LMFDB - Embedded newform 637.2.e.i.508.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			508.3
Root			$-0.906803 - 1.57063i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.i.79.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.906803 + 1.57063i) q^{2} +(-1.55139 + 2.68708i) q^{3} +(-0.644584 + 1.11645i) q^{4} +(1.40680 + 2.43665i) q^{5} -5.62721 q^{6} +1.28917 q^{8} +(-3.31361 - 5.73933i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	0.985164	+	0.171617i	$0.0548992\pi$
$2$	0.906803	+	1.57063i	0.641207	+	1.11060i	−0.343957	+	0.938985i	$0.611767\pi$
$3$	−1.55139	+	2.68708i	−0.895694	+	1.55139i	−0.0627507	+	0.998029i	$0.519987\pi$
$3$	−1.55139	+	2.68708i	−0.895694	+	1.55139i	−0.832943	+	0.553358i	$0.813346\pi$
$4$	−0.644584	+	1.11645i	−0.322292	+	0.558226i
$5$	1.40680	+	2.43665i	0.629142	+	1.08971i	0.987724	+	0.156207i	$0.0499268\pi$
$5$	1.40680	+	2.43665i	0.629142	+	1.08971i	−0.358583	+	0.933498i	$0.616740\pi$
$6$	−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	−0.999321	−	0.0368347i	$-0.988273\pi$
$11$	−1.55139	+	2.68708i	−0.467761	+	0.810186i	0.531560	+	0.847020i	$0.321606\pi$
$12$	−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	−0.896071	−	0.443911i	$-0.853591\pi$
$17$	−0.262219	+	0.454177i	−0.0635974	+	0.110154i	0.832474	+	0.554065i	$0.186924\pi$
$18$	6.00958	−	10.4089i	1.41647	−	2.45340i
$19$	0.406803	+	0.704604i	0.0933271	+	0.161647i	0.908909	−	0.416994i	$-0.136916\pi$
$19$	0.406803	+	0.704604i	0.0933271	+	0.161647i	−0.815582	+	0.578641i	$0.803583\pi$
$20$	−3.62721			−0.811069
$21$		0			0
$22$	−5.62721			−1.19973
$23$	−3.66902	−	6.35493i	−0.765044	−	1.32510i	−0.940223	−	0.340559i	$-0.889384\pi$
$23$	−3.66902	−	6.35493i	−0.765044	−	1.32510i	0.175179	−	0.984537i	$-0.443949\pi$
$24$	−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	−0.796733	−	0.604332i	$-0.793440\pi$
$31$	0.695972	−	1.20546i	0.125000	−	0.216507i	0.921733	+	0.387825i	$0.126774\pi$
$32$	−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	0.999979	+	0.00655099i	$0.00208526\pi$
$37$	3.07583	+	5.32749i	0.505663	+	0.875833i	−0.494316	+	0.869282i	$0.664581\pi$
$38$	−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	0.561903	−	0.827203i	$-0.310069\pi$
$47$	−2.98514	−	5.17041i	−0.435427	−	0.754183i	−0.997330	+	0.0730207i	$0.976736\pi$
$48$	−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	−0.767550	−	0.640989i	$-0.778524\pi$
$53$	1.24736	−	2.16049i	0.171338	−	0.296766i	0.938888	+	0.344223i	$0.111858\pi$
$54$	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	−0.974048	−	0.226341i	$-0.927324\pi$
$59$	−2.23527	+	3.87160i	−0.291007	+	0.504039i	0.683041	+	0.730380i	$0.260657\pi$
$60$	5.62721	−	9.74662i	0.726470	−	1.25828i
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	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	0.377512	+	0.926005i	$0.376780\pi$
$67$	−5.01916	+	8.69343i	−0.613188	+	1.06207i	−0.990700	+	0.136067i	$0.956554\pi$
$68$	−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	−0.926404	−	0.376530i	$-0.877117\pi$
$73$	−1.17153	+	2.02916i	−0.137118	+	0.237495i	0.789287	+	0.614025i	$0.210451\pi$
$74$	−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	0.941877	+	0.335958i	$0.109060\pi$
