LMFDB - Embedded newform 637.2.e.i.79.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(79,637)] 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("637.79"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,-1,-2,-3,2] 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$-0.906803 + 1.57063i$ of defining polynomial
Character	$\chi$	$=$	637.79
Dual form			637.2.e.i.508.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.906803 - 1.57063i) q^{2} +(-1.55139 - 2.68708i) q^{3} +(-0.644584 - 1.11645i) q^{4} +(1.40680 - 2.43665i) q^{5} -5.62721 q^{6} +1.28917 q^{8} +(-3.31361 + 5.73933i) q^{9} +(-2.55139 - 4.41913i) q^{10} +(-1.55139 - 2.68708i) q^{11} +(-2.00000 + 3.46410i) q^{12} -1.00000 q^{13} -8.72999 q^{15} +(2.45819 - 4.25771i) q^{16} +(-0.262219 - 0.454177i) q^{17} +(6.00958 + 10.4089i) q^{18} +(0.406803 - 0.704604i) q^{19} -3.62721 q^{20} -5.62721 q^{22} +(-3.66902 + 6.35493i) q^{23} +(-2.00000 - 3.46410i) q^{24} +(-1.45819 - 2.52566i) q^{25} +(-0.906803 + 1.57063i) q^{26} +11.2544 q^{27} +8.28917 q^{29} +(-7.91638 + 13.7116i) q^{30} +(0.695972 + 1.20546i) q^{31} +(-3.16902 - 5.48891i) q^{32} +(-4.81361 + 8.33741i) q^{33} -0.951124 q^{34} +8.54359 q^{36} +(3.07583 - 5.32749i) q^{37} +(-0.737781 - 1.27787i) q^{38} +(1.55139 + 2.68708i) q^{39} +(1.81361 - 3.14126i) q^{40} +4.20555 q^{41} +6.75971 q^{43} +(-2.00000 + 3.46410i) q^{44} +(9.32318 + 16.1482i) q^{45} +(6.65416 + 11.5253i) q^{46} +(-2.98514 + 5.17041i) q^{47} -15.2544 q^{48} -5.28917 q^{50} +(-0.813607 + 1.40921i) q^{51} +(0.644584 + 1.11645i) q^{52} +(1.24736 + 2.16049i) q^{53} +(10.2056 - 17.6765i) q^{54} -8.72999 q^{55} -2.52444 q^{57} +(7.51664 - 13.0192i) q^{58} +(-2.23527 - 3.87160i) q^{59} +(5.62721 + 9.74662i) q^{60} +(-1.00000 + 1.73205i) q^{61} +2.52444 q^{62} -1.66196 q^{64} +(-1.40680 + 2.43665i) q^{65} +(8.72999 + 15.1208i) q^{66} +(-5.01916 - 8.69343i) q^{67} +(-0.338044 + 0.585510i) q^{68} +22.7683 q^{69} -8.72999 q^{71} +(-4.27180 + 7.39897i) q^{72} +(-1.17153 - 2.02916i) q^{73} +(-5.57834 - 9.66196i) q^{74} +(-4.52444 + 7.83656i) q^{75} -1.04888 q^{76} +5.62721 q^{78} +(6.77180 - 11.7291i) q^{79} +(-6.91638 - 11.9795i) q^{80} +(-7.51916 - 13.0236i) q^{81} +(3.81361 - 6.60536i) q^{82} -16.4791 q^{83} -1.47556 q^{85} +(6.12972 - 10.6170i) q^{86} +(-12.8597 - 22.2737i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-5.32318 + 9.22003i) q^{89} +33.8172 q^{90} +9.45998 q^{92} +(2.15944 - 3.74027i) q^{93} +(5.41387 + 9.37710i) q^{94} +(-1.14458 - 1.98248i) q^{95} +(-9.83276 + 17.0308i) q^{96} +1.18639 q^{97} +20.5628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9} - 8 q^{10} - 2 q^{11} - 12 q^{12} - 6 q^{13} - 12 q^{15} + q^{16} + 4 q^{17} + 15 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 10 q^{23}+ \cdots + 28 q^{99}+O(q^{100}) $ 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9 - 8 * q^10 - 2 * q^11 - 12 * q^12 - 6 * q^13 - 12 * q^15 + q^16 + 4 * q^17 + 15 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 + 5 * q^25 + q^26 + 16 * q^27 + 48 * q^29 - 20 * q^30 - 4 * q^31 - 7 * q^32 - 16 * q^33 - 28 * q^34 - 2 * q^36 - 10 * q^38 + 2 * q^39 - 2 * q^40 - 4 * q^41 + 20 * q^43 - 12 * q^44 + 22 * q^45 + 18 * q^46 - 8 * q^47 - 40 * q^48 - 30 * q^50 + 8 * q^51 + 3 * q^52 - 8 * q^53 + 32 * q^54 - 12 * q^55 - 4 * q^57 - 12 * q^58 - 4 * q^59 + 8 * q^60 - 6 * q^61 + 4 * q^62 - 34 * q^64 - 2 * q^65 + 12 * q^66 + 12 * q^67 + 22 * q^68 + 12 * q^69 - 12 * q^71 + q^72 - 10 * q^73 - 30 * q^74 - 16 * q^75 + 16 * q^76 + 8 * q^78 + 14 * q^79 - 14 * q^80 - 3 * q^81 + 10 * q^82 + 24 * q^83 - 20 * q^85 + 26 * q^86 - 26 * q^87 - 12 * q^88 + 2 * q^89 + 56 * q^90 - 24 * q^92 + 22 * q^93 - 10 * q^94 - 6 * q^95 - 4 * q^96 + 20 * q^97 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.906803	−	1.57063i	0.641207	−	1.11060i	−0.343957	−	0.938985i	$-0.611767\pi$
$2$	0.906803	−	1.57063i	0.641207	−	1.11060i	0.985164	−	0.171617i	$-0.0548992\pi$
$3$	−1.55139	−	2.68708i	−0.895694	−	1.55139i	−0.832943	−	0.553358i	$-0.813346\pi$
$3$	−1.55139	−	2.68708i	−0.895694	−	1.55139i	−0.0627507	−	0.998029i	$-0.519987\pi$
$4$	−0.644584	−	1.11645i	−0.322292	−	0.558226i
$5$	1.40680	−	2.43665i	0.629142	−	1.08971i	−0.358583	−	0.933498i	$-0.616740\pi$
$5$	1.40680	−	2.43665i	0.629142	−	1.08971i	0.987724	−	0.156207i	$-0.0499268\pi$
$6$	−5.62721			−2.29730
$7$		0			0
$7$		0			0
$8$	1.28917			0.455790
$9$	−3.31361	+	5.73933i	−1.10454	+	1.91311i
$10$	−2.55139	−	4.41913i	−0.806820	−	1.39745i
$11$	−1.55139	−	2.68708i	−0.467761	−	0.810186i	0.531560	−	0.847020i	$-0.321606\pi$
$11$	−1.55139	−	2.68708i	−0.467761	−	0.810186i	−0.999321	+	0.0368347i	$0.988273\pi$
$12$	−2.00000	+	3.46410i	−0.577350	+	1.00000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−8.72999			−2.25407
$16$	2.45819	−	4.25771i	0.614548	−	1.06443i
$17$	−0.262219	−	0.454177i	−0.0635974	−	0.110154i	0.832474	−	0.554065i	$-0.186924\pi$
$17$	−0.262219	−	0.454177i	−0.0635974	−	0.110154i	−0.896071	+	0.443911i	$0.853591\pi$
$18$	6.00958	+	10.4089i	1.41647	+	2.45340i
$19$	0.406803	−	0.704604i	0.0933271	−	0.161647i	−0.815582	−	0.578641i	$-0.803583\pi$
$19$	0.406803	−	0.704604i	0.0933271	−	0.161647i	0.908909	+	0.416994i	$0.136916\pi$
$20$	−3.62721			−0.811069
$21$		0			0
$22$	−5.62721			−1.19973
$23$	−3.66902	+	6.35493i	−0.765044	+	1.32510i	0.175179	+	0.984537i	$0.443949\pi$
$23$	−3.66902	+	6.35493i	−0.765044	+	1.32510i	−0.940223	+	0.340559i	$0.889384\pi$
$24$	−2.00000	−	3.46410i	−0.408248	−	0.707107i
$25$	−1.45819	−	2.52566i	−0.291638	−	0.505132i
$26$	−0.906803	+	1.57063i	−0.177839	+	0.308026i
$27$	11.2544			2.16592
$28$		0			0
$29$	8.28917			1.53926			0.769630	−	0.638490i	$-0.220441\pi$
$29$	8.28917			1.53926			0.769630	+	0.638490i	$0.220441\pi$
$30$	−7.91638	+	13.7116i	−1.44533	+	2.50338i
$31$	0.695972	+	1.20546i	0.125000	+	0.216507i	0.921733	−	0.387825i	$-0.126774\pi$
$31$	0.695972	+	1.20546i	0.125000	+	0.216507i	−0.796733	+	0.604332i	$0.793440\pi$
$32$	−3.16902	−	5.48891i	−0.560209	−	0.970311i
$33$	−4.81361	+	8.33741i	−0.837941	+	1.45136i
$34$	−0.951124			−0.163116
$35$		0			0
$36$	8.54359			1.42393
$37$	3.07583	−	5.32749i	0.505663	−	0.875833i	−0.494316	−	0.869282i	$-0.664581\pi$
$37$	3.07583	−	5.32749i	0.505663	−	0.875833i	0.999979	−	0.00655099i	$-0.00208526\pi$
$38$	−0.737781	−	1.27787i	−0.119684	−	0.207299i
$39$	1.55139	+	2.68708i	0.248421	+	0.430277i
$40$	1.81361	−	3.14126i	0.286756	−	0.496677i
$41$	4.20555			0.656797			0.328398	−	0.944539i	$-0.393491\pi$
$41$	4.20555			0.656797			0.328398	+	0.944539i	$0.393491\pi$
$42$		0			0
$43$	6.75971			1.03085			0.515423	−	0.856936i	$-0.327635\pi$
$43$	6.75971			1.03085			0.515423	+	0.856936i	$0.327635\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$	9.32318	+	16.1482i	1.38982	+	2.40724i
$46$	6.65416	+	11.5253i	0.981103	+	1.69932i
$47$	−2.98514	+	5.17041i	−0.435427	+	0.754183i	−0.997330	−	0.0730207i	$-0.976736\pi$
$47$	−2.98514	+	5.17041i	−0.435427	+	0.754183i	0.561903	+	0.827203i	$0.310069\pi$
$48$	−15.2544			−2.20179
$49$		0			0
$50$	−5.28917			−0.748001
$51$	−0.813607	+	1.40921i	−0.113928	+	0.197329i
$52$	0.644584	+	1.11645i	0.0893878	+	0.154824i
$53$	1.24736	+	2.16049i	0.171338	+	0.296766i	0.938888	−	0.344223i	$-0.111858\pi$
$53$	1.24736	+	2.16049i	0.171338	+	0.296766i	−0.767550	+	0.640989i	$0.778524\pi$
$54$	10.2056	−	17.6765i	1.38880	−	2.40547i
$55$	−8.72999			−1.17715
$56$		0			0
$57$	−2.52444			−0.334370
$58$	7.51664	−	13.0192i	0.986984	−	1.70951i
$59$	−2.23527	−	3.87160i	−0.291007	−	0.504039i	0.683041	−	0.730380i	$-0.260657\pi$
$59$	−2.23527	−	3.87160i	−0.291007	−	0.504039i	−0.974048	+	0.226341i	$0.927324\pi$
$60$	5.62721	+	9.74662i	0.726470	+	1.25828i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	2.52444			0.320604
$63$		0			0
$64$	−1.66196			−0.207744
$65$	−1.40680	+	2.43665i	−0.174492	+	0.302230i
$66$	8.72999	+	15.1208i	1.07459	+	1.86124i
$67$	−5.01916	−	8.69343i	−0.613188	−	1.06207i	−0.990700	−	0.136067i	$-0.956554\pi$
