LMFDB - Embedded newform 2940.2.x.b.1273.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2940,2,Mod(97,2940)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2940.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2940, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 1, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2940.x (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$23.4760181943$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1273.1
Character	$\chi$	$=$	2940.1273
Dual form			2940.2.x.b.97.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{3} +(0.754578 - 2.10490i) q^{5} -1.00000i q^{9} +6.33122 q^{11} +(-1.38794 + 1.38794i) q^{13} +(0.954823 + 2.02196i) q^{15} +(5.29535 + 5.29535i) q^{17} -2.53368 q^{19} +(3.01557 + 3.01557i) q^{23} +(-3.86122 - 3.17663i) q^{25} +(0.707107 + 0.707107i) q^{27} -8.47255i q^{29} +5.78344i q^{31} +(-4.47685 + 4.47685i) q^{33} +(-5.28232 + 5.28232i) q^{37} -1.96284i q^{39} -5.07850i q^{41} +(5.60543 + 5.60543i) q^{43} +(-2.10490 - 0.754578i) q^{45} +(1.32422 + 1.32422i) q^{47} -7.48876 q^{51} +(2.43234 + 2.43234i) q^{53} +(4.77740 - 13.3266i) q^{55} +(1.79158 - 1.79158i) q^{57} -12.2495 q^{59} +10.9807i q^{61} +(1.87416 + 3.96877i) q^{65} +(3.00403 - 3.00403i) q^{67} -4.26466 q^{69} +6.80517 q^{71} +(6.47591 - 6.47591i) q^{73} +(4.97651 - 0.484084i) q^{75} -5.56831i q^{79} -1.00000 q^{81} +(1.29322 - 1.29322i) q^{83} +(15.1420 - 7.15044i) q^{85} +(5.99100 + 5.99100i) q^{87} -1.33158 q^{89} +(-4.08951 - 4.08951i) q^{93} +(-1.91186 + 5.33314i) q^{95} +(-7.58318 - 7.58318i) q^{97} -6.33122i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{5} - 16 q^{13} - 32 q^{19} + 16 q^{23} - 16 q^{25} + 16 q^{37} - 16 q^{43} - 8 q^{45} + 16 q^{47} + 24 q^{53} + 16 q^{57} - 64 q^{59} - 32 q^{65} + 32 q^{67} + 32 q^{71} + 16 q^{73} - 24 q^{81}+ \cdots - 16 q^{97}+O(q^{100}) $ 24 * q + 8 * q^5 - 16 * q^13 - 32 * q^19 + 16 * q^23 - 16 * q^25 + 16 * q^37 - 16 * q^43 - 8 * q^45 + 16 * q^47 + 24 * q^53 + 16 * q^57 - 64 * q^59 - 32 * q^65 + 32 * q^67 + 32 * q^71 + 16 * q^73 - 24 * q^81 + 48 * q^85 + 40 * q^87 - 144 * q^89 + 16 * q^93 - 64 * q^95 - 16 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times$.

$n$	$1081$	$1177$	$1471$	$1961$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	0.754578	−	2.10490i	0.337458	−	0.941341i
$5$	0.754578	−	2.10490i	0.337458	−	0.941341i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	6.33122			1.90893			0.954467	−	0.298318i	$-0.0964255\pi$
$11$	6.33122			1.90893			0.954467	+	0.298318i	$0.0964255\pi$
$12$		0			0
$13$	−1.38794	+	1.38794i	−0.384944	+	0.384944i	−0.872880	−	0.487936i	$-0.837750\pi$
$13$	−1.38794	+	1.38794i	−0.384944	+	0.384944i	0.487936	+	0.872880i	$0.337750\pi$
$14$		0			0
$15$	0.954823	+	2.02196i	0.246534	+	0.522067i
$16$		0			0
$17$	5.29535	+	5.29535i	1.28431	+	1.28431i	0.938190	+	0.346122i	$0.112502\pi$
$17$	5.29535	+	5.29535i	1.28431	+	1.28431i	0.346122	+	0.938190i	$0.387498\pi$
$18$		0			0
$19$	−2.53368			−0.581266			−0.290633	−	0.956835i	$-0.593866\pi$
$19$	−2.53368			−0.581266			−0.290633	+	0.956835i	$0.593866\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.01557	+	3.01557i	0.628789	+	0.628789i	0.947763	−	0.318974i	$-0.103338\pi$
$23$	3.01557	+	3.01557i	0.628789	+	0.628789i	−0.318974	+	0.947763i	$0.603338\pi$
$24$		0			0
$25$	−3.86122	−	3.17663i	−0.772245	−	0.635325i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$		−	8.47255i		−	1.57331i	−0.617391	−	0.786657i	$-0.711810\pi$
$29$		−	8.47255i		−	1.57331i	0.617391	−	0.786657i	$-0.288190\pi$
$30$		0			0
$31$			5.78344i			1.03874i	0.854550	+	0.519369i	$0.173833\pi$
$31$			5.78344i			1.03874i	−0.854550	+	0.519369i	$0.826167\pi$
$32$		0			0
$33$	−4.47685	+	4.47685i	−0.779319	+	0.779319i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.28232	+	5.28232i	−0.868407	+	0.868407i	−0.992296	−	0.123889i	$-0.960463\pi$
$37$	−5.28232	+	5.28232i	−0.868407	+	0.868407i	0.123889	+	0.992296i	$0.460463\pi$
$38$		0			0
$39$		−	1.96284i		−	0.314305i
$40$		0			0
$41$		−	5.07850i		−	0.793129i	−0.918007	−	0.396564i	$-0.870202\pi$
$41$		−	5.07850i		−	0.793129i	0.918007	−	0.396564i	$-0.129798\pi$
$42$		0			0
$43$	5.60543	+	5.60543i	0.854821	+	0.854821i	0.990722	−	0.135902i	$-0.0433931\pi$
$43$	5.60543	+	5.60543i	0.854821	+	0.854821i	−0.135902	+	0.990722i	$0.543393\pi$
$44$		0			0
$45$	−2.10490	−	0.754578i	−0.313780	−	0.112486i
$46$		0			0
$47$	1.32422	+	1.32422i	0.193157	+	0.193157i	0.797059	−	0.603902i	$-0.206388\pi$
$47$	1.32422	+	1.32422i	0.193157	+	0.193157i	−0.603902	+	0.797059i	$0.706388\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−7.48876			−1.04864
$52$		0			0
$53$	2.43234	+	2.43234i	0.334108	+	0.334108i	0.854144	−	0.520036i	$-0.174082\pi$
$53$	2.43234	+	2.43234i	0.334108	+	0.334108i	−0.520036	+	0.854144i	$0.674082\pi$
$54$		0			0
$55$	4.77740	−	13.3266i	0.644184	−	1.79696i
$56$		0			0
$57$	1.79158	−	1.79158i	0.237301	−	0.237301i
$58$		0			0
$59$	−12.2495			−1.59476			−0.797378	−	0.603481i	$-0.793780\pi$
$59$	−12.2495			−1.59476			−0.797378	+	0.603481i	$0.793780\pi$
$60$		0			0
$61$			10.9807i			1.40594i	0.711220	+	0.702970i	$0.248143\pi$
$61$			10.9807i			1.40594i	−0.711220	+	0.702970i	$0.751857\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.87416	+	3.96877i	0.232461	+	0.492266i
$66$		0			0
$67$	3.00403	−	3.00403i	0.367000	−	0.367000i	−0.499382	−	0.866382i	$-0.666440\pi$
$67$	3.00403	−	3.00403i	0.367000	−	0.367000i	0.866382	+	0.499382i	$0.166440\pi$
$68$		0			0
$69$	−4.26466			−0.513404
$70$		0			0
$71$	6.80517			0.807625			0.403812	−	0.914842i	$-0.367685\pi$
$71$	6.80517			0.807625			0.403812	+	0.914842i	$0.367685\pi$
$72$		0			0
$73$	6.47591	−	6.47591i	0.757948	−	0.757948i	−0.218001	−	0.975949i	$-0.569954\pi$
$73$	6.47591	−	6.47591i	0.757948	−	0.757948i	0.975949	+	0.218001i	$0.0699536\pi$
$74$		0			0