$79$	6.77180	+	11.7291i	0.761887	+	1.31963i	−0.179990	+	0.983668i	$0.557607\pi$
$80$	−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	−0.997118	−	0.0758606i	$-0.975830\pi$
$89$	−5.32318	−	9.22003i	−0.564256	−	0.977321i	0.432862	−	0.901460i	$-0.357504\pi$
$90$	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	−0.330777	−	0.943709i	$-0.607311\pi$
$101$	6.55139	−	11.3473i	0.651887	−	1.12910i	0.982664	−	0.185393i	$-0.0593559\pi$
$102$	1.47556	−	2.55575i	0.146102	−	0.253057i
$103$	2.20555	+	3.82012i	0.217319	+	0.376408i	0.953988	−	0.299846i	$-0.0969354\pi$
$103$	2.20555	+	3.82012i	0.217319	+	0.376408i	−0.736668	+	0.676254i	$0.763602\pi$
$104$	−1.28917			−0.126413
$105$		0			0
$106$	4.52444			0.439452
$107$	−0.289169	−	0.500855i	−0.0279550	−	0.0484194i	0.851709	−	0.524014i	$-0.175566\pi$
$107$	−0.289169	−	0.500855i	−0.0279550	−	0.0484194i	−0.879664	+	0.475595i	$0.842233\pi$
$108$	−7.25443	+	12.5650i	−0.698057	+	1.20907i
$109$	−2.78666	+	4.82663i	−0.266913	+	0.462307i	−0.968063	−	0.250707i	$-0.919337\pi$
$109$	−2.78666	+	4.82663i	−0.266913	+	0.462307i	0.701150	+	0.713014i	$0.252670\pi$
$110$	−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	0.993140	−	0.116934i	$-0.0373066\pi$
$131$	4.52444	+	7.83656i	0.395302	+	0.684683i	−0.597838	+	0.801617i	$0.703973\pi$
$132$	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	−0.700797	−	0.713361i	$-0.747172\pi$
$137$	3.12972	−	5.42084i	0.267390	−	0.463134i	0.968187	+	0.250227i	$0.0805053\pi$
$138$	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	0.636928	−	0.770923i	$-0.280205\pi$
$149$	−4.26222	−	7.38238i	−0.349175	−	0.604788i	−0.986103	+	0.166135i	$0.946871\pi$
$150$	8.20555	−	14.2124i	0.669980	−	1.16044i
$151$	5.99221	−	10.3788i	0.487639	−	0.844615i	−0.512260	−	0.858830i	$-0.671192\pi$
$151$	5.99221	−	10.3788i	0.487639	−	0.844615i	0.999899	+	0.0142150i	$0.00452494\pi$
$152$	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	0.488023	+	0.872831i	$0.337718\pi$
$157$	−6.41387	+	11.1091i	−0.511883	+	0.886607i	−0.999905	+	0.0137756i	$0.995615\pi$
$158$	−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	0.999500	+	0.0316196i	$0.0100665\pi$
$163$	6.72999	+	11.6567i	0.527133	+	0.913022i	−0.472367	+	0.881402i	$0.656600\pi$
$164$	−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	0.936683	+	0.350179i	$0.113879\pi$
$173$	10.1489	+	17.5784i	0.771605	+	1.33646i	−0.165078	+	0.986281i	$0.552788\pi$
$174$	−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	−0.583801	−	0.811897i	$-0.698435\pi$
$179$	5.50179	−	9.52937i	0.411223	−	0.712259i	0.995024	+	0.0996381i	$0.0317685\pi$
$180$	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	0.688835	−	0.724918i	$-0.258122\pi$
$191$	−3.91638	−	6.78337i	−0.283379	−	0.490828i	−0.972215	+	0.234090i	$0.924789\pi$
$192$	2.57834	−	4.46581i	0.186075	−	0.322292i
$193$	6.10278	−	10.5703i	0.439287	−	0.760868i	−0.558347	−	0.829607i	$-0.688564\pi$
$193$	6.10278	−	10.5703i	0.439287	−	0.760868i	0.997635	+	0.0687393i	$0.0218977\pi$
$194$	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	−0.173710	−	0.984797i	$-0.555576\pi$
$199$	10.8058	−	18.7162i	0.766004	−	1.32676i	0.939714	−	0.341961i	$-0.111091\pi$
