LMFDB - Embedded newform 637.2.f.g.295.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

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([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, 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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1485512441856.7
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 24x^{6} + 455x^{4} + 2904x^{2} + 14641 $ x^8 + 24x^6 + 455x^4 + 2904*x^2 + 14641
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			295.4
Root			$1.34203 + 2.32446i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.g.393.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.68406 q^{5} +(0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.68406 q^{5} +(0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.34203 + 2.32446i) q^{10} +(-2.89792 + 5.01934i) q^{11} +1.41421 q^{12} +(-2.75624 + 2.32446i) q^{13} +(1.89792 - 3.28729i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.75624 + 4.77395i) q^{17} -1.00000 q^{18} +(-1.41421 - 2.44949i) q^{19} +(1.34203 + 2.32446i) q^{20} +(-2.89792 - 5.01934i) q^{22} +(-0.897916 + 1.55524i) q^{23} +(-2.12132 + 3.67423i) q^{24} +2.20417 q^{25} +(-0.634922 - 3.54921i) q^{26} +5.65685 q^{27} +(4.39792 - 7.61741i) q^{29} +(1.89792 + 3.28729i) q^{30} +1.41421 q^{31} +(-2.50000 - 4.33013i) q^{32} +(4.09827 + 7.09841i) q^{33} -5.51249 q^{34} +(-0.500000 + 0.866025i) q^{36} +(3.39792 - 5.88536i) q^{37} +2.82843 q^{38} +(0.897916 + 5.01934i) q^{39} -8.05217 q^{40} +(4.87756 - 8.44819i) q^{41} +(0.897916 + 1.55524i) q^{43} -5.79583 q^{44} +(1.34203 + 2.32446i) q^{45} +(-0.897916 - 1.55524i) q^{46} -2.82843 q^{47} +(-0.707107 - 1.22474i) q^{48} +(-1.10208 + 1.90887i) q^{50} +7.79583 q^{51} +(-3.39116 - 1.22474i) q^{52} +6.59166 q^{53} +(-2.82843 + 4.89898i) q^{54} +(-7.77817 + 13.4722i) q^{55} -4.00000 q^{57} +(4.39792 + 7.61741i) q^{58} +(0.562738 + 0.974691i) q^{59} +3.79583 q^{60} +(0.779291 + 1.34977i) q^{61} +(-0.707107 + 1.22474i) q^{62} +7.00000 q^{64} +(-7.39792 + 6.23899i) q^{65} -8.19654 q^{66} +(-2.89792 + 5.01934i) q^{67} +(-2.75624 + 4.77395i) q^{68} +(1.26984 + 2.19944i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} +5.80122 q^{73} +(3.39792 + 5.88536i) q^{74} +(1.55858 - 2.69954i) q^{75} +(1.41421 - 2.44949i) q^{76} +(-4.79583 - 1.73205i) q^{78} -11.7958 q^{79} +(1.34203 - 2.32446i) q^{80} +(2.50000 - 4.33013i) q^{81} +(4.87756 + 8.44819i) q^{82} +9.89949 q^{83} +(7.39792 + 12.8136i) q^{85} -1.79583 q^{86} +(-6.21959 - 10.7726i) q^{87} +(8.69375 - 15.0580i) q^{88} +(6.07522 - 10.5226i) q^{89} -2.68406 q^{90} -1.79583 q^{92} +(1.00000 - 1.73205i) q^{93} +(1.41421 - 2.44949i) q^{94} +(-3.79583 - 6.57457i) q^{95} -7.07107 q^{96} +(-2.12132 - 3.67423i) q^{97} -5.79583 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 4 * q^4 - 24 * q^8 + 4 * q^9	$ 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} + 4 q^{9} - 4 q^{11} - 4 q^{15} + 4 q^{16} - 8 q^{18} - 4 q^{22} + 12 q^{23} + 56 q^{25} + 16 q^{29} - 4 q^{30} - 20 q^{32} - 4 q^{36} + 8 q^{37} - 12 q^{39} - 12 q^{43} - 8 q^{44} + 12 q^{46} - 28 q^{50} + 24 q^{51} - 24 q^{53} - 32 q^{57} + 16 q^{58} - 8 q^{60} + 56 q^{64} - 40 q^{65} - 4 q^{67} - 24 q^{71} - 12 q^{72} + 8 q^{74} - 56 q^{79} + 20 q^{81} + 40 q^{85} + 24 q^{86} + 12 q^{88} + 24 q^{92} + 8 q^{93} + 8 q^{95} - 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^4 - 24 * q^8 + 4 * q^9 - 4 * q^11 - 4 * q^15 + 4 * q^16 - 8 * q^18 - 4 * q^22 + 12 * q^23 + 56 * q^25 + 16 * q^29 - 4 * q^30 - 20 * q^32 - 4 * q^36 + 8 * q^37 - 12 * q^39 - 12 * q^43 - 8 * q^44 + 12 * q^46 - 28 * q^50 + 24 * q^51 - 24 * q^53 - 32 * q^57 + 16 * q^58 - 8 * q^60 + 56 * q^64 - 40 * q^65 - 4 * q^67 - 24 * q^71 - 12 * q^72 + 8 * q^74 - 56 * q^79 + 20 * q^81 + 40 * q^85 + 24 * q^86 + 12 * q^88 + 24 * q^92 + 8 * q^93 + 8 * q^95 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$	0.707107	−	1.22474i	0.408248	−	0.707107i	−0.586445	−	0.809989i	$-0.699473\pi$
$3$	0.707107	−	1.22474i	0.408248	−	0.707107i	0.994694	+	0.102882i	$0.0328064\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.68406			1.20035			0.600174	−	0.799870i	$-0.295098\pi$
$5$	2.68406			1.20035			0.600174	+	0.799870i	$0.295098\pi$
$6$	0.707107	+	1.22474i	0.288675	+	0.500000i
$7$		0			0
$7$		0			0
$8$	−3.00000			−1.06066
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.34203	+	2.32446i	−0.424387	+	0.735060i
$11$	−2.89792	+	5.01934i	−0.873754	+	1.51339i	−0.0156708	+	0.999877i	$0.504988\pi$
$11$	−2.89792	+	5.01934i	−0.873754	+	1.51339i	−0.858084	+	0.513510i	$0.828345\pi$
$12$	1.41421			0.408248
$13$	−2.75624	+	2.32446i	−0.764444	+	0.644690i
$13$	−2.75624	+	2.32446i	−0.764444	+	0.644690i
$14$		0			0
$15$	1.89792	−	3.28729i	0.490040	−	0.848774i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.75624	+	4.77395i	0.668487	+	1.15785i	0.978327	+	0.207065i	$0.0663911\pi$
$17$	2.75624	+	4.77395i	0.668487	+	1.15785i	−0.309840	+	0.950789i	$0.600276\pi$
$18$	−1.00000			−0.235702
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	0.656957	−	0.753928i	$-0.271843\pi$
$19$	−1.41421	−	2.44949i	−0.324443	−	0.561951i	−0.981399	+	0.191977i	$0.938510\pi$
$20$	1.34203	+	2.32446i	0.300087	+	0.519766i
$21$		0			0
$22$	−2.89792	−	5.01934i	−0.617838	−	1.07013i
$23$	−0.897916	+	1.55524i	−0.187228	+	0.324289i	−0.944325	−	0.329014i	$-0.893284\pi$
$23$	−0.897916	+	1.55524i	−0.187228	+	0.324289i	0.757097	+	0.653303i	$0.226617\pi$
$24$	−2.12132	+	3.67423i	−0.433013	+	0.750000i
$25$	2.20417			0.440834
$26$	−0.634922	−	3.54921i	−0.124519	−	0.696057i
$27$	5.65685			1.08866
$28$		0			0
$29$	4.39792	−	7.61741i	0.816672	−	1.41452i	−0.0914483	−	0.995810i	$-0.529150\pi$
$29$	4.39792	−	7.61741i	0.816672	−	1.41452i	0.908121	−	0.418708i	$-0.137517\pi$
$30$	1.89792	+	3.28729i	0.346510	+	0.600174i
$31$	1.41421			0.254000			0.127000	−	0.991903i	$-0.459465\pi$
$31$	1.41421			0.254000			0.127000	+	0.991903i	$0.459465\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$	4.09827	+	7.09841i	0.713418	+	1.23568i
$34$	−5.51249			−0.945383
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	3.39792	−	5.88536i	0.558614	−	0.967548i	−0.438999	−	0.898488i	$-0.644667\pi$
$37$	3.39792	−	5.88536i	0.558614	−	0.967548i	0.997613	−	0.0690599i	$-0.0220000\pi$
$38$	2.82843			0.458831
$39$	0.897916	+	5.01934i	0.143782	+	0.803737i
$40$	−8.05217			−1.27316
$41$	4.87756	−	8.44819i	0.761747	−	1.31939i	−0.180202	−	0.983630i	$-0.557675\pi$
$41$	4.87756	−	8.44819i	0.761747	−	1.31939i	0.941949	−	0.335755i	$-0.108992\pi$
$42$		0			0
$43$	0.897916	+	1.55524i	0.136931	+	0.237171i	0.926333	−	0.376705i	$-0.122943\pi$
$43$	0.897916	+	1.55524i	0.136931	+	0.237171i	−0.789403	+	0.613876i	$0.789610\pi$
$44$	−5.79583			−0.873754
$45$	1.34203	+	2.32446i	0.200058	+	0.346510i
$46$	−0.897916	−	1.55524i	−0.132390	−	0.229307i
$47$	−2.82843			−0.412568			−0.206284	−	0.978492i	$-0.566137\pi$
$47$	−2.82843			−0.412568			−0.206284	+	0.978492i	$0.566137\pi$
$48$	−0.707107	−	1.22474i	−0.102062	−	0.176777i
$49$		0			0
$50$	−1.10208	+	1.90887i	−0.155858	+	0.269954i
$51$	7.79583			1.09163
$52$	−3.39116	−	1.22474i	−0.470270	−	0.169842i
$53$	6.59166			0.905435			0.452717	−	0.891654i	$-0.350455\pi$
$53$	6.59166			0.905435			0.452717	+	0.891654i	$0.350455\pi$
$54$	−2.82843	+	4.89898i	−0.384900	+	0.666667i
$55$	−7.77817	+	13.4722i	−1.04881	+	1.81659i
$56$		0			0
$57$	−4.00000			−0.529813
$58$	4.39792	+	7.61741i	0.577475	+	1.00022i
$59$	0.562738	+	0.974691i	0.0732622	+	0.126894i	0.900329	−	0.435209i	$-0.143326\pi$
$59$	0.562738	+	0.974691i	0.0732622	+	0.126894i	−0.827067	+	0.562103i	$0.809992\pi$
$60$	3.79583			0.490040
$61$	0.779291	+	1.34977i	0.0997780	+	0.172821i	0.911593	−	0.411095i	$-0.134853\pi$
$61$	0.779291	+	1.34977i	0.0997780	+	0.172821i	−0.811815	+	0.583915i	$0.801520\pi$
$62$	−0.707107	+	1.22474i	−0.0898027	+	0.155543i
$63$		0			0
$64$	7.00000			0.875000
$65$	−7.39792	+	6.23899i	−0.917599	+	0.773852i
$66$	−8.19654			−1.00892
$67$	−2.89792	+	5.01934i	−0.354037	+	0.613210i	−0.986953	−	0.161011i	$-0.948525\pi$
