LMFDB - Embedded newform 637.2.f.g.393.3

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			393.3
Root			$-2.04914 + 3.54921i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.g.295.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.707107 + 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} -4.09827 q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.04914 + 3.54921i) q^{10} +(1.89792 + 3.28729i) q^{11} +1.41421 q^{12} +(0.634922 + 3.54921i) q^{13} +(-2.89792 - 5.01934i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.634922 + 1.09972i) q^{17} -1.00000 q^{18} +(-1.41421 + 2.44949i) q^{19} +(-2.04914 + 3.54921i) q^{20} +(1.89792 - 3.28729i) q^{22} +(3.89792 + 6.75139i) q^{23} +(-2.12132 - 3.67423i) q^{24} +11.7958 q^{25} +(2.75624 - 2.32446i) q^{26} +5.65685 q^{27} +(-0.397916 - 0.689210i) q^{29} +(-2.89792 + 5.01934i) q^{30} +1.41421 q^{31} +(-2.50000 + 4.33013i) q^{32} +(-2.68406 + 4.64893i) q^{33} +1.26984 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-1.39792 - 2.42126i) q^{37} +2.82843 q^{38} +(-3.89792 + 3.28729i) q^{39} +12.2948 q^{40} +(1.48640 + 2.57452i) q^{41} +(-3.89792 + 6.75139i) q^{43} +3.79583 q^{44} +(-2.04914 + 3.54921i) q^{45} +(3.89792 - 6.75139i) q^{46} -2.82843 q^{47} +(-0.707107 + 1.22474i) q^{48} +(-5.89792 - 10.2155i) q^{50} -1.79583 q^{51} +(3.39116 + 1.22474i) q^{52} -12.5917 q^{53} +(-2.82843 - 4.89898i) q^{54} +(-7.77817 - 13.4722i) q^{55} -4.00000 q^{57} +(-0.397916 + 0.689210i) q^{58} +(-6.21959 + 10.7726i) q^{59} -5.79583 q^{60} +(4.17046 - 7.22344i) q^{61} +(-0.707107 - 1.22474i) q^{62} +7.00000 q^{64} +(-2.60208 - 14.5456i) q^{65} +5.36812 q^{66} +(1.89792 + 3.28729i) q^{67} +(0.634922 + 1.09972i) q^{68} +(-5.51249 + 9.54790i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +12.5836 q^{73} +(-1.39792 + 2.42126i) q^{74} +(8.34091 + 14.4469i) q^{75} +(1.41421 + 2.44949i) q^{76} +(4.79583 + 1.73205i) q^{78} -2.20417 q^{79} +(-2.04914 - 3.54921i) q^{80} +(2.50000 + 4.33013i) q^{81} +(1.48640 - 2.57452i) q^{82} +9.89949 q^{83} +(2.60208 - 4.50694i) q^{85} +7.79583 q^{86} +(0.562738 - 0.974691i) q^{87} +(-5.69375 - 9.86186i) q^{88} +(-7.48944 - 12.9721i) q^{89} +4.09827 q^{90} +7.79583 q^{92} +(1.00000 + 1.73205i) q^{93} +(1.41421 + 2.44949i) q^{94} +(5.79583 - 10.0387i) q^{95} -7.07107 q^{96} +(-2.12132 + 3.67423i) q^{97} +3.79583 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

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	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	0.994694	−	0.102882i	$-0.0328064\pi$
$3$	0.707107	+	1.22474i	0.408248	+	0.707107i	−0.586445	+	0.809989i	$0.699473\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−4.09827			−1.83280			−0.916401	−	0.400260i	$-0.868920\pi$
$5$	−4.09827			−1.83280			−0.916401	+	0.400260i	$0.868920\pi$
$6$	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
$10$	2.04914	+	3.54921i	0.647994	+	1.12236i
$11$	1.89792	+	3.28729i	0.572243	+	0.991154i	0.996335	+	0.0855351i	$0.0272600\pi$
$11$	1.89792	+	3.28729i	0.572243	+	0.991154i	−0.424092	+	0.905619i	$0.639407\pi$
$12$	1.41421			0.408248
$13$	0.634922	+	3.54921i	0.176096	+	0.984373i
$13$	0.634922	+	3.54921i	0.176096	+	0.984373i
$14$		0			0
$15$	−2.89792	−	5.01934i	−0.748239	−	1.29599i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.634922	+	1.09972i	−0.153991	+	0.266721i	−0.932691	−	0.360676i	$-0.882546\pi$
$17$	−0.634922	+	1.09972i	−0.153991	+	0.266721i	0.778700	+	0.627396i	$0.215879\pi$
$18$	−1.00000			−0.235702
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	−0.981399	−	0.191977i	$-0.938510\pi$
$19$	−1.41421	+	2.44949i	−0.324443	+	0.561951i	0.656957	+	0.753928i	$0.271843\pi$
$20$	−2.04914	+	3.54921i	−0.458201	+	0.793627i
$21$		0			0
$22$	1.89792	−	3.28729i	0.404637	−	0.700852i
$23$	3.89792	+	6.75139i	0.812772	+	1.40776i	0.910917	+	0.412590i	$0.135376\pi$
$23$	3.89792	+	6.75139i	0.812772	+	1.40776i	−0.0981454	+	0.995172i	$0.531291\pi$
$24$	−2.12132	−	3.67423i	−0.433013	−	0.750000i
$25$	11.7958			2.35917
$26$	2.75624	−	2.32446i	0.540544	−	0.455865i
$27$	5.65685			1.08866
$28$		0			0
$29$	−0.397916	−	0.689210i	−0.0738911	−	0.127983i	0.826712	−	0.562625i	$-0.190208\pi$
$29$	−0.397916	−	0.689210i	−0.0738911	−	0.127983i	−0.900604	+	0.434642i	$0.856875\pi$
$30$	−2.89792	+	5.01934i	−0.529085	+	0.916401i
$31$	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
$33$	−2.68406	+	4.64893i	−0.467235	+	0.809274i
$34$	1.26984			0.217777
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.39792	−	2.42126i	−0.229816	−	0.398053i	0.727937	−	0.685643i	$-0.240479\pi$
$37$	−1.39792	−	2.42126i	−0.229816	−	0.398053i	−0.957753	+	0.287591i	$0.907146\pi$
$38$	2.82843			0.458831
$39$	−3.89792	+	3.28729i	−0.624166	+	0.526387i
$40$	12.2948			1.94398
$41$	1.48640	+	2.57452i	0.232136	+	0.402072i	0.958437	−	0.285306i	$-0.0920951\pi$
$41$	1.48640	+	2.57452i	0.232136	+	0.402072i	−0.726300	+	0.687378i	$0.758762\pi$
$42$		0			0
$43$	−3.89792	+	6.75139i	−0.594427	+	1.02958i	0.399201	+	0.916863i	$0.369288\pi$
$43$	−3.89792	+	6.75139i	−0.594427	+	1.02958i	−0.993628	+	0.112714i	$0.964046\pi$
$44$	3.79583			0.572243
$45$	−2.04914	+	3.54921i	−0.305467	+	0.529085i
$46$	3.89792	−	6.75139i	0.574716	−	0.995438i
$47$	−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
$50$	−5.89792	−	10.2155i	−0.834091	−	1.44469i
$51$	−1.79583			−0.251467
$52$	3.39116	+	1.22474i	0.470270	+	0.169842i
$53$	−12.5917			−1.72960			−0.864799	−	0.502118i	$-0.832554\pi$
$53$	−12.5917			−1.72960			−0.864799	+	0.502118i	$0.832554\pi$
$54$	−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
$58$	−0.397916	+	0.689210i	−0.0522489	+	0.0904977i
$59$	−6.21959	+	10.7726i	−0.809722	+	1.40248i	0.103335	+	0.994647i	$0.467049\pi$
$59$	−6.21959	+	10.7726i	−0.809722	+	1.40248i	−0.913057	+	0.407833i	$0.866285\pi$
$60$	−5.79583			−0.748239
$61$	4.17046	−	7.22344i	0.533972	−	0.924867i	−0.465240	−	0.885185i	$-0.654032\pi$
$61$	4.17046	−	7.22344i	0.533972	−	0.924867i	0.999212	−	0.0396825i	$-0.0126346\pi$
$62$	−0.707107	−	1.22474i	−0.0898027	−	0.155543i
$63$		0			0
$64$	7.00000			0.875000
$65$	−2.60208	−	14.5456i	−0.322749	−	1.80416i
$66$	5.36812			0.660769
$67$	1.89792	+	3.28729i	0.231867	+	0.401606i	0.958358	−	0.285571i	$-0.0921831\pi$
$67$	1.89792	+	3.28729i	0.231867	+	0.401606i	−0.726490	+	0.687177i	$0.758850\pi$
$68$	0.634922	+	1.09972i	0.0769956	+	0.133360i
$69$	−5.51249	+	9.54790i	−0.663625	+	1.14943i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	12.5836			1.47279			0.736397	−	0.676550i	$-0.236526\pi$
$73$	12.5836			1.47279			0.736397	+	0.676550i	$0.236526\pi$
$74$	−1.39792	+	2.42126i	−0.162504	+	0.281466i
$75$	8.34091	+	14.4469i	0.963126	+	1.66818i
$76$	1.41421	+	2.44949i	0.162221	+	0.280976i
$77$		0			0
$78$	4.79583	+	1.73205i	0.543021	+	0.196116i
$79$	−2.20417			−0.247988			−0.123994	−	0.992283i	$-0.539570\pi$
$79$	−2.20417			−0.247988			−0.123994	+	0.992283i	$0.539570\pi$
$80$	−2.04914	−	3.54921i	−0.229100	−	0.396813i
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	1.48640	−	2.57452i	0.164145	−	0.284308i
$83$	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
$85$	2.60208	−	4.50694i	0.282236	−	0.488847i
$86$	7.79583			0.840646
$87$	0.562738	−	0.974691i	0.0603318	−	0.104498i
$88$	−5.69375	−	9.86186i	−0.606955	−	1.05128i
$89$	−7.48944	−	12.9721i	−0.793879	−	1.37504i	−0.923549	−	0.383481i	$-0.874725\pi$
$89$	−7.48944	−	12.9721i	−0.793879	−	1.37504i	0.129670	−	0.991557i	$-0.458608\pi$
$90$	4.09827			0.431996
$91$		0			0
$92$	7.79583			0.812772
$93$	1.00000	+	1.73205i	0.103695	+	0.179605i
$94$	1.41421	+	2.44949i	0.145865	+	0.252646i
$95$	5.79583	−	10.0387i	0.594640	−	1.02995i
