LMFDB - Embedded newform 637.2.e.o.508.5

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + \cdots + 1 $ x^12 - 2x^11 + 9x^10 - 6x^9 + 34x^8 - 18x^7 + 85x^6 - 2x^5 + 92x^4 - 26x^3 + 43x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.5
Root			$1.17550 + 2.03602i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.o.79.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.588093 + 1.01861i) q^{2} +(1.67550 - 2.90205i) q^{3} +(0.308293 - 0.533979i) q^{4} +(1.57431 + 2.72679i) q^{5} +3.94140 q^{6} +3.07759 q^{8} +(-4.11459 - 7.12667i) q^{9} +O(q^{10})$	\(q+(0.588093 + 1.01861i) q^{2} +(1.67550 - 2.90205i) q^{3} +(0.308293 - 0.533979i) q^{4} +(1.57431 + 2.72679i) q^{5} +3.94140 q^{6} +3.07759 q^{8} +(-4.11459 - 7.12667i) q^{9} +(-1.85168 + 3.20721i) q^{10} +(0.386695 - 0.669775i) q^{11} +(-1.03309 - 1.78936i) q^{12} -1.00000 q^{13} +10.5510 q^{15} +(1.19333 + 2.06690i) q^{16} +(-2.87670 + 4.98259i) q^{17} +(4.83952 - 8.38230i) q^{18} +(-0.611490 - 1.05913i) q^{19} +1.94140 q^{20} +0.909650 q^{22} +(1.49591 + 2.59099i) q^{23} +(5.15650 - 8.93132i) q^{24} +(-2.45692 + 4.25550i) q^{25} +(-0.588093 - 1.01861i) q^{26} -17.5229 q^{27} -2.46882 q^{29} +(6.20499 + 10.7474i) q^{30} +(-3.06743 + 5.31295i) q^{31} +(1.67402 - 2.89949i) q^{32} +(-1.29581 - 2.24441i) q^{33} -6.76707 q^{34} -5.07399 q^{36} +(-2.49966 - 4.32954i) q^{37} +(0.719226 - 1.24574i) q^{38} +(-1.67550 + 2.90205i) q^{39} +(4.84509 + 8.39194i) q^{40} +2.55981 q^{41} -2.73150 q^{43} +(-0.238430 - 0.412974i) q^{44} +(12.9553 - 22.4392i) q^{45} +(-1.75947 + 3.04749i) q^{46} +(2.68585 + 4.65202i) q^{47} +7.99766 q^{48} -5.77958 q^{50} +(9.63981 + 16.6966i) q^{51} +(-0.308293 + 0.533979i) q^{52} +(4.89508 - 8.47852i) q^{53} +(-10.3051 - 17.8490i) q^{54} +2.43511 q^{55} -4.09820 q^{57} +(-1.45190 - 2.51476i) q^{58} +(1.25228 - 2.16902i) q^{59} +(3.25281 - 5.63402i) q^{60} +(-5.45835 - 9.45414i) q^{61} -7.21575 q^{62} +8.71122 q^{64} +(-1.57431 - 2.72679i) q^{65} +(1.52412 - 2.63985i) q^{66} +(-2.16259 + 3.74571i) q^{67} +(1.77373 + 3.07219i) q^{68} +10.0256 q^{69} +10.6649 q^{71} +(-12.6630 - 21.9330i) q^{72} +(-2.58725 + 4.48125i) q^{73} +(2.94007 - 5.09235i) q^{74} +(8.23312 + 14.2602i) q^{75} -0.754072 q^{76} -3.94140 q^{78} +(0.271019 + 0.469419i) q^{79} +(-3.75733 + 6.50789i) q^{80} +(-17.0159 + 29.4724i) q^{81} +(1.50540 + 2.60744i) q^{82} -15.2259 q^{83} -18.1153 q^{85} +(-1.60638 - 2.78233i) q^{86} +(-4.13650 + 7.16464i) q^{87} +(1.19009 - 2.06129i) q^{88} +(4.61604 + 7.99522i) q^{89} +30.4757 q^{90} +1.84471 q^{92} +(10.2790 + 17.8037i) q^{93} +(-3.15905 + 5.47164i) q^{94} +(1.92535 - 3.33481i) q^{95} +(-5.60963 - 9.71617i) q^{96} +1.26291 q^{97} -6.36436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * 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 $

$2$	0.588093	+	1.01861i	0.415845	+	0.720264i	0.995517	−	0.0945858i	$-0.0301527\pi$
$2$	0.588093	+	1.01861i	0.415845	+	0.720264i	−0.579672	+	0.814850i	$0.696819\pi$
$3$	1.67550	−	2.90205i	0.967349	−	1.67550i	0.264183	−	0.964473i	$-0.414898\pi$
$3$	1.67550	−	2.90205i	0.967349	−	1.67550i	0.703166	−	0.711025i	$-0.251769\pi$
$4$	0.308293	−	0.533979i	0.154146	−	0.266989i
$5$	1.57431	+	2.72679i	0.704054	+	1.21946i	0.967032	+	0.254655i	$0.0819619\pi$
$5$	1.57431	+	2.72679i	0.704054	+	1.21946i	−0.262978	+	0.964802i	$0.584705\pi$
$6$	3.94140			1.60907
$7$		0			0
$7$		0			0
$8$	3.07759			1.08809
$9$	−4.11459	−	7.12667i	−1.37153	−	2.37556i
$10$	−1.85168	+	3.20721i	−0.585554	+	1.01421i
$11$	0.386695	−	0.669775i	0.116593	−	0.201945i	−0.801823	−	0.597562i	$-0.796136\pi$
$11$	0.386695	−	0.669775i	0.116593	−	0.201945i	0.918415	+	0.395618i	$0.129469\pi$
$12$	−1.03309	−	1.78936i	−0.298227	−	0.516544i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	10.5510			2.72426
$16$	1.19333	+	2.06690i	0.298331	+	0.516725i
$17$	−2.87670	+	4.98259i	−0.697702	+	1.20846i	0.271559	+	0.962422i	$0.412461\pi$
$17$	−2.87670	+	4.98259i	−0.697702	+	1.20846i	−0.969261	+	0.246034i	$0.920873\pi$
$18$	4.83952	−	8.38230i	1.14069	−	1.97573i
$19$	−0.611490	−	1.05913i	−0.140285	−	0.242981i	0.787319	−	0.616546i	$-0.211469\pi$
$19$	−0.611490	−	1.05913i	−0.140285	−	0.242981i	−0.927604	+	0.373565i	$0.878135\pi$
$20$	1.94140			0.434109
$21$		0			0
$22$	0.909650			0.193938
$23$	1.49591	+	2.59099i	0.311919	+	0.540259i	0.978778	−	0.204925i	$-0.0656950\pi$
$23$	1.49591	+	2.59099i	0.311919	+	0.540259i	−0.666859	+	0.745184i	$0.732362\pi$
$24$	5.15650	−	8.93132i	1.05257	−	1.82310i
$25$	−2.45692	+	4.25550i	−0.491383	+	0.851101i
$26$	−0.588093	−	1.01861i	−0.115335	−	0.199765i
$27$	−17.5229			−3.37229
$28$		0			0
$29$	−2.46882			−0.458449			−0.229224	−	0.973374i	$-0.573619\pi$
$29$	−2.46882			−0.458449			−0.229224	+	0.973374i	$0.573619\pi$
$30$	6.20499	+	10.7474i	1.13287	+	1.96219i
$31$	−3.06743	+	5.31295i	−0.550927	+	0.954234i	0.447281	+	0.894394i	$0.352393\pi$
$31$	−3.06743	+	5.31295i	−0.550927	+	0.954234i	−0.998208	+	0.0598404i	$0.980941\pi$
$32$	1.67402	−	2.89949i	0.295928	−	0.512562i
$33$	−1.29581	−	2.24441i	−0.225572	−	0.390702i
$34$	−6.76707			−1.16054
$35$		0			0
$36$	−5.07399			−0.845665
$37$	−2.49966	−	4.32954i	−0.410942	−	0.711773i	0.584051	−	0.811717i	$-0.301467\pi$
$37$	−2.49966	−	4.32954i	−0.410942	−	0.711773i	−0.994993	+	0.0999443i	$0.968134\pi$
$38$	0.719226	−	1.24574i	0.116674	−	0.202085i
$39$	−1.67550	+	2.90205i	−0.268294	+	0.464700i
$40$	4.84509	+	8.39194i	0.766076	+	1.32688i
$41$	2.55981			0.399774			0.199887	−	0.979819i	$-0.435942\pi$
$41$	2.55981			0.399774			0.199887	+	0.979819i	$0.435942\pi$
$42$		0			0
$43$	−2.73150			−0.416550			−0.208275	−	0.978070i	$-0.566785\pi$
$43$	−2.73150			−0.416550			−0.208275	+	0.978070i	$0.566785\pi$
$44$	−0.238430	−	0.412974i	−0.0359447	−	0.0622581i
$45$	12.9553	−	22.4392i	1.93126	−	3.34504i
$46$	−1.75947	+	3.04749i	−0.259420	+	0.449328i
$47$	2.68585	+	4.65202i	0.391771	+	0.678567i	0.992683	−	0.120748i	$-0.0385293\pi$
$47$	2.68585	+	4.65202i	0.391771	+	0.678567i	−0.600912	+	0.799315i	$0.705196\pi$
$48$	7.99766			1.15436
$49$		0			0
$50$	−5.77958			−0.817357
$51$	9.63981	+	16.6966i	1.34984	+	2.33800i
$52$	−0.308293	+	0.533979i	−0.0427525	+	0.0740495i