$67$	−2.89792	+	5.01934i	−0.354037	+	0.613210i	0.632916	+	0.774221i	$0.281858\pi$
$68$	−2.75624	+	4.77395i	−0.334244	+	0.578927i
$69$	1.26984	+	2.19944i	0.152871	+	0.264781i
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−1.50000	−	2.59808i	−0.176777	−	0.306186i
$73$	5.80122			0.678982			0.339491	−	0.940609i	$-0.389745\pi$
$73$	5.80122			0.678982			0.339491	+	0.940609i	$0.389745\pi$
$74$	3.39792	+	5.88536i	0.395000	+	0.684160i
$75$	1.55858	−	2.69954i	0.179970	−	0.311716i
$76$	1.41421	−	2.44949i	0.162221	−	0.280976i
$77$		0			0
$78$	−4.79583	−	1.73205i	−0.543021	−	0.196116i
$79$	−11.7958			−1.32713			−0.663567	−	0.748117i	$-0.730958\pi$
$79$	−11.7958			−1.32713			−0.663567	+	0.748117i	$0.730958\pi$
$80$	1.34203	−	2.32446i	0.150043	−	0.259883i
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	4.87756	+	8.44819i	0.538637	+	0.932946i
$83$	9.89949			1.08661			0.543305	−	0.839535i	$-0.317173\pi$
$83$	9.89949			1.08661			0.543305	+	0.839535i	$0.317173\pi$
$84$		0			0
$85$	7.39792	+	12.8136i	0.802417	+	1.38983i
$86$	−1.79583			−0.193649
$87$	−6.21959	−	10.7726i	−0.666810	−	1.15495i
$88$	8.69375	−	15.0580i	0.926757	−	1.60519i
$89$	6.07522	−	10.5226i	0.643972	−	1.11539i	−0.340565	−	0.940221i	$-0.610618\pi$
$89$	6.07522	−	10.5226i	0.643972	−	1.11539i	0.984538	−	0.175172i	$-0.0560482\pi$
$90$	−2.68406			−0.282925
$91$		0			0
$92$	−1.79583			−0.187228
$93$	1.00000	−	1.73205i	0.103695	−	0.179605i
$94$	1.41421	−	2.44949i	0.145865	−	0.252646i
$95$	−3.79583	−	6.57457i	−0.389444	−	0.674537i
$96$	−7.07107			−0.721688
$97$	−2.12132	−	3.67423i	−0.215387	−	0.373062i	0.738005	−	0.674795i	$-0.235768\pi$
$97$	−2.12132	−	3.67423i	−0.215387	−	0.373062i	−0.953392	+	0.301733i	$0.902435\pi$
$98$		0			0
$99$	−5.79583			−0.582503
$100$	1.10208	+	1.90887i	0.110208	+	0.190887i
$101$	−1.48640	+	2.57452i	−0.147902	+	0.256174i	−0.930452	−	0.366414i	$-0.880585\pi$
$101$	−1.48640	+	2.57452i	−0.147902	+	0.256174i	0.782550	+	0.622588i	$0.213919\pi$
$102$	−3.89792	+	6.75139i	−0.385951	+	0.668487i
$103$	8.19654			0.807629			0.403815	−	0.914841i	$-0.367684\pi$
$103$	8.19654			0.807629			0.403815	+	0.914841i	$0.367684\pi$
$104$	8.26873	−	6.97339i	0.810815	−	0.683797i
$105$		0			0
$106$	−3.29583	+	5.70855i	−0.320119	+	0.554463i
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	−0.683793	−	0.729676i	$-0.739671\pi$
$107$	3.00000	−	5.19615i	0.290021	−	0.502331i	0.973814	+	0.227345i	$0.0730044\pi$
$108$	2.82843	+	4.89898i	0.272166	+	0.471405i
$109$	−17.5917			−1.68498			−0.842488	−	0.538715i	$-0.818910\pi$
$109$	−17.5917			−1.68498			−0.842488	+	0.538715i	$0.818910\pi$
$110$	−7.77817	−	13.4722i	−0.741620	−	1.28452i
$111$	−4.80538	−	8.32316i	−0.456106	−	0.789999i
$112$		0			0
$113$	8.29583	+	14.3688i	0.780406	+	1.35170i	0.931705	+	0.363215i	$0.118321\pi$
$113$	8.29583	+	14.3688i	0.780406	+	1.35170i	−0.151299	+	0.988488i	$0.548346\pi$
$114$	2.00000	−	3.46410i	0.187317	−	0.324443i
$115$	−2.41006	+	4.17434i	−0.224739	+	0.389260i
$116$	8.79583			0.816672
$117$	−3.39116	−	1.22474i	−0.313513	−	0.113228i
$118$	−1.12548			−0.103608
$119$		0			0
$120$	−5.69375	+	9.86186i	−0.519766	+	0.900260i
$121$	−11.2958	−	19.5650i	−1.02689	−	1.77863i
$122$	−1.55858			−0.141107
$123$	−6.89792	−	11.9475i	−0.621964	−	1.07727i
$124$	0.707107	+	1.22474i	0.0635001	+	0.109985i
$125$	−7.50417			−0.671194
$126$		0			0
$127$	−3.79583	+	6.57457i	−0.336826	+	0.583399i	−0.983834	−	0.179084i	$-0.942687\pi$
$127$	−3.79583	+	6.57457i	−0.336826	+	0.583399i	0.647008	+	0.762483i	$0.276020\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$	2.53969			0.223607
$130$	−1.70417	−	9.52628i	−0.149465	−	0.835510i
$131$	8.19654			0.716135			0.358068	−	0.933696i	$-0.383436\pi$
$131$	8.19654			0.716135			0.358068	+	0.933696i	$0.383436\pi$
$132$	−4.09827	+	7.09841i	−0.356709	+	0.617838i
$133$		0			0
$134$	−2.89792	−	5.01934i	−0.250342	−	0.433605i
$135$	15.1833			1.30677
$136$	−8.26873	−	14.3219i	−0.709038	−	1.22809i
$137$	4.60208	+	7.97104i	0.393183	+	0.681012i	0.992867	−	0.119224i	$-0.0380407\pi$
$137$	4.60208	+	7.97104i	0.393183	+	0.681012i	−0.599685	+	0.800236i	$0.704707\pi$
$138$	−2.53969			−0.216193
$139$	−7.63381	−	13.2221i	−0.647491	−	1.12149i	−0.983720	−	0.179707i	$-0.942485\pi$
$139$	−7.63381	−	13.2221i	−0.647491	−	1.12149i	0.336229	−	0.941780i	$-0.390848\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$	6.00000			0.503509
$143$	−3.67990	−	20.5706i	−0.307729	−	1.72020i
$144$	1.00000			0.0833333
$145$	11.8043	−	20.4456i	0.980291	−	1.69791i
$146$	−2.90061	+	5.02401i	−0.240056	+	0.415790i
$147$		0			0
$148$	6.79583			0.558614
$149$	−2.29583	−	3.97650i	−0.188082	−	0.325767i	0.756529	−	0.653960i	$-0.226894\pi$
$149$	−2.29583	−	3.97650i	−0.188082	−	0.325767i	−0.944611	+	0.328193i	$0.893560\pi$
$150$	1.55858	+	2.69954i	0.127258	+	0.220417i
$151$	−17.5917			−1.43159			−0.715795	−	0.698311i	$-0.753935\pi$
$151$	−17.5917			−1.43159			−0.715795	+	0.698311i	$0.753935\pi$
$152$	4.24264	+	7.34847i	0.344124	+	0.596040i
$153$	−2.75624	+	4.77395i	−0.222829	+	0.385951i
$154$		0			0
$155$	3.79583			0.304889
$156$	−3.89792	+	3.28729i	−0.312083	+	0.263194i
$157$	6.92670			0.552811			0.276405	−	0.961041i	$-0.410857\pi$
$157$	6.92670			0.552811			0.276405	+	0.961041i	$0.410857\pi$
$158$	5.89792	−	10.2155i	0.469213	−	0.812701i
$159$	4.66101	−	8.07311i	0.369642	−	0.640239i
$160$	−6.71015	−	11.6223i	−0.530484	−	0.918825i
$161$		0			0
$162$	2.50000	+	4.33013i	0.196419	+	0.340207i
$163$	6.69375	+	11.5939i	0.524295	+	0.908105i	0.999600	+	0.0282841i	$0.00900432\pi$
$163$	6.69375	+	11.5939i	0.524295	+	0.908105i	−0.475305	+	0.879821i	$0.657662\pi$
$164$	9.75513			0.761747
$165$	11.0000	+	19.0526i	0.856349	+	1.48324i
$166$	−4.94975	+	8.57321i	−0.384175	+	0.665410i
$167$	7.63381	−	13.2221i	0.590722	−	1.02316i	−0.403414	−	0.915018i	$-0.632176\pi$
$167$	7.63381	−	13.2221i	0.590722	−	1.02316i	0.994135	−	0.108142i	$-0.0344902\pi$
$168$		0			0
$169$	2.19375	−	12.8136i	0.168750	−	0.985659i
$170$	−14.7958			−1.13479
$171$	1.41421	−	2.44949i	0.108148	−	0.187317i
$172$	−0.897916	+	1.55524i	−0.0684654	+	0.118586i
$173$	4.66101	+	8.07311i	0.354370	+	0.613787i	0.987010	−	0.160659i	$-0.0513620\pi$
$173$	4.66101	+	8.07311i	0.354370	+	0.613787i	−0.632640	+	0.774446i	$0.718029\pi$
$174$	12.4392			0.943012
$175$		0			0
$176$	2.89792	+	5.01934i	0.218439	+	0.378347i
$177$	1.59166			0.119637
$178$	6.07522	+	10.5226i	0.455357	+	0.788702i
$179$	0.204168	−	0.353630i	0.0152603	−	0.0264316i	−0.858294	−	0.513158i	$-0.828476\pi$
$179$	0.204168	−	0.353630i	0.0152603	−	0.0264316i	0.873555	+	0.486726i	$0.161809\pi$
$180$	−1.34203	+	2.32446i	−0.100029	+	0.173255i
$181$	16.5375			1.22922			0.614610	−	0.788831i	$-0.289314\pi$
$181$	16.5375			1.22922			0.614610	+	0.788831i	$0.289314\pi$
$182$		0			0
$183$	2.20417			0.162937
$184$	2.69375	−	4.66571i	0.198586	−	0.343960i
$185$	9.12020	−	15.7967i	0.670531	−	1.16139i
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	−31.9494			−2.33637
$188$	−1.41421	−	2.44949i	−0.103142	−	0.178647i
$189$		0			0
$190$	7.59166			0.550757
$191$	12.8979	+	22.3398i	0.933260	+	1.61645i	0.777707	+	0.628627i	$0.216383\pi$
$191$	12.8979	+	22.3398i	0.933260	+	1.61645i	0.155553	+	0.987827i	$0.450284\pi$
$192$	4.94975	−	8.57321i	0.357217	−	0.618718i
$193$	−1.70417	+	2.95171i	−0.122669	+	0.212468i	−0.920819	−	0.389990i	$-0.872479\pi$
$193$	−1.70417	+	2.95171i	−0.122669	+	0.212468i	0.798151	+	0.602458i	$0.205812\pi$
$194$	4.24264			0.304604
$195$	2.41006	+	13.4722i	0.172588	+	0.964764i
$196$		0			0
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	−0.687618	−	0.726073i	$-0.741344\pi$
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	0.972606	+	0.232458i	$0.0746770\pi$
$198$	2.89792	−	5.01934i	0.205946	−	0.356709i
$199$	−11.0250	−	19.0958i	−0.781539	−	1.35367i	−0.931045	−	0.364905i	$-0.881101\pi$
$199$	−11.0250	−	19.0958i	−0.781539	−	1.35367i	0.149505	−	0.988761i	$-0.452232\pi$
$200$	−6.61251			−0.467575
$201$	4.09827	+	7.09841i	0.289070	+	0.500684i
$202$	−1.48640	−	2.57452i	−0.104583	−	0.181142i
