91153i
$567$		0			0
$568$			59.4751i			2.49552i
$569$		−	22.1027i		−	0.926592i	−0.886204	−	0.463296i	$-0.846667\pi$
$569$		−	22.1027i		−	0.926592i	0.886204	−	0.463296i	$-0.153333\pi$
$570$		−	6.25778i		−	0.262110i
$571$		−	24.2021i		−	1.01283i	−0.862291	−	0.506414i	$-0.830971\pi$
$571$		−	24.2021i		−	1.01283i	0.862291	−	0.506414i	$-0.169029\pi$
$572$	10.4253	+	8.28449i	0.435905	+	0.346392i
$573$			22.1638i			0.925906i
$574$		0			0
$575$	−3.06137			−0.127668
$576$	−4.23671			−0.176529
$577$		−	11.8243i		−	0.492252i	−0.969238	−	0.246126i	$-0.920842\pi$
$577$		−	11.8243i		−	0.492252i	0.969238	−	0.246126i	$-0.0791577\pi$
$578$		−	24.5293i		−	1.02029i
$579$	12.0456			0.500596
$580$	−36.6067			−1.52001
$581$		0			0
$582$			18.2723i			0.757410i
$583$	11.6752	+	9.27771i	0.483538	+	0.384244i
$584$		−	58.3972i		−	2.41649i
$585$			0.923385i			0.0381773i
$586$		−	53.4166i		−	2.20662i
$587$			3.24719i			0.134026i	0.997752	+	0.0670130i	$0.0213469\pi$
$587$			3.24719i			0.134026i	−0.997752	+	0.0670130i	$0.978653\pi$
$588$		0			0
$589$			16.2107i			0.667948i
$590$		−	36.1148i		−	1.48682i
$591$	0.892906			0.0367293
$592$	16.9189			0.695363
$593$	−8.89431			−0.365245			−0.182623	−	0.983183i	$-0.558459\pi$
$593$	−8.89431			−0.365245			−0.182623	+	0.983183i	$0.558459\pi$
$594$	−6.49940	−	5.16475i	−0.266674	−	0.211912i
$595$		0			0
$596$		−	5.44876i		−	0.223190i
$597$	−10.2153			−0.418083
$598$			1.78643i			0.0730525i
$599$	2.47961			0.101314			0.0506571	−	0.998716i	$-0.483868\pi$
$599$	2.47961			0.101314			0.0506571	+	0.998716i	$0.483868\pi$
$600$	22.8934			0.934621
$601$	−27.6199			−1.12664			−0.563319	−	0.826239i	$-0.690476\pi$
$601$	−27.6199			−1.12664			−0.563319	+	0.826239i	$0.690476\pi$
$602$		0			0
$603$	−12.4252			−0.505994
$604$		−	97.1032i		−	3.95107i
$605$	10.5113	−	2.43738i	0.427345	−	0.0990938i
$606$	13.2160			0.536862
$607$	1.81561			0.0736935			0.0368467	−	0.999321i	$-0.488269\pi$
$607$	1.81561			0.0736935			0.0368467	+	0.999321i	$0.488269\pi$
$608$			7.21529i			0.292618i
$609$		0			0
$610$	13.8151			0.559358
$611$			9.16181i			0.370647i
$612$	−22.0802			−0.892539
$613$		−	29.2846i		−	1.18279i	−0.806381	−	0.591397i	$-0.798577\pi$
$613$		−	29.2846i		−	1.18279i	0.806381	−	0.591397i	$-0.201423\pi$
$614$			62.5241i			2.52327i
$615$	3.73627			0.150661
$616$		0			0
$617$	2.57805			0.103788			0.0518941	−	0.998653i	$-0.483474\pi$
$617$	2.57805			0.103788			0.0518941	+	0.998653i	$0.483474\pi$
$618$			42.9636i			1.72825i
$619$		−	41.3547i		−	1.66219i	−0.556133	−	0.831093i	$-0.687715\pi$
$619$		−	41.3547i		−	1.66219i	0.556133	−	0.831093i	$-0.312285\pi$
$620$	26.6108			1.06871
$621$		−	0.758182i		−	0.0304248i
$622$	60.5076			2.42613