$75$	4.97651	−	0.484084i	0.574638	−	0.0558972i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		−	5.56831i		−	0.626484i	−0.949673	−	0.313242i	$-0.898585\pi$
$79$		−	5.56831i		−	0.626484i	0.949673	−	0.313242i	$-0.101415\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	1.29322	−	1.29322i	0.141949	−	0.141949i	−0.632561	−	0.774510i	$-0.717996\pi$
$83$	1.29322	−	1.29322i	0.141949	−	0.141949i	0.774510	+	0.632561i	$0.217996\pi$
$84$		0			0
$85$	15.1420	−	7.15044i	1.64238	−	0.775574i
$86$		0			0
$87$	5.99100	+	5.99100i	0.642303	+	0.642303i
$88$		0			0
$89$	−1.33158			−0.141147			−0.0705735	−	0.997507i	$-0.522483\pi$
$89$	−1.33158			−0.141147			−0.0705735	+	0.997507i	$0.522483\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−4.08951	−	4.08951i	−0.424063	−	0.424063i
$94$		0			0
$95$	−1.91186	+	5.33314i	−0.196153	+	0.547169i
$96$		0			0
$97$	−7.58318	−	7.58318i	−0.769956	−	0.769956i	0.208143	−	0.978098i	$-0.433258\pi$
$97$	−7.58318	−	7.58318i	−0.769956	−	0.769956i	−0.978098	+	0.208143i	$0.933258\pi$
$98$		0			0
$99$		−	6.33122i		−	0.636311i
$100$		0			0
$101$			17.8771i			1.77884i	0.457093	+	0.889419i	$0.348891\pi$
$101$			17.8771i			1.77884i	−0.457093	+	0.889419i	$0.651109\pi$
$102$		0			0
$103$	7.47105	−	7.47105i	0.736144	−	0.736144i	−0.235685	−	0.971829i	$-0.575733\pi$
$103$	7.47105	−	7.47105i	0.736144	−	0.736144i	0.971829	+	0.235685i	$0.0757334\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.2939	−	12.2939i	1.18849	−	1.18849i	0.211010	−	0.977484i	$-0.432325\pi$
$107$	12.2939	−	12.2939i	1.18849	−	1.18849i	0.977484	−	0.211010i	$-0.0676751\pi$
$108$		0			0
$109$		−	3.93872i		−	0.377261i	−0.982048	−	0.188630i	$-0.939595\pi$
$109$		−	3.93872i		−	0.377261i	0.982048	−	0.188630i	$-0.0604048\pi$
$110$		0			0
$111$		−	7.47032i		−	0.709052i
$112$		0			0
$113$	12.0500	+	12.0500i	1.13357	+	1.13357i	0.989580	+	0.143987i	$0.0459923\pi$
$113$	12.0500	+	12.0500i	1.13357	+	1.13357i	0.143987	+	0.989580i	$0.454008\pi$
$114$		0			0
$115$	8.62296	−	4.07199i	0.804095	−	0.379715i
$116$		0			0
$117$	1.38794	+	1.38794i	0.128315	+	0.128315i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	29.0843			2.64403
$122$		0			0
$123$	3.59104	+	3.59104i	0.323794	+	0.323794i
$124$		0			0
$125$	−9.60008	+	5.73048i	−0.858657	+	0.512550i
$126$		0			0
$127$	7.13365	−	7.13365i	0.633009	−	0.633009i	−0.315812	−	0.948822i	$-0.602277\pi$
$127$	7.13365	−	7.13365i	0.633009	−	0.633009i	0.948822	+	0.315812i	$0.102277\pi$
$128$		0			0
$129$	−7.92728			−0.697958
$130$		0			0
$131$			3.62791i			0.316972i	0.987361	+	0.158486i	$0.0506613\pi$
$131$			3.62791i			0.316972i	−0.987361	+	0.158486i	$0.949339\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	2.02196	−	0.954823i	0.174022	−	0.0821781i
$136$		0			0
$137$	1.96363	−	1.96363i	0.167764	−	0.167764i	−0.618232	−	0.785996i	$-0.712151\pi$
$137$	1.96363	−	1.96363i	0.167764	−	0.167764i	0.785996	+	0.618232i	$0.212151\pi$
$138$		0			0
$139$	7.91103			0.671004			0.335502	−	0.942039i	$-0.391094\pi$
$139$	7.91103			0.671004			0.335502	+	0.942039i	$0.391094\pi$
$140$		0			0
$141$	−1.87272			−0.157712
$142$		0			0
$143$	−8.78732	+	8.78732i	−0.734832	+	0.734832i
$144$		0			0
$145$	−17.8339	−	6.39320i	−1.48102	−	0.530927i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			4.62794i			0.379136i	0.981868	+	0.189568i	$0.0607087\pi$
$149$			4.62794i			0.379136i	−0.981868	+	0.189568i	$0.939291\pi$
$150$		0			0
$151$	−16.7181			−1.36050			−0.680251	−	0.732979i	$-0.738129\pi$
$151$	−16.7181			−1.36050			−0.680251	+	0.732979i	$0.738129\pi$
$152$		0			0
$153$	5.29535	−	5.29535i	0.428104	−	0.428104i
$154$		0			0
$155$	12.1736	+	4.36406i	0.977806	+	0.350530i
$156$		0			0
$157$	−3.24781	−	3.24781i	−0.259204	−	0.259204i	0.565526	−	0.824730i	$-0.308673\pi$
$157$	−3.24781	−	3.24781i	−0.259204	−	0.259204i	−0.824730	+	0.565526i	$0.808673\pi$
$158$		0			0
$159$	−3.43985			−0.272798
$160$		0			0
$161$		0			0
$162$		0			0
$163$	13.6375	+	13.6375i	1.06817	+	1.06817i	0.997499	+	0.0706738i	$0.0225149\pi$
$163$	13.6375	+	13.6375i	1.06817	+	1.06817i	0.0706738	+	0.997499i	$0.477485\pi$
$164$		0			0
$165$	6.04519	+	12.8014i	0.470617	+	0.996592i
$166$		0			0
$167$	4.68721	+	4.68721i	0.362707	+	0.362707i	0.864809	−	0.502102i	$-0.167440\pi$
$167$	4.68721	+	4.68721i	0.362707	+	0.362707i	−0.502102	+	0.864809i	$0.667440\pi$
$168$		0			0
$169$			9.14727i			0.703636i
$170$		0			0
$171$			2.53368i			0.193755i
$172$		0			0
$173$	−12.9851	+	12.9851i	−0.987236	+	0.987236i	−0.999920	−	0.0126836i	$-0.995963\pi$
$173$	−12.9851	+	12.9851i	−0.987236	+	0.987236i	0.0126836	+	0.999920i	$0.495963\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.66174	−	8.66174i	0.651056	−	0.651056i
$178$		0			0
$179$		−	6.36935i		−	0.476068i	−0.971257	−	0.238034i	$-0.923497\pi$
$179$		−	6.36935i		−	0.476068i	0.971257	−	0.238034i	$-0.0765029\pi$
$180$		0			0
$181$		−	6.59928i		−	0.490521i	−0.969457	−	0.245260i	$-0.921127\pi$
$181$		−	6.59928i		−	0.490521i	0.969457	−	0.245260i	$-0.0788734\pi$
$182$		0			0
$183$	−7.76455	−	7.76455i	−0.573972	−	0.573972i
$184$		0			0
$185$	7.13284	+	15.1047i	0.524417	+	1.11052i
$186$		0			0
$187$	33.5260	+	33.5260i	2.45166	+	2.45166i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.18382			−0.375088			−0.187544	−	0.982256i	$-0.560053\pi$
$191$	−5.18382			−0.375088			−0.187544	+	0.982256i	$0.560053\pi$
$192$		0			0
$193$	4.77205	+	4.77205i	0.343500	+	0.343500i	0.857681	−	0.514182i	$-0.171904\pi$
$193$	4.77205	+	4.77205i	0.343500	+	0.343500i	−0.514182	+	0.857681i	$0.671904\pi$
$194$		0			0
$195$	−4.13158	−	1.48111i	−0.295869	−	0.106065i
$196$		0			0
$197$	−1.65986	+	1.65986i	−0.118260	+	0.118260i	−0.763760	−	0.645500i	$-0.776649\pi$
$197$	−1.65986	+	1.65986i	−0.118260	+	0.118260i	0.645500	+	0.763760i	$0.276649\pi$
$198$		0			0
$199$	17.1345			1.21463			0.607316	−	0.794460i	$-0.292246\pi$
$199$	17.1345			1.21463			0.607316	+	0.794460i	$0.292246\pi$
$200$		0			0
$201$			4.24833i			0.299654i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−10.6898	−	3.83213i	−0.746605	−	0.267647i