$203$		0			0
$204$	3.89792	+	6.75139i	0.272909	+	0.472692i
$205$	13.0917	−	22.6754i	0.914361	−	1.58372i
$206$	−4.09827	+	7.09841i	−0.285540	+	0.494570i
$207$	−1.79583			−0.124819
$208$	0.634922	+	3.54921i	0.0440239	+	0.246093i
$209$	16.3931			1.13393
$210$		0			0
$211$	0.897916	−	1.55524i	0.0618151	−	0.107067i	−0.833462	−	0.552577i	$-0.813644\pi$
$211$	0.897916	−	1.55524i	0.0618151	−	0.107067i	0.895277	+	0.445510i	$0.146978\pi$
$212$	3.29583	+	5.70855i	0.226359	+	0.392065i
$213$	−8.48528			−0.581402
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$	2.41006	+	4.17434i	0.164365	+	0.284688i
$216$	−16.9706			−1.15470
$217$		0			0
$218$	8.79583	−	15.2348i	0.595729	−	1.03183i
$219$	4.10208	−	7.10502i	0.277193	−	0.480113i
$220$	−15.5563			−1.04881
$221$	−18.6937	−	6.75139i	−1.25748	−	0.454148i
$222$	9.61076			0.645032
$223$	−2.82843	+	4.89898i	−0.189405	+	0.328060i	−0.945052	−	0.326920i	$-0.893989\pi$
$223$	−2.82843	+	4.89898i	−0.189405	+	0.328060i	0.755647	+	0.654979i	$0.227323\pi$
$224$		0			0
$225$	1.10208	+	1.90887i	0.0734723	+	0.127258i
$226$	−16.5917			−1.10366
$227$	10.4622	+	18.1211i	0.694403	+	1.20274i	0.970382	+	0.241577i	$0.0776647\pi$
$227$	10.4622	+	18.1211i	0.694403	+	1.20274i	−0.275979	+	0.961164i	$0.589002\pi$
$228$	−2.00000	−	3.46410i	−0.132453	−	0.229416i
$229$	−12.7279			−0.841085			−0.420542	−	0.907273i	$-0.638160\pi$
$229$	−12.7279			−0.841085			−0.420542	+	0.907273i	$0.638160\pi$
$230$	−2.41006	−	4.17434i	−0.158915	−	0.275248i
$231$		0			0
$232$	−13.1937	+	22.8522i	−0.866212	+	1.50032i
$233$	−21.1833			−1.38777			−0.693883	−	0.720088i	$-0.744101\pi$
$233$	−21.1833			−1.38777			−0.693883	+	0.720088i	$0.744101\pi$
$234$	2.75624	−	2.32446i	0.180181	−	0.151955i
$235$	−7.59166			−0.495225
$236$	−0.562738	+	0.974691i	−0.0366311	+	0.0634470i
$237$	−8.34091	+	14.4469i	−0.541800	+	0.938426i
$238$		0			0
$239$	−19.7958			−1.28049			−0.640243	−	0.768172i	$-0.721166\pi$
$239$	−19.7958			−1.28049			−0.640243	+	0.768172i	$0.721166\pi$
$240$	−1.89792	−	3.28729i	−0.122510	−	0.212193i
$241$	2.19350	+	3.79926i	0.141296	+	0.244732i	0.927985	−	0.372618i	$-0.121540\pi$
$241$	2.19350	+	3.79926i	0.141296	+	0.244732i	−0.786689	+	0.617350i	$0.788206\pi$
$242$	22.5917			1.45225
$243$	4.94975	+	8.57321i	0.317526	+	0.549972i
$244$	−0.779291	+	1.34977i	−0.0498890	+	0.0864103i
$245$		0			0
$246$	13.7958			0.879590
$247$	9.59166	+	3.46410i	0.610303	+	0.220416i
$248$	−4.24264			−0.269408
$249$	7.00000	−	12.1244i	0.443607	−	0.768350i
$250$	3.75209	−	6.49881i	0.237303	−	0.411021i
$251$	−1.55858	−	2.69954i	−0.0983769	−	0.170394i	0.812636	−	0.582771i	$-0.198032\pi$
$251$	−1.55858	−	2.69954i	−0.0983769	−	0.170394i	−0.911013	+	0.412378i	$0.864698\pi$
$252$		0			0
$253$	−5.20417	−	9.01388i	−0.327183	−	0.566698i
$254$	−3.79583	−	6.57457i	−0.238172	−	0.412525i
$255$	20.9245			1.31034
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	7.70599	−	13.3472i	0.480686	−	0.832573i	−0.519068	−	0.854733i	$-0.673721\pi$
$257$	7.70599	−	13.3472i	0.480686	−	0.832573i	0.999754	+	0.0221596i	$0.00705419\pi$
$258$	−1.26984	+	2.19944i	−0.0790571	+	0.136931i
$259$		0			0
$260$	−9.10208	−	3.28729i	−0.564487	−	0.203869i
$261$	8.79583			0.544448
$262$	−4.09827	+	7.09841i	−0.253192	+	0.438542i
$263$	12.6937	−	21.9862i	0.782730	−	1.35573i	−0.147616	−	0.989045i	$-0.547160\pi$
$263$	12.6937	−	21.9862i	0.782730	−	1.35573i	0.930346	−	0.366683i	$-0.119507\pi$
$264$	−12.2948	−	21.2952i	−0.756694	−	1.31063i
$265$	17.6924			1.08684
$266$		0			0
$267$	−8.59166	−	14.8812i	−0.525801	−	0.910714i
$268$	−5.79583			−0.354037
$269$	−0.562738	−	0.974691i	−0.0343107	−	0.0594279i	0.848360	−	0.529420i	$-0.177590\pi$
$269$	−0.562738	−	0.974691i	−0.0343107	−	0.0594279i	−0.882671	+	0.469992i	$0.844257\pi$
$270$	−7.59166	+	13.1491i	−0.462014	+	0.800232i
$271$	−11.5877	+	20.0705i	−0.703903	+	1.21920i	0.263183	+	0.964746i	$0.415228\pi$
$271$	−11.5877	+	20.0705i	−0.703903	+	1.21920i	−0.967086	+	0.254450i	$0.918106\pi$
$272$	5.51249			0.334244
$273$		0			0
$274$	−9.20417			−0.556044
$275$	−6.38749	+	11.0635i	−0.385180	+	0.667152i
$276$	−1.26984	+	2.19944i	−0.0764357	+	0.132390i
$277$	3.09166	+	5.35492i	0.185760	+	0.321746i	0.943832	−	0.330425i	$-0.107192\pi$
$277$	3.09166	+	5.35492i	0.185760	+	0.321746i	−0.758072	+	0.652170i	$0.773859\pi$
$278$	15.2676			0.915690
$279$	0.707107	+	1.22474i	0.0423334	+	0.0733236i
$280$		0			0
$281$	15.2042			0.907005			0.453502	−	0.891255i	$-0.350174\pi$
$281$	15.2042			0.907005			0.453502	+	0.891255i	$0.350174\pi$
$282$	−2.00000	−	3.46410i	−0.119098	−	0.206284i
$283$	−14.7049	+	25.4696i	−0.874114	+	1.51401i	−0.0164104	+	0.999865i	$0.505224\pi$
$283$	−14.7049	+	25.4696i	−0.874114	+	1.51401i	−0.857704	+	0.514145i	$0.828109\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	−10.7362			−0.635960
$286$	19.6546	+	7.09841i	1.16220	+	0.419738i
$287$		0			0
$288$	2.50000	−	4.33013i	0.147314	−	0.255155i
$289$	−6.69375	+	11.5939i	−0.393750	+	0.681995i
$290$	11.8043	+	20.4456i	0.693170	+	1.20061i
$291$	−6.00000			−0.351726
$292$	2.90061	+	5.02401i	0.169745	+	0.294008i
$293$	−4.87756	−	8.44819i	−0.284950	−	0.493548i	0.687647	−	0.726045i	$-0.258644\pi$
$293$	−4.87756	−	8.44819i	−0.284950	−	0.493548i	−0.972597	+	0.232497i	$0.925310\pi$
$294$		0			0
$295$	1.51042	+	2.61613i	0.0879401	+	0.152317i
$296$	−10.1937	+	17.6561i	−0.592500	+	1.02624i
$297$	−16.3931	+	28.3937i	−0.951223	+	1.64757i
$298$	4.59166			0.265988
$299$	−1.14021	−	6.37378i	−0.0659403	−	0.368605i
$300$	3.11716			0.179970
$301$		0			0
$302$	8.79583	−	15.2348i	0.506143	−	0.876666i
$303$	2.10208	+	3.64092i	0.120762	+	0.209165i
$304$	−2.82843			−0.162221
$305$	2.09166	+	3.62287i	0.119768	+	0.207445i
$306$	−2.75624	−	4.77395i	−0.157564	−	0.272909i
$307$	−34.2004			−1.95192			−0.975960	−	0.217951i	$-0.930063\pi$
$307$	−34.2004			−1.95192			−0.975960	+	0.217951i	$0.930063\pi$
$308$		0			0
$309$	5.79583	−	10.0387i	0.329713	−	0.571080i
$310$	−1.89792	+	3.28729i	−0.107794	+	0.186705i
$311$	−11.8617			−0.672616			−0.336308	−	0.941752i	$-0.609178\pi$
$311$	−11.8617			−0.672616			−0.336308	+	0.941752i	$0.609178\pi$
$312$	−2.69375	−	15.0580i	−0.152503	−	0.852492i
$313$	−1.70295			−0.0962565			−0.0481283	−	0.998841i	$-0.515326\pi$
$313$	−1.70295			−0.0962565			−0.0481283	+	0.998841i	$0.515326\pi$
$314$	−3.46335	+	5.99870i	−0.195448	+	0.338526i
$315$		0			0
$316$	−5.89792	−	10.2155i	−0.331784	−	0.574666i
$317$	−12.5917			−0.707218			−0.353609	−	0.935393i	$-0.615046\pi$
$317$	−12.5917			−0.707218			−0.353609	+	0.935393i	$0.615046\pi$
$318$	4.66101	+	8.07311i	0.261376	+	0.452717i
$319$	25.4896	+	44.1492i	1.42714	+	2.47188i
$320$	18.7884			1.05030
$321$	−4.24264	−	7.34847i	−0.236801	−	0.410152i
$322$		0			0
$323$	7.79583	−	13.5028i	0.433772	−	0.751315i
$324$	5.00000			0.277778
$325$	−6.07522	+	5.12351i	−0.336993	+	0.284201i
$326$	−13.3875			−0.741465
$327$	−12.4392	+	21.5453i	−0.687888	+	1.19146i
$328$	−14.6327	+	25.3446i	−0.807955	+	1.39942i
$329$		0			0
$330$	−22.0000			−1.21106
$331$	−0.306253	−	0.530445i	−0.0168332	−	0.0291559i	0.857486	−	0.514507i	$-0.172025\pi$
$331$	−0.306253	−	0.530445i	−0.0168332	−	0.0291559i	−0.874319	+	0.485351i	$0.838692\pi$
$332$	4.94975	+	8.57321i	0.271653	+	0.470516i
$333$	6.79583			0.372409
$334$	7.63381	+	13.2221i	0.417703	+	0.723483i
$335$	−7.77817	+	13.4722i	−0.424967	+	0.736065i
$336$		0			0
$337$	−29.9792			−1.63307			−0.816534	−	0.577297i	$-0.804108\pi$
$337$	−29.9792			−1.63307			−0.816534	+	0.577297i	$0.804108\pi$
$338$	10.0000	+	8.30662i	0.543928	+	0.451821i
$339$	23.4642			1.27440
$340$	−7.39792	+	12.8136i	−0.401208	+	0.694913i
$341$	−4.09827	+	7.09841i	−0.221934	+	0.384401i
$342$	1.41421	+	2.44949i	0.0764719	+	0.132453i
$343$		0			0
$344$	−2.69375	−	4.66571i	−0.145237	−	0.251558i
$345$	3.40834	+	5.90341i	0.183499	+	0.317829i
$346$	−9.32202			−0.501155
$347$	−7.48958	−	12.9723i	−0.402062	−	0.696391i	0.591913	−	0.806002i	$-0.298373\pi$
$347$	−7.48958	−	12.9723i	−0.402062	−	0.696391i	−0.993975	+	0.109611i	$0.965040\pi$