$67$	−5.01916	−	8.69343i	−0.613188	−	1.06207i	0.377512	−	0.926005i	$-0.376780\pi$
$68$	−0.338044	+	0.585510i	−0.0409939	+	0.0710035i
$69$	22.7683			2.74098
$70$		0			0
$71$	−8.72999			−1.03606			−0.518029	−	0.855363i	$-0.673334\pi$
$71$	−8.72999			−1.03606			−0.518029	+	0.855363i	$0.673334\pi$
$72$	−4.27180	+	7.39897i	−0.503436	+	0.871977i
$73$	−1.17153	−	2.02916i	−0.137118	−	0.237495i	0.789287	−	0.614025i	$-0.210451\pi$
$73$	−1.17153	−	2.02916i	−0.137118	−	0.237495i	−0.926404	+	0.376530i	$0.877117\pi$
$74$	−5.57834	−	9.66196i	−0.648469	−	1.12318i
$75$	−4.52444	+	7.83656i	−0.522437	+	0.904888i
$76$	−1.04888			−0.120314
$77$		0			0
$78$	5.62721			0.637156
$79$	6.77180	−	11.7291i	0.761887	−	1.31963i	−0.179990	−	0.983668i	$-0.557607\pi$
$79$	6.77180	−	11.7291i	0.761887	−	1.31963i	0.941877	−	0.335958i	$-0.109060\pi$
$80$	−6.91638	−	11.9795i	−0.773275	−	1.33935i
$81$	−7.51916	−	13.0236i	−0.835462	−	1.44706i
$82$	3.81361	−	6.60536i	0.421142	−	0.729440i
$83$	−16.4791			−1.80882			−0.904410	−	0.426665i	$-0.859688\pi$
$83$	−16.4791			−1.80882			−0.904410	+	0.426665i	$0.859688\pi$
$84$		0			0
$85$	−1.47556			−0.160047
$86$	6.12972	−	10.6170i	0.660985	−	1.14486i
$87$	−12.8597	−	22.2737i	−1.37871	−	2.38799i
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	−5.32318	+	9.22003i	−0.564256	+	0.977321i	0.432862	+	0.901460i	$0.357504\pi$
$89$	−5.32318	+	9.22003i	−0.564256	+	0.977321i	−0.997118	+	0.0758606i	$0.975830\pi$
$90$	33.8172			3.56464
$91$		0			0
$92$	9.45998			0.986271
$93$	2.15944	−	3.74027i	0.223924	−	0.387848i
$94$	5.41387	+	9.37710i	0.558398	+	0.967174i
$95$	−1.14458	−	1.98248i	−0.117432	−	0.203398i
$96$	−9.83276	+	17.0308i	−1.00355	+	1.73820i
$97$	1.18639			0.120460			0.0602300	−	0.998185i	$-0.480817\pi$
$97$	1.18639			0.120460			0.0602300	+	0.998185i	$0.480817\pi$
$98$		0			0
$99$	20.5628			2.06663
$100$	−1.87985	+	3.25600i	−0.187985	+	0.325600i
$101$	6.55139	+	11.3473i	0.651887	+	1.12910i	0.982664	+	0.185393i	$0.0593559\pi$
$101$	6.55139	+	11.3473i	0.651887	+	1.12910i	−0.330777	+	0.943709i	$0.607311\pi$
$102$	1.47556	+	2.55575i	0.146102	+	0.253057i
$103$	2.20555	−	3.82012i	0.217319	−	0.376408i	−0.736668	−	0.676254i	$-0.763602\pi$
$103$	2.20555	−	3.82012i	0.217319	−	0.376408i	0.953988	+	0.299846i	$0.0969354\pi$
$104$	−1.28917			−0.126413
$105$		0			0
$106$	4.52444			0.439452
$107$	−0.289169	+	0.500855i	−0.0279550	+	0.0484194i	−0.879664	−	0.475595i	$-0.842233\pi$
$107$	−0.289169	+	0.500855i	−0.0279550	+	0.0484194i	0.851709	+	0.524014i	$0.175566\pi$
$108$	−7.25443	−	12.5650i	−0.698057	−	1.20907i
$109$	−2.78666	−	4.82663i	−0.266913	−	0.462307i	0.701150	−	0.713014i	$-0.252670\pi$
$109$	−2.78666	−	4.82663i	−0.266913	−	0.462307i	−0.968063	+	0.250707i	$0.919337\pi$
$110$	−7.91638	+	13.7116i	−0.754797	+	1.30735i
$111$	−19.0872			−1.81168
$112$		0			0
$113$	5.44584			0.512302			0.256151	−	0.966637i	$-0.417546\pi$
$113$	5.44584			0.512302			0.256151	+	0.966637i	$0.417546\pi$
$114$	−2.28917	+	3.96496i	−0.214400	+	0.371352i
$115$	10.3232	+	17.8803i	0.962642	+	1.66734i
$116$	−5.34307	−	9.25446i	−0.496091	−	0.859255i
$117$	3.31361	−	5.73933i	0.306343	−	0.530602i
$118$	−8.10780			−0.746383
$119$		0			0
$120$	−11.2544			−1.02738
$121$	0.686393	−	1.18887i	0.0623994	−	0.108079i
$122$	1.81361	+	3.14126i	0.164196	+	0.284396i
$123$	−6.52444	−	11.3007i	−0.588289	−	1.01895i
$124$	0.897225	−	1.55404i	0.0805732	−	0.139557i
$125$	5.86248			0.524356
$126$		0			0
$127$	−12.8816			−1.14306			−0.571530	−	0.820581i	$-0.693650\pi$
$127$	−12.8816			−1.14306			−0.571530	+	0.820581i	$0.693650\pi$
$128$	4.83098	−	8.36750i	0.427002	−	0.739589i
$129$	−10.4869	−	18.1639i	−0.923322	−	1.59924i
$130$	2.55139	+	4.41913i	0.223771	+	0.387584i
$131$	4.52444	−	7.83656i	0.395302	−	0.684683i	−0.597838	−	0.801617i	$-0.703973\pi$
$131$	4.52444	−	7.83656i	0.395302	−	0.684683i	0.993140	+	0.116934i	$0.0373066\pi$
$132$	12.4111			1.08025
$133$		0			0
$134$	−18.2056			−1.57272
$135$	15.8328	−	27.4232i	1.36267	−	2.36021i
$136$	−0.338044	−	0.585510i	−0.0289871	−	0.0502071i
$137$	3.12972	+	5.42084i	0.267390	+	0.463134i	0.968187	−	0.250227i	$-0.0805053\pi$
$137$	3.12972	+	5.42084i	0.267390	+	0.463134i	−0.700797	+	0.713361i	$0.747172\pi$
$138$	20.6464	−	35.7606i	1.75754	−	3.04414i
$139$	11.5733			0.981636			0.490818	−	0.871262i	$-0.336698\pi$
$139$	11.5733			0.981636			0.490818	+	0.871262i	$0.336698\pi$
$140$		0			0
$141$	18.5244			1.56004
$142$	−7.91638	+	13.7116i	−0.664328	+	1.15065i
$143$	1.55139	+	2.68708i	0.129734	+	0.224705i
$144$	16.2910	+	28.2168i	1.35758	+	2.35140i
$145$	11.6612	−	20.1978i	0.968412	−	1.67734i
$146$	−4.24940			−0.351683
$147$		0			0
$148$	−7.93051			−0.651884
$149$	−4.26222	+	7.38238i	−0.349175	+	0.604788i	−0.986103	−	0.166135i	$-0.946871\pi$
$149$	−4.26222	+	7.38238i	−0.349175	+	0.604788i	0.636928	+	0.770923i	$0.280205\pi$
$150$	8.20555	+	14.2124i	0.669980	+	1.16044i
$151$	5.99221	+	10.3788i	0.487639	+	0.844615i	0.999899	−	0.0142150i	$-0.00452494\pi$
$151$	5.99221	+	10.3788i	0.487639	+	0.844615i	−0.512260	+	0.858830i	$0.671192\pi$
$152$	0.524438	−	0.908353i	0.0425375	−	0.0736772i
$153$	3.47556			0.280983
$154$		0			0
$155$	3.91638			0.314571
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	−6.41387	−	11.1091i	−0.511883	−	0.886607i	−0.999905	−	0.0137756i	$-0.995615\pi$
$157$	−6.41387	−	11.1091i	−0.511883	−	0.886607i	0.488023	−	0.872831i	$-0.337718\pi$
$158$	−12.2814	−	21.2720i	−0.977054	−	1.69231i
$159$	3.87028	−	6.70351i	0.306933	−	0.531623i
$160$	−17.8328			−1.40980
$161$		0			0
$162$	−27.2736			−2.14282
$163$	6.72999	−	11.6567i	0.527133	−	0.913022i	−0.472367	−	0.881402i	$-0.656600\pi$
$163$	6.72999	−	11.6567i	0.527133	−	0.913022i	0.999500	−	0.0316196i	$-0.0100665\pi$
$164$	−2.71083	−	4.69530i	−0.211680	−	0.366641i
$165$	13.5436	+	23.4582i	1.05437	+	1.82622i
$166$	−14.9433	+	25.8826i	−1.15983	+	2.00888i
$167$	2.02972			0.157064			0.0785322	−	0.996912i	$-0.474977\pi$
$167$	2.02972			0.157064			0.0785322	+	0.996912i	$0.474977\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−1.33804	+	2.31756i	−0.102623	+	0.177749i
$171$	2.69597	+	4.66956i	0.206166	+	0.357090i
$172$	−4.35720	−	7.54689i	−0.332233	−	0.575445i
$173$	10.1489	−	17.5784i	0.771605	−	1.33646i	−0.165078	−	0.986281i	$-0.552788\pi$
$173$	10.1489	−	17.5784i	0.771605	−	1.33646i	0.936683	−	0.350179i	$-0.113879\pi$
$174$	−46.6449			−3.53614
$175$		0			0
$176$	−15.2544			−1.14985
$177$	−6.93554	+	12.0127i	−0.521307	+	0.902930i
$178$	9.65416	+	16.7215i	0.723610	+	1.25333i
$179$	5.50179	+	9.52937i	0.411223	+	0.712259i	0.995024	−	0.0996381i	$-0.0317685\pi$
$179$	5.50179	+	9.52937i	0.411223	+	0.712259i	−0.583801	+	0.811897i	$0.698435\pi$
$180$	12.0192	−	20.8178i	0.895855	−	1.55167i
$181$	−0.691675			−0.0514118			−0.0257059	−	0.999670i	$-0.508183\pi$
$181$	−0.691675			−0.0514118			−0.0257059	+	0.999670i	$0.508183\pi$
$182$		0			0
$183$	6.20555			0.458727
$184$	−4.72999	+	8.19258i	−0.348699	+	0.603965i
$185$	−8.65416	−	14.9894i	−0.636267	−	1.10205i
$186$	−3.91638	−	6.78337i	−0.287163	−	0.497381i
$187$	−0.813607	+	1.40921i	−0.0594968	+	0.103051i
$188$	7.69670			0.561339
$189$		0			0
$190$	−4.15165			−0.301192
$191$	−3.91638	+	6.78337i	−0.283379	+	0.490828i	−0.972215	−	0.234090i	$-0.924789\pi$
$191$	−3.91638	+	6.78337i	−0.283379	+	0.490828i	0.688835	+	0.724918i	$0.258122\pi$
$192$	2.57834	+	4.46581i	0.186075	+	0.322292i
$193$	6.10278	+	10.5703i	0.439287	+	0.760868i	0.997635	−	0.0687393i	$-0.0218977\pi$
$193$	6.10278	+	10.5703i	0.439287	+	0.760868i	−0.558347	+	0.829607i	$0.688564\pi$
$194$	1.07583	−	1.86338i	0.0772398	−	0.133783i
$195$	8.72999			0.625167
$196$		0			0
$197$	−18.8222			−1.34103			−0.670513	−	0.741898i	$-0.733926\pi$
$197$	−18.8222			−1.34103			−0.670513	+	0.741898i	$0.733926\pi$
$198$	18.6464	−	32.2965i	1.32514	−	2.29521i
$199$	10.8058	+	18.7162i	0.766004	+	1.32676i	0.939714	+	0.341961i	$0.111091\pi$
$199$	10.8058	+	18.7162i	0.766004	+	1.32676i	−0.173710	+	0.984797i	$0.555576\pi$