$200$	−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	−0.958009	−	0.286739i	$-0.907429\pi$
$227$	−3.47556	+	6.01985i	−0.230681	+	0.399551i	0.727328	+	0.686290i	$0.240762\pi$
$228$	1.62721	−	2.81842i	0.107765	−	0.186654i
$229$	−10.5436	−	18.2620i	−0.696740	−	1.20679i	−0.969590	−	0.244733i	$-0.921300\pi$
$229$	−10.5436	−	18.2620i	−0.696740	−	1.20679i	0.272850	−	0.962057i	$-0.412034\pi$
$230$	37.4444			2.46901
$231$		0			0
$232$	10.6861			0.701579
$233$	−3.04181	−	5.26857i	−0.199276	−	0.345155i	0.749018	−	0.662549i	$-0.230526\pi$
$233$	−3.04181	−	5.26857i	−0.199276	−	0.345155i	−0.948294	+	0.317394i	$0.897192\pi$
$234$	−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	−0.697478	−	0.716606i	$-0.745694\pi$
$241$	4.22041	−	7.30996i	0.271860	−	0.470876i	0.969338	+	0.245730i	$0.0790277\pi$
$242$	−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	0.999887	−	0.0150459i	$-0.00478944\pi$
$257$	7.80581	+	13.5201i	0.486913	+	0.843359i	−0.512974	+	0.858404i	$0.671456\pi$
$258$	−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	−0.531584	−	0.847005i	$-0.678403\pi$
$263$	7.58540	−	13.1383i	0.467736	−	0.810143i	0.999320	+	0.0368628i	$0.0117365\pi$
$264$	−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	−0.254731	−	0.967012i	$-0.581987\pi$
$269$	11.6464	−	20.1721i	0.710092	−	1.22991i	0.964822	−	0.262903i	$-0.0846799\pi$
$270$	−28.7144	+	49.7348i	−1.74750	+	3.02676i
$271$	6.37279	+	11.0380i	0.387119	+	0.670510i	0.992061	−	0.125760i	$-0.0401368\pi$
$271$	6.37279	+	11.0380i	0.387119	+	0.670510i	−0.604941	+	0.796270i	$0.706804\pi$
$272$	−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	−0.961850	−	0.273578i	$-0.911793\pi$
$277$	−4.06097	+	7.03380i	−0.244000	+	0.422620i	0.717850	+	0.696198i	$0.245126\pi$
$278$	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	−0.651468	−	0.758676i	$-0.725846\pi$
$283$	5.57331	−	9.65326i	0.331299	−	0.573827i	0.982767	+	0.184849i	$0.0591797\pi$
$284$	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	−0.859913	−	0.510440i	$-0.829482\pi$
$311$	0.213343	−	0.369521i	0.0120976	−	0.0209536i	0.872011	+	0.489487i	$0.162816\pi$
$312$	2.00000	−	3.46410i	0.113228	−	0.196116i
$313$	−9.07583	−	15.7198i	−0.512996	−	0.888535i	−0.999886	−	0.0150721i	$-0.995202\pi$
$313$	−9.07583	−	15.7198i	−0.512996	−	0.888535i	0.486890	−	0.873463i	$-0.338131\pi$
$314$	−23.2645			−1.31289
$315$		0			0
$316$	−17.4600			−0.982200
$317$	−4.71083	−	8.15940i	−0.264587	−	0.458278i	0.702869	−	0.711320i	$-0.251902\pi$
$317$	−4.71083	−	8.15940i	−0.264587	−	0.458278i	−0.967455	+	0.253042i	$0.918569\pi$
$318$	−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	0.999688	−	0.0249807i	$-0.00795244\pi$
$331$	8.70027	+	15.0693i	0.478210	+	0.828284i	−0.521478	+	0.853265i	$0.674619\pi$
$332$	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	0.294344	+	0.955700i	$0.404899\pi$
$347$	−12.6761	+	21.9556i	−0.680488	+	1.17864i	−0.974832	+	0.222940i	$0.928434\pi$
$348$	−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	0.178089	+	0.984014i	$0.443009\pi$
$353$	−14.3380	+	24.8342i	−0.763137	+	1.32179i	−0.941226	+	0.337778i	$0.890325\pi$
$354$	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	0.682724	−	0.730677i	$-0.260795\pi$