$623$		0			0
$624$		−	5.32926i		−	0.213341i
$625$	11.4926			0.459703
$626$	55.2510			2.20828
$627$	5.25896	−	6.61796i	0.210023	−	0.264296i
$628$		−	41.3702i		−	1.65085i
$629$	−15.4710			−0.616867
$630$		0			0
$631$	−2.44038			−0.0971500			−0.0485750	−	0.998820i	$-0.515468\pi$
$631$	−2.44038			−0.0971500			−0.0485750	+	0.998820i	$0.515468\pi$
$632$	43.4117			1.72682
$633$	5.90844			0.234839
$634$			17.2010i			0.683140i
$635$	5.01473			0.199003
$636$		−	19.1776i		−	0.760442i
$637$		0			0
$638$	−56.8670	−	45.1894i	−2.25139	−	1.78907i
$639$	−10.4898			−0.414970
$640$	−15.9563			−0.630729
$641$	−33.3107			−1.31569			−0.657846	−	0.753152i	$-0.728532\pi$
$641$	−33.3107			−1.31569			−0.657846	+	0.753152i	$0.728532\pi$
$642$			32.0115i			1.26339i
$643$			14.8370i			0.585116i	0.956248	+	0.292558i	$0.0945064\pi$
$643$			14.8370i			0.585116i	−0.956248	+	0.292558i	$0.905494\pi$
$644$		0			0
$645$			6.60543i			0.260088i
$646$		−	33.0255i		−	1.29937i
$647$		−	7.92987i		−	0.311756i	−0.987776	−	0.155878i	$-0.950179\pi$
$647$		−	7.92987i		−	0.311756i	0.987776	−	0.155878i	$-0.0498206\pi$
$648$			5.66981i			0.222731i
$649$	30.3505	−	38.1935i	1.19136	−	1.49922i
$650$		−	9.51383i		−	0.373163i
$651$		0			0
$652$	73.7247			2.88728
$653$	13.1483			0.514534			0.257267	−	0.966340i	$-0.417178\pi$
$653$	13.1483			0.514534			0.257267	+	0.966340i	$0.417178\pi$
$654$			4.45971i			0.174389i
$655$			11.9591i			0.467280i
$656$	−21.5637			−0.841919
$657$	10.2997			0.401829
$658$		0			0
$659$			1.07554i			0.0418972i	0.999781	+	0.0209486i	$0.00666864\pi$
$659$			1.07554i			0.0418972i	−0.999781	+	0.0209486i	$0.993331\pi$
$660$	−10.8638	−	8.63290i	−0.422872	−	0.336035i
$661$		−	50.8171i		−	1.97656i	−0.152668	−	0.988278i	$-0.548786\pi$
$661$		−	50.8171i		−	1.97656i	0.152668	−	0.988278i	$-0.451214\pi$
$662$			11.9537i			0.464593i
$663$			4.87317i			0.189258i
$664$		−	35.6569i		−	1.38376i
$665$		0			0
$666$			7.48027i			0.289855i
$667$		−	6.63376i		−	0.256860i
$668$	−21.0783			−0.815544
$669$	−13.1739			−0.509333
$670$	−30.5076			−1.17861
$671$	14.6103	+	11.6101i	0.564023	+	0.448201i
$672$		0			0
$673$		−	29.6755i		−	1.14391i	−0.820287	−	0.571953i	$-0.806186\pi$
$673$		−	29.6755i		−	1.14391i	0.820287	−	0.571953i	$-0.193814\pi$
$674$	40.8314			1.57277
$675$			4.03778i			0.155414i
$676$	51.6678			1.98722
$677$	−25.1420			−0.966285			−0.483143	−	0.875542i	$-0.660505\pi$
$677$	−25.1420			−0.966285			−0.483143	+	0.875542i	$0.660505\pi$
$678$	37.6838			1.44724
$679$		0			0
$680$	−28.7920			−1.10412
$681$			26.4288i			1.01275i
$682$	41.3387	+	32.8498i	1.58294	+	1.25788i
$683$	−0.905093			−0.0346324			−0.0173162	−	0.999850i	$-0.505512\pi$