$206$		0			0
$207$	3.01557	−	3.01557i	0.209596	−	0.209596i
$208$		0			0
$209$	−16.0413			−1.10960
$210$		0			0
$211$	6.35620			0.437579			0.218789	−	0.975772i	$-0.429789\pi$
$211$	6.35620			0.437579			0.218789	+	0.975772i	$0.429789\pi$
$212$		0			0
$213$	−4.81198	+	4.81198i	−0.329711	+	0.329711i
$214$		0			0
$215$	16.0286	−	7.56915i	1.09314	−	0.516212i
$216$		0			0
$217$		0			0
$218$		0			0
$219$			9.15831i			0.618862i
$220$		0			0
$221$	−14.6992			−0.988776
$222$		0			0
$223$	9.79765	−	9.79765i	0.656099	−	0.656099i	−0.298356	−	0.954455i	$-0.596438\pi$
$223$	9.79765	−	9.79765i	0.656099	−	0.656099i	0.954455	+	0.298356i	$0.0964381\pi$
$224$		0			0
$225$	−3.17663	+	3.86122i	−0.211775	+	0.257415i
$226$		0			0
$227$	−8.55902	−	8.55902i	−0.568082	−	0.568082i	0.363509	−	0.931591i	$-0.381579\pi$
$227$	−8.55902	−	8.55902i	−0.568082	−	0.568082i	−0.931591	+	0.363509i	$0.881579\pi$
$228$		0			0
$229$	−7.98457			−0.527635			−0.263818	−	0.964573i	$-0.584982\pi$
$229$	−7.98457			−0.527635			−0.263818	+	0.964573i	$0.584982\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−18.8962	−	18.8962i	−1.23793	−	1.23793i	−0.960844	−	0.277089i	$-0.910630\pi$
$233$	−18.8962	−	18.8962i	−1.23793	−	1.23793i	−0.277089	−	0.960844i	$-0.589370\pi$
$234$		0			0
$235$	3.78657	−	1.78812i	0.247009	−	0.116644i
$236$		0			0
$237$	3.93739	+	3.93739i	0.255761	+	0.255761i
$238$		0			0
$239$		−	20.8422i		−	1.34817i	−0.738654	−	0.674085i	$-0.764538\pi$
$239$		−	20.8422i		−	1.34817i	0.738654	−	0.674085i	$-0.235462\pi$
$240$		0			0
$241$		−	6.16316i		−	0.397004i	−0.980101	−	0.198502i	$-0.936392\pi$
$241$		−	6.16316i		−	0.397004i	0.980101	−	0.198502i	$-0.0636076\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.51658	−	3.51658i	0.223755	−	0.223755i
$248$		0			0
$249$			1.82888i			0.115901i
$250$		0			0
$251$		−	14.0646i		−	0.887751i	−0.896089	−	0.443875i	$-0.853603\pi$
$251$		−	14.0646i		−	0.887751i	0.896089	−	0.443875i	$-0.146397\pi$
$252$		0			0
$253$	19.0922	+	19.0922i	1.20032	+	1.20032i
$254$		0			0
$255$	−5.65085	+	15.7631i	−0.353870	+	0.987124i
$256$		0			0
$257$	11.3998	+	11.3998i	0.711103	+	0.711103i	0.966766	−	0.255663i	$-0.0822937\pi$
$257$	11.3998	+	11.3998i	0.711103	+	0.711103i	−0.255663	+	0.966766i	$0.582294\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−8.47255			−0.524438
$262$		0			0
$263$	7.18578	+	7.18578i	0.443094	+	0.443094i	0.893050	−	0.449956i	$-0.148561\pi$
$263$	7.18578	+	7.18578i	0.443094	+	0.443094i	−0.449956	+	0.893050i	$0.648561\pi$
$264$		0			0
$265$	6.95523	−	3.28445i	0.427256	−	0.201762i
$266$		0			0
$267$	0.941568	−	0.941568i	0.0576230	−	0.0576230i
$268$		0			0
$269$	16.6777			1.01686			0.508429	−	0.861104i	$-0.330226\pi$
$269$	16.6777			1.01686			0.508429	+	0.861104i	$0.330226\pi$
$270$		0			0
$271$		−	12.7773i		−	0.776166i	−0.921624	−	0.388083i	$-0.873137\pi$
$271$		−	12.7773i		−	0.776166i	0.921624	−	0.388083i	$-0.126863\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−24.4462	−	20.1119i	−1.47416	−	1.21279i
$276$		0			0
$277$	−14.7904	+	14.7904i	−0.888668	+	0.888668i	−0.994395	−	0.105727i	$-0.966283\pi$
$277$	−14.7904	+	14.7904i	−0.888668	+	0.888668i	0.105727	+	0.994395i	$0.466283\pi$
$278$		0			0
$279$	5.78344			0.346246
$280$		0			0
$281$	−10.4867			−0.625585			−0.312792	−	0.949822i	$-0.601264\pi$
$281$	−10.4867			−0.625585			−0.312792	+	0.949822i	$0.601264\pi$
$282$		0			0
$283$	3.52170	−	3.52170i	0.209343	−	0.209343i	−0.594645	−	0.803988i	$-0.702707\pi$
$283$	3.52170	−	3.52170i	0.209343	−	0.209343i	0.803988	+	0.594645i	$0.202707\pi$
$284$		0			0
$285$	−2.41921	−	5.12299i	−0.143302	−	0.303460i
$286$		0			0
$287$		0			0
$288$		0			0
$289$			39.0815i			2.29891i
$290$		0			0
$291$	10.7242			0.628666
$292$		0			0
$293$	−0.231971	+	0.231971i	−0.0135519	+	0.0135519i	−0.713850	−	0.700298i	$-0.753050\pi$
$293$	−0.231971	+	0.231971i	−0.0135519	+	0.0135519i	0.700298	+	0.713850i	$0.253050\pi$
$294$		0			0
$295$	−9.24324	+	25.7841i	−0.538162	+	1.50121i
$296$		0			0
$297$	4.47685	+	4.47685i	0.259773	+	0.259773i
$298$		0			0
$299$	−8.37083			−0.484097
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−12.6410	−	12.6410i	−0.726207	−	0.726207i
$304$		0			0
$305$	23.1134	+	8.28582i	1.32347	+	0.474445i
$306$		0			0
$307$	−10.5619	−	10.5619i	−0.602801	−	0.602801i	0.338254	−	0.941055i	$-0.390164\pi$
$307$	−10.5619	−	10.5619i	−0.602801	−	0.602801i	−0.941055	+	0.338254i	$0.890164\pi$
$308$		0			0
$309$			10.5657i			0.601059i
$310$		0			0
$311$			11.1728i			0.633552i	0.948500	+	0.316776i	$0.102600\pi$
$311$			11.1728i			0.633552i	−0.948500	+	0.316776i	$0.897400\pi$
$312$		0			0
$313$	5.10465	−	5.10465i	0.288532	−	0.288532i	−0.547968	−	0.836499i	$-0.684598\pi$
$313$	5.10465	−	5.10465i	0.288532	−	0.288532i	0.836499	+	0.547968i	$0.184598\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.41199	−	3.41199i	0.191636	−	0.191636i	−0.604766	−	0.796403i	$-0.706734\pi$
$317$	3.41199	−	3.41199i	0.191636	−	0.191636i	0.796403	+	0.604766i	$0.206734\pi$
$318$		0			0
$319$		−	53.6416i		−	3.00335i
$320$		0			0
$321$			17.3862i			0.970401i
$322$		0			0
$323$	−13.4167	−	13.4167i	−0.746526	−	0.746526i
$324$		0			0
$325$	9.76808	−	0.950178i	0.541836	−	0.0527064i
$326$		0			0
$327$	2.78509	+	2.78509i	0.154016	+	0.154016i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	28.0612			1.54239			0.771193	−	0.636602i	$-0.219661\pi$
$331$	28.0612			1.54239			0.771193	+	0.636602i	$0.219661\pi$
$332$		0			0
$333$	5.28232	+	5.28232i	0.289469	+	0.289469i
$334$		0			0
$335$	−4.05641	−	8.58995i	−0.221625	−	0.469319i
$336$		0			0
$337$	−3.75987	+	3.75987i	−0.204813	+	0.204813i	−0.802059	−	0.597245i	$-0.796262\pi$
$337$	−3.75987	+	3.75987i	−0.204813	+	0.204813i	0.597245	+	0.802059i	$0.296262\pi$
$338$		0			0
$339$	−17.0412			−0.925553
$340$		0			0
$341$			36.6162i			1.98288i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−3.21802	+	8.97669i	−0.173252	+	0.483289i
$346$		0			0