$359$	−5.52167	−	9.56381i	−0.291423	−	0.504759i	−0.974146	+	0.225918i	$0.927462\pi$
$360$	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	−0.249701	−	0.968323i	$-0.580332\pi$
$367$	13.6733	−	23.6829i	0.713741	−	1.23624i	0.963443	−	0.267914i	$-0.0863342\pi$
$368$	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	0.577732	−	0.816227i	$-0.303938\pi$
$373$	−8.07306	−	13.9829i	−0.418007	−	0.724009i	−0.995739	+	0.0922172i	$0.970605\pi$
$374$	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	−0.999024	−	0.0441810i	$-0.985932\pi$
$383$	−10.5244	−	18.2289i	−0.537774	−	0.931451i	0.461250	−	0.887270i	$-0.347401\pi$
$384$	−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	−0.450693	−	0.892679i	$-0.648823\pi$
$389$	10.8030	−	18.7114i	0.547736	−	0.948707i	0.998429	−	0.0560278i	$-0.0178435\pi$
$390$	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	−0.970183	−	0.242372i	$-0.922074\pi$
$397$	−13.8476	−	23.9848i	−0.694992	−	1.20376i	0.275191	−	0.961390i	$-0.411259\pi$
$398$	39.1950			1.96467
$399$		0			0
$400$	−14.3380			−0.716902
$401$	1.28917	+	2.23291i	0.0643780	+	0.111506i	0.896418	−	0.443210i	$-0.146160\pi$
$401$	1.28917	+	2.23291i	0.0643780	+	0.111506i	−0.832040	+	0.554716i	$0.812827\pi$
$402$	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	−0.616396	−	0.787436i	$-0.711408\pi$
$409$	7.55845	−	13.0916i	0.373742	−	0.647339i	0.990138	+	0.140097i	$0.0447414\pi$
$410$	−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	0.214225	+	0.976784i	$0.431277\pi$
$431$	−15.3380	+	26.5663i	−0.738808	+	1.27965i	−0.953033	+	0.302868i	$0.902056\pi$
$432$	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	0.936449	+	0.350805i	$0.114092\pi$
$439$	16.1758	+	28.0174i	0.772030	+	1.33720i	−0.164418	+	0.986391i	$0.552575\pi$
$440$	−11.2544			−0.536534
$441$		0			0
$442$	0.951124			0.0452404
$443$	−7.72292	−	13.3765i	−0.366927	−	0.635536i	0.622156	−	0.782893i	$-0.286257\pi$
$443$	−7.72292	−	13.3765i	−0.366927	−	0.635536i	−0.989083	+	0.147357i	$0.952923\pi$
$444$	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	0.912228	+	0.409683i	$0.134361\pi$
$457$	17.3353	+	30.0256i	0.810910	+	1.40454i	−0.101318	+	0.994854i	$0.532306\pi$
$458$	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	−0.874920	−	0.484268i	$-0.839086\pi$
$467$	−18.5166	−	32.0718i	−0.856848	−	1.48410i	0.0180717	−	0.999837i	$-0.494247\pi$
$468$	−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	−0.695626	−	0.718404i	$-0.744873\pi$
$479$	6.00430	−	10.3997i	0.274343	−	0.475177i	0.969969	+	0.243228i	$0.0782062\pi$
$480$	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	−0.964052	−	0.265714i	$-0.914392\pi$
$487$	−5.55918	+	9.62878i	−0.251911	+	0.436322i	0.712141	+	0.702036i	$0.247726\pi$
$488$	−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	0.727458	−	0.686152i	$-0.240701\pi$
$499$	−5.14888	−	8.91812i	−0.230496	−	0.399230i	−0.957954	+	0.286922i	$0.907368\pi$
$500$	−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	0.851637	+	0.524132i	$0.175610\pi$
$509$	19.8476	+	34.3771i	0.879730	+	1.52374i	0.0280937	+	0.999605i	$0.491056\pi$
$510$	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	−0.510067	−	0.860135i	$-0.670379\pi$