$96$	−7.07107			−0.721688
$97$	−2.12132	+	3.67423i	−0.215387	+	0.373062i	−0.953392	−	0.301733i	$-0.902435\pi$
$97$	−2.12132	+	3.67423i	−0.215387	+	0.373062i	0.738005	+	0.674795i	$0.235768\pi$
$98$		0			0
$99$	3.79583			0.381495
$100$	5.89792	−	10.2155i	0.589792	−	1.02155i
$101$	−4.87756	−	8.44819i	−0.485336	−	0.840626i	0.514522	−	0.857477i	$-0.327969\pi$
$101$	−4.87756	−	8.44819i	−0.485336	−	0.840626i	−0.999858	+	0.0168509i	$0.994636\pi$
$102$	0.897916	+	1.55524i	0.0889069	+	0.153991i
$103$	−5.36812			−0.528936			−0.264468	−	0.964394i	$-0.585196\pi$
$103$	−5.36812			−0.528936			−0.264468	+	0.964394i	$0.585196\pi$
$104$	−1.90477	−	10.6476i	−0.186778	−	1.04409i
$105$		0			0
$106$	6.29583	+	10.9047i	0.611505	+	1.05916i
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	2.82843	−	4.89898i	0.272166	−	0.471405i
$109$	1.59166			0.152454			0.0762268	−	0.997091i	$-0.475713\pi$
$109$	1.59166			0.152454			0.0762268	+	0.997091i	$0.475713\pi$
$110$	−7.77817	+	13.4722i	−0.741620	+	1.28452i
$111$	1.97695	−	3.42418i	0.187644	−	0.325009i
$112$		0			0
$113$	−1.29583	+	2.24445i	−0.121902	+	0.211140i	−0.920518	−	0.390701i	$-0.872233\pi$
$113$	−1.29583	+	2.24445i	−0.121902	+	0.211140i	0.798616	+	0.601841i	$0.205566\pi$
$114$	2.00000	+	3.46410i	0.187317	+	0.324443i
$115$	−15.9747	−	27.6690i	−1.48965	−	2.58015i
$116$	−0.795832			−0.0738911
$117$	3.39116	+	1.22474i	0.313513	+	0.113228i
$118$	12.4392			1.14512
$119$		0			0
$120$	8.69375	+	15.0580i	0.793627	+	1.37460i
$121$	−1.70417	+	2.95171i	−0.154924	+	0.268337i
$122$	−8.34091			−0.755151
$123$	−2.10208	+	3.64092i	−0.189539	+	0.328290i
$124$	0.707107	−	1.22474i	0.0635001	−	0.109985i
$125$	−27.8512			−2.49108
$126$		0			0
$127$	5.79583	+	10.0387i	0.514297	+	0.890788i	0.999862	+	0.0165881i	$0.00528038\pi$
$127$	5.79583	+	10.0387i	0.514297	+	0.890788i	−0.485566	+	0.874200i	$0.661386\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$	−11.0250			−0.970695
$130$	−11.2958	+	9.52628i	−0.990710	+	0.835510i
$131$	−5.36812			−0.469015			−0.234507	−	0.972114i	$-0.575348\pi$
$131$	−5.36812			−0.469015			−0.234507	+	0.972114i	$0.575348\pi$
$132$	2.68406	+	4.64893i	0.233617	+	0.404637i
$133$		0			0
$134$	1.89792	−	3.28729i	0.163955	−	0.283978i
$135$	−23.1833			−1.99530
$136$	1.90477	−	3.29915i	0.163332	−	0.282900i
$137$	9.39792	−	16.2777i	0.802918	−	1.39069i	−0.114769	−	0.993392i	$-0.536613\pi$
$137$	9.39792	−	16.2777i	0.802918	−	1.39069i	0.917688	−	0.397303i	$-0.130054\pi$
$138$	11.0250			0.938508
$139$	−0.851476	+	1.47480i	−0.0722212	+	0.125091i	−0.899875	−	0.436149i	$-0.856342\pi$
$139$	−0.851476	+	1.47480i	−0.0722212	+	0.125091i	0.827653	+	0.561240i	$0.189675\pi$
$140$		0			0
$141$	−2.00000	−	3.46410i	−0.168430	−	0.291730i
$142$	6.00000			0.503509
$143$	−10.4622	+	8.82327i	−0.874896	+	0.737839i
$144$	1.00000			0.0833333
$145$	1.63077	+	2.82457i	0.135428	+	0.234568i
$146$	−6.29178	−	10.8977i	−0.520711	−	0.901898i
$147$		0			0
$148$	−2.79583			−0.229816
$149$	7.29583	−	12.6368i	0.597698	−	1.03524i	−0.395462	−	0.918482i	$-0.629416\pi$
$149$	7.29583	−	12.6368i	0.597698	−	1.03524i	0.993160	−	0.116761i	$-0.0372511\pi$
$150$	8.34091	−	14.4469i	0.681033	−	1.17958i
$151$	1.59166			0.129528			0.0647639	−	0.997901i	$-0.479371\pi$
$151$	1.59166			0.129528			0.0647639	+	0.997901i	$0.479371\pi$
$152$	4.24264	−	7.34847i	0.344124	−	0.596040i
$153$	0.634922	+	1.09972i	0.0513304	+	0.0889069i
$154$		0			0
$155$	−5.79583			−0.465532
$156$	0.897916	+	5.01934i	0.0718908	+	0.401869i
$157$	0.144369			0.0115219			0.00576095	−	0.999983i	$-0.498166\pi$
$157$	0.144369			0.0115219			0.00576095	+	0.999983i	$0.498166\pi$
$158$	1.10208	+	1.90887i	0.0876771	+	0.151861i
$159$	−8.90365	−	15.4216i	−0.706105	−	1.22301i
$160$	10.2457	−	17.7460i	0.809992	−	1.40295i
$161$		0			0
$162$	2.50000	−	4.33013i	0.196419	−	0.340207i
$163$	−7.69375	+	13.3260i	−0.602621	+	1.04377i	0.389802	+	0.920899i	$0.372543\pi$
$163$	−7.69375	+	13.3260i	−0.602621	+	1.04377i	−0.992423	+	0.122871i	$0.960790\pi$
$164$	2.97280			0.232136
$165$	11.0000	−	19.0526i	0.856349	−	1.48324i
$166$	−4.94975	−	8.57321i	−0.384175	−	0.665410i
$167$	0.851476	+	1.47480i	0.0658892	+	0.114123i	0.897088	−	0.441852i	$-0.145678\pi$
$167$	0.851476	+	1.47480i	0.0658892	+	0.114123i	−0.831199	+	0.555975i	$0.812345\pi$
$168$		0			0
$169$	−12.1937	+	4.50694i	−0.937981	+	0.346688i
$170$	−5.20417			−0.399142
$171$	1.41421	+	2.44949i	0.108148	+	0.187317i
$172$	3.89792	+	6.75139i	0.297213	+	0.514789i
$173$	−8.90365	+	15.4216i	−0.676932	+	1.17248i	0.298968	+	0.954263i	$0.403358\pi$
$173$	−8.90365	+	15.4216i	−0.676932	+	1.17248i	−0.975900	+	0.218218i	$0.929976\pi$
$174$	−1.12548			−0.0853221
$175$		0			0
$176$	−1.89792	+	3.28729i	−0.143061	+	0.247789i
$177$	−17.5917			−1.32227
$178$	−7.48944	+	12.9721i	−0.561357	+	0.972299i
$179$	9.79583	+	16.9669i	0.732175	+	1.26816i	0.955952	+	0.293524i	$0.0948279\pi$
$179$	9.79583	+	16.9669i	0.732175	+	1.26816i	−0.223777	+	0.974640i	$0.571839\pi$
$180$	2.04914	+	3.54921i	0.152734	+	0.264542i
$181$	−3.80953			−0.283160			−0.141580	−	0.989927i	$-0.545218\pi$
$181$	−3.80953			−0.283160			−0.141580	+	0.989927i	$0.545218\pi$
$182$		0			0
$183$	11.7958			0.871973
$184$	−11.6937	−	20.2542i	−0.862074	−	1.49316i
$185$	5.72904	+	9.92299i	0.421207	+	0.729552i
$186$	1.00000	−	1.73205i	0.0733236	−	0.127000i
$187$	−4.82012			−0.352482
$188$	−1.41421	+	2.44949i	−0.103142	+	0.178647i
$189$		0			0
$190$	−11.5917			−0.840948
$191$	8.10208	−	14.0332i	0.586246	−	1.01541i	−0.408473	−	0.912771i	$-0.633938\pi$
$191$	8.10208	−	14.0332i	0.586246	−	1.01541i	0.994719	−	0.102638i	$-0.0327282\pi$
$192$	4.94975	+	8.57321i	0.357217	+	0.618718i
$193$	−11.2958	−	19.5650i	−0.813092	−	1.40832i	−0.910690	−	0.413090i	$-0.864449\pi$
$193$	−11.2958	−	19.5650i	−0.813092	−	1.40832i	0.0975983	−	0.995226i	$-0.468884\pi$
$194$	4.24264			0.304604
$195$	15.9747	−	13.4722i	1.14397	−	0.964764i
$196$		0			0
$197$	4.00000	+	6.92820i	0.284988	+	0.493614i	0.972606	−	0.232458i	$-0.0746770\pi$
$197$	4.00000	+	6.92820i	0.284988	+	0.493614i	−0.687618	+	0.726073i	$0.741344\pi$
$198$	−1.89792	−	3.28729i	−0.134879	−	0.233617i
$199$	2.53969	−	4.39887i	0.180034	−	0.311828i	−0.761858	−	0.647744i	$-0.775713\pi$
$199$	2.53969	−	4.39887i	0.180034	−	0.311828i	0.941892	+	0.335916i	$0.109046\pi$
$200$	−35.3875			−2.50227
$201$	−2.68406	+	4.64893i	−0.189319	+	0.327910i
$202$	−4.87756	+	8.44819i	−0.343184	+	0.594412i
$203$		0			0
$204$	−0.897916	+	1.55524i	−0.0628667	+	0.108888i
$205$	−6.09166	−	10.5511i	−0.425460	−	0.736919i
$206$	2.68406	+	4.64893i	0.187007	+	0.323906i
$207$	7.79583			0.541848
$208$	−2.75624	+	2.32446i	−0.191111	+	0.161172i
$209$	−10.7362			−0.742641
$210$		0			0
$211$	−3.89792	−	6.75139i	−0.268344	−	0.464785i	0.700091	−	0.714054i	$-0.253143\pi$
$211$	−3.89792	−	6.75139i	−0.268344	−	0.464785i	−0.968434	+	0.249269i	$0.919810\pi$
$212$	−6.29583	+	10.9047i	−0.432399	+	0.748938i
$213$	−8.48528			−0.581402
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$	15.9747	−	27.6690i	1.08947	−	1.88701i
$216$	−16.9706			−1.15470
$217$		0			0
$218$	−0.795832	−	1.37842i	−0.0539005	−	0.0933584i
$219$	8.89792	+	15.4116i	0.601265	+	1.04142i
$220$	−15.5563			−1.04881
$221$	−4.30625	−	1.55524i	−0.289670	−	0.104616i
$222$	−3.95390			−0.265369
$223$	−2.82843	−	4.89898i	−0.189405	−	0.328060i	0.755647	−	0.654979i	$-0.227323\pi$
$223$	−2.82843	−	4.89898i	−0.189405	−	0.328060i	−0.945052	+	0.326920i	$0.893989\pi$
$224$		0			0
$225$	5.89792	−	10.2155i	0.393194	−	0.681033i
$226$	2.59166			0.172395
$227$	3.67990	−	6.37378i	0.244244	−	0.423043i	−0.717675	−	0.696378i	$-0.754794\pi$
$227$	3.67990	−	6.37378i	0.244244	−	0.423043i	0.961919	+	0.273336i	$0.0881270\pi$