$683$	−0.905093			−0.0346324			−0.0173162	+	0.999850i	$0.505512\pi$
$684$	−10.8706			−0.415648
$685$		−	2.96427i		−	0.113259i
$686$		0			0
$687$	−11.0702			−0.422355
$688$		−	38.1229i		−	1.45342i
$689$	−4.23257			−0.161248
$690$		−	1.86156i		−	0.0708683i
$691$		−	4.67964i		−	0.178022i	−0.996031	−	0.0890109i	$-0.971629\pi$
$691$		−	4.67964i		−	0.178022i	0.996031	−	0.0890109i	$-0.0283706\pi$
$692$	4.94487			0.187976
$693$		0			0
$694$	−29.1637			−1.10704
$695$			11.4176i			0.433095i
$696$			49.6084i			1.88040i
$697$	19.7182			0.746880
$698$			30.9607i			1.17188i
$699$	−7.74230			−0.292841
$700$		0			0
$701$		−	0.533229i		−	0.0201398i	−0.999949	−	0.0100699i	$-0.996795\pi$
$701$		−	0.533229i		−	0.0201398i	0.999949	−	0.0100699i	$-0.00320540\pi$
$702$	2.35620			0.0889291
$703$	−7.61672			−0.287270
$704$	−11.0011	−	8.74202i	−0.414619	−	0.329477i
$705$		−	9.54712i		−	0.359565i
$706$	33.6164			1.26517
$707$		0			0
$708$	−62.7363			−2.35778
$709$	12.7072			0.477230			0.238615	−	0.971114i	$-0.423307\pi$
$709$	12.7072			0.477230			0.238615	+	0.971114i	$0.423307\pi$
$710$	−25.7555			−0.966588
$711$			7.65664i			0.287146i
$712$	−13.5180			−0.506608
$713$			4.82233i			0.180598i
$714$		0			0
$715$	−1.90531	+	2.39767i	−0.0712546	+	0.0896678i
$716$	−82.1199			−3.06896
$717$	12.7580			0.476458
$718$	4.95293			0.184842
$719$			32.2258i			1.20182i	0.799317	+	0.600909i	$0.205195\pi$
$719$			32.2258i			1.20182i	−0.799317	+	0.600909i	$0.794805\pi$
$720$			5.55339i			0.206963i
$721$		0			0
$722$			31.2984i			1.16480i
$723$			25.6106i			0.952467i
$724$			4.26322i			0.158441i
$725$			35.3289i			1.31208i
$726$	−6.21947	−	26.8217i	−0.230826	−	0.995447i
$727$			34.5072i			1.27980i	0.768457	+	0.639902i	$0.221025\pi$
$727$			34.5072i			1.27980i	−0.768457	+	0.639902i	$0.778975\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	25.2887			0.935978
$731$			34.8602i			1.28935i
$732$		−	23.9987i		−	0.887019i
$733$	−31.8974			−1.17816			−0.589078	−	0.808076i	$-0.700509\pi$
$733$	−31.8974			−1.17816			−0.589078	+	0.808076i	$0.700509\pi$
$734$	30.3205			1.11915
$735$		0			0
$736$			2.14639i			0.0791172i
$737$	−32.2635	−	25.6382i	−1.18844	−	0.944394i
$738$		−	9.53383i		−	0.350945i
$739$		−	43.2750i		−	1.59190i	−0.605365	−	0.795948i	$-0.706973\pi$
$739$		−	43.2750i		−	1.59190i	0.605365	−	0.795948i	$-0.293027\pi$
$740$			12.5033i			0.459630i
$741$			2.39918i			0.0881361i
$742$		0			0
$743$		−	50.2625i		−	1.84395i	−0.387246	−	0.921976i	$-0.626574\pi$
$743$		−	50.2625i		−	1.84395i	0.387246	−	0.921976i	$-0.373426\pi$
$744$		−	36.0622i		−	1.32210i
$745$	1.25313			0.0459113
$746$	37.8142			1.38447
$747$	6.28891			0.230099
$748$	−57.3337	−	45.5602i	−2.09633	−	1.66585i