$200$	−1.87985	−	3.25600i	−0.132926	−	0.230234i
$201$	−15.5733	+	26.9738i	−1.09846	+	1.90258i
$202$	23.7633			1.67198
$203$		0			0
$204$	2.09775			0.146872
$205$	5.91638	−	10.2475i	0.413218	−	0.715715i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$	−24.3154	−	42.1155i	−1.69004	−	2.92723i
$208$	−2.45819	+	4.25771i	−0.170445	+	0.295219i
$209$	−2.52444			−0.174619
$210$		0			0
$211$	−17.3764			−1.19624			−0.598119	−	0.801407i	$-0.704085\pi$
$211$	−17.3764			−1.19624			−0.598119	+	0.801407i	$0.704085\pi$
$212$	1.60806	−	2.78524i	0.110442	−	0.191291i
$213$	13.5436	+	23.4582i	0.927992	+	1.60733i
$214$	0.524438	+	0.908353i	0.0358498	+	0.0620937i
$215$	9.50958	−	16.4711i	0.648548	−	1.12332i
$216$	14.5089			0.987202
$217$		0			0
$218$	−10.1078			−0.684586
$219$	−3.63501	+	6.29602i	−0.245631	+	0.425445i
$220$	5.62721	+	9.74662i	0.379387	+	0.657117i
$221$	0.262219	+	0.454177i	0.0176388	+	0.0305512i
$222$	−17.3083	+	29.9789i	−1.16166	+	2.01205i
$223$	10.5486			0.706388			0.353194	−	0.935550i	$-0.385096\pi$
$223$	10.5486			0.706388			0.353194	+	0.935550i	$0.385096\pi$
$224$		0			0
$225$	19.3275			1.28850
$226$	4.93831	−	8.55340i	0.328491	−	0.568964i
$227$	−3.47556	−	6.01985i	−0.230681	−	0.399551i	0.727328	−	0.686290i	$-0.240762\pi$
$227$	−3.47556	−	6.01985i	−0.230681	−	0.399551i	−0.958009	+	0.286739i	$0.907429\pi$
$228$	1.62721	+	2.81842i	0.107765	+	0.186654i
$229$	−10.5436	+	18.2620i	−0.696740	+	1.20679i	0.272850	+	0.962057i	$0.412034\pi$
$229$	−10.5436	+	18.2620i	−0.696740	+	1.20679i	−0.969590	+	0.244733i	$0.921300\pi$
$230$	37.4444			2.46901
$231$		0			0
$232$	10.6861			0.701579
$233$	−3.04181	+	5.26857i	−0.199276	+	0.345155i	−0.948294	−	0.317394i	$-0.897192\pi$
$233$	−3.04181	+	5.26857i	−0.199276	+	0.345155i	0.749018	+	0.662549i	$0.230526\pi$
$234$	−6.00958	−	10.4089i	−0.392858	−	0.680451i
$235$	8.39901	+	14.5475i	0.547891	+	0.948975i
$236$	−2.88164	+	4.99115i	−0.187579	+	0.324896i
$237$	−42.0227			−2.72967
$238$		0			0
$239$	−14.2056			−0.918881			−0.459440	−	0.888209i	$-0.651950\pi$
$239$	−14.2056			−0.918881			−0.459440	+	0.888209i	$0.651950\pi$
$240$	−21.4600	+	37.1698i	−1.38524	+	2.39930i
$241$	4.22041	+	7.30996i	0.271860	+	0.470876i	0.969338	−	0.245730i	$-0.0790277\pi$
$241$	4.22041	+	7.30996i	0.271860	+	0.470876i	−0.697478	+	0.716606i	$0.745694\pi$
$242$	−1.24485	−	2.15614i	−0.0800218	−	0.138602i
$243$	−6.44861	+	11.1693i	−0.413679	+	0.716512i
$244$	2.57834			0.165061
$245$		0			0
$246$	−23.6655			−1.50886
$247$	−0.406803	+	0.704604i	−0.0258843	+	0.0448329i
$248$	0.897225	+	1.55404i	0.0569738	+	0.0986816i
$249$	25.5655	+	44.2808i	1.62015	+	2.80618i
$250$	5.31612	−	9.20779i	0.336221	−	0.582352i
$251$	23.9844			1.51388			0.756941	−	0.653483i	$-0.226693\pi$
$251$	23.9844			1.51388			0.756941	+	0.653483i	$0.226693\pi$
$252$		0			0
$253$	22.7683			1.43143
$254$	−11.6811	+	20.2323i	−0.732938	+	1.26949i
$255$	2.28917	+	3.96496i	0.143353	+	0.248295i
$256$	−10.4234	−	18.0539i	−0.651466	−	1.12837i
$257$	7.80581	−	13.5201i	0.486913	−	0.843359i	−0.512974	−	0.858404i	$-0.671456\pi$
$257$	7.80581	−	13.5201i	0.486913	−	0.843359i	0.999887	+	0.0150459i	$0.00478944\pi$
$258$	−38.0383			−2.36816
$259$		0			0
$260$	3.62721			0.224950
$261$	−27.4670	+	47.5743i	−1.70017	+	2.94478i
$262$	−8.20555	−	14.2124i	−0.506941	−	0.878047i
$263$	7.58540	+	13.1383i	0.467736	+	0.810143i	0.999320	−	0.0368628i	$-0.0117365\pi$
$263$	7.58540	+	13.1383i	0.467736	+	0.810143i	−0.531584	+	0.847005i	$0.678403\pi$
$264$	−6.20555	+	10.7483i	−0.381925	+	0.661514i
$265$	7.01916			0.431183
$266$		0			0
$267$	33.0333			2.02160
$268$	−6.47054	+	11.2073i	−0.395251	+	0.684595i
$269$	11.6464	+	20.1721i	0.710092	+	1.22991i	0.964822	+	0.262903i	$0.0846799\pi$
$269$	11.6464	+	20.1721i	0.710092	+	1.22991i	−0.254731	+	0.967012i	$0.581987\pi$
$270$	−28.7144	−	49.7348i	−1.74750	−	3.02676i
$271$	6.37279	−	11.0380i	0.387119	−	0.670510i	−0.604941	−	0.796270i	$-0.706804\pi$
$271$	6.37279	−	11.0380i	0.387119	−	0.670510i	0.992061	+	0.125760i	$0.0401368\pi$
$272$	−2.57834			−0.156335
$273$		0			0
$274$	11.3522			0.685810
$275$	−4.52444	+	7.83656i	−0.272834	+	0.472562i
$276$	−14.6761	−	25.4197i	−0.883397	−	1.53009i
$277$	−4.06097	−	7.03380i	−0.244000	−	0.422620i	0.717850	−	0.696198i	$-0.245126\pi$
$277$	−4.06097	−	7.03380i	−0.244000	−	0.422620i	−0.961850	+	0.273578i	$0.911793\pi$
$278$	10.4947	−	18.1774i	0.629431	−	1.09021i
$279$	−9.22471			−0.552269
$280$		0			0
$281$	19.0333			1.13543			0.567715	−	0.823225i	$-0.307827\pi$
$281$	19.0333			1.13543			0.567715	+	0.823225i	$0.307827\pi$
$282$	16.7980	−	29.0950i	1.00031	−	1.73258i
$283$	5.57331	+	9.65326i	0.331299	+	0.573827i	0.982767	−	0.184849i	$-0.0591797\pi$
$283$	5.57331	+	9.65326i	0.331299	+	0.573827i	−0.651468	+	0.758676i	$0.725846\pi$
$284$	5.62721	+	9.74662i	0.333914	+	0.578355i
$285$	−3.55139	+	6.15118i	−0.210366	+	0.364365i
$286$	5.62721			0.332744
$287$		0			0
$288$	42.0036			2.47508
$289$	8.36248	−	14.4842i	0.491911	−	0.852014i
$290$	−21.1489	−	36.6309i	−1.24191	−	2.15104i
$291$	−1.84056	−	3.18794i	−0.107895	−	0.186880i
$292$	−1.51030	+	2.61592i	−0.0883839	+	0.153085i
$293$	14.1758			0.828161			0.414080	−	0.910240i	$-0.364103\pi$
$293$	14.1758			0.828161			0.414080	+	0.910240i	$0.364103\pi$
$294$		0			0
$295$	−12.5783			−0.732339
$296$	3.96526	−	6.86803i	0.230476	−	0.399196i
$297$	−17.4600	−	30.2416i	−1.01313	−	1.75479i
$298$	7.72999	+	13.3887i	0.447786	+	0.775588i
$299$	3.66902	−	6.35493i	0.212185	−	0.367515i
$300$	11.6655			0.673509
$301$		0			0
$302$	21.7350			1.25071
$303$	20.3275	−	35.2082i	1.16778	−	2.02266i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	2.81361	+	4.87331i	0.161107	+	0.279045i
$306$	3.15165	−	5.45882i	0.180168	−	0.312060i
$307$	−13.5592			−0.773863			−0.386932	−	0.922108i	$-0.626465\pi$
$307$	−13.5592			−0.773863			−0.386932	+	0.922108i	$0.626465\pi$
$308$		0			0
$309$	−13.6867			−0.778606
$310$	3.55139	−	6.15118i	0.201705	−	0.349364i
$311$	0.213343	+	0.369521i	0.0120976	+	0.0209536i	0.872011	−	0.489487i	$-0.162816\pi$
$311$	0.213343	+	0.369521i	0.0120976	+	0.0209536i	−0.859913	+	0.510440i	$0.829482\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	−9.07583	+	15.7198i	−0.512996	+	0.888535i	0.486890	+	0.873463i	$0.338131\pi$
$313$	−9.07583	+	15.7198i	−0.512996	+	0.888535i	−0.999886	+	0.0150721i	$0.995202\pi$
$314$	−23.2645			−1.31289
$315$		0			0
$316$	−17.4600			−0.982200
$317$	−4.71083	+	8.15940i	−0.264587	+	0.458278i	−0.967455	−	0.253042i	$-0.918569\pi$
$317$	−4.71083	+	8.15940i	−0.264587	+	0.458278i	0.702869	+	0.711320i	$0.251902\pi$
$318$	−7.01916	−	12.1575i	−0.393615	−	0.681761i
$319$	−12.8597	−	22.2737i	−0.720006	−	1.24709i
$320$	−2.33804	+	4.04961i	−0.130701	+	0.226380i
$321$	1.79445			0.100156
$322$		0			0
$323$	−0.426686			−0.0237415
$324$	−9.69346	+	16.7896i	−0.538526	+	0.932754i
$325$	1.45819	+	2.52566i	0.0808859	+	0.140098i
$326$	−12.2056	−	21.1406i	−0.676003	−	1.17087i
$327$	−8.64637	+	14.9760i	−0.478145	+	0.828172i
$328$	5.42166			0.299361
$329$		0			0
$330$	49.1255			2.70427
$331$	8.70027	−	15.0693i	0.478210	−	0.828284i	−0.521478	−	0.853265i	$-0.674619\pi$
$331$	8.70027	−	15.0693i	0.478210	−	0.828284i	0.999688	+	0.0249807i	$0.00795244\pi$
$332$	10.6222	+	18.3982i	0.582968	+	1.00973i
$333$	20.3842	+	35.3064i	1.11704	+	1.93478i
$334$	1.84056	−	3.18794i	0.100711	−	0.174436i
$335$	−28.2439			−1.54313
$336$		0			0
$337$	22.0524			1.20127			0.600637	−	0.799522i	$-0.294914\pi$
$337$	22.0524			1.20127			0.600637	+	0.799522i	$0.294914\pi$
$338$	0.906803	−	1.57063i	0.0493236	−	0.0854310i
$339$	−8.44861	−	14.6334i	−0.458866	−	0.794779i
$340$	0.951124	+	1.64740i	0.0515819	+	0.0893426i
$341$	2.15944	−	3.74027i	0.116940	−	0.202547i
$342$	9.77886			0.528780
$343$		0			0
$344$	8.71440			0.469849
$345$	32.0305	−	55.4785i	1.72447	−	2.98686i
$346$	−18.4061	−	31.8803i	−0.989517	−	1.71389i
$347$	−12.6761	−	21.9556i	−0.680488	−	1.17864i	−0.974832	−	0.222940i	$-0.928434\pi$