$228$	−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	$0.638160\pi$
$230$	−15.9747	+	27.6690i	−1.05334	+	1.82444i
$231$		0			0
$232$	1.19375	+	2.06763i	0.0783733	+	0.135747i
$233$	17.1833			1.12572			0.562859	−	0.826553i	$-0.309702\pi$
$233$	17.1833			1.12572			0.562859	+	0.826553i	$0.309702\pi$
$234$	−0.634922	−	3.54921i	−0.0415062	−	0.232019i
$235$	11.5917			0.756157
$236$	6.21959	+	10.7726i	0.404861	+	0.701240i
$237$	−1.55858	−	2.69954i	−0.101241	−	0.175354i
$238$		0			0
$239$	−10.2042			−0.660053			−0.330026	−	0.943972i	$-0.607058\pi$
$239$	−10.2042			−0.660053			−0.330026	+	0.943972i	$0.607058\pi$
$240$	2.89792	−	5.01934i	0.187060	−	0.323997i
$241$	5.58467	−	9.67293i	0.359740	−	0.623088i	−0.628177	−	0.778070i	$-0.716199\pi$
$241$	5.58467	−	9.67293i	0.359740	−	0.623088i	0.987917	+	0.154982i	$0.0495320\pi$
$242$	3.40834			0.219096
$243$	4.94975	−	8.57321i	0.317526	−	0.549972i
$244$	−4.17046	−	7.22344i	−0.266986	−	0.462433i
$245$		0			0
$246$	4.20417			0.268048
$247$	−9.59166	−	3.46410i	−0.610303	−	0.220416i
$248$	−4.24264			−0.269408
$249$	7.00000	+	12.1244i	0.443607	+	0.768350i
$250$	13.9256	+	24.1198i	0.880731	+	1.52547i
$251$	−8.34091	+	14.4469i	−0.526474	+	0.911879i	0.473050	+	0.881035i	$0.343153\pi$
$251$	−8.34091	+	14.4469i	−0.526474	+	0.911879i	−0.999524	+	0.0308439i	$0.990181\pi$
$252$		0			0
$253$	−14.7958	+	25.6271i	−0.930206	+	1.61116i
$254$	5.79583	−	10.0387i	0.363663	−	0.629882i
$255$	7.35981			0.460889
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	4.31483	+	7.47350i	0.269151	+	0.466184i	0.968643	−	0.248457i	$-0.0799235\pi$
$257$	4.31483	+	7.47350i	0.269151	+	0.466184i	−0.699492	+	0.714641i	$0.746590\pi$
$258$	5.51249	+	9.54790i	0.343192	+	0.594427i
$259$		0			0
$260$	−13.8979	−	5.01934i	−0.861912	−	0.311286i
$261$	−0.795832			−0.0492607
$262$	2.68406	+	4.64893i	0.165822	+	0.287212i
$263$	−1.69375	−	2.93366i	−0.104441	−	0.180897i	0.809069	−	0.587714i	$-0.199972\pi$
$263$	−1.69375	−	2.93366i	−0.104441	−	0.180897i	−0.913510	+	0.406817i	$0.866639\pi$
$264$	8.05217	−	13.9468i	0.495577	−	0.858365i
$265$	51.6041			3.17001
$266$		0			0
$267$	10.5917	−	18.3453i	0.648199	−	1.12271i
$268$	3.79583			0.231867
$269$	6.21959	−	10.7726i	0.379215	−	0.656820i	−0.611733	−	0.791064i	$-0.709527\pi$
$269$	6.21959	−	10.7726i	0.379215	−	0.656820i	0.990948	+	0.134244i	$0.0428607\pi$
$270$	11.5917	+	20.0773i	0.705446	+	1.22187i
$271$	8.75928	+	15.1715i	0.532088	+	0.921604i	0.999298	+	0.0374577i	$0.0119260\pi$
$271$	8.75928	+	15.1715i	0.532088	+	0.921604i	−0.467210	+	0.884147i	$0.654741\pi$
$272$	−1.26984			−0.0769956
$273$		0			0
$274$	−18.7958			−1.13550
$275$	22.3875	+	38.7763i	1.35002	+	2.33830i
$276$	5.51249	+	9.54790i	0.331813	+	0.574716i
$277$	−16.0917	+	27.8716i	−0.966854	+	1.67464i	−0.262306	+	0.964985i	$0.584483\pi$
$277$	−16.0917	+	27.8716i	−0.966854	+	1.67464i	−0.704548	+	0.709656i	$0.748850\pi$
$278$	1.70295			0.102136
$279$	0.707107	−	1.22474i	0.0423334	−	0.0733236i
$280$		0			0
$281$	24.7958			1.47920			0.739598	−	0.673049i	$-0.235016\pi$
$281$	24.7958			1.47920			0.739598	+	0.673049i	$0.235016\pi$
$282$	−2.00000	+	3.46410i	−0.119098	+	0.206284i
$283$	−7.92254	−	13.7222i	−0.470946	−	0.815703i	0.528501	−	0.848932i	$-0.322754\pi$
$283$	−7.92254	−	13.7222i	−0.470946	−	0.815703i	−0.999448	+	0.0332294i	$0.989421\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$	16.3931			0.971043
$286$	12.8723	+	4.64893i	0.761155	+	0.274897i
$287$		0			0
$288$	2.50000	+	4.33013i	0.147314	+	0.255155i
$289$	7.69375	+	13.3260i	0.452573	+	0.783880i
$290$	1.63077	−	2.82457i	0.0957619	−	0.165865i
$291$	−6.00000			−0.351726
$292$	6.29178	−	10.8977i	0.368198	−	0.637738i
$293$	−1.48640	+	2.57452i	−0.0868363	+	0.150405i	−0.906172	−	0.422909i	$-0.861009\pi$
$293$	−1.48640	+	2.57452i	−0.0868363	+	0.150405i	0.819336	+	0.573314i	$0.194342\pi$
$294$		0			0
$295$	25.4896	−	44.1492i	1.48406	−	2.57047i
$296$	4.19375	+	7.26378i	0.243757	+	0.422199i
$297$	10.7362	+	18.5957i	0.622979	+	1.07903i
$298$	−14.5917			−0.845272
$299$	−21.4872	+	18.1211i	−1.24264	+	1.04797i
$300$	16.6818			0.963126
$301$		0			0
$302$	−0.795832	−	1.37842i	−0.0457950	−	0.0793192i
$303$	6.89792	−	11.9475i	0.396275	−	0.686368i
$304$	−2.82843			−0.162221
$305$	−17.0917	+	29.6036i	−0.978666	+	1.69510i
$306$	0.634922	−	1.09972i	0.0362961	−	0.0628667i
$307$	20.0583			1.14478			0.572392	−	0.819980i	$-0.306015\pi$
$307$	20.0583			1.14478			0.572392	+	0.819980i	$0.306015\pi$
$308$		0			0
$309$	−3.79583	−	6.57457i	−0.215937	−	0.374014i
$310$	2.89792	+	5.01934i	0.164591	+	0.285079i
$311$	28.8323			1.63493			0.817464	−	0.575980i	$-0.195379\pi$
$311$	28.8323			1.63493			0.817464	+	0.575980i	$0.195379\pi$
$312$	11.6937	−	9.86186i	0.662028	−	0.558318i
$313$	−15.2676			−0.862976			−0.431488	−	0.902119i	$-0.642011\pi$
$313$	−15.2676			−0.862976			−0.431488	+	0.902119i	$0.642011\pi$
$314$	−0.0721845	−	0.125027i	−0.00407360	−	0.00705569i
$315$		0			0
$316$	−1.10208	+	1.90887i	−0.0619971	+	0.107382i
$317$	6.59166			0.370225			0.185112	−	0.982717i	$-0.440735\pi$
$317$	6.59166			0.370225			0.185112	+	0.982717i	$0.440735\pi$
$318$	−8.90365	+	15.4216i	−0.499292	+	0.864799i
$319$	1.51042	−	2.61613i	0.0845674	−	0.146475i
$320$	−28.6879			−1.60370
$321$	−4.24264	+	7.34847i	−0.236801	+	0.410152i
$322$		0			0
$323$	−1.79583	−	3.11047i	−0.0999227	−	0.173071i
$324$	5.00000			0.277778
$325$	7.48944	+	41.8659i	0.415439	+	2.32230i
$326$	15.3875			0.852235
$327$	1.12548	+	1.94938i	0.0622390	+	0.107801i
$328$	−4.45919	−	7.72355i	−0.246218	−	0.426462i
$329$		0			0
$330$	−22.0000			−1.21106
$331$	−14.6937	+	25.4503i	−0.807641	+	1.39888i	0.106852	+	0.994275i	$0.465923\pi$
$331$	−14.6937	+	25.4503i	−0.807641	+	1.39888i	−0.914493	+	0.404601i	$0.867410\pi$
$332$	4.94975	−	8.57321i	0.271653	−	0.470516i
$333$	−2.79583			−0.153211
$334$	0.851476	−	1.47480i	0.0465907	−	0.0806974i
$335$	−7.77817	−	13.4722i	−0.424967	−	0.736065i
$336$		0			0
$337$	17.9792			0.979387			0.489694	−	0.871895i	$-0.337109\pi$
$337$	17.9792			0.979387			0.489694	+	0.871895i	$0.337109\pi$
$338$	10.0000	+	8.30662i	0.543928	+	0.451821i
$339$	−3.66517			−0.199064
$340$	−2.60208	−	4.50694i	−0.141118	−	0.244423i
$341$	2.68406	+	4.64893i	0.145350	+	0.251753i
$342$	1.41421	−	2.44949i	0.0764719	−	0.132453i
$343$		0			0
$344$	11.6937	−	20.2542i	0.630485	−	1.09203i
$345$	22.5917	−	39.1299i	1.21629	−	2.10668i
$346$	17.8073			0.957326
$347$	16.4896	−	28.5608i	0.885207	−	1.53322i	0.0397307	−	0.999210i	$-0.487350\pi$
$347$	16.4896	−	28.5608i	0.885207	−	1.53322i	0.845476	−	0.534013i	$-0.179317\pi$
$348$	−0.562738	−	0.974691i	−0.0301659	−	0.0522489i
$349$	13.2907	+	23.0201i	0.711433	+	1.23224i	0.964319	+	0.264742i	$0.0852867\pi$
$349$	13.2907	+	23.0201i	0.711433	+	1.23224i	−0.252887	+	0.967496i	$0.581380\pi$
$350$		0			0
$351$	3.59166	+	20.0773i	0.191709	+	1.07165i
$352$	−18.9792			−1.01159
$353$	2.61187	+	4.52390i	0.139016	+	0.240783i	0.927124	−	0.374754i	$-0.122273\pi$
$353$	2.61187	+	4.52390i	0.139016	+	0.240783i	−0.788108	+	0.615536i	$0.788939\pi$
$354$	8.79583	+	15.2348i	0.467493	+	0.809722i
$355$	12.2948	−	21.2952i	0.652541	−	1.13023i
$356$	−14.9789			−0.793879
$357$		0			0
$358$	9.79583	−	16.9669i	0.517726	−	0.896727i
$359$	−4.00000			−0.211112			−0.105556	−	0.994413i	$-0.533662\pi$
$359$	−4.00000			−0.211112			−0.105556	+	0.994413i	$0.533662\pi$
$360$	6.14741	−	10.6476i	0.323997	−	0.561179i
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	1.90477	+	3.29915i	0.100112	+	0.173400i
$363$	−4.82012			−0.252990
$364$		0			0
$365$	−51.5708			−2.69934
$366$	−5.89792	−	10.2155i	−0.308289	−	0.533972i