$53$	4.89508	−	8.47852i	0.672390	−	1.16461i	−0.304834	−	0.952406i	$-0.598601\pi$
$53$	4.89508	−	8.47852i	0.672390	−	1.16461i	0.977224	−	0.212209i	$-0.0680657\pi$
$54$	−10.3051	−	17.8490i	−1.40235	−	2.42894i
$55$	2.43511			0.328351
$56$		0			0
$57$	−4.09820			−0.542820
$58$	−1.45190	−	2.51476i	−0.190643	−	0.330204i
$59$	1.25228	−	2.16902i	0.163033	−	0.282382i	−0.772922	−	0.634501i	$-0.781206\pi$
$59$	1.25228	−	2.16902i	0.163033	−	0.282382i	0.935955	+	0.352119i	$0.114539\pi$
$60$	3.25281	−	5.63402i	0.419935	−	0.727349i
$61$	−5.45835	−	9.45414i	−0.698870	−	1.21048i	−0.968858	−	0.247615i	$-0.920353\pi$
$61$	−5.45835	−	9.45414i	−0.698870	−	1.21048i	0.269988	−	0.962864i	$-0.412980\pi$
$62$	−7.21575			−0.916401
$63$		0			0
$64$	8.71122			1.08890
$65$	−1.57431	−	2.72679i	−0.195269	−	0.338216i
$66$	1.52412	−	2.63985i	0.187606	−	0.324943i
$67$	−2.16259	+	3.74571i	−0.264202	+	0.457612i	−0.967354	−	0.253428i	$-0.918442\pi$
$67$	−2.16259	+	3.74571i	−0.264202	+	0.457612i	0.703152	+	0.711039i	$0.251775\pi$
$68$	1.77373	+	3.07219i	0.215097	+	0.372558i
$69$	10.0256			1.20694
$70$		0			0
$71$	10.6649			1.26570			0.632848	−	0.774276i	$-0.281886\pi$
$71$	10.6649			1.26570			0.632848	+	0.774276i	$0.281886\pi$
$72$	−12.6630	−	21.9330i	−1.49235	−	2.58483i
$73$	−2.58725	+	4.48125i	−0.302815	+	0.524491i	−0.976772	−	0.214279i	$-0.931260\pi$
$73$	−2.58725	+	4.48125i	−0.302815	+	0.524491i	0.673958	+	0.738770i	$0.264593\pi$
$74$	2.94007	−	5.09235i	0.341776	−	0.591974i
$75$	8.23312	+	14.2602i	0.950679	+	1.64662i
$76$	−0.754072			−0.0864979
$77$		0			0
$78$	−3.94140			−0.446275
$79$	0.271019	+	0.469419i	0.0304920	+	0.0528138i	0.880869	−	0.473361i	$-0.156959\pi$
$79$	0.271019	+	0.469419i	0.0304920	+	0.0528138i	−0.850377	+	0.526174i	$0.823626\pi$
$80$	−3.75733	+	6.50789i	−0.420083	+	0.727605i
$81$	−17.0159	+	29.4724i	−1.89066	+	3.27471i
$82$	1.50540	+	2.60744i	0.166244	+	0.287943i
$83$	−15.2259			−1.67125			−0.835627	−	0.549297i	$-0.814896\pi$
$83$	−15.2259			−1.67125			−0.835627	+	0.549297i	$0.814896\pi$
$84$		0			0
$85$	−18.1153			−1.96488
$86$	−1.60638	−	2.78233i	−0.173220	−	0.300026i
$87$	−4.13650	+	7.16464i	−0.443480	+	0.768130i
$88$	1.19009	−	2.06129i	0.126864	−	0.219735i
$89$	4.61604	+	7.99522i	0.489299	+	0.847492i	0.999924	−	0.0123122i	$-0.00391918\pi$
$89$	4.61604	+	7.99522i	0.489299	+	0.847492i	−0.510625	+	0.859804i	$0.670586\pi$
$90$	30.4757			3.21242
$91$		0			0
$92$	1.84471			0.192325
$93$	10.2790	+	17.8037i	1.06588	+	1.84616i
$94$	−3.15905	+	5.47164i	−0.325832	+	0.564357i
$95$	1.92535	−	3.33481i	0.197537	−	0.342144i
$96$	−5.60963	−	9.71617i	−0.572531	−	0.991652i
$97$	1.26291			0.128229			0.0641145	−	0.997943i	$-0.479578\pi$
$97$	1.26291			0.128229			0.0641145	+	0.997943i	$0.479578\pi$
$98$		0			0
$99$	−6.36436			−0.639642
$100$	1.51490	+	2.62388i	0.151490	+	0.262388i
$101$	0.302724	−	0.524333i	0.0301221	−	0.0521731i	−0.850571	−	0.525860i	$-0.823744\pi$
$101$	0.302724	−	0.524333i	0.0301221	−	0.0521731i	0.880693	+	0.473687i	$0.157077\pi$
$102$	−11.3382	+	19.6384i	−1.12265	+	1.94449i
$103$	3.82402	+	6.62340i	0.376792	+	0.652623i	0.990593	−	0.136838i	$-0.0436939\pi$
$103$	3.82402	+	6.62340i	0.376792	+	0.652623i	−0.613802	+	0.789460i	$0.710361\pi$
$104$	−3.07759			−0.301783
$105$		0			0
$106$	11.5150			1.11844
$107$	−2.41482	−	4.18260i	−0.233450	−	0.404347i	0.725371	−	0.688358i	$-0.241668\pi$
$107$	−2.41482	−	4.18260i	−0.233450	−	0.404347i	−0.958821	+	0.284011i	$0.908335\pi$
$108$	−5.40220	+	9.35688i	−0.519827	+	0.900366i
$109$	−3.61546	+	6.26216i	−0.346298	+	0.599806i	−0.985589	−	0.169159i	$-0.945895\pi$
$109$	−3.61546	+	6.26216i	−0.346298	+	0.599806i	0.639291	+	0.768965i	$0.279228\pi$
$110$	1.43207	+	2.48042i	0.136543	+	0.236499i
$111$	−16.7527			−1.59010
$112$		0			0
$113$	−9.19375			−0.864875			−0.432438	−	0.901664i	$-0.642346\pi$
$113$	−9.19375			−0.864875			−0.432438	+	0.901664i	$0.642346\pi$
$114$	−2.41012	−	4.17446i	−0.225729	−	0.390974i
$115$	−4.71006	+	8.15806i	−0.439215	+	0.760743i
$116$	−0.761120	+	1.31830i	−0.0706682	+	0.122401i
$117$	4.11459	+	7.12667i	0.380394	+	0.658861i
$118$	2.94583			0.271186
$119$		0			0
$120$	32.4718			2.96425
$121$	5.20093	+	9.00828i	0.472812	+	0.818935i
$122$	6.42004	−	11.1198i	0.581243	−	1.00674i
$123$	4.28895	−	7.42868i	0.386722	−	0.669821i
$124$	1.89133	+	3.27589i	0.169847	+	0.294183i
$125$	0.271305			0.0242663
$126$		0			0
$127$	−11.2118			−0.994888			−0.497444	−	0.867496i	$-0.665728\pi$
$127$	−11.2118			−0.994888			−0.497444	+	0.867496i	$0.665728\pi$
$128$	1.77497	+	3.07434i	0.156887	+	0.271736i
$129$	−4.57663	+	7.92695i	−0.402949	+	0.697929i
$130$	1.85168	−	3.20721i	0.162403	−	0.281291i
$131$	7.86899	+	13.6295i	0.687517	+	1.19081i	0.972639	+	0.232323i	$0.0746325\pi$
$131$	7.86899	+	13.6295i	0.687517	+	1.19081i	−0.285122	+	0.958491i	$0.592034\pi$
$132$	−1.59796			−0.139084
$133$		0			0
$134$	−5.08721			−0.439468
$135$	−27.5866	−	47.7814i	−2.37427	−	4.11236i
$136$	−8.85331	+	15.3344i	−0.759165	+	1.31491i
$137$	9.31050	−	16.1263i	0.795449	−	1.37776i	−0.127104	−	0.991889i	$-0.540568\pi$
$137$	9.31050	−	16.1263i	0.795449	−	1.37776i	0.922553	−	0.385869i	$-0.126098\pi$
$138$	5.89597	+	10.2121i	0.501899	+	0.869314i
$139$	11.9137			1.01050			0.505252	−	0.862972i	$-0.331399\pi$
$139$	11.9137			1.01050			0.505252	+	0.862972i	$0.331399\pi$
$140$		0			0
$141$	18.0005			1.51592
$142$	6.27198	+	10.8634i	0.526333	+	0.911635i
$143$	−0.386695	+	0.669775i	−0.0323370	+	0.0560094i
$144$	9.82008	−	17.0089i	0.818340	−	1.41741i
$145$	−3.88669	−	6.73195i	−0.322772	−	0.559058i
$146$	−6.08618			−0.503696
$147$		0			0
$148$	−3.08251			−0.253381
$149$	−5.68767	−	9.85133i	−0.465952	−	0.807053i	0.533292	−	0.845931i	$-0.320955\pi$
$149$	−5.68767	−	9.85133i	−0.465952	−	0.807053i	−0.999244	+	0.0388786i	$0.987621\pi$
$150$	−9.68368	+	16.7726i	−0.790669	+	1.36948i
$151$	1.84625	−	3.19780i	0.150246	−	0.260234i	−0.781072	−	0.624441i	$-0.785327\pi$
$151$	1.84625	−	3.19780i	0.150246	−	0.260234i	0.931318	+	0.364208i	$0.118660\pi$
$152$	−1.88192	−	3.25957i	−0.152644	−	0.264386i
$153$	47.3457			3.82767
$154$		0			0
$155$	−19.3164			−1.55153
$156$	1.03309	+	1.78936i	0.0827132	+	0.143264i