$749$		0			0
$750$			22.1904i			0.810279i
$751$	−37.1749			−1.35653			−0.678266	−	0.734816i	$-0.737268\pi$
$751$	−37.1749			−1.35653			−0.678266	+	0.734816i	$0.737268\pi$
$752$			55.1007i			2.00932i
$753$	6.48260			0.236239
$754$	20.6158			0.750782
$755$	22.3323			0.812756
$756$		0			0
$757$	−5.95539			−0.216452			−0.108226	−	0.994126i	$-0.534517\pi$
$757$	−5.95539			−0.216452			−0.108226	+	0.994126i	$0.534517\pi$
$758$			0.141893i			0.00515378i
$759$	1.56443	−	1.96870i	0.0567852	−	0.0714594i
$760$	−14.1750			−0.514181
$761$	25.6120			0.928435			0.464217	−	0.885721i	$-0.346336\pi$
$761$	25.6120			0.928435			0.464217	+	0.885721i	$0.346336\pi$
$762$		−	12.7961i		−	0.463553i
$763$		0			0
$764$	94.5325			3.42007
$765$		−	5.07812i		−	0.183600i
$766$	24.1513			0.872622
$767$			13.8461i			0.499954i
$768$			32.2424i			1.16345i
$769$	52.0469			1.87686			0.938429	−	0.345472i	$-0.112281\pi$
$769$	52.0469			1.87686			0.938429	+	0.345472i	$0.112281\pi$
$770$		0			0
$771$	−16.0976			−0.579742
$772$		−	51.3764i		−	1.84908i
$773$		−	35.1928i		−	1.26580i	−0.774235	−	0.632899i	$-0.781865\pi$
$773$		−	35.1928i		−	1.26580i	0.774235	−	0.632899i	$-0.218135\pi$
$774$	16.8551			0.605843
$775$		−	25.6818i		−	0.922519i
$776$	41.3899			1.48581
$777$		0			0
$778$		−	22.5734i		−	0.809295i
$779$	9.70774			0.347816
$780$	3.93840			0.141017
$781$	−27.2379	−	21.6446i	−0.974649	−	0.774506i
$782$		−	9.82440i		−	0.351320i
$783$	−8.74957			−0.312684
$784$		0			0
$785$	9.51454			0.339589
$786$	30.5160			1.08847
$787$	−3.43603			−0.122481			−0.0612406	−	0.998123i	$-0.519506\pi$
$787$	−3.43603			−0.122481			−0.0612406	+	0.998123i	$0.519506\pi$
$788$		−	3.80840i		−	0.135669i
$789$	6.25530			0.222695
$790$			18.7993i			0.668849i
$791$		0			0
$792$	−11.6991	+	14.7223i	−0.415708	+	0.523134i
$793$	−5.29660			−0.188088
$794$	36.5805			1.29819
$795$	4.41057			0.156427
$796$			43.5699i			1.54430i
$797$		−	20.0096i		−	0.708777i	−0.935098	−	0.354388i	$-0.884689\pi$
$797$		−	20.0096i		−	0.708777i	0.935098	−	0.354388i	$-0.115311\pi$
$798$		0			0
$799$		−	50.3851i		−	1.78250i
$800$		−	11.4309i		−	0.404142i
$801$		−	2.38421i		−	0.0842418i
$802$			35.6044i			1.25724i
$803$	26.7442	+	21.2523i	0.943784	+	0.749978i
$804$			52.9957i			1.86902i
$805$		0			0
$806$	−14.9863			−0.527872
$807$	−9.47772			−0.333631
$808$		−	29.9365i		−	1.05316i
$809$			15.6850i			0.551457i	0.961236	+	0.275728i	$0.0889190\pi$
$809$			15.6850i			0.551457i	−0.961236	+	0.275728i	$0.911081\pi$
$810$	−2.45529			−0.0862702
$811$	23.1967			0.814545			0.407272	−	0.913307i	$-0.366480\pi$
$811$	23.1967			0.814545			0.407272	+	0.913307i	$0.366480\pi$
$812$		0			0
$813$		−	18.6738i		−	0.654919i