$347$	2.47573	−	2.47573i	0.132904	−	0.132904i	−0.637525	−	0.770429i	$-0.720042\pi$
$347$	2.47573	−	2.47573i	0.132904	−	0.132904i	0.770429	+	0.637525i	$0.220042\pi$
$348$		0			0
$349$	8.83087			0.472706			0.236353	−	0.971667i	$-0.424048\pi$
$349$	8.83087			0.472706			0.236353	+	0.971667i	$0.424048\pi$
$350$		0			0
$351$	−1.96284			−0.104768
$352$		0			0
$353$	3.61944	−	3.61944i	0.192643	−	0.192643i	−0.604194	−	0.796837i	$-0.706505\pi$
$353$	3.61944	−	3.61944i	0.192643	−	0.192643i	0.796837	+	0.604194i	$0.206505\pi$
$354$		0			0
$355$	5.13503	−	14.3242i	0.272539	−	0.760250i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			27.0366i			1.42694i	0.700687	+	0.713469i	$0.252877\pi$
$359$			27.0366i			1.42694i	−0.700687	+	0.713469i	$0.747123\pi$
$360$		0			0
$361$	−12.5805			−0.662130
$362$		0			0
$363$	−20.5657	+	20.5657i	−1.07942	+	1.07942i
$364$		0			0
$365$	−8.74457	−	18.5177i	−0.457712	−	0.969262i
$366$		0			0
$367$	4.52234	+	4.52234i	0.236064	+	0.236064i	0.815218	−	0.579154i	$-0.196617\pi$
$367$	4.52234	+	4.52234i	0.236064	+	0.236064i	−0.579154	+	0.815218i	$0.696617\pi$
$368$		0			0
$369$	−5.07850			−0.264376
$370$		0			0
$371$		0			0
$372$		0			0
$373$	6.49055	+	6.49055i	0.336068	+	0.336068i	0.854885	−	0.518817i	$-0.173627\pi$
$373$	6.49055	+	6.49055i	0.336068	+	0.336068i	−0.518817	+	0.854885i	$0.673627\pi$
$374$		0			0
$375$	2.73622	−	10.8403i	0.141298	−	0.559793i
$376$		0			0
$377$	11.7594	+	11.7594i	0.605638	+	0.605638i
$378$		0			0
$379$		−	31.5827i		−	1.62229i	−0.584843	−	0.811146i	$-0.698844\pi$
$379$		−	31.5827i		−	1.62229i	0.584843	−	0.811146i	$-0.301156\pi$
$380$		0			0
$381$			10.0885i			0.516850i
$382$		0			0
$383$	1.03214	−	1.03214i	0.0527400	−	0.0527400i	−0.680245	−	0.732985i	$-0.738127\pi$
$383$	1.03214	−	1.03214i	0.0527400	−	0.0527400i	0.732985	+	0.680245i	$0.238127\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.60543	−	5.60543i	0.284940	−	0.284940i
$388$		0			0
$389$		−	0.0757408i		−	0.00384021i	−0.999998	−	0.00192011i	$-0.999389\pi$
$389$		−	0.0757408i		−	0.00384021i	0.999998	−	0.00192011i	$-0.000611189\pi$
$390$		0			0
$391$			31.9370i			1.61512i
$392$		0			0
$393$	−2.56532	−	2.56532i	−0.129403	−	0.129403i
$394$		0			0
$395$	−11.7207	−	4.20172i	−0.589734	−	0.211412i
$396$		0			0
$397$	−23.5494	−	23.5494i	−1.18191	−	1.18191i	−0.979248	−	0.202664i	$-0.935040\pi$
$397$	−23.5494	−	23.5494i	−1.18191	−	1.18191i	−0.202664	−	0.979248i	$-0.564960\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.6547			0.582010			0.291005	−	0.956722i	$-0.406010\pi$
$401$	11.6547			0.582010			0.291005	+	0.956722i	$0.406010\pi$
$402$		0			0
$403$	−8.02705	−	8.02705i	−0.399856	−	0.399856i
$404$		0			0
$405$	−0.754578	+	2.10490i	−0.0374953	+	0.104593i
$406$		0			0
$407$	−33.4435	+	33.4435i	−1.65773	+	1.65773i
$408$		0			0
$409$	0.154285			0.00762892			0.00381446	−	0.999993i	$-0.498786\pi$
$409$	0.154285			0.00762892			0.00381446	+	0.999993i	$0.498786\pi$
$410$		0			0
$411$			2.77699i			0.136979i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.74626	−	3.69792i	−0.0857205	−	0.181524i
$416$		0			0
$417$	−5.59394	+	5.59394i	−0.273936	+	0.273936i
$418$		0			0
$419$	35.2229			1.72075			0.860375	−	0.509662i	$-0.170229\pi$
$419$	35.2229			1.72075			0.860375	+	0.509662i	$0.170229\pi$
$420$		0			0
$421$	−5.36455			−0.261452			−0.130726	−	0.991419i	$-0.541731\pi$
$421$	−5.36455			−0.261452			−0.130726	+	0.991419i	$0.541731\pi$
$422$		0			0
$423$	1.32422	−	1.32422i	0.0643856	−	0.0643856i
$424$		0			0
$425$	−3.62519	−	37.2679i	−0.175847	−	1.80776i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		−	12.4271i		−	0.599988i
$430$		0			0
$431$	0.957776			0.0461344			0.0230672	−	0.999734i	$-0.492657\pi$
$431$	0.957776			0.0461344			0.0230672	+	0.999734i	$0.492657\pi$
$432$		0			0
$433$	−24.2660	+	24.2660i	−1.16615	+	1.16615i	−0.183047	+	0.983104i	$0.558596\pi$
$433$	−24.2660	+	24.2660i	−1.16615	+	1.16615i	−0.983104	+	0.183047i	$0.941404\pi$
$434$		0			0
$435$	17.1311	−	8.08979i	0.821375	−	0.387876i
$436$		0			0
$437$	−7.64048	−	7.64048i	−0.365494	−	0.365494i
$438$		0			0
$439$	−4.53062			−0.216235			−0.108117	−	0.994138i	$-0.534482\pi$
$439$	−4.53062			−0.216235			−0.108117	+	0.994138i	$0.534482\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.48523	−	8.48523i	−0.403145	−	0.403145i	0.476195	−	0.879340i	$-0.342016\pi$
$443$	−8.48523	−	8.48523i	−0.403145	−	0.403145i	−0.879340	+	0.476195i	$0.842016\pi$
$444$		0			0
$445$	−1.00478	+	2.80284i	−0.0476311	+	0.132867i
$446$		0			0
$447$	−3.27245	−	3.27245i	−0.154782	−	0.154782i
$448$		0			0
$449$		−	5.81337i		−	0.274350i	−0.990547	−	0.137175i	$-0.956198\pi$
$449$		−	5.81337i		−	0.274350i	0.990547	−	0.137175i	$-0.0438023\pi$
$450$		0			0
$451$		−	32.1531i		−	1.51403i
$452$		0			0
$453$	11.8215	−	11.8215i	0.555423	−	0.555423i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	19.0700	−	19.0700i	0.892057	−	0.892057i	−0.102659	−	0.994717i	$-0.532735\pi$
$457$	19.0700	−	19.0700i	0.892057	−	0.892057i	0.994717	+	0.102659i	$0.0327352\pi$
$458$		0			0
$459$			7.48876i			0.349545i
$460$		0			0
$461$		−	12.6645i		−	0.589845i	−0.955521	−	0.294923i	$-0.904706\pi$
$461$		−	12.6645i		−	0.589845i	0.955521	−	0.294923i	$-0.0952939\pi$
$462$		0			0
$463$	4.84858	+	4.84858i	0.225333	+	0.225333i	0.810740	−	0.585407i	$-0.199065\pi$
$463$	4.84858	+	4.84858i	0.225333	+	0.225333i	−0.585407	+	0.810740i	$0.699065\pi$
$464$		0			0
$465$	−11.6939	+	5.52217i	−0.542291	+	0.256084i
$466$		0			0
$467$	−21.7099	−	21.7099i	−1.00461	−	1.00461i	−0.999989	−	0.00462401i	$-0.998528\pi$
$467$	−21.7099	−	21.7099i	−1.00461	−	1.00461i	−0.00462401	−	0.999989i	$-0.501472\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	4.59310			0.211639
$472$		0			0
$473$	35.4892	+	35.4892i	1.63180	+	1.63180i
$474$		0			0
$475$	9.78310	+	8.04855i	0.448879	+	0.369293i
$476$		0			0
$477$	2.43234	−	2.43234i	0.111369	−	0.111369i
$478$		0			0