$367$	10.6066	+	18.3712i	0.553660	+	0.958967i	0.998006	+	0.0631123i	$0.0201026\pi$
$367$	10.6066	+	18.3712i	0.553660	+	0.958967i	−0.444346	+	0.895855i	$0.646564\pi$
$368$	−3.89792	+	6.75139i	−0.203193	+	0.351940i
$369$	2.97280			0.154758
$370$	5.72904	−	9.92299i	0.297839	−	0.515871i
$371$		0			0
$372$	2.00000			0.103695
$373$	−3.29583	+	5.70855i	−0.170652	+	0.295577i	−0.938648	−	0.344877i	$-0.887921\pi$
$373$	−3.29583	+	5.70855i	−0.170652	+	0.295577i	0.767996	+	0.640454i	$0.221254\pi$
$374$	2.41006	+	4.17434i	0.124621	+	0.215850i
$375$	−19.6937	−	34.1106i	−1.01698	−	1.76146i
$376$	8.48528			0.437595
$377$	2.19350	−	1.84988i	0.112971	−	0.0952737i
$378$		0			0
$379$	−12.6937	−	21.9862i	−0.652034	−	1.12936i	−0.982629	−	0.185583i	$-0.940583\pi$
$379$	−12.6937	−	21.9862i	−0.652034	−	1.12936i	0.330595	−	0.943773i	$-0.392751\pi$
$380$	−5.79583	−	10.0387i	−0.297320	−	0.514973i
$381$	−8.19654	+	14.1968i	−0.419922	+	0.727326i
$382$	−16.2042			−0.829077
$383$	6.07522	−	10.5226i	0.310429	−	0.537680i	−0.668026	−	0.744138i	$-0.732860\pi$
$383$	6.07522	−	10.5226i	0.310429	−	0.537680i	0.978455	+	0.206458i	$0.0661938\pi$
$384$	−2.12132	+	3.67423i	−0.108253	+	0.187500i
$385$		0			0
$386$	−11.2958	+	19.5650i	−0.574943	+	0.995830i
$387$	3.89792	+	6.75139i	0.198142	+	0.343192i
$388$	2.12132	+	3.67423i	0.107694	+	0.186531i
$389$	−0.387495			−0.0196468			−0.00982338	−	0.999952i	$-0.503127\pi$
$389$	−0.387495			−0.0196468			−0.00982338	+	0.999952i	$0.503127\pi$
$390$	−19.6546	−	7.09841i	−0.995250	−	0.359442i
$391$	−9.89949			−0.500639
$392$		0			0
$393$	−3.79583	−	6.57457i	−0.191474	−	0.331643i
$394$	4.00000	−	6.92820i	0.201517	−	0.349038i
$395$	9.03328			0.454514
$396$	1.89792	−	3.28729i	0.0953739	−	0.165192i
$397$	3.53553	−	6.12372i	0.177443	−	0.307341i	−0.763561	−	0.645736i	$-0.776551\pi$
$397$	3.53553	−	6.12372i	0.177443	−	0.307341i	0.941004	+	0.338395i	$0.109884\pi$
$398$	−5.07938			−0.254606
$399$		0			0
$400$	5.89792	+	10.2155i	0.294896	+	0.510774i
$401$	2.19375	+	3.79968i	0.109551	+	0.189747i	0.915588	−	0.402117i	$-0.131726\pi$
$401$	2.19375	+	3.79968i	0.109551	+	0.189747i	−0.806038	+	0.591864i	$0.798392\pi$
$402$	5.36812			0.267737
$403$	0.897916	+	5.01934i	0.0447284	+	0.250031i
$404$	−9.75513			−0.485336
$405$	−10.2457	−	17.7460i	−0.509112	−	0.881808i
$406$		0			0
$407$	5.30625	−	9.19070i	0.263021	−	0.455566i
$408$	5.38749			0.266721
$409$	9.39420	−	16.2712i	0.464513	−	0.804561i	−0.534666	−	0.845063i	$-0.679563\pi$
$409$	9.39420	−	16.2712i	0.464513	−	0.804561i	0.999179	+	0.0405026i	$0.0128959\pi$
$410$	−6.09166	+	10.5511i	−0.300846	+	0.521080i
$411$	26.5813			1.31116
$412$	−2.68406	+	4.64893i	−0.132234	+	0.229036i
$413$		0			0
$414$	−3.89792	−	6.75139i	−0.191572	−	0.331813i
$415$	−40.5708			−1.99154
$416$	−16.9558	−	6.12372i	−0.831328	−	0.300240i
$417$	−2.40834			−0.117937
$418$	5.36812	+	9.29785i	0.262563	+	0.454773i
$419$	−12.8576	−	22.2699i	−0.628133	−	1.08796i	−0.987926	−	0.154926i	$-0.950486\pi$
$419$	−12.8576	−	22.2699i	−0.628133	−	1.08796i	0.359794	−	0.933032i	$-0.382847\pi$
$420$		0			0
$421$	12.5917			0.613680			0.306840	−	0.951761i	$-0.400728\pi$
$421$	12.5917			0.613680			0.306840	+	0.951761i	$0.400728\pi$
$422$	−3.89792	+	6.75139i	−0.189748	+	0.328652i
$423$	−1.41421	+	2.44949i	−0.0687614	+	0.119098i
$424$	37.7750			1.83452
$425$	−7.48944	+	12.9721i	−0.363291	+	0.629239i
$426$	4.24264	+	7.34847i	0.205557	+	0.356034i
$427$		0			0
$428$	6.00000			0.290021
$429$	−18.2042	−	6.57457i	−0.878906	−	0.317423i
$430$	−31.9494			−1.54074
$431$	−16.5917	−	28.7376i	−0.799192	−	1.38424i	−0.920143	−	0.391583i	$-0.871928\pi$
$431$	−16.5917	−	28.7376i	−0.799192	−	1.38424i	0.120950	−	0.992659i	$-0.461406\pi$
$432$	2.82843	+	4.89898i	0.136083	+	0.235702i
$433$	−10.2457	+	17.7460i	−0.492376	+	0.852820i	−0.999961	−	0.00878126i	$-0.997205\pi$
$433$	−10.2457	+	17.7460i	−0.492376	+	0.852820i	0.507586	+	0.861601i	$0.330538\pi$
$434$		0			0
$435$	−2.30625	+	3.99455i	−0.110576	+	0.191524i
$436$	0.795832	−	1.37842i	0.0381134	−	0.0660144i
$437$	−22.0499			−1.05479
$438$	8.89792	−	15.4116i	0.425159	−	0.736397i
$439$	−10.0291	−	17.3710i	−0.478664	−	0.829070i	0.521037	−	0.853534i	$-0.325545\pi$
$439$	−10.0291	−	17.3710i	−0.478664	−	0.829070i	−0.999701	+	0.0244638i	$0.992212\pi$
$440$	23.3345	+	40.4166i	1.11243	+	1.92678i
$441$		0			0
$442$	0.806253	+	4.50694i	0.0383495	+	0.214373i
$443$	10.0000			0.475114			0.237557	−	0.971374i	$-0.423653\pi$
$443$	10.0000			0.475114			0.237557	+	0.971374i	$0.423653\pi$
$444$	−1.97695	−	3.42418i	−0.0938220	−	0.162504i
$445$	30.6937	+	53.1631i	1.45502	+	2.52017i
$446$	−2.82843	+	4.89898i	−0.133930	+	0.231973i
$447$	20.6357			0.976036
$448$		0			0
$449$	−11.7958	+	20.4310i	−0.556680	+	0.964198i	0.441091	+	0.897462i	$0.354592\pi$
$449$	−11.7958	+	20.4310i	−0.556680	+	0.964198i	−0.997771	+	0.0667352i	$0.978742\pi$
$450$	−11.7958			−0.556061
$451$	−5.64212	+	9.77243i	−0.265677	+	0.460166i
$452$	1.29583	+	2.24445i	0.0609508	+	0.105570i
$453$	1.12548	+	1.94938i	0.0528795	+	0.0915899i
$454$	−7.35981			−0.345413
$455$		0			0
$456$	12.0000			0.561951
$457$	−2.29583	−	3.97650i	−0.107394	−	0.186013i	0.807320	−	0.590115i	$-0.200917\pi$
$457$	−2.29583	−	3.97650i	−0.107394	−	0.186013i	−0.914714	+	0.404102i	$0.867584\pi$
$458$	6.36396	+	11.0227i	0.297368	+	0.515057i
$459$	−3.59166	+	6.22094i	−0.167644	+	0.290369i
$460$	−31.9494			−1.48965
$461$	12.0930	−	20.9457i	0.563227	−	0.975538i	−0.433985	−	0.900920i	$-0.642893\pi$
$461$	12.0930	−	20.9457i	0.563227	−	0.975538i	0.997212	−	0.0746180i	$-0.0237737\pi$
$462$		0			0
$463$	−17.3875			−0.808065			−0.404033	−	0.914745i	$-0.632392\pi$
$463$	−17.3875			−0.808065			−0.404033	+	0.914745i	$0.632392\pi$
$464$	0.397916	−	0.689210i	0.0184728	−	0.0319958i
$465$	−4.09827	−	7.09841i	−0.190053	−	0.329181i
$466$	−8.59166	−	14.8812i	−0.398001	−	0.689358i
$467$	31.9494			1.47844			0.739222	−	0.673462i	$-0.235194\pi$
$467$	31.9494			1.47844			0.739222	+	0.673462i	$0.235194\pi$
$468$	2.75624	−	2.32446i	0.127407	−	0.107448i
$469$		0			0
$470$	−5.79583	−	10.0387i	−0.267342	−	0.463050i
$471$	0.102084	+	0.176815i	0.00470379	+	0.00814721i
$472$	18.6588	−	32.3179i	0.858840	−	1.48755i
$473$	−29.5917			−1.36063
$474$	−1.55858	+	2.69954i	−0.0715881	+	0.123994i
$475$	−16.6818	+	28.8938i	−0.765415	+	1.32574i
$476$		0			0
$477$	−6.29583	+	10.9047i	−0.288266	+	0.499292i
$478$	5.10208	+	8.83707i	0.233364	+	0.404198i
$479$	−10.4622	−	18.1211i	−0.478032	−	0.827975i	0.521651	−	0.853159i	$-0.325316\pi$
$479$	−10.4622	−	18.1211i	−0.478032	−	0.827975i	−0.999683	+	0.0251838i	$0.991983\pi$
$480$	28.9792			1.32271
$481$	7.70599	−	6.49881i	0.351363	−	0.296320i
$482$	−11.1693			−0.508749
$483$		0			0
$484$	1.70417	+	2.95171i	0.0774622	+	0.134168i
$485$	8.69375	−	15.0580i	0.394763	−	0.683749i
$486$	−9.89949			−0.449050
$487$	−0.204168	+	0.353630i	−0.00925176	+	0.0160245i	−0.870614	−	0.491966i	$-0.836278\pi$
$487$	−0.204168	+	0.353630i	−0.00925176	+	0.0160245i	0.861362	+	0.507991i	$0.169612\pi$
$488$	−12.5114	+	21.6703i	−0.566363	+	0.980970i
$489$	−21.7612			−0.984076
$490$		0			0
$491$	−4.79583	−	8.30662i	−0.216433	−	0.374873i	0.737282	−	0.675585i	$-0.236109\pi$
$491$	−4.79583	−	8.30662i	−0.216433	−	0.374873i	−0.953715	+	0.300712i	$0.902776\pi$
$492$	2.10208	+	3.64092i	0.0947693	+	0.164145i
$493$	1.01058			0.0455143
$494$	1.79583	+	10.0387i	0.0807983	+	0.451661i
$495$	−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
$499$	25.7958			1.15478			0.577390	−	0.816468i	$-0.304071\pi$
$499$	25.7958			1.15478			0.577390	+	0.816468i	$0.304071\pi$
$500$	−13.9256	+	24.1198i	−0.622771	+	1.07867i
$501$	−1.20417	+	2.08568i	−0.0537983	+	0.0931814i