$814$	−15.4348	+	19.4234i	−0.540989	+	0.680788i
$815$			16.9556i			0.593928i
$816$			29.3081i			1.02599i
$817$			17.1625i			0.600441i
$818$			8.97653i			0.313857i
$819$		0			0
$820$		−	15.9358i		−	0.556503i
$821$		−	27.0909i		−	0.945478i	−0.881202	−	0.472739i	$-0.843265\pi$
$821$		−	27.0909i		−	0.945478i	0.881202	−	0.472739i	$-0.156735\pi$
$822$	−7.56393			−0.263823
$823$	45.6430			1.59102			0.795508	−	0.605943i	$-0.207204\pi$
$823$	45.6430			1.59102			0.795508	+	0.605943i	$0.207204\pi$
$824$	97.3202			3.39031
$825$	−8.33155	+	10.4845i	−0.290067	+	0.365025i
$826$		0			0
$827$		−	11.3712i		−	0.395415i	−0.980261	−	0.197707i	$-0.936650\pi$
$827$		−	11.3712i		−	0.395415i	0.980261	−	0.197707i	$-0.0633496\pi$
$828$	−3.23378			−0.112382
$829$			28.8085i			1.00056i	0.865863	+	0.500280i	$0.166770\pi$
$829$			28.8085i			1.00056i	−0.865863	+	0.500280i	$0.833230\pi$
$830$	15.4411			0.535969
$831$	−17.6196			−0.611217
$832$	3.98818			0.138265
$833$		0			0
$834$	29.1344			1.00884
$835$		−	4.84770i		−	0.167762i
$836$	−28.2268	−	22.4304i	−0.976243	−	0.775772i
$837$	6.36039			0.219847
$838$	−74.2678			−2.56554
$839$		−	12.9826i		−	0.448211i	−0.974565	−	0.224105i	$-0.928054\pi$
$839$		−	12.9826i		−	0.448211i	0.974565	−	0.224105i	$-0.0719460\pi$
$840$		0			0
$841$	−47.5550			−1.63983
$842$			16.5908i			0.571757i
$843$	−10.9532			−0.377249
$844$		−	25.2005i		−	0.867438i
$845$			11.8828i			0.408782i
$846$	−24.3614			−0.837562
$847$		0			0
$848$	−25.4554			−0.874141
$849$		−	27.6734i		−	0.949749i
$850$			52.3209i			1.79459i
$851$	−2.26581			−0.0776711
$852$			44.7408i			1.53279i
$853$	−38.9986			−1.33529			−0.667644	−	0.744481i	$-0.732697\pi$
$853$	−38.9986			−1.33529			−0.667644	+	0.744481i	$0.732697\pi$
$854$		0			0
$855$		−	2.50008i		−	0.0855010i
$856$	72.5117			2.47840
$857$	−0.497058			−0.0169792			−0.00848959	−	0.999964i	$-0.502702\pi$
$857$	−0.497058			−0.0169792			−0.00848959	+	0.999964i	$0.502702\pi$
$858$	6.11814	+	4.86178i	0.208870	+	0.165979i
$859$			22.7631i			0.776666i	0.921519	+	0.388333i	$0.126949\pi$
$859$			22.7631i			0.776666i	−0.921519	+	0.388333i	$0.873051\pi$
$860$	28.1733			0.960702
$861$		0			0
$862$	−90.0412			−3.06682
$863$	20.6980			0.704568			0.352284	−	0.935893i	$-0.385405\pi$
$863$	20.6980			0.704568			0.352284	+	0.935893i	$0.385405\pi$
$864$	2.83098			0.0963118
$865$			1.13725i			0.0386676i
$866$	−43.7357			−1.48620
$867$		−	9.79984i		−	0.332820i
$868$		0			0
$869$	−15.7987	+	19.8813i	−0.535934	+	0.674427i
$870$	−21.4828			−0.728334
$871$	11.6963			0.396315
$872$	10.1020			0.342098
$873$			7.30005i			0.247069i
$874$		−	4.83679i		−	0.163607i
$875$		0			0
$876$		−	43.9299i		−	1.48425i