$348$	6.21959	−	10.7726i	0.333405	−	0.577475i
$349$	6.50833	−	11.2728i	0.348383	−	0.603417i	−0.637579	−	0.770385i	$-0.720064\pi$
$349$	6.50833	−	11.2728i	0.348383	−	0.603417i	0.985962	+	0.166968i	$0.0533976\pi$
$350$		0			0
$351$	−15.5917	+	13.1491i	−0.832221	+	0.701849i
$352$	28.9792			1.54459
$353$	−7.56162	+	13.0971i	−0.402464	+	0.697089i	−0.994023	−	0.109173i	$-0.965180\pi$
$353$	−7.56162	+	13.0971i	−0.402464	+	0.697089i	0.591558	+	0.806262i	$0.298513\pi$
$354$	−0.795832	+	1.37842i	−0.0422980	+	0.0732622i
$355$	−8.05217	−	13.9468i	−0.427365	−	0.740218i
$356$	12.1504			0.643972
$357$		0			0
$358$	0.204168	+	0.353630i	0.0107906	+	0.0186899i
$359$	−4.00000			−0.211112			−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000			−0.211112			−0.105556	+	0.994413i	$0.533662\pi$
$360$	−4.02609	−	6.97339i	−0.212193	−	0.367530i
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$	−8.26873	+	14.3219i	−0.434595	+	0.752740i
$363$	−31.9494			−1.67691
$364$		0			0
$365$	15.5708			0.815014
$366$	−1.10208	+	1.90887i	−0.0576069	+	0.0997780i
$367$	10.6066	−	18.3712i	0.553660	−	0.958967i	−0.444346	−	0.895855i	$-0.646564\pi$
$367$	10.6066	−	18.3712i	0.553660	−	0.958967i	0.998006	−	0.0631123i	$-0.0201026\pi$
$368$	0.897916	+	1.55524i	0.0468071	+	0.0810723i
$369$	9.75513			0.507832
$370$	9.12020	+	15.7967i	0.474137	+	0.821229i
$371$		0			0
$372$	2.00000			0.103695
$373$	6.29583	+	10.9047i	0.325986	+	0.564624i	0.981711	−	0.190375i	$-0.0609705\pi$
$373$	6.29583	+	10.9047i	0.325986	+	0.564624i	−0.655726	+	0.754999i	$0.727637\pi$
$374$	15.9747	−	27.6690i	0.826033	−	1.43073i
$375$	−5.30625	+	9.19070i	−0.274014	+	0.474606i
$376$	8.48528			0.437595
$377$	5.58467	+	31.2182i	0.287625	+	1.60782i
$378$		0			0
$379$	1.69375	−	2.93366i	0.0870020	−	0.150692i	−0.819241	−	0.573450i	$-0.805605\pi$
$379$	1.69375	−	2.93366i	0.0870020	−	0.150692i	0.906243	+	0.422758i	$0.138938\pi$
$380$	3.79583	−	6.57457i	0.194722	−	0.337268i
$381$	5.36812	+	9.29785i	0.275017	+	0.476343i
$382$	−25.7958			−1.31983
$383$	−7.48944	−	12.9721i	−0.382692	−	0.662843i	0.608754	−	0.793359i	$-0.291670\pi$
$383$	−7.48944	−	12.9721i	−0.382692	−	0.662843i	−0.991446	+	0.130517i	$0.958336\pi$
$384$	−2.12132	−	3.67423i	−0.108253	−	0.187500i
$385$		0			0
$386$	−1.70417	−	2.95171i	−0.0867399	−	0.150238i
$387$	−0.897916	+	1.55524i	−0.0456436	+	0.0790571i
$388$	2.12132	−	3.67423i	0.107694	−	0.186531i
$389$	28.3875			1.43930			0.719652	−	0.694335i	$-0.244302\pi$
$389$	28.3875			1.43930			0.719652	+	0.694335i	$0.244302\pi$
$390$	−12.8723	−	4.64893i	−0.651814	−	0.235407i
$391$	−9.89949			−0.500639
$392$		0			0
$393$	5.79583	−	10.0387i	0.292361	−	0.506384i
$394$	4.00000	+	6.92820i	0.201517	+	0.349038i
$395$	−31.6607			−1.59302
$396$	−2.89792	−	5.01934i	−0.145626	−	0.252231i
$397$	3.53553	+	6.12372i	0.177443	+	0.307341i	0.941004	−	0.338395i	$-0.109884\pi$
$397$	3.53553	+	6.12372i	0.177443	+	0.307341i	−0.763561	+	0.645736i	$0.776551\pi$
$398$	22.0499			1.10526
$399$		0			0
$400$	1.10208	−	1.90887i	0.0551042	−	0.0954433i
$401$	−12.1937	+	21.1202i	−0.608927	+	1.05469i	0.382491	+	0.923959i	$0.375066\pi$
$401$	−12.1937	+	21.1202i	−0.608927	+	1.05469i	−0.991418	+	0.130733i	$0.958267\pi$
$402$	−8.19654			−0.408806
$403$	−3.89792	+	3.28729i	−0.194169	+	0.163751i
$404$	−2.97280			−0.147902
$405$	6.71015	−	11.6223i	0.333430	−	0.577517i
$406$		0			0
$407$	19.6937	+	34.1106i	0.976183	+	1.69080i
$408$	−23.3875			−1.15785
$409$	−14.3440	−	24.8445i	−0.709263	−	1.22848i	−0.965131	−	0.261767i	$-0.915695\pi$
$409$	−14.3440	−	24.8445i	−0.709263	−	1.22848i	0.255868	−	0.966712i	$-0.417639\pi$
$410$	13.0917	+	22.6754i	0.646551	+	1.11986i
$411$	13.0167			0.642064
$412$	4.09827	+	7.09841i	0.201907	+	0.349714i
$413$		0			0
$414$	0.897916	−	1.55524i	0.0441302	−	0.0764357i
$415$	26.5708			1.30431
$416$	16.9558	+	6.12372i	0.831328	+	0.300240i
$417$	−21.5917			−1.05735
$418$	−8.19654	+	14.1968i	−0.400906	+	0.694390i
$419$	14.2718	−	24.7194i	0.697221	−	1.20762i	−0.272205	−	0.962239i	$-0.587753\pi$
$419$	14.2718	−	24.7194i	0.697221	−	1.20762i	0.969426	−	0.245384i	$-0.0789139\pi$
$420$		0			0
$421$	−6.59166			−0.321258			−0.160629	−	0.987015i	$-0.551352\pi$
$421$	−6.59166			−0.321258			−0.160629	+	0.987015i	$0.551352\pi$
$422$	0.897916	+	1.55524i	0.0437099	+	0.0757077i
$423$	−1.41421	−	2.44949i	−0.0687614	−	0.119098i
$424$	−19.7750			−0.960358
$425$	6.07522	+	10.5226i	0.294692	+	0.510421i
$426$	4.24264	−	7.34847i	0.205557	−	0.356034i
$427$		0			0
$428$	6.00000			0.290021
$429$	−27.7958	−	10.0387i	−1.34200	−	0.484672i
$430$	−4.82012			−0.232447
$431$	2.59166	−	4.48889i	0.124836	−	0.216222i	−0.796833	−	0.604200i	$-0.793493\pi$
$431$	2.59166	−	4.48889i	0.124836	−	0.216222i	0.921669	+	0.387978i	$0.126826\pi$
$432$	2.82843	−	4.89898i	0.136083	−	0.235702i
$433$	6.71015	+	11.6223i	0.322469	+	0.558533i	0.980997	−	0.194024i	$-0.0621539\pi$
$433$	6.71015	+	11.6223i	0.322469	+	0.558533i	−0.658528	+	0.752556i	$0.728821\pi$
$434$		0			0
$435$	−16.6937	−	28.9144i	−0.800404	−	1.38634i
$436$	−8.79583	−	15.2348i	−0.421244	−	0.729616i
$437$	5.07938			0.242980
$438$	4.10208	+	7.10502i	0.196005	+	0.339491i
$439$	17.1002	−	29.6184i	0.816148	−	1.41361i	−0.0923531	−	0.995726i	$-0.529439\pi$
$439$	17.1002	−	29.6184i	0.816148	−	1.41361i	0.908501	−	0.417883i	$-0.137228\pi$
$440$	23.3345	−	40.4166i	1.11243	−	1.92678i
$441$		0			0
$442$	15.1937	−	12.8136i	0.722693	−	0.609479i
$443$	10.0000			0.475114			0.237557	−	0.971374i	$-0.423653\pi$
$443$	10.0000			0.475114			0.237557	+	0.971374i	$0.423653\pi$
$444$	4.80538	−	8.32316i	0.228053	−	0.395000i
$445$	16.3063	−	28.2433i	0.772991	−	1.33886i
$446$	−2.82843	−	4.89898i	−0.133930	−	0.231973i
$447$	−6.49359			−0.307136
$448$		0			0
$449$	−2.20417	−	3.81773i	−0.104021	−	0.180170i	0.809317	−	0.587372i	$-0.199838\pi$
$449$	−2.20417	−	3.81773i	−0.104021	−	0.180170i	−0.913338	+	0.407203i	$0.866504\pi$
$450$	−2.20417			−0.103905
$451$	28.2695	+	48.9643i	1.33116	+	2.30564i
$452$	−8.29583	+	14.3688i	−0.390203	+	0.675852i
$453$	−12.4392	+	21.5453i	−0.584444	+	1.01229i
$454$	−20.9245			−0.982034
$455$		0			0
$456$	12.0000			0.561951
$457$	7.29583	−	12.6368i	0.341285	−	0.591122i	−0.643387	−	0.765541i	$-0.722471\pi$
$457$	7.29583	−	12.6368i	0.341285	−	0.591122i	0.984672	+	0.174419i	$0.0558047\pi$
$458$	6.36396	−	11.0227i	0.297368	−	0.515057i
$459$	15.5917	+	27.0056i	0.727757	+	1.26051i
$460$	−4.82012			−0.224739
$461$	15.4842	+	26.8194i	0.721169	+	1.24910i	0.960531	+	0.278172i	$0.0897284\pi$
$461$	15.4842	+	26.8194i	0.721169	+	1.24910i	−0.239362	+	0.970930i	$0.576938\pi$
$462$		0			0
$463$	11.3875			0.529222			0.264611	−	0.964355i	$-0.414756\pi$
$463$	11.3875			0.529222			0.264611	+	0.964355i	$0.414756\pi$
$464$	−4.39792	−	7.61741i	−0.204168	−	0.353630i
$465$	2.68406	−	4.64893i	0.124470	−	0.215589i
$466$	10.5917	−	18.3453i	0.490649	−	0.849830i
$467$	4.82012			0.223048			0.111524	−	0.993762i	$-0.464427\pi$
$467$	4.82012			0.223048			0.111524	+	0.993762i	$0.464427\pi$
$468$	−0.634922	−	3.54921i	−0.0293493	−	0.164062i
$469$		0			0
$470$	3.79583	−	6.57457i	0.175089	−	0.303262i
$471$	4.89792	−	8.48344i	0.225684	−	0.390896i
$472$	−1.68821	−	2.92407i	−0.0777063	−	0.134591i
$473$	−10.4083			−0.478576
$474$	−8.34091	−	14.4469i	−0.383111	−	0.663567i
$475$	−3.11716	−	5.39909i	−0.143025	−	0.247727i
$476$		0			0
$477$	3.29583	+	5.70855i	0.150906	+	0.261376i
$478$	9.89792	−	17.1437i	0.452720	−	0.784134i
$479$	−3.67990	+	6.37378i	−0.168139	+	0.291225i	−0.937766	−	0.347269i	$-0.887109\pi$
$479$	−3.67990	+	6.37378i	−0.168139	+	0.291225i	0.769627	+	0.638494i	$0.220442\pi$
$480$	−18.9792			−0.866276
$481$	4.31483	+	24.1198i	0.196739	+	1.09977i
$482$	−4.38701			−0.199823
$483$		0			0
$484$	11.2958	−	19.5650i	0.513447	−	0.889316i
$485$	−5.69375	−	9.86186i	−0.258540	−	0.447804i
$486$	−9.89949			−0.449050
$487$	−9.79583	−	16.9669i	−0.443891	−	0.768843i	0.554083	−	0.832462i	$-0.313069\pi$
$487$	−9.79583	−	16.9669i	−0.443891	−	0.768843i	−0.997974	+	0.0636190i	$0.979736\pi$
$488$	−2.33787	−	4.04932i	−0.105831	−	0.183304i
$489$	18.9328			0.856170