$157$	0.560324	−	0.970509i	0.0447187	−	0.0774550i	−0.842800	−	0.538227i	$-0.819094\pi$
$157$	0.560324	−	0.970509i	0.0447187	−	0.0774550i	0.887518	+	0.460772i	$0.152428\pi$
$158$	−0.318769	+	0.552124i	−0.0253599	+	0.0439246i
$159$	−16.4034	−	28.4115i	−1.30087	−	2.25318i
$160$	10.5417			0.833396
$161$		0			0
$162$	−40.0277			−3.14488
$163$	10.1717	+	17.6180i	0.796712	+	1.37995i	0.921746	+	0.387794i	$0.126763\pi$
$163$	10.1717	+	17.6180i	0.796712	+	1.37995i	−0.125034	+	0.992152i	$0.539904\pi$
$164$	0.789170	−	1.36688i	0.0616238	−	0.106736i
$165$	4.08003	−	7.06681i	0.317630	−	0.550151i
$166$	−8.95422	−	15.5092i	−0.694982	−	1.20374i
$167$	−13.0063			−1.00646			−0.503228	−	0.864154i	$-0.667854\pi$
$167$	−13.0063			−1.00646			−0.503228	+	0.864154i	$0.667854\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−10.6535	−	18.4524i	−0.817085	−	1.41523i
$171$	−5.03206	+	8.71578i	−0.384811	+	0.666512i
$172$	−0.842102	+	1.45856i	−0.0642097	+	0.111214i
$173$	−12.9555	−	22.4396i	−0.984989	−	1.70605i	−0.641985	−	0.766717i	$-0.721889\pi$
$173$	−12.9555	−	22.4396i	−0.984989	−	1.70605i	−0.343004	−	0.939334i	$-0.611445\pi$
$174$	−9.73060			−0.737675
$175$		0			0
$176$	1.84581			0.139133
$177$	−4.19639	−	7.26836i	−0.315420	−	0.546324i
$178$	−5.42933	+	9.40387i	−0.406945	+	0.704850i
$179$	−4.82081	+	8.34989i	−0.360325	+	0.624100i	−0.988014	−	0.154363i	$-0.950667\pi$
$179$	−4.82081	+	8.34989i	−0.360325	+	0.624100i	0.627690	+	0.778464i	$0.284001\pi$
$180$	−7.98804	−	13.8357i	−0.595394	−	1.03125i
$181$	2.92683			0.217550			0.108775	−	0.994066i	$-0.465307\pi$
$181$	2.92683			0.217550			0.108775	+	0.994066i	$0.465307\pi$
$182$		0			0
$183$	−36.5818			−2.70421
$184$	4.60380	+	7.97402i	0.339397	+	0.587852i
$185$	7.87050	−	13.6321i	0.578651	−	1.00225i
$186$	−12.0900	+	20.9404i	−0.886480	+	1.53543i
$187$	2.22481	+	3.85348i	0.162694	+	0.281795i
$188$	3.31211			0.241560
$189$		0			0
$190$	4.52914			0.328579
$191$	8.06822	+	13.9746i	0.583796	+	1.01116i	0.995024	+	0.0996315i	$0.0317664\pi$
$191$	8.06822	+	13.9746i	0.583796	+	1.01116i	−0.411229	+	0.911532i	$0.634900\pi$
$192$	14.5956	−	25.2804i	1.05335	−	1.82445i
$193$	0.0431908	−	0.0748087i	0.00310894	−	0.00538485i	−0.864467	−	0.502690i	$-0.832344\pi$
$193$	0.0431908	−	0.0748087i	0.00310894	−	0.00538485i	0.867576	+	0.497305i	$0.165677\pi$
$194$	0.742709	+	1.28641i	0.0533234	+	0.0923588i
$195$	−10.5510			−0.755575
$196$		0			0
$197$	15.0589			1.07290			0.536451	−	0.843932i	$-0.319765\pi$
$197$	15.0589			1.07290			0.536451	+	0.843932i	$0.319765\pi$
$198$	−3.74284	−	6.48278i	−0.265992	−	0.460711i
$199$	7.72332	−	13.3772i	0.547492	−	0.948284i	−0.450954	−	0.892547i	$-0.648916\pi$
$199$	7.72332	−	13.3772i	0.547492	−	0.948284i	0.998446	−	0.0557363i	$-0.0177506\pi$
$200$	−7.56139	+	13.0967i	−0.534671	+	0.926077i
$201$	7.24682	+	12.5519i	0.511152	+	0.885340i
$202$	0.712119			0.0501045
$203$		0			0
$204$	11.8875			0.832294
$205$	4.02993	+	6.98005i	0.281463	+	0.487508i
$206$	−4.49776	+	7.79035i	−0.313374	+	0.542779i
$207$	12.3101	−	21.3217i	0.855611	−	1.48196i
$208$	−1.19333	−	2.06690i	−0.0827422	−	0.143314i
$209$	−0.945840			−0.0654251
$210$		0			0
$211$	−25.0561			−1.72493			−0.862466	−	0.506115i	$-0.831081\pi$
$211$	−25.0561			−1.72493			−0.862466	+	0.506115i	$0.831081\pi$
$212$	−3.01823	−	5.22773i	−0.207293	−	0.359042i
$213$	17.8691	−	30.9502i	1.22437	−	2.12067i
$214$	2.84028	−	4.91952i	0.194158	−	0.336291i
$215$	−4.30024	−	7.44823i	−0.293274	−	0.507965i
$216$	−53.9285			−3.66937
$217$		0			0
$218$	−8.50491			−0.576025
$219$	8.66987	+	15.0167i	0.585855	+	1.01473i
$220$	0.750728	−	1.30030i	0.0506141	−	0.0876661i
$221$	2.87670	−	4.98259i	0.193508	−	0.335165i
$222$	−9.85216	−	17.0644i	−0.661234	−	1.14529i
$223$	20.6640			1.38376			0.691881	−	0.722012i	$-0.256782\pi$
$223$	20.6640			1.38376			0.691881	+	0.722012i	$0.256782\pi$
$224$		0			0
$225$	40.4368			2.69579
$226$	−5.40678	−	9.36482i	−0.359654	−	0.622939i
$227$	0.491189	−	0.850764i	0.0326013	−	0.0564672i	−0.849264	−	0.527968i	$-0.822954\pi$
$227$	0.491189	−	0.850764i	0.0326013	−	0.0564672i	0.881866	+	0.471501i	$0.156287\pi$
$228$	−1.26345	+	2.18835i	−0.0836737	+	0.144927i
$229$	−7.13712	−	12.3619i	−0.471634	−	0.816895i	0.527839	−	0.849344i	$-0.323002\pi$
$229$	−7.13712	−	12.3619i	−0.471634	−	0.816895i	−0.999473	+	0.0324498i	$0.989669\pi$
$230$	−11.0798			−0.730581
$231$		0			0
$232$	−7.59802			−0.498835
$233$	−0.697671	−	1.20840i	−0.0457060	−	0.0791651i	0.842267	−	0.539060i	$-0.181220\pi$
$233$	−0.697671	−	1.20840i	−0.0457060	−	0.0791651i	−0.887973	+	0.459895i	$0.847887\pi$
$234$	−4.83952	+	8.38230i	−0.316369	+	0.547968i
$235$	−8.45672	+	14.6475i	−0.551655	+	0.955495i
$236$	−0.772139	−	1.33738i	−0.0502620	−	0.0870563i
$237$	1.81637			0.117986
$238$		0			0
$239$	2.54875			0.164865			0.0824326	−	0.996597i	$-0.473731\pi$
$239$	2.54875			0.164865			0.0824326	+	0.996597i	$0.473731\pi$
$240$	12.5908	+	21.8079i	0.812733	+	1.40770i
$241$	14.8373	−	25.6990i	0.955755	−	1.65542i	0.223124	−	0.974790i	$-0.428375\pi$
$241$	14.8373	−	25.6990i	0.955755	−	1.65542i	0.732631	−	0.680626i	$-0.238292\pi$
$242$	−6.11727	+	10.5954i	−0.393233	+	0.681099i
$243$	30.7358	+	53.2359i	1.97170	+	3.41509i
$244$	−6.73108			−0.430913
$245$		0			0
$246$	10.0892			0.643264
$247$	0.611490	+	1.05913i	0.0389082	+	0.0673909i
$248$	−9.44031	+	16.3511i	−0.599460	+	1.03830i
$249$	−25.5109	+	44.1861i	−1.61669	+	2.80018i
$250$	0.159553	+	0.276353i	0.0100910	+	0.0174781i
$251$	−18.0858			−1.14157			−0.570784	−	0.821100i	$-0.693361\pi$
$251$	−18.0858			−1.14157			−0.570784	+	0.821100i	$0.693361\pi$
$252$		0			0
$253$	2.31384			0.145470
$254$	−6.59359	−	11.4204i	−0.413719	−	0.716582i
$255$	−30.3521	+	52.5714i	−1.90072	+	3.29215i
$256$	6.62352	−	11.4723i	0.413970	−	0.717017i
$257$	7.37014	+	12.7655i	0.459737	+	0.796287i	0.998947	−	0.0458839i	$-0.0146104\pi$
$257$	7.37014	+	12.7655i	0.459737	+	0.796287i	−0.539210	+	0.842171i	$0.681277\pi$
$258$	−10.7659			−0.670257
$259$		0			0
$260$	−1.94140			−0.120400
$261$	10.1582	+	17.5945i	0.628776	+	1.08907i
$262$	−9.25540	+	16.0308i	−0.571800	+	0.990387i
$263$	4.07961	−	7.06609i	0.251560	−	0.435714i	−0.712396	−	0.701778i	$-0.752390\pi$