$877$		−	33.4507i		−	1.12955i	−0.825246	−	0.564774i	$-0.808963\pi$
$877$		−	33.4507i		−	1.12955i	0.825246	−	0.564774i	$-0.191037\pi$
$878$			81.4496i			2.74879i
$879$		−	21.3408i		−	0.719806i
$880$	−11.4589	+	14.4200i	−0.386278	+	0.486098i
$881$		−	39.1311i		−	1.31836i	−0.751984	−	0.659181i	$-0.770903\pi$
$881$		−	39.1311i		−	1.31836i	0.751984	−	0.659181i	$-0.229097\pi$
$882$		0			0
$883$	38.6223			1.29974			0.649872	−	0.760044i	$-0.274823\pi$
$883$	38.6223			1.29974			0.649872	+	0.760044i	$0.274823\pi$
$884$	20.7849			0.699073
$885$		−	14.4284i		−	0.485006i
$886$		−	6.66122i		−	0.223788i
$887$	11.7524			0.394607			0.197303	−	0.980343i	$-0.436782\pi$
$887$	11.7524			0.394607			0.197303	+	0.980343i	$0.436782\pi$
$888$	16.9441			0.568608
$889$		0			0
$890$		−	5.85393i		−	0.196224i
$891$	−2.59661	−	2.06340i	−0.0869897	−	0.0691264i
$892$			56.1891i			1.88135i
$893$		−	24.8058i		−	0.830094i
$894$		−	3.19762i		−	0.106944i
$895$		−	18.8864i		−	0.631302i
$896$		0			0
$897$			0.713705i			0.0238299i
$898$			101.451i			3.38546i
$899$	55.6507			1.85605
$900$	17.2218			0.574062
$901$	23.2768			0.775464
$902$	19.6721	−	24.7557i	0.655009	−	0.824273i
$903$		0			0
$904$		−	85.3604i		−	2.83904i
$905$	−0.980478			−0.0325922
$906$		−	56.9854i		−	1.89321i
$907$	32.9563			1.09429			0.547147	−	0.837036i	$-0.315714\pi$
$907$	32.9563			1.09429			0.547147	+	0.837036i	$0.315714\pi$
$908$	112.724			3.74086
$909$	5.27998			0.175126
$910$		0			0
$911$	2.79047			0.0924525			0.0462263	−	0.998931i	$-0.485280\pi$
$911$	2.79047			0.0924525			0.0462263	+	0.998931i	$0.485280\pi$
$912$			14.4291i			0.477795i
$913$	16.3298	+	12.9765i	0.540439	+	0.429460i
$914$	36.8945			1.22036
$915$	5.51935			0.182464
$916$			47.2164i			1.56007i
$917$		0			0
$918$	−12.9578			−0.427673
$919$			46.8792i			1.54640i	0.634160	+	0.773202i	$0.281346\pi$
$919$			46.8792i			1.54640i	−0.634160	+	0.773202i	$0.718654\pi$
$920$	−4.21676			−0.139022
$921$			24.9793i			0.823097i
$922$			12.5894i			0.414610i
$923$	9.87445			0.325021
$924$		0			0
$925$	12.0668			0.396755
$926$		−	7.03645i		−	0.231232i
$927$			17.1646i			0.563760i
$928$	24.7698			0.813110
$929$		−	46.6397i		−	1.53020i	−0.643912	−	0.765099i	$-0.722690\pi$
$929$		−	46.6397i		−	1.53020i	0.643912	−	0.765099i	$-0.277310\pi$
$930$	15.6166			0.512089
$931$		0			0
$932$			33.0223i			1.08168i
$933$	24.1737			0.791412
$934$	35.2086			1.15206
$935$	10.4782	−	13.1859i	0.342673	−	0.431225i
$936$		−	5.33721i		−	0.174452i
$937$	1.36302			0.0445280			0.0222640	−	0.999752i	$-0.492913\pi$
$937$	1.36302			0.0445280			0.0222640	+	0.999752i	$0.492913\pi$
$938$		0			0
$939$	22.0736			0.720346
$940$	−40.7201			−1.32814