$490$		0			0
$491$	4.79583	−	8.30662i	0.216433	−	0.374873i	−0.737282	−	0.675585i	$-0.763891\pi$
$491$	4.79583	−	8.30662i	0.216433	−	0.374873i	0.953715	+	0.300712i	$0.0972244\pi$
$492$	6.89792	−	11.9475i	0.310982	−	0.538637i
$493$	48.4869			2.18374
$494$	−7.79583	+	6.57457i	−0.350751	+	0.295804i
$495$	−15.5563			−0.699206
$496$	0.707107	−	1.22474i	0.0317500	−	0.0549927i
$497$		0			0
$498$	7.00000	+	12.1244i	0.313678	+	0.543305i
$499$	16.2042			0.725398			0.362699	−	0.931906i	$-0.381855\pi$
$499$	16.2042			0.725398			0.362699	+	0.931906i	$0.381855\pi$
$500$	−3.75209	−	6.49881i	−0.167798	−	0.290635i
$501$	−10.7958	−	18.6989i	−0.482322	−	0.835407i
$502$	3.11716			0.139126
$503$	−14.2718	−	24.7194i	−0.636347	−	1.10218i	−0.986228	−	0.165391i	$-0.947111\pi$
$503$	−14.2718	−	24.7194i	−0.636347	−	1.10218i	0.349881	−	0.936794i	$-0.386222\pi$
$504$		0			0
$505$	−3.98958	+	6.91015i	−0.177534	+	0.307498i
$506$	10.4083			0.462707
$507$	−14.1421	−	11.7473i	−0.628074	−	0.521718i
$508$	−7.59166			−0.336826
$509$	13.2185	−	22.8951i	0.585899	−	1.01481i	−0.408864	−	0.912595i	$-0.634075\pi$
$509$	13.2185	−	22.8951i	0.585899	−	1.01481i	0.994763	−	0.102211i	$-0.0325917\pi$
$510$	−10.4622	+	18.1211i	−0.463275	+	0.802417i
$511$		0			0
$512$	−11.0000			−0.486136
$513$	−8.00000	−	13.8564i	−0.353209	−	0.611775i
$514$	7.70599	+	13.3472i	0.339897	+	0.588718i
$515$	22.0000			0.969436
$516$	1.26984	+	2.19944i	0.0559018	+	0.0968247i
$517$	8.19654	−	14.1968i	0.360484	−	0.624376i
$518$		0			0
$519$	13.1833			0.578684
$520$	22.1937	−	18.7170i	0.973260	−	0.820794i
$521$	−25.0227			−1.09627			−0.548133	−	0.836391i	$-0.684661\pi$
$521$	−25.0227			−1.09627			−0.548133	+	0.836391i	$0.684661\pi$
$522$	−4.39792	+	7.61741i	−0.192492	+	0.333405i
$523$	14.2865	−	24.7450i	0.624705	−	1.08202i	−0.363893	−	0.931441i	$-0.618552\pi$
$523$	14.2865	−	24.7450i	0.624705	−	1.08202i	0.988598	−	0.150580i	$-0.0481142\pi$
$524$	4.09827	+	7.09841i	0.179034	+	0.310096i
$525$		0			0
$526$	12.6937	+	21.9862i	0.553474	+	0.958645i
$527$	3.89792	+	6.75139i	0.169796	+	0.294095i
$528$	8.19654			0.356709
$529$	9.88749	+	17.1256i	0.429891	+	0.744593i
$530$	−8.84620	+	15.3221i	−0.384255	+	0.665548i
$531$	−0.562738	+	0.974691i	−0.0244207	+	0.0422980i
$532$		0			0
$533$	6.19375	+	34.6230i	0.268281	+	1.49969i
$534$	17.1833			0.743595
$535$	8.05217	−	13.9468i	0.348126	−	0.602972i
$536$	8.69375	−	15.0580i	0.375513	−	0.650407i
$537$	−0.288738	−	0.500109i	−0.0124600	−	0.0215813i
$538$	1.12548			0.0485227
$539$		0			0
$540$	7.59166	+	13.1491i	0.326693	+	0.565849i
$541$	−12.5917			−0.541358			−0.270679	−	0.962670i	$-0.587248\pi$
$541$	−12.5917			−0.541358			−0.270679	+	0.962670i	$0.587248\pi$
$542$	−11.5877	−	20.0705i	−0.497735	−	0.862102i
$543$	11.6937	−	20.2542i	0.501827	−	0.869189i
$544$	13.7812	−	23.8698i	0.590865	−	1.02341i
$545$	−47.2170			−2.02256
$546$		0			0
$547$	−36.9792			−1.58111			−0.790557	−	0.612388i	$-0.790209\pi$
$547$	−36.9792			−1.58111			−0.790557	+	0.612388i	$0.790209\pi$
$548$	−4.60208	+	7.97104i	−0.196591	+	0.340506i
$549$	−0.779291	+	1.34977i	−0.0332593	+	0.0576069i
$550$	−6.38749	−	11.0635i	−0.272364	−	0.471748i
$551$	−24.8784			−1.05985
$552$	−3.80953	−	6.59831i	−0.162145	−	0.280843i
$553$		0			0
$554$	−6.18333			−0.262704
$555$	−12.8979	−	22.3398i	−0.547486	−	0.948274i
$556$	7.63381	−	13.2221i	0.323745	−	0.560744i
$557$	−10.2958	+	17.8329i	−0.436248	+	0.755604i	−0.997397	−	0.0721110i	$-0.977026\pi$
$557$	−10.2958	+	17.8329i	−0.436248	+	0.755604i	0.561148	+	0.827715i	$0.310360\pi$
$558$	−1.41421			−0.0598684
$559$	−6.08996	−	2.19944i	−0.257578	−	0.0930262i
$560$		0			0
$561$	−22.5917	+	39.1299i	−0.953821	+	1.65207i
$562$	−7.60208	+	13.1672i	−0.320675	+	0.555425i
$563$	−0.562738	−	0.974691i	−0.0237166	−	0.0410783i	0.853924	−	0.520399i	$-0.174217\pi$
$563$	−0.562738	−	0.974691i	−0.0237166	−	0.0410783i	−0.877640	+	0.479320i	$0.840883\pi$
$564$	−4.00000			−0.168430
$565$	22.2665	+	38.5667i	0.936758	+	1.62251i
$566$	−14.7049	−	25.4696i	−0.618092	−	1.07057i
$567$		0			0
$568$	9.00000	+	15.5885i	0.377632	+	0.654077i
$569$	−3.20417	+	5.54978i	−0.134326	+	0.232659i	−0.925340	−	0.379139i	$-0.876220\pi$
$569$	−3.20417	+	5.54978i	−0.134326	+	0.232659i	0.791014	+	0.611798i	$0.209554\pi$
$570$	5.36812	−	9.29785i	0.224846	−	0.389444i
$571$	15.1833			0.635402			0.317701	−	0.948191i	$-0.397089\pi$
$571$	15.1833			0.635402			0.317701	+	0.948191i	$0.397089\pi$
$572$	15.9747	−	13.4722i	0.667937	−	0.563301i
$573$	36.4808			1.52401
$574$		0			0
$575$	−1.97916	+	3.42800i	−0.0825366	+	0.142958i
$576$	3.50000	+	6.06218i	0.145833	+	0.252591i
$577$	9.17765			0.382071			0.191035	−	0.981583i	$-0.438816\pi$
$577$	9.17765			0.382071			0.191035	+	0.981583i	$0.438816\pi$
$578$	−6.69375	−	11.5939i	−0.278423	−	0.482243i
$579$	2.41006	+	4.17434i	0.100159	+	0.173480i
$580$	23.6085			0.980291
$581$		0			0
$582$	3.00000	−	5.19615i	0.124354	−	0.215387i
$583$	−19.1021	+	33.0858i	−0.791127	+	1.37027i
$584$	−17.4037			−0.720169
$585$	−9.10208	−	3.28729i	−0.376325	−	0.135913i
$586$	9.75513			0.402981
$587$	1.55858	−	2.69954i	0.0643296	−	0.111422i	−0.832067	−	0.554675i	$-0.812842\pi$
$587$	1.55858	−	2.69954i	0.0643296	−	0.111422i	0.896396	+	0.443253i	$0.146176\pi$
$588$		0			0
$589$	−2.00000	−	3.46410i	−0.0824086	−	0.142736i
$590$	−3.02084			−0.124366
$591$	−5.65685	−	9.79796i	−0.232692	−	0.403034i
$592$	−3.39792	−	5.88536i	−0.139653	−	0.241887i
$593$	1.55858			0.0640033			0.0320017	−	0.999488i	$-0.489812\pi$
$593$	1.55858			0.0640033			0.0320017	+	0.999488i	$0.489812\pi$
$594$	−16.3931	−	28.3937i	−0.672617	−	1.16501i
$595$		0			0
$596$	2.29583	−	3.97650i	0.0940409	−	0.162884i
$597$	−31.1833			−1.27625
$598$	6.08996	+	2.19944i	0.249037	+	0.0899416i
$599$	−14.4083			−0.588709			−0.294354	−	0.955696i	$-0.595105\pi$
$599$	−14.4083			−0.588709			−0.294354	+	0.955696i	$0.595105\pi$
$600$	−4.67575	+	8.09863i	−0.190887	+	0.330625i
$601$	−15.4842	+	26.8194i	−0.631612	+	1.09398i	0.355610	+	0.934634i	$0.384273\pi$
$601$	−15.4842	+	26.8194i	−0.631612	+	1.09398i	−0.987222	+	0.159350i	$0.949060\pi$
$602$		0			0
$603$	−5.79583			−0.236025
$604$	−8.79583	−	15.2348i	−0.357897	−	0.619896i
$605$	−30.3187	−	52.5135i	−1.23263	−	2.13498i
$606$	−4.20417			−0.170783
$607$	−17.9517	−	31.0932i	−0.728636	−	1.26203i	−0.957460	−	0.288566i	$-0.906821\pi$
$607$	−17.9517	−	31.0932i	−0.728636	−	1.26203i	0.228824	−	0.973468i	$-0.426512\pi$
$608$	−7.07107	+	12.2474i	−0.286770	+	0.496700i
$609$		0			0
$610$	−4.18333			−0.169378
$611$	7.79583	−	6.57457i	0.315386	−	0.265979i
$612$	−5.51249			−0.222829
$613$	2.98958	−	5.17810i	0.120748	−	0.209142i	−0.799315	−	0.600912i	$-0.794804\pi$
$613$	2.98958	−	5.17810i	0.120748	−	0.209142i	0.920063	+	0.391771i	$0.128137\pi$
$614$	17.1002	−	29.6184i	0.690108	−	1.19530i
$615$	−18.5144	−	32.0679i	−0.746573	−	1.29310i
$616$		0			0
$617$	12.1937	+	21.1202i	0.490902	+	0.850267i	0.999945	−	0.0104740i	$-0.00333405\pi$
$617$	12.1937	+	21.1202i	0.490902	+	0.850267i	−0.509043	+	0.860741i	$0.670001\pi$
$618$	5.79583	+	10.0387i	0.233143	+	0.403815i
$619$	−33.9116			−1.36302			−0.681512	−	0.731807i	$-0.738677\pi$
$619$	−33.9116			−1.36302			−0.681512	+	0.731807i	$0.738677\pi$
$620$	1.89792	+	3.28729i	0.0762221	+	0.132021i
$621$	−5.07938	+	8.79774i	−0.203828	+	0.353041i
$622$	5.93085	−	10.2725i	0.237806	−	0.411891i
$623$		0			0
$624$	4.79583	+	1.73205i	0.191987	+	0.0693375i
$625$	−31.1625			−1.24650
$626$	0.851476	−	1.47480i	0.0340318	−	0.0589448i
$627$	11.5917	−	20.0773i	0.462926	−	0.801812i
$628$	3.46335	+	5.99870i	0.138203	+	0.239374i
$629$	37.4619			1.49370
$630$		0			0
$631$	10.2042	+	17.6741i	0.406222	+	0.703596i	0.994463	−	0.105089i	$-0.0335128\pi$
$631$	10.2042	+	17.6741i	0.406222	+	0.703596i	−0.588241	+	0.808685i	$0.700179\pi$
$632$	35.3875			1.40764
$633$	−1.26984	−	2.19944i	−0.0504718	−	0.0874197i
$634$	6.29583	−	10.9047i	0.250039	−	0.433081i
$635$	−10.1882	+	17.6465i	−0.404308	+	0.700281i
$636$	9.32202			0.369642
$637$		0			0
$638$	−50.9792			−2.01828