$502$	16.6818			0.744546
$503$	12.8576	−	22.2699i	0.573290	−	0.992967i	−0.422935	−	0.906160i	$-0.639000\pi$
$503$	12.8576	−	22.2699i	0.573290	−	0.992967i	0.996225	−	0.0868074i	$-0.0276665\pi$
$504$		0			0
$505$	19.9896	+	34.6230i	0.889525	+	1.54070i
$506$	29.5917			1.31551
$507$	−14.1421	−	11.7473i	−0.628074	−	0.521718i
$508$	11.5917			0.514297
$509$	3.04498	+	5.27406i	0.134966	+	0.233769i	0.925585	−	0.378541i	$-0.123574\pi$
$509$	3.04498	+	5.27406i	0.134966	+	0.233769i	−0.790618	+	0.612309i	$0.790241\pi$
$510$	−3.67990	−	6.37378i	−0.162949	−	0.282236i
$511$		0			0
$512$	−11.0000			−0.486136
$513$	−8.00000	+	13.8564i	−0.353209	+	0.611775i
$514$	4.31483	−	7.47350i	0.190319	−	0.329642i
$515$	22.0000			0.969436
$516$	−5.51249	+	9.54790i	−0.242674	+	0.420323i
$517$	−5.36812	−	9.29785i	−0.236089	−	0.408919i
$518$		0			0
$519$	−25.1833			−1.10543
$520$	7.80625	+	43.6369i	0.342327	+	1.91360i
$521$	−4.67575			−0.204848			−0.102424	−	0.994741i	$-0.532660\pi$
$521$	−4.67575			−0.204848			−0.102424	+	0.994741i	$0.532660\pi$
$522$	0.397916	+	0.689210i	0.0174163	+	0.0301659i
$523$	21.0688	+	36.4923i	0.921276	+	1.59570i	0.797444	+	0.603393i	$0.206185\pi$
$523$	21.0688	+	36.4923i	0.921276	+	1.59570i	0.123832	+	0.992303i	$0.460482\pi$
$524$	−2.68406	+	4.64893i	−0.117254	+	0.203089i
$525$		0			0
$526$	−1.69375	+	2.93366i	−0.0738509	+	0.127913i
$527$	−0.897916	+	1.55524i	−0.0391138	+	0.0677471i
$528$	−5.36812			−0.233617
$529$	−18.8875	+	32.7141i	−0.821195	+	1.42235i
$530$	−25.8020	−	44.6904i	−1.12077	−	1.94123i
$531$	6.21959	+	10.7726i	0.269907	+	0.467493i
$532$		0			0
$533$	−8.19375	+	6.91015i	−0.354911	+	0.299312i
$534$	−21.1833			−0.916692
$535$	−12.2948	−	21.2952i	−0.531551	−	0.920674i
$536$	−5.69375	−	9.86186i	−0.245932	−	0.425967i
$537$	−13.8534	+	23.9948i	−0.597818	+	1.03545i
$538$	−12.4392			−0.536291
$539$		0			0
$540$	−11.5917	+	20.0773i	−0.498826	+	0.863992i
$541$	6.59166			0.283398			0.141699	−	0.989910i	$-0.454744\pi$
$541$	6.59166			0.283398			0.141699	+	0.989910i	$0.454744\pi$
$542$	8.75928	−	15.1715i	0.376243	−	0.651673i
$543$	−2.69375	−	4.66571i	−0.115600	−	0.200225i
$544$	−3.17461	−	5.49859i	−0.136110	−	0.235750i
$545$	−6.52307			−0.279418
$546$		0			0
$547$	10.9792			0.469435			0.234717	−	0.972064i	$-0.424584\pi$
$547$	10.9792			0.469435			0.234717	+	0.972064i	$0.424584\pi$
$548$	−9.39792	−	16.2777i	−0.401459	−	0.695347i
$549$	−4.17046	−	7.22344i	−0.177991	−	0.308289i
$550$	22.3875	−	38.7763i	0.954606	−	1.65343i
$551$	2.25095			0.0958938
$552$	16.5375	−	28.6437i	0.703881	−	1.21916i
$553$		0			0
$554$	32.1833			1.36734
$555$	−8.10208	+	14.0332i	−0.343914	+	0.595677i
$556$	0.851476	+	1.47480i	0.0361106	+	0.0625454i
$557$	−0.704168	−	1.21966i	−0.0298366	−	0.0516785i	0.850722	−	0.525617i	$-0.176165\pi$
$557$	−0.704168	−	1.21966i	−0.0298366	−	0.0516785i	−0.880558	+	0.473938i	$0.842832\pi$
$558$	−1.41421			−0.0598684
$559$	−26.4370	−	9.54790i	−1.11816	−	0.403833i
$560$		0			0
$561$	−3.40834	−	5.90341i	−0.143900	−	0.249242i
$562$	−12.3979	−	21.4738i	−0.522975	−	0.905818i
$563$	6.21959	−	10.7726i	0.262125	−	0.454013i	−0.704682	−	0.709524i	$-0.748910\pi$
$563$	6.21959	−	10.7726i	0.262125	−	0.454013i	0.966806	+	0.255511i	$0.0822435\pi$
$564$	−4.00000			−0.168430
$565$	5.31067	−	9.19835i	0.223422	−	0.386977i
$566$	−7.92254	+	13.7222i	−0.333009	+	0.576789i
$567$		0			0
$568$	9.00000	−	15.5885i	0.377632	−	0.654077i
$569$	−12.7958	−	22.1630i	−0.536429	−	0.929123i	−0.999093	−	0.0425886i	$-0.986440\pi$
$569$	−12.7958	−	22.1630i	−0.536429	−	0.929123i	0.462664	−	0.886534i	$-0.346894\pi$
$570$	−8.19654	−	14.1968i	−0.343315	−	0.594640i
$571$	−23.1833			−0.970192			−0.485096	−	0.874461i	$-0.661215\pi$
$571$	−23.1833			−0.970192			−0.485096	+	0.874461i	$0.661215\pi$
$572$	2.41006	+	13.4722i	0.100770	+	0.563301i
$573$	22.9162			0.957336
$574$		0			0
$575$	45.9792	+	79.6382i	1.91746	+	3.32114i
$576$	3.50000	−	6.06218i	0.145833	−	0.252591i
$577$	−24.7340			−1.02969			−0.514845	−	0.857283i	$-0.672151\pi$
$577$	−24.7340			−1.02969			−0.514845	+	0.857283i	$0.672151\pi$
$578$	7.69375	−	13.3260i	0.320018	−	0.554287i
$579$	15.9747	−	27.6690i	0.663887	−	1.14989i
$580$	3.26153			0.135428
$581$		0			0
$582$	3.00000	+	5.19615i	0.124354	+	0.215387i
$583$	−23.8979	−	41.3924i	−0.989751	−	1.71430i
$584$	−37.7507			−1.56213
$585$	−13.8979	−	5.01934i	−0.574608	−	0.207524i
$586$	2.97280			0.122805
$587$	8.34091	+	14.4469i	0.344266	+	0.596287i	0.985220	−	0.171293i	$-0.0547944\pi$
$587$	8.34091	+	14.4469i	0.344266	+	0.596287i	−0.640954	+	0.767579i	$0.721461\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$	−50.9792			−2.09878
$591$	−5.65685	+	9.79796i	−0.232692	+	0.403034i
$592$	1.39792	−	2.42126i	0.0574540	−	0.0995132i
$593$	8.34091			0.342520			0.171260	−	0.985226i	$-0.445216\pi$
$593$	8.34091			0.342520			0.171260	+	0.985226i	$0.445216\pi$
$594$	10.7362	−	18.5957i	0.440513	−	0.762991i
$595$		0			0
$596$	−7.29583	−	12.6368i	−0.298849	−	0.517621i
$597$	7.18333			0.293994
$598$	26.4370	+	9.54790i	1.08109	+	0.390443i
$599$	−33.5917			−1.37252			−0.686259	−	0.727357i	$-0.740748\pi$
$599$	−33.5917			−1.37252			−0.686259	+	0.727357i	$0.740748\pi$
$600$	−25.0227	−	43.3407i	−1.02155	−	1.76937i
$601$	−12.0930	−	20.9457i	−0.493284	−	0.854393i	0.506686	−	0.862130i	$-0.330870\pi$
$601$	−12.0930	−	20.9457i	−0.493284	−	0.854393i	−0.999970	+	0.00773797i	$0.997537\pi$
$602$		0			0
$603$	3.79583			0.154578
$604$	0.795832	−	1.37842i	0.0323819	−	0.0560871i
$605$	6.98415	−	12.0969i	0.283946	−	0.491809i
$606$	−13.7958			−0.560417
$607$	2.39532	−	4.14882i	0.0972231	−	0.168395i	−0.813311	−	0.581829i	$-0.802337\pi$
$607$	2.39532	−	4.14882i	0.0972231	−	0.168395i	0.910534	+	0.413434i	$0.135671\pi$
$608$	−7.07107	−	12.2474i	−0.286770	−	0.496700i
$609$		0			0
$610$	34.1833			1.38404
$611$	−1.79583	−	10.0387i	−0.0726516	−	0.406121i
$612$	1.26984			0.0513304
$613$	−20.9896	−	36.3550i	−0.847761	−	1.46837i	−0.883202	−	0.468994i	$-0.844617\pi$
$613$	−20.9896	−	36.3550i	−0.847761	−	1.46837i	0.0354405	−	0.999372i	$-0.488717\pi$
$614$	−10.0291	−	17.3710i	−0.404743	−	0.701035i
$615$	8.61491	−	14.9215i	0.347387	−	0.601692i
$616$		0			0
$617$	−2.19375	+	3.79968i	−0.0883169	+	0.152969i	−0.906800	−	0.421561i	$-0.861482\pi$
$617$	−2.19375	+	3.79968i	−0.0883169	+	0.152969i	0.818483	+	0.574531i	$0.194815\pi$
$618$	−3.79583	+	6.57457i	−0.152691	+	0.264468i
$619$	33.9116			1.36302			0.681512	−	0.731807i	$-0.261323\pi$
$619$	33.9116			1.36302			0.681512	+	0.731807i	$0.261323\pi$
$620$	−2.89792	+	5.01934i	−0.116383	+	0.201581i
$621$	22.0499	+	38.1916i	0.884834	+	1.53258i
$622$	−14.4161	−	24.9695i	−0.578034	−	1.00118i
$623$		0			0
$624$	−4.79583	−	1.73205i	−0.191987	−	0.0693375i
$625$	55.1625			2.20650
$626$	7.63381	+	13.2221i	0.305108	+	0.528463i
$627$	−7.59166	−	13.1491i	−0.303182	−	0.525126i
$628$	0.0721845	−	0.125027i	0.00288047	−	0.00498913i
$629$	3.55027			0.141559
$630$		0			0
$631$	19.7958	−	34.2874i	0.788060	−	1.36496i	−0.139095	−	0.990279i	$-0.544419\pi$
$631$	19.7958	−	34.2874i	0.788060	−	1.36496i	0.927154	−	0.374680i	$-0.122247\pi$
$632$	6.61251			0.263031
$633$	5.51249	−	9.54790i	0.219102	−	0.379495i
$634$	−3.29583	−	5.70855i	−0.130894	−	0.226715i
$635$	−23.7529	−	41.1412i	−0.942605	−	1.63264i
$636$	−17.8073			−0.706105
$637$		0			0
$638$	−3.02084			−0.119596
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$	−6.14741	−	10.6476i	−0.242998	−	0.420884i
$641$	2.39792	−	4.15331i	0.0947120	−	0.164046i	−0.814776	−	0.579775i	$-0.803140\pi$
$641$	2.39792	−	4.15331i	0.0947120	−	0.164046i	0.909488	+	0.415729i	$0.136474\pi$
$642$	8.48528			0.334887