$263$	4.07961	−	7.06609i	0.251560	−	0.435714i	0.963955	+	0.266064i	$0.0857232\pi$
$264$	−3.98798	−	6.90739i	−0.245443	−	0.425120i
$265$	30.8255			1.89360
$266$		0			0
$267$	30.9367			1.89329
$268$	1.33342	+	2.30955i	0.0814516	+	0.141078i
$269$	0.221291	−	0.383288i	0.0134924	−	0.0233695i	−0.859200	−	0.511639i	$-0.829038\pi$
$269$	0.221291	−	0.383288i	0.0134924	−	0.0233695i	0.872693	+	0.488270i	$0.162372\pi$
$270$	32.4470	−	56.1998i	1.97466	−	3.42021i
$271$	−10.5416	−	18.2585i	−0.640354	−	1.10913i	−0.985354	−	0.170523i	$-0.945454\pi$
$271$	−10.5416	−	18.2585i	−0.640354	−	1.10913i	0.345000	−	0.938603i	$-0.387879\pi$
$272$	−13.7314			−0.832586
$273$		0			0
$274$	21.9018			1.32313
$275$	1.90015	+	3.29116i	0.114584	+	0.198465i
$276$	3.09081	−	5.35345i	0.186045	−	0.322240i
$277$	−1.79710	+	3.11267i	−0.107977	+	0.187022i	−0.914951	−	0.403565i	$-0.867771\pi$
$277$	−1.79710	+	3.11267i	−0.107977	+	0.187022i	0.806973	+	0.590588i	$0.201104\pi$
$278$	7.00635	+	12.1354i	0.420213	+	0.727831i
$279$	50.4849			3.02245
$280$		0			0
$281$	−9.01252			−0.537642			−0.268821	−	0.963190i	$-0.586634\pi$
$281$	−9.01252			−0.537642			−0.268821	+	0.963190i	$0.586634\pi$
$282$	10.5860	+	18.3355i	0.630386	+	1.09186i
$283$	13.8706	−	24.0245i	0.824520	−	1.42811i	−0.0777659	−	0.996972i	$-0.524779\pi$
$283$	13.8706	−	24.0245i	0.824520	−	1.42811i	0.902286	−	0.431139i	$-0.141888\pi$
$284$	3.28792	−	5.69485i	0.195102	−	0.337927i
$285$	−6.45185	−	11.1749i	−0.382174	−	0.661945i
$286$	−0.909650			−0.0537887
$287$		0			0
$288$	−27.5516			−1.62349
$289$	−8.05080	−	13.9444i	−0.473576	−	0.820258i
$290$	4.57148	−	7.91803i	0.268446	−	0.464963i
$291$	2.11600	−	3.66502i	0.124042	−	0.214848i
$292$	1.59526	+	2.76307i	0.0933556	+	0.161697i
$293$	−12.7409			−0.744333			−0.372167	−	0.928166i	$-0.621385\pi$
$293$	−12.7409			−0.744333			−0.372167	+	0.928166i	$0.621385\pi$
$294$		0			0
$295$	7.88593			0.459137
$296$	−7.69295	−	13.3246i	−0.447143	−	0.774475i
$297$	−6.77603	+	11.7364i	−0.393185	+	0.681017i
$298$	6.68976	−	11.5870i	0.387527	−	0.671217i
$299$	−1.49591	−	2.59099i	−0.0865107	−	0.149841i
$300$	10.1528			0.586175
$301$		0			0
$302$	4.34307			0.249916
$303$	−1.01443	−	1.75704i	−0.0582773	−	0.100939i
$304$	1.45941	−	2.52778i	0.0837031	−	0.144978i
$305$	17.1863	−	29.7675i	0.984085	−	1.70448i
$306$	27.8437	+	48.2267i	1.59172	+	2.75694i
$307$	−10.1384			−0.578626			−0.289313	−	0.957235i	$-0.593427\pi$
$307$	−10.1384			−0.578626			−0.289313	+	0.957235i	$0.593427\pi$
$308$		0			0
$309$	25.6286			1.45796
$310$	−11.3598	−	19.6758i	−0.645195	−	1.11751i
$311$	10.3006	−	17.8412i	0.584096	−	1.01168i	−0.410892	−	0.911684i	$-0.634783\pi$
$311$	10.3006	−	17.8412i	0.584096	−	1.01168i	0.994987	−	0.0999994i	$-0.0318841\pi$
$312$	−5.15650	+	8.93132i	−0.291929	+	0.505636i
$313$	8.27280	+	14.3289i	0.467606	+	0.809918i	0.999315	−	0.0370095i	$-0.0117832\pi$
$313$	8.27280	+	14.3289i	0.467606	+	0.809918i	−0.531709	+	0.846927i	$0.678450\pi$
$314$	1.31809			0.0743841
$315$		0			0
$316$	0.334213			0.0188010
$317$	10.6170	+	18.3892i	0.596310	+	1.03284i	0.993361	+	0.115043i	$0.0367006\pi$
$317$	10.6170	+	18.3892i	0.596310	+	1.03284i	−0.397050	+	0.917797i	$0.629966\pi$
$318$	19.2934	−	33.4172i	1.08192	−	1.87394i
$319$	−0.954680	+	1.65355i	−0.0534518	+	0.0925813i
$320$	13.7142	+	23.7537i	0.766646	+	1.32787i
$321$	−16.1841			−0.903310
$322$		0			0
$323$	7.03629			0.391510
$324$	10.4918	+	18.1723i	0.582875	+	1.00957i
$325$	2.45692	−	4.25550i	0.136285	−	0.236053i
$326$	−11.9639	+	20.7220i	−0.662617	+	1.14769i
$327$	12.1154	+	20.9845i	0.669982	+	1.16044i
$328$	7.87804			0.434992
$329$		0			0
$330$	9.59774			0.528338
$331$	−8.12074	−	14.0655i	−0.446356	−	0.773111i	0.551789	−	0.833983i	$-0.313945\pi$
$331$	−8.12074	−	14.0655i	−0.446356	−	0.773111i	−0.998146	+	0.0608720i	$0.980612\pi$
$332$	−4.69402	+	8.13028i	−0.257618	+	0.446207i
$333$	−20.5702	+	35.6286i	−1.12724	+	1.95243i
$334$	−7.64890	−	13.2483i	−0.418529	−	0.724914i
$335$	−13.6184			−0.744050
$336$		0			0
$337$	6.42141			0.349797			0.174898	−	0.984586i	$-0.444040\pi$
$337$	6.42141			0.349797			0.174898	+	0.984586i	$0.444040\pi$
$338$	0.588093	+	1.01861i	0.0319881	+	0.0554049i
$339$	−15.4041	+	26.6807i	−0.836636	+	1.44910i
$340$	−5.58481	+	9.67318i	−0.302879	+	0.524602i
$341$	2.37232	+	4.10898i	0.128468	+	0.222514i
$342$	−11.8373			−0.640086
$343$		0			0
$344$	−8.40645			−0.453245
$345$	15.7834	+	27.3376i	0.849749	+	1.47181i
$346$	15.2381	−	26.3932i	0.819205	−	1.41890i
$347$	−7.24046	+	12.5408i	−0.388688	+	0.673228i	−0.992273	−	0.124071i	$-0.960405\pi$
$347$	−7.24046	+	12.5408i	−0.388688	+	0.673228i	0.603585	+	0.797298i	$0.293738\pi$
$348$	2.55051	+	4.41761i	0.136722	+	0.236809i
$349$	−1.74500			−0.0934079			−0.0467040	−	0.998909i	$-0.514872\pi$
$349$	−1.74500			−0.0934079			−0.0467040	+	0.998909i	$0.514872\pi$
$350$		0			0
$351$	17.5229			0.935306
$352$	−1.29467	−	2.24243i	−0.0690061	−	0.119522i
$353$	7.97900	−	13.8200i	0.424679	−	0.735566i	−0.571711	−	0.820455i	$-0.693720\pi$
$353$	7.97900	−	13.8200i	0.424679	−	0.735566i	0.996390	+	0.0848891i	$0.0270536\pi$
$354$	4.93574	−	8.54895i	0.262332	−	0.454372i
$355$	16.7899	+	29.0810i	0.891118	+	1.54346i
$356$	5.69237			0.301695
$357$		0			0
$358$	−11.3404			−0.599356
$359$	−4.40700	−	7.63315i	−0.232593	−	0.402862i	0.725978	−	0.687718i	$-0.241388\pi$
$359$	−4.40700	−	7.63315i	−0.232593	−	0.402862i	−0.958570	+	0.284856i	$0.908054\pi$
$360$	39.8711	−	69.0588i	2.10139	−	3.63972i
$361$	8.75216	−	15.1592i	0.460640	−	0.797852i
$362$	1.72125	+	2.98129i	0.0904670	+	0.156693i
$363$	34.8566			1.82950
$364$		0			0
$365$	−16.2926			−0.852792
$366$	−21.5135	−	37.2625i	−1.12453	−	1.94774i
$367$	−9.85399	+	17.0676i	−0.514374	+	0.890922i	0.485487	+	0.874244i	$0.338642\pi$
$367$	−9.85399	+	17.0676i	−0.514374	+	0.890922i	−0.999861	+	0.0166783i	$0.994691\pi$
$368$	−3.57022	+	6.18379i	−0.186110	+	0.322353i
$369$	−10.5325	−	18.2429i	−0.548302	−	0.949687i
$370$	18.5144			0.962515
$371$		0			0
$372$	12.6757			0.657205
$373$	0.182896	+	0.316785i	0.00947000	+	0.0164025i	0.870722	−	0.491776i	$-0.163652\pi$