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$	4.02609	−	6.97339i	0.159145	−	0.275647i
$641$	−2.39792	−	4.15331i	−0.0947120	−	0.164046i	0.814776	−	0.579775i	$-0.196860\pi$
$641$	−2.39792	−	4.15331i	−0.0947120	−	0.164046i	−0.909488	+	0.415729i	$0.863526\pi$
$642$	8.48528			0.334887
$643$	2.82843	+	4.89898i	0.111542	+	0.193197i	0.916392	−	0.400281i	$-0.131088\pi$
$643$	2.82843	+	4.89898i	0.111542	+	0.193197i	−0.804850	+	0.593478i	$0.797754\pi$
$644$		0			0
$645$	6.81667			0.268406
$646$	7.79583	+	13.5028i	0.306723	+	0.531260i
$647$	−0.981107	+	1.69933i	−0.0385713	+	0.0668074i	−0.884667	−	0.466224i	$-0.845614\pi$
$647$	−0.981107	+	1.69933i	−0.0385713	+	0.0668074i	0.846095	+	0.533032i	$0.178947\pi$
$648$	−7.50000	+	12.9904i	−0.294628	+	0.510310i
$649$	−6.52307			−0.256053
$650$	−1.39948	−	7.82305i	−0.0548920	−	0.306845i
$651$		0			0
$652$	−6.69375	+	11.5939i	−0.262147	+	0.454053i
$653$	−12.5917	+	21.8094i	−0.492750	+	0.853468i	−0.999965	−	0.00835161i	$-0.997342\pi$
$653$	−12.5917	+	21.8094i	−0.492750	+	0.853468i	0.507215	+	0.861819i	$0.330675\pi$
$654$	−12.4392	−	21.5453i	−0.486411	−	0.842488i
$655$	22.0000			0.859611
$656$	−4.87756	−	8.44819i	−0.190437	−	0.329846i
$657$	2.90061	+	5.02401i	0.113164	+	0.196005i
$658$		0			0
$659$	18.7958	+	32.5553i	0.732182	+	1.26818i	0.955949	+	0.293533i	$0.0948311\pi$
$659$	18.7958	+	32.5553i	0.732182	+	1.26818i	−0.223767	+	0.974643i	$0.571836\pi$
$660$	−11.0000	+	19.0526i	−0.428174	+	0.741620i
$661$	13.9256	−	24.1198i	0.541642	−	0.938152i	−0.457168	−	0.889381i	$-0.651136\pi$
$661$	13.9256	−	24.1198i	0.541642	−	0.938152i	0.998810	−	0.0487715i	$-0.0155306\pi$
$662$	0.612505			0.0238057
$663$	−21.4872	+	18.1211i	−0.834494	+	0.703766i
$664$	−29.6985			−1.15252
$665$		0			0
$666$	−3.39792	+	5.88536i	−0.131667	+	0.228053i
$667$	7.89792	+	13.6796i	0.305809	+	0.529676i
$668$	15.2676			0.590722
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$	−7.77817	−	13.4722i	−0.300497	−	0.520476i
$671$	−9.03328			−0.348726
$672$		0			0
$673$	−11.9896	+	20.7666i	−0.462164	+	0.800492i	−0.999069	−	0.0431511i	$-0.986260\pi$
$673$	−11.9896	+	20.7666i	−0.462164	+	0.800492i	0.536904	+	0.843643i	$0.319594\pi$
$674$	14.9896	−	25.9627i	0.577377	−	1.00005i
$675$	12.4687			0.479919
$676$	12.1937	−	4.50694i	0.468990	−	0.173344i
$677$	−34.7779			−1.33662			−0.668311	−	0.743882i	$-0.732982\pi$
$677$	−34.7779			−1.33662			−0.668311	+	0.743882i	$0.732982\pi$
$678$	−11.7321	+	20.3206i	−0.450568	+	0.780406i
$679$		0			0
$680$	−22.1937	−	38.4407i	−0.851091	−	1.47413i
$681$	29.5917			1.13395
$682$	−4.09827	−	7.09841i	−0.156931	−	0.271812i
$683$	−25.3875	−	43.9724i	−0.971425	−	1.68256i	−0.691259	−	0.722607i	$-0.742944\pi$
$683$	−25.3875	−	43.9724i	−0.971425	−	1.68256i	−0.280166	−	0.959952i	$-0.590390\pi$
$684$	2.82843			0.108148
$685$	12.3523	+	21.3947i	0.471956	+	0.817451i
$686$		0			0
$687$	−9.00000	+	15.5885i	−0.343371	+	0.594737i
$688$	1.79583			0.0684654
$689$	−18.1682	+	15.3221i	−0.692154	+	0.583725i
$690$	−6.81667			−0.259506
$691$	5.51249	−	9.54790i	0.209705	−	0.363219i	−0.741917	−	0.670492i	$-0.766083\pi$
$691$	5.51249	−	9.54790i	0.209705	−	0.363219i	0.951622	+	0.307273i	$0.0994164\pi$
$692$	−4.66101	+	8.07311i	−0.177185	+	0.306893i
$693$		0			0
$694$	14.9792			0.568601
$695$	−20.4896	−	35.4890i	−0.777214	−	1.34617i
$696$	18.6588	+	32.3179i	0.707259	+	1.22501i
$697$	53.7750			2.03687
$698$	6.50833	+	11.2728i	0.246344	+	0.426680i
$699$	−14.9789	+	25.9442i	−0.566553	+	0.981299i
$700$		0			0
$701$	−10.4083			−0.393117			−0.196559	−	0.980492i	$-0.562977\pi$
$701$	−10.4083			−0.393117			−0.196559	+	0.980492i	$0.562977\pi$
$702$	−3.59166	−	20.0773i	−0.135559	−	0.757771i
$703$	−19.2215			−0.724953
$704$	−20.2854	+	35.1354i	−0.764535	+	1.32421i
$705$	−5.36812	+	9.29785i	−0.202175	+	0.350177i
$706$	−7.56162	−	13.0971i	−0.284585	−	0.492916i
$707$		0			0
$708$	0.795832	+	1.37842i	0.0299092	+	0.0518042i
$709$	9.39792	+	16.2777i	0.352946	+	0.611321i	0.986764	−	0.162162i	$-0.0518466\pi$
$709$	9.39792	+	16.2777i	0.352946	+	0.611321i	−0.633818	+	0.773482i	$0.718513\pi$
$710$	16.1043			0.604385
$711$	−5.89792	−	10.2155i	−0.221189	−	0.383111i
$712$	−18.2257	+	31.5678i	−0.683036	+	1.18305i
$713$	−1.26984	+	2.19944i	−0.0475561	+	0.0823695i
$714$		0			0
$715$	−9.87707	−	55.2127i	−0.369382	−	2.06484i
$716$	0.408337			0.0152603
$717$	−13.9978	+	24.2448i	−0.522756	+	0.905440i
$718$	2.00000	−	3.46410i	0.0746393	−	0.129279i
$719$	14.5605	+	25.2195i	0.543015	+	0.940530i	0.998729	+	0.0504035i	$0.0160507\pi$
$719$	14.5605	+	25.2195i	0.543015	+	0.940530i	−0.455714	+	0.890126i	$0.650616\pi$
$720$	2.68406			0.100029
$721$		0			0
$722$	5.50000	+	9.52628i	0.204689	+	0.354531i
$723$	6.20417			0.230736
$724$	8.26873	+	14.3219i	0.307305	+	0.532268i
$725$	9.69375	−	16.7901i	0.360017	−	0.623567i
$726$	15.9747	−	27.6690i	0.592877	−	1.02689i
$727$	35.3259			1.31016			0.655082	−	0.755558i	$-0.272634\pi$
$727$	35.3259			1.31016			0.655082	+	0.755558i	$0.272634\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	−7.78541	+	13.4847i	−0.288151	+	0.499092i
$731$	−4.94975	+	8.57321i	−0.183073	+	0.317092i
$732$	1.10208	+	1.90887i	0.0407342	+	0.0705537i
$733$	−0.692369			−0.0255732			−0.0127866	−	0.999918i	$-0.504070\pi$
$733$	−0.692369			−0.0255732			−0.0127866	+	0.999918i	$0.504070\pi$
$734$	10.6066	+	18.3712i	0.391497	+	0.678092i
$735$		0			0
$736$	8.97916			0.330976
$737$	−16.7958	−	29.0912i	−0.618682	−	1.07159i
$738$	−4.87756	+	8.44819i	−0.179546	+	0.310982i
$739$	−7.59166	+	13.1491i	−0.279264	+	0.483699i	−0.971202	−	0.238258i	$-0.923424\pi$
$739$	−7.59166	+	13.1491i	−0.279264	+	0.483699i	0.691938	+	0.721957i	$0.256757\pi$
$740$	18.2404			0.670531
$741$	11.0250	−	9.29785i	0.405012	−	0.341565i
$742$		0			0
$743$	−4.59166	+	7.95299i	−0.168452	+	0.291767i	−0.937876	−	0.346971i	$-0.887210\pi$
$743$	−4.59166	+	7.95299i	−0.168452	+	0.291767i	0.769424	+	0.638738i	$0.220543\pi$
$744$	−3.00000	+	5.19615i	−0.109985	+	0.190500i
$745$	−6.16215	−	10.6731i	−0.225764	−	0.391034i
$746$	−12.5917			−0.461014
$747$	4.94975	+	8.57321i	0.181102	+	0.313678i
$748$	−15.9747	−	27.6690i	−0.584094	−	1.01168i
$749$		0			0
$750$	−5.30625	−	9.19070i	−0.193757	−	0.335597i
$751$	−0.897916	+	1.55524i	−0.0327654	+	0.0567514i	−0.881943	−	0.471356i	$-0.843765\pi$
$751$	−0.897916	+	1.55524i	−0.0327654	+	0.0567514i	0.849178	+	0.528107i	$0.177098\pi$
$752$	−1.41421	+	2.44949i	−0.0515711	+	0.0893237i
$753$	−4.40834			−0.160649
$754$	−29.8281	−	10.7726i	−1.08628	−	0.392317i
$755$	−47.2170			−1.71840
$756$		0			0
$757$	12.5917	−	21.8094i	0.457652	−	0.792676i	−0.541185	−	0.840904i	$-0.682024\pi$
$757$	12.5917	−	21.8094i	0.457652	−	0.792676i	0.998836	+	0.0482277i	$0.0153573\pi$
$758$	1.69375	+	2.93366i	0.0615197	+	0.106555i
$759$	−14.7196			−0.534288
$760$	11.3875	+	19.7237i	0.413068	+	0.715454i
$761$	4.66101	+	8.07311i	0.168961	+	0.292650i	0.938055	−	0.346486i	$-0.112625\pi$
$761$	4.66101	+	8.07311i	0.168961	+	0.292650i	−0.769094	+	0.639136i	$0.779292\pi$
$762$	−10.7362			−0.388933
$763$		0			0
$764$	−12.8979	+	22.3398i	−0.466630	+	0.808227i
$765$	−7.39792	+	12.8136i	−0.267472	+	0.463275i
$766$	14.9789			0.541209
$767$	−3.81667	−	1.37842i	−0.137812	−	0.0497719i
$768$	24.0416			0.867528
$769$	2.12132	−	3.67423i	0.0764968	−	0.132496i	−0.825239	−	0.564783i	$-0.808960\pi$
$769$	2.12132	−	3.67423i	0.0764968	−	0.132496i	0.901736	+	0.432287i	$0.142293\pi$
$770$		0			0
$771$	−10.8979	−	18.8757i	−0.392479	−	0.679793i
$772$	−3.40834			−0.122669
$773$	3.82427	+	6.62383i	0.137549	+	0.238243i	0.926568	−	0.376126i	$-0.122744\pi$
$773$	3.82427	+	6.62383i	0.137549	+	0.238243i	−0.789019	+	0.614369i	$0.789411\pi$
$774$	−0.897916	−	1.55524i	−0.0322749	−	0.0559018i
$775$	3.11716			0.111972
$776$	6.36396	+	11.0227i	0.228453	+	0.395692i
$777$		0			0
$778$	−14.1937	+	24.5843i	−0.508870	+	0.881390i
$779$	−27.5917			−0.988574
$780$	−10.4622	+	8.82327i	−0.374608	+	0.315924i
$781$	34.7750			1.24435
$782$	4.94975	−	8.57321i	0.177003	−	0.306578i
$783$	24.8784	−	43.0906i	0.889080	−	1.53993i
$784$		0			0
$785$	18.5917			0.663565