$347$	−12.6761	−	21.9556i	−0.680488	−	1.17864i	0.294344	−	0.955700i	$-0.404899\pi$
$348$	−16.5783	+	28.7145i	−0.888692	+	1.53926i
$349$	5.70529			0.305397			0.152699	−	0.988273i	$-0.451204\pi$
$349$	5.70529			0.305397			0.152699	+	0.988273i	$0.451204\pi$
$350$		0			0
$351$	−11.2544			−0.600717
$352$	−9.83276	+	17.0308i	−0.524088	+	0.907747i
$353$	−14.3380	−	24.8342i	−0.763137	−	1.32179i	−0.941226	−	0.337778i	$-0.890325\pi$
$353$	−14.3380	−	24.8342i	−0.763137	−	1.32179i	0.178089	−	0.984014i	$-0.443009\pi$
$354$	12.5783	+	21.7863i	0.668531	+	1.15793i
$355$	−12.2814	+	21.2720i	−0.651828	+	1.12900i
$356$	13.7250			0.727422
$357$		0			0
$358$	19.9561			1.05472
$359$	−5.52167	+	9.56381i	−0.291423	+	0.504759i	−0.974146	−	0.225918i	$-0.927462\pi$
$359$	−5.52167	+	9.56381i	−0.291423	+	0.504759i	0.682724	+	0.730677i	$0.260795\pi$
$360$	12.0192	+	20.8178i	0.633465	+	1.09719i
$361$	9.16902	+	15.8812i	0.482580	+	0.835853i
$362$	−0.627213	+	1.08636i	−0.0329656	+	0.0570981i
$363$	−4.25945			−0.223563
$364$		0			0
$365$	−6.59247			−0.345066
$366$	5.62721	−	9.74662i	0.294139	−	0.509464i
$367$	13.6733	+	23.6829i	0.713741	+	1.23624i	0.963443	+	0.267914i	$0.0863342\pi$
$367$	13.6733	+	23.6829i	0.713741	+	1.23624i	−0.249701	+	0.968323i	$0.580332\pi$
$368$	18.0383	+	31.2433i	0.940312	+	1.62867i
$369$	−13.9355	+	24.1371i	−0.725455	+	1.25653i
$370$	−31.3905			−1.63191
$371$		0			0
$372$	−5.56777			−0.288676
$373$	−8.07306	+	13.9829i	−0.418007	+	0.724009i	−0.995739	−	0.0922172i	$-0.970605\pi$
$373$	−8.07306	+	13.9829i	−0.418007	+	0.724009i	0.577732	+	0.816227i	$0.303938\pi$
$374$	1.47556	+	2.55575i	0.0762995	+	0.132155i
$375$	−9.09498	−	15.7530i	−0.469663	−	0.813480i
$376$	−3.84835	+	6.66554i	−0.198463	+	0.343749i
$377$	−8.28917			−0.426914
$378$		0			0
$379$	26.1305			1.34223			0.671117	−	0.741351i	$-0.265815\pi$
$379$	26.1305			1.34223			0.671117	+	0.741351i	$0.265815\pi$
$380$	−1.47556	+	2.55575i	−0.0756947	+	0.131107i
$381$	19.9844	+	34.6140i	1.02383	+	1.77333i
$382$	7.10278	+	12.3024i	0.363410	+	0.629444i
$383$	−10.5244	+	18.2289i	−0.537774	+	0.931451i	0.461250	+	0.887270i	$0.347401\pi$
$383$	−10.5244	+	18.2289i	−0.537774	+	0.931451i	−0.999024	+	0.0441810i	$0.985932\pi$
$384$	−29.9789			−1.52985
$385$		0			0
$386$	22.1361			1.12670
$387$	−22.3990	+	38.7962i	−1.13861	+	1.97212i
$388$	−0.764731	−	1.32455i	−0.0388233	−	0.0672440i
$389$	10.8030	+	18.7114i	0.547736	+	0.948707i	0.998429	+	0.0560278i	$0.0178435\pi$
$389$	10.8030	+	18.7114i	0.547736	+	0.948707i	−0.450693	+	0.892679i	$0.648823\pi$
$390$	7.91638	−	13.7116i	0.400862	−	0.694313i
$391$	3.84835			0.194619
$392$		0			0
$393$	−28.0766			−1.41628
$394$	−17.0680	+	29.5627i	−0.859875	+	1.48935i
$395$	−19.0532	−	33.0011i	−0.958669	−	1.66046i
$396$	−13.2544	−	22.9573i	−0.666060	−	1.15365i
$397$	−13.8476	+	23.9848i	−0.694992	+	1.20376i	0.275191	+	0.961390i	$0.411259\pi$
$397$	−13.8476	+	23.9848i	−0.694992	+	1.20376i	−0.970183	+	0.242372i	$0.922074\pi$
$398$	39.1950			1.96467
$399$		0			0
$400$	−14.3380			−0.716902
$401$	1.28917	−	2.23291i	0.0643780	−	0.111506i	−0.832040	−	0.554716i	$-0.812827\pi$
$401$	1.28917	−	2.23291i	0.0643780	−	0.111506i	0.896418	+	0.443210i	$0.146160\pi$
$402$	28.2439	+	48.9198i	1.40868	+	2.43990i
$403$	−0.695972	−	1.20546i	−0.0346688	−	0.0600482i
$404$	8.44584	−	14.6286i	0.420196	−	0.727801i
$405$	−42.3119			−2.10250
$406$		0			0
$407$	−19.0872			−0.946117
$408$	−1.04888	+	1.81671i	−0.0519271	+	0.0899404i
$409$	7.55845	+	13.0916i	0.373742	+	0.647339i	0.990138	−	0.140097i	$-0.0447414\pi$
$409$	7.55845	+	13.0916i	0.373742	+	0.647339i	−0.616396	+	0.787436i	$0.711408\pi$
$410$	−10.7300	−	18.5849i	−0.529916	−	0.917842i
$411$	9.71083	−	16.8197i	0.479000	−	0.829652i
$412$	−5.68665			−0.280161
$413$		0			0
$414$	−88.1971			−4.33465
$415$	−23.1829	+	40.1540i	−1.13800	+	1.97108i
$416$	3.16902	+	5.48891i	0.155374	+	0.269116i
$417$	−17.9547	−	31.0984i	−0.879245	−	1.52290i
$418$	−2.28917	+	3.96496i	−0.111967	+	0.193932i
$419$	9.99446			0.488261			0.244131	−	0.969742i	$-0.421497\pi$
$419$	9.99446			0.488261			0.244131	+	0.969742i	$0.421497\pi$
$420$		0			0
$421$	−25.9250			−1.26351			−0.631753	−	0.775170i	$-0.717664\pi$
$421$	−25.9250			−1.26351			−0.631753	+	0.775170i	$0.717664\pi$
$422$	−15.7569	+	27.2918i	−0.767036	+	1.32854i
$423$	−19.7832	−	34.2654i	−0.961890	−	1.66604i
$424$	1.60806	+	2.78524i	0.0780941	+	0.135263i
$425$	−0.764731	+	1.32455i	−0.0370949	+	0.0642502i
$426$	49.1255			2.38014
$427$		0			0
$428$	0.745574			0.0360387
$429$	4.81361	−	8.33741i	0.232403	−	0.402534i
$430$	−17.2466	−	29.8720i	−0.831706	−	1.44056i
$431$	−15.3380	−	26.5663i	−0.738808	−	1.27965i	−0.953033	−	0.302868i	$-0.902056\pi$
$431$	−15.3380	−	26.5663i	−0.738808	−	1.27965i	0.214225	−	0.976784i	$-0.431277\pi$
$432$	27.6655	−	47.9181i	1.33106	−	2.30546i
$433$	3.51941			0.169132			0.0845661	−	0.996418i	$-0.473050\pi$
$433$	3.51941			0.169132			0.0845661	+	0.996418i	$0.473050\pi$
$434$		0			0
$435$	−72.3643			−3.46960
$436$	−3.59247	+	6.22234i	−0.172048	+	0.297996i
$437$	2.98514	+	5.17041i	0.142799	+	0.247334i
$438$	6.59247	+	11.4185i	0.315000	+	0.545597i
$439$	16.1758	−	28.0174i	0.772030	−	1.33720i	−0.164418	−	0.986391i	$-0.552575\pi$
$439$	16.1758	−	28.0174i	0.772030	−	1.33720i	0.936449	−	0.350805i	$-0.114092\pi$
$440$	−11.2544			−0.536534
$441$		0			0
$442$	0.951124			0.0452404
$443$	−7.72292	+	13.3765i	−0.366927	+	0.635536i	−0.989083	−	0.147357i	$-0.952923\pi$
$443$	−7.72292	+	13.3765i	−0.366927	+	0.635536i	0.622156	+	0.782893i	$0.286257\pi$
$444$	12.3033	+	21.3099i	0.583889	+	1.01133i
$445$	14.9773	+	25.9415i	0.709994	+	1.22975i
$446$	9.56552	−	16.5680i	0.452941	−	0.784516i
$447$	26.4494			1.25101
$448$		0			0
$449$	−14.4705			−0.682907			−0.341453	−	0.939899i	$-0.610919\pi$
$449$	−14.4705			−0.682907			−0.341453	+	0.939899i	$0.610919\pi$
$450$	17.5262	−	30.3563i	0.826194	−	1.43101i
$451$	−6.52444	−	11.3007i	−0.307224	−	0.532127i
$452$	−3.51030	−	6.08003i	−0.165111	−	0.285980i
$453$	18.5925	−	32.2031i	0.873550	−	1.51303i
$454$	−12.6066			−0.591657
$455$		0			0
$456$	−3.25443			−0.152402
$457$	17.3353	−	30.0256i	0.810910	−	1.40454i	−0.101318	−	0.994854i	$-0.532306\pi$
$457$	17.3353	−	30.0256i	0.810910	−	1.40454i	0.912228	−	0.409683i	$-0.134361\pi$
$458$	19.1219	+	33.1202i	0.893509	+	1.54760i
$459$	−2.95112	−	5.11150i	−0.137747	−	0.238584i
$460$	13.3083	−	23.0507i	0.620504	−	1.07474i
$461$	−12.5400			−0.584047			−0.292024	−	0.956411i	$-0.594329\pi$
$461$	−12.5400			−0.584047			−0.292024	+	0.956411i	$0.594329\pi$
$462$		0			0
$463$	12.1517			0.564735			0.282368	−	0.959306i	$-0.408880\pi$
$463$	12.1517			0.564735			0.282368	+	0.959306i	$0.408880\pi$
$464$	20.3764	−	35.2929i	0.945949	−	1.63843i
$465$	−6.07583	−	10.5236i	−0.281760	−	0.488022i
$466$	5.51664	+	9.55511i	0.255554	+	0.442632i
$467$	−18.5166	+	32.0718i	−0.856848	+	1.48410i	0.0180717	+	0.999837i	$0.494247\pi$
$467$	−18.5166	+	32.0718i	−0.856848	+	1.48410i	−0.874920	+	0.484268i	$0.839086\pi$
$468$	−8.54359			−0.394928
$469$		0			0
$470$	30.4650			1.40525
$471$	−19.9008	+	34.4692i	−0.916980	+	1.58826i
$472$	−2.88164	−	4.99115i	−0.132638	−	0.229736i
$473$	−10.4869	−	18.1639i	−0.482189	−	0.835176i
$474$	−38.1063	+	66.0021i	−1.75028	+	3.03158i
$475$	−2.37279			−0.108871
$476$		0			0
$477$	−16.5330			−0.756996
$478$	−12.8816	+	22.3117i	−0.589192	+	1.02051i
$479$	6.00430	+	10.3997i	0.274343	+	0.475177i	0.969969	−	0.243228i	$-0.0782062\pi$
$479$	6.00430	+	10.3997i	0.274343	+	0.475177i	−0.695626	+	0.718404i	$0.744873\pi$
$480$	27.6655	+	47.9181i	1.26275	+	2.18715i
$481$	−3.07583	+	5.32749i	−0.140246	+	0.242912i
$482$	15.3083			0.697275
$483$		0			0
$484$	−1.76975			−0.0804434
$485$	1.66902	−	2.89083i	0.0757864	−	0.131266i
$486$	11.6952	+	20.2568i	0.530507	+	0.918865i
$487$	−5.55918	−	9.62878i	−0.251911	−	0.436322i	0.712141	−	0.702036i	$-0.247726\pi$
$487$	−5.55918	−	9.62878i	−0.251911	−	0.436322i	−0.964052	+	0.265714i	$0.914392\pi$