$373$	0.182896	+	0.316785i	0.00947000	+	0.0164025i	−0.861252	+	0.508179i	$0.830319\pi$
$374$	−2.61679	+	4.53241i	−0.135311	+	0.234366i
$375$	0.454571	−	0.787341i	0.0234740	−	0.0406581i
$376$	8.26594	+	14.3170i	0.426283	+	0.738344i
$377$	2.46882			0.127151
$378$		0			0
$379$	7.39215			0.379709			0.189855	−	0.981812i	$-0.439198\pi$
$379$	7.39215			0.379709			0.189855	+	0.981812i	$0.439198\pi$
$380$	−1.18714	−	2.05619i	−0.0608992	−	0.105481i
$381$	−18.7854	+	32.5372i	−0.962404	+	1.66693i
$382$	−9.48973	+	16.4367i	−0.485537	+	0.840974i
$383$	−1.67682	−	2.90433i	−0.0856814	−	0.148405i	0.820000	−	0.572364i	$-0.193973\pi$
$383$	−1.67682	−	2.90433i	−0.0856814	−	0.148405i	−0.905681	+	0.423959i	$0.860640\pi$
$384$	11.8958			0.607057
$385$		0			0
$386$	0.101601			0.00517135
$387$	11.2390	+	19.4665i	0.571311	+	0.989539i
$388$	0.389346	−	0.674367i	0.0197660	−	0.0342358i
$389$	1.29672	−	2.24598i	0.0657462	−	0.113876i	−0.831279	−	0.555856i	$-0.812391\pi$
$389$	1.29672	−	2.24598i	0.0657462	−	0.113876i	0.897025	+	0.441980i	$0.145724\pi$
$390$	−6.20499	−	10.7474i	−0.314202	−	0.544213i
$391$	−17.2131			−0.870506
$392$		0			0
$393$	52.7379			2.66027
$394$	8.85603	+	15.3391i	0.446160	+	0.772773i
$395$	−0.853338	+	1.47802i	−0.0429361	+	0.0743675i
$396$	−1.96209	+	3.39843i	−0.0985985	+	0.170778i
$397$	−16.7457	−	29.0044i	−0.840441	−	1.45569i	−0.889522	−	0.456892i	$-0.848962\pi$
$397$	−16.7457	−	29.0044i	−0.840441	−	1.45569i	0.0490806	−	0.998795i	$-0.484371\pi$
$398$	18.1681			0.910686
$399$		0			0
$400$	−11.7276			−0.586380
$401$	−19.7578	−	34.2215i	−0.986657	−	1.70894i	−0.634327	−	0.773065i	$-0.718723\pi$
$401$	−19.7578	−	34.2215i	−0.986657	−	1.70894i	−0.352330	−	0.935876i	$-0.614611\pi$
$402$	−8.52362	+	14.7633i	−0.425119	+	0.736328i
$403$	3.06743	−	5.31295i	0.152800	−	0.264657i
$404$	−0.186655	−	0.323296i	−0.00928644	−	0.0160846i
$405$	−107.153			−5.32449
$406$		0			0
$407$	−3.86643			−0.191652
$408$	29.6674	+	51.3854i	1.46876	+	2.54396i
$409$	−5.48996	+	9.50889i	−0.271461	+	0.470184i	−0.969236	−	0.246133i	$-0.920840\pi$
$409$	−5.48996	+	9.50889i	−0.271461	+	0.470184i	0.697775	+	0.716317i	$0.254173\pi$
$410$	−4.73995	+	8.20984i	−0.234090	+	0.405455i
$411$	−31.1994	−	54.0390i	−1.53895	−	2.66555i
$412$	4.71567			0.232324
$413$		0			0
$414$	28.9580			1.42321
$415$	−23.9702	−	41.5177i	−1.17665	−	2.03802i
$416$	−1.67402	+	2.89949i	−0.0820755	+	0.142159i
$417$	19.9613	−	34.5741i	0.977511	−	1.69310i
$418$	−0.556242	−	0.963439i	−0.0272067	−	0.0471234i
$419$	−31.5621			−1.54191			−0.770954	−	0.636891i	$-0.780220\pi$
$419$	−31.5621			−1.54191			−0.770954	+	0.636891i	$0.780220\pi$
$420$		0			0
$421$	−17.7055			−0.862914			−0.431457	−	0.902134i	$-0.642000\pi$
$421$	−17.7055			−0.862914			−0.431457	+	0.902134i	$0.642000\pi$
$422$	−14.7353	−	25.5223i	−0.717304	−	1.24241i
$423$	22.1023	−	38.2823i	1.07465	−	1.86135i
$424$	15.0650	−	26.0934i	0.731623	−	1.26721i
$425$	−14.1356	−	24.4836i	−0.685678	−	1.18763i
$426$	42.0348			2.03659
$427$		0			0
$428$	−2.97789			−0.143942
$429$	1.29581	+	2.24441i	0.0625624	+	0.108361i
$430$	5.05788	−	8.76050i	0.243913	−	0.422469i
$431$	10.7408	−	18.6036i	0.517367	−	0.896106i	−0.482429	−	0.875935i	$-0.660246\pi$
$431$	10.7408	−	18.6036i	0.517367	−	0.896106i	0.999797	−	0.0201713i	$-0.00642116\pi$
$432$	−20.9106	−	36.2182i	−1.00606	−	1.74255i
$433$	−34.7200			−1.66854			−0.834269	−	0.551358i	$-0.814110\pi$
$433$	−34.7200			−1.66854			−0.834269	+	0.551358i	$0.814110\pi$
$434$		0			0
$435$	−26.0486			−1.24893
$436$	2.22924	+	3.86116i	0.106761	+	0.184916i
$437$	1.82947	−	3.16873i	0.0875153	−	0.151581i
$438$	−10.1974	+	17.6624i	−0.487250	+	0.843941i
$439$	0.364253	+	0.630904i	0.0173848	+	0.0301114i	0.874587	−	0.484869i	$-0.161133\pi$
$439$	0.364253	+	0.630904i	0.0173848	+	0.0301114i	−0.857202	+	0.514980i	$0.827799\pi$
$440$	7.49428			0.357276
$441$		0			0
$442$	6.76707			0.321877
$443$	−0.418645	−	0.725115i	−0.0198904	−	0.0344513i	0.855909	−	0.517127i	$-0.172998\pi$
$443$	−0.418645	−	0.725115i	−0.0198904	−	0.0344513i	−0.875799	+	0.482675i	$0.839665\pi$
$444$	−5.16474	+	8.94560i	−0.245108	+	0.424539i
$445$	−14.5342	+	25.1739i	−0.688986	+	1.19336i
$446$	12.1523	+	21.0485i	0.575430	+	0.996674i
$447$	−38.1187			−1.80295
$448$		0			0
$449$	26.4312			1.24737			0.623683	−	0.781677i	$-0.285635\pi$
$449$	26.4312			1.24737			0.623683	+	0.781677i	$0.285635\pi$
$450$	23.7806	+	41.1892i	1.12103	+	1.94168i
$451$	0.989863	−	1.71449i	0.0466108	−	0.0807324i
$452$	−2.83437	+	4.90927i	−0.133317	+	0.230912i
$453$	−6.18678	−	10.7158i	−0.290680	−	0.503473i
$454$	1.15546			0.0542284
$455$		0			0
$456$	−12.6126			−0.590639
$457$	1.20237	+	2.08257i	0.0562447	+	0.0974186i	0.892777	−	0.450499i	$-0.148754\pi$
$457$	1.20237	+	2.08257i	0.0562447	+	0.0974186i	−0.836532	+	0.547918i	$0.815421\pi$
$458$	8.39459	−	14.5399i	0.392253	−	0.679403i
$459$	50.4082	−	87.3096i	2.35286	−	4.07526i
$460$	2.90415	+	5.03014i	0.135407	+	0.234532i
$461$	22.2702			1.03722			0.518612	−	0.855010i	$-0.326449\pi$
$461$	22.2702			1.03722			0.518612	+	0.855010i	$0.326449\pi$
$462$		0			0
$463$	32.3085			1.50151			0.750753	−	0.660583i	$-0.229691\pi$
$463$	32.3085			1.50151			0.750753	+	0.660583i	$0.229691\pi$
$464$	−2.94611	−	5.10281i	−0.136770	−	0.236892i
$465$	−32.3646	+	56.0571i	−1.50087	+	2.59958i
$466$	0.820592	−	1.42131i	0.0380132	−	0.0658407i
$467$	−6.43720	−	11.1496i	−0.297878	−	0.515940i	0.677772	−	0.735272i	$-0.262946\pi$
$467$	−6.43720	−	11.1496i	−0.297878	−	0.515940i	−0.975650	+	0.219332i	$0.929612\pi$
$468$	5.07399			0.234545
$469$		0			0
$470$	−19.8934			−0.917612
$471$	−1.87764	−	3.25217i	−0.0865172	−	0.149852i
$472$	3.85401	−	6.67535i	0.177395	−	0.307258i
$473$	−1.05626	+	1.82949i	−0.0485668	+	0.0841201i
$474$	1.06819	+	1.85017i	0.0490638	+	0.0849809i
$475$	6.00952			0.275736
$476$		0			0
$477$	−80.5649			−3.68881
$478$	1.49891	+	2.59618i	0.0685583	+	0.118747i
$479$	5.27093	−	9.12952i	0.240835	−	0.417138i	−0.720117	−	0.693852i	$-0.755912\pi$
$479$	5.27093	−	9.12952i	0.240835	−	0.417138i	0.960952	+	0.276714i	$0.0892454\pi$
$480$	17.6626	−	30.5926i	0.806185	−	1.39635i
$481$	2.49966	+	4.32954i	0.113975	+	0.197410i
$482$	34.9029			1.58978
$483$		0			0