$479$	−32.4440			−1.48241			−0.741203	−	0.671281i	$-0.765745\pi$
$479$	−32.4440			−1.48241			−0.741203	+	0.671281i	$0.765745\pi$
$480$		0			0
$481$		−	14.6630i		−	0.668576i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−21.6840	+	10.2398i	−0.984618	+	0.464963i
$486$		0			0
$487$	−13.2698	+	13.2698i	−0.601312	+	0.601312i	−0.940661	−	0.339348i	$-0.889793\pi$
$487$	−13.2698	+	13.2698i	−0.601312	+	0.601312i	0.339348	+	0.940661i	$0.389793\pi$
$488$		0			0
$489$	−19.2864			−0.872160
$490$		0			0
$491$	−13.5398			−0.611041			−0.305520	−	0.952186i	$-0.598830\pi$
$491$	−13.5398			−0.611041			−0.305520	+	0.952186i	$0.598830\pi$
$492$		0			0
$493$	44.8651	−	44.8651i	2.02062	−	2.02062i
$494$		0			0
$495$	−13.3266	−	4.77740i	−0.598986	−	0.214728i
$496$		0			0
$497$		0			0
$498$		0			0
$499$			15.4253i			0.690530i	0.938505	+	0.345265i	$0.112211\pi$
$499$			15.4253i			0.690530i	−0.938505	+	0.345265i	$0.887789\pi$
$500$		0			0
$501$	−6.62871			−0.296149
$502$		0			0
$503$	16.1450	−	16.1450i	0.719871	−	0.719871i	−0.248708	−	0.968579i	$-0.580006\pi$
$503$	16.1450	−	16.1450i	0.719871	−	0.719871i	0.968579	+	0.248708i	$0.0800058\pi$
$504$		0			0
$505$	37.6295	+	13.4897i	1.67449	+	0.600282i
$506$		0			0
$507$	−6.46810	−	6.46810i	−0.287258	−	0.287258i
$508$		0			0
$509$	−20.3648			−0.902653			−0.451327	−	0.892359i	$-0.649049\pi$
$509$	−20.3648			−0.902653			−0.451327	+	0.892359i	$0.649049\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.79158	−	1.79158i	−0.0791002	−	0.0791002i
$514$		0			0
$515$	−10.0883	−	21.3633i	−0.444545	−	0.941380i
$516$		0			0
$517$	8.38390	+	8.38390i	0.368723	+	0.368723i
$518$		0			0
$519$		−	18.3637i		−	0.806075i
$520$		0			0
$521$		−	19.2483i		−	0.843284i	−0.906762	−	0.421642i	$-0.861454\pi$
$521$		−	19.2483i		−	0.843284i	0.906762	−	0.421642i	$-0.138546\pi$
$522$		0			0
$523$	1.44992	−	1.44992i	0.0634004	−	0.0634004i	−0.674696	−	0.738096i	$-0.735725\pi$
$523$	1.44992	−	1.44992i	0.0634004	−	0.0634004i	0.738096	+	0.674696i	$0.235725\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−30.6254	+	30.6254i	−1.33406	+	1.33406i
$528$		0			0
$529$		−	4.81269i		−	0.209248i
$530$		0			0
$531$			12.2495i			0.531585i
$532$		0			0
$533$	7.04863	+	7.04863i	0.305310	+	0.305310i
$534$		0			0
$535$	−16.6007	−	35.1541i	−0.717711	−	1.51984i
$536$		0			0
$537$	4.50381	+	4.50381i	0.194354	+	0.194354i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−33.0674			−1.42168			−0.710838	−	0.703356i	$-0.751684\pi$
$541$	−33.0674			−1.42168			−0.710838	+	0.703356i	$0.751684\pi$
$542$		0			0
$543$	4.66640	+	4.66640i	0.200254	+	0.200254i
$544$		0			0
$545$	−8.29061	−	2.97207i	−0.355131	−	0.127309i
$546$		0			0
$547$	−15.9819	+	15.9819i	−0.683336	+	0.683336i	−0.960750	−	0.277415i	$-0.910522\pi$
$547$	−15.9819	+	15.9819i	−0.683336	+	0.683336i	0.277415	+	0.960750i	$0.410522\pi$
$548$		0			0
$549$	10.9807			0.468646
$550$		0			0
$551$			21.4667i			0.914513i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−15.7243	−	5.63694i	−0.667459	−	0.239275i
$556$		0			0
$557$	−30.2359	+	30.2359i	−1.28114	+	1.28114i	−0.341118	+	0.940021i	$0.610805\pi$
$557$	−30.2359	+	30.2359i	−1.28114	+	1.28114i	−0.940021	+	0.341118i	$0.889195\pi$
$558$		0			0
$559$	−15.5600			−0.658116
$560$		0			0
$561$	−47.4129			−2.00178
$562$		0			0
$563$	−6.77107	+	6.77107i	−0.285367	+	0.285367i	−0.835245	−	0.549878i	$-0.814674\pi$
$563$	−6.77107	+	6.77107i	−0.285367	+	0.285367i	0.549878	+	0.835245i	$0.314674\pi$
$564$		0			0
$565$	34.4567	−	16.2714i	1.44960	−	0.684542i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	42.8659i		−	1.79703i	−0.438942	−	0.898516i	$-0.644647\pi$
$569$		−	42.8659i		−	1.79703i	0.438942	−	0.898516i	$-0.355353\pi$
$570$		0			0
$571$	−31.2460			−1.30761			−0.653803	−	0.756665i	$-0.726828\pi$
$571$	−31.2460			−1.30761			−0.653803	+	0.756665i	$0.726828\pi$
$572$		0			0
$573$	3.66552	−	3.66552i	0.153129	−	0.153129i
$574$		0			0
$575$	−2.06445	−	21.2231i	−0.0860936	−	0.885065i
$576$		0			0
$577$	9.62174	+	9.62174i	0.400558	+	0.400558i	0.878430	−	0.477872i	$-0.158592\pi$
$577$	9.62174	+	9.62174i	0.400558	+	0.400558i	−0.477872	+	0.878430i	$0.658592\pi$
$578$		0			0
$579$	−6.74870			−0.280466
$580$		0			0
$581$		0			0
$582$		0			0
$583$	15.3997	+	15.3997i	0.637789	+	0.637789i
$584$		0			0
$585$	3.96877	−	1.87416i	0.164089	−	0.0774871i
$586$		0			0
$587$	7.44158	+	7.44158i	0.307147	+	0.307147i	0.843802	−	0.536655i	$-0.180312\pi$
$587$	7.44158	+	7.44158i	0.307147	+	0.307147i	−0.536655	+	0.843802i	$0.680312\pi$
$588$		0			0
$589$		−	14.6534i		−	0.603782i
$590$		0			0
$591$		−	2.34739i		−	0.0965588i
$592$		0			0
$593$	19.5676	−	19.5676i	0.803545	−	0.803545i	−0.180103	−	0.983648i	$-0.557643\pi$
$593$	19.5676	−	19.5676i	0.803545	−	0.803545i	0.983648	+	0.180103i	$0.0576431\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−12.1159	+	12.1159i	−0.495872	+	0.495872i
$598$		0			0
$599$		−	24.1242i		−	0.985687i	−0.870118	−	0.492844i	$-0.835957\pi$
$599$		−	24.1242i		−	0.985687i	0.870118	−	0.492844i	$-0.164043\pi$
$600$		0			0
$601$		−	21.4606i		−	0.875396i	−0.899122	−	0.437698i	$-0.855794\pi$
$601$		−	21.4606i		−	0.875396i	0.899122	−	0.437698i	$-0.144206\pi$
$602$		0			0
$603$	−3.00403	−	3.00403i	−0.122333	−	0.122333i
$604$		0			0
$605$	21.9464	−	61.2196i	0.892247	−	2.48893i
$606$		0			0
$607$	28.8570	+	28.8570i	1.17127	+	1.17127i	0.981908	+	0.189360i	$0.0606413\pi$
$607$	28.8570	+	28.8570i	1.17127	+	1.17127i	0.189360	+	0.981908i	$0.439359\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.67585			−0.148709
$612$		0			0
$613$	−21.3007	−	21.3007i	−0.860329	−	0.860329i	0.131047	−	0.991376i	$-0.458166\pi$
$613$	−21.3007	−	21.3007i	−0.860329	−	0.860329i	−0.991376	+	0.131047i	$0.958166\pi$
$614$		0			0
$615$	10.2685	−	4.84907i	0.414067	−	0.195533i
$616$		0			0
$617$	−14.2272	+	14.2272i	−0.572767	+	0.572767i	−0.932901	−	0.360134i	$-0.882731\pi$
$617$	−14.2272	+	14.2272i	−0.572767	+	0.572767i	0.360134	+	0.932901i	$0.382731\pi$