$643$	2.82843	−	4.89898i	0.111542	−	0.193197i	−0.804850	−	0.593478i	$-0.797754\pi$
$643$	2.82843	−	4.89898i	0.111542	−	0.193197i	0.916392	+	0.400281i	$0.131088\pi$
$644$		0			0
$645$	45.1833			1.77909
$646$	−1.79583	+	3.11047i	−0.0706560	+	0.122380i
$647$	19.3659	+	33.5427i	0.761351	+	1.31870i	0.942154	+	0.335180i	$0.108797\pi$
$647$	19.3659	+	33.5427i	0.761351	+	1.31870i	−0.180803	+	0.983519i	$0.557870\pi$
$648$	−7.50000	−	12.9904i	−0.294628	−	0.510310i
$649$	−47.2170			−1.85343
$650$	32.5122	−	27.4190i	1.27523	−	1.07546i
$651$		0			0
$652$	7.69375	+	13.3260i	0.301310	+	0.521885i
$653$	6.59166	+	11.4171i	0.257952	+	0.446785i	0.965693	−	0.259686i	$-0.0836191\pi$
$653$	6.59166	+	11.4171i	0.257952	+	0.446785i	−0.707741	+	0.706472i	$0.750286\pi$
$654$	1.12548	−	1.94938i	0.0440096	−	0.0762268i
$655$	22.0000			0.859611
$656$	−1.48640	+	2.57452i	−0.0580341	+	0.100518i
$657$	6.29178	−	10.8977i	0.245466	−	0.425159i
$658$		0			0
$659$	9.20417	−	15.9421i	0.358543	−	0.621016i	−0.629174	−	0.777264i	$-0.716607\pi$
$659$	9.20417	−	15.9421i	0.358543	−	0.621016i	0.987718	+	0.156249i	$0.0499401\pi$
$660$	−11.0000	−	19.0526i	−0.428174	−	0.741620i
$661$	3.75209	+	6.49881i	0.145939	+	0.252774i	0.929723	−	0.368260i	$-0.120046\pi$
$661$	3.75209	+	6.49881i	0.145939	+	0.252774i	−0.783784	+	0.621034i	$0.786713\pi$
$662$	29.3875			1.14218
$663$	−1.14021	−	6.37378i	−0.0442822	−	0.247537i
$664$	−29.6985			−1.15252
$665$		0			0
$666$	1.39792	+	2.42126i	0.0541681	+	0.0938220i
$667$	3.10208	−	5.37297i	0.120113	−	0.208042i
$668$	1.70295			0.0658892
$669$	4.00000	−	6.92820i	0.154649	−	0.267860i
$670$	−7.77817	+	13.4722i	−0.300497	+	0.520476i
$671$	31.6607			1.22225
$672$		0			0
$673$	11.9896	+	20.7666i	0.462164	+	0.800492i	0.999069	−	0.0431511i	$-0.0137397\pi$
$673$	11.9896	+	20.7666i	0.462164	+	0.800492i	−0.536904	+	0.843643i	$0.680406\pi$
$674$	−8.98958	−	15.5704i	−0.346266	−	0.599750i
$675$	66.7273			2.56833
$676$	−2.19375	+	12.8136i	−0.0843749	+	0.492829i
$677$	−7.64854			−0.293957			−0.146979	−	0.989140i	$-0.546955\pi$
$677$	−7.64854			−0.293957			−0.146979	+	0.989140i	$0.546955\pi$
$678$	1.83258	+	3.17413i	0.0703799	+	0.121902i
$679$		0			0
$680$	−7.80625	+	13.5208i	−0.299356	+	0.518500i
$681$	10.4083			0.398848
$682$	2.68406	−	4.64893i	0.102778	−	0.178017i
$683$	3.38749	−	5.86731i	0.129619	−	0.224506i	−0.793910	−	0.608035i	$-0.791958\pi$
$683$	3.38749	−	5.86731i	0.129619	−	0.224506i	0.923529	+	0.383529i	$0.125291\pi$
$684$	2.82843			0.108148
$685$	−38.5152	+	66.7103i	−1.47159	+	2.54887i
$686$		0			0
$687$	−9.00000	−	15.5885i	−0.343371	−	0.594737i
$688$	−7.79583			−0.297213
$689$	−7.99473	−	44.6904i	−0.304575	−	1.70257i
$690$	−45.1833			−1.72010
$691$	−1.26984	−	2.19944i	−0.0483072	−	0.0836705i	0.840861	−	0.541251i	$-0.182049\pi$
$691$	−1.26984	−	2.19944i	−0.0483072	−	0.0836705i	−0.889168	+	0.457581i	$0.848716\pi$
$692$	8.90365	+	15.4216i	0.338466	+	0.586240i
$693$		0			0
$694$	−32.9792			−1.25187
$695$	3.48958	−	6.04413i	0.132367	−	0.229267i
$696$	−1.68821	+	2.92407i	−0.0639916	+	0.110837i
$697$	−3.77499			−0.142988
$698$	13.2907	−	23.0201i	0.503059	−	0.871324i
$699$	12.1504	+	21.0452i	0.459572	+	0.796002i
$700$		0			0
$701$	−29.5917			−1.11766			−0.558831	−	0.829282i	$-0.688750\pi$
$701$	−29.5917			−1.11766			−0.558831	+	0.829282i	$0.688750\pi$
$702$	15.5917	−	13.1491i	0.588469	−	0.496283i
$703$	7.90781			0.298249
$704$	13.2854	+	23.0110i	0.500713	+	0.867260i
$705$	8.19654	+	14.1968i	0.308700	+	0.534684i
$706$	2.61187	−	4.52390i	0.0982992	−	0.170259i
$707$		0			0
$708$	−8.79583	+	15.2348i	−0.330568	+	0.572560i
$709$	4.60208	−	7.97104i	0.172835	−	0.299359i	−0.766575	−	0.642155i	$-0.778041\pi$
$709$	4.60208	−	7.97104i	0.172835	−	0.299359i	0.939410	+	0.342796i	$0.111374\pi$
$710$	−24.5896			−0.922832
$711$	−1.10208	+	1.90887i	−0.0413314	+	0.0715881i
$712$	22.4683	+	38.9163i	0.842036	+	1.45845i
$713$	5.51249	+	9.54790i	0.206444	+	0.357572i
$714$		0			0
$715$	42.8771	−	36.1602i	1.60351	−	1.35231i
$716$	19.5917			0.732175
$717$	−7.21544	−	12.4975i	−0.269465	−	0.466728i
$718$	2.00000	+	3.46410i	0.0746393	+	0.129279i
$719$	0.995845	−	1.72485i	0.0371387	−	0.0643262i	−0.846859	−	0.531818i	$-0.821509\pi$
$719$	0.995845	−	1.72485i	0.0371387	−	0.0643262i	0.883997	+	0.467492i	$0.154842\pi$
$720$	−4.09827			−0.152734
$721$		0			0
$722$	5.50000	−	9.52628i	0.204689	−	0.354531i
$723$	15.7958			0.587453
$724$	−1.90477	+	3.29915i	−0.0707901	+	0.122612i
$725$	−4.69375	−	8.12981i	−0.174321	−	0.301934i
$726$	2.41006	+	4.17434i	0.0894456	+	0.154924i
$727$	−32.4974			−1.20526			−0.602632	−	0.798020i	$-0.705881\pi$
$727$	−32.4974			−1.20526			−0.602632	+	0.798020i	$0.705881\pi$
$728$		0			0
$729$	29.0000			1.07407
$730$	25.7854	+	44.6616i	0.954361	+	1.65300i
$731$	−4.94975	−	8.57321i	−0.183073	−	0.317092i
$732$	5.89792	−	10.2155i	0.217993	−	0.377575i
$733$	33.2193			1.22698			0.613491	−	0.789702i	$-0.289765\pi$
$733$	33.2193			1.22698			0.613491	+	0.789702i	$0.289765\pi$
$734$	10.6066	−	18.3712i	0.391497	−	0.678092i
$735$		0			0
$736$	−38.9792			−1.43679
$737$	−7.20417	+	12.4780i	−0.265369	+	0.459633i
$738$	−1.48640	−	2.57452i	−0.0547151	−	0.0947693i
$739$	11.5917	+	20.0773i	0.426406	+	0.738557i	0.996551	−	0.0829873i	$-0.0264461\pi$
$739$	11.5917	+	20.0773i	0.426406	+	0.738557i	−0.570144	+	0.821545i	$0.693113\pi$
$740$	11.4581			0.421207
$741$	−2.53969	−	14.1968i	−0.0932978	−	0.521534i
$742$		0			0
$743$	14.5917	+	25.2735i	0.535316	+	0.927195i	0.999148	+	0.0412716i	$0.0131409\pi$
$743$	14.5917	+	25.2735i	0.535316	+	0.927195i	−0.463832	+	0.885923i	$0.653526\pi$
$744$	−3.00000	−	5.19615i	−0.109985	−	0.190500i
$745$	−29.9003	+	51.7888i	−1.09546	+	1.89740i
$746$	6.59166			0.241338
$747$	4.94975	−	8.57321i	0.181102	−	0.313678i
$748$	−2.41006	+	4.17434i	−0.0881205	+	0.152629i
$749$		0			0
$750$	−19.6937	+	34.1106i	−0.719114	+	1.24554i
$751$	3.89792	+	6.75139i	0.142237	+	0.246362i	0.928339	−	0.371735i	$-0.121237\pi$
$751$	3.89792	+	6.75139i	0.142237	+	0.246362i	−0.786102	+	0.618097i	$0.787904\pi$
$752$	−1.41421	−	2.44949i	−0.0515711	−	0.0893237i
$753$	−23.5917			−0.859728
$754$	−2.69880	−	0.974691i	−0.0982844	−	0.0354961i
$755$	−6.52307			−0.237399
$756$		0			0
$757$	−6.59166	−	11.4171i	−0.239578	−	0.414961i	0.721015	−	0.692919i	$-0.243676\pi$
$757$	−6.59166	−	11.4171i	−0.239578	−	0.414961i	−0.960593	+	0.277958i	$0.910342\pi$
$758$	−12.6937	+	21.9862i	−0.461058	+	0.798575i
$759$	−41.8489			−1.51902
$760$	−17.3875	+	30.1160i	−0.630711	+	1.09242i
$761$	−8.90365	+	15.4216i	−0.322757	+	0.559032i	−0.981056	−	0.193725i	$-0.937943\pi$
$761$	−8.90365	+	15.4216i	−0.322757	+	0.559032i	0.658299	+	0.752757i	$0.271276\pi$
$762$	16.3931			0.593859
$763$		0			0
$764$	−8.10208	−	14.0332i	−0.293123	−	0.507704i
$765$	−2.60208	−	4.50694i	−0.0940786	−	0.162949i
$766$	−12.1504			−0.439013
$767$	−42.1833	−	15.2348i	−1.52315	−	0.550098i
$768$	24.0416			0.867528
$769$	2.12132	+	3.67423i	0.0764968	+	0.132496i	0.901736	−	0.432287i	$-0.142293\pi$
$769$	2.12132	+	3.67423i	0.0764968	+	0.132496i	−0.825239	+	0.564783i	$0.808960\pi$
$770$		0			0
$771$	−6.10208	+	10.5691i	−0.219761	+	0.380638i
$772$	−22.5917			−0.813092
$773$	17.3889	−	30.1185i	0.625436	−	1.08329i	−0.363020	−	0.931781i	$-0.618254\pi$
$773$	17.3889	−	30.1185i	0.625436	−	1.08329i	0.988456	−	0.151506i	$-0.0484124\pi$
$774$	3.89792	−	6.75139i	0.140108	−	0.242674i
$775$	16.6818			0.599229
$776$	6.36396	−	11.0227i	0.228453	−	0.395692i
$777$		0			0
$778$	0.193747	+	0.335580i	0.00694618	+	0.0120311i
$779$	−8.40834			−0.301260
$780$	−3.67990	−	20.5706i	−0.131762	−	0.736546i
$781$	−22.7750			−0.814953
$782$	4.94975	+	8.57321i	0.177003	+	0.306578i
$783$	−2.25095	−	3.89876i	−0.0804424	−	0.139330i