$484$	6.41364			0.291529
$485$	1.98821	+	3.44369i	0.0902802	+	0.156370i
$486$	−36.1510	+	62.6154i	−1.63984	+	2.84029i
$487$	−19.1208	+	33.1182i	−0.866446	+	1.50073i	−0.000841391		1.00000i	$0.500268\pi$
$487$	−19.1208	+	33.1182i	−0.866446	+	1.50073i	−0.865604	+	0.500728i	$0.833066\pi$
$488$	−16.7986	−	29.0960i	−0.760436	−	1.31711i
$489$	68.1709			3.08280
$490$		0			0
$491$	−15.4291			−0.696306			−0.348153	−	0.937438i	$-0.613191\pi$
$491$	−15.4291			−0.696306			−0.348153	+	0.937438i	$0.613191\pi$
$492$	−2.64450	−	4.58042i	−0.119223	−	0.206501i
$493$	7.10206	−	12.3011i	0.319861	−	0.554015i
$494$	−0.719226	+	1.24574i	−0.0323595	+	0.0560483i
$495$	−10.0195	−	17.3543i	−0.450342	−	0.780016i
$496$	−14.6418			−0.657436
$497$		0			0
$498$	−60.0111			−2.68916
$499$	19.4106	+	33.6202i	0.868938	+	1.50505i	0.863083	+	0.505062i	$0.168530\pi$
$499$	19.4106	+	33.6202i	0.868938	+	1.50505i	0.00585522	+	0.999983i	$0.498136\pi$
$500$	0.0836414	−	0.144871i	0.00374056	−	0.00647884i
$501$	−21.7920	+	37.7448i	−0.973594	+	1.68631i
$502$	−10.6362	−	18.4224i	−0.474715	−	0.822230i
$503$	27.0935			1.20804			0.604020	−	0.796969i	$-0.293565\pi$
$503$	27.0935			1.20804			0.604020	+	0.796969i	$0.293565\pi$
$504$		0			0
$505$	1.90633			0.0848304
$506$	1.36075	+	2.35690i	0.0604929	+	0.104777i
$507$	1.67550	−	2.90205i	0.0744115	−	0.128884i
$508$	−3.45652	+	5.98687i	−0.153358	+	0.265624i
$509$	−7.88464	−	13.6566i	−0.349480	−	0.605318i	0.636677	−	0.771131i	$-0.280309\pi$
$509$	−7.88464	−	13.6566i	−0.349480	−	0.605318i	−0.986157	+	0.165813i	$0.946975\pi$
$510$	−71.3995			−3.16162
$511$		0			0
$512$	22.6809			1.00236
$513$	10.7151	+	18.5591i	0.473083	+	0.819404i
$514$	−8.66866	+	15.0146i	−0.382358	+	0.662264i
$515$	−12.0404	+	20.8546i	−0.530563	+	0.918963i
$516$	2.82188	+	4.88764i	0.124226	+	0.215166i
$517$	4.15441			0.182711
$518$		0			0
$519$	−86.8277			−3.81131
$520$	−4.84509	−	8.39194i	−0.212471	−	0.368011i
$521$	3.65369	−	6.32837i	0.160071	−	0.277251i	−0.774823	−	0.632178i	$-0.782161\pi$
$521$	3.65369	−	6.32837i	0.160071	−	0.277251i	0.934894	+	0.354927i	$0.115494\pi$
$522$	−11.9479	+	20.6944i	−0.522946	+	0.905769i
$523$	7.04128	+	12.1959i	0.307894	+	0.533288i	0.977901	−	0.209066i	$-0.0670425\pi$
$523$	7.04128	+	12.1959i	0.307894	+	0.533288i	−0.670008	+	0.742354i	$0.733709\pi$
$524$	9.70381			0.423913
$525$		0			0
$526$	9.59677			0.418439
$527$	−17.6482	−	30.5675i	−0.768766	−	1.33154i
$528$	3.09265	−	5.35663i	0.134590	−	0.233117i
$529$	7.02451	−	12.1668i	0.305413	−	0.528991i
$530$	18.1283	+	31.3991i	0.787442	+	1.36389i
$531$	−20.6105			−0.894419
$532$		0			0
$533$	−2.55981			−0.110877
$534$	18.1936	+	31.5123i	0.787316	+	1.36367i
$535$	7.60337	−	13.1694i	0.328723	−	0.569364i
$536$	−6.65556	+	11.5278i	−0.287477	+	0.497924i
$537$	16.1545	+	27.9805i	0.697119	+	1.20745i
$538$	0.520559			0.0224429
$539$		0			0
$540$	−34.0190			−1.46394
$541$	19.5875	+	33.9265i	0.842132	+	1.45862i	0.888088	+	0.459673i	$0.152033\pi$
$541$	19.5875	+	33.9265i	0.842132	+	1.45862i	−0.0459559	+	0.998943i	$0.514633\pi$
$542$	12.3988	−	21.4754i	0.532576	−	0.922448i
$543$	4.90390	−	8.49381i	0.210447	−	0.364504i
$544$	9.63130	+	16.6819i	0.412939	+	0.715231i
$545$	−22.7674			−0.975250
$546$		0			0
$547$	38.7917			1.65862			0.829308	−	0.558792i	$-0.188735\pi$
$547$	38.7917			1.65862			0.829308	+	0.558792i	$0.188735\pi$
$548$	−5.74072	−	9.94321i	−0.245231	−	0.424753i
$549$	−44.9177	+	77.7998i	−1.91704	+	3.32041i
$550$	−2.23494	+	3.87102i	−0.0952980	+	0.165061i
$551$	1.50966	+	2.61481i	0.0643136	+	0.111394i
$552$	30.8546			1.31326
$553$		0			0
$554$	−4.22746			−0.179607
$555$	−26.3740	−	45.6811i	−1.11951	−	1.93906i
$556$	3.67290	−	6.36165i	0.155766	−	0.269794i
$557$	13.7347	−	23.7891i	0.581956	−	1.00798i	−0.413291	−	0.910599i	$-0.635621\pi$
$557$	13.7347	−	23.7891i	0.581956	−	1.00798i	0.995247	−	0.0973791i	$-0.0310459\pi$
$558$	29.6898	+	51.4243i	1.25687	+	2.17696i
$559$	2.73150			0.115530
$560$		0			0
$561$	14.9107			0.629528
$562$	−5.30020	−	9.18022i	−0.223576	−	0.387244i
$563$	7.06050	−	12.2291i	0.297565	−	0.515397i	−0.678014	−	0.735049i	$-0.737159\pi$
$563$	7.06050	−	12.2291i	0.297565	−	0.515397i	0.975578	+	0.219652i	$0.0704923\pi$
$564$	5.54943	−	9.61189i	0.233673	−	0.404734i
$565$	−14.4738	−	25.0694i	−0.608919	−	1.05468i
$566$	32.6288			1.37149
$567$		0			0
$568$	32.8223			1.37720
$569$	4.14324	+	7.17631i	0.173694	+	0.300846i	0.939708	−	0.341977i	$-0.111096\pi$
$569$	4.14324	+	7.17631i	0.173694	+	0.300846i	−0.766015	+	0.642823i	$0.777763\pi$
$570$	7.58857	−	13.1438i	0.317850	−	0.550533i
$571$	11.7637	−	20.3753i	0.492295	−	0.852681i	−0.507665	−	0.861554i	$-0.669491\pi$
$571$	11.7637	−	20.3753i	0.492295	−	0.852681i	0.999961	+	0.00887373i	$0.00282463\pi$
$572$	0.238430	+	0.412974i	0.00996928	+	0.0172673i
$573$	54.0731			2.25894
$574$		0			0
$575$	−14.7013			−0.613087
$576$	−35.8431	−	62.0820i	−1.49346	−	2.58675i
$577$	−8.88658	+	15.3920i	−0.369953	+	0.640777i	−0.989558	−	0.144137i	$-0.953960\pi$
$577$	−8.88658	+	15.3920i	−0.369953	+	0.640777i	0.619605	+	0.784914i	$0.287293\pi$
$578$	9.46924	−	16.4012i	0.393869	−	0.682200i
$579$	−0.144732	−	0.250684i	−0.00601487	−	0.0104181i
$580$	−4.79296			−0.199017
$581$		0			0
$582$	4.97763			0.206329
$583$	−3.78580	−	6.55720i	−0.156792	−	0.271571i
$584$	−7.96250	+	13.7915i	−0.329491	+	0.570695i
$585$	−12.9553	+	22.4392i	−0.535635	+	0.927747i
$586$	−7.49286	−	12.9780i	−0.309527	−	0.536117i
$587$	6.64096			0.274102			0.137051	−	0.990564i	$-0.456238\pi$
$587$	6.64096			0.274102			0.137051	+	0.990564i	$0.456238\pi$
$588$		0			0
$589$	7.50282			0.309148
$590$	4.63766	+	8.03266i	0.190929	+	0.330700i
$591$	25.2311	−	43.7016i	1.03787	−	1.79764i
$592$	5.96583	−	10.3331i	0.245194	−	0.424688i
$593$	17.0252	+	29.4885i	0.699141	+	1.21095i	0.968765	+	0.247982i	$0.0797674\pi$
$593$	17.0252	+	29.4885i	0.699141	+	1.21095i	−0.269624	+	0.962966i	$0.586899\pi$
$594$	−15.9398			−0.654016
$595$		0			0
$596$	−7.01387			−0.287299
$597$	−25.8808	−	44.8269i	−1.05923	−	1.83464i
$598$	1.75947	−	3.04749i	0.0719500	−	0.124621i
$599$	−4.69221	+	8.12714i	−0.191718	+	0.332066i	−0.945820	−	0.324692i	$-0.894739\pi$