$618$		0			0
$619$	−38.8414			−1.56117			−0.780584	−	0.625050i	$-0.785078\pi$
$619$	−38.8414			−1.56117			−0.780584	+	0.625050i	$0.785078\pi$
$620$		0			0
$621$			4.26466i			0.171135i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	4.81810	+	24.5313i	0.192724	+	0.981253i
$626$		0			0
$627$	11.3429	−	11.3429i	0.452991	−	0.452991i
$628$		0			0
$629$	−55.9434			−2.23061
$630$		0			0
$631$	−27.8699			−1.10948			−0.554742	−	0.832022i	$-0.687183\pi$
$631$	−27.8699			−1.10948			−0.554742	+	0.832022i	$0.687183\pi$
$632$		0			0
$633$	−4.49451	+	4.49451i	−0.178641	+	0.178641i
$634$		0			0
$635$	−9.63274	−	20.3985i	−0.382264	−	0.809491i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		−	6.80517i		−	0.269208i
$640$		0			0
$641$	20.0250			0.790942			0.395471	−	0.918478i	$-0.370581\pi$
$641$	20.0250			0.790942			0.395471	+	0.918478i	$0.370581\pi$
$642$		0			0
$643$	20.9307	−	20.9307i	0.825426	−	0.825426i	−0.161454	−	0.986880i	$-0.551618\pi$
$643$	20.9307	−	20.9307i	0.825426	−	0.825426i	0.986880	+	0.161454i	$0.0516184\pi$
$644$		0			0
$645$	−5.98175	+	16.6861i	−0.235531	+	0.657016i
$646$		0			0
$647$	−17.5914	−	17.5914i	−0.691588	−	0.691588i	0.270993	−	0.962581i	$-0.412648\pi$
$647$	−17.5914	−	17.5914i	−0.691588	−	0.691588i	−0.962581	+	0.270993i	$0.912648\pi$
$648$		0			0
$649$	−77.5545			−3.04428
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.17807	−	4.17807i	−0.163500	−	0.163500i	0.620615	−	0.784115i	$-0.286883\pi$
$653$	−4.17807	−	4.17807i	−0.163500	−	0.163500i	−0.784115	+	0.620615i	$0.786883\pi$
$654$		0			0
$655$	7.63640	+	2.73754i	0.298379	+	0.106965i
$656$		0			0
$657$	−6.47591	−	6.47591i	−0.252649	−	0.252649i
$658$		0			0
$659$		−	31.8415i		−	1.24037i	−0.784457	−	0.620184i	$-0.787058\pi$
$659$		−	31.8415i		−	1.24037i	0.784457	−	0.620184i	$-0.212942\pi$
$660$		0			0
$661$		−	47.1727i		−	1.83481i	−0.397959	−	0.917403i	$-0.630281\pi$
$661$		−	47.1727i		−	1.83481i	0.397959	−	0.917403i	$-0.369719\pi$
$662$		0			0
$663$	10.3939	−	10.3939i	0.403666	−	0.403666i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	25.5496	−	25.5496i	0.989283	−	0.989283i
$668$		0			0
$669$			13.8560i			0.535703i
$670$		0			0
$671$			69.5214i			2.68384i
$672$		0			0
$673$	−31.6183	−	31.6183i	−1.21879	−	1.21879i	−0.968054	−	0.250740i	$-0.919326\pi$
$673$	−31.6183	−	31.6183i	−1.21879	−	1.21879i	−0.250740	−	0.968054i	$-0.580674\pi$
$674$		0			0
$675$	−0.484084	−	4.97651i	−0.0186324	−	0.191546i
$676$		0			0
$677$	14.4723	+	14.4723i	0.556214	+	0.556214i	0.928227	−	0.372013i	$-0.121332\pi$
$677$	14.4723	+	14.4723i	0.556214	+	0.556214i	−0.372013	+	0.928227i	$0.621332\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	12.1043			0.463837
$682$		0			0
$683$	−29.8762	−	29.8762i	−1.14318	−	1.14318i	−0.987865	−	0.155317i	$-0.950360\pi$
$683$	−29.8762	−	29.8762i	−1.14318	−	1.14318i	−0.155317	−	0.987865i	$-0.549640\pi$
$684$		0			0
$685$	−2.65153	−	5.61495i	−0.101310	−	0.214536i
$686$		0			0
$687$	5.64594	−	5.64594i	0.215406	−	0.215406i
$688$		0			0
$689$	−6.75186			−0.257225
$690$		0			0
$691$		−	4.46757i		−	0.169954i	−0.996383	−	0.0849772i	$-0.972918\pi$
$691$		−	4.46757i		−	0.169954i	0.996383	−	0.0849772i	$-0.0270818\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.96949	−	16.6519i	0.226436	−	0.631644i
$696$		0			0
$697$	26.8925	−	26.8925i	1.01862	−	1.01862i
$698$		0			0
$699$	26.7233			1.01077
$700$		0			0
$701$	−19.3528			−0.730944			−0.365472	−	0.930822i	$-0.619092\pi$
$701$	−19.3528			−0.730944			−0.365472	+	0.930822i	$0.619092\pi$
$702$		0			0
$703$	13.3837	−	13.3837i	0.504775	−	0.504775i
$704$		0			0
$705$	−1.41312	+	3.94190i	−0.0532211	+	0.148461i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			43.7646i			1.64361i	0.569766	+	0.821807i	$0.307034\pi$
$709$			43.7646i			1.64361i	−0.569766	+	0.821807i	$0.692966\pi$
$710$		0			0
$711$	−5.56831			−0.208828
$712$		0			0
$713$	−17.4404	+	17.4404i	−0.653147	+	0.653147i
$714$		0			0
$715$	11.8657	+	25.1272i	0.443753	+	0.939702i
$716$		0			0
$717$	14.7377	+	14.7377i	0.550388	+	0.550388i
$718$		0			0
$719$	−34.9331			−1.30278			−0.651392	−	0.758741i	$-0.725815\pi$
$719$	−34.9331			−1.30278			−0.651392	+	0.758741i	$0.725815\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	4.35801	+	4.35801i	0.162076	+	0.162076i
$724$		0			0
$725$	−26.9141	+	32.7144i	−0.999566	+	1.21498i
$726$		0			0
$727$	28.2450	+	28.2450i	1.04755	+	1.04755i	0.998812	+	0.0487357i	$0.0155192\pi$
$727$	28.2450	+	28.2450i	1.04755	+	1.04755i	0.0487357	+	0.998812i	$0.484481\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$			59.3655i			2.19571i
$732$		0			0
$733$	5.09170	−	5.09170i	0.188066	−	0.188066i	−0.606793	−	0.794860i	$-0.707544\pi$
$733$	5.09170	−	5.09170i	0.188066	−	0.188066i	0.794860	+	0.606793i	$0.207544\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.0191	−	19.0191i	0.700579	−	0.700579i
$738$		0			0
$739$			30.8524i			1.13493i	0.823399	+	0.567463i	$0.192075\pi$
$739$			30.8524i			1.13493i	−0.823399	+	0.567463i	$0.807925\pi$
$740$		0			0
$741$			4.97320i			0.182695i
$742$		0			0
$743$	24.1494	+	24.1494i	0.885954	+	0.885954i	0.994132	−	0.108178i	$-0.0345016\pi$
$743$	24.1494	+	24.1494i	0.885954	+	0.885954i	−0.108178	+	0.994132i	$0.534502\pi$
$744$		0			0
$745$	9.74136	+	3.49214i	0.356896	+	0.127942i
$746$		0			0
$747$	−1.29322	−	1.29322i	−0.0473163	−	0.0473163i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−20.0817			−0.732792			−0.366396	−	0.930459i	$-0.619409\pi$
$751$	−20.0817			−0.732792			−0.366396	+	0.930459i	$0.619409\pi$
$752$		0			0
$753$	9.94519	+	9.94519i	0.362423	+	0.362423i
$754$		0			0
$755$	−12.6151	+	35.1900i	−0.459112	+	1.28070i
$756$		0			0
$757$	−28.0669	+	28.0669i	−1.02011	+	1.02011i	−0.0203156	+	0.999794i	$0.506467\pi$
$757$	−28.0669	+	28.0669i	−1.02011	+	1.02011i	−0.999794	+	0.0203156i	$0.993533\pi$
$758$		0			0
$759$	−27.0005			−0.980055
$760$		0			0
$761$		−	22.1695i		−	0.803644i	−0.915718	−	0.401822i	$-0.868377\pi$