$488$	−1.28917	+	2.23291i	−0.0583579	+	0.101079i
$489$	−41.7633			−1.88860
$490$		0			0
$491$	0.0594386			0.00268243			0.00134121	−	0.999999i	$-0.499573\pi$
$491$	0.0594386			0.00268243			0.00134121	+	0.999999i	$0.499573\pi$
$492$	−8.41110	+	14.5685i	−0.379202	+	0.656797i
$493$	−2.17358	−	3.76475i	−0.0978930	−	0.169556i
$494$	0.737781	+	1.27787i	0.0331943	+	0.0574943i
$495$	28.9277	−	50.1043i	1.30021	−	2.25202i
$496$	6.84333			0.307274
$497$		0			0
$498$	92.7316			4.15540
$499$	−5.14888	+	8.91812i	−0.230496	+	0.399230i	−0.957954	−	0.286922i	$-0.907368\pi$
$499$	−5.14888	+	8.91812i	−0.230496	+	0.399230i	0.727458	+	0.686152i	$0.240701\pi$
$500$	−3.77886	−	6.54518i	−0.168996	−	0.292710i
$501$	−3.14888	−	5.45402i	−0.140682	−	0.243668i
$502$	21.7491	−	37.6706i	0.970712	−	1.68132i
$503$	9.32391			0.415733			0.207866	−	0.978157i	$-0.433348\pi$
$503$	9.32391			0.415733			0.207866	+	0.978157i	$0.433348\pi$
$504$		0			0
$505$	36.8661			1.64052
$506$	20.6464	−	35.7606i	0.917843	−	1.58975i
$507$	−1.55139	−	2.68708i	−0.0688995	−	0.119338i
$508$	8.30330	+	14.3817i	0.368399	+	0.638087i
$509$	19.8476	−	34.3771i	0.879730	−	1.52374i	0.0280937	−	0.999605i	$-0.491056\pi$
$509$	19.8476	−	34.3771i	0.879730	−	1.52374i	0.851637	−	0.524132i	$-0.175610\pi$
$510$	8.30330			0.367676
$511$		0			0
$512$	−18.4842			−0.816892
$513$	4.57834	−	7.92991i	0.202139	−	0.350114i
$514$	−14.1567	−	24.5201i	−0.624424	−	1.08153i
$515$	−6.20555	−	10.7483i	−0.273449	−	0.473628i
$516$	−13.5194	+	23.4163i	−0.595159	+	1.03085i
$517$	18.5244			0.814704
$518$		0			0
$519$	−62.9794			−2.76449
$520$	−1.81361	+	3.14126i	−0.0795319	+	0.137753i
$521$	11.1814	+	19.3667i	0.489865	+	0.848471i	0.999932	−	0.0116639i	$-0.00371283\pi$
$521$	11.1814	+	19.3667i	0.489865	+	0.848471i	−0.510067	+	0.860135i	$0.670379\pi$
$522$	49.8144	+	86.2811i	2.18032	+	3.77642i
$523$	−10.3275	+	17.8877i	−0.451589	+	0.782176i	−0.998485	−	0.0550252i	$-0.982476\pi$
$523$	−10.3275	+	17.8877i	−0.451589	+	0.782176i	0.546896	+	0.837201i	$0.315809\pi$
$524$	−11.6655			−0.509611
$525$		0			0
$526$	27.5139			1.19966
$527$	0.364994	−	0.632188i	0.0158994	−	0.0275386i
$528$	23.6655	+	40.9899i	1.02991	+	1.78386i
$529$	−15.4234	−	26.7142i	−0.670585	−	1.16149i
$530$	6.36499	−	11.0245i	0.276478	−	0.478873i
$531$	29.6272			1.28571
$532$		0			0
$533$	−4.20555			−0.182163
$534$	29.9547	−	51.8831i	1.29627	−	2.24520i
$535$	0.813607	+	1.40921i	0.0351753	+	0.0609254i
$536$	−6.47054	−	11.2073i	−0.279485	−	0.484082i
$537$	17.0708	−	29.5675i	0.736659	−	1.27593i
$538$	42.2439			1.82126
$539$		0			0
$540$	−40.8222			−1.75671
$541$	−2.81084	+	4.86851i	−0.120847	+	0.209314i	−0.920102	−	0.391679i	$-0.871894\pi$
$541$	−2.81084	+	4.86851i	−0.120847	+	0.209314i	0.799255	+	0.600992i	$0.205228\pi$
$542$	−11.5577	−	20.0186i	−0.496447	−	0.859871i
$543$	1.07306	+	1.85859i	0.0460492	+	0.0797596i
$544$	−1.66196	+	2.87859i	−0.0712558	+	0.123419i
$545$	−15.6811			−0.671705
$546$		0			0
$547$	−10.3970			−0.444542			−0.222271	−	0.974985i	$-0.571347\pi$
$547$	−10.3970			−0.444542			−0.222271	+	0.974985i	$0.571347\pi$
$548$	4.03474	−	6.98838i	0.172356	−	0.298529i
$549$	−6.62721	−	11.4787i	−0.282843	−	0.489898i
$550$	8.20555	+	14.2124i	0.349886	+	0.606020i
$551$	3.37206	−	5.84058i	0.143655	−	0.248817i
$552$	29.3522			1.24931
$553$		0			0
$554$	−14.7300			−0.625817
$555$	−26.8519	+	46.5089i	−1.13980	+	1.97419i
$556$	−7.45998	−	12.9211i	−0.316373	−	0.547975i
$557$	−7.32748	−	12.6916i	−0.310475	−	0.537759i	0.667990	−	0.744170i	$-0.267155\pi$
$557$	−7.32748	−	12.6916i	−0.310475	−	0.537759i	−0.978465	+	0.206411i	$0.933822\pi$
$558$	−8.36499	+	14.4886i	−0.354118	+	0.613351i
$559$	−6.75971			−0.285905
$560$		0			0
$561$	5.04888			0.213164
$562$	17.2594	−	29.8942i	0.728046	−	1.26101i
$563$	−12.3728	−	21.4303i	−0.521451	−	0.903179i	−0.999689	−	0.0249490i	$-0.992058\pi$
$563$	−12.3728	−	21.4303i	−0.521451	−	0.903179i	0.478238	−	0.878230i	$-0.341276\pi$
$564$	−11.9406	−	20.6817i	−0.502788	−	0.870855i
$565$	7.66123	−	13.2696i	0.322310	−	0.558258i
$566$	20.2156			0.849725
$567$		0			0
$568$	−11.2544			−0.472225
$569$	10.2665	−	17.7821i	0.430395	−	0.745466i	−0.566512	−	0.824053i	$-0.691708\pi$
$569$	10.2665	−	17.7821i	0.430395	−	0.745466i	0.996907	+	0.0785876i	$0.0250410\pi$
$570$	6.44082	+	11.1558i	0.269776	+	0.467266i
$571$	20.9476	+	36.2824i	0.876631	+	1.51837i	0.855015	+	0.518603i	$0.173548\pi$
$571$	20.9476	+	36.2824i	0.876631	+	1.51837i	0.0216158	+	0.999766i	$0.493119\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	24.3033			1.01529
$574$		0			0
$575$	21.4005			0.892464
$576$	5.50707	−	9.53852i	0.229461	−	0.397438i
$577$	−10.0872	−	17.4715i	−0.419935	−	0.727349i	0.575997	−	0.817452i	$-0.304614\pi$
$577$	−10.0872	−	17.4715i	−0.419935	−	0.727349i	−0.995932	+	0.0901025i	$0.971281\pi$
$578$	−15.1663	−	26.2687i	−0.630833	−	1.09263i
$579$	18.9355	−	32.7973i	0.786934	−	1.36301i
$580$	−30.0666			−1.24845
$581$		0			0
$582$	−6.67609			−0.276733
$583$	3.87028	−	6.70351i	0.160290	−	0.277631i
$584$	−1.51030	−	2.61592i	−0.0624968	−	0.108248i
$585$	−9.32318	−	16.1482i	−0.385466	−	0.667647i
$586$	12.8547	−	22.2650i	0.531022	−	0.919758i
$587$	18.7441			0.773653			0.386826	−	0.922153i	$-0.373571\pi$
$587$	18.7441			0.773653			0.386826	+	0.922153i	$0.373571\pi$
$588$		0			0
$589$	1.13249			0.0466636
$590$	−11.4061	+	19.7559i	−0.469581	+	0.813338i
$591$	29.2005	+	50.5768i	1.20115	+	2.08045i
$592$	−15.1219	−	26.1920i	−0.621508	−	1.07648i
$593$	−1.49042	+	2.58149i	−0.0612043	+	0.106009i	−0.895004	−	0.446058i	$-0.852827\pi$
$593$	−1.49042	+	2.58149i	−0.0612043	+	0.106009i	0.833800	+	0.552067i	$0.186161\pi$
$594$	−63.3311			−2.59850
$595$		0			0
$596$	10.9894			0.450145
$597$	33.5280	−	58.0722i	1.37221	−	2.37674i
$598$	−6.65416	−	11.5253i	−0.272109	−	0.471307i
$599$	−3.73705	−	6.47277i	−0.152692	−	0.264470i	0.779524	−	0.626372i	$-0.215461\pi$
$599$	−3.73705	−	6.47277i	−0.152692	−	0.264470i	−0.932216	+	0.361902i	$0.882128\pi$
$600$	−5.83276	+	10.1026i	−0.238122	+	0.412439i
$601$	−21.4700			−0.875780			−0.437890	−	0.899028i	$-0.644274\pi$
$601$	−21.4700			−0.875780			−0.437890	+	0.899028i	$0.644274\pi$
$602$		0			0
$603$	66.5260			2.70915
$604$	7.72496	−	13.3800i	0.314324	−	0.544426i
$605$	−1.93124	−	3.34501i	−0.0785161	−	0.135994i
$606$	−36.8661	−	63.8539i	−1.49758	−	2.59389i
$607$	−11.4522	+	19.8358i	−0.464830	+	0.805109i	−0.999194	−	0.0401456i	$-0.987218\pi$
$607$	−11.4522	+	19.8358i	−0.464830	+	0.805109i	0.534364	+	0.845254i	$0.320551\pi$
$608$	−5.15667			−0.209131
$609$		0			0
$610$	10.2056			0.413211
$611$	2.98514	−	5.17041i	0.120766	−	0.209173i
$612$	−2.24029	−	3.88030i	−0.0905585	−	0.156852i
$613$	10.0731	+	17.4470i	0.406847	+	0.704679i	0.994535	−	0.104408i	$-0.0332949\pi$
$613$	10.0731	+	17.4470i	0.406847	+	0.704679i	−0.587688	+	0.809088i	$0.699962\pi$
$614$	−12.2955	+	21.2964i	−0.496206	+	0.859455i
$615$	−36.7144			−1.48047
$616$		0			0
$617$	−13.7844			−0.554939			−0.277470	−	0.960734i	$-0.589496\pi$
$617$	−13.7844			−0.554939			−0.277470	+	0.960734i	$0.589496\pi$
$618$	−12.4111	+	21.4967i	−0.499248	+	0.864722i
$619$	−9.83276	−	17.0308i	−0.395212	−	0.684527i	0.597916	−	0.801559i	$-0.295996\pi$
$619$	−9.83276	−	17.0308i	−0.395212	−	0.684527i	−0.993128	+	0.117031i	$0.962662\pi$
$620$	−2.52444	−	4.37245i	−0.101384	−	0.175602i
$621$	−41.2927	+	71.5211i	−1.65702	+	2.87004i
$622$	0.773841			0.0310282
$623$		0			0
$624$	15.2544			0.610666
$625$	15.5383	−	26.9131i	0.621533	−	1.07653i
$626$	16.4600	+	28.5095i	0.657873	+	1.13947i
$627$	3.91638	+	6.78337i	0.156405	+	0.270902i
$628$	−8.26856	+	14.3216i	−0.329951	+	0.571493i
$629$	−3.22616			−0.128635
$630$		0			0
$631$	−16.1672			−0.643608			−0.321804	−	0.946806i	$-0.604289\pi$
$631$	−16.1672			−0.643608			−0.321804	+	0.946806i	$0.604289\pi$
$632$	8.72999	−	15.1208i	0.347260	−	0.601472i
$633$	26.9575	+	46.6917i	1.07146	+	1.85583i
$634$	8.54359	+	14.7979i	0.339309	+	0.587701i
$635$	−18.1219	+	31.3881i	−0.719147	+	1.24560i