$599$	−4.69221	+	8.12714i	−0.191718	+	0.332066i	0.754101	+	0.656758i	$0.228073\pi$
$600$	25.3382	+	43.8870i	1.03443	+	1.79168i
$601$	−8.80294			−0.359079			−0.179540	−	0.983751i	$-0.557461\pi$
$601$	−8.80294			−0.359079			−0.179540	+	0.983751i	$0.557461\pi$
$602$		0			0
$603$	35.5926			1.44944
$604$	−1.13837	−	1.97172i	−0.0463197	−	0.0802281i
$605$	−16.3758	+	28.3637i	−0.665770	+	1.15315i
$606$	1.19315	−	2.06660i	0.0484686	−	0.0839500i
$607$	8.88598	+	15.3910i	0.360671	+	0.624700i	0.988071	−	0.153997i	$-0.0492145\pi$
$607$	8.88598	+	15.3910i	0.360671	+	0.624700i	−0.627401	+	0.778697i	$0.715881\pi$
$608$	−4.09458			−0.166057
$609$		0			0
$610$	40.4286			1.63691
$611$	−2.68585	−	4.65202i	−0.108658	−	0.188201i
$612$	14.5963	−	25.2816i	0.590022	−	1.02195i
$613$	−5.30405	+	9.18688i	−0.214228	+	0.371055i	−0.953034	−	0.302865i	$-0.902057\pi$
$613$	−5.30405	+	9.18688i	−0.214228	+	0.371055i	0.738805	+	0.673919i	$0.235390\pi$
$614$	−5.96230	−	10.3270i	−0.240619	−	0.416764i
$615$	27.0086			1.08909
$616$		0			0
$617$	49.3483			1.98669			0.993344	−	0.115188i	$-0.0367469\pi$
$617$	49.3483			1.98669			0.993344	+	0.115188i	$0.0367469\pi$
$618$	15.0720	+	26.1054i	0.606284	+	1.05011i
$619$	3.71101	−	6.42767i	0.149158	−	0.258350i	−0.781758	−	0.623582i	$-0.785677\pi$
$619$	3.71101	−	6.42767i	0.149158	−	0.258350i	0.930917	+	0.365232i	$0.119010\pi$
$620$	−5.95510	+	10.3145i	−0.239163	+	0.414242i
$621$	−26.2127	−	45.4018i	−1.05188	−	1.82191i
$622$	24.2309			0.971573
$623$		0			0
$624$	−7.99766			−0.320163
$625$	12.7117	+	22.0173i	0.508468	+	0.880693i
$626$	−9.73036	+	16.8535i	−0.388903	+	0.673600i
$627$	−1.58475	+	2.74487i	−0.0632889	+	0.109620i
$628$	−0.345487	−	0.598402i	−0.0137864	−	0.0238788i
$629$	28.7631			1.14686
$630$		0			0
$631$	35.5184			1.41396			0.706982	−	0.707231i	$-0.250056\pi$
$631$	35.5184			1.41396			0.706982	+	0.707231i	$0.250056\pi$
$632$	0.834087	+	1.44468i	0.0331782	+	0.0574663i
$633$	−41.9814	+	72.7139i	−1.66861	+	2.89012i
$634$	−12.4876	+	21.6291i	−0.495945	+	0.859002i
$635$	−17.6509	−	30.5722i	−0.700454	−	1.21322i
$636$	−20.2282			−0.802099
$637$		0			0
$638$	−2.24576			−0.0889106
$639$	−43.8818	−	76.0056i	−1.73594	−	3.00673i
$640$	−5.58872	+	9.67994i	−0.220913	+	0.382633i
$641$	−18.5777	+	32.1775i	−0.733775	+	1.27093i	0.221484	+	0.975164i	$0.428910\pi$
$641$	−18.5777	+	32.1775i	−0.733775	+	1.27093i	−0.955259	+	0.295771i	$0.904424\pi$
$642$	−9.51778	−	16.4853i	−0.375637	−	0.650622i
$643$	−39.7694			−1.56835			−0.784176	−	0.620538i	$-0.786914\pi$
$643$	−39.7694			−1.56835			−0.784176	+	0.620538i	$0.786914\pi$
$644$		0			0
$645$	−28.8201			−1.13479
$646$	4.13799	+	7.16722i	0.162807	+	0.281990i
$647$	11.4877	−	19.8973i	0.451628	−	0.782243i	−0.546859	−	0.837224i	$-0.684177\pi$
$647$	11.4877	−	19.8973i	0.451628	−	0.782243i	0.998487	+	0.0549819i	$0.0175101\pi$
$648$	−52.3680	+	90.7040i	−2.05721	+	3.56319i
$649$	−0.968502	−	1.67749i	−0.0380170	−	0.0658474i
$650$	5.77958			0.226694
$651$		0			0
$652$	12.5435			0.491241
$653$	−9.08783	−	15.7406i	−0.355634	−	0.615976i	0.631592	−	0.775301i	$-0.282402\pi$
$653$	−9.08783	−	15.7406i	−0.355634	−	0.615976i	−0.987226	+	0.159324i	$0.949068\pi$
$654$	−14.2500	+	24.6816i	−0.557217	+	0.965129i
$655$	−24.7765	+	42.9141i	−0.968097	+	1.67679i
$656$	3.05468	+	5.29086i	0.119265	+	0.206574i
$657$	42.5819			1.66128
$658$		0			0
$659$	14.1044			0.549431			0.274716	−	0.961526i	$-0.411416\pi$
$659$	14.1044			0.549431			0.274716	+	0.961526i	$0.411416\pi$
$660$	−2.51569	−	4.35730i	−0.0979229	−	0.169607i
$661$	−6.42783	+	11.1333i	−0.250013	+	0.433036i	−0.963529	−	0.267603i	$-0.913768\pi$
$661$	−6.42783	+	11.1333i	−0.250013	+	0.433036i	0.713516	+	0.700639i	$0.247102\pi$
$662$	9.55150	−	16.5437i	0.371230	−	0.642989i
$663$	−9.63981	−	16.6966i	−0.374379	−	0.648444i
$664$	−46.8590			−1.81848
$665$		0			0
$666$	−48.3887			−1.87502
$667$	−3.69313	−	6.39670i	−0.142999	−	0.247681i
$668$	−4.00974	+	6.94507i	−0.155141	+	0.268713i
$669$	34.6224	−	59.9678i	1.33858	−	2.31849i
$670$	−8.00886	−	13.8718i	−0.309409	−	0.535913i
$671$	−8.44287			−0.325933
$672$		0			0
$673$	−45.6138			−1.75828			−0.879141	−	0.476561i	$-0.841883\pi$
$673$	−45.6138			−1.75828			−0.879141	+	0.476561i	$0.841883\pi$
$674$	3.77639	+	6.54090i	0.145461	+	0.251946i
$675$	43.0524	−	74.5690i	1.65709	−	2.87016i
$676$	0.308293	−	0.533979i	0.0118574	−	0.0205376i
$677$	5.12346	+	8.87409i	0.196910	+	0.341059i	0.947525	−	0.319681i	$-0.103576\pi$
$677$	5.12346	+	8.87409i	0.196910	+	0.341059i	−0.750615	+	0.660740i	$0.770243\pi$
$678$	−36.2362			−1.39164
$679$		0			0
$680$	−55.7515			−2.13797
$681$	−1.64597	−	2.85091i	−0.0630738	−	0.109247i
$682$	−2.79029	+	4.83293i	−0.106846	+	0.185062i
$683$	−1.45020	+	2.51182i	−0.0554904	+	0.0961122i	−0.892436	−	0.451173i	$-0.851006\pi$
$683$	−1.45020	+	2.51182i	−0.0554904	+	0.0961122i	0.836946	+	0.547286i	$0.184339\pi$
$684$	3.10269	+	5.37402i	0.118634	+	0.205481i
$685$	58.6305			2.24016
$686$		0			0
$687$	−47.8329			−1.82494
$688$	−3.25957	−	5.64574i	−0.124270	−	0.215242i
$689$	−4.89508	+	8.47852i	−0.186488	+	0.323006i
$690$	−18.5642	+	32.1541i	−0.706727	+	1.22409i
$691$	3.45735	+	5.98831i	0.131524	+	0.227806i	0.924264	−	0.381753i	$-0.124680\pi$
$691$	3.45735	+	5.98831i	0.131524	+	0.227806i	−0.792740	+	0.609560i	$0.791346\pi$
$692$	−15.9764			−0.607330
$693$		0			0
$694$	−17.0323			−0.646536
$695$	18.7558	+	32.4861i	0.711450	+	1.23227i
$696$	−12.7305	+	22.0498i	−0.482547	+	0.835797i
$697$	−7.36379	+	12.7545i	−0.278923	+	0.483110i
$698$	−1.02622	−	1.77747i	−0.0388432	−	0.0672784i
$699$	−4.67579			−0.176855
$700$		0			0
$701$	−26.0973			−0.985682			−0.492841	−	0.870119i	$-0.664042\pi$
$701$	−26.0973			−0.985682			−0.492841	+	0.870119i	$0.664042\pi$
$702$	10.3051	+	17.8490i	0.388942	+	0.673667i
$703$	−3.05704	+	5.29494i	−0.115298	+	0.199703i
$704$	3.36858	−	5.83456i	0.126958	−	0.219898i
$705$	28.3384	+	49.0836i	1.06729	+	1.84860i
$706$	18.7696			0.706402
$707$		0			0
$708$	−5.17487			−0.194483
$709$	1.69236	+	2.93126i	0.0635580	+	0.110086i	0.896053	−	0.443946i	$-0.146422\pi$
$709$	1.69236	+	2.93126i	0.0635580	+	0.110086i	−0.832495	+	0.554032i	$0.813089\pi$