$941$	−39.2445			−1.27934			−0.639668	−	0.768652i	$-0.720928\pi$
$941$	−39.2445			−1.27934			−0.639668	+	0.768652i	$0.720928\pi$
$942$		−	24.2783i		−	0.791029i
$943$	2.88785			0.0940412
$944$			83.2729i			2.71030i
$945$		0			0
$946$	43.7661	+	34.7787i	1.42296	+	1.13075i
$947$	16.8170			0.546479			0.273240	−	0.961946i	$-0.411905\pi$
$947$	16.8170			0.546479			0.273240	+	0.961946i	$0.411905\pi$
$948$	32.6569			1.06065
$949$	−9.69548			−0.314729
$950$			25.7589i			0.835728i
$951$			6.87207i			0.222842i
$952$		0			0
$953$			46.5459i			1.50777i	0.657007	+	0.753884i	$0.271822\pi$
$953$			46.5459i			1.50777i	−0.657007	+	0.753884i	$0.728178\pi$
$954$		−	11.2545i		−	0.364376i
$955$			21.7411i			0.703525i
$956$		−	54.4153i		−	1.75992i
$957$	−22.7192	−	18.0539i	−0.734409	−	0.583598i
$958$		−	100.437i		−	3.24497i
$959$		0			0
$960$	−4.15590			−0.134131
$961$	−9.45450			−0.304984
$962$		−	7.04147i		−	0.227026i
$963$			12.7891i			0.412123i
$964$	109.234			3.51818
$965$	11.8158			0.380365
$966$		0			0
$967$		−	41.2782i		−	1.32742i	−0.747991	−	0.663709i	$-0.768981\pi$
$967$		−	41.2782i		−	1.32742i	0.747991	−	0.663709i	$-0.231019\pi$
$968$	−60.7559	+	14.0882i	−1.95277	+	0.452812i
$969$		−	13.1942i		−	0.423859i
$970$			17.9238i			0.575497i
$971$		−	50.5652i		−	1.62272i	−0.584550	−	0.811358i	$-0.698729\pi$
$971$		−	50.5652i		−	1.62272i	0.584550	−	0.811358i	$-0.301271\pi$
$972$			4.26518i			0.136806i
$973$		0			0
$974$		−	6.51141i		−	0.208639i
$975$		−	3.80092i		−	0.121727i
$976$	−31.8547			−1.01964
$977$	9.56102			0.305884			0.152942	−	0.988235i	$-0.451125\pi$
$977$	9.56102			0.305884			0.152942	+	0.988235i	$0.451125\pi$
$978$	43.2656			1.38348
$979$	4.91957	−	6.19086i	0.157230	−	0.197861i
$980$		0			0
$981$			1.78172i			0.0568860i
$982$	−51.1957			−1.63372
$983$			4.45092i			0.141962i	0.997478	+	0.0709811i	$0.0226130\pi$
$983$			4.45092i			0.141962i	−0.997478	+	0.0709811i	$0.977387\pi$
$984$	−21.5958			−0.688449
$985$	0.875876			0.0279077
$986$	−113.376			−3.61061
$987$		0			0
$988$	10.2329			0.325553
$989$			5.10549i			0.162345i
$990$	−6.37544	−	5.06625i	−0.202625	−	0.161016i
$991$	−45.3069			−1.43922			−0.719610	−	0.694378i	$-0.755680\pi$
$991$	−45.3069			−1.43922			−0.719610	+	0.694378i	$0.755680\pi$
$992$	−18.0061			−0.571694
$993$			4.77568i			0.151552i
$994$		0			0
$995$	−10.0204			−0.317669
$996$		−	26.8233i		−	0.849929i
$997$	39.2102			1.24180			0.620900	−	0.783890i	$-0.286767\pi$
$997$	39.2102			1.24180			0.620900	+	0.783890i	$0.286767\pi$
$998$		−	84.4024i		−	2.67171i
$999$			2.98848i			0.0945514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.c.a.538.3		32
7.2	even	3		231.2.p.a.10.2	✓	32
7.3	odd	6		231.2.p.a.208.15	yes	32