$761$		−	22.1695i		−	0.803644i	0.915718	−	0.401822i	$-0.131623\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−7.15044	−	15.1420i	−0.258525	−	0.547458i
$766$		0			0
$767$	17.0016	−	17.0016i	0.613892	−	0.613892i
$768$		0			0
$769$	14.3998			0.519271			0.259636	−	0.965707i	$-0.416398\pi$
$769$	14.3998			0.519271			0.259636	+	0.965707i	$0.416398\pi$
$770$		0			0
$771$	−16.1218			−0.580613
$772$		0			0
$773$	−33.4490	+	33.4490i	−1.20308	+	1.20308i	−0.229851	+	0.973226i	$0.573824\pi$
$773$	−33.4490	+	33.4490i	−1.20308	+	1.20308i	−0.973226	+	0.229851i	$0.926176\pi$
$774$		0			0
$775$	18.3718	−	22.3312i	0.659936	−	0.802159i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			12.8673i			0.461019i
$780$		0			0
$781$	43.0850			1.54170
$782$		0			0
$783$	5.99100	−	5.99100i	0.214101	−	0.214101i
$784$		0			0
$785$	−9.28705	+	4.38560i	−0.331469	+	0.156529i
$786$		0			0
$787$	9.90434	+	9.90434i	0.353052	+	0.353052i	0.861244	−	0.508192i	$-0.169686\pi$
$787$	9.90434	+	9.90434i	0.353052	+	0.353052i	−0.508192	+	0.861244i	$0.669686\pi$
$788$		0			0
$789$	−10.1622			−0.361785
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−15.2406	−	15.2406i	−0.541208	−	0.541208i
$794$		0			0
$795$	−2.59563	+	7.24054i	−0.0920577	+	0.256796i
$796$		0			0
$797$	38.4353	+	38.4353i	1.36145	+	1.36145i	0.872074	+	0.489374i	$0.162775\pi$
$797$	38.4353	+	38.4353i	1.36145	+	1.36145i	0.489374	+	0.872074i	$0.337225\pi$
$798$		0			0
$799$			14.0244i			0.496147i
$800$		0			0
$801$			1.33158i			0.0470490i
$802$		0			0
$803$	41.0004	−	41.0004i	1.44687	−	1.44687i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−11.7929	+	11.7929i	−0.415131	+	0.415131i
$808$		0			0
$809$		−	3.23409i		−	0.113705i	−0.998383	−	0.0568523i	$-0.981894\pi$
$809$		−	3.23409i		−	0.113705i	0.998383	−	0.0568523i	$-0.0181064\pi$
$810$		0			0
$811$			6.02085i			0.211421i	0.994397	+	0.105710i	$0.0337116\pi$
$811$			6.02085i			0.211421i	−0.994397	+	0.105710i	$0.966288\pi$
$812$		0			0
$813$	9.03492	+	9.03492i	0.316868	+	0.316868i
$814$		0			0
$815$	38.9962	−	18.4151i	1.36598	−	0.645052i
$816$		0			0
$817$	−14.2024	−	14.2024i	−0.496878	−	0.496878i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	16.8092			0.586644			0.293322	−	0.956014i	$-0.405239\pi$
$821$	16.8092			0.586644			0.293322	+	0.956014i	$0.405239\pi$
$822$		0			0
$823$	−15.9221	−	15.9221i	−0.555009	−	0.555009i	0.372873	−	0.927882i	$-0.378373\pi$
$823$	−15.9221	−	15.9221i	−0.555009	−	0.555009i	−0.927882	+	0.372873i	$0.878373\pi$
$824$		0			0
$825$	31.5074	−	3.06484i	1.09695	−	0.106704i
$826$		0			0
$827$	−37.7327	+	37.7327i	−1.31209	+	1.31209i	−0.392225	+	0.919869i	$0.628295\pi$
$827$	−37.7327	+	37.7327i	−1.31209	+	1.31209i	−0.919869	+	0.392225i	$0.871705\pi$
$828$		0			0
$829$	−7.51937			−0.261158			−0.130579	−	0.991438i	$-0.541684\pi$
$829$	−7.51937			−0.261158			−0.130579	+	0.991438i	$0.541684\pi$
$830$		0			0
$831$		−	20.9168i		−	0.725594i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	13.4030	−	6.32925i	0.463829	−	0.219033i
$836$		0			0
$837$	−4.08951	+	4.08951i	−0.141354	+	0.141354i
$838$		0			0
$839$	−38.3742			−1.32483			−0.662413	−	0.749139i	$-0.730468\pi$
$839$	−38.3742			−1.32483			−0.662413	+	0.749139i	$0.730468\pi$
$840$		0			0
$841$	−42.7841			−1.47532
$842$		0			0
$843$	7.41522	−	7.41522i	0.255394	−	0.255394i
$844$		0			0
$845$	19.2541	+	6.90233i	0.662361	+	0.237447i
$846$		0			0
$847$		0			0
$848$		0			0
$849$			4.98044i			0.170928i
$850$		0			0
$851$	−31.8584			−1.09209
$852$		0			0
$853$	−3.39596	+	3.39596i	−0.116275	+	0.116275i	−0.762850	−	0.646575i	$-0.776201\pi$
$853$	−3.39596	+	3.39596i	−0.116275	+	0.116275i	0.646575	+	0.762850i	$0.276201\pi$
$854$		0			0
$855$	5.33314	+	1.91186i	0.182390	+	0.0653842i
$856$		0			0
$857$	15.3731	+	15.3731i	0.525135	+	0.525135i	0.919118	−	0.393983i	$-0.128903\pi$
$857$	15.3731	+	15.3731i	0.525135	+	0.525135i	−0.393983	+	0.919118i	$0.628903\pi$
$858$		0			0
$859$	31.1394			1.06246			0.531232	−	0.847227i	$-0.321729\pi$
$859$	31.1394			1.06246			0.531232	+	0.847227i	$0.321729\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.15275	−	1.15275i	−0.0392400	−	0.0392400i	0.687215	−	0.726455i	$-0.258833\pi$
$863$	−1.15275	−	1.15275i	−0.0392400	−	0.0392400i	−0.726455	+	0.687215i	$0.758833\pi$
$864$		0			0
$865$	17.5340	+	37.1305i	0.596175	+	1.26248i
$866$		0			0
$867$	−27.6348	−	27.6348i	−0.938526	−	0.938526i
$868$		0			0
$869$		−	35.2542i		−	1.19592i
$870$		0			0
$871$			8.33879i			0.282549i
$872$		0			0
$873$	−7.58318	+	7.58318i	−0.256652	+	0.256652i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−3.85591	+	3.85591i	−0.130205	+	0.130205i	−0.769206	−	0.639001i	$-0.779348\pi$
$877$	−3.85591	+	3.85591i	−0.130205	+	0.130205i	0.639001	+	0.769206i	$0.279348\pi$
$878$		0			0
$879$		−	0.328057i		−	0.0110651i
$880$		0			0
$881$			6.12351i			0.206306i	0.994665	+	0.103153i	$0.0328932\pi$
$881$			6.12351i			0.206306i	−0.994665	+	0.103153i	$0.967107\pi$
$882$		0			0
$883$	−11.2733	−	11.2733i	−0.379375	−	0.379375i	0.491501	−	0.870877i	$-0.336448\pi$
$883$	−11.2733	−	11.2733i	−0.379375	−	0.379375i	−0.870877	+	0.491501i	$0.836448\pi$
$884$		0			0
$885$	−11.6962	−	24.7681i	−0.393162	−	0.832570i
$886$		0			0
$887$	29.7983	+	29.7983i	1.00053	+	1.00053i	1.00000		0.000530546i	$0.000168878\pi$
$887$	29.7983	+	29.7983i	1.00053	+	1.00053i	0.000530546		1.00000i	$0.499831\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−6.33122			−0.212104
$892$		0			0
$893$	−3.35514	−	3.35514i	−0.112275	−	0.112275i
$894$		0			0
$895$	−13.4069	−	4.80617i	−0.448142	−	0.160653i
$896$		0			0
$897$	5.91907	−	5.91907i	0.197632	−	0.197632i
$898$		0			0
$899$	49.0005			1.63426
$900$		0			0
$901$			25.7602i			0.858196i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−13.8908	−	4.97967i	−0.461747	−	0.165530i
$906$		0			0
$907$	−6.89946	+	6.89946i	−0.229093	+	0.229093i	−0.812314	−	0.583221i	$-0.801792\pi$