$710$	−19.7481	+	34.2047i	−0.741133	+	1.28368i
$711$	2.23026	−	3.86293i	0.0836414	−	0.144871i
$712$	14.2063	+	24.6060i	0.532403	+	0.922150i
$713$	−18.3544			−0.687378
$714$		0			0
$715$	−2.43511			−0.0910681
$716$	2.97244	+	5.14842i	0.111085	+	0.192406i
$717$	4.27043	−	7.39661i	0.159482	−	0.276231i
$718$	5.18346	−	8.97801i	0.193445	−	0.335056i
$719$	−1.20787	−	2.09209i	−0.0450459	−	0.0780218i	0.842623	−	0.538503i	$-0.181010\pi$
$719$	−1.20787	−	2.09209i	−0.0450459	−	0.0780218i	−0.887669	+	0.460482i	$0.847677\pi$
$720$	61.8395			2.30462
$721$		0			0
$722$	20.5883			0.766219
$723$	−49.7198	−	86.1171i	−1.84910	−	3.20273i
$724$	0.902322	−	1.56287i	0.0335345	−	0.0580835i
$725$	6.06569	−	10.5061i	0.225274	−	0.390186i
$726$	20.4989	+	35.5052i	0.760787	+	1.31772i
$727$	−17.0150			−0.631050			−0.315525	−	0.948917i	$-0.602181\pi$
$727$	−17.0150			−0.631050			−0.315525	+	0.948917i	$0.602181\pi$
$728$		0			0
$729$	103.896			3.84799
$730$	−9.58155	−	16.5957i	−0.354629	−	0.614235i
$731$	7.85771	−	13.6100i	0.290628	−	0.503382i
$732$	−11.2779	+	19.5339i	−0.416844	+	0.721995i
$733$	2.09226	+	3.62391i	0.0772795	+	0.133852i	0.902075	−	0.431579i	$-0.142043\pi$
$733$	2.09226	+	3.62391i	0.0772795	+	0.133852i	−0.824796	+	0.565431i	$0.808710\pi$
$734$	−23.1803			−0.855599
$735$		0			0
$736$	10.0167			0.369221
$737$	1.67252	+	2.89689i	0.0616082	+	0.106708i
$738$	12.3882	−	21.4571i	0.456017	−	0.789845i
$739$	14.0397	−	24.3175i	0.516458	−	0.894532i	−0.483359	−	0.875422i	$-0.660583\pi$
$739$	14.0397	−	24.3175i	0.516458	−	0.894532i	0.999817	−	0.0191099i	$-0.00608325\pi$
$740$	−4.85284	−	8.40536i	−0.178394	−	0.308987i
$741$	4.09820			0.150551
$742$		0			0
$743$	−26.5210			−0.972961			−0.486481	−	0.873691i	$-0.661720\pi$
$743$	−26.5210			−0.972961			−0.486481	+	0.873691i	$0.661720\pi$
$744$	31.6344	+	54.7925i	1.15977	+	2.00879i
$745$	17.9083	−	31.0181i	0.656111	−	1.13642i
$746$	−0.215120	+	0.372599i	−0.00787610	+	0.0136418i
$747$	62.6481	+	108.510i	2.29217	+	3.97016i
$748$	2.74357			0.100315
$749$		0			0
$750$	1.06932			0.0390461
$751$	11.8581	+	20.5389i	0.432709	+	0.749474i	0.997106	−	0.0760297i	$-0.0242244\pi$
$751$	11.8581	+	20.5389i	0.432709	+	0.749474i	−0.564396	+	0.825504i	$0.690891\pi$
$752$	−6.41018	+	11.1028i	−0.233755	+	0.404876i
$753$	−30.3028	+	52.4860i	−1.10429	+	1.91269i
$754$	1.45190	+	2.51476i	0.0528750	+	0.0915821i
$755$	11.6263			0.423125
$756$		0			0
$757$	−52.3661			−1.90328			−0.951639	−	0.307219i	$-0.900602\pi$
$757$	−52.3661			−1.90328			−0.951639	+	0.307219i	$0.900602\pi$
$758$	4.34727	+	7.52970i	0.157900	+	0.273491i
$759$	3.87684	−	6.71488i	0.140720	−	0.243735i
$760$	5.92545	−	10.2632i	0.214939	−	0.372285i
$761$	11.9347	+	20.6716i	0.432634	+	0.749344i	0.997099	−	0.0761129i	$-0.0242509\pi$
$761$	11.9347	+	20.6716i	0.432634	+	0.749344i	−0.564465	+	0.825457i	$0.690918\pi$
$762$	−44.1902			−1.60084
$763$		0			0
$764$	9.94949			0.359960
$765$	74.5369	+	129.102i	2.69489	+	4.66768i
$766$	1.97225	−	3.41604i	0.0712603	−	0.123426i
$767$	−1.25228	+	2.16902i	−0.0452173	+	0.0783186i
$768$	−22.1954	−	38.4436i	−0.800907	−	1.38721i
$769$	−41.7599			−1.50590			−0.752950	−	0.658077i	$-0.771370\pi$
$769$	−41.7599			−1.50590			−0.752950	+	0.658077i	$0.771370\pi$
$770$		0			0
$771$	49.3946			1.77890
$772$	−0.0266308	−	0.0461260i	−0.000958465	−	0.00166011i
$773$	1.48589	−	2.57364i	0.0534438	−	0.0925674i	−0.838066	−	0.545569i	$-0.816314\pi$
$773$	1.48589	−	2.57364i	0.0534438	−	0.0925674i	0.891510	+	0.453002i	$0.149647\pi$
$774$	−13.2192	+	22.8963i	−0.475153	+	0.822989i
$775$	−15.0729	−	26.1070i	−0.541433	−	0.937789i
$776$	3.88672			0.139525
$777$		0

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)

\(f(q)\)	\(=\)	\(q+(0.588093 + 1.01861i) q^{2} +(1.67550 - 2.90205i) q^{3} +(0.308293 - 0.533979i) q^{4} +(1.57431 + 2.72679i) q^{5} +3.94140 q^{6} +3.07759 q^{8} +(-4.11459 - 7.12667i) q^{9} +O(q^{10})\)	\(q+(0.588093 + 1.01861i) q^{2} +(1.67550 - 2.90205i) q^{3} +(0.308293 - 0.533979i) q^{4} +(1.57431 + 2.72679i) q^{5} +3.94140 q^{6} +3.07759 q^{8} +(-4.11459 - 7.12667i) q^{9} +(-1.85168 + 3.20721i) q^{10} +(0.386695 - 0.669775i) q^{11} +(-1.03309 - 1.78936i) q^{12} -1.00000 q^{13} +10.5510 q^{15} +(1.19333 + 2.06690i) q^{16} +(-2.87670 + 4.98259i) q^{17} +(4.83952 - 8.38230i) q^{18} +(-0.611490 - 1.05913i) q^{19} +1.94140 q^{20} +0.909650 q^{22} +(1.49591 + 2.59099i) q^{23} +(5.15650 - 8.93132i) q^{24} +(-2.45692 + 4.25550i) q^{25} +(-0.588093 - 1.01861i) q^{26} -17.5229 q^{27} -2.46882 q^{29} +(6.20499 + 10.7474i) q^{30} +(-3.06743 + 5.31295i) q^{31} +(1.67402 - 2.89949i) q^{32} +(-1.29581 - 2.24441i) q^{33} -6.76707 q^{34} -5.07399 q^{36} +(-2.49966 - 4.32954i) q^{37} +(0.719226 - 1.24574i) q^{38} +(-1.67550 + 2.90205i) q^{39} +(4.84509 + 8.39194i) q^{40} +2.55981 q^{41} -2.73150 q^{43} +(-0.238430 - 0.412974i) q^{44} +(12.9553 - 22.4392i) q^{45} +(-1.75947 + 3.04749i) q^{46} +(2.68585 + 4.65202i) q^{47} +7.99766 q^{48} -5.77958 q^{50} +(9.63981 + 16.6966i) q^{51} +(-0.308293 + 0.533979i) q^{52} +(4.89508 - 8.47852i) q^{53} +(-10.3051 - 17.8490i) q^{54} +2.43511 q^{55} -4.09820 q^{57} +(-1.45190 - 2.51476i) q^{58} +(1.25228 - 2.16902i) q^{59} +(3.25281 - 5.63402i) q^{60} +(-5.45835 - 9.45414i) q^{61} -7.21575 q^{62} +8.71122 q^{64} +(-1.57431 - 2.72679i) q^{65} +(1.52412 - 2.63985i) q^{66} +(-2.16259 + 3.74571i) q^{67} +(1.77373 + 3.07219i) q^{68} +10.0256 q^{69} +10.6649 q^{71} +(-12.6630 - 21.9330i) q^{72} +(-2.58725 + 4.48125i) q^{73} +(2.94007 - 5.09235i) q^{74} +(8.23312 + 14.2602i) q^{75} -0.754072 q^{76} -3.94140 q^{78} +(0.271019 + 0.469419i) q^{79} +(-3.75733 + 6.50789i) q^{80} +(-17.0159 + 29.4724i) q^{81} +(1.50540 + 2.60744i) q^{82} -15.2259 q^{83} -18.1153 q^{85} +(-1.60638 - 2.78233i) q^{86} +(-4.13650 + 7.16464i) q^{87} +(1.19009 - 2.06129i) q^{88} +(4.61604 + 7.99522i) q^{89} +30.4757 q^{90} +1.84471 q^{92} +(10.2790 + 17.8037i) q^{93} +(-3.15905 + 5.47164i) q^{94} +(1.92535 - 3.33481i) q^{95} +(-5.60963 - 9.71617i) q^{96} +1.26291 q^{97} -6.36436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * q^99

Introduction

L-functions

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