$786$	5.79583	+	10.0387i	0.206730	+	0.358068i
$787$	12.7132	+	22.0199i	0.453176	+	0.784924i	0.998581	−	0.0532485i	$-0.0169575\pi$
$787$	12.7132	+	22.0199i	0.453176	+	0.784924i	−0.545405	+	0.838173i	$0.683624\pi$
$788$	8.00000			0.284988
$789$	−17.9517	−	31.0932i	−0.639096	−	1.10695i
$790$	15.8303	−	27.4190i	0.563219	−	0.975523i
$791$		0			0
$792$	17.3875			0.617838
$793$	−5.28541	−	1.90887i	−0.187690	−	0.0677858i
$794$	−7.07107			−0.250943
$795$	12.5104	−	21.6687i	0.443699	−	0.768509i
$796$	11.0250	−	19.0958i	0.390770	−	0.676833i
$797$	−13.1463	−	22.7700i	−0.465666	−	0.806556i	0.533566	−	0.845759i	$-0.320852\pi$
$797$	−13.1463	−	22.7700i	−0.465666	−	0.806556i	−0.999231	+	0.0392022i	$0.987518\pi$
$798$		0			0
$799$	−7.79583	−	13.5028i	−0.275797	−	0.477694i
$800$	−5.51042	−	9.54433i	−0.194823	−	0.337443i
$801$	12.1504			0.429315
$802$	−12.1937	−	21.1202i	−0.430576	−	0.745780i
$803$	−16.8115	+	29.1183i	−0.593263	+	1.02756i
$804$	−4.09827	+	7.09841i	−0.144535	+	0.250342i
$805$		0			0
$806$	−0.897916	−	5.01934i	−0.0316277	−	0.176799i
$807$	−1.59166			−0.0560292
$808$	4.45919	−	7.72355i	0.156874	−	0.271714i
$809$	−19.6833	+	34.0925i	−0.692029	+	1.19863i	0.279143	+	0.960250i	$0.409950\pi$
$809$	−19.6833	+	34.0925i	−0.692029	+	1.19863i	−0.971172	+	0.238380i	$0.923384\pi$
$810$	6.71015	+	11.6223i	0.235770	+	0.408366i
$811$	38.4725			1.35095			0.675476	−	0.737382i	$-0.263938\pi$
$811$	38.4725			1.35095			0.675476	+	0.737382i	$0.263938\pi$
$812$		0			0
$813$	16.3875	+	28.3840i	0.574735	+	0.995469i
$814$	−39.3875			−1.38053
$815$	17.9664	+	31.1187i	0.629336	+	1.09004i
$816$	3.89792	−	6.75139i	0.136454	−	0.236346i
$817$	2.53969	−	4.39887i	0.0888525	−	0.153897i
$818$	28.6879			1.00305
$819$		0			0
$820$	26.1833			0.914361
$821$	20.1833	−	34.9585i	0.704403	−	1.22006i	−0.262504	−	0.964931i	$-0.584548\pi$
$821$	20.1833	−	34.9585i	0.704403	−	1.22006i	0.966907	−	0.255131i	$-0.0821185\pi$
$822$	−6.50833	+	11.2728i	−0.227004	+	0.393183i
$823$	−18.3875	−	31.8481i	−0.640948	−	1.11015i	−0.985222	−	0.171285i	$-0.945208\pi$
$823$	−18.3875	−	31.8481i	−0.640948	−	1.11015i	0.344274	−	0.938869i	$-0.388125\pi$
$824$	−24.5896			−0.856620
$825$	9.03328	+	15.6461i	0.314498	+	0.544727i
$826$		0			0
$827$	26.9792			0.938157			0.469079	−	0.883156i	$-0.344586\pi$
$827$	26.9792			0.938157			0.469079	+	0.883156i	$0.344586\pi$
$828$	−0.897916	−	1.55524i	−0.0312047	−	0.0540482i
$829$	10.1013	−	17.4960i	0.350833	−	0.607661i	−0.635563	−	0.772049i	$-0.719232\pi$
$829$	10.1013	−	17.4960i	0.350833	−	0.607661i	0.986396	+	0.164389i	$0.0525651\pi$
$830$	−13.2854	+	23.0110i	−0.461143	+	0.798724i
$831$	8.74454			0.303345
$832$	−19.2937	+	16.2712i	−0.668889	+	0.564104i
$833$		0			0
$834$	10.7958	−	18.6989i	0.373829	−	0.647491i
$835$	20.4896	−	35.4890i	0.709071	−	1.22815i
$836$	8.19654	+	14.1968i	0.283483	+	0.491008i
$837$	8.00000			0.276520
$838$	14.2718	+	24.7194i	0.493010	+	0.853918i
$839$	2.82843	+	4.89898i	0.0976481	+	0.169132i	0.910711	−	0.413045i	$-0.135535\pi$
$839$	2.82843	+	4.89898i	0.0976481	+	0.169132i	−0.813063	+	0.582176i	$0.802201\pi$
$840$		0			0
$841$	−24.1833	−	41.8867i	−0.833908	−	1.44437i
$842$	3.29583	−	5.70855i	0.113582	−	0.196730i
$843$	10.7510	−	18.6212i	0.370283	−	0.641349i
$844$	1.79583			0.0618151
$845$	5.88815	−	34.3924i	0.202558	−	1.18313i
$846$	2.82843			0.0972433
$847$		0			0
$848$	3.29583	−	5.70855i	0.113179	−	0.196032i
$849$	20.7958	+	36.0194i	0.713711	+	1.23618i
$850$	−12.1504			−0.416757
$851$	6.10208	+	10.5691i	0.209177	+	0.362305i
$852$	−4.24264	−	7.34847i	−0.145350	−	0.251754i
$853$	13.1610			0.450625			0.225313	−	0.974287i	$-0.427660\pi$
$853$	13.1610			0.450625			0.225313	+	0.974287i	$0.427660\pi$
$854$		0			0
$855$	3.79583	−	6.57457i	0.129815	−	0.224846i
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	37.7507			1.28954			0.644769	−	0.764377i	$-0.276954\pi$
$857$	37.7507			1.28954			0.644769	+	0.764377i	$0.276954\pi$
$858$	22.5917	−	19.0526i	0.771267	−	0.650444i
$859$	−23.7529			−0.810438			−0.405219	−	0.914220i	$-0.632805\pi$
$859$	−23.7529			−0.810438			−0.405219	+	0.914220i	$0.632805\pi$
$860$	−2.41006	+	4.17434i	−0.0821823	+	0.142344i
$861$		0			0
$862$	2.59166	+	4.48889i	0.0882724	+	0.152892i
$863$	17.7958			0.605777			0.302889	−	0.953026i	$-0.402049\pi$
$863$	17.7958			0.605777			0.302889	+	0.953026i	$0.402049\pi$
$864$	−14.1421	−	24.4949i	−0.481125	−	0.833333i
$865$	12.5104	+	21.6687i	0.425367	+	0.736757i
$866$	−13.4203			−0.456040
$867$	9.46639	+	16.3963i	0.321495	+	0.556846i
$868$		0			0
$869$	34.1833	−	59.2073i	1.15959	−	2.00847i
$870$	33.3875			1.13194
$871$	−3.67990	−	20.5706i	−0.124689	−	0.697008i
$872$	52.7750			1.78719
$873$	2.12132	−	3.67423i	0.0717958	−	0.124354i
$874$	−2.53969	+	4.39887i	−0.0859063	+	0.148794i
$875$		0			0
$876$	8.20417			0.277193
$877$	2.39792	+	4.15331i	0.0809719	+	0.140247i	0.903668	−	0.428235i	$-0.140864\pi$
$877$	2.39792	+	4.15331i	0.0809719	+	0.140247i	−0.822696	+	0.568482i	$0.807531\pi$
$878$	17.1002	+	29.6184i	0.577104	+	0.999573i
$879$	−13.7958			−0.465322
$880$	7.77817	+	13.4722i	0.262202	+	0.454148i
$881$	−11.6599	+	20.1955i	−0.392832	+	0.680405i	−0.992822	−	0.119603i	$-0.961838\pi$
$881$	−11.6599	+	20.1955i	−0.392832	+	0.680405i	0.599990	+	0.800007i	$0.295171\pi$
$882$		0			0
$883$	−16.6125			−0.559055			−0.279528	−	0.960138i	$-0.590178\pi$
$883$	−16.6125			−0.559055			−0.279528	+	0.960138i	$0.590178\pi$
$884$	−3.50000	−	19.5650i	−0.117718	−	0.658041i
$885$	4.27212			0.143606
$886$	−5.00000	+	8.66025i	−0.167978	+	0.290947i
$887$	−14.2865	+	24.7450i	−0.479694	+	0.830854i	−0.999729	−	0.0232909i	$-0.992586\pi$
$887$	−14.2865	+	24.7450i	−0.479694	+	0.830854i	0.520035	+	0.854145i	$0.325919\pi$
$888$	14.4161	+	24.9695i	0.483774	+	0.837921i
$889$		0			0
$890$	16.3063	+	28.2433i	0.546587	+	0.946716i
$891$	14.4896	+	25.0967i	0.485419	+	0.840771i
$892$	−5.65685			−0.189405
$893$	4.00000	+	6.92820i	0.133855	+	0.231843i
$894$	3.24680	−	5.62362i	0.108589	−	0.188082i
$895$	0.548000	−	0.949164i	0.0183176	−	0.0317271i
$896$		0			0
$897$	−8.61251	−	3.11047i	−0.287563	−	0.103856i
$898$	4.40834			0.147108
$899$	6.21959	−	10.7726i	0.207435	−	0.359288i
$900$	−1.10208	+	1.90887i	−0.0367361	+	0.0636289i
$901$	18.1682	+	31.4683i	0.605271	+	1.04836i
$902$	−56.5391			−1.88255
$903$		0			0
$904$	−24.8875	−	43.1064i	−0.827746	−	1.43370i
$905$	44.3875			1.47549
$906$	−12.4392	−	21.5453i	−0.413264	−	0.715795i
$907$	−24.6937	+	42.7708i	−0.819942	+	1.42018i	0.0857816	+	0.996314i	$0.472661\pi$
$907$	−24.6937	+	42.7708i	−0.819942	+	1.42018i	−0.905724	+	0.423868i	$0.860672\pi$
$908$	−10.4622	+	18.1211i	−0.347201	+	0.601370i
$909$	−2.97280			−0.0986014
$910$		0			0
$911$	−43.1833			−1.43073			−0.715364	−	0.698752i	$-0.753739\pi$
$911$	−43.1833			−1.43073			−0.715364	+	0.698752i	$0.753739\pi$
$912$	−2.00000	+	3.46410i	−0.0662266	+	0.114708i
$913$	−28.6879	+	49.6889i	−0.949431	+	1.64446i
$914$	7.29583	+	12.6368i	0.241325	+	0.417987i
$915$	5.91612			0.195581
$916$	−6.36396	−	11.0227i	−0.210271	−	0.364200i
$917$		0			0
$918$	−31.1833			−1.02920
$919$	−5.00000	−	8.66025i	−0.164935	−	0.285675i	0.771697	−	0.635990i	$-0.219408\pi$
$919$	−5.00000	−	8.66025i	−0.164935	−	0.285675i	−0.936632	+	0.350315i	$0.886075\pi$
$920$	7.23017	−	12.5230i	0.238372	−	0.412872i
$921$	−24.1833	+	41.8867i	−0.796868	+	1.38022i
$922$	−30.9683			−1.01989
$923$	20.3470	+	7.34847i	0.669729	+	0.241878i
$924$		0			0
$925$	7.48958	−	12.9723i	0.246256	−	0.426528i
$926$	−5.69375	+	9.86186i	−0.187108	+	0.324081i
$927$	4.09827	+	7.09841i	0.134605	+	0.233143i
$928$	−43.9792			−1.44369
$929$	−14.0700	−	24.3699i	−0.461620	−	0.799550i	0.537422	−	0.843314i	$-0.319398\pi$
$929$	−14.0700	−	24.3699i	−0.461620	−	0.799550i	−0.999042	+	0.0437641i	$0.986065\pi$
$930$	2.68406	+	4.64893i	0.0880137	+	0.152444i
$931$		0			0
$932$	−10.5917	−	18.3453i	−0.346941	−	0.600920i
$933$	−8.38749	+	14.5276i	−0.274594	+	0.475611i
$934$	−2.41006	+	4.17434i	−0.0788595	+	0.136589i
$935$	−85.7541			−2.80446
$936$	10.1735	+	3.67423i	0.332531	+	0.120096i