$636$	−9.97887			−0.395688
$637$		0			0
$638$	−46.6449			−1.84669
$639$	28.9277	−	50.1043i	1.14436	−	1.98210i
$640$	−13.5925	−	23.5428i	−0.537290	−	0.930613i
$641$	14.5018	+	25.1178i	0.572786	+	0.992095i	0.996278	+	0.0861949i	$0.0274708\pi$
$641$	14.5018	+	25.1178i	0.572786	+	0.992095i	−0.423492	+	0.905900i	$0.639196\pi$
$642$	1.62721	−	2.81842i	0.0642210	−	0.111234i
$643$	39.2233			1.54681			0.773407	−	0.633910i	$-0.218551\pi$
$643$	39.2233			1.54681			0.773407	+	0.633910i	$0.218551\pi$
$644$		0			0
$645$	−59.0122			−2.32360
$646$	−0.386920	+	0.670166i	−0.0152232	+	0.0263673i
$647$	−5.99221	−	10.3788i	−0.235578	−	0.408033i	0.723863	−	0.689944i	$-0.242365\pi$
$647$	−5.99221	−	10.3788i	−0.235578	−	0.408033i	−0.959440	+	0.281911i	$0.909032\pi$
$648$	−9.69346	−	16.7896i	−0.380795	−	0.659556i
$649$	−6.93554	+	12.0127i	−0.272244	+	0.471540i
$650$	5.28917			0.207458
$651$		0			0
$652$	−17.3522			−0.679564
$653$	−22.6655	+	39.2578i	−0.886971	+	1.53628i	−0.0435323	+	0.999052i	$0.513861\pi$
$653$	−22.6655	+	39.2578i	−0.886971	+	1.53628i	−0.843438	+	0.537226i	$0.819472\pi$
$654$	15.6811	+	27.1605i	0.613180	+	1.06206i
$655$	−12.7300	−	22.0490i	−0.497402	−	0.861525i
$656$	10.3380	−	17.9060i	0.403633	−	0.699113i
$657$	15.5280			0.605805
$658$		0			0
$659$	6.12193			0.238477			0.119238	−	0.992866i	$-0.461955\pi$
$659$	6.12193			0.238477			0.119238	+	0.992866i	$0.461955\pi$
$660$	17.4600	−	30.2416i	0.679629	−	1.17715i
$661$	−13.7640	−	23.8400i	−0.535358	−	0.927267i	−0.999146	−	0.0413207i	$-0.986843\pi$
$661$	−13.7640	−	23.8400i	−0.535358	−	0.927267i	0.463788	−	0.885946i	$-0.346490\pi$
$662$	−15.7789	−	27.3298i	−0.613263	−	1.06220i
$663$	0.813607	−	1.40921i	0.0315979	−	0.0547291i
$664$	−21.2444			−0.824442
$665$		0			0
$666$	73.9377			2.86503
$667$	−30.4131	+	52.6771i	−1.17760	+	2.03967i
$668$	−1.30833	−	2.26609i	−0.0506206	−	0.0876775i
$669$	−16.3650	−	28.3450i	−0.632707	−	1.09588i
$670$	−25.6116	+	44.3606i	−0.989463	+	1.71380i
$671$	6.20555			0.239563
$672$		0			0
$673$	27.9547			1.07757			0.538787	−	0.842442i	$-0.318883\pi$
$673$	27.9547			1.07757			0.538787	+	0.842442i	$0.318883\pi$
$674$	19.9972	−	34.6362i	0.770265	−	1.33414i
$675$	−16.4111	−	28.4249i	−0.631664	−	1.09407i
$676$	−0.644584	−	1.11645i	−0.0247917	−	0.0429405i
$677$	−6.33025	+	10.9643i	−0.243291	+	0.421393i	−0.961650	−	0.274280i	$-0.911560\pi$
$677$	−6.33025	+	10.9643i	−0.243291	+	0.421393i	0.718359	+	0.695673i	$0.244894\pi$
$678$	−30.6449			−1.17691
$679$		0			0
$680$	−1.90225			−0.0729479
$681$	−10.7839	+	18.6782i	−0.413239	+	0.715752i
$682$	−3.91638	−	6.78337i	−0.149966	−	0.259749i
$683$	14.1517	+	24.5114i	0.541498	+	0.937902i	0.998818	+	0.0485999i	$0.0154759\pi$
$683$	14.1517	+	24.5114i	0.541498	+	0.937902i	−0.457320	+	0.889302i	$0.651191\pi$
$684$	3.47556	−	6.01985i	0.132891	−	0.230175i
$685$	17.6116			0.672906
$686$		0			0
$687$	65.4288			2.49626
$688$	16.6167	−	28.7809i	0.633504	−	1.09726i
$689$	−1.24736	−	2.16049i	−0.0475206	−	0.0823081i
$690$	−58.0908	−	100.616i	−2.21148	−	3.83039i
$691$	6.11763	−	10.5961i	0.232726	−	0.403093i	−0.725884	−	0.687818i	$-0.758569\pi$
$691$	6.11763	−	10.5961i	0.232726	−	0.403093i	0.958609	+	0.284725i	$0.0919022\pi$
$692$	−26.1672			−0.994729
$693$		0			0
$694$	−45.9789			−1.74533
$695$	16.2814	−	28.2002i	0.617588	−	1.06969i
$696$	−16.5783	−	28.7145i	−0.628400	−	1.08842i
$697$	−1.10278	−	1.91006i	−0.0417706	−	0.0723488i
$698$	5.17358	−	8.96090i	0.195823	−	0.339175i
$699$	18.8761			0.713960
$700$		0			0
$701$	51.0419			1.92783			0.963913	−	0.266219i	$-0.0857743\pi$
$701$	51.0419			1.92783			0.963913	+	0.266219i	$0.0857743\pi$
$702$	−10.2056	+	17.6765i	−0.385184	+	0.667158i
$703$	−2.50251	−	4.33448i	−0.0943840	−	0.163478i
$704$	2.57834	+	4.46581i	0.0971747	+	0.168312i
$705$	26.0602	−	45.1377i	0.981485	−	1.69998i
$706$	−52.0071			−1.95731
$707$		0			0
$708$	17.8822			0.672053
$709$	−21.2955	+	36.8849i	−0.799770	+	1.38524i	0.119996	+	0.992774i	$0.461712\pi$
$709$	−21.2955	+	36.8849i	−0.799770	+	1.38524i	−0.919766	+	0.392467i	$0.871622\pi$
$710$	22.2736	+	38.5790i	0.835913	+	1.44784i
$711$	44.8781	+	77.7312i	1.68306	+	2.91515i
$712$	−6.86248	+	11.8862i	−0.257182	+	0.445453i
$713$	−10.2141			−0.382523
$714$		0			0
$715$	8.72999			0.326483
$716$	7.09273	−	12.2850i	0.265068	−	0.459111i
$717$	22.0383	+	38.1715i	0.823036	+	1.42554i
$718$	10.0141	+	17.3450i	0.373724	+	0.647309i
$719$	−21.2466	+	36.8002i	−0.792366	+	1.37242i	0.132133	+	0.991232i	$0.457817\pi$
$719$	−21.2466	+	36.8002i	−0.792366	+	1.37242i	−0.924499	+	0.381186i	$0.875516\pi$
$720$	91.6727			3.41644
$721$		0			0
$722$	33.2580			1.23773
$723$	13.0950	−	22.6812i	0.487008	−	0.843522i
$724$	0.445843	+	0.772222i	0.0165696	+	0.0286994i
$725$	−12.0872	−	20.9356i	−0.448907	−	0.777530i
$726$	−3.86248	+	6.69002i	−0.143350	+	0.248290i
$727$	3.75614			0.139307			0.0696537	−	0.997571i	$-0.477811\pi$
$727$	3.75614			0.139307			0.0696537	+	0.997571i	$0.477811\pi$
$728$		0			0
$729$	−5.09775			−0.188806
$730$	−5.97807	+	10.3543i	−0.221258	+	0.383231i
$731$	−1.77252	−	3.07010i	−0.0655592	−	0.113552i
$732$	−4.00000	−	6.92820i	−0.147844	−	0.256074i
$733$	22.8910	−	39.6483i	0.845497	−	1.46444i	−0.0396921	−	0.999212i	$-0.512638\pi$
$733$	22.8910	−	39.6483i	0.845497	−	1.46444i	0.885189	−	0.465232i	$-0.154029\pi$
$734$	49.5960			1.83062
$735$		0			0
$736$	46.5089			1.71434
$737$	−15.5733	+	26.9738i	−0.573650	+	0.993592i
$738$	25.2736	+	43.7751i	0.930333	+	1.61138i
$739$	7.02695	+	12.1710i	0.258491	+	0.447719i	0.965838	−	0.259148i	$-0.0834416\pi$
$739$	7.02695	+	12.1710i	0.258491	+	0.447719i	−0.707347	+	0.706866i	$0.750108\pi$
$740$	−11.1567	+	19.3239i	−0.410127	+	0.710362i
$741$	2.52444			0.0927375
$742$		0			0
$743$	4.74557			0.174098			0.0870491	−	0.996204i	$-0.472256\pi$
$743$	4.74557			0.174098			0.0870491	+	0.996204i	$0.472256\pi$
$744$	2.78389	−	4.82183i	0.102062	−	0.176777i
$745$	11.9922	+	20.7711i	0.439360	+	0.760995i
$746$	14.6413	+	25.3596i	0.536058	+	0.928479i
$747$	54.6054	−	94.5793i	1.99791	−	3.46047i
$748$	2.09775			0.0767014
$749$		0			0
$750$	−32.9894			−1.20460
$751$	−18.0504	+	31.2642i	−0.658669	+	1.14085i	0.322292	+	0.946640i	$0.395547\pi$
$751$	−18.0504	+	31.2642i	−0.658669	+	1.14085i	−0.980961	+	0.194207i	$0.937787\pi$
$752$	14.6761	+	25.4197i	0.535182	+	0.926962i
$753$	−37.2091	−	64.4481i	−1.35598	−	2.34862i
$754$	−7.51664	+	13.0192i	−0.273740	+	0.474132i
$755$	33.7194			1.22718
$756$		0			0
$757$	−1.03474			−0.0376084			−0.0188042	−	0.999823i	$-0.505986\pi$
$757$	−1.03474			−0.0376084			−0.0188042	+	0.999823i	$0.505986\pi$
$758$	23.6952	−	41.0414i	0.860650	−	1.49069i
$759$	−35.3225	−	61.1803i	−1.28212	−	2.22070i
$760$	−1.47556	−	2.55575i	−0.0535243	−	0.0927067i
$761$	14.9207	−	25.8434i	0.540874	−	0.936822i	−0.457980	−	0.888963i	$-0.651427\pi$
$761$	14.9207	−	25.8434i	0.540874	−	0.936822i	0.998854	−	0.0478590i	$-0.0152398\pi$
$762$	72.4877			2.62595
$763$		0			0
$764$	10.0978			0.365324
$765$	4.88943	−	8.46874i	0.176778	−	0.306188i
$766$	19.0872	+	33.0600i	0.689648	+	1.19451i
$767$	2.23527	+	3.87160i	0.0807109	+	0.139795i
$768$	−32.3416	+	56.0173i	−1.16703	+	2.02135i
$769$	−23.6358			−0.852329			−0.426164	−	0.904646i	$-0.640136\pi$
$769$	−23.6358			−0.852329			−0.426164	+	0.904646i	$0.640136\pi$
$770$		0			0
$771$	−48.4394			−1.74450
$772$	7.86751	−	13.6269i	0.283158	−	0.490444i
$773$	6.51388	+	11.2824i	0.234288	+	0.405798i	0.959065	−	0.283184i	$-0.0913909\pi$
$773$	6.51388	+	11.2824i	0.234288	+	0.405798i	−0.724778	+	0.688983i	$0.758058\pi$
$774$	40.6230	+	70.3611i	1.46016	+	2.52908i
$775$	2.02972	−	3.51558i	0.0729097	−	0.126283i
$776$	1.52946			0.0549045
$777$		0			0
$778$	39.1849			1.40485
$779$	1.71083	−	2.96325i	0.0612969	−	0.106169i
$780$	−5.62721	−	9.74662i	−0.201487	−	0.348985i
$781$	13.5436	+	23.4582i	0.484628	+	0.839400i
$782$	3.48970	−	6.04433i	0.124791	−	0.216145i
$783$	93.2898			3.33391
$784$		0			0
$785$	−36.0922			−1.28819