$907$	−6.89946	+	6.89946i	−0.229093	+	0.229093i	0.583221	+	0.812314i	$0.301792\pi$
$908$		0			0
$909$	17.8771			0.592946
$910$		0			0
$911$	4.36075			0.144478			0.0722391	−	0.997387i	$-0.476986\pi$
$911$	4.36075			0.144478			0.0722391	+	0.997387i	$0.476986\pi$
$912$		0			0
$913$	8.18763	−	8.18763i	0.270971	−	0.270971i
$914$		0			0
$915$	−22.2026	+	10.4847i	−0.733995	+	0.346612i
$916$		0			0
$917$		0			0
$918$		0			0
$919$		−	11.6415i		−	0.384017i	−0.981393	−	0.192008i	$-0.938500\pi$
$919$		−	11.6415i		−	0.384017i	0.981393	−	0.192008i	$-0.0615001\pi$
$920$		0			0
$921$	14.9368			0.492185
$922$		0			0
$923$	−9.44513	+	9.44513i	−0.310890	+	0.310890i
$924$		0			0
$925$	37.1761	−	3.61626i	1.22234	−	0.118902i
$926$		0			0
$927$	−7.47105	−	7.47105i	−0.245381	−	0.245381i
$928$		0			0
$929$	−4.08768			−0.134112			−0.0670562	−	0.997749i	$-0.521361\pi$
$929$	−4.08768			−0.134112			−0.0670562	+	0.997749i	$0.521361\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−7.90037	−	7.90037i	−0.258646	−	0.258646i
$934$		0			0
$935$	95.8670	−	45.2710i	3.13518	−	1.48052i
$936$		0			0
$937$	16.2775	+	16.2775i	0.531763	+	0.531763i	0.921097	−	0.389334i	$-0.127295\pi$
$937$	16.2775	+	16.2775i	0.531763	+	0.531763i	−0.389334	+	0.921097i	$0.627295\pi$
$938$		0			0
$939$			7.21906i			0.235585i
$940$		0			0
$941$			18.7840i			0.612341i	0.951977	+	0.306171i	$0.0990478\pi$
$941$			18.7840i			0.612341i	−0.951977	+	0.306171i	$0.900952\pi$
$942$		0			0
$943$	15.3146	−	15.3146i	0.498711	−	0.498711i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−18.9735	+	18.9735i	−0.616556	+	0.616556i	−0.944646	−	0.328090i	$-0.893595\pi$
$947$	−18.9735	+	18.9735i	−0.616556	+	0.616556i	0.328090	+	0.944646i	$0.393595\pi$
$948$		0			0
$949$			17.9763i			0.583535i
$950$		0			0
$951$			4.82528i			0.156470i
$952$		0			0
$953$	22.9835	+	22.9835i	0.744510	+	0.744510i	0.973442	−	0.228933i	$-0.0735236\pi$
$953$	22.9835	+	22.9835i	0.744510	+	0.744510i	−0.228933	+	0.973442i	$0.573524\pi$
$954$		0			0
$955$	−3.91160	+	10.9114i	−0.126576	+	0.353086i
$956$		0			0
$957$	37.9303	+	37.9303i	1.22611	+	1.22611i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−2.44823			−0.0789752
$962$		0			0
$963$	−12.2939	−	12.2939i	−0.396165	−	0.396165i
$964$		0			0
$965$	13.6456	−	6.44381i	0.439267	−	0.207434i
$966$		0			0
$967$	9.83973	−	9.83973i	0.316424	−	0.316424i	−0.530968	−	0.847392i	$-0.678171\pi$
$967$	9.83973	−	9.83973i	0.316424	−	0.316424i	0.847392	+	0.530968i	$0.178171\pi$
$968$		0			0
$969$	18.9741			0.609536
$970$		0			0
$971$			11.7606i			0.377415i	0.982033	+	0.188708i	$0.0604298\pi$
$971$			11.7606i			0.377415i	−0.982033	+	0.188708i	$0.939570\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−6.23520	+	7.57895i	−0.199686	+	0.242721i
$976$		0			0
$977$	−35.8508	+	35.8508i	−1.14697	+	1.14697i	−0.159823	+	0.987146i	$0.551092\pi$
$977$	−35.8508	+	35.8508i	−1.14697	+	1.14697i	−0.987146	+	0.159823i	$0.948908\pi$
$978$		0			0
$979$	−8.43051			−0.269440
$980$		0			0
$981$	−3.93872			−0.125754
$982$		0			0
$983$	0.522567	−	0.522567i	0.0166673	−	0.0166673i	−0.698724	−	0.715391i	$-0.746248\pi$
$983$	0.522567	−	0.522567i	0.0166673	−	0.0166673i	0.715391	+	0.698724i	$0.246248\pi$
$984$		0			0
$985$	2.24134	+	4.74633i	0.0714151	+	0.151231i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			33.8071i			1.07500i
$990$		0			0
$991$	−52.0036			−1.65195			−0.825974	−	0.563708i	$-0.809374\pi$
$991$	−52.0036			−1.65195			−0.825974	+	0.563708i	$0.809374\pi$
$992$		0			0
$993$	−19.8423	+	19.8423i	−0.629676	+	0.629676i
$994$		0			0
$995$	12.9293	−	36.0664i	0.409887	−	1.14338i
$996$		0			0
$997$	11.4659	+	11.4659i	0.363130	+	0.363130i	0.864964	−	0.501834i	$-0.167341\pi$
$997$	11.4659	+	11.4659i	0.363130	+	0.363130i	−0.501834	+	0.864964i	$0.667341\pi$
$998$		0			0
$999$	−7.47032			−0.236351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2940.2.x.b.1273.1	yes	24
5.2	odd	4		2940.2.x.a.97.12	✓	24
7.6	odd	2		2940.2.x.a.1273.12	yes	24
35.27	even	4	inner	2940.2.x.b.97.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2940.2.x.a.97.12	✓	24	5.2	odd	4
2940.2.x.a.1273.12	yes	24	7.6	odd	2
2940.2.x.b.97.1	yes	24	35.27	even	4	inner
2940.2.x.b.1273.1	yes	24	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2940.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(0.754578 - 2.10490i) q^{5} -1.00000i q^{9} +6.33122 q^{11} +(-1.38794 + 1.38794i) q^{13} +(0.954823 + 2.02196i) q^{15} +(5.29535 + 5.29535i) q^{17} -2.53368 q^{19} +(3.01557 + 3.01557i) q^{23} +(-3.86122 - 3.17663i) q^{25} +(0.707107 + 0.707107i) q^{27} -8.47255i q^{29} +5.78344i q^{31} +(-4.47685 + 4.47685i) q^{33} +(-5.28232 + 5.28232i) q^{37} -1.96284i q^{39} -5.07850i q^{41} +(5.60543 + 5.60543i) q^{43} +(-2.10490 - 0.754578i) q^{45} +(1.32422 + 1.32422i) q^{47} -7.48876 q^{51} +(2.43234 + 2.43234i) q^{53} +(4.77740 - 13.3266i) q^{55} +(1.79158 - 1.79158i) q^{57} -12.2495 q^{59} +10.9807i q^{61} +(1.87416 + 3.96877i) q^{65} +(3.00403 - 3.00403i) q^{67} -4.26466 q^{69} +6.80517 q^{71} +(6.47591 - 6.47591i) q^{73} +(4.97651 - 0.484084i) q^{75} -5.56831i q^{79} -1.00000 q^{81} +(1.29322 - 1.29322i) q^{83} +(15.1420 - 7.15044i) q^{85} +(5.99100 + 5.99100i) q^{87} -1.33158 q^{89} +(-4.08951 - 4.08951i) q^{93} +(-1.91186 + 5.33314i) q^{95} +(-7.58318 - 7.58318i) q^{97} -6.33122i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{5} - 16 q^{13} - 32 q^{19} + 16 q^{23} - 16 q^{25} + 16 q^{37} - 16 q^{43} - 8 q^{45} + 16 q^{47} + 24 q^{53} + 16 q^{57} - 64 q^{59} - 32 q^{65} + 32 q^{67} + 32 q^{71} + 16 q^{73} - 24 q^{81}+ \cdots - 16 q^{97}+O(q^{100}) \) 24 * q + 8 * q^5 - 16 * q^13 - 32 * q^19 + 16 * q^23 - 16 * q^25 + 16 * q^37 - 16 * q^43 - 8 * q^45 + 16 * q^47 + 24 * q^53 + 16 * q^57 - 64 * q^59 - 32 * q^65 + 32 * q^67 + 32 * q^71 + 16 * q^73 - 24 * q^81 + 48 * q^85 + 40 * q^87 - 144 * q^89 + 16 * q^93 - 64 * q^95 - 16 * q^97

Introduction

L-functions

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