$521$	11.1814	−	19.3667i	0.489865	−	0.848471i	0.999932	+	0.0116639i	$0.00371283\pi$
$522$	49.8144	−	86.2811i	2.18032	−	3.77642i
$523$	−10.3275	−	17.8877i	−0.451589	−	0.782176i	0.546896	−	0.837201i	$-0.315809\pi$
$523$	−10.3275	−	17.8877i	−0.451589	−	0.782176i	−0.998485	+	0.0550252i	$0.982476\pi$
$524$	−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	0.799255	−	0.600992i	$-0.205228\pi$
$541$	−2.81084	−	4.86851i	−0.120847	−	0.209314i	−0.920102	+	0.391679i	$0.871894\pi$
$542$	−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	−0.978465	−	0.206411i	$-0.933822\pi$
$557$	−7.32748	+	12.6916i	−0.310475	+	0.537759i	0.667990	+	0.744170i	$0.267155\pi$
$558$	−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	0.478238	+	0.878230i	$0.341276\pi$
$563$	−12.3728	+	21.4303i	−0.521451	+	0.903179i	−0.999689	+	0.0249490i	$0.992058\pi$
$564$	−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	0.996907	−	0.0785876i	$-0.0250410\pi$
$569$	10.2665	+	17.7821i	0.430395	+	0.745466i	−0.566512	+	0.824053i	$0.691708\pi$
$570$	6.44082	−	11.1558i	0.269776	−	0.467266i
$571$	20.9476	−	36.2824i	0.876631	−	1.51837i	0.0216158	−	0.999766i	$-0.493119\pi$
$571$	20.9476	−	36.2824i	0.876631	−	1.51837i	0.855015	−	0.518603i	$-0.173548\pi$
$572$	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	−0.995932	−	0.0901025i	$-0.971281\pi$
$577$	−10.0872	+	17.4715i	−0.419935	+	0.727349i	0.575997	+	0.817452i	$0.304614\pi$
$578$	−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	0.833800	−	0.552067i	$-0.186161\pi$
$593$	−1.49042	−	2.58149i	−0.0612043	−	0.106009i	−0.895004	+	0.446058i	$0.852827\pi$
$594$	−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	−0.932216	−	0.361902i	$-0.882128\pi$
$599$	−3.73705	+	6.47277i	−0.152692	+	0.264470i	0.779524	+	0.626372i	$0.215461\pi$
$600$	−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	0.534364	−	0.845254i	$-0.320551\pi$
$607$	−11.4522	−	19.8358i	−0.464830	−	0.805109i	−0.999194	+	0.0401456i	$0.987218\pi$
$608$	−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	−0.587688	−	0.809088i	$-0.699962\pi$
$613$	10.0731	−	17.4470i	0.406847	−	0.704679i	0.994535	+	0.104408i	$0.0332949\pi$
$614$	−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	−0.993128	−	0.117031i	$-0.962662\pi$
$619$	−9.83276	+	17.0308i	−0.395212	+	0.684527i	0.597916	+	0.801559i	$0.295996\pi$
$620$	−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	−0.423492	−	0.905900i	$-0.639196\pi$
$641$	14.5018	−	25.1178i	0.572786	−	0.992095i	0.996278	−	0.0861949i	$-0.0274708\pi$
$642$	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	−0.959440	−	0.281911i	$-0.909032\pi$
$647$	−5.99221	+	10.3788i	−0.235578	+	0.408033i	0.723863	+	0.689944i	$0.242365\pi$
$648$	−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	−0.843438	−	0.537226i	$-0.819472\pi$
$653$	−22.6655	−	39.2578i	−0.886971	−	1.53628i	−0.0435323	−	0.999052i	$-0.513861\pi$
$654$	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	0.463788	+	0.885946i	$0.346490\pi$
$661$	−13.7640	+	23.8400i	−0.535358	+	0.927267i	−0.999146	+	0.0413207i	$0.986843\pi$
$662$	−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	0.718359	−	0.695673i	$-0.244894\pi$