$784$		0			0
$785$	−0.591663			−0.0211174
$786$	−3.79583	+	6.57457i	−0.135393	+	0.234507i
$787$	−21.1985	+	36.7168i	−0.755644	+	1.30881i	0.189410	+	0.981898i	$0.439342\pi$
$787$	−21.1985	+	36.7168i	−0.755644	+	1.30881i	−0.945054	+	0.326915i	$0.893991\pi$
$788$	8.00000			0.284988
$789$	2.39532	−	4.14882i	0.0852757	−	0.147702i
$790$	−4.51664	−	7.82305i	−0.160695	−	0.278332i
$791$		0			0
$792$	−11.3875			−0.404637
$793$	28.2854	+	10.2155i	1.00444	+	0.362763i
$794$	−7.07107			−0.250943
$795$	36.4896	+	63.2018i	1.29415	+	2.24154i
$796$	−2.53969	−	4.39887i	−0.0900169	−	0.155914i
$797$	0.418369	−	0.724636i	0.0148194	−	0.0256679i	−0.858521	−	0.512779i	$-0.828616\pi$
$797$	0.418369	−	0.724636i	0.0148194	−	0.0256679i	0.873340	+	0.487111i	$0.161949\pi$
$798$		0			0
$799$	1.79583	−	3.11047i	0.0635320	−	0.110041i
$800$	−29.4896	+	51.0774i	−1.04261	+	1.80586i
$801$	−14.9789			−0.529252
$802$	2.19375	−	3.79968i	0.0774639	−	0.134171i
$803$	23.8825	+	41.3657i	0.842796	+	1.45977i
$804$	2.68406	+	4.64893i	0.0946594	+	0.163955i
$805$		0			0
$806$	3.89792	−	3.28729i	0.137298	−	0.115790i
$807$	17.5917			0.619256
$808$	14.6327	+	25.3446i	0.514776	+	0.891619i
$809$	18.6833	+	32.3605i	0.656871	+	1.13773i	0.981421	+	0.191865i	$0.0614536\pi$
$809$	18.6833	+	32.3605i	0.656871	+	1.13773i	−0.324551	+	0.945868i	$0.605213\pi$
$810$	−10.2457	+	17.7460i	−0.359996	+	0.623532i
$811$	52.0372			1.82727			0.913636	−	0.406533i	$-0.133262\pi$
$811$	52.0372			1.82727			0.913636	+	0.406533i	$0.133262\pi$
$812$		0			0
$813$	−12.3875	+	21.4558i	−0.434448	+	0.752487i
$814$	−10.6125			−0.371968
$815$	31.5311	−	54.6134i	1.10449	−	1.91302i
$816$	−0.897916	−	1.55524i	−0.0314333	−	0.0544441i
$817$	−11.0250	−	19.0958i	−0.385715	−	0.668078i
$818$	−18.7884			−0.656921
$819$		0			0
$820$	−12.1833			−0.425460
$821$	−18.1833	−	31.4944i	−0.634602	−	1.09916i	−0.986599	−	0.163162i	$-0.947831\pi$
$821$	−18.1833	−	31.4944i	−0.634602	−	1.09916i	0.351997	−	0.936001i	$-0.385503\pi$
$822$	−13.2907	−	23.0201i	−0.463565	−	0.802918i
$823$	10.3875	−	17.9917i	0.362085	−	0.627150i	−0.626219	−	0.779648i	$-0.715398\pi$
$823$	10.3875	−	17.9917i	0.362085	−	0.627150i	0.988304	+	0.152497i	$0.0487316\pi$
$824$	16.1043			0.561022
$825$	−31.6607	+	54.8379i	−1.10228	+	1.90921i
$826$		0			0
$827$	−20.9792			−0.729517			−0.364758	−	0.931102i	$-0.618848\pi$
$827$	−20.9792			−0.729517			−0.364758	+	0.931102i	$0.618848\pi$
$828$	3.89792	−	6.75139i	0.135462	−	0.234627i
$829$	−13.6368	−	23.6197i	−0.473627	−	0.820346i	0.525917	−	0.850536i	$-0.323722\pi$
$829$	−13.6368	−	23.6197i	−0.473627	−	0.820346i	−0.999544	+	0.0301895i	$0.990389\pi$
$830$	20.2854	+	35.1354i	0.704117	+	1.21957i
$831$	−45.5141			−1.57887
$832$	4.44446	+	24.8445i	0.154084	+	0.861326i
$833$		0			0
$834$	1.20417	+	2.08568i	0.0416969	+	0.0722212i
$835$	−3.48958	−	6.04413i	−0.120762	−	0.209166i
$836$	−5.36812	+	9.29785i	−0.185660	+	0.321573i
$837$	8.00000			0.276520
$838$	−12.8576	+	22.2699i	−0.444157	+	0.769302i
$839$	2.82843	−	4.89898i	0.0976481	−	0.169132i	−0.813063	−	0.582176i	$-0.802201\pi$
$839$	2.82843	−	4.89898i	0.0976481	−	0.169132i	0.910711	+	0.413045i	$0.135535\pi$
$840$		0			0
$841$	14.1833	−	24.5662i	0.489080	−	0.847112i
$842$	−6.29583	−	10.9047i	−0.216969	−	0.375801i
$843$	17.5333	+	30.3686i	0.603879	+	1.04595i
$844$	−7.79583			−0.268344
$845$	49.9733	−	18.4707i	1.71913	−	0.635410i
$846$	2.82843			0.0972433
$847$		0			0
$848$	−6.29583	−	10.9047i	−0.216200	−	0.374469i
$849$	11.2042	−	19.4062i	0.384526	−	0.666019i
$850$	14.9789			0.513771
$851$	10.8979	−	18.8757i	0.373576	−	0.647052i
$852$	−4.24264	+	7.34847i	−0.145350	+	0.251754i
$853$	33.5080			1.14729			0.573646	−	0.819103i	$-0.305528\pi$
$853$	33.5080			1.14729			0.573646	+	0.819103i	$0.305528\pi$
$854$		0			0
$855$	−5.79583	−	10.0387i	−0.198213	−	0.343315i
$856$	−9.00000	−	15.5885i	−0.307614	−	0.532803i
$857$	17.4037			0.594498			0.297249	−	0.954800i	$-0.403931\pi$
$857$	17.4037			0.594498			0.297249	+	0.954800i	$0.403931\pi$
$858$	3.40834	+	19.0526i	0.116359	+	0.650444i
$859$	−10.1882			−0.347618			−0.173809	−	0.984779i	$-0.555608\pi$
$859$	−10.1882			−0.347618			−0.173809	+	0.984779i	$0.555608\pi$
$860$	−15.9747	−	27.6690i	−0.544733	−	0.943506i
$861$		0			0
$862$	−16.5917	+	28.7376i	−0.565114	+	0.978807i
$863$	8.20417			0.279273			0.139637	−	0.990203i	$-0.455407\pi$
$863$	8.20417			0.279273			0.139637	+	0.990203i	$0.455407\pi$
$864$	−14.1421	+	24.4949i	−0.481125	+	0.833333i
$865$	36.4896	−	63.2018i	1.24068	−	2.14893i
$866$	20.4914			0.696325
$867$	−10.8806	+	18.8458i	−0.369525	+	0.640035i
$868$		0			0
$869$	−4.18333	−	7.24573i	−0.141910	−	0.245795i
$870$	4.61251			0.156379
$871$	−10.4622	+	8.82327i	−0.354499	+	0.298965i
$872$	−4.77499			−0.161702
$873$	2.12132	+	3.67423i	0.0717958	+	0.124354i
$874$	11.0250	+	19.0958i	0.372925	+	0.645925i
$875$		0			0
$876$	17.7958			0.601265
$877$	−2.39792	+	4.15331i	−0.0809719	+	0.140247i	−0.903668	−	0.428235i	$-0.859136\pi$
$877$	−2.39792	+	4.15331i	−0.0809719	+	0.140247i	0.822696	+	0.568482i	$0.192469\pi$
$878$	−10.0291	+	17.3710i	−0.338467	+	0.586241i
$879$	−4.20417			−0.141803
$880$	7.77817	−	13.4722i	0.262202	−	0.454148i
$881$	5.29593	+	9.17282i	0.178424	+	0.309040i	0.941341	−	0.337457i	$-0.109567\pi$
$881$	5.29593	+	9.17282i	0.178424	+	0.309040i	−0.762917	+	0.646497i	$0.776233\pi$
$882$		0			0
$883$	−45.3875			−1.52741			−0.763705	−	0.645565i	$-0.776622\pi$
$883$	−45.3875			−1.52741			−0.763705	+	0.645565i	$0.776622\pi$
$884$	−3.50000	+	2.95171i	−0.117718	+	0.0992766i
$885$	72.0954			2.42346
$886$	−5.00000	−	8.66025i	−0.167978	−	0.290947i
$887$	−21.0688	−	36.4923i	−0.707422	−	1.22529i	−0.965810	−	0.259250i	$-0.916525\pi$
$887$	−21.0688	−	36.4923i	−0.707422	−	1.22529i	0.258388	−	0.966041i	$-0.416809\pi$
$888$	−5.93085	+	10.2725i	−0.199026	+	0.344724i
$889$		0			0
$890$	30.6937	−	53.1631i	1.02886	−	1.78203i
$891$	−9.48958	+	16.4364i	−0.317913	+	0.550641i
$892$	−5.65685			−0.189405
$893$	4.00000	−	6.92820i	0.133855	−	0.231843i
$894$	−10.3179	−	17.8711i	−0.345081	−	0.597698i
$895$	−40.1460	−	69.5349i	−1.34193	−	2.32429i
$896$		0			0
$897$	−37.3875	−	13.5028i	−1.24833	−	0.450845i
$898$	23.5917			0.787264
$899$	−0.562738	−	0.974691i	−0.0187684	−	0.0325078i
$900$	−5.89792	−	10.2155i	−0.196597	−	0.340516i
$901$	7.99473	−	13.8473i	0.266343	−	0.461320i
$902$	11.2842			0.375724
$903$		0			0
$904$	3.88749	−	6.73334i	0.129296	−	0.223947i
$905$	15.6125			0.518977
$906$	1.12548	−	1.94938i	0.0373914	−	0.0647639i
$907$	−10.3063	−	17.8510i	−0.342214	−	0.592731i	0.642630	−	0.766177i	$-0.277843\pi$
$907$	−10.3063	−	17.8510i	−0.342214	−	0.592731i	−0.984843	+	0.173446i	$0.944510\pi$
$908$	−3.67990	−	6.37378i	−0.122122	−	0.211521i
$909$	−9.75513			−0.323557
$910$		0			0
$911$	−4.81667			−0.159584			−0.0797918	−	0.996812i	$-0.525426\pi$
$911$	−4.81667			−0.159584			−0.0797918	+	0.996812i	$0.525426\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	18.7884	+	32.5425i	0.621806	+	1.07700i
$914$	−2.29583	+	3.97650i	−0.0759394	+	0.131531i
$915$	−48.3425			−1.59815
$916$	−6.36396	+	11.0227i	−0.210271	+	0.364200i
$917$		0			0
$918$	7.18333			0.237085
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	−0.936632	−	0.350315i	$-0.886075\pi$
$919$	−5.00000	+	8.66025i	−0.164935	+	0.285675i	0.771697	+	0.635990i	$0.219408\pi$
$920$	47.9242	+	83.0071i	1.58001	+	2.73666i
$921$	14.1833	+	24.5662i	0.467356	+	0.809485i
$922$	−24.1860			−0.796523
$923$	−20.3470	−	7.34847i	−0.669729	−	0.241878i
$924$		0			0
$925$	−16.4896	−	28.5608i	−0.542174	−	0.939073i
$926$	8.69375	+	15.0580i	0.285694	+	0.494837i
$927$	−2.68406	+	4.64893i	−0.0881560	+	0.152691i