$937$	−6.63796			−0.216853			−0.108426	−	0.994104i	$-0.534581\pi$
$937$	−6.63796			−0.216853			−0.108426	+	0.994104i	$0.534581\pi$
$938$		0			0
$939$	−1.20417	+	2.08568i	−0.0392966	+	0.0680636i
$940$	−3.79583	−	6.57457i	−0.123806	−	0.214439i
$941$	23.4642			0.764910			0.382455	−	0.923974i	$-0.375079\pi$
$941$	23.4642			0.764910			0.382455	+	0.923974i	$0.375079\pi$
$942$	4.89792	+	8.48344i	0.159583	+	0.276405i
$943$	8.75928	+	15.1715i	0.285241	+	0.494053i
$944$	1.12548			0.0366311
$945$		0			0
$946$	5.20417	−	9.01388i	0.169202	−	0.293067i
$947$	−14.1021	+	24.4255i	−0.458256	+	0.793723i	−0.998869	−	0.0475486i	$-0.984859\pi$
$947$	−14.1021	+	24.4255i	−0.458256	+	0.793723i	0.540613	+	0.841272i	$0.318192\pi$
$948$	−16.6818			−0.541800
$949$	−15.9896	+	13.4847i	−0.519044	+	0.437733i
$950$	6.23433			0.202268
$951$	−8.90365	+	15.4216i	−0.288721	+	0.500079i
$952$		0			0
$953$	2.40834	+	4.17136i	0.0780137	+	0.135124i	0.902393	−	0.430914i	$-0.141809\pi$
$953$	2.40834	+	4.17136i	0.0780137	+	0.135124i	−0.824379	+	0.566038i	$0.808476\pi$
$954$	−6.59166			−0.213413
$955$	34.6188	+	59.9614i	1.12024	+	1.94031i
$956$	−9.89792	−	17.1437i	−0.320121	−	0.554467i
$957$	72.0954			2.33051
$958$	−3.67990	−	6.37378i	−0.118892	−	0.205927i
$959$		0			0
$960$	13.2854	−	23.0110i	0.428785	−	0.742677i
$961$	−29.0000			−0.935484
$962$	−23.0458	−	8.32316i	−0.743026	−	0.268349i
$963$	6.00000			0.193347
$964$	−2.19350	+	3.79926i	−0.0706480	+	0.122366i
$965$	−4.57409	+	7.92255i	−0.147245	+	0.255036i
$966$		0			0
$967$	11.3875			0.366197			0.183099	−	0.983095i	$-0.441387\pi$
$967$	11.3875			0.366197			0.183099	+	0.983095i	$0.441387\pi$
$968$	33.8875	+	58.6949i	1.08919	+	1.88652i
$969$	−11.0250	−	19.0958i	−0.354173	−	0.613446i
$970$	11.3875			0.365630
$971$	−11.3137	−	19.5959i	−0.363074	−	0.628863i	0.625391	−	0.780312i	$-0.284940\pi$
$971$	−11.3137	−	19.5959i	−0.363074	−	0.628863i	−0.988465	+	0.151449i	$0.951606\pi$
$972$	−4.94975	+	8.57321i	−0.158763	+	0.274986i
$973$		0			0
$974$	19.5917			0.627757
$975$	1.97916	+	11.0635i	0.0633838	+	0.354314i
$976$	1.55858			0.0498890
$977$	−0.193747	+	0.335580i	−0.00619852	+	0.0107362i	−0.869108	−	0.494622i	$-0.835306\pi$
$977$	−0.193747	+	0.335580i	−0.00619852	+	0.0107362i	0.862910	+	0.505358i	$0.168640\pi$
$978$	−9.46639	+	16.3963i	−0.302702	+	0.524295i
$979$	35.2110	+	60.9872i	1.12535	+	1.94916i
$980$		0			0
$981$	−8.79583	−	15.2348i	−0.280829	−	0.486411i
$982$	4.79583	+	8.30662i	0.153041	+	0.265075i
$983$	−41.5602			−1.32556			−0.662782	−	0.748812i	$-0.730624\pi$
$983$	−41.5602			−1.32556			−0.662782	+	0.748812i	$0.730624\pi$
$984$	20.6937	+	35.8426i	0.659693	+	1.14262i
$985$	10.7362	−	18.5957i	0.342085	−	0.592508i
$986$	−24.2434	+	41.9909i	−0.772069	+	1.33726i
$987$		0			0
$988$	1.79583	+	10.0387i	0.0571330	+	0.319373i
$989$	−3.22501			−0.102549
$990$	7.77817	−	13.4722i	0.247207	−	0.428174i
$991$	−9.10208	+	15.7653i	−0.289137	+	0.500800i	−0.973604	−	0.228244i	$-0.926702\pi$
$991$	−9.10208	+	15.7653i	−0.289137	+	0.500800i	0.684467	+	0.729044i	$0.260035\pi$
$992$	−3.53553	−	6.12372i	−0.112253	−	0.194428i
$993$	−0.866213			−0.0274885
$994$		0			0
$995$	−29.5917	−	51.2543i	−0.938119	−	1.62487i
$996$	14.0000			0.443607
$997$	−2.75624	−	4.77395i	−0.0872911	−	0.151193i	0.819074	−	0.573688i	$-0.194488\pi$
$997$	−2.75624	−	4.77395i	−0.0872911	−	0.151193i	−0.906365	+	0.422495i	$0.861154\pi$
$998$	−8.10208	+	14.0332i	−0.256467	+	0.444214i
$999$	19.2215	−	33.2926i	0.608142	−	1.05333i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.g.295.4	yes	8
7.2	even	3		637.2.h.k.165.3		8
7.3	odd	6		637.2.g.h.373.4		8
7.4	even	3		637.2.g.h.373.1		8
7.5	odd	6		637.2.h.k.165.2		8
7.6	odd	2	inner	637.2.f.g.295.1	✓	8
13.3	even	3	inner	637.2.f.g.393.4	yes	8
13.4	even	6		8281.2.a.bn.1.1		4
13.9	even	3		8281.2.a.bv.1.2		4
91.3	odd	6		637.2.h.k.471.2		8
91.16	even	3		637.2.g.h.263.1		8
91.48	odd	6		8281.2.a.bv.1.3		4
91.55	odd	6	inner	637.2.f.g.393.1	yes	8
91.68	odd	6		637.2.g.h.263.4		8
91.69	odd	6		8281.2.a.bn.1.4		4
91.81	even	3		637.2.h.k.471.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.g.295.1	✓	8	7.6	odd	2	inner
637.2.f.g.295.4	yes	8	1.1	even	1	trivial
637.2.f.g.393.1	yes	8	91.55	odd	6	inner
637.2.f.g.393.4	yes	8	13.3	even	3	inner
637.2.g.h.263.1		8	91.16	even	3
637.2.g.h.263.4		8	91.68	odd	6
637.2.g.h.373.1		8	7.4	even	3
637.2.g.h.373.4		8	7.3	odd	6
637.2.h.k.165.2		8	7.5	odd	6
637.2.h.k.165.3		8	7.2	even	3
637.2.h.k.471.2		8	91.3	odd	6
637.2.h.k.471.3		8	91.81	even	3
8281.2.a.bn.1.1		4	13.4	even	6
8281.2.a.bn.1.4		4	91.69	odd	6
8281.2.a.bv.1.2		4	13.9	even	3
8281.2.a.bv.1.3		4	91.48	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.68406 q^{5} +(0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.707107 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +2.68406 q^{5} +(0.707107 + 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.34203 + 2.32446i) q^{10} +(-2.89792 + 5.01934i) q^{11} +1.41421 q^{12} +(-2.75624 + 2.32446i) q^{13} +(1.89792 - 3.28729i) q^{15} +(0.500000 - 0.866025i) q^{16} +(2.75624 + 4.77395i) q^{17} -1.00000 q^{18} +(-1.41421 - 2.44949i) q^{19} +(1.34203 + 2.32446i) q^{20} +(-2.89792 - 5.01934i) q^{22} +(-0.897916 + 1.55524i) q^{23} +(-2.12132 + 3.67423i) q^{24} +2.20417 q^{25} +(-0.634922 - 3.54921i) q^{26} +5.65685 q^{27} +(4.39792 - 7.61741i) q^{29} +(1.89792 + 3.28729i) q^{30} +1.41421 q^{31} +(-2.50000 - 4.33013i) q^{32} +(4.09827 + 7.09841i) q^{33} -5.51249 q^{34} +(-0.500000 + 0.866025i) q^{36} +(3.39792 - 5.88536i) q^{37} +2.82843 q^{38} +(0.897916 + 5.01934i) q^{39} -8.05217 q^{40} +(4.87756 - 8.44819i) q^{41} +(0.897916 + 1.55524i) q^{43} -5.79583 q^{44} +(1.34203 + 2.32446i) q^{45} +(-0.897916 - 1.55524i) q^{46} -2.82843 q^{47} +(-0.707107 - 1.22474i) q^{48} +(-1.10208 + 1.90887i) q^{50} +7.79583 q^{51} +(-3.39116 - 1.22474i) q^{52} +6.59166 q^{53} +(-2.82843 + 4.89898i) q^{54} +(-7.77817 + 13.4722i) q^{55} -4.00000 q^{57} +(4.39792 + 7.61741i) q^{58} +(0.562738 + 0.974691i) q^{59} +3.79583 q^{60} +(0.779291 + 1.34977i) q^{61} +(-0.707107 + 1.22474i) q^{62} +7.00000 q^{64} +(-7.39792 + 6.23899i) q^{65} -8.19654 q^{66} +(-2.89792 + 5.01934i) q^{67} +(-2.75624 + 4.77395i) q^{68} +(1.26984 + 2.19944i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-1.50000 - 2.59808i) q^{72} +5.80122 q^{73} +(3.39792 + 5.88536i) q^{74} +(1.55858 - 2.69954i) q^{75} +(1.41421 - 2.44949i) q^{76} +(-4.79583 - 1.73205i) q^{78} -11.7958 q^{79} +(1.34203 - 2.32446i) q^{80} +(2.50000 - 4.33013i) q^{81} +(4.87756 + 8.44819i) q^{82} +9.89949 q^{83} +(7.39792 + 12.8136i) q^{85} -1.79583 q^{86} +(-6.21959 - 10.7726i) q^{87} +(8.69375 - 15.0580i) q^{88} +(6.07522 - 10.5226i) q^{89} -2.68406 q^{90} -1.79583 q^{92} +(1.00000 - 1.73205i) q^{93} +(1.41421 - 2.44949i) q^{94} +(-3.79583 - 6.57457i) q^{95} -7.07107 q^{96} +(-2.12132 - 3.67423i) q^{97} -5.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 4 * q^4 - 24 * q^8 + 4 * q^9	\( 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} + 4 q^{9} - 4 q^{11} - 4 q^{15} + 4 q^{16} - 8 q^{18} - 4 q^{22} + 12 q^{23} + 56 q^{25} + 16 q^{29} - 4 q^{30} - 20 q^{32} - 4 q^{36} + 8 q^{37} - 12 q^{39} - 12 q^{43} - 8 q^{44} + 12 q^{46} - 28 q^{50} + 24 q^{51} - 24 q^{53} - 32 q^{57} + 16 q^{58} - 8 q^{60} + 56 q^{64} - 40 q^{65} - 4 q^{67} - 24 q^{71} - 12 q^{72} + 8 q^{74} - 56 q^{79} + 20 q^{81} + 40 q^{85} + 24 q^{86} + 12 q^{88} + 24 q^{92} + 8 q^{93} + 8 q^{95} - 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^4 - 24 * q^8 + 4 * q^9 - 4 * q^11 - 4 * q^15 + 4 * q^16 - 8 * q^18 - 4 * q^22 + 12 * q^23 + 56 * q^25 + 16 * q^29 - 4 * q^30 - 20 * q^32 - 4 * q^36 + 8 * q^37 - 12 * q^39 - 12 * q^43 - 8 * q^44 + 12 * q^46 - 28 * q^50 + 24 * q^51 - 24 * q^53 - 32 * q^57 + 16 * q^58 - 8 * q^60 + 56 * q^64 - 40 * q^65 - 4 * q^67 - 24 * q^71 - 12 * q^72 + 8 * q^74 - 56 * q^79 + 20 * q^81 + 40 * q^85 + 24 * q^86 + 12 * q^88 + 24 * q^92 + 8 * q^93 + 8 * q^95 - 8 * q^99

Introduction

L-functions

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