$677$	−6.33025	−	10.9643i	−0.243291	−	0.421393i	−0.961650	+	0.274280i	$0.911560\pi$
$678$	−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	−0.457320	−	0.889302i	$-0.651191\pi$
$683$	14.1517	−	24.5114i	0.541498	−	0.937902i	0.998818	−	0.0485999i	$-0.0154759\pi$
$684$	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	0.958609	−	0.284725i	$-0.0919022\pi$
$691$	6.11763	+	10.5961i	0.232726	+	0.403093i	−0.725884	+	0.687818i	$0.758569\pi$
$692$	−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	−0.919766	−	0.392467i	$-0.871622\pi$
$709$	−21.2955	−	36.8849i	−0.799770	−	1.38524i	0.119996	−	0.992774i	$-0.461712\pi$
$710$	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	−0.924499	−	0.381186i	$-0.875516\pi$
$719$	−21.2466	−	36.8002i	−0.792366	−	1.37242i	0.132133	−	0.991232i	$-0.457817\pi$
$720$	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	0.885189	+	0.465232i	$0.154029\pi$
$733$	22.8910	+	39.6483i	0.845497	+	1.46444i	−0.0396921	+	0.999212i	$0.512638\pi$
$734$	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	−0.707347	−	0.706866i	$-0.750108\pi$
$739$	7.02695	−	12.1710i	0.258491	−	0.447719i	0.965838	+	0.259148i	$0.0834416\pi$
$740$	−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	−0.980961	−	0.194207i	$-0.937787\pi$
$751$	−18.0504	−	31.2642i	−0.658669	−	1.14085i	0.322292	−	0.946640i	$-0.395547\pi$
$752$	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	0.998854	+	0.0478590i	$0.0152398\pi$
$761$	14.9207	+	25.8434i	0.540874	+	0.936822i	−0.457980	+	0.888963i	$0.651427\pi$
$762$	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	−0.724778	−	0.688983i	$-0.758058\pi$
$773$	6.51388	−	11.2824i	0.234288	−	0.405798i	0.959065	+	0.283184i	$0.0913909\pi$
$774$	40.6230	−	70.3611i	1.46016	−	2.52908i
$775$	2.02972	+	3.51558i	0.0729097	+	0.126283i
$776$	1.52946

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.906803 + 1.57063i) q^{2} +(-1.55139 + 2.68708i) q^{3} +(-0.644584 + 1.11645i) q^{4} +(1.40680 + 2.43665i) q^{5} -5.62721 q^{6} +1.28917 q^{8} +(-3.31361 - 5.73933i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) 6 * q - q^2 - 2 * q^3 - 3 * q^4 + 2 * q^5 - 8 * q^6 + 6 * q^8 - 7 * q^9	\( 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9} - 8 q^{10} - 2 q^{11} - 12 q^{12} - 6 q^{13} - 12 q^{15} + q^{16} + 4 q^{17} + 15 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} + 5 q^{25} + q^{26} + 16 q^{27} + 48 q^{29} - 20 q^{30} - 4 q^{31} - 7 q^{32} - 16 q^{33} - 28 q^{34} - 2 q^{36} - 10 q^{38} + 2 q^{39} - 2 q^{40} - 4 q^{41} + 20 q^{43} - 12 q^{44} + 22 q^{45} + 18 q^{46} - 8 q^{47} - 40 q^{48} - 30 q^{50} + 8 q^{51} + 3 q^{52} - 8 q^{53} + 32 q^{54} - 12 q^{55} - 4 q^{57} - 12 q^{58} - 4 q^{59} + 8 q^{60} - 6 q^{61} + 4 q^{62} - 34 q^{64} - 2 q^{65} + 12 q^{66} + 12 q^{67} + 22 q^{68} + 12 q^{69} - 12 q^{71} + q^{72} - 10 q^{73} - 30 q^{74} - 16 q^{75} + 16 q^{76} + 8 q^{78} + 14 q^{79} - 14 q^{80} - 3 q^{81} + 10 q^{82} + 24 q^{83} - 20 q^{85} + 26 q^{86} - 26 q^{87} - 12 q^{88} + 2 q^{89} + 56 q^{90} - 24 q^{92} + 22 q^{93} - 10 q^{94} - 6 q^{95} - 4 q^{96} + 20 q^{97} + 28 q^{99}+O(q^{100}) \) 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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