$928$	3.97916			0.130622
$929$	−10.6788	+	18.4962i	−0.350360	+	0.606841i	−0.986312	−	0.164887i	$-0.947274\pi$
$929$	−10.6788	+	18.4962i	−0.350360	+	0.606841i	0.635953	+	0.771728i	$0.280607\pi$
$930$	−4.09827	+	7.09841i	−0.134388	+	0.232766i
$931$		0			0
$932$	8.59166	−	14.8812i	0.281429	−	0.487450i
$933$	20.3875	+	35.3122i	0.667457	+	1.15607i
$934$	−15.9747	−	27.6690i	−0.522709	−	0.905358i
$935$	19.7541			0.646030
$936$	−10.1735	−	3.67423i	−0.332531	−	0.120096i
$937$	13.7090			0.447854			0.223927	−	0.974606i	$-0.428112\pi$
$937$	13.7090			0.447854			0.223927	+	0.974606i	$0.428112\pi$
$938$		0			0
$939$	−10.7958	−	18.6989i	−0.352309	−	0.610216i
$940$	5.79583	−	10.0387i	0.189039	−	0.327425i
$941$	−3.66517			−0.119481			−0.0597405	−	0.998214i	$-0.519027\pi$
$941$	−3.66517			−0.119481			−0.0597405	+	0.998214i	$0.519027\pi$
$942$	0.102084	−	0.176815i	0.00332608	−	0.00576095i
$943$	−11.5877	+	20.0705i	−0.377348	+	0.653585i
$944$	−12.4392			−0.404861
$945$		0			0
$946$	14.7958	+	25.6271i	0.481054	+	0.833210i
$947$	−18.8979	−	32.7322i	−0.614100	−	1.06365i	−0.990542	−	0.137212i	$-0.956186\pi$
$947$	−18.8979	−	32.7322i	−0.614100	−	1.06365i	0.376442	−	0.926440i	$-0.377147\pi$
$948$	−3.11716			−0.101241
$949$	7.98958	+	44.6616i	0.259353	+	1.44978i
$950$	33.3636			1.08246
$951$	4.66101	+	8.07311i	0.151144	+	0.261788i
$952$		0			0
$953$	21.5917	−	37.3979i	0.699423	−	1.21144i	−0.269244	−	0.963072i	$-0.586774\pi$
$953$	21.5917	−	37.3979i	0.699423	−	1.21144i	0.968667	−	0.248364i	$-0.0798928\pi$
$954$	12.5917			0.407670
$955$	−33.2045	+	57.5120i	−1.07447	+	1.86104i
$956$	−5.10208	+	8.83707i	−0.165013	+	0.285811i
$957$	4.27212			0.138098
$958$	−10.4622	+	18.1211i	−0.338019	+	0.585467i
$959$		0			0
$960$	−20.2854	−	35.1354i	−0.654709	−	1.13399i
$961$	−29.0000			−0.935484
$962$	−9.48113	−	3.42418i	−0.305684	−	0.110400i
$963$	6.00000			0.193347
$964$	−5.58467	−	9.67293i	−0.179870	−	0.311544i
$965$	46.2934	+	80.1825i	1.49024	+	2.58117i
$966$		0			0
$967$	−17.3875			−0.559144			−0.279572	−	0.960125i	$-0.590193\pi$
$967$	−17.3875			−0.559144			−0.279572	+	0.960125i	$0.590193\pi$
$968$	5.11251	−	8.85512i	0.164322	−	0.284614i
$969$	2.53969	−	4.39887i	0.0815866	−	0.141312i
$970$	−17.3875			−0.558279
$971$	−11.3137	+	19.5959i	−0.363074	+	0.628863i	−0.988465	−	0.151449i	$-0.951606\pi$
$971$	−11.3137	+	19.5959i	−0.363074	+	0.628863i	0.625391	+	0.780312i	$0.284940\pi$
$972$	−4.94975	−	8.57321i	−0.158763	−	0.274986i
$973$		0			0
$974$	0.408337			0.0130840
$975$	−45.9792	+	38.7763i	−1.47251	+	1.24183i
$976$	8.34091			0.266986
$977$	14.1937	+	24.5843i	0.454098	+	0.786521i	0.998636	−	0.0522152i	$-0.0166282\pi$
$977$	14.1937	+	24.5843i	0.454098	+	0.786521i	−0.544538	+	0.838736i	$0.683295\pi$
$978$	10.8806	+	18.8458i	0.347923	+	0.602621i
$979$	28.4286	−	49.2398i	0.908583	−	1.57371i
$980$		0			0
$981$	0.795832	−	1.37842i	0.0254089	−	0.0440096i
$982$	−4.79583	+	8.30662i	−0.153041	+	0.265075i
$983$	−0.866213			−0.0276279			−0.0138140	−	0.999905i	$-0.504397\pi$
$983$	−0.866213			−0.0276279			−0.0138140	+	0.999905i	$0.504397\pi$
$984$	6.30625	−	10.9228i	0.201036	−	0.348205i
$985$	−16.3931	−	28.3937i	−0.522327	−	0.904697i
$986$	−0.505291	−	0.875190i	−0.0160918	−	0.0278717i
$987$		0			0
$988$	−7.79583	+	6.57457i	−0.248018	+	0.209165i
$989$	−60.7750			−1.93253
$990$	7.77817	+	13.4722i	0.247207	+	0.428174i
$991$	−13.8979	−	24.0719i	−0.441482	−	0.764669i	0.556318	−	0.830970i	$-0.312214\pi$
$991$	−13.8979	−	24.0719i	−0.441482	−	0.764669i	−0.997800	+	0.0663006i	$0.978880\pi$
$992$	−3.53553	+	6.12372i	−0.112253	+	0.194428i
$993$	−41.5602			−1.31887
$994$		0			0
$995$	−10.4083	+	18.0278i	−0.329966	+	0.571519i
$996$	14.0000			0.443607
$997$	0.634922	−	1.09972i	0.0201082	−	0.0348284i	−0.855796	−	0.517313i	$-0.826932\pi$
$997$	0.634922	−	1.09972i	0.0201082	−	0.0348284i	0.875904	+	0.482485i	$0.160266\pi$
$998$	−12.8979	−	22.3398i	−0.408276	−	0.707155i
$999$	−7.90781	−	13.6967i	−0.250192	−	0.433345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.g.393.3	yes	8
7.2	even	3		637.2.g.h.263.2		8
7.3	odd	6		637.2.h.k.471.1		8
7.4	even	3		637.2.h.k.471.4		8
7.5	odd	6		637.2.g.h.263.3		8
7.6	odd	2	inner	637.2.f.g.393.2	yes	8
13.3	even	3		8281.2.a.bv.1.1		4
13.9	even	3	inner	637.2.f.g.295.3	yes	8
13.10	even	6		8281.2.a.bn.1.2		4
91.9	even	3		637.2.h.k.165.4		8
91.48	odd	6	inner	637.2.f.g.295.2	✓	8
91.55	odd	6		8281.2.a.bv.1.4		4
91.61	odd	6		637.2.h.k.165.1		8
91.62	odd	6		8281.2.a.bn.1.3		4
91.74	even	3		637.2.g.h.373.2		8
91.87	odd	6		637.2.g.h.373.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.g.295.2	✓	8	91.48	odd	6	inner
637.2.f.g.295.3	yes	8	13.9	even	3	inner
637.2.f.g.393.2	yes	8	7.6	odd	2	inner
637.2.f.g.393.3	yes	8	1.1	even	1	trivial
637.2.g.h.263.2		8	7.2	even	3
637.2.g.h.263.3		8	7.5	odd	6
637.2.g.h.373.2		8	91.74	even	3
637.2.g.h.373.3		8	91.87	odd	6
637.2.h.k.165.1		8	91.61	odd	6
637.2.h.k.165.4		8	91.9	even	3
637.2.h.k.471.1		8	7.3	odd	6
637.2.h.k.471.4		8	7.4	even	3
8281.2.a.bn.1.2		4	13.10	even	6
8281.2.a.bn.1.3		4	91.62	odd	6
8281.2.a.bv.1.1		4	13.3	even	3
8281.2.a.bv.1.4		4	91.55	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} -4.09827 q^{5} +(0.707107 - 1.22474i) q^{6} -3.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(2.04914 + 3.54921i) q^{10} +(1.89792 + 3.28729i) q^{11} +1.41421 q^{12} +(0.634922 + 3.54921i) q^{13} +(-2.89792 - 5.01934i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.634922 + 1.09972i) q^{17} -1.00000 q^{18} +(-1.41421 + 2.44949i) q^{19} +(-2.04914 + 3.54921i) q^{20} +(1.89792 - 3.28729i) q^{22} +(3.89792 + 6.75139i) q^{23} +(-2.12132 - 3.67423i) q^{24} +11.7958 q^{25} +(2.75624 - 2.32446i) q^{26} +5.65685 q^{27} +(-0.397916 - 0.689210i) q^{29} +(-2.89792 + 5.01934i) q^{30} +1.41421 q^{31} +(-2.50000 + 4.33013i) q^{32} +(-2.68406 + 4.64893i) q^{33} +1.26984 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-1.39792 - 2.42126i) q^{37} +2.82843 q^{38} +(-3.89792 + 3.28729i) q^{39} +12.2948 q^{40} +(1.48640 + 2.57452i) q^{41} +(-3.89792 + 6.75139i) q^{43} +3.79583 q^{44} +(-2.04914 + 3.54921i) q^{45} +(3.89792 - 6.75139i) q^{46} -2.82843 q^{47} +(-0.707107 + 1.22474i) q^{48} +(-5.89792 - 10.2155i) q^{50} -1.79583 q^{51} +(3.39116 + 1.22474i) q^{52} -12.5917 q^{53} +(-2.82843 - 4.89898i) q^{54} +(-7.77817 - 13.4722i) q^{55} -4.00000 q^{57} +(-0.397916 + 0.689210i) q^{58} +(-6.21959 + 10.7726i) q^{59} -5.79583 q^{60} +(4.17046 - 7.22344i) q^{61} +(-0.707107 - 1.22474i) q^{62} +7.00000 q^{64} +(-2.60208 - 14.5456i) q^{65} +5.36812 q^{66} +(1.89792 + 3.28729i) q^{67} +(0.634922 + 1.09972i) q^{68} +(-5.51249 + 9.54790i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-1.50000 + 2.59808i) q^{72} +12.5836 q^{73} +(-1.39792 + 2.42126i) q^{74} +(8.34091 + 14.4469i) q^{75} +(1.41421 + 2.44949i) q^{76} +(4.79583 + 1.73205i) q^{78} -2.20417 q^{79} +(-2.04914 - 3.54921i) q^{80} +(2.50000 + 4.33013i) q^{81} +(1.48640 - 2.57452i) q^{82} +9.89949 q^{83} +(2.60208 - 4.50694i) q^{85} +7.79583 q^{86} +(0.562738 - 0.974691i) q^{87} +(-5.69375 - 9.86186i) q^{88} +(-7.48944 - 12.9721i) q^{89} +4.09827 q^{90} +7.79583 q^{92} +(1.00000 + 1.73205i) q^{93} +(1.41421 + 2.44949i) q^{94} +(5.79583 - 10.0387i) q^{95} -7.07107 q^{96} +(-2.12132 + 3.67423i) q^{97} +3.79583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{4} - 24 q^{8} + 4 q^{9} - 4 q^{11} - 4 q^{15} + 4 q^{16} - 8 q^{18} - 4 q^{22} + 12 q^{23} + 56 q^{25} + 16 q^{29} - 4 q^{30} - 20 q^{32} - 4 q^{36} + 8 q^{37} - 12 q^{39} - 12 q^{43}+ \cdots - 8 q^{99}+O(q^{100}) \) 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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