$786$	−25.4600	+	44.0980i	−0.908127	+	1.57292i
$787$	23.1071	+	40.0226i	0.823678	+	1.42665i	0.902925	+	0.429797i	$0.141415\pi$
$787$	23.1071	+	40.0226i	0.823678	+	1.42665i	−0.0792472	+	0.996855i	$0.525252\pi$
$788$	12.1325	+	21.0141i	0.432202	+	0.748596i
$789$	23.5358	−	40.7652i	0.837897	−	1.45128i
$790$	−69.1099			−2.45882
$791$		0			0
$792$	26.5089			0.941951
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$	25.1141	+	43.4990i	0.891267	+	1.54372i
$795$	−10.8894	−	18.8610i	−0.386208	−	0.668932i
$796$	13.9305	−	24.1284i	0.493754	−	0.855207i
$797$	−53.1155			−1.88145			−0.940723	−	0.339176i	$-0.889852\pi$
$797$	−53.1155			−1.88145			−0.940723	+	0.339176i	$0.889852\pi$
$798$		0			0
$799$	3.13104			0.110768
$800$	−9.24208	+	16.0077i	−0.326757	+	0.565959i
$801$	−35.2779	−	61.1031i	−1.24648	−	2.15897i
$802$	−2.33804	−	4.04961i	−0.0825592	−	0.142997i
$803$	−3.63501	+	6.29602i	−0.128277	+	0.222182i
$804$	40.1533			1.41610
$805$		0			0
$806$	−2.52444			−0.0889195
$807$	36.1361	−	62.5895i	1.27205	−	2.20325i
$808$	8.44584	+	14.6286i	0.297124	+	0.514633i
$809$	27.2318	+	47.1668i	0.957418	+	1.65830i	0.728735	+	0.684796i	$0.240109\pi$
$809$	27.2318	+	47.1668i	0.957418	+	1.65830i	0.228683	+	0.973501i	$0.426558\pi$
$810$	−38.3686	+	66.4563i	−1.34813	+	2.33504i
$811$	−38.0978			−1.33779			−0.668897	−	0.743356i	$-0.733233\pi$
$811$	−38.0978			−1.33779			−0.668897	+	0.743356i	$0.733233\pi$
$812$		0			0
$813$	−39.5466			−1.38696
$814$	−17.3083	+	29.9789i	−0.606656	+	1.05076i
$815$	−18.9355	−	32.7973i	−0.663283	−	1.14884i
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$	2.74987	−	4.76292i	0.0962058	−	0.166633i
$818$	27.4161			0.958582
$819$		0			0
$820$	−15.2544			−0.532708
$821$	1.15165	−	1.99472i	0.0401929	−	0.0696161i	−0.845229	−	0.534404i	$-0.820536\pi$
$821$	1.15165	−	1.99472i	0.0401929	−	0.0696161i	0.885422	+	0.464788i	$0.153869\pi$
$822$	−17.6116	−	30.5042i	−0.614276	−	1.06396i
$823$	−11.8086	−	20.4531i	−0.411621	−	0.712949i	0.583446	−	0.812152i	$-0.301704\pi$
$823$	−11.8086	−	20.4531i	−0.411621	−	0.712949i	−0.995067	+	0.0992029i	$0.968371\pi$
$824$	2.84333	−	4.92478i	0.0990519	−	0.171563i
$825$	28.0766			0.977503
$826$		0			0
$827$	−48.1643			−1.67484			−0.837419	−	0.546562i	$-0.815936\pi$
$827$	−48.1643			−1.67484			−0.837419	+	0.546562i	$0.815936\pi$
$828$	−31.3466	+	54.2940i	−1.08937	+	1.88685i
$829$	6.53580	+	11.3203i	0.226998	+	0.393172i	0.956917	−	0.290362i	$-0.0937757\pi$
$829$	6.53580	+	11.3203i	0.226998	+	0.393172i	−0.729919	+	0.683533i	$0.760442\pi$
$830$	42.0447	+	72.8235i	1.45939	+	2.52774i
$831$	−12.6003	+	21.8243i	−0.437098	+	0.757076i
$832$	1.66196			0.0576179
$833$		0			0
$834$	−65.1255			−2.25511
$835$	2.85542	−	4.94573i	0.0988157	−	0.171154i
$836$	1.62721	+	2.81842i	0.0562783	+	0.0974769i
$837$	7.83276	+	13.5667i	0.270740	+	0.468935i
$838$	9.06301	−	15.6976i	0.313076	−	0.542264i
$839$	17.6756			0.610229			0.305114	−	0.952316i	$-0.401305\pi$
$839$	17.6756			0.610229			0.305114	+	0.952316i	$0.401305\pi$
$840$		0			0
$841$	39.7103			1.36932
$842$	−23.5089	+	40.7185i	−0.810169	+	1.40325i
$843$	−29.5280	−	51.1440i	−1.01700	−	1.76149i
$844$	11.2005	+	19.3999i	0.385538	+	0.667771i
$845$	1.40680	−	2.43665i	0.0483955	−	0.0838235i
$846$	−71.7577			−2.46708
$847$		0			0
$848$	12.2650			0.421181
$849$	17.2927	−	29.9519i	0.593485	−	1.02795i
$850$	1.38692	+	2.40222i	0.0475710	+	0.0823953i
$851$	22.5705	+	39.0933i	0.773708	+	1.34010i
$852$	17.4600	−	30.2416i	0.598169	−	1.03606i
$853$	5.48970			0.187964			0.0939818	−	0.995574i	$-0.470040\pi$
$853$	5.48970			0.187964			0.0939818	+	0.995574i	$0.470040\pi$
$854$		0			0
$855$	15.1708			0.518831
$856$	−0.372787	+	0.645686i	−0.0127416	+	0.0220691i
$857$	−5.52444	−	9.56861i	−0.188711	−	0.326857i	0.756110	−	0.654445i	$-0.227098\pi$
$857$	−5.52444	−	9.56861i	−0.188711	−	0.326857i	−0.944821	+	0.327588i	$0.893764\pi$
$858$	−8.72999	−	15.1208i	−0.298037	−	0.516215i
$859$	22.6308	−	39.1977i	0.772152	−	1.33741i	−0.164229	−	0.986422i	$-0.552514\pi$
$859$	22.6308	−	39.1977i	0.772152	−	1.33741i	0.936381	−	0.350985i	$-0.114153\pi$
$860$	−24.5189			−0.836087
$861$		0			0
$862$	−55.6344			−1.89491
$863$	2.95112	−	5.11150i	0.100457	−	0.173997i	−0.811416	−	0.584469i	$-0.801303\pi$
$863$	2.95112	−	5.11150i	0.100457	−	0.173997i	0.911873	+	0.410472i	$0.134636\pi$
$864$	−35.6655	−	61.7745i	−1.21337	−	2.10161i
$865$	−28.5550	−	49.4586i	−0.970898	−	1.68164i
$866$	3.19142	−	5.52770i	0.108449	−	0.187839i
$867$	−51.8938			−1.76241
$868$		0			0
$869$	−42.0227			−1.42552
$870$	−65.6202	+	113.658i	−2.22473	+	3.85335i
$871$	5.01916	+	8.69343i	0.170068	+	0.294566i
$872$	−3.59247	−	6.22234i	−0.121656	−	0.210715i
$873$	−3.93124	+	6.80911i	−0.133052	+	0.230453i
$874$	10.8277			0.366254
$875$		0			0
$876$	9.37227			0.316660
$877$	2.45364	−	4.24982i	0.0828534	−	0.143506i	−0.821621	−	0.570034i	$-0.806930\pi$
$877$	2.45364	−	4.24982i	0.0828534	−	0.143506i	0.904474	+	0.426528i	$0.140263\pi$
$878$	−29.3366	−	50.8125i	−0.990062	−	1.71484i
$879$	−21.9922	−	38.0916i	−0.741779	−	1.28480i
$880$	−21.4600	+	37.1698i	−0.723416	+	1.25299i
$881$	−44.2822			−1.49190			−0.745952	−	0.665999i	$-0.768005\pi$
$881$	−44.2822			−1.49190			−0.745952	+	0.665999i	$0.768005\pi$
$882$		0			0
$883$	−58.8605			−1.98081			−0.990407	−	0.138181i	$-0.955874\pi$
$883$	−58.8605			−1.98081			−0.990407	+	0.138181i	$0.955874\pi$
$884$	0.338044	−	0.585510i	0.0113697	−	0.0196928i
$885$	19.5139	+	33.7990i	0.655952	+	1.13614i
$886$	14.0063	+	24.2597i	0.470552	+	0.815020i
$887$	−5.06446	+	8.77191i	−0.170048	+	0.294532i	−0.938436	−	0.345452i	$-0.887726\pi$
$887$	−5.06446	+	8.77191i	−0.170048	+	0.294532i	0.768388	+	0.639984i	$0.221059\pi$
$888$	−24.6066			−0.825744
$889$		0			0
$890$	54.3260			1.82101
$891$	−23.3303	+	40.4092i	−0.781593	+	1.35376i
$892$	−6.79947	−	11.7770i	−0.227663	−	0.394324i
$893$	2.42873	+	4.20668i	0.0812743	+	0.140771i
$894$	23.9844	−	41.5422i	0.802159	−	1.38938i
$895$	30.9597			1.03487
$896$		0			0
$897$	−22.7683			−0.760211
$898$	−13.1219	+	22.7279i	−0.437885	+	0.758438i
$899$	5.76903	+	9.99225i	0.192408	+	0.333260i
$900$	−12.4582	−	21.5782i	−0.415273	−	0.719274i
$901$	0.654163	−	1.13304i	0.0217933	−	0.0377471i
$902$	−23.6655			−0.787976
$903$		0			0
$904$	7.02061			0.233502
$905$	−0.973050	+	1.68537i	−0.0323453	+	0.0560237i
$906$	−33.7194	−	58.4038i	−1.12025	−	1.94033i
$907$	−18.9773	−	32.8697i	−0.630132	−	1.09142i	−0.987524	−	0.157467i	$-0.949667\pi$
$907$	−18.9773	−	32.8697i	−0.630132	−	1.09142i	0.357392	−	0.933955i	$-0.383666\pi$
$908$	−4.48059	+	7.76060i	−0.148693	+	0.257545i
$909$	−86.8349			−2.88013
$910$		0			0
$911$	5.57477			0.184700			0.0923501	−	0.995727i	$-0.470562\pi$
$911$	5.57477			0.184700			0.0923501	+	0.995727i	$0.470562\pi$
$912$	−6.20555	+	10.7483i	−0.205486	+	0.355913i
$913$	25.5655	+	44.2808i	0.846095	+	1.46548i
$914$	−31.4394	−	54.4546i	−1.03992	−	1.80120i
$915$	8.72999	−	15.1208i	0.288605	−	0.499878i
$916$	27.1849			0.898216
$917$		0			0
$918$	−10.7044			−0.353296
$919$	−7.89220	+	13.6697i	−0.260340	+	0.450922i	−0.966332	−	0.257298i	$-0.917168\pi$
$919$	−7.89220	+	13.6697i	−0.260340	+	0.450922i	0.705992	+	0.708219i	$0.250501\pi$
$920$	13.3083	+	23.0507i	0.438762	+	0.759959i
$921$	21.0355	+	36.4346i	0.693145	+	1.20056i
$922$	−11.3713	+	19.6957i	−0.374495	+	0.648644i
$923$	8.72999			0.287351
$924$		0			0
$925$	−17.9406			−0.589882
$926$	11.0192	−	19.0857i	0.362112	−	0.627196i
$927$	14.6167	+	25.3168i	0.480074	+	0.831512i
$928$	−26.2686	−	45.4985i	−0.862308	−	1.49356i
$929$	−22.6315	+	39.1989i	−0.742516	+	1.28608i	0.208831	+	0.977952i	$0.433034\pi$
$929$	−22.6315	+	39.1989i	−0.742516	+	1.28608i	−0.951346	+	0.308123i	$0.900299\pi$
$930$	−22.0383			−0.722665
$931$		0			0
$932$	7.84281			0.256900
$933$	0.661956	−	1.14654i	0.0216715	−	0.0375361i
$934$	33.5819	+	58.1656i	1.09883	+	1.90324i
$935$	2.28917	+	3.96496i	0.0748638	+	0.129668i
$936$	4.27180	−	7.39897i	0.139628	−	0.241843i