7.6	odd	2	inner	1617.2.c.a.538.4		32
11.10	odd	2	inner	1617.2.c.a.538.29		32
21.2	odd	6		693.2.bg.b.10.15		32
21.17	even	6		693.2.bg.b.208.2		32
77.10	even	6		231.2.p.a.208.2	yes	32
77.65	odd	6		231.2.p.a.10.15	yes	32
77.76	even	2	inner	1617.2.c.a.538.30		32
231.65	even	6		693.2.bg.b.10.2		32
231.164	odd	6		693.2.bg.b.208.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.p.a.10.2	✓	32	7.2	even	3
231.2.p.a.10.15	yes	32	77.65	odd	6
231.2.p.a.208.2	yes	32	77.10	even	6
231.2.p.a.208.15	yes	32	7.3	odd	6
693.2.bg.b.10.2		32	231.65	even	6
693.2.bg.b.10.15		32	21.2	odd	6
693.2.bg.b.208.2		32	21.17	even	6
693.2.bg.b.208.15		32	231.164	odd	6
1617.2.c.a.538.3		32	1.1	even	1	trivial
1617.2.c.a.538.4		32	7.6	odd	2	inner
1617.2.c.a.538.29		32	11.10	odd	2	inner
1617.2.c.a.538.30		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)

\(f(q)\)	\(=\)	\(q-2.50303i q^{2} -1.00000i q^{3} -4.26518 q^{4} -0.980927i q^{5} -2.50303 q^{6} +5.66981i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.50303i q^{2} -1.00000i q^{3} -4.26518 q^{4} -0.980927i q^{5} -2.50303 q^{6} +5.66981i q^{8} -1.00000 q^{9} -2.45529 q^{10} +(-2.59661 - 2.06340i) q^{11} +4.26518i q^{12} +0.941338 q^{13} -0.980927 q^{15} +5.66137 q^{16} -5.17686 q^{17} +2.50303i q^{18} -2.54869 q^{19} +4.18383i q^{20} +(-5.16475 + 6.49940i) q^{22} -0.758182 q^{23} +5.66981 q^{24} +4.03778 q^{25} -2.35620i q^{26} +1.00000i q^{27} +8.74957i q^{29} +2.45529i q^{30} -6.36039i q^{31} -2.83098i q^{32} +(-2.06340 + 2.59661i) q^{33} +12.9578i q^{34} +4.26518 q^{36} +2.98848 q^{37} +6.37946i q^{38} -0.941338i q^{39} +5.56167 q^{40} -3.80891 q^{41} -6.73386i q^{43} +(11.0750 + 8.80076i) q^{44} +0.980927i q^{45} +1.89775i q^{46} +9.73275i q^{47} -5.66137i q^{48} -10.1067i q^{50} +5.17686i q^{51} -4.01497 q^{52} -4.49633 q^{53} +2.50303 q^{54} +(-2.02404 + 2.54709i) q^{55} +2.54869i q^{57} +21.9005 q^{58} +14.7090i q^{59} +4.18383 q^{60} -5.62667 q^{61} -15.9203 q^{62} +4.23671 q^{64} -0.923385i q^{65} +(6.49940 + 5.16475i) q^{66} +12.4252 q^{67} +22.0802 q^{68} +0.758182i q^{69} +10.4898 q^{71} -5.66981i q^{72} -10.2997 q^{73} -7.48027i q^{74} -4.03778i q^{75} +10.8706 q^{76} -2.35620 q^{78} -7.65664i q^{79} -5.55339i q^{80} +1.00000 q^{81} +9.53383i q^{82} -6.28891 q^{83} +5.07812i q^{85} -16.8551 q^{86} +8.74957 q^{87} +(11.6991 - 14.7223i) q^{88} +2.38421i q^{89} +2.45529 q^{90} +3.23378 q^{92} -6.36039 q^{93} +24.3614 q^{94} +2.50008i q^{95} -2.83098 q^{96} -7.30005i q^{97} +(2.59661 + 2.06340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 24 q^{4} - 32 q^{9}+O(q^{10}) \) 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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