$937$	−53.6188			−1.75165			−0.875824	−	0.482630i	$-0.839682\pi$
$937$	−53.6188			−1.75165			−0.875824	+	0.482630i	$0.839682\pi$
$938$		0			0
$939$	56.3205			1.83795
$940$	10.8277	−	18.7542i	0.353162	−	0.611694i
$941$	10.3876	+	17.9919i	0.338628	+	0.586520i	0.984175	−	0.177200i	$-0.0567040\pi$
$941$	10.3876	+	17.9919i	0.338628	+	0.586520i	−0.645547	+	0.763720i	$0.723371\pi$
$942$	36.0922	+	62.5135i	1.17595	+	2.03680i
$943$	−15.4303	+	26.7260i	−0.502478	+	0.870318i
$944$	−21.9789			−0.715351
$945$		0			0
$946$	−38.0383			−1.23673
$947$	5.43026	−	9.40548i	0.176460	−	0.305637i	−0.764206	−	0.644972i	$-0.776869\pi$
$947$	5.43026	−	9.40548i	0.176460	−	0.305637i	0.940665	+	0.339335i	$0.110202\pi$
$948$	27.0872	+	46.9164i	0.879751	+	1.52377i
$949$	1.17153	+	2.02916i	0.0380296	+	0.0658692i
$950$	−2.15165	+	3.72677i	−0.0698088	+	0.120912i
$951$	29.2333			0.947955
$952$		0			0
$953$	−25.7180			−0.833087			−0.416543	−	0.909116i	$-0.636759\pi$
$953$	−25.7180			−0.833087			−0.416543	+	0.909116i	$0.636759\pi$
$954$	−14.9922	+	25.9673i	−0.485391	+	0.840721i
$955$	11.0192	+	19.0857i	0.356572	+	0.617600i
$956$	9.15667	+	15.8598i	0.296148	+	0.512943i
$957$	−39.9008	+	69.1102i	−1.28981	+	2.23402i
$958$	21.7789			0.703643
$959$		0			0
$960$	14.5089			0.468271
$961$	14.5312	−	25.1689i	0.468750	−	0.811899i
$962$	5.57834	+	9.66196i	0.179853	+	0.311514i
$963$	−1.91638	−	3.31927i	−0.0617545	−	0.106962i
$964$	5.44082	−	9.42378i	0.175237	−	0.303519i
$965$	34.3416			1.10550
$966$		0			0
$967$	33.5038			1.07741			0.538705	−	0.842494i	$-0.318914\pi$
$967$	33.5038			1.07741			0.538705	+	0.842494i	$0.318914\pi$
$968$	0.884877	−	1.53265i	0.0284410	−	0.0492613i
$969$	0.661956	+	1.14654i	0.0212651	+	0.0368322i
$970$	−3.02695	−	5.24283i	−0.0971895	−	0.168337i
$971$	1.01916	−	1.76523i	0.0327063	−	0.0566490i	−0.849209	−	0.528057i	$-0.822921\pi$
$971$	1.01916	−	1.76523i	0.0327063	−	0.0566490i	0.881915	+	0.471408i	$0.156254\pi$
$972$	16.6267			0.533302
$973$		0			0
$974$	−20.1643			−0.646107
$975$	4.52444	−	7.83656i	0.144898	−	0.250971i
$976$	4.91638	+	8.51542i	0.157370	+	0.272572i
$977$	−7.57054	−	13.1126i	−0.242203	−	0.419508i	0.719138	−	0.694867i	$-0.244537\pi$
$977$	−7.57054	−	13.1126i	−0.242203	−	0.419508i	−0.961342	+	0.275359i	$0.911203\pi$
$978$	−37.8711	+	65.5946i	−1.21098	+	2.09748i
$979$	33.0333			1.05575
$980$		0			0
$981$	36.9355			1.17926
$982$	0.0538991	−	0.0933560i	0.00171999	−	0.00297911i
$983$	24.6562	+	42.7058i	0.786411	+	1.36210i	0.928153	+	0.372200i	$0.121396\pi$
$983$	24.6562	+	42.7058i	0.786411	+	1.36210i	−0.141742	+	0.989904i	$0.545270\pi$
$984$	−8.41110	−	14.5685i	−0.268136	−	0.464425i
$985$	−26.4791	+	45.8632i	−0.843695	+	1.46132i
$986$	−7.88403			−0.251079
$987$		0			0
$988$	1.04888			0.0333692
$989$	−24.8015	+	42.9575i	−0.788642	+	1.36597i
$990$	−52.4635	−	90.8695i	−1.66740	−	2.88802i
$991$	−2.71585	−	4.70400i	−0.0862720	−	0.149427i	0.819661	−	0.572850i	$-0.194162\pi$
$991$	−2.71585	−	4.70400i	−0.0862720	−	0.149427i	−0.905933	+	0.423422i	$0.860829\pi$
$992$	4.41110	−	7.64025i	0.140053	−	0.242578i
$993$	−53.9900			−1.71332
$994$		0			0
$995$	60.8066			1.92770
$996$	32.9583	−	57.0854i	1.04432	−	1.80882i
$997$	−26.8030	−	46.4242i	−0.848861	−	1.47027i	−0.882226	−	0.470827i	$-0.843956\pi$
$997$	−26.8030	−	46.4242i	−0.848861	−	1.47027i	0.0333647	−	0.999443i	$-0.489378\pi$
$998$	9.33804	+	16.1740i	0.295591	+	0.511978i
$999$	34.6167	−	59.9578i	1.09522	−	1.89698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.i.79.3		6
7.2	even	3		637.2.a.j.1.1		3
7.3	odd	6		637.2.e.j.508.3		6
7.4	even	3	inner	637.2.e.i.508.3		6
7.5	odd	6		91.2.a.d.1.1	✓	3
7.6	odd	2		637.2.e.j.79.3		6
21.2	odd	6		5733.2.a.x.1.3		3
21.5	even	6		819.2.a.i.1.3		3
28.19	even	6		1456.2.a.t.1.3		3
35.19	odd	6		2275.2.a.m.1.3		3
56.5	odd	6		5824.2.a.by.1.3		3
56.19	even	6		5824.2.a.bs.1.1		3
91.5	even	12		1183.2.c.f.337.5		6
91.12	odd	6		1183.2.a.i.1.3		3
91.47	even	12		1183.2.c.f.337.2		6
91.51	even	6		8281.2.a.bg.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.d.1.1	✓	3	7.5	odd	6
637.2.a.j.1.1		3	7.2	even	3
637.2.e.i.79.3		6	1.1	even	1	trivial
637.2.e.i.508.3		6	7.4	even	3	inner
637.2.e.j.79.3		6	7.6	odd	2
637.2.e.j.508.3		6	7.3	odd	6
819.2.a.i.1.3		3	21.5	even	6
1183.2.a.i.1.3		3	91.12	odd	6
1183.2.c.f.337.2		6	91.47	even	12
1183.2.c.f.337.5		6	91.5	even	12
1456.2.a.t.1.3		3	28.19	even	6
2275.2.a.m.1.3		3	35.19	odd	6
5733.2.a.x.1.3		3	21.2	odd	6
5824.2.a.bs.1.1		3	56.19	even	6
5824.2.a.by.1.3		3	56.5	odd	6
8281.2.a.bg.1.3		3	91.51	even	6

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.906803 - 1.57063i) q^{2} +(-1.55139 - 2.68708i) q^{3} +(-0.644584 - 1.11645i) q^{4} +(1.40680 - 2.43665i) q^{5} -5.62721 q^{6} +1.28917 q^{8} +(-3.31361 + 5.73933i) q^{9} +(-2.55139 - 4.41913i) q^{10} +(-1.55139 - 2.68708i) q^{11} +(-2.00000 + 3.46410i) q^{12} -1.00000 q^{13} -8.72999 q^{15} +(2.45819 - 4.25771i) q^{16} +(-0.262219 - 0.454177i) q^{17} +(6.00958 + 10.4089i) q^{18} +(0.406803 - 0.704604i) q^{19} -3.62721 q^{20} -5.62721 q^{22} +(-3.66902 + 6.35493i) q^{23} +(-2.00000 - 3.46410i) q^{24} +(-1.45819 - 2.52566i) q^{25} +(-0.906803 + 1.57063i) q^{26} +11.2544 q^{27} +8.28917 q^{29} +(-7.91638 + 13.7116i) q^{30} +(0.695972 + 1.20546i) q^{31} +(-3.16902 - 5.48891i) q^{32} +(-4.81361 + 8.33741i) q^{33} -0.951124 q^{34} +8.54359 q^{36} +(3.07583 - 5.32749i) q^{37} +(-0.737781 - 1.27787i) q^{38} +(1.55139 + 2.68708i) q^{39} +(1.81361 - 3.14126i) q^{40} +4.20555 q^{41} +6.75971 q^{43} +(-2.00000 + 3.46410i) q^{44} +(9.32318 + 16.1482i) q^{45} +(6.65416 + 11.5253i) q^{46} +(-2.98514 + 5.17041i) q^{47} -15.2544 q^{48} -5.28917 q^{50} +(-0.813607 + 1.40921i) q^{51} +(0.644584 + 1.11645i) q^{52} +(1.24736 + 2.16049i) q^{53} +(10.2056 - 17.6765i) q^{54} -8.72999 q^{55} -2.52444 q^{57} +(7.51664 - 13.0192i) q^{58} +(-2.23527 - 3.87160i) q^{59} +(5.62721 + 9.74662i) q^{60} +(-1.00000 + 1.73205i) q^{61} +2.52444 q^{62} -1.66196 q^{64} +(-1.40680 + 2.43665i) q^{65} +(8.72999 + 15.1208i) q^{66} +(-5.01916 - 8.69343i) q^{67} +(-0.338044 + 0.585510i) q^{68} +22.7683 q^{69} -8.72999 q^{71} +(-4.27180 + 7.39897i) q^{72} +(-1.17153 - 2.02916i) q^{73} +(-5.57834 - 9.66196i) q^{74} +(-4.52444 + 7.83656i) q^{75} -1.04888 q^{76} +5.62721 q^{78} +(6.77180 - 11.7291i) q^{79} +(-6.91638 - 11.9795i) q^{80} +(-7.51916 - 13.0236i) q^{81} +(3.81361 - 6.60536i) q^{82} -16.4791 q^{83} -1.47556 q^{85} +(6.12972 - 10.6170i) q^{86} +(-12.8597 - 22.2737i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-5.32318 + 9.22003i) q^{89} +33.8172 q^{90} +9.45998 q^{92} +(2.15944 - 3.74027i) q^{93} +(5.41387 + 9.37710i) q^{94} +(-1.14458 - 1.98248i) q^{95} +(-9.83276 + 17.0308i) q^{96} +1.18639 q^{97} +20.5628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9} - 8 q^{10} - 2 q^{11} - 12 q^{12} - 6 q^{13} - 12 q^{15} + q^{16} + 4 q^{17} + 15 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 10 q^{23}+ \cdots + 28 q^{99}+O(q^{100}) \) 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9 - 8 * q^10 - 2 * q^11 - 12 * q^12 - 6 * q^13 - 12 * q^15 + q^16 + 4 * q^17 + 15 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 + 5 * q^25 + q^26 + 16 * q^27 + 48 * q^29 - 20 * q^30 - 4 * q^31 - 7 * q^32 - 16 * q^33 - 28 * q^34 - 2 * q^36 - 10 * q^38 + 2 * q^39 - 2 * q^40 - 4 * q^41 + 20 * q^43 - 12 * q^44 + 22 * q^45 + 18 * q^46 - 8 * q^47 - 40 * q^48 - 30 * q^50 + 8 * q^51 + 3 * q^52 - 8 * q^53 + 32 * q^54 - 12 * q^55 - 4 * q^57 - 12 * q^58 - 4 * q^59 + 8 * q^60 - 6 * q^61 + 4 * q^62 - 34 * q^64 - 2 * q^65 + 12 * q^66 + 12 * q^67 + 22 * q^68 + 12 * q^69 - 12 * q^71 + q^72 - 10 * q^73 - 30 * q^74 - 16 * q^75 + 16 * q^76 + 8 * q^78 + 14 * q^79 - 14 * q^80 - 3 * q^81 + 10 * q^82 + 24 * q^83 - 20 * q^85 + 26 * q^86 - 26 * q^87 - 12 * q^88 + 2 * q^89 + 56 * q^90 - 24 * q^92 + 22 * q^93 - 10 * q^94 - 6 * q^95 - 4 * q^96 + 20 * q^97 + 28 * q^99

Introduction

L-functions

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